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 988)

Label	Polynomial	Discriminant	Galois group	Class group
16.6.331051355413671875.1	x^16 - x^15 - 3x^14 + 10x^13 - 16x^12 + 10x^11 + 10x^10 - 34x^9 + 45x^8 - 34x^7 + 10x^6 + 10x^5 - 16x^4 + 10x^3 - 3x^2 - x + 1	\( -\,5^{8}\cdot 59\cdot 119851^{2} \)	16T1905	Trivial
16.6.378431998703576723.1	x^16 - 3x^14 - 4x^13 + x^12 + 4x^11 + 6x^9 + 7x^8 - 5x^7 - 14x^6 - x^5 + 12x^4 - 6x^2 + 1	\( -\,79\cdot 4501009\cdot 1064267693 \)	$S_{16}$ (as 16T1954)	Trivial
16.6.453554270824333667.1	x^16 - 2x^14 - 3x^13 - 2x^12 + 13x^11 + 9x^10 - x^9 - 14x^8 - 40x^7 - 13x^6 + 3x^5 + 2x^4 + 5x^3 - 5x^2 - x + 1	\( -\,89^{2}\cdot 107\cdot 731531^{2} \)	16T1948	Trivial
16.6.505241847543359375.1	x^16 - x^15 - 3x^14 + 10x^13 - 13x^12 + 6x^11 + 12x^10 - 33x^9 + 41x^8 - 33x^7 + 12x^6 + 6x^5 - 13x^4 + 10x^3 - 3x^2 - x + 1	\( -\,5^{8}\cdot 71^{3}\cdot 1901^{2} \)	16T1905	Trivial
16.6.555286069887735611.1	x^16 - 3x^14 - 4x^13 + 8x^12 + 6x^11 - 9x^10 - 5x^9 + 12x^8 - 13x^7 - 6x^6 + 30x^5 - 10x^4 - 15x^3 + 9x^2 + x - 1	\( -\,89^{2}\cdot 131\cdot 731531^{2} \)	16T1948	Trivial
16.6.561298201600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 61x^12 - 2x^11 - 107x^10 + 172x^9 - 129x^8 + 34x^7 + 21x^6 - 20x^5 + 8x^4 - 6x^3 + 3x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 31 \)	16T1823	Trivial
16.6.716416589069289243.1	x^16 - 5x^15 + 11x^14 - 16x^13 + 15x^12 - 2x^11 - 19x^10 + 40x^9 - 49x^8 + 40x^7 - 19x^6 - 2x^5 + 15x^4 - 16x^3 + 11x^2 - 5x + 1	\( -\,3^{6}\cdot 19^{4}\cdot 67\cdot 103^{4} \)	16T1879	Trivial
16.6.779934549194921875.1	x^16 - 5x^15 + 11x^14 - 15x^13 + 11x^12 + 5x^11 - 28x^10 + 50x^9 - 59x^8 + 50x^7 - 28x^6 + 5x^5 + 11x^4 - 15x^3 + 11x^2 - 5x + 1	\( -\,5^{8}\cdot 139\cdot 119851^{2} \)	16T1905	Trivial
16.6.832833149900000000.1	x^16 - 2x^15 - 2x^14 - x^13 + 6x^12 + 9x^11 - 5x^10 - 16x^9 - 15x^8 + 19x^7 + 15x^6 + 4x^5 - 16x^4 - x^3 + x^2 + 3x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 59\cdot 109^{4} \)	16T1887	Trivial
16.6.847267028262109375.1	x^16 - 7x^15 + 19x^14 - 27x^13 + 19x^12 + 6x^11 - 38x^10 + 66x^9 - 77x^8 + 66x^7 - 38x^6 + 6x^5 + 19x^4 - 27x^3 + 19x^2 - 7x + 1	\( -\,5^{8}\cdot 151\cdot 119851^{2} \)	16T1905	Trivial
16.6.998084115966796875.1	x^16 - x^15 - 7x^14 + 5x^13 + 20x^12 - 8x^11 - 25x^10 + 9x^9 + 6x^8 - 25x^7 + 31x^5 + 13x^4 - 11x^3 - 8x^2 + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179 \)	16T1771	Trivial
16.6.998084115966796875.2	x^16 - x^15 - 4x^14 + 2x^13 + 7x^12 + 10x^11 - 22x^10 - 13x^9 + 27x^8 - 3x^7 - 5x^6 - 5x^4 + 9x^3 + x^2 - 4x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179 \)	16T1771	Trivial
16.6.1071708625152734375.1	x^16 - 2x^15 - x^14 + 4x^12 - 2x^10 + 4x^9 + 4x^8 - 3x^7 - 18x^6 + 19x^4 - 9x^2 + x + 1	\( -\,5^{8}\cdot 191\cdot 119851^{2} \)	16T1905	Trivial
16.6.1184384858154296875.1	x^16 - 3x^15 - 3x^14 + 15x^13 - 29x^11 + 15x^10 + 8x^9 - 9x^8 + 25x^7 - 15x^6 - 18x^5 + 13x^4 - 3x^3 - 2x^2 + 5x + 1	\( -\,5^{12}\cdot 19^{3}\cdot 29^{4} \)	16T1561	Trivial
16.6.1357983683758204983.1	x^16 - x^15 - 3x^14 - 5x^13 + 10x^12 + 12x^11 - 11x^10 - 2x^9 - x^8 + 3x^7 - 20x^6 + 14x^5 + 5x^4 - 6x^3 + 5x^2 + x - 1	\( -\,3^{6}\cdot 19^{4}\cdot 103^{4}\cdot 127 \)	16T1879	Trivial
16.6.1486297102695988131.1	x^16 - x^15 + x^14 - x^13 + 2x^12 + 2x^11 - 11x^10 - 15x^9 - 6x^8 + 14x^7 + 31x^6 + 24x^5 - 17x^3 - 17x^2 - 7x - 1	\( -\,3^{6}\cdot 19^{4}\cdot 103^{4}\cdot 139 \)	16T1879	Trivial
16.6.1873431282147923539.1	x^16 - 7x^15 + 18x^14 - 12x^13 - 39x^12 + 98x^11 - 63x^10 - 73x^9 + 143x^8 - 54x^7 - 36x^6 + 30x^5 - 13x^4 + 8x^3 + 7x^2 - 8x + 1	\( -\,19^{5}\cdot 607^{2}\cdot 1433^{2} \)	16T1948	Trivial
16.6.2162271712669470583.1	x^16 - 2x^15 - 2x^14 + 2x^13 + 9x^12 + 9x^11 - 21x^10 - 33x^9 + 9x^8 + 39x^7 + 15x^6 - 12x^5 - 10x^4 - 6x^3 - x^2 + 3x + 1	\( -\,103\cdot 12037^{4} \)	16T1944	Trivial
16.6.2255320901676777119.1	x^16 - 3x^15 + 4x^14 - 7x^13 + 12x^12 - 21x^11 + 28x^10 - 30x^9 + 34x^8 - 38x^7 + 51x^6 - 51x^5 + 27x^4 + 3x^3 - 17x^2 + 9x - 1	\( -\,167\cdot 13504915578902857 \)	$S_{16}$ (as 16T1954)	Trivial
16.6.2330215146663215871.1	x^16 - x^15 - x^14 + 7x^13 - 3x^12 - 5x^11 - 5x^10 - 11x^9 + 17x^8 - 6x^7 - 17x^6 + 25x^5 + 2x^4 - 19x^3 + 4x^2 + 8x + 1	\( -\,3\cdot 37\cdot 12037^{4} \)	16T1944	Trivial
16.6.2696120875100000000.1	x^16 - 4x^14 + 2x^12 - 14x^11 - 6x^10 + 40x^9 + 35x^8 - 30x^7 - 24x^6 + 8x^5 - 13x^4 - 8x^3 + 11x^2 + 4x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 109^{4}\cdot 191 \)	16T1887	Trivial
16.6.2743959120100000000.1	x^16 - 8x^14 + 21x^12 - 11x^10 - 30x^8 + 41x^6 - 21x^4 + 7x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 37^{4} \)	16T1778	Trivial
16.6.2925657431985881088.1	x^16 - 4x^15 + 2x^14 + 12x^13 - 9x^12 - 12x^11 - 8x^10 + 16x^9 + 5x^8 + 16x^7 - 8x^6 - 12x^5 - 9x^4 + 12x^3 + 2x^2 - 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 47^{3} \)	16T905	Trivial
16.6.2925657431985881088.2	x^16 - 6x^14 + 14x^12 - 4x^11 - 22x^10 + 16x^9 + 44x^8 - 16x^7 - 66x^6 - 12x^5 + 45x^4 + 20x^3 - 10x^2 - 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 47^{3} \)	16T905	Trivial
16.6.2971284994465234375.1	x^16 - 5x^15 + 10x^14 - 12x^13 + 8x^12 + 3x^11 - 14x^10 + 22x^9 - 25x^8 + 22x^7 - 14x^6 + 3x^5 + 8x^4 - 12x^3 + 10x^2 - 5x + 1	\( -\,5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{3} \)	16T1823	Trivial (GRH)
16.6.2972348402500000000.1	x^16 - 5x^15 + 10x^14 - 5x^13 - 12x^12 + 2x^11 + 64x^10 - 100x^9 - 23x^8 + 218x^7 - 218x^6 + 24x^5 + 88x^4 - 49x^3 + 2x^2 + 5x - 1	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1823	Trivial
16.6.2972348402500000000.2	x^16 - 7x^14 + 10x^12 + 41x^10 - 181x^8 + 305x^6 - 270x^4 + 125x^2 - 25	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1823	Trivial
16.6.3028085707763671875.1	x^16 - x^15 - 3x^14 + x^13 + x^12 + 5x^11 - 12x^10 + 10x^9 - 3x^8 + 10x^7 - 12x^6 + 5x^5 + x^4 + x^3 - 3x^2 - x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 179^{2} \)	16T1771	Trivial
16.6.3028085707763671875.2	x^16 - 2x^15 - 6x^14 + x^13 + 11x^12 + 24x^11 + 20x^10 + 5x^9 + 2x^8 - 15x^7 - 20x^6 - 17x^5 - 4x^4 + 13x^3 + 11x^2 + 6x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 179^{2} \)	16T1771	Trivial
16.6.3613648921600000000.1	x^16 - 11x^14 + 46x^12 - 98x^10 + 123x^8 - 90x^6 + 32x^4 - x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 109^{4} \)	16T1870	Trivial
16.6.3625256545900000000.1	x^16 - x^15 - 4x^14 - x^13 + 11x^12 + 3x^11 - 21x^10 - 5x^9 + 44x^8 + 39x^7 - 45x^6 - 18x^5 + 60x^4 + 20x^3 - 15x^2 - 8x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{5} \)	16T1581	Trivial
16.6.3745595669067333632.1	x^16 - 6x^15 + 15x^14 - 22x^13 + 20x^12 - 4x^11 - 21x^10 + 44x^9 - 53x^8 + 44x^7 - 21x^6 - 4x^5 + 20x^4 - 22x^3 + 15x^2 - 6x + 1	\( -\,2^{24}\cdot 41^{6}\cdot 47 \)	16T1722	Trivial (GRH)
16.6.4053375385600000000.1	x^16 - 4x^15 + 4x^14 + 8x^13 - 36x^12 + 68x^11 - 52x^10 - 64x^9 + 230x^8 - 312x^7 + 244x^6 - 80x^5 - 76x^4 + 136x^3 - 96x^2 + 32x - 4	\( -\,2^{36}\cdot 5^{8}\cdot 151 \)	16T1590	Trivial
16.6.4770074402500000000.1	x^16 - x^15 - 5x^14 + 7x^13 + 3x^12 - 10x^11 + 14x^10 - 29x^9 + 19x^8 + 42x^7 - 84x^6 + 71x^5 - 44x^4 + 24x^3 - 4x^2 - 4x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{4}\cdot 19^{4} \)	16T1719	Trivial (GRH)
16.6.4813668526738671875.1	x^16 - 2x^15 - 5x^14 + 11x^13 - 21x^11 + 21x^10 + 9x^9 - 29x^8 + 9x^7 + 21x^6 - 21x^5 + 11x^3 - 5x^2 - 2x + 1	\( -\,5^{8}\cdot 11\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial
16.6.4852425925537109375.1	x^16 - 5x^15 + 7x^14 - 3x^13 + 7x^12 - 2x^11 - 31x^10 + 46x^9 - 40x^8 + 34x^7 - 13x^6 + x^5 + 12x^4 - 32x^3 + 27x^2 - 9x + 1	\( -\,5^{12}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial
16.6.5127117209600000000.1	x^16 - 8x^14 - 8x^13 + 8x^12 + 48x^11 + 62x^10 - 24x^9 - 141x^8 - 152x^7 - 26x^6 + 108x^5 + 146x^4 + 100x^3 + 42x^2 + 12x + 1	\( -\,2^{36}\cdot 5^{8}\cdot 191 \)	16T1590	Trivial
16.6.5424849633958428672.1	x^16 - 4x^15 + 20x^13 - 28x^12 + 20x^10 - 16x^9 + 54x^8 - 128x^7 + 136x^6 - 56x^5 - 36x^4 + 72x^3 - 48x^2 + 16x - 2	\( -\,2^{44}\cdot 3^{8}\cdot 47 \)	16T1577	Trivial
16.6.5567497578575422279.1	x^16 - 6x^15 + 16x^14 - 17x^13 - 30x^12 + 148x^11 - 291x^10 + 338x^9 - 221x^8 + 33x^7 + 108x^6 - 139x^5 + 102x^4 - 59x^3 + 20x^2 - 5x + 1	\( -\,37^{3}\cdot 643^{5} \)	16T1760	Trivial
16.6.5661124198400000000.1	x^16 - 2x^15 - 4x^14 + 6x^13 + 6x^12 + 20x^11 - 70x^10 + 50x^9 - 13x^8 - 16x^7 + 90x^6 - 114x^5 + 90x^4 - 70x^3 + 14x^2 + 12x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 59 \)	16T1719	Trivial (GRH)
16.6.5802498457600000000.1	x^16 - 2x^15 - x^14 - 2x^13 + 6x^12 + 4x^11 + 5x^10 - 8x^9 - 7x^8 - 8x^7 + 5x^6 + 4x^5 + 6x^4 - 2x^3 - x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 31 \)	16T1577	Trivial
16.6.5925801293676171875.1	x^16 - 3x^15 + 5x^13 - 2x^11 - 6x^10 + 3x^9 + 5x^8 + 3x^7 - 6x^6 - 2x^5 + 5x^3 - 3x + 1	\( -\,5^{8}\cdot 11^{3}\cdot 106759^{2} \)	16T1905	Trivial
16.6.6146647162089373696.1	x^16 - 4x^14 + 14x^10 - 41x^8 + 54x^6 - 34x^4 + 10x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial (GRH)
16.6.6146647162089373696.2	x^16 - 4x^14 + 12x^12 - 22x^10 + 23x^8 - 14x^6 - 2x^4 + 6x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial (GRH)
16.6.6226566414068750000.1	x^16 - 3x^15 + 4x^14 - 8x^13 - 2x^12 + 38x^11 - 58x^10 + 51x^9 - 17x^8 - 33x^7 + 62x^6 - 80x^5 + 66x^4 - 30x^3 + 10x^2 - x - 1	\( -\,2^{4}\cdot 5^{8}\cdot 251^{5} \)	16T1675	Trivial
16.6.6349180148041908224.1	x^16 - 8x^15 + 30x^14 - 66x^13 + 81x^12 - 34x^11 - 46x^10 + 80x^9 - 46x^8 + 24x^7 - 8x^6 - 42x^5 + 20x^4 + 4x^3 - 8x^2 + 1	\( -\,2^{24}\cdot 59\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.6.6349180148041908224.2	x^16 - 6x^15 + 10x^14 + 12x^13 - 57x^12 + 56x^11 - 46x^10 + 134x^9 - 161x^8 + 70x^7 - 54x^6 + 76x^5 - 31x^4 - 18x^3 + 22x^2 - 10x + 1	\( -\,2^{24}\cdot 59\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.6.6350601601600000000.1	x^16 - x^14 + 3x^12 - 13x^8 - 13x^6 + 4x^4 + 4x^2 - 1	\( -\,2^{12}\cdot 5^{8}\cdot 251^{4} \)	16T1759	Trivial
16.6.6350601601600000000.2	x^16 - 7x^14 + 25x^12 - 47x^10 + 43x^8 + 3x^6 - 27x^4 + 11x^2 - 1	\( -\,2^{12}\cdot 5^{8}\cdot 251^{4} \)	16T1759	Trivial
16.6.6492723609600000000.1	x^16 - 4x^15 + 6x^14 - 8x^13 + 16x^12 - 30x^11 + 18x^10 + 10x^9 - 9x^8 - 10x^7 - 3x^6 + 30x^5 - 4x^4 - 14x^3 - x^2 + 2x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 151 \)	16T1577	Trivial