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 212)

Label	Polynomial	Discriminant	Galois group	Class group
16.6.229672602410888671875.1	x^16 - 5x^15 + 6x^14 + 5x^13 - 13x^12 - 5x^11 + 38x^10 - 25x^9 - 25x^8 + 35x^7 + 22x^6 - 55x^5 + 12x^4 + 20x^3 - 11x^2 + 1	\( -\,3^{8}\cdot 5^{14}\cdot 179^{3} \)	16T1251	Trivial
16.6.229672602410888671875.2	x^16 - x^15 - 4x^14 - 9x^13 + 13x^12 + 49x^11 + 34x^10 - 32x^9 - 132x^8 - 91x^7 + 141x^6 + 163x^5 - 67x^4 - 97x^3 + 14x^2 + 18x + 1	\( -\,3^{8}\cdot 5^{14}\cdot 179^{3} \)	16T1251	Trivial
16.6.229672602410888671875.3	x^16 - 3x^15 + 4x^14 - 8x^13 - 2x^12 + 2x^11 - 19x^10 + 16x^9 + 18x^8 + 22x^7 + 19x^6 + 11x^5 - 17x^4 - 76x^3 - 9x^2 + 41x + 1	\( -\,3^{8}\cdot 5^{14}\cdot 179^{3} \)	16T1251	Trivial
16.6.229672602410888671875.4	x^16 - 4x^15 + 4x^14 + 21x^13 - 94x^12 + 188x^11 - 219x^10 + 118x^9 + 67x^8 - 163x^7 + 81x^6 + 7x^5 + 26x^4 - 36x^3 - 11x^2 + 4x + 1	\( -\,3^{8}\cdot 5^{14}\cdot 179^{3} \)	16T1251	Trivial
16.12.673301391207980597248.1	x^16 - 4x^15 + 2x^14 - 4x^13 + 13x^12 + 76x^11 - 80x^10 - 232x^9 + 81x^8 + 320x^7 + 36x^6 - 180x^5 - 51x^4 + 44x^3 + 14x^2 - 4x - 1	\( 2^{44}\cdot 337^{3} \)	16T1251	Trivial
16.12.673301391207980597248.2	x^16 - 12x^14 - 4x^13 + 48x^12 + 32x^11 - 78x^10 - 84x^9 + 78x^8 + 84x^7 - 88x^6 + 12x^5 + 37x^4 - 36x^3 + 6x^2 + 4x - 1	\( 2^{44}\cdot 337^{3} \)	16T1251	Trivial
16.10.744139231811279296875.1	x^16 - 3x^15 - 4x^14 + 19x^13 - 7x^12 - 36x^11 + 53x^10 + 6x^9 - 74x^8 + 51x^7 + 16x^6 - 61x^5 + 15x^4 + 23x^3 - 5x^2 - 4x + 1	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial
16.2.744139231811279296875.1	x^16 - 3x^15 + 7x^14 - 9x^13 + 9x^12 - 6x^11 - 11x^10 + 3x^9 - 77x^8 + 75x^7 - 15x^6 + 285x^5 + 132x^4 + 189x^3 + 9x^2 - 9x - 9	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial
16.2.744139231811279296875.2	x^16 - 6x^15 + 22x^14 - 54x^13 + 91x^12 - 135x^11 + 178x^10 - 210x^9 + 217x^8 - 210x^7 + 178x^6 - 135x^5 + 91x^4 - 54x^3 + 22x^2 - 6x + 1	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial
16.10.744139231811279296875.2	x^16 - 2x^15 - 3x^14 + 23x^13 - 18x^12 - 78x^11 + 142x^10 + 92x^9 - 471x^8 + 100x^7 + 781x^6 - 429x^5 - 567x^4 + 445x^3 + 105x^2 - 151x + 31	\( -\,3^{12}\cdot 5^{12}\cdot 179^{3} \)	16T1251	Trivial
16.4.10772822259327689555968.1	x^16 + 4x^14 - 8x^13 - 2x^12 - 32x^11 - 60x^10 - 112x^9 - 117x^8 - 64x^7 - 60x^6 + 16x^5 + 282x^4 + 464x^3 + 272x^2 + 24x - 31	\( 2^{48}\cdot 337^{3} \)	16T1251	Trivial
16.4.10772822259327689555968.2	x^16 + 4x^14 - 8x^13 - 2x^12 - 48x^11 - 52x^10 - 72x^9 + 127x^8 + 320x^7 + 356x^6 + 24x^5 - 258x^4 - 176x^3 + 56x^2 + 112x + 17	\( 2^{48}\cdot 337^{3} \)	16T1251	Trivial
16.8.44125479974206216421244928.1	x^16 + 20x^14 - 42x^12 - 248x^10 + 521x^8 + 664x^6 - 1866x^4 + 644x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[2]$
16.16.44125479974206216421244928.1	x^16 - 28x^14 + 322x^12 - 1968x^10 + 6901x^8 - 13920x^6 + 15086x^4 - 7020x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	Trivial (GRH)
16.0.44125479974206216421244928.1	x^16 + 32x^14 + 392x^12 + 2352x^10 + 7418x^8 + 12240x^6 + 9800x^4 + 3136x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[5, 30]$ (GRH)
16.0.44125479974206216421244928.2	x^16 + 28x^14 + 322x^12 + 1968x^10 + 6901x^8 + 13920x^6 + 15086x^4 + 7020x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[5, 30]$ (GRH)
16.8.44125479974206216421244928.2	x^16 - 4x^14 - 58x^12 + 120x^10 + 1001x^8 - 72x^6 - 2698x^4 - 788x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	Trivial
16.16.44125479974206216421244928.2	x^16 - 32x^14 + 392x^12 - 2352x^10 + 7418x^8 - 12240x^6 + 9800x^4 - 3136x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	Trivial (GRH)
16.8.44125479974206216421244928.3	x^16 - 20x^14 - 42x^12 + 248x^10 + 521x^8 - 664x^6 - 1866x^4 - 644x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	Trivial
16.8.44125479974206216421244928.4	x^16 - 12x^14 - 22x^12 + 240x^10 - 23x^8 - 864x^6 - 22x^4 + 828x^2 + 337	\( 2^{60}\cdot 337^{3} \)	16T1251	$[2]$
16.6.8196894918367374985699192631.1	x^16 - 7x^15 + 9x^14 - 21x^13 + 110x^12 - 39x^11 - 862x^10 + 1504x^9 + 2682x^8 - 7391x^7 - 3952x^6 + 16319x^5 + 2139x^4 - 16095x^3 - 1475x^2 + 5474x + 2116	\( -\,71^{3}\cdot 73^{12} \)	16T1251	Trivial (GRH)
16.6.8196894918367374985699192631.2	x^16 - 6x^15 - 6x^14 + 121x^13 - 236x^12 - 740x^11 + 2962x^10 + 715x^9 - 10578x^8 + 13538x^7 + 14824x^6 - 46025x^5 - 8119x^4 + 15254x^3 - 31268x^2 - 3872x + 4096	\( -\,71^{3}\cdot 73^{12} \)	16T1251	Trivial (GRH)
16.2.18920881198502041761781608367.1	x^16 - 7x^15 + 14x^14 - 32x^13 + 230x^12 - 385x^11 - 1511x^10 + 7653x^9 - 13411x^8 - 5374x^7 + 77730x^6 - 138149x^5 + 19172x^4 + 256782x^3 - 390293x^2 + 256600x - 74332	\( -\,23^{3}\cdot 41^{15} \)	16T1251	Trivial (GRH)
16.10.18920881198502041761781608367.2	x^16 - 3x^15 - 15x^14 + 49x^13 - 133x^12 - 16x^11 + 3470x^10 - 2240x^9 - 21278x^8 + 11842x^7 + 39764x^6 - 28240x^5 - 20887x^4 + 25123x^3 - 3299x^2 - 3627x + 961	\( -\,23^{3}\cdot 41^{15} \)	16T1251	Trivial (GRH)
16.10.18920881198502041761781608367.3	x^16 - x^15 - 29x^14 + 58x^13 + 256x^12 - 924x^11 + 70x^10 + 4842x^9 - 12094x^8 + 3264x^7 + 52780x^6 - 94204x^5 - 21343x^4 + 184271x^3 - 170813x^2 + 58286x + 6988	\( -\,23^{3}\cdot 41^{15} \)	16T1251	Trivial (GRH)
16.2.18920881198502041761781608367.3	x^16 - 5x^15 + 13x^14 - 7x^13 + 18x^12 + 294x^11 - 376x^10 + 1761x^9 + 8341x^8 + 77x^7 - 24408x^6 - 34756x^5 - 23123x^4 - 6266x^3 - 1488x^2 - 3464x - 1712	\( -\,23^{3}\cdot 41^{15} \)	16T1251	Trivial (GRH)
16.0.29811439152025391709947927861.1	x^16 - 5x^15 + 51x^14 - 169x^13 + 835x^12 - 1901x^11 + 5482x^10 - 9231x^9 + 16470x^8 - 26311x^7 + 41306x^6 - 62540x^5 + 69921x^4 - 60530x^3 + 54598x^2 - 36337x + 11221	\( 37^{14}\cdot 149^{3} \)	16T1251	Trivial (GRH)
16.0.29811439152025391709947927861.2	x^16 - 3x^15 - 12x^14 + 12x^13 + 74x^12 + 161x^11 + 356x^10 - 149x^9 - 2979x^8 - 8125x^7 - 7220x^6 + 5520x^5 + 35483x^4 + 68939x^3 + 80299x^2 + 64115x + 28349	\( 37^{14}\cdot 149^{3} \)	16T1251	Trivial (GRH)
16.6.55165324595664289089457824787.1	x^16 - 5x^15 - 11x^14 + 49x^13 - 60x^12 - 363x^11 + 1312x^10 + 4861x^9 + 1271x^8 - 9814x^7 - 12797x^6 - 12306x^5 - 11875x^4 + 6369x^3 + 22546x^2 + 17112x + 6173	\( -\,43^{3}\cdot 97^{12} \)	16T1251	Trivial (GRH)
16.6.55165324595664289089457824787.2	x^16 - 4x^15 - 27x^14 + 110x^13 + 62x^12 - 221x^11 + 915x^10 - 3330x^9 - 6013x^8 + 3563x^7 - 16425x^6 + 59112x^5 + 7052x^4 + 94968x^3 + 28272x^2 + 32384x + 7744	\( -\,43^{3}\cdot 97^{12} \)	16T1251	Trivial (GRH)
16.10.319384536834647064600389984779.1	x^16 - 2x^15 - 34x^14 - 28x^13 + 447x^12 + 1510x^11 - 891x^10 - 9164x^9 - 20367x^8 - 41894x^7 + 30286x^6 + 243758x^5 + 103863x^4 - 261716x^3 - 172416x^2 + 15600x + 10000	\( -\,41^{15}\cdot 59^{3} \)	16T1251	Trivial (GRH)
16.2.319384536834647064600389984779.2	x^16 - 3x^15 - 15x^14 + 8x^13 + 236x^12 + 148x^11 - 3049x^10 - 2896x^9 + 20706x^8 + 35171x^7 - 18743x^6 - 31766x^5 + 88173x^4 + 108558x^3 - 59961x^2 - 129620x - 48116	\( -\,41^{15}\cdot 59^{3} \)	16T1251	Trivial (GRH)
16.10.319384536834647064600389984779.3	x^16 - 5x^15 - 28x^14 + 116x^13 + 387x^12 - 526x^11 - 4189x^10 - 5086x^9 + 27980x^8 + 55181x^7 - 75863x^6 - 268128x^5 + 198769x^4 + 930707x^3 - 1189053x^2 + 92599x + 138713	\( -\,41^{15}\cdot 59^{3} \)	16T1251	Trivial (GRH)
16.2.319384536834647064600389984779.3	x^16 - 6x^15 + 22x^14 + 23x^13 - 406x^12 + 1292x^11 - 960x^10 - 6567x^9 + 22888x^8 - 27610x^7 - 1347x^6 + 35119x^5 - 21289x^4 - 16607x^3 + 17565x^2 + 198x - 4924	\( -\,41^{15}\cdot 59^{3} \)	16T1251	Trivial (GRH)
16.10.652030299991134977060343848687.1	x^16 - 2x^15 - 35x^14 + 98x^13 + 284x^12 - 1346x^11 + 1119x^10 + 3286x^9 - 13412x^8 + 24976x^7 - 12710x^6 - 39068x^5 + 63642x^4 - 14482x^3 - 30961x^2 + 17114x - 2311	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.6.652030299991134977060343848687.2	x^16 - x^15 - 33x^14 + 35x^13 + 572x^12 - 921x^11 - 4655x^10 + 11534x^9 + 17884x^8 - 63378x^7 - 22060x^6 + 180456x^5 - 14955x^4 - 304112x^3 - 41221x^2 + 112076x - 17251	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.10.652030299991134977060343848687.2	x^16 - 6x^15 - 20x^14 + 89x^13 + 96x^12 - 586x^11 - 267x^10 + 1092x^9 - 2077x^8 - 2043x^7 + 15508x^6 + 19365x^5 - 11930x^4 - 17369x^3 + 3002x^2 + 1321x - 103	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.6.652030299991134977060343848687.3	x^16 - 6x^15 - 21x^14 + 181x^13 - 211x^12 - 930x^11 + 3516x^10 - 8756x^9 + 11469x^8 - 1733x^7 - 12193x^6 + 39909x^5 - 42541x^4 + 28413x^3 - 5137x^2 - 4173x + 4759	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.6.652030299991134977060343848687.5	x^16 - 6x^15 + 18x^14 - 40x^13 - 96x^12 + 1812x^11 - 9812x^10 + 30348x^9 - 45268x^8 - 82210x^7 + 549035x^6 - 956679x^5 + 375334x^4 + 641845x^3 - 486895x^2 - 152393x + 74303	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.2.652030299991134977060343848687.6	x^16 - 8x^15 + 36x^14 - 85x^13 + 162x^12 - 1356x^11 + 8450x^10 - 27976x^9 + 57332x^8 - 81596x^7 + 88676x^6 - 81156x^5 + 63944x^4 - 32841x^3 + 3178x^2 - 79x + 3727	\( -\,17^{12}\cdot 47^{9} \)	16T1251	$[2]$ (GRH)
16.6.652030299991134977060343848687.6	x^16 - 26x^14 - 3x^13 + 137x^12 - 953x^11 + 3699x^10 + 19111x^9 - 31887x^8 - 224360x^7 + 216515x^6 + 782415x^5 - 505143x^4 - 920155x^3 + 78893x^2 + 372274x + 184301	\( -\,17^{12}\cdot 47^{9} \)	16T1251	Trivial (GRH)
16.2.652030299991134977060343848687.9	x^16 - 4x^15 + 50x^14 - 166x^13 + 803x^12 - 2002x^11 + 5292x^10 - 9793x^9 + 16001x^8 - 31872x^7 + 36105x^6 - 121028x^5 + 19354x^4 - 270587x^3 - 246861x^2 - 344185x + 822209	\( -\,17^{12}\cdot 47^{9} \)	16T1251	$[2]$ (GRH)
16.2.889185000234066487453260499987.1	x^16 - x^15 - 29x^14 - 24x^13 + 297x^12 + 675x^11 - 94x^10 - 1677x^9 - 9060x^8 - 35891x^7 - 38281x^6 + 77422x^5 + 146265x^4 - 211133x^3 - 755227x^2 - 735228x - 251312	\( -\,41^{15}\cdot 83^{3} \)	16T1251	Trivial (GRH)
16.10.889185000234066487453260499987.1	x^16 - 2x^15 - 34x^14 + 13x^13 + 283x^12 + 321x^11 - 317x^10 - 1538x^9 - 2450x^8 - 156x^7 + 5235x^6 + 7188x^5 + 1732x^4 - 5179x^3 - 6407x^2 - 3301x - 701	\( -\,41^{15}\cdot 83^{3} \)	16T1251	Trivial (GRH)
16.2.889185000234066487453260499987.2	x^16 - 8x^15 + 30x^14 - 29x^13 - 245x^12 + 581x^11 + 2744x^10 - 28528x^9 + 111413x^8 - 281217x^7 + 494529x^6 - 612816x^5 + 601056x^4 - 485575x^3 + 13789x^2 + 297312x - 142336	\( -\,41^{15}\cdot 83^{3} \)	16T1251	Trivial (GRH)
16.10.889185000234066487453260499987.3	x^16 - 5x^15 - 28x^14 + 75x^13 + 469x^12 - 608x^11 - 3820x^10 + 3893x^9 + 13876x^8 - 13699x^7 - 22522x^6 + 19446x^5 + 21526x^4 - 16434x^3 - 873x^2 + 1210x + 92	\( -\,41^{15}\cdot 83^{3} \)	16T1251	Trivial (GRH)
16.0.6065133898851787352862994830253.1	x^16 - 8x^15 + 21x^14 - 7x^13 - 24x^12 - 129x^11 + 1767x^10 - 6866x^9 + 20099x^8 - 42049x^7 + 65360x^6 - 74807x^5 + 63255x^4 - 38636x^3 + 16492x^2 - 4469x + 703	\( 37^{3}\cdot 149^{12} \)	16T1251	$[3, 3]$ (GRH)
16.0.6065133898851787352862994830253.2	x^16 - 3x^15 - 18x^14 + 124x^13 - 167x^12 - 2066x^11 + 14604x^10 - 47496x^9 + 98643x^8 - 123761x^7 + 93551x^6 - 31491x^5 + 52452x^4 - 130628x^3 + 90463x^2 - 18586x + 4409	\( 37^{3}\cdot 149^{12} \)	16T1251	$[3, 3]$ (GRH)
16.6.10009146154007580091982470826143.3	x^16 - 3x^15 - 15x^14 + 90x^13 + 195x^12 - 1328x^11 - 712x^10 + 10183x^9 + 780x^8 - 44205x^7 - 22884x^6 + 161836x^5 + 94405x^4 - 501358x^3 + 62219x^2 + 666313x - 439133	\( -\,23^{5}\cdot 41^{15} \)	16T1251	Trivial (GRH)
16.6.10009146154007580091982470826143.4	x^16 - 8x^15 + 30x^14 - 70x^13 - 122x^12 + 1278x^11 - 5046x^10 + 12800x^9 - 15113x^8 - 1146x^7 + 70466x^6 - 168868x^5 + 150097x^4 - 38060x^3 - 365215x^2 + 358976x - 235652	\( -\,23^{5}\cdot 41^{15} \)	16T1251	$[2, 2]$ (GRH)