TABLE OF CLASS NUMBERS AND FUNDAMENRAL

UNITS OF REAL 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 real biquadratic bicyclic number fields with discriminants ≦ 10^{8}. There exist exactly 3603 such fields.

Let K be a real biquadratic bicyclic number field. Then K contains three real quadratic subfields k_{1}, k_{2}, k_{3}. 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}{4}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.) We also know that we can take as a system of fundamenral units of K one of the following: ε_{1}, ε_{2}, ε_{3}; \sqrt{ε_{i}}, ε_{j}, ε_{k}; \sqrt{ε_{i}ε_{j}}, ε_{j}, ε_{k}; \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}; \sqrt{ε_{i}}, \sqrt{ε_{j}}, ε_{k}; \sqrt{ε_{i}ε_{j}}, ε_{j}, \sqrt{ε_{k}}; \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}. Here ε_{i} is the fundamenral unit of k_{i}, and {i, j, k} = {1, 2, 3}.

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 system of fundamental units of K (in terms of ε_{1}, ε_{2}, ε_{3}); an approximate value of the regulator R of K.

In Table 2, for each K, we give the narrow class numbers h_{i+} = h_{+}(k_{i}) (i = 1, 2, 3) and h_{+} = h_{+}(K); generators of the group E_{K}^{+} of totally positive units in K; the index Q_{+} = [E_{K} : E_{K}^{+}].

We note h_{+} = 16h/Q_{+}. In Tabe 3, 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. 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}).

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 3

Table 1

d_{1} d_{2} d_{3}  d h_{1} h_{2} h_{3} h Q Fundamental units  R
5 8 40  1600 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1.5425
8 12 24  2304 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  2.6609
5 12 60  3600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2.6153
5 13 65  4225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3.1926
12 21 28  7056 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  5.7129
5 17 85  7225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  4.4540
8 13 104 10816 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  4.8701
5 21 105 11025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  6.6448
8 28 56 12544 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  8.2970
5 24 120 14400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  6.8152
12 33 44 17424 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  15.0904
8 17 136 18496 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  15.6866
5 28 140 19600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  6.6026
5 29 145 21025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  5.0410
12 13 156 24336 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  12.3095
5 33 165 27225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  9.4281
8 21 168 28224 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  8.9943
21 24 56 28224 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 12.2124
8 44 88 30976 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  15.7665
5 37 185 34225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  11.7814
12 17 204 41616 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  25.4075
5 41 205 42025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  15.0533
5 44 220 48400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  14.9273
13 17 221 48841 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  13.5324
12 57 76 51984 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  43.8358
21 33 77 53361 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 13.1034
8 29 232 53824 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  15.3554
8 60 120 57600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  11.2356
12 40 120 57600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  14.7950
24 40 60 57600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  17.2036
8 33 264 69696 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  32.8462
24 33 88 69696 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 52.4473
5 53 265 70225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  17.7921
13 21 273 74529 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  27.2634
12 69 92 76176 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  16.4005
5 56 280 78400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  20.3492
5 57 285 81225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  15.5518
8 37 296 87616 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  19.5658
8 76 152 92416 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  22.1111
5 61 305 93025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  24.2820
28 44 77 94864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  18.1046
13 24 312 97344 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  25.5450
8 41 328 107584 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  21.2133
12 56 168 112896 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 14.5824
24 28 168 112896 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  20.6696
5 69 345 119025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  29.4530
12 29 348 121104 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  17.4633
17 21 357 127449 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  19.3090
13 28 364 132496 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  53.2870
5 73 365 133225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  21.7462

4 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 92 184 135424 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  36.8207
12 93 124 138384 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  35.5511
13 29 377 142129 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  24.1841
5 76 380 144400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  24.4398
5 77 385 148225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  25.5744
21 57 133 159201 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 46.1066
17 24 408 166464 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  50.9802
12 105 140 176400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  28.7597
21 60 140 176400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  16.0220
28 60 105 176400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.3491
8 53 424 179776 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  31.1456
13 33 429 184041 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  45.5243
5 88 440 193600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  21.4950
12 37 444 197136 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  41.8736
5 89 445 198025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  20.2556
8 57 456 207936 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  76.7594
24 57 152 207936 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 56.3410
5 92 460 211600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  28.7579
5 93 465 216225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  33.5799
17 28 476 226576 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  63.5702
13 37 481 231361 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  86.1696
21 69 161 233289 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 50.7453
5 97 485 235225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  33.9640
8 61 488 238144 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  19.9786
12 41 492 242064 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  60.2201
17 29 493 243049 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  32.5008
8 124 248 246016 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  34.1837
5 101 505 255025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  21.3213
12 129 172 266256 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  121.4901
5 104 520 270400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  10.5408
8 65 520 270400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  23.1804
13 40 520 270400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  20.5802
40 65 104 270400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  23.3504
12 88 264 278784 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 38.3099
24 44 264 278784 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 33.3994
28 76 133 283024 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  83.1650
13 41 533 284089 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  31.1804
5 109 545 297025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  44.3128
8 69 552 304704 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  25.7655
24 69 184 304704 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 79.6011
8 140 280 313600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  27.1622
28 40 280 313600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  62.6170
40 56 140 313600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  30.6409
17 33 561 314721 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  222.2854
12 141 188 318096 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  31.5392
5 113 565 319225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  40.5418
13 44 572 327184 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  22.7182
8 73 584 341056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  76.6251
21 29 609 370881 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  72.3022
8 77 616 379456 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  41.0490

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 5

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
56 77 88 379456 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 44.3921
5 124 620 384400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  47.9350
8 156 312 389376 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  32.1547
12 104 312 389376 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  28.4034
24 104 156 389376 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  41.4719
33 57 209 393129 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 250.1151
17 37 629 395641 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  33.6189
12 53 636 404496 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  40.8071
28 92 161 414736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  107.8851
5 129 645 416025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  48.6050
21 93 217 423801 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 83.6204
12 165 220 435600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  34.9257
33 60 220 435600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  81.8632
44 60 165 435600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  31.6102
5 133 665 442225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  50.6857
5 136 680 462400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  26.6545
8 85 680 462400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  25.3890
17 40 680 462400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  49.6644
40 85 136 462400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  68.2714
5 137 685 469225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  52.0650
8 172 344 473344 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  77.5454
13 53 689 474721 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  25.1160
24 29 696 484416 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  60.2159
17 41 697 485809 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  97.1575
5 141 705 497025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  65.9995
12 177 236 501264 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  107.6549
8 89 712 506944 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  98.2840
13 56 728 529984 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  32.4061
12 61 732 535824 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  66.4142
13 57 741 549081 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  75.0655
8 93 744 553536 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  57.0571
24 93 248 553536 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 37.3190
5 149 745 555025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  67.4835
17 44 748 559504 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  101.8350
8 188 376 565504 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  61.4322
33 69 253 576081 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 92.7275
5 152 760 577600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  47.8525
8 97 776 602176 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  98.0626
21 37 777 603729 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  47.6327
5 156 780 608400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  25.0795
12 65 780 608400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  48.7181
13 60 780 608400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  32.8472
60 65 156 608400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  89.6399
5 157 785 616225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  20.7719
13 61 793 628849 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  79.5102
12 201 268 646416 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  209.4950
5 161 805 648025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  70.5064
8 101 808 652864 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  46.2206
28 29 812 659344 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  43.1993
8 204 408 665856 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  21.5450

6 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 136 408 665856 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 29.6987
24 136 204 665856 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 44.8484
44 76 209 698896 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  199.6225
5 168 840 705600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  25.4510
8 105 840 705600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  63.0757
21 40 840 705600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  46.2717
21 120 280 705600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  60.1935
24 105 280 705600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.6376
40 105 168 705600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  104.3825
56 105 120 705600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  92.5623
12 213 284 725904 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  49.9918
5 172 860 739600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  38.1280
21 41 861 741321 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  90.3762
5 173 865 748225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.3796
28 124 217 753424 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  352.0419
8 109 872 760384 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  60.9975
12 73 876 767376 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  100.9099
8 220 440 774400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  34.1351
40 44 440 774400 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  40.6822
40 88 220 774400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  112.6271
5 177 885 783225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  61.8030
24 37 888 788544 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  65.0861
13 69 897 804609 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  54.4940
17 53 901 811801 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  33.7202
21 129 301 815409 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 163.8718
8 113 904 817216 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  44.0647
5 181 905 819025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  45.4448
12 152 456 831744 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 43.2221
24 76 456 831744 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 101.8966
5 184 920 846400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  54.0551
12 77 924 853776 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  28.9080
21 44 924 853776 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  47.1214
28 33 924 853776 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  106.4942
5 188 940 883600 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  19.8625
8 236 472 891136 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  81.8263
12 237 316 898704 1 1 3 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  29.0317
13 73 949 900601 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  190.4279
17 56 952 906304 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  143.2605
29 33 957 915849 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  43.2955
5 193 965 931225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  49.8416
17 57 969 938961 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  409.5180
24 41 984 968256 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  230.4939
5 197 985 970225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  21.5092
21 141 329 974169 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 126.3916
13 76 988 976144 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  167.7952
12 249 332 992016 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  111.8596
13 77 1001 1002001 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  76.0477
5 201 1005 1010025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  99.9298
44 92 253 1024144 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  87.2300
5 204 1020 1040400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  30.7118

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 7

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 85 1020 1040400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  40.3245
17 60 1020 1040400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  59.9030
60 85 204 1040400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  83.9753
33 93 341 1046529 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 72.4710
8 129 1032 1065024 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  114.7171
24 129 344 1065024 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 237.6408
28 37 1036 1073296 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  197.8997
17 61 1037 1075369 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  78.0051
5 209 1045 1092025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  50.3734
8 133 1064 1132096 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  65.6090
56 133 152 1132096 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 75.4105
5 213 1065 1134225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  78.1362
12 89 1068 1140624 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  154.2381
8 268 536 1149184 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  127.4323
29 37 1073 1151329 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  93.7124
5 217 1085 1177225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  53.3406
12 273 364 1192464 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  154.4887
21 156 364 1192464 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  98.7279
28 156 273 1192464 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  157.7290
8 137 1096 1201216 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  114.2022
12 184 552 1218816 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 64.5754
24 92 552 1218816 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  40.3138
5 221 1105 1221025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  56.9855
13 85 1105 1221025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  115.6206
17 65 1105 1221025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  254.7459
65 85 221 1221025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  66.3370
21 53 1113 1238769 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  87.1947
8 141 1128 1272384 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  78.2083
24 141 376 1272384 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 183.6854
8 284 568 1290496 1 1 3 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  44.1072
12 285 380 1299600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  32.4706
57 60 380 1299600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  102.6671
60 76 285 1299600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  68.0701
13 88 1144 1308736 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  198.9594
5 229 1145 1311025 1 3 4 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  20.4292
28 41 1148 1317904 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  146.3837
21 165 385 1334025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  97.5367
33 105 385 1334025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  410.3741
77 105 165 1334025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  49.2695
13 89 1157 1338649 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  69.6519
5 232 1160 1345600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  17.9521
8 145 1160 1345600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  39.5413
29 40 1160 1345600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  21.1309
40 145 232 1345600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  122.3133
12 97 1164 1354896 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  156.2736
5 233 1165 1357225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  77.5515
17 69 1173 1375929 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  75.6565
5 236 1180 1392400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  102.0002
5 237 1185 1404225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  76.2190
29 41 1189 1413721 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  139.1285

8 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 149 1192 1420864 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  98.6737
13 92 1196 1430416 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  62.1685
28 172 301 1449616 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  245.7715
5 241 1205 1452025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  99.2381
13 93 1209 1461681 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  149.2229
12 101 1212 1468944 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  67.3363
33 37 1221 1490841 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  67.8130
28 88 616 1517824 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  176.3749
44 56 616 1517824 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 108.4827
12 309 412 1527696 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  146.2880
21 177 413 1535121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 75.5781
5 248 1240 1537600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  66.7670
17 73 1241 1540081 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  579.2625
5 249 1245 1550025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  88.3108
8 157 1256 1577536 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  64.1388
13 97 1261 1590121 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  251.2689
8 316 632 1597696 1 3 1 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  43.1550
5 253 1265 1600225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  93.7165
24 53 1272 1617984 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  48.3610
29 44 1276 1628176 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  168.2891
21 61 1281 1640961 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  243.2055
12 321 428 1648656 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  60.3895
5 257 1285 1651225 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  33.9164
8 161 1288 1658944 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  114.8267
56 161 184 1658944 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 369.4192
17 76 1292 1669264 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  87.4903
12 109 1308 1710864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  89.0096
17 77 1309 1713481 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  106.8169
57 69 437 1718721 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 55.8920
13 101 1313 1723969 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.9842
28 188 329 1731856 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  194.2817
5 264 1320 1742400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  50.4479
8 165 1320 1742400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  48.5769
24 165 440 1742400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  43.8458
33 40 1320 1742400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  149.9322
33 120 440 1742400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  88.3832
40 165 264 1742400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  90.6006
88 120 165 1742400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  94.4813
8 332 664 1763584 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  98.6511
5 268 1340 1795600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  78.4738
5 269 1345 1809025 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  45.0482
33 41 1353 1830609 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  581.7665
12 113 1356 1838736 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  235.8171
44 124 341 1860496 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  135.0013
5 273 1365 1863225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  50.6035
13 105 1365 1863225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  76.0278
21 65 1365 1863225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  62.8198
65 105 273 1863225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  356.3765
12 345 460 1904400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  193.4062
60 69 460 1904400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  102.4949

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 9

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
60 92 345 1904400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  151.9474
8 173 1384 1915456 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  23.6816
5 277 1385 1918225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  92.7353
8 348 696 1937664 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.5705
12 232 696 1937664 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  111.0574
24 232 348 1937664 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  97.5913
5 281 1405 1974025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  117.9508
21 201 469 1979649 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 90.5487
8 177 1416 2005056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  272.1001
24 177 472 2005056 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 358.5267
13 109 1417 2007889 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  291.3451
33 129 473 2013561 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 205.9005
5 284 1420 2016400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  123.1541
12 357 476 2039184 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  42.4643
21 204 476 2039184 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  79.0878
28 204 357 2039184 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  75.0115
8 181 1448 2096704 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  46.0092
8 364 728 2119936 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.6311
28 104 728 2119936 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  51.0734
56 104 364 2119936 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  126.6571
77 133 209 2140369 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 128.8082
24 61 1464 2143296 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  242.1218
5 293 1465 2146225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  76.7874
13 113 1469 2157961 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  83.3034
5 296 1480 2190400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  55.5875
8 185 1480 2190400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  112.2857
37 40 1480 2190400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  117.5042
40 185 296 2190400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  159.1764
28 53 1484 2202256 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  88.4782
12 248 744 2214144 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 61.2448
24 124 744 2214144 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  176.7834
21 213 497 2223081 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 98.7632
17 88 1496 2238016 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  220.6883
5 301 1505 2265025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  164.0496
17 89 1513 2289169 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  709.6008
37 41 1517 2301289 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  75.9219
8 380 760 2310400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  88.7176
40 76 760 2310400 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  244.9050
40 152 380 2310400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  68.1919
12 381 508 2322576 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  161.1038
21 73 1533 2350089 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  149.7303
29 53 1537 2362369 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  166.6595
28 220 385 2371600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  349.0071
44 140 385 2371600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  180.4301
77 140 220 2371600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  56.1008
8 193 1544 2383936 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  327.2913
5 309 1545 2387025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  158.5745
33 141 517 2405601 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 186.1216
5 312 1560 2433600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  45.4427
13 120 1560 2433600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  74.7352

10 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
24 65 1560 2433600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  128.8901
65 120 312 2433600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  159.9798
17 92 1564 2446096 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  267.5982
5 313 1565 2449225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  128.4481
12 393 524 2471184 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  240.7178
8 197 1576 2483776 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  120.3868
5 316 1580 2496400 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  28.1443
17 93 1581 2499561 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  94.8705
5 317 1585 2512225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  118.3933
12 133 1596 2547216 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.0616
21 76 1596 2547216 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  67.3680
28 57 1596 2547216 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  116.6240
5 321 1605 2576025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  41.7629
8 201 1608 2585664 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  163.2034
24 201 536 2585664 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 399.4072
13 124 1612 2598544 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  270.3526
29 56 1624 2637376 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  208.2809
37 44 1628 2650384 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  127.9923
5 328 1640 2689600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  28.3348
8 205 1640 2689600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  33.7259
40 41 1640 2689600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  76.9559
40 205 328 2689600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  79.1479
12 137 1644 2702736 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  247.2397
5 329 1645 2706025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  150.7832
8 412 824 2715904 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  134.2036
17 97 1649 2719201 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  749.9697
28 236 413 2729104 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  79.2794
29 57 1653 2732409 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  136.5904
21 237 553 2752281 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 189.5605
5 332 1660 2755600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  85.5091
12 417 556 2782224 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  470.7972
8 209 1672 2795584 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  224.3339
88 152 209 2795584 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 294.2911
13 129 1677 2812329 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  92.4981
12 280 840 2822400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  66.5022
24 140 840 2822400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  46.1264
28 120 840 2822400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  69.4472
56 60 840 2822400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  56.9708
60 168 280 2822400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  83.5757
120 140 168 2822400 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  49.8531
5 337 1685 2839225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  76.6113
8 213 1704 2903616 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  91.4079
24 213 568 2903616 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 55.6274
5 341 1705 2907025 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  41.0923
28 61 1708 2917264 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  97.8019
8 428 856 2930944 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  186.3615
12 429 572 2944656 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  41.6357
33 156 572 2944656 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  95.1265
44 156 429 2944656 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  116.5377
17 101 1717 2948089 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  145.0350

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 11

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 344 1720 2958400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  148.9049
13 133 1729 2989441 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  395.5475
8 217 1736 3013696 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  154.3171
56 217 248 3013696 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 260.7156
5 348 1740 3027600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  21.9905
12 145 1740 3027600 1 4 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  47.5443
29 60 1740 3027600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  38.5900
60 145 348 3027600 2 4 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  52.8188
21 249 581 3038049 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 229.9914
5 349 1745 3045025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  85.0704
76 92 437 3055504 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  68.6406
33 53 1749 3059001 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  124.7253
24 73 1752 3069504 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  224.0267
5 353 1765 3115225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.6076
57 93 589 3122289 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 293.8607
8 221 1768 3125824 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  35.6308
13 136 1768 3125824 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  75.8967
17 104 1768 3125824 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  72.4305
104 136 221 3125824 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  53.1194
29 61 1769 3129361 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  233.3619
77 161 253 3136441 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 165.5790
8 444 888 3154176 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  64.0725
12 296 888 3154176 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  66.8423
24 296 444 3154176 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  130.3024
13 137 1781 3171961 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  104.3165
5 357 1785 3186225 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  16.4857
17 105 1785 3186225 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  107.4991
21 85 1785 3186225 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  40.3141
85 105 357 3186225 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  57.2779
12 149 1788 3196944 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  61.6174
41 44 1804 3254416 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  456.8231
12 453 604 3283344 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  144.7376
5 364 1820 3312400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  37.6118
13 140 1820 3312400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  28.7284
28 65 1820 3312400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  74.5952
65 140 364 3312400 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  110.8268
8 229 1832 3356224 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  25.6569
13 141 1833 3359889 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  200.0596
8 460 920 3385600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  70.8139
40 92 920 3385600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  73.2593
40 184 460 3385600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  303.0112
21 88 1848 3415104 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  83.4161
21 264 616 3415104 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  162.5844
24 77 1848 3415104 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  44.6147
33 56 1848 3415104 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  115.9529
33 168 616 3415104 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  265.7780
77 168 264 3415104 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  69.2597
17 109 1853 3433609 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  87.6945
12 465 620 3459600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  169.5591
60 93 620 3459600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  86.2744

12 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
60 124 465 3459600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  343.0524
8 233 1864 3474496 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  404.3670
5 373 1865 3478225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  116.3655
21 89 1869 3493161 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  219.8195
28 268 469 3519376 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  132.7818
5 376 1880 3534400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  119.4325
12 157 1884 3549456 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  233.9571
5 377 1885 3553225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  41.0909
13 145 1885 3553225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  105.5979
29 65 1885 3553225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  63.5614
65 145 377 3553225 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  216.9777
44 172 473 3579664 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  136.6396
8 237 1896 3594816 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  98.5148
24 237 632 3594816 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  96.0668
8 476 952 3625216 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  48.5817
28 136 952 3625216 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 118.2950
56 136 476 3625216 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  79.1651
5 381 1905 3629025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  174.3539
17 113 1921 3690241 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1003.2227
8 241 1928 3717184 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  227.4288
12 161 1932 3732624 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  100.3253
21 92 1932 3732624 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  45.8938
28 69 1932 3732624 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  67.4064
13 149 1937 3751969 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  43.9852
5 389 1945 3783025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  221.2829
33 177 649 3790809 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1587.9562
12 489 652 3825936 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  576.3844
37 53 1961 3845521 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  226.3780
5 393 1965 3861225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  86.3496
8 492 984 3873024 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  58.5637
12 328 984 3873024 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  92.1187
24 328 492 3873024 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  72.9255
13 152 1976 3904576 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  122.2986
5 397 1985 3940225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  172.9503
28 284 497 3952144 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  359.9222
8 249 1992 3968064 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  375.5736
24 249 664 3968064 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 837.9699
21 285 665 3980025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  90.6205
57 105 665 3980025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  514.3230
105 133 285 3980025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  128.5164
29 69 2001 4004001 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  258.6116
12 501 668 4016016 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  78.5084
5 401 2005 4020025 1 5 4 10 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  21.3014
33 61 2013 4052169 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  182.6836
8 253 2024 4096576 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  59.7176
88 184 253 4096576 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 485.6241
8 508 1016 4129024 1 1 3 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  88.2621
21 97 2037 4149369 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  190.4389
5 408 2040 4161600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  64.3222
17 120 2040 4161600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  162.9341

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 13

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
24 85 2040 4161600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  127.5364
85 120 408 4161600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  144.9067
13 157 2041 4165681 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  486.3701
28 73 2044 4177936 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  969.9966
5 409 2045 4182025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  151.1346
8 257 2056 4227136 1 3 4 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  55.8074
5 412 2060 4243600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  131.1254
12 344 1032 4260096 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  81.7404
24 172 1032 4260096 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 126.6209
5 413 2065 4264225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  122.6271
44 188 517 4276624 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  126.5909
37 56 2072 4293184 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  143.3935
12 173 2076 4309776 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  116.5125
5 417 2085 4347225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  89.7534
13 161 2093 4380649 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  141.9881
8 524 1048 4393216 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  168.2626
5 421 2105 4431025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  217.0518
17 124 2108 4443664 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  233.9144
37 57 2109 4447881 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  332.5409
29 73 2117 4481689 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  114.2126
5 424 2120 4494400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  33.1245
8 265 2120 4494400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  63.4787
40 53 2120 4494400 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  27.3748
40 265 424 4494400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  307.4362
21 101 2121 4498641 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  265.6004
28 152 1064 4528384 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  86.0640
56 76 1064 4528384 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 143.1431
24 89 2136 4562496 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  500.7591
69 93 713 4575321 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 175.1569
5 428 2140 4579600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.0998
5 429 2145 4601025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  104.7864
13 165 2145 4601025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  133.7756
33 65 2145 4601025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  465.0641
65 165 429 4601025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  141.4361
12 537 716 4613904 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  415.0120
8 269 2152 4631104 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  106.4015
21 309 721 4678569 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 509.7281
5 433 2165 4687225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  150.2537
12 181 2172 4717584 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  266.5639
41 53 2173 4721929 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  116.0951
8 273 2184 4769856 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  186.0170
13 168 2184 4769856 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  112.7680
21 104 2184 4769856 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  105.0077
21 312 728 4769856 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  58.2863
24 273 728 4769856 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  133.1700
56 273 312 4769856 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  230.9260
104 168 273 4769856 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  219.3570
5 437 2185 4774225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  105.8412
17 129 2193 4809249 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1083.1370
29 76 2204 4857616 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  186.7849

14 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
33 201 737 4888521 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1062.2627
28 316 553 4892944 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  391.3796
8 277 2216 4910656 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  177.0007
5 444 2220 4928400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  100.6584
12 185 2220 4928400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  212.1182
37 60 2220 4928400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  168.5722
60 185 444 4928400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  258.7028
8 556 1112 4946176 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  141.5836
29 77 2233 4986289 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  71.4251
13 172 2236 4999696 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  438.4434
12 561 748 5035536 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  296.4632
33 204 748 5035536 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  286.3259
44 204 561 5035536 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  382.0945
5 449 2245 5040025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  231.8550
21 321 749 5049009 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  89.9573
8 281 2248 5053504 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  511.2731
13 173 2249 5058001 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  79.1518
12 376 1128 5089536 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 170.0557
24 188 1128 5089536 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  88.4742
37 61 2257 5094049 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  462.4087
17 133 2261 5112121 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  163.0126
5 453 2265 5130225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  132.9404
5 456 2280 5198400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  87.2674
8 285 2280 5198400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  59.3127
24 285 760 5198400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  149.8822
40 57 2280 5198400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  246.9507
40 285 456 5198400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  156.9568
57 120 760 5198400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  407.5579
120 152 285 5198400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  75.2402
5 457 2285 5221225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  134.3789
8 572 1144 5234944 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  78.0064
44 104 1144 5234944 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  192.8662
88 104 572 5234944 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  87.7928
21 109 2289 5239521 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  271.4509
12 573 764 5253264 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  146.1064
41 56 2296 5271616 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  199.3233
13 177 2301 5294601 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  225.1509
5 461 2305 5313025 1 1 16 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  25.9179
12 193 2316 5363856 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  263.9264
28 332 581 5400976 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  124.4451
24 97 2328 5419584 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  254.6178
17 137 2329 5424241 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1206.3197
44 53 2332 5438224 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  195.8189
41 57 2337 5461569 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  998.4558
33 213 781 5489649 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 307.4938
8 293 2344 5494336 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  114.1624
5 469 2345 5499025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  69.1991
13 181 2353 5536609 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  542.9239
76 124 589 5550736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  714.6426
5 472 2360 5569600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  119.9998

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 15

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 197 2364 5588496 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  111.6033
5 473 2365 5593225 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  62.7886
21 113 2373 5631129 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  134.2701
5 476 2380 5664400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  110.9732
17 140 2380 5664400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  218.4029
28 85 2380 5664400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  257.3865
85 140 476 5664400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  120.0150
77 217 341 5697769 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 194.8039
12 597 796 5702544 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  292.7935
13 184 2392 5721664 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  385.8788
17 141 2397 5745609 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  85.5404
5 481 2405 5784025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  54.2124
13 185 2405 5784025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  45.6912
37 65 2405 5784025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  53.8558
65 185 481 5784025 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  394.8000
8 301 2408 5798464 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  127.7758
56 301 344 5798464 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 339.1621
33 73 2409 5803281 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1897.3263
21 345 805 5832225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  216.9130
69 105 805 5832225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  206.3410
105 161 345 5832225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  843.9192
8 604 1208 5837056 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  308.9892
24 101 2424 5875776 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  250.8833
12 609 812 5934096 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  174.7344
21 348 812 5934096 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  59.7359
28 348 609 5934096 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  312.1927
5 488 2440 5953600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  70.7034
8 305 2440 5953600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  288.2742
40 61 2440 5953600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  316.5131
40 305 488 5953600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  154.9140
13 188 2444 5973136 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  142.5316
5 489 2445 5978025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  238.8656
57 129 817 6007401 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 388.8106
5 492 2460 6051600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  29.1692
12 205 2460 6051600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  54.6118
41 60 2460 6051600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  94.6333
60 205 492 6051600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  85.3145
5 493 2465 6076225 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.4635
17 145 2465 6076225 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  148.3128
29 85 2465 6076225 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  81.0354
85 145 493 6076225 2 4 2 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  66.1724
8 309 2472 6110784 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  148.9831
24 309 824 6110784 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 228.4388
8 620 1240 6150400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  157.0409
40 124 1240 6150400 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  418.3823
40 248 620 6150400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.2370
5 497 2485 6175225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  159.1603
28 89 2492 6210064 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  272.6988
41 61 2501 6255001 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  140.3682
8 313 2504 6270016 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  133.4616

16 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 501 2505 6275025 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  74.9767
12 209 2508 6290064 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  214.9436
33 76 2508 6290064 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  318.3113
44 57 2508 6290064 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  243.8251
13 193 2509 6295081 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  541.5423
12 633 844 6411024 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  733.6209
17 149 2533 6416089 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  86.4135
8 317 2536 6431296 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  202.6093
5 508 2540 6451600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  85.4800
8 636 1272 6471936 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  74.5503
12 424 1272 6471936 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  127.0379
24 424 636 6471936 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  324.8054
5 509 2545 6477025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  133.5144
29 88 2552 6512704 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  223.3756
37 69 2553 6517809 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  318.1497
13 197 2561 6558721 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  176.1804
8 321 2568 6594624 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  99.9925
24 321 856 6594624 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 388.6781
28 184 1288 6635776 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 193.3580
56 92 1288 6635776 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 85.1617
12 645 860 6656400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  57.1248
60 129 860 6656400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  192.6316
60 172 645 6656400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  176.8914
29 89 2581 6661561 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  288.5576
17 152 2584 6677056 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  115.6397
5 517 2585 6682225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  203.8384
44 236 649 6739216 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  737.0457
12 217 2604 6780816 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  340.4338
21 124 2604 6780816 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  204.8595
28 93 2604 6780816 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  151.9450
5 521 2605 6786025 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  73.2807
33 237 869 6796449 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 179.7047
8 652 1304 6801664 1 1 3 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  106.5732
13 201 2613 6827769 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  223.8880
24 109 2616 6843456 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  425.9711
5 524 2620 6864400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  202.4310
8 329 2632 6927424 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  220.2601
56 329 376 6927424 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 798.2726
12 440 1320 6969600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  53.0005
24 220 1320 6969600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  127.9223
44 120 1320 6969600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  99.5694
60 88 1320 6969600 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  132.8006
60 264 440 6969600 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  75.0689
120 220 264 6969600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  155.8203
12 221 2652 7033104 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  37.9396
13 204 2652 7033104 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  58.6274
17 156 2652 7033104 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  87.3099
156 204 221 7033104 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  97.4006
28 380 665 7075600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  246.5353
76 140 665 7075600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  295.2151

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 17

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
133 140 380 7075600 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  111.2592
5 533 2665 7102225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  109.4171
13 205 2665 7102225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  325.6325
41 65 2665 7102225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  836.9077
65 205 533 7102225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  131.0341
21 381 889 7112889 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 533.6452
29 92 2668 7118224 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  244.6183
17 157 2669 7123561 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  113.2786
8 668 1336 7139584 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  166.5262
12 669 892 7160976 1 1 3 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  101.5340
57 141 893 7177041 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 231.9429
5 536 2680 7182400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  196.9876
44 61 2684 7203856 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  256.0324
5 537 2685 7209225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  216.3065
8 337 2696 7268416 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  272.3086
29 93 2697 7273809 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  250.6048
37 73 2701 7295401 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  557.7151
5 541 2705 7317025 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  63.2474
24 113 2712 7354944 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  242.9063
28 97 2716 7376656 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1254.4116
13 209 2717 7382089 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  183.8928
12 681 908 7420176 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  247.1671
8 341 2728 7441984 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  145.6246
88 248 341 7441984 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 162.5501
17 161 2737 7491169 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1420.8875
33 249 913 7502121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2204.1084
12 229 2748 7551504 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  90.7974
21 393 917 7568001 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 203.3503
5 552 2760 7617600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  69.8444
8 345 2760 7617600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  267.8369
24 345 920 7617600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  226.9535
40 69 2760 7617600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  186.9061
40 345 552 7617600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  314.3372
69 120 920 7617600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  103.4348
120 184 345 7617600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  634.2401
5 553 2765 7645225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  191.4137
13 213 2769 7667361 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  350.3778
5 556 2780 7728400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  201.7780
5 557 2785 7756225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  182.9528
8 349 2792 7795264 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  159.7914
12 233 2796 7817616 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  433.7553
5 561 2805 7868025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  105.9120
17 165 2805 7868025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  85.1206
33 85 2805 7868025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  134.3070
85 165 561 7868025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  313.4414
37 76 2812 7907344 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  425.7506
29 97 2813 7912969 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  121.9736
12 705 940 7952400 1 2 6 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  155.6555
60 141 940 7952400 2 1 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  97.9109
60 188 705 7952400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  246.1803

18 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 217 2821 7958041 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  690.9003
8 353 2824 7974976 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  233.1346
28 101 2828 7997584 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  141.5752
41 69 2829 8003241 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  314.2843
12 472 1416 8020224 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 230.8775
24 236 1416 8020224 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 210.0598
5 568 2840 8065600 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  42.7146
5 569 2845 8094025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  214.7738
37 77 2849 8116801 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.7916
92 124 713 8133904 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  502.0676
8 357 2856 8156736 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  46.7492
17 168 2856 8156736 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  123.0021
21 136 2856 8156736 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  120.0188
21 408 952 8156736 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  167.2925
24 357 952 8156736 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  135.6441
56 357 408 8156736 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  106.1849
136 168 357 8156736 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  81.3959
5 572 2860 8179600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  72.9205
13 220 2860 8179600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  295.3578
44 65 2860 8179600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  396.4810
65 220 572 8179600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  182.7904
8 716 1432 8202496 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  373.6011
5 573 2865 8208225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  203.7240
12 717 956 8225424 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  117.9727
21 137 2877 8277129 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  210.0185
28 412 721 8317456 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1376.3384
5 577 2885 8323225 1 7 2 7 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  34.6780
12 241 2892 8363664 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  305.6577
5 581 2905 8439025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  342.7039
21 417 973 8520561 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 427.8673
5 584 2920 8526400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  43.5380
8 365 2920 8526400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  41.4504
40 73 2920 8526400 2 1 12 6 1 ε_{1}, ε_{2}, ε_{3}  222.4683
40 365 584 8526400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  121.5466
17 172 2924 8549776 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  270.1003
8 732 1464 8573184 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  174.8210
12 488 1464 8573184 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  117.4147
24 488 732 8573184 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  97.5884
29 101 2929 8579041 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  428.9061
33 89 2937 8625969 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1535.9679
17 173 2941 8649481 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  70.6334
5 589 2945 8673025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  128.1893
44 268 737 8690704 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  689.2549
12 741 988 8785296 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  174.5585
57 156 988 8785296 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  538.1868
76 156 741 8785296 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  250.8632
5 593 2965 8791225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  212.3404
69 129 989 8803089 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 387.2357
53 56 2968 8809024 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  268.4295
13 229 2977 8862529 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  232.6878

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 19

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 373 2984 8904256 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  264.0022
5 597 2985 8910225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  222.3899
8 748 1496 8952064 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  63.0889
44 136 1496 8952064 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 112.0837
88 136 748 8952064 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 206.1832
41 73 2993 8958049 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  502.1024
28 428 749 8976016 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  198.2417
21 429 1001 9018009 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  227.1836
33 273 1001 9018009 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  812.2121
77 273 429 9018009 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  158.3456
5 601 3005 9030025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  204.9390
17 177 3009 9054081 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1402.8470
12 753 1004 9072144 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  565.2624
8 377 3016 9096256 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  230.0260
13 232 3016 9096256 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  268.3801
29 104 3016 9096256 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  161.7997
104 232 377 9096256 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  300.5451
5 604 3020 9120400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  164.6809
53 57 3021 9126441 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  89.9579
13 233 3029 9174841 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  102.8810
12 253 3036 9217296 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  138.9096
33 92 3036 9217296 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  207.5959
44 69 3036 9217296 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  134.9142
5 609 3045 9272025 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  86.3929
21 145 3045 9272025 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  127.7113
29 105 3045 9272025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  93.0344
105 145 609 9272025 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  785.0771
8 381 3048 9290304 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  126.8528
24 381 1016 9290304 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 108.8445
28 109 3052 9314704 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  649.7616
8 764 1528 9339136 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  390.5028
133 161 437 9357481 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 157.8234
5 613 3065 9394225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  211.0606
13 236 3068 9412624 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  183.7947
17 181 3077 9467929 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  205.8471
5 616 3080 9486400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  110.8499
8 385 3080 9486400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  231.6784
40 77 3080 9486400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  85.8516
40 385 616 9486400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  943.0840
56 385 440 9486400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  309.1098
77 280 440 9486400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  101.5402
88 280 385 9486400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  904.0993
13 237 3081 9492561 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  100.7498
12 257 3084 9511056 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  205.5521
5 617 3085 9517225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  275.5337
12 777 1036 9659664 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  230.4571
21 444 1036 9659664 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 143.3766
28 444 777 9659664 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  215.5165
8 389 3112 9684544 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  256.0958
41 76 3116 9709456 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  823.0852

20 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 780 1560 9734400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  59.4504
12 520 1560 9734400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  126.3102
24 520 780 9734400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  144.6633
40 156 1560 9734400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  72.0207
40 312 780 9734400 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.4929
60 104 1560 9734400 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  48.3127
60 312 520 9734400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  182.2998
104 120 780 9734400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  47.5860
120 156 520 9734400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  228.9115
44 284 781 9759376 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  495.8399
17 184 3128 9784384 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  332.6193
21 149 3129 9790641 1 1 10 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  96.4908
13 241 3133 9815689 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  667.2216
33 285 1045 9828225 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  99.1107
57 165 1045 9828225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  133.6959
165 209 285 9828225 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 82.8502
8 393 3144 9884736 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  237.9897
24 393 1048 9884736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 805.9468
5 629 3145 9891025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  67.2974
17 185 3145 9891025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  446.8772
37 85 3145 9891025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  239.0653
85 185 629 9891025 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  69.9092
12 789 1052 9960336 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  171.1735
41 77 3157 9966649 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  198.7235
5 632 3160 9985600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  216.3993
29 109 3161 9991921 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  281.2333
28 113 3164 10010896 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  248.5505
5 633 3165 10017225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  188.5306
21 453 1057 10055241 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 319.1791
8 397 3176 10086976 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  158.0806
5 636 3180 10112400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  71.9999
12 265 3180 10112400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  235.1230
53 60 3180 10112400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  77.0010
60 265 636 10112400 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  305.8956
8 796 1592 10137856 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  142.5567
21 152 3192 10188864 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  73.1045
21 456 1064 10188864 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  172.5872
24 133 3192 10188864 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  128.0704
56 57 3192 10188864 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  210.4883
57 168 1064 10188864 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  268.6306
133 168 456 10188864 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  255.9481
17 188 3196 10214416 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  128.9342
33 97 3201 10246401 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  703.3918
5 641 3205 10272025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  320.7940
8 401 3208 10291264 1 5 2 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  131.3565
44 73 3212 10316944 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  439.6210
12 536 1608 10342656 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 110.8227
24 268 1608 10342656 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 176.1309
28 460 805 10368400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  311.0713
92 140 805 10368400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  139.5969

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 21

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
140 161 460 10368400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  385.1235
13 248 3224 10394176 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  188.6882
12 269 3228 10419984 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  247.9257
53 61 3233 10452289 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  209.9190
13 249 3237 10478169 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  278.0121
69 141 1081 10517049 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 807.2600
5 649 3245 10530025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  137.5349
8 812 1624 10549504 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  155.2344
28 232 1624 10549504 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  544.4902
56 232 812 10549504 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  170.3170
12 813 1084 10575504 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  288.6143
21 465 1085 10595025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  113.5402
93 105 1085 10595025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  103.7000
105 217 465 10595025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1448.3983
37 88 3256 10601536 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  886.3833
5 652 3260 10627600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  227.3738
5 653 3265 10660225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  281.6709
76 172 817 10679824 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  336.8456
8 409 3272 10705984 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  260.5609
29 113 3277 10738729 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  356.7797
17 193 3281 10764961 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  502.7607
24 137 3288 10810944 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  359.1054
13 253 3289 10817521 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  798.9663
37 89 3293 10843849 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  251.5751
21 157 3297 10870209 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  385.8845
8 413 3304 10916416 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  194.3378
56 413 472 10916416 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 186.2702
5 661 3305 10923025 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  128.4014
77 301 473 10962721 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 113.0681
5 664 3320 11022400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  265.8802
12 277 3324 11048976 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  347.9823
33 101 3333 11108889 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  201.4179
8 417 3336 11128896 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  778.3994
24 417 1112 11128896 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 370.1172
5 668 3340 11155600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  139.6977
13 257 3341 11162281 1 3 4 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  46.9396
44 152 1672 11182336 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 143.2924
76 88 1672 11182336 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 387.4796
5 669 3345 11189025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  373.6435
17 197 3349 11215801 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  232.3886
57 177 1121 11309769 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2234.6728
5 673 3365 11323225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  147.3720
8 421 3368 11343424 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  93.0955
12 281 3372 11370384 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  285.0986
8 844 1688 11397376 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  392.3044
5 677 3385 11458225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  165.3612
12 849 1132 11532816 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  912.3058
33 309 1133 11553201 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 150.6323
37 92 3404 11587216 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  320.9715
5 681 3405 11594025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  257.6452

22 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 568 1704 11614464 1 3 2 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  90.0303
24 284 1704 11614464 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  245.1587
56 61 3416 11669056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  367.9445
17 201 3417 11675889 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1575.6645
21 489 1141 11716929 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 770.1236
8 429 3432 11778624 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  127.1770
13 264 3432 11778624 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  168.6141
24 429 1144 11778624 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  317.8949
33 104 3432 11778624 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  256.6667
33 312 1144 11778624 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  497.4346
88 312 429 11778624 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  277.3984
104 264 429 11778624 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  224.0651
8 860 1720 11833600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  122.8045
40 172 1720 11833600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  500.7462
40 344 860 11833600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  161.9062
37 93 3441 11840481 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  684.8044
12 861 1148 11861136 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  116.0918
21 492 1148 11861136 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.4894
28 492 861 11861136 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  211.0794
5 689 3445 11868025 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  87.6390
13 265 3445 11868025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  191.3533
53 65 3445 11868025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  92.9457
65 265 689 11868025 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  558.4834
8 433 3464 11999296 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  468.0165
28 248 1736 12054784 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  73.9313
56 124 1736 12054784 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 150.5552
44 316 869 12082576 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  164.1729
57 61 3477 12089529 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  170.6265
5 696 3480 12110400 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  36.6076
24 145 3480 12110400 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  139.1004
29 120 3480 12110400 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  48.5481
120 145 696 12110400 2 4 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  156.6288
13 268 3484 12138256 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  669.4462
5 697 3485 12145225 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  43.7668
17 205 3485 12145225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  128.4922
41 85 3485 12145225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  149.8838
85 205 697 12145225 2 2 6 6 1 ε_{1}, ε_{2}, ε_{3}  185.3139
8 437 3496 12222016 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  47.8138
152 184 437 12222016 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 141.3155
13 269 3497 12229009 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  252.9910
8 876 1752 12278016 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.1409
12 584 1752 12278016 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  47.5894
24 584 876 12278016 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  64.9521
5 701 3505 12285025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  357.8966
21 501 1169 12299049 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 538.5412
12 293 3516 12362256 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  143.3318
33 321 1177 12467961 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1030.4112
12 885 1180 12531600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  219.2896
60 177 1180 12531600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  736.7975
60 236 885 12531600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  157.3158

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 23

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 709 3545 12567025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  212.3147
17 209 3553 12623809 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2032.7747
28 508 889 12645136 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1988.8991
5 712 3560 12673600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  45.6813
8 445 3560 12673600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  63.1652
40 89 3560 12673600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  147.7351
40 445 712 12673600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  178.8784
5 713 3565 12709225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  284.8974
8 892 1784 12730624 1 3 1 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  103.3648
76 188 893 12759184 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  205.9493
24 149 3576 12787776 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  120.5129
5 716 3580 12816400 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  100.8987
5 717 3585 12852225 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  36.2373
12 897 1196 12873744 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  125.4908
69 156 1196 12873744 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  84.5875
92 156 897 12873744 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  214.6509
37 97 3589 12880921 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  941.5248
8 449 3592 12902464 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  260.9513
29 124 3596 12931216 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  108.1665
33 109 3597 12938409 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  361.1092
13 277 3601 12967201 1 1 20 10 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  90.0129
5 721 3605 12996025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  292.5444
41 88 3608 13017664 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  372.6792
12 301 3612 13046544 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  187.3901
21 172 3612 13046544 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  196.6375
28 129 3612 13046544 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  409.4033
77 329 517 13097161 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 311.2215
17 213 3621 13111641 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  245.2981
8 453 3624 13133376 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.4542
24 453 1208 13133376 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 183.0997
8 908 1816 13191424 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  205.0848
21 173 3633 13198689 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  211.1883
5 728 3640 13249600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  45.2332
13 280 3640 13249600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  175.0935
56 65 3640 13249600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  222.4739
65 280 728 13249600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  137.7338
41 89 3649 13315201 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3105.6691
44 332 913 13337104 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  527.7048
13 281 3653 13344409 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  254.8715
8 457 3656 13366336 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  418.9688
53 69 3657 13373649 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  345.5992
5 732 3660 13395600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  36.3522
12 305 3660 13395600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  99.5462
60 61 3660 13395600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  83.0022
60 305 732 13395600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  195.5396
5 733 3665 13432225 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  85.1643
28 524 917 13454224 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  195.1276
12 921 1228 13571856 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  904.3463
5 737 3685 13579225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  239.2935
8 461 3688 13601344 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  213.6919

24 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
17 217 3689 13608721 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2117.1078
13 284 3692 13630864 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  151.1994
8 924 1848 13660416 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  78.8908
12 616 1848 13660416 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.0560
24 616 924 13660416 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  245.5239
28 264 1848 13660416 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  120.0533
44 168 1848 13660416 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  86.8373
56 264 924 13660416 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  166.2873
88 168 924 13660416 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  195.5543
5 741 3705 13727025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  204.8616
13 285 3705 13727025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  261.6321
57 65 3705 13727025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1226.9435
65 285 741 13727025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  172.8860
5 744 3720 13838400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  44.4587
8 465 3720 13838400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  87.7758
24 465 1240 13838400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  681.7131
40 93 3720 13838400 2 1 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  58.8108
40 465 744 13838400 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  362.5001
93 120 1240 13838400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  298.3051
120 248 465 13838400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  309.6959
33 113 3729 13905441 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1860.3131
12 933 1244 13927824 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  272.1707
37 101 3737 13965169 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  183.3719
5 748 3740 13987600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  123.8025
17 220 3740 13987600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  343.8672
44 85 3740 13987600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  209.5043
85 220 748 13987600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  371.8811
29 129 3741 13995081 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  489.8088
5 749 3745 14025025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  425.8683
8 469 3752 14077504 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  76.8390
56 469 536 14077504 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 178.5979
12 313 3756 14107536 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  632.5798
21 537 1253 14130081 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 160.3170
8 940 1880 14137600 1 6 2 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  64.7706
40 188 1880 14137600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  134.8925
40 376 940 14137600 2 1 6 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  251.1291
5 753 3765 14175225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  269.6761
24 157 3768 14197824 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  301.4993
41 92 3772 14227984 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  234.9082
8 473 3784 14318656 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  292.2450
88 344 473 14318656 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 306.5693
5 757 3785 14326225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  309.3655
12 632 1896 14379264 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 163.4758
24 316 1896 14379264 1 3 2 6 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  149.6932
33 345 1265 14402025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  941.9247
69 165 1265 14402025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  212.9632
165 253 345 14402025 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  366.5233
21 181 3801 14447601 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  793.0462
12 317 3804 14470416 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  235.5292
5 761 3805 14478025 1 3 4 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  62.7088

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 25

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 293 3809 14508481 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  237.2156
41 93 3813 14538969 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  173.6716
57 201 1273 14584761 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3197.5791
5 764 3820 14592400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  356.2144
8 956 1912 14622976 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  514.0829
12 957 1276 14653584 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  154.3125
33 348 1276 14653584 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  525.9237
44 348 957 14653584 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  82.7190
28 137 3836 14714896 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  341.4765
5 769 3845 14784025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  176.4164
8 481 3848 14807104 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  210.5856
13 296 3848 14807104 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  87.8648
37 104 3848 14807104 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  95.1296
104 296 481 14807104 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  596.2936
29 133 3857 14876449 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  358.5431
21 184 3864 14930496 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  394.0975
21 552 1288 14930496 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  92.1215
24 161 3864 14930496 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  537.8322
56 69 3864 14930496 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  254.9370
69 168 1288 14930496 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  135.5944
161 168 552 14930496 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 148.9434
5 773 3865 14938225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  245.8426
53 73 3869 14969161 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  173.0042
12 969 1292 15023376 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  161.5358
57 204 1292 15023376 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  188.4300
76 204 969 15023376 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  459.4904
5 776 3880 15054400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  153.8206
8 485 3880 15054400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  178.7215
40 97 3880 15054400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  908.4589
40 485 776 15054400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  164.2427
5 777 3885 15093225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  61.4242
21 185 3885 15093225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  80.5296
37 105 3885 15093225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  114.8766
105 185 777 15093225 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  528.2432
28 556 973 15147664 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  752.2725
17 229 3893 15155449 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  86.7045
5 781 3905 15249025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  169.9775
8 489 3912 15303744 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  511.3752
24 489 1304 15303744 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 348.0907
13 301 3913 15311569 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  875.7089
44 89 3916 15335056 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  557.7785
21 561 1309 15421329 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  506.8899
33 357 1309 15421329 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  262.8560
77 357 561 15421329 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  178.1428
8 493 3944 15555136 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  95.4614
17 232 3944 15555136 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  254.7550
29 136 3944 15555136 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  160.9354
136 232 493 15555136 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  423.2284
5 789 3945 15563025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  341.8410
12 329 3948 15586704 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  268.2918

26 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
21 188 3948 15586704 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  94.7596
28 141 3948 15586704 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  192.4960
8 988 1976 15618304 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  252.5326
76 104 1976 15618304 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  320.5816
104 152 988 15618304 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  239.7943
92 172 989 15649936 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  395.4174
17 233 3961 15689521 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2362.0019
5 793 3965 15721225 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  36.2075
13 305 3965 15721225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  68.1633
61 65 3965 15721225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 84.2961
65 305 793 15721225 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  347.2074
12 993 1324 15776784 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  409.4082
29 137 3973 15784729 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  111.3461
8 497 3976 15808576 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  200.1374
56 497 568 15808576 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 282.5496
41 97 3977 15816529 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 1925.9250
5 796 3980 15840400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  388.7509
12 664 1992 15872256 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 369.7582
24 332 1992 15872256 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 149.5586
5 797 3985 15880225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  283.4536
93 129 1333 15992001 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 399.1726
28 572 1001 16032016 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  256.2219
44 364 1001 16032016 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  702.4287
77 364 572 16032016 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  111.7825
8 501 4008 16064064 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  358.4145
24 501 1336 16064064 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 763.0445
21 573 1337 16088121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 226.1025
17 236 4012 16096144 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  286.0291
8 1004 2008 16128256 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  317.1517
13 309 4017 16136289 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  207.3984
12 1005 1340 16160400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  140.1804
60 201 1340 16160400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  405.4897
60 268 1005 16160400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  355.5903
53 76 4028 16224784 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 157.1717
17 237 4029 16232841 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  331.4591
37 109 4033 16265089 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1257.0866
5 808 4040 16321600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  66.2031
8 505 4040 16321600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  204.8957
40 101 4040 16321600 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  85.7679
40 505 808 16321600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  470.0292
12 337 4044 16353936 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  549.3879
5 809 4045 16362025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  170.7799
57 213 1349 16378209 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 237.1258
44 184 2024 16386304 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 145.3638
88 92 2024 16386304 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}} 104.0914
21 193 4053 16426809 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  248.1325
5 812 4060 16483600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  61.3847
28 145 4060 16483600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  474.2402
29 140 4060 16483600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  109.9353
140 145 812 16483600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  149.2665

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 27

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 813 4065 16524225 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  78.6686
13 313 4069 16556761 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  943.5305
69 177 1357 16573041 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 517.3039
8 509 4072 16581184 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  228.4456
8 1020 2040 16646400 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  38.4483
12 680 2040 16646400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  108.0952
24 680 1020 16646400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  103.5595
40 204 2040 16646400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  210.8680
40 408 1020 16646400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  133.7779
60 136 2040 16646400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  110.3696
60 408 680 16646400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  142.8113
120 136 1020 16646400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  90.9350
120 204 680 16646400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  185.4687
53 77 4081 16654561 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 238.9478
5 817 4085 16687225 1 5 2 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  63.9003
56 73 4088 16711744 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 397.4570
29 141 4089 16719921 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  732.7727
12 341 4092 16744464 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  61.6026
33 124 4092 16744464 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  255.3440
44 93 4092 16744464 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 83.8007
17 241 4097 16785409 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  381.5770
5 821 4105 16851025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  405.6030
13 316 4108 16875664 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  235.2687
5 824 4120 16974400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  317.2156
13 317 4121 16982641 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  271.5101
133 217 589 16999129 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1249.1063
8 517 4136 17106496 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  169.3199
88 376 517 17106496 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 845.6647
21 197 4137 17114769 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  311.5723
41 101 4141 17147881 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  569.5865
8 1036 2072 17172736 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  213.9568
28 296 2072 17172736 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  208.7357
56 296 1036 17172736 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  434.4632
5 829 4145 17181025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  447.1529
24 173 4152 17239104 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  203.2439
57 73 4161 17313921 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 876.2475
12 1041 1388 17338896 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  647.7762
8 521 4168 17372224 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  252.1238
28 149 4172 17405584 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  317.7638
13 321 4173 17413929 1 3 4 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  83.7155
21 597 1393 17464041 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 127.7497
44 380 1045 17472400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  119.3067
76 220 1045 17472400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  276.3437
209 220 380 17472400 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 258.2854
37 113 4181 17480761 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  505.5977
12 349 4188 17539344 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  323.8562
33 381 1397 17564481 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 235.0932
8 1052 2104 17707264 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  514.5723
61 69 4209 17715681 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 998.2914
17 248 4216 17774656 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  738.3616

28 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 844 4220 17808400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  211.4870
28 604 1057 17875984 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  2475.6125
17 249 4233 17918289 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1749.9854
12 353 4236 17943696 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  725.3422
5 849 4245 18020025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  231.2357
12 1065 1420 18147600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  720.8484
60 213 1420 18147600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  256.0630
60 284 1065 18147600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  690.9782
8 533 4264 18181696 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  87.0632
13 328 4264 18181696 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  217.6881
41 104 4264 18181696 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  302.8169
104 328 533 18181696 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  83.9677
5 853 4265 18190225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  295.6365
44 97 4268 18215824 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 294.6224
8 1068 2136 18249984 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  118.1349
12 712 2136 18249984 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 168.0712
24 712 1068 18249984 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 156.8574
13 329 4277 18292729 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  212.7065
5 856 4280 18318400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  419.5283
5 857 4285 18361225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  280.9713
8 537 4296 18455616 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  549.1160
24 537 1432 18455616 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1204.9801
17 253 4301 18498601 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  297.2814
5 861 4305 18533025 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  61.7926
21 205 4305 18533025 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.1110
41 105 4305 18533025 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  339.3862
105 205 861 18533025 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 114.9141
12 1077 1436 18558864 1 1 3 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  51.0247
13 332 4316 18627856 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  240.1264
29 149 4321 18671041 1 1 10 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  159.9049
33 393 1441 18688329 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3917.8227
92 188 1081 18696976 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  844.8514
8 541 4328 18731584 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  367.6788
8 1084 2168 18800896 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  368.2543
28 620 1085 18835600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  120.2134
124 140 1085 18835600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  138.9266
140 217 620 18835600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  487.9962
24 181 4344 18870336 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  239.4286
5 869 4345 18879025 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  76.6194
5 872 4360 19009600 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  50.1523
8 545 4360 19009600 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  122.2239
40 109 4360 19009600 2 1 12 6 1 ε_{1}, ε_{2}, ε_{3}  169.5866
40 545 872 19009600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  374.2723
12 728 2184 19079424 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  76.1210
24 364 2184 19079424 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  267.5739
28 312 2184 19079424 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  187.1006
56 156 2184 19079424 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  192.7322
156 168 728 19079424 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  101.6198
168 312 364 19079424 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  244.6437
17 257 4369 19088161 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  857.3681

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 29

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
93 141 1457 19105641 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 535.2070
5 876 4380 19184400 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  31.6953
12 365 4380 19184400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  51.1583
60 73 4380 19184400 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 208.5135
60 365 876 19184400 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  60.7791
13 337 4381 19193161 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  983.8803
5 877 4385 19228225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  284.7170
21 209 4389 19263321 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  224.9008
33 133 4389 19263321 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  247.4967
57 77 4389 19263321 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 156.5110
28 157 4396 19324816 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  854.6943
12 1101 1468 19395216 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  189.2897
5 881 4405 19404025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  531.0068
29 152 4408 19430464 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  240.2022
8 553 4424 19571776 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  452.7540
56 553 632 19571776 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 913.6801
21 633 1477 19633761 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 552.4424
13 341 4433 19651489 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  360.3050
5 888 4440 19713600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  90.9472
24 185 4440 19713600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  373.6095
37 120 4440 19713600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  255.3429
120 185 888 19713600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  345.8177
44 101 4444 19749136 1 1 10 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  95.0975
5 889 4445 19758025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  446.4966
12 1113 1484 19820304 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  303.0693
21 636 1484 19820304 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  200.7569
28 636 1113 19820304 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  617.7842
61 73 4453 19829209 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 1028.7041
8 557 4456 19855936 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  356.7672
5 892 4460 19891600 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  94.1591
5 893 4465 19936225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  305.8644
41 109 4469 19971961 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  553.3940
13 344 4472 19998784 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  214.7641
12 373 4476 20034576 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  436.8879
76 236 1121 20106256 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1354.0772
5 897 4485 20115225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  57.3662
13 345 4485 20115225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  95.5649
65 69 4485 20115225 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 75.1143
65 345 897 20115225 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  748.8196
8 561 4488 20142144 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  119.6617
17 264 4488 20142144 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  99.8752
24 561 1496 20142144 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  560.1202
33 136 4488 20142144 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  159.3070
33 408 1496 20142144 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  358.2294
88 408 561 20142144 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  879.3908
136 264 561 20142144 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 286.6048
57 237 1501 20277009 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 541.2905
5 901 4505 20295025 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  49.9620
17 265 4505 20295025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  499.5208
53  85 4505 20295025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  110.1223

30 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
85 265 901 20295025 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  170.1562
21 645 1505 20385225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  257.9145
105 129 1505 20385225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1561.1574
105 301 645 20385225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  428.2900
5 904 4520 20430400 1 8 4 16 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  22.1782
8 565 4520 20430400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  68.4518
40 113 4520 20430400 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  180.9858
40 565 904 20430400 2 2 8 16 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  70.9435
33 137 4521 20439441 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2482.3046
12 377 4524 20466576 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  218.6275
13 348 4524 20466576 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  129.9332
29 156 4524 20466576 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  174.0926
156 348 377 20466576 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  193.4730
8 1132 2264 20502784 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  326.6898
44 412 1133 20539024 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  179.9685
13 349 4537 20584369 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1176.0179
5 908 4540 20611600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  180.5572
77 413 649 20638849 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 317.4365
12 1137 1516 20684304 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1388.3153
8 569 4552 20720704 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  533.1657
29 157 4553 20729809 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  281.6881
17 268 4556 20757136 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  269.4759
12 760 2280 20793600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  180.9097
24 380 2280 20793600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  118.7547
60 152 2280 20793600 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  105.5999
60 456 760 20793600 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  363.5572
76 120 2280 20793600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  214.0992
120 380 456 20793600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  205.2388
28 652 1141 20830096 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1083.6990
5 913 4565 20839225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  330.0524
17 269 4573 20912329 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  343.8812
8 573 4584 21013056 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  184.3378
24 573 1528 21013056 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 403.7882
5 917 4585 21022225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  369.7880
33 417 1529 21040569 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2365.9114
37 124 4588 21049744 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  945.6857
13 353 4589 21058921 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  361.4583
8 1148 2296 21086464 1 2 6 12 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  39.4809
28 328 2296 21086464 1 4 6 12 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  112.9148
56 328 1148 21086464 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  125.0621
12 1149 1532 21123216 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  228.6559
5 921 4605 21206025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  372.9421
8 577 4616 21307456 1 7 4 14 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  52.8574
5 924 4620 21344400 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  40.8011
12 385 4620 21344400 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  135.1760
21 220 4620 21344400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  137.0217
28 165 4620 21344400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  119.5737
33 140 4620 21344400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  160.0930
44 105 4620 21344400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  222.6072
60  77 4620 21344400 2 1 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  38.0401

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 31

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
60 385 924 21344400 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  252.1825
105 220 924 21344400 2 2 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  229.4261
140 165 924 21344400 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  63.7109
69 201 1541 21372129 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 622.9646
24 193 4632 21455424 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  535.4763
41 113 4633 21464689 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2210.3366
61 76 4636 21492496 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 1526.8864
13 357 4641 21538881 1 2 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  49.1615
17 273 4641 21538881 1 2 12 12 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  213.3688
21 221 4641 21538881 1 2 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  59.2520
221 273 357 21538881 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  115.8286
5 929 4645 21576025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  578.5925
8 581 4648 21603904 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  273.8603
56 581 664 21603904 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 657.7016
8 1164 2328 21678336 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  66.8030
12 776 2328 21678336 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  46.7959
24 776 1164 21678336 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  87.0269
53 88 4664 21752896 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 493.4449
5 933 4665 21762225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  347.7613
12 389 4668 21790224 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  279.6158
29 161 4669 21799561 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  176.5366
28 668 1169 21864976 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  540.1872
21 669 1561 21930489 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1208.9772
5 937 4685 21949225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  311.0191
12 1173 1564 22014864 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  243.9706
69 204 1564 22014864 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  488.9740
92 204 1173 22014864 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  200.1093
61 77 4697 22061809 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 381.5448
5 941 4705 22137025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  188.3908
44 428 1177 22165264 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1004.7571
17 277 4709 22174681 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  383.0974
8 589 4712 22202944 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  314.9825
152 248 589 22202944 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 318.2090
53 89 4717 22250089 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 400.5297
8 1180 2360 22278400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  250.9031
40 236 2360 22278400 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  237.0181
40 472 1180 22278400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  737.4430
24 197 4728 22353984 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  272.2580
57 249 1577 22382361 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3142.8720
12 1185 1580 22467600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  276.7081
60 237 1580 22467600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  103.2883
60 316 1185 22467600 2 3 2 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  381.8673
8 593 4744 22505536 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  403.5201
5 949 4745 22515025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  127.6477
13 365 4745 22515025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  89.8581
65 73 4745 22515025 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 543.2093
65 365 949 22515025 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  170.1153
5 952 4760 22657600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  95.3848
17 280 4760 22657600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  256.7303
56  85 4760 22657600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  148.0519

32 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
85 280 952 22657600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  552.7119
12 397 4764 22695696 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  187.8551
5 953 4765 22705225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  91.3941
21 681 1589 22724289 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 753.2643
37 129 4773 22781529 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  382.9630
8 597 4776 22810176 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  396.5311
24 597 1592 22810176 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 140.6971
17 281 4777 22819729 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1196.4437
5 956 4780 22848400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  360.7961
8 1196 2392 22886656 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  177.2783
92 104 2392 22886656 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  267.8560
104 184 1196 22886656 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  335.5029
5 957 4785 22896225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  73.3714
29 165 4785 22896225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  187.2169
33 145 4785 22896225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  1081.2912
145 165 957 22896225 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  111.7355
44 109 4796 23001616 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  690.1806
209 253 437 23107249 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 262.0628
8 601 4808 23116864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  585.2709
21 229 4809 23126481 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  375.1862
12 401 4812 23155344 1 5 2 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  132.8876
28 344 2408 23193856 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  198.9125
56 172 2408 23193856 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 217.3835
17 284 4828 23309584 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  543.3027
12 1209 1612 23386896 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  689.3872
93 156 1612 23386896 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  371.5181
124 156 1209 23386896 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1163.9554
28 173 4844 23464336 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  83.3084
5 969 4845 23474025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  127.5035
17 285 4845 23474025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  91.7498
57 85 4845 23474025 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 195.2841
85 285 969 23474025 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  214.0379
8 1212 2424 23503104 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  274.3184
12 808 2424 23503104 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  420.4024
24 808 1212 23503104 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  341.8941
13 373 4849 23512801 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1290.0912
5 973 4865 23668225 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  87.6904
8 609 4872 23736384 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  161.6839
21 232 4872 23736384 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  108.5130
21 696 1624 23736384 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  464.5673
24 609 1624 23736384 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1194.1401
29 168 4872 23736384 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  70.2545
56 609 696 23736384 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  759.4579
168 232 609 23736384 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  482.4647
53 92 4876 23775376 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 586.1967
12 1221 1628 23853456 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  80.3322
33 444 1628 23853456 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 209.5681
44 444 1221 23853456 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  135.7626
5 977 4885 23863225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  405.7616
13 376 4888 23892544 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1108.2090

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 33

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
21 233 4893 23941449 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  267.1856
69 213 1633 24000201 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 757.0447
8 613 4904 24049216 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  86.1315
12 409 4908 24088464 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  537.2362
8 1228 2456 24127744 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  456.4644
33 149 4917 24176889 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  332.0490
5 984 4920 24206400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  80.1476
24 205 4920 24206400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  118.7911
41 120 4920 24206400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  177.0269
120 205 984 24206400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  280.8268
37 133 4921 24216241 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1581.5320
53 93 4929 24295041 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 644.4947
21 705 1645 24354225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  417.3492
105 141 1645 24354225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  471.2312
105 329 705 24354225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1770.8768
8 617 4936 24364096 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1114.5569
5 988 4940 24403600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  143.7340
13 380 4940 24403600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  129.0532
65 76 4940 24403600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 401.2615
65 380 988 24403600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  582.8728
12 824 2472 24443136 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 152.5760
24 412 2472 24443136 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  296.0560
5 989 4945 24453025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  496.7566
13 381 4953 24532209 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  326.9361
12 413 4956 24561936 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  63.4854
21 236 4956 24561936 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  127.9954
28 177 4956 24561936 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  381.0155
5 993 4965 24651225 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  148.4498
44 113 4972 24720784 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  560.6960
8 1244 2488 24760576 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  367.3195
12 1245 1660 24800400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  252.8102
60 249 1660 24800400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1197.4501
60 332 1245 24800400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  115.9522
17 293 4981 24810361 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  150.6075
33 453 1661 24830289 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 285.1573
56 89 4984 24840256 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 1616.8307
5 997 4985 24850225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  340.3626
29 172 4988 24880144 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  420.8021
161 217 713 24910081 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2581.5355
5 1001 5005 25050025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  235.6049
13 385 5005 25050025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  488.4213
65 77 5005 25050025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 203.8584
65 385 1001 25050025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1967.9083
28 716 1253 25120144 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  228.4548
24 209 5016 25160256 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  707.8438
33 152 5016 25160256 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  444.6429
33 456 1672 25160256 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  649.4094
57 88 5016 25160256 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 921.0078
57 264 1672 25160256 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  618.3371
209 264 456 25160256 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  849.3537

34 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
29 173 5017 25170289 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  393.3987
21 717 1673 25190361 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 253.3426
5 1004 5020 25200400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  483.3006
12 1257 1676 25280784 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  323.5973
8 629 5032 25321024 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  140.1389
17 296 5032 25321024 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  460.6815
37 136 5032 25321024 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  522.6404
136 296 629 25321024 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  243.7761
69 73 5037 25371369 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 210.2753
5 1009 5045 25452025 1 7 4 14 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  28.6562
12 421 5052 25522704 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  430.2136
13 389 5057 25573249 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  326.0653
44 460 1265 25603600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  597.6987
92 220 1265 25603600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  518.8282
220 253 460 25603600 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  602.3233
21 241 5061 25613721 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1059.8204
8 633 5064 25644096 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  754.7496
24 633 1688 25644096 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 777.0974
5 1013 5065 25654225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  390.3837
28 181 5068 25684624 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  832.1183
37 137 5069 25694761 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  596.9884
57 89 5073 25735329 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 682.2506
5 1016 5080 25806400 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  166.6995
41 124 5084 25847056 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  739.8915
76 268 1273 25928464 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  2708.5874
8 1276 2552 26050816 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  341.3012
44 232 2552 26050816 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  359.1700
88 232 1276 26050816 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1078.7316
5 1021 5105 26061025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  295.0542
13 393 5109 26101881 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  383.4566
33 465 1705 26163225 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  602.4974
93 165 1705 26163225 1 2 8 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  130.7894
165 341 465 26163225 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 149.1758
17 301 5117 26183689 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  293.2855
12 1281 1708 26255376 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  268.9163
21 732 1708 26255376 1 2 6 6 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  103.9411
28 732 1281 26255376 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  807.0968
8 641 5128 26296384 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  997.9879
29 177 5133 26347689 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  430.2967
12 856 2568 26378496 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 344.4737
24 428 2568 26378496 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 162.1721
53 97 5141 26429881 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 375.4249
77 469 737 26615281 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 182.7632
5 1032 5160 26625600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  81.2146
8 645 5160 26625600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  115.4341
24 645 1720 26625600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  345.5881
40 129 5160 26625600 2 1 8 4 1 ε_{1}, ε_{2}, ε_{3}  512.5760
40 645 1032 26625600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.9727
120 129 1720 26625600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1002.2121
120 344 645 26625600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  297.5670

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 35

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 397 5161 26635921 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1233.0451
5 1033 5165 26677225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  321.0804
8 1292 2584 26708224 1 4 8 16 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  40.5040
76 136 2584 26708224 1 2 8 16 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 158.8166
136 152 1292 26708224 2 1 4 8 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  65.5075
12 1293 1724 26749584 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  191.7035
5 1036 5180 26832400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  118.0642
28 185 5180 26832400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  232.6678
37 140 5180 26832400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  105.6178
140 185 1036 26832400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  698.3913
33 157 5181 26842761 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  362.8943
5 1037 5185 26884225 1 2 20 10 1 ε_{1}, ε_{2}, ε_{3}  48.6102
17 305 5185 26884225 1 2 20 10 1 ε_{1}, ε_{2}, ε_{3}  286.7245
61 85 5185 26884225 1 2 20 10 1 ε_{1}, ε_{2}, ε_{3} 160.9347
85 305 1037 26884225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  309.2055
21 741 1729 26904969 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  553.7439
57 273 1729 26904969 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  2671.5152
133 273 741 26904969 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  412.8836
8 649 5192 26956864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  489.8192
88 472 649 26956864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2815.4907
12 433 5196 26998416 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  459.4295
5 1041 5205 27092025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  364.8393
21 248 5208 27123264 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  102.5051
21 744 1736 27123264 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  166.3749
24 217 5208 27123264 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  491.6929
56 93 5208 27123264 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 154.8258
93 168 1736 27123264 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  121.0533
168 217 744 27123264 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 496.5116
13 401 5213 27175369 1 5 2 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  51.9174
37 141 5217 27217089 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  545.3665
8 653 5224 27290176 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  445.2847
8 1308 2616 27373824 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  178.7397
12 872 2616 27373824 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  273.4763
24 872 1308 27373824 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  173.1512
28 748 1309 27415696 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  524.8168
44 476 1309 27415696 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  382.9161
77 476 748 27415696 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  194.4661
5 1048 5240 27457600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  356.6345
12 437 5244 27499536 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  103.1102
57  92 5244 27499536 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  568.8531
69  76 5244 27499536 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  482.6280
5 1049 5245 27510025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  329.8567
29 181 5249 27552001 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  188.4076
17 309 5253 27594009 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  375.8979
5 1052 5260 27667600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  256.9541
28 376 2632 27709696 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  343.6283
56 188 2632 27709696 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 126.1276
12 1317 1756 27751824 1 1 5 5 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  115.6509
21 753 1757 27783441 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 294.0814
5 1057 5285 27931225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  397.5763

36 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 661 5288 27962944 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  279.0970
41 129 5289 27973521 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  4522.3133
8 1324 2648 28047616 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  701.6654
13 408 5304 28132416 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  108.2799
17 312 5304 28132416 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  166.7775
24 221 5304 28132416 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  105.8157
221 312 408 28132416 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  133.8497
5 1061 5305 28143025 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  164.9323
21 253 5313 28227969 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  401.2258
33 161 5313 28227969 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1310.7860
69 77 5313 28227969 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 239.0640
12 1329 1772 28259856 1 1 3 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  373.3836
13 409 5317 28270489 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1350.7073
5 1064 5320 28302400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  204.7685
8 665 5320 28302400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  530.6801
40 133 5320 28302400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  552.0999
40 665 1064 28302400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  536.8951
56 665 760 28302400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  802.8511
133 280 760 28302400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  740.4268
152 280 665 28302400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  547.0414
17 313 5321 28313041 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3239.4923
124 172 1333 28430224 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  807.1563
29 184 5336 28472896 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  802.3584
5 1068 5340 28515600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  93.0929
12 445 5340 28515600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  183.1349
60 89 5340 28515600 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 325.2789
60 445 1068 28515600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  213.1794
5 1069 5345 28569025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  519.5402
28 764 1337 28601104 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1005.0052
8 669 5352 28643904 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  386.4609
24 669 1784 28643904 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 556.1698
53 101 5353 28654609 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  157.9883
13 412 5356 28686736 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  392.6482
8 1340 2680 28729600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  203.4707
40 268 2680 28729600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  679.6502
40 536 1340 28729600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  324.7931
5 1073 5365 28783225 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  93.0381
29 185 5365 28783225 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  137.0558
37 145 5365 28783225 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  134.1928
145 185 1073 28783225 4 2 2 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  356.6578
61 88 5368 28815424 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 337.0332
13 413 5369 28826161 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  119.8875
17 316 5372 28858384 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  288.3589
33 489 1793 28933641 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3041.9012
8 673 5384 28987456 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1154.8999
5 1077 5385 28998225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  245.7648
12 449 5388 29030544 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  848.4726
17 317 5389 29041321 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  320.3578
76 284 1349 29116816 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  499.1804
21 257 5397 29127609 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  90.4059

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 37

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
28 193 5404 29203216 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  786.5218
5 1081 5405 29214025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  624.8777
12 1353 1804 29289744 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  882.8850
33 492 1804 29289744 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  772.2102
44 492 1353 29289744 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  601.2183
8 677 5416 29333056 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  215.2467
5 1084 5420 29376400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  380.5492
13 417 5421 29387241 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  372.8054
8 1356 2712 29419776 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  77.4444
12 904 2712 29419776 1 8 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  64.6189
24 904 1356 29419776 1 8 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  190.0840
92 236 1357 29463184 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  369.4561
61  89 5429 29474041 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  601.0360
56  97 5432 29506624 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  989.6123
8 681 5448 29680704 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1175.9617
24 681 1816 29680704 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2678.4503
69 237 1817 29713401 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 440.1963
29 188 5452 29724304 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  236.7912
41 133 5453 29735209 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  347.5851
44 248 2728 29767936 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 212.6395
88 124 2728 29767936 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  704.0249
17 321 5457 29778849 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1096.2266
12 1365 1820 29811600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  92.2740
21 780 1820 29811600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  101.2876
28 780 1365 29811600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  133.1755
60 273 1820 29811600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  291.6247
60 364 1365 29811600 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  120.0026
105 156 1820 29811600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  334.5305
105 364 780 29811600 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  236.4480
140 156 1365 29811600 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  69.9839
140 273 780 29811600 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  120.2076
5 1093 5465 29866225 1 5 2 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  88.5546
77 497 781 29888089 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 600.9500
13 421 5473 29953729 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1254.2534
5 1096 5480 30030400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  65.8026
8 685 5480 30030400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.3190
40 137 5480 30030400 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  127.6917
40 685 1096 30030400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  383.1378
12 457 5484 30074256 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  531.5633
5 1097 5485 30085225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  341.2301
93 177 1829 30107169 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 719.5281
24 229 5496 30206016 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  328.9447
5 1101 5505 30305025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  193.3726
33 501 1837 30371121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 673.7736
8 689 5512 30382144 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  214.1009
13 424 5512 30382144 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  243.9371
53 104 5512 30382144 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  103.2531
104 424 689 30382144 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  444.5615
37 149 5513 30393169 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  130.8551
28 197 5516 30426256 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  412.3610

38 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 920 2760 30470400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  109.4744
24 460 2760 30470400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  282.6799
60 184 2760 30470400 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  355.7389
60 552 920 30470400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  97.5701
92 120 2760 30470400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  190.9923
120 460 552 30470400 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  216.6692
21 789 1841 30503529 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 660.0709
57 97 5529 30569841 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 1510.4384
12 461 5532 30603024 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  229.4790
5 1109 5545 30747025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  345.1299
73 76 5548 30780304 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 1333.6042
8 1388 2776 30824704 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  653.3574
12 1389 1852 30869136 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  625.6333
5 1112 5560 30913600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  295.6377
13 428 5564 30958096 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  302.0375
5 1113 5565 30969225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  161.3460
21 265 5565 30969225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  349.0199
53 105 5565 30969225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  205.1726
105 265 1113 30969225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  2346.5276
28 796 1393 31047184 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  594.9149
8 697 5576 31091776 1 6 4 12 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  99.5701
17 328 5576 31091776 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  245.5945
41 136 5576 31091776 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  357.9856
136 328 697 31091776 2 4 6 12 1 ε_{1}, ε_{2}, ε_{3}  274.1633
5 1117 5585 31192225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  323.0936
44 508 1397 31225744 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  387.6966
24 233 5592 31270464 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  792.5777
17 329 5593 31281649 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  3458.6023
29 193 5597 31326409 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  564.1408
12 1401 1868 31404816 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  978.4832
5 1121 5605 31416025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  225.4265
8 701 5608 31449664 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  501.3648
61 92 5612 31494544 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 337.9812
41 137 5617 31550689 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2654.9906
73 77 5621 31595641 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 144.6212
37 152 5624 31629376 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  107.4704
12 469 5628 31674384 1 3 4 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  98.1019
21 268 5628 31674384 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  321.2562
28 201 5628 31674384 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  684.0812
13 433 5629 31685641 1 1 12 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  241.3677
5 1128 5640 31809600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  119.0518
8 705 5640 31809600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  337.0322
24 705 1880 31809600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  486.9437
40 141 5640 31809600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  279.1638
40 705 1128 31809600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  803.8518
120 141 1880 31809600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  263.4166
120 376 705 31809600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1233.0335
17 332 5644 31854736 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  440.2255
5 1129 5645 31866025 1 9 2 9 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  39.3427
21 269 5649 31911201 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  685.1087

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 39

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
56 101 5656 31990336 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  683.6397
5 1132 5660 32035600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  329.2709
5 1133 5665 32092225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  278.2618
8 709 5672 32171584 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  345.6713
61 93 5673 32182929 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 566.6243
12 473 5676 32216976 1 3 4 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  137.8954
33 172 5676 32216976 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  687.4983
44 129 5676 32216976 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  633.3569
8 1420 2840 32262400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  200.0476
40 284 2840 32262400 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  252.5079
40 568 1420 32262400 2 3 2 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  297.4946
13 437 5681 32273761 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  298.4532
5 1137 5685 32319225 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  159.2566
21 813 1897 32387481 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 149.3521
8 713 5704 32535616 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  478.8944
184 248 713 32535616 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 844.2141
5 1141 5705 32547025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  529.1845
33 173 5709 32592681 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  356.7669
12 952 2856 32626944 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  238.8230
24 476 2856 32626944 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  226.5416
28 408 2856 32626944 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  264.9977
56 204 2856 32626944 1 2 4 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  282.3240
168 204 952 32626944 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  301.6581
168 408 476 32626944 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  189.4859
29 197 5713 32638369 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  150.7831
133 301 817 32706961 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 337.6332
5 1144 5720 32718400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  273.2535
13 440 5720 32718400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  181.9824
65 88 5720 32718400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 676.3034
65 440 1144 32718400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  578.2361
69 249 1909 32798529 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1194.0499
17 337 5729 32821441 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3274.0814
8 717 5736 32901696 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  257.0862
24 717 1912 32901696 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 449.0329
5 1148 5740 32947600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  88.7475
28 205 5740 32947600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  302.1079
41 140 5740 32947600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  299.0286
140 205 1148 32947600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  118.4586
8 1436 2872 32993536 1 3 1 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  257.0567
5 1149 5745 33005025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  676.4587
12 1437 1916 33039504 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  225.3769
57 101 5757 33143049 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  243.1770
44 524 1441 33223696 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1663.4528
5 1153 5765 33235225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  429.2665
8 721 5768 33269824 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  535.9091
56 721 824 33269824 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1516.2897
12 481 5772 33315984 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  330.1480
13 444 5772 33315984 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  132.0428
37 156 5772 33315984 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  168.8382
156 444 481 33315984 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  722.3514

40 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
53 109 5777 33373729 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  109.9066
41 141 5781 33419961 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  683.9891
24 241 5784 33454656 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  685.8509
5 1157 5785 33466225 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  98.9904
13 445 5785 33466225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  354.9164
65 89 5785 33466225 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 934.9817
65 445 1157 33466225 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  142.7838
17 341 5797 33605209 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  477.4778
37 157 5809 33744481 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  796.3086
21 277 5817 33837489 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  381.4871
5 1164 5820 33872400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  131.8980
12 485 5820 33872400 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  107.3526
60 97 5820 33872400 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 414.4000
60 485 1164 33872400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  198.7682
124 188 1457 33965584 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1109.1882
29 201 5829 33977241 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  546.8193
13 449 5837 34070569 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  313.3409
12 1461 1948 34152336 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  682.4793
5 1169 5845 34164025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  646.5734
17 344 5848 34199104 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  358.8100
28 209 5852 34245904 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  362.6168
44 133 5852 34245904 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  176.5706
76 77 5852 34245904 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 145.7697
8 733 5864 34386496 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  113.5773
5 1173 5865 34398225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  81.2105
17 345 5865 34398225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  599.0615
69 85 5865 34398225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3} 213.7094
85 345 1173 34398225 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  235.9246
57 309 1957 34468641 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 332.7382
8 1468 2936 34480384 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  361.8001
5 1177 5885 34633225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  268.5446
13 453 5889 34680321 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  639.3344
12 1473 1964 34715664 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1001.6193
8 737 5896 34762816 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1386.2534
88 536 737 34762816 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1507.2807
21 281 5901 34821801 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  307.7000
5 1181 5905 34869025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  635.0206
33 537 1969 34892649 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 5571.0815
28 844 1477 34904464 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1281.8206
12 493 5916 34999056 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  396.7341
17 348 5916 34999056 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  539.3074
29 204 5916 34999056 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  485.2141
204 348 493 34999056 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  349.1811
61 97 5917 35010889 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 1184.5522
8 741 5928 35141184 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  97.6888
13 456 5928 35141184 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  183.5607
24 741 1976 35141184 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  299.9413
57 104 5928 35141184 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  266.0493
57 312 1976 35141184 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  633.3516
104 456 741 35141184 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  388.0294

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 41

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
152 312 741 35141184 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  220.8255
17 349 5933 35200489 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  178.7335
8 1484 2968 35236096 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  287.7357
28 424 2968 35236096 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  999.4772
56 424 1484 35236096 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  496.8431
13 457 5941 35295481 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1441.6874
21 849 1981 35319249 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1670.6345
5 1189 5945 35343025 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  184.5605
29 205 5945 35343025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  233.9869
41 145 5945 35343025 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  999.0865
145 205 1189 35343025 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  485.6810
37 161 5957 35485849 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  338.3420
5 1192 5960 35521600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  156.0948
8 745 5960 35521600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  358.1231
40 149 5960 35521600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  178.1010
40 745 1192 35521600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1689.1895
12 497 5964 35569296 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  457.5680
21 284 5964 35569296 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  327.8248
28 213 5964 35569296 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  280.8930
5 1193 5965 35581225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  493.0034
33 181 5973 35676729 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  345.6737
5 1196 5980 35760400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  70.4681
13 460 5980 35760400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  200.9417
65 92 5980 35760400 2 1 12 6 1 ε_{1}, ε_{2}, ε_{3} 234.1452
65 460 1196 35760400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  576.2461
12 1497 1996 35856144 1 1 5 5 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  376.8821
53 113 5989 35868121 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  857.6603
8 749 5992 35904064 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  453.8155
56 749 856 35904064 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 900.1596
13 461 5993 35916049 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  460.7053
17 353 6001 36012001 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1709.3672
76 316 1501 36048016 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  645.5741
5 1201 6005 36060025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  517.9831
28 860 1505 36240400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  421.2343
140 172 1505 36240400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  745.0731
140 301 860 36240400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  222.5927
8 753 6024 36288576 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1190.5678
24 753 2008 36288576 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1416.4718
44 137 6028 36336784 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  786.0293
12 1509 2012 36433296 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  88.5786
5 1208 6040 36481600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  397.0758
5 1209 6045 36542025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  229.7215
13 465 6045 36542025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  318.6670
65 93 6045 36542025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 240.4863
65 465 1209 36542025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  2135.6752
8 757 6056 36675136 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  481.7063
5 1212 6060 36723600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  56.7853
12 505 6060 36723600 1 4 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  134.6699
60 101 6060 36723600 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  85.6192
60 505 1212 36723600 2 4 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  260.0082

42 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
29 209 6061 36735721 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  940.2091
129 141 2021 36759969 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 208.2081
8 1516 3032 36772096 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  683.9847
5 1213 6065 36784225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  560.5936
24 253 6072 36869184 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  262.8201
33 184 6072 36869184 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  629.1561
33 552 2024 36869184 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  156.5177
69 88 6072 36869184 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 292.7898
69 264 2024 36869184 1 2 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  140.9301
253 264 552 36869184 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  332.9842
77 553 869 37002889 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 657.6222
5 1217 6085 37027225 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  86.6441
8 761 6088 37063744 1 3 12 18 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  56.6617
12 1016 3048 37161216 1 3 2 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  77.5822
24 508 3048 37161216 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  347.9448
13 469 6097 37173409 1 3 14 21 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  75.1642
57 321 2033 37197801 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 884.3743
56 109 6104 37258816 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  724.0626
5 1221 6105 37271025 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  154.1623
33 185 6105 37271025 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  847.5040
37 165 6105 37271025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  287.3466
165 185 1221 37271025 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  178.7434
12 509 6108 37307664 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  124.5499
41 149 6109 37319881 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  775.6595
44 556 1529 37405456 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1840.5873
8 1532 3064 37552384 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  437.4675
12 1533 2044 37601424 1 2 2 4 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  187.5396
21 876 2044 37601424 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  357.7914
28 876 1533 37601424 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  172.4574
13 472 6136 37650496 1 1 14 7 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  195.9420
5 1228 6140 37699600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  271.0565
69 89 6141 37711881 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 972.6165
5 1229 6145 37761025 1 3 4 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  90.8214
13 473 6149 37810201 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  131.0330
8 769 6152 37847104 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  958.7220
21 293 6153 37859409 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  125.5046
28 440 3080 37945600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  111.8000
44 280 3080 37945600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  201.1263
56 220 3080 37945600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  190.3723
88 140 3080 37945600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  160.0128
140 440 616 37945600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  197.4143
220 280 616 37945600 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  686.9588
61 101 6161 37957921 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  990.7761
92 268 1541 37994896 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  621.9744
24 257 6168 38044224 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  245.7453
29 213 6177 38155329 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  329.2144
12 1545 2060 38192400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  532.2954
60 309 2060 38192400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  367.9690
60 412 1545 38192400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1039.0077
8 773 6184 38241856 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  98.9527

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 43

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
5 1237 6185 38254225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  164.0461
13 476 6188 38291344 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  71.5546
17 364 6188 38291344 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  184.3699
28 221 6188 38291344 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  81.7964
221 364 476 38291344 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  238.6922
21 885 2065 38378025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  531.5254
105 177 2065 38378025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  3205.6953
105 413 885 38378025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  198.2452
12 517 6204 38489616 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  369.1155
33 188 6204 38489616 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  528.5119
44 141 6204 38489616 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  475.0563
5 1241 6205 38502025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  400.6483
17 365 6205 38502025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  285.0018
73 85 6205 38502025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3} 781.9625
85 365 1241 38502025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  469.7279
57 109 6213 38601369 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1097.9400
8 777 6216 38638656 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  136.3289
21 296 6216 38638656 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  176.9646
21 888 2072 38638656 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  75.5381
24 777 2072 38638656 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  236.6893
37 168 6216 38638656 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  205.7556
56 777 888 38638656 1 4 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  236.3330
168 296 777 38638656 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  176.9888
5 1244 6220 38688400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  615.0363
93 201 2077 38825361 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 895.0243
41 152 6232 38837824 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  869.9486
28 892 1561 38987536 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1032.7041
5 1249 6245 39000025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  215.6137
8 781 6248 39037504 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  498.4658
88 568 781 39037504 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 632.8547
133 329 893 39075001 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 613.3078
12 521 6252 39087504 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1254.4869
8 1564 3128 39137536 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  106.9917
92 136 3128 39137536 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 120.9677
136 184 1564 39137536 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 756.6253
5 1253 6265 39250225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  297.8132
12 1569 2092 39388176 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1712.1051
21 897 2093 39425841 1 4 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  131.1105
69 273 2093 39425841 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 138.2891
161 273 897 39425841 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1039.2707
5 1256 6280 39438400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  221.9868
8 785 6280 39438400 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  241.1733
40 157 6280 39438400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  662.6783
40 785 1256 39438400 2 6 2 6 1 ε_{1}, ε_{2}, ε_{3}  198.7278
5 1257 6285 39501225 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  116.7821
12 1048 3144 39538944 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 185.7083
24 524 3144 39538944 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 168.0669
29 217 6293 39601849 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  542.4463
33 573 2101 39727809 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 259.8800
5 1261 6305 39753025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  294.5084

44 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 485 6305 39753025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  245.3966
65 97 6305 39753025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 1404.9732
65 485 1261 39753025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  474.0151
76 332 1577 39790864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  982.3322
8 789 6312 39841344 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  250.2564
24 789 2104 39841344 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1106.9010
8 1580 3160 39942400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  236.7187
40 316 3160 39942400 2 3 2 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  430.1741
40 632 1580 39942400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  202.1763
12 1581 2108 39992976 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  123.3674
93 204 2108 39992976 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  215.8455
124 204 1581 39992976 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  496.8998
56 113 6328 40043584 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  832.3657
17 373 6341 40208281 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  456.8734
8 793 6344 40246336 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  325.3162
13 488 6344 40246336 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  75.1038
61 104 6344 40246336 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  172.2017
104 488 793 40246336 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  259.8089
28 908 1589 40398736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  265.0878
13 489 6357 40411449 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  871.7234
5 1272 6360 40449600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  66.7058
24 265 6360 40449600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  556.9509
53 120 6360 40449600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  156.8614
120 265 1272 40449600 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  311.7673
37 172 6364 40500496 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1661.4817
5 1273 6365 40513225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  351.6112
33 193 6369 40564161 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  5269.1029
8 797 6376 40653376 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  327.6708
5 1276 6380 40704400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  117.4870
29 220 6380 40704400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  122.1104
44 145 6380 40704400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  272.3254
145 220 1276 40704400 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  1124.7779
8 1596 3192 40755456 1 8 4 8 1 ε_{1}, ε_{2}, ε_{3}  70.4825
12 1064 3192 40755456 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  103.1179
24 1064 1596 40755456 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  122.1346
28 456 3192 40755456 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 114.4416
56 456 1596 40755456 1 2 8 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  191.2556
76 168 3192 40755456 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  205.7909
152 168 1596 40755456 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  103.3897
5 1277 6385 40768225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  555.8095
77 581 913 40844881 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 665.6251
17 376 6392 40857664 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  516.3101
12 533 6396 40908816 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  72.4200
13 492 6396 40908816 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  115.1169
41 156 6396 40908816 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  285.1535
156 492 533 40908816 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  269.8495
37 173 6401 40972801 1 1 12 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  65.0227
5 1281 6405 41024025 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  174.1161
21 305 6405 41024025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  184.2907
61 105 6405 41024025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  275.8265

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 45

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
105 305 1281 41024025 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1285.3322
13 493 6409 41075281 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  409.3687
17 377 6409 41075281 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  936.3457
29 221 6409 41075281 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  323.9969
221 377 493 41075281 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  156.4652
28 229 6412 41113744 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  386.0117
12 1605 2140 41216400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  282.5495
60 321 2140 41216400 2 3 2 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  375.1252
60 428 1605 41216400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  223.3306
73 88 6424 41267776 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 2888.8199
41 157 6437 41434969 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  309.9412
5 1288 6440 41473600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  40.2592
8 805 6440 41473600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  82.9274
40 161 6440 41473600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  236.6825
40 805 1288 41473600 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  171.2598
56 805 920 41473600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  257.5266
161 280 920 41473600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  651.5573
184 280 805 41473600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  976.8420
57 113 6441 41486481 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4418.8383
5 1289 6445 41538025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  332.2272
21 921 2149 41563809 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1703.0881
8 1612 3224 41576704 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  406.0527
104 124 3224 41576704 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  605.5925
104 248 1612 41576704 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  315.5524
24 269 6456 41679936 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  633.4781
5 1292 6460 41731600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  108.2564
17 380 6460 41731600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  286.5088
76 85 6460 41731600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 404.3196
85 380 1292 41731600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  137.9375
13 497 6461 41744521 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  517.2830
5 1293 6465 41796225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  334.8849
8 809 6472 41886784 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  706.5628
17 381 6477 41951529 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  483.3972
209 341 589 41977441 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 983.7231
5 1297 6485 42055225 1 11 2 11 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  29.7262
12 541 6492 42146064 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  431.2518
73 89 6497 42211009 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 1442.3380
33 197 6501 42263001 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  368.3528
8 813 6504 42302016 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  500.5699
24 813 2168 42302016 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 306.4995
5 1301 6505 42315025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  824.7799
8 1628 3256 42406144 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  450.1338
44 296 3256 42406144 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  793.6200
88 296 1628 42406144 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  456.8443
13 501 6513 42419169 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  823.0464
5 1304 6520 42510400 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  150.4145
28 233 6524 42562576 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  670.6744
21 933 2177 42653961 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 174.1554
92 284 1633 42667024 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1878.3991
8 817 6536 42719296 1 5 2 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  203.9551

46 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
152 344 817 42719296 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 279.4844
5 1308 6540 42771600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  72.1757
12 545 6540 42771600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  269.1254
60 109 6540 42771600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  283.5754
60 545 1308 42771600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  207.3775
5 1309 6545 42837025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  369.7785
17 385 6545 42837025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1677.5796
77 85 6545 42837025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3} 317.7937
85 385 1309 42837025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1254.5472
37 177 6549 42889401 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  449.6841
57 345 2185 42968025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  3927.0547
69 285 2185 42968025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  658.1995
285 345 437 42968025 2 2 1 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  163.7742
44 149 6556 42981136 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  365.3895
12 1641 2188 43086096 1 5 1 5 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  399.2615
5 1313 6565 43099225 1 4 8 16 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  30.0986
13 505 6565 43099225 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  155.1829
65 101 6565 43099225 2 1 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  73.1656
65 505 1313 43099225 2 4 4 8 1 ε_{1}, ε_{2}, ε_{3}  583.9771
33 597 2189 43125489 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 489.7381
8 821 6568 43138624 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  545.9417
53 124 6572 43191184 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  308.7741
21 313 6573 43204329 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  466.3993
8 1644 3288 43243776 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  97.3872
12 1096 3288 43243776 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  200.8687
24 1096 1644 43243776 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  419.0419
28 940 1645 43296400 1 6 2 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  255.1473
140 188 1645 43296400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  230.5010
140 329 940 43296400 2 1 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  344.5122
5 1317 6585 43362225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  389.3125
41 161 6601 43573201 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2034.2554
93 213 2201 43599609 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 653.8871
13 508 6604 43612816 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1506.8942
5 1321 6605 43626025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  782.9187
28 472 3304 43665664 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  989.6441
56 236 3304 43665664 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 635.2375
12 1653 2204 43718544 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  186.0105
57 348 2204 43718544 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  447.1311
76 348 1653 43718544 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  340.6878
17 389 6613 43731769 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  554.0459
13 509 6617 43784689 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  530.1090
5 1324 6620 43824400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  466.5503
8 829 6632 43983424 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  345.9527
12 553 6636 44036496 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1043.0778
21 316 6636 44036496 1 3 4 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  226.1126
28 237 6636 44036496 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  341.9690
8 1660 3320 44089600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  386.5574
40 332 3320 44089600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  233.4637
40 664 1660 44089600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1390.6173
29 229 6641 44102881 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  241.8648

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 47

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
44 604 1661 44142736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  978.6436
5 1329 6645 44156025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  650.3243
24 277 6648 44195904 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  673.6280
61 109 6649 44209201 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1343.3868
21 317 6657 44315649 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  481.6807
5 1333 6665 44422225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  410.8565
12 1112 3336 44515584 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 261.3215
24 556 3336 44515584 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1007.2071
5 1336 6680 44622400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  597.5032
17 393 6681 44635761 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1272.0986
12 557 6684 44675856 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  241.2864
5 1337 6685 44689225 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  155.7658
28 956 1673 44782864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1333.0784
69 97 6693 44796249 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 895.8949
37 181 6697 44849809 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1788.1766
21 957 2233 44876601 1 2 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  106.7569
33 609 2233 44876601 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1064.2913
77 609 957 44876601 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  210.1025
8 1676 3352 44943616 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  445.8387
12 1677 2236 44997264 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  202.7943
129 156 2236 44997264 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 845.6440
156 172 1677 44997264 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  257.0273
73 92 6716 45104656 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 481.9197
13 517 6721 45171841 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1669.4725
24 281 6744 45481536 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1668.8452
5 1349 6745 45495025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  301.2084
28 241 6748 45535504 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  3312.6478
17 397 6749 45549001 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  438.0097
12 1689 2252 45643536 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  817.6759
29 233 6757 45657049 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  213.0158
76 89 6764 45751696 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 2007.4449
5 1353 6765 45765225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  114.0993
33 205 6765 45765225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  186.8428
41 165 6765 45765225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  138.1307
165 205 1353 45765225 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  351.6301
13 521 6773 45873529 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  391.1381
5 1356 6780 45968400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  307.7536
12 565 6780 45968400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  396.2795
60 113 6780 45968400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  795.6832
60 565 1356 45968400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  576.6409
21 969 2261 46009089 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  405.0225
57 357 2261 46009089 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  253.6733
133 357 969 46009089 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  518.9850
5 1357 6785 46036225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  551.0301
73 93 6789 46090521 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 786.9471
8 849 6792 46131264 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1445.8616
24 849 2264 46131264 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1557.9086
5 1361 6805 46308025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  297.1348
37 184 6808 46348864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1816.2077
13 524 6812 46403344 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  361.1435

48 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
17 401 6817 46471489 1 5 2 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  632.0393
44 620 1705 46512400 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  282.2608
124 220 1705 46512400 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  630.9694
220 341 620 46512400 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 180.9904
8 853 6824 46566976 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  372.7292
12 569 6828 46621584 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  830.3736
8 1708 3416 46676224 1 6 2 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.4694
28 488 3416 46676224 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  252.9153
56 488 1708 46676224 1 2 6 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  101.3866
53 129 6837 46744569 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  418.0258
29 236 6844 46840336 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  707.5332
12 1713 2284 46949904 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1993.5730
77 89 6853 46963609 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 505.9742
8 857 6856 47004736 1 1 12 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  176.3565
12 1144 3432 47114496 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  265.9911
24 572 3432 47114496 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  105.5597
44 312 3432 47114496 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  202.3557
88 156 3432 47114496 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  338.8995
156 264 1144 47114496 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  530.5272
264 312 572 47114496 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  144.1966
5 1373 6865 47128225 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  209.4178
29 237 6873 47238129 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  470.0823
8 861 6888 47444544 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  62.4864
21 328 6888 47444544 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  92.6990
21 984 2296 47444544 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  266.9380
24 861 2296 47444544 1 2 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  224.0635
41 168 6888 47444544 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  138.4794
56 861 984 47444544 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  569.9796
168 328 861 47444544 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  261.3666
61 113 6893 47513449 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  237.9369
8 1724 3448 47554816 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  826.5688
5 1381 6905 47679025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  467.2951
44 157 6908 47720464 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  347.8143
28 988 1729 47831056 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2142.8052
76 364 1729 47831056 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3016.2270
133 364 988 47831056 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1000.0691
5 1384 6920 47886400 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  119.6011
8 865 6920 47886400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  853.5429
40 173 6920 47886400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  222.3409
40 865 1384 47886400 2 2 6 6 1 ε_{1}, ε_{2}, ε_{3}  773.9778
161 301 989 47927929 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1165.9381
12 577 6924 47941776 1 7 4 14 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  153.1603
5 1388 6940 48163600 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  118.3080
5 1389 6945 48233025 1 1 10 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  146.2042
21 993 2317 48316401 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 249.7782
8 869 6952 48330304 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  690.8097
88 632 869 48330304 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 623.1231
17 409 6953 48344209 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  841.0336
37 188 6956 48385936 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  410.5728
8 1740 3480 48441600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  95.4758

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 49

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 1160 3480 48441600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  88.6419
24 1160 1740 48441600 1 4 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  91.8034
40 348 3480 48441600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  139.6703
40 696 1740 48441600 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  164.6114
60 232 3480 48441600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  208.2288
60 696 1160 48441600 2 2 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  116.0605
120 232 1740 48441600 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  185.4634
120 348 1160 48441600 2 2 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  87.7094
33 633 2321 48483369 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3798.6533
5 1393 6965 48511225 1 5 2 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  89.0515
13 536 6968 48553024 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  366.0396
69 101 6969 48566961 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1128.5642
12 581 6972 48608784 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  134.9011
21 332 6972 48608784 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  92.8666
28 249 6972 48608784 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  535.9272
13 537 6981 48734361 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  428.8770
5 1397 6985 48790225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  466.9833
29 241 6989 48846121 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  416.1118
76 184 3496 48888064 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 560.9095
92 152 3496 48888064 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  148.5340
12 1749 2332 48944016 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  363.2265
33 636 2332 48944016 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1004.1463
44 636 1749 48944016 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  391.0147
17 412 7004 49056016 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  608.6252
5 1401 7005 49070025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  644.5553
8 877 7016 49224256 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  617.0183
17 413 7021 49294441 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  505.4679
8 1756 3512 49336576 1 5 1 5 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  100.0338
28 1004 1757 49392784 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  302.6350
24 293 7032 49449024 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  91.9264
13 541 7033 49463089 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1623.7359
21 1005 2345 49491225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  404.7970
105 201 2345 49491225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2101.8306
105 469 1005 49491225 2 3 2 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  275.8841
12 1761 2348 49617936 1 7 1 7 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  154.9138
5 1409 7045 49632025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  368.3366
8 881 7048 49674304 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  375.5400
53 133 7049 49688401 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  168.1866
41 172 7052 49730704 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  326.1161
12 589 7068 49956624 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  312.6269
57 124 7068 49956624 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  711.0980
76 93 7068 49956624 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 304.6669
21 337 7077 50083929 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  483.8780
5 1416 7080 50126400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  179.0498
8 885 7080 50126400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  136.4276
24 885 2360 50126400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  234.7246
40 177 7080 50126400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  603.6060
40 885 1416 50126400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  523.5863
120 177 2360 50126400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  678.2452
120 472 885 50126400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  450.5654

50 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1}  d_{2}  d_{3}  d h_{1} h_{2} h_{3} h Q Fundamental units  R
73  97 7081 50140561 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  11238.4151
28 253 7084 50183056 1 1 12 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  288.3974
44 161 7084 50183056 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  416.8943
77 92 7084 50183056 1 1 12 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 116.9956
5 1417 7085 50197225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  328.9781
13 545 7085 50197225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  308.4465
65 109 7085 50197225 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  482.0431
65 545 1417 50197225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  2013.5135
8 1772 3544 50239744 1 3 1 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  346.8314
17 417 7089 50253921 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4018.9831
41 173 7093 50310649 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  257.4039
33 645 2365 50339025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  469.0113
129 165 2365 50339025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  674.7495
165 473 645 50339025 2 3 2 6 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  127.9026
69 309 2369 50509449 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1198.9420
8 889 7112 50580544 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  490.8633
56 889 1016 50580544 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  948.0017
12 593 7116 50637456 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  953.3092
12 1785 2380 50979600 1 8 4 8 1 ε_{1}, ε_{2}, ε_{3}  322.6812
21 1020 2380 50979600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  114.2111
28 1020 1785 50979600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  223.4354
60 357 2380 50979600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  255.4086
60 476 1785 50979600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  263.4090
105 204 2380 50979600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  853.8649
105 476 1020 50979600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  334.7059
140 204 1785 50979600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  265.7832
140 357 1020 50979600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  101.0199
37 193 7141 50993881 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2300.9142
8 893 7144 51036736 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  634.4825
152 376 893 51036736 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  508.7806
5 1429 7145 51051025 1 5 2 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  112.7472
8 1788 3576 51151104 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  64.1318
12 1192 3576 51151104 1 2 6 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  229.2954
24 1192 1788 51151104 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  355.2336
17 421 7157 51222649 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  329.4991
5 1432 7160 51265600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  299.5061
21 341 7161 51279921 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  475.7662
33 217 7161 51279921 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3277.1553
77 93 7161 51279921 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 397.0479
5 1433 7165 51337225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  586.5942
44 652 1793 51437584 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1894.0226
8 897 7176 51494976 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  425.8558
13 552 7176 51494976 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  184.9975
24 897 2392 51494976 1 4 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  486.2720
69 104 7176 51494976 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  253.5606
69 312 2392 51494976 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  224.4864
104 552 897 51494976 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  297.8784
184 312 897 51494976 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  713.5289
5 1436 7180 51552400 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  184.8656
5 1437 7185 51624225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  393.0973

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 51

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 1797 2396 51667344 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  525.9566
13 553 7189 51681721 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1818.5325
29 248 7192 51724864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  463.0249
28 257 7196 51782416 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  299.7553
5 1441 7205 51912025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  390.5374
8 901 7208 51955264 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  107.3603
17 424 7208 51955264 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  280.0586
53 136 7208 51955264 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  124.2155
136 424 901 51955264 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  625.4214
12 601 7212 52012944 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1131.4554
8 1804 3608 52070656 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  121.2284
44 328 3608 52070656 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  129.8528
88 328 1804 52070656 1 4 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  634.5378
29 249 7221 52142841 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  243.7579
21 344 7224 52186176 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  160.0199
21 1032 2408 52186176 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  141.3348
24 301 7224 52186176 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  236.2236
56 129 7224 52186176 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  364.1025
129 168 2408 52186176 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  490.6389
168 301 1032 52186176 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  407.8751
13 556 7228 52243984 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1501.1893
57 381 2413 52403121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 837.0187
5 1448 7240 52417600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  69.8230
8 905 7240 52417600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  462.7174
40 181 7240 52417600 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  520.2664
40 905 1448 52417600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  174.1870
13 557 7241 52432081 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  518.6985
12 1208 3624 52533504 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 134.5401
24 604 3624 52533504 1 1 6 6 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  322.2512
41 177 7257 52664049 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  3157.7661
53 137 7261 52722121 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1024.8976
5 1453 7265 52780225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  588.1127
92 316 1817 52823824 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  618.7992
17 428 7276 52940176 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1236.1292
8 1820 3640 52998400 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  100.7799
28 520 3640 52998400 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  309.0313
40 364 3640 52998400 2 2 8 16 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  172.5863
40 728 1820 52998400 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  70.3839
56 520 1820 52998400 1 4 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  156.2697
104 140 3640 52998400 2 2 8 16 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  67.5177
104 280 1820 52998400 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  139.5438
140 520 728 52998400 2 4 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  93.6211
280 364 520 52998400 2 2 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  474.4594
12 1821 2428 53056656 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  770.4998
5 1457 7285 53071225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  576.9499
21 1041 2429 53100369 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 320.1890
37 197 7289 53129521 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  371.2410
13 561 7293 53187849 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  200.5945
17 429 7293 53187849 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  126.2805
33 221 7293 53187849 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.3722

52 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
221 429 561 53187849 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  372.9704
8 913 7304 53348416 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  952.4676
88 664 913 53348416 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 4534.3858
5 1461 7305 53363025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  848.9764
77 665 1045 53509225 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  204.2686
133 385 1045 53509225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  573.4871
209 385 665 53509225 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1422.2526
124 236 1829 53523856 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1017.6101
5 1464 7320 53582400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  162.0542
24 305 7320 53582400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  368.8333
61 120 7320 53582400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  264.4800
120 305 1464 53582400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  613.0641
21 349 7329 53714241 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1790.0311
12 1833 2444 53758224 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  549.2491
141 156 2444 53758224 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  536.4490
156 188 1833 53758224 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  569.7602
8 917 7336 53816896 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  506.4972
56 917 1048 53816896 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 460.9062
29 253 7337 53831569 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  674.9721
5 1468 7340 53875600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  504.3127
5 1469 7345 53949025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  319.4887
13 565 7345 53949025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  958.4876
65 113 7345 53949025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  2854.4156
65 565 1469 53949025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  302.1238
93 237 2449 53978409 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1062.1070
44 668 1837 53993104 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  299.0413
12 613 7356 54110736 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  538.3330
33 669 2453 54154881 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 395.4311
17 433 7361 54184321 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4461.6809
28 1052 1841 54228496 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1410.3300
5 1473 7365 54243225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  406.6066
8 921 7368 54287424 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1468.2961
24 921 2456 54287424 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2260.2953
76 97 7372 54346384 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 3503.8742
73 101 7373 54361129 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  519.8706
69 321 2461 54508689 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 669.6670
13 568 7384 54523456 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  501.0151
5 1477 7385 54538225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  604.6077
13 569 7397 54715609 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  276.4995
12 617 7404 54819216 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  394.3430
5 1481 7405 54834025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  493.8049
8 1852 3704 54878464 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  1015.2257
21 353 7413 54952569 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  440.9654
5 1484 7420 55056400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  258.2669
28 265 7420 55056400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1719.2021
53 140 7420 55056400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  321.6037
140 265 1484 55056400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  757.6989
41 181 7421 55071241 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  879.2084
12 1857 2476 55175184 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  2349.4700
17 437 7429 55190041 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  410.7964

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 53

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 929 7432 55234624 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  962.2679
37 201 7437 55308969 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  517.6026
12 1240 3720 55353600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  181.5056
24 620 3720 55353600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  136.7913
60 248 3720 55353600 2 1 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  95.8796
60 744 1240 55353600 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 284.6245
120 124 3720 55353600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  238.0104
120 620 744 55353600 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 184.4755
5 1489 7445 55428025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  306.9130
13 573 7449 55487601 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  227.4610
29 257 7453 55547209 1 3 6 9 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  63.4641
21 1065 2485 55577025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  667.4457
105 213 2485 55577025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  425.5855
105 497 1065 55577025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2450.3558
8 933 7464 55711296 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  217.4036
24 933 2488 55711296 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 657.0543
5 1493 7465 55726225 1 1 18 9 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  50.5317
57 393 2489 55756089 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 5384.5647
77 97 7469 55785961 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 424.2148
8 1868 3736 55830784 1 1 3 3 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  206.4140
53 141 7473 55845729 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  299.2314
12 1869 2492 55890576 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  190.6929
21 1068 2492 55890576 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  189.3837
28 1068 1869 55890576 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  476.6923
5 1496 7480 55950400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  296.7119
17 440 7480 55950400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  547.6067
85 88 7480 55950400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 923.6535
85 440 1496 55950400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  291.1041
5 1497 7485 56025225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  551.8903
33 681 2497 56115081 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 6924.3210
8 937 7496 56190016 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1069.3873
13 577 7501 56265001 1 7 2 7 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  274.7001
28 536 3752 56310016 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  363.8410
56 268 3752 56310016 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 407.9568
5 1501 7505 56325025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  468.3715
24 313 7512 56430144 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  925.2506
69 109 7521 56565441 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1551.0984
8 941 7528 56670784 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  111.0013
28 269 7532 56731024 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  268.4724
8 1884 3768 56791296 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  358.2133
12 1256 3768 56791296 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  219.2554
24 1256 1884 56791296 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  515.5244
21 1077 2513 56836521 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 345.6744
41 184 7544 56911936 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1088.7478
5 1509 7545 56927025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  198.1646
12 629 7548 56972304 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  166.2092
17 444 7548 56972304 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  523.7414
37 204 7548 56972304 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  449.6862
204 444 629 56972304 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  378.4814
13 581 7553 57047809 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  517.4477

54 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
33 229 7557 57108249 1 3 4 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  162.6600
61 124 7564 57214096 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2464.8754
5 1513 7565 57229225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  105.3867
17 445 7565 57229225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  114.0047
85 89 7565 57229225 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 136.3101
85 445 1513 57229225 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  660.2192
161 329 1081 57259489 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 7401.2281
44 344 3784 57274624 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 956.4325
88 172 3784 57274624 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1699.3989
12 1893 2524 57335184 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  642.7764
5 1516 7580 57456400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  673.3685
5 1517 7585 57532225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  118.1100
37 205 7585 57532225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  627.9116
41 185 7585 57532225 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  1369.1407
185 205 1517 57532225 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  135.3444
28 1084 1897 57577744 1 1 5 5 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  824.7495
8 949 7592 57638464 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  309.2116
13 584 7592 57638464 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  228.6335
73 104 7592 57638464 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  598.3607
104 584 949 57638464 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  545.1474
24 317 7608 57881664 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  320.1189
129 177 2537 57927321 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2878.6618
44 173 7612 57942544 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  327.5451
12 1905 2540 58064400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  346.4426
60 381 2540 58064400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  173.7862
60 508 1905 58064400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1576.8504
8 953 7624 58125376 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  940.3752
17 449 7633 58262689 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3469.4223
92 332 1909 58308496 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  439.8876
5 1528 7640 58369600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  337.7117
5 1529 7645 58446025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  428.2657
8 957 7656 58614336 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  70.8975
24 957 2552 58614336 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  178.5701
29 264 7656 58614336 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  187.8720
33 232 7656 58614336 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  474.3625
33 696 2552 58614336 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  692.5749
88 696 957 58614336 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  327.1619
232 264 957 58614336 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  176.7324
13 589 7657 58629649 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1849.7211
5 1532 7660 58675600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  427.4525
8 1916 3832 58736896 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  523.3060
5 1533 7665 58752225 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  97.9045
21 365 7665 58752225 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  150.7408
73 105 7665 58752225 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  1102.8508
105 365 1533 58752225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  323.7639
56 137 7672 58859584 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  756.2383
76 101 7676 58920976 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  900.5052
5 1537 7685 59059225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  138.0104
29 265 7685 59059225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  172.6420
53 145 7685 59059225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  139.3162

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 55

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
145 265 1537 59059225 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  3078.3741
33 233 7689 59120721 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  3674.3188
12 641 7692 59166864 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1507.4919
17 453 7701 59305401 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  463.8835
5 1541 7705 59367025 1 1 10 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  176.6060
21 1101 2569 59397849 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 749.4177
41 188 7708 59413264 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1221.2517
13 593 7709 59428681 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  203.5310
12 1929 2572 59536656 1 3 1 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  739.3579
93 249 2573 59582961 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 594.3181
5 1544 7720 59598400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  393.2858
8 965 7720 59598400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  200.9152
40 193 7720 59598400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  1819.3594
40 965 1544 59598400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  307.7087
8 1932 3864 59721984 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  77.7193
12 1288 3864 59721984 1 4 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  198.6027
24 1288 1932 59721984 1 4 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  112.2529
28 552 3864 59721984 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  293.1467
56 552 1932 59721984 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  116.8943
92 168 3864 59721984 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  293.7776
168 184 1932 59721984 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  265.9774
37 209 7733 59799289 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  452.8668
5 1549 7745 59985025 1 1 12 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  135.5565
8 969 7752 60093504 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  249.3035
17 456 7752 60093504 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  263.9463
24 969 2584 60093504 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  503.3492
57 136 7752 60093504 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  400.8662
57 408 2584 60093504 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  388.8129
136 456 969 60093504 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1109.0953
152 408 969 60093504 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 391.0768
33 705 2585 60140025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2287.2271
141 165 2585 60140025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  613.8073
165 517 705 60140025 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  619.8055
28 277 7756 60155536 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1918.6767
13 597 7761 60233121 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  523.9696
12 1941 2588 60279696 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  586.4820
5 1553 7765 60295225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  466.1947
17 457 7769 60357361 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4323.6194
29 268 7772 60403984 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  455.3087
77 101 7777 60481729 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  823.0389
8 973 7784 60590656 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  490.3034
56 973 1112 60590656 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 417.2307
12 649 7788 60652944 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  610.7318
33 236 7788 60652944 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  349.8519
44 177 7788 60652944 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  460.8126
8 1948 3896 60715264 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  981.8161
69 113 7797 60793209 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  692.7466
29 269 7801 60855601 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1235.3040
5 1561 7805 60918025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  561.5816
57 137 7809 60980481 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  5585.4228

56 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 601 7813 61042969 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1910.8032
8 977 7816 61089856 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  662.6347
5 1564 7820 61152400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  274.9639
17 460 7820 61152400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  559.9193
85 92 7820 61152400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 296.1207
85 460 1564 61152400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1125.7686
12 1304 3912 61214976 1 3 2 6 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 105.5527
24 652 3912 61214976 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 529.5880
76 412 1957 61277584 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  518.9850
88 89 7832 61340224 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 484.6052
21 373 7833 61355889 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  307.8650
12 653 7836 61402896 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  597.6143
17 461 7837 61418569 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  295.1461
253 341 713 61512649 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 684.8369
5 1569 7845 61544025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  612.3149
133 413 1121 61575409 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 706.4099
13 604 7852 61653904 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1654.2737
8 1964 3928 61716736 1 1 5 5 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  223.7308
12 1965 2620 61779600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  271.9383
60 393 2620 61779600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1598.5057
60 524 1965 61779600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  201.0634
28 281 7868 61905424 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  688.0669
61 129 7869 61921161 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1905.7140
44 716 1969 62031376 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  3512.7893
5 1576 7880 62094400 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  139.0297
8 985 7880 62094400 1 6 4 12 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  83.3299
40 197 7880 62094400 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  85.4827
40 985 1576 62094400 2 6 2 12 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  499.5542
37 213 7881 62110161 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  189.6080
5 1577 7885 62173225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  584.9506
33 717 2629 62204769 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 763.6645
21 376 7896 62346816 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  709.5682
21 1128 2632 62346816 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  215.3511
24 329 7896 62346816 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1045.2102
56 141 7896 62346816 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  529.0707
141 168 2632 62346816 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  277.7531
168 329 1128 62346816 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 423.3621
53 149 7897 62362609 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  476.0459
5 1581 7905 62489025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  348.4076
17 465 7905 62489025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  2336.7509
85 93 7905 62489025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3} 800.3755
85 465 1581 62489025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  616.2532
12 1977 2636 62536464 1 1 3 3 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  417.1193
8 989 7912 62599744 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  660.0661
184 344 989 62599744 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1238.9370
41 193 7913 62615569 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  4366.2243
13 609 7917 62678889 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  150.2339
21 377 7917 62678889 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  86.4191
29 273 7917 62678889 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  107.6817
273 377 609 62678889 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1253.4379

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 57

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
57 417 2641 62773929 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 9755.0469
28 1132 1981 62789776 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1610.1545
77 721 1133 62900761 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 384.7039
12 661 7932 62916624 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  772.8446
8 993 7944 63107136 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  362.7048
24 993 2648 63107136 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 431.6007
5 1589 7945 63123025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  981.8766
28 568 3976 63234304 1 3 8 24 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  121.0092
56 284 3976 63234304 1 1 8 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 232.4730
33 241 7953 63250209 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  6852.0849
73 109 7957 63313849 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  775.2480
21 1137 2653 63345681 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 996.7063
5 1592 7960 63361600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  249.4991
44 181 7964 63425296 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  818.9573
13 613 7969 63504961 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2064.7299
17 469 7973 63568729 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  146.2481
8 997 7976 63616576 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  402.0934
5 1596 7980 63680400 1 8 8 16 1 ε_{1}, ε_{2}, ε_{3}  39.6921
12 665 7980 63680400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  300.9933
21 380 7980 63680400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  152.6521
28 285 7980 63680400 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  87.6058
57 140 7980 63680400 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  158.2220
60 133 7980 63680400 2 1 8 4 1 ε_{1}, ε_{2}, ε_{3}  237.8047
60 665 1596 63680400 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  311.1068
76 105 7980 63680400 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  574.4305
105 380 1596 63680400 2 2 8 16 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  141.6099
140 285 1596 63680400 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  103.4447
8 1996 3992 63744256 1 5 1 5 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  171.6936
5 1597 7985 63760225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  551.9762
12 2001 2668 64064016 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1232.7786
69 348 2668 64064016 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  496.8149
92 348 2001 64064016 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  760.2775
5 1601 8005 64080025 1 7 8 28 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  30.9023
8 1001 8008 64128064 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  869.7968
13 616 8008 64128064 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  862.7361
56 1001 1144 64128064 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1380.1617
77 104 8008 64128064 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  342.2277
77 728 1144 64128064 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  242.8021
88 728 1001 64128064 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  694.5187
104 616 1001 64128064 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1436.3334
12 1336 4008 64256256 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 848.6835
24 668 4008 64256256 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  264.5825
13 617 8021 64336441 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  335.8818
17 472 8024 64384576 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  785.0031
37 217 8029 64464841 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2051.7117
29 277 8033 64529089 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1055.3351
5 1608 8040 64641600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  80.9351
8 1005 8040 64641600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  166.2457
24 1005 2680 64641600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  559.2530
40 201 8040 64641600 2 1 8 4 1 ε_{1}, ε_{2}, ε_{3}  633.2336

58 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
40 1005 1608 64641600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  182.3882
120 201 2680 64641600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1391.2291
120 536 1005 64641600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  583.0289
17 473 8041 64657681 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1495.1252
21 1149 2681 64689849 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1209.2739
5 1609 8045 64722025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  896.1932
8 2012 4024 64770304 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  492.3350
12 2013 2684 64834704 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  200.1906
33 732 2684 64834704 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  614.9545
44 732 2013 64834704 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  268.2525
53 152 8056 64899136 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  771.8640
5 1612 8060 64963600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  181.7958
13 620 8060 64963600 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  198.6997
65 124 8060 64963600 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  596.2506
65 620 1612 64963600 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  973.0878
5 1613 8065 65044225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  518.4300
8 1009 8072 65157184 1 7 2 7 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  228.2575
12 673 8076 65221776 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  611.4189
41 197 8077 65237929 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  283.3514
172 188 2021 65351056 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  153.7186
24 337 8088 65415744 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  776.3064
8 1013 8104 65674816 1 1 14 7 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  54.1584
5 1621 8105 65691025 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  246.6904
61 133 8113 65820769 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  728.5532
5 1624 8120 65934400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  132.2723
29 280 8120 65934400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  151.4274
56 145 8120 65934400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  319.6503
145 280 1624 65934400 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  1470.7040
12 677 8124 65999376 1 1 10 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  75.0364
76 428 2033 66129424 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1125.7973
5 1628 8140 66259600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  110.6481
37 220 8140 66259600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  346.0100
44 185 8140 66259600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  394.0600
185 220 1628 66259600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  436.8506
12 2037 2716 66389904 1 2 2 4 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  208.5377
21 1164 2716 66389904 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  484.4260
28 1164 2037 66389904 1 4 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  229.6442
29 281 8149 66406201 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  776.8676
33 741 2717 66438801 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  283.3046
57 429 2717 66438801 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  382.3049
209 429 741 66438801 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  626.4870
5 1633 8165 66667225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  576.7908
8 1021 8168 66716224 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  494.2914
21 389 8169 66732561 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1311.7484
8 2044 4088 66846976 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  153.5272
28 584 4088 66846976 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 119.6754
56 584 2044 66846976 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 440.4793
13 629 8177 66863329 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  303.0314
17 481 8177 66863329 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  2387.5002
37 221 8177 66863329 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  530.5600

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 59

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
221 481 629 66863329 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  504.0235
24 341 8184 66977856 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  387.3108
33 248 8184 66977856 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  556.1790
33 744 2728 66977856 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1081.4631
88 93 8184 66977856 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 604.3392
93 264 2728 66977856 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  481.3493
264 341 744 66977856 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  526.4669
5 1637 8185 66994225 1 1 14 7 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  90.2508
89 92 8188 67043344 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3} 1237.0815
12 2049 2732 67174416 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1355.7413
28 293 8204 67305616 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  383.8575
5 1641 8205 67322025 1 5 2 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  130.3849
21 1173 2737 67420521 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  592.5945
69 357 2737 67420521 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  637.7055
161 357 1173 67420521 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  332.4459
13 632 8216 67502656 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  348.9927
5 1644 8220 67568400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  124.1693
12 685 8220 67568400 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  195.8454
60 137 8220 67568400 2 1 12 6 1 ε_{1}, ε_{2}, ε_{3}  377.4182
60 685 1644 67568400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  629.9083
13 633 8229 67716441 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  317.6313
29 284 8236 67831696 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1354.6868
77 749 1177 67881121 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 918.1979
8 2060 4120 67897600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  519.8700
40 412 4120 67897600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1336.2323
40 824 2060 67897600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  444.5164
41 201 8241 67914081 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  7204.5885
5 1649 8245 67980025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  168.5820
17 485 8245 67980025 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  144.6646
85 97 8245 67980025 2 1 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3} 375.9153
85 485 1649 67980025 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  321.0668
73 113 8249 68046001 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  3703.3941
28 1180 2065 68227600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2611.3429
140 236 2065 68227600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1070.0676
140 413 1180 68227600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  309.9327
8 1033 8264 68293696 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2067.1441
5 1653 8265 68310225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  164.6610
29 285 8265 68310225 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  219.6782
57 145 8265 68310225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  1711.5211
145 285 1653 68310225 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  261.3193
12 689 8268 68359824 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  110.4489
13 636 8268 68359824 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  147.6952
53 156 8268 68359824 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  120.6010
156 636 689 68359824 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  329.6979
44 376 4136 68425984 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 473.8375
88 188 4136 68425984 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  282.7658
89 93 8277 68508729 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 209.7695
33 753 2761 68608089 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 8231.3915
76 109 8284 68624656 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2812.3931
5 1657 8285 68641225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  193.2492

60 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
12 2073 2764 68757264 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  2750.3474
21 1185 2765 68807025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  407.9554
105 237 2765 68807025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  273.3442
105 553 1185 68807025 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  4475.6427
8 1037 8296 68823616 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  387.6192
17 488 8296 68823616 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  560.7598
61 136 8296 68823616 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1347.2674
136 488 1037 68823616 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  267.0887
8 2076 4152 68956416 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  523.0102
12 1384 4152 68956416 1 6 2 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  237.3412
24 1384 2076 68956416 1 6 2 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  412.2654
5 1661 8305 68973025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  429.8719
124 268 2077 69022864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1769.5407
17 489 8313 69105969 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  3715.4236
141 177 2773 69205761 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1851.3112
53 157 8321 69239041 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  188.0127
8 1041 8328 69355584 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1346.4247
24 1041 2776 69355584 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 4225.4098
13 641 8333 69438889 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  385.9533
21 397 8337 69505569 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  882.9503
12 2085 2780 69555600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  144.0563
60 417 2780 69555600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  869.5985
60 556 2085 69555600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  382.9269
56 149 8344 69622336 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1028.0453
5 1669 8345 69639025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  422.5571
61 137 8357 69839449 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  459.9061
5 1672 8360 69889600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  113.6923
8 1045 8360 69889600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  171.2831
40 209 8360 69889600 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  441.9290
40 1045 1672 69889600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  370.1160
88 760 1045 69889600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  631.6799
152 440 1045 69889600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  147.1563
209 440 760 69889600 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 493.9625
12 697 8364 69956496 1 6 4 12 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  192.8989
17 492 8364 69956496 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  302.4824
41 204 8364 69956496 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  503.1256
204 492 697 69956496 2 2 6 12 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  282.3084
5 1673 8365 69973225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  787.0560
8 2092 4184 70023424 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  676.0705
28 1196 2093 70090384 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  219.6879
92 364 2093 70090384 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  368.0544
161 364 1196 70090384 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1089.9989
24 349 8376 70157376 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1721.5280
5 1676 8380 70224400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  893.4712
5 1677 8385 70308225 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  177.6238
13 645 8385 70308225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  287.6801
65 129 8385 70308225 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1438.8151
65 645 1677 70308225 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  199.7519
8 1049 8392 70425664 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  821.3824
77 109 8393 70442449 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  534.4028

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 61

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
44 764 2101 70627216 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  511.1256
12 701 8412 70761744 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  295.3304
21 401 8421 70913241 1 5 2 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  238.2129
8 2108 4216 71098624 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  223.6237
124 136 4216 71098624 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1241.5848
136 248 2108 71098624 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 143.0439
12 2109 2812 71166096 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  451.0926
57 444 2812 71166096 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1067.9546
76 444 2109 71166096 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  869.1321
13 649 8437 71182969 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1962.5665
5 1688 8440 71233600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  625.6595
5 1689 8445 71318025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  716.0432
17 497 8449 71385601 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  5303.9350
8 1057 8456 71503936 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  599.2204
56 1057 1208 71503936 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2209.4514
21 1209 2821 71622369 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1060.1601
93 273 2821 71622369 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  894.0150
217 273 1209 71622369 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  4284.0289
5 1693 8465 71656225 1 1 14 7 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  70.9306
24 353 8472 71774784 1 1 6 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  454.3719
37 229 8473 71791729 1 3 8 12 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  192.5893
13 652 8476 71842576 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1496.6419
33 257 8481 71927361 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1731.9057
12 2121 2828 71978256 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  634.9610
21 1212 2828 71978256 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  227.8508
28 1212 2121 71978256 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1334.7637
5 1697 8485 71995225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  741.0145
8 1061 8488 72046144 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  740.1425
13 653 8489 72063121 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  588.1783
44 193 8492 72114064 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1682.0608
57 149 8493 72131049 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  806.5167
29 293 8497 72199009 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  477.0617
12 709 8508 72386064 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  750.3011
17 501 8517 72539289 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  493.5028
5 1704 8520 72590400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  125.3864
8 1065 8520 72590400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  359.5558
24 1065 2840 72590400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  680.8167
40 213 8520 72590400 2 1 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  168.1862
40 1065 1704 72590400 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  831.8420
120 213 2840 72590400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  207.9845
120 568 1065 72590400 2 3 2 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  661.2303
53 161 8533 72812089 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  684.4224
88 97 8536 72863296 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 1100.3748
5 1708 8540 72931600 1 6 4 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  44.6847
28 305 8540 72931600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  367.2495
61 140 8540 72931600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  174.9117
140 305 1708 72931600 2 2 6 12 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  164.4805
5 1709 8545 73017025 1 1 12 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  164.6895
21 1221 2849 73051209 1 4 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  128.6936
33 777 2849 73051209 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  539.6405

62 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
77 777 1221 73051209 1 4 4 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  94.7426
8 1069 8552 73136704 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  347.1087
12 713 8556 73205136 1 1 12 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  251.9173
69 124 8556 73205136 1 1 12 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  305.1515
92 93 8556 73205136 1 1 12 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 154.0987
8 2140 4280 73273600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  411.9518
40 428 4280 73273600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  428.7669
40 856 2140 73273600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1524.3770
5 1713 8565 73359225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  439.7231
41 209 8569 73427761 1 1 10 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1671.3150
12 2145 2860 73616400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  687.2747
33 780 2860 73616400 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  304.1698
44 780 2145 73616400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  436.2471
60 429 2860 73616400 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  244.9579
60 572 2145 73616400 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  143.3881
156 165 2860 73616400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  477.5443
156 220 2145 73616400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  443.4371
165 572 780 73616400 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  54.1483
220 429 780 73616400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  343.5911
8 1073 8584 73685056 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  538.5852
29 296 8584 73685056 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  392.7745
37 232 8584 73685056 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  705.3694
232 296 1073 73685056 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  537.8308
5 1717 8585 73702225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  195.0342
17 505 8585 73702225 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  543.2839
85 101 8585 73702225 2 1 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  232.5134
85 505 1717 73702225 2 4 2 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  376.9911
76 113 8588 73753744 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  904.6891
21 409 8589 73770921 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2020.3212
12 1432 4296 73822464 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  551.8299
24 716 4296 73822464 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  575.8841
13 661 8593 73839649 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2242.4072
28 1228 2149 73891216 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1580.7799
61 141 8601 73977201 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  877.2361
5 1721 8605 74046025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  564.2401
57 453 2869 74080449 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  959.5179
8 1077 8616 74235456 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  291.9459
24 1077 2872 74235456 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}}  598.4405
5 1724 8620 74304400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  634.2280
37 233 8621 74321641 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  716.9761
12 2157 2876 74442384 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  683.0283
13 664 8632 74511424 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1768.0630
89 97 8633 74528689 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 5380.7184
17 508 8636 74580496 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  737.0978
129 201 2881 74701449 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 13166.2878
5 1729 8645 74736025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  280.2447
13 665 8645 74736025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  221.3684
65 133 8645 74736025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  259.4009
65 665 1729 74736025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  3645.8238
8 1081 8648 74787904 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  440.5050

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 63

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
184 376 1081 74787904 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 7881.6525
12 721 8652 74857104 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  939.9991
21 412 8652 74857104 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  381.8391
28 309 8652 74857104 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  441.5767
17 509 8653 74874409 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  129.6942
5 1733 8665 75082225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  647.3767
44 197 8668 75134224 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  778.8165
33 789 2893 75325041 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1047.1892
5 1736 8680 75342400 1 4 12 12 1 ε_{1}, ε_{2}, ε_{3}  74.6006
8 1085 8680 75342400 1 2 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  43.2518
40 217 8680 75342400 2 1 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  404.7580
40 1085 1736 75342400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  140.3891
56 1085 1240 75342400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  340.9803
217 280 1240 75342400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2828.6753
248 280 1085 75342400 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  210.2561
13 668 8684 75411856 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  426.3506
8 2172 4344 75481344 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  181.0178
12 1448 4344 75481344 1 2 6 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  69.7571
24 1448 2172 75481344 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  235.3221
13 669 8697 75637809 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  861.6580
77 113 8701 75707401 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  470.2267
5 1741 8705 75777025 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  516.4301
28 1244 2177 75829264 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  447.4787
21 1245 2905 75951225 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  697.5020
105 249 2905 75951225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  5930.2948
105 581 1245 75951225 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  427.9426
12 2181 2908 76108176 1 1 5 5 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  229.0713
29 301 8729 76195441 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1386.9274
37 236 8732 76247824 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  507.2173
41 213 8733 76265289 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  527.4749
76 460 2185 76387600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  3253.1695
92 380 2185 76387600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1219.1669
380 437 460 76387600 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  204.6256
8 1093 8744 76457536 1 5 2 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  146.8435
5 1749 8745 76475025 1 2 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  75.3782
33 265 8745 76475025 1 2 12 12 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  680.5002
53 165 8745 76475025 1 2 12 12 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  95.0793
165 265 1749 76475025 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  398.8857
13 673 8749 76545001 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2306.6757
8 2188 4376 76597504 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  1116.6876
44 796 2189 76667536 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1009.1381
5 1752 8760 76737600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  128.8733
24 365 8760 76737600 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  141.9504
73 120 8760 76737600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  497.5683
120 365 1752 76737600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  232.0857
69 381 2921 76790169 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1312.7985
28 313 8764 76807696 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  4626.3801
5 1753 8765 76825225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  820.3458
37 237 8769 76895361 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  317.0121
12 2193 2924 76947984 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  475.9184

64 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
129 204 2924 76947984 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  699.6257
172 204 2193 76947984 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1010.5001
8 1097 8776 77018176 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1486.1350
5 1756 8780 77088400 1 5 2 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  116.5901
5 1757 8785 77176225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  473.8196
17 517 8789 77246521 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  256.9876
56 157 8792 77299264 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  665.4746
12 733 8796 77369616 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  242.6126
21 1257 2933 77422401 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 228.3526
13 677 8801 77457601 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  242.6629
124 284 2201 77510416 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  3212.8144
5 1761 8805 77528025 1 7 2 7 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  125.0792
8 1101 8808 77580864 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  217.3002
24 1101 2936 77580864 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 227.8965
8 2204 4408 77721856 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  290.4624
76 232 4408 77721856 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1044.4002
152 232 2204 77721856 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  442.7654
57 465 2945 78057225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1031.3902
93 285 2945 78057225 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  165.9750
285 465 589 78057225 2 2 1 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 448.4126
5 1768 8840 78145600 1 8 8 16 1 ε_{1}, ε_{2}, ε_{3}  32.6922
8 1105 8840 78145600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  175.4006
13 680 8840 78145600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  70.7757
17 520 8840 78145600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  180.3031
40 221 8840 78145600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  89.3472
40 1105 1768 78145600 2 4 8 32 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  148.8767
65 136 8840 78145600 2 2 8 8 1 ε_{1}, ε_{2}, ε_{3}  214.3628
65 680 1768 78145600 2 4 8 16 1 ε_{1}, ε_{2}, ε_{3}  135.3258
85 104 8840 78145600 2 2 8 16 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  46.4244
85 520 1768 78145600 2 4 8 16 1 ε_{1}, ε_{2}, ε_{3}  156.4688
104 680 1105 78145600 2 4 4 16 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  165.0784
136 520 1105 78145600 2 4 4 8 1 ε_{1}, ε_{2}, ε_{3}  881.3342
221 520 680 78145600 2 4 4 8 1 ε_{1}, ε_{2}, ε_{3}  166.9537
21 421 8841 78163281 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1269.8564
12 737 8844 78216336 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  443.1037
33 268 8844 78216336 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  738.3894
44 201 8844 78216336 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  695.7184
5 1769 8845 78234025 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  252.4184
29 305 8845 78234025 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  307.7593
61 145 8845 78234025 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  632.3096
145 305 1769 78234025 4 2 2 4 1 ε_{1}, ε_{2}, ε_{3}  1693.0036
28 632 4424 78287104 1 1 4 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  246.3112
56 316 4424 78287104 1 3 4 12 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 159.1214
13 681 8853 78375609 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  937.8912
77 805 1265 78411025 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  411.2423
161 385 1265 78411025 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  3167.4011
253 385 805 78411025 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1332.8615
17 521 8857 78446449 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  5263.7823
5 1772 8860 78499600 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  207.2399
12 2217 2956 78641424 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  2247.7699

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 65

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 1109 8872 78712384 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  413.0140
28 317 8876 78783376 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  554.1410
33 269 8877 78801129 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  506.2119
8 2220 4440 78854400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  239.6545
12 1480 4440 78854400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  283.2407
24 1480 2220 78854400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  487.2646
40 444 4440 78854400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  192.4420
40 888 2220 78854400 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  169.8275
60 296 4440 78854400 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  152.4611
60 888 1480 78854400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  304.8506
120 296 2220 78854400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  225.5620
120 444 1480 78854400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  511.0764
5 1777 8885 78943225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  404.9656
88 101 8888 78996544 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  354.5458
41 217 8897 79156609 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  4008.8700
8 1113 8904 79281216 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  459.0368
21 424 8904 79281216 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  518.1558
21 1272 2968 79281216 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  337.6596
24 1113 2968 79281216 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1303.2875
53 168 8904 79281216 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  235.5323
56 1113 1272 79281216 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  516.5254
168 424 1113 79281216 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  828.7164
5 1781 8905 79299025 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  125.3582
13 685 8905 79299025 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  385.6886
65 137 8905 79299025 2 1 12 6 1 ε_{1}, ε_{2}, ε_{3}  1102.3982
65 685 1781 79299025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  394.1890
17 524 8908 79352464 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1701.8186
133 469 1273 79405921 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 869.9667
12 2229 2972 79495056 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  317.0115
37 241 8917 79512889 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1939.8588
5 1784 8920 79566400 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  219.6661
92 97 8924 79637776 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3} 1407.7166
28 1276 2233 79780624 1 2 6 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  937.8158
44 812 2233 79780624 1 2 6 6 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  281.3699
77 812 1276 79780624 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  353.1554
8 1117 8936 79852096 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  805.5226
5 1788 8940 79923600 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  76.8966
12 745 8940 79923600 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  630.7725
60 149 8940 79923600 2 1 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  238.2241
60 745 1788 79923600 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  400.5245
33 813 2981 79977249 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 179.8282
8 2236 4472 79995136 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  330.4043
104 172 4472 79995136 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  369.9086
104 344 2236 79995136 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  953.5807
5 1789 8945 80013025 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  363.2289
57 157 8949 80084601 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  377.1253
24 373 8952 80138304 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  555.8989
29 309 8961 80299521 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1865.7364
5 1793 8965 80371225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  669.2736
8 1121 8968 80425024 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2194.2616

66 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
152 472 1121 80425024 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1912.8353
12 1496 4488 80568576 1 2 8 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  113.7080
24 748 4488 80568576 1 2 8 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  182.3599
44 408 4488 80568576 1 2 8 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  155.6394
88 204 4488 80568576 1 2 8 8 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  269.5886
204 264 1496 80568576 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 197.5738
264 408 748 80568576 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 209.8254
5 1797 8985 80730225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  721.4553
209 473 817 80766169 1 3 5 15 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 385.4960
12 749 8988 80784144 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  262.6268
21 428 8988 80784144 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  249.5439
28 321 8988 80784144 1 3 4 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  353.5905
89 101 8989 80802121 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1235.9088
5 1801 9005 81090025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  500.1539
8 2252 4504 81144064 1 1 5 5 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  126.2253
12 2253 3004 81216144 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1160.0494
5 1804 9020 81360400 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  156.8801
41 220 9020 81360400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  382.9426
44 205 9020 81360400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  200.0128
205 220 1804 81360400 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  715.0681
93 97 9021 81378441 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}} 285.8567
8 1129 9032 81577024 1 9 4 18 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  114.3478
69 393 3013 81703521 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1277.0499
28 1292 2261 81793936 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  149.7961
76 476 2261 81793936 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  241.2149
133 476 1292 81793936 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  202.3754
13 696 9048 81866304 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  232.0683
24 377 9048 81866304 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  343.1344
29 312 9048 81866304 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  187.1356
312 377 696 81866304 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  456.9011
21 1293 3017 81920601 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 495.3237
73 124 9052 81938704 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1513.6624
12 2265 3020 82083600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  566.4480
60 453 3020 82083600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  160.8815
60 604 2265 82083600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2502.0959
13 697 9061 82101721 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  352.8559
17 533 9061 82101721 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  348.0864
41 221 9061 82101721 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  595.5749
221 533 697 82101721 2 2 6 6 1 ε_{1}, ε_{2}, ε_{3}  189.1845
8 1133 9064 82156096 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  351.0842
88 824 1133 82156096 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 322.3516
29 313 9077 82391929 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  614.4674
5 1816 9080 82446400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  901.8279
12 757 9084 82519056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1145.1648
5 1817 9085 82537225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  460.0389
61 149 9089 82609921 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  607.4973
21 433 9093 82682649 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1076.2643
8 1137 9096 82737216 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1205.1201
24 1137 3032 82737216 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1313.0807
5 1821 9105 82901025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  778.5437

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 67

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
17 536 9112 83028544 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  907.4695
13 701 9113 83046769 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  708.5778
53 172 9116 83101456 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  925.9702
8 1141 9128 83320384 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  583.2521
56 1141 1304 83320384 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 461.7262
17 537 9129 83338641 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  5573.5525
12 761 9132 83393424 1 3 2 3 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  367.0510
8 2284 4568 83466496 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  889.4712
33 277 9141 83557881 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  861.0331
5 1829 9145 83631025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  590.0125
12 2289 3052 83832336 1 4 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  864.6624
21 1308 3052 83832336 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 200.6527
28 1308 2289 83832336 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  523.5096
129 213 3053 83887281 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 364.7638
5 1832 9160 83905600 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  94.2897
8 1145 9160 83905600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  503.7183
40 229 9160 83905600 2 3 4 12 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  180.1118
40 1145 1832 83905600 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  305.4437
29 316 9164 83978896 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  547.4430
5 1833 9165 83997225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  314.9790
13 705 9165 83997225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  640.5516
65 141 9165 83997225 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  597.6029
65 705 1833 83997225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  2316.0810
12 1528 4584 84052224 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 550.0004
24 764 4584 84052224 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  603.0143
53 173 9169 84070561 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  759.1640
37 248 9176 84198976 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  378.4173
21 437 9177 84217329 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  226.2279
57 161 9177 84217329 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2728.3559
69 133 9177 84217329 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  786.8791
5 1837 9185 84364225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  637.2801
8 1149 9192 84492864 1 1 6 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  213.1492
24 1149 3064 84492864 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1780.6716
29 317 9193 84511249 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  973.1433
17 541 9197 84584809 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  585.1674
12 2301 3068 84713616 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}}, ε_{3}  233.5194
156 177 3068 84713616 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1013.6783
156 236 2301 84713616 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  437.5793
5 1841 9205 84732025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1126.6475
37 249 9213 84879369 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  781.5587
13 709 9217 84953089 1 1 18 9 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  218.7539
21 1317 3073 84989961 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1436.6481
8 1153 9224 85082176 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  592.7613
12 769 9228 85155984 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  804.3622
5 1848 9240 85377600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  62.9157
21 440 9240 85377600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  171.8700
21 1320 3080 85377600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  91.1578
24 385 9240 85377600 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  409.2384
33 280 9240 85377600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  698.7715
33 840 3080 85377600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  167.9461

68 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
56 165 9240 85377600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  255.3925
77 120 9240 85377600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  99.0412
77 840 1320 85377600 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  191.0405
88 105 9240 85377600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  773.0153
105 264 3080 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  463.5236
105 440 1848 85377600 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  146.7022
105 616 1320 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  1011.6627
120 385 1848 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  669.4262
165 168 3080 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  180.0945
165 280 1848 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  283.5241
165 616 840 85377600 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  221.4981
168 385 1320 85377600 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  426.5773
264 385 840 85377600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  961.5315
8 1157 9256 85673536 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  406.8263
13 712 9256 85673536 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1054.8793
89 104 9256 85673536 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1747.3189
104 712 1157 85673536 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  315.0432
5 1852 9260 85747600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  631.3522
8 2316 4632 85821696 1 4 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  90.7600
12 1544 4632 85821696 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 125.6434
24 1544 2316 85821696 1 2 4 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 187.6426
5 1853 9265 85840225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  302.1912
17 545 9265 85840225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  2893.4459
85 109 9265 85840225 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  2052.3416
85 545 1853 85840225 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  275.0725
28 1324 2317 85895824 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1866.3587
13 713 9269 85914361 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  675.7528
61 152 9272 85969984 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  487.6126
33 281 9273 85988529 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4916.3036
12 773 9276 86044176 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  489.3696
44 844 2321 86192656 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  3899.9740
5 1857 9285 86211225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  697.7937
57 489 3097 86322681 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 8149.3777
92 101 9292 86341264 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  577.6302
28 664 4648 86415616 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1071.1305
56 332 4648 86415616 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 305.6551
21 1329 3101 86545809 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 949.5944
5 1861 9305 86583025 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  221.0170
13 716 9308 86638864 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  636.5810
29 321 9309 86657481 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  388.9337
5 1864 9320 86862400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  390.0439
8 1165 9320 86862400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  250.9432
40 233 9320 86862400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  741.5763
40 1165 1864 86862400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1164.9472
13 717 9321 86881041 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  186.4136
8 2332 4664 87011584 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  616.0345
44 424 4664 87011584 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1130.0689
88 424 2332 87011584 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1787.7797
217 301 1333 87067561 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1809.2451
24 389 9336 87160896 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  773.3090

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 69

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
33 849 3113 87216921 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 4292.4484
5 1868 9340 87235600 1 1 10 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  130.4131
5 1869 9345 87329025 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  108.6491
21 445 9345 87329025 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  212.2700
89 105 9345 87329025 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  676.7707
105 445 1869 87329025 2 4 2 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  272.6830
12 2337 3116 87385104 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  939.8403
57 492 3116 87385104 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1065.7583
76 492 2337 87385104 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1347.0569
8 1169 9352 87459904 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  834.6204
56 1169 1336 87459904 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 3704.0227
37 253 9361 87628321 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  3499.6805
5 1873 9365 87703225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  717.0648
12 781 9372 87834384 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  491.4727
33 284 9372 87834384 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  675.1494
44 213 9372 87834384 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  255.9710
13 721 9373 87853129 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2169.7844
28 1340 2345 87984400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  676.8981
140 268 2345 87984400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  980.7961
140 469 1340 87984400 2 3 2 6 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  146.8039
53 177 9381 88003161 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1015.7914
8 1173 9384 88059456 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  181.5714
17 552 9384 88059456 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  349.2754
24 1173 3128 88059456 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  189.3165
69 136 9384 88059456 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  501.6323
69 408 3128 88059456 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  251.2620
136 552 1173 88059456 2 2 2 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  216.6747
184 408 1173 88059456 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  643.1608
5 1877 9385 88078225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  463.3739
41 229 9389 88153321 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  369.0897
8 2348 4696 88209664 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  767.9614
93 101 9393 88228449 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  677.8140
17 553 9401 88378801 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  4615.9179
8 1177 9416 88661056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2473.7309
88 856 1177 88661056 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 7417.5752
73 129 9417 88679889 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  7495.7061
5 1884 9420 88736400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  364.0552
12 785 9420 88736400 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  242.0907
60 157 9420 88736400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  505.1617
60 785 1884 88736400 2 6 2 6 1 ε_{1}, ε_{2}, ε_{3}  550.4938
76 248 4712 88811776 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 329.4926
124 152 4712 88811776 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  403.4262
21 449 9429 88906041 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1266.6958
28 337 9436 89038096 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2790.2848
133 497 1349 89170249 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 732.8335
12 2361 3148 89189136 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  2023.7284
5 1889 9445 89208025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  788.6990
141 201 3149 89245809 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1360.3499
8 1181 9448 89264704 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  112.0613
17 556 9452 89340304 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1697.5091

70 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
69 137 9453 89359209 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  655.4784
8 2364 4728 89415936 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  399.1391
12 1576 4728 89415936 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  961.2796
24 1576 2364 89415936 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1193.9746
44 860 2365 89491600 1 2 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  338.9403
172 220 2365 89491600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1159.6411
220 473 860 89491600 2 3 2 6 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  239.3764
5 1893 9465 89586225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  581.0849
17 557 9469 89661961 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  692.8557
21 1353 3157 89699841 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  626.0445
33 861 3157 89699841 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  580.5854
77 861 1353 89699841 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  553.5346
92 412 2369 89794576 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  2204.1335
5 1896 9480 89870400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  198.0249
8 1185 9480 89870400 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  513.9597
24 1185 3160 89870400 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1948.2118
40 237 9480 89870400 2 1 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  252.6268
40 1185 1896 89870400 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  853.1636
120 237 3160 89870400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  625.4078
120 632 1185 89870400 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1086.7026
5 1897 9485 89965225 1 5 2 5 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  145.2589
12 2373 3164 90098064 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  93.8420
21 1356 3164 90098064 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  233.2794
28 1356 2373 90098064 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  196.7539
161 413 1357 90231001 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 566.9981
5 1901 9505 90345025 1 3 14 21 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  60.3808
37 257 9509 90421081 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  202.1992
8 1189 9512 90478144 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  132.6890
29 328 9512 90478144 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  70.6668
41 232 9512 90478144 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  326.1093
232 328 1189 90478144 2 4 2 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  310.7348
12 793 9516 90554256 1 4 8 16 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  197.7868
13 732 9516 90554256 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  135.9738
61 156 9516 90554256 1 2 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  237.0468
156 732 793 90554256 2 2 4 16 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 244.4354
57 501 3173 90611361 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 300.2003
8 2380 4760 90630400 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  91.3656
28 680 4760 90630400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  177.8650
40 476 4760 90630400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  196.4222
40 952 2380 90630400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  769.5470
56 680 2380 90630400 1 4 4 4 1 ε_{1}, ε_{2}, ε_{3}  466.3399
136 140 4760 90630400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  103.7352
136 280 2380 90630400 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  555.8131
140 680 952 90630400 2 4 2 4 1 ε_{1}, ε_{2}, ε_{3}  324.9263
280 476 680 90630400 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  444.3680
24 397 9528 90782784 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1062.4993
13 733 9529 90801841 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  759.7704
29 329 9541 91030681 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1712.9148
8 1193 9544 91087936 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1280.0722
5 1909 9545 91107025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1037.6027

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 71

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
28 341 9548 91164304 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  203.2930
44 217 9548 91164304 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  619.6089
77 124 9548 91164304 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  228.7395
12 1592 4776 91240704 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 215.5248
24 796 4776 91240704 1 1 2 2 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1359.0091
41 233 9553 91259809 1 1 10 5 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1034.5025
5 1912 9560 91393600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  386.9194
12 797 9564 91470096 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  625.7427
5 1913 9565 91489225 1 1 6 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  178.0873
61 157 9577 91718929 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2754.7410
93 309 3193 91757241 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2240.8317
5 1916 9580 91776400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  702.5426
13 737 9581 91795561 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  653.9631
8 2396 4792 91853056 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  1402.9546
12 2397 3196 91929744 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  69.1120
141 204 3196 91929744 1 2 8 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  325.8535
188 204 2397 91929744 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  81.7920
69 417 3197 91987281 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 773.0825
88 109 9592 92006464 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2600.4584
53 181 9593 92025649 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1015.6455
21 457 9597 92102409 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  687.8715
5 1921 9605 92256025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  331.1253
17 565 9605 92256025 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  253.5560
85 113 9605 92256025 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  342.7148
85 565 1921 92256025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1651.3829
8 1201 9608 92313664 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  441.0114
24 401 9624 92621376 1 5 2 5 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  482.7475
29 332 9628 92698384 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  394.7773
12 2409 3212 92852496 1 2 2 4 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  407.7429
33 876 3212 92852496 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  366.4767
44 876 2409 92852496 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  966.9543
5 1928 9640 92929600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  77.1751
8 1205 9640 92929600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  112.9685
40 241 9640 92929600 2 1 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  796.4958
40 1205 1928 92929600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  137.3094
5 1929 9645 93026025 1 3 2 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  323.3221
76 508 2413 93161104 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1802.0246
17 568 9656 93238336 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  616.6097
5 1932 9660 93315600 1 4 8 8 1 ε_{1}, ε_{2}, ε_{3}  47.5855
12 805 9660 93315600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  250.4748
21 460 9660 93315600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  316.1052
28 345 9660 93315600 1 2 8 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  344.1436
60 161 9660 93315600 2 1 8 4 1 ε_{1}, ε_{2}, ε_{3}  542.8891
60 805 1932 93315600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  227.2647
69 140 9660 93315600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  104.1752
92 105 9660 93315600 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  445.7821
105 460 1932 93315600 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  257.4172
140 345 1932 93315600 2 2 4 4 1 ε_{1}, ε_{2}, ε_{3}  356.7225
5 1933 9665 93412225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  487.9185
33 293 9669 93489561 1 1 10 5 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  123.5117

72 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
8 1209 9672 93547584 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  770.7697
13 744 9672 93547584 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  541.5545
24 1209 3224 93547584 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  1388.8307
93 104 9672 93547584 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  366.9158
93 312 3224 93547584 1 2 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  512.6047
104 744 1209 93547584 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1650.1287
248 312 1209 93547584 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  836.8159
17 569 9673 93566929 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2996.0678
41 236 9676 93624976 1 1 12 6 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  503.1405
21 461 9681 93721761 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1285.2326
5 1937 9685 93799225 1 6 4 6 1 ε_{1}, ε_{2}, ε_{3}  135.5725
13 745 9685 93799225 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  1282.1946
65 149 9685 93799225 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  718.2225
65 745 1937 93799225 2 2 6 6 1 ε_{1}, ε_{2}, ε_{3}  848.1147
56 173 9688 93857344 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  586.2132
89 109 9701 94109401 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1024.4863
8 1213 9704 94167616 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  665.4085
5 1941 9705 94187025 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  999.6681
12 809 9708 94245264 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1418.0841
73 133 9709 94264681 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  2317.0337
8 2428 4856 94322944 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  762.2898
28 1388 2429 94400656 1 1 3 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  227.5522
41 237 9717 94420089 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  475.7920
21 1389 3241 94536729 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 2061.8781
13 748 9724 94556176 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  517.3201
17 572 9724 94556176 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  354.7495
44 221 9724 94556176 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  431.4711
221 572 748 94556176 2 2 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  139.4746
12 2433 3244 94711824 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  2588.8348
33 885 3245 94770225 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  169.3805
165 177 3245 94770225 2 1 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  242.8007
165 649 885 94770225 2 1 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 494.9979
8 1217 9736 94789696 1 1 8 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  335.8623
13 749 9737 94809169 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  761.8840
5 1948 9740 94867600 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  613.0679
17 573 9741 94887081 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  691.6898
12 1624 4872 94945536 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  320.7008
24 812 4872 94945536 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  142.1911
28 696 4872 94945536 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  289.1031
56 348 4872 94945536 1 2 4 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  179.2306
168 348 1624 94945536 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 243.7310
168 696 812 94945536 2 2 2 8 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 122.9757
5 1949 9745 94965025 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  306.8830
53 184 9752 95101504 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  625.4073
8 1221 9768 95413824 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  44.3510
24 1221 3256 95413824 1 4 2 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  485.0148
33 296 9768 95413824 1 2 4 4 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  241.4069
33 888 3256 95413824 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 649.0674
37 264 9768 95413824 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  171.7018
88 888 1221 95413824 1 2 4 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  242.0474

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 73

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
264 296 1221 95413824 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  154.1393
28 349 9772 95491984 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2034.7486
29 337 9773 95511529 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  1032.1422
8 2444 4888 95570176 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  699.6214
104 188 4888 95570176 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  641.0780
104 376 2444 95570176 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  922.9931
77 889 1397 95628841 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 787.8415
12 2445 3260 95648400 1 2 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  352.8767
60 489 3260 95648400 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1224.3436
60 652 2445 95648400 2 1 2 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  815.6438
5 1957 9785 95746225 1 3 2 3 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  196.6100
13 753 9789 95824521 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  524.8754
124 316 2449 95961616 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  2956.5697
97 101 9797 95981209 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  256.9220
12 817 9804 96118416 1 5 8 20 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  163.0397
57 172 9804 96118416 1 1 8 4 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  957.8290
76 129 9804 96118416 1 1 8 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1151.9628
5 1961 9805 96138025 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  204.3975
37 265 9805 96138025 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  430.7408
53 185 9805 96138025 1 2 12 6 1 ε_{1}, ε_{2}, ε_{3}  177.5045
185 265 1961 96138025 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  4270.6479
21 1401 3269 96177249 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 1241.1066
17 577 9809 96216481 1 7 2 7 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  788.1915
44 892 2453 96275344 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  149.4584
24 409 9816 96353856 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  2383.0570
5 1964 9820 96432400 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  663.6812
61 161 9821 96452041 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1224.5983
209 517 893 96491329 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 820.6893
8 1229 9832 96668224 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  267.7925
8 2460 4920 96825600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  66.9582
12 1640 4920 96825600 1 4 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  92.3219
24 1640 2460 96825600 1 4 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  128.6045
40 492 4920 96825600 2 2 4 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  137.7405
40 984 2460 96825600 2 2 4 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  242.3717
60 328 4920 96825600 2 4 4 8 1 ε_{1}, ε_{2}, ε_{3}  164.5355
60 984 1640 96825600 2 2 4 8 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  253.7824
120 328 2460 96825600 2 4 4 8 1 ε_{1}, ε_{2}, ε_{3}  197.1103
120 492 1640 96825600 2 2 4 8 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  172.7789
13 757 9841 96845281 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1336.3134
92 428 2461 96904336 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1004.7792
5 1969 9845 96924025 1 1 4 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  481.4106
12 821 9852 97061904 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  370.5248
57 173 9861 97239321 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  559.8610
5 1973 9865 97318225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  975.7668
33 897 3289 97357689 1 4 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  2410.2198
69 429 3289 97357689 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 711.0742
253 429 897 97357689 1 2 4 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  531.1885
12 2469 3292 97535376 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1445.6085
17 581 9877 97555129 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  781.1182
5 1976 9880 97614400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  352.3900

74 REAL BIQUADRATIC BICYCLIC NUMBER FIELDS

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
13 760 9880 97614400 1 2 4 2 1 ε_{1}, ε_{2}, ε_{3}  849.9588
65 152 9880 97614400 2 1 4 2 1 ε_{1}, ε_{2}, ε_{3}  735.8545
65 760 1976 97614400 2 2 2 2 1 ε_{1}, ε_{2}, ε_{3}  1525.7392
41 241 9881 97634161 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  4656.3811
28 353 9884 97693456 1 1 2 1 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1447.4176
5 1977 9885 97713225 1 1 2 1 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  640.0070
29 341 9889 97792321 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1520.4664
13 761 9893 97871449 1 3 2 3 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  245.9046
8 1237 9896 97930816 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  620.8275
8 2476 4952 98089216 1 1 1 1 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  526.6818
5 1981 9905 98109025 1 1 6 3 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  433.8435
21 472 9912 98247744 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  457.5910
21 1416 3304 98247744 1 2 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1105.5196
24 413 9912 98247744 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  206.4991
56 177 9912 98247744 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  874.3449
168 177 3304 98247744 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  2049.9100
168 413 1416 98247744 2 1 2 2 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  352.1791
37 268 9916 98327056 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  3298.1211
12 2481 3308 98485776 1 1 1 1 4 \sqrt{ε_{1}ε_{3}}, \sqrt{ε_{2}}, ε_{3}  1000.8593
8 1241 9928 98565184 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  553.9524
17 584 9928 98565184 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  413.9013
73 136 9928 98565184 1 2 8 4 1 ε_{1}, ε_{2}, ε_{3}  1135.0671
136 584 1241 98565184 2 2 2 4 2 \sqrt{ε_{1}ε_{2}}, ε_{2}, ε_{3}  868.8211
13 764 9932 98644624 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  408.0436
21 473 9933 98664489 1 3 4 6 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  92.1549
33 301 9933 98664489 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  437.8453
77 129 9933 98664489 1 1 4 2 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  259.6674
28 1420 2485 98803600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  901.3877
140 284 2485 98803600 2 1 2 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  493.5430
140 497 1420 98803600 2 1 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  1053.0519
88 113 9944 98883136 1 1 4 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1418.5113
12 829 9948 98962704 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1420.5495
93 321 3317 99022401 1 3 1 3 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 174.8080
37 269 9953 99062209 1 1 8 4 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  206.6085
76 524 2489 99121936 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  2984.6260
5 1992 9960 99201600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  85.0231
8 1245 9960 99201600 1 2 8 8 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  67.0661
24 1245 3320 99201600 1 2 2 2 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  317.9522
40 249 9960 99201600 2 1 8 8 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  418.2992
40 1245 1992 99201600 2 2 2 4 2 ε_{1}, \sqrt{ε_{2}ε_{3}}, ε_{3}  256.3257
120 249 3320 99201600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  1295.1573
120 664 1245 99201600 2 1 2 2 2 \sqrt{ε_{1}ε_{3}}, ε_{2}, ε_{3}  747.0200
53 188 9964 99281296 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  750.1562
5 1993 9965 99301225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  700.2426
8 2492 4984 99361024 1 2 2 4 4 ε_{1}, \sqrt{ε_{2}}, \sqrt{ε_{3}}  216.2791
28 712 4984 99361024 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 769.1894
56 712 2492 99361024 1 2 2 4 4 \sqrt{ε_{1}ε_{2}}, \sqrt{ε_{2}ε_{3}}, \sqrt{ε_{3}ε_{1}} 195.6556
29 344 9976 99520576 1 1 2 1 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  1532.2554
5 1996 9980 99600400 1 5 6 15 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  66.5805
5 1997 9985 99700225 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  558.1499

REAL BIQUADRATIC BICYCLIC NUMBER FIELDS 75

Continued

d_{1} d_{2} d_{3} d h_{1} h_{2} h_{3} h Q Fundamental units R
44 908 2497 99760144 1 1 1 1 4 \sqrt{ε_{1}ε_{2}}, ε_{2}, \sqrt{ε_{3}}  1078.2301
8 1249 9992 99840064 1 1 4 2 2 ε_{1}, ε_{2}, \sqrt{ε_{3}}  769.7216
13 769 9997 99940009 1 1 2 1 2 \sqrt{ε_{1}ε_{2}ε_{3}}, ε_{2}, ε_{3}  2324.1902