| 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 |
| 38.2.108...821.1 |
$x^{38} - x - 1$ |
$38$ |
[2,18] |
$624808693\cdot 17\!\cdots\!97$ |
$2$ |
$38.0097638537$ |
$1.0423372472169321e+30$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
trivial |
$2$ |
$19$ |
$900165801403525.9$ |
| 38.0.282...776.1 |
$x^{38} - 2 x^{19} + 2$ |
$38$ |
[0,19] |
$-\,2^{56}\cdot 19^{38}$ |
$2$ |
$52.7687434194$ |
$61.08583685562279$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
trivial |
$4$ |
$18$ |
$1117851098845078000$ |
| 38.0.176...083.1 |
$x^{38} - 3 x^{19} + 3$ |
$38$ |
[0,19] |
$-\,3^{37}\cdot 19^{38}$ |
$2$ |
$55.3756750125$ |
$64.10365739999646$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
trivial |
$6$ |
$18$ |
$3410189640739071500$ |
| 38.2.290...489.1 |
$x^{38} - 4 x - 1$ |
$38$ |
[2,18] |
$11149\cdot 365159\cdot 14342233\cdot 49\!\cdots\!63$ |
$4$ |
$67.2919716533$ |
$5.386439829939296e+34$ |
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.290...352.1 |
$x^{38} - 2 x - 1$ |
$38$ |
[2,18] |
$2^{39}\cdot 199\cdot 28308359\cdot 2683125188231\cdot 180622253751001441\cdot 1933097818431428689$ |
$6$ |
$67.291971654$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.789...744.1 |
$x^{38} - 4 x + 4$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 3\cdot 1061\cdot 24469\cdot 188414113\cdot 393131311\cdot 49\!\cdots\!91$ |
$7$ |
$69.087701074$ |
|
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.2.768...792.1 |
$x^{38} - 4 x - 4$ |
$38$ |
[2,18] |
$2^{38}\cdot 727\cdot 5261563\cdot 73\!\cdots\!93$ |
$4$ |
$73.35163813$ |
|
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.144...440.1 |
$x^{38} - 2 x + 2$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 5\cdot 41\cdot 367\cdot 263591\cdot 73599203\cdot 4905513061473881\cdot 73660168063921443246200957$ |
$8$ |
$74.5873673916$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.147...971.1 |
$x^{38} - x + 2$ |
$38$ |
[0,19] |
$-\,27991188787\cdot 52\!\cdots\!33$ |
$2$ |
$74.626272613$ |
$3.845415349377665e+35$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.147...488.1 |
$x^{38} + 2$ |
$38$ |
[0,19] |
$-\,2^{75}\cdot 19^{38}$ |
$2$ |
$74.626272613$ |
$86.388418950132$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
trivial |
$2$ |
$18$ |
$584782896068373250000$ |
| 38.2.147...488.1 |
$x^{38} - 2$ |
$38$ |
[2,18] |
$2^{75}\cdot 19^{38}$ |
$2$ |
$74.626272613$ |
$86.388418950132$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
trivial |
$2$ |
$19$ |
$541671220201208600000$ |
| 38.2.150...536.1 |
$x^{38} - 2 x - 2$ |
$38$ |
[2,18] |
$2^{38}\cdot 3\cdot 18\!\cdots\!23$ |
$3$ |
$74.6644415557$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.284...125.1 |
$x^{38} - 5$ |
$38$ |
[2,18] |
$5^{37}\cdot 19^{38}$ |
$2$ |
$91.0604218291$ |
$105.41282038213063$ |
|
|
? |
$C_2\times F_{19}$ (as 38T9) |
not computed |
$2$ |
$19$ |
|
| 38.2.142...317.1 |
$x^{38} - 3 x - 1$ |
$38$ |
[2,18] |
$487\cdot 521\cdot 4519\cdot 26317\cdot 11892563\cdot 39\!\cdots\!79$ |
$6$ |
$100.93795748$ |
$1.1940863530449824e+38$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.470...339.1 |
$x^{38} - 3 x + 3$ |
$38$ |
[0,19] |
$-\,3^{37}\cdot 11\cdot 71\cdot 7880009\cdot 21435017\cdot 79\!\cdots\!21$ |
$6$ |
$110.664319059$ |
$2.9782896001353043e+30$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.484...304.1 |
$x^{38} - 2 x + 3$ |
$38$ |
[0,19] |
$-\,2^{39}\cdot 523\cdot 599\cdot 213961453\cdot 35576001825507809\cdot 36\!\cdots\!27$ |
$6$ |
$110.751350008$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.2.484...352.1 |
$x^{38} - 3$ |
$38$ |
[2,18] |
$2^{38}\cdot 3^{37}\cdot 19^{38}$ |
$3$ |
$110.751350025$ |
$128.20731479999293$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
not computed |
$2$ |
$19$ |
|
| 38.2.498...365.1 |
$x^{38} - 3 x - 3$ |
$38$ |
[2,18] |
$3^{37}\cdot 5\cdot 22\!\cdots\!71$ |
$3$ |
$110.835921845$ |
$3.0672730378801607e+30$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.948...304.1 |
$x^{38} - 4 x - 3$ |
$38$ |
[2,18] |
$2^{38}\cdot 40980168689701\cdot 203965927976641\cdot 41\!\cdots\!51$ |
$4$ |
$112.728018653$ |
|
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.319...232.1 |
$x^{38} - 4 x - 2$ |
$38$ |
[2,18] |
$2^{75}\cdot 3\cdot 23\cdot 277\cdot 1513583473\cdot 5473293451459721\cdot 5332978185985420820488513531$ |
$7$ |
$123.65319833$ |
|
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.797...824.1 |
$x^{38} - 4 x + 2$ |
$38$ |
[2,18] |
$2^{75}\cdot 7\cdot 47\cdot 64\!\cdots\!17$ |
$4$ |
$134.583943306$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.797...008.1 |
$x^{38} - 4 x + 1$ |
$38$ |
[2,18] |
$2^{38}\cdot 3\cdot 811\cdot 2302291\cdot 51\!\cdots\!69$ |
$5$ |
$134.583943307$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.508...072.1 |
$x^{38} - 2 x + 4$ |
$38$ |
[0,19] |
$-\,2^{36}\cdot 3\cdot 7\cdot 269683\cdot 243410960929\cdot 53\!\cdots\!41$ |
$6$ |
$141.304573961$ |
$5.3373085180131776e+35$ |
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.2.508...096.1 |
$x^{38} - 2 x - 4$ |
$38$ |
[2,18] |
$2^{36}\cdot 101\cdot 919\cdot 1949\cdot 3539\cdot 185240700233\cdot 17140715362231\cdot 36\!\cdots\!23$ |
$8$ |
$141.304573961$ |
$5.337308518013939e+35$ |
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.203...853.1 |
$x^{38} - x - 4$ |
$38$ |
[2,18] |
$773\cdot 4813\cdot 6781\cdot 44087\cdot 282407\cdot 4622799406751\cdot 23120981570369\cdot 60\!\cdots\!47$ |
$8$ |
$146.554751687$ |
$1.4256016038422806e+41$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.250...631.1 |
$x^{38} - x^{37} + 3 x^{36} - 11 x^{35} + 44 x^{34} + 732 x^{33} - 116 x^{32} + 2069 x^{31} + 2818 x^{30} - 12880 x^{29} + 93246 x^{28} - 145805 x^{27} + 92780 x^{26} + 2105124 x^{25} - 3183002 x^{24} - 3104601 x^{23} + 12583923 x^{22} + 9706311 x^{21} + 21916307 x^{20} - 49619666 x^{19} + 22159929 x^{18} - 196911474 x^{17} + 1026982112 x^{16} + 311788273 x^{15} - 1106984612 x^{14} - 334730951 x^{13} - 1752540110 x^{12} + 3801710744 x^{11} + 7280378790 x^{10} + 1308968234 x^{9} - 6926602921 x^{8} - 6856588968 x^{7} + 18604485712 x^{6} + 18058309277 x^{5} + 9272912074 x^{4} - 5214869030 x^{3} - 1463327624 x^{2} + 5326526527 x + 2048986499$ |
$38$ |
[0,19] |
$-\,191^{37}$ |
$1$ |
$166.343629548$ |
$166.34362954768946$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.2.383...821.1 |
$x^{38} - 5 x + 1$ |
$38$ |
[2,18] |
$3\cdot 4921063777787\cdot 26\!\cdots\!61$ |
$3$ |
$168.229929133$ |
$1.9595753946993848e+42$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.383...429.1 |
$x^{38} - 5 x - 1$ |
$38$ |
[2,18] |
$163\cdot 315952440047\cdot 735114279983971219\cdot 10\!\cdots\!31$ |
$4$ |
$168.229929133$ |
$1.9595753946993848e+42$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.912...125.1 |
$x^{38} - 5 x - 5$ |
$38$ |
[2,18] |
$5^{37}\cdot 131\cdot 181\cdot 2011\cdot 898776624172831\cdot 29\!\cdots\!71$ |
$6$ |
$172.105717768$ |
$1.6972337346715754e+30$ |
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.0.195...488.1 |
$x^{38} - 2 x + 5$ |
$38$ |
[0,19] |
$-\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357$ |
$9$ |
$175.59654618$ |
|
|
|
? |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.744...875.1 |
$x^{38} - 5 x + 5$ |
$38$ |
[0,19] |
$-\,5^{37}\cdot 23\cdot 139\cdot 299699\cdot 9433691167\cdot 85263102703\cdot 14613295519063\cdot 90847825344374471$ |
$8$ |
$181.879952061$ |
$4.847778484353784e+30$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.782...987.1 |
$x^{38} - 3 x + 5$ |
$38$ |
[0,19] |
$-\,313\cdot 1019481121\cdot 8471154741571\cdot 28\!\cdots\!89$ |
$4$ |
$182.120843657$ |
$8.847761675350612e+42$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$18$ |
|
| 38.0.782...000.1 |
$x^{38} + 5$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 5^{37}\cdot 19^{38}$ |
$3$ |
$182.120843658$ |
$210.82564076426127$ |
|
|
✓ |
$C_2\times F_{19}$ (as 38T9) |
not computed |
$2$ |
$18$ |
|
| 38.2.782...517.1 |
$x^{38} - x - 5$ |
$38$ |
[2,18] |
$3\cdot 4441\cdot 68315627\cdot 8533124051989\cdot 10\!\cdots\!93$ |
$5$ |
$182.120843658$ |
$8.847761676156376e+42$ |
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.2.782...048.1 |
$x^{38} - 2 x - 5$ |
$38$ |
[2,18] |
$2^{39}\cdot 3\cdot 17\cdot 929\cdot 26261\cdot 1587413\cdot 12103709\cdot 158015743\cdot 1243193510457304691\cdot 30321616657803787127474779$ |
$10$ |
$182.120843658$ |
|
|
|
✓ |
$S_{38}$ (as 38T76) |
not computed |
$2$ |
$19$ |
|
| 38.38.206...109.1 |
$x^{38} - x^{37} - 111 x^{36} + 252 x^{35} + 5215 x^{34} - 18518 x^{33} - 127217 x^{32} + 667591 x^{31} + 1483161 x^{30} - 13721975 x^{29} + 465004 x^{28} + 166721208 x^{27} - 256518740 x^{26} - 1121099509 x^{25} + 3587854285 x^{24} + 2545487107 x^{23} - 24194172078 x^{22} + 18477975516 x^{21} + 81929300895 x^{20} - 167013913064 x^{19} - 73340427022 x^{18} + 542830510766 x^{17} - 389253844535 x^{16} - 713755295161 x^{15} + 1324741808499 x^{14} - 116683382685 x^{13} - 1503618080692 x^{12} + 1234820609168 x^{11} + 402888989840 x^{10} - 1097103201368 x^{9} + 414161581992 x^{8} + 265775405099 x^{7} - 274544542564 x^{6} + 51663795877 x^{5} + 34067812864 x^{4} - 20708103251 x^{3} + 4233902513 x^{2} - 281738990 x - 6131569$ |
$38$ |
[38,0] |
$229^{37}$ |
$1$ |
$198.488133851$ |
$198.48813385059066$ |
|
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$37$ |
|
| 38.0.152...747.1 |
$x^{38} - x^{37} + 91 x^{36} - 24 x^{35} + 5113 x^{34} - 166 x^{33} + 173717 x^{32} + 27194 x^{31} + 4239797 x^{30} + 1325317 x^{29} + 74027272 x^{28} + 40999344 x^{27} + 983326589 x^{26} + 743120555 x^{25} + 10059741791 x^{24} + 9563481092 x^{23} + 81070213075 x^{22} + 87547591746 x^{21} + 511882174610 x^{20} + 601337789804 x^{19} + 2539884758984 x^{18} + 3042827513863 x^{17} + 9675050790560 x^{16} + 11543123809355 x^{15} + 28268796522511 x^{14} + 31776668507252 x^{13} + 60600608962241 x^{12} + 63076854532617 x^{11} + 95016529831875 x^{10} + 85766481354393 x^{9} + 98440678914956 x^{8} + 74640315704381 x^{7} + 67352150639088 x^{6} + 40110464366364 x^{5} + 23287561297245 x^{4} + 7350839404496 x^{3} + 1810153278801 x^{2} + 182761486103 x + 13841287201$ |
$38$ |
[0,19] |
$-\,3^{19}\cdot 191^{36}$ |
$2$ |
$250.922500573$ |
$250.92250057347005$ |
✓ |
✓ |
|
$C_{38}$ (as 38T1) |
not computed |
$6$ |
$18$ |
|
| 38.0.223...259.1 |
$x^{38} - 209 x^{35} + 190 x^{34} + 1292 x^{33} + 11818 x^{32} - 17860 x^{31} - 124165 x^{30} + 92378 x^{29} - 315590 x^{28} + 461434 x^{27} + 19355661 x^{26} + 42336256 x^{25} - 170675214 x^{24} - 2184021538 x^{23} + 4055379323 x^{22} + 20028771815 x^{21} - 37281886089 x^{20} - 119372774190 x^{19} + 206222273796 x^{18} + 638565435242 x^{17} - 1510749792677 x^{16} - 1246896758667 x^{15} + 6615154002166 x^{14} + 1497131351993 x^{13} + 895955914113 x^{12} - 6914578071407 x^{11} + 51068057863185 x^{10} + 80278712330599 x^{9} - 10972845112675 x^{8} + 78343381011053 x^{7} + 257531197354487 x^{6} + 248070995565179 x^{5} + 172436840306532 x^{4} + 97988777901672 x^{3} + 65070800259551 x^{2} + 24610290628033 x + 5454582062023$ |
$38$ |
[0,19] |
$-\,19^{73}$ |
$1$ |
$286.123131947$ |
$286.1231319470719$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.38.290...677.1 |
$x^{38} - x^{37} - 188 x^{36} + 180 x^{35} + 15133 x^{34} - 12829 x^{33} - 695929 x^{32} + 470210 x^{31} + 20560148 x^{30} - 9452291 x^{29} - 414286793 x^{28} + 90520176 x^{27} + 5875939616 x^{26} + 191303612 x^{25} - 59496127537 x^{24} - 16762796308 x^{23} + 430644226744 x^{22} + 224673611403 x^{21} - 2206305371572 x^{20} - 1655031822292 x^{19} + 7828656065108 x^{18} + 7607383848877 x^{17} - 18551523651529 x^{16} - 22355418258850 x^{15} + 27686404325779 x^{14} + 41724858463028 x^{13} - 23225313872578 x^{12} - 48637857116067 x^{11} + 6837701957301 x^{10} + 34223650023543 x^{9} + 4693738691921 x^{8} - 13444562674843 x^{7} - 4790142874347 x^{6} + 2352031466145 x^{5} + 1507820068977 x^{4} + 14043380009 x^{3} - 154333274880 x^{2} - 38062864399 x - 2836879451$ |
$38$ |
[38,0] |
$3^{19}\cdot 191^{37}$ |
$2$ |
$288.115617892$ |
$288.1156178920137$ |
|
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$37$ |
|
| 38.0.360...904.1 |
$x^{38} + 181 x^{36} + 14302 x^{34} + 655785 x^{32} + 19564842 x^{30} + 403491764 x^{28} + 5961216274 x^{26} + 64460499272 x^{24} + 516273473421 x^{22} + 3076728313208 x^{20} + 13620343868498 x^{18} + 44444158242663 x^{16} + 105381413708670 x^{14} + 177560394917737 x^{12} + 205585970435602 x^{10} + 155336297697903 x^{8} + 70268784621098 x^{6} + 16089414412134 x^{4} + 1207108975793 x^{2} + 13841287201$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 191^{36}$ |
$2$ |
$289.740346504$ |
$289.7403465036539$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$4$ |
$18$ |
|
| 38.0.104...707.1 |
$x^{38} - x^{37} + 109 x^{36} - 318 x^{35} + 7607 x^{34} - 26082 x^{33} + 346271 x^{32} - 1277601 x^{31} + 11625429 x^{30} - 40847577 x^{29} + 278354747 x^{28} - 890102893 x^{27} + 4876149460 x^{26} - 13377962627 x^{25} + 59213347219 x^{24} - 129738898417 x^{23} + 497734200105 x^{22} - 864588650146 x^{21} + 3071362959747 x^{20} - 3938571660134 x^{19} + 13635086341776 x^{18} - 11900678948488 x^{17} + 45427254629183 x^{16} - 23117165748554 x^{15} + 104447793269632 x^{14} - 20670309199584 x^{13} + 172563580620384 x^{12} + 14666610274324 x^{11} + 167592119930922 x^{10} + 69948796872392 x^{9} + 125341715722354 x^{8} + 63681900889938 x^{7} + 64136735752211 x^{6} + 36520042111943 x^{5} + 22298249070088 x^{4} + 8329262399475 x^{3} + 2645555104756 x^{2} + 468857415513 x + 63175314409$ |
$38$ |
[0,19] |
$-\,3^{19}\cdot 229^{36}$ |
$2$ |
$297.98488963$ |
$297.98488962998783$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$6$ |
$18$ |
|
| 38.38.249...125.1 |
$x^{38} - 17 x^{37} - 64 x^{36} + 2589 x^{35} - 5411 x^{34} - 156768 x^{33} + 733103 x^{32} + 4788192 x^{31} - 35074270 x^{30} - 69778288 x^{29} + 937716801 x^{28} - 3988006 x^{27} - 15662818901 x^{26} + 18940301798 x^{25} + 169186329709 x^{24} - 366424944806 x^{23} - 1167394423359 x^{22} + 3780063487716 x^{21} + 4693995261962 x^{20} - 24515638087910 x^{19} - 6315614627194 x^{18} + 103828189076722 x^{17} - 36155927083660 x^{16} - 285274970106320 x^{15} + 223944436674986 x^{14} + 486329219734937 x^{13} - 571966582999537 x^{12} - 458764738319995 x^{11} + 781485719820911 x^{10} + 160103399248715 x^{9} - 557488639455834 x^{8} + 53135732479684 x^{7} + 180915511892981 x^{6} - 38184876354047 x^{5} - 25486623807243 x^{4} + 6173666606950 x^{3} + 1214949029058 x^{2} - 273982926995 x + 184740541$ |
$38$ |
[38,0] |
$5^{19}\cdot 191^{36}$ |
$2$ |
$323.939555303$ |
$323.93955530325684$ |
|
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$37$ |
|
| 38.38.687...664.1 |
$x^{38} - 191 x^{36} + 15662 x^{34} - 730575 x^{32} + 21705622 x^{30} - 436357836 x^{28} + 6157331558 x^{26} - 62411853712 x^{24} + 460944322269 x^{22} - 2499589479956 x^{20} + 9974553348782 x^{18} - 29202012585177 x^{16} + 62167403988174 x^{14} - 94680464008195 x^{12} + 100459885220950 x^{10} - 71207905317537 x^{8} + 31469275400290 x^{6} - 7629511512714 x^{4} + 744125807285 x^{2} - 1101076991$ |
$38$ |
[38,0] |
$2^{38}\cdot 191^{37}$ |
$2$ |
$332.687259095$ |
$332.6872590953789$ |
|
✓ |
|
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$37$ |
|
| 38.0.239...903.1 |
$x^{38} - x^{37} + 118 x^{36} - 435 x^{35} + 6131 x^{34} - 35235 x^{33} + 222008 x^{32} - 1286466 x^{31} + 5995377 x^{30} - 26936649 x^{29} + 103513172 x^{28} - 328397860 x^{27} + 831795745 x^{26} - 841346468 x^{25} - 6703672958 x^{24} + 58117415411 x^{23} - 303731983764 x^{22} + 1218275129036 x^{21} - 3767355799065 x^{20} + 7961894667643 x^{19} - 2218796696910 x^{18} - 81504663492211 x^{17} + 502603614584717 x^{16} - 2027971305796085 x^{15} + 6509260330141933 x^{14} - 17551631941921428 x^{13} + 40524896388301467 x^{12} - 80503012777500047 x^{11} + 136388077021556601 x^{10} - 193370722349898757 x^{9} + 226309207994588218 x^{8} - 220960831577107827 x^{7} + 187038155057537519 x^{6} - 141423416677434751 x^{5} + 93202974532409581 x^{4} - 51592635735804780 x^{3} + 25439606449082092 x^{2} - 11768916674310345 x + 3447647463127489$ |
$38$ |
[0,19] |
$-\,3^{19}\cdot 229^{37}$ |
$2$ |
$343.791532529$ |
$343.79153252875494$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.0.247...624.1 |
$x^{38} + 217 x^{36} + 20630 x^{34} + 1139565 x^{32} + 40850264 x^{30} + 1004488522 x^{28} + 17454519530 x^{26} + 217550145613 x^{24} + 1954462763213 x^{22} + 12621446315235 x^{20} + 58044125409037 x^{18} + 187171442808726 x^{16} + 413962321806804 x^{14} + 609555286857416 x^{12} + 575420256350720 x^{10} + 333058518278260 x^{8} + 111675903836641 x^{6} + 20190511272319 x^{4} + 1811471395871 x^{2} + 63175314409$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 229^{36}$ |
$2$ |
$344.083312485$ |
$344.0833124846288$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$4$ |
$18$ |
|
| 38.0.105...139.1 |
$x^{38} - x^{37} + 6 x^{36} - 46 x^{35} - 866 x^{34} - 2262 x^{33} - 8218 x^{32} - 21902 x^{31} + 431634 x^{30} + 845654 x^{29} + 12392062 x^{28} + 22625646 x^{27} + 131347110 x^{26} + 99749222 x^{25} + 35665294 x^{24} - 866315187 x^{23} - 258426421 x^{22} + 17785842992 x^{21} + 90256146871 x^{20} + 153552360949 x^{19} + 435041961961 x^{18} - 1392669637447 x^{17} + 1076840441256 x^{16} - 9935143209215 x^{15} + 31070017846749 x^{14} - 17675958023404 x^{13} + 138250934902501 x^{12} - 327233950365006 x^{11} + 433153745352823 x^{10} - 1944991946784557 x^{9} + 5889532748622531 x^{8} - 11577094600459131 x^{7} + 25495193933767723 x^{6} - 50712315827213047 x^{5} + 74651226530405679 x^{4} - 82308207923451862 x^{3} + 77528185035084423 x^{2} - 59368882440546583 x + 25758699005655811$ |
$38$ |
[0,19] |
$-\,419^{37}$ |
$1$ |
$357.444312198$ |
$357.44431219766653$ |
✓ |
✓ |
|
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.0.477...875.1 |
$x^{38} - x^{37} + 194 x^{36} - 202 x^{35} + 16279 x^{34} - 7863 x^{33} + 772861 x^{32} + 402596 x^{31} + 23045822 x^{30} + 40384193 x^{29} + 479536671 x^{28} + 1351816180 x^{27} + 7928555878 x^{26} + 25902608554 x^{25} + 111456458601 x^{24} + 341385389946 x^{23} + 1297163210108 x^{22} + 3493633650369 x^{21} + 12095301942774 x^{20} + 29754895552994 x^{19} + 90602135732080 x^{18} + 209292172135889 x^{17} + 578704163180687 x^{16} + 1150796400064466 x^{15} + 3249066298571457 x^{14} + 4892053641982278 x^{13} + 14078439508345248 x^{12} + 18448183569455711 x^{11} + 46083907583218775 x^{10} + 65495333977938485 x^{9} + 111449247373051429 x^{8} + 177739871270855783 x^{7} + 253288222342260757 x^{6} + 334042708854918147 x^{5} + 456173375797126253 x^{4} + 247500381632980217 x^{3} + 331215018154218380 x^{2} + 303420818935344453 x + 79580728329881359$ |
$38$ |
[0,19] |
$-\,5^{19}\cdot 191^{37}$ |
$2$ |
$371.955663293$ |
$371.95566329267626$ |
✓ |
✓ |
|
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.38.261...857.1 |
$x^{38} - x^{37} - 222 x^{36} + 479 x^{35} + 21047 x^{34} - 66053 x^{33} - 1110228 x^{32} + 4495506 x^{31} + 35823405 x^{30} - 180946047 x^{29} - 731415663 x^{28} + 4712734359 x^{27} + 9238434306 x^{26} - 83665939703 x^{25} - 59973164681 x^{24} + 1044644450973 x^{23} - 101098208429 x^{22} - 9336414182461 x^{21} + 6288159462034 x^{20} + 60150648390199 x^{19} - 67252981484387 x^{18} - 278611442416743 x^{17} + 417500804951451 x^{16} + 915079337067075 x^{15} - 1716002791423036 x^{14} - 2065408719688167 x^{13} + 4825202788269126 x^{12} + 2982003177766905 x^{11} - 9269437748788275 x^{10} - 2187058821094830 x^{9} + 11855288436035595 x^{8} - 411608485430453 x^{7} - 9515695267587717 x^{6} + 2357948299236310 x^{5} + 4196479083397002 x^{4} - 1892165812751211 x^{3} - 650631784472963 x^{2} + 526610168112801 x - 83497743723127$ |
$38$ |
[38,0] |
$457^{37}$ |
$1$ |
$388.972058577$ |
$388.9720585765065$ |
|
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$37$ |
|
| 38.0.566...896.1 |
$x^{38} + 229 x^{36} + 22442 x^{34} + 1242325 x^{32} + 43174744 x^{30} + 989928070 x^{28} + 15310092242 x^{26} + 160462320009 x^{24} + 1129846290713 x^{22} + 5241767939799 x^{20} + 15619544332617 x^{18} + 29338707057674 x^{16} + 34962128493052 x^{14} + 26729901012072 x^{12} + 13161379227544 x^{10} + 4139430890096 x^{8} + 811133080337 x^{6} + 94183964323 x^{4} + 5864318791 x^{2} + 149876149$ |
$38$ |
[0,19] |
$-\,2^{38}\cdot 229^{37}$ |
$2$ |
$396.976267701$ |
$396.9762677011813$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$2$ |
$18$ |
|
| 38.0.136...787.1 |
$x^{38} + 171 x^{36} - 266 x^{35} + 17765 x^{34} - 38323 x^{33} + 1208419 x^{32} - 3128616 x^{31} + 60877083 x^{30} - 164538138 x^{29} + 2281935169 x^{28} - 6108816122 x^{27} + 65770773122 x^{26} - 164067939585 x^{25} + 1434043198618 x^{24} - 3182597959136 x^{23} + 23807715304970 x^{22} - 44488778447299 x^{21} + 291967423046375 x^{20} - 424722852053838 x^{19} + 2667130160996125 x^{18} - 2974990157993691 x^{17} + 18341053997864450 x^{16} - 14685757775285777 x^{15} + 92760878311304464 x^{14} - 59049250104163667 x^{13} + 342353164732402796 x^{12} - 172475502215832115 x^{11} + 890393108976853995 x^{10} - 452012764582067042 x^{9} + 1563583757111096932 x^{8} - 707974172043966504 x^{7} + 1816769368682524829 x^{6} - 831929210861393479 x^{5} + 1134167336866808190 x^{4} - 228910989279510535 x^{3} + 271437005032832706 x^{2} - 30519054068376079 x + 49228485006254761$ |
$38$ |
[0,19] |
$-\,3^{19}\cdot 19^{72}$ |
$2$ |
$458.629712312$ |
$458.62971231173134$ |
✓ |
✓ |
? |
$C_{38}$ (as 38T1) |
not computed |
$6$ |
$18$ |
|
