| 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 |
| 30.0.457...771.1 |
$x^{30} + 6 x^{28} - x^{27} + 14 x^{26} - x^{25} + 8 x^{24} + 13 x^{23} - 39 x^{22} + 37 x^{21} - 93 x^{20} + 30 x^{19} + 10 x^{18} - 13 x^{17} + 349 x^{16} + 77 x^{15} + 721 x^{14} + 575 x^{13} + 1026 x^{12} + 1233 x^{11} + 1137 x^{10} + 993 x^{9} + 501 x^{8} - 41 x^{7} - 253 x^{6} - 186 x^{5} - 58 x^{4} + 6 x^{3} + 14 x^{2} + 6 x + 1$ |
$30$ |
[0,15] |
$-\,3^{20}\cdot 11^{27}$ |
$2$ |
$18.002559423165124$ |
$37.44683262965639$ |
|
|
? |
$S_3\times C_{15}$ (as 30T15) |
trivial |
$22$ |
$14$ |
$27376181.549941503$ |
| 30.0.131...536.1 |
$x^{30} + 6 x^{28} + 25 x^{26} + 45 x^{24} - 44 x^{22} - 197 x^{20} - 20 x^{18} + 411 x^{16} + 283 x^{14} - 424 x^{12} - 397 x^{10} + 348 x^{8} + 358 x^{6} + 8 x^{4} - 7 x^{2} + 1$ |
$30$ |
[0,15] |
$-\,2^{40}\cdot 11^{26}$ |
$2$ |
$20.13323926187899$ |
$21.808547634345086$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$4$ |
$14$ |
$18931497.119988322$ |
| 30.10.144...896.1 |
$x^{30} - 15 x^{28} + 104 x^{26} - 482 x^{24} + 1708 x^{22} - 4753 x^{20} + 10608 x^{18} - 18925 x^{16} + 26563 x^{14} - 28460 x^{12} + 22463 x^{10} - 12716 x^{8} + 5049 x^{6} - 1331 x^{4} + 198 x^{2} - 11$ |
$30$ |
[10,10] |
$2^{40}\cdot 11^{27}$ |
$2$ |
$21.808547634345086$ |
$21.808547634345086$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$2$ |
$19$ |
$397294072.2356694$ |
| 30.0.218...571.1 |
$x^{30} - x^{29} - 7 x^{28} + 10 x^{27} + 7 x^{26} - 19 x^{25} + 56 x^{24} - 38 x^{23} - 238 x^{22} + 196 x^{21} + 1084 x^{20} + 255 x^{19} - 3219 x^{18} - 4472 x^{17} + 2252 x^{16} + 12483 x^{15} + 13641 x^{14} + 1966 x^{13} - 11281 x^{12} - 13340 x^{11} - 5077 x^{10} + 3378 x^{9} + 6156 x^{8} + 4833 x^{7} + 3411 x^{6} + 3672 x^{5} + 4671 x^{4} + 4536 x^{3} + 2997 x^{2} + 1215 x + 243$ |
$30$ |
[0,15] |
$-\,3^{10}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$23.877737944442764$ |
$39.66094555677728$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$22$ |
$14$ |
$2830009383.1065817$ |
| 30.0.107...171.1 |
$x^{30} - x^{29} - 4 x^{28} + 2 x^{27} + 14 x^{26} - 18 x^{25} - 22 x^{24} + 80 x^{23} + 2 x^{22} - 292 x^{21} + 107 x^{20} + 966 x^{19} - 524 x^{18} - 1689 x^{17} + 1837 x^{16} + 1003 x^{15} - 6747 x^{14} + 4493 x^{13} + 13850 x^{12} - 15662 x^{11} - 11779 x^{10} + 28372 x^{9} - 4752 x^{8} - 31522 x^{7} + 29972 x^{6} + 5164 x^{5} - 25670 x^{4} + 15150 x^{3} + 3000 x^{2} - 8125 x + 3125$ |
$30$ |
[0,15] |
$-\,11^{27}\cdot 31^{10}$ |
$2$ |
$27.18779466419903$ |
$85.40721213930478$ |
|
|
? |
$S_3\times C_{15}$ (as 30T15) |
trivial |
$22$ |
$14$ |
$10842704727.78492$ |
| 30.0.177...271.1 |
$x^{30} - x^{29} + x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$30$ |
[0,15] |
$-\,31^{29}$ |
$1$ |
$27.6471034373$ |
$27.647103437285644$ |
✓ |
✓ |
✓ |
$C_{30}$ (as 30T1) |
$[9]$ |
$62$ |
$14$ |
$4316173757.895952$ |
| 30.0.182...875.1 |
$x^{30} - 10 x^{27} - 54 x^{25} + 90 x^{24} + 315 x^{23} + 15 x^{22} - 240 x^{21} + 504 x^{20} - 4740 x^{19} + 8375 x^{18} - 14580 x^{17} + 25140 x^{16} - 34179 x^{15} + 51465 x^{14} - 61710 x^{13} + 70215 x^{12} - 67800 x^{11} + 45276 x^{10} - 22840 x^{9} - 3240 x^{8} + 16350 x^{7} - 10730 x^{6} + 4956 x^{5} + 2280 x^{4} - 4065 x^{3} - 420 x^{2} + 780 x + 169$ |
$30$ |
[0,15] |
$-\,3^{35}\cdot 5^{38}$ |
$2$ |
$27.669637490247258$ |
$29.194595979271636$ |
|
|
? |
$D_{30}$ (as 30T14) |
trivial |
$6$ |
$14$ |
$17149795938.655872$ |
| 30.10.531...753.1 |
$x^{30} - 7 x^{29} + 24 x^{28} - 23 x^{27} - 141 x^{26} + 633 x^{25} - 1481 x^{24} + 2556 x^{23} - 3432 x^{22} + 2970 x^{21} + 2520 x^{20} - 16434 x^{19} + 36814 x^{18} - 58793 x^{17} + 75906 x^{16} - 86484 x^{15} + 87441 x^{14} - 74977 x^{13} + 56249 x^{12} - 35409 x^{11} + 19416 x^{10} - 7865 x^{9} + 726 x^{8} + 1323 x^{7} - 1451 x^{6} + 413 x^{5} - 168 x^{4} + 17 x^{3} - 15 x^{2} + x + 1$ |
$30$ |
[10,10] |
$3^{15}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$28.6756579034896$ |
$39.66094555677728$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$2$ |
$19$ |
$26520700757.33144$ |
| 30.2.605...125.1 |
$x^{30} - 4 x^{29} - 4 x^{28} + 32 x^{27} + 29 x^{26} - 207 x^{25} - 80 x^{24} + 808 x^{23} + 324 x^{22} - 2807 x^{21} - 784 x^{20} + 6744 x^{19} + 2549 x^{18} - 11743 x^{17} - 5231 x^{16} + 15441 x^{15} + 10445 x^{14} - 10233 x^{13} - 7776 x^{12} + 6706 x^{11} + 5598 x^{10} - 2410 x^{9} - 2278 x^{8} + 1045 x^{7} + 940 x^{6} - 185 x^{5} - 176 x^{4} + 44 x^{3} + 30 x^{2} - 6 x - 1$ |
$30$ |
[2,14] |
$5^{15}\cdot 239^{14}$ |
$2$ |
$28.80076493748214$ |
$34.56877203488721$ |
|
|
? |
$D_{30}$ (as 30T14) |
trivial |
$2$ |
$15$ |
$5581738694.683278$ |
| 30.0.141...987.1 |
$x^{30} - 5 x^{29} + 14 x^{28} - 37 x^{27} + 83 x^{26} - 152 x^{25} + 241 x^{24} - 335 x^{23} + 465 x^{22} - 620 x^{21} + 812 x^{20} - 1084 x^{19} + 1348 x^{18} - 1578 x^{17} + 1736 x^{16} - 1826 x^{15} + 1986 x^{14} - 2009 x^{13} + 2111 x^{12} - 2179 x^{11} + 1810 x^{10} - 1551 x^{9} + 1376 x^{8} - 959 x^{7} + 887 x^{6} - 765 x^{5} + 462 x^{4} - 285 x^{3} + 146 x^{2} - 13 x + 1$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 439^{14}$ |
$2$ |
$29.628573118259904$ |
$36.29049462324811$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$6$ |
$14$ |
$18103283853.50697$ |
| 30.0.203...531.1 |
$x^{30} - x + 1$ |
$30$ |
[0,15] |
$-\,7\cdot 4547\cdot 625861750823\cdot 40306090892659\cdot 253230129277627$ |
$5$ |
$29.9874531212$ |
$1.4259153058351249e+22$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$11086740597.223595$ |
| 30.2.208...469.1 |
$x^{30} - x - 1$ |
$30$ |
[2,14] |
$4421\cdot 22659339443160463\cdot 2080906233684319160584903$ |
$3$ |
$30.0123965237$ |
$1.4438103000318644e+22$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$12534500381.926157$ |
| 30.0.104...371.1 |
$x^{30} - x^{29} + 3 x^{28} - 4 x^{27} + 9 x^{26} - 14 x^{25} + 28 x^{24} - 47 x^{23} + 89 x^{22} - 155 x^{21} + 286 x^{20} + 132 x^{19} + 285 x^{18} + 265 x^{17} + 437 x^{16} + 378 x^{15} + 761 x^{14} + 432 x^{13} + 1468 x^{12} + 157 x^{11} + 3211 x^{10} - 1429 x^{9} + 636 x^{8} - 283 x^{7} + 126 x^{6} - 56 x^{5} + 25 x^{4} - 11 x^{3} + 5 x^{2} - 2 x + 1$ |
$30$ |
[0,15] |
$-\,7^{20}\cdot 11^{27}$ |
$2$ |
$31.670295092$ |
$31.670295092032053$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 2]$ |
$22$ |
$14$ |
$4697581952.048968$ |
| 30.0.132...687.1 |
$x^{30} - x^{29} + 5 x^{28} - 6 x^{27} + 20 x^{26} - 27 x^{25} + 75 x^{24} - 46 x^{23} + 211 x^{22} - 109 x^{21} + 617 x^{20} - 357 x^{19} + 1911 x^{18} - 1372 x^{17} + 2909 x^{16} - 2210 x^{15} + 4354 x^{14} - 2262 x^{13} + 5693 x^{12} + 2042 x^{11} + 3092 x^{10} + 1302 x^{9} + 2375 x^{8} + 290 x^{7} + 1798 x^{6} - 511 x^{5} + 146 x^{4} - 41 x^{3} + 12 x^{2} - 3 x + 1$ |
$30$ |
[0,15] |
$-\,7^{25}\cdot 11^{24}$ |
$2$ |
$34.4637486944$ |
$34.463748694396095$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 10]$ |
$14$ |
$14$ |
$4697581952.048968$ |
| 30.2.140...000.1 |
$x^{30} - x^{29} + 11 x^{28} + 4 x^{27} + 44 x^{26} - 6 x^{25} - 74 x^{24} - 446 x^{23} - 1543 x^{22} + 183 x^{21} - 1721 x^{20} + 7116 x^{19} + 11884 x^{18} - 3168 x^{17} + 7664 x^{16} - 18756 x^{15} + 17109 x^{14} - 3363 x^{13} - 2431 x^{12} + 11594 x^{11} - 15080 x^{10} + 6868 x^{9} + 3884 x^{8} - 3768 x^{7} + 2512 x^{6} - 1864 x^{5} - 1696 x^{4} + 656 x^{3} + 448 x^{2} + 16 x - 16$ |
$30$ |
[2,14] |
$2^{20}\cdot 5^{15}\cdot 131^{14}$ |
$3$ |
$34.53278493432046$ |
$40.62630398353121$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$145673548066.95038$ |
| 30.0.290...763.1 |
$x^{30} - 4 x^{27} + 47 x^{24} + 4 x^{21} + 1159 x^{18} - 1525 x^{15} + 4898 x^{12} + 2458 x^{9} + 1824 x^{6} - 42 x^{3} + 1$ |
$30$ |
[0,15] |
$-\,3^{45}\cdot 11^{24}$ |
$2$ |
$35.3831122505$ |
$35.383112250454936$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[31]$ |
$18$ |
$14$ |
$15853905121.091976$ |
| 30.2.698...512.1 |
$x^{30} - 16 x^{28} + 152 x^{26} - 960 x^{24} + 4656 x^{22} - 18272 x^{20} + 59264 x^{18} - 161280 x^{16} + 368896 x^{14} - 701952 x^{12} + 1121280 x^{10} - 1376256 x^{8} + 1417216 x^{6} - 884736 x^{4} + 524288 x^{2} - 32768$ |
$30$ |
[2,14] |
$2^{45}\cdot 239^{14}$ |
$2$ |
$36.43040622302421$ |
$43.726422218150894$ |
|
|
? |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
|
| 30.0.159...171.1 |
$x^{30} + 3 x^{28} - x^{27} + 9 x^{26} - 6 x^{25} + 28 x^{24} - 27 x^{23} + 90 x^{22} - 109 x^{21} + 297 x^{20} + 507 x^{19} + 1000 x^{18} + 1224 x^{17} + 2493 x^{16} + 2672 x^{15} + 6255 x^{14} + 5523 x^{13} + 16093 x^{12} + 10314 x^{11} + 42756 x^{10} + 14849 x^{9} + 5157 x^{8} + 1791 x^{7} + 622 x^{6} + 216 x^{5} + 75 x^{4} + 26 x^{3} + 9 x^{2} + 3 x + 1$ |
$30$ |
[0,15] |
$-\,3^{40}\cdot 11^{27}$ |
$2$ |
$37.4468326297$ |
$37.44683262965639$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[93]$ |
$22$ |
$14$ |
$15853905121.091976$ |
| 30.2.301...125.1 |
$x^{30} - 5 x^{29} + 8 x^{28} + 19 x^{27} - 63 x^{26} - 52 x^{25} + 265 x^{24} - 211 x^{23} - 393 x^{22} + 858 x^{21} - 86 x^{20} - 2380 x^{19} + 4186 x^{18} + 8272 x^{17} - 3336 x^{16} - 13036 x^{15} + 7176 x^{14} + 23259 x^{13} + 6583 x^{12} - 9115 x^{11} - 7328 x^{10} + 1279 x^{9} + 4440 x^{8} + 2429 x^{7} - 349 x^{6} - 1189 x^{5} - 88 x^{4} + 271 x^{3} + 100 x^{2} - 13 x - 1$ |
$30$ |
[2,14] |
$5^{15}\cdot 439^{14}$ |
$2$ |
$38.25032341963645$ |
$46.850827100489916$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$748323688575.9082$ |
| 30.2.812...137.1 |
$x^{30} - 9 x^{29} + 29 x^{28} - 62 x^{27} + 140 x^{26} - 289 x^{25} + 749 x^{24} - 2505 x^{23} + 6556 x^{22} - 13979 x^{21} + 24020 x^{20} - 33363 x^{19} + 38542 x^{18} - 41923 x^{17} + 47672 x^{16} - 60161 x^{15} + 70650 x^{14} - 64907 x^{13} + 32243 x^{12} + 11892 x^{11} - 39347 x^{10} + 39493 x^{9} - 24068 x^{8} + 9526 x^{7} + 164 x^{6} - 4686 x^{5} + 4431 x^{4} - 2269 x^{3} + 729 x^{2} - 213 x + 43$ |
$30$ |
[2,14] |
$17^{15}\cdot 127^{14}$ |
$2$ |
$39.53661926232569$ |
$46.46504062195577$ |
|
|
? |
$D_{30}$ (as 30T14) |
trivial |
$2$ |
$15$ |
$1232398776399.036$ |
| 30.0.893...671.1 |
$x^{30} - 3 x^{29} - 5 x^{28} + 23 x^{27} - 7 x^{26} - 43 x^{25} + 380 x^{24} - 1004 x^{23} - 505 x^{22} + 4147 x^{21} - 3960 x^{20} + 145 x^{19} + 33797 x^{18} - 104422 x^{17} + 76694 x^{16} + 164546 x^{15} - 470105 x^{14} + 125016 x^{13} + 1685293 x^{12} - 1720079 x^{11} - 1513677 x^{10} - 5549753 x^{9} + 23270864 x^{8} - 21911244 x^{7} + 5984424 x^{6} - 15339818 x^{5} + 45492605 x^{4} - 53109297 x^{3} + 35921397 x^{2} - 13035410 x + 2348809$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 7^{15}\cdot 11^{27}$ |
$3$ |
$39.66094555677728$ |
$39.66094555677728$ |
|
✓ |
? |
$C_5\times S_3$ (as 30T2) |
$[2, 22]$ |
$2$ |
$14$ |
$9800307802.95059$ |
| 30.0.109...375.1 |
$x^{30} - 7 x^{29} + 48 x^{28} - 257 x^{27} + 1124 x^{26} - 4108 x^{25} + 12894 x^{24} - 35106 x^{23} + 82734 x^{22} - 166828 x^{21} + 288975 x^{20} - 424231 x^{19} + 515389 x^{18} - 443551 x^{17} + 184757 x^{16} + 79835 x^{15} - 29816 x^{14} - 348911 x^{13} + 993639 x^{12} - 2148173 x^{11} + 1765791 x^{10} + 384577 x^{9} - 1489368 x^{8} + 2068027 x^{7} - 1731374 x^{6} - 444980 x^{5} + 2213182 x^{4} - 1190713 x^{3} - 21588 x^{2} + 127306 x + 52081$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 5^{25}\cdot 47^{14}$ |
$3$ |
$39.93447365182815$ |
$45.40300106204512$ |
|
|
? |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$14$ |
|
| 30.2.110...000.1 |
$x^{30} - 3 x^{29} + 21 x^{28} - 42 x^{27} + 225 x^{26} - 359 x^{25} + 651 x^{24} - 2808 x^{23} - 1822 x^{22} - 11536 x^{21} - 10414 x^{20} - 26496 x^{19} - 25330 x^{18} - 33066 x^{17} - 28312 x^{16} - 19700 x^{15} - 18200 x^{14} + 6446 x^{13} - 8210 x^{12} + 13412 x^{11} - 5750 x^{10} + 6200 x^{9} - 4422 x^{8} + 1276 x^{7} - 711 x^{6} + 161 x^{5} - 113 x^{4} - 42 x^{3} + 3 x^{2} - 3 x - 1$ |
$30$ |
[2,14] |
$2^{20}\cdot 5^{15}\cdot 179^{14}$ |
$3$ |
$39.94873948168138$ |
$47.489563898943345$ |
|
|
|
$D_{30}$ (as 30T14) |
$[3, 3]$ |
$2$ |
$15$ |
$383760855207.4596$ |
| 30.0.337...000.1 |
$x^{30} - 2 x^{15} + 2$ |
$30$ |
[0,15] |
$-\,2^{44}\cdot 3^{30}\cdot 5^{30}$ |
$3$ |
$41.457386399$ |
$63.38224664768071$ |
|
|
✓ |
$D_6\times F_5$ (as 30T51) |
trivial |
$4$ |
$14$ |
$4813633304417.372$ |
| 30.0.607...847.1 |
$x^{30} - 6 x^{29} + 38 x^{28} - 178 x^{27} + 694 x^{26} - 2325 x^{25} + 6840 x^{24} - 17890 x^{23} + 42428 x^{22} - 92148 x^{21} + 185209 x^{20} - 348333 x^{19} + 617591 x^{18} - 1037914 x^{17} + 1659175 x^{16} - 2519432 x^{15} + 3620042 x^{14} - 4892313 x^{13} + 6168845 x^{12} - 7195888 x^{11} + 7698034 x^{10} - 7475970 x^{9} + 6524456 x^{8} - 5050948 x^{7} + 3416179 x^{6} - 1976201 x^{5} + 950326 x^{4} - 363451 x^{3} + 103267 x^{2} - 19350 x + 1849$ |
$30$ |
[0,15] |
$-\,17^{14}\cdot 127^{15}$ |
$2$ |
$42.277700430231675$ |
$46.46504062195577$ |
|
|
? |
$D_{30}$ (as 30T14) |
$[5]$ |
$2$ |
$14$ |
$588337897727.5111$ |
| 30.0.822...187.1 |
$x^{30} - x^{29} + 15 x^{28} - 12 x^{27} + 131 x^{26} - 92 x^{25} + 755 x^{24} - 449 x^{23} + 3202 x^{22} - 1648 x^{21} + 10173 x^{20} - 4368 x^{19} + 24856 x^{18} - 8980 x^{17} + 46255 x^{16} - 13276 x^{15} + 65515 x^{14} - 15154 x^{13} + 68312 x^{12} - 11198 x^{11} + 51310 x^{10} - 6592 x^{9} + 25719 x^{8} - 1518 x^{7} + 8148 x^{6} - 588 x^{5} + 1330 x^{4} + 56 x^{3} + 92 x^{2} - 8 x + 1$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 31^{28}$ |
$2$ |
$42.7069157518$ |
$42.70691575177761$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[755]$ |
$6$ |
$14$ |
$4316173757.895952$ |
| 30.0.112...787.1 |
$x^{30} - x^{29} + 23 x^{28} - 12 x^{27} + 335 x^{26} - 144 x^{25} + 2773 x^{24} - 863 x^{23} + 16295 x^{22} - 4775 x^{21} + 62257 x^{20} - 15750 x^{19} + 170334 x^{18} - 52802 x^{17} + 293956 x^{16} - 111720 x^{15} + 369164 x^{14} - 135917 x^{13} + 276687 x^{12} - 78965 x^{11} + 139349 x^{10} - 31906 x^{9} + 42847 x^{8} - 4541 x^{7} + 8009 x^{6} - 477 x^{5} + 1036 x^{4} + 2 x^{3} + 63 x^{2} - 6 x + 1$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 7^{20}\cdot 11^{24}$ |
$3$ |
$43.1592082322$ |
$43.15920823215784$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 122]$ |
$6$ |
$14$ |
$4697581952.048968$ |
| 30.2.119...125.1 |
$x^{30} - 5 x^{29} + 11 x^{28} - 4 x^{27} - 19 x^{26} + 37 x^{25} + 129 x^{24} - 1314 x^{23} + 6565 x^{22} - 21133 x^{21} + 56331 x^{20} - 116407 x^{19} + 192164 x^{18} - 249788 x^{17} + 240591 x^{16} - 123362 x^{15} + 65684 x^{14} - 91823 x^{13} + 137991 x^{12} - 356197 x^{11} - 307772 x^{10} + 22452 x^{9} + 102955 x^{8} + 347102 x^{7} + 442668 x^{6} - 57105 x^{5} - 325253 x^{4} - 81893 x^{3} + 80109 x^{2} + 46065 x + 6845$ |
$30$ |
[2,14] |
$5^{15}\cdot 571^{14}$ |
$2$ |
$43.2429373044137$ |
$53.43220002957018$ |
|
|
|
$D_{30}$ (as 30T14) |
$[5]$ |
$2$ |
$15$ |
$9816173974474.957$ |
| 30.0.131...875.1 |
$x^{30} + 3$ |
$30$ |
[0,15] |
$-\,3^{59}\cdot 5^{30}$ |
$2$ |
$43.3818903138$ |
$55.22732047661838$ |
|
|
|
$S_3\times F_5$ (as 30T32) |
trivial |
$6$ |
$14$ |
$19051205214911.367$ |
| 30.30.175...397.1 |
$x^{30} - x^{29} - 30 x^{28} + 29 x^{27} + 405 x^{26} - 377 x^{25} - 3250 x^{24} + 2901 x^{23} + 17249 x^{22} - 14697 x^{21} - 63734 x^{20} + 51590 x^{19} + 168035 x^{18} - 128611 x^{17} - 318629 x^{16} + 229651 x^{15} + 432159 x^{14} - 292608 x^{13} - 411241 x^{12} + 261924 x^{11} + 264472 x^{10} - 159873 x^{9} - 107406 x^{8} + 63143 x^{7} + 24051 x^{6} - 14609 x^{5} - 2010 x^{4} + 1562 x^{3} - 72 x^{2} - 24 x + 1$ |
$30$ |
[30,0] |
$7^{25}\cdot 11^{27}$ |
$2$ |
$43.8027909818$ |
$43.80279098179992$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$864355592506536.0$ |
| 30.2.305...688.1 |
$x^{30} - 24 x^{28} + 342 x^{26} - 3240 x^{24} + 23571 x^{22} - 138753 x^{20} + 675054 x^{18} - 2755620 x^{16} + 9454401 x^{14} - 26985393 x^{12} + 64658655 x^{10} - 119042784 x^{8} + 183878586 x^{6} - 172186884 x^{4} + 153055008 x^{2} - 14348907$ |
$30$ |
[2,14] |
$2^{30}\cdot 3^{15}\cdot 239^{14}$ |
$3$ |
$44.61795318436113$ |
$53.55371135598354$ |
|
|
? |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
|
| 30.0.380...059.1 |
$x^{30} - 6 x^{29} + 25 x^{28} - 72 x^{27} + 234 x^{26} - 520 x^{25} + 1111 x^{24} - 2189 x^{23} + 3903 x^{22} - 4957 x^{21} + 4623 x^{20} - 10333 x^{19} + 8702 x^{18} + 8683 x^{17} - 6137 x^{16} + 9595 x^{15} - 28557 x^{14} + 23199 x^{13} - 20007 x^{12} + 4195 x^{11} + 12906 x^{10} - 27137 x^{9} + 36711 x^{8} - 24629 x^{7} + 24367 x^{6} - 23558 x^{5} + 11264 x^{4} + 26568 x^{3} - 14144 x^{2} - 4128 x + 4928$ |
$30$ |
[0,15] |
$-\,11^{12}\cdot 19^{29}$ |
$2$ |
$44.94543157691572$ |
$57.1248172219452$ |
|
|
|
$C_3\times D_{10}$ (as 30T5) |
$[11]$ |
$2$ |
$14$ |
$2589248825821.8447$ |
| 30.30.387...553.1 |
$x^{30} - 30 x^{28} - x^{27} + 405 x^{26} + 27 x^{25} - 3250 x^{24} - 324 x^{23} + 17250 x^{22} + 2278 x^{21} - 63756 x^{20} - 10416 x^{19} + 168244 x^{18} + 32508 x^{17} - 319752 x^{16} - 70720 x^{15} + 435915 x^{14} + 107592 x^{13} - 419353 x^{12} - 113139 x^{11} + 275835 x^{10} + 79936 x^{9} - 117504 x^{8} - 36027 x^{7} + 29442 x^{6} + 9423 x^{5} - 3555 x^{4} - 1173 x^{3} + 108 x^{2} + 36 x + 1$ |
$30$ |
[30,0] |
$3^{45}\cdot 11^{27}$ |
$2$ |
$44.9712851592$ |
$44.971285159244935$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$1458908175124897.5$ |
| 30.2.515...625.1 |
$x^{30} - 10 x^{29} + 36 x^{28} - 34 x^{27} - 129 x^{26} + 673 x^{25} - 2345 x^{24} + 3400 x^{23} + 8195 x^{22} - 23985 x^{21} - 13829 x^{20} + 36240 x^{19} + 94321 x^{18} + 102411 x^{17} + 62946 x^{16} + 325659 x^{15} + 1299805 x^{14} + 3826146 x^{13} + 7335516 x^{12} + 9580506 x^{11} + 8499204 x^{10} + 5247290 x^{9} + 1937111 x^{8} + 388946 x^{7} - 47819 x^{6} - 74039 x^{5} - 43685 x^{4} - 5057 x^{3} + 3493 x^{2} + 123 x + 169$ |
$30$ |
[2,14] |
$3^{15}\cdot 5^{25}\cdot 47^{15}$ |
$3$ |
$45.40300106204512$ |
$45.40300106204512$ |
|
|
? |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
|
| 30.0.675...203.1 |
$x^{30} - x^{29} + 12 x^{28} - 45 x^{27} + 210 x^{26} - 744 x^{25} + 2465 x^{24} - 6965 x^{23} + 19758 x^{22} - 48686 x^{21} + 121619 x^{20} - 306546 x^{19} + 810012 x^{18} - 2087415 x^{17} + 5002572 x^{16} - 11311375 x^{15} + 24424402 x^{14} - 49257771 x^{13} + 88022499 x^{12} - 134078913 x^{11} + 172501038 x^{10} - 188691174 x^{9} + 176841252 x^{8} - 141293241 x^{7} + 95362353 x^{6} - 55362204 x^{5} + 28414476 x^{4} - 12173571 x^{3} + 3774762 x^{2} - 708588 x + 59049$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 1117^{14}$ |
$2$ |
$45.81265290342043$ |
$57.88782255362521$ |
|
|
|
$D_{30}$ (as 30T14) |
trivial |
$6$ |
$14$ |
$3232250515402658.0$ |
| 30.2.114...125.1 |
$x^{30} - 3 x^{29} + 9 x^{28} + 14 x^{27} - 113 x^{26} + 370 x^{25} - 643 x^{24} - 15 x^{23} + 3880 x^{22} - 13302 x^{21} + 28770 x^{20} - 44390 x^{19} + 53641 x^{18} - 46319 x^{17} + 35868 x^{16} - 26390 x^{15} + 12095 x^{14} + 43878 x^{13} + 45313 x^{12} - 6914 x^{11} - 59831 x^{10} - 94496 x^{9} - 64150 x^{8} - 2932 x^{7} + 54993 x^{6} + 69070 x^{5} + 52989 x^{4} + 26576 x^{3} + 8569 x^{2} + 484 x - 121$ |
$30$ |
[2,14] |
$5^{15}\cdot 11^{14}\cdot 61^{14}$ |
$3$ |
$46.62535787186501$ |
$57.92236183029832$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$16637349953072.254$ |
| 30.0.214...923.1 |
$x^{30} - 6 x^{29} + 7 x^{28} + 64 x^{27} - 269 x^{26} + 169 x^{25} + 1697 x^{24} - 5426 x^{23} + 2993 x^{22} + 23602 x^{21} - 68143 x^{20} + 32587 x^{19} + 255113 x^{18} - 722972 x^{17} + 638195 x^{16} + 912175 x^{15} - 3578530 x^{14} + 6806701 x^{13} - 13186196 x^{12} + 20272003 x^{11} - 4641245 x^{10} - 65229024 x^{9} + 170166391 x^{8} - 258098865 x^{7} + 369027093 x^{6} - 495862722 x^{5} + 471214449 x^{4} - 297134325 x^{3} + 130881204 x^{2} - 35973639 x + 5861241$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 1213^{14}$ |
$2$ |
$47.609724432602746$ |
$60.32412452742269$ |
|
|
|
$D_{30}$ (as 30T14) |
$[7]$ |
$6$ |
$14$ |
$828216417792195.4$ |
| 30.0.249...171.1 |
$x^{30} - x^{29} + 5 x^{28} - 10 x^{27} + 31 x^{26} - 76 x^{25} + 210 x^{24} - 545 x^{23} + 1461 x^{22} - 3851 x^{21} + 10240 x^{20} + 18326 x^{19} + 26485 x^{18} + 36579 x^{17} + 51035 x^{16} + 68796 x^{15} + 98765 x^{14} + 125384 x^{13} + 200880 x^{12} + 201891 x^{11} + 476245 x^{10} + 130439 x^{9} + 35726 x^{8} + 9785 x^{7} + 2680 x^{6} + 734 x^{5} + 201 x^{4} + 55 x^{3} + 15 x^{2} + 4 x + 1$ |
$30$ |
[0,15] |
$-\,11^{27}\cdot 13^{20}$ |
$2$ |
$47.8500414346$ |
$47.8500414346374$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[427]$ |
$22$ |
$14$ |
$85915831770.81862$ |
| 30.30.254...797.1 |
$x^{30} - x^{29} - 30 x^{28} + 30 x^{27} + 404 x^{26} - 404 x^{25} - 3223 x^{24} + 3223 x^{23} + 16927 x^{22} - 16927 x^{21} - 61503 x^{20} + 61503 x^{19} + 158101 x^{18} - 158101 x^{17} - 288950 x^{16} + 288950 x^{15} + 371908 x^{14} - 371908 x^{13} - 329002 x^{12} + 329002 x^{11} + 191674 x^{10} - 191674 x^{9} - 68664 x^{8} + 68664 x^{7} + 13548 x^{6} - 13548 x^{5} - 1208 x^{4} + 1208 x^{3} + 32 x^{2} - 32 x + 1$ |
$30$ |
[30,0] |
$3^{15}\cdot 31^{29}$ |
$2$ |
$47.8861878355$ |
$47.88618783549088$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$3165460564789336.0$ |
| 30.2.347...912.1 |
$x^{30} - 6 x^{28} + 68 x^{26} - 536 x^{24} + 1904 x^{22} - 4192 x^{20} + 2240 x^{18} + 23936 x^{16} - 82432 x^{14} + 138752 x^{12} + 235520 x^{10} - 1073152 x^{8} + 2486272 x^{6} - 2449408 x^{4} + 2015232 x^{2} - 32768$ |
$30$ |
[2,14] |
$2^{45}\cdot 439^{14}$ |
$2$ |
$48.38325729765269$ |
$59.262129560116215$ |
|
|
|
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
|
| 30.2.553...125.1 |
$x^{30} - 5 x^{29} + 2 x^{28} + 21 x^{27} + 40 x^{26} - 46 x^{25} + 39 x^{24} - 296 x^{23} - 1612 x^{22} - 2561 x^{21} + 962 x^{20} + 4669 x^{19} + 19325 x^{18} + 55780 x^{17} + 98099 x^{16} + 110152 x^{15} + 94739 x^{14} + 50734 x^{13} + 40862 x^{12} + 44242 x^{11} + 25838 x^{10} + 20656 x^{9} + 3131 x^{8} + 2527 x^{7} + 6736 x^{6} + 1305 x^{5} + 3768 x^{4} - 512 x^{3} + 661 x^{2} - 25 x - 1$ |
$30$ |
[2,14] |
$5^{15}\cdot 751^{14}$ |
$2$ |
$49.14171468572467$ |
$61.27805479941412$ |
|
|
|
$D_{30}$ (as 30T14) |
$[4]$ |
$2$ |
$15$ |
$26934148162576.97$ |
| 30.0.615...784.1 |
$x^{30} + 29 x^{28} + 378 x^{26} + 2925 x^{24} + 14950 x^{22} + 53130 x^{20} + 134596 x^{18} + 245157 x^{16} + 319770 x^{14} + 293930 x^{12} + 184756 x^{10} + 75582 x^{8} + 18564 x^{6} + 2380 x^{4} + 120 x^{2} + 1$ |
$30$ |
[0,15] |
$-\,2^{30}\cdot 31^{28}$ |
$2$ |
$49.3136986111$ |
$49.31369861109494$ |
✓ |
✓ |
✓ |
$C_{30}$ (as 30T1) |
$[2, 2542]$ |
$4$ |
$14$ |
$4316173757.895952$ |
| 30.0.843...984.1 |
$x^{30} + 45 x^{28} + 850 x^{26} + 8863 x^{24} + 56474 x^{22} + 230106 x^{20} + 610963 x^{18} + 1061766 x^{16} + 1203495 x^{14} + 883132 x^{12} + 414061 x^{10} + 121105 x^{8} + 21162 x^{6} + 2035 x^{4} + 90 x^{2} + 1$ |
$30$ |
[0,15] |
$-\,2^{30}\cdot 7^{20}\cdot 11^{24}$ |
$3$ |
$49.8359609817$ |
$49.83596098169488$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 362]$ |
$4$ |
$14$ |
$4697581952.048968$ |
| 30.0.266...291.1 |
$x^{30} - 5 x^{29} + 23 x^{28} - 62 x^{27} + 198 x^{26} - 367 x^{25} + 397 x^{24} + 1188 x^{23} - 7770 x^{22} + 27186 x^{21} - 70571 x^{20} + 106780 x^{19} + 113195 x^{18} - 1691169 x^{17} + 8127778 x^{16} - 29421234 x^{15} + 90493414 x^{14} - 242325966 x^{13} + 570478488 x^{12} - 1182396448 x^{11} + 2168615679 x^{10} - 3480425904 x^{9} + 4808261059 x^{8} - 5571332106 x^{7} + 5293750647 x^{6} - 4028704993 x^{5} + 2404982206 x^{4} - 1088744723 x^{3} + 357808383 x^{2} - 76833878 x + 8961073$ |
$30$ |
[0,15] |
$-\,11^{15}\cdot 19^{28}$ |
$2$ |
$51.784490002099986$ |
$51.784490002099986$ |
|
✓ |
|
$C_3\times D_5$ (as 30T4) |
$[2, 2]$ |
$2$ |
$14$ |
$22790934759037.23$ |
| 30.2.275...081.1 |
$x^{30} - 4 x - 1$ |
$30$ |
[2,14] |
$1657\cdot 56091358577718162989\cdot 29663564839667553243668426797$ |
$3$ |
$51.8419577315$ |
$5.250744721994074e+25$ |
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$72802108759548.89$ |
| 30.2.275...456.1 |
$x^{30} - 2 x - 1$ |
$30$ |
[2,14] |
$2^{31}\cdot 309259\cdot 14808181703558627\cdot 280341823437737461079$ |
$4$ |
$51.8419578606$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$90634957909906.56$ |
| 30.2.493...181.1 |
$x^{30} - 9 x^{29} + 51 x^{28} - 225 x^{27} + 938 x^{26} - 3065 x^{25} + 9027 x^{24} - 23897 x^{23} + 55855 x^{22} - 110855 x^{21} + 206236 x^{20} - 276419 x^{19} + 363187 x^{18} - 228654 x^{17} - 26451 x^{16} + 1021780 x^{15} - 676090 x^{14} + 4072978 x^{13} + 297137 x^{12} + 7819653 x^{11} - 19045735 x^{10} + 54647605 x^{9} - 99924364 x^{8} + 139085676 x^{7} - 209111579 x^{6} + 87062190 x^{5} - 13968112 x^{4} - 6858710 x^{3} - 581573 x^{2} - 428582 x - 60395$ |
$30$ |
[2,14] |
$3^{15}\cdot 7^{25}\cdot 47^{14}$ |
$3$ |
$52.85929028008203$ |
$60.09770990472659$ |
|
|
|
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
|
| 30.30.595...341.1 |
$x^{30} - x^{29} - 29 x^{28} + 28 x^{27} + 378 x^{26} - 351 x^{25} - 2925 x^{24} + 2600 x^{23} + 14950 x^{22} - 12650 x^{21} - 53130 x^{20} + 42504 x^{19} + 134596 x^{18} - 100947 x^{17} - 245157 x^{16} + 170544 x^{15} + 319770 x^{14} - 203490 x^{13} - 293930 x^{12} + 167960 x^{11} + 184756 x^{10} - 92378 x^{9} - 75582 x^{8} + 31824 x^{7} + 18564 x^{6} - 6188 x^{5} - 2380 x^{4} + 560 x^{3} + 120 x^{2} - 15 x - 1$ |
$30$ |
[30,0] |
$61^{29}$ |
$1$ |
$53.1886344501$ |
$53.18863445009107$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$17190292874679612$ |
| 30.0.885...327.1 |
$x^{30} - 4 x^{29} - 32 x^{28} + 92 x^{27} + 588 x^{26} - 752 x^{25} - 6717 x^{24} - 805 x^{23} + 44049 x^{22} + 54263 x^{21} - 93757 x^{20} - 350454 x^{19} - 591742 x^{18} + 307201 x^{17} + 3600412 x^{16} + 5669890 x^{15} - 632841 x^{14} - 17605194 x^{13} - 34361042 x^{12} - 23087625 x^{11} + 45815379 x^{10} + 119941341 x^{9} + 85868062 x^{8} - 30516460 x^{7} - 62011703 x^{6} + 46150369 x^{5} + 155790202 x^{4} + 147686157 x^{3} + 67768188 x^{2} + 10788948 x + 751689$ |
$30$ |
[0,15] |
$-\,3^{14}\cdot 7^{25}\cdot 53^{14}$ |
$3$ |
$53.8973018694987$ |
$63.81854946060407$ |
|
|
|
$D_{30}$ (as 30T14) |
$[3]$ |
$2$ |
$14$ |
$44958053496730.96$ |
| 30.30.150...497.1 |
$x^{30} - x^{29} - 52 x^{28} + 51 x^{27} + 1142 x^{26} - 1092 x^{25} - 13898 x^{24} + 12856 x^{23} + 103478 x^{22} - 91664 x^{21} - 491678 x^{20} + 412467 x^{19} + 1512708 x^{18} - 1191563 x^{17} - 3007832 x^{16} + 2225799 x^{15} + 3819257 x^{14} - 2692049 x^{13} - 3042474 x^{12} + 2079355 x^{11} + 1471733 x^{10} - 992749 x^{9} - 403229 x^{8} + 274849 x^{7} + 52970 x^{6} - 38754 x^{5} - 1790 x^{4} + 2057 x^{3} - 72 x^{2} - 24 x + 1$ |
$30$ |
[30,0] |
$3^{15}\cdot 7^{20}\cdot 11^{27}$ |
$3$ |
$54.8545601901$ |
$54.854560190098766$ |
|
✓ |
? |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$25852981457107600$ |
