-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1296, 0, 768, 0, 1056, 0, 0, 0, 72, 0, -64, 0, -8, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1936465405881733890441216, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[8, 2]]], [11, [[4, 2], [2, 4]]], [13, [[4, 2], [2, 4]]], [17, [[8, 1], [4, 1], [2, 2]]], [19, [[4, 2], [2, 2], [1, 4]]], [23, [[8, 2]]], [29, [[8, 2]]], [31, [[8, 2]]], [37, [[4, 4]]], [41, [[8, 1], [2, 1], [1, 6]]], [43, [[4, 1], [2, 5], [1, 2]]], [47, [[8, 2]]], [53, [[8, 2]]], [59, [[4, 1], [2, 5], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9660, 1792], 'galois_label': '16T1455', 'galt': 1455, 'grd': 68.76674068410085, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 262, 'label': '16.0.1936465405881733890441216.262', 'local_algs': ['2.1.16.68f1.1309', '3.1.2.1a1.1', 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\\frac{53}{1712} a^{4} - \\frac{5543}{10272} a^{3} - \\frac{5111}{1712} a^{2} + \\frac{6853}{2568} a - \\frac{397}{214} \\)', '\\( -\\frac{305}{123264} a^{15} + \\frac{41}{20544} a^{14} - \\frac{39}{13696} a^{13} - \\frac{39}{6848} a^{12} + \\frac{925}{30816} a^{11} - \\frac{275}{10272} a^{10} + \\frac{10705}{61632} a^{9} - \\frac{169}{2568} a^{8} - \\frac{479}{3424} a^{7} + \\frac{1019}{1712} a^{6} - \\frac{2887}{3424} a^{5} - \\frac{105}{1712} a^{4} - \\frac{325}{321} a^{3} - \\frac{57}{856} a^{2} - \\frac{9961}{5136} a - \\frac{929}{428} \\)', '\\( -\\frac{275}{246528} a^{15} + \\frac{67}{41088} a^{14} + \\frac{71}{13696} a^{13} + \\frac{25}{13696} a^{12} + \\frac{2189}{123264} a^{11} + \\frac{83}{20544} a^{10} + \\frac{1525}{30816} a^{9} - \\frac{1457}{20544} a^{8} - \\frac{2835}{6848} a^{7} - \\frac{99}{3424} a^{6} - \\frac{599}{3424} a^{5} - \\frac{3439}{3424} a^{4} - \\frac{22333}{10272} a^{3} - \\frac{375}{1712} a^{2} + \\frac{127}{321} a - \\frac{5111}{1712} \\)', '\\( -\\frac{275}{246528} a^{15} - \\frac{67}{41088} a^{14} + \\frac{71}{13696} a^{13} - \\frac{25}{13696} a^{12} + \\frac{2189}{123264} a^{11} - \\frac{83}{20544} a^{10} + \\frac{1525}{30816} a^{9} + \\frac{1457}{20544} a^{8} - \\frac{2835}{6848} a^{7} + \\frac{99}{3424} a^{6} - \\frac{599}{3424} a^{5} + \\frac{3439}{3424} a^{4} - \\frac{22333}{10272} a^{3} + \\frac{375}{1712} a^{2} + \\frac{127}{321} a + \\frac{5111}{1712} \\)', '\\( -\\frac{191}{82176} a^{15} + \\frac{11}{41088} a^{14} + \\frac{53}{13696} a^{13} + \\frac{15}{3424} a^{12} + \\frac{827}{41088} a^{11} + \\frac{7}{5136} a^{10} + \\frac{1351}{10272} a^{9} - \\frac{61}{5136} a^{8} - \\frac{2273}{6848} a^{7} - \\frac{473}{3424} a^{6} + \\frac{867}{3424} a^{5} + \\frac{205}{856} a^{4} - \\frac{10471}{3424} a^{3} - \\frac{1413}{856} a^{2} - \\frac{281}{428} a + \\frac{1085}{428} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/4*a^5 - 1/2*a^3 - 1/2*a', '1/4*a^6 - 1/2*a^2', '1/4*a^7 - 1/2*a^3', '1/32*a^8 + 1/8*a^4 - 1/2*a^2 + 3/8', '1/32*a^9 - 1/8*a^5 - 1/8*a', '1/64*a^10 + 1/16*a^6 - 1/4*a^4 - 1/2*a^3 + 3/16*a^2', '1/64*a^11 + 1/16*a^7 - 5/16*a^3 - 1/2*a', '1/128*a^12 - 1/64*a^8 - 1/8*a^6 - 3/32*a^4 - 1/2*a^3 - 1/4*a^2 + 7/16', '1/128*a^13 - 1/64*a^9 - 1/8*a^7 - 3/32*a^5 - 1/4*a^3 + 7/16*a', '1/41088*a^14 - 7/6848*a^12 - 85/20544*a^10 - 157/10272*a^8 - 257/3424*a^6 + 261/1712*a^4 - 111/1712*a^2 - 7/856', '1/246528*a^15 - 19/6848*a^13 - 85/123264*a^11 - 799/61632*a^9 - 371/6848*a^7 - 5/856*a^5 - 1/4*a^4 + 1601/10272*a^3 - 1/2*a^2 - 863/5136*a - 1/2']}
Number field data - 16.0.1936465405881733890441216.262