Table

d Cl_{+}(K) K_{1,nar} K_{2,nar} l_{w} Γ
5 {1} K  0 {1}
8 {1} K  0 {1}
12 C_{2} K(\sqrt{−3}) 1 C_{2}
13 {1} K  0 {1}
17 {1} K  0 {1}
21  C_{2} K(\sqrt{−3})  1 C_{2}
24  C_{2} K(\sqrt{−3})  1 C_{2}
28  C_{2} K(\sqrt{−1})  1 C_{2}
29 {1} K  0 {1}
33 C_{2} K(\sqrt{−3}) 1 C_{2}
37 {1} K  0 {1}
40 C_{2} K(\sqrt{5}) 1 C_{2}
41 {1} K  0 {1}
44 C_{2} K(\sqrt{−11}) 1 C_{2}
53 {1} K  0 {1}
56  C_{2} K(\sqrt{−7})  1 C_{2}
57  C_{2} K(\sqrt{−3})  1 C_{2}
60  V_{4} K(ζ_{12})  1 V_{4}
61 {1} K  0 {1}
65  C_{2} K(\sqrt{5})  1 C_{2}
69  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{1}) 2 D_{3}
73 {1} K  0 {1}
76  C_{2} K(\sqrt{−1})  1 C_{2}
77  C_{2} K(\sqrt{−7})  1 C_{2}
85  C_{2} K(\sqrt{5})  1 C_{2}
88  C_{2} K(\sqrt{−2})  1 C_{2}
89 {1} K  0 {1}
92  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{1}) 2 D_{3}
93  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{2}) 2 D_{3}
97 {1} K  0 {1}
101 {1} K  0 {1}
104  C_{2} K(\sqrt{2})  1 C_{2}
105  V_{4} K(\sqrt{−3}, \sqrt{5})  1 V_{4}
109 {1} K  0 {1}
113 {1} K  0 {1}
120  V_{4} K(\sqrt{−3}, \sqrt{5})  1 V_{4}
124  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{2}) 2 D_{3}
129  C_{2} K(\sqrt{−3})  1 C_{2}
133  C_{2} K(\sqrt{−7})  1 C_{2}
136  C_{4} K(\sqrt{−(5 + 2\sqrt{2})})  1 C_{4}

Continued

d Cl_{+}(K) K_{1,nar} K_{2,nar} l_{w} Γ
137 {1} K  0 {1}
140  V_{4} K(\sqrt{−1}, \sqrt{5})  1 V_{4}
141  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{1})  2 D_{5}
145  C_{4} K(\sqrt{7 + 2\sqrt{5}})  1 C_{4}
149 {1} K  0 {1}
152  C_{2} K(\sqrt{−2})  1 C_{2}
156  V_{4} K(ζ_{12})  K_{1,nar}(\sqrt{(−1 + \sqrt{13})/2}) 2 D_{4}
157 {1} K  0 {1}
161  C_{2} K(\sqrt{−7})  K_{1,nar}(α_{1})  2 D_{3}
165  V_{4} K(\sqrt{−3}, \sqrt{5})  K_{1,nar}(\sqrt{3 + 2\sqrt{5}})  2 D_{4}
168  V_{4} K(\sqrt{−3}, \sqrt{2})  K_{1,nar}(\sqrt{−1 + 2\sqrt{2}})  2 D_{4}
172  C_{2} K(\sqrt{−1})  1 C_{2}
173 {1} K  0 {1}
177 C_{2} K(\sqrt{−3}) K_{1,nar}(α_{4}) 2 D_{3}
181 {1} K  0 {1}
184  C_{2} K(\sqrt{−2})  K_{1,nar}(α_{1})  2 D_{3}
185  C_{2} K(\sqrt{5})  1 C_{2}
188  C_{2} K(\sqrt{−1})  K_{1,nar}(γ_{1})  2 D_{5}
193 {1} K  0 {1}
197 {1} K  0 {1}
201  C_{2} K(\sqrt{−3})  1 C_{2}
204  V_{4} K(ζ_{12})  K_{1,nar}(\sqrt{(1 + \sqrt{17})/2})  2 D_{4}
205  C_{4} K(\sqrt{−(13 + \sqrt{5})/2})  1 C_{4}
209  C_{2} K(\sqrt{−11})  1 C_{2}
213  C_{2} K(\sqrt{−3})  KQ(\sqrt{−71})_{1}  2 D_{7}
217  C_{2} K(\sqrt{−7})  K_{1,nar}(α_{2})  2 D_{3}
220  V_{4} K(\sqrt{−1}, \sqrt{5})  K_{1,nar}(\sqrt{3 + 2\sqrt{5}})  2 D_{4}
221  C_{4} K(\sqrt{−(9 + \sqrt{13})/2})  1 C_{4}
229  C_{3} K(a_{2})  2 A_{4}
232  C_{2} K(\sqrt{2})  1 C_{2}
233 {1} K  0 {1}
236  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{4})  2 D_{3}
237  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{2})  2 D_{5}
241 {1} K  0 {1}
248  C_{2} K(\sqrt{−2})  K_{1,nar}(α_{2})  2 D_{3}
249  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{6})  2 D_{3}
253  C_{2} K(\sqrt{−11})  K_{1,nar}(α_{1})  2 D_{3}
257  C_{3} K(a_{3})  2 A_{4}
264  V_{4} K(\sqrt{2}, \sqrt{−3})  1 V_{4}
265  C_{2} K(\sqrt{5})  1 C_{2}

Continued

d Cl_{+}(K)  K_{1,nar}  K_{2,nar}  l_{w}  Γ
268  C_{2} K(\sqrt{−1})  1  C_{2}
269 {1} K  0 {1}
273 V_{4} K(\sqrt{−3}, \sqrt{−7}) K_{1,nar}(\sqrt{(−1 + \sqrt{13})/2}) 2 D_{4}
277 {1} K  0 {1}
280 V_{4} K(\sqrt{5}, \sqrt{−7}) 1 V_{4}
281 {1} K  0 {1}
284  C_{2} K(\sqrt{−1})  KQ(\sqrt{−71})_{1}  2 D_{7}
285  V_{4} K(\sqrt{−3}, \sqrt{5})  KQ(\sqrt{−95})_{1}  2 D_{8}
293 {1} K  0 {1}
296  C_{2} K(\sqrt{2})  1  C_{2}
301  C_{2} K  1  C_{2}
305  C_{4} K(\sqrt{−(7 + 3\sqrt{5})/2})  1  C_{4}
309  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{3})  2 D_{5}
312  V_{4} K(\sqrt{−2}, \sqrt{−3})  K_{1,nar}(α_{8}, \sqrt{(−1 + \sqrt{13})/2}) 2 D_{12}
313 {1} K  0 {1}
316 C_{6} K(\sqrt{−1}, a_{4}) K_{1,nar}(γ_{2}) 2 D_{5} × C_{3}
317 {1} K  0 {1}
321  C_{6} K(\sqrt{−3}, a_{5})  K_{1,nar}(α_{9})  2 D_{3} × C_{3}
328  C_{4} K(\sqrt{7 + 2\sqrt{2}})  1  C_{4}
329  C_{2} K(\sqrt{−7})  K_{1,nar}(γ_{1})  2 D_{5}
332  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{6})  3  S_{4}
337 {1} K  0 {1}
341  C_{2} K(\sqrt{−11})  K_{1,nar}(α_{2})  3  S_{4}
344  C_{2} K(\sqrt{−2})  1  C_{2}
345  V_{4} K(\sqrt{−3}, \sqrt{5})  K_{1,nar}(α_{1})  2 D_{6}
348  V_{4} K(ζ_{12})  K_{1,nar}(α_{11}, \sqrt[3]{(5 + \sqrt{29})/2})) 2 D_{3} × D_{3}
349 {1} K  0 {1}
353 {1} K  0 {1}
357  V_{4} K(\sqrt{−3}, \sqrt{−7})  K_{1,nar}(γ_{4})  2 D_{10}
364  V_{4} K(\sqrt{−1}, \sqrt{−7})  1  V_{4}
365  C_{2} K(\sqrt{5})  1  C_{2}
373 {1} K  0 {1}
376  C_{2} K(\sqrt{−2})  K_{1,nar}(γ_{1})  2 D_{5}
377  C_{4} K(\sqrt{−(9 + 2\sqrt{13})})  1  C_{4}
380  V_{4} K(\sqrt{−1}, \sqrt{5})  KQ(\sqrt{−95})_{1}  2 D_{8}
381  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{5})  2 D_{5}
385  V_{4} K(\sqrt{5}, \sqrt{−7})  K_{1,nar}(\sqrt{3 + 2\sqrt{5}})  2 D_{4}
389 {1} K  0 {1}
393 C_{2} K(\sqrt{−3}) K_{1,nar}(γ_{6}) 2 D_{5}
397 {1} K  0 {1}

Continued

d Cl_{+}(K)  K_{1,nar}  K_{2,nar}  l_{w}  Γ
401  C_{5}  1  C_{5}
408  V_{4} K(\sqrt{−2}, \sqrt{−3}) K_{1,nar}(\sqrt{(3 + \sqrt{17})/2})  2  D_{4}
409 {1} K  0  {1}
412  C_{2} K(\sqrt{−1})  K_{1,nar}(γ_{3})  2  D_{5}
413  C_{2} K(\sqrt{−7})  K_{1,nar}(α_{4})  2  D_{3}
417  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{13})  2  D_{3}
421 {1} K  0  {1}
424  C_{2} K(\sqrt{2})  1  C_{2}
428  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{9})  2  D_{3}
429  V_{4} K(\sqrt{−3}, \sqrt{−11}) K_{1,nar}(γ_{7}, \sqrt{(−1 + \sqrt{13})/2}) 2 D_{4} ⋏ D_{5}
433 {1} K  0  {1}
437  C_{2} K(\sqrt{−19})  K_{1,nar}(α_{1})  3  S_{4}
440  V_{4} K(\sqrt{−2}, \sqrt{5})  K_{1,nar}(\sqrt{3 + 2\sqrt{5}})  2  D_{4}
444  V_{4} K(ζ_{12})  KQ(\sqrt{−111})_{1}  2  D_{8}
445  C_{4} K(\sqrt{13 + 4\sqrt{5}})  1  C_{4}
449 {1} K  0  {1}
453  C_{2} K(\sqrt{−3})  KQ(\sqrt{−151})_{1}  2  D_{7}
456  V_{4} K(\sqrt{2}, \sqrt{−3})  K_{1,nar}(α_{15})  2  D_{6}
457 {1} K  0  {1}
460  V_{4} K(\sqrt{−1}, \sqrt{5})  K_{1,nar}(α_{1})  2  D_{6}
461 {1} K  0  {1}
465  V_{4} K(\sqrt{−3}, \sqrt{5})  K_{1,nar}(α_{3}, \sqrt{(−1 + 5\sqrt{5})/2})) 2 D_{4} ⋏ D_{6}
469  C_{6} K(\sqrt{−7}, a_{7})  1  C_{6}
472  C_{2} K(\sqrt{−2})  K_{1,nar}(α_{4})  3  S_{4}
473  C_{6} K(\sqrt{−11}, a_{8})  1  C_{6}
476  V_{4} K(\sqrt{−1}, \sqrt{−7}) K_{1,nar}(γ_{4}, \sqrt{(1 + \sqrt{17})/2})  2 D_{4} ⋏ D_{10}
481  C_{2} K(\sqrt{13})  1  C_{2}
485  C_{2} K(\sqrt{5})  1  C_{2}
488  C_{2} K(\sqrt{2})  1  C_{2}
489  C_{2} K(\sqrt{−3})  1  C_{2}
492  V_{4} K(ζ_{12})  KQ(\sqrt{−41})_{1}  2  D_{8}
493  C_{2} K(\sqrt{17})  1  C_{2}
497  C_{2} K(\sqrt{−7})  KQ(\sqrt{−71})_{1}  2  D_{7}
501  C_{2} K(\sqrt{−3})  KQ(\sqrt{−167})_{1}  2 D_{11}
505  C_{8}  1  C_{8}
508  C_{2} K(\sqrt{−1})  K_{1,nar}(γ_{5})  2  D_{5}
509 {1} K  0  {1}
517  C_{2} K(\sqrt{−11})  K_{1,nar}(γ_{1})  2  D_{5}
520  V_{4} K(\sqrt{2}, \sqrt{5})  K(\sqrt{(1 + \sqrt{2})(3\sqrt{2} + \sqrt{5})})  2  Q_{8}
521 {1} K  0  {1}

Continued

d Cl_{+}(K)  K_{1,nar}  K_{2,nar}  l_{w}  Γ
524  C_{2} K(\sqrt{−1})  K_{1,nar}(γ_{6})  2 D_{5}
533  C_{2} K(\sqrt{13})  1  C_{2}
536  C_{2} K(\sqrt{−2})  1  C_{2}
537  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{9})  2 D_{5}
541 {1} K  0 {1}
545  C_{4} K(\sqrt{−(21 + \sqrt{5})/2})  1  C_{4}
552  V_{4} K(\sqrt{2}, \sqrt{−3})  K_{1,nar}(\sqrt{−3 + 4\sqrt{2}})  2 Q_{12}
553  C_{2} K(\sqrt{−7})  K_{1,nar}(γ_{2})  2 D_{5}
556  C_{2} K(\sqrt{−1})  K_{1,nar}(α_{13})  2 D_{3}
557 {1} K  0 {1}
561  V_{4} K(\sqrt{−3}, \sqrt{−11})  1  V_{4}
565  C_{2} K(\sqrt{5})  1  C_{2}
568  C_{6} K(\sqrt{−2}, a_{10})  KQ(\sqrt{−71})_{1}  2 D_{7} × C_{3}
569 {1} K  0 {1}
572  V_{4} K(\sqrt{−1}, \sqrt{−11})  K_{1,nar}(γ_{7})  2 D_{10}
573  C_{2} K(\sqrt{−3})  KQ(\sqrt{−191})_{1}  2 D_{13}
577  C_{7}  1  C_{7}
581  C_{2} K(\sqrt{−7})  K_{1,nar}(α_{6})  2 D_{3}
584  C_{4} K(\sqrt{−(9 + 2\sqrt{2})})  1  C_{4}
589  C_{2} K(\sqrt{−19})  K_{1,nar}(α_{2})  2 D_{3}
593 {1} K  0 {1}
597 C_{2} K(\sqrt{−3}) KQ(\sqrt{−199})_{1} 3 S_{4} ⋏ D_{9}
601 {1} K  0 {1}
604  C_{2} K(\sqrt{−1})  KQ(\sqrt{−151})_{1}  2 D_{7}
609  V_{4} K(\sqrt{−3}, \sqrt{−7})  K_{1,nar}(α_{7}, \sqrt{(−1 + \sqrt{29})/2}) 2 D_{4} ⋏ D_{6}
613 {1} K  0 {1}
616 V_{4} K(\sqrt{2}, \sqrt{−7}) K_{1,nar}(\sqrt{−1 + 2\sqrt{2}}) 2 D_{4}
617 {1} K  0 {1}
620  V_{4} K(\sqrt{−1}, \sqrt{5})  K_{1,nar}(α_{2}, \sqrt{(−1 + 5\sqrt{5})/2}) 2 D_{4} ⋏ D_{6}
629  C_{2} K(\sqrt{17})  1  C_{2}
632  C_{2} K(\sqrt{−2})  K_{1,nar}(γ_{2})  2 D_{5}
633  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{21})  2 D_{3}
636  V_{4} K(ζ_{12})  K_{1,nar}(α_{22}, γ_{8})  2 D_{5} × D_{3}
641 {1} K  0 {1}?
645  V_{4} K(\sqrt{−3}, \sqrt{5})  KQ(\sqrt{−215})_{1}  2 D_{14}
649  C_{2} K(\sqrt{−11})  K_{1,nar}(α_{4})  2 D_{3}
652  C_{2} K(\sqrt{−1})  1  C_{2}
653 {1} K  0 A_{5}
661 {1} K  0 {1}?
664  C_{2} K(\sqrt{−2})  K_{1,nar}(α_{6})  2 D_{3}

Continued

d Cl_{+}(K)  K_{1,nar}  K_{2,nar}  l_{w}  Γ
665  V_{4}  K(\sqrt{5}, \sqrt{−7})  KQ(\sqrt{−95})_{1}  2  D_{8}
668  C_{2} K(\sqrt{−1})  KQ(\sqrt{−167})_{1}  2  D_{11}
669  C_{2} K(\sqrt{−3})  KQ(\sqrt{−223})_{1}  2  D_{7}
673  {1} K  0  {1}?
677  {1} K  0  {1}?
680  V_{4}  K(\sqrt{2}, \sqrt{5})  K_{1,nar}(\sqrt{−(5 + 2\sqrt{2})})  2  D_{4}
681  C_{2} K(\sqrt{−3})  K_{1,nar}(γ_{10})  2  D_{5}
685  C_{2} K(\sqrt{5})  1  C_{2}
689  C_{8}  1  C_{8}
696  V_{4}  K(\sqrt{−2}, \sqrt{−3})  K_{1,nar}(\sqrt[3]{(5 + \sqrt{29})/2}))  2  D_{6}
697  C_{6} K(\sqrt{17}, a_{12})  2  A_{4} × C_{2}
701  {1} K  0  {1}?
705  V_{4}  K(\sqrt{−3}, \sqrt{5})  K_{1,nar}(γ_{1})  2  D_{10}
709  {1} K  0  {1}?
712  C_{4} K(\sqrt{−(11 + 4\sqrt{2})})  1  C_{4}
713  C_{2} K(\sqrt{−23})  K_{1,nar}(α_{1}, α_{2})  2  D_{3} ⋏ D_{3}
716  C_{2} K(\sqrt{−1})  K_{1,nar}(γ_{9})  2  D_{5}
717  C_{2} K(\sqrt{−3})  K_{1,nar}(α_{25}, γ_{11})  3  S_{4} ⋏ D_{5}
721  C_{2} K(\sqrt{−7})  K_{1,nar}(γ_{3})  2  D_{5}
728  V_{4}  K(\sqrt{−2}, \sqrt{−7})  K_{1,nar}(α_{8})  2  D_{6}
732  V_{4}  K(\sqrt{−1}, \sqrt{−3})  K_{1,nar}(α_{27})Q(\sqrt{−183})_{1}  2  D_{8} ⋏ D_{6}
733  C_{3} K(a_{13})  1  C_{3}
737  C_{2} K(\sqrt{−11})  1  C_{2}
741  V_{4}  K(\sqrt{−3}, \sqrt{13})  K_{1,nar}(α_{4}, \sqrt{(−1 + \sqrt{13})/2})  2  D_{4} ⋏ D_{6}
744  V_{4}  K(\sqrt{2}, \sqrt{−3})  KQ(\sqrt{−62})_{2}  2  D_{8} ⋉ C_{3}
745  C_{4} K(\sqrt{−(13 + 2\sqrt{5})})  1  C_{4}
748  V_{4}  K(\sqrt{−1}, \sqrt{−11})  K_{1,nar}(\sqrt{(1 + \sqrt{17})/2})  2  D_{4}
749  C_{2} K(\sqrt{−7})  K_{1,nar}(α_{9})  4  S̃_{4}
753  C_{2} K(\sqrt{−3})  KQ(\sqrt{−251})_{1}  2  D_{7}
757  {1} K  0  {1}?
760  V_{4}  K(\sqrt{−2}, \sqrt{5})  KQ(\sqrt{−95})_{1}  2  D_{8}
761  C_{3} K(a_{15})  2  A_{4}
764  C_{2} K(\sqrt{−1})  KQ(\sqrt{−191})_{1}  2  D_{13}
769  {1} K  0  {1}?
773  {1} K  0  {1}?
776  C_{4} K(\sqrt{−(13 + 6\sqrt{2})})  ≧ 2  C_{4} ⋉ C_{3}^{2}?
777 C_{4} × C_{2} K(\sqrt{−3}, \sqrt{(11 + \sqrt{37})/2})  2 (C_{4} × C_{2}) ⋉ C_{8}
780  C_{2}^{3} K(\sqrt{−1}, \sqrt{−3}, \sqrt{5})  2  C_{2}^{3} ⋉ C_{4}^{2}
781  C_{2} K(\sqrt{−11})  KQ(\sqrt{−71})_{1}  2  D_{7}
785  C_{6} K(\sqrt{5}, a_{16})  1  C_{6}

Continued

d Cl_{+}(K) K_{1,nar} K_{2,nar} l_{w} Γ
789  C_{2} K(\sqrt{−3}) KQ(\sqrt{−263})_{1} 2 D_{13}
793 C_{8} 1 C_{8}
796  C_{2} K(\sqrt{−1}) KQ(\sqrt{−199})_{1} 2 D_{9}
797 {1} K  0 {1}?