| 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 |
| 9.3.426083629572608.1 |
$x^{9} - 3 x^{8} - 15 x^{7} + 37 x^{6} + 29 x^{5} - 35 x^{4} + 335 x^{3} - 189 x^{2} - 350 x - 322$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{2}\cdot 19^{8}$ |
$3$ |
$42.218172264$ |
$141.7795371895746$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[9]$ |
$2$ |
$5$ |
$6385.89290769$ |
| 9.1.1113034787454976.1 |
$x^{9} - 19 x^{5} - 76 x^{4} - 38 x^{3} + 228 x^{2} + 456 x + 304$ |
$9$ |
[1,4] |
$2^{16}\cdot 19^{8}$ |
$2$ |
$46.9714864776$ |
$109.58720601631192$ |
|
|
|
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[9]$ |
$2$ |
$4$ |
$11784.0495373$ |
| 9.1.3756492407660544.1 |
$x^{9} - 3 x^{8} + 4 x^{7} + 18 x^{6} + 10 x^{5} - 320 x^{4} + 316 x^{3} + 1350 x^{2} - 7019 x + 9995$ |
$9$ |
[1,4] |
$2^{13}\cdot 3^{3}\cdot 19^{8}$ |
$3$ |
$53.7689295648$ |
$106.52760230477175$ |
|
|
|
$S_3\wr S_3$ (as 9T31) |
$[9]$ |
$2$ |
$4$ |
$19868.0877124$ |
| 9.5.6114082694760000.1 |
$x^{9} - x^{8} - 8 x^{7} - 31 x^{6} - 112 x^{5} + 365 x^{4} + 1101 x^{3} - 1472 x^{2} - 1610 x + 1310$ |
$9$ |
[5,2] |
$2^{6}\cdot 3^{2}\cdot 5^{4}\cdot 19^{8}$ |
$4$ |
$56.7592714153$ |
$84.21746423992032$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[9]$ |
$2$ |
$6$ |
$17845.6733875$ |
| 9.5.17982892873895481.1 |
$x^{9} - x^{8} - 27 x^{7} + 45 x^{6} + 192 x^{5} - 376 x^{4} - 267 x^{3} + 276 x^{2} + 423 x + 531$ |
$9$ |
[5,2] |
$3^{2}\cdot 7^{6}\cdot 19^{8}$ |
$3$ |
$63.9875535998$ |
$86.82188052060228$ |
|
|
|
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25) |
$[9]$ |
$2$ |
$6$ |
$27843.7285838$ |
| 9.3.20878097849057792.3 |
$x^{9} - 38 x^{7} - 38 x^{6} + 171 x^{5} - 646 x^{4} - 171 x^{3} + 3914 x^{2} - 4541 x + 1748$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{4}\cdot 19^{8}$ |
$3$ |
$65.0577429284$ |
$141.7795371895746$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[9]$ |
$2$ |
$5$ |
$41799.8473316$ |
| 9.1.114897217668536241.1 |
$x^{9} - 2 x^{8} - 13 x^{7} - 39 x^{6} + 127 x^{5} + 185 x^{4} + 2178 x^{3} - 449 x^{2} + 24992 x + 22592$ |
$9$ |
[1,4] |
$3^{4}\cdot 17^{4}\cdot 19^{8}$ |
$3$ |
$78.6303023783$ |
$97.82614855618401$ |
|
|
|
$D_{9}$ (as 9T3) |
$[9]$ |
$2$ |
$4$ |
$291204.143728$ |
| 9.3.1023026794603831808.3 |
$x^{9} - 4 x^{8} + 5 x^{7} - 46 x^{6} - 381 x^{5} + 1056 x^{4} - 49 x^{3} + 2074 x^{2} + 29152 x + 52648$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{6}\cdot 19^{8}$ |
$3$ |
$100.25327218$ |
$141.7795371895746$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
$[3, 9]$ |
$2$ |
$5$ |
$38054.4761857$ |
| 9.9.642...801.2 |
$x^{9} - 4 x^{8} - 52 x^{7} - 84 x^{6} + 56 x^{5} + 182 x^{4} + 84 x^{3} - 16 x^{2} - 13 x - 1$ |
$9$ |
[9,0] |
$3^{8}\cdot 7^{8}\cdot 19^{8}$ |
$3$ |
$205.104839264$ |
$334.21797094964006$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
$[9]$ |
$2$ |
$8$ |
$9716024.4267$ |
| 9.9.596...761.2 |
$x^{9} - x^{8} - 312 x^{7} + 1565 x^{6} + 22118 x^{5} - 146182 x^{4} - 420319 x^{3} + 3575354 x^{2} + 518192 x - 17159528$ |
$9$ |
[9,0] |
$19^{8}\cdot 37^{8}$ |
$2$ |
$339.333671102$ |
$339.33367110228545$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[9]$ |
$2$ |
$8$ |
$84671913.5934$ |
| 10.2.634...000.1 |
$x^{10} - 5700 x^{7} + 10830000 x^{4} - 6859000000 x - 47502004500$ |
$10$ |
[2,4] |
$2^{12}\cdot 3^{14}\cdot 5^{19}\cdot 19^{8}$ |
$4$ |
$2400.22326181$ |
$13069.939519129885$ |
|
|
? |
$S_{10}$ (as 10T45) |
$[2]$ |
$2$ |
$5$ |
$35499371082600$ |
| 18.0.673...131.1 |
$x^{18} - 6 x^{17} + 29 x^{16} - 128 x^{15} + 741 x^{14} - 2860 x^{13} + 6513 x^{12} - 34248 x^{11} + 118173 x^{10} + 193226 x^{9} + 2021877 x^{8} + 2748886 x^{7} + 4497608 x^{6} + 6272856 x^{5} + 34795840 x^{4} + 94166304 x^{3} + 277514880 x^{2} + 202315392 x + 44160768$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 17^{9}\cdot 19^{16}$ |
$3$ |
$97.8261485562$ |
$97.82614855618401$ |
|
✓ |
|
$D_9$ (as 18T5) |
$[18]$ |
$2$ |
$8$ |
$763198679918$ |
| 18.18.326...125.1 |
$x^{18} - 81 x^{16} + 2457 x^{14} - 450 x^{13} - 35799 x^{12} + 18036 x^{11} + 270387 x^{10} - 227047 x^{9} - 1034208 x^{8} + 1198881 x^{7} + 1683324 x^{6} - 2571156 x^{5} - 445626 x^{4} + 1440903 x^{3} - 215973 x^{2} - 79857 x + 14269$ |
$18$ |
[18,0] |
$3^{44}\cdot 5^{9}\cdot 19^{8}$ |
$3$ |
$121.371392975$ |
$712.4007850468525$ |
|
|
? |
$C_9\times D_9$ (as 18T74) |
trivial |
$2$ |
$17$ |
$9817904742040$ |
| 27.27.278...849.1 |
$x^{27} - 9 x^{26} - 36 x^{25} + 441 x^{24} + 378 x^{23} - 8235 x^{22} - 1647 x^{21} + 81891 x^{20} + 8019 x^{19} - 489621 x^{18} - 87885 x^{17} + 1845909 x^{16} + 591453 x^{15} - 4427514 x^{14} - 2082537 x^{13} + 6631281 x^{12} + 4052430 x^{11} - 5937300 x^{10} - 4424841 x^{9} + 2963061 x^{8} + 2683422 x^{7} - 721620 x^{6} - 883440 x^{5} + 42336 x^{4} + 145242 x^{3} + 12150 x^{2} - 9099 x - 1509$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{8}$ |
$2$ |
$57.1794860246354$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1845726979276938.2$ |
| 27.27.990...361.1 |
$x^{27} - 99 x^{25} - 48 x^{24} + 3753 x^{23} + 3249 x^{22} - 69339 x^{21} - 74286 x^{20} + 682488 x^{19} + 723114 x^{18} - 3915387 x^{17} - 3437613 x^{16} + 14011512 x^{15} + 8318637 x^{14} - 32171256 x^{13} - 8873247 x^{12} + 46716687 x^{11} - 1132533 x^{10} - 40329039 x^{9} + 11719143 x^{8} + 17687556 x^{7} - 9949521 x^{6} - 1946151 x^{5} + 2657682 x^{4} - 673626 x^{3} + 45486 x^{2} + 3249 x - 361$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{16}$ |
$2$ |
$77.39875893058758$ |
$212.09372094764964$ |
|
|
? |
$C_9^2.C_3$ (as 27T112) |
trivial |
$2$ |
$26$ |
$190873621455186500$ |
| 27.27.990...361.2 |
$x^{27} - 9 x^{26} - 54 x^{25} + 780 x^{24} - 432 x^{23} - 21780 x^{22} + 64575 x^{21} + 217296 x^{20} - 1247445 x^{19} + 19374 x^{18} + 9433674 x^{17} - 12087774 x^{16} - 30763836 x^{15} + 71593578 x^{14} + 34852194 x^{13} - 180656406 x^{12} + 25262640 x^{11} + 232115463 x^{10} - 89066520 x^{9} - 156750336 x^{8} + 67857723 x^{7} + 53078022 x^{6} - 19125909 x^{5} - 7172685 x^{4} + 2619018 x^{3} + 247698 x^{2} - 143370 x + 11607$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{16}$ |
$2$ |
$77.39875893058758$ |
$212.09372094764964$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
trivial |
$2$ |
$26$ |
$129312577589579410$ |
| 27.27.990...361.3 |
$x^{27} - 9 x^{26} - 54 x^{25} + 651 x^{24} + 1044 x^{23} - 20862 x^{22} - 5127 x^{21} + 392805 x^{20} - 126657 x^{19} - 4857378 x^{18} + 2649987 x^{17} + 41709384 x^{16} - 23830170 x^{15} - 255584943 x^{14} + 119736639 x^{13} + 1124792841 x^{12} - 317017170 x^{11} - 3502388043 x^{10} + 170591364 x^{9} + 7391454030 x^{8} + 1468199223 x^{7} - 9653289549 x^{6} - 4190530887 x^{5} + 6357903066 x^{4} + 4027341045 x^{3} - 1071738720 x^{2} - 711775062 x + 116833319$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{16}$ |
$2$ |
$77.39875893058758$ |
$212.09372094764964$ |
|
|
|
$C_9^2:C_3$ (as 27T108) |
trivial |
$2$ |
$26$ |
$286344648123180700$ |
| 27.27.403...281.1 |
$x^{27} - 117 x^{25} - 144 x^{24} + 5454 x^{23} + 12321 x^{22} - 127080 x^{21} - 415908 x^{20} + 1499193 x^{19} + 7118643 x^{18} - 6881679 x^{17} - 66517326 x^{16} - 25844319 x^{15} + 338054688 x^{14} + 452971134 x^{13} - 806211819 x^{12} - 2101675842 x^{11} + 72795897 x^{10} + 4152980271 x^{9} + 3389225814 x^{8} - 2166315039 x^{7} - 4727639052 x^{6} - 2245523607 x^{5} + 227410506 x^{4} + 469499994 x^{3} + 82966464 x^{2} - 18766224 x - 4931621$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{12}$ |
$2$ |
$81.53478118184302$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$274519020102255230$ |
| 27.27.815...609.9 |
$x^{27} - 81 x^{25} - 18 x^{24} + 2511 x^{23} + 972 x^{22} - 40626 x^{21} - 18873 x^{20} + 388746 x^{19} + 177723 x^{18} - 2354427 x^{17} - 916272 x^{16} + 9332928 x^{15} + 2674134 x^{14} - 24427818 x^{13} - 4212630 x^{12} + 41782311 x^{11} + 2689146 x^{10} - 45453738 x^{9} + 1329696 x^{8} + 29868912 x^{7} - 3123144 x^{6} - 10731447 x^{5} + 1676997 x^{4} + 1711539 x^{3} - 292410 x^{2} - 77976 x + 13357$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{10}$ |
$2$ |
$83.68495107025696$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$320110532571514240$ |
| 27.27.815...609.10 |
$x^{27} - 81 x^{25} - 90 x^{24} + 2511 x^{23} + 4536 x^{22} - 39600 x^{21} - 92988 x^{20} + 349893 x^{19} + 1017738 x^{18} - 1758591 x^{17} - 6549093 x^{16} + 4672692 x^{15} + 25803846 x^{14} - 4242348 x^{13} - 63419616 x^{12} - 8199792 x^{11} + 98254890 x^{10} + 25070082 x^{9} - 96883128 x^{8} - 24099201 x^{7} + 60870528 x^{6} + 8104374 x^{5} - 22874670 x^{4} + 1305585 x^{3} + 3859812 x^{2} - 1091664 x + 84113$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{10}$ |
$2$ |
$83.68495107025696$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$385388460717378800$ |
| 27.27.363...529.3 |
$x^{27} - 117 x^{25} - 81 x^{24} + 5373 x^{23} + 5553 x^{22} - 127944 x^{21} - 140346 x^{20} + 1791414 x^{19} + 1736451 x^{18} - 15762681 x^{17} - 11394765 x^{16} + 89620614 x^{15} + 38266209 x^{14} - 328348899 x^{13} - 47589471 x^{12} + 755784945 x^{11} - 57893247 x^{10} - 1056691137 x^{9} + 231787251 x^{8} + 875182446 x^{7} - 263973042 x^{6} - 408194613 x^{5} + 141503697 x^{4} + 94435434 x^{3} - 35371863 x^{2} - 7654644 x + 2956229$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{12}$ |
$2$ |
$88.4474314157294$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$767808676666832900$ |
| 27.27.294...849.1 |
$x^{27} - 135 x^{25} - 9 x^{24} + 7047 x^{23} - 1998 x^{22} - 196326 x^{21} + 145638 x^{20} + 3259251 x^{19} - 3940164 x^{18} - 33522579 x^{17} + 56259495 x^{16} + 212739093 x^{15} - 471794301 x^{14} - 784939248 x^{13} + 2409017733 x^{12} + 1315272492 x^{11} - 7464051504 x^{10} + 935223966 x^{9} + 13355743644 x^{8} - 7963749414 x^{7} - 11841408684 x^{6} + 12597987753 x^{5} + 2375041743 x^{4} - 6952232943 x^{3} + 2088421461 x^{2} + 284456448 x - 117721017$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{12}$ |
$2$ |
$104.08061637618087$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$7638767070101032000$ |
| 27.27.294...849.7 |
$x^{27} - 135 x^{25} - 27 x^{24} + 7047 x^{23} + 3348 x^{22} - 187164 x^{21} - 125793 x^{20} + 2815992 x^{19} + 1976769 x^{18} - 26075115 x^{17} - 15605838 x^{16} + 155938356 x^{15} + 62760420 x^{14} - 611741727 x^{13} - 91912158 x^{12} + 1546030152 x^{11} - 196588782 x^{10} - 2359374894 x^{9} + 967201479 x^{8} + 1846195173 x^{7} - 1315759329 x^{6} - 406946997 x^{5} + 567947943 x^{4} - 107694603 x^{3} - 26667792 x^{2} + 7778106 x - 61731$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{12}$ |
$2$ |
$104.08061637618087$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$6037098075027638000$ |
| 27.27.131...969.2 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1314 x^{24} + 7740 x^{23} - 68076 x^{22} - 239166 x^{21} + 1714032 x^{20} + 4990779 x^{19} - 22424565 x^{18} - 67949397 x^{17} + 139167009 x^{16} + 521720982 x^{15} - 259125408 x^{14} - 1876452975 x^{13} - 322111764 x^{12} + 3304120158 x^{11} + 1504663875 x^{10} - 3180640551 x^{9} - 1866753171 x^{8} + 1770577101 x^{7} + 1116671832 x^{6} - 573082407 x^{5} - 338304879 x^{4} + 102031929 x^{3} + 44766450 x^{2} - 8037450 x - 1183123$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$11959041246274464000$ |
| 27.27.131...969.5 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1152 x^{24} + 8748 x^{23} - 53568 x^{22} - 299961 x^{21} + 1145826 x^{20} + 5967756 x^{19} - 11122377 x^{18} - 64116414 x^{17} + 40038543 x^{16} + 341380242 x^{15} - 21808332 x^{14} - 928546470 x^{13} - 170651646 x^{12} + 1278782856 x^{11} + 375962418 x^{10} - 839220759 x^{9} - 271274076 x^{8} + 239523237 x^{7} + 68849766 x^{6} - 29543454 x^{5} - 5065389 x^{4} + 1859094 x^{3} + 44577 x^{2} - 39771 x + 2427$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$14754752089330426000$ |
| 27.27.131...969.7 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1872 x^{24} + 2106 x^{23} - 111753 x^{22} + 379287 x^{21} + 1612305 x^{20} - 11898603 x^{19} + 6695106 x^{18} + 107593056 x^{17} - 216909630 x^{16} - 369397431 x^{15} + 1331515098 x^{14} + 337538367 x^{13} - 3791098422 x^{12} + 806496507 x^{11} + 5702765337 x^{10} - 2023744905 x^{9} - 4502257263 x^{8} + 1475327898 x^{7} + 1639440171 x^{6} - 350905878 x^{5} - 160087995 x^{4} + 29332107 x^{3} + 4044492 x^{2} - 734751 x + 21387$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$11922122740913914000$ |
| 27.27.131...969.12 |
$x^{27} - 9 x^{26} - 144 x^{25} + 972 x^{24} + 9072 x^{23} - 33939 x^{22} - 287172 x^{21} + 446148 x^{20} + 4797252 x^{19} - 948495 x^{18} - 43262856 x^{17} - 27538407 x^{16} + 210610332 x^{15} + 252437067 x^{14} - 552609999 x^{13} - 960981732 x^{12} + 719899245 x^{11} + 1951953849 x^{10} - 222050403 x^{9} - 2223658170 x^{8} - 547065360 x^{7} + 1363938678 x^{6} + 690220035 x^{5} - 371729358 x^{4} - 306346419 x^{3} + 7322238 x^{2} + 46515114 x + 9191829$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$21775391337291145000$ |
| 27.27.106...489.2 |
$x^{27} - 216 x^{25} - 54 x^{24} + 17577 x^{23} - 1674 x^{22} - 751446 x^{21} + 467046 x^{20} + 19163736 x^{19} - 22819158 x^{18} - 306171738 x^{17} + 544106781 x^{16} + 3067005042 x^{15} - 7492395267 x^{14} - 18175020570 x^{13} + 62548234650 x^{12} + 49971914820 x^{11} - 313892502399 x^{10} + 48114826206 x^{9} + 885539561175 x^{8} - 712809280062 x^{7} - 1162258177779 x^{6} + 1686232267110 x^{5} + 276057575064 x^{4} - 1320639000219 x^{3} + 355272769656 x^{2} + 281352613320 x - 112116329189$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{14}$ |
$2$ |
$129.44710568273106$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$130102874105020090000$ |
| 27.27.106...489.10 |
$x^{27} - 216 x^{25} - 99 x^{24} + 17577 x^{23} + 13986 x^{22} - 738630 x^{21} - 969975 x^{20} + 18381924 x^{19} + 36391563 x^{18} - 281369214 x^{17} - 801684594 x^{16} + 2501189811 x^{15} + 10785939912 x^{14} - 8785266075 x^{13} - 87323224914 x^{12} - 52562328840 x^{11} + 379549230111 x^{10} + 703767475968 x^{9} - 455709844179 x^{8} - 2687267920338 x^{7} - 2449968465528 x^{6} + 2010946525029 x^{5} + 6575807857752 x^{4} + 6674032187829 x^{3} + 3533336322723 x^{2} + 970335761256 x + 106993150037$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{14}$ |
$2$ |
$129.44710568273106$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$142084898352538880000$ |
| 27.27.473...809.4 |
$x^{27} - 198 x^{25} - 234 x^{24} + 15957 x^{23} + 34857 x^{22} - 664605 x^{21} - 2060424 x^{20} + 14909967 x^{19} + 61408524 x^{18} - 164914623 x^{17} - 969682860 x^{16} + 509316831 x^{15} + 7881823827 x^{14} + 4987250568 x^{13} - 30694701609 x^{12} - 45067675860 x^{11} + 41145793425 x^{10} + 121189746357 x^{9} + 34092403551 x^{8} - 95018229873 x^{7} - 74437098228 x^{6} + 10022089581 x^{5} + 25924612491 x^{4} + 5241208824 x^{3} - 2001751137 x^{2} - 781144074 x - 68912373$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$389272223027587500000$ |
| 27.27.473...809.5 |
$x^{27} - 198 x^{25} - 198 x^{24} + 15957 x^{23} + 28566 x^{22} - 671706 x^{21} - 1614870 x^{20} + 15931323 x^{19} + 45904695 x^{18} - 218499525 x^{17} - 714238614 x^{16} + 1768536378 x^{15} + 6406124436 x^{14} - 8491221657 x^{13} - 33616662570 x^{12} + 24197393817 x^{11} + 100415043225 x^{10} - 43624161405 x^{9} - 155806925652 x^{8} + 61105024917 x^{7} + 96957229824 x^{6} - 58997665035 x^{5} - 2068254918 x^{4} + 5643925623 x^{3} - 181762056 x^{2} - 163515672 x - 4287597$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$380921386531835540000$ |
| 27.27.473...809.8 |
$x^{27} - 198 x^{25} - 261 x^{24} + 15957 x^{23} + 39798 x^{22} - 653067 x^{21} - 2354373 x^{20} + 13795839 x^{19} + 68282040 x^{18} - 128625003 x^{17} - 1020022524 x^{16} + 17217990 x^{15} + 7566935193 x^{14} + 7502170482 x^{13} - 24774464097 x^{12} - 43165902780 x^{11} + 20935131912 x^{10} + 75968172036 x^{9} + 25647134895 x^{8} - 29829689559 x^{7} - 24029279100 x^{6} - 5321891241 x^{5} + 84272562 x^{4} + 163197270 x^{3} + 17369154 x^{2} + 467856 x - 1083$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$361319951347960800000$ |
| 27.27.190...561.1 |
$x^{27} - 252 x^{25} - 153 x^{24} + 26676 x^{23} + 32148 x^{22} - 1560717 x^{21} - 2766096 x^{20} + 55372023 x^{19} + 127624767 x^{18} - 1224408393 x^{17} - 3450315051 x^{16} + 16693678179 x^{15} + 56072843757 x^{14} - 134677099638 x^{13} - 546076812150 x^{12} + 596270531925 x^{11} + 3157615221048 x^{10} - 1158142431219 x^{9} - 10597232739906 x^{8} - 348324575220 x^{7} + 19755125421237 x^{6} + 4626276516927 x^{5} - 19184037556914 x^{4} - 5979749371812 x^{3} + 8367062889969 x^{2} + 2393976700566 x - 1004382513469$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{18}$ |
$2$ |
$156.8593376663821$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$1598701524418741700000$ |
| 27.27.190...561.6 |
$x^{27} - 252 x^{25} - 153 x^{24} + 26676 x^{23} + 33687 x^{22} - 1553364 x^{21} - 3053889 x^{20} + 54186993 x^{19} + 148881606 x^{18} - 1139298615 x^{17} - 4252897908 x^{16} + 13262322753 x^{15} + 72283381614 x^{14} - 53627977755 x^{13} - 701974235448 x^{12} - 488492465364 x^{11} + 3407798185731 x^{10} + 6269229941286 x^{9} - 4735327044591 x^{8} - 21572290559160 x^{7} - 11921681283597 x^{6} + 17866911359250 x^{5} + 19771712417475 x^{4} - 3798660234969 x^{3} - 9596654035785 x^{2} - 293848572726 x + 1654650680651$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{18}$ |
$2$ |
$156.8593376663821$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$1824559286708386400000$ |
| 27.27.383...529.3 |
$x^{27} - 216 x^{25} - 333 x^{24} + 18954 x^{23} + 52893 x^{22} - 852030 x^{21} - 3281148 x^{20} + 20969388 x^{19} + 104103432 x^{18} - 285990831 x^{17} - 1907406333 x^{16} + 1938725496 x^{15} + 21440798577 x^{14} - 1499373828 x^{13} - 151838594145 x^{12} - 75166183575 x^{11} + 679464549387 x^{10} + 578776504776 x^{9} - 1884091171959 x^{8} - 2042571007674 x^{7} + 3079526987592 x^{6} + 3783386874411 x^{5} - 2688697902708 x^{4} - 3407929857954 x^{3} + 1078232166144 x^{2} + 1068270819867 x - 237554461961$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$1869498757230685000000$ |
| 27.27.383...529.4 |
$x^{27} - 216 x^{25} - 351 x^{24} + 18954 x^{23} + 59913 x^{22} - 831717 x^{21} - 4007556 x^{20} + 17484066 x^{19} + 132803388 x^{18} - 84624993 x^{17} - 2255595849 x^{16} - 3006320904 x^{15} + 17933159025 x^{14} + 53663373558 x^{13} - 39156972282 x^{12} - 344264498109 x^{11} - 278000308116 x^{10} + 859172869167 x^{9} + 1710748857222 x^{8} - 126820721979 x^{7} - 2922899699187 x^{6} - 2110999635981 x^{5} + 1299946892481 x^{4} + 2155024024596 x^{3} + 402933114171 x^{2} - 497532476466 x - 204171695243$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$2522949704045501000000$ |
| 27.27.383...529.6 |
$x^{27} - 216 x^{25} - 126 x^{24} + 18954 x^{23} + 24975 x^{22} - 875052 x^{21} - 1892970 x^{20} + 22692042 x^{19} + 71110521 x^{18} - 316638477 x^{17} - 1432046169 x^{16} + 1812081357 x^{15} + 15499723005 x^{14} + 5402467638 x^{13} - 85210703568 x^{12} - 119880614304 x^{11} + 187324337502 x^{10} + 524296119381 x^{9} + 69677940285 x^{8} - 774118036773 x^{7} - 608211900027 x^{6} + 298745384301 x^{5} + 521853502770 x^{4} + 104853930822 x^{3} - 111313030545 x^{2} - 61038316449 x - 8866910519$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$2914941073381261000000$ |
| 27.27.383...529.16 |
$x^{27} - 216 x^{25} - 117 x^{24} + 18954 x^{23} + 18252 x^{22} - 880956 x^{21} - 1129626 x^{20} + 23786271 x^{19} + 36121014 x^{18} - 388008063 x^{17} - 663083280 x^{16} + 3881919906 x^{15} + 7441348176 x^{14} - 23461467102 x^{13} - 52175347803 x^{12} + 79089740955 x^{11} + 224088111090 x^{10} - 105212273862 x^{9} - 546189714900 x^{8} - 126600712695 x^{7} + 613151491185 x^{6} + 468570328389 x^{5} - 106598016765 x^{4} - 228661747884 x^{3} - 76816019277 x^{2} - 4211844399 x + 983011303$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$2798550781651066600000$ |
| 27.27.171...049.1 |
$x^{27} - 252 x^{25} - 189 x^{24} + 26676 x^{23} + 37278 x^{22} - 1542249 x^{21} - 2997459 x^{20} + 53109180 x^{19} + 127595412 x^{18} - 1115642646 x^{17} - 3116503386 x^{16} + 14106344724 x^{15} + 44288457588 x^{14} - 103097199771 x^{13} - 357917273712 x^{12} + 414062657892 x^{11} + 1585147569417 x^{10} - 865139058768 x^{9} - 3663417923046 x^{8} + 907297669062 x^{7} + 4289785218828 x^{6} - 435357630576 x^{5} - 2278964378115 x^{4} + 94666216968 x^{3} + 374720442165 x^{2} - 29638905030 x - 7668478603$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{18}$ |
$2$ |
$170.15812526953377$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$5070048917270998000000$ |
| 27.27.171...049.4 |
$x^{27} - 252 x^{25} - 99 x^{24} + 26676 x^{23} + 20178 x^{22} - 1570293 x^{21} - 1699569 x^{20} + 57017214 x^{19} + 78127848 x^{18} - 1334373021 x^{17} - 2172073635 x^{16} + 20370285396 x^{15} + 38161629846 x^{14} - 199882736190 x^{13} - 428779146348 x^{12} + 1195373405592 x^{11} + 3027247806195 x^{10} - 3753781201236 x^{9} - 12644875257885 x^{8} + 2816072475219 x^{7} + 26896341027078 x^{6} + 12429019112103 x^{5} - 18143533711233 x^{4} - 18014727041253 x^{3} - 4242597548580 x^{2} + 87223063374 x + 82189154107$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{18}$ |
$2$ |
$170.15812526953377$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
$2$ |
$26$ |
$5564427432512092000000$ |
| 27.27.339...889.3 |
$x^{27} - 342 x^{25} - 171 x^{24} + 46683 x^{23} + 46341 x^{22} - 3355533 x^{21} - 5157702 x^{20} + 141070896 x^{19} + 304568499 x^{18} - 3604128696 x^{17} - 10433737881 x^{16} + 54778016538 x^{15} + 214528692105 x^{14} - 430357812705 x^{13} - 2623389763455 x^{12} + 484674058620 x^{11} + 17799029177004 x^{10} + 18223177602711 x^{9} - 52998728674194 x^{8} - 120973089602043 x^{7} - 8984984026869 x^{6} + 206976085874100 x^{5} + 232910749406520 x^{4} + 69514606972872 x^{3} - 34096952904768 x^{2} - 26350368234912 x - 4632246391616$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
|
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$2$ |
$26$ |
$16996392881398743000000$ |
| 27.27.339...889.6 |
$x^{27} - 198 x^{25} - 240 x^{24} + 14211 x^{23} + 27828 x^{22} - 470235 x^{21} - 1095210 x^{20} + 7805736 x^{19} + 17721963 x^{18} - 75980394 x^{17} - 145128888 x^{16} + 462567705 x^{15} + 653137839 x^{14} - 1750939695 x^{13} - 1685642442 x^{12} + 4004759304 x^{11} + 2575237032 x^{10} - 5330234694 x^{9} - 2406041811 x^{8} + 3884585238 x^{7} + 1396307361 x^{6} - 1366755093 x^{5} - 467018919 x^{4} + 163985460 x^{3} + 65743461 x^{2} + 1605852 x - 707723$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$2$ |
$26$ |
$5839873155237562000000$ |
| 27.27.339...889.7 |
$x^{27} - 198 x^{25} - 69 x^{24} + 16947 x^{23} + 10215 x^{22} - 822495 x^{21} - 626499 x^{20} + 24996195 x^{19} + 20626740 x^{18} - 496209987 x^{17} - 393964668 x^{16} + 6511386444 x^{15} + 4364596737 x^{14} - 55763583489 x^{13} - 25774577970 x^{12} + 298557947277 x^{11} + 57580976835 x^{10} - 910210926315 x^{9} + 71942819904 x^{8} + 1311914075382 x^{7} - 284784790380 x^{6} - 772175021373 x^{5} + 205559479314 x^{4} + 123582042393 x^{3} - 20629945359 x^{2} - 2138965308 x + 140428837$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$2$ |
$26$ |
$6419023085158092000000$ |
| 27.27.339...889.9 |
$x^{27} - 342 x^{25} - 513 x^{24} + 33345 x^{23} + 97470 x^{22} - 1260270 x^{21} - 5221827 x^{20} + 21068226 x^{19} + 127768179 x^{18} - 110794149 x^{17} - 1625812596 x^{16} - 1238190651 x^{15} + 10625545845 x^{14} + 21661040763 x^{13} - 26176910337 x^{12} - 123140488707 x^{11} - 62085384675 x^{10} + 266388984264 x^{9} + 452485760760 x^{8} + 50424782157 x^{7} - 565685907975 x^{6} - 671734642302 x^{5} - 292929027750 x^{4} + 19194328485 x^{3} + 68592894498 x^{2} + 24847653465 x + 2988651493$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2.C_3$ (as 27T112) |
$[3]$ |
$2$ |
$26$ |
$14434686400004354000000$ |
| 27.27.339...889.11 |
$x^{27} - 342 x^{25} - 171 x^{24} + 46170 x^{23} + 54207 x^{22} - 3268665 x^{21} - 5858460 x^{20} + 134311095 x^{19} + 307109616 x^{18} - 3351895830 x^{17} - 8921016477 x^{16} + 51614085105 x^{15} + 150995085174 x^{14} - 490758149016 x^{13} - 1497559744062 x^{12} + 2913712319943 x^{11} + 8540208558981 x^{10} - 11433313439043 x^{9} - 27388259069094 x^{8} + 30252509997111 x^{7} + 45148147517106 x^{6} - 48196927157832 x^{5} - 28168971334749 x^{4} + 32756642210241 x^{3} - 1498948623333 x^{2} - 870715261152 x + 60790706549$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$2$ |
$26$ |
$7310010199955040000000$ |
| 27.27.339...889.12 |
$x^{27} - 342 x^{25} - 171 x^{24} + 46170 x^{23} + 57969 x^{22} - 3279438 x^{21} - 6520230 x^{20} + 134909595 x^{19} + 352381467 x^{18} - 3333620205 x^{17} - 10418795730 x^{16} + 50121757674 x^{15} + 178009616952 x^{14} - 463992065019 x^{13} - 1806600296394 x^{12} + 2715560049888 x^{11} + 11011380121971 x^{10} - 10515068124774 x^{9} - 39561865551387 x^{8} + 28232252708814 x^{7} + 77396652420660 x^{6} - 50679118012977 x^{5} - 64451687339025 x^{4} + 46443797067753 x^{3} + 3010733343882 x^{2} - 6428032239168 x + 953773526008$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
|
$C_9^2:C_3$ (as 27T104) |
$[3]$ |
$2$ |
$26$ |
$38146196077994220000000$ |
| 27.27.138...969.7 |
$x^{27} - 378 x^{25} - 180 x^{24} + 55404 x^{23} + 24111 x^{22} - 4270554 x^{21} - 1205037 x^{20} + 193978638 x^{19} + 34664778 x^{18} - 5500402929 x^{17} - 826631784 x^{16} + 100060233273 x^{15} + 17341462773 x^{14} - 1173646133964 x^{13} - 242321726520 x^{12} + 8757504551097 x^{11} + 1781259610428 x^{10} - 40408055580087 x^{9} - 5139431874873 x^{8} + 110255393136807 x^{7} - 2797660463697 x^{6} - 161409309518763 x^{5} + 35414591654925 x^{4} + 96140161943631 x^{3} - 36022701760533 x^{2} - 4256570175237 x - 76637740149$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$44379744372833940000000$ |
| 27.27.138...969.24 |
$x^{27} - 378 x^{25} - 315 x^{24} + 55404 x^{23} + 46683 x^{22} - 4306122 x^{21} - 1723680 x^{20} + 200227491 x^{19} - 63211860 x^{18} - 5833394820 x^{17} + 6874981299 x^{16} + 104966539623 x^{15} - 226015385400 x^{14} - 1055343919599 x^{13} + 3654734759361 x^{12} + 3876220236258 x^{11} - 29069793915759 x^{10} + 18853994432151 x^{9} + 89826955537563 x^{8} - 164552770500552 x^{7} - 15360483925809 x^{6} + 285084705066885 x^{5} - 252928677028653 x^{4} - 2994487658343 x^{3} + 113841340568514 x^{2} - 57484656305685 x + 8459366908491$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$41808458497309560000000$ |
| 27.27.138...969.26 |
$x^{27} - 378 x^{25} - 513 x^{24} + 55404 x^{23} + 119529 x^{22} - 4213269 x^{21} - 11188530 x^{20} + 187674894 x^{19} + 564813855 x^{18} - 5181539058 x^{17} - 17108570007 x^{16} + 90541039644 x^{15} + 324183358323 x^{14} - 999376119261 x^{13} - 3875525392122 x^{12} + 6883130455848 x^{11} + 28927459576170 x^{10} - 29696195966094 x^{9} - 132253465860747 x^{8} + 85388283789075 x^{7} + 357696434522934 x^{6} - 187333813486665 x^{5} - 527171693484474 x^{4} + 309232011262428 x^{3} + 317779448060151 x^{2} - 256552668287964 x + 31559929488873$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$2$ |
$26$ |
$58913118392700195000000$ |
| 27.27.138...969.27 |
$x^{27} - 378 x^{25} - 18 x^{24} + 55404 x^{23} - 39501 x^{22} - 4348530 x^{21} + 7442604 x^{20} + 201518712 x^{19} - 560792619 x^{18} - 5579090460 x^{17} + 22367172438 x^{16} + 85766616873 x^{15} - 509251811157 x^{14} - 498924299331 x^{13} + 6562951486776 x^{12} - 4053952736253 x^{11} - 43741290249000 x^{10} + 74889249020109 x^{9} + 117207205935372 x^{8} - 353698342106850 x^{7} - 51675639694047 x^{6} + 690611312567574 x^{5} - 186204036367638 x^{4} - 604512053961813 x^{3} + 147108894400044 x^{2} + 233132005533258 x + 33274751851323$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$2$ |
$26$ |
$46311770302077570000000$ |
