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 52)

Label	Polynomial	Discriminant	Galois group	Class group
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
16.0.839480269605146341.1	x^16 - 8x^15 + 35x^14 - 105x^13 + 238x^12 - 427x^11 + 627x^10 - 770x^9 + 808x^8 - 735x^7 + 587x^6 - 410x^5 + 250x^4 - 129x^3 + 56x^2 - 18x + 5	\( 229^{6}\cdot 5821 \)	16T1849	Trivial
16.0.1567652491871535501.1	x^16 - x^15 + x^14 - 3x^13 + 6x^12 - 5x^11 + 5x^10 - 8x^9 + 9x^8 - 8x^7 + 5x^6 - 5x^5 + 6x^4 - 3x^3 + x^2 - x + 1	\( 3^{15}\cdot 23\cdot 41^{6} \)	16T1849	Trivial
16.0.3517279555986929069.1	x^16 - 7x^15 + 22x^14 - 39x^13 + 41x^12 - 22x^11 - 2x^10 + 13x^9 - 3x^8 - 36x^7 + 105x^6 - 162x^5 + 180x^4 - 154x^3 + 83x^2 - 14x + 5	\( 29^{3}\cdot 229^{6} \)	16T1849	Trivial
16.2.7883701662020620563.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 48x^12 - 15x^11 - 18x^10 + 13x^9 + 15x^8 - 17x^7 - 3x^6 + 6x^5 - 6x^4 + 14x^3 - 3x^2 - 5x - 1	\( -\,3^{14}\cdot 41^{6}\cdot 347 \)	16T1849	Trivial
16.4.278586303061013037056.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 30x^12 + 2x^11 - 16x^10 + 14x^9 - 18x^8 + 10x^7 + 8x^6 - 4x^5 - 5x^4 + 2x + 1	\( 2^{24}\cdot 23^{6}\cdot 223\cdot 503 \)	16T1849	Trivial (GRH)
16.0.370331990045141172224.1	x^16 + 9x^14 + 35x^12 + 81x^10 + 127x^8 + 139x^6 + 104x^4 + 50x^2 + 11	\( 2^{16}\cdot 11\cdot 283^{6} \)	16T1849	Trivial (GRH)
16.4.370331990045141172224.1	x^16 - 9x^14 + 35x^12 - 81x^10 + 127x^8 - 139x^6 + 104x^4 - 50x^2 + 11	\( 2^{16}\cdot 11\cdot 283^{6} \)	16T1849	Trivial (GRH)
16.2.3314339292766522775891.1	x^16 - x^15 - 13x^13 + 20x^12 - 8x^11 + 60x^10 - 110x^9 + 37x^8 - 120x^7 + 20x^6 - 72x^5 + 11x^4 - 26x^3 + 6x^2 - 5x + 1	\( -\,19^{6}\cdot 59\cdot 103^{6} \)	16T1849	Trivial
16.6.3314339292766522775891.1	x^16 - 3x^15 + 3x^14 - 6x^13 + 27x^12 - 52x^11 + 8x^10 - 30x^9 + 3x^8 + 143x^7 - 23x^6 + 146x^5 - 250x^4 + 44x^3 + 75x^2 + 16x + 1	\( -\,19^{6}\cdot 59\cdot 103^{6} \)	16T1849	Trivial
16.2.3763741230768763152283.1	x^16 - x^15 + 4x^14 - 12x^13 + 5x^12 - 34x^11 + 24x^10 - 10x^9 + 93x^8 + 10x^7 + 66x^6 + 24x^5 + 16x^4 + 5x^3 + 8x^2 - 3x + 1	\( -\,19^{6}\cdot 67\cdot 103^{6} \)	16T1849	Trivial
16.6.3763741230768763152283.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 39x^12 + 39x^11 - 162x^10 + 238x^9 - 179x^8 + 3x^7 + 155x^6 - 187x^5 + 155x^4 - 116x^3 + 92x^2 - 48x - 59	\( -\,19^{6}\cdot 67\cdot 103^{6} \)	16T1849	Trivial
16.0.78883055671993920640108.1	x^16 - 2x^15 + 10x^14 - 18x^13 + 38x^12 - 52x^11 + 66x^10 - 131x^9 + 101x^8 + 29x^7 - 111x^6 + 199x^5 - 15x^4 - 199x^3 + 305x^2 - 228x + 536	\( 2^{2}\cdot 43\cdot 2777^{6} \)	16T1849	$[9]$ (GRH)
16.0.78883055671993920640108.2	x^16 - 2x^15 + 12x^14 - 28x^13 + 74x^12 - 114x^11 + 278x^10 - 119x^9 + 632x^8 + 319x^7 + 868x^6 + 791x^5 + 771x^4 + 565x^3 + 300x^2 + 68x + 16	\( 2^{2}\cdot 43\cdot 2777^{6} \)	16T1849	$[9]$ (GRH)
16.6.643505441877074224453347.1	x^16 - 7x^15 + 24x^14 - 63x^13 + 125x^12 - 191x^11 + 235x^10 - 139x^9 - 127x^8 + 707x^7 - 1655x^6 + 2611x^5 - 3529x^4 + 3624x^3 - 2670x^2 + 1328x - 257	\( -\,3^{7}\cdot 17^{8}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.12.3646530837303420605235633.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 81x^12 + 304x^11 - 401x^10 - 162x^9 + 1211x^8 - 1672x^7 + 282x^6 + 2201x^5 - 1968x^4 - 305x^3 + 570x^2 + 20x - 1	\( 3^{6}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.8.3646530837303420605235633.1	x^16 - 3x^15 - 8x^14 + 33x^13 - 2x^12 - 64x^11 + 40x^10 - 319x^9 + 653x^8 + 1110x^7 - 2680x^6 - 863x^5 + 2720x^4 + 655x^3 - 479x^2 - 986x + 289	\( 3^{6}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.8.6220552604811717503049021.1	x^16 - 8x^15 + 23x^14 - 21x^13 - 83x^12 + 407x^11 - 725x^10 + 347x^9 + 1103x^8 - 2875x^7 + 2751x^6 - 291x^5 - 2539x^4 + 3287x^3 - 1955x^2 + 578x - 68	\( 3^{6}\cdot 17^{8}\cdot 29\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.10.10081585256074162849769103.1	x^16 - 4x^15 - 15x^14 + 72x^13 + 72x^12 - 481x^11 - 135x^10 + 1569x^9 + 225x^8 - 2904x^7 - 577x^6 + 3049x^5 + 803x^4 - 1431x^3 - 339x^2 + 51x - 87	\( -\,3^{6}\cdot 17^{8}\cdot 47\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.10.10081585256074162849769103.2	x^16 - 5x^15 - 13x^14 + 95x^13 + 13x^12 - 639x^11 + 390x^10 + 1931x^9 - 1837x^8 - 2740x^7 + 3740x^6 - 226x^5 - 777x^4 + 230x^3 - 21x^2 - 6x + 1	\( -\,3^{6}\cdot 17^{8}\cdot 47\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.6.10296087070033187591253552.1	x^16 - 3x^15 - 15x^14 + 61x^13 - 7x^12 - 101x^11 - 205x^10 + 251x^9 + 715x^8 + 216x^7 - 1848x^6 - 192x^5 + 1080x^4 + 75x^3 - 96x^2 + 24x - 3	\( -\,2^{4}\cdot 3^{7}\cdot 17^{8}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.2.10939592511910261815706899.1	x^16 - 4x^15 + 6x^14 - 8x^13 + 6x^12 - 2x^11 - 4x^10 + 9x^9 - 11x^8 + 9x^7 - 4x^6 - 2x^5 + 6x^4 - 8x^3 + 6x^2 - 4x + 1	\( -\,3^{7}\cdot 17^{9}\cdot 59^{6} \)	16T1849	$[6]$ (GRH)
16.10.18661657814435152509147063.1	x^16 - 2x^15 - 12x^14 + 94x^12 + 108x^11 - 296x^10 - 578x^9 - 301x^8 + 1308x^7 + 3117x^6 - 579x^5 - 4749x^4 - 1599x^3 + 1437x^2 + 537x - 87	\( -\,3^{7}\cdot 17^{8}\cdot 29\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.12.20806675954025399923991553.1	x^16 - 8x^15 + 10x^14 + 62x^13 - 175x^12 - 39x^11 + 594x^10 - 658x^9 - 225x^8 + 1421x^7 - 1338x^6 - 342x^5 + 1133x^4 - 327x^3 - 203x^2 + 102x - 9	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 97 \)	16T1849	Trivial (GRH)
16.4.20806675954025399923991553.1	x^16 - 3x^15 + 14x^14 - 48x^13 + 109x^12 - 252x^11 + 406x^10 - 81x^9 - 1043x^8 + 5544x^7 - 14548x^6 + 27171x^5 - 38465x^4 + 31413x^3 - 16716x^2 + 3648x + 501	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 97 \)	16T1849	Trivial (GRH)
16.8.23380697721533696821804941.1	x^16 - 8x^15 + 31x^14 - 77x^13 - 21x^12 + 763x^11 - 2888x^10 + 6564x^9 - 10216x^8 + 11303x^7 - 8837x^6 + 4643x^5 - 1422x^4 + 108x^3 + 64x^2 - 8x - 1	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 109 \)	16T1849	Trivial (GRH)
16.8.23380697721533696821804941.2	x^16 - 4x^15 - 2x^14 + 12x^13 - 56x^12 + 3x^11 + 37x^10 - 78x^9 + 7x^8 + 63x^7 + 1000x^6 - 1021x^5 + 403x^4 + 2031x^3 - 4047x^2 + 780x + 87	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 109 \)	16T1849	Trivial (GRH)
16.4.24238704977369795787742737.1	x^16 - x^15 + x^14 + 23x^13 - 36x^12 - 177x^11 - 7x^10 - 215x^9 - 1217x^8 - 1409x^7 - 943x^6 - 636x^5 - 908x^4 - 163x^3 + 336x^2 - 85x + 29	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 113 \)	16T1849	Trivial (GRH)
16.10.25770504732800472143822848.1	x^16 - 6x^15 + 15x^14 - 32x^13 - 42x^12 + 518x^11 - 979x^10 - 198x^9 + 2711x^8 - 2458x^7 - 2011x^6 + 3972x^5 + 56x^4 - 2250x^3 + 179x^2 + 446x + 69	\( -\,2^{16}\cdot 7\cdot 19^{6}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.4.25770504732800472143822848.1	x^16 + 4x^14 + 9x^12 + 13x^10 + x^8 - 15x^6 - 14x^4 - 5x^2 + 7	\( 2^{16}\cdot 7\cdot 19^{6}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.4.25770504732800472143822848.2	x^16 - 4x^14 + 9x^12 - 13x^10 + x^8 + 15x^6 - 14x^4 + 5x^2 + 7	\( 2^{16}\cdot 7\cdot 19^{6}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.0.69948512846172710104662016.1	x^16 + 13x^14 + 98x^12 + 417x^10 + 946x^8 + 1406x^6 + 1368x^4 + 513x^2 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	$[2]$ (GRH)
16.4.69948512846172710104662016.1	x^16 - 2x^14 - 79x^12 + 223x^10 + 116x^8 + 152x^6 + 57x^4 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.8.69948512846172710104662016.1	x^16 - 9x^14 + 18x^12 - 50x^10 + 60x^8 - 95x^6 + 152x^4 - 95x^2 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.0.69948512846172710104662016.2	x^16 + 5x^14 + 32x^12 + 99x^10 + 363x^8 + 817x^6 + 779x^4 + 266x^2 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	$[2]$ (GRH)
16.4.69948512846172710104662016.2	x^16 + 8x^14 + 29x^12 + 44x^10 - 220x^8 + 133x^6 - 57x^4 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.8.69948512846172710104662016.2	x^16 - 5x^14 + 32x^12 - 99x^10 + 363x^8 - 817x^6 + 779x^4 - 266x^2 + 19	\( 2^{16}\cdot 19^{7}\cdot 103^{6} \)	16T1849	Trivial (GRH)
16.6.113900463212242137728242419.1	x^16 - 7x^15 + 20x^14 - 51x^13 + 119x^12 - 109x^11 - 37x^10 + 275x^9 - 1134x^8 + 1612x^7 - 338x^6 - 757x^5 + 2501x^4 - 2994x^3 - 2052x^2 + 3408x + 1856	\( -\,3^{8}\cdot 17^{8}\cdot 59^{7} \)	16T1849	Trivial (GRH)
16.6.175033480190564189051310384.1	x^16 - 10x^14 - 59x^12 + 174x^10 + 932x^8 + 981x^6 + 51x^4 - 255x^2 - 51	\( -\,2^{4}\cdot 3^{7}\cdot 17^{9}\cdot 59^{6} \)	16T1849	$[2]$ (GRH)
16.14.878599429976165341120303104.1	x^16 - 26x^14 + 193x^12 - 406x^10 - 428x^8 + 2533x^6 - 3035x^4 + 1233x^2 - 81	\( -\,2^{12}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.2.878599429976165341120303104.1	x^16 + 24x^14 + 197x^12 + 703x^10 + 998x^8 - 39x^6 - 1173x^4 - 558x^2 - 9	\( -\,2^{12}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1849	$[2]$ (GRH)
16.14.886106993464731207072258819.1	x^16 - 4x^15 - 6x^14 + 52x^13 - 38x^12 - 258x^11 + 454x^10 + 603x^9 - 1685x^8 - 645x^7 + 3056x^6 + 217x^5 - 2838x^4 + 42x^3 + 1219x^2 + 6x - 167	\( -\,3^{11}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.0.134425712786353297191406374912.1	x^16 - 3x^15 + 7x^14 - 11x^13 - 67x^12 + 160x^11 - 80x^10 + 98x^9 + 2181x^8 - 1261x^7 + 14531x^6 - 13409x^5 + 47122x^4 - 17549x^3 + 62369x^2 - 47493x + 17807	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	$[2, 140]$ (GRH)
16.12.134425712786353297191406374912.1	x^16 - 6x^15 - 18x^14 + 191x^13 - 145x^12 - 1962x^11 + 4253x^10 + 8338x^9 - 29606x^8 - 13845x^7 + 92317x^6 + 7646x^5 - 138825x^4 - 16350x^3 + 84536x^2 + 29283x + 549	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.16.134425712786353297191406374912.1	x^16 - 47x^14 + 788x^12 - 6525x^10 + 29670x^8 - 75330x^6 + 100215x^4 - 55080x^2 + 1377	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.4.134425712786353297191406374912.1	x^16 + 29x^14 + 208x^12 - 582x^10 - 11202x^8 - 37656x^6 - 43758x^4 - 11934x^2 + 1377	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.8.134425712786353297191406374912.1	x^16 - 17x^14 - 199x^12 + 2872x^10 + 6167x^8 - 79955x^6 - 105536x^4 + 105162x^2 + 128673	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.0.134425712786353297191406374912.2	x^16 + 45x^14 + 768x^12 + 6413x^10 + 28812x^8 + 70782x^6 + 89029x^4 + 44574x^2 + 153	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	$[2, 200]$ (GRH)
16.12.134425712786353297191406374912.2	x^16 - 3x^15 - 28x^14 + 92x^13 + 217x^12 - 884x^11 - 74x^10 + 2513x^9 - 3321x^8 + 1262x^7 + 6383x^6 - 10049x^5 + 3286x^4 + 4948x^3 - 5472x^2 - 935x + 643	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)
16.16.134425712786353297191406374912.2	x^16 - 51x^14 + 994x^12 - 9597x^10 + 49425x^8 - 136495x^6 + 189941x^4 - 104499x^2 + 153	\( 2^{12}\cdot 3^{8}\cdot 17^{9}\cdot 59^{6} \)	16T1849	Trivial (GRH)