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 80)

Label	Polynomial	Discriminant	Galois group	Class group
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
16.0.96489516623265792.1	x^16 - 4x^15 + 9x^14 - 10x^13 - 9x^12 + 30x^11 - 24x^10 - 2x^9 + 45x^8 - 36x^7 - 24x^6 + 30x^5 - 4x^4 - 14x^3 + 6x^2 + 6x + 1	\( 2^{16}\cdot 3^{12}\cdot 13^{4}\cdot 97 \)	16T1778	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
16.0.152812774400000000.1	x^16 - 2x^15 + 3x^14 - 2x^13 + 6x^11 - 4x^10 - 4x^9 + 15x^8 - 4x^7 - 4x^6 + 6x^5 - 2x^3 + 3x^2 - 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11\cdot 13^{4}\cdot 19 \)	16T1778	Trivial
16.0.201317633448542208.1	x^16 - 4x^15 + 11x^14 - 20x^13 + 12x^12 + 28x^11 - 83x^10 + 124x^9 - 101x^8 - 40x^7 + 246x^6 - 354x^5 + 290x^4 - 150x^3 + 50x^2 - 10x + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{6}\cdot 97 \)	16T1778	Trivial
16.4.742362137600000000.1	x^16 - 4x^15 + 6x^14 - 2x^13 - 4x^12 + 14x^11 - 35x^10 + 54x^9 - 59x^8 + 66x^7 - 33x^6 - 48x^5 + 89x^4 - 70x^3 + 35x^2 - 10x + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 41 \)	16T1778	Trivial
16.2.2020065264100000000.1	x^16 + 7x^14 + 20x^12 + 31x^10 + 27x^8 + 15x^6 + 8x^4 + x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 13^{4}\cdot 29^{4} \)	16T1778	Trivial
16.2.2020065264100000000.2	x^16 + 3x^14 - 3x^12 - 14x^10 - 9x^8 + 2x^6 + 8x^4 - 6x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 13^{4}\cdot 29^{4} \)	16T1778	Trivial
16.2.2743959120100000000.1	x^16 + 9x^14 + 30x^12 + 43x^10 + 15x^8 - 19x^6 - 4x^4 - 3x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 37^{4} \)	16T1778	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
16.0.4647728283417578125.1	x^16 - 3x^15 + x^14 + 6x^13 - 6x^12 - 4x^11 + 12x^10 - 12x^9 - 4x^8 + 29x^7 - 17x^6 - 23x^5 + 24x^4 + 3x^3 - 6x^2 - x + 1	\( 5^{8}\cdot 13^{4}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	Trivial
16.4.4647728283417578125.1	x^16 + x^14 - 3x^13 + 3x^12 - 2x^11 - 4x^10 + x^9 - 3x^8 + 15x^7 - 16x^6 + 17x^5 + 6x^4 - 19x^3 + 2x^2 + x + 1	\( 5^{8}\cdot 13^{4}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	Trivial
16.6.8321090236900000000.1	x^16 - x^15 - 7x^14 + 6x^13 + 19x^12 - 4x^11 - 71x^10 + 91x^9 - 29x^8 - x^7 - 28x^6 + 30x^5 + 11x^4 - 34x^3 + 21x^2 - 2x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 7^{6}\cdot 29^{4} \)	16T1778	Trivial
16.6.8321090236900000000.2	x^16 - 7x^15 + 19x^14 - 26x^13 + 11x^12 + 27x^11 - 55x^10 + 49x^9 - 34x^8 + 27x^7 - 15x^6 - 33x^5 + 77x^4 - 52x^3 + 6x^2 + 5x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 7^{6}\cdot 29^{4} \)	16T1778	Trivial
16.4.10302537958400000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 69x^12 - 50x^11 + 13x^10 + 12x^9 - 17x^8 + 18x^7 - 19x^6 + 12x^5 - 2x^4 - 2x^3 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 569 \)	16T1778	Trivial (GRH)
16.0.20680626457900000000.1	x^16 - 3x^15 + 7x^14 - 6x^13 + 8x^12 - 3x^11 - 13x^10 + 36x^9 - 13x^8 - 33x^7 + 35x^6 + 24x^5 + 12x^3 + 6x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 17^{4}\cdot 19^{5} \)	16T1778	Trivial
16.0.30183550321100000000.1	x^16 - 2x^15 + 2x^14 - 5x^13 + 17x^12 - 25x^11 + 26x^10 - 8x^9 + 4x^8 - 8x^7 + 26x^6 - 25x^5 + 17x^4 - 5x^3 + 2x^2 - 2x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{5}\cdot 37^{4} \)	16T1778	Trivial
16.4.30183550321100000000.1	x^16 + 2x^14 - 7x^12 - 16x^10 + 11x^8 + 50x^6 - 31x^4 - 22x^2 + 11	\( 2^{8}\cdot 5^{8}\cdot 11^{5}\cdot 37^{4} \)	16T1778	Trivial (GRH)
16.4.30183550321100000000.2	x^16 + 3x^14 - 2x^12 - 11x^10 - 7x^8 - 17x^6 - 38x^4 - 11x^2 + 11	\( 2^{8}\cdot 5^{8}\cdot 11^{5}\cdot 37^{4} \)	16T1778	Trivial (GRH)
16.4.30183550321100000000.3	x^16 - x^15 - x^14 + 6x^13 - 11x^12 + 10x^11 - 19x^10 + 25x^9 - 36x^8 + 25x^7 - 19x^6 + 10x^5 - 11x^4 + 6x^3 - x^2 - x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{5}\cdot 37^{4} \)	16T1778	Trivial (GRH)
16.2.126254275295538671875.1	x^16 - 8x^15 + 37x^14 - 119x^13 + 289x^12 - 551x^11 + 836x^10 - 1012x^9 + 959x^8 - 679x^7 + 316x^6 - 46x^5 - 46x^4 + 27x^3 - 7x^2 + 3x - 1	\( -\,5^{8}\cdot 11^{4}\cdot 37^{4}\cdot 11779 \)	16T1778	Trivial (GRH)
16.0.155153686758400000000.1	x^16 - 8x^15 + 30x^14 - 68x^13 + 104x^12 - 124x^11 + 142x^10 - 162x^9 + 153x^8 - 114x^7 + 89x^6 - 66x^5 + 26x^4 - 12x^3 + 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11\cdot 19\cdot 29^{4}\cdot 41 \)	16T1778	$[2]$
16.6.315330395110400000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 26x^12 + 26x^11 - 72x^10 + 74x^9 - 35x^8 - 18x^7 + 44x^6 - 26x^5 - 3x^4 + 12x^3 - x^2 - 4x - 1	\( -\,2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 139\cdot 1061 \)	16T1778	Trivial (GRH)
16.6.341391029632900000000.1	x^16 - 4x^15 + 2x^14 + 6x^13 - 23x^12 + 14x^11 + 26x^10 - 73x^9 - 12x^8 + 64x^7 - 67x^6 - 36x^5 + 112x^4 + 31x^3 - 46x^2 - 7x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1778	Trivial (GRH)
16.6.341391029632900000000.2	x^16 - 5x^15 - x^14 + 46x^13 - 73x^12 - 86x^11 + 357x^10 - 250x^9 - 392x^8 + 858x^7 - 511x^6 - 269x^5 + 721x^4 - 641x^3 + 328x^2 - 93x + 11	\( -\,2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1778	Trivial (GRH)
16.8.377978757818547265625.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 98x^12 + 42x^11 + 208x^10 - 138x^9 - 289x^8 + 158x^7 + 302x^6 - 80x^5 - 201x^4 + 2x^3 + 59x^2 + 10x - 1	\( 5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 61\cdot 9341 \)	16T1778	Trivial (GRH)
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)
16.6.497995639706091520000.1	x^16 - 4x^15 + 6x^14 - 4x^13 - 28x^12 + 14x^11 - 18x^10 - 32x^9 + x^8 - 14x^7 + 91x^6 + 146x^5 + 61x^4 + 26x^3 + 30x^2 + 12x + 1	\( -\,2^{24}\cdot 5^{4}\cdot 7^{5}\cdot 41^{4} \)	16T1778	Trivial
16.0.1676300377913588514816.1	x^16 - 6x^13 + 5x^12 - 6x^11 - 5x^10 - 48x^9 + 54x^8 + 18x^7 + 61x^6 - 60x^5 + 126x^4 + 102x^3 + 178x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 73^{4}\cdot 107\cdot 1283 \)	16T1778	$[2]$
16.8.1676300377913588514816.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 11x^12 + 66x^11 - 63x^10 - 4x^9 + 51x^8 - 26x^7 - 15x^6 + 12x^5 + 8x^4 - 10x^3 - x^2 + 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 73^{4}\cdot 107\cdot 1283 \)	16T1778	Trivial (GRH)
16.10.1824644755865600000000.1	x^16 - 6x^15 + 3x^14 + 38x^13 - 44x^12 - 110x^11 + 146x^10 + 224x^9 - 223x^8 - 296x^7 + 48x^6 + 112x^5 + 58x^4 + 16x^3 - 19x^2 - 8x + 1	\( -\,2^{20}\cdot 5^{8}\cdot 71\cdot 89^{4} \)	16T1778	Trivial (GRH)
16.6.1824644755865600000000.1	x^16 - 4x^15 + 10x^13 - 19x^12 + 16x^11 - 4x^10 - 4x^9 + 9x^8 - 4x^7 - 4x^6 + 16x^5 - 19x^4 + 10x^3 - 4x + 1	\( -\,2^{20}\cdot 5^{8}\cdot 71\cdot 89^{4} \)	16T1778	Trivial (GRH)
16.0.2340675787025285120000.1	x^16 - 2x^14 - 2x^12 + x^10 - 5x^8 + 42x^6 + 68x^4 + 22x^2 + 2	\( 2^{29}\cdot 5^{4}\cdot 17^{8} \)	16T1778	Trivial
16.8.2340675787025285120000.1	x^16 + 2x^14 - 2x^12 - x^10 - 5x^8 - 42x^6 + 68x^4 - 22x^2 + 2	\( 2^{29}\cdot 5^{4}\cdot 17^{8} \)	16T1778	Trivial (GRH)
16.8.2340675787025285120000.2	x^16 - 9x^14 + 34x^12 - 80x^10 + 143x^8 - 184x^6 + 144x^4 - 56x^2 + 8	\( 2^{29}\cdot 5^{4}\cdot 17^{8} \)	16T1778	Trivial (GRH)
16.4.2730154452582400000000.1	x^16 - 4x^15 + 6x^14 - 10x^13 - 16x^12 - 22x^11 - 52x^10 - 130x^9 - 110x^8 - 306x^7 - 134x^6 - 348x^5 - 275x^4 - 76x^3 - 24x^2 + 18x + 1	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	Trivial (GRH)
16.4.2730154452582400000000.2	x^16 - 4x^15 - 4x^14 + 38x^13 - 19x^12 - 160x^11 + 108x^10 + 434x^9 - 47x^8 - 586x^7 - 326x^6 + 34x^5 - 11x^4 - 132x^3 - 126x^2 - 58x - 11	\( 2^{24}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	Trivial (GRH)
16.4.3652209588853100000000.1	x^16 - 2x^15 - 2x^14 + 8x^13 + 4x^12 - 20x^11 - 30x^10 - 38x^9 + 26x^8 + 162x^7 + 10x^6 - 404x^5 - 363x^4 + 236x^3 + 544x^2 + 308x + 59	\( 2^{8}\cdot 5^{8}\cdot 11^{7}\cdot 37^{4} \)	16T1778	Trivial (GRH)
16.0.132743767502689448828125.1	x^16 - 6x^15 + 34x^14 - 123x^13 + 393x^12 - 961x^11 + 2084x^10 - 3574x^9 + 5443x^8 - 6426x^7 + 7206x^6 - 6774x^5 + 8385x^4 - 9171x^3 + 10419x^2 - 6860x + 3301	\( 5^{8}\cdot 13^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	$[2, 2]$ (GRH)
16.4.132743767502689448828125.1	x^16 - x^15 + 3x^14 - 4x^13 - 44x^12 + 36x^11 - 80x^10 + 307x^9 + 511x^8 - 166x^7 - 30x^6 - 3204x^5 - 2132x^4 - 608x^3 + 2949x^2 + 6340x + 5171	\( 5^{8}\cdot 13^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1778	$[2]$ (GRH)
16.10.480265781941912000000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 17x^12 + 80x^11 - 196x^10 + 199x^9 - 28x^8 - 202x^7 + 287x^6 - 180x^5 + 30x^4 + 35x^3 - 18x^2 - x + 1	\( -\,2^{12}\cdot 5^{9}\cdot 179\cdot 761^{4} \)	16T1778	Trivial (GRH)
16.10.585531072079462400000000.1	x^16 - 2x^15 - 7x^14 + 22x^13 - 32x^12 - 54x^11 + 291x^10 - 82x^9 - 581x^8 + 492x^7 + 314x^6 - 704x^5 + 38x^4 + 472x^3 - 80x^2 - 88x - 4	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.14.585531072079462400000000.1	x^16 - 4x^15 - 16x^14 + 74x^13 + 51x^12 - 454x^11 + 240x^10 + 1142x^9 - 1240x^8 - 868x^7 + 1356x^6 + 106x^5 - 513x^4 + 78x^3 + 60x^2 - 18x + 1	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.2.585531072079462400000000.1	x^16 - 2x^15 + 11x^14 - 16x^13 + 43x^12 - 8x^11 - 3x^10 + 52x^9 - 70x^8 + 332x^7 - 499x^6 + 576x^5 + 7x^4 - 78x^3 + 186x^2 + 140x + 19	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	$[2]$ (GRH)
16.6.585531072079462400000000.1	x^16 - 2x^15 + 15x^14 - 26x^13 + 38x^12 - 178x^11 + 65x^10 - 182x^9 + 479x^8 + 292x^7 + 16x^6 + 92x^5 - 734x^4 + 736x^3 + 44x^2 - 448x + 76	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.10.585531072079462400000000.2	x^16 - 2x^15 - 21x^14 + 22x^13 + 145x^12 + 28x^11 - 348x^10 - 848x^9 - 318x^8 + 1224x^7 + 1394x^6 + 332x^5 - 261x^4 - 214x^3 - 57x^2 - 2x + 1	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.14.585531072079462400000000.2	x^16 - 18x^14 + 112x^12 - 244x^10 - 169x^8 + 1472x^6 - 2014x^4 + 890x^2 - 89	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.2.585531072079462400000000.2	x^16 - 4x^15 + 14x^14 - 38x^13 + 54x^12 - 110x^11 + 66x^10 - 66x^9 + 248x^8 - 346x^7 - 188x^6 - 618x^5 + 195x^4 + 458x^3 + 526x^2 - 520x + 4	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	$[2]$ (GRH)
16.6.585531072079462400000000.2	x^16 - 4x^15 + 8x^14 + 16x^13 - 127x^12 + 390x^11 - 811x^10 + 852x^9 + 588x^8 - 4210x^7 + 8887x^6 - 11988x^5 + 12505x^4 - 10558x^3 + 6563x^2 - 2332x + 131	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.10.585531072079462400000000.3	x^16 - 16x^14 + 72x^12 + 16x^10 - 677x^8 + 644x^6 + 1098x^4 - 89	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)