| 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 |
| 36.0.110...853.1 |
$x^{36} - x^{35} + 3 x^{34} - 4 x^{33} + 9 x^{32} - 14 x^{31} + 28 x^{30} - 47 x^{29} + 89 x^{28} - 155 x^{27} + 286 x^{26} - 507 x^{25} + 924 x^{24} + 442 x^{23} + 899 x^{22} + 909 x^{21} + 1331 x^{20} + 1386 x^{19} + 2185 x^{18} + 1918 x^{17} + 3838 x^{16} + 2183 x^{15} + 7411 x^{14} + 793 x^{13} + 16212 x^{12} - 7215 x^{11} + 3211 x^{10} - 1429 x^{9} + 636 x^{8} - 283 x^{7} + 126 x^{6} - 56 x^{5} + 25 x^{4} - 11 x^{3} + 5 x^{2} - 2 x + 1$ |
$36$ |
[0,18] |
$7^{24}\cdot 13^{33}$ |
$2$ |
$38.4161141302$ |
$38.416114130176354$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
$[2, 74]$ |
$26$ |
$17$ |
$4866030378143.887$ |
| 36.0.459...733.1 |
$x^{36} + 3 x^{34} - x^{33} + 9 x^{32} - 6 x^{31} + 28 x^{30} - 27 x^{29} + 90 x^{28} - 109 x^{27} + 297 x^{26} - 417 x^{25} + 1000 x^{24} + 1845 x^{23} + 3417 x^{22} + 4535 x^{21} + 8406 x^{20} + 10188 x^{19} + 20683 x^{18} + 22158 x^{17} + 51861 x^{16} + 45791 x^{15} + 133425 x^{14} + 85512 x^{13} + 354484 x^{12} + 123111 x^{11} + 42756 x^{10} + 14849 x^{9} + 5157 x^{8} + 1791 x^{7} + 622 x^{6} + 216 x^{5} + 75 x^{4} + 26 x^{3} + 9 x^{2} + 3 x + 1$ |
$36$ |
[0,18] |
$3^{48}\cdot 13^{33}$ |
$2$ |
$45.423062587$ |
$45.423062587011394$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[3, 3, 9, 9]$ |
$26$ |
$17$ |
$20980577392492.816$ |
| 36.0.113...125.1 |
$x^{36} + 15 x^{34} - 4 x^{33} + 171 x^{32} + 132 x^{31} + 1809 x^{30} + 1683 x^{29} + 17889 x^{28} + 12647 x^{27} + 85860 x^{26} + 52491 x^{25} + 358026 x^{24} + 22707 x^{23} + 1329663 x^{22} + 118787 x^{21} + 4193811 x^{20} + 697212 x^{19} + 3532755 x^{18} + 635940 x^{17} + 2414307 x^{16} + 853087 x^{15} + 1609083 x^{14} + 558075 x^{13} + 908302 x^{12} + 274491 x^{11} + 259680 x^{10} + 62761 x^{9} + 63297 x^{8} + 693 x^{7} + 10925 x^{6} + 846 x^{5} + 1881 x^{4} + 286 x^{3} + 45 x^{2} + 6 x + 1$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{27}\cdot 7^{24}$ |
$3$ |
$52.9404793803$ |
$52.940479380274844$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[14, 518]$ |
$10$ |
$17$ |
$13624539961495.691$ |
| 36.36.129...597.1 |
$x^{36} - x^{35} - 36 x^{34} + 35 x^{33} + 594 x^{32} - 560 x^{31} - 5952 x^{30} + 5426 x^{29} + 40454 x^{28} - 35554 x^{27} - 197288 x^{26} + 166634 x^{25} + 712180 x^{24} - 576199 x^{23} - 1934944 x^{22} + 1494700 x^{21} + 3983738 x^{20} - 2928983 x^{19} - 6208136 x^{18} + 4331906 x^{17} + 7259749 x^{16} - 4795428 x^{15} - 6263633 x^{14} + 3907332 x^{13} + 3879994 x^{12} - 2278575 x^{11} - 1655004 x^{10} + 908896 x^{9} + 456052 x^{8} - 230058 x^{7} - 73571 x^{6} + 32327 x^{5} + 6018 x^{4} - 1922 x^{3} - 216 x^{2} + 24 x + 1$ |
$36$ |
[36,0] |
$7^{30}\cdot 13^{33}$ |
$2$ |
$53.1328493368$ |
$53.13284933680473$ |
|
✓ |
✓ |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$48664971049465540000$ |
| 36.36.334...357.1 |
$x^{36} - 36 x^{34} - x^{33} + 594 x^{32} + 33 x^{31} - 5952 x^{30} - 495 x^{29} + 40455 x^{28} + 4467 x^{27} - 197316 x^{26} - 27054 x^{25} + 712529 x^{24} + 116154 x^{23} - 1937496 x^{22} - 364067 x^{21} + 3995883 x^{20} + 845295 x^{19} - 6247579 x^{18} - 1459998 x^{17} + 7348878 x^{16} + 1867585 x^{15} - 6403833 x^{14} - 1746123 x^{13} + 4030936 x^{12} + 1165464 x^{11} - 1761969 x^{10} - 534544 x^{9} + 502173 x^{8} + 158337 x^{7} - 83631 x^{6} - 27162 x^{5} + 6471 x^{4} + 2145 x^{3} - 108 x^{2} - 36 x + 1$ |
$36$ |
[36,0] |
$3^{54}\cdot 13^{33}$ |
$2$ |
$54.550234478$ |
$54.55023447801447$ |
|
✓ |
✓ |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$63356932035659470000$ |
| 36.36.830...125.1 |
$x^{36} - 60 x^{34} - 4 x^{33} + 1566 x^{32} + 192 x^{31} - 23491 x^{30} - 3897 x^{29} + 225594 x^{28} + 44322 x^{27} - 1463265 x^{26} - 315834 x^{25} + 6595406 x^{24} + 1493037 x^{23} - 20954832 x^{22} - 4829603 x^{21} + 47178711 x^{20} + 10844637 x^{19} - 75203780 x^{18} - 16934940 x^{17} + 84384807 x^{16} + 18269987 x^{15} - 65933622 x^{14} - 13456680 x^{13} + 35213992 x^{12} + 6642171 x^{11} - 12459300 x^{10} - 2131789 x^{9} + 2769012 x^{8} + 423228 x^{7} - 351580 x^{6} - 47619 x^{5} + 21066 x^{4} + 2501 x^{3} - 360 x^{2} - 24 x + 1$ |
$36$ |
[36,0] |
$3^{54}\cdot 5^{27}\cdot 7^{24}$ |
$3$ |
$63.5781781125$ |
$63.57817811250523$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$982275678999294500000$ |
| 36.36.427...117.1 |
$x^{36} - x^{35} - 62 x^{34} + 61 x^{33} + 1673 x^{32} - 1613 x^{31} - 25920 x^{30} + 24367 x^{29} + 256293 x^{28} - 233479 x^{27} - 1701570 x^{26} + 1490905 x^{25} + 7778369 x^{24} - 6496035 x^{23} - 24747903 x^{22} + 19486869 x^{21} + 54933520 x^{20} - 40274564 x^{19} - 84897695 x^{18} + 57204830 x^{17} + 90928152 x^{16} - 55712580 x^{15} - 66860091 x^{14} + 37010766 x^{13} + 33119347 x^{12} - 16533426 x^{11} - 10663861 x^{10} + 4809468 x^{9} + 2090230 x^{8} - 852134 x^{7} - 220627 x^{6} + 79647 x^{5} + 10022 x^{4} - 2741 x^{3} - 216 x^{2} + 24 x + 1$ |
$36$ |
[36,0] |
$3^{18}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$66.5386615028$ |
$66.53866150283011$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$2899632352845428700000$ |
| 36.0.774...125.1 |
$x^{36} + 20 x^{34} - 8 x^{33} + 297 x^{32} + 296 x^{31} + 4101 x^{30} + 5256 x^{29} + 51773 x^{28} + 53598 x^{27} + 332705 x^{26} + 342662 x^{25} + 1750974 x^{24} + 1731140 x^{23} + 8191554 x^{22} + 7356788 x^{21} + 32849307 x^{20} + 24190390 x^{19} + 78438432 x^{18} + 37935396 x^{17} + 151542669 x^{16} - 46316204 x^{15} + 205249519 x^{14} - 67004790 x^{13} + 240290549 x^{12} - 33283168 x^{11} + 136087020 x^{10} - 14642248 x^{9} + 73074896 x^{8} + 3567392 x^{7} + 38305280 x^{6} + 2431744 x^{5} + 14561024 x^{4} + 1893376 x^{3} + 246784 x^{2} + 30720 x + 4096$ |
$36$ |
[0,18] |
$5^{27}\cdot 7^{24}\cdot 13^{24}$ |
$3$ |
$67.6480213151$ |
$67.64802131514648$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[2, 26426]$ |
$10$ |
$17$ |
$101496132655168.33$ |
| 36.36.133...125.1 |
$x^{36} - 3 x^{35} - 69 x^{34} + 194 x^{33} + 2100 x^{32} - 5496 x^{31} - 37141 x^{30} + 90237 x^{29} + 423339 x^{28} - 958293 x^{27} - 3261144 x^{26} + 6959373 x^{25} + 17329413 x^{24} - 35601552 x^{23} - 63680853 x^{22} + 129922520 x^{21} + 159349053 x^{20} - 337769112 x^{19} - 259925101 x^{18} + 616092369 x^{17} + 246176712 x^{16} - 763692862 x^{15} - 79242273 x^{14} + 608220999 x^{13} - 78776304 x^{12} - 281930013 x^{11} + 88315116 x^{10} + 63028536 x^{9} - 29887359 x^{8} - 4534752 x^{7} + 3622138 x^{6} - 118797 x^{5} - 108390 x^{4} + 1113 x^{3} + 1272 x^{2} + 69 x + 1$ |
$36$ |
[36,0] |
$3^{48}\cdot 5^{27}\cdot 7^{30}$ |
$3$ |
$73.2213181479$ |
$73.22131814786569$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$16003335917605122000000$ |
| 36.0.281...413.1 |
$x^{36} - x^{35} + 7 x^{34} - 6 x^{33} + 41 x^{32} - 28 x^{31} + 232 x^{30} - 113 x^{29} + 1309 x^{28} - 363 x^{27} + 7426 x^{26} - 441 x^{25} + 42456 x^{24} - 101318 x^{23} + 352967 x^{22} - 663683 x^{21} + 2072259 x^{20} - 3583588 x^{19} + 11371361 x^{18} - 18367076 x^{17} + 61510126 x^{16} - 92113055 x^{15} + 332604279 x^{14} - 454711727 x^{13} + 1805546016 x^{12} - 2205586425 x^{11} + 2694284257 x^{10} - 3288980695 x^{9} + 4015581262 x^{8} - 4889475633 x^{7} + 5960098340 x^{6} - 7187883304 x^{5} + 8722143913 x^{4} - 10128755357 x^{3} + 12146435707 x^{2} - 11863960458 x + 13841287201$ |
$36$ |
[0,18] |
$13^{33}\cdot 19^{24}$ |
$2$ |
$74.7510229493$ |
$74.75102294928078$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$26$ |
$17$ |
|
| 36.36.757...808.1 |
$x^{36} - 65 x^{34} + 1859 x^{32} - 30940 x^{30} + 334113 x^{28} - 2472002 x^{26} + 12905893 x^{24} - 48291581 x^{22} + 130412230 x^{20} - 254526168 x^{18} + 358202936 x^{16} - 361633805 x^{14} + 259562875 x^{12} - 130409526 x^{10} + 44665010 x^{8} - 9967789 x^{6} + 1337973 x^{4} - 92274 x^{2} + 2197$ |
$36$ |
[36,0] |
$2^{36}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$76.8322282604$ |
$76.83222826035271$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$31901682379687710000000$ |
| 36.0.322...125.1 |
$x^{36} - 3 x^{35} + 27 x^{34} - 91 x^{33} + 546 x^{32} - 879 x^{31} + 6766 x^{30} - 8742 x^{29} + 79572 x^{28} - 109299 x^{27} + 677004 x^{26} - 773109 x^{25} + 4800131 x^{24} - 1125369 x^{23} + 20272767 x^{22} - 7098692 x^{21} + 86239137 x^{20} - 79515333 x^{19} + 179581154 x^{18} - 149538474 x^{17} + 288977244 x^{16} - 145690029 x^{15} + 279084165 x^{14} - 159459888 x^{13} + 279984346 x^{12} - 206283594 x^{11} + 180939411 x^{10} - 94040687 x^{9} + 79247853 x^{8} - 16999917 x^{7} + 2966770 x^{6} - 471501 x^{5} + 68880 x^{4} - 4902 x^{3} + 336 x^{2} - 21 x + 1$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{27}\cdot 13^{24}$ |
$3$ |
$79.9867549246$ |
$79.986754924587$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[10, 20410]$ |
$10$ |
$17$ |
$478341710831896.44$ |
| 36.0.420...125.1 |
$x^{36} - 9 x^{35} + 52 x^{34} - 208 x^{33} + 763 x^{32} - 2473 x^{31} + 7774 x^{30} - 21073 x^{29} + 55175 x^{28} - 126998 x^{27} + 301106 x^{26} - 609219 x^{25} + 1314509 x^{24} - 2161107 x^{23} + 4589322 x^{22} - 5937815 x^{21} + 16165015 x^{20} - 18096988 x^{19} + 93286907 x^{18} - 201850025 x^{17} + 928905669 x^{16} - 2319599256 x^{15} + 7079450070 x^{14} - 15030668107 x^{13} + 33733591464 x^{12} - 57654424490 x^{11} + 98895340726 x^{10} - 131090685506 x^{9} + 175257385390 x^{8} - 177210083687 x^{7} + 186781470161 x^{6} - 135288523899 x^{5} + 123224165522 x^{4} - 71789180593 x^{3} + 47347720069 x^{2} - 20963341532 x + 32332243789$ |
$36$ |
[0,18] |
$5^{18}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$85.9010426265$ |
$85.90104262646453$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.699...125.1 |
$x^{36} + 26 x^{34} - 14 x^{33} + 495 x^{32} + 476 x^{31} + 8655 x^{30} + 11760 x^{29} + 134201 x^{28} + 164766 x^{27} + 1245581 x^{26} + 1641584 x^{25} + 10003278 x^{24} + 17605574 x^{23} + 73281546 x^{22} + 115896662 x^{21} + 420977265 x^{20} + 540199534 x^{19} + 1258004478 x^{18} + 1344337974 x^{17} + 2875411227 x^{16} + 1250872126 x^{15} + 4489581151 x^{14} + 2102836554 x^{13} + 7030264277 x^{12} + 4148560640 x^{11} + 5060682060 x^{10} + 2659981016 x^{9} + 2836346576 x^{8} + 701556128 x^{7} + 885129728 x^{6} + 244545280 x^{5} + 290205440 x^{4} + 99398656 x^{3} + 61465600 x^{2} + 14751744 x + 9834496$ |
$36$ |
[0,18] |
$5^{27}\cdot 7^{24}\cdot 19^{24}$ |
$3$ |
$87.1221525744$ |
$87.12215257437191$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$10$ |
$17$ |
|
| 36.0.976...125.1 |
$x^{36} + 30 x^{34} - 4 x^{33} + 261 x^{32} - 153 x^{31} - 151 x^{30} - 2232 x^{29} - 12486 x^{28} - 17223 x^{27} - 40545 x^{26} - 69369 x^{25} + 219791 x^{24} + 80127 x^{23} + 2244003 x^{22} + 3598192 x^{21} + 11476701 x^{20} + 27824757 x^{19} + 55944685 x^{18} + 122149350 x^{17} + 246367347 x^{16} + 364897592 x^{15} + 821493693 x^{14} + 857521695 x^{13} + 1993614817 x^{12} + 1740513231 x^{11} + 3580401840 x^{10} + 2916789821 x^{9} + 5006204397 x^{8} + 3581139363 x^{7} + 5853643895 x^{6} + 2918077776 x^{5} + 5636834421 x^{4} + 1219028741 x^{3} + 3957820605 x^{2} + 187966461 x + 1759249171$ |
$36$ |
[0,18] |
$3^{54}\cdot 5^{27}\cdot 7^{30}$ |
$3$ |
$87.9341868705$ |
$87.93418687047121$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.315...488.1 |
$x^{36} - 75 x^{34} - 12 x^{33} + 2466 x^{32} + 708 x^{31} - 46837 x^{30} - 17640 x^{29} + 571011 x^{28} + 242208 x^{27} - 4707315 x^{26} - 2006406 x^{25} + 26995916 x^{24} + 10295208 x^{23} - 109335657 x^{22} - 31916038 x^{21} + 314149779 x^{20} + 51886254 x^{19} - 635559496 x^{18} - 8009280 x^{17} + 884137635 x^{16} - 135354640 x^{15} - 806374134 x^{14} + 261081888 x^{13} + 440313718 x^{12} - 223846182 x^{11} - 116564358 x^{10} + 92545112 x^{9} + 3573618 x^{8} - 15365958 x^{7} + 3090085 x^{6} + 371922 x^{5} - 162048 x^{4} + 8268 x^{3} + 1335 x^{2} - 120 x + 1$ |
$36$ |
[36,0] |
$2^{36}\cdot 3^{48}\cdot 13^{33}$ |
$3$ |
$90.846125174$ |
$90.84612517402279$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$1056313367466610800000000$ |
| 36.0.502...933.1 |
$x^{36} - x^{35} + 55 x^{34} - 56 x^{33} + 1322 x^{32} - 1379 x^{31} + 18345 x^{30} - 19781 x^{29} + 163941 x^{28} - 185158 x^{27} + 1002183 x^{26} - 1208558 x^{25} + 4408145 x^{24} - 5825079 x^{23} + 15017355 x^{22} - 22388250 x^{21} + 45074515 x^{20} - 76386185 x^{19} + 138221149 x^{18} - 246519877 x^{17} + 444193428 x^{16} - 703532376 x^{15} + 1351689873 x^{14} - 1601650713 x^{13} + 3605252587 x^{12} - 2754343527 x^{11} + 8327023718 x^{10} - 3127376355 x^{9} + 17005484365 x^{8} - 1760009807 x^{7} + 30454580477 x^{6} - 1674794190 x^{5} + 45670623647 x^{4} - 8083073282 x^{3} + 45711370125 x^{2} - 12457929369 x + 21305513503$ |
$36$ |
[0,18] |
$3^{18}\cdot 7^{30}\cdot 13^{33}$ |
$3$ |
$92.0287946022$ |
$92.02879460224813$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.911...125.1 |
$x^{36} - 9 x^{35} - 50 x^{34} + 617 x^{33} + 853 x^{32} - 18792 x^{31} - 857 x^{30} + 335261 x^{29} - 196141 x^{28} - 3888989 x^{27} + 3669506 x^{26} + 30780881 x^{25} - 36431516 x^{24} - 169652114 x^{23} + 234314708 x^{22} + 651588327 x^{21} - 1036003947 x^{20} - 1707996749 x^{19} + 3202795146 x^{18} + 2878146054 x^{17} - 6878941470 x^{16} - 2583494750 x^{15} + 9996118628 x^{14} - 21924592 x^{13} - 9335764683 x^{12} + 2679130010 x^{11} + 5110286208 x^{10} - 2690155249 x^{9} - 1371167792 x^{8} + 1122925954 x^{7} + 110647669 x^{6} - 212313517 x^{5} + 12391295 x^{4} + 16680904 x^{3} - 1356543 x^{2} - 505872 x + 2521$ |
$36$ |
[36,0] |
$5^{27}\cdot 7^{30}\cdot 13^{24}$ |
$3$ |
$93.5631363519$ |
$93.56313635186852$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$949930772610205500000000$ |
| 36.36.235...125.1 |
$x^{36} - 12 x^{35} - 18 x^{34} + 701 x^{33} - 1014 x^{32} - 17841 x^{31} + 46936 x^{30} + 258882 x^{29} - 903138 x^{28} - 2337941 x^{27} + 10357989 x^{26} + 13221999 x^{25} - 78595284 x^{24} - 41557041 x^{23} + 412140267 x^{22} + 15579817 x^{21} - 1517917803 x^{20} + 487842723 x^{19} + 3915786614 x^{18} - 2406058791 x^{17} - 6918173706 x^{16} + 6167942709 x^{15} + 7929872535 x^{14} - 9724914267 x^{13} - 5143540984 x^{12} + 9570453009 x^{11} + 944334231 x^{10} - 5631020628 x^{9} + 964975548 x^{8} + 1795533942 x^{7} - 646510065 x^{6} - 255756294 x^{5} + 139324140 x^{4} + 10150922 x^{3} - 10886424 x^{2} + 71286 x + 288991$ |
$36$ |
[36,0] |
$3^{54}\cdot 5^{27}\cdot 13^{24}$ |
$3$ |
$96.0590499135$ |
$96.05904991354265$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$1731579138067769200000000$ |
| 36.0.107...797.1 |
$x^{36} - 9 x^{35} + 16 x^{34} + 26 x^{33} + 181 x^{32} - 1445 x^{31} + 2604 x^{30} - 2755 x^{29} + 9910 x^{28} - 30401 x^{27} + 82223 x^{26} - 197798 x^{25} + 452764 x^{24} - 1456052 x^{23} + 2709150 x^{22} + 1162726 x^{21} - 8566260 x^{20} - 8520187 x^{19} + 71726367 x^{18} - 146575781 x^{17} + 219113520 x^{16} - 450921336 x^{15} + 971562775 x^{14} - 1564444576 x^{13} + 2406821450 x^{12} - 4029586993 x^{11} + 5513868716 x^{10} - 4668590893 x^{9} + 1306426495 x^{8} + 1351057679 x^{7} - 782004588 x^{6} - 648398298 x^{5} + 17515236 x^{4} + 769014408 x^{3} + 45608456 x^{2} - 600274541 x + 239345231$ |
$36$ |
[0,18] |
$7^{24}\cdot 37^{33}$ |
$2$ |
$100.211356374$ |
$100.21135637396078$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[3, 3, 117, 117]$ |
$2$ |
$17$ |
$10004315800200082$ |
| 36.0.175...125.1 |
$x^{36} - 3 x^{35} + 9 x^{34} - 13 x^{33} + 153 x^{32} - 567 x^{31} + 1779 x^{30} - 3546 x^{29} + 13113 x^{28} - 47895 x^{27} + 161433 x^{26} - 415143 x^{25} + 1104025 x^{24} - 3273684 x^{23} + 10489914 x^{22} - 30772058 x^{21} + 84771678 x^{20} - 222454680 x^{19} + 611810329 x^{18} - 1550727096 x^{17} + 3898113045 x^{16} - 8261897447 x^{15} + 17439706425 x^{14} - 31141822035 x^{13} + 56950578528 x^{12} - 87157837233 x^{11} + 133566120075 x^{10} - 164805518158 x^{9} + 193914680868 x^{8} - 179069923941 x^{7} + 186530283006 x^{6} - 188488040397 x^{5} + 232594560831 x^{4} - 140326122819 x^{3} + 227273426838 x^{2} - 163796723415 x + 254886323381$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{18}\cdot 13^{33}$ |
$3$ |
$101.569055691$ |
$101.56905569078494$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.291...125.1 |
$x^{36} - 3 x^{35} + 33 x^{34} - 97 x^{33} + 744 x^{32} - 1893 x^{31} + 13664 x^{30} - 33576 x^{29} + 238560 x^{28} - 588745 x^{27} + 2734752 x^{26} - 6216015 x^{25} + 25176457 x^{24} - 48643407 x^{23} + 187250949 x^{22} - 366416386 x^{21} + 1263887211 x^{20} - 2483705709 x^{19} + 5333249622 x^{18} - 8164618602 x^{17} + 15104700468 x^{16} - 13400914841 x^{15} + 15331684227 x^{14} - 12098329740 x^{13} + 10527569472 x^{12} - 4556162778 x^{11} + 4668826305 x^{10} - 1640038211 x^{9} + 1696221807 x^{8} - 449229501 x^{7} + 699314280 x^{6} - 75367485 x^{5} + 187711800 x^{4} + 52035172 x^{3} + 18826488 x^{2} + 3495057 x + 1874161$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{27}\cdot 19^{24}$ |
$3$ |
$103.012891301$ |
$103.01289130105687$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$10$ |
$17$ |
|
| 36.0.357...013.1 |
$x^{36} - x^{35} + 11 x^{34} - 13 x^{33} + 115 x^{32} - 157 x^{31} + 1203 x^{30} - 1853 x^{29} + 12627 x^{28} - 21533 x^{27} + 132979 x^{26} - 247293 x^{25} + 1404819 x^{24} + 345266 x^{23} + 11724580 x^{22} + 2966632 x^{21} + 117041296 x^{20} + 6421664 x^{19} + 1187724352 x^{18} - 187177344 x^{17} + 12115794176 x^{16} - 4485772800 x^{15} + 124146295808 x^{14} - 72077670400 x^{13} + 1277654446080 x^{12} - 1005260783616 x^{11} + 790941073408 x^{10} - 622313340928 x^{9} + 489637806080 x^{8} - 385242628096 x^{7} + 303113961472 x^{6} - 238437793792 x^{5} + 187636383744 x^{4} - 147102629888 x^{3} + 115964116992 x^{2} - 85899345920 x + 68719476736$ |
$36$ |
[0,18] |
$13^{33}\cdot 31^{24}$ |
$2$ |
$103.599072871$ |
$103.59907287094359$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$26$ |
$17$ |
|
| 36.0.373...125.1 |
$x^{36} - 9 x^{35} + 40 x^{34} - 93 x^{33} - 2 x^{32} + 978 x^{31} - 5277 x^{30} + 18201 x^{29} - 33611 x^{28} - 40454 x^{27} + 580156 x^{26} - 2428654 x^{25} + 6063184 x^{24} - 9282144 x^{23} + 10683683 x^{22} - 22090573 x^{21} + 50749698 x^{20} - 64733864 x^{19} + 165821771 x^{18} - 765022581 x^{17} + 2271992540 x^{16} - 3472565480 x^{15} + 1952471023 x^{14} + 519332948 x^{13} + 4974249937 x^{12} - 18527494830 x^{11} + 34673056498 x^{10} - 65961793774 x^{9} + 116764727313 x^{8} - 134118855581 x^{7} + 125862271939 x^{6} - 122395204267 x^{5} + 95870943525 x^{4} - 37664181986 x^{3} + 53097299592 x^{2} + 996547853 x + 10152422981$ |
$36$ |
[0,18] |
$5^{27}\cdot 7^{24}\cdot 13^{30}$ |
$3$ |
$103.731897806$ |
$103.73189780646314$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.782...000.1 |
$x^{36} - 105 x^{34} - 16 x^{33} + 4761 x^{32} + 1248 x^{31} - 123596 x^{30} - 41868 x^{29} + 2056674 x^{28} + 805868 x^{27} - 23292630 x^{26} - 9998316 x^{25} + 186077966 x^{24} + 84929628 x^{23} - 1071803142 x^{22} - 510857842 x^{21} + 4507244436 x^{20} + 2215904058 x^{19} - 13908705320 x^{18} - 6983909430 x^{17} + 31442289642 x^{16} + 15977803388 x^{15} - 51621469782 x^{14} - 26292514800 x^{13} + 60523405652 x^{12} + 30554706504 x^{11} - 49300418040 x^{10} - 24331055976 x^{9} + 26726967447 x^{8} + 12667223022 x^{7} - 9004822995 x^{6} - 4006725276 x^{5} + 1671476916 x^{4} + 681310144 x^{3} - 129046575 x^{2} - 47460006 x + 405901$ |
$36$ |
[36,0] |
$2^{36}\cdot 3^{48}\cdot 5^{27}\cdot 7^{24}$ |
$4$ |
$105.880958761$ |
$105.88095876054969$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.0.891...392.1 |
$x^{36} + 91 x^{34} + 3731 x^{32} + 91364 x^{30} + 1493765 x^{28} + 17271618 x^{26} + 145978105 x^{24} + 919646455 x^{22} + 4365494770 x^{20} + 15684015256 x^{18} + 42607368076 x^{16} + 86981860147 x^{14} + 131846926939 x^{12} + 145558267218 x^{10} + 113655085362 x^{8} + 60003090875 x^{6} + 19902563681 x^{4} + 3618647942 x^{2} + 258474853$ |
$36$ |
[0,18] |
$2^{36}\cdot 7^{30}\cdot 13^{33}$ |
$3$ |
$106.265698674$ |
$106.26569867360946$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.968...568.1 |
$x^{36} + 24 x^{34} - 12 x^{33} + 360 x^{32} - 84 x^{31} + 2630 x^{30} - 2412 x^{29} + 11523 x^{28} + 96 x^{27} + 91002 x^{26} - 46908 x^{25} - 220219 x^{24} - 320856 x^{23} + 4474812 x^{22} + 8165264 x^{21} - 7129761 x^{20} - 66767160 x^{19} - 67476264 x^{18} + 267892788 x^{17} + 928023510 x^{16} + 143463500 x^{15} - 3773616390 x^{14} - 5967524316 x^{13} + 4254421520 x^{12} + 24836211816 x^{11} + 27413396142 x^{10} - 22088255944 x^{9} - 97921001331 x^{8} - 98513884404 x^{7} + 41560681778 x^{6} + 245496957708 x^{5} + 373399441383 x^{4} + 324953099232 x^{3} + 191526766890 x^{2} + 65880963516 x + 12160977767$ |
$36$ |
[0,18] |
$2^{99}\cdot 3^{48}\cdot 7^{24}$ |
$3$ |
$106.51060569$ |
$106.51060568991636$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
$[3, 3, 234, 22698]$ |
$2$ |
$17$ |
$160258501280890.78$ |
| 36.36.968...568.1 |
$x^{36} - 96 x^{34} - 16 x^{33} + 3960 x^{32} + 1152 x^{31} - 93164 x^{30} - 35748 x^{29} + 1399617 x^{28} + 633928 x^{27} - 14244732 x^{26} - 7185408 x^{25} + 101630814 x^{24} + 55109544 x^{23} - 518477394 x^{22} - 295082980 x^{21} + 1910373432 x^{20} + 1121373960 x^{19} - 5094003336 x^{18} - 3042649560 x^{17} + 9770946912 x^{16} + 5873901604 x^{15} - 13272355962 x^{14} - 7951933872 x^{13} + 12401306684 x^{12} + 7325904048 x^{11} - 7580888508 x^{10} - 4344012424 x^{9} + 2779199601 x^{8} + 1490571564 x^{7} - 523046756 x^{6} - 234531744 x^{5} + 40444434 x^{4} + 8023128 x^{3} - 1974252 x^{2} + 134520 x - 3023$ |
$36$ |
[36,0] |
$2^{99}\cdot 3^{48}\cdot 7^{24}$ |
$3$ |
$106.51060569$ |
$106.51060568991636$ |
|
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$18065118890547987000000000$ |
| 36.0.182...037.1 |
$x^{36} - 9 x^{35} - 6 x^{34} + 302 x^{33} - 624 x^{32} - 3513 x^{31} + 13674 x^{30} + 14298 x^{29} - 120915 x^{28} + 16960 x^{27} + 705036 x^{26} - 447510 x^{25} - 3860961 x^{24} + 5881605 x^{23} + 13497015 x^{22} - 42557253 x^{21} - 7820376 x^{20} + 134349147 x^{19} + 12019540 x^{18} - 618372375 x^{17} + 715410807 x^{16} + 1940709560 x^{15} - 2960870652 x^{14} + 293208303 x^{13} + 14694026311 x^{12} - 2381175957 x^{11} - 10114588962 x^{10} + 31085975417 x^{9} + 12400497834 x^{8} - 49757150475 x^{7} - 290397941 x^{6} + 69843766965 x^{5} + 69916985034 x^{4} + 43030484656 x^{3} + 31088478201 x^{2} + 10559306385 x + 6300259631$ |
$36$ |
[0,18] |
$3^{48}\cdot 7^{24}\cdot 13^{27}$ |
$3$ |
$108.397154178$ |
$108.39715417800616$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.198...352.1 |
$x^{36} - 12 x^{35} - 36 x^{34} + 940 x^{33} - 927 x^{32} - 31316 x^{31} + 80914 x^{30} + 576272 x^{29} - 2182273 x^{28} - 6302752 x^{27} + 33144748 x^{26} + 39516048 x^{25} - 323192934 x^{24} - 95894188 x^{23} + 2132039314 x^{22} - 522495128 x^{21} - 9735028662 x^{20} + 5836708324 x^{19} + 30988574904 x^{18} - 26088563508 x^{17} - 68587862405 x^{16} + 69170933872 x^{15} + 104690525460 x^{14} - 116627921592 x^{13} - 109205998641 x^{12} + 126071424492 x^{11} + 77381360212 x^{10} - 85597408092 x^{9} - 36970755407 x^{8} + 34634932836 x^{7} + 11547553650 x^{6} - 7464917976 x^{5} - 2116489012 x^{4} + 652490564 x^{3} + 169180380 x^{2} - 2159532 x - 771471$ |
$36$ |
[36,0] |
$2^{54}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$108.657179233$ |
$108.65717923313618$ |
|
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.0.198...352.1 |
$x^{36} - 12 x^{35} + 120 x^{34} - 828 x^{33} + 5157 x^{32} - 26740 x^{31} + 128546 x^{30} - 546200 x^{29} + 2177147 x^{28} - 7884176 x^{27} + 26975312 x^{26} - 85116720 x^{25} + 254822270 x^{24} - 709486284 x^{23} + 1879297474 x^{22} - 4653122096 x^{21} + 10982223270 x^{20} - 24295546348 x^{19} + 51310501256 x^{18} - 101716601500 x^{17} + 192953738019 x^{16} - 343875076752 x^{15} + 588444243076 x^{14} - 945622774200 x^{13} + 1470275270855 x^{12} - 2150175684852 x^{11} + 3090474193456 x^{10} - 4158681286228 x^{9} + 5602128086021 x^{8} - 6986616644348 x^{7} + 9425727731754 x^{6} - 11556021388336 x^{5} + 15742746932912 x^{4} - 16012210942028 x^{3} + 15548809804884 x^{2} - 8434770285524 x + 3561903327529$ |
$36$ |
[0,18] |
$2^{54}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$108.657179233$ |
$108.65717923313618$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.230...752.1 |
$x^{36} + 78 x^{34} + 2691 x^{32} + 54444 x^{30} + 722475 x^{28} + 6665490 x^{26} + 44226585 x^{24} + 215382726 x^{22} + 778931478 x^{20} + 2103342228 x^{18} + 4241564028 x^{16} + 6356268126 x^{14} + 7002607950 x^{12} + 5568808401 x^{10} + 3105527607 x^{8} + 1160101683 x^{6} + 269070984 x^{4} + 33633873 x^{2} + 1601613$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 13^{33}$ |
$3$ |
$109.100468956$ |
$109.10046895602893$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.249...533.1 |
$x^{36} - x^{35} + 13 x^{34} - 36 x^{33} + 203 x^{32} - 778 x^{31} + 3610 x^{30} - 15179 x^{29} + 67057 x^{28} - 288915 x^{27} + 1260568 x^{26} - 5465175 x^{25} + 23770056 x^{24} + 93314596 x^{23} + 252043001 x^{22} + 606261535 x^{21} + 1391793921 x^{20} + 3110871488 x^{19} + 6921778679 x^{18} + 15098946046 x^{17} + 33742811734 x^{16} + 71304975349 x^{15} + 167520358953 x^{14} + 316968416161 x^{13} + 908921162436 x^{12} + 1051975883013 x^{11} + 1217338347379 x^{10} + 1408239461981 x^{9} + 1628085993424 x^{8} + 1880065729179 x^{7} + 2166332110118 x^{6} + 2485510712366 x^{5} + 2829751588081 x^{4} + 3166723749013 x^{3} + 3449677471933 x^{2} + 3423740047332 x + 3138428376721$ |
$36$ |
[0,18] |
$13^{33}\cdot 37^{24}$ |
$2$ |
$116.568861719$ |
$116.56886171941974$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$26$ |
$17$ |
|
| 36.0.449...917.1 |
$x^{36} - 3 x^{35} - 27 x^{34} + 137 x^{33} + 207 x^{32} - 1893 x^{31} + 1057 x^{30} + 9420 x^{29} - 18840 x^{28} + 12544 x^{27} + 65883 x^{26} - 229239 x^{25} + 159200 x^{24} + 167631 x^{23} - 2700417 x^{22} + 3836034 x^{21} + 19377618 x^{20} - 3061389 x^{19} - 51896833 x^{18} - 32759037 x^{17} + 96376791 x^{16} + 334585913 x^{15} + 313578288 x^{14} + 434132280 x^{13} + 951065917 x^{12} - 818916783 x^{11} - 3390929529 x^{10} - 4188723253 x^{9} - 861415446 x^{8} + 4170559728 x^{7} + 4762776347 x^{6} + 1981536447 x^{5} + 1704283443 x^{4} + 3516565010 x^{3} + 2834392743 x^{2} + 713505450 x + 104897357$ |
$36$ |
[0,18] |
$3^{48}\cdot 37^{33}$ |
$2$ |
$118.489514506$ |
$118.48951450631344$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.494...125.1 |
$x^{36} - x^{35} - 127 x^{34} + 126 x^{33} + 7328 x^{32} - 7203 x^{31} - 254655 x^{30} + 247577 x^{29} + 5956273 x^{28} - 5715774 x^{27} - 99258341 x^{26} + 93783066 x^{25} + 1216750731 x^{24} - 1128384881 x^{23} - 11167777905 x^{22} + 10123730642 x^{21} + 77372149977 x^{20} - 68170119347 x^{19} - 404867699989 x^{18} + 343756885869 x^{17} + 1590272002452 x^{16} - 1283637936946 x^{15} - 4628193618151 x^{14} + 3471389732603 x^{13} + 9777925862459 x^{12} - 6544984186949 x^{11} - 14568115911700 x^{10} + 8066810405369 x^{9} + 14716307928191 x^{8} - 5774232219857 x^{7} - 9516669187523 x^{6} + 1798484654352 x^{5} + 3510763848149 x^{4} + 66623171786 x^{3} - 532421593101 x^{2} - 84148737831 x + 7203054951$ |
$36$ |
[36,0] |
$5^{18}\cdot 7^{30}\cdot 13^{33}$ |
$3$ |
$118.808662955$ |
$118.80866295535$ |
|
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.36.747...117.1 |
$x^{36} - 3 x^{35} - 108 x^{34} + 314 x^{33} + 5133 x^{32} - 14553 x^{31} - 141455 x^{30} + 394602 x^{29} + 2507526 x^{28} - 6965157 x^{27} - 29988882 x^{26} + 84226455 x^{25} + 246806857 x^{24} - 714893316 x^{23} - 1398775770 x^{22} + 4292785887 x^{21} + 5364342456 x^{20} - 18168287730 x^{19} - 13333973109 x^{18} + 53510458269 x^{17} + 19430031183 x^{16} - 107555904357 x^{15} - 11332618518 x^{14} + 143867150712 x^{13} - 9214998883 x^{12} - 123510493746 x^{11} + 19994463534 x^{10} + 64078960801 x^{9} - 12437043336 x^{8} - 17931881889 x^{7} + 2702218315 x^{6} + 2080472373 x^{5} + 14312169 x^{4} - 34504929 x^{3} + 1294671 x^{2} + 21021 x + 53$ |
$36$ |
[36,0] |
$3^{48}\cdot 7^{18}\cdot 13^{33}$ |
$3$ |
$120.178127392$ |
$120.17812739215435$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.36.822...125.1 |
$x^{36} - 9 x^{35} - 74 x^{34} + 909 x^{33} + 1441 x^{32} - 38540 x^{31} + 29909 x^{30} + 883449 x^{29} - 1940661 x^{28} - 11622649 x^{27} + 41000690 x^{26} + 82185945 x^{25} - 475474126 x^{24} - 170531710 x^{23} + 3313200544 x^{22} - 1874661149 x^{21} - 14012133789 x^{20} + 17229198563 x^{19} + 34707820890 x^{18} - 66363236954 x^{17} - 44892472008 x^{16} + 142697506526 x^{15} + 15401207070 x^{14} - 183495454624 x^{13} + 32402227403 x^{12} + 145220963746 x^{11} - 46806011656 x^{10} - 71694298121 x^{9} + 27858490170 x^{8} + 21853214932 x^{7} - 8861546511 x^{6} - 3909998733 x^{5} + 1545247949 x^{4} + 363308426 x^{3} - 136694687 x^{2} - 12769152 x + 4591091$ |
$36$ |
[36,0] |
$5^{27}\cdot 7^{30}\cdot 19^{24}$ |
$3$ |
$120.497564927$ |
$120.49756492669414$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$92625495286396430000000000$ |
| 36.36.127...125.1 |
$x^{36} - 114 x^{34} - x^{33} + 5859 x^{32} + 111 x^{31} - 180048 x^{30} - 5526 x^{29} + 3699240 x^{28} + 163470 x^{27} - 53820756 x^{26} - 3208830 x^{25} + 572790581 x^{24} + 44143254 x^{23} - 4540870752 x^{22} - 437624579 x^{21} + 27043916778 x^{20} + 3163735311 x^{19} - 121104847513 x^{18} - 16681810230 x^{17} + 405277633206 x^{16} + 63503538493 x^{15} - 1000011221073 x^{14} - 170766196161 x^{13} + 1779851366683 x^{12} + 312383052333 x^{11} - 2211527198037 x^{10} - 364422057685 x^{9} + 1829938769694 x^{8} + 239262351117 x^{7} - 941144446491 x^{6} - 61365660075 x^{5} + 268847902749 x^{4} - 9408191247 x^{3} - 32267765898 x^{2} + 5446221264 x - 98828729$ |
$36$ |
[36,0] |
$3^{54}\cdot 5^{18}\cdot 13^{33}$ |
$3$ |
$121.978032481$ |
$121.97803248139311$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.36.132...853.1 |
$x^{36} - x^{35} - 97 x^{34} + 98 x^{33} + 4058 x^{32} - 4149 x^{31} - 96839 x^{30} + 100351 x^{29} + 1472129 x^{28} - 1547896 x^{27} - 15099705 x^{26} + 16117232 x^{25} + 108034873 x^{24} - 116987282 x^{23} - 549690124 x^{22} + 602644282 x^{21} + 2008422826 x^{20} - 2221244124 x^{19} - 5280367442 x^{18} + 5859024782 x^{17} + 9939296148 x^{16} - 10975518510 x^{15} - 13230545958 x^{14} + 14360136230 x^{13} + 12203357336 x^{12} - 12756349726 x^{11} - 7568837976 x^{10} + 7354733074 x^{9} + 3020402597 x^{8} - 2560846304 x^{7} - 717542006 x^{6} + 475096085 x^{5} + 83002961 x^{4} - 35766984 x^{3} - 1884048 x^{2} + 471498 x + 18773$ |
$36$ |
[36,0] |
$13^{33}\cdot 19^{30}$ |
$2$ |
$122.107612667$ |
$122.10761266703042$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$129475995156478280000000000$ |
| 36.0.155...125.1 |
$x^{36} - 3 x^{35} - 3 x^{34} + 8 x^{33} - 15 x^{32} - 210 x^{31} - 385 x^{30} + 5415 x^{29} + 6351 x^{28} - 36200 x^{27} + 130713 x^{26} + 121467 x^{25} - 1894259 x^{24} + 441060 x^{23} + 14119596 x^{22} - 22878764 x^{21} - 43702461 x^{20} + 226149234 x^{19} - 26520393 x^{18} - 976832769 x^{17} + 3135439767 x^{16} - 4935139658 x^{15} + 2592680742 x^{14} + 2242273917 x^{13} + 11620240143 x^{12} - 26596418232 x^{11} + 69063367278 x^{10} - 65694612305 x^{9} + 136411565292 x^{8} - 109764491523 x^{7} + 123111472419 x^{6} - 18291665040 x^{5} + 69893697486 x^{4} - 64890324348 x^{3} + 101791204893 x^{2} - 51149414124 x + 22848924331$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{27}\cdot 13^{30}$ |
$3$ |
$122.65218888$ |
$122.65218888006295$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.212...125.1 |
$x^{36} - 12 x^{35} - 42 x^{34} + 1061 x^{33} - 1350 x^{32} - 37617 x^{31} + 129380 x^{30} + 647814 x^{29} - 3761226 x^{28} - 4267081 x^{27} + 57623793 x^{26} - 33213237 x^{25} - 505422576 x^{24} + 881990283 x^{23} + 2405576283 x^{22} - 7520229251 x^{21} - 4085328615 x^{20} + 33458575323 x^{19} - 14028012138 x^{18} - 80883403815 x^{17} + 85769496648 x^{16} + 98511159201 x^{15} - 181248893193 x^{14} - 38964520557 x^{13} + 195904466188 x^{12} - 32629612377 x^{11} - 118260246567 x^{10} + 43807175472 x^{9} + 40452413076 x^{8} - 20325698838 x^{7} - 7481712385 x^{6} + 4554136782 x^{5} + 636738900 x^{4} - 467339570 x^{3} - 14193342 x^{2} + 15094344 x + 143461$ |
$36$ |
[36,0] |
$3^{54}\cdot 5^{27}\cdot 19^{24}$ |
$3$ |
$123.711988023$ |
$123.71198802296776$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.0.570...000.1 |
$x^{36} - 12 x^{35} + 132 x^{34} - 964 x^{33} + 6462 x^{32} - 35316 x^{31} + 178450 x^{30} - 786024 x^{29} + 3224823 x^{28} - 11908044 x^{27} + 41299005 x^{26} - 131377506 x^{25} + 394830604 x^{24} - 1099808568 x^{23} + 2908195344 x^{22} - 7183606822 x^{21} + 16934574060 x^{20} - 37490949888 x^{19} + 79573970631 x^{18} - 159170870298 x^{17} + 307045487688 x^{16} - 559522976788 x^{15} + 986494828509 x^{14} - 1636097978718 x^{13} + 2640055694434 x^{12} - 4009568149062 x^{11} + 6031372465950 x^{10} - 8462912247118 x^{9} + 11730030510336 x^{8} - 14696441624388 x^{7} + 19080633257687 x^{6} - 22224248926686 x^{5} + 28052657251047 x^{4} - 27230959523324 x^{3} + 25534530115587 x^{2} - 13710464052024 x + 6311298334321$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 5^{27}\cdot 7^{24}$ |
$4$ |
$127.156356225$ |
$127.15635622501046$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.0.706...072.1 |
$x^{36} - 12 x^{35} + 114 x^{34} - 760 x^{33} + 4383 x^{32} - 21156 x^{31} + 90754 x^{30} - 342108 x^{29} + 1163349 x^{28} - 3564384 x^{27} + 10049106 x^{26} - 26143512 x^{25} + 63374392 x^{24} - 142650108 x^{23} + 302605242 x^{22} - 610491148 x^{21} + 1185262668 x^{20} - 2187042156 x^{19} + 3793817988 x^{18} - 6146155488 x^{17} + 9744782631 x^{16} - 15541129312 x^{15} + 23994963972 x^{14} - 33027263592 x^{13} + 41712329035 x^{12} - 53997803892 x^{11} + 81557728002 x^{10} - 120007128040 x^{9} + 143740618215 x^{8} - 131526335532 x^{7} + 150054670958 x^{6} - 234723540492 x^{5} + 430616836146 x^{4} - 504014501660 x^{3} + 443927747412 x^{2} - 219262177512 x + 66191511889$ |
$36$ |
[0,18] |
$2^{99}\cdot 3^{54}\cdot 7^{24}$ |
$3$ |
$127.912522491$ |
$127.91252249119998$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.706...072.1 |
$x^{36} - 12 x^{35} - 30 x^{34} + 872 x^{33} - 1233 x^{32} - 25380 x^{31} + 78226 x^{30} + 379620 x^{29} - 1758891 x^{28} - 2937888 x^{27} + 22076274 x^{26} + 6821832 x^{25} - 173279528 x^{24} + 79991748 x^{23} + 885664602 x^{22} - 877781932 x^{21} - 2962642644 x^{20} + 4262622420 x^{19} + 6317132340 x^{18} - 12265171104 x^{17} - 7935268665 x^{16} + 22118582240 x^{15} + 4488876612 x^{14} - 25142360904 x^{13} + 1143439675 x^{12} + 17833884876 x^{11} - 3207637326 x^{10} - 7708877992 x^{9} + 1857934743 x^{8} + 1926063060 x^{7} - 485300914 x^{6} - 247363308 x^{5} + 56713698 x^{4} + 12546916 x^{3} - 2193228 x^{2} - 170472 x + 3457$ |
$36$ |
[36,0] |
$2^{99}\cdot 3^{54}\cdot 7^{24}$ |
$3$ |
$127.912522491$ |
$127.91252249119998$ |
|
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
trivial |
$2$ |
$35$ |
$361611812727349340000000000$ |
| 36.36.821...625.1 |
$x^{36} - 9 x^{35} - 65 x^{34} + 767 x^{33} + 1348 x^{32} - 27862 x^{31} + 1248 x^{30} + 570596 x^{29} - 539471 x^{28} - 7345274 x^{27} + 11035141 x^{26} + 62715081 x^{25} - 119635996 x^{24} - 365138709 x^{23} + 822660108 x^{22} + 1467238032 x^{21} - 3815197767 x^{20} - 4065525074 x^{19} + 12253153691 x^{18} + 7632713374 x^{17} - 27502514595 x^{16} - 9230490750 x^{15} + 42972000803 x^{14} + 6151376608 x^{13} - 45930613858 x^{12} - 541428095 x^{11} + 32430382933 x^{10} - 2537946464 x^{9} - 14234297497 x^{8} + 1972347494 x^{7} + 3506699274 x^{6} - 611541017 x^{5} - 408560825 x^{4} + 74320909 x^{3} + 14619917 x^{2} - 1560887 x - 127399$ |
$36$ |
[36,0] |
$5^{27}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$128.452019397$ |
$128.45201939711583$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[2]$ |
$2$ |
$35$ |
$291218721617730900000000000$ |
| 36.36.821...625.2 |
$x^{36} - 9 x^{35} - 65 x^{34} + 767 x^{33} + 1348 x^{32} - 27862 x^{31} + 1248 x^{30} + 570596 x^{29} - 539471 x^{28} - 7345079 x^{27} + 11033971 x^{26} + 62716641 x^{25} - 119639181 x^{24} - 365203449 x^{23} + 823243158 x^{22} + 1467032372 x^{21} - 3822699612 x^{20} - 4052765184 x^{19} + 12292532381 x^{18} + 7514841399 x^{17} - 27583235170 x^{16} - 8685061710 x^{15} + 42894256903 x^{14} + 4650174763 x^{13} - 45171089573 x^{12} + 2033087095 x^{11} + 30731222743 x^{10} - 5227780689 x^{9} - 12313025417 x^{8} + 3507716589 x^{7} + 2347697989 x^{6} - 949622917 x^{5} - 86946285 x^{4} + 56606849 x^{3} + 1187472 x^{2} - 996492 x - 54664$ |
$36$ |
[36,0] |
$5^{27}\cdot 7^{24}\cdot 13^{33}$ |
$3$ |
$128.452019397$ |
$128.45201939711583$ |
|
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
$[2]$ |
$2$ |
$35$ |
$837390418804361600000000000$ |
| 36.0.827...272.1 |
$x^{36} + 42 x^{34} - 12 x^{33} + 1062 x^{32} - 228 x^{31} + 18566 x^{30} - 3600 x^{29} + 244113 x^{28} - 26424 x^{27} + 2554524 x^{26} - 61164 x^{25} + 21412793 x^{24} + 1371384 x^{23} + 149530704 x^{22} + 27331592 x^{21} + 868074111 x^{20} + 236070696 x^{19} + 4266665390 x^{18} + 1820606652 x^{17} + 18620376480 x^{16} + 10373579276 x^{15} + 68331137634 x^{14} + 47710693968 x^{13} + 248970781930 x^{12} + 256259966832 x^{11} + 858443199054 x^{10} + 837202367648 x^{9} + 2334611060583 x^{8} + 3325143168012 x^{7} + 10600537969942 x^{6} + 18337221438216 x^{5} + 35763130408821 x^{4} + 38912147678040 x^{3} + 41429002968336 x^{2} + 21093689536332 x + 9724193509447$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{48}\cdot 13^{33}$ |
$3$ |
$128.47582231$ |
$128.47582231014687$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$17$ |
|
| 36.36.827...272.1 |
$x^{36} - 114 x^{34} - 12 x^{33} + 5742 x^{32} + 1020 x^{31} - 168842 x^{30} - 36360 x^{29} + 3229485 x^{28} + 703864 x^{27} - 42416064 x^{26} - 7921692 x^{25} + 393837365 x^{24} + 49313304 x^{23} - 2622544680 x^{22} - 102135304 x^{21} + 12569299335 x^{20} - 808250712 x^{19} - 43114770166 x^{18} + 7549082028 x^{17} + 104325807096 x^{16} - 29535704788 x^{15} - 174043844046 x^{14} + 65924502360 x^{13} + 194157715726 x^{12} - 88530910560 x^{11} - 139310773122 x^{10} + 71713506368 x^{9} + 60595492083 x^{8} - 33960132372 x^{7} - 14319635826 x^{6} + 8664074736 x^{5} + 1436547993 x^{4} - 990979704 x^{3} - 26527284 x^{2} + 33492924 x - 126541$ |
$36$ |
[36,0] |
$2^{54}\cdot 3^{48}\cdot 13^{33}$ |
$3$ |
$128.47582231$ |
$128.47582231014687$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
not computed |
$2$ |
$35$ |
|
| 36.0.919...053.1 |
$x^{36} - x^{35} + 15 x^{34} - 37 x^{33} + 255 x^{32} - 893 x^{31} + 4759 x^{30} - 19301 x^{29} + 93071 x^{28} - 401357 x^{27} + 1858759 x^{26} - 8222325 x^{25} + 37455807 x^{24} + 144852694 x^{23} + 445307204 x^{22} + 1282984056 x^{21} + 3792495248 x^{20} + 10606823904 x^{19} + 32224237120 x^{18} + 85931335552 x^{17} + 280353392896 x^{16} + 664891407872 x^{15} + 2572605408256 x^{14} + 4493047158784 x^{13} + 26204297293824 x^{12} + 16117519663104 x^{11} + 9913428803584 x^{10} + 6097468129280 x^{9} + 3750377816064 x^{8} + 2306745565184 x^{7} + 1418798825472 x^{6} + 872616558592 x^{5} + 536602476544 x^{4} + 329638739968 x^{3} + 201863462912 x^{2} + 120259084288 x + 68719476736$ |
$36$ |
[0,18] |
$13^{33}\cdot 43^{24}$ |
$2$ |
$128.852755406$ |
$128.85275540558848$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
not computed |
$26$ |
$17$ |
|
| 36.36.109...957.1 |
$x^{36} - 9 x^{35} - 74 x^{34} + 906 x^{33} + 1465 x^{32} - 38375 x^{31} + 28176 x^{30} + 881049 x^{29} - 1892871 x^{28} - 11630750 x^{27} + 40364678 x^{26} + 82284019 x^{25} - 470447773 x^{24} - 160121713 x^{23} + 3263481172 x^{22} - 2057742341 x^{21} - 13374176751 x^{20} + 18261358636 x^{19} + 29791639547 x^{18} - 67146393883 x^{17} - 26075281081 x^{16} + 131524497452 x^{15} - 18736332340 x^{14} - 147685422825 x^{13} + 62851529470 x^{12} + 98707302558 x^{11} - 60074993232 x^{10} - 39397313544 x^{9} + 29752270500 x^{8} + 8975560111 x^{7} - 8221358547 x^{6} - 1005405651 x^{5} + 1224100668 x^{4} + 27696257 x^{3} - 85804113 x^{2} + 2030710 x + 1923169$ |
$36$ |
[36,0] |
$3^{18}\cdot 13^{33}\cdot 19^{24}$ |
$3$ |
$129.472569666$ |
$129.47256966590146$ |
|
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[2, 2]$ |
$2$ |
$35$ |
$98353320439532980000000000$ |
