| 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 |
| 32.0.352...129.1 |
$x^{32} - x^{31} + x^{29} - x^{28} + x^{26} - x^{25} + x^{23} - x^{22} + x^{20} - x^{19} + x^{17} - x^{16} + x^{15} - x^{13} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ |
$32$ |
[0,16] |
$3^{16}\cdot 17^{30}$ |
$2$ |
$24.666440964$ |
$24.666440964016477$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[5]$ |
$102$ |
$15$ |
$9977645145.96466$ |
| 32.0.351...304.1 |
$x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 17^{30}$ |
$2$ |
$28.482352661$ |
$28.48235266104985$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[8]$ |
$68$ |
$15$ |
$36938367173.77557$ |
| 32.0.125...625.1 |
$x^{32} - x^{31} + 2 x^{30} - 3 x^{29} + 5 x^{28} - 8 x^{27} + 13 x^{26} - 21 x^{25} + 34 x^{24} - 55 x^{23} + 89 x^{22} - 144 x^{21} + 233 x^{20} - 377 x^{19} + 610 x^{18} - 987 x^{17} + 1597 x^{16} + 987 x^{15} + 610 x^{14} + 377 x^{13} + 233 x^{12} + 144 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$32$ |
[0,16] |
$5^{16}\cdot 17^{30}$ |
$2$ |
$31.8442383546$ |
$31.844238354614745$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[17]$ |
$34$ |
$15$ |
$42597284566.379654$ |
| 32.0.146...976.1 |
$x^{32} + 1$ |
$32$ |
[0,16] |
$2^{160}$ |
$1$ |
$32.0$ |
$32.0$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[17]$ |
$64$ |
$15$ |
$211230625393.46567$ |
| 32.0.272...249.1 |
$x^{32} - x^{31} - x^{30} + 3 x^{29} - x^{28} - 5 x^{27} + 7 x^{26} + 3 x^{25} - 17 x^{24} + 11 x^{23} + 23 x^{22} - 45 x^{21} - x^{20} + 91 x^{19} - 89 x^{18} - 93 x^{17} + 271 x^{16} - 186 x^{15} - 356 x^{14} + 728 x^{13} - 16 x^{12} - 1440 x^{11} + 1472 x^{10} + 1408 x^{9} - 4352 x^{8} + 1536 x^{7} + 7168 x^{6} - 10240 x^{5} - 4096 x^{4} + 24576 x^{3} - 16384 x^{2} - 32768 x + 65536$ |
$32$ |
[0,16] |
$7^{16}\cdot 17^{30}$ |
$2$ |
$37.6786109476$ |
$37.67861094758833$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[3, 15]$ |
$34$ |
$15$ |
$308154877506.37555$ |
| 32.0.230...944.1 |
$x^{32} - 2 x^{30} + 4 x^{28} - 8 x^{26} + 16 x^{24} - 32 x^{22} + 64 x^{20} - 128 x^{18} + 256 x^{16} - 512 x^{14} + 1024 x^{12} - 2048 x^{10} + 4096 x^{8} - 8192 x^{6} + 16384 x^{4} - 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 17^{30}$ |
$2$ |
$40.2801294216$ |
$40.28012942155011$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[3, 24]$ |
$34$ |
$15$ |
$598124168304.8442$ |
| 32.0.230...944.2 |
$x^{32} + 2 x^{30} + 4 x^{28} + 8 x^{26} + 16 x^{24} + 32 x^{22} + 64 x^{20} + 128 x^{18} + 256 x^{16} + 512 x^{14} + 1024 x^{12} + 2048 x^{10} + 4096 x^{8} + 8192 x^{6} + 16384 x^{4} + 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 17^{30}$ |
$2$ |
$40.2801294216$ |
$40.28012942155011$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.376...689.1 |
$x^{32} - x^{31} - 2 x^{30} + 5 x^{29} + x^{28} - 16 x^{27} + 13 x^{26} + 35 x^{25} - 74 x^{24} - 31 x^{23} + 253 x^{22} - 160 x^{21} - 599 x^{20} + 1079 x^{19} + 718 x^{18} - 3955 x^{17} + 1801 x^{16} - 11865 x^{15} + 6462 x^{14} + 29133 x^{13} - 48519 x^{12} - 38880 x^{11} + 184437 x^{10} - 67797 x^{9} - 485514 x^{8} + 688905 x^{7} + 767637 x^{6} - 2834352 x^{5} + 531441 x^{4} + 7971615 x^{3} - 9565938 x^{2} - 14348907 x + 43046721$ |
$32$ |
[0,16] |
$11^{16}\cdot 17^{30}$ |
$2$ |
$47.2326384616$ |
$47.232638461641514$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.32.488...625.1 |
$x^{32} - x^{31} - 32 x^{30} + 31 x^{29} + 464 x^{28} - 433 x^{27} - 4033 x^{26} + 3600 x^{25} + 23426 x^{24} - 19826 x^{23} - 95978 x^{22} + 76152 x^{21} + 285340 x^{20} - 209188 x^{19} - 623732 x^{18} + 414544 x^{17} + 1004699 x^{16} - 590154 x^{15} - 1183593 x^{14} + 593422 x^{13} + 1001431 x^{12} - 407890 x^{11} - 589403 x^{10} + 181071 x^{9} + 228888 x^{8} - 46882 x^{7} - 53690 x^{6} + 5686 x^{5} + 6516 x^{4} - 116 x^{3} - 304 x^{2} - 16 x + 1$ |
$32$ |
[32,0] |
$5^{24}\cdot 17^{30}$ |
$2$ |
$47.6182430125$ |
$47.618243012491206$ |
|
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$34401098890034160$ |
| 32.0.151...184.1 |
$x^{32} + 33 x^{30} + 494 x^{28} + 4436 x^{26} + 26623 x^{24} + 112607 x^{22} + 344863 x^{20} + 773397 x^{18} + 1269578 x^{16} + 1508868 x^{14} + 1269578 x^{12} + 729146 x^{10} + 270216 x^{8} + 59244 x^{6} + 6648 x^{4} + 288 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$49.332881928$ |
$49.332881928032954$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[2, 3088]$ |
$4$ |
$15$ |
$19955290291.92932$ |
| 32.32.151...184.1 |
$x^{32} - 31 x^{30} + 434 x^{28} - 3628 x^{26} + 20175 x^{24} - 78705 x^{22} + 221355 x^{20} - 454195 x^{18} + 680390 x^{16} - 737276 x^{14} + 566618 x^{12} - 298870 x^{10} + 102752 x^{8} - 21204 x^{6} + 2280 x^{4} - 96 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{32}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$49.332881928$ |
$49.332881928032954$ |
|
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$57026536947552560$ |
| 32.0.151...184.2 |
$x^{32} + 17 x^{30} + 170 x^{28} + 1139 x^{26} + 5712 x^{24} + 21930 x^{22} + 66453 x^{20} + 158576 x^{18} + 300254 x^{16} + 442459 x^{14} + 505172 x^{12} + 427142 x^{10} + 265013 x^{8} + 107508 x^{6} + 29478 x^{4} + 3468 x^{2} + 289$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$49.332881928$ |
$49.332881928032954$ |
✓ |
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
$[2, 1930]$ |
$6$ |
$15$ |
$73876734347.55115$ |
| 32.0.151...184.3 |
$x^{32} + 3 x^{30} + 9 x^{28} + 27 x^{26} + 81 x^{24} + 243 x^{22} + 729 x^{20} + 2187 x^{18} + 6561 x^{16} + 19683 x^{14} + 59049 x^{12} + 177147 x^{10} + 531441 x^{8} + 1594323 x^{6} + 4782969 x^{4} + 14348907 x^{2} + 43046721$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$49.332881928$ |
$49.332881928032954$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.545...009.1 |
$x^{32} - x^{31} + 4 x^{30} - 7 x^{29} + 19 x^{28} - 40 x^{27} + 97 x^{26} - 217 x^{25} + 508 x^{24} - 1159 x^{23} + 2683 x^{22} - 6160 x^{21} + 14209 x^{20} - 32689 x^{19} + 75316 x^{18} - 173383 x^{17} + 399331 x^{16} + 520149 x^{15} + 677844 x^{14} + 882603 x^{13} + 1150929 x^{12} + 1496880 x^{11} + 1955907 x^{10} + 2534733 x^{9} + 3332988 x^{8} + 4271211 x^{7} + 5727753 x^{6} + 7085880 x^{5} + 10097379 x^{4} + 11160261 x^{3} + 19131876 x^{2} + 14348907 x + 43046721$ |
$32$ |
[0,16] |
$13^{16}\cdot 17^{30}$ |
$2$ |
$51.3472914826$ |
$51.34729148263172$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.157...424.1 |
$x^{32} - 16 x^{30} + 152 x^{28} - 960 x^{26} + 4524 x^{24} - 16160 x^{22} + 45184 x^{20} - 97984 x^{18} + 166158 x^{16} - 213664 x^{14} + 207712 x^{12} - 142016 x^{10} + 68568 x^{8} - 18816 x^{6} + 3424 x^{4} - 128 x^{2} + 4$ |
$32$ |
[0,16] |
$2^{158}\cdot 3^{16}$ |
$2$ |
$53.0757611413$ |
$53.07576114126626$ |
✓ |
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
$[3, 51]$ |
$6$ |
$15$ |
$12949932335324.246$ |
| 32.0.157...424.2 |
$x^{32} + 16 x^{30} + 152 x^{28} + 960 x^{26} + 4524 x^{24} + 16160 x^{22} + 45184 x^{20} + 97984 x^{18} + 166158 x^{16} + 213664 x^{14} + 207712 x^{12} + 142016 x^{10} + 68568 x^{8} + 18816 x^{6} + 3424 x^{4} + 128 x^{2} + 4$ |
$32$ |
[0,16] |
$2^{158}\cdot 3^{16}$ |
$2$ |
$53.0757611413$ |
$53.07576114126626$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[3, 1203]$ |
$6$ |
$15$ |
$211230625393.46567$ |
| 32.32.538...625.1 |
$x^{32} - x^{31} - 49 x^{30} + 48 x^{29} + 1025 x^{28} - 977 x^{27} - 12023 x^{26} + 11046 x^{25} + 87635 x^{24} - 76589 x^{23} - 417686 x^{22} + 341097 x^{21} + 1341822 x^{20} - 1000725 x^{19} - 2965533 x^{18} + 1964808 x^{17} + 4562969 x^{16} - 2594590 x^{15} - 4899810 x^{14} + 2282032 x^{13} + 3639474 x^{12} - 1295443 x^{11} - 1825949 x^{10} + 442548 x^{9} + 590580 x^{8} - 76972 x^{7} - 112748 x^{6} + 3238 x^{5} + 10596 x^{4} + 496 x^{3} - 304 x^{2} - 16 x + 1$ |
$32$ |
[32,0] |
$3^{16}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$55.1558387585$ |
$55.155838758526286$ |
|
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$471152520983870500$ |
| 32.0.538...625.1 |
$x^{32} - x^{31} + 31 x^{30} - 27 x^{29} + 430 x^{28} - 322 x^{27} + 3532 x^{26} - 2244 x^{25} + 19175 x^{24} - 10199 x^{23} + 72729 x^{22} - 31933 x^{21} + 198487 x^{20} - 70755 x^{19} + 395067 x^{18} - 112047 x^{17} + 574754 x^{16} - 122995 x^{15} + 602425 x^{14} - 49738 x^{13} + 418484 x^{12} + 205417 x^{11} + 119371 x^{10} + 637343 x^{9} - 115465 x^{8} + 904978 x^{7} - 113658 x^{6} + 500408 x^{5} + 20116 x^{4} + 527946 x^{3} - 601474 x^{2} - 781826 x + 3188011$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$55.1558387585$ |
$55.155838758526286$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[17, 816]$ |
$2$ |
$15$ |
$19955290291.92932$ |
| 32.0.538...625.2 |
$x^{32} - x^{31} - 17 x^{30} + 18 x^{29} + 169 x^{28} - 187 x^{27} - 1121 x^{26} + 1308 x^{25} + 5525 x^{24} - 6833 x^{23} - 20622 x^{22} + 27455 x^{21} + 59620 x^{20} - 87075 x^{19} - 131121 x^{18} + 218196 x^{17} + 213179 x^{16} - 427804 x^{15} - 227834 x^{14} + 534224 x^{13} + 198782 x^{12} - 308057 x^{11} - 317867 x^{10} + 2204306 x^{9} - 1621426 x^{8} - 7260650 x^{7} + 8774568 x^{6} + 2492744 x^{5} - 11237834 x^{4} + 11294784 x^{3} - 60418 x^{2} - 12691334 x + 12752041$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$55.1558387585$ |
$55.155838758526286$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[2, 170]$ |
$6$ |
$15$ |
$3942730660019.478$ |
| 32.0.538...625.3 |
$x^{32} - x^{31} - 3 x^{30} + 7 x^{29} + 5 x^{28} - 33 x^{27} + 13 x^{26} + 119 x^{25} - 171 x^{24} - 305 x^{23} + 989 x^{22} + 231 x^{21} - 4187 x^{20} + 3263 x^{19} + 13485 x^{18} - 26537 x^{17} - 27403 x^{16} - 106148 x^{15} + 215760 x^{14} + 208832 x^{13} - 1071872 x^{12} + 236544 x^{11} + 4050944 x^{10} - 4997120 x^{9} - 11206656 x^{8} + 31195136 x^{7} + 13631488 x^{6} - 138412032 x^{5} + 83886080 x^{4} + 469762048 x^{3} - 805306368 x^{2} - 1073741824 x + 4294967296$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$55.1558387585$ |
$55.155838758526286$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.32.629...696.1 |
$x^{32} - 32 x^{30} + 464 x^{28} - 4032 x^{26} + 23400 x^{24} - 95680 x^{22} + 283360 x^{20} - 615296 x^{18} + 980628 x^{16} - 1136960 x^{14} + 940576 x^{12} - 537472 x^{10} + 201552 x^{8} - 45696 x^{6} + 5440 x^{4} - 256 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{160}\cdot 3^{16}$ |
$2$ |
$55.4256258422$ |
$55.42562584220407$ |
|
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$969667117813122800$ |
| 32.0.629...696.1 |
$x^{32} + 32 x^{30} + 464 x^{28} + 4032 x^{26} + 23400 x^{24} + 95680 x^{22} + 283360 x^{20} + 615296 x^{18} + 980628 x^{16} + 1136960 x^{14} + 940576 x^{12} + 537472 x^{10} + 201552 x^{8} + 45696 x^{6} + 5440 x^{4} + 256 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{160}\cdot 3^{16}$ |
$2$ |
$55.4256258422$ |
$55.42562584220407$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[13634]$ |
$2$ |
$15$ |
$47233168152.25636$ |
| 32.0.629...696.2 |
$x^{32} + 43046721$ |
$32$ |
[0,16] |
$2^{160}\cdot 3^{16}$ |
$2$ |
$55.4256258422$ |
$55.42562584220407$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$32$ |
$15$ |
|
| 32.0.151...984.1 |
$x^{32} + 32 x^{30} + 463 x^{28} + 4004 x^{26} + 23051 x^{24} + 93128 x^{22} + 271214 x^{20} + 575832 x^{18} + 891311 x^{16} + 995824 x^{14} + 786798 x^{12} + 425128 x^{10} + 149106 x^{8} + 31248 x^{6} + 3396 x^{4} + 144 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 17^{30}$ |
$2$ |
$56.9647053221$ |
$56.9647053220997$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[2, 6, 2328]$ |
$2$ |
$15$ |
$36938367173.77557$ |
| 32.32.151...984.1 |
$x^{32} - 32 x^{30} + 463 x^{28} - 4004 x^{26} + 23051 x^{24} - 93128 x^{22} + 271214 x^{20} - 575832 x^{18} + 891311 x^{16} - 995824 x^{14} + 786798 x^{12} - 425128 x^{10} + 149106 x^{8} - 31248 x^{6} + 3396 x^{4} - 144 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{64}\cdot 17^{30}$ |
$2$ |
$56.9647053221$ |
$56.9647053220997$ |
|
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[2]$ |
$2$ |
$31$ |
$471833271145334340$ |
| 32.0.151...984.2 |
$x^{32} + 51 x^{28} + 1003 x^{24} + 9554 x^{20} + 45407 x^{16} + 99994 x^{12} + 83810 x^{8} + 17340 x^{4} + 289$ |
$32$ |
[0,16] |
$2^{64}\cdot 17^{30}$ |
$2$ |
$56.9647053221$ |
$56.9647053220997$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[2, 2, 776]$ |
$4$ |
$15$ |
$598124168304.8442$ |
| 32.0.236...169.1 |
$x^{32} - x^{31} - 4 x^{30} + 9 x^{29} + 11 x^{28} - 56 x^{27} + x^{26} + 279 x^{25} - 284 x^{24} - 1111 x^{23} + 2531 x^{22} + 3024 x^{21} - 15679 x^{20} + 559 x^{19} + 77836 x^{18} - 80631 x^{17} - 308549 x^{16} - 403155 x^{15} + 1945900 x^{14} + 69875 x^{13} - 9799375 x^{12} + 9450000 x^{11} + 39546875 x^{10} - 86796875 x^{9} - 110937500 x^{8} + 544921875 x^{7} + 9765625 x^{6} - 2734375000 x^{5} + 2685546875 x^{4} + 10986328125 x^{3} - 24414062500 x^{2} - 30517578125 x + 152587890625$ |
$32$ |
[0,16] |
$17^{30}\cdot 19^{16}$ |
$2$ |
$62.0758484619$ |
$62.07584846190154$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.536...000.1 |
$x^{32} - 5 x^{30} + 25 x^{28} - 125 x^{26} + 625 x^{24} - 3125 x^{22} + 15625 x^{20} - 78125 x^{18} + 390625 x^{16} - 1953125 x^{14} + 9765625 x^{12} - 48828125 x^{10} + 244140625 x^{8} - 1220703125 x^{6} + 6103515625 x^{4} - 30517578125 x^{2} + 152587890625$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$63.6884767092$ |
$63.68847670922949$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.32.536...000.1 |
$x^{32} - 51 x^{30} + 1122 x^{28} - 14025 x^{26} + 110704 x^{24} - 581910 x^{22} + 2100605 x^{20} - 5308080 x^{18} + 9493310 x^{16} - 12057369 x^{14} + 10821316 x^{12} - 6760866 x^{10} + 2859077 x^{8} - 780300 x^{6} + 126582 x^{4} - 10404 x^{2} + 289$ |
$32$ |
[32,0] |
$2^{32}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$63.6884767092$ |
$63.68847670922949$ |
|
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$4821130960706681000$ |
| 32.0.536...000.2 |
$x^{32} + 29 x^{30} + 382 x^{28} + 3020 x^{26} + 15959 x^{24} + 59435 x^{22} + 160295 x^{20} + 316785 x^{18} + 459050 x^{16} + 483196 x^{14} + 362466 x^{12} + 186394 x^{10} + 67392 x^{8} - 7500 x^{6} + 103392 x^{4} - 510024 x^{2} + 2550409$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$63.6884767092$ |
$63.68847670922949$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[40, 1360]$ |
$2$ |
$15$ |
$73876734347.55115$ |
| 32.0.536...000.3 |
$x^{32} - 35 x^{30} + 562 x^{28} - 5492 x^{26} + 36551 x^{24} - 175781 x^{22} + 633251 x^{20} - 1751511 x^{18} + 3794486 x^{16} - 6572932 x^{14} + 9351378 x^{12} - 11350102 x^{10} + 12349464 x^{8} - 12678924 x^{6} + 12744816 x^{4} - 12751752 x^{2} + 12752041$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 17^{30}$ |
$3$ |
$63.6884767092$ |
$63.68847670922949$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[2, 2, 136]$ |
$4$ |
$15$ |
$10897700797646.188$ |
| 32.0.117...529.1 |
$x^{32} - x^{31} + 34 x^{30} - 33 x^{29} + 679 x^{28} - 646 x^{27} + 9079 x^{26} - 8433 x^{25} + 90746 x^{24} - 82313 x^{23} + 693327 x^{22} - 611014 x^{21} + 4170679 x^{20} - 3559665 x^{19} + 19686714 x^{18} - 16127049 x^{17} + 73305359 x^{16} - 57178411 x^{15} + 210412060 x^{14} - 153240517 x^{13} + 460124585 x^{12} - 306932144 x^{11} + 721594375 x^{10} - 414305095 x^{9} + 778203968 x^{8} - 360876953 x^{7} + 463378521 x^{6} - 98875264 x^{5} + 118464295 x^{4} - 24204327 x^{3} + 19379456 x^{2} - 449753 x + 10201$ |
$32$ |
[0,16] |
$3^{16}\cdot 7^{16}\cdot 17^{30}$ |
$3$ |
$65.2612685198$ |
$65.26126851984391$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$6$ |
$15$ |
|
| 32.32.117...529.1 |
$x^{32} - x^{31} - 62 x^{30} + 57 x^{29} + 1741 x^{28} - 1456 x^{27} - 29279 x^{26} + 21999 x^{25} + 328550 x^{24} - 218555 x^{23} - 2594055 x^{22} + 1501280 x^{21} + 14806525 x^{20} - 7300125 x^{19} - 61804530 x^{18} + 25303905 x^{17} + 188675045 x^{16} - 62155621 x^{15} - 417033506 x^{14} + 106258835 x^{13} + 653702339 x^{12} - 122456240 x^{11} - 702418817 x^{10} + 90494753 x^{9} + 490797914 x^{8} - 39835109 x^{7} - 205111641 x^{6} + 9562400 x^{5} + 44453923 x^{4} - 1257219 x^{3} - 3752014 x^{2} + 103231 x + 76603$ |
$32$ |
[32,0] |
$3^{16}\cdot 7^{16}\cdot 17^{30}$ |
$3$ |
$65.2612685198$ |
$65.26126851984391$ |
|
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$7704904687609626000$ |
| 32.0.117...529.2 |
$x^{32} - 14 x^{31} + 90 x^{30} - 354 x^{29} + 1060 x^{28} - 3122 x^{27} + 9718 x^{26} - 27548 x^{25} + 68323 x^{24} - 162420 x^{23} + 388682 x^{22} - 885302 x^{21} + 1883356 x^{20} - 3859590 x^{19} + 7747823 x^{18} - 14894504 x^{17} + 27483236 x^{16} - 48703184 x^{15} + 83847191 x^{14} - 137630031 x^{13} + 219099037 x^{12} - 329935717 x^{11} + 485458653 x^{10} - 661629418 x^{9} + 894648443 x^{8} - 1078358227 x^{7} + 1337537651 x^{6} - 1342929253 x^{5} + 1540908056 x^{4} - 1158250822 x^{3} + 1251370063 x^{2} - 517957627 x + 555187123$ |
$32$ |
[0,16] |
$3^{16}\cdot 7^{16}\cdot 17^{30}$ |
$3$ |
$65.2612685198$ |
$65.26126851984391$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$2$ |
$15$ |
|
| 32.0.117...529.3 |
$x^{32} - x^{31} + 6 x^{30} - 11 x^{29} + 41 x^{28} - 96 x^{27} + 301 x^{26} - 781 x^{25} + 2286 x^{24} - 6191 x^{23} + 17621 x^{22} - 48576 x^{21} + 136681 x^{20} - 379561 x^{19} + 1062966 x^{18} - 2960771 x^{17} + 8275601 x^{16} + 14803855 x^{15} + 26574150 x^{14} + 47445125 x^{13} + 85425625 x^{12} + 151800000 x^{11} + 275328125 x^{10} + 483671875 x^{9} + 892968750 x^{8} + 1525390625 x^{7} + 2939453125 x^{6} + 4687500000 x^{5} + 10009765625 x^{4} + 13427734375 x^{3} + 36621093750 x^{2} + 30517578125 x + 152587890625$ |
$32$ |
[0,16] |
$3^{16}\cdot 7^{16}\cdot 17^{30}$ |
$3$ |
$65.2612685198$ |
$65.26126851984391$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.502...889.1 |
$x^{32} - x^{31} - 5 x^{30} + 11 x^{29} + 19 x^{28} - 85 x^{27} - 29 x^{26} + 539 x^{25} - 365 x^{24} - 2869 x^{23} + 5059 x^{22} + 12155 x^{21} - 42509 x^{20} - 30421 x^{19} + 285475 x^{18} - 102949 x^{17} - 1609901 x^{16} - 617694 x^{15} + 10277100 x^{14} - 6570936 x^{13} - 55091664 x^{12} + 94517280 x^{11} + 236032704 x^{10} - 803136384 x^{9} - 613059840 x^{8} + 5431878144 x^{7} - 1753519104 x^{6} - 30837749760 x^{5} + 41358864384 x^{4} + 143667634176 x^{3} - 391820820480 x^{2} - 470184984576 x + 2821109907456$ |
$32$ |
[0,16] |
$17^{30}\cdot 23^{16}$ |
$2$ |
$68.298282375$ |
$68.2982823749864$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.32.557...000.1 |
$x^{32} - 48 x^{30} + 984 x^{28} - 11328 x^{26} + 81260 x^{24} - 382560 x^{22} + 1217920 x^{20} - 2670144 x^{18} + 4067918 x^{16} - 4305120 x^{14} + 3129696 x^{12} - 1524288 x^{10} + 475992 x^{8} - 88704 x^{6} + 8800 x^{4} - 384 x^{2} + 4$ |
$32$ |
[32,0] |
$2^{158}\cdot 5^{16}$ |
$2$ |
$68.5205129958$ |
$68.52051299580233$ |
|
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
trivial |
$2$ |
$31$ |
$17279702978410850000$ |
| 32.0.557...000.1 |
$x^{32} + 48 x^{30} + 984 x^{28} + 11328 x^{26} + 81260 x^{24} + 382560 x^{22} + 1217920 x^{20} + 2670144 x^{18} + 4067918 x^{16} + 4305120 x^{14} + 3129696 x^{12} + 1524288 x^{10} + 475992 x^{8} + 88704 x^{6} + 8800 x^{4} + 384 x^{2} + 4$ |
$32$ |
[0,16] |
$2^{158}\cdot 5^{16}$ |
$2$ |
$68.5205129958$ |
$68.52051299580233$ |
✓ |
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
$[17, 5729]$ |
$2$ |
$15$ |
$323273529801.8212$ |
| 32.32.992...624.1 |
$x^{32} - 2 x^{31} - 63 x^{30} + 124 x^{29} + 1712 x^{28} - 3300 x^{27} - 26300 x^{26} + 49300 x^{25} + 251803 x^{24} - 454306 x^{23} - 1565501 x^{22} + 2676696 x^{21} + 6411521 x^{20} - 10146346 x^{19} - 17289475 x^{18} + 24432604 x^{17} + 30419036 x^{16} - 36405466 x^{15} - 34405772 x^{14} + 32406588 x^{13} + 24527010 x^{12} - 16635294 x^{11} - 10672826 x^{10} + 4758978 x^{9} + 2732732 x^{8} - 704616 x^{7} - 385884 x^{6} + 43964 x^{5} + 26192 x^{4} - 328 x^{3} - 624 x^{2} - 32 x + 1$ |
$32$ |
[32,0] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
|
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[2]$ |
$2$ |
$31$ |
$10078657704407090000$ |
| 32.0.992...624.1 |
$x^{32} - 6 x^{30} + 36 x^{28} - 216 x^{26} + 1296 x^{24} - 7776 x^{22} + 46656 x^{20} - 279936 x^{18} + 1679616 x^{16} - 10077696 x^{14} + 60466176 x^{12} - 362797056 x^{10} + 2176782336 x^{8} - 13060694016 x^{6} + 78364164096 x^{4} - 470184984576 x^{2} + 2821109907456$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.0.992...624.2 |
$x^{32} + 6 x^{30} + 36 x^{28} + 216 x^{26} + 1296 x^{24} + 7776 x^{22} + 46656 x^{20} + 279936 x^{18} + 1679616 x^{16} + 10077696 x^{14} + 60466176 x^{12} + 362797056 x^{10} + 2176782336 x^{8} + 13060694016 x^{6} + 78364164096 x^{4} + 470184984576 x^{2} + 2821109907456$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
| 32.32.992...624.2 |
$x^{32} - 62 x^{30} + 1736 x^{28} - 29024 x^{26} + 322800 x^{24} - 2518560 x^{22} + 14166720 x^{20} - 58136960 x^{18} + 174179840 x^{16} - 377485312 x^{14} + 580216832 x^{12} - 612085760 x^{10} + 420872192 x^{8} - 173703168 x^{6} + 37355520 x^{4} - 3145728 x^{2} + 65536$ |
$32$ |
[32,0] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
|
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$2$ |
$31$ |
|
| 32.0.992...624.3 |
$x^{32} + 62 x^{30} + 1736 x^{28} + 29024 x^{26} + 322800 x^{24} + 2518560 x^{22} + 14166720 x^{20} + 58136960 x^{18} + 174179840 x^{16} + 377485312 x^{14} + 580216832 x^{12} + 612085760 x^{10} + 420872192 x^{8} + 173703168 x^{6} + 37355520 x^{4} + 3145728 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$2$ |
$15$ |
|
| 32.0.992...624.4 |
$x^{32} - 34 x^{30} + 680 x^{28} - 9112 x^{26} + 91392 x^{24} - 701760 x^{22} + 4252992 x^{20} - 20297728 x^{18} + 76865024 x^{16} - 226539008 x^{14} + 517296128 x^{12} - 874786816 x^{10} + 1085493248 x^{8} - 880705536 x^{6} + 482967552 x^{4} - 113639424 x^{2} + 18939904$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
not computed |
$6$ |
$15$ |
|
| 32.0.992...624.5 |
$x^{32} + 34 x^{30} + 680 x^{28} + 9112 x^{26} + 91392 x^{24} + 701760 x^{22} + 4252992 x^{20} + 20297728 x^{18} + 76865024 x^{16} + 226539008 x^{14} + 517296128 x^{12} + 874786816 x^{10} + 1085493248 x^{8} + 880705536 x^{6} + 482967552 x^{4} + 113639424 x^{2} + 18939904$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
|
$C_2\times C_{16}$ (as 32T32) |
not computed |
$6$ |
$15$ |
|
| 32.0.992...624.6 |
$x^{32} - 2 x^{31} + x^{30} + 4 x^{29} + 108 x^{28} - 228 x^{27} + 404 x^{26} - 124 x^{25} + 5275 x^{24} - 10178 x^{23} + 29827 x^{22} - 29120 x^{21} + 181429 x^{20} - 275498 x^{19} + 1000869 x^{18} - 1175244 x^{17} + 4552448 x^{16} - 5579162 x^{15} + 19519380 x^{14} - 22301852 x^{13} + 72254162 x^{12} - 77576350 x^{11} + 231999798 x^{10} - 231692214 x^{9} + 641213764 x^{8} - 584431816 x^{7} + 1459356196 x^{6} - 1174733284 x^{5} + 2600147168 x^{4} - 1662828840 x^{3} + 3077744976 x^{2} - 1174279296 x + 1761923521$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{30}$ |
$3$ |
$69.7672306936$ |
$69.76723069357476$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[6, 99888]$ |
$2$ |
$15$ |
$19955290291.92932$ |
| 32.0.223...000.1 |
$x^{32} + 152587890625$ |
$32$ |
[0,16] |
$2^{160}\cdot 5^{16}$ |
$2$ |
$71.55417528$ |
$71.55417527999327$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$32$ |
$15$ |
|
| 32.0.223...000.2 |
$x^{32} - 32 x^{30} + 464 x^{28} - 4032 x^{26} + 23400 x^{24} - 95680 x^{22} + 283360 x^{20} - 615296 x^{18} + 980628 x^{16} - 1136960 x^{14} + 940576 x^{12} - 537472 x^{10} + 201552 x^{8} - 45696 x^{6} + 5440 x^{4} - 256 x^{2} + 4870849$ |
$32$ |
[0,16] |
$2^{160}\cdot 5^{16}$ |
$2$ |
$71.55417528$ |
$71.55417527999327$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[17, 34]$ |
$2$ |
$15$ |
$67435414427975.664$ |
| 32.0.223...000.3 |
$x^{32} + 32 x^{30} + 464 x^{28} + 4032 x^{26} + 23400 x^{24} + 95680 x^{22} + 283360 x^{20} + 615296 x^{18} + 980628 x^{16} + 1136960 x^{14} + 940576 x^{12} + 537472 x^{10} + 201552 x^{8} + 45696 x^{6} + 5440 x^{4} + 256 x^{2} + 4870849$ |
$32$ |
[0,16] |
$2^{160}\cdot 5^{16}$ |
$2$ |
$71.55417528$ |
$71.55417527999327$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[17, 11458]$ |
$2$ |
$15$ |
$211230625393.46567$ |
| 32.0.116...704.1 |
$x^{32} + 7 x^{30} + 49 x^{28} + 343 x^{26} + 2401 x^{24} + 16807 x^{22} + 117649 x^{20} + 823543 x^{18} + 5764801 x^{16} + 40353607 x^{14} + 282475249 x^{12} + 1977326743 x^{10} + 13841287201 x^{8} + 96889010407 x^{6} + 678223072849 x^{4} + 4747561509943 x^{2} + 33232930569601$ |
$32$ |
[0,16] |
$2^{32}\cdot 7^{16}\cdot 17^{30}$ |
$3$ |
$75.3572218952$ |
$75.35722189517666$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
not computed |
$34$ |
$15$ |
|
