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 104)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3207314697265625.1	x^16 - 2x^15 - x^14 + x^13 + 11x^12 - 11x^11 - 10x^10 + 5x^9 + 22x^8 - 10x^7 - 15x^6 + 3x^5 + 11x^4 - 2x^3 - 4x^2 + x + 1	\( 5^{12}\cdot 181^{2}\cdot 401 \)	16T1771	Trivial
16.0.7105708251953125.1	x^16 - 2x^15 + 4x^14 - 5x^13 + 3x^12 + 5x^11 - 14x^10 + 17x^9 - 12x^8 - 3x^7 + 31x^6 - 60x^5 + 68x^4 - 50x^3 + 24x^2 - 7x + 1	\( 5^{12}\cdot 181\cdot 401^{2} \)	16T1771	Trivial
16.2.401647199580061696.1	x^16 - 4x^14 - 4x^13 + 12x^12 + 8x^11 - 14x^10 - 12x^9 + 6x^8 + 12x^7 + 4x^6 - 4x^5 - 7x^4 - 4x^3 + 2x^2 + 4x + 1	\( -\,2^{44}\cdot 17^{2}\cdot 79 \)	16T1771	Trivial
16.6.998084115966796875.1	x^16 - x^15 - 7x^14 + 5x^13 + 20x^12 - 8x^11 - 25x^10 + 9x^9 + 6x^8 - 25x^7 + 31x^5 + 13x^4 - 11x^3 - 8x^2 + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179 \)	16T1771	Trivial
16.6.998084115966796875.2	x^16 - x^15 - 4x^14 + 2x^13 + 7x^12 + 10x^11 - 22x^10 - 13x^9 + 27x^8 - 3x^7 - 5x^6 - 5x^4 + 9x^3 + x^2 - 4x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 179 \)	16T1771	Trivial
16.4.1866478162754404352.1	x^16 - 4x^15 + 6x^14 - 4x^13 + 3x^12 - 4x^11 - 4x^10 + 8x^9 - 3x^8 + 8x^7 - 4x^6 - 4x^5 + 3x^4 - 4x^3 + 6x^2 - 4x + 1	\( 2^{44}\cdot 17\cdot 79^{2} \)	16T1771	Trivial
16.6.3028085707763671875.1	x^16 - x^15 - 3x^14 + x^13 + x^12 + 5x^11 - 12x^10 + 10x^9 - 3x^8 + 10x^7 - 12x^6 + 5x^5 + x^4 + x^3 - 3x^2 - x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 179^{2} \)	16T1771	Trivial
16.6.3028085707763671875.2	x^16 - 2x^15 - 6x^14 + x^13 + 11x^12 + 24x^11 + 20x^10 + 5x^9 + 2x^8 - 15x^7 - 20x^6 - 17x^5 - 4x^4 + 13x^3 + 11x^2 + 6x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 179^{2} \)	16T1771	Trivial
16.2.4327959241903046656.1	x^16 + 4x^14 + 6x^12 - 4x^10 - 11x^8 + 12x^4 - 4	\( -\,2^{52}\cdot 31^{2} \)	16T1771	Trivial
16.4.5692982583251953125.1	x^16 - x^15 - 2x^14 + 5x^13 - 5x^12 - 3x^11 + 20x^10 - 16x^9 - 29x^8 + 45x^7 - 20x^6 + 11x^5 - 7x^4 + 4x^3 - 3x^2 + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 1021 \)	16T1771	Trivial
16.8.5692982583251953125.1	x^16 - 4x^15 + 4x^14 - x^13 - 3x^12 + 30x^11 - 40x^10 - 25x^9 + 63x^8 - 32x^7 + 4x^6 + 34x^5 - 46x^4 + 6x^3 + 17x^2 - 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 1021 \)	16T1771	Trivial
16.4.6085489282470703125.1	x^16 - 2x^15 - 4x^14 + 8x^13 + 4x^12 + 7x^11 - 48x^10 + 34x^9 + 28x^8 + 7x^7 - 82x^6 + 29x^5 + 64x^4 - 71x^3 + 34x^2 - 9x + 1	\( 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 1021 \)	16T1771	Trivial
16.4.6085489282470703125.2	x^16 - 3x^15 + 11x^14 - 21x^13 + 40x^12 - 48x^11 + 45x^10 + 5x^9 - 79x^8 + 170x^7 - 205x^6 + 183x^5 - 105x^4 + 36x^3 + x^2 - 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 1021 \)	16T1771	Trivial
16.2.17311836967612186624.1	x^16 - 4x^14 + 6x^12 + 4x^10 - 11x^8 + 12x^4 - 4	\( -\,2^{54}\cdot 31^{2} \)	16T1771	Trivial
16.6.24483801782013657088.1	x^16 - 4x^15 + 2x^14 + 16x^13 - 41x^12 + 24x^11 + 54x^10 - 100x^9 + 40x^8 + 28x^7 + 6x^6 - 32x^5 + x^4 + 8x^3 - 2x^2 - 4x - 1	\( -\,2^{44}\cdot 79^{2}\cdot 223 \)	16T1771	Trivial
16.6.35740566642812256256.1	x^16 - 4x^14 - 14x^12 - 32x^11 - 24x^10 - 48x^9 - 47x^8 - 48x^7 - 24x^6 - 32x^5 - 14x^4 - 4x^2 + 1	\( -\,2^{60}\cdot 31 \)	16T1771	Trivial
16.2.43107820312500000000.1	x^16 + 10x^14 + 40x^12 + 80x^10 + 75x^8 + 10x^6 - 35x^4 - 25x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{15}\cdot 29^{2} \)	16T1771	Trivial
16.0.52401279790283203125.1	x^16 - 2x^15 + 3x^14 - 3x^13 + 2x^12 + 2x^11 - 16x^10 + 29x^9 - 18x^8 - 22x^7 + 71x^6 - 94x^5 + 82x^4 - 51x^3 + 22x^2 - 6x + 1	\( 3^{8}\cdot 5^{12}\cdot 179^{2}\cdot 1021 \)	16T1771	$[2]$
16.4.52401279790283203125.1	x^16 - 2x^15 + 4x^14 - 6x^12 + 16x^11 - 12x^10 + 6x^9 + 6x^8 + 2x^7 + 4x^6 - 25x^5 + 36x^4 - 35x^3 + 5x - 5	\( 3^{8}\cdot 5^{12}\cdot 179^{2}\cdot 1021 \)	16T1771	Trivial
16.8.52401279790283203125.1	x^16 - 3x^15 - x^14 + 14x^13 - 24x^12 + 21x^11 - 20x^10 + 35x^9 - 28x^8 - 20x^7 + 60x^6 - 33x^5 - 14x^4 + 17x^3 - 4x^2 - x + 1	\( 3^{8}\cdot 5^{12}\cdot 179^{2}\cdot 1021 \)	16T1771	Trivial (GRH)
16.4.52401279790283203125.2	x^16 - 5x^15 + 9x^14 + 3x^13 - 52x^12 + 114x^11 - 91x^10 - 89x^9 + 299x^8 - 291x^7 + 28x^6 + 215x^5 - 223x^4 + 97x^3 - 16x^2 + x + 1	\( 3^{8}\cdot 5^{12}\cdot 179^{2}\cdot 1021 \)	16T1771	Trivial
16.0.53578799887939453125.1	x^16 - 4x^15 + 9x^14 - 15x^13 + 21x^12 - 27x^11 + 30x^10 - 28x^9 + 22x^8 - 9x^7 - 5x^6 + 11x^5 - 4x^4 - 5x^3 + x^2 + 2x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021 \)	16T1771	$[2]$
16.8.53578799887939453125.1	x^16 - x^15 - 6x^14 + 11x^13 - 3x^12 - 20x^11 + 25x^10 - 2x^8 - 28x^7 + 54x^6 - 29x^5 - 21x^4 + 29x^3 - 8x^2 - 2x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021 \)	16T1771	Trivial (GRH)
16.4.53578799887939453125.1	x^16 - 4x^15 + 6x^14 - 12x^13 + 26x^12 - 27x^11 + 10x^10 - 10x^9 + 42x^8 - 45x^7 + 40x^6 - x^5 + 6x^4 - 9x^3 + 14x^2 - 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021 \)	16T1771	Trivial
16.4.53578799887939453125.2	x^16 - x^15 + 14x^13 - 16x^12 + 12x^11 + 26x^10 - 17x^9 - 4x^8 + 36x^7 - 11x^6 - 19x^5 + 29x^4 - 22x^3 + 5x^2 - 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2}\cdot 1021 \)	16T1771	Trivial
16.6.77594076562500000000.1	x^16 - 9x^14 + 32x^12 - 57x^10 + 55x^8 - 33x^6 + 12x^4 + 9x^2 - 9	\( -\,2^{8}\cdot 3^{10}\cdot 5^{14}\cdot 29^{2} \)	16T1771	Trivial
16.10.98517546059326171875.1	x^16 - 6x^15 + 14x^14 - 8x^13 - 51x^12 + 161x^11 - 164x^10 - 81x^9 + 335x^8 - 221x^7 - 58x^6 + 17x^5 + 115x^4 - 29x^3 - 27x^2 + 2x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.6.98517546059326171875.1	x^16 - 3x^15 - 2x^14 + 11x^13 - 8x^12 + 2x^10 + 7x^9 - 15x^8 + 7x^7 + 2x^6 - 8x^4 + 11x^3 - 2x^2 - 3x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59\cdot 1021^{2} \)	16T1771	Trivial
16.8.101857123891845703125.1	x^16 - x^15 - 7x^14 + 4x^13 + 7x^12 + 7x^10 + 12x^9 + 15x^8 + 12x^7 + 7x^6 + 7x^4 + 4x^3 - 7x^2 - x + 1	\( 3^{8}\cdot 5^{12}\cdot 61\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.8.101857123891845703125.2	x^16 - 5x^15 + 4x^14 + 15x^13 - 30x^12 + 5x^11 + 66x^10 - 130x^9 + 34x^8 + 235x^7 - 194x^6 - 145x^5 + 110x^4 + 60x^3 - 21x^2 - 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 61\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.6.116076040678637830144.1	x^16 - 4x^15 + 6x^14 - 4x^13 + x^12 + 4x^11 - 64x^9 + 141x^8 - 48x^7 - 156x^6 + 100x^5 + 249x^4 - 372x^3 + 134x^2 + 28x - 17	\( -\,2^{44}\cdot 17^{4}\cdot 79 \)	16T1771	Trivial
16.0.134166736498994446336.1	x^16 - 4x^15 + 10x^14 - 16x^13 + 15x^12 - 16x^11 + 26x^10 - 28x^9 + 26x^8 - 76x^7 + 170x^6 - 208x^5 + 203x^4 - 224x^3 + 226x^2 - 132x + 31	\( 2^{52}\cdot 31^{3} \)	16T1771	Trivial
16.4.134166736498994446336.1	x^16 - 4x^15 + 2x^14 + 20x^13 - 77x^12 + 152x^11 - 232x^10 + 264x^9 - 223x^8 + 100x^7 + 22x^6 - 84x^5 + 75x^4 - 16x^3 - 20x^2 + 16x - 4	\( 2^{52}\cdot 31^{3} \)	16T1771	Trivial
16.4.163260010786376953125.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 183x^12 - 279x^11 + 323x^10 - 273x^9 + 140x^8 + 11x^7 - 103x^6 + 109x^5 - 59x^4 + 11x^3 + 7x^2 - 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 179^{2}\cdot 3181 \)	16T1771	Trivial
16.8.175362884561548533629.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 86x^12 + 61x^11 + 141x^10 - 144x^9 - 157x^8 + 161x^7 + 125x^6 - 94x^5 - 66x^4 + 27x^3 + 17x^2 - 4x - 1	\( 13^{3}\cdot 17^{12}\cdot 137 \)	16T1771	Trivial (GRH)
16.6.221803285190185546875.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 182x^12 - 273x^11 + 303x^10 - 228x^9 + 70x^8 + 87x^7 - 154x^6 + 119x^5 - 38x^4 - 16x^3 + 23x^2 - 10x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 39779 \)	16T1771	Trivial (GRH)
16.4.281571595683837890625.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 24x^12 + 38x^11 - 93x^10 + 69x^9 + 16x^8 - 60x^7 + 32x^6 + 4x^5 - 11x^4 + 5x^3 - x + 1	\( 3^{10}\cdot 5^{12}\cdot 29\cdot 61^{2}\cdot 181 \)	16T1771	Trivial
16.4.284048656000000000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 159x^12 - 226x^11 + 239x^10 - 172x^9 + 48x^8 + 70x^7 - 125x^6 + 110x^5 - 58x^4 + 14x^3 + 4x^2 - 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 41^{2}\cdot 59\cdot 179 \)	16T1771	Trivial (GRH)
16.6.298892216010498046875.1	x^16 - x^15 - 7x^14 + 19x^13 - 23x^12 + 15x^11 - 8x^10 + 12x^9 - 15x^8 + 12x^7 - 8x^6 + 15x^5 - 23x^4 + 19x^3 - 7x^2 - x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.10.298892216010498046875.1	x^16 - x^15 - 13x^14 + 65x^12 + 56x^11 - 119x^10 - 220x^9 - 21x^8 + 220x^7 + 179x^6 + 48x^5 + 30x^4 - 5x^3 - 32x^2 - 8x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.10.298892216010498046875.2	x^16 - 6x^15 + 11x^14 + 11x^13 - 75x^12 + 65x^11 + 125x^10 - 187x^9 - 68x^8 + 128x^7 + 63x^6 - 20x^5 - 88x^4 + 33x^3 + 16x^2 - 9x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.6.298892216010498046875.2	x^16 - 3x^15 + 4x^14 - 6x^13 + 6x^12 - 24x^11 + 85x^10 - 150x^9 + 222x^8 - 405x^7 + 490x^6 - 288x^5 + 191x^4 - 228x^3 + 126x^2 - 21x + 1	\( -\,3^{8}\cdot 5^{12}\cdot 179\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.8.302231793843017578125.1	x^16 - 6x^15 + 7x^14 + 21x^13 - 69x^12 + 75x^11 + 8x^10 - 135x^9 + 197x^8 - 135x^7 + 8x^6 + 75x^5 - 69x^4 + 21x^3 + 7x^2 - 6x + 1	\( 3^{8}\cdot 5^{12}\cdot 181\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.4.302231793843017578125.1	x^16 - 7x^15 + 18x^14 - 21x^13 + 7x^12 + 10x^11 - 3x^10 - 27x^9 + 45x^8 - 27x^7 - 3x^6 + 10x^5 + 7x^4 - 21x^3 + 18x^2 - 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 181\cdot 1021^{2} \)	16T1771	Trivial
16.12.302231793843017578125.1	x^16 - x^15 - 10x^14 - 4x^13 + 28x^12 + 43x^11 + 14x^10 - 28x^9 - 114x^8 - 156x^7 + 37x^6 + 162x^5 + 25x^4 - 51x^3 - 11x^2 + 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 181\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.8.302231793843017578125.2	x^16 - 5x^15 - x^14 + 47x^13 - 77x^12 - 49x^11 + 179x^10 + 14x^9 - 166x^8 - 169x^7 + 263x^6 + 235x^5 - 318x^4 - 102x^3 + 164x^2 + 14x - 29	\( 3^{8}\cdot 5^{12}\cdot 181\cdot 1021^{2} \)	16T1771	Trivial (GRH)
16.8.421877331274658203125.1	x^16 - 8x^15 + 25x^14 - 35x^13 + 7x^12 + 49x^11 - 75x^10 + 45x^9 + 4x^8 - 33x^7 + 37x^6 - 27x^5 + 8x^4 + 7x^3 - 7x^2 + 2x + 1	\( 3^{8}\cdot 5^{12}\cdot 29\cdot 59^{2}\cdot 2609 \)	16T1771	Trivial (GRH)
16.8.428173719224853515625.1	x^16 - 7x^15 + 16x^14 - x^13 - 66x^12 + 152x^11 - 151x^10 - 64x^9 + 446x^8 - 635x^7 + 380x^6 + 70x^5 - 315x^4 + 280x^3 - 140x^2 + 40x - 5	\( 3^{8}\cdot 5^{13}\cdot 149\cdot 599^{2} \)	16T1771	Trivial (GRH)
16.4.495643256553955078125.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 47x^12 - 9x^11 - 37x^10 + 53x^9 - 35x^8 + 9x^7 - x^6 + 11x^5 - 17x^4 + 11x^3 - 3x + 1	\( 3^{8}\cdot 5^{13}\cdot 181^{2}\cdot 1889 \)	16T1771	Trivial (GRH)
16.6.532536595697021484375.1	x^16 - 4x^15 + 4x^14 - 14x^13 + 71x^12 - 132x^11 + 186x^10 - 357x^9 + 482x^8 - 468x^7 + 531x^6 - 408x^5 + 116x^4 - 31x^3 + 34x^2 - 11x + 1	\( -\,3^{8}\cdot 5^{14}\cdot 149^{2}\cdot 599 \)	16T1771	Trivial (GRH)