| 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 |
| 32.0.168...625.1 |
$x^{32} - x^{31} + 8 x^{30} - 9 x^{29} + 44 x^{28} - 38 x^{27} + 192 x^{26} - 145 x^{25} + 766 x^{24} - 556 x^{23} + 2257 x^{22} - 1493 x^{21} + 5640 x^{20} - 2513 x^{19} + 11628 x^{18} - 4801 x^{17} + 21029 x^{16} - 8919 x^{15} + 26197 x^{14} - 7798 x^{13} + 27196 x^{12} - 90 x^{11} + 19367 x^{10} - 2094 x^{9} + 12428 x^{8} - 3657 x^{7} + 3055 x^{6} - 664 x^{5} + 741 x^{4} + 134 x^{3} + 26 x^{2} + 4 x + 1$ |
$32$ |
[0,16] |
$5^{24}\cdot 17^{28}$ |
$2$ |
$39.8905761936$ |
$39.89057619356904$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[365]$ |
$10$ |
$15$ |
$42597284566.379654$ |
| 32.0.126...000.1 |
$x^{32} - 8 x^{30} + 44 x^{28} - 208 x^{26} + 910 x^{24} - 2800 x^{22} + 7440 x^{20} - 17664 x^{18} + 35492 x^{16} - 44096 x^{14} + 49952 x^{12} - 50240 x^{10} + 37432 x^{8} - 5696 x^{6} + 864 x^{4} - 128 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[85]$ |
$10$ |
$15$ |
$2660439411454.7925$ |
| 32.0.126...000.2 |
$x^{32} + 8 x^{30} + 44 x^{28} + 208 x^{26} + 910 x^{24} + 2800 x^{22} + 7440 x^{20} + 17664 x^{18} + 35492 x^{16} + 44096 x^{14} + 49952 x^{12} + 50240 x^{10} + 37432 x^{8} + 5696 x^{6} + 864 x^{4} + 128 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}$ |
$2$ |
$49.0590050814$ |
$49.05900508138431$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[3, 615]$ |
$10$ |
$15$ |
$323273529801.8212$ |
| 32.0.202...000.1 |
$x^{32} + 32 x^{30} + 464 x^{28} + 4032 x^{26} + 23400 x^{24} + 95680 x^{22} + 283360 x^{20} + 615296 x^{18} + 980627 x^{16} + 1136944 x^{14} + 940472 x^{12} + 537120 x^{10} + 200892 x^{8} + 45024 x^{6} + 5104 x^{4} + 192 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 5^{24}$ |
$2$ |
$53.4992243981$ |
$53.49922439811376$ |
✓ |
✓ |
✓ |
$C_4\times C_8$ (as 32T43) |
$[3, 4182]$ |
$2$ |
$15$ |
$24306760628.406784$ |
| 32.32.202...000.1 |
$x^{32} - 32 x^{30} + 464 x^{28} - 4032 x^{26} + 23400 x^{24} - 95680 x^{22} + 283360 x^{20} - 615296 x^{18} + 980627 x^{16} - 1136944 x^{14} + 940472 x^{12} - 537120 x^{10} + 200892 x^{8} - 45024 x^{6} + 5104 x^{4} - 192 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{128}\cdot 5^{24}$ |
$2$ |
$53.4992243981$ |
$53.49922439811376$ |
|
✓ |
✓ |
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$261659034550885400$ |
| 32.0.727...625.1 |
$x^{32} - x^{31} + x^{30} - 2 x^{29} - 157 x^{28} + 136 x^{27} + 194 x^{26} + 123 x^{25} + 6029 x^{24} - 784 x^{23} - 15683 x^{22} - 28328 x^{21} - 43829 x^{20} - 60297 x^{19} + 259309 x^{18} + 488309 x^{17} + 580886 x^{16} + 27606 x^{15} - 197086 x^{14} - 6589011 x^{13} - 48880 x^{12} - 11329204 x^{11} + 10963461 x^{10} + 3190803 x^{9} + 31270930 x^{8} + 19525837 x^{7} + 28309424 x^{6} + 9007615 x^{5} + 7220745 x^{4} - 102743 x^{3} + 1319440 x^{2} + 211141 x + 330991$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$69.0925047105$ |
$69.09250471045908$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 2482]$ |
$2$ |
$15$ |
$5880820493631.187$ |
| 32.32.727...625.1 |
$x^{32} - 4 x^{31} - 57 x^{30} + 246 x^{29} + 1318 x^{28} - 6334 x^{27} - 15812 x^{26} + 89642 x^{25} + 102376 x^{24} - 771912 x^{23} - 299890 x^{22} + 4237982 x^{21} - 283286 x^{20} - 15130884 x^{19} + 5324168 x^{18} + 35220860 x^{17} - 18558598 x^{16} - 52954720 x^{15} + 32826914 x^{14} + 50625606 x^{13} - 32389886 x^{12} - 30305480 x^{11} + 17702718 x^{10} + 11166940 x^{9} - 5039008 x^{8} - 2410058 x^{7} + 624842 x^{6} + 256798 x^{5} - 16252 x^{4} - 6488 x^{3} + 67 x^{2} + 46 x + 1$ |
$32$ |
[32,0] |
$3^{16}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$69.0925047105$ |
$69.09250471045908$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$24920675451007074000$ |
| 32.0.727...625.3 |
$x^{32} - x^{31} - 9 x^{30} + 8 x^{29} + 78 x^{28} + 81 x^{27} - 811 x^{26} - 417 x^{25} + 6444 x^{24} + 736 x^{23} - 208 x^{22} - 31498 x^{21} - 10544 x^{20} - 22352 x^{19} + 161874 x^{18} + 175569 x^{17} - 155159 x^{16} - 641829 x^{15} + 1310904 x^{14} - 657436 x^{13} + 1201420 x^{12} - 5443694 x^{11} + 4223756 x^{10} - 6671092 x^{9} + 16511370 x^{8} + 1917717 x^{7} + 1253609 x^{6} - 32655165 x^{5} + 45419760 x^{4} - 19509848 x^{3} - 39942885 x^{2} - 51358169 x + 112550881$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$69.0925047105$ |
$69.09250471045908$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 170]$ |
$10$ |
$15$ |
$324074432504351.1$ |
| 32.32.725...000.1 |
$x^{32} - 4 x^{31} - 62 x^{30} + 254 x^{29} + 1634 x^{28} - 6922 x^{27} - 23918 x^{26} + 106300 x^{25} + 212831 x^{24} - 1015754 x^{23} - 1179608 x^{22} + 6296568 x^{21} + 3963550 x^{20} - 25646062 x^{19} - 7114737 x^{18} + 68207746 x^{17} + 2809454 x^{16} - 115984606 x^{15} + 13245392 x^{14} + 121984038 x^{13} - 25600339 x^{12} - 75984420 x^{11} + 19655062 x^{10} + 26633854 x^{9} - 7358192 x^{8} - 4774168 x^{7} + 1309965 x^{6} + 357464 x^{5} - 89234 x^{4} - 7564 x^{3} + 1651 x^{2} - 74 x + 1$ |
$32$ |
[32,0] |
$2^{32}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$79.7811523871$ |
$79.78115238713808$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$228509556238802780000$ |
| 32.0.725...000.1 |
$x^{32} - 17 x^{30} + 221 x^{28} - 2686 x^{26} + 32062 x^{24} - 145945 x^{22} + 525402 x^{20} - 1687182 x^{18} + 4815029 x^{16} - 9305222 x^{14} + 16320986 x^{12} - 25297037 x^{10} + 29310958 x^{8} - 7182806 x^{6} + 1753941 x^{4} - 417605 x^{2} + 83521$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$79.7811523871$ |
$79.78115238713808$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.725...000.2 |
$x^{32} - 7 x^{30} - 94 x^{28} + 739 x^{26} + 1632 x^{24} - 21915 x^{22} + 61832 x^{20} - 161567 x^{18} + 517344 x^{16} + 629743 x^{14} - 3440334 x^{12} - 4579907 x^{10} + 12169433 x^{8} + 32864424 x^{6} + 28638896 x^{4} + 6817920 x^{2} + 2027776$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$79.7811523871$ |
$79.78115238713808$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 2, 10, 730]$ |
$2$ |
$15$ |
$39925225682933.99$ |
| 32.0.877...296.1 |
$x^{32} + 60 x^{30} + 1542 x^{28} + 22360 x^{26} + 203404 x^{24} + 1224784 x^{22} + 5034128 x^{20} + 14374848 x^{18} + 28730096 x^{16} + 40097856 x^{14} + 38567232 x^{12} + 24884992 x^{10} + 10286208 x^{8} + 2526720 x^{6} + 327168 x^{4} + 18432 x^{2} + 256$ |
$32$ |
[0,16] |
$2^{88}\cdot 17^{28}$ |
$2$ |
$80.2555904562$ |
$80.25559045617275$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[8, 72488]$ |
$2$ |
$15$ |
$303826092469.64355$ |
| 32.32.877...296.1 |
$x^{32} - 60 x^{30} + 1542 x^{28} - 22360 x^{26} + 203404 x^{24} - 1224784 x^{22} + 5034128 x^{20} - 14374848 x^{18} + 28730096 x^{16} - 40097856 x^{14} + 38567232 x^{12} - 24884992 x^{10} + 10286208 x^{8} - 2526720 x^{6} + 327168 x^{4} - 18432 x^{2} + 256$ |
$32$ |
[32,0] |
$2^{88}\cdot 17^{28}$ |
$2$ |
$80.2555904562$ |
$80.25559045617275$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$216292366437755300000$ |
| 32.0.153...801.1 |
$x^{32} - 4 x^{31} - 9 x^{30} + 90 x^{29} - 46 x^{28} - 558 x^{27} + 1218 x^{26} + 1208 x^{25} - 1596 x^{24} + 6274 x^{23} - 6246 x^{22} + 55176 x^{21} + 119832 x^{20} - 5090 x^{19} + 698130 x^{18} + 815952 x^{17} + 1621632 x^{16} + 5502716 x^{15} + 2685146 x^{14} + 9810462 x^{13} + 10151814 x^{12} - 16856174 x^{11} + 13433300 x^{10} - 17714304 x^{9} + 33195458 x^{8} + 175428026 x^{7} + 842388 x^{6} - 165678188 x^{5} + 111572666 x^{4} + 47363710 x^{3} + 50770223 x^{2} - 14835712 x + 34431289$ |
$32$ |
[0,16] |
$13^{24}\cdot 17^{28}$ |
$2$ |
$81.6771020686$ |
$81.67710206860912$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 2, 2, 2, 6, 1020]$ |
$2$ |
$15$ |
$2356853515467.5938$ |
| 32.32.545...000.1 |
$x^{32} - 56 x^{30} + 1316 x^{28} - 17104 x^{26} + 136570 x^{24} - 705040 x^{22} + 2417360 x^{20} - 5581792 x^{18} + 8730872 x^{16} - 9255712 x^{14} + 6621008 x^{12} - 3155840 x^{10} + 976032 x^{8} - 186432 x^{6} + 20096 x^{4} - 1024 x^{2} + 16$ |
$32$ |
[32,0] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$370118030677416540000$ |
| 32.0.545...000.1 |
$x^{32} + 56 x^{30} + 1316 x^{28} + 17104 x^{26} + 136570 x^{24} + 705040 x^{22} + 2417360 x^{20} + 5581792 x^{18} + 8730872 x^{16} + 9255712 x^{14} + 6621008 x^{12} + 3155840 x^{10} + 976032 x^{8} + 186432 x^{6} + 20096 x^{4} + 1024 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[3, 3, 42, 1722]$ |
$2$ |
$15$ |
$1099105261005.4811$ |
| 32.32.545...000.2 |
$x^{32} - 8 x^{31} - 36 x^{30} + 440 x^{29} + 134 x^{28} - 9792 x^{27} + 11652 x^{26} + 113616 x^{25} - 240255 x^{24} - 732960 x^{23} + 2231260 x^{22} + 2495960 x^{21} - 11792220 x^{20} - 2751040 x^{19} + 37734684 x^{18} - 9662688 x^{17} - 73953556 x^{16} + 40994896 x^{15} + 87563076 x^{14} - 65186904 x^{13} - 61202386 x^{12} + 52549560 x^{11} + 25065416 x^{10} - 22254968 x^{9} - 6034148 x^{8} + 4705064 x^{7} + 803092 x^{6} - 427104 x^{5} - 38980 x^{4} + 16600 x^{3} + 376 x^{2} - 192 x + 1$ |
$32$ |
[32,0] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$1022818136839327000000$ |
| 32.0.545...000.4 |
$x^{32} - 8 x^{31} + 28 x^{30} - 40 x^{29} + 54 x^{28} - 512 x^{27} + 2516 x^{26} - 5296 x^{25} + 3985 x^{24} - 2080 x^{23} + 37260 x^{22} - 153000 x^{21} + 294260 x^{20} - 227840 x^{19} - 382084 x^{18} + 1259168 x^{17} + 717500 x^{16} - 10742192 x^{15} + 22324164 x^{14} - 3197336 x^{13} - 76009730 x^{12} + 176356600 x^{11} - 141389160 x^{10} - 339377432 x^{9} + 1611662172 x^{8} - 3467919192 x^{7} + 4930199252 x^{6} - 5279972480 x^{5} + 4642269708 x^{4} - 2995482536 x^{3} + 970581784 x^{2} - 206749664 x + 295089121$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[14, 21182]$ |
$2$ |
$15$ |
$1099105261005.4811$ |
| 32.0.545...000.5 |
$x^{32} - 24 x^{30} + 396 x^{28} - 5616 x^{26} + 73710 x^{24} - 680400 x^{22} + 5423760 x^{20} - 38631168 x^{18} + 232863012 x^{16} - 867941568 x^{14} + 2949615648 x^{12} - 8899865280 x^{10} + 19892899512 x^{8} - 9081263808 x^{6} + 4132485216 x^{4} - 1836660096 x^{2} + 688747536$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.545...000.6 |
$x^{32} + 24 x^{30} + 396 x^{28} + 5616 x^{26} + 73710 x^{24} + 680400 x^{22} + 5423760 x^{20} + 38631168 x^{18} + 232863012 x^{16} + 867941568 x^{14} + 2949615648 x^{12} + 8899865280 x^{10} + 19892899512 x^{8} + 9081263808 x^{6} + 4132485216 x^{4} + 1836660096 x^{2} + 688747536$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$84.9726893697$ |
$84.97268936973735$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.857...625.1 |
$x^{32} - x^{31} - 2 x^{30} - 6 x^{29} - 21 x^{28} - 406 x^{27} + 417 x^{26} + 1503 x^{25} + 2405 x^{24} + 5907 x^{23} + 51558 x^{22} - 80653 x^{21} - 292681 x^{20} - 304226 x^{19} - 38117 x^{18} - 2136490 x^{17} + 7115533 x^{16} + 17827751 x^{15} - 1285999 x^{14} - 34006613 x^{13} + 23039126 x^{12} + 24562491 x^{11} - 146418413 x^{10} - 215674134 x^{9} + 198051499 x^{8} + 330667302 x^{7} + 301645453 x^{6} + 191861363 x^{5} + 93574213 x^{4} + 82119327 x^{3} + 57690613 x^{2} + 32860640 x + 12117361$ |
$32$ |
[0,16] |
$5^{24}\cdot 41^{28}$ |
$2$ |
$86.1813668691$ |
$86.18136686908747$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[24, 120]$ |
$10$ |
$15$ |
$960117309726421.5$ |
| 32.32.873...000.2 |
$x^{32} - 96 x^{30} + 4176 x^{28} - 108864 x^{26} + 1895400 x^{24} - 23250240 x^{22} + 206569440 x^{20} - 1345652352 x^{18} + 6433893747 x^{16} - 22378468752 x^{14} + 55533931128 x^{12} - 95149196640 x^{10} + 106762245372 x^{8} - 71782798752 x^{6} + 24412273776 x^{4} - 2754990144 x^{2} + 43046721$ |
$32$ |
[32,0] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$31$ |
|
| 32.0.873...000.5 |
$x^{32} - 16 x^{30} + 56 x^{28} + 256 x^{26} - 1460 x^{24} - 1760 x^{22} + 12800 x^{20} + 10048 x^{18} + 12827 x^{16} + 536128 x^{14} + 2598488 x^{12} + 4206560 x^{10} + 8338152 x^{8} - 605472 x^{6} + 4540976 x^{4} - 921344 x^{2} + 34093921$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[2, 24, 1968]$ |
$2$ |
$15$ |
$20225182375589.523$ |
| 32.0.873...000.6 |
$x^{32} + 16 x^{30} + 56 x^{28} - 256 x^{26} - 1460 x^{24} + 1760 x^{22} + 12800 x^{20} - 10048 x^{18} + 12827 x^{16} - 536128 x^{14} + 2598488 x^{12} - 4206560 x^{10} + 8338152 x^{8} + 605472 x^{6} + 4540976 x^{4} + 921344 x^{2} + 34093921$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.873...000.7 |
$x^{32} + 96 x^{30} + 4176 x^{28} + 108864 x^{26} + 1895400 x^{24} + 23250240 x^{22} + 206569440 x^{20} + 1345652352 x^{18} + 6433893747 x^{16} + 22378468752 x^{14} + 55533931128 x^{12} + 95149196640 x^{10} + 106762245372 x^{8} + 71782798752 x^{6} + 24412273776 x^{4} + 2754990144 x^{2} + 43046721$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.873...000.10 |
$x^{32} - 48 x^{30} + 984 x^{28} - 11328 x^{26} + 81260 x^{24} - 382560 x^{22} + 1217920 x^{20} - 2670144 x^{18} + 4129467 x^{16} - 5233056 x^{14} + 14823352 x^{12} - 99845280 x^{10} + 479321832 x^{8} - 1275041376 x^{6} + 1668661744 x^{4} - 832092288 x^{2} + 779470561$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[2, 8, 272]$ |
$2$ |
$15$ |
$459974601348790.56$ |
| 32.0.873...000.11 |
$x^{32} + 48 x^{30} + 984 x^{28} + 11328 x^{26} + 81260 x^{24} + 382560 x^{22} + 1217920 x^{20} + 2670144 x^{18} + 4129467 x^{16} + 5233056 x^{14} + 14823352 x^{12} + 99845280 x^{10} + 479321832 x^{8} + 1275041376 x^{6} + 1668661744 x^{4} + 832092288 x^{2} + 779470561$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$92.6633748231$ |
$92.66337482306153$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.224...776.2 |
$x^{32} - 8 x^{30} - 124 x^{28} + 736 x^{26} + 4997 x^{24} - 15672 x^{22} - 27588 x^{20} + 201200 x^{18} + 376952 x^{16} - 3438736 x^{14} + 6156800 x^{12} - 2082176 x^{10} + 382501 x^{8} - 16686272 x^{6} + 26615832 x^{4} - 10774256 x^{2} + 3243601$ |
$32$ |
[0,16] |
$2^{96}\cdot 17^{28}$ |
$2$ |
$95.4405191892$ |
$95.44051918922511$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.224...776.3 |
$x^{32} + 8 x^{30} - 124 x^{28} - 736 x^{26} + 4997 x^{24} + 15672 x^{22} - 27588 x^{20} - 201200 x^{18} + 376952 x^{16} + 3438736 x^{14} + 6156800 x^{12} + 2082176 x^{10} + 382501 x^{8} + 16686272 x^{6} + 26615832 x^{4} + 10774256 x^{2} + 3243601$ |
$32$ |
[0,16] |
$2^{96}\cdot 17^{28}$ |
$2$ |
$95.4405191892$ |
$95.44051918922511$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 2, 2, 6, 4182]$ |
$2$ |
$15$ |
$38649094918357.02$ |
| 32.0.115...976.1 |
$x^{32} - 8 x^{31} + 76 x^{30} - 376 x^{29} + 1990 x^{28} - 7200 x^{27} + 27220 x^{26} - 78416 x^{25} + 230321 x^{24} - 549536 x^{23} + 1299116 x^{22} - 2640872 x^{21} + 5132100 x^{20} - 8981104 x^{19} + 14525436 x^{18} - 22097552 x^{17} + 30299804 x^{16} - 38582432 x^{15} + 45545668 x^{14} - 51444648 x^{13} + 48961614 x^{12} - 37727976 x^{11} + 45640456 x^{10} - 34775816 x^{9} - 15710452 x^{8} - 19426712 x^{7} + 45725380 x^{6} + 54746128 x^{5} - 17251700 x^{4} - 60652600 x^{3} - 26861080 x^{2} + 26719104 x + 19747393$ |
$32$ |
[0,16] |
$2^{124}\cdot 13^{24}$ |
$2$ |
$100.449723914$ |
$100.44972391405638$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[45, 45]$ |
$2$ |
$15$ |
$2849230308504732.5$ |
| 32.0.115...976.2 |
$x^{32} - 8 x^{31} + 12 x^{30} + 104 x^{29} - 426 x^{28} + 32 x^{27} + 2948 x^{26} - 5200 x^{25} - 351 x^{24} + 12896 x^{23} - 26884 x^{22} + 106392 x^{21} - 108044 x^{20} - 106160 x^{19} + 1069852 x^{18} - 1263952 x^{17} + 2202572 x^{16} + 2415456 x^{15} - 5967804 x^{14} + 18098136 x^{13} - 15688322 x^{12} - 17522856 x^{11} + 52305080 x^{10} - 101764328 x^{9} + 173545612 x^{8} + 103143400 x^{7} - 285976060 x^{6} - 53577424 x^{5} + 350995068 x^{4} - 163307832 x^{3} + 89896776 x^{2} - 55119136 x + 58281889$ |
$32$ |
[0,16] |
$2^{124}\cdot 13^{24}$ |
$2$ |
$100.449723914$ |
$100.44972391405638$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
$[5, 87965]$ |
$2$ |
$15$ |
$9664872226004.74$ |
| 32.32.561...625.1 |
$x^{32} - 4 x^{31} - 97 x^{30} + 416 x^{29} + 3953 x^{28} - 18474 x^{27} - 87837 x^{26} + 461322 x^{25} + 1146281 x^{24} - 7186022 x^{23} - 8540945 x^{22} + 73242962 x^{21} + 26561229 x^{20} - 497884694 x^{19} + 105769163 x^{18} + 2251615110 x^{17} - 1474815293 x^{16} - 6592149900 x^{15} + 6946567999 x^{14} + 11614969466 x^{13} - 17900177751 x^{12} - 9777588040 x^{11} + 26279937053 x^{10} - 1494801150 x^{9} - 20290513343 x^{8} + 9449532252 x^{7} + 5947593437 x^{6} - 5889335682 x^{5} + 731994753 x^{4} + 828328332 x^{3} - 384738348 x^{2} + 63812896 x - 3700304$ |
$32$ |
[32,0] |
$5^{24}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$105.540544263$ |
$105.54054426325722$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$16668045472879155000000$ |
| 32.0.561...625.2 |
$x^{32} - x^{31} - 6 x^{30} + 5 x^{29} - 546 x^{28} + 556 x^{27} + 4802 x^{26} - 4187 x^{25} + 57950 x^{24} + 71120 x^{23} - 710547 x^{22} - 1199025 x^{21} + 81720 x^{20} - 12009033 x^{19} + 32840498 x^{18} + 115457045 x^{17} + 148502093 x^{16} + 90690253 x^{15} + 77390757 x^{14} - 4980292302 x^{13} - 6297437270 x^{12} - 14252605152 x^{11} + 651843825 x^{10} + 45573354048 x^{9} + 154455067964 x^{8} + 270487093719 x^{7} + 331005058977 x^{6} + 207815025774 x^{5} + 32016319033 x^{4} - 98707729302 x^{3} - 79785142736 x^{2} + 5111337362 x + 18479977261$ |
$32$ |
[0,16] |
$5^{24}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$105.540544263$ |
$105.54054426325722$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.561...625.3 |
$x^{32} - x^{31} - 26 x^{30} + 25 x^{29} + 554 x^{28} + 166 x^{27} - 12048 x^{26} - 2967 x^{25} + 243900 x^{24} - 34760 x^{23} - 1239627 x^{22} - 566845 x^{21} + 4462190 x^{20} - 23080013 x^{19} + 12321838 x^{18} + 133745895 x^{17} + 71438063 x^{16} - 731908967 x^{15} + 958307527 x^{14} + 715528798 x^{13} - 3048724550 x^{12} - 8181879192 x^{11} + 18801912335 x^{10} - 5205488012 x^{9} - 6043816216 x^{8} + 13428234259 x^{7} + 130340525677 x^{6} - 276022878046 x^{5} + 163663111613 x^{4} - 110147425102 x^{3} + 183684061184 x^{2} - 1310299091478 x + 1791981145201$ |
$32$ |
[0,16] |
$5^{24}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$105.540544263$ |
$105.54054426325722$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.184...616.1 |
$x^{32} + 80 x^{30} + 2744 x^{28} + 53120 x^{26} + 644748 x^{24} + 5172960 x^{22} + 28278912 x^{20} + 107218880 x^{18} + 283997723 x^{16} + 523451648 x^{14} + 659656088 x^{12} + 548056352 x^{10} + 280891560 x^{8} + 78474144 x^{6} + 9153840 x^{4} + 160256 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 13^{24}$ |
$2$ |
$109.541200672$ |
$109.54120067236873$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.32.184...616.1 |
$x^{32} - 80 x^{30} + 2744 x^{28} - 53120 x^{26} + 644748 x^{24} - 5172960 x^{22} + 28278912 x^{20} - 107218880 x^{18} + 283997723 x^{16} - 523451648 x^{14} + 659656088 x^{12} - 548056352 x^{10} + 280891560 x^{8} - 78474144 x^{6} + 9153840 x^{4} - 160256 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{128}\cdot 13^{24}$ |
$2$ |
$109.541200672$ |
$109.54120067236873$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$29157260098603590000000$ |
| 32.32.475...000.1 |
$x^{32} - 4 x^{31} - 102 x^{30} + 404 x^{29} + 4549 x^{28} - 17812 x^{27} - 117028 x^{26} + 451980 x^{25} + 1929761 x^{24} - 7327884 x^{23} - 21441958 x^{22} + 79690868 x^{21} + 164374860 x^{20} - 594024912 x^{19} - 876219412 x^{18} + 3049830256 x^{17} + 3236345879 x^{16} - 10699434056 x^{15} - 8173761298 x^{14} + 25146964908 x^{13} + 13793063056 x^{12} - 38328647620 x^{11} - 14997610308 x^{10} + 36075446764 x^{9} + 9895657258 x^{8} - 19452177308 x^{7} - 3540548500 x^{6} + 5285519244 x^{5} + 538535816 x^{4} - 555932464 x^{3} - 5956104 x^{2} + 14755336 x - 522239$ |
$32$ |
[32,0] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$31$ |
|
| 32.0.475...000.1 |
$x^{32} + 14 x^{30} - 376 x^{28} - 5912 x^{26} + 26112 x^{24} + 701280 x^{22} + 3957248 x^{20} + 20680576 x^{18} + 132440064 x^{16} - 322428416 x^{14} - 3522902016 x^{12} + 9379649536 x^{10} + 49845997568 x^{8} - 269225361408 x^{6} + 469219672064 x^{4} - 223409602560 x^{2} + 132892327936$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.475...000.2 |
$x^{32} - 14 x^{30} - 376 x^{28} + 5912 x^{26} + 26112 x^{24} - 701280 x^{22} + 3957248 x^{20} - 20680576 x^{18} + 132440064 x^{16} + 322428416 x^{14} - 3522902016 x^{12} - 9379649536 x^{10} + 49845997568 x^{8} + 269225361408 x^{6} + 469219672064 x^{4} + 223409602560 x^{2} + 132892327936$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.475...000.3 |
$x^{32} - 4 x^{31} + 58 x^{30} - 196 x^{29} + 1769 x^{28} - 5332 x^{27} + 36592 x^{26} - 99500 x^{25} + 565421 x^{24} - 1397804 x^{23} + 6873202 x^{22} - 15497652 x^{21} + 67844200 x^{20} - 139719472 x^{19} + 555470148 x^{18} - 1043995424 x^{17} + 3821729999 x^{16} - 6530125576 x^{15} + 22197557342 x^{14} - 34192038852 x^{13} + 108414578156 x^{12} - 148455171060 x^{11} + 440639227972 x^{10} - 525717928076 x^{9} + 1465891189858 x^{8} - 1474785975388 x^{7} + 3846333624060 x^{6} - 3081196575196 x^{5} + 7536247963216 x^{4} - 4320797259664 x^{3} + 9841464291016 x^{2} - 3060156463304 x + 6460791592081$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.475...000.5 |
$x^{32} - 34 x^{30} + 884 x^{28} - 21488 x^{26} + 512992 x^{24} - 4670240 x^{22} + 33625728 x^{20} - 215959296 x^{18} + 1232647424 x^{16} - 4764273664 x^{14} + 16712689664 x^{12} - 51808331776 x^{10} + 120057683968 x^{8} - 58841546752 x^{6} + 28736569344 x^{4} - 13684080640 x^{2} + 5473632256$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.475...000.6 |
$x^{32} + 34 x^{30} + 884 x^{28} + 21488 x^{26} + 512992 x^{24} + 4670240 x^{22} + 33625728 x^{20} + 215959296 x^{18} + 1232647424 x^{16} + 4764273664 x^{14} + 16712689664 x^{12} + 51808331776 x^{10} + 120057683968 x^{8} + 58841546752 x^{6} + 28736569344 x^{4} + 13684080640 x^{2} + 5473632256$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$112.827587728$ |
$112.8275877276453$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.721...136.1 |
$x^{32} - 8 x^{31} + 12 x^{30} + 48 x^{29} + 30 x^{28} - 984 x^{27} + 1096 x^{26} + 2456 x^{25} + 2917 x^{24} - 10632 x^{23} + 6216 x^{22} - 151880 x^{21} + 49206 x^{20} + 562864 x^{19} + 734604 x^{18} + 1498456 x^{17} + 539142 x^{16} - 23901944 x^{15} - 28776348 x^{14} - 9443456 x^{13} - 11820722 x^{12} + 421923464 x^{11} + 905081912 x^{10} + 1134683112 x^{9} + 3831594961 x^{8} + 442166472 x^{7} + 6109266600 x^{6} - 781734536 x^{5} + 4368859022 x^{4} - 1030498048 x^{3} + 646464852 x^{2} + 118091240 x + 449086927$ |
$32$ |
[0,16] |
$2^{124}\cdot 17^{24}$ |
$2$ |
$122.836638792$ |
$122.83663879218146$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
$[2, 4, 180, 7380]$ |
$2$ |
$15$ |
$38649094918357.02$ |
| 32.32.721...136.1 |
$x^{32} - 8 x^{31} - 52 x^{30} + 528 x^{29} + 942 x^{28} - 14808 x^{27} - 4040 x^{26} + 232952 x^{25} - 101787 x^{24} - 2290952 x^{23} + 1894744 x^{22} + 14880024 x^{21} - 15740682 x^{20} - 65768208 x^{19} + 78677084 x^{18} + 200834584 x^{17} - 255633450 x^{16} - 425796088 x^{15} + 553415588 x^{14} + 624757920 x^{13} - 797607810 x^{12} - 627979512 x^{11} + 749016552 x^{10} + 424971976 x^{9} - 437179375 x^{8} - 187713208 x^{7} + 144420248 x^{6} + 50201368 x^{5} - 21676018 x^{4} - 6390976 x^{3} + 552740 x^{2} + 49768 x - 2753$ |
$32$ |
[32,0] |
$2^{124}\cdot 17^{24}$ |
$2$ |
$122.836638792$ |
$122.83663879218146$ |
|
✓ |
|
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$269323465797089430000000$ |
| 32.32.421...000.1 |
$x^{32} - 96 x^{30} + 3696 x^{28} - 75184 x^{26} + 899720 x^{24} - 6660000 x^{22} + 31193320 x^{20} - 93050912 x^{18} + 175529272 x^{16} - 205236512 x^{14} + 144210848 x^{12} - 58587840 x^{10} + 13396712 x^{8} - 1684032 x^{6} + 108576 x^{4} - 2944 x^{2} + 16$ |
$32$ |
[32,0] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
trivial |
$2$ |
$31$ |
$398446588986736840000000$ |
| 32.32.421...000.2 |
$x^{32} - 8 x^{31} - 76 x^{30} + 760 x^{29} + 1954 x^{28} - 30352 x^{27} - 7628 x^{26} + 666456 x^{25} - 634585 x^{24} - 8827760 x^{23} + 15632420 x^{22} + 72455680 x^{21} - 182544660 x^{20} - 357343720 x^{19} + 1267393024 x^{18} + 888389032 x^{17} - 5510095721 x^{16} + 176836216 x^{15} + 14927443376 x^{14} - 8043244424 x^{13} - 23836615436 x^{12} + 23589054160 x^{11} + 18807108516 x^{10} - 31998194928 x^{9} - 1328020573 x^{8} + 20765809224 x^{7} - 7738765748 x^{6} - 4658045344 x^{5} + 3842975350 x^{4} - 498020920 x^{3} - 286773844 x^{2} + 103141288 x - 9793409$ |
$32$ |
[32,0] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
|
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$31$ |
|
| 32.0.421...000.2 |
$x^{32} - 8 x^{31} - 12 x^{30} + 280 x^{29} - 206 x^{28} - 5712 x^{27} + 12196 x^{26} + 71064 x^{25} - 240585 x^{24} - 567280 x^{23} + 2902260 x^{22} + 2536640 x^{21} - 22883300 x^{20} - 4950760 x^{19} + 120802336 x^{18} + 38552968 x^{17} - 478813865 x^{16} - 813999752 x^{15} + 2360618384 x^{14} + 6386853784 x^{13} - 14042867340 x^{12} - 20749097200 x^{11} + 38583306500 x^{10} + 52356953808 x^{9} + 54615249427 x^{8} - 483652890552 x^{7} + 223883790332 x^{6} + 456373127360 x^{5} + 603312953478 x^{4} - 1277065516216 x^{3} - 954628846756 x^{2} + 858240692296 x + 1117847129071$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.421...000.3 |
$x^{32} + 96 x^{30} + 3696 x^{28} + 75184 x^{26} + 899720 x^{24} + 6660000 x^{22} + 31193320 x^{20} + 93050912 x^{18} + 175529272 x^{16} + 205236512 x^{14} + 144210848 x^{12} + 58587840 x^{10} + 13396712 x^{8} + 1684032 x^{6} + 108576 x^{4} + 2944 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$2$ |
$15$ |
|
| 32.0.421...000.4 |
$x^{32} - 56 x^{30} + 2156 x^{28} - 71344 x^{26} + 2184910 x^{24} - 47059600 x^{22} + 875308560 x^{20} - 14547063552 x^{18} + 204604317092 x^{16} - 1779432654272 x^{14} + 14110203638048 x^{12} - 99340895568320 x^{10} + 518107062507832 x^{8} - 551879803278272 x^{6} + 585984734941536 x^{4} - 607687873272704 x^{2} + 531726889113616$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
✓ |
✓ |
? |
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
| 32.0.421...000.5 |
$x^{32} + 56 x^{30} + 2156 x^{28} + 71344 x^{26} + 2184910 x^{24} + 47059600 x^{22} + 875308560 x^{20} + 14547063552 x^{18} + 204604317092 x^{16} + 1779432654272 x^{14} + 14110203638048 x^{12} + 99340895568320 x^{10} + 518107062507832 x^{8} + 551879803278272 x^{6} + 585984734941536 x^{4} + 607687873272704 x^{2} + 531726889113616$ |
$32$ |
[0,16] |
$2^{124}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$129.797927014$ |
$129.79792701359696$ |
✓ |
✓ |
|
$C_4\times C_8$ (as 32T43) |
not computed |
$10$ |
$15$ |
|
