Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 130)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6634204312890625.1	x^16 - 7x^15 + 27x^14 - 73x^13 + 160x^12 - 304x^11 + 509x^10 - 730x^9 + 869x^8 - 839x^7 + 654x^6 - 416x^5 + 221x^4 - 98x^3 + 34x^2 - 8x + 1	\( 5^{8}\cdot 19^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.23045377697175681.1	x^16 - x^15 + 11x^13 - 14x^12 + 6x^11 + 23x^10 - 44x^9 + 45x^8 - 44x^7 + 23x^6 + 6x^5 - 14x^4 + 11x^3 - x + 1	\( 3^{8}\cdot 37^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.117033789351264256.1	x^16 - 8x^15 + 32x^14 - 82x^13 + 153x^12 - 226x^11 + 274x^10 - 254x^9 + 144x^8 - 16x^7 - 36x^6 + 26x^5 - 7x^4 + 2x^3 + 2x^2 - 2x + 1	\( 2^{24}\cdot 17^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.288230376151711744.4	x^16 + 6x^8 + 1	\( 2^{58} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.523300059815673856.1	x^16 + 7x^14 + 17x^12 - 2x^10 - 30x^8 - 2x^6 + 17x^4 + 7x^2 + 1	\( 2^{16}\cdot 41^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.1257791680575160641.1	x^16 + 2x^14 - 14x^13 - 6x^12 - 21x^11 + 45x^10 + 43x^9 + 120x^8 + 96x^7 + 142x^6 + 99x^5 + 101x^4 + 58x^3 + 61x^2 + 5x + 25	\( 3^{8}\cdot 61^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.11378694989371408384.2	x^16 + 2x^14 - 21x^12 - 14x^10 + 217x^8 - 308x^6 + 168x^4 - 40x^2 + 4	\( 2^{24}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	Trivial
16.0.11378694989371408384.3	x^16 + 2x^14 - 14x^10 + 49x^4 - 26x^2 + 4	\( 2^{24}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	Trivial
16.0.14309137159611744256.1	x^16 - 2x^15 - x^14 - 10x^13 + 33x^12 - 28x^11 + 22x^10 - 72x^9 + 218x^8 - 128x^7 + 126x^6 - 204x^5 + 137x^4 - 78x^3 + 63x^2 - 14x + 1	\( 2^{24}\cdot 31^{8} \)	$D_{8}$ (as 16T13)	$[3]$
16.0.18446744073709551616.3	x^16 - 8x^14 + 52x^12 - 168x^10 + 264x^8 - 168x^6 + 52x^4 - 8x^2 + 1	\( 2^{64} \)	$D_{8}$ (as 16T13)	Trivial
16.0.29960650073923649536.3	x^16 - 3x^12 + 64x^8 + 37x^4 + 1	\( 2^{32}\cdot 17^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.43527014496875390625.3	x^16 - 7x^15 + 26x^14 - 74x^13 + 158x^12 - 246x^11 + 372x^10 - 634x^9 + 798x^8 - 656x^7 + 663x^6 - 741x^5 + 379x^4 + 10x^3 - 75x^2 + 50x + 25	\( 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.44499647686531640625.1	x^16 - 7x^15 + 26x^14 - 62x^13 + 86x^12 - 71x^11 + 78x^10 - 126x^9 + 175x^8 - 126x^7 + 78x^6 - 71x^5 + 86x^4 - 62x^3 + 26x^2 - 7x + 1	\( 3^{12}\cdot 5^{8}\cdot 11^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.44499647686531640625.3	x^16 - 3x^15 - x^14 + 16x^13 - 28x^12 - 12x^11 + 98x^10 - 102x^9 - 62x^8 + 303x^7 - 203x^6 - 79x^5 + 414x^4 - 283x^3 + 181x^2 - 40x + 25	\( 3^{12}\cdot 5^{8}\cdot 11^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.57355639689187890625.1	x^16 + 6x^14 - 7x^13 + 27x^12 - 43x^11 + 137x^10 - 155x^9 + 402x^8 - 413x^7 + 649x^6 - 349x^5 + 574x^4 + 206x^3 + 527x^2 + 546x + 441	\( 5^{8}\cdot 59^{8} \)	$D_{8}$ (as 16T13)	$[3]$
16.0.63880676485490517601.1	x^16 - 8x^15 + 26x^14 - 36x^13 + 38x^11 + 74x^10 - 280x^9 + 266x^8 - 100x^7 + 296x^6 - 702x^5 + 573x^4 + 72x^3 - 172x^2 + 16	\( 13^{8}\cdot 23^{8} \)	$D_{8}$ (as 16T13)	$[3]$
16.0.101415451701035401216.1	x^16 - 4x^15 + 4x^14 + 20x^13 - 38x^12 + 4x^11 + 140x^10 - 116x^9 - 198x^8 + 116x^7 + 140x^6 - 4x^5 - 38x^4 - 20x^3 + 4x^2 + 4x + 1	\( 2^{44}\cdot 7^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.101415451701035401216.5	x^16 - 4x^15 + 8x^14 - 8x^13 + 16x^12 - 56x^11 + 156x^10 - 376x^9 + 643x^8 - 796x^7 + 944x^6 - 912x^5 + 486x^4 - 216x^3 + 156x^2 + 14	\( 2^{44}\cdot 7^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.109951162777600000000.9	x^16 - 4x^14 - 4x^12 + 32x^10 + 99x^8 + 96x^6 + 44x^4 - 20x^2 + 25	\( 2^{48}\cdot 5^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.109951162777600000000.10	x^16 - 4x^14 + 20x^12 + 35x^8 - 64x^6 + 36x^4 + 60x^2 + 25	\( 2^{48}\cdot 5^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.145383138964293121969.1	x^16 - 3x^15 + 6x^14 - 21x^13 + 28x^12 + 77x^11 - 224x^10 + 25x^9 + 548x^8 - 809x^7 + 434x^6 - 91x^5 + 189x^4 - 308x^3 + 244x^2 - 144x + 64	\( 7^{14}\cdot 11^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.358914725543104304161.1	x^16 - 4x^15 + 12x^14 - 36x^13 + 66x^12 - 44x^11 + 18x^10 + 102x^9 - 104x^8 + 180x^7 - 266x^6 + 92x^5 + 413x^4 - 826x^3 + 732x^2 - 336x + 64	\( 7^{8}\cdot 53^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.399487099562283237376.1	x^16 - 2x^15 + 11x^14 - 26x^13 + 81x^12 - 160x^11 + 334x^10 - 532x^9 + 834x^8 - 932x^7 + 1142x^6 - 848x^5 - 119x^4 + 630x^3 - 189x^2 - 162x + 81	\( 2^{24}\cdot 47^{8} \)	$D_{8}$ (as 16T13)	$[5]$
16.0.434779213849600000000.3	x^16 + x^14 - 4x^12 - 18x^10 + 14x^8 + 61x^6 + 244x^4 - 20x^2 + 25	\( 2^{16}\cdot 5^{8}\cdot 19^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.592620628869750390625.1	x^16 + 2x^14 - 10x^13 + 7x^12 + 97x^10 + 388x^8 - 280x^7 + 881x^6 - 1030x^5 + 1488x^4 - 1080x^3 + 624x^2 - 320x + 256	\( 5^{8}\cdot 79^{8} \)	$D_{8}$ (as 16T13)	$[5]$
16.0.642366916348420476801.1	x^16 - 2x^15 + 12x^14 - 46x^13 + 172x^12 - 387x^11 + 625x^10 - 636x^9 + 444x^8 - 362x^7 + 367x^6 - 294x^5 + 163x^4 - 78x^3 + 57x^2 - 36x + 9	\( 3^{8}\cdot 7^{8}\cdot 19^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.642366916348420476801.3	x^16 - 4x^15 + 18x^14 - 53x^13 + 131x^12 - 306x^11 + 614x^10 - 1160x^9 + 2220x^8 - 4198x^7 + 7075x^6 - 9966x^5 + 11478x^4 - 10161x^3 + 6507x^2 - 2916x + 729	\( 3^{8}\cdot 7^{8}\cdot 19^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.752931165277996622401.1	x^16 - 8x^15 + 14x^14 + 42x^13 - 163x^12 + 68x^11 + 358x^10 - 459x^9 + 3x^8 + 58x^7 + 583x^6 - 1006x^5 + 960x^4 - 715x^3 + 143x^2 + 121x + 121	\( 11^{8}\cdot 37^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.767858691933644783616.4	x^16 - 6x^13 + 9x^12 - 54x^11 + 18x^10 + 126x^9 - 196x^8 + 444x^7 + 540x^6 - 3762x^5 + 7785x^4 - 8262x^3 + 5202x^2 - 1734x + 289	\( 2^{24}\cdot 3^{8}\cdot 17^{8} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.1306642885859619140625.2	x^16 - x^15 + 7x^14 + 20x^12 - 4x^11 + 111x^10 - 245x^9 + 484x^8 - 445x^7 + 474x^6 + 163x^5 - 175x^4 + 58x^2 - 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 13^{8} \)	$D_{8}$ (as 16T13)	$[4]$
16.0.1306642885859619140625.5	x^16 - x^14 + 56x^10 + 274x^8 + 651x^6 + 945x^4 + 594x^2 + 81	\( 3^{8}\cdot 5^{12}\cdot 13^{8} \)	$D_{8}$ (as 16T13)	$[4]$
16.0.1510301872762105430016.1	x^16 - 3x^14 + 18x^12 - 56x^10 + 141x^8 - 324x^6 + 406x^4 - 111x^2 + 9	\( 2^{16}\cdot 3^{8}\cdot 37^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.1738211555063394140625.2	x^16 - 2x^15 + 2x^14 + 21x^13 - 14x^12 - 28x^11 + 112x^10 + 47x^9 - 38x^8 + 192x^7 + 119x^6 + 7x^5 - 35x^4 - 21x^3 + 177x^2 + 108x + 81	\( 3^{8}\cdot 5^{8}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.1738211555063394140625.3	x^16 - 13x^14 + 84x^12 - 329x^10 + 819x^8 - 1288x^6 + 1246x^4 - 720x^2 + 225	\( 3^{8}\cdot 5^{8}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.1742237986263159341056.1	x^16 - 4x^15 + 8x^14 - 34x^13 + 36x^12 + 32x^11 + 162x^10 - 112x^9 - 16x^8 - 310x^7 - 144x^6 + 44x^5 + 265x^4 + 120x^3 + 32x^2 + 16x + 4	\( 2^{16}\cdot 113^{8} \)	$D_{8}$ (as 16T13)	Trivial
16.0.1891079497931380752384.2	x^16 + 72x^12 + 80x^10 + 366x^8 + 288x^6 + 88x^4 - 48x^2 + 9	\( 2^{58}\cdot 3^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.1891079497931380752384.4	x^16 + 72x^12 - 80x^10 + 366x^8 - 288x^6 + 88x^4 + 48x^2 + 9	\( 2^{58}\cdot 3^{8} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.1891079497931380752384.8	x^16 + 486x^8 + 6561	\( 2^{58}\cdot 3^{8} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.2421961621595988176961.1	x^16 - 2x^15 + 15x^14 - 37x^13 + 107x^12 - 261x^11 + 518x^10 - 934x^9 + 1884x^8 - 2843x^7 + 4132x^6 - 6093x^5 + 6762x^4 - 6354x^3 + 5616x^2 - 3159x + 729	\( 3^{8}\cdot 157^{8} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.2912945917279080546304.3	x^16 + 21x^12 + 112x^8 - 147x^4 + 49	\( 2^{32}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	Trivial
16.0.2912945917279080546304.4	x^16 + 4x^14 - 14x^12 + 56x^10 + 21x^8 - 84x^6 + 280x^4 + 312x^2 + 100	\( 2^{32}\cdot 7^{14} \)	$D_{8}$ (as 16T13)	$[2, 2]$
16.0.3433371692450636169216.3	x^16 + 9x^14 + 38x^12 + 74x^10 + 21x^8 + 173x^6 + 1092x^4 + 1664x^2 + 1024	\( 2^{16}\cdot 3^{8}\cdot 41^{8} \)	$D_{8}$ (as 16T13)	$[2]$ (GRH)
16.0.3663139112860606529536.1	x^16 + 6x^14 + 56x^12 - 70x^10 + 270x^8 - 70x^6 + 56x^4 + 6x^2 + 1	\( 2^{32}\cdot 31^{8} \)	$D_{8}$ (as 16T13)	$[6]$
16.0.4229909006359687890625.4	x^16 - 2x^15 + 13x^14 - 25x^13 + 89x^12 - 129x^11 + 282x^10 - 436x^9 + 449x^8 - 735x^7 + 199x^6 - 100x^5 + 365x^4 + 1275x^3 - 275x^2 + 125x + 625	\( 5^{8}\cdot 101^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.9534424039639863880321.1	x^16 - 2x^15 - 5x^14 + 21x^13 + 27x^12 - 59x^11 - 10x^10 - 92x^9 + 552x^8 + 843x^7 - 1950x^6 - 3761x^5 + 64x^4 + 3822x^3 + 5642x^2 + 3549x + 1521	\( 13^{8}\cdot 43^{8} \)	$D_{8}$ (as 16T13)	$[2]$
16.0.13345917567985773647041.1	x^16 - 2x^15 - 5x^14 + 17x^13 - 17x^12 - 18x^11 + 165x^10 - 312x^9 - 532x^8 + 1736x^7 + 809x^6 - 3224x^5 + 1091x^4 - 168x^3 - 7551x^2 + 810x + 18225	\( 11^{8}\cdot 53^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.50787142148496295121281.4	x^16 + 2x^14 + 53x^12 + 354x^10 + 1160x^8 + 1833x^6 + 2729x^4 + 2678x^2 + 8281	\( 13^{8}\cdot 53^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)
16.0.53112317075112629735569.1	x^16 + 9x^14 + 7x^12 - 238x^10 - 1113x^8 + 462x^6 + 12222x^4 + 24684x^2 + 14641	\( 7^{14}\cdot 23^{8} \)	$D_{8}$ (as 16T13)	$[3]$ (GRH)
16.0.76060599125298737496849.1	x^16 - 3x^15 - 5x^14 + 2x^13 + 78x^12 - 30x^11 - 224x^10 - 384x^9 + 1120x^8 + 682x^7 - 1206x^6 - 1930x^5 + 1543x^4 + 1899x^3 - 2115x^2 - 324x + 1296	\( 3^{8}\cdot 23^{14} \)	$D_{8}$ (as 16T13)	$[3]$ (GRH)
16.0.156381544652244701169601.1	x^16 - 8x^15 + 28x^14 - 29x^13 + 105x^12 - 186x^11 + 94x^10 - 283x^9 + 245x^8 - 227x^7 + 784x^6 - 802x^5 + 599x^4 - 64x^3 + 133x^2 - 78x + 13	\( 13^{8}\cdot 61^{8} \)	$D_{8}$ (as 16T13)	Trivial (GRH)