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 92)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.30588194928937669.1	x^16 - x^15 - 2x^14 + 3x^13 + 4x^12 - 9x^11 + 4x^10 + 2x^9 - 3x^8 + 5x^7 - 3x^6 - 8x^5 + 19x^4 - 20x^3 + 13x^2 - 5x + 1	\( 17^{2}\cdot 29\cdot 283^{4}\cdot 569 \)	16T1879	Trivial
16.0.41268653593021184.1	x^16 - 5x^15 + 15x^14 - 31x^13 + 52x^12 - 75x^11 + 97x^10 - 107x^9 + 91x^8 - 49x^7 + 5x^6 + 16x^5 - 12x^4 + x^3 + 5x^2 - 4x + 1	\( 2^{8}\cdot 11\cdot 73^{2}\cdot 229^{4} \)	16T1879	Trivial
16.2.46569375736056031.1	x^16 - 2x^15 + 5x^14 - 8x^13 + 12x^12 - 17x^11 + 20x^10 - 23x^9 + 23x^8 - 23x^7 + 20x^6 - 17x^5 + 12x^4 - 8x^3 + 5x^2 - 2x + 1	\( -\,37^{2}\cdot 199\cdot 643^{4} \)	16T1879	Trivial
16.0.62661751274285761.1	x^16 - x^15 + x^14 - 5x^12 + 9x^11 - 4x^10 + 3x^9 + 4x^8 - 8x^7 + 16x^6 - 9x^5 + 13x^4 - 7x^3 + 5x^2 - 2x + 1	\( 13^{2}\cdot 17\cdot 23\cdot 79\cdot 331^{4} \)	16T1879	Trivial
16.0.63141730482005821.1	x^16 - 8x^15 + 31x^14 - 77x^13 + 140x^12 - 203x^11 + 249x^10 - 266x^9 + 250x^8 - 207x^7 + 152x^6 - 99x^5 + 58x^4 - 30x^3 + 13x^2 - 4x + 1	\( 23\cdot 29^{2}\cdot 229^{4}\cdot 1187 \)	16T1879	Trivial
16.2.75417294303354643.1	x^16 + 4x^14 - x^13 + 7x^12 - 8x^11 + 3x^10 - 18x^9 - 7x^8 - 15x^7 - 4x^6 - 2x^5 - 7x^4 - 5x^3 + x^2 - x - 1	\( -\,149^{2}\cdot 283\cdot 331^{4} \)	16T1879	Trivial
16.0.143242243542613181.1	x^16 - 5x^15 + 14x^14 - 27x^13 + 43x^12 - 63x^11 + 88x^10 - 110x^9 + 120x^8 - 116x^7 + 104x^6 - 85x^5 + 60x^4 - 35x^3 + 17x^2 - 6x + 1	\( 149\cdot 283^{2}\cdot 331^{4} \)	16T1879	Trivial
16.2.183992172742975744.1	x^16 + x^14 + 3x^12 - 8x^10 + x^8 + 14x^6 - 4x^2 - 1	\( -\,2^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4} \)	16T1879	Trivial
16.0.250467723553382437.1	x^16 - 3x^15 + 2x^14 + 2x^13 - x^12 - 7x^11 + 10x^10 - x^9 - 5x^8 - x^7 + 10x^6 - 7x^5 - x^4 + 2x^3 + 2x^2 - 3x + 1	\( 37\cdot 199^{2}\cdot 643^{4} \)	16T1879	Trivial
16.4.311502095702824709.1	x^16 - x^15 - 6x^14 + 6x^13 + 11x^12 - 13x^11 - 2x^10 + 15x^9 - 9x^8 - 15x^7 - 2x^6 + 13x^5 + 11x^4 - 6x^3 - 6x^2 + x + 1	\( 23^{2}\cdot 563^{4}\cdot 5861 \)	16T1879	Trivial
16.2.320501104309234339.1	x^16 - 3x^12 - 4x^11 - 10x^10 - 10x^9 - 22x^7 - 5x^6 + 5x^5 - 7x^4 + x^3 + 7x^2 - 3x + 1	\( -\,67^{2}\cdot 283^{4}\cdot 11131 \)	16T1879	Trivial
16.2.347222681549178551.1	x^16 - 4x^15 + 7x^14 - x^13 - 19x^12 + 41x^11 - 33x^10 - 16x^9 + 72x^8 - 82x^7 + 34x^6 + 32x^5 - 66x^4 + 56x^3 - 28x^2 + 8x - 1	\( -\,59^{2}\cdot 283^{4}\cdot 15551 \)	16T1879	Trivial
16.4.599756696007540736.1	x^16 + 3x^14 - 4x^13 + x^12 - 4x^11 - x^10 + 12x^9 - 29x^8 + 42x^7 - 49x^6 + 60x^5 - 58x^4 + 42x^3 - 24x^2 + 8x - 1	\( 2^{16}\cdot 7^{3}\cdot 41\cdot 47\cdot 61^{4} \)	16T1879	Trivial
16.6.716416589069289243.1	x^16 - 5x^15 + 11x^14 - 16x^13 + 15x^12 - 2x^11 - 19x^10 + 40x^9 - 49x^8 + 40x^7 - 19x^6 - 2x^5 + 15x^4 - 16x^3 + 11x^2 - 5x + 1	\( -\,3^{6}\cdot 19^{4}\cdot 67\cdot 103^{4} \)	16T1879	Trivial
16.4.951657857121891681.1	x^16 - 4x^15 + 7x^14 - 9x^13 + 9x^12 - 9x^11 + 16x^10 - 17x^9 + 6x^8 + 15x^7 - 25x^6 + 14x^5 + 10x^4 - 18x^3 + x^2 + 5x - 1	\( 3^{6}\cdot 19^{4}\cdot 89\cdot 103^{4} \)	16T1879	Trivial
16.4.1287945209200830208.1	x^16 - x^15 - 7x^14 + 13x^13 + 10x^12 - 49x^11 + 30x^10 + 57x^9 - 93x^8 + 10x^7 + 81x^6 - 70x^5 + 13x^4 + 13x^3 - 10x^2 + 4x - 1	\( 2^{8}\cdot 7^{3}\cdot 19^{4}\cdot 103^{4} \)	16T1879	Trivial
16.6.1357983683758204983.1	x^16 - x^15 - 3x^14 - 5x^13 + 10x^12 + 12x^11 - 11x^10 - 2x^9 - x^8 + 3x^7 - 20x^6 + 14x^5 + 5x^4 - 6x^3 + 5x^2 + x - 1	\( -\,3^{6}\cdot 19^{4}\cdot 103^{4}\cdot 127 \)	16T1879	Trivial
16.6.1486297102695988131.1	x^16 - x^15 + x^14 - x^13 + 2x^12 + 2x^11 - 11x^10 - 15x^9 - 6x^8 + 14x^7 + 31x^6 + 24x^5 - 17x^3 - 17x^2 - 7x - 1	\( -\,3^{6}\cdot 19^{4}\cdot 103^{4}\cdot 139 \)	16T1879	Trivial
16.4.1678767231102662853.1	x^16 - 4x^15 + 8x^14 - 11x^13 + 6x^12 + 8x^11 - 28x^10 + 46x^9 - 53x^8 + 46x^7 - 28x^6 + 8x^5 + 6x^4 - 11x^3 + 8x^2 - 4x + 1	\( 3^{6}\cdot 19^{4}\cdot 103^{4}\cdot 157 \)	16T1879	Trivial
16.4.2618616687908826112.1	x^16 + x^14 - x^13 - 5x^12 - 8x^11 - 28x^10 - 51x^9 - 50x^8 - 46x^7 - 64x^6 - 57x^5 - 31x^4 - 22x^3 - 17x^2 - 7x - 1	\( 2^{10}\cdot 43\cdot 2777^{4} \)	16T1879	Trivial
16.2.3136946269772161467.1	x^16 + 2x^14 + 7x^12 - 2x^11 + x^10 + 9x^9 - 9x^8 + 9x^7 + x^6 - 2x^5 + 7x^4 + 2x^2 + 1	\( -\,3^{3}\cdot 19^{4}\cdot 89^{2}\cdot 103^{4} \)	16T1879	Trivial
16.2.3495851282116539136.1	x^16 + x^14 - 7x^12 - 2x^10 + 19x^8 - 18x^6 - 22x^4 + 38x^2 - 19	\( -\,2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{4} \)	16T1879	Trivial
16.0.3495851282116539136.1	x^16 - x^15 + 4x^14 - 7x^13 + 17x^12 - 21x^11 + 32x^10 - 43x^9 + 52x^8 - 43x^7 + 32x^6 - 21x^5 + 17x^4 - 7x^3 + 4x^2 - x + 1	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{4} \)	16T1879	Trivial
16.4.3495851282116539136.1	x^16 - 5x^14 + 7x^12 - 13x^10 + 60x^8 - 127x^6 + 135x^4 - 76x^2 + 19	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{4} \)	16T1879	Trivial
16.4.4282263258518041549.1	x^16 - 2x^15 + 3x^14 + x^13 - 7x^12 + 19x^11 - 35x^10 + 52x^9 - 56x^8 + 37x^7 - 12x^6 - 12x^5 + 8x^4 + 6x^3 - 7x^2 + 4x - 1	\( 149^{2}\cdot 331^{4}\cdot 16069 \)	16T1879	Trivial
16.6.6728856603171684352.1	x^16 - 4x^14 - 10x^13 - 9x^12 + 4x^11 + 7x^10 + 16x^9 + 4x^8 - 4x^6 - 32x^5 + 29x^4 + 10x^3 - 20x^2 + 8x - 1	\( -\,2^{16}\cdot 7\cdot 19^{4}\cdot 103^{4} \)	16T1879	Trivial
16.0.8163317900823533749.1	x^16 - x^15 - 2x^14 + 5x^13 + 10x^12 - 30x^11 + 29x^10 - 17x^8 - 16x^7 + 15x^6 + 18x^5 + x^4 - 9x^3 - 8x^2 + 2x + 3	\( 7\cdot 19^{4}\cdot 43^{3}\cdot 103^{4} \)	16T1879	Trivial
16.2.8294667542637416704.1	x^16 - 4x^15 + 7x^14 - 6x^13 + 5x^12 - 16x^11 + 50x^10 - 100x^9 + 155x^8 - 190x^7 + 184x^6 - 138x^5 + 64x^4 - 6x^3 - 12x^2 + 6x - 1	\( -\,2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4} \)	16T1879	Trivial
16.2.8332582876366199175.1	x^16 - 3x^15 + 7x^14 - 16x^13 + 30x^12 - 60x^11 + 133x^10 - 258x^9 + 424x^8 - 567x^7 + 578x^6 - 459x^5 + 282x^4 - 132x^3 + 44x^2 - 10x + 1	\( -\,3^{4}\cdot 5^{2}\cdot 1327^{5} \)	16T1879	Trivial
16.8.8564920714097025129.1	x^16 - x^15 + 5x^13 - 12x^12 - 4x^11 + 9x^10 - 24x^9 + 6x^8 + 40x^7 + 30x^6 + 20x^5 - 18x^4 - 26x^3 - x^2 + 5x + 1	\( 3^{8}\cdot 19^{4}\cdot 89\cdot 103^{4} \)	16T1879	Trivial
16.8.15108905079923965677.1	x^16 - 4x^15 - 2x^14 + 18x^13 - 3x^12 - 10x^11 - 13x^10 - 20x^9 + 38x^8 + 16x^7 - 20x^6 + 3x^5 - 5x^4 - 8x^3 + 4x^2 + 5x + 1	\( 3^{8}\cdot 19^{4}\cdot 103^{4}\cdot 157 \)	16T1879	Trivial
16.6.15336535719789789184.1	x^16 - 7x^14 + 14x^12 + x^10 - 29x^8 + 21x^6 + 3x^4 - 2x^2 - 1	\( -\,2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1879	Trivial
16.6.15336535719789789184.2	x^16 - 5x^14 + 16x^12 - 35x^10 + 40x^8 - 24x^6 + 8x^4 + x^2 - 1	\( -\,2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1879	Trivial
16.4.16343010957417578496.1	x^16 - 2x^15 - x^14 + 4x^13 + 3x^12 - 2x^11 - 12x^10 + 8x^9 + 23x^8 - 24x^7 - 26x^6 + 48x^5 - 8x^4 - 28x^3 + 24x^2 - 8x + 1	\( 2^{16}\cdot 3^{2}\cdot 41^{2}\cdot 53^{4}\cdot 2089 \)	16T1879	Trivial
16.2.18928664138721239296.1	x^16 + 7x^14 + 18x^12 + 23x^10 + 21x^8 + 15x^6 - 2x^4 - 9x^2 - 1	\( -\,2^{8}\cdot 19^{4}\cdot 71^{2}\cdot 103^{4} \)	16T1879	Trivial
16.4.23527485718490325229.1	x^16 - x^15 + 6x^13 - 15x^12 + 17x^11 - 8x^10 - 13x^9 + 19x^8 - 13x^7 - 8x^6 + 17x^5 - 15x^4 + 6x^3 - x + 1	\( 7\cdot 19^{4}\cdot 43\cdot 73^{2}\cdot 103^{4} \)	16T1879	Trivial
16.6.28232516427949453203.1	x^16 - 3x^15 + 4x^14 - 14x^13 + 17x^12 - 13x^11 + 36x^10 + 2x^9 + 15x^8 - x^7 - 23x^6 - 13x^5 - 17x^4 + 6x^3 + 7x^2 + 4x + 1	\( -\,3^{5}\cdot 19^{4}\cdot 89^{2}\cdot 103^{4} \)	16T1879	Trivial
16.0.41540647987478977309.1	x^16 - 2x^15 + 2x^14 - 3x^13 + x^12 - 3x^11 + 5x^10 + 14x^9 + 4x^8 - 23x^7 - 26x^6 - 3x^5 + 25x^4 + 28x^3 + 17x^2 + 8x + 3	\( 7\cdot 19^{4}\cdot 43\cdot 97^{2}\cdot 103^{4} \)	16T1879	Trivial
16.0.41540647987478977309.2	x^16 - 3x^15 + 8x^14 - 16x^13 + 42x^12 - 85x^11 + 125x^10 - 110x^9 + 50x^8 - x^7 + 8x^6 - 29x^5 + 24x^4 - 2x^3 - 5x^2 + x + 1	\( 7\cdot 19^{4}\cdot 43\cdot 97^{2}\cdot 103^{4} \)	16T1879	Trivial
16.0.45037320663223833301.1	x^16 - 3x^15 + 5x^14 - 11x^13 + 22x^12 - 26x^11 + 26x^10 - 35x^9 + 43x^8 - 35x^7 + 26x^6 - 26x^5 + 22x^4 - 11x^3 + 5x^2 - 3x + 1	\( 7\cdot 19^{4}\cdot 43\cdot 101^{2}\cdot 103^{4} \)	16T1879	Trivial
16.8.56300258790039761408.1	x^16 - 2x^14 - 6x^12 + 10x^10 + 12x^8 - 13x^6 - 9x^4 + 4x^2 + 2	\( 2^{9}\cdot 43^{2}\cdot 2777^{4} \)	16T1879	Trivial
16.6.57143225305764736243.1	x^16 + 3x^14 - 3x^13 + 7x^12 + 13x^11 + 16x^10 - 48x^9 - 133x^8 - 38x^7 + 152x^6 + 138x^5 - 10x^4 - 46x^3 - 8x^2 + 4x + 1	\( -\,7^{2}\cdot 19^{4}\cdot 43^{3}\cdot 103^{4} \)	16T1879	Trivial
16.8.68204009994461277281.1	x^16 - 4x^14 - 9x^12 - x^11 + 32x^10 + 2x^9 + 2x^8 + 49x^7 + 18x^6 - 43x^5 - 50x^4 - 12x^3 + 9x^2 + 6x + 1	\( 37^{3}\cdot 643^{4}\cdot 7877 \)	16T1879	Trivial
16.8.72207435208103458129.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 99x^12 + 48x^11 + 206x^10 - 183x^9 - 228x^8 + 250x^7 + 138x^6 - 165x^5 - 37x^4 + 46x^3 + x^2 - 2x + 1	\( 53\cdot 109^{2}\cdot 491^{4}\cdot 1973 \)	16T1879	Trivial
16.6.74993245887295792575.1	x^16 - 3x^15 + 6x^13 + 9x^12 + x^11 - 26x^10 - 72x^9 - 48x^8 + 90x^7 + 176x^6 + 76x^5 - 73x^4 - 95x^3 - 37x^2 - x + 1	\( -\,3^{6}\cdot 5^{2}\cdot 1327^{5} \)	16T1879	Trivial
16.8.97010591798158738273.1	x^16 - 8x^14 - 3x^13 + 11x^12 + 4x^11 + 22x^10 + 12x^9 - 84x^8 - 8x^7 + 99x^6 - 24x^5 - 46x^4 + 24x^3 + 4x^2 - 6x + 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 73\cdot 103^{4} \)	16T1879	Trivial
16.10.128860300270118047744.1	x^16 - 5x^14 + 4x^12 + 13x^10 - 22x^8 + 12x^6 - 15x^4 + 14x^2 - 1	\( -\,2^{12}\cdot 23^{2}\cdot 2777^{4} \)	16T1879	Trivial
16.8.128904484992073939897.1	x^16 - 5x^15 + 8x^14 - 4x^13 - 3x^12 + 12x^11 - 18x^10 + 21x^9 - 25x^8 + 21x^7 - 18x^6 + 12x^5 - 3x^4 - 4x^3 + 8x^2 - 5x + 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 97\cdot 103^{4} \)	16T1879	Trivial
16.8.128904484992073939897.2	x^16 - x^15 - 5x^14 - 5x^13 + 20x^12 + 40x^11 - 63x^10 - 82x^9 + 119x^8 + 57x^7 - 129x^6 + 16x^5 + 73x^4 - 36x^3 - 14x^2 + 11x - 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 97\cdot 103^{4} \)	16T1879	Trivial
16.4.134220133857726473501.1	x^16 - 4x^15 + 7x^14 - 9x^13 + 9x^12 - 7x^11 + 6x^10 - 5x^9 + 5x^8 - 5x^7 + 6x^6 - 7x^5 + 9x^4 - 9x^3 + 7x^2 - 4x + 1	\( 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 101\cdot 103^{4} \)	16T1879	Trivial