| 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 |
| 21.7.105...767.1 |
$x^{21} - x^{20} - 6 x^{19} + 11 x^{18} + 47 x^{17} - 45 x^{16} - 170 x^{15} + 162 x^{14} + 400 x^{13} - 307 x^{12} - 750 x^{11} + 395 x^{10} + 733 x^{9} - 371 x^{8} - 425 x^{7} + 197 x^{6} + 204 x^{5} - 78 x^{4} - 36 x^{3} + 17 x^{2} - 1$ |
$21$ |
[7,7] |
$-\,17^{3}\cdot 23^{8}\cdot 64879^{3}$ |
$3$ |
$24.0976852901$ |
$5036.634689949233$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$13$ |
$2726200.25314$ |
| 21.7.130...811.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5144 x^{7} - 588 x^{6} + 2051 x^{5} + 392 x^{4} - 329 x^{3} - 98 x^{2} - 7 x - 1$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 19^{3}\cdot 23^{7}$ |
$3$ |
$30.3170126207$ |
|
|
|
✓ |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$13$ |
$51827131.3445$ |
| 21.7.133...103.1 |
$x^{21} - x^{20} - 9 x^{19} + 10 x^{18} + 28 x^{17} - 211 x^{16} + 324 x^{15} + 384 x^{14} - 1692 x^{13} + 1991 x^{12} + 2315 x^{11} - 1214 x^{10} - 9164 x^{9} - 5328 x^{8} + 34796 x^{7} - 21283 x^{6} - 16215 x^{5} + 19798 x^{4} - 2184 x^{3} - 3057 x^{2} + 711 x - 41$ |
$21$ |
[7,7] |
$-\,3^{7}\cdot 29^{19}$ |
$2$ |
$30.3502600324$ |
$39.49131773649383$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$35353252.3989$ |
| 21.7.204...187.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5146 x^{7} - 588 x^{6} + 2065 x^{5} + 392 x^{4} - 357 x^{3} - 98 x^{2} + 7 x + 3$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 11^{3}\cdot 31^{7}$ |
$3$ |
$30.9734076341$ |
|
|
|
✓ |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$13$ |
$74853328.7428$ |
| 21.7.231...543.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5143 x^{7} - 882 x^{6} + 2044 x^{5} + 588 x^{4} - 315 x^{3} - 147 x^{2} - 14 x + 1$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 23^{10}$ |
$2$ |
$31.1558688265$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$13$ |
$62978395.9714$ |
| 21.7.277...279.1 |
$x^{21} - x^{20} - 6 x^{19} + 9 x^{18} + 49 x^{17} - 53 x^{16} - 173 x^{15} + 212 x^{14} + 363 x^{13} - 424 x^{12} - 649 x^{11} + 526 x^{10} + 562 x^{9} - 475 x^{8} - 233 x^{7} + 217 x^{6} + 94 x^{5} - 67 x^{4} - 14 x^{3} + 14 x^{2} - 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 71^{3}\cdot 283583^{3}$ |
$3$ |
$31.4288919779$ |
$21519.55015793778$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$13$ |
$47881465.0911$ |
| 21.7.393...568.1 |
$x^{21} + 3 x^{19} - 36 x^{16} + 51 x^{15} - 108 x^{14} - 210 x^{13} + 1028 x^{12} - 1872 x^{11} + 2298 x^{10} - 147 x^{9} - 2556 x^{8} + 3279 x^{7} - 2508 x^{6} - 828 x^{5} + 1272 x^{4} + 432 x^{3} + 288 x^{2} - 192 x - 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 593^{3}\cdot 1033^{3}$ |
$4$ |
$31.955406697$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$41507831.5952$ |
| 21.7.393...568.2 |
$x^{21} - 21 x^{19} - 2 x^{18} + 189 x^{17} + 36 x^{16} - 957 x^{15} - 270 x^{14} + 3015 x^{13} + 1112 x^{12} - 6183 x^{11} - 2814 x^{10} + 8375 x^{9} + 4644 x^{8} - 7335 x^{7} - 5074 x^{6} + 3780 x^{5} + 3552 x^{4} - 864 x^{3} - 1440 x^{2} + 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 593^{3}\cdot 1033^{3}$ |
$4$ |
$31.955406697$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$48678144.712$ |
| 21.7.755...368.1 |
$x^{21} - 2 x^{20} + x^{19} - 23 x^{18} - 7 x^{17} + 6 x^{16} + 62 x^{15} + 71 x^{14} + 134 x^{13} - 981 x^{12} + 565 x^{11} + 2065 x^{10} - 3120 x^{9} + 5036 x^{8} - 9383 x^{7} + 9486 x^{6} + 1068 x^{5} - 13797 x^{4} + 16346 x^{3} - 9327 x^{2} + 2191 x - 49$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 23^{9}\cdot 233^{6}$ |
$3$ |
$32.9617879071$ |
$207.05554810243555$ |
|
|
|
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$13$ |
$136509280.84$ |
| 21.7.755...368.2 |
$x^{21} - x^{20} - 8 x^{19} + 9 x^{18} + 83 x^{17} - 107 x^{16} - 370 x^{15} + 627 x^{14} + 1058 x^{13} - 1940 x^{12} - 2492 x^{11} + 3886 x^{10} + 3386 x^{9} - 5684 x^{8} - 3489 x^{7} + 3367 x^{6} + 2392 x^{5} - 347 x^{4} - 529 x^{3} + 71 x^{2} - 1$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 23^{9}\cdot 233^{6}$ |
$3$ |
$32.9617879071$ |
$207.05554810243555$ |
|
|
|
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$13$ |
$136509280.84$ |
| 21.7.999...896.1 |
$x^{21} - 3 x^{19} - 10 x^{18} - 79 x^{17} + 237 x^{16} + 265 x^{15} - 691 x^{14} - 190 x^{13} - 2867 x^{12} + 8917 x^{11} - 86 x^{10} - 12167 x^{9} - 1656 x^{8} + 3245 x^{7} + 25876 x^{6} - 21636 x^{5} - 3866 x^{4} + 177 x^{3} + 4752 x^{2} + 2525 x - 2917$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 29^{19}$ |
$2$ |
$33.40478353734483$ |
$45.60064585163551$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$109720182.39051026$ |
| 21.7.457...607.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5141 x^{7} - 882 x^{6} + 2030 x^{5} + 588 x^{4} - 287 x^{3} - 147 x^{2} - 28 x - 3$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 31^{10}$ |
$2$ |
$35.9145372621$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$13$ |
$312384901.42$ |
| 21.7.878...263.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 58 x^{16} - 894 x^{15} - 452 x^{14} + 2477 x^{13} + 1803 x^{12} - 3795 x^{11} - 3826 x^{10} + 2581 x^{9} + 3988 x^{8} - 3 x^{7} - 1577 x^{6} - 413 x^{5} + 231 x^{4} + 106 x^{3} - 5 x^{2} - 8 x - 1$ |
$21$ |
[7,7] |
$-\,11\cdot 23^{7}\cdot 59\cdot 64079789\cdot 6204687157589$ |
$5$ |
$37.0468641591$ |
$2436165269401.3257$ |
|
|
✓ |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$13$ |
$330361715.756$ |
| 21.7.138...288.1 |
$x^{21} - 3 x^{19} - 2 x^{18} - 27 x^{17} - 36 x^{16} + 15 x^{15} + 54 x^{14} + 360 x^{13} + 872 x^{12} + 621 x^{11} - 426 x^{10} - 1745 x^{9} - 3636 x^{8} - 2913 x^{7} + 5854 x^{6} + 18252 x^{5} + 22104 x^{4} + 15056 x^{3} + 6048 x^{2} + 1344 x + 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6}$ |
$4$ |
$37.8616297577$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$13$ |
$435235767.296$ |
| 21.7.138...288.2 |
$x^{21} - 3 x^{19} - 10 x^{18} - 36 x^{17} - 18 x^{16} + 124 x^{15} + 252 x^{14} + 618 x^{13} + 982 x^{12} - 144 x^{11} - 1332 x^{10} - 2358 x^{9} - 4626 x^{8} - 2493 x^{7} + 4586 x^{6} + 5472 x^{5} + 1344 x^{4} + 624 x^{3} + 576 x^{2} - 192 x - 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6}$ |
$4$ |
$37.8616297577$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$13$ |
$301411030.106$ |
| 21.7.139...039.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 53 x^{16} - 899 x^{15} - 382 x^{14} + 2557 x^{13} + 1438 x^{12} - 4286 x^{11} - 3003 x^{10} + 3982 x^{9} + 3413 x^{8} - 1742 x^{7} - 1959 x^{6} + 181 x^{5} + 487 x^{4} + 54 x^{3} - 44 x^{2} - 13 x - 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 709\cdot 743\cdot 681493\cdot 1139465977607$ |
$5$ |
$37.8687180123$ |
$3067346393582.2656$ |
|
|
? |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$13$ |
$509897342.37$ |
| 21.7.307...488.1 |
$x^{21} - 3 x^{19} - 2 x^{18} - 27 x^{17} - 36 x^{16} + 96 x^{15} + 216 x^{14} + 225 x^{13} + 248 x^{12} - 999 x^{11} - 3954 x^{10} - 4655 x^{9} - 684 x^{8} + 5847 x^{7} + 14366 x^{6} + 22572 x^{5} + 23256 x^{4} + 15184 x^{3} + 6048 x^{2} + 1344 x + 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 61^{3}\cdot 42899^{3}$ |
$4$ |
$39.3217832313$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$403309102.408$ |
| 21.7.640...887.1 |
$x^{21} - 3 x^{20} - 17 x^{19} + 29 x^{18} + 208 x^{17} - 102 x^{16} - 1409 x^{15} - x^{14} + 3951 x^{13} + 2695 x^{12} - 3516 x^{11} - 6803 x^{10} - 5950 x^{9} - 1331 x^{8} + 8064 x^{7} + 12913 x^{6} + 7673 x^{5} + 1263 x^{4} - 612 x^{3} - 375 x^{2} - 90 x - 9$ |
$21$ |
[7,7] |
$-\,3^{21}\cdot 29^{9}\cdot 59^{6}$ |
$3$ |
$40.7212378647$ |
$611.6307435196422$ |
|
|
|
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$13$ |
$5132288610.41$ |
| 21.7.209...328.1 |
$x^{21} + 3 x^{19} - 4 x^{18} - 36 x^{17} - 84 x^{16} - 460 x^{15} - 504 x^{14} - 861 x^{13} - 1196 x^{12} - 108 x^{11} - 2400 x^{10} + 6543 x^{9} + 6354 x^{8} - 6891 x^{7} - 1444 x^{6} - 1908 x^{5} - 1128 x^{4} + 2128 x^{3} - 288 x^{2} + 576 x - 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6}$ |
$4$ |
$43.0823524279$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$13$ |
$1457394853.22$ |
| 21.7.241...839.1 |
$x^{21} - 2 x^{20} - 7 x^{19} + 30 x^{18} + 67 x^{17} - 166 x^{16} - 306 x^{15} + 883 x^{14} + 1278 x^{13} - 2134 x^{12} - 3557 x^{11} + 2894 x^{10} + 3853 x^{9} - 3155 x^{8} - 310 x^{7} + 967 x^{6} + 11 x^{5} - 146 x^{4} + 8 x^{3} + 21 x^{2} - 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 577^{9}$ |
$2$ |
$43.3780816068$ |
$115.19982638875807$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$13$ |
$2208285999.6$ |
| 21.7.307...043.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5147 x^{7} - 588 x^{6} + 2072 x^{5} + 392 x^{4} - 371 x^{3} - 98 x^{2} + 14 x + 5$ |
$21$ |
[7,7] |
$-\,7^{24}\cdot 107^{7}$ |
$2$ |
$43.882118985$ |
$230.14587517526783$ |
|
|
✓ |
$C_7^3:(C_3\times S_4)$ (as 21T69) |
trivial |
$2$ |
$13$ |
$5014793055.23$ |
| 21.7.357...016.1 |
$x^{21} - 21 x^{19} - 10 x^{18} + 189 x^{17} + 180 x^{16} - 945 x^{15} - 1350 x^{14} + 2835 x^{13} + 5704 x^{12} - 5103 x^{11} - 15798 x^{10} + 4015 x^{9} + 30996 x^{8} + 7605 x^{7} - 39738 x^{6} - 29376 x^{5} + 22320 x^{4} + 33088 x^{3} + 3456 x^{2} - 11136 x - 4736$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 17\cdot 107^{3}\cdot 21557^{3}$ |
$5$ |
$44.1974016907$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$1492827697.55$ |
| 21.7.814...452.1 |
$x^{21} - 3 x^{20} - 2 x^{19} + 16 x^{18} - 12 x^{17} - 27 x^{16} + 46 x^{15} + 13 x^{14} - 76 x^{13} + 26 x^{12} + 79 x^{11} - 73 x^{10} - 38 x^{9} + 86 x^{8} - 17 x^{7} - 47 x^{6} + 34 x^{5} + 6 x^{4} - 15 x^{3} + 4 x^{2} + 2 x - 1$ |
$21$ |
[7,7] |
$-\,2^{2}\cdot 37\cdot 139\cdot 51194111\cdot 77344387584200382269131$ |
$5$ |
$45.96476198$ |
$2.2652666506726595e+17$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$13$ |
$6523034612.32$ |
| 21.7.911...744.1 |
$x^{21} - 9 x^{19} - 6 x^{18} + 27 x^{17} + 36 x^{16} - 15 x^{15} - 54 x^{14} - 441 x^{13} - 1088 x^{12} + 135 x^{11} + 3570 x^{10} + 7507 x^{9} + 12348 x^{8} + 13593 x^{7} + 2914 x^{6} - 13932 x^{5} - 20952 x^{4} - 14928 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[7,7] |
$-\,2^{33}\cdot 3^{21}\cdot 317^{6}$ |
$3$ |
$46.2122114022$ |
|
|
|
? |
$C_3^7.C_2^4:\GL(3,2)$ (as 21T136) |
trivial |
$2$ |
$13$ |
$8151096814.97$ |
| 21.7.195...007.1 |
$x^{21} + 18 x^{19} - 20 x^{18} + 115 x^{17} - 188 x^{16} + 227 x^{15} - 571 x^{14} - 633 x^{13} + 412 x^{12} - 2156 x^{11} + 1703 x^{10} + 2628 x^{9} + 1031 x^{8} + 1528 x^{7} - 391 x^{6} + 241 x^{5} - 147 x^{4} + 21 x^{3} - 10 x^{2} - x + 1$ |
$21$ |
[7,7] |
$-\,31^{7}\cdot 577^{9}$ |
$2$ |
$47.9161181809$ |
$133.74228949737625$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$13$ |
$3294250109.26$ |
| 21.7.319...832.1 |
$x^{21} - 3 x^{19} - 2 x^{18} - 18 x^{17} - 24 x^{16} - 62 x^{15} - 108 x^{14} + 252 x^{13} + 848 x^{12} + 1350 x^{11} + 2004 x^{10} + 2224 x^{9} + 1440 x^{8} - 1707 x^{7} - 10142 x^{6} - 20412 x^{5} - 22680 x^{4} - 15120 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 11^{12}\cdot 29^{6}$ |
$4$ |
$49.0588600175$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$13$ |
$4802711026.12$ |
| 21.7.467...416.1 |
$x^{21} + 16 x^{19} - 6 x^{18} + 60 x^{17} + 24 x^{16} - 262 x^{15} + 630 x^{14} - 2088 x^{13} + 2404 x^{12} - 2916 x^{11} - 68 x^{10} + 6420 x^{9} - 11568 x^{8} + 16832 x^{7} - 14508 x^{6} + 9552 x^{5} - 4776 x^{4} + 204 x^{3} + 360 x^{2} - 600 x + 500$ |
$21$ |
[7,7] |
$-\,2^{20}\cdot 11^{7}\cdot 73^{12}$ |
$3$ |
$49.9553549451$ |
$112.10031078443632$ |
|
|
? |
$C_{21}:C_6$ (as 21T11) |
trivial |
$2$ |
$13$ |
$11785083997.5$ |
| 21.7.716...967.1 |
$x^{21} - x^{20} - 12 x^{19} + 23 x^{18} + 209 x^{17} - 147 x^{16} - 1451 x^{15} + 840 x^{14} + 5070 x^{13} - 2978 x^{12} - 15769 x^{11} + 12105 x^{10} + 20201 x^{9} - 20848 x^{8} - 11002 x^{7} + 12758 x^{6} + 6317 x^{5} + 686 x^{4} - 267 x^{3} - 53 x^{2} + 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 29^{18}$ |
$2$ |
$50.9792306286$ |
$85.9701958689459$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$9787612489.51$ |
| 21.7.887...816.1 |
$x^{21} - 4 x^{20} - 12 x^{19} + 58 x^{18} + 74 x^{17} - 382 x^{16} - 686 x^{15} + 4800 x^{14} - 12932 x^{13} + 28358 x^{12} - 26452 x^{11} - 81018 x^{10} + 310564 x^{9} - 409604 x^{8} + 110816 x^{7} + 349094 x^{6} - 498694 x^{5} + 323368 x^{4} - 122288 x^{3} + 28698 x^{2} - 4026 x + 266$ |
$21$ |
[7,7] |
$-\,2^{20}\cdot 7^{12}\cdot 11^{19}$ |
$3$ |
$51.5016127648$ |
$65.62985136179203$ |
|
|
? |
$C_{21}:C_6$ (as 21T11) |
$[2]$ |
$2$ |
$13$ |
$16693350374.1$ |
| 21.7.127...232.1 |
$x^{21} - 3 x^{20} - 2 x^{19} + 16 x^{18} - 12 x^{17} - 27 x^{16} + 46 x^{15} + 13 x^{14} - 76 x^{13} + 26 x^{12} + 79 x^{11} - 73 x^{10} - 38 x^{9} + 86 x^{8} - 18 x^{7} - 47 x^{6} + 35 x^{5} + 6 x^{4} - 15 x^{3} + 4 x^{2} + 2 x - 1$ |
$21$ |
[7,7] |
$-\,2^{7}\cdot 43\cdot 5795579\cdot 27741107\cdot 364589707\cdot 3964080223$ |
$6$ |
$52.4051071617$ |
$3.998323662720794e+17$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$13$ |
$32741866392.3$ |
| 21.7.243...728.1 |
$x^{21} - 6 x^{20} + 36 x^{19} - 114 x^{18} + 327 x^{17} - 693 x^{16} + 1251 x^{15} - 2007 x^{14} + 2295 x^{13} - 2524 x^{12} + 1179 x^{11} + 198 x^{10} - 1188 x^{9} + 3231 x^{8} - 2097 x^{7} + 618 x^{6} + 438 x^{5} - 1026 x^{4} + 44 x^{3} - 6 x^{2} + 45 x + 9$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{33}\cdot 547^{6}$ |
$3$ |
$54.0419148345$ |
|
|
|
? |
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$13$ |
$20747070689.6$ |
| 21.7.778...000.1 |
$x^{21} + 7 x^{19} - 70 x^{17} - 651 x^{15} - 106 x^{14} + 147 x^{13} + 1106 x^{12} + 12593 x^{11} + 11676 x^{10} + 28469 x^{9} - 1918 x^{8} - 7394 x^{7} - 60760 x^{6} - 185780 x^{5} + 120540 x^{4} + 233205 x^{3} + 168070 x^{2} - 432040 x + 140680$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 5^{6}\cdot 7^{21}\cdot 23^{7}$ |
$4$ |
$57.1134960008$ |
|
|
|
|
$C_7^3:(C_6\times S_3)$ (as 21T55) |
trivial |
$2$ |
$13$ |
$63196703282.5$ |
| 21.7.778...000.2 |
$x^{21} + 7 x^{19} - 70 x^{17} - 651 x^{15} - 36 x^{14} + 147 x^{13} - 462 x^{12} + 12593 x^{11} - 3640 x^{10} + 28469 x^{9} - 20258 x^{8} - 9958 x^{7} - 50470 x^{6} - 66220 x^{5} - 34300 x^{4} - 31675 x^{3} + 3500 x - 1000$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 5^{6}\cdot 7^{21}\cdot 23^{7}$ |
$4$ |
$57.1134960008$ |
|
|
|
|
$C_7^3:(C_6\times S_3)$ (as 21T55) |
trivial |
$2$ |
$13$ |
$56983942300.0$ |
| 21.7.177...264.1 |
$x^{21} - 2 x^{20} + 4 x^{19} + 70 x^{18} - 226 x^{17} - 406 x^{16} + 1741 x^{15} - 48 x^{14} - 4521 x^{13} + 7056 x^{12} - 14691 x^{11} + 29502 x^{10} - 17641 x^{9} - 46606 x^{8} + 128156 x^{7} - 152086 x^{6} + 57937 x^{5} + 104248 x^{4} - 179097 x^{3} + 119110 x^{2} - 36110 x + 3596$ |
$21$ |
[7,7] |
$-\,2^{36}\cdot 3^{18}\cdot 13^{16}$ |
$3$ |
$59.3924500662$ |
$86.95752969217298$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
trivial |
$2$ |
$13$ |
$260777898205$ |
| 21.7.419...016.1 |
$x^{21} - 6 x^{20} + 6 x^{19} + 14 x^{18} + 117 x^{17} - 756 x^{16} + 993 x^{15} - 72 x^{14} + 5994 x^{13} - 27152 x^{12} + 37740 x^{11} - 31386 x^{10} + 134624 x^{9} - 240930 x^{8} + 143181 x^{7} + 237822 x^{6} - 396504 x^{5} + 2869290 x^{4} - 6027167 x^{3} - 6344232 x^{2} + 4802307 x + 1646714$ |
$21$ |
[7,7] |
$-\,2^{30}\cdot 3^{27}\cdot 13^{15}$ |
$3$ |
$69.0491421275$ |
$101.07244310208699$ |
|
|
|
$S_3\times F_7$ (as 21T15) |
trivial |
$2$ |
$13$ |
$1564637139010$ |
| 21.7.109...648.1 |
$x^{21} - 37 x^{19} - 7 x^{18} + 631 x^{17} - 160 x^{16} - 7660 x^{15} + 5137 x^{14} + 56640 x^{13} - 76851 x^{12} - 243751 x^{11} + 479095 x^{10} + 411482 x^{9} - 1347008 x^{8} + 92559 x^{7} + 992616 x^{6} - 416686 x^{5} + 955747 x^{4} + 870892 x^{3} - 1275931 x^{2} - 1256035 x - 284261$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 7^{12}\cdot 23^{7}\cdot 211^{6}$ |
$4$ |
$72.2651413477$ |
$23981.217627612627$ |
|
|
? |
$C_7\wr S_3$ (as 21T32) |
$[7]$ |
$2$ |
$13$ |
$34482408278.3$ |
| 21.7.806...192.1 |
$x^{21} - 6 x^{19} - 24 x^{18} + 262 x^{17} - 1188 x^{16} - 1310 x^{15} + 16498 x^{14} - 8820 x^{13} - 84272 x^{12} + 91788 x^{11} + 198880 x^{10} - 311512 x^{9} - 182624 x^{8} + 380216 x^{7} + 267120 x^{6} + 75760 x^{5} - 599792 x^{4} - 519200 x^{3} + 413824 x^{2} + 381312 x + 45152$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 7^{24}\cdot 107^{7}$ |
$3$ |
$79.4901472056$ |
$461.2829834966581$ |
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
$2$ |
$13$ |
$3153077248290$ |
| 21.7.828...288.1 |
$x^{21} + 36 x^{19} - 24 x^{18} + 495 x^{17} - 660 x^{16} + 3433 x^{15} - 6426 x^{14} + 13923 x^{13} - 26656 x^{12} + 35424 x^{11} - 43824 x^{10} + 40730 x^{9} - 11304 x^{8} - 26121 x^{7} + 55258 x^{6} - 74196 x^{5} + 71496 x^{4} - 45744 x^{3} + 18144 x^{2} - 4032 x + 384$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{26}\cdot 337\cdot 8388019^{3}$ |
$4$ |
$79.5913271888$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$911621400346$ |
| 21.7.127...944.1 |
$x^{21} - 3 x^{20} + x^{19} - 42 x^{18} - 157 x^{17} + 310 x^{16} + 5798 x^{15} - 3709 x^{14} - 92464 x^{13} + 474108 x^{12} - 2368117 x^{11} + 9006061 x^{10} - 20442035 x^{9} + 24167098 x^{8} + 18849199 x^{7} - 129416738 x^{6} + 120608306 x^{5} + 151200437 x^{4} - 174966569 x^{3} - 172336121 x^{2} + 129418146 x + 31235087$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 29^{6}\cdot 31^{7}\cdot 379^{6}$ |
$4$ |
$81.2322223036$ |
$29339.501842851583$ |
|
|
? |
$C_7\wr S_3$ (as 21T32) |
$[7]$ |
$2$ |
$13$ |
$105149816421$ |
| 21.7.310...000.1 |
$x^{21} - 63 x^{19} - 84 x^{18} + 1512 x^{17} + 3850 x^{16} - 15029 x^{15} - 63668 x^{14} + 19355 x^{13} + 408198 x^{12} + 542696 x^{11} - 448728 x^{10} - 1801933 x^{9} - 2364768 x^{8} - 3841877 x^{7} - 7427812 x^{6} - 9136848 x^{5} - 5209666 x^{4} + 684425 x^{3} + 2417492 x^{2} + 819441 x - 32894$ |
$21$ |
[7,7] |
$-\,2^{20}\cdot 5^{7}\cdot 7^{35}$ |
$3$ |
$84.7582475598$ |
$129.90531209989487$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$13$ |
$84536711969500$ |
| 21.7.374...392.1 |
$x^{21} + 39 x^{19} - 26 x^{18} + 594 x^{17} - 792 x^{16} + 4692 x^{15} - 8856 x^{14} + 22266 x^{13} - 44944 x^{12} + 68904 x^{11} - 103632 x^{10} + 118468 x^{9} - 86544 x^{8} + 29091 x^{7} + 50834 x^{6} - 134244 x^{5} + 156456 x^{4} - 105584 x^{3} + 42336 x^{2} - 9408 x + 896$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 7^{2}\cdot 71^{3}\cdot 547\cdot 283583^{3}$ |
$6$ |
$85.5250992016$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$13$ |
$1320972873570$ |
| 21.7.117...328.1 |
$x^{21} + 36 x^{19} - 24 x^{18} + 477 x^{17} - 636 x^{16} + 2912 x^{15} - 5400 x^{14} + 7893 x^{13} - 12248 x^{12} - 3132 x^{11} + 43512 x^{10} - 108421 x^{9} + 221076 x^{8} - 313047 x^{7} + 275646 x^{6} - 152172 x^{5} + 57816 x^{4} - 19024 x^{3} + 6048 x^{2} - 1344 x + 128$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 97\cdot 577^{9}$ |
$4$ |
$90.3185920954$ |
|
|
|
? |
$C_3^7:C_2\wr D_7$ (as 21T131) |
trivial |
$2$ |
$13$ |
$2316032975570$ |
| 21.7.231...048.1 |
$x^{21} - 21 x^{17} - 280 x^{15} - 138 x^{14} + 98 x^{13} + 1792 x^{12} + 2352 x^{11} + 1008 x^{10} + 13279 x^{9} - 44576 x^{8} + 4321 x^{7} + 142296 x^{6} - 106484 x^{5} + 32928 x^{4} + 355376 x^{3} - 154252 x^{2} - 254912 x + 83900$ |
$21$ |
[7,7] |
$-\,2^{6}\cdot 7^{30}\cdot 107^{7}$ |
$3$ |
$93.272312364$ |
|
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
$2$ |
$13$ |
$13512231302100$ |
| 21.7.629...496.1 |
$x^{21} + 33 x^{19} - 22 x^{18} + 396 x^{17} - 528 x^{16} + 2174 x^{15} - 3996 x^{14} + 5580 x^{13} - 8368 x^{12} + 1944 x^{11} + 15984 x^{10} - 38466 x^{9} + 69768 x^{8} - 97614 x^{7} + 98940 x^{6} - 79704 x^{5} + 55728 x^{4} - 31392 x^{3} + 12096 x^{2} - 2688 x + 256$ |
$21$ |
[7,7] |
$-\,2^{45}\cdot 3^{21}\cdot 61\cdot 809^{6}$ |
$4$ |
$109.155009637$ |
|
|
|
|
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$13$ |
$273459852214000$ |
| 21.7.802...592.1 |
$x^{21} - 21 x^{19} - 5 x^{18} + 189 x^{17} + 90 x^{16} - 1177 x^{15} - 675 x^{14} + 6315 x^{13} + 1984 x^{12} - 25983 x^{11} + 2517 x^{10} + 76399 x^{9} - 31374 x^{8} - 174051 x^{7} + 139683 x^{6} + 290088 x^{5} - 453996 x^{4} - 67056 x^{3} + 594000 x^{2} - 499968 x + 147136$ |
$21$ |
[7,7] |
$-\,2^{13}\cdot 3^{21}\cdot 97\cdot 149^{6}\cdot 211^{6}$ |
$5$ |
$110.426268934$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
$[2]$ |
$2$ |
$13$ |
$58510470637000$ |
| 21.7.384...288.1 |
$x^{21} - 28 x^{15} - 24 x^{14} + 147 x^{9} + 252 x^{8} + 108 x^{7} + 343 x^{3} + 882 x^{2} + 756 x + 216$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 3^{18}\cdot 7^{35}$ |
$3$ |
$118.98261768$ |
|
|
|
? |
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$13$ |
$83199751120200$ |
| 21.7.428...608.1 |
$x^{21} - 63 x^{15} - 54 x^{14} + 9261 x^{3} + 23814 x^{2} + 20412 x + 5832$ |
$21$ |
[7,7] |
$-\,2^{12}\cdot 3^{44}\cdot 7^{21}\cdot 19$ |
$4$ |
$119.588890847$ |
|
|
|
|
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$13$ |
$227380547912000$ |
| 21.7.569...976.1 |
$x^{21} - 49 x^{19} - 98 x^{18} + 826 x^{17} + 2968 x^{16} - 7448 x^{15} - 44616 x^{14} + 22197 x^{13} + 371224 x^{12} + 210063 x^{11} - 1736602 x^{10} - 2769312 x^{9} + 3364144 x^{8} + 7470434 x^{7} - 27811420 x^{6} - 80806096 x^{5} + 4000752 x^{4} + 229127416 x^{3} + 240065168 x^{2} - 1757728 x - 66831808$ |
$21$ |
[7,7] |
$-\,2^{36}\cdot 3^{7}\cdot 7^{35}$ |
$3$ |
$121.223989536$ |
$201.24844413870787$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$13$ |
$23977211379700000$ |
| 21.7.109...192.1 |
$x^{21} - 54 x^{19} - 142 x^{18} + 1125 x^{17} + 5550 x^{16} - 6017 x^{15} - 77418 x^{14} - 70674 x^{13} + 434534 x^{12} + 848124 x^{11} - 983280 x^{10} - 3192759 x^{9} + 1467252 x^{8} + 8862276 x^{7} + 2890596 x^{6} - 11439792 x^{5} - 12529152 x^{4} - 3350624 x^{3} + 785664 x^{2} + 160896 x - 49664$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}\cdot 661$ |
$5$ |
$125.053050438$ |
|
|
|
|
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$13$ |
$647248138887000$ |
| 21.7.118...503.1 |
$x^{21} - 5 x^{20} - 109 x^{19} + 701 x^{18} + 4296 x^{17} - 39756 x^{16} - 48624 x^{15} + 1154631 x^{14} - 1521502 x^{13} - 17113929 x^{12} + 59548164 x^{11} + 83276272 x^{10} - 794402904 x^{9} + 960360912 x^{8} + 3742318991 x^{7} - 13615721957 x^{6} + 9795702580 x^{5} + 34213837684 x^{4} - 101142508280 x^{3} + 124128246896 x^{2} - 77759450304 x + 20461436081$ |
$21$ |
[7,7] |
$-\,7^{3}\cdot 4591^{2}\cdot 1057681^{3}\cdot 117508201^{2}$ |
$4$ |
$125.510884169$ |
$180319772830.39352$ |
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T149) |
$[3]$ |
$2$ |
$13$ |
$35696540240900$ |
