| 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 |
| 22.8.147...499.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 112 x^{18} + 381 x^{17} - 87 x^{16} - 834 x^{15} + 674 x^{14} + 1020 x^{13} - 1213 x^{12} - 834 x^{11} + 1220 x^{10} + 511 x^{9} - 776 x^{8} - 247 x^{7} + 323 x^{6} + 85 x^{5} - 89 x^{4} - 18 x^{3} + 16 x^{2} + x - 1$ |
$22$ |
[8,7] |
$-\,97\cdot 2381^{2}\cdot 2467\cdot 104446171^{2}$ |
$4$ |
$19.0750493033$ |
$243947516.5618645$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$439864.358869$ |
| 22.8.806...447.1 |
$x^{22} - 9 x^{21} + 29 x^{20} - 38 x^{19} - 4 x^{18} + 86 x^{17} - 143 x^{16} + 138 x^{15} - 79 x^{14} - 37 x^{13} + 184 x^{12} - 257 x^{11} + 184 x^{10} - 37 x^{9} - 79 x^{8} + 138 x^{7} - 143 x^{6} + 86 x^{5} - 4 x^{4} - 38 x^{3} + 29 x^{2} - 9 x + 1$ |
$22$ |
[8,7] |
$-\,23^{20}\cdot 47$ |
$2$ |
$20.6033976441$ |
$118.57232216797493$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$918526.809002$ |
| 22.8.104...544.1 |
$x^{22} - 2 x^{20} - x^{18} - 2 x^{16} + 18 x^{12} - 24 x^{10} - 3 x^{8} + 36 x^{6} - 27 x^{4} + 4 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 19457^{2}\cdot 8095783^{2}$ |
$3$ |
$20.8434457974$ |
|
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$967898.03203$ |
| 22.8.156...136.1 |
$x^{22} - x^{20} - 4 x^{18} + x^{16} + 5 x^{14} + 7 x^{12} - 7 x^{10} - 5 x^{8} + 7 x^{6} - 3 x^{4} - x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 610429790897^{2}$ |
$2$ |
$23.5749849842$ |
|
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$4235240.70716$ |
| 22.8.274...864.1 |
$x^{22} - 2 x^{20} - x^{18} + 4 x^{16} - x^{14} - 5 x^{12} - x^{10} + 8 x^{8} + 3 x^{6} - 5 x^{4} - x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2}$ |
$4$ |
$24.1850829808$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$6351542.86721$ |
| 22.8.871...207.1 |
$x^{22} - x^{21} + x^{20} - x^{19} - 22 x^{18} + 22 x^{17} - 91 x^{16} + 68 x^{15} - 229 x^{14} - 162 x^{13} + 484 x^{12} - 1105 x^{11} + 852 x^{10} - 461 x^{9} - 114 x^{8} + 1264 x^{7} - 735 x^{6} + 574 x^{5} + 622 x^{4} + 298 x^{3} - 459 x^{2} - 162 x + 47$ |
$22$ |
[8,7] |
$-\,23^{21}\cdot 47^{2}$ |
$2$ |
$28.3034914521$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$28009585.914$ |
| 22.8.871...207.2 |
$x^{22} - 4 x^{21} - 7 x^{20} + 51 x^{19} - 43 x^{18} - 150 x^{17} + 416 x^{16} - 192 x^{15} - 1256 x^{14} + 1988 x^{13} + 2076 x^{12} - 5521 x^{11} - 1238 x^{10} + 8241 x^{9} - 2466 x^{8} - 6627 x^{7} + 5601 x^{6} + 2988 x^{5} - 5397 x^{4} + 566 x^{3} + 3417 x^{2} - 2306 x - 1609$ |
$22$ |
[8,7] |
$-\,23^{21}\cdot 47^{2}$ |
$2$ |
$28.3034914521$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$27806400.2764$ |
| 22.8.178...423.1 |
$x^{22} - 2 x^{21} - 14 x^{20} + 31 x^{19} + 70 x^{18} - 232 x^{17} - 279 x^{16} + 727 x^{15} + 777 x^{14} - 691 x^{13} - 405 x^{12} + 301 x^{11} - 1802 x^{10} - 2957 x^{9} + 1747 x^{8} + 4390 x^{7} + 52 x^{6} - 990 x^{5} - 739 x^{4} - 86 x^{3} + 40 x^{2} + 61 x - 47$ |
$22$ |
[8,7] |
$-\,23^{20}\cdot 47^{3}$ |
$2$ |
$29.2380053103$ |
$118.57232216797493$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$44250455.5687$ |
| 22.8.237...576.1 |
$x^{22} - x^{20} - 6 x^{18} + 5 x^{16} + 10 x^{14} - 8 x^{12} + 5 x^{8} - 10 x^{6} - 2 x^{4} + 4 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2}$ |
$5$ |
$29.6245630228$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$63144845.0704$ |
| 22.8.128...496.1 |
$x^{22} + 3 x^{20} - x^{18} - 7 x^{16} - 2 x^{14} - 4 x^{12} - 2 x^{10} + 16 x^{8} + 4 x^{6} - 9 x^{4} - x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 17524013040643^{2}$ |
$2$ |
$31.9887068235$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$149601967.313$ |
| 22.8.719...104.1 |
$x^{22} + 7 x^{20} - 7 x^{18} - 166 x^{16} - 458 x^{14} - 375 x^{12} + 144 x^{10} + 285 x^{8} + 29 x^{6} - 51 x^{4} - 9 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$279947596.769$ |
| 22.8.719...104.2 |
$x^{22} + 10 x^{20} + 35 x^{18} + 39 x^{16} - 42 x^{14} - 112 x^{12} - 14 x^{10} + 85 x^{8} + 24 x^{6} - 22 x^{4} - 4 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
✓ |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$284715946.713$ |
| 22.8.719...104.3 |
$x^{22} + 5 x^{20} - 20 x^{18} - 113 x^{16} + 75 x^{14} + 721 x^{12} + 196 x^{10} - 1492 x^{8} - 981 x^{6} + 372 x^{4} + 84 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$260618630.211$ |
| 22.8.719...104.4 |
$x^{22} - 4 x^{20} - 45 x^{18} - 45 x^{16} + 223 x^{14} + 469 x^{12} + 26 x^{10} - 571 x^{8} - 421 x^{6} - 34 x^{4} + 33 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$14$ |
$245941420.248$ |
| 22.8.138...424.1 |
$x^{22} + 11 x^{20} + 43 x^{18} + 62 x^{16} - 16 x^{14} - 116 x^{12} - 53 x^{10} + 56 x^{8} + 32 x^{6} - 10 x^{4} - 4 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 233^{2}\cdot 246572816873^{2}$ |
$3$ |
$35.6349006082$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$525272724.88$ |
| 22.8.172...867.1 |
$x^{22} - 11 x^{21} + 62 x^{20} - 235 x^{19} + 656 x^{18} - 1401 x^{17} + 2307 x^{16} - 2850 x^{15} + 2370 x^{14} - 664 x^{13} - 1547 x^{12} + 2938 x^{11} - 2660 x^{10} + 1125 x^{9} + 394 x^{8} - 967 x^{7} + 681 x^{6} - 193 x^{5} - 53 x^{4} + 68 x^{3} - 22 x^{2} + x + 1$ |
$22$ |
[8,7] |
$-\,137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 1849643$ |
$5$ |
$35.989529397$ |
$13357983455.871616$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$418659910.553$ |
| 22.8.197...632.1 |
$x^{22} - 3 x^{21} - 2 x^{20} + 17 x^{19} - 15 x^{18} - 29 x^{17} + 62 x^{16} - x^{15} - 98 x^{14} + 77 x^{13} + 66 x^{12} - 131 x^{11} + 24 x^{10} + 98 x^{9} - 81 x^{8} - 17 x^{7} + 57 x^{6} - 25 x^{5} - 12 x^{4} + 14 x^{3} - 3 x^{2} - 2 x + 1$ |
$22$ |
[8,7] |
$-\,2^{6}\cdot 673\cdot 683\cdot 4730027\cdot 141935338646968028959691$ |
$5$ |
$49.5739103748$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$14$ |
$50370489046.5$ |
| 22.8.565...896.1 |
$x^{22} + 16 x^{20} + 62 x^{18} - 216 x^{16} - 1948 x^{14} - 3000 x^{12} + 4363 x^{10} + 9892 x^{8} - 2285 x^{6} - 747 x^{4} + 4 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$29044854880.9$ |
| 22.8.565...896.2 |
$x^{22} + 16 x^{20} + 46 x^{18} - 346 x^{16} - 2536 x^{14} - 5981 x^{12} - 4843 x^{10} + 1475 x^{8} + 2688 x^{6} - 302 x^{4} - 144 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$34544260341.0$ |
| 22.8.565...896.3 |
$x^{22} + 9 x^{20} - 34 x^{18} - 335 x^{16} + 207 x^{14} + 3414 x^{12} + 981 x^{10} - 8064 x^{8} + 51 x^{6} + 3070 x^{4} + 710 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$40384558136.4$ |
| 22.8.565...896.4 |
$x^{22} + 9 x^{20} - 9 x^{18} - 259 x^{16} - 351 x^{14} + 1960 x^{12} + 4198 x^{10} - 1414 x^{8} - 4092 x^{6} - 774 x^{4} + 197 x^{2} + 25$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$26006566433.6$ |
| 22.8.565...896.5 |
$x^{22} - 7 x^{20} - 72 x^{18} - 36 x^{16} + 711 x^{14} + 1469 x^{12} - 353 x^{10} - 3136 x^{8} - 2011 x^{6} + 858 x^{4} + 1172 x^{2} + 289$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$43490276888.5$ |
| 22.8.565...896.6 |
$x^{22} + 6 x^{20} - 87 x^{18} - 904 x^{16} - 2836 x^{14} - 3349 x^{12} - 591 x^{10} + 1601 x^{8} + 959 x^{6} + 43 x^{4} - 47 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$39083872328.2$ |
| 22.8.565...896.7 |
$x^{22} + x^{20} - 89 x^{18} + 172 x^{16} + 1434 x^{14} - 3373 x^{12} - 5614 x^{10} + 7890 x^{8} + 12675 x^{6} + 3940 x^{4} + 219 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$33967070400.7$ |
| 22.8.565...896.8 |
$x^{22} + 4 x^{20} - 67 x^{18} - 65 x^{16} + 801 x^{14} + 697 x^{12} - 3324 x^{10} - 3913 x^{8} + 3601 x^{6} + 7419 x^{4} + 3784 x^{2} + 625$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$46640307074.3$ |
| 22.8.565...896.9 |
$x^{22} + 8 x^{20} - 58 x^{18} - 428 x^{16} + 1165 x^{14} + 6751 x^{12} - 4689 x^{10} - 33802 x^{8} - 37548 x^{6} - 16383 x^{4} - 2545 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 1297^{10}$ |
$2$ |
$51.999924379508414$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$14$ |
$44156910311.00117$ |
| 22.8.168...875.1 |
$x^{22} + 49 x^{20} + 685 x^{18} + 1815 x^{16} - 17505 x^{14} - 55752 x^{12} + 164457 x^{10} + 203115 x^{8} - 250965 x^{6} - 61270 x^{4} + 1001 x^{2} + 44$ |
$22$ |
[8,7] |
$-\,3^{20}\cdot 5^{20}\cdot 11^{17}$ |
$3$ |
$74.797382692$ |
$101.490943175476$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$12048790117700$ |
| 22.8.840...375.1 |
$x^{22} - 5 x^{21} + 5 x^{20} + 95 x^{19} - 410 x^{18} + 45 x^{17} + 4290 x^{16} - 18810 x^{15} - 10695 x^{14} + 249935 x^{13} - 321475 x^{12} - 1866185 x^{11} + 4561585 x^{10} + 11295680 x^{9} - 23786070 x^{8} - 42468195 x^{7} + 60552030 x^{6} + 77724405 x^{5} - 83970865 x^{4} - 64754635 x^{3} + 60087775 x^{2} + 19479130 x - 16767520$ |
$22$ |
[8,7] |
$-\,3^{20}\cdot 5^{21}\cdot 11^{17}$ |
$3$ |
$80.4744032946584$ |
$109.1939690656762$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
$[2]$ |
$2$ |
$14$ |
$22251499761686.65$ |
| 22.8.158...744.1 |
$x^{22} + 22 x^{20} - 66 x^{18} - 1892 x^{16} + 2684 x^{14} + 50908 x^{12} - 77924 x^{10} - 384824 x^{8} + 646272 x^{6} + 36080 x^{4} + 660 x^{2} + 4$ |
$22$ |
[8,7] |
$-\,2^{36}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$82.8176105784$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$14$ |
$21328458038300$ |
| 22.8.632...976.1 |
$x^{22} + 22 x^{20} - 22 x^{18} - 1738 x^{16} + 1100 x^{14} + 22000 x^{12} + 4840 x^{10} - 87120 x^{8} - 57596 x^{6} + 104544 x^{4} + 94380 x^{2} + 484$ |
$22$ |
[8,7] |
$-\,2^{38}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$88.2041581953$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$14$ |
$74479018733000$ |
| 22.8.156...000.1 |
$x^{22} + 26 x^{20} - 110 x^{18} - 3315 x^{16} - 14415 x^{14} - 13548 x^{12} + 20277 x^{10} + 30555 x^{8} + 10620 x^{6} + 670 x^{4} - 94 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$62716281487400$ |
| 22.8.156...000.2 |
$x^{22} - 19 x^{20} - 170 x^{18} + 3015 x^{16} + 10980 x^{14} - 127398 x^{12} - 271758 x^{10} + 1040880 x^{8} + 1659690 x^{6} + 598255 x^{4} + 77051 x^{2} + 3136$ |
$22$ |
[8,7] |
$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$41702856594400$ |
| 22.8.156...000.3 |
$x^{22} + 26 x^{20} - 20 x^{18} - 3330 x^{16} - 12255 x^{14} + 78192 x^{12} + 447987 x^{10} + 277980 x^{8} - 1318755 x^{6} - 2129930 x^{4} - 884209 x^{2} + 8836$ |
$22$ |
[8,7] |
$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$187763627752000$ |
| 22.8.156...000.4 |
$x^{22} - 19 x^{20} - 395 x^{18} + 615 x^{16} + 20850 x^{14} + 16842 x^{12} - 223773 x^{10} - 144525 x^{8} + 284565 x^{6} + 250165 x^{4} + 38861 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$70053485057500$ |
| 22.8.156...000.5 |
$x^{22} + 44 x^{20} + 415 x^{18} - 2265 x^{16} - 52410 x^{14} - 232827 x^{12} + 61662 x^{10} + 2529105 x^{8} + 4141035 x^{6} - 550070 x^{4} + 15791 x^{2} + 64$ |
$22$ |
[8,7] |
$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$163889571344000$ |
| 22.8.220...963.1 |
$x^{22} - 33 x^{20} - 66 x^{19} - 165 x^{17} - 1584 x^{16} - 5379 x^{15} + 11517 x^{14} + 66462 x^{13} + 1452 x^{12} - 124158 x^{11} + 531795 x^{10} + 1346697 x^{9} - 72006 x^{8} - 136224 x^{7} + 4245747 x^{6} + 2948682 x^{5} - 3930531 x^{4} - 687159 x^{3} + 4962870 x^{2} + 314622 x - 2099481$ |
$22$ |
[8,7] |
$-\,3^{21}\cdot 11^{32}$ |
$2$ |
$93.3656062498$ |
|
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$14$ |
$97875809452100$ |
| 22.8.252...904.1 |
$x^{22} - 11 x^{20} - 297 x^{18} + 1639 x^{16} + 20130 x^{14} + 39776 x^{12} + 10890 x^{10} - 19096 x^{8} - 10527 x^{6} + 231 x^{4} + 715 x^{2} + 49$ |
$22$ |
[8,7] |
$-\,2^{40}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$93.9410527374$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$14$ |
$122487476263000$ |
| 22.8.286...348.1 |
$x^{22} - 4 x^{21} - 8 x^{20} + 47 x^{19} + 7 x^{18} - 218 x^{17} + 124 x^{16} + 494 x^{15} - 557 x^{14} - 508 x^{13} + 1073 x^{12} + 9 x^{11} - 1074 x^{10} + 507 x^{9} + 535 x^{8} - 513 x^{7} - 87 x^{6} + 233 x^{5} - 23 x^{4} - 50 x^{3} + 10 x^{2} + 5 x - 1$ |
$22$ |
[8,7] |
$-\,2^{2}\cdot 71\!\cdots\!37$ |
$2$ |
$94.4716826404$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$14$ |
$65059933732500$ |
| 22.8.442...832.1 |
$x^{22} + 44 x^{20} + 330 x^{18} - 1122 x^{16} - 10428 x^{14} - 9548 x^{12} + 33044 x^{10} + 58124 x^{8} + 25432 x^{6} + 748 x^{4} - 836 x^{2} + 28$ |
$22$ |
[8,7] |
$-\,2^{38}\cdot 7^{11}\cdot 11^{22}$ |
$3$ |
$96.3612903217$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$14$ |
$184763637962000$ |
| 22.8.176...328.1 |
$x^{22} - 440 x^{18} + 1760 x^{16} + 29216 x^{14} - 54208 x^{12} - 381568 x^{10} + 2816 x^{8} + 1143296 x^{6} + 1216512 x^{4} + 405504 x^{2} + 28672$ |
$22$ |
[8,7] |
$-\,2^{40}\cdot 7^{11}\cdot 11^{22}$ |
$3$ |
$102.628733624$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$14$ |
$499478032980000$ |
| 22.8.412...904.1 |
$x^{22} + 13 x^{20} - 175 x^{18} - 443 x^{16} + 4918 x^{14} + 5154 x^{12} - 30529 x^{10} - 31931 x^{8} - 8640 x^{6} - 37 x^{4} + 149 x^{2} + 9$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$693934097341000$ |
| 22.8.412...904.2 |
$x^{22} - 7 x^{20} - 305 x^{18} + 1628 x^{16} + 16707 x^{14} - 32324 x^{12} - 356150 x^{10} - 370911 x^{8} + 918618 x^{6} + 1408022 x^{4} + 86679 x^{2} + 729$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$726368944674000$ |
| 22.8.412...904.3 |
$x^{22} - 10 x^{20} - 462 x^{18} + 3723 x^{16} + 44062 x^{14} - 61606 x^{12} - 1444979 x^{10} - 4726237 x^{8} - 6044709 x^{6} - 2432660 x^{4} + 446695 x^{2} + 52441$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
|
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$2237018414480000$ |
| 22.8.412...904.4 |
$x^{22} + 53 x^{20} + 1013 x^{18} + 7634 x^{16} + 4909 x^{14} - 175743 x^{12} - 326231 x^{10} + 1362553 x^{8} + 1192125 x^{6} - 2661192 x^{4} - 168308 x^{2} + 109561$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$1133954855610000$ |
| 22.8.412...904.5 |
$x^{22} + 10 x^{20} - 224 x^{18} - 1796 x^{16} + 5190 x^{14} + 71141 x^{12} + 187010 x^{10} + 147260 x^{8} + 4176 x^{6} - 5361 x^{4} - 167 x^{2} + 1$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
|
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$1226201594170000$ |
| 22.8.412...904.6 |
$x^{22} + 13 x^{20} - 136 x^{18} - 1229 x^{16} + 6421 x^{14} + 15324 x^{12} - 43922 x^{10} - 84593 x^{8} - 33311 x^{6} - 3209 x^{4} + 35 x^{2} + 9$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
|
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$1292107867650000$ |
| 22.8.412...904.7 |
$x^{22} + 54 x^{20} + 856 x^{18} + 3656 x^{16} - 429 x^{14} - 22607 x^{12} - 6522 x^{10} + 46131 x^{8} - 7022 x^{6} - 12568 x^{4} + 1984 x^{2} + 9$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.42642228905491$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$759035868919358.4$ |
| 22.8.412...904.8 |
$x^{22} - 9 x^{20} - 214 x^{18} + 797 x^{16} + 14307 x^{14} + 18880 x^{12} - 108938 x^{10} - 284353 x^{8} - 147121 x^{6} + 66241 x^{4} + 22699 x^{2} + 49$ |
$22$ |
[8,7] |
$-\,2^{22}\cdot 74843^{8}$ |
$2$ |
$118.42642228905491$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$14$ |
$493967748555922.4$ |
| 22.8.333...000.1 |
$x^{22} + 11 x^{20} - 495 x^{18} - 7865 x^{16} - 24585 x^{14} + 129107 x^{12} + 801867 x^{10} + 572385 x^{8} - 2731740 x^{6} - 3375130 x^{4} - 45419 x^{2} + 1681$ |
$22$ |
[8,7] |
$-\,2^{32}\cdot 5^{20}\cdot 11^{22}$ |
$3$ |
$130.221224171$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
$[2]$ |
$2$ |
$14$ |
$2018919861370000$ |
| 22.8.333...000.2 |
$x^{22} - 55 x^{20} - 110 x^{19} + 1265 x^{18} + 5390 x^{17} - 12155 x^{16} - 108680 x^{15} - 54615 x^{14} + 1156650 x^{13} + 2584725 x^{12} - 6092700 x^{11} - 26435475 x^{10} + 3812050 x^{9} + 118802475 x^{8} + 110680350 x^{7} - 162157050 x^{6} - 354485450 x^{5} - 248457000 x^{4} - 122510850 x^{3} - 86390975 x^{2} - 35201100 x - 4085775$ |
$22$ |
[8,7] |
$-\,2^{32}\cdot 5^{20}\cdot 11^{22}$ |
$3$ |
$130.221224171$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
$[2]$ |
$2$ |
$14$ |
$4300530737910000$ |
