| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 8.2.425927596977747.1 |
$x^{8} - 3 x^{7} - 14 x^{6} + 72 x^{5} + 120 x^{4} - 1758 x^{3} + 3051 x^{2} + 4167 x - 19539$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
? |
$\textrm{GL(2,3)}$ (as 8T23) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$2817.87768675$ |
| 8.2.425927596977747.4 |
$x^{8} - 3 x^{7} - 14 x^{6} - 10 x^{5} + 120 x^{4} - 118 x^{3} - 803 x^{2} - 1245 x - 392$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
|
$\textrm{GL(2,3)}$ (as 8T23) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$24017.7979781$ |
| 8.2.425927596977747.5 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 112 x^{4} - 217 x^{3} + 44 x^{2} + 64 x - 373$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
? |
$\textrm{GL(2,3)}$ (as 8T23) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$2817.87768675$ |
| 8.2.425927596977747.6 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} - 11 x^{4} + 29 x^{3} + 3 x^{2} - 18 x - 168$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
|
$Q_8:S_4$ (as 8T40) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$95011.3480969$ |
| 8.2.425927596977747.10 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 235 x^{4} - 463 x^{3} - 120 x^{2} + 351 x - 2259$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$5517.38273149$ |
| 8.2.425927596977747.11 |
$x^{8} - x^{7} + 3 x^{6} - 93 x^{5} - 489 x^{4} - 1464 x^{3} - 2307 x^{2} - 3858 x - 2196$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
|
$Q_8:S_4$ (as 8T40) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$5054.83273927$ |
| 8.2.425927596977747.13 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 112 x^{4} - 217 x^{3} - 448 x^{2} + 556 x - 496$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
|
$\textrm{GL(2,3)}$ (as 8T23) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$24017.7979781$ |
| 8.2.425927596977747.16 |
$x^{8} - x^{7} + 3 x^{6} - 52 x^{5} - 161 x^{4} + 258 x^{3} + 1711 x^{2} + 4547 x + 4323$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 41^{7}$ |
$2$ |
$67.4010981593$ |
$92.85971330020284$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[8]$ |
$[2, 8]$ |
$2$ |
$4$ |
$8911.01642272$ |
| 8.0.799...913.1 |
$x^{8} - x^{7} + 44 x^{6} - 1405 x^{5} - 10780 x^{4} + 74263 x^{3} + 675587 x^{2} + 1473700 x + 2097988$ |
$8$ |
[0,4] |
$17^{7}\cdot 41^{7}$ |
$2$ |
$307.488360475$ |
$307.48836047472827$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[5, 120]$ |
$[5, 120]$ |
$2$ |
$3$ |
$11973.8491431$ |
| 8.8.861...049.3 |
$x^{8} - x^{7} - 1596 x^{6} + 399 x^{5} + 763833 x^{4} + 130515 x^{3} - 118151146 x^{2} - 32663105 x + 5076740025$ |
$8$ |
[8,0] |
$41^{7}\cdot 89^{7}$ |
$2$ |
$1308.88692819$ |
$1308.8869281912066$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[8]$ |
$2$ |
$7$ |
$91638809746.7$ |
| 8.0.157...553.2 |
$x^{8} - x^{7} + 249 x^{6} - 22930 x^{5} - 180602 x^{4} - 3118202 x^{3} + 113326121 x^{2} + 2385614475 x + 10297018121$ |
$8$ |
[0,4] |
$41^{7}\cdot 97^{7}$ |
$2$ |
$1411.2733551$ |
$1411.2733551005474$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[16136]$ |
$[16136]$ |
$2$ |
$3$ |
$201135.757908$ |
| 8.8.176...473.3 |
$x^{8} - x^{7} - 2457 x^{6} - 28875 x^{5} + 1064896 x^{4} + 13828164 x^{3} - 130233600 x^{2} - 1150743232 x + 7570851328$ |
$8$ |
[8,0] |
$41^{7}\cdot 137^{7}$ |
$2$ |
$1909.04590196$ |
$1909.0459019607583$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[8]$ |
$2$ |
$7$ |
$1316364511280$ |
| 8.0.194...217.1 |
$x^{8} - x^{7} + 495 x^{6} - 10015 x^{5} - 1067432 x^{4} + 39716056 x^{3} + 821747696 x^{2} - 5368502448 x + 98333552384$ |
$8$ |
[0,4] |
$41^{7}\cdot 193^{7}$ |
$2$ |
$2576.60900343$ |
$2576.6090034307076$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[7739528]$ |
$[7739528]$ |
$2$ |
$3$ |
$850774.809401$ |
| 8.8.726...337.2 |
$x^{8} - x^{7} - 4179 x^{6} + 32092 x^{5} + 4784621 x^{4} - 38578692 x^{3} - 1683561978 x^{2} + 10133407476 x - 7855398549$ |
$8$ |
[8,0] |
$41^{7}\cdot 233^{7}$ |
$2$ |
$3038.24159769$ |
$3038.241597686726$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[20]$ |
$[40]$ |
$2$ |
$7$ |
$584329939391$ |
| 8.0.144...633.1 |
$x^{8} - x^{7} + 659 x^{6} + 39349 x^{5} + 4725294 x^{4} + 116837999 x^{3} + 2561433169 x^{2} + 31660957266 x + 222868971593$ |
$8$ |
[0,4] |
$41^{7}\cdot 257^{7}$ |
$2$ |
$3310.37625014$ |
$3310.376250144458$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[3, 95448]$ |
$[3, 95448]$ |
$2$ |
$3$ |
$129037.570656$ |
| 8.8.269...041.3 |
$x^{8} - x^{7} - 5040 x^{6} - 10261 x^{5} + 8270441 x^{4} + 37596643 x^{3} - 4674850474 x^{2} - 30953318553 x + 416258961577$ |
$8$ |
[8,0] |
$41^{7}\cdot 281^{7}$ |
$2$ |
$3579.34783582$ |
$3579.3478358151997$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[4]$ |
$[8]$ |
$2$ |
$7$ |
$98266257946.2$ |
| 8.8.573...377.3 |
$x^{8} - x^{7} - 5614 x^{6} + 46319 x^{5} + 9416596 x^{4} - 125034203 x^{3} - 4078131554 x^{2} + 36856567917 x + 675987039547$ |
$8$ |
[8,0] |
$41^{7}\cdot 313^{7}$ |
$2$ |
$3933.5725986$ |
$3933.5725986031202$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[8]$ |
$2$ |
$7$ |
$211171894295$ |
| 8.8.810...233.1 |
$x^{8} - x^{7} - 8197 x^{6} - 339901 x^{5} - 2102231 x^{4} + 70711933 x^{3} + 759334585 x^{2} - 226884287 x - 13980435166$ |
$8$ |
[8,0] |
$41^{7}\cdot 457^{7}$ |
$2$ |
$5477.88044711$ |
$5477.8804471081385$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[4]$ |
$[8]$ |
$2$ |
$7$ |
$74306247643200$ |
| 16.4.118...625.1 |
$x^{16} - 6 x^{15} + 12 x^{14} + 2 x^{13} - 60 x^{12} + 138 x^{11} - 143 x^{10} - 4 x^{9} + 276 x^{8} - 550 x^{7} + 715 x^{6} - 720 x^{5} + 575 x^{4} - 350 x^{3} + 150 x^{2} - 40 x + 5$ |
$16$ |
[4,6] |
$5^{14}\cdot 41^{7}$ |
$2$ |
$20.7582955549$ |
$105.38641435597748$ |
|
|
? |
$C_8^2:C_4$ (as 16T694) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$23378.6928393$ |
| 16.0.243...000.1 |
$x^{16} - 4 x^{14} + 6 x^{12} - 9 x^{10} + 96 x^{8} - 205 x^{6} + 410 x^{2} + 205$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{11}\cdot 41^{7}$ |
$3$ |
$21.7094995983$ |
$298.077792944188$ |
|
|
|
$\OD_{16}^2:C_4$ (as 16T1106) |
trivial |
trivial |
$2$ |
$7$ |
$41222.420892$ |
| 16.0.243...000.2 |
$x^{16} - 7 x^{15} + 35 x^{14} - 128 x^{13} + 382 x^{12} - 949 x^{11} + 2006 x^{10} - 3634 x^{9} + 5667 x^{8} - 7558 x^{7} + 8570 x^{6} - 8157 x^{5} + 6326 x^{4} - 3850 x^{3} + 1655 x^{2} - 425 x + 125$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{11}\cdot 41^{7}$ |
$3$ |
$21.7094995983$ |
$298.077792944188$ |
|
|
? |
$\OD_{16}^2:C_4$ (as 16T1106) |
trivial |
trivial |
$2$ |
$7$ |
$21560.1445594$ |
| 16.0.243...000.3 |
$x^{16} - 4 x^{15} + 11 x^{14} - 22 x^{13} + 20 x^{12} - 8 x^{11} - 6 x^{10} - 19 x^{9} + 113 x^{8} - 155 x^{7} + 244 x^{6} - 289 x^{5} + 213 x^{4} - 136 x^{3} + 90 x^{2} - 32 x + 4$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{11}\cdot 41^{7}$ |
$3$ |
$21.7094995983$ |
$172.36273373817494$ |
|
|
|
$C_8^2:(C_2\times C_4)$ (as 16T816) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$20042.3917058$ |
| 16.0.243...000.4 |
$x^{16} - 2 x^{15} - 2 x^{14} + 5 x^{13} + x^{12} - 5 x^{11} + 12 x^{10} - 12 x^{9} - 15 x^{8} + 29 x^{7} + 49 x^{6} - 50 x^{5} - 6 x^{4} + 15 x^{3} + 25 x^{2} - 40 x + 20$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{11}\cdot 41^{7}$ |
$3$ |
$21.7094995983$ |
$172.36273373817494$ |
|
|
|
$C_8^2:(C_2\times C_4)$ (as 16T816) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$20042.3917058$ |
| 16.0.779...000.1 |
$x^{16} - 4 x^{14} - 7 x^{12} + 53 x^{10} - 71 x^{8} - 82 x^{6} + 533 x^{4} - 984 x^{2} + 656$ |
$16$ |
[0,8] |
$2^{12}\cdot 5^{10}\cdot 41^{7}$ |
$3$ |
$23.3464948621$ |
|
|
|
? |
$C_2^7.D_4:D_4$ (as 16T1734) |
trivial |
trivial |
$2$ |
$7$ |
$34016.0404209$ |
| 16.0.389...000.1 |
$x^{16} - 3 x^{15} + 5 x^{13} + 18 x^{12} - 67 x^{11} + 69 x^{10} - 20 x^{9} - 24 x^{8} + 88 x^{7} + 477 x^{6} - 1045 x^{5} - 370 x^{4} + 617 x^{3} + 1484 x^{2} + 475 x + 295$ |
$16$ |
[0,8] |
$2^{12}\cdot 5^{11}\cdot 41^{7}$ |
$3$ |
$25.8170913855$ |
$354.47623219353625$ |
|
|
|
$\OD_{16}^2:(C_2\times C_4)$ (as 16T1397) |
trivial |
trivial |
$2$ |
$7$ |
$199752.583811$ |
| 16.8.608...000.1 |
$x^{16} - x^{14} - 4 x^{13} - 26 x^{12} - 62 x^{11} - 181 x^{10} - 6 x^{9} + 331 x^{8} + 84 x^{7} - 209 x^{6} - 36 x^{5} + 96 x^{4} + 14 x^{3} - 19 x^{2} - 2 x + 1$ |
$16$ |
[8,4] |
$2^{8}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$26.5473431584$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1601) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$528904.348363$ |
| 16.0.608...000.1 |
$x^{16} - x^{14} - 9 x^{13} - 21 x^{12} + 23 x^{11} + 4 x^{10} + 74 x^{9} + 206 x^{8} - 121 x^{7} + 76 x^{6} + 214 x^{5} - 439 x^{4} + 59 x^{3} + 121 x^{2} - 537 x + 711$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$26.5473431584$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1601) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$28255.5270125$ |
| 16.4.608...000.3 |
$x^{16} + 4 x^{14} - 24 x^{12} - 46 x^{10} - 199 x^{8} - 410 x^{6} - 615 x^{4} - 205 x^{2} + 205$ |
$16$ |
[4,6] |
$2^{8}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$26.5473431584$ |
$354.47623219353625$ |
|
|
? |
$C_2^7.D_4:D_4$ (as 16T1734) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$84733.4458413$ |
| 16.4.304...000.1 |
$x^{16} + 8 x^{14} + 13 x^{12} - 30 x^{11} - 144 x^{10} + 155 x^{9} - 220 x^{8} + 190 x^{7} + 1631 x^{6} - 3140 x^{5} - 72 x^{4} + 4825 x^{3} - 4322 x^{2} + 725 x + 691$ |
$16$ |
[4,6] |
$2^{8}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$29.3566631055$ |
$354.47623219353625$ |
|
|
|
$C_2^7.C_4^2:C_4$ (as 16T1715) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$233757.678636$ |
| 16.4.304...000.2 |
$x^{16} - 7 x^{15} + 22 x^{14} - 41 x^{13} + 31 x^{12} + 43 x^{11} - 180 x^{10} + 447 x^{9} - 646 x^{8} + 751 x^{7} - 1680 x^{6} + 2881 x^{5} - 3219 x^{4} + 2317 x^{3} - 882 x^{2} + 121 x + 121$ |
$16$ |
[4,6] |
$2^{8}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$29.3566631055$ |
$354.47623219353625$ |
|
|
? |
$C_2^7.C_4^2:C_4$ (as 16T1715) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$205927.032646$ |
| 16.0.398...000.1 |
$x^{16} - 4 x^{14} - 8 x^{13} + 7 x^{12} + 44 x^{11} - 98 x^{10} - 940 x^{9} - 1793 x^{8} + 1968 x^{7} + 15908 x^{6} + 35752 x^{5} + 45756 x^{4} + 36736 x^{3} + 18368 x^{2} + 5248 x + 656$ |
$16$ |
[0,8] |
$2^{20}\cdot 5^{9}\cdot 41^{7}$ |
$3$ |
$29.8573362639$ |
$316.1146474714332$ |
|
|
|
$C_2^7.D_4:D_4$ (as 16T1713) |
trivial |
trivial |
$2$ |
$7$ |
$329751.08725$ |
| 16.0.398...000.3 |
$x^{16} - 6 x^{15} + 13 x^{14} - 38 x^{13} + 181 x^{12} - 458 x^{11} + 553 x^{10} - 126 x^{9} - 532 x^{8} + 126 x^{7} + 553 x^{6} + 458 x^{5} + 181 x^{4} + 38 x^{3} + 13 x^{2} + 6 x + 1$ |
$16$ |
[0,8] |
$2^{20}\cdot 5^{9}\cdot 41^{7}$ |
$3$ |
$29.857336263913524$ |
|
|
|
? |
$C_2^7.D_4:D_4$ (as 16T1713) |
trivial |
trivial |
$2$ |
$7$ |
$344867.59797738655$ |
| 16.4.311...000.4 |
$x^{16} - 34 x^{12} + 151 x^{8} + 246 x^{4} + 41$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{12}\cdot 41^{7}$ |
$3$ |
$33.9508331454$ |
$316.1146474714332$ |
|
|
|
$\OD_{16}^2:(C_2\times C_4)$ (as 16T1397) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$2505349.51666$ |
| 16.4.311...000.8 |
$x^{16} + 31 x^{12} - 54 x^{8} - 164 x^{4} + 41$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{12}\cdot 41^{7}$ |
$3$ |
$33.95083314539379$ |
$316.1146474714332$ |
|
|
? |
$\OD_{16}^2:(C_2\times C_4)$ (as 16T1397) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$1717135.559166074$ |
| 16.8.155...000.1 |
$x^{16} - 13 x^{14} + 59 x^{12} - 92 x^{10} - 109 x^{8} + 410 x^{6} + 410 x^{4} - 1640 x^{2} + 205$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$37.5436127395$ |
$386.55907225309664$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1601) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$4432882.9202$ |
| 16.0.155...000.1 |
$x^{16} + 9 x^{14} - 49 x^{12} - 191 x^{10} + 506 x^{8} + 1025 x^{6} + 615 x^{4} + 410 x^{2} + 205$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$37.5436127395$ |
$386.55907225309664$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1601) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$285326.723261$ |
| 16.8.155...000.2 |
$x^{16} - 9 x^{14} + 21 x^{12} + 61 x^{10} - 384 x^{8} + 205 x^{6} + 1845 x^{4} - 2665 x^{2} + 205$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$37.543612739529465$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1601) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$9779594.466297263$ |
| 16.8.155...000.3 |
$x^{16} - 4 x^{14} - 24 x^{12} + 11 x^{10} + 96 x^{8} + 410 x^{4} - 615 x^{2} + 205$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{13}\cdot 41^{7}$ |
$3$ |
$37.543612739529465$ |
$386.55907225309664$ |
|
|
|
$C_2^7.C_4\wr C_2$ (as 16T1601) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$11340318.11347551$ |
| 16.0.268...125.1 |
$x^{16} - 3 x^{15} + 22 x^{14} - 26 x^{13} + 170 x^{12} - 215 x^{11} + 1077 x^{10} - 1195 x^{9} + 3442 x^{8} - 7745 x^{7} + 10933 x^{6} - 26066 x^{5} - 13818 x^{4} - 58627 x^{3} + 154904 x^{2} + 531130 x + 532121$ |
$16$ |
[0,8] |
$5^{11}\cdot 41^{11}$ |
$2$ |
$38.8446112511$ |
$86.18136686908747$ |
|
|
|
$C_8^2:C_4$ (as 16T664) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1135187.57575$ |
| 16.12.779...000.1 |
$x^{16} - 4 x^{15} - 12 x^{14} + 72 x^{13} - 79 x^{12} - 54 x^{11} + 180 x^{10} - 134 x^{9} - 11 x^{8} - 98 x^{7} - 20 x^{6} + 358 x^{5} - 19 x^{4} - 126 x^{3} - 8 x^{2} + 8 x + 1$ |
$16$ |
[12,2] |
$2^{16}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$41.5165911098$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1635) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$13$ |
$43556373.2795$ |
| 16.4.779...000.4 |
$x^{16} - 4 x^{15} - 12 x^{14} + 22 x^{13} - 14 x^{12} - 134 x^{11} + 105 x^{10} + 66 x^{9} - 561 x^{8} + 132 x^{7} + 420 x^{6} - 1072 x^{5} - 224 x^{4} + 704 x^{3} - 768 x^{2} - 512 x + 256$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$41.5165911098$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1635) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$9$ |
$2326901.42476$ |
| 16.4.779...000.7 |
$x^{16} - 6 x^{15} + 3 x^{14} + 78 x^{13} - 289 x^{12} + 204 x^{11} + 1330 x^{10} - 4666 x^{9} + 7249 x^{8} - 6472 x^{7} + 6465 x^{6} - 13568 x^{5} + 23401 x^{4} - 23524 x^{3} + 13292 x^{2} - 3688 x + 361$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$41.51659110984125$ |
|
|
|
|
$C_2^7.D_4:D_4$ (as 16T1713) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$5962295.566858462$ |
| 16.4.134...625.1 |
$x^{16} - x^{15} + 16 x^{14} - 4 x^{13} + 21 x^{12} + 198 x^{11} - 1107 x^{10} - 857 x^{9} - 4743 x^{8} - 14819 x^{7} + 2152 x^{6} - 41841 x^{5} + 28386 x^{4} - 37713 x^{3} + 31819 x^{2} + 6612 x - 3249$ |
$16$ |
[4,6] |
$5^{12}\cdot 41^{11}$ |
$2$ |
$42.9552652091$ |
$86.18136686908747$ |
|
|
|
$C_8^2:C_4$ (as 16T664) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$3645871.00169$ |
| 16.4.199...000.1 |
$x^{16} - 2 x^{15} - 12 x^{14} - 44 x^{13} + 185 x^{12} + 186 x^{11} + 848 x^{10} - 2102 x^{9} - 2724 x^{8} - 5320 x^{7} + 2090 x^{6} + 7230 x^{5} + 530 x^{4} - 80 x^{3} - 10240 x^{2} - 3590 x + 9505$ |
$16$ |
[4,6] |
$2^{24}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$58.713326211$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1635) |
$[2, 2, 2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$9$ |
$14903965.1216$ |
| 16.12.199...000.1 |
$x^{16} - 18 x^{14} - 87 x^{12} + 2224 x^{10} - 2350 x^{8} - 13366 x^{6} + 17548 x^{4} - 2788 x^{2} + 41$ |
$16$ |
[12,2] |
$2^{24}\cdot 5^{14}\cdot 41^{7}$ |
$3$ |
$58.713326211$ |
$298.077792944188$ |
|
|
? |
$C_2^7.C_4\wr C_2$ (as 16T1635) |
$[2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$13$ |
$402684973.582$ |
| 16.8.177...201.1 |
$x^{16} - 5 x^{15} - 88 x^{14} + 584 x^{13} + 4158 x^{12} - 27910 x^{11} - 146023 x^{10} + 677150 x^{9} + 3364332 x^{8} - 7669946 x^{7} - 45948558 x^{6} + 15988021 x^{5} + 357512186 x^{4} + 368488064 x^{3} - 1206628366 x^{2} - 2236180544 x - 927690517$ |
$16$ |
[8,4] |
$41^{13}\cdot 61^{8}$ |
$2$ |
$159.606950934$ |
$201.30325259286246$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
$[4]$ |
$[4]$ |
$2$ |
$11$ |
$151512570997$ |
| 16.0.219...841.1 |
$x^{16} - 6 x^{15} + 18 x^{14} - 914 x^{13} - 11643 x^{12} - 4505 x^{11} - 666621 x^{10} + 6544220 x^{9} + 192945359 x^{8} - 92956623 x^{7} + 18779161722 x^{6} - 108041397253 x^{5} + 710394592157 x^{4} - 4082313435256 x^{3} + 20830100827364 x^{2} - 22248194975662 x + 244550645566343$ |
$16$ |
[0,8] |
$41^{11}\cdot 43^{12}$ |
$2$ |
$215.719916335$ |
$432.799964339086$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
$[10]$ |
$[10]$ |
$2$ |
$7$ |
$82497909972.1$ |
| 16.8.245...041.4 |
$x^{16} - 4 x^{15} - 62 x^{14} - 365 x^{13} - 36296 x^{12} + 239825 x^{11} + 2824948 x^{10} - 12911947 x^{9} - 72705899 x^{8} + 196796199 x^{7} + 1652715612 x^{6} - 4402541455 x^{5} - 34785033579 x^{4} - 24368392662 x^{3} + 617809678981 x^{2} + 1809057925185 x + 981554628449$ |
$16$ |
[8,4] |
$41^{13}\cdot 61^{12}$ |
$2$ |
$446.050735523$ |
$562.5786556087241$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
$[4]$ |
$[2, 4]$ |
$2$ |
$11$ |
$251939001427000$ |
| 16.0.229...168.4 |
$x^{16} + 656 x^{14} + 174824 x^{12} + 24260192 x^{10} + 1873874004 x^{8} + 80765299104 x^{6} + 1894303058256 x^{4} + 22247465019968 x^{2} + 100501518711458$ |
$16$ |
[0,8] |
$2^{79}\cdot 41^{14}$ |
$2$ |
$789.807908724$ |
$789.807908724367$ |
✓ |
✓ |
? |
$C_{16}$ (as 16T1) |
$[8, 108312968]$ |
$[108312968, 8]$ |
$2$ |
$7$ |
$85463586.75547288$ |
| 16.16.229...168.4 |
$x^{16} - 656 x^{14} + 174824 x^{12} - 24260192 x^{10} + 1873874004 x^{8} - 80765299104 x^{6} + 1894303058256 x^{4} - 22247465019968 x^{2} + 100501518711458$ |
$16$ |
[16,0] |
$2^{79}\cdot 41^{14}$ |
$2$ |
$789.807908724$ |
$789.807908724367$ |
|
✓ |
? |
$C_{16}$ (as 16T1) |
$[4, 4]$ |
$[8, 8]$ |
$2$ |
$15$ |
$102928314007091120$ |
