| 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 |
| 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 |
$2$ |
$26$ |
$1845726979276938.2$ |
| 27.27.278...849.2 |
$x^{27} - 9 x^{26} - 36 x^{25} + 414 x^{24} + 540 x^{23} - 7425 x^{22} - 6669 x^{21} + 70335 x^{20} + 71874 x^{19} - 379365 x^{18} - 511623 x^{17} + 1129005 x^{16} + 2129508 x^{15} - 1468449 x^{14} - 4908276 x^{13} - 613476 x^{12} + 5606361 x^{11} + 3772170 x^{10} - 2092104 x^{9} - 3238029 x^{8} - 690525 x^{7} + 712836 x^{6} + 456705 x^{5} + 61128 x^{4} - 25884 x^{3} - 10584 x^{2} - 1377 x - 57$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{8}$ |
$2$ |
$57.1794860246354$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$2463155124765665.5$ |
| 27.27.278...849.3 |
$x^{27} - 9 x^{26} - 36 x^{25} + 405 x^{24} + 504 x^{23} - 6408 x^{22} - 5526 x^{21} + 46836 x^{20} + 39951 x^{19} - 181389 x^{18} - 166248 x^{17} + 397512 x^{16} + 395784 x^{15} - 506772 x^{14} - 552078 x^{13} + 372978 x^{12} + 456291 x^{11} - 149211 x^{10} - 220551 x^{9} + 26451 x^{8} + 59688 x^{7} + 144 x^{6} - 8244 x^{5} - 576 x^{4} + 477 x^{3} + 45 x^{2} - 9 x - 1$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{8}$ |
$2$ |
$57.1794860246354$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1720496116352301.0$ |
| 27.27.576...169.1 |
$x^{27} - 90 x^{25} - 27 x^{24} + 3321 x^{23} + 2331 x^{22} - 66708 x^{21} - 74250 x^{20} + 801783 x^{19} + 1210986 x^{18} - 5939001 x^{17} - 11418210 x^{16} + 26746641 x^{15} + 65575413 x^{14} - 67212999 x^{13} - 232389027 x^{12} + 60931980 x^{11} + 497525553 x^{10} + 114003132 x^{9} - 599594805 x^{8} - 362697273 x^{7} + 329247756 x^{6} + 354182463 x^{5} - 872793 x^{4} - 114481404 x^{3} - 49947003 x^{2} - 7314012 x - 181781$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{8}$ |
$2$ |
$69.66307714093857$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$27075886950323990$ |
| 27.27.576...169.2 |
$x^{27} - 90 x^{25} - 54 x^{24} + 3321 x^{23} + 3771 x^{22} - 64197 x^{21} - 103653 x^{20} + 689949 x^{19} + 1431282 x^{18} - 4043439 x^{17} - 10629720 x^{16} + 11616192 x^{15} + 43272711 x^{14} - 8991252 x^{13} - 95880114 x^{12} - 28105110 x^{11} + 112980438 x^{10} + 72817596 x^{9} - 63677259 x^{8} - 66729537 x^{7} + 9676980 x^{6} + 27002970 x^{5} + 4339323 x^{4} - 4210452 x^{3} - 1365633 x^{2} + 132534 x + 68561$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{8}$ |
$2$ |
$69.66307714093857$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$39608374769790800$ |
| 27.27.576...169.3 |
$x^{27} - 90 x^{25} - 99 x^{24} + 3321 x^{23} + 6939 x^{22} - 61758 x^{21} - 193131 x^{20} + 557847 x^{19} + 2681391 x^{18} - 1316817 x^{17} - 19042155 x^{16} - 14760324 x^{15} + 61979175 x^{14} + 110624751 x^{13} - 50973660 x^{12} - 263246922 x^{11} - 137047923 x^{10} + 214627986 x^{9} + 285707007 x^{8} + 38509452 x^{7} - 134788077 x^{6} - 99467433 x^{5} - 18592389 x^{4} + 8439885 x^{3} + 5100894 x^{2} + 998001 x + 69819$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{8}$ |
$2$ |
$69.66307714093857$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$38143597557545870$ |
| 27.27.120...129.1 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 2448 x^{18} - 6069411 x^{17} + 94311 x^{16} + 34988868 x^{15} - 1507977 x^{14} - 137978073 x^{13} + 12994236 x^{12} + 367382223 x^{11} - 65496303 x^{10} - 639184476 x^{9} + 195746949 x^{8} + 679326399 x^{7} - 334312353 x^{6} - 373524534 x^{5} + 293287230 x^{4} + 42597639 x^{3} - 98512929 x^{2} + 32905872 x - 3509281$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$21979660026260440000$ |
| 27.27.120...129.2 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 1746 x^{18} - 6069411 x^{17} + 63882 x^{16} + 34988868 x^{15} - 950454 x^{14} - 137978073 x^{13} + 7427862 x^{12} + 367382223 x^{11} - 32754186 x^{10} - 639641559 x^{9} + 80815968 x^{8} + 685847142 x^{7} - 102226536 x^{6} - 406332936 x^{5} + 51464160 x^{4} + 109559529 x^{3} - 2280798 x^{2} - 9318132 x - 522728$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
|
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$41372886827155580000$ |
| 27.27.120...129.3 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 2439 x^{18} - 6069411 x^{17} + 89208 x^{16} + 34988868 x^{15} - 1329858 x^{14} - 137978073 x^{13} + 10475244 x^{12} + 367382223 x^{11} - 47188683 x^{10} - 639729039 x^{9} + 122544414 x^{8} + 686821329 x^{7} - 175065867 x^{6} - 409227795 x^{5} + 122227380 x^{4} + 110436759 x^{3} - 31668003 x^{2} - 7037334 x - 130321$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$11169850458960992000$ |
| 27.27.120...129.4 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 1881 x^{18} - 6069411 x^{17} + 68256 x^{16} + 34988868 x^{15} - 1008774 x^{14} - 137978073 x^{13} + 7898148 x^{12} + 367382223 x^{11} - 35701533 x^{10} - 639734871 x^{9} + 95193306 x^{8} + 686673585 x^{7} - 146462013 x^{6} - 407011635 x^{5} + 120442140 x^{4} + 103418919 x^{3} - 42462549 x^{2} - 3011310 x + 2034577$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$21644917067226534000$ |
| 27.27.120...129.5 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 1926 x^{18} - 6069411 x^{17} + 73251 x^{16} + 34988868 x^{15} - 1148337 x^{14} - 137978073 x^{13} + 9601092 x^{12} + 367382223 x^{11} - 46181529 x^{10} - 639398874 x^{9} + 128154069 x^{8} + 682693731 x^{7} - 194014035 x^{6} - 393174486 x^{5} + 138894750 x^{4} + 91917459 x^{3} - 31668003 x^{2} - 7037334 x + 2215457$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$15463930720726591000$ |
| 27.27.120...129.6 |
$x^{27} - 81 x^{25} + 2835 x^{23} - 56628 x^{21} + 717822 x^{19} - 2547 x^{18} - 6069411 x^{17} + 97416 x^{16} + 34988868 x^{15} - 1539972 x^{14} - 137978073 x^{13} + 13035519 x^{12} + 367382223 x^{11} - 63887346 x^{10} - 639213960 x^{9} + 182634669 x^{8} + 680194395 x^{7} - 290626299 x^{6} - 381682773 x^{5} + 227787390 x^{4} + 71546229 x^{3} - 63336006 x^{2} + 3518667 x + 2476099$ |
$27$ |
[27,0] |
$3^{94}\cdot 19^{8}$ |
$2$ |
$109.64245937216903$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$16761359861579436000$ |
| 27.27.131...969.1 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1179 x^{24} + 8424 x^{23} - 55377 x^{22} - 274770 x^{21} + 1210734 x^{20} + 5422086 x^{19} - 12748809 x^{18} - 62954388 x^{17} + 54854766 x^{16} + 405117225 x^{15} + 7928955 x^{14} - 1392693777 x^{13} - 742641318 x^{12} + 2507826150 x^{11} + 2141963568 x^{10} - 2385005094 x^{9} - 2712466035 x^{8} + 1138097601 x^{7} + 1777446351 x^{6} - 197814987 x^{5} - 602138853 x^{4} - 25209081 x^{3} + 92334330 x^{2} + 9229194 x - 3954579$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$11299048665263497000$ |
| 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...969.3 |
$x^{27} - 9 x^{26} - 144 x^{25} + 900 x^{24} + 9774 x^{23} - 27378 x^{22} - 346653 x^{21} + 90153 x^{20} + 6100137 x^{19} + 8607171 x^{18} - 45005895 x^{17} - 128080251 x^{16} + 53541369 x^{15} + 527673744 x^{14} + 382961115 x^{13} - 696520170 x^{12} - 1032920802 x^{11} + 91154160 x^{10} + 770021307 x^{9} + 221022054 x^{8} - 214930260 x^{7} - 92320875 x^{6} + 23081463 x^{5} + 9674613 x^{4} - 1417167 x^{3} - 178092 x^{2} + 16443 x + 321$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$17387588880329714000$ |
| 27.27.131...969.4 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1152 x^{24} + 7992 x^{23} - 53541 x^{22} - 202482 x^{21} + 1212084 x^{20} + 2341710 x^{19} - 15263673 x^{18} - 9524196 x^{17} + 108099279 x^{16} - 36528660 x^{15} - 390101427 x^{14} + 438049161 x^{13} + 468295578 x^{12} - 1094174109 x^{11} + 467195391 x^{10} + 272433717 x^{9} - 250032474 x^{8} + 10460340 x^{7} + 36869346 x^{6} - 8055207 x^{5} - 1531548 x^{4} + 628245 x^{3} - 29052 x^{2} - 7776 x + 699$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$15209940687473095000$ |
| 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...969.6 |
$x^{27} - 9 x^{26} - 144 x^{25} + 927 x^{24} + 9126 x^{23} - 28620 x^{22} - 285651 x^{21} + 278127 x^{20} + 4695138 x^{19} + 1602309 x^{18} - 41742081 x^{17} - 52937523 x^{16} + 189563859 x^{15} + 420669558 x^{14} - 296826174 x^{13} - 1460583423 x^{12} - 640173996 x^{11} + 1871837154 x^{10} + 2327028903 x^{9} + 277411662 x^{8} - 916280181 x^{7} - 431133264 x^{6} + 54390879 x^{5} + 56423169 x^{4} + 1553535 x^{3} - 1611954 x^{2} + 1053 x + 5667$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$9799124893329762000$ |
| 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...969.8 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1080 x^{24} + 8334 x^{23} - 43803 x^{22} - 240957 x^{21} + 763956 x^{20} + 3903570 x^{19} - 6213252 x^{18} - 36624186 x^{17} + 18953046 x^{16} + 197669853 x^{15} + 36663372 x^{14} - 589708953 x^{13} - 382785741 x^{12} + 898681680 x^{11} + 889177248 x^{10} - 628660896 x^{9} - 896337207 x^{8} + 106516584 x^{7} + 403743699 x^{6} + 74897694 x^{5} - 63119475 x^{4} - 26464158 x^{3} - 1876050 x^{2} + 388710 x + 35171$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$20656084157365380000$ |
| 27.27.131...969.9 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1242 x^{24} + 7362 x^{23} - 62163 x^{22} - 154314 x^{21} + 1490634 x^{20} + 1147383 x^{19} - 19460316 x^{18} + 5689242 x^{17} + 142484445 x^{16} - 153280089 x^{15} - 548516025 x^{14} + 1015757568 x^{13} + 807287913 x^{12} - 2902462479 x^{11} + 671552928 x^{10} + 3224454132 x^{9} - 2356967277 x^{8} - 1116287280 x^{7} + 1634434722 x^{6} - 194321358 x^{5} - 333474363 x^{4} + 129689019 x^{3} - 7936686 x^{2} - 1773342 x + 165797$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$11822013149204924000$ |
| 27.27.131...969.10 |
$x^{27} - 9 x^{26} - 144 x^{25} + 1017 x^{24} + 9144 x^{23} - 39942 x^{22} - 311013 x^{21} + 642429 x^{20} + 5965236 x^{19} - 2162577 x^{18} - 62493561 x^{17} - 53777907 x^{16} + 310666383 x^{15} + 586956312 x^{14} - 422532351 x^{13} - 1802492766 x^{12} - 600743043 x^{11} + 2078789715 x^{10} + 1758504927 x^{9} - 756052659 x^{8} - 1222488405 x^{7} - 33888618 x^{6} + 340829280 x^{5} + 62266230 x^{4} - 36438975 x^{3} - 8727867 x^{2} + 662463 x + 174221$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$16374461404304407000$ |
| 27.27.131...969.11 |
$x^{27} - 9 x^{26} - 144 x^{25} + 990 x^{24} + 9828 x^{23} - 39420 x^{22} - 381663 x^{21} + 591732 x^{20} + 8426619 x^{19} + 1497300 x^{18} - 100468890 x^{17} - 138028428 x^{16} + 583157466 x^{15} + 1454543217 x^{14} - 1130591763 x^{13} - 6328420839 x^{12} - 2824992477 x^{11} + 11064908340 x^{10} + 14034140973 x^{9} - 2248879869 x^{8} - 14377341348 x^{7} - 9048273120 x^{6} - 59122899 x^{5} + 2191309038 x^{4} + 987810561 x^{3} + 185008536 x^{2} + 14995908 x + 403653$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{14}$ |
$2$ |
$110.00380666902184$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$17820717588267616000$ |
| 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 |
$2$ |
$26$ |
$21775391337291145000$ |
| 27.27.248...849.3 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 13590 x^{18} - 21561876 x^{17} + 571050 x^{16} + 154457145 x^{15} - 10023750 x^{14} - 752212980 x^{13} + 95787090 x^{12} + 2461248585 x^{11} - 542660310 x^{10} - 5236988664 x^{9} + 1853854290 x^{8} + 6765728499 x^{7} - 3692274030 x^{6} - 4485999510 x^{5} + 3857139000 x^{4} + 614349369 x^{3} - 1560118320 x^{2} + 578920500 x - 69893000$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
|
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$474997658671351100000$ |
| 27.27.248...849.4 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 14841 x^{18} - 21561876 x^{17} + 618030 x^{16} + 154457145 x^{15} - 10685439 x^{14} - 752212980 x^{13} + 99813897 x^{12} + 2461248585 x^{11} - 548268345 x^{10} - 5238344586 x^{9} + 1802416779 x^{8} + 6787064142 x^{7} - 3437669889 x^{6} - 4598899497 x^{5} + 3446430120 x^{4} + 851122359 x^{3} - 1366263369 x^{2} + 404818776 x - 35609059$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$278938331637223560000$ |
| 27.27.248...849.5 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 13896 x^{18} - 21561876 x^{17} + 583119 x^{16} + 154457145 x^{15} - 10207944 x^{14} - 752212980 x^{13} + 97047666 x^{12} + 2461248585 x^{11} - 544723542 x^{10} - 5237061699 x^{9} + 1831466700 x^{8} + 6768794430 x^{7} - 3554436006 x^{6} - 4520390085 x^{5} + 3569516910 x^{4} + 755388189 x^{3} - 1366263369 x^{2} + 404818776 x - 31860737$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$277544536638652740000$ |
| 27.27.248...849.6 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 16380 x^{18} - 21561876 x^{17} + 681696 x^{16} + 154457145 x^{15} - 11770434 x^{14} - 752212980 x^{13} + 109645272 x^{12} + 2461248585 x^{11} - 598992894 x^{10} - 5238091227 x^{9} + 1949176872 x^{8} + 6783857352 x^{7} - 3651574770 x^{6} - 4589252154 x^{5} + 3556210230 x^{4} + 858145329 x^{3} - 1353289356 x^{2} + 372771855 x - 31293971$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$238623929120542600000$ |
| 27.27.248...849.10 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 6282 x^{18} - 21561876 x^{17} + 267786 x^{16} + 154457145 x^{15} - 4805568 x^{14} - 752212980 x^{13} + 47254050 x^{12} + 2461248585 x^{11} - 275881788 x^{10} - 5238854013 x^{9} + 964392642 x^{8} + 6799417776 x^{7} - 1927694376 x^{6} - 4703024268 x^{5} + 1946101950 x^{4} + 1198944189 x^{3} - 706584708 x^{2} + 49197753 x + 9066887$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$189262285479713570000$ |
| 27.27.248...849.12 |
$x^{27} - 108 x^{25} + 4941 x^{23} - 126774 x^{21} + 2035395 x^{19} - 7254 x^{18} - 21561876 x^{17} + 305775 x^{16} + 154457145 x^{15} - 5383422 x^{14} - 752212980 x^{13} + 51386832 x^{12} + 2461248585 x^{11} - 287240904 x^{10} - 5238990939 x^{9} + 943137918 x^{8} + 6802942248 x^{7} - 1719175104 x^{6} - 4735059201 x^{5} + 1502486010 x^{4} + 1319883129 x^{3} - 422262315 x^{2} - 100133766 x + 30624641$ |
$27$ |
[27,0] |
$3^{94}\cdot 37^{8}$ |
$2$ |
$133.57991888690358$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$270061919689455170000$ |
| 27.27.473...809.3 |
$x^{27} - 198 x^{25} - 324 x^{24} + 15957 x^{23} + 49725 x^{22} - 644769 x^{21} - 3032019 x^{20} + 12560013 x^{19} + 93063924 x^{18} - 54306693 x^{17} - 1478243016 x^{16} - 2056022262 x^{15} + 10541021913 x^{14} + 34015124034 x^{13} - 8049345858 x^{12} - 175164475860 x^{11} - 224281584594 x^{10} + 199424923134 x^{9} + 729122375853 x^{8} + 500318360757 x^{7} - 305360617968 x^{6} - 605228405058 x^{5} - 254515772601 x^{4} + 28848540294 x^{3} + 37095532227 x^{2} + 1618768764 x - 1370987389$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$477398611390585900000$ |
| 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...809.6 |
$x^{27} - 198 x^{25} - 324 x^{24} + 15957 x^{23} + 50697 x^{22} - 635265 x^{21} - 3097143 x^{20} + 11489031 x^{19} + 91993104 x^{18} - 17075205 x^{17} - 1326457602 x^{16} - 2433538962 x^{15} + 6935920569 x^{14} + 30091046472 x^{13} + 20048000670 x^{12} - 82335812580 x^{11} - 201197080152 x^{10} - 169635330966 x^{9} - 11908368009 x^{8} + 76050281961 x^{7} + 46711958166 x^{6} + 5360869494 x^{5} - 2868369903 x^{4} - 574299738 x^{3} + 48003975 x^{2} + 8993232 x - 325261$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$423447292814985600000$ |
| 27.27.473...809.7 |
$x^{27} - 198 x^{25} - 351 x^{24} + 15957 x^{23} + 54666 x^{22} - 628191 x^{21} - 3320568 x^{20} + 10748718 x^{19} + 97483116 x^{18} + 10246662 x^{17} - 1371557484 x^{16} - 2851583688 x^{15} + 6714620064 x^{14} + 32323968747 x^{13} + 22618940013 x^{12} - 85813277472 x^{11} - 190061000811 x^{10} - 104390822466 x^{9} + 66445669386 x^{8} + 75457381698 x^{7} - 4904615673 x^{6} - 13930587846 x^{5} + 1516854132 x^{4} + 370139076 x^{3} - 32593968 x^{2} - 2098854 x - 6859$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$179168037776802940000$ |
| 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 |
$2$ |
$26$ |
$361319951347960800000$ |
| 27.27.473...809.9 |
$x^{27} - 198 x^{25} - 324 x^{24} + 15957 x^{23} + 51129 x^{22} - 635886 x^{21} - 3164049 x^{20} + 11359485 x^{19} + 95026734 x^{18} - 5080239 x^{17} - 1361703780 x^{16} - 2636302725 x^{15} + 7043298138 x^{14} + 30376529946 x^{13} + 10980699507 x^{12} - 110623392846 x^{11} - 186652654974 x^{10} + 33543026664 x^{9} + 371930987223 x^{8} + 351664456248 x^{7} + 42064344891 x^{6} - 91842793731 x^{5} - 24631208334 x^{4} + 11341992582 x^{3} + 1682517393 x^{2} - 673004358 x + 34458533$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$294275878678997140000$ |
| 27.27.473...809.10 |
$x^{27} - 198 x^{25} - 324 x^{24} + 15957 x^{23} + 49932 x^{22} - 640503 x^{21} - 3037851 x^{20} + 12035106 x^{19} + 91062213 x^{18} - 36445059 x^{17} - 1348741980 x^{16} - 2111402664 x^{15} + 7993816857 x^{14} + 28308501261 x^{13} + 4240071711 x^{12} - 108535038075 x^{11} - 170171826822 x^{10} + 21357476946 x^{9} + 314235482400 x^{8} + 337295653029 x^{7} + 109009291356 x^{6} - 45411916302 x^{5} - 40125705579 x^{4} - 5215837383 x^{3} + 2382137559 x^{2} + 677929842 x + 37662769$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
|
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$716086447716255000000$ |
| 27.27.473...809.11 |
$x^{27} - 198 x^{25} - 351 x^{24} + 15957 x^{23} + 53964 x^{22} - 633321 x^{21} - 3260952 x^{20} + 11293011 x^{19} + 96050397 x^{18} - 11416302 x^{17} - 1373475078 x^{16} - 2377555272 x^{15} + 7791530697 x^{14} + 28219382388 x^{13} - 201270933 x^{12} - 115955392752 x^{11} - 144053041095 x^{10} + 110901440043 x^{9} + 377335104156 x^{8} + 240459812343 x^{7} - 92712784959 x^{6} - 174750707502 x^{5} - 58091031585 x^{4} + 9395149545 x^{3} + 8403317568 x^{2} + 1343883870 x + 46167929$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{16}$ |
$2$ |
$136.81389372177443$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$340613162319737650000$ |
| 27.27.148...121.1 |
$x^{27} - 9 x^{26} - 207 x^{25} + 1746 x^{24} + 15138 x^{23} - 106965 x^{22} - 603000 x^{21} + 3031254 x^{20} + 14178654 x^{19} - 47178009 x^{18} - 206967996 x^{17} + 437065938 x^{16} + 1951501077 x^{15} - 2469116664 x^{14} - 12205873089 x^{13} + 8113340367 x^{12} + 51157068741 x^{11} - 11503322586 x^{10} - 142259699883 x^{9} - 15412712787 x^{8} + 252637716510 x^{7} + 93396799143 x^{6} - 261835947369 x^{5} - 153140469174 x^{4} + 126082509264 x^{3} + 99346891194 x^{2} - 9056985669 x - 12370359097$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1413310487466431200000$ |
| 27.27.148...121.2 |
$x^{27} - 9 x^{26} - 207 x^{25} + 1440 x^{24} + 14571 x^{23} - 75267 x^{22} - 504243 x^{21} + 1928547 x^{20} + 9880497 x^{19} - 28166697 x^{18} - 118471176 x^{17} + 250441344 x^{16} + 911246229 x^{15} - 1391357448 x^{14} - 4617698967 x^{13} + 4823922528 x^{12} + 15572158245 x^{11} - 10086999165 x^{10} - 34753163961 x^{9} + 11336304123 x^{8} + 50169183741 x^{7} - 3520769526 x^{6} - 44553463002 x^{5} - 5816827341 x^{4} + 21857309784 x^{3} + 6234267753 x^{2} - 4461923952 x - 1787785381$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1126446222211834700000$ |
| 27.27.148...121.3 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2826 x^{24} + 5814 x^{23} - 261504 x^{22} + 1136322 x^{21} + 5499783 x^{20} - 66559284 x^{19} + 185384712 x^{18} + 375796512 x^{17} - 3660023160 x^{16} + 7299156483 x^{15} + 9114202908 x^{14} - 66356119557 x^{13} + 95294961954 x^{12} + 72223522002 x^{11} - 391799892249 x^{10} + 384046921056 x^{9} + 213840147114 x^{8} - 729026209944 x^{7} + 439648499853 x^{6} + 191579774787 x^{5} - 342969049890 x^{4} + 116848576062 x^{3} + 12879475245 x^{2} - 8825772654 x - 627216479$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
|
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$3044395581000423300000$ |
| 27.27.148...121.4 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2997 x^{24} + 3042 x^{23} - 265239 x^{22} + 1507536 x^{21} + 2738466 x^{20} - 67344633 x^{19} + 311771703 x^{18} - 469848474 x^{17} - 1132781373 x^{16} + 5723367561 x^{15} - 5655563352 x^{14} - 13512930939 x^{13} + 35828321940 x^{12} - 5011416387 x^{11} - 67140321030 x^{10} + 55974129948 x^{9} + 49903098399 x^{8} - 73744660836 x^{7} - 9623795355 x^{6} + 37914584130 x^{5} - 3163693779 x^{4} - 7107748938 x^{3} + 1132924338 x^{2} + 294335946 x - 53358427$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
|
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$4097645205246278000000$ |
| 27.27.148...121.5 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2430 x^{24} + 10710 x^{23} - 225468 x^{22} + 315414 x^{21} + 7950735 x^{20} - 37833984 x^{19} - 54831156 x^{18} + 783048348 x^{17} - 1255479606 x^{16} - 4678904349 x^{15} + 17166505788 x^{14} + 360698841 x^{13} - 71443118016 x^{12} + 63985353966 x^{11} + 131367906603 x^{10} - 186726076974 x^{9} - 125389355328 x^{8} + 221468125464 x^{7} + 84852314937 x^{6} - 110706914601 x^{5} - 47612921652 x^{4} + 8590327038 x^{3} + 3577157847 x^{2} - 347145012 x - 36661159$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1319961692625717200000$ |
| 27.27.148...121.6 |
$x^{27} - 9 x^{26} - 207 x^{25} + 1053 x^{24} + 18243 x^{23} - 30609 x^{22} - 762219 x^{21} - 337455 x^{20} + 14394222 x^{19} + 18865533 x^{18} - 140044365 x^{17} - 229479687 x^{16} + 759195621 x^{15} + 1236308715 x^{14} - 2365739316 x^{13} - 3134665098 x^{12} + 4117878882 x^{11} + 3436020873 x^{10} - 3337466076 x^{9} - 1457794890 x^{8} + 973936881 x^{7} + 163558872 x^{6} - 89092071 x^{5} - 1104831 x^{4} + 2410083 x^{3} - 230292 x^{2} + 7272 x - 73$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1237064429700766000000$ |
| 27.27.148...121.7 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2547 x^{24} + 8946 x^{23} - 228753 x^{22} + 543510 x^{21} + 6493329 x^{20} - 41016366 x^{19} + 25612518 x^{18} + 436127823 x^{17} - 1213591986 x^{16} - 630634644 x^{15} + 6847124634 x^{14} - 5902301997 x^{13} - 13253346027 x^{12} + 22909008852 x^{11} + 5873437782 x^{10} - 29173581276 x^{9} + 6810318666 x^{8} + 14563732563 x^{7} - 5320103328 x^{6} - 3216998556 x^{5} + 1057509531 x^{4} + 305135028 x^{3} - 53992962 x^{2} - 7854129 x + 661267$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1198421747127336800000$ |
| 27.27.148...121.8 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2907 x^{24} + 4122 x^{23} - 255951 x^{22} + 1297107 x^{21} + 3569580 x^{20} - 61861851 x^{19} + 247983885 x^{18} - 243350172 x^{17} - 1297390842 x^{16} + 4674740247 x^{15} - 3281538969 x^{14} - 11850636087 x^{13} + 27052744176 x^{12} - 7648551396 x^{11} - 38281553226 x^{10} + 46513389417 x^{9} - 2308941486 x^{8} - 28965908223 x^{7} + 17460108009 x^{6} + 542724507 x^{5} - 3567273012 x^{4} + 1076115096 x^{3} - 56626326 x^{2} - 17057889 x + 1810349$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$2377461209797079600000$ |
| 27.27.148...121.9 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2889 x^{24} + 4770 x^{23} - 265212 x^{22} + 1328670 x^{21} + 4238262 x^{20} - 70591950 x^{19} + 282418605 x^{18} - 153349398 x^{17} - 2795913981 x^{16} + 11260778301 x^{15} - 15465981762 x^{14} - 19153773153 x^{13} + 119720767365 x^{12} - 230892699834 x^{11} + 224259801912 x^{10} - 59486501883 x^{9} - 122461162776 x^{8} + 166911581889 x^{7} - 92436758946 x^{6} + 16913584557 x^{5} + 7716008547 x^{4} - 5251784238 x^{3} + 1211997132 x^{2} - 117436815 x + 3709691$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1434823113874317800000$ |
| 27.27.148...121.10 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2799 x^{24} + 5922 x^{23} - 254160 x^{22} + 1067706 x^{21} + 5184450 x^{20} - 60066783 x^{19} + 169760046 x^{18} + 173607633 x^{17} - 1995002874 x^{16} + 2806251156 x^{15} + 6814404873 x^{14} - 21984532803 x^{13} - 1750133259 x^{12} + 67700695032 x^{11} - 42064801020 x^{10} - 108704725638 x^{9} + 106963312905 x^{8} + 98762533614 x^{7} - 111025954818 x^{6} - 56131777134 x^{5} + 46914875073 x^{4} + 20807085114 x^{3} - 3017697426 x^{2} - 1193105691 x + 86840011$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1130213042200532100000$ |
| 27.27.148...121.11 |
$x^{27} - 9 x^{26} - 207 x^{25} + 2853 x^{24} + 4716 x^{23} - 246015 x^{22} + 1098981 x^{21} + 4187772 x^{20} - 50356287 x^{19} + 105780981 x^{18} + 482960412 x^{17} - 2960821908 x^{16} + 3823880805 x^{15} + 12119523849 x^{14} - 46008777645 x^{13} + 26747251893 x^{12} + 119429355303 x^{11} - 223788026142 x^{10} - 15927568029 x^{9} + 386604080271 x^{8} - 267114033063 x^{7} - 207108431559 x^{6} + 272866304493 x^{5} + 23627296278 x^{4} - 100842494571 x^{3} + 2550966498 x^{2} + 13937054031 x + 1395604241$ |
$27$ |
[27,0] |
$3^{78}\cdot 37^{14}$ |
$2$ |
$155.41463976624786$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
trivial |
$2$ |
$26$ |
$1622706228315206500000$ |
