| 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 |
| 21.21.129...449.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - x^{14} + 2940 x^{13} + 14 x^{12} - 5733 x^{11} - 77 x^{10} + 7007 x^{9} + 210 x^{8} - 5147 x^{7} - 294 x^{6} + 2072 x^{5} + 196 x^{4} - 371 x^{3} - 49 x^{2} + 14 x + 1$ |
$21$ |
[21,0] |
$7^{38}$ |
$1$ |
$33.8240046076$ |
$33.82400460756605$ |
|
✓ |
✓ |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$1694541833.65$ |
| 21.21.467...001.1 |
$x^{21} - x^{20} - 20 x^{19} + 19 x^{18} + 171 x^{17} - 153 x^{16} - 816 x^{15} + 680 x^{14} + 2380 x^{13} - 1820 x^{12} - 4368 x^{11} + 3003 x^{10} + 5005 x^{9} - 3003 x^{8} - 3432 x^{7} + 1716 x^{6} + 1287 x^{5} - 495 x^{4} - 220 x^{3} + 55 x^{2} + 11 x - 1$ |
$21$ |
[21,0] |
$43^{20}$ |
$1$ |
$35.9487872153$ |
$35.948787215302666$ |
|
✓ |
✓ |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$2620717953.48$ |
| 21.21.142...689.1 |
$x^{21} - 4 x^{20} - 46 x^{19} + 192 x^{18} + 752 x^{17} - 3392 x^{16} - 5652 x^{15} + 29504 x^{14} + 19392 x^{13} - 138787 x^{12} - 17833 x^{11} + 362514 x^{10} - 59599 x^{9} - 524134 x^{8} + 180953 x^{7} + 401883 x^{6} - 198823 x^{5} - 141878 x^{4} + 97061 x^{3} + 10664 x^{2} - 16800 x + 2843$ |
$21$ |
[21,0] |
$7^{14}\cdot 29^{18}$ |
$2$ |
$65.5968057063$ |
$65.59680570632788$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$2231765965710$ |
| 21.21.481...721.1 |
$x^{21} - 3 x^{20} - 54 x^{19} + 142 x^{18} + 1131 x^{17} - 2619 x^{16} - 12066 x^{15} + 24246 x^{14} + 72072 x^{13} - 121339 x^{12} - 250395 x^{11} + 331947 x^{10} + 508726 x^{9} - 470445 x^{8} - 589995 x^{7} + 290104 x^{6} + 363423 x^{5} - 39813 x^{4} - 91517 x^{3} - 11880 x^{2} + 3264 x + 289$ |
$21$ |
[21,0] |
$3^{28}\cdot 29^{18}$ |
$2$ |
$77.5614056385$ |
$77.56140563852703$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$25788034339300$ |
| 21.21.171...001.1 |
$x^{21} - 4 x^{20} - 64 x^{19} + 186 x^{18} + 1724 x^{17} - 3096 x^{16} - 24588 x^{15} + 21110 x^{14} + 195304 x^{13} - 27551 x^{12} - 844197 x^{11} - 320638 x^{10} + 1805255 x^{9} + 1352446 x^{8} - 1520495 x^{7} - 1550169 x^{6} + 381991 x^{5} + 548114 x^{4} - 51323 x^{3} - 71820 x^{2} + 6678 x + 1757$ |
$21$ |
[21,0] |
$7^{14}\cdot 43^{18}$ |
$2$ |
$91.9421197726$ |
$91.94211977258162$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$140330847878000$ |
| 21.21.828...529.1 |
$x^{21} - 4 x^{20} - 60 x^{19} + 224 x^{18} + 1382 x^{17} - 4786 x^{16} - 16074 x^{15} + 51216 x^{14} + 104984 x^{13} - 301449 x^{12} - 405653 x^{11} + 1007842 x^{10} + 952245 x^{9} - 1910342 x^{8} - 1353475 x^{7} + 1951543 x^{6} + 1093353 x^{5} - 915746 x^{4} - 403833 x^{3} + 109604 x^{2} + 19366 x + 521$ |
$21$ |
[21,0] |
$13^{14}\cdot 29^{18}$ |
$2$ |
$99.1089556288$ |
$99.10895562881393$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$117685929270000$ |
| 21.21.119...201.1 |
$x^{21} - x^{20} - 60 x^{19} + 133 x^{18} + 1305 x^{17} - 4493 x^{16} - 10801 x^{15} + 62425 x^{14} - 2588 x^{13} - 380273 x^{12} + 489841 x^{11} + 832624 x^{10} - 2307149 x^{9} + 540263 x^{8} + 3165855 x^{7} - 3188668 x^{6} - 157753 x^{5} + 1481414 x^{4} - 380716 x^{3} - 205872 x^{2} + 50035 x + 14459$ |
$21$ |
[21,0] |
$127^{20}$ |
$1$ |
$100.837621071$ |
$100.83762107060207$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$399125736989601.2$ |
| 21.21.577...689.1 |
$x^{21} - 3 x^{20} - 72 x^{19} + 262 x^{18} + 1785 x^{17} - 7923 x^{16} - 17502 x^{15} + 107772 x^{14} + 38604 x^{13} - 717609 x^{12} + 440313 x^{11} + 2251605 x^{10} - 3001988 x^{9} - 2337081 x^{8} + 6238701 x^{7} - 1893950 x^{6} - 3157635 x^{5} + 2597691 x^{4} - 495851 x^{3} - 66246 x^{2} + 18912 x + 251$ |
$21$ |
[21,0] |
$3^{28}\cdot 43^{18}$ |
$2$ |
$108.712001601$ |
$108.71200160070175$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$520470899652557.25$ |
| 21.21.606...561.1 |
$x^{21} - 84 x^{19} - 56 x^{18} + 2730 x^{17} + 3234 x^{16} - 43722 x^{15} - 70242 x^{14} + 365904 x^{13} + 743141 x^{12} - 1518279 x^{11} - 4067070 x^{10} + 2152563 x^{9} + 10909626 x^{8} + 3233979 x^{7} - 11269811 x^{6} - 9277107 x^{5} + 1051050 x^{4} + 3366867 x^{3} + 948738 x^{2} - 66192 x - 38809$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{36}$ |
$2$ |
$121.590927175$ |
$121.59092717489902$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$2419977962290507.0$ |
| 21.21.168...481.1 |
$x^{21} - 4 x^{20} - 74 x^{19} + 326 x^{18} + 1940 x^{17} - 9666 x^{16} - 22526 x^{15} + 138634 x^{14} + 103892 x^{13} - 1050735 x^{12} + 79957 x^{11} + 4265962 x^{10} - 2409705 x^{9} - 8725818 x^{8} + 7775839 x^{7} + 7456241 x^{6} - 8733417 x^{5} - 1687630 x^{4} + 3268313 x^{3} - 336298 x^{2} - 152624 x + 21401$ |
$21$ |
[21,0] |
$19^{14}\cdot 29^{18}$ |
$2$ |
$127.639883413$ |
$127.63988341292236$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$1584733822664509.5$ |
| 21.21.316...849.1 |
$x^{21} - x^{20} - 106 x^{19} + 19 x^{18} + 4514 x^{17} + 2212 x^{16} - 98469 x^{15} - 101273 x^{14} + 1161058 x^{13} + 1687220 x^{12} - 7173629 x^{11} - 12696230 x^{10} + 21408857 x^{9} + 41742773 x^{8} - 33331528 x^{7} - 62993456 x^{6} + 29458695 x^{5} + 39416874 x^{4} - 12941586 x^{3} - 5181015 x^{2} - 313502 x + 8771$ |
$21$ |
[21,0] |
$7^{14}\cdot 43^{20}$ |
$2$ |
$131.547602325$ |
$131.54760232535784$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$2941850439885216.0$ |
| 21.21.316...849.2 |
$x^{21} - x^{20} - 106 x^{19} + 19 x^{18} + 4514 x^{17} + 2212 x^{16} - 98469 x^{15} - 98564 x^{14} + 1181526 x^{13} + 1663441 x^{12} - 7722653 x^{11} - 13739797 x^{10} + 24767415 x^{9} + 55808804 x^{8} - 26783273 x^{7} - 97849256 x^{6} - 9722475 x^{5} + 58173689 x^{4} + 9727326 x^{3} - 14175798 x^{2} - 678013 x + 910567$ |
$21$ |
[21,0] |
$7^{14}\cdot 43^{20}$ |
$2$ |
$131.547602325$ |
$131.54760232535784$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$2201310310593683.5$ |
| 21.21.994...561.1 |
$x^{21} - 4 x^{20} - 78 x^{19} + 218 x^{18} + 2534 x^{17} - 4502 x^{16} - 43774 x^{15} + 43542 x^{14} + 429292 x^{13} - 196925 x^{12} - 2399473 x^{11} + 392282 x^{10} + 7477031 x^{9} - 739098 x^{8} - 12783623 x^{7} + 2345155 x^{6} + 10795899 x^{5} - 3647782 x^{4} - 2993437 x^{3} + 1434512 x^{2} - 61380 x - 23557$ |
$21$ |
[21,0] |
$13^{14}\cdot 43^{18}$ |
$2$ |
$138.913585362$ |
$138.91358536199056$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$4188365147703962.5$ |
| 21.21.142...889.1 |
$x^{21} - 4 x^{20} - 100 x^{19} + 456 x^{18} + 3776 x^{17} - 20240 x^{16} - 65058 x^{15} + 451646 x^{14} + 423688 x^{13} - 5452225 x^{12} + 1655193 x^{11} + 35371490 x^{10} - 39386623 x^{9} - 111354014 x^{8} + 208156183 x^{7} + 105332901 x^{6} - 422345627 x^{5} + 144428798 x^{4} + 234723315 x^{3} - 152780306 x^{2} - 25641148 x + 26494201$ |
$21$ |
[21,0] |
$7^{14}\cdot 71^{18}$ |
$2$ |
$141.316074058$ |
$141.31607405847367$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$4244799371179891.5$ |
| 21.21.297...489.1 |
$x^{21} - 126 x^{19} - 126 x^{18} + 6174 x^{17} + 11760 x^{16} - 145530 x^{15} - 403956 x^{14} + 1638168 x^{13} + 6429192 x^{12} - 6395823 x^{11} - 48369027 x^{10} - 21758891 x^{9} + 148886451 x^{8} + 200914581 x^{7} - 81540704 x^{6} - 293313510 x^{5} - 130714458 x^{4} + 46911963 x^{3} + 32454954 x^{2} - 2195739 x - 1148581$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{38}$ |
$2$ |
$146.347968334$ |
$146.3479683340138$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$7412107993664674.0$ |
| 21.21.297...489.2 |
$x^{21} - 126 x^{19} - 63 x^{18} + 6174 x^{17} + 5145 x^{16} - 151263 x^{15} - 153909 x^{14} + 2036391 x^{13} + 2323482 x^{12} - 15568182 x^{11} - 19772382 x^{10} + 67561690 x^{9} + 96070968 x^{8} - 159797400 x^{7} - 258336281 x^{6} + 184053996 x^{5} + 356224953 x^{4} - 78664992 x^{3} - 218834343 x^{2} + 6835059 x + 48473999$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{38}$ |
$2$ |
$146.347968334$ |
$146.3479683340138$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$2623927281262563.0$ |
| 21.21.104...689.1 |
$x^{21} - 7 x^{20} - 70 x^{19} + 462 x^{18} + 2135 x^{17} - 12411 x^{16} - 36610 x^{15} + 175044 x^{14} + 373940 x^{13} - 1403661 x^{12} - 2218069 x^{11} + 6566007 x^{10} + 6982234 x^{9} - 17907827 x^{8} - 9448729 x^{7} + 26548844 x^{6} + 686581 x^{5} - 16732429 x^{4} + 5281647 x^{3} + 1717044 x^{2} - 573440 x - 71167$ |
$21$ |
[21,0] |
$7^{36}\cdot 13^{14}$ |
$2$ |
$155.370441098$ |
$155.37044109805885$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$24318621275742050$ |
| 21.21.106...961.1 |
$x^{21} - 129 x^{19} - 86 x^{18} + 6579 x^{17} + 7998 x^{16} - 169635 x^{15} - 282897 x^{14} + 2351541 x^{13} + 4822837 x^{12} - 17262522 x^{11} - 42117210 x^{10} + 60860609 x^{9} + 187574256 x^{8} - 66235308 x^{7} - 399918748 x^{6} - 118626723 x^{5} + 303277839 x^{4} + 245278579 x^{3} + 53399808 x^{2} - 44247 x - 722701$ |
$21$ |
[21,0] |
$3^{28}\cdot 43^{20}$ |
$2$ |
$155.541368743$ |
$155.5413687430282$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$104145016649537420$ |
| 21.21.106...961.2 |
$x^{21} - 129 x^{19} - 86 x^{18} + 6579 x^{17} + 7998 x^{16} - 169635 x^{15} - 279414 x^{14} + 2373600 x^{13} + 4785298 x^{12} - 17868564 x^{11} - 43218999 x^{10} + 64742219 x^{9} + 202286448 x^{8} - 64709754 x^{7} - 440981770 x^{6} - 148287951 x^{5} + 334614390 x^{4} + 261995044 x^{3} + 27998289 x^{2} - 12075690 x + 521117$ |
$21$ |
[21,0] |
$3^{28}\cdot 43^{20}$ |
$2$ |
$155.541368743$ |
$155.5413687430282$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$3551271732999900.0$ |
| 21.21.305...201.1 |
$x^{21} - x^{20} - 100 x^{19} + 67 x^{18} + 3859 x^{17} - 1091 x^{16} - 75232 x^{15} - 6133 x^{14} + 794170 x^{13} + 286211 x^{12} - 4477546 x^{11} - 2182156 x^{10} + 12688535 x^{9} + 4651760 x^{8} - 18320520 x^{7} - 1508898 x^{6} + 11921203 x^{5} - 2662713 x^{4} - 1452380 x^{3} + 378406 x^{2} - 6036 x - 1759$ |
$21$ |
[21,0] |
$211^{20}$ |
$1$ |
$163.531845679$ |
$163.5318456792314$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$66095963290529660$ |
| 21.21.480...521.1 |
$x^{21} - 3 x^{20} - 108 x^{19} + 220 x^{18} + 4893 x^{17} - 5637 x^{16} - 119292 x^{15} + 48774 x^{14} + 1686642 x^{13} + 326899 x^{12} - 13945275 x^{11} - 9596163 x^{10} + 64179378 x^{9} + 72399831 x^{8} - 139946343 x^{7} - 231646188 x^{6} + 66234471 x^{5} + 266883405 x^{4} + 109853705 x^{3} - 40148160 x^{2} - 34962030 x - 5904559$ |
$21$ |
[21,0] |
$3^{28}\cdot 71^{18}$ |
$2$ |
$167.091571385$ |
$167.09157138479483$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$82999008884616240$ |
| 21.21.159...681.1 |
$x^{21} - 4 x^{20} - 102 x^{19} + 425 x^{18} + 3920 x^{17} - 17149 x^{16} - 73530 x^{15} + 346443 x^{14} + 712451 x^{13} - 3821466 x^{12} - 3325067 x^{11} + 23337412 x^{10} + 4524633 x^{9} - 75328115 x^{8} + 12733514 x^{7} + 114123433 x^{6} - 29226462 x^{5} - 71499935 x^{4} + 6060357 x^{3} + 17526365 x^{2} + 3735328 x + 144611$ |
$21$ |
[21,0] |
$29^{18}\cdot 31^{14}$ |
$2$ |
$176.898897984$ |
$176.89889798439629$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$51659455204894376$ |
| 21.21.201...529.1 |
$x^{21} - 4 x^{20} - 92 x^{19} + 320 x^{18} + 3272 x^{17} - 9934 x^{16} - 56698 x^{15} + 153364 x^{14} + 503792 x^{13} - 1226011 x^{12} - 2281327 x^{11} + 4808330 x^{10} + 5496701 x^{9} - 8919502 x^{8} - 7230861 x^{7} + 7111669 x^{6} + 4936501 x^{5} - 2093106 x^{4} - 1493691 x^{3} + 73346 x^{2} + 122402 x + 12691$ |
$21$ |
[21,0] |
$19^{14}\cdot 43^{18}$ |
$2$ |
$178.903245701$ |
$178.90324570144705$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$1907344761740974800$ |
| 21.21.511...761.1 |
$x^{21} - 189 x^{19} - 154 x^{18} + 14364 x^{17} + 22050 x^{16} - 563108 x^{15} - 1214079 x^{14} + 12183605 x^{13} + 33155136 x^{12} - 143285772 x^{11} - 476613326 x^{10} + 825207138 x^{9} + 3516028369 x^{8} - 1670183867 x^{7} - 12232226328 x^{6} - 1210816971 x^{5} + 16657769884 x^{4} + 4239732917 x^{3} - 4978400147 x^{2} - 940891777 x + 36861817$ |
$21$ |
[21,0] |
$7^{38}\cdot 13^{14}$ |
$2$ |
$187.005304772$ |
$187.0053047720693$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$108700043286586450$ |
| 21.21.511...761.2 |
$x^{21} - 189 x^{19} - 63 x^{18} + 14273 x^{17} + 7672 x^{16} - 559650 x^{15} - 347577 x^{14} + 12591922 x^{13} + 7983444 x^{12} - 170719178 x^{11} - 106682856 x^{10} + 1419969761 x^{9} + 876942010 x^{8} - 7150956164 x^{7} - 4423657378 x^{6} + 20583982601 x^{5} + 12754970620 x^{4} - 29178026367 x^{3} - 16933928459 x^{2} + 12876797381 x + 3691462039$ |
$21$ |
[21,0] |
$7^{38}\cdot 13^{14}$ |
$2$ |
$187.005304772$ |
$187.0053047720693$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$28334278031696510$ |
| 21.21.183...289.1 |
$x^{21} - x^{20} - 192 x^{19} + 277 x^{18} + 14834 x^{17} - 26598 x^{16} - 597785 x^{15} + 1228287 x^{14} + 13705276 x^{13} - 30630118 x^{12} - 184175217 x^{11} + 434797030 x^{10} + 1426797465 x^{9} - 3526931287 x^{8} - 5827035514 x^{7} + 15440417206 x^{6} + 9213729365 x^{5} - 30297922744 x^{4} + 2645891174 x^{3} + 12032834277 x^{2} - 399661124 x - 1092874069$ |
$21$ |
[21,0] |
$13^{14}\cdot 43^{20}$ |
$2$ |
$198.752749338$ |
$198.75274933826643$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$1940642799270161000$ |
| 21.21.183...289.2 |
$x^{21} - x^{20} - 192 x^{19} + 277 x^{18} + 14834 x^{17} - 26598 x^{16} - 597785 x^{15} + 1210958 x^{14} + 13738816 x^{13} - 29260009 x^{12} - 186891957 x^{11} + 392209615 x^{10} + 1521281881 x^{9} - 2924408106 x^{8} - 7272568707 x^{7} + 11518541404 x^{6} + 19001737751 x^{5} - 20453992557 x^{4} - 21439276738 x^{3} + 9354769810 x^{2} + 732657661 x - 357231187$ |
$21$ |
[21,0] |
$13^{14}\cdot 43^{20}$ |
$2$ |
$198.752749338$ |
$198.75274933826643$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$47107157976503970$ |
| 21.21.211...721.1 |
$x^{21} - 7 x^{20} - 84 x^{19} + 602 x^{18} + 2639 x^{17} - 19901 x^{16} - 37646 x^{15} + 319090 x^{14} + 232456 x^{13} - 2582937 x^{12} - 497623 x^{11} + 10297315 x^{10} + 976654 x^{9} - 20496567 x^{8} - 4195819 x^{7} + 18273234 x^{6} + 6621433 x^{5} - 4948475 x^{4} - 1775109 x^{3} + 562184 x^{2} + 131824 x - 26753$ |
$21$ |
[21,0] |
$7^{36}\cdot 19^{14}$ |
$2$ |
$200.097608352$ |
$200.09760835180217$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$832088128597863300$ |
| 21.21.612...121.1 |
$x^{21} - 4 x^{20} - 154 x^{19} + 792 x^{18} + 7952 x^{17} - 51926 x^{16} - 145220 x^{15} + 1418338 x^{14} + 61944 x^{13} - 16336335 x^{12} + 18143395 x^{11} + 79537118 x^{10} - 132545343 x^{9} - 176540462 x^{8} + 368567997 x^{7} + 170444833 x^{6} - 445036167 x^{5} - 52948234 x^{4} + 208339119 x^{3} - 3670640 x^{2} - 25278358 x + 1626227$ |
$21$ |
[21,0] |
$7^{14}\cdot 113^{18}$ |
$2$ |
$210.465161204$ |
$210.46516120423587$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$350292924482315400$ |
| 21.21.827...729.1 |
$x^{21} - 4 x^{20} - 114 x^{19} + 488 x^{18} + 4946 x^{17} - 23362 x^{16} - 100260 x^{15} + 557394 x^{14} + 893184 x^{13} - 6986867 x^{12} - 1446343 x^{11} + 45520578 x^{10} - 23590055 x^{9} - 154124034 x^{8} + 143234027 x^{7} + 261729665 x^{6} - 315720051 x^{5} - 199051958 x^{4} + 300106465 x^{3} + 36273150 x^{2} - 102144250 x + 15389375$ |
$21$ |
[21,0] |
$13^{14}\cdot 71^{18}$ |
$2$ |
$213.511745926$ |
$213.5117459255851$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$30398950792448647000$ |
| 21.21.501...881.1 |
$x^{21} - 4 x^{20} - 172 x^{19} + 666 x^{18} + 11408 x^{17} - 43140 x^{16} - 378976 x^{15} + 1422996 x^{14} + 6835412 x^{13} - 26070729 x^{12} - 67235959 x^{11} + 269546118 x^{10} + 339303301 x^{9} - 1526878622 x^{8} - 740975509 x^{7} + 4442293901 x^{6} + 269281123 x^{5} - 5893987054 x^{4} + 618720777 x^{3} + 3268069590 x^{2} - 387607364 x - 585814321$ |
$21$ |
[21,0] |
$7^{14}\cdot 127^{18}$ |
$2$ |
$232.626413797$ |
$232.62641379733722$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$688733692772026100$ |
| 21.21.103...329.1 |
$x^{21} - 273 x^{19} - 707 x^{18} + 28329 x^{17} + 138600 x^{16} - 1256010 x^{15} - 9720649 x^{14} + 15415400 x^{13} + 295555148 x^{12} + 459394712 x^{11} - 3492190380 x^{10} - 14219288965 x^{9} - 1746076850 x^{8} + 95156654696 x^{7} + 227577402612 x^{6} + 180231411857 x^{5} - 72622185076 x^{4} - 206563651595 x^{3} - 96402059663 x^{2} + 11414547333 x + 12861176609$ |
$21$ |
[21,0] |
$7^{38}\cdot 19^{14}$ |
$2$ |
$240.839338355$ |
$240.83933835506394$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$1030828564219823600$ |
| 21.21.103...329.2 |
$x^{21} - 273 x^{19} - 574 x^{18} + 28462 x^{17} + 108276 x^{16} - 1365336 x^{15} - 7387297 x^{14} + 29273335 x^{13} + 236399408 x^{12} - 136995908 x^{11} - 3677713942 x^{10} - 4292878786 x^{9} + 24629746463 x^{8} + 60756994317 x^{7} - 36501637424 x^{6} - 239196844705 x^{5} - 155322145538 x^{4} + 236480949201 x^{3} + 369969955635 x^{2} + 170427535873 x + 24521880853$ |
$21$ |
[21,0] |
$7^{38}\cdot 19^{14}$ |
$2$ |
$240.839338355$ |
$240.83933835506394$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$644113238376879900$ |
| 21.21.356...801.1 |
$x^{21} - x^{20} - 160 x^{19} + 75 x^{18} + 9107 x^{17} - 4485 x^{16} - 253705 x^{15} + 195358 x^{14} + 3811310 x^{13} - 4575964 x^{12} - 30765519 x^{11} + 53760107 x^{10} + 115833483 x^{9} - 301059030 x^{8} - 85146670 x^{7} + 682493117 x^{6} - 370577748 x^{5} - 444734752 x^{4} + 545440112 x^{3} - 159561140 x^{2} - 12506848 x + 7333121$ |
$21$ |
[21,0] |
$337^{20}$ |
$1$ |
$255.426864524$ |
$255.4268645244068$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$3025545659707238400$ |
| 21.21.373...121.1 |
$x^{21} - x^{20} - 278 x^{19} - 325 x^{18} + 30572 x^{17} + 90706 x^{16} - 1619293 x^{15} - 7475214 x^{14} + 39793032 x^{13} + 274015207 x^{12} - 273602661 x^{11} - 4607226493 x^{10} - 4412589549 x^{9} + 30914338952 x^{8} + 60233241889 x^{7} - 74040616576 x^{6} - 218112157253 x^{5} + 55980136111 x^{4} + 294993180914 x^{3} - 10861258704 x^{2} - 116080052977 x - 14284976423$ |
$21$ |
[21,0] |
$19^{14}\cdot 43^{20}$ |
$2$ |
$255.96857108$ |
$255.9685710799544$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$864898073802425300$ |
| 21.21.373...121.2 |
$x^{21} - x^{20} - 278 x^{19} - 325 x^{18} + 30572 x^{17} + 90706 x^{16} - 1619293 x^{15} - 7441717 x^{14} + 40623104 x^{13} + 278806912 x^{12} - 309578439 x^{11} - 5095633178 x^{10} - 5354762119 x^{9} + 40289615751 x^{8} + 110934247984 x^{7} - 35893590814 x^{6} - 526207863829 x^{5} - 789731658124 x^{4} - 300252270554 x^{3} + 314047983523 x^{2} + 333487382586 x + 88392158713$ |
$21$ |
[21,0] |
$19^{14}\cdot 43^{20}$ |
$2$ |
$255.96857108$ |
$255.9685710799544$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$725348753199178600$ |
| 21.21.200...921.1 |
$x^{21} - 7 x^{20} - 112 x^{19} + 777 x^{18} + 4781 x^{17} - 33873 x^{16} - 95998 x^{15} + 737571 x^{14} + 879809 x^{13} - 8504538 x^{12} - 2454739 x^{11} + 52185714 x^{10} - 9150197 x^{9} - 173794943 x^{8} + 70295426 x^{7} + 311945270 x^{6} - 155083208 x^{5} - 285286645 x^{4} + 142672320 x^{3} + 109049556 x^{2} - 46336661 x - 5373811$ |
$21$ |
[21,0] |
$7^{36}\cdot 31^{14}$ |
$2$ |
$277.319639131$ |
$277.3196391306286$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$7030134349554524000$ |
| 21.21.326...129.1 |
$x^{21} - 3 x^{20} - 180 x^{19} + 246 x^{18} + 13731 x^{17} + 1647 x^{16} - 557982 x^{15} - 788016 x^{14} + 12481956 x^{13} + 32581845 x^{12} - 140147985 x^{11} - 580762089 x^{10} + 459856514 x^{9} + 4704604611 x^{8} + 3799626111 x^{7} - 13678950530 x^{6} - 26746513641 x^{5} - 2530942323 x^{4} + 29275076935 x^{3} + 22576339788 x^{2} + 2145270072 x - 1693276957$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{14}\cdot 29^{18}$ |
$3$ |
$283.82089453$ |
$283.82089453046984$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$1679101587664927000$ |
| 21.21.326...129.2 |
$x^{21} - 3 x^{20} - 180 x^{19} + 295 x^{18} + 13605 x^{17} - 5157 x^{16} - 551346 x^{15} - 398277 x^{14} + 12659553 x^{13} + 21281696 x^{12} - 159042903 x^{11} - 417305250 x^{10} + 922946239 x^{9} + 3784485999 x^{8} - 675851490 x^{7} - 14780825192 x^{6} - 12395275152 x^{5} + 16098793473 x^{4} + 29396147584 x^{3} + 14346185940 x^{2} + 2403226995 x + 72232579$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{14}\cdot 29^{18}$ |
$3$ |
$283.82089453$ |
$283.82089453046984$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$4220636828185508400$ |
| 21.21.373...401.1 |
$x^{21} - x^{20} - 180 x^{19} + 325 x^{18} + 12681 x^{17} - 28085 x^{16} - 466147 x^{15} + 1104481 x^{14} + 9994129 x^{13} - 23230778 x^{12} - 131326631 x^{11} + 274701966 x^{10} + 1071723493 x^{9} - 1796606075 x^{8} - 5285574412 x^{7} + 5900535983 x^{6} + 14227077020 x^{5} - 7395125885 x^{4} - 15613111936 x^{3} + 1522403319 x^{2} + 2278571400 x - 206124161$ |
$21$ |
[21,0] |
$379^{20}$ |
$1$ |
$285.658312714$ |
$285.6583127137164$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$6959071739608064000$ |
| 21.21.305...401.1 |
$x^{21} - x^{20} - 200 x^{19} + 67 x^{18} + 16134 x^{17} + 828 x^{16} - 697221 x^{15} - 222713 x^{14} + 17859943 x^{13} + 9863681 x^{12} - 280861686 x^{11} - 223777460 x^{10} + 2686381285 x^{9} + 2906746078 x^{8} - 14625774577 x^{7} - 21119020890 x^{6} + 36814363818 x^{5} + 75239240850 x^{4} - 8634241360 x^{3} - 86032090549 x^{2} - 56191978934 x - 10850554247$ |
$21$ |
[21,0] |
$421^{20}$ |
$1$ |
$315.73031417$ |
$315.7303141696199$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$262575512314938100000$ |
| 21.21.983...129.1 |
$x^{21} - 441 x^{19} - 938 x^{18} + 74949 x^{17} + 303702 x^{16} - 5958638 x^{15} - 35693127 x^{14} + 209014400 x^{13} + 1889261640 x^{12} - 1478858493 x^{11} - 45340006873 x^{10} - 78589262157 x^{9} + 392624985032 x^{8} + 1524423979489 x^{7} + 495742766778 x^{6} - 5115634476204 x^{5} - 7304874384850 x^{4} + 1192289177177 x^{3} + 7245219154649 x^{2} + 2766193463894 x - 330316678789$ |
$21$ |
[21,0] |
$7^{38}\cdot 31^{14}$ |
$2$ |
$333.784491235$ |
$333.7844912351955$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$17576256199406360000$ |
| 21.21.983...129.2 |
$x^{21} - 441 x^{19} - 504 x^{18} + 75383 x^{17} + 143990 x^{16} - 6403488 x^{15} - 15018669 x^{14} + 295491070 x^{13} + 777025536 x^{12} - 7503654305 x^{11} - 21936726567 x^{10} + 99101537213 x^{9} + 338432862404 x^{8} - 543595119755 x^{7} - 2634639635474 x^{6} - 388511337004 x^{5} + 7568631421988 x^{4} + 10342548829935 x^{3} + 4902119383049 x^{2} + 606314747948 x - 64432726399$ |
$21$ |
[21,0] |
$7^{38}\cdot 31^{14}$ |
$2$ |
$333.784491235$ |
$333.7844912351955$ |
|
✓ |
|
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$97078377381360090000$ |
| 21.21.135...961.1 |
$x^{21} - 4 x^{20} - 262 x^{19} + 498 x^{18} + 28760 x^{17} - 1460 x^{16} - 1645358 x^{15} - 2346530 x^{14} + 50774140 x^{13} + 131954593 x^{12} - 804361037 x^{11} - 2979538158 x^{10} + 5552672841 x^{9} + 30745724450 x^{8} - 7081032431 x^{7} - 143924148549 x^{6} - 65958243269 x^{5} + 278406118274 x^{4} + 185139245847 x^{3} - 190583514332 x^{2} - 112640151504 x + 4073697629$ |
$21$ |
[21,0] |
$7^{14}\cdot 197^{18}$ |
$2$ |
$338.9097242$ |
$338.90972420019415$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[7]$ |
$2$ |
$20$ |
$9941186336646355000$ |
| 21.21.204...801.1 |
$x^{21} - x^{20} - 220 x^{19} + 59 x^{18} + 19731 x^{17} + 10669 x^{16} - 933778 x^{15} - 1261590 x^{14} + 24832342 x^{13} + 53278874 x^{12} - 359999966 x^{11} - 1090202912 x^{10} + 2403675074 x^{9} + 11114459489 x^{8} - 1212682637 x^{7} - 49217032511 x^{6} - 53493754115 x^{5} + 42961970730 x^{4} + 119457363636 x^{3} + 84397161408 x^{2} + 23424596481 x + 1888668673$ |
$21$ |
[21,0] |
$463^{20}$ |
$1$ |
$345.659552112$ |
$345.6595521122571$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$62050086594131485000$ |
| 21.21.466...769.1 |
$x^{21} - 4 x^{20} - 280 x^{19} + 1434 x^{18} + 28400 x^{17} - 174768 x^{16} - 1259964 x^{15} + 9241088 x^{14} + 24220628 x^{13} - 224432817 x^{12} - 225043591 x^{11} + 2800292150 x^{10} + 1310509833 x^{9} - 18643709590 x^{8} - 7862755157 x^{7} + 62071423969 x^{6} + 36855850475 x^{5} - 78614032446 x^{4} - 59296509039 x^{3} + 18479082734 x^{2} + 15129157356 x - 692122129$ |
$21$ |
[21,0] |
$7^{14}\cdot 211^{18}$ |
$2$ |
$359.451911857$ |
$359.4519118565782$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
trivial |
$2$ |
$20$ |
$115303717001291800000$ |
| 21.21.808...649.1 |
$x^{21} - x^{20} - 314 x^{19} + 641 x^{18} + 39405 x^{17} - 119809 x^{16} - 2475109 x^{15} + 10025575 x^{14} + 78717981 x^{13} - 415588104 x^{12} - 1066077495 x^{11} + 8308415958 x^{10} + 1043228987 x^{9} - 70546887095 x^{8} + 59456573110 x^{7} + 267134979239 x^{6} - 357627209452 x^{5} - 425427767421 x^{4} + 739147737632 x^{3} + 189916353207 x^{2} - 511171099198 x + 73391024141$ |
$21$ |
[21,0] |
$7^{14}\cdot 127^{20}$ |
$2$ |
$368.995682569$ |
$368.99568256878683$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$84153812913585720000$ |
| 21.21.808...649.2 |
$x^{21} - x^{20} - 314 x^{19} + 641 x^{18} + 36738 x^{17} - 95806 x^{16} - 2134622 x^{15} + 6573588 x^{14} + 67487244 x^{13} - 249054401 x^{12} - 1162017486 x^{11} + 5450875699 x^{10} + 9285707168 x^{9} - 67555921271 x^{8} + 824221871 x^{7} + 429237041242 x^{6} - 490449416375 x^{5} - 989353991611 x^{4} + 2305780509364 x^{3} - 753973198685 x^{2} - 1273935520834 x + 833882527031$ |
$21$ |
[21,0] |
$7^{14}\cdot 127^{20}$ |
$2$ |
$368.995682569$ |
$368.99568256878683$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$45298926008459270000$ |
| 21.21.391...961.1 |
$x^{21} - 3 x^{20} - 198 x^{19} + 415 x^{18} + 15879 x^{17} - 16779 x^{16} - 665196 x^{15} - 7383 x^{14} + 15300921 x^{13} + 15483570 x^{12} - 181736895 x^{11} - 349626786 x^{10} + 881813437 x^{9} + 2667813231 x^{8} - 254106018 x^{7} - 5442055226 x^{6} - 2142757218 x^{5} + 3764283285 x^{4} + 1543507294 x^{3} - 828477006 x^{2} - 96455373 x + 3324797$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{14}\cdot 43^{18}$ |
$3$ |
$397.810448205$ |
$397.81044820547436$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$286692515494192970000$ |
| 21.21.391...961.2 |
$x^{21} - 3 x^{20} - 198 x^{19} + 366 x^{18} + 16005 x^{17} - 9597 x^{16} - 671202 x^{15} - 438534 x^{14} + 14998752 x^{13} + 27946195 x^{12} - 155865357 x^{11} - 508309275 x^{10} + 311371348 x^{9} + 3072449295 x^{8} + 3830424663 x^{7} - 635242124 x^{6} - 4505239431 x^{5} - 2657813739 x^{4} + 449118201 x^{3} + 909084162 x^{2} + 287915376 x + 27487873$ |
$21$ |
[21,0] |
$3^{28}\cdot 7^{14}\cdot 43^{18}$ |
$3$ |
$397.810448205$ |
$397.81044820547436$ |
|
✓ |
? |
$C_{21}$ (as 21T1) |
$[3]$ |
$2$ |
$20$ |
$232239644387987300000$ |
