| 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 |
| 39.39.128...161.1 |
$x^{39} - x^{38} - 38 x^{37} + 37 x^{36} + 666 x^{35} - 630 x^{34} - 7140 x^{33} + 6545 x^{32} + 52360 x^{31} - 46376 x^{30} - 278256 x^{29} + 237336 x^{28} + 1107568 x^{27} - 906192 x^{26} - 3365856 x^{25} + 2629575 x^{24} + 7888725 x^{23} - 5852925 x^{22} - 14307150 x^{21} + 10015005 x^{20} + 20030010 x^{19} - 13123110 x^{18} - 21474180 x^{17} + 13037895 x^{16} + 17383860 x^{15} - 9657700 x^{14} - 10400600 x^{13} + 5200300 x^{12} + 4457400 x^{11} - 1961256 x^{10} - 1307504 x^{9} + 490314 x^{8} + 245157 x^{7} - 74613 x^{6} - 26334 x^{5} + 5985 x^{4} + 1330 x^{3} - 190 x^{2} - 20 x + 1$ |
$39$ |
[39,0] |
$79^{38}$ |
$1$ |
$70.626874312$ |
$70.626874311955$ |
|
✓ |
✓ |
$C_{39}$ (as 39T1) |
trivial |
$2$ |
$38$ |
$536916737153376600000000$ |
| 39.39.270...889.1 |
$x^{39} - 78 x^{37} + 2691 x^{35} - 26 x^{34} - 54301 x^{33} + 1573 x^{32} + 714415 x^{31} - 41041 x^{30} - 6470152 x^{29} + 608296 x^{28} + 41530255 x^{27} - 5687020 x^{26} - 191726951 x^{25} + 35251762 x^{24} + 639669732 x^{23} - 148392244 x^{22} - 1537691324 x^{21} + 427950341 x^{20} + 2636840661 x^{19} - 844358905 x^{18} - 3171548939 x^{17} + 1129454313 x^{16} + 2610137920 x^{15} - 1007230666 x^{14} - 1417531106 x^{13} + 581665721 x^{12} + 480801555 x^{11} - 206676184 x^{10} - 93363413 x^{9} + 41256709 x^{8} + 9129731 x^{7} - 3966105 x^{6} - 427921 x^{5} + 161980 x^{4} + 7137 x^{3} - 1833 x^{2} + 78 x - 1$ |
$39$ |
[39,0] |
$13^{74}$ |
$1$ |
$129.90806214$ |
$129.9080621398409$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
trivial |
$2$ |
$38$ |
$80306583605632290000000000000$ |
| 39.39.278...849.1 |
$x^{39} - x^{38} - 76 x^{37} + 71 x^{36} + 2556 x^{35} - 2222 x^{34} - 50313 x^{33} + 40520 x^{32} + 646279 x^{31} - 479776 x^{30} - 5720417 x^{29} + 3892342 x^{28} + 35931891 x^{27} - 22265255 x^{26} - 162617513 x^{25} + 91086546 x^{24} + 533275855 x^{23} - 267613697 x^{22} - 1265136580 x^{21} + 562372122 x^{20} + 2154121978 x^{19} - 835520674 x^{18} - 2594978102 x^{17} + 861831376 x^{16} + 2164301236 x^{15} - 603623323 x^{14} - 1211061590 x^{13} + 280758113 x^{12} + 434291871 x^{11} - 84841877 x^{10} - 93357668 x^{9} + 15992102 x^{8} + 10935603 x^{7} - 1639529 x^{6} - 599706 x^{5} + 67036 x^{4} + 11826 x^{3} - 272 x^{2} - 49 x - 1$ |
$39$ |
[39,0] |
$157^{38}$ |
$1$ |
$137.90961089$ |
$137.9096108902142$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
trivial |
$2$ |
$38$ |
$216984792046842040000000000000$ |
| 39.39.111...929.1 |
$x^{39} - 10 x^{38} - 55 x^{37} + 838 x^{36} + 433 x^{35} - 29490 x^{34} + 36492 x^{33} + 574075 x^{32} - 1308560 x^{31} - 6805710 x^{30} + 21722262 x^{29} + 50319569 x^{28} - 220059875 x^{27} - 219014481 x^{26} + 1482194078 x^{25} + 368114118 x^{24} - 6887826619 x^{23} + 1579984745 x^{22} + 22412813436 x^{21} - 12656284391 x^{20} - 51075711901 x^{19} + 41988060380 x^{18} + 80500790810 x^{17} - 83924117638 x^{16} - 85491405725 x^{15} + 107935481554 x^{14} + 58560262932 x^{13} - 89832821948 x^{12} - 24031853409 x^{11} + 47511398377 x^{10} + 5015492400 x^{9} - 15459668136 x^{8} - 163687701 x^{7} + 2936606920 x^{6} - 133518320 x^{5} - 294156298 x^{4} + 23663051 x^{3} + 11997840 x^{2} - 1233420 x - 17513$ |
$39$ |
[39,0] |
$7^{26}\cdot 53^{36}$ |
$2$ |
$142.901885013$ |
$142.90188501299207$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
trivial |
$2$ |
$38$ |
$688762923023490700000000000000$ |
| 39.39.766...761.1 |
$x^{39} - 3 x^{38} - 108 x^{37} + 298 x^{36} + 5118 x^{35} - 12960 x^{34} - 141273 x^{33} + 327258 x^{32} + 2542896 x^{31} - 5364720 x^{30} - 31665816 x^{29} + 60457005 x^{28} + 282448421 x^{27} - 483720000 x^{26} - 1843142403 x^{25} + 2798088433 x^{24} + 8906870079 x^{23} - 11806339326 x^{22} - 32037019809 x^{21} + 36413436990 x^{20} + 85660814031 x^{19} - 81805437661 x^{18} - 168975543573 x^{17} + 132746230803 x^{16} + 242513964655 x^{15} - 153550437819 x^{14} - 248180206443 x^{13} + 124178901378 x^{12} + 176350634529 x^{11} - 68071818495 x^{10} - 84005722509 x^{9} + 23987475126 x^{8} + 25531114500 x^{7} - 4940743725 x^{6} - 4581690405 x^{5} + 488059458 x^{4} + 422630171 x^{3} - 11643372 x^{2} - 14496000 x - 430019$ |
$39$ |
[39,0] |
$3^{52}\cdot 53^{36}$ |
$2$ |
$168.966628034$ |
$168.96662803404803$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
trivial |
$2$ |
$38$ |
$14858926187187562000000000000000$ |
| 39.39.193...529.1 |
$x^{39} - 10 x^{38} - 91 x^{37} + 1036 x^{36} + 3946 x^{35} - 48394 x^{34} - 113775 x^{33} + 1340155 x^{32} + 2502275 x^{31} - 24308912 x^{30} - 43149237 x^{29} + 301161228 x^{28} + 566666743 x^{27} - 2578642861 x^{26} - 5471311188 x^{25} + 15078823676 x^{24} + 37876474410 x^{23} - 57546616634 x^{22} - 184436616929 x^{21} + 124709319279 x^{20} + 618742359228 x^{19} - 54324200102 x^{18} - 1388110537758 x^{17} - 483581361681 x^{16} + 1979142956060 x^{15} + 1427263115288 x^{14} - 1609144180429 x^{13} - 1887910006886 x^{12} + 509773426670 x^{11} + 1295640832119 x^{10} + 171082251210 x^{9} - 429221222404 x^{8} - 160917420416 x^{7} + 56100044133 x^{6} + 37303198473 x^{5} - 296394467 x^{4} - 3173168574 x^{3} - 345469686 x^{2} + 87223662 x + 14066053$ |
$39$ |
[39,0] |
$7^{26}\cdot 79^{36}$ |
$2$ |
$206.563921539$ |
$206.5639215386565$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.108...489.1 |
$x^{39} - 10 x^{38} - 81 x^{37} + 1050 x^{36} + 2269 x^{35} - 47944 x^{34} - 10490 x^{33} + 1262097 x^{32} - 921080 x^{31} - 21400660 x^{30} + 27475516 x^{29} + 247428139 x^{28} - 406156179 x^{27} - 2015287011 x^{26} + 3799253180 x^{25} + 11792160578 x^{24} - 24197312569 x^{23} - 50158998143 x^{22} + 108120625100 x^{21} + 156174553989 x^{20} - 342706955337 x^{19} - 357124870516 x^{18} + 769896542138 x^{17} + 599267077900 x^{16} - 1212025785075 x^{15} - 732019943274 x^{14} + 1306427105242 x^{13} + 636966693014 x^{12} - 927524873227 x^{11} - 377238926259 x^{10} + 408532943088 x^{9} + 139924561470 x^{8} - 102630494231 x^{7} - 28423351128 x^{6} + 13445073140 x^{5} + 2704930022 x^{4} - 804059407 x^{3} - 106744516 x^{2} + 15239414 x + 1788197$ |
$39$ |
[39,0] |
$13^{26}\cdot 53^{36}$ |
$2$ |
$215.907717282$ |
$215.90771728173132$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.133...161.1 |
$x^{39} - 3 x^{38} - 144 x^{37} + 544 x^{36} + 8607 x^{35} - 39873 x^{34} - 273219 x^{33} + 1586748 x^{32} + 4768863 x^{31} - 38339003 x^{30} - 36770526 x^{29} + 590401068 x^{28} - 186548878 x^{27} - 5865182265 x^{26} + 7401235119 x^{25} + 36650142262 x^{24} - 80182575711 x^{23} - 129404499477 x^{22} + 478911168431 x^{21} + 133680753126 x^{20} - 1717086418740 x^{19} + 841783459401 x^{18} + 3624110595294 x^{17} - 4051561096485 x^{16} - 3908165428785 x^{15} + 8158071470571 x^{14} + 524362618785 x^{13} - 8608241123601 x^{12} + 3464219056332 x^{11} + 4466815249788 x^{10} - 3609335878022 x^{9} - 703907774076 x^{8} + 1408564281330 x^{7} - 178984846489 x^{6} - 212099031525 x^{5} + 49542152886 x^{4} + 13836139901 x^{3} - 2992803492 x^{2} - 474072537 x + 17616187$ |
$39$ |
[39,0] |
$3^{52}\cdot 79^{36}$ |
$2$ |
$244.240370186$ |
$244.24037018618242$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.120...489.1 |
$x^{39} - x^{38} - 196 x^{37} + 37 x^{36} + 17177 x^{35} + 9403 x^{34} - 882381 x^{33} - 1067223 x^{32} + 29336001 x^{31} + 53273410 x^{30} - 658772565 x^{29} - 1583577890 x^{28} + 10123695780 x^{27} + 30773254905 x^{26} - 105181421187 x^{25} - 406462457224 x^{24} + 701275142050 x^{23} + 3703719049533 x^{22} - 2495293357664 x^{21} - 23296951876563 x^{20} - 582451600575 x^{19} + 100148494787668 x^{18} + 52233018535617 x^{17} - 288162921569191 x^{16} - 262264312267859 x^{15} + 535079835460586 x^{14} + 679366178486570 x^{13} - 600819998721797 x^{12} - 1028790083129260 x^{11} + 359936453258218 x^{10} + 916306649955834 x^{9} - 86249482058917 x^{8} - 469190872234743 x^{7} + 4041363119341 x^{6} + 135236928048853 x^{5} - 4445757797975 x^{4} - 19527462450618 x^{3} + 2244998319481 x^{2} + 789598736860 x - 116423735903$ |
$39$ |
[39,0] |
$7^{26}\cdot 79^{38}$ |
$2$ |
$258.445324451$ |
$258.44532445081165$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.120...489.2 |
$x^{39} - x^{38} - 196 x^{37} + 37 x^{36} + 17177 x^{35} + 9403 x^{34} - 882381 x^{33} - 1067223 x^{32} + 29336001 x^{31} + 53273410 x^{30} - 658679661 x^{29} - 1582974014 x^{28} + 10115860876 x^{27} + 30713447955 x^{26} - 104944361700 x^{25} - 404054826285 x^{24} + 698746620334 x^{23} + 3652383956122 x^{22} - 2514455451909 x^{21} - 22664595762180 x^{20} + 201147288071 x^{19} + 95542005646477 x^{18} + 43535191283083 x^{17} - 268603953306336 x^{16} - 212548013703570 x^{15} + 489275966728363 x^{14} + 517783387282365 x^{13} - 549595953418310 x^{12} - 723715965685304 x^{11} + 343123809068303 x^{10} + 580854022082499 x^{9} - 85745300820944 x^{8} - 252040837202603 x^{7} - 10510715956375 x^{6} + 52566975147352 x^{5} + 6905591385122 x^{4} - 5057933882725 x^{3} - 892913278781 x^{2} + 181524069429 x + 36571406327$ |
$39$ |
[39,0] |
$7^{26}\cdot 79^{38}$ |
$2$ |
$258.445324451$ |
$258.44532445081165$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.677...529.1 |
$x^{39} - x^{38} - 152 x^{37} + 131 x^{36} + 10058 x^{35} - 7664 x^{34} - 385412 x^{33} + 259301 x^{32} + 9584688 x^{31} - 5543314 x^{30} - 164185853 x^{29} + 77293037 x^{28} + 2005287415 x^{27} - 697581260 x^{26} - 17813421285 x^{25} + 3767883715 x^{24} + 116209225455 x^{23} - 7694298355 x^{22} - 557397698695 x^{21} - 45743080985 x^{20} + 1952302482609 x^{19} + 442964945371 x^{18} - 4917326782303 x^{17} - 1782021019971 x^{16} + 8684112089102 x^{15} + 4202789024049 x^{14} - 10349426133993 x^{13} - 6090366989496 x^{12} + 7867872784032 x^{11} + 5300624795924 x^{10} - 3522617600307 x^{9} - 2593891521982 x^{8} + 842025983515 x^{7} + 645145821500 x^{6} - 97379198250 x^{5} - 71168573750 x^{4} + 4180068750 x^{3} + 2855312500 x^{2} - 13984375 x - 9765625$ |
$39$ |
[39,0] |
$313^{38}$ |
$1$ |
$270.119552273$ |
$270.11955227277815$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
$[7]$ |
$2$ |
$38$ |
$77156139939904980000000000000000000000$ |
| 39.39.832...801.1 |
$x^{39} - 237 x^{37} - 158 x^{36} + 24885 x^{35} + 31758 x^{34} - 1521777 x^{33} - 2797074 x^{32} + 59981382 x^{31} + 142319290 x^{30} - 1593020385 x^{29} - 4645069176 x^{28} + 28911926408 x^{27} + 102131256564 x^{26} - 354430642254 x^{25} - 1546711782640 x^{24} + 2789344797921 x^{23} + 16230796918608 x^{22} - 11865055676615 x^{21} - 117384643087056 x^{20} + 1203314824617 x^{19} + 577307993368452 x^{18} + 284377372208856 x^{17} - 1897069485800418 x^{16} - 1634584478920060 x^{15} + 4091661940360473 x^{14} + 4742867841110748 x^{13} - 5697404621999031 x^{12} - 8186462453659176 x^{11} + 5033143416507438 x^{10} + 8729302726558491 x^{9} - 2808785515834836 x^{8} - 5719188124989093 x^{7} + 1072119182609331 x^{6} + 2216792963213496 x^{5} - 346349054137671 x^{4} - 464961302461611 x^{3} + 86786523385245 x^{2} + 39491507056968 x - 9364853836691$ |
$39$ |
[39,0] |
$3^{52}\cdot 79^{38}$ |
$2$ |
$305.584737386$ |
$305.58473738571735$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.832...801.2 |
$x^{39} - 237 x^{37} - 158 x^{36} + 24885 x^{35} + 31758 x^{34} - 1521777 x^{33} - 2797074 x^{32} + 59981382 x^{31} + 142319290 x^{30} - 1593173961 x^{29} - 4645709076 x^{28} + 28932877445 x^{27} + 102241716102 x^{26} - 355443646614 x^{25} - 1553454595933 x^{24} + 2810177785458 x^{23} + 16432247086167 x^{22} - 11967377146298 x^{21} - 120635759398347 x^{20} - 1823113254630 x^{19} + 605746157617644 x^{18} + 341698986985275 x^{17} - 2017784741258409 x^{16} - 2057859861184228 x^{15} + 4196664129873231 x^{14} + 6285983642002179 x^{13} - 4725650025499719 x^{12} - 10914822027031086 x^{11} + 1465701883750416 x^{10} + 10558980638642454 x^{9} + 2159465693586741 x^{8} - 5293388896015467 x^{7} - 2202937031211426 x^{6} + 1157156267855625 x^{5} + 698944716032751 x^{4} - 59632171643934 x^{3} - 73740757923315 x^{2} - 5146532589771 x + 1075512295747$ |
$39$ |
[39,0] |
$3^{52}\cdot 79^{38}$ |
$2$ |
$305.584737386$ |
$305.58473738571735$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.189...089.1 |
$x^{39} - 10 x^{38} - 117 x^{37} + 1248 x^{36} + 6574 x^{35} - 70508 x^{34} - 238767 x^{33} + 2376429 x^{32} + 6246879 x^{31} - 53084512 x^{30} - 122075225 x^{29} + 827367236 x^{28} + 1790293625 x^{27} - 9246368917 x^{26} - 19595581406 x^{25} + 75169877668 x^{24} + 158901467338 x^{23} - 447662704038 x^{22} - 947228275523 x^{21} + 1958725720367 x^{20} + 4113180518714 x^{19} - 6305779770878 x^{18} - 12855958984538 x^{17} + 14959051199327 x^{16} + 28441505512102 x^{15} - 26161675308530 x^{14} - 43445251987869 x^{13} + 33478011120120 x^{12} + 44089907326138 x^{11} - 30444285645115 x^{10} - 27975777878380 x^{9} + 18404264085338 x^{8} + 10144928480062 x^{7} - 6624071325699 x^{6} - 1906724813303 x^{5} + 1267027871999 x^{4} + 154439956714 x^{3} - 106661114208 x^{2} - 3009281044 x + 2198272487$ |
$39$ |
[39,0] |
$13^{26}\cdot 79^{36}$ |
$2$ |
$312.093467263$ |
$312.09346726335514$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.156...969.1 |
$x^{39} - 10 x^{38} - 163 x^{37} + 1930 x^{36} + 10036 x^{35} - 159252 x^{34} - 244026 x^{33} + 7427095 x^{32} - 2389017 x^{31} - 217511108 x^{30} + 326735317 x^{29} + 4189088926 x^{28} - 10153118781 x^{27} - 53678089242 x^{26} + 179337849315 x^{25} + 446153115950 x^{24} - 2052054489049 x^{23} - 2151039397974 x^{22} + 15813321949956 x^{21} + 2821647348255 x^{20} - 82489984035674 x^{19} + 33701919033939 x^{18} + 286106777644803 x^{17} - 243663734729882 x^{16} - 630941672277082 x^{15} + 788875500248585 x^{14} + 805762979991898 x^{13} - 1416423805872644 x^{12} - 462194605752742 x^{11} + 1418910665071105 x^{10} - 50123800376408 x^{9} - 755859394498746 x^{8} + 182503268720113 x^{7} + 191800233365760 x^{6} - 72017807491341 x^{5} - 18496135085754 x^{4} + 9851455470329 x^{3} + 124863566729 x^{2} - 388373575025 x + 27293535527$ |
$39$ |
[39,0] |
$7^{26}\cdot 131^{36}$ |
$2$ |
$329.460206465$ |
$329.4602064654238$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.118...449.1 |
$x^{39} - x^{38} - 354 x^{37} + 511 x^{36} + 56045 x^{35} - 103251 x^{34} - 5247131 x^{33} + 11548919 x^{32} + 323858271 x^{31} - 818077472 x^{30} - 13915010959 x^{29} + 39315623658 x^{28} + 428683737326 x^{27} - 1332897877353 x^{26} - 9615971778232 x^{25} + 32610615529383 x^{24} + 157954520735238 x^{23} - 583064031850378 x^{22} - 1895313576585435 x^{21} + 7659727015753552 x^{20} + 16422194396956823 x^{19} - 73899082723108593 x^{18} - 100210603740569843 x^{17} + 520414495467180616 x^{16} + 408676600606594002 x^{15} - 2642936340868695765 x^{14} - 971974365656650043 x^{13} + 9496075566431610394 x^{12} + 586468002053107902 x^{11} - 23471590571480299925 x^{10} + 3789203055222994557 x^{9} + 38292325977191105354 x^{8} - 12389487729343041691 x^{7} - 38551672930076472707 x^{6} + 17045767379408771012 x^{5} + 21043564296778861782 x^{4} - 11248804489468062285 x^{3} - 4368569542269920485 x^{2} + 2837239422181036677 x - 221647485396299581$ |
$39$ |
[39,0] |
$13^{26}\cdot 79^{38}$ |
$2$ |
$390.480083865$ |
$390.4800838648001$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.118...449.2 |
$x^{39} - x^{38} - 354 x^{37} + 511 x^{36} + 56045 x^{35} - 103251 x^{34} - 5247131 x^{33} + 11548919 x^{32} + 323858271 x^{31} - 818077472 x^{30} - 13912915879 x^{29} + 39305918508 x^{28} + 428252335706 x^{27} - 1330679343737 x^{26} - 9579637340859 x^{25} + 32404331102658 x^{24} + 156314779697940 x^{23} - 572661461636511 x^{22} - 1851957964341868 x^{21} + 7341898588148461 x^{20} + 15740944592310945 x^{19} - 67699689278718824 x^{18} - 94298948980717131 x^{17} + 441371170652289465 x^{16} + 391057744594350035 x^{15} - 1980375180524138330 x^{14} - 1121115212503618422 x^{13} + 5873379572582775725 x^{12} + 2334047970653280778 x^{11} - 10818653588566378140 x^{10} - 3849139231012138630 x^{9} + 11165439791508447499 x^{8} + 4690051537532888413 x^{7} - 5357278100940296591 x^{6} - 2992545959704021257 x^{5} + 706803441870504299 x^{4} + 694897163472669662 x^{3} + 124066763635805181 x^{2} + 4291829198615412 x - 176560760826029$ |
$39$ |
[39,0] |
$13^{26}\cdot 79^{38}$ |
$2$ |
$390.480083865$ |
$390.4800838648001$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.150...769.1 |
$x^{39} - 13 x^{38} - 182 x^{37} + 2730 x^{36} + 14677 x^{35} - 259233 x^{34} - 697762 x^{33} + 14757002 x^{32} + 22070763 x^{31} - 562769506 x^{30} - 502430448 x^{29} + 15217824882 x^{28} + 8836227920 x^{27} - 301252971368 x^{26} - 128531515099 x^{25} + 4444891875554 x^{24} + 1611389606593 x^{23} - 49312156872550 x^{22} - 17208326212714 x^{21} + 412126532724114 x^{20} + 148945309469346 x^{19} - 2584439781741701 x^{18} - 990752940639891 x^{17} + 12045290627585839 x^{16} + 4853248692356259 x^{15} - 41087556662763260 x^{14} - 16875632381268701 x^{13} + 100344648053329030 x^{12} + 39971524926664279 x^{11} - 170232014288977485 x^{10} - 60718951748161707 x^{9} + 192451677172291043 x^{8} + 52833922982995011 x^{7} - 136584375299797074 x^{6} - 19036514040517506 x^{5} + 55032005931718101 x^{4} - 2939818026931279 x^{3} - 9750856549065099 x^{2} + 2629380133737812 x - 141031288821697$ |
$39$ |
[39,0] |
$7^{26}\cdot 13^{72}$ |
$2$ |
$416.78252133$ |
$416.78252132992753$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.110...889.1 |
$x^{39} - x^{38} - 266 x^{37} + 201 x^{36} + 30249 x^{35} - 20577 x^{34} - 1955719 x^{33} + 1451515 x^{32} + 80733464 x^{31} - 73319589 x^{30} - 2263189338 x^{29} + 2590988751 x^{28} + 44569388886 x^{27} - 63687593067 x^{26} - 626428894665 x^{25} + 1097818462656 x^{24} + 6291493806807 x^{23} - 13394812097448 x^{22} - 44496937680997 x^{21} + 116206956876955 x^{20} + 212799596796731 x^{19} - 715024587078660 x^{18} - 615613322642382 x^{17} + 3085798869034590 x^{16} + 605869572443830 x^{15} - 9130534820399395 x^{14} + 2644115229153457 x^{13} + 17760841353343332 x^{12} - 12225754395203670 x^{11} - 20865350159842410 x^{10} + 23224133468755773 x^{9} + 11651476867778808 x^{8} - 23071484201964822 x^{7} + 1000224610088400 x^{6} + 11129065111375902 x^{5} - 4226325744669057 x^{4} - 1602614683727208 x^{3} + 1322681130702459 x^{2} - 264907416527640 x + 15539564953953$ |
$39$ |
[39,0] |
$547^{38}$ |
$1$ |
$465.353005424$ |
$465.3530054237375$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
$[2, 2]$ |
$2$ |
$38$ |
$6525765843490048000000000000000000000000000000$ |
| 39.39.253...961.1 |
$x^{39} - 390 x^{37} - 286 x^{36} + 65546 x^{35} + 88920 x^{34} - 6280378 x^{33} - 11653265 x^{32} + 382930899 x^{31} + 856590241 x^{30} - 15717114465 x^{29} - 39435109363 x^{28} + 448686972500 x^{27} + 1199990267358 x^{26} - 9100383506097 x^{25} - 24822667931009 x^{24} + 133188687315944 x^{23} + 353619732471278 x^{22} - 1423517779177858 x^{21} - 3471118652598805 x^{20} + 11204722304355203 x^{19} + 23164264288822098 x^{18} - 65107276882797305 x^{17} - 101594264051122518 x^{16} + 276580892395972736 x^{15} + 271196926808388100 x^{14} - 832291995419335689 x^{13} - 347469449614272362 x^{12} + 1664092769802147698 x^{11} - 107016937117947402 x^{10} - 1979883098807303638 x^{9} + 914796793672703903 x^{8} + 1120784114904201293 x^{7} - 985117898592833785 x^{6} - 96010311784372778 x^{5} + 330848508619272800 x^{4} - 78098712119608596 x^{3} - 28407282472861357 x^{2} + 14411976246188482 x - 1643796985453897$ |
$39$ |
[39,0] |
$7^{26}\cdot 13^{74}$ |
$2$ |
$475.373313566$ |
$475.3733135663388$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.253...961.2 |
$x^{39} - 390 x^{37} - 377 x^{36} + 65455 x^{35} + 112125 x^{34} - 6254079 x^{33} - 14263418 x^{32} + 380924713 x^{31} + 1033279390 x^{30} - 15735345587 x^{29} - 47974546815 x^{28} + 457822132534 x^{27} + 1520603688668 x^{26} - 9602929351899 x^{25} - 34139726254127 x^{24} + 147079561332782 x^{23} + 554786638604653 x^{22} - 1650975560722670 x^{21} - 6598530446060852 x^{20} + 13495970265024962 x^{19} + 57595923527804103 x^{18} - 78681583686823273 x^{17} - 366959544536418691 x^{16} + 311465144437682807 x^{15} + 1681821358187714354 x^{14} - 734434831693408538 x^{13} - 5396067856183792892 x^{12} + 500544557333199483 x^{11} + 11554845389791749045 x^{10} + 2391742500244971471 x^{9} - 15095999493316201044 x^{8} - 7224331708988341766 x^{7} + 9804310922264413685 x^{6} + 7359453991472534068 x^{5} - 1374497594327824447 x^{4} - 1935220066468897533 x^{3} - 225397097195334857 x^{2} + 30401302690706818 x - 653320975578181$ |
$39$ |
[39,0] |
$7^{26}\cdot 13^{74}$ |
$2$ |
$475.373313566$ |
$475.3733135663388$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.103...321.1 |
$x^{39} - 273 x^{37} - 182 x^{36} + 32916 x^{35} + 40482 x^{34} - 2316834 x^{33} - 3952806 x^{32} + 106181673 x^{31} + 224718143 x^{30} - 3349110687 x^{29} - 8318087427 x^{28} + 74929320141 x^{27} + 212338381011 x^{26} - 1206809157840 x^{25} - 3860615205330 x^{24} + 14025312563028 x^{23} + 50874859479912 x^{22} - 116266057517948 x^{21} - 489362521182600 x^{20} + 664421816490900 x^{19} + 3429684774229909 x^{18} - 2392139407741278 x^{17} - 17327097772488816 x^{16} + 3760495385256844 x^{15} + 61790220910015260 x^{14} + 8390784874919109 x^{13} - 150278137860645691 x^{12} - 58889345017035585 x^{11} + 236344730286375750 x^{10} + 133821224934649850 x^{9} - 222021635494235226 x^{8} - 145266045302980407 x^{7} + 112906095976866894 x^{6} + 69192173959102974 x^{5} - 31218629333468928 x^{4} - 12581772617130626 x^{3} + 3902254369099281 x^{2} + 508628454555390 x - 74582793628487$ |
$39$ |
[39,0] |
$3^{52}\cdot 13^{72}$ |
$2$ |
$492.802017596$ |
$492.80201759580734$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.174...249.1 |
$x^{39} - 468 x^{37} - 429 x^{36} + 94302 x^{35} + 150579 x^{34} - 10877178 x^{33} - 23126805 x^{32} + 804503037 x^{31} + 2063650381 x^{30} - 40442681214 x^{29} - 119678631189 x^{28} + 1426153141465 x^{27} + 4775548173669 x^{26} - 35796898561242 x^{25} - 135274459055463 x^{24} + 639534035211318 x^{23} + 2764323417100050 x^{22} - 7982985062501423 x^{21} - 40969565914828005 x^{20} + 65860628821697658 x^{19} + 438528752332665930 x^{18} - 298043599765412943 x^{17} - 3338994626047440672 x^{16} - 78429613481451596 x^{15} + 17529509839348545363 x^{14} + 10385292113264182764 x^{13} - 59680983047763845157 x^{12} - 66690131644525453272 x^{11} + 114548751172900486065 x^{10} + 205291995294759812569 x^{9} - 69848700129376819794 x^{8} - 304768906927191533463 x^{7} - 109317071033620364590 x^{6} + 147814957917242282979 x^{5} + 127696294768806174450 x^{4} + 20371231882178434231 x^{3} - 7573798888698559374 x^{2} - 1545897989187597630 x + 139962979452437479$ |
$39$ |
[39,0] |
$3^{52}\cdot 13^{74}$ |
$2$ |
$562.079540402$ |
$562.0795404019609$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.174...249.2 |
$x^{39} - 468 x^{37} - 312 x^{36} + 94302 x^{35} + 118638 x^{34} - 10878699 x^{33} - 19307574 x^{32} + 805821744 x^{31} + 1800372886 x^{30} - 40680500211 x^{29} - 108237264603 x^{28} + 1446005621320 x^{27} + 4459027282749 x^{26} - 36740305683120 x^{25} - 130171431648258 x^{24} + 667319579204967 x^{23} + 2739095618686947 x^{22} - 8508852916909748 x^{21} - 41760228787431102 x^{20} + 72335202029643423 x^{19} + 459027912672556227 x^{18} - 350556005056037274 x^{17} - 3583579320625784766 x^{16} + 223936776371258899 x^{15} + 19350977144085682407 x^{14} + 8850830449501775865 x^{13} - 69386406134656900614 x^{12} - 59318124902891828415 x^{11} + 155603230401068027877 x^{10} + 183666623582194428403 x^{9} - 199867410901172997567 x^{8} - 299712026978452810761 x^{7} + 126091751205245716982 x^{6} + 247052928867978365847 x^{5} - 26149175806607388015 x^{4} - 89715453239778791906 x^{3} - 3866411569558451472 x^{2} + 10712801222330860887 x + 1727305433480995147$ |
$39$ |
[39,0] |
$3^{52}\cdot 13^{74}$ |
$2$ |
$562.079540402$ |
$562.0795404019609$ |
|
✓ |
? |
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.310...121.1 |
$x^{39} - x^{38} - 418 x^{37} + 257 x^{36} + 76656 x^{35} - 25124 x^{34} - 8202516 x^{33} + 1019926 x^{32} + 574247527 x^{31} + 5687450 x^{30} - 27929902375 x^{29} - 2377460296 x^{28} + 977447780026 x^{27} + 104572804788 x^{26} - 25143771161526 x^{25} - 1960796376209 x^{24} + 481506512358468 x^{23} - 367850835644 x^{22} - 6909840978182031 x^{21} + 881254692222165 x^{20} + 74394563155392672 x^{19} - 22215332285440559 x^{18} - 597860125935944916 x^{17} + 304123644173622296 x^{16} + 3535952790750419585 x^{15} - 2666822697362825632 x^{14} - 14955842277567387623 x^{13} + 15573247852725031688 x^{12} + 42764798476196161371 x^{11} - 60196114411581821386 x^{10} - 72785367486446956468 x^{9} + 147412192602412912773 x^{8} + 44677485895471467253 x^{7} - 205734048952896741833 x^{6} + 58393246255856725398 x^{5} + 122604532156110799892 x^{4} - 93030852218962216732 x^{3} + 3463394079889685056 x^{2} + 14915576173796699171 x - 3730889337449273077$ |
$39$ |
[39,0] |
$859^{38}$ |
$1$ |
$722.374771146$ |
$722.3747711464864$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
| 39.39.843...529.1 |
$x^{39} - x^{38} - 456 x^{37} + 889 x^{36} + 90828 x^{35} - 253868 x^{34} - 10385180 x^{33} + 37136294 x^{32} + 753123799 x^{31} - 3270550490 x^{30} - 36099160776 x^{29} + 186756003421 x^{28} + 1153888467019 x^{27} - 7173288778188 x^{26} - 24081982466754 x^{25} + 188571229295629 x^{24} + 304007530489979 x^{23} - 3415756724968728 x^{22} - 1675569173908960 x^{21} + 42720685818403975 x^{20} - 10554063966988809 x^{19} - 369187803799463938 x^{18} + 273182269941204948 x^{17} + 2201019540853979395 x^{16} - 2354043730739816544 x^{15} - 9001671285085868002 x^{14} + 11514879338270450671 x^{13} + 24991289927843292457 x^{12} - 34615393263055948671 x^{11} - 46331426122390477259 x^{10} + 64085787618282944397 x^{9} + 55701401545562743601 x^{8} - 70426823322220439228 x^{7} - 40617153217434411375 x^{6} + 42835827891298341241 x^{5} + 15065589607445769980 x^{4} - 13137613446326251666 x^{3} - 1795725529019100898 x^{2} + 1568527642769879023 x - 143456380943806673$ |
$39$ |
[39,0] |
$937^{38}$ |
$1$ |
$786.214664148$ |
$786.2146641483995$ |
|
✓ |
|
$C_{39}$ (as 39T1) |
not computed |
$2$ |
$38$ |
|
