| 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 |
| 33.33.271...161.1 |
$x^{33} - x^{32} - 32 x^{31} + 31 x^{30} + 465 x^{29} - 435 x^{28} - 4060 x^{27} + 3654 x^{26} + 23751 x^{25} - 20475 x^{24} - 98280 x^{23} + 80730 x^{22} + 296010 x^{21} - 230230 x^{20} - 657800 x^{19} + 480700 x^{18} + 1081575 x^{17} - 735471 x^{16} - 1307504 x^{15} + 817190 x^{14} + 1144066 x^{13} - 646646 x^{12} - 705432 x^{11} + 352716 x^{10} + 293930 x^{9} - 125970 x^{8} - 77520 x^{7} + 27132 x^{6} + 11628 x^{5} - 3060 x^{4} - 816 x^{3} + 136 x^{2} + 17 x - 1$ |
$33$ |
[33,0] |
$67^{32}$ |
$1$ |
$58.9846766001$ |
$58.98467660010086$ |
|
✓ |
✓ |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$3985748844865106400$ |
| 33.33.277...001.1 |
$x^{33} - x^{32} - 52 x^{31} + 47 x^{30} + 1159 x^{29} - 945 x^{28} - 14589 x^{27} + 10741 x^{26} + 115099 x^{25} - 76770 x^{24} - 597580 x^{23} + 362822 x^{22} + 2088771 x^{21} - 1160546 x^{20} - 4956062 x^{19} + 2531215 x^{18} + 7980244 x^{17} - 3753538 x^{16} - 8674935 x^{15} + 3750773 x^{14} + 6304834 x^{13} - 2497276 x^{12} - 3006793 x^{11} + 1087323 x^{10} + 908614 x^{9} - 298518 x^{8} - 163557 x^{7} + 48112 x^{6} + 15777 x^{5} - 3955 x^{4} - 691 x^{3} + 126 x^{2} + 12 x - 1$ |
$33$ |
[33,0] |
$7^{22}\cdot 23^{30}$ |
$2$ |
$63.2897076721$ |
$63.289707672053964$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$15716532070591353000$ |
| 33.33.700...569.1 |
$x^{33} - 63 x^{31} - 4 x^{30} + 1710 x^{29} + 204 x^{28} - 26254 x^{27} - 4392 x^{26} + 251754 x^{25} + 52248 x^{24} - 1572192 x^{23} - 377544 x^{22} + 6479940 x^{21} + 1717920 x^{20} - 17548167 x^{19} - 4953616 x^{18} + 30725595 x^{17} + 8949468 x^{16} - 34072421 x^{15} - 9933084 x^{14} + 23552382 x^{13} + 6584132 x^{12} - 10086444 x^{11} - 2580438 x^{10} + 2636960 x^{9} + 587106 x^{8} - 404862 x^{7} - 74061 x^{6} + 33768 x^{5} + 4755 x^{4} - 1326 x^{3} - 135 x^{2} + 18 x + 1$ |
$33$ |
[33,0] |
$3^{44}\cdot 23^{30}$ |
$2$ |
$74.8335019768$ |
$74.83350197679573$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$176588774716401650000$ |
| 33.33.228...681.1 |
$x^{33} - 8 x^{32} - 48 x^{31} + 488 x^{30} + 889 x^{29} - 13082 x^{28} - 6681 x^{27} + 203003 x^{26} - 17780 x^{25} - 2022483 x^{24} + 832653 x^{23} + 13572345 x^{22} - 8326527 x^{21} - 62657637 x^{20} + 47704277 x^{19} + 199663335 x^{18} - 178099102 x^{17} - 433344046 x^{16} + 447058648 x^{15} + 617907878 x^{14} - 750473359 x^{13} - 533823452 x^{12} + 817138243 x^{11} + 221279551 x^{10} - 544192951 x^{9} + 11597098 x^{8} + 199867737 x^{7} - 43176794 x^{6} - 33036600 x^{5} + 11713378 x^{4} + 1505253 x^{3} - 925381 x^{2} + 72350 x + 1013$ |
$33$ |
[33,0] |
$13^{22}\cdot 23^{30}$ |
$2$ |
$95.6232054578$ |
$95.623205457779$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$22765796489209540000000$ |
| 33.33.964...489.1 |
$x^{33} - 8 x^{32} - 70 x^{31} + 734 x^{30} + 1439 x^{29} - 27994 x^{28} + 11289 x^{27} + 571079 x^{26} - 1005928 x^{25} - 6614661 x^{24} + 19440415 x^{23} + 40980613 x^{22} - 194665653 x^{21} - 82258867 x^{20} + 1125872365 x^{19} - 536982871 x^{18} - 3781576926 x^{17} + 4155619240 x^{16} + 6998281772 x^{15} - 12201861484 x^{14} - 5994133153 x^{13} + 18812121252 x^{12} + 75160599 x^{11} - 16337602363 x^{10} + 3902636199 x^{9} + 8090155706 x^{8} - 3031301627 x^{7} - 2187750082 x^{6} + 1012187926 x^{5} + 277584302 x^{4} - 153651191 x^{3} - 8485173 x^{2} + 8057502 x - 470213$ |
$33$ |
[33,0] |
$19^{22}\cdot 23^{30}$ |
$2$ |
$123.150675121$ |
$123.1506751207494$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$859641744829651100000000$ |
| 33.33.236...601.1 |
$x^{33} - 8 x^{32} - 86 x^{31} + 690 x^{30} + 3527 x^{29} - 25876 x^{28} - 92162 x^{27} + 549745 x^{26} + 1676544 x^{25} - 7221169 x^{24} - 21518451 x^{23} + 59984529 x^{22} + 192193744 x^{21} - 307177110 x^{20} - 1170053321 x^{19} + 864215343 x^{18} + 4741699040 x^{17} - 637264044 x^{16} - 12404482875 x^{15} - 3656463713 x^{14} + 19997642137 x^{13} + 12376322490 x^{12} - 18399788371 x^{11} - 16849661483 x^{10} + 8289542908 x^{9} + 11391691466 x^{8} - 842642325 x^{7} - 3707258605 x^{6} - 522452271 x^{5} + 463178377 x^{4} + 128777001 x^{3} - 2389174 x^{2} - 1929880 x + 90889$ |
$33$ |
[33,0] |
$7^{22}\cdot 67^{30}$ |
$2$ |
$167.288734484$ |
$167.28873448442988$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$503657750536712100000000000$ |
| 33.33.365...601.1 |
$x^{33} - x^{32} - 96 x^{31} + 217 x^{30} + 3795 x^{29} - 13403 x^{28} - 74197 x^{27} + 394231 x^{26} + 599821 x^{25} - 6350170 x^{24} + 2832807 x^{23} + 56803105 x^{22} - 104532088 x^{21} - 244229488 x^{20} + 932758015 x^{19} + 5618002 x^{18} - 3890173018 x^{17} + 4529747891 x^{16} + 6495127532 x^{15} - 18110944809 x^{14} + 4574986912 x^{13} + 26694143816 x^{12} - 29645825157 x^{11} - 6037403432 x^{10} + 30417132332 x^{9} - 15468969217 x^{8} - 6737165737 x^{7} + 8515927088 x^{6} - 1017730658 x^{5} - 1409177433 x^{4} + 395068072 x^{3} + 75602260 x^{2} - 21210003 x - 2947097$ |
$33$ |
[33,0] |
$199^{32}$ |
$1$ |
$169.508258478$ |
$169.50825847800346$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$194708110268326050000000000$ |
| 33.33.458...889.1 |
$x^{33} - 8 x^{32} - 114 x^{31} + 1061 x^{30} + 5059 x^{29} - 60653 x^{28} - 96801 x^{27} + 1959353 x^{26} - 29225 x^{25} - 39423204 x^{24} + 40518048 x^{23} + 513641811 x^{22} - 918583926 x^{21} - 4362858468 x^{20} + 10893040871 x^{19} + 23607826158 x^{18} - 79952364670 x^{17} - 75116228962 x^{16} + 381639679930 x^{15} + 98812353215 x^{14} - 1205788951741 x^{13} + 175885903114 x^{12} + 2530475990857 x^{11} - 987113141315 x^{10} - 3498652499635 x^{9} + 1841635007257 x^{8} + 3110258033850 x^{7} - 1787906886467 x^{6} - 1685908305594 x^{5} + 902138910730 x^{4} + 495599994390 x^{3} - 195854103442 x^{2} - 57250484608 x + 8460460991$ |
$33$ |
[33,0] |
$23^{30}\cdot 31^{22}$ |
$2$ |
$170.677206312$ |
$170.677206311906$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$478444878328119400000000000$ |
| 33.33.225...481.1 |
$x^{33} - 8 x^{32} - 136 x^{31} + 1010 x^{30} + 9089 x^{29} - 56260 x^{28} - 391707 x^{27} + 1778015 x^{26} + 11776892 x^{25} - 33684927 x^{24} - 250499393 x^{23} + 352249669 x^{22} + 3723230595 x^{21} - 869647969 x^{20} - 37516024451 x^{19} - 27213591295 x^{18} + 241140895308 x^{17} + 392273336476 x^{16} - 846902299600 x^{15} - 2477173011886 x^{14} + 614677458641 x^{13} + 7779541229922 x^{12} + 5903210349213 x^{11} - 9094078083973 x^{10} - 16773542913789 x^{9} - 4693562989906 x^{8} + 8584245508513 x^{7} + 7302900918860 x^{6} + 488836631314 x^{5} - 1567611092278 x^{4} - 601455629303 x^{3} - 17378174655 x^{2} + 24259321620 x + 3109630591$ |
$33$ |
[33,0] |
$23^{30}\cdot 37^{22}$ |
$2$ |
$192.044649724$ |
$192.04464972398003$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.596...969.1 |
$x^{33} - 3 x^{32} - 120 x^{31} + 450 x^{30} + 5757 x^{29} - 26439 x^{28} - 139216 x^{27} + 813933 x^{26} + 1676889 x^{25} - 14588595 x^{24} - 5289417 x^{23} + 158067366 x^{22} - 111316484 x^{21} - 1026324261 x^{20} + 1580724570 x^{19} + 3707180205 x^{18} - 9398785623 x^{17} - 5392982019 x^{16} + 29700176281 x^{15} - 7076803698 x^{14} - 50183067855 x^{13} + 37619683596 x^{12} + 40721934162 x^{11} - 52500002157 x^{10} - 9740363856 x^{9} + 32585743542 x^{8} - 5020929429 x^{7} - 9149246964 x^{6} + 3064214298 x^{5} + 963373038 x^{4} - 501812162 x^{3} + 1428300 x^{2} + 21340050 x - 2255257$ |
$33$ |
[33,0] |
$3^{44}\cdot 67^{30}$ |
$2$ |
$197.801543145$ |
$197.80154314512671$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$5218493771929612000000000000$ |
| 33.33.613...201.1 |
$x^{33} - 8 x^{32} - 158 x^{31} + 1201 x^{30} + 11799 x^{29} - 79637 x^{28} - 553517 x^{27} + 3047297 x^{26} + 18045183 x^{25} - 73486076 x^{24} - 423467260 x^{23} + 1134885507 x^{22} + 7181937070 x^{21} - 10577693296 x^{20} - 86925920617 x^{19} + 42552529394 x^{18} + 731936029174 x^{17} + 221162562802 x^{16} - 4103969993350 x^{15} - 4008861317997 x^{14} + 14099364740759 x^{13} + 23658856478442 x^{12} - 23960117693331 x^{11} - 70854886167335 x^{10} + 459363050377 x^{9} + 105795614045209 x^{8} + 56031098946162 x^{7} - 67912012997243 x^{6} - 66884906075414 x^{5} + 8079131079686 x^{4} + 24981654176414 x^{3} + 4742963910394 x^{2} - 1938599990280 x - 418925179289$ |
$33$ |
[33,0] |
$23^{30}\cdot 43^{22}$ |
$2$ |
$212.28209586$ |
$212.28209586019705$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.106...889.1 |
$x^{33} - x^{32} - 166 x^{31} + 31 x^{30} + 12056 x^{29} + 6466 x^{28} - 499793 x^{27} - 584740 x^{26} + 12983561 x^{25} + 22545996 x^{24} - 218817971 x^{23} - 498814134 x^{22} + 2391704632 x^{21} + 6888744208 x^{20} - 16302268943 x^{19} - 60873620056 x^{18} + 60970794078 x^{17} + 341619629535 x^{16} - 59392601981 x^{15} - 1175181902675 x^{14} - 406185859598 x^{13} + 2319674937703 x^{12} + 1532280908714 x^{11} - 2407172936531 x^{10} - 1914990089276 x^{9} + 1318064593414 x^{8} + 880459878203 x^{7} - 500254090591 x^{6} - 126270280983 x^{5} + 98927128189 x^{4} - 8375694534 x^{3} - 3305868170 x^{2} + 625295808 x - 24571849$ |
$33$ |
[33,0] |
$7^{22}\cdot 67^{32}$ |
$2$ |
$215.842963887$ |
$215.84296388660744$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.106...889.2 |
$x^{33} - x^{32} - 166 x^{31} + 31 x^{30} + 12056 x^{29} + 6466 x^{28} - 499793 x^{27} - 584740 x^{26} + 12983561 x^{25} + 22519732 x^{24} - 218988687 x^{23} - 497212030 x^{22} + 2404876028 x^{21} + 6861757948 x^{20} - 16687359215 x^{19} - 60999502470 x^{18} + 66428973399 x^{17} + 350436717444 x^{16} - 97922207025 x^{15} - 1282471520334 x^{14} - 299209598192 x^{13} + 2904925438202 x^{12} + 1667373272694 x^{11} - 3878119747536 x^{10} - 3171263867777 x^{9} + 2800536792860 x^{8} + 2837059467987 x^{7} - 963126440972 x^{6} - 1120340176018 x^{5} + 176411491936 x^{4} + 160346257228 x^{3} - 27513840644 x^{2} - 1420033359 x + 92241043$ |
$33$ |
[33,0] |
$7^{22}\cdot 67^{32}$ |
$2$ |
$215.842963887$ |
$215.84296388660744$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
$[3]$ |
$2$ |
$32$ |
$2873827831811995000000000000$ |
| 33.33.118...249.1 |
$x^{33} - 8 x^{32} - 116 x^{31} + 1072 x^{30} + 5007 x^{29} - 59420 x^{28} - 90148 x^{27} + 1807185 x^{26} - 22554 x^{25} - 33533077 x^{24} + 30987203 x^{23} + 397774975 x^{22} - 620888184 x^{21} - 3064646220 x^{20} + 6410478765 x^{19} + 15227509843 x^{18} - 40385752376 x^{17} - 47126502322 x^{16} + 162998575211 x^{15} + 81953781823 x^{14} - 427869988653 x^{13} - 45802829578 x^{12} + 727374495587 x^{11} - 105270881315 x^{10} - 778209959832 x^{9} + 249662858736 x^{8} + 487414494739 x^{7} - 229613689017 x^{6} - 148659543549 x^{5} + 99441822253 x^{4} + 8651377149 x^{3} - 15544432294 x^{2} + 2900591056 x - 88092733$ |
$33$ |
[33,0] |
$7^{22}\cdot 89^{30}$ |
$2$ |
$216.55660119$ |
$216.55660119019367$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.194...281.1 |
$x^{33} - 8 x^{32} - 108 x^{31} + 826 x^{30} + 5517 x^{29} - 37410 x^{28} - 174850 x^{27} + 974941 x^{26} + 3753002 x^{25} - 16170687 x^{24} - 56209081 x^{23} + 178946863 x^{22} + 592568182 x^{21} - 1351731560 x^{20} - 4397140947 x^{19} + 7038388451 x^{18} + 22835380012 x^{17} - 25350973354 x^{16} - 82027847149 x^{15} + 63440275941 x^{14} + 199922687695 x^{13} - 111827183164 x^{12} - 320812557227 x^{11} + 142179324189 x^{10} + 323210228406 x^{9} - 130110920902 x^{8} - 188148415319 x^{7} + 77322457297 x^{6} + 52579210647 x^{5} - 22741173483 x^{4} - 3948105037 x^{3} + 1212304894 x^{2} + 227068790 x + 8672509$ |
$33$ |
[33,0] |
$13^{22}\cdot 67^{30}$ |
$2$ |
$252.753340421$ |
$252.75334042094067$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.267...841.1 |
$x^{33} - 201 x^{31} - 134 x^{30} + 17487 x^{29} + 22110 x^{28} - 861687 x^{27} - 1554534 x^{26} + 26459037 x^{25} + 61127718 x^{24} - 525017025 x^{23} - 1484472234 x^{22} + 6740683807 x^{21} + 23212311336 x^{20} - 53976965718 x^{19} - 236603093887 x^{18} + 238566048363 x^{17} + 1560447894561 x^{16} - 286240447964 x^{15} - 6509647282689 x^{14} - 2289097051344 x^{13} + 16594056412925 x^{12} + 11906847973017 x^{11} - 24622684612068 x^{10} - 24919584215523 x^{9} + 19258042021938 x^{8} + 26552533093695 x^{7} - 5285639627900 x^{6} - 14010626855421 x^{5} - 1812694476681 x^{4} + 2783095185303 x^{3} + 1020301549110 x^{2} + 80878788432 x + 703500067$ |
$33$ |
[33,0] |
$3^{44}\cdot 67^{32}$ |
$2$ |
$255.211873444$ |
$255.21187344365075$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.267...841.2 |
$x^{33} - 201 x^{31} - 134 x^{30} + 17487 x^{29} + 22110 x^{28} - 861687 x^{27} - 1554534 x^{26} + 26459037 x^{25} + 61060182 x^{24} - 525472893 x^{23} - 1479852048 x^{22} + 6781467109 x^{21} + 23142227058 x^{20} - 55275281400 x^{19} - 237908569591 x^{18} + 256540684815 x^{17} + 1607669922021 x^{16} - 384257671040 x^{15} - 7002763432065 x^{14} - 2330964630558 x^{13} + 18790066832900 x^{12} + 14115431940957 x^{11} - 28558726323942 x^{10} - 31399034523306 x^{9} + 21599565380280 x^{8} + 32182755692400 x^{7} - 8169702508646 x^{6} - 16809267910761 x^{5} + 1974777473349 x^{4} + 4512897235854 x^{3} - 547717175874 x^{2} - 515631486780 x + 102306835297$ |
$33$ |
[33,0] |
$3^{44}\cdot 67^{32}$ |
$2$ |
$255.211873444$ |
$255.21187344365075$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.298...681.1 |
$x^{33} - 3 x^{32} - 150 x^{31} + 378 x^{30} + 9687 x^{29} - 20259 x^{28} - 356924 x^{27} + 608835 x^{26} + 8367087 x^{25} - 11392799 x^{24} - 131654085 x^{23} + 139517502 x^{22} + 1429876464 x^{21} - 1144629303 x^{20} - 10866675378 x^{19} + 6321530429 x^{18} + 58029594807 x^{17} - 23073983745 x^{16} - 216880006359 x^{15} + 52038465948 x^{14} + 559616885679 x^{13} - 55951112920 x^{12} - 969959674314 x^{11} - 29098948383 x^{10} + 1074317235504 x^{9} + 167558013330 x^{8} - 693751861143 x^{7} - 194929659142 x^{6} + 217064440848 x^{5} + 87344653842 x^{4} - 20763764254 x^{3} - 10943386668 x^{2} + 463085148 x + 394127189$ |
$33$ |
[33,0] |
$3^{44}\cdot 89^{30}$ |
$2$ |
$256.055675391$ |
$256.0556753908071$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$391930822437712850000000000000$ |
| 33.33.431...961.1 |
$x^{33} - x^{32} - 160 x^{31} + 127 x^{30} + 10849 x^{29} - 5947 x^{28} - 413016 x^{27} + 118107 x^{26} + 9866153 x^{25} - 311795 x^{24} - 156418516 x^{23} - 30572191 x^{22} + 1696328846 x^{21} + 645059522 x^{20} - 12788859303 x^{19} - 6539712577 x^{18} + 67632545787 x^{17} + 39220743072 x^{16} - 252575482403 x^{15} - 146537401384 x^{14} + 670475622740 x^{13} + 343137082097 x^{12} - 1269500051881 x^{11} - 487547125457 x^{10} + 1698429690588 x^{9} + 367945862575 x^{8} - 1552342739498 x^{7} - 54894829630 x^{6} + 900256719370 x^{5} - 121808299470 x^{4} - 284076623751 x^{3} + 78469286329 x^{2} + 32809035298 x - 11929082177$ |
$33$ |
[33,0] |
$331^{32}$ |
$1$ |
$277.632030723$ |
$277.6320307232831$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$2249458248958823000000000000000$ |
| 33.33.119...449.1 |
$x^{33} - 11 x^{32} - 132 x^{31} + 1672 x^{30} + 6930 x^{29} - 108592 x^{28} - 178156 x^{27} + 3996894 x^{26} + 1844139 x^{25} - 93027924 x^{24} + 18084198 x^{23} + 1444297455 x^{22} - 855342411 x^{21} - 15352935246 x^{20} + 12969912978 x^{19} + 112761226974 x^{18} - 113656432329 x^{17} - 569856225147 x^{16} + 634286675935 x^{15} + 1947780966208 x^{14} - 2300361984558 x^{13} - 4350475066289 x^{12} + 5355715367049 x^{11} + 5954891146325 x^{10} - 7704320537793 x^{9} - 4383135863612 x^{8} + 6391533808968 x^{7} + 1195860701409 x^{6} - 2744512475650 x^{5} + 145506995579 x^{4} + 515513855593 x^{3} - 94026824265 x^{2} - 30998629574 x + 7577750599$ |
$33$ |
[33,0] |
$7^{22}\cdot 11^{60}$ |
$2$ |
$286.312256051$ |
$286.3122560511772$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.873...409.1 |
$x^{33} - x^{32} - 300 x^{31} + 433 x^{30} + 39392 x^{29} - 72192 x^{28} - 2984153 x^{27} + 6485636 x^{26} + 144860331 x^{25} - 357729656 x^{24} - 4739669905 x^{23} + 12909408240 x^{22} + 107287869164 x^{21} - 315033430920 x^{20} - 1703147326109 x^{19} + 5283844260566 x^{18} + 19108503148571 x^{17} - 61242330267096 x^{16} - 152647487143611 x^{15} + 489240390400026 x^{14} + 878121079251490 x^{13} - 2664350540682474 x^{12} - 3689093459713802 x^{11} + 9646685091663910 x^{10} + 11364071406107235 x^{9} - 21997467965527856 x^{8} - 24801640551393011 x^{7} + 27838156837825430 x^{6} + 34243335729709568 x^{5} - 12822438553586336 x^{4} - 22500329928610950 x^{3} - 3950367838190814 x^{2} + 1433024492530567 x + 315890005221779$ |
$33$ |
[33,0] |
$13^{22}\cdot 67^{32}$ |
$2$ |
$326.11299438$ |
$326.1129943796312$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.873...409.2 |
$x^{33} - x^{32} - 300 x^{31} + 433 x^{30} + 39392 x^{29} - 72192 x^{28} - 2984153 x^{27} + 6485636 x^{26} + 144860331 x^{25} - 358196512 x^{24} - 4737666605 x^{23} + 12983509436 x^{22} + 106955941516 x^{21} - 319817342676 x^{20} - 1680727775657 x^{19} + 5447962104586 x^{18} + 18298306892962 x^{17} - 64528340390635 x^{16} - 135334358355851 x^{15} + 528898840721217 x^{14} + 650547522824832 x^{13} - 2954479054797901 x^{12} - 1829759678630894 x^{11} + 10940132786146607 x^{10} + 1988618561887006 x^{9} - 25655283542767342 x^{8} + 3493450525717951 x^{7} + 35251613885785939 x^{6} - 13002855201605431 x^{5} - 24464261884516557 x^{4} + 13219885452415850 x^{3} + 5866180865966940 x^{2} - 4214342480887616 x + 360625176548807$ |
$33$ |
[33,0] |
$13^{22}\cdot 67^{32}$ |
$2$ |
$326.11299438$ |
$326.1129943796312$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.144...241.1 |
$x^{33} - x^{32} - 192 x^{31} + 409 x^{30} + 15372 x^{29} - 47108 x^{28} - 664958 x^{27} + 2610041 x^{26} + 16908632 x^{25} - 82566570 x^{24} - 257440569 x^{23} + 1615294942 x^{22} + 2235888539 x^{21} - 20426291889 x^{20} - 8215547427 x^{19} + 171033576249 x^{18} - 30119712292 x^{17} - 959026697321 x^{16} + 482008128932 x^{15} + 3615890185103 x^{14} - 2329240823315 x^{13} - 9171653462413 x^{12} + 5801368765632 x^{11} + 15508197069166 x^{10} - 7754711015299 x^{9} - 16764042648709 x^{8} + 5101268818647 x^{7} + 10477113462512 x^{6} - 1311338013785 x^{5} - 3158585276742 x^{4} + 151875061213 x^{3} + 407404883932 x^{2} - 12108757758 x - 15673387271$ |
$33$ |
[33,0] |
$397^{32}$ |
$1$ |
$331.161071626$ |
$331.1610716260621$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.299...481.1 |
$x^{33} - 198 x^{31} - 88 x^{30} + 16500 x^{29} + 12672 x^{28} - 767778 x^{27} - 757746 x^{26} + 22354497 x^{25} + 25239423 x^{24} - 431474868 x^{23} - 525348783 x^{22} + 5687836869 x^{21} + 7225040196 x^{20} - 51815376558 x^{19} - 67410260049 x^{18} + 325326665763 x^{17} + 429771174723 x^{16} - 1383513593077 x^{15} - 1855194763851 x^{14} + 3841738634745 x^{13} + 5275486801024 x^{12} - 6494206038078 x^{11} - 9369700675533 x^{10} + 5765703181788 x^{9} + 9428309081928 x^{8} - 1695923602263 x^{7} - 4455495029205 x^{6} - 352916325432 x^{5} + 665621580294 x^{4} + 84512905389 x^{3} - 28282285053 x^{2} - 3992061348 x - 126686997$ |
$33$ |
[33,0] |
$3^{44}\cdot 11^{60}$ |
$2$ |
$338.534487949$ |
$338.5344879487777$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$1383473472152591500000000000000000$ |
| 33.33.198...081.1 |
$x^{33} - x^{32} - 224 x^{31} + 159 x^{30} + 21325 x^{29} - 7901 x^{28} - 1132606 x^{27} - 33149 x^{26} + 37089947 x^{25} + 18323632 x^{24} - 781070288 x^{23} - 797096725 x^{22} + 10645175728 x^{21} + 17186085873 x^{20} - 90626504470 x^{19} - 213351348451 x^{18} + 424789196171 x^{17} + 1554506047014 x^{16} - 536588718261 x^{15} - 6282532031836 x^{14} - 4114024022131 x^{13} + 11512222917539 x^{12} + 18101684222486 x^{11} - 1491679119790 x^{10} - 21152129527475 x^{9} - 14284279230133 x^{8} + 2241066960907 x^{7} + 5769638127754 x^{6} + 1343595105723 x^{5} - 598044769496 x^{4} - 250097496007 x^{3} + 934259347 x^{2} + 6767585596 x + 509248489$ |
$33$ |
[33,0] |
$463^{32}$ |
$1$ |
$384.419854034$ |
$384.41985403404107$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.977...769.1 |
$x^{33} - 11 x^{32} - 154 x^{31} + 1870 x^{30} + 9790 x^{29} - 136466 x^{28} - 331628 x^{27} + 5647818 x^{26} + 6285609 x^{25} - 147450798 x^{24} - 56474286 x^{23} + 2554436199 x^{22} - 172542777 x^{21} - 30060392670 x^{20} + 11356146252 x^{19} + 241782778908 x^{18} - 150485460213 x^{17} - 1317959825523 x^{16} + 1115197659829 x^{15} + 4739104722814 x^{14} - 5133584320546 x^{13} - 10580613968177 x^{12} + 14678412368203 x^{11} + 12611946333679 x^{10} - 24751179933865 x^{9} - 3703919800064 x^{8} + 21789096498620 x^{7} - 6749089207179 x^{6} - 6959318830992 x^{5} + 5135155439513 x^{4} - 749916660471 x^{3} - 286400294719 x^{2} + 105877549382 x - 9610946509$ |
$33$ |
[33,0] |
$11^{60}\cdot 13^{22}$ |
$2$ |
$432.583696346$ |
$432.58369634642736$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.176...721.1 |
$x^{33} - x^{32} - 320 x^{31} + 187 x^{30} + 43914 x^{29} - 11540 x^{28} - 3460853 x^{27} + 73732 x^{26} + 175969767 x^{25} + 26532806 x^{24} - 6125565450 x^{23} - 1606043451 x^{22} + 150795115936 x^{21} + 48276231954 x^{20} - 2668704786185 x^{19} - 883418455033 x^{18} + 34121303671429 x^{17} + 10279731034763 x^{16} - 313568423387915 x^{15} - 74802553335500 x^{14} + 2038896549985192 x^{13} + 312519177752992 x^{12} - 9116099992077474 x^{11} - 548476468520710 x^{10} + 26784429195477322 x^{9} - 555377424998222 x^{8} - 48372244456751422 x^{7} + 3264254358246161 x^{6} + 48927115610873873 x^{5} - 3753848630151356 x^{4} - 23333379191567542 x^{3} + 1429857798242251 x^{2} + 3214304531610982 x - 123565152645239$ |
$33$ |
[33,0] |
$661^{32}$ |
$1$ |
$542.926211601$ |
$542.9262116008858$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.370...521.1 |
$x^{33} - x^{32} - 352 x^{31} + 191 x^{30} + 53325 x^{29} - 5539 x^{28} - 4599401 x^{27} - 1367903 x^{26} + 251321055 x^{25} + 163093214 x^{24} - 9156555829 x^{23} - 8651258355 x^{22} + 228148662892 x^{21} + 270435185408 x^{20} - 3927285173382 x^{19} - 5404967120470 x^{18} + 46634682382594 x^{17} + 71223740777055 x^{16} - 376895709459825 x^{15} - 622196848535392 x^{14} + 2013236272760588 x^{13} + 3547264695384956 x^{12} - 6728485806509359 x^{11} - 12649524720509365 x^{10} + 12694495286118886 x^{9} + 25874769644564343 x^{8} - 11006437794195958 x^{7} - 25594970973829515 x^{6} + 3112971959916868 x^{5} + 9093258572218301 x^{4} - 614354748354538 x^{3} - 828504839088097 x^{2} + 72659140639036 x + 6976214555677$ |
$33$ |
[33,0] |
$727^{32}$ |
$1$ |
$595.417022871$ |
$595.4170228714686$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.772...081.1 |
$x^{33} - x^{32} - 416 x^{31} + 191 x^{30} + 75041 x^{29} - 455 x^{28} - 7743543 x^{27} - 2848629 x^{26} + 508227609 x^{25} + 337409090 x^{24} - 22349514267 x^{23} - 19659185366 x^{22} + 677362414344 x^{21} + 686515260612 x^{20} - 14372485033281 x^{19} - 15355370903390 x^{18} + 215100287692371 x^{17} + 226362584032972 x^{16} - 2270604728714300 x^{15} - 2220809582843956 x^{14} + 16760941278978266 x^{13} + 14435255865873138 x^{12} - 84825828453165930 x^{11} - 60863271644854248 x^{10} + 283890115111513251 x^{9} + 158147521995659556 x^{8} - 588624189480318666 x^{7} - 223667714966856312 x^{6} + 664314630903472785 x^{5} + 111992084480027030 x^{4} - 294174458035494256 x^{3} + 41938540757020584 x^{2} + 465346809949645 x - 179323516281983$ |
$33$ |
[33,0] |
$859^{32}$ |
$1$ |
$699.977821956$ |
$699.977821955724$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
| 33.33.748...281.1 |
$x^{33} - x^{32} - 480 x^{31} + 841 x^{30} + 100035 x^{29} - 246593 x^{28} - 11847949 x^{27} + 37295911 x^{26} + 875724109 x^{25} - 3347342666 x^{24} - 41716339229 x^{23} + 189165664796 x^{22} + 1275541327262 x^{21} - 6871211052240 x^{20} - 24098937075303 x^{19} + 160178686172920 x^{18} + 256597803886120 x^{17} - 2370647282193365 x^{16} - 1144274665359647 x^{15} + 22181360108245463 x^{14} - 3662194677145606 x^{13} - 130789225558009551 x^{12} + 66804186840965828 x^{11} + 481862849875948438 x^{10} - 303652517115261327 x^{9} - 1087338804330243466 x^{8} + 584492973328394885 x^{7} + 1438876527722391781 x^{6} - 333389199283077303 x^{5} - 972604385085778092 x^{4} - 184507168180810153 x^{3} + 139410765528126540 x^{2} + 51754392829849123 x + 3664635831529441$ |
$33$ |
[33,0] |
$991^{32}$ |
$1$ |
$804.050902502$ |
$804.0509025017632$ |
|
✓ |
? |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
|
