LMFDB - Global number field search results

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Results (displaying all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.125468737884127232.1	x¹⁶ - 4x¹⁵ + 20x¹³ - 21x¹² - 32x¹¹ + 62x¹⁰ + 4x⁹ - 59x⁸ + 20x⁷ + 12x⁶ + 8x⁵ - 9x⁴ - 8x³ + 2x² + 4x + 1	$ -\,2^{32}\cdot 7^{4}\cdot 23^{3} $	16T1567	Trivial
16.2.2007499806146035712.1	x¹⁶ - 4x¹⁵ + 6x¹⁴ - 8x¹³ + 16x¹² - 16x¹¹ - 10x¹⁰ + 40x⁹ - 37x⁸ + 4x⁷ + 22x⁶ - 20x⁵ + 2x⁴ + 8x³ - 4x² + 1	$ -\,2^{36}\cdot 7^{4}\cdot 23^{3} $	16T1567	Trivial
16.2.2107060827100000000.1	x¹⁶ - 3x¹⁵ + 7x¹⁴ - 11x¹³ + 9x¹² - 4x¹¹ - 9x¹⁰ + 8x⁹ - 12x⁸ - 2x⁷ + 5x⁶ + 7x⁵ + 3x⁴ - 13x³ - 3x² + 2x - 1	$ -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{3} $	16T1567	Trivial
16.4.3726679716405444608.1	x¹⁶ - 2x¹⁵ + x¹⁴ + 4x¹³ - 15x¹² + 16x¹¹ + 11x¹⁰ - 68x⁹ + 114x⁸ - 84x⁷ - 35x⁶ + 184x⁵ - 255x⁴ + 198x³ - 86x² + 16x - 1	$ 2^{28}\cdot 17^{3}\cdot 41^{4} $	16T1567	Trivial
16.4.4874651380100000000.1	x¹⁶ - 5x¹⁵ + 8x¹⁴ - 4x¹³ - 10x¹² + 18x¹¹ - 3x¹⁰ - 21x⁹ + 6x⁸ + 73x⁷ - 166x⁶ + 197x⁵ - 143x⁴ + 55x³ - 4x² - 4x + 1	$ 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} $	16T1567	Trivial
16.0.9141231334400000000.1	x¹⁶ + 4x¹² + 10x⁸ + 27x⁴ + 29	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} $	16T1567	Trivial
16.0.9141231334400000000.2	x¹⁶ - 5x¹² - 6x⁸ + 40x⁴ + 29	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} $	16T1567	Trivial
16.0.11208269900102565888.1	x¹⁶ - 13x¹² + 62x⁸ - 128x⁴ + 97	$ 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{3} $	16T1567	Trivial
16.0.11208269900102565888.2	x¹⁶ + 7x¹² + 14x⁸ + 32x⁴ + 97	$ 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{3} $	16T1567	Trivial
16.2.24099609881600000000.1	x¹⁶ - 9x¹⁴ + 34x¹² - 67x¹⁰ + 65x⁸ - 7x⁶ - 49x⁴ + 44x² - 11	$ -\,2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	Trivial
16.0.110267976046400000000.1	x¹⁶ - 6x¹² + 23x⁸ - 42x⁴ + 29	$ 2^{12}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} $	16T1567	Trivial
16.6.539407571737600000000.1	x¹⁶ - 8x¹⁵ + 29x¹⁴ - 62x¹³ + 89x¹² - 134x¹¹ + 206x¹⁰ - 182x⁹ + 153x⁸ - 190x⁷ + 152x⁶ - 86x⁵ + 36x⁴ - 8x³ + 14x² - 10x + 1	$ -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 31^{3} $	16T1567	Trivial
16.0.1764287616742400000000.1	x¹⁶ - 9x¹² + 28x⁸ - 33x⁴ + 29	$ 2^{16}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} $	16T1567	Trivial
16.4.2340155221606400000000.1	x¹⁶ - 2x¹⁵ - 2x¹⁴ - 2x¹³ - 10x¹² - 4x¹¹ + 62x¹⁰ + 78x⁹ + 43x⁸ - 76x⁷ - 102x⁶ + 2x⁵ + 90x⁴ - 46x³ + 12x² - 4x + 1	$ 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} $	16T1567	Trivial
16.4.2340155221606400000000.2	x¹⁶ - 2x¹⁵ + 6x¹⁴ - 18x¹³ + 14x¹² - 66x¹¹ + 20x¹⁰ - 62x⁹ + 136x⁸ + 176x⁷ + 448x⁶ + 496x⁵ + 463x⁴ + 282x³ + 110x² + 24x + 1	$ 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} $	16T1567	Trivial
16.6.6169500129689600000000.1	x¹⁶ - 2x¹⁵ - 10x¹³ + 22x¹² + 36x¹¹ - 102x¹⁰ - 22x⁹ + 356x⁸ - 516x⁷ + 106x⁶ + 422x⁵ - 431x⁴ + 80x³ + 104x² - 32x - 11	$ -\,2^{24}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	Trivial
16.4.176270963105382400000000.1	x¹⁶ - 7x¹² - 100x⁸ + 331x⁴ + 19	$ 2^{20}\cdot 5^{8}\cdot 19^{3}\cdot 89^{4} $	16T1567	Trivial
16.4.176270963105382400000000.2	x¹⁶ - 4x¹² - 65x⁸ - 82x⁴ + 19	$ 2^{20}\cdot 5^{8}\cdot 19^{3}\cdot 89^{4} $	16T1567	Trivial
16.0.544631207982822400000000.1	x¹⁶ + 4x¹⁴ - 38x¹² - 71x¹⁰ + 503x⁸ - 801x⁶ - 415x⁴ + 27709x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	$[2]$
16.4.544631207982822400000000.1	x¹⁶ - 5x¹⁴ - 47x¹² + 517x¹⁰ - 2210x⁸ + 4298x⁶ + 1817x⁴ - 22671x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	Trivial (GRH)
16.8.544631207982822400000000.1	x¹⁶ - 4x¹⁴ - 38x¹² + 71x¹⁰ + 503x⁸ + 801x⁶ - 415x⁴ - 27709x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	Trivial (GRH)
16.0.544631207982822400000000.2	x¹⁶ + 19x¹⁴ + 123x¹² + 538x¹⁰ + 2745x⁸ + 12717x⁶ + 35577x⁴ + 50380x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	$[2]$
16.4.544631207982822400000000.2	x¹⁶ + 5x¹⁴ - 47x¹² - 517x¹⁰ - 2210x⁸ - 4298x⁶ + 1817x⁴ + 22671x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	Trivial (GRH)
16.8.544631207982822400000000.2	x¹⁶ - 19x¹⁴ + 123x¹² - 538x¹⁰ + 2745x⁸ - 12717x⁶ + 35577x⁴ - 50380x² + 27709	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1567	Trivial (GRH)
16.0.1579392033200537600000000.1	x¹⁶ - 14x¹⁴ + 81x¹² - 236x¹⁰ + 333x⁸ + 52x⁶ - 561x⁴ + 572x² + 1331	$ 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	$[2]$
16.8.1579392033200537600000000.1	x¹⁶ - 10x¹⁴ - 10x¹² + 210x¹⁰ + 192x⁸ - 890x⁶ - 1005x⁴ + 11	$ 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	Trivial (GRH)
16.0.1579392033200537600000000.2	x¹⁶ + 9x¹² + 27x⁸ + 31x⁴ + 11	$ 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	$[2]$
16.8.1579392033200537600000000.2	x¹⁶ - 4x¹⁴ - 57x¹² + 154x¹⁰ + 463x⁸ + 108x⁶ - 163x⁴ - 22x² + 11	$ 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} $	16T1567	Trivial (GRH)
16.12.3555504469700818662400000000.1	x¹⁶ - 8x¹⁴ - 248x¹² + 3871x¹⁰ - 17965x⁸ + 3111x⁶ + 219263x⁴ - 639065x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)
16.16.3555504469700818662400000000.1	x¹⁶ - 69x¹⁴ + 1892x¹² - 26405x¹⁰ + 199643x⁸ - 811944x⁶ + 1706860x⁴ - 1679828x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)
16.4.3555504469700818662400000000.1	x¹⁶ + 26x¹⁴ - 14x¹² - 4513x¹⁰ - 23250x⁸ + 124439x⁶ + 931395x⁴ + 1497238x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.1	x¹⁶ - 2x¹⁴ - 431x¹² + 2729x¹⁰ + 15235x⁸ - 86598x⁶ - 186775x⁴ + 346921x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	$[2]$ (GRH)
16.12.3555504469700818662400000000.2	x¹⁶ - 52x¹⁴ + 955x¹² - 6586x¹⁰ - 2625x⁸ + 207227x⁶ - 501921x⁴ - 748619x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)
16.16.3555504469700818662400000000.2	x¹⁶ - 63x¹⁴ + 1581x¹² - 20451x¹⁰ + 147060x⁸ - 592904x⁶ + 1298869x⁴ - 1405943x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)
16.4.3555504469700818662400000000.2	x¹⁶ + 10x¹⁴ - 383x¹² - 6659x¹⁰ - 32698x⁸ - 2214x⁶ + 395405x⁴ + 949468x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.2	x¹⁶ + 10x¹⁴ - 349x¹² - 245x¹⁰ + 25490x⁸ - 37535x⁶ - 508772x⁴ + 1095540x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)
16.8.3555504469700818662400000000.3	x¹⁶ + 6x¹⁴ - 324x¹² - 2883x¹⁰ + 7650x⁸ + 68059x⁶ - 91760x⁴ - 419957x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.4	x¹⁶ - 5x¹⁴ - 612x¹² + 4592x¹⁰ + 47842x⁸ - 127667x⁶ - 532890x⁴ + 164331x² + 566029	$ 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} $	16T1567	Trivial (GRH)

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Results (displaying all 38 matches)

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
16.2.125468737884127232.1	x¹⁶ - 4x¹⁵ + 20x¹³ - 21x¹² - 32x¹¹ + 62x¹⁰ + 4x⁹ - 59x⁸ + 20x⁷ + 12x⁶ + 8x⁵ - 9x⁴ - 8x³ + 2x² + 4x + 1	\( -\,2^{32}\cdot 7^{4}\cdot 23^{3} \)	16T1567	Trivial
16.2.2007499806146035712.1	x¹⁶ - 4x¹⁵ + 6x¹⁴ - 8x¹³ + 16x¹² - 16x¹¹ - 10x¹⁰ + 40x⁹ - 37x⁸ + 4x⁷ + 22x⁶ - 20x⁵ + 2x⁴ + 8x³ - 4x² + 1	\( -\,2^{36}\cdot 7^{4}\cdot 23^{3} \)	16T1567	Trivial
16.2.2107060827100000000.1	x¹⁶ - 3x¹⁵ + 7x¹⁴ - 11x¹³ + 9x¹² - 4x¹¹ - 9x¹⁰ + 8x⁹ - 12x⁸ - 2x⁷ + 5x⁶ + 7x⁵ + 3x⁴ - 13x³ - 3x² + 2x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{3} \)	16T1567	Trivial
16.4.3726679716405444608.1	x¹⁶ - 2x¹⁵ + x¹⁴ + 4x¹³ - 15x¹² + 16x¹¹ + 11x¹⁰ - 68x⁹ + 114x⁸ - 84x⁷ - 35x⁶ + 184x⁵ - 255x⁴ + 198x³ - 86x² + 16x - 1	\( 2^{28}\cdot 17^{3}\cdot 41^{4} \)	16T1567	Trivial
16.4.4874651380100000000.1	x¹⁶ - 5x¹⁵ + 8x¹⁴ - 4x¹³ - 10x¹² + 18x¹¹ - 3x¹⁰ - 21x⁹ + 6x⁸ + 73x⁷ - 166x⁶ + 197x⁵ - 143x⁴ + 55x³ - 4x² - 4x + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{3} \)	16T1567	Trivial
16.0.9141231334400000000.1	x¹⁶ + 4x¹² + 10x⁸ + 27x⁴ + 29	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} \)	16T1567	Trivial
16.0.9141231334400000000.2	x¹⁶ - 5x¹² - 6x⁸ + 40x⁴ + 29	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} \)	16T1567	Trivial
16.0.11208269900102565888.1	x¹⁶ - 13x¹² + 62x⁸ - 128x⁴ + 97	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{3} \)	16T1567	Trivial
16.0.11208269900102565888.2	x¹⁶ + 7x¹² + 14x⁸ + 32x⁴ + 97	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{3} \)	16T1567	Trivial
16.2.24099609881600000000.1	x¹⁶ - 9x¹⁴ + 34x¹² - 67x¹⁰ + 65x⁸ - 7x⁶ - 49x⁴ + 44x² - 11	\( -\,2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	Trivial
16.0.110267976046400000000.1	x¹⁶ - 6x¹² + 23x⁸ - 42x⁴ + 29	\( 2^{12}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} \)	16T1567	Trivial
16.6.539407571737600000000.1	x¹⁶ - 8x¹⁵ + 29x¹⁴ - 62x¹³ + 89x¹² - 134x¹¹ + 206x¹⁰ - 182x⁹ + 153x⁸ - 190x⁷ + 152x⁶ - 86x⁵ + 36x⁴ - 8x³ + 14x² - 10x + 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 31^{3} \)	16T1567	Trivial
16.0.1764287616742400000000.1	x¹⁶ - 9x¹² + 28x⁸ - 33x⁴ + 29	\( 2^{16}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} \)	16T1567	Trivial
16.4.2340155221606400000000.1	x¹⁶ - 2x¹⁵ - 2x¹⁴ - 2x¹³ - 10x¹² - 4x¹¹ + 62x¹⁰ + 78x⁹ + 43x⁸ - 76x⁷ - 102x⁶ + 2x⁵ + 90x⁴ - 46x³ + 12x² - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} \)	16T1567	Trivial
16.4.2340155221606400000000.2	x¹⁶ - 2x¹⁵ + 6x¹⁴ - 18x¹³ + 14x¹² - 66x¹¹ + 20x¹⁰ - 62x⁹ + 136x⁸ + 176x⁷ + 448x⁶ + 496x⁵ + 463x⁴ + 282x³ + 110x² + 24x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} \)	16T1567	Trivial
16.6.6169500129689600000000.1	x¹⁶ - 2x¹⁵ - 10x¹³ + 22x¹² + 36x¹¹ - 102x¹⁰ - 22x⁹ + 356x⁸ - 516x⁷ + 106x⁶ + 422x⁵ - 431x⁴ + 80x³ + 104x² - 32x - 11	\( -\,2^{24}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	Trivial
16.4.176270963105382400000000.1	x¹⁶ - 7x¹² - 100x⁸ + 331x⁴ + 19	\( 2^{20}\cdot 5^{8}\cdot 19^{3}\cdot 89^{4} \)	16T1567	Trivial
16.4.176270963105382400000000.2	x¹⁶ - 4x¹² - 65x⁸ - 82x⁴ + 19	\( 2^{20}\cdot 5^{8}\cdot 19^{3}\cdot 89^{4} \)	16T1567	Trivial
16.0.544631207982822400000000.1	x¹⁶ + 4x¹⁴ - 38x¹² - 71x¹⁰ + 503x⁸ - 801x⁶ - 415x⁴ + 27709x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	$[2]$
16.4.544631207982822400000000.1	x¹⁶ - 5x¹⁴ - 47x¹² + 517x¹⁰ - 2210x⁸ + 4298x⁶ + 1817x⁴ - 22671x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	Trivial (GRH)
16.8.544631207982822400000000.1	x¹⁶ - 4x¹⁴ - 38x¹² + 71x¹⁰ + 503x⁸ + 801x⁶ - 415x⁴ - 27709x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	Trivial (GRH)
16.0.544631207982822400000000.2	x¹⁶ + 19x¹⁴ + 123x¹² + 538x¹⁰ + 2745x⁸ + 12717x⁶ + 35577x⁴ + 50380x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	$[2]$
16.4.544631207982822400000000.2	x¹⁶ + 5x¹⁴ - 47x¹² - 517x¹⁰ - 2210x⁸ - 4298x⁶ + 1817x⁴ + 22671x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	Trivial (GRH)
16.8.544631207982822400000000.2	x¹⁶ - 19x¹⁴ + 123x¹² - 538x¹⁰ + 2745x⁸ - 12717x⁶ + 35577x⁴ - 50380x² + 27709	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1567	Trivial (GRH)
16.0.1579392033200537600000000.1	x¹⁶ - 14x¹⁴ + 81x¹² - 236x¹⁰ + 333x⁸ + 52x⁶ - 561x⁴ + 572x² + 1331	\( 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	$[2]$
16.8.1579392033200537600000000.1	x¹⁶ - 10x¹⁴ - 10x¹² + 210x¹⁰ + 192x⁸ - 890x⁶ - 1005x⁴ + 11	\( 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	Trivial (GRH)
16.0.1579392033200537600000000.2	x¹⁶ + 9x¹² + 27x⁸ + 31x⁴ + 11	\( 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	$[2]$
16.8.1579392033200537600000000.2	x¹⁶ - 4x¹⁴ - 57x¹² + 154x¹⁰ + 463x⁸ + 108x⁶ - 163x⁴ - 22x² + 11	\( 2^{32}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4} \)	16T1567	Trivial (GRH)
16.12.3555504469700818662400000000.1	x¹⁶ - 8x¹⁴ - 248x¹² + 3871x¹⁰ - 17965x⁸ + 3111x⁶ + 219263x⁴ - 639065x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)
16.16.3555504469700818662400000000.1	x¹⁶ - 69x¹⁴ + 1892x¹² - 26405x¹⁰ + 199643x⁸ - 811944x⁶ + 1706860x⁴ - 1679828x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)
16.4.3555504469700818662400000000.1	x¹⁶ + 26x¹⁴ - 14x¹² - 4513x¹⁰ - 23250x⁸ + 124439x⁶ + 931395x⁴ + 1497238x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.1	x¹⁶ - 2x¹⁴ - 431x¹² + 2729x¹⁰ + 15235x⁸ - 86598x⁶ - 186775x⁴ + 346921x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	$[2]$ (GRH)
16.12.3555504469700818662400000000.2	x¹⁶ - 52x¹⁴ + 955x¹² - 6586x¹⁰ - 2625x⁸ + 207227x⁶ - 501921x⁴ - 748619x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)
16.16.3555504469700818662400000000.2	x¹⁶ - 63x¹⁴ + 1581x¹² - 20451x¹⁰ + 147060x⁸ - 592904x⁶ + 1298869x⁴ - 1405943x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)
16.4.3555504469700818662400000000.2	x¹⁶ + 10x¹⁴ - 383x¹² - 6659x¹⁰ - 32698x⁸ - 2214x⁶ + 395405x⁴ + 949468x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.2	x¹⁶ + 10x¹⁴ - 349x¹² - 245x¹⁰ + 25490x⁸ - 37535x⁶ - 508772x⁴ + 1095540x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)
16.8.3555504469700818662400000000.3	x¹⁶ + 6x¹⁴ - 324x¹² - 2883x¹⁰ + 7650x⁸ + 68059x⁶ - 91760x⁴ - 419957x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	$[2]$ (GRH)
16.8.3555504469700818662400000000.4	x¹⁶ - 5x¹⁴ - 612x¹² + 4592x¹⁰ + 47842x⁸ - 127667x⁶ - 532890x⁴ + 164331x² + 566029	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{4}\cdot 31^{5} \)	16T1567	Trivial (GRH)