| 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 |
| 16.0.2779733938787757.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 26 x^{13} + 39 x^{12} - 53 x^{11} + 74 x^{10} - 107 x^{9} + 153 x^{8} - 196 x^{7} + 213 x^{6} - 191 x^{5} + 138 x^{4} - 77 x^{3} + 31 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 7^{2}\cdot 37^{2}\cdot 151^{2}\cdot 277$ |
$5$ |
$9.23103083876$ |
$5700.840201233499$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$6$ |
$7$ |
$20.5837782538$ |
| 16.0.3006123291015625.1 |
$x^{16} - x^{15} - 3 x^{14} + 6 x^{13} + x^{12} - 10 x^{11} + 8 x^{10} + 5 x^{9} - 13 x^{8} + 5 x^{7} + 8 x^{6} - 10 x^{5} + x^{4} + 6 x^{3} - 3 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 11^{4}\cdot 29^{2}$ |
$3$ |
$9.2763136443$ |
$59.72041882063591$ |
|
|
? |
$D_4^2:C_4$ (as 16T547) |
trivial |
$10$ |
$7$ |
$35.8754367412$ |
| 16.0.3091162921500672.1 |
$x^{16} - 2 x^{15} + 8 x^{14} - 18 x^{13} + 35 x^{12} - 62 x^{11} + 92 x^{10} - 118 x^{9} + 138 x^{8} - 142 x^{7} + 127 x^{6} - 104 x^{5} + 77 x^{4} - 46 x^{3} + 20 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{8}\cdot 193^{3}$ |
$3$ |
$9.29250104192$ |
$179.373633178251$ |
|
|
? |
$C_4\wr C_2^2$ (as 16T1202) |
trivial |
$12$ |
$7$ |
$43.8698041698$ |
| 16.0.3100665090835456.1 |
$x^{16} + 2 x^{14} + 4 x^{12} + 6 x^{10} + 8 x^{8} + 7 x^{6} + 5 x^{4} + 3 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{10}\cdot 1740113^{2}$ |
$2$ |
$9.29428378397$ |
$4838.602746804308$ |
|
|
? |
$C_2^7.S_8$ (as 16T1945) |
trivial |
$2$ |
$7$ |
$7.31402076949$ |
| 16.0.3143861048180736.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 8 x^{13} - 4 x^{12} + 30 x^{11} - 56 x^{10} + 58 x^{9} - 18 x^{8} - 48 x^{7} + 98 x^{6} - 102 x^{5} + 73 x^{4} - 40 x^{3} + 18 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{8}\cdot 13^{4}$ |
$3$ |
$9.30232393605$ |
$21.005585720479342$ |
|
|
? |
$C_2\wr C_2^2$ (as 16T149) |
trivial |
$12$ |
$7$ |
$44.6663869612$ |
| 16.0.3207314697265625.1 |
$x^{16} - 2 x^{15} - x^{14} + x^{13} + 11 x^{12} - 11 x^{11} - 10 x^{10} + 5 x^{9} + 22 x^{8} - 10 x^{7} - 15 x^{6} + 3 x^{5} + 11 x^{4} - 2 x^{3} - 4 x^{2} + x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 181^{2}\cdot 401$ |
$3$ |
$9.31394884654$ |
$900.8219853969824$ |
|
|
? |
$C_4^4.C_2\wr C_4$ (as 16T1771) |
trivial |
$10$ |
$7$ |
$37.3668375913$ |
| 16.0.3243658447265625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 30 x^{13} + 57 x^{12} - 100 x^{11} + 157 x^{10} - 215 x^{9} + 250 x^{8} - 240 x^{7} + 183 x^{6} - 110 x^{5} + 57 x^{4} - 30 x^{3} + 16 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{14}$ |
$2$ |
$9.3205103882$ |
$9.320510388204081$ |
|
✓ |
? |
$C_8: C_2$ (as 16T6) |
trivial |
$30$ |
$7$ |
$112.874368042$ |
| 16.0.3345005787800625.1 |
$x^{16} - 5 x^{15} + 12 x^{14} - 19 x^{13} + 21 x^{12} - 16 x^{11} + 6 x^{10} + 12 x^{9} - 28 x^{8} + 21 x^{7} + x^{6} - 20 x^{5} + 28 x^{4} - 20 x^{3} + 10 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{4}\cdot 13^{8}$ |
$3$ |
$9.33845014563$ |
$13.96424004376894$ |
|
|
? |
$D_8:C_2$ (as 16T47) |
trivial |
$6$ |
$7$ |
$22.9306095521$ |
| 16.0.3347302586328125.1 |
$x^{16} - 6 x^{15} + 20 x^{14} - 45 x^{13} + 76 x^{12} - 98 x^{11} + 94 x^{10} - 58 x^{9} + 8 x^{8} + 28 x^{7} - 37 x^{6} + 28 x^{5} - 13 x^{4} + 6 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 61^{2}\cdot 101\cdot 151^{2}$ |
$4$ |
$9.33885077346$ |
$2156.7463921379353$ |
|
|
✓ |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$7$ |
$7.65571718077$ |
| 16.0.3571460308796416.1 |
$x^{16} - 2 x^{14} + 4 x^{10} - 4 x^{8} + x^{6} + 3 x^{4} - 3 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{10}\cdot 1867553^{2}$ |
$2$ |
$9.37676138074$ |
$5012.653784966714$ |
|
|
? |
$C_2^7.S_8$ (as 16T1945) |
trivial |
$2$ |
$7$ |
$7.9464198774$ |
| 16.0.3692461181640625.1 |
$x^{16} - 2 x^{15} - 2 x^{14} + 9 x^{13} - 3 x^{12} - 15 x^{11} + 17 x^{10} + 8 x^{9} - 25 x^{8} + 8 x^{7} + 17 x^{6} - 15 x^{5} - 3 x^{4} + 9 x^{3} - 2 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 3889^{2}$ |
$2$ |
$9.39630804632$ |
$208.51940394717084$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$40.8735633138$ |
| 16.0.3750900906670801.1 |
$x^{16} - 4 x^{15} + 10 x^{14} - 18 x^{13} + 29 x^{12} - 43 x^{11} + 58 x^{10} - 73 x^{9} + 85 x^{8} - 88 x^{7} + 81 x^{6} - 65 x^{5} + 45 x^{4} - 26 x^{3} + 12 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$13^{2}\cdot 43^{2}\cdot 331^{4}$ |
$3$ |
$9.40553436247$ |
$430.1499738463319$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$8.20527213707$ |
| 16.0.3914091521024229.1 |
$x^{16} - 2 x^{15} + x^{14} - x^{13} + 4 x^{12} - 4 x^{11} + 5 x^{10} - 8 x^{9} + 6 x^{8} - 5 x^{7} + 8 x^{6} - 7 x^{5} + 7 x^{4} - 7 x^{3} + 4 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 61\cdot 98893^{2}$ |
$3$ |
$9.43060241959$ |
$4254.1061340779925$ |
|
|
✓ |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$6$ |
$7$ |
$25.217952399$ |
| 16.0.4045039500390625.1 |
$x^{16} - 5 x^{15} + 10 x^{14} - 6 x^{13} - 12 x^{12} + 27 x^{11} - 16 x^{10} - 14 x^{9} + 32 x^{8} - 27 x^{7} + 16 x^{6} - 11 x^{5} + 8 x^{4} - 3 x^{3} + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 11^{4}\cdot 29^{4}$ |
$3$ |
$9.45001880937$ |
$39.93745109543172$ |
|
|
? |
$C_2\wr D_4$ (as 16T388) |
trivial |
$2$ |
$7$ |
$8.56826776068$ |
| 16.0.4096000000000000.1 |
$x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 47 x^{12} - 30 x^{11} - 18 x^{10} + 72 x^{9} - 95 x^{8} + 72 x^{7} - 18 x^{6} - 30 x^{5} + 47 x^{4} - 36 x^{3} + 18 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 5^{12}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
|
✓ |
? |
$C_2^2 : C_4$ (as 16T10) |
trivial |
$20$ |
$7$ |
$87.2940978199$ |
| 16.0.4186494384765625.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 6 x^{13} - 5 x^{12} + 15 x^{11} - 6 x^{10} - 17 x^{9} + 26 x^{8} - 7 x^{7} - 16 x^{6} + 17 x^{5} - 2 x^{4} - 9 x^{3} + 9 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 41^{2}\cdot 101^{2}$ |
$3$ |
$9.47034187384$ |
$215.16920661222215$ |
|
|
? |
$C_2^2\wr C_2^2.D_4$ (as 16T1720) |
trivial |
$10$ |
$7$ |
$43.5759224128$ |
| 16.0.4393378612917909.1 |
$x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 6 x^{11} + 4 x^{10} - x^{8} + 4 x^{6} + 6 x^{5} + 6 x^{4} + 6 x^{3} + 5 x^{2} + 3 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 61\cdot 104773^{2}$ |
$3$ |
$9.49893496957$ |
$4378.75084927197$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$6$ |
$7$ |
$27.0045913409$ |
| 16.0.4540317078515625.1 |
$x^{16} - 3 x^{15} + 4 x^{14} - 3 x^{13} + 11 x^{10} - 24 x^{9} + 29 x^{8} - 24 x^{7} + 11 x^{6} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{8}\cdot 11^{6}$ |
$3$ |
$9.51848624089$ |
$23.393227447460962$ |
|
|
? |
$D_4:D_4$ (as 16T141) |
trivial |
$6$ |
$7$ |
$27.6507723749$ |
| 16.0.4559007230078125.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 6 x^{13} + 11 x^{12} - 19 x^{11} + 26 x^{10} - 30 x^{9} + 33 x^{8} - 30 x^{7} + 26 x^{6} - 19 x^{5} + 11 x^{4} - 6 x^{3} + 3 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 11^{4}\cdot 59^{2}\cdot 229$ |
$4$ |
$9.52093044767$ |
$862.0353821044703$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$7$ |
$9.23010708309$ |
| 16.0.4897760256000000.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 6 x^{13} - 10 x^{12} + 28 x^{11} - 8 x^{10} - 90 x^{9} + 253 x^{8} - 396 x^{7} + 433 x^{6} - 352 x^{5} + 218 x^{4} - 102 x^{3} + 35 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{14}\cdot 5^{6}$ |
$3$ |
$9.5636757927$ |
$17.487937673507474$ |
|
|
? |
$D_8:C_4$ (as 16T114) |
trivial |
$12$ |
$7$ |
$59.5214550029$ |
| 16.0.4919707275390625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 29 x^{13} + 50 x^{12} - 77 x^{11} + 112 x^{10} - 149 x^{9} + 176 x^{8} - 182 x^{7} + 159 x^{6} - 118 x^{5} + 73 x^{4} - 36 x^{3} + 15 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 67^{4}$ |
$2$ |
$9.56634862885$ |
$27.369376545007917$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$10$ |
$7$ |
$48.4508350282$ |
| 16.0.5190614520439741.1 |
$x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 15 x^{12} - 15 x^{11} + 12 x^{10} - 5 x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} + 3 x^{4} - 5 x^{3} - x^{2} + 1$ |
$16$ |
[0,8] |
$617^{2}\cdot 2389^{3}$ |
$2$ |
$9.59845147343$ |
$8487.986777006932$ |
|
|
? |
$C_2^8.S_8$ (as 16T1948) |
trivial |
$2$ |
$7$ |
$10.0160978095$ |
| 16.0.5236602731044893.1 |
$x^{16} - 7 x^{15} + 26 x^{14} - 66 x^{13} + 125 x^{12} - 180 x^{11} + 195 x^{10} - 148 x^{9} + 60 x^{8} + 21 x^{7} - 58 x^{6} + 51 x^{5} - 22 x^{4} - 2 x^{3} + 9 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 13^{4}\cdot 181^{2}\cdot 853$ |
$4$ |
$9.6037445943$ |
$2453.839236787936$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$6$ |
$7$ |
$29.7678343854$ |
| 16.0.5415791883780096.1 |
$x^{16} - 4 x^{15} + 11 x^{14} - 24 x^{13} + 46 x^{12} - 84 x^{11} + 143 x^{10} - 208 x^{9} + 259 x^{8} - 284 x^{7} + 278 x^{6} - 234 x^{5} + 160 x^{4} - 84 x^{3} + 32 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{10}\cdot 7^{2}\cdot 13^{4}$ |
$4$ |
$9.62396141075$ |
$43.49022283071465$ |
|
|
? |
$D_4^2:C_2^2$ (as 16T595) |
trivial |
$12$ |
$7$ |
$63.1744988972$ |
| 16.0.5455162516701184.1 |
$x^{16} - 4 x^{13} + 3 x^{12} + 8 x^{10} - 8 x^{9} + x^{8} - 8 x^{7} + 8 x^{6} + 3 x^{4} - 4 x^{3} + 1$ |
$16$ |
[0,8] |
$2^{32}\cdot 7^{4}\cdot 23^{2}$ |
$3$ |
$9.628319226$ |
$50.75431016179808$ |
|
|
? |
$D_4^2:C_2^2$ (as 16T509) |
trivial |
$8$ |
$7$ |
$40.8921494432$ |
| 16.0.5572562780160000.1 |
$x^{16} - 2 x^{14} - 7 x^{12} + 4 x^{10} + 34 x^{8} + 50 x^{6} + 32 x^{4} + 8 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$9.64114102734$ |
$14.416868484808525$ |
|
|
? |
$C_4:D_4$ (as 16T43) |
trivial |
$12$ |
$7$ |
$62.6647388247$ |
| 16.0.5575888916015625.1 |
$x^{16} - 5 x^{15} + 15 x^{14} - 30 x^{13} + 49 x^{12} - 70 x^{11} + 90 x^{10} - 105 x^{9} + 111 x^{8} - 105 x^{7} + 90 x^{6} - 70 x^{5} + 49 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{12}\cdot 59^{2}$ |
$3$ |
$9.64150058785$ |
$44.48505546908213$ |
|
|
? |
$C_2^5:C_4$ (as 16T261) |
trivial |
$30$ |
$7$ |
$155.628338249$ |
| 16.0.5605632412826517.1 |
$x^{16} - 4 x^{15} + 11 x^{14} - 24 x^{13} + 46 x^{12} - 75 x^{11} + 104 x^{10} - 121 x^{9} + 121 x^{8} - 107 x^{7} + 86 x^{6} - 63 x^{5} + 43 x^{4} - 27 x^{3} + 14 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$3^{10}\cdot 37^{7}$ |
$2$ |
$9.64470699747$ |
$34.197332740531884$ |
|
|
? |
$C_2^4.D_8$ (as 16T675) |
trivial |
$6$ |
$7$ |
$32.1900879299$ |
| 16.0.5821863490955437.1 |
$x^{16} - 4 x^{15} + 10 x^{14} - 17 x^{13} + 23 x^{12} - 27 x^{11} + 30 x^{10} - 30 x^{9} + 25 x^{8} - 14 x^{7} + 6 x^{6} - 7 x^{5} + 15 x^{4} - 20 x^{3} + 15 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$19^{2}\cdot 101^{2}\cdot 277\cdot 2389^{2}$ |
$4$ |
$9.66754886986$ |
$35635.71252269274$ |
|
|
? |
$C_2^8.S_8$ (as 16T1948) |
trivial |
$2$ |
$7$ |
$10.6211653408$ |
| 16.0.5850424087444225.1 |
$x^{16} - x^{15} - 2 x^{14} + 6 x^{13} + x^{12} - 16 x^{11} + 16 x^{10} + 5 x^{9} - 19 x^{8} + 5 x^{7} + 16 x^{6} - 16 x^{5} + x^{4} + 6 x^{3} - 2 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{2}\cdot 37^{2}\cdot 643^{4}$ |
$3$ |
$9.67050623513$ |
$344.8985358043725$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$10.6388599051$ |
| 16.0.5960322509765625.1 |
$x^{16} - 5 x^{15} + 11 x^{14} - 10 x^{13} - 10 x^{12} + 45 x^{11} - 56 x^{10} - 10 x^{9} + 159 x^{8} - 315 x^{7} + 374 x^{6} - 300 x^{5} + 160 x^{4} - 50 x^{3} + 6 x^{2} + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{12}\cdot 61^{2}$ |
$3$ |
$9.68176105277$ |
$45.23275582376457$ |
|
|
? |
$C_2^5:C_4$ (as 16T261) |
trivial |
$30$ |
$7$ |
$161.821613678$ |
| 16.0.6158959248447369.1 |
$x^{16} - 3 x^{15} + 2 x^{14} + 6 x^{13} - 10 x^{12} - 3 x^{11} + 23 x^{10} - 24 x^{9} + 7 x^{8} + 6 x^{7} + x^{6} - 15 x^{5} + 20 x^{4} - 15 x^{3} + 7 x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$3^{12}\cdot 7^{4}\cdot 13^{6}$ |
$3$ |
$9.70161884492$ |
$41.29024647011401$ |
|
|
? |
$C_4^2:D_4$ (as 16T211) |
trivial |
$6$ |
$7$ |
$33.7844971841$ |
| 16.0.6158959248447369.2 |
$x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 17 x^{12} - 18 x^{11} + 13 x^{10} + 3 x^{9} - 29 x^{8} + 45 x^{7} - 34 x^{6} + 3 x^{5} + 23 x^{4} - 27 x^{3} + 17 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$3^{12}\cdot 7^{4}\cdot 13^{6}$ |
$3$ |
$9.70161884492$ |
$41.29024647011401$ |
|
|
? |
$C_4^2:D_4$ (as 16T211) |
trivial |
$6$ |
$7$ |
$33.0234170129$ |
| 16.0.6298009600000000.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 10 x^{13} + 11 x^{12} - 12 x^{11} + 10 x^{10} - 4 x^{9} + x^{8} - 4 x^{7} + 10 x^{6} - 12 x^{5} + 11 x^{4} - 10 x^{3} + 8 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 5^{8}\cdot 31^{2}$ |
$3$ |
$9.71516559153$ |
$35.21363372331802$ |
|
|
? |
$C_2\wr D_4$ (as 16T396) |
trivial |
$4$ |
$7$ |
$22.3523537457$ |
| 16.0.6468474822995241.1 |
$x^{16} - 4 x^{15} + 9 x^{14} - 14 x^{13} + 16 x^{12} - 9 x^{11} - 8 x^{10} + 27 x^{9} - 35 x^{8} + 27 x^{7} - 8 x^{6} - 9 x^{5} + 16 x^{4} - 14 x^{3} + 9 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$9.73139538561$ |
$202.7239502377556$ |
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$11.6239832087$ |
| 16.0.6472705322265625.1 |
$x^{16} - x^{15} + x^{14} + x^{13} + 3 x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 9 x^{7} + 6 x^{6} + 8 x^{5} + 8 x^{4} + 3 x^{3} + 4 x^{2} + 3 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 19^{2}\cdot 271^{2}$ |
$3$ |
$9.73179304548$ |
$239.93242815578742$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$56.3298547938$ |
| 16.0.6561000000000000.1 |
$x^{16} - 5 x^{15} + 15 x^{14} - 32 x^{13} + 56 x^{12} - 85 x^{11} + 114 x^{10} - 134 x^{9} + 131 x^{8} - 98 x^{7} + 42 x^{6} + 9 x^{5} - 28 x^{4} + 18 x^{3} - x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$9.74003746425$ |
$16.3807251762544$ |
|
|
? |
$C_4 \times D_4$ (as 16T19) |
trivial |
$30$ |
$7$ |
$175.01473438$ |
| 16.0.6634204312890625.1 |
$x^{16} - 7 x^{15} + 27 x^{14} - 73 x^{13} + 160 x^{12} - 304 x^{11} + 509 x^{10} - 730 x^{9} + 869 x^{8} - 839 x^{7} + 654 x^{6} - 416 x^{5} + 221 x^{4} - 98 x^{3} + 34 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 19^{8}$ |
$2$ |
$9.74679434481$ |
$9.746794344808963$ |
|
✓ |
? |
$D_{8}$ (as 16T13) |
trivial |
$2$ |
$7$ |
$11.4915268613$ |
| 16.0.6741949462890625.1 |
$x^{16} + x^{14} - 5 x^{13} + 2 x^{12} - 5 x^{11} + 13 x^{10} - 10 x^{9} + 15 x^{8} - 20 x^{7} + 17 x^{6} - 20 x^{5} + 17 x^{4} - 10 x^{3} + 9 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$5^{14}\cdot 1051^{2}$ |
$2$ |
$9.75661332423$ |
$132.55622019828223$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$58.1502195758$ |
| 16.0.6788091008176384.1 |
$x^{16} - 2 x^{14} - 4 x^{12} + 10 x^{10} + 3 x^{8} - 12 x^{6} - x^{4} + 5 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 47^{2}\cdot 331^{4}$ |
$3$ |
$9.76077335363$ |
$419.53231474906187$ |
|
|
? |
$C_2\wr C_2^3.S_4$ (as 16T1852) |
trivial |
$2$ |
$7$ |
$11.7319712743$ |
| 16.0.6884340550074368.1 |
$x^{16} - 6 x^{15} + 22 x^{14} - 56 x^{13} + 110 x^{12} - 174 x^{11} + 232 x^{10} - 266 x^{9} + 259 x^{8} - 202 x^{7} + 112 x^{6} - 30 x^{5} - 14 x^{4} + 20 x^{3} - 6 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 17^{7}$ |
$2$ |
$9.7693663658$ |
$33.74331915933294$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
trivial |
$4$ |
$7$ |
$23.5886655901$ |
| 16.0.6926910400390625.1 |
$x^{16} - 7 x^{15} + 25 x^{14} - 55 x^{13} + 75 x^{12} - 46 x^{11} - 43 x^{10} + 140 x^{9} - 160 x^{8} + 80 x^{7} + 37 x^{6} - 109 x^{5} + 110 x^{4} - 70 x^{3} + 30 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$5^{15}\cdot 61^{3}$ |
$2$ |
$9.77313106739$ |
$98.69195574460448$ |
|
|
? |
$C_4\wr C_4$ (as 16T1192) |
trivial |
$10$ |
$7$ |
$65.2827160145$ |
| 16.0.7058653305387264.1 |
$x^{16} - 2 x^{15} + 2 x^{14} - 3 x^{13} + 11 x^{12} - 19 x^{11} + 10 x^{10} + 21 x^{9} - 44 x^{8} + 21 x^{7} + 40 x^{6} - 89 x^{5} + 92 x^{4} - 60 x^{3} + 26 x^{2} - 7 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 3^{14}\cdot 7^{8}$ |
$3$ |
$9.78464595129$ |
$13.837579007333664$ |
|
|
? |
$D_8:C_2$ (as 16T47) |
trivial |
$6$ |
$7$ |
$37.0149239843$ |
| 16.0.7105708251953125.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 5 x^{13} + 3 x^{12} + 5 x^{11} - 14 x^{10} + 17 x^{9} - 12 x^{8} - 3 x^{7} + 31 x^{6} - 60 x^{5} + 68 x^{4} - 50 x^{3} + 24 x^{2} - 7 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 181\cdot 401^{2}$ |
$3$ |
$9.78870996517$ |
$900.8219853969824$ |
|
|
? |
$C_4^4.C_2\wr C_4$ (as 16T1771) |
trivial |
$10$ |
$7$ |
$60.6835925321$ |
| 16.0.7213895789838336.1 |
$x^{16} - 8 x^{15} + 36 x^{14} - 108 x^{13} + 244 x^{12} - 436 x^{11} + 636 x^{10} - 780 x^{9} + 831 x^{8} - 780 x^{7} + 636 x^{6} - 436 x^{5} + 244 x^{4} - 108 x^{3} + 36 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{8}$ |
$2$ |
$9.79795897113$ |
$9.797958971132712$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$168.461389974$ |
| 16.0.7380528100000000.1 |
$x^{16} + 2 x^{14} + 2 x^{12} + 4 x^{6} + 5 x^{4} + 4 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 71^{2}$ |
$4$ |
$9.81195312751$ |
$176.7484087622856$ |
|
|
? |
$C_2^2.C_2^2\wr D_4$ (as 16T1728) |
trivial |
$2$ |
$7$ |
$12.3463543204$ |
| 16.0.7771775074107392.1 |
$x^{16} - 6 x^{15} + 17 x^{14} - 28 x^{13} + 26 x^{12} - 10 x^{11} - 3 x^{10} + 2 x^{9} + x^{8} + 6 x^{7} - 10 x^{6} + 2 x^{5} + 6 x^{4} - 4 x^{3} - 2 x^{2} + 2 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 17^{9}$ |
$2$ |
$9.84368060738$ |
$23.86012979730628$ |
|
|
? |
$D_8:C_8$ (as 16T260) |
trivial |
$4$ |
$7$ |
$25.2889722607$ |
| 16.0.8067379209183488.1 |
$x^{16} - 3 x^{15} + 3 x^{14} + x^{13} + x^{12} - 18 x^{11} + 36 x^{10} - 33 x^{9} + 23 x^{8} - 42 x^{7} + 92 x^{6} - 129 x^{5} + 120 x^{4} - 76 x^{3} + 32 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 17^{3}\cdot 283^{4}$ |
$3$ |
$9.86667400786$ |
$473.73165033466563$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1851) |
trivial |
$2$ |
$7$ |
$13.0020519042$ |
| 16.0.8084777718513664.1 |
$x^{16} - 4 x^{15} + 6 x^{14} - 14 x^{12} + 24 x^{11} - 18 x^{10} + 15 x^{8} - 20 x^{7} + 22 x^{6} - 24 x^{5} + 24 x^{4} - 20 x^{3} + 12 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{36}\cdot 7^{6}$ |
$2$ |
$9.8680026001$ |
$20.471092479852693$ |
|
|
? |
$D_4:D_4$ (as 16T141) |
trivial |
$8$ |
$7$ |
$60.0447869363$ |
| 16.0.8148125331379089.1 |
$x^{16} - x^{15} - 6 x^{14} + 4 x^{13} + 15 x^{12} - 6 x^{11} - 20 x^{10} + 7 x^{9} + 21 x^{8} - 7 x^{7} - 20 x^{6} + 6 x^{5} + 15 x^{4} - 4 x^{3} - 6 x^{2} + x + 1$ |
$16$ |
[0,8] |
$3^{12}\cdot 7^{6}\cdot 19^{4}$ |
$3$ |
$9.87281743569$ |
$42.76035198975074$ |
|
|
? |
$C_2\wr D_4$ (as 16T388) |
trivial |
$6$ |
$7$ |
$41.5444168882$ |
