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 511)

Label	Polynomial	Discriminant	Galois group	Class group
16.10.17156774645460546875.1	x^16 - 4x^15 + 2x^14 + 11x^13 - 22x^12 + 31x^11 - 39x^10 - 30x^9 + 189x^8 - 211x^7 - 4x^6 + 166x^5 - 112x^4 + 3x^3 + 28x^2 - 11x + 1	\( -\,5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 179 \)	16T1823	Trivial (GRH)
16.10.28263782809600000000.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 4x^11 + 2x^10 - 8x^9 + 7x^8 - 4x^7 + 13x^6 + 28x^5 - 25x^4 - 28x^3 + 3x^2 + 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 151 \)	16T1577	Trivial
16.10.29670049912965746743.1	x^16 - 5x^15 + 4x^14 + 9x^13 - 3x^12 - 11x^11 - 29x^10 + 40x^9 + 50x^8 - 86x^7 - 23x^6 + 87x^5 + 2x^4 - 41x^3 - 2x^2 + 7x + 1	\( -\,127\cdot 483345053^{2} \)	16T1948	Trivial
16.10.32473519196080620451.1	x^16 - 2x^15 - 9x^14 + 21x^13 + 27x^12 - 69x^11 - 54x^10 + 71x^9 + 53x^8 - 10x^7 + 25x^6 + 33x^5 - 31x^4 - 47x^3 - 12x^2 + 3x + 1	\( -\,139\cdot 483345053^{2} \)	16T1948	Trivial
16.10.34570892146577734375.1	x^16 - 2x^15 - 5x^14 + 8x^13 + 12x^12 + 10x^11 - 46x^10 - 68x^9 + 131x^8 + 66x^7 - 170x^6 + 13x^5 + 86x^4 - 34x^3 - 9x^2 + 7x - 1	\( -\,5^{8}\cdot 79\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.10.34978167156257421875.1	x^16 - 3x^15 - 3x^14 + 9x^13 + 18x^12 - 29x^11 - 79x^10 + 103x^9 + 59x^8 - 145x^7 + 96x^6 + 10x^5 - 87x^4 + 59x^3 - 6x^2 - 5x + 1	\( -\,5^{8}\cdot 29^{8}\cdot 179 \)	16T1461	Trivial
16.10.37248296550400000000.1	x^16 - 8x^14 - 2x^13 + 27x^12 - 6x^11 - 41x^10 + 58x^9 + 23x^8 - 96x^7 + 20x^6 + 42x^5 - 56x^4 - 8x^3 + 34x^2 + 12x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 199 \)	16T1577	Trivial
16.10.37248296550400000000.2	x^16 - 6x^15 + 9x^14 + 8x^13 - 17x^12 - 32x^11 + 31x^10 + 96x^9 - 63x^8 - 144x^7 + 52x^6 + 126x^5 + x^4 - 52x^3 - 14x^2 + 4x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 199 \)	16T1577	Trivial
16.10.39165688288992519439.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 102x^12 + 66x^11 + 180x^10 - 218x^9 - 124x^8 + 242x^7 + 19x^6 - 125x^5 + 16x^4 + 33x^3 - 9x^2 - 3x + 1	\( -\,17\cdot 263\cdot 1117^{2}\cdot 83791^{2} \)	16T1948	Trivial
16.10.43104723599206637824.1	x^16 - 3x^14 - 12x^12 + 26x^10 + 42x^8 - 33x^6 - 14x^4 + 10x^2 - 1	\( -\,2^{8}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.50024641296100000000.1	x^16 - 8x^14 + 12x^12 + 40x^10 - 116x^8 + 48x^6 + 47x^4 + 2x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.10.57326416091160546875.1	x^16 - 2x^15 - 9x^14 + 10x^13 + 26x^12 - 18x^11 - 34x^10 + 32x^9 + 20x^8 - 43x^7 - 22x^6 + 24x^5 + 29x^4 - 5x^3 - 12x^2 + x + 1	\( -\,5^{8}\cdot 131\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.10.60827265928788671875.1	x^16 - 2x^15 - 8x^14 + 16x^13 + 12x^12 - 15x^11 - 30x^10 - 15x^9 + 94x^8 - 21x^7 - 89x^6 + 58x^5 + 13x^4 - 17x^3 + 7x^2 - 4x + 1	\( -\,5^{8}\cdot 139\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.10.72998530305426171875.1	x^16 - x^15 - 6x^14 + 7x^13 + 6x^12 - 19x^11 + 15x^10 + 16x^9 - 27x^8 + 16x^7 + 15x^6 - 19x^5 + 6x^4 + 7x^3 - 6x^2 - x + 1	\( -\,5^{8}\cdot 11\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.10.82837504000000000000.1	x^16 - 10x^14 + 27x^12 - 30x^10 - 40x^9 + 64x^8 + 100x^7 - 110x^6 - 80x^5 + 78x^4 + 20x^3 - 20x^2 + 1	\( -\,2^{32}\cdot 5^{12}\cdot 79 \)	16T1379	Trivial (GRH)
16.10.87083639710999609375.1	x^16 - x^15 - 11x^14 + 13x^13 + 44x^12 - 60x^11 - 86x^10 + 135x^9 + 105x^8 - 190x^7 - 69x^6 + 140x^5 + 34x^4 - 46x^3 - 14x^2 + 3x + 1	\( -\,5^{8}\cdot 199\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.10.98517546059326171875.1	x^16 - 6x^15 + 14x^14 - 8x^13 - 51x^12 + 161x^11 - 164x^10 - 81x^9 + 335x^8 - 221x^7 - 58x^6 + 17x^5 + 115x^4 - 29x^3 - 27x^2 + 2x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.10.128860300270118047744.1	x^16 - 5x^14 + 4x^12 + 13x^10 - 22x^8 + 12x^6 - 15x^4 + 14x^2 - 1	\( -\,2^{12}\cdot 23^{2}\cdot 2777^{4} \)	16T1879	Trivial
16.10.165351052032100000000.1	x^16 - 6x^14 + 5x^12 + 28x^10 - 53x^8 + 10x^6 + 17x^4 - 2x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 139^{2} \)	16T1823	Trivial (GRH)
16.10.177617204783918359375.1	x^16 - 7x^15 + 16x^14 - 6x^13 - 37x^12 + 100x^11 - 141x^10 + 6x^9 + 314x^8 - 377x^7 + 31x^6 + 222x^5 - 167x^4 + 42x^3 + 12x^2 - 9x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 31\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.10.191782344451157658131.1	x^16 - 3x^15 - 8x^14 + 24x^13 + 13x^12 - 39x^11 - 19x^10 - 11x^9 + 67x^8 + 20x^7 - 43x^6 - 7x^5 - 13x^4 + 22x^3 + 2x^2 - 6x + 1	\( -\,17^{15}\cdot 67 \)	16T1351	Trivial (GRH)
16.10.202794005063232421875.1	x^16 - 10x^14 - 10x^13 + 29x^12 + 70x^11 + 25x^10 - 105x^9 - 179x^8 - 105x^7 + 25x^6 + 70x^5 + 29x^4 - 10x^3 - 10x^2 + 1	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.10.202794005063232421875.2	x^16 - 8x^15 + 29x^14 - 63x^13 + 76x^12 - x^11 - 163x^10 + 276x^9 - 183x^8 - 77x^7 + 243x^6 - 172x^5 + 26x^4 + 31x^3 - 14x^2 - x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 179 \)	16T1616	Trivial (GRH)
16.10.234092152286547152896.1	x^16 - 8x^14 + 14x^12 + 11x^10 - 27x^8 - 8x^6 + 13x^4 + 4x^2 - 1	\( -\,2^{12}\cdot 31^{2}\cdot 2777^{4} \)	16T1879	Trivial
16.10.269468244377600000000.1	x^16 - 4x^14 - 8x^13 - 4x^12 + 40x^11 + 22x^10 - 24x^9 - 64x^8 + 124x^6 - 52x^5 - 75x^4 + 32x^3 + 16x^2 - 4x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 71\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.10.277226992409600000000.1	x^16 - 8x^15 + 20x^14 - 73x^12 + 74x^11 + 85x^10 - 150x^9 - 35x^8 + 138x^7 - 11x^6 - 74x^5 + 24x^4 + 22x^3 - 11x^2 - 2x + 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 61\cdot 251 \)	16T1823	Trivial (GRH)
16.10.277795632642462908416.1	x^16 - 3x^14 + x^12 - 3x^10 + 19x^8 - 18x^6 - 2x^4 + 5x^2 - 1	\( -\,2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.10.298892216010498046875.1	x^16 - x^15 - 13x^14 + 65x^12 + 56x^11 - 119x^10 - 220x^9 - 21x^8 + 220x^7 + 179x^6 + 48x^5 + 30x^4 - 5x^3 - 32x^2 - 8x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.10.298892216010498046875.2	x^16 - 6x^15 + 11x^14 + 11x^13 - 75x^12 + 65x^11 + 125x^10 - 187x^9 - 68x^8 + 128x^7 + 63x^6 - 20x^5 - 88x^4 + 33x^3 + 16x^2 - 9x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.10.302613890996463717568.1	x^16 - 13x^14 - 7x^13 + 66x^12 + 67x^11 - 146x^10 - 236x^9 + 92x^8 + 355x^7 + 108x^6 - 194x^5 - 136x^4 + 10x^3 + 37x^2 + 5x - 1	\( -\,2^{6}\cdot 43^{3}\cdot 2777^{4} \)	16T1879	Trivial
16.10.310723820569600000000.1	x^16 - 6x^14 + 5x^12 + 18x^10 - 13x^8 - 25x^6 + 17x^4 + 3x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{2} \)	16T1823	Trivial (GRH)
16.10.310723820569600000000.2	x^16 - 10x^14 + 38x^12 - 68x^10 + 57x^8 - 17x^6 - 5x^4 + 6x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{2} \)	16T1823	Trivial (GRH)
16.10.310723820569600000000.3	x^16 - 7x^14 + 15x^12 + 4x^10 - 63x^8 + 95x^6 - 57x^4 + 14x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{2} \)	16T1823	Trivial (GRH)
16.10.329356056319413671875.1	x^16 - 3x^15 - 10x^14 + 37x^13 + 3x^12 - 105x^11 + 120x^10 - 24x^9 - 57x^8 - 24x^7 + 120x^6 - 105x^5 + 3x^4 + 37x^3 - 10x^2 - 3x + 1	\( -\,5^{8}\cdot 19\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.10.329713973555412533248.1	x^16 - 12x^13 - 11x^12 + 44x^11 - 3x^10 - 90x^9 + 18x^8 + 146x^7 + 141x^6 - 14x^5 - 151x^4 - 68x^3 + 25x^2 + 16x + 1	\( -\,2^{16}\cdot 7^{3}\cdot 19^{4}\cdot 103^{4} \)	16T1879	Trivial
16.10.338045647814554296875.1	x^16 - 4x^15 - 4x^14 + 29x^13 - 7x^12 - 59x^11 + 28x^10 + 27x^9 + 26x^8 - 15x^7 - 81x^6 + 42x^5 + 54x^4 - 16x^3 - 18x^2 - 5x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 59\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.10.367725112345600000000.1	x^16 - 6x^14 + 15x^12 - 17x^10 - 10x^8 + 51x^6 - 44x^4 + 12x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1905	Trivial
16.10.367725112345600000000.2	x^16 + 3x^14 - 6x^12 - 18x^10 + 20x^8 + 21x^6 - 29x^4 + 10x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1905	Trivial
16.10.367725112345600000000.3	x^16 - 9x^14 + 29x^12 - 38x^10 + 10x^8 + 22x^6 - 24x^4 + 9x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1905	Trivial
16.10.367725112345600000000.4	x^16 - 8x^14 + 25x^12 - 41x^10 + 43x^8 - 31x^6 + 8x^4 + 5x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1905	Trivial
16.10.389849374503958585088.1	x^16 - x^15 - 14x^14 + 22x^13 + 48x^12 - 112x^11 - 5x^10 + 159x^9 - 116x^8 + 29x^7 - 24x^6 - 39x^5 + 143x^4 - 143x^3 + 66x^2 - 14x + 1	\( -\,2^{8}\cdot 19^{4}\cdot 47^{3}\cdot 103^{4} \)	16T1851	Trivial (GRH)
16.10.463927926730170763651.1	x^16 - 5x^15 + 2x^14 + 28x^13 - 32x^12 - 88x^11 + 157x^10 + 116x^9 - 389x^8 + 108x^7 + 357x^6 - 311x^5 - 30x^4 + 109x^3 - 18x^2 - 5x + 1	\( -\,7^{2}\cdot 19\cdot 163^{8} \)	16T1845	Trivial
16.10.497995639706091520000.1	x^16 - 2x^15 - 3x^14 - 4x^13 + 21x^12 + 8x^11 + x^10 - 32x^9 - 57x^8 + 32x^7 + 40x^6 + 16x^5 + 10x^4 - 20x^3 - 13x^2 + 2x + 1	\( -\,2^{24}\cdot 5^{4}\cdot 7^{5}\cdot 41^{4} \)	16T1778	Trivial (GRH)
16.10.573094435225600000000.1	x^16 - 2x^15 - 11x^14 + 16x^13 + 57x^12 - 54x^11 - 147x^10 + 96x^9 + 142x^8 - 58x^7 - 46x^6 + 102x^5 - 61x^4 - 70x^3 + 17x^2 + 10x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 151\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.10.672488745723457421875.1	x^16 - 6x^15 + 10x^14 + 9x^13 - 75x^12 + 132x^11 - 13x^10 - 297x^9 + 296x^8 + 225x^7 - 338x^6 - 122x^5 + 191x^4 + 43x^3 - 72x^2 + 16x - 1	\( -\,5^{8}\cdot 119851^{3} \)	16T1651	Trivial (GRH)
16.10.672488745723457421875.2	x^16 - x^15 - 11x^14 + 6x^13 + 38x^12 - 18x^11 - 51x^10 + 48x^9 + 63x^8 - 27x^7 - 60x^6 - 33x^5 - 23x^4 - 10x^3 + 15x^2 + 5x - 1	\( -\,5^{8}\cdot 119851^{3} \)	16T1651	Trivial (GRH)
16.10.724907530649600000000.1	x^16 - 4x^15 - 4x^14 + 36x^13 - 32x^12 - 24x^11 - 12x^10 + 26x^9 + 87x^8 - 24x^7 - 48x^6 - 42x^5 + 15x^4 + 34x^3 - x^2 - 6x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 191\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.10.732780301186512843008.1	x^16 - 34x^12 + 102x^10 - 51x^8 - 136x^6 + 153x^4 - 17x^2 - 17	\( -\,2^{8}\cdot 17^{15} \)	16T1351	Trivial (GRH)
16.10.744139231811279296875.1	x^16 - 3x^15 - 4x^14 + 19x^13 - 7x^12 - 36x^11 + 53x^10 + 6x^9 - 74x^8 + 51x^7 + 16x^6 - 61x^5 + 15x^4 + 23x^3 - 5x^2 - 4x + 1	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial
16.10.744139231811279296875.2	x^16 - 2x^15 - 3x^14 + 23x^13 - 18x^12 - 78x^11 + 142x^10 + 92x^9 - 471x^8 + 100x^7 + 781x^6 - 429x^5 - 567x^4 + 445x^3 + 105x^2 - 151x + 31	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial