LMFDB - Global number field search results

Further refine search

Results (displaying matches 1-50 of 67) Next

Label	Polynomial	Discriminant	Galois group	Class group
16.0.281792804290560000.2	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 20x¹² + 16x¹¹ + 6x¹⁰ - 28x⁹ + 15x⁸ + 32x⁷ + 18x⁶ + 40x⁵ + 58x⁴ + 48x³ + 26x² + 8x + 1	$ 2^{36}\cdot 3^{8}\cdot 5^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.403275801600000000.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ + 6x¹³ - 17x¹² + 2x¹¹ + 48x¹⁰ - 116x⁹ + 153x⁸ - 116x⁷ + 48x⁶ + 2x⁵ - 17x⁴ + 6x³ + 2x² - 2x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.403275801600000000.2	x¹⁶ - 6x¹⁵ + 16x¹⁴ - 28x¹³ + 42x¹² - 58x¹¹ + 74x¹⁰ - 76x⁹ + 42x⁸ + 12x⁷ - 50x⁶ + 74x⁵ - 15x⁴ - 58x³ + 10x² + 20x + 4	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.687970713600000000.4	x¹⁶ - x¹² - 3x⁸ - 4x⁴ + 16	$ 2^{28}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1082535236962615296.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 16x¹³ + 18x¹² - 4x¹¹ - 34x¹⁰ + 68x⁹ - 49x⁸ - 8x⁷ + 50x⁶ - 68x⁵ + 72x⁴ - 56x³ + 28x² - 8x + 1	$ 2^{36}\cdot 3^{8}\cdot 7^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1549224319426560000.1	x¹⁶ - 4x¹⁵ + 17x¹⁴ - 42x¹³ + 94x¹² - 170x¹¹ + 261x¹⁰ - 334x⁹ + 363x⁸ - 334x⁷ + 261x⁶ - 170x⁵ + 94x⁴ - 42x³ + 17x² - 4x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{4}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1549224319426560000.3	x¹⁶ - 6x¹⁵ + 9x¹⁴ + 12x¹³ - 35x¹² - 4x¹¹ + 28x¹⁰ + 46x⁹ - 49x⁸ - 68x⁷ + 105x⁶ - 30x⁵ + 55x⁴ - 114x³ + 90x² - 28x + 4	$ 2^{16}\cdot 3^{8}\cdot 5^{4}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.2174327193600000000.1	x¹⁶ - 2x¹⁴ + 2x¹² - 12x¹¹ + 18x¹⁰ + 24x⁹ - 37x⁸ - 48x⁷ + 90x⁶ - 48x⁵ + 56x⁴ - 84x³ + 52x² - 12x + 1	$ 2^{36}\cdot 3^{4}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.3782285936100000000.2	x¹⁶ + 15x¹² + 32x⁸ + 15x⁴ + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.3782285936100000000.3	x¹⁶ - x¹⁵ - 11x¹³ + 6x¹² + 22x¹⁰ + 10x⁹ + 21x⁸ - 10x⁷ + 22x⁶ + 6x⁴ + 11x³ + x + 1	$ 2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.4508684868648960000.1	x¹⁶ - 8x¹⁴ + 44x¹² - 24x¹¹ - 168x¹⁰ + 252x⁹ + 335x⁸ - 1536x⁷ + 2352x⁶ - 2028x⁵ + 1052x⁴ - 336x³ + 76x² - 12x + 1	$ 2^{40}\cdot 3^{8}\cdot 5^{4} $	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.4508684868648960000.2	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 64x¹³ + 186x¹² - 416x¹¹ + 808x¹⁰ - 1280x⁹ + 1766x⁸ - 2024x⁷ + 2000x⁶ - 1592x⁵ + 1036x⁴ - 464x³ + 144x² + 4	$ 2^{40}\cdot 3^{8}\cdot 5^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.4508684868648960000.3	x¹⁶ - 4x¹⁵ - 4x¹⁴ + 24x¹³ + 36x¹² - 164x¹¹ + 80x¹⁰ + 16x⁹ + 401x⁸ - 644x⁷ - 12x⁶ + 576x⁵ - 278x⁴ - 168x³ + 204x² - 72x + 9	$ 2^{40}\cdot 3^{8}\cdot 5^{4} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.10152996499793903616.5	x¹⁶ + 3x¹² + 89x⁸ - 72x⁴ + 16	$ 2^{28}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.2	x¹⁶ - 12x¹⁴ + 63x¹² - 180x¹⁰ + 296x⁸ - 270x⁶ + 123x⁴ - 18x² + 1	$ 2^{32}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.3	x¹⁶ + 2x¹⁴ + 5x¹² - 12x¹⁰ + 20x⁸ + 90x⁶ + 53x⁴ - 16x² + 1	$ 2^{32}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.5	x¹⁶ - 6x¹⁴ + 2x¹² + 60x¹⁰ + 111x⁸ + 60x⁶ + 2x⁴ - 6x² + 1	$ 2^{32}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.7	x¹⁶ - 2x¹⁴ + 2x¹² + 12x¹⁰ + 23x⁸ + 12x⁶ + 2x⁴ - 2x² + 1	$ 2^{32}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.12	x¹⁶ - 2x¹⁴ + 5x¹² + 12x¹⁰ + 20x⁸ - 90x⁶ + 53x⁴ + 16x² + 1	$ 2^{32}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.11953891353600000000.1	x¹⁶ - x¹⁴ + 11x¹² + 33x¹⁰ + 56x⁸ + 33x⁶ + 11x⁴ - x² + 1	$ 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11953891353600000000.2	x¹⁶ - 8x¹⁵ + 38x¹⁴ - 126x¹³ + 292x¹² - 478x¹¹ + 542x¹⁰ - 378x⁹ + 76x⁸ + 138x⁷ - 124x⁶ - 26x⁵ + 145x⁴ - 150x³ + 86x² - 28x + 4	$ 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.32088482764780732416.1	x¹⁶ + 12x¹⁴ + 12x¹² - 20x¹⁰ - 6x⁸ - 20x⁶ + 12x⁴ + 12x² + 1	$ 2^{36}\cdot 3^{4}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.34789235097600000000.1	x¹⁶ - 8x¹⁵ + 44x¹⁴ - 164x¹³ + 468x¹² - 1036x¹¹ + 1828x¹⁰ - 2572x⁹ + 2887x⁸ - 2572x⁷ + 1828x⁶ - 1036x⁵ + 468x⁴ - 164x³ + 44x² - 8x + 1	$ 2^{40}\cdot 3^{4}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.34789235097600000000.3	x¹⁶ - 4x¹⁵ + 4x¹⁴ + 20x¹³ - 70x¹² + 60x¹¹ + 128x¹⁰ - 364x⁹ + 282x⁸ + 188x⁷ - 460x⁶ + 60x⁵ + 526x⁴ - 612x³ + 320x² - 84x + 9	$ 2^{40}\cdot 3^{4}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.34789235097600000000.4	x¹⁶ - 4x¹⁵ + 16x¹⁴ - 32x¹³ + 70x¹² - 116x¹¹ + 240x¹⁰ - 408x⁹ + 609x⁸ - 692x⁷ + 812x⁶ - 1224x⁵ + 1668x⁴ - 1528x³ + 868x² - 280x + 41	$ 2^{40}\cdot 3^{4}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.162447943996702457856.2	x¹⁶ + 8x¹⁴ + 42x¹² + 94x¹⁰ + 47x⁸ - 38x⁶ + 30x⁴ - 10x² + 1	$ 2^{32}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.162447943996702457856.7	x¹⁶ - 8x¹⁴ + 42x¹² - 94x¹⁰ + 47x⁸ + 38x⁶ + 30x⁴ + 10x² + 1	$ 2^{32}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.176120502681600000000.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 8x¹³ - 12x¹² + 72x¹¹ - 52x¹⁰ - 60x⁹ + 187x⁸ - 60x⁷ - 52x⁶ + 72x⁵ - 12x⁴ - 8x³ + 10x² - 4x + 1	$ 2^{36}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.176120502681600000000.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 4x¹³ + 18x¹² - 20x¹¹ - 110x¹⁰ + 56x⁹ + 447x⁸ - 448x⁷ - 262x⁶ + 280x⁵ + 136x⁴ - 48x³ - 60x² + 9	$ 2^{36}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.176120502681600000000.8	x¹⁶ - 4x¹⁴ + 42x¹² + 4x¹⁰ - 27x⁸ - 64x⁶ + 148x⁴ - 120x² + 36	$ 2^{36}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.176120502681600000000.9	x¹⁶ + 4x¹⁴ + 42x¹² - 4x¹⁰ - 27x⁸ + 64x⁶ + 148x⁴ + 120x² + 36	$ 2^{36}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.2	x¹⁶ - 4x¹⁵ + 7x¹⁴ - 8x¹³ + 60x¹¹ - 67x¹⁰ - 138x⁹ + 379x⁸ - 138x⁷ - 67x⁶ + 60x⁵ - 8x³ + 7x² - 4x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.968265199641600000000.2	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 20x¹³ + 2x¹² + 102x¹¹ - 350x¹⁰ + 690x⁹ - 921x⁸ + 976x⁷ - 642x⁶ - 54x⁵ + 573x⁴ - 374x³ - 73x² + 84x + 1	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.8.968265199641600000000.3	x¹⁶ - 2x¹⁴ - 4x¹³ - 20x¹² + 6x¹¹ + 54x¹⁰ + 26x⁹ + 40x⁸ + 40x⁷ - 212x⁶ - 222x⁵ + 233x⁴ + 206x³ - 58x² - 28x + 4	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.968265199641600000000.4	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 36x¹³ + 135x¹² - 242x¹¹ + 612x¹⁰ - 690x⁹ + 985x⁸ - 1434x⁷ + 1322x⁶ - 1108x⁵ + 856x⁴ - 536x³ + 264x² - 80x + 16	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.5	x¹⁶ + 54x¹² + 737x⁸ + 1896x⁴ + 16	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.6	x¹⁶ + 6x¹⁴ + 29x¹² + 65x¹⁰ + 18x⁸ - 31x⁶ + 60x⁴ + 20x² + 16	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.7	x¹⁶ + 18x¹⁴ + 113x¹² + 279x¹⁰ + 298x⁸ + 333x⁶ + 387x⁴ - 81x² + 81	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.9	x¹⁶ + 8x¹⁴ - 4x¹³ + 28x¹² - 24x¹¹ + 141x¹⁰ - 218x⁹ + 489x⁸ - 664x⁷ + 568x⁶ - 440x⁵ + 148x⁴ - 288x³ + 768x² - 576x + 144	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.10	x¹⁶ - 6x¹⁴ + 17x¹² + 61x¹⁰ - 102x⁸ - 71x⁶ + 228x⁴ - 320x² + 256	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.11	x¹⁶ - 6x¹⁵ + 7x¹⁴ + 24x¹³ - 73x¹² + 60x¹¹ + 156x¹⁰ - 858x⁹ + 1439x⁸ - 252x⁷ - 618x⁶ - 1716x⁵ + 1802x⁴ + 762x³ + 550x² - 378x + 301	$ 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.2599167103947239325696.1	x¹⁶ - 4x¹⁵ + 14x¹⁴ - 8x¹³ + 32x¹¹ - 4x¹⁰ - 12x⁹ + 43x⁸ - 12x⁷ - 4x⁶ + 32x⁵ - 8x³ + 14x² - 4x + 1	$ 2^{36}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2, 2]$
16.8.2599167103947239325696.1	x¹⁶ - 8x¹⁴ + 4x¹² + 8x¹⁰ + 204x⁸ - 464x⁶ + 352x⁴ - 160x² + 16	$ 2^{36}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2599167103947239325696.4	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 156x¹² - 280x¹¹ + 448x¹⁰ - 544x⁹ + 524x⁸ - 592x⁷ + 800x⁶ - 736x⁵ + 448x⁴ - 160x³ + 16	$ 2^{36}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[8]$
16.0.2599167103947239325696.6	x¹⁶ - 12x¹⁴ - 12x¹³ + 68x¹² + 24x¹¹ - 214x¹⁰ + 228x⁹ + 711x⁸ - 960x⁷ - 562x⁶ + 3708x⁵ - 1128x⁴ - 5196x³ + 4880x² - 816x + 58	$ 2^{36}\cdot 3^{8}\cdot 7^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[2, 2]$
16.8.2817928042905600000000.1	x¹⁶ - 4x¹⁴ - 26x¹² - 88x¹¹ - 40x¹⁰ + 132x⁹ + 177x⁸ - 32x⁷ - 148x⁶ + 20x⁵ + 116x⁴ + 32x³ - 16x² - 4x + 1	$ 2^{40}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2817928042905600000000.2	x¹⁶ + 8x¹⁴ + 40x¹² + 64x¹⁰ + 18x⁸ + 104x⁶ + 280x⁴ - 32x² + 1	$ 2^{40}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.2817928042905600000000.3	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 120x¹² - 64x¹¹ - 128x¹⁰ + 320x⁹ - 238x⁸ - 136x⁷ + 512x⁶ - 496x⁵ + 232x⁴ + 32x³ + 1	$ 2^{40}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.2817928042905600000000.3	x¹⁶ + 4x¹⁴ - 30x¹² - 64x¹¹ - 16x¹⁰ + 384x⁹ + 154x⁸ - 768x⁷ - 128x⁶ + 552x⁵ + 100x⁴ - 160x³ - 48x² + 16x + 4	$ 2^{40}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2817928042905600000000.4	x¹⁶ - 4x¹⁴ + 8x¹² + 36x¹⁰ + 398x⁸ - 876x⁶ + 968x⁴ + 44x² + 1	$ 2^{40}\cdot 3^{8}\cdot 5^{8} $	$Q_8 : C_2^2$ (as 16T23)	$[4]$

Introduction	Features
Universe	News

Degree	Signature	Galois group	Class number	Class group

Regulator	Num. ramified primes	Ramified primes		Unramified primes

CM field	Discriminant		Root discriminant

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Further refine search

Results (displaying matches 1-50 of 67) Next

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
16.0.281792804290560000.2	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 20x¹² + 16x¹¹ + 6x¹⁰ - 28x⁹ + 15x⁸ + 32x⁷ + 18x⁶ + 40x⁵ + 58x⁴ + 48x³ + 26x² + 8x + 1	\( 2^{36}\cdot 3^{8}\cdot 5^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.403275801600000000.1	x¹⁶ - 2x¹⁵ + 2x¹⁴ + 6x¹³ - 17x¹² + 2x¹¹ + 48x¹⁰ - 116x⁹ + 153x⁸ - 116x⁷ + 48x⁶ + 2x⁵ - 17x⁴ + 6x³ + 2x² - 2x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.403275801600000000.2	x¹⁶ - 6x¹⁵ + 16x¹⁴ - 28x¹³ + 42x¹² - 58x¹¹ + 74x¹⁰ - 76x⁹ + 42x⁸ + 12x⁷ - 50x⁶ + 74x⁵ - 15x⁴ - 58x³ + 10x² + 20x + 4	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.687970713600000000.4	x¹⁶ - x¹² - 3x⁸ - 4x⁴ + 16	\( 2^{28}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1082535236962615296.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 16x¹³ + 18x¹² - 4x¹¹ - 34x¹⁰ + 68x⁹ - 49x⁸ - 8x⁷ + 50x⁶ - 68x⁵ + 72x⁴ - 56x³ + 28x² - 8x + 1	\( 2^{36}\cdot 3^{8}\cdot 7^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1549224319426560000.1	x¹⁶ - 4x¹⁵ + 17x¹⁴ - 42x¹³ + 94x¹² - 170x¹¹ + 261x¹⁰ - 334x⁹ + 363x⁸ - 334x⁷ + 261x⁶ - 170x⁵ + 94x⁴ - 42x³ + 17x² - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{4}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.1549224319426560000.3	x¹⁶ - 6x¹⁵ + 9x¹⁴ + 12x¹³ - 35x¹² - 4x¹¹ + 28x¹⁰ + 46x⁹ - 49x⁸ - 68x⁷ + 105x⁶ - 30x⁵ + 55x⁴ - 114x³ + 90x² - 28x + 4	\( 2^{16}\cdot 3^{8}\cdot 5^{4}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.2174327193600000000.1	x¹⁶ - 2x¹⁴ + 2x¹² - 12x¹¹ + 18x¹⁰ + 24x⁹ - 37x⁸ - 48x⁷ + 90x⁶ - 48x⁵ + 56x⁴ - 84x³ + 52x² - 12x + 1	\( 2^{36}\cdot 3^{4}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.3782285936100000000.2	x¹⁶ + 15x¹² + 32x⁸ + 15x⁴ + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.3782285936100000000.3	x¹⁶ - x¹⁵ - 11x¹³ + 6x¹² + 22x¹⁰ + 10x⁹ + 21x⁸ - 10x⁷ + 22x⁶ + 6x⁴ + 11x³ + x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.4508684868648960000.1	x¹⁶ - 8x¹⁴ + 44x¹² - 24x¹¹ - 168x¹⁰ + 252x⁹ + 335x⁸ - 1536x⁷ + 2352x⁶ - 2028x⁵ + 1052x⁴ - 336x³ + 76x² - 12x + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{4} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.4508684868648960000.2	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 64x¹³ + 186x¹² - 416x¹¹ + 808x¹⁰ - 1280x⁹ + 1766x⁸ - 2024x⁷ + 2000x⁶ - 1592x⁵ + 1036x⁴ - 464x³ + 144x² + 4	\( 2^{40}\cdot 3^{8}\cdot 5^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.4508684868648960000.3	x¹⁶ - 4x¹⁵ - 4x¹⁴ + 24x¹³ + 36x¹² - 164x¹¹ + 80x¹⁰ + 16x⁹ + 401x⁸ - 644x⁷ - 12x⁶ + 576x⁵ - 278x⁴ - 168x³ + 204x² - 72x + 9	\( 2^{40}\cdot 3^{8}\cdot 5^{4} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.10152996499793903616.5	x¹⁶ + 3x¹² + 89x⁸ - 72x⁴ + 16	\( 2^{28}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.2	x¹⁶ - 12x¹⁴ + 63x¹² - 180x¹⁰ + 296x⁸ - 270x⁶ + 123x⁴ - 18x² + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.3	x¹⁶ + 2x¹⁴ + 5x¹² - 12x¹⁰ + 20x⁸ + 90x⁶ + 53x⁴ - 16x² + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.5	x¹⁶ - 6x¹⁴ + 2x¹² + 60x¹⁰ + 111x⁸ + 60x⁶ + 2x⁴ - 6x² + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.7	x¹⁶ - 2x¹⁴ + 2x¹² + 12x¹⁰ + 23x⁸ + 12x⁶ + 2x⁴ - 2x² + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11007531417600000000.12	x¹⁶ - 2x¹⁴ + 5x¹² + 12x¹⁰ + 20x⁸ - 90x⁶ + 53x⁴ + 16x² + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.11953891353600000000.1	x¹⁶ - x¹⁴ + 11x¹² + 33x¹⁰ + 56x⁸ + 33x⁶ + 11x⁴ - x² + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.11953891353600000000.2	x¹⁶ - 8x¹⁵ + 38x¹⁴ - 126x¹³ + 292x¹² - 478x¹¹ + 542x¹⁰ - 378x⁹ + 76x⁸ + 138x⁷ - 124x⁶ - 26x⁵ + 145x⁴ - 150x³ + 86x² - 28x + 4	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.32088482764780732416.1	x¹⁶ + 12x¹⁴ + 12x¹² - 20x¹⁰ - 6x⁸ - 20x⁶ + 12x⁴ + 12x² + 1	\( 2^{36}\cdot 3^{4}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.34789235097600000000.1	x¹⁶ - 8x¹⁵ + 44x¹⁴ - 164x¹³ + 468x¹² - 1036x¹¹ + 1828x¹⁰ - 2572x⁹ + 2887x⁸ - 2572x⁷ + 1828x⁶ - 1036x⁵ + 468x⁴ - 164x³ + 44x² - 8x + 1	\( 2^{40}\cdot 3^{4}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.34789235097600000000.3	x¹⁶ - 4x¹⁵ + 4x¹⁴ + 20x¹³ - 70x¹² + 60x¹¹ + 128x¹⁰ - 364x⁹ + 282x⁸ + 188x⁷ - 460x⁶ + 60x⁵ + 526x⁴ - 612x³ + 320x² - 84x + 9	\( 2^{40}\cdot 3^{4}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.34789235097600000000.4	x¹⁶ - 4x¹⁵ + 16x¹⁴ - 32x¹³ + 70x¹² - 116x¹¹ + 240x¹⁰ - 408x⁹ + 609x⁸ - 692x⁷ + 812x⁶ - 1224x⁵ + 1668x⁴ - 1528x³ + 868x² - 280x + 41	\( 2^{40}\cdot 3^{4}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.162447943996702457856.2	x¹⁶ + 8x¹⁴ + 42x¹² + 94x¹⁰ + 47x⁸ - 38x⁶ + 30x⁴ - 10x² + 1	\( 2^{32}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2]$
16.0.162447943996702457856.7	x¹⁶ - 8x¹⁴ + 42x¹² - 94x¹⁰ + 47x⁸ + 38x⁶ + 30x⁴ + 10x² + 1	\( 2^{32}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial
16.0.176120502681600000000.1	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 8x¹³ - 12x¹² + 72x¹¹ - 52x¹⁰ - 60x⁹ + 187x⁸ - 60x⁷ - 52x⁶ + 72x⁵ - 12x⁴ - 8x³ + 10x² - 4x + 1	\( 2^{36}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.176120502681600000000.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ + 4x¹³ + 18x¹² - 20x¹¹ - 110x¹⁰ + 56x⁹ + 447x⁸ - 448x⁷ - 262x⁶ + 280x⁵ + 136x⁴ - 48x³ - 60x² + 9	\( 2^{36}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.176120502681600000000.8	x¹⁶ - 4x¹⁴ + 42x¹² + 4x¹⁰ - 27x⁸ - 64x⁶ + 148x⁴ - 120x² + 36	\( 2^{36}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.176120502681600000000.9	x¹⁶ + 4x¹⁴ + 42x¹² - 4x¹⁰ - 27x⁸ + 64x⁶ + 148x⁴ + 120x² + 36	\( 2^{36}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.2	x¹⁶ - 4x¹⁵ + 7x¹⁴ - 8x¹³ + 60x¹¹ - 67x¹⁰ - 138x⁹ + 379x⁸ - 138x⁷ - 67x⁶ + 60x⁵ - 8x³ + 7x² - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.968265199641600000000.2	x¹⁶ - 4x¹⁵ + 10x¹⁴ - 20x¹³ + 2x¹² + 102x¹¹ - 350x¹⁰ + 690x⁹ - 921x⁸ + 976x⁷ - 642x⁶ - 54x⁵ + 573x⁴ - 374x³ - 73x² + 84x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.8.968265199641600000000.3	x¹⁶ - 2x¹⁴ - 4x¹³ - 20x¹² + 6x¹¹ + 54x¹⁰ + 26x⁹ + 40x⁸ + 40x⁷ - 212x⁶ - 222x⁵ + 233x⁴ + 206x³ - 58x² - 28x + 4	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.968265199641600000000.4	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 36x¹³ + 135x¹² - 242x¹¹ + 612x¹⁰ - 690x⁹ + 985x⁸ - 1434x⁷ + 1322x⁶ - 1108x⁵ + 856x⁴ - 536x³ + 264x² - 80x + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.5	x¹⁶ + 54x¹² + 737x⁸ + 1896x⁴ + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.6	x¹⁶ + 6x¹⁴ + 29x¹² + 65x¹⁰ + 18x⁸ - 31x⁶ + 60x⁴ + 20x² + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.7	x¹⁶ + 18x¹⁴ + 113x¹² + 279x¹⁰ + 298x⁸ + 333x⁶ + 387x⁴ - 81x² + 81	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.9	x¹⁶ + 8x¹⁴ - 4x¹³ + 28x¹² - 24x¹¹ + 141x¹⁰ - 218x⁹ + 489x⁸ - 664x⁷ + 568x⁶ - 440x⁵ + 148x⁴ - 288x³ + 768x² - 576x + 144	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.10	x¹⁶ - 6x¹⁴ + 17x¹² + 61x¹⁰ - 102x⁸ - 71x⁶ + 228x⁴ - 320x² + 256	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.968265199641600000000.11	x¹⁶ - 6x¹⁵ + 7x¹⁴ + 24x¹³ - 73x¹² + 60x¹¹ + 156x¹⁰ - 858x⁹ + 1439x⁸ - 252x⁷ - 618x⁶ - 1716x⁵ + 1802x⁴ + 762x³ + 550x² - 378x + 301	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.2599167103947239325696.1	x¹⁶ - 4x¹⁵ + 14x¹⁴ - 8x¹³ + 32x¹¹ - 4x¹⁰ - 12x⁹ + 43x⁸ - 12x⁷ - 4x⁶ + 32x⁵ - 8x³ + 14x² - 4x + 1	\( 2^{36}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2, 2]$
16.8.2599167103947239325696.1	x¹⁶ - 8x¹⁴ + 4x¹² + 8x¹⁰ + 204x⁸ - 464x⁶ + 352x⁴ - 160x² + 16	\( 2^{36}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2599167103947239325696.4	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 156x¹² - 280x¹¹ + 448x¹⁰ - 544x⁹ + 524x⁸ - 592x⁷ + 800x⁶ - 736x⁵ + 448x⁴ - 160x³ + 16	\( 2^{36}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[8]$
16.0.2599167103947239325696.6	x¹⁶ - 12x¹⁴ - 12x¹³ + 68x¹² + 24x¹¹ - 214x¹⁰ + 228x⁹ + 711x⁸ - 960x⁷ - 562x⁶ + 3708x⁵ - 1128x⁴ - 5196x³ + 4880x² - 816x + 58	\( 2^{36}\cdot 3^{8}\cdot 7^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[2, 2]$
16.8.2817928042905600000000.1	x¹⁶ - 4x¹⁴ - 26x¹² - 88x¹¹ - 40x¹⁰ + 132x⁹ + 177x⁸ - 32x⁷ - 148x⁶ + 20x⁵ + 116x⁴ + 32x³ - 16x² - 4x + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2817928042905600000000.2	x¹⁶ + 8x¹⁴ + 40x¹² + 64x¹⁰ + 18x⁸ + 104x⁶ + 280x⁴ - 32x² + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.0.2817928042905600000000.3	x¹⁶ - 8x¹⁵ + 32x¹⁴ - 80x¹³ + 120x¹² - 64x¹¹ - 128x¹⁰ + 320x⁹ - 238x⁸ - 136x⁷ + 512x⁶ - 496x⁵ + 232x⁴ + 32x³ + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$
16.8.2817928042905600000000.3	x¹⁶ + 4x¹⁴ - 30x¹² - 64x¹¹ - 16x¹⁰ + 384x⁹ + 154x⁸ - 768x⁷ - 128x⁶ + 552x⁵ + 100x⁴ - 160x³ - 48x² + 16x + 4	\( 2^{40}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	Trivial (GRH)
16.0.2817928042905600000000.4	x¹⁶ - 4x¹⁴ + 8x¹² + 36x¹⁰ + 398x⁸ - 876x⁶ + 968x⁴ + 44x² + 1	\( 2^{40}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2^2$ (as 16T23)	$[4]$