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 72)

Label	Polynomial	Discriminant	Galois group	Class group
16.10.463927926730170763651.1	x^16 - 5x^15 + 2x^14 + 28x^13 - 32x^12 - 88x^11 + 157x^10 + 116x^9 - 389x^8 + 108x^7 + 357x^6 - 311x^5 - 30x^4 + 109x^3 - 18x^2 - 5x + 1	\( -\,7^{2}\cdot 19\cdot 163^{8} \)	16T1845	Trivial
16.2.463927926730170763651.1	x^16 - 7x^15 + 15x^14 - 47x^12 + 75x^11 - 28x^10 - 63x^9 + 109x^8 - 63x^7 - 28x^6 + 75x^5 - 47x^4 + 15x^2 - 7x + 1	\( -\,7^{2}\cdot 19\cdot 163^{8} \)	16T1845	Trivial
16.0.566228018786860007424.1	x^16 + 8x^14 + 28x^12 + 48x^10 + 26x^8 - 24x^6 - 28x^4 + 21	\( 2^{32}\cdot 3^{3}\cdot 7^{9}\cdot 11^{2} \)	16T1845	Trivial
16.0.566228018786860007424.2	x^16 - 8x^14 + 28x^12 - 48x^10 + 26x^8 + 24x^6 - 28x^4 + 21	\( 2^{32}\cdot 3^{3}\cdot 7^{9}\cdot 11^{2} \)	16T1845	Trivial
16.10.1259232943981892072767.1	x^16 - 2x^15 - 7x^14 + 19x^13 + 4x^12 - 57x^11 + 53x^10 + 61x^9 - 125x^8 + 10x^7 + 102x^6 - 68x^5 - 35x^4 + 41x^3 + 3x^2 - 8x + 1	\( -\,7\cdot 19^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.2.1259232943981892072767.1	x^16 - 4x^15 + 7x^14 - 11x^13 + 7x^12 - 2x^11 - 8x^10 + 15x^9 - 17x^8 + 15x^7 - 8x^6 - 2x^5 + 7x^4 - 11x^3 + 7x^2 - 4x + 1	\( -\,7\cdot 19^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.2173136077841326208681.1	x^16 + 5x^14 - 14x^13 + 5x^12 - 30x^11 + 35x^10 + 9x^9 - 59x^8 - 6x^7 + 139x^6 - 55x^5 - 311x^4 + 284x^3 + 123x^2 - 216x + 27	\( 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial
16.8.2173136077841326208681.1	x^16 - 3x^15 - 2x^14 + 22x^13 - 33x^12 - 10x^11 + 96x^10 - 147x^9 + 55x^8 + 150x^7 - 190x^6 + 35x^5 + 79x^4 - 71x^3 - 17x^2 + 5x + 1	\( 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.2.2391894788726981380800.1	x^16 - 6x^15 + 23x^14 - 64x^13 + 151x^12 - 274x^11 + 431x^10 - 511x^9 + 515x^8 - 356x^7 + 173x^6 - 28x^5 - 73x^4 + 41x^3 - 43x^2 + 42x + 27	\( -\,2^{6}\cdot 3\cdot 5^{2}\cdot 163^{8} \)	16T1845	Trivial
16.6.2391894788726981380800.1	x^16 - 8x^15 + 25x^14 - 34x^13 - 15x^12 + 163x^11 - 378x^10 + 545x^9 - 551x^8 + 392x^7 - 151x^6 - 67x^5 + 178x^4 - 161x^3 + 83x^2 - 24x + 3	\( -\,2^{6}\cdot 3\cdot 5^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.3247495487111195345557.1	x^16 - 5x^15 + 5x^14 + 20x^13 - 51x^12 + 12x^11 + 43x^10 + 68x^9 - 160x^8 - 100x^7 + 343x^6 - 161x^5 + 51x^4 - 304x^3 + 413x^2 - 210x + 36	\( 7^{3}\cdot 19\cdot 163^{8} \)	16T1845	$[2]$
16.8.3247495487111195345557.1	x^16 - 4x^15 + 27x^13 - 38x^12 - 42x^11 + 87x^10 - 11x^9 + 94x^8 - 21x^7 - 238x^6 + 201x^5 + 58x^4 - 84x^3 - 3x^2 + 8x + 1	\( 7^{3}\cdot 19\cdot 163^{8} \)	16T1845	Trivial
16.4.4910418720965427142464.1	x^16 - x^14 - 5x^13 + 9x^12 + 2x^11 - 12x^10 + 123x^9 - 268x^8 + 218x^7 + 326x^6 - 943x^5 + 913x^4 - 440x^3 + 139x^2 - 23x + 1	\( 2^{6}\cdot 3^{8}\cdot 61^{9} \)	16T1845	Trivial
16.8.4910418720965427142464.1	x^16 - 2x^15 - x^14 + 7x^13 - 25x^12 + 5x^11 + 53x^10 - 85x^9 - 121x^8 - 179x^7 - 188x^6 + 129x^5 + 125x^4 + 48x^3 + 12x^2 - 64x + 16	\( 2^{6}\cdot 3^{8}\cdot 61^{9} \)	16T1845	Trivial
16.2.5995682937075633327872.1	x^16 + 11x^14 + 36x^12 + 31x^10 - 41x^8 - 117x^6 - 195x^4 - 183x^2 - 47	\( -\,2^{8}\cdot 47\cdot 163^{8} \)	16T1845	Trivial
16.6.5995682937075633327872.1	x^16 - 3x^15 - 6x^14 + 42x^13 - 50x^12 - 101x^11 + 375x^10 - 437x^9 - 35x^8 + 919x^7 - 1599x^6 + 1564x^5 - 961x^4 + 326x^3 - 12x^2 - 28x + 6	\( -\,2^{8}\cdot 47\cdot 163^{8} \)	16T1845	Trivial
16.6.17307213524714210420160.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 265x^12 - 498x^11 + 763x^10 - 966x^9 + 1007x^8 - 850x^7 + 543x^6 - 218x^5 + 5x^4 + 60x^3 - 28x^2 + 1	\( -\,2^{6}\cdot 3^{8}\cdot 5\cdot 43\cdot 61^{8} \)	16T1845	Trivial (GRH)
16.0.19558224700571935878129.1	x^16 - 2x^15 + 2x^14 - 12x^13 + 50x^12 - 80x^11 + 75x^10 - 279x^9 + 871x^8 - 1145x^7 + 453x^6 + 863x^5 - 800x^4 - 166x^3 + 603x^2 + 40x + 43	\( 3^{2}\cdot 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	$[2]$
16.4.19558224700571935878129.1	x^16 + 5x^14 - 9x^13 + 22x^12 - 30x^11 - 74x^10 + 47x^9 + 39x^8 - 80x^7 - 296x^6 - 504x^5 - 446x^4 - 163x^3 - 84x^2 - 68x + 1	\( 3^{2}\cdot 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.25545436343604161146944.1	x^16 - 6x^15 + 21x^14 - 53x^13 + 106x^12 - 202x^11 + 421x^10 - 886x^9 + 1743x^8 - 2942x^7 + 3850x^6 - 4087x^5 + 3505x^4 - 2278x^3 + 1064x^2 - 270x + 6	\( 2^{6}\cdot 3^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.25545436343604161146944.2	x^16 - 7x^15 + 14x^14 - 3x^13 + 15x^12 - 79x^11 - 18x^10 + 198x^9 - 142x^8 + 182x^7 - 208x^6 - 175x^5 + 379x^4 - 258x^3 + 128x^2 - 30x + 6	\( 2^{6}\cdot 3^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.10.27629872989696861796087.1	x^16 - x^15 - 18x^14 + 3x^13 + 130x^12 + 52x^11 - 436x^10 - 310x^9 + 686x^8 + 528x^7 - 586x^6 - 297x^5 + 275x^4 - 30x^3 + 13x^2 - 8x + 1	\( -\,7\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.6.27629872989696861796087.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 80x^12 + 66x^11 - 484x^10 + 1100x^9 - 1481x^8 + 1194x^7 - 252x^6 - 712x^5 + 1056x^4 - 774x^3 + 315x^2 - 61x + 3	\( -\,7\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.0.34770177245461219338896.1	x^16 - 8x^15 + 32x^14 - 76x^13 + 126x^12 - 172x^11 + 233x^10 - 231x^9 + 93x^8 + 47x^7 + 54x^6 + 61x^5 - 243x^4 + 36x^3 + 394x^2 + 216x + 36	\( 2^{4}\cdot 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	$[2]$
16.4.34770177245461219338896.1	x^16 - 2x^15 + 5x^14 - 10x^13 - 11x^12 + 31x^11 - 71x^10 + 260x^9 - 261x^8 + 105x^7 - 247x^6 - 155x^5 - 3x^4 - 154x^3 - 27x^2 - 21x - 7	\( 2^{4}\cdot 7^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.146958015819385736036352.1	x^16 + 5x^14 + 7x^12 - 5x^10 - 23x^8 - 19x^6 + 3x^4 + 8x^2 + 2	\( 2^{15}\cdot 3^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.8.189461986215064195173168.1	x^16 + 2x^14 - 18x^12 - 18x^10 + 80x^8 + 13x^6 - 58x^4 - x^2 + 3	\( 2^{4}\cdot 3\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.8.189461986215064195173168.2	x^16 - 5x^15 - 2x^14 + 30x^13 - 43x^12 + 32x^11 + 33x^10 - 81x^9 + 118x^8 - 81x^7 + 33x^6 + 32x^5 - 43x^4 + 30x^3 - 2x^2 - 5x + 1	\( 2^{4}\cdot 3\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.10.248668856907271756164783.1	x^16 - 5x^15 - 7x^14 + 67x^13 - 31x^12 - 311x^11 + 408x^10 + 519x^9 - 1290x^8 + 122x^7 + 1493x^6 - 1028x^5 - 363x^4 + 518x^3 - 20x^2 - 75x + 3	\( -\,3^{2}\cdot 7\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.6.248668856907271756164783.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 28x^12 + 62x^11 - 149x^10 + 215x^9 - 276x^8 - 482x^7 + 1619x^6 - 2235x^5 + 5374x^4 - 3835x^3 - 1515x^2 + 425x - 289	\( -\,3^{2}\cdot 7\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.10.311822852312293154555839.1	x^16 - 7x^15 + 6x^14 + 66x^13 - 185x^12 - 20x^11 + 718x^10 - 936x^9 - 71x^8 + 1018x^7 - 919x^6 + 714x^5 - 622x^4 + 188x^3 + 67x^2 - 18x + 1	\( -\,79\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.6.311822852312293154555839.1	x^16 - x^15 - 4x^14 + 6x^13 + 27x^12 + 16x^11 - 151x^10 - 375x^9 + 63x^8 + 1215x^7 + 1172x^6 - 916x^5 - 2182x^4 - 677x^3 + 977x^2 + 773x + 139	\( -\,79\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial
16.0.355698456099933128632236.1	x^16 - 5x^14 - 33x^13 - 27x^12 + 101x^11 + 385x^10 + 755x^9 + 639x^8 + 472x^7 + 677x^6 + 433x^5 + 291x^4 + 224x^3 + 127x^2 + 34x + 16	\( 2^{2}\cdot 3^{8}\cdot 19\cdot 61^{10} \)	16T1845	$[2]$ (GRH)
16.8.355698456099933128632236.1	x^16 - 7x^15 + 16x^14 + 12x^13 - 144x^12 + 289x^11 - 132x^10 - 332x^9 + 433x^8 + 137x^7 - 326x^6 - 26x^5 + 131x^4 + 15x^3 - 24x^2 - 4x + 1	\( 2^{2}\cdot 3^{8}\cdot 19\cdot 61^{10} \)	16T1845	Trivial (GRH)
16.4.391888042185028629430272.1	x^16 + 8x^14 + 26x^12 + 44x^10 + 33x^8 - 12x^6 - 41x^4 - 26x^2 + 3	\( 2^{18}\cdot 3\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.8.440874047458157208109056.1	x^16 - 11x^14 + 49x^12 - 117x^10 + 167x^8 - 147x^6 + 77x^4 - 24x^2 + 6	\( 2^{15}\cdot 3^{3}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.12.443165289567129799607376.1	x^16 - 3x^15 - 8x^14 + 23x^13 + 21x^12 - 81x^11 - 18x^10 + 188x^9 - 17x^8 - 266x^7 + 26x^6 + 194x^5 + 8x^4 - 60x^3 - 10x^2 + 5x + 1	\( 2^{4}\cdot 3^{8}\cdot 19^{2}\cdot 61^{9} \)	16T1845	Trivial (GRH)
16.4.443165289567129799607376.1	x^16 - 4x^15 + 3x^14 - 10x^13 + 37x^12 + 8x^11 - 118x^10 + 108x^9 + 372x^8 - 33x^7 - 573x^6 - 810x^5 - 251x^4 + 1055x^3 + 910x^2 - 278x - 353	\( 2^{4}\cdot 3^{8}\cdot 19^{2}\cdot 61^{9} \)	16T1845	Trivial (GRH)
16.2.465131363476694405041800.1	x^16 - 4x^15 + 8x^14 - 13x^13 - x^12 - 46x^11 + 145x^10 - 390x^9 + 602x^8 - 517x^7 + 493x^6 - 185x^5 + 192x^4 - 27x^3 + 21x^2 + 1	\( -\,2^{3}\cdot 3^{8}\cdot 5^{2}\cdot 43^{2}\cdot 61^{8} \)	16T1845	Trivial (GRH)
16.10.485496339676102000131243.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 145x^12 + 415x^11 - 509x^10 - 139x^9 + 1899x^8 - 4199x^7 + 5633x^6 - 5231x^5 + 3393x^4 - 1479x^3 + 405x^2 - 62x + 4	\( -\,3\cdot 41\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.6.485496339676102000131243.1	x^16 - 5x^15 + 6x^14 + 6x^13 - 2x^12 - 77x^11 + 51x^10 + 635x^9 - 1380x^8 - 141x^7 + 2288x^6 - 949x^5 - 1122x^4 + 705x^3 + 337x^2 + 30x + 4	\( -\,3\cdot 41\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.12.509179087952985024527889.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 64x^12 + 162x^11 - 603x^10 + 815x^9 - 349x^8 - 568x^7 + 911x^6 - 287x^5 - 239x^4 + 150x^3 - 9x + 1	\( 3\cdot 43\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.509179087952985024527889.1	x^16 - 5x^15 + 3x^14 + 13x^13 + 19x^12 - 96x^11 - 59x^10 + 264x^9 + 187x^8 - 608x^7 + 92x^6 + 336x^5 - 128x^4 + 47x^3 - 18x^2 + 1	\( 3\cdot 43\cdot 89^{2}\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.4.670966851462478045125201.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 139x^12 - 288x^11 + 509x^10 - 620x^9 - 68x^8 + 1968x^7 - 4651x^6 + 6446x^5 - 6067x^4 + 3938x^3 - 1694x^2 + 435x - 50	\( 3^{2}\cdot 41^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.8.670966851462478045125201.1	x^16 - 4x^15 - 7x^14 + 33x^13 + 48x^12 - 170x^11 - 162x^10 + 543x^9 + 50x^8 - 691x^7 + 385x^6 + 165x^5 - 400x^4 + 145x^3 + 62x^2 - 36x + 16	\( 3^{2}\cdot 41^{2}\cdot 89\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.8.682852575316793870103293.1	x^16 - 3x^15 + 6x^14 - 20x^13 + 17x^12 - 16x^11 + 95x^10 - 105x^9 + 388x^8 - 402x^7 - 776x^6 + 61x^5 + 303x^4 + 2909x^3 - 2537x^2 - 376x + 519	\( 89^{2}\cdot 163^{8}\cdot 173 \)	16T1845	Trivial (GRH)
16.8.682852575316793870103293.2	x^16 - 7x^15 + 13x^14 + 17x^13 - 106x^12 + 241x^11 - 564x^10 + 999x^9 - 300x^8 - 1788x^7 + 2175x^6 - 122x^5 - 631x^4 - 229x^3 + 235x^2 + 56x + 3	\( 89^{2}\cdot 163^{8}\cdot 173 \)	16T1845	Trivial (GRH)
16.0.738023621864438968135929.1	x^16 - 7x^15 + 28x^14 - 79x^13 + 184x^12 - 347x^11 + 534x^10 - 527x^9 + 276x^8 + 166x^7 - 257x^6 + 65x^5 + 318x^4 - 6x^3 - 21x^2 + 1	\( 3^{2}\cdot 43^{2}\cdot 89\cdot 163^{8} \)	16T1845	$[2]$ (GRH)
16.6.812386634223132183022759.1	x^16 - 3x^15 - 8x^14 + 7x^13 + 17x^12 + 126x^11 + 174x^10 - 442x^9 - 1015x^8 - 175x^7 + 1400x^6 + 2623x^5 + 902x^4 - 3853x^3 - 3383x^2 + 1730x + 1900	\( -\,7^{5}\cdot 97\cdot 163^{8} \)	16T1845	Trivial (GRH)
16.6.812386634223132183022759.2	x^16 - 7x^15 + 14x^14 + 5x^13 - 82x^12 + 51x^11 + 323x^10 - 129x^9 - 512x^8 + 207x^7 + 376x^6 - 575x^5 - 51x^4 + 925x^3 + 199x^2 - 198x + 4	\( -\,7^{5}\cdot 97\cdot 163^{8} \)	16T1845	Trivial (GRH)