| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 9.3.426083629572608.2 |
$x^{9} - 3 x^{8} + 23 x^{7} - 39 x^{6} + 86 x^{5} - 16 x^{4} - 235 x^{3} - 569 x^{2} - 616 x - 208$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{2}\cdot 19^{8}$ |
$3$ |
$42.218172264$ |
$141.7795371895746$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[9]$ |
$[9]$ |
$2$ |
$5$ |
$7279.92359983$ |
| 9.5.2717370086560000.1 |
$x^{9} - 3 x^{8} + 4 x^{7} + 18 x^{6} - 66 x^{5} + 60 x^{4} + 88 x^{3} - 322 x^{2} + 49 x + 343$ |
$9$ |
[5,2] |
$2^{8}\cdot 5^{4}\cdot 19^{8}$ |
$3$ |
$51.8687069101$ |
$84.81635197329787$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[9]$ |
$[9]$ |
$2$ |
$6$ |
$10371.8007682$ |
| 9.5.2717370086560000.2 |
$x^{9} - 3 x^{8} + 4 x^{7} - 20 x^{6} + 10 x^{5} + 60 x^{4} - 26 x^{3} - 18 x^{2} + 11 x + 1$ |
$9$ |
[5,2] |
$2^{8}\cdot 5^{4}\cdot 19^{8}$ |
$3$ |
$51.8687069101$ |
$102.82507438926143$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[9]$ |
$[9]$ |
$2$ |
$6$ |
$13210.5041848$ |
| 9.3.20878097849057792.1 |
$x^{9} - 3 x^{8} + 23 x^{7} - 96 x^{6} + 143 x^{5} - 244 x^{4} - 2515 x^{3} + 7468 x^{2} - 8596 x + 419$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{4}\cdot 19^{8}$ |
$3$ |
$65.0577429284$ |
$141.7795371895746$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
$[9]$ |
$[9]$ |
$2$ |
$5$ |
$11013.0136007$ |
| 9.3.1023026794603831808.2 |
$x^{9} - 3 x^{8} - 91 x^{7} + 341 x^{6} + 1701 x^{5} - 5127 x^{4} - 14029 x^{3} + 39179 x^{2} - 30142 x + 7658$ |
$9$ |
[3,3] |
$-\,2^{9}\cdot 7^{6}\cdot 19^{8}$ |
$3$ |
$100.25327218$ |
$141.7795371895746$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3, 9]$ |
$[3, 9]$ |
$2$ |
$5$ |
$85375.9082975$ |
| 9.9.642...801.3 |
$x^{9} - 133 x^{7} - 133 x^{6} + 5586 x^{5} + 9443 x^{4} - 71953 x^{3} - 132468 x^{2} + 123557 x + 237937$ |
$9$ |
[9,0] |
$3^{8}\cdot 7^{8}\cdot 19^{8}$ |
$3$ |
$205.104839264$ |
$334.21797094964006$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
$[9]$ |
$[9]$ |
$2$ |
$8$ |
$5046683.2949$ |
| 9.1.431...489.3 |
$x^{9} - 513 x^{4} + 2223 x^{3} - 6156 x^{2} + 8208 x - 399$ |
$9$ |
[1,4] |
$3^{26}\cdot 19^{8}$ |
$2$ |
$327.3558896148253$ |
$393.1337853329599$ |
|
|
? |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
$[18]$ |
$[18]$ |
$2$ |
$4$ |
$9556659.520339727$ |
| 9.9.596...761.1 |
$x^{9} - x^{8} - 312 x^{7} + 862 x^{6} + 31257 x^{5} - 113141 x^{4} - 1205570 x^{3} + 4881528 x^{2} + 14499456 x - 60964864$ |
$9$ |
[9,0] |
$19^{8}\cdot 37^{8}$ |
$2$ |
$339.333671102$ |
$339.33367110228545$ |
|
✓ |
|
$C_9$ (as 9T1) |
$[9]$ |
$[9]$ |
$2$ |
$8$ |
$18511275002.2$ |
| 12.2.129...467.3 |
$x^{12} - 8 x^{9} - 57 x^{3} - 57$ |
$12$ |
[2,5] |
$-\,3^{27}\cdot 19^{8}$ |
$2$ |
$84.3383739935$ |
$393.1337853329599$ |
|
|
? |
$C_3^3:S_4$ (as 12T177) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$8563417.83371$ |
| 18.0.618...448.1 |
$x^{18} + 3 x^{16} - 6 x^{15} + 162 x^{14} - 720 x^{13} - 441 x^{12} + 3114 x^{11} - 558 x^{10} + 1392 x^{9} - 6669 x^{8} - 9234 x^{7} + 19209 x^{6} - 6156 x^{5} + 15732 x^{4} - 13452 x^{3} - 2052 x^{2} + 4104 x + 912$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{33}\cdot 19^{8}$ |
$3$ |
$51.3617074045$ |
$403.44005880356065$ |
|
|
|
$D_9\wr C_2$ (as 18T211) |
$[3]$ |
$[3]$ |
$6$ |
$8$ |
$677587243.462$ |
| 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 |
trivial |
$2$ |
$26$ |
$1720496116352301.0$ |
| 27.27.403...281.2 |
$x^{27} - 9 x^{26} - 54 x^{25} + 747 x^{24} - 396 x^{23} - 18144 x^{22} + 49374 x^{21} + 143370 x^{20} - 765126 x^{19} + 241197 x^{18} + 3940596 x^{17} - 6851223 x^{16} - 3085029 x^{15} + 19311318 x^{14} - 14393484 x^{13} - 12138795 x^{12} + 22911579 x^{11} - 5137074 x^{10} - 10821168 x^{9} + 7438311 x^{8} + 890325 x^{7} - 2382309 x^{6} + 549288 x^{5} + 213705 x^{4} - 105993 x^{3} + 7533 x^{2} + 1458 x + 3$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{12}$ |
$2$ |
$81.53478118184302$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$259306124696432350$ |
| 27.27.815...609.3 |
$x^{27} - 81 x^{25} - 27 x^{24} + 2511 x^{23} + 1674 x^{22} - 40302 x^{21} - 40581 x^{20} + 369198 x^{19} + 508797 x^{18} - 1942785 x^{17} - 3606525 x^{16} + 5249880 x^{15} + 14560560 x^{14} - 3030534 x^{13} - 30964491 x^{12} - 18397206 x^{11} + 24706080 x^{10} + 38474772 x^{9} + 12230433 x^{8} - 14029524 x^{7} - 18235098 x^{6} - 10406718 x^{5} - 3622806 x^{4} - 816183 x^{3} - 116964 x^{2} - 9747 x - 361$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{10}$ |
$2$ |
$83.68495107025696$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
trivial |
$2$ |
$26$ |
$266386962493922140$ |
| 27.27.815...609.7 |
$x^{27} - 81 x^{25} - 9 x^{24} + 2511 x^{23} + 243 x^{22} - 40743 x^{21} - 2025 x^{20} + 388935 x^{19} + 630 x^{18} - 2297565 x^{17} + 78327 x^{16} + 8546157 x^{15} - 440559 x^{14} - 19928835 x^{13} + 942075 x^{12} + 28513053 x^{11} - 503253 x^{10} - 24116016 x^{9} - 951102 x^{8} + 11417841 x^{7} + 1386981 x^{6} - 2737881 x^{5} - 610470 x^{4} + 229311 x^{3} + 87723 x^{2} + 9747 x + 361$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{10}$ |
$2$ |
$83.68495107025696$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
trivial |
$2$ |
$26$ |
$423972567161809100$ |
| 27.27.363...529.2 |
$x^{27} - 117 x^{25} - 81 x^{24} + 5373 x^{23} + 7047 x^{22} - 124668 x^{21} - 232524 x^{20} + 1562382 x^{19} + 3804126 x^{18} - 10257516 x^{17} - 33239565 x^{16} + 28582371 x^{15} + 154892655 x^{14} + 12049344 x^{13} - 367483959 x^{12} - 218030130 x^{11} + 413211753 x^{10} + 387045675 x^{9} - 201033414 x^{8} - 266767182 x^{7} + 38879928 x^{6} + 83512296 x^{5} - 2007882 x^{4} - 11088837 x^{3} + 370386 x + 20577$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{12}$ |
$2$ |
$88.4474314157294$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$801120709352538800$ |
| 27.27.722...169.3 |
$x^{27} - 99 x^{25} - 18 x^{24} + 3780 x^{23} + 1053 x^{22} - 71640 x^{21} - 20169 x^{20} + 738927 x^{19} + 148341 x^{18} - 4413852 x^{17} - 308484 x^{16} + 15826905 x^{15} - 1255311 x^{14} - 34463340 x^{13} + 7824276 x^{12} + 45097317 x^{11} - 16528176 x^{10} - 34029798 x^{9} + 17105985 x^{8} + 13356639 x^{7} - 8847027 x^{6} - 2027376 x^{5} + 2066364 x^{4} - 45486 x^{3} - 175446 x^{2} + 25992 x + 361$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{16}$ |
$2$ |
$98.8009094950624$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
trivial |
trivial |
$2$ |
$26$ |
$3297458367799525400$ |
| 27.27.722...169.5 |
$x^{27} - 99 x^{25} - 81 x^{24} + 4050 x^{23} + 5634 x^{22} - 89838 x^{21} - 160191 x^{20} + 1210248 x^{19} + 2487465 x^{18} - 10528299 x^{17} - 23555934 x^{16} + 61473816 x^{15} + 142991568 x^{14} - 248378697 x^{13} - 566763768 x^{12} + 716104395 x^{11} + 1459128465 x^{10} - 1511977554 x^{9} - 2357818794 x^{8} + 2315360862 x^{7} + 2177918415 x^{6} - 2351210328 x^{5} - 852930729 x^{4} + 1279751859 x^{3} - 67195818 x^{2} - 211236984 x + 45408024$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{16}$ |
$2$ |
$98.8009094950624$ |
$270.741453963268$ |
|
|
|
$C_9^2:C_3$ (as 27T108) |
trivial |
trivial |
$2$ |
$26$ |
$14449197646184610000$ |
| 27.27.722...169.6 |
$x^{27} - 99 x^{25} - 81 x^{24} + 4050 x^{23} + 5733 x^{22} - 89622 x^{21} - 166806 x^{20} + 1193508 x^{19} + 2663292 x^{18} - 10041975 x^{17} - 26061597 x^{16} + 54084051 x^{15} + 164483703 x^{14} - 181644750 x^{13} - 683419284 x^{12} + 338368131 x^{11} + 1865911302 x^{10} - 156675615 x^{9} - 3263383323 x^{8} - 700347942 x^{7} + 3436236621 x^{6} + 1565095284 x^{5} - 1877639337 x^{4} - 1320036210 x^{3} + 297049572 x^{2} + 407512323 x + 81751699$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{16}$ |
$2$ |
$98.8009094950624$ |
$270.741453963268$ |
|
|
? |
$C_9^2.C_3$ (as 27T112) |
trivial |
trivial |
$2$ |
$26$ |
$2408945105764801000$ |
| 27.27.294...849.13 |
$x^{27} - 135 x^{25} - 63 x^{24} + 7047 x^{23} + 5832 x^{22} - 187605 x^{21} - 219672 x^{20} + 2848608 x^{19} + 4397661 x^{18} - 25829928 x^{17} - 51292791 x^{16} + 137995452 x^{15} + 362095920 x^{14} - 382041360 x^{13} - 1549240506 x^{12} + 173460690 x^{11} + 3852744912 x^{10} + 1972487907 x^{9} - 4900954734 x^{8} - 5236789158 x^{7} + 1887071526 x^{6} + 4823624601 x^{5} + 1313067105 x^{4} - 1267792290 x^{3} - 870036714 x^{2} - 145561698 x + 4506363$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{12}$ |
$2$ |
$104.08061637618087$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
trivial |
$2$ |
$26$ |
$6323138894532765000$ |
| 27.27.294...849.14 |
$x^{27} - 135 x^{25} - 162 x^{24} + 7047 x^{23} + 15849 x^{22} - 177282 x^{21} - 575181 x^{20} + 2187216 x^{19} + 10030059 x^{18} - 11284434 x^{17} - 94923387 x^{16} - 18566721 x^{15} + 504367236 x^{14} + 541169343 x^{13} - 1402042338 x^{12} - 2841375672 x^{11} + 1197214263 x^{10} + 6830265483 x^{9} + 3356277363 x^{8} - 6703753185 x^{7} - 8772970491 x^{6} - 926354880 x^{5} + 5025416742 x^{4} + 4225685139 x^{3} + 1505063511 x^{2} + 244454760 x + 14383323$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{12}$ |
$2$ |
$104.08061637618087$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
trivial |
$2$ |
$26$ |
$8321765635095911000$ |
| 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 |
trivial |
$2$ |
$26$ |
$11299048665263497000$ |
| 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 |
trivial |
$2$ |
$26$ |
$17387588880329714000$ |
| 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 |
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 |
trivial |
$2$ |
$26$ |
$11822013149204924000$ |
| 27.27.106...489.1 |
$x^{27} - 216 x^{25} - 225 x^{24} + 20169 x^{23} + 42147 x^{22} - 1052784 x^{21} - 3350241 x^{20} + 32803515 x^{19} + 147589191 x^{18} - 584539902 x^{17} - 3923616375 x^{16} + 4183739010 x^{15} + 63705507588 x^{14} + 44260281576 x^{13} - 596838291084 x^{12} - 1263982834593 x^{11} + 2544638382594 x^{10} + 11251792495779 x^{9} + 2560126629276 x^{8} - 42358622516919 x^{7} - 60447934931013 x^{6} + 38512784059794 x^{5} + 158397991520580 x^{4} + 93680190421164 x^{3} - 87328255096854 x^{2} - 131165933857722 x - 46697177581633$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{14}$ |
$2$ |
$129.44710568273106$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$126645346215724990000$ |
| 27.27.106...489.7 |
$x^{27} - 216 x^{25} - 351 x^{24} + 17577 x^{23} + 50706 x^{22} - 696798 x^{21} - 2878659 x^{20} + 14105529 x^{19} + 84548493 x^{18} - 114455430 x^{17} - 1390549086 x^{16} - 769853286 x^{15} + 12476626830 x^{14} + 24924651345 x^{13} - 47451872601 x^{12} - 209268727659 x^{11} - 85005220392 x^{10} + 670322974317 x^{9} + 1220257194435 x^{8} + 83000997621 x^{7} - 2234735627400 x^{6} - 3241549009818 x^{5} - 2116301526378 x^{4} - 615547456488 x^{3} - 18451889748 x^{2} + 17783343018 x - 671022829$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{14}$ |
$2$ |
$129.44710568273106$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$132107914802734320000$ |
| 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 |
$[2, 2]$ |
$2$ |
$26$ |
$179168037776802940000$ |
| 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 |
$[2, 2]$ |
$2$ |
$26$ |
$716086447716255000000$ |
| 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 |
$[2, 2]$ |
$2$ |
$26$ |
$340613162319737650000$ |
| 27.27.465...041.4 |
$x^{27} - 198 x^{25} - 45 x^{24} + 15579 x^{23} + 6030 x^{22} - 632286 x^{21} - 310068 x^{20} + 14600934 x^{19} + 8164416 x^{18} - 203233293 x^{17} - 125229636 x^{16} + 1766356578 x^{15} + 1183824531 x^{14} - 9713177811 x^{13} - 7005475422 x^{12} + 33422250969 x^{11} + 25588183383 x^{10} - 69016853337 x^{9} - 55151595630 x^{8} + 78171347961 x^{7} + 64267220736 x^{6} - 40048806510 x^{5} - 34581622104 x^{4} + 4926877416 x^{3} + 6161769765 x^{2} + 646708653 x - 2336381$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{22}$ |
$2$ |
$148.90231979619955$ |
$212.09372094764964$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$406394478302227500000$ |
| 27.27.465...041.5 |
$x^{27} - 198 x^{25} - 126 x^{24} + 16776 x^{23} + 19278 x^{22} - 795249 x^{21} - 1233891 x^{20} + 23215230 x^{19} + 43148010 x^{18} - 434324403 x^{17} - 906977322 x^{16} + 5265287784 x^{15} + 11923977321 x^{14} - 40805433558 x^{13} - 98885834082 x^{12} + 192901535685 x^{11} + 508119571197 x^{10} - 495140867637 x^{9} - 1536761691900 x^{8} + 460460407959 x^{7} + 2431663293402 x^{6} + 415706899014 x^{5} - 1459761679503 x^{4} - 745064356392 x^{3} - 81518448537 x^{2} + 8509434516 x + 1202926393$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{22}$ |
$2$ |
$148.90231979619955$ |
$212.09372094764964$ |
|
|
|
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$944239243915202100000$ |
| 27.27.465...041.6 |
$x^{27} - 198 x^{25} - 45 x^{24} + 15237 x^{23} + 4833 x^{22} - 600480 x^{21} - 183699 x^{20} + 13726098 x^{19} + 3453195 x^{18} - 194571288 x^{17} - 36243630 x^{16} + 1777900104 x^{15} + 222681924 x^{14} - 10706727312 x^{13} - 807257232 x^{12} + 42821702532 x^{11} + 1666449261 x^{10} - 112769868543 x^{9} - 1730530440 x^{8} + 189660239523 x^{7} + 401161077 x^{6} - 190580666364 x^{5} + 1426883472 x^{4} + 99216536310 x^{3} - 3465425070 x^{2} - 18374841090 x + 3271584133$ |
$27$ |
[27,0] |
$3^{64}\cdot 19^{22}$ |
$2$ |
$148.90231979619955$ |
$212.09372094764964$ |
|
|
? |
$C_9^2.C_3$ (as 27T112) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$194249351595459200000$ |
| 27.27.190...561.2 |
$x^{27} - 9 x^{26} - 171 x^{25} + 1827 x^{24} + 8433 x^{23} - 124389 x^{22} - 104823 x^{21} + 3918834 x^{20} - 2569968 x^{19} - 64252308 x^{18} + 89129079 x^{17} + 562282668 x^{16} - 1046356191 x^{15} - 2468599038 x^{14} + 6093605916 x^{13} + 4104735093 x^{12} - 18070771140 x^{11} + 4291171425 x^{10} + 23744268153 x^{9} - 21421070622 x^{8} - 4874467032 x^{7} + 16766623575 x^{6} - 9694169019 x^{5} + 1758763854 x^{4} + 457190010 x^{3} - 276885648 x^{2} + 49444398 x - 3162129$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{18}$ |
$2$ |
$156.8593376663821$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$1820137830367464800000$ |
| 27.27.190...561.4 |
$x^{27} - 9 x^{26} - 171 x^{25} + 1953 x^{24} + 7299 x^{23} - 135972 x^{22} + 2331 x^{21} + 4411557 x^{20} - 6531948 x^{19} - 80808069 x^{18} + 181696527 x^{17} + 920389176 x^{16} - 2511828594 x^{15} - 6847170354 x^{14} + 20921969682 x^{13} + 34010504388 x^{12} - 111099635775 x^{11} - 113325677451 x^{10} + 378840677886 x^{9} + 252102714957 x^{8} - 805776156774 x^{7} - 372759279390 x^{6} + 991316828322 x^{5} + 365587258383 x^{4} - 598889953575 x^{3} - 219609858852 x^{2} + 118781944614 x + 46868205099$ |
$27$ |
[27,0] |
$3^{76}\cdot 19^{18}$ |
$2$ |
$156.8593376663821$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$1568529793068684800000$ |
| 27.27.383...529.9 |
$x^{27} - 216 x^{25} - 216 x^{24} + 18954 x^{23} + 38286 x^{22} - 860175 x^{21} - 2639385 x^{20} + 20954511 x^{19} + 90504999 x^{18} - 245730591 x^{17} - 1638260370 x^{16} + 574266906 x^{15} + 15500618703 x^{14} + 14073911838 x^{13} - 74058178644 x^{12} - 139203301032 x^{11} + 142968879036 x^{10} + 526920200223 x^{9} + 91035508203 x^{8} - 860830584777 x^{7} - 713082436488 x^{6} + 372352379274 x^{5} + 706228134903 x^{4} + 262277919513 x^{3} + 802256076 x^{2} - 9627072912 x - 760162393$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$2464791236362595500000$ |
| 27.27.383...529.17 |
$x^{27} - 216 x^{25} - 18 x^{24} + 18954 x^{23} + 3780 x^{22} - 882513 x^{21} - 277020 x^{20} + 24105357 x^{19} + 9226989 x^{18} - 408013524 x^{17} - 151933671 x^{16} + 4439250801 x^{15} + 1252161180 x^{14} - 31614258555 x^{13} - 3955099356 x^{12} + 146740929048 x^{11} - 11620217448 x^{10} - 428633907384 x^{9} + 131907232917 x^{8} + 722643457230 x^{7} - 387873404604 x^{6} - 578099394765 x^{5} + 438077560167 x^{4} + 127121228487 x^{3} - 158245010991 x^{2} + 25939613124 x + 2052686071$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
trivial |
$2$ |
$26$ |
$2276352581014484400000$ |
| 27.27.383...529.18 |
$x^{27} - 216 x^{25} - 99 x^{24} + 18954 x^{23} + 14445 x^{22} - 901908 x^{21} - 827982 x^{20} + 26122473 x^{19} + 24655806 x^{18} - 488663280 x^{17} - 419133312 x^{16} + 6093359964 x^{15} + 4133335392 x^{14} - 51294613500 x^{13} - 22020245757 x^{12} + 289946153340 x^{11} + 41208434829 x^{10} - 1069377228912 x^{9} + 156336597126 x^{8} + 2412544212477 x^{7} - 967011855561 x^{6} - 2925996805188 x^{5} + 1726683788907 x^{4} + 1447328605554 x^{3} - 943453145376 x^{2} - 206915212935 x + 102914102737$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$2655591585059051700000$ |
| 27.27.383...529.19 |
$x^{27} - 216 x^{25} - 126 x^{24} + 18954 x^{23} + 19953 x^{22} - 895761 x^{21} - 1265058 x^{20} + 25398117 x^{19} + 42600888 x^{18} - 455785623 x^{17} - 853539660 x^{16} + 5321387646 x^{15} + 10815347124 x^{14} - 40653844893 x^{13} - 89377838307 x^{12} + 199068780465 x^{11} + 484834006890 x^{10} - 583536360171 x^{9} - 1692454751910 x^{8} + 820864268640 x^{7} + 3585908602908 x^{6} + 115334866926 x^{5} - 4019197380750 x^{4} - 1642533694713 x^{3} + 1597893539373 x^{2} + 1133520980715 x + 129651019739$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{16}$ |
$2$ |
$160.9959063758093$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
trivial |
$2$ |
$26$ |
$2691722582948657500000$ |
| 27.27.171...049.5 |
$x^{27} - 252 x^{25} - 27 x^{24} + 26676 x^{23} + 9234 x^{22} - 1554219 x^{21} - 1071657 x^{20} + 54770958 x^{19} + 59861514 x^{18} - 1201883589 x^{17} - 1817742141 x^{16} + 16231398660 x^{15} + 31126869054 x^{14} - 129011136048 x^{13} - 298368100674 x^{12} + 562414844016 x^{11} + 1573739557155 x^{10} - 1175038843806 x^{9} - 4495178021841 x^{8} + 468668851065 x^{7} + 6519867102090 x^{6} + 2089275385923 x^{5} - 3866005175571 x^{4} - 2596880633121 x^{3} + 129564356274 x^{2} + 436962142728 x + 83694622299$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{18}$ |
$2$ |
$170.15812526953377$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$5299518409690694000000$ |
| 27.27.171...049.6 |
$x^{27} - 252 x^{25} - 324 x^{24} + 26676 x^{23} + 64638 x^{22} - 1515231 x^{21} - 5266971 x^{20} + 49079736 x^{19} + 226357716 x^{18} - 880909749 x^{17} - 5551058601 x^{16} + 7233888069 x^{15} + 79194920832 x^{14} + 7001328582 x^{13} - 652750244703 x^{12} - 597410765226 x^{11} + 3009364582419 x^{10} + 4461720498882 x^{9} - 7163270610597 x^{8} - 14308275820797 x^{7} + 7326546142509 x^{6} + 20682161639280 x^{5} - 1641081658131 x^{4} - 12195540309096 x^{3} - 1227050668242 x^{2} + 2334698890506 x + 558763928637$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{18}$ |
$2$ |
$170.15812526953377$ |
|
|
|
? |
$C_3^4.C_3\wr C_3$ (as 27T692) |
trivial |
trivial |
$2$ |
$26$ |
$4616095758962743000000$ |
| 27.27.339...889.1 |
$x^{27} - 342 x^{25} - 513 x^{24} + 44118 x^{23} + 90801 x^{22} - 2981727 x^{21} - 6472008 x^{20} + 121330485 x^{19} + 246648804 x^{18} - 3201655572 x^{17} - 5627251755 x^{16} + 56927792115 x^{15} + 81002443500 x^{14} - 692022165066 x^{13} - 752454403308 x^{12} + 5731732794843 x^{11} + 4553687358927 x^{10} - 31742437777359 x^{9} - 18268295333976 x^{8} + 113548681613889 x^{7} + 51224687886906 x^{6} - 248339818016604 x^{5} - 106571714729175 x^{4} + 301723261505325 x^{3} + 147597401495655 x^{2} - 156503134770876 x - 93694152498679$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$8335393731184680000000$ |
| 27.27.339...889.4 |
$x^{27} - 342 x^{25} - 513 x^{24} + 44118 x^{23} + 83790 x^{22} - 3010113 x^{21} - 5281848 x^{20} + 124989372 x^{19} + 161892768 x^{18} - 3370580829 x^{17} - 2293774506 x^{16} + 60134818284 x^{15} + 2369261772 x^{14} - 699812389836 x^{13} + 380590290252 x^{12} + 5104534817484 x^{11} - 5326597180323 x^{10} - 21771205924011 x^{9} + 32666335127838 x^{8} + 47416860042858 x^{7} - 99286773058350 x^{6} - 32748128208990 x^{5} + 139511854250577 x^{4} - 30930526756359 x^{3} - 68624984741040 x^{2} + 34775795254410 x - 522845636543$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
? |
$C_9^2:C_3$ (as 27T108) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$10298688172283046000000$ |
| 27.27.339...889.5 |
$x^{27} - 198 x^{25} - 102 x^{24} + 13527 x^{23} + 17316 x^{22} - 436719 x^{21} - 923103 x^{20} + 7147215 x^{19} + 21933108 x^{18} - 54450810 x^{17} - 258536961 x^{16} + 80438451 x^{15} + 1505641401 x^{14} + 1250223165 x^{13} - 3827702793 x^{12} - 6807180132 x^{11} + 2152757358 x^{10} + 12634058130 x^{9} + 6236992431 x^{8} - 8249914710 x^{7} - 9629166999 x^{6} - 741030696 x^{5} + 3566696760 x^{4} + 1918570632 x^{3} + 197938368 x^{2} - 91131552 x - 19336384$ |
$27$ |
[27,0] |
$3^{70}\cdot 19^{22}$ |
$2$ |
$190.0764925052974$ |
$270.741453963268$ |
|
|
|
$C_9^2:C_3$ (as 27T104) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$22719306079717260000000$ |
| 27.27.138...969.2 |
$x^{27} - 378 x^{25} - 711 x^{24} + 60021 x^{23} + 213921 x^{22} - 5089302 x^{21} - 26695494 x^{20} + 239961906 x^{19} + 1784544372 x^{18} - 5534111646 x^{17} - 68507699562 x^{16} + 5317578792 x^{15} + 1488046067748 x^{14} + 2763959450931 x^{13} - 16268917640211 x^{12} - 60151814966142 x^{11} + 52736759471412 x^{10} + 510345847517235 x^{9} + 353601343013661 x^{8} - 1837773148346811 x^{7} - 2928454659769284 x^{6} + 2273231099637648 x^{5} + 6964865146017486 x^{4} + 1067798135043999 x^{3} - 5320689854748084 x^{2} - 2765198058285744 x - 118039856126597$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
trivial |
$2$ |
$26$ |
$51686710043462970000000$ |
| 27.27.138...969.21 |
$x^{27} - 378 x^{25} - 243 x^{24} + 55404 x^{23} + 58995 x^{22} - 4169664 x^{21} - 5712768 x^{20} + 180277947 x^{19} + 290727018 x^{18} - 4720060674 x^{17} - 8625116709 x^{16} + 76248291753 x^{15} + 155970499806 x^{14} - 754420694859 x^{13} - 1747866846537 x^{12} + 4389478561512 x^{11} + 12125089990539 x^{10} - 13026346787403 x^{9} - 50311748066175 x^{8} + 6729218405478 x^{7} + 112225410342099 x^{6} + 60281722114659 x^{5} - 93275305496235 x^{4} - 113159356049241 x^{3} - 32993182253538 x^{2} + 2991412343385 x + 1379902735611$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^6.C_3^3:C_9$ (as 27T1470) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$47525692125712920000000$ |
| 27.27.138...969.22 |
$x^{27} - 378 x^{25} - 846 x^{24} + 55404 x^{23} + 226233 x^{22} - 3954033 x^{21} - 23397417 x^{20} + 138293514 x^{19} + 1206745119 x^{18} - 1666266066 x^{17} - 33363480312 x^{16} - 33137623512 x^{15} + 479132265312 x^{14} + 1323999817803 x^{13} - 2755707718707 x^{12} - 16063167837078 x^{11} - 7192562957793 x^{10} + 76338652404573 x^{9} + 141644422142379 x^{8} - 60811633364859 x^{7} - 440341308656118 x^{6} - 415668127121424 x^{5} + 136596331344159 x^{4} + 516088793213226 x^{3} + 364262566231629 x^{2} + 96026241580839 x + 4534329056661$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$42036208643320840000000$ |
| 27.27.138...969.23 |
$x^{27} - 378 x^{25} - 531 x^{24} + 55404 x^{23} + 138510 x^{22} - 4125375 x^{21} - 14461983 x^{20} + 170744868 x^{19} + 796499361 x^{18} - 3879129528 x^{17} - 25287882021 x^{16} + 37948301190 x^{15} + 469731196089 x^{14} + 211707442449 x^{13} - 4837682543148 x^{12} - 9160529891382 x^{11} + 22029685724619 x^{10} + 86525718391728 x^{9} + 16737331285575 x^{8} - 308264870450808 x^{7} - 467712477374400 x^{6} + 97738857739080 x^{5} + 947196672790635 x^{4} + 1091589596100054 x^{3} + 564828189743781 x^{2} + 128344927038480 x + 8376377974407$ |
$27$ |
[27,0] |
$3^{82}\cdot 19^{18}$ |
$2$ |
$200.23376909867972$ |
|
|
|
? |
$C_3^7.C_3\wr C_3$ (as 27T1459) |
trivial |
$[2, 2]$ |
$2$ |
$26$ |
$42991505614374950000000$ |
| 27.27.617...689.5 |
$x^{27} - 513 x^{25} + 116964 x^{23} - 15617943 x^{21} + 1354686795 x^{19} - 1028850 x^{18} - 80025043581 x^{17} + 351866700 x^{16} + 3282297025608 x^{15} - 50141004750 x^{14} - 93545465229828 x^{13} + 3853057653900 x^{12} + 1824136571981646 x^{11} - 172561939213950 x^{10} - 23532332269224030 x^{9} + 4539706400859300 x^{8} + 189157232975424048 x^{7} - 67086772368254100 x^{6} - 846158627393377569 x^{5} + 496616366881881000 x^{4} + 1549004532090187059 x^{3} - 1415356645613360850 x^{2} + 367661650281552567 x - 29349414176093387$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{20}$ |
$2$ |
$211.6290005905609$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$32622736520754870000000$ |
| 27.27.617...689.7 |
$x^{27} - 513 x^{25} - 342 x^{24} + 106191 x^{23} + 149796 x^{22} - 11541816 x^{21} - 24582447 x^{20} + 714621825 x^{19} + 1993601961 x^{18} - 25712839422 x^{17} - 88399578258 x^{16} + 530166982239 x^{15} + 2264300549451 x^{14} - 5740901700273 x^{13} - 33893808221313 x^{12} + 19958315538708 x^{11} + 285815993148162 x^{10} + 182634862421520 x^{9} - 1193167984564197 x^{8} - 1944804108936825 x^{7} + 1378862387759556 x^{6} + 5425595065450053 x^{5} + 3234703718736684 x^{4} - 1803646350108549 x^{3} - 2205124372321704 x^{2} - 180719412704064 x + 221579183765493$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{20}$ |
$2$ |
$211.6290005905609$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$28642439101801417000000$ |
| 27.27.617...689.10 |
$x^{27} - 513 x^{25} - 342 x^{24} + 107730 x^{23} + 146718 x^{22} - 12248046 x^{21} - 25010289 x^{20} + 834938793 x^{19} + 2254547847 x^{18} - 35586150795 x^{17} - 119951484741 x^{16} + 954168730758 x^{15} + 3966390152379 x^{14} - 15513607609578 x^{13} - 82986861836061 x^{12} + 131843333553894 x^{11} + 1085837349661794 x^{10} - 144032576230986 x^{9} - 8448649391292588 x^{8} - 7433903024321445 x^{7} + 34325921490970401 x^{6} + 60807387572360784 x^{5} - 45486709840746738 x^{4} - 169126075823361777 x^{3} - 66168284295433779 x^{2} + 105384927812028633 x + 77038681754077993$ |
$27$ |
[27,0] |
$3^{78}\cdot 19^{20}$ |
$2$ |
$211.6290005905609$ |
|
|
|
? |
$C_9\wr C_3$ (as 27T434) |
$[3]$ |
$[3]$ |
$2$ |
$26$ |
$41350661916579610000000$ |
