| 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 |
| 28.0.305...909.1 |
$x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$28$ |
[0,14] |
$29^{27}$ |
$1$ |
$25.7139916164$ |
$25.713991616408272$ |
✓ |
✓ |
✓ |
$C_{28}$ (as 28T1) |
$[2, 2, 2]$ |
$58$ |
$13$ |
$487075979.1876791$ |
| 28.28.146...821.1 |
$x^{28} - x^{27} - 28 x^{26} + 28 x^{25} + 349 x^{24} - 349 x^{23} - 2551 x^{22} + 2551 x^{21} + 12123 x^{20} - 12123 x^{19} - 39236 x^{18} + 39236 x^{17} + 88045 x^{16} - 88045 x^{15} - 136763 x^{14} + 136763 x^{13} + 144247 x^{12} - 144247 x^{11} - 99295 x^{10} + 99295 x^{9} + 41703 x^{8} - 41703 x^{7} - 9569 x^{6} + 9569 x^{5} + 987 x^{4} - 987 x^{3} - 28 x^{2} + 28 x + 1$ |
$28$ |
[28,0] |
$3^{14}\cdot 29^{27}$ |
$2$ |
$44.537939945$ |
$44.53793994501929$ |
|
✓ |
✓ |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$114482618238342.14$ |
| 28.28.819...504.1 |
$x^{28} - 29 x^{26} + 377 x^{24} - 2900 x^{22} + 14674 x^{20} - 51359 x^{18} + 127281 x^{16} - 224808 x^{14} + 281010 x^{12} - 243542 x^{10} + 140998 x^{8} - 51272 x^{6} + 10556 x^{4} - 1015 x^{2} + 29$ |
$28$ |
[28,0] |
$2^{28}\cdot 29^{27}$ |
$2$ |
$51.4279832328$ |
$51.427983232816544$ |
|
✓ |
✓ |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$822416597953191.9$ |
| 28.0.186...125.1 |
$x^{28} - x^{27} + 30 x^{26} - 30 x^{25} + 407 x^{24} - 407 x^{23} + 3307 x^{22} - 3307 x^{21} + 17981 x^{20} - 17981 x^{19} + 69340 x^{18} - 69340 x^{17} + 196621 x^{16} - 196621 x^{15} + 421429 x^{14} - 421429 x^{13} + 702439 x^{12} - 702439 x^{11} + 945981 x^{10} - 945981 x^{9} + 1086979 x^{8} - 1086979 x^{7} + 1138251 x^{6} - 1138251 x^{5} + 1148807 x^{4} - 1148807 x^{3} + 1149822 x^{2} - 1149822 x + 1149851$ |
$28$ |
[0,14] |
$5^{14}\cdot 29^{27}$ |
$2$ |
$57.4982332271$ |
$57.498233227148596$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2, 2, 2, 1514]$ |
$2$ |
$13$ |
$487075979.1876791$ |
| 28.0.596...125.1 |
$x^{28} - x^{27} + 13 x^{26} - 18 x^{25} + 139 x^{24} + 6 x^{23} + 1195 x^{22} + 162 x^{21} + 10698 x^{20} - 2678 x^{19} + 31811 x^{18} - 10412 x^{17} + 82335 x^{16} - 59127 x^{15} + 217167 x^{14} - 143196 x^{13} + 464676 x^{12} - 285512 x^{11} + 357781 x^{10} - 176521 x^{9} + 256648 x^{8} + 112508 x^{7} + 36201 x^{6} + 9801 x^{5} + 2858 x^{4} + 449 x^{3} + 67 x^{2} + 9 x + 1$ |
$28$ |
[0,14] |
$5^{21}\cdot 29^{24}$ |
$2$ |
$59.9392771877$ |
$59.93927718771197$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2, 842]$ |
$10$ |
$13$ |
$34681517373.86067$ |
| 28.28.207...741.1 |
$x^{28} - x^{27} - 57 x^{26} + 57 x^{25} + 1451 x^{24} - 1451 x^{23} - 21749 x^{22} + 21749 x^{21} + 213035 x^{20} - 213035 x^{19} - 1430453 x^{18} + 1430453 x^{17} + 6715531 x^{16} - 6715531 x^{15} - 22059893 x^{14} + 22059893 x^{13} + 49878667 x^{12} - 49878667 x^{11} - 74814837 x^{10} + 74814837 x^{9} + 69567115 x^{8} - 69567115 x^{7} - 35437941 x^{6} + 35437941 x^{5} + 7799435 x^{4} - 7799435 x^{3} - 515445 x^{2} + 515445 x - 40309$ |
$28$ |
[28,0] |
$7^{14}\cdot 29^{27}$ |
$2$ |
$68.0328270318$ |
$68.03282703181608$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$40658806140034130$ |
| 28.0.134...536.1 |
$x^{28} + 58 x^{26} + 1508 x^{24} + 23200 x^{22} + 234784 x^{20} + 1643488 x^{18} + 8145984 x^{16} + 28775424 x^{14} + 71938560 x^{12} + 124693504 x^{10} + 144381952 x^{8} + 105005056 x^{6} + 43237376 x^{4} + 8314880 x^{2} + 475136$ |
$28$ |
[0,14] |
$2^{42}\cdot 29^{27}$ |
$2$ |
$72.7301513733$ |
$72.7301513733453$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2, 2, 48802]$ |
$2$ |
$13$ |
$487075979.1876791$ |
| 28.28.134...536.1 |
$x^{28} - 58 x^{26} + 1508 x^{24} - 23200 x^{22} + 234784 x^{20} - 1643488 x^{18} + 8145984 x^{16} - 28775424 x^{14} + 71938560 x^{12} - 124693504 x^{10} + 144381952 x^{8} - 105005056 x^{6} + 43237376 x^{4} - 8314880 x^{2} + 475136$ |
$28$ |
[28,0] |
$2^{42}\cdot 29^{27}$ |
$2$ |
$72.7301513733$ |
$72.7301513733453$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$170028857236944540$ |
| 28.0.502...125.1 |
$x^{28} - x^{27} + 18 x^{26} - 23 x^{25} + 29 x^{24} - 149 x^{23} - 795 x^{22} - 8 x^{21} - 2927 x^{20} + 667 x^{19} + 13846 x^{18} - 647 x^{17} + 109320 x^{16} + 98963 x^{15} + 313397 x^{14} + 494999 x^{13} + 789626 x^{12} + 291678 x^{11} + 1921156 x^{10} - 425111 x^{9} + 1044768 x^{8} + 1156338 x^{7} - 1030264 x^{6} + 642721 x^{5} + 1780368 x^{4} - 4481806 x^{3} + 897127 x^{2} + 1339909 x + 1148111$ |
$28$ |
[0,14] |
$5^{21}\cdot 29^{26}$ |
$2$ |
$76.2374745349$ |
$76.23747453486138$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2, 2, 2, 562]$ |
$2$ |
$13$ |
$34681517373.86067$ |
| 28.0.761...125.1 |
$x^{28} - x^{27} + 19 x^{26} - 2 x^{25} + 271 x^{24} - 992 x^{23} + 5175 x^{22} - 15390 x^{21} + 63548 x^{20} - 148986 x^{19} + 389755 x^{18} - 780480 x^{17} + 1682463 x^{16} - 2675897 x^{15} + 5128339 x^{14} - 7532046 x^{13} + 13393480 x^{12} - 18209154 x^{11} + 29065829 x^{10} - 34016343 x^{9} + 48229826 x^{8} - 40181120 x^{7} + 44171883 x^{6} - 25868717 x^{5} + 23880346 x^{4} + 7983325 x^{3} + 12353145 x^{2} + 823543 x + 5764801$ |
$28$ |
[0,14] |
$5^{21}\cdot 43^{24}$ |
$2$ |
$84.0123866236$ |
$84.01238662362125$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[22709]$ |
$10$ |
$13$ |
$263819853122.8475$ |
| 28.28.115...069.1 |
$x^{28} - x^{27} - 86 x^{26} + 86 x^{25} + 3307 x^{24} - 3307 x^{23} - 74993 x^{22} + 74993 x^{21} + 1113601 x^{20} - 1113601 x^{19} - 11366636 x^{18} + 11366636 x^{17} + 81421213 x^{16} - 81421213 x^{15} - 410233883 x^{14} + 410233883 x^{13} + 1433472727 x^{12} - 1433472727 x^{11} - 3360164459 x^{10} + 3360164459 x^{9} + 4965626443 x^{8} - 4965626443 x^{7} - 4117054541 x^{6} + 4117054541 x^{5} + 1492836655 x^{4} - 1492836655 x^{3} - 125401190 x^{2} + 125401190 x + 13304911$ |
$28$ |
[28,0] |
$11^{14}\cdot 29^{27}$ |
$2$ |
$85.283662054$ |
$85.2836620539706$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$1525104928454641200$ |
| 28.28.145...625.1 |
$x^{28} - x^{27} - 57 x^{26} + 57 x^{25} + 1364 x^{24} - 1364 x^{23} - 17950 x^{22} + 18037 x^{21} + 142913 x^{20} - 145523 x^{19} - 713109 x^{18} + 743298 x^{17} + 2232740 x^{16} - 2405667 x^{15} - 4269698 x^{14} + 4803704 x^{13} + 4711051 x^{12} - 5646852 x^{11} - 2718459 x^{10} + 3724759 x^{9} + 602998 x^{8} - 1290327 x^{7} + 67136 x^{6} + 201056 x^{5} - 39932 x^{4} - 7831 x^{3} + 2582 x^{2} - 146 x + 1$ |
$28$ |
[28,0] |
$5^{21}\cdot 29^{27}$ |
$2$ |
$85.9799129786$ |
$85.97991297859014$ |
|
✓ |
|
$C_{28}$ (as 28T1) |
$[4]$ |
$2$ |
$27$ |
$1266343040764484400$ |
| 28.28.145...625.2 |
$x^{28} - x^{27} - 57 x^{26} + 57 x^{25} + 1364 x^{24} - 1364 x^{23} - 17950 x^{22} + 18037 x^{21} + 142913 x^{20} - 145523 x^{19} - 713109 x^{18} + 743298 x^{17} + 2232740 x^{16} - 2405812 x^{15} - 4269553 x^{14} + 4796744 x^{13} + 4718011 x^{12} - 5558257 x^{11} - 2806909 x^{10} + 3434904 x^{9} + 899378 x^{8} - 1037302 x^{7} - 179219 x^{6} + 128266 x^{5} + 22273 x^{4} - 2466 x^{3} - 463 x^{2} - x + 1$ |
$28$ |
[28,0] |
$5^{21}\cdot 29^{27}$ |
$2$ |
$85.9799129786$ |
$85.97991297859014$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
$[4]$ |
$2$ |
$27$ |
$238735871646007500$ |
| 28.0.391...376.1 |
$x^{28} + 87 x^{26} + 3393 x^{24} + 78300 x^{22} + 1188594 x^{20} + 12480237 x^{18} + 92787849 x^{16} + 491655096 x^{14} + 1843706610 x^{12} + 4793637186 x^{10} + 8325790902 x^{8} + 9082680984 x^{6} + 5609891196 x^{4} + 1618237845 x^{2} + 138706101$ |
$28$ |
[0,14] |
$2^{28}\cdot 3^{14}\cdot 29^{27}$ |
$3$ |
$89.07587989$ |
$89.07587989003858$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.120...701.1 |
$x^{28} - x^{27} + 88 x^{26} - 88 x^{25} + 3481 x^{24} - 3481 x^{23} + 81781 x^{22} - 81781 x^{21} + 1270375 x^{20} - 1270375 x^{19} + 13750612 x^{18} - 13750612 x^{17} + 106538461 x^{16} - 106538461 x^{15} + 598193557 x^{14} - 598193557 x^{13} + 2441900167 x^{12} - 2441900167 x^{11} + 7235537353 x^{10} - 7235537353 x^{9} + 15561328255 x^{8} - 15561328255 x^{7} + 24644009239 x^{6} - 24644009239 x^{5} + 30253900435 x^{4} - 30253900435 x^{3} + 31872138280 x^{2} - 31872138280 x + 32010844381$ |
$28$ |
[0,14] |
$13^{14}\cdot 29^{27}$ |
$2$ |
$92.7131152698$ |
$92.71311526981118$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.175...125.1 |
$x^{28} + 21 x^{26} - 21 x^{25} + 350 x^{24} + 875 x^{23} + 5964 x^{22} + 15191 x^{21} + 74431 x^{20} + 149541 x^{19} + 491337 x^{18} + 902447 x^{17} + 2521988 x^{16} + 4058887 x^{15} + 10825963 x^{14} + 16164904 x^{13} + 40448583 x^{12} + 53367559 x^{11} + 103699603 x^{10} + 109113760 x^{9} + 196642418 x^{8} + 95224249 x^{7} + 208289837 x^{6} + 114584232 x^{5} + 234771859 x^{4} + 151478789 x^{3} + 168609280 x^{2} + 76664532 x + 88529281$ |
$28$ |
[0,14] |
$5^{21}\cdot 7^{48}$ |
$2$ |
$93.9651909019$ |
$93.96519090194225$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[43793]$ |
$10$ |
$13$ |
$1494941023922.2002$ |
| 28.28.271...417.1 |
$x^{28} - x^{27} - 54 x^{26} + 49 x^{25} + 1225 x^{24} - 1001 x^{23} - 15311 x^{22} + 11161 x^{21} + 116343 x^{20} - 74822 x^{19} - 560240 x^{18} + 313492 x^{17} + 1732121 x^{16} - 830930 x^{15} - 3415294 x^{14} + 1402578 x^{13} + 4180450 x^{12} - 1539463 x^{11} - 3009246 x^{10} + 1130459 x^{9} + 1156658 x^{8} - 526380 x^{7} - 185425 x^{6} + 123876 x^{5} - 2990 x^{4} - 8671 x^{3} + 1761 x^{2} - 106 x + 1$ |
$28$ |
[28,0] |
$113^{27}$ |
$1$ |
$95.4452265981$ |
$95.44522659812843$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$5378761397781380000$ |
| 28.28.891...125.1 |
$x^{28} - x^{27} - 115 x^{26} + 115 x^{25} + 5917 x^{24} - 5917 x^{23} - 179683 x^{22} + 179683 x^{21} + 3576861 x^{20} - 3576861 x^{19} - 49014755 x^{18} + 49014755 x^{17} + 472328221 x^{16} - 472328221 x^{15} - 3210926051 x^{14} + 3210926051 x^{13} + 15205345309 x^{12} - 15205345309 x^{11} - 48637728739 x^{10} + 48637728739 x^{9} + 99209390109 x^{8} - 99209390109 x^{7} - 115840964579 x^{6} + 115840964579 x^{5} + 61259327517 x^{4} - 61259327517 x^{3} - 6856169443 x^{2} + 6856169443 x + 928458781$ |
$28$ |
[28,0] |
$3^{14}\cdot 5^{14}\cdot 29^{27}$ |
$3$ |
$99.5898612949$ |
$99.58986129486638$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.28.285...125.1 |
$x^{28} - 3 x^{27} - 76 x^{26} + 240 x^{25} + 2304 x^{24} - 7603 x^{23} - 36878 x^{22} + 128066 x^{21} + 343545 x^{20} - 1282732 x^{19} - 1916913 x^{18} + 8047861 x^{17} + 6204946 x^{16} - 32326986 x^{15} - 9514433 x^{14} + 82829451 x^{13} - 3555519 x^{12} - 130526538 x^{11} + 39192998 x^{10} + 114771575 x^{9} - 59689322 x^{8} - 42555117 x^{7} + 33120187 x^{6} - 652569 x^{5} - 2759285 x^{4} + 199864 x^{3} + 57190 x^{2} + 86 x - 59$ |
$28$ |
[28,0] |
$3^{14}\cdot 5^{21}\cdot 29^{24}$ |
$3$ |
$103.817873458$ |
$103.8178734580713$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$23509806182109426000$ |
| 28.0.514...461.1 |
$x^{28} - x^{27} + 117 x^{26} - 117 x^{25} + 6149 x^{24} - 6149 x^{23} + 191749 x^{22} - 191749 x^{21} + 3948293 x^{20} - 3948293 x^{19} + 56539909 x^{18} - 56539909 x^{17} + 577882885 x^{16} - 577882885 x^{15} + 4261137157 x^{14} - 4261137157 x^{13} + 22677408517 x^{12} - 22677408517 x^{11} + 86520482565 x^{10} - 86520482565 x^{9} + 234367601413 x^{8} - 234367601413 x^{7} + 449417956101 x^{6} - 449417956101 x^{5} + 626518248197 x^{4} - 626518248197 x^{3} + 694633745157 x^{2} - 694633745157 x + 702418373381$ |
$28$ |
[0,14] |
$17^{14}\cdot 29^{27}$ |
$2$ |
$106.021503491$ |
$106.02150349069831$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.28.857...125.1 |
$x^{28} - 84 x^{26} - 21 x^{25} + 2870 x^{24} + 1365 x^{23} - 52311 x^{22} - 35384 x^{21} + 558551 x^{20} + 476021 x^{19} - 3616123 x^{18} - 3640098 x^{17} + 14278698 x^{16} + 16439787 x^{15} - 33849902 x^{14} - 44286151 x^{13} + 45977568 x^{12} + 70220969 x^{11} - 31909787 x^{10} - 63232365 x^{9} + 7294518 x^{8} + 30363184 x^{7} + 2492042 x^{6} - 6990543 x^{5} - 1496096 x^{4} + 540274 x^{3} + 194915 x^{2} + 17822 x + 361$ |
$28$ |
[28,0] |
$5^{21}\cdot 7^{50}$ |
$2$ |
$107.976972437$ |
$107.9769724365677$ |
|
✓ |
|
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$98168811512269490000$ |
| 28.28.140...125.1 |
$x^{28} - x^{27} - 81 x^{26} + 98 x^{25} + 2666 x^{24} - 3722 x^{23} - 46935 x^{22} + 73335 x^{21} + 486583 x^{20} - 833426 x^{19} - 3079355 x^{18} + 5705690 x^{17} + 11981008 x^{16} - 23840492 x^{15} - 28489796 x^{14} + 60403709 x^{13} + 41941965 x^{12} - 91572889 x^{11} - 41957881 x^{10} + 83155937 x^{9} + 31487031 x^{8} - 43876845 x^{7} - 17209192 x^{6} + 11875118 x^{5} + 5608146 x^{4} - 990770 x^{3} - 732425 x^{2} - 84867 x - 2789$ |
$28$ |
[28,0] |
$5^{21}\cdot 43^{26}$ |
$2$ |
$109.90555421$ |
$109.90555421034314$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$34667735947885390000$ |
| 28.28.243...989.1 |
$x^{28} - x^{27} - 144 x^{26} + 144 x^{25} + 9281 x^{24} - 9281 x^{23} - 353219 x^{22} + 353219 x^{21} + 8818031 x^{20} - 8818031 x^{19} - 151678844 x^{18} + 151678844 x^{17} + 1837086781 x^{16} - 1837086781 x^{15} - 15726038219 x^{14} + 15726038219 x^{13} + 94043493031 x^{12} - 94043493031 x^{11} - 381624475719 x^{10} + 381624475719 x^{9} + 995309118031 x^{8} - 995309118031 x^{7} - 1508206506969 x^{6} + 1508206506969 x^{5} + 1068941930531 x^{4} - 1068941930531 x^{3} - 170071741344 x^{2} + 170071741344 x + 6930211781$ |
$28$ |
[28,0] |
$19^{14}\cdot 29^{27}$ |
$2$ |
$112.084690891$ |
$112.08469089097576$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.28.500...000.1 |
$x^{28} - 145 x^{26} + 9425 x^{24} - 362500 x^{22} + 9171250 x^{20} - 160496875 x^{18} + 1988765625 x^{16} - 17563125000 x^{14} + 109769531250 x^{12} - 475667968750 x^{10} + 1376933593750 x^{8} - 2503515625000 x^{6} + 2577148437500 x^{4} - 1239013671875 x^{2} + 177001953125$ |
$28$ |
[28,0] |
$2^{28}\cdot 5^{14}\cdot 29^{27}$ |
$3$ |
$114.996466454$ |
$114.99646645429719$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.0.990...029.1 |
$x^{28} - x^{27} + 146 x^{26} - 146 x^{25} + 9571 x^{24} - 9571 x^{23} + 372071 x^{22} - 372071 x^{21} + 9543321 x^{20} - 9543321 x^{19} + 170040196 x^{18} - 170040196 x^{17} + 2158805821 x^{16} - 2158805821 x^{15} + 19721930821 x^{14} - 19721930821 x^{13} + 129491462071 x^{12} - 129491462071 x^{11} + 605159430821 x^{10} - 605159430821 x^{9} + 1982093024571 x^{8} - 1982093024571 x^{7} + 4485608649571 x^{6} - 4485608649571 x^{5} + 7062757087071 x^{4} - 7062757087071 x^{3} + 8301770758946 x^{2} - 8301770758946 x + 8478772712071$ |
$28$ |
[0,14] |
$3^{14}\cdot 7^{14}\cdot 29^{27}$ |
$3$ |
$117.836313002$ |
$117.8363130016508$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.28.160...000.1 |
$x^{28} - 4 x^{27} - 77 x^{26} + 298 x^{25} + 2444 x^{24} - 9196 x^{23} - 42045 x^{22} + 154538 x^{21} + 436038 x^{20} - 1566292 x^{19} - 2887069 x^{18} + 10049582 x^{17} + 12680015 x^{16} - 41758048 x^{15} - 38007063 x^{14} + 112864436 x^{13} + 79251721 x^{12} - 195680358 x^{11} - 115037594 x^{10} + 209457056 x^{9} + 112205318 x^{8} - 127991098 x^{7} - 66955254 x^{6} + 37949294 x^{5} + 20053613 x^{4} - 3584684 x^{3} - 1768008 x^{2} + 148696 x + 31321$ |
$28$ |
[28,0] |
$2^{28}\cdot 5^{21}\cdot 29^{24}$ |
$3$ |
$119.878554375$ |
$119.87855437542395$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$258467010943663670000$ |
| 28.0.189...232.1 |
$x^{28} - 4 x^{27} - 14 x^{26} + 64 x^{25} + 191 x^{24} - 772 x^{23} - 690 x^{22} + 4028 x^{21} - 654 x^{20} - 16648 x^{19} + 22712 x^{18} + 37484 x^{17} + 113927 x^{16} + 252872 x^{15} + 1432704 x^{14} - 2924152 x^{13} + 10716934 x^{12} - 2935524 x^{11} + 20038 x^{10} + 11010404 x^{9} + 19222670 x^{8} - 54174868 x^{7} + 364501416 x^{6} - 435001108 x^{5} + 473363957 x^{4} - 376661420 x^{3} + 493240074 x^{2} - 18656684 x + 186649783$ |
$28$ |
[0,14] |
$2^{77}\cdot 29^{24}$ |
$2$ |
$120.591441419$ |
$120.59144141897728$ |
✓ |
✓ |
|
$C_{28}$ (as 28T1) |
$[2, 2, 772186]$ |
$2$ |
$13$ |
$297452739458.56445$ |
| 28.28.189...232.1 |
$x^{28} - 4 x^{27} - 70 x^{26} + 272 x^{25} + 2007 x^{24} - 7620 x^{23} - 31106 x^{22} + 115948 x^{21} + 290042 x^{20} - 1063528 x^{19} - 1718136 x^{18} + 6176908 x^{17} + 6666823 x^{16} - 23204920 x^{15} - 17269984 x^{14} + 56540840 x^{13} + 30251654 x^{12} - 88343908 x^{11} - 35706314 x^{10} + 86510324 x^{9} + 26775430 x^{8} - 51247828 x^{7} - 10970104 x^{6} + 17598492 x^{5} + 1821397 x^{4} - 3152012 x^{3} + 46562 x^{2} + 211268 x - 23953$ |
$28$ |
[28,0] |
$2^{77}\cdot 29^{24}$ |
$2$ |
$120.591441419$ |
$120.59144141897728$ |
|
✓ |
|
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$614883944308310100000$ |
| 28.0.309...253.1 |
$x^{28} - 3 x^{27} - 34 x^{26} + 144 x^{25} + 434 x^{24} - 2347 x^{23} - 1826 x^{22} + 20510 x^{21} - 1765 x^{20} - 109438 x^{19} + 155561 x^{18} + 274375 x^{17} - 755172 x^{16} + 932048 x^{15} - 239571 x^{14} - 6022955 x^{13} + 13616855 x^{12} - 2683804 x^{11} - 29709892 x^{10} + 50763183 x^{9} - 10828500 x^{8} + 60669907 x^{7} + 337407873 x^{6} - 138342771 x^{5} - 258957409 x^{4} - 71603500 x^{3} + 372018822 x^{2} + 287060780 x + 118082201$ |
$28$ |
[0,14] |
$13^{21}\cdot 29^{24}$ |
$2$ |
$122.727393985$ |
$122.7273939845637$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 14, 9422]$ |
$2$ |
$13$ |
$1523489837639.8035$ |
| 28.28.353...381.1 |
$x^{28} - x^{27} - 173 x^{26} + 173 x^{25} + 13399 x^{24} - 13399 x^{23} - 613001 x^{22} + 613001 x^{21} + 18404503 x^{20} - 18404503 x^{19} - 380963081 x^{18} + 380963081 x^{17} + 5557459255 x^{16} - 5557459255 x^{15} - 57374393033 x^{14} + 57374393033 x^{13} + 414614499127 x^{12} - 414614499127 x^{11} - 2039727740105 x^{10} + 2039727740105 x^{9} + 6485882143543 x^{8} - 6485882143543 x^{7} - 12115448511689 x^{6} + 12115448511689 x^{5} + 10862665827127 x^{4} - 10862665827127 x^{3} - 2393938599113 x^{2} + 2393938599113 x - 121377840329$ |
$28$ |
[28,0] |
$23^{14}\cdot 29^{27}$ |
$2$ |
$123.319971584$ |
$123.31997158416979$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$260881845825591150000$ |
| 28.28.642...384.1 |
$x^{28} - 174 x^{26} + 13572 x^{24} - 626400 x^{22} + 19017504 x^{20} - 399367584 x^{18} + 5938422336 x^{16} - 62931852288 x^{14} + 471988892160 x^{12} - 2454342239232 x^{10} + 8525609883648 x^{8} - 18601330655232 x^{6} + 22978114338816 x^{4} - 13256604426240 x^{2} + 2272560758784$ |
$28$ |
[28,0] |
$2^{42}\cdot 3^{14}\cdot 29^{27}$ |
$3$ |
$125.972317421$ |
$125.9723174208094$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.0.642...384.1 |
$x^{28} + 174 x^{26} + 13572 x^{24} + 626400 x^{22} + 19017504 x^{20} + 399367584 x^{18} + 5938422336 x^{16} + 62931852288 x^{14} + 471988892160 x^{12} + 2454342239232 x^{10} + 8525609883648 x^{8} + 18601330655232 x^{6} + 22978114338816 x^{4} + 13256604426240 x^{2} + 2272560758784$ |
$28$ |
[0,14] |
$2^{42}\cdot 3^{14}\cdot 29^{27}$ |
$3$ |
$125.972317421$ |
$125.9723174208094$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.128...125.1 |
$x^{28} - x^{27} + 31 x^{26} - 64 x^{25} + 743 x^{24} + 360 x^{23} + 14247 x^{22} + 17824 x^{21} + 211772 x^{20} + 351618 x^{19} + 2950835 x^{18} + 5926264 x^{17} + 35579743 x^{16} + 98555653 x^{15} + 337486035 x^{14} + 730923194 x^{13} + 2193380028 x^{12} + 3489008888 x^{11} + 6547998985 x^{10} + 8180911099 x^{9} + 13300322412 x^{8} - 1313161326 x^{7} + 8126173929 x^{6} - 251536057 x^{5} + 8464009280 x^{4} + 3624030723 x^{3} + 1759162063 x^{2} + 629981485 x + 352275361$ |
$28$ |
[0,14] |
$5^{21}\cdot 71^{24}$ |
$2$ |
$129.127984859$ |
$129.12798485937523$ |
✓ |
✓ |
|
$C_{28}$ (as 28T1) |
$[2, 2, 2, 2, 14, 2758]$ |
$10$ |
$13$ |
$18641852176931.93$ |
| 28.28.240...125.1 |
$x^{28} - x^{27} - 127 x^{26} + 122 x^{25} + 6844 x^{24} - 6239 x^{23} - 208000 x^{22} + 174427 x^{21} + 3978918 x^{20} - 2921373 x^{19} - 50486029 x^{18} + 30063653 x^{17} + 435121500 x^{16} - 184317982 x^{15} - 2557698883 x^{14} + 574396734 x^{13} + 10101792966 x^{12} - 102364842 x^{11} - 25756963009 x^{10} - 5196774016 x^{9} + 39074109508 x^{8} + 15087293028 x^{7} - 29974362484 x^{6} - 15060917194 x^{5} + 8518851558 x^{4} + 3872502094 x^{3} - 1071658158 x^{2} - 256197636 x + 42607381$ |
$28$ |
[28,0] |
$3^{14}\cdot 5^{21}\cdot 29^{26}$ |
$3$ |
$132.047179335$ |
$132.04717933511836$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2]$ |
$2$ |
$27$ |
$322489910135565840000$ |
| 28.0.555...896.1 |
$x^{28} + 203 x^{26} + 18473 x^{24} + 994700 x^{22} + 35232274 x^{20} + 863190713 x^{18} + 14974482369 x^{16} + 185139054744 x^{14} + 1619966729010 x^{12} + 9827798155994 x^{10} + 39828445158502 x^{8} + 101381496767096 x^{6} + 146108627693756 x^{4} + 98342345563105 x^{2} + 19668469112621$ |
$28$ |
[0,14] |
$2^{28}\cdot 7^{14}\cdot 29^{27}$ |
$3$ |
$136.065654064$ |
$136.06565406363217$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.28.231...789.1 |
$x^{28} - x^{27} - 231 x^{26} + 231 x^{25} + 23897 x^{24} - 23897 x^{23} - 1460903 x^{22} + 1460903 x^{21} + 58643801 x^{20} - 58643801 x^{19} - 1624287911 x^{18} + 1624287911 x^{17} + 31741662553 x^{16} - 31741662553 x^{15} - 439714884263 x^{14} + 439714884263 x^{13} + 4274850583897 x^{12} - 4274850583897 x^{11} - 28412803328679 x^{10} + 28412803328679 x^{9} + 122982646371673 x^{8} - 122982646371673 x^{7} - 317440480029351 x^{6} + 317440480029351 x^{5} + 407962316395865 x^{4} - 407962316395865 x^{3} - 150039834700455 x^{2} + 150039834700455 x - 22496485878439$ |
$28$ |
[28,0] |
$29^{27}\cdot 31^{14}$ |
$2$ |
$143.169446148$ |
$143.16944614794792$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.28.364...125.1 |
$x^{28} - 3 x^{27} - 100 x^{26} + 212 x^{25} + 4256 x^{24} - 5523 x^{23} - 99700 x^{22} + 59618 x^{21} + 1402407 x^{20} - 36832 x^{19} - 12199271 x^{18} - 5368181 x^{17} + 65218506 x^{16} + 54518578 x^{15} - 204434963 x^{14} - 248307765 x^{13} + 329592453 x^{12} + 566561234 x^{11} - 164293830 x^{10} - 586030579 x^{9} - 118191520 x^{8} + 199817979 x^{7} + 70371961 x^{6} - 24893187 x^{5} - 10823713 x^{4} + 572142 x^{3} + 491878 x^{2} + 43812 x + 811$ |
$28$ |
[28,0] |
$3^{14}\cdot 5^{21}\cdot 43^{24}$ |
$3$ |
$145.513722097$ |
$145.51372209723195$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$1634421464198991000000$ |
| 28.0.554...861.1 |
$x^{28} - x^{27} + 233 x^{26} - 233 x^{25} + 24361 x^{24} - 24361 x^{23} + 1509161 x^{22} - 1509161 x^{21} + 61613865 x^{20} - 61613865 x^{19} + 1744545577 x^{18} - 1744545577 x^{17} + 35110496041 x^{16} - 35110496041 x^{15} + 506567042857 x^{14} - 506567042857 x^{13} + 5221132511017 x^{12} - 5221132511017 x^{11} + 37908786423593 x^{10} - 37908786423593 x^{9} + 189304236123945 x^{8} - 189304236123945 x^{7} + 629727362524969 x^{6} - 629727362524969 x^{5} + 1355130158950185 x^{4} - 1355130158950185 x^{3} + 1913132310046505 x^{2} - 1913132310046505 x + 2040675658868521$ |
$28$ |
[0,14] |
$3^{14}\cdot 11^{14}\cdot 29^{27}$ |
$3$ |
$147.715635733$ |
$147.715635733011$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.696...625.1 |
$x^{28} - x^{27} + 88 x^{26} - 88 x^{25} + 3394 x^{24} - 3394 x^{23} + 75865 x^{22} - 80998 x^{21} + 1100638 x^{20} - 1451393 x^{19} + 11305361 x^{18} - 20452367 x^{17} + 85342680 x^{16} - 210052337 x^{15} + 497984202 x^{14} - 1476922586 x^{13} + 2539665866 x^{12} - 6840651052 x^{11} + 12213543141 x^{10} - 20170505866 x^{9} + 46647651823 x^{8} - 56641660997 x^{7} + 104743069711 x^{6} - 140023586864 x^{5} + 212356160468 x^{4} - 260927965161 x^{3} + 188267474927 x^{2} - 67387744281 x + 9200187361$ |
$28$ |
[0,14] |
$3^{14}\cdot 5^{21}\cdot 29^{27}$ |
$3$ |
$148.921577709$ |
$148.92157770926886$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.696...625.2 |
$x^{28} - x^{27} + 88 x^{26} - 88 x^{25} + 3394 x^{24} - 3394 x^{23} + 75865 x^{22} - 67948 x^{21} + 1087588 x^{20} - 790193 x^{19} + 10659821 x^{18} - 5999927 x^{17} + 78712410 x^{16} - 38454407 x^{15} + 503292507 x^{14} - 288729656 x^{13} + 2653721996 x^{12} - 2087317747 x^{11} + 11671511826 x^{10} - 12321166201 x^{9} + 39843676753 x^{8} - 39322573172 x^{7} + 96931321441 x^{6} - 93383072609 x^{5} + 163068261008 x^{4} - 47326599591 x^{3} + 119652295787 x^{2} + 25984132239 x + 24797115841$ |
$28$ |
[0,14] |
$3^{14}\cdot 5^{21}\cdot 29^{27}$ |
$3$ |
$148.921577709$ |
$148.92157770926886$ |
✓ |
✓ |
|
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.28.864...777.1 |
$x^{28} - 3 x^{27} - 90 x^{26} + 251 x^{25} + 3319 x^{24} - 8554 x^{23} - 66698 x^{22} + 158075 x^{21} + 814194 x^{20} - 1759929 x^{19} - 6351581 x^{18} + 12347113 x^{17} + 32407795 x^{16} - 55419172 x^{15} - 108806380 x^{14} + 158408220 x^{13} + 238211940 x^{12} - 281263173 x^{11} - 332007770 x^{10} + 294247369 x^{9} + 283623445 x^{8} - 164124215 x^{7} - 141255320 x^{6} + 39437768 x^{5} + 37970686 x^{4} - 617338 x^{3} - 4146895 x^{2} - 804372 x - 43367$ |
$28$ |
[28,0] |
$17^{21}\cdot 29^{24}$ |
$2$ |
$150.079263311$ |
$150.07926331072795$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$4582667171549212600000$ |
| 28.28.126...125.1 |
$x^{28} - x^{27} - 260 x^{26} + 260 x^{25} + 30277 x^{24} - 30277 x^{23} - 2083823 x^{22} + 2083823 x^{21} + 94192291 x^{20} - 94192291 x^{19} - 2938505300 x^{18} + 2938505300 x^{17} + 64703836621 x^{16} - 64703836621 x^{15} - 1010545858331 x^{14} + 1010545858331 x^{13} + 11086013209879 x^{12} - 11086013209879 x^{11} - 83267147522159 x^{10} + 83267147522159 x^{9} + 408362479450039 x^{8} - 408362479450039 x^{7} - 1200607208822609 x^{6} + 1200607208822609 x^{5} + 1780718978270827 x^{4} - 1780718978270827 x^{3} - 799274837483108 x^{2} + 799274837483108 x - 135847856289239$ |
$28$ |
[28,0] |
$5^{14}\cdot 7^{14}\cdot 29^{27}$ |
$3$ |
$152.126025945$ |
$152.126025944626$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$27$ |
|
| 28.28.134...000.1 |
$x^{28} - 145 x^{26} + 8555 x^{24} - 272600 x^{22} + 5210575 x^{20} - 62582000 x^{18} + 480954125 x^{16} - 2365022500 x^{14} + 7347186250 x^{12} - 14139312500 x^{10} + 16449434375 x^{8} - 11274656250 x^{6} + 4349546875 x^{4} - 854140625 x^{2} + 65703125$ |
$28$ |
[28,0] |
$2^{28}\cdot 5^{21}\cdot 29^{26}$ |
$3$ |
$152.47494907$ |
$152.47494906972275$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
$[2, 2]$ |
$2$ |
$27$ |
$1362591492474554000000$ |
| 28.28.159...112.1 |
$x^{28} - 116 x^{26} + 5162 x^{24} - 117160 x^{22} + 1511944 x^{20} - 11760544 x^{18} + 56876888 x^{16} - 173227904 x^{14} + 331475104 x^{12} - 392753728 x^{10} + 281553344 x^{8} - 117551616 x^{6} + 26535232 x^{4} - 2798848 x^{2} + 107648$ |
$28$ |
[28,0] |
$2^{77}\cdot 29^{26}$ |
$2$ |
$153.38167852$ |
$153.3816785195779$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
$[2]$ |
$2$ |
$27$ |
$2831606619659909500000$ |
| 28.0.159...112.1 |
$x^{28} + 116 x^{26} + 5162 x^{24} + 117160 x^{22} + 1511944 x^{20} + 11760544 x^{18} + 56876888 x^{16} + 173227904 x^{14} + 331475104 x^{12} + 392753728 x^{10} + 281553344 x^{8} + 117551616 x^{6} + 26535232 x^{4} + 2798848 x^{2} + 107648$ |
$28$ |
[0,14] |
$2^{77}\cdot 29^{26}$ |
$2$ |
$153.38167852$ |
$153.3816785195779$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.260...773.1 |
$x^{28} - x^{27} + 51 x^{26} - 64 x^{25} + 310 x^{24} - 1155 x^{23} - 7876 x^{22} - 36341 x^{21} - 5884 x^{20} - 28565 x^{19} + 2289507 x^{18} + 6735427 x^{17} + 12889086 x^{16} - 44127190 x^{15} - 68765767 x^{14} + 112739846 x^{13} - 244119948 x^{12} + 661911232 x^{11} + 656858657 x^{10} - 1574285300 x^{9} + 36632420 x^{8} - 3142097964 x^{7} + 12498470472 x^{6} - 11788049168 x^{5} + 11576546984 x^{4} - 220732122 x^{3} - 16100534512 x^{2} + 12497398748 x + 15073109483$ |
$28$ |
[0,14] |
$13^{21}\cdot 29^{26}$ |
$2$ |
$156.098421813$ |
$156.09842181323828$ |
✓ |
✓ |
|
$C_{28}$ (as 28T1) |
$[2, 2, 2, 2, 1801972]$ |
$2$ |
$13$ |
$1523489837639.8035$ |
| 28.28.404...125.1 |
$x^{28} - 3 x^{27} - 111 x^{26} + 355 x^{25} + 5014 x^{24} - 16873 x^{23} - 121463 x^{22} + 430221 x^{21} + 1739875 x^{20} - 6558612 x^{19} - 15281943 x^{18} + 62805921 x^{17} + 82351466 x^{16} - 386151006 x^{15} - 261479693 x^{14} + 1531368941 x^{13} + 426084076 x^{12} - 3886142713 x^{11} - 137358612 x^{10} + 6204587325 x^{9} - 603585672 x^{8} - 6078001902 x^{7} + 902850052 x^{6} + 3489342686 x^{5} - 463454290 x^{4} - 1069073901 x^{3} + 59014540 x^{2} + 137225481 x + 9342001$ |
$28$ |
[28,0] |
$5^{21}\cdot 7^{14}\cdot 29^{24}$ |
$3$ |
$158.584421204$ |
$158.58442120365285$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$9549725081294820000000$ |
| 28.28.837...125.1 |
$x^{28} - 7 x^{27} - 91 x^{26} + 623 x^{25} + 3640 x^{24} - 23205 x^{23} - 85141 x^{22} + 472657 x^{21} + 1298689 x^{20} - 5765676 x^{19} - 13490477 x^{18} + 43240799 x^{17} + 95742934 x^{16} - 195423844 x^{15} - 451889985 x^{14} + 487358557 x^{13} + 1342231212 x^{12} - 484759443 x^{11} - 2289033110 x^{10} - 289531417 x^{9} + 1935821398 x^{8} + 834820998 x^{7} - 668407222 x^{6} - 463370698 x^{5} + 34038536 x^{4} + 68490877 x^{3} + 8311506 x^{2} - 1013901 x - 63209$ |
$28$ |
[28,0] |
$3^{14}\cdot 5^{21}\cdot 7^{48}$ |
$3$ |
$162.752484785$ |
$162.7524847850728$ |
|
✓ |
? |
$C_{28}$ (as 28T1) |
trivial |
$2$ |
$27$ |
$16515401085022949000000$ |
| 28.0.892...613.1 |
$x^{28} - x^{27} + 4 x^{26} - 20 x^{25} + 110 x^{24} + 544 x^{23} - 1294 x^{22} + 5613 x^{21} + 45738 x^{20} + 7993 x^{19} - 127473 x^{18} + 913848 x^{17} + 1222711 x^{16} - 5830816 x^{15} + 905534 x^{14} + 26658338 x^{13} - 35698128 x^{12} - 34599131 x^{11} + 407111869 x^{10} + 111504745 x^{9} - 1148132126 x^{8} + 383663419 x^{7} + 2357319562 x^{6} - 93877796 x^{5} - 1271425197 x^{4} - 977493727 x^{3} - 474592366 x^{2} + 529082650 x + 493619587$ |
$28$ |
[0,14] |
$197^{27}$ |
$1$ |
$163.125179961$ |
$163.12517996059472$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
| 28.0.129...073.1 |
$x^{28} - x^{27} + 59 x^{26} - 64 x^{25} + 1338 x^{24} - 2583 x^{23} + 18024 x^{22} - 49859 x^{21} + 201884 x^{20} - 608973 x^{19} + 2001244 x^{18} - 5335265 x^{17} + 17538561 x^{16} - 32869029 x^{15} + 105198385 x^{14} - 175996687 x^{13} + 432226710 x^{12} - 906030787 x^{11} + 1606739712 x^{10} - 2466399578 x^{9} + 6832621830 x^{8} - 3024360615 x^{7} + 14632734546 x^{6} - 3903580904 x^{5} + 14821845636 x^{4} - 4978220620 x^{3} + 4490511812 x^{2} - 3736246457 x + 805522987$ |
$28$ |
[0,14] |
$3^{14}\cdot 113^{27}$ |
$2$ |
$165.315981808$ |
$165.31598180788282$ |
✓ |
✓ |
? |
$C_{28}$ (as 28T1) |
not computed |
$2$ |
$13$ |
|
