Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
9.9.16983563041.1 |
$x^{9} - x^{8} - 8 x^{7} + 7 x^{6} + 21 x^{5} - 15 x^{4} - 20 x^{3} + 10 x^{2} + 5 x - 1$ |
$9$ |
[9,0] |
$19^{8}$ |
$1$ |
$13.698400752$ |
$13.69840075203899$ |
|
✓ |
✓ |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$87.132402653$ |
9.9.31381059609.1 |
$x^{9} - 9 x^{7} + 27 x^{5} - 30 x^{3} + 9 x - 1$ |
$9$ |
[9,0] |
$3^{22}$ |
$1$ |
$14.665484$ |
$14.665483999969616$ |
|
✓ |
✓ |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$159.898566189$ |
9.9.3512479453921.1 |
$x^{9} - x^{8} - 16 x^{7} + 11 x^{6} + 66 x^{5} - 32 x^{4} - 73 x^{3} + 7 x^{2} + 7 x - 1$ |
$9$ |
[9,0] |
$37^{8}$ |
$1$ |
$24.7717727963$ |
$24.771772796308063$ |
|
✓ |
? |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$1598.24730552$ |
9.9.806460091894081.1 |
$x^{9} - x^{8} - 32 x^{7} + 11 x^{6} + 278 x^{5} + 34 x^{4} - 427 x^{3} - 150 x^{2} - 8 x + 1$ |
$9$ |
[9,0] |
$73^{8}$ |
$1$ |
$45.3196958723$ |
$45.319695872342585$ |
|
✓ |
? |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$15512.1980357$ |
9.9.1998099208210609.1 |
$x^{9} - x^{8} - 46 x^{7} + 7 x^{6} + 572 x^{5} - 72 x^{4} - 2281 x^{3} + 770 x^{2} + 1050 x - 77$ |
$9$ |
[9,0] |
$7^{6}\cdot 19^{8}$ |
$2$ |
$50.1266360901$ |
$50.12663609011925$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$29669.763917$ |
9.9.1998099208210609.2 |
$x^{9} - x^{8} - 46 x^{7} + 7 x^{6} + 572 x^{5} + 460 x^{4} - 1483 x^{3} - 1757 x^{2} + 385 x + 721$ |
$9$ |
[9,0] |
$7^{6}\cdot 19^{8}$ |
$2$ |
$50.1266360901$ |
$50.12663609011925$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$17066.6537031$ |
9.9.3691950281939241.1 |
$x^{9} - 63 x^{7} + 1323 x^{5} - 10290 x^{3} + 21609 x - 12691$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{6}$ |
$2$ |
$53.6654893413$ |
$53.665489341339345$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$17156.8683251$ |
9.9.3691950281939241.2 |
$x^{9} - 63 x^{7} + 1323 x^{5} - 10290 x^{3} + 21609 x - 5831$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{6}$ |
$2$ |
$53.6654893413$ |
$53.665489341339345$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$40597.2195867$ |
9.9.9025761726072081.1 |
$x^{9} - 57 x^{7} - 38 x^{6} + 855 x^{5} + 228 x^{4} - 4902 x^{3} + 1710 x^{2} + 9063 x - 7201$ |
$9$ |
[9,0] |
$3^{12}\cdot 19^{8}$ |
$2$ |
$59.2695377956$ |
$59.269537795580746$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$58633.710835$ |
9.9.9025761726072081.2 |
$x^{9} - 57 x^{7} - 38 x^{6} + 855 x^{5} + 1254 x^{4} - 3192 x^{3} - 7524 x^{2} - 4275 x - 703$ |
$9$ |
[9,0] |
$3^{12}\cdot 19^{8}$ |
$2$ |
$59.2695377956$ |
$59.269537795580746$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$86043.1062668$ |
9.9.19925626416901921.1 |
$x^{9} - x^{8} - 48 x^{7} + 73 x^{6} + 660 x^{5} - 1454 x^{4} - 2149 x^{3} + 8350 x^{2} - 7432 x + 2008$ |
$9$ |
[9,0] |
$109^{8}$ |
$1$ |
$64.7210830126$ |
$64.72108301255068$ |
|
✓ |
|
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$120939.78896$ |
9.9.67675234241018881.1 |
$x^{9} - x^{8} - 56 x^{7} + 118 x^{6} + 573 x^{5} - 1249 x^{4} - 1582 x^{3} + 2700 x^{2} + 1576 x - 32$ |
$9$ |
[9,0] |
$127^{8}$ |
$1$ |
$74.1391755032$ |
$74.13917550324533$ |
|
✓ |
|
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$64259015.2682$ |
9.9.81976414938366169.1 |
$x^{9} - x^{8} - 84 x^{7} + 121 x^{6} + 1940 x^{5} - 3682 x^{4} - 13415 x^{3} + 34419 x^{2} - 2009 x - 26411$ |
$9$ |
[9,0] |
$13^{6}\cdot 19^{8}$ |
$2$ |
$75.7353730656$ |
$75.73537306555289$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$421404.034925$ |
9.9.81976414938366169.2 |
$x^{9} - x^{8} - 84 x^{7} + 121 x^{6} + 1940 x^{5} - 1706 x^{4} - 17861 x^{3} + 3544 x^{2} + 58012 x + 23977$ |
$9$ |
[9,0] |
$13^{6}\cdot 19^{8}$ |
$2$ |
$75.7353730656$ |
$75.73537306555289$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$53619.2496249$ |
9.9.151470380950257681.1 |
$x^{9} - 117 x^{7} + 4563 x^{5} - 65910 x^{3} + 257049 x - 195533$ |
$9$ |
[9,0] |
$3^{22}\cdot 13^{6}$ |
$2$ |
$81.0821585694$ |
$81.0821585694425$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$233016.463019$ |
9.9.151470380950257681.2 |
$x^{9} - 117 x^{7} + 4563 x^{5} - 65910 x^{3} + 257049 x - 41743$ |
$9$ |
[9,0] |
$3^{22}\cdot 13^{6}$ |
$2$ |
$81.0821585694$ |
$81.0821585694425$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$214694.556945$ |
9.9.413239695274351729.1 |
$x^{9} - x^{8} - 90 x^{7} + 11 x^{6} + 2730 x^{5} + 1226 x^{4} - 30339 x^{3} - 14830 x^{2} + 103200 x + 1849$ |
$9$ |
[9,0] |
$7^{6}\cdot 37^{8}$ |
$2$ |
$90.6474896409$ |
$90.64748964092182$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$135908.267095$ |
9.9.413239695274351729.2 |
$x^{9} - x^{8} - 90 x^{7} + 11 x^{6} + 1953 x^{5} + 1485 x^{4} - 12986 x^{3} - 15866 x^{2} + 20579 x + 28267$ |
$9$ |
[9,0] |
$7^{6}\cdot 37^{8}$ |
$2$ |
$90.6474896409$ |
$90.64748964092182$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$483519.35341$ |
9.9.498311414318121121.1 |
$x^{9} - x^{8} - 72 x^{7} + 73 x^{6} + 1482 x^{5} - 1034 x^{4} - 9637 x^{3} + 1173 x^{2} + 10087 x - 853$ |
$9$ |
[9,0] |
$163^{8}$ |
$1$ |
$92.5526763305$ |
$92.55267633047686$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[2, 2]$ |
$2$ |
$8$ |
$160679.065001$ |
9.9.1151936657823500641.1 |
$x^{9} - x^{8} - 80 x^{7} - 53 x^{6} + 1668 x^{5} + 3314 x^{4} - 4261 x^{3} - 10795 x^{2} - 2933 x + 1949$ |
$9$ |
[9,0] |
$181^{8}$ |
$1$ |
$101.584021087$ |
$101.58402108741569$ |
|
✓ |
? |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$1356171.33617$ |
9.9.1476349596018920529.1 |
$x^{9} - 171 x^{7} + 9747 x^{5} - 205770 x^{3} + 1172889 x - 1118017$ |
$9$ |
[9,0] |
$3^{22}\cdot 19^{6}$ |
$2$ |
$104.423633576$ |
$104.4236335758831$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$784138.972462$ |
9.9.1476349596018920529.2 |
$x^{9} - 171 x^{7} + 9747 x^{5} - 205770 x^{3} + 1172889 x - 733913$ |
$9$ |
[9,0] |
$3^{22}\cdot 19^{6}$ |
$2$ |
$104.423633576$ |
$104.4236335758831$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$399809.251389$ |
9.9.1866675593471230161.1 |
$x^{9} - 111 x^{7} - 74 x^{6} + 3663 x^{5} + 3774 x^{4} - 40848 x^{3} - 30636 x^{2} + 137529 x - 42661$ |
$9$ |
[9,0] |
$3^{12}\cdot 37^{8}$ |
$2$ |
$107.181236014$ |
$107.18123601368417$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$380116.876345$ |
9.9.1866675593471230161.2 |
$x^{9} - 111 x^{7} - 74 x^{6} + 3663 x^{5} + 5772 x^{4} - 37518 x^{3} - 84582 x^{2} + 39627 x + 129833$ |
$9$ |
[9,0] |
$3^{12}\cdot 37^{8}$ |
$2$ |
$107.181236014$ |
$107.18123601368417$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$1103271.33407$ |
9.9.2459374191553118401.1 |
$x^{9} - x^{8} - 88 x^{7} + 325 x^{6} + 775 x^{5} - 3447 x^{4} - 1602 x^{3} + 7354 x^{2} - 3333 x - 121$ |
$9$ |
[9,0] |
$199^{8}$ |
$1$ |
$110.515948869$ |
$110.51594886908097$ |
|
✓ |
? |
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$2331050.1092$ |
9.9.150...921.1 |
$x^{9} - x^{8} - 198 x^{7} - 107 x^{6} + 10319 x^{5} + 973 x^{4} - 189602 x^{3} + 170782 x^{2} + 815941 x - 1009547$ |
$9$ |
[9,0] |
$19^{8}\cdot 31^{6}$ |
$2$ |
$135.17955011$ |
$135.17955010958042$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$6898775.79927$ |
9.9.150...921.2 |
$x^{9} - x^{8} - 198 x^{7} - 107 x^{6} + 10319 x^{5} + 24533 x^{4} - 118922 x^{3} - 460626 x^{2} - 367949 x + 57721$ |
$9$ |
[9,0] |
$19^{8}\cdot 31^{6}$ |
$2$ |
$135.17955011$ |
$135.17955010958042$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$785284.164362$ |
9.9.169...089.1 |
$x^{9} - x^{8} - 164 x^{7} + 233 x^{6} + 8539 x^{5} - 16127 x^{4} - 140932 x^{3} + 331342 x^{2} + 98797 x - 419359$ |
$9$ |
[9,0] |
$13^{6}\cdot 37^{8}$ |
$2$ |
$136.957553526$ |
$136.95755352640347$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$1396236.99081$ |
9.9.169...089.2 |
$x^{9} - x^{8} - 164 x^{7} + 233 x^{6} + 7096 x^{5} - 13722 x^{4} - 95237 x^{3} + 217826 x^{2} + 113708 x - 70153$ |
$9$ |
[9,0] |
$13^{6}\cdot 37^{8}$ |
$2$ |
$136.957553526$ |
$136.95755352640347$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$3194362.61761$ |
9.9.278...729.1 |
$x^{9} - 279 x^{7} + 25947 x^{5} - 893730 x^{3} + 8311689 x - 8609599$ |
$9$ |
[9,0] |
$3^{22}\cdot 31^{6}$ |
$2$ |
$144.722991037$ |
$144.7229910367496$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$3358979.96303$ |
9.9.278...729.2 |
$x^{9} - 279 x^{7} + 25947 x^{5} - 893730 x^{3} + 8311689 x - 566029$ |
$9$ |
[9,0] |
$3^{22}\cdot 31^{6}$ |
$2$ |
$144.722991037$ |
$144.7229910367496$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$2452297.55299$ |
9.9.290...361.1 |
$x^{9} - x^{8} - 120 x^{7} + 543 x^{6} + 858 x^{5} - 6780 x^{4} + 7217 x^{3} + 2818 x^{2} - 4068 x + 261$ |
$9$ |
[9,0] |
$271^{8}$ |
$1$ |
$145.425099517$ |
$145.42509951704676$ |
|
✓ |
|
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$190161211.995$ |
9.9.435...769.1 |
$x^{9} - x^{8} - 236 x^{7} + 653 x^{6} + 15050 x^{5} - 54792 x^{4} - 284735 x^{3} + 1266246 x^{2} + 191050 x - 3107603$ |
$9$ |
[9,0] |
$19^{8}\cdot 37^{6}$ |
$2$ |
$152.102966246$ |
$152.10296624610643$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$1312040.91922$ |
9.9.435...769.2 |
$x^{9} - x^{8} - 236 x^{7} + 653 x^{6} + 15050 x^{5} - 37920 x^{4} - 378937 x^{3} + 524581 x^{2} + 3505695 x + 855911$ |
$9$ |
[9,0] |
$19^{8}\cdot 37^{6}$ |
$2$ |
$152.102966246$ |
$152.10296624610643$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$4822443.93517$ |
9.9.789...001.1 |
$x^{9} - x^{8} - 136 x^{7} + 365 x^{6} + 3572 x^{5} - 11176 x^{4} + 1999 x^{3} + 15708 x^{2} - 8316 x - 1944$ |
$9$ |
[9,0] |
$307^{8}$ |
$1$ |
$162.476167778$ |
$162.4761677783451$ |
|
✓ |
|
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$235679015.694$ |
9.9.805...081.2 |
$x^{9} - 333 x^{7} + 36963 x^{5} - 1519590 x^{3} + 16867449 x - 21932749$ |
$9$ |
[9,0] |
$3^{22}\cdot 37^{6}$ |
$2$ |
$162.841170893$ |
$162.84117089348263$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$2734333.08957$ |
9.9.805...081.3 |
$x^{9} - 333 x^{7} + 36963 x^{5} - 1519590 x^{3} + 16867449 x - 16360919$ |
$9$ |
[9,0] |
$3^{22}\cdot 37^{6}$ |
$2$ |
$162.841170893$ |
$162.84117089348263$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$5545508.09504$ |
9.9.948...569.1 |
$x^{9} - x^{8} - 178 x^{7} + 595 x^{6} + 6775 x^{5} - 25005 x^{4} - 46928 x^{3} + 74456 x^{2} + 85329 x + 18397$ |
$9$ |
[9,0] |
$7^{6}\cdot 73^{8}$ |
$2$ |
$165.838621882$ |
$165.83862188216773$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$5808098.73819$ |
9.9.948...569.2 |
$x^{9} - x^{8} - 178 x^{7} - 427 x^{6} + 7286 x^{5} + 23540 x^{4} - 109781 x^{3} - 397197 x^{2} + 545229 x + 2104299$ |
$9$ |
[9,0] |
$7^{6}\cdot 73^{8}$ |
$2$ |
$165.838621882$ |
$165.83862188216773$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$103368266.058$ |
9.9.107...009.1 |
$x^{9} - x^{8} - 274 x^{7} + 577 x^{6} + 20123 x^{5} - 67883 x^{4} - 409774 x^{3} + 2059534 x^{2} - 1701977 x - 1290899$ |
$9$ |
[9,0] |
$19^{8}\cdot 43^{6}$ |
$2$ |
$168.131403336$ |
$168.13140333606742$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$3270598.89555$ |
9.9.107...009.2 |
$x^{9} - x^{8} - 274 x^{7} + 577 x^{6} + 20123 x^{5} - 22131 x^{4} - 586246 x^{3} - 123490 x^{2} + 6054621 x + 8405257$ |
$9$ |
[9,0] |
$19^{8}\cdot 43^{6}$ |
$2$ |
$168.131403336$ |
$168.13140333606742$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$7178955.86747$ |
9.9.165...401.1 |
$x^{9} - x^{8} - 238 x^{7} - 285 x^{6} + 15680 x^{5} + 55764 x^{4} - 208901 x^{3} - 1310052 x^{2} - 1827386 x - 343139$ |
$9$ |
[9,0] |
$19^{6}\cdot 37^{8}$ |
$2$ |
$176.384122441$ |
$176.3841224409683$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$5458915.67791$ |
9.9.165...401.2 |
$x^{9} - x^{8} - 238 x^{7} - 285 x^{6} + 17789 x^{5} + 49437 x^{4} - 365670 x^{3} - 1055566 x^{2} + 1831729 x + 2605243$ |
$9$ |
[9,0] |
$19^{6}\cdot 37^{8}$ |
$2$ |
$176.384122441$ |
$176.3841224409683$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$4298056.78822$ |
9.9.198...841.1 |
$x^{9} - 387 x^{7} + 49923 x^{5} - 2385210 x^{3} + 30769209 x - 35698643$ |
$9$ |
[9,0] |
$3^{22}\cdot 43^{6}$ |
$2$ |
$180.001187741$ |
$180.00118774087656$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$4865245.74368$ |
9.9.198...841.2 |
$x^{9} - 387 x^{7} + 49923 x^{5} - 2385210 x^{3} + 30769209 x - 5644997$ |
$9$ |
[9,0] |
$3^{22}\cdot 43^{6}$ |
$2$ |
$180.001187741$ |
$180.00118774087656$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3]$ |
$2$ |
$8$ |
$11739683.2351$ |
9.9.425...161.1 |
$x^{9} - x^{8} - 168 x^{7} + 591 x^{6} + 5776 x^{5} - 20434 x^{4} - 69977 x^{3} + 148399 x^{2} + 389543 x + 65245$ |
$9$ |
[9,0] |
$379^{8}$ |
$1$ |
$195.940288063$ |
$195.9402880627296$ |
|
✓ |
|
$C_9$ (as 9T1) |
trivial |
$2$ |
$8$ |
$67087578.0834$ |
9.9.428...721.1 |
$x^{9} - 219 x^{7} - 730 x^{6} + 9855 x^{5} + 36792 x^{4} - 148482 x^{3} - 484866 x^{2} + 609039 x + 810081$ |
$9$ |
[9,0] |
$3^{12}\cdot 73^{8}$ |
$2$ |
$196.086935695$ |
$196.08693569504558$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[3, 3]$ |
$2$ |
$8$ |
$4758026.42602$ |
9.9.428...721.2 |
$x^{9} - 219 x^{7} - 584 x^{6} + 9855 x^{5} + 30222 x^{4} - 139284 x^{3} - 437562 x^{2} + 561735 x + 1779813$ |
$9$ |
[9,0] |
$3^{12}\cdot 73^{8}$ |
$2$ |
$196.086935695$ |
$196.08693569504558$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[3, 3]$ |
$2$ |
$8$ |
$17216132.8683$ |
9.9.532...969.5 |
$x^{9} - 171 x^{7} - 342 x^{6} + 3591 x^{5} + 10260 x^{4} - 13566 x^{3} - 70794 x^{2} - 73701 x - 21869$ |
$9$ |
[9,0] |
$3^{22}\cdot 19^{8}$ |
$2$ |
$200.893677054$ |
$200.8936770541996$ |
|
✓ |
? |
$C_9$ (as 9T1) |
$[9]$ |
$2$ |
$8$ |
$3014820.24187$ |
9.9.532...969.6 |
$x^{9} - 171 x^{7} - 342 x^{6} + 3591 x^{5} + 5130 x^{4} - 26904 x^{3} - 18468 x^{2} + 68913 x - 2375$ |
$9$ |
[9,0] |
$3^{22}\cdot 19^{8}$ |
$2$ |
$200.893677054$ |
$200.8936770541996$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[9]$ |
$2$ |
$8$ |
$22548077.9628$ |