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nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-989, -785, 1152, -134, -349, 182, -26, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 498053903884848, 'disc_rad': 426, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1], [2, 2]]], [7, [[8, 1]]], [11, [[2, 2], [1, 4]]], [13, [[4, 2]]], [17, [[2, 3], [1, 2]]], [19, [[4, 1], [2, 2]]], [23, [[2, 2], [1, 4]]], [29, [[4, 1], [2, 2]]], [31, [[8, 1]]], [37, [[2, 2], [1, 4]]], [41, [[2, 3], [1, 2]]], [43, [[2, 1], [1, 6]]], [47, [[4, 1], [2, 1], [1, 2]]], [53, [[4, 1], [2, 2]]], [59, [[4, 1], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [192, 96, 96], 'galois_label': '8T35', 'galt': 35, 'grd': 157.6992747634948, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.4.498053903884848.1', 'local_algs': ['2.2.2.4a2.2', '2.4.1.0a1.1', '3.2.2.2a1.2', '3.1.4.3a1.1', '71.2.4.6a1.2'], 'minimal_sibling': [-41, 28, -19, -26, 34, -28, 14, -4, 1], 'monogenic': 0, 'narrow_class_group': [6], 'narrow_class_number': 6, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 71], 'rd': 68.7320889663, 'regulator': {'__RealLiteral__': 0, 'data': '20825.5219384', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-53.-1.1', '-33.-111.-44.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{24812}{12380555} a^{7} - \\frac{359979}{24761110} a^{6} - \\frac{276971}{12380555} a^{5} + \\frac{13967309}{24761110} a^{4} - \\frac{55078803}{24761110} a^{3} + \\frac{94144493}{24761110} a^{2} - \\frac{28312088}{12380555} a - \\frac{1143179}{1076570} \\)', '\\( \\frac{301647}{24761110} a^{7} - \\frac{100261}{12380555} a^{6} - \\frac{7872461}{24761110} a^{5} + \\frac{38054437}{24761110} a^{4} - \\frac{27632409}{24761110} a^{3} - \\frac{51774858}{12380555} a^{2} + \\frac{220866027}{24761110} a + \\frac{3959234}{538285} \\)', '\\( \\frac{211107}{24761110} a^{7} - \\frac{368141}{12380555} a^{6} - \\frac{4935741}{24761110} a^{5} + \\frac{37760027}{24761110} a^{4} - \\frac{100794109}{24761110} a^{3} + \\frac{56895512}{12380555} a^{2} - \\frac{12661723}{24761110} a - \\frac{2143486}{538285} \\)', '\\( \\frac{19556}{12380555} a^{7} - \\frac{567986}{12380555} a^{6} + \\frac{262712}{12380555} a^{5} + \\frac{16400891}{12380555} a^{4} - \\frac{69230972}{12380555} a^{3} + \\frac{76492832}{12380555} a^{2} + \\frac{40743746}{12380555} a - \\frac{1223311}{538285} \\)', '\\( \\frac{36138}{12380555} a^{7} - \\frac{5734403}{12380555} a^{6} - \\frac{3272504}{12380555} a^{5} + \\frac{172212968}{12380555} a^{4} - \\frac{457035006}{12380555} a^{3} - \\frac{366290339}{12380555} a^{2} + \\frac{1654968113}{12380555} a + \\frac{43714007}{538285} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/24761110*a^7 - 3574411/24761110*a^6 + 4788647/24761110*a^5 + 4801398/12380555*a^4 - 1041291/12380555*a^3 + 3359247/24761110*a^2 - 941209/24761110*a - 98961/1076570']}
Number field data - 8.4.498053903884848.1