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 2247)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.13972911310408283.1	x^16 - 2x^15 + 2x^14 - 7x^13 + 10x^12 - 10x^11 + 19x^10 - 18x^9 + 18x^8 - 22x^7 + 13x^6 - 14x^5 + 8x^4 - 3x^3 + 4x^2 + x + 1	\( -\,4271\cdot 22247\cdot 147057059 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.15968672198702159.1	x^16 - x^14 + x^12 - 3x^11 - 4x^10 + 5x^9 + 3x^8 - x^7 - 2x^6 + 2x^5 - 5x^3 + 3x^2 + x - 1	\( -\,15968672198702159 \)	$S_{16}$ (as 16T1954)	Trivial
16.2.17695129757421875.1	x^16 - x^15 - 2x^14 + 5x^13 - 3x^12 - 7x^11 + 12x^10 + x^9 - 15x^8 + 13x^7 + 8x^6 - 19x^5 + 2x^4 + 10x^3 - 3x^2 - 2x + 1	\( -\,5^{8}\cdot 11^{4}\cdot 59\cdot 229^{2} \)	16T1823	Trivial
16.2.17968112315819999.1	x^16 - x^15 - 4x^14 + 5x^13 + 7x^12 - 9x^11 - 10x^10 + 11x^9 + 14x^8 - 14x^7 - 13x^6 + 17x^5 + 4x^4 - 11x^3 + 2x^2 + 3x - 1	\( -\,43^{2}\cdot 71\cdot 369959^{2} \)	16T1948	Trivial
16.2.19666546293359375.1	x^16 - 3x^15 + 5x^14 - 4x^13 - x^12 + 6x^11 - 6x^10 - 8x^9 + 20x^8 - 19x^7 + 11x^6 + 4x^5 - 14x^4 + 4x^3 + 5x^2 - x - 1	\( -\,5^{8}\cdot 31^{2}\cdot 71\cdot 859^{2} \)	16T1905	Trivial
16.2.21004976369198027.1	x^16 - 4x^15 + 6x^14 - x^13 - 6x^12 + 2x^11 + 10x^10 - 18x^9 + 19x^8 - 18x^7 + 10x^6 + 2x^5 - 6x^4 - x^3 + 6x^2 - 4x + 1	\( -\,43^{2}\cdot 83\cdot 369959^{2} \)	16T1948	Trivial
16.2.26611481600000000.1	x^16 - 2x^15 + 4x^13 - 2x^12 + 7x^10 - 20x^9 - 11x^8 + 28x^7 + x^6 - 4x^5 + 11x^4 - 10x^3 - 5x^2 + 4x - 1	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 71 \)	16T1719	Trivial
16.2.32297047507421875.1	x^16 - 5x^15 + 13x^14 - 22x^13 + 26x^12 - 20x^11 + 4x^10 + 12x^9 - 19x^8 + 12x^7 + 4x^6 - 20x^5 + 26x^4 - 22x^3 + 13x^2 - 5x + 1	\( -\,5^{8}\cdot 29^{6}\cdot 139 \)	16T1722	Trivial
16.2.36286162879296875.1	x^16 - 2x^15 + x^14 + 3x^13 - 11x^12 + 16x^11 - 17x^10 + 16x^9 - 13x^8 + 16x^7 - 17x^6 + 16x^5 - 11x^4 + 3x^3 + x^2 - 2x + 1	\( -\,5^{8}\cdot 31^{2}\cdot 131\cdot 859^{2} \)	16T1905	Trivial
16.2.36973431874322432.1	x^16 - 2x^15 + 3x^14 + 6x^13 - 9x^12 + 14x^11 + 6x^10 - 6x^9 + 21x^8 - 6x^7 + 6x^6 + 14x^5 - 9x^4 + 6x^3 + 3x^2 - 2x + 1	\( -\,2^{16}\cdot 47\cdot 331^{4} \)	16T1848	Trivial
16.2.45287535480859375.1	x^16 - 3x^15 + 6x^14 - 11x^13 + 14x^12 - 16x^11 + 13x^10 - 8x^9 + 7x^8 - 8x^7 + 13x^6 - 16x^5 + 14x^4 - 11x^3 + 6x^2 - 3x + 1	\( -\,5^{8}\cdot 11^{4}\cdot 151\cdot 229^{2} \)	16T1823	Trivial
16.2.46569375736056031.1	x^16 - 2x^15 + 5x^14 - 8x^13 + 12x^12 - 17x^11 + 20x^10 - 23x^9 + 23x^8 - 23x^7 + 20x^6 - 17x^5 + 12x^4 - 8x^3 + 5x^2 - 2x + 1	\( -\,37^{2}\cdot 199\cdot 643^{4} \)	16T1879	Trivial
16.2.47375394326171875.1	x^16 - 5x^15 + 8x^14 + 4x^13 - 29x^12 + 31x^11 + 4x^10 - 19x^9 - 23x^8 + 59x^7 - 30x^6 - 16x^5 + 20x^4 - 6x^2 + x + 1	\( -\,5^{10}\cdot 19^{3}\cdot 29^{4} \)	16T1561	Trivial
16.2.60840256363671875.1	x^16 - x^15 + x^14 - 2x^12 - 2x^11 + 3x^10 - 3x^9 + 3x^8 + 14x^7 - 22x^6 + 6x^5 + 5x^4 + 2x^3 - 5x^2 + 1	\( -\,5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 131 \)	16T1823	Trivial
16.2.63474986914349056.1	x^16 - 6x^15 + 15x^14 - 18x^13 + 5x^12 + 8x^11 + 4x^10 - 22x^9 + 25x^8 - 22x^7 + 4x^6 + 8x^5 + 5x^4 - 18x^3 + 15x^2 - 6x + 1	\( -\,2^{16}\cdot 151\cdot 283^{4} \)	16T1848	Trivial
16.2.66221484488898283.1	x^16 - x^15 - 3x^13 + 10x^12 - 11x^11 + 17x^10 - 30x^9 + 27x^8 - 20x^7 + 47x^6 - 70x^5 + 35x^4 + 13x^3 - 21x^2 + 8x - 1	\( -\,191^{2}\cdot 283^{5} \)	16T1847	Trivial
16.2.67969704100000000.1	x^16 - 3x^14 + x^12 + 3x^10 + 2x^8 - x^6 - 9x^4 - 4x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{2} \)	16T1823	Trivial
16.2.75417294303354643.1	x^16 + 4x^14 - x^13 + 7x^12 - 8x^11 + 3x^10 - 18x^9 - 7x^8 - 15x^7 - 4x^6 - 2x^5 - 7x^4 - 5x^3 + x^2 - x - 1	\( -\,149^{2}\cdot 283\cdot 331^{4} \)	16T1879	Trivial
16.2.80157081600000000.1	x^16 - 2x^15 + x^14 - 3x^12 - 2x^11 + 19x^10 - 4x^9 - 37x^8 + 28x^7 + 19x^6 - 30x^5 + 6x^4 + 10x^3 - 6x^2 + 1	\( -\,2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151 \)	16T1577	Trivial
16.2.86899140707421875.1	x^16 - 5x^15 + 10x^14 - 9x^13 - 2x^12 + 17x^11 - 21x^10 + 11x^9 + x^8 - 7x^7 + 2x^6 + 5x^5 - 12x^4 + 14x^3 - 9x^2 + 4x - 1	\( -\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131 \)	16T1778	Trivial
16.2.98118744033289079.1	x^16 - 7x^15 + 27x^14 - 70x^13 + 129x^12 - 168x^11 + 134x^10 - 6x^9 - 152x^8 + 231x^7 - 187x^6 + 88x^5 - 18x^4 - 4x^3 + 5x^2 - 3x + 1	\( -\,191\cdot 283^{6} \)	16T1849	Trivial
16.2.98251000757421875.1	x^16 - x^15 - x^14 + 5x^13 - 2x^12 - 8x^11 + 13x^10 + 5x^9 - 24x^8 + 12x^7 + 28x^6 - 25x^5 - 21x^4 + 16x^3 + 8x^2 - 4x - 1	\( -\,5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 2939 \)	16T1823	Trivial
16.2.115558273191796875.1	x^16 + 2x^14 - 5x^13 - x^12 - 10x^11 + 3x^10 - 4x^9 + 9x^8 - 4x^7 + 8x^6 - x^5 + 7x^4 + 4x^2 - x + 1	\( -\,3^{4}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 691 \)	16T1823	Trivial
16.2.117614702500000000.1	x^16 + 3x^14 - 5x^10 - x^8 - x^6 - 8x^4 - 7x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 19^{6} \)	16T1774	Trivial
16.2.118740047226171875.1	x^16 - x^15 - 2x^14 + 3x^13 - x^12 - 2x^11 - 2x^10 + 9x^9 + x^8 + x^7 - x^6 - 2x^5 + 2x^4 + 10x^3 + 3x^2 - 2x - 1	\( -\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 179 \)	16T1778	Trivial
16.2.118893936100000000.1	x^16 - x^14 - 4x^12 + 4x^10 + 7x^8 + 2x^6 - 4x^4 - 5x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{2} \)	16T1823	Trivial
16.2.122484747687109375.1	x^16 - 2x^15 - x^14 + 3x^13 - 2x^10 - 6x^9 + 7x^8 + 6x^7 - 5x^6 + 2x^5 - 3x^3 - 1	\( -\,5^{8}\cdot 79\cdot 251^{4} \)	16T1759	Trivial
16.2.125468737884127232.1	x^16 - 4x^15 + 20x^13 - 21x^12 - 32x^11 + 62x^10 + 4x^9 - 59x^8 + 20x^7 + 12x^6 + 8x^5 - 9x^4 - 8x^3 + 2x^2 + 4x + 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1567	Trivial
16.2.125468737884127232.2	x^16 - 4x^15 + 6x^14 - 8x^13 + 19x^12 - 40x^11 + 62x^10 - 76x^9 + 90x^8 - 104x^7 + 80x^6 - 12x^5 - 46x^4 + 52x^3 - 28x^2 + 8x - 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1781	Trivial
16.2.125468737884127232.3	x^16 - 4x^15 + 6x^14 - 19x^12 + 44x^11 - 48x^10 + 8x^9 + 53x^8 - 76x^7 + 36x^6 + 28x^5 - 43x^4 + 12x^3 + 4x^2 - 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1781	Trivial
16.2.142966494557221347.1	x^16 - 2x^15 + x^14 + 2x^13 - 3x^12 - 7x^11 + 38x^10 - 84x^9 + 105x^8 - 84x^7 + 38x^6 - 7x^5 - 3x^4 + 2x^3 + x^2 - 2x + 1	\( -\,3^{3}\cdot 19^{6}\cdot 103^{4} \)	16T1758	Trivial
16.2.145380128593826227.1	x^16 - x^15 - 2x^14 + 2x^13 - 2x^12 + 7x^11 + 5x^10 - 24x^9 + x^8 + 35x^7 - 15x^6 - 42x^5 + 36x^4 + 23x^3 - 28x^2 + 6x - 1	\( -\,283^{7} \)	16T1691	Trivial
16.2.145380128593826227.2	x^16 - 2x^15 + x^14 - 5x^13 + 15x^12 - 13x^11 - 3x^10 + 9x^9 - x^8 + 4x^7 - 17x^6 + 4x^5 + 16x^4 - 2x^3 - 9x^2 + 2x + 1	\( -\,283^{7} \)	16T1692	Trivial
16.2.173942237590234375.1	x^16 - x^15 + 2x^14 - 4x^13 + 2x^12 - 3x^11 + 2x^10 + x^8 + 2x^6 - 3x^5 + 2x^4 - 4x^3 + 2x^2 - x + 1	\( -\,5^{8}\cdot 31\cdot 119851^{2} \)	16T1905	Trivial
16.2.183992172742975744.1	x^16 + x^14 + 3x^12 - 8x^10 + x^8 + 14x^6 - 4x^2 - 1	\( -\,2^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4} \)	16T1879	Trivial
16.2.190802976100000000.1	x^16 - x^15 - x^14 - 3x^12 - 6x^11 + 5x^10 - x^9 - 4x^8 - x^7 + 5x^6 - 6x^5 - 3x^4 - x^2 - x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T1719	Trivial
16.2.194097037021484375.1	x^16 - 3x^15 + 3x^14 - 6x^12 + 10x^11 - 2x^10 - 6x^9 + 7x^8 + 9x^7 - 4x^6 - 12x^5 + 7x^4 + 7x^3 - 4x^2 - 3x + 1	\( -\,5^{10}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial
16.2.195238297600000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 + 10x^12 - 26x^11 + 52x^10 - 54x^9 - 12x^8 + 82x^7 - 54x^6 - 24x^5 + 49x^4 - 32x^3 + 16x^2 - 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 31^{3} \)	16T1477	Trivial
16.2.195238297600000000.2	x^16 - 6x^15 + 14x^14 - 14x^13 + 2x^12 - 4x^11 + 40x^10 - 78x^9 + 79x^8 - 52x^7 + 36x^6 - 34x^5 + 26x^4 - 18x^3 + 10x^2 - 4x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 31^{3} \)	16T972	Trivial
16.2.195238297600000000.3	x^16 - 6x^15 + 18x^14 - 36x^13 + 51x^12 - 46x^11 + 18x^10 - 4x^9 + 44x^8 - 118x^7 + 160x^6 - 138x^5 + 72x^4 - 16x^3 - 4x^2 + 4x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 31^{3} \)	16T972	Trivial
16.2.199224773165828807.1	x^16 - 3x^15 + 6x^14 - 8x^13 + 7x^12 - 4x^11 + 3x^9 - 5x^8 + 3x^7 - 4x^5 + 7x^4 - 8x^3 + 6x^2 - 3x + 1	\( -\,47\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.2.217453542400000000.1	x^16 - 2x^15 - x^14 + 4x^13 - 4x^12 + 4x^11 - x^10 + 8x^9 - 14x^8 - 8x^7 + 14x^6 + 6x^5 - 4x^4 - 4x^3 - x^2 + 2x + 1	\( -\,2^{16}\cdot 5^{8}\cdot 31^{2}\cdot 8839 \)	16T1823	Trivial
16.2.284452595367842719.1	x^16 - x^15 - 2x^14 - 4x^13 + 9x^12 + 4x^11 + 2x^10 - 11x^9 - 5x^8 - 5x^7 + 12x^6 + 2x^5 + 4x^4 - 6x^3 - x^2 - x + 1	\( -\,1321^{2}\cdot 3347^{2}\cdot 14551 \)	16T1948	Trivial
16.2.300956572229230751.1	x^16 - 3x^15 + 3x^14 - x^13 - x^12 + 6x^11 - 12x^10 + 16x^9 - 17x^8 + 16x^7 - 12x^6 + 6x^5 - x^4 - x^3 + 3x^2 - 3x + 1	\( -\,71\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.2.316940672000000000.1	x^16 - 4x^15 + 6x^14 - 2x^13 - 7x^12 + 37x^10 - 64x^9 + 32x^8 + 14x^7 + 8x^6 - 82x^5 + 119x^4 - 90x^3 + 40x^2 - 10x + 1	\( -\,2^{16}\cdot 5^{9}\cdot 19^{5} \)	16T1782	Trivial
16.2.319040277384290048.1	x^16 - x^15 + 2x^14 - 7x^13 + x^12 + x^11 + x^10 + 13x^9 - 12x^8 - 11x^7 + 5x^6 - 8x^5 - 6x^4 - 8x^3 + 3x^2 - 6x + 1	\( -\,2^{8}\cdot 47^{3}\cdot 331^{4} \)	16T1758	Trivial
16.2.319040277384290048.2	x^16 - 6x^15 + 15x^14 - 23x^13 + 29x^12 - 34x^11 + 28x^10 - 14x^9 + x^8 + 40x^7 - 80x^6 + 58x^5 - 30x^4 + 29x^3 - 20x^2 + 6x - 1	\( -\,2^{8}\cdot 47^{3}\cdot 331^{4} \)	16T1851	Trivial
16.2.320444825600000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 260x^12 - 468x^11 + 658x^10 - 716x^9 + 574x^8 - 288x^7 + 8x^6 + 140x^5 - 145x^4 + 84x^3 - 32x^2 + 8x - 1	\( -\,2^{32}\cdot 5^{8}\cdot 191 \)	16T1590	Trivial
16.2.320501104309234339.1	x^16 - 3x^12 - 4x^11 - 10x^10 - 10x^9 - 22x^7 - 5x^6 + 5x^5 - 7x^4 + x^3 + 7x^2 - 3x + 1	\( -\,67^{2}\cdot 283^{4}\cdot 11131 \)	16T1879	Trivial
16.2.331051355413671875.1	x^16 - 4x^15 + 6x^14 - 5x^13 + x^12 + 2x^11 + x^10 - 8x^9 + 11x^8 - 8x^7 + x^6 + 2x^5 + x^4 - 5x^3 + 6x^2 - 4x + 1	\( -\,5^{8}\cdot 59\cdot 119851^{2} \)	16T1905	Trivial