TABLE OF CLASS NUMBERS AND FUNDAMENRAL UNITS OF IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS WITH DISCRIMINANTS ≦ 10^{8}

By Ken Yamamura Department of Mathematics, National Defense Academy

August in 2000

Typeset by AMS-TEX

This is a table of class numbers and fundamenral units of imaginary biquadratic bicyclic number fields with discriminants ≦ 10^{8}. There exist exactly 13076 such fields.

Let K be a imaginary biquadratic bicyclic number field. Then K contains three quadratic subfields k_{1}, k_{2}, k_{3}, one real and two imaginary. We take k_{1} as real. We know that the class number h(K) and fundamenral units of K can be expressed in terms of those of k_{1}, k_{2}, k_{3}. In fact, we know the following class number relation:

h(K) = \frac{Q}{2}h(k_{1})h(k_{2})h(k_{3}),

where Q = [E_{K} : E_{k_{1}}E_{k_{2}}E_{k_{3}}] is the unit index. (As usual, E_{K} denotes the group of units in K. This index coincides with Hasse’s unit index [E_{K} : E_{k_{1}}W_{K}] of K except for the case K = Q(\sqrt{−1}, \sqrt{2}), in which case Q = 2 but [E_{K} : E_{k_{1}}W_{K}] = 1, where W_{K} is the group of roots of unity in K.) We also know that we can take as a fundamenral unit of K one of the following:

ε_{1};

\sqrt{−1}\sqrt{ε_{1}};
\sqrt{i}\sqrt{ε_{1}}.

Here ε_{1} is the fundamenral unit of k_{1}.

For each K, the fundamental data are the discriminants d_{i} of subfields of k_{i} (i = 1, 2, 3). K is determined by them. For the discriminant d of K, we have d = d_{1}d_{2}d_{3}. In Table 1, for each K, we give

the class numbers h_{i} = h(k_{i}) (i = 1, 2, 3) and h = h(K); A fundamental unit ε of K (in terms of ε_{1}); An approximate value of the regulator R of K.

In Table 2, the nonquadratic fundamental units are given explicitly in the form

a + b_{1}\sqrt{d_{1}} + b_{2}\sqrt{d_{2}} + b_{3}\sqrt{d_{3}},

where a and b_{1}, b_{2}, b_{3} are rational numbers. (We take \sqrt{i} = (\sqrt{2} + \sqrt{−2})/2.) The fields are ordered by discriminants. For some d, there exist several fields with the same discrimiannt d. They are ordered lexicographically with respect to (d_{1}, |d_{2}|, |d_{3}|).

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 3

Table 1

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
12 −3  −4  144 1 1 1 1 2  1  \sqrt{i}\sqrt{ε_{1}} 1.3170
5 −3 −15  225 1 1 2 1 1  1  ε_{1} 0.9624
8 −4  −8  256 1 1 1 1 2  1  ε_{1} 1.7627
5 −4 −20  400 1 1 2 1 1  1  ε_{1} 0.9624
21 −3  −7  441 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 1.5668
8 −3 −24  576 1 1 2 1 1  1  ε_{1} 1.7627
24 −3  −8  576 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 2.2924
28 −4  −7  784 1 1 1 1 2  1  \sqrt{i}\sqrt{ε_{1}} 2.7687
33 −3 −11 1089 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 3.8282
5 −7 −35 1225 1 1 2 1 1  1  ε_{1} 0.9624
13 −3 −39 1521 1 1 4 2 1  2  ε_{1} 2.3895
5 −8 −40 1600 1 1 2 1 1  1  ε_{1} 0.9624
44 −4 −11 1936 1 1 1 1 2  1  \sqrt{i}\sqrt{ε_{1}} 2.9932
12 −8 −24 2304 1 1 2 2 2  2 \sqrt{−1}\sqrt{ε_{1}} 1.3170
24 −4 −24 2304 1 1 2 2 2  2  \sqrt{i}\sqrt{ε_{1}} 2.2924
17 −3 −51 2601 1 1 2 1 1  1  ε_{1} 4.1894
13 −4 −52 2704 1 1 2 1 1  1  ε_{1} 2.3895
5 −11 −55 3025 1 1 4 2 1  2  ε_{1} 0.9624
8 −7 −56 3136 1 1 4 2 1  2  ε_{1} 1.7627
56 −7  −8 3136 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 3.4001
57 −3 −19 3249 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 5.7104
12 −15 −20 3600 1 2 2 2 1  2  ε_{1} 2.6339
60 −3 −20 3600 2 1 2 2 1  1  ε_{1} 4.1269
60 −4 −15 3600 2 1 2 2 1  1  ε_{1} 4.1269
17 −4 −68 4624 1 1 4 2 1  2  ε_{1} 4.1894
69 −3 −23 4761 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 3.2173
76 −4 −19 5776 1 1 1 1 2 1 \sqrt{i}\sqrt{ε_{1}} 5.8289
77 −7 −11 5929 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 2.1846
8 −20 −40 6400 1 2 2 2 1  2  ε_{1} 1.7627
40 −4 −40 6400 2 1 2 2 1  1  ε_{1} 3.6369
40 −8 −20 6400 2 1 2 2 1  1  ε_{1} 3.6369
12 −7 −84 7056 1 1 4 2 1  2  ε_{1} 2.6339
21 −4 −84 7056 1 1 4 2 1  2  ε_{1} 3.1336
28 −3 −84 7056 1 1 4 2 1  2  ε_{1} 5.5373
29 −3 −87 7569 1 1 6 3 1  3  ε_{1} 3.2945
8 −11 −88 7744 1 1 2 1 1  1  ε_{1} 1.7627
88 −8 −11 7744 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 5.9763
13 −7 −91 8281 1 1 2 1 1  1  ε_{1} 2.3895
92 −4 −23 8464 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 3.8708
93 −3 −31 8649 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 3.3661
5 −19 −95 9025 1 1 8 4 1  4  ε_{1} 0.9624
13 −8 −104 10816 1 1 6 3 1  3  ε_{1} 2.3895
21 −15 −35 11025 1 2 2 2 1  2  ε_{1} 3.1336
105 −3 −35 11025 2 1 2 2 1  1  ε_{1} 8.8131
105 −7 −15 11025 2 1 2 2 1  1  ε_{1} 8.8131
37 −3 −111 12321 1 1 8 4 1  4  ε_{1} 4.9836
28 −8 −56 12544 1 1 4 4 2  4 \sqrt{−1}\sqrt{ε_{1}} 2.7687
56 −4 −56 12544 1 1 4 4 2  4  \sqrt{i}\sqrt{ε_{1}} 3.4001
5 −23 −115 13225 1 3 2 3 1  3  ε_{1} 0.9624
29 −4 −116 13456 1 1 6 3 1  3  ε_{1} 3.2945

4 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
17 −7 −119 14161 1 1 10 5 1  5  ε_{1} 4.1894
5 −24 −120 14400 1 2 4 4 1  4  ε_{1} 0.9624
8 −15 −120 14400 1 2 4 4 1  4  ε_{1} 1.7627
24 −15 −40 14400 1 2 2 2 1  2  ε_{1} 4.5849
40 −3 −120 14400 2 1 4 4 1  2  ε_{1} 3.6369
40 −15 −24 14400 2 2 2 4 1  2  ε_{1} 3.6369
120 −3 −40 14400 2 1 2 2 1  1  ε_{1} 6.1779
120 −8 −15 14400 2 1 2 2 1  1  ε_{1} 6.1779
41 −3 −123 15129 1 1 2 1 1  1  ε_{1} 8.3183
124 −4 −31 15376 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 8.0196
129 −3 −43 16641 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 10.4255
12 −11 −132 17424 1 1 4 2 1  2  ε_{1} 2.6339
33 −4 −132 17424 1 1 4 2 1  2  ε_{1} 7.6563
44 −3 −132 17424 1 1 4 2 1  2  ε_{1} 5.9864
133 −7 −19 17689 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 5.1533
17 −8 −136 18496 1 1 4 2 1  2  ε_{1} 4.1894
28 −20 −35 19600 1 2 2 2 1  2  ε_{1} 5.5373
140 −4 −35 19600 2 1 2 2 1  1  ε_{1} 4.9558
140 −7 −20 19600 2 1 2 2 1  1  ε_{1} 4.9558
141 −3 −47 19881 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 5.2470
13 −11 −143 20449 1 1 10 5 1  5  ε_{1} 2.3895
37 −4 −148 21904 1 1 2 1 1  1  ε_{1} 4.9836
8 −19 −152 23104 1 1 6 3 1  3  ε_{1} 1.7627
152 −8 −19 23104 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 4.3039
5 −31 −155 24025 1 3 4 6 1  6  ε_{1} 0.9624
12 −39 −52 24336 1 4 2 4 1  4  ε_{1} 2.6339
156 −3 −52 24336 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 3.9116
156 −4 −39 24336 2 1 4 4 1  2  ε_{1} 7.8232
53 −3 −159 25281 1 1 10 5 1  5  ε_{1} 3.9314
161 −7 −23 25921 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 10.0669
41 −4 −164 26896 1 1 8 4 1  4  ε_{1} 8.3183
33 −15 −55 27225 1 2 4 4 1  4  ε_{1} 7.6563
165 −3 −55 27225 2 1 4 4 1  2  ε_{1} 5.1180
165 −11 −15 27225 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 2.5590
21 −8 −168 28224 1 1 4 2 1  2  ε_{1} 3.1336
21 −24 −56 28224 1 2 4 4 1  4  ε_{1} 3.1336
24 −7 −168 28224 1 1 4 2 1  2  ε_{1} 4.5849
56 −3 −168 28224 1 1 4 2 1  2  ε_{1} 6.8002
168 −3 −56 28224 2 1 4 4 1  2  ε_{1} 6.5132
168 −7 −24 28224 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 3.2566
172 −4 −43 29584 1 1 1 1 2 1 \sqrt{i}\sqrt{ε_{1}} 8.8485
44 −8 −88 30976 1 1 2 2 2  2 \sqrt{−1}\sqrt{ε_{1}} 2.9932
88 −4 −88 30976 1 1 2 2 2 2 \sqrt{i}\sqrt{ε_{1}} 5.9763
177 −3 −59 31329 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 11.7348
61 −3 −183 33489 1 1 8 4 1  4  ε_{1} 7.3284
8 −23 −184 33856 1 3 4 6 1  6  ε_{1} 1.7627
184 −8 −23 33856 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 10.7928
17 −11 −187 34969 1 1 2 1 1  1  ε_{1} 4.1894
188 −4 −47 35344 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 4.5642
5 −39 −195 38025 1 4 4 8 1  8  ε_{1} 0.9624

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 5

Continued

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
13 −15 −195 38025 1 2 4 4 1  4  ε_{1} 2.3895
65 −3 −195 38025 2 1 4 4 1  2  ε_{1} 5.5529
65 −15 −39 38025 2 2 4 8 1  4  ε_{1} 5.5529
201 −3 −67 40401 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 13.8453
29 −7 −203 41209 1 1 4 2 1  2  ε_{1} 3.2945
12 −51 −68 41616 1 2 4 4 1  4  ε_{1} 2.6339
204 −3 −68 41616 2 1 4 4 1  2  ε_{1} 9.2101
204 −4 −51 41616 2 1 2 4 2  2  \sqrt{i}\sqrt{ε_{1}} 4.6051
8 −52 −104 43264 1 2 6 6 1  6  ε_{1} 1.7627
104 −4 −104 43264 2 1 6 6 1  3  ε_{1} 4.6249
104 −8 −52 43264 2 1 2 2 1  1  ε_{1} 4.6249
209 −11 −19 43681 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 11.4415
53 −4 −212 44944 1 1 6 3 1 3 ε_{1} 3.9314
213 −3 −71 45369 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 4.2903
5 −43 −215 46225 1 1 14 7 1 7 ε_{1} 0.9624
217 −7 −31 47089 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 15.8552
73 −3 −219 47961 1 1 4 2 1  2  ε_{1} 15.3334
44 −20 −55 48400 1 2 4 4 1  4  ε_{1} 5.9864
220 −4 −55 48400 2 1 4 4 1  2  ε_{1} 10.3635
220 −11 −20 48400 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 5.1818
12 −19 −228 51984 1 1 4 2 1  2  ε_{1} 2.6339
57 −4 −228 51984 1 1 4 2 1  2  ε_{1} 11.4208
76 −3 −228 51984 1 1 4 2 1  2  ε_{1} 11.6579
21 −11 −231 53361 1 1 12 6 1  6  ε_{1} 3.1336
33 −7 −231 53361 1 1 12 6 1  6  ε_{1} 7.6563
77 −3 −231 53361 1 1 12 6 1  6  ε_{1} 4.3693
29 −8 −232 53824 1 1 2 1 1  1  ε_{1} 3.2945
5 −47 −235 55225 1 5 2 5 1  5  ε_{1} 0.9624
236 −4 −59 55696 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 6.9660
237 −3 −79 56169 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 4.3436
12 −40 −120 57600 1 2 4 4 1  4  ε_{1} 2.6339
24 −20 −120 57600 1 2 4 4 1  4  ε_{1} 4.5849
60 −8 −120 57600 2 1 4 4 1  2  ε_{1} 4.1269
60 −24 −40 57600 2 2 2 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 2.0634
120 −4 −120 57600 2 1 4 4 1 2 ε_{1} 6.1779
120 −20 −24 57600 2 2 2 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 3.0890
61 −4 −244 59536 1 1 6 3 1  3  ε_{1} 7.3284
13 −19 −247 61009 1 1 6 3 1  3  ε_{1} 2.3895
8 −31 −248 61504 1 3 8 12 1 12  ε_{1} 1.7627
248 −8 −31 61504 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 4.8362
249 −3 −83 62001 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 16.6550
253 −11 −23 64009 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 7.5289
5 −51 −255 65025 1 2 12 12 1 12  ε_{1} 0.9624
17 −15 −255 65025 1 2 12 12 1 12  ε_{1} 4.1894
85 −3 −255 65025 2 1 12 12 1  6  ε_{1} 4.4187
85 −15 −51 65025 2 2 2 4 1  2  ε_{1} 4.4187
37 −7 −259 67081 1 1 4 2 1  2  ε_{1} 4.9836
5 −52 −260 67600 1 2 8 8 1  8  ε_{1} 0.9624
13 −20 −260 67600 1 2 8 8 1  8  ε_{1} 2.3895
65 −4 −260 67600 2 1 8 8 1  4  ε_{1} 5.5529

6 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
65 −20 −52 67600 2 2 2 4 1  2  ε_{1} 5.5529
24 −11 −264 69696 1 1 8 4 1  4  ε_{1} 4.5849
33 −8 −264 69696 1 1 8 4 1  4  ε_{1} 7.6563
33 −24 −88 69696 1 2 2 2 1  2  ε_{1} 7.6563
88 −3 −264 69696 1 1 8 4 1  4  ε_{1} 11.9527
264 −3 −88 69696 2 1 2 2 1  1  ε_{1} 9.7350
264 −11 −24 69696 2 1 2 2 1  1  ε_{1} 9.7350
89 −3 −267 71289 1 1 2 1 1  1  ε_{1} 13.8155
268 −4 −67 71824 1 1 1 1 2  1  \sqrt{i}\sqrt{ε_{1}} 11.4895
8 −68 −136 73984 1 4 4 8 1  8  ε_{1} 1.7627
136 −4 −136 73984 2 1 4 8 2  4  \sqrt{i}\sqrt{ε_{1}} 4.2483
136 −8 −68 73984 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 4.2483
21 −39 −91 74529 1 4 2 4 1 4 ε_{1} 3.1336
273 −3 −91 74529 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 7.2821
273 −7 −39 74529 2 1 4 4 1 2 ε_{1} 14.5641
12 −23 −276 76176 1 3 8 12 1 12  ε_{1} 2.6339
69 −4 −276 76176 1 1 8 4 1  4  ε_{1} 6.4345
92 −3 −276 76176 1 1 8 4 1  4  ε_{1} 7.7415
5 −56 −280 78400 1 4 4 8 1  8  ε_{1} 0.9624
8 −35 −280 78400 1 2 4 4 1  4  ε_{1} 1.7627
40 −7 −280 78400 2 1 4 4 1  2  ε_{1} 3.6369
40 −35 −56 78400 2 2 4 8 1  4  ε_{1} 3.6369
56 −35 −40 78400 1 2 2 2 1  2  ε_{1} 6.8002
280 −7 −40 78400 2 1 2 2 1  1  ε_{1} 12.4372
280 −8 −35 78400 2 1 2 2 1  1  ε_{1} 12.4372
284 −4 −71 80656 1 1 7 7 2  7  \sqrt{i}\sqrt{ε_{1}} 8.8479
57 −15 −95 81225 1 2 8 8 1  8  ε_{1} 11.4208
285 −3 −95 81225 2 1 8 8 1  4  ε_{1} 5.6595
285 −15 −19 81225 2 2 1 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 2.8297
41 −7 −287 82369 1 1 14 7 1  7  ε_{1} 8.3183
97 −3 −291 84681 1 1 4 2 1  2  ε_{1} 18.6488
73 −4 −292 85264 1 1 4 2 1  2  ε_{1} 15.3334
5 −59 −295 87025 1 3 8 12 1 12  ε_{1} 0.9624
37 −8 −296 87616 1 1 10 5 1 5 ε_{1} 4.9836
13 −23 −299 89401 1 3 8 12 1 12  ε_{1} 2.3895
301 −7 −43 90601 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 10.0321
101 −3 −303 91809 1 1 10 5 1 5 ε_{1} 5.9964
76 −8 −152 92416 1 1 6 6 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.8289
152 −4 −152 92416 1 1 6 6 2  6  \sqrt{i}\sqrt{ε_{1}} 4.3039
28 −11 −308 94864 1 1 8 4 1  4  ε_{1} 5.5373
44 −7 −308 94864 1 1 8 4 1  4  ε_{1} 5.9864
77 −4 −308 94864 1 1 8 4 1  4  ε_{1} 4.3693
309 −3 −103 95481 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 8.5262
8 −39 −312 97344 1 4 4 8 1  8  ε_{1} 1.7627
13 −24 −312 97344 1 2 4 4 1  4  ε_{1} 2.3895
24 −39 −104 97344 1 4 6 12 1 12  ε_{1} 4.5849
104 −3 −312 97344 2 1 4 4 1  2  ε_{1} 4.6249
104 −24 −39 97344 2 2 4 8 1  4  ε_{1} 4.6249
312 −3 −104 97344 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 4.6634
312 −8 −39 97344 2 1 4 4 1  2  ε_{1} 9.3267

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 7

Continued

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
316 −4 −79 99856 3 1 5 15 2  5  \sqrt{i}\sqrt{ε_{1}} 5.0751
29 −11 −319 101761 1 1 10 5 1  5  ε_{1} 3.2945
321 −3 −107 103041 3 1 3 9 2  3 \sqrt{−1}\sqrt{ε_{1}} 6.0638
17 −19 −323 104329 1 1 4 2 1  2  ε_{1} 4.1894
109 −3 −327 106929 1 1 12 6 1  6  ε_{1} 11.1291
41 −8 −328 107584 1 1 4 2 1  2  ε_{1} 8.3183
329 −7 −47 108241 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 15.3743
332 −4 −83 110224 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 5.0998
5 −67 −335 112225 1 1 18 9 1  9  ε_{1} 0.9624
8 −84 −168 112896 1 4 4 8 1  8  ε_{1} 1.7627
12 −56 −168 112896 1 4 4 8 1  8  ε_{1} 2.6339
24 −56 −84 112896 1 4 4 8 1  8  ε_{1} 4.5849
28 −24 −168 112896 1 2 4 4 1  4  ε_{1} 5.5373
56 −24 −84 112896 1 2 4 4 1  4  ε_{1} 6.8002
168 −4 −168 112896 2 1 4 4 1  2  ε_{1} 6.5132
168 −8 −84 112896 2 1 4 4 1  2  ε_{1} 6.5132
113 −3 −339 114921 1 1 6 3 1  3  ε_{1} 14.6946
5 −68 −340 115600 1 4 4 8 1  8  ε_{1} 0.9624
17 −20 −340 115600 1 2 4 4 1  4  ε_{1} 4.1894
85 −4 −340 115600 2 1 4 4 1  2  ε_{1} 4.4187
85 −20 −68 115600 2 2 4 8 1  4  ε_{1} 4.4187
341 −11 −31 116281 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 5.6240
8 −43 −344 118336 1 1 10 5 1 5 ε_{1} 1.7627
344 −8 −43 118336 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 9.9432
69 −15 −115 119025 1 2 2 2 1  2  ε_{1} 6.4345
345 −3 −115 119025 2 1 2 2 1  1  ε_{1} 19.0241
345 −15 −23 119025 2 2 3 6 1  3  ε_{1} 19.0241
12 −87 −116 121104 1 6 6 18 1 18  ε_{1} 2.6339
348 −3 −116 121104 2 1 6 6 1  3  ε_{1} 8.0501
348 −4 −87 121104 2 1 6 6 1  3  ε_{1} 8.0501
5 −71 −355 126025 1 7 4 14 1 14  ε_{1} 0.9624
89 −4 −356 126736 1 1 12 6 1 6 ε_{1} 13.8155
21 −51 −119 127449 1 2 10 10 1 10  ε_{1} 3.1336
357 −3 −119 127449 2 1 10 10 1  5  ε_{1} 5.8833
357 −7 −51 127449 2 1 2 2 1  1  ε_{1} 5.8833
28 −52 −91 132496 1 2 2 2 1  2  ε_{1} 5.5373
364 −4 −91 132496 2 1 2 2 1  1  ε_{1} 16.1090
364 −7 −52 132496 2 1 2 2 1  1  ε_{1} 16.1090
92 −8 −184 135424 1 1 4 4 2  4 \sqrt{−1}\sqrt{ε_{1}} 3.8708
184 −4 −184 135424 1 1 4 4 2  4  \sqrt{i}\sqrt{ε_{1}} 10.7928
53 −7 −371 137641 1 1 8 4 1  4  ε_{1} 3.9314
12 −31 −372 138384 1 3 4 6 1  6  ε_{1} 2.6339
93 −4 −372 138384 1 1 4 2 1  2  ε_{1} 6.7322
124 −3 −372 138384 1 1 4 2 1  2  ε_{1} 16.0392
8 −47 −376 141376 1 5 8 20 1 20  ε_{1} 1.7627
376 −8 −47 141376 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 15.2710
76 −20 −95 144400 1 2 8 8 1  8  ε_{1} 11.6579
380 −4 −95 144400 2 1 8 8 1  4  ε_{1} 8.7131
380 −19 −20 144400 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 4.3565
381 −3 −127 145161 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 7.6158

8 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
77 −35 −55 148225 1 2 4 4 1  4  ε_{1} 4.3693
385 −7 −55 148225 2 1 4 4 1  2  ε_{1} 24.3270
385 −11 −35 148225 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 12.1635
97 −4 −388 150544 1 1 4 2 1 2 ε_{1} 18.6488
17 −23 −391 152881 1 3 14 21 1 21  ε_{1} 4.1894
393 −3 −131 154449 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 18.3468
5 −79 −395 156025 1 5 8 20 1 20  ε_{1} 0.9624
21 −19 −399 159201 1 1 16 8 1  8  ε_{1} 3.1336
57 −7 −399 159201 1 1 16 8 1  8  ε_{1} 11.4208
133 −3 −399 159201 1 1 16 8 1  8  ε_{1} 10.3065
13 −31 −403 162409 1 3 2 3 1  3  ε_{1} 2.3895
101 −4 −404 163216 1 1 14 7 1  7  ε_{1} 5.9964
37 −11 −407 165649 1 1 16 8 1  8  ε_{1} 4.9836
8 −51 −408 166464 1 2 4 4 1  4  ε_{1} 1.7627
17 −24 −408 166464 1 2 4 4 1  4  ε_{1} 4.1894
24 −51 −136 166464 1 2 4 4 1  4  ε_{1} 4.5849
136 −3 −408 166464 2 1 4 4 1  2  ε_{1} 8.4966
136 −24 −51 166464 2 2 2 4 1  2  ε_{1} 8.4966
408 −3 −136 166464 2 1 4 4 1  2  ε_{1} 10.6165
408 −8 −51 166464 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 5.3082
137 −3 −411 168921 1 1 6 3 1  3  ε_{1} 16.3142
412 −4 −103 169744 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 13.0282
413 −7 −59 170569 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 4.1106
5 −83 −415 172225 1 3 10 15 1 15  ε_{1} 0.9624
417 −3 −139 173889 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 18.9551
5 −84 −420 176400 1 4 8 16 1 16  ε_{1} 0.9624
12 −35 −420 176400 1 2 8 8 1  8  ε_{1} 2.6339
21 −20 −420 176400 1 2 8 8 1  8  ε_{1} 3.1336
28 −15 −420 176400 1 2 8 8 1  8  ε_{1} 5.5373
60 −7 −420 176400 2 1 8 8 1  4  ε_{1} 4.1269
60 −35 −84 176400 2 2 4 8 1  4  ε_{1} 4.1269
105 −4 −420 176400 2 1 8 8 1  4  ε_{1} 8.8131
105 −20 −84 176400 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.4066
140 −3 −420 176400 2 1 8 8 1  4  ε_{1} 4.9558
140 −15 −84 176400 2 2 4 8 1  4  ε_{1} 4.9558
53 −8 −424 179776 1 1 6 3 1  3  ε_{1} 3.9314
61 −7 −427 182329 1 1 2 1 1  1  ε_{1} 7.3284
428 −4 −107 183184 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 7.5622
33 −39 −143 184041 1 4 10 20 1 20  ε_{1} 7.6563
429 −3 −143 184041 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 4.9767
429 −11 −39 184041 2 1 4 4 1 2 ε_{1} 9.9534
5 −87 −435 189225 1 6 4 12 1 12  ε_{1} 0.9624
29 −15 −435 189225 1 2 4 4 1  4  ε_{1} 3.2945
145 −3 −435 189225 4 1 4 8 1  2  ε_{1} 6.3596
145 −15 −87 189225 4 2 6 24 1  6  ε_{1} 6.3596
109 −4 −436 190096 1 1 6 3 1  3  ε_{1} 11.1291
437 −19 −23 190969 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 3.0422
5 −88 −440 193600 1 2 12 12 1 12  ε_{1} 0.9624
8 −55 −440 193600 1 4 12 24 1 24  ε_{1} 1.7627
40 −11 −440 193600 2 1 12 12 1  6  ε_{1} 3.6369

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 9

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
40 −55 −88 193600 2 4 2 8 1  4  ε_{1} 3.6369
88 −40 −55 193600 1 2 4 4 1  4  ε_{1} 11.9527
440  −8 −55 193600 2 1 4 4 1  2  ε_{1} 7.4742
440 −11 −40 193600 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 3.7371
12 −111 −148 197136 1 8 2 8 1  8  ε_{1} 2.6339
444  −3 −148 197136 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 6.3801
444  −4 −111 197136 2 1 8 8 1  4  ε_{1} 12.7602
149  −3 −447 199809 1 1 14 7 1  7  ε_{1} 8.2223
41 −11 −451 203401 1 1 6 3 1  3  ε_{1} 8.3183
113  −4 −452 204304 1 1 8 4 1  4  ε_{1} 14.6946
453  −3 −151 205209 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 5.0039
5 −91 −455 207025 1 2 20 20 1 20  ε_{1} 0.9624
13 −35 −455 207025 1 2 20 20 1 20  ε_{1} 2.3895
65  −7 −455 207025 2 1 20 20 1 10  ε_{1} 5.5529
65 −35 −91 207025 2 2 2 4 1  2  ε_{1} 5.5529
24 −19 −456 207936 1 1 8 4 1  4  ε_{1} 4.5849
57  −8 −456 207936 1 1 8 4 1  4  ε_{1} 11.4208
57 −24 −152 207936 1 2 6 6 1  6  ε_{1} 11.4208
152  −3 −456 207936 1 1 8 4 1  4  ε_{1} 8.6078
456  −3 −152 207936 2 1 6 6 1  3  ε_{1} 15.2512
456 −19 −24 207936 2 1 2 2 1  1  ε_{1} 15.2512
92 −20 −115 211600 1 2 2 2 1  2  ε_{1} 7.7415
460  −4 −115 211600 2 1 2 2 1  1  ε_{1} 15.4391
460 −20 −23 211600 2 2 3 6 1  3  ε_{1} 15.4391
8 −116 −232 215296 1 6 2 6 1  6  ε_{1} 1.7627
232  −4 −232 215296 2 1 2 2 1  1  ε_{1} 10.5766
232  −8 −116 215296 2 1 6 6 1  3  ε_{1} 10.5766
93 −15 −155 216225 1 2 4 4 1  4  ε_{1} 6.7322
465  −3 −155 216225 2 1 4 4 1  2  ε_{1} 20.7308
465 −15 −31 216225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 10.3654
469  −7 −67 219961 3 1 1 3 2  1 \sqrt{−1}\sqrt{ε_{1}} 4.1742
157  −3 −471 221841 1 1 16 8 1  8  ε_{1} 10.7226
8 −59 −472 222784 1 3 6 9 1  9  ε_{1} 1.7627
472  −8 −59 222784 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 13.3275
473 −11 −43 223729 3 1 1 3 2  1 \sqrt{−1}\sqrt{ε_{1}} 5.1590
28 −68 −119 226576 1 4 10 20 1 20  ε_{1} 5.5373
476  −4 −119 226576 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 5.4806
476  −7 −68 226576 2 1 4 4 1  2  ε_{1} 10.9612
21 −23 −483 233289 1 3 4 6 1  6  ε_{1} 3.1336
69  −7 −483 233289 1 1 4 2 1  2  ε_{1} 6.4345
161  −3 −483 233289 1 1 4 2 1  2  ε_{1} 20.1338
61  −8 −488 238144 1 1 10 5 1  5  ε_{1} 7.3284
489  −3 −163 239121 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 23.4436
12 −123 −164 242064 1 2 8 8 1  8  ε_{1} 2.6339
492  −3 −164 242064 2 1 8 8 1  4  ε_{1} 10.9943
492  −4 −123 242064 2 1 2 4 2  2  \sqrt{i}\sqrt{ε_{1}} 5.4972
124  −8 −248 246016 1 1 8 8 2  8 \sqrt{−1}\sqrt{ε_{1}} 8.0196
248  −4 −248 246016 1 1 8 8 2  8  \sqrt{i}\sqrt{ε_{1}} 4.8362
497  −7 −71 247009 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 14.6926
501  −3 −167 251001 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 10.2480

10 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
508  −4 −127 258064 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 16.0627
73  −7 −511 261121 1 1 14 7 1  7  ε_{1} 15.3334
5 −103 −515 265225 1 5 6 15 1 15  ε_{1} 0.9624
12 −43 −516 266256 1 1 12 6 1  6  ε_{1} 2.6339
129  −4 −516 266256 1 1 12 6 1  6  ε_{1} 20.8511
172  −3 −516 266256 1 1 12 6 1  6  ε_{1} 17.6970
517 −11 −47 267289 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 9.2661
173 −3 −519 269361 1 1 18 9 1 9 ε_{1} 5.1416
5 −104 −520 270400 1 6 4 12 1 12  ε_{1} 0.9624
13 −40 −520 270400 1 2 4 4 1  4  ε_{1} 2.3895
65  −8 −520 270400 2 1 4 4 1  2  ε_{1} 5.5529
65 −40 −104 270400 2 2 6 12 1  6  ε_{1} 5.5529
524  −4 −131 274576 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 9.9627
17 −31 −527 277729 1 3 18 27 1 27  ε_{1} 4.1894
8 −132 −264 278784 1 4 8 16 1 16  ε_{1} 1.7627
12 −88 −264 278784 1 2 8 8 1  8  ε_{1} 2.6339
24 −88 −132 278784 1 2 4 4 1  4  ε_{1} 4.5849
44 −24 −264 278784 1 2 8 8 1  8  ε_{1} 5.9864
88 −24 −132 278784 1 2 4 4 1  4  ε_{1} 11.9527
264  −4 −264 278784 2 1 8 16 2  8  \sqrt{i}\sqrt{ε_{1}} 4.8675
264  −8 −132 278784 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 4.8675
28 −19 −532 283024 1 1 4 2 1  2  ε_{1} 5.5373
76  −7 −532 283024 1 1 4 2 1  2  ε_{1} 11.6579
133  −4 −532 283024 1 1 4 2 1  2  ε_{1} 10.3065
5 −107 −535 286225 1 3 14 21 1 21  ε_{1} 0.9624
8 −67 −536 287296 1 1 14 7 1  7  ε_{1} 1.7627
536  −8 −67 287296 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 12.5840
537  −3 −179 288369 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 19.7680
181  −3 −543 294849 1 1 12 6 1  6  ε_{1} 14.3479
137  −4 −548 300304 1 1 8 4 1  4  ε_{1} 16.3142
29 −19 −551 303601 1 1 26 13 1 13  ε_{1} 3.2945
24 −23 −552 304704 1 3 8 12 1 12  ε_{1} 4.5849
69  −8 −552 304704 1 1 8 4 1  4  ε_{1} 6.4345
69 −24 −184 304704 1 2 4 4 1  4  ε_{1} 6.4345
184  −3 −552 304704 1 1 8 4 1  4  ε_{1} 21.5856
552  −3 −184 304704 2 1 4 4 1  2  ε_{1} 9.0864
552 −23 −24 304704 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 4.5432
553 −7 −79 305809 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 27.8536
5 −111 −555 308025 1 8 4 16 1 16  ε_{1} 0.9624
37 −15 −555 308025 1 2 4 4 1  4  ε_{1} 4.9836
185  −3 −555 308025 2 1 4 4 1  2  ε_{1} 9.8254
185 −15 −111 308025 2 2 8 16 1  8  ε_{1} 9.8254
556  −4 −139 309136 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 18.8598
13 −43 −559 312481 1 1 16 8 1  8  ε_{1} 2.3895
28 −40 −280 313600 1 2 4 4 1  4  ε_{1} 5.5373
56 −20 −280 313600 1 2 4 4 1  4  ε_{1} 6.8002
140  −8 −280 313600 2 1 4 4 1  2  ε_{1} 4.9558
140 −40 −56 313600 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 2.4779
280 −4 −280 313600 2 1 4 4 1 2 ε_{1} 12.4372
280 −20 −56 313600 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 6.2186

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 11

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
33 −51 −187 314721 1 2 2 2 1  2  ε_{1} 7.6563
561  −3 −187 314721 2 1 2 2 1  1  ε_{1} 27.7201
561 −11 −51 314721 2 1 2 2 1  1  ε_{1} 27.7201
12 −47 −564 318096 1 5 8 20 1 20  ε_{1} 2.6339
141  −4 −564 318096 1 1 8 4 1  4  ε_{1} 10.4940
188  −3 −564 318096 1 1 8 4 1  4  ε_{1} 9.1285
8 −71 −568 322624 1 7 4 14 1 14  ε_{1} 1.7627
568 −8 −71 322624 3 1 7 21 2 7 \sqrt{−1}\sqrt{ε_{1}} 5.6560
44 −52 −143 327184 1 2 10 10 1 10  ε_{1} 5.9864
572  −4 −143 327184 2 1 10 10 1  5  ε_{1} 6.3526
572 −11 −52 327184 2 1 2 2 1  1  ε_{1} 6.3526
573  −3 −191 328329 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 6.6412
193 −3 −579 335241 1 1 8 4 1 4 ε_{1} 30.1526
5 −116 −580 336400 1 6 8 24 1 24  ε_{1} 0.9624
29 −20 −580 336400 1 2 8 8 1  8  ε_{1} 3.2945
145  −4 −580 336400 4 1 8 16 1  4  ε_{1} 6.3596
145 −20 −116 336400 4 2 6 24 1  6  ε_{1} 6.3596
581  −7 −83 337561 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 8.8136
53 −11 −583 339889 1 1 8 4 1  4  ε_{1} 3.9314
73  −8 −584 341056 1 1 16 8 1  8  ε_{1} 15.3334
589 −19 −31 346921 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 15.2878
197 −3 −591 349281 1 1 22 11 1 11 ε_{1} 6.6670
8 −148 −296 350464 1 2 10 10 1 10  ε_{1} 1.7627
296  −4 −296 350464 2 1 10 10 1  5  ε_{1} 8.9090
296  −8 −148 350464 2 1 2 2 1  1  ε_{1} 8.9090
5 −119 −595 354025 1 10 4 20 1 20  ε_{1} 0.9624
17 −35 −595 354025 1 2 4 4 1  4  ε_{1} 4.1894
85  −7 −595 354025 2 1 4 4 1  2  ε_{1} 4.4187
85 −35 −119 354025 2 2 10 20 1 10  ε_{1} 4.4187
149  −4 −596 355216 1 1 14 7 1  7  ε_{1} 8.2223
597  −3 −199 356409 1 1 9 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 9.1849
604  −4 −151 364816 1 1 7 7 2  7  \sqrt{i}\sqrt{ε_{1}} 21.9635
21 −87 −203 370881 1 6 4 12 1 12  ε_{1} 3.1336
609  −3 −203 370881 2 1 4 4 1  2  ε_{1} 28.0146
609  −7 −87 370881 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 14.0073
13 −47 −611 373321 1 5 10 25 1 25  ε_{1} 2.3895
5 −123 −615 378225 1 2 20 20 1 20  ε_{1} 0.9624
41 −15 −615 378225 1 2 20 20 1 20  ε_{1} 8.3183
205  −3 −615 378225 2 1 20 20 1 10  ε_{1} 7.5213
205 −15 −123 378225 2 2 2 4 1  2  ε_{1} 7.5213
56 −11 −616 379456 1 1 8 4 1  4  ε_{1} 6.8002
77  −8 −616 379456 1 1 8 4 1  4  ε_{1} 4.3693
77 −56 −88 379456 1 4 2 4 1  4  ε_{1} 4.3693
88  −7 −616 379456 1 1 8 4 1  4  ε_{1} 11.9527
616  −7 −88 379456 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 10.6594
616 −11 −56 379456 2 1 4 4 1  2  ε_{1} 21.3187
124 −20 −155 384400 1 2 4 4 1  4  ε_{1} 16.0392
620  −4 −155 384400 2 1 4 4 1  2  ε_{1} 12.4212
620 −20 −31 384400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.2106
89  −7 −623 388129 1 1 22 11 1 11  ε_{1} 13.8155

12 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −104 −312 389376 1 6 4 12 1 12  ε_{1} 2.6339
24 −52 −312 389376 1 2 4 4 1  4  ε_{1} 4.5849
156  −8 −312 389376 2 1 4 4 1  2  ε_{1} 7.8232
156 −24 −104 389376 2 2 6 12 1  6  ε_{1} 7.8232
312  −4 −312 389376 2 1 4 4 1  2  ε_{1} 9.3267
312 −24 −52 389376 2 2 2 4 1  2  ε_{1} 9.3267
33 −19 −627 393129 1 1 4 2 1  2  ε_{1} 7.6563
57 −11 −627 393129 1 1 4 2 1  2  ε_{1} 11.4208
209  −3 −627 393129 1 1 4 2 1  2  ε_{1} 22.8829
157  −4 −628 394384 1 1 6 3 1  3  ε_{1} 10.7226
8 −79 −632 399424 1 5 8 20 1 20  ε_{1} 1.7627
632  −8 −79 399424 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 9.6477
633  −3 −211 400689 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 20.5972
5 −127 −635 403225 1 5 10 25 1 25  ε_{1} 0.9624
12 −159 −212 404496 1 10 6 30 1 30  ε_{1} 2.6339
636  −3 −212 404496 2 1 6 6 1  3  ε_{1} 15.7631
636  −4 −159 404496 2 1 10 10 1  5  ε_{1} 15.7631
28 −23 −644 414736 1 3 16 24 1 24  ε_{1} 5.5373
92  −7 −644 414736 1 1 16 8 1  8  ε_{1} 7.7415
161  −4 −644 414736 1 1 16 8 1  8  ε_{1} 20.1338
129 −15 −215 416025 1 2 14 14 1 14  ε_{1} 20.8511
645  −3 −215 416025 2 1 14 14 1  7  ε_{1} 9.6883
645 −15 −43 416025 2 2 1 2 1  1  ε_{1} 9.6883
649 −11 −59 421201 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 35.3485
21 −31 −651 423801 1 3 8 12 1 12  ε_{1} 3.1336
93  −7 −651 423801 1 1 8 4 1  4  ε_{1} 6.7322
217  −3 −651 423801 1 1 8 4 1  4  ε_{1} 31.7104
652  −4 −163 425104 1 1 1 1 2  1  \sqrt{i}\sqrt{ε_{1}} 18.6688
5 −131 −655 429025 1 5 12 30 1 30  ε_{1} 0.9624
8 −164 −328 430336 1 8 4 16 1 16  ε_{1} 1.7627
328  −4 −328 430336 4 1 4 8 1  2  ε_{1} 5.7869
328  −8 −164 430336 4 1 8 16 1  4  ε_{1} 5.7869
5 −132 −660 435600 1 4 8 16 1 16  ε_{1} 0.9624
12 −55 −660 435600 1 4 8 16 1 16  ε_{1} 2.6339
33 −20 −660 435600 1 2 8 8 1  8  ε_{1} 7.6563
44 −15 −660 435600 1 2 8 8 1  8  ε_{1} 5.9864
60 −11 −660 435600 2 1 8 8 1  4  ε_{1} 4.1269
60 −55 −132 435600 2 4 4 16 1  8  ε_{1} 4.1269
165  −4 −660 435600 2 1 8 8 1  4  ε_{1} 5.1180
165 −20 −132 435600 2 2 4 8 1  4  ε_{1} 5.1180
220  −3 −660 435600 2 1 8 8 1  4  ε_{1} 10.3635
220 −15 −132 435600 2 2 4 8 1  4  ε_{1} 10.3635
13 −51 −663 439569 1 2 16 16 1 16  ε_{1} 2.3895
17 −39 −663 439569 1 4 16 32 1 32  ε_{1} 4.1894
221  −3 −663 439569 2 1 16 16 1  8  ε_{1} 5.4072
221 −39 −51 439569 2 4 2 8 1  4  ε_{1} 5.4072
8 −83 −664 440896 1 3 10 15 1 15  ε_{1} 1.7627
664  −8 −83 440896 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 21.9476
133 −35 −95 442225 1 2 8 8 1  8  ε_{1} 10.3065
665  −7 −95 442225 2 1 8 8 1  4  ε_{1} 20.4394

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 13

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
665 −19 −35 442225 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 10.2197
29 −23 −667 444889 1 3 4 6 1  6  ε_{1} 3.2945
668  −4 −167 446224 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 5.8171
669  −3 −223 447561 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 12.6290
61 −11 −671 450241 1 1 30 15 1 15  ε_{1} 7.3284
97 −7 −679 461041 1 1 18 9 1 9 ε_{1} 18.6488
5 −136 −680 462400 1 4 12 24 1 24  ε_{1} 0.9624
17 −40 −680 462400 1 2 12 12 1 12  ε_{1} 4.1894
85  −8 −680 462400 2 1 12 12 1  6  ε_{1} 4.4187
85 −40 −136 462400 2 2 4 8 1  4  ε_{1} 4.4187
681  −3 −227 463761 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 30.6984
229  −3 −687 471969 3 1 12 18 1  6  ε_{1} 5.4249
172  −8 −344 473344 1 1 10 10 2 10 \sqrt{−1}\sqrt{ε_{1}} 8.8485
344  −4 −344 473344 1 1 10 10 2 10  \sqrt{i}\sqrt{ε_{1}} 9.9432
173  −4 −692 478864 1 1 14 7 1  7  ε_{1} 5.1416
5 −139 −695 483025 1 3 24 36 1 36  ε_{1} 0.9624
8 −87 −696 484416 1 6 12 36 1 36  ε_{1} 1.7627
24 −87 −232 484416 1 6 2 6 1 6 ε_{1} 4.5849
29 −24 −696 484416 1 2 12 12 1 12  ε_{1} 3.2945
232  −3 −696 484416 2 1 12 12 1  6  ε_{1} 10.5766
232 −24 −87 484416 2 2 6 12 1  6  ε_{1} 10.5766
696  −3 −232 484416 2 1 2 2 1  1  ε_{1} 15.9463
696  −8 −87 484416 2 1 6 6 1  3  ε_{1} 15.9463
233  −3 −699 488601 1 1 10 5 1  5  ε_{1} 21.4863
37 −19 −703 494209 1 1 14 7 1  7  ε_{1} 4.9836
141 −15 −235 497025 1 2 2 2 1  2  ε_{1} 10.4940
705  −3 −235 497025 2 1 2 2 1  1  ε_{1} 26.1393
705 −15 −47 497025 2 2 5 10 1  5  ε_{1} 26.1393
101  −7 −707 499849 1 1 6 3 1  3  ε_{1} 5.9964
12 −59 −708 501264 1 3 4 6 1  6  ε_{1} 2.6339
177  −4 −708 501264 1 1 4 2 1  2  ε_{1} 23.4697
236  −3 −708 501264 1 1 4 2 1  2  ε_{1} 13.9320
89  −8 −712 506944 1 1 8 4 1  4  ε_{1} 13.8155
713 −23 −31 508369 1 3 3 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 16.1738
5 −143 −715 511225 1 10 4 20 1 20  ε_{1} 0.9624
13 −55 −715 511225 1 4 4 8 1  8  ε_{1} 2.3895
65 −11 −715 511225 2 1 4 4 1  2  ε_{1} 5.5529
65 −55 −143 511225 2 4 10 40 1 20  ε_{1} 5.5529
716 −4 −179 512656 1 1 5 5 2 5 \sqrt{i}\sqrt{ε_{1}} 15.9414
717  −3 −239 514089 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 5.4848
721  −7 −103 519841 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 38.1568
241  −3 −723 522729 1 1 4 2 1  2  ε_{1} 37.5430
181  −4 −724 524176 1 1 10 5 1  5  ε_{1} 14.3479
8 −91 −728 529984 1 2 12 12 1 12  ε_{1} 1.7627
13 −56 −728 529984 1 4 12 24 1 24  ε_{1} 2.3895
56 −91 −104 529984 1 2 6 6 1  6  ε_{1} 6.8002
104  −7 −728 529984 2 1 12 12 1  6  ε_{1} 4.6249
104 −56 −91 529984 2 4 2 8 1  4  ε_{1} 4.6249
728  −7 −104 529984 2 1 6 6 1  3  ε_{1} 7.9773
728  −8 −91 529984 2 1 2 2 1  1  ε_{1} 7.9773

14 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
17 −43 −731 534361 1 1 12 6 1  6  ε_{1} 4.1894
12 −183 −244 535824 1 8 6 24 1 24  ε_{1} 2.6339
732  −3 −244 535824 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.8814
732  −4 −183 535824 2 1 8 8 1  4  ε_{1} 13.7628
737 −11 −67 543169 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 20.0419
5 −148 −740 547600 1 2 16 16 1 16  ε_{1} 0.9624
37 −20 −740 547600 1 2 16 16 1 16  ε_{1} 4.9836
185  −4 −740 547600 2 1 16 16 1  8  ε_{1} 9.8254
185 −20 −148 547600 2 2 2 4 1  2  ε_{1} 9.8254
57 −39 −247 549081 1 4 6 12 1 12  ε_{1} 11.4208
741  −3 −247 549081 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.5012
741 −19 −39 549081 2 1 4 4 1  2  ε_{1} 11.0025
24 −31 −744 553536 1 3 12 18 1 18  ε_{1} 4.5849
93  −8 −744 553536 1 1 12 6 1  6  ε_{1} 6.7322
93 −24 −248 553536 1 2 8 8 1  8  ε_{1} 6.7322
248  −3 −744 553536 1 1 12 6 1  6  ε_{1} 9.6724
744  −3 −248 553536 2 1 8 8 1  4  ε_{1} 19.2319
744 −24 −31 553536 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.6159
44 −68 −187 559504 1 4 2 4 1  4  ε_{1} 5.9864
748  −4 −187 559504 2 1 2 4 2  2  \sqrt{i}\sqrt{ε_{1}} 8.1209
748 −11 −68 559504 2 1 4 4 1  2  ε_{1} 16.2418
749  −7 −107 561001 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 9.4685
188  −8 −376 565504 1 1 8 8 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.5642
376  −4 −376 565504 1 1 8 8 2  8  \sqrt{i}\sqrt{ε_{1}} 15.2710
753  −3 −251 567009 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 27.1482
5 −151 −755 570025 1 7 12 42 1 42  ε_{1} 0.9624
33 −23 −759 576081 1 3 24 36 1 36  ε_{1} 7.6563
69 −11 −759 576081 1 1 24 12 1 12  ε_{1} 6.4345
253 −3 −759 576081 1 1 24 12 1 12 ε_{1} 15.0577
5 −152 −760 577600 1 6 4 12 1 12  ε_{1} 0.9624
8 −95 −760 577600 1 8 4 16 1 16  ε_{1} 1.7627
40 −19 −760 577600 2 1 4 4 1 2 ε_{1} 3.6369
40 −95 −152 577600 2 8 6 48 1 24  ε_{1} 3.6369
152 −40 −95 577600 1 2 8 8 1  8  ε_{1} 8.6078
760  −8 −95 577600 2 1 8 8 1  4  ε_{1} 23.1051
760 −19 −40 577600 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 11.5525
109  −7 −763 582169 1 1 4 2 1  2  ε_{1} 11.1291
764  −4 −191 583696 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 16.7052
13 −59 −767 588289 1 3 22 33 1 33  ε_{1} 2.3895
257  −3 −771 594441 3 1 6 9 1  3  ε_{1} 6.9334
193  −4 −772 595984 1 1 4 2 1  2  ε_{1} 30.1526
97  −8 −776 602176 1 1 20 10 1 10  ε_{1} 18.6488
21 −111 −259 603729 1 8 4 16 1 16  ε_{1} 3.1336
777  −3 −259 603729 4 1 4 8 1  2  ε_{1} 12.2006
777  −7 −111 603729 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 6.1003
41 −19 −779 606841 1 1 10 5 1  5  ε_{1} 8.3183
12 −195 −260 608400 1 4 8 16 1 16  ε_{1} 2.6339
60 −39 −260 608400 2 4 8 32 1 16  ε_{1} 4.1269
60 −52 −195 608400 2 2 4 8 1  4  ε_{1} 4.1269
156 −15 −260 608400 2 2 8 16 1  8  ε_{1} 7.8232

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 15

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
156 −20 −195 608400 2 2 4 8 1  4  ε_{1} 7.8232
780  −3 −260 608400 4 1 8 16 1  4  ε_{1} 6.6619
780  −4 −195 608400 4 1 4 8 1  2  ε_{1} 6.6619
780 −15 −52 608400 4 2 2 8 1  2  ε_{1} 6.6619
780 −20 −39 608400 4 2 4 16 1  4  ε_{1} 6.6619
781 −11 −71 609961 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 18.7224
197 −4 −788 620944 1 1 10 5 1 5 ε_{1} 6.6670
789  −3 −263 622521 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 10.3680
113 −7 −791 625681 1 1 32 16 1 16 ε_{1} 14.6946
5 −159 −795 632025 1 10 4 20 1 20  ε_{1} 0.9624
53 −15 −795 632025 1 2 4 4 1  4  ε_{1} 3.9314
265  −3 −795 632025 2 1 4 4 1  2  ε_{1} 18.8092
265 −15 −159 632025 2 2 10 20 1 10  ε_{1} 18.8092
796 −4 −199 633616 1 1 9 9 2 9 \sqrt{i}\sqrt{ε_{1}} 24.2055
17 −47 −799 638401 1 5 16 40 1 40  ε_{1} 4.1894
73 −11 −803 644809 1 1 10 5 1  5  ε_{1} 15.3334
12 −67 −804 646416 1 1 12 6 1  6  ε_{1} 2.6339
201  −4 −804 646416 1 1 12 6 1  6  ε_{1} 27.6905
268  −3 −804 646416 1 1 12 6 1  6  ε_{1} 22.9790
161 −35 −115 648025 1 2 2 2 1  2  ε_{1} 20.1338
805  −7 −115 648025 2 1 2 2 1  1  ε_{1} 14.5545
805 −23 −35 648025 2 3 2 6 1  3  ε_{1} 14.5545
269  −3 −807 651249 1 1 14 7 1  7  ε_{1} 10.1998
101  −8 −808 652864 1 1 6 3 1  3  ε_{1} 5.9964
28 −116 −203 659344 1 6 4 12 1 12  ε_{1} 5.5373
812  −4 −203 659344 2 1 4 4 1  2  ε_{1} 9.4722
812  −7 −116 659344 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 4.7361
813  −3 −271 660969 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 8.3742
5 −163 −815 664225 1 1 30 15 1 15  ε_{1} 0.9624
12 −136 −408 665856 1 4 4 8 1  8  ε_{1} 2.6339
24 −68 −408 665856 1 4 4 8 1  8  ε_{1} 4.5849
204  −8 −408 665856 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 4.6051
204 −24 −136 665856 2 2 4 8 1  4  ε_{1} 9.2101
408  −4 −408 665856 2 1 4 8 2  4  \sqrt{i}\sqrt{ε_{1}} 5.3082
408 −24 −68 665856 2 2 4 8 1  4  ε_{1} 10.6165
817 −19 −43 667489 5 1 1 5 2  1 \sqrt{−1}\sqrt{ε_{1}} 6.5309
5 −164 −820 672400 1 8 8 32 1 32  ε_{1} 0.9624
41 −20 −820 672400 1 2 8 8 1  8  ε_{1} 8.3183
205  −4 −820 672400 2 1 8 8 1  4  ε_{1} 7.5213
205 −20 −164 672400 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 3.7607
8 −103 −824 678976 1 5 20 50 1 50  ε_{1} 1.7627
824  −8 −103 678976 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 11.6875
277  −3 −831 690561 1 1 28 14 1 14  ε_{1} 15.7365
5 −167 −835 697225 1 11 6 33 1 33  ε_{1} 0.9624
44 −19 −836 698896 1 1 20 10 1 10  ε_{1} 5.9864
76 −11 −836 698896 1 1 20 10 1 10  ε_{1} 11.6579
209 −4 −836 698896 1 1 20 10 1 10 ε_{1} 22.8829
5 −168 −840 705600 1 4 8 16 1 16  ε_{1} 0.9624
21 −40 −840 705600 1 2 8 8 1  8  ε_{1} 3.1336
21 −120 −280 705600 1 4 4 8 1  8  ε_{1} 3.1336

16 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
24 −35 −840 705600 1 2 8 8 1  8  ε_{1} 4.5849
56 −15 −840 705600 1 2 8 8 1  8  ε_{1} 6.8002
105  −8 −840 705600 2 1 8 8 1  4  ε_{1} 8.8131
105 −24 −280 705600 2 2 4 8 1  4  ε_{1} 8.8131
105 −40 −168 705600 2 2 4 8 1  4  ε_{1} 8.8131
105 −56 −120 705600 2 4 4 16 1  8  ε_{1} 8.8131
120  −7 −840 705600 2 1 8 8 1  4  ε_{1} 6.1779
120 −35 −168 705600 2 2 4 8 1  4  ε_{1} 6.1779
168 −15 −280 705600 2 2 4 8 1  4  ε_{1} 6.5132
168 −35 −120 705600 2 2 4 8 1  4  ε_{1} 6.5132
280  −3 −840 705600 2 1 8 8 1  4  ε_{1} 12.4372
280 −15 −168 705600 2 2 4 8 1  4  ε_{1} 12.4372
840  −3 −280 705600 4 1 4 8 1  2  ε_{1} 8.1203
840  −7 −120 705600 4 1 4 8 1  2  ε_{1} 8.1203
840 −15 −56 705600 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.0601
840 −24 −35 705600 4 2 2 8 1  2  ε_{1} 8.1203
281  −3 −843 710649 1 1 6 3 1  3  ε_{1} 29.1405
844  −4 −211 712336 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 27.0453
8 −212 −424 719104 1 6 6 18 1 18  ε_{1} 1.7627
424  −4 −424 719104 2 1 6 6 1  3  ε_{1} 17.9769
424  −8 −212 719104 2 1 6 6 1  3  ε_{1} 17.9769
849  −3 −283 720801 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 35.6385
37 −23 −851 724201 1 3 10 15 1 15  ε_{1} 4.9836
12 −71 −852 725904 1 7 8 28 1 28  ε_{1} 2.6339
213  −4 −852 725904 1 1 8 4 1  4  ε_{1} 8.5805
284  −3 −852 725904 1 1 8 4 1  4  ε_{1} 17.6959
8 −107 −856 732736 1 3 6 9 1  9  ε_{1} 1.7627
856  −8 −107 732736 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 27.9608
172 −20 −215 739600 1 2 14 14 1 14  ε_{1} 17.6970
860  −4 −215 739600 2 1 14 14 1  7  ε_{1} 8.9544
860 −20 −43 739600 2 2 1 2 1  1  ε_{1} 8.9544
21 −123 −287 741321 1 2 14 14 1 14  ε_{1} 3.1336
861  −3 −287 741321 2 1 14 14 1  7  ε_{1} 13.8688
861  −7 −123 741321 2 1 2 2 1  1  ε_{1} 13.8688
28 −31 −868 753424 1 3 8 12 1 12  ε_{1} 5.5373
124  −7 −868 753424 1 1 8 4 1  4  ε_{1} 16.0392
217  −4 −868 753424 1 1 8 4 1  4  ε_{1} 31.7104
869 −11 −79 755161 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 10.8072
13 −67 −871 758641 1 1 22 11 1 11  ε_{1} 2.3895
109  −8 −872 760384 1 1 10 5 1  5  ε_{1} 11.1291
12 −219 −292 767376 1 4 4 8 1  8  ε_{1} 2.6339
876  −3 −292 767376 4 1 4 8 1  2  ε_{1} 9.9943
876  −4 −219 767376 4 1 4 8 1  2  ε_{1} 9.9943
293  −3 −879 772641 1 1 22 11 1 11  ε_{1} 5.6733
44 −40 −440 774400 1 2 12 12 1 12  ε_{1} 5.9864
88 −20 −440 774400 1 2 12 12 1 12  ε_{1} 11.9527
220  −8 −440 774400 2 1 12 12 1  6  ε_{1} 10.3635
220 −40 −88 774400 2 2 2 4 1  2  ε_{1} 10.3635
440  −4 −440 774400 2 1 12 12 1  6  ε_{1} 7.4742
440 −20 −88 774400 2 2 2 4 1  2  ε_{1} 7.4742

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 17

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
13 −68 −884 781456 1 4 16 32 1 32  ε_{1} 2.3895
17 −52 −884 781456 1 2 16 16 1 16  ε_{1} 4.1894
221 −4 −884 781456 2 1 16 16 1 8 ε_{1} 5.4072
221 −52 −68 781456 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 2.7036
177 −15 −295 783225 1 2 8 8 1  8  ε_{1} 23.4697
885  −3 −295 783225 2 1 8 8 1  4  ε_{1} 10.9445
885 −15 −59 783225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.4723
8 −111 −888 788544 1 8 12 48 1 48  ε_{1} 1.7627
24 −111 −296 788544 1 8 10 40 1 40  ε_{1} 4.5849
37 −24 −888 788544 1 2 12 12 1 12  ε_{1} 4.9836
296  −3 −888 788544 2 1 12 12 1  6  ε_{1} 8.9090
296 −24 −111 788544 2 2 8 16 1  8  ε_{1} 8.9090
888  −3 −296 788544 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 5.6971
888  −8 −111 788544 2 1 8 8 1  4  ε_{1} 11.3942
889  −7 −127 790321 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 44.7223
892  −4 −223 795664 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 6.1048
893 −19 −47 797449 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 7.7411
5 −179 −895 801025 1 5 16 40 1 40  ε_{1} 0.9624
69 −39 −299 804609 1 4 8 16 1 16  ε_{1} 6.4345
897  −3 −299 804609 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.0884
897 −23 −39 804609 4 3 4 24 1  6  ε_{1} 14.1768
29 −31 −899 808201 1 3 14 21 1 21  ε_{1} 3.2945
21 −43 −903 815409 1 1 16 8 1  8  ε_{1} 3.1336
129  −7 −903 815409 1 1 16 8 1  8  ε_{1} 20.8511
301  −3 −903 815409 1 1 16 8 1  8  ε_{1} 20.0642
113  −8 −904 817216 1 1 8 4 1  4  ε_{1} 14.6946
908  −4 −227 824464 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 6.1137
8 −228 −456 831744 1 4 8 16 1 16  ε_{1} 1.7627
12 −152 −456 831744 1 6 8 24 1 24  ε_{1} 2.6339
24 −152 −228 831744 1 6 4 12 1 12  ε_{1} 4.5849
76 −24 −456 831744 1 2 8 8 1  8  ε_{1} 11.6579
152 −24 −228 831744 1 2 4 4 1  4  ε_{1} 8.6078
456  −4 −456 831744 2 1 8 16 2  8  \sqrt{i}\sqrt{ε_{1}} 7.6256
456  −8 −228 831744 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 7.6256
913 −11 −83 833569 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 34.5698
5 −183 −915 837225 1 8 8 32 1 32  ε_{1} 0.9624
61 −15 −915 837225 1 2 8 8 1  8  ε_{1} 7.3284
305  −3 −915 837225 2 1 8 8 1  4  ε_{1} 13.7710
305 −15 −183 837225 2 2 8 16 1  8  ε_{1} 13.7710
229  −4 −916 839056 3 1 10 15 1  5  ε_{1} 5.4249
917  −7 −131 840889 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 7.0741
5 −184 −920 846400 1 4 20 40 1 40  ε_{1} 0.9624
8 −115 −920 846400 1 2 20 20 1 20  ε_{1} 1.7627
40 −23 −920 846400 2 3 20 60 1 30  ε_{1} 3.6369
40 −115 −184 846400 2 2 4 8 1  4  ε_{1} 3.6369
184 −40 −115 846400 1 2 2 2 1  2  ε_{1} 21.5856
920  −8 −115 846400 2 1 2 2 1  1  ε_{1} 10.4080
920 −23 −40 846400 2 3 2 6 1  3  ε_{1} 10.4080
921  −3 −307 848241 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 36.1570
13 −71 −923 851929 1 7 10 35 1 35  ε_{1} 2.3895

18 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −231 −308 853776 1 12 8 48 1 48  ε_{1} 2.6339
21 −132 −308 853776 1 4 8 16 1 16  ε_{1} 3.1336
28 −132 −231 853776 1 4 12 24 1 24  ε_{1} 5.5373
33 −84 −308 853776 1 4 8 16 1 16  ε_{1} 7.6563
44 −84 −231 853776 1 4 12 24 1 24  ε_{1} 5.9864
77 −84 −132 853776 1 4 4 8 1  8  ε_{1} 4.3693
924  −3 −308 853776 4 1 8 16 1  4  ε_{1} 10.0477
924  −4 −231 853776 4 1 12 24 1  6  ε_{1} 10.0477
924  −7 −132 853776 4 1 4 8 1  2  ε_{1} 10.0477
924 −11 −84 853776 4 1 4 8 1  2  ε_{1} 10.0477
233  −4 −932 868624 1 1 12 6 1  6  ε_{1} 21.4863
933  −3 −311 870489 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 11.9219
5 −187 −935 874225 1 2 28 28 1 28  ε_{1} 0.9624
17 −55 −935 874225 1 4 28 56 1 56  ε_{1} 4.1894
85 −11 −935 874225 2 1 28 28 1 14  ε_{1} 4.4187
85 −55 −187 874225 2 4 2 8 1  4  ε_{1} 4.4187
313  −3 −939 881721 1 1 8 4 1  4  ε_{1} 38.7035
188 −20 −235 883600 1 2 2 2 1  2  ε_{1} 9.1285
940  −4 −235 883600 6 1 2 6 1  1  ε_{1} 9.0433
940 −20 −47 883600 6 2 5 30 1  5  ε_{1} 9.0433
41 −23 −943 889249 1 3 16 24 1 24  ε_{1} 8.3183
236  −8 −472 891136 1 1 6 6 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.9660
472  −4 −472 891136 1 1 6 6 2  6  \sqrt{i}\sqrt{ε_{1}} 13.3275
12 −79 −948 898704 1 5 12 30 1 30  ε_{1} 2.6339
237  −4 −948 898704 1 1 12 6 1  6  ε_{1} 8.6873
316  −3 −948 898704 3 1 12 18 1  6  ε_{1} 10.1503
317  −3 −951 904401 1 1 26 13 1 13  ε_{1} 8.9775
8 −119 −952 906304 1 10 8 40 1 40  ε_{1} 1.7627
17 −56 −952 906304 1 4 8 16 1 16  ε_{1} 4.1894
56 −119 −136 906304 1 10 4 20 1 20  ε_{1} 6.8002
136 −7 −952 906304 2 1 8 8 1 4 ε_{1} 8.4966
136 −56 −119 906304 2 4 10 40 1 20  ε_{1} 8.4966
952 −7 −136 906304 2 1 4 4 1 2 ε_{1} 20.1146
952  −8 −119 906304 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 10.0573
5 −191 −955 912025 1 13 4 26 1 26  ε_{1} 0.9624
956 −4 −239 913936 1 1 15 15 2 15 \sqrt{i}\sqrt{ε_{1}} 16.3324
33 −87 −319 915849 1 6 10 30 1 30  ε_{1} 7.6563
957  −3 −319 915849 2 1 10 10 1  5  ε_{1} 6.8659
957 −11 −87 915849 2 1 6 6 1  3  ε_{1} 6.8659
137  −7 −959 919681 1 1 36 18 1 18  ε_{1} 16.3142
241  −4 −964 929296 1 1 12 6 1  6  ε_{1} 37.5430
57 −51 −323 938961 1 2 4 4 1  4  ε_{1} 11.4208
969  −3 −323 938961 2 1 4 4 1  2  ε_{1} 34.2358
969 −19 −51 938961 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 17.1179
973 −7 −139 946729 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 14.4069
8 −244 −488 952576 1 6 10 30 1 30  ε_{1} 1.7627
488  −4 −488 952576 2 1 10 10 1  5  ε_{1} 6.1862
488  −8 −244 952576 2 1 6 6 1  3  ε_{1} 6.1862
89 −11 −979 958441 1 1 8 4 1  4  ε_{1} 13.8155
8 −123 −984 968256 1 2 12 12 1 12  ε_{1} 1.7627

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 19

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
24 −123 −328 968256 1 2 4 4 1  4  ε_{1} 4.5849
41 −24 −984 968256 1 2 12 12 1 12  ε_{1} 8.3183
328  −3 −984 968256 4 1 12 24 1  6  ε_{1} 5.7869
328 −24 −123 968256 4 2 2 8 1  2  ε_{1} 5.7869
984  −3 −328 968256 2 1 4 4 1  2  ε_{1} 24.1747
984  −8 −123 968256 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 12.0873
21 −47 −987 974169 1 5 8 20 1 20  ε_{1} 3.1336
141  −7 −987 974169 1 1 8 4 1  4  ε_{1} 10.4940
329  −3 −987 974169 1 1 8 4 1  4  ε_{1} 30.7485
76 −52 −247 976144 1 2 6 6 1  6  ε_{1} 11.6579
988  −4 −247 976144 2 1 6 6 1  3  ε_{1} 24.0940
988 −19  −52 976144 2 1 2 2 1  1  ε_{1} 24.0940
989 −23  −43 978121 1 3 1 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 11.5449
993  −3 −331 986049 3 1 3 9 2  3 \sqrt{−1}\sqrt{ε_{1}} 8.5743
5 −199 −995 990025 1 9 8 36 1 36  ε_{1} 0.9624
12 −83 −996 992016 1 3 12 18 1 18  ε_{1} 2.6339
249  −4 −996 992016 1 1 12 6 1  6  ε_{1} 33.3101
332  −3 −996 992016 1 1 12 6 1  6  ε_{1} 10.1997
77 −91 −143 1002001 1 2 10 10 1 10  ε_{1} 4.3693
1001  −7 −143 1002001 2 1 10 10 1  5  ε_{1} 29.1356
1001 −11  −91 1002001 2 1 2 2 1  1  ε_{1} 29.1356
17 −59 −1003 1006009 1 3 4 6 1  6  ε_{1} 4.1894
1004  −4 −251 1008016 1 1 7 7 2  7  \sqrt{i}\sqrt{ε_{1}} 15.8102
201 −15 −335 1010025 1 2 18 18 1 18  ε_{1} 27.6905
1005  −3 −335 1010025 2 1 18 18 1  9  ε_{1} 14.9988
1005 −15  −67 1010025 2 2 1 2 1  1  ε_{1} 14.9988
53 −19 −1007 1014049 1 1 30 15 1 15  ε_{1} 3.9314
337  −3 −1011 1022121 1 1 12 6 1  6  ε_{1} 42.8642
44 −23 −1012 1024144 1 3 4 6 1  6  ε_{1} 5.9864
92 −11 −1012 1024144 1 1 4 2 1  2  ε_{1} 7.7415
253  −4 −1012 1024144 1 1 4 2 1  2  ε_{1} 15.0577
5 −203 −1015 1030225 1 4 16 32 1 32  ε_{1} 0.9624
29 −35 −1015 1030225 1 2 16 16 1 16  ε_{1} 3.2945
145  −7 −1015 1030225 4 1 16 32 1  8  ε_{1} 6.3596
145 −35 −203 1030225 4 2 4 16 1  4  ε_{1} 6.3596
8 −127 −1016 1032256 1 5 16 40 1 40  ε_{1} 1.7627
1016 −8 −127 1032256 3 1 5 15 2 5 \sqrt{−1}\sqrt{ε_{1}} 6.2344
12 −255 −340 1040400 1 12 4 24 1 24  ε_{1} 2.6339
60 −51 −340 1040400 2 2 4 8 1 4 ε_{1} 4.1269
60 −68 −255 1040400 2 4 12 48 1 24  ε_{1} 4.1269
204 −15 −340 1040400 2 2 4 8 1 4 ε_{1} 9.2101
204 −20 −255 1040400 2 2 12 24 1 12  ε_{1} 9.2101
1020  −3 −340 1040400 4 1 4 8 1  2  ε_{1} 6.9295
1020  −4 −255 1040400 4 1 12 24 1  6  ε_{1} 6.9295
1020 −15  −68 1040400 4 2 4 16 1  4  ε_{1} 6.9295
1020 −20  −51 1040400 4 2 2 8 1  2  ε_{1} 6.9295
33 −31 −1023 1046529 1 3 16 24 1 24  ε_{1} 7.6563
93 −11 −1023 1046529 1 1 16 8 1  8  ε_{1} 6.7322
341  −3 −1023 1046529 1 1 16 8 1  8  ε_{1} 11.2480
13 −79 −1027 1054729 1 5 4 10 1 10  ε_{1} 2.3895

20 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
257  −4 −1028 1056784 3 1 16 24 1  8  ε_{1} 6.9334
24 −43 −1032 1065024 1 1 8 4 1  4  ε_{1} 4.5849
129  −8 −1032 1065024 1 1 8 4 1  4  ε_{1} 20.8511
129 −24 −344 1065024 1 2 10 10 1 10  ε_{1} 20.8511
344  −3 −1032 1065024 1 1 8 4 1  4  ε_{1} 19.8864
1032  −3 −344 1065024 2 1 10 10 1  5  ε_{1} 12.4844
1032 −24  −43 1065024 2 2 1 2 1  1  ε_{1} 12.4844
28 −148 −259 1073296 1 2 4 4 1  4  ε_{1} 5.5373
1036  −4 −259 1073296 2 1 4 4 1  2  ε_{1} 28.6857
1036  −7 −148 1073296 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 14.3429
8 −260 −520 1081600 1 8 4 16 1 16  ε_{1} 1.7627
40 −52 −520 1081600 2 2 4 8 1 4 ε_{1} 3.6369
40 −104 −260 1081600 2 6 8 48 1 24  ε_{1} 3.6369
104 −20 −520 1081600 2 2 4 8 1  4  ε_{1} 4.6249
104 −40 −260 1081600 2 2 8 16 1  8  ε_{1} 4.6249
520  −4 −520 1081600 4 1 4 8 1  2  ε_{1} 9.4726
520  −8 −260 1081600 4 1 8 16 1  4  ε_{1} 9.4726
520 −20 −104 1081600 4 2 6 24 1  6  ε_{1} 9.4726
520 −40  −52 1081600 4 2 2 8 1  2  ε_{1} 9.4726
1041  −3 −347 1083681 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 34.9718
149  −7 −1043 1087849 1 1 8 4 1  4  ε_{1} 8.2223
209 −55  −95 1092025 1 4 8 16 1 16  ε_{1} 22.8829
1045 −11  −95 1092025 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.5746
1045 −19  −55 1092025 4 1 4 8 1  2  ε_{1} 9.1492
349  −3 −1047 1096209 1 1 16 8 1  8  ε_{1} 19.6424
8 −131 −1048 1098304 1 5 6 15 1 15  ε_{1} 1.7627
1048  −8 −131 1098304 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 19.1624
1052  −4 −263 1106704 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 12.5363
5 −211 −1055 1113025 1 3 36 54 1 54  ε_{1} 0.9624
1057  −7 −151 1117249 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 40.7111
353  −3 −1059 1121481 1 1 6 3 1  3  ε_{1} 23.7346
5 −212 −1060 1123600 1 6 8 24 1 24  ε_{1} 0.9624
53 −20 −1060 1123600 1 2 8 8 1  8  ε_{1} 3.9314
265  −4 −1060 1123600 2 1 8 8 1  4  ε_{1} 18.8092
265 −20 −212 1123600 2 2 6 12 1  6  ε_{1} 18.8092
56 −19 −1064 1132096 1 1 20 10 1 10  ε_{1} 6.8002
133 −8 −1064 1132096 1 1 20 10 1 10 ε_{1} 10.3065
133 −56 −152 1132096 1 4 6 12 1 12  ε_{1} 10.3065
152  −7 −1064 1132096 1 1 20 10 1 10  ε_{1} 8.6078
1064  −7 −152 1132096 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 7.2226
1064 −19  −56 1132096 2 1 4 4 1  2  ε_{1} 14.4451
213 −15 −355 1134225 1 2 4 4 1  4  ε_{1} 8.5805
1065  −3 −355 1134225 2 1 4 4 1  2  ε_{1} 37.8470
1065 −15  −71 1134225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 18.9235
97 −11 −1067 1138489 1 1 12 6 1 6 ε_{1} 18.6488
12 −267 −356 1140624 1 2 12 12 1 12  ε_{1} 2.6339
1068  −3 −356 1140624 2 1 12 12 1  6  ε_{1} 16.9544
1068  −4 −267 1140624 2 1 2 4 2  2  \sqrt{i}\sqrt{ε_{1}} 8.4772
268  −8 −536 1149184 1 1 14 14 2 14 \sqrt{−1}\sqrt{ε_{1}} 11.4895
536  −4 −536 1149184 1 1 14 14 2 14  \sqrt{i}\sqrt{ε_{1}} 12.5840

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 21

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
269  −4 −1076 1157776 1 1 22 11 1 11  ε_{1} 10.1998
1077  −3 −359 1159929 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 5.8889
13 −83 −1079 1164241 1 3 34 51 1 51  ε_{1} 2.3895
1081 −23  −47 1168561 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 47.8206
1084  −4 −271 1175056 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 26.1698
217 −35 −155 1177225 1 2 4 4 1  4  ε_{1} 31.7104
1085  −7 −155 1177225 2 1 4 4 1  2  ε_{1} 6.9912
1085 −31  −35 1177225 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 3.4956
12 −91 −1092 1192464 1 2 8 8 1  8  ε_{1} 2.6339
13 −84 −1092 1192464 1 4 8 16 1 16  ε_{1} 2.3895
21 −52 −1092 1192464 1 2 8 8 1 8 ε_{1} 3.1336
28 −39 −1092 1192464 1 4 8 16 1 16  ε_{1} 5.5373
156  −7 −1092 1192464 2 1 8 8 1  4  ε_{1} 7.8232
156 −84  −91 1192464 2 4 2 8 1  4  ε_{1} 7.8232
273  −4 −1092 1192464 2 1 8 8 1  4  ε_{1} 14.5641
273 −52  −84 1192464 2 2 4 8 1  4  ε_{1} 14.5641
364  −3 −1092 1192464 2 1 8 8 1  4  ε_{1} 16.1090
364 −39  −84 1192464 2 4 4 16 1  8  ε_{1} 16.1090
5 −219 −1095 1199025 1 4 28 56 1 56  ε_{1} 0.9624
73 −15 −1095 1199025 1 2 28 28 1 28  ε_{1} 15.3334
365  −3 −1095 1199025 2 1 28 28 1 14  ε_{1} 5.8944
365 −15 −219 1199025 2 2 4 8 1  4  ε_{1} 5.8944
137  −8 −1096 1201216 1 1 12 6 1  6  ε_{1} 16.3142
157  −7 −1099 1207801 1 1 6 3 1  3  ε_{1} 10.7226
1101  −3 −367 1212201 3 1 9 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 5.8999
8 −276 −552 1218816 1 8 8 32 1 32  ε_{1} 1.7627
12 −184 −552 1218816 1 4 8 16 1 16  ε_{1} 2.6339
24 −184 −276 1218816 1 4 8 16 1 16  ε_{1} 4.5849
92 −24 −552 1218816 1 2 8 8 1  8  ε_{1} 7.7415
184 −24 −276 1218816 1 2 8 8 1  8  ε_{1} 21.5856
552  −4 −552 1218816 2 1 8 8 1  4  ε_{1} 9.0864
552  −8 −276 1218816 2 1 8 8 1  4  ε_{1} 9.0864
277  −4 −1108 1227664 1 1 6 3 1  3  ε_{1} 15.7365
101 −11 −1111 1234321 1 1 22 11 1 11  ε_{1} 5.9964
8 −139 −1112 1236544 1 3 14 21 1 21  ε_{1} 1.7627
1112 −8 −139 1236544 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 8.5176
21 −159 −371 1238769 1 10 8 40 1 40  ε_{1} 3.1336
1113 −3 −371 1238769 2 1 8 8 1 4 ε_{1} 28.3110
1113  −7 −159 1238769 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 14.1555
5 −223 −1115 1243225 1 7 10 35 1 35  ε_{1} 0.9624
373  −3 −1119 1252161 1 1 32 16 1 16  ε_{1} 18.4673
1121 −19  −59 1256641 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 33.3480
281  −4 −1124 1263376 1 1 20 10 1 10  ε_{1} 29.1405
24 −47 −1128 1272384 1 5 8 20 1 20  ε_{1} 4.5849
141  −8 −1128 1272384 1 1 8 4 1  4  ε_{1} 10.4940
141 −24 −376 1272384 1 2 8 8 1  8  ε_{1} 10.4940
376  −3 −1128 1272384 1 1 8 4 1  4  ε_{1} 30.5420
1128  −3 −376 1272384 2 1 8 8 1  4  ε_{1} 16.9115
1128 −24  −47 1272384 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 8.4557
13 −87 −1131 1279161 1 6 8 24 1 24  ε_{1} 2.3895

22 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
29 −39 −1131 1279161 1 4 8 16 1 16  ε_{1} 3.2945
377  −3 −1131 1279161 2 1 8 8 1  4  ε_{1} 12.2884
377 −39  −87 1279161 2 4 6 24 1 12  ε_{1} 12.2884
1132  −4 −283 1281424 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 19.4379
1133 −11 −103 1283689 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 4.6150
5 −227 −1135 1288225 1 5 18 45 1 45  ε_{1} 0.9624
284  −8 −568 1290496 1 1 4 4 2  4 \sqrt{−1}\sqrt{ε_{1}} 8.8479
568  −4 −568 1290496 3 1 4 12 2  4  \sqrt{i}\sqrt{ε_{1}} 5.6560
1137  −3 −379 1292769 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 27.8941
17 −67 −1139 1297321 1 1 16 8 1  8  ε_{1} 4.1894
5 −228 −1140 1299600 1 4 16 32 1 32  ε_{1} 0.9624
12 −95 −1140 1299600 1 8 16 64 1 64  ε_{1} 2.6339
57 −20 −1140 1299600 1 2 16 16 1 16  ε_{1} 11.4208
60 −19 −1140 1299600 2 1 16 16 1 8 ε_{1} 4.1269
60 −95 −228 1299600 2 8 4 32 1 16  ε_{1} 4.1269
76 −15 −1140 1299600 1 2 16 16 1 16  ε_{1} 11.6579
285  −4 −1140 1299600 2 1 16 16 1  8  ε_{1} 5.6595
285 −20 −228 1299600 2 2 4 8 1  4  ε_{1} 5.6595
380  −3 −1140 1299600 2 1 16 16 1  8  ε_{1} 8.7131
380 −15 −228 1299600 2 2 4 8 1  4  ε_{1} 8.7131
1141  −7 −163 1301881 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 20.9664
8 −143 −1144 1308736 1 10 12 60 1 60  ε_{1} 1.7627
13 −88 −1144 1308736 1 2 12 12 1 12  ε_{1} 2.3895
88 −104 −143 1308736 1 6 10 30 1 30  ε_{1} 11.9527
104 −11 −1144 1308736 2 1 12 12 1 6 ε_{1} 4.6249
104 −88 −143 1308736 2 2 10 20 1 10  ε_{1} 4.6249
1144  −8 −143 1308736 2 1 10 10 1  5  ε_{1} 27.8642
1144 −11 −104 1308736 2 1 6 6 1  3  ε_{1} 27.8642
37 −31 −1147 1315609 1 3 6 9 1  9  ε_{1} 4.9836
28 −164 −287 1317904 1 8 14 56 1 56  ε_{1} 5.5373
1148  −4 −287 1317904 2 1 14 28 2 14  \sqrt{i}\sqrt{ε_{1}} 6.3561
1148  −7 −164 1317904 2 1 8 8 1  4  ε_{1} 12.7122
1149  −3 −383 1320201 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 16.4838
5 −231 −1155 1334025 1 12 8 48 1 48  ε_{1} 0.9624
21 −55 −1155 1334025 1 4 8 16 1 16  ε_{1} 3.1336
33 −35 −1155 1334025 1 2 8 8 1  8  ε_{1} 7.6563
77 −15 −1155 1334025 1 2 8 8 1  8  ε_{1} 4.3693
105 −11 −1155 1334025 2 1 8 8 1  4  ε_{1} 8.8131
105 −55 −231 1334025 2 4 12 48 1 24  ε_{1} 8.8131
165 −7 −1155 1334025 2 1 8 8 1 4 ε_{1} 5.1180
165 −35 −231 1334025 2 2 12 24 1 12  ε_{1} 5.1180
385 −3 −1155 1334025 2 1 8 8 1 4 ε_{1} 24.3270
385 −15 −231 1334025 2 2 12 24 1 12  ε_{1} 24.3270
61 −19 −1159 1343281 1 1 16 8 1 8 ε_{1} 7.3284
5 −232 −1160 1345600 1 2 20 20 1 20  ε_{1} 0.9624
29 −40 −1160 1345600 1 2 20 20 1 20  ε_{1} 3.2945
145  −8 −1160 1345600 4 1 20 40 1 10  ε_{1} 6.3596
145 −40 −232 1345600 4 2 2 8 1  2  ε_{1} 6.3596
12 −291 −388 1354896 1 4 4 8 1  8  ε_{1} 2.6339
1164  −3 −388 1354896 4 1 4 8 1  2  ε_{1} 12.7261

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 23

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
1164  −4 −291 1354896 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 6.3630
389  −3 −1167 1361889 1 1 22 11 1 11  ε_{1} 15.6986
8 −292 −584 1364224 1 4 16 32 1 32  ε_{1} 1.7627
584  −4 −584 1364224 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 5.6699
584  −8 −292 1364224 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.6699
1169  −7 −167 1366561 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 33.5404
293 −4 −1172 1373584 1 1 18 9 1 9 ε_{1} 5.6733
69 −51 −391 1375929 1 2 14 14 1 14  ε_{1} 6.4345
1173  −3 −391 1375929 2 1 14 14 1  7  ε_{1} 11.2262
1173 −23  −51 1375929 2 3 2 6 1  3  ε_{1} 11.2262
1177 −11 −107 1385329 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 44.3891
236 −20 −295 1392400 1 2 8 8 1  8  ε_{1} 13.9320
1180  −4 −295 1392400 2 1 8 8 1  4  ε_{1} 30.4285
1180 −20  −59 1392400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 15.2142
237 −15 −395 1404225 1 2 8 8 1  8  ε_{1} 8.6873
1185  −3 −395 1404225 2 1 8 8 1  4  ε_{1} 36.4648
1185 −15  −79 1404225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 18.2324
397  −3 −1191 1418481 1 1 24 12 1 12  ε_{1} 16.2905
149  −8 −1192 1420864 1 1 6 3 1  3  ε_{1} 8.2223
5 −239 −1195 1428025 1 15 8 60 1 60  ε_{1} 0.9624
92 −52 −299 1430416 1 2 8 8 1  8  ε_{1} 7.7415
1196  −4 −299 1430416 2 1 8 8 1  4  ε_{1} 13.4428
1196 −23  −52 1430416 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.7214
109 −11 −1199 1437601 1 1 38 19 1 19  ε_{1} 11.1291
401  −3 −1203 1447209 5 1 6 15 1  3  ε_{1} 7.3790
28 −43 −1204 1449616 1 1 8 4 1  4  ε_{1} 5.5373
172  −7 −1204 1449616 1 1 8 4 1  4  ε_{1} 17.6970
301  −4 −1204 1449616 1 1 8 4 1  4  ε_{1} 20.0642
17 −71 −1207 1456849 1 7 18 63 1 63  ε_{1} 4.1894
8 −151 −1208 1459264 1 7 12 42 1 42  ε_{1} 1.7627
1208  −8 −151 1459264 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 15.9618
93 −39 −403 1461681 1 4 2 4 1  4  ε_{1} 6.7322
1209  −3 −403 1461681 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 18.5522
1209 −31  −39 1461681 2 3 4 12 1  6  ε_{1} 37.1044
173  −7 −1211 1466521 1 1 14 7 1  7  ε_{1} 5.1416
12 −303 −404 1468944 1 10 14 70 1 70  ε_{1} 2.6339
1212  −3 −404 1468944 2 1 14 14 1  7  ε_{1} 17.0535
1212  −4 −303 1468944 2 1 10 10 1  5  ε_{1} 17.0535
53 −23 −1219 1485961 1 3 6 9 1  9  ε_{1} 3.9314
5 −244 −1220 1488400 1 6 16 48 1 48  ε_{1} 0.9624
61 −20 −1220 1488400 1 2 16 16 1 16  ε_{1} 7.3284
305 −4 −1220 1488400 2 1 16 16 1 8 ε_{1} 13.7710
305 −20 −244 1488400 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.8855
33 −111 −407 1490841 1 8 16 64 1 64  ε_{1} 7.6563
1221  −3 −407 1490841 4 1 16 32 1  8  ε_{1} 7.1091
1221 −11 −111 1490841 4 1 8 16 1  4  ε_{1} 7.1091
409  −3 −1227 1505529 1 1 4 2 1  2  ε_{1} 52.2684
1228  −4 −307 1507984 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 18.9920
8 −308 −616 1517824 1 8 8 32 1 32  ε_{1} 1.7627
28 −88 −616 1517824 1 2 8 8 1  8  ε_{1} 5.5373

24 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
44 −56 −616 1517824 1 4 8 16 1 16  ε_{1} 5.9864
56 −88 −308 1517824 1 2 8 8 1 8 ε_{1} 6.8002
88 −56 −308 1517824 1 4 8 16 1 16  ε_{1} 11.9527
616  −4 −616 1517824 2 1 8 8 1  4  ε_{1} 21.3187
616  −8 −308 1517824 2 1 8 8 1  4  ε_{1} 21.3187
5 −247 −1235 1525225 1 6 12 36 1 36  ε_{1} 0.9624
13 −95 −1235 1525225 1 8 12 48 1 48  ε_{1} 2.3895
65 −19 −1235 1525225 2 1 12 12 1 6 ε_{1} 5.5529
65 −95 −247 1525225 2 8 6 48 1 24  ε_{1} 5.5529
12 −103 −1236 1527696 1 5 12 30 1 30  ε_{1} 2.6339
309  −4 −1236 1527696 1 1 12 6 1  6  ε_{1} 17.0523
412  −3 −1236 1527696 1 1 12 6 1  6  ε_{1} 26.0564
21 −59 −1239 1535121 1 3 32 48 1 48  ε_{1} 3.1336
177  −7 −1239 1535121 1 1 32 16 1 16  ε_{1} 23.4697
413  −3 −1239 1535121 1 1 32 16 1 16  ε_{1} 8.2212
5 −248 −1240 1537600 1 8 8 32 1 32  ε_{1} 0.9624
8 −155 −1240 1537600 1 4 8 16 1 16  ε_{1} 1.7627
40 −31 −1240 1537600 2 3 8 24 1 12  ε_{1} 3.6369
40 −155 −248 1537600 2 4 8 32 1 16  ε_{1} 3.6369
248 −40 −155 1537600 1 2 4 4 1  4  ε_{1} 9.6724
1240  −8 −155 1537600 2 1 4 4 1  2  ε_{1} 28.6893
1240 −31  −40 1537600 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 14.3446
113 −11 −1243 1545049 1 1 4 2 1  2  ε_{1} 14.6946
1244  −4 −311 1547536 1 1 19 19 2 19  \sqrt{i}\sqrt{ε_{1}} 17.3350
249 −15 −415 1550025 1 2 10 10 1 10  ε_{1} 33.3101
1245  −3 −415 1550025 2 1 10 10 1  5  ε_{1} 11.0187
1245 −15  −83 1550025 2 2 3 6 1  3  ε_{1} 11.0187
29 −43 −1247 1555009 1 1 26 13 1 13  ε_{1} 3.2945
313  −4 −1252 1567504 1 1 8 4 1  4  ε_{1} 38.7035
1253  −7 −179 1570009 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 5.1761
5 −251 −1255 1575025 1 7 12 42 1 42  ε_{1} 0.9624
157  −8 −1256 1577536 1 1 26 13 1 13  ε_{1} 10.7226
1257  −3 −419 1580049 3 1 9 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 12.2200
421  −3 −1263 1595169 1 1 20 10 1 10  ε_{1} 26.0114
316  −8 −632 1597696 3 1 8 24 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.0751
632  −4 −632 1597696 1 1 8 8 2  8  \sqrt{i}\sqrt{ε_{1}} 9.6477
253 −55 −115 1600225 1 4 2 4 1  4  ε_{1} 15.0577
1265 −11 −115 1600225 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 12.9336
1265 −23  −55 1600225 2 3 4 12 1  6  ε_{1} 25.8672
181  −7 −1267 1605289 1 1 6 3 1  3  ε_{1} 14.3479
317  −4 −1268 1607824 1 1 10 5 1  5  ε_{1} 8.9775
41 −31 −1271 1615441 1 3 40 60 1 60  ε_{1} 8.3183
8 −159 −1272 1617984 1 10 12 60 1 60  ε_{1} 1.7627
24 −159 −424 1617984 1 10 6 30 1 30  ε_{1} 4.5849
53 −24 −1272 1617984 1 2 12 12 1 12  ε_{1} 3.9314
424 −3 −1272 1617984 2 1 12 12 1 6 ε_{1} 17.9769
424 −24 −159 1617984 2 2 10 20 1 10  ε_{1} 17.9769
1272  −3 −424 1617984 2 1 6 6 1  3  ε_{1} 10.7319
1272  −8 −159 1617984 2 1 10 10 1  5  ε_{1} 10.7319
1273 −19  −67 1620529 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 40.4439

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 25

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
44 −116 −319 1628176 1 6 10 30 1 30  ε_{1} 5.9864
1276  −4 −319 1628176 2 1 10 10 1  5  ε_{1} 34.1320
1276 −11 −116 1628176 2 1 6 6 1  3  ε_{1} 34.1320
21 −183 −427 1640961 1 8 2 8 1  8  ε_{1} 3.1336
1281  −3 −427 1640961 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 21.1811
1281  −7 −183 1640961 2 1 8 8 1  4  ε_{1} 42.3622
12 −107 −1284 1648656 1 3 20 30 1 30  ε_{1} 2.6339
321  −4 −1284 1648656 3 1 20 30 1 10  ε_{1} 12.1276
428  −3 −1284 1648656 1 1 20 10 1 10  ε_{1} 15.1243
56 −23 −1288 1658944 1 3 8 12 1 12  ε_{1} 6.8002
161  −8 −1288 1658944 1 1 8 4 1  4  ε_{1} 20.1338
161 −56 −184 1658944 1 4 4 8 1  8  ε_{1} 20.1338
184  −7 −1288 1658944 1 1 8 4 1  4  ε_{1} 21.5856
1288  −7 −184 1658944 4 1 4 8 1  2  ε_{1} 12.9416
1288 −23  −56 1658944 4 3 4 24 1  6  ε_{1} 12.9416
76 −68 −323 1669264 1 4 4 8 1  8  ε_{1} 11.6579
1292  −4 −323 1669264 4 1 4 8 1  2  ε_{1} 7.1655
1292 −19  −68 1669264 4 1 4 8 1  2  ε_{1} 7.1655
1293  −3 −431 1671849 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 7.4536
5 −259 −1295 1677025 1 4 36 72 1 72  ε_{1} 0.9624
37 −35 −1295 1677025 1 2 36 36 1 36  ε_{1} 4.9836
185  −7 −1295 1677025 2 1 36 36 1 18  ε_{1} 9.8254
185 −35 −259 1677025 2 2 4 8 1  4  ε_{1} 9.8254
433  −3 −1299 1687401 1 1 8 4 1  4  ε_{1} 46.7895
8 −163 −1304 1700416 1 1 22 11 1 11  ε_{1} 1.7627
1304 −8 −163 1700416 3 1 1 3 2 1 \sqrt{−1}\sqrt{ε_{1}} 6.4770
12 −327 −436 1710864 1 12 6 36 1 36  ε_{1} 2.6339
1308  −3 −436 1710864 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.0730
1308  −4 −327 1710864 2 1 12 12 1  6  ε_{1} 12.1461
77 −119 −187 1713481 1 10 2 10 1 10  ε_{1} 4.3693
1309  −7 −187 1713481 2 1 2 2 1  1  ε_{1} 23.3418
1309 −11 −119 1713481 2 1 10 10 1  5  ε_{1} 23.3418
57 −23 −1311 1718721 1 3 28 42 1 42  ε_{1} 11.4208
69 −19 −1311 1718721 1 1 28 14 1 14  ε_{1} 6.4345
437 −3 −1311 1718721 1 1 28 14 1 14 ε_{1} 6.0845
5 −263 −1315 1729225 1 13 6 39 1 39  ε_{1} 0.9624
28 −47 −1316 1731856 1 5 24 60 1 60  ε_{1} 5.5373
188  −7 −1316 1731856 1 1 24 12 1 12  ε_{1} 9.1285
329  −4 −1316 1731856 1 1 24 12 1 12  ε_{1} 30.7485
1317  −3 −439 1734489 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 12.9525
5 −264 −1320 1742400 1 8 8 32 1 32  ε_{1} 0.9624
24 −55 −1320 1742400 1 4 8 16 1 16  ε_{1} 4.5849
33 −40 −1320 1742400 1 2 8 8 1 8 ε_{1} 7.6563
33 −120 −440 1742400 1 4 12 24 1 24  ε_{1} 7.6563
88 −15 −1320 1742400 1 2 8 8 1  8  ε_{1} 11.9527
120 −11 −1320 1742400 2 1 8 8 1  4  ε_{1} 6.1779
120 −55 −264 1742400 2 4 8 32 1 16  ε_{1} 6.1779
165 −8 −1320 1742400 2 1 8 8 1 4 ε_{1} 5.1180
165 −24 −440 1742400 2 2 12 24 1 12  ε_{1} 5.1180
165 −40 −264 1742400 2 2 8 16 1  8  ε_{1} 5.1180

26 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
165 −88 −120 1742400 2 2 4 8 1  4  ε_{1} 5.1180
264 −15 −440 1742400 2 2 12 24 1 12  ε_{1} 9.7350
264 −55 −120 1742400 2 4 4 16 1  8  ε_{1} 9.7350
440  −3 −1320 1742400 2 1 8 8 1  4  ε_{1} 7.4742
440 −15 −264 1742400 2 2 8 16 1  8  ε_{1} 7.4742
1320  −3 −440 1742400 4 1 12 24 1  6  ε_{1} 10.7689
1320 −11 −120 1742400 4 1 4 8 1  2  ε_{1} 10.7689
1320 −15  −88 1742400 4 2 2 8 1  2  ε_{1} 10.7689
1320 −24  −55 1742400 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.3845
1324  −4 −331 1752976 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 36.2564
332  −8 −664 1763584 1 1 10 10 2 10 \sqrt{−1}\sqrt{ε_{1}} 5.0998
664  −4 −664 1763584 1 1 10 10 2 10  \sqrt{i}\sqrt{ε_{1}} 21.9476
1329  −3 −443 1766241 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 41.7896
1333 −31  −43 1776889 1 3 1 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 11.3745
5 −267 −1335 1782225 1 2 28 28 1 28  ε_{1} 0.9624
89 −15 −1335 1782225 1 2 28 28 1 28  ε_{1} 13.8155
445  −3 −1335 1782225 4 1 28 56 1 14  ε_{1} 6.0936
445 −15 −267 1782225 4 2 2 8 1  2  ε_{1} 6.0936
8 −167 −1336 1784896 1 11 12 66 1 66  ε_{1} 1.7627
1336  −8 −167 1784896 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 32.4800
1337  −7 −191 1787569 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 21.7293
13 −103 −1339 1792921 1 5 8 20 1 20  ε_{1} 2.3895
268 −20 −335 1795600 1 2 18 18 1 18  ε_{1} 22.9790
1340  −4 −335 1795600 2 1 18 18 1  9  ε_{1} 14.1934
1340 −20  −67 1795600 2 2 1 2 1  1  ε_{1} 14.1934
17 −79 −1343 1803649 1 5 34 85 1 85  ε_{1} 4.1894
449  −3 −1347 1814409 1 1 6 3 1  3  ε_{1} 39.5058
337  −4 −1348 1817104 1 1 8 4 1  4  ε_{1} 42.8642
1349 −19  −71 1819801 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 9.6789
193  −7 −1351 1825201 1 1 24 12 1 12  ε_{1} 30.1526
33 −123 −451 1830609 1 2 6 6 1  6  ε_{1} 7.6563
1353  −3 −451 1830609 2 1 6 6 1  3  ε_{1} 36.5389
1353 −11 −123 1830609 2 1 2 2 1  1  ε_{1} 36.5389
5 −271 −1355 1836025 1 11 12 66 1 66  ε_{1} 0.9624
12 −339 −452 1838736 1 6 8 24 1 24  ε_{1} 2.6339
1356  −3 −452 1838736 2 1 8 8 1  4  ε_{1} 24.3711
1356  −4 −339 1838736 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 12.1856
1357 −23  −59 1841449 1 3 3 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 13.7019
8 −340 −680 1849600 1 4 12 24 1 24  ε_{1} 1.7627
40 −68 −680 1849600 2 4 12 48 1 24  ε_{1} 3.6369
40 −136 −340 1849600 2 4 4 16 1 8 ε_{1} 3.6369
136 −20 −680 1849600 2 2 12 24 1 12  ε_{1} 8.4966
136 −40 −340 1849600 2 2 4 8 1  4  ε_{1} 8.4966
680  −4 −680 1849600 4 1 12 24 1  6  ε_{1} 6.5191
680  −8 −340 1849600 4 1 4 8 1  2  ε_{1} 6.5191
680 −20 −136 1849600 4 2 4 16 1  4  ε_{1} 6.5191
680 −40  −68 1849600 4 2 4 16 1  4  ε_{1} 6.5191
29 −47 −1363 1857769 1 5 6 15 1 15  ε_{1} 3.2945
44 −31 −1364 1860496 1 3 28 42 1 42  ε_{1} 5.9864
124 −11 −1364 1860496 1 1 28 14 1 14  ε_{1} 16.0392

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 27

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
341  −4 −1364 1860496 1 1 28 14 1 14  ε_{1} 11.2480
21 −195 −455 1863225 1 4 20 40 1 40  ε_{1} 3.1336
105 −39 −455 1863225 2 4 20 80 1 40  ε_{1} 8.8131
105 −91 −195 1863225 2 2 4 8 1 4 ε_{1} 8.8131
273 −15 −455 1863225 2 2 20 40 1 20  ε_{1} 14.5641
273 −35 −195 1863225 2 2 4 8 1  4  ε_{1} 14.5641
1365  −3 −455 1863225 4 1 20 40 1 10  ε_{1} 7.2204
1365  −7 −195 1863225 4 1 4 8 1  2  ε_{1} 7.2204
1365 −15  −91 1863225 4 2 2 8 1  2  ε_{1} 7.2204
1365 −35  −39 1863225 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 3.6102
457  −3 −1371 1879641 1 1 12 6 1  6  ε_{1} 50.9909
197  −7 −1379 1901641 1 1 16 8 1  8  ε_{1} 6.6670
5 −276 −1380 1904400 1 8 8 32 1 32  ε_{1} 0.9624
12 −115 −1380 1904400 1 2 8 8 1 8 ε_{1} 2.6339
60 −23 −1380 1904400 2 3 8 24 1 12  ε_{1} 4.1269
60 −115 −276 1904400 2 2 8 16 1  8  ε_{1} 4.1269
69 −20 −1380 1904400 1 2 8 8 1  8  ε_{1} 6.4345
92 −15 −1380 1904400 1 2 8 8 1  8  ε_{1} 7.7415
345  −4 −1380 1904400 2 1 8 8 1  4  ε_{1} 19.0241
345 −20 −276 1904400 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 9.5121
460  −3 −1380 1904400 2 1 8 8 1  4  ε_{1} 15.4391
460 −15 −276 1904400 2 2 8 16 1  8  ε_{1} 15.4391
461  −3 −1383 1912689 1 1 18 9 1  9  ε_{1} 11.7998
173  −8 −1384 1915456 1 1 10 5 1  5  ε_{1} 5.1416
73 −19 −1387 1923769 1 1 4 2 1  2  ε_{1} 15.3334
1388  −4 −347 1926544 1 1 5 5 2  5  \sqrt{i}\sqrt{ε_{1}} 14.0649
1389  −3 −463 1929321 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 14.0402
13 −107 −1391 1934881 1 3 44 66 1 66  ε_{1} 2.3895
12 −232 −696 1937664 1 2 12 12 1 12  ε_{1} 2.6339
24 −116 −696 1937664 1 6 12 36 1 36  ε_{1} 4.5849
348 −8 −696 1937664 2 1 12 12 1 6 ε_{1} 8.0501
348 −24 −232 1937664 2 2 2 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 4.0250
696 −4 −696 1937664 2 1 12 12 1 6 ε_{1} 15.9463
696 −24 −116 1937664 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.9732
1393  −7 −199 1940449 5 1 9 45 2  9 \sqrt{−1}\sqrt{ε_{1}} 8.8771
349  −4 −1396 1948816 1 1 14 7 1  7  ε_{1} 19.6424
1397 −11 −127 1951609 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 8.0637
1401 −3 −467 1962801 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 49.5505
61 −23 −1403 1968409 1 3 14 21 1 21  ε_{1} 7.3284
21 −67 −1407 1979649 1 1 24 12 1 12  ε_{1} 3.1336
201  −7 −1407 1979649 1 1 24 12 1 12  ε_{1} 27.6905
469  −3 −1407 1979649 3 1 24 36 1 12  ε_{1} 8.3483
17 −83 −1411 1990921 1 3 4 6 1  6  ε_{1} 4.1894
353  −4 −1412 1993744 1 1 16 8 1  8  ε_{1} 23.7346
5 −283 −1415 2002225 1 3 34 51 1 51  ε_{1} 0.9624
24 −59 −1416 2005056 1 3 16 24 1 24  ε_{1} 4.5849
177  −8 −1416 2005056 1 1 16 8 1  8  ε_{1} 23.4697
177 −24 −472 2005056 1 2 6 6 1  6  ε_{1} 23.4697
472  −3 −1416 2005056 1 1 16 8 1  8  ε_{1} 26.6550
1416  −3 −472 2005056 2 1 6 6 1  3  ε_{1} 26.3082

28 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
1416 −24  −59 2005056 2 2 3 6 1  3  ε_{1} 26.3082
33 −43 −1419 2013561 1 1 12 6 1  6  ε_{1} 7.6563
129 −11 −1419 2013561 1 1 12 6 1  6  ε_{1} 20.8511
473  −3 −1419 2013561 3 1 12 18 1  6  ε_{1} 10.3180
284 −20 −355 2016400 1 2 4 4 1  4  ε_{1} 17.6959
1420  −4 −355 2016400 2 1 4 4 1  2  ε_{1} 28.9248
1420 −20  −71 2016400 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 14.4624
8 −356 −712 2027776 1 12 8 48 1 48  ε_{1} 1.7627
712 −4 −712 2027776 2 1 8 16 2 8 \sqrt{i}\sqrt{ε_{1}} 8.0715
712  −8 −356 2027776 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.0715
12 −119 −1428 2039184 1 10 8 40 1 40  ε_{1} 2.6339
17 −84 −1428 2039184 1 4 8 16 1 16  ε_{1} 4.1894
21 −68 −1428 2039184 1 4 8 16 1 16  ε_{1} 3.1336
28 −51 −1428 2039184 1 2 8 8 1  8  ε_{1} 5.5373
204  −7 −1428 2039184 2 1 8 8 1  4  ε_{1} 9.2101
204 −84 −119 2039184 2 4 10 40 1 20  ε_{1} 9.2101
357 −4 −1428 2039184 2 1 8 8 1 4 ε_{1} 5.8833
357 −68  −84 2039184 2 4 4 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 2.9417
476  −3 −1428 2039184 2 1 8 8 1  4  ε_{1} 10.9612
476 −51  −84 2039184 2 2 4 8 1  4  ε_{1} 10.9612
8 −179 −1432 2050624 1 5 6 15 1 15  ε_{1} 1.7627
1432 −8 −179 2050624 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 26.5902
5 −287 −1435 2059225 1 14 4 28 1 28  ε_{1} 0.9624
41 −35 −1435 2059225 1 2 4 4 1  4  ε_{1} 8.3183
205  −7 −1435 2059225 2 1 4 4 1  2  ε_{1} 7.5213
205 −35 −287 2059225 2 2 14 28 1 14  ε_{1} 7.5213
1436 −4 −359 2062096 3 1 19 57 2 19 \sqrt{i}\sqrt{ε_{1}} 6.5792
1437  −3 −479 2064969 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 10.9675
1441 −11 −131 2076481 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 55.7820
13 −111 −1443 2082249 1 8 8 32 1 32  ε_{1} 2.3895
37 −39 −1443 2082249 1 4 8 16 1 16  ε_{1} 4.9836
481 −3 −1443 2082249 2 1 8 8 1 4 ε_{1} 28.9443
481 −39 −111 2082249 2 4 8 32 1 16  ε_{1} 28.9443
181 −8 −1448 2096704 1 1 18 9 1 9 ε_{1} 14.3479
5 −291 −1455 2117025 1 4 28 56 1 56  ε_{1} 0.9624
97 −15 −1455 2117025 1 2 28 28 1 28  ε_{1} 18.6488
485  −3 −1455 2117025 2 1 28 28 1 14  ε_{1} 7.5694
485 −15 −291 2117025 2 2 4 8 1  4  ε_{1} 7.5694
28 −104 −728 2119936 1 6 12 36 1 36  ε_{1} 5.5373
56 −52 −728 2119936 1 2 12 12 1 12  ε_{1} 6.8002
364 −8 −728 2119936 2 1 12 12 1 6 ε_{1} 16.1090
364 −56 −104 2119936 2 4 6 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 8.0545
728  −4 −728 2119936 2 1 12 12 1  6  ε_{1} 7.9773
728 −52  −56 2119936 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 3.9886
1457 −31  −47 2122849 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 30.3028
5 −292 −1460 2131600 1 4 20 40 1 40  ε_{1} 0.9624
73 −20 −1460 2131600 1 2 20 20 1 20  ε_{1} 15.3334
365  −4 −1460 2131600 2 1 20 20 1 10  ε_{1} 5.8944
365 −20 −292 2131600 2 2 4 8 1  4  ε_{1} 5.8944
1461  −3 −487 2134521 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 16.0572

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 29

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
77 −19 −1463 2140369 1 1 32 16 1 16  ε_{1} 4.3693
133 −11 −1463 2140369 1 1 32 16 1 16  ε_{1} 10.3065
209 −7 −1463 2140369 1 1 32 16 1 16 ε_{1} 22.8829
8 −183 −1464 2143296 1 8 12 48 1 48  ε_{1} 1.7627
24 −183 −488 2143296 1 8 10 40 1 40  ε_{1} 4.5849
61 −24 −1464 2143296 1 2 12 12 1 12  ε_{1} 7.3284
488  −3 −1464 2143296 2 1 12 12 1  6  ε_{1} 6.1862
488 −24 −183 2143296 2 2 8 16 1  8  ε_{1} 6.1862
1464  −3 −488 2143296 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 14.4121
1464  −8 −183 2143296 2 1 8 8 1  4  ε_{1} 28.8241
1468  −4 −367 2155024 1 1 9 9 2  9  \sqrt{i}\sqrt{ε_{1}} 24.3619
1473  −3 −491 2169729 1 1 9 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 29.3020
1477  −7 −211 2181529 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 17.1185
17 −87 −1479 2187441 1 6 28 84 1 84  ε_{1} 4.1894
29 −51 −1479 2187441 1 2 28 28 1 28  ε_{1} 3.2945
493  −3 −1479 2187441 2 1 28 28 1 14  ε_{1} 9.4192
493 −51  −87 2187441 2 2 6 12 1  6  ε_{1} 9.4192
5 −296 −1480 2190400 1 10 12 60 1 60  ε_{1} 0.9624
37 −40 −1480 2190400 1 2 12 12 1 12  ε_{1} 4.9836
185 −8 −1480 2190400 2 1 12 12 1 6 ε_{1} 9.8254
185 −40 −296 2190400 2 2 10 20 1 10  ε_{1} 9.8254
28 −212 −371 2202256 1 6 8 24 1 24  ε_{1} 5.5373
1484  −4 −371 2202256 2 1 8 8 1  4  ε_{1} 16.2572
1484  −7 −212 2202256 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 8.1286
8 −372 −744 2214144 1 4 12 24 1 24  ε_{1} 1.7627
12 −248 −744 2214144 1 8 12 48 1 48  ε_{1} 2.6339
24 −248 −372 2214144 1 8 4 16 1 16  ε_{1} 4.5849
124 −24 −744 2214144 1 2 12 12 1 12  ε_{1} 16.0392
248 −24 −372 2214144 1 2 4 4 1  4  ε_{1} 9.6724
744  −4 −744 2214144 2 1 12 12 1  6  ε_{1} 19.2319
744  −8 −372 2214144 2 1 4 4 1  2  ε_{1} 19.2319
21 −71 −1491 2223081 1 7 12 42 1 42  ε_{1} 3.1336
213  −7 −1491 2223081 1 1 12 6 1  6  ε_{1} 8.5805
497  −3 −1491 2223081 1 1 12 6 1  6  ε_{1} 29.3851
373  −4 −1492 2226064 1 1 10 5 1  5  ε_{1} 18.4673
5 −299 −1495 2235025 1 8 20 80 1 80  ε_{1} 0.9624
13 −115 −1495 2235025 1 2 20 20 1 20  ε_{1} 2.3895
65 −23 −1495 2235025 2 3 20 60 1 30  ε_{1} 5.5529
65 −115 −299 2235025 2 2 8 16 1 8 ε_{1} 5.5529
8 −187 −1496 2238016 1 2 28 28 1 28  ε_{1} 1.7627
17 −88 −1496 2238016 1 2 28 28 1 28  ε_{1} 4.1894
88 −136 −187 2238016 1 4 2 4 1 4 ε_{1} 11.9527
136 −11 −1496 2238016 2 1 28 28 1 14  ε_{1} 8.4966
136 −88 −187 2238016 2 2 2 4 1  2  ε_{1} 8.4966
1496  −8 −187 2238016 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 8.8143
1496 −11 −136 2238016 2 1 4 4 1  2  ε_{1} 17.6287
1497  −3 −499 2241009 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 31.4384
1501 −19  −79 2253001 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 21.8227
301 −35 −215 2265025 1 2 14 14 1 14  ε_{1} 20.0642
1505  −7 −215 2265025 2 1 14 14 1  7  ε_{1} 33.9818

30 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
1505 −35  −43 2265025 2 2 1 2 1  1  ε_{1} 33.9818
137 −11 −1507 2271049 1 1 4 2 1  2  ε_{1} 16.3142
13 −116 −1508 2274064 1 6 16 48 1 48  ε_{1} 2.3895
29 −52 −1508 2274064 1 2 16 16 1 16  ε_{1} 3.2945
377 −4 −1508 2274064 2 1 16 16 1 8 ε_{1} 12.2884
377 −52 −116 2274064 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.1442
1509  −3 −503 2277081 3 1 21 63 2 21 \sqrt{−1}\sqrt{ε_{1}} 6.2246
5 −303 −1515 2295225 1 10 12 60 1 60  ε_{1} 0.9624
101 −15 −1515 2295225 1 2 12 12 1 12  ε_{1} 5.9964
505 −3 −1515 2295225 4 1 12 24 1 6 ε_{1} 14.7779
505 −15 −303 2295225 4 2 10 40 1 10  ε_{1} 14.7779
1516  −4 −379 2298256 1 1 3 3 2  3  \sqrt{i}\sqrt{ε_{1}} 37.7923
76 −40 −760 2310400 1 2 4 4 1  4  ε_{1} 11.6579
152 −20 −760 2310400 1 2 4 4 1  4  ε_{1} 8.6078
380  −8 −760 2310400 2 1 4 4 1  2  ε_{1} 8.7131
380 −40 −152 2310400 2 2 6 12 1  6  ε_{1} 8.7131
760  −4 −760 2310400 2 1 4 4 1  2  ε_{1} 23.1051
760 −20 −152 2310400 2 2 6 12 1  6  ε_{1} 23.1051
12 −127 −1524 2322576 1 5 20 50 1 50  ε_{1} 2.6339
381  −4 −1524 2322576 1 1 20 10 1 10  ε_{1} 15.2316
508  −3 −1524 2322576 1 1 20 10 1 10  ε_{1} 32.1254
509  −3 −1527 2331729 1 1 14 7 1  7  ε_{1} 13.6596
8 −191 −1528 2334784 1 13 8 52 1 52  ε_{1} 1.7627
1528  −8 −191 2334784 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 26.5223
1529 −11 −139 2337841 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 32.6048
1532 −4 −383 2347024 1 1 17 17 2 17 \sqrt{i}\sqrt{ε_{1}} 10.5331
21 −219 −511 2350089 1 4 14 28 1 28  ε_{1} 3.1336
1533  −3 −511 2350089 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 6.2324
1533 −7 −219 2350089 2 1 4 4 1 2 ε_{1} 12.4649
5 −307 −1535 2356225 1 3 38 57 1 57  ε_{1} 0.9624
5 −308 −1540 2371600 1 8 8 32 1 32  ε_{1} 0.9624
28 −55 −1540 2371600 1 4 8 16 1 16  ε_{1} 5.5373
44 −35 −1540 2371600 1 2 8 8 1  8  ε_{1} 5.9864
77 −20 −1540 2371600 1 2 8 8 1  8  ε_{1} 4.3693
140 −11 −1540 2371600 2 1 8 8 1  4  ε_{1} 4.9558
140 −55 −308 2371600 2 4 8 32 1 16  ε_{1} 4.9558
220  −7 −1540 2371600 2 1 8 8 1  4  ε_{1} 10.3635
220 −35 −308 2371600 2 2 8 16 1  8  ε_{1} 10.3635
385  −4 −1540 2371600 2 1 8 8 1  4  ε_{1} 24.3270
385 −20 −308 2371600 2 2 8 16 1  8  ε_{1} 24.3270
1541 −23  −67 2374681 1 3 1 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 13.9854
193  −8 −1544 2383936 1 1 20 10 1 10  ε_{1} 30.1526
309 −15 −515 2387025 1 2 6 6 1  6  ε_{1} 17.0523
1545  −3 −515 2387025 2 1 6 6 1  3  ε_{1} 38.6495
1545 −15 −103 2387025 2 2 5 10 1  5  ε_{1} 38.6495
13 −119 −1547 2393209 1 10 12 60 1 60  ε_{1} 2.3895
17 −91 −1547 2393209 1 2 12 12 1 12  ε_{1} 4.1894
221 −7 −1547 2393209 2 1 12 12 1 6 ε_{1} 5.4072
221 −91 −119 2393209 2 2 10 20 1 10  ε_{1} 5.4072
33 −47 −1551 2405601 1 5 32 80 1 80  ε_{1} 7.6563

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 31

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
141 −11 −1551 2405601 1 1 32 16 1 16  ε_{1} 10.4940
517 −3 −1551 2405601 1 1 32 16 1 16 ε_{1} 18.5321
8 −388 −776 2408704 1 4 20 40 1 40  ε_{1} 1.7627
776  −4 −776 2408704 2 1 20 40 2 20  \sqrt{i}\sqrt{ε_{1}} 5.9661
776  −8 −388 2408704 2 1 4 8 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.9661
5 −311 −1555 2418025 1 19 4 38 1 38  ε_{1} 0.9624
389 −4 −1556 2421136 1 1 22 11 1 11 ε_{1} 15.6986
5 −312 −1560 2433600 1 4 16 32 1 32  ε_{1} 0.9624
8 −195 −1560 2433600 1 4 16 32 1 32  ε_{1} 1.7627
13 −120 −1560 2433600 1 4 16 32 1 32  ε_{1} 2.3895
24 −195 −520 2433600 1 4 4 8 1 8 ε_{1} 4.5849
40 −39 −1560 2433600 2 4 16 64 1 32  ε_{1} 3.6369
40 −195 −312 2433600 2 4 4 16 1 8 ε_{1} 3.6369
65 −24 −1560 2433600 2 2 16 32 1 16  ε_{1} 5.5529
65 −120 −312 2433600 2 4 4 16 1 8 ε_{1} 5.5529
104 −15 −1560 2433600 2 2 16 32 1 16  ε_{1} 4.6249
104 −120 −195 2433600 2 4 4 16 1  8  ε_{1} 4.6249
120 −39 −520 2433600 2 4 4 16 1  8  ε_{1} 6.1779
120 −104 −195 2433600 2 6 4 24 1 12  ε_{1} 6.1779
312 −15 −520 2433600 2 2 4 8 1  4  ε_{1} 9.3267
312 −40 −195 2433600 2 2 4 8 1  4  ε_{1} 9.3267
520  −3 −1560 2433600 4 1 16 32 1  8  ε_{1} 9.4726
520 −15 −312 2433600 4 2 4 16 1  4  ε_{1} 9.4726
520 −24 −195 2433600 4 2 4 16 1  4  ε_{1} 9.4726
520 −39 −120 2433600 4 4 4 32 1  8  ε_{1} 9.4726
1560  −3 −520 2433600 4 1 4 8 1  2  ε_{1} 10.1251
1560  −8 −195 2433600 4 1 4 8 1  2  ε_{1} 10.1251
1560 −15 −104 2433600 4 2 6 24 1  6  ε_{1} 10.1251
1560 −39  −40 2433600 4 4 2 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.0626
1561  −7 −223 2436721 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 61.0992
521  −3 −1563 2442969 1 1 6 3 1  3  ε_{1} 38.7273
92 −68 −391 2446096 1 4 14 28 1 28  ε_{1} 7.7415
1564  −4 −391 2446096 2 1 14 28 2 14  \sqrt{i}\sqrt{ε_{1}} 16.5018
1564 −23  −68 2446096 2 3 4 12 1  6  ε_{1} 33.0036
1569  −3 −523 2461761 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 50.3487
12 −131 −1572 2471184 1 5 12 30 1 30  ε_{1} 2.6339
393  −4 −1572 2471184 1 1 12 6 1  6  ε_{1} 36.6935
524  −3 −1572 2471184 1 1 12 6 1  6  ε_{1} 19.9254
197  −8 −1576 2483776 1 1 10 5 1  5  ε_{1} 6.6670
1577 −19  −83 2486929 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 33.0456
316 −20 −395 2496400 3 2 8 24 1  8  ε_{1} 10.1503
1580  −4 −395 2496400 2 1 8 8 1  4  ε_{1} 11.5241
1580 −20  −79 2496400 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 5.7620
93 −51 −527 2499561 1 2 18 18 1 18  ε_{1} 6.7322
1581  −3 −527 2499561 2 1 18 18 1  9  ε_{1} 13.4549
1581 −31  −51 2499561 2 3 2 6 1  3  ε_{1} 13.4549
397  −4 −1588 2521744 1 1 6 3 1  3  ε_{1} 16.2905
1589  −7 −227 2524921 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 15.6609
37 −43 −1591 2531281 1 1 22 11 1 11  ε_{1} 4.9836
8 −199 −1592 2534464 1 9 20 90 1 90  ε_{1} 1.7627

32 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
1592  −8 −199 2534464 1 1 9 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 6.6821
5 −319 −1595 2544025 1 10 16 80 1 80  ε_{1} 0.9624
29 −55 −1595 2544025 1 4 16 32 1 32  ε_{1} 3.2945
145 −11 −1595 2544025 4 1 16 32 1 8 ε_{1} 6.3596
145 −55 −319 2544025 4 4 10 80 1 20  ε_{1} 6.3596
12 −399 −532 2547216 1 16 4 32 1 32  ε_{1} 2.6339
21 −228 −532 2547216 1 4 4 8 1 8 ε_{1} 3.1336
28 −228 −399 2547216 1 4 16 32 1 32  ε_{1} 5.5373
57 −84 −532 2547216 1 4 4 8 1 8 ε_{1} 11.4208
76 −84 −399 2547216 1 4 16 32 1 32  ε_{1} 11.6579
133 −84 −228 2547216 1 4 4 8 1  8  ε_{1} 10.3065
1596  −3 −532 2547216 8 1 4 16 1  2  ε_{1} 7.3765
1596  −4 −399 2547216 8 1 16 64 1  8  ε_{1} 7.3765
1596  −7 −228 2547216 8 1 4 16 1  2  ε_{1} 7.3765
1596 −19  −84 2547216 8 1 4 16 1  2  ε_{1} 7.3765
13 −123 −1599 2556801 1 2 36 36 1 36  ε_{1} 2.3895
41 −39 −1599 2556801 1 4 36 72 1 72  ε_{1} 8.3183
533  −3 −1599 2556801 2 1 36 36 1 18  ε_{1} 6.2748
533 −39 −123 2556801 2 4 2 8 1  4  ε_{1} 6.2748
229  −7 −1603 2569609 3 1 6 9 1  3  ε_{1} 5.4249
401  −4 −1604 2572816 5 1 20 50 1 10  ε_{1} 7.3790
321 −15 −535 2576025 3 2 14 42 1 14  ε_{1} 12.1276
1605  −3 −535 2576025 2 1 14 14 1  7  ε_{1} 14.3124
1605 −15 −107 2576025 2 2 3 6 1  3  ε_{1} 14.3124
24 −67 −1608 2585664 1 1 16 8 1  8  ε_{1} 4.5849
201  −8 −1608 2585664 1 1 16 8 1  8  ε_{1} 27.6905
201 −24 −536 2585664 1 2 14 14 1 14  ε_{1} 27.6905
536  −3 −1608 2585664 1 1 16 8 1  8  ε_{1} 25.1680
1608  −3 −536 2585664 2 1 14 14 1  7  ε_{1} 13.3742
1608 −24  −67 2585664 2 2 1 2 1  1  ε_{1} 13.3742
124 −52 −403 2598544 1 2 2 2 1  2  ε_{1} 16.0392
1612  −4 −403 2598544 2 1 2 2 1  1  ε_{1} 28.2160
1612 −31  −52 2598544 2 3 2 6 1  3  ε_{1} 28.2160
5 −323 −1615 2608225 1 4 24 48 1 48  ε_{1} 0.9624
17 −95 −1615 2608225 1 8 24 96 1 96  ε_{1} 4.1894
85 −19 −1615 2608225 2 1 24 24 1 12  ε_{1} 4.4187
85 −95 −323 2608225 2 8 4 32 1 16  ε_{1} 4.4187
8 −404 −808 2611456 1 14 6 42 1 42  ε_{1} 1.7627
808  −4 −808 2611456 2 1 6 6 1  3  ε_{1} 17.4909
808  −8 −404 2611456 2 1 14 14 1  7  ε_{1} 17.4909
541  −3 −1623 2634129 1 1 28 14 1 14  ε_{1} 28.2989
8 −203 −1624 2637376 1 4 16 32 1 32  ε_{1} 1.7627
29 −56 −1624 2637376 1 4 16 32 1 32  ε_{1} 3.2945
56 −203 −232 2637376 1 4 2 4 1  4  ε_{1} 6.8002
232  −7 −1624 2637376 2 1 16 16 1  8  ε_{1} 10.5766
232 −56 −203 2637376 2 4 4 16 1  8  ε_{1} 10.5766
1624  −7 −232 2637376 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 18.5941
1624  −8 −203 2637376 2 1 4 4 1  2  ε_{1} 37.1882
44 −148 −407 2650384 1 2 16 16 1 16  ε_{1} 5.9864
1628  −4 −407 2650384 2 1 16 16 1  8  ε_{1} 17.1607

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 33

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
1628 −11 −148 2650384 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 8.5804
233 −7 −1631 2660161 1 1 44 22 1 22 ε_{1} 21.4863
1633 −23  −71 2666689 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 54.8465
5 −327 −1635 2673225 1 12 8 48 1 48  ε_{1} 0.9624
109 −15 −1635 2673225 1 2 8 8 1  8  ε_{1} 11.1291
545  −3 −1635 2673225 2 1 8 8 1  4  ε_{1} 16.5487
545 −15 −327 2673225 2 2 12 24 1 12  ε_{1} 16.5487
409 −4 −1636 2676496 1 1 16 8 1 8 ε_{1} 52.2684
149 −11 −1639 2686321 1 1 22 11 1 11  ε_{1} 8.2223
5 −328 −1640 2689600 1 4 16 32 1 32  ε_{1} 0.9624
41 −40 −1640 2689600 1 2 16 16 1 16  ε_{1} 8.3183
205  −8 −1640 2689600 2 1 16 16 1  8  ε_{1} 7.5213
205 −40 −328 2689600 2 2 4 8 1  4  ε_{1} 7.5213
1641  −3 −547 2692881 5 1 3 15 2  3 \sqrt{−1}\sqrt{ε_{1}} 9.0768
53 −31 −1643 2699449 1 3 10 15 1 15  ε_{1} 3.9314
12 −411 −548 2702736 1 6 8 24 1 24  ε_{1} 2.6339
1644  −3 −548 2702736 2 1 8 8 1  4  ε_{1} 23.0150
1644  −4 −411 2702736 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 11.5075
329 −35 −235 2706025 1 2 2 2 1  2  ε_{1} 30.7485
1645  −7 −235 2706025 2 1 2 2 1  1  ε_{1} 20.3809
1645 −35  −47 2706025 2 2 5 10 1  5  ε_{1} 20.3809
412  −8 −824 2715904 1 1 20 20 2 20 \sqrt{−1}\sqrt{ε_{1}} 13.0282
824 −4 −824 2715904 1 1 20 20 2 20 \sqrt{i}\sqrt{ε_{1}} 11.6875
13 −127 −1651 2725801 1 5 8 20 1 20  ε_{1} 2.3895
28 −59 −1652 2729104 1 3 20 30 1 30  ε_{1} 5.5373
236  −7 −1652 2729104 1 1 20 10 1 10  ε_{1} 13.9320
413  −4 −1652 2729104 1 1 20 10 1 10  ε_{1} 8.2212
57 −87 −551 2732409 1 6 26 78 1 78  ε_{1} 11.4208
1653  −3 −551 2732409 2 1 26 26 1 13  ε_{1} 14.5210
1653 −19  −87 2732409 2 1 6 6 1  3  ε_{1} 14.5210
5 −331 −1655 2739025 1 3 44 66 1 66  ε_{1} 0.9624
21 −79 −1659 2752281 1 5 8 20 1 20  ε_{1} 3.1336
237  −7 −1659 2752281 1 1 8 4 1  4  ε_{1} 8.6873
553  −3 −1659 2752281 1 1 8 4 1  4  ε_{1} 55.7072
332 −20 −415 2755600 1 2 10 10 1 10  ε_{1} 10.1997
1660  −4 −415 2755600 2 1 10 10 1  5  ε_{1} 34.8434
1660 −20  −83 2755600 2 2 3 6 1  3  ε_{1} 34.8434
1661 −11 −151 2758921 1 1 7 7 2  7 \sqrt{−1}\sqrt{ε_{1}} 14.8862
12 −139 −1668 2782224 1 3 12 18 1 18  ε_{1} 2.6339
417  −4 −1668 2782224 1 1 12 6 1  6  ε_{1} 37.9102
556  −3 −1668 2782224 1 1 12 6 1  6  ε_{1} 37.7195
557  −3 −1671 2792241 1 1 38 19 1 19  ε_{1} 10.9277
88 −19 −1672 2795584 1 1 8 4 1  4  ε_{1} 11.9527
152 −11 −1672 2795584 1 1 8 4 1  4  ε_{1} 8.6078
209  −8 −1672 2795584 1 1 8 4 1  4  ε_{1} 22.8829
209 −88 −152 2795584 1 2 6 6 1  6  ε_{1} 22.8829
1672 −11 −152 2795584 2 1 6 6 1  3  ε_{1} 22.2461
1672 −19  −88 2795584 2 1 2 2 1  1  ε_{1} 22.2461
1673  −7 −239 2798929 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 29.4806
1676  −4 −419 2808976 1 1 9 9 2  9  \sqrt{i}\sqrt{ε_{1}} 20.1077

34 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
129 −39 −559 2812329 1 4 16 32 1 32  ε_{1} 20.8511
1677  −3 −559 2812329 4 1 16 32 1  8  ε_{1} 7.4260
1677 −39  −43 2812329 4 4 1 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 3.7130
73 −23 −1679 2819041 1 3 52 78 1 78  ε_{1} 15.3334
8 −420 −840 2822400 1 8 8 32 1 32  ε_{1} 1.7627
12 −280 −840 2822400 1 4 8 16 1 16  ε_{1} 2.6339
24 −280 −420 2822400 1 4 8 16 1 16  ε_{1} 4.5849
28 −120 −840 2822400 1 4 8 16 1 16  ε_{1} 5.5373
40 −84 −840 2822400 2 4 8 32 1 16  ε_{1} 3.6369
40 −168 −420 2822400 2 4 8 32 1 16  ε_{1} 3.6369
56 −120 −420 2822400 1 4 8 16 1 16  ε_{1} 6.8002
60 −56 −840 2822400 2 4 8 32 1 16  ε_{1} 4.1269
60 −168 −280 2822400 2 4 4 16 1 8 ε_{1} 4.1269
120 −56 −420 2822400 2 4 8 32 1 16  ε_{1} 6.1779
120 −84 −280 2822400 2 4 4 16 1  8  ε_{1} 6.1779
140 −24 −840 2822400 2 2 8 16 1  8  ε_{1} 4.9558
140 −120 −168 2822400 2 4 4 16 1  8  ε_{1} 4.9558
168 −20 −840 2822400 2 2 8 16 1  8  ε_{1} 6.5132
168 −40 −420 2822400 2 2 8 16 1  8  ε_{1} 6.5132
280 −24 −420 2822400 2 2 8 16 1  8  ε_{1} 12.4372
280 −84 −120 2822400 2 4 4 16 1  8  ε_{1} 12.4372
840  −4 −840 2822400 4 1 8 16 1  4  ε_{1} 8.1203
840  −8 −420 2822400 4 1 8 16 1  4  ε_{1} 8.1203
840 −20 −168 2822400 4 2 4 16 1  4  ε_{1} 8.1203
840 −40  −84 2822400 4 2 4 16 1  4  ε_{1} 8.1203
421  −4 −1684 2835856 1 1 10 5 1  5  ε_{1} 26.0114
241  −7 −1687 2845969 1 1 18 9 1  9  ε_{1} 37.5430
8 −211 −1688 2849344 1 3 10 15 1 15  ε_{1} 1.7627
1688  −8 −211 2849344 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 16.4578
1689  −3 −563 2852721 1 1 9 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 52.5183
89 −19 −1691 2859481 1 1 18 9 1  9  ε_{1} 13.8155
5 −339 −1695 2873025 1 6 20 60 1 60  ε_{1} 0.9624
113 −15 −1695 2873025 1 2 20 20 1 20  ε_{1} 14.6946
565  −3 −1695 2873025 2 1 20 20 1 10  ε_{1} 11.4667
565 −15 −339 2873025 2 2 6 12 1  6  ε_{1} 11.4667
13 −131 −1703 2900209 1 5 28 70 1 70  ε_{1} 2.3895
24 −71 −1704 2903616 1 7 24 84 1 84  ε_{1} 4.5849
213  −8 −1704 2903616 1 1 24 12 1 12  ε_{1} 8.5805
213 −24 −568 2903616 1 2 4 4 1  4  ε_{1} 8.5805
568  −3 −1704 2903616 3 1 24 36 1 12  ε_{1} 11.3120
1704  −3 −568 2903616 2 1 4 4 1  2  ε_{1} 24.1735
1704 −24  −71 2903616 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 12.0867
341 −55 −155 2907025 1 4 4 8 1  8  ε_{1} 11.2480
1705 −11 −155 2907025 8 1 4 16 1  2  ε_{1} 15.1837
1705 −31  −55 2907025 8 3 4 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.5919
569  −3 −1707 2913849 1 1 10 5 1  5  ε_{1} 44.9587
28 −244 −427 2917264 1 6 2 6 1  6  ε_{1} 5.5373
1708  −4 −427 2917264 6 1 2 6 1  1  ε_{1} 9.6404
1708  −7 −244 2917264 6 1 6 18 1  3  ε_{1} 9.6404
29 −59 −1711 2927521 1 3 28 42 1 42  ε_{1} 3.2945

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 35

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
428  −8 −856 2930944 1 1 6  6 2  6 \sqrt{−1}\sqrt{ε_{1}} 7.5622
856  −4 −856 2930944 1 1 6  6 2  6  \sqrt{i}\sqrt{ε_{1}} 27.9608
1713  −3 −571 2934369 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 31.9773
12 −143 −1716 2944656 1 10 16 80 1 80  ε_{1} 2.6339
13 −132 −1716 2944656 1 4 16 32 1 32  ε_{1} 2.3895
33 −52 −1716 2944656 1 2 16 16 1 16  ε_{1} 7.6563
44 −39 −1716 2944656 1 4 16 32 1 32  ε_{1} 5.9864
156 −11 −1716 2944656 2 1 16 16 1 8 ε_{1} 7.8232
156 −132 −143 2944656 2 4 10 40 1 20  ε_{1} 7.8232
429  −4 −1716 2944656 2 1 16 16 1  8  ε_{1} 9.9534
429 −52 −132 2944656 2 2 4  8 1  4  ε_{1} 9.9534
572  −3 −1716 2944656 2 1 16 16 1  8  ε_{1} 6.3526
572 −39 −132 2944656 2 4 4 16 1  8  ε_{1} 6.3526
5 −344 −1720 2958400 1 10 12 60 1 60  ε_{1} 0.9624
8 −215 −1720 2958400 1 14 12 84 1 84  ε_{1} 1.7627
40 −43 −1720 2958400 2 1 12 12 1 6 ε_{1} 3.6369
40 −215 −344 2958400 2 14 10 140 1 70  ε_{1} 3.6369
344 −40 −215 2958400 1 2 14 14 1 14  ε_{1} 19.8864
1720  −8 −215 2958400 2 1 14 14 1  7  ε_{1} 31.1205
1720 −40  −43 2958400 2 2 1  2 1  1  ε_{1} 31.1205
1724  −4 −431 2972176 1 1 21 21 2 21  \sqrt{i}\sqrt{ε_{1}} 19.5296
157 −11 −1727 2982529 1 1 36 18 1 18  ε_{1} 10.7226
133 −91 −247 2989441 1 2 6  6 1  6  ε_{1} 10.3065
1729  −7 −247 2989441 2 1 6  6 1  3  ε_{1} 64.2443
1729 −19  −91 2989441 2 1 2  2 1  1  ε_{1} 64.2443
577  −3 −1731 2996361 7 1 8 28 1  4  ε_{1} 7.7433
433  −4 −1732 2999824 1 1 12  6 1  6  ε_{1} 46.7895
5 −347 −1735 3010225 1 5 26 65 1 65  ε_{1} 0.9624
56 −31 −1736 3013696 1 3 24 36 1 36  ε_{1} 6.8002
217 −8 −1736 3013696 1 1 24 12 1 12 ε_{1} 31.7104
217 −56 −248 3013696 1 4 8 16 1 16  ε_{1} 31.7104
248  −7 −1736 3013696 1 1 24 12 1 12  ε_{1} 9.6724
1736  −7 −248 3013696 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.5214
1736 −31  −56 3013696 4 3 4 24 1  6  ε_{1} 11.0429
37 −47 −1739 3024121 1 5 20 50 1 50  ε_{1} 4.9836
12 −435 −580 3027600 1 4 8 16 1 16  ε_{1} 2.6339
60 −87 −580 3027600 2 6 8 48 1 24  ε_{1} 4.1269
60 −116 −435 3027600 2 6 4 24 1 12  ε_{1} 4.1269
348 −15 −580 3027600 2 2 8 16 1  8  ε_{1} 8.0501
348 −20 −435 3027600 2 2 4  8 1  4  ε_{1} 8.0501
1740  −3 −580 3027600 4 1 8 16 1  4  ε_{1} 11.3535
1740  −4 −435 3027600 4 1 4  8 1  2  ε_{1} 11.3535
1740 −15 −116 3027600 4 2 6 24 1  6  ε_{1} 11.3535
1740 −20  −87 3027600 4 2 6 24 1  6  ε_{1} 11.3535
21 −83 −1743 3038049 1 3 24 36 1 36  ε_{1} 3.1336
249  −7 −1743 3038049 1 1 24 12 1 12  ε_{1} 33.3101
581  −3 −1743 3038049 1 1 24 12 1 12  ε_{1} 17.6272
8 −436 −872 3041536 1 6 10 30 1 30  ε_{1} 1.7627
872  −4 −872 3041536 2 1 10 10 1  5  ε_{1} 12.4372
872  −8 −436 3041536 2 1 6  6 1  3  ε_{1} 12.4372

36 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
76 −23 −1748 3055504 1 3 20 30 1 30  ε_{1} 11.6579
92 −19 −1748 3055504 1 1 20 10 1 10  ε_{1} 7.7415
437 −4 −1748 3055504 1 1 20 10 1 10 ε_{1} 6.0845
33 −159 −583 3059001 1 10 8 40 1 40  ε_{1} 7.6563
1749 −3 −583 3059001 2 1 8 8 1 4 ε_{1} 16.5746
1749 −11 −159 3059001 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 8.2873
17 −103 −1751 3066001 1 5 48 120 1 120  ε_{1} 4.1894
8 −219 −1752 3069504 1 4 8 16 1 16  ε_{1} 1.7627
24 −219 −584 3069504 1 4 16 32 1 32  ε_{1} 4.5849
73 −24 −1752 3069504 1 2 8  8 1  8  ε_{1} 15.3334
584  −3 −1752 3069504 2 1 8  8 1  4  ε_{1} 11.3397
584 −24 −219 3069504 2 2 4  8 1  4  ε_{1} 11.3397
1752  −3 −584 3069504 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.3733
1752  −8 −219 3069504 4 1 4  8 1  2  ε_{1} 12.7466
1756  −4 −439 3083536 5 1 15 75 2 15  \sqrt{i}\sqrt{ε_{1}} 6.7799
1757  −7 −251 3087049 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 6.9137
1761  −3 −587 3101121 7 1 7 49 2  7 \sqrt{−1}\sqrt{ε_{1}} 7.7622
41 −43 −1763 3108169 1 1 12  6 1  6  ε_{1} 8.3183
57 −31 −1767 3122289 1 3 32 48 1 48  ε_{1} 11.4208
93 −19 −1767 3122289 1 1 32 16 1 16  ε_{1} 6.7322
589 −3 −1767 3122289 1 1 32 16 1 16 ε_{1} 30.5757
13 −136 −1768 3125824 1 4 8 16 1 16  ε_{1} 2.3895
17 −104 −1768 3125824 1 6 8 24 1 24  ε_{1} 4.1894
221 −8 −1768 3125824 2 1 8 8 1 4 ε_{1} 5.4072
221 −104 −136 3125824 2 6 4 24 1 12  ε_{1} 5.4072
77 −23 −1771 3136441 1 3 8 12 1 12  ε_{1} 4.3693
161 −11 −1771 3136441 1 1 8  4 1  4  ε_{1} 20.1338
253  −7 −1771 3136441 1 1 8  4 1  4  ε_{1} 15.0577
1772  −4 −443 3139984 3 1 5 15 2  5  \sqrt{i}\sqrt{ε_{1}} 6.7845
12 −296 −888 3154176 1 10 12 60 1 60  ε_{1} 2.6339
24 −148 −888 3154176 1 2 12 12 1 12  ε_{1} 4.5849
444 −8 −888 3154176 2 1 12 12 1 6 ε_{1} 12.7602
444 −24 −296 3154176 2 2 10 20 1 10  ε_{1} 12.7602
888  −4 −888 3154176 2 1 12 12 1  6  ε_{1} 11.3942
888 −24 −148 3154176 2 2 2  4 1  2  ε_{1} 11.3942
593  −3 −1779 3164841 1 1 10  5 1  5  ε_{1} 27.9978
5 −356 −1780 3168400 1 12 8 48 1 48  ε_{1} 0.9624
89 −20 −1780 3168400 1 2 8  8 1  8  ε_{1} 13.8155
445  −4 −1780 3168400 4 1 8 16 1  4  ε_{1} 6.0936
445 −20 −356 3168400 4 2 12 48 1 12  ε_{1} 6.0936
8 −223 −1784 3182656 1 7 32 112 1 112  ε_{1} 1.7627
1784 −8 −223 3182656 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 19.2106
21 −255 −595 3186225 1 12 4 24 1 24  ε_{1} 3.1336
105 −51 −595 3186225 2 2 4 8 1 4 ε_{1} 8.8131
105 −119 −255 3186225 2 10 12 120 1 60  ε_{1} 8.8131
357 −15 −595 3186225 2 2 4 8 1 4 ε_{1} 5.8833
357 −35 −255 3186225 2 2 12 24 1 12  ε_{1} 5.8833
1785  −3 −595 3186225 8 1 4 16 1  2  ε_{1} 11.6461
1785  −7 −255 3186225 8 1 12 48 1  6  ε_{1} 11.6461
1785 −15 −119 3186225 8 2 10 80 1 10  ε_{1} 11.6461

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 37

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
1785 −35  −51 3186225 8 2 2 16 1  2  ε_{1} 11.6461
12 −447 −596 3196944 1 14 14 98 1 98  ε_{1} 2.6339
1788  −3 −596 3196944 2 1 14 14 1  7  ε_{1} 11.3807
1788  −4 −447 3196944 2 1 14 14 1  7  ε_{1} 11.3807
1793 −11 −163 3214849 1 1 1 1 2  1 \sqrt{−1}\sqrt{ε_{1}} 33.8946
5 −359 −1795 3222025 1 19 8 76 1 76  ε_{1} 0.9624
449 −4 −1796 3225616 1 1 20 10 1 10 ε_{1} 39.5058
1797  −3 −599 3229209 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 12.6663
257  −7 −1799 3236401 3 1 50 75 1 25  ε_{1} 6.9334
601  −3 −1803 3250809 1 1 8 4 1  4  ε_{1} 66.5240
44 −164 −451 3254416 1 8 6 24 1 24  ε_{1} 5.9864
1804  −4 −451 3254416 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 18.3475
1804 −11 −164 3254416 2 1 8 8 1  4  ε_{1} 36.6950
13 −139 −1807 3265249 1 3 12 18 1 18  ε_{1} 2.3895
8 −452 −904 3268864 1 8 8 32 1 32  ε_{1} 1.7627
904  −4 −904 3268864 8 1 8 32 1  4  ε_{1} 6.8046
904  −8 −452 3268864 8 1 8 32 1  4  ε_{1} 6.8046
12 −151 −1812 3283344 1 7 12 42 1 42  ε_{1} 2.6339
453  −4 −1812 3283344 1 1 12 6 1  6  ε_{1} 10.0078
604  −3 −1812 3283344 1 1 12 6 1  6  ε_{1} 43.9269
8 −227 −1816 3297856 1 5 14 35 1 35  ε_{1} 1.7627
1816 −8 −227 3297856 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 38.0602
1817 −23  −79 3301489 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 31.4996
17 −107 −1819 3308761 1 3 10 15 1 15  ε_{1} 4.1894
28 −260 −455 3312400 1 8 20 80 1 80  ε_{1} 5.5373
140 −52 −455 3312400 2 2 20 40 1 20  ε_{1} 4.9558
140 −91 −260 3312400 2 2 8 16 1 8 ε_{1} 4.9558
364 −20 −455 3312400 2 2 20 40 1 20  ε_{1} 16.1090
364 −35 −260 3312400 2 2 8 16 1  8  ε_{1} 16.1090
1820  −4 −455 3312400 4 1 20 40 1 10  ε_{1} 9.7039
1820  −7 −260 3312400 4 1 8 16 1  4  ε_{1} 9.7039
1820 −20  −91 3312400 4 2 2 8 1  2  ε_{1} 9.7039
1820 −35  −52 3312400 4 2 2 8 1  2  ε_{1} 9.7039
1821  −3 −607 3316041 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 22.0638
457  −4 −1828 3341584 1 1 8 4 1  4  ε_{1} 50.9909
1829 −31  −59 3345241 1 3 3 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 18.2156
229  −8 −1832 3356224 3 1 26 39 1 13  ε_{1} 5.4249
141 −39 −611 3359889 1 4 10 20 1 20  ε_{1} 10.4940
1833  −3 −611 3359889 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 15.9565
1833 −39 −47 3359889 2 4 5 20 1 10 ε_{1} 31.9129
5 −367 −1835 3367225 1 9 10 45 1 45  ε_{1} 0.9624
1837 −11 −167 3374569 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 17.1746
613 −3 −1839 3381921 1 1 40 20 1 20 ε_{1} 23.0010
92 −40 −920 3385600 1 2 20 20 1 20  ε_{1} 7.7415
184 −20 −920 3385600 1 2 20 20 1 20  ε_{1} 21.5856
460 −8 −920 3385600 2 1 20 20 1 10 ε_{1} 15.4391
460 −40 −184 3385600 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.7196
920 −4 −920 3385600 2 1 20 20 1 10 ε_{1} 10.4080
920 −20 −184 3385600 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.2040
1841  −7 −263 3389281 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 40.6333

38 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
97 −19 −1843 3396649 1 1 6  3 1  3  ε_{1} 18.6488
461  −4 −1844 3400336 1 1 30 15 1 15  ε_{1} 11.7998
8 −231 −1848 3415104 1 12 8 48 1 48  ε_{1} 1.7627
21 −88 −1848 3415104 1 2 8 8 1 8 ε_{1} 3.1336
21 −264 −616 3415104 1 8 8 32 1 32  ε_{1} 3.1336
24 −231 −616 3415104 1 12 8 48 1 48  ε_{1} 4.5849
33 −56 −1848 3415104 1 4 8 16 1 16  ε_{1} 7.6563
33 −168 −616 3415104 1 4 8 16 1 16  ε_{1} 7.6563
56 −231 −264 3415104 1 12 8 48 1 48  ε_{1} 6.8002
77 −24 −1848 3415104 1 2 8 8 1 8 ε_{1} 4.3693
77 −168 −264 3415104 1 4 8 16 1 16  ε_{1} 4.3693
88 −168 −231 3415104 1 4 12 24 1 24  ε_{1} 11.9527
168 −11 −1848 3415104 2 1 8 8 1 4 ε_{1} 6.5132
168 −88 −231 3415104 2 2 12 24 1 12  ε_{1} 6.5132
264 −7 −1848 3415104 2 1 8 8 1 4 ε_{1} 9.7350
264 −56 −231 3415104 2 4 12 48 1 24  ε_{1} 9.7350
616 −3 −1848 3415104 2 1 8 8 1 4 ε_{1} 21.3187
616 −24 −231 3415104 2 2 12 24 1 12  ε_{1} 21.3187
1848  −3 −616 3415104 4 1 8 16 1  4  ε_{1} 8.9084
1848  −7 −264 3415104 4 1 8 16 1  4  ε_{1} 8.9084
1848  −8 −231 3415104 4 1 12 24 1  6  ε_{1} 8.9084
1848 −11 −168 3415104 4 1 4  8 1  2  ε_{1} 8.9084
617  −3 −1851 3426201 1 1 14  7 1  7  ε_{1} 36.4449
1852  −4 −463 3429904 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 33.8356
5 −371 −1855 3441025 1 8 28 112 1 112  ε_{1} 0.9624
53 −35 −1855 3441025 1 2 28 28 1 28  ε_{1} 3.9314
265  −7 −1855 3441025 2 1 28 28 1 14  ε_{1} 18.8092
265 −35 −371 3441025 2 2 8 16 1  8  ε_{1} 18.8092
1857  −3 −619 3448449 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 43.0086
5 −372 −1860 3459600 1 4 16 32 1 32  ε_{1} 0.9624
12 −155 −1860 3459600 1 4 16 32 1 32  ε_{1} 2.6339
60 −31 −1860 3459600 2 3 16 48 1 24  ε_{1} 4.1269
60 −155 −372 3459600 2 4 4 16 1 8 ε_{1} 4.1269
93 −20 −1860 3459600 1 2 16 16 1 16  ε_{1} 6.7322
124 −15 −1860 3459600 1 2 16 16 1 16  ε_{1} 16.0392
465  −4 −1860 3459600 2 1 16 16 1  8  ε_{1} 20.7308
465 −20 −372 3459600 2 2 4  8 1  4  ε_{1} 20.7308
620  −3 −1860 3459600 2 1 16 16 1  8  ε_{1} 12.4212
620 −15 −372 3459600 2 2 4  8 1  4  ε_{1} 12.4212
233  −8 −1864 3474496 1 1 8  4 1  4  ε_{1} 21.4863
1868  −4 −467 3489424 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 14.9946
21 −267 −623 3493161 1 2 22 22 1 22  ε_{1} 3.1336
1869  −3 −623 3493161 2 1 22 22 1 11  ε_{1} 20.3103
1869  −7 −267 3493161 2 1 2  2 1  1  ε_{1} 20.3103
28 −67 −1876 3519376 1 1 16  8 1  8  ε_{1} 5.5373
268  −7 −1876 3519376 1 1 16  8 1  8  ε_{1} 22.9790
469  −4 −1876 3519376 3 1 16 24 1  8  ε_{1} 8.3483
5 −376 −1880 3534400 1 8 20 80 1 80  ε_{1} 0.9624
8 −235 −1880 3534400 1 2 20 20 1 20  ε_{1} 1.7627
40 −47 −1880 3534400 2 5 20 100 1 50  ε_{1} 3.6369

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 39

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
40 −235 −376 3534400 2 2 8 16 1  8  ε_{1} 3.6369
376 −40 −235 3534400 1 2 2 2 1  2  ε_{1} 30.5420
1880  −8 −235 3534400 2 1 2 2 1  1  ε_{1} 16.2524
1880 −40  −47 3534400 2 2 5 10 1  5  ε_{1} 16.2524
269  −7 −1883 3545689 1 1 14 7 1  7  ε_{1} 10.1998
12 −471 −628 3549456 1 16 6 48 1 48  ε_{1} 2.6339
1884  −3 −628 3549456 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 16.5677
1884  −4 −471 3549456 2 1 16 16 1  8  ε_{1} 33.1355
17 −111 −1887 3560769 1 8 20 80 1 80  ε_{1} 4.1894
37 −51 −1887 3560769 1 2 20 20 1 20  ε_{1} 4.9836
629  −3 −1887 3560769 2 1 20 20 1 10  ε_{1} 6.4409
629 −51 −111 3560769 2 2 8 16 1  8  ε_{1} 6.4409
61 −31 −1891 3575881 1 3 10 15 1 15  ε_{1} 7.3284
44 −43 −1892 3579664 1 1 12 6 1  6  ε_{1} 5.9864
172 −11 −1892 3579664 1 1 12 6 1  6  ε_{1} 17.6970
473  −4 −1892 3579664 3 1 12 18 1  6  ε_{1} 10.3180
1893  −3 −631 3583449 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 9.2197
5 −379 −1895 3591025 1 3 48 72 1 72  ε_{1} 0.9624
24 −79 −1896 3594816 1 5 20 50 1 50  ε_{1} 4.5849
237  −8 −1896 3594816 1 1 20 10 1 10  ε_{1} 8.6873
237 −24 −632 3594816 1 2 8 8 1  8  ε_{1} 8.6873
632  −3 −1896 3594816 1 1 20 10 1 10  ε_{1} 19.2954
1896  −3 −632 3594816 2 1 8 8 1  4  ε_{1} 25.7329
1896 −24  −79 3594816 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 12.8664
1897  −7 −271 3598609 5 1 11 55 2 11 \sqrt{−1}\sqrt{ε_{1}} 11.3829
173 −11 −1903 3621409 1 1 22 11 1 11  ε_{1} 5.1416
28 −136 −952 3625216 1 4 8 16 1 16  ε_{1} 5.5373
56 −68 −952 3625216 1 4 8 16 1 16  ε_{1} 6.8002
476  −8 −952 3625216 2 1 8 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.4806
476 −56 −136 3625216 2 4 4 16 1  8  ε_{1} 10.9612
952  −4 −952 3625216 2 1 8 16 2  8  \sqrt{i}\sqrt{ε_{1}} 10.0573
952 −56  −68 3625216 2 4 4 16 1  8  ε_{1} 20.1146
381 −15 −635 3629025 1 2 10 10 1 10  ε_{1} 15.2316
1905  −3 −635 3629025 2 1 10 10 1  5  ε_{1} 47.5752
1905 −15 −127 3629025 2 2 5 10 1  5  ε_{1} 47.5752
1909 −23  −83 3644281 1 3 3 9 2  9 \sqrt{−1}\sqrt{ε_{1}} 22.2838
8 −239 −1912 3655744 1 15 8 60 1 60  ε_{1} 1.7627
1912  −8 −239 3655744 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 35.7127
5 −383 −1915 3667225 1 17 6 51 1 51  ε_{1} 0.9624
1916 −4 −479 3671056 1 1 25 25 2 25 \sqrt{i}\sqrt{ε_{1}} 15.6037
101 −19 −1919 3682561 1 1 44 22 1 22  ε_{1} 5.9964
641 −3 −1923 3697929 1 1 10 5 1 5 ε_{1} 50.0066
13 −148 −1924 3701776 1 2 16 16 1 16  ε_{1} 2.3895
37 −52 −1924 3701776 1 2 16 16 1 16  ε_{1} 4.9836
481  −4 −1924 3701776 2 1 16 16 1  8  ε_{1} 28.9443
481 −52 −148 3701776 2 2 2 4 1  2  ε_{1} 28.9443
41 −47 −1927 3713329 1 5 18 45 1 45  ε_{1} 8.3183
241  −8 −1928 3717184 1 1 20 10 1 10  ε_{1} 37.5430
1929  −3 −643 3721041 3 1 3 9 2  3 \sqrt{−1}\sqrt{ε_{1}} 19.3512
12 −483 −644 3732624 1 4 16 32 1 32  ε_{1} 2.6339

40 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
21 −276 −644 3732624 1 8 16 64 1 64  ε_{1} 3.1336
28 −276 −483 3732624 1 8 4 16 1 16  ε_{1} 5.5373
69 −84 −644 3732624 1 4 16 32 1 32  ε_{1} 6.4345
92 −84 −483 3732624 1 4 4 8 1 8 ε_{1} 7.7415
161 −84 −276 3732624 1 4 8 16 1 16  ε_{1} 20.1338
1932  −3 −644 3732624 4 1 16 32 1  8  ε_{1} 7.5673
1932  −4 −483 3732624 4 1 4 8 1  2  ε_{1} 7.5673
1932  −7 −276 3732624 4 1 8 16 1  4  ε_{1} 7.5673
1932 −23  −84 3732624 4 3 4 24 1  6  ε_{1} 7.5673
277  −7 −1939 3759721 1 1 8 4 1  4  ε_{1} 15.7365
5 −388 −1940 3763600 1 4 20 40 1 40  ε_{1} 0.9624
97 −20 −1940 3763600 1 2 20 20 1 20  ε_{1} 18.6488
485  −4 −1940 3763600 2 1 20 20 1 10  ε_{1} 7.5694
485 −20 −388 3763600 2 2 4 8 1  4  ε_{1} 7.5694
1941  −3 −647 3767481 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 23.0769
29 −67 −1943 3775249 1 1 32 16 1 16  ε_{1} 3.2945
33 −59 −1947 3790809 1 3 8 12 1 12  ε_{1} 7.6563
177 −11 −1947 3790809 1 1 8 4 1  4  ε_{1} 23.4697
649  −3 −1947 3790809 1 1 8 4 1  4  ε_{1} 70.6969
1948  −4 −487 3794704 1 1 7 7 2  7  \sqrt{i}\sqrt{ε_{1}} 32.2736
5 −391 −1955 3822025 1 14 12 84 1 84  ε_{1} 0.9624
17 −115 −1955 3822025 1 2 12 12 1 12  ε_{1} 4.1894
85 −23 −1955 3822025 2 3 12 36 1 18  ε_{1} 4.4187
85 −115 −391 3822025 2 2 14 28 1 14  ε_{1} 4.4187
12 −163 −1956 3825936 1 1 20 10 1 10  ε_{1} 2.6339
489  −4 −1956 3825936 1 1 20 10 1 10  ε_{1} 46.8872
652  −3 −1956 3825936 1 1 20 10 1 10  ε_{1} 37.3376
1957 −19 −103 3829849 3 1 5 15 2  5 \sqrt{−1}\sqrt{ε_{1}} 6.8341
653 −3 −1959 3837681 1 1 42 21 1 21 ε_{1} 14.8304
13 −151 −1963 3853369 1 7 6 21 1 21  ε_{1} 2.3895
1964 −4 −491 3857296 1 1 9 9 2 9 \sqrt{i}\sqrt{ε_{1}} 25.9557
393 −15 −655 3861225 1 2 12 12 1 12  ε_{1} 36.6935
1965 −3 −655 3861225 2 1 12 12 1 6 ε_{1} 9.7806
1965 −15 −131 3861225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 4.8903
281 −7 −1967 3869089 1 1 36 18 1 18 ε_{1} 29.1405
12 −328 −984 3873024 1 4 12 24 1 24  ε_{1} 2.6339
24 −164 −984 3873024 1 8 12 48 1 48  ε_{1} 4.5849
492  −8 −984 3873024 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.4972
492 −24 −328 3873024 2 2 4 8 1  4  ε_{1} 10.9943
984  −4 −984 3873024 2 1 12 24 2 12  \sqrt{i}\sqrt{ε_{1}} 12.0873
984 −24 −164 3873024 2 2 8 16 1  8  ε_{1} 24.1747
1969 −11 −179 3876961 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 73.6184
17 −116 −1972 3888784 1 6 12 36 1 36  ε_{1} 4.1894
29 −68 −1972 3888784 1 4 12 24 1 24  ε_{1} 3.2945
493 −4 −1972 3888784 2 1 12 12 1 6 ε_{1} 9.4192
493 −68 −116 3888784 2 4 6 24 1 12  ε_{1} 9.4192
8 −247 −1976 3904576 1 6 28 84 1 84  ε_{1} 1.7627
13 −152 −1976 3904576 1 6 28 84 1 84  ε_{1} 2.3895
104 −19 −1976 3904576 2 1 28 28 1 14  ε_{1} 4.6249
104 −152 −247 3904576 2 6 6 36 1 18  ε_{1} 4.6249

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 41

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
152 −104 −247 3904576 1 6 6 18 1 18  ε_{1} 8.6078
1976  −8 −247 3904576 2 1 6  6 1  3  ε_{1} 23.7837
1976 −19 −104 3904576 2 1 6  6 1  3  ε_{1} 23.7837
1977  −3 −659 3908529 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 33.7631
1981  −7 −283 3924361 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 29.9191
661  −3 −1983 3932289 1 1 16  8 1  8  ε_{1} 28.7949
28 −71 −1988 3952144 1 7 24 84 1 84  ε_{1} 5.5373
284  −7 −1988 3952144 1 1 24 12 1 12  ε_{1} 17.6959
497  −4 −1988 3952144 1 1 24 12 1 12  ε_{1} 29.3851
181 −11 −1991 3964081 1 1 56 28 1 28  ε_{1} 14.3479
24 −83 −1992 3968064 1 3 8 12 1 12  ε_{1} 4.5849
249 −8 −1992 3968064 1 1 8 4 1 4 ε_{1} 33.3101
249 −24 −664 3968064 1 2 10 10 1 10  ε_{1} 33.3101
664  −3 −1992 3968064 1 1 8  4 1  4  ε_{1} 43.8951
1992  −3 −664 3968064 2 1 10 10 1  5  ε_{1} 25.5852
1992 −24  −83 3968064 2 2 3  6 1  3  ε_{1} 25.5852
5 −399 −1995 3980025 1 16 8 64 1 64  ε_{1} 0.9624
21 −95 −1995 3980025 1 8 8 32 1 32  ε_{1} 3.1336
57 −35 −1995 3980025 1 2 8  8 1  8  ε_{1} 11.4208
105 −19 −1995 3980025 2 1 8  8 1  4  ε_{1} 8.8131
105 −95 −399 3980025 2 8 16 128 1 64  ε_{1} 8.8131
133 −15 −1995 3980025 1 2 8  8 1  8  ε_{1} 10.3065
285  −7 −1995 3980025 2 1 8  8 1  4  ε_{1} 5.6595
285 −35 −399 3980025 2 2 16 32 1 16  ε_{1} 5.6595
665 −3 −1995 3980025 2 1 8 8 1 4 ε_{1} 20.4394
665 −15 −399 3980025 2 2 16 32 1 16  ε_{1} 20.4394
1996 −4 −499 3984016 5 1 3 15 2 3 \sqrt{i}\sqrt{ε_{1}} 9.1028
69 −87 −667 4004001 1 6 4 12 1 12  ε_{1} 6.4345
2001 −3 −667 4004001 2 1 4 4 1 2 ε_{1} 48.7984
2001 −23  −87 4004001 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 24.3992
12 −167 −2004 4016016 1 11 16 88 1 88  ε_{1} 2.6339
501  −4 −2004 4016016 1 1 16  8 1  8  ε_{1} 20.4959
668  −3 −2004 4016016 1 1 16  8 1  8  ε_{1} 11.6342
8 −251 −2008 4032064 1 7 14 49 1 49  ε_{1} 1.7627
2008  −8 −251 4032064 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 22.7599
2012  −4 −503 4048144 1 1 21 21 2 21  \sqrt{i}\sqrt{ε_{1}} 10.8056
33 −183 −671 4052169 1 8 30 120 1 120  ε_{1} 7.6563
2013  −3 −671 4052169 2 1 30 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 6.5117
2013 −11 −183 4052169 2 1 8 8 1 4 ε_{1} 13.0235
5 −403 −2015 4060225 1 2 52 52 1 52  ε_{1} 0.9624
13 −155 −2015 4060225 1 4 52 104 1 104  ε_{1} 2.3895
65 −31 −2015 4060225 2 3 52 156 1 78  ε_{1} 5.5529
65 −155 −403 4060225 2 4 2  8 1  4  ε_{1} 5.5529
673  −3 −2019 4076361 1 1 16  8 1  8  ε_{1} 64.4243
5 −404 −2020 4080400 1 14 8 56 1 56  ε_{1} 0.9624
101 −20 −2020 4080400 1 2 8  8 1  8  ε_{1} 5.9964
505  −4 −2020 4080400 4 1 8 16 1  4  ε_{1} 14.7779
505 −20 −404 4080400 4 2 14 112 2 28 \sqrt{−1}\sqrt{ε_{1}} 7.3889
2021 −43 −47 4084441 3 1 5 15 2 5 \sqrt{−1}\sqrt{ε_{1}} 3.8062
88 −23 −2024 4096576 1 3 28 42 1 42  ε_{1} 11.9527

42 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
184 −11 −2024 4096576 1 1 28 14 1 14  ε_{1} 21.5856
253  −8 −2024 4096576 1 1 28 14 1 14  ε_{1} 15.0577
253 −88 −184 4096576 1 2 4 4 1  4  ε_{1} 15.0577
2024 −11 −184 4096576 6 1 4 12 1  2  ε_{1} 8.9994
2024 −23  −88 4096576 6 3 2 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 4.4997
677  −3 −2031 4124961 1 1 38 19 1 19  ε_{1} 7.9032
508  −8 −1016 4129024 1 1 16 16 2 16 \sqrt{−1}\sqrt{ε_{1}} 16.0627
1016 −4 −1016 4129024 3 1 16 48 2 16 \sqrt{i}\sqrt{ε_{1}} 6.2344
2033 −19 −107 4133089 1 1 3 3 2  3 \sqrt{−1}\sqrt{ε_{1}} 25.5402
5 −407 −2035 4141225 1 16 8 64 1 64  ε_{1} 0.9624
37 −55 −2035 4141225 1 4 8 16 1 16  ε_{1} 4.9836
185 −11 −2035 4141225 2 1 8 8 1 4 ε_{1} 9.8254
185 −55 −407 4141225 2 4 16 64 1 32  ε_{1} 9.8254
509 −4 −2036 4145296 1 1 30 15 1 15 ε_{1} 13.6596
21 −291 −679 4149369 1 4 18 36 1 36  ε_{1} 3.1336
2037  −3 −679 4149369 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 6.5177
2037 −7 −291 4149369 2 1 4 4 1 2 ε_{1} 13.0353
5 −408 −2040 4161600 1 4 16 32 1 32  ε_{1} 0.9624
8 −255 −2040 4161600 1 12 16 96 1 96  ε_{1} 1.7627
17 −120 −2040 4161600 1 4 16 32 1 32  ε_{1} 4.1894
24 −255 −680 4161600 1 12 12 72 1 72  ε_{1} 4.5849
40 −51 −2040 4161600 2 2 16 32 1 16  ε_{1} 3.6369
40 −255 −408 4161600 2 12 4 48 1 24  ε_{1} 3.6369
85 −24 −2040 4161600 2 2 16 32 1 16  ε_{1} 4.4187
85 −120 −408 4161600 2 4 4 16 1 8 ε_{1} 4.4187
120 −51 −680 4161600 2 2 12 24 1 12  ε_{1} 6.1779
120 −136 −255 4161600 2 4 12 48 1 24  ε_{1} 6.1779
136 −15 −2040 4161600 2 2 16 32 1 16  ε_{1} 8.4966
136 −120 −255 4161600 2 4 12 48 1 24  ε_{1} 8.4966
408 −15 −680 4161600 2 2 12 24 1 12  ε_{1} 10.6165
408 −40 −255 4161600 2 2 12 24 1 12  ε_{1} 10.6165
680  −3 −2040 4161600 4 1 16 32 1  8  ε_{1} 6.5191
680 −15 −408 4161600 4 2 4 16 1  4  ε_{1} 6.5191
680 −24 −255 4161600 4 2 12 48 1 12  ε_{1} 6.5191
680 −51 −120 4161600 4 2 4 16 1  4  ε_{1} 6.5191
2040  −3 −680 4161600 4 1 12 24 1  6  ε_{1} 12.5905
2040  −8 −255 4161600 4 1 12 24 1  6  ε_{1} 12.5905
2040 −15 −136 4161600 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 6.2953
2040 −40 −51 4161600 4 2 2 8 1 2 ε_{1} 12.5905
28 −292 −511 4177936 1 4 14 28 1 28  ε_{1} 5.5373
2044  −4 −511 4177936 2 1 14 28 2 14  \sqrt{i}\sqrt{ε_{1}} 22.8488
2044  −7 −292 4177936 2 1 4 4 1  2  ε_{1} 45.6975
89 −23 −2047 4190209 1 3 18 27 1 27  ε_{1} 13.8155
2049  −3 −683 4198401 1 1 5 5 2  5 \sqrt{−1}\sqrt{ε_{1}} 52.4030
293  −7 −2051 4206601 1 1 18 9 1  9  ε_{1} 5.6733
5 −411 −2055 4223025 1 6 28 84 1 84  ε_{1} 0.9624
137 −15 −2055 4223025 1 2 28 28 1 28  ε_{1} 16.3142
685  −3 −2055 4223025 2 1 28 28 1 14  ε_{1} 13.2640
685 −15 −411 4223025 2 2 6 12 1  6  ε_{1} 13.2640
257  −8 −2056 4227136 3 1 16 24 1  8  ε_{1} 6.9334

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 43

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
29 −71 −2059 4239481 1 7 8 28 1 28  ε_{1} 3.2945
412 −20 −515 4243600 1 2 6  6 1  6  ε_{1} 26.0564
2060  −4 −515 4243600 2 1 6  6 1  3  ε_{1} 20.9154
2060 −20 −103 4243600 2 2 5 10 1  5  ε_{1} 20.9154
8 −516 −1032 4260096 1 12 8 48 1 48  ε_{1} 1.7627
12 −344 −1032 4260096 1 10 8 40 1 40  ε_{1} 2.6339
24 −344 −516 4260096 1 10 12 60 1 60  ε_{1} 4.5849
172 −24 −1032 4260096 1 2 8 8 1 8 ε_{1} 17.6970
344 −24 −516 4260096 1 2 12 12 1 12  ε_{1} 19.8864
1032 −4 −1032 4260096 2 1 8 16 2 8 \sqrt{i}\sqrt{ε_{1}} 6.2422
1032  −8 −516 4260096 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.2422
413 −35 −295 4264225 1 2 8  8 1  8  ε_{1} 8.2212
2065  −7 −295 4264225 2 1 8  8 1  4  ε_{1} 61.9933
2065 −35  −59 4264225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 30.9966
13 −159 −2067 4272489 1 10 8 40 1 40  ε_{1} 2.3895
53 −39 −2067 4272489 1 4 8 16 1 16  ε_{1} 3.9314
689 −3 −2067 4272489 4 1 8 16 1 4 ε_{1} 10.6942
689 −39 −159 4272489 4 4 10 80 1 20  ε_{1} 10.6942
44 −47 −2068 4276624 1 5 12 30 1 30  ε_{1} 5.9864
188 −11 −2068 4276624 1 1 12  6 1  6  ε_{1} 9.1285
517  −4 −2068 4276624 1 1 12  6 1  6  ε_{1} 18.5321
109 −19 −2071 4289041 1 1 30 15 1 15  ε_{1} 11.1291
8 −259 −2072 4293184 1 4 16 32 1 32  ε_{1} 1.7627
37 −56 −2072 4293184 1 4 16 32 1 32  ε_{1} 4.9836
56 −259 −296 4293184 1 4 10 20 1 20  ε_{1} 6.8002
296  −7 −2072 4293184 2 1 16 16 1  8  ε_{1} 8.9090
296 −56 −259 4293184 2 4 4 16 1  8  ε_{1} 8.9090
2072  −7 −296 4293184 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 8.4625
2072  −8 −259 4293184 2 1 4  4 1  2  ε_{1} 16.9251
2073  −3 −691 4297329 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 45.8204
12 −519 −692 4309776 1 18 14 126 1 126  ε_{1} 2.6339
2076  −3 −692 4309776 2 1 14 14 1  7  ε_{1} 34.4136
2076  −4 −519 4309776 2 1 18 18 1  9  ε_{1} 34.4136
2077 −31  −67 4313929 1 3 1  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 19.2046
521  −4 −2084 4343056 1 1 32 16 1 16  ε_{1} 38.7273
417 −15 −695 4347225 1 2 24 24 1 24  ε_{1} 37.9102
2085 −3 −695 4347225 2 1 24 24 1 12 ε_{1} 9.8399
2085 −15 −139 4347225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 4.9199
17 −123 −2091 4372281 1 2 12 12 1 12  ε_{1} 4.1894
41 −51 −2091 4372281 1 2 12 12 1 12  ε_{1} 8.3183
697  −3 −2091 4372281 6 1 12 36 1  6  ε_{1} 11.1519
697 −51 −123 4372281 6 2 2 12 1  2  ε_{1} 11.1519
2092  −4 −523 4376464 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 25.8208
161 −91 −299 4380649 1 2 8  8 1  8  ε_{1} 20.1338
2093  −7 −299 4380649 2 1 8  8 1  4  ε_{1} 11.8053
2093 −23  −91 4380649 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.9026
5 −419 −2095 4389025 1 9 16 72 1 72  ε_{1} 0.9624
524  −8 −1048 4393216 1 1 6  6 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.9627
1048  −4 −1048 4393216 1 1 6  6 2  6  \sqrt{i}\sqrt{ε_{1}} 19.1624
2101 −11 −191 4414201 3 1 13 39 2 13 \sqrt{−1}\sqrt{ε_{1}} 10.2220

44 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q h^{−}  ε  R
701  −3 −2103 4422609 1 1 34 17 1 17  ε_{1} 20.1350
8 −263 −2104 4426816 1 13 12 78 1 78  ε_{1} 1.7627
2104  −8 −263 4426816 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 46.5712
124 −68 −527 4443664 1 4 18 36 1 36  ε_{1} 16.0392
2108  −4 −527 4443664 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 6.9622
2108 −31  −68 4443664 2 3 4 12 1  6  ε_{1} 13.9245
57 −111 −703 4447881 1 8 14 56 1 56  ε_{1} 11.4208
2109  −3 −703 4447881 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 11.6852
2109 −19 −111 4447881 2 1 8 8 1 4 ε_{1} 23.3705
13 −163 −2119 4490161 1 1 34 17 1 17  ε_{1} 2.3895
5 −424 −2120 4494400 1 6 28 84 1 84  ε_{1} 0.9624
53 −40 −2120 4494400 1 2 28 28 1 28  ε_{1} 3.9314
265  −8 −2120 4494400 2 1 28 28 1 14  ε_{1} 18.8092
265 −40 −424 4494400 2 2 6 12 1  6  ε_{1} 18.8092
21 −303 −707 4498641 1 10 6 30 1 30  ε_{1} 3.1336
2121  −3 −707 4498641 2 1 6 6 1  3  ε_{1} 56.5394
2121  −7 −303 4498641 2 1 10 10 1  5  ε_{1} 56.5394
193 −11 −2123 4507129 1 1 14 7 1  7  ε_{1} 30.1526
709  −3 −2127 4524129 1 1 28 14 1 14  ε_{1} 34.8251
8 −532 −1064 4528384 1 4 20 40 1 40  ε_{1} 1.7627
28 −152 −1064 4528384 1 6 20 60 1 60  ε_{1} 5.5373
56 −152 −532 4528384 1 6 4 12 1 12  ε_{1} 6.8002
76 −56 −1064 4528384 1 4 20 40 1 40  ε_{1} 11.6579
152 −56 −532 4528384 1 4 4 8 1  8  ε_{1} 8.6078
1064  −4 −1064 4528384 2 1 20 20 1 10  ε_{1} 14.4451
1064  −8 −532 4528384 2 1 4 4 1  2  ε_{1} 14.4451
13 −164 −2132 4545424 1 8 12 48 1 48  ε_{1} 2.3895
41 −52 −2132 4545424 1 2 12 12 1 12  ε_{1} 8.3183
533  −4 −2132 4545424 2 1 12 12 1  6  ε_{1} 6.2748
533 −52 −164 4545424 2 2 8 16 1  8  ε_{1} 6.2748
5 −427 −2135 4558225 1 2 44 44 1 44  ε_{1} 0.9624
61 −35 −2135 4558225 1 2 44 44 1 44  ε_{1} 7.3284
305  −7 −2135 4558225 2 1 44 44 1 22  ε_{1} 13.7710
305 −35 −427 4558225 2 2 2 4 1  2  ε_{1} 13.7710
8 −267 −2136 4562496 1 2 20 20 1 20  ε_{1} 1.7627
24 −267 −712 4562496 1 2 8 8 1 8 ε_{1} 4.5849
89 −24 −2136 4562496 1 2 20 20 1 20  ε_{1} 13.8155
712  −3 −2136 4562496 2 1 20 20 1 10  ε_{1} 16.1431
712 −24 −267 4562496 2 2 2 4 1  2  ε_{1} 16.1431
2136  −3 −712 4562496 2 1 8 8 1  4  ε_{1} 31.6224
2136  −8 −267 4562496 2 1 2 4 2  2 \sqrt{−1}\sqrt{ε_{1}} 15.8112
69 −31 −2139 4575321 1 3 8 12 1 12  ε_{1} 6.4345
93 −23 −2139 4575321 1 3 8 12 1 12  ε_{1} 6.7322
713 −3 −2139 4575321 1 1 8 4 1 4 ε_{1} 32.3476
428 −20 −535 4579600 1 2 14 14 1 14  ε_{1} 15.1243
2140  −4 −535 4579600 2 1 14 14 1  7  ε_{1} 29.9807
2140 −20 −107 4579600 2 2 3 6 1  3  ε_{1} 29.9807
33 −195 −715 4601025 1 4 4 8 1  8  ε_{1} 7.6563
165 −39 −715 4601025 2 4 4 16 1  8  ε_{1} 5.1180
165 −143 −195 4601025 2 10 4 40 1 20  ε_{1} 5.1180

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 45

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
429 −15 −715 4601025 2 2 4  8 1  4  ε_{1} 9.9534
429 −55 −195 4601025 2 4 4 16 1  8  ε_{1} 9.9534
2145  −3 −715 4601025 4 1 4  8 1  2  ε_{1} 21.8775
2145 −11 −195 4601025 4 1 4  8 1  2  ε_{1} 21.8775
2145 −15 −143 4601025 4 2 10 40 1 10  ε_{1} 21.8775
2145 −39  −55 4601025 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 10.9388
113 −19 −2147 4609609 1 1 14 7 1 7 ε_{1} 14.6946
12 −179 −2148 4613904 1 5 12 30 1 30  ε_{1} 2.6339
537  −4 −2148 4613904 1 1 12  6 1  6  ε_{1} 39.5359
716  −3 −2148 4613904 1 1 12  6 1  6  ε_{1} 31.8828
2149  −7 −307 4618201 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 30.0629
269  −8 −2152 4631104 1 1 10  5 1  5  ε_{1} 10.1998
5 −431 −2155 4644025 1 21 12 126 1 126  ε_{1} 0.9624
2157  −3 −719 4652649 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 18.9171
17 −127 −2159 4661281 1 5 60 150 1 150  ε_{1} 4.1894
21 −103 −2163 4678569 1 5 8 20 1 20  ε_{1} 3.1336
309  −7 −2163 4678569 1 1 8  4 1  4  ε_{1} 17.0523
721  −3 −2163 4678569 1 1 8  4 1  4  ε_{1} 76.3136
541  −4 −2164 4682896 1 1 10  5 1  5  ε_{1} 28.2989
197 −11 −2167 4695889 1 1 18  9 1  9  ε_{1} 6.6670
8 −271 −2168 4700224 1 11 24 132 1 132  ε_{1} 1.7627
2168  −8 −271 4700224 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 15.9657
13 −167 −2171 4713241 1 11 14 77 1 77  ε_{1} 2.3895
12 −543 −724 4717584 1 12 10 60 1 60  ε_{1} 2.6339
2172  −3 −724 4717584 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 14.1072
2172 −4 −543 4717584 2 1 12 12 1 6 ε_{1} 28.2144
2177  −7 −311 4739329 3 1 19 57 2 19 \sqrt{−1}\sqrt{ε_{1}} 9.3235
5 −436 −2180 4752400 1 6 32 96 1 96  ε_{1} 0.9624
109 −20 −2180 4752400 1 2 32 32 1 32  ε_{1} 11.1291
545 −4 −2180 4752400 2 1 32 32 1 16 ε_{1} 16.5487
545 −20 −436 4752400 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.2744
2181  −3 −727 4756761 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 23.8815
37 −59 −2183 4765489 1 3 42 63 1 63  ε_{1} 4.9836
13 −168 −2184 4769856 1 4 24 48 1 48  ε_{1} 2.3895
21 −104 −2184 4769856 1 6 24 72 1 72  ε_{1} 3.1336
21 −312 −728 4769856 1 4 12 24 1 24  ε_{1} 3.1336
24 −91 −2184 4769856 1 2 24 24 1 24  ε_{1} 4.5849
56 −39 −2184 4769856 1 4 24 48 1 48  ε_{1} 6.8002
168 −39 −728 4769856 2 4 12 48 1 24  ε_{1} 6.5132
168 −91 −312 4769856 2 2 4  8 1  4  ε_{1} 6.5132
273  −8 −2184 4769856 2 1 24 24 1 12  ε_{1} 14.5641
273 −24 −728 4769856 2 2 12 24 1 12  ε_{1} 14.5641
273 −56 −312 4769856 2 4 4 16 1 8 ε_{1} 14.5641
273 −104 −168 4769856 2 6 4 24 1 12  ε_{1} 14.5641
312  −7 −2184 4769856 2 1 24 24 1 12  ε_{1} 9.3267
312 −91 −168 4769856 2 2 4  8 1  4  ε_{1} 9.3267
728  −3 −2184 4769856 2 1 24 24 1 12  ε_{1} 7.9773
728 −39 −168 4769856 2 4 4 16 1  8  ε_{1} 7.9773
2184  −3 −728 4769856 4 1 12 24 1  6  ε_{1} 14.4913
2184  −7 −312 4769856 4 1 4  8 1  2  ε_{1} 14.4913

46 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2184 −24  −91 4769856 4 2 2  8 1  2  ε_{1} 14.4913
2184 −39  −56 4769856 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 7.2457
437 −95 −115 4774225 1 8 2  8 1  8  ε_{1} 6.0845
2185 −19 −115 4774225 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 36.1488
2185 −23  −95 4774225 2 3 8 24 1 12  ε_{1} 72.2976
2188  −4 −547 4787344 1 1 3  3 2  3  \sqrt{i}\sqrt{ε_{1}} 33.4005
2189 −11 −199 4791721 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 13.9283
313  −7 −2191 4800481 1 1 30 15 1 15  ε_{1} 38.7035
8 −548 −1096 4804864 1 8 12 48 1 48  ε_{1} 1.7627
1096  −4 −1096 4804864 4 1 12 24 1  6  ε_{1} 15.8847
1096  −8 −548 4804864 4 1 8 16 1  4  ε_{1} 15.8847
129 −51 −731 4809249 1 2 12 12 1 12  ε_{1} 20.8511
2193  −3 −731 4809249 2 1 12 12 1  6  ε_{1} 49.5975
2193 −43  −51 4809249 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 24.7988
5 −439 −2195 4818025 1 15 16 120 1 120  ε_{1} 0.9624
733 −3 −2199 4835601 3 1 36 54 1 18 ε_{1} 6.5944
2201 −31  −71 4844401 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 45.2783
76 −116 −551 4857616 1 6 26 78 1 78  ε_{1} 11.6579
2204  −4 −551 4857616 2 1 26 26 1 13  ε_{1} 19.4535
2204 −19 −116 4857616 2 1 6  6 1  3  ε_{1} 19.4535
33 −67 −2211 4888521 1 1 16  8 1  8  ε_{1} 7.6563
201 −11 −2211 4888521 1 1 16  8 1  8  ε_{1} 27.6905
737  −3 −2211 4888521 1 1 16  8 1  8  ε_{1} 40.0839
28 −79 −2212 4892944 1 5 8 20 1 20  ε_{1} 5.5373
316  −7 −2212 4892944 3 1 8 12 1  4  ε_{1} 10.1503
553  −4 −2212 4892944 1 1 8  4 1  4  ε_{1} 55.7072
5 −443 −2215 4906225 1 5 22 55 1 55  ε_{1} 0.9624
277  −8 −2216 4910656 1 1 22 11 1 11  ε_{1} 15.7365
2217  −3 −739 4915089 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 31.8238
317  −7 −2219 4923961 1 1 24 12 1 12  ε_{1} 8.9775
12 −555 −740 4928400 1 4 16 32 1 32  ε_{1} 2.6339
60 −111 −740 4928400 2 8 16 128 1 64  ε_{1} 4.1269
60 −148 −555 4928400 2 2 4 8 1 4 ε_{1} 4.1269
444 −15 −740 4928400 2 2 16 32 1 16  ε_{1} 12.7602
444 −20 −555 4928400 2 2 4  8 1  4  ε_{1} 12.7602
2220  −3 −740 4928400 4 1 16 32 1  8  ε_{1} 16.3929
2220  −4 −555 4928400 4 1 4  8 1  2  ε_{1} 16.3929
2220 −15 −148 4928400 4 2 2  8 1  2  ε_{1} 16.3929
2220 −20 −111 4928400 4 2 8 32 1  8  ε_{1} 16.3929
556  −8 −1112 4946176 1 1 14 14 2 14 \sqrt{−1}\sqrt{ε_{1}} 18.8598
1112 −4 −1112 4946176 1 1 14 14 2 14 \sqrt{i}\sqrt{ε_{1}} 8.5176
17 −131 −2227 4959529 1 5 6 15 1 15  ε_{1} 4.1894
557 −4 −2228 4963984 1 1 18 9 1 9 ε_{1} 10.9277
2229  −3 −743 4968441 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 16.9855
97 −23 −2231 4977361 1 3 58 87 1 87  ε_{1} 18.6488
77 −203 −319 4986289 1 4 10 20 1 20  ε_{1} 4.3693
2233  −7 −319 4986289 6 1 10 60 2 10 \sqrt{−1}\sqrt{ε_{1}} 9.9240
2233 −11 −203 4986289 6 1 4 12 1 2 ε_{1} 19.8480
5 −447 −2235 4995225 1 14 12 84 1 84  ε_{1} 0.9624
149 −15 −2235 4995225 1 2 12 12 1 12  ε_{1} 8.2223

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 47

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
745  −3 −2235 4995225 2 1 12 12 1  6  ε_{1} 34.1114
745 −15 −447 4995225 2 2 14 28 1 14  ε_{1} 34.1114
172 −52 −559 4999696 1 2 16 16 1 16  ε_{1} 17.6970
2236  −4 −559 4999696 2 1 16 16 1  8  ε_{1} 41.4726
2236 −43  −52 4999696 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 20.7363
12 −187 −2244 5035536 1 2 16 16 1 16  ε_{1} 2.6339
17 −132 −2244 5035536 1 4 16 32 1 32  ε_{1} 4.1894
33 −68 −2244 5035536 1 4 16 32 1 32  ε_{1} 7.6563
44 −51 −2244 5035536 1 2 16 16 1 16  ε_{1} 5.9864
204 −11 −2244 5035536 2 1 16 16 1  8  ε_{1} 9.2101
204 −132 −187 5035536 2 4 2  8 1  4  ε_{1} 9.2101
561  −4 −2244 5035536 2 1 16 16 1  8  ε_{1} 27.7201
561 −68 −132 5035536 2 4 4 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 13.8601
748  −3 −2244 5035536 2 1 16 16 1  8  ε_{1} 16.2418
748 −51 −132 5035536 2 2 4  8 1  4  ε_{1} 16.2418
21 −107 −2247 5049009 1 3 20 30 1 30  ε_{1} 3.1336
321  −7 −2247 5049009 3 1 20 30 1 10  ε_{1} 12.1276
749  −3 −2247 5049009 1 1 20 10 1 10  ε_{1} 18.9369
281  −8 −2248 5053504 1 1 8  4 1  4  ε_{1} 29.1405
2252  −4 −563 5071504 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 11.8222
2253  −3 −751 5076009 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 15.2023
5 −451 −2255 5085025 1 6 40 120 1 120  ε_{1} 0.9624
41 −55 −2255 5085025 1 4 40 80 1 80  ε_{1} 8.3183
205 −11 −2255 5085025 2 1 40 40 1 20  ε_{1} 7.5213
205 −55 −451 5085025 2 4 6 24 1 12  ε_{1} 7.5213
8 −564 −1128 5089536 1 8 8 32 1 32  ε_{1} 1.7627
12 −376 −1128 5089536 1 8 8 32 1 32  ε_{1} 2.6339
24 −376 −564 5089536 1 8 8 32 1 32  ε_{1} 4.5849
188 −24 −1128 5089536 1 2 8  8 1  8  ε_{1} 9.1285
376 −24 −564 5089536 1 2 8  8 1  8  ε_{1} 30.5420
1128  −4 −1128 5089536 2 1 8  8 1  4  ε_{1} 16.9115
1128  −8 −564 5089536 2 1 8  8 1  4  ε_{1} 16.9115
5 −452 −2260 5107600 1 8 12 48 1 48  ε_{1} 0.9624
113 −20 −2260 5107600 1 2 12 12 1 12  ε_{1} 14.6946
565  −4 −2260 5107600 2 1 12 12 1  6  ε_{1} 11.4667
565 −20 −452 5107600 2 2 8 16 1  8  ε_{1} 11.4667
133 −119 −323 5112121 1 10 4 20 1 20  ε_{1} 10.3065
2261 −7 −323 5112121 2 1 4 4 1 2 ε_{1} 15.1013
2261 −19 −119 5112121 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 7.5507
73 −31 −2263 5121169 1 3 22 33 1 33  ε_{1} 15.3334
8 −283 −2264 5125696 1 3 30 45 1 45  ε_{1} 1.7627
2264 −8 −283 5125696 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 19.0689
453 −15 −755 5130225 1 2 12 12 1 12  ε_{1} 10.0078
2265 −3 −755 5130225 2 1 12 12 1 6 ε_{1} 55.2093
2265 −15 −151 5130225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 27.6046
757  −3 −2271 5157441 1 1 44 22 1 22  ε_{1} 29.6460
569  −4 −2276 5180176 1 1 32 16 1 16  ε_{1} 44.9587
53 −43 −2279 5193841 1 1 56 28 1 28  ε_{1} 3.9314
5 −456 −2280 5198400 1 8 16 64 1 64  ε_{1} 0.9624
24 −95 −2280 5198400 1 8 16 64 1 64  ε_{1} 4.5849

48 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
57 −40 −2280 5198400 1 2 16 16 1 16  ε_{1} 11.4208
57 −120 −760 5198400 1 4 4  8 1  8  ε_{1} 11.4208
120 −19 −2280 5198400 2 1 16 16 1  8  ε_{1} 6.1779
120 −95 −456 5198400 2 8 8 64 1 32  ε_{1} 6.1779
152 −15 −2280 5198400 1 2 16 16 1 16  ε_{1} 8.6078
285  −8 −2280 5198400 2 1 16 16 1  8  ε_{1} 5.6595
285 −24 −760 5198400 2 2 4  8 1  4  ε_{1} 5.6595
285 −40 −456 5198400 2 2 8 16 1  8  ε_{1} 5.6595
285 −120 −152 5198400 2 4 6 24 1 12  ε_{1} 5.6595
456 −15 −760 5198400 2 2 4 8 1 4 ε_{1} 15.2512
456 −95 −120 5198400 2 8 4 32 1 16  ε_{1} 15.2512
760  −3 −2280 5198400 2 1 16 16 1  8  ε_{1} 23.1051
760 −15 −456 5198400 2 2 8 16 1  8  ε_{1} 23.1051
2280  −3 −760 5198400 4 1 4  8 1  2  ε_{1} 11.8908
2280 −15 −152 5198400 4 2 6 24 1  6  ε_{1} 11.8908
2280 −19 −120 5198400 4 1 4  8 1  2  ε_{1} 11.8908
2280 −24  −95 5198400 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.9454
761  −3 −2283 5212089 3 1 6  9 1  3  ε_{1} 14.7555
2284  −4 −571 5216656 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 47.3389
44 −104 −1144 5234944 1 6 12 36 1 36  ε_{1} 5.9864
88 −52 −1144 5234944 1 2 12 12 1 12  ε_{1} 11.9527
572 −8 −1144 5234944 2 1 12 12 1 6 ε_{1} 6.3526
572 −88 −104 5234944 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 3.1763
1144  −4 −1144 5234944 2 1 12 12 1  6  ε_{1} 27.8642
1144 −52  −88 5234944 2 2 2  8 2  4 \sqrt{−1}\sqrt{ε_{1}} 13.9321
21 −327 −763 5239521 1 12 4 24 1 24  ε_{1} 3.1336
2289  −3 −763 5239521 4 1 4  8 1  2  ε_{1} 31.1350
2289  −7 −327 5239521 4 1 12 24 1  6  ε_{1} 31.1350
29 −79 −2291 5248681 1 5 18 45 1 45  ε_{1} 3.2945
12 −191 −2292 5253264 1 13 16 104 1 104  ε_{1} 2.6339
573  −4 −2292 5253264 1 1 16  8 1  8  ε_{1} 13.2824
764  −3 −2292 5253264 1 1 16  8 1  8  ε_{1} 33.4104
8 −287 −2296 5271616 1 14 16 112 1 112  ε_{1} 1.7627
41 −56 −2296 5271616 1 4 16 32 1 32  ε_{1} 8.3183
56 −287 −328 5271616 1 14 4 28 1 28  ε_{1} 6.8002
328 −7 −2296 5271616 4 1 16 32 1 8 ε_{1} 5.7869
328 −56 −287 5271616 4 4 14 112 1 28  ε_{1} 5.7869
2296 −7 −328 5271616 6 1 4 12 1 2 ε_{1} 14.0950
2296  −8 −287 5271616 6 1 14 84 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.0475
177 −39 −767 5294601 1 4 22 44 1 44  ε_{1} 23.4697
2301  −3 −767 5294601 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 8.0294
2301 −39  −59 5294601 2 4 3 12 1  6  ε_{1} 16.0589
769  −3 −2307 5322249 1 1 8  4 1  4  ε_{1} 76.0544
577  −4 −2308 5326864 7 1 8 28 1  4  ε_{1} 7.7433
5 −463 −2315 5359225 1 7 18 63 1 63  ε_{1} 0.9624
12 −579 −772 5363856 1 8 4 16 1 16  ε_{1} 2.6339
2316  −3 −772 5363856 4 1 4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 6.6464
2316  −4 −579 5363856 4 1 8 16 1  4  ε_{1} 13.2928
2317  −7 −331 5368489 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 18.5926
773  −3 −2319 5377761 1 1 30 15 1 15  ε_{1} 9.8691

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 49

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8 −580 −1160 5382400 1 8 20 80 1 80  ε_{1} 1.7627
40 −116 −1160 5382400 2 6 20 120 1 60  ε_{1} 3.6369
40 −232 −580 5382400 2 2 8 16 1 8 ε_{1} 3.6369
232 −20 −1160 5382400 2 2 20 40 1 20  ε_{1} 10.5766
232 −40 −580 5382400 2 2 8 16 1  8  ε_{1} 10.5766
1160  −4 −1160 5382400 4 1 20 40 1 10  ε_{1} 7.0544
1160  −8 −580 5382400 4 1 8 16 1  4  ε_{1} 7.0544
1160 −20 −232 5382400 4 2 2  8 1  2  ε_{1} 7.0544
1160 −40 −116 5382400 4 2 6 24 1  6  ε_{1} 7.0544
2321 −11 −211 5387041 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 48.1760
101 −23 −2323 5396329 1 3 8 12 1 12  ε_{1} 5.9964
28 −83 −2324 5400976 1 3 28 42 1 42  ε_{1} 5.5373
332  −7 −2324 5400976 1 1 28 14 1 14  ε_{1} 10.1997
581  −4 −2324 5400976 1 1 28 14 1 14  ε_{1} 17.6272
13 −179 −2327 5414929 1 5 48 120 1 120  ε_{1} 2.3895
8 −291 −2328 5419584 1 4 16 32 1 32  ε_{1} 1.7627
24 −291 −776 5419584 1 4 20 40 1 40  ε_{1} 4.5849
97 −24 −2328 5419584 1 2 16 16 1 16  ε_{1} 18.6488
776  −3 −2328 5419584 2 1 16 16 1  8  ε_{1} 11.9323
776 −24 −291 5419584 2 2 4  8 1  4  ε_{1} 11.9323
2328  −3 −776 5419584 4 1 20 40 1 10  ε_{1} 11.9117
2328  −8 −291 5419584 4 1 4  8 1  2  ε_{1} 11.9117
44 −212 −583 5438224 1 6 8 24 1 24  ε_{1} 5.9864
2332 −4 −583 5438224 2 1 8 8 1 4 ε_{1} 33.2808
2332 −11 −212 5438224 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 16.6404
5 −467 −2335 5452225 1 7 14 49 1 49  ε_{1} 0.9624
57 −123 −779 5461569 1 2 10 10 1 10  ε_{1} 11.4208
2337  −3 −779 5461569 2 1 10 10 1  5  ε_{1} 42.0396
2337 −19 −123 5461569 2 1 2  2 1  1  ε_{1} 42.0396
33 −71 −2343 5489649 1 7 32 112 1 112  ε_{1} 7.6563
213 −11 −2343 5489649 1 1 32 16 1 16  ε_{1} 8.5805
781  −3 −2343 5489649 1 1 32 16 1 16  ε_{1} 37.4447
293  −8 −2344 5494336 1 1 18  9 1  9  ε_{1} 5.6733
469 −35 −335 5499025 3 2 18 54 1 18  ε_{1} 8.3483
2345  −7 −335 5499025 2 1 18 18 1  9  ε_{1} 34.4505
2345 −35  −67 5499025 2 2 1  2 1  1  ε_{1} 34.4505
2348  −4 −587 5513104 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 15.1543
5 −471 −2355 5546025 1 16 12 96 1 96  ε_{1} 0.9624
157 −15 −2355 5546025 1 2 12 12 1 12  ε_{1} 10.7226
785 −3 −2355 5546025 6 1 12 36 1 6 ε_{1} 8.0513
785 −15 −471 5546025 6 2 16 96 1 16  ε_{1} 8.0513
76 −31 −2356 5550736 1 3 16 24 1 24  ε_{1} 11.6579
124 −19 −2356 5550736 1 1 16  8 1  8  ε_{1} 16.0392
589  −4 −2356 5550736 1 1 16  8 1  8  ε_{1} 30.5757
337  −7 −2359 5564881 1 1 28 14 1 14  ε_{1} 42.8642
5 −472 −2360 5569600 1 6 20 60 1 60  ε_{1} 0.9624
8 −295 −2360 5569600 1 8 20 80 1 80  ε_{1} 1.7627
40 −59 −2360 5569600 2 3 20 60 1 30  ε_{1} 3.6369
40 −295 −472 5569600 2 8 6 48 1 24  ε_{1} 3.6369
472 −40 −295 5569600 1 2 8  8 1  8  ε_{1} 26.6550

50 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2360  −8 −295 5569600 2 1 8  8 1  4  ε_{1} 18.7110
2360 −40  −59 5569600 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.3555
2361  −3 −787 5574321 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 61.5628
17 −139 −2363 5583769 1 3 10 15 1 15  ε_{1} 4.1894
12 −591 −788 5588496 1 22 10 110 1 110  ε_{1} 2.6339
2364  −3 −788 5588496 2 1 10 10 1  5  ε_{1} 25.4219
2364  −4 −591 5588496 2 1 22 22 1 11  ε_{1} 25.4219
473 −55 −215 5593225 3 4 14 84 1 28  ε_{1} 10.3180
2365 −11 −215 5593225 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 12.6458
2365 −43 −55 5593225 2 1 4 4 1 2 ε_{1} 25.2916
2369 −23 −103 5612161 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 43.7076
593 −4 −2372 5626384 1 1 24 12 1 12 ε_{1} 27.9978
21 −339 −791 5631129 1 6 32 96 1 96  ε_{1} 3.1336
2373  −3 −791 5631129 2 1 32 32 1 16  ε_{1} 11.6637
2373  −7 −339 5631129 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.8319
13 −183 −2379 5659641 1 8 16 64 1 64  ε_{1} 2.3895
61 −39 −2379 5659641 1 4 16 32 1 32  ε_{1} 7.3284
793 −3 −2379 5659641 4 1 16 32 1 8 ε_{1} 18.1618
793 −39 −183 5659641 4 4 8 64 1 16  ε_{1} 18.1618
28 −340 −595 5664400 1 4 4  8 1  8  ε_{1} 5.5373
140 −68 −595 5664400 2 4 4 16 1  8  ε_{1} 4.9558
140 −119 −340 5664400 2 10 4 40 1 20  ε_{1} 4.9558
476 −20 −595 5664400 2 2 4  8 1  4  ε_{1} 10.9612
476 −35 −340 5664400 2 2 4  8 1  4  ε_{1} 10.9612
2380  −4 −595 5664400 4 1 4  8 1  2  ε_{1} 21.0389
2380  −7 −340 5664400 4 1 4  8 1  2  ε_{1} 21.0389
2380 −20 −119 5664400 4 2 10 40 1 10  ε_{1} 21.0389
2380 −35 −68 5664400 4 2 4 16 1 4 ε_{1} 21.0389
8 −596 −1192 5683456 1 14 6 42 1 42  ε_{1} 1.7627
1192  −4 −1192 5683456 2 1 6  6 1  3  ε_{1} 27.2320
1192  −8 −596 5683456 2 1 14 14 1  7  ε_{1} 27.2320
77 −31 −2387 5697769 1 3 12 18 1 18  ε_{1} 4.3693
217 −11 −2387 5697769 1 1 12  6 1  6  ε_{1} 31.7104
341  −7 −2387 5697769 1 1 12  6 1  6  ε_{1} 11.2480
12 −199 −2388 5702544 1 9 12 54 1 54  ε_{1} 2.6339
597  −4 −2388 5702544 1 1 12  6 1  6  ε_{1} 18.3698
796  −3 −2388 5702544 1 1 12  6 1  6  ε_{1} 48.4110
797  −3 −2391 5716881 1 1 34 17 1 17  ε_{1} 11.8107
8 −299 −2392 5721664 1 8 8 32 1 32  ε_{1} 1.7627
13 −184 −2392 5721664 1 4 8 16 1 16  ε_{1} 2.3895
104 −23 −2392 5721664 2 3 8 24 1 12  ε_{1} 4.6249
104 −184 −299 5721664 2 4 8 32 1 16  ε_{1} 4.6249
184 −104 −299 5721664 1 6 8 24 1 24  ε_{1} 21.5856
2392 −8 −299 5721664 2 1 8 8 1 4 ε_{1} 29.9250
2392 −23 −104 5721664 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 14.9625
5 −479 −2395 5736025 1 25 8 100 1 100  ε_{1} 0.9624
2396 −4 −599 5740816 1 1 25 25 2 25 \sqrt{i}\sqrt{ε_{1}} 31.5304
141 −51 −799 5745609 1 2 16 16 1 16  ε_{1} 10.4940
2397 −3 −799 5745609 2 1 16 16 1 8 ε_{1} 7.7828
2397 −47  −51 5745609 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 3.8914

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 51

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
601  −4 −2404 5779216 1 1 20 10 1 10  ε_{1} 66.5240
29 −83 −2407 5793649 1 3 20 30 1 30  ε_{1} 3.2945
56 −43 −2408 5798464 1 1 24 12 1 12  ε_{1} 6.8002
301 −8 −2408 5798464 1 1 24 12 1 12 ε_{1} 20.0642
301 −56 −344 5798464 1 4 10 20 1 20  ε_{1} 20.0642
344 −7 −2408 5798464 1 1 24 12 1 12 ε_{1} 19.8864
2408  −7 −344 5798464 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 7.2255
2408 −43 −56 5798464 2 1 4 4 1 2 ε_{1} 14.4510
33 −219 −803 5803281 1 4 10 20 1 20  ε_{1} 7.6563
2409  −3 −803 5803281 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 32.3231
2409 −11 −219 5803281 2 1 4  4 1  2  ε_{1} 64.6462
2413 −19 −127 5822569 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 19.2465
5 −483 −2415 5832225 1 4 40 80 1 80  ε_{1} 0.9624
21 −115 −2415 5832225 1 2 40 40 1 40  ε_{1} 3.1336
69 −35 −2415 5832225 1 2 40 40 1 40  ε_{1} 6.4345
105 −23 −2415 5832225 2 3 40 120 1 60  ε_{1} 8.8131
105 −115 −483 5832225 2 2 4 8 1 4 ε_{1} 8.8131
161 −15 −2415 5832225 1 2 40 40 1 40  ε_{1} 20.1338
345  −7 −2415 5832225 2 1 40 40 1 20  ε_{1} 19.0241
345 −35 −483 5832225 2 2 4  8 1  4  ε_{1} 19.0241
805  −3 −2415 5832225 2 1 40 40 1 20  ε_{1} 14.5545
805 −15 −483 5832225 2 2 4  8 1  4  ε_{1} 14.5545
604  −8 −1208 5837056 1 1 12 12 2 12 \sqrt{−1}\sqrt{ε_{1}} 21.9635
1208 −4 −1208 5837056 1 1 12 12 2 12 \sqrt{i}\sqrt{ε_{1}} 15.9618
41 −59 −2419 5851561 1 3 8 12 1 12  ε_{1} 8.3183
8 −303 −2424 5875776 1 10 12 60 1 60  ε_{1} 1.7627
24 −303 −808 5875776 1 10 6 30 1 30  ε_{1} 4.5849
101 −24 −2424 5875776 1 2 12 12 1 12  ε_{1} 5.9964
808 −3 −2424 5875776 2 1 12 12 1 6 ε_{1} 17.4909
808 −24 −303 5875776 2 2 10 20 1 10  ε_{1} 17.4909
2424  −3 −808 5875776 2 1 6  6 1  3  ε_{1} 36.5016
2424  −8 −303 5875776 2 1 10 10 1  5  ε_{1} 36.5016
809  −3 −2427 5890329 1 1 14  7 1  7  ε_{1} 54.9782
2428  −4 −607 5895184 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 26.5167
2429  −7 −347 5900041 3 1 5 15 2  5 \sqrt{−1}\sqrt{ε_{1}} 5.8435
13 −187 −2431 5909761 1 2 28 28 1 28  ε_{1} 2.3895
17 −143 −2431 5909761 1 10 28 140 1 140  ε_{1} 4.1894
221 −11 −2431 5909761 2 1 28 28 1 14  ε_{1} 5.4072
221 −143 −187 5909761 2 10 2 20 1 10  ε_{1} 5.4072
2433 −3 −811 5919489 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 46.2934
5 −487 −2435 5929225 1 7 22 77 1 77  ε_{1} 0.9624
12 −203 −2436 5934096 1 4 16 32 1 32  ε_{1} 2.6339
21 −116 −2436 5934096 1 6 16 48 1 48  ε_{1} 3.1336
28 −87 −2436 5934096 1 6 16 48 1 48  ε_{1} 5.5373
29 −84 −2436 5934096 1 4 16 32 1 32  ε_{1} 3.2945
348  −7 −2436 5934096 2 1 16 16 1  8  ε_{1} 8.0501
348 −84 −203 5934096 2 4 4 16 1  8  ε_{1} 8.0501
609  −4 −2436 5934096 2 1 16 16 1  8  ε_{1} 28.0146
609 −84 −116 5934096 2 4 6 24 1 12  ε_{1} 28.0146
812  −3 −2436 5934096 2 1 16 16 1  8  ε_{1} 9.4722

52 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
812 −84  −87 5934096 2 4 6 24 1 12  ε_{1} 9.4722
5 −488 −2440 5953600 1 10 12 60 1 60  ε_{1} 0.9624
61 −40 −2440 5953600 1 2 12 12 1 12  ε_{1} 7.3284
305 −8 −2440 5953600 2 1 12 12 1 6 ε_{1} 13.7710
305 −40 −488 5953600 2 2 10 20 1 10  ε_{1} 13.7710
349 −7 −2443 5968249 1 1 6 3 1 3 ε_{1} 19.6424
188 −52 −611 5973136 1 2 10 10 1 10  ε_{1} 9.1285
2444  −4 −611 5973136 2 1 10 10 1  5  ε_{1} 26.1373
2444 −47  −52 5973136 2 5 2 10 1  5  ε_{1} 26.1373
489 −15 −815 5978025 1 2 30 30 1 30  ε_{1} 46.8872
2445  −3 −815 5978025 2 1 30 30 1 15  ε_{1} 21.1735
2445 −15 −163 5978025 2 2 1  2 1  1  ε_{1} 21.1735
2449 −31  −79 5997601 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 72.6419
57 −43 −2451 6007401 1 1 8  4 1  4  ε_{1} 11.4208
129 −19 −2451 6007401 1 1 8  4 1  4  ε_{1} 20.8511
817  −3 −2451 6007401 5 1 8 20 1  4  ε_{1} 13.0618
613  −4 −2452 6012304 1 1 10  5 1  5  ε_{1} 23.0010
2453 −11 −223 6017209 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 8.1792
5 −491 −2455 6027025 1 9 28 126 1 126  ε_{1} 0.9624
8 −307 −2456 6031936 1 3 34 51 1 51  ε_{1} 1.7627
2456 −8 −307 6031936 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 27.2695
12 −615 −820 6051600 1 20 8 80 1 80  ε_{1} 2.6339
60 −123 −820 6051600 2 2 8 16 1 8 ε_{1} 4.1269
60 −164 −615 6051600 2 8 20 160 1 80  ε_{1} 4.1269
492 −15 −820 6051600 2 2 8 16 1 8 ε_{1} 10.9943
492 −20 −615 6051600 2 2 20 40 1 20  ε_{1} 10.9943
2460  −3 −820 6051600 4 1 8 16 1  4  ε_{1} 11.0268
2460  −4 −615 6051600 4 1 20 40 1 10  ε_{1} 11.0268
2460 −15 −164 6051600 4 2 8 32 1  8  ε_{1} 11.0268
2460 −20 −123 6051600 4 2 2  8 1  2  ε_{1} 11.0268
2461 −23 −107 6056521 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 34.3264
821  −3 −2463 6066369 1 1 34 17 1 17  ε_{1} 19.3842
617  −4 −2468 6091024 1 1 12  6 1  6  ε_{1} 36.4449
2469  −3 −823 6095961 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 23.0607
353  −7 −2471 6105841 1 1 62 31 1 31  ε_{1} 23.7346
24 −103 −2472 6110784 1 5 12 30 1 30  ε_{1} 4.5849
309 −8 −2472 6110784 1 1 12 6 1 6 ε_{1} 17.0523
309 −24 −824 6110784 1 2 20 20 1 20  ε_{1} 17.0523
824  −3 −2472 6110784 1 1 12  6 1  6  ε_{1} 23.3749
2472  −3 −824 6110784 2 1 20 20 1 10  ε_{1} 19.8255
2472 −24 −103 6110784 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 9.9127
2476 −4 −619 6130576 1 1 5 5 2 5 \sqrt{i}\sqrt{ε_{1}} 41.4804
37 −67 −2479 6145441 1 1 24 12 1 12  ε_{1} 4.9836
124 −40 −1240 6150400 1 2 8  8 1  8  ε_{1} 16.0392
248 −20 −1240 6150400 1 2 8  8 1  8  ε_{1} 9.6724
620  −8 −1240 6150400 2 1 8  8 1  4  ε_{1} 12.4212
620 −40 −248 6150400 2 2 8 16 1  8  ε_{1} 12.4212
1240  −4 −1240 6150400 2 1 8  8 1  4  ε_{1} 28.6893
1240 −20 −248 6150400 2 2 8 16 1  8  ε_{1} 28.6893
2481  −3 −827 6155361 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 52.7617

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 53

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
13 −191 −2483 6165289 1 13 20 130 1 130  ε_{1} 2.3895
497 −35 −355 6175225 1 2 4  4 1  4  ε_{1} 29.3851
2485  −7 −355 6175225 2 1 4  4 1  2  ε_{1} 22.5113
2485 −35  −71 6175225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 11.2557
829 −3 −2487 6185169 1 1 20 10 1 10 ε_{1} 34.4976
8 −311 −2488 6190144 1 19 12 114 1 114  ε_{1} 1.7627
2488  −8 −311 6190144 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 24.0414
2489 −19 −131 6195121 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 51.3953
53 −47 −2491 6205081 1 5 12 30 1 30  ε_{1} 3.9314
28 −356 −623 6210064 1 12 22 132 1 132  ε_{1} 5.5373
2492  −4 −623 6210064 2 1 22 44 2 22  \sqrt{i}\sqrt{ε_{1}} 7.1293
2492  −7 −356 6210064 2 1 12 12 1  6  ε_{1} 14.2586
5 −499 −2495 6225025 1 3 56 84 1 84  ε_{1} 0.9624
2497 −11 −227 6235009 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 58.9210
313  −8 −2504 6270016 1 1 36 18 1 18  ε_{1} 38.7035
501 −15 −835 6275025 1 2 6  6 1  6  ε_{1} 20.4959
2505  −3 −835 6275025 6 1 6 18 1  3  ε_{1} 15.2038
2505 −15 −167 6275025 6 2 11 66 1 11  ε_{1} 15.2038
109 −23 −2507 6285049 1 3 14 21 1 21  ε_{1} 11.1291
12 −627 −836 6290064 1 4 20 40 1 40  ε_{1} 2.6339
33 −228 −836 6290064 1 4 20 40 1 40  ε_{1} 7.6563
44 −228 −627 6290064 1 4 4 8 1 8 ε_{1} 5.9864
57 −132 −836 6290064 1 4 20 40 1 40  ε_{1} 11.4208
76 −132 −627 6290064 1 4 4  8 1  8  ε_{1} 11.6579
209 −132 −228 6290064 1 4 4  8 1  8  ε_{1} 22.8829
2508  −3 −836 6290064 4 1 20 40 1 10  ε_{1} 14.2650
2508  −4 −627 6290064 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 7.1325
2508 −11 −228 6290064 4 1 4  8 1  2  ε_{1} 14.2650
2508 −19 −132 6290064 4 1 4  8 1  2  ε_{1} 14.2650
8 −628 −1256 6310144 1 6 26 78 1 78  ε_{1} 1.7627
1256  −4 −1256 6310144 2 1 26 26 1 13  ε_{1} 13.5734
1256  −8 −628 6310144 2 1 6  6 1  3  ε_{1} 13.5734
2513  −7 −359 6315169 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 37.4647
5 −503 −2515 6325225 1 21 6 63 1 63  ε_{1} 0.9624
17 −148 −2516 6330256 1 2 36 36 1 36  ε_{1} 4.1894
37 −68 −2516 6330256 1 4 36 72 1 72  ε_{1} 4.9836
629  −4 −2516 6330256 2 1 36 36 1 18  ε_{1} 6.4409
629 −68 −148 6330256 2 4 2  8 1  4  ε_{1} 6.4409
2517  −3 −839 6335289 1 1 33 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 18.6283
229 −11 −2519 6345361 3 1 64 96 1 32  ε_{1} 5.4249
2524 −4 −631 6370576 1 1 13 13 2 13 \sqrt{i}\sqrt{ε_{1}} 52.9385
12 −211 −2532 6411024 1 3 20 30 1 30  ε_{1} 2.6339
633  −4 −2532 6411024 1 1 20 10 1 10  ε_{1} 41.1944
844  −3 −2532 6411024 1 1 20 10 1 10  ε_{1} 54.0906
317  −8 −2536 6431296 1 1 14  7 1  7  ε_{1} 8.9775
2537 −43  −59 6436369 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 23.5296
508 −20 −635 6451600 1 2 10 10 1 10  ε_{1} 32.1254
2540  −4 −635 6451600 2 1 10 10 1  5  ε_{1} 11.0588
2540 −20 −127 6451600 2 2 5 10 1  5  ε_{1} 11.0588
12 −424 −1272 6471936 1 6 12 36 1 36  ε_{1} 2.6339

54 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
24 −212 −1272 6471936 1 6 12 36 1 36  ε_{1} 4.5849
636 −8 −1272 6471936 2 1 12 12 1 6 ε_{1} 15.7631
636 −24 −424 6471936 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.8816
1272 −4 −1272 6471936 2 1 12 12 1 6 ε_{1} 10.7319
1272 −24 −212 6471936 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.3660
8 −319 −2552 6512704 1 10 20 100 1 100  ε_{1} 1.7627
29 −88 −2552 6512704 1 2 20 20 1 20  ε_{1} 3.2945
88 −232 −319 6512704 1 2 10 10 1 10  ε_{1} 11.9527
232 −11 −2552 6512704 2 1 20 20 1 10  ε_{1} 10.5766
232 −88 −319 6512704 2 2 10 20 1 10  ε_{1} 10.5766
2552  −8 −319 6512704 2 1 10 10 1  5  ε_{1} 22.6906
2552 −11 −232 6512704 2 1 2  2 1  1  ε_{1} 22.6906
69 −111 −851 6517809 1 8 10 40 1 40  ε_{1} 6.4345
2553  −3 −851 6517809 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 19.8429
2553 −23 −111 6517809 2 3 8 24 1 12  ε_{1} 39.6857
5 −511 −2555 6528025 1 14 12 84 1 84  ε_{1} 0.9624
73 −35 −2555 6528025 1 2 12 12 1 12  ε_{1} 15.3334
365 −7 −2555 6528025 2 1 12 12 1 6 ε_{1} 5.8944
365 −35 −511 6528025 2 2 14 28 1 14  ε_{1} 5.8944
853  −3 −2559 6548481 1 1 40 20 1 20  ε_{1} 20.4426
233 −11 −2563 6568969 1 1 6  3 1  3  ε_{1} 21.4863
641  −4 −2564 6574096 1 1 28 14 1 14  ε_{1} 50.0066
17 −151 −2567 6589489 1 7 44 154 1 154  ε_{1} 4.1894
24 −107 −2568 6594624 1 3 16 24 1 24  ε_{1} 4.5849
321  −8 −2568 6594624 3 1 16 24 1  8  ε_{1} 12.1276
321 −24 −856 6594624 3 2 6 18 1  6  ε_{1} 12.1276
856  −3 −2568 6594624 1 1 16  8 1  8  ε_{1} 55.9217
2568  −3 −856 6594624 2 1 6  6 1  3  ε_{1} 18.7096
2568 −24 −107 6594624 2 2 3  6 1  3  ε_{1} 18.7096
2569  −7 −367 6599761 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 81.0712
857  −3 −2571 6610041 1 1 14  7 1  7  ε_{1} 33.2056
2572  −4 −643 6615184 1 1 3  3 2  3  \sqrt{i}\sqrt{ε_{1}} 29.0118
2573 −31  −83 6620329 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 10.6010
8 −644 −1288 6635776 1 16 8 64 1 64  ε_{1} 1.7627
28 −184 −1288 6635776 1 4 8 16 1 16  ε_{1} 5.5373
56 −184 −644 6635776 1 4 16 32 1 32  ε_{1} 6.8002
92 −56 −1288 6635776 1 4 8 16 1 16  ε_{1} 7.7415
184 −56 −644 6635776 1 4 16 32 1 32  ε_{1} 21.5856
1288 −4 −1288 6635776 4 1 8 32 2 8 \sqrt{i}\sqrt{ε_{1}} 6.4708
1288  −8 −644 6635776 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.4708
2577 −3 −859 6640929 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 53.6282
5 −516 −2580 6656400 1 12 16 96 1 96  ε_{1} 0.9624
12 −215 −2580 6656400 1 14 16 112 1 112  ε_{1} 2.6339
60 −43 −2580 6656400 2 1 16 16 1 8 ε_{1} 4.1269
60 −215 −516 6656400 2 14 12 168 1 84  ε_{1} 4.1269
129 −20 −2580 6656400 1 2 16 16 1 16  ε_{1} 20.8511
172 −15 −2580 6656400 1 2 16 16 1 16  ε_{1} 17.6970
645 −4 −2580 6656400 2 1 16 16 1 8 ε_{1} 9.6883
645 −20 −516 6656400 2 2 12 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 4.8441
860  −3 −2580 6656400 2 1 16 16 1  8  ε_{1} 8.9544

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 55

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
860 −15 −516 6656400 2 2 12 24 1 12  ε_{1} 8.9544
8 −323 −2584 6677056 1 4 16 32 1 32  ε_{1} 1.7627
17 −152 −2584 6677056 1 6 16 48 1 48  ε_{1} 4.1894
136 −19 −2584 6677056 2 1 16 16 1 8 ε_{1} 8.4966
136 −152 −323 6677056 2 6 4 24 1 12  ε_{1} 8.4966
152 −136 −323 6677056 1 4 4  8 1  8  ε_{1} 8.6078
2584  −8 −323 6677056 8 1 4 16 1  2  ε_{1} 12.8269
2584 −19 −136 6677056 8 1 4 16 1  2  ε_{1} 12.8269
517 −55 −235 6682225 1 4 2  4 1  4  ε_{1} 18.5321
2585 −11 −235 6682225 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 22.8573
2585 −47  −55 6682225 2 5 4 20 1 10  ε_{1} 45.7146
13 −199 −2587 6692569 1 9 8 36 1 36  ε_{1} 2.3895
2588 −4 −647 6697744 1 1 23 23 2 23 \sqrt{i}\sqrt{ε_{1}} 19.2977
2589  −3 −863 6702921 3 1 21 63 2 21 \sqrt{−1}\sqrt{ε_{1}} 6.7627
5 −519 −2595 6734025 1 18 12 108 1 108  ε_{1} 0.9624
173 −15 −2595 6734025 1 2 12 12 1 12  ε_{1} 5.1416
865 −3 −2595 6734025 2 1 12 12 1 6 ε_{1} 40.7237
865 −15 −519 6734025 2 2 18 36 1 18  ε_{1} 40.7237
44 −59 −2596 6739216 1 3 20 30 1 30  ε_{1} 5.9864
236 −11 −2596 6739216 1 1 20 10 1 10  ε_{1} 13.9320
649 −4 −2596 6739216 1 1 20 10 1 10 ε_{1} 70.6969
113 −23 −2599 6754801 1 3 30 45 1 45  ε_{1} 14.6946
137 −19 −2603 6775609 1 1 20 10 1 10  ε_{1} 16.3142
12 −651 −868 6780816 1 8 8 32 1 32  ε_{1} 2.6339
21 −372 −868 6780816 1 4 8 16 1 16  ε_{1} 3.1336
28 −372 −651 6780816 1 4 8 16 1 16  ε_{1} 5.5373
93 −84 −868 6780816 1 4 8 16 1 16  ε_{1} 6.7322
124 −84 −651 6780816 1 4 8 16 1 16  ε_{1} 16.0392
217 −84 −372 6780816 1 4 4  8 1  8  ε_{1} 31.7104
2604  −3 −868 6780816 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 8.1519
2604  −4 −651 6780816 4 1 8 16 1  4  ε_{1} 16.3038
2604  −7 −372 6780816 4 1 4  8 1  2  ε_{1} 16.3038
2604 −31  −84 6780816 4 3 4 24 1  6  ε_{1} 16.3038
33 −79 −2607 6796449 1 5 28 70 1 70  ε_{1} 7.6563
237 −11 −2607 6796449 1 1 28 14 1 14  ε_{1} 8.6873
869 −3 −2607 6796449 1 1 28 14 1 14 ε_{1} 21.6145
652  −8 −1304 6801664 1 1 22 22 2 22 \sqrt{−1}\sqrt{ε_{1}} 18.6688
1304  −4 −1304 6801664 3 1 22 66 2 22  \sqrt{i}\sqrt{ε_{1}} 6.4770
373  −7 −2611 6817321 1 1 8  4 1  4  ε_{1} 18.4673
653  −4 −2612 6822544 1 1 14  7 1  7  ε_{1} 14.8304
201 −39 −871 6827769 1 4 22 44 1 44  ε_{1} 27.6905
2613  −3 −871 6827769 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 6.7673
2613 −39 −67 6827769 2 4 1 4 1 2 ε_{1} 13.5347
5 −523 −2615 6838225 1 5 46 115 1 115  ε_{1} 0.9624
8 −327 −2616 6843456 1 12 28 168 1 168  ε_{1} 1.7627
24 −327 −872 6843456 1 12 10 60 1 60  ε_{1} 4.5849
109 −24 −2616 6843456 1 2 28 28 1 28  ε_{1} 11.1291
872 −3 −2616 6843456 2 1 28 28 1 14 ε_{1} 12.4372
872 −24 −327 6843456 2 2 12 24 1 12  ε_{1} 12.4372
2616  −3 −872 6843456 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 16.6965

56 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2616  −8 −327 6843456 2 1 12 12 1  6  ε_{1} 33.3930
524 −20 −655 6864400 1 2 12 12 1 12  ε_{1} 19.9254
2620 −4 −655 6864400 2 1 12 12 1 6 ε_{1} 42.2244
2620 −20 −131 6864400 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 21.1122
61 −43 −2623 6880129 1 1 22 11 1 11  ε_{1} 7.3284
37 −71 −2627 6901129 1 7 12 42 1 42  ε_{1} 4.9836
2629 −11 −239 6911641 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 36.3708
877 −3 −2631 6922161 1 1 48 24 1 24 ε_{1} 26.1741
56 −47 −2632 6927424 1 5 8 20 1 20  ε_{1} 6.8002
329 −8 −2632 6927424 1 1 8 4 1 4 ε_{1} 30.7485
329 −56 −376 6927424 1 4 8 16 1 16  ε_{1} 30.7485
376  −7 −2632 6927424 1 1 8  4 1  4  ε_{1} 30.5420
2632  −7 −376 6927424 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 8.1274
2632 −47  −56 6927424 4 5 4 40 1 10  ε_{1} 16.2548
5 −527 −2635 6943225 1 18 12 108 1 108  ε_{1} 0.9624
17 −155 −2635 6943225 1 4 12 24 1 24  ε_{1} 4.1894
85 −31 −2635 6943225 2 3 12 36 1 18  ε_{1} 4.4187
85 −155 −527 6943225 2 4 18 72 1 36  ε_{1} 4.4187
2636 −4 −659 6948496 3 1 11 33 2 11 \sqrt{i}\sqrt{ε_{1}} 9.3809
13 −203 −2639 6964321 1 4 64 128 1 128  ε_{1} 2.3895
29 −91 −2639 6964321 1 2 64 64 1 64  ε_{1} 3.2945
377  −7 −2639 6964321 2 1 64 64 1 32  ε_{1} 12.2884
377 −91 −203 6964321 2 2 4  8 1  4  ε_{1} 12.2884
8 −660 −1320 6969600 1 8 8 32 1 32  ε_{1} 1.7627
12 −440 −1320 6969600 1 12 8 48 1 48  ε_{1} 2.6339
24 −440 −660 6969600 1 12 8 48 1 48  ε_{1} 4.5849
40 −132 −1320 6969600 2 4 8 32 1 16  ε_{1} 3.6369
40 −264 −660 6969600 2 8 8 64 1 32  ε_{1} 3.6369
44 −120 −1320 6969600 1 4 8 16 1 16  ε_{1} 5.9864
60 −88 −1320 6969600 2 2 8 16 1 8 ε_{1} 4.1269
60 −264 −440 6969600 2 8 12 96 1 48  ε_{1} 4.1269
88 −120 −660 6969600 1 4 8 16 1 16  ε_{1} 11.9527
120 −88 −660 6969600 2 2 8 16 1 8 ε_{1} 6.1779
120 −132 −440 6969600 2 4 12 48 1 24  ε_{1} 6.1779
220 −24 −1320 6969600 2 2 8 16 1 8 ε_{1} 10.3635
220 −120 −264 6969600 2 4 8 32 1 16  ε_{1} 10.3635
264 −20 −1320 6969600 2 2 8 16 1  8  ε_{1} 9.7350
264 −40 −660 6969600 2 2 8 16 1  8  ε_{1} 9.7350
440 −24 −660 6969600 2 2 8 16 1  8  ε_{1} 7.4742
440 −120 −132 6969600 2 4 4 16 1  8  ε_{1} 7.4742
1320  −4 −1320 6969600 4 1 8 16 1  4  ε_{1} 10.7689
1320  −8 −660 6969600 4 1 8 16 1  4  ε_{1} 10.7689
1320 −20 −264 6969600 4 2 8 32 1  8  ε_{1} 10.7689
1320 −40 −132 6969600 4 2 4 16 1  4  ε_{1} 10.7689
2641 −19 −139 6974881 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 90.1230
881  −3 −2643 6985449 1 1 10  5 1  5  ε_{1} 52.1657
661  −4 −2644 6990736 1 1 18  9 1  9  ε_{1} 28.7949
8 −331 −2648 7011904 1 3 22 33 1 33  ε_{1} 1.7627
2648  −8 −331 7011904 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 21.9576
2649  −3 −883 7017201 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 60.5577

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 57

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
241 −11 −2651 7027801 1 1 26 13 1 13  ε_{1} 37.5430
12 −663 −884 7033104 1 16 16 128 1 128  ε_{1} 2.6339
156 −51 −884 7033104 2 2 16 32 1 16  ε_{1} 7.8232
156 −68 −663 7033104 2 4 16 64 1 32  ε_{1} 7.8232
204 −39 −884 7033104 2 4 16 64 1 32  ε_{1} 9.2101
204 −52 −663 7033104 2 2 16 32 1 16  ε_{1} 9.2101
2652  −3 −884 7033104 4 1 16 32 1  8  ε_{1} 10.6557
2652  −4 −663 7033104 4 1 16 32 1  8  ε_{1} 10.6557
2652 −39  −68 7033104 4 4 4 32 1  8  ε_{1} 10.6557
2652 −51  −52 7033104 4 2 2 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.3279
2653  −7 −379 7038409 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 22.8056
5 −532 −2660 7075600 1 4 24 48 1 48  ε_{1} 0.9624
28 −95 −2660 7075600 1 8 24 96 1 96  ε_{1} 5.5373
76 −35 −2660 7075600 1 2 24 24 1 24  ε_{1} 11.6579
133 −20 −2660 7075600 1 2 24 24 1 24  ε_{1} 10.3065
140 −19 −2660 7075600 2 1 24 24 1 12  ε_{1} 4.9558
140 −95 −532 7075600 2 8 4 32 1 16  ε_{1} 4.9558
380  −7 −2660 7075600 2 1 24 24 1 12  ε_{1} 8.7131
380 −35 −532 7075600 2 2 4  8 1  4  ε_{1} 8.7131
665  −4 −2660 7075600 2 1 24 24 1 12  ε_{1} 20.4394
665 −20 −532 7075600 2 2 4  8 1  4  ε_{1} 20.4394
2661  −3 −887 7080921 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 27.5365
21 −127 −2667 7112889 1 5 8 20 1 20  ε_{1} 3.1336
381  −7 −2667 7112889 1 1 8  4 1  4  ε_{1} 15.2316
889  −3 −2667 7112889 1 1 8  4 1  4  ε_{1} 89.4446
92 −116 −667 7118224 1 6 4 12 1 12  ε_{1} 7.7415
2668 −4 −667 7118224 2 1 4 4 1 2 ε_{1} 38.3652
2668 −23 −116 7118224 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 19.1826
668  −8 −1336 7139584 1 1 12 12 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.8171
1336 −4 −1336 7139584 1 1 12 12 2 12 \sqrt{i}\sqrt{ε_{1}} 32.4800
12 −223 −2676 7160976 1 7 12 42 1 42  ε_{1} 2.6339
669  −4 −2676 7160976 1 1 12  6 1  6  ε_{1} 25.2580
892  −3 −2676 7160976 3 1 12 18 1  6  ε_{1} 12.2096
57 −47 −2679 7177041 1 5 52 130 1 130  ε_{1} 11.4208
141 −19 −2679 7177041 1 1 52 26 1 26  ε_{1} 10.4940
893 −3 −2679 7177041 1 1 52 26 1 26 ε_{1} 15.4822
5 −536 −2680 7182400 1 14 12 84 1 84  ε_{1} 0.9624
8 −335 −2680 7182400 1 18 12 108 1 108  ε_{1} 1.7627
40 −67 −2680 7182400 2 1 12 12 1 6 ε_{1} 3.6369
40 −335 −536 7182400 2 18 14 252 1 126  ε_{1} 3.6369
536 −40 −335 7182400 1 2 18 18 1 18  ε_{1} 25.1680
2680  −8 −335 7182400 2 1 18 18 1  9  ε_{1} 32.5300
2680 −40  −67 7182400 2 2 1  2 1  1  ε_{1} 32.5300
2681  −7 −383 7187761 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 46.8226
44 −244 −671 7203856 1 6 30 90 1 90  ε_{1} 5.9864
2684  −4 −671 7203856 2 1 30 30 1 15  ε_{1} 23.3440
2684 −11 −244 7203856 2 1 6  6 1  3  ε_{1} 23.3440
537 −15 −895 7209225 1 2 16 16 1 16  ε_{1} 39.5359
2685 −3 −895 7209225 2 1 16 16 1 8 ε_{1} 22.7390
2685 −15 −179 7209225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 11.3695

58 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
673  −4 −2692 7246864 1 1 12  6 1  6  ε_{1} 64.4243
337  −8 −2696 7268416 1 1 24 12 1 12  ε_{1} 42.8642
93 −87 −899 7273809 1 6 14 42 1 42  ε_{1} 6.7322
2697  −3 −899 7273809 2 1 14 14 1  7  ε_{1} 45.1967
2697 −31  −87 7273809 2 3 6 18 1  9  ε_{1} 45.1967
17 −159 −2703 7306209 1 10 28 140 1 140  ε_{1} 4.1894
53 −51 −2703 7306209 1 2 28 28 1 28  ε_{1} 3.9314
901 −3 −2703 7306209 4 1 28 56 1 14 ε_{1} 8.1892
901 −51 −159 7306209 4 2 10 40 1 10  ε_{1} 8.1892
677 −4 −2708 7333264 1 1 30 15 1 15 ε_{1} 7.9032
8 −339 −2712 7354944 1 6 20 60 1 60  ε_{1} 1.7627
24 −339 −904 7354944 1 6 8 24 1 24  ε_{1} 4.5849
113 −24 −2712 7354944 1 2 20 20 1 20  ε_{1} 14.6946
904  −3 −2712 7354944 8 1 20 80 1 10  ε_{1} 6.8046
904 −24 −339 7354944 8 2 6 48 1  6  ε_{1} 6.8046
2712  −3 −904 7354944 2 1 8  8 1  4  ε_{1} 14.4216
2712  −8 −339 7354944 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 7.2108
5 −543 −2715 7371225 1 12 8 48 1 48  ε_{1} 0.9624
181 −15 −2715 7371225 1 2 8  8 1  8  ε_{1} 14.3479
905  −3 −2715 7371225 4 1 8 16 1  4  ε_{1} 13.1640
905 −15 −543 7371225 4 2 12 48 1 12  ε_{1} 13.1640
28 −388 −679 7376656 1 4 18 36 1 36  ε_{1} 5.5373
2716  −4 −679 7376656 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 24.2952
2716  −7 −388 7376656 2 1 4  4 1  2  ε_{1} 48.5904
209 −143 −247 7382089 1 10 6 30 1 30  ε_{1} 22.8829
2717 −11 −247 7382089 2 1 6  6 1  3  ε_{1} 13.4525
2717 −19 −143 7382089 2 1 10 10 1  5  ε_{1} 13.4525
2721  −3 −907 7403841 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 64.5176
389  −7 −2723 7414729 1 1 12  6 1  6  ε_{1} 15.6986
12 −227 −2724 7420176 1 5 20 50 1 50  ε_{1} 2.6339
681  −4 −2724 7420176 1 1 20 10 1 10  ε_{1} 61.3969
908  −3 −2724 7420176 1 1 20 10 1 10  ε_{1} 12.2274
88 −31 −2728 7441984 1 3 12 18 1 18  ε_{1} 11.9527
248 −11 −2728 7441984 1 1 12  6 1  6  ε_{1} 9.6724
341  −8 −2728 7441984 1 1 12  6 1  6  ε_{1} 11.2480
341 −88 −248 7441984 1 2 8  8 1  8  ε_{1} 11.2480
2728 −11 −248 7441984 2 1 8  8 1  4  ε_{1} 29.3785
2728 −31  −88 7441984 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 14.6892
2732  −4 −683 7463824 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 19.6449
2733  −3 −911 7469289 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 17.0743
5 −547 −2735 7480225 1 3 62 93 1 93  ε_{1} 0.9624
161 −119 −391 7491169 1 10 14 70 1 70  ε_{1} 20.1338
2737 −7 −391 7491169 2 1 14 14 1 7 ε_{1} 67.3814
2737 −23 −119 7491169 2 3 10 30 1 15  ε_{1} 67.3814
33 −83 −2739 7502121 1 3 16 24 1 24  ε_{1} 7.6563
249 −11 −2739 7502121 1 1 16  8 1  8  ε_{1} 33.3101
913  −3 −2739 7502121 1 1 16  8 1  8  ε_{1} 69.1395
5 −548 −2740 7507600 1 8 12 48 1 48  ε_{1} 0.9624
137 −20 −2740 7507600 1 2 12 12 1 12  ε_{1} 16.3142
685  −4 −2740 7507600 2 1 12 12 1  6  ε_{1} 13.2640

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 59

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
685 −20 −548 7507600 2 2 8 16 1  8  ε_{1} 13.2640
13 −211 −2743 7524049 1 3 20 30 1 30  ε_{1} 2.3895
41 −67 −2747 7546009 1 1 18 9 1 9 ε_{1} 8.3183
12 −687 −916 7551504 1 12 10 60 1 60  ε_{1} 2.6339
2748  −3 −916 7551504 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 12.7089
2748 −4 −687 7551504 2 1 12 12 1 6 ε_{1} 25.4178
21 −131 −2751 7568001 1 5 40 100 1 100  ε_{1} 3.1336
393  −7 −2751 7568001 1 1 40 20 1 20  ε_{1} 36.6935
917  −3 −2751 7568001 1 1 40 20 1 20  ε_{1} 14.1482
5 −551 −2755 7590025 1 26 8 104 1 104  ε_{1} 0.9624
29 −95 −2755 7590025 1 8 8 32 1 32  ε_{1} 3.2945
145 −19 −2755 7590025 4 1 8 16 1 4 ε_{1} 6.3596
145 −95 −551 7590025 4 8 26 416 1 104  ε_{1} 6.3596
13 −212 −2756 7595536 1 6 40 120 1 120  ε_{1} 2.3895
53 −52 −2756 7595536 1 2 40 40 1 40  ε_{1} 3.9314
689 −4 −2756 7595536 4 1 40 80 1 20 ε_{1} 10.6942
689 −52 −212 7595536 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.3471
2757  −3 −919 7601049 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 9.5957
89 −31 −2759 7612081 1 3 54 81 1 81  ε_{1} 13.8155
5 −552 −2760 7617600 1 8 16 64 1 64  ε_{1} 0.9624
24 −115 −2760 7617600 1 2 16 16 1 16  ε_{1} 4.5849
69 −40 −2760 7617600 1 2 16 16 1 16  ε_{1} 6.4345
69 −120 −920 7617600 1 4 20 40 1 40  ε_{1} 6.4345
120 −23 −2760 7617600 2 3 16 48 1 24  ε_{1} 6.1779
120 −115 −552 7617600 2 2 8 16 1 8 ε_{1} 6.1779
184 −15 −2760 7617600 1 2 16 16 1 16  ε_{1} 21.5856
345 −8 −2760 7617600 2 1 16 16 1 8 ε_{1} 19.0241
345 −24 −920 7617600 2 2 20 40 1 20  ε_{1} 19.0241
345 −40 −552 7617600 2 2 8 16 1  8  ε_{1} 19.0241
345 −120 −184 7617600 2 4 4 16 1  8  ε_{1} 19.0241
552 −15 −920 7617600 2 2 20 40 1 20  ε_{1} 9.0864
552 −115 −120 7617600 2 2 4  8 1  4  ε_{1} 9.0864
920  −3 −2760 7617600 2 1 16 16 1  8  ε_{1} 10.4080
920 −15 −552 7617600 2 2 8 16 1  8  ε_{1} 10.4080
2760  −3 −920 7617600 4 1 20 40 1 10  ε_{1} 15.9737
2760 −15 −184 7617600 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.9868
2760 −23 −120 7617600 4 3 4 24 1  6  ε_{1} 15.9737
2760 −24 −115 7617600 4 2 2  8 1  2  ε_{1} 15.9737
2761 −11 −251 7623121 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 79.2029
2764  −4 −691 7639696 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 45.5781
553 −35 −395 7645225 1 2 8  8 1  8  ε_{1} 55.7072
2765  −7 −395 7645225 2 1 8  8 1  4  ε_{1} 14.2809
2765 −35  −79 7645225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 7.1405
8 −692 −1384 7661824 1 14 10 70 1 70  ε_{1} 1.7627
1384  −4 −1384 7661824 6 1 10 30 1  5  ε_{1} 10.4516
1384  −8 −692 7661824 6 1 14 42 1  7  ε_{1} 10.4516
213 −39 −923 7667361 1 4 10 20 1 20  ε_{1} 8.5805
2769  −3 −923 7667361 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 34.1775
2769 −39 −71 7667361 2 4 7 28 1 14 ε_{1} 68.3549
17 −163 −2771 7678441 1 1 26 13 1 13  ε_{1} 4.1894

60 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
2773 −47  −59 7689529 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 30.0671
8 −347 −2776 7706176 1 5 10 25 1 25  ε_{1} 1.7627
2776  −8 −347 7706176 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 52.7054
397  −7 −2779 7722841 1 1 14  7 1  7  ε_{1} 16.2905
556 −20 −695 7728400 1 2 24 24 1 24  ε_{1} 37.7195
2780 −4 −695 7728400 2 1 24 24 1 12 ε_{1} 22.2332
2780 −20 −139 7728400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 11.1166
929 −3 −2787 7767369 1 1 6 3 1 3 ε_{1} 51.6295
17 −164 −2788 7772944 1 8 8 32 1 32  ε_{1} 4.1894
41 −68 −2788 7772944 1 4 8 16 1 16  ε_{1} 8.3183
697 −4 −2788 7772944 6 1 8 24 1 4 ε_{1} 11.1519
697 −68 −164 7772944 6 4 8 96 1 16  ε_{1} 11.1519
349 −8 −2792 7795264 1 1 26 13 1 13 ε_{1} 19.6424
5 −559 −2795 7812025 1 16 12 96 1 96  ε_{1} 0.9624
13 −215 −2795 7812025 1 14 12 84 1 84  ε_{1} 2.3895
65 −43 −2795 7812025 2 1 12 12 1 6 ε_{1} 5.5529
65 −215 −559 7812025 2 14 16 224 1 112  ε_{1} 5.5529
12 −699 −932 7817616 1 10 12 60 1 60  ε_{1} 2.6339
2796  −3 −932 7817616 2 1 12 12 1  6  ε_{1} 30.6578
2796  −4 −699 7817616 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 15.3289
701  −4 −2804 7862416 1 1 34 17 1 17  ε_{1} 20.1350
33 −255 −935 7868025 1 12 28 168 1 168  ε_{1} 7.6563
165 −51 −935 7868025 2 2 28 56 1 28  ε_{1} 5.1180
165 −187 −255 7868025 2 2 12 24 1 12  ε_{1} 5.1180
561 −15 −935 7868025 2 2 28 56 1 28  ε_{1} 27.7201
561 −55 −255 7868025 2 4 12 48 1 24  ε_{1} 27.7201
2805  −3 −935 7868025 4 1 28 56 1 14  ε_{1} 7.9399
2805 −11 −255 7868025 4 1 12 24 1  6  ε_{1} 7.9399
2805 −15 −187 7868025 4 2 2  8 1  2  ε_{1} 7.9399
2805 −51  −55 7868025 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 3.9699
401  −7 −2807 7879249 5 1 52 130 1 26  ε_{1} 7.3790
937  −3 −2811 7901721 1 1 16  8 1  8  ε_{1} 69.0381
76 −148 −703 7907344 1 2 14 14 1 14  ε_{1} 11.6579
2812  −4 −703 7907344 2 1 14 14 1  7  ε_{1} 29.3127
2812 −19 −148 7907344 2 1 2  2 1  1  ε_{1} 29.3127
5 −563 −2815 7924225 1 9 22 99 1 99  ε_{1} 0.9624
5 −564 −2820 7952400 1 8 24 96 1 96  ε_{1} 0.9624
12 −235 −2820 7952400 1 2 24 24 1 24  ε_{1} 2.6339
60 −47 −2820 7952400 2 5 24 120 1 60  ε_{1} 4.1269
60 −235 −564 7952400 2 2 8 16 1 8 ε_{1} 4.1269
141 −20 −2820 7952400 1 2 24 24 1 24  ε_{1} 10.4940
188 −15 −2820 7952400 1 2 24 24 1 24  ε_{1} 9.1285
705 −4 −2820 7952400 2 1 24 24 1 12 ε_{1} 26.1393
705 −20 −564 7952400 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 13.0696
940  −3 −2820 7952400 6 1 24 72 1 12  ε_{1} 9.0433
940 −15 −564 7952400 6 2 8 48 1  8  ε_{1} 9.0433
217 −91 −403 7958041 1 2 2  2 1  2  ε_{1} 31.7104
2821  −7 −403 7958041 2 1 2  2 1  1  ε_{1} 36.4722
2821 −31  −91 7958041 2 3 2  6 1  3  ε_{1} 36.4722
941  −3 −2823 7969329 1 1 26 13 1 13  ε_{1} 14.0688

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 61

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
353  −8 −2824 7974976 1 1 24 12 1 12  ε_{1} 23.7346
257 −11 −2827 7991929 3 1 8 12 1  4  ε_{1} 6.9334
28 −404 −707 7997584 1 14 6 42 1 42  ε_{1} 5.5373
2828  −4 −707 7997584 2 1 6  6 1  3  ε_{1} 17.0551
2828  −7 −404 7997584 2 1 14 14 1  7  ε_{1} 17.0551
69 −123 −943 8003241 1 2 16 16 1 16  ε_{1} 6.4345
2829 −3 −943 8003241 2 1 16 16 1 8 ε_{1} 23.4873
2829 −23 −123 8003241 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 11.7436
149 −19 −2831 8014561 1 1 68 34 1 34  ε_{1} 8.2223
8 −708 −1416 8020224 1 4 16 32 1 32  ε_{1} 1.7627
12 −472 −1416 8020224 1 6 16 48 1 48  ε_{1} 2.6339
24 −472 −708 8020224 1 6 4 12 1 12  ε_{1} 4.5849
236 −24 −1416 8020224 1 2 16 16 1 16  ε_{1} 13.9320
472 −24 −708 8020224 1 2 4  4 1  4  ε_{1} 26.6550
1416  −4 −1416 8020224 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 13.1541
1416  −8 −708 8020224 2 1 4  8 2  4 \sqrt{−1}\sqrt{ε_{1}} 13.1541
709  −4 −2836 8042896 1 1 10  5 1  5  ε_{1} 34.8251
17 −167 −2839 8059921 1 11 26 143 1 143  ε_{1} 4.1894
5 −568 −2840 8065600 1 4 32 64 1 64  ε_{1} 0.9624
8 −355 −2840 8065600 1 4 32 64 1 64  ε_{1} 1.7627
40 −71 −2840 8065600 2 7 32 224 1 112  ε_{1} 3.6369
40 −355 −568 8065600 2 4 4 16 1  8  ε_{1} 3.6369
568 −40 −355 8065600 3 2 4 12 1  4  ε_{1} 11.3120
2840  −8 −355 8065600 2 1 4  4 1  2  ε_{1} 15.6940
2840 −40  −71 8065600 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.8470
2841 −3 −947 8071281 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 61.4522
13 −219 −2847 8105409 1 4 32 64 1 64  ε_{1} 2.3895
73 −39 −2847 8105409 1 4 32 64 1 64  ε_{1} 15.3334
949  −3 −2847 8105409 2 1 32 32 1 16  ε_{1} 20.7893
949 −39 −219 8105409 2 4 4 16 1  8  ε_{1} 20.7893
77 −259 −407 8116801 1 4 16 32 1 32  ε_{1} 4.3693
2849  −7 −407 8116801 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 11.5540
2849 −11 −259 8116801 4 1 4 8 1 2 ε_{1} 23.1079
92 −31 −2852 8133904 1 3 24 36 1 36  ε_{1} 7.7415
124 −23 −2852 8133904 1 3 24 36 1 36  ε_{1} 16.0392
713 −4 −2852 8133904 1 1 24 12 1 12 ε_{1} 32.3476
5 −571 −2855 8151025 1 5 60 150 1 150  ε_{1} 0.9624
17 −168 −2856 8156736 1 4 24 48 1 48  ε_{1} 4.1894
21 −136 −2856 8156736 1 4 24 48 1 48  ε_{1} 3.1336
21 −408 −952 8156736 1 4 8 16 1 16  ε_{1} 3.1336
24 −119 −2856 8156736 1 10 24 120 1 120  ε_{1} 4.5849
56 −51 −2856 8156736 1 2 24 24 1 24  ε_{1} 6.8002
168 −51 −952 8156736 2 2 8 16 1 8 ε_{1} 6.5132
168 −119 −408 8156736 2 10 4 40 1 20  ε_{1} 6.5132
357  −8 −2856 8156736 2 1 24 24 1 12  ε_{1} 5.8833
357 −24 −952 8156736 2 2 8 16 1  8  ε_{1} 5.8833
357 −56 −408 8156736 2 4 4 16 1  8  ε_{1} 5.8833
357 −136 −168 8156736 2 4 4 16 1  8  ε_{1} 5.8833
408  −7 −2856 8156736 2 1 24 24 1 12  ε_{1} 10.6165
408 −119 −168 8156736 2 10 4 40 1 20  ε_{1} 10.6165

62 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
952  −3 −2856 8156736 2 1 24 24 1 12  ε_{1} 20.1146
952 −51 −168 8156736 2 2 4  8 1  4  ε_{1} 20.1146
2856  −3 −952 8156736 4 1 8 16 1  4  ε_{1} 18.0311
2856  −7 −408 8156736 4 1 4  8 1  2  ε_{1} 18.0311
2856 −24 −119 8156736 4 2 10 40 1 10  ε_{1} 18.0311
2856 −51  −56 8156736 4 2 4 16 1  4  ε_{1} 18.0311
953  −3 −2859 8173881 1 1 18  9 1  9  ε_{1} 44.8537
44 −260 −715 8179600 1 8 4 16 1 16  ε_{1} 5.9864
220 −52 −715 8179600 2 2 4 8 1 4 ε_{1} 10.3635
220 −143 −260 8179600 2 10 8 80 1 40  ε_{1} 10.3635
572 −20 −715 8179600 2 2 4 8 1 4 ε_{1} 6.3526
572 −55 −260 8179600 2 4 8 32 1 16  ε_{1} 6.3526
2860  −4 −715 8179600 4 1 4  8 1  2  ε_{1} 23.8539
2860 −11 −260 8179600 4 1 8 16 1  4  ε_{1} 23.8539
2860 −20 −143 8179600 4 2 10 40 1 10  ε_{1} 23.8539
2860 −52  −55 8179600 4 2 4 16 1  4  ε_{1} 23.8539
409  −7 −2863 8196769 1 1 22 11 1 11  ε_{1} 52.2684
716  −8 −1432 8202496 1 1 6  6 2  6 \sqrt{−1}\sqrt{ε_{1}} 15.9414
1432  −4 −1432 8202496 1 1 6  6 2  6  \sqrt{i}\sqrt{ε_{1}} 26.5902
573 −15 −955 8208225 1 2 4  4 1  4  ε_{1} 13.2824
2865  −3 −955 8208225 2 1 4  4 1  2  ε_{1} 63.7471
2865 −15 −191 8208225 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 31.8736
61 −47 −2867 8219689 1 5 12 30 1 30  ε_{1} 7.3284
12 −239 −2868 8225424 1 15 16 120 1 120  ε_{1} 2.6339
717  −4 −2868 8225424 1 1 16  8 1  8  ε_{1} 10.9696
956  −3 −2868 8225424 1 1 16  8 1  8  ε_{1} 32.6648
2869 −19 −151 8231161 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 33.5797
8 −359 −2872 8248384 1 19 12 114 1 114  ε_{1} 1.7627
2872  −8 −359 8248384 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 44.3295
2876 −4 −719 8271376 1 1 31 31 2 31 \sqrt{i}\sqrt{ε_{1}} 27.4165
21 −411 −959 8277129 1 6 36 108 1 108  ε_{1} 3.1336
2877  −3 −959 8277129 2 1 36 36 1 18  ε_{1} 16.4327
2877  −7 −411 8277129 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 8.2164
2881 −43  −67 8300161 1 1 1  1 2  1 \sqrt{−1}\sqrt{ε_{1}} 91.2144
28 −103 −2884 8317456 1 5 16 40 1 40  ε_{1} 5.5373
412  −7 −2884 8317456 1 1 16  8 1  8  ε_{1} 26.0564
721  −4 −2884 8317456 1 1 16  8 1  8  ε_{1} 76.3136
12 −723 −964 8363664 1 4 12 24 1 24  ε_{1} 2.6339
2892  −3 −964 8363664 4 1 12 24 1  6  ε_{1} 12.3642
2892  −4 −723 8363664 4 1 4  8 1  2  ε_{1} 12.3642
2893 −11 −263 8369449 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 26.3839
5 −579 −2895 8381025 1 8 36 144 1 144  ε_{1} 0.9624
193 −15 −2895 8381025 1 2 36 36 1 36  ε_{1} 30.1526
965  −3 −2895 8381025 2 1 36 36 1 18  ε_{1} 6.8701
965 −15 −579 8381025 2 2 8 16 1  8  ε_{1} 6.8701
8 −724 −1448 8386816 1 10 18 90 1 90  ε_{1} 1.7627
1448  −4 −1448 8386816 2 1 18 18 1  9  ε_{1} 7.2766
1448  −8 −724 8386816 2 1 10 10 1  5  ε_{1} 7.2766
13 −223 −2899 8404201 1 7 10 35 1 35  ε_{1} 2.3895
2901  −3 −967 8415801 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 16.9088

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 63

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
581 −35 −415 8439025 1 2 10 10 1 10  ε_{1} 17.6272
2905  −7 −415 8439025 2 1 10 10 1  5  ε_{1} 80.8035
2905 −35  −83 8439025 2 2 3  6 1  3  ε_{1} 80.8035
2908  −4 −727 8456464 5 1 13 65 2 13  \sqrt{i}\sqrt{ε_{1}} 7.2834
41 −71 −2911 8473921 1 7 42 147 1 147  ε_{1} 8.3183
2913  −3 −971 8485569 7 1 15 105 2 15 \sqrt{−1}\sqrt{ε_{1}} 8.2651
5 −583 −2915 8497225 1 8 24 96 1 96  ε_{1} 0.9624
53 −55 −2915 8497225 1 4 24 48 1 48  ε_{1} 3.9314
265 −11 −2915 8497225 2 1 24 24 1 12  ε_{1} 18.8092
265 −55 −583 8497225 2 4 8 32 1 16  ε_{1} 18.8092
21 −139 −2919 8520561 1 3 40 60 1 60  ε_{1} 3.1336
417  −7 −2919 8520561 1 1 40 20 1 20  ε_{1} 37.9102
973  −3 −2919 8520561 1 1 40 20 1 20  ε_{1} 28.8137
5 −584 −2920 8526400 1 16 12 96 1 96  ε_{1} 0.9624
73 −40 −2920 8526400 1 2 12 12 1 12  ε_{1} 15.3334
365 −8 −2920 8526400 2 1 12 12 1 6 ε_{1} 5.8944
365 −40 −584 8526400 2 2 16 32 1 16  ε_{1} 5.8944
2921 −23 −127 8532241 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 53.5791
37 −79 −2923 8543929 1 5 6 15 1 15  ε_{1} 4.9836
172 −68 −731 8549776 1 4 12 24 1 24  ε_{1} 17.6970
2924  −4 −731 8549776 4 1 12 48 2 12  \sqrt{i}\sqrt{ε_{1}} 7.2862
2924 −43  −68 8549776 4 1 4  8 1  2  ε_{1} 14.5724
12 −488 −1464 8573184 1 10 12 60 1 60  ε_{1} 2.6339
24 −244 −1464 8573184 1 6 12 36 1 36  ε_{1} 4.5849
732 −8 −1464 8573184 2 1 12 12 1 6 ε_{1} 13.7628
732 −24 −488 8573184 2 2 10 20 1 10  ε_{1} 13.7628
1464  −4 −1464 8573184 2 1 12 12 1  6  ε_{1} 28.8241
1464 −24 −244 8573184 2 2 6 12 1  6  ε_{1} 28.8241
977  −3 −2931 8590761 1 1 14  7 1  7  ε_{1} 46.8295
733  −4 −2932 8596624 3 1 14 21 1  7  ε_{1} 6.5944
2933  −7 −419 8602489 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 11.9268
5 −587 −2935 8614225 1 7 22 77 1 77  ε_{1} 0.9624
8 −367 −2936 8620096 1 9 40 180 1 180  ε_{1} 1.7627
2936  −8 −367 8620096 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 16.8499
33 −267 −979 8625969 1 2 8  8 1  8  ε_{1} 7.6563
2937  −3 −979 8625969 2 1 8  8 1  4  ε_{1} 58.0837
2937 −11 −267 8625969 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 29.0418
589 −95 −155 8673025 1 8 4 16 1 16  ε_{1} 30.5757
2945 −19 −155 8673025 4 1 4 8 1 2 ε_{1} 17.4249
2945 −31  −95 8673025 4 3 8 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 8.7124
421 −7 −2947 8684809 1 1 8 4 1 4 ε_{1} 26.0114
44 −67 −2948 8690704 1 1 20 10 1 10  ε_{1} 5.9864
268 −11 −2948 8690704 1 1 20 10 1 10  ε_{1} 22.9790
737 −4 −2948 8690704 1 1 20 10 1 10 ε_{1} 40.0839
2949  −3 −983 8696601 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 29.0223
13 −227 −2951 8708401 1 5 54 135 1 135  ε_{1} 2.3895
5 −591 −2955 8732025 1 22 12 132 1 132  ε_{1} 0.9624
197 −15 −2955 8732025 1 2 12 12 1 12  ε_{1} 6.6670
985 −3 −2955 8732025 6 1 12 36 1 6 ε_{1} 13.4088
985 −15 −591 8732025 6 2 22 132 1 22  ε_{1} 13.4088

64 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2956  −4 −739 8737936 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 53.6326
269 −11 −2959 8755681 1 1 40 20 1 20  ε_{1} 10.1998
8 −740 −1480 8761600 1 16 12 96 1 96  ε_{1} 1.7627
40 −148 −1480 8761600 2 2 12 24 1 12  ε_{1} 3.6369
40 −296 −740 8761600 2 10 16 160 1 80  ε_{1} 3.6369
296 −20 −1480 8761600 2 2 12 24 1 12  ε_{1} 8.9090
296 −40 −740 8761600 2 2 16 32 1 16  ε_{1} 8.9090
1480  −4 −1480 8761600 4 1 12 24 1  6  ε_{1} 12.9662
1480  −8 −740 8761600 4 1 16 32 1  8  ε_{1} 12.9662
1480 −20 −296 8761600 4 2 10 40 1 10  ε_{1} 12.9662
1480 −40 −148 8761600 4 2 2 8 1 2 ε_{1} 12.9662
12 −247 −2964 8785296 1 6 24 72 1 72  ε_{1} 2.6339
13 −228 −2964 8785296 1 4 24 48 1 48  ε_{1} 2.3895
57 −52 −2964 8785296 1 2 24 24 1 24  ε_{1} 11.4208
76 −39 −2964 8785296 1 4 24 48 1 48  ε_{1} 11.6579
156 −19 −2964 8785296 2 1 24 24 1 12  ε_{1} 7.8232
156 −228 −247 8785296 2 4 6 24 1 12  ε_{1} 7.8232
741  −4 −2964 8785296 2 1 24 24 1 12  ε_{1} 11.0025
741 −52 −228 8785296 2 2 4  8 1  4  ε_{1} 11.0025
988  −3 −2964 8785296 2 1 24 24 1 12  ε_{1} 24.0940
988 −39 −228 8785296 2 4 4 16 1  8  ε_{1} 24.0940
69 −43 −2967 8803089 1 1 44 22 1 22  ε_{1} 6.4345
129 −23 −2967 8803089 1 3 44 66 1 66  ε_{1} 20.8511
989 −3 −2967 8803089 1 1 44 22 1 22 ε_{1} 23.0897
8 −371 −2968 8809024 1 8 8 32 1 32  ε_{1} 1.7627
53 −56 −2968 8809024 1 4 8 16 1 16  ε_{1} 3.9314
56 −371 −424 8809024 1 8 6 24 1 24  ε_{1} 6.8002
424 −7 −2968 8809024 2 1 8 8 1 4 ε_{1} 17.9769
424 −56 −371 8809024 2 4 8 32 1 16  ε_{1} 17.9769
2968  −7 −424 8809024 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 20.0812
2968  −8 −371 8809024 2 1 8  8 1  4  ε_{1} 40.1623
2972  −4 −743 8832784 1 1 21 21 2 21  \sqrt{i}\sqrt{ε_{1}} 14.1718
2973  −3 −991 8838729 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 18.5389
5 −596 −2980 8880400 1 14 16 112 1 112  ε_{1} 0.9624
149 −20 −2980 8880400 1 2 16 16 1 16  ε_{1} 8.2223
745 −4 −2980 8880400 2 1 16 16 1 8 ε_{1} 34.1114
745 −20 −596 8880400 2 2 14 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 17.0557
2981 −11 −271 8886361 3 1 11 33 2 11 \sqrt{−1}\sqrt{ε_{1}} 5.6095
157 −19 −2983 8898289 1 1 20 10 1 10  ε_{1} 10.7226
373  −8 −2984 8904256 1 1 26 13 1 13  ε_{1} 18.4673
597 −15 −995 8910225 1 2 8  8 1  8  ε_{1} 18.3698
2985  −3 −995 8910225 2 1 8  8 1  4  ε_{1} 50.3157
2985 −15 −199 8910225 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 25.1578
29 −103 −2987 8922169 1 5 20 50 1 50  ε_{1} 3.2945
997 −3 −2991 8946081 1 1 48 24 1 24 ε_{1} 24.0849
44 −136 −1496 8952064 1 4 28 56 1 56  ε_{1} 5.9864
88 −68 −1496 8952064 1 4 28 56 1 56  ε_{1} 11.9527
748  −8 −1496 8952064 2 1 28 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 8.1209
748 −88 −136 8952064 2 2 4  8 1  4  ε_{1} 16.2418
1496  −4 −1496 8952064 2 1 28 56 2 28  \sqrt{i}\sqrt{ε_{1}} 8.8143

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 65

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1496 −68  −88 8952064 2 4 2  8 1  4  ε_{1} 17.6287
5 −599 −2995 8970025 1 25 8 100 1 100  ε_{1} 0.9624
28 −107 −2996 8976016 1 3 32 48 1 48  ε_{1} 5.5373
428  −7 −2996 8976016 1 1 32 16 1 16  ε_{1} 15.1243
749  −4 −2996 8976016 1 1 32 16 1 16  ε_{1} 18.9369
13 −231 −3003 9018009 1 12 8 48 1 48  ε_{1} 2.3895
21 −143 −3003 9018009 1 10 8 40 1 40  ε_{1} 3.1336
33 −91 −3003 9018009 1 2 8 8 1 8 ε_{1} 7.6563
77 −39 −3003 9018009 1 4 8 16 1 16  ε_{1} 4.3693
273 −11 −3003 9018009 2 1 8 8 1 4 ε_{1} 14.5641
273 −143 −231 9018009 2 10 12 120 1 60  ε_{1} 14.5641
429 −7 −3003 9018009 2 1 8 8 1 4 ε_{1} 9.9534
429 −91 −231 9018009 2 2 12 24 1 12  ε_{1} 9.9534
1001 −3 −3003 9018009 2 1 8 8 1 4 ε_{1} 29.1356
1001 −39 −231 9018009 2 4 12 48 1 24  ε_{1} 29.1356
3004 −4 −751 9024016 1 1 15 15 2 15 \sqrt{i}\sqrt{ε_{1}} 57.9421
97 −31 −3007 9042049 1 3 20 30 1 30  ε_{1} 18.6488
177 −51 −1003 9054081 1 2 4  4 1  4  ε_{1} 23.4697
3009  −3 −1003 9054081 2 1 4  4 1  2  ε_{1} 57.0701
3009 −51  −59 9054081 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 28.5351
12 −251 −3012 9072144 1 7 12 42 1 42  ε_{1} 2.6339
753  −4 −3012 9072144 1 1 12  6 1  6  ε_{1} 54.2964
1004  −3 −3012 9072144 1 1 12  6 1  6  ε_{1} 31.6204
3013 −23 −131 9078169 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 21.6352
13 −232 −3016 9096256 1 2 20 20 1 20  ε_{1} 2.3895
29 −104 −3016 9096256 1 6 20 60 1 60  ε_{1} 3.2945
377  −8 −3016 9096256 2 1 20 20 1 10  ε_{1} 12.2884
377 −104 −232 9096256 2 6 2 12 1  6  ε_{1} 12.2884
3017  −7 −431 9102289 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 42.4143
604 −20 −755 9120400 1 2 12 12 1 12  ε_{1} 43.9269
3020 −4 −755 9120400 2 1 12 12 1 6 ε_{1} 15.5814
3020 −20 −151 9120400 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.7907
57 −159 −1007 9126441 1 10 30 150 1 150  ε_{1} 11.4208
3021  −3 −1007 9126441 6 1 30 90 1 15  ε_{1} 8.0140
3021 −19 −159 9126441 6 1 10 30 1  5  ε_{1} 8.0140
1009  −3 −3027 9162729 7 1 12 42 1  6  ε_{1} 13.9694
757  −4 −3028 9168784 1 1 10  5 1  5  ε_{1} 29.6460
433  −7 −3031 9186961 1 1 34 17 1 17  ε_{1} 46.7895
8 −379 −3032 9193024 1 3 22 33 1 33  ε_{1} 1.7627
3032 −8 −379 9193024 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 20.5344
5 −607 −3035 9211225 1 13 18 117 1 117  ε_{1} 0.9624
12 −759 −1012 9217296 1 24 4 48 1 48  ε_{1} 2.6339
33 −276 −1012 9217296 1 8 4 16 1 16  ε_{1} 7.6563
44 −276 −759 9217296 1 8 24 96 1 96  ε_{1} 5.9864
69 −132 −1012 9217296 1 4 4 8 1 8 ε_{1} 6.4345
92 −132 −759 9217296 1 4 24 48 1 48  ε_{1} 7.7415
253 −132 −276 9217296 1 4 8 16 1 16  ε_{1} 15.0577
3036  −3 −1012 9217296 4 1 4  8 1  2  ε_{1} 14.0098
3036  −4 −759 9217296 4 1 24 48 1 12  ε_{1} 14.0098
3036 −11 −276 9217296 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.0049

66 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3036 −23 −132 9217296 4 3 4 24 1  6  ε_{1} 14.0098
1013  −3 −3039 9235521 1 1 42 21 1 21  ε_{1} 13.6553
17 −179 −3043 9259849 1 5 12 30 1 30  ε_{1} 4.1894
761 −4 −3044 9265936 3 1 40 60 1 20 ε_{1} 14.7555
21 −435 −1015 9272025 1 4 16 32 1 32  ε_{1} 3.1336
105 −87 −1015 9272025 2 6 16 96 1 48  ε_{1} 8.8131
105 −203 −435 9272025 2 4 4 16 1 8 ε_{1} 8.8131
609 −15 −1015 9272025 2 2 16 32 1 16  ε_{1} 28.0146
609 −35 −435 9272025 2 2 4  8 1  4  ε_{1} 28.0146
3045  −3 −1015 9272025 4 1 16 32 1  8  ε_{1} 12.8171
3045  −7 −435 9272025 4 1 4  8 1  2  ε_{1} 12.8171
3045 −15 −203 9272025 4 2 4 16 1  4  ε_{1} 12.8171
3045 −35  −87 9272025 4 2 6 24 1  6  ε_{1} 12.8171
277 −11 −3047 9284209 1 1 38 19 1 19  ε_{1} 15.7365
24 −127 −3048 9290304 1 5 12 30 1 30  ε_{1} 4.5849
381 −8 −3048 9290304 1 1 12 6 1 6 ε_{1} 15.2316
381 −24 −1016 9290304 1 2 16 16 1 16  ε_{1} 15.2316
1016  −3 −3048 9290304 3 1 12 18 1  6  ε_{1} 12.4688
3048  −3 −1016 9290304 2 1 16 16 1  8  ε_{1} 18.8984
3048 −24 −127 9290304 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 9.4492
28 −436 −763 9314704 1 6 4 12 1 12  ε_{1} 5.5373
3052  −4 −763 9314704 2 1 4  4 1  2  ε_{1} 42.1751
3052  −7 −436 9314704 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 21.0875
3053 −43  −71 9320809 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 8.1551
5 −611 −3055 9333025 1 10 36 180 1 180  ε_{1} 0.9624
13 −235 −3055 9333025 1 2 36 36 1 36  ε_{1} 2.3895
65 −47 −3055 9333025 2 5 36 180 1 90  ε_{1} 5.5529
65 −235 −611 9333025 2 2 10 20 1 10  ε_{1} 5.5529
764  −8 −1528 9339136 1 1 8  8 2  8 \sqrt{−1}\sqrt{ε_{1}} 16.7052
1528  −4 −1528 9339136 1 1 8  8 2  8  \sqrt{i}\sqrt{ε_{1}} 26.5223
3057  −3 −1019 9345249 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 36.3160
133 −23 −3059 9357481 1 3 24 36 1 36  ε_{1} 10.3065
161 −19 −3059 9357481 1 1 24 12 1 12  ε_{1} 20.1338
437  −7 −3059 9357481 1 1 24 12 1 12  ε_{1} 6.0845
1021  −3 −3063 9381969 1 1 16  8 1  8  ε_{1} 36.5338
8 −383 −3064 9388096 1 17 24 204 1 204  ε_{1} 1.7627
3064  −8 −383 9388096 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 47.1228
236 −52 −767 9412624 1 2 22 22 1 22  ε_{1} 13.9320
3068  −4 −767 9412624 2 1 22 22 1 11  ε_{1} 22.0834
3068 −52  −59 9412624 2 2 3  6 1  3  ε_{1} 22.0834
37 −83 −3071 9431041 1 3 76 114 1 114  ε_{1} 4.9836
3073  −7 −439 9443329 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 70.7920
769 −4 −3076 9461776 1 1 20 10 1 10 ε_{1} 76.0544
5 −616 −3080 9486400 1 8 32 128 1 128  ε_{1} 0.9624
56 −55 −3080 9486400 1 4 32 64 1 64  ε_{1} 6.8002
77 −40 −3080 9486400 1 2 32 32 1 32  ε_{1} 4.3693
77 −280 −440 9486400 1 4 12 24 1 24  ε_{1} 4.3693
88 −35 −3080 9486400 1 2 32 32 1 32  ε_{1} 11.9527
280 −11 −3080 9486400 2 1 32 32 1 16  ε_{1} 12.4372
280 −55 −616 9486400 2 4 8 32 1 16  ε_{1} 12.4372

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 67

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
385  −8 −3080 9486400 2 1 32 32 1 16  ε_{1} 24.3270
385 −40 −616 9486400 2 2 8 16 1  8  ε_{1} 24.3270
385 −56 −440 9486400 2 4 12 48 1 24  ε_{1} 24.3270
385 −88 −280 9486400 2 2 4  8 1  4  ε_{1} 24.3270
440  −7 −3080 9486400 2 1 32 32 1 16  ε_{1} 7.4742
440 −35 −616 9486400 2 2 8 16 1  8  ε_{1} 7.4742
616 −35 −440 9486400 2 2 12 24 1 12  ε_{1} 21.3187
616 −55 −280 9486400 2 4 4 16 1  8  ε_{1} 21.3187
3080  −7 −440 9486400 4 1 12 24 1  6  ε_{1} 10.8053
3080 −11 −280 9486400 4 1 4  8 1  2  ε_{1} 10.8053
3080 −35  −88 9486400 4 2 2  8 1  2  ε_{1} 10.8053
3080 −55  −56 9486400 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.4027
237 −39 −1027 9492561 1 4 4  8 1  8  ε_{1} 8.6873
3081  −3 −1027 9492561 8 1 4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 9.7069
3081 −39  −79 9492561 8 4 5 80 1 10  ε_{1} 19.4137
12 −771 −1028 9511056 1 6 16 48 1 48  ε_{1} 2.6339
3084  −3 −1028 9511056 2 1 16 16 1  8  ε_{1} 45.0228
3084  −4 −771 9511056 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 22.5114
8 −772 −1544 9535744 1 4 20 40 1 40  ε_{1} 1.7627
1544  −4 −1544 9535744 2 1 20 40 2 20  \sqrt{i}\sqrt{ε_{1}} 12.3154
1544  −8 −772 9535744 2 1 4  8 2  4 \sqrt{−1}\sqrt{ε_{1}} 12.3154
281 −11 −3091 9554281 1 1 10  5 1  5  ε_{1} 29.1405
773  −4 −3092 9560464 1 1 26 13 1 13  ε_{1} 9.8691
3093  −3 −1031 9566649 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 12.0682
5 −619 −3095 9579025 1 5 48 120 1 120  ε_{1} 0.9624
3097 −19 −163 9591409 1 1 1  1 2  1 \sqrt{−1}\sqrt{ε_{1}} 60.8741
1033  −3 −3099 9603801 1 1 20 10 1 10  ε_{1} 80.9246
3101  −7 −443 9616201 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 14.5030
29 −107 −3103 9628609 1 3 20 30 1 30  ε_{1} 3.2945
13 −239 −3107 9653449 1 15 18 135 1 135  ε_{1} 2.3895
12 −259 −3108 9659664 1 4 16 32 1 32  ε_{1} 2.6339
21 −148 −3108 9659664 1 2 16 16 1 16  ε_{1} 3.1336
28 −111 −3108 9659664 1 8 16 64 1 64  ε_{1} 5.5373
37 −84 −3108 9659664 1 4 16 32 1 32  ε_{1} 4.9836
444  −7 −3108 9659664 2 1 16 16 1  8  ε_{1} 12.7602
444 −84 −259 9659664 2 4 4 16 1  8  ε_{1} 12.7602
777  −4 −3108 9659664 4 1 16 32 1  8  ε_{1} 12.2006
777 −84 −148 9659664 4 4 2 16 1  4  ε_{1} 12.2006
1036  −3 −3108 9659664 2 1 16 16 1  8  ε_{1} 28.6857
1036 −84 −111 9659664 2 4 8 32 1 16  ε_{1} 28.6857
17 −183 −3111 9678321 1 8 52 208 1 208  ε_{1} 4.1894
61 −51 −3111 9678321 1 2 52 52 1 52  ε_{1} 7.3284
1037  −3 −3111 9678321 2 1 52 52 1 26  ε_{1} 10.1629
1037 −51 −183 9678321 2 2 8 16 1  8  ε_{1} 10.1629
389  −8 −3112 9684544 1 1 14  7 1  7  ε_{1} 15.6986
3113 −11 −283 9690769 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 31.4626
5 −623 −3115 9703225 1 22 12 132 1 132  ε_{1} 0.9624
89 −35 −3115 9703225 1 2 12 12 1 12  ε_{1} 13.8155
445 −7 −3115 9703225 4 1 12 24 1 6 ε_{1} 6.0936
445 −35 −623 9703225 4 2 22 88 1 22  ε_{1} 6.0936

68 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
76 −164 −779 9709456 1 8 10 40 1 40  ε_{1} 11.6579
3116  −4 −779 9709456 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 16.9755
3116 −19 −164 9709456 2 1 8  8 1  4  ε_{1} 33.9511
3117  −3 −1039 9715689 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 22.2577
12 −520 −1560 9734400 1 4 16 32 1 32  ε_{1} 2.6339
24 −260 −1560 9734400 1 8 16 64 1 64  ε_{1} 4.5849
60 −104 −1560 9734400 2 6 16 96 1 48  ε_{1} 4.1269
60 −312 −520 9734400 2 4 4 16 1 8 ε_{1} 4.1269
120 −52 −1560 9734400 2 2 16 32 1 16  ε_{1} 6.1779
120 −260 −312 9734400 2 8 4 32 1 16  ε_{1} 6.1779
156 −40 −1560 9734400 2 2 16 32 1 16  ε_{1} 7.8232
156 −120 −520 9734400 2 4 4 16 1 8 ε_{1} 7.8232
312 −20 −1560 9734400 2 2 16 32 1 16  ε_{1} 9.3267
312 −120 −260 9734400 2 4 8 32 1 16  ε_{1} 9.3267
780  −8 −1560 9734400 4 1 16 32 1  8  ε_{1} 6.6619
780 −24 −520 9734400 4 2 4 16 1  4  ε_{1} 6.6619
780 −40 −312 9734400 4 2 4 16 1  4  ε_{1} 6.6619
780 −104 −120 9734400 4 6 4 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 3.3309
1560  −4 −1560 9734400 4 1 16 32 1  8  ε_{1} 10.1251
1560 −20 −312 9734400 4 2 4 16 1  4  ε_{1} 10.1251
1560 −24 −260 9734400 4 2 8 32 1  8  ε_{1} 10.1251
1560 −52 −120 9734400 4 2 4 16 1  4  ε_{1} 10.1251
44 −71 −3124 9759376 1 7 20 70 1 70  ε_{1} 5.9864
284 −11 −3124 9759376 1 1 20 10 1 10  ε_{1} 17.6959
781 −4 −3124 9759376 1 1 20 10 1 10 ε_{1} 37.4447
53 −59 −3127 9778129 1 3 24 36 1 36  ε_{1} 3.9314
8 −391 −3128 9784384 1 14 24 168 1 168  ε_{1} 1.7627
17 −184 −3128 9784384 1 4 24 48 1 48  ε_{1} 4.1894
136 −23 −3128 9784384 2 3 24 72 1 36  ε_{1} 8.4966
136 −184 −391 9784384 2 4 14 56 1 28  ε_{1} 8.4966
184 −136 −391 9784384 1 4 14 28 1 28  ε_{1} 21.5856
3128  −8 −391 9784384 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.3563
3128 −23 −136 9784384 2 3 4 12 1 6 ε_{1} 14.7126
21 −447 −1043 9790641 1 14 8 56 1 56  ε_{1} 3.1336
3129 −3 −1043 9790641 10 1 8 40 1 4 ε_{1} 14.9799
3129  −7 −447 9790641 10 1 14 140 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.4900
101 −31 −3131 9803161 1 3 20 30 1 30  ε_{1} 5.9964
5 −627 −3135 9828225 1 4 40 80 1 80  ε_{1} 0.9624
33 −95 −3135 9828225 1 8 40 160 1 160  ε_{1} 7.6563
57 −55 −3135 9828225 1 4 40 80 1 80  ε_{1} 11.4208
165 −19 −3135 9828225 2 1 40 40 1 20  ε_{1} 5.1180
165 −95 −627 9828225 2 8 4 32 1 16  ε_{1} 5.1180
209 −15 −3135 9828225 1 2 40 40 1 40  ε_{1} 22.8829
285 −11 −3135 9828225 2 1 40 40 1 20  ε_{1} 5.6595
285 −55 −627 9828225 2 4 4 16 1  8  ε_{1} 5.6595
1045  −3 −3135 9828225 4 1 40 80 1 20  ε_{1} 9.1492
1045 −15 −627 9828225 4 2 4 16 1  4  ε_{1} 9.1492
73 −43 −3139 9853321 1 1 10  5 1  5  ε_{1} 15.3334
5 −628 −3140 9859600 1 6 16 48 1 48  ε_{1} 0.9624
157 −20 −3140 9859600 1 2 16 16 1 16  ε_{1} 10.7226

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 69

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
785  −4 −3140 9859600 6 1 16 48 1  8  ε_{1} 8.0513
785 −20 −628 9859600 6 2 6 36 1  6  ε_{1} 8.0513
449  −7 −3143 9878449 1 1 56 28 1 28  ε_{1} 39.5058
24 −131 −3144 9884736 1 5 16 40 1 40  ε_{1} 4.5849
393  −8 −3144 9884736 1 1 16  8 1  8  ε_{1} 36.6935
393 −24 −1048 9884736 1 2 6  6 1  6  ε_{1} 36.6935
1048  −3 −3144 9884736 1 1 16  8 1  8  ε_{1} 38.3249
3144  −3 −1048 9884736 6 1 6 18 1  3  ε_{1} 14.7177
3144 −24 −131 9884736 6 2 5 30 1  5  ε_{1} 14.7177
1049  −3 −3147 9903609 1 1 10  5 1  5  ε_{1} 57.5072
3148  −4 −787 9909904 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 24.9610
3149 −47  −67 9916201 1 5 1  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 18.7257
137 −23 −3151 9928801 1 3 22 33 1 33  ε_{1} 16.3142
8 −788 −1576 9935104 1 10 10 50 1 50  ε_{1} 1.7627
1576  −4 −1576 9935104 2 1 10 10 1  5  ε_{1} 40.9752
1576  −8 −788 9935104 2 1 10 10 1  5  ε_{1} 40.9752
3153  −3 −1051 9941409 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 38.1748
5 −631 −3155 9954025 1 13 20 130 1 130  ε_{1} 0.9624
12 −263 −3156 9960336 1 13 32 208 1 208  ε_{1} 2.6339
789  −4 −3156 9960336 1 1 32 16 1 16  ε_{1} 20.7360
1052  −3 −3156 9960336 1 1 32 16 1 16  ε_{1} 25.0726
77 −287 −451 9966649 1 14 6 42 1 42  ε_{1} 4.3693
3157  −7 −451 9966649 2 1 6  6 1  3  ε_{1} 21.8709
3157 −11 −287 9966649 2 1 14 14 1  7  ε_{1} 21.8709
5 −632 −3160 9985600 1 8 16 64 1 64  ε_{1} 0.9624
8 −395 −3160 9985600 1 8 16 64 1 64  ε_{1} 1.7627
40 −79 −3160 9985600 2 5 16 80 1 40  ε_{1} 3.6369
40 −395 −632 9985600 2 8 8 64 1 32  ε_{1} 3.6369
632 −40 −395 9985600 1 2 8  8 1  8  ε_{1} 19.2954
3160  −8 −395 9985600 2 1 8  8 1  4  ε_{1} 46.6118
3160 −40  −79 9985600 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 23.3059
28 −452 −791 10010896 1 8 32 128 1 128  ε_{1} 5.5373
3164  −4 −791 10010896 4 1 32 64 1 16  ε_{1} 12.2185
3164  −7 −452 10010896 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 6.1092
633 −15 −1055 10017225 1 2 36 36 1 36  ε_{1} 41.1944
3165 −3 −1055 10017225 2 1 36 36 1 18 ε_{1} 19.0212
3165 −15 −211 10017225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.5106
21 −151 −3171 10055241 1 7 16 56 1 56  ε_{1} 3.1336
453  −7 −3171 10055241 1 1 16  8 1  8  ε_{1} 10.0078
1057  −3 −3171 10055241 1 1 16  8 1  8  ε_{1} 81.4221
13 −244 −3172 10061584 1 6 8 24 1 24  ε_{1} 2.3895
61 −52 −3172 10061584 1 2 8  8 1  8  ε_{1} 7.3284
793  −4 −3172 10061584 4 1 8 16 1  4  ε_{1} 18.1618
793 −52 −244 10061584 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 9.0809
3173 −19 −167 10067929 3 1 11 33 2 11 \sqrt{−1}\sqrt{ε_{1}} 5.1299
397 −8 −3176 10086976 1 1 42 21 1 21 ε_{1} 16.2905
12 −795 −1060 10112400 1 4 8 16 1 16  ε_{1} 2.6339
60 −159 −1060 10112400 2 10 8 80 1 40  ε_{1} 4.1269
60 −212 −795 10112400 2 6 4 24 1 12  ε_{1} 4.1269
636 −15 −1060 10112400 2 2 8 16 1  8  ε_{1} 15.7631

70 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
636 −20 −795 10112400 2 2 4  8 1  4  ε_{1} 15.7631
3180  −3 −1060 10112400 4 1 8 16 1  4  ε_{1} 18.9838
3180  −4 −795 10112400 4 1 4  8 1  2  ε_{1} 18.9838
3180 −15 −212 10112400 4 2 6 24 1  6  ε_{1} 18.9838
3180 −20 −159 10112400 4 2 10 40 1 10  ε_{1} 18.9838
1061 −3 −3183 10131489 1 1 34 17 1 17 ε_{1} 24.9704
796  −8 −1592 10137856 1 1 20 20 2 20 \sqrt{−1}\sqrt{ε_{1}} 24.2055
1592  −4 −1592 10137856 1 1 20 20 2 20  \sqrt{i}\sqrt{ε_{1}} 6.6821
797  −4 −3188 10163344 1 1 30 15 1 15  ε_{1} 11.8107
3189  −3 −1063 10169721 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 27.1290
8 −399 −3192 10188864 1 16 16 128 1 128  ε_{1} 1.7627
21 −152 −3192 10188864 1 6 16 48 1 48  ε_{1} 3.1336
21 −456 −1064 10188864 1 8 20 80 1 80  ε_{1} 3.1336
24 −399 −1064 10188864 1 16 20 160 1 160  ε_{1} 4.5849
56 −399 −456 10188864 1 16 8 64 1 64  ε_{1} 6.8002
57 −56 −3192 10188864 1 4 16 32 1 32  ε_{1} 11.4208
57 −168 −1064 10188864 1 4 20 40 1 40  ε_{1} 11.4208
133 −24 −3192 10188864 1 2 16 16 1 16  ε_{1} 10.3065
133 −168 −456 10188864 1 4 8 16 1 16  ε_{1} 10.3065
152 −168 −399 10188864 1 4 16 32 1 32  ε_{1} 8.6078
168 −19 −3192 10188864 2 1 16 16 1 8 ε_{1} 6.5132
168 −152 −399 10188864 2 6 16 96 1 48  ε_{1} 6.5132
456 −7 −3192 10188864 2 1 16 16 1 8 ε_{1} 15.2512
456 −56 −399 10188864 2 4 16 64 1 32  ε_{1} 15.2512
1064 −3 −3192 10188864 2 1 16 16 1 8 ε_{1} 14.4451
1064 −24 −399 10188864 2 2 16 32 1 16  ε_{1} 14.4451
3192  −3 −1064 10188864 4 1 20 40 1 10  ε_{1} 10.8410
3192  −7 −456 10188864 4 1 8 16 1  4  ε_{1} 10.8410
3192  −8 −399 10188864 4 1 16 32 1  8  ε_{1} 10.8410
3192 −19 −168 10188864 4 1 4  8 1  2  ε_{1} 10.8410
3193 −31 −103 10195249 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 78.0780
188 −68 −799 10214416 1 4 16 32 1 32  ε_{1} 9.1285
3196  −4 −799 10214416 8 1 16 64 1  8  ε_{1} 13.4858
3196 −47  −68 10214416 8 5 4 80 1 10  ε_{1} 13.4858
3197 −23 −139 10220809 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 12.6769
457  −7 −3199 10233601 1 1 32 16 1 16  ε_{1} 50.9909
33 −291 −1067 10246401 1 4 12 24 1 24  ε_{1} 7.6563
3201  −3 −1067 10246401 8 1 12 48 1  6  ε_{1} 19.7054
3201 −11 −291 10246401 8 1 4 16 1  2  ε_{1} 19.7054
1069  −3 −3207 10284849 1 1 32 16 1 16  ε_{1} 36.9734
401  −8 −3208 10291264 5 1 12 30 1  6  ε_{1} 7.3790
44 −292 −803 10316944 1 4 10 20 1 20  ε_{1} 5.9864
3212  −4 −803 10316944 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 9.5786
3212 −11 −292 10316944 2 1 4  4 1  2  ε_{1} 19.1572
5 −643 −3215 10336225 1 3 50 75 1 75  ε_{1} 0.9624
8 −804 −1608 10342656 1 12 16 96 1 96  ε_{1} 1.7627
12 −536 −1608 10342656 1 14 16 112 1 112  ε_{1} 2.6339
24 −536 −804 10342656 1 14 12 84 1 84  ε_{1} 4.5849
268 −24 −1608 10342656 1 2 16 16 1 16  ε_{1} 22.9790
536 −24 −804 10342656 1 2 12 12 1 12  ε_{1} 25.1680

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 71

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1608  −4 −1608 10342656 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 6.6871
1608  −8 −804 10342656 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.6871
29 −111 −3219 10361961 1 8 20 80 1 80  ε_{1} 3.2945
37 −87 −3219 10361961 1 6 20 60 1 60  ε_{1} 4.9836
1073 −3 −3219 10361961 2 1 20 20 1 10 ε_{1} 22.8314
1073 −87 −111 10361961 2 6 8 48 1 24  ε_{1} 22.8314
5 −644 −3220 10368400 1 16 16 128 1 128  ε_{1} 0.9624
28 −115 −3220 10368400 1 2 16 16 1 16  ε_{1} 5.5373
92 −35 −3220 10368400 1 2 16 16 1 16  ε_{1} 7.7415
140 −23 −3220 10368400 2 3 16 48 1 24  ε_{1} 4.9558
140 −115 −644 10368400 2 2 16 32 1 16  ε_{1} 4.9558
161 −20 −3220 10368400 1 2 16 16 1 16  ε_{1} 20.1338
460 −7 −3220 10368400 2 1 16 16 1 8 ε_{1} 15.4391
460 −35 −644 10368400 2 2 16 32 1 16  ε_{1} 15.4391
805 −4 −3220 10368400 2 1 16 16 1 8 ε_{1} 14.5545
805 −20 −644 10368400 2 2 16 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 7.2772
293 −11 −3223 10387729 1 1 30 15 1 15  ε_{1} 5.6733
8 −403 −3224 10394176 1 2 28 28 1 28  ε_{1} 1.7627
13 −248 −3224 10394176 1 8 28 112 1 112  ε_{1} 2.3895
104 −31 −3224 10394176 2 3 28 84 1 42  ε_{1} 4.6249
104 −248 −403 10394176 2 8 2 16 1  8  ε_{1} 4.6249
248 −104 −403 10394176 1 6 2  6 1  6  ε_{1} 9.6724
3224  −8 −403 10394176 2 1 2  2 1  1  ε_{1} 32.6555
3224 −31 −104 10394176 2 3 6 18 1  9  ε_{1} 32.6555
461  −7 −3227 10413529 1 1 14  7 1  7  ε_{1} 11.7998
12 −807 −1076 10419984 1 14 22 154 1 154  ε_{1} 2.6339
3228  −3 −1076 10419984 2 1 22 22 1 11  ε_{1} 36.9137
3228  −4 −807 10419984 2 1 14 14 1  7  ε_{1} 36.9137
5 −647 −3235 10465225 1 23 6 69 1 69  ε_{1} 0.9624
809 −4 −3236 10471696 1 1 32 16 1 16 ε_{1} 54.9782
249 −39 −1079 10478169 1 4 34 68 1 68  ε_{1} 33.3101
3237  −3 −1079 10478169 2 1 34 68 2 34 \sqrt{−1}\sqrt{ε_{1}} 6.9856
3237 −39 −83 10478169 2 4 3 12 1 6 ε_{1} 13.9713
41 −79 −3239 10491121 1 5 70 175 1 175  ε_{1} 8.3183
3241 −7 −463 10504081 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 93.7294
69 −47 −3243 10517049 1 5 8 20 1 20  ε_{1} 6.4345
141 −23 −3243 10517049 1 3 8 12 1 12  ε_{1} 10.4940
1081  −3 −3243 10517049 1 1 8  4 1  4  ε_{1} 95.6412
3244  −4 −811 10523536 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 42.4633
649 −55 −295 10530025 1 4 8 16 1 16  ε_{1} 70.6969
3245 −11 −295 10530025 4 1 8 16 1 4 ε_{1} 8.0855
3245 −55  −59 10530025 4 4 3 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 4.0427
17 −191 −3247 10543009 1 13 32 208 1 208  ε_{1} 4.1894
28 −232 −1624 10549504 1 2 16 16 1 16  ε_{1} 5.5373
56 −116 −1624 10549504 1 6 16 48 1 48  ε_{1} 6.8002
812  −8 −1624 10549504 2 1 16 16 1  8  ε_{1} 9.4722
812 −56 −232 10549504 2 4 2  8 1  4  ε_{1} 9.4722
1624  −4 −1624 10549504 2 1 16 16 1  8  ε_{1} 37.1882
1624 −56 −116 10549504 2 4 6 24 1 12  ε_{1} 37.1882
12 −271 −3252 10575504 1 11 12 66 1 66  ε_{1} 2.6339

72 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
813  −4 −3252 10575504 1 1 12  6 1  6  ε_{1} 16.7485
1084  −3 −3252 10575504 1 1 12  6 1  6  ε_{1} 52.3396
5 −651 −3255 10595025 1 8 40 160 1 160  ε_{1} 0.9624
21 −155 −3255 10595025 1 4 40 80 1 80  ε_{1} 3.1336
93 −35 −3255 10595025 1 2 40 40 1 40  ε_{1} 6.7322
105 −31 −3255 10595025 2 3 40 120 1 60  ε_{1} 8.8131
105 −155 −651 10595025 2 4 8 32 1 16  ε_{1} 8.8131
217 −15 −3255 10595025 1 2 40 40 1 40  ε_{1} 31.7104
465  −7 −3255 10595025 2 1 40 40 1 20  ε_{1} 20.7308
465 −35 −651 10595025 2 2 8 16 1  8  ε_{1} 20.7308
1085  −3 −3255 10595025 2 1 40 40 1 20  ε_{1} 6.9912
1085 −15 −651 10595025 2 2 8 16 1  8  ε_{1} 6.9912
8 −407 −3256 10601536 1 16 12 96 1 96  ε_{1} 1.7627
37 −88 −3256 10601536 1 2 12 12 1 12  ε_{1} 4.9836
88 −296 −407 10601536 1 10 16 80 1 80  ε_{1} 11.9527
296 −11 −3256 10601536 2 1 12 12 1 6 ε_{1} 8.9090
296 −88 −407 10601536 2 2 16 32 1 16  ε_{1} 8.9090
3256 −8 −407 10601536 2 1 16 16 1 8 ε_{1} 59.5218
3256 −11 −296 10601536 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 29.7609
652 −20 −815 10627600 1 2 30 30 1 30  ε_{1} 37.3376
3260  −4 −815 10627600 2 1 30 30 1 15  ε_{1} 25.3098
3260 −20 −163 10627600 2 2 1  2 1  1  ε_{1} 25.3098
3261  −3 −1087 10634121 3 1 9 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 6.9893
13 −251 −3263 10647169 1 7 48 168 1 168  ε_{1} 2.3895
76 −43 −3268 10679824 1 1 12  6 1  6  ε_{1} 11.6579
172 −19 −3268 10679824 1 1 12  6 1  6  ε_{1} 17.6970
817  −4 −3268 10679824 5 1 12 30 1  6  ε_{1} 13.0618
3269  −7 −467 10686361 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 15.9863
409  −8 −3272 10705984 1 1 28 14 1 14  ε_{1} 52.2684
3273  −3 −1091 10712529 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 58.1058
1093 −3 −3279 10751841 5 1 52 130 1 26 ε_{1} 6.9948
8 −820 −1640 10758400 1 8 16 64 1 64  ε_{1} 1.7627
40 −164 −1640 10758400 2 8 16 128 1 64  ε_{1} 3.6369
40 −328 −820 10758400 2 4 8 32 1 16  ε_{1} 3.6369
328 −20 −1640 10758400 4 2 16 64 1 16  ε_{1} 5.7869
328 −40 −820 10758400 4 2 8 32 1  8  ε_{1} 5.7869
1640  −4 −1640 10758400 4 1 16 32 1  8  ε_{1} 10.1751
1640  −8 −820 10758400 4 1 8 16 1  4  ε_{1} 10.1751
1640 −20 −328 10758400 4 2 4 16 1  4  ε_{1} 10.1751
1640 −40 −164 10758400 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.0876
821 −4 −3284 10784656 1 1 30 15 1 15 ε_{1} 19.3842
173 −19 −3287 10804369 1 1 34 17 1 17  ε_{1} 5.1416
8 −411 −3288 10810944 1 6 20 60 1 60  ε_{1} 1.7627
24 −411 −1096 10810944 1 6 12 36 1 36  ε_{1} 4.5849
137 −24 −3288 10810944 1 2 20 20 1 20  ε_{1} 16.3142
1096  −3 −3288 10810944 4 1 20 40 1 10  ε_{1} 15.8847
1096 −24 −411 10810944 4 2 6 24 1  6  ε_{1} 15.8847
3288  −3 −1096 10810944 2 1 12 12 1  6  ε_{1} 19.2040
3288  −8 −411 10810944 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.6020
253 −143 −299 10817521 1 10 8 40 1 40  ε_{1} 15.0577

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 73

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3289 −11 −299 10817521 2 1 8  8 1  4  ε_{1} 88.8213
3289 −23 −143 10817521 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 44.4106
1097  −3 −3291 10830681 1 1 10  5 1  5  ε_{1} 35.1082
3292  −4 −823 10837264 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 47.6000
5 −659 −3295 10857025 1 11 32 176 1 176  ε_{1} 0.9624
21 −471 −1099 10870209 1 16 6 48 1 48  ε_{1} 3.1336
3297  −3 −1099 10870209 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 22.9690
3297  −7 −471 10870209 2 1 16 16 1  8  ε_{1} 45.9381
56 −59 −3304 10916416 1 3 12 18 1 18  ε_{1} 6.8002
413 −8 −3304 10916416 1 1 12 6 1 6 ε_{1} 8.2212
413 −56 −472 10916416 1 4 6 12 1 12  ε_{1} 8.2212
472  −7 −3304 10916416 1 1 12  6 1  6  ε_{1} 26.6550
3304  −7 −472 10916416 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 26.8202
3304 −56  −59 10916416 2 4 3 12 1  6  ε_{1} 53.6403
3308  −4 −827 10942864 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 14.4040
3309  −3 −1103 10949481 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 19.3575
77 −43 −3311 10962721 1 1 72 36 1 36  ε_{1} 4.3693
301 −11 −3311 10962721 1 1 72 36 1 36  ε_{1} 20.0642
473 −7 −3311 10962721 3 1 72 108 1 36 ε_{1} 10.3180
5 −663 −3315 10989225 1 16 8 64 1 64  ε_{1} 0.9624
13 −255 −3315 10989225 1 12 8 48 1 48  ε_{1} 2.3895
17 −195 −3315 10989225 1 4 8 16 1 16  ε_{1} 4.1894
65 −51 −3315 10989225 2 2 8 16 1 8 ε_{1} 5.5529
65 −255 −663 10989225 2 12 16 192 1 96  ε_{1} 5.5529
85 −39 −3315 10989225 2 4 8 32 1 16  ε_{1} 4.4187
85 −195 −663 10989225 2 4 16 64 1 32  ε_{1} 4.4187
221 −15 −3315 10989225 2 2 8 16 1 8 ε_{1} 5.4072
221 −195 −255 10989225 2 4 12 48 1 24  ε_{1} 5.4072
1105 −3 −3315 10989225 4 1 8 16 1 4 ε_{1} 21.9008
1105 −15 −663 10989225 4 2 16 64 1 16  ε_{1} 21.9008
1105 −39 −255 10989225 4 4 12 96 1 24  ε_{1} 21.9008
1105 −51 −195 10989225 4 2 4 16 1  4  ε_{1} 21.9008
829  −4 −3316 10995856 1 1 22 11 1 11  ε_{1} 34.4976
3317 −31 −107 11002489 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 8.5643
5 −664 −3320 11022400 1 10 20 100 1 100  ε_{1} 0.9624
8 −415 −3320 11022400 1 10 20 100 1 100  ε_{1} 1.7627
40 −83 −3320 11022400 2 3 20 60 1 30  ε_{1} 3.6369
40 −415 −664 11022400 2 10 10 100 1 50  ε_{1} 3.6369
664 −40 −415 11022400 1 2 10 10 1 10  ε_{1} 43.8951
3320  −8 −415 11022400 2 1 10 10 1  5  ε_{1} 25.1746
3320 −40  −83 11022400 2 2 3  6 1  3  ε_{1} 25.1746
12 −831 −1108 11048976 1 28 6 84 1 84  ε_{1} 2.6339
3324  −3 −1108 11048976 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 16.7910
3324  −4 −831 11048976 2 1 28 28 1 14  ε_{1} 33.5820
1109  −3 −3327 11068929 1 1 26 13 1 13  ε_{1} 23.1586
33 −303 −1111 11108889 1 10 22 110 1 110  ε_{1} 7.6563
3333  −3 −1111 11108889 2 1 22 22 1 11  ε_{1} 17.5486
3333 −11 −303 11108889 2 1 10 10 1  5  ε_{1} 17.5486
5 −667 −3335 11122225 1 4 64 128 1 128  ε_{1} 0.9624
29 −115 −3335 11122225 1 2 64 64 1 64  ε_{1} 3.2945

74 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
145 −23 −3335 11122225 4 3 64 384 1 96  ε_{1} 6.3596
145 −115 −667 11122225 4 2 4 16 1 4 ε_{1} 6.3596
24 −139 −3336 11128896 1 3 16 24 1 24  ε_{1} 4.5849
417 −8 −3336 11128896 1 1 16 8 1 8 ε_{1} 37.9102
417 −24 −1112 11128896 1 2 14 14 1 14  ε_{1} 37.9102
1112  −3 −3336 11128896 1 1 16  8 1  8  ε_{1} 17.0352
3336  −3 −1112 11128896 2 1 14 14 1  7  ε_{1} 46.5925
3336 −24 −139 11128896 2 2 3  6 1  3  ε_{1} 46.5925
3337 −47  −71 11135569 1 5 7 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 69.7694
668 −20 −835 11155600 1 2 6  6 1  6  ε_{1} 11.6342
3340  −4 −835 11155600 2 1 6  6 1  3  ε_{1} 49.9052
3340 −20 −167 11155600 2 2 11 22 1 11  ε_{1} 49.9052
8 −836 −1672 11182336 1 20 8 80 1 80  ε_{1} 1.7627
44 −152 −1672 11182336 1 6 8 24 1 24  ε_{1} 5.9864
76 −88 −1672 11182336 1 2 8 8 1 8 ε_{1} 11.6579
88 −152 −836 11182336 1 6 20 60 1 60  ε_{1} 11.9527
152 −88 −836 11182336 1 2 20 20 1 20  ε_{1} 8.6078
1672 −4 −1672 11182336 2 1 8 16 2 8 \sqrt{i}\sqrt{ε_{1}} 11.1230
1672  −8 −836 11182336 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 11.1230
669 −15 −1115 11189025 1 2 10 10 1 10  ε_{1} 25.2580
3345  −3 −1115 11189025 2 1 10 10 1  5  ε_{1} 61.4826
3345 −15 −223 11189025 2 2 7 14 1  7  ε_{1} 61.4826
1117  −3 −3351 11229201 1 1 60 30 1 30  ε_{1} 31.6567
8 −419 −3352 11235904 1 9 14 63 1 63  ε_{1} 1.7627
3352 −8 −419 11235904 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 25.1568
3353  −7 −479 11242609 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 46.7014
5 −671 −3355 11256025 1 30 8 120 1 120  ε_{1} 0.9624
61 −55 −3355 11256025 1 4 8 16 1 16  ε_{1} 7.3284
305 −11 −3355 11256025 2 1 8 8 1 4 ε_{1} 13.7710
305 −55 −671 11256025 2 4 30 120 1 60  ε_{1} 13.7710
3356 −4 −839 11262736 3 1 33 99 2 33 \sqrt{i}\sqrt{ε_{1}} 7.4265
57 −59 −3363 11309769 1 3 16 24 1 24  ε_{1} 11.4208
177 −19 −3363 11309769 1 1 16  8 1  8  ε_{1} 23.4697
1121  −3 −3363 11309769 1 1 16  8 1  8  ε_{1} 66.6959
13 −259 −3367 11336689 1 4 20 40 1 40  ε_{1} 2.3895
37 −91 −3367 11336689 1 2 20 20 1 20  ε_{1} 4.9836
481  −7 −3367 11336689 2 1 20 20 1 10  ε_{1} 28.9443
481 −91 −259 11336689 2 2 4  8 1  4  ε_{1} 28.9443
421  −8 −3368 11343424 1 1 26 13 1 13  ε_{1} 26.0114
3369  −3 −1123 11350161 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 78.3493
12 −843 −1124 11370384 1 6 20 60 1 60  ε_{1} 2.6339
3372  −3 −1124 11370384 2 1 20 20 1 10  ε_{1} 14.8579
3372  −4 −843 11370384 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 7.4289
844  −8 −1688 11397376 1 1 10 10 2 10 \sqrt{−1}\sqrt{ε_{1}} 27.0453
1688  −4 −1688 11397376 1 1 10 10 2 10  \sqrt{i}\sqrt{ε_{1}} 16.4578
3377 −11 −307 11404129 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 31.8850
109 −31 −3379 11417641 1 3 16 24 1 24  ε_{1} 11.1291
17 −199 −3383 11444689 1 9 46 207 1 207  ε_{1} 4.1894
1129 −3 −3387 11471769 9 1 12 54 1 6 ε_{1} 11.6342
5 −679 −3395 11526025 1 18 20 180 1 180  ε_{1} 0.9624

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 75

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
97 −35 −3395 11526025 1 2 20 20 1 20  ε_{1} 18.6488
485 −7 −3395 11526025 2 1 20 20 1 10 ε_{1} 7.5694
485 −35 −679 11526025 2 2 18 36 1 18  ε_{1} 7.5694
12 −283 −3396 11532816 1 3 28 42 1 42  ε_{1} 2.6339
849  −4 −3396 11532816 1 1 28 14 1 14  ε_{1} 71.2770
1132  −3 −3396 11532816 1 1 28 14 1 14  ε_{1} 38.8758
3397 −43  −79 11539609 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 32.1618
33 −103 −3399 11553201 1 5 40 100 1 100  ε_{1} 7.6563
309 −11 −3399 11553201 1 1 40 20 1 20  ε_{1} 17.0523
1133  −3 −3399 11553201 1 1 40 20 1 20  ε_{1} 9.2300
3401 −19 −179 11566801 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 44.3000
41 −83 −3403 11580409 1 3 8 12 1 12  ε_{1} 8.3183
92 −148 −851 11587216 1 2 10 10 1 10  ε_{1} 7.7415
3404  −4 −851 11587216 2 1 10 10 1  5  ε_{1} 33.2782
3404 −23 −148 11587216 2 3 2  6 1  3  ε_{1} 33.2782
681 −15 −1135 11594025 1 2 18 18 1 18  ε_{1} 61.3969
3405  −3 −1135 11594025 2 1 18 18 1  9  ε_{1} 17.4409
3405 −15 −227 11594025 2 2 5 10 1  5  ε_{1} 17.4409
8 −852 −1704 11614464 1 8 24 96 1 96  ε_{1} 1.7627
12 −568 −1704 11614464 1 4 24 48 1 48  ε_{1} 2.6339
24 −568 −852 11614464 1 4 8 16 1 16  ε_{1} 4.5849
284 −24 −1704 11614464 1 2 24 24 1 24  ε_{1} 17.6959
568 −24 −852 11614464 3 2 8 24 1  8  ε_{1} 11.3120
1704  −4 −1704 11614464 2 1 24 24 1 12  ε_{1} 24.1735
1704  −8 −852 11614464 2 1 8  8 1  4  ε_{1} 24.1735
3409  −7 −487 11621281 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 96.8819
853  −4 −3412 11641744 1 1 10  5 1  5  ε_{1} 20.4426
5 −683 −3415 11662225 1 5 38 95 1 95  ε_{1} 0.9624
8 −427 −3416 11669056 1 2 44 44 1 44  ε_{1} 1.7627
56 −427 −488 11669056 1 2 10 10 1 10  ε_{1} 6.8002
61 −56 −3416 11669056 1 4 44 88 1 88  ε_{1} 7.3284
488  −7 −3416 11669056 2 1 44 44 1 22  ε_{1} 6.1862
488 −56 −427 11669056 2 4 2  8 1  4  ε_{1} 6.1862
3416  −7 −488 11669056 2 1 10 10 1  5  ε_{1} 29.5333
3416  −8 −427 11669056 2 1 2  2 1  1  ε_{1} 29.5333
201 −51 −1139 11675889 1 2 16 16 1 16  ε_{1} 27.6905
3417  −3 −1139 11675889 2 1 16 16 1  8  ε_{1} 54.3298
3417 −51  −67 11675889 2 2 1  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 27.1649
13 −263 −3419 11689561 1 13 28 182 1 182  ε_{1} 2.3895
3421 −11 −311 11703241 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 32.9607
21 −163 −3423 11716929 1 1 40 20 1 20  ε_{1} 3.1336
489  −7 −3423 11716929 1 1 40 20 1 20  ε_{1} 46.8872
1141  −3 −3423 11716929 1 1 40 20 1 20  ε_{1} 41.9327
149 −23 −3427 11744329 1 3 6  9 1  9  ε_{1} 8.2223
857  −4 −3428 11751184 1 1 32 16 1 16  ε_{1} 33.2056
73 −47 −3431 11771761 1 5 66 165 1 165  ε_{1} 15.3334
13 −264 −3432 11778624 1 8 16 64 1 64  ε_{1} 2.3895
24 −143 −3432 11778624 1 10 16 80 1 80  ε_{1} 4.5849
33 −104 −3432 11778624 1 6 16 48 1 48  ε_{1} 7.6563
33 −312 −1144 11778624 1 4 12 24 1 24  ε_{1} 7.6563

76 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
88 −39 −3432 11778624 1 4 16 32 1 32  ε_{1} 11.9527
264 −39 −1144 11778624 2 4 12 48 1 24  ε_{1} 9.7350
264 −143 −312 11778624 2 10 4 40 1 20  ε_{1} 9.7350
312 −11 −3432 11778624 2 1 16 16 1 8 ε_{1} 9.3267
312 −143 −264 11778624 2 10 8 80 1 40  ε_{1} 9.3267
429 −8 −3432 11778624 2 1 16 16 1 8 ε_{1} 9.9534
429 −24 −1144 11778624 2 2 12 24 1 12  ε_{1} 9.9534
429 −88 −312 11778624 2 2 4 8 1 4 ε_{1} 9.9534
429 −104 −264 11778624 2 6 8 48 1 24  ε_{1} 9.9534
1144 −3 −3432 11778624 2 1 16 16 1 8 ε_{1} 27.8642
1144 −39 −264 11778624 2 4 8 32 1 16  ε_{1} 27.8642
3432  −3 −1144 11778624 4 1 12 24 1  6  ε_{1} 14.4970
3432 −11 −312 11778624 4 1 4  8 1  2  ε_{1} 14.4970
3432 −24 −143 11778624 4 2 10 40 1 10  ε_{1} 14.4970
3432 −39 −88 11778624 4 4 2 32 2 8 \sqrt{−1}\sqrt{ε_{1}} 7.2485
5 −687 −3435 11799225 1 12 16 96 1 96  ε_{1} 0.9624
229 −15 −3435 11799225 3 2 16 48 1 16  ε_{1} 5.4249
1145 −3 −3435 11799225 4 1 16 32 1 8 ε_{1} 15.6513
1145 −15 −687 11799225 4 2 12 48 1 12  ε_{1} 15.6513
3436  −4 −859 11806096 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 56.6773
3437  −7 −491 11812969 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 11.7416
181 −19 −3439 11826721 1 1 30 15 1 15  ε_{1} 14.3479
172 −40 −1720 11833600 1 2 12 12 1 12  ε_{1} 17.6970
344 −20 −1720 11833600 1 2 12 12 1 12  ε_{1} 19.8864
860 −8 −1720 11833600 2 1 12 12 1 6 ε_{1} 8.9544
860 −40 −344 11833600 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 4.4772
1720 −4 −1720 11833600 2 1 12 12 1 6 ε_{1} 31.1205
1720 −20 −344 11833600 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 15.5603
93 −111 −1147 11840481 1 8 6 24 1 24  ε_{1} 6.7322
3441 −3 −1147 11840481 2 1 6 12 2 6 \sqrt{−1}\sqrt{ε_{1}} 40.8225
3441 −31 −111 11840481 2 3 8 24 1 12  ε_{1} 81.6449
313 −11 −3443 11854249 1 1 16 8 1 8 ε_{1} 38.7035
12 −287 −3444 11861136 1 14 24 168 1 168  ε_{1} 2.6339
21 −164 −3444 11861136 1 8 24 96 1 96  ε_{1} 3.1336
28 −123 −3444 11861136 1 2 24 24 1 24  ε_{1} 5.5373
41 −84 −3444 11861136 1 4 24 48 1 48  ε_{1} 8.3183
492 −7 −3444 11861136 2 1 24 24 1 12 ε_{1} 10.9943
492 −84 −287 11861136 2 4 14 56 1 28  ε_{1} 10.9943
861 −4 −3444 11861136 2 1 24 24 1 12 ε_{1} 13.8688
861 −84 −164 11861136 2 4 8 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 6.9344
1148  −3 −3444 11861136 2 1 24 24 1 12  ε_{1} 12.7122
1148 −84 −123 11861136 2 4 2  8 1  4  ε_{1} 12.7122
8 −431 −3448 11888704 1 21 8 84 1 84  ε_{1} 1.7627
3448  −8 −431 11888704 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 48.0203
17 −203 −3451 11909401 1 4 12 24 1 24  ε_{1} 4.1894
29 −119 −3451 11909401 1 10 12 60 1 60  ε_{1} 3.2945
493 −7 −3451 11909401 2 1 12 12 1 6 ε_{1} 9.4192
493 −119 −203 11909401 2 10 4 40 1 20  ε_{1} 9.4192
3452 −4 −863 11916304 1 1 21 21 2 21 \sqrt{i}\sqrt{ε_{1}} 24.3355
3453  −3 −1151 11923209 1 1 41 41 2 41 \sqrt{−1}\sqrt{ε_{1}} 16.9741

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 77

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −691 −3455 11937025 1 5 52 130 1 130  ε_{1} 0.9624
1153 −3 −3459 11964681 1 1 12 6 1 6 ε_{1} 79.7231
5 −692 −3460 11971600 1 14 16 112 1 112  ε_{1} 0.9624
173 −20 −3460 11971600 1 2 16 16 1 16  ε_{1} 5.1416
865 −4 −3460 11971600 2 1 16 16 1 8 ε_{1} 40.7237
865 −20 −692 11971600 2 2 14 28 1 14  ε_{1} 40.7237
433 −8 −3464 11999296 1 1 44 22 1 22 ε_{1} 46.7895
13 −267 −3471 12047841 1 2 60 60 1 60  ε_{1} 2.3895
89 −39 −3471 12047841 1 4 60 120 1 120  ε_{1} 13.8155
1157  −3 −3471 12047841 2 1 60 60 1 30  ε_{1} 8.4394
1157 −39 −267 12047841 2 4 2  8 1  4  ε_{1} 8.4394
8 −868 −1736 12054784 1 8 24 96 1 96  ε_{1} 1.7627
28 −248 −1736 12054784 1 8 24 96 1 96  ε_{1} 5.5373
56 −248 −868 12054784 1 8 8 32 1 32  ε_{1} 6.8002
124 −56 −1736 12054784 1 4 24 48 1 48  ε_{1} 16.0392
248 −56 −868 12054784 1 4 8 16 1 16  ε_{1} 9.6724
1736  −4 −1736 12054784 4 1 24 48 1 12  ε_{1} 11.0429
1736  −8 −868 12054784 4 1 8 16 1  4  ε_{1} 11.0429
3473 −23 −151 12061729 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 36.4796
44 −79 −3476 12082576 1 5 32 80 1 80  ε_{1} 5.9864
316 −11 −3476 12082576 3 1 32 48 1 16  ε_{1} 10.1503
869 −4 −3476 12082576 1 1 32 16 1 16 ε_{1} 21.6145
57 −183 −1159 12089529 1 8 16 64 1 64  ε_{1} 11.4208
3477  −3 −1159 12089529 4 1 16 32 1  8  ε_{1} 8.1545
3477 −19 −183 12089529 4 1 8 16 1  4  ε_{1} 8.1545
5 −696 −3480 12110400 1 12 16 96 1 96  ε_{1} 0.9624
8 −435 −3480 12110400 1 4 16 32 1 32  ε_{1} 1.7627
24 −435 −1160 12110400 1 4 20 40 1 40  ε_{1} 4.5849
29 −120 −3480 12110400 1 4 16 32 1 32  ε_{1} 3.2945
40 −87 −3480 12110400 2 6 16 96 1 48  ε_{1} 3.6369
40 −435 −696 12110400 2 4 12 48 1 24  ε_{1} 3.6369
120 −87 −1160 12110400 2 6 20 120 1 60  ε_{1} 6.1779
120 −232 −435 12110400 2 2 4 8 1 4 ε_{1} 6.1779
145 −24 −3480 12110400 4 2 16 64 1 16  ε_{1} 6.3596
145 −120 −696 12110400 4 4 12 96 1 24  ε_{1} 6.3596
232 −15 −3480 12110400 2 2 16 32 1 16  ε_{1} 10.5766
232 −120 −435 12110400 2 4 4 16 1 8 ε_{1} 10.5766
696 −15 −1160 12110400 2 2 20 40 1 20  ε_{1} 15.9463
696 −40 −435 12110400 2 2 4  8 1  4  ε_{1} 15.9463
1160  −3 −3480 12110400 4 1 16 32 1  8  ε_{1} 7.0544
1160 −15 −696 12110400 4 2 12 48 1 12  ε_{1} 7.0544
1160 −24 −435 12110400 4 2 4 16 1 4 ε_{1} 7.0544
1160 −87 −120 12110400 4 6 4 48 1 12  ε_{1} 7.0544
3480  −3 −1160 12110400 8 1 20 80 1 10  ε_{1} 9.5412
3480  −8 −435 12110400 8 1 4 16 1  2  ε_{1} 9.5412
3480 −15 −232 12110400 8 2 2 16 1  2  ε_{1} 9.5412
3480 −40  −87 12110400 8 2 6 48 1  6  ε_{1} 9.5412
268 −52 −871 12138256 1 2 22 22 1 22  ε_{1} 22.9790
3484  −4 −871 12138256 2 1 22 22 1 11  ε_{1} 48.7678
3484 −52  −67 12138256 2 2 1  2 1  1  ε_{1} 48.7678

78 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
317 −11 −3487 12159169 1 1 28 14 1 14  ε_{1} 8.9775
3489  −3 −1163 12173121 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 61.5588
3493  −7 −499 12201049 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 26.8706
5 −699 −3495 12215025 1 10 36 180 1 180  ε_{1} 0.9624
233 −15 −3495 12215025 1 2 36 36 1 36  ε_{1} 21.4863
1165 −3 −3495 12215025 2 1 36 36 1 18 ε_{1} 15.0011
1165 −15 −699 12215025 2 2 10 20 1 10  ε_{1} 15.0011
152 −23 −3496 12222016 1 3 20 30 1 30  ε_{1} 8.6078
184 −19 −3496 12222016 1 1 20 10 1 10  ε_{1} 21.5856
437 −8 −3496 12222016 1 1 20 10 1 10 ε_{1} 6.0845
437 −152 −184 12222016 1 6 4 12 1 12  ε_{1} 6.0845
3496 −19 −184 12222016 6 1 4 12 1 2 ε_{1} 17.8319
3496 −23 −152 12222016 6 3 6 108 2 18 \sqrt{−1}\sqrt{ε_{1}} 8.9160
113 −31 −3503 12271009 1 3 52 78 1 78  ε_{1} 14.6946
12 −584 −1752 12278016 1 16 8 64 1 64  ε_{1} 2.6339
24 −292 −1752 12278016 1 4 8 16 1 16  ε_{1} 4.5849
876 −8 −1752 12278016 4 1 8 16 1 4 ε_{1} 9.9943
876 −24 −584 12278016 4 2 16 128 2 32 \sqrt{−1}\sqrt{ε_{1}} 4.9972
1752  −4 −1752 12278016 4 1 8 16 1  4  ε_{1} 12.7466
1752 −24 −292 12278016 4 2 4 16 1  4  ε_{1} 12.7466
21 −167 −3507 12299049 1 11 8 44 1 44  ε_{1} 3.1336
501  −7 −3507 12299049 1 1 8  4 1  4  ε_{1} 20.4959
1169  −3 −3507 12299049 1 1 8  4 1  4  ε_{1} 67.0808
877  −4 −3508 12306064 1 1 10  5 1  5  ε_{1} 26.1741
8 −439 −3512 12334144 1 15 20 150 1 150  ε_{1} 1.7627
3512  −8 −439 12334144 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 16.7403
3513 −3 −1171 12341169 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 50.8639
5 −703 −3515 12355225 1 14 20 140 1 140  ε_{1} 0.9624
37 −95 −3515 12355225 1 8 20 80 1 80  ε_{1} 4.9836
185 −19 −3515 12355225 2 1 20 20 1 10  ε_{1} 9.8254
185 −95 −703 12355225 2 8 14 112 1 56  ε_{1} 9.8254
12 −879 −1172 12362256 1 22 18 198 1 198  ε_{1} 2.6339
3516  −3 −1172 12362256 2 1 18 18 1  9  ε_{1} 38.3676
3516  −4 −879 12362256 2 1 22 22 1 11  ε_{1} 38.3676
3521  −7 −503 12397441 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 60.4861
13 −271 −3523 12411529 1 11 6 33 1 33  ε_{1} 2.3895
881 −4 −3524 12418576 1 1 40 20 1 20 ε_{1} 52.1657
33 −107 −3531 12467961 1 3 16 24 1 24  ε_{1} 7.6563
321 −11 −3531 12467961 3 1 16 24 1  8  ε_{1} 12.1276
1177  −3 −3531 12467961 1 1 16  8 1  8  ε_{1} 88.7782
3532  −4 −883 12475024 1 1 3  3 2  3  \sqrt{i}\sqrt{ε_{1}} 52.5993
5 −707 −3535 12496225 1 6 28 84 1 84  ε_{1} 0.9624
101 −35 −3535 12496225 1 2 28 28 1 28  ε_{1} 5.9964
505  −7 −3535 12496225 4 1 28 56 1 14  ε_{1} 14.7779
505 −35 −707 12496225 4 2 6 24 1  6  ε_{1} 14.7779
8 −884 −1768 12503296 1 16 8 64 1 64  ε_{1} 1.7627
104 −68 −1768 12503296 2 4 8 32 1 16  ε_{1} 4.6249
104 −136 −884 12503296 2 4 16 64 1 32  ε_{1} 4.6249
136 −52 −1768 12503296 2 2 8 16 1 8 ε_{1} 8.4966
136 −104 −884 12503296 2 6 16 96 1 48  ε_{1} 8.4966

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 79

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1768  −4 −1768 12503296 8 1 8 32 1  4  ε_{1} 7.4765
1768  −8 −884 12503296 8 1 16 64 1  8  ε_{1} 7.4765
1768 −52 −136 12503296 8 2 4 32 1  4  ε_{1} 7.4765
1768 −68 −104 12503296 8 4 6 96 1 12  ε_{1} 7.4765
5 −708 −3540 12531600 1 4 24 48 1 48  ε_{1} 0.9624
12 −295 −3540 12531600 1 8 24 96 1 96  ε_{1} 2.6339
60 −59 −3540 12531600 2 3 24 72 1 36  ε_{1} 4.1269
60 −295 −708 12531600 2 8 4 32 1 16  ε_{1} 4.1269
177 −20 −3540 12531600 1 2 24 24 1 24  ε_{1} 23.4697
236 −15 −3540 12531600 1 2 24 24 1 24  ε_{1} 13.9320
885  −4 −3540 12531600 2 1 24 24 1 12  ε_{1} 10.9445
885 −20 −708 12531600 2 2 4  8 1  4  ε_{1} 10.9445
1180  −3 −3540 12531600 2 1 24 24 1 12  ε_{1} 30.4285
1180 −15 −708 12531600 2 2 4  8 1  4  ε_{1} 30.4285
1181  −3 −3543 12552849 1 1 18  9 1  9  ε_{1} 20.5528
8 −443 −3544 12559936 1 5 18 45 1 45  ε_{1} 1.7627
3544  −8 −443 12559936 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 58.0020
3548  −4 −887 12588304 1 1 29 29 2 29  \sqrt{i}\sqrt{ε_{1}} 13.7520
53 −67 −3551 12609601 1 1 58 29 1 29  ε_{1} 3.9314
209 −187 −323 12623809 1 2 4  4 1  4  ε_{1} 22.8829
3553 −11 −323 12623809 2 1 4  4 1  2  ε_{1} 84.8172
3553 −19 −187 12623809 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 42.4086
28 −127 −3556 12645136 1 5 16 40 1 40  ε_{1} 5.5373
508  −7 −3556 12645136 1 1 16  8 1  8  ε_{1} 32.1254
889  −4 −3556 12645136 1 1 16  8 1  8  ε_{1} 89.4446
5 −712 −3560 12673600 1 8 24 96 1 96  ε_{1} 0.9624
89 −40 −3560 12673600 1 2 24 24 1 24  ε_{1} 13.8155
445  −8 −3560 12673600 4 1 24 48 1 12  ε_{1} 6.0936
445 −40 −712 12673600 4 2 8 32 1  8  ε_{1} 6.0936
3561  −3 −1187 12680721 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 65.8075
509  −7 −3563 12694969 1 1 22 11 1 11  ε_{1} 13.6596
713 −115 −155 12709225 1 2 4  4 1  4  ε_{1} 32.3476
3565 −23 −155 12709225 2 3 4 12 1  6  ε_{1} 36.6050
3565 −31 −115 12709225 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 18.3025
29 −123 −3567 12723489 1 2 20 20 1 20  ε_{1} 3.2945
41 −87 −3567 12723489 1 6 20 60 1 60  ε_{1} 8.3183
1189  −3 −3567 12723489 2 1 20 20 1 10  ε_{1} 20.3076
1189 −87 −123 12723489 2 6 2 12 1  6  ε_{1} 20.3076
892  −8 −1784 12730624 3 1 32 96 2 32 \sqrt{−1}\sqrt{ε_{1}} 6.1048
1784  −4 −1784 12730624 1 1 32 32 2 32  \sqrt{i}\sqrt{ε_{1}} 19.2106
3569 −43  −83 12737761 3 1 3  9 2  3 \sqrt{−1}\sqrt{ε_{1}} 18.2582
76 −47 −3572 12759184 1 5 28 70 1 70  ε_{1} 11.6579
188 −19 −3572 12759184 1 1 28 14 1 14  ε_{1} 9.1285
893 −4 −3572 12759184 1 1 28 14 1 14 ε_{1} 15.4822
8 −447 −3576 12787776 1 14 28 196 1 196  ε_{1} 1.7627
24 −447 −1192 12787776 1 14 6 42 1 42  ε_{1} 4.5849
149 −24 −3576 12787776 1 2 28 28 1 28  ε_{1} 8.2223
1192 −3 −3576 12787776 2 1 28 28 1 14 ε_{1} 27.2320
1192 −24 −447 12787776 2 2 14 28 1 14  ε_{1} 27.2320
3576  −3 −1192 12787776 6 1 6 18 1  3  ε_{1} 12.7872

80 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3576  −8 −447 12787776 6 1 14 42 1  7  ε_{1} 12.7872
1193  −3 −3579 12809241 1 1 14  7 1  7  ε_{1} 42.5195
716 −20 −895 12816400 1 2 16 16 1 16  ε_{1} 31.8828
3580 −4 −895 12816400 6 1 16 48 1 8 ε_{1} 13.1529
3580 −20 −179 12816400 6 2 5 60 2 10 \sqrt{−1}\sqrt{ε_{1}} 6.5765
717 −15 −1195 12852225 1 2 8  8 1  8  ε_{1} 10.9696
3585  −3 −1195 12852225 10 1 8 40 1  4  ε_{1} 13.7297
3585 −15 −239 12852225 10 2 15 300 2 30 \sqrt{−1}\sqrt{ε_{1}} 6.8648
17 −211 −3587 12866569 1 3 22 33 1 33  ε_{1} 4.1894
12 −299 −3588 12873744 1 8 16 64 1 64  ε_{1} 2.6339
13 −276 −3588 12873744 1 8 16 64 1 64  ε_{1} 2.3895
69 −52 −3588 12873744 1 2 16 16 1 16  ε_{1} 6.4345
92 −39 −3588 12873744 1 4 16 32 1 32  ε_{1} 7.7415
156 −23 −3588 12873744 2 3 16 48 1 24  ε_{1} 7.8232
156 −276 −299 12873744 2 8 8 64 1 32  ε_{1} 7.8232
897  −4 −3588 12873744 4 1 16 32 1  8  ε_{1} 14.1768
897 −52 −276 12873744 4 2 8 32 1  8  ε_{1} 14.1768
1196  −3 −3588 12873744 2 1 16 16 1  8  ε_{1} 13.4428
1196 −39 −276 12873744 2 4 8 32 1 16  ε_{1} 13.4428
449 −8 −3592 12902464 1 1 12 6 1 6 ε_{1} 39.5058
5 −719 −3595 12924025 1 31 8 124 1 124  ε_{1} 0.9624
124 −116 −899 12931216 1 6 14 42 1 42  ε_{1} 16.0392
3596  −4 −899 12931216 6 1 14 42 1  7  ε_{1} 8.1881
3596 −31 −116 12931216 6 3 6 54 1  9  ε_{1} 8.1881
33 −327 −1199 12938409 1 12 38 228 1 228  ε_{1} 7.6563
3597  −3 −1199 12938409 2 1 38 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 8.4760
3597 −11 −327 12938409 2 1 12 12 1 6 ε_{1} 16.9519
61 −59 −3599 12952801 1 3 66 99 1 99  ε_{1} 7.3284
1201 −3 −3603 12981609 1 1 16 8 1 8 ε_{1} 109.1299
17 −212 −3604 12988816 1 6 24 72 1 72  ε_{1} 4.1894
53 −68 −3604 12988816 1 4 24 48 1 48  ε_{1} 3.9314
901 −4 −3604 12988816 4 1 24 48 1 12 ε_{1} 8.1892
901 −68 −212 12988816 4 4 6 48 1 12  ε_{1} 8.1892
721 −35 −515 12996025 1 2 6  6 1  6  ε_{1} 76.3136
3605  −7 −515 12996025 2 1 6  6 1  3  ε_{1} 15.9325
3605 −35 −103 12996025 2 2 5 10 1  5  ε_{1} 15.9325
8 −451 −3608 13017664 1 6 28 84 1 84  ε_{1} 1.7627
41 −88 −3608 13017664 1 2 28 28 1 28  ε_{1} 8.3183
88 −328 −451 13017664 1 4 6 12 1 12  ε_{1} 11.9527
328 −11 −3608 13017664 4 1 28 56 1 14  ε_{1} 5.7869
328 −88 −451 13017664 4 2 6 24 1  6  ε_{1} 5.7869
3608  −8 −451 13017664 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 7.4967
3608 −11 −328 13017664 2 1 4  4 1  2  ε_{1} 14.9933
157 −23 −3611 13039321 1 3 26 39 1 39  ε_{1} 10.7226
12 −903 −1204 13046544 1 16 8 64 1 64  ε_{1} 2.6339
21 −516 −1204 13046544 1 12 8 48 1 48  ε_{1} 3.1336
28 −516 −903 13046544 1 12 16 96 1 96  ε_{1} 5.5373
129 −84 −1204 13046544 1 4 8 16 1 16  ε_{1} 20.8511
172 −84 −903 13046544 1 4 16 32 1 32  ε_{1} 17.6970
301 −84 −516 13046544 1 4 12 24 1 24  ε_{1} 20.0642

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 81

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3612  −3 −1204 13046544 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.0917
3612  −4 −903 13046544 4 1 16 32 1  8  ε_{1} 14.1835
3612  −7 −516 13046544 4 1 12 24 1  6  ε_{1} 14.1835
3612 −43  −84 13046544 4 1 4  8 1  2  ε_{1} 14.1835
5 −723 −3615 13068225 1 4 48 96 1 96  ε_{1} 0.9624
241 −15 −3615 13068225 1 2 48 48 1 48  ε_{1} 37.5430
1205  −3 −3615 13068225 2 1 48 48 1 24  ε_{1} 10.9861
1205 −15 −723 13068225 2 2 4  8 1  4  ε_{1} 10.9861
77 −47 −3619 13097161 1 5 12 30 1 30  ε_{1} 4.3693
329 −11 −3619 13097161 1 1 12  6 1  6  ε_{1} 30.7485
517  −7 −3619 13097161 1 1 12  6 1  6  ε_{1} 18.5321
5 −724 −3620 13104400 1 10 24 120 1 120  ε_{1} 0.9624
181 −20 −3620 13104400 1 2 24 24 1 24  ε_{1} 14.3479
905 −4 −3620 13104400 4 1 24 48 1 12 ε_{1} 13.1640
905 −20 −724 13104400 4 2 10 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 6.5820
213 −51 −1207 13111641 1 2 18 18 1 18  ε_{1} 8.5805
3621  −3 −1207 13111641 2 1 18 18 1  9  ε_{1} 27.2951
3621 −51  −71 13111641 2 2 7 14 1  7  ε_{1} 27.2951
24 −151 −3624 13133376 1 7 28 98 1 98  ε_{1} 4.5849
453 −8 −3624 13133376 1 1 28 14 1 14 ε_{1} 10.0078
453 −24 −1208 13133376 1 2 12 12 1 12  ε_{1} 10.0078
1208  −3 −3624 13133376 1 1 28 14 1 14  ε_{1} 31.9236
3624  −3 −1208 13133376 6 1 12 36 1  6  ε_{1} 12.8005
3624 −24 −151 13133376 6 2 7 84 2 14 \sqrt{−1}\sqrt{ε_{1}} 6.4003
3628 −4 −907 13162384 1 1 3 3 2 3 \sqrt{i}\sqrt{ε_{1}} 46.9585
3629 −19 −191 13169641 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 16.9102
908  −8 −1816 13191424 1 1 14 14 2 14 \sqrt{−1}\sqrt{ε_{1}} 6.1137
1816 −4 −1816 13191424 1 1 14 14 2 14 \sqrt{i}\sqrt{ε_{1}} 38.0602
21 −519 −1211 13198689 1 18 14 126 1 126  ε_{1} 3.1336
3633  −3 −1211 13198689 2 1 14 14 1  7  ε_{1} 52.4307
3633  −7 −519 13198689 2 1 18 18 1  9  ε_{1} 52.4307
5 −727 −3635 13213225 1 13 10 65 1 65  ε_{1} 0.9624
1213 −3 −3639 13242321 1 1 60 30 1 30 ε_{1} 37.5314
5 −728 −3640 13249600 1 12 16 96 1 96  ε_{1} 0.9624
8 −455 −3640 13249600 1 20 16 160 1 160  ε_{1} 1.7627
13 −280 −3640 13249600 1 4 16 32 1 32  ε_{1} 2.3895
40 −91 −3640 13249600 2 2 16 32 1 16  ε_{1} 3.6369
40 −455 −728 13249600 2 20 12 240 1 120  ε_{1} 3.6369
56 −455 −520 13249600 1 20 4 40 1 40  ε_{1} 6.8002
65 −56 −3640 13249600 2 4 16 64 1 32  ε_{1} 5.5529
65 −280 −728 13249600 2 4 12 48 1 24  ε_{1} 5.5529
104 −35 −3640 13249600 2 2 16 32 1 16  ε_{1} 4.6249
104 −280 −455 13249600 2 4 20 80 1 40  ε_{1} 4.6249
280 −91 −520 13249600 2 2 4 8 1 4 ε_{1} 12.4372
280 −104 −455 13249600 2 6 20 120 1 60  ε_{1} 12.4372
520 −7 −3640 13249600 4 1 16 32 1 8 ε_{1} 9.4726
520 −35 −728 13249600 4 2 12 48 1 12  ε_{1} 9.4726
520 −56 −455 13249600 4 4 20 160 1 40  ε_{1} 9.4726
520 −91 −280 13249600 4 2 4 16 1  4  ε_{1} 9.4726
728 −35 −520 13249600 2 2 4  8 1  4  ε_{1} 7.9773

82 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
728 −40 −455 13249600 2 2 20 40 1 20  ε_{1} 7.9773
3640  −7 −520 13249600 8 1 4 16 1  2  ε_{1} 11.7833
3640  −8 −455 13249600 8 1 20 80 1 10  ε_{1} 11.7833
3640 −35 −104 13249600 8 2 6 48 1  6  ε_{1} 11.7833
3640 −40  −91 13249600 8 2 2 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.8916
3641 −11 −331 13256881 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 63.0703
3644  −4 −911 13278736 1 1 31 31 2 31  \sqrt{i}\sqrt{ε_{1}} 34.2426
521  −7 −3647 13300609 1 1 54 27 1 27  ε_{1} 38.7273
1217  −3 −3651 13329801 1 1 18  9 1  9  ε_{1} 35.6550
44 −83 −3652 13337104 1 3 12 18 1 18  ε_{1} 5.9864
332 −11 −3652 13337104 1 1 12  6 1  6  ε_{1} 10.1997
913  −4 −3652 13337104 1 1 12  6 1  6  ε_{1} 69.1395
5 −731 −3655 13359025 1 12 20 120 1 120  ε_{1} 0.9624
17 −215 −3655 13359025 1 14 20 140 1 140  ε_{1} 4.1894
85 −43 −3655 13359025 2 1 20 20 1 10  ε_{1} 4.4187
85 −215 −731 13359025 2 14 12 168 1 84  ε_{1} 4.4187
457 −8 −3656 13366336 1 1 36 18 1 18 ε_{1} 50.9909
69 −159 −1219 13373649 1 10 6 30 1 30  ε_{1} 6.4345
3657 −3 −1219 13373649 2 1 6 6 1 3 ε_{1} 54.6466
3657 −23 −159 13373649 2 3 10 30 1 15  ε_{1} 54.6466
12 −915 −1220 13395600 1 8 16 64 1 64  ε_{1} 2.6339
60 −183 −1220 13395600 2 8 16 128 1 64  ε_{1} 4.1269
60 −244 −915 13395600 2 6 8 48 1 24  ε_{1} 4.1269
732 −15 −1220 13395600 2 2 16 32 1 16  ε_{1} 13.7628
732 −20 −915 13395600 2 2 8 16 1  8  ε_{1} 13.7628
3660  −3 −1220 13395600 4 1 16 32 1  8  ε_{1} 10.9778
3660  −4 −915 13395600 4 1 8 16 1  4  ε_{1} 10.9778
3660 −15 −244 13395600 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.4889
3660 −20 −183 13395600 4 2 8 32 1  8  ε_{1} 10.9778
3661  −7 −523 13402921 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 37.3968
8 −916 −1832 13424896 1 10 26 130 1 130  ε_{1} 1.7627
1832  −4 −1832 13424896 2 1 26 26 1 13  ε_{1} 10.7320
1832  −8 −916 13424896 2 1 10 10 1  5  ε_{1} 10.7320
193 −19 −3667 13446889 1 1 10  5 1  5  ε_{1} 30.1526
28 −131 −3668 13454224 1 5 20 50 1 50  ε_{1} 5.5373
524  −7 −3668 13454224 1 1 20 10 1 10  ε_{1} 19.9254
917  −4 −3668 13454224 1 1 20 10 1 10  ε_{1} 14.1482
3669  −3 −1223 13461561 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 27.6825
3676 −4 −919 13512976 1 1 19 19 2 19 \sqrt{i}\sqrt{ε_{1}} 64.3629
13 −283 −3679 13535041 1 3 32 48 1 48  ε_{1} 2.3895
29 −127 −3683 13564489 1 5 10 25 1 25  ε_{1} 3.2945
12 −307 −3684 13571856 1 3 20 30 1 30  ε_{1} 2.6339
921  −4 −3684 13571856 1 1 20 10 1 10  ε_{1} 72.3140
1228  −3 −3684 13571856 1 1 20 10 1 10  ε_{1} 37.9840
737 −55 −335 13579225 1 4 18 36 1 36  ε_{1} 40.0839
3685 −11 −335 13579225 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 12.4058
3685 −55  −67 13579225 2 4 1  4 1  2  ε_{1} 24.8116
1229  −3 −3687 13593969 3 1 42 63 1 21  ε_{1} 7.1123
461  −8 −3688 13601344 1 1 18  9 1  9  ε_{1} 11.7998
217 −119 −527 13608721 1 10 18 90 1 90  ε_{1} 31.7104

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 83

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3689  −7 −527 13608721 2 1 18 18 1  9  ε_{1} 63.7451
3689 −31 −119 13608721 2 3 10 30 1 15  ε_{1} 63.7451
284 −52 −923 13630864 1 2 10 10 1 10  ε_{1} 17.6959
3692  −4 −923 13630864 2 1 10 10 1  5  ε_{1} 14.3030
3692 −52  −71 13630864 2 2 7 14 1  7  ε_{1} 14.3030
3693  −3 −1231 13638249 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 23.2902
5 −739 −3695 13653025 1 5 72 180 1 180  ε_{1} 0.9624
12 −616 −1848 13660416 1 8 8 32 1 32  ε_{1} 2.6339
24 −308 −1848 13660416 1 8 8 32 1 32  ε_{1} 4.5849
28 −264 −1848 13660416 1 8 8 32 1 32  ε_{1} 5.5373
44 −168 −1848 13660416 1 4 8 16 1 16  ε_{1} 5.9864
56 −132 −1848 13660416 1 4 8 16 1 16  ε_{1} 6.8002
88 −84 −1848 13660416 1 4 8 16 1 16  ε_{1} 11.9527
168 −132 −616 13660416 2 4 8 32 1 16  ε_{1} 6.5132
168 −264 −308 13660416 2 8 8 64 1 32  ε_{1} 6.5132
264 −84 −616 13660416 2 4 8 32 1 16  ε_{1} 9.7350
264 −168 −308 13660416 2 4 8 32 1 16  ε_{1} 9.7350
616 −84 −264 13660416 2 4 8 32 1 16  ε_{1} 21.3187
616 −132 −168 13660416 2 4 4 16 1  8  ε_{1} 21.3187
924  −8 −1848 13660416 4 1 8 16 1  4  ε_{1} 10.0477
924 −24 −616 13660416 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.0238
924 −56 −264 13660416 4 4 8 64 1 16  ε_{1} 10.0477
924 −88 −168 13660416 4 2 4 16 1  4  ε_{1} 10.0477
1848  −4 −1848 13660416 4 1 8 16 1  4  ε_{1} 8.9084
1848 −24 −308 13660416 4 2 8 32 1  8  ε_{1} 8.9084
1848 −56 −132 13660416 4 4 4 32 1  8  ε_{1} 8.9084
1848 −84  −88 13660416 4 4 2 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.4542
8 −463 −3704 13719616 1 7 40 140 1 140  ε_{1} 1.7627
3704 −8 −463 13719616 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 34.0430
57 −195 −1235 13727025 1 4 12 24 1 24  ε_{1} 11.4208
285 −39 −1235 13727025 2 4 12 48 1 24  ε_{1} 5.6595
285 −195 −247 13727025 2 4 6 24 1 12  ε_{1} 5.6595
741 −15 −1235 13727025 2 2 12 24 1 12  ε_{1} 11.0025
741 −95 −195 13727025 2 8 4 32 1 16  ε_{1} 11.0025
3705  −3 −1235 13727025 4 1 12 24 1  6  ε_{1} 38.6931
3705 −15 −247 13727025 4 2 6 24 1  6  ε_{1} 38.6931
3705 −19 −195 13727025 4 1 4  8 1  2  ε_{1} 38.6931
3705 −39  −95 13727025 4 4 8 128 2 32 \sqrt{−1}\sqrt{ε_{1}} 19.3465
337 −11 −3707 13741849 1 1 14  7 1  7  ε_{1} 42.8642
1237  −3 −3711 13771521 1 1 36 18 1 18  ε_{1} 28.1466
3713 −47  −79 13786369 1 5 5 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 24.6297
5 −743 −3715 13801225 1 21 14 147 1 147  ε_{1} 0.9624
929 −4 −3716 13808656 1 1 36 18 1 18 ε_{1} 51.6295
5 −744 −3720 13838400 1 12 24 144 1 144  ε_{1} 0.9624
24 −155 −3720 13838400 1 4 24 48 1 48  ε_{1} 4.5849
93 −40 −3720 13838400 1 2 24 24 1 24  ε_{1} 6.7322
93 −120 −1240 13838400 1 4 8 16 1 16  ε_{1} 6.7322
120 −31 −3720 13838400 2 3 24 72 1 36  ε_{1} 6.1779
120 −155 −744 13838400 2 4 12 48 1 24  ε_{1} 6.1779
248 −15 −3720 13838400 1 2 24 24 1 24  ε_{1} 9.6724

84 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
465  −8 −3720 13838400 2 1 24 24 1 12  ε_{1} 20.7308
465 −24 −1240 13838400 2 2 8 16 1  8  ε_{1} 20.7308
465 −40 −744 13838400 2 2 12 24 1 12  ε_{1} 20.7308
465 −120 −248 13838400 2 4 8 32 1 16  ε_{1} 20.7308
744 −15 −1240 13838400 2 2 8 16 1  8  ε_{1} 19.2319
744 −120 −155 13838400 2 4 4 16 1  8  ε_{1} 19.2319
1240  −3 −3720 13838400 2 1 24 24 1 12  ε_{1} 28.6893
1240 −15 −744 13838400 2 2 12 24 1 12  ε_{1} 28.6893
3720  −3 −1240 13838400 4 1 8 16 1  4  ε_{1} 9.6079
3720 −15 −248 13838400 4 2 8 32 1  8  ε_{1} 9.6079
3720 −24 −155 13838400 4 2 4 16 1  4  ε_{1} 9.6079
3720 −31 −120 13838400 4 3 4 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 4.8040
17 −219 −3723 13860729 1 4 12 24 1 24  ε_{1} 4.1894
73 −51 −3723 13860729 1 2 12 12 1 12  ε_{1} 15.3334
1241  −3 −3723 13860729 2 1 12 12 1  6  ε_{1} 36.0697
1241 −51 −219 13860729 2 2 4  8 1  4  ε_{1} 36.0697
8 −932 −1864 13897984 1 12 8 48 1 48  ε_{1} 1.7627
1864 −4 −1864 13897984 2 1 8 16 2 8 \sqrt{i}\sqrt{ε_{1}} 21.3527
1864  −8 −932 13897984 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 21.3527
33 −339 −1243 13905441 1 6 4 12 1 12  ε_{1} 7.6563
3729 −3 −1243 13905441 2 1 4 4 1 2 ε_{1} 66.1405
3729 −11 −339 13905441 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 33.0702
13 −287 −3731 13920361 1 14 28 196 1 196  ε_{1} 2.3895
41 −91 −3731 13920361 1 2 28 28 1 28  ε_{1} 8.3183
533 −7 −3731 13920361 2 1 28 28 1 14 ε_{1} 6.2748
533 −91 −287 13920361 2 2 14 28 1 14  ε_{1} 6.2748
12 −311 −3732 13927824 1 19 16 152 1 152  ε_{1} 2.6339
933  −4 −3732 13927824 1 1 16  8 1  8  ε_{1} 23.8438
1244  −3 −3732 13927824 1 1 16  8 1  8  ε_{1} 34.6700
8 −467 −3736 13957696 1 7 26 91 1 91  ε_{1} 1.7627
3736 −8 −467 13957696 3 1 7 21 2 7 \sqrt{−1}\sqrt{ε_{1}} 15.6187
44 −340 −935 13987600 1 4 28 56 1 56  ε_{1} 5.9864
220 −68 −935 13987600 2 4 28 112 1 56  ε_{1} 10.3635
220 −187 −340 13987600 2 2 4 8 1 4 ε_{1} 10.3635
748 −20 −935 13987600 2 2 28 56 1 28  ε_{1} 16.2418
748 −55 −340 13987600 2 4 4 16 1  8  ε_{1} 16.2418
3740  −4 −935 13987600 4 1 28 56 1 14  ε_{1} 15.8402
3740 −11 −340 13987600 4 1 4  8 1  2  ε_{1} 15.8402
3740 −20 −187 13987600 4 2 2  8 1  2  ε_{1} 15.8402
3740 −55  −68 13987600 4 4 4 32 1  8  ε_{1} 15.8402
129 −87 −1247 13995081 1 6 26 78 1 78  ε_{1} 20.8511
3741  −3 −1247 13995081 2 1 26 26 1 13  ε_{1} 28.5215
3741 −43  −87 13995081 2 1 6  6 1  3  ε_{1} 28.5215
197 −19 −3743 14010049 1 1 56 28 1 28  ε_{1} 6.6670
749 −35 −535 14025025 1 2 14 14 1 14  ε_{1} 18.9369
3745  −7 −535 14025025 2 1 14 14 1  7  ε_{1} 93.4672
3745 −35 −107 14025025 2 2 3  6 1  3  ε_{1} 93.4672
1249  −3 −3747 14040009 1 1 12  6 1  6  ε_{1} 102.5410
937  −4 −3748 14047504 1 1 20 10 1 10  ε_{1} 69.0381
3749 −23 −163 14055001 1 3 1  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 24.5392

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 85

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
56 −67 −3752 14077504 1 1 16  8 1  8  ε_{1} 6.8002
469  −8 −3752 14077504 3 1 16 24 1  8  ε_{1} 8.3483
469 −56 −536 14077504 3 4 14 84 1 28  ε_{1} 8.3483
536 −7 −3752 14077504 1 1 16 8 1 8 ε_{1} 25.1680
3752  −7 −536 14077504 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.4430
3752 −56 −67 14077504 2 4 1 4 1 2 ε_{1} 20.8859
5 −751 −3755 14100025 1 15 20 150 1 150  ε_{1} 0.9624
12 −939 −1252 14107536 1 8 8 32 1 32  ε_{1} 2.6339
3756  −3 −1252 14107536 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 12.4106
3756  −4 −939 14107536 4 1 8 16 1  4  ε_{1} 24.8212
21 −179 −3759 14130081 1 5 52 130 1 130  ε_{1} 3.1336
537  −7 −3759 14130081 1 1 52 26 1 26  ε_{1} 39.5359
1253  −3 −3759 14130081 1 1 52 26 1 26  ε_{1} 10.3522
188 −40 −1880 14137600 1 2 20 20 1 20  ε_{1} 9.1285
376 −20 −1880 14137600 1 2 20 20 1 20  ε_{1} 30.5420
940 −8 −1880 14137600 6 1 20 60 1 10 ε_{1} 9.0433
940 −40 −376 14137600 6 2 8 96 2 16 \sqrt{−1}\sqrt{ε_{1}} 4.5217
1880 −4 −1880 14137600 2 1 20 20 1 10 ε_{1} 16.2524
1880 −20 −376 14137600 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 8.1262
53 −71 −3763 14160169 1 7 6 21 1 21  ε_{1} 3.9314
941 −4 −3764 14167696 1 1 46 23 1 23 ε_{1} 14.0688
753 −15 −1255 14175225 1 2 12 12 1 12  ε_{1} 54.2964
3765 −3 −1255 14175225 2 1 12 12 1 6 ε_{1} 20.6426
3765 −15 −251 14175225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.3213
8 −471 −3768 14197824 1 16 12 96 1 96  ε_{1} 1.7627
24 −471 −1256 14197824 1 16 26 208 1 208  ε_{1} 4.5849
157 −24 −3768 14197824 1 2 12 12 1 12  ε_{1} 10.7226
1256 −3 −3768 14197824 2 1 12 12 1 6 ε_{1} 13.5734
1256 −24 −471 14197824 2 2 16 32 1 16  ε_{1} 13.5734
3768  −3 −1256 14197824 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 12.2656
3768 −8 −471 14197824 2 1 16 16 1 8 ε_{1} 24.5312
92 −164 −943 14227984 1 8 16 64 1 64  ε_{1} 7.7415
3772 −4 −943 14227984 4 1 16 32 1 8 ε_{1} 14.5915
3772 −23 −164 14227984 4 3 8 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 7.2957
3777  −3 −1259 14265729 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 58.6129
3781 −19 −199 14295961 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 38.6077
13 −291 −3783 14311089 1 4 48 96 1 96  ε_{1} 2.3895
97 −39 −3783 14311089 1 4 48 96 1 96  ε_{1} 18.6488
1261  −3 −3783 14311089 2 1 48 48 1 24  ε_{1} 22.5547
1261 −39 −291 14311089 2 4 4 16 1  8  ε_{1} 22.5547
88 −43 −3784 14318656 1 1 16  8 1  8  ε_{1} 11.9527
344 −11 −3784 14318656 1 1 16  8 1  8  ε_{1} 19.8864
473  −8 −3784 14318656 3 1 16 24 1  8  ε_{1} 10.3180
473 −88 −344 14318656 3 2 10 30 1 10  ε_{1} 10.3180
3784 −11 −344 14318656 2 1 10 10 1  5  ε_{1} 64.2717
3784 −43  −88 14318656 2 1 2  2 1  1  ε_{1} 64.2717
541  −7 −3787 14341369 1 1 8  4 1  4  ε_{1} 28.2989
3788  −4 −947 14348944 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 24.0198
17 −223 −3791 14371681 1 7 68 238 1 238  ε_{1} 4.1894
8 −948 −1896 14379264 1 12 20 120 1 120  ε_{1} 1.7627

86 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −632 −1896 14379264 1 8 20 80 1 80  ε_{1} 2.6339
24 −632 −948 14379264 1 8 12 48 1 48  ε_{1} 4.5849
316 −24 −1896 14379264 3 2 20 60 1 20  ε_{1} 10.1503
632 −24 −948 14379264 1 2 12 12 1 12  ε_{1} 19.2954
1896  −4 −1896 14379264 2 1 20 20 1 10  ε_{1} 25.7329
1896  −8 −948 14379264 2 1 12 12 1  6  ε_{1} 25.7329
5 −759 −3795 14402025 1 24 16 192 1 192  ε_{1} 0.9624
33 −115 −3795 14402025 1 2 16 16 1 16  ε_{1} 7.6563
69 −55 −3795 14402025 1 4 16 32 1 32  ε_{1} 6.4345
165 −23 −3795 14402025 2 3 16 48 1 24  ε_{1} 5.1180
165 −115 −759 14402025 2 2 24 48 1 24  ε_{1} 5.1180
253 −15 −3795 14402025 1 2 16 16 1 16  ε_{1} 15.0577
345 −11 −3795 14402025 2 1 16 16 1 8 ε_{1} 19.0241
345 −55 −759 14402025 2 4 24 96 1 48  ε_{1} 19.0241
1265 −3 −3795 14402025 2 1 16 16 1 8 ε_{1} 25.8672
1265 −15 −759 14402025 2 2 24 48 1 24  ε_{1} 25.8672
13 −292 −3796 14409616 1 4 12 24 1 24  ε_{1} 2.3895
73 −52 −3796 14409616 1 2 12 12 1 12  ε_{1} 15.3334
949  −4 −3796 14409616 2 1 12 12 1  6  ε_{1} 20.7893
949 −52 −292 14409616 2 2 4  8 1  4  ε_{1} 20.7893
29 −131 −3799 14432401 1 5 46 115 1 115  ε_{1} 3.2945
21 −543 −1267 14447601 1 12 6 36 1 36  ε_{1} 3.1336
3801  −3 −1267 14447601 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 35.2774
3801  −7 −543 14447601 2 1 12 12 1  6  ε_{1} 70.5548
12 −951 −1268 14470416 1 26 10 130 1 130  ε_{1} 2.6339
3804  −3 −1268 14470416 2 1 10 10 1  5  ε_{1} 39.8425
3804  −4 −951 14470416 2 1 26 26 1 13  ε_{1} 39.8425
37 −103 −3811 14523721 1 5 10 25 1 25  ε_{1} 4.9836
953 −4 −3812 14531344 1 1 32 16 1 16 ε_{1} 44.8537
93 −123 −1271 14538969 1 2 40 40 1 40  ε_{1} 6.7322
3813 −3 −1271 14538969 2 1 40 40 1 20 ε_{1} 12.4051
3813 −31 −123 14538969 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.2025
5 −763 −3815 14554225 1 4 56 112 1 112  ε_{1} 0.9624
109 −35 −3815 14554225 1 2 56 56 1 56  ε_{1} 11.1291
545  −7 −3815 14554225 2 1 56 56 1 28  ε_{1} 16.5487
545 −35 −763 14554225 2 2 4  8 1  4  ε_{1} 16.5487
3817 −11 −347 14569489 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 85.1723
57 −67 −3819 14584761 1 1 16  8 1  8  ε_{1} 11.4208
201 −19 −3819 14584761 1 1 16  8 1  8  ε_{1} 27.6905
1273  −3 −3819 14584761 1 1 16  8 1  8  ε_{1} 80.8877
764 −20 −955 14592400 1 2 4  4 1  4  ε_{1} 33.4104
3820  −4 −955 14592400 2 1 4  4 1  2  ε_{1} 44.3122
3820 −20 −191 14592400 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 22.1561
956  −8 −1912 14622976 1 1 8  8 2  8 \sqrt{−1}\sqrt{ε_{1}} 16.3324
1912  −4 −1912 14622976 1 1 8  8 2  8  \sqrt{i}\sqrt{ε_{1}} 35.7127
89 −43 −3827 14645929 1 1 22 11 1 11  ε_{1} 13.8155
12 −319 −3828 14653584 1 10 16 80 1 80  ε_{1} 2.6339
29 −132 −3828 14653584 1 4 16 32 1 32  ε_{1} 3.2945
33 −116 −3828 14653584 1 6 16 48 1 48  ε_{1} 7.6563
44 −87 −3828 14653584 1 6 16 48 1 48  ε_{1} 5.9864

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 87

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
348 −11 −3828 14653584 2 1 16 16 1  8  ε_{1} 8.0501
348 −132 −319 14653584 2 4 10 40 1 20  ε_{1} 8.0501
957 −4 −3828 14653584 2 1 16 16 1 8 ε_{1} 6.8659
957 −116 −132 14653584 2 6 4 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 3.4329
1276 −3 −3828 14653584 2 1 16 16 1 8 ε_{1} 34.1320
1276 −87 −132 14653584 2 6 4 24 1 12  ε_{1} 34.1320
3829  −7 −547 14661241 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 39.8711
1277  −3 −3831 14676561 1 1 42 21 1 21  ε_{1} 17.5930
8 −479 −3832 14684224 1 25 16 200 1 200  ε_{1} 1.7627
3832  −8 −479 14684224 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 38.0511
5 −767 −3835 14707225 1 22 12 132 1 132  ε_{1} 0.9624
13 −295 −3835 14707225 1 8 12 48 1 48  ε_{1} 2.3895
65 −59 −3835 14707225 2 3 12 36 1 18  ε_{1} 5.5529
65 −295 −767 14707225 2 8 22 176 1 88  ε_{1} 5.5529
28 −548 −959 14714896 1 8 36 144 1 144  ε_{1} 5.5373
3836  −4 −959 14714896 4 1 36 144 2 36  \sqrt{i}\sqrt{ε_{1}} 7.5601
3836  −7 −548 14714896 4 1 8 16 1  4  ε_{1} 15.1202
3837  −3 −1279 14722569 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 18.5681
349 −11 −3839 14737921 1 1 82 41 1 41  ε_{1} 19.6424
3841 −23 −167 14753281 1 3 11 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 91.1269
13 −296 −3848 14807104 1 10 28 140 1 140  ε_{1} 2.3895
37 −104 −3848 14807104 1 6 28 84 1 84  ε_{1} 4.9836
481 −8 −3848 14807104 2 1 28 28 1 14 ε_{1} 28.9443
481 −104 −296 14807104 2 6 10 60 1 30  ε_{1} 28.9443
3849  −3 −1283 14814801 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 69.2808
5 −771 −3855 14861025 1 6 44 132 1 132  ε_{1} 0.9624
257 −15 −3855 14861025 3 2 44 132 1 44  ε_{1} 6.9334
1285  −3 −3855 14861025 2 1 44 44 1 22  ε_{1} 20.3309
1285 −15 −771 14861025 2 2 6 12 1  6  ε_{1} 20.3309
8 −964 −1928 14868736 1 12 20 120 1 120  ε_{1} 1.7627
1928 −4 −1928 14868736 2 1 20 40 2 20 \sqrt{i}\sqrt{ε_{1}} 6.8732
1928  −8 −964 14868736 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.8732
133 −203 −551 14876449 1 4 26 52 1 52  ε_{1} 10.3065
3857  −7 −551 14876449 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 21.1191
3857 −19 −203 14876449 2 1 4 4 1 2 ε_{1} 42.2382
17 −227 −3859 14891881 1 5 10 25 1 25  ε_{1} 4.1894
5 −772 −3860 14899600 1 4 44 88 1 88  ε_{1} 0.9624
193 −20 −3860 14899600 1 2 44 44 1 44  ε_{1} 30.1526
965  −4 −3860 14899600 2 1 44 44 1 22  ε_{1} 6.8701
965 −20 −772 14899600 2 2 4  8 1  4  ε_{1} 6.8701
8 −483 −3864 14930496 1 4 24 48 1 48  ε_{1} 1.7627
21 −184 −3864 14930496 1 4 24 48 1 48  ε_{1} 3.1336
21 −552 −1288 14930496 1 8 8 32 1 32  ε_{1} 3.1336
24 −483 −1288 14930496 1 4 8 16 1 16  ε_{1} 4.5849
56 −483 −552 14930496 1 4 8 16 1 16  ε_{1} 6.8002
69 −56 −3864 14930496 1 4 24 48 1 48  ε_{1} 6.4345
69 −168 −1288 14930496 1 4 8 16 1 16  ε_{1} 6.4345
161 −24 −3864 14930496 1 2 24 24 1 24  ε_{1} 20.1338
161 −168 −552 14930496 1 4 8 16 1 16  ε_{1} 20.1338
168 −23 −3864 14930496 2 3 24 72 1 36  ε_{1} 6.5132

88 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
168 −184 −483 14930496 2 4 4 16 1  8  ε_{1} 6.5132
184 −168 −483 14930496 1 4 4  8 1  8  ε_{1} 21.5856
552  −7 −3864 14930496 2 1 24 24 1 12  ε_{1} 9.0864
552 −56 −483 14930496 2 4 4 16 1  8  ε_{1} 9.0864
1288  −3 −3864 14930496 4 1 24 48 1 12  ε_{1} 12.9416
1288 −24 −483 14930496 4 2 4 16 1  4  ε_{1} 12.9416
3864  −3 −1288 14930496 4 1 8 16 1  4  ε_{1} 23.3053
3864  −7 −552 14930496 4 1 8 16 1  4  ε_{1} 23.3053
3864  −8 −483 14930496 4 1 4  8 1  2  ε_{1} 23.3053
3864 −23 −168 14930496 4 3 4 24 1  6  ε_{1} 23.3053
1289  −3 −3867 14953689 1 1 14  7 1  7  ε_{1} 68.0567
3868  −4 −967 14961424 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 43.6764
3873  −3 −1291 15000129 3 1 9 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 22.9770
12 −323 −3876 15023376 1 4 24 48 1 48  ε_{1} 2.6339
17 −228 −3876 15023376 1 4 24 48 1 48  ε_{1} 4.1894
57 −68 −3876 15023376 1 4 24 48 1 48  ε_{1} 11.4208
76 −51 −3876 15023376 1 2 24 24 1 24  ε_{1} 11.6579
204 −19 −3876 15023376 2 1 24 24 1 12  ε_{1} 9.2101
204 −228 −323 15023376 2 4 4 16 1  8  ε_{1} 9.2101
969  −4 −3876 15023376 2 1 24 24 1 12  ε_{1} 34.2358
969 −68 −228 15023376 2 4 4 16 1  8  ε_{1} 34.2358
1292  −3 −3876 15023376 4 1 24 48 1 12  ε_{1} 7.1655
1292 −51 −228 15023376 4 2 4 16 1  4  ε_{1} 7.1655
5 −776 −3880 15054400 1 20 12 120 1 120  ε_{1} 0.9624
97 −40 −3880 15054400 1 2 12 12 1 12  ε_{1} 18.6488
485 −8 −3880 15054400 2 1 12 12 1 6 ε_{1} 7.5694
485 −40 −776 15054400 2 2 20 40 1 20  ε_{1} 7.5694
353 −11 −3883 15077689 1 1 8  4 1  4  ε_{1} 23.7346
3884  −4 −971 15085456 1 1 15 15 2 15  \sqrt{i}\sqrt{ε_{1}} 30.8483
21 −555 −1295 15093225 1 4 36 72 1 72  ε_{1} 3.1336
105 −111 −1295 15093225 2 8 36 288 1 144  ε_{1} 8.8131
105 −259 −555 15093225 2 4 4 16 1 8 ε_{1} 8.8131
777 −15 −1295 15093225 4 2 36 144 1 36  ε_{1} 12.2006
777 −35 −555 15093225 4 2 4 16 1  4  ε_{1} 12.2006
3885  −3 −1295 15093225 4 1 36 72 1 18  ε_{1} 10.4622
3885  −7 −555 15093225 4 1 4  8 1  2  ε_{1} 10.4622
3885 −15 −259 15093225 4 2 4 16 1  4  ε_{1} 10.4622
3885 −35 −111 15093225 4 2 8 32 1  8  ε_{1} 10.4622
1297  −3 −3891 15139881 11 1 24 132 1 12  ε_{1} 8.5537
28 −139 −3892 15147664 1 3 12 18 1 18  ε_{1} 5.5373
556  −7 −3892 15147664 1 1 12  6 1  6  ε_{1} 37.7195
973  −4 −3892 15147664 1 1 12  6 1  6  ε_{1} 28.8137
5 −779 −3895 15171025 1 10 32 160 1 160  ε_{1} 0.9624
41 −95 −3895 15171025 1 8 32 128 1 128  ε_{1} 8.3183
205 −19 −3895 15171025 2 1 32 32 1 16  ε_{1} 7.5213
205 −95 −779 15171025 2 8 10 80 1 40  ε_{1} 7.5213
8 −487 −3896 15178816 1 7 36 126 1 126  ε_{1} 1.7627
3896  −8 −487 15178816 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 34.5162
557  −7 −3899 15202201 1 1 24 12 1 12  ε_{1} 10.9277
3901 −47  −83 15217801 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 44.5631

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 89

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1301  −3 −3903 15233409 1 1 26 13 1 13  ε_{1} 25.9645
781 −55 −355 15249025 1 4 4  8 1  8  ε_{1} 37.4447
3905 −11 −355 15249025 4 1 4  8 1  2  ε_{1} 18.8666
3905 −55  −71 15249025 4 4 7 56 1 14  ε_{1} 18.8666
977  −4 −3908 15272464 1 1 20 10 1 10  ε_{1} 46.8295
3909  −3 −1303 15280281 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 26.8891
24 −163 −3912 15303744 1 1 24 12 1 12  ε_{1} 4.5849
489 −8 −3912 15303744 1 1 24 12 1 12 ε_{1} 46.8872
489 −24 −1304 15303744 1 2 22 22 1 22  ε_{1} 46.8872
1304  −3 −3912 15303744 3 1 24 36 1 12  ε_{1} 12.9539
3912  −3 −1304 15303744 2 1 22 22 1 11  ε_{1} 24.7489
3912 −24 −163 15303744 2 2 1  2 1  1  ε_{1} 24.7489
301 −91 −559 15311569 1 2 16 16 1 16  ε_{1} 20.0642
3913  −7 −559 15311569 2 1 16 16 1  8  ε_{1} 73.0611
3913 −43  −91 15311569 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 36.5305
44 −356 −979 15335056 1 12 8 48 1 48  ε_{1} 5.9864
3916 −4 −979 15335056 4 1 8 16 1 4 ε_{1} 26.9765
3916 −11 −356 15335056 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 13.4883
3921  −3 −1307 15374241 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 85.1687
17 −231 −3927 15421329 1 12 40 240 1 240  ε_{1} 4.1894
21 −187 −3927 15421329 1 2 40 40 1 40  ε_{1} 3.1336
33 −119 −3927 15421329 1 10 40 200 1 200  ε_{1} 7.6563
77 −51 −3927 15421329 1 2 40 40 1 40  ε_{1} 4.3693
357 −11 −3927 15421329 2 1 40 40 1 20  ε_{1} 5.8833
357 −187 −231 15421329 2 2 12 24 1 12  ε_{1} 5.8833
561 −7 −3927 15421329 2 1 40 40 1 20 ε_{1} 27.7201
561 −119 −231 15421329 2 10 12 120 1 60  ε_{1} 27.7201
1309 −3 −3927 15421329 2 1 40 40 1 20 ε_{1} 23.3418
1309 −51 −231 15421329 2 2 12 24 1 12  ε_{1} 23.3418
8 −491 −3928 15429184 1 9 10 45 1 45  ε_{1} 1.7627
3928  −8 −491 15429184 5 1 9 45 2  9 \sqrt{−1}\sqrt{ε_{1}} 9.7798
3932  −4 −983 15460624 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 13.2502
5 −787 −3935 15484225 1 5 66 165 1 165  ε_{1} 0.9624
3937 −31 −127 15499969 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 65.0659
13 −303 −3939 15515721 1 10 16 80 1 80  ε_{1} 2.3895
101 −39 −3939 15515721 1 4 16 32 1 32  ε_{1} 5.9964
1313 −3 −3939 15515721 4 1 16 32 1 8 ε_{1} 14.2328
1313 −39 −303 15515721 4 4 10 80 1 20  ε_{1} 14.2328
5 −788 −3940 15523600 1 10 24 120 1 120  ε_{1} 0.9624
197 −20 −3940 15523600 1 2 24 24 1 24  ε_{1} 6.6670
985 −4 −3940 15523600 6 1 24 72 1 12 ε_{1} 13.4088
985 −20 −788 15523600 6 2 10 60 1 10  ε_{1} 13.4088
3941 −7 −563 15531481 3 1 9 27 2 9 \sqrt{−1}\sqrt{ε_{1}} 6.3368
17 −232 −3944 15555136 1 2 44 44 1 44  ε_{1} 4.1894
29 −136 −3944 15555136 1 4 44 88 1 88  ε_{1} 3.2945
493  −8 −3944 15555136 2 1 44 44 1 22  ε_{1} 9.4192
493 −136 −232 15555136 2 4 2  8 1  4  ε_{1} 9.4192
789 −15 −1315 15563025 1 2 6  6 1  6  ε_{1} 20.7360
3945  −3 −1315 15563025 2 1 6  6 1  3  ε_{1} 68.5161
3945 −15 −263 15563025 2 2 13 26 1 13  ε_{1} 68.5161

90 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −987 −1316 15586704 1 8 24 96 1 96  ε_{1} 2.6339
21 −564 −1316 15586704 1 8 24 96 1 96  ε_{1} 3.1336
28 −564 −987 15586704 1 8 8 32 1 32  ε_{1} 5.5373
141 −84 −1316 15586704 1 4 24 48 1 48  ε_{1} 10.4940
188 −84 −987 15586704 1 4 8 16 1 16  ε_{1} 9.1285
329 −84 −564 15586704 1 4 8 16 1 16  ε_{1} 30.7485
3948  −3 −1316 15586704 4 1 24 48 1 12  ε_{1} 13.2508
3948  −4 −987 15586704 4 1 8 16 1  4  ε_{1} 13.2508
3948  −7 −564 15586704 4 1 8 16 1  4  ε_{1} 13.2508
3948 −47  −84 15586704 4 5 4 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 6.6254
3949 −11 −359 15594601 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 47.1241
76 −104 −1976 15618304 1 6 28 84 1 84  ε_{1} 11.6579
152 −52 −1976 15618304 1 2 28 28 1 28  ε_{1} 8.6078
988 −8 −1976 15618304 2 1 28 28 1 14 ε_{1} 24.0940
988 −104 −152 15618304 2 6 6 72 2 36 \sqrt{−1}\sqrt{ε_{1}} 12.0470
1976 −4 −1976 15618304 2 1 28 28 1 14 ε_{1} 23.7837
1976 −52 −152 15618304 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 11.8918
3953 −59 −67 15626209 1 3 1 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 44.2592
5 −791 −3955 15642025 1 32 12 192 1 192  ε_{1} 0.9624
113 −35 −3955 15642025 1 2 12 12 1 12  ε_{1} 14.6946
565 −7 −3955 15642025 2 1 12 12 1 6 ε_{1} 11.4667
565 −35 −791 15642025 2 2 32 64 1 32  ε_{1} 11.4667
92 −43 −3956 15649936 1 1 36 18 1 18  ε_{1} 7.7415
172 −23 −3956 15649936 1 3 36 54 1 54  ε_{1} 17.6970
989 −4 −3956 15649936 1 1 36 18 1 18 ε_{1} 23.0897
3957  −3 −1319 15657849 3 1 45 135 2 45 \sqrt{−1}\sqrt{ε_{1}} 7.1861
37 −107 −3959 15673681 1 3 68 102 1 102  ε_{1} 4.9836
1321  −3 −3963 15705369 1 1 8  4 1  4  ε_{1} 106.0524
3964  −4 −991 15713296 1 1 17 17 2 17  \sqrt{i}\sqrt{ε_{1}} 68.8018
12 −331 −3972 15776784 1 3 12 18 1 18  ε_{1} 2.6339
993  −4 −3972 15776784 3 1 12 18 1  6  ε_{1} 17.1487
1324  −3 −3972 15776784 1 1 12  6 1  6  ε_{1} 72.5128
56 −71 −3976 15808576 1 7 16 56 1 56  ε_{1} 6.8002
497  −8 −3976 15808576 1 1 16  8 1  8  ε_{1} 29.3851
497 −56 −568 15808576 1 4 4  8 1  8  ε_{1} 29.3851
568  −7 −3976 15808576 3 1 16 24 1  8  ε_{1} 11.3120
3976  −7 −568 15808576 8 1 4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 7.7275
3976 −56  −71 15808576 8 4 7 112 1 14  ε_{1} 15.4551
173 −23 −3979 15832441 1 3 20 30 1 30  ε_{1} 5.1416
796 −20 −995 15840400 1 2 8  8 1  8  ε_{1} 48.4110
3980  −4 −995 15840400 2 1 8  8 1  4  ε_{1} 33.3750
3980 −20 −199 15840400 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 16.6875
3981  −3 −1327 15848361 3 1 15 45 2 15 \sqrt{−1}\sqrt{ε_{1}} 7.1892
569 −7 −3983 15864289 1 1 44 22 1 22 ε_{1} 44.9587
8 −996 −1992 15872256 1 12 8 48 1 48  ε_{1} 1.7627
12 −664 −1992 15872256 1 10 8 40 1 40  ε_{1} 2.6339
24 −664 −996 15872256 1 10 12 60 1 60  ε_{1} 4.5849
332 −24 −1992 15872256 1 2 8 8 1 8 ε_{1} 10.1997
664 −24 −996 15872256 1 2 12 12 1 12  ε_{1} 43.8951
1992  −4 −1992 15872256 2 1 8 16 2  8  \sqrt{i}\sqrt{ε_{1}} 12.7926

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 91

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
1992  −8 −996 15872256 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 12.7926
997 −4 −3988 15904144 1 1 14 7 1 7 ε_{1} 24.0849
13 −307 −3991 15928081 1 3 30 45 1 45  ε_{1} 2.3895
8 −499 −3992 15936064 1 3 26 39 1 39  ε_{1} 1.7627
3992 −8 −499 15936064 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 21.4004
5 −799 −3995 15960025 1 16 28 224 1 224  ε_{1} 0.9624
17 −235 −3995 15960025 1 2 28 28 1 28  ε_{1} 4.1894
85 −47 −3995 15960025 2 5 28 140 1 70  ε_{1} 4.4187
85 −235 −799 15960025 2 2 16 32 1 16  ε_{1} 4.4187
3997 −7 −571 15976009 5 1 5 25 2 5 \sqrt{−1}\sqrt{ε_{1}} 6.3439
93 −43 −3999 15992001 1 1 48 24 1 24  ε_{1} 6.7322
129 −31 −3999 15992001 1 3 48 72 1 72  ε_{1} 20.8511
1333 −3 −3999 15992001 1 1 48 24 1 24 ε_{1} 22.7491
13 −308 −4004 16032016 1 8 40 160 1 160  ε_{1} 2.3895
28 −143 −4004 16032016 1 10 40 200 1 200  ε_{1} 5.5373
44 −91 −4004 16032016 1 2 40 40 1 40  ε_{1} 5.9864
77 −52 −4004 16032016 1 2 40 40 1 40  ε_{1} 4.3693
364 −11 −4004 16032016 2 1 40 40 1 20  ε_{1} 16.1090
364 −143 −308 16032016 2 10 8 80 1 40  ε_{1} 16.1090
572  −7 −4004 16032016 2 1 40 40 1 20  ε_{1} 6.3526
572 −91 −308 16032016 2 2 8 16 1  8  ε_{1} 6.3526
1001  −4 −4004 16032016 2 1 40 40 1 20  ε_{1} 29.1356
1001 −52 −308 16032016 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 14.5678
24 −167 −4008 16064064 1 11 16 88 1 88  ε_{1} 4.5849
501 −8 −4008 16064064 1 1 16 8 1 8 ε_{1} 20.4959
501 −24 −1336 16064064 1 2 12 12 1 12  ε_{1} 20.4959
1336  −3 −4008 16064064 1 1 16  8 1  8  ε_{1} 64.9600
4008  −3 −1336 16064064 2 1 12 12 1  6  ε_{1} 39.6815
4008 −24 −167 16064064 2 2 11 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 19.8407
4009 −19 −211 16072081 11 1 3 33 2  3 \sqrt{−1}\sqrt{ε_{1}} 8.9356
21 −191 −4011 16088121 1 13 20 130 1 130  ε_{1} 3.1336
573  −7 −4011 16088121 1 1 20 10 1 10  ε_{1} 13.2824
1337  −3 −4011 16088121 1 1 20 10 1 10  ε_{1} 43.4587
236 −68 −1003 16096144 1 4 4  8 1  8  ε_{1} 13.9320
4012  −4 −1003 16096144 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 9.8010
4012 −59  −68 16096144 4 3 4 24 1  6  ε_{1} 19.6020
5 −803 −4015 16120225 1 10 20 100 1 100  ε_{1} 0.9624
73 −55 −4015 16120225 1 4 20 40 1 40  ε_{1} 15.3334
365 −11 −4015 16120225 2 1 20 20 1 10  ε_{1} 5.8944
365 −55 −803 16120225 2 4 10 40 1 20  ε_{1} 5.8944
1004  −8 −2008 16128256 1 1 14 14 2 14 \sqrt{−1}\sqrt{ε_{1}} 15.8102
2008 −4 −2008 16128256 1 1 14 14 2 14 \sqrt{i}\sqrt{ε_{1}} 22.7599
309 −39 −1339 16136289 1 4 8 16 1 16  ε_{1} 17.0523
4017 −3 −1339 16136289 4 1 8 16 1 4 ε_{1} 20.3597
4017 −39 −103 16136289 4 4 5 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 10.1798
5 −804 −4020 16160400 1 12 16 96 1 96  ε_{1} 0.9624
12 −335 −4020 16160400 1 18 16 144 1 144  ε_{1} 2.6339
60 −67 −4020 16160400 2 1 16 16 1 8 ε_{1} 4.1269
60 −335 −804 16160400 2 18 12 216 1 108  ε_{1} 4.1269
201 −20 −4020 16160400 1 2 16 16 1 16  ε_{1} 27.6905

92 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
268  −15 −4020 16160400 1 2 16 16 1 16  ε_{1} 22.9790
1005  −4 −4020 16160400 2 1 16 16 1  8  ε_{1} 14.9988
1005  −20 −804 16160400 2 2 12 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 7.4994
1340  −3 −4020 16160400 2 1 16 16 1  8  ε_{1} 14.1934
1340  −15 −804 16160400 2 2 12 24 1 12  ε_{1} 14.1934
8 −503 −4024 16192576 1 21 20 210 1 210  ε_{1} 1.7627
4024  −8 −503 16192576 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 51.6954
76 −212 −1007 16224784 1 6 30 90 1 90  ε_{1} 11.6579
4028  −4 −1007 16224784 2 1 30 30 1 15  ε_{1} 13.7171
4028  −19 −212 16224784 2 1 6  6 1  3  ε_{1} 13.7171
237  −51 −1343 16232841 1 2 34 34 1 34  ε_{1} 8.6873
4029  −3 −1343 16232841 2 1 34 34 1 17  ε_{1} 36.4294
4029  −51  −79 16232841 2 2 5 10 1  5  ε_{1} 36.4294
29 −139 −4031 16248961 1 3 84 126 1 126  ε_{1} 3.2945
5 −807 −4035 16281225 1 14 12 84 1 84  ε_{1} 0.9624
269  −15 −4035 16281225 1 2 12 12 1 12  ε_{1} 10.1998
1345  −3 −4035 16281225 6 1 12 36 1  6  ε_{1} 18.3560
1345  −15 −807 16281225 6 2 14 84 1 14  ε_{1} 18.3560
1009  −4 −4036 16289296 7 1 20 70 1 10  ε_{1} 13.9694
4037  −11 −367 16297369 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 14.3147
577  −7 −4039 16313521 7 1 42 147 1 21  ε_{1} 7.7433
5 −808 −4040 16321600 1 6 28 84 1 84  ε_{1} 0.9624
101  −40 −4040 16321600 1 2 28 28 1 28  ε_{1} 5.9964
505  −8 −4040 16321600 4 1 28 56 1 14  ε_{1} 14.7779
505  −40 −808 16321600 4 2 6 24 1  6  ε_{1} 14.7779
13 −311 −4043 16345849 1 19 16 152 1 152  ε_{1} 2.3895
12 −1011 −1348 16353936 1 12 8 48 1 48  ε_{1} 2.6339
4044  −3 −1348 16353936 4 1 8 16 1  4  ε_{1} 19.4644
4044  −4 −1011 16353936 4 1 12 24 1  6  ε_{1} 19.4644
57  −71 −4047 16378209 1 7 40 140 1 140  ε_{1} 11.4208
213  −19 −4047 16378209 1 1 40 20 1 20  ε_{1} 8.5805
1349  −3 −4047 16378209 1 1 40 20 1 20  ε_{1} 19.3578
8 −1012 −2024 16386304 1 4 28 56 1 56  ε_{1} 1.7627
44 −184 −2024 16386304 1 4 28 56 1 56  ε_{1} 5.9864
88 −184 −1012 16386304 1 4 4  8 1  8  ε_{1} 11.9527
92  −88 −2024 16386304 1 2 28 28 1 28  ε_{1} 7.7415
184  −88 −1012 16386304 1 2 4  4 1  4  ε_{1} 21.5856
2024  −4 −2024 16386304 6 1 28 84 1 14  ε_{1} 8.9994
2024  −8 −1012 16386304 6 1 4 12 1  2  ε_{1} 8.9994
1013  −4 −4052 16418704 1 1 26 13 1 13  ε_{1} 13.6553
21 −579 −1351 16426809 1 8 24 96 1 96  ε_{1} 3.1336
4053  −3 −1351 16426809 4 1 24 48 1 12  ε_{1} 10.5045
4053  −7 −579 16426809 4 1 8 16 1  4  ε_{1} 10.5045
5 −811 −4055 16443025 1 7 68 238 1 238  ε_{1} 0.9624
28 −580 −1015 16483600 1 8 16 64 1 64  ε_{1} 5.5373
140 −116 −1015 16483600 2 6 16 96 1 48  ε_{1} 4.9558
140 −203 −580 16483600 2 4 8 32 1 16  ε_{1} 4.9558
812  −20 −1015 16483600 2 2 16 32 1 16  ε_{1} 9.4722
812  −35 −580 16483600 2 2 8 16 1  8  ε_{1} 9.4722
4060  −4 −1015 16483600 4 1 16 32 1  8  ε_{1} 26.9340

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 93

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
4060  −7 −580 16483600 4 1 8 16 1  4  ε_{1} 26.9340
4060 −20 −203 16483600 4 2 4 16 1  4  ε_{1} 26.9340
4060 −35 −116 16483600 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 13.4670
4061 −31 −131 16491721 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 21.9283
17 −239 −4063 16507969 1 15 24 180 1 180  ε_{1} 4.1894
813 −15 −1355 16524225 1 2 12 12 1 12  ε_{1} 16.7485
4065 −3 −1355 16524225 6 1 12 36 1 6 ε_{1} 19.5218
4065 −15 −271 16524225 6 2 11 132 2 22 \sqrt{−1}\sqrt{ε_{1}} 9.7609
69 −59 −4071 16573041 1 3 40 60 1 60  ε_{1} 6.4345
177 −23 −4071 16573041 1 3 40 60 1 60  ε_{1} 23.4697
1357  −3 −4071 16573041 1 1 40 20 1 20  ε_{1} 27.4038
509  −8 −4072 16581184 1 1 18  9 1  9  ε_{1} 13.6596
4076  −4 −1019 16613776 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 30.1308
12 −680 −2040 16646400 1 12 16 96 1 96  ε_{1} 2.6339
24 −340 −2040 16646400 1 4 16 32 1 32  ε_{1} 4.5849
60 −136 −2040 16646400 2 4 16 64 1 32  ε_{1} 4.1269
60 −408 −680 16646400 2 4 12 48 1 24  ε_{1} 4.1269
120 −68 −2040 16646400 2 4 16 64 1 32  ε_{1} 6.1779
120 −340 −408 16646400 2 4 4 16 1 8 ε_{1} 6.1779
204 −40 −2040 16646400 2 2 16 32 1 16  ε_{1} 9.2101
204 −120 −680 16646400 2 4 12 48 1 24  ε_{1} 9.2101
408 −20 −2040 16646400 2 2 16 32 1 16  ε_{1} 10.6165
408 −120 −340 16646400 2 4 4 16 1  8  ε_{1} 10.6165
1020  −8 −2040 16646400 4 1 16 32 1  8  ε_{1} 6.9295
1020 −24 −680 16646400 4 2 12 48 1 12  ε_{1} 6.9295
1020 −40 −408 16646400 4 2 4 16 1 4 ε_{1} 6.9295
1020 −120 −136 16646400 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 3.4648
2040  −4 −2040 16646400 4 1 16 32 1  8  ε_{1} 12.5905
2040 −20 −408 16646400 4 2 4 16 1  4  ε_{1} 12.5905
2040 −24 −340 16646400 4 2 4 16 1  4  ε_{1} 12.5905
2040 −68 −120 16646400 4 4 4 32 1  8  ε_{1} 12.5905
77 −371 −583 16654561 1 8 8 32 1 32  ε_{1} 4.3693
4081  −7 −583 16654561 4 1 8 16 1  4  ε_{1} 55.6417
4081 −11 −371 16654561 4 1 8 16 1  4  ε_{1} 55.6417
1361  −3 −4083 16670889 1 1 10  5 1  5  ε_{1} 61.8173
1021  −4 −4084 16679056 1 1 22 11 1 11  ε_{1} 36.5338
817 −95 −215 16687225 5 8 14 280 1 56  ε_{1} 13.0618
4085 −19 −215 16687225 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.1664
4085 −43 −95 16687225 2 1 8 8 1 4 ε_{1} 20.3327
61 −67 −4087 16703569 1 1 30 15 1 15  ε_{1} 7.3284
8 −511 −4088 16711744 1 14 32 224 1 224  ε_{1} 1.7627
56 −511 −584 16711744 1 14 16 112 1 112  ε_{1} 6.8002
73 −56 −4088 16711744 1 4 32 64 1 64  ε_{1} 15.3334
584 −7 −4088 16711744 2 1 32 32 1 16 ε_{1} 11.3397
584 −56 −511 16711744 2 4 14 56 1 28  ε_{1} 11.3397
4088 −7 −584 16711744 2 1 16 16 1 8 ε_{1} 15.2473
4088  −8 −511 16711744 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.6236
141 −87 −1363 16719921 1 6 6 18 1 18  ε_{1} 10.4940
4089  −3 −1363 16719921 2 1 6  6 1  3  ε_{1} 84.7821
4089 −47  −87 16719921 2 5 6 30 1 15  ε_{1} 84.7821

94 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −1023 −1364 16744464 1 16 28 224 1 224  ε_{1} 2.6339
33 −372 −1364 16744464 1 4 28 56 1 56  ε_{1} 7.6563
44 −372 −1023 16744464 1 4 16 32 1 32  ε_{1} 5.9864
93 −132 −1364 16744464 1 4 28 56 1 56  ε_{1} 6.7322
124 −132 −1023 16744464 1 4 16 32 1 32  ε_{1} 16.0392
341 −132 −372 16744464 1 4 4  8 1  8  ε_{1} 11.2480
4092  −3 −1364 16744464 8 1 28 112 1 14  ε_{1} 8.3173
4092  −4 −1023 16744464 8 1 16 64 1  8  ε_{1} 8.3173
4092  −11 −372 16744464 8 1 4 16 1  2  ε_{1} 8.3173
4092  −31 −132 16744464 8 3 4 48 1  6  ε_{1} 8.3173
4101  −3 −1367 16818201 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 26.4630
373  −11 −4103 16834609 1 1 42 21 1 21  ε_{1} 18.4673
316  −52 −1027 16875664 3 2 4 12 1  4  ε_{1} 10.1503
4108  −4 −1027 16875664 2 1 4  4 1  2  ε_{1} 38.8003
4108  −52  −79 16875664 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 19.4001
4109  −7 −587 16883881 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 19.9280
8 −1028 −2056 16908544 1 16 16 128 1 128  ε_{1} 1.7627
2056 −4 −2056 16908544 4 1 16 64 2 16 \sqrt{i}\sqrt{ε_{1}} 9.1324
2056  −8 −1028 16908544 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 9.1324
5 −823 −4115 16933225 1 9 22 99 1 99  ε_{1} 0.9624
4117  −23 −179 16949689 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 34.9727
1373 −3 −4119 16966161 3 1 54 81 1 27 ε_{1} 7.2233
5 −824 −4120 16974400 1 20 12 120 1 120  ε_{1} 0.9624
8 −515 −4120 16974400 1 6 12 36 1 36  ε_{1} 1.7627
40 −103 −4120 16974400 2 5 12 60 1 30  ε_{1} 3.6369
40 −515 −824 16974400 2 6 20 120 1 60  ε_{1} 3.6369
824  −40 −515 16974400 1 2 6  6 1  6  ε_{1} 23.3749
4120  −8 −515 16974400 2 1 6  6 1  3  ε_{1} 56.4024
4120  −40 −103 16974400 2 2 5 10 1  5  ε_{1} 56.4024
133  −31 −4123 16999129 1 3 8 12 1 12  ε_{1} 10.3065
217  −19 −4123 16999129 1 1 8  4 1  4  ε_{1} 31.7104
589  −7 −4123 16999129 1 1 8  4 1  4  ε_{1} 30.5757
4124  −4 −1031 17007376 1 1 35 35 2 35  \sqrt{i}\sqrt{ε_{1}} 34.8038
1033  −4 −4132 17073424 1 1 12  6 1  6  ε_{1} 80.9246
5 −827 −4135 17098225 1 7 46 161 1 161  ε_{1} 0.9624
88  −47 −4136 17106496 1 5 44 110 1 110  ε_{1} 11.9527
376  −11 −4136 17106496 1 1 44 22 1 22  ε_{1} 30.5420
517  −8 −4136 17106496 1 1 44 22 1 22  ε_{1} 18.5321
517  −88 −376 17106496 1 2 8  8 1  8  ε_{1} 18.5321
4136  −11 −376 17106496 2 1 8  8 1  4  ε_{1} 20.7326
4136  −47  −88 17106496 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 10.3663
21 −591 −1379 17114769 1 22 16 176 1 176  ε_{1} 3.1336
4137 −3 −1379 17114769 2 1 16 16 1 8 ε_{1} 59.6551
4137  −7 −591 17114769 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 29.8276
1381 −3 −4143 17164449 1 1 44 22 1 22 ε_{1} 50.0922
28 −296 −2072 17172736 1 10 16 80 1 80  ε_{1} 5.5373
56 −148 −2072 17172736 1 2 16 16 1 16  ε_{1} 6.8002
1036  −8 −2072 17172736 2 1 16 16 1  8  ε_{1} 28.6857
1036  −56 −296 17172736 2 4 10 40 1 20  ε_{1} 28.6857
2072  −4 −2072 17172736 2 1 16 16 1  8  ε_{1} 16.9251

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 95

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2072 −56 −148 17172736 2 4 2  8 1  4  ε_{1} 16.9251
13 −319 −4147 17197609 1 10 12 60 1 60  ε_{1} 2.3895
29 −143 −4147 17197609 1 10 12 60 1 60  ε_{1} 3.2945
377 −11 −4147 17197609 2 1 12 12 1 6 ε_{1} 12.2884
377 −143 −319 17197609 2 10 10 100 1 50  ε_{1} 12.2884
17 −244 −4148 17205904 1 6 20 60 1 60  ε_{1} 4.1894
61 −68 −4148 17205904 1 4 20 40 1 40  ε_{1} 7.3284
1037 −4 −4148 17205904 2 1 20 20 1 10 ε_{1} 10.1629
1037 −68 −244 17205904 2 4 6 24 1 12  ε_{1} 10.1629
593 −7 −4151 17230801 1 1 74 37 1 37 ε_{1} 27.9978
8 −519 −4152 17239104 1 18 12 108 1 108  ε_{1} 1.7627
24 −519 −1384 17239104 1 18 10 90 1 90  ε_{1} 4.5849
173 −24 −4152 17239104 1 2 12 12 1 12  ε_{1} 5.1416
1384 −3 −4152 17239104 6 1 12 36 1 6 ε_{1} 10.4516
1384 −24 −519 17239104 6 2 18 108 1 18  ε_{1} 10.4516
4152  −3 −1384 17239104 2 1 10 10 1  5  ε_{1} 34.4866
4152  −8 −519 17239104 2 1 18 18 1  9  ε_{1} 34.4866
5 −831 −4155 17264025 1 28 12 168 1 168  ε_{1} 0.9624
277 −15 −4155 17264025 1 2 12 12 1 12  ε_{1} 15.7365
1385 −3 −4155 17264025 2 1 12 12 1 6 ε_{1} 24.4924
1385 −15 −831 17264025 2 2 28 56 1 28  ε_{1} 24.4924
4156  −4 −1039 17272336 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 62.1561
57 −219 −1387 17313921 1 4 4  8 1  8  ε_{1} 11.4208
4161  −3 −1387 17313921 8 1 4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 10.0074
4161 −19 −219 17313921 8 1 4 16 1  2  ε_{1} 20.0148
181 −23 −4163 17330569 1 3 22 33 1 33  ε_{1} 14.3479
12 −347 −4164 17338896 1 5 36 90 1 90  ε_{1} 2.6339
1041  −4 −4164 17338896 1 1 36 18 1 18  ε_{1} 69.9435
1388  −3 −4164 17338896 1 1 36 18 1 18  ε_{1} 28.1297
521  −8 −4168 17372224 1 1 12  6 1  6  ε_{1} 38.7273
4169 −11 −379 17380561 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 72.6389
97 −43 −4171 17397241 1 1 16  8 1  8  ε_{1} 18.6488
28 −596 −1043 17405584 1 14 8 56 1 56  ε_{1} 5.5373
4172 −4 −1043 17405584 2 1 8 8 1 4 ε_{1} 27.9172
4172  −7 −596 17405584 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 13.9586
321 −39 −1391 17413929 3 4 44 264 1 88  ε_{1} 12.1276
4173  −3 −1391 17413929 4 1 44 88 1 22  ε_{1} 11.5553
4173 −39 −107 17413929 4 4 3 24 1  6  ε_{1} 11.5553
21 −199 −4179 17464041 1 9 16 72 1 72  ε_{1} 3.1336
597  −7 −4179 17464041 1 1 16  8 1  8  ε_{1} 18.3698
1393  −3 −4179 17464041 5 1 16 40 1  8  ε_{1} 17.7542
5 −836 −4180 17472400 1 20 16 160 1 160  ε_{1} 0.9624
44 −95 −4180 17472400 1 8 16 64 1 64  ε_{1} 5.9864
76 −55 −4180 17472400 1 4 16 32 1 32  ε_{1} 11.6579
209 −20 −4180 17472400 1 2 16 16 1 16  ε_{1} 22.8829
220 −19 −4180 17472400 2 1 16 16 1 8 ε_{1} 10.3635
220 −95 −836 17472400 2 8 20 160 1 80  ε_{1} 10.3635
380 −11 −4180 17472400 2 1 16 16 1 8 ε_{1} 8.7131
380 −55 −836 17472400 2 4 20 80 1 40  ε_{1} 8.7131
1045  −4 −4180 17472400 4 1 16 32 1  8  ε_{1} 9.1492

96 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1045  −20 −836 17472400 4 2 20 80 1 20  ε_{1} 9.1492
89  −47 −4183 17497489 1 5 28 70 1 70  ε_{1} 13.8155
8 −523 −4184 17505856 1 5 42 105 1 105  ε_{1} 1.7627
4184  −8 −523 17505856 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 29.7072
53  −79 −4187 17530969 1 5 14 35 1 35  ε_{1} 3.9314
12 −1047 −1396 17539344 1 16 14 112 1 112  ε_{1} 2.6339
4188  −3 −1396 17539344 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 12.5195
4188  −4 −1047 17539344 2 1 16 16 1  8  ε_{1} 25.0389
4189  −59  −71 17547721 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 41.9621
33 −127 −4191 17564481 1 5 60 150 1 150  ε_{1} 7.6563
381  −11 −4191 17564481 1 1 60 30 1 30  ε_{1} 15.2316
1397  −3 −4191 17564481 1 1 60 30 1 30  ε_{1} 16.1274
4193  −7 −599 17581249 3 1 25 75 2 25 \sqrt{−1}\sqrt{ε_{1}} 10.5541
5 −839 −4195 17598025 1 33 8 132 1 132  ε_{1} 0.9624
1049 −4 −4196 17606416 1 1 44 22 1 22 ε_{1} 57.5072
4197  −3 −1399 17614809 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 18.9190
13 −323 −4199 17631601 1 4 88 176 1 176  ε_{1} 2.3895
17 −247 −4199 17631601 1 6 88 264 1 264  ε_{1} 4.1894
221 −19 −4199 17631601 2 1 88 88 1 44 ε_{1} 5.4072
221 −247 −323 17631601 2 6 4 24 1 12  ε_{1} 5.4072
4204  −4 −1051 17673616 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 62.8173
601  −7 −4207 17698849 1 1 26 13 1 13  ε_{1} 66.5240
1052  −8 −2104 17707264 1 1 12 12 2 12 \sqrt{−1}\sqrt{ε_{1}} 12.5363
2104 −4 −2104 17707264 1 1 12 12 2 12 \sqrt{i}\sqrt{ε_{1}} 46.5712
69 −183 −1403 17715681 1 8 14 56 1 56  ε_{1} 6.4345
4209  −3 −1403 17715681 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 42.3407
4209 −23 −183 17715681 2 3 8 24 1 12 ε_{1} 84.6814
4213  −11 −383 17749369 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 24.2396
5 −843 −4215 17766225 1 6 44 132 1 132  ε_{1} 0.9624
281  −15 −4215 17766225 1 2 44 44 1 44  ε_{1} 29.1405
1405  −3 −4215 17766225 2 1 44 44 1 22  ε_{1} 16.8228
1405  −15 −843 17766225 2 2 6 12 1  6  ε_{1} 16.8228
8 −527 −4216 17774656 1 18 16 144 1 144  ε_{1} 1.7627
17 −248 −4216 17774656 1 8 16 64 1 64  ε_{1} 4.1894
136 −31 −4216 17774656 2 3 16 48 1 24 ε_{1} 8.4966
136 −248 −527 17774656 2 8 18 144 1 72  ε_{1} 8.4966
248 −136 −527 17774656 1 4 18 36 1 36  ε_{1} 9.6724
4216  −8 −527 17774656 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 36.4425
4216  −31 −136 17774656 2 3 4 12 1  6  ε_{1} 72.8851
844  −20 −1055 17808400 1 2 36 36 1 36  ε_{1} 54.0906
4220  −4 −1055 17808400 2 1 36 36 1 18  ε_{1} 16.2501
4220  −20 −211 17808400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 8.1250
41 −103 −4223 17833729 1 5 44 110 1 110  ε_{1} 8.3183
1409 −3 −4227 17867529 1 1 10 5 1 5 ε_{1} 77.6008
28 −151 −4228 17875984 1 7 16 56 1 56  ε_{1} 5.5373
604  −7 −4228 17875984 1 1 16  8 1  8  ε_{1} 43.9269
1057  −4 −4228 17875984 1 1 16  8 1  8  ε_{1} 81.4221
249  −51 −1411 17918289 1 2 4  4 1  4  ε_{1} 33.3101
4233  −3 −1411 17918289 2 1 4  4 1  2  ε_{1} 50.1608
4233  −51  −83 17918289 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 25.0804

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 97

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −1059 −1412 17943696 1 6 16 48 1 48  ε_{1} 2.6339
4236  −3 −1412 17943696 2 1 16 16 1  8  ε_{1} 46.4108
4236  −4 −1059 17943696 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 23.2054
4237  −19 −223 17952169 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 31.5663
8 −1060 −2120 17977600 1 8 28 112 1 112  ε_{1} 1.7627
40 −212 −2120 17977600 2 6 28 168 1 84  ε_{1} 3.6369
40 −424 −1060 17977600 2 6 8 48 1 24  ε_{1} 3.6369
424  −20 −2120 17977600 2 2 28 56 1 28  ε_{1} 17.9769
424  −40 −1060 17977600 2 2 8 16 1  8  ε_{1} 17.9769
2120  −4 −2120 17977600 4 1 28 56 1 14  ε_{1} 7.6582
2120  −8 −1060 17977600 4 1 8 16 1  4  ε_{1} 7.6582
2120  −20 −424 17977600 4 2 6 24 1  6  ε_{1} 7.6582
2120  −40 −212 17977600 4 2 6 24 1  6  ε_{1} 7.6582
1061  −4 −4244 18011536 1 1 26 13 1 13  ε_{1} 24.9704
849  −15 −1415 18020025 1 2 34 34 1 34  ε_{1} 71.2770
4245  −3 −1415 18020025 2 1 34 34 1 17  ε_{1} 13.4834
4245  −15 −283 18020025 2 2 3  6 1  3  ε_{1} 13.4834
137  −31 −4247 18037009 1 3 62 93 1 93  ε_{1} 16.3142
4249  −7 −607 18054001 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 111.5585
13 −327 −4251 18071001 1 12 16 96 1 96  ε_{1} 2.3895
109  −39 −4251 18071001 1 4 16 32 1 32  ε_{1} 11.1291
1417  −3 −4251 18071001 2 1 16 16 1  8  ε_{1} 43.8225
1417  −39 −327 18071001 2 4 12 48 1 24  ε_{1} 43.8225
4252  −4 −1063 18079504 1 1 19 19 2 19  \sqrt{i}\sqrt{ε_{1}} 35.7889
5 −851 −4255 18105025 1 10 36 180 1 180  ε_{1} 0.9624
37 −115 −4255 18105025 1 2 36 36 1 36  ε_{1} 4.9836
185 −23 −4255 18105025 2 3 36 108 1 54 ε_{1} 9.8254
185 −115 −851 18105025 2 2 10 20 1 10  ε_{1} 9.8254
5 −852 −4260 18147600 1 8 16 64 1 64  ε_{1} 0.9624
12 −355 −4260 18147600 1 4 16 32 1 32  ε_{1} 2.6339
60 −71 −4260 18147600 2 7 16 112 1 56 ε_{1} 4.1269
60 −355 −852 18147600 2 4 8 32 1 16  ε_{1} 4.1269
213  −20 −4260 18147600 1 2 16 16 1 16  ε_{1} 8.5805
284  −15 −4260 18147600 1 2 16 16 1 16  ε_{1} 17.6959
1065  −4 −4260 18147600 2 1 16 16 1  8  ε_{1} 37.8470
1065  −20 −852 18147600 2 2 8 16 1  8  ε_{1} 37.8470
1420  −3 −4260 18147600 2 1 16 16 1  8  ε_{1} 28.9248
1420  −15 −852 18147600 2 2 8 16 1  8  ε_{1} 28.9248
13 −328 −4264 18181696 1 4 20 40 1 40  ε_{1} 2.3895
41 −104 −4264 18181696 1 6 20 60 1 60  ε_{1} 8.3183
533 −8 −4264 18181696 2 1 20 20 1 10 ε_{1} 6.2748
533 −104 −328 18181696 2 6 4 24 1 12  ε_{1} 6.2748
17 −251 −4267 18207289 1 7 8 28 1 28  ε_{1} 4.1894
44 −388 −1067 18215824 1 4 12 24 1 24  ε_{1} 5.9864
4268  −4 −1067 18215824 4 1 12 24 1  6  ε_{1} 10.5562
4268  −11 −388 18215824 4 1 4  8 1  2  ε_{1} 10.5562
4269  −3 −1423 18224361 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 24.6718
12 −712 −2136 18249984 1 8 20 80 1 80  ε_{1} 2.6339
24 −356 −2136 18249984 1 12 20 120 1 120  ε_{1} 4.5849
1068  −8 −2136 18249984 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 8.4772

98 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1068  −24 −712 18249984 2 2 8 16 1  8  ε_{1} 16.9544
2136  −4 −2136 18249984 2 1 20 40 2 20  \sqrt{i}\sqrt{ε_{1}} 15.8112
2136  −24 −356 18249984 2 2 12 24 1 12  ε_{1} 31.6224
1069  −4 −4276 18284176 1 1 30 15 1 15  ε_{1} 36.9734
329  −91 −611 18292729 1 2 10 10 1 10  ε_{1} 30.7485
4277  −7 −611 18292729 2 1 10 10 1  5  ε_{1} 11.5799
4277  −47  −91 18292729 2 5 2 10 1  5  ε_{1} 11.5799
389  −11 −4279 18309841 1 1 28 14 1 14  ε_{1} 15.6986
5 −856 −4280 18318400 1 6 36 108 1 108  ε_{1} 0.9624
8 −535 −4280 18318400 1 14 36 252 1 252  ε_{1} 1.7627
40 −107 −4280 18318400 2 3 36 108 1 54  ε_{1} 3.6369
40 −535 −856 18318400 2 14 6 84 1 42  ε_{1} 3.6369
856  −40 −535 18318400 1 2 14 14 1 14  ε_{1} 55.9217
4280  −8 −535 18318400 2 1 14 14 1  7  ε_{1} 31.1799
4280  −40 −107 18318400 2 2 3  6 1  3  ε_{1} 31.1799
4281  −3 −1427 18326961 3 1 15 45 2 15 \sqrt{−1}\sqrt{ε_{1}} 29.5007
1429  −3 −4287 18378369 5 1 48 120 1 24  ε_{1} 10.4836
613  −7 −4291 18412681 1 1 12  6 1  6  ε_{1} 23.0010
29 −148 −4292 18421264 1 2 24 24 1 24  ε_{1} 3.2945
37 −116 −4292 18421264 1 6 24 72 1 72  ε_{1} 4.9836
1073  −4 −4292 18421264 2 1 24 24 1 12  ε_{1} 22.8314
1073 −116 −148 18421264 2 6 2 12 1  6  ε_{1} 22.8314
5 −859 −4295 18447025 1 7 48 168 1 168  ε_{1} 0.9624
24 −179 −4296 18455616 1 5 32 80 1 80  ε_{1} 4.5849
537  −8 −4296 18455616 1 1 32 16 1 16  ε_{1} 39.5359
537  −24 −1432 18455616 1 2 6  6 1  6  ε_{1} 39.5359
1432  −3 −4296 18455616 1 1 32 16 1 16  ε_{1} 53.1804
4296  −3 −1432 18455616 2 1 6  6 1  3  ε_{1} 31.5168
4296  −24 −179 18455616 2 2 5 10 1  5  ε_{1} 31.5168
1433  −3 −4299 18481401 1 1 18  9 1  9  ε_{1} 46.3372
253 −187 −391 18498601 1 2 14 14 1 14  ε_{1} 15.0577
4301  −11 −391 18498601 2 1 14 14 1  7  ε_{1} 18.8501
4301  −23 −187 18498601 2 3 2  6 1  3  ε_{1} 18.8501
13 −331 −4303 18515809 1 3 34 51 1 51  ε_{1} 2.3895
8 −1076 −2152 18524416 1 22 10 110 1 110  ε_{1} 1.7627
2152  −4 −2152 18524416 2 1 10 10 1  5  ε_{1} 23.6715
2152  −8 −1076 18524416 2 1 22 22 1 11  ε_{1} 23.6715
21 −615 −1435 18533025 1 20 4 40 1 40  ε_{1} 3.1336
105 −123 −1435 18533025 2 2 4 8 1 4 ε_{1} 8.8131
105 −287 −615 18533025 2 14 20 280 1 140  ε_{1} 8.8131
861  −15 −1435 18533025 2 2 4  8 1  4  ε_{1} 13.8688
861  −35 −615 18533025 2 2 20 40 1 20  ε_{1} 13.8688
4305  −3 −1435 18533025 8 1 4 16 1  2  ε_{1} 18.5179
4305  −7 −615 18533025 8 1 20 80 1 10  ε_{1} 18.5179
4305  −15 −287 18533025 8 2 14 112 1 14  ε_{1} 18.5179
4305  −35 −123 18533025 8 2 2 16 1  2  ε_{1} 18.5179
73  −59 −4307 18550249 1 3 18 27 1 27  ε_{1} 15.3334
12 −359 −4308 18558864 1 19 24 228 1 228  ε_{1} 2.6339
1077  −4 −4308 18558864 1 1 24 12 1 12  ε_{1} 11.7777
1436  −3 −4308 18558864 3 1 24 36 1 12  ε_{1} 13.1585

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 99

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
4309 −31 −139 18567481 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 42.8287
4313 −19 −227 18601969 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 55.7170
5 −863 −4315 18619225 1 21 14 147 1 147  ε_{1} 0.9624
332 −52 −1079 18627856 1 2 34 34 1 34  ε_{1} 10.1997
4316  −4 −1079 18627856 2 1 34 34 1 17  ε_{1} 39.4096
4316 −52  −83 18627856 2 2 3  6 1  3  ε_{1} 39.4096
4317  −3 −1439 18636489 1 1 39 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 23.9450
617 −7 −4319 18653761 1 1 84 42 1 42 ε_{1} 36.4449
33 −131 −4323 18688329 1 5 8 20 1 20  ε_{1} 7.6563
393 −11 −4323 18688329 1 1 8  4 1  4  ε_{1} 36.6935
1441  −3 −4323 18688329 1 1 8  4 1  4  ε_{1} 111.5641
92 −47 −4324 18696976 1 5 16 40 1 40  ε_{1} 7.7415
188 −23 −4324 18696976 1 3 16 24 1 24  ε_{1} 9.1285
1081  −4 −4324 18696976 1 1 16  8 1  8  ε_{1} 95.6412
541  −8 −4328 18731584 1 1 22 11 1 11  ε_{1} 28.2989
61 −71 −4331 18757561 1 7 34 119 1 119  ε_{1} 7.3284
4333 −7 −619 18774889 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 30.7095
1084  −8 −2168 18800896 1 1 24 24 2 24 \sqrt{−1}\sqrt{ε_{1}} 26.1698
2168 −4 −2168 18800896 1 1 24 24 2 24 \sqrt{i}\sqrt{ε_{1}} 15.9657
5 −868 −4340 18835600 1 8 32 128 1 128  ε_{1} 0.9624
28 −155 −4340 18835600 1 4 32 64 1 64  ε_{1} 5.5373
124 −35 −4340 18835600 1 2 32 32 1 32  ε_{1} 16.0392
140 −31 −4340 18835600 2 3 32 96 1 48  ε_{1} 4.9558
140 −155 −868 18835600 2 4 8 32 1 16  ε_{1} 4.9558
217 −20 −4340 18835600 1 2 32 32 1 32  ε_{1} 31.7104
620  −7 −4340 18835600 2 1 32 32 1 16  ε_{1} 12.4212
620 −35 −868 18835600 2 2 8 16 1  8  ε_{1} 12.4212
1085  −4 −4340 18835600 2 1 32 32 1 16  ε_{1} 6.9912
1085 −20 −868 18835600 2 2 8 16 1  8  ε_{1} 6.9912
4341  −3 −1447 18844281 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 32.9368
101 −43 −4343 18861649 1 1 64 32 1 32  ε_{1} 5.9964
8 −543 −4344 18870336 1 12 28 168 1 168  ε_{1} 1.7627
24 −543 −1448 18870336 1 12 18 108 1 108  ε_{1} 4.5849
181 −24 −4344 18870336 1 2 28 28 1 28  ε_{1} 14.3479
1448 −3 −4344 18870336 2 1 28 28 1 14 ε_{1} 7.2766
1448 −24 −543 18870336 2 2 12 24 1 12  ε_{1} 7.2766
4344  −3 −1448 18870336 6 1 18 108 2 18 \sqrt{−1}\sqrt{ε_{1}} 7.2793
4344 −8 −543 18870336 6 1 12 36 1 6 ε_{1} 14.5586
869 −55 −395 18879025 1 4 8 16 1 16  ε_{1} 21.6145
4345 −11 −395 18879025 12 1 8 96 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.3664
4345 −55  −79 18879025 12 4 5 120 1 10  ε_{1} 14.7329
4348  −4 −1087 18905104 7 1 9 63 2  9  \sqrt{i}\sqrt{ε_{1}} 7.6852
229 −19 −4351 18931201 3 1 44 66 1 22  ε_{1} 5.4249
4353  −3 −1451 18948609 5 1 13 65 2 13 \sqrt{−1}\sqrt{ε_{1}} 8.6666
5 −871 −4355 18966025 1 22 20 220 1 220  ε_{1} 0.9624
13 −335 −4355 18966025 1 18 20 180 1 180  ε_{1} 2.3895
65 −67 −4355 18966025 2 1 20 20 1 10  ε_{1} 5.5529
65 −335 −871 18966025 2 18 22 396 1 198  ε_{1} 5.5529
1453 −3 −4359 19000881 1 1 60 30 1 30 ε_{1} 43.6833
5 −872 −4360 19009600 1 10 12 60 1 60  ε_{1} 0.9624

100 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
109  −40 −4360 19009600 1 2 12 12 1 12  ε_{1} 11.1291
545  −8 −4360 19009600 2 1 12 12 1  6  ε_{1} 16.5487
545  −40 −872 19009600 2 2 10 20 1 10  ε_{1} 16.5487
4364  −4 −1091 19044496 3 1 17 51 2 17  \sqrt{i}\sqrt{ε_{1}} 7.6871
397  −11 −4367 19070689 1 1 68 34 1 34  ε_{1} 16.2905
8 −1092 −2184 19079424 1 8 24 96 1 96  ε_{1} 1.7627
12 −728 −2184 19079424 1 12 24 144 1 144  ε_{1} 2.6339
24 −728 −1092 19079424 1 12 8 48 1 48  ε_{1} 4.5849
28 −312 −2184 19079424 1 4 24 48 1 48  ε_{1} 5.5373
56 −312 −1092 19079424 1 4 8 16 1 16  ε_{1} 6.8002
104 −84 −2184 19079424 2 4 24 96 1 48 ε_{1} 4.6249
104 −168 −1092 19079424 2 4 8 32 1 16  ε_{1} 4.6249
156 −56 −2184 19079424 2 4 24 96 1 48 ε_{1} 7.8232
156 −168 −728 19079424 2 4 12 48 1 24  ε_{1} 7.8232
168 −52 −2184 19079424 2 2 24 48 1 24 ε_{1} 6.5132
168 −104 −1092 19079424 2 6 8 48 1 24  ε_{1} 6.5132
312  −56 −1092 19079424 2 4 8 32 1 16  ε_{1} 9.3267
312  −84 −728 19079424 2 4 12 48 1 24  ε_{1} 9.3267
364  −24 −2184 19079424 2 2 24 48 1 24  ε_{1} 16.1090
364 −168 −312 19079424 2 4 4 16 1  8  ε_{1} 16.1090
728  −24 −1092 19079424 2 2 8 16 1  8  ε_{1} 7.9773
728  −84 −312 19079424 2 4 4 16 1  8  ε_{1} 7.9773
2184  −4 −2184 19079424 4 1 24 48 1 12  ε_{1} 14.4913
2184  −8 −1092 19079424 4 1 8 16 1  4  ε_{1} 14.4913
2184  −52 −168 19079424 4 2 4 16 1  4  ε_{1} 14.4913
2184  −84 −104 19079424 4 4 6 48 1 12  ε_{1} 14.4913
93  −47 −4371 19105641 1 5 20 50 1 50  ε_{1} 6.7322
141  −31 −4371 19105641 1 3 20 30 1 30  ε_{1} 10.4940
1457  −3 −4371 19105641 1 1 20 10 1 10  ε_{1} 60.6057
1093  −4 −4372 19114384 5 1 10 25 1  5  ε_{1} 6.9948
8 −547 −4376 19149376 1 3 26 39 1 39  ε_{1} 1.7627
4376 −8 −547 19149376 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 37.9332
4377  −3 −1459 19158129 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 66.6649
29 −151 −4379 19175641 1 7 16 56 1 56  ε_{1} 3.2945
12 −1095 −1460 19184400 1 28 20 280 1 280  ε_{1} 2.6339
60 −219 −1460 19184400 2 4 20 80 1 40  ε_{1} 4.1269
60 −292 −1095 19184400 2 4 28 112 1 56  ε_{1} 4.1269
876  −15 −1460 19184400 4 2 20 80 1 20  ε_{1} 9.9943
876  −20 −1095 19184400 4 2 28 112 1 28  ε_{1} 9.9943
4380  −3 −1460 19184400 4 1 20 40 1 10  ε_{1} 13.1806
4380  −4 −1095 19184400 4 1 28 56 1 14  ε_{1} 13.1806
4380  −15 −292 19184400 4 2 4 16 1  4  ε_{1} 13.1806
4380  −20 −219 19184400 4 2 4 16 1  4  ε_{1} 13.1806
41 −107 −4387 19245769 1 3 8 12 1 12  ε_{1} 8.3183
1097 −4 −4388 19254544 1 1 36 18 1 18 ε_{1} 35.1082
21 −627 −1463 19263321 1 4 32 64 1 64  ε_{1} 3.1336
33 −399 −1463 19263321 1 16 32 256 1 256  ε_{1} 7.6563
57 −231 −1463 19263321 1 12 32 192 1 192  ε_{1} 11.4208
77 −399 −627 19263321 1 16 4 32 1 32  ε_{1} 4.3693
133 −231 −627 19263321 1 12 4 24 1 24  ε_{1} 10.3065

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 101

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
209 −231 −399 19263321 1 12 16 96 1 96  ε_{1} 22.8829
4389  −3 −1463 19263321 4 1 32 64 1 16  ε_{1} 12.5457
4389  −7 −627 19263321 4 1 4  8 1  2  ε_{1} 12.5457
4389 −11 −399 19263321 4 1 16 32 1  8  ε_{1} 12.5457
4389 −19 −231 19263321 4 1 12 24 1  6  ε_{1} 12.5457
4393 −23 −191 19298449 1 3 13 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 99.2906
5 −879 −4395 19316025 1 22 20 220 1 220  ε_{1} 0.9624
293 −15 −4395 19316025 1 2 20 20 1 20  ε_{1} 5.6733
1465 −3 −4395 19316025 2 1 20 20 1 10 ε_{1} 56.2532
1465 −15 −879 19316025 2 2 22 44 1 22  ε_{1} 56.2532
28 −628 −1099 19324816 1 6 6 18 1 18  ε_{1} 5.5373
4396  −4 −1099 19324816 2 1 6  6 1  3  ε_{1} 57.5798
4396  −7 −628 19324816 2 1 6  6 1  3  ε_{1} 57.5798
53 −83 −4399 19351201 1 3 50 75 1 75  ε_{1} 3.9314
17 −259 −4403 19386409 1 4 20 40 1 40  ε_{1} 4.1894
37 −119 −4403 19386409 1 10 20 100 1 100  ε_{1} 4.9836
629 −7 −4403 19386409 2 1 20 20 1 10 ε_{1} 6.4409
629 −119 −259 19386409 2 10 4 40 1 20  ε_{1} 6.4409
12 −367 −4404 19395216 1 9 28 126 1 126  ε_{1} 2.6339
1101  −4 −4404 19395216 3 1 28 42 1 14  ε_{1} 11.7998
1468  −3 −4404 19395216 1 1 28 14 1 14  ε_{1} 48.7238
13 −339 −4407 19421649 1 6 40 120 1 120  ε_{1} 2.3895
113 −39 −4407 19421649 1 4 40 80 1 80  ε_{1} 14.6946
1469 −3 −4407 19421649 2 1 40 40 1 20 ε_{1} 9.4897
1469 −39 −339 19421649 2 4 6 24 1 12  ε_{1} 9.4897
8 −551 −4408 19430464 1 26 20 260 1 260  ε_{1} 1.7627
29 −152 −4408 19430464 1 6 20 60 1 60  ε_{1} 3.2945
152 −232 −551 19430464 1 2 26 26 1 26  ε_{1} 8.6078
232 −19 −4408 19430464 2 1 20 20 1 10  ε_{1} 10.5766
232 −152 −551 19430464 2 6 26 156 1 78  ε_{1} 10.5766
4408  −8 −551 19430464 2 1 26 26 1 13  ε_{1} 33.8815
4408 −19 −232 19430464 2 1 2  2 1  1  ε_{1} 33.8815
401 −11 −4411 19456921 5 1 12 30 1  6  ε_{1} 7.3790
4412  −4 −1103 19465744 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 29.1770
4413  −3 −1471 19474569 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 11.1855
5 −883 −4415 19492225 1 3 66 99 1 99  ε_{1} 0.9624
4417  −7 −631 19509889 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 83.3968
5 −884 −4420 19536400 1 16 16 128 1 128  ε_{1} 0.9624
13 −340 −4420 19536400 1 4 16 32 1 32  ε_{1} 2.3895
17 −260 −4420 19536400 1 8 16 64 1 64  ε_{1} 4.1894
65 −68 −4420 19536400 2 4 16 64 1 32  ε_{1} 5.5529
65 −340 −884 19536400 2 4 16 64 1 32  ε_{1} 5.5529
85 −52 −4420 19536400 2 2 16 32 1 16  ε_{1} 4.4187
85 −260 −884 19536400 2 8 16 128 1 64  ε_{1} 4.4187
221 −20 −4420 19536400 2 2 16 32 1 16  ε_{1} 5.4072
221 −260 −340 19536400 2 8 4 32 1 16  ε_{1} 5.4072
1105 −4 −4420 19536400 4 1 16 32 1 8 ε_{1} 21.9008
1105 −20 −884 19536400 4 2 16 64 1 16  ε_{1} 21.9008
1105 −52 −340 19536400 4 2 4 16 1 4 ε_{1} 21.9008
1105 −68 −260 19536400 4 4 8 64 1 16  ε_{1} 21.9008

102 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
56  −79 −4424 19571776 1 5 48 120 1 120  ε_{1} 6.8002
553  −8 −4424 19571776 1 1 48 24 1 24  ε_{1} 55.7072
553  −56 −632 19571776 1 4 8 16 1 16  ε_{1} 55.7072
632  −7 −4424 19571776 1 1 48 24 1 24  ε_{1} 19.2954
4424  −7 −632 19571776 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 9.2213
4424  −56  −79 19571776 4 4 5 40 1 10  ε_{1} 18.4426
233  −19 −4427 19598329 1 1 16  8 1  8  ε_{1} 21.4863
4429  −43 −103 19616041 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 37.4394
21 −211 −4431 19633761 1 3 48 72 1 72  ε_{1} 3.1336
633  −7 −4431 19633761 1 1 48 24 1 24  ε_{1} 41.1944
1477  −3 −4431 19633761 1 1 48 24 1 24  ε_{1} 34.2370
8 −1108 −2216 19642624 1 6 22 66 1 66  ε_{1} 1.7627
2216  −4 −2216 19642624 2 1 22 22 1 11  ε_{1} 25.5233
2216  −8 −1108 19642624 2 1 6  6 1  3  ε_{1} 25.5233
341 −143 −403 19651489 1 10 2 10 1 10  ε_{1} 11.2480
4433  −11 −403 19651489 2 1 2  2 1  1  ε_{1} 53.6220
4433  −31 −143 19651489 2 3 10 30 1 15  ε_{1} 53.6220
5 −887 −4435 19669225 1 29 10 145 1 145  ε_{1} 0.9624
1109  −4 −4436 19678096 1 1 50 25 1 25  ε_{1} 23.1586
193  −23 −4439 19704721 1 3 76 114 1 114  ε_{1} 30.1526
5 −888 −4440 19713600 1 12 16 96 1 96  ε_{1} 0.9624
8 −555 −4440 19713600 1 4 16 32 1 32  ε_{1} 1.7627
24 −555 −1480 19713600 1 4 12 24 1 24  ε_{1} 4.5849
37 −120 −4440 19713600 1 4 16 32 1 32  ε_{1} 4.9836
40 −111 −4440 19713600 2 8 16 128 1 64  ε_{1} 3.6369
40 −555 −888 19713600 2 4 12 48 1 24  ε_{1} 3.6369
120 −111 −1480 19713600 2 8 12 96 1 48  ε_{1} 6.1779
120 −296 −555 19713600 2 10 4 40 1 20  ε_{1} 6.1779
185 −24 −4440 19713600 2 2 16 32 1 16 ε_{1} 9.8254
185 −120 −888 19713600 2 4 12 48 1 24  ε_{1} 9.8254
296  −15 −4440 19713600 2 2 16 32 1 16  ε_{1} 8.9090
296 −120 −555 19713600 2 4 4 16 1  8  ε_{1} 8.9090
888  −15 −1480 19713600 2 2 12 24 1 12  ε_{1} 11.3942
888  −40 −555 19713600 2 2 4  8 1  4  ε_{1} 11.3942
1480  −3 −4440 19713600 4 1 16 32 1  8  ε_{1} 12.9662
1480  −15 −888 19713600 4 2 12 48 1 12  ε_{1} 12.9662
1480  −24 −555 19713600 4 2 4 16 1  4  ε_{1} 12.9662
1480 −111 −120 19713600 4 8 4 64 1 16  ε_{1} 12.9662
4440  −3 −1480 19713600 4 1 12 24 1  6  ε_{1} 16.5871
4440  −8 −555 19713600 4 1 4  8 1  2  ε_{1} 16.5871
4440  −15 −296 19713600 4 2 10 40 1 10  ε_{1} 16.5871
4440  −40 −111 19713600 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 8.2935
1481 −3 −4443 19740249 1 1 14 7 1 7 ε_{1} 77.8029
44 −404 −1111 19749136 1 14 22 154 1 154  ε_{1} 5.9864
4444  −4 −1111 19749136 10 1 22 110 1 11  ε_{1} 10.5966
4444  −11 −404 19749136 10 1 14 70 1  7  ε_{1} 10.5966
889  −35 −635 19758025 1 2 10 10 1 10  ε_{1} 89.4446
4445  −7 −635 19758025 2 1 10 10 1  5  ε_{1} 20.7471
4445  −35 −127 19758025 2 2 5 10 1  5  ε_{1} 20.7471
4449  −3 −1483 19793601 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 94.4406

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 103

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
12 −371 −4452 19820304 1 8 16 64 1 64  ε_{1} 2.6339
21 −212 −4452 19820304 1 6 16 48 1 48  ε_{1} 3.1336
28 −159 −4452 19820304 1 10 16 80 1 80  ε_{1} 5.5373
53  −84 −4452 19820304 1 4 16 32 1 32  ε_{1} 3.9314
636  −7 −4452 19820304 2 1 16 16 1  8  ε_{1} 15.7631
636  −84 −371 19820304 2 4 8 32 1 16  ε_{1} 15.7631
1113  −4 −4452 19820304 2 1 16 16 1  8  ε_{1} 28.3110
1113  −84 −212 19820304 2 4 6 24 1 12  ε_{1} 28.3110
1484  −3 −4452 19820304 2 1 16 16 1  8  ε_{1} 16.2572
1484  −84 −159 19820304 2 4 10 40 1 20  ε_{1} 16.2572
557  −8 −4456 19855936 1 1 22 11 1 11  ε_{1} 10.9277
892  −20 −1115 19891600 3 2 10 30 1 10  ε_{1} 12.2096
4460  −4 −1115 19891600 2 1 10 10 1  5  ε_{1} 32.0520
4460  −20 −223 19891600 2 2 7 14 1  7  ε_{1} 32.0520
4461  −3 −1487 19900521 1 1 37 37 2 37 \sqrt{−1}\sqrt{ε_{1}} 27.2863
893  −95 −235 19936225 1 8 2  8 1  8  ε_{1} 15.4822
4465  −19 −235 19936225 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 41.0544
4465  −47  −95 19936225 2 5 8 40 1 20  ε_{1} 82.1089
1489  −3 −4467 19954089 3 1 12 18 1  6  ε_{1} 38.2173
1117  −4 −4468 19963024 1 1 14  7 1  7  ε_{1} 31.6567
17 −263 −4471 19989841 1 13 44 286 1 286  ε_{1} 4.1894
8 −559 −4472 19998784 1 16 36 288 1 288  ε_{1} 1.7627
13 −344 −4472 19998784 1 10 36 180 1 180  ε_{1} 2.3895
104 −43 −4472 19998784 2 1 36 36 1 18 ε_{1} 4.6249
104 −344 −559 19998784 2 10 16 160 1 80  ε_{1} 4.6249
344 −104 −559 19998784 1 6 16 48 1 48  ε_{1} 19.8864
4472  −8 −559 19998784 2 1 16 16 1  8  ε_{1} 18.0782
4472  −43 −104 19998784 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 9.0391
12 −1119 −1492 20034576 1 32 10 160 1 160  ε_{1} 2.6339
4476  −3 −1492 20034576 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 17.9636
4476  −4 −1119 20034576 2 1 32 32 1 16  ε_{1} 35.9273
1493  −3 −4479 20061441 1 1 70 35 1 35  ε_{1} 15.5303
76  −59 −4484 20106256 1 3 44 66 1 66  ε_{1} 11.6579
236  −19 −4484 20106256 1 1 44 22 1 22  ε_{1} 13.9320
1121  −4 −4484 20106256 1 1 44 22 1 22  ε_{1} 66.6959
69 −195 −1495 20115225 1 4 20 40 1 40  ε_{1} 6.4345
345 −39 −1495 20115225 2 4 20 80 1 40 ε_{1} 19.0241
345 −195 −299 20115225 2 4 8 32 1 16  ε_{1} 19.0241
897  −15 −1495 20115225 4 2 20 80 1 20  ε_{1} 14.1768
897 −115 −195 20115225 4 2 4 16 1  4  ε_{1} 14.1768
4485  −3 −1495 20115225 4 1 20 40 1 10  ε_{1} 8.4089
4485  −15 −299 20115225 4 2 8 32 1  8  ε_{1} 8.4089
4485  −23 −195 20115225 4 3 4 24 1  6  ε_{1} 8.4089
4485  −39 −115 20115225 4 4 2 16 1  4  ε_{1} 8.4089
641  −7 −4487 20133169 1 1 60 30 1 30  ε_{1} 50.0066
17 −264 −4488 20142144 1 8 16 64 1 64  ε_{1} 4.1894
24 −187 −4488 20142144 1 2 16 16 1 16  ε_{1} 4.5849
33 −136 −4488 20142144 1 4 16 32 1 32  ε_{1} 7.6563
33 −408 −1496 20142144 1 4 28 56 1 56  ε_{1} 7.6563
88  −51 −4488 20142144 1 2 16 16 1 16  ε_{1} 11.9527

104 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
264  −51 −1496 20142144 2 2 28 56 1 28  ε_{1} 9.7350
264 −187 −408 20142144 2 2 4  8 1  4  ε_{1} 9.7350
408  −11 −4488 20142144 2 1 16 16 1  8  ε_{1} 10.6165
408 −187 −264 20142144 2 2 8 16 1  8  ε_{1} 10.6165
561  −8 −4488 20142144 2 1 16 16 1  8  ε_{1} 27.7201
561  −24 −1496 20142144 2 2 28 56 1 28  ε_{1} 27.7201
561  −88 −408 20142144 2 2 4  8 1  4  ε_{1} 27.7201
561 −136 −264 20142144 2 4 8 32 1 16  ε_{1} 27.7201
1496  −3 −4488 20142144 2 1 16 16 1  8  ε_{1} 17.6287
1496  −51 −264 20142144 2 2 8 16 1  8  ε_{1} 17.6287
4488  −3 −1496 20142144 8 1 28 112 1 14  ε_{1} 9.7956
4488  −11 −408 20142144 8 1 4 16 1  2  ε_{1} 9.7956
4488  −24 −187 20142144 8 2 2 16 1  2  ε_{1} 9.7956
4488  −51  −88 20142144 8 2 2 16 1  2  ε_{1} 9.7956
4492  −4 −1123 20178064 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 38.0357
5 −899 −4495 20205025 1 14 32 224 1 224  ε_{1} 0.9624
29 −155 −4495 20205025 1 4 32 64 1 64  ε_{1} 3.2945
145 −31 −4495 20205025 4 3 32 192 1 48 ε_{1} 6.3596
145 −155 −899 20205025 4 4 14 112 1 28  ε_{1} 6.3596
8 −1124 −2248 20214016 1 20 8 80 1 80  ε_{1} 1.7627
2248 −4 −2248 20214016 2 1 8 16 2 8 \sqrt{i}\sqrt{ε_{1}} 19.9065
2248  −8 −1124 20214016 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 19.9065
4497  −3 −1499 20223009 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 59.6924
409  −11 −4499 20241001 1 1 34 17 1 17  ε_{1} 52.2684
4501  −7 −643 20259001 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 45.5480
57  −79 −4503 20277009 1 5 24 60 1 60  ε_{1} 11.4208
237  −19 −4503 20277009 1 1 24 12 1 12  ε_{1} 8.6873
1501  −3 −4503 20277009 1 1 24 12 1 12  ε_{1} 43.6455
8 −563 −4504 20286016 1 9 22 99 1 99  ε_{1} 1.7627
4504 −8 −563 20286016 5 1 9 45 2 9 \sqrt{−1}\sqrt{ε_{1}} 12.1140
13 −347 −4511 20349121 1 5 84 210 1 210  ε_{1} 2.3895
5 −903 −4515 20385225 1 16 16 128 1 128  ε_{1} 0.9624
21 −215 −4515 20385225 1 14 16 112 1 112  ε_{1} 3.1336
105 −43 −4515 20385225 2 1 16 16 1 8 ε_{1} 8.8131
105 −215 −903 20385225 2 14 16 224 1 112  ε_{1} 8.8131
129  −35 −4515 20385225 1 2 16 16 1 16  ε_{1} 20.8511
301  −15 −4515 20385225 1 2 16 16 1 16  ε_{1} 20.0642
645  −7 −4515 20385225 2 1 16 16 1  8  ε_{1} 9.6883
645  −35 −903 20385225 2 2 16 32 1 16  ε_{1} 9.6883
1505  −3 −4515 20385225 2 1 16 16 1  8  ε_{1} 33.9818
1505  −15 −903 20385225 2 2 16 32 1 16  ε_{1} 33.9818
1129  −4 −4516 20394256 9 1 16 72 1  8  ε_{1} 11.6342
5 −904 −4520 20430400 1 8 44 176 1 176  ε_{1} 0.9624
113  −40 −4520 20430400 1 2 44 44 1 44  ε_{1} 14.6946
565  −8 −4520 20430400 2 1 44 44 1 22  ε_{1} 11.4667
565  −40 −904 20430400 2 2 8 16 1  8  ε_{1} 11.4667
33 −411 −1507 20439441 1 6 4 12 1 12  ε_{1} 7.6563
4521  −3 −1507 20439441 2 1 4  4 1  2  ε_{1} 79.4930
4521  −11 −411 20439441 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 39.7465
12 −1131 −1508 20466576 1 8 16 64 1 64  ε_{1} 2.6339

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 105

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
156  −87 −1508 20466576 2 6 16 96 1 48  ε_{1} 7.8232
156 −116 −1131 20466576 2 6 8 48 1 24  ε_{1} 7.8232
348  −39 −1508 20466576 2 4 16 64 1 32  ε_{1} 8.0501
348  −52 −1131 20466576 2 2 8 16 1  8  ε_{1} 8.0501
4524  −3 −1508 20466576 4 1 16 32 1  8  ε_{1} 27.0190
4524  −4 −1131 20466576 4 1 8 16 1  4  ε_{1} 27.0190
4524  −39 −116 20466576 4 4 6 48 1 12  ε_{1} 27.0190
4524  −52  −87 20466576 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 13.5095
1132  −8 −2264 20502784 1 1 30 30 2 30 \sqrt{−1}\sqrt{ε_{1}} 19.4379
2264 −4 −2264 20502784 1 1 30 30 2 30 \sqrt{i}\sqrt{ε_{1}} 19.0689
4529  −7 −647 20511841 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 55.7992
197 −23 −4531 20529961 1 3 12 18 1 18 ε_{1} 6.6670
44 −103 −4532 20539024 1 5 28 70 1 70  ε_{1} 5.9864
412  −11 −4532 20539024 1 1 28 14 1 14  ε_{1} 26.0564
1133  −4 −4532 20539024 1 1 28 14 1 14  ε_{1} 9.2300
4533  −3 −1511 20548089 1 1 49 49 2 49 \sqrt{−1}\sqrt{ε_{1}} 28.3387
5 −907 −4535 20566225 1 3 70 105 1 105  ε_{1} 0.9624
17 −267 −4539 20602521 1 2 20 20 1 20  ε_{1} 4.1894
89  −51 −4539 20602521 1 2 20 20 1 20  ε_{1} 13.8155
1513  −3 −4539 20602521 2 1 20 20 1 10  ε_{1} 49.0402
1513  −51 −267 20602521 2 2 2  4 1  2  ε_{1} 49.0402
908  −20 −1135 20611600 1 2 18 18 1 18  ε_{1} 12.2274
4540  −4 −1135 20611600 2 1 18 18 1  9  ε_{1} 61.3728
4540  −20 −227 20611600 2 2 5 10 1  5  ε_{1} 61.3728
4541  −19 −239 20620681 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 22.3419
77  −59 −4543 20638849 1 3 28 42 1 42  ε_{1} 4.3693
413  −11 −4543 20638849 1 1 28 14 1 14  ε_{1} 8.2212
649  −7 −4543 20638849 1 1 28 14 1 14  ε_{1} 70.6969
12 −379 −4548 20684304 1 3 20 30 1 30  ε_{1} 2.6339
1137  −4 −4548 20684304 1 1 20 10 1 10  ε_{1} 55.7882
1516  −3 −4548 20684304 1 1 20 10 1 10  ε_{1} 75.5847
37 −123 −4551 20711601 1 2 56 56 1 56  ε_{1} 4.9836
41 −111 −4551 20711601 1 8 56 224 1 224  ε_{1} 8.3183
1517  −3 −4551 20711601 2 1 56 56 1 28  ε_{1} 7.3258
1517 −111 −123 20711601 2 8 2 16 1  8  ε_{1} 7.3258
569  −8 −4552 20720704 1 1 12  6 1  6  ε_{1} 44.9587
5 −911 −4555 20748025 1 31 12 186 1 186  ε_{1} 0.9624
268  −68 −1139 20757136 1 4 16 32 1 32  ε_{1} 22.9790
4556  −4 −1139 20757136 4 1 16 32 1  8  ε_{1} 11.1968
4556  −67  −68 20757136 4 1 4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.5984
97  −47 −4559 20784481 1 5 72 180 1 180  ε_{1} 18.6488
8 −1140 −2280 20793600 1 16 16 128 1 128  ε_{1} 1.7627
12 −760 −2280 20793600 1 4 16 32 1 32  ε_{1} 2.6339
24 −760 −1140 20793600 1 4 16 32 1 32  ε_{1} 4.5849
40 −228 −2280 20793600 2 4 16 64 1 32  ε_{1} 3.6369
40 −456 −1140 20793600 2 8 16 128 1 64  ε_{1} 3.6369
60 −152 −2280 20793600 2 6 16 96 1 48  ε_{1} 4.1269
60 −456 −760 20793600 2 8 4 32 1 16  ε_{1} 4.1269
76 −120 −2280 20793600 1 4 16 32 1 32  ε_{1} 11.6579
120 −152 −1140 20793600 2 6 16 96 1 48  ε_{1} 6.1779

106 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
120 −228 −760 20793600 2 4 4 16 1  8  ε_{1} 6.1779
152 −120 −1140 20793600 1 4 16 32 1 32  ε_{1} 8.6078
380 −24 −2280 20793600 2 2 16 32 1 16  ε_{1} 8.7131
380 −120 −456 20793600 2 4 8 32 1 16  ε_{1} 8.7131
456 −20 −2280 20793600 2 2 16 32 1 16  ε_{1} 15.2512
456 −40 −1140 20793600 2 2 16 32 1 16  ε_{1} 15.2512
760 −24 −1140 20793600 2 2 16 32 1 16  ε_{1} 23.1051
760 −120 −228 20793600 2 4 4 16 1  8  ε_{1} 23.1051
2280  −4 −2280 20793600 4 1 16 32 1  8  ε_{1} 11.8908
2280  −8 −1140 20793600 4 1 16 32 1  8  ε_{1} 11.8908
2280 −20 −456 20793600 4 2 8 32 1  8  ε_{1} 11.8908
2280 −40 −228 20793600 4 2 4 16 1  4  ε_{1} 11.8908
28 −163 −4564 20830096 1 1 24 12 1 12  ε_{1} 5.5373
652  −7 −4564 20830096 1 1 24 12 1 12  ε_{1} 37.3376
1141  −4 −4564 20830096 1 1 24 12 1 12  ε_{1} 41.9327
913 −55 −415 20839225 1 4 10 20 1 20  ε_{1} 69.1395
4565 −11 −415 20839225 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 9.9202
4565 −55 −83 20839225 2 4 3 12 1 6 ε_{1} 19.8404
8 −571 −4568 20866624 1 5 18 45 1 45  ε_{1} 1.7627
4568  −8 −571 20866624 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 21.3184
4569  −3 −1523 20875761 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 79.6518
653  −7 −4571 20894041 1 1 28 14 1 14  ε_{1} 14.8304
4577 −23 −199 20948929 1 3 9 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 49.4373
241 −19 −4579 20967241 1 1 10 5 1 5 ε_{1} 37.5430
5 −916 −4580 20976400 1 10 24 120 1 120  ε_{1} 0.9624
229 −20 −4580 20976400 3 2 24 72 1 24  ε_{1} 5.4249
1145 −4 −4580 20976400 4 1 24 48 1 12 ε_{1} 15.6513
1145 −20 −916 20976400 4 2 10 40 1 10  ε_{1} 15.6513
24 −191 −4584 21013056 1 13 32 208 1 208  ε_{1} 4.5849
573  −8 −4584 21013056 1 1 32 16 1 16  ε_{1} 13.2824
573 −24 −1528 21013056 1 2 8  8 1  8  ε_{1} 13.2824
1528  −3 −4584 21013056 1 1 32 16 1 16  ε_{1} 53.0447
4584  −3 −1528 21013056 2 1 8  8 1  4  ε_{1} 31.4926
4584 −24 −191 21013056 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 15.7463
917 −35 −655 21022225 1 2 12 12 1 12  ε_{1} 14.1482
4585 −7 −655 21022225 2 1 12 12 1 6 ε_{1} 108.6286
4585 −35 −131 21022225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 54.3143
33 −139 −4587 21040569 1 3 12 18 1 18  ε_{1} 7.6563
417 −11 −4587 21040569 1 1 12  6 1  6  ε_{1} 37.9102
1529  −3 −4587 21040569 1 1 12  6 1  6  ε_{1} 65.2096
124 −148 −1147 21049744 1 2 6  6 1  6  ε_{1} 16.0392
4588  −4 −1147 21049744 2 1 6  6 1  3  ε_{1} 47.3243
4588 −31 −148 21049744 2 3 2  6 1  3  ε_{1} 47.3243
28 −328 −2296 21086464 1 4 16 32 1 32  ε_{1} 5.5373
56 −164 −2296 21086464 1 8 16 64 1 64  ε_{1} 6.8002
1148  −8 −2296 21086464 2 1 16 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.3561
1148 −56 −328 21086464 2 4 4 16 1  8  ε_{1} 12.7122
2296  −4 −2296 21086464 6 1 16 96 2 16  \sqrt{i}\sqrt{ε_{1}} 7.0475
2296 −56 −164 21086464 6 4 8 96 1 16  ε_{1} 14.0950
4593  −3 −1531 21095649 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 63.8543

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 107

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −919 −4595 21114025 1 19 24 228 1 228  ε_{1} 0.9624
12 −383 −4596 21123216 1 17 16 136 1 136  ε_{1} 2.6339
1149  −4 −4596 21123216 1 1 16  8 1  8  ε_{1} 32.9675
1532  −3 −4596 21123216 1 1 16  8 1  8  ε_{1} 21.0661
4601  −43 −107 21169201 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 75.4372
4604  −4 −1151 21196816 1 1 41 41 2 41  \sqrt{i}\sqrt{ε_{1}} 25.6046
921  −15 −1535 21206025 1 2 38 38 1 38  ε_{1} 72.3140
4605  −3 −1535 21206025 2 1 38 38 1 19  ε_{1} 21.4345
4605  −15 −307 21206025 2 2 3  6 1  3  ε_{1} 21.4345
17 −271 −4607 21224449 1 11 40 220 1 220  ε_{1} 4.1894
4609 −11 −419 21242881 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 107.0081
29 −159 −4611 21261321 1 10 28 140 1 140  ε_{1} 3.2945
53  −87 −4611 21261321 1 6 28 84 1 84  ε_{1} 3.9314
1537  −3 −4611 21261321 2 1 28 28 1 14  ε_{1} 51.4699
1537  −87 −159 21261321 2 6 10 60 1 30  ε_{1} 51.4699
1153  −4 −4612 21270544 1 1 16  8 1  8  ε_{1} 79.7231
4613  −7 −659 21279769 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 13.7126
5 −923 −4615 21298225 1 10 36 180 1 180  ε_{1} 0.9624
13 −355 −4615 21298225 1 4 36 72 1 72  ε_{1} 2.3895
65 −71 −4615 21298225 2 7 36 252 1 126 ε_{1} 5.5529
65 −355 −923 21298225 2 4 10 40 1 20  ε_{1} 5.5529
577  −8 −4616 21307456 7 1 56 196 1 28  ε_{1} 7.7433
149  −31 −4619 21335161 1 3 36 54 1 54  ε_{1} 8.2223
12 −1155 −1540 21344400 1 8 8 32 1 32  ε_{1} 2.6339
21 −660 −1540 21344400 1 8 8 32 1 32  ε_{1} 3.1336
28 −660 −1155 21344400 1 8 8 32 1 32  ε_{1} 5.5373
33 −420 −1540 21344400 1 8 8 32 1 32  ε_{1} 7.6563
44 −420 −1155 21344400 1 8 8 32 1 32  ε_{1} 5.9864
60 −231 −1540 21344400 2 12 8 96 1 48  ε_{1} 4.1269
60 −308 −1155 21344400 2 8 8 64 1 32  ε_{1} 4.1269
77 −420 −660 21344400 1 8 8 32 1 32  ε_{1} 4.3693
105 −132 −1540 21344400 2 4 8 32 1 16  ε_{1} 8.8131
105 −308 −660 21344400 2 8 8 64 1 32  ε_{1} 8.8131
140 −132 −1155 21344400 2 4 8 32 1 16  ε_{1} 4.9558
140 −231 −660 21344400 2 12 8 96 1 48  ε_{1} 4.9558
165 −84 −1540 21344400 2 4 8 32 1 16 ε_{1} 5.1180
165 −308 −420 21344400 2 8 8 64 1 32  ε_{1} 5.1180
220 −84 −1155 21344400 2 4 8 32 1 16 ε_{1} 10.3635
220 −231 −420 21344400 2 12 8 96 1 48  ε_{1} 10.3635
385 −84 −660 21344400 2 4 8 32 1 16 ε_{1} 24.3270
385 −132 −420 21344400 2 4 8 32 1 16  ε_{1} 24.3270
924  −15 −1540 21344400 4 2 8 32 1  8  ε_{1} 10.0477
924  −20 −1155 21344400 4 2 8 32 1  8  ε_{1} 10.0477
924  −35 −660 21344400 4 2 8 32 1  8  ε_{1} 10.0477
924  −55 −420 21344400 4 4 8 64 1 16  ε_{1} 10.0477
4620  −3 −1540 21344400 8 1 8 32 1  4  ε_{1} 8.4386
4620  −4 −1155 21344400 8 1 8 32 1  4  ε_{1} 8.4386
4620  −7 −660 21344400 8 1 8 32 1  4  ε_{1} 8.4386
4620  −11 −420 21344400 8 1 8 32 1  4  ε_{1} 8.4386
4620  −15 −308 21344400 8 2 8 64 1  8  ε_{1} 8.4386

108 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
4620 −20 −231 21344400 8 2 12 96 1 12  ε_{1} 8.4386
4620 −35 −132 21344400 8 2 4 32 1  4  ε_{1} 8.4386
4620 −55  −84 21344400 8 4 4 64 1  8  ε_{1} 8.4386
69 −67 −4623 21372129 1 1 36 18 1 18  ε_{1} 6.4345
201 −23 −4623 21372129 1 3 36 54 1 54  ε_{1} 27.6905
1541  −3 −4623 21372129 1 1 36 18 1 18  ε_{1} 27.9708
661  −7 −4627 21409129 1 1 10  5 1  5  ε_{1} 28.7949
13 −356 −4628 21418384 1 12 28 168 1 168  ε_{1} 2.3895
89 −52 −4628 21418384 1 2 28 28 1 28  ε_{1} 13.8155
1157 −4 −4628 21418384 2 1 28 28 1 14 ε_{1} 8.4394
1157 −52 −356 21418384 2 2 12 24 1 12  ε_{1} 8.4394
4629  −3 −1543 21427641 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 36.4893
421 −11 −4631 21446161 1 1 76 38 1 38  ε_{1} 26.0114
8 −579 −4632 21455424 1 8 24 96 1 96  ε_{1} 1.7627
24 −579 −1544 21455424 1 8 20 80 1 80  ε_{1} 4.5849
193 −24 −4632 21455424 1 2 24 24 1 24  ε_{1} 30.1526
1544  −3 −4632 21455424 2 1 24 24 1 12  ε_{1} 24.6308
1544 −24 −579 21455424 2 2 8 16 1  8  ε_{1} 24.6308
4632  −3 −1544 21455424 4 1 20 40 1 10  ε_{1} 15.4935
4632  −8 −579 21455424 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.7467
76 −244 −1159 21492496 1 6 16 48 1 48  ε_{1} 11.6579
4636 −4 −1159 21492496 2 1 16 16 1 8 ε_{1} 71.4885
4636 −19 −244 21492496 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 35.7442
21 −663 −1547 21538881 1 16 12 96 1 96  ε_{1} 3.1336
273 −51 −1547 21538881 2 2 12 24 1 12  ε_{1} 14.5641
273 −119 −663 21538881 2 10 16 160 1 80  ε_{1} 14.5641
357 −39 −1547 21538881 2 4 12 48 1 24  ε_{1} 5.8833
357 −91 −663 21538881 2 2 16 32 1 16  ε_{1} 5.8833
4641  −3 −1547 21538881 12 1 12 72 1  6  ε_{1} 13.9879
4641  −7 −663 21538881 12 1 16 96 1  8  ε_{1} 13.9879
4641 −39 −119 21538881 12 4 10 240 1 20  ε_{1} 13.9879
4641 −51  −91 21538881 12 2 2 24 1  2  ε_{1} 13.9879
1549  −3 −4647 21594609 1 1 32 16 1 16  ε_{1} 54.4816
56 −83 −4648 21603904 1 3 12 18 1 18  ε_{1} 6.8002
581 −8 −4648 21603904 1 1 12 6 1 6 ε_{1} 17.6272
581 −56 −664 21603904 1 4 10 20 1 20  ε_{1} 17.6272
664 −7 −4648 21603904 1 1 12 6 1 6 ε_{1} 43.8951
4648  −7 −664 21603904 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 17.6273
4648 −56  −83 21603904 2 4 3 12 1  6  ε_{1} 35.2546
4652  −4 −1163 21641104 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 21.6478
12 −776 −2328 21678336 1 20 16 160 1 160  ε_{1} 2.6339
24 −388 −2328 21678336 1 4 16 32 1 32  ε_{1} 4.5849
1164  −8 −2328 21678336 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.3630
1164 −24 −776 21678336 4 2 20 80 1 20  ε_{1} 12.7261
2328 −4 −2328 21678336 4 1 16 32 1 8 ε_{1} 11.9117
2328 −24 −388 21678336 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.9558
1553 −3 −4659 21706281 1 1 14 7 1 7 ε_{1} 38.0572
5 −932 −4660 21715600 1 12 20 120 1 120  ε_{1} 0.9624
233 −20 −4660 21715600 1 2 20 20 1 20  ε_{1} 21.4863
1165  −4 −4660 21715600 2 1 20 20 1 10  ε_{1} 15.0011

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 109

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1165  −20 −932 21715600 2 2 12 24 1 12  ε_{1} 15.0011
4661  −59  −79 21724921 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 14.2527
8 −583 −4664 21752896 1 8 36 144 1 144  ε_{1} 1.7627
53 −88 −4664 21752896 1 2 36 36 1 36 ε_{1} 3.9314
88 −424 −583 21752896 1 6 8 24 1 24  ε_{1} 11.9527
424  −11 −4664 21752896 2 1 36 36 1 18  ε_{1} 17.9769
424  −88 −583 21752896 2 2 8 16 1  8  ε_{1} 17.9769
4664  −8 −583 21752896 2 1 8  8 1  4  ε_{1} 42.0031
4664  −11 −424 21752896 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 21.0015
933  −15 −1555 21762225 1 2 4  4 1  4  ε_{1} 23.8438
4665  −3 −1555 21762225 2 1 4  4 1  2  ε_{1} 60.6178
4665  −15 −311 21762225 2 2 19 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 30.3089
13 −359 −4667 21780889 1 19 22 209 1 209  ε_{1} 2.3895
12 −1167 −1556 21790224 1 22 22 242 1 242  ε_{1} 2.6339
4668  −3 −1556 21790224 2 1 22 22 1 11  ε_{1} 27.0494
4668  −4 −1167 21790224 2 1 22 22 1 11  ε_{1} 27.0494
161 −203 −667 21799561 1 4 4  8 1  8  ε_{1} 20.1338
4669  −7 −667 21799561 8 1 4 16 1  2  ε_{1} 10.6460
4669  −23 −203 21799561 8 3 4 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.3230
28 −167 −4676 21864976 1 11 48 264 1 264  ε_{1} 5.5373
668  −7 −4676 21864976 1 1 48 24 1 24  ε_{1} 11.6342
1169  −4 −4676 21864976 1 1 48 24 1 24  ε_{1} 67.0808
4677  −3 −1559 21874329 1 1 51 51 2 51 \sqrt{−1}\sqrt{ε_{1}} 22.4447
4681  −31 −151 21911761 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 106.0305
21 −223 −4683 21930489 1 7 16 56 1 56  ε_{1} 3.1336
669  −7 −4683 21930489 1 1 16  8 1  8  ε_{1} 25.2580
1561  −3 −4683 21930489 1 1 16  8 1  8  ε_{1} 122.1985
4684  −4 −1171 21939856 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 25.3728
109  −43 −4687 21967969 1 1 16  8 1  8  ε_{1} 11.1291
8 −1172 −2344 21977344 1 18 18 162 1 162  ε_{1} 1.7627
2344  −4 −2344 21977344 2 1 18 18 1  9  ε_{1} 45.6621
2344  −8 −1172 21977344 2 1 18 18 1  9  ε_{1} 45.6621
12 −391 −4692 22014864 1 14 24 168 1 168  ε_{1} 2.6339
17 −276 −4692 22014864 1 8 24 96 1 96  ε_{1} 4.1894
69  −68 −4692 22014864 1 4 24 48 1 48  ε_{1} 6.4345
92  −51 −4692 22014864 1 2 24 24 1 24  ε_{1} 7.7415
204  −23 −4692 22014864 2 3 24 72 1 36  ε_{1} 9.2101
204 −276 −391 22014864 2 8 14 112 1 56  ε_{1} 9.2101
1173 −4 −4692 22014864 2 1 24 24 1 12 ε_{1} 11.2262
1173  −68 −276 22014864 2 4 8 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 5.6131
1564  −3 −4692 22014864 2 1 24 24 1 12  ε_{1} 33.0036
1564  −51 −276 22014864 2 2 8 16 1  8  ε_{1} 33.0036
5 −939 −4695 22043025 1 8 44 176 1 176  ε_{1} 0.9624
313  −15 −4695 22043025 1 2 44 44 1 44  ε_{1} 38.7035
1565  −3 −4695 22043025 2 1 44 44 1 22  ε_{1} 13.7934
1565  −15 −939 22043025 2 2 8 16 1  8  ε_{1} 13.7934
8 −587 −4696 22052416 1 7 30 105 1 105  ε_{1} 1.7627
4696 −8 −587 22052416 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 57.4969
77 −427 −671 22061809 1 2 30 30 1 30  ε_{1} 4.3693
4697  −7 −671 22061809 2 1 30 30 1 15  ε_{1} 47.6632

110 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
4697 −11 −427 22061809 2 1 2  2 1  1  ε_{1} 47.6632
37 −127 −4699 22080601 1 5 12 30 1 30  ε_{1} 4.9836
4701  −3 −1567 22099401 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 35.4460
44 −107 −4708 22165264 1 3 12 18 1 18  ε_{1} 5.9864
428 −11 −4708 22165264 1 1 12  6 1  6  ε_{1} 15.1243
1177  −4 −4708 22165264 1 1 12  6 1  6  ε_{1} 88.7782
673  −7 −4711 22193521 1 1 44 22 1 22  ε_{1} 64.4243
152 −31 −4712 22202944 1 3 16 24 1 24  ε_{1} 8.6078
248 −19 −4712 22202944 1 1 16  8 1  8  ε_{1} 9.6724
589  −8 −4712 22202944 1 1 16  8 1  8  ε_{1} 30.5757
589 −152 −248 22202944 1 6 8 24 1 24  ε_{1} 30.5757
4712 −19 −248 22202944 2 1 8 8 1 4 ε_{1} 23.3765
4712 −31 −152 22202944 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 11.6883
4713  −3 −1571 22212369 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 71.6132
5 −943 −4715 22231225 1 16 24 192 1 192  ε_{1} 0.9624
41 −115 −4715 22231225 1 2 24 24 1 24  ε_{1} 8.3183
205 −23 −4715 22231225 2 3 24 72 1 36  ε_{1} 7.5213
205 −115 −943 22231225 2 2 16 32 1 16  ε_{1} 7.5213
236 −40 −2360 22278400 1 2 20 20 1 20  ε_{1} 13.9320
472 −20 −2360 22278400 1 2 20 20 1 20  ε_{1} 26.6550
1180  −8 −2360 22278400 2 1 20 20 1 10  ε_{1} 30.4285
1180 −40 −472 22278400 2 2 6 12 1  6  ε_{1} 30.4285
2360  −4 −2360 22278400 2 1 20 20 1 10  ε_{1} 18.7110
2360 −20 −472 22278400 2 2 6 12 1  6  ε_{1} 18.7110
1181  −4 −4724 22316176 1 1 46 23 1 23  ε_{1} 20.5528
29 −163 −4727 22344529 1 1 54 27 1 27  ε_{1} 3.2945
8 −591 −4728 22353984 1 22 20 220 1 220  ε_{1} 1.7627
24 −591 −1576 22353984 1 22 10 110 1 110  ε_{1} 4.5849
197 −24 −4728 22353984 1 2 20 20 1 20  ε_{1} 6.6670
1576 −3 −4728 22353984 2 1 20 20 1 10 ε_{1} 40.9752
1576 −24 −591 22353984 2 2 22 44 1 22  ε_{1} 40.9752
4728  −3 −1576 22353984 2 1 10 10 1  5  ε_{1} 35.6276
4728  −8 −591 22353984 2 1 22 22 1 11  ε_{1} 35.6276
57 −83 −4731 22382361 1 3 20 30 1 30  ε_{1} 11.4208
249 −19 −4731 22382361 1 1 20 10 1 10  ε_{1} 33.3101
1577 −3 −4731 22382361 1 1 20 10 1 10 ε_{1} 66.0912
5 −947 −4735 22420225 1 5 42 105 1 105  ε_{1} 0.9624
4737  −3 −1579 22439169 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 43.1627
677  −7 −4739 22458121 1 1 26 13 1 13  ε_{1} 7.9032
5 −948 −4740 22467600 1 12 16 96 1 96  ε_{1} 0.9624
12 −395 −4740 22467600 1 8 16 64 1 64  ε_{1} 2.6339
60 −79 −4740 22467600 2 5 16 80 1 40  ε_{1} 4.1269
60 −395 −948 22467600 2 8 12 96 1 48  ε_{1} 4.1269
237 −20 −4740 22467600 1 2 16 16 1 16  ε_{1} 8.6873
316 −15 −4740 22467600 3 2 16 48 1 16  ε_{1} 10.1503
1185 −4 −4740 22467600 2 1 16 16 1 8 ε_{1} 36.4648
1185 −20 −948 22467600 2 2 12 24 1 12  ε_{1} 36.4648
1580 −3 −4740 22467600 2 1 16 16 1 8 ε_{1} 11.5241
1580 −15 −948 22467600 2 2 12 24 1 12  ε_{1} 11.5241
4741 −11 −431 22477081 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 50.7871

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 111

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
593  −8 −4744 22505536 1 1 24 12 1 12  ε_{1} 27.9978
101  −47 −4747 22534009 1 5 8 20 1 20  ε_{1} 5.9964
4748  −4 −1187 22543504 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 25.0824
4749  −3 −1583 22553001 3 1 33 99 2 33 \sqrt{−1}\sqrt{ε_{1}} 7.3683
5 −951 −4755 22610025 1 26 12 156 1 156  ε_{1} 0.9624
317  −15 −4755 22610025 1 2 12 12 1 12  ε_{1} 8.9775
1585  −3 −4755 22610025 2 1 12 12 1  6  ε_{1} 54.8106
1585  −15 −951 22610025 2 2 26 52 1 26  ε_{1} 54.8106
29 −164 −4756 22619536 1 8 20 80 1 80  ε_{1} 3.2945
41 −116 −4756 22619536 1 6 20 60 1 60  ε_{1} 8.3183
1189 −4 −4756 22619536 2 1 20 20 1 10 ε_{1} 20.3076
1189 −116 −164 22619536 2 6 8 48 1 24  ε_{1} 20.3076
4757 −67 −71 22629049 5 1 7 35 2 7 \sqrt{−1}\sqrt{ε_{1}} 4.2339
5 −952 −4760 22657600 1 8 40 160 1 160  ε_{1} 0.9624
8 −595 −4760 22657600 1 4 40 80 1 80  ε_{1} 1.7627
17 −280 −4760 22657600 1 4 40 80 1 80  ε_{1} 4.1894
40 −119 −4760 22657600 2 10 40 400 1 200  ε_{1} 3.6369
40 −595 −952 22657600 2 4 8 32 1 16  ε_{1} 3.6369
56 −595 −680 22657600 1 4 12 24 1 24  ε_{1} 6.8002
85 −56 −4760 22657600 2 4 40 160 1 80 ε_{1} 4.4187
85 −280 −952 22657600 2 4 8 32 1 16  ε_{1} 4.4187
136  −35 −4760 22657600 2 2 40 80 1 40  ε_{1} 8.4966
136 −280 −595 22657600 2 4 4 16 1  8  ε_{1} 8.4966
280 −119 −680 22657600 2 10 12 120 1 60  ε_{1} 12.4372
280 −136 −595 22657600 2 4 4 16 1  8  ε_{1} 12.4372
680  −7 −4760 22657600 4 1 40 80 1 20  ε_{1} 6.5191
680  −35 −952 22657600 4 2 8 32 1  8  ε_{1} 6.5191
680  −56 −595 22657600 4 4 4 32 1  8  ε_{1} 6.5191
680 −119 −280 22657600 4 10 4 80 1 20  ε_{1} 6.5191
952  −35 −680 22657600 2 2 12 24 1 12  ε_{1} 20.1146
952  −40 −595 22657600 2 2 4  8 1  4  ε_{1} 20.1146
4760  −7 −680 22657600 4 1 12 24 1  6  ε_{1} 9.8544
4760  −8 −595 22657600 4 1 4  8 1  2  ε_{1} 9.8544
4760  −35 −136 22657600 4 2 4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 4.9272
4760  −40 −119 22657600 4 2 10 40 1 10  ε_{1} 9.8544
433  −11 −4763 22686169 1 1 20 10 1 10  ε_{1} 46.7895
12 −1191 −1588 22695696 1 24 6 72 1 72  ε_{1} 2.6339
4764  −3 −1588 22695696 6 1 6 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 8.7562
4764  −4 −1191 22695696 6 1 24 72 1 12  ε_{1} 17.5124
21 −227 −4767 22724289 1 5 32 80 1 80  ε_{1} 3.1336
681  −7 −4767 22724289 1 1 32 16 1 16  ε_{1} 61.3969
1589  −3 −4767 22724289 1 1 32 16 1 16  ε_{1} 31.3219
4769  −19 −251 22743361 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 69.2965
13 −367 −4771 22762441 1 9 12 54 1 54  ε_{1} 2.3895
1193 −4 −4772 22771984 1 1 36 18 1 18 ε_{1} 42.5195
129 −111 −1591 22781529 1 8 22 88 1 88  ε_{1} 20.8511
4773  −3 −1591 22781529 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 7.3709
4773 −43 −111 22781529 2 1 8 8 1 4 ε_{1} 14.7417
24 −199 −4776 22810176 1 9 28 126 1 126  ε_{1} 4.5849
597  −8 −4776 22810176 1 1 28 14 1 14  ε_{1} 18.3698

112 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
597  −24 −1592 22810176 1 2 20 20 1 20  ε_{1} 18.3698
1592  −3 −4776 22810176 1 1 28 14 1 14  ε_{1} 13.3642
4776  −3 −1592 22810176 2 1 20 20 1 10  ε_{1} 48.9826
4776  −24 −199 22810176 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 24.4913
956  −20 −1195 22848400 1 2 8  8 1  8  ε_{1} 32.6648
4780  −4 −1195 22848400 2 1 8  8 1  4  ε_{1} 45.9066
4780  −20 −239 22848400 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 22.9533
4781 −7 −683 22857961 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 22.5743
92 −104 −2392 22886656 1 6 8 24 1 24  ε_{1} 7.7415
184  −52 −2392 22886656 1 2 8  8 1  8  ε_{1} 21.5856
1196  −8 −2392 22886656 2 1 8  8 1  4  ε_{1} 13.4428
1196 −104 −184 22886656 2 6 4 24 1 12  ε_{1} 13.4428
2392  −4 −2392 22886656 2 1 8  8 1  4  ε_{1} 29.9250
2392  −52 −184 22886656 2 2 4  8 1  4  ε_{1} 29.9250
33 −435 −1595 22896225 1 4 16 32 1 32  ε_{1} 7.6563
165 −87 −1595 22896225 2 6 16 96 1 48 ε_{1} 5.1180
165 −319 −435 22896225 2 10 4 40 1 20  ε_{1} 5.1180
957  −15 −1595 22896225 2 2 16 32 1 16  ε_{1} 6.8659
957  −55 −435 22896225 2 4 4 16 1  8  ε_{1} 6.8659
4785  −3 −1595 22896225 4 1 16 32 1  8  ε_{1} 44.4144
4785  −11 −435 22896225 4 1 4  8 1  2  ε_{1} 44.4144
4785  −15 −319 22896225 4 2 10 40 1 10  ε_{1} 44.4144
4785  −55  −87 22896225 4 4 6 48 1 12  ε_{1} 44.4144
1597  −3 −4791 22953681 1 1 68 34 1 34  ε_{1} 36.8543
8 −599 −4792 22963264 1 25 12 150 1 150  ε_{1} 1.7627
4792  −8 −599 22963264 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 50.4840
5 −959 −4795 22992025 1 36 12 216 1 216  ε_{1} 0.9624
137  −35 −4795 22992025 1 2 12 12 1 12  ε_{1} 16.3142
685  −7 −4795 22992025 2 1 12 12 1  6  ε_{1} 13.2640
685  −35 −959 22992025 2 2 36 72 1 36  ε_{1} 13.2640
44 −436 −1199 23001616 1 6 38 114 1 114  ε_{1} 5.9864
4796  −4 −1199 23001616 2 1 38 38 1 19  ε_{1} 41.4376
4796  −11 −436 23001616 2 1 6  6 1  3  ε_{1} 41.4376
1601  −3 −4803 23068809 7 1 14 49 1  7  ε_{1} 8.7644
1201  −4 −4804 23078416 1 1 16  8 1  8  ε_{1} 109.1299
209  −23 −4807 23107249 1 3 40 60 1 60  ε_{1} 22.8829
253  −19 −4807 23107249 1 1 40 20 1 20  ε_{1} 15.0577
437  −11 −4807 23107249 1 1 40 20 1 20  ε_{1} 6.0845
601  −8 −4808 23116864 1 1 24 12 1 12  ε_{1} 66.5240
21 −687 −1603 23126481 1 12 6 36 1 36  ε_{1} 3.1336
4809  −3 −1603 23126481 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 44.1407
4809  −7 −687 23126481 2 1 12 12 1  6  ε_{1} 88.2814
17 −283 −4811 23145721 1 3 22 33 1 33  ε_{1} 4.1894
12 −1203 −1604 23155344 1 6 20 60 1 60  ε_{1} 2.6339
4812  −3 −1604 23155344 2 1 20 20 1 10  ε_{1} 27.3492
4812  −4 −1203 23155344 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 13.6746
8 −1204 −2408 23193856 1 8 24 96 1 96  ε_{1} 1.7627
28 −344 −2408 23193856 1 10 24 120 1 120  ε_{1} 5.5373
56 −344 −1204 23193856 1 10 8 40 1 40  ε_{1} 6.8002
172  −56 −2408 23193856 1 4 24 48 1 48  ε_{1} 17.6970

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 113

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
344 −56 −1204 23193856 1 4 8 16 1 16  ε_{1} 19.8864
2408  −4 −2408 23193856 2 1 24 24 1 12  ε_{1} 14.4510
2408  −8 −1204 23193856 2 1 8  8 1  4  ε_{1} 14.4510
61 −79 −4819 23222761 1 5 18 45 1 45  ε_{1} 7.3284
5 −964 −4820 23232400 1 12 40 240 1 240  ε_{1} 0.9624
241 −20 −4820 23232400 1 2 40 40 1 40  ε_{1} 37.5430
1205 −4 −4820 23232400 2 1 40 40 1 20 ε_{1} 10.9861
1205 −20 −964 23232400 2 2 12 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 5.4930
4821  −3 −1607 23242041 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 24.5338
13 −371 −4823 23261329 1 8 48 192 1 192  ε_{1} 2.3895
53 −91 −4823 23261329 1 2 48 48 1 48  ε_{1} 3.9314
689  −7 −4823 23261329 4 1 48 96 1 24  ε_{1} 10.6942
689 −91 −371 23261329 4 2 8 32 1  8  ε_{1} 10.6942
1609  −3 −4827 23299929 1 1 12  6 1  6  ε_{1} 122.7907
284 −68 −1207 23309584 1 4 18 36 1 36  ε_{1} 17.6959
4828  −4 −1207 23309584 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 14.6570
4828 −68  −71 23309584 2 4 7 28 1 14  ε_{1} 29.3140
4829 −11 −439 23319241 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 16.3205
5 −967 −4835 23377225 1 11 30 165 1 165  ε_{1} 0.9624
12 −403 −4836 23386896 1 2 40 40 1 40  ε_{1} 2.6339
13 −372 −4836 23386896 1 4 40 80 1 80  ε_{1} 2.3895
93 −52 −4836 23386896 1 2 40 40 1 40  ε_{1} 6.7322
124 −39 −4836 23386896 1 4 40 80 1 80  ε_{1} 16.0392
156 −31 −4836 23386896 2 3 40 120 1 60  ε_{1} 7.8232
156 −372 −403 23386896 2 4 2  8 1  4  ε_{1} 7.8232
1209  −4 −4836 23386896 2 1 40 40 1 20  ε_{1} 37.1044
1209 −52 −372 23386896 2 2 4  8 1  4  ε_{1} 37.1044
1612  −3 −4836 23386896 2 1 40 40 1 20  ε_{1} 28.2160
1612 −39 −372 23386896 2 4 4 16 1  8  ε_{1} 28.2160
4837  −7 −691 23396569 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 33.1213
1613  −3 −4839 23415921 1 1 58 29 1 29  ε_{1} 15.9940
4841 −47 −103 23435281 3 5 5 75 2 25 \sqrt{−1}\sqrt{ε_{1}} 24.5476
29 −167 −4843 23454649 1 11 8 44 1 44  ε_{1} 3.2945
28 −692 −1211 23464336 1 14 14 98 1 98  ε_{1} 5.5373
4844  −4 −1211 23464336 6 1 14 42 1  7  ε_{1} 11.7044
4844  −7 −692 23464336 6 1 14 42 1  7  ε_{1} 11.7044
57 −255 −1615 23474025 1 12 24 144 1 144  ε_{1} 11.4208
285 −51 −1615 23474025 2 2 24 48 1 24  ε_{1} 5.6595
285 −255 −323 23474025 2 12 4 48 1 24  ε_{1} 5.6595
969 −15 −1615 23474025 2 2 24 48 1 24  ε_{1} 34.2358
969 −95 −255 23474025 2 8 12 96 1 48  ε_{1} 34.2358
4845  −3 −1615 23474025 4 1 24 48 1 12  ε_{1} 15.4787
4845 −15 −323 23474025 4 2 4 16 1  4  ε_{1} 15.4787
4845 −19 −255 23474025 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.7394
4845 −51 −95 23474025 4 2 8 32 1 8 ε_{1} 15.4787
37 −131 −4847 23493409 1 5 74 185 1 185  ε_{1} 4.9836
12 −808 −2424 23503104 1 6 12 36 1 36  ε_{1} 2.6339
24 −404 −2424 23503104 1 14 12 84 1 84  ε_{1} 4.5849
1212 −8 −2424 23503104 2 1 12 12 1 6 ε_{1} 17.0535
1212 −24 −808 23503104 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.5267

114 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2424  −4 −2424 23503104 2 1 12 12 1  6  ε_{1} 36.5016
2424  −24 −404 23503104 2 2 14 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 18.2508
1213  −4 −4852 23541904 1 1 10  5 1  5  ε_{1} 37.5314
4853  −23 −211 23551609 3 3 3 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 5.3423
5 −971 −4855 23571025 1 15 20 150 1 150  ε_{1} 0.9624
8 −607 −4856 23580736 1 13 40 260 1 260  ε_{1} 1.7627
4856  −8 −607 23580736 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 32.6167
4857  −3 −1619 23590449 3 1 15 45 2 15 \sqrt{−1}\sqrt{ε_{1}} 13.9058
113  −43 −4859 23609881 1 1 30 15 1 15  ε_{1} 14.6946
1621  −3 −4863 23648769 1 1 52 26 1 26  ε_{1} 58.4091
973  −35 −695 23668225 1 2 24 24 1 24  ε_{1} 28.8137
4865  −7 −695 23668225 10 1 24 120 1 12  ε_{1} 12.6487
4865  −35 −139 23668225 10 2 3 60 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.3244
157  −31 −4867 23687689 1 3 8 12 1 12  ε_{1} 10.7226
1217  −4 −4868 23697424 1 1 32 16 1 16  ε_{1} 35.6550
21 −232 −4872 23736384 1 2 24 24 1 24  ε_{1} 3.1336
21 −696 −1624 23736384 1 12 16 96 1 96  ε_{1} 3.1336
24 −203 −4872 23736384 1 4 24 48 1 48  ε_{1} 4.5849
29 −168 −4872 23736384 1 4 24 48 1 48  ε_{1} 3.2945
56  −87 −4872 23736384 1 6 24 72 1 72  ε_{1} 6.8002
168  −87 −1624 23736384 2 6 16 96 1 48  ε_{1} 6.5132
168 −203 −696 23736384 2 4 12 48 1 24  ε_{1} 6.5132
609  −8 −4872 23736384 2 1 24 24 1 12  ε_{1} 28.0146
609  −24 −1624 23736384 2 2 16 32 1 16  ε_{1} 28.0146
609  −56 −696 23736384 2 4 12 48 1 24  ε_{1} 28.0146
609 −168 −232 23736384 2 4 2  8 1  4  ε_{1} 28.0146
696  −7 −4872 23736384 2 1 24 24 1 12  ε_{1} 15.9463
696 −168 −203 23736384 2 4 4 16 1  8  ε_{1} 15.9463
1624  −3 −4872 23736384 2 1 24 24 1 12  ε_{1} 37.1882
1624  −87 −168 23736384 2 6 4 24 1 12  ε_{1} 37.1882
4872  −3 −1624 23736384 4 1 16 32 1  8  ε_{1} 13.0964
4872  −7 −696 23736384 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.5482
4872  −24 −203 23736384 4 2 4 16 1  4  ε_{1} 13.0964
4872  −56  −87 23736384 4 4 6 48 1 12  ε_{1} 13.0964
4873  −11 −443 23746129 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 93.3877
92 −212 −1219 23775376 1 6 6 18 1 18  ε_{1} 7.7415
4876  −4 −1219 23775376 2 1 6  6 1  3  ε_{1} 77.0415
4876  −23 −212 23775376 2 3 6 18 1  9  ε_{1} 77.0415
17 −287 −4879 23804641 1 14 52 364 1 364  ε_{1} 4.1894
41 −119 −4879 23804641 1 10 52 260 1 260  ε_{1} 8.3183
697 −7 −4879 23804641 6 1 52 156 1 26 ε_{1} 11.1519
697 −119 −287 23804641 6 10 14 420 1 70  ε_{1} 11.1519
8 −1220 −2440 23814400 1 16 12 96 1 96  ε_{1} 1.7627
40 −244 −2440 23814400 2 6 12 72 1 36  ε_{1} 3.6369
40 −488 −1220 23814400 2 10 16 160 1 80  ε_{1} 3.6369
488  −20 −2440 23814400 2 2 12 24 1 12  ε_{1} 6.1862
488  −40 −1220 23814400 2 2 16 32 1 16  ε_{1} 6.1862
2440  −4 −2440 23814400 4 1 12 24 1  6  ε_{1} 23.7509
2440  −8 −1220 23814400 4 1 16 32 1  8  ε_{1} 23.7509
2440  −20 −488 23814400 4 2 10 40 1 10  ε_{1} 23.7509

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 115

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2440  −40 −244 23814400 4 2 6 24 1  6  ε_{1} 23.7509
4881  −3 −1627 23824161 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 92.3088
257  −19 −4883 23843689 3 1 18 27 1  9  ε_{1} 6.9334
12 −407 −4884 23853456 1 16 32 256 1 256  ε_{1} 2.6339
33 −148 −4884 23853456 1 2 32 32 1 32  ε_{1} 7.6563
37 −132 −4884 23853456 1 4 32 64 1 64  ε_{1} 4.9836
44 −111 −4884 23853456 1 8 32 128 1 128  ε_{1} 5.9864
444 −11 −4884 23853456 2 1 32 32 1 16 ε_{1} 12.7602
444 −132 −407 23853456 2 4 16 64 1 32  ε_{1} 12.7602
1221 −4 −4884 23853456 4 1 32 64 1 16 ε_{1} 7.1091
1221 −132 −148 23853456 4 4 2 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 3.5545
1628 −3 −4884 23853456 2 1 32 32 1 16 ε_{1} 17.1607
1628 −111 −132 23853456 2 8 4 32 1 16  ε_{1} 17.1607
8 −611 −4888 23892544 1 10 12 60 1 60  ε_{1} 1.7627
13 −376 −4888 23892544 1 8 12 48 1 48  ε_{1} 2.3895
104 −47 −4888 23892544 2 5 12 60 1 30 ε_{1} 4.6249
104 −376 −611 23892544 2 8 10 80 1 40  ε_{1} 4.6249
376 −104 −611 23892544 1 6 10 30 1 30  ε_{1} 30.5420
4888  −8 −611 23892544 2 1 10 10 1  5  ε_{1} 60.7397
4888  −47 −104 23892544 2 5 6 30 1 15  ε_{1} 60.7397
73  −67 −4891 23921881 1 1 20 10 1 10  ε_{1} 15.3334
4892  −4 −1223 23931664 3 1 35 105 2 35  \sqrt{i}\sqrt{ε_{1}} 7.8030
21 −699 −1631 23941449 1 10 44 220 1 220  ε_{1} 3.1336
4893 −3 −1631 23941449 2 1 44 44 1 22 ε_{1} 15.8733
4893  −7 −699 23941449 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 7.9367
5 −979 −4895 23961025 1 8 64 256 1 256  ε_{1} 0.9624
89  −55 −4895 23961025 1 4 64 128 1 128  ε_{1} 13.8155
445  −11 −4895 23961025 4 1 64 128 1 32  ε_{1} 6.0936
445  −55 −979 23961025 4 4 8 64 1 16  ε_{1} 6.0936
4897  −59  −83 23980609 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 96.8010
69  −71 −4899 24000201 1 7 16 56 1 56  ε_{1} 6.4345
213  −23 −4899 24000201 1 3 16 24 1 24  ε_{1} 8.5805
1633  −3 −4899 24000201 1 1 16  8 1  8  ε_{1} 109.6930
613  −8 −4904 24049216 1 1 42 21 1 21  ε_{1} 23.0010
701  −7 −4907 24078649 1 1 12  6 1  6  ε_{1} 20.1350
12 −1227 −1636 24088464 1 4 16 32 1 32  ε_{1} 2.6339
4908  −3 −1636 24088464 4 1 16 32 1  8  ε_{1} 15.6093
4908  −4 −1227 24088464 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 7.8047
1637  −3 −4911 24117921 1 1 50 25 1 25  ε_{1} 17.2406
1228  −8 −2456 24127744 1 1 34 34 2 34 \sqrt{−1}\sqrt{ε_{1}} 18.9920
2456 −4 −2456 24127744 1 1 34 34 2 34 \sqrt{i}\sqrt{ε_{1}} 27.2695
5 −983 −4915 24157225 1 27 10 135 1 135  ε_{1} 0.9624
1229 −4 −4916 24167056 3 1 38 57 1 19 ε_{1} 7.1123
33 −447 −1639 24176889 1 14 22 154 1 154  ε_{1} 7.6563
4917  −3 −1639 24176889 2 1 22 22 1 11  ε_{1} 21.0984
4917  −11 −447 24176889 2 1 14 14 1  7  ε_{1} 21.0984
5 −984 −4920 24206400 1 12 24 144 1 144  ε_{1} 0.9624
8 −615 −4920 24206400 1 20 24 240 1 240  ε_{1} 1.7627
24 −615 −1640 24206400 1 20 16 160 1 160  ε_{1} 4.5849
40 −123 −4920 24206400 2 2 24 48 1 24  ε_{1} 3.6369

116 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
40 −615 −984 24206400 2 20 12 240 1 120  ε_{1} 3.6369
41 −120 −4920 24206400 1 4 24 48 1 48  ε_{1} 8.3183
120 −123 −1640 24206400 2 2 16 32 1 16  ε_{1} 6.1779
120 −328 −615 24206400 2 4 20 80 1 40  ε_{1} 6.1779
205 −24 −4920 24206400 2 2 24 48 1 24 ε_{1} 7.5213
205 −120 −984 24206400 2 4 12 48 1 24  ε_{1} 7.5213
328 −15 −4920 24206400 4 2 24 96 1 24 ε_{1} 5.7869
328 −120 −615 24206400 4 4 20 160 1 40  ε_{1} 5.7869
984  −15 −1640 24206400 2 2 16 32 1 16  ε_{1} 24.1747
984  −40 −615 24206400 2 2 20 40 1 20  ε_{1} 24.1747
1640  −3 −4920 24206400 4 1 24 48 1 12  ε_{1} 10.1751
1640  −15 −984 24206400 4 2 12 48 1 12  ε_{1} 10.1751
1640  −24 −615 24206400 4 2 20 80 1 20  ε_{1} 10.1751
1640 −120 −123 24206400 4 4 2 16 1  4  ε_{1} 10.1751
4920  −3 −1640 24206400 4 1 16 32 1  8  ε_{1} 13.7792
4920  −8 −615 24206400 4 1 20 40 1 10  ε_{1} 13.7792
4920  −15 −328 24206400 4 2 4 16 1  4  ε_{1} 13.7792
4920  −40 −123 24206400 4 2 2  8 1  2  ε_{1} 13.7792
133 −259 −703 24216241 1 4 14 28 1 28  ε_{1} 10.3065
4921  −7 −703 24216241 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 61.5824
4921  −19 −259 24216241 2 1 4  4 1  2  ε_{1} 123.1647
4924  −4 −1231 24245776 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 56.6739
13 −379 −4927 24275329 1 3 34 51 1 51  ε_{1} 2.3895
93 −159 −1643 24295041 1 10 10 50 1 50  ε_{1} 6.7322
4929  −3 −1643 24295041 2 1 10 10 1  5  ε_{1} 97.4025
4929  −31 −159 24295041 2 3 10 30 1 15  ε_{1} 97.4025
5 −987 −4935 24354225 1 8 48 192 1 192  ε_{1} 0.9624
21 −235 −4935 24354225 1 2 48 48 1 48  ε_{1} 3.1336
105  −47 −4935 24354225 2 5 48 240 1 120  ε_{1} 8.8131
105 −235 −987 24354225 2 2 8 16 1  8  ε_{1} 8.8131
141  −35 −4935 24354225 1 2 48 48 1 48  ε_{1} 10.4940
329  −15 −4935 24354225 1 2 48 48 1 48  ε_{1} 30.7485
705  −7 −4935 24354225 2 1 48 48 1 24  ε_{1} 26.1393
705  −35 −987 24354225 2 2 8 16 1  8  ε_{1} 26.1393
1645  −3 −4935 24354225 2 1 48 48 1 24  ε_{1} 20.3809
1645  −15 −987 24354225 2 2 8 16 1  8  ε_{1} 20.3809
617  −8 −4936 24364096 1 1 24 12 1 12  ε_{1} 36.4449
449  −11 −4939 24393721 1 1 16  8 1  8  ε_{1} 39.5058
76 −260 −1235 24403600 1 8 12 48 1 48  ε_{1} 11.6579
380 −52 −1235 24403600 2 2 12 24 1 12 ε_{1} 8.7131
380 −247 −260 24403600 2 6 8 48 1 24  ε_{1} 8.7131
988  −20 −1235 24403600 2 2 12 24 1 12  ε_{1} 24.0940
988  −95 −260 24403600 2 8 8 64 1 32  ε_{1} 24.0940
4940  −4 −1235 24403600 4 1 12 24 1  6  ε_{1} 12.3969
4940  −19 −260 24403600 4 1 8 16 1  4  ε_{1} 12.3969
4940  −20 −247 24403600 4 2 6 24 1  6  ε_{1} 12.3969
4940  −52  −95 24403600 4 2 8 32 1  8  ε_{1} 12.3969
8 −1236 −2472 24443136 1 12 12 72 1 72  ε_{1} 1.7627
12 −824 −2472 24443136 1 20 12 120 1 120  ε_{1} 2.6339
24 −824 −1236 24443136 1 20 12 120 1 120  ε_{1} 4.5849

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 117

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
412  −24 −2472 24443136 1 2 12 12 1 12  ε_{1} 26.0564
824  −24 −1236 24443136 1 2 12 12 1 12  ε_{1} 23.3749
2472  −4 −2472 24443136 2 1 12 12 1  6  ε_{1} 19.8255
2472  −8 −1236 24443136 2 1 12 12 1  6  ε_{1} 19.8255
989 −115 −215 24453025 1 2 14 14 1 14  ε_{1} 23.0897
4945  −23 −215 24453025 2 3 14 42 1 21  ε_{1} 89.4167
4945  −43 −115 24453025 2 1 2  2 1  1  ε_{1} 89.4167
17 −291 −4947 24472809 1 4 12 24 1 24  ε_{1} 4.1894
97  −51 −4947 24472809 1 2 12 12 1 12  ε_{1} 18.6488
1649  −3 −4947 24472809 2 1 12 12 1  6  ε_{1} 38.3972
1649  −51 −291 24472809 2 2 4  8 1  4  ε_{1} 38.3972
1237  −4 −4948 24482704 1 1 14  7 1  7  ε_{1} 28.1466
8 −619 −4952 24522304 1 5 42 105 1 105  ε_{1} 1.7627
4952  −8 −619 24522304 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 14.4061
381  −39 −1651 24532209 1 4 8 16 1 16  ε_{1} 15.2316
4953  −3 −1651 24532209 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 17.9654
4953  −39 −127 24532209 4 4 5 40 1 10  ε_{1} 35.9307
5 −991 −4955 24552025 1 17 28 238 1 238  ε_{1} 0.9624
12 −1239 −1652 24561936 1 32 20 320 1 320  ε_{1} 2.6339
21 −708 −1652 24561936 1 4 20 40 1 40  ε_{1} 3.1336
28 −708 −1239 24561936 1 4 32 64 1 64  ε_{1} 5.5373
177  −84 −1652 24561936 1 4 20 40 1 40  ε_{1} 23.4697
236  −84 −1239 24561936 1 4 32 64 1 64  ε_{1} 13.9320
413  −84 −708 24561936 1 4 4  8 1  8  ε_{1} 8.2212
4956  −3 −1652 24561936 8 1 20 80 1 10  ε_{1} 11.7272
4956  −4 −1239 24561936 8 1 32 128 1 16  ε_{1} 11.7272
4956  −7 −708 24561936 8 1 4 16 1  2  ε_{1} 11.7272
4956  −59  −84 24561936 8 3 4 48 1  6  ε_{1} 11.7272
709  −7 −4963 24631369 1 1 12  6 1  6  ε_{1} 34.8251
17 −292 −4964 24641296 1 4 32 64 1 64  ε_{1} 4.1894
73  −68 −4964 24641296 1 4 32 64 1 64  ε_{1} 15.3334
1241  −4 −4964 24641296 2 1 32 32 1 16  ε_{1} 36.0697
1241  −68 −292 24641296 2 4 4 16 1  8  ε_{1} 36.0697
993  −15 −1655 24651225 3 2 44 132 1 44  ε_{1} 17.1487
4965  −3 −1655 24651225 2 1 44 44 1 22  ε_{1} 35.9785
4965  −15 −331 24651225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 17.9893
1657  −3 −4971 24710841 1 1 16  8 1  8  ε_{1} 89.0247
44 −452 −1243 24720784 1 8 4 16 1 16  ε_{1} 5.9864
4972  −4 −1243 24720784 4 1 4  8 1  2  ε_{1} 25.4953
4972  −11 −452 24720784 4 1 8 16 1  4  ε_{1} 25.4953
1244  −8 −2488 24760576 1 1 12 12 2 12 \sqrt{−1}\sqrt{ε_{1}} 17.3350
2488 −4 −2488 24760576 1 1 12 12 2 12 \sqrt{i}\sqrt{ε_{1}} 24.0414
13 −383 −4979 24790441 1 17 30 255 1 255  ε_{1} 2.3895
5 −996 −4980 24800400 1 12 32 192 1 192  ε_{1} 0.9624
12 −415 −4980 24800400 1 10 32 160 1 160  ε_{1} 2.6339
60 −83 −4980 24800400 2 3 32 96 1 48 ε_{1} 4.1269
60 −415 −996 24800400 2 10 12 120 1 60  ε_{1} 4.1269
249  −20 −4980 24800400 1 2 32 32 1 32  ε_{1} 33.3101
332  −15 −4980 24800400 1 2 32 32 1 32  ε_{1} 10.1997
1245  −4 −4980 24800400 2 1 32 32 1 16  ε_{1} 11.0187

118 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
1245  −20 −996 24800400 2 2 12 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 5.5094
1660  −3 −4980 24800400 2 1 32 32 1 16  ε_{1} 34.8434
1660  −15 −996 24800400 2 2 12 24 1 12  ε_{1} 34.8434
33 −151 −4983 24830289 1 7 52 182 1 182  ε_{1} 7.6563
453  −11 −4983 24830289 1 1 52 26 1 26  ε_{1} 10.0078
1661  −3 −4983 24830289 1 1 52 26 1 26  ε_{1} 29.7725
8 −623 −4984 24840256 1 22 16 176 1 176  ε_{1} 1.7627
56 −623 −712 24840256 1 22 8 88 1 88  ε_{1} 6.8002
89  −56 −4984 24840256 1 4 16 32 1 32  ε_{1} 13.8155
712  −7 −4984 24840256 2 1 16 16 1  8  ε_{1} 16.1431
712  −56 −623 24840256 2 4 22 88 1 44  ε_{1} 16.1431
4984  −7 −712 24840256 2 1 8  8 1  4  ε_{1} 68.8395
4984  −8 −623 24840256 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 34.4198
172 −116 −1247 24880144 1 6 26 78 1 78  ε_{1} 17.6970
4988  −4 −1247 24880144 2 1 26 26 1 13  ε_{1} 28.8704
4988  −43 −116 24880144 2 1 6  6 1  3  ε_{1} 28.8704
4989  −3 −1663 24890121 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 28.1738
161  −31 −4991 24910081 1 3 92 138 1 138  ε_{1} 20.1338
217  −23 −4991 24910081 1 3 92 138 1 138  ε_{1} 31.7104
713  −7 −4991 24910081 1 1 92 46 1 46  ε_{1} 32.3476
1249  −4 −4996 24960016 1 1 32 16 1 16  ε_{1} 102.5410
4997  −19 −263 24970009 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 15.7350
5001  −3 −1667 25010001 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 77.9339
77 −455 −715 25050025 1 20 4 40 1 40  ε_{1} 4.3693
385 −91 −715 25050025 2 2 4 8 1 4 ε_{1} 24.3270
385 −143 −455 25050025 2 10 20 200 1 100  ε_{1} 24.3270
1001  −35 −715 25050025 2 2 4  8 1  4  ε_{1} 29.1356
1001  −55 −455 25050025 2 4 20 80 1 40  ε_{1} 29.1356
5005  −7 −715 25050025 4 1 4  8 1  2  ε_{1} 16.8045
5005  −11 −455 25050025 4 1 20 40 1 10  ε_{1} 16.8045
5005  −35 −143 25050025 4 2 10 40 1 10  ε_{1} 16.8045
5005  −55  −91 25050025 4 4 2 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 8.4022
1669  −3 −5007 25070049 1 1 36 18 1 18  ε_{1} 41.9610
8 −1252 −2504 25080064 1 8 36 144 1 144  ε_{1} 1.7627
2504  −4 −2504 25080064 4 1 36 72 1 18  ε_{1} 7.8248
2504  −8 −1252 25080064 4 1 8 16 1  4  ε_{1} 7.8248
28 −179 −5012 25120144 1 5 32 80 1 80  ε_{1} 5.5373
716  −7 −5012 25120144 1 1 32 16 1 16  ε_{1} 31.8828
1253  −4 −5012 25120144 1 1 32 16 1 16  ε_{1} 10.3522
5 −1003 −5015 25150225 1 4 88 176 1 176  ε_{1} 0.9624
17 −295 −5015 25150225 1 8 88 352 1 352  ε_{1} 4.1894
85 −59 −5015 25150225 2 3 88 264 1 132 ε_{1} 4.4187
85 −295 −1003 25150225 2 8 4 32 1 16  ε_{1} 4.4187
8 −627 −5016 25160256 1 4 24 48 1 48  ε_{1} 1.7627
24 −627 −1672 25160256 1 4 8 16 1 16  ε_{1} 4.5849
33 −152 −5016 25160256 1 6 24 72 1 72  ε_{1} 7.6563
33 −456 −1672 25160256 1 8 8 32 1 32  ε_{1} 7.6563
57 −88 −5016 25160256 1 2 24 24 1 24 ε_{1} 11.4208
57 −264 −1672 25160256 1 8 8 32 1 32  ε_{1} 11.4208
88 −456 −627 25160256 1 8 4 16 1 16  ε_{1} 11.9527

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 119

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
152 −264 −627 25160256 1 8 4 16 1 16  ε_{1} 8.6078
209 −24 −5016 25160256 1 2 24 24 1 24 ε_{1} 22.8829
209 −264 −456 25160256 1 8 8 32 1 32  ε_{1} 22.8829
264 −19 −5016 25160256 2 1 24 24 1 12 ε_{1} 9.7350
264 −152 −627 25160256 2 6 4 24 1 12  ε_{1} 9.7350
456  −11 −5016 25160256 2 1 24 24 1 12  ε_{1} 15.2512
456  −88 −627 25160256 2 2 4  8 1  4  ε_{1} 15.2512
1672  −3 −5016 25160256 2 1 24 24 1 12  ε_{1} 22.2461
1672  −24 −627 25160256 2 2 4  8 1  4  ε_{1} 22.2461
5016  −3 −1672 25160256 4 1 8 16 1  4  ε_{1} 26.9873
5016  −8 −627 25160256 4 1 4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 13.4937
5016  −11 −456 25160256 4 1 8 16 1  4  ε_{1} 26.9873
5016  −19 −264 25160256 4 1 8 16 1  4  ε_{1} 26.9873
21 −239 −5019 25190361 1 15 20 150 1 150  ε_{1} 3.1336
717  −7 −5019 25190361 1 1 20 10 1 10  ε_{1} 10.9696
1673  −3 −5019 25190361 1 1 20 10 1 10  ε_{1} 58.9611
1004  −20 −1255 25200400 1 2 12 12 1 12  ε_{1} 31.6204
5020  −4 −1255 25200400 2 1 12 12 1  6  ε_{1} 63.5249
5020  −20 −251 25200400 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 31.7625
457 −11 −5027 25270729 1 1 14 7 1 7 ε_{1} 50.9909
12 −419 −5028 25280784 1 9 20 90 1 90  ε_{1} 2.6339
1257  −4 −5028 25280784 3 1 20 30 1 10  ε_{1} 24.4399
1676  −3 −5028 25280784 1 1 20 10 1 10  ε_{1} 40.2155
5029  −47 −107 25290841 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 31.6685
17 −296 −5032 25321024 1 10 12 60 1 60  ε_{1} 4.1894
37 −136 −5032 25321024 1 4 12 24 1 24  ε_{1} 4.9836
629 −8 −5032 25321024 2 1 12 12 1 6 ε_{1} 6.4409
629 −136 −296 25321024 2 4 10 40 1 20  ε_{1} 6.4409
5033  −7 −719 25331089 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 42.3528
5 −1007 −5035 25351225 1 30 12 180 1 180  ε_{1} 0.9624
53  −95 −5035 25351225 1 8 12 48 1 48  ε_{1} 3.9314
265  −19 −5035 25351225 2 1 12 12 1  6  ε_{1} 18.8092
265  −95 −1007 25351225 2 8 30 240 1 120  ε_{1} 18.8092
5036  −4 −1259 25361296 1 1 15 15 2 15  \sqrt{i}\sqrt{ε_{1}} 33.0374
69 −219 −1679 25371369 1 4 52 104 1 104  ε_{1} 6.4345
5037  −3 −1679 25371369 4 1 52 104 1 26  ε_{1} 8.5250
5037  −23 −219 25371369 4 3 4 24 1  6  ε_{1} 8.5250
13 −388 −5044 25441936 1 4 20 40 1 40  ε_{1} 2.3895
97  −52 −5044 25441936 1 2 20 20 1 20  ε_{1} 18.6488
1261  −4 −5044 25441936 2 1 20 20 1 10  ε_{1} 22.5547
1261  −52 −388 25441936 2 2 4  8 1  4  ε_{1} 22.5547
8 −631 −5048 25482304 1 13 36 234 1 234  ε_{1} 1.7627
5048  −8 −631 25482304 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 25.5412
12 −1263 −1684 25522704 1 20 10 100 1 100  ε_{1} 2.6339
5052  −3 −1684 25522704 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 12.5588
5052  −4 −1263 25522704 2 1 20 20 1 10  ε_{1} 25.1176
5053  −31 −163 25532809 1 3 1  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 33.5889
5 −1011 −5055 25553025 1 12 36 216 1 216  ε_{1} 0.9624
337  −15 −5055 25553025 1 2 36 36 1 36  ε_{1} 42.8642
1685  −3 −5055 25553025 2 1 36 36 1 18  ε_{1} 7.4283

120 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1685  −15 −1011 25553025 2 2 12 24 1 12  ε_{1} 7.4283
5 −1012 −5060 25603600 1 4 40 80 1 80  ε_{1} 0.9624
44 −115 −5060 25603600 1 2 40 40 1 40  ε_{1} 5.9864
92  −55 −5060 25603600 1 4 40 80 1 80  ε_{1} 7.7415
220  −23 −5060 25603600 2 3 40 120 1 60  ε_{1} 10.3635
220 −115 −1012 25603600 2 2 4  8 1  4  ε_{1} 10.3635
253  −20 −5060 25603600 1 2 40 40 1 40  ε_{1} 15.0577
460  −11 −5060 25603600 2 1 40 40 1 20  ε_{1} 15.4391
460  −55 −1012 25603600 2 4 4 16 1  8  ε_{1} 15.4391
1265  −4 −5060 25603600 2 1 40 40 1 20  ε_{1} 25.8672
1265  −20 −1012 25603600 2 2 4  8 1  4  ε_{1} 25.8672
21 −723 −1687 25613721 1 4 18 36 1 36  ε_{1} 3.1336
5061  −3 −1687 25613721 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 18.0173
5061  −7 −723 25613721 2 1 4  4 1  2  ε_{1} 36.0346
61  −83 −5063 25633969 1 3 36 54 1 54  ε_{1} 7.3284
24 −211 −5064 25644096 1 3 32 48 1 48  ε_{1} 4.5849
633  −8 −5064 25644096 1 1 32 16 1 16  ε_{1} 41.1944
633  −24 −1688 25644096 1 2 10 10 1 10  ε_{1} 41.1944
1688  −3 −5064 25644096 1 1 32 16 1 16  ε_{1} 32.9156
5064  −3 −1688 25644096 2 1 10 10 1  5  ε_{1} 41.5753
5064  −24 −211 25644096 2 2 3  6 1  3  ε_{1} 41.5753
28 −724 −1267 25684624 1 10 6 30 1 30  ε_{1} 5.5373
5068  −4 −1267 25684624 2 1 6  6 1  3  ε_{1} 41.8945
5068  −7 −724 25684624 2 1 10 10 1  5  ε_{1} 41.8945
461  −11 −5071 25715041 1 1 50 25 1 25  ε_{1} 11.7998
8 −1268 −2536 25725184 1 10 14 70 1 70  ε_{1} 1.7627
2536  −4 −2536 25725184 2 1 14 14 1  7  ε_{1} 51.2121
2536  −8 −1268 25725184 2 1 10 10 1  5  ε_{1} 51.2121
57 −267 −1691 25735329 1 2 18 18 1 18  ε_{1} 11.4208
5073  −3 −1691 25735329 6 1 18 54 1  9  ε_{1} 17.2957
5073  −19 −267 25735329 6 1 2  6 1  1  ε_{1} 17.2957
1693  −3 −5079 25796241 1 1 64 32 1 32  ε_{1} 28.2648
5 −1016 −5080 25806400 1 16 20 160 1 160  ε_{1} 0.9624
8 −635 −5080 25806400 1 10 20 100 1 100  ε_{1} 1.7627
40 −127 −5080 25806400 2 5 20 100 1 50  ε_{1} 3.6369
40 −635 −1016 25806400 2 10 16 160 1 80  ε_{1} 3.6369
1016  −40 −635 25806400 3 2 10 30 1 10  ε_{1} 12.4688
5080  −8 −635 25806400 2 1 10 10 1  5  ε_{1} 55.5652
5080  −40 −127 25806400 2 2 5 10 1  5  ε_{1} 55.5652
13 −391 −5083 25836889 1 14 8 56 1 56  ε_{1} 2.3895
17 −299 −5083 25836889 1 8 8 32 1 32  ε_{1} 4.1894
221 −23 −5083 25836889 2 3 8 24 1 12 ε_{1} 5.4072
221 −299 −391 25836889 2 8 14 112 1 56  ε_{1} 5.4072
124 −164 −1271 25847056 1 8 40 160 1 160  ε_{1} 16.0392
5084 −4 −1271 25847056 4 1 40 80 1 20 ε_{1} 22.1826
5084  −31 −164 25847056 4 3 8 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 11.0913
5089  −7 −727 25897921 3 1 13 39 2 13 \sqrt{−1}\sqrt{ε_{1}} 38.2546
1697  −3 −5091 25918281 1 1 14  7 1  7  ε_{1} 47.7607
76  −67 −5092 25928464 1 1 20 10 1 10  ε_{1} 11.6579
268  −19 −5092 25928464 1 1 20 10 1 10  ε_{1} 22.9790

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 121

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1273  −4 −5092 25928464 1 1 20 10 1 10  ε_{1} 80.8877
5093  −11 −463 25938649 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 18.3518
5 −1019 −5095 25959025 1 13 48 312 1 312  ε_{1} 0.9624
5097  −3 −1699 25979409 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 78.2251
44 −232 −2552 26050816 1 2 20 20 1 20  ε_{1} 5.9864
88 −116 −2552 26050816 1 6 20 60 1 60  ε_{1} 11.9527
1276  −8 −2552 26050816 2 1 20 20 1 10  ε_{1} 34.1320
1276  −88 −232 26050816 2 2 2  8 2  4 \sqrt{−1}\sqrt{ε_{1}} 17.0660
2552  −4 −2552 26050816 2 1 20 20 1 10  ε_{1} 22.6906
2552  −88 −116 26050816 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 11.3453
1277  −4 −5108 26091664 1 1 34 17 1 17  ε_{1} 17.5930
393  −39 −1703 26101881 1 4 28 56 1 56  ε_{1} 36.6935
5109  −3 −1703 26101881 4 1 28 56 1 14  ε_{1} 17.4934
5109  −39 −131 26101881 4 4 5 40 1 10  ε_{1} 17.4934
269  −19 −5111 26122321 1 1 78 39 1 39  ε_{1} 10.1998
5 −1023 −5115 26163225 1 16 16 128 1 128  ε_{1} 0.9624
33 −155 −5115 26163225 1 4 16 32 1 32  ε_{1} 7.6563
93  −55 −5115 26163225 1 4 16 32 1 32  ε_{1} 6.7322
165  −31 −5115 26163225 2 3 16 48 1 24  ε_{1} 5.1180
165 −155 −1023 26163225 2 4 16 64 1 32  ε_{1} 5.1180
341  −15 −5115 26163225 1 2 16 16 1 16  ε_{1} 11.2480
465  −11 −5115 26163225 2 1 16 16 1  8  ε_{1} 20.7308
465  −55 −1023 26163225 2 4 16 64 1 32  ε_{1} 20.7308
1705  −3 −5115 26163225 8 1 16 64 1  8  ε_{1} 15.1837
1705  −15 −1023 26163225 8 2 16 128 1 16  ε_{1} 15.1837
5116  −4 −1279 26173456 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 63.9008
301 −119 −731 26183689 1 10 12 60 1 60  ε_{1} 20.0642
5117 −7 −731 26183689 2 1 12 12 1 6 ε_{1} 13.9564
5117  −43 −119 26183689 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 6.9782
109 −47 −5123 26245129 1 5 26 65 1 65 ε_{1} 11.1291
12 −427 −5124 26255376 1 2 24 24 1 24  ε_{1} 2.6339
21 −244 −5124 26255376 1 6 24 72 1 72  ε_{1} 3.1336
28 −183 −5124 26255376 1 8 24 96 1 96  ε_{1} 5.5373
61  −84 −5124 26255376 1 4 24 48 1 48  ε_{1} 7.3284
732  −7 −5124 26255376 2 1 24 24 1 12  ε_{1} 13.7628
732  −84 −427 26255376 2 4 2  8 1  4  ε_{1} 13.7628
1281  −4 −5124 26255376 2 1 24 24 1 12  ε_{1} 42.3622
1281  −84 −244 26255376 2 4 6 24 1 12  ε_{1} 42.3622
1708  −3 −5124 26255376 6 1 24 72 1 12  ε_{1} 9.6404
1708  −84 −183 26255376 6 4 8 96 1 16  ε_{1} 9.6404
1709  −3 −5127 26286129 1 1 38 19 1 19  ε_{1} 31.0005
641  −8 −5128 26296384 1 1 12  6 1  6  ε_{1} 50.0066
5129  −23 −223 26306641 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 58.7635
733  −7 −5131 26327161 3 1 10 15 1  5  ε_{1} 6.5944
5132  −4 −1283 26337424 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 28.9375
177  −87 −1711 26347689 1 6 28 84 1 84  ε_{1} 23.4697
5133  −3 −1711 26347689 2 1 28 28 1 14  ε_{1} 22.2606
5133  −59  −87 26347689 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 11.1303
5 −1027 −5135 26368225 1 4 56 112 1 112  ε_{1} 0.9624
13 −395 −5135 26368225 1 8 56 224 1 224  ε_{1} 2.3895

122 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
65  −79 −5135 26368225 2 5 56 280 1 140  ε_{1} 5.5529
65 −395 −1027 26368225 2 8 4 32 1 16  ε_{1} 5.5529
8 −1284 −2568 26378496 1 20 16 160 1 160  ε_{1} 1.7627
12 −856 −2568 26378496 1 6 16 48 1 48  ε_{1} 2.6339
24 −856 −1284 26378496 1 6 20 60 1 60  ε_{1} 4.5849
428  −24 −2568 26378496 1 2 16 16 1 16  ε_{1} 15.1243
856  −24 −1284 26378496 1 2 20 20 1 20  ε_{1} 55.9217
2568  −4 −2568 26378496 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 9.3548
2568  −8 −1284 26378496 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 9.3548
5137 −11 −467 26388769 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 77.7221
5 −1028 −5140 26419600 1 16 12 96 1 96  ε_{1} 0.9624
257  −20 −5140 26419600 3 2 12 36 1 12  ε_{1} 6.9334
1285  −4 −5140 26419600 2 1 12 12 1  6  ε_{1} 20.3309
1285  −20 −1028 26419600 2 2 16 32 1 16  ε_{1} 20.3309
37 −139 −5143 26450449 1 3 40 60 1 60  ε_{1} 4.9836
8 −643 −5144 26460736 1 3 58 87 1 87  ε_{1} 1.7627
5144 −8 −643 26460736 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 24.6497
5149  −19 −271 26512201 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 56.0022
17 −303 −5151 26532801 1 10 68 340 1 340  ε_{1} 4.1894
101  −51 −5151 26532801 1 2 68 68 1 68  ε_{1} 5.9964
1717  −3 −5151 26532801 2 1 68 68 1 34  ε_{1} 23.0932
1717  −51 −303 26532801 2 2 10 20 1 10  ε_{1} 23.0932
5 −1031 −5155 26574025 1 35 12 210 1 210  ε_{1} 0.9624
1289  −4 −5156 26584336 1 1 36 18 1 18  ε_{1} 68.0567
77  −67 −5159 26615281 1 1 88 44 1 44  ε_{1} 4.3693
469  −11 −5159 26615281 3 1 88 132 1 44  ε_{1} 8.3483
737  −7 −5159 26615281 1 1 88 44 1 44  ε_{1} 40.0839
5 −1032 −5160 26625600 1 8 16 64 1 64  ε_{1} 0.9624
24 −215 −5160 26625600 1 14 16 112 1 112  ε_{1} 4.5849
120 −43 −5160 26625600 2 1 16 16 1 8 ε_{1} 6.1779
120 −215 −1032 26625600 2 14 8 112 1 56  ε_{1} 6.1779
129 −40 −5160 26625600 1 2 16 16 1 16 ε_{1} 20.8511
129 −120 −1720 26625600 1 4 12 24 1 24  ε_{1} 20.8511
344  −15 −5160 26625600 1 2 16 16 1 16  ε_{1} 19.8864
645  −8 −5160 26625600 2 1 16 16 1  8  ε_{1} 9.6883
645  −24 −1720 26625600 2 2 12 24 1 12  ε_{1} 9.6883
645  −40 −1032 26625600 2 2 8 16 1  8  ε_{1} 9.6883
645 −120 −344 26625600 2 4 10 40 1 20  ε_{1} 9.6883
1032 −15 −1720 26625600 2 2 12 24 1 12 ε_{1} 12.4844
1032 −120 −215 26625600 2 4 14 56 1 28  ε_{1} 12.4844
1720  −3 −5160 26625600 2 1 16 16 1  8  ε_{1} 31.1205
1720  −15 −1032 26625600 2 2 8 16 1  8  ε_{1} 31.1205
5160  −3 −1720 26625600 8 1 12 48 1  6  ε_{1} 13.5185
5160  −15 −344 26625600 8 2 10 80 1 10  ε_{1} 13.5185
5160  −24 −215 26625600 8 2 14 224 2 28 \sqrt{−1}\sqrt{ε_{1}} 6.7593
5160  −43 −120 26625600 8 1 4 16 1  2  ε_{1} 13.5185
1721  −3 −5163 26656569 1 1 10  5 1  5  ε_{1} 72.7737
5164  −4 −1291 26666896 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 69.4273
76 −136 −2584 26708224 1 4 16 32 1 32  ε_{1} 11.6579
152  −68 −2584 26708224 1 4 16 32 1 32  ε_{1} 8.6078

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 123

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1292  −8 −2584 26708224 4 1 16 32 1  8  ε_{1} 7.1655
1292 −136 −152 26708224 4 4 6 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 3.5827
2584 −4 −2584 26708224 8 1 16 64 1 8 ε_{1} 12.8269
2584  −68 −152 26708224 8 4 6 192 2 24 \sqrt{−1}\sqrt{ε_{1}} 6.4135
5169 −3 −1723 26718561 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 75.7515
12 −431 −5172 26749584 1 21 24 252 1 252  ε_{1} 2.6339
1293  −4 −5172 26749584 1 1 24 12 1 12  ε_{1} 14.9071
1724  −3 −5172 26749584 1 1 24 12 1 12  ε_{1} 39.0593
5173  −7 −739 26759929 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 34.3686
8 −647 −5176 26790976 1 23 28 322 1 322  ε_{1} 1.7627
5176  −8 −647 26790976 7 1 23 161 2 23 \sqrt{−1}\sqrt{ε_{1}} 7.8594
5177  −31 −167 26801329 1 3 11 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 58.3825
28 −740 −1295 26832400 1 16 36 288 1 288  ε_{1} 5.5373
140 −148 −1295 26832400 2 2 36 72 1 36  ε_{1} 4.9558
140 −259 −740 26832400 2 4 16 64 1 32  ε_{1} 4.9558
1036  −20 −1295 26832400 2 2 36 72 1 36  ε_{1} 28.6857
1036  −35 −740 26832400 2 2 16 32 1 16  ε_{1} 28.6857
5180  −4 −1295 26832400 4 1 36 72 1 18  ε_{1} 8.5529
5180  −7 −740 26832400 4 1 16 32 1  8  ε_{1} 8.5529
5180  −20 −259 26832400 4 2 4 16 1  4  ε_{1} 8.5529
5180  −35 −148 26832400 4 2 2  8 1  2  ε_{1} 8.5529
33 −471 −1727 26842761 1 16 36 288 1 288  ε_{1} 7.6563
5181  −3 −1727 26842761 4 1 36 144 2 36 \sqrt{−1}\sqrt{ε_{1}} 8.8407
5181  −11 −471 26842761 4 1 16 32 1  8  ε_{1} 17.6814
73  −71 −5183 26863489 1 7 80 280 1 280  ε_{1} 15.3334
13 −399 −5187 26904969 1 16 16 128 1 128  ε_{1} 2.3895
21 −247 −5187 26904969 1 6 16 48 1 48  ε_{1} 3.1336
57  −91 −5187 26904969 1 2 16 16 1 16  ε_{1} 11.4208
133  −39 −5187 26904969 1 4 16 32 1 32  ε_{1} 10.3065
273  −19 −5187 26904969 2 1 16 16 1  8  ε_{1} 14.5641
273 −247 −399 26904969 2 6 16 96 1 48  ε_{1} 14.5641
741  −7 −5187 26904969 2 1 16 16 1  8  ε_{1} 11.0025
741  −91 −399 26904969 2 2 16 32 1 16  ε_{1} 11.0025
1729  −3 −5187 26904969 2 1 16 16 1  8  ε_{1} 64.2443
1729  −39 −399 26904969 2 4 16 64 1 32  ε_{1} 64.2443
1297  −4 −5188 26915344 11 1 12 66 1  6  ε_{1} 8.5537
29 −179 −5191 26946481 1 5 40 100 1 100  ε_{1} 3.2945
88  −59 −5192 26956864 1 3 32 48 1 48  ε_{1} 11.9527
472  −11 −5192 26956864 1 1 32 16 1 16  ε_{1} 26.6550
649  −8 −5192 26956864 1 1 32 16 1 16  ε_{1} 70.6969
649  −88 −472 26956864 1 2 6  6 1  6  ε_{1} 70.6969
5192  −11 −472 26956864 2 1 6  6 1  3  ε_{1} 15.7219
5192  −59  −88 26956864 2 3 2  6 1  3  ε_{1} 15.7219
5 −1039 −5195 26988025 1 23 16 184 1 184  ε_{1} 0.9624
12 −1299 −1732 26998416 1 8 12 48 1 48  ε_{1} 2.6339
5196  −3 −1732 26998416 8 1 12 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.4559
5196  −4 −1299 26998416 8 1 8 32 1  4  ε_{1} 14.9118
1733  −3 −5199 27029601 1 1 74 37 1 37  ε_{1} 24.1150
5201  −7 −743 27050401 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 77.2147
1301  −4 −5204 27081616 1 1 50 25 1 25  ε_{1} 25.9645

124 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1041  −15 −1735 27092025 1 2 26 26 1 26  ε_{1} 69.9435
5205  −3 −1735 27092025 2 1 26 26 1 13  ε_{1} 21.6794
5205  −15 −347 27092025 2 2 5 10 1  5  ε_{1} 21.6794
41 −127 −5207 27112849 1 5 56 140 1 140  ε_{1} 8.3183
8 −651 −5208 27123264 1 8 16 64 1 64  ε_{1} 1.7627
21 −248 −5208 27123264 1 8 16 64 1 64  ε_{1} 3.1336
21 −744 −1736 27123264 1 12 24 144 1 144  ε_{1} 3.1336
24 −651 −1736 27123264 1 8 24 96 1 96  ε_{1} 4.5849
56 −651 −744 27123264 1 8 12 48 1 48  ε_{1} 6.8002
93 −56 −5208 27123264 1 4 16 32 1 32 ε_{1} 6.7322
93 −168 −1736 27123264 1 4 24 48 1 48  ε_{1} 6.7322
168 −31 −5208 27123264 2 3 16 48 1 24 ε_{1} 6.5132
168 −248 −651 27123264 2 8 8 64 1 32  ε_{1} 6.5132
217 −24 −5208 27123264 1 2 16 16 1 16 ε_{1} 31.7104
217 −168 −744 27123264 1 4 12 24 1 24  ε_{1} 31.7104
248 −168 −651 27123264 1 4 8 16 1 16  ε_{1} 9.6724
744  −7 −5208 27123264 2 1 16 16 1  8  ε_{1} 19.2319
744  −56 −651 27123264 2 4 8 32 1 16  ε_{1} 19.2319
1736  −3 −5208 27123264 4 1 16 32 1  8  ε_{1} 11.0429
1736  −24 −651 27123264 4 2 8 32 1  8  ε_{1} 11.0429
5208  −3 −1736 27123264 4 1 24 48 1 12  ε_{1} 13.5278
5208  −7 −744 27123264 4 1 12 24 1  6  ε_{1} 13.5278
5208  −8 −651 27123264 4 1 8 16 1  4  ε_{1} 13.5278
5208  −31 −168 27123264 4 3 4 24 1  6  ε_{1} 13.5278
5212  −4 −1303 27164944 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 59.5540
5 −1043 −5215 27196225 1 8 32 128 1 128  ε_{1} 0.9624
149  −35 −5215 27196225 1 2 32 32 1 32  ε_{1} 8.2223
745  −7 −5215 27196225 2 1 32 32 1 16  ε_{1} 34.1114
745  −35 −1043 27196225 2 2 8 16 1  8  ε_{1} 34.1114
141 −111 −1739 27217089 1 8 20 80 1 80  ε_{1} 10.4940
5217 −3 −1739 27217089 4 1 20 40 1 10 ε_{1} 41.7127
5217  −47 −111 27217089 4 5 8 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 20.8563
17 −307 −5219 27237961 1 3 24 36 1 36  ε_{1} 4.1894
5221  −23 −227 27258841 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 36.0685
1741  −3 −5223 27279729 1 1 32 16 1 16  ε_{1} 50.3527
653  −8 −5224 27290176 1 1 18  9 1  9  ε_{1} 14.8304
5228  −4 −1307 27331984 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 19.7855
12 −872 −2616 27373824 1 10 28 140 1 140  ε_{1} 2.6339
24 −436 −2616 27373824 1 6 28 84 1 84  ε_{1} 4.5849
1308  −8 −2616 27373824 2 1 28 28 1 14  ε_{1} 12.1461
1308  −24 −872 27373824 2 2 10 20 1 10  ε_{1} 12.1461
2616  −4 −2616 27373824 2 1 28 28 1 14  ε_{1} 33.3930
2616  −24 −436 27373824 2 2 6 12 1  6  ε_{1} 33.3930
5 −1047 −5235 27405225 1 16 24 192 1 192  ε_{1} 0.9624
349  −15 −5235 27405225 1 2 24 24 1 24  ε_{1} 19.6424
1745  −3 −5235 27405225 4 1 24 48 1 12  ε_{1} 18.0002
1745  −15 −1047 27405225 4 2 16 64 1 16  ε_{1} 18.0002
17 −308 −5236 27415696 1 8 24 96 1 96  ε_{1} 4.1894
28 −187 −5236 27415696 1 2 24 24 1 24  ε_{1} 5.5373
44 −119 −5236 27415696 1 10 24 120 1 120  ε_{1} 5.9864

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 125

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
77  −68 −5236 27415696 1 4 24 48 1 48  ε_{1} 4.3693
476  −11 −5236 27415696 2 1 24 24 1 12  ε_{1} 10.9612
476 −187 −308 27415696 2 2 8 16 1  8  ε_{1} 10.9612
748  −7 −5236 27415696 2 1 24 24 1 12  ε_{1} 16.2418
748 −119 −308 27415696 2 10 8 80 1 40  ε_{1} 16.2418
1309 −4 −5236 27415696 2 1 24 24 1 12 ε_{1} 23.3418
1309  −68 −308 27415696 2 4 8 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 11.6709
5 −1048 −5240 27457600 1 6 36 108 1 108  ε_{1} 0.9624
8 −655 −5240 27457600 1 12 36 216 1 216  ε_{1} 1.7627
40 −131 −5240 27457600 2 5 36 180 1 90  ε_{1} 3.6369
40 −655 −1048 27457600 2 12 6 72 1 36  ε_{1} 3.6369
1048  −40 −655 27457600 1 2 12 12 1 12  ε_{1} 38.3249
5240  −8 −655 27457600 2 1 12 12 1  6  ε_{1} 38.6755
5240  −40 −131 27457600 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 19.3378
5241 −3 −1747 27468081 5 1 5 25 2 5 \sqrt{−1}\sqrt{ε_{1}} 16.1271
12 −1311 −1748 27499536 1 28 20 280 1 280  ε_{1} 2.6339
57 −276 −1748 27499536 1 8 20 80 1 80  ε_{1} 11.4208
69 −228 −1748 27499536 1 4 20 40 1 40  ε_{1} 6.4345
76 −276 −1311 27499536 1 8 28 112 1 112  ε_{1} 11.6579
92 −228 −1311 27499536 1 4 28 56 1 56  ε_{1} 7.7415
437 −228 −276 27499536 1 4 8 16 1 16  ε_{1} 6.0845
5244  −3 −1748 27499536 4 1 20 40 1 10  ε_{1} 25.7357
5244  −4 −1311 27499536 4 1 28 56 1 14  ε_{1} 25.7357
5244  −19 −276 27499536 4 1 8 16 1  4  ε_{1} 25.7357
5244  −23 −228 27499536 4 3 4 24 1  6  ε_{1} 25.7357
89  −59 −5251 27573001 1 3 14 21 1 21  ε_{1} 13.8155
13 −404 −5252 27583504 1 14 24 168 1 168  ε_{1} 2.3895
101  −52 −5252 27583504 1 2 24 24 1 24  ε_{1} 5.9964
1313  −4 −5252 27583504 4 1 24 48 1 12  ε_{1} 14.2328
1313  −52 −404 27583504 4 2 14 56 1 14  ε_{1} 14.2328
309  −51 −1751 27594009 1 2 48 48 1 48  ε_{1} 17.0523
5253  −3 −1751 27594009 2 1 48 48 1 24  ε_{1} 21.0471
5253  −51 −103 27594009 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 10.5236
5 −1051 −5255 27615025 1 5 92 230 1 230  ε_{1} 0.9624
5257  −7 −751 27636049 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 85.2354
1753  −3 −5259 27657081 1 1 12  6 1  6  ε_{1} 97.8840
1052  −20 −1315 27667600 1 2 6  6 1  6  ε_{1} 25.0726
5260  −4 −1315 27667600 2 1 6  6 1  3  ε_{1} 42.5942
5260  −20 −263 27667600 2 2 13 26 1 13  ε_{1} 42.5942
277  −19 −5263 27699169 1 1 28 14 1 14  ε_{1} 15.7365
8 −1316 −2632 27709696 1 24 8 96 1 96  ε_{1} 1.7627
28 −376 −2632 27709696 1 8 8 32 1 32  ε_{1} 5.5373
56 −376 −1316 27709696 1 8 24 96 1 96  ε_{1} 6.8002
188  −56 −2632 27709696 1 4 8 16 1 16  ε_{1} 9.1285
376  −56 −1316 27709696 1 4 24 48 1 48  ε_{1} 30.5420
2632  −4 −2632 27709696 4 1 8 16 1  4  ε_{1} 16.2548
2632  −8 −1316 27709696 4 1 24 48 1 12  ε_{1} 16.2548
229  −23 −5267 27741289 3 3 14 63 1 21  ε_{1} 5.4249
12 −439 −5268 27751824 1 15 20 150 1 150  ε_{1} 2.6339
1317  −4 −5268 27751824 1 1 20 10 1 10  ε_{1} 25.9049

126 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1756  −3 −5268 27751824 5 1 20 50 1 10  ε_{1} 13.5598
5269  −11 −479 27762361 5 1 25 125 2 25 \sqrt{−1}\sqrt{ε_{1}} 9.3907
21 −251 −5271 27783441 1 7 64 224 1 224  ε_{1} 3.1336
753  −7 −5271 27783441 1 1 64 32 1 32  ε_{1} 54.2964
1757  −3 −5271 27783441 1 1 64 32 1 32  ε_{1} 13.8275
8 −659 −5272 27793984 1 11 10 55 1 55  ε_{1} 1.7627
5272  −8 −659 27793984 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 58.3882
5276 −4 −1319 27836176 1 1 45 45 2 45 \sqrt{i}\sqrt{ε_{1}} 21.6096
5277  −3 −1759 27846729 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 14.1369
1321  −4 −5284 27920656 1 1 24 12 1 12  ε_{1} 106.0524
1057  −35 −755 27931225 1 2 12 12 1 12  ε_{1} 81.4221
5285  −7 −755 27931225 2 1 12 12 1  6  ε_{1} 20.2942
5285  −35 −151 27931225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.1471
17 −311 −5287 27952369 1 19 34 323 1 323  ε_{1} 4.1894
661 −8 −5288 27962944 1 1 42 21 1 21 ε_{1} 28.7949
129 −123 −1763 27973521 1 2 12 12 1 12  ε_{1} 20.8511
5289  −3 −1763 27973521 2 1 12 12 1  6  ε_{1} 104.2940
5289  −43 −123 27973521 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 52.1470
13 −407 −5291 27994681 1 16 36 288 1 288  ε_{1} 2.3895
37 −143 −5291 27994681 1 10 36 180 1 180  ε_{1} 4.9836
481 −11 −5291 27994681 2 1 36 36 1 18 ε_{1} 28.9443
481 −143 −407 27994681 2 10 16 160 1 80  ε_{1} 28.9443
5293 −67 −79 28015849 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 31.1171
5 −1059 −5295 28037025 1 6 60 180 1 180  ε_{1} 0.9624
353  −15 −5295 28037025 1 2 60 60 1 60  ε_{1} 23.7346
1765  −3 −5295 28037025 6 1 60 180 1 30  ε_{1} 8.8619
1765  −15 −1059 28037025 6 2 6 36 1  6  ε_{1} 8.8619
1324  −8 −2648 28047616 1 1 22 22 2 22 \sqrt{−1}\sqrt{ε_{1}} 36.2564
2648  −4 −2648 28047616 1 1 22 22 2 22  \sqrt{i}\sqrt{ε_{1}} 21.9576
757  −7 −5299 28079401 1 1 12  6 1  6  ε_{1} 29.6460
8 −663 −5304 28132416 1 16 40 320 1 320  ε_{1} 1.7627
13 −408 −5304 28132416 1 4 40 80 1 80  ε_{1} 2.3895
17 −312 −5304 28132416 1 4 40 80 1 80  ε_{1} 4.1894
24 −663 −1768 28132416 1 16 8 64 1 64  ε_{1} 4.5849
104 −51 −5304 28132416 2 2 40 80 1 40 ε_{1} 4.6249
104 −408 −663 28132416 2 4 16 64 1 32  ε_{1} 4.6249
136 −39 −5304 28132416 2 4 40 160 1 80 ε_{1} 8.4966
136 −312 −663 28132416 2 4 16 64 1 32  ε_{1} 8.4966
221  −24 −5304 28132416 2 2 40 80 1 40  ε_{1} 5.4072
221 −312 −408 28132416 2 4 4 16 1  8  ε_{1} 5.4072
312  −51 −1768 28132416 2 2 8 16 1  8  ε_{1} 9.3267
312 −136 −663 28132416 2 4 16 64 1 32  ε_{1} 9.3267
408 −39 −1768 28132416 2 4 8 32 1 16 ε_{1} 10.6165
408 −104 −663 28132416 2 6 16 96 1 48  ε_{1} 10.6165
1768  −3 −5304 28132416 8 1 40 160 1 20  ε_{1} 7.4765
1768  −24 −663 28132416 8 2 16 128 1 16  ε_{1} 7.4765
1768  −39 −408 28132416 8 4 4 64 1  8  ε_{1} 7.4765
1768  −51 −312 28132416 8 2 4 32 1  4  ε_{1} 7.4765
5304  −3 −1768 28132416 4 1 8 16 1  4  ε_{1} 17.0732
5304  −8 −663 28132416 4 1 16 32 1  8  ε_{1} 17.0732

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 127

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
5304  −39 −136 28132416 4 4 4 32 1  8  ε_{1} 17.0732
5304  −51 −104 28132416 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.5366
29 −183 −5307 28164249 1 8 12 48 1 48  ε_{1} 3.2945
61  −87 −5307 28164249 1 6 12 36 1 36  ε_{1} 7.3284
1769  −3 −5307 28164249 2 1 12 12 1  6  ε_{1} 38.6629
1769  −87 −183 28164249 2 6 8 48 1 24  ε_{1} 38.6629
5308  −4 −1327 28174864 5 1 15 75 2 15  \sqrt{i}\sqrt{ε_{1}} 11.7757
113  −47 −5311 28206721 1 5 46 115 1 115  ε_{1} 14.6946
21 −759 −1771 28227969 1 24 8 96 1 96  ε_{1} 3.1336
33 −483 −1771 28227969 1 4 8 16 1 16  ε_{1} 7.6563
69 −231 −1771 28227969 1 12 8 48 1 48  ε_{1} 6.4345
77 −483 −759 28227969 1 4 24 48 1 48  ε_{1} 4.3693
161 −231 −759 28227969 1 12 24 144 1 144  ε_{1} 20.1338
253 −231 −483 28227969 1 12 4 24 1 24  ε_{1} 15.0577
5313  −3 −1771 28227969 4 1 8 16 1  4  ε_{1} 34.0131
5313  −7 −759 28227969 4 1 24 48 1 12  ε_{1} 34.0131
5313  −11 −483 28227969 4 1 4  8 1  2  ε_{1} 34.0131
5313  −23 −231 28227969 4 3 12 72 1 18  ε_{1} 34.0131
5 −1063 −5315 28249225 1 19 18 171 1 171  ε_{1} 0.9624
12 −443 −5316 28259856 1 5 36 90 1 90  ε_{1} 2.6339
1329  −4 −5316 28259856 1 1 36 18 1 18  ε_{1} 83.5792
1772  −3 −5316 28259856 3 1 36 54 1 18  ε_{1} 13.5689
5 −1064 −5320 28302400 1 20 24 240 1 240  ε_{1} 0.9624
56  −95 −5320 28302400 1 8 24 96 1 96  ε_{1} 6.8002
133  −40 −5320 28302400 1 2 24 24 1 24  ε_{1} 10.3065
133 −280 −760 28302400 1 4 4  8 1  8  ε_{1} 10.3065
152  −35 −5320 28302400 1 2 24 24 1 24  ε_{1} 8.6078
280  −19 −5320 28302400 2 1 24 24 1 12  ε_{1} 12.4372
280  −95 −1064 28302400 2 8 20 160 1 80  ε_{1} 12.4372
665  −8 −5320 28302400 2 1 24 24 1 12  ε_{1} 20.4394
665  −40 −1064 28302400 2 2 20 40 1 20  ε_{1} 20.4394
665  −56 −760 28302400 2 4 4 16 1  8  ε_{1} 20.4394
665 −152 −280 28302400 2 6 4 24 1 12  ε_{1} 20.4394
760  −7 −5320 28302400 2 1 24 24 1 12  ε_{1} 23.1051
760  −35 −1064 28302400 2 2 20 40 1 20  ε_{1} 23.1051
1064  −35 −760 28302400 2 2 4  8 1  4  ε_{1} 14.4451
1064  −95 −280 28302400 2 8 4 32 1 16  ε_{1} 14.4451
5320  −7 −760 28302400 4 1 4  8 1  2  ε_{1} 29.4581
5320  −19 −280 28302400 4 1 4  8 1  2  ε_{1} 29.4581
5320  −35 −152 28302400 4 2 6 24 1  6  ε_{1} 29.4581
5320  −56  −95 28302400 4 4 8 128 2 32 \sqrt{−1}\sqrt{ε_{1}} 14.7291
761  −7 −5327 28376929 3 1 58 87 1 29  ε_{1} 14.7555
1777  −3 −5331 28419561 1 1 20 10 1 10  ε_{1} 95.2359
124  −43 −5332 28430224 1 1 20 10 1 10  ε_{1} 16.0392
172  −31 −5332 28430224 1 3 20 30 1 30  ε_{1} 17.6970
1333  −4 −5332 28430224 1 1 20 10 1 10  ε_{1} 22.7491
5 −1067 −5335 28462225 1 12 32 192 1 192  ε_{1} 0.9624
97  −55 −5335 28462225 1 4 32 64 1 64  ε_{1} 18.6488
485  −11 −5335 28462225 2 1 32 32 1 16  ε_{1} 7.5694
485  −55 −1067 28462225 2 4 12 48 1 24  ε_{1} 7.5694

128 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8 −667 −5336 28472896 1 4 32 64 1 64  ε_{1} 1.7627
29 −184 −5336 28472896 1 4 32 64 1 64  ε_{1} 3.2945
184 −232 −667 28472896 1 2 4  4 1  4  ε_{1} 21.5856
232  −23 −5336 28472896 2 3 32 96 1 48  ε_{1} 10.5766
232 −184 −667 28472896 2 4 4 16 1  8  ε_{1} 10.5766
5336  −8 −667 28472896 2 1 4  4 1  2  ε_{1} 45.1314
5336  −23 −232 28472896 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 22.5657
281  −19 −5339 28504921 1 1 34 17 1 17  ε_{1} 29.1405
12 −1335 −1780 28515600 1 28 8 112 1 112  ε_{1} 2.6339
60 −267 −1780 28515600 2 2 8 16 1 8 ε_{1} 4.1269
60 −356 −1335 28515600 2 12 28 336 1 168  ε_{1} 4.1269
1068  −15 −1780 28515600 2 2 8 16 1  8  ε_{1} 16.9544
1068  −20 −1335 28515600 2 2 28 56 1 28  ε_{1} 16.9544
5340  −3 −1780 28515600 4 1 8 16 1  4  ε_{1} 22.8206
5340  −4 −1335 28515600 4 1 28 56 1 14  ε_{1} 22.8206
5340  −15 −356 28515600 4 2 12 48 1 12  ε_{1} 22.8206
5340  −20 −267 28515600 4 2 2  8 1  2  ε_{1} 22.8206
13 −411 −5343 28547649 1 6 36 108 1 108  ε_{1} 2.3895
137  −39 −5343 28547649 1 4 36 72 1 72  ε_{1} 16.3142
1781  −3 −5343 28547649 2 1 36 36 1 18  ε_{1} 10.7038
1781  −39 −411 28547649 2 4 6 24 1 12  ε_{1} 10.7038
28 −191 −5348 28601104 1 13 24 156 1 156  ε_{1} 5.5373
764  −7 −5348 28601104 1 1 24 12 1 12  ε_{1} 33.4104
1337  −4 −5348 28601104 1 1 24 12 1 12  ε_{1} 43.4587
5349  −3 −1783 28611801 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 35.6052
24 −223 −5352 28643904 1 7 20 70 1 70  ε_{1} 4.5849
669  −8 −5352 28643904 1 1 20 10 1 10  ε_{1} 25.2580
669  −24 −1784 28643904 1 2 32 32 1 32  ε_{1} 25.2580
1784  −3 −5352 28643904 1 1 20 10 1 10  ε_{1} 38.4213
5352  −3 −1784 28643904 2 1 32 32 1 16  ε_{1} 34.7197
5352  −24 −223 28643904 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 17.3599
412  −52 −1339 28686736 1 2 8  8 1  8  ε_{1} 26.0564
5356  −4 −1339 28686736 6 1 8 24 1  4  ε_{1} 25.2254
5356  −52 −103 28686736 6 2 5 60 2 10 \sqrt{−1}\sqrt{ε_{1}} 12.6127
5357  −11 −487 28697449 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 18.7825
233  −23 −5359 28718881 1 3 48 72 1 72  ε_{1} 21.4863
268  −40 −2680 28729600 1 2 12 12 1 12  ε_{1} 22.9790
536  −20 −2680 28729600 1 2 12 12 1 12  ε_{1} 25.1680
1340  −8 −2680 28729600 2 1 12 12 1  6  ε_{1} 14.1934
1340  −40 −536 28729600 2 2 14 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 7.0967
2680 −4 −2680 28729600 2 1 12 12 1 6 ε_{1} 32.5300
2680  −20 −536 28729600 2 2 14 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 16.2650
5361  −3 −1787 28740321 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 81.1308
173  −31 −5363 28761769 1 3 16 24 1 24  ε_{1} 5.1416
1789  −3 −5367 28804689 1 1 40 20 1 20  ε_{1} 54.0623
8 −671 −5368 28815424 1 30 20 300 1 300  ε_{1} 1.7627
61 −88 −5368 28815424 1 2 20 20 1 20 ε_{1} 7.3284
88 −488 −671 28815424 1 10 30 150 1 150  ε_{1} 11.9527
488  −11 −5368 28815424 2 1 20 20 1 10  ε_{1} 6.1862
488  −88 −671 28815424 2 2 30 60 1 30  ε_{1} 6.1862

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 129

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
5368  −8 −671 28815424 6 1 30 90 1 15  ε_{1} 15.3906
5368  −11 −488 28815424 6 1 10 30 1  5  ε_{1} 15.3906
413  −91 −767 28826161 1 2 22 22 1 22  ε_{1} 8.2212
5369  −7 −767 28826161 6 1 22 66 1 11  ε_{1} 24.4110
5369  −59  −91 28826161 6 3 2 18 1  3  ε_{1} 24.4110
41 −131 −5371 28847641 1 5 12 30 1 30  ε_{1} 8.3183
316  −68 −1343 28858384 3 4 34 204 1 68  ε_{1} 10.1503
5372  −4 −1343 28858384 2 1 34 68 2 34  \sqrt{i}\sqrt{ε_{1}} 13.5622
5372  −68  −79 28858384 2 4 5 20 1 10  ε_{1} 27.1245
5377  −19 −283 28912129 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 103.3756
33 −163 −5379 28933641 1 1 24 12 1 12  ε_{1} 7.6563
489  −11 −5379 28933641 1 1 24 12 1 12  ε_{1} 46.8872
1793  −3 −5379 28933641 1 1 24 12 1 12  ε_{1} 67.7891
5 −1076 −5380 28944400 1 22 16 176 1 176  ε_{1} 0.9624
269  −20 −5380 28944400 1 2 16 16 1 16  ε_{1} 10.1998
1345  −4 −5380 28944400 6 1 16 48 1  8  ε_{1} 18.3560
1345  −20 −1076 28944400 6 2 22 264 2 44 \sqrt{−1}\sqrt{ε_{1}} 9.1780
769  −7 −5383 28976689 1 1 22 11 1 11  ε_{1} 76.0544
673  −8 −5384 28987456 1 1 28 14 1 14  ε_{1} 64.4243
1077  −15 −1795 28998225 1 2 8  8 1  8  ε_{1} 11.7777
5385  −3 −1795 28998225 2 1 8  8 1  4  ε_{1} 86.7264
5385  −15 −359 28998225 2 2 19 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 43.3632
12 −1347 −1796 29030544 1 6 20 60 1 60  ε_{1} 2.6339
5388  −3 −1796 29030544 2 1 20 20 1 10  ε_{1} 32.6163
5388  −4 −1347 29030544 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 16.3082
8 −1348 −2696 29073664 1 8 24 96 1 96  ε_{1} 1.7627
2696  −4 −2696 29073664 4 1 24 96 2 24  \sqrt{i}\sqrt{ε_{1}} 7.2079
2696  −8 −1348 29073664 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.2079
5 −1079 −5395 29106025 1 34 12 204 1 204  ε_{1} 0.9624
13 −415 −5395 29106025 1 10 12 60 1 60  ε_{1} 2.3895
65 −83 −5395 29106025 2 3 12 36 1 18 ε_{1} 5.5529
65 −415 −1079 29106025 2 10 34 340 1 170  ε_{1} 5.5529
76  −71 −5396 29116816 1 7 56 196 1 196  ε_{1} 11.6579
284  −19 −5396 29116816 1 1 56 28 1 28  ε_{1} 17.6959
1349  −4 −5396 29116816 1 1 56 28 1 28  ε_{1} 19.3578
21 −771 −1799 29127609 1 6 50 150 1 150  ε_{1} 3.1336
5397  −3 −1799 29127609 2 1 50 50 1 25  ε_{1} 16.6443
5397  −7 −771 29127609 2 1 6  6 1  3  ε_{1} 16.6443
5401  −11 −491 29170801 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 133.5621
1801  −3 −5403 29192409 1 1 16  8 1  8  ε_{1} 138.6334
28 −772 −1351 29203216 1 4 24 48 1 48  ε_{1} 5.5373
5404  −4 −1351 29203216 8 1 24 96 1 12  ε_{1} 18.8428
5404  −7 −772 29203216 8 1 4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 9.4214
1081 −115 −235 29214025 1 2 2  2 1  2  ε_{1} 95.6412
5405  −23 −235 29214025 2 3 2  6 1  3  ε_{1} 27.1546
5405  −47 −115 29214025 2 5 2 10 1  5  ε_{1} 27.1546
773  −7 −5411 29278921 1 1 34 17 1 17  ε_{1} 9.8691
12 −451 −5412 29289744 1 6 16 48 1 48  ε_{1} 2.6339
33 −164 −5412 29289744 1 8 16 64 1 64  ε_{1} 7.6563
41 −132 −5412 29289744 1 4 16 32 1 32  ε_{1} 8.3183

130 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
44 −123 −5412 29289744 1 2 16 16 1 16  ε_{1} 5.9864
492 −11 −5412 29289744 2 1 16 16 1 8 ε_{1} 10.9943
492 −132 −451 29289744 2 4 6 24 1 12  ε_{1} 10.9943
1353 −4 −5412 29289744 2 1 16 16 1 8 ε_{1} 36.5389
1353 −132 −164 29289744 2 4 8 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 18.2694
1804  −3 −5412 29289744 2 1 16 16 1  8  ε_{1} 36.6950
1804 −123 −132 29289744 2 2 4  8 1  4  ε_{1} 36.6950
677  −8 −5416 29333056 1 1 22 11 1 11  ε_{1} 7.9032
1084  −20 −1355 29376400 1 2 12 12 1 12  ε_{1} 52.3396
5420  −4 −1355 29376400 2 1 12 12 1  6  ε_{1} 30.2186
5420  −20 −271 29376400 2 2 11 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 15.1093
417  −39 −1807 29387241 1 4 12 24 1 24  ε_{1} 37.9102
5421  −3 −1807 29387241 4 1 12 24 1  6  ε_{1} 16.4617
5421  −39 −139 29387241 4 4 3 24 1  6  ε_{1} 16.4617
17 −319 −5423 29408929 1 10 68 340 1 340  ε_{1} 4.1894
29 −187 −5423 29408929 1 2 68 68 1 68  ε_{1} 3.2945
493 −11 −5423 29408929 2 1 68 68 1 34 ε_{1} 9.4192
493 −187 −319 29408929 2 2 10 20 1 10  ε_{1} 9.4192
12 −904 −2712 29419776 1 8 20 80 1 80  ε_{1} 2.6339
24 −452 −2712 29419776 1 8 20 80 1 80  ε_{1} 4.5849
1356  −8 −2712 29419776 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 12.1856
1356  −24 −904 29419776 2 2 8 16 1  8  ε_{1} 24.3711
2712  −4 −2712 29419776 2 1 20 40 2 20  \sqrt{i}\sqrt{ε_{1}} 7.2108
2712  −24 −452 29419776 2 2 8 16 1  8  ε_{1} 14.4216
92  −59 −5428 29463184 1 3 16 24 1 24  ε_{1} 7.7415
236  −23 −5428 29463184 1 3 16 24 1 24  ε_{1} 13.9320
1357  −4 −5428 29463184 1 1 16  8 1  8  ε_{1} 27.4038
8 −679 −5432 29506624 1 18 24 216 1 216  ε_{1} 1.7627
56 −679 −776 29506624 1 18 20 180 1 180  ε_{1} 6.8002
97  −56 −5432 29506624 1 4 24 48 1 48  ε_{1} 18.6488
776  −7 −5432 29506624 2 1 24 24 1 12  ε_{1} 11.9323
776  −56 −679 29506624 2 4 18 72 1 36  ε_{1} 11.9323
5432  −7 −776 29506624 2 1 20 20 1 10  ε_{1} 31.2144
5432  −8 −679 29506624 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 15.6072
5433  −3 −1811 29517489 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 66.9360
5 −1087 −5435 29539225 1 9 26 117 1 117  ε_{1} 0.9624
1361 −4 −5444 29637136 1 1 60 30 1 30 ε_{1} 61.8173
13 −419 −5447 29669809 1 9 60 270 1 270  ε_{1} 2.3895
24 −227 −5448 29680704 1 5 24 60 1 60  ε_{1} 4.5849
681  −8 −5448 29680704 1 1 24 12 1 12  ε_{1} 61.3969
681  −24 −1816 29680704 1 2 14 14 1 14  ε_{1} 61.3969
1816  −3 −5448 29680704 1 1 24 12 1 12  ε_{1} 76.1204
5448  −3 −1816 29680704 2 1 14 14 1  7  ε_{1} 43.4627
5448  −24 −227 29680704 2 2 5 10 1  5  ε_{1} 43.4627
69  −79 −5451 29713401 1 5 28 70 1 70  ε_{1} 6.4345
237  −23 −5451 29713401 1 3 28 42 1 42  ε_{1} 8.6873
1817  −3 −5451 29713401 1 1 28 14 1 14  ε_{1} 62.9992
188 −116 −1363 29724304 1 6 6 18 1 18  ε_{1} 9.1285
5452  −4 −1363 29724304 2 1 6  6 1  3  ε_{1} 31.4951
5452  −47 −116 29724304 2 5 6 30 1 15  ε_{1} 31.4951

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 131

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
133 −287 −779 29735209 1 14 10 70 1 70  ε_{1} 10.3065
5453  −7 −779 29735209 2 1 10 10 1  5  ε_{1} 16.2172
5453  −19 −287 29735209 2 1 14 14 1  7  ε_{1} 16.2172
5 −1091 −5455 29757025 1 17 36 306 1 306  ε_{1} 0.9624
8 −1364 −2728 29767936 1 28 12 168 1 168  ε_{1} 1.7627
44 −248 −2728 29767936 1 8 12 48 1 48  ε_{1} 5.9864
88 −248 −1364 29767936 1 8 28 112 1 112  ε_{1} 11.9527
124  −88 −2728 29767936 1 2 12 12 1 12  ε_{1} 16.0392
248  −88 −1364 29767936 1 2 28 28 1 28  ε_{1} 9.6724
2728  −4 −2728 29767936 2 1 12 12 1  6  ε_{1} 29.3785
2728  −8 −1364 29767936 2 1 28 28 1 14  ε_{1} 29.3785
321  −51 −1819 29778849 3 2 10 30 1 10  ε_{1} 12.1276
5457  −3 −1819 29778849 2 1 10 10 1  5  ε_{1} 86.3043
5457  −51 −107 29778849 2 2 3  6 1  3  ε_{1} 86.3043
53 −103 −5459 29800681 1 5 34 85 1 85  ε_{1} 3.9314
5 −1092 −5460 29811600 1 8 16 64 1 64  ε_{1} 0.9624
12 −455 −5460 29811600 1 20 16 160 1 160  ε_{1} 2.6339
13 −420 −5460 29811600 1 8 16 64 1 64  ε_{1} 2.3895
21 −260 −5460 29811600 1 8 16 64 1 64  ε_{1} 3.1336
28 −195 −5460 29811600 1 4 16 32 1 32  ε_{1} 5.5373
60 −91 −5460 29811600 2 2 16 32 1 16 ε_{1} 4.1269
60 −455 −1092 29811600 2 20 8 160 1 80  ε_{1} 4.1269
65 −84 −5460 29811600 2 4 16 64 1 32 ε_{1} 5.5529
65 −420 −1092 29811600 2 8 8 64 1 32  ε_{1} 5.5529
105 −52 −5460 29811600 2 2 16 32 1 16 ε_{1} 8.8131
105 −260 −1092 29811600 2 8 8 64 1 32  ε_{1} 8.8131
140 −39 −5460 29811600 2 4 16 64 1 32 ε_{1} 4.9558
140 −195 −1092 29811600 2 4 8 32 1 16  ε_{1} 4.9558
156 −35 −5460 29811600 2 2 16 32 1 16 ε_{1} 7.8232
156 −420 −455 29811600 2 8 20 160 1 80  ε_{1} 7.8232
273 −20 −5460 29811600 2 2 16 32 1 16 ε_{1} 14.5641
273 −260 −420 29811600 2 8 8 64 1 32  ε_{1} 14.5641
364 −15 −5460 29811600 2 2 16 32 1 16 ε_{1} 16.1090
364 −195 −420 29811600 2 4 8 32 1 16  ε_{1} 16.1090
780  −7 −5460 29811600 4 1 16 32 1  8  ε_{1} 6.6619
780  −35 −1092 29811600 4 2 8 32 1  8  ε_{1} 6.6619
780  −84 −455 29811600 4 4 20 160 1 40  ε_{1} 6.6619
780  −91 −420 29811600 4 2 8 32 1  8  ε_{1} 6.6619
1365  −4 −5460 29811600 4 1 16 32 1  8  ε_{1} 7.2204
1365  −20 −1092 29811600 4 2 8 32 1  8  ε_{1} 7.2204
1365  −52 −420 29811600 4 2 8 32 1  8  ε_{1} 7.2204
1365  −84 −260 29811600 4 4 8 64 1 16  ε_{1} 7.2204
1820  −3 −5460 29811600 4 1 16 32 1  8  ε_{1} 9.7039
1820  −15 −1092 29811600 4 2 8 32 1  8  ε_{1} 9.7039
1820  −39 −420 29811600 4 4 8 64 1 16  ε_{1} 9.7039
1820  −84 −195 29811600 4 4 4 32 1  8  ε_{1} 9.7039
5461  −43 −127 29822521 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 58.3813
8 −683 −5464 29855296 1 5 18 45 1 45  ε_{1} 1.7627
5464  −8 −683 29855296 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 77.5075
77  −71 −5467 29888089 1 7 8 28 1 28  ε_{1} 4.3693

132 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
497  −11 −5467 29888089 1 1 8  4 1  4  ε_{1} 29.3851
781  −7 −5467 29888089 1 1 8  4 1  4  ε_{1} 37.4447
5468  −4 −1367 29899024 3 1 25 75 2 25  \sqrt{i}\sqrt{ε_{1}} 7.9143
5469  −3 −1823 29909961 1 1 45 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 36.7333
5 −1096 −5480 30030400 1 12 44 264 1 264  ε_{1} 0.9624
137  −40 −5480 30030400 1 2 44 44 1 44  ε_{1} 16.3142
685  −8 −5480 30030400 2 1 44 44 1 22  ε_{1} 13.2640
685  −40 −1096 30030400 2 2 12 24 1 12  ε_{1} 13.2640
12 −1371 −1828 30074256 1 12 8 48 1 48  ε_{1} 2.6339
5484  −3 −1828 30074256 4 1 8 16 1  4  ε_{1} 15.8314
5484  −4 −1371 30074256 4 1 12 48 2 12  \sqrt{i}\sqrt{ε_{1}} 7.9157
93  −59 −5487 30107169 1 3 52 78 1 78  ε_{1} 6.7322
177  −31 −5487 30107169 1 3 52 78 1 78  ε_{1} 23.4697
1829  −3 −5487 30107169 1 1 52 26 1 26  ε_{1} 36.4312
5489  −11 −499 30129121 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 85.0361
1373  −4 −5492 30162064 3 1 18 27 1  9  ε_{1} 7.2233
5493  −3 −1831 30173049 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 15.7344
5 −1099 −5495 30195025 1 6 84 252 1 252  ε_{1} 0.9624
157  −35 −5495 30195025 1 2 84 84 1 84  ε_{1} 10.7226
785  −7 −5495 30195025 6 1 84 252 1 42  ε_{1} 8.0513
785  −35 −1099 30195025 6 2 6 36 1  6  ε_{1} 8.0513
8 −687 −5496 30206016 1 12 28 168 1 168  ε_{1} 1.7627
24 −687 −1832 30206016 1 12 26 156 1 156  ε_{1} 4.5849
229  −24 −5496 30206016 3 2 28 84 1 28  ε_{1} 5.4249
1832  −3 −5496 30206016 2 1 28 28 1 14  ε_{1} 10.7320
1832  −24 −687 30206016 2 2 12 24 1 12  ε_{1} 10.7320
5496  −3 −1832 30206016 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 26.4504
5496 −8 −687 30206016 2 1 12 12 1 6 ε_{1} 52.9008
5497  −23 −239 30217009 3 3 15 135 2 45 \sqrt{−1}\sqrt{ε_{1}} 32.1055
1101  −15 −1835 30305025 3 2 10 30 1 10  ε_{1} 11.7998
5505  −3 −1835 30305025 2 1 10 10 1  5  ε_{1} 68.1106
5505  −15 −367 30305025 2 2 9 18 1  9  ε_{1} 68.1106
5509  −7 −787 30349081 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 53.7263
33 −167 −5511 30371121 1 11 56 308 1 308  ε_{1} 7.6563
501  −11 −5511 30371121 1 1 56 28 1 28  ε_{1} 20.4959
1837  −3 −5511 30371121 1 1 56 28 1 28  ε_{1} 34.3491
13 −424 −5512 30382144 1 6 20 60 1 60  ε_{1} 2.3895
53 −104 −5512 30382144 1 6 20 60 1 60  ε_{1} 3.9314
689 −8 −5512 30382144 4 1 20 40 1 10 ε_{1} 10.6942
689 −104 −424 30382144 4 6 6 72 1 18  ε_{1} 10.6942
5 −1103 −5515 30415225 1 23 10 115 1 115  ε_{1} 0.9624
28 −788 −1379 30426256 1 10 16 80 1 80  ε_{1} 5.5373
5516 −4 −1379 30426256 2 1 16 16 1 8 ε_{1} 44.6797
5516  −7 −788 30426256 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 22.3399
8 −1380 −2760 30470400 1 8 16 64 1 64  ε_{1} 1.7627
12 −920 −2760 30470400 1 20 16 160 1 160  ε_{1} 2.6339
24 −920 −1380 30470400 1 20 8 80 1 80  ε_{1} 4.5849
40 −276 −2760 30470400 2 8 16 128 1 64  ε_{1} 3.6369
40 −552 −1380 30470400 2 8 8 64 1 32  ε_{1} 3.6369
60 −184 −2760 30470400 2 4 16 64 1 32  ε_{1} 4.1269

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 133

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
60 −552 −920 30470400 2 8 20 160 1 80  ε_{1} 4.1269
92 −120 −2760 30470400 1 4 16 32 1 32  ε_{1} 7.7415
120 −184 −1380 30470400 2 4 8 32 1 16  ε_{1} 6.1779
120 −276 −920 30470400 2 8 20 160 1 80  ε_{1} 6.1779
184 −120 −1380 30470400 1 4 8 16 1 16  ε_{1} 21.5856
460 −24 −2760 30470400 2 2 16 32 1 16 ε_{1} 15.4391
460 −120 −552 30470400 2 4 8 32 1 16  ε_{1} 15.4391
552  −20 −2760 30470400 2 2 16 32 1 16  ε_{1} 9.0864
552  −40 −1380 30470400 2 2 8 16 1  8  ε_{1} 9.0864
920  −24 −1380 30470400 2 2 8 16 1  8  ε_{1} 10.4080
920 −120 −276 30470400 2 4 8 32 1 16  ε_{1} 10.4080
2760  −4 −2760 30470400 4 1 16 32 1  8  ε_{1} 15.9737
2760  −8 −1380 30470400 4 1 8 16 1  4  ε_{1} 15.9737
2760  −20 −552 30470400 4 2 8 32 1  8  ε_{1} 15.9737
2760  −40 −276 30470400 4 2 8 32 1  8  ε_{1} 15.9737
21 −263 −5523 30503529 1 13 12 78 1 78  ε_{1} 3.1336
789  −7 −5523 30503529 1 1 12  6 1  6  ε_{1} 20.7360
1841  −3 −5523 30503529 1 1 12  6 1  6  ε_{1} 81.2666
1381  −4 −5524 30514576 1 1 26 13 1 13  ε_{1} 50.0922
8 −691 −5528 30558784 1 5 38 95 1 95  ε_{1} 1.7627
5528 −8 −691 30558784 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 17.0739
57 −291 −1843 30569841 1 4 6 12 1 12  ε_{1} 11.4208
5529  −3 −1843 30569841 6 1 6 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 14.1836
5529  −19 −291 30569841 6 1 4 12 1  2  ε_{1} 28.3671
12 −1383 −1844 30603024 1 18 30 270 1 270  ε_{1} 2.6339
5532  −3 −1844 30603024 2 1 30 30 1 15  ε_{1} 29.5343
5532  −4 −1383 30603024 2 1 18 18 1  9  ε_{1} 29.5343
5533  −11 −503 30614089 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 29.3578
29 −191 −5539 30680521 1 13 18 117 1 117  ε_{1} 3.2945
5 −1108 −5540 30691600 1 6 48 144 1 144  ε_{1} 0.9624
277  −20 −5540 30691600 1 2 48 48 1 48  ε_{1} 15.7365
1385  −4 −5540 30691600 2 1 48 48 1 24  ε_{1} 24.4924
1385  −20 −1108 30691600 2 2 6 12 1  6  ε_{1} 24.4924
5541  −3 −1847 30702681 1 1 43 43 2 43 \sqrt{−1}\sqrt{ε_{1}} 34.7851
241  −23 −5543 30724849 1 3 78 117 1 117  ε_{1} 37.5430
76 −292 −1387 30780304 1 4 4  8 1  8  ε_{1} 11.6579
5548  −4 −1387 30780304 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 14.9211
5548  −19 −292 30780304 4 1 4  8 1  2  ε_{1} 29.8421
5549  −31 −179 30791401 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 21.7720
13 −427 −5551 30813601 1 2 52 52 1 52  ε_{1} 2.3895
61  −91 −5551 30813601 1 2 52 52 1 52  ε_{1} 7.3284
793  −7 −5551 30813601 4 1 52 104 1 26  ε_{1} 18.1618
793  −91 −427 30813601 4 2 2  8 1  2  ε_{1} 18.1618
1388  −8 −2776 30824704 1 1 10 10 2 10 \sqrt{−1}\sqrt{ε_{1}} 14.0649
2776 −4 −2776 30824704 1 1 10 10 2 10 \sqrt{i}\sqrt{ε_{1}} 52.7054
5 −1111 −5555 30858025 1 22 24 264 1 264  ε_{1} 0.9624
101  −55 −5555 30858025 1 4 24 48 1 48  ε_{1} 5.9964
505  −11 −5555 30858025 4 1 24 48 1 12  ε_{1} 14.7779
505  −55 −1111 30858025 4 4 22 176 1 44  ε_{1} 14.7779
12 −463 −5556 30869136 1 7 28 98 1 98  ε_{1} 2.6339

134 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1389  −4 −5556 30869136 1 1 28 14 1 14  ε_{1} 28.0804
1852  −3 −5556 30869136 1 1 28 14 1 14  ε_{1} 67.6713
17 −327 −5559 30902481 1 12 44 264 1 264  ε_{1} 4.1894
109  −51 −5559 30902481 1 2 44 44 1 44  ε_{1} 11.1291
1853  −3 −5559 30902481 2 1 44 44 1 22  ε_{1} 7.5235
1853  −51 −327 30902481 2 2 12 24 1 12  ε_{1} 7.5235
5 −1112 −5560 30913600 1 14 20 140 1 140  ε_{1} 0.9624
8 −695 −5560 30913600 1 24 20 240 1 240  ε_{1} 1.7627
40 −139 −5560 30913600 2 3 20 60 1 30  ε_{1} 3.6369
40 −695 −1112 30913600 2 24 14 336 1 168  ε_{1} 3.6369
1112  −40 −695 30913600 1 2 24 24 1 24  ε_{1} 17.0352
5560  −8 −695 30913600 2 1 24 24 1 12  ε_{1} 72.1285
5560  −40 −139 30913600 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 36.0642
5561  −67  −83 30924721 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 64.4519
428  −52 −1391 30958096 1 2 44 44 1 44  ε_{1} 15.1243
5564  −4 −1391 30958096 2 1 44 44 1 22  ε_{1} 33.4298
5564  −52 −107 30958096 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 16.7149
21 −795 −1855 30969225 1 4 28 56 1 56  ε_{1} 3.1336
105 −159 −1855 30969225 2 10 28 280 1 140  ε_{1} 8.8131
105 −371 −795 30969225 2 8 4 32 1 16  ε_{1} 8.8131
1113  −15 −1855 30969225 2 2 28 56 1 28  ε_{1} 28.3110
1113  −35 −795 30969225 2 2 4  8 1  4  ε_{1} 28.3110
5565  −3 −1855 30969225 4 1 28 56 1 14  ε_{1} 11.8431
5565  −7 −795 30969225 4 1 4  8 1  2  ε_{1} 11.8431
5565  −15 −371 30969225 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.9216
5565  −35 −159 30969225 4 2 10 40 1 10  ε_{1} 11.8431
293  −19 −5567 30991489 1 1 54 27 1 27  ε_{1} 5.6733
28 −199 −5572 31047184 1 9 16 72 1 72  ε_{1} 5.5373
796  −7 −5572 31047184 1 1 16  8 1  8  ε_{1} 48.4110
1393  −4 −5572 31047184 5 1 16 40 1  8  ε_{1} 17.7542
17 −328 −5576 31091776 1 4 48 96 1 96  ε_{1} 4.1894
41 −136 −5576 31091776 1 4 48 96 1 96  ε_{1} 8.3183
697  −8 −5576 31091776 6 1 48 144 1 24  ε_{1} 11.1519
697 −136 −328 31091776 6 4 4 48 1  8  ε_{1} 11.1519
797  −7 −5579 31125241 1 1 30 15 1 15  ε_{1} 11.8107
1861  −3 −5583 31169889 1 1 32 16 1 16  ε_{1} 44.0966
8 −1396 −2792 31181056 1 14 26 182 1 182  ε_{1} 1.7627
2792  −4 −2792 31181056 2 1 26 26 1 13  ε_{1} 18.4599
2792  −8 −1396 31181056 2 1 14 14 1  7  ε_{1} 18.4599
37 −151 −5587 31214569 1 7 8 28 1 28  ε_{1} 4.9836
44 −127 −5588 31225744 1 5 24 60 1 60  ε_{1} 5.9864
508  −11 −5588 31225744 1 1 24 12 1 12  ε_{1} 32.1254
1397  −4 −5588 31225744 1 1 24 12 1 12  ε_{1} 16.1274
8 −699 −5592 31270464 1 10 20 100 1 100  ε_{1} 1.7627
24 −699 −1864 31270464 1 10 8 40 1 40  ε_{1} 4.5849
233  −24 −5592 31270464 1 2 20 20 1 20  ε_{1} 21.4863
1864  −3 −5592 31270464 2 1 20 20 1 10  ε_{1} 42.7055
1864  −24 −699 31270464 2 2 10 20 1 10  ε_{1} 42.7055
5592  −3 −1864 31270464 2 1 8  8 1  4  ε_{1} 32.1820
5592  −8 −699 31270464 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 16.0910

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 135

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
329 −119 −799 31281649 1 10 16 80 1 80  ε_{1} 30.7485
5593 −7 −799 31281649 2 1 16 16 1 8 ε_{1} 107.3945
5593  −47 −119 31281649 2 5 10 100 2 50 \sqrt{−1}\sqrt{ε_{1}} 53.6973
5 −1119 −5595 31304025 1 32 12 192 1 192  ε_{1} 0.9624
373  −15 −5595 31304025 1 2 12 12 1 12  ε_{1} 18.4673
1865  −3 −5595 31304025 2 1 12 12 1  6  ε_{1} 26.1887
1865  −15 −1119 31304025 2 2 32 64 1 32  ε_{1} 26.1887
5596  −4 −1399 31315216 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 53.3278
509  −11 −5599 31348801 1 1 56 28 1 28  ε_{1} 13.6596
5601  −3 −1867 31371201 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 96.9626
13 −431 −5603 31393609 1 21 22 231 1 231  ε_{1} 2.3895
12 −467 −5604 31404816 1 7 28 98 1 98  ε_{1} 2.6339
1401  −4 −5604 31404816 1 1 28 14 1 14  ε_{1} 99.1010
1868  −3 −5604 31404816 1 1 28 14 1 14  ε_{1} 29.9891
1121  −95 −295 31416025 1 8 8 32 1 32  ε_{1} 66.6959
5605  −19 −295 31416025 4 1 8 16 1  4  ε_{1} 14.0475
5605  −59  −95 31416025 4 3 8 48 1 12  ε_{1} 14.0475
701  −8 −5608 31449664 1 1 14  7 1  7  ε_{1} 20.1350
5609  −71  −79 31460881 1 7 5 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 73.3118
181  −31 −5611 31483321 1 3 10 15 1 15  ε_{1} 14.3479
92 −244 −1403 31494544 1 6 14 42 1 42  ε_{1} 7.7415
5612  −4 −1403 31494544 2 1 14 14 1  7  ε_{1} 23.8295
5612  −23 −244 31494544 2 3 6 18 1  9  ε_{1} 23.8295
5613  −3 −1871 31505769 3 1 45 135 2 45 \sqrt{−1}\sqrt{ε_{1}} 7.5353
5 −1123 −5615 31528225 1 5 62 155 1 155  ε_{1} 0.9624
1873 −3 −5619 31573161 1 1 28 14 1 14 ε_{1} 122.3244
5 −1124 −5620 31584400 1 20 24 240 1 240  ε_{1} 0.9624
281  −20 −5620 31584400 1 2 24 24 1 24  ε_{1} 29.1405
1405  −4 −5620 31584400 2 1 24 24 1 12  ε_{1} 16.8228
1405  −20 −1124 31584400 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 8.4114
77 −511 −803 31595641 1 14 10 70 1 70  ε_{1} 4.3693
5621  −7 −803 31595641 6 1 10 30 1  5  ε_{1} 8.6346
5621  −11 −511 31595641 6 1 14 42 1  7  ε_{1} 8.6346
8 −703 −5624 31629376 1 14 44 308 1 308  ε_{1} 1.7627
37 −152 −5624 31629376 1 6 44 132 1 132  ε_{1} 4.9836
152 −296 −703 31629376 1 10 14 70 1 70  ε_{1} 8.6078
296 −19 −5624 31629376 2 1 44 44 1 22 ε_{1} 8.9090
296 −152 −703 31629376 2 6 14 84 1 42  ε_{1} 8.9090
5624  −8 −703 31629376 6 1 14 42 1  7  ε_{1} 10.0212
5624  −19 −296 31629376 6 1 10 30 1  5  ε_{1} 10.0212
17 −331 −5627 31663129 1 3 28 42 1 42  ε_{1} 4.1894
12 −1407 −1876 31674384 1 24 16 192 1 192  ε_{1} 2.6339
21 −804 −1876 31674384 1 12 16 96 1 96  ε_{1} 3.1336
28 −804 −1407 31674384 1 12 24 144 1 144  ε_{1} 5.5373
201  −84 −1876 31674384 1 4 16 32 1 32  ε_{1} 27.6905
268  −84 −1407 31674384 1 4 24 48 1 48  ε_{1} 22.9790
469  −84 −804 31674384 3 4 12 72 1 24  ε_{1} 8.3483
5628  −3 −1876 31674384 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 8.9229
5628  −4 −1407 31674384 4 1 24 48 1 12  ε_{1} 17.8458
5628  −7 −804 31674384 4 1 12 24 1  6  ε_{1} 17.8458

136 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
5628  −67  −84 31674384 4 1 4  8 1  2  ε_{1} 17.8458
1877  −3 −5631 31708161 1 1 74 37 1 37  ε_{1} 14.7593
5633  −43 −131 31730689 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 48.9856
1409  −4 −5636 31764496 1 1 36 18 1 18  ε_{1} 77.6008
5637  −3 −1879 31775769 3 1 27 81 2 27 \sqrt{−1}\sqrt{ε_{1}} 7.5374
5 −1128 −5640 31809600 1 8 32 128 1 128  ε_{1} 0.9624
24 −235 −5640 31809600 1 2 32 32 1 32  ε_{1} 4.5849
120  −47 −5640 31809600 2 5 32 160 1 80  ε_{1} 6.1779
120 −235 −1128 31809600 2 2 8 16 1  8  ε_{1} 6.1779
141  −40 −5640 31809600 1 2 32 32 1 32  ε_{1} 10.4940
141 −120 −1880 31809600 1 4 20 40 1 40  ε_{1} 10.4940
376  −15 −5640 31809600 1 2 32 32 1 32  ε_{1} 30.5420
705  −8 −5640 31809600 2 1 32 32 1 16  ε_{1} 26.1393
705  −24 −1880 31809600 2 2 20 40 1 20  ε_{1} 26.1393
705  −40 −1128 31809600 2 2 8 16 1  8  ε_{1} 26.1393
705 −120 −376 31809600 2 4 8 32 1 16  ε_{1} 26.1393
1128  −15 −1880 31809600 2 2 20 40 1 20  ε_{1} 16.9115
1128 −120 −235 31809600 2 4 2  8 1  4  ε_{1} 16.9115
1880  −3 −5640 31809600 2 1 32 32 1 16  ε_{1} 16.2524
1880  −15 −1128 31809600 2 2 8 16 1  8  ε_{1} 16.2524
5640  −3 −1880 31809600 4 1 20 40 1 10  ε_{1} 14.6291
5640  −15 −376 31809600 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 7.3146
5640  −24 −235 31809600 4 2 2  8 1  2  ε_{1} 14.6291
5640  −47 −120 31809600 4 5 4 40 1 10  ε_{1} 14.6291
332  −68 −1411 31854736 1 4 4  8 1  8  ε_{1} 10.1997
5644  −4 −1411 31854736 4 1 4 16 2  4  \sqrt{i}\sqrt{ε_{1}} 20.6046
5644  −68  −83 31854736 4 4 3 24 1  6  ε_{1} 41.2093
8 −1412 −2824 31899904 1 16 24 192 1 192  ε_{1} 1.7627
2824 −4 −2824 31899904 4 1 24 96 2 24 \sqrt{i}\sqrt{ε_{1}} 11.1446
2824  −8 −1412 31899904 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 11.1446
21 −807 −1883 31911201 1 14 14 98 1 98  ε_{1} 3.1336
5649  −3 −1883 31911201 2 1 14 14 1  7  ε_{1} 85.7401
5649  −7 −807 31911201 2 1 14 14 1  7  ε_{1} 85.7401
5 −1131 −5655 31979025 1 8 56 224 1 224  ε_{1} 0.9624
13 −435 −5655 31979025 1 4 56 112 1 112  ε_{1} 2.3895
29 −195 −5655 31979025 1 4 56 112 1 112  ε_{1} 3.2945
65 −87 −5655 31979025 2 6 56 336 1 168 ε_{1} 5.5529
65 −435 −1131 31979025 2 4 8 32 1 16  ε_{1} 5.5529
145 −39 −5655 31979025 4 4 56 448 1 112 ε_{1} 6.3596
145 −195 −1131 31979025 4 4 8 64 1 16  ε_{1} 6.3596
377  −15 −5655 31979025 2 2 56 112 1 56  ε_{1} 12.2884
377 −195 −435 31979025 2 4 4 16 1  8  ε_{1} 12.2884
1885  −3 −5655 31979025 4 1 56 112 1 28  ε_{1} 13.8978
1885  −15 −1131 31979025 4 2 8 32 1  8  ε_{1} 13.8978
1885  −39 −435 31979025 4 4 4 32 1  8  ε_{1} 13.8978
1885  −87 −195 31979025 4 6 4 48 1 12  ε_{1} 13.8978
8 −707 −5656 31990336 1 6 28 84 1 84  ε_{1} 1.7627
56 −707 −808 31990336 1 6 6 18 1 18  ε_{1} 6.8002
101  −56 −5656 31990336 1 4 28 56 1 56  ε_{1} 5.9964
808  −7 −5656 31990336 2 1 28 28 1 14  ε_{1} 17.4909

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 137

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
808  −56 −707 31990336 2 4 6 24 1 12  ε_{1} 17.4909
5656  −7 −808 31990336 2 1 6  6 1  3  ε_{1} 67.0616
5656  −8 −707 31990336 2 1 6  6 1  3  ε_{1} 67.0616
1132  −20 −1415 32035600 1 2 34 34 1 34  ε_{1} 38.8758
5660  −4 −1415 32035600 2 1 34 34 1 17  ε_{1} 35.2020
5660  −20 −283 32035600 2 2 3  6 1  3  ε_{1} 35.2020
809  −7 −5663 32069569 1 1 56 28 1 28  ε_{1} 54.9782
1133  −55 −515 32092225 1 4 6 12 1 12  ε_{1} 9.2300
5665  −11 −515 32092225 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 62.6489
5665  −55 −103 32092225 2 4 5 20 1 10  ε_{1} 125.2978
1889  −3 −5667 32114889 1 1 10  5 1  5  ε_{1} 73.3811
13 −436 −5668 32126224 1 6 16 48 1 48  ε_{1} 2.3895
109  −52 −5668 32126224 1 2 16 16 1 16  ε_{1} 11.1291
1417  −4 −5668 32126224 2 1 16 16 1  8  ε_{1} 43.8225
1417  −52 −436 32126224 2 2 6 12 1  6  ε_{1} 43.8225
53 −107 −5671 32160241 1 3 44 66 1 66  ε_{1} 3.9314
709 −8 −5672 32171584 1 1 34 17 1 17 ε_{1} 34.8251
93 −183 −1891 32182929 1 8 10 40 1 40  ε_{1} 6.7322
5673  −3 −1891 32182929 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 22.9697
5673 −31 −183 32182929 2 3 8 24 1 12 ε_{1} 45.9395
12 −1419 −1892 32216976 1 12 12 72 1 72  ε_{1} 2.6339
33 −516 −1892 32216976 1 12 12 72 1 72  ε_{1} 7.6563
44 −516 −1419 32216976 1 12 12 72 1 72  ε_{1} 5.9864
129 −132 −1892 32216976 1 4 12 24 1 24  ε_{1} 20.8511
172 −132 −1419 32216976 1 4 12 24 1 24  ε_{1} 17.6970
473 −132 −516 32216976 3 4 12 72 1 24  ε_{1} 10.3180
5676  −3 −1892 32216976 4 1 12 24 1  6  ε_{1} 20.2960
5676  −4 −1419 32216976 4 1 12 48 2 12  \sqrt{i}\sqrt{ε_{1}} 10.1480
5676  −11 −516 32216976 4 1 12 24 1  6  ε_{1} 20.2960
5676  −43 −132 32216976 4 1 4  8 1  2  ε_{1} 20.2960
5677  −7 −811 32228329 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 39.1754
284  −40 −2840 32262400 1 2 32 32 1 32  ε_{1} 17.6959
568  −20 −2840 32262400 3 2 32 96 1 32  ε_{1} 11.3120
1420  −8 −2840 32262400 2 1 32 32 1 16  ε_{1} 28.9248
1420  −40 −568 32262400 2 2 4  8 1  4  ε_{1} 28.9248
2840  −4 −2840 32262400 2 1 32 32 1 16  ε_{1} 15.6940
2840  −20 −568 32262400 2 2 4  8 1  4  ε_{1} 15.6940
437 −247 −299 32273761 1 6 8 24 1 24  ε_{1} 6.0845
5681 −19 −299 32273761 2 1 8 8 1 4 ε_{1} 82.1107
5681  −23 −247 32273761 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 41.0554
1137  −15 −1895 32319225 1 2 48 48 1 48  ε_{1} 55.7882
5685  −3 −1895 32319225 6 1 48 144 1 24  ε_{1} 11.8645
5685  −15 −379 32319225 6 2 3 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 5.9322
21 −271 −5691 32387481 1 11 24 132 1 132  ε_{1} 3.1336
813  −7 −5691 32387481 1 1 24 12 1 12  ε_{1} 16.7485
1897  −3 −5691 32387481 5 1 24 60 1 12  ε_{1} 22.7658
5692  −4 −1423 32398864 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 55.2212
5 −1139 −5695 32433025 1 16 44 352 1 352  ε_{1} 0.9624
17 −335 −5695 32433025 1 18 44 396 1 396  ε_{1} 4.1894
85  −67 −5695 32433025 2 1 44 44 1 22  ε_{1} 4.4187

138 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
85 −335 −1139 32433025 2 18 16 288 1 144  ε_{1} 4.4187
41 −139 −5699 32478601 1 3 24 36 1 36  ε_{1} 8.3183
1901  −3 −5703 32524209 3 1 54 81 1 27  ε_{1} 12.1553
184  −31 −5704 32535616 1 3 32 48 1 48  ε_{1} 21.5856
248  −23 −5704 32535616 1 3 32 48 1 48  ε_{1} 9.6724
713  −8 −5704 32535616 1 1 32 16 1 16  ε_{1} 32.3476
713 −184 −248 32535616 1 4 8 16 1 16  ε_{1} 32.3476
5704  −23 −248 32535616 4 3 8 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 16.7972
5704  −31 −184 32535616 4 3 4 24 1  6  ε_{1} 33.5945
1141  −35 −815 32547025 1 2 30 30 1 30  ε_{1} 41.9327
5705  −7 −815 32547025 2 1 30 30 1 15  ε_{1} 52.4503
5705  −35 −163 32547025 2 2 1  2 1  1  ε_{1} 52.4503
13 −439 −5707 32569849 1 15 8 60 1 60  ε_{1} 2.3895
5708 −4 −1427 32581264 1 1 15 15 2 15 \sqrt{i}\sqrt{ε_{1}} 23.6543
33 −519 −1903 32592681 1 18 22 198 1 198  ε_{1} 7.6563
5709  −3 −1903 32592681 2 1 22 22 1 11  ε_{1} 36.2512
5709  −11 −519 32592681 2 1 18 18 1  9  ε_{1} 36.2512
8 −1428 −2856 32626944 1 8 24 96 1 96  ε_{1} 1.7627
12 −952 −2856 32626944 1 8 24 96 1 96  ε_{1} 2.6339
24 −952 −1428 32626944 1 8 8 32 1 32  ε_{1} 4.5849
28 −408 −2856 32626944 1 4 24 48 1 48  ε_{1} 5.5373
56 −408 −1428 32626944 1 4 8 16 1 16  ε_{1} 6.8002
136 −84 −2856 32626944 2 4 24 96 1 48 ε_{1} 8.4966
136 −168 −1428 32626944 2 4 8 32 1 16  ε_{1} 8.4966
168 −68 −2856 32626944 2 4 24 96 1 48 ε_{1} 6.5132
168 −136 −1428 32626944 2 4 8 32 1 16  ε_{1} 6.5132
204 −56 −2856 32626944 2 4 24 96 1 48 ε_{1} 9.2101
204 −168 −952 32626944 2 4 8 32 1 16  ε_{1} 9.2101
408  −56 −1428 32626944 2 4 8 32 1 16  ε_{1} 10.6165
408  −84 −952 32626944 2 4 8 32 1 16  ε_{1} 10.6165
476  −24 −2856 32626944 2 2 24 48 1 24  ε_{1} 10.9612
476 −168 −408 32626944 2 4 4 16 1  8  ε_{1} 10.9612
952  −24 −1428 32626944 2 2 8 16 1  8  ε_{1} 20.1146
952  −84 −408 32626944 2 4 4 16 1  8  ε_{1} 20.1146
2856  −4 −2856 32626944 4 1 24 48 1 12  ε_{1} 18.0311
2856  −8 −1428 32626944 4 1 8 16 1  4  ε_{1} 18.0311
2856  −68 −168 32626944 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 9.0155
2856  −84 −136 32626944 4 4 4 32 1  8  ε_{1} 18.0311
1429  −4 −5716 32672656 5 1 22 55 1 11  ε_{1} 10.4836
133  −43 −5719 32706961 1 1 56 28 1 28  ε_{1} 10.3065
301  −19 −5719 32706961 1 1 56 28 1 28  ε_{1} 20.0642
817  −7 −5719 32706961 5 1 56 140 1 28  ε_{1} 13.0618
5 −1144 −5720 32718400 1 12 32 192 1 192  ε_{1} 0.9624
8 −715 −5720 32718400 1 4 32 64 1 64  ε_{1} 1.7627
13 −440 −5720 32718400 1 12 32 192 1 192  ε_{1} 2.3895
40 −143 −5720 32718400 2 10 32 320 1 160  ε_{1} 3.6369
40 −715 −1144 32718400 2 4 12 48 1 24  ε_{1} 3.6369
65 −88 −5720 32718400 2 2 32 64 1 32 ε_{1} 5.5529
65 −440 −1144 32718400 2 12 12 144 1 72  ε_{1} 5.5529
88 −520 −715 32718400 1 4 4  8 1  8  ε_{1} 11.9527

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 139

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
104  −55 −5720 32718400 2 4 32 128 1 64  ε_{1} 4.6249
104 −440 −715 32718400 2 12 4 48 1 24  ε_{1} 4.6249
440 −104 −715 32718400 2 6 4 24 1 12  ε_{1} 7.4742
440 −143 −520 32718400 2 10 4 40 1 20  ε_{1} 7.4742
520  −11 −5720 32718400 4 1 32 64 1 16  ε_{1} 9.4726
520  −55 −1144 32718400 4 4 12 96 1 24  ε_{1} 9.4726
520  −88 −715 32718400 4 2 4 16 1  4  ε_{1} 9.4726
520 −143 −440 32718400 4 10 12 240 1 60  ε_{1} 9.4726
1144  −40 −715 32718400 2 2 4  8 1  4  ε_{1} 27.8642
1144  −55 −520 32718400 2 4 4 16 1  8  ε_{1} 27.8642
5720  −8 −715 32718400 4 1 4  8 1  2  ε_{1} 20.3790
5720  −11 −520 32718400 4 1 4  8 1  2  ε_{1} 20.3790
5720  −40 −143 32718400 4 2 10 40 1 10  ε_{1} 20.3790
5720  −55 −104 32718400 4 4 6 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 10.1895
5721  −3 −1907 32729841 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 110.9506
97  −59 −5723 32752729 1 3 14 21 1 21  ε_{1} 18.6488
69  −83 −5727 32798529 1 3 40 60 1 60  ε_{1} 6.4345
249  −23 −5727 32798529 1 3 40 60 1 60  ε_{1} 33.3101
1909  −3 −5727 32798529 1 1 40 20 1 20  ε_{1} 44.5676
521  −11 −5731 32844361 1 1 20 10 1 10  ε_{1} 38.7273
1433  −4 −5732 32855824 1 1 36 18 1 18  ε_{1} 46.3372
5 −1147 −5735 32890225 1 6 52 156 1 156  ε_{1} 0.9624
37 −155 −5735 32890225 1 4 52 104 1 104  ε_{1} 4.9836
185 −31 −5735 32890225 2 3 52 156 1 78 ε_{1} 9.8254
185 −155 −1147 32890225 2 4 6 24 1 12  ε_{1} 9.8254
24 −239 −5736 32901696 1 15 32 240 1 240  ε_{1} 4.5849
717  −8 −5736 32901696 1 1 32 16 1 16  ε_{1} 10.9696
717  −24 −1912 32901696 1 2 8  8 1  8  ε_{1} 10.9696
1912  −3 −5736 32901696 1 1 32 16 1 16  ε_{1} 71.4254
5736  −3 −1912 32901696 2 1 8  8 1  4  ε_{1} 53.1814
5736  −24 −239 32901696 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 26.5907
1913 −3 −5739 32936121 1 1 22 11 1 11 ε_{1} 59.7641
28 −820 −1435 32947600 1 8 4 16 1 16  ε_{1} 5.5373
140 −164 −1435 32947600 2 8 4 32 1 16  ε_{1} 4.9558
140 −287 −820 32947600 2 14 8 112 1 56  ε_{1} 4.9558
1148  −20 −1435 32947600 2 2 4  8 1  4  ε_{1} 12.7122
1148  −35 −820 32947600 2 2 8 16 1  8  ε_{1} 12.7122
5740  −4 −1435 32947600 4 1 4  8 1  2  ε_{1} 29.0154
5740  −7 −820 32947600 4 1 8 16 1  4  ε_{1} 29.0154
5740  −20 −287 32947600 4 2 14 56 1 14  ε_{1} 29.0154
5740  −35 −164 32947600 4 2 8 32 1  8  ε_{1} 29.0154
1436  −8 −2872 32993536 3 1 12 36 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.5792
2872  −4 −2872 32993536 1 1 12 12 2 12  \sqrt{i}\sqrt{ε_{1}} 44.3295
1149  −15 −1915 33005025 1 2 6  6 1  6  ε_{1} 32.9675
5745  −3 −1915 33005025 2 1 6  6 1  3  ε_{1} 85.2803
5745  −15 −383 33005025 2 2 17 34 1 17  ε_{1} 85.2803
821  −7 −5747 33028009 1 1 24 12 1 12  ε_{1} 19.3842
12 −479 −5748 33039504 1 25 24 300 1 300  ε_{1} 2.6339
1437  −4 −5748 33039504 1 1 24 12 1 12  ε_{1} 21.9351
1916  −3 −5748 33039504 1 1 24 12 1 12  ε_{1} 31.2075

140 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8 −719 −5752 33085504 1 31 16 248 1 248  ε_{1} 1.7627
5752  −8 −719 33085504 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 31.0943
5753 −11 −523 33097009 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 34.8031
5 −1151 −5755 33120025 1 41 12 246 1 246  ε_{1} 0.9624
5756 −4 −1439 33131536 1 1 39 39 2 39 \sqrt{i}\sqrt{ε_{1}} 44.6936
57 −303 −1919 33143049 1 10 44 220 1 220  ε_{1} 11.4208
5757 −3 −1919 33143049 2 1 44 44 1 22 ε_{1} 14.2034
5757  −19 −303 33143049 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 7.1017
13 −443 −5759 33166081 1 5 108 270 1 270  ε_{1} 2.3895
5761 −7 −823 33189121 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 124.3522
17 −339 −5763 33212169 1 6 12 36 1 36  ε_{1} 4.1894
113  −51 −5763 33212169 1 2 12 12 1 12  ε_{1} 14.6946
1921  −3 −5763 33212169 2 1 12 12 1  6  ε_{1} 65.1846
1921  −51 −339 33212169 2 2  6 12 1  6  ε_{1} 65.1846
44 −131 −5764 33223696 1 5 28 70 1 70  ε_{1} 5.9864
524  −11 −5764 33223696 1 1 28 14 1 14  ε_{1} 19.9254
1441  −4 −5764 33223696 1 1 28 14 1 14  ε_{1} 111.5641
73  −79 −5767 33258289 1 5 36 90 1 90  ε_{1} 15.3334
56 −103 −5768 33269824 1 5 24 60 1 60  ε_{1} 6.8002
721  −8 −5768 33269824 1 1 24 12 1 12  ε_{1} 76.3136
721  −56 −824 33269824 1 4 20 40 1 40  ε_{1} 76.3136
824  −7 −5768 33269824 1 1 24 12 1 12  ε_{1} 23.3749
5768  −7 −824 33269824 4 1 20 40 1 10  ε_{1} 15.9353
5768  −56 −103 33269824 4 4  5 40 1 10  ε_{1} 15.9353
29 −199 −5771 33304441 1 9 44 198 1 198  ε_{1} 3.2945
12 −1443 −1924 33315984 1 8 16 64 1 64  ε_{1} 2.6339
156 −111 −1924 33315984 2 8 16 128 1 64  ε_{1} 7.8232
156 −148 −1443 33315984 2 2  8 16 1  8  ε_{1} 7.8232
444  −39 −1924 33315984 2 4 16 64 1 32  ε_{1} 12.7602
444  −52 −1443 33315984 2 2  8 16 1  8  ε_{1} 12.7602
5772  −3 −1924 33315984 8 1 16 64 1  8  ε_{1} 8.6611
5772  −4 −1443 33315984 8 1  8 32 1  4  ε_{1} 8.6611
5772  −39 −148 33315984 8 4  2 32 1  4  ε_{1} 8.6611
5772  −52 −111 33315984 8 2  8 64 1  8  ε_{1} 8.6611
5773  −23 −251 33327529 1 3  7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 34.2075
141 −123 −1927 33419961 1 2 18 18 1 18  ε_{1} 10.4940
5781  −3 −1927 33419961 2 1 18 18 1  9  ε_{1} 31.3427
5781  −47 −123 33419961 2 5  2 10 1  5  ε_{1} 31.3427
8 −723 −5784 33454656 1 4 32 64 1 64  ε_{1} 1.7627
24 −723 −1928 33454656 1 4 20 40 1 40  ε_{1} 4.5849
241  −24 −5784 33454656 1 2 32 32 1 32  ε_{1} 37.5430
1928  −3 −5784 33454656 2 1 32 32 1 16  ε_{1} 13.7463
1928  −24 −723 33454656 2 2  4  8 1  4  ε_{1} 13.7463
5784  −3 −1928 33454656 8 1 20 80 1 10  ε_{1} 15.9380
5784  −8 −723 33454656 8 1  4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 7.9690
5788  −4 −1447 33500944 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 40.1026
5789  −7 −827 33512521 1 1  7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 28.2830
5793  −3 −1931 33558849 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 70.7241
5 −1159 −5795 33582025 1 16 32 256 1 256  ε_{1} 0.9624
61  −95 −5795 33582025 1 8 32 128 1 128  ε_{1} 7.3284

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 141

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
305  −19 −5795 33582025 2 1 32 32 1 16  ε_{1} 13.7710
305  −95 −1159 33582025 2 8 16 128 1 64  ε_{1} 13.7710
341 −187 −527 33605209 1 2 18 18 1 18  ε_{1} 11.2480
5797  −11 −527 33605209 2 1 18 18 1  9  ε_{1} 40.5306
5797  −31 −187 33605209 2 3 2  6 1  3  ε_{1} 40.5306
1933  −3 −5799 33628401 1 1 80 40 1 40  ε_{1} 41.0311
829  −7 −5803 33674809 1 1 10  5 1  5  ε_{1} 34.4976
5804  −4 −1451 33686416 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 38.7134
13 −447 −5811 33767721 1 14 12 84 1 84  ε_{1} 2.3895
149  −39 −5811 33767721 1 4 12 24 1 24  ε_{1} 8.2223
1937  −3 −5811 33767721 6 1 12 36 1  6  ε_{1} 8.9549
1937  −39 −447 33767721 6 4 14 168 1 28  ε_{1} 8.9549
1453  −4 −5812 33779344 1 1 14  7 1  7  ε_{1} 43.6833
5 −1163 −5815 33814225 1 7 50 175 1 175  ε_{1} 0.9624
8 −727 −5816 33825856 1 13 60 390 1 390  ε_{1} 1.7627
5816  −8 −727 33825856 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 27.3210
21 −831 −1939 33837489 1 28 8 112 1 112  ε_{1} 3.1336
5817  −3 −1939 33837489 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 15.4724
5817  −7 −831 33837489 4 1 28 56 1 14  ε_{1} 30.9448
12 −1455 −1940 33872400 1 28 20 280 1 280  ε_{1} 2.6339
60 −291 −1940 33872400 2 4 20 80 1 40  ε_{1} 4.1269
60 −388 −1455 33872400 2 4 28 112 1 56  ε_{1} 4.1269
1164  −15 −1940 33872400 4 2 20 80 1 20  ε_{1} 12.7261
1164  −20 −1455 33872400 4 2 28 112 1 28  ε_{1} 12.7261
5820  −3 −1940 33872400 4 1 20 40 1 10  ε_{1} 21.5381
5820  −4 −1455 33872400 4 1 28 56 1 14  ε_{1} 21.5381
5820  −15 −388 33872400 4 2 4 16 1  4  ε_{1} 21.5381
5820  −20 −291 33872400 4 2 4 16 1  4  ε_{1} 21.5381
124  −47 −5828 33965584 1 5 24 60 1 60  ε_{1} 16.0392
188  −31 −5828 33965584 1 3 24 36 1 36  ε_{1} 9.1285
1457  −4 −5828 33965584 1 1 24 12 1 12  ε_{1} 60.6057
201  −87 −1943 33977241 1 6 32 96 1 96  ε_{1} 27.6905
5829  −3 −1943 33977241 2 1 32 32 1 16  ε_{1} 23.9766
5829  −67  −87 33977241 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 11.9883
5833  −19 −307 34023889 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 119.6057
5 −1167 −5835 34047225 1 22 12 132 1 132  ε_{1} 0.9624
389  −15 −5835 34047225 1 2 12 12 1 12  ε_{1} 15.6986
1945  −3 −5835 34047225 2 1 12 12 1  6  ε_{1} 58.5840
1945  −15 −1167 34047225 2 2 22 44 1 22  ε_{1} 58.5840
5836  −4 −1459 34058896 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 60.5416
8 −1460 −2920 34105600 1 20 12 120 1 120  ε_{1} 1.7627
40 −292 −2920 34105600 2 4 12 48 1 24  ε_{1} 3.6369
40 −584 −1460 34105600 2 16 20 320 1 160  ε_{1} 3.6369
584  −20 −2920 34105600 2 2 12 24 1 12  ε_{1} 11.3397
584  −40 −1460 34105600 2 2 20 40 1 20  ε_{1} 11.3397
2920  −4 −2920 34105600 12 1 12 72 1  6  ε_{1} 7.9787
2920  −8 −1460 34105600 12 1 20 120 1 10  ε_{1} 7.9787
2920  −20 −584 34105600 12 2 16 192 1 16  ε_{1} 7.9787
2920  −40 −292 34105600 12 2 4 48 1  4  ε_{1} 7.9787
12 −487 −5844 34152336 1 7 28 98 1 98  ε_{1} 2.6339

142 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1461  −4 −5844 34152336 1 1 28 14 1 14  ε_{1} 32.1144
1948  −3 −5844 34152336 1 1 28 14 1 14  ε_{1} 64.5472
1169  −35 −835 34164025 1 2 6  6 1  6  ε_{1} 67.0808
5845  −7 −835 34164025 2 1 6  6 1  3  ε_{1} 40.0602
5845  −35 −167 34164025 2 2 11 22 1 11  ε_{1} 40.0602
1949  −3 −5847 34187409 1 1 50 25 1 25  ε_{1} 24.0447
8 −731 −5848 34199104 1 12 16 96 1 96  ε_{1} 1.7627
17 −344 −5848 34199104 1 10 16 80 1 80  ε_{1} 4.1894
136 −43 −5848 34199104 2 1 16 16 1 8 ε_{1} 8.4966
136 −344 −731 34199104 2 10 12 120 1 60  ε_{1} 8.4966
344 −136 −731 34199104 1 4 12 24 1 24  ε_{1} 19.8864
5848  −8 −731 34199104 4 1 12 24 1  6  ε_{1} 17.2272
5848  −43 −136 34199104 4 1 4  8 1  2  ε_{1} 17.2272
28 −836 −1463 34245904 1 20 32 320 1 320  ε_{1} 5.5373
44 −532 −1463 34245904 1 4 32 64 1 64  ε_{1} 5.9864
76 −308 −1463 34245904 1 8 32 128 1 128  ε_{1} 11.6579
77 −532 −836 34245904 1 4 20 40 1 40  ε_{1} 4.3693
133 −308 −836 34245904 1 8 20 80 1 80  ε_{1} 10.3065
209 −308 −532 34245904 1 8 4 16 1 16  ε_{1} 22.8829
5852  −4 −1463 34245904 4 1 32 64 1 16  ε_{1} 11.4471
5852  −7 −836 34245904 4 1 20 40 1 10  ε_{1} 11.4471
5852  −11 −532 34245904 4 1 4  8 1  2  ε_{1} 11.4471
5852  −19 −308 34245904 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 5.7236
5853  −3 −1951 34257609 3 1 33 99 2 33 \sqrt{−1}\sqrt{ε_{1}} 10.3486
5 −1171 −5855 34281025 1 7 76 266 1 266  ε_{1} 0.9624
5 −1172 −5860 34339600 1 18 16 144 1 144  ε_{1} 0.9624
293  −20 −5860 34339600 1 2 16 16 1 16  ε_{1} 5.6733
1465  −4 −5860 34339600 2 1 16 16 1  8  ε_{1} 56.2532
1465  −20 −1172 34339600 2 2 18 36 1 18  ε_{1} 56.2532
13 −451 −5863 34374769 1 6 28 84 1 84  ε_{1} 2.3895
41 −143 −5863 34374769 1 10 28 140 1 140  ε_{1} 8.3183
533 −11 −5863 34374769 2 1 28 28 1 14 ε_{1} 6.2748
533 −143 −451 34374769 2 10 6 60 1 30  ε_{1} 6.2748
733 −8 −5864 34386496 3 1 58 87 1 29 ε_{1} 6.5944
69 −255 −1955 34398225 1 12 12 72 1 72  ε_{1} 6.4345
345 −51 −1955 34398225 2 2 12 24 1 12 ε_{1} 19.0241
345 −255 −391 34398225 2 12 14 168 1 84  ε_{1} 19.0241
1173 −15 −1955 34398225 2 2 12 24 1 12 ε_{1} 11.2262
1173 −115 −255 34398225 2 2 12 24 1 12  ε_{1} 11.2262
5865  −3 −1955 34398225 8 1 12 48 1  6  ε_{1} 15.0329
5865  −15 −391 34398225 8 2 14 112 1 14  ε_{1} 15.0329
5865  −23 −255 34398225 8 3 12 144 1 18  ε_{1} 15.0329
5865  −51 −115 34398225 8 2 2 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 7.5164
57 −103 −5871 34468641 1 5 72 180 1 180  ε_{1} 11.4208
309  −19 −5871 34468641 1 1 72 36 1 36  ε_{1} 17.0523
1957  −3 −5871 34468641 3 1 72 108 1 36  ε_{1} 13.6682
1468  −8 −2936 34480384 1 1 40 40 2 40 \sqrt{−1}\sqrt{ε_{1}} 24.3619
2936 −4 −2936 34480384 1 1 40 40 2 40 \sqrt{i}\sqrt{ε_{1}} 16.8499
5873  −7 −839 34492129 1 1 33 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 51.7994
13 −452 −5876 34527376 1 8 56 224 1 224  ε_{1} 2.3895

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 143

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
113  −52 −5876 34527376 1 2 56 56 1 56  ε_{1} 14.6946
1469  −4 −5876 34527376 2 1 56 56 1 28  ε_{1} 9.4897
1469  −52 −452 34527376 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 4.7449
37 −159 −5883 34609689 1 10 16 80 1 80  ε_{1} 4.9836
53 −111 −5883 34609689 1 8 16 64 1 64  ε_{1} 3.9314
1961 −3 −5883 34609689 2 1 16 16 1 8 ε_{1} 46.2171
1961 −111 −159 34609689 2 8 10 80 1 40  ε_{1} 46.2171
5884  −4 −1471 34621456 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 73.4345
1177  −55 −535 34633225 1 4 14 28 1 28  ε_{1} 88.7782
5885  −11 −535 34633225 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 6.2860
5885  −55 −107 34633225 2 4 3 12 1  6  ε_{1} 12.5720
453  −39 −1963 34680321 1 4 6 12 1 12  ε_{1} 10.0078
5889  −3 −1963 34680321 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 53.4697
5889  −39 −151 34680321 2 4 7 28 1 14  ε_{1} 106.9393
137  −43 −5891 34703881 1 1 26 13 1 13  ε_{1} 16.3142
12 −491 −5892 34715664 1 9 28 126 1 126  ε_{1} 2.6339
1473  −4 −5892 34715664 1 1 28 14 1 14  ε_{1} 58.6040
1964  −3 −5892 34715664 1 1 28 14 1 14  ε_{1} 51.9115
5893  −71  −83 34727449 1 7 3 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 24.2033
88  −67 −5896 34762816 1 1 16  8 1  8  ε_{1} 11.9527
536  −11 −5896 34762816 1 1 16  8 1  8  ε_{1} 25.1680
737  −8 −5896 34762816 1 1 16  8 1  8  ε_{1} 40.0839
737  −88 −536 34762816 1 2 14 14 1 14  ε_{1} 40.0839
5896  −11 −536 34762816 2 1 14 14 1  7  ε_{1} 78.4770
5896  −67  −88 34762816 2 1 2  2 1  1  ε_{1} 78.4770
17 −347 −5899 34798201 1 5 18 45 1 45  ε_{1} 4.1894
21 −843 −1967 34821801 1 6 36 108 1 108  ε_{1} 3.1336
5901  −3 −1967 34821801 6 1 36 108 1 18  ε_{1} 13.4787
5901  −7 −843 34821801 6 1 6 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 6.7393
33 −179 −5907 34892649 1 5 16 40 1 40  ε_{1} 7.6563
537  −11 −5907 34892649 1 1 16  8 1  8  ε_{1} 39.5359
1969  −3 −5907 34892649 1 1 16  8 1  8  ε_{1} 147.2368
28 −211 −5908 34904464 1 3 16 24 1 24  ε_{1} 5.5373
844  −7 −5908 34904464 1 1 16  8 1  8  ε_{1} 54.0906
1477  −4 −5908 34904464 1 1 16  8 1  8  ε_{1} 34.2370
5909  −19 −311 34916281 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 24.2422
257 −23 −5911 34939921 3 3 56 252 1 84 ε_{1} 6.9334
8 −739 −5912 34951744 1 5 30 75 1 75  ε_{1} 1.7627
5912 −8 −739 34951744 3 1 5 15 2 5 \sqrt{−1}\sqrt{ε_{1}} 12.3860
12 −1479 −1972 34999056 1 28 12 168 1 168  ε_{1} 2.6339
204 −87 −1972 34999056 2 6 12 72 1 36 ε_{1} 9.2101
204 −116 −1479 34999056 2 6 28 168 1 84  ε_{1} 9.2101
348  −51 −1972 34999056 2 2 12 24 1 12  ε_{1} 8.0501
348  −68 −1479 34999056 2 4 28 112 1 56  ε_{1} 8.0501
5916  −3 −1972 34999056 4 1 12 24 1  6  ε_{1} 31.9825
5916  −4 −1479 34999056 4 1 28 56 1 14  ε_{1} 31.9825
5916  −51 −116 34999056 4 2 6 24 1  6  ε_{1} 31.9825
5916  −68  −87 34999056 4 4 6 48 1 12  ε_{1} 31.9825
1973  −3 −5919 35034561 1 1 54 27 1 27  ε_{1} 24.1684
5921  −31 −191 35058241 1 3 13 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 61.1414

144 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1481  −4 −5924 35093776 1 1 52 26 1 26  ε_{1} 77.8029
13 −456 −5928 35141184 1 8 24 96 1 96  ε_{1} 2.3895
24 −247 −5928 35141184 1 6 24 72 1 72  ε_{1} 4.5849
57 −104 −5928 35141184 1 6 24 72 1 72  ε_{1} 11.4208
57 −312 −1976 35141184 1 4 28 56 1 56  ε_{1} 11.4208
152  −39 −5928 35141184 1 4 24 48 1 48  ε_{1} 8.6078
312  −19 −5928 35141184 2 1 24 24 1 12  ε_{1} 9.3267
312 −247 −456 35141184 2 6 8 48 1 24  ε_{1} 9.3267
456 −39 −1976 35141184 2 4 28 112 1 56 ε_{1} 15.2512
456 −247 −312 35141184 2 6 4 24 1 12  ε_{1} 15.2512
741  −8 −5928 35141184 2 1 24 24 1 12  ε_{1} 11.0025
741  −24 −1976 35141184 2 2 28 56 1 28  ε_{1} 11.0025
741 −104 −456 35141184 2 6 8 48 1 24  ε_{1} 11.0025
741 −152 −312 35141184 2 6 4 24 1 12  ε_{1} 11.0025
1976  −3 −5928 35141184 2 1 24 24 1 12  ε_{1} 23.7837
1976  −39 −456 35141184 2 4 8 32 1 16  ε_{1} 23.7837
5928  −3 −1976 35141184 4 1 28 56 1 14  ε_{1} 10.0738
5928  −19 −312 35141184 4 1 4  8 1  2  ε_{1} 10.0738
5928  −24 −247 35141184 4 2 6 24 1  6  ε_{1} 10.0738
5928  −39 −152 35141184 4 4 6 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 5.0369
5932 −4 −1483 35188624 1 1 7 7 2 7 \sqrt{i}\sqrt{ε_{1}} 54.1144
5 −1187 −5935 35224225 1 9 42 189 1 189  ε_{1} 0.9624
28 −424 −2968 35236096 1 6 8 24 1 24  ε_{1} 5.5373
56 −212 −2968 35236096 1 6 8 24 1 24  ε_{1} 6.8002
1484  −8 −2968 35236096 2 1 8  8 1  4  ε_{1} 16.2572
1484  −56 −424 35236096 2 4 6 24 1 12  ε_{1} 16.2572
2968  −4 −2968 35236096 2 1 8  8 1  4  ε_{1} 40.1623
2968  −56 −212 35236096 2 4 6 24 1 12  ε_{1} 40.1623
5937  −3 −1979 35247969 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 81.2487
21 −283 −5943 35319249 1 3 32 48 1 48  ε_{1} 3.1336
849  −7 −5943 35319249 1 1 32 16 1 16  ε_{1} 71.2770
1981  −3 −5943 35319249 1 1 32 16 1 16  ε_{1} 59.8382
8 −743 −5944 35331136 1 21 20 210 1 210  ε_{1} 1.7627
5944  −8 −743 35331136 5 1 21 105 2 21 \sqrt{−1}\sqrt{ε_{1}} 17.4518
313  −19 −5947 35366809 1 1 8  4 1  4  ε_{1} 38.7035
5948  −4 −1487 35378704 1 1 37 37 2 37  \sqrt{i}\sqrt{ε_{1}} 16.5786
541  −11 −5951 35414401 1 1 90 45 1 45  ε_{1} 28.2989
5 −1191 −5955 35462025 1 24 20 240 1 240  ε_{1} 0.9624
397  −15 −5955 35462025 1 2 20 20 1 20  ε_{1} 16.2905
1985  −3 −5955 35462025 2 1 20 20 1 10  ε_{1} 44.1245
1985  −15 −1191 35462025 2 2 24 48 1 24  ε_{1} 44.1245
1489  −4 −5956 35473936 3 1 20 30 1 10  ε_{1} 38.2173
161 −259 −851 35485849 1 4 10 20 1 20  ε_{1} 20.1338
5957  −7 −851 35485849 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 6.7441
5957  −23 −259 35485849 2 3 4 12 1  6  ε_{1} 13.4881
101  −59 −5959 35509681 1 3 42 63 1 63  ε_{1} 5.9964
5 −1192 −5960 35521600 1 6 36 108 1 108  ε_{1} 0.9624
149  −40 −5960 35521600 1 2 36 36 1 36  ε_{1} 8.2223
745  −8 −5960 35521600 2 1 36 36 1 18  ε_{1} 34.1114
745  −40 −1192 35521600 2 2 6 12 1  6  ε_{1} 34.1114

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 145

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
5961  −3 −1987 35533521 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 96.4527
89  −67 −5963 35557369 1 1 24 12 1 12  ε_{1} 13.8155
12 −1491 −1988 35569296 1 12 24 144 1 144  ε_{1} 2.6339
21 −852 −1988 35569296 1 8 24 96 1 96  ε_{1} 3.1336
28 −852 −1491 35569296 1 8 12 48 1 48  ε_{1} 5.5373
213  −84 −1988 35569296 1 4 24 48 1 48  ε_{1} 8.5805
284  −84 −1491 35569296 1 4 12 24 1 24  ε_{1} 17.6959
497  −84 −852 35569296 1 4 8 16 1 16  ε_{1} 29.3851
5964  −3 −1988 35569296 4 1 24 48 1 12  ε_{1} 23.6476
5964  −4 −1491 35569296 4 1 12 24 1  6  ε_{1} 23.6476
5964  −7 −852 35569296 4 1 8 16 1  4  ε_{1} 23.6476
5964  −71  −84 35569296 4 7 4 56 1 14  ε_{1} 23.6476
8 −1492 −2984 35617024 1 10 26 130 1 130  ε_{1} 1.7627
2984  −4 −2984 35617024 2 1 26 26 1 13  ε_{1} 32.4394
2984  −8 −1492 35617024 2 1 10 10 1  5  ε_{1} 32.4394
5969  −47 −127 35628961 1 5 5 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 59.3779
853  −7 −5971 35652841 1 1 14  7 1  7  ε_{1} 20.4426
1493  −4 −5972 35664784 1 1 22 11 1 11  ε_{1} 15.5303
33 −543 −1991 35676729 1 12 56 336 1 336  ε_{1} 7.6563
5973 −3 −1991 35676729 4 1 56 112 1 28 ε_{1} 12.5868
5973  −11 −543 35676729 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 6.2934
5977  −43 −139 35724529 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 95.5307
1993  −3 −5979 35748441 1 1 24 12 1 12  ε_{1} 101.9612
92 −260 −1495 35760400 1 8 20 80 1 80  ε_{1} 7.7415
460 −52 −1495 35760400 2 2 20 40 1 20 ε_{1} 15.4391
460 −260 −299 35760400 2 8 8 64 1 32  ε_{1} 15.4391
1196  −20 −1495 35760400 2 2 20 40 1 20  ε_{1} 13.4428
1196 −115 −260 35760400 2 2 8 16 1  8  ε_{1} 13.4428
5980  −4 −1495 35760400 12 1 20 120 1 10  ε_{1} 10.8934
5980  −20 −299 35760400 12 2 8 96 1  8  ε_{1} 10.8934
5980  −23 −260 35760400 12 3 8 144 1 12  ε_{1} 10.8934
5980  −52 −115 35760400 12 2 2 24 1  2  ε_{1} 10.8934
193  −31 −5983 35796289 1 3 44 66 1 66  ε_{1} 30.1526
12 −499 −5988 35856144 1 3 20 30 1 30  ε_{1} 2.6339
1497  −4 −5988 35856144 1 1 20 10 1 10  ε_{1} 62.8769
1996  −3 −5988 35856144 5 1 20 50 1 10  ε_{1} 18.2055
1997  −3 −5991 35892081 1 1 70 35 1 35  ε_{1} 18.2454
56 −107 −5992 35904064 1 3 16 24 1 24  ε_{1} 6.8002
749  −8 −5992 35904064 1 1 16  8 1  8  ε_{1} 18.9369
749  −56 −856 35904064 1 4 6 12 1 12  ε_{1} 18.9369
856  −7 −5992 35904064 1 1 16  8 1  8  ε_{1} 55.9217
5992  −7 −856 35904064 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 27.1900
5992  −56 −107 35904064 2 4 3 12 1  6  ε_{1} 54.3801
5 −1199 −5995 35940025 1 38 16 304 1 304  ε_{1} 0.9624
109  −55 −5995 35940025 1 4 16 32 1 32  ε_{1} 11.1291
545  −11 −5995 35940025 2 1 16 16 1  8  ε_{1} 16.5487
545  −55 −1199 35940025 2 4 38 152 1 76  ε_{1} 16.5487
5996  −4 −1499 35952016 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 50.1469
5997  −3 −1999 35964009 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 18.7824
857  −7 −5999 35988001 1 1 90 45 1 45  ε_{1} 33.2056

146 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
76  −79 −6004 36048016 1 5 24 60 1 60  ε_{1} 11.6579
316  −19 −6004 36048016 3 1 24 36 1 12  ε_{1} 10.1503
1501  −4 −6004 36048016 1 1 24 12 1 12  ε_{1} 43.6455
8 −751 −6008 36096064 1 15 24 180 1 180  ε_{1} 1.7627
6008  −8 −751 36096064 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 23.2025
6009  −3 −2003 36108081 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 102.2817
6013  −7 −859 36156169 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 25.1283
5 −1203 −6015 36180225 1 6 36 108 1 108  ε_{1} 0.9624
401  −15 −6015 36180225 5 2 36 180 1 36  ε_{1} 7.3790
2005  −3 −6015 36180225 4 1 36 72 1 18  ε_{1} 11.9979
2005  −15 −1203 36180225 4 2 6 24 1  6  ε_{1} 11.9979
6017  −11 −547 36204289 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 52.7023
13 −463 −6019 36228361 1 7 22 77 1 77  ε_{1} 2.3895
5 −1204 −6020 36240400 1 8 40 160 1 160  ε_{1} 0.9624
28 −215 −6020 36240400 1 14 40 280 1 280  ε_{1} 5.5373
140 −43 −6020 36240400 2 1 40 40 1 20 ε_{1} 4.9558
140 −215 −1204 36240400 2 14 8 112 1 56  ε_{1} 4.9558
172  −35 −6020 36240400 1 2 40 40 1 40  ε_{1} 17.6970
301  −20 −6020 36240400 1 2 40 40 1 40  ε_{1} 20.0642
860  −7 −6020 36240400 2 1 40 40 1 20  ε_{1} 8.9544
860  −35 −1204 36240400 2 2 8 16 1  8  ε_{1} 8.9544
1505  −4 −6020 36240400 2 1 40 40 1 20  ε_{1} 33.9818
1505  −20 −1204 36240400 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 16.9909
317 −19 −6023 36276529 1 1 82 41 1 41 ε_{1} 8.9775
24 −251 −6024 36288576 1 7 24 84 1 84  ε_{1} 4.5849
753  −8 −6024 36288576 1 1 24 12 1 12  ε_{1} 54.2964
753  −24 −2008 36288576 1 2 14 14 1 14  ε_{1} 54.2964
2008  −3 −6024 36288576 1 1 24 12 1 12  ε_{1} 45.5198
6024  −3 −2008 36288576 2 1 14 14 1  7  ε_{1} 49.7568
6024  −24 −251 36288576 2 2 7 14 1  7  ε_{1} 49.7568
44 −548 −1507 36336784 1 8 4 16 1 16  ε_{1} 5.9864
6028  −4 −1507 36336784 4 1 4  8 1  2  ε_{1} 32.1932
6028  −11 −548 36336784 4 1 8 16 1  4  ε_{1} 32.1932
37 −163 −6031 36372961 1 1 50 25 1 25  ε_{1} 4.9836
8 −1508 −3016 36385024 1 16 20 160 1 160  ε_{1} 1.7627
104 −116 −3016 36385024 2 6 20 120 1 60  ε_{1} 4.6249
104 −232 −1508 36385024 2 2 16 32 1 16  ε_{1} 4.6249
232 −52 −3016 36385024 2 2 20 40 1 20 ε_{1} 10.5766
232 −104 −1508 36385024 2 6 16 96 1 48  ε_{1} 10.5766
3016  −4 −3016 36385024 4 1 20 40 1 10  ε_{1} 21.2385
3016  −8 −1508 36385024 4 1 16 32 1  8  ε_{1} 21.2385
3016  −52 −232 36385024 4 2 2  8 1  2  ε_{1} 21.2385
3016 −104 −116 36385024 4 6 6 72 1 18  ε_{1} 21.2385
6033 −3 −2011 36397089 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 68.5920
5 −1207 −6035 36421225 1 18 28 252 1 252  ε_{1} 0.9624
17 −355 −6035 36421225 1 4 28 56 1 56  ε_{1} 4.1894
85 −71 −6035 36421225 2 7 28 196 1 98 ε_{1} 4.4187
85 −355 −1207 36421225 2 4 18 72 1 36  ε_{1} 4.4187
12 −503 −6036 36433296 1 21 40 420 1 420  ε_{1} 2.6339
1509  −4 −6036 36433296 3 1 40 60 1 20  ε_{1} 12.4491

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 147

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2012  −3 −6036 36433296 1 1 40 20 1 20  ε_{1} 21.6112
5 −1208 −6040 36481600 1 12 16 96 1 96  ε_{1} 0.9624
8 −755 −6040 36481600 1 12 16 96 1 96  ε_{1} 1.7627
40 −151 −6040 36481600 2 7 16 112 1 56  ε_{1} 3.6369
40 −755 −1208 36481600 2 12 12 144 1 72  ε_{1} 3.6369
1208  −40 −755 36481600 1 2 12 12 1 12  ε_{1} 31.9236
6040  −8 −755 36481600 2 1 12 12 1  6  ε_{1} 51.6957
6040  −40 −151 36481600 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 25.8479
6041  −7 −863 36493681 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 68.0736
6044 −4 −1511 36529936 1 1 49 49 2 49 \sqrt{i}\sqrt{ε_{1}} 38.8815
93 −195 −2015 36542025 1 4 52 104 1 104  ε_{1} 6.7322
465  −39 −2015 36542025 2 4 52 208 1 104  ε_{1} 20.7308
465 −195 −403 36542025 2 4 2  8 1  4  ε_{1} 20.7308
1209  −15 −2015 36542025 2 2 52 104 1 52  ε_{1} 37.1044
1209 −155 −195 36542025 2 4 4 16 1  8  ε_{1} 37.1044
6045  −3 −2015 36542025 4 1 52 104 1 26  ε_{1} 12.8659
6045  −15 −403 36542025 4 2 2  8 1  2  ε_{1} 12.8659
6045  −31 −195 36542025 4 3 4 24 1  6  ε_{1} 12.8659
6045  −39 −155 36542025 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.4329
6049  −23 −263 36590401 1 3 13 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 144.3425
2017 −3 −6051 36614601 1 1 20 10 1 10 ε_{1} 121.2470
17 −356 −6052 36626704 1 12 16 96 1 96  ε_{1} 4.1894
89  −68 −6052 36626704 1 4 16 32 1 32  ε_{1} 13.8155
1513  −4 −6052 36626704 2 1 16 16 1  8  ε_{1} 49.0402
1513  −68 −356 36626704 2 4 12 96 2 48 \sqrt{−1}\sqrt{ε_{1}} 24.5201
5 −1211 −6055 36663025 1 14 36 252 1 252  ε_{1} 0.9624
173  −35 −6055 36663025 1 2 36 36 1 36  ε_{1} 5.1416
865  −7 −6055 36663025 2 1 36 36 1 18  ε_{1} 40.7237
865  −35 −1211 36663025 2 2 14 28 1 14  ε_{1} 40.7237
757  −8 −6056 36675136 1 1 50 25 1 25  ε_{1} 29.6460
73  −83 −6059 36711481 1 3 26 39 1 39  ε_{1} 15.3334
12 −1515 −2020 36723600 1 12 8 48 1 48  ε_{1} 2.6339
60 −303 −2020 36723600 2 10 8 80 1 40  ε_{1} 4.1269
60 −404 −1515 36723600 2 14 12 168 1 84  ε_{1} 4.1269
1212  −15 −2020 36723600 2 2 8 16 1  8  ε_{1} 17.0535
1212  −20 −1515 36723600 2 2 12 24 1 12  ε_{1} 17.0535
6060  −3 −2020 36723600 4 1 8 16 1  4  ε_{1} 13.8394
6060  −4 −1515 36723600 4 1 12 24 1  6  ε_{1} 13.8394
6060  −15 −404 36723600 4 2 14 56 1 14  ε_{1} 13.8394
6060  −20 −303 36723600 4 2 10 40 1 10  ε_{1} 13.8394
209 −319 −551 36735721 1 10 26 130 1 130  ε_{1} 22.8829
6061  −11 −551 36735721 2 1 26 26 1 13  ε_{1} 49.8872
6061  −19 −319 36735721 2 1 10 10 1  5  ε_{1} 49.8872
129  −47 −6063 36759969 1 5 36 90 1 90  ε_{1} 20.8511
141  −43 −6063 36759969 1 1 36 18 1 18  ε_{1} 10.4940
2021  −3 −6063 36759969 3 1 36 54 1 18  ε_{1} 7.6123
1516  −8 −3032 36772096 1 1 22 22 2 22 \sqrt{−1}\sqrt{ε_{1}} 37.7923
3032 −4 −3032 36772096 1 1 22 22 2 22 \sqrt{i}\sqrt{ε_{1}} 20.5344
37 −164 −6068 36820624 1 8 48 192 1 192  ε_{1} 4.9836
41 −148 −6068 36820624 1 2 48 48 1 48  ε_{1} 8.3183

148 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1517  −4 −6068 36820624 2 1 48 48 1 24  ε_{1} 7.3258
1517 −148 −164 36820624 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 3.6629
13 −467 −6071 36857041 1 7 96 336 1 336  ε_{1} 2.3895
8 −759 −6072 36869184 1 24 24 288 1 288  ε_{1} 1.7627
24 −759 −2024 36869184 1 24 28 336 1 336  ε_{1} 4.5849
33 −184 −6072 36869184 1 4 24 48 1 48  ε_{1} 7.6563
33 −552 −2024 36869184 1 8 28 112 1 112  ε_{1} 7.6563
69 −88 −6072 36869184 1 2 24 24 1 24 ε_{1} 6.4345
69 −264 −2024 36869184 1 8 28 112 1 112  ε_{1} 6.4345
88 −552 −759 36869184 1 8 24 96 1 96  ε_{1} 11.9527
184 −264 −759 36869184 1 8 24 96 1 96  ε_{1} 21.5856
253 −24 −6072 36869184 1 2 24 24 1 24 ε_{1} 15.0577
253 −264 −552 36869184 1 8 8 32 1 32  ε_{1} 15.0577
264 −23 −6072 36869184 2 3 24 72 1 36 ε_{1} 9.7350
264 −184 −759 36869184 2 4 24 96 1 48  ε_{1} 9.7350
552  −11 −6072 36869184 2 1 24 24 1 12  ε_{1} 9.0864
552  −88 −759 36869184 2 2 24 48 1 24  ε_{1} 9.0864
2024  −3 −6072 36869184 6 1 24 72 1 12  ε_{1} 8.9994
2024  −24 −759 36869184 6 2 24 144 1 24  ε_{1} 8.9994
6072  −3 −2024 36869184 4 1 28 112 2 28 \sqrt{−1}\sqrt{ε_{1}} 7.6138
6072  −8 −759 36869184 4 1 24 48 1 12  ε_{1} 15.2276
6072  −11 −552 36869184 4 1 8 16 1  4  ε_{1} 15.2276
6072  −23 −264 36869184 4 3 8 48 1 12  ε_{1} 15.2276
6077  −59 −103 36929929 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 23.9183
6081  −3 −2027 36978561 11 1 11 121 2 11 \sqrt{−1}\sqrt{ε_{1}} 9.0009
77  −79 −6083 37002889 1 5 24 60 1 60  ε_{1} 4.3693
553  −11 −6083 37002889 1 1 24 12 1 12  ε_{1} 55.7072
869  −7 −6083 37002889 1 1 24 12 1 12  ε_{1} 21.6145
2029  −3 −6087 37051569 7 1 36 126 1 18  ε_{1} 7.6143
761  −8 −6088 37063744 3 1 20 30 1 10  ε_{1} 14.7555
6092  −4 −1523 37112464 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 8.0209
5 −1219 −6095 37149025 1 6 84 252 1 252  ε_{1} 0.9624
53 −115 −6095 37149025 1 2 84 84 1 84  ε_{1} 3.9314
265  −23 −6095 37149025 2 3 84 252 1 126  ε_{1} 18.8092
265 −115 −1219 37149025 2 2 6 12 1  6  ε_{1} 18.8092
8 −1524 −3048 37161216 1 20 12 120 1 120  ε_{1} 1.7627
12 −1016 −3048 37161216 1 16 12 96 1 96  ε_{1} 2.6339
24 −1016 −1524 37161216 1 16 20 160 1 160  ε_{1} 4.5849
508  −24 −3048 37161216 1 2 12 12 1 12  ε_{1} 32.1254
1016  −24 −1524 37161216 3 2 20 60 1 20  ε_{1} 12.4688
3048  −4 −3048 37161216 2 1 12 12 1  6  ε_{1} 18.8984
3048  −8 −1524 37161216 2 1 20 20 1 10  ε_{1} 18.8984
469  −91 −871 37173409 3 2 22 66 1 22  ε_{1} 8.3483
6097  −7 −871 37173409 14 1 22 154 1 11  ε_{1} 15.0717
6097  −67  −91 37173409 14 1 2 14 1  1  ε_{1} 15.0717
57 −107 −6099 37197801 1 3 16 24 1 24  ε_{1} 11.4208
321  −19 −6099 37197801 3 1 16 24 1  8  ε_{1} 12.1276
2033  −3 −6099 37197801 1 1 16  8 1  8  ε_{1} 51.0805
17 −359 −6103 37246609 1 19 28 266 1 266  ε_{1} 4.1894
8 −763 −6104 37258816 1 4 48 96 1 96  ε_{1} 1.7627

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 149

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
56 −763 −872 37258816 1 4 10 20 1 20  ε_{1} 6.8002
109  −56 −6104 37258816 1 4 48 96 1 96  ε_{1} 11.1291
872  −7 −6104 37258816 2 1 48 48 1 24  ε_{1} 12.4372
872  −56 −763 37258816 2 4 4 16 1  8  ε_{1} 12.4372
6104  −7 −872 37258816 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 19.1350
6104 −8 −763 37258816 2 1 4 4 1 2 ε_{1} 38.2699
33 −555 −2035 37271025 1 4 8 16 1 16  ε_{1} 7.6563
165 −111 −2035 37271025 2 8 8 64 1 32  ε_{1} 5.1180
165 −407 −555 37271025 2 16 4 64 1 32  ε_{1} 5.1180
1221  −15 −2035 37271025 4 2 8 32 1  8  ε_{1} 7.1091
1221  −55 −555 37271025 4 4 4 32 1  8  ε_{1} 7.1091
6105  −3 −2035 37271025 4 1 8 16 1  4  ε_{1} 45.0640
6105  −11 −555 37271025 4 1 4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 22.5320
6105  −15 −407 37271025 4 2 16 64 1 16  ε_{1} 45.0640
6105  −55 −111 37271025 4 4 8 64 1 16  ε_{1} 45.0640
197  −31 −6107 37295449 1 3 30 45 1 45  ε_{1} 6.6670
12 −1527 −2036 37307664 1 14 30 210 1 210  ε_{1} 2.6339
6108  −3 −2036 37307664 6 1 30 90 1 15  ε_{1} 13.8473
6108  −4 −1527 37307664 6 1 14 42 1  7  ε_{1} 13.8473
5 −1223 −6115 37393225 1 35 10 175 1 175  ε_{1} 0.9624
44 −139 −6116 37405456 1 3 52 78 1 78  ε_{1} 5.9864
556  −11 −6116 37405456 1 1 52 26 1 26  ε_{1} 37.7195
1529  −4 −6116 37405456 1 1 52 26 1 26  ε_{1} 65.2096
6117  −3 −2039 37417689 1 1 45 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 16.1456
29 −211 −6119 37442161 1 3 82 123 1 123  ε_{1} 3.2945
13 −471 −6123 37491129 1 16 16 128 1 128  ε_{1} 2.3895
157  −39 −6123 37491129 1 4 16 32 1 32  ε_{1} 10.7226
2041  −3 −6123 37491129 2 1 16 16 1  8  ε_{1} 75.9301
2041  −39 −471 37491129 2 4 16 64 1 32  ε_{1} 75.9301
6124  −4 −1531 37503376 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 69.9166
557  −11 −6127 37540129 1 1 22 11 1 11  ε_{1} 10.9277
1532  −8 −3064 37552384 1 1 24 24 2 24 \sqrt{−1}\sqrt{ε_{1}} 10.5331
3064 −4 −3064 37552384 1 1 24 24 2 24 \sqrt{i}\sqrt{ε_{1}} 47.1228
12 −511 −6132 37601424 1 14 24 168 1 168  ε_{1} 2.6339
21 −292 −6132 37601424 1 4 24 48 1 48  ε_{1} 3.1336
28 −219 −6132 37601424 1 4 24 48 1 48  ε_{1} 5.5373
73  −84 −6132 37601424 1 4 24 48 1 48  ε_{1} 15.3334
876  −7 −6132 37601424 4 1 24 48 1 12  ε_{1} 9.9943
876  −84 −511 37601424 4 4 14 112 1 28  ε_{1} 9.9943
1533  −4 −6132 37601424 2 1 24 24 1 12  ε_{1} 12.4649
1533  −84 −292 37601424 2 4 4 16 1  8  ε_{1} 12.4649
2044  −3 −6132 37601424 2 1 24 24 1 12  ε_{1} 45.6975
2044  −84 −219 37601424 2 4 4 16 1  8  ε_{1} 45.6975
5 −1227 −6135 37638225 1 4 72 144 1 144  ε_{1} 0.9624
409  −15 −6135 37638225 1 2 72 72 1 72  ε_{1} 52.2684
2045  −3 −6135 37638225 2 1 72 72 1 36  ε_{1} 12.0176
2045  −15 −1227 37638225 2 2 4  8 1  4  ε_{1} 12.0176
8 −767 −6136 37650496 1 22 20 220 1 220  ε_{1} 1.7627
13 −472 −6136 37650496 1 6 20 60 1 60  ε_{1} 2.3895
104  −59 −6136 37650496 2 3 20 60 1 30  ε_{1} 4.6249

150 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
104 −472 −767 37650496 2 6 22 132 1 66  ε_{1} 4.6249
472 −104 −767 37650496 1 6 22 66 1 66  ε_{1} 26.6550
6136  −8 −767 37650496 14 1 22 154 1 11  ε_{1} 12.3055
6136  −59 −104 37650496 14 3 6 126 1  9  ε_{1} 12.3055
877  −7 −6139 37687321 1 1 20 10 1 10  ε_{1} 26.1741
1228  −20 −1535 37699600 1 2 38 38 1 38  ε_{1} 37.9840
6140  −4 −1535 37699600 2 1 38 38 1 19  ε_{1} 29.6588
6140  −20 −307 37699600 2 2 3  6 1  3  ε_{1} 29.6588
69 −267 −2047 37711881 1 2 18 18 1 18  ε_{1} 6.4345
6141  −3 −2047 37711881 2 1 18 18 1  9  ε_{1} 43.7640
6141  −23 −267 37711881 2 3 2  6 1  3  ε_{1} 43.7640
29 −212 −6148 37797904 1 6 16 48 1 48  ε_{1} 3.2945
53 −116 −6148 37797904 1 6 16 48 1 48  ε_{1} 3.9314
1537 −4 −6148 37797904 2 1 16 16 1 8 ε_{1} 51.4699
1537 −116 −212 37797904 2 6 6 72 2 36 \sqrt{−1}\sqrt{ε_{1}} 25.7350
473 −143 −559 37810201 3 10 16 240 1 80  ε_{1} 10.3180
6149 −11 −559 37810201 2 1 16 16 1 8 ε_{1} 21.2584
6149  −43 −143 37810201 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 10.6292
769 −8 −6152 37847104 1 1 44 22 1 22 ε_{1} 76.0544
21 −879 −2051 37859409 1 22 18 198 1 198  ε_{1} 3.1336
6153  −3 −2051 37859409 6 1 18 54 1  9  ε_{1} 28.2384
6153  −7 −879 37859409 6 1 22 66 1 11  ε_{1} 28.2384
5 −1231 −6155 37884025 1 27 28 378 1 378  ε_{1} 0.9624
6157  −47 −131 37908649 5 5 5 125 2 25 \sqrt{−1}\sqrt{ε_{1}} 7.0707
2053 −3 −6159 37933281 1 1 80 40 1 40 ε_{1} 48.1240
8 −1540 −3080 37945600 1 8 32 128 1 128  ε_{1} 1.7627
28 −440 −3080 37945600 1 12 32 192 1 192  ε_{1} 5.5373
40 −308 −3080 37945600 2 8 32 256 1 128  ε_{1} 3.6369
40 −616 −1540 37945600 2 8 8 64 1 32  ε_{1} 3.6369
44 −280 −3080 37945600 1 4 32 64 1 64  ε_{1} 5.9864
56 −440 −1540 37945600 1 12 8 48 1 48  ε_{1} 6.8002
88 −280 −1540 37945600 1 4 8 16 1 16  ε_{1} 11.9527
140 −88 −3080 37945600 2 2 32 64 1 32 ε_{1} 4.9558
140 −440 −616 37945600 2 12 8 96 1 48  ε_{1} 4.9558
220 −56 −3080 37945600 2 4 32 128 1 64 ε_{1} 10.3635
220 −280 −616 37945600 2 4 8 32 1 16  ε_{1} 10.3635
280 −88 −1540 37945600 2 2 8 16 1 8 ε_{1} 12.4372
280 −308 −440 37945600 2 8 12 96 1 48  ε_{1} 12.4372
440 −56 −1540 37945600 2 4 8 32 1 16 ε_{1} 7.4742
440 −280 −308 37945600 2 4 8 32 1 16  ε_{1} 7.4742
616  −20 −3080 37945600 2 2 32 64 1 32  ε_{1} 21.3187
616  −40 −1540 37945600 2 2 8 16 1  8  ε_{1} 21.3187
3080  −4 −3080 37945600 4 1 32 64 1 16  ε_{1} 10.8053
3080  −8 −1540 37945600 4 1 8 16 1  4  ε_{1} 10.8053
3080  −20 −616 37945600 4 2 8 32 1  8  ε_{1} 10.8053
3080  −40 −308 37945600 4 2 8 32 1  8  ε_{1} 10.8053
92  −67 −6164 37994896 1 1 36 18 1 18  ε_{1} 7.7415
268  −23 −6164 37994896 1 3 36 54 1 54  ε_{1} 22.9790
1541  −4 −6164 37994896 1 1 36 18 1 18  ε_{1} 27.9708
881  −7 −6167 38031889 1 1 66 33 1 33  ε_{1} 52.1657

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 151

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8 −771 −6168 38044224 1 6 20 60 1 60  ε_{1} 1.7627
24 −771 −2056 38044224 1 6 16 48 1 48  ε_{1} 4.5849
257  −24 −6168 38044224 3 2 20 60 1 20  ε_{1} 6.9334
2056  −3 −6168 38044224 4 1 20 40 1 10  ε_{1} 18.2648
2056  −24 −771 38044224 4 2 6 24 1  6  ε_{1} 18.2648
6168  −3 −2056 38044224 2 1 16 16 1  8  ε_{1} 30.9223
6168  −8 −771 38044224 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 15.4611
6169  −31 −199 38056561 1 3 9 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 148.7978
6172  −4 −1543 38093584 1 1 19 19 2 19  \sqrt{i}\sqrt{ε_{1}} 57.8488
213  −87 −2059 38155329 1 6 8 24 1 24  ε_{1} 8.5805
6177  −3 −2059 38155329 2 1 8  8 1  4  ε_{1} 46.5843
6177  −71  −87 38155329 2 7 6 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 23.2921
37 −167 −6179 38180041 1 11 42 231 1 231  ε_{1} 4.9836
5 −1236 −6180 38192400 1 12 24 144 1 144  ε_{1} 0.9624
12 −515 −6180 38192400 1 6 24 72 1 72  ε_{1} 2.6339
60 −103 −6180 38192400 2 5 24 120 1 60  ε_{1} 4.1269
60 −515 −1236 38192400 2 6 12 72 1 36  ε_{1} 4.1269
309  −20 −6180 38192400 1 2 24 24 1 24  ε_{1} 17.0523
412  −15 −6180 38192400 1 2 24 24 1 24  ε_{1} 26.0564
1545  −4 −6180 38192400 2 1 24 24 1 12  ε_{1} 38.6495
1545  −20 −1236 38192400 2 2 12 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 19.3248
2060  −3 −6180 38192400 2 1 24 24 1 12  ε_{1} 20.9154
2060  −15 −1236 38192400 2 2 12 24 1 12  ε_{1} 20.9154
6181  −7 −883 38204761 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 43.0351
773  −8 −6184 38241856 1 1 34 17 1 17  ε_{1} 9.8691
269  −23 −6187 38278969 1 3 12 18 1 18  ε_{1} 10.1998
28 −884 −1547 38291344 1 16 12 96 1 96  ε_{1} 5.5373
364 −68 −1547 38291344 2 4 12 48 1 24 ε_{1} 16.1090
364 −119 −884 38291344 2 10 16 160 1 80  ε_{1} 16.1090
476  −52 −1547 38291344 2 2 12 24 1 12  ε_{1} 10.9612
476  −91 −884 38291344 2 2 16 32 1 16  ε_{1} 10.9612
6188  −4 −1547 38291344 4 1 12 24 1  6  ε_{1} 10.9276
6188  −7 −884 38291344 4 1 16 32 1  8  ε_{1} 10.9276
6188  −52 −119 38291344 4 2 10 40 1 10  ε_{1} 10.9276
6188  −68  −91 38291344 4 4 2 16 1  4  ε_{1} 10.9276
6189  −3 −2063 38303721 1 1 45 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 41.1881
41 −151 −6191 38328481 1 7 98 343 1 343  ε_{1} 8.3183
6193 −11 −563 38353249 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 81.4617
5 −1239 −6195 38378025 1 32 16 256 1 256  ε_{1} 0.9624
21 −295 −6195 38378025 1 8 16 64 1 64  ε_{1} 3.1336
105 −59 −6195 38378025 2 3 16 48 1 24 ε_{1} 8.8131
105 −295 −1239 38378025 2 8 32 256 1 128  ε_{1} 8.8131
177  −35 −6195 38378025 1 2 16 16 1 16  ε_{1} 23.4697
413  −15 −6195 38378025 1 2 16 16 1 16  ε_{1} 8.2212
885  −7 −6195 38378025 2 1 16 16 1  8  ε_{1} 10.9445
885  −35 −1239 38378025 2 2 32 64 1 32  ε_{1} 10.9445
2065  −3 −6195 38378025 2 1 16 16 1  8  ε_{1} 61.9933
2065  −15 −1239 38378025 2 2 32 64 1 32  ε_{1} 61.9933
1549  −4 −6196 38390416 1 1 18  9 1  9  ε_{1} 54.4816
12 −1551 −2068 38489616 1 32 12 192 1 192  ε_{1} 2.6339

152 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
33 −564 −2068 38489616 1 8 12 48 1 48  ε_{1} 7.6563
44 −564 −1551 38489616 1 8 32 128 1 128  ε_{1} 5.9864
141 −132 −2068 38489616 1 4 12 24 1 24  ε_{1} 10.4940
188 −132 −1551 38489616 1 4 32 64 1 64  ε_{1} 9.1285
517 −132 −564 38489616 1 4 8 16 1 16  ε_{1} 18.5321
6204  −3 −2068 38489616 4 1 12 24 1  6  ε_{1} 30.2479
6204  −4 −1551 38489616 4 1 32 64 1 16  ε_{1} 30.2479
6204  −11 −564 38489616 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 15.1240
6204  −47 −132 38489616 4 5 4 40 1 10  ε_{1} 30.2479
2069  −3 −6207 38526849 1 1 50 25 1 25  ε_{1} 32.7815
6209  −7 −887 38551681 3 1 29 87 2 29 \sqrt{−1}\sqrt{ε_{1}} 25.3254
1553 −4 −6212 38588944 1 1 40 20 1 20 ε_{1} 38.0572
57 −327 −2071 38601369 1 12 30 180 1 180  ε_{1} 11.4208
6213  −3 −2071 38601369 2 1 30 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 17.2763
6213 −19 −327 38601369 2 1 12 12 1 6 ε_{1} 34.5527
5 −1243 −6215 38626225 1 4 96 192 1 192  ε_{1} 0.9624
113  −55 −6215 38626225 1 4 96 192 1 192  ε_{1} 14.6946
565  −11 −6215 38626225 2 1 96 96 1 48  ε_{1} 11.4667
565  −55 −1243 38626225 2 4 4 16 1  8  ε_{1} 11.4667
21 −296 −6216 38638656 1 10 24 120 1 120  ε_{1} 3.1336
21 −888 −2072 38638656 1 12 16 96 1 96  ε_{1} 3.1336
24 −259 −6216 38638656 1 4 24 48 1 48  ε_{1} 4.5849
37 −168 −6216 38638656 1 4 24 48 1 48  ε_{1} 4.9836
56 −111 −6216 38638656 1 8 24 96 1 96  ε_{1} 6.8002
168 −111 −2072 38638656 2 8 16 128 1 64  ε_{1} 6.5132
168 −259 −888 38638656 2 4 12 48 1 24  ε_{1} 6.5132
777  −8 −6216 38638656 4 1 24 48 1 12  ε_{1} 12.2006
777  −24 −2072 38638656 4 2 16 64 1 16  ε_{1} 12.2006
777  −56 −888 38638656 4 4 12 96 1 24  ε_{1} 12.2006
777 −168 −296 38638656 4 4 10 80 1 20  ε_{1} 12.2006
888  −7 −6216 38638656 2 1 24 24 1 12  ε_{1} 11.3942
888 −168 −259 38638656 2 4 4 16 1  8  ε_{1} 11.3942
2072  −3 −6216 38638656 2 1 24 24 1 12  ε_{1} 16.9251
2072 −111 −168 38638656 2 8 4 32 1 16  ε_{1} 16.9251
6216 −3 −2072 38638656 4 1 16 32 1 8 ε_{1} 25.3557
6216  −7 −888 38638656 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 12.6779
6216  −24 −259 38638656 4 2 4 16 1  4  ε_{1} 25.3557
6216  −56 −111 38638656 4 4 8 64 1 16  ε_{1} 25.3557
1244  −20 −1555 38688400 1 2 4  4 1  4  ε_{1} 34.6700
6220  −4 −1555 38688400 2 1 4  4 1  2  ε_{1} 73.7293
6220  −20 −311 38688400 2 2 19 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 36.8647
8 −1556 −3112 38738176 1 22 14 154 1 154  ε_{1} 1.7627
3112  −4 −3112 38738176 2 1 14 14 1  7  ε_{1} 37.0178
3112  −8 −1556 38738176 2 1 22 22 1 11  ε_{1} 37.0178
13 −479 −6227 38775529 1 25 18 225 1 225  ε_{1} 2.3895
93  −67 −6231 38825361 1 1 64 32 1 32  ε_{1} 6.7322
201  −31 −6231 38825361 1 3 64 96 1 96  ε_{1} 27.6905
2077  −3 −6231 38825361 1 1 64 32 1 32  ε_{1} 38.4093
8 −779 −6232 38837824 1 10 12 60 1 60  ε_{1} 1.7627
41 −152 −6232 38837824 1 6 12 36 1 36  ε_{1} 8.3183

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 153

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
152 −328 −779 38837824 1 4 10 20 1 20  ε_{1} 8.6078
328 −19 −6232 38837824 4 1 12 24 1 6 ε_{1} 5.7869
328 −152 −779 38837824 4 6 10 120 1 30  ε_{1} 5.7869
6232  −8 −779 38837824 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 24.2997
6232 −19 −328 38837824 2 1 4 4 1 2 ε_{1} 48.5994
6233  −23 −271 38850289 1 3 11 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 34.8798
5 −1247 −6235 38875225 1 26 12 156 1 156  ε_{1} 0.9624
29 −215 −6235 38875225 1 14 12 84 1 84  ε_{1} 3.2945
145 −43 −6235 38875225 4 1 12 24 1 6 ε_{1} 6.3596
145 −215 −1247 38875225 4 14 26 728 1 182  ε_{1} 6.3596
6236 −4 −1559 38887696 1 1 51 51 2 51 \sqrt{i}\sqrt{ε_{1}} 35.9846
17 −367 −6239 38925121 1 9 90 405 1 405  ε_{1} 4.1894
2081 −3 −6243 38975049 5 1 22 55 1 11 ε_{1} 18.0042
28 −223 −6244 38987536 1 7 32 112 1 112  ε_{1} 5.5373
892  −7 −6244 38987536 3 1 32 48 1 16  ε_{1} 12.2096
1561  −4 −6244 38987536 1 1 32 16 1 16  ε_{1} 122.1985
88  −71 −6248 39037504 1 7 28 98 1 98  ε_{1} 11.9527
568  −11 −6248 39037504 3 1 28 42 1 14  ε_{1} 11.3120
781  −8 −6248 39037504 1 1 28 14 1 14  ε_{1} 37.4447
781  −88 −568 39037504 1 2 4  4 1  4  ε_{1} 37.4447
6248  −11 −568 39037504 2 1 4  4 1  2  ε_{1} 30.2075
6248  −71  −88 39037504 2 7 2 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 15.1037
6249  −3 −2083 39050001 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 99.6867
133  −47 −6251 39075001 1 5 24 60 1 60  ε_{1} 10.3065
329  −19 −6251 39075001 1 1 24 12 1 12  ε_{1} 30.7485
893  −7 −6251 39075001 1 1 24 12 1 12  ε_{1} 15.4822
12 −1563 −2084 39087504 1 6 32 96 1 96  ε_{1} 2.6339
6252  −3 −2084 39087504 2 1 32 32 1 16  ε_{1} 49.1935
6252  −4 −1563 39087504 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 24.5967
92 −136 −3128 39137536 1 4 24 48 1 48  ε_{1} 7.7415
184 −68 −3128 39137536 1 4 24 48 1 48 ε_{1} 21.5856
1564  −8 −3128 39137536 2 1 24 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 16.5018
1564 −136 −184 39137536 2 4 4 16 1  8  ε_{1} 33.0036
3128  −4 −3128 39137536 2 1 24 48 2 24  \sqrt{i}\sqrt{ε_{1}} 7.3563
3128  −68 −184 39137536 2 4 4 16 1  8  ε_{1} 14.7126
569  −11 −6259 39175081 1 1 10  5 1  5  ε_{1} 44.9587
5 −1252 −6260 39187600 1 8 28 112 1 112  ε_{1} 0.9624
313  −20 −6260 39187600 1 2 28 28 1 28  ε_{1} 38.7035
1565  −4 −6260 39187600 2 1 28 28 1 14  ε_{1} 13.7934
1565  −20 −1252 39187600 2 2 8 16 1  8  ε_{1} 13.7934
6261  −3 −2087 39200121 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 18.7103
1253  −35 −895 39250225 1 2 16 16 1 16  ε_{1} 10.3522
6265  −7 −895 39250225 2 1 16 16 1  8  ε_{1} 119.5648
6265  −35 −179 39250225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 59.7824
2089  −3 −6267 39275289 3 1 12 18 1  6  ε_{1} 45.6146
6268  −4 −1567 39287824 3 1 15 45 2 15  \sqrt{i}\sqrt{ε_{1}} 15.4772
12 −523 −6276 39388176 1 5 28 70 1 70  ε_{1} 2.6339
1569  −4 −6276 39388176 1 1 28 14 1 14  ε_{1} 100.6975
2092  −3 −6276 39388176 1 1 28 14 1 14  ε_{1} 51.6416
13 −483 −6279 39425841 1 4 56 112 1 112  ε_{1} 2.3895

154 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
21 −299 −6279 39425841 1 8 56 224 1 224  ε_{1} 3.1336
69  −91 −6279 39425841 1 2 56 56 1 56  ε_{1} 6.4345
161  −39 −6279 39425841 1 4 56 112 1 112  ε_{1} 20.1338
273  −23 −6279 39425841 2 3 56 168 1 84  ε_{1} 14.5641
273 −299 −483 39425841 2 8 4 32 1 16  ε_{1} 14.5641
897  −7 −6279 39425841 4 1 56 112 1 28  ε_{1} 14.1768
897  −91 −483 39425841 4 2 4 16 1  4  ε_{1} 14.1768
2093  −3 −6279 39425841 2 1 56 56 1 28  ε_{1} 11.8053
2093  −39 −483 39425841 2 4 4 16 1  8  ε_{1} 11.8053
5 −1256 −6280 39438400 1 26 20 260 1 260  ε_{1} 0.9624
157  −40 −6280 39438400 1 2 20 20 1 20  ε_{1} 10.7226
785  −8 −6280 39438400 6 1 20 60 1 10  ε_{1} 8.0513
785  −40 −1256 39438400 6 2 26 156 1 26  ε_{1} 8.0513
6281  −11 −571 39450961 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 87.1732
61 −103 −6283 39476089 1 5 12 30 1 30  ε_{1} 7.3284
6284  −4 −1571 39488656 1 1 17 17 2 17  \sqrt{i}\sqrt{ε_{1}} 28.6819
1257  −15 −2095 39501225 3 2 16 48 1 16  ε_{1} 24.4399
6285  −3 −2095 39501225 2 1 16 16 1  8  ε_{1} 19.8596
6285  −15 −419 39501225 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 9.9298
8 −1572 −3144 39538944 1 12 16 96 1 96  ε_{1} 1.7627
12 −1048 −3144 39538944 1 6 16 48 1 48  ε_{1} 2.6339
24 −1048 −1572 39538944 1 6 12 36 1 36  ε_{1} 4.5849
524  −24 −3144 39538944 1 2 16 16 1 16  ε_{1} 19.9254
1048  −24 −1572 39538944 1 2 12 12 1 12  ε_{1} 38.3249
3144  −4 −3144 39538944 6 1 16 96 2 16  \sqrt{i}\sqrt{ε_{1}} 7.3588
3144  −8 −1572 39538944 6 1 12 72 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.3588
6289 −19 −331 39551521 3 1 3 9 2 3 \sqrt{−1}\sqrt{ε_{1}} 42.2432
217 −203 −899 39601849 1 4 14 28 1 28  ε_{1} 31.7104
6293  −7 −899 39601849 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.3849
6293 −31 −203 39601849 2 3 4 12 1 6 ε_{1} 20.7697
5 −1259 −6295 39627025 1 15 24 180 1 180  ε_{1} 0.9624
8 −787 −6296 39639616 1 5 54 135 1 135  ε_{1} 1.7627
6296 −8 −787 39639616 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 36.3624
6297  −3 −2099 39652209 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 78.3569
33 −191 −6303 39727809 1 13 48 312 1 312  ε_{1} 7.6563
573  −11 −6303 39727809 1 1 48 24 1 24  ε_{1} 13.2824
2101  −3 −6303 39727809 3 1 48 72 1 24  ε_{1} 20.4440
17 −371 −6307 39778249 1 8 8 32 1 32  ε_{1} 4.1894
53 −119 −6307 39778249 1 10 8 40 1 40  ε_{1} 3.9314
901 −7 −6307 39778249 4 1 8 16 1 4 ε_{1} 8.1892
901 −119 −371 39778249 4 10 8 160 1 40  ε_{1} 8.1892
76  −83 −6308 39790864 1 3 28 42 1 42  ε_{1} 11.6579
332  −19 −6308 39790864 1 1 28 14 1 14  ε_{1} 10.1997
1577  −4 −6308 39790864 1 1 28 14 1 14  ε_{1} 66.0912
24 −263 −6312 39841344 1 13 16 104 1 104  ε_{1} 4.5849
789  −8 −6312 39841344 1 1 16  8 1  8  ε_{1} 20.7360
789  −24 −2104 39841344 1 2 12 12 1 12  ε_{1} 20.7360
2104  −3 −6312 39841344 1 1 16  8 1  8  ε_{1} 93.1423
6312  −3 −2104 39841344 2 1 12 12 1  6  ε_{1} 27.3861
6312  −24 −263 39841344 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 13.6930

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 155

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
6313  −59 −107 39853969 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 78.9654
5 −1263 −6315 39879225 1 20 16 160 1 160  ε_{1} 0.9624
421  −15 −6315 39879225 1 2 16 16 1 16  ε_{1} 26.0114
2105  −3 −6315 39879225 2 1 16 16 1  8  ε_{1} 34.6812
2105  −15 −1263 39879225 2 2 20 40 1 20  ε_{1} 34.6812
6316  −4 −1579 39891856 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 76.5193
89  −71 −6319 39929761 1 7 52 182 1 182  ε_{1} 13.8155
316  −40 −3160 39942400 3 2 16 48 1 16  ε_{1} 10.1503
632  −20 −3160 39942400 1 2 16 16 1 16  ε_{1} 19.2954
1580  −8 −3160 39942400 2 1 16 16 1  8  ε_{1} 11.5241
1580  −40 −632 39942400 2 2 8 16 1  8  ε_{1} 11.5241
3160  −4 −3160 39942400 2 1 16 16 1  8  ε_{1} 46.6118
3160  −20 −632 39942400 2 2 8 16 1  8  ε_{1} 46.6118
12 −527 −6324 39992976 1 18 40 360 1 360  ε_{1} 2.6339
17 −372 −6324 39992976 1 4 40 80 1 80  ε_{1} 4.1894
93  −68 −6324 39992976 1 4 40 80 1 80  ε_{1} 6.7322
124  −51 −6324 39992976 1 2 40 40 1 40  ε_{1} 16.0392
204  −31 −6324 39992976 2 3 40 120 1 60  ε_{1} 9.2101
204 −372 −527 39992976 2 4 18 72 1 36  ε_{1} 9.2101
1581 −4 −6324 39992976 2 1 40 40 1 20 ε_{1} 13.4549
1581  −68 −372 39992976 2 4 4 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.7274
2108  −3 −6324 39992976 2 1 40 40 1 20  ε_{1} 13.9245
2108  −51 −372 39992976 2 2 4  8 1  4  ε_{1} 13.9245
8 −791 −6328 40043584 1 32 16 256 1 256  ε_{1} 1.7627
56 −791 −904 40043584 1 32 8 128 1 128  ε_{1} 6.8002
113  −56 −6328 40043584 1 4 16 32 1 32  ε_{1} 14.6946
904  −7 −6328 40043584 8 1 16 64 1  8  ε_{1} 6.8046
904  −56 −791 40043584 8 4 32 512 1 64  ε_{1} 6.8046
6328  −7 −904 40043584 4 1 8 16 1  4  ε_{1} 33.3194
6328  −8 −791 40043584 4 1 32 64 1 16  ε_{1} 33.3194
13 −487 −6331 40081561 1 7 18 63 1 63  ε_{1} 2.3895
6332 −4 −1583 40094224 1 1 33 33 2 33 \sqrt{i}\sqrt{ε_{1}} 32.8708
6333  −3 −2111 40106889 1 1 49 49 2 49 \sqrt{−1}\sqrt{ε_{1}} 17.4053
5 −1267 −6335 40132225 1 6 92 276 1 276  ε_{1} 0.9624
181  −35 −6335 40132225 1 2 92 92 1 92  ε_{1} 14.3479
905  −7 −6335 40132225 4 1 92 184 1 46  ε_{1} 13.1640
905  −35 −1267 40132225 4 2 6 24 1  6  ε_{1} 13.1640
2113  −3 −6339 40182921 1 1 20 10 1 10  ε_{1} 104.9750
5 −1268 −6340 40195600 1 10 24 120 1 120  ε_{1} 0.9624
317  −20 −6340 40195600 1 2 24 24 1 24  ε_{1} 8.9775
1585  −4 −6340 40195600 2 1 24 24 1 12  ε_{1} 54.8106
1585  −20 −1268 40195600 2 2 10 20 1 10  ε_{1} 54.8106
13 −488 −6344 40246336 1 10 44 220 1 220  ε_{1} 2.3895
61 −104 −6344 40246336 1 6 44 132 1 132  ε_{1} 7.3284
793 −8 −6344 40246336 4 1 44 88 1 22 ε_{1} 18.1618
793 −104 −488 40246336 4 6 10 120 1 30  ε_{1} 18.1618
577  −11 −6347 40284409 7 1 28 98 1 14  ε_{1} 7.7433
6349  −7 −907 40309801 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 45.6871
29 −219 −6351 40335201 1 4 44 88 1 88  ε_{1} 3.2945
73  −87 −6351 40335201 1 6 44 132 1 132  ε_{1} 15.3334

156 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2117  −3 −6351 40335201 2 1 44 44 1 22  ε_{1} 9.0438
2117  −87 −219 40335201 2 6 4 24 1 12  ε_{1} 9.0438
8 −1588 −3176 40347904 1 6 42 126 1 126  ε_{1} 1.7627
3176  −4 −3176 40347904 2 1 42 42 1 21  ε_{1} 22.0198
3176  −8 −1588 40347904 2 1 6  6 1  3  ε_{1} 22.0198
5 −1271 −6355 40386025 1 40 16 320 1 320  ε_{1} 0.9624
41 −155 −6355 40386025 1 4 16 32 1 32  ε_{1} 8.3183
205 −31 −6355 40386025 2 3 16 48 1 24 ε_{1} 7.5213
205 −155 −1271 40386025 2 4 40 160 1 80  ε_{1} 7.5213
28 −227 −6356 40398736 1 5 52 130 1 130  ε_{1} 5.5373
908  −7 −6356 40398736 1 1 52 26 1 26  ε_{1} 12.2274
1589  −4 −6356 40398736 1 1 52 26 1 26  ε_{1} 31.3219
489  −39 −2119 40411449 1 4 34 68 1 68  ε_{1} 46.8872
6357  −3 −2119 40411449 2 1 34 68 2 34 \sqrt{−1}\sqrt{ε_{1}} 15.5612
6357 −39 −163 40411449 2 4 1 4 1 2 ε_{1} 31.1224
5 −1272 −6360 40449600 1 12 32 192 1 192  ε_{1} 0.9624
8 −795 −6360 40449600 1 4 32 64 1 64  ε_{1} 1.7627
24 −795 −2120 40449600 1 4 28 56 1 56  ε_{1} 4.5849
40 −159 −6360 40449600 2 10 32 320 1 160  ε_{1} 3.6369
40 −795 −1272 40449600 2 4 12 48 1 24  ε_{1} 3.6369
53 −120 −6360 40449600 1 4 32 64 1 64  ε_{1} 3.9314
120 −159 −2120 40449600 2 10 28 280 1 140  ε_{1} 6.1779
120 −424 −795 40449600 2 6 4 24 1 12  ε_{1} 6.1779
265 −24 −6360 40449600 2 2 32 64 1 32 ε_{1} 18.8092
265 −120 −1272 40449600 2 4 12 48 1 24  ε_{1} 18.8092
424  −15 −6360 40449600 2 2 32 64 1 32  ε_{1} 17.9769
424 −120 −795 40449600 2 4 4 16 1  8  ε_{1} 17.9769
1272  −15 −2120 40449600 2 2 28 56 1 28  ε_{1} 10.7319
1272  −40 −795 40449600 2 2 4  8 1  4  ε_{1} 10.7319
2120  −3 −6360 40449600 4 1 32 64 1 16  ε_{1} 7.6582
2120  −15 −1272 40449600 4 2 12 48 1 12  ε_{1} 7.6582
2120  −24 −795 40449600 4 2 4 16 1  4  ε_{1} 7.6582
2120 −120 −159 40449600 4 4 10 80 1 20  ε_{1} 7.6582
6360  −3 −2120 40449600 8 1 28 112 1 14  ε_{1} 12.9167
6360  −8 −795 40449600 8 1 4 16 1  2  ε_{1} 12.9167
6360  −15 −424 40449600 8 2 6 48 1  6  ε_{1} 12.9167
6360  −40 −159 40449600 8 2 10 160 2 20 \sqrt{−1}\sqrt{ε_{1}} 6.4583
172 −148 −1591 40500496 1 2 22 22 1 22  ε_{1} 17.6970
6364  −4 −1591 40500496 2 1 22 22 1 11  ε_{1} 75.3556
6364  −43 −148 40500496 2 1 2  2 1  1  ε_{1} 75.3556
1273  −95 −335 40513225 1 8 18 72 1 72  ε_{1} 80.8877
6365  −19 −335 40513225 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 9.0332
6365 −67 −95 40513225 2 1 8 8 1 4 ε_{1} 18.0665
33 −579 −2123 40564161 1 8 14 56 1 56  ε_{1} 7.6563
6369  −3 −2123 40564161 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 45.6479
6369  −11 −579 40564161 2 1 8  8 1  4  ε_{1} 91.2957
277  −23 −6371 40589641 1 3 36 54 1 54  ε_{1} 15.7365
797  −8 −6376 40653376 1 1 34 17 1 17  ε_{1} 11.8107
6377  −7 −911 40666129 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 43.8307
44 −580 −1595 40704400 1 8 16 64 1 64  ε_{1} 5.9864

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 157

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
220 −116 −1595 40704400 2 6 16 96 1 48  ε_{1} 10.3635
220 −319 −580 40704400 2 10 8 80 1 40  ε_{1} 10.3635
1276  −20 −1595 40704400 2 2 16 32 1 16  ε_{1} 34.1320
1276  −55 −580 40704400 2 4 8 32 1 16  ε_{1} 34.1320
6380  −4 −1595 40704400 4 1 16 32 1  8  ε_{1} 14.3061
6380  −11 −580 40704400 4 1 8 16 1  4  ε_{1} 14.3061
6380  −20 −319 40704400 4 2 10 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 7.1531
6380 −55 −116 40704400 4 4 6 48 1 12 ε_{1} 14.3061
13 −491 −6383 40742689 1 9 72 324 1 324  ε_{1} 2.3895
12 −1064 −3192 40755456 1 20 16 160 1 160  ε_{1} 2.6339
24 −532 −3192 40755456 1 4 16 32 1 32  ε_{1} 4.5849
28 −456 −3192 40755456 1 8 16 64 1 64  ε_{1} 5.5373
56 −228 −3192 40755456 1 4 16 32 1 32  ε_{1} 6.8002
76 −168 −3192 40755456 1 4 16 32 1 32  ε_{1} 11.6579
152 −84 −3192 40755456 1 4 16 32 1 32 ε_{1} 8.6078
168 −228 −1064 40755456 2 4 20 80 1 40  ε_{1} 6.5132
168 −456 −532 40755456 2 8 4 32 1 16  ε_{1} 6.5132
456  −84 −1064 40755456 2 4 20 80 1 40  ε_{1} 15.2512
456 −168 −532 40755456 2 4 4 16 1  8  ε_{1} 15.2512
1064  −84 −456 40755456 2 4 8 32 1 16  ε_{1} 14.4451
1064 −168 −228 40755456 2 4 4 16 1  8  ε_{1} 14.4451
1596  −8 −3192 40755456 8 1 16 64 1  8  ε_{1} 7.3765
1596  −24 −1064 40755456 8 2 20 160 1 20  ε_{1} 7.3765
1596  −56 −456 40755456 8 4 8 128 1 16  ε_{1} 7.3765
1596 −152 −168 40755456 8 6 4 192 2 24 \sqrt{−1}\sqrt{ε_{1}} 3.6883
3192  −4 −3192 40755456 4 1 16 32 1  8  ε_{1} 10.8410
3192  −24 −532 40755456 4 2 4 16 1  4  ε_{1} 10.8410
3192  −56 −228 40755456 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.4205
3192  −84 −152 40755456 4 4 6 48 1 12  ε_{1} 10.8410
2129  −3 −6387 40793769 1 1 18  9 1  9  ε_{1} 97.3639
1597  −4 −6388 40806544 1 1 14  7 1  7  ε_{1} 36.8543
77  −83 −6391 40844881 1 3 48 72 1 72  ε_{1} 4.3693
581  −11 −6391 40844881 1 1 48 24 1 24  ε_{1} 17.6272
913  −7 −6391 40844881 1 1 48 24 1 24  ε_{1} 69.1395
8 −799 −6392 40857664 1 16 32 256 1 256  ε_{1} 1.7627
17 −376 −6392 40857664 1 8 32 128 1 128  ε_{1} 4.1894
136 −47 −6392 40857664 2 5 32 160 1 80 ε_{1} 8.4966
136 −376 −799 40857664 2 8 16 128 1 64  ε_{1} 8.4966
376 −136 −799 40857664 1 4 16 32 1 32  ε_{1} 30.5420
6392  −8 −799 40857664 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 8.0703
6392 −47 −136 40857664 4 5 4 40 1 10 ε_{1} 16.1406
6393  −3 −2131 40870449 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 82.8956
5 −1279 −6395 40896025 1 23 16 184 1 184  ε_{1} 0.9624
12 −1599 −2132 40908816 1 36 12 216 1 216  ε_{1} 2.6339
156 −123 −2132 40908816 2 2 12 24 1 12  ε_{1} 7.8232
156 −164 −1599 40908816 2 8 36 288 1 144  ε_{1} 7.8232
492  −39 −2132 40908816 2 4 12 48 1 24  ε_{1} 10.9943
492  −52 −1599 40908816 2 2 36 72 1 36  ε_{1} 10.9943
6396  −3 −2132 40908816 12 1 12 72 1  6  ε_{1} 8.7637
6396  −4 −1599 40908816 12 1 36 216 1 18  ε_{1} 8.7637

158 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
6396  −39 −164 40908816 12 4  8 192 1 16  ε_{1} 8.7637
6396  −52 −123 40908816 12 2  2 24 1  2  ε_{1} 8.7637
337  −19 −6403 40998409 1 1 10  5 1  5  ε_{1} 42.8642
1601  −4 −6404 41011216 7 1 56 196 1 28  ε_{1} 8.7644
21 −915 −2135 41024025 1 8 44 176 1 176  ε_{1} 3.1336
105 −183 −2135 41024025 2 8 44 352 1 176  ε_{1} 8.8131
105 −427 −915 41024025 2 2  8 16 1  8  ε_{1} 8.8131
1281  −15 −2135 41024025 2 2 44 88 1 44  ε_{1} 42.3622
1281  −35 −915 41024025 2 2  8 16 1  8  ε_{1} 42.3622
6405  −3 −2135 41024025 4 1 44 88 1 22  ε_{1} 17.0826
6405  −7 −915 41024025 4 1  8 16 1  4  ε_{1} 17.0826
6405  −15 −427 41024025 4 2  2  8 1  2  ε_{1} 17.0826
6405  −35 −183 41024025 4 2  8 32 1  8  ε_{1} 17.0826
149  −43 −6407 41049649 1 1 46 23 1 23  ε_{1} 8.2223
2137  −3 −6411 41100921 1 1 24 12 1 12  ε_{1} 126.0100
28 −916 −1603 41113744 1 10  6 30 1 30  ε_{1} 5.5373
6412  −4 −1603 41113744 2 1  6  6 1  3  ε_{1} 51.4004
6412  −7 −916 41113744 2 1 10 10 1  5  ε_{1} 51.4004
5 −1283 −6415 41152225 1 11 50 275 1 275  ε_{1} 0.9624
8 −1604 −3208 41165056 1 20 12 120 1 120  ε_{1} 1.7627
3208 −4 −3208 41165056 2 1 12 24 2 12 \sqrt{i}\sqrt{ε_{1}} 20.1973
3208  −8 −1604 41165056 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 20.1973
5 −1284 −6420 41216400 1 20 16 160 1 160  ε_{1} 0.9624
12 −535 −6420 41216400 1 14 16 112 1 112  ε_{1} 2.6339
60 −107 −6420 41216400 2 3 16 48 1 24  ε_{1} 4.1269
60 −535 −1284 41216400 2 14 20 280 1 140  ε_{1} 4.1269
321  −20 −6420 41216400 3 2 16 48 1 16  ε_{1} 12.1276
428  −15 −6420 41216400 1 2 16 16 1 16  ε_{1} 15.1243
1605  −4 −6420 41216400 2 1 16 16 1  8  ε_{1} 14.3124
1605  −20 −1284 41216400 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 7.1562
2140  −3 −6420 41216400 2 1 16 16 1  8  ε_{1} 29.9807
2140  −15 −1284 41216400 2 2 20 40 1 20  ε_{1} 29.9807
2141  −3 −6423 41254929 1 1 38 19 1 19  ε_{1} 27.5414
8 −803 −6424 41267776 1 10 28 140 1 140  ε_{1} 1.7627
73 −88 −6424 41267776 1 2 28 28 1 28 ε_{1} 15.3334
88 −584 −803 41267776 1 16 10 80 1 80  ε_{1} 11.9527
584  −11 −6424 41267776 2 1 28 28 1 14  ε_{1} 11.3397
584  −88 −803 41267776 2 2 10 20 1 10  ε_{1} 11.3397
6424  −8 −803 41267776 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 31.5244
6424  −11 −584 41267776 2 1 16 16 1  8  ε_{1} 63.0488
6428  −4 −1607 41319184 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 33.2445
6429  −3 −2143 41332041 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 32.8277
109 −59 −6431 41357761 1 3 114 171 1 171 ε_{1} 11.1291
6433  −7 −919 41383489 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 105.4851
1609  −4 −6436 41422096 1 1 28 14 1 14  ε_{1} 122.7907
137  −47 −6439 41460721 1 5 62 155 1 155  ε_{1} 16.3142
5 −1288 −6440 41473600 1 8 32 128 1 128  ε_{1} 0.9624
56 −115 −6440 41473600 1 2 32 32 1 32  ε_{1} 6.8002
161 −40 −6440 41473600 1 2 32 32 1 32 ε_{1} 20.1338
161 −280 −920 41473600 1 4 20 40 1 40  ε_{1} 20.1338

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 159

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
184  −35 −6440 41473600 1 2 32 32 1 32  ε_{1} 21.5856
280  −23 −6440 41473600 2 3 32 96 1 48  ε_{1} 12.4372
280 −115 −1288 41473600 2 2 8 16 1  8  ε_{1} 12.4372
805  −8 −6440 41473600 2 1 32 32 1 16  ε_{1} 14.5545
805  −40 −1288 41473600 2 2 8 16 1  8  ε_{1} 14.5545
805  −56 −920 41473600 2 4 20 80 1 40  ε_{1} 14.5545
805 −184 −280 41473600 2 4 4 16 1  8  ε_{1} 14.5545
920  −7 −6440 41473600 2 1 32 32 1 16  ε_{1} 10.4080
920  −35 −1288 41473600 2 2 8 16 1  8  ε_{1} 10.4080
1288  −35 −920 41473600 4 2 20 80 1 20  ε_{1} 12.9416
1288 −115 −280 41473600 4 2 4 16 1  4  ε_{1} 12.9416
6440  −7 −920 41473600 4 1 20 40 1 10  ε_{1} 12.9292
6440  −23 −280 41473600 4 3 4 24 1  6  ε_{1} 12.9292
6440  −35 −184 41473600 4 2 4 16 1  4  ε_{1} 12.9292
6440  −56 −115 41473600 4 4 2 16 1  4  ε_{1} 12.9292
57 −339 −2147 41486481 1 6 14 42 1 42  ε_{1} 11.4208
6441  −3 −2147 41486481 2 1 14 14 1  7  ε_{1} 105.3204
6441  −19 −339 41486481 2 1 6  6 1  3  ε_{1} 105.3204
17 −379 −6443 41512249 1 3 26 39 1 39  ε_{1} 4.1894
21 −307 −6447 41563809 1 3 48 72 1 72  ε_{1} 3.1336
921  −7 −6447 41563809 1 1 48 24 1 24  ε_{1} 72.3140
2149  −3 −6447 41563809 1 1 48 24 1 24  ε_{1} 60.1259
124 −104 −3224 41576704 1 6 28 84 1 84  ε_{1} 16.0392
248  −52 −3224 41576704 1 2 28 28 1 28  ε_{1} 9.6724
1612  −8 −3224 41576704 2 1 28 28 1 14  ε_{1} 28.2160
1612 −104 −248 41576704 2 6 8 96 2 48 \sqrt{−1}\sqrt{ε_{1}} 14.1080
3224 −4 −3224 41576704 2 1 28 28 1 14 ε_{1} 32.6555
3224  −52 −248 41576704 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 16.3278
1613 −4 −6452 41628304 1 1 42 21 1 21 ε_{1} 15.9940
5 −1291 −6455 41667025 1 9 60 270 1 270  ε_{1} 0.9624
8 −807 −6456 41679936 1 14 28 196 1 196  ε_{1} 1.7627
24 −807 −2152 41679936 1 14 10 70 1 70  ε_{1} 4.5849
269  −24 −6456 41679936 1 2 28 28 1 28  ε_{1} 10.1998
2152  −3 −6456 41679936 2 1 28 28 1 14  ε_{1} 23.6715
2152  −24 −807 41679936 2 2 14 28 1 14  ε_{1} 23.6715
6456  −3 −2152 41679936 2 1 10 10 1  5  ε_{1} 54.1843
6456  −8 −807 41679936 2 1 14 14 1  7  ε_{1} 54.1843
6457  −11 −587 41692849 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 93.3844
2153  −3 −6459 41718681 5 1 30 75 1 15  ε_{1} 12.2798
76 −340 −1615 41731600 1 4 24 48 1 48  ε_{1} 11.6579
380  −68 −1615 41731600 2 4 24 96 1 48  ε_{1} 8.7131
380 −323 −340 41731600 2 4 4 16 1  8  ε_{1} 8.7131
1292  −20 −1615 41731600 4 2 24 96 1 24  ε_{1} 7.1655
1292  −95 −340 41731600 4 8 4 64 1 16  ε_{1} 7.1655
6460  −4 −1615 41731600 4 1 24 48 1 12  ε_{1} 31.3958
6460  −19 −340 41731600 4 1 4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 15.6979
6460  −20 −323 41731600 4 2 4 16 1  4  ε_{1} 31.3958
6460  −68  −95 41731600 4 4 8 64 1 16  ε_{1} 31.3958
497  −91 −923 41744521 1 2 10 10 1 10  ε_{1} 29.3851
6461  −7 −923 41744521 2 1 10 10 1  5  ε_{1} 29.4679

160 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
6461  −71  −91 41744521 2 7 2 14 1  7  ε_{1} 29.4679
281  −23 −6463 41770369 1 3 30 45 1 45  ε_{1} 29.1405
1293  −15 −2155 41796225 1 2 12 12 1 12  ε_{1} 14.9071
6465  −3 −2155 41796225 2 1 12 12 1  6  ε_{1} 93.3674
6465  −15 −431 41796225 2 2 21 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 46.6837
29 −223 −6467 41822089 1 7 20 70 1 70  ε_{1} 3.2945
809  −8 −6472 41886784 1 1 12  6 1  6  ε_{1} 54.9782
6476  −4 −1619 41938576 1 1 15 15 2 15  \sqrt{i}\sqrt{ε_{1}} 46.4971
381  −51 −2159 41951529 1 2 60 60 1 60  ε_{1} 15.2316
6477  −3 −2159 41951529 2 1 60 60 1 30  ε_{1} 30.3015
6477  −51 −127 41951529 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 15.1508
209  −31 −6479 41977441 1 3 84 126 1 126  ε_{1} 22.8829
341  −19 −6479 41977441 1 1 84 42 1 42  ε_{1} 11.2480
589  −11 −6479 41977441 1 1 84 42 1 42  ε_{1} 30.5757
2161  −3 −6483 42029289 1 1 12  6 1  6  ε_{1} 148.1166
1621  −4 −6484 42042256 1 1 18  9 1  9  ε_{1} 58.4091
13 −499 −6487 42081169 1 3 42 63 1 63  ε_{1} 2.3895
8 −811 −6488 42094144 1 7 30 105 1 105  ε_{1} 1.7627
6488 −8 −811 42094144 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 29.3649
12 −1623 −2164 42146064 1 28 10 140 1 140  ε_{1} 2.6339
6492  −3 −2164 42146064 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 11.5715
6492  −4 −1623 42146064 2 1 28 28 1 14  ε_{1} 23.1430
6493  −43 −151 42159049 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 39.5158
5 −1299 −6495 42185025 1 8 52 208 1 208  ε_{1} 0.9624
433  −15 −6495 42185025 1 2 52 52 1 52  ε_{1} 46.7895
2165  −3 −6495 42185025 2 1 52 52 1 26  ε_{1} 13.3466
2165  −15 −1299 42185025 2 2 8 16 1  8  ε_{1} 13.3466
97  −67 −6499 42237001 1 1 14  7 1  7  ε_{1} 18.6488
33 −591 −2167 42263001 1 22 18 198 1 198  ε_{1} 7.6563
6501  −3 −2167 42263001 2 1 18 18 1  9  ε_{1} 28.8653
6501  −11 −591 42263001 2 1 22 22 1 11  ε_{1} 28.8653
929  −7 −6503 42289009 1 1 82 41 1 41  ε_{1} 51.6295
24 −271 −6504 42302016 1 11 20 110 1 110  ε_{1} 4.5849
813  −8 −6504 42302016 1 1 20 10 1 10  ε_{1} 16.7485
813  −24 −2168 42302016 1 2 24 24 1 24  ε_{1} 16.7485
2168  −3 −6504 42302016 1 1 20 10 1 10  ε_{1} 31.9314
6504  −3 −2168 42302016 2 1 24 24 1 12  ε_{1} 67.8202
6504  −24 −271 42302016 2 2 11 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 33.9101
6508  −4 −1627 42354064 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 10.2848
6509  −23 −283 42367081 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 26.5647
17 −383 −6511 42393121 1 17 44 374 1 374  ε_{1} 4.1894
44 −296 −3256 42406144 1 10 12 60 1 60  ε_{1} 5.9864
88 −148 −3256 42406144 1 2 12 12 1 12  ε_{1} 11.9527
1628  −8 −3256 42406144 2 1 12 12 1  6  ε_{1} 17.1607
1628  −88 −296 42406144 2 2 10 20 1 10  ε_{1} 17.1607
3256  −4 −3256 42406144 2 1 12 12 1  6  ε_{1} 59.5218
3256  −88 −148 42406144 2 2 2  4 1  2  ε_{1} 59.5218
501  −39 −2171 42419169 1 4 14 28 1 28  ε_{1} 20.4959
6513  −3 −2171 42419169 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 33.6105
6513  −39 −167 42419169 2 4 11 44 1 22  ε_{1} 67.2210

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 161

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −1303 −6515 42445225 1 11 26 143 1 143  ε_{1} 0.9624
41 −159 −6519 42497361 1 10 68 340 1 340  ε_{1} 8.3183
53 −123 −6519 42497361 1 2 68 68 1 68  ε_{1} 3.9314
2173 −3 −6519 42497361 2 1 68 68 1 34 ε_{1} 14.2001
2173 −123 −159 42497361 2 2 10 20 1 10  ε_{1} 14.2001
5 −1304 −6520 42510400 1 22 28 308 1 308  ε_{1} 0.9624
8 −815 −6520 42510400 1 30 28 420 1 420  ε_{1} 1.7627
40 −163 −6520 42510400 2 1 28 28 1 14  ε_{1} 3.6369
40 −815 −1304 42510400 2 30 22 660 1 330  ε_{1} 3.6369
1304  −40 −815 42510400 3 2 30 90 1 30  ε_{1} 12.9539
6520  −8 −815 42510400 2 1 30 30 1 15  ε_{1} 48.2594
6520  −40 −163 42510400 2 2 1  2 1  1  ε_{1} 48.2594
593  −11 −6523 42549529 1 1 14  7 1  7  ε_{1} 27.9978
28 −932 −1631 42562576 1 12 44 264 1 264  ε_{1} 5.5373
6524  −4 −1631 42562576 4 1 44 88 1 22  ε_{1} 22.5481
6524  −7 −932 42562576 4 1 12 24 1  6  ε_{1} 22.5481
61 −107 −6527 42601729 1 3 80 120 1 120  ε_{1} 7.3284
21 −311 −6531 42653961 1 19 24 228 1 228  ε_{1} 3.1336
933  −7 −6531 42653961 1 1 24 12 1 12  ε_{1} 23.8438
2177  −3 −6531 42653961 3 1 24 36 1 12  ε_{1} 18.6470
92  −71 −6532 42667024 1 7 16 56 1 56  ε_{1} 7.7415
284  −23 −6532 42667024 1 3 16 24 1 24  ε_{1} 17.6959
1633  −4 −6532 42667024 1 1 16  8 1  8  ε_{1} 109.6930
6533  −47 −139 42680089 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 16.2673
5 −1307 −6535 42706225 1 11 30 165 1 165  ε_{1} 0.9624
152  −43 −6536 42719296 1 1 64 32 1 32  ε_{1} 8.6078
344  −19 −6536 42719296 1 1 64 32 1 32  ε_{1} 19.8864
817  −8 −6536 42719296 5 1 64 160 1 32  ε_{1} 13.0618
817 −152 −344 42719296 5 6 10 150 1 30  ε_{1} 13.0618
6536  −19 −344 42719296 2 1 10 10 1  5  ε_{1} 35.4326
6536  −43 −152 42719296 2 1 6  6 1  3  ε_{1} 35.4326
6537  −3 −2179 42732369 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 65.3256
13 −503 −6539 42758521 1 21 28 294 1 294  ε_{1} 2.3895
12 −1635 −2180 42771600 1 8 32 128 1 128  ε_{1} 2.6339
60 −327 −2180 42771600 2 12 32 384 1 192  ε_{1} 4.1269
60 −436 −1635 42771600 2 6 8 48 1 24  ε_{1} 4.1269
1308  −15 −2180 42771600 2 2 32 64 1 32  ε_{1} 12.1461
1308  −20 −1635 42771600 2 2 8 16 1  8  ε_{1} 12.1461
6540  −3 −2180 42771600 4 1 32 64 1 16  ε_{1} 24.6972
6540  −4 −1635 42771600 4 1 8 16 1  4  ε_{1} 24.6972
6540  −15 −436 42771600 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 12.3486
6540  −20 −327 42771600 4 2 12 48 1 12  ε_{1} 24.6972
6541  −31 −211 42784681 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 43.9719
8 −1636 −3272 42823936 1 16 28 224 1 224  ε_{1} 1.7627
3272  −4 −3272 42823936 4 1 28 56 1 14  ε_{1} 11.3120
3272  −8 −1636 42823936 4 1 16 32 1  8  ε_{1} 11.3120
77 −595 −935 42837025 1 4 28 56 1 56  ε_{1} 4.3693
385 −119 −935 42837025 2 10 28 280 1 140  ε_{1} 24.3270
385 −187 −595 42837025 2 2 4  8 1  4  ε_{1} 24.3270
1309  −35 −935 42837025 2 2 28 56 1 28  ε_{1} 23.3418

162 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1309  −55 −595 42837025 2 4 4 16 1  8  ε_{1} 23.3418
6545  −7 −935 42837025 4 1 28 56 1 14  ε_{1} 32.9208
6545  −11 −595 42837025 4 1 4  8 1  2  ε_{1} 32.9208
6545  −35 −187 42837025 4 2 2  8 1  2  ε_{1} 32.9208
6545  −55 −119 42837025 4 4 10 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 16.4604
1637 −4 −6548 42876304 1 1 38 19 1 19 ε_{1} 17.2406
177 −111 −2183 42889401 1 8 42 168 1 168  ε_{1} 23.4697
6549  −3 −2183 42889401 6 1 42 252 2 42 \sqrt{−1}\sqrt{ε_{1}} 7.6894
6549 −59 −111 42889401 6 3 8 72 1 12 ε_{1} 15.3787
5 −1311 −6555 42968025 1 28 24 336 1 336  ε_{1} 0.9624
57 −115 −6555 42968025 1 2 24 24 1 24  ε_{1} 11.4208
69  −95 −6555 42968025 1 8 24 96 1 96  ε_{1} 6.4345
285  −23 −6555 42968025 2 3 24 72 1 36  ε_{1} 5.6595
285 −115 −1311 42968025 2 2 28 56 1 28  ε_{1} 5.6595
345  −19 −6555 42968025 2 1 24 24 1 12  ε_{1} 19.0241
345  −95 −1311 42968025 2 8 28 224 1 112  ε_{1} 19.0241
437  −15 −6555 42968025 1 2 24 24 1 24  ε_{1} 6.0845
2185  −3 −6555 42968025 2 1 24 24 1 12  ε_{1} 72.2976
2185  −15 −1311 42968025 2 2 28 56 1 28  ε_{1} 72.2976
44 −596 −1639 42981136 1 14 22 154 1 154  ε_{1} 5.9864
6556  −4 −1639 42981136 6 1 22 66 1 11  ε_{1} 29.6930
6556  −11 −596 42981136 6 1 14 42 1  7  ε_{1} 29.6930
6557  −79  −83 42994249 3 5 3 45 2 15 \sqrt{−1}\sqrt{ε_{1}} 4.3943
937  −7 −6559 43020481 1 1 38 19 1 19  ε_{1} 69.0381
12 −547 −6564 43086096 1 3 44 66 1 66  ε_{1} 2.6339
1641  −4 −6564 43086096 5 1 44 110 1 22  ε_{1} 18.1536
2188  −3 −6564 43086096 1 1 44 22 1 22  ε_{1} 66.8009
33 −199 −6567 43125489 1 9 32 144 1 144  ε_{1} 7.6563
597  −11 −6567 43125489 1 1 32 16 1 16  ε_{1} 18.3698
2189  −3 −6567 43125489 1 1 32 16 1 16  ε_{1} 27.8566
821  −8 −6568 43138624 1 1 14  7 1  7  ε_{1} 19.3842
124 −212 −1643 43191184 1 6 10 30 1 30  ε_{1} 16.0392
6572  −4 −1643 43191184 2 1 10 10 1  5  ε_{1} 19.5869
6572  −31 −212 43191184 2 3 6 18 1  9  ε_{1} 19.5869
21 −939 −2191 43204329 1 8 30 120 1 120  ε_{1} 3.1336
6573  −3 −2191 43204329 2 1 30 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 7.6912
6573 −7 −939 43204329 2 1 8 8 1 4 ε_{1} 15.3824
12 −1096 −3288 43243776 1 12 20 120 1 120  ε_{1} 2.6339
24 −548 −3288 43243776 1 8 20 80 1 80  ε_{1} 4.5849
1644  −8 −3288 43243776 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 11.5075
1644  −24 −1096 43243776 2 2 12 24 1 12  ε_{1} 23.0150
3288  −4 −3288 43243776 2 1 20 40 2 20  \sqrt{i}\sqrt{ε_{1}} 9.6020
3288  −24 −548 43243776 2 2 8 16 1  8  ε_{1} 19.2040
5 −1316 −6580 43296400 1 24 16 192 1 192  ε_{1} 0.9624
28 −235 −6580 43296400 1 2 16 16 1 16  ε_{1} 5.5373
140 −47 −6580 43296400 2 5 16 80 1 40 ε_{1} 4.9558
140 −235 −1316 43296400 2 2 24 48 1 24  ε_{1} 4.9558
188  −35 −6580 43296400 1 2 16 16 1 16  ε_{1} 9.1285
329  −20 −6580 43296400 1 2 16 16 1 16  ε_{1} 30.7485
940  −7 −6580 43296400 6 1 16 48 1  8  ε_{1} 9.0433

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 163

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
940  −35 −1316 43296400 6 2 24 144 1 24  ε_{1} 9.0433
1645  −4 −6580 43296400 2 1 16 16 1  8  ε_{1} 20.3809
1645  −20 −1316 43296400 2 2 24 96 2 48 \sqrt{−1}\sqrt{ε_{1}} 10.1904
29 −227 −6583 43335889 1 5 36 90 1 90  ε_{1} 3.2945
8 −823 −6584 43349056 1 9 44 198 1 198  ε_{1} 1.7627
6584  −8 −823 43349056 3 1 9 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 11.9911
1317  −15 −2195 43362225 1 2 16 16 1 16  ε_{1} 25.9049
6585  −3 −2195 43362225 2 1 16 16 1  8  ε_{1} 62.4611
6585  −15 −439 43362225 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 31.2305
941 −7 −6587 43388569 1 1 26 13 1 13 ε_{1} 14.0688
6589  −11 −599 43414921 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 52.0209
6593 −19 −347 43467649 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 41.1997
5 −1319 −6595 43494025 1 45 16 360 1 360  ε_{1} 0.9624
17 −388 −6596 43507216 1 4 48 96 1 96  ε_{1} 4.1894
97  −68 −6596 43507216 1 4 48 96 1 96  ε_{1} 18.6488
1649  −4 −6596 43507216 2 1 48 48 1 24  ε_{1} 38.3972
1649  −68 −388 43507216 2 4 4 16 1  8  ε_{1} 38.3972
161 −287 −943 43573201 1 14 16 112 1 112  ε_{1} 20.1338
6601 −7 −943 43573201 6 1 16 48 1 8 ε_{1} 48.5857
6601  −23 −287 43573201 6 3 14 252 2 42 \sqrt{−1}\sqrt{ε_{1}} 24.2928
93  −71 −6603 43599609 1 7 12 42 1 42  ε_{1} 6.7322
213  −31 −6603 43599609 1 3 12 18 1 18  ε_{1} 8.5805
2201  −3 −6603 43599609 1 1 12  6 1  6  ε_{1} 90.5566
508  −52 −1651 43612816 1 2 8  8 1  8  ε_{1} 32.1254
6604  −4 −1651 43612816 2 1 8  8 1  4  ε_{1} 78.5203
6604  −52 −127 43612816 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 39.2602
8 −1652 −3304 43665664 1 20 12 120 1 120  ε_{1} 1.7627
28 −472 −3304 43665664 1 6 12 36 1 36  ε_{1} 5.5373
56 −472 −1652 43665664 1 6 20 60 1 60  ε_{1} 6.8002
236  −56 −3304 43665664 1 4 12 24 1 24  ε_{1} 13.9320
472  −56 −1652 43665664 1 4 20 40 1 40  ε_{1} 26.6550
3304  −4 −3304 43665664 2 1 12 12 1  6  ε_{1} 53.6403
3304  −8 −1652 43665664 2 1 20 20 1 10  ε_{1} 53.6403
6609  −3 −2203 43678881 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 119.1997
601  −11 −6611 43705321 1 1 42 21 1 21  ε_{1} 66.5240
12 −551 −6612 43718544 1 26 16 208 1 208  ε_{1} 2.6339
29 −228 −6612 43718544 1 4 16 32 1 32  ε_{1} 3.2945
57 −116 −6612 43718544 1 6 16 48 1 48  ε_{1} 11.4208
76  −87 −6612 43718544 1 6 16 48 1 48  ε_{1} 11.6579
348  −19 −6612 43718544 2 1 16 16 1  8  ε_{1} 8.0501
348 −228 −551 43718544 2 4 26 104 1 52  ε_{1} 8.0501
1653 −4 −6612 43718544 2 1 16 16 1 8 ε_{1} 14.5210
1653 −116 −228 43718544 2 6 4 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 7.2605
2204  −3 −6612 43718544 2 1 16 16 1  8  ε_{1} 19.4535
2204  −87 −228 43718544 2 6 4 24 1 12  ε_{1} 19.4535
8 −827 −6616 43771456 1 7 22 77 1 77  ε_{1} 1.7627
6616  −8 −827 43771456 9 1 7 63 2  7 \sqrt{−1}\sqrt{ε_{1}} 10.3013
1324  −20 −1655 43824400 1 2 44 44 1 44  ε_{1} 72.5128
6620  −4 −1655 43824400 2 1 44 44 1 22  ε_{1} 26.7410
6620  −20 −331 43824400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 13.3705

164 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
6621  −3 −2207 43837641 1 1 39 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 33.2608
37 −179 −6623 43864129 1 5 42 105 1 105  ε_{1} 4.9836
1657  −4 −6628 43930384 1 1 16  8 1  8  ε_{1} 89.0247
6629  −7 −947 43943641 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 25.8449
349  −19 −6631 43970161 1 1 44 22 1 22  ε_{1} 19.6424
829  −8 −6632 43983424 1 1 42 21 1 21  ε_{1} 34.4976
5 −1327 −6635 44023225 1 15 30 225 1 225  ε_{1} 0.9624
12 −1659 −2212 44036496 1 8 8 32 1 32  ε_{1} 2.6339
21 −948 −2212 44036496 1 12 8 48 1 48  ε_{1} 3.1336
28 −948 −1659 44036496 1 12 8 48 1 48  ε_{1} 5.5373
237  −84 −2212 44036496 1 4 8 16 1 16  ε_{1} 8.6873
316  −84 −1659 44036496 3 4 8 48 1 16  ε_{1} 10.1503
553  −84 −948 44036496 1 4 12 24 1 24  ε_{1} 55.7072
6636  −3 −2212 44036496 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 14.2178
6636  −4 −1659 44036496 4 1 8 16 1  4  ε_{1} 28.4357
6636  −7 −948 44036496 4 1 12 24 1  6  ε_{1} 28.4357
6636  −79  −84 44036496 4 5 4 40 1 10  ε_{1} 28.4357
2213  −3 −6639 44076321 3 1 90 135 1 45  ε_{1} 7.7012
332  −40 −3320 44089600 1 2 20 20 1 20  ε_{1} 10.1997
664  −20 −3320 44089600 1 2 20 20 1 20  ε_{1} 43.8951
1660  −8 −3320 44089600 2 1 20 20 1 10  ε_{1} 34.8434
1660  −40 −664 44089600 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 17.4217
3320 −4 −3320 44089600 2 1 20 20 1 10 ε_{1} 25.1746
3320  −20 −664 44089600 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 12.5873
13 −511 −6643 44129449 1 14 12 84 1 84  ε_{1} 2.3895
73  −91 −6643 44129449 1 2 12 12 1 12  ε_{1} 15.3334
949  −7 −6643 44129449 2 1 12 12 1  6  ε_{1} 20.7893
949  −91 −511 44129449 2 2 14 28 1 14  ε_{1} 20.7893
44 −151 −6644 44142736 1 7 48 168 1 168  ε_{1} 5.9864
604  −11 −6644 44142736 1 1 48 24 1 24  ε_{1} 43.9269
1661  −4 −6644 44142736 1 1 48 24 1 24  ε_{1} 29.7725
1329  −15 −2215 44156025 1 2 22 22 1 22  ε_{1} 83.5792
6645  −3 −2215 44156025 2 1 22 22 1 11  ε_{1} 32.3389
6645  −15 −443 44156025 2 2 5 10 1  5  ε_{1} 32.3389
8 −831 −6648 44195904 1 28 20 280 1 280  ε_{1} 1.7627
24 −831 −2216 44195904 1 28 22 308 1 308  ε_{1} 4.5849
277  −24 −6648 44195904 1 2 20 20 1 20  ε_{1} 15.7365
2216  −3 −6648 44195904 2 1 20 20 1 10  ε_{1} 25.5233
2216  −24 −831 44195904 2 2 28 56 1 28  ε_{1} 25.5233
6648  −3 −2216 44195904 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 18.6731
6648  −8 −831 44195904 2 1 28 28 1 14  ε_{1} 37.3461
6652  −4 −1663 44249104 1 1 17 17 2 17  \sqrt{i}\sqrt{ε_{1}} 54.1981
21 −951 −2219 44315649 1 26 24 312 1 312  ε_{1} 3.1336
6657 −3 −2219 44315649 2 1 24 24 1 12 ε_{1} 68.4888
6657  −7 −951 44315649 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 34.2444
2221 −3 −6663 44395569 1 1 60 30 1 30 ε_{1} 60.0993
1333 −155 −215 44422225 1 4 14 28 1 28  ε_{1} 22.7491
6665  −31 −215 44422225 2 3 14 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 37.5310
6665  −43 −155 44422225 2 1 4  4 1  2  ε_{1} 75.0619
113  −59 −6667 44448889 1 3 10 15 1 15  ε_{1} 14.6946

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 165

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
6668  −4 −1667 44462224 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 27.0227
953  −7 −6671 44502241 1 1 88 44 1 44  ε_{1} 44.8537
8 −1668 −3336 44515584 1 12 16 96 1 96  ε_{1} 1.7627
12 −1112 −3336 44515584 1 14 16 112 1 112  ε_{1} 2.6339
24 −1112 −1668 44515584 1 14 12 84 1 84  ε_{1} 4.5849
556  −24 −3336 44515584 1 2 16 16 1 16  ε_{1} 37.7195
1112  −24 −1668 44515584 1 2 12 12 1 12  ε_{1} 17.0352
3336  −4 −3336 44515584 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 23.2963
3336  −8 −1668 44515584 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 23.2963
1669 −4 −6676 44568976 1 1 26 13 1 13 ε_{1} 41.9610
6677  −11 −607 44582329 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 11.6867
5 −1336 −6680 44622400 1 12 28 168 1 168  ε_{1} 0.9624
8 −835 −6680 44622400 1 6 28 84 1 84  ε_{1} 1.7627
40 −167 −6680 44622400 2 11 28 308 1 154  ε_{1} 3.6369
40 −835 −1336 44622400 2 6 12 72 1 36  ε_{1} 3.6369
1336  −40 −835 44622400 1 2 6  6 1  6  ε_{1} 64.9600
6680  −8 −835 44622400 2 1 6  6 1  3  ε_{1} 38.2286
6680  −40 −167 44622400 2 2 11 22 1 11  ε_{1} 38.2286
393  −51 −2227 44635761 1 2 6  6 1  6  ε_{1} 36.6935
6681  −3 −2227 44635761 6 1 6 18 1  3  ε_{1} 33.1007
6681  −51 −131 44635761 6 2 5 30 1  5  ε_{1} 33.1007
41 −163 −6683 44662489 1 1 32 16 1 16  ε_{1} 8.3183
12 −1671 −2228 44675856 1 38 18 342 1 342  ε_{1} 2.6339
6684  −3 −2228 44675856 2 1 18 18 1  9  ε_{1} 33.5322
6684  −4 −1671 44675856 2 1 38 38 1 19  ε_{1} 33.5322
1337  −35 −955 44689225 1 2 4  4 1  4  ε_{1} 43.4587
6685  −7 −955 44689225 6 1 4 12 1  2  ε_{1} 14.8967
6685  −35 −191 44689225 6 2 13 156 2 26 \sqrt{−1}\sqrt{ε_{1}} 7.4483
28 −239 −6692 44782864 1 15 32 240 1 240  ε_{1} 5.5373
956  −7 −6692 44782864 1 1 32 16 1 16  ε_{1} 32.6648
1673  −4 −6692 44782864 1 1 32 16 1 16  ε_{1} 58.9611
69 −291 −2231 44796249 1 4 58 116 1 116  ε_{1} 6.4345
6693  −3 −2231 44796249 2 1 58 116 2 58 \sqrt{−1}\sqrt{ε_{1}} 14.9320
6693 −23 −291 44796249 2 3 4 12 1 6 ε_{1} 29.8641
5 −1339 −6695 44823025 1 8 92 368 1 368  ε_{1} 0.9624
13 −515 −6695 44823025 1 6 92 276 1 276  ε_{1} 2.3895
65 −103 −6695 44823025 2 5 92 460 1 230  ε_{1} 5.5529
65 −515 −1339 44823025 2 6 8 48 1 24  ε_{1} 5.5529
21 −319 −6699 44876601 1 10 24 120 1 120  ε_{1} 3.1336
29 −231 −6699 44876601 1 12 24 144 1 144  ε_{1} 3.2945
33 −203 −6699 44876601 1 4 24 48 1 48  ε_{1} 7.6563
77  −87 −6699 44876601 1 6 24 72 1 72  ε_{1} 4.3693
609  −11 −6699 44876601 2 1 24 24 1 12  ε_{1} 28.0146
609 −231 −319 44876601 2 12 10 120 1 60  ε_{1} 28.0146
957 −7 −6699 44876601 2 1 24 24 1 12 ε_{1} 6.8659
957 −203 −231 44876601 2 4 12 48 1 24  ε_{1} 6.8659
2233  −3 −6699 44876601 6 1 24 72 1 12  ε_{1} 19.8480
2233  −87 −231 44876601 6 6 12 216 1 36  ε_{1} 19.8480
1676  −8 −3352 44943616 1 1 14 14 2 14 \sqrt{−1}\sqrt{ε_{1}} 20.1077
3352  −4 −3352 44943616 1 1 14 14 2 14  \sqrt{i}\sqrt{ε_{1}} 25.1568

166 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
353  −19 −6707 44983849 1 1 28 14 1 14  ε_{1} 23.7346
12 −559 −6708 44997264 1 16 16 128 1 128  ε_{1} 2.6339
13 −516 −6708 44997264 1 12 16 96 1 96  ε_{1} 2.3895
129  −52 −6708 44997264 1 2 16 16 1 16  ε_{1} 20.8511
156  −43 −6708 44997264 2 1 16 16 1  8  ε_{1} 7.8232
156 −516 −559 44997264 2 12 16 192 1 96  ε_{1} 7.8232
172  −39 −6708 44997264 1 4 16 32 1 32  ε_{1} 17.6970
1677  −4 −6708 44997264 4 1 16 32 1  8  ε_{1} 7.4260
1677  −52 −516 44997264 4 2 12 48 1 12  ε_{1} 7.4260
2236  −3 −6708 44997264 2 1 16 16 1  8  ε_{1} 41.4726
2236  −39 −516 44997264 2 4 12 48 1 24  ε_{1} 41.4726
2237  −3 −6711 45037521 1 1 74 37 1 37  ε_{1} 28.0891
8 −839 −6712 45050944 1 33 20 330 1 330  ε_{1} 1.7627
6712  −8 −839 45050944 1 1 33 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 44.4198
5 −1343 −6715 45091225 1 34 12 204 1 204  ε_{1} 0.9624
17 −395 −6715 45091225 1 8 12 48 1 48  ε_{1} 4.1894
85 −79 −6715 45091225 2 5 12 60 1 30 ε_{1} 4.4187
85 −395 −1343 45091225 2 8 34 272 1 136  ε_{1} 4.4187
92 −292 −1679 45104656 1 4 52 104 1 104  ε_{1} 7.7415
6716  −4 −1679 45104656 4 1 52 208 2 52  \sqrt{i}\sqrt{ε_{1}} 8.1197
6716  −23 −292 45104656 4 3 4 24 1  6  ε_{1} 16.2394
6717  −3 −2239 45118089 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 26.2173
517 −143 −611 45171841 1 10 10 50 1 50  ε_{1} 18.5321
6721  −11 −611 45171841 2 1 10 10 1  5  ε_{1} 150.8004
6721  −47 −143 45171841 2 5 10 50 1 25  ε_{1} 150.8004
6729  −3 −2243 45279441 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 102.7203
53 −127 −6731 45306361 1 5 34 85 1 85  ε_{1} 3.9314
5 −1347 −6735 45360225 1 6 44 132 1 132  ε_{1} 0.9624
449  −15 −6735 45360225 1 2 44 44 1 44  ε_{1} 39.5058
2245  −3 −6735 45360225 2 1 44 44 1 22  ε_{1} 24.3921
2245  −15 −1347 45360225 2 2 6 12 1  6  ε_{1} 24.3921
8 −1684 −3368 45373696 1 10 26 130 1 130  ε_{1} 1.7627
3368  −4 −3368 45373696 6 1 26 78 1 13  ε_{1} 8.1215
3368  −8 −1684 45373696 6 1 10 30 1  5  ε_{1} 8.1215
293  −23 −6739 45414121 1 3 18 27 1 27  ε_{1} 5.6733
5 −1348 −6740 45427600 1 8 52 208 1 208  ε_{1} 0.9624
337  −20 −6740 45427600 1 2 52 52 1 52  ε_{1} 42.8642
1685  −4 −6740 45427600 2 1 52 52 1 26  ε_{1} 7.4283
1685  −20 −1348 45427600 2 2 8 16 1  8  ε_{1} 7.4283
613  −11 −6743 45468049 1 1 54 27 1 27  ε_{1} 23.0010
8 −843 −6744 45481536 1 6 44 132 1 132  ε_{1} 1.7627
24 −843 −2248 45481536 1 6 8 24 1 24  ε_{1} 4.5849
281  −24 −6744 45481536 1 2 44 44 1 44  ε_{1} 29.1405
2248  −3 −6744 45481536 2 1 44 44 1 22  ε_{1} 39.8131
2248  −24 −843 45481536 2 2 6 12 1  6  ε_{1} 39.8131
6744  −3 −2248 45481536 2 1 8  8 1  4  ε_{1} 49.9635
6744  −8 −843 45481536 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 24.9817
1349  −95 −355 45495025 1 8 4 16 1 16  ε_{1} 19.3578
6745  −19 −355 45495025 4 1 4  8 1  2  ε_{1} 64.6703
6745  −71  −95 45495025 4 7 8 224 2 56 \sqrt{−1}\sqrt{ε_{1}} 32.3351

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 167

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
13 −519 −6747 45522009 1 18 16 144 1 144  ε_{1} 2.3895
173  −39 −6747 45522009 1 4 16 32 1 32  ε_{1} 5.1416
2249  −3 −6747 45522009 4 1 16 32 1  8  ε_{1} 25.7696
2249  −39 −519 45522009 4 4 18 144 1 36  ε_{1} 25.7696
28 −964 −1687 45535504 1 12 18 108 1 108  ε_{1} 5.5373
6748  −4 −1687 45535504 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 31.8696
6748  −7 −964 45535504 2 1 12 12 1  6  ε_{1} 63.7392
157  −43 −6751 45576001 1 1 66 33 1 33  ε_{1} 10.7226
6753  −3 −2251 45603009 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 50.2319
5 −1351 −6755 45630025 1 24 20 240 1 240  ε_{1} 0.9624
193  −35 −6755 45630025 1 2 20 20 1 20  ε_{1} 30.1526
965  −7 −6755 45630025 2 1 20 20 1 10  ε_{1} 6.8701
965  −35 −1351 45630025 2 2 24 48 1 24  ε_{1} 6.8701
12 −563 −6756 45643536 1 9 36 162 1 162  ε_{1} 2.6339
1689  −4 −6756 45643536 1 1 36 18 1 18  ε_{1} 105.0367
2252  −3 −6756 45643536 1 1 36 18 1 18  ε_{1} 23.6444
76 −356 −1691 45751696 1 12 18 108 1 108  ε_{1} 11.6579
6764  −4 −1691 45751696 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 24.9280
6764  −19 −356 45751696 2 1 12 12 1  6  ε_{1} 49.8560
33 −615 −2255 45765225 1 20 40 400 1 400  ε_{1} 7.6563
165 −123 −2255 45765225 2 2 40 80 1 40  ε_{1} 5.1180
165 −451 −615 45765225 2 6 20 120 1 60  ε_{1} 5.1180
1353  −15 −2255 45765225 2 2 40 80 1 40  ε_{1} 36.5389
1353  −55 −615 45765225 2 4 20 80 1 40  ε_{1} 36.5389
6765  −3 −2255 45765225 4 1 40 80 1 20  ε_{1} 12.9784
6765  −11 −615 45765225 4 1 20 40 1 10  ε_{1} 12.9784
6765  −15 −451 45765225 4 2 6 24 1  6  ε_{1} 12.9784
6765  −55 −123 45765225 4 4 2 16 1  4  ε_{1} 12.9784
101  −67 −6767 45792289 1 1 86 43 1 43  ε_{1} 5.9964
6769  −7 −967 45819361 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 151.2225
37 −183 −6771 45846441 1 8 16 64 1 64  ε_{1} 4.9836
61 −111 −6771 45846441 1 8 16 64 1 64  ε_{1} 7.3284
2257 −3 −6771 45846441 2 1 16 16 1 8 ε_{1} 50.6448
2257 −111 −183 45846441 2 8 8 64 1 32  ε_{1} 50.6448
1693 −4 −6772 45859984 1 1 22 11 1 11 ε_{1} 28.2648
12 −1695 −2260 45968400 1 20 12 120 1 120  ε_{1} 2.6339
60 −339 −2260 45968400 2 6 12 72 1 36  ε_{1} 4.1269
60 −452 −1695 45968400 2 8 20 160 1 80  ε_{1} 4.1269
1356  −15 −2260 45968400 2 2 12 24 1 12  ε_{1} 24.3711
1356  −20 −1695 45968400 2 2 20 40 1 20  ε_{1} 24.3711
6780  −3 −2260 45968400 4 1 12 24 1  6  ε_{1} 26.2417
6780  −4 −1695 45968400 4 1 20 40 1 10  ε_{1} 26.2417
6780  −15 −452 45968400 4 2 8 32 1  8  ε_{1} 26.2417
6780  −20 −339 45968400 4 2 6 24 1  6  ε_{1} 26.2417
17 −399 −6783 46009089 1 16 56 448 1 448  ε_{1} 4.1894
21 −323 −6783 46009089 1 4 56 112 1 112  ε_{1} 3.1336
57 −119 −6783 46009089 1 10 56 280 1 280  ε_{1} 11.4208
133  −51 −6783 46009089 1 2 56 56 1 56  ε_{1} 10.3065
357  −19 −6783 46009089 2 1 56 56 1 28  ε_{1} 5.8833
357 −323 −399 46009089 2 4 16 64 1 32  ε_{1} 5.8833

168 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
969  −7 −6783 46009089 2 1 56 56 1 28  ε_{1} 34.2358
969 −119 −399 46009089 2 10 16 160 1 80  ε_{1} 34.2358
2261  −3 −6783 46009089 2 1 56 56 1 28  ε_{1} 15.1013
2261  −51 −399 46009089 2 2 16 32 1 16  ε_{1} 15.1013
1357 −115 −295 46036225 1 2 8  8 1  8  ε_{1} 27.4038
6785  −23 −295 46036225 2 3 8 24 1 12  ε_{1} 83.5715
6785  −59 −115 46036225 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 41.7857
617  −11 −6787 46063369 1 1 12  6 1  6  ε_{1} 36.4449
1697  −4 −6788 46076944 1 1 28 14 1 14  ε_{1} 47.7607
93 −219 −2263 46090521 1 4 22 44 1 44  ε_{1} 6.7322
6789  −3 −2263 46090521 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 15.2468
6789 −31 −219 46090521 2 3 4 12 1 6 ε_{1} 30.4937
24 −283 −6792 46131264 1 3 16 24 1 24  ε_{1} 4.5849
849  −8 −6792 46131264 1 1 16  8 1  8  ε_{1} 71.2770
849  −24 −2264 46131264 1 2 30 30 1 30  ε_{1} 71.2770
2264  −3 −6792 46131264 1 1 16  8 1  8  ε_{1} 38.1379
6792  −3 −2264 46131264 2 1 30 30 1 15  ε_{1} 46.0307
6792  −24 −283 46131264 2 2 3  6 1  3  ε_{1} 46.0307
6796  −4 −1699 46185616 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 77.6876
6797  −7 −971 46199209 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 12.6591
13 −523 −6799 46226401 1 5 44 110 1 110  ε_{1} 2.3895
6801  −3 −2267 46253601 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 117.3092
2269 −3 −6807 46335249 1 1 40 20 1 20 ε_{1} 66.2649
8 −851 −6808 46348864 1 10 20 100 1 100  ε_{1} 1.7627
37 −184 −6808 46348864 1 4 20 40 1 40  ε_{1} 4.9836
184 −296 −851 46348864 1 10 10 50 1 50  ε_{1} 21.5856
296 −23 −6808 46348864 2 3 20 60 1 30 ε_{1} 8.9090
296 −184 −851 46348864 2 4 10 40 1 20  ε_{1} 8.9090
6808  −8 −851 46348864 2 1 10 10 1  5  ε_{1} 67.5338
6808  −23 −296 46348864 2 3 10 30 1 15  ε_{1} 67.5338
6809  −11 −619 46362481 9 1 5 45 2  5 \sqrt{−1}\sqrt{ε_{1}} 9.2005
524  −52 −1703 46403344 1 2 28 28 1 28  ε_{1} 19.9254
6812  −4 −1703 46403344 2 1 28 28 1 14  ε_{1} 30.3404
6812  −52 −131 46403344 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 15.1702
5 −1363 −6815 46444225 1 6 92 276 1 276  ε_{1} 0.9624
29 −235 −6815 46444225 1 2 92 92 1 92  ε_{1} 3.2945
145  −47 −6815 46444225 4 5 92 920 1 230  ε_{1} 6.3596
145 −235 −1363 46444225 4 2 6 24 1  6  ε_{1} 6.3596
2273  −3 −6819 46498761 1 1 22 11 1 11  ε_{1} 41.8730
5 −1364 −6820 46512400 1 28 16 224 1 224  ε_{1} 0.9624
44 −155 −6820 46512400 1 4 16 32 1 32  ε_{1} 5.9864
124  −55 −6820 46512400 1 4 16 32 1 32  ε_{1} 16.0392
220  −31 −6820 46512400 2 3 16 48 1 24  ε_{1} 10.3635
220 −155 −1364 46512400 2 4 28 112 1 56  ε_{1} 10.3635
341  −20 −6820 46512400 1 2 16 16 1 16  ε_{1} 11.2480
620  −11 −6820 46512400 2 1 16 16 1  8  ε_{1} 12.4212
620  −55 −1364 46512400 2 4 28 112 1 56  ε_{1} 12.4212
1705  −4 −6820 46512400 8 1 16 64 1  8  ε_{1} 15.1837
1705  −20 −1364 46512400 8 2 28 224 1 28  ε_{1} 15.1837
6821  −19 −359 46526041 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 30.9719

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 169

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
853  −8 −6824 46566976 1 1 58 29 1 29  ε_{1} 20.4426
12 −1707 −2276 46621584 1 10 32 160 1 160  ε_{1} 2.6339
6828  −3 −2276 46621584 2 1 32 32 1 16  ε_{1} 28.0490
6828  −4 −1707 46621584 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 14.0245
28 −488 −3416 46676224 1 10 44 220 1 220  ε_{1} 5.5373
56 −244 −3416 46676224 1 6 44 132 1 132  ε_{1} 6.8002
1708 −8 −3416 46676224 6 1 44 132 1 22 ε_{1} 9.6404
1708  −56 −488 46676224 6 4 10 240 2 40 \sqrt{−1}\sqrt{ε_{1}} 4.8202
3416  −4 −3416 46676224 2 1 44 44 1 22  ε_{1} 29.5333
3416  −56 −244 46676224 2 4  6 48 2 24 \sqrt{−1}\sqrt{ε_{1}} 14.7666
5 −1367 −6835 46717225 1 25 18 225 1 225  ε_{1} 0.9624
1709 −4 −6836 46730896 1 1 42 21 1 21 ε_{1} 31.0005
129 −159 −2279 46744569 1 10 56 280 1 280  ε_{1} 20.8511
6837 −3 −2279 46744569 2 1 56 56 1 28 ε_{1} 20.3978
6837  −43 −159 46744569 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 10.1989
977  −7 −6839 46771921 1 1 108 54 1 54  ε_{1} 46.8295
2281  −3 −6843 46826649 1 1 12  6 1  6  ε_{1} 146.8485
236 −116 −1711 46840336 1 6 28 84 1 84  ε_{1} 13.9320
6844  −4 −1711 46840336 2 1 28 28 1 14  ε_{1} 61.6605
6844  −59 −116 46840336 2 3  6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 30.8303
41 −167 −6847 46881409 1 11 26 143 1 143  ε_{1} 8.3183
13 −527 −6851 46936201 1 18 36 324 1 324  ε_{1} 2.3895
17 −403 −6851 46936201 1 2 36 36 1 36  ε_{1} 4.1894
221 −31 −6851 46936201 2 3 36 108 1 54 ε_{1} 5.4072
221 −403 −527 46936201 2 2 18 36 1 18  ε_{1} 5.4072
12 −571 −6852 46949904 1 5 36 90 1 90  ε_{1} 2.6339
1713  −4 −6852 46949904 1 1 36 18 1 18  ε_{1} 63.9547
2284  −3 −6852 46949904 1 1 36 18 1 18  ε_{1} 94.6777
77 −623 −979 46963609 1 22  8 88 1 88  ε_{1} 4.3693
6853  −7 −979 46963609 2 1  8  8 1  4  ε_{1} 33.5282
6853  −11 −623 46963609 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 16.7641
5 −1371 −6855 46991025 1 12 60 360 1 360  ε_{1} 0.9624
457  −15 −6855 46991025 1 2 60 60 1 60  ε_{1} 50.9909
2285  −3 −6855 46991025 2 1 60 60 1 30  ε_{1} 10.9530
2285  −15 −1371 46991025 2 2 12 24 1 12  ε_{1} 10.9530
857  −8 −6856 47004736 1 1 20 10 1 10  ε_{1} 33.2056
6861  −3 −2287 47073321 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 36.8928
8 −1716 −3432 47114496 1 16 16 128 1 128  ε_{1} 1.7627
12 −1144 −3432 47114496 1 12 16 96 1 96  ε_{1} 2.6339
24 −1144 −1716 47114496 1 12 16 96 1 96  ε_{1} 4.5849
44 −312 −3432 47114496 1 4 16 32 1 32  ε_{1} 5.9864
88 −312 −1716 47114496 1 4 16 32 1 32  ε_{1} 11.9527
104 −132 −3432 47114496 2 4 16 64 1 32  ε_{1} 4.6249
104 −264 −1716 47114496 2 8 16 128 1 64  ε_{1} 4.6249
156 −88 −3432 47114496 2 2 16 32 1 16 ε_{1} 7.8232
156 −264 −1144 47114496 2 8 12 96 1 48  ε_{1} 7.8232
264 −52 −3432 47114496 2 2 16 32 1 16 ε_{1} 9.7350
264 −104 −1716 47114496 2 6 16 96 1 48  ε_{1} 9.7350
312 −88 −1716 47114496 2 2 16 32 1 16 ε_{1} 9.3267
312 −132 −1144 47114496 2 4 12 48 1 24  ε_{1} 9.3267

170 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
572  −24 −3432 47114496 2 2 16 32 1 16  ε_{1} 6.3526
572 −264 −312 47114496 2 8 4 32 1 16  ε_{1} 6.3526
1144  −24 −1716 47114496 2 2 16 32 1 16  ε_{1} 27.8642
1144 −132 −312 47114496 2 4 4 16 1  8  ε_{1} 27.8642
3432  −4 −3432 47114496 4 1 16 32 1  8  ε_{1} 14.4970
3432  −8 −1716 47114496 4 1 16 32 1  8  ε_{1} 14.4970
3432  −52 −264 47114496 4 2 8 32 1  8  ε_{1} 14.4970
3432 −104 −132 47114496 4 6 4 48 1 12  ε_{1} 14.4970
17 −404 −6868 47169424 1 14 16 112 1 112  ε_{1} 4.1894
101  −68 −6868 47169424 1 4 16 32 1 32  ε_{1} 5.9964
1717  −4 −6868 47169424 2 1 16 16 1  8  ε_{1} 23.0932
1717  −68 −404 47169424 2 4 14 112 2 56 \sqrt{−1}\sqrt{ε_{1}} 11.5466
8 −859 −6872 47224384 1 7 46 161 1 161  ε_{1} 1.7627
6872  −8 −859 47224384 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 19.4330
237  −87 −2291 47238129 1 6 18 54 1 54  ε_{1} 8.6873
6873  −3 −2291 47238129 2 1 18 18 1  9  ε_{1} 65.7001
6873  −79  −87 47238129 2 5 6 30 1 15  ε_{1} 65.7001
2293  −3 −6879 47320641 1 1 64 32 1 32  ε_{1} 49.0472
6881  −7 −983 47348161 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 79.0839
1721  −4 −6884 47389456 1 1 52 26 1 26  ε_{1} 72.7737
97  −71 −6887 47430769 1 7 78 273 1 273  ε_{1} 18.6488
21 −328 −6888 47444544 1 4 24 48 1 48  ε_{1} 3.1336
21 −984 −2296 47444544 1 12 16 96 1 96  ε_{1} 3.1336
24 −287 −6888 47444544 1 14 24 168 1 168  ε_{1} 4.5849
41 −168 −6888 47444544 1 4 24 48 1 48  ε_{1} 8.3183
56 −123 −6888 47444544 1 2 24 24 1 24  ε_{1} 6.8002
168 −123 −2296 47444544 2 2 16 32 1 16  ε_{1} 6.5132
168 −287 −984 47444544 2 14 12 168 1 84  ε_{1} 6.5132
861  −8 −6888 47444544 2 1 24 24 1 12  ε_{1} 13.8688
861  −24 −2296 47444544 2 2 16 32 1 16  ε_{1} 13.8688
861  −56 −984 47444544 2 4 12 48 1 24  ε_{1} 13.8688
861 −168 −328 47444544 2 4 4 16 1  8  ε_{1} 13.8688
984  −7 −6888 47444544 2 1 24 24 1 12  ε_{1} 24.1747
984 −168 −287 47444544 2 4 14 56 1 28  ε_{1} 24.1747
2296  −3 −6888 47444544 6 1 24 72 1 12  ε_{1} 14.0950
2296 −123 −168 47444544 6 2 4 24 1  4  ε_{1} 14.0950
6888  −3 −2296 47444544 4 1 16 32 1  8  ε_{1} 10.2239
6888  −7 −984 47444544 4 1 12 24 1  6  ε_{1} 10.2239
6888  −24 −287 47444544 4 2 14 56 1 14  ε_{1} 10.2239
6888  −56 −123 47444544 4 4 2 16 1  4  ε_{1} 10.2239
2297  −3 −6891 47485881 1 1 26 13 1 13  ε_{1} 82.6380
6892  −4 −1723 47499664 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 48.4079
5 −1379 −6895 47541025 1 16 28 224 1 224  ε_{1} 0.9624
197  −35 −6895 47541025 1 2 28 28 1 28  ε_{1} 6.6670
985  −7 −6895 47541025 6 1 28 84 1 14  ε_{1} 13.4088
985  −35 −1379 47541025 6 2 16 96 1 16  ε_{1} 13.4088
1724  −8 −3448 47554816 1 1 8  8 2  8 \sqrt{−1}\sqrt{ε_{1}} 19.5296
3448  −4 −3448 47554816 1 1 8  8 2  8  \sqrt{i}\sqrt{ε_{1}} 48.0203
6901  −67 −103 47623801 3 1 5 15 2  5 \sqrt{−1}\sqrt{ε_{1}} 17.7139
8 −863 −6904 47665216 1 21 24 252 1 252  ε_{1} 1.7627

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 171

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
6904  −8 −863 47665216 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 91.4834
44 −628 −1727 47720464 1 6 36 108 1 108  ε_{1} 5.9864
6908  −4 −1727 47720464 2 1 36 36 1 18  ε_{1} 21.6739
6908  −11 −628 47720464 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 10.8370
6913  −31 −223 47789569 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 129.3285
5 −1383 −6915 47817225 1 18 28 252 1 252  ε_{1} 0.9624
461  −15 −6915 47817225 1 2 28 28 1 28  ε_{1} 11.7998
2305  −3 −6915 47817225 16 1 28 224 1 14  ε_{1} 9.1289
2305  −15 −1383 47817225 16 2 18 288 1 18  ε_{1} 9.1289
13 −532 −6916 47831056 1 4 24 48 1 48  ε_{1} 2.3895
28 −247 −6916 47831056 1 6 24 72 1 72  ε_{1} 5.5373
76  −91 −6916 47831056 1 2 24 24 1 24  ε_{1} 11.6579
133  −52 −6916 47831056 1 2 24 24 1 24  ε_{1} 10.3065
364  −19 −6916 47831056 2 1 24 24 1 12  ε_{1} 16.1090
364 −247 −532 47831056 2 6 4 24 1 12  ε_{1} 16.1090
988  −7 −6916 47831056 2 1 24 24 1 12  ε_{1} 24.0940
988  −91 −532 47831056 2 2 4  8 1  4  ε_{1} 24.0940
1729  −4 −6916 47831056 2 1 24 24 1 12  ε_{1} 64.2443
1729  −52 −532 47831056 2 2 4 16 2  8 \sqrt{−1}\sqrt{ε_{1}} 32.1222
17 −407 −6919 47872561 1 16 68 544 1 544  ε_{1} 4.1894
37 −187 −6919 47872561 1 2 68 68 1 68  ε_{1} 4.9836
629 −11 −6919 47872561 2 1 68 68 1 34 ε_{1} 6.4409
629 −187 −407 47872561 2 2 16 32 1 16  ε_{1} 6.4409
5 −1384 −6920 47886400 1 10 36 180 1 180  ε_{1} 0.9624
173  −40 −6920 47886400 1 2 36 36 1 36  ε_{1} 5.1416
865  −8 −6920 47886400 2 1 36 36 1 18  ε_{1} 40.7237
865  −40 −1384 47886400 2 2 10 20 1 10  ε_{1} 40.7237
161  −43 −6923 47927929 1 1 16  8 1  8  ε_{1} 20.1338
301  −23 −6923 47927929 1 3 16 24 1 24  ε_{1} 20.0642
989  −7 −6923 47927929 1 1 16  8 1  8  ε_{1} 23.0897
12 −1731 −2308 47941776 1 8 8 32 1 32  ε_{1} 2.6339
6924  −3 −2308 47941776 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 15.0193
6924  −4 −1731 47941776 4 1 8 16 1  4  ε_{1} 30.0386
2309  −3 −6927 47983329 1 1 38 19 1 19  ε_{1} 19.5444
8 −1732 −3464 47997184 1 12 44 264 1 264  ε_{1} 1.7627
3464 −4 −3464 47997184 2 1 44 88 2 44 \sqrt{i}\sqrt{ε_{1}} 11.3489
3464  −8 −1732 47997184 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 11.3489
29 −239 −6931 48038761 1 15 12 90 1 90  ε_{1} 3.2945
1733 −4 −6932 48052624 1 1 34 17 1 17 ε_{1} 24.1150
6933  −3 −2311 48066489 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 24.0573
5 −1387 −6935 48094225 1 4 88 176 1 176  ε_{1} 0.9624
73  −95 −6935 48094225 1 8 88 352 1 352  ε_{1} 15.3334
365  −19 −6935 48094225 2 1 88 88 1 44  ε_{1} 5.8944
365  −95 −1387 48094225 2 8 4 32 1 16  ε_{1} 5.8944
6937  −7 −991 48121969 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 94.3311
1388  −20 −1735 48163600 1 2 26 26 1 26  ε_{1} 28.1297
6940  −4 −1735 48163600 6 1 26 78 1 13  ε_{1} 17.4800
6940  −20 −347 48163600 6 2 5 30 1  5  ε_{1} 17.4800
6941  −11 −631 48177481 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 32.9798
53 −131 −6943 48205249 1 5 48 120 1 120  ε_{1} 3.9314

172 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1389  −15 −2315 48233025 1 2 18 18 1 18  ε_{1} 28.0804
6945  −3 −2315 48233025 10 1 18 90 1  9  ε_{1} 21.6396
6945  −15 −463 48233025 10 2 7 70 1  7  ε_{1} 21.6396
21 −331 −6951 48316401 1 3 80 120 1 120  ε_{1} 3.1336
993  −7 −6951 48316401 3 1 80 120 1 40  ε_{1} 17.1487
2317  −3 −6951 48316401 1 1 80 40 1 40  ε_{1} 37.1853
88  −79 −6952 48330304 1 5 16 40 1 40  ε_{1} 11.9527
632  −11 −6952 48330304 1 1 16  8 1  8  ε_{1} 19.2954
869  −8 −6952 48330304 1 1 16  8 1  8  ε_{1} 21.6145
869  −88 −632 48330304 1 2 8  8 1  8  ε_{1} 21.6145
6952  −11 −632 48330304 2 1 8  8 1  4  ε_{1} 72.5243
6952  −79  −88 48330304 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 36.2622
5 −1391 −6955 48372025 1 44 12 264 1 264  ε_{1} 0.9624
13 −535 −6955 48372025 1 14 12 84 1 84  ε_{1} 2.3895
65 −107 −6955 48372025 2 3 12 36 1 18  ε_{1} 5.5529
65 −535 −1391 48372025 2 14 44 616 1 308  ε_{1} 5.5529
188 −148 −1739 48385936 1 2 20 20 1 20  ε_{1} 9.1285
6956 −4 −1739 48385936 2 1 20 20 1 10 ε_{1} 36.1004
6956  −47 −148 48385936 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 18.0502
12 −1160 −3480 48441600 1 20 16 160 1 160  ε_{1} 2.6339
24 −580 −3480 48441600 1 8 16 64 1 64  ε_{1} 4.5849
60 −232 −3480 48441600 2 2 16 32 1 16  ε_{1} 4.1269
60 −696 −1160 48441600 2 12 20 240 1 120  ε_{1} 4.1269
120 −116 −3480 48441600 2 6 16 96 1 48  ε_{1} 6.1779
120 −580 −696 48441600 2 8 12 96 1 48  ε_{1} 6.1779
348 −40 −3480 48441600 2 2 16 32 1 16 ε_{1} 8.0501
348 −120 −1160 48441600 2 4 20 80 1 40  ε_{1} 8.0501
696 −20 −3480 48441600 2 2 16 32 1 16 ε_{1} 15.9463
696 −120 −580 48441600 2 4 8 32 1 16  ε_{1} 15.9463
1740 −8 −3480 48441600 4 1 16 32 1 8 ε_{1} 11.3535
1740  −24 −1160 48441600 4 2 20 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 5.6767
1740  −40 −696 48441600 4 2 12 48 1 12  ε_{1} 11.3535
1740 −120 −232 48441600 4 4 2 16 1  4  ε_{1} 11.3535
3480  −4 −3480 48441600 8 1 16 64 1  8  ε_{1} 9.5412
3480  −20 −696 48441600 8 2 12 96 1 12  ε_{1} 9.5412
3480  −24 −580 48441600 8 2 8 64 1  8  ε_{1} 9.5412
3480 −116 −120 48441600 8 6 4 192 2 24 \sqrt{−1}\sqrt{ε_{1}} 4.7706
33 −211 −6963 48483369 1 3 12 18 1 18  ε_{1} 7.6563
633  −11 −6963 48483369 1 1 12  6 1  6  ε_{1} 41.1944
2321  −3 −6963 48483369 1 1 12  6 1  6  ε_{1} 96.3520
1741  −4 −6964 48497296 1 1 26 13 1 13  ε_{1} 50.3527
1393  −35 −995 48511225 5 2 8 40 1  8  ε_{1} 17.7542
6965  −7 −995 48511225 2 1 8  8 1  4  ε_{1} 20.8465
6965  −35 −199 48511225 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 10.4233
8 −871 −6968 48553024 1 22 44 484 1 484  ε_{1} 1.7627
13 −536 −6968 48553024 1 14 44 308 1 308  ε_{1} 2.3895
104 −67 −6968 48553024 2 1 44 44 1 22 ε_{1} 4.6249
104 −536 −871 48553024 2 14 22 308 1 154  ε_{1} 4.6249
536 −104 −871 48553024 1 6 22 66 1 66  ε_{1} 25.1680
6968  −8 −871 48553024 2 1 22 22 1 11  ε_{1} 24.3460

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 173

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
6968  −67 −104 48553024 2 1 6  6 1  3  ε_{1} 24.3460
69 −303 −2323 48566961 1 10 8 40 1 40  ε_{1} 6.4345
6969 −3 −2323 48566961 2 1 8 8 1 4 ε_{1} 116.9970
6969  −23 −303 48566961 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 58.4985
12 −1743 −2324 48608784 1 24 28 336 1 336  ε_{1} 2.6339
21 −996 −2324 48608784 1 12 28 168 1 168  ε_{1} 3.1336
28 −996 −1743 48608784 1 12 24 144 1 144  ε_{1} 5.5373
249  −84 −2324 48608784 1 4 28 56 1 56  ε_{1} 33.3101
332  −84 −1743 48608784 1 4 24 48 1 48  ε_{1} 10.1997
581  −84 −996 48608784 1 4 12 24 1 24  ε_{1} 17.6272
6972  −3 −2324 48608784 8 1 28 112 1 14  ε_{1} 11.6223
6972  −4 −1743 48608784 8 1 24 96 1 12  ε_{1} 11.6223
6972  −7 −996 48608784 8 1 12 48 1  6  ε_{1} 11.6223
6972  −83  −84 48608784 8 3 4 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.8111
6973  −19 −367 48622729 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 34.3138
997  −7 −6979 48706441 1 1 14  7 1  7  ε_{1} 24.0849
5 −1396 −6980 48720400 1 14 40 280 1 280  ε_{1} 0.9624
349  −20 −6980 48720400 1 2 40 40 1 40  ε_{1} 19.6424
1745  −4 −6980 48720400 4 1 40 80 1 20  ε_{1} 18.0002
1745  −20 −1396 48720400 4 2 14 56 1 14  ε_{1} 18.0002
537  −39 −2327 48734361 1 4 48 96 1 96  ε_{1} 39.5359
6981  −3 −2327 48734361 4 1 48 96 1 24  ε_{1} 18.1589
6981  −39 −179 48734361 4 4 5 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 9.0794
1397 −55 −635 48790225 1 4 10 20 1 20 ε_{1} 16.1274
6985  −11 −635 48790225 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 60.1729
6985 −55 −127 48790225 2 4 5 20 1 10 ε_{1} 120.3458
17 −411 −6987 48818169 1 6 12 36 1 36  ε_{1} 4.1894
137  −51 −6987 48818169 1 2 12 12 1 12  ε_{1} 16.3142
2329  −3 −6987 48818169 2 1 12 12 1  6  ε_{1} 70.5997
2329  −51 −411 48818169 2 2 6 12 1  6  ε_{1} 70.5997
6988  −4 −1747 48832144 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 62.5382
8 −1748 −3496 48888064 1 20 20 200 1 200  ε_{1} 1.7627
76 −184 −3496 48888064 1 4 20 40 1 40  ε_{1} 11.6579
92 −152 −3496 48888064 1 6 20 60 1 60  ε_{1} 7.7415
152 −184 −1748 48888064 1 4 20 40 1 40  ε_{1} 8.6078
184 −152 −1748 48888064 1 6 20 60 1 60  ε_{1} 21.5856
3496  −4 −3496 48888064 6 1 20 60 1 10  ε_{1} 17.8319
3496  −8 −1748 48888064 6 1 20 60 1 10  ε_{1} 17.8319
5 −1399 −6995 48930025 1 27 32 432 1 432  ε_{1} 0.9624
12 −583 −6996 48944016 1 8 40 160 1 160  ε_{1} 2.6339
33 −212 −6996 48944016 1 6 40 120 1 120  ε_{1} 7.6563
44 −159 −6996 48944016 1 10 40 200 1 200  ε_{1} 5.9864
53 −132 −6996 48944016 1 4 40 80 1 80  ε_{1} 3.9314
636 −11 −6996 48944016 2 1 40 40 1 20 ε_{1} 15.7631
636 −132 −583 48944016 2 4 8 32 1 16  ε_{1} 15.7631
1749 −4 −6996 48944016 2 1 40 40 1 20 ε_{1} 16.5746
1749 −132 −212 48944016 2 4 6 24 1 12  ε_{1} 16.5746
2332 −3 −6996 48944016 2 1 40 40 1 20 ε_{1} 33.2808
2332 −132 −159 48944016 2 4 10 40 1 20  ε_{1} 33.2808
2333  −3 −6999 48986001 1 1 66 33 1 33  ε_{1} 25.5432

174 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
149  −47 −7003 49042009 1 5 16 40 1 40  ε_{1} 8.2223
412  −68 −1751 49056016 1 4 48 96 1 96  ε_{1} 26.0564
7004  −4 −1751 49056016 4 1 48 96 1 24  ε_{1} 22.3019
7004  −68 −103 49056016 4 4  5 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 11.1510
1401  −15 −2335 49070025 1 2 14 14 1 14  ε_{1} 99.1010
7005  −3 −2335 49070025 2 1 14 14 1  7  ε_{1} 27.0319
7005  −15 −467 49070025 2 2  7 14 1  7  ε_{1} 27.0319
7009  −43 −163 49126081 1 1  1  1 2  1 \sqrt{−1}\sqrt{ε_{1}} 147.5425
1753  −4 −7012 49168144 1 1 20 10 1 10  ε_{1} 97.8840
5 −1403 −7015 49210225 1 14 28 196 1 196  ε_{1} 0.9624
61 −115 −7015 49210225 1 2 28 28 1 28  ε_{1} 7.3284
305 −23 −7015 49210225 2 3 28 84 1 42 ε_{1} 13.7710
305 −115 −1403 49210225 2 2 14 28 1 14  ε_{1} 13.7710
877 −8 −7016 49224256 1 1 38 19 1 19 ε_{1} 26.1741
7017  −3 −2339 49238289 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 68.2679
413 −119 −1003 49294441 1 10  4 20 1 20  ε_{1} 8.2212
7021  −7 −1003 49294441 2 1  4  4 1  2  ε_{1} 58.7034
7021  −59 −119 49294441 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 29.3517
2341 −3 −7023 49322529 1 1 44 22 1 22 ε_{1} 60.9631
1756  −8 −3512 49336576 5 1 20 100 2 20 \sqrt{−1}\sqrt{ε_{1}} 6.7799
3512 −4 −3512 49336576 1 1 20 20 2 20 \sqrt{i}\sqrt{ε_{1}} 16.7403
28 −251 −7028 49392784 1 7 28 98 1 98  ε_{1} 5.5373
1004  −7 −7028 49392784 1 1 28 14 1 14  ε_{1} 31.6204
1757  −4 −7028 49392784 1 1 28 14 1 14  ε_{1} 13.8275
89  −79 −7031 49434961 1 5 108 270 1 270  ε_{1} 13.8155
8 −879 −7032 49449024 1 22 20 220 1 220  ε_{1} 1.7627
24 −879 −2344 49449024 1 22 18 198 1 198  ε_{1} 4.5849
293  −24 −7032 49449024 1 2 20 20 1 20  ε_{1} 5.6733
2344  −3 −7032 49449024 2 1 20 20 1 10  ε_{1} 45.6621
2344  −24 −879 49449024 2 2 22 44 1 22  ε_{1} 45.6621
7032  −3 −2344 49449024 6 1 18 54 1  9  ε_{1} 14.1363
7032  −8 −879 49449024 6 1 22 66 1 11  ε_{1} 14.1363
5 −1407 −7035 49491225 1 24 16 192 1 192  ε_{1} 0.9624
21 −335 −7035 49491225 1 18 16 144 1 144  ε_{1} 3.1336
105 −67 −7035 49491225 2 1 16 16 1 8 ε_{1} 8.8131
105 −335 −1407 49491225 2 18 24 432 1 216  ε_{1} 8.8131
201  −35 −7035 49491225 1 2 16 16 1 16  ε_{1} 27.6905
469  −15 −7035 49491225 3 2 16 48 1 16  ε_{1} 8.3483
1005  −7 −7035 49491225 2 1 16 16 1  8  ε_{1} 14.9988
1005  −35 −1407 49491225 2 2 24 48 1 24  ε_{1} 14.9988
2345  −3 −7035 49491225 2 1 16 16 1  8  ε_{1} 34.4505
2345  −15 −1407 49491225 2 2 24 48 1 24  ε_{1} 34.4505
7036  −4 −1759 49505296 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 88.7292
7037  −31 −227 49519369 1 3  5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 21.8392
7041  −3 −2347 49575681 1 1  5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 98.4554
12 −587 −7044 49617936 1 7 20 70 1 70  ε_{1} 2.6339
1761  −4 −7044 49617936 7 1 20 70 1 10  ε_{1} 15.5243
2348  −3 −7044 49617936 1 1 20 10 1 10  ε_{1} 30.3085
881  −8 −7048 49674304 1 1 24 12 1 12  ε_{1} 52.1657
133 −371 −1007 49688401 1 8 30 120 1 120  ε_{1} 10.3065

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 175

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
7049  −7 −1007 49688401 10 1 30 300 2 30 \sqrt{−1}\sqrt{ε_{1}} 8.3015
7049  −19 −371 49688401 10 1 8 40 1  4  ε_{1} 16.6030
641  −11 −7051 49716601 1 1 16  8 1  8  ε_{1} 50.0066
172 −164 −1763 49730704 1 8 12 48 1 48  ε_{1} 17.6970
7052  −4 −1763 49730704 4 1 12 24 1  6  ε_{1} 8.8614
7052  −43 −164 49730704 4 1 8 16 1  4  ε_{1} 8.8614
7053  −3 −2351 49744809 3 1 63 189 2 63 \sqrt{−1}\sqrt{ε_{1}} 9.1491
5 −1411 −7055 49773025 1 4 92 184 1 184  ε_{1} 0.9624
17 −415 −7055 49773025 1 10 92 460 1 460  ε_{1} 4.1894
85 −83 −7055 49773025 2 3 92 276 1 138 ε_{1} 4.4187
85 −415 −1411 49773025 2 10 4 40 1 20  ε_{1} 4.4187
13 −543 −7059 49829481 1 12 32 192 1 192  ε_{1} 2.3895
181  −39 −7059 49829481 1 4 32 64 1 64  ε_{1} 14.3479
2353  −3 −7059 49829481 2 1 32 32 1 16  ε_{1} 63.3429
2353  −39 −543 49829481 2 4 12 48 1 24  ε_{1} 63.3429
5 −1412 −7060 49843600 1 16 20 160 1 160  ε_{1} 0.9624
353  −20 −7060 49843600 1 2 20 20 1 20  ε_{1} 23.7346
1765  −4 −7060 49843600 6 1 20 60 1 10  ε_{1} 8.8619
1765  −20 −1412 49843600 6 2 16 96 1 16  ε_{1} 8.8619
7061  −23 −307 49857721 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 14.9571
1009  −7 −7063 49885969 7 1 40 140 1 20  ε_{1} 13.9694
8 −883 −7064 49900096 1 3 50 75 1 75  ε_{1} 1.7627
7064 −8 −883 49900096 5 1 3 15 2 3 \sqrt{−1}\sqrt{ε_{1}} 8.1691
37 −191 −7067 49942489 1 13 14 91 1 91  ε_{1} 4.9836
12 −1767 −2356 49956624 1 32 16 256 1 256  ε_{1} 2.6339
57 −372 −2356 49956624 1 4 16 32 1 32  ε_{1} 11.4208
76 −372 −1767 49956624 1 4 32 64 1 64  ε_{1} 11.6579
93 −228 −2356 49956624 1 4 16 32 1 32  ε_{1} 6.7322
124 −228 −1767 49956624 1 4 32 64 1 64  ε_{1} 16.0392
589 −228 −372 49956624 1 4 4 8 1 8 ε_{1} 30.5757
7068  −3 −2356 49956624 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 7.7639
7068  −4 −1767 49956624 4 1 32 64 1 16  ε_{1} 15.5277
7068  −19 −372 49956624 4 1 4  8 1  2  ε_{1} 15.5277
7068  −31 −228 49956624 4 3 4 24 1  6  ε_{1} 15.5277
2357  −3 −7071 49999041 1 1 70 35 1 35  ε_{1} 21.6629
7073  −11 −643 50027329 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 58.0312
29 −244 −7076 50069776 1 6 64 192 1 192  ε_{1} 3.2945
61 −116 −7076 50069776 1 6 64 192 1 192  ε_{1} 7.3284
1769 −4 −7076 50069776 2 1 64 64 1 32 ε_{1} 38.6629
1769 −116 −244 50069776 2 6 6 36 1 18  ε_{1} 38.6629
21 −1011 −2359 50083929 1 12 28 168 1 168  ε_{1} 3.1336
7077  −3 −2359 50083929 4 1 28 56 1 14  ε_{1} 14.4098
7077  −7 −1011 50083929 4 1 12 24 1  6  ε_{1} 14.4098
5 −1416 −7080 50126400 1 16 40 320 1 320  ε_{1} 0.9624
24 −295 −7080 50126400 1 8 40 160 1 160  ε_{1} 4.5849
120 −59 −7080 50126400 2 3 40 120 1 60 ε_{1} 6.1779
120 −295 −1416 50126400 2 8 16 128 1 64  ε_{1} 6.1779
177 −40 −7080 50126400 1 2 40 40 1 40 ε_{1} 23.4697
177 −120 −2360 50126400 1 4 20 40 1 40  ε_{1} 23.4697
472  −15 −7080 50126400 1 2 40 40 1 40  ε_{1} 26.6550

176 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
885  −8 −7080 50126400 2 1 40 40 1 20  ε_{1} 10.9445
885  −24 −2360 50126400 2 2 20 40 1 20  ε_{1} 10.9445
885  −40 −1416 50126400 2 2 16 32 1 16  ε_{1} 10.9445
885 −120 −472 50126400 2 4 6 24 1 12  ε_{1} 10.9445
1416 −15 −2360 50126400 2 2 20 40 1 20 ε_{1} 26.3082
1416 −120 −295 50126400 2 4 8 32 1 16  ε_{1} 26.3082
2360  −3 −7080 50126400 2 1 40 40 1 20  ε_{1} 18.7110
2360  −15 −1416 50126400 2 2 16 32 1 16  ε_{1} 18.7110
7080  −3 −2360 50126400 4 1 20 40 1 10  ε_{1} 14.1431
7080  −15 −472 50126400 4 2 6 24 1  6  ε_{1} 14.1431
7080  −24 −295 50126400 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 7.0716
7080 −59 −120 50126400 4 3 4 24 1 6 ε_{1} 14.1431
28 −1012 −1771 50183056 1 4 8 16 1 16  ε_{1} 5.5373
44 −644 −1771 50183056 1 16 8 64 1 64  ε_{1} 5.9864
77 −644 −1012 50183056 1 16 4 32 1 32  ε_{1} 4.3693
92 −308 −1771 50183056 1 8 8 32 1 32  ε_{1} 7.7415
161 −308 −1012 50183056 1 8 4 16 1 16  ε_{1} 20.1338
253 −308 −644 50183056 1 8 16 64 1 64  ε_{1} 15.0577
7084  −4 −1771 50183056 12 1 8 48 1  4  ε_{1} 13.8354
7084  −7 −1012 50183056 12 1 4 48 2  4 \sqrt{−1}\sqrt{ε_{1}} 6.9177
7084  −11 −644 50183056 12 1 16 96 1  8  ε_{1} 13.8354
7084  −23 −308 50183056 12 3 8 144 1 12  ε_{1} 13.8354
373  −19 −7087 50225569 1 1 30 15 1 15  ε_{1} 18.4673
1772  −8 −3544 50239744 3 1 18 54 2 18 \sqrt{−1}\sqrt{ε_{1}} 6.7845
3544  −4 −3544 50239744 1 1 18 18 2 18  \sqrt{i}\sqrt{ε_{1}} 58.0020
417  −51 −2363 50253921 1 2 10 10 1 10  ε_{1} 37.9102
7089  −3 −2363 50253921 2 1 10 10 1  5  ε_{1} 101.2199
7089  −51 −139 50253921 2 2 3  6 1  3  ε_{1} 101.2199
1013  −7 −7091 50282281 1 1 38 19 1 19  ε_{1} 13.6553
5 −1419 −7095 50339025 1 12 56 336 1 336  ε_{1} 0.9624
33 −215 −7095 50339025 1 14 56 392 1 392  ε_{1} 7.6563
129  −55 −7095 50339025 1 4 56 112 1 112  ε_{1} 20.8511
165  −43 −7095 50339025 2 1 56 56 1 28  ε_{1} 5.1180
165 −215 −1419 50339025 2 14 12 168 1 84  ε_{1} 5.1180
473  −15 −7095 50339025 3 2 56 168 1 56  ε_{1} 10.3180
645  −11 −7095 50339025 2 1 56 56 1 28  ε_{1} 9.6883
645  −55 −1419 50339025 2 4 12 48 1 24  ε_{1} 9.6883
2365  −3 −7095 50339025 2 1 56 56 1 28  ε_{1} 25.2916
2365  −15 −1419 50339025 2 2 12 24 1 12  ε_{1} 25.2916
8 −887 −7096 50353216 1 29 20 290 1 290  ε_{1} 1.7627
7096  −8 −887 50353216 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 74.6013
7097  −47 −151 50367409 1 5 7 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 47.0366
229 −31 −7099 50395801 3 3 14 63 1 21 ε_{1} 5.4249
69 −103 −7107 50509449 1 5 12 30 1 30  ε_{1} 6.4345
309  −23 −7107 50509449 1 3 12 18 1 18  ε_{1} 17.0523
2369  −3 −7107 50509449 1 1 12  6 1  6  ε_{1} 87.4153
1777  −4 −7108 50523664 1 1 24 12 1 12  ε_{1} 95.2359
13 −547 −7111 50566321 1 3 52 78 1 78  ε_{1} 2.3895
56 −127 −7112 50580544 1 5 40 100 1 100  ε_{1} 6.8002
889  −8 −7112 50580544 1 1 40 20 1 20  ε_{1} 89.4446

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 177

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
889  −56 −1016 50580544 1 4 16 32 1 32  ε_{1} 89.4446
1016  −7 −7112 50580544 3 1 40 60 1 20  ε_{1} 12.4688
7112  −7 −1016 50580544 4 1 16 32 1  8  ε_{1} 12.4531
7112  −56 −127 50580544 4 4 5 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 6.2265
7113  −3 −2371 50594769 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 75.6350
5 −1423 −7115 50623225 1 9 30 135 1 135  ε_{1} 0.9624
12 −1779 −2372 50637456 1 10 24 120 1 120  ε_{1} 2.6339
7116  −3 −2372 50637456 2 1 24 24 1 12  ε_{1} 51.7093
7116  −4 −1779 50637456 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 25.8546
7117  −11 −647 50651689 3 1 23 69 2 23 \sqrt{−1}\sqrt{ε_{1}} 8.6692
8 −1780 −3560 50694400 1 8 24 96 1 96  ε_{1} 1.7627
40 −356 −3560 50694400 2 12 24 288 1 144  ε_{1} 3.6369
40 −712 −1780 50694400 2 8 8 64 1 32  ε_{1} 3.6369
712  −20 −3560 50694400 2 2 24 48 1 24  ε_{1} 16.1431
712  −40 −1780 50694400 2 2 8 16 1  8  ε_{1} 16.1431
3560  −4 −3560 50694400 4 1 24 48 1 12  ε_{1} 11.7611
3560  −8 −1780 50694400 4 1 8 16 1  4  ε_{1} 11.7611
3560  −20 −712 50694400 4 2 8 32 1  8  ε_{1} 11.7611
3560  −40 −356 50694400 4 2 12 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 5.8805
17 −419 −7123 50737129 1 9 10 45 1 45  ε_{1} 4.1894
13 −548 −7124 50751376 1 8 68 272 1 272  ε_{1} 2.3895
137  −52 −7124 50751376 1 2 68 68 1 68  ε_{1} 16.3142
1781  −4 −7124 50751376 2 1 68 68 1 34  ε_{1} 10.7038
1781  −52 −548 50751376 2 2 8 16 1  8  ε_{1} 10.7038
2377  −3 −7131 50851161 1 1 20 10 1 10  ε_{1} 132.3131
7132  −4 −1783 50865424 1 1 17 17 2 17  \sqrt{i}\sqrt{ε_{1}} 54.7531
7133  −7 −1019 50879689 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 20.8811
5 −1427 −7135 50908225 1 15 38 285 1 285  ε_{1} 0.9624
5 −1428 −7140 50979600 1 8 32 128 1 128  ε_{1} 0.9624
12 −595 −7140 50979600 1 4 32 64 1 64  ε_{1} 2.6339
17 −420 −7140 50979600 1 8 32 128 1 128  ε_{1} 4.1894
21 −340 −7140 50979600 1 4 32 64 1 64  ε_{1} 3.1336
28 −255 −7140 50979600 1 12 32 192 1 192  ε_{1} 5.5373
60 −119 −7140 50979600 2 10 32 320 1 160  ε_{1} 4.1269
60 −595 −1428 50979600 2 4 8 32 1 16  ε_{1} 4.1269
85 −84 −7140 50979600 2 4 32 128 1 64 ε_{1} 4.4187
85 −420 −1428 50979600 2 8 8 64 1 32  ε_{1} 4.4187
105 −68 −7140 50979600 2 4 32 128 1 64 ε_{1} 8.8131
105 −340 −1428 50979600 2 4 8 32 1 16  ε_{1} 8.8131
140 −51 −7140 50979600 2 2 32 64 1 32 ε_{1} 4.9558
140 −255 −1428 50979600 2 12 8 96 1 48  ε_{1} 4.9558
204 −35 −7140 50979600 2 2 32 64 1 32 ε_{1} 9.2101
204 −420 −595 50979600 2 8 4 32 1 16  ε_{1} 9.2101
357 −20 −7140 50979600 2 2 32 64 1 32 ε_{1} 5.8833
357 −340 −420 50979600 2 4 8 32 1 16  ε_{1} 5.8833
476 −15 −7140 50979600 2 2 32 64 1 32 ε_{1} 10.9612
476 −255 −420 50979600 2 12 8 96 1 48  ε_{1} 10.9612
1020  −7 −7140 50979600 4 1 32 64 1 16  ε_{1} 6.9295
1020  −35 −1428 50979600 4 2 8 32 1  8  ε_{1} 6.9295
1020  −84 −595 50979600 4 4 4 32 1  8  ε_{1} 6.9295

178 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
1020 −119 −420 50979600 4 10 8 160 1 40  ε_{1} 6.9295
1785  −4 −7140 50979600 8 1 32 128 1 16  ε_{1} 11.6461
1785  −20 −1428 50979600 8 2 8 64 1  8  ε_{1} 11.6461
1785  −68 −420 50979600 8 4 8 128 1 16  ε_{1} 11.6461
1785  −84 −340 50979600 8 4 4 128 2 16 \sqrt{−1}\sqrt{ε_{1}} 5.8230
2380  −3 −7140 50979600 4 1 32 64 1 16  ε_{1} 21.0389
2380  −15 −1428 50979600 4 2 8 32 1  8  ε_{1} 21.0389
2380  −51 −420 50979600 4 2 8 32 1  8  ε_{1} 21.0389
2380  −84 −255 50979600 4 4 12 96 1 24  ε_{1} 21.0389
2381  −3 −7143 51022449 1 1 46 23 1 23  ε_{1} 40.1861
152  −47 −7144 51036736 1 5 20 50 1 50  ε_{1} 8.6078
376  −19 −7144 51036736 1 1 20 10 1 10  ε_{1} 30.5420
893  −8 −7144 51036736 1 1 20 10 1 10  ε_{1} 15.4822
893 −152 −376 51036736 1 6 8 24 1 24  ε_{1} 15.4822
7144 −19 −376 51036736 2 1 8 8 1 4 ε_{1} 92.9944
7144  −47 −152 51036736 2 5 6 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 46.4972
1021  −7 −7147 51079609 1 1 14  7 1  7  ε_{1} 36.5338
7148  −4 −1787 51093904 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 12.9772
7149  −3 −2383 51108201 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 43.1132
12 −1192 −3576 51151104 1 6 28 84 1 84  ε_{1} 2.6339
24 −596 −3576 51151104 1 14 28 196 1 196  ε_{1} 4.5849
1788 −8 −3576 51151104 2 1 28 28 1 14 ε_{1} 11.3807
1788  −24 −1192 51151104 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.6903
3576 −4 −3576 51151104 6 1 28 84 1 14 ε_{1} 12.7872
3576  −24 −596 51151104 6 2 14 168 2 28 \sqrt{−1}\sqrt{ε_{1}} 6.3936
7153  −23 −311 51165409 1 3 19 57 2 57 \sqrt{−1}\sqrt{ε_{1}} 111.7798
1789 −4 −7156 51208336 1 1 26 13 1 13 ε_{1} 54.0623
5 −1432 −7160 51265600 1 6 52 156 1 156  ε_{1} 0.9624
8 −895 −7160 51265600 1 16 52 416 1 416  ε_{1} 1.7627
40 −179 −7160 51265600 2 5 52 260 1 130  ε_{1} 3.6369
40 −895 −1432 51265600 2 16 6 96 1 48  ε_{1} 3.6369
1432  −40 −895 51265600 1 2 16 16 1 16  ε_{1} 53.1804
7160  −8 −895 51265600 2 1 16 16 1  8  ε_{1} 23.4071
7160  −40 −179 51265600 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 11.7036
21 −1023 −2387 51279921 1 16 12 96 1 96  ε_{1} 3.1336
33 −651 −2387 51279921 1 8 12 48 1 48  ε_{1} 7.6563
77 −651 −1023 51279921 1 8 16 64 1 64  ε_{1} 4.3693
93 −231 −2387 51279921 1 12 12 72 1 72  ε_{1} 6.7322
217 −231 −1023 51279921 1 12 16 96 1 96  ε_{1} 31.7104
341 −231 −651 51279921 1 12 8 48 1 48  ε_{1} 11.2480
7161  −3 −2387 51279921 4 1 12 24 1  6  ε_{1} 53.9926
7161  −7 −1023 51279921 4 1 16 32 1  8  ε_{1} 53.9926
7161  −11 −651 51279921 4 1 8 16 1  4  ε_{1} 53.9926
7161  −31 −231 51279921 4 3 12 72 1 18  ε_{1} 53.9926
13 −551 −7163 51308569 1 26 20 260 1 260  ε_{1} 2.3895
29 −247 −7163 51308569 1 6 20 60 1 60  ε_{1} 3.2945
377 −19 −7163 51308569 2 1 20 20 1 10 ε_{1} 12.2884
377 −247 −551 51308569 2 6 26 156 1 78  ε_{1} 12.2884
2389  −3 −7167 51365889 1 1 64 32 1 32  ε_{1} 66.6117
7169  −67 −107 51394561 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 84.7911

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 179

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
101  −71 −7171 51423241 1 7 20 70 1 70  ε_{1} 5.9964
44 −163 −7172 51437584 1 1 36 18 1 18  ε_{1} 5.9864
652  −11 −7172 51437584 1 1 36 18 1 18  ε_{1} 37.3376
1793  −4 −7172 51437584 1 1 36 18 1 18  ε_{1} 67.7891
13 −552 −7176 51494976 1 8 32 128 1 128  ε_{1} 2.3895
24 −299 −7176 51494976 1 8 32 128 1 128  ε_{1} 4.5849
69 −104 −7176 51494976 1 6 32 96 1 96  ε_{1} 6.4345
69 −312 −2392 51494976 1 4 8 16 1 16  ε_{1} 6.4345
184  −39 −7176 51494976 1 4 32 64 1 64  ε_{1} 21.5856
312  −23 −7176 51494976 2 3 32 96 1 48  ε_{1} 9.3267
312 −299 −552 51494976 2 8 8 64 1 32  ε_{1} 9.3267
552 −39 −2392 51494976 2 4 8 32 1 16 ε_{1} 9.0864
552 −299 −312 51494976 2 8 4 32 1 16  ε_{1} 9.0864
897  −8 −7176 51494976 4 1 32 64 1 16  ε_{1} 14.1768
897  −24 −2392 51494976 4 2 8 32 1  8  ε_{1} 14.1768
897 −104 −552 51494976 4 6 8 96 1 24  ε_{1} 14.1768
897 −184 −312 51494976 4 4 4 32 1  8  ε_{1} 14.1768
2392  −3 −7176 51494976 2 1 32 32 1 16  ε_{1} 29.9250
2392  −39 −552 51494976 2 4 8 32 1 16  ε_{1} 29.9250
7176  −3 −2392 51494976 4 1 8 16 1  4  ε_{1} 34.0819
7176  −23 −312 51494976 4 3 4 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 17.0410
7176  −24 −299 51494976 4 2 8 32 1  8  ε_{1} 34.0819
7176  −39 −184 51494976 4 4 4 32 1  8  ε_{1} 34.0819
2393  −3 −7179 51538041 1 1 22 11 1 11  ε_{1} 54.7353
1436  −20 −1795 51552400 3 2 8 24 1  8  ε_{1} 13.1585
7180  −4 −1795 51552400 2 1 8  8 1  4  ε_{1} 58.3907
7180  −20 −359 51552400 2 2 19 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 29.1953
7181  −43 −167 51566761 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 20.1574
653 −11 −7183 51595489 1 1 32 16 1 16 ε_{1} 14.8304
8 −1796 −3592 51609856 1 20 12 120 1 120  ε_{1} 1.7627
3592 −4 −3592 51609856 6 1 12 72 2 12 \sqrt{i}\sqrt{ε_{1}} 7.4944
3592  −8 −1796 51609856 6 1 20 120 2 20 \sqrt{−1}\sqrt{ε_{1}} 7.4944
1437  −15 −2395 51624225 1 2 8  8 1  8  ε_{1} 21.9351
7185  −3 −2395 51624225 2 1 8  8 1  4  ε_{1} 74.4826
7185  −15 −479 51624225 2 2 25 100 2 50 \sqrt{−1}\sqrt{ε_{1}} 37.2413
12 −599 −7188 51667344 1 25 24 300 1 300  ε_{1} 2.6339
1797  −4 −7188 51667344 1 1 24 12 1 12  ε_{1} 25.3325
2396  −3 −7188 51667344 1 1 24 12 1 12  ε_{1} 63.0608
553  −91 −1027 51681721 1 2 4  4 1  4  ε_{1} 55.7072
7189  −7 −1027 51681721 2 1 4  4 1  2  ε_{1} 54.6460
7189  −79  −91 51681721 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 27.3230
8 −899 −7192 51724864 1 14 20 140 1 140  ε_{1} 1.7627
29 −248 −7192 51724864 1 8 20 80 1 80  ε_{1} 3.2945
232 −31 −7192 51724864 2 3 20 60 1 30 ε_{1} 10.5766
232 −248 −899 51724864 2 8 14 112 1 56  ε_{1} 10.5766
248 −232 −899 51724864 1 2 14 14 1 14  ε_{1} 9.6724
7192  −8 −899 51724864 2 1 14 14 1  7  ε_{1} 58.1224
7192  −31 −232 51724864 2 3 2  6 1  3  ε_{1} 58.1224
5 −1439 −7195 51768025 1 39 16 312 1 312  ε_{1} 0.9624
28 −1028 −1799 51782416 1 16 50 400 1 400  ε_{1} 5.5373

180 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7196  −4 −1799 51782416 2 1 50 100 2 50  \sqrt{i}\sqrt{ε_{1}} 15.6153
7196  −7 −1028 51782416 2 1 16 16 1  8  ε_{1} 31.2306
7197  −3 −2399 51796809 1 1 59 59 2 59 \sqrt{−1}\sqrt{ε_{1}} 25.9876
313  −23 −7199 51825601 1 3 114 171 1 171  ε_{1} 38.7035
7201  −19 −379 51854401 1 1  3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 133.0705
1801  −4 −7204 51897616 1 1 28 14 1 14  ε_{1} 138.6334
1441  −55 −655 51912025 1 4 12 24 1 24  ε_{1} 111.5641
7205  −11 −655 51912025 4 1 12 24 1  6  ε_{1} 14.5490
7205  −55 −131 51912025 4 4  5 40 1 10  ε_{1} 14.5490
17 −424 −7208 51955264 1 6 32 96 1 96  ε_{1} 4.1894
53 −136 −7208 51955264 1 4 32 64 1 64  ε_{1} 3.9314
901  −8 −7208 51955264 4 1 32 64 1 16  ε_{1} 8.1892
901 −136 −424 51955264 4 4  6 48 1 12  ε_{1} 8.1892
12 −1803 −2404 52012944 1 8 20 80 1 80  ε_{1} 2.6339
7212  −3 −2404 52012944 4 1 20 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 12.9148
7212 −4 −1803 52012944 4 1 8 16 1 4 ε_{1} 25.8296
5 −1443 −7215 52056225 1 8 72 288 1 288  ε_{1} 0.9624
13 −555 −7215 52056225 1 4 72 144 1 144  ε_{1} 2.3895
37 −195 −7215 52056225 1 4 72 144 1 144  ε_{1} 4.9836
65 −111 −7215 52056225 2 8 72 576 1 288  ε_{1} 5.5529
65 −555 −1443 52056225 2 4  8 32 1 16  ε_{1} 5.5529
185  −39 −7215 52056225 2 4 72 288 1 144  ε_{1} 9.8254
185 −195 −1443 52056225 2 4  8 32 1 16  ε_{1} 9.8254
481  −15 −7215 52056225 2 2 72 144 1 72  ε_{1} 28.9443
481 −195 −555 52056225 2 4  4 16 1  8  ε_{1} 28.9443
2405  −3 −7215 52056225 4 1 72 144 1 36  ε_{1} 7.7845
2405  −15 −1443 52056225 4 2  8 32 1  8  ε_{1} 7.7845
2405  −39 −555 52056225 4 4  4 32 1  8  ε_{1} 7.7845
2405 −111 −195 52056225 4 8  4 64 1 16  ε_{1} 7.7845
44 −328 −3608 52070656 1 4 28 56 1 56  ε_{1} 5.9864
88 −164 −3608 52070656 1 8 28 112 1 112  ε_{1} 11.9527
1804  −8 −3608 52070656 2 1 28 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 18.3475
1804  −88 −328 52070656 2 2  4  8 1  4  ε_{1} 36.6950
3608  −4 −3608 52070656 2 1 28 56 2 28  \sqrt{i}\sqrt{ε_{1}} 7.4967
3608  −88 −164 52070656 2 2  8 16 1  8  ε_{1} 14.9933
7217  −7 −1031 52085089 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 65.6980
249  −87 −2407 52142841 1 6 20 60 1 60  ε_{1} 33.3101
7221  −3 −2407 52142841 10 1 20 100 1 10  ε_{1} 8.8850
7221  −83  −87 52142841 10 3  6 180 2 18 \sqrt{−1}\sqrt{ε_{1}} 4.4425
233  −31 −7223 52171729 1 3 84 126 1 126  ε_{1} 21.4863
8 −903 −7224 52186176 1 16 40 320 1 320  ε_{1} 1.7627
21 −344 −7224 52186176 1 10 40 200 1 200  ε_{1} 3.1336
21 −1032 −2408 52186176 1 8 24 96 1 96  ε_{1} 3.1336
24 −903 −2408 52186176 1 16 24 192 1 192  ε_{1} 4.5849
56 −903 −1032 52186176 1 16  8 64 1 64  ε_{1} 6.8002
129  −56 −7224 52186176 1 4 40 80 1 80  ε_{1} 20.8511
129 −168 −2408 52186176 1 4 24 48 1 48  ε_{1} 20.8511
168 −43 −7224 52186176 2 1 40 40 1 20 ε_{1} 6.5132
168 −344 −903 52186176 2 10 16 160 1 80  ε_{1} 6.5132
301  −24 −7224 52186176 1 2 40 40 1 40  ε_{1} 20.0642

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 181

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
301 −168 −1032 52186176 1 4  8 16 1 16  ε_{1} 20.0642
344 −168 −903 52186176 1 4 16 32 1 32  ε_{1} 19.8864
1032  −7 −7224 52186176 2 1 40 40 1 20  ε_{1} 12.4844
1032  −56 −903 52186176 2 4 16 64 1 32  ε_{1} 12.4844
2408  −3 −7224 52186176 2 1 40 40 1 20  ε_{1} 14.4510
2408  −24 −903 52186176 2 2 16 32 1 16  ε_{1} 14.4510
7224  −3 −2408 52186176 12 1 24 144 1 12  ε_{1} 10.2715
7224  −7 −1032 52186176 12 1  8 48 1  4  ε_{1} 10.2715
7224  −8 −903 52186176 12 1 16 96 1  8  ε_{1} 10.2715
7224  −43 −168 52186176 12 1  4 48 2  4 \sqrt{−1}\sqrt{ε_{1}} 5.1358
556  −52 −1807 52243984 1 2 12 12 1 12  ε_{1} 37.7195
7228  −4 −1807 52243984 2 1 12 12 1  6  ε_{1} 66.6220
7228  −52 −139 52243984 2 2  3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 33.3110
1033  −7 −7231 52287361 1 1 44 22 1 22  ε_{1} 80.9246
7233  −3 −2411 52316289 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 72.9154
5 −1447 −7235 52345225 1 23 22 253 1 253  ε_{1} 0.9624
57 −127 −7239 52403121 1 5 48 120 1 120  ε_{1} 11.4208
381  −19 −7239 52403121 1 1 48 24 1 24  ε_{1} 15.2316
2413  −3 −7239 52403121 1 1 48 24 1 24  ε_{1} 38.4931
5 −1448 −7240 52417600 1 18 20 180 1 180  ε_{1} 0.9624
181  −40 −7240 52417600 1 2 20 20 1 20  ε_{1} 14.3479
905  −8 −7240 52417600 4 1 20 40 1 10  ε_{1} 13.1640
905  −40 −1448 52417600 4 2 18 72 1 18  ε_{1} 13.1640
7244  −4 −1811 52475536 3 1 23 69 2 23  \sqrt{i}\sqrt{ε_{1}} 12.5892
8 −1812 −3624 52533504 1 12 28 168 1 168  ε_{1} 1.7627
12 −1208 −3624 52533504 1 12 28 168 1 168  ε_{1} 2.6339
24 −1208 −1812 52533504 1 12 12 72 1 72  ε_{1} 4.5849
604  −24 −3624 52533504 1 2 28 28 1 28  ε_{1} 43.9269
1208  −24 −1812 52533504 1 2 12 12 1 12  ε_{1} 31.9236
3624  −4 −3624 52533504 6 1 28 84 1 14  ε_{1} 12.8005
3624  −8 −1812 52533504 6 1 12 36 1  6  ε_{1} 12.8005
7249  −11 −659 52548001 3 1 11 33 2 11 \sqrt{−1}\sqrt{ε_{1}} 51.7229
2417 −3 −7251 52577001 1 1 34 17 1 17 ε_{1} 72.4854
5 −1451 −7255 52635025 1 13 60 390 1 390  ε_{1} 0.9624
8 −907 −7256 52649536 1 3 46 69 1 69  ε_{1} 1.7627
7256  −8 −907 52649536 1 1  3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 41.9028
177 −123 −2419 52664049 1 2  8  8 1  8  ε_{1} 23.4697
7257  −3 −2419 52664049 2 1  8  8 1  4  ε_{1} 64.6995
7257  −59 −123 52664049 2 3  2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 32.3497
17 −427 −7259 52693081 1 2 36 36 1 36  ε_{1} 4.1894
61 −119 −7259 52693081 1 10 36 180 1 180  ε_{1} 7.3284
1037  −7 −7259 52693081 2 1 36 36 1 18  ε_{1} 10.1629
1037 −119 −427 52693081 2 10  2 20 1 10  ε_{1} 10.1629
92  −79 −7268 52823824 1 5 40 100 1 100  ε_{1} 7.7415
316  −23 −7268 52823824 3 3 40 180 1 60  ε_{1} 10.1503
1817  −4 −7268 52823824 1 1 40 20 1 20  ε_{1} 62.9992
7269  −3 −2423 52838361 1 1 33 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 30.6968
661 −11 −7271 52867441 1 1 116 58 1 58 ε_{1} 28.7949
7273  −7 −1039 52896529 3 1 23 69 2 23 \sqrt{−1}\sqrt{ε_{1}} 30.7877
428  −68 −1819 52940176 1 4 10 20 1 20  ε_{1} 15.1243

182 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7276  −4 −1819 52940176 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 39.0179
7276  −68 −107 52940176 2 4 3 12 1  6  ε_{1} 78.0357
7277  −19 −383 52954729 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 23.4740
29 −251 −7279 52983841 1 7 70 245 1 245  ε_{1} 3.2945
28 −520 −3640 52998400 1 4 16 32 1 32  ε_{1} 5.5373
56 −260 −3640 52998400 1 8 16 64 1 64  ε_{1} 6.8002
140 −104 −3640 52998400 2 6 16 96 1 48  ε_{1} 4.9558
140 −520 −728 52998400 2 4 12 48 1 24  ε_{1} 4.9558
280 −52 −3640 52998400 2 2 16 32 1 16 ε_{1} 12.4372
280 −260 −728 52998400 2 8 12 96 1 48  ε_{1} 12.4372
364  −40 −3640 52998400 2 2 16 32 1 16  ε_{1} 16.1090
364 −280 −520 52998400 2 4 4 16 1  8  ε_{1} 16.1090
728  −20 −3640 52998400 2 2 16 32 1 16  ε_{1} 7.9773
728 −260 −280 52998400 2 8 4 32 1 16  ε_{1} 7.9773
1820  −8 −3640 52998400 4 1 16 32 1  8  ε_{1} 9.7039
1820  −40 −728 52998400 4 2 12 48 1 12  ε_{1} 9.7039
1820  −56 −520 52998400 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 4.8520
1820 −104 −280 52998400 4 6 4 48 1 12  ε_{1} 9.7039
3640  −4 −3640 52998400 8 1 16 64 1  8  ε_{1} 11.7833
3640  −20 −728 52998400 8 2 12 96 1 12  ε_{1} 11.7833
3640  −52 −280 52998400 8 2 4 32 1  4  ε_{1} 11.7833
3640  −56 −260 52998400 8 4 8 128 1 16  ε_{1} 11.7833
12 −607 −7284 53056656 1 13 36 234 1 234  ε_{1} 2.6339
1821  −4 −7284 53056656 1 1 36 18 1 18  ε_{1} 44.1276
2428  −3 −7284 53056656 1 1 36 18 1 18  ε_{1} 53.0335
1457 −155 −235 53071225 1 4 2  4 1  4  ε_{1} 60.6057
7285  −31 −235 53071225 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 19.7828
7285  −47 −155 53071225 2 5 4 20 1 10  ε_{1} 39.5657
21 −347 −7287 53100369 1 5 36 90 1 90  ε_{1} 3.1336
1041  −7 −7287 53100369 1 1 36 18 1 18  ε_{1} 69.9435
2429  −3 −7287 53100369 3 1 36 54 1 18  ε_{1} 11.6871
8 −911 −7288 53114944 1 31 16 248 1 248  ε_{1} 1.7627
7288  −8 −911 53114944 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 54.9646
317  −23 −7291 53158681 1 3 12 18 1 18  ε_{1} 8.9775
7292  −4 −1823 53173264 1 1 45 45 2 45  \sqrt{i}\sqrt{ε_{1}} 27.3998
33 −663 −2431 53187849 1 16 28 224 1 224  ε_{1} 7.6563
429 −51 −2431 53187849 2 2 28 56 1 28 ε_{1} 9.9534
429 −187 −663 53187849 2 2 16 32 1 16  ε_{1} 9.9534
561 −39 −2431 53187849 2 4 28 112 1 56 ε_{1} 27.7201
561 −143 −663 53187849 2 10 16 160 1 80  ε_{1} 27.7201
7293  −3 −2431 53187849 4 1 28 56 1 14  ε_{1} 12.1136
7293  −11 −663 53187849 4 1 16 32 1  8  ε_{1} 12.1136
7293  −39 −187 53187849 4 4 2 16 1  4  ε_{1} 12.1136
7293  −51 −143 53187849 4 2 10 40 1 10  ε_{1} 12.1136
5 −1459 −7295 53217025 1 11 80 440 1 440  ε_{1} 0.9624
109  −67 −7303 53333809 1 1 30 15 1 15  ε_{1} 11.1291
88  −83 −7304 53348416 1 3 56 84 1 84  ε_{1} 11.9527
664  −11 −7304 53348416 1 1 56 28 1 28  ε_{1} 43.8951
913  −8 −7304 53348416 1 1 56 28 1 28  ε_{1} 69.1395
913  −88 −664 53348416 1 2 10 10 1 10  ε_{1} 69.1395

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 183

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7304  −11 −664 53348416 2 1 10 10 1  5  ε_{1} 31.2603
7304  −83  −88 53348416 2 3 2  6 1  3  ε_{1} 31.2603
1461  −15 −2435 53363025 1 2 22 22 1 22  ε_{1} 32.1144
7305  −3 −2435 53363025 2 1 22 22 1 11  ε_{1} 109.8725
7305  −15 −487 53363025 2 2 7 14 1  7  ε_{1} 109.8725
2437  −3 −7311 53450721 1 1 88 44 1 44  ε_{1} 42.8377
8 −1828 −3656 53465344 1 8 36 144 1 144  ε_{1} 1.7627
3656  −4 −3656 53465344 4 1 36 72 1 18  ε_{1} 18.6448
3656  −8 −1828 53465344 4 1 8 16 1  4  ε_{1} 18.6448
7313  −71 −103 53479969 1 7 5 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 47.5946
5 −1463 −7315 53509225 1 32 16 256 1 256  ε_{1} 0.9624
77  −95 −7315 53509225 1 8 16 64 1 64  ε_{1} 4.3693
133  −55 −7315 53509225 1 4 16 32 1 32  ε_{1} 10.3065
209  −35 −7315 53509225 1 2 16 16 1 16  ε_{1} 22.8829
385  −19 −7315 53509225 2 1 16 16 1  8  ε_{1} 24.3270
385  −95 −1463 53509225 2 8 32 256 1 128  ε_{1} 24.3270
665  −11 −7315 53509225 2 1 16 16 1  8  ε_{1} 20.4394
665  −55 −1463 53509225 2 4 32 128 1 64  ε_{1} 20.4394
1045  −7 −7315 53509225 4 1 16 32 1  8  ε_{1} 9.1492
1045  −35 −1463 53509225 4 2 32 128 1 32  ε_{1} 9.1492
124  −59 −7316 53523856 1 3 40 60 1 60  ε_{1} 16.0392
236  −31 −7316 53523856 1 3 40 60 1 60  ε_{1} 13.9320
1829  −4 −7316 53523856 1 1 40 20 1 20  ε_{1} 36.4312
13 −563 −7319 53567761 1 9 88 396 1 396  ε_{1} 2.3895
5 −1464 −7320 53582400 1 12 24 144 1 144  ε_{1} 0.9624
8 −915 −7320 53582400 1 8 24 96 1 96  ε_{1} 1.7627
24 −915 −2440 53582400 1 8 12 48 1 48  ε_{1} 4.5849
40 −183 −7320 53582400 2 8 24 192 1 96  ε_{1} 3.6369
40 −915 −1464 53582400 2 8 12 96 1 48  ε_{1} 3.6369
61 −120 −7320 53582400 1 4 24 48 1 48  ε_{1} 7.3284
120 −183 −2440 53582400 2 8 12 96 1 48  ε_{1} 6.1779
120 −488 −915 53582400 2 10 8 80 1 40  ε_{1} 6.1779
305 −24 −7320 53582400 2 2 24 48 1 24 ε_{1} 13.7710
305 −120 −1464 53582400 2 4 12 48 1 24  ε_{1} 13.7710
488 −15 −7320 53582400 2 2 24 48 1 24 ε_{1} 6.1862
488 −120 −915 53582400 2 4 8 32 1 16  ε_{1} 6.1862
1464  −15 −2440 53582400 2 2 12 24 1 12  ε_{1} 28.8241
1464  −40 −915 53582400 2 2 8 16 1  8  ε_{1} 28.8241
2440  −3 −7320 53582400 4 1 24 48 1 12  ε_{1} 23.7509
2440  −15 −1464 53582400 4 2 12 48 1 12  ε_{1} 23.7509
2440  −24 −915 53582400 4 2 8 32 1  8  ε_{1} 23.7509
2440 −120 −183 53582400 4 4 8 64 1 16  ε_{1} 23.7509
7320  −3 −2440 53582400 4 1 12 24 1  6  ε_{1} 23.3667
7320  −8 −915 53582400 4 1 8 16 1  4  ε_{1} 23.3667
7320  −15 −488 53582400 4 2 10 40 1 10  ε_{1} 23.3667
7320  −40 −183 53582400 4 2 8 32 1  8  ε_{1} 23.3667
2441  −3 −7323 53626329 1 1 18  9 1  9  ε_{1} 82.9144
7324  −4 −1831 53640976 1 1 19 19 2 19  \sqrt{i}\sqrt{ε_{1}} 91.1453
17 −431 −7327 53684929 1 21 34 357 1 357  ε_{1} 4.1894
21 −1047 −2443 53714241 1 16 6 48 1 48  ε_{1} 3.1336

184 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7329  −3 −2443 53714241 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 58.1638
7329  −7 −1047 53714241 2 1 16 16 1  8  ε_{1} 116.3277
12 −611 −7332 53758224 1 10 24 120 1 120  ε_{1} 2.6339
13 −564 −7332 53758224 1 8 24 96 1 96  ε_{1} 2.3895
141  −52 −7332 53758224 1 2 24 24 1 24  ε_{1} 10.4940
156  −47 −7332 53758224 2 5 24 120 1 60  ε_{1} 7.8232
156 −564 −611 53758224 2 8 10 80 1 40  ε_{1} 7.8232
188  −39 −7332 53758224 1 4 24 48 1 48  ε_{1} 9.1285
1833  −4 −7332 53758224 2 1 24 24 1 12  ε_{1} 31.9129
1833  −52 −564 53758224 2 2 8 16 1  8  ε_{1} 31.9129
2444  −3 −7332 53758224 2 1 24 24 1 12  ε_{1} 26.1373
2444  −39 −564 53758224 2 4 8 32 1 16  ε_{1} 26.1373
56 −131 −7336 53816896 1 5 36 90 1 90  ε_{1} 6.8002
917  −8 −7336 53816896 1 1 36 18 1 18  ε_{1} 14.1482
917  −56 −1048 53816896 1 4 6 12 1 12  ε_{1} 14.1482
1048  −7 −7336 53816896 1 1 36 18 1 18  ε_{1} 38.3249
7336  −7 −1048 53816896 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 40.6177
7336  −56 −131 53816896 2 4 5 20 1 10  ε_{1} 81.2353
253 −319 −667 53831569 1 10 4 20 1 20  ε_{1} 15.0577
7337 −11 −667 53831569 2 1 4 4 1 2 ε_{1} 54.4254
7337  −23 −319 53831569 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 27.2127
41 −179 −7339 53860921 1 5 18 45 1 45  ε_{1} 8.3183
1468  −20 −1835 53875600 1 2 10 10 1 10  ε_{1} 48.7238
7340  −4 −1835 53875600 2 1 10 10 1  5  ε_{1} 43.0182
7340  −20 −367 53875600 2 2 9 18 1  9  ε_{1} 43.0182
7341  −3 −2447 53890281 1 1 37 37 2 37 \sqrt{−1}\sqrt{ε_{1}} 40.8236
1049  −7 −7343 53919649 1 1 74 37 1 37  ε_{1} 57.5072
93  −79 −7347 53978409 1 5 16 40 1 40  ε_{1} 6.7322
237  −31 −7347 53978409 1 3 16 24 1 24  ε_{1} 8.6873
2449  −3 −7347 53978409 1 1 16  8 1  8  ε_{1} 145.2838
44 −167 −7348 53993104 1 11 24 132 1 132  ε_{1} 5.9864
668  −11 −7348 53993104 1 1 24 12 1 12  ε_{1} 11.6342
1837  −4 −7348 53993104 1 1 24 12 1 12  ε_{1} 34.3491
8 −919 −7352 54051904 1 19 28 266 1 266  ε_{1} 1.7627
7352  −8 −919 54051904 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 31.5255
5 −1471 −7355 54096025 1 23 36 414 1 414  ε_{1} 0.9624
12 −1839 −2452 54110736 1 40 10 200 1 200  ε_{1} 2.6339
7356  −3 −2452 54110736 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 17.7719
7356  −4 −1839 54110736 2 1 40 40 1 20  ε_{1} 35.5437
7357  −7 −1051 54125449 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 48.2315
33 −223 −7359 54154881 1 7 72 252 1 252  ε_{1} 7.6563
669  −11 −7359 54154881 1 1 72 36 1 36  ε_{1} 25.2580
2453  −3 −7359 54154881 1 1 72 36 1 36  ε_{1} 16.3584
37 −199 −7363 54213769 1 9 10 45 1 45  ε_{1} 4.9836
28 −263 −7364 54228496 1 13 40 260 1 260  ε_{1} 5.5373
1052  −7 −7364 54228496 1 1 40 20 1 20  ε_{1} 25.0726
1841  −4 −7364 54228496 1 1 40 20 1 20  ε_{1} 81.2666
1473  −15 −2455 54243225 1 2 28 28 1 28  ε_{1} 58.6040
7365  −3 −2455 54243225 2 1 28 28 1 14  ε_{1} 28.8364
7365  −15 −491 54243225 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 14.4182

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 185

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
53 −139 −7367 54272689 1 3 94 141 1 141  ε_{1} 3.9314
24 −307 −7368 54287424 1 3 16 24 1 24  ε_{1} 4.5849
921  −8 −7368 54287424 1 1 16  8 1  8  ε_{1} 72.3140
921  −24 −2456 54287424 1 2 34 34 1 34  ε_{1} 72.3140
2456  −3 −7368 54287424 1 1 16  8 1  8  ε_{1} 54.5389
7368  −3 −2456 54287424 2 1 34 34 1 17  ε_{1} 46.0746
7368  −24 −307 54287424 2 2  3  6 1  3  ε_{1} 46.0746
76 −388 −1843 54346384 1 4  6 12 1 12  ε_{1} 11.6579
7372  −4 −1843 54346384 2 1  6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 32.2336
7372  −19 −388 54346384 2 1  4  4 1  2  ε_{1} 64.4672
8 −1844 −3688 54405376 1 30 18 270 1 270  ε_{1} 1.7627
3688  −4 −3688 54405376 2 1 18 18 1  9  ε_{1} 41.0944
3688  −8 −1844 54405376 2 1 30 30 1 15  ε_{1} 41.0944
7377  −3 −2459 54420129 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 55.4775
157 −47 −7379 54449641 1 5 28 70 1 70 ε_{1} 10.7226
69 −107 −7383 54508689 1 3 56 84 1 84  ε_{1} 6.4345
321  −23 −7383 54508689 3 3 56 252 1 84  ε_{1} 12.1276
2461  −3 −7383 54508689 1 1 56 28 1 28  ε_{1} 68.6527
8 −923 −7384 54523456 1 10 28 140 1 140  ε_{1} 1.7627
13 −568 −7384 54523456 1 4 28 56 1 56  ε_{1} 2.3895
104 −71 −7384 54523456 2 7 28 196 1 98 ε_{1} 4.6249
104 −568 −923 54523456 2 4 10 40 1 20  ε_{1} 4.6249
568 −104 −923 54523456 3 6 10 90 1 30  ε_{1} 11.3120
7384  −8 −923 54523456 2 1 10 10 1  5  ε_{1} 74.1415
7384  −71 −104 54523456 2 7  6 42 1 21  ε_{1} 74.1415
1477  −35 −1055 54538225 1 2 36 36 1 36  ε_{1} 34.2370
7385  −7 −1055 54538225 2 1 36 36 1 18  ε_{1} 73.3959
7385  −35 −211 54538225 2 2  3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 36.6979
89  −83 −7387 54567769 1 3 10 15 1 15  ε_{1} 13.8155
7388  −4 −1847 54582544 3 1 43 129 2 43  \sqrt{i}\sqrt{ε_{1}} 8.2150
389  −19 −7391 54626881 1 1 120 60 1 60  ε_{1} 15.6986
5 −1479 −7395 54686025 1 28 16 224 1 224  ε_{1} 0.9624
17 −435 −7395 54686025 1 4 16 32 1 32  ε_{1} 4.1894
29 −255 −7395 54686025 1 12 16 96 1 96  ε_{1} 3.2945
85 −87 −7395 54686025 2 6 16 96 1 48 ε_{1} 4.4187
85 −435 −1479 54686025 2 4 28 112 1 56  ε_{1} 4.4187
145 −51 −7395 54686025 4 2 16 64 1 16 ε_{1} 6.3596
145 −255 −1479 54686025 4 12 28 672 1 168  ε_{1} 6.3596
493  −15 −7395 54686025 2 2 16 32 1 16  ε_{1} 9.4192
493 −255 −435 54686025 2 12  4 48 1 24  ε_{1} 9.4192
2465  −3 −7395 54686025 4 1 16 32 1  8  ε_{1} 22.2667
2465  −15 −1479 54686025 4 2 28 112 1 28  ε_{1} 22.2667
2465  −51 −435 54686025 4 2  4 16 1  4  ε_{1} 22.2667
2465  −87 −255 54686025 4 6 12 144 1 36  ε_{1} 22.2667
7401  −3 −2467 54774801 1 1  7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 128.1416
673  −11 −7403 54804409 1 1 22 11 1 11  ε_{1} 64.4243
12 −1851 −2468 54819216 1 14 12 84 1 84  ε_{1} 2.6339
7404  −3 −2468 54819216 6 1 12 36 1  6  ε_{1} 16.4322
7404  −4 −1851 54819216 6 1 14 84 2 14  \sqrt{i}\sqrt{ε_{1}} 8.2161
1852  −8 −3704 54878464 1 1 40 40 2 40 \sqrt{−1}\sqrt{ε_{1}} 33.8356

186 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3704  −4 −3704 54878464 1 1 40 40 2 40  \sqrt{i}\sqrt{ε_{1}} 34.0430
7409  −31 −239 54893281 1 3 15 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 67.5794
17 −436 −7412 54937744 1 6 36 108 1 108  ε_{1} 4.1894
109  −68 −7412 54937744 1 4 36 72 1 72  ε_{1} 11.1291
1853  −4 −7412 54937744 2 1 36 36 1 18  ε_{1} 7.5235
1853  −68 −436 54937744 2 4  6 24 1 12  ε_{1} 7.5235
21 −1059 −2471 54952569 1 6 62 186 1 186  ε_{1} 3.1336
7413  −3 −2471 54952569 2 1 62 62 1 31  ε_{1} 23.7159
7413  −7 −1059 54952569 2 1  6  6 1  3  ε_{1} 23.7159
5 −1483 −7415 54982225 1 7 58 203 1 203  ε_{1} 0.9624
2473 −3 −7419 55041561 1 1 24 12 1 12 ε_{1} 145.8308
28 −1060 −1855 55056400 1 8 28 112 1 112  ε_{1} 5.5373
140 −212 −1855 55056400 2 6 28 168 1 84  ε_{1} 4.9558
140 −371 −1060 55056400 2 8  8 64 1 32  ε_{1} 4.9558
1484  −20 −1855 55056400 2 2 28 56 1 28  ε_{1} 16.2572
1484  −35 −1060 55056400 2 2  8 16 1  8  ε_{1} 16.2572
7420  −4 −1855 55056400 4 1 28 56 1 14  ε_{1} 33.0132
7420  −7 −1060 55056400 4 1  8 16 1  4  ε_{1} 33.0132
7420  −20 −371 55056400 4 2  8 32 1  8  ε_{1} 33.0132
7420  −35 −212 55056400 4 2  6 24 1  6  ε_{1} 33.0132
13 −571 −7423 55100929 1 5 40 100 1 100  ε_{1} 2.3895
1061 −7 −7427 55160329 1 1 28 14 1 14 ε_{1} 24.9704
12 −619 −7428 55175184 1 5 20 50 1 50  ε_{1} 2.6339
1857  −4 −7428 55175184 1 1 20 10 1 10  ε_{1} 86.0172
2476  −3 −7428 55175184 1 1 20 10 1 10  ε_{1} 82.9608
437 −323 −391 55190041 1 4 14 28 1 28  ε_{1} 6.0845
7429  −19 −391 55190041 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 32.2313
7429  −23 −323 55190041 2 3  4 12 1  6  ε_{1} 64.4626
2477  −3 −7431 55219761 1 1 70 35 1 35  ε_{1} 12.9447
929  −8 −7432 55234624 1 1 20 10 1 10  ε_{1} 51.6295
5 −1487 −7435 55279225 1 37 10 185 1 185  ε_{1} 0.9624
201 −111 −2479 55308969 1 8 24 96 1 96  ε_{1} 27.6905
7437  −3 −2479 55308969 4 1 24 48 1 12  ε_{1} 15.0033
7437  −67 −111 55308969 4 1  8 16 1  4  ε_{1} 15.0033
173  −43 −7439 55338721 1 1 116 58 1 58  ε_{1} 5.1416
8 −1860 −3720 55353600 1 16 24 192 1 192  ε_{1} 1.7627
12 −1240 −3720 55353600 1 8 24 96 1 96  ε_{1} 2.6339
24 −1240 −1860 55353600 1 8 16 64 1 64  ε_{1} 4.5849
40 −372 −3720 55353600 2 4 24 96 1 48  ε_{1} 3.6369
40 −744 −1860 55353600 2 12 16 192 1 96  ε_{1} 3.6369
60 −248 −3720 55353600 2 8 24 192 1 96  ε_{1} 4.1269
60 −744 −1240 55353600 2 12 8 96 1 48 ε_{1} 4.1269
120 −248 −1860 55353600 2 8 16 128 1 64  ε_{1} 6.1779
120 −372 −1240 55353600 2 4 8 32 1 16 ε_{1} 6.1779
124 −120 −3720 55353600 1 4 24 48 1 48  ε_{1} 16.0392
248 −120 −1860 55353600 1 4 16 32 1 32  ε_{1} 9.6724
620 −24 −3720 55353600 2 2 24 48 1 24 ε_{1} 12.4212
620 −120 −744 55353600 2 4 12 48 1 24  ε_{1} 12.4212
744  −20 −3720 55353600 2 2 24 48 1 24  ε_{1} 19.2319
744  −40 −1860 55353600 2 2 16 32 1 16  ε_{1} 19.2319

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 187

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1240  −24 −1860 55353600 2 2 16 32 1 16  ε_{1} 28.6893
1240 −120 −372 55353600 2 4 4 16 1  8  ε_{1} 28.6893
3720  −4 −3720 55353600 4 1 24 48 1 12  ε_{1} 9.6079
3720  −8 −1860 55353600 4 1 16 32 1  8  ε_{1} 9.6079
3720  −20 −744 55353600 4 2 12 48 1 12  ε_{1} 9.6079
3720  −40 −372 55353600 4 2 4 16 1  4  ε_{1} 9.6079
7441  −7 −1063 55368481 3 1 19 57 2 19 \sqrt{−1}\sqrt{ε_{1}} 49.8182
1861  −4 −7444 55413136 1 1 38 19 1 19  ε_{1} 44.0966
677  −11 −7447 55457809 1 1 42 21 1 21  ε_{1} 7.9032
573  −39 −2483 55487601 1 4 20 40 1 40  ε_{1} 13.2824
7449  −3 −2483 55487601 8 1 20 160 2 20 \sqrt{−1}\sqrt{ε_{1}} 14.3334
7449 −39 −191 55487601 8 4 13 208 1 26 ε_{1} 28.6668
5 −1491 −7455 55577025 1 12 56 336 1 336  ε_{1} 0.9624
21 −355 −7455 55577025 1 4 56 112 1 112  ε_{1} 3.1336
105 −71 −7455 55577025 2 7 56 392 1 196 ε_{1} 8.8131
105 −355 −1491 55577025 2 4 12 48 1 24  ε_{1} 8.8131
213  −35 −7455 55577025 1 2 56 56 1 56  ε_{1} 8.5805
497  −15 −7455 55577025 1 2 56 56 1 56  ε_{1} 29.3851
1065  −7 −7455 55577025 2 1 56 56 1 28  ε_{1} 37.8470
1065  −35 −1491 55577025 2 2 12 24 1 12  ε_{1} 37.8470
2485  −3 −7455 55577025 2 1 56 56 1 28  ε_{1} 22.5113
2485  −15 −1491 55577025 2 2 12 24 1 12  ε_{1} 22.5113
5 −1492 −7460 55651600 1 10 48 240 1 240  ε_{1} 0.9624
373  −20 −7460 55651600 1 2 48 48 1 48  ε_{1} 18.4673
1865  −4 −7460 55651600 2 1 48 48 1 24  ε_{1} 26.1887
1865  −20 −1492 55651600 2 2 10 20 1 10  ε_{1} 26.1887
17 −439 −7463 55696369 1 15 66 495 1 495  ε_{1} 4.1894
24 −311 −7464 55711296 1 19 32 304 1 304  ε_{1} 4.5849
933  −8 −7464 55711296 1 1 32 16 1 16  ε_{1} 23.8438
933  −24 −2488 55711296 1 2 12 12 1 12  ε_{1} 23.8438
2488  −3 −7464 55711296 1 1 32 16 1 16  ε_{1} 48.0828
7464  −3 −2488 55711296 6 1 12 36 1  6  ε_{1} 20.6901
7464  −24 −311 55711296 6 2 19 228 2 38 \sqrt{−1}\sqrt{ε_{1}} 10.3450
57 −131 −7467 55756089 1 5 20 50 1 50  ε_{1} 11.4208
393  −19 −7467 55756089 1 1 20 10 1 10  ε_{1} 36.6935
2489  −3 −7467 55756089 1 1 20 10 1 10  ε_{1} 102.7906
7468  −4 −1867 55771024 1 1 5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 39.7062
77 −679 −1067 55785961 1 18 12 108 1 108  ε_{1} 4.3693
7469 −7 −1067 55785961 2 1 12 12 1 6 ε_{1} 20.8250
7469  −11 −679 55785961 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 10.4125
241 −31 −7471 55815841 1 3 58 87 1 87 ε_{1} 37.5430
1868  −8 −3736 55830784 1 1 26 26 2 26 \sqrt{−1}\sqrt{ε_{1}} 14.9946
3736 −4 −3736 55830784 3 1 26 78 2 26 \sqrt{i}\sqrt{ε_{1}} 15.6187
141 −159 −2491 55845729 1 10 12 60 1 60  ε_{1} 10.4940
7473 −3 −2491 55845729 6 1 12 36 1 6 ε_{1} 29.0118
7473  −47 −159 55845729 6 5 10 300 2 50 \sqrt{−1}\sqrt{ε_{1}} 14.5059
12 −623 −7476 55890576 1 22 40 440 1 440  ε_{1} 2.6339
21 −356 −7476 55890576 1 12 40 240 1 240  ε_{1} 3.1336
28 −267 −7476 55890576 1 2 40 40 1 40  ε_{1} 5.5373
89  −84 −7476 55890576 1 4 40 80 1 80  ε_{1} 13.8155

188 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1068  −7 −7476 55890576 2 1 40 40 1 20  ε_{1} 16.9544
1068  −84 −623 55890576 2 4 22 88 1 44  ε_{1} 16.9544
1869  −4 −7476 55890576 2 1 40 40 1 20  ε_{1} 20.3103
1869  −84 −356 55890576 2 4 12 96 2 48 \sqrt{−1}\sqrt{ε_{1}} 10.1551
2492  −3 −7476 55890576 2 1 40 40 1 20  ε_{1} 14.2586
2492  −84 −267 55890576 2 4 2  8 1  4  ε_{1} 14.2586
5 −1496 −7480 55950400 1 28 16 224 1 224  ε_{1} 0.9624
8 −935 −7480 55950400 1 28 16 224 1 224  ε_{1} 1.7627
17 −440 −7480 55950400 1 12 16 96 1 96  ε_{1} 4.1894
40 −187 −7480 55950400 2 2 16 32 1 16  ε_{1} 3.6369
40 −935 −1496 55950400 2 28 28 784 1 392  ε_{1} 3.6369
85 −88 −7480 55950400 2 2 16 32 1 16 ε_{1} 4.4187
85 −440 −1496 55950400 2 12 28 336 1 168  ε_{1} 4.4187
88 −680 −935 55950400 1 12 28 168 1 168  ε_{1} 11.9527
136 −55 −7480 55950400 2 4 16 64 1 32 ε_{1} 8.4966
136 −440 −935 55950400 2 12 28 336 1 168  ε_{1} 8.4966
440 −136 −935 55950400 2 4 28 112 1 56  ε_{1} 7.4742
440 −187 −680 55950400 2 2 12 24 1 12  ε_{1} 7.4742
680  −11 −7480 55950400 4 1 16 32 1  8  ε_{1} 6.5191
680  −55 −1496 55950400 4 4 28 224 1 56  ε_{1} 6.5191
680  −88 −935 55950400 4 2 28 112 1 28  ε_{1} 6.5191
680 −187 −440 55950400 4 2 12 48 1 12  ε_{1} 6.5191
1496  −40 −935 55950400 2 2 28 56 1 28  ε_{1} 17.6287
1496  −55 −680 55950400 2 4 12 48 1 24  ε_{1} 17.6287
7480  −8 −935 55950400 4 1 28 56 1 14  ε_{1} 34.9767
7480  −11 −680 55950400 4 1 12 24 1  6  ε_{1} 34.9767
7480  −40 −187 55950400 4 2 2  8 1  2  ε_{1} 34.9767
7480  −55 −136 55950400 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 17.4884
1069  −7 −7483 55995289 1 1 10  5 1  5  ε_{1} 36.9734
7484  −4 −1871 56010256 1 1 45 45 2 45  \sqrt{i}\sqrt{ε_{1}} 58.6606
1497  −15 −2495 56025225 1 2 56 56 1 56  ε_{1} 62.8769
7485  −3 −2495 56025225 2 1 56 56 1 28  ε_{1} 36.4801
7485  −15 −499 56025225 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 18.2400
33 −227 −7491 56115081 1 5 16 40 1 40  ε_{1} 7.6563
681  −11 −7491 56115081 1 1 16  8 1  8  ε_{1} 61.3969
2497  −3 −7491 56115081 1 1 16  8 1  8  ε_{1} 117.8419
1873  −4 −7492 56130064 1 1 12  6 1  6  ε_{1} 122.3244
7493  −59 −127 56145049 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 14.6841
5 −1499 −7495 56175025 1 13 48 312 1 312  ε_{1} 0.9624
937 −8 −7496 56190016 1 1 56 28 1 28 ε_{1} 69.0381
41 −183 −7503 56295009 1 8 40 160 1 160  ε_{1} 8.3183
61 −123 −7503 56295009 1 2 40 40 1 40  ε_{1} 7.3284
2501  −3 −7503 56295009 4 1 40 80 1 20  ε_{1} 9.2105
2501 −123 −183 56295009 4 2 8 32 1  8  ε_{1} 9.2105
8 −1876 −3752 56310016 1 16 16 128 1 128  ε_{1} 1.7627
28 −536 −3752 56310016 1 14 16 112 1 112  ε_{1} 5.5373
56 −536 −1876 56310016 1 14 16 112 1 112  ε_{1} 6.8002
268  −56 −3752 56310016 1 4 16 32 1 32  ε_{1} 22.9790
536  −56 −1876 56310016 1 4 16 32 1 32  ε_{1} 25.1680
3752  −4 −3752 56310016 2 1 16 16 1  8  ε_{1} 20.8859

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 189

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3752  −8 −1876 56310016 2 1 16 16 1  8  ε_{1} 20.8859
1501  −95 −395 56325025 1 8 8 32 1 32  ε_{1} 43.6455
7505  −19 −395 56325025 4 1 8 16 1  4  ε_{1} 44.6010
7505  −79  −95 56325025 4 5 8 80 1 20  ε_{1} 44.6010
1877  −4 −7508 56370064 1 1 34 17 1 17  ε_{1} 14.7593
7509  −3 −2503 56385081 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 24.9484
29 −259 −7511 56415121 1 4 96 192 1 192  ε_{1} 3.2945
37 −203 −7511 56415121 1 4 96 192 1 192  ε_{1} 4.9836
1073  −7 −7511 56415121 2 1 96 96 1 48  ε_{1} 22.8314
1073 −203 −259 56415121 2 4 4 16 1  8  ε_{1} 22.8314
8 −939 −7512 56430144 1 8 24 96 1 96  ε_{1} 1.7627
24 −939 −2504 56430144 1 8 36 144 1 144  ε_{1} 4.5849
313  −24 −7512 56430144 1 2 24 24 1 24  ε_{1} 38.7035
2504  −3 −7512 56430144 4 1 24 48 1 12  ε_{1} 7.8248
2504  −24 −939 56430144 4 2 8 32 1  8  ε_{1} 7.8248
7512  −3 −2504 56430144 4 1 36 72 1 18  ε_{1} 20.8566
7512  −8 −939 56430144 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 10.4283
7513  −11 −683 56445169 5 1 5 25 2  5 \sqrt{−1}\sqrt{ε_{1}} 25.1731
7516  −4 −1879 56490256 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 81.2254
73 −103 −7519 56535361 1 5 50 125 1 125  ε_{1} 15.3334
69 −327 −2507 56565441 1 12 14 84 1 84  ε_{1} 6.4345
7521  −3 −2507 56565441 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 43.3204
7521 −23 −327 56565441 2 3 12 36 1 18 ε_{1} 86.6408
13 −579 −7527 56655729 1 8 40 160 1 160  ε_{1} 2.3895
193  −39 −7527 56655729 1 4 40 80 1 80  ε_{1} 30.1526
2509  −3 −7527 56655729 2 1 40 40 1 20  ε_{1} 30.0646
2509  −39 −579 56655729 2 4 8 32 1 16  ε_{1} 30.0646
941  −8 −7528 56670784 1 1 18  9 1  9  ε_{1} 14.0688
17 −443 −7531 56715961 1 5 24 60 1 60  ε_{1} 4.1894
28 −1076 −1883 56731024 1 22 14 154 1 154  ε_{1} 5.5373
7532  −4 −1883 56731024 2 1 14 14 1  7  ε_{1} 19.0138
7532  −7 −1076 56731024 2 1 22 22 1 11  ε_{1} 19.0138
5 −1507 −7535 56776225 1 4 96 192 1 192  ε_{1} 0.9624
137  −55 −7535 56776225 1 4 96 192 1 192  ε_{1} 16.3142
685  −11 −7535 56776225 2 1 96 96 1 48  ε_{1} 13.2640
685  −55 −1507 56776225 2 4 4 16 1  8  ε_{1} 13.2640
12 −1256 −3768 56791296 1 26 12 156 1 156  ε_{1} 2.6339
24 −628 −3768 56791296 1 6 12 36 1 36  ε_{1} 4.5849
1884  −8 −3768 56791296 2 1 12 12 1  6  ε_{1} 33.1355
1884  −24 −1256 56791296 2 2 26 52 1 26  ε_{1} 33.1355
3768  −4 −3768 56791296 2 1 12 12 1  6  ε_{1} 24.5312
3768  −24 −628 56791296 2 2 6 12 1  6  ε_{1} 24.5312
21 −359 −7539 56836521 1 19 28 266 1 266  ε_{1} 3.1336
1077  −7 −7539 56836521 1 1 28 14 1 14  ε_{1} 11.7777
2513  −3 −7539 56836521 1 1 28 14 1 14  ε_{1} 74.9293
5 −1508 −7540 56851600 1 16 16 128 1 128  ε_{1} 0.9624
13 −580 −7540 56851600 1 8 16 64 1 64  ε_{1} 2.3895
29 −260 −7540 56851600 1 8 16 64 1 64  ε_{1} 3.2945
65 −116 −7540 56851600 2 6 16 96 1 48  ε_{1} 5.5529
65 −580 −1508 56851600 2 8 16 128 1 64  ε_{1} 5.5529

190 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
145  −52 −7540 56851600 4 2 16 64 1 16  ε_{1} 6.3596
145 −260 −1508 56851600 4 8 16 256 1 64  ε_{1} 6.3596
377 −20 −7540 56851600 2 2 16 32 1 16 ε_{1} 12.2884
377 −260 −580 56851600 2 8 8 64 1 32  ε_{1} 12.2884
1885  −4 −7540 56851600 4 1 16 32 1  8  ε_{1} 13.8978
1885  −20 −1508 56851600 4 2 16 64 1 16  ε_{1} 13.8978
1885  −52 −580 56851600 4 2 8 32 1  8  ε_{1} 13.8978
1885 −116 −260 56851600 4 6 8 192 2 48 \sqrt{−1}\sqrt{ε_{1}} 6.9489
397 −19 −7543 56896849 1 1 36 18 1 18 ε_{1} 16.2905
8 −943 −7544 56911936 1 16 64 512 1 512  ε_{1} 1.7627
41 −184 −7544 56911936 1 4 64 128 1 128  ε_{1} 8.3183
184 −328 −943 56911936 1 4 16 32 1 32  ε_{1} 21.5856
328 −23 −7544 56911936 4 3 64 384 1 96 ε_{1} 5.7869
328 −184 −943 56911936 4 4 16 128 1 32  ε_{1} 5.7869
7544  −8 −943 56911936 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 12.1272
7544  −23 −328 56911936 4 3 4 24 1  6  ε_{1} 24.2544
1509  −15 −2515 56927025 3 2 6 18 1  6  ε_{1} 12.4491
7545  −3 −2515 56927025 2 1 6  6 1  3  ε_{1} 66.1579
7545  −15 −503 56927025 2 2 21 42 1 21  ε_{1} 66.1579
12 −1887 −2516 56972304 1 20 36 360 1 360  ε_{1} 2.6339
204 −111 −2516 56972304 2 8 36 288 1 144  ε_{1} 9.2101
204 −148 −1887 56972304 2 2 20 40 1 20  ε_{1} 9.2101
444  −51 −2516 56972304 2 2 36 72 1 36  ε_{1} 12.7602
444  −68 −1887 56972304 2 4 20 80 1 40  ε_{1} 12.7602
7548  −3 −2516 56972304 4 1 36 72 1 18  ε_{1} 19.5945
7548  −4 −1887 56972304 4 1 20 40 1 10  ε_{1} 19.5945
7548  −51 −148 56972304 4 2 2  8 1  2  ε_{1} 19.5945
7548  −68 −111 56972304 4 4 8 64 1 16  ε_{1} 19.5945
581  −91 −1079 57047809 1 2 34 34 1 34  ε_{1} 17.6272
7553  −7 −1079 57047809 2 1 34 34 1 17  ε_{1} 49.1396
7553  −83  −91 57047809 2 3 2  6 1  3  ε_{1} 49.1396
5 −1511 −7555 57078025 1 49 12 294 1 294  ε_{1} 0.9624
1889 −4 −7556 57093136 1 1 72 36 1 36 ε_{1} 73.3811
33 −687 −2519 57108249 1 12 64 384 1 384  ε_{1} 7.6563
7557  −3 −2519 57108249 4 1 64 256 2 64 \sqrt{−1}\sqrt{ε_{1}} 7.8324
7557  −11 −687 57108249 4 1 12 24 1  6  ε_{1} 15.6648
2521  −3 −7563 57198969 1 1 24 12 1 12  ε_{1} 171.5360
124 −244 −1891 57214096 1 6 10 30 1 30  ε_{1} 16.0392
7564  −4 −1891 57214096 2 1 10 10 1  5  ε_{1} 83.8803
7564  −31 −244 57214096 2 3 6 18 1  9  ε_{1} 83.8803
161  −47 −7567 57259489 1 5 44 110 1 110  ε_{1} 20.1338
329  −23 −7567 57259489 1 3 44 66 1 66  ε_{1} 30.7485
1081  −7 −7567 57259489 1 1 44 22 1 22  ε_{1} 95.6412
8 −1892 −3784 57274624 1 12 16 96 1 96  ε_{1} 1.7627
44 −344 −3784 57274624 1 10 16 80 1 80  ε_{1} 5.9864
88 −344 −1892 57274624 1 10 12 60 1 60  ε_{1} 11.9527
172  −88 −3784 57274624 1 2 16 16 1 16  ε_{1} 17.6970
344  −88 −1892 57274624 1 2 12 12 1 12  ε_{1} 19.8864
3784  −4 −3784 57274624 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 32.1358
3784  −8 −1892 57274624 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 32.1358

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 191

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
113  −67 −7571 57320041 1 1 18  9 1  9  ε_{1} 14.6946
12 −631 −7572 57335184 1 13 20 130 1 130  ε_{1} 2.6339
1893  −4 −7572 57335184 1 1 20 10 1 10  ε_{1} 18.4394
2524  −3 −7572 57335184 1 1 20 10 1 10  ε_{1} 105.8769
8 −947 −7576 57395776 1 5 30 75 1 75  ε_{1} 1.7627
7576 −8 −947 57395776 1 1 5 5 2 5 \sqrt{−1}\sqrt{ε_{1}} 89.0081
13 −583 −7579 57441241 1 8 16 64 1 64  ε_{1} 2.3895
53 −143 −7579 57441241 1 10 16 80 1 80  ε_{1} 3.9314
689 −11 −7579 57441241 4 1 16 32 1 8 ε_{1} 10.6942
689 −143 −583 57441241 4 10 8 160 1 40  ε_{1} 10.6942
1516  −20 −1895 57456400 1 2 48 48 1 48  ε_{1} 75.5847
7580  −4 −1895 57456400 2 1 48 48 1 24  ε_{1} 37.0265
7580  −20 −379 57456400 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 18.5133
28 −271 −7588 57577744 1 11 16 88 1 88  ε_{1} 5.5373
1084  −7 −7588 57577744 1 1 16  8 1  8  ε_{1} 52.3396
1897  −4 −7588 57577744 5 1 16 40 1  8  ε_{1} 22.7658
13 −584 −7592 57638464 1 16 28 224 1 224  ε_{1} 2.3895
73 −104 −7592 57638464 1 6 28 84 1 84  ε_{1} 15.3334
949 −8 −7592 57638464 2 1 28 28 1 14 ε_{1} 20.7893
949 −104 −584 57638464 2 6 16 96 1 48  ε_{1} 20.7893
7593  −3 −2531 57653649 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 72.8599
7597  −71 −107 57714409 1 7 3 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 40.9140
17 −447 −7599 57744801 1 14 52 364 1 364  ε_{1} 4.1894
149  −51 −7599 57744801 1 2 52 52 1 52  ε_{1} 8.2223
2533  −3 −7599 57744801 4 1 52 104 1 26  ε_{1} 10.0345
2533  −51 −447 57744801 4 2 14 56 1 14  ε_{1} 10.0345
7601  −11 −691 57775201 3 1 5 15 2  5 \sqrt{−1}\sqrt{ε_{1}} 26.9557
1901  −4 −7604 57820816 3 1 42 63 1 21  ε_{1} 12.1553
8 −951 −7608 57881664 1 26 36 468 1 468  ε_{1} 1.7627
24 −951 −2536 57881664 1 26 14 182 1 182  ε_{1} 4.5849
317  −24 −7608 57881664 1 2 36 36 1 36  ε_{1} 8.9775
2536  −3 −7608 57881664 2 1 36 36 1 18  ε_{1} 51.2121
2536  −24 −951 57881664 2 2 26 52 1 26  ε_{1} 51.2121
7608  −3 −2536 57881664 2 1 14 14 1  7  ε_{1} 31.1092
7608  −8 −951 57881664 2 1 26 26 1 13  ε_{1} 31.1092
7609  −7 −1087 57896881 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 148.7296
129  −59 −7611 57927321 1 3 20 30 1 30  ε_{1} 20.8511
177  −43 −7611 57927321 1 1 20 10 1 10  ε_{1} 23.4697
2537  −3 −7611 57927321 1 1 20 10 1 10  ε_{1} 47.0592
44 −692 −1903 57942544 1 14 22 154 1 154  ε_{1} 5.9864
7612  −4 −1903 57942544 2 1 22 22 1 11  ε_{1} 42.5658
7612  −11 −692 57942544 2 1 14 14 1  7  ε_{1} 42.5658
7613  −23 −331 57957769 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 18.2273
5 −1523 −7615 57988225 1 7 50 175 1 175  ε_{1} 0.9624
7617  −3 −2539 58018689 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 104.2719
401 −19 −7619 58049161 5 1 46 115 1 23 ε_{1} 7.3790
5 −1524 −7620 58064400 1 20 24 240 1 240  ε_{1} 0.9624
12 −635 −7620 58064400 1 10 24 120 1 120  ε_{1} 2.6339
60 −127 −7620 58064400 2 5 24 120 1 60  ε_{1} 4.1269
60 −635 −1524 58064400 2 10 20 200 1 100  ε_{1} 4.1269

192 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
381  −20 −7620 58064400 1 2 24 24 1 24  ε_{1} 15.2316
508  −15 −7620 58064400 1 2 24 24 1 24  ε_{1} 32.1254
1905  −4 −7620 58064400 2 1 24 24 1 12  ε_{1} 47.5752
1905  −20 −1524 58064400 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 23.7876
2540  −3 −7620 58064400 2 1 24 24 1 12  ε_{1} 11.0588
2540  −15 −1524 58064400 2 2 20 40 1 20  ε_{1} 11.0588
953  −8 −7624 58125376 1 1 20 10 1 10  ε_{1} 44.8537
29 −263 −7627 58171129 1 13 10 65 1 65  ε_{1} 3.2945
7628 −4 −1907 58186384 3 1 13 39 2 13 \sqrt{i}\sqrt{ε_{1}} 10.4436
7629  −3 −2543 58201641 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 26.6857
13 −587 −7631 58232161 1 7 106 371 1 371  ε_{1} 2.3895
5 −1527 −7635 58293225 1 14 20 140 1 140  ε_{1} 0.9624
509  −15 −7635 58293225 1 2 20 20 1 20  ε_{1} 13.6596
2545  −3 −7635 58293225 4 1 20 40 1 10  ε_{1} 40.6241
2545  −15 −1527 58293225 4 2 14 56 1 14  ε_{1} 40.6241
92  −83 −7636 58308496 1 3 28 42 1 42  ε_{1} 7.7415
332  −23 −7636 58308496 1 3 28 42 1 42  ε_{1} 10.1997
1909  −4 −7636 58308496 1 1 28 14 1 14  ε_{1} 44.5676
7637  −7 −1091 58323769 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 17.1327
5 −1528 −7640 58369600 1 8 56 224 1 224  ε_{1} 0.9624
8 −955 −7640 58369600 1 4 56 112 1 112  ε_{1} 1.7627
40 −191 −7640 58369600 2 13 56 728 1 364  ε_{1} 3.6369
40 −955 −1528 58369600 2 4  8 32 1 16  ε_{1} 3.6369
1528  −40 −955 58369600 1 2  4  4 1  4  ε_{1} 53.0447
7640  −8 −955 58369600 2 1  4  4 1  2  ε_{1} 26.4605
7640  −40 −191 58369600 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 13.2302
1529  −55 −695 58446025 1 4 24 48 1 48  ε_{1} 65.2096
7645  −11 −695 58446025 4 1 24 48 1 12  ε_{1} 27.2958
7645  −55 −139 58446025 4 4  3 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 13.6479
2549  −3 −7647 58476609 1 1 66 33 1 33  ε_{1} 36.3065
1093  −7 −7651 58537801 5 1 20 50 1 10  ε_{1} 6.9948
1913  −4 −7652 58553104 1 1 36 18 1 18  ε_{1} 59.7641
7653  −3 −2551 58568409 1 1 41 41 2 41 \sqrt{−1}\sqrt{ε_{1}} 20.8677
5 −1531 −7655 58599025 1 11 76 418 1 418  ε_{1} 0.9624
24 −319 −7656 58614336 1 10 48 240 1 240  ε_{1} 4.5849
29 −264 −7656 58614336 1 8 48 192 1 192  ε_{1} 3.2945
33 −232 −7656 58614336 1 2 48 48 1 48  ε_{1} 7.6563
33 −696 −2552 58614336 1 12 20 120 1 120  ε_{1} 7.6563
88  −87 −7656 58614336 1 6 48 144 1 144  ε_{1} 11.9527
264  −87 −2552 58614336 2 6 20 120 1 60  ε_{1} 9.7350
264 −319 −696 58614336 2 10 12 120 1 60  ε_{1} 9.7350
696 −11 −7656 58614336 2 1 48 48 1 24 ε_{1} 15.9463
696 −264 −319 58614336 2 8 10 80 1 40  ε_{1} 15.9463
957  −8 −7656 58614336 2 1 48 48 1 24  ε_{1} 6.8659
957  −24 −2552 58614336 2 2 20 40 1 20  ε_{1} 6.8659
957  −88 −696 58614336 2 2 12 24 1 12  ε_{1} 6.8659
957 −232 −264 58614336 2 2  8 16 1  8  ε_{1} 6.8659
2552  −3 −7656 58614336 2 1 48 48 1 24  ε_{1} 22.6906
2552  −87 −264 58614336 2 6  8 48 1 24  ε_{1} 22.6906
7656  −3 −2552 58614336 8 1 20 80 1 10  ε_{1} 11.7158

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 193

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7656  −11 −696 58614336 8 1 12 48 1  6  ε_{1} 11.7158
7656  −24 −319 58614336 8 2 10 80 1 10  ε_{1} 11.7158
7656  −87  −88 58614336 8 6  2 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.8579
589 −247 −403 58629649 1 6  2  6 1  6  ε_{1} 30.5757
7657  −19 −403 58629649 2 1  2  2 1  1  ε_{1} 101.2694
7657  −31 −247 58629649 2 3  6 18 1  9  ε_{1} 101.2694
1532  −20 −1915 58675600 1 2  6  6 1  6  ε_{1} 21.0661
7660  −4 −1915 58675600 2 1  6  6 1  3  ε_{1} 84.3329
7660  −20 −383 58675600 2 2 17 34 1 17  ε_{1} 84.3329
7661  −47 −163 58690921 1 5  1  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 30.7744
97  −79 −7663 58721569 1 5 44 110 1 110  ε_{1} 18.6488
1916  −8 −3832 58736896 1 1 16 16 2 16 \sqrt{−1}\sqrt{ε_{1}} 15.6037
3832 −4 −3832 58736896 1 1 16 16 2 16 \sqrt{i}\sqrt{ε_{1}} 38.0511
21 −1095 −2555 58752225 1 28 12 168 1 168  ε_{1} 3.1336
105 −219 −2555 58752225 2 4 12 48 1 24  ε_{1} 8.8131
105 −511 −1095 58752225 2 14 28 392 1 196  ε_{1} 8.8131
1533  −15 −2555 58752225 2 2 12 24 1 12  ε_{1} 12.4649
1533  −35 −1095 58752225 2 2 28 56 1 28  ε_{1} 12.4649
7665  −3 −2555 58752225 12 1 12 72 1  6  ε_{1} 16.3222
7665  −7 −1095 58752225 12 1 28 168 1 14  ε_{1} 16.3222
7665  −15 −511 58752225 12 2 14 168 1 14  ε_{1} 16.3222
7665  −35 −219 58752225 12 2  4 96 2  8 \sqrt{−1}\sqrt{ε_{1}} 8.1611
17 −451 −7667 58782889 1 6 20 60 1 60  ε_{1} 4.1894
41 −187 −7667 58782889 1 2 20 20 1 20  ε_{1} 8.3183
697  −11 −7667 58782889 6 1 20 60 1 10  ε_{1} 11.1519
697 −187 −451 58782889 6 2  6 36 1  6  ε_{1} 11.1519
2557  −3 −7671 58844241 3 1 84 126 1 42  ε_{1} 19.0946
8 −959 −7672 58859584 1 36 16 288 1 288  ε_{1} 1.7627
56 −959 −1096 58859584 1 36 12 216 1 216  ε_{1} 6.8002
137  −56 −7672 58859584 1 4 16 32 1 32  ε_{1} 16.3142
1096  −7 −7672 58859584 4 1 16 32 1  8  ε_{1} 15.8847
1096  −56 −959 58859584 4 4 36 288 1 72  ε_{1} 15.8847
7672  −7 −1096 58859584 4 1 12 24 1  6  ε_{1} 27.2668
7672  −8 −959 58859584 4 1 36 72 1 18  ε_{1} 27.2668
76 −404 −1919 58920976 1 14 44 308 1 308  ε_{1} 11.6579
7676 −4 −1919 58920976 2 1 44 44 1 22 ε_{1} 51.5268
7676  −19 −404 58920976 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 25.7634
1097 −7 −7679 58967041 1 1 106 53 1 53 ε_{1} 35.1082
13 −591 −7683 59028489 1 22 12 132 1 132  ε_{1} 2.3895
197  −39 −7683 59028489 1 4 12 24 1 24  ε_{1} 6.6670
2561  −3 −7683 59028489 2 1 12 12 1  6  ε_{1} 44.2362
2561  −39 −591 59028489 2 4 22 88 1 44  ε_{1} 44.2362
17 −452 −7684 59043856 1 8 40 160 1 160  ε_{1} 4.1894
113  −68 −7684 59043856 1 4 40 80 1 80  ε_{1} 14.6946
1921  −4 −7684 59043856 2 1 40 40 1 20  ε_{1} 65.1846
1921  −68 −452 59043856 2 4  8 32 1 16  ε_{1} 65.1846
33 −699 −2563 59120721 1 10  6 30 1 30  ε_{1} 7.6563
7689  −3 −2563 59120721 2 1  6  6 1  3  ε_{1} 89.3416
7689  −11 −699 59120721 2 1 10 10 1  5  ε_{1} 89.3416
12 −1923 −2564 59166864 1 10 28 140 1 140  ε_{1} 2.6339

194 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7692  −3 −2564 59166864 2 1 28 28 1 14  ε_{1} 45.7811
7692  −4 −1923 59166864 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 22.8905
8 −1924 −3848 59228416 1 16 28 224 1 224  ε_{1} 1.7627
104 −148 −3848 59228416 2 2 28 56 1 28  ε_{1} 4.6249
104 −296 −1924 59228416 2 10 16 160 1 80  ε_{1} 4.6249
296 −52 −3848 59228416 2 2 28 56 1 28 ε_{1} 8.9090
296 −104 −1924 59228416 2 6 16 96 1 48  ε_{1} 8.9090
3848  −4 −3848 59228416 4 1 28 56 1 14  ε_{1} 8.2548
3848  −8 −1924 59228416 4 1 16 32 1  8  ε_{1} 8.2548
3848  −52 −296 59228416 4 2 10 40 1 10  ε_{1} 8.2548
3848 −104 −148 59228416 4 6 2 24 1  6  ε_{1} 8.2548
7697  −43 −179 59243809 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 64.1512
453  −51 −2567 59305401 1 2 44 44 1 44  ε_{1} 10.0078
7701  −3 −2567 59305401 2 1 44 44 1 22  ε_{1} 44.2564
7701  −51 −151 59305401 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 22.1282
1541 −115 −335 59367025 1 2 18 18 1 18  ε_{1} 27.9708
7705  −23 −335 59367025 10 3 18 270 1 27  ε_{1} 26.2419
7705  −67 −115 59367025 10 1 2 10 1  1  ε_{1} 26.2419
21 −367 −7707 59397849 1 9 16 72 1 72  ε_{1} 3.1336
1101  −7 −7707 59397849 3 1 16 24 1  8  ε_{1} 11.7998
2569  −3 −7707 59397849 1 1 16  8 1  8  ε_{1} 162.1424
188 −164 −1927 59413264 1 8 18 72 1 72  ε_{1} 9.1285
7708  −4 −1927 59413264 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 32.1666
7708  −47 −164 59413264 2 5 8 40 1 20  ε_{1} 64.3331
701  −11 −7711 59459521 1 1 34 17 1 17  ε_{1} 20.1350
5 −1543 −7715 59521225 1 19 18 171 1 171  ε_{1} 0.9624
12 −643 −7716 59536656 1 3 28 42 1 42  ε_{1} 2.6339
1929  −4 −7716 59536656 3 1 28 42 1 14  ε_{1} 38.7025
2572  −3 −7716 59536656 1 1 28 14 1 14  ε_{1} 58.0236
93  −83 −7719 59582961 1 3 96 144 1 144  ε_{1} 6.7322
249  −31 −7719 59582961 1 3 96 144 1 144  ε_{1} 33.3101
2573  −3 −7719 59582961 1 1 96 48 1 48  ε_{1} 21.2020
5 −1544 −7720 59598400 1 20 20 200 1 200  ε_{1} 0.9624
193  −40 −7720 59598400 1 2 20 20 1 20  ε_{1} 30.1526
965  −8 −7720 59598400 2 1 20 20 1 10  ε_{1} 6.8701
965  −40 −1544 59598400 2 2 20 40 1 20  ε_{1} 6.8701
7721  −7 −1103 59613841 3 1 23 69 2 23 \sqrt{−1}\sqrt{ε_{1}} 29.0057
7724 −4 −1931 59660176 1 1 21 21 2 21 \sqrt{i}\sqrt{ε_{1}} 25.3943
12 −1288 −3864 59721984 1 8 24 96 1 96  ε_{1} 2.6339
24 −644 −3864 59721984 1 16 24 192 1 192  ε_{1} 4.5849
28 −552 −3864 59721984 1 8 24 96 1 96  ε_{1} 5.5373
56 −276 −3864 59721984 1 8 24 96 1 96  ε_{1} 6.8002
92 −168 −3864 59721984 1 4 24 48 1 48  ε_{1} 7.7415
168 −276 −1288 59721984 2 8 8 64 1 32  ε_{1} 6.5132
168 −552 −644 59721984 2 8 16 128 1 64  ε_{1} 6.5132
184  −84 −3864 59721984 1 4 24 48 1 48  ε_{1} 21.5856
552  −84 −1288 59721984 2 4 8 32 1 16  ε_{1} 9.0864
552 −168 −644 59721984 2 4 16 64 1 32  ε_{1} 9.0864
1288 −84 −552 59721984 4 4 8 64 1 16 ε_{1} 12.9416
1288 −168 −276 59721984 4 4 8 64 1 16  ε_{1} 12.9416

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 195

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1932  −8 −3864 59721984 4 1 24 48 1 12  ε_{1} 7.5673
1932  −24 −1288 59721984 4 2  8 32 1  8  ε_{1} 7.5673
1932  −56 −552 59721984 4 4  8 64 1 16  ε_{1} 7.5673
1932 −168 −184 59721984 4 4  4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 3.7837
3864  −4 −3864 59721984 4 1 24 48 1 12  ε_{1} 23.3053
3864  −24 −644 59721984 4 2 16 64 1 16  ε_{1} 23.3053
3864  −56 −276 59721984 4 4  8 64 1 16  ε_{1} 23.3053
3864  −84 −184 59721984 4 4  4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 11.6527
7729  −59 −131 59737441 1 3  5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 153.2507
1933  −4 −7732 59783824 1 1 18  9 1  9  ε_{1} 41.0311
209 −407 −703 59799289 1 16 14 112 1 112  ε_{1} 22.8829
7733  −11 −703 59799289 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 7.9424
7733 −19 −407 59799289 2 1 16 16 1 8 ε_{1} 15.8847
5 −1547 −7735 59830225 1 12 48 288 1 288  ε_{1} 0.9624
13 −595 −7735 59830225 1 4 48 96 1 96  ε_{1} 2.3895
17 −455 −7735 59830225 1 20 48 480 1 480  ε_{1} 4.1894
65 −119 −7735 59830225 2 10 48 480 1 240  ε_{1} 5.5529
65 −595 −1547 59830225 2 4 12 48 1 24  ε_{1} 5.5529
85 −91 −7735 59830225 2 2 48 96 1 48 ε_{1} 4.4187
85 −455 −1547 59830225 2 20 12 240 1 120  ε_{1} 4.4187
221  −35 −7735 59830225 2 2 48 96 1 48  ε_{1} 5.4072
221 −455 −595 59830225 2 20  4 80 1 40  ε_{1} 5.4072
1105  −7 −7735 59830225 4 1 48 96 1 24  ε_{1} 21.9008
1105  −35 −1547 59830225 4 2 12 48 1 12  ε_{1} 21.9008
1105  −91 −595 59830225 4 2  4 16 1  4  ε_{1} 21.9008
1105 −119 −455 59830225 4 10 20 400 1 100  ε_{1} 21.9008
8 −967 −7736 59845696 1 11 52 286 1 286  ε_{1} 1.7627
7736  −8 −967 59845696 7 1 11 77 2 11 \sqrt{−1}\sqrt{ε_{1}} 8.2610
7737  −3 −2579 59861169 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 99.2661
109 −71 −7739 59892121 1 7 40 140 1 140 ε_{1} 11.1291
29 −267 −7743 59954049 1 2 52 52 1 52  ε_{1} 3.2945
89  −87 −7743 59954049 1 6 52 156 1 156  ε_{1} 13.8155
2581  −3 −7743 59954049 2 1 52 52 1 26  ε_{1} 25.3595
2581  −87 −267 59954049 2 6  2 12 1  6  ε_{1} 25.3595
61 −127 −7747 60016009 1 5 16 40 1 40  ε_{1} 7.3284
13 −596 −7748 60031504 1 14 48 336 1 336  ε_{1} 2.3895
149  −52 −7748 60031504 1 2 48 48 1 48  ε_{1} 8.2223
1937  −4 −7748 60031504 6 1 48 144 1 24  ε_{1} 8.9549
1937  −52 −596 60031504 6 2 14 84 1 14  ε_{1} 8.9549
337  −23 −7751 60078001 1 3 110 165 1 165  ε_{1} 42.8642
17 −456 −7752 60093504 1 8 32 128 1 128  ε_{1} 4.1894
24 −323 −7752 60093504 1 4 32 64 1 64  ε_{1} 4.5849
57 −136 −7752 60093504 1 4 32 64 1 64  ε_{1} 11.4208
57 −408 −2584 60093504 1 4 16 32 1 32  ε_{1} 11.4208
152  −51 −7752 60093504 1 2 32 32 1 32  ε_{1} 8.6078
408  −19 −7752 60093504 2 1 32 32 1 16  ε_{1} 10.6165
408 −323 −456 60093504 2 4  8 32 1 16  ε_{1} 10.6165
456  −51 −2584 60093504 2 2 16 32 1 16  ε_{1} 15.2512
456 −323 −408 60093504 2 4  4 16 1  8  ε_{1} 15.2512
969  −8 −7752 60093504 2 1 32 32 1 16  ε_{1} 34.2358

196 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
969  −24 −2584 60093504 2 2 16 32 1 16  ε_{1} 34.2358
969 −136 −456 60093504 2 4 8 32 1 16  ε_{1} 34.2358
969 −152 −408 60093504 2 6 4 24 1 12  ε_{1} 34.2358
2584  −3 −7752 60093504 8 1 32 128 1 16  ε_{1} 12.8269
2584  −51 −456 60093504 8 2 8 64 1  8  ε_{1} 12.8269
7752  −3 −2584 60093504 4 1 16 32 1  8  ε_{1} 16.5241
7752  −19 −408 60093504 4 1 4  8 1  2  ε_{1} 16.5241
7752  −24 −323 60093504 4 2 4 16 1  4  ε_{1} 16.5241
7752  −51 −152 60093504 4 2 6 24 1  6  ε_{1} 16.5241
5 −1551 −7755 60140025 1 32 16 256 1 256  ε_{1} 0.9624
33 −235 −7755 60140025 1 2 16 16 1 16  ε_{1} 7.6563
141  −55 −7755 60140025 1 4 16 32 1 32  ε_{1} 10.4940
165  −47 −7755 60140025 2 5 16 80 1 40  ε_{1} 5.1180
165 −235 −1551 60140025 2 2 32 64 1 32  ε_{1} 5.1180
517  −15 −7755 60140025 1 2 16 16 1 16  ε_{1} 18.5321
705  −11 −7755 60140025 2 1 16 16 1  8  ε_{1} 26.1393
705  −55 −1551 60140025 2 4 32 128 1 64  ε_{1} 26.1393
2585  −3 −7755 60140025 2 1 16 16 1  8  ε_{1} 45.7146
2585  −15 −1551 60140025 2 2 32 64 1 32  ε_{1} 45.7146
28 −1108 −1939 60155536 1 6 8 24 1 24  ε_{1} 5.5373
7756  −4 −1939 60155536 2 1 8  8 1  4  ε_{1} 88.0752
7756  −7 −1108 60155536 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 44.0376
8 −1940 −3880 60217600 1 20 12 120 1 120  ε_{1} 1.7627
40 −388 −3880 60217600 2 4 12 48 1 24  ε_{1} 3.6369
40 −776 −1940 60217600 2 20 20 400 1 200  ε_{1} 3.6369
776  −20 −3880 60217600 2 2 12 24 1 12  ε_{1} 11.9323
776  −40 −1940 60217600 2 2 20 40 1 20  ε_{1} 11.9323
3880  −4 −3880 60217600 4 1 12 24 1  6  ε_{1} 26.7889
3880  −8 −1940 60217600 4 1 20 40 1 10  ε_{1} 26.7889
3880  −20 −776 60217600 4 2 20 80 1 20  ε_{1} 26.7889
3880  −40 −388 60217600 4 2 4 16 1  4  ε_{1} 26.7889
597  −39 −2587 60233121 1 4 8 16 1 16  ε_{1} 18.3698
7761  −3 −2587 60233121 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 23.8737
7761  −39 −199 60233121 4 4 9 72 1 18  ε_{1} 47.7473
1109  −7 −7763 60264169 1 1 22 11 1 11  ε_{1} 23.1586
12 −647 −7764 60279696 1 23 24 276 1 276  ε_{1} 2.6339
1941  −4 −7764 60279696 1 1 24 12 1 12  ε_{1} 46.1538
2588  −3 −7764 60279696 1 1 24 12 1 12  ε_{1} 38.5954
8 −971 −7768 60341824 1 15 22 165 1 165  ε_{1} 1.7627
7768  −8 −971 60341824 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 44.0833
409 −19 −7771 60388441 1 1 18 9 1 9 ε_{1} 52.2684
268 −116 −1943 60403984 1 6 32 96 1 96  ε_{1} 22.9790
7772  −4 −1943 60403984 2 1 32 32 1 16  ε_{1} 24.0575
7772  −67 −116 60403984 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 12.0288
7773  −3 −2591 60419529 1 1 57 57 2 57 \sqrt{−1}\sqrt{ε_{1}} 19.8774
77 −707 −1111 60481729 1 6 22 66 1 66  ε_{1} 4.3693
7777  −7 −1111 60481729 2 1 22 22 1 11  ε_{1} 125.6538
7777  −11 −707 60481729 2 1 6  6 1  3  ε_{1} 125.6538
2593  −3 −7779 60512841 1 1 24 12 1 12  ε_{1} 108.9624
5 −1556 −7780 60528400 1 22 16 176 1 176  ε_{1} 0.9624

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 197

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
389  −20 −7780 60528400 1 2 16 16 1 16  ε_{1} 15.6986
1945  −4 −7780 60528400 2 1 16 16 1  8  ε_{1} 58.5840
1945  −20 −1556 60528400 2 2 22 88 2 44 \sqrt{−1}\sqrt{ε_{1}} 29.2920
7781  −31 −251 60543961 1 3 7 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 31.3010
181 −43 −7783 60575089 1 1 44 22 1 22 ε_{1} 14.3479
56 −139 −7784 60590656 1 3 68 102 1 102  ε_{1} 6.8002
973  −8 −7784 60590656 1 1 68 34 1 34  ε_{1} 28.8137
973  −56 −1112 60590656 1 4 14 28 1 28  ε_{1} 28.8137
1112  −7 −7784 60590656 1 1 68 34 1 34  ε_{1} 17.0352
7784  −7 −1112 60590656 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 19.3066
7784 −56 −139 60590656 2 4 3 12 1 6 ε_{1} 38.6131
13 −599 −7787 60637369 1 25 28 350 1 350  ε_{1} 2.3895
12 −1947 −2596 60652944 1 8 20 80 1 80  ε_{1} 2.6339
33 −708 −2596 60652944 1 4 20 40 1 40  ε_{1} 7.6563
44 −708 −1947 60652944 1 4 8 16 1 16  ε_{1} 5.9864
177 −132 −2596 60652944 1 4 20 40 1 40  ε_{1} 23.4697
236 −132 −1947 60652944 1 4 8 16 1 16  ε_{1} 13.9320
649 −132 −708 60652944 1 4 4  8 1  8  ε_{1} 70.6969
7788  −3 −2596 60652944 8 1 20 80 1 10  ε_{1} 13.1192
7788  −4 −1947 60652944 8 1 8 32 1  4  ε_{1} 13.1192
7788  −11 −708 60652944 8 1 4 32 2  4 \sqrt{−1}\sqrt{ε_{1}} 6.5596
7788  −59 −132 60652944 8 3 4 48 1  6  ε_{1} 13.1192
1948  −8 −3896 60715264 1 1 36 36 2 36 \sqrt{−1}\sqrt{ε_{1}} 32.2736
3896 −4 −3896 60715264 1 1 36 36 2 36 \sqrt{i}\sqrt{ε_{1}} 34.5162
5 −1559 −7795 60762025 1 51 16 408 1 408  ε_{1} 0.9624
1949 −4 −7796 60777616 1 1 70 35 1 35 ε_{1} 24.0447
69 −339 −2599 60793209 1 6 30 90 1 90  ε_{1} 6.4345
7797  −3 −2599 60793209 2 1 30 30 1 15  ε_{1} 29.3062
7797  −23 −339 60793209 2 3 6 18 1  9  ε_{1} 29.3062
709  −11 −7799 60824401 1 1 96 48 1 48  ε_{1} 34.8251
7804  −4 −1951 60902416 1 1 33 33 2 33  \sqrt{i}\sqrt{ε_{1}} 82.1023
1561  −35 −1115 60918025 1 2 10 10 1 10  ε_{1} 122.1985
7805  −7 −1115 60918025 2 1 10 10 1  5  ε_{1} 19.1003
7805  −35 −223 60918025 2 2 7 14 1  7  ε_{1} 19.1003
37 −211 −7807 60949249 1 3 36 54 1 54  ε_{1} 4.9836
57 −411 −2603 60980481 1 6 20 60 1 60  ε_{1} 11.4208
7809  −3 −2603 60980481 2 1 20 20 1 10  ε_{1} 119.9094
7809  −19 −411 60980481 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 59.9547
73 −107 −7811 61011721 1 3 42 63 1 63  ε_{1} 15.3334
5 −1563 −7815 61074225 1 6 52 156 1 156  ε_{1} 0.9624
521  −15 −7815 61074225 1 2 52 52 1 52  ε_{1} 38.7273
2605  −3 −7815 61074225 8 1 52 208 1 26  ε_{1} 7.8644
2605  −15 −1563 61074225 8 2 6 48 1  6  ε_{1} 7.8644
977  −8 −7816 61089856 1 1 28 14 1 14  ε_{1} 46.8295
1117  −7 −7819 61136761 1 1 16  8 1  8  ε_{1} 31.6567
92 −340 −1955 61152400 1 4 12 24 1 24  ε_{1} 7.7415
460 −68 −1955 61152400 2 4 12 48 1 24 ε_{1} 15.4391
460 −340 −391 61152400 2 4 14 56 1 28  ε_{1} 15.4391
1564  −20 −1955 61152400 2 2 12 24 1 12  ε_{1} 33.0036
1564 −115 −340 61152400 2 2 4  8 1  4  ε_{1} 33.0036

198 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7820  −4 −1955 61152400 4 1 12 24 1  6  ε_{1} 17.3132
7820  −20 −391 61152400 4 2 14 56 1 14  ε_{1} 17.3132
7820  −23 −340 61152400 4 3 4 24 1  6  ε_{1} 17.3132
7820  −68 −115 61152400 4 4 2 16 1  4  ε_{1} 17.3132
8 −1956 −3912 61214976 1 20 24 240 1 240  ε_{1} 1.7627
12 −1304 −3912 61214976 1 22 24 264 1 264  ε_{1} 2.6339
24 −1304 −1956 61214976 1 22 20 220 1 220  ε_{1} 4.5849
652  −24 −3912 61214976 1 2 24 24 1 24  ε_{1} 37.3376
1304  −24 −1956 61214976 3 2 20 60 1 20  ε_{1} 12.9539
3912  −4 −3912 61214976 2 1 24 48 2 24  \sqrt{i}\sqrt{ε_{1}} 12.3744
3912  −8 −1956 61214976 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 12.3744
2609 −3 −7827 61261929 1 1 18 9 1 9 ε_{1} 88.6929
76 −103 −7828 61277584 1 5 16 40 1 40  ε_{1} 11.6579
412  −19 −7828 61277584 1 1 16  8 1  8  ε_{1} 26.0564
1957  −4 −7828 61277584 3 1 16 24 1  8  ε_{1} 13.6682
41 −191 −7831 61324561 1 13 66 429 1 429  ε_{1} 8.3183
8 −979 −7832 61340224 1 8 32 128 1 128  ε_{1} 1.7627
88 −712 −979 61340224 1 8 8 32 1 32  ε_{1} 11.9527
89  −88 −7832 61340224 1 2 32 32 1 32  ε_{1} 13.8155
712  −11 −7832 61340224 2 1 32 32 1 16  ε_{1} 16.1431
712  −88 −979 61340224 2 2 8 16 1  8  ε_{1} 16.1431
7832  −8 −979 61340224 4 1 8 16 1  4  ε_{1} 11.7386
7832  −11 −712 61340224 4 1 8 16 1  4  ε_{1} 11.7386
21 −1119 −2611 61355889 1 32 8 128 1 128  ε_{1} 3.1336
7833  −3 −2611 61355889 8 1 8 64 2  8 \sqrt{−1}\sqrt{ε_{1}} 10.6400
7833  −7 −1119 61355889 8 1 32 128 1 16  ε_{1} 21.2801
5 −1567 −7835 61387225 1 15 30 225 1 225  ε_{1} 0.9624
12 −1959 −2612 61402896 1 42 14 294 1 294  ε_{1} 2.6339
7836  −3 −2612 61402896 2 1 14 14 1  7  ε_{1} 61.1967
7836  −4 −1959 61402896 2 1 42 42 1 21  ε_{1} 61.1967
253  −31 −7843 61512649 1 3 16 24 1 24  ε_{1} 15.0577
341  −23 −7843 61512649 1 3 16 24 1 24  ε_{1} 11.2480
713  −11 −7843 61512649 1 1 16  8 1  8  ε_{1} 32.3476
37 −212 −7844 61528336 1 6 32 96 1 96  ε_{1} 4.9836
53 −148 −7844 61528336 1 2 32 32 1 32  ε_{1} 3.9314
1961 −4 −7844 61528336 2 1 32 32 1 16 ε_{1} 46.2171
1961 −148 −212 61528336 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 23.1086
1569  −15 −2615 61544025 1 2 46 46 1 46  ε_{1} 100.6975
7845  −3 −2615 61544025 2 1 46 46 1 23  ε_{1} 25.2726
7845  −15 −523 61544025 2 2 5 10 1  5  ε_{1} 25.2726
133  −59 −7847 61575409 1 3 56 84 1 84  ε_{1} 10.3065
413  −19 −7847 61575409 1 1 56 28 1 28  ε_{1} 8.2212
1121  −7 −7847 61575409 1 1 56 28 1 28  ε_{1} 66.6959
7849  −47 −167 61606801 1 5 11 55 2 55 \sqrt{−1}\sqrt{ε_{1}} 162.7152
2617  −3 −7851 61638201 1 1 20 10 1 10  ε_{1} 116.1277
604  −52 −1963 61653904 1 2 6  6 1  6  ε_{1} 43.9269
7852  −4 −1963 61653904 2 1 6  6 1  3  ε_{1} 63.0412
7852  −52 −151 61653904 2 2 7 14 1  7  ε_{1} 63.0412
5 −1571 −7855 61701025 1 17 44 374 1 374  ε_{1} 0.9624
1964  −8 −3928 61716736 1 1 10 10 2 10 \sqrt{−1}\sqrt{ε_{1}} 25.9557

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 199

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3928  −4 −3928 61716736 5 1 10 50 2 10  \sqrt{i}\sqrt{ε_{1}} 9.7798
29 −271 −7859 61763881 1 11 34 187 1 187  ε_{1} 3.2945
5 −1572 −7860 61779600 1 12 40 240 1 240  ε_{1} 0.9624
12 −655 −7860 61779600 1 12 40 240 1 240  ε_{1} 2.6339
60 −131 −7860 61779600 2 5 40 200 1 100  ε_{1} 4.1269
60 −655 −1572 61779600 2 12 12 144 1 72  ε_{1} 4.1269
393  −20 −7860 61779600 1 2 40 40 1 40  ε_{1} 36.6935
524  −15 −7860 61779600 1 2 40 40 1 40  ε_{1} 19.9254
1965  −4 −7860 61779600 2 1 40 40 1 20  ε_{1} 9.7806
1965  −20 −1572 61779600 2 2 12 24 1 12  ε_{1} 9.7806
2620  −3 −7860 61779600 2 1 40 40 1 20  ε_{1} 42.2244
2620  −15 −1572 61779600 2 2 12 24 1 12  ε_{1} 42.2244
7861  −7 −1123 61795321 5 1  5 25 2  5 \sqrt{−1}\sqrt{ε_{1}} 10.6073
2621  −3 −7863 61826769 1 1 34 17 1 17  ε_{1} 24.5957
8 −983 −7864 61842496 1 27 36 486 1 486  ε_{1} 1.7627
7864  −8 −983 61842496 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 72.0583
28 −1124 −1967 61905424 1 20 36 360 1 360  ε_{1} 5.5373
7868  −4 −1967 61905424 4 1 36 72 1 18  ε_{1} 17.0567
7868  −7 −1124 61905424 4 1 20 40 1 10  ε_{1} 17.0567
129 −183 −2623 61921161 1 8 22 88 1 88  ε_{1} 20.8511
7869  −3 −2623 61921161 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 24.9429
7869 −43 −183 61921161 2 1 8 8 1 4 ε_{1} 49.8859
17 −463 −7871 61952641 1 7 120 420 1 420  ε_{1} 4.1894
44 −179 −7876 62031376 1 5 20 50 1 50  ε_{1} 5.9864
716  −11 −7876 62031376 1 1 20 10 1 10  ε_{1} 31.8828
1969  −4 −7876 62031376 1 1 20 10 1 10  ε_{1} 147.2368
5 −1576 −7880 62094400 1 10 52 260 1 260  ε_{1} 0.9624
197  −40 −7880 62094400 1 2 52 52 1 52  ε_{1} 6.6670
985  −8 −7880 62094400 6 1 52 156 1 26  ε_{1} 13.4088
985  −40 −1576 62094400 6 2 10 60 1 10  ε_{1} 13.4088
213 −111 −2627 62110161 1 8 12 48 1 48  ε_{1} 8.5805
7881  −3 −2627 62110161 12 1 12 72 1  6  ε_{1} 17.7363
7881  −71 −111 62110161 12 7  8 672 2 56 \sqrt{−1}\sqrt{ε_{1}} 8.8681
1577  −95 −415 62173225 1 8 10 40 1 40  ε_{1} 66.0912
7885  −19 −415 62173225 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 18.3924
7885 −83 −95 62173225 2 3 8 24 1 12 ε_{1} 36.7849
33 −239 −7887 62204769 1 15 72 540 1 540  ε_{1} 7.6563
717  −11 −7887 62204769 1 1 72 36 1 36  ε_{1} 10.9696
2629  −3 −7887 62204769 1 1 72 36 1 36  ε_{1} 72.7415
8 −1972 −3944 62220544 1 12 44 264 1 264  ε_{1} 1.7627
136 −116 −3944 62220544 2 6 44 264 1 132  ε_{1} 8.4966
136 −232 −1972 62220544 2 2 12 24 1 12  ε_{1} 8.4966
232 −68 −3944 62220544 2 4 44 176 1 88 ε_{1} 10.5766
232 −136 −1972 62220544 2 4 12 48 1 24  ε_{1} 10.5766
3944  −4 −3944 62220544 4 1 44 88 1 22  ε_{1} 11.4988
3944  −8 −1972 62220544 4 1 12 24 1  6  ε_{1} 11.4988
3944  −68 −232 62220544 4 4  2 16 1  4  ε_{1} 11.4988
3944 −116 −136 62220544 4 6  4 48 1 12  ε_{1} 11.4988
13 −607 −7891 62267881 1 13 12 78 1 78  ε_{1} 2.3895
1973  −4 −7892 62283664 1 1 42 21 1 21  ε_{1} 24.1684

200 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −1579 −7895 62331025 1 9 112 504 1 504  ε_{1} 0.9624
8 −987 −7896 62346816 1 8 32 128 1 128  ε_{1} 1.7627
21 −376 −7896 62346816 1 8 32 128 1 128  ε_{1} 3.1336
21 −1128 −2632 62346816 1 8  8 32 1 32  ε_{1} 3.1336
24 −987 −2632 62346816 1 8  8 32 1 32  ε_{1} 4.5849
56 −987 −1128 62346816 1 8  8 32 1 32  ε_{1} 6.8002
141  −56 −7896 62346816 1 4 32 64 1 64  ε_{1} 10.4940
141 −168 −2632 62346816 1 4  8 16 1 16  ε_{1} 10.4940
168  −47 −7896 62346816 2 5 32 160 1 80  ε_{1} 6.5132
168 −376 −987 62346816 2 8  8 64 1 32  ε_{1} 6.5132
329  −24 −7896 62346816 1 2 32 32 1 32  ε_{1} 30.7485
329 −168 −1128 62346816 1 4  8 16 1 16  ε_{1} 30.7485
376 −168 −987 62346816 1 4  8 16 1 16  ε_{1} 30.5420
1128  −7 −7896 62346816 2 1 32 32 1 16  ε_{1} 16.9115
1128  −56 −987 62346816 2 4  8 32 1 16  ε_{1} 16.9115
2632  −3 −7896 62346816 4 1 32 64 1 16  ε_{1} 16.2548
2632  −24 −987 62346816 4 2  8 32 1  8  ε_{1} 16.2548
7896  −3 −2632 62346816 4 1  8 16 1  4  ε_{1} 29.6560
7896  −7 −1128 62346816 4 1  8 16 1  4  ε_{1} 29.6560
7896  −8 −987 62346816 4 1  8 16 1  4  ε_{1} 29.6560
7896  −47 −168 62346816 4 5  4 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 14.8280
2633  −3 −7899 62394201 1 1 22 11 1 11  ε_{1} 81.4628
1129  −7 −7903 62457409 9 1 44 198 1 22  ε_{1} 11.6342
93 −255 −2635 62489025 1 12 12 72 1 72  ε_{1} 6.7322
465 −51 −2635 62489025 2 2 12 24 1 12 ε_{1} 20.7308
465 −255 −527 62489025 2 12 18 216 1 108  ε_{1} 20.7308
1581 −15 −2635 62489025 2 2 12 24 1 12 ε_{1} 13.4549
1581 −155 −255 62489025 2 4 12 48 1 24  ε_{1} 13.4549
7905  −3 −2635 62489025 4 1 12 24 1  6  ε_{1} 53.8111
7905  −15 −527 62489025 4 2 18 72 1 18  ε_{1} 53.8111
7905  −31 −255 62489025 4 3 12 72 1 18  ε_{1} 53.8111
7905  −51 −155 62489025 4 2  4 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 26.9056
12 −659 −7908 62536464 1 11 36 198 1 198  ε_{1} 2.6339
1977  −4 −7908 62536464 1 1 36 18 1 18  ε_{1} 67.5262
2636  −3 −7908 62536464 3 1 36 54 1 18  ε_{1} 18.7619
7909  −11 −719 62552281 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 50.3859
184  −43 −7912 62599744 1 1 12  6 1  6  ε_{1} 21.5856
344  −23 −7912 62599744 1 3 12 18 1 18  ε_{1} 19.8864
989  −8 −7912 62599744 1 1 12  6 1  6  ε_{1} 23.0897
989 −184 −344 62599744 1 4 10 20 1 20  ε_{1} 23.0897
7912  −23 −344 62599744 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 32.4346
7912 −43 −184 62599744 2 1 4 4 1 2 ε_{1} 64.8692
5 −1583 −7915 62647225 1 33 14 231 1 231  ε_{1} 0.9624
7916 −4 −1979 62663056 1 1 23 23 2 23 \sqrt{i}\sqrt{ε_{1}} 33.6072
21 −1131 −2639 62678889 1 8 64 256 1 256  ε_{1} 3.1336
273  −87 −2639 62678889 2 6 64 384 1 192  ε_{1} 14.5641
273 −203 −1131 62678889 2 4  8 32 1 16  ε_{1} 14.5641
609  −39 −2639 62678889 2 4 64 256 1 128  ε_{1} 28.0146
609  −91 −1131 62678889 2 2  8 16 1  8  ε_{1} 28.0146
7917  −3 −2639 62678889 4 1 64 128 1 32  ε_{1} 8.9770

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 201

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7917  −7 −1131 62678889 4 1 8 16 1  4  ε_{1} 8.9770
7917  −39 −203 62678889 4 4 4 32 1  8  ε_{1} 8.9770
7917  −87  −91 62678889 4 6 2 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 4.4885
57 −139 −7923 62773929 1 3 16 24 1 24  ε_{1} 11.4208
417  −19 −7923 62773929 1 1 16  8 1  8  ε_{1} 37.9102
2641  −3 −7923 62773929 1 1 16  8 1  8  ε_{1} 180.2460
28 −283 −7924 62789776 1 3 20 30 1 30  ε_{1} 5.5373
1132  −7 −7924 62789776 1 1 20 10 1 10  ε_{1} 38.8758
1981  −4 −7924 62789776 1 1 20 10 1 10  ε_{1} 59.8382
8 −991 −7928 62853184 1 17 24 204 1 204  ε_{1} 1.7627
7928  −8 −991 62853184 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 27.5004
77 −103 −7931 62900761 1 5 44 110 1 110  ε_{1} 4.3693
721  −11 −7931 62900761 1 1 44 22 1 22  ε_{1} 76.3136
1133  −7 −7931 62900761 1 1 44 22 1 22  ε_{1} 9.2300
12 −1983 −2644 62916624 1 16 18 144 1 144  ε_{1} 2.6339
7932  −3 −2644 62916624 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 20.3800
7932 −4 −1983 62916624 2 1 16 16 1 8 ε_{1} 40.7600
17 −467 −7939 63027721 1 7 20 70 1 70  ε_{1} 4.1894
5 −1588 −7940 63043600 1 6 40 120 1 120  ε_{1} 0.9624
397  −20 −7940 63043600 1 2 40 40 1 40  ε_{1} 16.2905
1985  −4 −7940 63043600 2 1 40 40 1 20  ε_{1} 44.1245
1985  −20 −1588 63043600 2 2 6 12 1  6  ε_{1} 44.1245
7941  −3 −2647 63059481 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 29.9567
24 −331 −7944 63107136 1 3 48 72 1 72  ε_{1} 4.5849
993  −8 −7944 63107136 3 1 48 72 1 24  ε_{1} 17.1487
993  −24 −2648 63107136 3 2 22 66 1 22  ε_{1} 17.1487
2648  −3 −7944 63107136 1 1 48 24 1 24  ε_{1} 43.9153
7944  −3 −2648 63107136 2 1 22 22 1 11  ε_{1} 47.9947
7944  −24 −331 63107136 2 2 3  6 1  3  ε_{1} 47.9947
1589  −35 −1135 63123025 1 2 18 18 1 18  ε_{1} 31.3219
7945  −7 −1135 63123025 2 1 18 18 1  9  ε_{1} 130.2875
7945  −35 −227 63123025 2 2 5 10 1  5  ε_{1} 130.2875
7948  −4 −1987 63170704 3 1 7 21 2  7  \sqrt{i}\sqrt{ε_{1}} 15.2805
8 −1988 −3976 63234304 1 24 16 192 1 192  ε_{1} 1.7627
28 −568 −3976 63234304 1 4 16 32 1 32  ε_{1} 5.5373
56 −568 −1988 63234304 1 4 24 48 1 48  ε_{1} 6.8002
284  −56 −3976 63234304 1 4 16 32 1 32  ε_{1} 17.6959
568  −56 −1988 63234304 3 4 24 144 1 48  ε_{1} 11.3120
3976  −4 −3976 63234304 8 1 16 64 1  8  ε_{1} 15.4551
3976  −8 −1988 63234304 8 1 24 96 1 12  ε_{1} 15.4551
33 −723 −2651 63250209 1 4 26 52 1 52  ε_{1} 7.6563
7953  −3 −2651 63250209 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 47.6763
7953 −11 −723 63250209 2 1 4 4 1 2 ε_{1} 95.3527
5 −1591 −7955 63282025 1 22 44 484 1 484  ε_{1} 0.9624
37 −215 −7955 63282025 1 14 44 308 1 308  ε_{1} 4.9836
185 −43 −7955 63282025 2 1 44 44 1 22 ε_{1} 9.8254
185 −215 −1591 63282025 2 14 22 308 1 154  ε_{1} 9.8254
21 −379 −7959 63345681 1 3 80 120 1 120  ε_{1} 3.1336
1137  −7 −7959 63345681 1 1 80 40 1 40  ε_{1} 55.7882
2653  −3 −7959 63345681 1 1 80 40 1 40  ε_{1} 45.6112

202 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −1592 −7960 63361600 1 20 24 240 1 240  ε_{1} 0.9624
8 −995 −7960 63361600 1 8 24 96 1 96  ε_{1} 1.7627
40 −199 −7960 63361600 2 9 24 216 1 108  ε_{1} 3.6369
40 −995 −1592 63361600 2 8 20 160 1 80  ε_{1} 3.6369
1592  −40 −995 63361600 1 2 8  8 1  8  ε_{1} 13.3642
7960  −8 −995 63361600 2 1 8  8 1  4  ε_{1} 77.5924
7960  −40 −199 63361600 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 38.7962
7961 −19 −419 63377521 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 83.9549
44 −724 −1991 63425296 1 10 56 280 1 280  ε_{1} 5.9864
7964 −4 −1991 63425296 2 1 56 56 1 28 ε_{1} 38.1385
7964  −11 −724 63425296 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 19.0692
257  −31 −7967 63473089 3 3 44 198 1 66  ε_{1} 6.9334
2657  −3 −7971 63536841 1 1 30 15 1 15  ε_{1} 68.2494
1993  −4 −7972 63552784 1 1 24 12 1 12  ε_{1} 101.9612
469 −119 −1139 63568729 3 10 16 240 1 80  ε_{1} 8.3483
7973 −7 −1139 63568729 2 1 16 16 1 8 ε_{1} 16.7262
7973  −67 −119 63568729 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 8.3631
997 −8 −7976 63616576 1 1 54 27 1 27 ε_{1} 24.0849
7977  −3 −2659 63632529 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 81.7740
101 −79 −7979 63664441 1 5 44 110 1 110 ε_{1} 5.9964
12 −1995 −2660 63680400 1 8 24 96 1 96  ε_{1} 2.6339
21 −1140 −2660 63680400 1 16 24 192 1 192  ε_{1} 3.1336
28 −1140 −1995 63680400 1 16 8 64 1 64  ε_{1} 5.5373
57 −420 −2660 63680400 1 8 24 96 1 96  ε_{1} 11.4208
60 −399 −2660 63680400 2 16 24 384 1 192  ε_{1} 4.1269
60 −532 −1995 63680400 2 4 8 32 1 16  ε_{1} 4.1269
76 −420 −1995 63680400 1 8 8 32 1 32  ε_{1} 11.6579
105 −228 −2660 63680400 2 4 24 96 1 48  ε_{1} 8.8131
105 −532 −1140 63680400 2 4 16 64 1 32  ε_{1} 8.8131
133 −420 −1140 63680400 1 8 16 64 1 64  ε_{1} 10.3065
140 −228 −1995 63680400 2 4 8 32 1 16  ε_{1} 4.9558
140 −399 −1140 63680400 2 16 16 256 1 128  ε_{1} 4.9558
285 −84 −2660 63680400 2 4 24 96 1 48 ε_{1} 5.6595
285 −420 −532 63680400 2 8 4 32 1 16  ε_{1} 5.6595
380 −84 −1995 63680400 2 4 8 32 1 16 ε_{1} 8.7131
380 −399 −420 63680400 2 16 8 128 1 64  ε_{1} 8.7131
665 −84 −1140 63680400 2 4 16 64 1 32 ε_{1} 20.4394
665 −228 −420 63680400 2 4 8 32 1 16  ε_{1} 20.4394
1596  −15 −2660 63680400 8 2 24 192 1 24  ε_{1} 7.3765
1596  −20 −1995 63680400 8 2 8 64 1  8  ε_{1} 7.3765
1596  −35 −1140 63680400 8 2 16 128 1 16  ε_{1} 7.3765
1596  −95 −420 63680400 8 8 8 256 1 32  ε_{1} 7.3765
7980  −3 −2660 63680400 8 1 24 96 1 12  ε_{1} 11.1819
7980  −4 −1995 63680400 8 1 8 32 1  4  ε_{1} 11.1819
7980  −7 −1140 63680400 8 1 16 64 1  8  ε_{1} 11.1819
7980  −15 −532 63680400 8 2 4 32 1  4  ε_{1} 11.1819
7980  −19 −420 63680400 8 1 8 32 1  4  ε_{1} 11.1819
7980  −20 −399 63680400 8 2 16 128 1 16  ε_{1} 11.1819
7980  −35 −228 63680400 8 2 4 32 1  4  ε_{1} 11.1819
7980  −84  −95 63680400 8 4 8 128 1 16  ε_{1} 11.1819

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 203

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
7981  −23 −347 63696361 1 3  5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 68.4007
1996  −8 −3992 63744256 5 1 26 130 2 26 \sqrt{−1}\sqrt{ε_{1}} 9.1028
3992  −4 −3992 63744256 1 1 26 26 2 26  \sqrt{i}\sqrt{ε_{1}} 21.4004
1997  −4 −7988 63808144 1 1 42 21 1 21  ε_{1} 18.2454
7989  −3 −2663 63824121 1 1 43 43 2 43 \sqrt{−1}\sqrt{ε_{1}} 47.6126
61 −131 −7991 63856081 1 5 100 250 1 250  ε_{1} 7.3284
5 −1599 −7995 63920025 1 36 16 288 1 288  ε_{1} 0.9624
13 −615 −7995 63920025 1 20 16 160 1 160  ε_{1} 2.3895
41 −195 −7995 63920025 1 4 16 32 1 32  ε_{1} 8.3183
65 −123 −7995 63920025 2 2 16 32 1 16  ε_{1} 5.5529
65 −615 −1599 63920025 2 20 36 720 1 360  ε_{1} 5.5529
205 −39 −7995 63920025 2 4 16 64 1 32 ε_{1} 7.5213
205 −195 −1599 63920025 2 4 36 144 1 72  ε_{1} 7.5213
533 −15 −7995 63920025 2 2 16 32 1 16 ε_{1} 6.2748
533 −195 −615 63920025 2 4 20 80 1 40  ε_{1} 6.2748
2665  −3 −7995 63920025 4 1 16 32 1  8  ε_{1} 36.2370
2665  −15 −1599 63920025 4 2 36 144 1 36  ε_{1} 36.2370
2665  −39 −615 63920025 4 4 20 160 1 40  ε_{1} 36.2370
2665 −123 −195 63920025 4 2  4 16 1  4  ε_{1} 36.2370
7996  −4 −1999 63936016 1 1 27 27 2 27  \sqrt{i}\sqrt{ε_{1}} 91.8872
7997  −11 −727 63952009 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 15.9532
421 −19 −7999 63984001 1 1 74 37 1 37 ε_{1} 26.0114
53 −151 −8003 64048009 1 7 26 91 1 91  ε_{1} 3.9314
12 −667 −8004 64064016 1 4 48 96 1 96  ε_{1} 2.6339
29 −276 −8004 64064016 1 8 48 192 1 192  ε_{1} 3.2945
69 −116 −8004 64064016 1 6 48 144 1 144  ε_{1} 6.4345
92  −87 −8004 64064016 1 6 48 144 1 144  ε_{1} 7.7415
348  −23 −8004 64064016 2 3 48 144 1 72  ε_{1} 8.0501
348 −276 −667 64064016 2 8  4 32 1 16  ε_{1} 8.0501
2001  −4 −8004 64064016 2 1 48 48 1 24  ε_{1} 48.7984
2001 −116 −276 64064016 2 6  8 48 1 24  ε_{1} 48.7984
2668  −3 −8004 64064016 2 1 48 48 1 24  ε_{1} 38.3652
2668  −87 −276 64064016 2 6  8 48 1 24  ε_{1} 38.3652
17 −471 −8007 64112049 1 16 64 512 1 512  ε_{1} 4.1894
157  −51 −8007 64112049 1 2 64 64 1 64  ε_{1} 10.7226
2669  −3 −8007 64112049 4 1 64 128 1 32  ε_{1} 10.0868
2669  −51 −471 64112049 4 2 16 64 1 16  ε_{1} 10.0868
13 −616 −8008 64128064 1 8 16 64 1 64  ε_{1} 2.3895
56 −143 −8008 64128064 1 10 16 80 1 80  ε_{1} 6.8002
77 −104 −8008 64128064 1 6 16 48 1 48  ε_{1} 4.3693
77 −728 −1144 64128064 1 12 12 72 1 72  ε_{1} 4.3693
88  −91 −8008 64128064 1 2 16 16 1 16  ε_{1} 11.9527
616  −91 −1144 64128064 2 2 12 24 1 12  ε_{1} 21.3187
616 −143 −728 64128064 2 10 12 120 1 60  ε_{1} 21.3187
728  −11 −8008 64128064 2 1 16 16 1  8  ε_{1} 7.9773
728 −143 −616 64128064 2 10  8 80 1 40  ε_{1} 7.9773
1001  −8 −8008 64128064 2 1 16 16 1  8  ε_{1} 29.1356
1001  −56 −1144 64128064 2 4 12 48 1 24  ε_{1} 29.1356
1001  −88 −728 64128064 2 2 12 24 1 12  ε_{1} 29.1356
1001 −104 −616 64128064 2 6  8 48 1 24  ε_{1} 29.1356

204 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1144  −7 −8008 64128064 2 1 16 16 1  8  ε_{1} 27.8642
1144  −91 −616 64128064 2 2 8 16 1  8  ε_{1} 27.8642
8008  −7 −1144 64128064 4 1 12 24 1  6  ε_{1} 33.8715
8008  −11 −728 64128064 4 1 12 24 1  6  ε_{1} 33.8715
8008  −56 −143 64128064 4 4 10 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 16.9357
8008  −88  −91 64128064 4 2 2  8 1  2  ε_{1} 33.8715
8012  −4 −2003 64192144 1 1 9  9 2  9  \sqrt{i}\sqrt{ε_{1}} 36.7008
8013  −3 −2671 64208169 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 21.7236
5 −1603 −8015 64240225 1 6 92 276 1 276  ε_{1} 0.9624
229  −35 −8015 64240225 3 2 92 276 1 92  ε_{1} 5.4249
1145  −7 −8015 64240225 4 1 92 184 1 46  ε_{1} 15.6513
1145  −35 −1603 64240225 4 2 6 24 1  6  ε_{1} 15.6513
8 −2004 −4008 64256256 1 16 16 128 1 128  ε_{1} 1.7627
12 −1336 −4008 64256256 1 12 16 96 1 96  ε_{1} 2.6339
24 −1336 −2004 64256256 1 12 16 96 1 96  ε_{1} 4.5849
668  −24 −4008 64256256 1 2 16 16 1 16  ε_{1} 11.6342
1336  −24 −2004 64256256 1 2 16 16 1 16  ε_{1} 64.9600
4008  −4 −4008 64256256 2 1 16 16 1  8  ε_{1} 39.6815
4008  −8 −2004 64256256 2 1 16 16 1  8  ε_{1} 39.6815
5 −1604 −8020 64320400 1 20 32 320 1 320  ε_{1} 0.9624
401  −20 −8020 64320400 5 2 32 160 1 32  ε_{1} 7.3790
2005  −4 −8020 64320400 4 1 32 64 1 16  ε_{1} 11.9979
2005  −20 −1604 64320400 4 2 20 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 5.9989
113 −71 −8023 64368529 1 7 22 77 1 77 ε_{1} 14.6946
8 −1003 −8024 64384576 1 4 48 96 1 96  ε_{1} 1.7627
17 −472 −8024 64384576 1 6 48 144 1 144  ε_{1} 4.1894
136 −59 −8024 64384576 2 3 48 144 1 72 ε_{1} 8.4966
136 −472 −1003 64384576 2 6 4 24 1 12  ε_{1} 8.4966
472 −136 −1003 64384576 1 4 4  8 1  8  ε_{1} 26.6550
8024  −8 −1003 64384576 4 1 4  8 1  2  ε_{1} 28.1189
8024  −59 −136 64384576 4 3 4 24 1  6  ε_{1} 28.1189
349  −23 −8027 64432729 1 3 28 42 1 42  ε_{1} 19.6424
217 −259 −1147 64464841 1 4 6 12 1 12  ε_{1} 31.7104
8029  −7 −1147 64464841 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 25.9660
8029  −31 −259 64464841 2 3 4 12 1  6  ε_{1} 51.9320
2677  −3 −8031 64496961 3 1 60 90 1 30  ε_{1} 16.4734
5 −1607 −8035 64561225 1 27 14 189 1 189  ε_{1} 0.9624
5 −1608 −8040 64641600 1 16 32 256 1 256  ε_{1} 0.9624
24 −335 −8040 64641600 1 18 32 288 1 288  ε_{1} 4.5849
120 −67 −8040 64641600 2 1 32 32 1 16 ε_{1} 6.1779
120 −335 −1608 64641600 2 18 16 288 1 144  ε_{1} 6.1779
201 −40 −8040 64641600 1 2 32 32 1 32 ε_{1} 27.6905
201 −120 −2680 64641600 1 4 12 24 1 24  ε_{1} 27.6905
536  −15 −8040 64641600 1 2 32 32 1 32  ε_{1} 25.1680
1005  −8 −8040 64641600 2 1 32 32 1 16  ε_{1} 14.9988
1005  −24 −2680 64641600 2 2 12 24 1 12  ε_{1} 14.9988
1005  −40 −1608 64641600 2 2 16 32 1 16  ε_{1} 14.9988
1005 −120 −536 64641600 2 4 14 56 1 28  ε_{1} 14.9988
1608 −15 −2680 64641600 2 2 12 24 1 12 ε_{1} 13.3742
1608 −120 −335 64641600 2 4 18 72 1 36  ε_{1} 13.3742

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 205

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2680  −3 −8040 64641600 2 1 32 32 1 16  ε_{1} 32.5300
2680  −15 −1608 64641600 2 2 16 32 1 16  ε_{1} 32.5300
8040  −3 −2680 64641600 8 1 12 48 1  6  ε_{1} 12.5757
8040  −15 −536 64641600 8 2 14 224 2 28 \sqrt{−1}\sqrt{ε_{1}} 6.2879
8040  −24 −335 64641600 8 2 18 144 1 18  ε_{1} 12.5757
8040  −67 −120 64641600 8 1 4 16 1  2  ε_{1} 12.5757
473 −187 −731 64657681 3 2 12 36 1 12  ε_{1} 10.3180
8041  −11 −731 64657681 2 1 12 12 1  6  ε_{1} 138.3521
8041  −43 −187 64657681 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 69.1760
21 −383 −8043 64689849 1 17 16 136 1 136  ε_{1} 3.1336
1149  −7 −8043 64689849 1 1 16  8 1  8  ε_{1} 32.9675
2681  −3 −8043 64689849 1 1 16  8 1  8  ε_{1} 93.6451
8044  −4 −2011 64705936 1 1 7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 100.5330
13 −619 −8047 64754209 1 5 34 85 1 85  ε_{1} 2.3895
2012  −8 −4024 64770304 1 1 20 20 2 20 \sqrt{−1}\sqrt{ε_{1}} 10.8056
4024  −4 −4024 64770304 1 1 20 20 2 20  \sqrt{i}\sqrt{ε_{1}} 51.6954
8049  −3 −2683 64786401 5 1 5 25 2  5 \sqrt{−1}\sqrt{ε_{1}} 17.8891
97  −83 −8051 64818601 1 3 34 51 1 51  ε_{1} 18.6488
12 −671 −8052 64834704 1 30 16 240 1 240  ε_{1} 2.6339
33 −244 −8052 64834704 1 6 16 48 1 48  ε_{1} 7.6563
44 −183 −8052 64834704 1 8 16 64 1 64  ε_{1} 5.9864
61 −132 −8052 64834704 1 4 16 32 1 32  ε_{1} 7.3284
732 −11 −8052 64834704 2 1 16 16 1 8 ε_{1} 13.7628
732 −132 −671 64834704 2 4 30 120 1 60  ε_{1} 13.7628
2013 −4 −8052 64834704 2 1 16 16 1 8 ε_{1} 13.0235
2013 −132 −244 64834704 2 4 6 24 1 12  ε_{1} 13.0235
2684 −3 −8052 64834704 2 1 16 16 1 8 ε_{1} 23.3440
2684 −132 −183 64834704 2 4 8 32 1 16  ε_{1} 23.3440
8 −1007 −8056 64899136 1 30 36 540 1 540  ε_{1} 1.7627
53 −152 −8056 64899136 1 6 36 108 1 108  ε_{1} 3.9314
152 −424 −1007 64899136 1 6 30 90 1 90  ε_{1} 8.6078
424 −19 −8056 64899136 2 1 36 36 1 18 ε_{1} 17.9769
424 −152 −1007 64899136 2 6 30 180 1 90  ε_{1} 17.9769
8056  −8 −1007 64899136 2 1 30 30 1 15  ε_{1} 91.2344
8056  −19 −424 64899136 2 1 6  6 1  3  ε_{1} 91.2344
8057  −7 −1151 64915249 3 1 41 123 2 41 \sqrt{−1}\sqrt{ε_{1}} 25.4044
124 −260 −2015 64963600 1 8 52 208 1 208  ε_{1} 16.0392
620  −52 −2015 64963600 2 2 52 104 1 52  ε_{1} 12.4212
620 −260 −403 64963600 2 8 2 16 1  8  ε_{1} 12.4212
1612  −20 −2015 64963600 2 2 52 104 1 52  ε_{1} 28.2160
1612 −155 −260 64963600 2 4 8 32 1 16  ε_{1} 28.2160
8060  −4 −2015 64963600 4 1 52 104 1 26  ε_{1} 13.3891
8060  −20 −403 64963600 4 2 2  8 1  2  ε_{1} 13.3891
8060  −31 −260 64963600 4 3 8 48 1 12  ε_{1} 13.3891
8060  −52 −155 64963600 4 2 4 16 1  4  ε_{1} 13.3891
8061  −3 −2687 64979721 1 1 51 51 2 51 \sqrt{−1}\sqrt{ε_{1}} 50.6390
733  −11 −8063 65011969 3 1 86 129 1 43  ε_{1} 6.5944
2689  −3 −8067 65076489 1 1 20 10 1 10  ε_{1} 180.6914
2017  −4 −8068 65092624 1 1 12  6 1  6  ε_{1} 121.2470
1153  −7 −8071 65141041 1 1 66 33 1 33  ε_{1} 79.7231

206 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1009  −8 −8072 65157184 7 1 28 98 1 14  ε_{1} 13.9694
12 −2019 −2692 65221776 1 16 12 96 1 96  ε_{1} 2.6339
8076  −3 −2692 65221776 8 1 12 48 1  6  ε_{1} 14.4128
8076  −4 −2019 65221776 8 1 16 64 1  8  ε_{1} 14.4128
2693  −3 −8079 65270241 1 1 50 25 1 25  ε_{1} 16.7837
8 −2020 −4040 65286400 1 8 28 112 1 112  ε_{1} 1.7627
40 −404 −4040 65286400 2 14 28 392 1 196  ε_{1} 3.6369
40 −808 −2020 65286400 2 6 8 48 1 24  ε_{1} 3.6369
808  −20 −4040 65286400 2 2 28 56 1 28  ε_{1} 17.4909
808  −40 −2020 65286400 2 2 8 16 1  8  ε_{1} 17.4909
4040  −4 −4040 65286400 4 1 28 56 1 14  ε_{1} 15.7311
4040  −8 −2020 65286400 4 1 8 16 1  4  ε_{1} 15.7311
4040  −20 −808 65286400 4 2 6 24 1  6  ε_{1} 15.7311
4040  −40 −404 65286400 4 2 14 56 1 14  ε_{1} 15.7311
137  −59 −8083 65334889 1 3 16 24 1 24  ε_{1} 16.3142
172  −47 −8084 65351056 1 5 68 170 1 170  ε_{1} 17.6970
188  −43 −8084 65351056 1 1 68 34 1 34  ε_{1} 9.1285
2021  −4 −8084 65351056 3 1 68 102 1 34  ε_{1} 7.6123
8 −1011 −8088 65415744 1 12 24 144 1 144  ε_{1} 1.7627
24 −1011 −2696 65415744 1 12 24 144 1 144  ε_{1} 4.5849
337  −24 −8088 65415744 1 2 24 24 1 24  ε_{1} 42.8642
2696  −3 −8088 65415744 4 1 24 48 1 12  ε_{1} 14.4157
2696  −24 −1011 65415744 4 2 12 48 1 12  ε_{1} 14.4157
8088  −3 −2696 65415744 4 1 24 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 7.9003
8088 −8 −1011 65415744 4 1 12 24 1 6 ε_{1} 15.8005
5 −1619 −8095 65529025 1 15 56 420 1 420  ε_{1} 0.9624
8097  −3 −2699 65561409 7 1 15 105 2 15 \sqrt{−1}\sqrt{ε_{1}} 9.2871
13 −623 −8099 65593801 1 22 28 308 1 308  ε_{1} 2.3895
89  −91 −8099 65593801 1 2 28 28 1 28  ε_{1} 13.8155
1157  −7 −8099 65593801 2 1 28 28 1 14  ε_{1} 8.4394
1157  −91 −623 65593801 2 2 22 44 1 22  ε_{1} 8.4394
37 −219 −8103 65658609 1 4 48 96 1 96  ε_{1} 4.9836
73 −111 −8103 65658609 1 8 48 192 1 192  ε_{1} 15.3334
2701 −3 −8103 65658609 2 1 48 48 1 24 ε_{1} 29.1941
2701 −111 −219 65658609 2 8 4 32 1 16  ε_{1} 29.1941
1013  −8 −8104 65674816 1 1 34 17 1 17  ε_{1} 13.6553
8108  −4 −2027 65739664 5 1 11 55 2 11  \sqrt{i}\sqrt{ε_{1}} 8.3070
133 −427 −1159 65820769 1 2 16 16 1 16  ε_{1} 10.3065
8113  −7 −1159 65820769 6 1 16 48 1  8  ε_{1} 38.5832
8113  −19 −427 65820769 6 1 2 12 2  2 \sqrt{−1}\sqrt{ε_{1}} 19.2916
5 −1623 −8115 65853225 1 28 24 336 1 336  ε_{1} 0.9624
541  −15 −8115 65853225 1 2 24 24 1 24  ε_{1} 28.2989
2705  −3 −8115 65853225 8 1 24 96 1 12  ε_{1} 9.2890
2705  −15 −1623 65853225 8 2 28 224 1 28  ε_{1} 9.2890
2029  −4 −8116 65869456 7 1 34 119 1 17  ε_{1} 7.6143
353  −23 −8119 65918161 1 3 52 78 1 78  ε_{1} 23.7346
5 −1624 −8120 65934400 1 16 40 320 1 320  ε_{1} 0.9624
8 −1015 −8120 65934400 1 16 40 320 1 320  ε_{1} 1.7627
29 −280 −8120 65934400 1 4 40 80 1 80  ε_{1} 3.2945
40 −203 −8120 65934400 2 4 40 160 1 80  ε_{1} 3.6369

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 207

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
40 −1015 −1624 65934400 2 16 16 256 1 128  ε_{1} 3.6369
56 −1015 −1160 65934400 1 16 20 160 1 160  ε_{1} 6.8002
145 −56 −8120 65934400 4 4 40 320 1 80 ε_{1} 6.3596
145 −280 −1624 65934400 4 4 16 128 1 32  ε_{1} 6.3596
232 −35 −8120 65934400 2 2 40 80 1 40 ε_{1} 10.5766
232 −280 −1015 65934400 2 4 16 64 1 32  ε_{1} 10.5766
280 −203 −1160 65934400 2 4 20 80 1 40  ε_{1} 12.4372
280 −232 −1015 65934400 2 2 16 32 1 16  ε_{1} 12.4372
1160  −7 −8120 65934400 4 1 40 80 1 20  ε_{1} 7.0544
1160  −35 −1624 65934400 4 2 16 64 1 16  ε_{1} 7.0544
1160  −56 −1015 65934400 4 4 16 128 1 32  ε_{1} 7.0544
1160 −203 −280 65934400 4 4 4 32 1  8  ε_{1} 7.0544
1624  −35 −1160 65934400 2 2 20 40 1 20  ε_{1} 37.1882
1624  −40 −1015 65934400 2 2 16 32 1 16  ε_{1} 37.1882
8120  −7 −1160 65934400 4 1 20 40 1 10  ε_{1} 14.7828
8120  −8 −1015 65934400 4 1 16 32 1  8  ε_{1} 14.7828
8120  −35 −232 65934400 4 2 2  8 1  2  ε_{1} 14.7828
8120  −40 −203 65934400 4 2 4 16 1  4  ε_{1} 14.7828
8121  −3 −2707 65950641 5 1 7 35 2  7 \sqrt{−1}\sqrt{ε_{1}} 26.5996
12 −2031 −2708 65999376 1 38 30 570 1 570  ε_{1} 2.6339
8124  −3 −2708 65999376 10 1 30 150 1 15  ε_{1} 14.4187
8124  −4 −2031 65999376 10 1 38 190 1 19  ε_{1} 14.4187
8129  −11 −739 66080641 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 100.9753
173  −47 −8131 66113161 1 5 12 30 1 30  ε_{1} 5.1416
76 −107 −8132 66129424 1 3 28 42 1 42  ε_{1} 11.6579
428  −19 −8132 66129424 1 1 28 14 1 14  ε_{1} 15.1243
2033  −4 −8132 66129424 1 1 28 14 1 14  ε_{1} 51.0805
8133  −3 −2711 66145689 1 1 53 53 2 53 \sqrt{−1}\sqrt{ε_{1}} 22.0226
5 −1627 −8135 66178225 1 7 94 329 1 329  ε_{1} 0.9624
8137  −79 −103 66210769 1 5 5 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 100.3875
2713 −3 −8139 66243321 3 1 36 54 1 18 ε_{1} 45.8142
44 −740 −2035 66259600 1 16 8 64 1 64  ε_{1} 5.9864
220 −148 −2035 66259600 2 2 8 16 1 8 ε_{1} 10.3635
220 −407 −740 66259600 2 16 16 256 1 128  ε_{1} 10.3635
1628  −20 −2035 66259600 2 2 8 16 1  8  ε_{1} 17.1607
1628  −55 −740 66259600 2 4 16 64 1 32  ε_{1} 17.1607
8140  −4 −2035 66259600 8 1 8 32 1  4  ε_{1} 13.3990
8140  −11 −740 66259600 8 1 16 64 1  8  ε_{1} 13.3990
8140  −20 −407 66259600 8 2 16 128 1 16  ε_{1} 13.3990
8140  −55 −148 66259600 8 4 2 32 1  4  ε_{1} 13.3990
8141  −7 −1163 66275881 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 36.3675
17 −479 −8143 66308449 1 25 22 275 1 275  ε_{1} 4.1894
8 −2036 −4072 66324736 1 30 18 270 1 270  ε_{1} 1.7627
4072  −4 −4072 66324736 2 1 18 18 1  9  ε_{1} 37.9503
4072  −8 −2036 66324736 2 1 30 30 1 15  ε_{1} 37.9503
12 −679 −8148 66389904 1 18 24 216 1 216  ε_{1} 2.6339
21 −388 −8148 66389904 1 4 24 48 1 48  ε_{1} 3.1336
28 −291 −8148 66389904 1 4 24 48 1 48  ε_{1} 5.5373
97  −84 −8148 66389904 1 4 24 48 1 48  ε_{1} 18.6488
1164  −7 −8148 66389904 4 1 24 48 1 12  ε_{1} 12.7261

208 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1164  −84 −679 66389904 4 4 18 144 1 36  ε_{1} 12.7261
2037  −4 −8148 66389904 2 1 24 24 1 12  ε_{1} 13.0353
2037  −84 −388 66389904 2 4  4 16 1  8  ε_{1} 13.0353
2716  −3 −8148 66389904 2 1 24 24 1 12  ε_{1} 48.5904
2716  −84 −291 66389904 2 4  4 16 1  8  ε_{1} 48.5904
13 −627 −8151 66438801 1 4 88 176 1 176  ε_{1} 2.3895
33 −247 −8151 66438801 1 6 88 264 1 264  ε_{1} 7.6563
57 −143 −8151 66438801 1 10 88 440 1 440  ε_{1} 11.4208
209  −39 −8151 66438801 1 4 88 176 1 176  ε_{1} 22.8829
429  −19 −8151 66438801 2 1 88 88 1 44  ε_{1} 9.9534
429 −247 −627 66438801 2 6  4 24 1 12  ε_{1} 9.9534
741  −11 −8151 66438801 2 1 88 88 1 44  ε_{1} 11.0025
741 −143 −627 66438801 2 10  4 40 1 20  ε_{1} 11.0025
2717  −3 −8151 66438801 2 1 88 88 1 44  ε_{1} 13.4525
2717  −39 −627 66438801 2 4  4 16 1  8  ε_{1} 13.4525
8 −1019 −8152 66455104 1 13 18 117 1 117  ε_{1} 1.7627
8152  −8 −1019 66455104 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 79.4556
8153  −31 −263 66471409 1 3 13 39 2 39 \sqrt{−1}\sqrt{ε_{1}} 32.1745
5 −1631 −8155 66504025 1 44 12 264 1 264  ε_{1} 0.9624
233  −35 −8155 66504025 1 2 12 12 1 12  ε_{1} 21.4863
1165  −7 −8155 66504025 2 1 12 12 1  6  ε_{1} 15.0011
1165  −35 −1631 66504025 2 2 44 88 1 44  ε_{1} 15.0011
8156  −4 −2039 66520336 1 1 45 45 2 45  \sqrt{i}\sqrt{ε_{1}} 54.2361
8157  −3 −2719 66536649 1 1 41 41 2 41 \sqrt{−1}\sqrt{ε_{1}} 22.4954
41 −199 −8159 66569281 1 9 106 477 1 477  ε_{1} 8.3183
13 −628 −8164 66650896 1 6 32 96 1 96  ε_{1} 2.3895
157  −52 −8164 66650896 1 2 32 32 1 32  ε_{1} 10.7226
2041  −4 −8164 66650896 2 1 32 32 1 16  ε_{1} 75.9301
2041  −52 −628 66650896 2 2  6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 37.9650
1633 −115 −355 66667225 1 2  4  4 1  4  ε_{1} 109.6930
8165  −23 −355 66667225 2 3  4 12 1  6  ε_{1} 21.8541
8165  −71 −115 66667225 2 7  2 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 10.9271
1021  −8 −8168 66716224 1 1 50 25 1 25  ε_{1} 36.5338
21 −1167 −2723 66732561 1 22 12 132 1 132  ε_{1} 3.1336
8169 −3 −2723 66732561 2 1 12 12 1 6 ε_{1} 106.6608
8169  −7 −1167 66732561 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 53.3304
8173  −11 −743 66797929 3 1 21 63 2 21 \sqrt{−1}\sqrt{ε_{1}} 17.3520
28 −584 −4088 66846976 1 16 32 256 1 256  ε_{1} 5.5373
56 −292 −4088 66846976 1 4 32 64 1 64  ε_{1} 6.8002
2044  −8 −4088 66846976 2 1 32 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 22.8488
2044  −56 −584 66846976 2 4 16 64 1 32  ε_{1} 45.6975
4088  −4 −4088 66846976 2 1 32 64 2 32  \sqrt{i}\sqrt{ε_{1}} 7.6236
4088  −56 −292 66846976 2 4  4 16 1  8  ε_{1} 15.2473
5 −1636 −8180 66912400 1 16 48 384 1 384  ε_{1} 0.9624
409  −20 −8180 66912400 1 2 48 48 1 48  ε_{1} 52.2684
2045  −4 −8180 66912400 2 1 48 48 1 24  ε_{1} 12.0176
2045  −20 −1636 66912400 2 2 16 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 6.0088
8 −1023 −8184 66977856 1 16 32 256 1 256  ε_{1} 1.7627
24 −1023 −2728 66977856 1 16 12 96 1 96  ε_{1} 4.5849
33 −248 −8184 66977856 1 8 32 128 1 128  ε_{1} 7.6563

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 209

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
33 −744 −2728 66977856 1 12 12 72 1 72  ε_{1} 7.6563
88 −744 −1023 66977856 1 12 16 96 1 96  ε_{1} 11.9527
93 −88 −8184 66977856 1 2 32 32 1 32 ε_{1} 6.7322
93 −264 −2728 66977856 1 8 12 48 1 48  ε_{1} 6.7322
248 −264 −1023 66977856 1 8 16 64 1 64  ε_{1} 9.6724
264 −31 −8184 66977856 2 3 32 96 1 48 ε_{1} 9.7350
264 −248 −1023 66977856 2 8 16 128 1 64  ε_{1} 9.7350
341 −24 −8184 66977856 1 2 32 32 1 32 ε_{1} 11.2480
341 −264 −744 66977856 1 8 12 48 1 48  ε_{1} 11.2480
744  −11 −8184 66977856 2 1 32 32 1 16  ε_{1} 19.2319
744  −88 −1023 66977856 2 2 16 32 1 16  ε_{1} 19.2319
2728  −3 −8184 66977856 2 1 32 32 1 16  ε_{1} 29.3785
2728  −24 −1023 66977856 2 2 16 32 1 16  ε_{1} 29.3785
8184  −3 −2728 66977856 4 1 12 24 1  6  ε_{1} 30.0412
8184  −8 −1023 66977856 4 1 16 32 1  8  ε_{1} 30.0412
8184  −11 −744 66977856 4 1 12 24 1  6  ε_{1} 30.0412
8184  −31 −264 66977856 4 3 8 48 1 12  ε_{1} 30.0412
2729  −3 −8187 67026969 1 1 14  7 1  7  ε_{1} 97.3655
92 −356 −2047 67043344 1 12 18 108 1 108  ε_{1} 7.7415
8188  −4 −2047 67043344 2 1 18 36 2 18  \sqrt{i}\sqrt{ε_{1}} 23.1331
8188  −23 −356 67043344 2 3 12 36 1 18  ε_{1} 46.2663
8189  −19 −431 67059721 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 28.8616
8193  −3 −2731 67125249 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 84.2210
5 −1639 −8195 67158025 1 22 32 352 1 352  ε_{1} 0.9624
149  −55 −8195 67158025 1 4 32 64 1 64  ε_{1} 8.2223
745  −11 −8195 67158025 2 1 32 32 1 16  ε_{1} 34.1114
745  −55 −1639 67158025 2 4 22 88 1 44  ε_{1} 34.1114
12 −683 −8196 67174416 1 5 36 90 1 90  ε_{1} 2.6339
2049  −4 −8196 67174416 1 1 36 18 1 18  ε_{1} 104.8060
2732  −3 −8196 67174416 1 1 36 18 1 18  ε_{1} 39.2897
8197  −7 −1171 67190809 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 26.4042
8201  −59 −139 67256401 1 3 3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 83.0815
13 −631 −8203 67289209 1 13 18 117 1 117  ε_{1} 2.3895
28 −1172 −2051 67305616 1 18 18 162 1 162  ε_{1} 5.5373
8204  −4 −2051 67305616 2 1 18 18 1  9  ε_{1} 48.8758
8204  −7 −1172 67305616 2 1 18 18 1  9  ε_{1} 48.8758
1641  −15 −2735 67322025 5 2 62 310 1 62  ε_{1} 18.1536
8205  −3 −2735 67322025 2 1 62 62 1 31  ε_{1} 29.8509
8205  −15 −547 67322025 2 2 3  6 1  3  ε_{1} 29.8509
29 −283 −8207 67354849 1 3 96 144 1 144  ε_{1} 3.2945
17 −483 −8211 67420521 1 4 24 48 1 48  ε_{1} 4.1894
21 −391 −8211 67420521 1 14 24 168 1 168  ε_{1} 3.1336
69 −119 −8211 67420521 1 10 24 120 1 120  ε_{1} 6.4345
161  −51 −8211 67420521 1 2 24 24 1 24  ε_{1} 20.1338
357  −23 −8211 67420521 2 3 24 72 1 36  ε_{1} 5.8833
357 −391 −483 67420521 2 14 4 56 1 28  ε_{1} 5.8833
1173 −7 −8211 67420521 2 1 24 24 1 12 ε_{1} 11.2262
1173 −119 −483 67420521 2 10 4 40 1 20  ε_{1} 11.2262
2737  −3 −8211 67420521 2 1 24 24 1 12  ε_{1} 67.3814
2737  −51 −483 67420521 2 2 4  8 1  4  ε_{1} 67.3814

210 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2053  −4 −8212 67436944 1 1 18  9 1  9  ε_{1} 48.1240
8213  −43 −191 67453369 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 26.9700
5 −1643 −8215 67486225 1 10 36 180 1 180  ε_{1} 0.9624
53 −155 −8215 67486225 1 4 36 72 1 72  ε_{1} 3.9314
265 −31 −8215 67486225 2 3 36 108 1 54 ε_{1} 18.8092
265 −155 −1643 67486225 2 4 10 40 1 20  ε_{1} 18.8092
8 −1027 −8216 67502656 1 4 72 144 1 144  ε_{1} 1.7627
13 −632 −8216 67502656 1 8 72 288 1 288  ε_{1} 2.3895
104 −79 −8216 67502656 2 5 72 360 1 180 ε_{1} 4.6249
104 −632 −1027 67502656 2 8 4 32 1 16  ε_{1} 4.6249
632 −104 −1027 67502656 1 6 4 12 1 12  ε_{1} 19.2954
8216 −8 −1027 67502656 2 1 4 4 1 2 ε_{1} 30.2769
8216  −79 −104 67502656 2 5 6 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 15.1384
12 −2055 −2740 67568400 1 28 12 168 1 168  ε_{1} 2.6339
60 −411 −2740 67568400 2 6 12 72 1 36  ε_{1} 4.1269
60 −548 −2055 67568400 2 8 28 224 1 112  ε_{1} 4.1269
1644  −15 −2740 67568400 2 2 12 24 1 12  ε_{1} 23.0150
1644  −20 −2055 67568400 2 2 28 56 1 28  ε_{1} 23.0150
8220  −3 −2740 67568400 12 1 12 72 1  6  ε_{1} 11.2116
8220  −4 −2055 67568400 12 1 28 168 1 14  ε_{1} 11.2116
8220  −15 −548 67568400 12 2 8 96 1  8  ε_{1} 11.2116
8220  −20 −411 67568400 12 2 6 72 1  6  ε_{1} 11.2116
2741  −3 −8223 67617729 1 1 58 29 1 29  ε_{1} 36.7532
433  −19 −8227 67683529 1 1 10  5 1  5  ε_{1} 46.7895
633  −39 −2743 67716441 1 4 20 40 1 40  ε_{1} 41.1944
8229  −3 −2743 67716441 8 1 20 80 1 10  ε_{1} 12.9072
8229  −39 −211 67716441 8 4 3 48 1  6  ε_{1} 12.9072
284 −116 −2059 67831696 1 6 8 24 1 24  ε_{1} 17.6959
8236 −4 −2059 67831696 2 1 8 8 1 4 ε_{1} 92.9485
8236  −71 −116 67831696 2 7 6 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 46.4743
77 −107 −8239 67881121 1 3 64 96 1 96  ε_{1} 4.3693
749  −11 −8239 67881121 1 1 64 32 1 32  ε_{1} 18.9369
1177  −7 −8239 67881121 1 1 64 32 1 32  ε_{1} 88.7782
412  −40 −4120 67897600 1 2 12 12 1 12  ε_{1} 26.0564
824  −20 −4120 67897600 1 2 12 12 1 12  ε_{1} 23.3749
2060  −8 −4120 67897600 2 1 12 12 1  6  ε_{1} 20.9154
2060  −40 −824 67897600 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 10.4577
4120 −4 −4120 67897600 2 1 12 12 1 6 ε_{1} 56.4024
4120  −20 −824 67897600 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 28.2012
201 −123 −2747 67914081 1 2 18 18 1 18  ε_{1} 27.6905
8241  −3 −2747 67914081 2 1 18 18 1  9  ε_{1} 125.1140
8241  −67 −123 67914081 2 1 2  2 1  1  ε_{1} 125.1140
2749  −3 −8247 68013009 1 1 40 20 1 20  ε_{1} 50.9777
8 −1031 −8248 68029504 1 35 12 210 1 210  ε_{1} 1.7627
8248  −8 −1031 68029504 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 62.2956
37 −223 −8251 68079001 1 7 20 70 1 70  ε_{1} 4.9836
8252 −4 −2063 68095504 1 1 45 45 2 45 \sqrt{i}\sqrt{ε_{1}} 26.5705
5 −1651 −8255 68145025 1 8 68 272 1 272  ε_{1} 0.9624
13 −635 −8255 68145025 1 10 68 340 1 340  ε_{1} 2.3895
65 −127 −8255 68145025 2 5 68 340 1 170  ε_{1} 5.5529

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 211

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
65 −635 −1651 68145025 2 10  8 80 1 40  ε_{1} 5.5529
8257  −23 −359 68178049 1 3 19 57 2 57 \sqrt{−1}\sqrt{ε_{1}} 114.7232
2753 −3 −8259 68211081 1 1 30 15 1 15 ε_{1} 93.2433
5 −1652 −8260 68227600 1 20 24 240 1 240  ε_{1} 0.9624
28 −295 −8260 68227600 1 8 24 96 1 96  ε_{1} 5.5373
140 −59 −8260 68227600 2 3 24 72 1 36 ε_{1} 4.9558
140 −295 −1652 68227600 2 8 20 160 1 80  ε_{1} 4.9558
236  −35 −8260 68227600 1 2 24 24 1 24  ε_{1} 13.9320
413  −20 −8260 68227600 1 2 24 24 1 24  ε_{1} 8.2212
1180  −7 −8260 68227600 2 1 24 24 1 12  ε_{1} 30.4285
1180  −35 −1652 68227600 2 2 20 40 1 20  ε_{1} 30.4285
2065  −4 −8260 68227600 2 1 24 24 1 12  ε_{1} 61.9933
2065  −20 −1652 68227600 2 2 20 40 1 20  ε_{1} 61.9933
8261  −11 −751 68244121 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 34.7861
1033  −8 −8264 68293696 1 1 56 28 1 28  ε_{1} 80.9246
57 −435 −2755 68310225 1 4  8 16 1 16  ε_{1} 11.4208
285  −87 −2755 68310225 2 6  8 48 1 24  ε_{1} 5.6595
285 −435 −551 68310225 2 4 26 104 1 52  ε_{1} 5.6595
1653  −15 −2755 68310225 2 2  8 16 1  8  ε_{1} 14.5210
1653  −95 −435 68310225 2 8  4 32 1 16  ε_{1} 14.5210
8265  −3 −2755 68310225 4 1  8 16 1  4  ε_{1} 47.1288
8265  −15 −551 68310225 4 2 26 104 1 26  ε_{1} 47.1288
8265  −19 −435 68310225 4 1  4  8 1  2  ε_{1} 47.1288
8265  −87  −95 68310225 4 6  8 96 1 24  ε_{1} 47.1288
1181  −7 −8267 68343289 1 1 30 15 1 15  ε_{1} 20.5528
12 −2067 −2756 68359824 1 8 40 160 1 160  ε_{1} 2.6339
156 −159 −2756 68359824 2 10 40 400 1 200  ε_{1} 7.8232
156 −212 −2067 68359824 2 6  8 48 1 24  ε_{1} 7.8232
636  −39 −2756 68359824 2 4 40 160 1 80  ε_{1} 15.7631
636  −52 −2067 68359824 2 2  8 16 1  8  ε_{1} 15.7631
8268  −3 −2756 68359824 4 1 40 80 1 20  ε_{1} 15.6846
8268  −4 −2067 68359824 4 1  8 16 1  4  ε_{1} 15.6846
8268  −39 −212 68359824 4 4  6 48 1 12  ε_{1} 15.6846
8268  −52 −159 68359824 4 2 10 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 7.8423
8 −2068 −4136 68425984 1 12 44 264 1 264  ε_{1} 1.7627
44 −376 −4136 68425984 1 8 44 176 1 176  ε_{1} 5.9864
88 −376 −2068 68425984 1 8 12 48 1 48  ε_{1} 11.9527
188  −88 −4136 68425984 1 2 44 44 1 44  ε_{1} 9.1285
376  −88 −2068 68425984 1 2 12 12 1 12  ε_{1} 30.5420
4136  −4 −4136 68425984 2 1 44 44 1 22  ε_{1} 20.7326
4136  −8 −2068 68425984 2 1 12 12 1  6  ε_{1} 20.7326
2069  −4 −8276 68492176 1 1 38 19 1 19  ε_{1} 32.7815
93 −267 −2759 68508729 1 2 54 54 1 54  ε_{1} 6.7322
8277  −3 −2759 68508729 6 1 54 162 1 27  ε_{1} 9.0215
8277  −31 −267 68508729 6 3  2 18 1  3  ε_{1} 9.0215
17 −487 −8279 68541841 1 7 126 441 1 441  ε_{1} 4.1894
33 −251 −8283 68608089 1 7 16 56 1 56  ε_{1} 7.6563
753  −11 −8283 68608089 1 1 16  8 1  8  ε_{1} 54.2964
2761  −3 −8283 68608089 1 1 16  8 1  8  ε_{1} 158.4057
76 −436 −2071 68624656 1 6 30 90 1 90  ε_{1} 11.6579

212 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
8284  −4 −2071 68624656 2 1 30 30 1 15  ε_{1} 86.7077
8284  −19 −436 68624656 2 1 6  6 1  3  ε_{1} 86.7077
12 −691 −8292 68757264 1 5 20 50 1 50  ε_{1} 2.6339
2073  −4 −8292 68757264 1 1 20 10 1 10  ε_{1} 91.6409
2764  −3 −8292 68757264 1 1 20 10 1 10  ε_{1} 91.1562
5 −1659 −8295 68807025 1 8 64 256 1 256  ε_{1} 0.9624
21 −395 −8295 68807025 1 8 64 256 1 256  ε_{1} 3.1336
105 −79 −8295 68807025 2 5 64 320 1 160 ε_{1} 8.8131
105 −395 −1659 68807025 2 8 8 64 1 32  ε_{1} 8.8131
237  −35 −8295 68807025 1 2 64 64 1 64  ε_{1} 8.6873
553  −15 −8295 68807025 1 2 64 64 1 64  ε_{1} 55.7072
1185  −7 −8295 68807025 2 1 64 64 1 32  ε_{1} 36.4648
1185  −35 −1659 68807025 2 2 8 16 1  8  ε_{1} 36.4648
2765  −3 −8295 68807025 2 1 64 64 1 32  ε_{1} 14.2809
2765  −15 −1659 68807025 2 2 8 16 1  8  ε_{1} 14.2809
17 −488 −8296 68823616 1 10 20 100 1 100  ε_{1} 4.1894
61 −136 −8296 68823616 1 4 20 40 1 40  ε_{1} 7.3284
1037 −8 −8296 68823616 2 1 20 20 1 10 ε_{1} 10.1629
1037 −136 −488 68823616 2 4 10 40 1 20  ε_{1} 10.1629
193 −43 −8299 68873401 1 1 16 8 1 8 ε_{1} 30.1526
8301  −3 −2767 68906601 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 25.4224
12 −1384 −4152 68956416 1 10 12 60 1 60  ε_{1} 2.6339
24 −692 −4152 68956416 1 14 12 84 1 84  ε_{1} 4.5849
2076 −8 −4152 68956416 2 1 12 12 1 6 ε_{1} 34.4136
2076  −24 −1384 68956416 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 17.2068
4152 −4 −4152 68956416 2 1 12 12 1 6 ε_{1} 34.4866
4152  −24 −692 68956416 2 2 14 56 2 28 \sqrt{−1}\sqrt{ε_{1}} 17.2433
1661  −55 −755 68973025 1 4 12 24 1 24  ε_{1} 29.7725
8305  −11 −755 68973025 4 1 12 24 1  6  ε_{1} 60.0092
8305  −55 −151 68973025 4 4 7 56 1 14  ε_{1} 60.0092
124  −67 −8308 69022864 1 1 16  8 1  8  ε_{1} 16.0392
268  −31 −8308 69022864 1 3 16 24 1 24  ε_{1} 22.9790
2077  −4 −8308 69022864 1 1 16  8 1  8  ε_{1} 38.4093
8309  −7 −1187 69039481 5 1 9 45 2  9 \sqrt{−1}\sqrt{ε_{1}} 7.0775
8 −1039 −8312 69089344 1 23 40 460 1 460  ε_{1} 1.7627
8312  −8 −1039 69089344 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 23.9971
489  −51 −2771 69105969 1 2 26 26 1 26  ε_{1} 46.8872
8313  −3 −2771 69105969 2 1 26 26 1 13  ε_{1} 75.6589
8313  −51 −163 69105969 2 2 1  2 1  1  ε_{1} 75.6589
5 −1663 −8315 69139225 1 17 38 323 1 323  ε_{1} 0.9624
141  −59 −8319 69205761 1 3 80 120 1 120  ε_{1} 10.4940
177  −47 −8319 69205761 1 5 80 200 1 200  ε_{1} 23.4697
2773  −3 −8319 69205761 1 1 80 40 1 40  ε_{1} 60.1342
29 −287 −8323 69272329 1 14 12 84 1 84  ε_{1} 3.2945
41 −203 −8323 69272329 1 4 12 24 1 24  ε_{1} 8.3183
1189 −7 −8323 69272329 2 1 12 12 1 6 ε_{1} 20.3076
1189 −203 −287 69272329 2 4 14 56 1 28  ε_{1} 20.3076
2081  −4 −8324 69288976 5 1 60 150 1 30  ε_{1} 18.0042
757  −11 −8327 69338929 1 1 52 26 1 26  ε_{1} 29.6460
24 −347 −8328 69355584 1 5 24 60 1 60  ε_{1} 4.5849

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 213

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1041  −8 −8328 69355584 1 1 24 12 1 12  ε_{1} 69.9435
1041  −24 −2776 69355584 1 2 10 10 1 10  ε_{1} 69.9435
2776  −3 −8328 69355584 1 1 24 12 1 12  ε_{1} 105.4108
8328  −3 −2776 69355584 2 1 10 10 1  5  ε_{1} 43.6822
8328  −24 −347 69355584 2 2  5 10 1  5  ε_{1} 43.6822
2777  −3 −8331 69405561 3 1 18 27 1  9  ε_{1} 18.6981
8332  −4 −2083 69422224 1 1  7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 80.8128
5 −1667 −8335 69472225 1 13 50 325 1 325  ε_{1} 0.9624
8 −2084 −4168 69488896 1 32 12 192 1 192  ε_{1} 1.7627
4168  −4 −4168 69488896 4 1 12 24 1  6  ε_{1} 14.7729
4168  −8 −2084 69488896 4 1 32 64 1 16  ε_{1} 14.7729
21 −1191 −2779 69505569 1 24 14 168 1 168  ε_{1} 3.1336
8337  −3 −2779 69505569 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 34.5930
8337  −7 −1191 69505569 2 1 24 24 1 12  ε_{1} 69.1860
269  −31 −8339 69538921 1 3 26 39 1 39  ε_{1} 10.1998
5 −1668 −8340 69555600 1 12 32 192 1 192  ε_{1} 0.9624
12 −695 −8340 69555600 1 24 32 384 1 384  ε_{1} 2.6339
60 −139 −8340 69555600 2 3 32 96 1 48  ε_{1} 4.1269
60 −695 −1668 69555600 2 24 12 288 1 144  ε_{1} 4.1269
417  −20 −8340 69555600 1 2 32 32 1 32  ε_{1} 37.9102
556  −15 −8340 69555600 1 2 32 32 1 32  ε_{1} 37.7195
2085  −4 −8340 69555600 2 1 32 32 1 16  ε_{1} 9.8399
2085  −20 −1668 69555600 2 2 12 24 1 12  ε_{1} 9.8399
2780  −3 −8340 69555600 2 1 32 32 1 16  ε_{1} 22.2332
2780  −15 −1668 69555600 2 2 12 24 1 12  ε_{1} 22.2332
8341  −19 −439 69572281 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 63.6351
8 −1043 −8344 69622336 1 8 24 96 1 96  ε_{1} 1.7627
56 −1043 −1192 69622336 1 8  6 24 1 24  ε_{1} 6.8002
149  −56 −8344 69622336 1 4 24 48 1 48  ε_{1} 8.2223
1192  −7 −8344 69622336 2 1 24 24 1 12  ε_{1} 27.2320
1192  −56 −1043 69622336 2 4  8 32 1 16  ε_{1} 27.2320
8344  −7 −1192 69622336 2 1  6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 36.7731
8344  −8 −1043 69622336 2 1  8  8 1  4  ε_{1} 73.5462
17 −491 −8347 69672409 1 9 12 54 1 54  ε_{1} 4.1894
8348  −4 −2087 69689104 1 1 35 35 2 35  \sqrt{i}\sqrt{ε_{1}} 33.1124
1193  −7 −8351 69739201 1 1 118 59 1 59  ε_{1} 42.5195
5 −1671 −8355 69806025 1 38 20 380 1 380  ε_{1} 0.9624
557  −15 −8355 69806025 1 2 20 20 1 20  ε_{1} 10.9277
2785  −3 −8355 69806025 2 1 20 20 1 10  ε_{1} 69.5831
2785  −15 −1671 69806025 2 2 38 76 1 38  ε_{1} 69.5831
2089  −4 −8356 69822736 3 1 44 66 1 22  ε_{1} 45.6146
13 −643 −8359 69872881 1 3 58 87 1 87  ε_{1} 2.3895
5 −1672 −8360 69889600 1 8 48 192 1 192  ε_{1} 0.9624
88  −95 −8360 69889600 1 8 48 192 1 192  ε_{1} 11.9527
152  −55 −8360 69889600 1 4 48 96 1 96  ε_{1} 8.6078
209  −40 −8360 69889600 1 2 48 48 1 48  ε_{1} 22.8829
209 −440 −760 69889600 1 12  4 24 1 24  ε_{1} 22.8829
440  −19 −8360 69889600 2 1 48 48 1 24  ε_{1} 7.4742
440  −95 −1672 69889600 2 8  8 64 1 32  ε_{1} 7.4742
760  −11 −8360 69889600 2 1 48 48 1 24  ε_{1} 23.1051

214 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
760  −55 −1672 69889600 2 4 8 32 1 16  ε_{1} 23.1051
1045  −8 −8360 69889600 4 1 48 96 1 24  ε_{1} 9.1492
1045  −40 −1672 69889600 4 2 8 32 1  8  ε_{1} 9.1492
1045  −88 −760 69889600 4 2 4 16 1  4  ε_{1} 9.1492
1045 −152 −440 69889600 4 6 12 144 1 36  ε_{1} 9.1492
1672  −55 −760 69889600 2 4 4 16 1  8  ε_{1} 22.2461
1672  −95 −440 69889600 2 8 12 96 1 48  ε_{1} 22.2461
8360  −11 −760 69889600 4 1 4  8 1  2  ε_{1} 21.2408
8360  −19 −440 69889600 4 1 12 24 1  6  ε_{1} 21.2408
8360  −55 −152 69889600 4 4 6 48 1 12  ε_{1} 21.2408
8360  −88  −95 69889600 4 2 8 32 1  8  ε_{1} 21.2408
12 −2091 −2788 69956496 1 12 8 48 1 48  ε_{1} 2.6339
204 −123 −2788 69956496 2 2 8 16 1 8 ε_{1} 9.2101
204 −164 −2091 69956496 2 8 12 96 1 48  ε_{1} 9.2101
492  −51 −2788 69956496 2 2 8 16 1  8  ε_{1} 10.9943
492  −68 −2091 69956496 2 4 12 48 1 24  ε_{1} 10.9943
8364  −3 −2788 69956496 4 1 8 16 1  4  ε_{1} 26.2687
8364  −4 −2091 69956496 4 1 12 48 2 12  \sqrt{i}\sqrt{ε_{1}} 13.1343
8364  −51 −164 69956496 4 2 8 32 1  8  ε_{1} 26.2687
8364  −68 −123 69956496 4 4 2 16 1  4  ε_{1} 26.2687
1673  −35 −1195 69973225 1 2 8  8 1  8  ε_{1} 58.9611
8365  −7 −1195 69973225 2 1 8  8 1  4  ε_{1} 55.4796
8365  −35 −239 69973225 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 27.7398
2789 −3 −8367 70006689 1 1 30 15 1 15 ε_{1} 25.9778
2092  −8 −4184 70023424 1 1 42 42 2 42 \sqrt{−1}\sqrt{ε_{1}} 25.8208
4184  −4 −4184 70023424 1 1 42 42 2 42  \sqrt{i}\sqrt{ε_{1}} 29.7072
761  −11 −8371 70073641 3 1 22 33 1 11  ε_{1} 14.7555
13 −644 −8372 70090384 1 16 40 320 1 320  ε_{1} 2.3895
28 −299 −8372 70090384 1 8 40 160 1 160  ε_{1} 5.5373
92  −91 −8372 70090384 1 2 40 40 1 40  ε_{1} 7.7415
161  −52 −8372 70090384 1 2 40 40 1 40  ε_{1} 20.1338
364  −23 −8372 70090384 2 3 40 120 1 60  ε_{1} 16.1090
364 −299 −644 70090384 2 8 16 128 1 64  ε_{1} 16.1090
1196  −7 −8372 70090384 2 1 40 40 1 20  ε_{1} 13.4428
1196  −91 −644 70090384 2 2 16 32 1 16  ε_{1} 13.4428
2093  −4 −8372 70090384 2 1 40 40 1 20  ε_{1} 11.8053
2093  −52 −644 70090384 2 2 16 32 1 16  ε_{1} 11.8053
8373  −3 −2791 70107129 3 1 39 117 2 39 \sqrt{−1}\sqrt{ε_{1}} 10.7067
8 −1047 −8376 70157376 1 16 28 224 1 224  ε_{1} 1.7627
24 −1047 −2792 70157376 1 16 26 208 1 208  ε_{1} 4.5849
349  −24 −8376 70157376 1 2 28 28 1 28  ε_{1} 19.6424
2792  −3 −8376 70157376 2 1 28 28 1 14  ε_{1} 18.4599
2792  −24 −1047 70157376 2 2 16 32 1 16  ε_{1} 18.4599
8376  −3 −2792 70157376 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 38.2317
8376  −8 −1047 70157376 2 1 16 16 1  8  ε_{1} 76.4634
1676  −20 −2095 70224400 1 2 16 16 1 16  ε_{1} 40.2155
8380  −4 −2095 70224400 2 1 16 16 1  8  ε_{1} 92.3382
8380  −20 −419 70224400 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 46.1691
101 −83 −8383 70274689 1 3 26 39 1 39 ε_{1} 5.9964
129 −195 −2795 70308225 1 4 12 24 1 24  ε_{1} 20.8511

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 215

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
645  −39 −2795 70308225 2 4 12 48 1 24  ε_{1} 9.6883
645 −195 −559 70308225 2 4 16 64 1 32  ε_{1} 9.6883
1677 −15 −2795 70308225 4 2 12 48 1 12 ε_{1} 7.4260
1677 −195 −215 70308225 4 4 14 112 1 28  ε_{1} 7.4260
8385  −3 −2795 70308225 4 1 12 24 1  6  ε_{1} 49.7064
8385  −15 −559 70308225 4 2 16 64 1 16  ε_{1} 49.7064
8385  −39 −215 70308225 4 4 14 112 1 28  ε_{1} 49.7064
8385  −43 −195 70308225 4 1  4  8 1  2  ε_{1} 49.7064
2797  −3 −8391 70408881 1 1 76 38 1 38  ε_{1} 56.8635
1049  −8 −8392 70425664 1 1 24 12 1 12  ε_{1} 57.5072
77 −763 −1199 70442449 1 4 38 76 1 76  ε_{1} 4.3693
8393  −7 −1199 70442449 2 1 38 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 21.9801
8393 −11 −763 70442449 2 1 4 4 1 2 ε_{1} 43.9602
5 −1679 −8395 70476025 1 52 12 312 1 312  ε_{1} 0.9624
73 −115 −8395 70476025 1 2 12 12 1 12  ε_{1} 15.3334
365 −23 −8395 70476025 2 3 12 36 1 18 ε_{1} 5.8944
365 −115 −1679 70476025 2 2 52 104 1 52  ε_{1} 5.8944
8396 −4 −2099 70492816 3 1 19 57 2 19 \sqrt{i}\sqrt{ε_{1}} 14.9340
37 −227 −8399 70543201 1 5 134 335 1 335  ε_{1} 4.9836
8401  −31 −271 70576801 1 3 11 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 171.8436
2801 −3 −8403 70610409 1 1 18 9 1 9 ε_{1} 101.9618
44 −191 −8404 70627216 1 13 20 130 1 130  ε_{1} 5.9864
764  −11 −8404 70627216 1 1 20 10 1 10  ε_{1} 33.4104
2101  −4 −8404 70627216 3 1 20 30 1 10  ε_{1} 20.4440
1201  −7 −8407 70677649 1 1 36 18 1 18  ε_{1} 109.1299
8 −1051 −8408 70694464 1 5 26 65 1 65  ε_{1} 1.7627
8408  −8 −1051 70694464 1 1  5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 38.9688
8409  −3 −2803 70711281 1 1  9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 131.1610
13 −647 −8411 70744921 1 23 40 460 1 460  ε_{1} 2.3895
12 −2103 −2804 70761744 1 34 34 578 1 578  ε_{1} 2.6339
8412  −3 −2804 70761744 2 1 34 34 1 17  ε_{1} 22.2749
8412  −4 −2103 70761744 2 1 34 34 1 17  ε_{1} 22.2749
8413  −47 −179 70778569 1 5  5 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 34.2785
8417  −19 −443 70845889 1 1  5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 43.5525
5 −1684 −8420 70896400 1 10 48 240 1 240  ε_{1} 0.9624
421  −20 −8420 70896400 1 2 48 48 1 48  ε_{1} 26.0114
2105  −4 −8420 70896400 2 1 48 48 1 24  ε_{1} 34.6812
2105  −20 −1684 70896400 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 17.3406
21 −1203 −2807 70913241 1 6 52 156 1 156  ε_{1} 3.1336
8421  −3 −2807 70913241 2 1 52 52 1 26  ε_{1} 41.2082
8421  −7 −1203 70913241 2 1  6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 20.6041
124 −136 −4216 71098624 1 4 16 32 1 32  ε_{1} 16.0392
248 −68 −4216 71098624 1 4 16 32 1 32 ε_{1} 9.6724
2108  −8 −4216 71098624 2 1 16 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.9622
2108 −136 −248 71098624 2 4  8 32 1 16  ε_{1} 13.9245
4216  −4 −4216 71098624 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 36.4425
4216  −68 −248 71098624 2 4  8 32 1 16  ε_{1} 72.8851
5 −1687 −8435 71149225 1 18 28 252 1 252  ε_{1} 0.9624
241  −35 −8435 71149225 1 2 28 28 1 28  ε_{1} 37.5430
1205  −7 −8435 71149225 2 1 28 28 1 14  ε_{1} 10.9861

216 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1205  −35 −1687 71149225 2 2 18 36 1 18  ε_{1} 10.9861
12 −703 −8436 71166096 1 14 40 280 1 280  ε_{1} 2.6339
37 −228 −8436 71166096 1 4 40 80 1 80  ε_{1} 4.9836
57 −148 −8436 71166096 1 2 40 40 1 40  ε_{1} 11.4208
76 −111 −8436 71166096 1 8 40 160 1 160  ε_{1} 11.6579
444 −19 −8436 71166096 2 1 40 40 1 20 ε_{1} 12.7602
444 −228 −703 71166096 2 4 14 56 1 28  ε_{1} 12.7602
2109  −4 −8436 71166096 2 1 40 40 1 20  ε_{1} 23.3705
2109 −148 −228 71166096 2 2 4  8 1  4  ε_{1} 23.3705
2812  −3 −8436 71166096 2 1 40 40 1 20  ε_{1} 29.3127
2812 −111 −228 71166096 2 8 4 32 1 16  ε_{1} 29.3127
649 −143 −767 71182969 1 10 22 110 1 110  ε_{1} 70.6969
8437  −11 −767 71182969 2 1 22 22 1 11  ε_{1} 46.4699
8437  −59 −143 71182969 2 3 10 30 1 15  ε_{1} 46.4699
29 −291 −8439 71216721 1 4 68 136 1 136  ε_{1} 3.2945
97  −87 −8439 71216721 1 6 68 204 1 204  ε_{1} 18.6488
2813  −3 −8439 71216721 2 1 68 68 1 34  ε_{1} 7.9413
2813  −87 −291 71216721 2 6 4 24 1 12  ε_{1} 7.9413
5 −1688 −8440 71233600 1 10 28 140 1 140  ε_{1} 0.9624
8 −1055 −8440 71233600 1 36 28 504 1 504  ε_{1} 1.7627
40 −211 −8440 71233600 2 3 28 84 1 42  ε_{1} 3.6369
40 −1055 −1688 71233600 2 36 10 360 1 180  ε_{1} 3.6369
1688  −40 −1055 71233600 1 2 36 36 1 36  ε_{1} 32.9156
8440  −8 −1055 71233600 2 1 36 36 1 18  ε_{1} 79.0006
8440  −40 −211 71233600 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 39.5003
8441  −23 −367 71250481 13 3 9 351 2 27 \sqrt{−1}\sqrt{ε_{1}} 7.2930
8444  −4 −2111 71301136 1 1 49 49 2 49  \sqrt{i}\sqrt{ε_{1}} 41.8781
1689  −15 −2815 71318025 1 2 22 22 1 22  ε_{1} 105.0367
8445  −3 −2815 71318025 2 1 22 22 1 11  ε_{1} 28.3330
8445  −15 −563 71318025 2 2 9 18 1  9  ε_{1} 28.3330
497 −119 −1207 71385601 1 10 18 90 1 90  ε_{1} 29.3851
8449  −7 −1207 71385601 2 1 18 18 1  9  ε_{1} 172.3362
8449  −71 −119 71385601 2 7 10 70 1 35  ε_{1} 172.3362
2113  −4 −8452 71436304 1 1 16  8 1  8  ε_{1} 104.9750
8453  −79 −107 71453209 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 28.4665
5 −1691 −8455 71487025 1 18 56 504 1 504  ε_{1} 0.9624
89  −95 −8455 71487025 1 8 56 224 1 224  ε_{1} 13.8155
445  −19 −8455 71487025 4 1 56 112 1 28  ε_{1} 6.0936
445  −95 −1691 71487025 4 8 18 288 1 72  ε_{1} 6.0936
56 −151 −8456 71503936 1 7 56 196 1 196  ε_{1} 6.8002
1057  −8 −8456 71503936 1 1 56 28 1 28  ε_{1} 81.4221
1057  −56 −1208 71503936 1 4 12 24 1 24  ε_{1} 81.4221
1208  −7 −8456 71503936 1 1 56 28 1 28  ε_{1} 31.9236
8456  −7 −1208 71503936 4 1 12 24 1  6  ε_{1} 16.6999
8456  −56 −151 71503936 4 4 7 56 1 14  ε_{1} 16.6999
8457  −3 −2819 71520849 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 95.3031
769 −11 −8459 71554681 1 1 42 21 1 21 ε_{1} 76.0544
13 −651 −8463 71622369 1 8 48 192 1 192  ε_{1} 2.3895
21 −403 −8463 71622369 1 2 48 48 1 48  ε_{1} 3.1336
93  −91 −8463 71622369 1 2 48 48 1 48  ε_{1} 6.7322

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 217

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
217  −39 −8463 71622369 1 4 48 96 1 96  ε_{1} 31.7104
273  −31 −8463 71622369 2 3 48 144 1 72  ε_{1} 14.5641
273 −403 −651 71622369 2 2 8 16 1  8  ε_{1} 14.5641
1209  −7 −8463 71622369 2 1 48 48 1 24  ε_{1} 37.1044
1209  −91 −651 71622369 2 2 8 16 1  8  ε_{1} 37.1044
2821  −3 −8463 71622369 2 1 48 48 1 24  ε_{1} 36.4722
2821  −39 −651 71622369 2 4 8 32 1 16  ε_{1} 36.4722
29 −292 −8468 71707024 1 4 36 72 1 72  ε_{1} 3.2945
73 −116 −8468 71707024 1 6 36 108 1 108  ε_{1} 15.3334
2117 −4 −8468 71707024 2 1 36 36 1 18 ε_{1} 9.0438
2117 −116 −292 71707024 2 6 4 24 1 12  ε_{1} 9.0438
197 −43 −8471 71757841 1 1 80 40 1 40 ε_{1} 6.6670
8 −1059 −8472 71774784 1 6 20 60 1 60  ε_{1} 1.7627
24 −1059 −2824 71774784 1 6 24 72 1 72  ε_{1} 4.5849
353  −24 −8472 71774784 1 2 20 20 1 20  ε_{1} 23.7346
2824  −3 −8472 71774784 4 1 20 40 1 10  ε_{1} 22.2892
2824  −24 −1059 71774784 4 2 6 24 1  6  ε_{1} 22.2892
8472  −3 −2824 71774784 6 1 24 72 1 12  ε_{1} 16.7018
8472  −8 −1059 71774784 6 1 6 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 8.3509
652  −52 −2119 71842576 1 2 34 34 1 34  ε_{1} 37.3376
8476  −4 −2119 71842576 2 1 34 34 1 17  ε_{1} 67.0996
8476  −52 −163 71842576 2 2 1  2 1  1  ε_{1} 67.0996
61 −139 −8479 71893441 1 3 50 75 1 75  ε_{1} 7.3284
33 −771 −2827 71927361 1 6 8 24 1 24  ε_{1} 7.6563
8481  −3 −2827 71927361 2 1 8  8 1  4  ε_{1} 130.5015
8481  −11 −771 71927361 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 65.2508
17 −499 −8483 71961289 1 3 30 45 1 45  ε_{1} 4.1894
12 −707 −8484 71978256 1 6 40 120 1 120  ε_{1} 2.6339
21 −404 −8484 71978256 1 14 40 280 1 280  ε_{1} 3.1336
28 −303 −8484 71978256 1 10 40 200 1 200  ε_{1} 5.5373
101  −84 −8484 71978256 1 4 40 80 1 80  ε_{1} 5.9964
1212  −7 −8484 71978256 2 1 40 40 1 20  ε_{1} 17.0535
1212  −84 −707 71978256 2 4 6 24 1 12  ε_{1} 17.0535
2121  −4 −8484 71978256 2 1 40 40 1 20  ε_{1} 56.5394
2121  −84 −404 71978256 2 4 14 112 2 56 \sqrt{−1}\sqrt{ε_{1}} 28.2697
2828  −3 −8484 71978256 2 1 40 40 1 20  ε_{1} 17.0551
2828  −84 −303 71978256 2 4 10 40 1 20  ε_{1} 17.0551
1061  −8 −8488 72046144 1 1 18  9 1  9  ε_{1} 24.9704
1213  −7 −8491 72097081 1 1 20 10 1 10  ε_{1} 37.5314
44 −772 −2123 72114064 1 4 14 28 1 28  ε_{1} 5.9864
8492  −4 −2123 72114064 2 1 14 28 2 14  \sqrt{i}\sqrt{ε_{1}} 18.6371
8492  −11 −772 72114064 2 1 4  4 1  2  ε_{1} 37.2741
57 −447 −2831 72131049 1 14 68 476 1 476  ε_{1} 11.4208
8493 −3 −2831 72131049 2 1 68 68 1 34 ε_{1} 34.3545
8493  −19 −447 72131049 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 17.1772
5 −1699 −8495 72165025 1 11 64 352 1 352  ε_{1} 0.9624
2833  −3 −8499 72233001 1 1 24 12 1 12  ε_{1} 116.2557
773  −11 −8503 72301009 1 1 48 24 1 24  ε_{1} 9.8691
8 −1063 −8504 72318016 1 19 60 570 1 570  ε_{1} 1.7627
8504  −8 −1063 72318016 1 1 19 19 2 19 \sqrt{−1}\sqrt{ε_{1}} 43.1859

218 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
181  −47 −8507 72369049 1 5 18 45 1 45  ε_{1} 14.3479
12 −2127 −2836 72386064 1 28 10 140 1 140  ε_{1} 2.6339
8508  −3 −2836 72386064 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 16.3595
8508  −4 −2127 72386064 2 1 28 28 1 14  ε_{1} 32.7191
8509  −67 −127 72403081 1 1  5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 60.9142
2837  −3 −8511 72437121 1 1 94 47 1 47  ε_{1} 32.7460
5 −1703 −8515 72505225 1 28 16 224 1 224  ε_{1} 0.9624
13 −655 −8515 72505225 1 12 16 96 1 96  ε_{1} 2.3895
65 −131 −8515 72505225 2 5 16 80 1 40  ε_{1} 5.5529
65 −655 −1703 72505225 2 12 28 336 1 168  ε_{1} 5.5529
2129  −4 −8516 72522256 1 1 56 28 1 28  ε_{1} 97.3639
501  −51 −2839 72539289 1 2 26 26 1 26  ε_{1} 20.4959
8517  −3 −2839 72539289 2 1 26 26 1 13  ε_{1} 22.9894
8517  −51 −167 72539289 2 2 11 22 1 11  ε_{1} 22.9894
1217  −7 −8519 72573361 1 1 110 55 1 55  ε_{1} 35.6550
5 −1704 −8520 72590400 1 24 32 384 1 384  ε_{1} 0.9624
24 −355 −8520 72590400 1 4 32 64 1 64  ε_{1} 4.5849
120 −71 −8520 72590400 2 7 32 224 1 112 ε_{1} 6.1779
120 −355 −1704 72590400 2 4 24 96 1 48  ε_{1} 6.1779
213 −40 −8520 72590400 1 2 32 32 1 32 ε_{1} 8.5805
213 −120 −2840 72590400 1 4 32 64 1 64  ε_{1} 8.5805
568  −15 −8520 72590400 3 2 32 96 1 32  ε_{1} 11.3120
1065  −8 −8520 72590400 2 1 32 32 1 16  ε_{1} 37.8470
1065  −24 −2840 72590400 2 2 32 64 1 32  ε_{1} 37.8470
1065  −40 −1704 72590400 2 2 24 48 1 24  ε_{1} 37.8470
1065 −120 −568 72590400 2 4  4 16 1  8  ε_{1} 37.8470
1704  −15 −2840 72590400 2 2 32 64 1 32  ε_{1} 24.1735
1704 −120 −355 72590400 2 4  4 16 1  8  ε_{1} 24.1735
2840  −3 −8520 72590400 2 1 32 32 1 16  ε_{1} 15.6940
2840  −15 −1704 72590400 2 2 24 48 1 24  ε_{1} 15.6940
8520  −3 −2840 72590400 4 1 32 64 1 16  ε_{1} 21.5578
8520  −15 −568 72590400 4 2  4 16 1  4  ε_{1} 21.5578
8520  −24 −355 72590400 4 2  4 16 1  4  ε_{1} 21.5578
8520  −71 −120 72590400 4 7  4 112 2 28 \sqrt{−1}\sqrt{ε_{1}} 10.7789
8524  −4 −2131 72658576 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 68.9769
8 −2132 −4264 72726784 1 12 20 120 1 120  ε_{1} 1.7627
104 −164 −4264 72726784 2 8 20 160 1 80  ε_{1} 4.6249
104 −328 −2132 72726784 2 4 12 48 1 24  ε_{1} 4.6249
328 −52 −4264 72726784 4 2 20 80 1 20 ε_{1} 5.7869
328 −104 −2132 72726784 4 6 12 144 1 36  ε_{1} 5.7869
4264  −4 −4264 72726784 4 1 20 40 1 10  ε_{1} 31.4853
4264  −8 −2132 72726784 4 1 12 24 1  6  ε_{1} 31.4853
4264  −52 −328 72726784 4 2  4 16 1  4  ε_{1} 31.4853
4264 −104 −164 72726784 4 6  8 96 1 24  ε_{1} 31.4853
8529  −3 −2843 72743841 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 113.5685
449  −19 −8531 72777961 1 1 50 25 1 25  ε_{1} 39.5058
161 −371 −1219 72812089 1 8  6 24 1 24  ε_{1} 20.1338
8533  −7 −1219 72812089 2 1  6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 17.2933
8533  −23 −371 72812089 2 3  8 24 1 12  ε_{1} 34.5866
5 −1707 −8535 72846225 1 10 52 260 1 260  ε_{1} 0.9624

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 219

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
569  −15 −8535 72846225 1 2 52 52 1 52  ε_{1} 44.9587
2845  −3 −8535 72846225 2 1 52 52 1 26  ε_{1} 19.8546
2845  −15 −1707 72846225 2 2 10 20 1 10  ε_{1} 19.8546
8 −1067 −8536 72863296 1 12 32 192 1 192  ε_{1} 1.7627
88 −776 −1067 72863296 1 20 12 120 1 120  ε_{1} 11.9527
97  −88 −8536 72863296 1 2 32 32 1 32  ε_{1} 18.6488
776  −11 −8536 72863296 2 1 32 32 1 16  ε_{1} 11.9323
776  −88 −1067 72863296 2 2 12 24 1 12  ε_{1} 11.9323
8536  −8 −1067 72863296 8 1 12 48 1  6  ε_{1} 19.7463
8536  −11 −776 72863296 8 1 20 160 2 20 \sqrt{−1}\sqrt{ε_{1}} 9.8731
28 −1220 −2135 72931600 1 16 44 352 1 352  ε_{1} 5.5373
140 −244 −2135 72931600 2 6 44 264 1 132  ε_{1} 4.9558
140 −427 −1220 72931600 2 2 16 32 1 16  ε_{1} 4.9558
1708  −20 −2135 72931600 6 2 44 264 1 44  ε_{1} 9.6404
1708  −35 −1220 72931600 6 2 16 96 1 16  ε_{1} 9.6404
8540  −4 −2135 72931600 4 1 44 88 1 22  ε_{1} 19.2644
8540  −7 −1220 72931600 4 1 16 32 1  8  ε_{1} 19.2644
8540  −20 −427 72931600 4 2 2  8 1  2  ε_{1} 19.2644
8540  −35 −244 72931600 4 2 6 24 1  6  ε_{1} 19.2644
21 −407 −8547 73051209 1 16 16 128 1 128  ε_{1} 3.1336
33 −259 −8547 73051209 1 4 16 32 1 32  ε_{1} 7.6563
37 −231 −8547 73051209 1 12 16 96 1 96  ε_{1} 4.9836
77 −111 −8547 73051209 1 8 16 64 1 64  ε_{1} 4.3693
777 −11 −8547 73051209 4 1 16 32 1 8 ε_{1} 12.2006
777 −231 −407 73051209 4 12 16 384 1 96  ε_{1} 12.2006
1221 −7 −8547 73051209 4 1 16 32 1 8 ε_{1} 7.1091
1221 −231 −259 73051209 4 12 4 96 1 24  ε_{1} 7.1091
2849 −3 −8547 73051209 4 1 16 32 1 8 ε_{1} 23.1079
2849 −111 −231 73051209 4 8 12 192 1 48  ε_{1} 23.1079
2137 −4 −8548 73068304 1 1 16 8 1 8 ε_{1} 126.0100
8549  −83 −103 73085401 1 3 5 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 32.8410
17 −503 −8551 73119601 1 21 50 525 1 525  ε_{1} 4.1894
1069 −8 −8552 73136704 1 1 42 21 1 21 ε_{1} 36.9734
8553  −3 −2851 73153809 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 65.9478
5 −1711 −8555 73188025 1 28 32 448 1 448  ε_{1} 0.9624
29 −295 −8555 73188025 1 8 32 128 1 128  ε_{1} 3.2945
145 −59 −8555 73188025 4 3 32 192 1 48 ε_{1} 6.3596
145 −295 −1711 73188025 4 8 28 448 1 112  ε_{1} 6.3596
12 −2139 −2852 73205136 1 8 24 96 1 96  ε_{1} 2.6339
69 −372 −2852 73205136 1 4 24 48 1 48  ε_{1} 6.4345
92 −372 −2139 73205136 1 4 8 16 1 16  ε_{1} 7.7415
93 −276 −2852 73205136 1 8 24 96 1 96  ε_{1} 6.7322
124 −276 −2139 73205136 1 8 8 32 1 32  ε_{1} 16.0392
713 −276 −372 73205136 1 8 4 16 1 16  ε_{1} 32.3476
8556  −3 −2852 73205136 12 1 24 144 1 12  ε_{1} 11.8270
8556  −4 −2139 73205136 12 1 8 48 1  4  ε_{1} 11.8270
8556  −23 −372 73205136 12 3 4 144 2 12 \sqrt{−1}\sqrt{ε_{1}} 5.9135
8556  −31 −276 73205136 12 3 8 144 1 12  ε_{1} 11.8270
8557  −43 −199 73222249 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 35.4975
428  −40 −4280 73273600 1 2 36 36 1 36  ε_{1} 15.1243

220 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
856  −20 −4280 73273600 1 2 36 36 1 36  ε_{1} 55.9217
2140  −8 −4280 73273600 2 1 36 36 1 18  ε_{1} 29.9807
2140  −40 −856 73273600 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 14.9903
4280 −4 −4280 73273600 2 1 36 36 1 18 ε_{1} 31.1799
4280  −20 −856 73273600 2 2 6 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 15.5900
8561  −7 −1223 73290721 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 90.2883
2141  −4 −8564 73342096 1 1 78 39 1 39  ε_{1} 27.5414
1713  −15 −2855 73359225 1 2 60 60 1 60  ε_{1} 63.9547
8565  −3 −2855 73359225 2 1 60 60 1 30  ε_{1} 28.5759
8565  −15 −571 73359225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 14.2880
13 −659 −8567 73393489 1 11 84 462 1 462  ε_{1} 2.3895
209 −451 −779 73427761 1 6 10 30 1 30  ε_{1} 22.8829
8569  −11 −779 73427761 10 1 10 50 1  5  ε_{1} 35.1217
8569  −19 −451 73427761 10 1 6 30 1  3  ε_{1} 35.1217
2857  −3 −8571 73462041 3 1 36 54 1 18  ε_{1} 49.4792
8572  −4 −2143 73479184 3 1 13 39 2 13  \sqrt{i}\sqrt{ε_{1}} 24.4239
373  −23 −8579 73599241 1 3 42 63 1 63  ε_{1} 18.4673
5 −1716 −8580 73616400 1 16 32 256 1 256  ε_{1} 0.9624
12 −715 −8580 73616400 1 4 32 64 1 64  ε_{1} 2.6339
13 −660 −8580 73616400 1 8 32 128 1 128  ε_{1} 2.3895
33 −260 −8580 73616400 1 8 32 128 1 128  ε_{1} 7.6563
44 −195 −8580 73616400 1 4 32 64 1 64  ε_{1} 5.9864
60 −143 −8580 73616400 2 10 32 320 1 160  ε_{1} 4.1269
60 −715 −1716 73616400 2 4 16 64 1 32  ε_{1} 4.1269
65 −132 −8580 73616400 2 4 32 128 1 64  ε_{1} 5.5529
65 −660 −1716 73616400 2 8 16 128 1 64  ε_{1} 5.5529
156 −55 −8580 73616400 2 4 32 128 1 64 ε_{1} 7.8232
156 −660 −715 73616400 2 8 4 32 1 16  ε_{1} 7.8232
165 −52 −8580 73616400 2 2 32 64 1 32 ε_{1} 5.1180
165 −260 −1716 73616400 2 8 16 128 1 64  ε_{1} 5.1180
220 −39 −8580 73616400 2 4 32 128 1 64 ε_{1} 10.3635
220 −195 −1716 73616400 2 4 16 64 1 32  ε_{1} 10.3635
429 −20 −8580 73616400 2 2 32 64 1 32 ε_{1} 9.9534
429 −260 −660 73616400 2 8 8 64 1 32  ε_{1} 9.9534
572 −15 −8580 73616400 2 2 32 64 1 32 ε_{1} 6.3526
572 −195 −660 73616400 2 4 8 32 1 16  ε_{1} 6.3526
780  −11 −8580 73616400 4 1 32 64 1 16  ε_{1} 6.6619
780  −55 −1716 73616400 4 4 16 128 1 32  ε_{1} 6.6619
780 −132 −715 73616400 4 4 4 32 1  8  ε_{1} 6.6619
780 −143 −660 73616400 4 10 8 160 1 40  ε_{1} 6.6619
2145  −4 −8580 73616400 4 1 32 64 1 16  ε_{1} 21.8775
2145  −20 −1716 73616400 4 2 16 64 1 16  ε_{1} 21.8775
2145  −52 −660 73616400 4 2 8 32 1  8  ε_{1} 21.8775
2145 −132 −260 73616400 4 4 8 64 1 16  ε_{1} 21.8775
2860  −3 −8580 73616400 4 1 32 64 1 16  ε_{1} 23.8539
2860  −15 −1716 73616400 4 2 16 64 1 16  ε_{1} 23.8539
2860  −39 −660 73616400 4 4 8 64 1 16  ε_{1} 23.8539
2860 −132 −195 73616400 4 4 4 32 1  8  ε_{1} 23.8539
2861  −3 −8583 73667889 1 1 50 25 1 25  ε_{1} 37.2320
29 −296 −8584 73685056 1 10 28 140 1 140  ε_{1} 3.2945

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 221

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
37 −232 −8584 73685056 1 2 28 28 1 28  ε_{1} 4.9836
1073 −8 −8584 73685056 2 1 28 28 1 14 ε_{1} 22.8314
1073 −232 −296 73685056 2 2 10 20 1 10  ε_{1} 22.8314
277 −31 −8587 73736569 1 3 18 27 1 27 ε_{1} 15.7365
76 −452 −2147 73753744 1 8 14 56 1 56  ε_{1} 11.6579
8588  −4 −2147 73753744 2 1 14 28 2 14  \sqrt{i}\sqrt{ε_{1}} 10.5621
8588  −19 −452 73753744 2 1  8  8 1  4  ε_{1} 21.1243
21 −1227 −2863 73770921 1 4 22 44 1 44  ε_{1} 3.1336
8589  −3 −2863 73770921 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 24.6699
8589 −7 −1227 73770921 2 1 4 4 1 2 ε_{1} 49.3398
8 −2148 −4296 73822464 1 12 32 192 1 192  ε_{1} 1.7627
12 −1432 −4296 73822464 1 6 32 96 1 96  ε_{1} 2.6339
24 −1432 −2148 73822464 1 6 12 36 1 36  ε_{1} 4.5849
716  −24 −4296 73822464 1 2 32 32 1 32  ε_{1} 31.8828
1432  −24 −2148 73822464 1 2 12 12 1 12  ε_{1} 53.1804
4296  −4 −4296 73822464 2 1 32 64 2 32  \sqrt{i}\sqrt{ε_{1}} 15.7584
4296  −8 −2148 73822464 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 15.7584
28 −307 −8596 73891216 1 3 28 42 1 42  ε_{1} 5.5373
1228  −7 −8596 73891216 1 1 28 14 1 14  ε_{1} 37.9840
2149  −4 −8596 73891216 1 1 28 14 1 14  ε_{1} 60.1259
141 −183 −2867 73977201 1 8 12 48 1 48  ε_{1} 10.4940
8601  −3 −2867 73977201 4 1 12 24 1  6  ε_{1} 45.6273
8601  −47 −183 73977201 4 5  8 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 22.8136
1229  −7 −8603 74011609 3 1 24 36 1 12  ε_{1} 7.1123
57 −151 −8607 74080449 1 7 40 140 1 140  ε_{1} 11.4208
453  −19 −8607 74080449 1 1 40 20 1 20  ε_{1} 10.0078
2869  −3 −8607 74080449 1 1 40 20 1 20  ε_{1} 67.1594
109  −79 −8611 74149321 1 5 14 35 1 35  ε_{1} 11.1291
2153  −4 −8612 74166544 5 1 32 80 1 16  ε_{1} 12.2798
5 −1723 −8615 74218225 1 5 118 295 1 295  ε_{1} 0.9624
24 −359 −8616 74235456 1 19 40 380 1 380  ε_{1} 4.5849
1077  −8 −8616 74235456 1 1 40 20 1 20  ε_{1} 11.7777
1077  −24 −2872 74235456 1 2 12 12 1 12  ε_{1} 11.7777
2872  −3 −8616 74235456 1 1 40 20 1 20  ε_{1} 88.6590
8616  −3 −2872 74235456 2 1 12 12 1  6  ε_{1} 56.2484
8616  −24 −359 74235456 2 2 19 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 28.1242
8617  −7 −1231 74252689 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 119.9899
1724  −20 −2155 74304400 1 2 12 12 1 12  ε_{1} 39.0593
8620  −4 −2155 74304400 2 1 12 12 1  6  ε_{1} 67.4862
8620  −20 −431 74304400 2 2 21 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 33.7431
12 −719 −8628 74442384 1 31 24 372 1 372  ε_{1} 2.6339
2157  −4 −8628 74442384 1 1 24 12 1 12  ε_{1} 37.8342
2876  −3 −8628 74442384 1 1 24 12 1 12  ε_{1} 54.8331
8 −1079 −8632 74511424 1 34 20 340 1 340  ε_{1} 1.7627
13 −664 −8632 74511424 1 10 20 100 1 100  ε_{1} 2.3895
104 −83 −8632 74511424 2 3 20 60 1 30 ε_{1} 4.6249
104 −664 −1079 74511424 2 10 34 340 1 170  ε_{1} 4.6249
664 −104 −1079 74511424 1 6 34 102 1 102  ε_{1} 43.8951
8632  −8 −1079 74511424 2 1 34 34 1 17  ε_{1} 67.4263
8632  −83 −104 74511424 2 3  6 18 1  9  ε_{1} 67.4263

222 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −1727 −8635 74563225 1 36 16 288 1 288  ε_{1} 0.9624
157  −55 −8635 74563225 1 4 16 32 1 32  ε_{1} 10.7226
785  −11 −8635 74563225 6 1 16 48 1  8  ε_{1} 8.0513
785  −55 −1727 74563225 6 4 36 432 1 72  ε_{1} 8.0513
508  −68 −2159 74580496 1 4 60 120 1 120  ε_{1} 32.1254
8636  −4 −2159 74580496 4 1 60 120 1 30  ε_{1} 21.9069
8636  −68 −127 74580496 4 4 5 40 1 10  ε_{1} 21.9069
8637  −3 −2879 74597769 3 1 57 171 2 57 \sqrt{−1}\sqrt{ε_{1}} 7.9659
53 −163 −8639 74632321 1 1 88 44 1 44  ε_{1} 3.9314
129  −67 −8643 74701449 1 1 16  8 1  8  ε_{1} 20.8511
201  −43 −8643 74701449 1 1 16  8 1  8  ε_{1} 27.6905
2881  −3 −8643 74701449 1 1 16  8 1  8  ε_{1} 182.4288
2161  −4 −8644 74718736 1 1 36 18 1 18  ε_{1} 148.1166
133 −455 −1235 74736025 1 20 12 120 1 120  ε_{1} 10.3065
665 −91 −1235 74736025 2 2 12 24 1 12 ε_{1} 20.4394
665 −247 −455 74736025 2 6 20 120 1 60  ε_{1} 20.4394
1729  −35 −1235 74736025 2 2 12 24 1 12  ε_{1} 64.2443
1729  −95 −455 74736025 2 8 20 160 1 80  ε_{1} 64.2443
8645  −7 −1235 74736025 4 1 12 24 1  6  ε_{1} 9.0650
8645  −19 −455 74736025 4 1 20 40 1 10  ε_{1} 9.0650
8645  −35 −247 74736025 4 2 6 24 1  6  ε_{1} 9.0650
8645  −91  −95 74736025 4 2 8 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 4.5325
184  −47 −8648 74787904 1 5 56 140 1 140  ε_{1} 21.5856
376  −23 −8648 74787904 1 3 56 84 1 84  ε_{1} 30.5420
1081  −8 −8648 74787904 1 1 56 28 1 28  ε_{1} 95.6412
1081 −184 −376 74787904 1 4 8 16 1 16  ε_{1} 95.6412
8648 −23 −376 74787904 4 3 8 48 1 12 ε_{1} 10.4514
8648  −47 −184 74787904 4 5 4 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 5.2257
41 −211 −8651 74839801 1 3 38 57 1 57  ε_{1} 8.3183
12 −2163 −2884 74857104 1 8 16 64 1 64  ε_{1} 2.6339
21 −1236 −2884 74857104 1 12 16 96 1 96  ε_{1} 3.1336
28 −1236 −2163 74857104 1 12 8 48 1 48  ε_{1} 5.5373
309  −84 −2884 74857104 1 4 16 32 1 32  ε_{1} 17.0523
412  −84 −2163 74857104 1 4 8 16 1 16  ε_{1} 26.0564
721  −84 −1236 74857104 1 4 12 24 1 24  ε_{1} 76.3136
8652  −3 −2884 74857104 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 9.3531
8652  −4 −2163 74857104 4 1 8 16 1  4  ε_{1} 18.7061
8652  −7 −1236 74857104 4 1 12 24 1  6  ε_{1} 18.7061
8652  −84 −103 74857104 4 4 5 40 1 10  ε_{1} 18.7061
5 −1731 −8655 74909025 1 8 84 336 1 336  ε_{1} 0.9624
577  −15 −8655 74909025 7 2 84 588 1 84  ε_{1} 7.7433
2885  −3 −8655 74909025 2 1 84 84 1 42  ε_{1} 18.6133
2885  −15 −1731 74909025 2 2 8 16 1  8  ε_{1} 18.6133
8 −2164 −4328 74926336 1 10 22 110 1 110  ε_{1} 1.7627
4328  −4 −4328 74926336 2 1 22 22 1 11  ε_{1} 29.4829
4328  −8 −2164 74926336 2 1 10 10 1  5  ε_{1} 29.4829
8657  −11 −787 74943649 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 59.9664
1237  −7 −8659 74978281 1 1 22 11 1 11  ε_{1} 28.1466
5 −1732 −8660 74995600 1 12 28 168 1 168  ε_{1} 0.9624
433  −20 −8660 74995600 1 2 28 28 1 28  ε_{1} 46.7895

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 223

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2165  −4 −8660 74995600 2 1 28 28 1 14  ε_{1} 13.3466
2165  −20 −1732 74995600 2 2 12 24 1 12  ε_{1} 13.3466
8661  −3 −2887 75012921 7 1 25 175 2 25 \sqrt{−1}\sqrt{ε_{1}} 7.9673
44 −788 −2167 75134224 1 10 18 90 1 90  ε_{1} 5.9864
8668  −4 −2167 75134224 2 1 18 18 1  9  ε_{1} 78.0546
8668  −11 −788 75134224 2 1 10 10 1  5  ε_{1} 78.0546
13 −667 −8671 75186241 1 4 64 128 1 128  ε_{1} 2.3895
29 −299 −8671 75186241 1 8 64 256 1 256  ε_{1} 3.2945
377 −23 −8671 75186241 2 3 64 192 1 96 ε_{1} 12.2884
377 −299 −667 75186241 2 8 4 32 1 16  ε_{1} 12.2884
33 −263 −8679 75325041 1 13 88 572 1 572  ε_{1} 7.6563
789  −11 −8679 75325041 1 1 88 44 1 44  ε_{1} 20.7360
2893  −3 −8679 75325041 1 1 88 44 1 44  ε_{1} 52.7678
5 −1736 −8680 75342400 1 24 16 192 1 192  ε_{1} 0.9624
56 −155 −8680 75342400 1 4 16 32 1 32  ε_{1} 6.8002
217 −40 −8680 75342400 1 2 16 16 1 16 ε_{1} 31.7104
217 −280 −1240 75342400 1 4 8 16 1 16  ε_{1} 31.7104
248  −35 −8680 75342400 1 2 16 16 1 16  ε_{1} 9.6724
280  −31 −8680 75342400 2 3 16 48 1 24  ε_{1} 12.4372
280 −155 −1736 75342400 2 4 24 96 1 48  ε_{1} 12.4372
1085  −8 −8680 75342400 2 1 16 16 1  8  ε_{1} 6.9912
1085  −40 −1736 75342400 2 2 24 48 1 24  ε_{1} 6.9912
1085  −56 −1240 75342400 2 4 8 32 1 16  ε_{1} 6.9912
1085 −248 −280 75342400 2 8 4 32 1 16  ε_{1} 6.9912
1240  −7 −8680 75342400 2 1 16 16 1  8  ε_{1} 28.6893
1240  −35 −1736 75342400 2 2 24 48 1 24  ε_{1} 28.6893
1736  −35 −1240 75342400 4 2 8 32 1  8  ε_{1} 11.0429
1736 −155 −280 75342400 4 4 4 32 1  8  ε_{1} 11.0429
8680  −7 −1240 75342400 12 1 8 48 1  4  ε_{1} 14.0386
8680  −31 −280 75342400 12 3 4 144 2 12 \sqrt{−1}\sqrt{ε_{1}} 7.0193
8680  −35 −248 75342400 12 2 8 96 1  8  ε_{1} 14.0386
8680  −56 −155 75342400 12 4 4 96 1  8  ε_{1} 14.0386
457  −19 −8683 75394489 1 1 16  8 1  8  ε_{1} 50.9909
668  −52 −2171 75411856 1 2 14 14 1 14  ε_{1} 11.6342
8684  −4 −2171 75411856 2 1 14 14 1  7  ε_{1} 61.3449
8684  −52 −167 75411856 2 2 11 22 1 11  ε_{1} 61.3449
17 −511 −8687 75463969 1 14 84 588 1 588  ε_{1} 4.1894
73 −119 −8687 75463969 1 10 84 420 1 420  ε_{1} 15.3334
1241 −7 −8687 75463969 2 1 84 84 1 42 ε_{1} 36.0697
1241 −119 −511 75463969 2 10 14 140 1 70  ε_{1} 36.0697
12 −1448 −4344 75481344 1 18 28 252 1 252  ε_{1} 2.6339
24 −724 −4344 75481344 1 10 28 140 1 140  ε_{1} 4.5849
2172  −8 −4344 75481344 2 1 28 28 1 14  ε_{1} 28.2144
2172  −24 −1448 75481344 2 2 18 36 1 18  ε_{1} 28.2144
4344  −4 −4344 75481344 6 1 28 84 1 14  ε_{1} 14.5586
4344  −24 −724 75481344 6 2 10 60 1 10  ε_{1} 14.5586
2897  −3 −8691 75533481 1 1 26 13 1 13  ε_{1} 60.1961
41 −212 −8692 75550864 1 6 20 60 1 60  ε_{1} 8.3183
53 −164 −8692 75550864 1 8 20 80 1 80  ε_{1} 3.9314
2173  −4 −8692 75550864 2 1 20 20 1 10  ε_{1} 14.2001

224 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2173 −164 −212 75550864 2 8  6 48 1 24  ε_{1} 14.2001
5 −1739 −8695 75603025 1 20 36 360 1 360  ε_{1} 0.9624
37 −235 −8695 75603025 1 2 36 36 1 36  ε_{1} 4.9836
185 −47 −8695 75603025 2 5 36 180 1 90 ε_{1} 9.8254
185 −235 −1739 75603025 2 2 20 40 1 20  ε_{1} 9.8254
8 −1087 −8696 75620416 1 9 64 288 1 288  ε_{1} 1.7627
8696  −8 −1087 75620416 1 1  9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 57.8603
669  −39 −2899 75637809 1 4 10 20 1 20  ε_{1} 25.2580
8697  −3 −2899 75637809 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 28.5532
8697  −39 −223 75637809 2 4  7 28 1 14  ε_{1} 57.1063
77 −791 −1243 75707401 1 32  4 64 1 64  ε_{1} 4.3693
8701  −7 −1243 75707401 4 1  4 16 2  4 \sqrt{−1}\sqrt{ε_{1}} 14.6477
8701  −11 −791 75707401 4 1 32 64 1 16  ε_{1} 29.2954
28 −311 −8708 75829264 1 19 40 380 1 380  ε_{1} 5.5373
1244  −7 −8708 75829264 1 1 40 20 1 20  ε_{1} 34.6700
2177  −4 −8708 75829264 3 1 40 60 1 20  ε_{1} 18.6470
8709  −3 −2903 75846681 1 1 59 59 2 59 \sqrt{−1}\sqrt{ε_{1}} 44.6387
281 −31 −8711 75881521 1 3 132 198 1 198 ε_{1} 29.1405
5 −1743 −8715 75951225 1 24 16 192 1 192  ε_{1} 0.9624
21 −415 −8715 75951225 1 10 16 80 1 80  ε_{1} 3.1336
105 −83 −8715 75951225 2 3 16 48 1 24 ε_{1} 8.8131
105 −415 −1743 75951225 2 10 24 240 1 120  ε_{1} 8.8131
249  −35 −8715 75951225 1 2 16 16 1 16  ε_{1} 33.3101
581  −15 −8715 75951225 1 2 16 16 1 16  ε_{1} 17.6272
1245  −7 −8715 75951225 2 1 16 16 1  8  ε_{1} 11.0187
1245  −35 −1743 75951225 2 2 24 48 1 24  ε_{1} 11.0187
2905  −3 −8715 75951225 2 1 16 16 1  8  ε_{1} 80.8035
2905  −15 −1743 75951225 2 2 24 48 1 24  ε_{1} 80.8035
8716  −4 −2179 75968656 1 1  7  7 2  7  \sqrt{i}\sqrt{ε_{1}} 95.9771
8717  −23 −379 75986089 1 3  3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 21.5808
8 −2180 −4360 76038400 1 32 12 192 1 192  ε_{1} 1.7627
40 −436 −4360 76038400 2 6 12 72 1 36  ε_{1} 3.6369
40 −872 −2180 76038400 2 10 32 320 1 160  ε_{1} 3.6369
872  −20 −4360 76038400 2 2 12 24 1 12  ε_{1} 12.4372
872  −40 −2180 76038400 2 2 32 64 1 32  ε_{1} 12.4372
4360  −4 −4360 76038400 12 1 12 72 1  6  ε_{1} 8.3798
4360  −8 −2180 76038400 12 1 32 192 1 16  ε_{1} 8.3798
4360  −20 −872 76038400 12 2 10 120 1 10  ε_{1} 8.3798
4360  −40 −436 76038400 12 2  6 72 1  6  ε_{1} 8.3798
13 −671 −8723 76090729 1 30 28 420 1 420  ε_{1} 2.3895
61 −143 −8723 76090729 1 10 28 140 1 140  ε_{1} 7.3284
793 −11 −8723 76090729 4 1 28 56 1 14 ε_{1} 18.1618
793 −143 −671 76090729 4 10 30 600 1 150  ε_{1} 18.1618
12 −727 −8724 76108176 1 13 36 234 1 234  ε_{1} 2.6339
2181  −4 −8724 76108176 1 1 36 18 1 18  ε_{1} 47.7630
2908  −3 −8724 76108176 5 1 36 90 1 18  ε_{1} 14.5669
2909  −3 −8727 76160529 1 1 50 25 1 25  ε_{1} 44.9226
8 −1091 −8728 76177984 1 17 22 187 1 187  ε_{1} 1.7627
8728  −8 −1091 76177984 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 52.0974
301 −203 −1247 76195441 1 4 26 52 1 52  ε_{1} 20.0642

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 225

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8729  −7 −1247 76195441 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 41.9640
8729 −43 −203 76195441 2 1 4 4 1 2 ε_{1} 83.9281
236 −148 −2183 76247824 1 2 42 42 1 42  ε_{1} 13.9320
8732  −4 −2183 76247824 2 1 42 42 1 21  ε_{1} 29.2213
8732  −59 −148 76247824 2 3  2  6 1  3  ε_{1} 29.2213
213 −123 −2911 76265289 1 2 42 42 1 42  ε_{1} 8.5805
8733  −3 −2911 76265289 2 1 42 42 1 21  ε_{1} 29.5607
8733  −71 −123 76265289 2 7  2 14 1  7  ε_{1} 29.5607
5 −1747 −8735 76300225 1 5 106 265 1 265  ε_{1} 0.9624
5 −1748 −8740 76387600 1 20 24 240 1 240  ε_{1} 0.9624
76 −115 −8740 76387600 1 2 24 24 1 24  ε_{1} 11.6579
92  −95 −8740 76387600 1 8 24 96 1 96  ε_{1} 7.7415
380  −23 −8740 76387600 2 3 24 72 1 36  ε_{1} 8.7131
380 −115 −1748 76387600 2 2 20 40 1 20  ε_{1} 8.7131
437  −20 −8740 76387600 1 2 24 24 1 24  ε_{1} 6.0845
460  −19 −8740 76387600 2 1 24 24 1 12  ε_{1} 15.4391
460  −95 −1748 76387600 2 8 20 160 1 80  ε_{1} 15.4391
2185  −4 −8740 76387600 2 1 24 24 1 12  ε_{1} 72.2976
2185  −20 −1748 76387600 2 2 20 40 1 20  ε_{1} 72.2976
1249  −7 −8743 76440049 1 1 26 13 1 13  ε_{1} 102.5410
1093  −8 −8744 76457536 5 1 42 105 1 21  ε_{1} 6.9948
33 −795 −2915 76475025 1 4 24 48 1 48  ε_{1} 7.6563
165 −159 −2915 76475025 2 10 24 240 1 120  ε_{1} 5.1180
165 −583 −795 76475025 2 8  4 32 1 16  ε_{1} 5.1180
1749  −15 −2915 76475025 2 2 24 48 1 24  ε_{1} 16.5746
1749  −55 −795 76475025 2 4  4 16 1  8  ε_{1} 16.5746
8745  −3 −2915 76475025 12 1 24 144 1 12  ε_{1} 18.9015
8745  −11 −795 76475025 12 1  4 48 2  4 \sqrt{−1}\sqrt{ε_{1}} 9.4508
8745  −15 −583 76475025 12 2  8 96 1  8  ε_{1} 18.9015
8745  −55 −159 76475025 12 4 10 240 1 20  ε_{1} 18.9015
2917  −3 −8751 76580001 3 1 72 108 1 36  ε_{1} 9.3644
2188  −8 −4376 76597504 1 1 26 26 2 26 \sqrt{−1}\sqrt{ε_{1}} 33.4005
4376 −4 −4376 76597504 1 1 26 26 2 26 \sqrt{i}\sqrt{ε_{1}} 37.9332
5 −1751 −8755 76650025 1 48 20 480 1 480  ε_{1} 0.9624
17 −515 −8755 76650025 1 6 20 60 1 60  ε_{1} 4.1894
85 −103 −8755 76650025 2 5 20 100 1 50  ε_{1} 4.4187
85 −515 −1751 76650025 2 6 48 288 1 144  ε_{1} 4.4187
44 −199 −8756 76667536 1 9 60 270 1 270  ε_{1} 5.9864
796  −11 −8756 76667536 1 1 60 30 1 30  ε_{1} 48.4110
2189  −4 −8756 76667536 1 1 60 30 1 30  ε_{1} 27.8566
461  −19 −8759 76720081 1 1 108 54 1 54  ε_{1} 11.7998
5 −1752 −8760 76737600 1 8 24 96 1 96  ε_{1} 0.9624
8 −1095 −8760 76737600 1 28 24 336 1 336  ε_{1} 1.7627
24 −1095 −2920 76737600 1 28 12 168 1 168  ε_{1} 4.5849
40 −219 −8760 76737600 2 4 24 96 1 48  ε_{1} 3.6369
40 −1095 −1752 76737600 2 28 8 224 1 112 ε_{1} 3.6369
73 −120 −8760 76737600 1 4 24 48 1 48  ε_{1} 15.3334
120 −219 −2920 76737600 2 4 12 48 1 24  ε_{1} 6.1779
120 −584 −1095 76737600 2 16 28 448 1 224  ε_{1} 6.1779
365  −24 −8760 76737600 2 2 24 48 1 24  ε_{1} 5.8944

226 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
365 −120 −1752 76737600 2 4 8 32 1 16  ε_{1} 5.8944
584 −15 −8760 76737600 2 2 24 48 1 24 ε_{1} 11.3397
584 −120 −1095 76737600 2 4 28 112 1 56  ε_{1} 11.3397
1752  −15 −2920 76737600 4 2 12 48 1 12  ε_{1} 12.7466
1752  −40 −1095 76737600 4 2 28 112 1 28  ε_{1} 12.7466
2920  −3 −8760 76737600 12 1 24 144 1 12  ε_{1} 7.9787
2920  −15 −1752 76737600 12 2 8 96 1  8  ε_{1} 7.9787
2920  −24 −1095 76737600 12 2 28 336 1 28  ε_{1} 7.9787
2920 −120 −219 76737600 12 4 4 96 1  8  ε_{1} 7.9787
8760  −3 −2920 76737600 4 1 12 24 1  6  ε_{1} 21.0102
8760  −8 −1095 76737600 4 1 28 56 1 14  ε_{1} 21.0102
8760  −15 −584 76737600 4 2 16 64 1 16  ε_{1} 21.0102
8760  −40 −219 76737600 4 2 4 16 1  4  ε_{1} 21.0102
69 −127 −8763 76790169 1 5 24 60 1 60  ε_{1} 6.4345
381  −23 −8763 76790169 1 3 24 36 1 36  ε_{1} 15.2316
2921  −3 −8763 76790169 1 1 24 12 1 12  ε_{1} 107.1582
28 −1252 −2191 76807696 1 8 30 120 1 120  ε_{1} 5.5373
8764  −4 −2191 76807696 2 1 30 60 2 30  \sqrt{i}\sqrt{ε_{1}} 43.1739
8764  −7 −1252 76807696 2 1 8  8 1  4  ε_{1} 86.3478
797  −11 −8767 76860289 1 1 36 18 1 18  ε_{1} 11.8107
237 −111 −2923 76895361 1 8 6 24 1 24  ε_{1} 8.6873
8769  −3 −2923 76895361 6 1 6 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 14.6448
8769  −79 −111 76895361 6 5 8 120 1 20  ε_{1} 29.2895
12 −731 −8772 76947984 1 12 24 144 1 144  ε_{1} 2.6339
17 −516 −8772 76947984 1 12 24 144 1 144  ε_{1} 4.1894
129  −68 −8772 76947984 1 4 24 48 1 48  ε_{1} 20.8511
172  −51 −8772 76947984 1 2 24 24 1 24  ε_{1} 17.6970
204  −43 −8772 76947984 2 1 24 24 1 12  ε_{1} 9.2101
204 −516 −731 76947984 2 12 12 144 1 72  ε_{1} 9.2101
2193  −4 −8772 76947984 2 1 24 24 1 12  ε_{1} 49.5975
2193  −68 −516 76947984 2 4 12 48 1 24  ε_{1} 49.5975
2924  −3 −8772 76947984 4 1 24 48 1 12  ε_{1} 14.5724
2924  −51 −516 76947984 4 2 12 48 1 12  ε_{1} 14.5724
8773  −31 −283 76965529 7 3 3 63 2  9 \sqrt{−1}\sqrt{ε_{1}} 5.6383
1097  −8 −8776 77018176 1 1 32 16 1 16  ε_{1} 35.1082
8777  −67 −131 77035729 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 31.4039
1756  −20 −2195 77088400 5 2 16 80 1 16  ε_{1} 13.5598
8780  −4 −2195 77088400 2 1 16 16 1  8  ε_{1} 35.7356
8780  −20 −439 77088400 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 17.8678
8781  −3 −2927 77105961 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 40.3391
1757  −35 −1255 77176225 1 2 12 12 1 12  ε_{1} 13.8275
8785  −7 −1255 77176225 2 1 12 12 1  6  ε_{1} 142.4177
8785  −35 −251 77176225 2 2 7 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 71.2088
29 −303 −8787 77211369 1 10 12 60 1 60  ε_{1} 3.2945
101  −87 −8787 77211369 1 6 12 36 1 36  ε_{1} 5.9964
2929  −3 −8787 77211369 2 1 12 12 1  6  ε_{1} 86.8448
2929  −87 −303 77211369 2 6 10 60 1 30  ε_{1} 86.8448
517 −187 −799 77246521 1 2 16 16 1 16  ε_{1} 18.5321
8789 −11 −799 77246521 6 1 16 48 1 8 ε_{1} 13.2401
8789  −47 −187 77246521 6 5 2 60 2 10 \sqrt{−1}\sqrt{ε_{1}} 6.6201

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 227

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
149  −59 −8791 77281681 1 3 82 123 1 123  ε_{1} 8.2223
8 −1099 −8792 77299264 1 6 36 108 1 108  ε_{1} 1.7627
56 −1099 −1256 77299264 1 6 26 78 1 78  ε_{1} 6.8002
157  −56 −8792 77299264 1 4 36 72 1 72  ε_{1} 10.7226
1256  −7 −8792 77299264 2 1 36 36 1 18  ε_{1} 13.5734
1256  −56 −1099 77299264 2 4 6 24 1 12  ε_{1} 13.5734
8792  −7 −1256 77299264 2 1 26 26 1 13  ε_{1} 36.5065
8792  −8 −1099 77299264 2 1 6  6 1  3  ε_{1} 36.5065
5 −1759 −8795 77352025 1 27 32 432 1 432  ε_{1} 0.9624
12 −2199 −2932 77369616 1 36 14 252 1 252  ε_{1} 2.6339
8796  −3 −2932 77369616 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 27.9361
8796  −4 −2199 77369616 2 1 36 36 1 18  ε_{1} 55.8722
8797  −19 −463 77387209 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 35.5132
21 −419 −8799 77422401 1 9 80 360 1 360  ε_{1} 3.1336
1257  −7 −8799 77422401 3 1 80 120 1 40  ε_{1} 24.4399
2933  −3 −8799 77422401 1 1 80 40 1 40  ε_{1} 23.8535
124  −71 −8804 77510416 1 7 64 224 1 224  ε_{1} 16.0392
284  −31 −8804 77510416 1 3 64 96 1 96  ε_{1} 17.6959
2201  −4 −8804 77510416 1 1 64 32 1 32  ε_{1} 90.5566
1761  −15 −2935 77528025 7 2 22 154 1 22  ε_{1} 15.5243
8805  −3 −2935 77528025 2 1 22 22 1 11  ε_{1} 33.4862
8805  −15 −587 77528025 2 2 7 14 1  7  ε_{1} 33.4862
24 −367 −8808 77580864 1 9 20 90 1 90  ε_{1} 4.5849
1101  −8 −8808 77580864 3 1 20 30 1 10  ε_{1} 11.7998
1101  −24 −2936 77580864 3 2 40 120 1 40  ε_{1} 11.7998
2936  −3 −8808 77580864 1 1 20 10 1 10  ε_{1} 33.6998
8808  −3 −2936 77580864 2 1 40 40 1 20  ε_{1} 41.7884
8808  −24 −367 77580864 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 20.8942
8809  −23 −383 77598481 1 3 17 51 2 51 \sqrt{−1}\sqrt{ε_{1}} 147.6911
8812 −4 −2203 77651344 1 1 5 5 2 5 \sqrt{i}\sqrt{ε_{1}} 51.2252
8813  −7 −1259 77668969 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 23.4801
5 −1763 −8815 77704225 1 12 48 288 1 288  ε_{1} 0.9624
41 −215 −8815 77704225 1 14 48 336 1 336  ε_{1} 8.3183
205 −43 −8815 77704225 2 1 48 48 1 24 ε_{1} 7.5213
205 −215 −1763 77704225 2 14 12 168 1 84  ε_{1} 7.5213
76 −232 −4408 77721856 1 2 20 20 1 20  ε_{1} 11.6579
152 −116 −4408 77721856 1 6 20 60 1 60  ε_{1} 8.6078
2204 −8 −4408 77721856 2 1 20 20 1 10 ε_{1} 19.4535
2204 −152 −232 77721856 2 6 2 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 9.7268
4408 −4 −4408 77721856 2 1 20 20 1 10 ε_{1} 33.8815
4408 −116 −152 77721856 2 6 6 72 2 36 \sqrt{−1}\sqrt{ε_{1}} 16.9407
8817  −3 −2939 77739489 1 1 29 29 2 29 \sqrt{−1}\sqrt{ε_{1}} 95.2543
17 −519 −8823 77845329 1 18 60 540 1 540  ε_{1} 4.1894
173  −51 −8823 77845329 1 2 60 60 1 60  ε_{1} 5.1416
2941  −3 −8823 77845329 6 1 60 180 1 30  ε_{1} 13.1164
2941  −51 −519 77845329 6 2 18 108 1 18  ε_{1} 13.1164
8 −1103 −8824 77862976 1 23 32 368 1 368  ε_{1} 1.7627
8824  −8 −1103 77862976 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 97.2728
13 −679 −8827 77915929 1 18 12 108 1 108  ε_{1} 2.3895
97  −91 −8827 77915929 1 2 12 12 1 12  ε_{1} 18.6488

228 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1261  −7 −8827 77915929 2 1 12 12 1  6  ε_{1} 22.5547
1261  −91 −679 77915929 2 2 18 36 1 18  ε_{1} 22.5547
8828  −4 −2207 77933584 3 1 39 117 2 39  \sqrt{i}\sqrt{ε_{1}} 8.3930
5 −1767 −8835 78057225 1 32 16 256 1 256  ε_{1} 0.9624
57 −155 −8835 78057225 1 4 16 32 1 32  ε_{1} 11.4208
93  −95 −8835 78057225 1 8 16 64 1 64  ε_{1} 6.7322
285  −31 −8835 78057225 2 3 16 48 1 24  ε_{1} 5.6595
285 −155 −1767 78057225 2 4 32 128 1 64  ε_{1} 5.6595
465  −19 −8835 78057225 2 1 16 16 1  8  ε_{1} 20.7308
465  −95 −1767 78057225 2 8 32 256 1 128  ε_{1} 20.7308
589  −15 −8835 78057225 1 2 16 16 1 16  ε_{1} 30.5757
2945  −3 −8835 78057225 4 1 16 32 1  8  ε_{1} 17.4249
2945  −15 −1767 78057225 4 2 32 128 1 32  ε_{1} 17.4249
5 −1768 −8840 78145600 1 8 56 224 1 224  ε_{1} 0.9624
13 −680 −8840 78145600 1 12 56 336 1 336  ε_{1} 2.3895
17 −520 −8840 78145600 1 4 56 112 1 112  ε_{1} 4.1894
65 −136 −8840 78145600 2 4 56 224 1 112  ε_{1} 5.5529
65 −680 −1768 78145600 2 12 8 96 1 48  ε_{1} 5.5529
85 −104 −8840 78145600 2 6 56 336 1 168  ε_{1} 4.4187
85 −520 −1768 78145600 2 4 8 32 1 16  ε_{1} 4.4187
221 −40 −8840 78145600 2 2 56 112 1 56 ε_{1} 5.4072
221 −520 −680 78145600 2 4 12 48 1 24  ε_{1} 5.4072
1105  −8 −8840 78145600 4 1 56 112 1 28  ε_{1} 21.9008
1105  −40 −1768 78145600 4 2 8 32 1  8  ε_{1} 21.9008
1105 −104 −680 78145600 4 6 12 144 1 36  ε_{1} 21.9008
1105 −136 −520 78145600 4 4 4 32 1 8 ε_{1} 21.9008
21 −1263 −2947 78163281 1 20 8 80 1 80  ε_{1} 3.1336
8841  −3 −2947 78163281 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 31.1586
8841  −7 −1263 78163281 4 1 20 40 1 10  ε_{1} 62.3172
37 −239 −8843 78198649 1 15 26 195 1 195  ε_{1} 4.9836
12 −2211 −2948 78216336 1 16 20 160 1 160  ε_{1} 2.6339
33 −804 −2948 78216336 1 12 20 120 1 120  ε_{1} 7.6563
44 −804 −2211 78216336 1 12 16 96 1 96  ε_{1} 5.9864
201 −132 −2948 78216336 1 4 20 40 1 40  ε_{1} 27.6905
268 −132 −2211 78216336 1 4 16 32 1 32  ε_{1} 22.9790
737 −132 −804 78216336 1 4 12 24 1 24  ε_{1} 40.0839
8844  −3 −2948 78216336 8 1 20 80 1 10  ε_{1} 16.7878
8844  −4 −2211 78216336 8 1 16 128 2 16  \sqrt{i}\sqrt{ε_{1}} 8.3939
8844  −11 −804 78216336 8 1 12 48 1  6  ε_{1} 16.7878
8844  −67 −132 78216336 8 1 4 16 1  2  ε_{1} 16.7878
8 −2212 −4424 78287104 1 8 48 192 1 192  ε_{1} 1.7627
28 −632 −4424 78287104 1 8 48 192 1 192  ε_{1} 5.5373
56 −632 −2212 78287104 1 8 8 32 1 32  ε_{1} 6.8002
316  −56 −4424 78287104 3 4 48 288 1 96  ε_{1} 10.1503
632  −56 −2212 78287104 1 4 8 16 1 16  ε_{1} 19.2954
4424  −4 −4424 78287104 4 1 48 96 1 24  ε_{1} 18.4426
4424  −8 −2212 78287104 4 1 8 16 1  4  ε_{1} 18.4426
53 −167 −8851 78340201 1 11 22 121 1 121  ε_{1} 3.9314
2213  −4 −8852 78357904 3 1 42 63 1 21  ε_{1} 7.7012
681  −39 −2951 78375609 1 4 54 108 1 108  ε_{1} 61.3969

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 229

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8853  −3 −2951 78375609 2 1 54 108 2 54 \sqrt{−1}\sqrt{ε_{1}} 12.7857
8853 −39 −227 78375609 2 4 5 20 1 10 ε_{1} 25.5714
5 −1771 −8855 78411025 1 8 88 352 1 352  ε_{1} 0.9624
77 −115 −8855 78411025 1 2 88 88 1 88  ε_{1} 4.3693
161  −55 −8855 78411025 1 4 88 176 1 176  ε_{1} 20.1338
253  −35 −8855 78411025 1 2 88 88 1 88  ε_{1} 15.0577
385  −23 −8855 78411025 2 3 88 264 1 132  ε_{1} 24.3270
385 −115 −1771 78411025 2 2  8 16 1  8  ε_{1} 24.3270
805  −11 −8855 78411025 2 1 88 88 1 44  ε_{1} 14.5545
805  −55 −1771 78411025 2 4  8 32 1 16  ε_{1} 14.5545
1265  −7 −8855 78411025 2 1 88 88 1 44  ε_{1} 25.8672
1265  −35 −1771 78411025 2 2  8 16 1  8  ε_{1} 25.8672
2953  −3 −8859 78481881 1 1 16  8 1  8  ε_{1} 122.8368
1772  −20 −2215 78499600 3 2 22 66 1 22  ε_{1} 13.5689
8860  −4 −2215 78499600 2 1 22 22 1 11  ε_{1} 63.4778
8860  −20 −443 78499600 2 2  5 10 1  5  ε_{1} 63.4778
12 −739 −8868 78641424 1 5 28 70 1 70  ε_{1} 2.6339
2217  −4 −8868 78641424 1 1 28 14 1 14  ε_{1} 63.6475
2956  −3 −8868 78641424 1 1 28 14 1 14  ε_{1} 107.2651
2957  −3 −8871 78694641 1 1 46 23 1 23  ε_{1} 21.9926
1109  −8 −8872 78712384 1 1 26 13 1 13  ε_{1} 23.1586
8873  −19 −467 78730129 1 1  7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 68.9716
28 −1268 −2219 78783376 1 10 24 120 1 120  ε_{1} 5.5373
8876 −4 −2219 78783376 2 1 24 24 1 12 ε_{1} 44.5886
8876  −7 −1268 78783376 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 22.2943
33 −807 −2959 78801129 1 14 40 280 1 280  ε_{1} 7.6563
8877 −3 −2959 78801129 2 1 40 40 1 20 ε_{1} 25.9286
8877  −11 −807 78801129 2 1 14 28 2 14 \sqrt{−1}\sqrt{ε_{1}} 12.9643
13 −683 −8879 78836641 1 5 130 325 1 325  ε_{1} 2.3895
12 −1480 −4440 78854400 1 12 16 96 1 96  ε_{1} 2.6339
24 −740 −4440 78854400 1 16 16 128 1 128  ε_{1} 4.5849
60 −296 −4440 78854400 2 10 16 160 1 80  ε_{1} 4.1269
60 −888 −1480 78854400 2 12 12 144 1 72  ε_{1} 4.1269
120 −148 −4440 78854400 2 2 16 32 1 16  ε_{1} 6.1779
120 −740 −888 78854400 2 16 12 192 1 96  ε_{1} 6.1779
444 −40 −4440 78854400 2 2 16 32 1 16 ε_{1} 12.7602
444 −120 −1480 78854400 2 4 12 48 1 24  ε_{1} 12.7602
888 −20 −4440 78854400 2 2 16 32 1 16 ε_{1} 11.3942
888 −120 −740 78854400 2 4 16 64 1 32  ε_{1} 11.3942
2220  −8 −4440 78854400 4 1 16 32 1  8  ε_{1} 16.3929
2220  −24 −1480 78854400 4 2 12 48 1 12  ε_{1} 16.3929
2220  −40 −888 78854400 4 2 12 48 1 12  ε_{1} 16.3929
2220 −120 −296 78854400 4 4 10 160 2 40 \sqrt{−1}\sqrt{ε_{1}} 8.1964
4440  −4 −4440 78854400 4 1 16 32 1  8  ε_{1} 16.5871
4440  −20 −888 78854400 4 2 12 48 1 12  ε_{1} 16.5871
4440  −24 −740 78854400 4 2 16 64 1 16  ε_{1} 16.5871
4440 −120 −148 78854400 4 4  2 16 1  4  ε_{1} 16.5871
8881  −83 −107 78872161 1 3  3  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 149.8903
2221  −4 −8884 78925456 1 1 18  9 1  9  ε_{1} 60.0993
8 −1111 −8888 78996544 1 22 52 572 1 572  ε_{1} 1.7627

230 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
88 −808 −1111 78996544 1 6 22 66 1 66  ε_{1} 11.9527
101  −88 −8888 78996544 1 2 52 52 1 52  ε_{1} 5.9964
808  −11 −8888 78996544 2 1 52 52 1 26  ε_{1} 17.4909
808  −88 −1111 78996544 2 2 22 44 1 22  ε_{1} 17.4909
8888  −8 −1111 78996544 2 1 22 22 1 11  ε_{1} 19.7867
8888  −11 −808 78996544 2 1 6  6 1  3  ε_{1} 19.7867
8889  −3 −2963 79014321 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 122.9658
17 −523 −8891 79049881 1 5 32 80 1 80  ε_{1} 4.1894
5 −1779 −8895 79121025 1 10 92 460 1 460  ε_{1} 0.9624
593  −15 −8895 79121025 1 2 92 92 1 92  ε_{1} 27.9978
2965  −3 −8895 79121025 2 1 92 92 1 46  ε_{1} 31.5212
2965  −15 −1779 79121025 2 2 10 20 1 10  ε_{1} 31.5212
217 −287 −1271 79156609 1 14 40 280 1 280  ε_{1} 31.7104
8897 −7 −1271 79156609 2 1 40 40 1 20 ε_{1} 60.7923
8897  −31 −287 79156609 2 3 14 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 30.3961
809 −11 −8899 79192201 1 1 14 7 1 7 ε_{1} 54.9782
29 −307 −8903 79263409 1 3 70 105 1 105  ε_{1} 3.2945
21 −424 −8904 79281216 1 6 40 120 1 120  ε_{1} 3.1336
21 −1272 −2968 79281216 1 12 8 48 1 48  ε_{1} 3.1336
24 −371 −8904 79281216 1 8 40 160 1 160  ε_{1} 4.5849
53 −168 −8904 79281216 1 4 40 80 1 80  ε_{1} 3.9314
56 −159 −8904 79281216 1 10 40 200 1 200  ε_{1} 6.8002
168 −159 −2968 79281216 2 10 8 80 1 40  ε_{1} 6.5132
168 −371 −1272 79281216 2 8 12 96 1 48  ε_{1} 6.5132
1113  −8 −8904 79281216 2 1 40 40 1 20  ε_{1} 28.3110
1113  −24 −2968 79281216 2 2 8 16 1  8  ε_{1} 28.3110
1113  −56 −1272 79281216 2 4 12 48 1 24  ε_{1} 28.3110
1113 −168 −424 79281216 2 4 6 24 1 12  ε_{1} 28.3110
1272 −7 −8904 79281216 2 1 40 40 1 20 ε_{1} 10.7319
1272 −168 −371 79281216 2 4 8 32 1 16  ε_{1} 10.7319
2968 −3 −8904 79281216 2 1 40 40 1 20 ε_{1} 40.1623
2968 −159 −168 79281216 2 10 4 40 1 20  ε_{1} 40.1623
8904 −3 −2968 79281216 4 1 8 16 1 4 ε_{1} 36.7928
8904  −7 −1272 79281216 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 18.3964
8904  −24 −371 79281216 4 2 8 32 1  8  ε_{1} 36.7928
8904  −56 −159 79281216 4 4 10 80 1 20  ε_{1} 36.7928
2969  −3 −8907 79334649 1 1 22 11 1 11  ε_{1} 103.7478
524  −68 −2227 79352464 1 4 6 12 1 12  ε_{1} 19.9254
8908  −4 −2227 79352464 2 1 6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 40.7739
8908  −68 −131 79352464 2 4 5 20 1 10  ε_{1} 81.5477
8909  −59 −151 79370281 3 3 7 63 2 21 \sqrt{−1}\sqrt{ε_{1}} 9.6226
133  −67 −8911 79405921 1 1 44 22 1 22  ε_{1} 10.3065
469  −19 −8911 79405921 3 1 44 66 1 22  ε_{1} 8.3483
1273  −7 −8911 79405921 1 1 44 22 1 22  ε_{1} 80.8877
8 −2228 −4456 79423744 1 18 22 198 1 198  ε_{1} 1.7627
4456  −4 −4456 79423744 2 1 22 22 1 11  ε_{1} 74.0843
4456  −8 −2228 79423744 2 1 18 18 1  9  ε_{1} 74.0843
8913  −3 −2971 79441569 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 91.7928
5 −1783 −8915 79477225 1 17 22 187 1 187  ε_{1} 0.9624
12 −743 −8916 79495056 1 21 48 504 1 504  ε_{1} 2.6339

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 231

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2229  −4 −8916 79495056 1 1 48 24 1 24  ε_{1} 33.9709
2972  −3 −8916 79495056 1 1 48 24 1 24  ε_{1} 28.3436
5 −1784 −8920 79566400 1 32 20 320 1 320  ε_{1} 0.9624
8 −1115 −8920 79566400 1 10 20 100 1 100  ε_{1} 1.7627
40 −223 −8920 79566400 2 7 20 140 1 70  ε_{1} 3.6369
40 −1115 −1784 79566400 2 10 32 320 1 160  ε_{1} 3.6369
1784  −40 −1115 79566400 1 2 10 10 1 10  ε_{1} 38.4213
8920  −8 −1115 79566400 6 1 10 30 1  5  ε_{1} 23.7621
8920  −40 −223 79566400 6 2 7 42 1  7  ε_{1} 23.7621
8921  −11 −811 79584241 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 80.9599
92 −388 −2231 79637776 1 4 58 116 1 116  ε_{1} 7.7415
8924  −4 −2231 79637776 2 1 58 116 2 58  \sqrt{i}\sqrt{ε_{1}} 19.5015
8924  −23 −388 79637776 2 3 4 12 1  6  ε_{1} 39.0030
113  −79 −8927 79691329 1 5 82 205 1 205  ε_{1} 14.6946
13 −687 −8931 79762761 1 12 32 192 1 192  ε_{1} 2.3895
229  −39 −8931 79762761 3 4 32 192 1 64  ε_{1} 5.4249
2977  −3 −8931 79762761 2 1 32 32 1 16  ε_{1} 71.8005
2977  −39 −687 79762761 2 4 12 48 1 24  ε_{1} 71.8005
28 −319 −8932 79780624 1 10 16 80 1 80  ε_{1} 5.5373
29 −308 −8932 79780624 1 8 16 64 1 64  ε_{1} 3.2945
44 −203 −8932 79780624 1 4 16 32 1 32  ε_{1} 5.9864
77 −116 −8932 79780624 1 6 16 48 1 48  ε_{1} 4.3693
812 −11 −8932 79780624 2 1 16 16 1 8 ε_{1} 9.4722
812 −308 −319 79780624 2 8 10 80 1 40  ε_{1} 9.4722
1276 −7 −8932 79780624 2 1 16 16 1 8 ε_{1} 34.1320
1276 −203 −308 79780624 2 4 8 32 1 16  ε_{1} 34.1320
2233 −4 −8932 79780624 6 1 16 48 1 8 ε_{1} 19.8480
2233 −116 −308 79780624 6 6 8 144 1 24  ε_{1} 19.8480
5 −1787 −8935 79834225 1 7 46 161 1 161  ε_{1} 0.9624
1117  −8 −8936 79852096 1 1 34 17 1 17  ε_{1} 31.6567
1277  −7 −8939 79905721 1 1 38 19 1 19  ε_{1} 17.5930
12 −2235 −2980 79923600 1 12 16 96 1 96  ε_{1} 2.6339
60 −447 −2980 79923600 2 14 16 224 1 112  ε_{1} 4.1269
60 −596 −2235 79923600 2 14 12 168 1 84  ε_{1} 4.1269
1788  −15 −2980 79923600 2 2 16 32 1 16  ε_{1} 11.3807
1788  −20 −2235 79923600 2 2 12 24 1 12  ε_{1} 11.3807
8940  −3 −2980 79923600 4 1 16 32 1  8  ε_{1} 28.0822
8940  −4 −2235 79923600 4 1 12 24 1  6  ε_{1} 28.0822
8940  −15 −596 79923600 4 2 14 56 1 14  ε_{1} 28.0822
8940  −20 −447 79923600 4 2 14 56 1 14  ε_{1} 28.0822
33 −271 −8943 79977249 1 11 60 330 1 330  ε_{1} 7.6563
813  −11 −8943 79977249 1 1 60 30 1 30  ε_{1} 16.7485
2981  −3 −8943 79977249 3 1 60 90 1 30  ε_{1} 11.2189
172 −104 −4472 79995136 1 6 36 108 1 108  ε_{1} 17.6970
344  −52 −4472 79995136 1 2 36 36 1 36  ε_{1} 19.8864
2236  −8 −4472 79995136 2 1 36 36 1 18  ε_{1} 41.4726
2236 −104 −344 79995136 2 6 10 60 1 30  ε_{1} 41.4726
4472  −4 −4472 79995136 2 1 36 36 1 18  ε_{1} 18.0782
4472  −52 −344 79995136 2 2 10 20 1 10  ε_{1} 18.0782
389  −23 −8947 80048809 1 3 10 15 1 15  ε_{1} 15.6986

232 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2237  −4 −8948 80066704 1 1 30 15 1 15  ε_{1} 28.0891
57 −471 −2983 80084601 1 16 20 160 1 160  ε_{1} 11.4208
8949 −3 −2983 80084601 4 1 20 40 1 10 ε_{1} 12.3182
8949  −19 −471 80084601 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.1591
8 −1119 −8952 80138304 1 32 28 448 1 448  ε_{1} 1.7627
24 −1119 −2984 80138304 1 32 26 416 1 416  ε_{1} 4.5849
373  −24 −8952 80138304 1 2 28 28 1 28  ε_{1} 18.4673
2984  −3 −8952 80138304 2 1 28 28 1 14  ε_{1} 32.4394
2984  −24 −1119 80138304 2 2 32 64 1 32  ε_{1} 32.4394
8952  −3 −2984 80138304 2 1 26 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 13.1309
8952 −8 −1119 80138304 2 1 32 32 1 16 ε_{1} 26.2618
8953  −7 −1279 80156209 1 1 23 23 2 23 \sqrt{−1}\sqrt{ε_{1}} 120.9485
8956  −4 −2239 80209936 1 1 35 35 2 35  \sqrt{i}\sqrt{ε_{1}} 81.5072
309  −87 −2987 80299521 1 6 20 60 1 60  ε_{1} 17.0523
8961  −3 −2987 80299521 2 1 20 20 1 10  ε_{1} 132.8442
8961  −87 −103 80299521 2 6 5 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 66.4221
1793 −55 −815 80371225 1 4 30 60 1 60 ε_{1} 67.7891
8965  −11 −815 80371225 2 1 30 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 20.5167
8965  −55 −163 80371225 2 4 1  4 1  2  ε_{1} 41.0334
152  −59 −8968 80425024 1 3 16 24 1 24  ε_{1} 8.6078
472  −19 −8968 80425024 1 1 16  8 1  8  ε_{1} 26.6550
1121  −8 −8968 80425024 1 1 16  8 1  8  ε_{1} 66.6959
1121 −152 −472 80425024 1 6 6 18 1 18  ε_{1} 66.6959
8968  −19 −472 80425024 2 1 6  6 1  3  ε_{1} 74.6551
8968  −59 −152 80425024 2 3 6 18 1  9  ε_{1} 74.6551
8972  −4 −2243 80496784 1 1 15 15 2 15  \sqrt{i}\sqrt{ε_{1}} 22.8553
8 −2244 −4488 80568576 1 16 16 128 1 128  ε_{1} 1.7627
12 −1496 −4488 80568576 1 28 16 224 1 224  ε_{1} 2.6339
24 −1496 −2244 80568576 1 28 16 224 1 224  ε_{1} 4.5849
44 −408 −4488 80568576 1 4 16 32 1 32  ε_{1} 5.9864
88 −408 −2244 80568576 1 4 16 32 1 32  ε_{1} 11.9527
136 −132 −4488 80568576 2 4 16 64 1 32  ε_{1} 8.4966
136 −264 −2244 80568576 2 8 16 128 1 64  ε_{1} 8.4966
204 −88 −4488 80568576 2 2 16 32 1 16 ε_{1} 9.2101
204 −264 −1496 80568576 2 8 28 224 1 112  ε_{1} 9.2101
264 −68 −4488 80568576 2 4 16 64 1 32 ε_{1} 9.7350
264 −136 −2244 80568576 2 4 16 64 1 32  ε_{1} 9.7350
408 −88 −2244 80568576 2 2 16 32 1 16 ε_{1} 10.6165
408 −132 −1496 80568576 2 4 28 112 1 56  ε_{1} 10.6165
748 −24 −4488 80568576 2 2 16 32 1 16 ε_{1} 16.2418
748 −264 −408 80568576 2 8 4 32 1 16  ε_{1} 16.2418
1496  −24 −2244 80568576 2 2 16 32 1 16  ε_{1} 17.6287
1496 −132 −408 80568576 2 4 4 16 1  8  ε_{1} 17.6287
4488  −4 −4488 80568576 8 1 16 64 1  8  ε_{1} 9.7956
4488  −8 −2244 80568576 8 1 16 64 1  8  ε_{1} 9.7956
4488  −68 −264 80568576 8 4 8 128 1 16  ε_{1} 9.7956
4488 −132 −136 80568576 8 4 4 128 2 16 \sqrt{−1}\sqrt{ε_{1}} 4.8978
8977  −47 −191 80586529 1 5 13 65 2 65 \sqrt{−1}\sqrt{ε_{1}} 115.3091
41 −219 −8979 80622441 1 4 24 48 1 48  ε_{1} 8.3183
73 −123 −8979 80622441 1 2 24 24 1 24  ε_{1} 15.3334

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 233

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2993  −3 −8979 80622441 6 1 24 72 1 12  ε_{1} 15.7464
2993 −123 −219 80622441 6 2 4 24 1  4  ε_{1} 15.7464
5 −1796 −8980 80640400 1 20 32 320 1 320  ε_{1} 0.9624
449  −20 −8980 80640400 1 2 32 32 1 32  ε_{1} 39.5058
2245  −4 −8980 80640400 2 1 32 32 1 16  ε_{1} 24.3921
2245  −20 −1796 80640400 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 12.1961
8981  −7 −1283 80658361 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 28.0254
13 −691 −8983 80694289 1 5 38 95 1 95  ε_{1} 2.3895
8 −1123 −8984 80712256 1 5 78 195 1 195  ε_{1} 1.7627
8984  −8 −1123 80712256 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 46.8028
1797  −15 −2995 80730225 1 2 8  8 1  8  ε_{1} 25.3325
8985  −3 −2995 80730225 2 1 8  8 1  4  ε_{1} 118.3654
8985  −15 −599 80730225 2 2 25 100 2 50 \sqrt{−1}\sqrt{ε_{1}} 59.1827
209  −43 −8987 80766169 1 1 32 16 1 16  ε_{1} 22.8829
473  −19 −8987 80766169 3 1 32 48 1 16  ε_{1} 10.3180
817  −11 −8987 80766169 5 1 32 80 1 16  ε_{1} 13.0618
12 −2247 −2996 80784144 1 20 32 320 1 320  ε_{1} 2.6339
21 −1284 −2996 80784144 1 20 32 320 1 320  ε_{1} 3.1336
28 −1284 −2247 80784144 1 20 20 200 1 200  ε_{1} 5.5373
321  −84 −2996 80784144 3 4 32 192 1 64  ε_{1} 12.1276
428  −84 −2247 80784144 1 4 20 40 1 40  ε_{1} 15.1243
749  −84 −1284 80784144 1 4 20 40 1 40  ε_{1} 18.9369
8988  −3 −2996 80784144 4 1 32 64 1 16  ε_{1} 21.0614
8988  −4 −2247 80784144 4 1 20 40 1 10  ε_{1} 21.0614
8988  −7 −1284 80784144 4 1 20 40 1 10  ε_{1} 21.0614
8988  −84 −107 80784144 4 4 3 24 1  6  ε_{1} 21.0614
5 −1799 −8995 80910025 1 50 20 500 1 500  ε_{1} 0.9624
257  −35 −8995 80910025 3 2 20 60 1 20  ε_{1} 6.9334
1285  −7 −8995 80910025 2 1 20 20 1 10  ε_{1} 20.3309
1285  −35 −1799 80910025 2 2 50 100 1 50  ε_{1} 20.3309
13 −692 −8996 80928016 1 14 40 280 1 280  ε_{1} 2.3895
173  −52 −8996 80928016 1 2 40 40 1 40  ε_{1} 5.1416
2249  −4 −8996 80928016 4 1 40 80 1 20  ε_{1} 25.7696
2249  −52 −692 80928016 4 2 14 56 1 14  ε_{1} 25.7696
8997  −3 −2999 80946009 1 1 73 73 2 73 \sqrt{−1}\sqrt{ε_{1}} 35.3821
3001  −3 −9003 81054009 1 1 12  6 1  6  ε_{1} 170.2925
9004  −4 −2251 81072016 7 1 7 49 2  7  \sqrt{i}\sqrt{ε_{1}} 12.8067
2252  −8 −4504 81144064 1 1 22 22 2 22 \sqrt{−1}\sqrt{ε_{1}} 11.8222
4504 −4 −4504 81144064 5 1 22 110 2 22 \sqrt{i}\sqrt{ε_{1}} 12.1140
12 −751 −9012 81216144 1 15 36 270 1 270  ε_{1} 2.6339
2253  −4 −9012 81216144 1 1 36 18 1 18  ε_{1} 30.4046
3004  −3 −9012 81216144 1 1 36 18 1 18  ε_{1} 115.8843
5 −1803 −9015 81270225 1 8 72 288 1 288  ε_{1} 0.9624
601  −15 −9015 81270225 1 2 72 72 1 72  ε_{1} 66.5240
3005  −3 −9015 81270225 2 1 72 72 1 36  ε_{1} 12.8038
3005  −15 −1803 81270225 2 2 8 16 1  8  ε_{1} 12.8038
9017  −71 −127 81306289 1 7 5 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 59.8581
29 −311 −9019 81342361 1 19 30 285 1 285  ε_{1} 3.2945
44 −820 −2255 81360400 1 8 40 160 1 160  ε_{1} 5.9864
220 −164 −2255 81360400 2 8 40 320 1 160  ε_{1} 10.3635

234 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
220 −451 −820 81360400 2 6 8 48 1 24  ε_{1} 10.3635
1804  −20 −2255 81360400 2 2 40 80 1 40  ε_{1} 36.6950
1804  −55 −820 81360400 2 4 8 32 1 16  ε_{1} 36.6950
9020  −4 −2255 81360400 4 1 40 80 1 20  ε_{1} 17.7687
9020  −11 −820 81360400 4 1 8 16 1  4  ε_{1} 17.7687
9020  −20 −451 81360400 4 2 6 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.8843
9020 −55 −164 81360400 4 4 8 64 1 16 ε_{1} 17.7687
93 −291 −3007 81378441 1 4 20 40 1 40  ε_{1} 6.7322
9021  −3 −3007 81378441 8 1 20 80 1 10  ε_{1} 9.1075
9021  −31 −291 81378441 8 3 4 48 1  6  ε_{1} 9.1075
1289  −7 −9023 81414529 1 1 80 40 1 40  ε_{1} 68.0567
37 −244 −9028 81504784 1 6 24 72 1 72  ε_{1} 4.9836
61 −148 −9028 81504784 1 2 24 24 1 24  ε_{1} 7.3284
2257  −4 −9028 81504784 2 1 24 24 1 12  ε_{1} 50.6448
2257 −148 −244 81504784 2 2 6 12 1  6  ε_{1} 50.6448
821  −11 −9031 81558961 1 1 54 27 1 27  ε_{1} 19.3842
1129  −8 −9032 81577024 9 1 28 126 1 14  ε_{1} 11.6342
9033  −3 −3011 81595089 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 46.5979
5 −1807 −9035 81631225 1 12 40 240 1 240  ε_{1} 0.9624
13 −695 −9035 81631225 1 24 40 480 1 480  ε_{1} 2.3895
65 −139 −9035 81631225 2 3 40 120 1 60  ε_{1} 5.5529
65 −695 −1807 81631225 2 24 12 288 1 144  ε_{1} 5.5529
9037 −7 −1291 81667369 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 27.8535
69 −131 −9039 81703521 1 5 80 200 1 200  ε_{1} 6.4345
393  −23 −9039 81703521 1 3 80 120 1 120  ε_{1} 36.6935
3013  −3 −9039 81703521 1 1 80 40 1 40  ε_{1} 43.2704
8 −2260 −4520 81721600 1 12 44 264 1 264  ε_{1} 1.7627
40 −452 −4520 81721600 2 8 44 352 1 176  ε_{1} 3.6369
40 −904 −2260 81721600 2 8 12 96 1 48  ε_{1} 3.6369
904  −20 −4520 81721600 8 2 44 352 1 44  ε_{1} 6.8046
904  −40 −2260 81721600 8 2 12 96 1 12  ε_{1} 6.8046
4520  −4 −4520 81721600 4 1 44 88 1 22  ε_{1} 13.5462
4520  −8 −2260 81721600 4 1 12 24 1  6  ε_{1} 13.5462
4520  −20 −904 81721600 4 2 8 32 1  8  ε_{1} 13.5462
4520  −40 −452 81721600 4 2 8 32 1  8  ε_{1} 13.5462
17 −532 −9044 81793936 1 4 72 144 1 144  ε_{1} 4.1894
28 −323 −9044 81793936 1 4 72 144 1 144  ε_{1} 5.5373
76 −119 −9044 81793936 1 10 72 360 1 360  ε_{1} 11.6579
133  −68 −9044 81793936 1 4 72 144 1 144  ε_{1} 10.3065
476  −19 −9044 81793936 2 1 72 72 1 36  ε_{1} 10.9612
476 −323 −532 81793936 2 4 4 16 1  8  ε_{1} 10.9612
1292  −7 −9044 81793936 4 1 72 144 1 36  ε_{1} 7.1655
1292 −119 −532 81793936 4 10 4 80 1 20  ε_{1} 7.1655
2261  −4 −9044 81793936 2 1 72 72 1 36  ε_{1} 15.1013
2261  −68 −532 81793936 2 4 4 16 1  8  ε_{1} 15.1013
109  −83 −9047 81848209 1 3 88 132 1 132  ε_{1} 11.1291
8 −1131 −9048 81866304 1 8 24 96 1 96  ε_{1} 1.7627
13 −696 −9048 81866304 1 12 24 144 1 144  ε_{1} 2.3895
24 −1131 −3016 81866304 1 8 20 80 1 80  ε_{1} 4.5849
29 −312 −9048 81866304 1 4 24 48 1 48  ε_{1} 3.2945

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 235

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
104  −87 −9048 81866304 2 6 24 144 1 72  ε_{1} 4.6249
104 −696 −1131 81866304 2 12  8 96 1 48  ε_{1} 4.6249
232  −39 −9048 81866304 2 4 24 96 1 48  ε_{1} 10.5766
232 −312 −1131 81866304 2 4  8 32 1 16  ε_{1} 10.5766
312  −87 −3016 81866304 2 6 20 120 1 60  ε_{1} 9.3267
312 −232 −1131 81866304 2 2  8 16 1  8  ε_{1} 9.3267
377  −24 −9048 81866304 2 2 24 48 1 24  ε_{1} 12.2884
377 −312 −696 81866304 2 4 12 48 1 24  ε_{1} 12.2884
696  −39 −3016 81866304 2 4 20 80 1 40  ε_{1} 15.9463
696 −104 −1131 81866304 2 6  8 48 1 24  ε_{1} 15.9463
3016  −3 −9048 81866304 4 1 24 48 1 12  ε_{1} 21.2385
3016  −24 −1131 81866304 4 2  8 32 1  8  ε_{1} 21.2385
3016  −39 −696 81866304 4 4 12 96 1 24  ε_{1} 21.2385
3016  −87 −312 81866304 4 6  4 48 1 12  ε_{1} 21.2385
9048  −3 −3016 81866304 4 1 20 40 1 10  ε_{1} 24.3615
9048  −8 −1131 81866304 4 1  8 16 1  4  ε_{1} 24.3615
9048  −39 −232 81866304 4 4  2 16 1  4  ε_{1} 24.3615
9048  −87 −104 81866304 4 6  6 72 1 18  ε_{1} 24.3615
21 −431 −9051 81920601 1 21 20 210 1 210  ε_{1} 3.1336
1293  −7 −9051 81920601 1 1 20 10 1 10  ε_{1} 14.9071
3017  −3 −9051 81920601 1 1 20 10 1 10  ε_{1} 84.8285
124 −292 −2263 81938704 1 4 22 44 1 44  ε_{1} 16.0392
9052  −4 −2263 81938704 6 1 22 132 2 22  \sqrt{i}\sqrt{ε_{1}} 12.3094
9052  −31 −292 81938704 6 3  4 36 1  6  ε_{1} 24.6188
9053  −11 −823 81956809 1 1  9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 27.5002
5 −1811 −9055 81993025 1 23 36 414 1 414  ε_{1} 0.9624
9057 −3 −3019 82029249 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 88.3083
5 −1812 −9060 82083600 1 12 32 192 1 192  ε_{1} 0.9624
12 −755 −9060 82083600 1 12 32 192 1 192  ε_{1} 2.6339
60 −151 −9060 82083600 2 7 32 224 1 112  ε_{1} 4.1269
60 −755 −1812 82083600 2 12 12 144 1 72  ε_{1} 4.1269
453  −20 −9060 82083600 1 2 32 32 1 32  ε_{1} 10.0078
604  −15 −9060 82083600 1 2 32 32 1 32  ε_{1} 43.9269
2265  −4 −9060 82083600 2 1 32 32 1 16  ε_{1} 55.2093
2265  −20 −1812 82083600 2 2 12 24 1 12  ε_{1} 55.2093
3020  −3 −9060 82083600 2 1 32 32 1 16  ε_{1} 15.5814
3020  −15 −1812 82083600 2 2 12 24 1 12  ε_{1} 15.5814
88 −103 −9064 82156096 1 5 36 90 1 90  ε_{1} 11.9527
824  −11 −9064 82156096 1 1 36 18 1 18  ε_{1} 23.3749
1133  −8 −9064 82156096 1 1 36 18 1 18  ε_{1} 9.2300
1133  −88 −824 82156096 1 2 20 20 1 20  ε_{1} 9.2300
9064  −11 −824 82156096 2 1 20 20 1 10  ε_{1} 86.3133
9064  −88 −103 82156096 2 2  5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 43.1566
9068  −4 −2267 82228624 1 1 11 11 2 11  \sqrt{i}\sqrt{ε_{1}} 30.7331
9069  −3 −3023 82246761 1 1 47 47 2 47 \sqrt{−1}\sqrt{ε_{1}} 49.3548
193  −47 −9071 82283041 1 5 138 345 1 345  ε_{1} 30.1526
9073  −43 −211 82319329 3 1  3  9 2  3 \sqrt{−1}\sqrt{ε_{1}} 46.9059
2269  −4 −9076 82373776 1 1 30 15 1 15  ε_{1} 66.2649
1297  −7 −9079 82428241 11 1 52 286 1 26  ε_{1} 8.5537
5 −1816 −9080 82446400 1 14 28 196 1 196  ε_{1} 0.9624

236 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
8 −1135 −9080 82446400 1 18 28 252 1 252  ε_{1} 1.7627
40 −227 −9080 82446400 2 5 28 140 1 70  ε_{1} 3.6369
40 −1135 −1816 82446400 2 18 14 252 1 126  ε_{1} 3.6369
1816  −40 −1135 82446400 1 2 18 18 1 18  ε_{1} 76.1204
9080  −8 −1135 82446400 2 1 18 18 1  9  ε_{1} 49.2398
9080  −40 −227 82446400 2 2 5 10 1  5  ε_{1} 49.2398
293  −31 −9083 82500889 1 3 24 36 1 36  ε_{1} 5.6733
12 −2271 −3028 82519056 1 44 10 220 1 220  ε_{1} 2.6339
9084  −3 −3028 82519056 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 29.3313
9084  −4 −2271 82519056 2 1 44 44 1 22  ε_{1} 58.6625
1817 −115 −395 82537225 1 2 8  8 1  8  ε_{1} 62.9992
9085  −23 −395 82537225 2 3 8 24 1 12  ε_{1} 30.3496
9085  −79 −115 82537225 2 5 2 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 15.1748
13 −699 −9087 82573569 1 10 32 160 1 160  ε_{1} 2.3895
233  −39 −9087 82573569 1 4 32 64 1 64  ε_{1} 21.4863
3029  −3 −9087 82573569 4 1 32 64 1 16  ε_{1} 8.0153
3029  −39 −699 82573569 4 4 10 80 1 20  ε_{1} 8.0153
2273  −4 −9092 82664464 1 1 48 24 1 24  ε_{1} 41.8730
21 −1299 −3031 82682649 1 8 34 136 1 136  ε_{1} 3.1336
9093  −3 −3031 82682649 2 1 34 68 2 34 \sqrt{−1}\sqrt{ε_{1}} 14.6811
9093 −7 −1299 82682649 2 1 8 8 1 4 ε_{1} 29.3621
5 −1819 −9095 82719025 1 10 76 380 1 380  ε_{1} 0.9624
17 −535 −9095 82719025 1 14 76 532 1 532  ε_{1} 4.1894
85 −107 −9095 82719025 2 3 76 228 1 114  ε_{1} 4.4187
85 −535 −1819 82719025 2 14 10 140 1 70  ε_{1} 4.4187
24 −379 −9096 82737216 1 3 56 84 1 84  ε_{1} 4.5849
1137  −8 −9096 82737216 1 1 56 28 1 28  ε_{1} 55.7882
1137  −24 −3032 82737216 1 2 22 22 1 22  ε_{1} 55.7882
3032  −3 −9096 82737216 1 1 56 28 1 28  ε_{1} 41.0689
9096  −3 −3032 82737216 2 1 22 22 1 11  ε_{1} 49.0183
9096  −24 −379 82737216 2 2 3  6 1  3  ε_{1} 49.0183
9097  −11 −827 82755409 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 147.6550
9101  −19 −479 82828201 7 1 25 175 2 25 \sqrt{−1}\sqrt{ε_{1}} 6.1675
8 −2276 −4552 82882816 1 32 12 192 1 192  ε_{1} 1.7627
4552  −4 −4552 82882816 4 1 12 24 1  6  ε_{1} 26.9103
4552  −8 −2276 82882816 4 1 32 64 1 16  ε_{1} 26.9103
1821  −15 −3035 82901025 1 2 18 18 1 18  ε_{1} 44.1276
9105  −3 −3035 82901025 2 1 18 18 1  9  ε_{1} 73.3274
9105  −15 −607 82901025 2 2 13 26 1 13  ε_{1} 73.3274
1301  −7 −9107 82937449 1 1 26 13 1 13  ε_{1} 25.9645
3037  −3 −9111 83010321 1 1 64 32 1 32  ε_{1} 41.9128
8 −1139 −9112 83028544 1 16 24 192 1 192  ε_{1} 1.7627
17 −536 −9112 83028544 1 14 24 168 1 168  ε_{1} 4.1894
136 −67 −9112 83028544 2 1 24 24 1 12 ε_{1} 8.4966
136 −536 −1139 83028544 2 14 16 224 1 112  ε_{1} 8.4966
536 −136 −1139 83028544 1 4 16 32 1 32  ε_{1} 25.1680
9112  −8 −1139 83028544 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 17.2131
9112 −67 −136 83028544 4 1 4 8 1 2 ε_{1} 34.4262
5 −1823 −9115 83083225 1 45 14 315 1 315  ε_{1} 0.9624
172 −212 −2279 83101456 1 6 56 168 1 168  ε_{1} 17.6970

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 237

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
9116  −4 −2279 83101456 2 1 56 56 1 28  ε_{1} 53.2360
9116  −43 −212 83101456 2 1  6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 26.6180
829  −11 −9119 83156161 1 1 124 62 1 62  ε_{1} 34.4976
9121  −7 −1303 83192641 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 162.5212
3041  −3 −9123 83229129 1 1 18  9 1  9  ε_{1} 107.3317
2281  −4 −9124 83247376 1 1 20 10 1 10  ε_{1} 146.8485
56 −163 −9128 83320384 1 1 40 20 1 20  ε_{1} 6.8002
1141  −8 −9128 83320384 1 1 40 20 1 20  ε_{1} 41.9327
1141  −56 −1304 83320384 1 4 22 44 1 44  ε_{1} 41.9327
1304  −7 −9128 83320384 3 1 40 60 1 20  ε_{1} 12.9539
9128  −7 −1304 83320384 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 15.7813
9128  −56 −163 83320384 2 4  1  4 1  2  ε_{1} 31.5626
537  −51 −3043 83338641 1 2 12 12 1 12  ε_{1} 39.5359
9129  −3 −3043 83338641 2 1 12 12 1  6  ε_{1} 134.6002
9129  −51 −179 83338641 2 2  5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 67.3001
397  −23 −9131 83375161 1 3 40 60 1 60  ε_{1} 16.2905
12 −2283 −3044 83393424 1 6 40 120 1 120  ε_{1} 2.6339
9132  −3 −3044 83393424 2 1 40 40 1 20  ε_{1} 37.7772
9132  −4 −2283 83393424 2 1  6 12 2  6  \sqrt{i}\sqrt{ε_{1}} 18.8886
2284  −8 −4568 83466496 1 1 18 18 2 18 \sqrt{−1}\sqrt{ε_{1}} 47.3389
4568 −4 −4568 83466496 1 1 18 18 2 18 \sqrt{i}\sqrt{ε_{1}} 21.3184
13 −703 −9139 83521321 1 14 12 84 1 84  ε_{1} 2.3895
37 −247 −9139 83521321 1 6 12 36 1 36  ε_{1} 4.9836
481 −19 −9139 83521321 2 1 12 12 1 6 ε_{1} 28.9443
481 −247 −703 83521321 2 6 14 84 1 42  ε_{1} 28.9443
5 −1828 −9140 83539600 1 8 60 240 1 240  ε_{1} 0.9624
457  −20 −9140 83539600 1 2 60 60 1 60  ε_{1} 50.9909
2285  −4 −9140 83539600 2 1 60 60 1 30  ε_{1} 10.9530
2285  −20 −1828 83539600 2 2  8 16 1  8  ε_{1} 10.9530
33 −831 −3047 83557881 1 28 38 532 1 532  ε_{1} 7.6563
9141  −3 −3047 83557881 2 1 38 76 2 38 \sqrt{−1}\sqrt{ε_{1}} 14.2929
9141 −11 −831 83557881 2 1 28 28 1 14 ε_{1} 28.5858
41 −223 −9143 83594449 1 7 72 252 1 252  ε_{1} 8.3183
1829 −155 −295 83631025 1 4  8 16 1 16  ε_{1} 36.4312
9145  −31 −295 83631025 4 3  8 48 1 12  ε_{1} 67.3103
9145  −59 −155 83631025 4 3  4 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 33.6552
3049  −3 −9147 83667609 1 1 20 10 1 10  ε_{1} 188.1231
9148  −4 −2287 83685904 1 1 29 29 2 29  \sqrt{i}\sqrt{ε_{1}} 57.1816
9149  −7 −1307 83704201 3 1 11 33 2 11 \sqrt{−1}\sqrt{ε_{1}} 9.3729
5 −1831 −9155 83814025 1 19 36 342 1 342  ε_{1} 0.9624
12 −763 −9156 83832336 1 4 32 64 1 64  ε_{1} 2.6339
21 −436 −9156 83832336 1 6 32 96 1 96  ε_{1} 3.1336
28 −327 −9156 83832336 1 12 32 192 1 192  ε_{1} 5.5373
109  −84 −9156 83832336 1 4 32 64 1 64  ε_{1} 11.1291
1308  −7 −9156 83832336 2 1 32 32 1 16  ε_{1} 12.1461
1308  −84 −763 83832336 2 4  4 16 1  8  ε_{1} 12.1461
2289  −4 −9156 83832336 4 1 32 64 1 16  ε_{1} 31.1350
2289  −84 −436 83832336 4 4  6 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 15.5675
3052  −3 −9156 83832336 2 1 32 32 1 16  ε_{1} 42.1751
3052  −84 −327 83832336 2 4 12 48 1 24  ε_{1} 42.1751

238 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
129  −71 −9159 83887281 1 7 96 336 1 336  ε_{1} 20.8511
213  −43 −9159 83887281 1 1 96 48 1 48  ε_{1} 8.5805
3053  −3 −9159 83887281 1 1 96 48 1 48  ε_{1} 16.3101
5 −1832 −9160 83905600 1 26 20 260 1 260  ε_{1} 0.9624
229  −40 −9160 83905600 3 2 20 60 1 20  ε_{1} 5.4249
1145  −8 −9160 83905600 4 1 20 40 1 10  ε_{1} 15.6513
1145  −40 −1832 83905600 4 2 26 104 1 26  ε_{1} 15.6513
316 −116 −2291 83978896 3 6 18 162 1 54  ε_{1} 10.1503
9164  −4 −2291 83978896 2 1 18 18 1  9  ε_{1} 65.4842
9164  −79 −116 83978896 2 5 6 30 1 15  ε_{1} 65.4842
141 −195 −3055 83997225 1 4 36 72 1 72  ε_{1} 10.4940
705 −39 −3055 83997225 2 4 36 144 1 72 ε_{1} 26.1393
705 −195 −611 83997225 2 4 10 40 1 20  ε_{1} 26.1393
1833  −15 −3055 83997225 2 2 36 72 1 36  ε_{1} 31.9129
1833 −195 −235 83997225 2 4 2  8 1  4  ε_{1} 31.9129
9165  −3 −3055 83997225 4 1 36 72 1 18  ε_{1} 20.5106
9165  −15 −611 83997225 4 2 10 40 1 10  ε_{1} 20.5106
9165  −39 −235 83997225 4 4 2 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 10.2553
9165  −47 −195 83997225 4 5 4 40 1 10  ε_{1} 20.5106
89 −103 −9167 84033889 1 5 54 135 1 135  ε_{1} 13.8155
8 −2292 −4584 84052224 1 16 32 256 1 256  ε_{1} 1.7627
12 −1528 −4584 84052224 1 8 32 128 1 128  ε_{1} 2.6339
24 −1528 −2292 84052224 1 8 16 64 1 64  ε_{1} 4.5849
764  −24 −4584 84052224 1 2 32 32 1 32  ε_{1} 33.4104
1528  −24 −2292 84052224 1 2 16 16 1 16  ε_{1} 53.0447
4584  −4 −4584 84052224 2 1 32 32 1 16  ε_{1} 31.4926
4584  −8 −2292 84052224 2 1 16 16 1  8  ε_{1} 31.4926
2293  −4 −9172 84125584 1 1 14  7 1  7  ε_{1} 49.0472
8 −1147 −9176 84198976 1 6 76 228 1 228  ε_{1} 1.7627
37 −248 −9176 84198976 1 8 76 304 1 304  ε_{1} 4.9836
248 −296 −1147 84198976 1 10 6 30 1 30  ε_{1} 9.6724
296 −31 −9176 84198976 2 3 76 228 1 114 ε_{1} 8.9090
296 −248 −1147 84198976 2 8 6 48 1 24  ε_{1} 8.9090
9176  −8 −1147 84198976 2 1 6  6 1  3  ε_{1} 31.4019
9176  −31 −296 84198976 2 3 10 30 1 15  ε_{1} 31.4019
21 −1311 −3059 84217329 1 28 24 336 1 336  ε_{1} 3.1336
57 −483 −3059 84217329 1 4 24 48 1 48  ε_{1} 11.4208
69 −399 −3059 84217329 1 16 24 192 1 192  ε_{1} 6.4345
133 −483 −1311 84217329 1 4 28 56 1 56  ε_{1} 10.3065
161 −399 −1311 84217329 1 16 28 224 1 224  ε_{1} 20.1338
437 −399 −483 84217329 1 16 4 32 1 32  ε_{1} 6.0845
9177  −3 −3059 84217329 4 1 24 48 1 12  ε_{1} 47.4612
9177  −7 −1311 84217329 4 1 28 56 1 14  ε_{1} 47.4612
9177  −19 −483 84217329 4 1 4  8 1  2  ε_{1} 47.4612
9177  −23 −399 84217329 4 3 16 96 1 24  ε_{1} 47.4612
137  −67 −9179 84254041 1 1 38 19 1 19  ε_{1} 16.3142
3061  −3 −9183 84327489 1 1 40 20 1 20  ε_{1} 80.0933
1837  −55 −835 84364225 1 4 6 12 1 12  ε_{1} 34.3491
9185  −11 −835 84364225 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 38.5548
9185  −55 −167 84364225 2 4 11 44 1 22  ε_{1} 77.1096

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 239

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2297  −4 −9188 84419344 1 1 40 20 1 20  ε_{1} 82.6380
13 −707 −9191 84474481 1 6 124 372 1 372  ε_{1} 2.3895
101  −91 −9191 84474481 1 2 124 124 1 124  ε_{1} 5.9964
1313  −7 −9191 84474481 4 1 124 248 1 62  ε_{1} 14.2328
1313  −91 −707 84474481 4 2  6 24 1  6  ε_{1} 14.2328
24 −383 −9192 84492864 1 17 32 272 1 272  ε_{1} 4.5849
1149  −8 −9192 84492864 1 1 32 16 1 16  ε_{1} 32.9675
1149  −24 −3064 84492864 1 2 24 24 1 24  ε_{1} 32.9675
3064  −3 −9192 84492864 1 1 32 16 1 16  ε_{1} 94.2457
9192  −3 −3064 84492864 6 1 24 72 1 12  ε_{1} 14.6713
9192  −24 −383 84492864 6 2 17 204 2 34 \sqrt{−1}\sqrt{ε_{1}} 7.3356
5 −1839 −9195 84548025 1 40 20 400 1 400  ε_{1} 0.9624
613  −15 −9195 84548025 1 2 20 20 1 20  ε_{1} 23.0010
3065  −3 −9195 84548025 2 1 20 20 1 10  ε_{1} 38.1377
3065  −15 −1839 84548025 2 2 40 80 1 40  ε_{1} 38.1377
9201  −3 −3067 84658401 1 1  7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 129.6545
12 −767 −9204 84713616 1 22 48 528 1 528  ε_{1} 2.6339
13 −708 −9204 84713616 1 4 48 96 1 96  ε_{1} 2.3895
156 −59 −9204 84713616 2 3 48 144 1 72 ε_{1} 7.8232
156 −708 −767 84713616 2 4 22 88 1 44  ε_{1} 7.8232
177  −52 −9204 84713616 1 2 48 48 1 48  ε_{1} 23.4697
236  −39 −9204 84713616 1 4 48 96 1 96  ε_{1} 13.9320
2301  −4 −9204 84713616 2 1 48 48 1 24  ε_{1} 16.0589
2301  −52 −708 84713616 2 2  4  8 1  4  ε_{1} 16.0589
3068  −3 −9204 84713616 2 1 48 48 1 24  ε_{1} 22.0834
3068  −39 −708 84713616 2 4  4 16 1  8  ε_{1} 22.0834
1841  −35 −1315 84732025 1 2  6  6 1  6  ε_{1} 81.2666
9205  −7 −1315 84732025 2 1  6  6 1  3  ε_{1} 57.6195
9205  −35 −263 84732025 2 2 13 26 1 13  ε_{1} 57.6195
8 −1151 −9208 84787264 1 41 16 328 1 328  ε_{1} 1.7627
9208  −8 −1151 84787264 7 1 41 287 2 41 \sqrt{−1}\sqrt{ε_{1}} 8.4351
61 −151 −9211 84842521 1 7 18 63 1 63  ε_{1} 7.3284
249 −111 −3071 84879369 1 8 76 304 1 304  ε_{1} 33.3101
9213  −3 −3071 84879369 4 1 76 304 2 76 \sqrt{−1}\sqrt{ε_{1}} 9.4162
9213 −83 −111 84879369 4 3 8 48 1 12 ε_{1} 18.8324
5 −1843 −9215 84916225 1 6 116 348 1 348  ε_{1} 0.9624
97  −95 −9215 84916225 1 8 116 464 1 464  ε_{1} 18.6488
485  −19 −9215 84916225 2 1 116 116 1 58  ε_{1} 7.5694
485  −95 −1843 84916225 2 8  6 48 1 24  ε_{1} 7.5694
21 −439 −9219 84989961 1 15 16 120 1 120  ε_{1} 3.1336
1317  −7 −9219 84989961 1 1 16  8 1  8  ε_{1} 25.9049
3073  −3 −9219 84989961 1 1 16  8 1  8  ε_{1} 141.5841
5 −1844 −9220 85008400 1 30 24 360 1 360  ε_{1} 0.9624
461  −20 −9220 85008400 1 2 24 24 1 24  ε_{1} 11.7998
2305  −4 −9220 85008400 16 1 24 192 1 12  ε_{1} 9.1289
2305  −20 −1844 85008400 16 2 30 480 1 30  ε_{1} 9.1289
401  −23 −9223 85063729 5 3 34 255 1 51  ε_{1} 7.3790
1153  −8 −9224 85082176 1 1 64 32 1 32  ε_{1} 79.7231
12 −2307 −3076 85155984 1 8 20 80 1 80  ε_{1} 2.6339
9228  −3 −3076 85155984 4 1 20 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 8.0307

240 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
9228  −4 −2307 85155984 4 1  8 16 1  4  ε_{1} 16.0615
9229  −11 −839 85174441 5 1 33 165 2 33 \sqrt{−1}\sqrt{ε_{1}} 12.1483
17 −543 −9231 85211361 1 12 100 600 1 600  ε_{1} 4.1894
181  −51 −9231 85211361 1 2 100 100 1 100  ε_{1} 14.3479
3077  −3 −9231 85211361 2 1 100 100 1 50  ε_{1} 13.6981
3077  −51 −543 85211361 2 2 12 24 1 12  ε_{1} 13.6981
8 −2308 −4616 85229824 1 8 56 224 1 224  ε_{1} 1.7627
4616  −4 −4616 85229824 4 1 56 224 2 56  \sqrt{i}\sqrt{ε_{1}} 7.7450
4616  −8 −2308 85229824 4 1  8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 7.7450
9233  −7 −1319 85248289 1 1 45 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 70.8402
5 −1847 −9235 85285225 1 43 14 301 1 301  ε_{1} 0.9624
2309 −4 −9236 85303696 1 1 66 33 1 33 ε_{1} 19.5444
9237  −3 −3079 85322169 1 1 41 41 2 41 \sqrt{−1}\sqrt{ε_{1}} 19.0511
5 −1848 −9240 85377600 1 8 32 128 1 128  ε_{1} 0.9624
8 −1155 −9240 85377600 1 8 32 128 1 128  ε_{1} 1.7627
21 −440 −9240 85377600 1 12 32 192 1 192  ε_{1} 3.1336
21 −1320 −3080 85377600 1 8 32 128 1 128  ε_{1} 3.1336
24 −1155 −3080 85377600 1 8 32 128 1 128  ε_{1} 4.5849
33 −280 −9240 85377600 1 4 32 64 1 64  ε_{1} 7.6563
33 −840 −3080 85377600 1 8 32 128 1 128  ε_{1} 7.6563
40 −231 −9240 85377600 2 12 32 384 1 192  ε_{1} 3.6369
40 −1155 −1848 85377600 2 8  8 64 1 32  ε_{1} 3.6369
56 −1155 −1320 85377600 1 8  8 32 1 32  ε_{1} 6.8002
77 −120 −9240 85377600 1 4 32 64 1 64  ε_{1} 4.3693
77 −840 −1320 85377600 1 8  8 32 1 32  ε_{1} 4.3693
88 −840 −1155 85377600 1 8  8 32 1 32  ε_{1} 11.9527
105  −88 −9240 85377600 2 2 32 64 1 32  ε_{1} 8.8131
105 −264 −3080 85377600 2 8 32 256 1 128  ε_{1} 8.8131
105 −440 −1848 85377600 2 12  8 96 1 48  ε_{1} 8.8131
105 −616 −1320 85377600 2 8  8 64 1 32  ε_{1} 8.8131
120 −231 −3080 85377600 2 12 32 384 1 192  ε_{1} 6.1779
120 −616 −1155 85377600 2 8  8 64 1 32  ε_{1} 6.1779
165  −56 −9240 85377600 2 4 32 128 1 64  ε_{1} 5.1180
165 −168 −3080 85377600 2 4 32 128 1 64  ε_{1} 5.1180
165 −280 −1848 85377600 2 4  8 32 1 16  ε_{1} 5.1180
165 −616 −840 85377600 2 8  8 64 1 32  ε_{1} 5.1180
168  −55 −9240 85377600 2 4 32 128 1 64  ε_{1} 6.5132
168 −440 −1155 85377600 2 12  8 96 1 48  ε_{1} 6.5132
264  −35 −9240 85377600 2 2 32 64 1 32  ε_{1} 9.7350
264 −280 −1155 85377600 2 4  8 32 1 16  ε_{1} 9.7350
280 −231 −1320 85377600 2 12  8 96 1 48  ε_{1} 12.4372
280 −264 −1155 85377600 2 8  8 64 1 32  ε_{1} 12.4372
385  −24 −9240 85377600 2 2 32 64 1 32  ε_{1} 24.3270
385 −120 −1848 85377600 2 4  8 32 1 16  ε_{1} 24.3270
385 −168 −1320 85377600 2 4  8 32 1 16  ε_{1} 24.3270
385 −264 −840 85377600 2 8  8 64 1 32  ε_{1} 24.3270
440 −168 −1155 85377600 2 4  8 32 1 16  ε_{1} 7.4742
440 −231 −840 85377600 2 12  8 96 1 48  ε_{1} 7.4742
616  −15 −9240 85377600 2 2 32 64 1 32  ε_{1} 21.3187
616 −120 −1155 85377600 2 4  8 32 1 16  ε_{1} 21.3187

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 241

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
840  −11 −9240 85377600 4 1 32 64 1 16  ε_{1} 8.1203
840  −55 −1848 85377600 4 4 8 64 1 16  ε_{1} 8.1203
840  −88 −1155 85377600 4 2 8 32 1  8  ε_{1} 8.1203
840 −231 −440 85377600 4 12 12 288 1 72  ε_{1} 8.1203
1320  −7 −9240 85377600 4 1 32 64 1 16  ε_{1} 10.7689
1320  −35 −1848 85377600 4 2 8 32 1  8  ε_{1} 10.7689
1320  −56 −1155 85377600 4 4 8 64 1 16  ε_{1} 10.7689
1320 −231 −280 85377600 4 12 4 96 1 24  ε_{1} 10.7689
1848  −15 −3080 85377600 4 2 32 128 1 32  ε_{1} 8.9084
1848  −35 −1320 85377600 4 2 8 32 1  8  ε_{1} 8.9084
1848  −40 −1155 85377600 4 2 8 32 1  8  ε_{1} 8.9084
1848  −55 −840 85377600 4 4 8 64 1 16  ε_{1} 8.9084
3080  −3 −9240 85377600 4 1 32 64 1 16  ε_{1} 10.8053
3080  −15 −1848 85377600 4 2 8 32 1  8  ε_{1} 10.8053
3080  −24 −1155 85377600 4 2 8 32 1  8  ε_{1} 10.8053
3080 −120 −231 85377600 4 4 12 96 1 24  ε_{1} 10.8053
9240  −3 −3080 85377600 8 1 32 128 1 16  ε_{1} 14.6765
9240  −7 −1320 85377600 8 1 8 32 1  4  ε_{1} 14.6765
9240  −8 −1155 85377600 8 1 8 32 1  4  ε_{1} 14.6765
9240  −11 −840 85377600 8 1 8 32 1  4  ε_{1} 14.6765
9240  −15 −616 85377600 8 2 8 64 1  8  ε_{1} 14.6765
9240  −35 −264 85377600 8 2 8 64 1  8  ε_{1} 14.6765
9240  −40 −231 85377600 8 2 12 96 1 12  ε_{1} 14.6765
9240  −55 −168 85377600 8 4 4 64 1  8  ε_{1} 14.6765
9244  −4 −2311 85451536 1 1 29 29 2 29  \sqrt{i}\sqrt{ε_{1}} 110.3032
1321  −7 −9247 85507009 1 1 54 27 1 27  ε_{1} 106.0524
9249  −3 −3083 85544001 1 1 13 13 2 13 \sqrt{−1}\sqrt{ε_{1}} 138.3979
9253 −19 −487 85618009 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 28.9710
5 −1851 −9255 85655025 1 14 52 364 1 364  ε_{1} 0.9624
617  −15 −9255 85655025 1 2 52 52 1 52  ε_{1} 36.4449
3085  −3 −9255 85655025 2 1 52 52 1 26  ε_{1} 31.4218
3085  −15 −1851 85655025 2 2 14 28 1 14  ε_{1} 31.4218
13 −712 −9256 85673536 1 8 28 112 1 112  ε_{1} 2.3895
89 −104 −9256 85673536 1 6 28 84 1 84  ε_{1} 13.8155
1157 −8 −9256 85673536 2 1 28 28 1 14 ε_{1} 8.4394
1157 −104 −712 85673536 2 6 8 48 1 24  ε_{1} 8.4394
197  −47 −9259 85729081 1 5 24 60 1 60  ε_{1} 6.6670
1852  −20 −2315 85747600 1 2 18 18 1 18  ε_{1} 67.6713
9260  −4 −2315 85747600 2 1 18 18 1  9  ε_{1} 38.7758
9260  −20 −463 85747600 2 2 7 14 1  7  ε_{1} 38.7758
157  −59 −9263 85803169 1 3 62 93 1 93  ε_{1} 10.7226
12 −1544 −4632 85821696 1 20 24 240 1 240  ε_{1} 2.6339
24 −772 −4632 85821696 1 4 24 48 1 48  ε_{1} 4.5849
2316  −8 −4632 85821696 4 1 24 48 1 12  ε_{1} 13.2928
2316  −24 −1544 85821696 4 2 20 80 1 20  ε_{1} 13.2928
4632  −4 −4632 85821696 4 1 24 96 2 24  \sqrt{i}\sqrt{ε_{1}} 7.7467
4632  −24 −772 85821696 4 2 4 16 1  4  ε_{1} 15.4935
3089  −3 −9267 85877289 1 1 22 11 1 11  ε_{1} 115.7114
28 −331 −9268 85895824 1 3 24 36 1 36  ε_{1} 5.5373
1324  −7 −9268 85895824 1 1 24 12 1 12  ε_{1} 72.5128

242 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2317  −4 −9268 85895824 1 1 24 12 1 12  ε_{1} 37.1853
713 −299 −403 85914361 1 8 2  8 1  8  ε_{1} 32.3476
9269  −23 −403 85914361 2 3 2 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 17.4849
9269  −31 −299 85914361 2 3 8 24 1 12  ε_{1} 34.9699
73 −127 −9271 85951441 1 5 60 150 1 150  ε_{1} 15.3334
8 −1159 −9272 85969984 1 16 36 288 1 288  ε_{1} 1.7627
61 −152 −9272 85969984 1 6 36 108 1 108  ε_{1} 7.3284
152 −488 −1159 85969984 1 10 16 80 1 80  ε_{1} 8.6078
488 −19 −9272 85969984 2 1 36 36 1 18 ε_{1} 6.1862
488 −152 −1159 85969984 2 6 16 96 1 48  ε_{1} 6.1862
9272 −8 −1159 85969984 2 1 16 16 1 8 ε_{1} 30.9195
9272  −19 −488 85969984 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 15.4598
33 −843 −3091 85988529 1 6 10 30 1 30  ε_{1} 7.6563
9273  −3 −3091 85988529 2 1 10 10 1  5  ε_{1} 88.1415
9273  −11 −843 85988529 2 1 6  6 1  3  ε_{1} 88.1415
12 −2319 −3092 86044176 1 30 26 390 1 390  ε_{1} 2.6339
9276  −3 −3092 86044176 2 1 26 26 1 13  ε_{1} 75.3043
9276  −4 −2319 86044176 2 1 30 30 1 15  ε_{1} 75.3043
44 −211 −9284 86192656 1 3 60 90 1 90  ε_{1} 5.9864
844  −11 −9284 86192656 1 1 60 30 1 30  ε_{1} 54.0906
2321  −4 −9284 86192656 1 1 60 30 1 30  ε_{1} 96.3520
1857  −15 −3095 86211225 1 2 48 48 1 48  ε_{1} 86.0172
9285  −3 −3095 86211225 2 1 48 48 1 24  ε_{1} 33.7160
9285  −15 −619 86211225 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 16.8580
37 −251 −9287 86248369 1 7 78 273 1 273  ε_{1} 4.9836
9289  −7 −1327 86285521 7 1 15 105 2 15 \sqrt{−1}\sqrt{ε_{1}} 24.6083
57 −163 −9291 86322681 1 1 32 16 1 16  ε_{1} 11.4208
489  −19 −9291 86322681 1 1 32 16 1 16  ε_{1} 46.8872
3097  −3 −9291 86322681 1 1 32 16 1 16  ε_{1} 121.7482
92 −404 −2323 86341264 1 14 8 56 1 56  ε_{1} 7.7415
9292 −4 −2323 86341264 2 1 8 8 1 4 ε_{1} 49.7724
9292  −23 −404 86341264 2 3 14 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 24.8862
8 −2324 −4648 86415616 1 28 12 168 1 168  ε_{1} 1.7627
28 −664 −4648 86415616 1 10 12 60 1 60  ε_{1} 5.5373
56 −664 −2324 86415616 1 10 28 140 1 140  ε_{1} 6.8002
332  −56 −4648 86415616 1 4 12 24 1 24  ε_{1} 10.1997
664  −56 −2324 86415616 1 4 28 56 1 56  ε_{1} 43.8951
4648  −4 −4648 86415616 2 1 12 12 1  6  ε_{1} 35.2546
4648  −8 −2324 86415616 2 1 28 28 1 14  ε_{1} 35.2546
17 −547 −9299 86471401 1 3 50 75 1 75  ε_{1} 4.1894
9301  −71 −131 86508601 3 7 5 105 2 35 \sqrt{−1}\sqrt{ε_{1}} 15.8365
21 −443 −9303 86545809 1 5 68 170 1 170  ε_{1} 3.1336
1329  −7 −9303 86545809 1 1 68 34 1 34  ε_{1} 83.5792
3101  −3 −9303 86545809 1 1 68 34 1 34  ε_{1} 29.0059
8 −1163 −9304 86564416 1 7 22 77 1 77  ε_{1} 1.7627
9304 −8 −1163 86564416 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 111.2289
41 −227 −9307 86620249 1 5 10 25 1 25  ε_{1} 8.3183
716  −52 −2327 86638864 1 2 48 48 1 48  ε_{1} 31.8828
9308  −4 −2327 86638864 2 1 48 48 1 24  ε_{1} 33.4230
9308  −52 −179 86638864 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 16.7115

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 243

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
321  −87 −3103 86657481 3 6 20 180 1 60  ε_{1} 12.1276
9309  −3 −3103 86657481 2 1 20 20 1 10  ε_{1} 38.9384
9309  −87 −107 86657481 2 6 3 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 19.4692
9313 −67 −139 86731969 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 86.7949
17 −548 −9316 86787856 1 8 32 128 1 128  ε_{1} 4.1894
137  −68 −9316 86787856 1 4 32 64 1 64  ε_{1} 16.3142
2329  −4 −9316 86787856 2 1 32 32 1 16  ε_{1} 70.5997
2329  −68 −548 86787856 2 4 8 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 35.2999
5 −1864 −9320 86862400 1 8 60 240 1 240  ε_{1} 0.9624
233  −40 −9320 86862400 1 2 60 60 1 60  ε_{1} 21.4863
1165  −8 −9320 86862400 2 1 60 60 1 30  ε_{1} 15.0011
1165  −40 −1864 86862400 2 2 8 16 1  8  ε_{1} 15.0011
717  −39 −3107 86881041 1 4 18 36 1 36  ε_{1} 10.9696
9321  −3 −3107 86881041 10 1 18 180 2 18 \sqrt{−1}\sqrt{ε_{1}} 14.2235
9321  −39 −239 86881041 10 4 15 300 1 30  ε_{1} 28.4470
3109  −3 −9327 86992929 1 1 56 28 1 28  ε_{1} 74.1167
44 −424 −4664 87011584 1 6 36 108 1 108  ε_{1} 5.9864
88 −212 −4664 87011584 1 6 36 108 1 108  ε_{1} 11.9527
2332  −8 −4664 87011584 2 1 36 36 1 18  ε_{1} 33.2808
2332  −88 −424 87011584 2 2 6 12 1  6  ε_{1} 33.2808
4664  −4 −4664 87011584 2 1 36 36 1 18  ε_{1} 42.0031
4664  −88 −212 87011584 2 2 6 12 1  6  ε_{1} 42.0031
9329  −19 −491 87030241 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 83.9848
217  −43 −9331 87067561 1 1 20 10 1 10  ε_{1} 31.7104
301  −31 −9331 87067561 1 3 20 30 1 30  ε_{1} 20.0642
1333  −7 −9331 87067561 1 1 20 10 1 10  ε_{1} 22.7491
2333  −4 −9332 87086224 1 1 34 17 1 17  ε_{1} 25.5432
5 −1867 −9335 87142225 1 5 98 245 1 245  ε_{1} 0.9624
8 −1167 −9336 87160896 1 22 44 484 1 484  ε_{1} 1.7627
24 −1167 −3112 87160896 1 22 14 154 1 154  ε_{1} 4.5849
389  −24 −9336 87160896 1 2 44 44 1 44  ε_{1} 15.6986
3112  −3 −9336 87160896 2 1 44 44 1 22  ε_{1} 37.0178
3112  −24 −1167 87160896 2 2 22 44 1 22  ε_{1} 37.0178
9336  −3 −3112 87160896 2 1 14 14 1  7  ε_{1} 42.9758
9336  −8 −1167 87160896 2 1 22 22 1 11  ε_{1} 42.9758
33 −283 −9339 87216921 1 3 20 30 1 30  ε_{1} 7.6563
849  −11 −9339 87216921 1 1 20 10 1 10  ε_{1} 71.2770
3113  −3 −9339 87216921 1 1 20 10 1 10  ε_{1} 62.9252
1868  −20 −2335 87235600 1 2 14 14 1 14  ε_{1} 29.9891
9340  −4 −2335 87235600 10 1 14 70 1  7  ε_{1} 18.0739
9340  −20 −467 87235600 10 2 7 70 1  7  ε_{1} 18.0739
21 −1335 −3115 87329025 1 28 12 168 1 168  ε_{1} 3.1336
105 −267 −3115 87329025 2 2 12 24 1 12  ε_{1} 8.8131
105 −623 −1335 87329025 2 22 28 616 1 308  ε_{1} 8.8131
1869  −15 −3115 87329025 2 2 12 24 1 12  ε_{1} 20.3103
1869  −35 −1335 87329025 2 2 28 56 1 28  ε_{1} 20.3103
9345  −3 −3115 87329025 8 1 12 48 1  6  ε_{1} 22.2333
9345  −7 −1335 87329025 8 1 28 112 1 14  ε_{1} 22.2333
9345  −15 −623 87329025 8 2 22 176 1 22  ε_{1} 22.2333
9345  −35 −267 87329025 8 2 2 16 1  2  ε_{1} 22.2333

244 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
13 −719 −9347 87366409 1 31 24 372 1 372  ε_{1} 2.3895
12 −779 −9348 87385104 1 10 32 160 1 160  ε_{1} 2.6339
41 −228 −9348 87385104 1 4 32 64 1 64  ε_{1} 8.3183
57 −164 −9348 87385104 1 8 32 128 1 128  ε_{1} 11.4208
76 −123 −9348 87385104 1 2 32 32 1 32  ε_{1} 11.6579
492 −19 −9348 87385104 2 1 32 32 1 16 ε_{1} 10.9943
492 −228 −779 87385104 2 4 10 40 1 20  ε_{1} 10.9943
2337 −4 −9348 87385104 2 1 32 32 1 16 ε_{1} 42.0396
2337 −164 −228 87385104 2 8 4 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 21.0198
3116  −3 −9348 87385104 2 1 32 32 1 16  ε_{1} 33.9511
3116 −123 −228 87385104 2 2 4  8 1  4  ε_{1} 33.9511
56 −167 −9352 87459904 1 11 24 132 1 132  ε_{1} 6.8002
1169  −8 −9352 87459904 1 1 24 12 1 12  ε_{1} 67.0808
1169  −56 −1336 87459904 1 4 12 24 1 24  ε_{1} 67.0808
1336  −7 −9352 87459904 1 1 24 12 1 12  ε_{1} 64.9600
9352  −7 −1336 87459904 4 1 12 24 1  6  ε_{1} 28.2333
9352  −56 −167 87459904 4 4 11 88 1 22  ε_{1} 28.2333
9353  −47 −199 87478609 1 5 9 45 2 45 \sqrt{−1}\sqrt{ε_{1}} 68.3866
5 −1871 −9355 87516025 1 45 12 270 1 270  ε_{1} 0.9624
9356 −4 −2339 87534736 1 1 19 19 2 19 \sqrt{i}\sqrt{ε_{1}} 50.9875
9357  −3 −3119 87553449 1 1 69 69 2 69 \sqrt{−1}\sqrt{ε_{1}} 20.8755
253 −407 −851 87628321 1 16 10 80 1 80  ε_{1} 15.0577
9361  −11 −851 87628321 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 93.2737
9361  −23 −407 87628321 2 3 16 48 1 24  ε_{1} 186.5473
3121  −3 −9363 87665769 5 1 20 50 1 10  ε_{1} 34.0856
2341  −4 −9364 87684496 1 1 30 15 1 15  ε_{1} 60.9631
17 −551 −9367 87740689 1 26 28 364 1 364  ε_{1} 4.1894
29 −323 −9367 87740689 1 4 28 56 1 56  ε_{1} 3.2945
493 −19 −9367 87740689 2 1 28 28 1 14 ε_{1} 9.4192
493 −323 −551 87740689 2 4 26 104 1 52  ε_{1} 9.4192
8 −1171 −9368 87759424 1 7 42 147 1 147  ε_{1} 1.7627
9368 −8 −1171 87759424 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 33.8500
12 −2343 −3124 87834384 1 32 20 320 1 320  ε_{1} 2.6339
33 −852 −3124 87834384 1 8 20 80 1 80  ε_{1} 7.6563
44 −852 −2343 87834384 1 8 32 128 1 128  ε_{1} 5.9864
213 −132 −3124 87834384 1 4 20 40 1 40  ε_{1} 8.5805
284 −132 −2343 87834384 1 4 32 64 1 64  ε_{1} 17.6959
781 −132 −852 87834384 1 4 8 16 1 16  ε_{1} 37.4447
9372  −3 −3124 87834384 4 1 20 40 1 10  ε_{1} 19.9327
9372  −4 −2343 87834384 4 1 32 64 1 16  ε_{1} 19.9327
9372  −11 −852 87834384 4 1 8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 9.9664
9372  −71 −132 87834384 4 7 4 56 1 14  ε_{1} 19.9327
721  −91 −1339 87853129 1 2 8  8 1  8  ε_{1} 76.3136
9373  −7 −1339 87853129 2 1 8  8 1  4  ε_{1} 47.5951
9373  −91 −103 87853129 2 2 5 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 23.7976
113 −83 −9379 87965641 1 3 24 36 1 36 ε_{1} 14.6946
5 −1876 −9380 87984400 1 16 56 448 1 448  ε_{1} 0.9624
28 −335 −9380 87984400 1 18 56 504 1 504  ε_{1} 5.5373
140 −67 −9380 87984400 2 1 56 56 1 28 ε_{1} 4.9558
140 −335 −1876 87984400 2 18 16 288 1 144  ε_{1} 4.9558

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 245

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
268  −35 −9380 87984400 1 2 56 56 1 56  ε_{1} 22.9790
469  −20 −9380 87984400 3 2 56 168 1 56  ε_{1} 8.3483
1340  −7 −9380 87984400 2 1 56 56 1 28  ε_{1} 14.1934
1340  −35 −1876 87984400 2 2 16 32 1 16  ε_{1} 14.1934
2345  −4 −9380 87984400 2 1 56 56 1 28  ε_{1} 34.4505
2345  −20 −1876 87984400 2 2 16 64 2 32 \sqrt{−1}\sqrt{ε_{1}} 17.2253
177 −159 −3127 88003161 1 10 24 120 1 120  ε_{1} 23.4697
9381 −3 −3127 88003161 2 1 24 24 1 12 ε_{1} 44.0358
9381  −59 −159 88003161 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 22.0179
853 −11 −9383 88040689 1 1 102 51 1 51 ε_{1} 20.4426
17 −552 −9384 88059456 1 8 24 96 1 96  ε_{1} 4.1894
24 −391 −9384 88059456 1 14 24 168 1 168  ε_{1} 4.5849
69 −136 −9384 88059456 1 4 24 48 1 48  ε_{1} 6.4345
69 −408 −3128 88059456 1 4 24 48 1 48  ε_{1} 6.4345
184  −51 −9384 88059456 1 2 24 24 1 24  ε_{1} 21.5856
408  −23 −9384 88059456 2 3 24 72 1 36  ε_{1} 10.6165
408 −391 −552 88059456 2 14  8 112 1 56  ε_{1} 10.6165
552  −51 −3128 88059456 2 2 24 48 1 24  ε_{1} 9.0864
552 −391 −408 88059456 2 14  4 56 1 28  ε_{1} 9.0864
1173  −8 −9384 88059456 2 1 24 24 1 12  ε_{1} 11.2262
1173  −24 −3128 88059456 2 2 24 48 1 24  ε_{1} 11.2262
1173 −136 −552 88059456 2 4  8 32 1 16  ε_{1} 11.2262
1173 −184 −408 88059456 2 4  4 16 1  8  ε_{1} 11.2262
3128  −3 −9384 88059456 2 1 24 24 1 12  ε_{1} 14.7126
3128  −51 −552 88059456 2 2  8 16 1  8  ε_{1} 14.7126
9384  −3 −3128 88059456 4 1 24 48 1 12  ε_{1} 36.7015
9384  −23 −408 88059456 4 3  4 24 1  6  ε_{1} 36.7015
9384  −24 −391 88059456 4 2 14 56 1 14  ε_{1} 36.7015
9384  −51 −184 88059456 4 2  4 16 1  4  ε_{1} 36.7015
9388  −4 −2347 88134544 1 1  5  5 2  5  \sqrt{i}\sqrt{ε_{1}} 75.5510
2348  −8 −4696 88209664 1 1 30 30 2 30 \sqrt{−1}\sqrt{ε_{1}} 15.1543
4696 −4 −4696 88209664 1 1 30 30 2 30 \sqrt{i}\sqrt{ε_{1}} 57.4969
93 −303 −3131 88228449 1 10 20 100 1 100  ε_{1} 6.7322
9393 −3 −3131 88228449 2 1 20 20 1 10 ε_{1} 67.1613
9393  −31 −303 88228449 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 33.5806
5 −1879 −9395 88266025 1 27 24 324 1 324  ε_{1} 0.9624
13 −723 −9399 88341201 1 4 96 192 1 192  ε_{1} 2.3895
241  −39 −9399 88341201 1 4 96 192 1 192  ε_{1} 37.5430
3133  −3 −9399 88341201 2 1 96 96 1 48  ε_{1} 29.7502
3133  −39 −723 88341201 2 4  4 16 1  8  ε_{1} 29.7502
553 −119 −1343 88378801 1 10 34 170 1 170  ε_{1} 55.7072
9401  −7 −1343 88378801 2 1 34 34 1 17  ε_{1} 79.1139
9401  −79 −119 88378801 2 5 10 50 1 25  ε_{1} 79.1139
9404  −4 −2351 88435216 1 1 63 63 2 63  \sqrt{i}\sqrt{ε_{1}} 23.0994
409  −23 −9407 88491649 1 3 92 138 1 138  ε_{1} 52.2684
3137  −3 −9411 88566921 9 1 30 135 1 15  ε_{1} 9.4372
13 −724 −9412 88585744 1 10 16 80 1 80  ε_{1} 2.3895
181  −52 −9412 88585744 1 2 16 16 1 16  ε_{1} 14.3479
2353  −4 −9412 88585744 2 1 16 16 1  8  ε_{1} 63.3429
2353  −52 −724 88585744 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 31.6715

246 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
5 −1883 −9415 88642225 1 14 52 364 1 364  ε_{1} 0.9624
269  −35 −9415 88642225 1 2 52 52 1 52  ε_{1} 10.1998
1345  −7 −9415 88642225 6 1 52 156 1 26  ε_{1} 18.3560
1345  −35 −1883 88642225 6 2 14 84 1 14  ε_{1} 18.3560
88 −107 −9416 88661056 1 3 56 84 1 84  ε_{1} 11.9527
856  −11 −9416 88661056 1 1 56 28 1 28  ε_{1} 55.9217
1177  −8 −9416 88661056 1 1 56 28 1 28  ε_{1} 88.7782
1177  −88 −856 88661056 1 2 6  6 1  6  ε_{1} 88.7782
9416  −11 −856 88661056 2 1 6  6 1  3  ε_{1} 63.2290
9416  −88 −107 88661056 2 2 3  6 1  3  ε_{1} 63.2290
129 −219 −3139 88679889 1 4 10 20 1 20  ε_{1} 20.8511
9417  −3 −3139 88679889 2 1 10 20 2 10 \sqrt{−1}\sqrt{ε_{1}} 46.8895
9417 −43 −219 88679889 2 1 4 4 1 2 ε_{1} 93.7790
12 −2355 −3140 88736400 1 12 16 96 1 96  ε_{1} 2.6339
60 −471 −3140 88736400 2 16 16 256 1 128  ε_{1} 4.1269
60 −628 −2355 88736400 2 6 12 72 1 36  ε_{1} 4.1269
1884  −15 −3140 88736400 2 2 16 32 1 16  ε_{1} 33.1355
1884  −20 −2355 88736400 2 2 12 24 1 12  ε_{1} 33.1355
9420  −3 −3140 88736400 4 1 16 32 1  8  ε_{1} 22.8317
9420  −4 −2355 88736400 4 1 12 24 1  6  ε_{1} 22.8317
9420  −15 −628 88736400 4 2 6 24 1  6  ε_{1} 22.8317
9420  −20 −471 88736400 4 2 16 64 1 16  ε_{1} 22.8317
8 −2356 −4712 88811776 1 16 16 128 1 128  ε_{1} 1.7627
76 −248 −4712 88811776 1 8 16 64 1 64  ε_{1} 11.6579
124 −152 −4712 88811776 1 6 16 48 1 48  ε_{1} 16.0392
152 −248 −2356 88811776 1 8 16 64 1 64  ε_{1} 8.6078
248 −152 −2356 88811776 1 6 16 48 1 48  ε_{1} 9.6724
4712  −4 −4712 88811776 2 1 16 16 1  8  ε_{1} 23.3765
4712  −8 −2356 88811776 2 1 16 16 1  8  ε_{1} 23.3765
857  −11 −9427 88868329 1 1 14  7 1  7  ε_{1} 33.2056
2357  −4 −9428 88887184 1 1 42 21 1 21  ε_{1} 21.6629
21 −1347 −3143 88906041 1 6 56 168 1 168  ε_{1} 3.1336
9429  −3 −3143 88906041 2 1 56 56 1 28  ε_{1} 40.9287
9429  −7 −1347 88906041 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 20.4644
5 −1887 −9435 89019225 1 20 32 320 1 320  ε_{1} 0.9624
17 −555 −9435 89019225 1 4 32 64 1 64  ε_{1} 4.1894
37 −255 −9435 89019225 1 12 32 192 1 192  ε_{1} 4.9836
85 −111 −9435 89019225 2 8 32 256 1 128  ε_{1} 4.4187
85 −555 −1887 89019225 2 4 20 80 1 40  ε_{1} 4.4187
185 −51 −9435 89019225 2 2 32 64 1 32 ε_{1} 9.8254
185 −255 −1887 89019225 2 12 20 240 1 120  ε_{1} 9.8254
629 −15 −9435 89019225 2 2 32 64 1 32 ε_{1} 6.4409
629 −255 −555 89019225 2 12 4 48 1 24  ε_{1} 6.4409
3145  −3 −9435 89019225 4 1 32 64 1 16  ε_{1} 43.4253
3145  −15 −1887 89019225 4 2 20 80 1 20  ε_{1} 43.4253
3145  −51 −555 89019225 4 2 4 16 1  4  ε_{1} 43.4253
3145 −111 −255 89019225 4 8 12 192 1 48  ε_{1} 43.4253
28 −1348 −2359 89038096 1 8 28 112 1 112  ε_{1} 5.5373
9436  −4 −2359 89038096 4 1 28 56 1 14  ε_{1} 47.0234
9436  −7 −1348 89038096 4 1 8 16 1  4  ε_{1} 47.0234

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 247

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
133  −71 −9443 89170249 1 7 20 70 1 70  ε_{1} 10.3065
497  −19 −9443 89170249 1 1 20 10 1 10  ε_{1} 29.3851
1349  −7 −9443 89170249 1 1 20 10 1 10  ε_{1} 19.3578
12 −787 −9444 89189136 1 5 36 90 1 90  ε_{1} 2.6339
2361  −4 −9444 89189136 1 1 36 18 1 18  ε_{1} 123.1256
3148  −3 −9444 89189136 1 1 36 18 1 18  ε_{1} 49.9220
141  −67 −9447 89245809 1 1 44 22 1 22  ε_{1} 10.4940
201  −47 −9447 89245809 1 5 44 110 1 110  ε_{1} 27.6905
3149  −3 −9447 89245809 1 1 44 22 1 22  ε_{1} 37.4515
1181  −8 −9448 89264704 1 1 26 13 1 13  ε_{1} 20.5528
9449  −11 −859 89283601 1 1  7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 76.0021
13 −727 −9451 89321401 1 13 24 156 1 156  ε_{1} 2.3895
556  −68 −2363 89340304 1 4 10 20 1 20  ε_{1} 37.7195
9452  −4 −2363 89340304 2 1 10 20 2 10  \sqrt{i}\sqrt{ε_{1}} 21.4843
9452  −68 −139 89340304 2 4  3 12 1  6  ε_{1} 42.9687
69 −411 −3151 89359209 1 6 22 66 1 66  ε_{1} 6.4345
9453  −3 −3151 89359209 2 1 22 22 1 11  ε_{1} 24.9767
9453  −23 −411 89359209 2 3  6 18 1  9  ε_{1} 24.9767
5 −1891 −9455 89397025 1 10 120 600 1 600  ε_{1} 0.9624
61 −155 −9455 89397025 1 4 120 240 1 240  ε_{1} 7.3284
305 −31 −9455 89397025 2 3 120 360 1 180 ε_{1} 13.7710
305 −155 −1891 89397025 2 4 10 40 1 20  ε_{1} 13.7710
12 −1576 −4728 89415936 1 10 20 100 1 100  ε_{1} 2.6339
24 −788 −4728 89415936 1 10 20 100 1 100  ε_{1} 4.5849
2364 −8 −4728 89415936 2 1 20 20 1 10 ε_{1} 25.4219
2364  −24 −1576 89415936 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 12.7109
4728 −4 −4728 89415936 2 1 20 20 1 10 ε_{1} 35.6276
4728  −24 −788 89415936 2 2 10 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 17.8138
5 −1892 −9460 89491600 1 12 32 192 1 192  ε_{1} 0.9624
44 −215 −9460 89491600 1 14 32 224 1 224  ε_{1} 5.9864
172  −55 −9460 89491600 1 4 32 64 1 64  ε_{1} 17.6970
220  −43 −9460 89491600 2 1 32 32 1 16  ε_{1} 10.3635
220 −215 −1892 89491600 2 14 12 168 1 84  ε_{1} 10.3635
473  −20 −9460 89491600 3 2 32 96 1 32  ε_{1} 10.3180
860  −11 −9460 89491600 2 1 32 32 1 16  ε_{1} 8.9544
860  −55 −1892 89491600 2 4 12 48 1 24  ε_{1} 8.9544
2365  −4 −9460 89491600 2 1 32 32 1 16  ε_{1} 25.2916
2365  −20 −1892 89491600 2 2 12 24 1 12  ε_{1} 25.2916
1893  −15 −3155 89586225 1 2 20 20 1 20  ε_{1} 18.4394
9465  −3 −3155 89586225 2 1 20 20 1 10  ε_{1} 130.9745
9465  −15 −631 89586225 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 65.4872
21 −451 −9471 89699841 1 6 72 216 1 216  ε_{1} 3.1336
33 −287 −9471 89699841 1 14 72 504 1 504  ε_{1} 7.6563
41 −231 −9471 89699841 1 12 72 432 1 432  ε_{1} 8.3183
77 −123 −9471 89699841 1 2 72 72 1 72  ε_{1} 4.3693
861  −11 −9471 89699841 2 1 72 72 1 36  ε_{1} 13.8688
861 −231 −451 89699841 2 12  6 72 1 36  ε_{1} 13.8688
1353  −7 −9471 89699841 2 1 72 72 1 36  ε_{1} 36.5389
1353 −231 −287 89699841 2 12 14 168 1 84  ε_{1} 36.5389
3157  −3 −9471 89699841 2 1 72 72 1 36  ε_{1} 21.8709

248 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
3157 −123 −231 89699841 2 2 12 24 1 12  ε_{1} 21.8709
92 −103 −9476 89794576 1 5 72 180 1 180  ε_{1} 7.7415
412  −23 −9476 89794576 1 3 72 108 1 108  ε_{1} 26.0564
2369  −4 −9476 89794576 1 1 72 36 1 36  ε_{1} 87.4153
5 −1896 −9480 89870400 1 20 24 240 1 240  ε_{1} 0.9624
24 −395 −9480 89870400 1 8 24 96 1 96  ε_{1} 4.5849
120 −79 −9480 89870400 2 5 24 120 1 60 ε_{1} 6.1779
120 −395 −1896 89870400 2 8 20 160 1 80  ε_{1} 6.1779
237 −40 −9480 89870400 1 2 24 24 1 24 ε_{1} 8.6873
237 −120 −3160 89870400 1 4 16 32 1 32  ε_{1} 8.6873
632  −15 −9480 89870400 1 2 24 24 1 24  ε_{1} 19.2954
1185  −8 −9480 89870400 2 1 24 24 1 12  ε_{1} 36.4648
1185  −24 −3160 89870400 2 2 16 32 1 16  ε_{1} 36.4648
1185  −40 −1896 89870400 2 2 20 40 1 20  ε_{1} 36.4648
1185 −120 −632 89870400 2 4 8 32 1 16  ε_{1} 36.4648
1896 −15 −3160 89870400 2 2 16 32 1 16 ε_{1} 25.7329
1896 −120 −395 89870400 2 4 8 32 1 16  ε_{1} 25.7329
3160  −3 −9480 89870400 2 1 24 24 1 12  ε_{1} 46.6118
3160  −15 −1896 89870400 2 2 20 40 1 20  ε_{1} 46.6118
9480  −3 −3160 89870400 4 1 16 32 1  8  ε_{1} 31.9835
9480  −15 −632 89870400 4 2 8 32 1  8  ε_{1} 31.9835
9480  −24 −395 89870400 4 2 8 32 1  8  ε_{1} 31.9835
9480  −79 −120 89870400 4 5 4 80 2 20 \sqrt{−1}\sqrt{ε_{1}} 15.9917
9481 −19 −499 89889361 1 1 3 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 148.2448
29 −327 −9483 89927289 1 12 16 96 1 96  ε_{1} 3.2945
109  −87 −9483 89927289 1 6 16 48 1 48  ε_{1} 11.1291
3161  −3 −9483 89927289 4 1 16 32 1  8  ε_{1} 30.6820
3161  −87 −327 89927289 4 6 12 144 1 36  ε_{1} 30.6820
9484  −4 −2371 89946256 1 1 13 13 2 13  \sqrt{i}\sqrt{ε_{1}} 75.0232
1897  −35 −1355 89965225 5 2 12 60 1 12  ε_{1} 22.7658
9485  −7 −1355 89965225 2 1 12 12 1  6  ε_{1} 26.5188
9485  −35 −271 89965225 2 2 11 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 13.2594
53 −179 −9487 90003169 1 5 38 95 1 95  ε_{1} 3.9314
8 −2372 −4744 90022144 1 24 24 288 1 288  ε_{1} 1.7627
4744 −4 −4744 90022144 4 1 24 96 2 24 \sqrt{i}\sqrt{ε_{1}} 16.3524
4744  −8 −2372 90022144 4 1 24 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 16.3524
9489 −3 −3163 90041121 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 131.0561
12 −791 −9492 90098064 1 32 24 384 1 384  ε_{1} 2.6339
21 −452 −9492 90098064 1 8 24 96 1 96  ε_{1} 3.1336
28 −339 −9492 90098064 1 6 24 72 1 72  ε_{1} 5.5373
113  −84 −9492 90098064 1 4 24 48 1 48  ε_{1} 14.6946
1356  −7 −9492 90098064 2 1 24 24 1 12  ε_{1} 24.3711
1356  −84 −791 90098064 2 4 32 128 1 64  ε_{1} 24.3711
2373  −4 −9492 90098064 2 1 24 24 1 12  ε_{1} 11.6637
2373  −84 −452 90098064 2 4 8 32 1 16  ε_{1} 11.6637
3164  −3 −9492 90098064 4 1 24 48 1 12  ε_{1} 12.2185
3164  −84 −339 90098064 4 4 6 48 1 12  ε_{1} 12.2185
9493  −11 −863 90117049 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 45.9040
8 −1187 −9496 90174016 1 9 22 99 1 99  ε_{1} 1.7627
9496  −8 −1187 90174016 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 101.2633

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 249

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
161  −59 −9499 90231001 1 3 28 42 1 42  ε_{1} 20.1338
413  −23 −9499 90231001 1 3 28 42 1 42  ε_{1} 8.2212
1357  −7 −9499 90231001 1 1 28 14 1 14  ε_{1} 27.4038
9501  −3 −3167 90269001 1 1 53 53 2 53 \sqrt{−1}\sqrt{ε_{1}} 45.1727
13 −731 −9503 90307009 1 12 80 480 1 480  ε_{1} 2.3895
17 −559 −9503 90307009 1 16 80 640 1 640  ε_{1} 4.1894
221 −43 −9503 90307009 2 1 80 80 1 40 ε_{1} 5.4072
221 −559 −731 90307009 2 16 12 192 1 96  ε_{1} 5.4072
3169  −3 −9507 90383049 1 1 16  8 1  8  ε_{1} 181.5975
2377  −4 −9508 90402064 1 1 16  8 1  8  ε_{1} 132.3131
29 −328 −9512 90478144 1 4 60 120 1 120  ε_{1} 3.2945
41 −232 −9512 90478144 1 2 60 60 1 60  ε_{1} 8.3183
1189  −8 −9512 90478144 2 1 60 60 1 30  ε_{1} 20.3076
1189 −232 −328 90478144 2 2 4  8 1  4  ε_{1} 20.3076
5 −1903 −9515 90535225 1 22 28 308 1 308  ε_{1} 0.9624
173  −55 −9515 90535225 1 4 28 56 1 56  ε_{1} 5.1416
865  −11 −9515 90535225 2 1 28 28 1 14  ε_{1} 40.7237
865  −55 −1903 90535225 2 4 22 88 1 44  ε_{1} 40.7237
12 −2379 −3172 90554256 1 16 8 64 1 64  ε_{1} 2.6339
156 −183 −3172 90554256 2 8 8 64 1 32  ε_{1} 7.8232
156 −244 −2379 90554256 2 6 16 96 1 48  ε_{1} 7.8232
732  −39 −3172 90554256 2 4 8 32 1 16  ε_{1} 13.7628
732  −52 −2379 90554256 2 2 16 32 1 16  ε_{1} 13.7628
9516  −3 −3172 90554256 8 1 8 32 1  4  ε_{1} 16.5385
9516  −4 −2379 90554256 8 1 16 64 1  8  ε_{1} 16.5385
9516  −39 −244 90554256 8 4 6 192 2 24 \sqrt{−1}\sqrt{ε_{1}} 8.2692
9516  −52 −183 90554256 8 2 8 64 1  8  ε_{1} 16.5385
9517  −31 −307 90573289 3 3 3 27 2  9 \sqrt{−1}\sqrt{ε_{1}} 16.7294
57 −167 −9519 90611361 1 11 96 528 1 528  ε_{1} 11.4208
501  −19 −9519 90611361 1 1 96 48 1 48  ε_{1} 20.4959
3173  −3 −9519 90611361 3 1 96 144 1 48  ε_{1} 10.2597
28 −680 −4760 90630400 1 12 40 240 1 240  ε_{1} 5.5373
56 −340 −4760 90630400 1 4 40 80 1 80  ε_{1} 6.8002
140 −136 −4760 90630400 2 4 40 160 1 80  ε_{1} 4.9558
140 −680 −952 90630400 2 12 8 96 1 48  ε_{1} 4.9558
280 −68 −4760 90630400 2 4 40 160 1 80 ε_{1} 12.4372
280 −340 −952 90630400 2 4 8 32 1 16  ε_{1} 12.4372
476 −40 −4760 90630400 2 2 40 80 1 40 ε_{1} 10.9612
476 −280 −680 90630400 2 4 12 48 1 24  ε_{1} 10.9612
952  −20 −4760 90630400 2 2 40 80 1 40  ε_{1} 20.1146
952 −280 −340 90630400 2 4 4 16 1  8  ε_{1} 20.1146
2380  −8 −4760 90630400 4 1 40 80 1 20  ε_{1} 21.0389
2380  −40 −952 90630400 4 2 8 32 1  8  ε_{1} 21.0389
2380  −56 −680 90630400 4 4 12 96 1 24  ε_{1} 21.0389
2380 −136 −280 90630400 4 4 4 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 10.5194
4760  −4 −4760 90630400 4 1 40 80 1 20  ε_{1} 9.8544
4760  −20 −952 90630400 4 2 8 32 1  8  ε_{1} 9.8544
4760  −56 −340 90630400 4 4 4 32 1  8  ε_{1} 9.8544
4760  −68 −280 90630400 4 4 4 32 1  8  ε_{1} 9.8544
89 −107 −9523 90687529 1 3 12 18 1 18  ε_{1} 13.8155

250 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2381  −4 −9524 90706576 1 1 38 19 1 19  ε_{1} 40.1861
1361  −7 −9527 90763729 1 1 66 33 1 33  ε_{1} 61.8173
8 −1191 −9528 90782784 1 24 28 336 1 336  ε_{1} 1.7627
24 −1191 −3176 90782784 1 24 42 504 1 504  ε_{1} 4.5849
397  −24 −9528 90782784 1 2 28 28 1 28  ε_{1} 16.2905
3176  −3 −9528 90782784 2 1 28 28 1 14  ε_{1} 22.0198
3176  −24 −1191 90782784 2 2 24 48 1 24  ε_{1} 22.0198
9528  −3 −3176 90782784 2 1 42 84 2 42 \sqrt{−1}\sqrt{ε_{1}} 28.4510
9528  −8 −1191 90782784 2 1 24 24 1 12  ε_{1} 56.9020
9532  −4 −2383 90859024 1 1 29 29 2 29  \sqrt{i}\sqrt{ε_{1}} 45.1109
5 −1907 −9535 90916225 1 13 34 221 1 221  ε_{1} 0.9624
329 −203 −1363 91030681 1 4 6 12 1 12  ε_{1} 30.7485
9541  −7 −1363 91030681 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 33.8187
9541  −47 −203 91030681 2 5 4 20 1 10  ε_{1} 67.6375
3181  −3 −9543 91068849 5 1 52 130 1 26  ε_{1} 12.6701
1193  −8 −9544 91087936 1 1 32 16 1 16  ε_{1} 42.5195
1909 −115 −415 91107025 1 2 10 10 1 10  ε_{1} 44.5676
9545  −23 −415 91107025 2 3 10 30 1 15  ε_{1} 96.7622
9545  −83 −115 91107025 2 3 2  6 1  3  ε_{1} 96.7622
28 −1364 −2387 91164304 1 28 12 168 1 168  ε_{1} 5.5373
44 −868 −2387 91164304 1 8 12 48 1 48  ε_{1} 5.9864
77 −868 −1364 91164304 1 8 28 112 1 112  ε_{1} 4.3693
124 −308 −2387 91164304 1 8 12 48 1 48  ε_{1} 16.0392
217 −308 −1364 91164304 1 8 28 112 1 112  ε_{1} 31.7104
341 −308 −868 91164304 1 8 8 32 1 32  ε_{1} 11.2480
9548  −4 −2387 91164304 4 1 12 24 1  6  ε_{1} 13.0559
9548  −7 −1364 91164304 4 1 28 56 1 14  ε_{1} 13.0559
9548  −11 −868 91164304 4 1 8 16 1  4  ε_{1} 13.0559
9548  −31 −308 91164304 4 3 8 48 1 12  ε_{1} 13.0559
8 −2388 −4776 91240704 1 12 28 168 1 168  ε_{1} 1.7627
12 −1592 −4776 91240704 1 20 28 280 1 280  ε_{1} 2.6339
24 −1592 −2388 91240704 1 20 12 120 1 120  ε_{1} 4.5849
796  −24 −4776 91240704 1 2 28 28 1 28  ε_{1} 48.4110
1592  −24 −2388 91240704 1 2 12 12 1 12  ε_{1} 13.3642
4776  −4 −4776 91240704 2 1 28 28 1 14  ε_{1} 48.9826
4776  −8 −2388 91240704 2 1 12 12 1  6  ε_{1} 48.9826
2389  −4 −9556 91317136 1 1 34 17 1 17  ε_{1} 66.6117
9557  −19 −503 91336249 1 1 21 21 2 21 \sqrt{−1}\sqrt{ε_{1}} 28.7886
5 −1912 −9560 91393600 1 8 48 192 1 192  ε_{1} 0.9624
8 −1195 −9560 91393600 1 8 48 192 1 192  ε_{1} 1.7627
40 −239 −9560 91393600 2 15 48 720 1 360  ε_{1} 3.6369
40 −1195 −1912 91393600 2 8 8 64 1 32  ε_{1} 3.6369
1912  −40 −1195 91393600 1 2 8  8 1  8  ε_{1} 71.4254
9560  −8 −1195 91393600 2 1 8  8 1  4  ε_{1} 22.5145
9560  −40 −239 91393600 2 2 15 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 11.2572
9561 −3 −3187 91412721 1 1 7 7 2 7 \sqrt{−1}\sqrt{ε_{1}} 98.8820
73 −131 −9563 91450969 1 5 18 45 1 45  ε_{1} 15.3334
12 −2391 −3188 91470096 1 34 30 510 1 510  ε_{1} 2.6339
9564  −3 −3188 91470096 2 1 30 30 1 15  ε_{1} 80.4594
9564  −4 −2391 91470096 2 1 34 34 1 17  ε_{1} 80.4594

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 251

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
9569  −7 −1367 91565761 1 1 25 25 2 25 \sqrt{−1}\sqrt{ε_{1}} 96.4412
17 −563 −9571 91604041 1 9 20 90 1 90  ε_{1} 4.1894
2393 −4 −9572 91623184 1 1 60 30 1 30 ε_{1} 54.7353
9573  −3 −3191 91642329 1 1 69 69 2 69 \sqrt{−1}\sqrt{ε_{1}} 36.9119
93 −103 −9579 91757241 1 5 32 80 1 80  ε_{1} 6.7322
309  −31 −9579 91757241 1 3 32 48 1 48  ε_{1} 17.0523
3193  −3 −9579 91757241 1 1 32 16 1 16  ε_{1} 156.1559
1916  −20 −2395 91776400 1 2 8  8 1  8  ε_{1} 31.2075
9580  −4 −2395 91776400 2 1 8  8 1  4  ε_{1} 93.5637
9580  −20 −479 91776400 2 2 25 100 2 50 \sqrt{−1}\sqrt{ε_{1}} 46.7819
737 −143 −871 91795561 1 10 22 110 1 110  ε_{1} 40.0839
9581  −11 −871 91795561 2 1 22 22 1 11  ε_{1} 27.3106
9581  −67 −143 91795561 2 1 10 10 1  5  ε_{1} 27.3106
2396  −8 −4792 91853056 1 1 12 12 2 12 \sqrt{−1}\sqrt{ε_{1}} 31.5304
4792 −4 −4792 91853056 1 1 12 12 2 12 \sqrt{i}\sqrt{ε_{1}} 50.4840
12 −799 −9588 91929744 1 16 32 256 1 256  ε_{1} 2.6339
17 −564 −9588 91929744 1 8 32 128 1 128  ε_{1} 4.1894
141  −68 −9588 91929744 1 4 32 64 1 64  ε_{1} 10.4940
188  −51 −9588 91929744 1 2 32 32 1 32  ε_{1} 9.1285
204  −47 −9588 91929744 2 5 32 160 1 80  ε_{1} 9.2101
204 −564 −799 91929744 2 8 16 128 1 64  ε_{1} 9.2101
2397  −4 −9588 91929744 2 1 32 32 1 16  ε_{1} 7.7828
2397  −68 −564 91929744 2 4 8 32 1 16  ε_{1} 7.7828
3196  −3 −9588 91929744 8 1 32 128 1 16  ε_{1} 13.4858
3196  −51 −564 91929744 8 2 8 64 1  8  ε_{1} 13.4858
9589  −43 −223 91948921 1 1 7  7 2  7 \sqrt{−1}\sqrt{ε_{1}} 46.5041
69 −139 −9591 91987281 1 3 80 120 1 120  ε_{1} 6.4345
417  −23 −9591 91987281 1 3 80 120 1 120  ε_{1} 37.9102
3197  −3 −9591 91987281 1 1 80 40 1 40  ε_{1} 25.3537
8 −1199 −9592 92006464 1 38 20 380 1 380  ε_{1} 1.7627
88 −872 −1199 92006464 1 10 38 190 1 190  ε_{1} 11.9527
109  −88 −9592 92006464 1 2 20 20 1 20  ε_{1} 11.1291
872  −11 −9592 92006464 2 1 20 20 1 10  ε_{1} 12.4372
872  −88 −1199 92006464 2 2 38 76 1 38  ε_{1} 12.4372
9592  −8 −1199 92006464 2 1 38 38 1 19  ε_{1} 78.1962
9592  −11 −872 92006464 2 1 10 10 1  5  ε_{1} 78.1962
5 −1919 −9595 92064025 1 44 16 352 1 352  ε_{1} 0.9624
101  −95 −9595 92064025 1 8 16 64 1 64  ε_{1} 5.9964
505  −19 −9595 92064025 4 1 16 32 1  8  ε_{1} 14.7779
505  −95 −1919 92064025 4 8 44 704 1 176  ε_{1} 14.7779
9596  −4 −2399 92083216 5 1 59 295 2 59  \sqrt{i}\sqrt{ε_{1}} 8.4764
21 −1371 −3199 92102409 1 12 32 192 1 192  ε_{1} 3.1336
9597 −3 −3199 92102409 4 1 32 64 1 16 ε_{1} 17.2199
9597  −7 −1371 92102409 4 1 12 48 2 12 \sqrt{−1}\sqrt{ε_{1}} 8.6100
29 −331 −9599 92140801 1 3 98 147 1 147  ε_{1} 3.2945
13 −739 −9607 92294449 1 5 42 105 1 105  ε_{1} 2.3895
1201 −8 −9608 92313664 1 1 40 20 1 20 ε_{1} 109.1299
9609  −3 −3203 92332881 1 1 11 11 2 11 \sqrt{−1}\sqrt{ε_{1}} 97.8774
1373 −7 −9611 92371321 3 1 44 66 1 22 ε_{1} 7.2233
5 −1923 −9615 92448225 1 10 36 180 1 180  ε_{1} 0.9624

252 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
641  −15 −9615 92448225 1 2 36 36 1 36  ε_{1} 50.0066
3205  −3 −9615 92448225 2 1 36 36 1 18  ε_{1} 26.6620
3205  −15 −1923 92448225 2 2 10 20 1 10  ε_{1} 26.6620
8 −2404 −4808 92467456 1 20 24 240 1 240  ε_{1} 1.7627
4808 −4 −4808 92467456 2 1 24 48 2 24 \sqrt{i}\sqrt{ε_{1}} 9.9820
4808  −8 −2404 92467456 2 1 20 40 2 20 \sqrt{−1}\sqrt{ε_{1}} 9.9820
9617 −59 −163 92486689 1 3 1 3 2 3 \sqrt{−1}\sqrt{ε_{1}} 62.2217
5 −1924 −9620 92544400 1 16 40 320 1 320  ε_{1} 0.9624
13 −740 −9620 92544400 1 16 40 320 1 320  ε_{1} 2.3895
37 −260 −9620 92544400 1 8 40 160 1 160  ε_{1} 4.9836
65 −148 −9620 92544400 2 2 40 80 1 40  ε_{1} 5.5529
65 −740 −1924 92544400 2 16 16 256 1 128  ε_{1} 5.5529
185 −52 −9620 92544400 2 2 40 80 1 40 ε_{1} 9.8254
185 −260 −1924 92544400 2 8 16 128 1 64  ε_{1} 9.8254
481 −20 −9620 92544400 2 2 40 80 1 40 ε_{1} 28.9443
481 −260 −740 92544400 2 8 16 128 1 64  ε_{1} 28.9443
2405  −4 −9620 92544400 4 1 40 80 1 20  ε_{1} 7.7845
2405  −20 −1924 92544400 4 2 16 64 1 16  ε_{1} 7.7845
2405  −52 −740 92544400 4 2 16 64 1 16  ε_{1} 7.7845
2405 −148 −260 92544400 4 2 8 32 1  8  ε_{1} 7.7845
8 −1203 −9624 92621376 1 6 60 180 1 180  ε_{1} 1.7627
24 −1203 −3208 92621376 1 6 12 36 1 36  ε_{1} 4.5849
401  −24 −9624 92621376 5 2 60 300 1 60  ε_{1} 7.3790
3208  −3 −9624 92621376 2 1 60 60 1 30  ε_{1} 40.3946
3208  −24 −1203 92621376 2 2 6 12 1  6  ε_{1} 40.3946
9624  −3 −3208 92621376 2 1 12 12 1  6  ε_{1} 57.0763
9624  −8 −1203 92621376 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 28.5381
3209  −3 −9627 92679129 1 1 18  9 1  9  ε_{1} 91.5160
332 −116 −2407 92698384 1 6 20 60 1 60  ε_{1} 10.1997
9628 −4 −2407 92698384 2 1 20 20 1 10 ε_{1} 46.9940
9628  −83 −116 92698384 2 3 6 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 23.4970
5 −1927 −9635 92833225 1 18 44 396 1 396  ε_{1} 0.9624
41 −235 −9635 92833225 1 2 44 44 1 44  ε_{1} 8.3183
205 −47 −9635 92833225 2 5 44 220 1 110 ε_{1} 7.5213
205 −235 −1927 92833225 2 2 18 36 1 18  ε_{1} 7.5213
12 −803 −9636 92852496 1 10 40 200 1 200  ε_{1} 2.6339
33 −292 −9636 92852496 1 4 40 80 1 80  ε_{1} 7.6563
44 −219 −9636 92852496 1 4 40 80 1 80  ε_{1} 5.9864
73 −132 −9636 92852496 1 4 40 80 1 80  ε_{1} 15.3334
876 −11 −9636 92852496 4 1 40 80 1 20 ε_{1} 9.9943
876 −132 −803 92852496 4 4 10 80 1 20  ε_{1} 9.9943
2409  −4 −9636 92852496 2 1 40 40 1 20  ε_{1} 64.6462
2409 −132 −292 92852496 2 4 4 16 1  8  ε_{1} 64.6462
3212  −3 −9636 92852496 2 1 40 40 1 20  ε_{1} 19.1572
3212 −132 −219 92852496 2 4 4 16 1  8  ε_{1} 19.1572
9637  −23 −419 92871769 1 3 9 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 48.8812
5 −1928 −9640 92929600 1 20 16 160 1 160  ε_{1} 0.9624
241  −40 −9640 92929600 1 2 16 16 1 16  ε_{1} 37.5430
1205  −8 −9640 92929600 2 1 16 16 1  8  ε_{1} 10.9861
1205  −40 −1928 92929600 2 2 20 40 1 20  ε_{1} 10.9861

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 253

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
9641  −31 −311 92948881 1 3 19 57 2 57 \sqrt{−1}\sqrt{ε_{1}} 112.3806
9644  −4 −2411 93006736 1 1 23 23 2 23  \sqrt{i}\sqrt{ε_{1}} 31.6887
1929  −15 −3215 93026025 3 2 50 150 1 50  ε_{1} 38.7025
9645  −3 −3215 93026025 2 1 50 50 1 25  ε_{1} 34.7209
9645  −15 −643 93026025 2 2 3  6 1  3  ε_{1} 34.7209
877  −11 −9647 93064609 1 1 86 43 1 43  ε_{1} 26.1741
3217  −3 −9651 93141801 1 1 28 14 1 14  ε_{1} 161.2872
76 −127 −9652 93161104 1 5 24 60 1 60  ε_{1} 11.6579
508  −19 −9652 93161104 1 1 24 12 1 12  ε_{1} 32.1254
2413  −4 −9652 93161104 1 1 24 12 1 12  ε_{1} 38.4931
5 −1931 −9655 93219025 1 21 52 546 1 546  ε_{1} 0.9624
8 −1207 −9656 93238336 1 18 72 648 1 648  ε_{1} 1.7627
17 −568 −9656 93238336 1 4 72 144 1 144  ε_{1} 4.1894
136 −71 −9656 93238336 2 7 72 504 1 252 ε_{1} 8.4966
136 −568 −1207 93238336 2 4 18 72 1 36  ε_{1} 8.4966
568 −136 −1207 93238336 3 4 18 108 1 36  ε_{1} 11.3120
9656  −8 −1207 93238336 2 1 18 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 26.0224
9656 −71 −136 93238336 2 7 4 28 1 14 ε_{1} 52.0449
13 −743 −9659 93296281 1 21 38 399 1 399  ε_{1} 2.3895
12 −2415 −3220 93315600 1 40 16 320 1 320  ε_{1} 2.6339
21 −1380 −3220 93315600 1 8 16 64 1 64  ε_{1} 3.1336
28 −1380 −2415 93315600 1 8 40 160 1 160  ε_{1} 5.5373
60 −483 −3220 93315600 2 4 16 64 1 32  ε_{1} 4.1269
60 −644 −2415 93315600 2 16 40 640 1 320  ε_{1} 4.1269
69 −420 −3220 93315600 1 8 16 64 1 64  ε_{1} 6.4345
92 −420 −2415 93315600 1 8 40 160 1 160  ε_{1} 7.7415
105 −276 −3220 93315600 2 8 16 128 1 64  ε_{1} 8.8131
105 −644 −1380 93315600 2 16 8 128 1 64  ε_{1} 8.8131
140 −276 −2415 93315600 2 8 40 320 1 160  ε_{1} 4.9558
140 −483 −1380 93315600 2 4 8 32 1 16  ε_{1} 4.9558
161 −420 −1380 93315600 1 8 8 32 1 32  ε_{1} 20.1338
345 −84 −3220 93315600 2 4 16 64 1 32 ε_{1} 19.0241
345 −420 −644 93315600 2 8 16 128 1 64  ε_{1} 19.0241
460 −84 −2415 93315600 2 4 40 160 1 80 ε_{1} 15.4391
460 −420 −483 93315600 2 8 4 32 1 16  ε_{1} 15.4391
805 −84 −1380 93315600 2 4 8 32 1 16 ε_{1} 14.5545
805 −276 −420 93315600 2 8 8 64 1 32  ε_{1} 14.5545
1932  −15 −3220 93315600 4 2 16 64 1 16  ε_{1} 7.5673
1932  −20 −2415 93315600 4 2 40 160 1 40  ε_{1} 7.5673
1932  −35 −1380 93315600 4 2 8 32 1  8  ε_{1} 7.5673
1932 −115 −420 93315600 4 2 8 32 1  8  ε_{1} 7.5673
9660  −3 −3220 93315600 8 1 16 64 1  8  ε_{1} 13.0676
9660  −4 −2415 93315600 8 1 40 160 1 20  ε_{1} 13.0676
9660  −7 −1380 93315600 8 1 8 32 1  4  ε_{1} 13.0676
9660  −15 −644 93315600 8 2 16 128 1 16  ε_{1} 13.0676
9660  −20 −483 93315600 8 2 4 32 1  4  ε_{1} 13.0676
9660  −23 −420 93315600 8 3 8 96 1 12  ε_{1} 13.0676
9660  −35 −276 93315600 8 2 8 64 1  8  ε_{1} 13.0676
9660  −84 −115 93315600 8 4 2 32 1  4  ε_{1} 13.0676
3221  −3 −9663 93373569 3 1 54 81 1 27  ε_{1} 16.4262

254 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
1381  −7 −9667 93450889 1 1 12  6 1  6  ε_{1} 50.0922
2417  −4 −9668 93470224 1 1 36 18 1 18  ε_{1} 72.4854
33 −879 −3223 93489561 1 22 30 330 1 330  ε_{1} 7.6563
9669  −3 −3223 93489561 10 1 30 150 1 15  ε_{1} 11.3739
9669  −11 −879 93489561 10 1 22 110 1 11  ε_{1} 11.3739
509  −19 −9671 93528241 1 1 126 63 1 63  ε_{1} 13.6596
13 −744 −9672 93547584 1 12 24 144 1 144  ε_{1} 2.3895
24 −403 −9672 93547584 1 2 24 24 1 24  ε_{1} 4.5849
93 −104 −9672 93547584 1 6 24 72 1 72  ε_{1} 6.7322
93 −312 −3224 93547584 1 4 28 56 1 56  ε_{1} 6.7322
248  −39 −9672 93547584 1 4 24 48 1 48  ε_{1} 9.6724
312  −31 −9672 93547584 2 3 24 72 1 36  ε_{1} 9.3267
312 −403 −744 93547584 2 2 12 24 1 12  ε_{1} 9.3267
744  −39 −3224 93547584 2 4 28 112 1 56  ε_{1} 19.2319
744 −312 −403 93547584 2 4  2  8 1  4  ε_{1} 19.2319
1209  −8 −9672 93547584 2 1 24 24 1 12  ε_{1} 37.1044
1209  −24 −3224 93547584 2 2 28 56 1 28  ε_{1} 37.1044
1209 −104 −744 93547584 2 6 12 72 1 36  ε_{1} 37.1044
1209 −248 −312 93547584 2 8  4 32 1 16  ε_{1} 37.1044
3224  −3 −9672 93547584 2 1 24 24 1 12  ε_{1} 32.6555
3224  −39 −744 93547584 2 4 12 48 1 24  ε_{1} 32.6555
9672  −3 −3224 93547584 4 1 28 56 1 14  ε_{1} 23.5689
9672  −24 −403 93547584 4 2  2  8 1  2  ε_{1} 23.5689
9672  −31 −312 93547584 4 3  4 24 1  6  ε_{1} 23.5689
9672  −39 −248 93547584 4 4  8 128 2 32 \sqrt{−1}\sqrt{ε_{1}} 11.7844
236 −164 −2419 93624976 1 8  8 32 1 32  ε_{1} 13.9320
9676  −4 −2419 93624976 12 1  8 48 1  4  ε_{1} 17.3661
9676  −59 −164 93624976 12 3  8 288 2 24 \sqrt{−1}\sqrt{ε_{1}} 8.6830
21 −1383 −3227 93721761 1 18 14 126 1 126  ε_{1} 3.1336
9681  −3 −3227 93721761 2 1 14 14 1  7  ε_{1} 139.0348
9681  −7 −1383 93721761 2 1 18 18 1  9  ε_{1} 139.0348
421  −23 −9683 93760489 1 3 18 27 1 27  ε_{1} 26.0114
3229  −3 −9687 93837969 3 1 60 90 1 30  ε_{1} 24.8609
8 −1211 −9688 93857344 1 14 20 140 1 140  ε_{1} 1.7627
56 −1211 −1384 93857344 1 14 10 70 1 70  ε_{1} 6.8002
173  −56 −9688 93857344 1 4 20 40 1 40  ε_{1} 5.1416
1384  −7 −9688 93857344 6 1 20 60 1 10  ε_{1} 10.4516
1384  −56 −1211 93857344 6 4 14 168 1 28  ε_{1} 10.4516
9688  −7 −1384 93857344 2 1 10 10 1  5  ε_{1} 67.0649
9688  −8 −1211 93857344 2 1 14 14 1  7  ε_{1} 67.0649
881  −11 −9691 93915481 1 1 20 10 1 10  ε_{1} 52.1657
9692  −4 −2423 93934864 1 1 33 33 2 33  \sqrt{i}\sqrt{ε_{1}} 42.4154
5 −1939 −9695 93993025 1 8 92 368 1 368  ε_{1} 0.9624
277  −35 −9695 93993025 1 2 92 92 1 92  ε_{1} 15.7365
1385  −7 −9695 93993025 2 1 92 92 1 46  ε_{1} 24.4924
1385  −35 −1939 93993025 2 2  8 16 1  8  ε_{1} 24.4924
53 −183 −9699 94070601 1 8 28 112 1 112  ε_{1} 3.9314
61 −159 −9699 94070601 1 10 28 140 1 140  ε_{1} 7.3284
3233  −3 −9699 94070601 2 1 28 28 1 14  ε_{1} 29.1440
3233 −159 −183 94070601 2 10  8 80 1 40  ε_{1} 29.1440

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 255

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
313  −31 −9703 94148209 1 3 34  51 1 51  ε_{1} 38.7035
1213  −8 −9704 94167616 1 1 54  27 1 27  ε_{1} 37.5314
1941  −15 −3235 94187025 1 2 6  6 1  6  ε_{1} 46.1538
9705  −3 −3235 94187025 2 1 6  6 1  3  ε_{1} 90.0207
9705  −15 −647 94187025 2 2 23  46 1 23  ε_{1} 90.0207
17 −571 −9707 94225849 1 5 26  65 1 65  ε_{1} 4.1894
12 −2427 −3236 94245264 1 14 32 224 1 224  ε_{1} 2.6339
9708  −3 −3236 94245264 2 1 32  32 1 16  ε_{1} 39.1714
9708  −4 −2427 94245264 2 1 14  28 2 14  \sqrt{i}\sqrt{ε_{1}} 19.5857
133 −511 −1387 94264681 1 14 4  28 1 28  ε_{1} 10.3065
9709  −7 −1387 94264681 2 1 4  4 1  2  ε_{1} 58.6466
9709  −19 −511 94264681 2 1 14  28 2 14 \sqrt{−1}\sqrt{ε_{1}} 29.3233
2428  −8 −4856 94322944 1 1 40  40 2 40 \sqrt{−1}\sqrt{ε_{1}} 26.5167
4856  −4 −4856 94322944 1 1 40  40 2 40  \sqrt{i}\sqrt{ε_{1}} 32.6167
9713  −11 −883 94342369 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 66.2045
5 −1943 −9715 94381225 1 32 24 384 1 384  ε_{1} 0.9624
29 −335 −9715 94381225 1 18 24 216 1 216  ε_{1} 3.2945
145 −67 −9715 94381225 4 1 24 48 1 12 ε_{1} 6.3596
145 −335 −1943 94381225 4 18 32 1152 1 288  ε_{1} 6.3596
28 −347 −9716 94400656 1 5 56 140 1 140  ε_{1} 5.5373
1388  −7 −9716 94400656 1 1 56  28 1 28  ε_{1} 28.1297
2429  −4 −9716 94400656 3 1 56  84 1 28  ε_{1} 11.6871
237 −123 −3239 94420089 1 2 70  70 1 70  ε_{1} 8.6873
9717  −3 −3239 94420089 2 1 70  70 1 35  ε_{1} 26.3367
9717  −79 −123 94420089 2 5 2  10 1  5  ε_{1} 26.3367
21 −463 −9723 94536729 1 7 24  84 1 84  ε_{1} 3.1336
1389  −7 −9723 94536729 1 1 24  12 1 12  ε_{1} 28.0804
3241  −3 −9723 94536729 1 1 24  12 1 12  ε_{1} 187.4588
44 −884 −2431 94556176 1 16 28 224 1 224  ε_{1} 5.9864
572  −68 −2431 94556176 2 4 28 112 1 56  ε_{1} 6.3526
572 −187 −884 94556176 2 2 16  32 1 16  ε_{1} 6.3526
748  −52 −2431 94556176 2 2 28  56 1 28  ε_{1} 16.2418
748 −143 −884 94556176 2 10 16 160 1 80  ε_{1} 16.2418
9724  −4 −2431 94556176 4 1 28  56 1 14  ε_{1} 53.3180
9724  −11 −884 94556176 4 1 16  32 1  8  ε_{1} 53.3180
9724  −52 −187 94556176 4 2 2  8 1  2  ε_{1} 53.3180
9724  −68 −143 94556176 4 4 10  80 1 20  ε_{1} 53.3180
137  −71 −9727 94614529 1 7 38 133 1 133  ε_{1} 16.3142
37 −263 −9731 94692361 1 13 32 208 1 208  ε_{1} 4.9836
12 −811 −9732 94711824 1 7 20  70 1 70  ε_{1} 2.6339
2433  −4 −9732 94711824 1 1 20  10 1 10  ε_{1} 92.5868
3244  −3 −9732 94711824 1 1 20  10 1 10  ε_{1} 84.9265
5 −1947 −9735 94770225 1 8 64 256 1 256  ε_{1} 0.9624
33 −295 −9735 94770225 1 8 64 256 1 256  ε_{1} 7.6563
165  −59 −9735 94770225 2 3 64 192 1 96  ε_{1} 5.1180
165 −295 −1947 94770225 2 8 8  64 1 32  ε_{1} 5.1180
177  −55 −9735 94770225 1 4 64 128 1 128  ε_{1} 23.4697
649  −15 −9735 94770225 1 2 64  64 1 64  ε_{1} 70.6969
885  −11 −9735 94770225 2 1 64  64 1 32  ε_{1} 10.9445
885  −55 −1947 94770225 2 4 8  32 1 16  ε_{1} 10.9445

256 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
3245  −3 −9735 94770225 4 1 64 128 1 32  ε_{1} 8.0855
3245  −15 −1947 94770225 4 2 8 32 1  8  ε_{1} 8.0855
1217  −8 −9736 94789696 1 1 32 16 1 16  ε_{1} 35.6550
749  −91 −1391 94809169 1 2 44 44 1 44  ε_{1} 18.9369
9737  −7 −1391 94809169 2 1 44 44 1 22  ε_{1} 67.3484
9737  −91 −107 94809169 2 2 3 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 33.6742
1948  −20 −2435 94867600 1 2 22 22 1 22  ε_{1} 64.5472
9740  −4 −2435 94867600 2 1 22 22 1 11  ε_{1} 39.4752
9740  −20 −487 94867600 2 2 7 14 1  7  ε_{1} 39.4752
573  −51 −3247 94887081 1 2 32 32 1 32  ε_{1} 13.2824
9741  −3 −3247 94887081 2 1 32 32 1 16  ε_{1} 49.7212
9741  −51 −191 94887081 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 24.8606
8 −2436 −4872 94945536 1 16 24 192 1 192  ε_{1} 1.7627
12 −1624 −4872 94945536 1 16 24 192 1 192  ε_{1} 2.6339
24 −1624 −2436 94945536 1 16 16 128 1 128  ε_{1} 4.5849
28 −696 −4872 94945536 1 12 24 144 1 144  ε_{1} 5.5373
56 −696 −2436 94945536 1 12 16 96 1 96  ε_{1} 6.8002
168 −116 −4872 94945536 2 6 24 144 1 72  ε_{1} 6.5132
168 −232 −2436 94945536 2 2 16 32 1 16  ε_{1} 6.5132
232 −84 −4872 94945536 2 4 24 96 1 48 ε_{1} 10.5766
232 −168 −2436 94945536 2 4 16 64 1 32  ε_{1} 10.5766
348 −56 −4872 94945536 2 4 24 96 1 48 ε_{1} 8.0501
348 −168 −1624 94945536 2 4 16 64 1 32  ε_{1} 8.0501
696  −56 −2436 94945536 2 4 16 64 1 32  ε_{1} 15.9463
696  −84 −1624 94945536 2 4 16 64 1 32  ε_{1} 15.9463
812  −24 −4872 94945536 2 2 24 48 1 24  ε_{1} 9.4722
812 −168 −696 94945536 2 4 12 48 1 24  ε_{1} 9.4722
1624  −24 −2436 94945536 2 2 16 32 1 16  ε_{1} 37.1882
1624  −84 −696 94945536 2 4 12 48 1 24  ε_{1} 37.1882
4872  −4 −4872 94945536 4 1 24 48 1 12  ε_{1} 13.0964
4872  −8 −2436 94945536 4 1 16 32 1  8  ε_{1} 13.0964
4872  −84 −232 94945536 4 4 2 16 1  4  ε_{1} 13.0964
4872 −116 −168 94945536 4 6 4 48 1 12  ε_{1} 13.0964
2437 −4 −9748 95023504 1 1 18 9 1 9 ε_{1} 42.8377
8 −1219 −9752 95101504 1 6 28 84 1 84  ε_{1} 1.7627
53 −184 −9752 95101504 1 4 28 56 1 56  ε_{1} 3.9314
184 −424 −1219 95101504 1 6 6 18 1 18  ε_{1} 21.5856
424 −23 −9752 95101504 2 3 28 84 1 42 ε_{1} 17.9769
424 −184 −1219 95101504 2 4 6 24 1 12  ε_{1} 17.9769
9752  −8 −1219 95101504 2 1 6  6 1  3  ε_{1} 29.4786
9752  −23 −424 95101504 2 3 6 18 1  9  ε_{1} 29.4786
9753  −3 −3251 95121009 1 1 31 31 2 31 \sqrt{−1}\sqrt{ε_{1}} 102.3386
5 −1951 −9755 95160025 1 33 20 330 1 330  ε_{1} 0.9624
9757  −11 −887 95199049 5 1 29 145 2 29 \sqrt{−1}\sqrt{ε_{1}} 6.7901
3253  −3 −9759 95238081 5 1 92 230 1 46  ε_{1} 8.0867
9761  −43 −227 95277121 1 1 5  5 2  5 \sqrt{−1}\sqrt{ε_{1}} 78.9311
13 −751 −9763 95316169 1 15 16 120 1 120  ε_{1} 2.3895
2441 −4 −9764 95335696 1 1 76 38 1 38 ε_{1} 82.9144
24 −407 −9768 95413824 1 16 32 256 1 256  ε_{1} 4.5849
33 −296 −9768 95413824 1 10 32 160 1 160  ε_{1} 7.6563

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 257

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
33 −888 −3256 95413824 1 12 12 72 1 72  ε_{1} 7.6563
37 −264 −9768 95413824 1 8 32 128 1 128  ε_{1} 4.9836
88 −111 −9768 95413824 1 8 32 128 1 128  ε_{1} 11.9527
264 −111 −3256 95413824 2 8 12 96 1 48  ε_{1} 9.7350
264 −407 −888 95413824 2 16 12 192 1 96  ε_{1} 9.7350
888 −11 −9768 95413824 2 1 32 32 1 16 ε_{1} 11.3942
888 −264 −407 95413824 2 8 16 128 1 64  ε_{1} 11.3942
1221  −8 −9768 95413824 4 1 32 64 1 16  ε_{1} 7.1091
1221  −24 −3256 95413824 4 2 12 48 1 12  ε_{1} 7.1091
1221  −88 −888 95413824 4 2 12 48 1 12  ε_{1} 7.1091
1221 −264 −296 95413824 4 8 10 160 1 40  ε_{1} 7.1091
3256 −3 −9768 95413824 2 1 32 32 1 16 ε_{1} 59.5218
3256 −111 −264 95413824 2 8 8 64 1 32  ε_{1} 59.5218
9768  −3 −3256 95413824 4 1 12 24 1  6  ε_{1} 14.1567
9768  −11 −888 95413824 4 1 12 24 1  6  ε_{1} 14.1567
9768  −24 −407 95413824 4 2 16 64 1 16  ε_{1} 14.1567
9768  −88 −111 95413824 4 2 8 32 1  8  ε_{1} 14.1567
3257  −3 −9771 95472441 1 1 26 13 1 13  ε_{1} 82.5257
28 −1396 −2443 95491984 1 14 6 42 1 42  ε_{1} 5.5373
9772  −4 −2443 95491984 2 1 6  6 1  3  ε_{1} 74.8302
9772  −7 −1396 95491984 2 1 14 14 1  7  ε_{1} 74.8302
188 −104 −4888 95570176 1 6 12 36 1 36  ε_{1} 9.1285
376  −52 −4888 95570176 1 2 12 12 1 12  ε_{1} 30.5420
2444  −8 −4888 95570176 2 1 12 12 1  6  ε_{1} 26.1373
2444 −104 −376 95570176 2 6 8 96 2 48 \sqrt{−1}\sqrt{ε_{1}} 13.0687
4888 −4 −4888 95570176 2 1 12 12 1 6 ε_{1} 60.7397
4888  −52 −376 95570176 2 2 8 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 30.3698
9777 −3 −3259 95589729 1 1 9 9 2 9 \sqrt{−1}\sqrt{ε_{1}} 98.3190
77 −127 −9779 95628841 1 5 48 120 1 120  ε_{1} 4.3693
889  −11 −9779 95628841 1 1 48 24 1 24  ε_{1} 89.4446
1397  −7 −9779 95628841 1 1 48 24 1 24  ε_{1} 16.1274
5 −1956 −9780 95648400 1 20 32 320 1 320  ε_{1} 0.9624
12 −815 −9780 95648400 1 30 32 480 1 480  ε_{1} 2.6339
60 −163 −9780 95648400 2 1 32 32 1 16  ε_{1} 4.1269
60 −815 −1956 95648400 2 30 20 600 1 300  ε_{1} 4.1269
489  −20 −9780 95648400 1 2 32 32 1 32  ε_{1} 46.8872
652  −15 −9780 95648400 1 2 32 32 1 32  ε_{1} 37.3376
2445  −4 −9780 95648400 2 1 32 32 1 16  ε_{1} 21.1735
2445  −20 −1956 95648400 2 2 20 80 2 40 \sqrt{−1}\sqrt{ε_{1}} 10.5868
3260  −3 −9780 95648400 2 1 32 32 1 16  ε_{1} 25.3098
3260  −15 −1956 95648400 2 2 20 40 1 20  ε_{1} 25.3098
8 −1223 −9784 95726656 1 35 28 490 1 490  ε_{1} 1.7627
9784  −8 −1223 95726656 1 1 35 35 2 35 \sqrt{−1}\sqrt{ε_{1}} 88.2908
1957  −95 −515 95746225 3 8 6 72 1 24  ε_{1} 13.6682
9785  −19 −515 95746225 2 1 6 12 2  6 \sqrt{−1}\sqrt{ε_{1}} 29.8922
9785  −95 −103 95746225 2 8 5 40 1 20  ε_{1} 59.7844
9788  −4 −2447 95804944 1 1 37 37 2 37  \sqrt{i}\sqrt{ε_{1}} 43.0501
753  −39 −3263 95824521 1 4 48 96 1 96  ε_{1} 54.2964
9789  −3 −3263 95824521 4 1 48 192 2 48 \sqrt{−1}\sqrt{ε_{1}} 8.0910
9789  −39 −251 95824521 4 4 7 56 1 14  ε_{1} 16.1820

258 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
9793  −7 −1399 95902849 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 146.5900
5 −1959 −9795 95942025 1 42 20 420 1 420  ε_{1} 0.9624
653  −15 −9795 95942025 1 2 20 20 1 20  ε_{1} 14.8304
3265  −3 −9795 95942025 2 1 20 20 1 10  ε_{1} 78.9377
3265  −15 −1959 95942025 2 2 42 84 1 42  ε_{1} 78.9377
124  −79 −9796 95961616 1 5 40 100 1 100  ε_{1} 16.0392
316  −31 −9796 95961616 3 3 40 180 1 60  ε_{1} 10.1503
2449  −4 −9796 95961616 1 1 40 20 1 20  ε_{1} 145.2838
41 −239 −9799 96020401 1 15 66 495 1 495  ε_{1} 8.3183
12 −2451 −3268 96118416 1 8 12 48 1 48  ε_{1} 2.6339
57 −516 −3268 96118416 1 12 12 72 1 72  ε_{1} 11.4208
76 −516 −2451 96118416 1 12 8 48 1 48  ε_{1} 11.6579
129 −228 −3268 96118416 1 4 12 24 1 24  ε_{1} 20.8511
172 −228 −2451 96118416 1 4 8 16 1 16  ε_{1} 17.6970
817 −228 −516 96118416 5 4 12 120 1 24  ε_{1} 13.0618
9804  −3 −3268 96118416 8 1 12 96 2 12 \sqrt{−1}\sqrt{ε_{1}} 9.4781
9804  −4 −2451 96118416 8 1 8 32 1  4  ε_{1} 18.9561
9804  −19 −516 96118416 8 1 12 48 1  6  ε_{1} 18.9561
9804  −43 −228 96118416 8 1 4 16 1  2  ε_{1} 18.9561
21 −467 −9807 96177249 1 7 64 224 1 224  ε_{1} 3.1336
1401  −7 −9807 96177249 1 1 64 32 1 32  ε_{1} 99.1010
3269  −3 −9807 96177249 1 1 64 32 1 32  ε_{1} 31.9726
8 −2452 −4904 96196864 1 10 42 210 1 210  ε_{1} 1.7627
4904  −4 −4904 96196864 10 1 42 210 1 21  ε_{1} 8.4974
4904  −8 −2452 96196864 10 1 10 50 1  5  ε_{1} 8.4974
44 −223 −9812 96275344 1 7 52 182 1 182  ε_{1} 5.9864
892  −11 −9812 96275344 3 1 52 78 1 26  ε_{1} 12.2096
2453  −4 −9812 96275344 1 1 52 26 1 26  ε_{1} 16.3584
9813  −3 −3271 96294969 3 1 27 81 2 27 \sqrt{−1}\sqrt{ε_{1}} 8.0922
5 −1963 −9815 96334225 1 6 76 228 1 228  ε_{1} 0.9624
13 −755 −9815 96334225 1 12 76 456 1 456  ε_{1} 2.3895
65 −151 −9815 96334225 2 7 76 532 1 266  ε_{1} 5.5529
65 −755 −1963 96334225 2 12 6 72 1 36  ε_{1} 5.5529
8 −1227 −9816 96353856 1 4 32 64 1 64  ε_{1} 1.7627
24 −1227 −3272 96353856 1 4 28 56 1 56  ε_{1} 4.5849
409  −24 −9816 96353856 1 2 32 32 1 32  ε_{1} 52.2684
3272  −3 −9816 96353856 4 1 32 64 1 16  ε_{1} 11.3120
3272  −24 −1227 96353856 4 2 4 16 1  4  ε_{1} 11.3120
9816  −3 −3272 96353856 4 1 28 56 1 14  ε_{1} 39.7767
9816  −8 −1227 96353856 4 1 4  8 1  2  ε_{1} 39.7767
1964  −20 −2455 96432400 1 2 28 28 1 28  ε_{1} 51.9115
9820  −4 −2455 96432400 2 1 28 28 1 14  ε_{1} 53.1361
9820  −20 −491 96432400 2 2 9 36 2 18 \sqrt{−1}\sqrt{ε_{1}} 26.5681
161 −427 −1403 96452041 1 2 14 14 1 14  ε_{1} 20.1338
9821  −7 −1403 96452041 2 1 14 14 1  7  ε_{1} 33.1984
9821  −23 −427 96452041 2 3 2  6 1  3  ε_{1} 33.1984
209  −47 −9823 96491329 1 5 24 60 1 60  ε_{1} 22.8829
517  −19 −9823 96491329 1 1 24 12 1 12  ε_{1} 18.5321
893  −11 −9823 96491329 1 1 24 12 1 12  ε_{1} 15.4822
317  −31 −9827 96569929 1 3 28 42 1 42  ε_{1} 8.9775

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 259

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q h^{−} ε R
29 −339 −9831 96648561 1 6 108 324 1 324  ε_{1} 3.2945
113  −87 −9831 96648561 1 6 108 324 1 324  ε_{1} 14.6946
3277  −3 −9831 96648561 2 1 108 108 1 54  ε_{1} 29.4793
3277  −87 −339 96648561 2 6  6 36 1 18  ε_{1} 29.4793
1229  −8 −9832 96668224 3 1 18 27 1  9  ε_{1} 7.1123
5 −1967 −9835 96727225 1 36 16 288 1 288  ε_{1} 0.9624
281  −35 −9835 96727225 1 2 16 16 1 16  ε_{1} 29.1405
1405  −7 −9835 96727225 2 1 16 16 1  8  ε_{1} 16.8228
1405  −35 −1967 96727225 2 2 36 72 1 36  ε_{1} 16.8228
9836  −4 −2459 96746896 3 1 19 57 2 19  \sqrt{i}\sqrt{ε_{1}} 14.1671
12 −1640 −4920 96825600 1 16 24 192 1 192  ε_{1} 2.6339
24 −820 −4920 96825600 1 8 24 96 1 96  ε_{1} 4.5849
60 −328 −4920 96825600 2 4 24 96 1 48  ε_{1} 4.1269
60 −984 −1640 96825600 2 12 16 192 1 96  ε_{1} 4.1269
120 −164 −4920 96825600 2 8 24 192 1 96  ε_{1} 6.1779
120 −820 −984 96825600 2 8 12 96 1 48  ε_{1} 6.1779
492 −40 −4920 96825600 2 2 24 48 1 24 ε_{1} 10.9943
492 −120 −1640 96825600 2 4 16 64 1 32  ε_{1} 10.9943
984  −20 −4920 96825600 2 2 24 48 1 24  ε_{1} 24.1747
984 −120 −820 96825600 2 4  8 32 1 16  ε_{1} 24.1747
2460  −8 −4920 96825600 4 1 24 48 1 12  ε_{1} 11.0268
2460  −24 −1640 96825600 4 2 16 64 1 16  ε_{1} 11.0268
2460  −40 −984 96825600 4 2 12 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 5.5134
2460 −120 −328 96825600 4 4  4 32 1  8  ε_{1} 11.0268
4920  −4 −4920 96825600 4 1 24 48 1 12  ε_{1} 13.7792
4920  −20 −984 96825600 4 2 12 96 2 24 \sqrt{−1}\sqrt{ε_{1}} 6.8896
4920  −24 −820 96825600 4 2  8 32 1  8  ε_{1} 13.7792
4920 −120 −164 96825600 4 4  8 64 1 16  ε_{1} 13.7792
17 −579 −9843 96884649 1 8 12 48 1 48  ε_{1} 4.1894
193  −51 −9843 96884649 1 2 12 12 1 12  ε_{1} 30.1526
3281  −3 −9843 96884649 6 1 12 36 1  6  ε_{1} 15.9199
3281  −51 −579 96884649 6 2  8 48 1  8  ε_{1} 15.9199
92 −107 −9844 96904336 1 3 36 54 1 54  ε_{1} 7.7415
428  −23 −9844 96904336 1 3 36 54 1 54  ε_{1} 15.1243
2461  −4 −9844 96904336 1 1 36 18 1 18  ε_{1} 68.6527
1969  −55 −895 96924025 1 4 16 32 1 32  ε_{1} 147.2368
9845  −11 −895 96924025 4 1 16 64 2 16 \sqrt{−1}\sqrt{ε_{1}} 6.7946
9845  −55 −179 96924025 4 4  5 40 1 10  ε_{1} 13.5892
229  −43 −9847 96963409 3 1 44 66 1 22  ε_{1} 5.4249
8 −1231 −9848 96983104 1 27 32 432 1 432  ε_{1} 1.7627
9848  −8 −1231 96983104 1 1 27 27 2 27 \sqrt{−1}\sqrt{ε_{1}} 28.1396
12 −2463 −3284 97061904 1 34 30 510 1 510  ε_{1} 2.6339
9852  −3 −3284 97061904 2 1 30 30 1 15  ε_{1} 29.0287
9852  −4 −2463 97061904 2 1 34 34 1 17  ε_{1} 29.0287
9853  −59 −167 97081609 1 3 11 33 2 33 \sqrt{−1}\sqrt{ε_{1}} 50.3248
5 −1972 −9860 97219600 1 12 32 192 1 192  ε_{1} 0.9624
17 −580 −9860 97219600 1 8 32 128 1 128  ε_{1} 4.1894
29 −340 −9860 97219600 1 4 32 64 1 64  ε_{1} 3.2945
85 −116 −9860 97219600 2 6 32 192 1 96  ε_{1} 4.4187
85 −580 −1972 97219600 2 8 12 96 1 48  ε_{1} 4.4187

260 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
145  −68 −9860 97219600 4 4 32 256 1 64  ε_{1} 6.3596
145 −340 −1972 97219600 4 4 12 96 1 24  ε_{1} 6.3596
493 −20 −9860 97219600 2 2 32 64 1 32 ε_{1} 9.4192
493 −340 −580 97219600 2 4 8 32 1 16  ε_{1} 9.4192
2465  −4 −9860 97219600 4 1 32 64 1 16  ε_{1} 22.2667
2465  −20 −1972 97219600 4 2 12 48 1 12  ε_{1} 22.2667
2465  −68 −580 97219600 4 4 8 64 1 16  ε_{1} 22.2667
2465 −116 −340 97219600 4 6 4 48 1 12  ε_{1} 22.2667
57 −519 −3287 97239321 1 18 34 306 1 306  ε_{1} 11.4208
9861  −3 −3287 97239321 2 1 34 34 1 17  ε_{1} 38.1366
9861  −19 −519 97239321 2 1 18 18 1  9  ε_{1} 38.1366
1409  −7 −9863 97278769 1 1 96 48 1 48  ε_{1} 77.6008
13 −759 −9867 97357689 1 24 16 192 1 192  ε_{1} 2.3895
33 −299 −9867 97357689 1 8 16 64 1 64  ε_{1} 7.6563
69 −143 −9867 97357689 1 10 16 80 1 80  ε_{1} 6.4345
253  −39 −9867 97357689 1 4 16 32 1 32  ε_{1} 15.0577
429  −23 −9867 97357689 2 3 16 48 1 24  ε_{1} 9.9534
429 −299 −759 97357689 2 8 24 192 1 96  ε_{1} 9.9534
897 −11 −9867 97357689 4 1 16 32 1 8 ε_{1} 14.1768
897 −143 −759 97357689 4 10 24 480 1 120  ε_{1} 14.1768
3289  −3 −9867 97357689 2 1 16 16 1  8  ε_{1} 88.8213
3289  −39 −759 97357689 2 4 24 96 1 48  ε_{1} 88.8213
9868  −4 −2467 97377424 7 1 7 49 2  7  \sqrt{i}\sqrt{ε_{1}} 10.7011
9869  −71 −139 97397161 3 7 3 63 2 21 \sqrt{−1}\sqrt{ε_{1}} 8.1539
8 −2468 −4936 97456384 1 12 24 144 1 144  ε_{1} 1.7627
4936 −4 −4936 97456384 2 1 24 48 2 24 \sqrt{i}\sqrt{ε_{1}} 34.6980
4936  −8 −2468 97456384 2 1 12 24 2 12 \sqrt{−1}\sqrt{ε_{1}} 34.6980
12 −823 −9876 97535376 1 9 52 234 1 234  ε_{1} 2.6339
2469  −4 −9876 97535376 1 1 52 26 1 26  ε_{1} 46.1213
3292  −3 −9876 97535376 1 1 52 26 1 26  ε_{1} 95.2000
581 −119 −1411 97555129 1 10 4 20 1 20  ε_{1} 17.6272
9877 −7 −1411 97555129 2 1 4 4 1 2 ε_{1} 42.3097
9877  −83 −119 97555129 2 3 10 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 21.1548
37 −267 −9879 97594641 1 2 76 76 1 76  ε_{1} 4.9836
89 −111 −9879 97594641 1 8 76 304 1 304  ε_{1} 13.8155
3293  −3 −9879 97594641 2 1 76 76 1 38  ε_{1} 14.6157
3293 −111 −267 97594641 2 8 2 16 1  8  ε_{1} 14.6157
5 −1976 −9880 97614400 1 28 32 448 1 448  ε_{1} 0.9624
8 −1235 −9880 97614400 1 12 32 192 1 192  ε_{1} 1.7627
13 −760 −9880 97614400 1 4 32 64 1 64  ε_{1} 2.3895
40 −247 −9880 97614400 2 6 32 192 1 96  ε_{1} 3.6369
40 −1235 −1976 97614400 2 12 28 336 1 168  ε_{1} 3.6369
65 −152 −9880 97614400 2 6 32 192 1 96  ε_{1} 5.5529
65 −760 −1976 97614400 2 4 28 112 1 56  ε_{1} 5.5529
104 −95 −9880 97614400 2 8 32 256 1 128 ε_{1} 4.6249
104 −760 −1235 97614400 2 4 12 48 1 24  ε_{1} 4.6249
152 −520 −1235 97614400 1 4 12 24 1 24  ε_{1} 8.6078
520  −19 −9880 97614400 4 1 32 64 1 16  ε_{1} 9.4726
520  −95 −1976 97614400 4 8 28 448 1 112  ε_{1} 9.4726
520 −152 −1235 97614400 4 6 12 144 1 36  ε_{1} 9.4726

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 261

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
520 −247 −760 97614400 4 6  4 48 1 12  ε_{1} 9.4726
760 −104 −1235 97614400 2 6 12 72 1 36  ε_{1} 23.1051
760 −247 −520 97614400 2 6  4 24 1 12  ε_{1} 23.1051
1976  −40 −1235 97614400 2 2 12 24 1 12  ε_{1} 23.7837
1976  −95 −520 97614400 2 8  4 32 1 16  ε_{1} 23.7837
9880  −8 −1235 97614400 4 1 12 24 1  6  ε_{1} 30.7899
9880  −19 −520 97614400 4 1  4  8 1  2  ε_{1} 30.7899
9880  −40 −247 97614400 4 2  6 24 1  6  ε_{1} 30.7899
9880  −95 −104 97614400 4 8  6 192 2 48 \sqrt{−1}\sqrt{ε_{1}} 15.3949
28 −1412 −2471 97693456 1 16 62 496 1 496  ε_{1} 5.5373
9884  −4 −2471 97693456 2 1 62 124 2 62  \sqrt{i}\sqrt{ε_{1}} 22.0264
9884  −7 −1412 97693456 2 1 16 16 1  8  ε_{1} 44.0527
1977  −15 −3295 97713225 1 2 32 32 1 32  ε_{1} 67.5262
9885  −3 −3295 97713225 2 1 32 32 1 16  ε_{1} 39.3918
9885  −15 −659 97713225 2 2 11 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 19.6959
341 −319 −899 97792321 1 10 14 70 1 70  ε_{1} 11.2480
9889  −11 −899 97792321 2 1 14 14 1  7  ε_{1} 164.1257
9889  −31 −319 97792321 2 3 10 30 1 15  ε_{1} 164.1257
2473  −4 −9892 97851664 1 1 20 10 1 10  ε_{1} 145.8308
5 −1979 −9895 97911025 1 23 56 644 1 644  ε_{1} 0.9624
1237 −8 −9896 97930816 1 1 78 39 1 39 ε_{1} 28.1466
9897  −3 −3299 97950609 3 1 27 81 2 27 \sqrt{−1}\sqrt{ε_{1}} 23.1985
521  −19 −9899 97990201 1 1 30 15 1 15  ε_{1} 38.7273
3301  −3 −9903 98069409 1 1 56 28 1 28  ε_{1} 85.2238
2476  −8 −4952 98089216 1 1 42 42 2 42 \sqrt{−1}\sqrt{ε_{1}} 41.4804
4952  −4 −4952 98089216 1 1 42 42 2 42  \sqrt{i}\sqrt{ε_{1}} 14.4061
1981  −35 −1415 98109025 1 2 34 34 1 34  ε_{1} 59.8382
9905  −7 −1415 98109025 6 1 34 102 1 17  ε_{1} 30.1334
9905  −35 −283 98109025 6 2  3 18 1  3  ε_{1} 30.1334
2477  −4 −9908 98168464 1 1 38 19 1 19  ε_{1} 12.9447
17 −583 −9911 98227921 1 8 136 544 1 544  ε_{1} 4.1894
53 −187 −9911 98227921 1 2 136 136 1 136  ε_{1} 3.9314
901  −11 −9911 98227921 4 1 136 272 1 68  ε_{1} 8.1892
901 −187 −583 98227921 4 2  8 32 1  8  ε_{1} 8.1892
8 −1239 −9912 98247744 1 32 32 512 1 512  ε_{1} 1.7627
21 −472 −9912 98247744 1 6 32 96 1 96  ε_{1} 3.1336
21 −1416 −3304 98247744 1 16 12 96 1 96  ε_{1} 3.1336
24 −1239 −3304 98247744 1 32 12 192 1 192  ε_{1} 4.5849
56 −1239 −1416 98247744 1 32 16 256 1 256  ε_{1} 6.8002
168 −59 −9912 98247744 2 3 32 96 1 48 ε_{1} 6.5132
168 −472 −1239 98247744 2 6 32 192 1 96  ε_{1} 6.5132
177 −56 −9912 98247744 1 4 32 64 1 64 ε_{1} 23.4697
177 −168 −3304 98247744 1 4 12 24 1 24  ε_{1} 23.4697
413 −24 −9912 98247744 1 2 32 32 1 32 ε_{1} 8.2212
413 −168 −1416 98247744 1 4 16 32 1 32  ε_{1} 8.2212
472 −168 −1239 98247744 1 4 32 64 1 64  ε_{1} 26.6550
1416  −7 −9912 98247744 2 1 32 32 1 16  ε_{1} 26.3082
1416  −56 −1239 98247744 2 4 32 128 1 64  ε_{1} 26.3082
3304  −3 −9912 98247744 2 1 32 32 1 16  ε_{1} 53.6403
3304  −24 −1239 98247744 2 2 32 64 1 32  ε_{1} 53.6403

262 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
9912  −3 −3304 98247744 4 1 12 24 1  6  ε_{1} 21.9137
9912  −7 −1416 98247744 4 1 16 32 1  8  ε_{1} 21.9137
9912  −8 −1239 98247744 4 1 32 64 1 16  ε_{1} 21.9137
9912  −59 −168 98247744 4 3 4 24 1  6  ε_{1} 21.9137
9913  −23 −431 98267569 1 3 21 63 2 63 \sqrt{−1}\sqrt{ε_{1}} 130.4199
5 −1983 −9915 98307225 1 16 24 192 1 192  ε_{1} 0.9624
661  −15 −9915 98307225 1 2 24 24 1 24  ε_{1} 28.7949
3305  −3 −9915 98307225 6 1 24 72 1 12  ε_{1} 18.5331
3305  −15 −1983 98307225 6 2 16 96 1 16  ε_{1} 18.5331
268 −148 −2479 98327056 1 2 24 24 1 24  ε_{1} 22.9790
9916  −4 −2479 98327056 2 1 24 24 1 12  ε_{1} 115.2009
9916  −67 −148 98327056 2 1 2  4 2  2 \sqrt{−1}\sqrt{ε_{1}} 57.6005
9917  −47 −211 98346889 1 5 3 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 15.9684
13 −763 −9919 98386561 1 4 68 136 1 136  ε_{1} 2.3895
109  −91 −9919 98386561 1 2 68 68 1 68  ε_{1} 11.1291
1417  −7 −9919 98386561 2 1 68 68 1 34  ε_{1} 43.8225
1417  −91 −763 98386561 2 2 4  8 1  4  ε_{1} 43.8225
9921  −3 −3307 98426241 1 1 9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 123.1694
12 −827 −9924 98485776 1 7 52 182 1 182  ε_{1} 2.6339
2481  −4 −9924 98485776 1 1 52 26 1 26  ε_{1} 105.5235
3308  −3 −9924 98485776 1 1 52 26 1 26  ε_{1} 28.8079
17 −584 −9928 98565184 1 16 24 192 1 192  ε_{1} 4.1894
73 −136 −9928 98565184 1 4 24 48 1 48  ε_{1} 15.3334
1241 −8 −9928 98565184 2 1 24 24 1 12 ε_{1} 36.0697
1241 −136 −584 98565184 2 4 16 64 1 32  ε_{1} 36.0697
764  −52 −2483 98644624 1 2 20 20 1 20  ε_{1} 33.4104
9932  −4 −2483 98644624 2 1 20 20 1 10  ε_{1} 20.4443
9932  −52 −191 98644624 2 2 13 52 2 26 \sqrt{−1}\sqrt{ε_{1}} 10.2222
21 −1419 −3311 98664489 1 12 72 432 1 432  ε_{1} 3.1336
33 −903 −3311 98664489 1 16 72 576 1 576  ε_{1} 7.6563
77 −903 −1419 98664489 1 16 12 96 1 96  ε_{1} 4.3693
129 −231 −3311 98664489 1 12 72 432 1 432  ε_{1} 20.8511
301 −231 −1419 98664489 1 12 12 72 1 72  ε_{1} 20.0642
473 −231 −903 98664489 3 12 16 288 1 96  ε_{1} 10.3180
9933  −3 −3311 98664489 4 1 72 144 1 36  ε_{1} 11.4009
9933  −7 −1419 98664489 4 1 12 24 1  6  ε_{1} 11.4009
9933  −11 −903 98664489 4 1 16 32 1  8  ε_{1} 11.4009
9933  −43 −231 98664489 4 1 12 24 1  6  ε_{1} 11.4009
5 −1987 −9935 98704225 1 7 94 329 1 329  ε_{1} 0.9624
9937  −19 −523 98743969 3 1 5 15 2  5 \sqrt{−1}\sqrt{ε_{1}} 49.7096
3313  −3 −9939 98783721 1 1 28 14 1 14  ε_{1} 153.9682
5 −1988 −9940 98803600 1 24 24 288 1 288  ε_{1} 0.9624
28 −355 −9940 98803600 1 4 24 48 1 48  ε_{1} 5.5373
140 −71 −9940 98803600 2 7 24 168 1 84 ε_{1} 4.9558
140 −355 −1988 98803600 2 4 24 96 1 48  ε_{1} 4.9558
284  −35 −9940 98803600 1 2 24 24 1 24  ε_{1} 17.6959
497  −20 −9940 98803600 1 2 24 24 1 24  ε_{1} 29.3851
1420  −7 −9940 98803600 2 1 24 24 1 12  ε_{1} 28.9248
1420  −35 −1988 98803600 2 2 24 48 1 24  ε_{1} 28.9248
2485  −4 −9940 98803600 2 1 24 24 1 12  ε_{1} 22.5113

IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS 263

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2485  −20 −1988 98803600 2 2 24 48 1 24  ε_{1} 22.5113
61 −163 −9943 98863249 1 1 56 28 1 28  ε_{1} 7.3284
8 −1243 −9944 98883136 1 4 56 112 1 112  ε_{1} 1.7627
88 −904 −1243 98883136 1 8  4 16 1 16  ε_{1} 11.9527
113  −88 −9944 98883136 1 2 56 56 1 56  ε_{1} 14.6946
904  −11 −9944 98883136 8 1 56 224 1 28  ε_{1} 6.8046
904  −88 −1243 98883136 8 2  4 32 1  4  ε_{1} 6.8046
9944  −8 −1243 98883136 4 1  4  8 1  2  ε_{1} 32.3050
9944  −11 −904 98883136 4 1  8 32 2  8 \sqrt{−1}\sqrt{ε_{1}} 16.1525
12 −2487 −3316 98962704 1 20 22 220 1 220  ε_{1} 2.6339
9948  −3 −3316 98962704 2 1 22 44 2 22 \sqrt{−1}\sqrt{ε_{1}} 31.2677
9948 −4 −2487 98962704 2 1 20 20 1 10 ε_{1} 62.5353
93 −107 −9951 99022401 1 3 76 114 1 114  ε_{1} 6.7322
321  −31 −9951 99022401 3 3 76 342 1 114  ε_{1} 12.1276
3317  −3 −9951 99022401 1 1 76 38 1 38  ε_{1} 17.1285
5 −1991 −9955 99102025 1 56 16 448 1 448  ε_{1} 0.9624
181  −55 −9955 99102025 1 4 16 32 1 32  ε_{1} 14.3479
905  −11 −9955 99102025 4 1 16 32 1  8  ε_{1} 13.1640
905  −55 −1991 99102025 4 4 56 448 1 112  ε_{1} 13.1640
76 −131 −9956 99121936 1 5 44 110 1 110  ε_{1} 11.6579
524  −19 −9956 99121936 1 1 44 22 1 22  ε_{1} 19.9254
2489  −4 −9956 99121936 1 1 44 22 1 22  ε_{1} 102.7906
9957  −3 −3319 99141849 1 1 41 41 2 41 \sqrt{−1}\sqrt{ε_{1}} 20.9146
433 −23 −9959 99181681 1 3 130 195 1 195 ε_{1} 46.7895
5 −1992 −9960 99201600 1 8 32 128 1 128  ε_{1} 0.9624
24 −415 −9960 99201600 1 10 32 160 1 160  ε_{1} 4.5849
120  −83 −9960 99201600 2 3 32 96 1 48  ε_{1} 6.1779
120 −415 −1992 99201600 2 10  8 80 1 40  ε_{1} 6.1779
249  −40 −9960 99201600 1 2 32 32 1 32  ε_{1} 33.3101
249 −120 −3320 99201600 1 4 20 40 1 40  ε_{1} 33.3101
664  −15 −9960 99201600 1 2 32 32 1 32  ε_{1} 43.8951
1245  −8 −9960 99201600 2 1 32 32 1 16  ε_{1} 11.0187
1245  −24 −3320 99201600 2 2 20 40 1 20  ε_{1} 11.0187
1245  −40 −1992 99201600 2 2  8 16 1  8  ε_{1} 11.0187
1245 −120 −664 99201600 2 4 10 40 1 20  ε_{1} 11.0187
1992 −15 −3320 99201600 2 2 20 40 1 20 ε_{1} 25.5852
1992 −120 −415 99201600 2 4 10 40 1 20  ε_{1} 25.5852
3320  −3 −9960 99201600 2 1 32 32 1 16  ε_{1} 25.1746
3320  −15 −1992 99201600 2 2  8 16 1  8  ε_{1} 25.1746
9960  −3 −3320 99201600 8 1 20 80 1 10  ε_{1} 13.8115
9960  −15 −664 99201600 8 2 10 80 1 10  ε_{1} 13.8115
9960  −24 −415 99201600 8 2 10 80 1 10  ε_{1} 13.8115
9960  −83 −120 99201600 8 3  4 48 1  6  ε_{1} 13.8115
9961  −7 −1423 99221521 1 1  9  9 2  9 \sqrt{−1}\sqrt{ε_{1}} 184.0130
188 −212 −2491 99281296 1 6 12 36 1 36  ε_{1} 9.1285
9964  −4 −2491 99281296 2 1 12 12 1  6  ε_{1} 83.6106
9964  −47 −212 99281296 2 5  6 60 2 30 \sqrt{−1}\sqrt{ε_{1}} 41.8053
28 −712 −4984 99361024 1 8 16 64 1 64  ε_{1} 5.5373
56 −356 −4984 99361024 1 12 16 96 1 96  ε_{1} 6.8002
2492  −8 −4984 99361024 2 1 16 32 2 16 \sqrt{−1}\sqrt{ε_{1}} 7.1293

264 IMAGINARY BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3}  h Q h^{−}  ε  R
2492  −56 −712 99361024 2 4 8 32 1 16  ε_{1} 14.2586
4984  −4 −4984 99361024 2 1 16 32 2 16  \sqrt{i}\sqrt{ε_{1}} 34.4198
4984  −56 −356 99361024 2 4 12 48 1 24  ε_{1} 68.8395
9969  −3 −3323 99380961 1 1 17 17 2 17 \sqrt{−1}\sqrt{ε_{1}} 136.1815
8 −1247 −9976 99520576 1 26 20 260 1 260  ε_{1} 1.7627
29 −344 −9976 99520576 1 10 20 100 1 100  ε_{1} 3.2945
232 −43 −9976 99520576 2 1 20 20 1 10 ε_{1} 10.5766
232 −344 −1247 99520576 2 10 26 260 1 130  ε_{1} 10.5766
344 −232 −1247 99520576 1 2 26 26 1 26  ε_{1} 19.8864
9976  −8 −1247 99520576 2 1 26 26 1 13  ε_{1} 93.5515
9976  −43 −232 99520576 2 1 2  2 1  1  ε_{1} 93.5515
9977  −11 −907 99540529 1 1 3  3 2  3 \sqrt{−1}\sqrt{ε_{1}} 72.3163
17 −587 −9979 99580441 1 7 20 70 1 70  ε_{1} 4.1894
1996  −20 −2495 99600400 5 2 56 280 1 56  ε_{1} 18.2055
9980  −4 −2495 99600400 6 1 56 168 1 28  ε_{1} 15.1998
9980  −20 −499 99600400 6 2 3 36 2  6 \sqrt{−1}\sqrt{ε_{1}} 7.5999
149  −67 −9983 99660289 1 1 92 46 1 46  ε_{1} 8.2223
3329  −3 −9987 99740169 1 1 26 13 1 13  ε_{1} 118.1791
44 −227 −9988 99760144 1 5 28 70 1 70  ε_{1} 5.9864
908  −11 −9988 99760144 1 1 28 14 1 14  ε_{1} 12.2274
2497  −4 −9988 99760144 1 1 28 14 1 14  ε_{1} 117.8419
9989  −7 −1427 99780121 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 31.8874
97 −103 −9991 99820081 1 5 32 80 1 80  ε_{1} 18.6488
1249 −8 −9992 99840064 1 1 40 20 1 20 ε_{1} 102.5410
9993  −3 −3331 99860049 1 1 15 15 2 15 \sqrt{−1}\sqrt{ε_{1}} 101.5209
5 −1999 −9995 99900025 1 27 40 540 1 540  ε_{1} 0.9624