| 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 |
| 32.0.146...776.1 |
$x^{32} - x^{16} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}$ |
$2$ |
$27.7128129211$ |
$27.712812921102035$ |
✓ |
✓ |
✓ |
$C_2^2\times C_8$ (as 32T37) |
$[3, 3]$ |
$96$ |
$15$ |
$47233168152.25636$ |
| 32.0.519...000.1 |
$x^{32} + 2207 x^{16} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 5^{16}$ |
$2$ |
$35.77708764$ |
$35.77708763999664$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[17]$ |
$32$ |
$15$ |
$323273529801.8212$ |
| 32.0.524...056.1 |
$x^{32} - 15 x^{30} + 134 x^{28} - 793 x^{26} + 3496 x^{24} - 11638 x^{22} + 30241 x^{20} - 60672 x^{18} + 94862 x^{16} - 111861 x^{14} + 99380 x^{12} - 61666 x^{10} + 26973 x^{8} - 6636 x^{6} + 1086 x^{4} - 36 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 17^{28}$ |
$3$ |
$41.3269570841$ |
$41.32695708412257$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[40]$ |
$12$ |
$15$ |
$550321919281.4646$ |
| 32.0.113...056.1 |
$x^{32} + 449 x^{16} + 65536$ |
$32$ |
[0,16] |
$2^{128}\cdot 7^{16}$ |
$2$ |
$42.332020977$ |
$42.33202097703345$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[136]$ |
$32$ |
$15$ |
$2002471224006.0598$ |
| 32.0.186...625.1 |
$x^{32} - x^{31} + 23 x^{30} - 12 x^{29} + 329 x^{28} - 122 x^{27} + 2779 x^{26} - 327 x^{25} + 16520 x^{24} - 338 x^{23} + 64543 x^{22} + 7650 x^{21} + 180555 x^{20} + 24855 x^{19} + 346044 x^{18} + 50946 x^{17} + 490499 x^{16} + 64136 x^{15} + 494181 x^{14} + 64009 x^{13} + 369102 x^{12} + 46478 x^{11} + 187873 x^{10} + 28296 x^{9} + 67299 x^{8} + 9995 x^{7} + 13558 x^{6} + 2674 x^{5} + 1791 x^{4} + 184 x^{3} + 62 x^{2} - 4 x + 1$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{16}\cdot 17^{28}$ |
$3$ |
$46.2049426717$ |
$46.20494267165728$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[2040]$ |
$6$ |
$15$ |
$42597284566.379654$ |
| 32.0.522...256.1 |
$x^{32} + 43 x^{28} + 691 x^{24} + 5146 x^{20} + 17903 x^{16} + 25954 x^{12} + 11826 x^{8} + 876 x^{4} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 17^{28}$ |
$2$ |
$47.7202595946$ |
$47.72025959461256$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[24, 24]$ |
$8$ |
$15$ |
$303826092469.64355$ |
| 32.0.156...416.1 |
$x^{32} - 353 x^{16} + 43046721$ |
$32$ |
[0,16] |
$2^{128}\cdot 11^{16}$ |
$2$ |
$53.0659966457$ |
$53.0659966456864$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.185...000.1 |
$x^{32} + 45 x^{30} + 862 x^{28} + 9243 x^{26} + 61576 x^{24} + 268554 x^{22} + 790441 x^{20} + 1599264 x^{18} + 2244206 x^{16} + 2182743 x^{14} + 1454308 x^{12} + 646998 x^{10} + 183789 x^{8} + 30996 x^{6} + 2766 x^{4} + 108 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{16}\cdot 17^{28}$ |
$3$ |
$53.3528721787$ |
$53.352872178745116$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[8, 40, 40]$ |
$4$ |
$15$ |
$42597284566.379654$ |
| 32.0.202...000.2 |
$x^{32} + 29375 x^{16} + 390625$ |
$32$ |
[0,16] |
$2^{128}\cdot 5^{24}$ |
$2$ |
$53.4992243981$ |
$53.49922439811376$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[3, 246]$ |
$16$ |
$15$ |
$2660439411454.7925$ |
| 32.0.405...161.1 |
$x^{32} - x^{31} - 22 x^{30} + 9 x^{29} + 266 x^{28} - 2 x^{27} - 2597 x^{26} - 54 x^{25} + 20774 x^{24} + 1099 x^{23} - 128438 x^{22} - 27858 x^{21} + 651009 x^{20} + 153366 x^{19} - 2755230 x^{18} - 386184 x^{17} + 9170393 x^{16} + 1793642 x^{15} - 23184576 x^{14} - 6931256 x^{13} + 46258944 x^{12} + 5607104 x^{11} - 67085888 x^{10} + 6766080 x^{9} + 65201664 x^{8} + 3431936 x^{7} - 34820096 x^{6} - 14815232 x^{5} + 13553664 x^{4} + 2523136 x^{3} - 753664 x^{2} + 131072 x + 65536$ |
$32$ |
[0,16] |
$3^{16}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$54.6704254438$ |
$54.67042544381368$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[15, 15]$ |
$6$ |
$15$ |
$8912832207192.955$ |
| 32.0.139...000.1 |
$x^{32} - 24 x^{30} + 372 x^{28} - 3360 x^{26} + 21794 x^{24} - 91200 x^{22} + 277384 x^{20} - 571296 x^{18} + 868896 x^{16} - 931104 x^{14} + 740368 x^{12} - 405120 x^{10} + 161928 x^{8} - 41472 x^{6} + 7072 x^{4} - 384 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$56.8246622038$ |
$56.82466220378493$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[340]$ |
$6$ |
$15$ |
$10112591187794.762$ |
| 32.0.139...000.2 |
$x^{32} + 24 x^{30} + 372 x^{28} + 3360 x^{26} + 21794 x^{24} + 91200 x^{22} + 277384 x^{20} + 571296 x^{18} + 868896 x^{16} + 931104 x^{14} + 740368 x^{12} + 405120 x^{10} + 161928 x^{8} + 41472 x^{6} + 7072 x^{4} + 384 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$56.8246622038$ |
$56.82466220378493$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[21, 840]$ |
$6$ |
$15$ |
$323273529801.8212$ |
| 32.0.226...496.1 |
$x^{32} + 625279 x^{16} + 43046721$ |
$32$ |
[0,16] |
$2^{128}\cdot 13^{16}$ |
$2$ |
$57.6888204074$ |
$57.688820407423826$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.343...016.1 |
$x^{32} - 30 x^{30} + 536 x^{28} - 6344 x^{26} + 55936 x^{24} - 372416 x^{22} + 1935424 x^{20} - 7766016 x^{18} + 24284672 x^{16} - 57272832 x^{14} + 101765120 x^{12} - 126291968 x^{10} + 110481408 x^{8} - 54362112 x^{6} + 17793024 x^{4} - 1179648 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{28}$ |
$3$ |
$58.4451432$ |
$58.445143199977$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[3, 120]$ |
$6$ |
$15$ |
$12886153151831.549$ |
| 32.0.343...016.2 |
$x^{32} + 30 x^{30} + 536 x^{28} + 6344 x^{26} + 55936 x^{24} + 372416 x^{22} + 1935424 x^{20} + 7766016 x^{18} + 24284672 x^{16} + 57272832 x^{14} + 101765120 x^{12} + 126291968 x^{10} + 110481408 x^{8} + 54362112 x^{6} + 17793024 x^{4} + 1179648 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 17^{28}$ |
$3$ |
$58.4451432$ |
$58.445143199977$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[8, 1640]$ |
$6$ |
$15$ |
$303826092469.64355$ |
| 32.32.223...000.1 |
$x^{32} - 48 x^{30} + 984 x^{28} - 11328 x^{26} + 81260 x^{24} - 382560 x^{22} + 1217920 x^{20} - 2670144 x^{18} + 4065711 x^{16} - 4291632 x^{14} + 3096208 x^{12} - 1480992 x^{10} + 444972 x^{8} - 76608 x^{6} + 6448 x^{4} - 192 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
|
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
trivial |
$2$ |
$31$ |
$3365113553891366400$ |
| 32.0.223...000.1 |
$x^{32} - 390625 x^{16} + 152587890625$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$48$ |
$15$ |
|
| 32.0.223...000.2 |
$x^{32} + 48 x^{30} + 984 x^{28} + 11328 x^{26} + 81260 x^{24} + 382560 x^{22} + 1217920 x^{20} + 2670144 x^{18} + 4065711 x^{16} + 4291632 x^{14} + 3096208 x^{12} + 1480992 x^{10} + 444972 x^{8} + 76608 x^{6} + 6448 x^{4} + 192 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[42, 714]$ |
$2$ |
$15$ |
$82239790500.5115$ |
| 32.0.223...000.3 |
$x^{32} - 223 x^{16} + 65536$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[3, 4080]$ |
$16$ |
$15$ |
$34585710193758.383$ |
| 32.0.223...000.4 |
$x^{32} + 32 x^{30} + 464 x^{28} + 4032 x^{26} + 23400 x^{24} + 95680 x^{22} + 283360 x^{20} + 615296 x^{18} + 978421 x^{16} + 1101648 x^{14} + 711048 x^{12} - 239392 x^{10} - 1255068 x^{8} - 1437408 x^{6} - 736112 x^{4} - 140992 x^{2} + 4866436$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[7, 9520]$ |
$2$ |
$15$ |
$94466336304.51273$ |
| 32.0.223...000.5 |
$x^{32} - 32 x^{30} + 464 x^{28} - 4032 x^{26} + 23400 x^{24} - 95680 x^{22} + 283360 x^{20} - 615296 x^{18} + 978421 x^{16} - 1101648 x^{14} + 711048 x^{12} + 239392 x^{10} - 1255068 x^{8} + 1437408 x^{6} - 736112 x^{4} + 140992 x^{2} + 4866436$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[3, 240]$ |
$2$ |
$15$ |
$16643930584707.18$ |
| 32.0.223...000.6 |
$x^{32} - 16 x^{30} + 152 x^{28} - 960 x^{26} + 4524 x^{24} - 16160 x^{22} + 45184 x^{20} - 97984 x^{18} + 163951 x^{16} - 248976 x^{14} + 666768 x^{12} - 918880 x^{10} - 1388052 x^{8} + 2947392 x^{6} - 738128 x^{4} - 141376 x^{2} + 4879681$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[6, 102]$ |
$6$ |
$15$ |
$14682543572799.25$ |
| 32.0.223...000.7 |
$x^{32} + 16 x^{30} + 152 x^{28} + 960 x^{26} + 4524 x^{24} + 16160 x^{22} + 45184 x^{20} + 97984 x^{18} + 163951 x^{16} + 248976 x^{14} + 666768 x^{12} + 918880 x^{10} - 1388052 x^{8} - 2947392 x^{6} - 738128 x^{4} + 141376 x^{2} + 4879681$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[14, 14]$ |
$6$ |
$15$ |
$34585710193758.383$ |
| 32.0.223...000.8 |
$x^{32} - 16 x^{31} + 104 x^{30} - 320 x^{29} + 260 x^{28} + 1232 x^{27} - 3472 x^{26} + 208 x^{25} + 11050 x^{24} - 10400 x^{23} - 19240 x^{22} + 32240 x^{21} + 21840 x^{20} - 58800 x^{19} - 18600 x^{18} + 76960 x^{17} + 29237 x^{16} - 181936 x^{15} + 2343360 x^{14} - 14637840 x^{13} + 83608980 x^{12} - 315275168 x^{11} + 945709544 x^{10} - 2176666960 x^{9} + 3968694340 x^{8} - 5704396048 x^{7} + 6462476552 x^{6} - 5703032384 x^{5} + 3845008700 x^{4} - 1914237040 x^{3} + 663710864 x^{2} - 143187248 x + 57526849$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$16$ |
$15$ |
|
| 32.0.223...000.9 |
$x^{32} - 81343 x^{16} + 4294967296$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$61.9677335393$ |
$61.96773353931867$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.404...736.1 |
$x^{32} - 45 x^{30} + 991 x^{28} - 13806 x^{26} + 134311 x^{24} - 955614 x^{22} + 5086474 x^{20} - 20412324 x^{18} + 61603217 x^{16} - 138056868 x^{14} + 224682160 x^{12} - 255944832 x^{10} + 193736448 x^{8} - 88639488 x^{6} + 22093824 x^{4} - 1769472 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$63.1279696934$ |
$63.127969693394384$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[3, 120]$ |
$4$ |
$15$ |
$20780022383218.207$ |
| 32.0.165...336.1 |
$x^{32} + 3437249 x^{16} + 4294967296$ |
$32$ |
[0,16] |
$2^{128}\cdot 17^{16}$ |
$2$ |
$65.9696900099$ |
$65.96969000988257$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.304...336.1 |
$x^{32} - 8 x^{31} + 4 x^{30} + 80 x^{29} + 234 x^{28} - 2264 x^{27} + 1136 x^{26} + 10616 x^{25} + 22459 x^{24} - 162808 x^{23} + 119568 x^{22} + 179256 x^{21} + 890618 x^{20} - 3819200 x^{19} + 4810220 x^{18} - 5531224 x^{17} + 16043315 x^{16} - 34704128 x^{15} + 51652776 x^{14} - 70800080 x^{13} + 94104568 x^{12} - 109734560 x^{11} + 111890280 x^{10} - 102977936 x^{9} + 84840210 x^{8} - 61558848 x^{7} + 39138560 x^{6} - 21489824 x^{5} + 9918048 x^{4} - 3743168 x^{3} + 1107472 x^{2} - 230048 x + 24964$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$67.2358470491$ |
$67.23584704905538$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[584]$ |
$6$ |
$15$ |
$94813681955904.33$ |
| 32.0.304...336.2 |
$x^{32} - 16 x^{31} + 168 x^{30} - 1280 x^{29} + 7916 x^{28} - 40992 x^{27} + 183240 x^{26} - 716976 x^{25} + 2483598 x^{24} - 7665216 x^{23} + 21161272 x^{22} - 52347824 x^{21} + 115997916 x^{20} - 229791536 x^{19} + 405338832 x^{18} - 632761344 x^{17} + 866628755 x^{16} - 1028800288 x^{15} + 1041246888 x^{14} - 878355456 x^{13} + 599463788 x^{12} - 322075968 x^{11} + 142388096 x^{10} - 73052800 x^{9} + 58308178 x^{8} - 43372256 x^{7} + 18813856 x^{6} - 1013184 x^{5} - 2770312 x^{4} + 344192 x^{3} + 226720 x^{2} + 172032 x + 116092$ |
$32$ |
[0,16] |
$2^{124}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$67.2358470491$ |
$67.23584704905538$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[3, 408]$ |
$6$ |
$15$ |
$36503341566423.26$ |
| 32.0.560...321.1 |
$x^{32} - 6 x^{31} + 12 x^{30} - 8 x^{29} - 61 x^{28} + 506 x^{27} - 1228 x^{26} + 369 x^{25} + 4169 x^{24} - 17726 x^{23} + 39027 x^{22} - 19516 x^{21} - 109778 x^{20} + 448827 x^{19} - 649829 x^{18} - 336490 x^{17} + 1298951 x^{16} - 2098612 x^{15} + 7358296 x^{14} - 9364589 x^{13} - 18829429 x^{12} + 74949056 x^{11} + 31923685 x^{10} - 307629712 x^{9} - 163392606 x^{8} + 1472291823 x^{7} - 87681207 x^{6} - 5684845246 x^{5} + 4210930219 x^{4} + 12988964210 x^{3} - 17053058431 x^{2} - 12778402507 x + 23670130201$ |
$32$ |
[0,16] |
$3^{16}\cdot 11^{16}\cdot 17^{28}$ |
$3$ |
$68.5330051876$ |
$68.53300518757732$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
not computed |
$6$ |
$15$ |
|
| 32.0.727...625.2 |
$x^{32} - x^{31} - 11 x^{30} + 22 x^{29} + 125 x^{28} - 275 x^{27} - 94 x^{26} + 1509 x^{25} + 761 x^{24} - 9994 x^{23} + 7117 x^{22} + 14365 x^{21} - 21524 x^{20} - 49605 x^{19} + 175483 x^{18} - 33646 x^{17} + 320975 x^{16} + 904191 x^{15} - 1392802 x^{14} - 8705985 x^{13} - 464629 x^{12} + 21128450 x^{11} + 15851367 x^{10} - 21617481 x^{9} - 24556589 x^{8} - 1571294 x^{7} + 11656076 x^{6} + 28090720 x^{5} + 24696960 x^{4} - 3964352 x^{3} + 7184704 x^{2} + 33890176 x + 18800896$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$69.0925047105$ |
$69.09250471045908$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[2, 8760]$ |
$6$ |
$15$ |
$162037216252175.56$ |
| 32.0.981...536.1 |
$x^{32} - 697729 x^{16} + 152587890625$ |
$32$ |
[0,16] |
$2^{128}\cdot 19^{16}$ |
$2$ |
$69.7423830967$ |
$69.74238309665078$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.143...625.1 |
$x^{32} - 14 x^{31} + 78 x^{30} - 188 x^{29} + 49 x^{28} + 296 x^{27} + 3226 x^{26} - 21675 x^{25} + 63975 x^{24} - 129988 x^{23} + 275925 x^{22} - 780056 x^{21} + 2403348 x^{20} - 6843359 x^{19} + 18026035 x^{18} - 44145382 x^{17} + 102440247 x^{16} - 225677648 x^{15} + 478360878 x^{14} - 961434547 x^{13} + 1830768541 x^{12} - 3240171528 x^{11} + 5352278301 x^{10} - 8101027726 x^{9} + 11338690706 x^{8} - 14331413831 x^{7} + 16632009985 x^{6} - 17012899062 x^{5} + 15839257061 x^{4} - 12277480374 x^{3} + 8585381539 x^{2} - 4158477603 x + 1842570739$ |
$32$ |
[0,16] |
$5^{16}\cdot 7^{16}\cdot 17^{28}$ |
$3$ |
$70.579215758$ |
$70.57921575798821$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[3, 182040]$ |
$2$ |
$15$ |
$42597284566.379654$ |
| 32.32.486...376.1 |
$x^{32} - 64 x^{30} + 1856 x^{28} - 32256 x^{26} + 374400 x^{24} - 3061760 x^{22} + 18135040 x^{20} - 78757888 x^{18} + 251040319 x^{16} - 582109152 x^{14} + 962963040 x^{12} - 1099478272 x^{10} + 820815552 x^{8} - 364686336 x^{6} + 79473664 x^{4} - 4710400 x^{2} + 37249$ |
$32$ |
[32,0] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
|
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
trivial |
$2$ |
$31$ |
$51823553187063560000$ |
| 32.0.486...376.1 |
$x^{32} + 13590431 x^{16} + 152587890625$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.486...376.2 |
$x^{32} + 277727 x^{16} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[24, 816]$ |
$16$ |
$15$ |
$94813681955904.33$ |
| 32.0.486...376.3 |
$x^{32} - 5764801 x^{16} + 33232930569601$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$48$ |
$15$ |
|
| 32.0.486...376.4 |
$x^{32} - 16 x^{31} + 184 x^{30} - 1520 x^{29} + 10332 x^{28} - 58576 x^{27} + 287336 x^{26} - 1231568 x^{25} + 4678390 x^{24} - 15845360 x^{23} + 48150984 x^{22} - 131699184 x^{21} + 325050908 x^{20} - 724744720 x^{19} + 1460287592 x^{18} - 2657464016 x^{17} + 4362326951 x^{16} - 6446364592 x^{15} + 8552171016 x^{14} - 10150858480 x^{13} + 10733886004 x^{12} - 10060579408 x^{11} + 8306946984 x^{10} - 5997987856 x^{9} + 3753175770 x^{8} - 2012511408 x^{7} + 911516648 x^{6} - 342110896 x^{5} + 103611084 x^{4} - 24348880 x^{3} + 4169416 x^{2} - 463120 x + 25054$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[4, 24, 24]$ |
$2$ |
$15$ |
$56335773768373.43$ |
| 32.0.486...376.5 |
$x^{32} + 64 x^{30} + 1856 x^{28} + 32256 x^{26} + 374400 x^{24} + 3061760 x^{22} + 18135040 x^{20} + 78757888 x^{18} + 251040319 x^{16} + 582109152 x^{14} + 962963040 x^{12} + 1099478272 x^{10} + 820815552 x^{8} + 364686336 x^{6} + 79473664 x^{4} + 4710400 x^{2} + 37249$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[2, 2, 6, 7446]$ |
$2$ |
$15$ |
$374180447387.275$ |
| 32.0.486...376.6 |
$x^{32} + 48 x^{30} + 1128 x^{28} + 16800 x^{26} + 175124 x^{24} + 1338720 x^{22} + 7679056 x^{20} + 33321408 x^{18} + 109128129 x^{16} + 266433984 x^{14} + 474418816 x^{12} + 595027968 x^{10} + 501224448 x^{8} + 258048000 x^{6} + 68485120 x^{4} + 3145728 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[8, 8, 19856]$ |
$2$ |
$15$ |
$94466336304.51273$ |
| 32.0.486...376.7 |
$x^{32} - 32 x^{30} + 608 x^{28} - 7680 x^{26} + 72384 x^{24} - 517120 x^{22} + 2891776 x^{20} - 12541952 x^{18} + 42535999 x^{16} - 109410336 x^{14} + 213070656 x^{12} - 292113152 x^{10} + 276113088 x^{8} - 134830080 x^{6} + 46443520 x^{4} - 7872512 x^{2} + 923521$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[8, 272]$ |
$6$ |
$15$ |
$56808797853492.48$ |
| 32.0.486...376.8 |
$x^{32} + 32 x^{30} + 608 x^{28} + 7680 x^{26} + 72384 x^{24} + 517120 x^{22} + 2891776 x^{20} + 12541952 x^{18} + 42535999 x^{16} + 109410336 x^{14} + 213070656 x^{12} + 292113152 x^{10} + 276113088 x^{8} + 134830080 x^{6} + 46443520 x^{4} + 7872512 x^{2} + 923521$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
not computed |
$6$ |
$15$ |
|
| 32.0.486...376.9 |
$x^{32} - 16 x^{31} + 152 x^{30} - 1040 x^{29} + 5660 x^{28} - 25648 x^{27} + 99848 x^{26} - 340496 x^{25} + 1032070 x^{24} - 2809040 x^{23} + 6920264 x^{22} - 15521584 x^{21} + 31841628 x^{20} - 59944080 x^{19} + 103821240 x^{18} - 165701168 x^{17} + 243967235 x^{16} - 331507312 x^{15} + 412923000 x^{14} - 461181840 x^{13} + 521407068 x^{12} - 811933616 x^{11} + 915761288 x^{10} + 616194800 x^{9} - 2353432250 x^{8} + 200955248 x^{7} + 3097052168 x^{6} - 1972643120 x^{5} - 538044580 x^{4} + 656503280 x^{3} - 66006472 x^{2} - 29392688 x + 46058146$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$73.3212111193$ |
$73.32121111929344$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[2, 6, 1752]$ |
$16$ |
$15$ |
$56808797853492.48$ |
| 32.0.812...801.1 |
$x^{32} - 6 x^{31} + 60 x^{30} - 224 x^{29} + 1535 x^{28} - 4738 x^{27} + 25964 x^{26} - 65115 x^{25} + 297875 x^{24} - 640430 x^{23} + 2525043 x^{22} - 4605832 x^{21} + 15332596 x^{20} - 24484833 x^{19} + 69153169 x^{18} - 95340760 x^{17} + 215848229 x^{16} - 262803136 x^{15} + 483174616 x^{14} - 502558589 x^{13} + 676121303 x^{12} - 589256116 x^{11} + 629711197 x^{10} - 456787822 x^{9} + 331102182 x^{8} - 161825433 x^{7} + 79124517 x^{6} - 28239532 x^{5} + 11237683 x^{4} - 3082612 x^{3} + 787679 x^{2} - 101101 x + 10201$ |
$32$ |
[0,16] |
$3^{16}\cdot 13^{16}\cdot 17^{28}$ |
$3$ |
$74.5032314129$ |
$74.50323141285185$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
not computed |
$6$ |
$15$ |
|
| 32.0.121...000.1 |
$x^{32} - 2 x^{31} - 11 x^{30} + 18 x^{29} + 160 x^{28} - 204 x^{27} - 85 x^{26} - 478 x^{25} + 6534 x^{24} - 6664 x^{23} + 40562 x^{22} - 44612 x^{21} + 393657 x^{20} - 342938 x^{19} + 2686108 x^{18} - 1863692 x^{17} + 16372434 x^{16} - 7017350 x^{15} + 81158763 x^{14} - 18587306 x^{13} + 328619726 x^{12} - 26993986 x^{11} + 1066070798 x^{10} + 3685932 x^{9} + 2730786641 x^{8} + 132064062 x^{7} + 5372660276 x^{6} + 339375200 x^{5} + 7725637406 x^{4} + 460160520 x^{3} + 7334969884 x^{2} + 342344184 x + 3492717761$ |
$32$ |
[0,16] |
$2^{48}\cdot 5^{16}\cdot 17^{28}$ |
$3$ |
$75.4523554267$ |
$75.45235542673952$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[12, 48, 1968]$ |
$2$ |
$15$ |
$42597284566.379654$ |
| 32.32.121...000.1 |
$x^{32} - 2 x^{31} - 75 x^{30} + 138 x^{29} + 2388 x^{28} - 4028 x^{27} - 42773 x^{26} + 66098 x^{25} + 481690 x^{24} - 682632 x^{23} - 3607182 x^{22} + 4693052 x^{21} + 18500129 x^{20} - 22098426 x^{19} - 65844764 x^{18} + 72088572 x^{17} + 162802674 x^{16} - 162666214 x^{15} - 276907093 x^{14} + 250455230 x^{13} + 317228010 x^{12} - 256163602 x^{11} - 236469810 x^{10} + 166790036 x^{9} + 108780553 x^{8} - 64933250 x^{7} - 28450908 x^{6} + 13786936 x^{5} + 3719918 x^{4} - 1375256 x^{3} - 182100 x^{2} + 44248 x + 1361$ |
$32$ |
[32,0] |
$2^{48}\cdot 5^{16}\cdot 17^{28}$ |
$3$ |
$75.4523554267$ |
$75.45235542673952$ |
|
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
trivial |
$2$ |
$31$ |
$83633567199842760000$ |
| 32.0.208...216.1 |
$x^{32} - 3322751 x^{16} + 2821109907456$ |
$32$ |
[0,16] |
$2^{128}\cdot 23^{16}$ |
$2$ |
$76.733304373$ |
$76.7333043730035$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
not computed |
$32$ |
$15$ |
|
| 32.0.559...896.1 |
$x^{32} - 12 x^{30} + 218 x^{28} - 2352 x^{26} + 24189 x^{24} - 202718 x^{22} + 1499568 x^{20} - 9556173 x^{18} + 52856810 x^{16} - 251354668 x^{14} + 1019045945 x^{12} - 3471939654 x^{10} + 9723925436 x^{8} - 21689088233 x^{6} + 36301701182 x^{4} - 41004582111 x^{2} + 23670130201$ |
$32$ |
[0,16] |
$2^{32}\cdot 11^{16}\cdot 17^{28}$ |
$3$ |
$79.1350979868$ |
$79.13509798684356$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[17, 136]$ |
$4$ |
$15$ |
$107850976760852.73$ |
| 32.0.725...000.3 |
$x^{32} - 23 x^{30} + 114 x^{28} + 675 x^{26} - 5812 x^{24} + 2385 x^{22} + 62416 x^{20} - 141927 x^{18} + 763268 x^{16} - 6766397 x^{14} + 26657386 x^{12} - 48774875 x^{10} + 42559893 x^{8} - 31754380 x^{6} + 49669184 x^{4} - 46720448 x^{2} + 18800896$ |
$32$ |
[0,16] |
$2^{32}\cdot 5^{24}\cdot 17^{28}$ |
$3$ |
$79.7811523871$ |
$79.78115238713808$ |
✓ |
✓ |
|
$C_2^2\times C_8$ (as 32T37) |
$[2, 4, 4, 584]$ |
$4$ |
$15$ |
$218851674878883.47$ |
| 32.32.225...576.1 |
$x^{32} - 60 x^{30} + 1499 x^{28} - 20332 x^{26} + 164371 x^{24} - 824692 x^{22} + 2624266 x^{20} - 5396088 x^{18} + 7298927 x^{16} - 6560964 x^{14} + 3912050 x^{12} - 1521784 x^{10} + 372978 x^{8} - 54264 x^{6} + 4236 x^{4} - 144 x^{2} + 1$ |
$32$ |
[32,0] |
$2^{64}\cdot 3^{16}\cdot 17^{28}$ |
$3$ |
$82.6539141682$ |
$82.65391416824514$ |
|
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[2]$ |
$2$ |
$31$ |
$151446630849813740000$ |
