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
16.0.4559007230078125.1	x^16 - 2x^15 + 3x^14 - 6x^13 + 11x^12 - 19x^11 + 26x^10 - 30x^9 + 33x^8 - 30x^7 + 26x^6 - 19x^5 + 11x^4 - 6x^3 + 3x^2 - 2x + 1	\( 5^{8}\cdot 11^{4}\cdot 59^{2}\cdot 229 \)	16T1823	Trivial
16.0.5236602731044893.1	x^16 - 7x^15 + 26x^14 - 66x^13 + 125x^12 - 180x^11 + 195x^10 - 148x^9 + 60x^8 + 21x^7 - 58x^6 + 51x^5 - 22x^4 - 2x^3 + 9x^2 - 5x + 1	\( 3^{8}\cdot 13^{4}\cdot 181^{2}\cdot 853 \)	16T1823	Trivial
16.0.8575915274724096.1	x^16 - 7x^15 + 20x^14 - 29x^13 + 19x^12 + 5x^11 - 18x^10 - 5x^9 + 50x^8 - 58x^7 + 21x^6 + 10x^5 - 18x^4 + 11x^3 - 2x + 1	\( 2^{8}\cdot 3^{8}\cdot 13^{4}\cdot 19\cdot 97^{2} \)	16T1823	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
16.0.29862086714453125.1	x^16 - 3x^15 + 3x^14 + x^13 - 4x^12 + 2x^11 + 5x^10 - 9x^9 + 3x^8 + 9x^7 - 9x^6 - 4x^5 + 9x^4 - x^3 - 4x^2 + x + 1	\( 5^{8}\cdot 11^{4}\cdot 151^{2}\cdot 229 \)	16T1823	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
16.2.60840256363671875.1	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
16.2.67969704100000000.1	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
16.2.98251000757421875.1	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
16.2.118893936100000000.1	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
16.0.156383420761328125.1	x^16 - 3x^15 + 4x^14 + x^13 - 5x^12 + 12x^10 - 5x^9 - 8x^8 + 10x^7 + 11x^6 - 8x^5 - x^4 + 7x^3 + x^2 - 2x + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31^{3} \)	16T1823	Trivial
16.0.189837888276953125.1	x^16 - 2x^15 + 3x^14 - 8x^13 + 9x^12 - 5x^11 + 12x^10 - 7x^9 - 2x^8 - 11x^7 + 7x^6 + 5x^5 + 6x^4 - 7x^3 - x^2 + 1	\( 5^{8}\cdot 11^{4}\cdot 29^{3}\cdot 1361 \)	16T1823	Trivial
16.4.194392038625390625.1	x^16 - 7x^15 + 23x^14 - 45x^13 + 55x^12 - 32x^11 - 28x^10 + 94x^9 - 123x^8 + 94x^7 - 28x^6 - 32x^5 + 55x^4 - 45x^3 + 23x^2 - 7x + 1	\( 5^{8}\cdot 29^{4}\cdot 41\cdot 131^{2} \)	16T1823	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
16.4.289217423320703125.1	x^16 - x^15 - 5x^14 + 12x^13 - 2x^12 - 22x^11 + 28x^10 - 4x^9 - 13x^8 - 4x^7 + 28x^6 - 22x^5 - 2x^4 + 12x^3 - 5x^2 - x + 1	\( 5^{8}\cdot 29^{4}\cdot 61\cdot 131^{2} \)	16T1823	Trivial
16.0.399698962570703125.1	x^16 - x^15 - x^14 + 3x^12 + 7x^11 - 2x^10 - 11x^9 + 8x^8 + 20x^7 - 7x^6 - 19x^5 + 12x^4 + 35x^3 + 25x^2 + 8x + 1	\( 5^{8}\cdot 11^{4}\cdot 29^{2}\cdot 83101 \)	16T1823	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
16.2.638966001996484375.1	x^16 - x^13 + 2x^12 - 6x^11 + 4x^10 - x^9 + x^8 - x^7 + 4x^6 - 6x^5 + 2x^4 - x^3 + 1	\( -\,5^{8}\cdot 29^{2}\cdot 31\cdot 89^{4} \)	16T1823	Trivial
16.4.683032622823828125.1	x^16 - x^15 - 2x^14 - 4x^13 - 5x^12 - x^11 + 6x^10 + 13x^9 + 15x^8 + 13x^7 + 6x^6 - x^5 - 5x^4 - 4x^3 - 2x^2 - x + 1	\( 5^{8}\cdot 29\cdot 31^{2}\cdot 89^{4} \)	16T1823	Trivial
16.2.848687193023046875.1	x^16 - 2x^15 + 4x^14 - 8x^13 + 11x^12 - 15x^11 + 18x^10 - 20x^9 + 21x^8 - 20x^7 + 18x^6 - 15x^5 + 11x^4 - 8x^3 + 4x^2 - 2x + 1	\( -\,5^{8}\cdot 29^{4}\cdot 131^{2}\cdot 179 \)	16T1823	Trivial
16.4.871313047442948096.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 20x^12 - 44x^11 + 63x^10 - 72x^9 + 41x^8 + 6x^7 - 27x^6 + 20x^5 - 15x^4 + 22x^3 - 12x^2 + 4x - 1	\( 2^{24}\cdot 7^{4}\cdot 23^{2}\cdot 31\cdot 1319 \)	16T1823	Trivial
16.2.1159656546191796875.1	x^16 - 2x^15 + 3x^14 - x^13 - 4x^12 + 11x^11 - 19x^10 + 25x^9 - 27x^8 + 25x^7 - 19x^6 + 11x^5 - 4x^4 - x^3 + 3x^2 - 2x + 1	\( -\,5^{8}\cdot 29^{4}\cdot 131\cdot 179^{2} \)	16T1823	Trivial
16.4.1660007570433203125.1	x^16 - 4x^15 + 3x^14 + 10x^13 - 18x^12 - 11x^11 + 49x^10 - 19x^9 - 50x^8 + 35x^7 + 45x^6 - 47x^5 - 19x^4 + 33x^3 - 7x^2 - 3x + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 101^{2} \)	16T1823	Trivial
16.4.1660007570433203125.2	x^16 + 2x^14 - 8x^13 + 5x^12 - 11x^11 - 8x^10 + 16x^9 - 25x^8 + 16x^7 - 8x^6 - 11x^5 + 5x^4 - 8x^3 + 2x^2 + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 101^{2} \)	16T1823	Trivial
16.0.1933393779464453125.1	x^16 - 6x^15 + 18x^14 - 35x^13 + 46x^12 - 37x^11 + 11x^10 + 4x^9 + 20x^8 - 73x^7 + 111x^6 - 100x^5 + 55x^4 - 16x^3 + 2x^2 - x + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 109^{2} \)	16T1823	Trivial
16.4.1933393779464453125.1	x^16 - 3x^15 - 2x^14 + 19x^13 - 20x^12 - 27x^11 + 74x^10 - 28x^9 - 77x^8 + 87x^7 + 7x^6 - 55x^5 + 21x^4 - 2x^3 + 11x^2 - 6x + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 109^{2} \)	16T1823	Trivial
16.4.2107060827100000000.1	x^16 - 7x^15 + 20x^14 - 31x^13 + 24x^12 + 7x^11 - 46x^10 + 57x^9 - 15x^8 - 53x^7 + 78x^6 - 30x^5 - 19x^4 + 27x^3 - 17x^2 + 6x - 1	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{3} \)	16T1823	Trivial
16.4.2957525616198828125.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 50x^12 - 27x^11 + 6x^10 + 3x^9 - 10x^8 + 11x^7 - 5x^6 + 4x^5 - 4x^4 + x + 1	\( 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 88469 \)	16T1823	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
16.4.3605577469136328125.1	x^16 - x^15 - 3x^14 + 3x^13 - 4x^12 + 30x^11 - 40x^10 + 29x^9 - 69x^8 + 64x^7 - 33x^6 + 35x^5 - 12x^4 + 20x^3 - 4x^2 + 4x - 1	\( 5^{8}\cdot 11^{4}\cdot 59^{2}\cdot 61\cdot 2969 \)	16T1823	Trivial
16.4.3612766206370703125.1	x^16 - 3x^15 + 8x^14 - 5x^13 - 3x^12 + 25x^11 - 21x^10 + 15x^9 + 27x^8 + 4x^7 + 46x^6 + 23x^5 + 14x^4 + 11x^3 - x^2 - x - 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 149^{2} \)	16T1823	Trivial
16.0.5214028287839453125.1	x^16 - 4x^15 + 5x^14 + 4x^13 - 12x^12 - 6x^11 + 30x^10 - 9x^9 - 32x^8 + 23x^7 + 20x^6 - 27x^5 + 3x^4 + 7x^3 - 3x + 1	\( 5^{8}\cdot 19\cdot 29^{4}\cdot 31\cdot 179^{2} \)	16T1823	Trivial
16.8.9680638207773828125.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 15x^12 + 7x^11 - 59x^10 - 48x^9 + 99x^8 + 100x^7 - 63x^6 - 89x^5 + 3x^4 + 31x^3 + 7x^2 - 3x - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101 \)	16T1823	Trivial
16.8.9680638207773828125.2	x^16 - 4x^15 + 4x^14 + 6x^13 - 33x^12 + 38x^11 + 10x^10 - 84x^9 + 103x^8 + 14x^7 - 80x^6 + 22x^5 + 3x^4 - 7x^3 + 9x^2 - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101 \)	16T1823	Trivial
16.4.10447421432151953125.1	x^16 - 3x^15 + 3x^14 - 7x^13 + 6x^12 - 9x^11 + 11x^10 - 8x^9 + 13x^8 - 8x^7 + 11x^6 - 9x^5 + 6x^4 - 7x^3 + 3x^2 - 3x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 109 \)	16T1823	Trivial
16.8.10447421432151953125.1	x^16 - 2x^15 - 4x^14 + 10x^13 - x^12 + 2x^10 - 51x^9 + 37x^8 + 75x^7 - 59x^6 - 38x^5 + 25x^4 + x^3 - x^2 + 5x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 109 \)	16T1823	Trivial
16.4.10980785807539453125.1	x^16 - x^15 - 3x^14 + x^13 + 5x^12 + 5x^11 - 6x^10 - 5x^9 - 4x^8 + x^7 + 21x^6 - 13x^5 - 16x^4 + 16x^3 - 4x + 1	\( 3^{4}\cdot 5^{8}\cdot 11^{4}\cdot 41^{2}\cdot 59\cdot 239 \)	16T1823	Trivial (GRH)
16.6.13138522584100000000.1	x^16 - 2x^14 - 2x^12 + 6x^10 - 6x^8 - 8x^6 + 7x^4 + 4x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 431^{2} \)	16T1823	Trivial (GRH)
16.8.14281337554042578125.1	x^16 - x^15 - 6x^14 + 4x^13 + 4x^12 + 2x^11 - 15x^9 + 40x^8 + 5x^7 - 75x^6 + 16x^5 + 41x^4 - 12x^3 - 4x^2 + 2x - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 149 \)	16T1823	Trivial
16.6.17156774645460546875.1	x^16 - 3x^15 + 8x^13 - 14x^12 + 20x^11 - 22x^10 + 20x^9 - 19x^8 + 20x^7 - 22x^6 + 20x^5 - 14x^4 + 8x^3 - 3x + 1	\( -\,5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 179 \)	16T1823	Trivial
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)
16.6.19655390233600000000.1	x^16 - 4x^14 + 9x^12 - 26x^10 + 48x^8 - 37x^6 + 9x^4 + 2x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{2} \)	16T1823	Trivial (GRH)
16.6.19655390233600000000.2	x^16 - 3x^12 - 4x^10 - 3x^8 + x^6 + 5x^4 + 3x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{2} \)	16T1823	Trivial (GRH)
16.4.21752712986034765625.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 10x^12 + 60x^11 - 44x^10 - 44x^9 + 90x^8 - 8x^7 - 75x^6 + 27x^5 + 30x^4 - 11x^3 - 7x^2 + 3x + 1	\( 5^{8}\cdot 11^{4}\cdot 29\cdot 41\cdot 61\cdot 229^{2} \)	16T1823	Trivial (GRH)
16.4.22894843174253515625.1	x^16 - 5x^15 + 9x^14 - 3x^13 - 14x^12 + 27x^11 - 27x^10 + 36x^9 - 62x^8 + 72x^7 - 32x^6 - 32x^5 + 66x^4 - 56x^3 + 28x^2 - 8x + 1	\( 5^{8}\cdot 29^{4}\cdot 139^{2}\cdot 4289 \)	16T1823	Trivial
16.4.36554776626933203125.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 48x^12 - 15x^11 - 24x^10 + 43x^9 - 38x^8 + 15x^7 + 11x^6 - 22x^5 + 11x^4 + 4x^3 - 6x^2 + 2x + 1	\( 5^{8}\cdot 29^{4}\cdot 31\cdot 41^{2}\cdot 2539 \)	16T1823	Trivial
16.8.57922757880019140625.1	x^16 - 3x^15 - 2x^14 + 26x^13 - 15x^12 - 75x^11 + 42x^10 + 107x^9 + 7x^8 - 128x^7 - 74x^6 + 89x^5 + 38x^4 + 21x^3 - 7x^2 - 7x - 1	\( 5^{8}\cdot 11^{4}\cdot 151\cdot 229^{2}\cdot 1279 \)	16T1823	Trivial (GRH)