Ima­gi­nä­r­qua­dra­ti­sche Zahl­kör­per mit klei­nem Ex­po­nen­ten

Hier sind Listen mit imaginärquadratischen Körpern mit Klassengruppenexponent bis 8. Für Exponent 1 ist die Liste vollständig. Für die Exponenten 2,4,8 sind die Listen vollständig, vorausgesetzt, es gibt keine Siegel-Nullstellen. Ohne diese Annahme könnte ein Körper fehlen. Für die Exponenten 3 und 5 sind die Listen unter der Annahme der verallgemeinerten Riemann-Vermutung vollständig. Ohne diese Annahme ist bekannt, dass es endlich viele Körper mit Exponent 3 oder 5 gibt. Für Exponent 6 ist die Liste bis zur Diskriminante 3.1·1020. vollständig. Es ist bekannt, dass es mit Exponent 6 endlich viele Körper gibt. Für Exponent 7 ist die Liste bis zur Diskriminante 3.1·1020. vollständig. Es ist nicht bekannt, ob es nur endlich viele Körper mit Exponent 7 gibt. Unter der Annahme der verallgemeinerten Riemann-Vermutung konergiert der Exponent nach unendlich, daher gibt es dann nur endlich viele Körper mit gegebenem Exponenten.

Der wissenschaftliche Inhalt steht in der Arbeit:

A.-S. Elsenhans, J. Klüners, F. Nicolae, Imaginary quadratic number fields with class groups of small exponent , Acta Arith., 193, 2020, 217-233.

Die folgende Tabelle enthält alle Körper mit Exponent 1.

Diskriminante Faktorisierung Klassengruppe
-3 -3 C1
-4 -2^2 C1
-7 -7 C1
-8 -2^3 C1
-11 -11 C1
-19 -19 C1
-43 -43 C1
-67 -67 C1
-163 -163 C1

Die folgende Tabelle ist vollständig, sofern es keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung könnte ein Körper fehlen.

Diskriminante Faktorisierung Klassengruppe
-15 -3 * 5 C2
-20 -2^2 * 5 C2
-24 -2^3 * 3 C2
-35 -5 * 7 C2
-40 -2^3 * 5 C2
-51 -3 * 17 C2
-52 -2^2 * 13 C2
-84 -2^2 * 3 * 7 C2 x C2
-88 -2^3 * 11 C2
-91 -7 * 13 C2
-115 -5 * 23 C2
-120 -2^3 * 3 * 5 C2 x C2
-123 -3 * 41 C2
-132 -2^2 * 3 * 11 C2 x C2
-148 -2^2 * 37 C2
-168 -2^3 * 3 * 7 C2 x C2
-187 -11 * 17 C2
-195 -3 * 5 * 13 C2 x C2
-228 -2^2 * 3 * 19 C2 x C2
-232 -2^3 * 29 C2
-235 -5 * 47 C2
-267 -3 * 89 C2
-280 -2^3 * 5 * 7 C2 x C2
-312 -2^3 * 3 * 13 C2 x C2
-340 -2^2 * 5 * 17 C2 x C2
-372 -2^2 * 3 * 31 C2 x C2
-403 -13 * 31 C2
-408 -2^3 * 3 * 17 C2 x C2
-420 -2^2 * 3 * 5 * 7 C2 x C2 x C2
-427 -7 * 61 C2
-435 -3 * 5 * 29 C2 x C2
-483 -3 * 7 * 23 C2 x C2
-520 -2^3 * 5 * 13 C2 x C2
-532 -2^2 * 7 * 19 C2 x C2
-555 -3 * 5 * 37 C2 x C2
-595 -5 * 7 * 17 C2 x C2
-627 -3 * 11 * 19 C2 x C2
-660 -2^2 * 3 * 5 * 11 C2 x C2 x C2
-708 -2^2 * 3 * 59 C2 x C2
-715 -5 * 11 * 13 C2 x C2
-760 -2^3 * 5 * 19 C2 x C2
-795 -3 * 5 * 53 C2 x C2
-840 -2^3 * 3 * 5 * 7 C2 x C2 x C2
-1012 -2^2 * 11 * 23 C2 x C2
-1092 -2^2 * 3 * 7 * 13 C2 x C2 x C2
-1155 -3 * 5 * 7 * 11 C2 x C2 x C2
-1320 -2^3 * 3 * 5 * 11 C2 x C2 x C2
-1380 -2^2 * 3 * 5 * 23 C2 x C2 x C2
-1428 -2^2 * 3 * 7 * 17 C2 x C2 x C2
-1435 -5 * 7 * 41 C2 x C2
-1540 -2^2 * 5 * 7 * 11 C2 x C2 x C2
-1848 -2^3 * 3 * 7 * 11 C2 x C2 x C2
-1995 -3 * 5 * 7 * 19 C2 x C2 x C2
-3003 -3 * 7 * 11 * 13 C2 x C2 x C2
-3315 -3 * 5 * 13 * 17 C2 x C2 x C2
-5460 -2^2 * 3 * 5 * 7 * 13 C2 x C2 x C2 x C2

Die folgende Tabelle ist vollständig unter der Annahme, dass die verallgemeinerte Riemann-Vermutung wahr ist. Ohne Vermutung ist bekannt, dass die Liste endlich ist.

Diskriminante Faktorisierung Klassengruppe
-23 -23 C3
-31 -31 C3
-59 -59 C3
-83 -83 C3
-107 -107 C3
-139 -139 C3
-211 -211 C3
-283 -283 C3
-307 -307 C3
-331 -331 C3
-379 -379 C3
-499 -499 C3
-547 -547 C3
-643 -643 C3
-883 -883 C3
-907 -907 C3
-4027 -4027 C3 x C3

Die folgende Tabelle ist vollständig, sofern keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung könnte ein Köper fehlen.

Diskriminante Faktorisierung Klassengruppe
-39 -3 * 13 C4
-55 -5 * 11 C4
-56 -2^3 * 7 C4
-68 -2^2 * 17 C4
-136 -2^3 * 17 C4
-155 -5 * 31 C4
-184 -2^3 * 23 C4
-203 -7 * 29 C4
-219 -3 * 73 C4
-259 -7 * 37 C4
-260 -2^2 * 5 * 13 C2 x C4
-264 -2^3 * 3 * 11 C2 x C4
-276 -2^2 * 3 * 23 C2 x C4
-291 -3 * 97 C4
-292 -2^2 * 73 C4
-308 -2^2 * 7 * 11 C2 x C4
-323 -17 * 19 C4
-328 -2^3 * 41 C4
-355 -5 * 71 C4
-388 -2^2 * 97 C4
-456 -2^3 * 3 * 19 C2 x C4
-552 -2^3 * 3 * 23 C2 x C4
-564 -2^2 * 3 * 47 C2 x C4
-568 -2^3 * 71 C4
-580 -2^2 * 5 * 29 C2 x C4
-616 -2^3 * 7 * 11 C2 x C4
-651 -3 * 7 * 31 C2 x C4
-667 -23 * 29 C4
-723 -3 * 241 C4
-763 -7 * 109 C4
-772 -2^2 * 193 C4
-820 -2^2 * 5 * 41 C2 x C4
-852 -2^2 * 3 * 71 C2 x C4
-868 -2^2 * 7 * 31 C2 x C4
-915 -3 * 5 * 61 C2 x C4
-952 -2^3 * 7 * 17 C2 x C4
-955 -5 * 191 C4
-987 -3 * 7 * 47 C2 x C4
-1003 -17 * 59 C4
-1027 -13 * 79 C4
-1032 -2^3 * 3 * 43 C2 x C4
-1060 -2^2 * 5 * 53 C2 x C4
-1128 -2^3 * 3 * 47 C2 x C4
-1131 -3 * 13 * 29 C2 x C4
-1140 -2^2 * 3 * 5 * 19 C2 x C2 x C4
-1204 -2^2 * 7 * 43 C2 x C4
-1227 -3 * 409 C4
-1240 -2^3 * 5 * 31 C2 x C4
-1243 -11 * 113 C4
-1288 -2^3 * 7 * 23 C2 x C4
-1387 -19 * 73 C4
-1411 -17 * 83 C4
-1443 -3 * 13 * 37 C2 x C4
-1507 -11 * 137 C4
-1555 -5 * 311 C4
-1560 -2^3 * 3 * 5 * 13 C2 x C2 x C4
-1635 -3 * 5 * 109 C2 x C4
-1659 -3 * 7 * 79 C2 x C4
-1672 -2^3 * 11 * 19 C2 x C4
-1716 -2^2 * 3 * 11 * 13 C2 x C2 x C4
-1752 -2^3 * 3 * 73 C2 x C4
-1768 -2^3 * 13 * 17 C2 x C4
-1771 -7 * 11 * 23 C2 x C4
-1780 -2^2 * 5 * 89 C2 x C4
-1860 -2^2 * 3 * 5 * 31 C2 x C2 x C4
-1947 -3 * 11 * 59 C2 x C4
-1992 -2^3 * 3 * 83 C2 x C4
-2020 -2^2 * 5 * 101 C2 x C4
-2035 -5 * 11 * 37 C2 x C4
-2040 -2^3 * 3 * 5 * 17 C2 x C2 x C4
-2067 -3 * 13 * 53 C2 x C4
-2139 -3 * 23 * 31 C2 x C4
-2163 -3 * 7 * 103 C2 x C4
-2212 -2^2 * 7 * 79 C2 x C4
-2244 -2^2 * 3 * 11 * 17 C2 x C2 x C4
-2280 -2^3 * 3 * 5 * 19 C2 x C2 x C4
-2379 -3 * 13 * 61 C4 x C4
-2392 -2^3 * 13 * 23 C2 x C4
-2436 -2^2 * 3 * 7 * 29 C2 x C2 x C4
-2451 -3 * 19 * 43 C2 x C4
-2580 -2^2 * 3 * 5 * 43 C2 x C2 x C4
-2632 -2^3 * 7 * 47 C2 x C4
-2667 -3 * 7 * 127 C2 x C4
-2715 -3 * 5 * 181 C2 x C4
-2755 -5 * 19 * 29 C2 x C4
-2760 -2^3 * 3 * 5 * 23 C2 x C2 x C4
-2788 -2^2 * 17 * 41 C2 x C4
-2968 -2^3 * 7 * 53 C2 x C4
-3108 -2^2 * 3 * 7 * 37 C2 x C2 x C4
-3172 -2^2 * 13 * 61 C2 x C4
-3192 -2^3 * 3 * 7 * 19 C2 x C2 x C4
-3220 -2^2 * 5 * 7 * 23 C2 x C2 x C4
-3243 -3 * 23 * 47 C2 x C4
-3355 -5 * 11 * 61 C2 x C4
-3432 -2^3 * 3 * 11 * 13 C2 x C2 x C4
-3480 -2^3 * 3 * 5 * 29 C2 x C2 x C4
-3507 -3 * 7 * 167 C2 x C4
-3588 -2^2 * 3 * 13 * 23 C2 x C2 x C4
-3640 -2^3 * 5 * 7 * 13 C2 x C2 x C4
-3795 -3 * 5 * 11 * 23 C2 x C2 x C4
-3828 -2^2 * 3 * 11 * 29 C2 x C2 x C4
-4020 -2^2 * 3 * 5 * 67 C2 x C2 x C4
-4123 -7 * 19 * 31 C2 x C4
-4180 -2^2 * 5 * 11 * 19 C2 x C2 x C4
-4260 -2^2 * 3 * 5 * 71 C2 x C2 x C4
-4323 -3 * 11 * 131 C2 x C4
-4420 -2^2 * 5 * 13 * 17 C2 x C2 x C4
-4440 -2^3 * 3 * 5 * 37 C2 x C2 x C4
-4452 -2^2 * 3 * 7 * 53 C2 x C2 x C4
-4488 -2^3 * 3 * 11 * 17 C2 x C2 x C4
-4515 -3 * 5 * 7 * 43 C2 x C2 x C4
-4740 -2^2 * 3 * 5 * 79 C2 x C2 x C4
-5083 -13 * 17 * 23 C2 x C4
-5115 -3 * 5 * 11 * 31 C2 x C2 x C4
-5160 -2^3 * 3 * 5 * 43 C2 x C2 x C4
-5187 -3 * 7 * 13 * 19 C2 x C2 x C4
-5208 -2^3 * 3 * 7 * 31 C2 x C2 x C4
-5412 -2^2 * 3 * 11 * 41 C2 x C2 x C4
-5467 -7 * 11 * 71 C2 x C4
-6052 -2^2 * 17 * 89 C4 x C4
-6123 -3 * 13 * 157 C4 x C4
-6195 -3 * 5 * 7 * 59 C2 x C2 x C4
-6307 -7 * 17 * 53 C2 x C4
-6328 -2^3 * 7 * 113 C4 x C4
-6355 -5 * 31 * 41 C4 x C4
-6360 -2^3 * 3 * 5 * 53 C2 x C4 x C4
-6420 -2^2 * 3 * 5 * 107 C2 x C2 x C4
-6580 -2^2 * 5 * 7 * 47 C2 x C2 x C4
-6612 -2^2 * 3 * 19 * 29 C2 x C2 x C4
-6708 -2^2 * 3 * 13 * 43 C2 x C2 x C4
-6820 -2^2 * 5 * 11 * 31 C2 x C2 x C4
-7035 -3 * 5 * 7 * 67 C2 x C2 x C4
-7140 -2^2 * 3 * 5 * 7 * 17 C2 x C2 x C2 x C4
-7315 -5 * 7 * 11 * 19 C2 x C2 x C4
-7395 -3 * 5 * 17 * 29 C2 x C2 x C4
-7480 -2^3 * 5 * 11 * 17 C2 x C2 x C4
-7540 -2^2 * 5 * 13 * 29 C2 x C2 x C4
-7672 -2^3 * 7 * 137 C4 x C4
-7755 -3 * 5 * 11 * 47 C2 x C2 x C4
-7995 -3 * 5 * 13 * 41 C2 x C2 x C4
-8008 -2^3 * 7 * 11 * 13 C2 x C2 x C4
-8052 -2^2 * 3 * 11 * 61 C2 x C2 x C4
-8547 -3 * 7 * 11 * 37 C2 x C2 x C4
-8580 -2^2 * 3 * 5 * 11 * 13 C2 x C2 x C2 x C4
-8680 -2^3 * 5 * 7 * 31 C2 x C2 x C4
-8715 -3 * 5 * 7 * 83 C2 x C2 x C4
-8835 -3 * 5 * 19 * 31 C2 x C2 x C4
-8932 -2^2 * 7 * 11 * 29 C2 x C2 x C4
-9240 -2^3 * 3 * 5 * 7 * 11 C2 x C2 x C2 x C4
-9595 -5 * 19 * 101 C4 x C4
-9867 -3 * 11 * 13 * 23 C2 x C2 x C4
-9955 -5 * 11 * 181 C4 x C4
-10168 -2^3 * 31 * 41 C4 x C4
-10803 -3 * 13 * 277 C4 x C4
-10920 -2^3 * 3 * 5 * 7 * 13 C2 x C2 x C2 x C4
-10948 -2^2 * 7 * 17 * 23 C2 x C2 x C4
-11067 -3 * 7 * 17 * 31 C2 x C2 x C4
-11715 -3 * 5 * 11 * 71 C2 x C2 x C4
-12180 -2^2 * 3 * 5 * 7 * 29 C2 x C2 x C2 x C4
-12595 -5 * 11 * 229 C4 x C4
-13195 -5 * 7 * 13 * 29 C2 x C2 x C4
-14008 -2^3 * 17 * 103 C4 x C4
-14155 -5 * 19 * 149 C4 x C4
-14280 -2^3 * 3 * 5 * 7 * 17 C2 x C2 x C2 x C4
-14547 -3 * 13 * 373 C4 x C4
-14763 -3 * 7 * 19 * 37 C2 x C2 x C4
-14820 -2^2 * 3 * 5 * 13 * 19 C2 x C2 x C2 x C4
-16555 -5 * 7 * 11 * 43 C2 x C2 x C4
-17220 -2^2 * 3 * 5 * 7 * 41 C2 x C2 x C2 x C4
-17427 -3 * 37 * 157 C4 x C4
-19240 -2^3 * 5 * 13 * 37 C2 x C4 x C4
-19320 -2^3 * 3 * 5 * 7 * 23 C2 x C2 x C2 x C4
-19380 -2^2 * 3 * 5 * 17 * 19 C2 x C2 x C2 x C4
-19635 -3 * 5 * 7 * 11 * 17 C2 x C2 x C2 x C4
-19947 -3 * 61 * 109 C4 x C4
-20020 -2^2 * 5 * 7 * 11 * 13 C2 x C2 x C2 x C4
-20148 -2^2 * 3 * 23 * 73 C2 x C4 x C4
-20155 -5 * 29 * 139 C4 x C4
-23640 -2^3 * 3 * 5 * 197 C2 x C4 x C4
-25608 -2^3 * 3 * 11 * 97 C2 x C4 x C4
-30340 -2^2 * 5 * 37 * 41 C2 x C4 x C4
-31395 -3 * 5 * 7 * 13 * 23 C2 x C2 x C2 x C4
-33915 -3 * 5 * 7 * 17 * 19 C2 x C2 x C2 x C4
-34840 -2^3 * 5 * 13 * 67 C2 x C4 x C4
-40755 -3 * 5 * 11 * 13 * 19 C2 x C2 x C2 x C4
-42420 -2^2 * 3 * 5 * 7 * 101 C2 x C2 x C4 x C4
-43435 -5 * 7 * 17 * 73 C2 x C4 x C4
-44115 -3 * 5 * 17 * 173 C2 x C4 x C4
-46852 -2^2 * 13 * 17 * 53 C2 x C4 x C4
-53592 -2^3 * 3 * 7 * 11 * 29 C2 x C2 x C4 x C4
-57387 -3 * 11 * 37 * 47 C2 x C4 x C4
-57715 -5 * 7 * 17 * 97 C2 x C4 x C4
-58548 -2^2 * 3 * 7 * 17 * 41 C2 x C2 x C4 x C4
-73140 -2^2 * 3 * 5 * 23 * 53 C2 x C2 x C4 x C4
-82555 -5 * 11 * 19 * 79 C2 x C4 x C4
-92568 -2^3 * 3 * 7 * 19 * 29 C2 x C2 x C4 x C4
-105315 -3 * 5 * 7 * 17 * 59 C2 x C2 x C4 x C4
-111435 -3 * 5 * 17 * 19 * 23 C2 x C2 x C4 x C4
-198660 -2^2 * 3 * 5 * 7 * 11 * 43 C2 x C2 x C2 x C4 x C4
-207480 -2^3 * 3 * 5 * 7 * 13 * 19 C2 x C2 x C2 x C4 x C4
-228228 -2^2 * 3 * 7 * 11 * 13 * 19 C2 x C2 x C2 x C4 x C4
-264180 -2^2 * 3 * 5 * 7 * 17 * 37 C2 x C2 x C2 x C4 x C4
-435435 -3 * 5 * 7 * 11 * 13 * 29 C2 x C2 x C2 x C4 x C4

Die folgende Tabelle ist vollständig unter der Annahme, dass die verallgemeinerte Riemann-Vermutung wahr ist. Ohne Annahme einer Vermutung ist bekannt, dass die Liste endlich ist.

Diskriminante Faktorisierung Klassengruppe
-47 -47 C5
-79 -79 C5
-103 -103 C5
-127 -127 C5
-131 -131 C5
-179 -179 C5
-227 -227 C5
-347 -347 C5
-443 -443 C5
-523 -523 C5
-571 -571 C5
-619 -619 C5
-683 -683 C5
-691 -691 C5
-739 -739 C5
-787 -787 C5
-947 -947 C5
-1051 -1051 C5
-1123 -1123 C5
-1723 -1723 C5
-1747 -1747 C5
-1867 -1867 C5
-2203 -2203 C5
-2347 -2347 C5
-2683 -2683 C5
-12451 -12451 C5 x C5
-37363 -37363 C5 x C5

Die folgende Tabelle ist nur bis zur Diskriminante 3.1 * 10 ^ 20 vollständig. Es ist bekannt, dass es nur eine endliche Anzahl von Körpern mit Exponent 6 gibt.

Diskriminante Faktorisierung Klassengruppe
-87 -3 * 29 C6
-104 -2^3 * 13 C6
-116 -2^2 * 29 C6
-152 -2^3 * 19 C6
-212 -2^2 * 53 C6
-231 -3 * 7 * 11 C2 x C6
-244 -2^2 * 61 C6
-247 -13 * 19 C6
-255 -3 * 5 * 17 C2 x C6
-339 -3 * 113 C6
-411 -3 * 137 C6
-424 -2^3 * 53 C6
-436 -2^2 * 109 C6
-440 -2^3 * 5 * 11 C2 x C6
-451 -11 * 41 C6
-472 -2^3 * 59 C6
-515 -5 * 103 C6
-516 -2^2 * 3 * 43 C2 x C6
-628 -2^2 * 157 C6
-680 -2^3 * 5 * 17 C2 x C6
-696 -2^3 * 3 * 29 C2 x C6
-707 -7 * 101 C6
-728 -2^3 * 7 * 13 C2 x C6
-744 -2^3 * 3 * 31 C2 x C6
-771 -3 * 257 C6
-804 -2^2 * 3 * 67 C2 x C6
-808 -2^3 * 101 C6
-835 -5 * 167 C6
-843 -3 * 281 C6
-856 -2^3 * 107 C6
-888 -2^3 * 3 * 37 C2 x C6
-948 -2^2 * 3 * 79 C2 x C6
-984 -2^3 * 3 * 41 C2 x C6
-996 -2^2 * 3 * 83 C2 x C6
-1048 -2^3 * 131 C6
-1059 -3 * 353 C6
-1099 -7 * 157 C6
-1108 -2^2 * 277 C6
-1144 -2^3 * 11 * 13 C2 x C6
-1147 -31 * 37 C6
-1192 -2^3 * 149 C6
-1203 -3 * 401 C6
-1219 -23 * 53 C6
-1235 -5 * 13 * 19 C2 x C6
-1236 -2^2 * 3 * 103 C2 x C6
-1267 -7 * 181 C6
-1272 -2^3 * 3 * 53 C2 x C6
-1315 -5 * 263 C6
-1347 -3 * 449 C6
-1363 -29 * 47 C6
-1419 -3 * 11 * 43 C2 x C6
-1432 -2^3 * 179 C6
-1464 -2^3 * 3 * 61 C2 x C6
-1480 -2^3 * 5 * 37 C2 x C6
-1491 -3 * 7 * 71 C2 x C6
-1515 -3 * 5 * 101 C2 x C6
-1547 -7 * 13 * 17 C2 x C6
-1563 -3 * 521 C6
-1572 -2^2 * 3 * 131 C2 x C6
-1588 -2^2 * 397 C6
-1603 -7 * 229 C6
-1668 -2^2 * 3 * 139 C2 x C6
-1720 -2^3 * 5 * 43 C2 x C6
-1812 -2^2 * 3 * 151 C2 x C6
-1843 -19 * 97 C6
-1892 -2^2 * 11 * 43 C2 x C6
-1915 -5 * 383 C6
-1955 -5 * 17 * 23 C2 x C6
-1963 -13 * 151 C6
-1972 -2^2 * 17 * 29 C2 x C6
-2068 -2^2 * 11 * 47 C2 x C6
-2091 -3 * 17 * 41 C2 x C6
-2132 -2^2 * 13 * 41 C2 x C6
-2148 -2^2 * 3 * 179 C2 x C6
-2184 -2^3 * 3 * 7 * 13 C2 x C2 x C6
-2227 -17 * 131 C6
-2235 -3 * 5 * 149 C2 x C6
-2260 -2^2 * 5 * 113 C2 x C6
-2283 -3 * 761 C6
-2355 -3 * 5 * 157 C2 x C6
-2387 -7 * 11 * 31 C2 x C6
-2388 -2^2 * 3 * 199 C2 x C6
-2424 -2^3 * 3 * 101 C2 x C6
-2440 -2^3 * 5 * 61 C2 x C6
-2443 -7 * 349 C6
-2472 -2^3 * 3 * 103 C2 x C6
-2515 -5 * 503 C6
-2555 -5 * 7 * 73 C2 x C6
-2563 -11 * 233 C6
-2595 -3 * 5 * 173 C2 x C6
-2635 -5 * 17 * 31 C2 x C6
-2660 -2^2 * 5 * 7 * 19 C2 x C2 x C6
-2676 -2^2 * 3 * 223 C2 x C6
-2680 -2^3 * 5 * 67 C2 x C6
-2728 -2^3 * 11 * 31 C2 x C6
-2740 -2^2 * 5 * 137 C2 x C6
-2787 -3 * 929 C6
-2795 -5 * 13 * 43 C2 x C6
-2820 -2^2 * 3 * 5 * 47 C2 x C2 x C6
-2856 -2^3 * 3 * 7 * 17 C2 x C2 x C6
-2920 -2^3 * 5 * 73 C2 x C6
-2923 -37 * 79 C6
-2955 -3 * 5 * 197 C2 x C6
-2964 -2^2 * 3 * 13 * 19 C2 x C2 x C6
-3012 -2^2 * 3 * 251 C2 x C6
-3048 -2^3 * 3 * 127 C2 x C6
-3115 -5 * 7 * 89 C2 x C6
-3235 -5 * 647 C6
-3252 -2^2 * 3 * 271 C2 x C6
-3256 -2^3 * 11 * 37 C2 x C6
-3268 -2^2 * 19 * 43 C2 x C6
-3304 -2^3 * 7 * 59 C2 x C6
-3427 -23 * 149 C6
-3444 -2^2 * 3 * 7 * 41 C2 x C2 x C6
-3451 -7 * 17 * 29 C2 x C6
-3523 -13 * 271 C6
-3540 -2^2 * 3 * 5 * 59 C2 x C2 x C6
-3619 -7 * 11 * 47 C2 x C6
-3652 -2^2 * 11 * 83 C2 x C6
-3720 -2^3 * 3 * 5 * 31 C2 x C2 x C6
-3723 -3 * 17 * 73 C2 x C6
-3763 -53 * 71 C6
-3768 -2^3 * 3 * 157 C2 x C6
-3796 -2^2 * 13 * 73 C2 x C6
-3835 -5 * 13 * 59 C2 x C6
-3864 -2^3 * 3 * 7 * 23 C2 x C2 x C6
-3876 -2^2 * 3 * 17 * 19 C2 x C2 x C6
-3880 -2^3 * 5 * 97 C2 x C6
-3892 -2^2 * 7 * 139 C2 x C6
-3955 -5 * 7 * 113 C2 x C6
-3972 -2^2 * 3 * 331 C2 x C6
-4035 -3 * 5 * 269 C2 x C6
-4120 -2^3 * 5 * 103 C2 x C6
-4147 -11 * 13 * 29 C2 x C6
-4152 -2^3 * 3 * 173 C2 x C6
-4155 -3 * 5 * 277 C2 x C6
-4360 -2^3 * 5 * 109 C2 x C6
-4587 -3 * 11 * 139 C2 x C6
-4648 -2^3 * 7 * 83 C2 x C6
-4692 -2^2 * 3 * 17 * 23 C2 x C2 x C6
-4708 -2^2 * 11 * 107 C2 x C6
-4755 -3 * 5 * 317 C2 x C6
-4795 -5 * 7 * 137 C2 x C6
-4872 -2^3 * 3 * 7 * 29 C2 x C2 x C6
-4888 -2^3 * 13 * 47 C2 x C6
-4920 -2^3 * 3 * 5 * 41 C2 x C2 x C6
-4947 -3 * 17 * 97 C2 x C6
-5016 -2^3 * 3 * 11 * 19 C2 x C2 x C6
-5032 -2^3 * 17 * 37 C2 x C6
-5035 -5 * 19 * 53 C2 x C6
-5124 -2^2 * 3 * 7 * 61 C2 x C2 x C6
-5140 -2^2 * 5 * 257 C2 x C6
-5236 -2^2 * 7 * 11 * 17 C2 x C2 x C6
-5307 -3 * 29 * 61 C2 x C6
-5320 -2^3 * 5 * 7 * 19 C2 x C2 x C6
-5395 -5 * 13 * 83 C2 x C6
-5523 -3 * 7 * 263 C2 x C6
-5595 -3 * 5 * 373 C2 x C6
-5763 -3 * 17 * 113 C2 x C6
-5811 -3 * 13 * 149 C2 x C6
-5835 -3 * 5 * 389 C2 x C6
-5928 -2^3 * 3 * 13 * 19 C2 x C2 x C6
-6072 -2^3 * 3 * 11 * 23 C2 x C2 x C6
-6132 -2^2 * 3 * 7 * 73 C2 x C2 x C6
-6180 -2^2 * 3 * 5 * 103 C2 x C2 x C6
-6216 -2^3 * 3 * 7 * 37 C2 x C2 x C6
-6232 -2^3 * 19 * 41 C2 x C6
-6235 -5 * 29 * 43 C2 x C6
-6555 -3 * 5 * 19 * 23 C2 x C2 x C6
-6603 -3 * 31 * 71 C2 x C6
-6643 -7 * 13 * 73 C2 x C6
-6699 -3 * 7 * 11 * 29 C2 x C2 x C6
-6715 -5 * 17 * 79 C2 x C6
-6888 -2^3 * 3 * 7 * 41 C2 x C2 x C6
-6916 -2^2 * 7 * 13 * 19 C2 x C2 x C6
-6955 -5 * 13 * 107 C2 x C6
-6963 -3 * 11 * 211 C2 x C6
-6987 -3 * 17 * 137 C2 x C6
-7107 -3 * 23 * 103 C2 x C6
-7320 -2^3 * 3 * 5 * 61 C2 x C2 x C6
-7332 -2^2 * 3 * 13 * 47 C2 x C2 x C6
-7620 -2^2 * 3 * 5 * 127 C2 x C2 x C6
-7683 -3 * 13 * 197 C2 x C6
-7912 -2^3 * 23 * 43 C2 x C6
-8148 -2^2 * 3 * 7 * 97 C2 x C2 x C6
-8155 -5 * 7 * 233 C2 x C6
-8211 -3 * 7 * 17 * 23 C2 x C2 x C6
-8260 -2^2 * 5 * 7 * 59 C2 x C2 x C6
-8323 -7 * 29 * 41 C2 x C6
-8395 -5 * 23 * 73 C2 x C6
-8740 -2^2 * 5 * 19 * 23 C2 x C2 x C6
-8760 -2^3 * 3 * 5 * 73 C2 x C2 x C6
-8772 -2^2 * 3 * 17 * 43 C2 x C2 x C6
-8787 -3 * 29 * 101 C2 x C6
-8827 -7 * 13 * 97 C2 x C6
-9048 -2^3 * 3 * 13 * 29 C2 x C2 x C6
-9139 -13 * 19 * 37 C2 x C6
-9384 -2^3 * 3 * 17 * 23 C2 x C2 x C6
-9480 -2^3 * 3 * 5 * 79 C2 x C2 x C6
-9492 -2^2 * 3 * 7 * 113 C2 x C2 x C6
-9672 -2^3 * 3 * 13 * 31 C2 x C2 x C6
-9748 -2^2 * 2437 C3 x C6
-9843 -3 * 17 * 193 C2 x C6
-9940 -2^2 * 5 * 7 * 71 C2 x C2 x C6
-10120 -2^3 * 5 * 11 * 23 C2 x C2 x C6
-10212 -2^2 * 3 * 23 * 37 C2 x C2 x C6
-10248 -2^3 * 3 * 7 * 61 C2 x C2 x C6
-10360 -2^3 * 5 * 7 * 37 C2 x C2 x C6
-10452 -2^2 * 3 * 13 * 67 C2 x C2 x C6
-10488 -2^3 * 3 * 19 * 23 C2 x C2 x C6
-10707 -3 * 43 * 83 C2 x C6
-10740 -2^2 * 3 * 5 * 179 C2 x C2 x C6
-10788 -2^2 * 3 * 29 * 31 C2 x C2 x C6
-10795 -5 * 17 * 127 C2 x C6
-10915 -5 * 37 * 59 C2 x C6
-11155 -5 * 23 * 97 C2 x C6
-11220 -2^2 * 3 * 5 * 11 * 17 C2 x C2 x C2 x C6
-11235 -3 * 5 * 7 * 107 C2 x C2 x C6
-11620 -2^2 * 5 * 7 * 83 C2 x C2 x C6
-11748 -2^2 * 3 * 11 * 89 C2 x C2 x C6
-11803 -11 * 29 * 37 C2 x C6
-11928 -2^3 * 3 * 7 * 71 C2 x C2 x C6
-12067 -11 * 1097 C3 x C6
-12243 -3 * 7 * 11 * 53 C2 x C2 x C6
-12376 -2^3 * 7 * 13 * 17 C2 x C2 x C6
-12408 -2^3 * 3 * 11 * 47 C2 x C2 x C6
-12628 -2^2 * 7 * 11 * 41 C2 x C2 x C6
-12760 -2^3 * 5 * 11 * 29 C2 x C2 x C6
-13035 -3 * 5 * 11 * 79 C2 x C2 x C6
-13080 -2^3 * 3 * 5 * 109 C2 x C2 x C6
-13395 -3 * 5 * 19 * 47 C2 x C2 x C6
-13668 -2^2 * 3 * 17 * 67 C2 x C2 x C6
-13780 -2^2 * 5 * 13 * 53 C2 x C2 x C6
-14212 -2^2 * 11 * 17 * 19 C2 x C2 x C6
-14235 -3 * 5 * 13 * 73 C2 x C2 x C6
-14260 -2^2 * 5 * 23 * 31 C2 x C2 x C6
-14443 -11 * 13 * 101 C2 x C6
-14532 -2^2 * 3 * 7 * 173 C2 x C2 x C6
-14595 -3 * 5 * 7 * 139 C2 x C2 x C6
-14835 -3 * 5 * 23 * 43 C2 x C2 x C6
-14952 -2^3 * 3 * 7 * 89 C2 x C2 x C6
-14980 -2^2 * 5 * 7 * 107 C2 x C2 x C6
-15283 -17 * 29 * 31 C2 x C6
-15540 -2^2 * 3 * 5 * 7 * 37 C2 x C2 x C2 x C6
-15544 -2^3 * 29 * 67 C6 x C6
-15555 -3 * 5 * 17 * 61 C2 x C2 x C6
-15640 -2^3 * 5 * 17 * 23 C2 x C2 x C6
-15652 -2^2 * 7 * 13 * 43 C2 x C2 x C6
-15960 -2^3 * 3 * 5 * 7 * 19 C2 x C2 x C2 x C6
-16107 -3 * 7 * 13 * 59 C2 x C2 x C6
-16627 -13 * 1279 C3 x C6
-16872 -2^3 * 3 * 19 * 37 C2 x C2 x C6
-17043 -3 * 13 * 19 * 23 C2 x C2 x C6
-17131 -37 * 463 C3 x C6
-17160 -2^3 * 3 * 5 * 11 * 13 C2 x C2 x C2 x C6
-17556 -2^2 * 3 * 7 * 11 * 19 C2 x C2 x C2 x C6
-17940 -2^2 * 3 * 5 * 13 * 23 C2 x C2 x C2 x C6
-18040 -2^3 * 5 * 11 * 41 C2 x C2 x C6
-18088 -2^3 * 7 * 17 * 19 C2 x C2 x C6
-18340 -2^2 * 5 * 7 * 131 C2 x C2 x C6
-18555 -3 * 5 * 1237 C6 x C6
-18795 -3 * 5 * 7 * 179 C2 x C2 x C6
-18915 -3 * 5 * 13 * 97 C2 x C2 x C6
-19140 -2^2 * 3 * 5 * 11 * 29 C2 x C2 x C2 x C6
-19651 -43 * 457 C3 x C6
-19803 -3 * 7 * 23 * 41 C2 x C2 x C6
-20355 -3 * 5 * 23 * 59 C2 x C2 x C6
-20568 -2^3 * 3 * 857 C6 x C6
-20955 -3 * 5 * 11 * 127 C2 x C2 x C6
-20995 -5 * 13 * 17 * 19 C2 x C2 x C6
-21112 -2^3 * 7 * 13 * 29 C2 x C2 x C6
-21252 -2^2 * 3 * 7 * 11 * 23 C2 x C2 x C2 x C6
-22260 -2^2 * 3 * 5 * 7 * 53 C2 x C2 x C2 x C6
-22395 -3 * 5 * 1493 C6 x C6
-22440 -2^3 * 3 * 5 * 11 * 17 C2 x C2 x C2 x C6
-22443 -3 * 7481 C3 x C6
-23115 -3 * 5 * 23 * 67 C2 x C2 x C6
-23188 -2^2 * 11 * 17 * 31 C2 x C2 x C6
-23683 -11 * 2153 C3 x C6
-24115 -5 * 7 * 13 * 53 C2 x C2 x C6
-24123 -3 * 11 * 17 * 43 C2 x C2 x C6
-24180 -2^2 * 3 * 5 * 13 * 31 C2 x C2 x C2 x C6
-24340 -2^2 * 5 * 1217 C6 x C6
-24360 -2^3 * 3 * 5 * 7 * 29 C2 x C2 x C2 x C6
-24388 -2^2 * 7 * 13 * 67 C2 x C2 x C6
-24420 -2^2 * 3 * 5 * 11 * 37 C2 x C2 x C2 x C6
-24915 -3 * 5 * 11 * 151 C2 x C2 x C6
-24955 -5 * 7 * 23 * 31 C2 x C2 x C6
-25347 -3 * 7 * 17 * 71 C2 x C2 x C6
-25707 -3 * 11 * 19 * 41 C2 x C2 x C6
-25755 -3 * 5 * 17 * 101 C2 x C2 x C6
-25795 -5 * 7 * 11 * 67 C2 x C2 x C6
-26040 -2^3 * 3 * 5 * 7 * 31 C2 x C2 x C2 x C6
-26187 -3 * 7 * 29 * 43 C2 x C2 x C6
-26520 -2^3 * 3 * 5 * 13 * 17 C2 x C2 x C2 x C6
-26760 -2^3 * 3 * 5 * 223 C2 x C6 x C6
-27060 -2^2 * 3 * 5 * 11 * 41 C2 x C2 x C2 x C6
-27115 -5 * 11 * 17 * 29 C2 x C2 x C6
-27156 -2^2 * 3 * 31 * 73 C2 x C6 x C6
-27435 -3 * 5 * 31 * 59 C2 x C2 x C6
-27640 -2^3 * 5 * 691 C6 x C6
-28644 -2^2 * 3 * 7 * 11 * 31 C2 x C2 x C2 x C6
-29172 -2^2 * 3 * 11 * 13 * 17 C2 x C2 x C2 x C6
-29640 -2^3 * 3 * 5 * 13 * 19 C2 x C2 x C2 x C6
-30360 -2^3 * 3 * 5 * 11 * 23 C2 x C2 x C2 x C6
-30660 -2^2 * 3 * 5 * 7 * 73 C2 x C2 x C2 x C6
-31620 -2^2 * 3 * 5 * 17 * 31 C2 x C2 x C2 x C6
-31908 -2^2 * 3 * 2659 C6 x C6
-32968 -2^3 * 13 * 317 C6 x C6
-33060 -2^2 * 3 * 5 * 19 * 29 C2 x C2 x C2 x C6
-34027 -7 * 4861 C3 x C6
-34507 -11 * 3137 C3 x C6
-34827 -3 * 13 * 19 * 47 C2 x C2 x C6
-34867 -7 * 17 * 293 C6 x C6
-34980 -2^2 * 3 * 5 * 11 * 53 C2 x C2 x C2 x C6
-35112 -2^3 * 3 * 7 * 11 * 19 C2 x C2 x C2 x C6
-36120 -2^3 * 3 * 5 * 7 * 43 C2 x C2 x C2 x C6
-36708 -2^2 * 3 * 7 * 19 * 23 C2 x C2 x C2 x C6
-37128 -2^3 * 3 * 7 * 13 * 17 C2 x C2 x C2 x C6
-37219 -7 * 13 * 409 C6 x C6
-37555 -5 * 7 * 29 * 37 C2 x C2 x C6
-38280 -2^3 * 3 * 5 * 11 * 29 C2 x C2 x C2 x C6
-39480 -2^3 * 3 * 5 * 7 * 47 C2 x C2 x C2 x C6
-39732 -2^2 * 3 * 7 * 11 * 43 C2 x C2 x C2 x C6
-40299 -3 * 7 * 19 * 101 C2 x C6 x C6
-40692 -2^2 * 3 * 3391 C6 x C6
-41412 -2^2 * 3 * 7 * 17 * 29 C2 x C2 x C2 x C6
-41860 -2^2 * 5 * 7 * 13 * 23 C2 x C2 x C2 x C6
-42315 -3 * 5 * 7 * 13 * 31 C2 x C2 x C2 x C6
-42427 -7 * 11 * 19 * 29 C2 x C2 x C6
-42619 -17 * 23 * 109 C6 x C6
-43428 -2^2 * 3 * 7 * 11 * 47 C2 x C2 x C2 x C6
-43827 -3 * 7 * 2087 C6 x C6
-44004 -2^2 * 3 * 19 * 193 C2 x C6 x C6
-45220 -2^2 * 5 * 7 * 17 * 19 C2 x C2 x C2 x C6
-45835 -5 * 89 * 103 C6 x C6
-46587 -3 * 53 * 293 C6 x C6
-46740 -2^2 * 3 * 5 * 19 * 41 C2 x C2 x C2 x C6
-47355 -3 * 5 * 7 * 11 * 41 C2 x C2 x C2 x C6
-48052 -2^2 * 41 * 293 C6 x C6
-48472 -2^3 * 73 * 83 C6 x C6
-49128 -2^3 * 3 * 23 * 89 C2 x C6 x C6
-49812 -2^2 * 3 * 7 * 593 C2 x C6 x C6
-50388 -2^2 * 3 * 13 * 17 * 19 C2 x C2 x C2 x C6
-51051 -3 * 7 * 11 * 13 * 17 C2 x C2 x C2 x C6
-51348 -2^2 * 3 * 11 * 389 C2 x C6 x C6
-52360 -2^3 * 5 * 7 * 11 * 17 C2 x C2 x C2 x C6
-54195 -3 * 5 * 3613 C6 x C6
-58920 -2^3 * 3 * 5 * 491 C2 x C6 x C6
-60099 -3 * 13 * 23 * 67 C2 x C6 x C6
-63492 -2^2 * 3 * 11 * 13 * 37 C2 x C2 x C2 x C6
-64155 -3 * 5 * 7 * 13 * 47 C2 x C2 x C2 x C6
-67480 -2^3 * 5 * 7 * 241 C2 x C6 x C6
-70035 -3 * 5 * 7 * 23 * 29 C2 x C2 x C2 x C6
-72435 -3 * 5 * 11 * 439 C2 x C6 x C6
-78180 -2^2 * 3 * 5 * 1303 C2 x C6 x C6
-78708 -2^2 * 3 * 7 * 937 C2 x C6 x C6
-81867 -3 * 29 * 941 C6 x C6
-83395 -5 * 13 * 1283 C6 x C6
-84072 -2^3 * 3 * 31 * 113 C2 x C6 x C6
-86955 -3 * 5 * 11 * 17 * 31 C2 x C2 x C2 x C6
-87720 -2^3 * 3 * 5 * 17 * 43 C2 x C2 x C6 x C6
-87780 -2^2 * 3 * 5 * 7 * 11 * 19 C2 x C2 x C2 x C2 x C6
-92827 -7 * 89 * 149 C6 x C6
-94395 -3 * 5 * 7 * 29 * 31 C2 x C2 x C2 x C6
-95448 -2^3 * 3 * 41 * 97 C2 x C6 x C6
-100488 -2^3 * 3 * 53 * 79 C2 x C6 x C6
-106260 -2^2 * 3 * 5 * 7 * 11 * 23 C2 x C2 x C2 x C2 x C6
-107848 -2^3 * 13 * 17 * 61 C2 x C6 x C6
-112795 -5 * 17 * 1327 C6 x C6
-115780 -2^2 * 5 * 7 * 827 C2 x C6 x C6
-116083 -11 * 61 * 173 C6 x C6
-117480 -2^3 * 3 * 5 * 11 * 89 C2 x C2 x C6 x C6
-119112 -2^3 * 3 * 7 * 709 C2 x C6 x C6
-121720 -2^3 * 5 * 17 * 179 C2 x C6 x C6
-125652 -2^2 * 3 * 37 * 283 C2 x C6 x C6
-132328 -2^3 * 7 * 17 * 139 C2 x C6 x C6
-137067 -3 * 7 * 61 * 107 C2 x C6 x C6
-138468 -2^2 * 3 * 11 * 1049 C2 x C6 x C6
-145860 -2^2 * 3 * 5 * 11 * 13 * 17 C2 x C2 x C2 x C2 x C6
-148852 -2^2 * 11 * 17 * 199 C2 x C6 x C6
-152355 -3 * 5 * 7 * 1451 C2 x C6 x C6
-154212 -2^2 * 3 * 71 * 181 C2 x C6 x C6
-180840 -2^3 * 3 * 5 * 11 * 137 C2 x C2 x C6 x C6
-183012 -2^2 * 3 * 101 * 151 C2 x C6 x C6
-183768 -2^3 * 3 * 13 * 19 * 31 C2 x C2 x C6 x C6
-192003 -3 * 7 * 41 * 223 C2 x C6 x C6
-195960 -2^3 * 3 * 5 * 23 * 71 C2 x C2 x C6 x C6
-198795 -3 * 5 * 29 * 457 C2 x C6 x C6
-199348 -2^2 * 19 * 43 * 61 C2 x C6 x C6
-204568 -2^3 * 7 * 13 * 281 C2 x C6 x C6
-211432 -2^3 * 13 * 19 * 107 C2 x C6 x C6
-214008 -2^3 * 3 * 37 * 241 C2 x C6 x C6
-224580 -2^2 * 3 * 5 * 19 * 197 C2 x C2 x C6 x C6
-231240 -2^3 * 3 * 5 * 41 * 47 C2 x C2 x C6 x C6
-287155 -5 * 11 * 23 * 227 C2 x C6 x C6
-303160 -2^3 * 5 * 11 * 13 * 53 C2 x C2 x C6 x C6
-315723 -3 * 19 * 29 * 191 C2 x C6 x C6
-341715 -3 * 5 * 11 * 19 * 109 C2 x C2 x C6 x C6
-343380 -2^2 * 3 * 5 * 59 * 97 C2 x C2 x C6 x C6
-352968 -2^3 * 3 * 7 * 11 * 191 C2 x C2 x C6 x C6
-393108 -2^2 * 3 * 17 * 41 * 47 C2 x C2 x C6 x C6
-394420 -2^2 * 5 * 13 * 37 * 41 C2 x C2 x C6 x C6
-397155 -3 * 5 * 11 * 29 * 83 C2 x C2 x C6 x C6
-404547 -3 * 11 * 13 * 23 * 41 C2 x C2 x C6 x C6
-419640 -2^3 * 3 * 5 * 13 * 269 C2 x C2 x C6 x C6
-423640 -2^3 * 5 * 7 * 17 * 89 C2 x C2 x C6 x C6
-453435 -3 * 5 * 19 * 37 * 43 C2 x C2 x C6 x C6
-458920 -2^3 * 5 * 7 * 11 * 149 C2 x C2 x C6 x C6
-507892 -2^2 * 7 * 11 * 17 * 97 C2 x C2 x C6 x C6
-512715 -3 * 5 * 7 * 19 * 257 C2 x C2 x C6 x C6
-522795 -3 * 5 * 7 * 13 * 383 C2 x C2 x C6 x C6
-603460 -2^2 * 5 * 11 * 13 * 211 C2 x C2 x C6 x C6
-668980 -2^2 * 5 * 13 * 31 * 83 C2 x C2 x C6 x C6
-680043 -3 * 7 * 13 * 47 * 53 C2 x C2 x C6 x C6
-697620 -2^2 * 3 * 5 * 7 * 11 * 151 C2 x C2 x C2 x C6 x C6
-740355 -3 * 5 * 7 * 11 * 641 C2 x C2 x C6 x C6
-740532 -2^2 * 3 * 13 * 47 * 101 C2 x C2 x C6 x C6
-742980 -2^2 * 3 * 5 * 7 * 29 * 61 C2 x C2 x C2 x C6 x C6
-820120 -2^3 * 5 * 7 * 29 * 101 C2 x C2 x C6 x C6
-899283 -3 * 7 * 11 * 17 * 229 C2 x C2 x C6 x C6
-941640 -2^3 * 3 * 5 * 7 * 19 * 59 C2 x C2 x C2 x C6 x C6
-1162392 -2^3 * 3 * 7 * 11 * 17 * 37 C2 x C2 x C2 x C6 x C6
-1172395 -5 * 7 * 19 * 41 * 43 C2 x C2 x C6 x C6
-1185240 -2^3 * 3 * 5 * 7 * 17 * 83 C2 x C2 x C2 x C6 x C6
-1196052 -2^2 * 3 * 11 * 13 * 17 * 41 C2 x C2 x C2 x C6 x C6
-1199220 -2^2 * 3 * 5 * 11 * 23 * 79 C2 x C2 x C2 x C6 x C6
-1282260 -2^2 * 3 * 5 * 7 * 43 * 71 C2 x C2 x C2 x C6 x C6
-1702155 -3 * 5 * 7 * 13 * 29 * 43 C2 x C2 x C2 x C6 x C6
-3892980 -2^2 * 3 * 5 * 7 * 13 * 23 * 31 C2 x C2 x C2 x C2 x C6 x C6
-4696692 -2^2 * 3 * 7 * 11 * 13 * 17 * 23 C2 x C2 x C2 x C2 x C6 x C6
-5761140 -2^2 * 3 * 5 * 7 * 11 * 29 * 43 C2 x C2 x C2 x C2 x C6 x C6

Die folgende Tabelle ist nur bis zur Diskriminante 3.1 * 10 ^ 20 vollständig.

Diskriminante Faktorisierung Klassengruppe
-71 -71 C7
-151 -151 C7
-223 -223 C7
-251 -251 C7
-463 -463 C7
-467 -467 C7
-487 -487 C7
-587 -587 C7
-811 -811 C7
-827 -827 C7
-859 -859 C7
-1163 -1163 C7
-1171 -1171 C7
-1483 -1483 C7
-1523 -1523 C7
-1627 -1627 C7
-1787 -1787 C7
-1987 -1987 C7
-2011 -2011 C7
-2083 -2083 C7
-2179 -2179 C7
-2251 -2251 C7
-2467 -2467 C7
-2707 -2707 C7
-3019 -3019 C7
-3067 -3067 C7
-3187 -3187 C7
-3907 -3907 C7
-4603 -4603 C7
-5107 -5107 C7
-5923 -5923 C7
-63499 -63499 C7 x C7
-118843 -118843 C7 x C7

Die folgende Tabelle ist vollständig, sofern es keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung  könnte ein Körper fehlen.  

Diskriminante Faktorisierung Klassengruppe
-95 -5 * 19 C8
-111 -3 * 37 C8
-164 -2^2 * 41 C8
-183 -3 * 61 C8
-248 -2^3 * 31 C8
-295 -5 * 59 C8
-299 -13 * 23 C8
-371 -7 * 53 C8
-376 -2^3 * 47 C8
-395 -5 * 79 C8
-399 -3 * 7 * 19 C2 x C8
-452 -2^2 * 113 C8
-548 -2^2 * 137 C8
-579 -3 * 193 C8
-583 -11 * 53 C8
-632 -2^3 * 79 C8
-644 -2^2 * 7 * 23 C2 x C8
-663 -3 * 13 * 17 C2 x C8
-712 -2^3 * 89 C8
-740 -2^2 * 5 * 37 C2 x C8
-884 -2^2 * 13 * 17 C2 x C8
-903 -3 * 7 * 43 C2 x C8
-904 -2^3 * 113 C8
-939 -3 * 313 C8
-979 -11 * 89 C8
-995 -5 * 199 C8
-1015 -5 * 7 * 29 C2 x C8
-1023 -3 * 11 * 31 C2 x C8
-1043 -7 * 149 C8
-1195 -5 * 239 C8
-1220 -2^2 * 5 * 61 C2 x C8
-1252 -2^2 * 313 C8
-1299 -3 * 433 C8
-1339 -13 * 103 C8
-1348 -2^2 * 337 C8
-1416 -2^3 * 3 * 59 C2 x C8
-1508 -2^2 * 13 * 29 C2 x C8
-1528 -2^3 * 191 C8
-1595 -5 * 11 * 29 C2 x C8
-1608 -2^3 * 3 * 67 C2 x C8
-1624 -2^3 * 7 * 29 C2 x C8
-1640 -2^3 * 5 * 41 C2 x C8
-1651 -13 * 127 C8
-1731 -3 * 577 C8
-1795 -5 * 359 C8
-1803 -3 * 601 C8
-1828 -2^2 * 457 C8
-1864 -2^3 * 233 C8
-1876 -2^2 * 7 * 67 C2 x C8
-1912 -2^3 * 239 C8
-1924 -2^2 * 13 * 37 C2 x C8
-1939 -7 * 277 C8
-2004 -2^2 * 3 * 167 C2 x C8
-2059 -29 * 71 C8
-2072 -2^3 * 7 * 37 C2 x C8
-2211 -3 * 11 * 67 C2 x C8
-2248 -2^3 * 281 C8
-2292 -2^2 * 3 * 191 C2 x C8
-2296 -2^3 * 7 * 41 C2 x C8
-2307 -3 * 769 C8
-2308 -2^2 * 577 C8
-2323 -23 * 101 C8
-2328 -2^3 * 3 * 97 C2 x C8
-2356 -2^2 * 19 * 31 C2 x C8
-2395 -5 * 479 C8
-2419 -41 * 59 C8
-2568 -2^3 * 3 * 107 C2 x C8
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-73320 -2^3 * 3 * 5 * 13 * 47 C2 x C2 x C2 x C8
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-77995 -5 * 19 * 821 C4 x C8
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-94963 -11 * 89 * 97 C4 x C8
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-112884 -2^2 * 3 * 23 * 409 C2 x C8 x C8
-112980 -2^2 * 3 * 5 * 7 * 269 C2 x C2 x C4 x C8
-113883 -3 * 7 * 11 * 17 * 29 C2 x C2 x C2 x C8
-116932 -2^2 * 23 * 31 * 41 C2 x C4 x C8
-117028 -2^2 * 17 * 1721 C8 x C8
-117096 -2^3 * 3 * 7 * 17 * 41 C2 x C2 x C4 x C8
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-121560 -2^3 * 3 * 5 * 1013 C2 x C8 x C8
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-125643 -3 * 7 * 31 * 193 C2 x C4 x C8
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-131560 -2^3 * 5 * 11 * 13 * 23 C2 x C2 x C2 x C8
-132483 -3 * 13 * 43 * 79 C2 x C4 x C8
-133315 -5 * 7 * 13 * 293 C2 x C4 x C8
-138292 -2^2 * 7 * 11 * 449 C2 x C4 x C8
-139780 -2^2 * 5 * 29 * 241 C2 x C4 x C8
-139867 -7 * 13 * 29 * 53 C2 x C4 x C8
-140595 -3 * 5 * 7 * 13 * 103 C2 x C2 x C2 x C8
-143115 -3 * 5 * 7 * 29 * 47 C2 x C2 x C2 x C8
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-152395 -5 * 29 * 1051 C8 x C8
-155155 -5 * 7 * 11 * 13 * 31 C2 x C2 x C2 x C8
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-159960 -2^3 * 3 * 5 * 31 * 43 C2 x C2 x C4 x C8
-160563 -3 * 13 * 23 * 179 C2 x C4 x C8
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-173755 -5 * 19 * 31 * 59 C2 x C4 x C8
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-183540 -2^2 * 3 * 5 * 7 * 19 * 23 C2 x C2 x C2 x C2 x C8
-184008 -2^3 * 3 * 11 * 17 * 41 C2 x C2 x C4 x C8
-185235 -3 * 5 * 53 * 233 C2 x C4 x C8
-185640 -2^3 * 3 * 5 * 7 * 13 * 17 C2 x C2 x C2 x C2 x C8
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-189267 -3 * 13 * 23 * 211 C2 x C4 x C8
-189987 -3 * 7 * 83 * 109 C2 x C4 x C8
-193323 -3 * 13 * 4957 C8 x C8
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-196168 -2^3 * 7 * 31 * 113 C2 x C4 x C8
-198835 -5 * 7 * 13 * 19 * 23 C2 x C2 x C2 x C8
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-218395 -5 * 31 * 1409 C8 x C8
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-263112 -2^3 * 3 * 19 * 577 C2 x C8 x C8
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-557832 -2^3 * 3 * 11 * 2113 C2 x C8 x C8
-559083 -3 * 7 * 79 * 337 C2 x C8 x C8
-563640 -2^3 * 3 * 5 * 7 * 11 * 61 C2 x C2 x C2 x C4 x C8
-563955 -3 * 5 * 7 * 41 * 131 C2 x C2 x C4 x C8
-566040 -2^3 * 3 * 5 * 53 * 89 C2 x C2 x C8 x C8
-568888 -2^3 * 17 * 47 * 89 C4 x C4 x C8
-585915 -3 * 5 * 11 * 53 * 67 C2 x C2 x C4 x C8
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-603988 -2^2 * 7 * 11 * 37 * 53 C2 x C2 x C4 x C8
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-644280 -2^3 * 3 * 5 * 7 * 13 * 59 C2 x C2 x C2 x C4 x C8
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-1232340 -2^2 * 3 * 5 * 19 * 23 * 47 C2 x C2 x C2 x C4 x C8
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-1390180 -2^2 * 5 * 11 * 71 * 89 C2 x C2 x C8 x C8
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-1928595 -3 * 5 * 19 * 67 * 101 C2 x C2 x C8 x C8
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-1937635 -5 * 7 * 23 * 29 * 83 C2 x C2 x C8 x C8
-2043195 -3 * 5 * 7 * 11 * 29 * 61 C2 x C2 x C2 x C4 x C8
-2045323 -7 * 37 * 53 * 149 C4 x C4 x C8
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-2103220 -2^2 * 5 * 7 * 83 * 181 C2 x C2 x C8 x C8
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-2188920 -2^3 * 3 * 5 * 17 * 29 * 37 C2 x C2 x C4 x C4 x C8
-2209467 -3 * 13 * 181 * 313 C4 x C8 x C8
-2229123 -3 * 13 * 61 * 937 C4 x C8 x C8
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-2401867 -13 * 23 * 29 * 277 C4 x C8 x C8
-2420635 -5 * 7 * 23 * 31 * 97 C2 x C2 x C8 x C8
-2443155 -3 * 5 * 11 * 13 * 17 * 67 C2 x C2 x C2 x C4 x C8
-2523928 -2^3 * 11 * 23 * 29 * 43 C2 x C2 x C8 x C8
-2999560 -2^3 * 5 * 31 * 41 * 59 C2 x C2 x C8 x C8
-3040888 -2^3 * 41 * 73 * 127 C4 x C8 x C8
-3081540 -2^2 * 3 * 5 * 7 * 11 * 23 * 29 C2 x C2 x C2 x C2 x C4 x C8
-3121035 -3 * 5 * 19 * 47 * 233 C2 x C2 x C8 x C8
-3352020 -2^2 * 3 * 5 * 7 * 23 * 347 C2 x C2 x C2 x C8 x C8
-3452020 -2^2 * 5 * 11 * 13 * 17 * 71 C2 x C2 x C2 x C8 x C8
-3468595 -5 * 13 * 17 * 43 * 73 C2 x C2 x C8 x C8
-3536260 -2^2 * 5 * 7 * 13 * 29 * 67 C2 x C2 x C2 x C8 x C8
-3598980 -2^2 * 3 * 5 * 7 * 11 * 19 * 41 C2 x C2 x C2 x C2 x C4 x C8
-3608760 -2^3 * 3 * 5 * 17 * 29 * 61 C2 x C2 x C2 x C8 x C8
-4800772 -2^2 * 41 * 73 * 401 C4 x C8 x C8
-4886995 -5 * 31 * 41 * 769 C4 x C8 x C8
-4903395 -3 * 5 * 7 * 17 * 41 * 67 C2 x C2 x C2 x C8 x C8
-5358340 -2^2 * 5 * 13 * 37 * 557 C2 x C4 x C8 x C8
-5692440 -2^3 * 3 * 5 * 13 * 41 * 89 C2 x C2 x C4 x C8 x C8
-6005748 -2^2 * 3 * 7 * 19 * 53 * 71 C2 x C2 x C2 x C8 x C8
-6174168 -2^3 * 3 * 7 * 11 * 13 * 257 C2 x C2 x C2 x C8 x C8
-6585987 -3 * 17 * 29 * 61 * 73 C2 x C2 x C8 x C8
-7538388 -2^2 * 3 * 11 * 13 * 23 * 191 C2 x C2 x C2 x C8 x C8
-11148180 -2^2 * 3 * 5 * 29 * 43 * 149 C2 x C2 x C4 x C8 x C8
-12517428 -2^2 * 3 * 7 * 11 * 19 * 23 * 31 C2 x C2 x C2 x C4 x C4 x C8
-15337315 -5 * 7 * 17 * 149 * 173 C2 x C4 x C8 x C8
-15898740 -2^2 * 3 * 5 * 11 * 13 * 17 * 109 C2 x C2 x C2 x C2 x C8 x C8
-17168515 -5 * 7 * 13 * 97 * 389 C2 x C4 x C8 x C8
-28663635 -3 * 5 * 7 * 11 * 13 * 23 * 83 C2 x C2 x C2 x C2 x C8 x C8
-29493555 -3 * 5 * 7 * 13 * 17 * 31 * 41 C2 x C2 x C2 x C2 x C8 x C8
-31078723 -13 * 43 * 53 * 1049 C8 x C8 x C8
-430950520 -2^3 * 5 * 7 * 11 * 13 * 47 * 229 C2 x C2 x C2 x C8 x C8 x C8
C-Programme

Die folgenden zwei C-Programme können verwendet werden, um alle imaginärquadratischen Zahlkörper mit einem Exponenten kleiner oder gleich 8 und einer Diskriminantenschranke von 3.1·1020 zu berechnen.

Smallest Split fixed.c 

No small split.c

List of fields

Julia Programme

Die folgende Datei enthält den Julia-Code. Sie müssen Julia einschließlich des Hecke- und des Markdown-Pakets installieren. Die Funktion M1 berechnet die imaginärquadratischen Zahlkörper eines gegebenen Exponenten. Die Funktionen M2a, M2b, M3a und M3b berechnen die entsprechenden Familien.

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