-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3, 0, 0, 0, 12, 0, 0, 0, 14, 0, 8, 0, -4, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 363087263602825104457728, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1], [4, 2]]], [7, [[8, 1], [4, 2]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[8, 1], [4, 1], [2, 1], [1, 2]]], [19, [[4, 2], [2, 1], [1, 6]]], [23, [[8, 2]]], [29, [[8, 1], [4, 2]]], [31, [[8, 1], [4, 2]]], [37, [[4, 2], [2, 4]]], [41, [[8, 1], [2, 2], [1, 4]]], [43, [[4, 1], [2, 6]]], [47, [[8, 2]]], [53, [[8, 1], [4, 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': '16T1444', 'galt': 1444, 'grd': 68.76674068410085, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 9, 'label': '16.0.363087263602825104457728.9', 'local_algs': ['2.1.16.64c1.29', 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'9,0,0,0,-36,0,0,0,102,0,24,0,-192,0,-192,0,241,0,112,0,144,0,-32,0,2,0,-16,0,4,0,0,0,1', '9,0,0,0,-72,0,0,0,228,0,0,0,-312,0,0,0,106,0,0,0,152,0,0,0,44,0,0,0,8,0,0,0,1', '9,0,72,0,864,0,14328,0,153624,0,553176,0,855624,0,378024,0,-109034,0,-94952,0,3072,0,7784,0,-232,0,-184,0,24,0,-8,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['2.0.1', '3.0.2.0.1', '2.-8.16.-8.8.-8.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{28}{501} a^{14} - \\frac{214}{501} a^{12} - \\frac{17}{167} a^{10} + \\frac{1079}{501} a^{8} - \\frac{483}{167} a^{6} - \\frac{901}{167} a^{4} + \\frac{354}{167} a^{2} - \\frac{463}{167} \\)', '\\( -\\frac{35}{501} a^{14} + \\frac{17}{501} a^{12} + \\frac{63}{167} a^{10} - \\frac{472}{501} a^{8} - \\frac{106}{167} a^{6} + \\frac{166}{167} a^{4} - \\frac{192}{167} a^{2} + \\frac{36}{167} \\)', '\\( \\frac{214}{501} a^{15} - \\frac{26}{501} a^{14} - \\frac{61}{501} a^{13} - \\frac{16}{501} a^{12} - \\frac{285}{167} a^{11} - \\frac{20}{167} a^{10} + \\frac{1841}{501} a^{9} + \\frac{179}{501} a^{8} + \\frac{901}{167} a^{7} - \\frac{136}{167} a^{6} - \\frac{242}{167} a^{5} - \\frac{559}{167} a^{4} + \\frac{463}{167} a^{3} + \\frac{53}{167} a^{2} - \\frac{139}{167} a - \\frac{250}{167} \\)', '\\( \\frac{214}{501} a^{15} + \\frac{26}{501} a^{14} - \\frac{61}{501} a^{13} + \\frac{16}{501} a^{12} - \\frac{285}{167} a^{11} + \\frac{20}{167} a^{10} + \\frac{1841}{501} a^{9} - \\frac{179}{501} a^{8} + \\frac{901}{167} a^{7} + \\frac{136}{167} a^{6} - \\frac{242}{167} a^{5} + \\frac{559}{167} a^{4} + \\frac{463}{167} a^{3} - \\frac{53}{167} a^{2} - \\frac{139}{167} a + \\frac{250}{167} \\)', '\\( -\\frac{160}{501} a^{15} - \\frac{178}{501} a^{14} - \\frac{137}{501} a^{13} - \\frac{71}{501} a^{12} + \\frac{288}{167} a^{11} + \\frac{287}{167} a^{10} - \\frac{941}{501} a^{9} - \\frac{1241}{501} a^{8} - \\frac{1248}{167} a^{7} - \\frac{1188}{167} a^{6} - \\frac{100}{167} a^{5} + \\frac{181}{167} a^{4} - \\frac{162}{167} a^{3} - \\frac{485}{167} a^{2} - \\frac{74}{167} a - \\frac{170}{167} \\)', '\\( -\\frac{419}{501} a^{15} - \\frac{190}{501} a^{14} + \\frac{89}{501} a^{13} + \\frac{307}{501} a^{12} + \\frac{654}{167} a^{11} + \\frac{342}{167} a^{10} - \\frac{3532}{501} a^{9} - \\frac{2777}{501} a^{8} - \\frac{2166}{167} a^{7} - \\frac{480}{167} a^{6} + \\frac{928}{167} a^{5} + \\frac{2094}{167} a^{4} + \\frac{154}{167} a^{3} + \\frac{413}{167} a^{2} + \\frac{660}{167} a + \\frac{768}{167} \\)', '\\( \\frac{799}{501} a^{15} - \\frac{91}{501} a^{14} + \\frac{299}{501} a^{13} - \\frac{56}{501} a^{12} - \\frac{1171}{167} a^{11} + \\frac{97}{167} a^{10} + \\frac{5078}{501} a^{9} - \\frac{626}{501} a^{8} + \\frac{4963}{167} a^{7} - \\frac{476}{167} a^{6} + \\frac{729}{167} a^{5} - \\frac{203}{167} a^{4} + \\frac{1191}{167} a^{3} - \\frac{900}{167} a^{2} + \\frac{476}{167} a - \\frac{708}{167} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', '1/501*a^14 - 115/501*a^12 + 65/167*a^10 + 128/501*a^8 - 59/167*a^6 - 62/167*a^4 - 47/167*a^2 + 61/167', '1/501*a^15 - 115/501*a^13 + 65/167*a^11 + 128/501*a^9 - 59/167*a^7 - 62/167*a^5 - 47/167*a^3 + 61/167*a']}
Number field data - 16.0.363087263602825104457728.9