| 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 |
| 32.0.146...416.1 |
$x^{32} - 4 x^{30} + 10 x^{28} - 32 x^{26} + 83 x^{24} - 208 x^{22} + 458 x^{20} - 956 x^{18} + 2113 x^{16} - 3824 x^{14} + 7328 x^{12} - 13312 x^{10} + 21248 x^{8} - 32768 x^{6} + 40960 x^{4} - 65536 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{72}\cdot 3^{16}\cdot 13^{8}\cdot 97^{4}$ |
$4$ |
$27.7147153518$ |
$292.57395390451063$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[4]$ |
$24$ |
$15$ |
$32664023933.600838$ |
| 32.0.103...616.1 |
$x^{32} - 4 x^{31} + 8 x^{30} - 16 x^{29} + 25 x^{28} - 24 x^{27} + 24 x^{26} - 20 x^{25} - 36 x^{23} + 152 x^{22} - 256 x^{21} + 425 x^{20} - 584 x^{19} + 296 x^{18} + 4 x^{17} + 113 x^{16} + 8 x^{15} + 1184 x^{14} - 4672 x^{13} + 6800 x^{12} - 8192 x^{11} + 9728 x^{10} - 4608 x^{9} - 10240 x^{7} + 24576 x^{6} - 49152 x^{5} + 102400 x^{4} - 131072 x^{3} + 131072 x^{2} - 131072 x + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 41^{8}\cdot 113^{4}$ |
$4$ |
$31.6556611366$ |
$471.5760808183553$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 6]$ |
$24$ |
$15$ |
$137041291644.51082$ |
| 32.0.133...000.1 |
$x^{32} - 2 x^{31} - 16 x^{30} + 24 x^{29} + 141 x^{28} - 120 x^{27} - 852 x^{26} - 70 x^{25} + 4216 x^{24} + 4978 x^{23} - 15640 x^{22} - 47344 x^{21} + 45797 x^{20} + 270436 x^{19} - 110380 x^{18} - 986938 x^{17} + 284105 x^{16} + 1973876 x^{15} - 441520 x^{14} - 2163488 x^{13} + 732752 x^{12} + 1515008 x^{11} - 1000960 x^{10} - 637184 x^{9} + 1079296 x^{8} + 35840 x^{7} - 872448 x^{6} + 245760 x^{5} + 577536 x^{4} - 196608 x^{3} - 262144 x^{2} + 65536 x + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 13^{8}\cdot 97^{4}$ |
$5$ |
$36.8487642351$ |
$388.99871465083277$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[20]$ |
$12$ |
$15$ |
$564327334704.2394$ |
| 32.0.103...000.1 |
$x^{32} + 5 x^{30} + 8 x^{28} - 5 x^{26} - 29 x^{24} + 15 x^{22} + 88 x^{20} - 255 x^{18} - 1131 x^{16} - 1020 x^{14} + 1408 x^{12} + 960 x^{10} - 7424 x^{8} - 5120 x^{6} + 32768 x^{4} + 81920 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 521^{4}$ |
$5$ |
$39.289801989$ |
$952.1239415118181$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[24]$ |
$12$ |
$15$ |
$716680193852.9397$ |
| 32.0.493...000.1 |
$x^{32} + 7 x^{30} + 23 x^{28} + 46 x^{26} + 55 x^{24} + 10 x^{22} - 218 x^{20} - 924 x^{18} - 2271 x^{16} - 3696 x^{14} - 3488 x^{12} + 640 x^{10} + 14080 x^{8} + 47104 x^{6} + 94208 x^{4} + 114688 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 769^{4}$ |
$5$ |
$41.2492367589$ |
$1156.7454343977329$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 18]$ |
$12$ |
$15$ |
$1024801800652.4087$ |
| 32.0.169...256.1 |
$x^{32} - 12 x^{31} + 72 x^{30} - 300 x^{29} + 1035 x^{28} - 3260 x^{27} + 9600 x^{26} - 26564 x^{25} + 69933 x^{24} - 174072 x^{23} + 400688 x^{22} - 851404 x^{21} + 1702949 x^{20} - 3206248 x^{19} + 5512736 x^{18} - 8563800 x^{17} + 12691211 x^{16} - 18904816 x^{15} + 26519464 x^{14} - 30813896 x^{13} + 27904797 x^{12} - 21762500 x^{11} + 20377800 x^{10} - 16601336 x^{9} - 10360556 x^{8} + 56257376 x^{7} - 83781376 x^{6} + 68810112 x^{5} - 15839936 x^{4} - 31786496 x^{3} + 44255232 x^{2} - 29503488 x + 9834496$ |
$32$ |
[0,16] |
$2^{64}\cdot 7^{16}\cdot 23^{8}\cdot 137^{4}$ |
$4$ |
$42.8677847392$ |
$594.0639696194341$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 48]$ |
$8$ |
$15$ |
$5074359259636.912$ |
| 32.0.170...000.1 |
$x^{32} + 8 x^{30} + 30 x^{28} + 74 x^{26} + 143 x^{24} + 226 x^{22} + 207 x^{20} - 185 x^{18} - 923 x^{16} - 740 x^{14} + 3312 x^{12} + 14464 x^{10} + 36608 x^{8} + 75776 x^{6} + 122880 x^{4} + 131072 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$5$ |
$42.8817065677$ |
$1351.0218355008183$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[30]$ |
$12$ |
$15$ |
$1780421557670.7527$ |
| 32.0.262...000.1 |
$x^{32} + 5 x^{30} + 8 x^{28} + 5 x^{26} + x^{24} - 40 x^{22} - 152 x^{20} - 240 x^{18} - 336 x^{16} - 960 x^{14} - 2432 x^{12} - 2560 x^{10} + 256 x^{8} + 5120 x^{6} + 32768 x^{4} + 81920 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{40}\cdot 3^{16}\cdot 5^{16}\cdot 31^{4}\cdot 89^{8}$ |
$5$ |
$43.4611123476$ |
$575.395516145199$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 6, 12]$ |
$12$ |
$15$ |
$2519992645123.5127$ |
| 32.0.290...176.1 |
$x^{32} - 4 x^{31} + 42 x^{30} - 134 x^{29} + 754 x^{28} - 1990 x^{27} + 7802 x^{26} - 17690 x^{25} + 53094 x^{24} - 108182 x^{23} + 256762 x^{22} - 492454 x^{21} + 925356 x^{20} - 1701130 x^{19} + 2638782 x^{18} - 4227686 x^{17} + 6633341 x^{16} - 6962910 x^{15} + 13367372 x^{14} - 10724860 x^{13} + 11545802 x^{12} - 23539896 x^{11} + 3955128 x^{10} - 7435992 x^{9} + 19530996 x^{8} + 2533056 x^{7} - 5443776 x^{6} - 1219904 x^{5} + 651552 x^{4} + 141056 x^{3} - 11264 x^{2} - 2816 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 7^{16}\cdot 13^{8}\cdot 97^{4}$ |
$5$ |
$43.6000458247$ |
$460.2694862795056$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 36]$ |
$12$ |
$15$ |
$1934945357870.7947$ |
| 32.0.385...000.1 |
$x^{32} - 12 x^{30} + 102 x^{28} - 452 x^{26} + 1409 x^{24} - 1772 x^{22} + 2946 x^{20} - 15768 x^{18} + 33540 x^{16} - 20668 x^{14} + 94478 x^{12} - 7132 x^{10} + 205785 x^{8} + 131700 x^{6} + 83794 x^{4} + 9720 x^{2} + 2025$ |
$32$ |
[0,16] |
$2^{72}\cdot 5^{16}\cdot 31^{8}\cdot 89^{4}$ |
$4$ |
$43.9862224969$ |
$558.699577131565$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 24]$ |
$8$ |
$15$ |
$2307780676559.752$ |
| 32.0.389...000.1 |
$x^{32} + 9 x^{30} + 40 x^{28} + 119 x^{26} + 271 x^{24} + 495 x^{22} + 752 x^{20} + 1105 x^{18} + 1941 x^{16} + 4420 x^{14} + 12032 x^{12} + 31680 x^{10} + 69376 x^{8} + 121856 x^{6} + 163840 x^{4} + 147456 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1289^{4}$ |
$5$ |
$44.0004116244$ |
$1497.6181088648734$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[38]$ |
$12$ |
$15$ |
$2224349047480.508$ |
| 32.0.662...096.1 |
$x^{32} - 8 x^{29} + 5 x^{28} + 4 x^{27} + 32 x^{26} - 24 x^{25} - 24 x^{24} - 68 x^{23} + 40 x^{22} + 156 x^{21} + 21 x^{20} - 664 x^{18} + 604 x^{17} - 111 x^{16} + 1208 x^{15} - 2656 x^{14} + 336 x^{12} + 4992 x^{11} + 2560 x^{10} - 8704 x^{9} - 6144 x^{8} - 12288 x^{7} + 32768 x^{6} + 8192 x^{5} + 20480 x^{4} - 65536 x^{3} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 7^{4}\cdot 23^{4}\cdot 137^{8}$ |
$5$ |
$44.7356750354$ |
$1028.948978326914$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[7, 28]$ |
$24$ |
$15$ |
$2545609047879.0273$ |
| 32.0.103...000.1 |
$x^{32} - 9 x^{28} + 25 x^{24} + 119 x^{20} - 991 x^{16} + 1904 x^{12} + 6400 x^{8} - 36864 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 29^{8}\cdot 521^{4}$ |
$4$ |
$45.3679555095$ |
$1099.4180278674714$ |
✓ |
|
? |
$D_4^2:C_2^3$ (as 32T12882) |
$[78]$ |
$8$ |
$15$ |
$2023301967377.3625$ |
| 32.0.119...000.1 |
$x^{32} + 5 x^{30} - 2 x^{28} + 29 x^{26} + 210 x^{24} - 901 x^{22} - 4431 x^{20} + 4007 x^{18} + 45913 x^{16} + 21602 x^{14} - 46434 x^{12} + 2224 x^{10} + 76721 x^{8} + 36772 x^{6} + 12160 x^{4} + 2112 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 89^{8}\cdot 181^{4}$ |
$5$ |
$45.5651651508$ |
$983.1276621070124$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 42]$ |
$12$ |
$15$ |
$3049689592222.7627$ |
| 32.0.305...000.1 |
$x^{32} + 12 x^{30} + 78 x^{28} + 422 x^{26} + 1873 x^{24} + 6131 x^{22} + 14681 x^{20} + 21599 x^{18} + 6878 x^{16} - 48739 x^{14} - 31214 x^{12} + 52985 x^{10} + 79497 x^{8} + 4744 x^{6} - 3280 x^{4} + 640 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 89^{8}\cdot 229^{4}$ |
$5$ |
$46.9248142485$ |
$1105.8300050188545$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 6, 18]$ |
$12$ |
$15$ |
$3573311276880.186$ |
| 32.0.492...000.1 |
$x^{32} - 3 x^{28} + 14 x^{24} + 60 x^{20} - 95 x^{16} + 960 x^{12} + 3584 x^{8} - 12288 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 29^{8}\cdot 769^{4}$ |
$4$ |
$47.6305158933$ |
$1335.6945758668035$ |
✓ |
|
? |
$D_4^2:C_2^3$ (as 32T12882) |
$[84]$ |
$8$ |
$15$ |
$2768304842151.426$ |
| 32.0.798...096.1 |
$x^{32} - 8 x^{31} + 60 x^{30} - 300 x^{29} + 1366 x^{28} - 5048 x^{27} + 16998 x^{26} - 49604 x^{25} + 131986 x^{24} - 313392 x^{23} + 675510 x^{22} - 1317928 x^{21} + 2318518 x^{20} - 3690480 x^{19} + 5269876 x^{18} - 6736676 x^{17} + 7939762 x^{16} - 7715504 x^{15} + 8672926 x^{14} - 8814852 x^{13} + 3813094 x^{12} - 12262392 x^{11} + 7728078 x^{10} + 26031328 x^{9} + 15492289 x^{8} - 26327288 x^{7} - 27826880 x^{6} - 1184288 x^{5} + 10222864 x^{4} + 6175232 x^{3} + 1676416 x^{2} + 225792 x + 12544$ |
$32$ |
[0,16] |
$2^{64}\cdot 7^{16}\cdot 41^{8}\cdot 113^{4}$ |
$4$ |
$48.3548211107$ |
$720.3443620935753$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[12, 12]$ |
$8$ |
$15$ |
$5703953342528.085$ |
| 32.0.170...000.1 |
$x^{32} - 4 x^{28} + 14 x^{24} + 21 x^{20} - 255 x^{16} + 336 x^{12} + 3584 x^{8} - 16384 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$4$ |
$49.5155296603$ |
$1560.0256408149194$ |
✓ |
|
? |
$D_4^2:C_2^3$ (as 32T12882) |
$[138]$ |
$8$ |
$15$ |
$3793239043715.9175$ |
| 32.0.240...000.1 |
$x^{32} - 2 x^{31} - 7 x^{30} + 6 x^{29} + 41 x^{28} + 140 x^{27} + 178 x^{26} - 2824 x^{25} + 684 x^{24} + 10324 x^{23} + 9232 x^{22} - 2516 x^{21} - 12401 x^{20} - 32042 x^{19} - 31601 x^{18} + 6402 x^{17} + 66991 x^{16} + 65484 x^{15} - 7418 x^{14} - 55672 x^{13} - 53412 x^{12} - 80560 x^{11} + 544 x^{10} + 118368 x^{9} + 65792 x^{8} - 23616 x^{7} + 10688 x^{6} + 2560 x^{5} - 3520 x^{4} + 2048 x^{3} - 384 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 41^{8}\cdot 113^{4}$ |
$5$ |
$50.051995015$ |
$745.6272527208216$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 6, 24]$ |
$6$ |
$15$ |
$9642731609916.342$ |
| 32.0.388...000.1 |
$x^{32} - x^{28} + x^{24} - 57 x^{20} + 161 x^{16} - 912 x^{12} + 256 x^{8} - 4096 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 29^{8}\cdot 1289^{4}$ |
$4$ |
$50.8072989916$ |
$1729.300436592786$ |
✓ |
|
? |
$D_4^2:C_2^3$ (as 32T12882) |
$[150]$ |
$8$ |
$15$ |
$3273323441082.3687$ |
| 32.0.789...000.1 |
$x^{32} + 4 x^{30} + 2 x^{28} - 6 x^{26} + 3 x^{24} + 6 x^{22} - 53 x^{20} - 181 x^{18} - 427 x^{16} - 724 x^{14} - 848 x^{12} + 384 x^{10} + 768 x^{8} - 6144 x^{6} + 8192 x^{4} + 65536 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{16}\cdot 101^{8}\cdot 401^{4}$ |
$5$ |
$51.9456296921$ |
$1558.8649717021676$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[210]$ |
$12$ |
$15$ |
$6738898358917.929$ |
| 32.0.804...625.1 |
$x^{32} - 6 x^{31} + 56 x^{29} + 24 x^{28} - 590 x^{27} + 214 x^{26} + 2129 x^{25} + 4244 x^{24} - 16360 x^{23} - 30577 x^{22} + 73623 x^{21} + 290255 x^{20} - 961869 x^{19} + 316357 x^{18} + 2979762 x^{17} - 5207851 x^{16} - 5517191 x^{15} + 35764951 x^{14} - 55566005 x^{13} + 34291363 x^{12} - 208731 x^{11} + 7674508 x^{10} + 4344517 x^{9} + 2817291 x^{8} + 710478 x^{7} + 745052 x^{6} + 149632 x^{5} + 86608 x^{4} + 26048 x^{3} + 7552 x^{2} + 1280 x + 256$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 521^{4}$ |
$5$ |
$51.9755225619$ |
$1259.541583275439$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 94]$ |
$6$ |
$15$ |
$5821898177846.913$ |
| 32.0.111...016.1 |
$x^{32} - 2 x^{31} - x^{30} + 14 x^{29} - 6 x^{28} - 82 x^{27} + 171 x^{26} + 426 x^{25} - 1103 x^{24} + 612 x^{23} + 1870 x^{22} + 1692 x^{21} - 15101 x^{20} + 12498 x^{19} + 60665 x^{18} - 224090 x^{17} + 470294 x^{16} - 1196922 x^{15} + 3481149 x^{14} - 4522026 x^{13} + 9950863 x^{12} - 12441624 x^{11} + 17394098 x^{10} - 19804208 x^{9} + 30506508 x^{8} - 11192944 x^{7} + 24538416 x^{6} - 26063296 x^{5} + 410816 x^{4} - 22830080 x^{3} + 11063808 x^{2} + 9834496$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 7^{16}\cdot 23^{8}\cdot 137^{4}$ |
$5$ |
$52.5020995073$ |
$727.5768000699308$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 4, 48]$ |
$6$ |
$15$ |
$17203826154694.41$ |
| 32.0.118...000.1 |
$x^{32} - 29 x^{28} + 707 x^{24} - 9485 x^{20} + 58946 x^{16} - 110740 x^{12} + 61457 x^{8} + 6896 x^{4} + 256$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 89^{8}\cdot 181^{4}$ |
$4$ |
$52.614120731$ |
$1135.218040730502$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 104]$ |
$8$ |
$15$ |
$11519211186268.066$ |
| 32.0.304...000.1 |
$x^{32} + 12 x^{28} + 442 x^{24} + 4491 x^{20} + 22291 x^{16} - 93453 x^{12} + 82801 x^{8} - 8160 x^{4} + 256$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 89^{8}\cdot 229^{4}$ |
$4$ |
$54.1841082761$ |
$1276.9025021512018$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 104]$ |
$8$ |
$15$ |
$11215015279939.906$ |
| 32.0.381...625.1 |
$x^{32} - 2 x^{31} - 20 x^{30} + 24 x^{29} + 286 x^{28} - 250 x^{27} - 2682 x^{26} + 1817 x^{25} + 19614 x^{24} - 14252 x^{23} - 106581 x^{22} + 99261 x^{21} + 427695 x^{20} - 593179 x^{19} - 962589 x^{18} + 2289866 x^{17} - 85839 x^{16} - 3519833 x^{15} + 7206071 x^{14} - 1530693 x^{13} + 140965 x^{12} + 5408365 x^{11} + 271976 x^{10} + 335065 x^{9} + 2939829 x^{8} - 637412 x^{7} + 550944 x^{6} + 18112 x^{5} + 35760 x^{4} + 7872 x^{3} + 4288 x^{2} + 384 x + 256$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 769^{4}$ |
$5$ |
$54.5676111177$ |
$1530.2303748128907$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 64]$ |
$6$ |
$15$ |
$8904823132081.674$ |
| 32.0.681...000.1 |
$x^{32} - 2 x^{31} + 29 x^{30} - 66 x^{29} + 434 x^{28} - 900 x^{27} + 4199 x^{26} - 7280 x^{25} + 27121 x^{24} - 36992 x^{23} + 121503 x^{22} - 101408 x^{21} + 374230 x^{20} - 78542 x^{19} + 859493 x^{18} + 544286 x^{17} + 2622903 x^{16} + 1417108 x^{15} + 7344212 x^{14} + 2680136 x^{13} + 23550888 x^{12} + 25845264 x^{11} - 9805072 x^{10} + 39727584 x^{9} + 163102208 x^{8} + 23268800 x^{7} - 74171200 x^{6} + 172395904 x^{5} + 284707712 x^{4} + 125751552 x^{3} + 10893312 x^{2} - 2704384 x + 92416$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 521^{4}$ |
$5$ |
$55.5641708358$ |
$1346.5065911461406$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 150]$ |
$6$ |
$15$ |
$12350581001475.229$ |
| 32.0.681...000.2 |
$x^{32} - 2 x^{31} - 35 x^{30} + 54 x^{29} + 582 x^{28} - 724 x^{27} - 5801 x^{26} + 6656 x^{25} + 38405 x^{24} - 49984 x^{23} - 177937 x^{22} + 300832 x^{21} + 590114 x^{20} - 1365710 x^{19} - 1185291 x^{18} + 4579318 x^{17} + 154147 x^{16} - 11942188 x^{15} + 7662420 x^{14} + 16564120 x^{13} - 23303048 x^{12} - 2384240 x^{11} + 68187376 x^{10} - 79122656 x^{9} + 115265728 x^{8} - 58417728 x^{7} + 58682560 x^{6} - 14078848 x^{5} + 11490944 x^{4} - 313088 x^{3} + 444416 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 521^{4}$ |
$5$ |
$55.5641708358$ |
$1346.5065911461406$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
not computed |
$6$ |
$15$ |
|
| 32.0.112...000.1 |
$x^{32} + 3 x^{30} - x^{28} - 10 x^{26} - x^{24} + 34 x^{22} + 70 x^{20} - 108 x^{18} - 623 x^{16} - 432 x^{14} + 1120 x^{12} + 2176 x^{10} - 256 x^{8} - 10240 x^{6} - 4096 x^{4} + 49152 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{8}\cdot 29^{16}\cdot 281^{4}$ |
$5$ |
$56.4443417958$ |
$699.242447224137$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 3, 54]$ |
$12$ |
$15$ |
$14409622230084.635$ |
| 32.0.132...625.1 |
$x^{32} - 4 x^{31} - 14 x^{30} + 48 x^{29} + 241 x^{28} - 612 x^{27} - 2200 x^{26} + 4670 x^{25} + 17272 x^{24} - 34668 x^{23} - 88792 x^{22} + 189324 x^{21} + 359948 x^{20} - 993844 x^{19} - 512835 x^{18} + 3355546 x^{17} - 2357503 x^{16} - 5180748 x^{15} + 15750611 x^{14} - 15792228 x^{13} + 10494454 x^{12} + 1373482 x^{11} - 2133533 x^{10} + 2981588 x^{9} + 2260261 x^{8} - 1760530 x^{7} + 2108768 x^{6} - 399864 x^{5} + 210384 x^{4} + 65504 x^{3} + 16640 x^{2} + 2176 x + 256$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$5$ |
$56.7271656861$ |
$1787.2338962765898$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 174]$ |
$6$ |
$15$ |
$9898476863353.523$ |
| 32.0.301...625.1 |
$x^{32} - 6 x^{31} - 4 x^{30} + 56 x^{29} + 186 x^{28} - 958 x^{27} - 1098 x^{26} + 6187 x^{25} + 12914 x^{24} - 53084 x^{23} - 45771 x^{22} + 250489 x^{21} + 210183 x^{20} - 1343675 x^{19} + 432927 x^{18} + 3735782 x^{17} - 4733917 x^{16} - 7945401 x^{15} + 34353397 x^{14} - 53496679 x^{13} + 52302241 x^{12} - 28481985 x^{11} + 8401560 x^{10} + 3267183 x^{9} - 363465 x^{8} - 2158930 x^{7} + 4307708 x^{6} - 2643232 x^{5} + 1313520 x^{4} - 282816 x^{3} + 44416 x^{2} - 4096 x + 256$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 1289^{4}$ |
$5$ |
$58.2070733714$ |
$1981.1625375016558$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[380]$ |
$6$ |
$15$ |
$14470191696026.596$ |
| 32.0.323...000.1 |
$x^{32} - 6 x^{31} - 5 x^{30} + 74 x^{29} + 129 x^{28} - 1066 x^{27} - 668 x^{26} + 7244 x^{25} + 10351 x^{24} - 57310 x^{23} - 37362 x^{22} + 204376 x^{21} + 380968 x^{20} - 1269788 x^{19} + 212448 x^{18} + 374616 x^{17} + 5694817 x^{16} - 22871144 x^{15} + 55852968 x^{14} - 91074688 x^{13} + 102128488 x^{12} - 85136864 x^{11} + 62345728 x^{10} - 37807360 x^{9} + 24126896 x^{8} - 12214656 x^{7} + 6620672 x^{6} - 2134016 x^{5} + 1276544 x^{4} - 280576 x^{3} + 48640 x^{2} - 4096 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 769^{4}$ |
$5$ |
$58.335230062$ |
$1635.8850815384312$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 210]$ |
$6$ |
$15$ |
$15835487316233.826$ |
| 32.0.323...000.2 |
$x^{32} - 12 x^{31} + 102 x^{30} - 632 x^{29} + 3259 x^{28} - 14196 x^{27} + 54054 x^{26} - 181168 x^{25} + 538850 x^{24} - 1421372 x^{23} + 3301686 x^{22} - 6656356 x^{21} + 11242330 x^{20} - 14675868 x^{19} + 10736660 x^{18} + 10164980 x^{17} - 54031327 x^{16} + 110396848 x^{15} - 138789976 x^{14} + 83526288 x^{13} + 68196328 x^{12} - 240215264 x^{11} + 278975616 x^{10} - 118651264 x^{9} - 65191888 x^{8} + 93478528 x^{7} - 24294144 x^{6} - 16443648 x^{5} + 13102720 x^{4} - 3280384 x^{3} + 364032 x^{2} - 15360 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 769^{4}$ |
$5$ |
$58.335230062$ |
$1635.8850815384312$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
not computed |
$6$ |
$15$ |
|
| 32.0.524...256.1 |
$x^{32} - 4 x^{31} - 12 x^{30} + 32 x^{29} + 238 x^{28} - 436 x^{27} - 1752 x^{26} + 2180 x^{25} + 12832 x^{24} - 19600 x^{23} - 49714 x^{22} + 123516 x^{21} + 139502 x^{20} - 681160 x^{19} - 49208 x^{18} + 2842960 x^{17} - 4085902 x^{16} - 1791724 x^{15} + 15066016 x^{14} - 16647948 x^{13} + 54648 x^{12} + 31538976 x^{11} - 37592014 x^{10} + 17627156 x^{9} + 19990921 x^{8} - 35629052 x^{7} + 31635244 x^{6} - 15719312 x^{5} + 5344480 x^{4} - 815552 x^{3} + 89408 x^{2} - 5888 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 7^{16}\cdot 41^{8}\cdot 113^{4}$ |
$5$ |
$59.2223191624$ |
$882.2380631099522$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 6, 108]$ |
$6$ |
$15$ |
$59356071958917.54$ |
| 32.0.788...000.1 |
$x^{32} - 12 x^{28} + 86 x^{24} - 427 x^{20} + 1809 x^{16} - 6832 x^{12} + 22016 x^{8} - 49152 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{16}\cdot 101^{8}\cdot 401^{4}$ |
$4$ |
$59.981646572$ |
$1800.0222220850496$ |
✓ |
|
? |
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 192]$ |
$8$ |
$15$ |
$18060264289735.246$ |
| 32.0.802...000.1 |
$x^{32} - 36 x^{30} + 576 x^{28} - 5474 x^{26} + 34020 x^{24} - 130166 x^{22} + 187427 x^{20} + 377425 x^{18} + 1235554 x^{16} - 19352440 x^{14} + 35136537 x^{12} + 25383639 x^{10} + 8167525 x^{8} + 1500436 x^{6} + 160416 x^{4} + 8704 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 521^{4}$ |
$5$ |
$60.0161638848$ |
$1454.3933443192045$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 84]$ |
$4$ |
$15$ |
$20661660535943.168$ |
| 32.0.922...625.1 |
$x^{32} - 2 x^{31} - 18 x^{30} + 48 x^{29} + 188 x^{28} - 530 x^{27} - 1260 x^{26} + 2484 x^{25} + 9755 x^{24} - 11858 x^{23} - 67320 x^{22} + 77464 x^{21} + 245214 x^{20} - 151056 x^{19} - 505449 x^{18} - 437870 x^{17} + 1660069 x^{16} - 2306224 x^{15} + 5411604 x^{14} - 4977908 x^{13} + 2763805 x^{12} - 6379754 x^{11} + 5902238 x^{10} + 4026816 x^{9} + 1973385 x^{8} - 3666630 x^{7} - 6023357 x^{6} - 740934 x^{5} - 664887 x^{4} + 1401626 x^{3} + 465968 x^{2} + 1135240 x + 1263376$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 89^{8}\cdot 181^{4}$ |
$5$ |
$60.2770477183$ |
$1300.555650481747$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[15, 90]$ |
$6$ |
$15$ |
$51309842707789.04$ |
| 32.0.111...000.1 |
$x^{32} - 4 x^{31} - 16 x^{30} + 68 x^{29} + 238 x^{28} - 892 x^{27} - 2226 x^{26} + 7118 x^{25} + 19549 x^{24} - 50808 x^{23} - 109802 x^{22} + 227718 x^{21} + 574539 x^{20} - 1048794 x^{19} - 1359471 x^{18} + 2416530 x^{17} + 2821509 x^{16} - 13345460 x^{15} + 30689972 x^{14} - 39794800 x^{13} + 35198576 x^{12} - 23067760 x^{11} + 19734256 x^{10} - 9181312 x^{9} + 8098064 x^{8} - 2113856 x^{7} + 2290048 x^{6} - 169088 x^{5} + 467456 x^{4} + 122368 x^{3} + 31232 x^{2} + 3072 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$5$ |
$60.6438910057$ |
$1910.6334028274498$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[528]$ |
$6$ |
$15$ |
$21820415730078.887$ |
| 32.0.111...000.2 |
$x^{32} - 8 x^{31} + 64 x^{30} - 332 x^{29} + 1604 x^{28} - 6256 x^{27} + 22310 x^{26} - 68580 x^{25} + 189272 x^{24} - 457172 x^{23} + 954788 x^{22} - 1681104 x^{21} + 2211865 x^{20} - 1508956 x^{19} - 2584912 x^{18} + 11838608 x^{17} - 24128969 x^{16} + 31887592 x^{15} - 15354096 x^{14} - 32328344 x^{13} + 86966400 x^{12} - 105636528 x^{11} + 18312240 x^{10} + 107553536 x^{9} - 98914352 x^{8} + 2393408 x^{7} + 40426432 x^{6} - 24013312 x^{5} + 5360768 x^{4} - 207104 x^{3} - 36096 x^{2} + 1536 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$5$ |
$60.6438910057$ |
$1910.6334028274498$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 276]$ |
$6$ |
$15$ |
$14816072342282.787$ |
| 32.0.169...936.1 |
$x^{32} + 18 x^{30} + 203 x^{28} + 1492 x^{26} + 8025 x^{24} + 25714 x^{22} + 62137 x^{20} + 123428 x^{18} + 139579 x^{16} - 16686 x^{14} + 1661 x^{12} + 76916 x^{10} + 9756 x^{8} - 10192 x^{6} + 3152 x^{4} - 1088 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 17^{16}\cdot 47^{8}\cdot 53^{4}$ |
$5$ |
$61.429082941$ |
$712.856226738604$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[12, 84]$ |
$12$ |
$15$ |
$182938558023068.47$ |
| 32.0.172...000.1 |
$x^{32} + 14 x^{30} + 109 x^{28} + 698 x^{26} + 3468 x^{24} + 10052 x^{22} + 23637 x^{20} + 66932 x^{18} + 81853 x^{16} - 83068 x^{14} - 23268 x^{12} + 308752 x^{10} + 118928 x^{8} - 217472 x^{6} - 106496 x^{4} - 24576 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{56}\cdot 3^{16}\cdot 5^{16}\cdot 31^{4}\cdot 89^{8}$ |
$5$ |
$61.4632945178$ |
$967.6960537591174$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 6, 48]$ |
$6$ |
$15$ |
$51163178113729.83$ |
| 32.0.172...000.2 |
$x^{32} - 14 x^{30} + 109 x^{28} - 698 x^{26} + 3468 x^{24} - 10052 x^{22} + 23637 x^{20} - 66932 x^{18} + 81853 x^{16} + 83068 x^{14} - 23268 x^{12} - 308752 x^{10} + 118928 x^{8} + 217472 x^{6} - 106496 x^{4} + 24576 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{56}\cdot 3^{16}\cdot 5^{16}\cdot 31^{4}\cdot 89^{8}$ |
$5$ |
$61.4632945178$ |
$967.6960537591174$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[4, 12, 24]$ |
$6$ |
$15$ |
$46284791623985.1$ |
| 32.0.236...625.1 |
$x^{32} - 4 x^{31} - 18 x^{30} + 72 x^{29} + 311 x^{28} - 1090 x^{27} - 2862 x^{26} + 8691 x^{25} + 24872 x^{24} - 66988 x^{23} - 86403 x^{22} + 207758 x^{21} + 395325 x^{20} - 595053 x^{19} - 1119168 x^{18} + 799235 x^{17} + 3298870 x^{16} - 4221332 x^{15} + 4111698 x^{14} - 7461943 x^{13} + 5469898 x^{12} + 2888264 x^{11} - 9443335 x^{10} + 9992412 x^{9} - 3874794 x^{8} - 4061403 x^{7} + 6823432 x^{6} - 2937855 x^{5} - 1141251 x^{4} + 2061220 x^{3} - 477856 x^{2} - 165184 x + 215296$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 7^{16}\cdot 89^{8}\cdot 229^{4}$ |
$5$ |
$62.0756944097$ |
$1462.8755927965988$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[1590]$ |
$6$ |
$15$ |
$63453830199620.586$ |
| 32.0.255...000.1 |
$x^{32} - 2 x^{31} - 23 x^{30} + 42 x^{29} + 346 x^{28} - 572 x^{27} - 3527 x^{26} + 4836 x^{25} + 28629 x^{24} - 32008 x^{23} - 174899 x^{22} + 146000 x^{21} + 849156 x^{20} - 634310 x^{19} - 2606613 x^{18} + 1920590 x^{17} + 3714309 x^{16} - 7098700 x^{15} + 16456044 x^{14} - 13605776 x^{13} + 10205664 x^{12} - 5756368 x^{11} + 11590288 x^{10} + 846848 x^{9} + 5276304 x^{8} - 270528 x^{7} + 1105024 x^{6} + 65152 x^{5} + 110848 x^{4} + 10752 x^{3} + 8704 x^{2} + 1024 x + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1289^{4}$ |
$5$ |
$62.2259788693$ |
$2117.9518408122503$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 180]$ |
$6$ |
$15$ |
$16449571016975.969$ |
| 32.0.255...000.2 |
$x^{32} - 2 x^{31} - 39 x^{30} + 78 x^{29} + 678 x^{28} - 1336 x^{27} - 6933 x^{26} + 13256 x^{25} + 46161 x^{24} - 84484 x^{23} - 207785 x^{22} + 363100 x^{21} + 629290 x^{20} - 1071214 x^{19} - 1236459 x^{18} + 2000398 x^{17} + 1905251 x^{16} - 877660 x^{15} - 6200876 x^{14} - 2748360 x^{13} + 11687032 x^{12} - 12604592 x^{11} + 40542960 x^{10} - 4541024 x^{9} + 55107776 x^{8} + 1846464 x^{7} + 23026880 x^{6} + 1271424 x^{5} + 3919488 x^{4} + 158976 x^{3} + 231424 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 29^{8}\cdot 1289^{4}$ |
$5$ |
$62.2259788693$ |
$2117.9518408122503$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 300]$ |
$6$ |
$15$ |
$21293667756063.02$ |
| 32.0.381...000.1 |
$x^{32} - 44 x^{30} + 868 x^{28} - 9906 x^{26} + 69988 x^{24} - 299086 x^{22} + 650567 x^{20} - 58759 x^{18} - 2384362 x^{16} + 1399292 x^{14} + 4696121 x^{12} + 4850223 x^{10} + 3856809 x^{8} + 1033776 x^{6} + 130272 x^{4} + 8000 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 769^{4}$ |
$5$ |
$63.0092499357$ |
$1766.9578376407287$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 86]$ |
$4$ |
$15$ |
$33723689221921.4$ |
| 32.0.781...000.1 |
$x^{32} - 6 x^{31} - 3 x^{30} + 38 x^{29} + 240 x^{28} - 870 x^{27} - 1253 x^{26} + 5504 x^{25} + 8960 x^{24} - 30532 x^{23} - 82591 x^{22} + 273588 x^{21} + 232111 x^{20} - 1662294 x^{19} + 1506913 x^{18} + 3228344 x^{17} - 8242121 x^{16} + 2035750 x^{15} + 20473926 x^{14} - 37183070 x^{13} + 23899872 x^{12} + 19231684 x^{11} - 44051780 x^{10} + 29086832 x^{9} + 22770705 x^{8} - 53249356 x^{7} + 38434576 x^{6} + 9011088 x^{5} - 26789548 x^{4} + 18764896 x^{3} + 5552960 x^{2} - 14383456 x + 9709456$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 89^{8}\cdot 181^{4}$ |
$5$ |
$64.4388745281$ |
$1390.3524732958906$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 6, 144]$ |
$6$ |
$15$ |
$72117810971857.08$ |
| 32.0.781...000.2 |
$x^{32} - 6 x^{31} - 19 x^{30} + 146 x^{29} + 236 x^{28} - 1994 x^{27} - 1515 x^{26} + 17532 x^{25} + 248 x^{24} - 102760 x^{23} + 62939 x^{22} + 452232 x^{21} - 621557 x^{20} - 1332326 x^{19} + 3689491 x^{18} + 75956 x^{17} - 11152569 x^{16} + 15594526 x^{15} + 12008686 x^{14} - 58161950 x^{13} + 9977818 x^{12} + 131342300 x^{11} - 70421448 x^{10} - 200370404 x^{9} + 221182489 x^{8} + 64149492 x^{7} - 233429156 x^{6} + 127683800 x^{5} + 51958176 x^{4} - 115466320 x^{3} + 71910480 x^{2} - 21408800 x + 2671600$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 89^{8}\cdot 181^{4}$ |
$5$ |
$64.4388745281$ |
$1390.3524732958906$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 312]$ |
$6$ |
$15$ |
$36960168098647.56$ |
| 32.0.112...000.1 |
$x^{32} - 11 x^{28} + 62 x^{24} - 260 x^{20} + 1041 x^{16} - 4160 x^{12} + 15872 x^{8} - 45056 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{8}\cdot 29^{16}\cdot 281^{4}$ |
$4$ |
$65.1763118601$ |
$807.4156302673364$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 186]$ |
$8$ |
$15$ |
$70769362065553.12$ |
| 32.0.131...000.1 |
$x^{32} - 44 x^{30} + 874 x^{28} - 10054 x^{26} + 71163 x^{24} - 296956 x^{22} + 554793 x^{20} + 537460 x^{18} - 3539799 x^{16} - 66968 x^{14} + 9372831 x^{12} + 10803870 x^{10} + 6888129 x^{8} + 2624028 x^{6} + 464976 x^{4} + 14784 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 7^{16}\cdot 29^{8}\cdot 1049^{4}$ |
$5$ |
$65.5028887584$ |
$2063.7199422402255$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[2, 2, 114]$ |
$4$ |
$15$ |
$37277164025166.29$ |
