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nf_fields • Show schema
{'class_group': [5, 5], 'class_number': 25, 'cm': True, 'coeffs': [21103, 13522, 1439, 76, 704, -20, 41, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 698538609674161, 'disc_rad': 5141, 'disc_sign': 1, 'frobs': [[2, [[2, 4]]], [3, [[2, 4]]], [5, [[4, 2]]], [7, [[2, 4]]], [11, [[2, 4]]], [13, [[2, 4]]], [17, [[2, 4]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[2, 4]]], [37, [[2, 4]]], [41, [[4, 2]]], [43, [[1, 8]]], [47, [[1, 8]]], [53, [0]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '8T4', 'galt': 4, 'grd': 71.7007670809734, 'inessentialp': [2, 3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.0.698538609674161.2', 'local_algs': ['53.2.1.1', '53.2.1.1', '53.2.1.1', '53.2.1.1', '97.4.2.1', '97.4.2.1'], 'minimal_sibling': [36, -6, -1, -1, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [53, 97], 'rd': 71.700767081, 'regulator': {'__RealLiteral__': 0, 'data': '1501.69967042', 'prec': 44}, 'relative_class_number': 25, 'res': {'sib': ['36,-6,-1,-1,1', '6,-11,12,-2,1']}, 'subfield_mults': [1, 1, 1, 1, 2, 2], 'subfields': ['-1285.-1.1', '-13.-1.1', '-24.-1.1', '121.0.-75.0.1', '36.-6.-1.-1.1', '6.-11.12.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{36965}{155064192} a^{7} - \\frac{21701}{155064192} a^{6} + \\frac{153889}{19383024} a^{5} + \\frac{303529}{38766048} a^{4} + \\frac{5448665}{38766048} a^{3} + \\frac{797111}{4845756} a^{2} - \\frac{76272229}{155064192} a - \\frac{130283051}{155064192} \\)', '\\( \\frac{4897479}{34165810304} a^{7} - \\frac{90384455}{34165810304} a^{6} - \\frac{25485}{4270726288} a^{5} - \\frac{894820397}{8541452576} a^{4} - \\frac{1951693277}{8541452576} a^{3} - \\frac{2235517145}{1067681572} a^{2} - \\frac{217254492103}{34165810304} a - \\frac{222443701257}{34165810304} \\)', '\\( \\frac{90471}{1615252} a^{7} - \\frac{1557353}{1615252} a^{6} + \\frac{1070289}{403813} a^{5} - \\frac{8065006}{403813} a^{4} + \\frac{1338857}{403813} a^{3} + \\frac{135991}{403813} a^{2} - \\frac{525489139}{1615252} a - \\frac{955208755}{1615252} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2', '1/2*a^4 - 1/2*a', '1/2*a^5 - 1/2*a^2', '1/4*a^6 - 1/4', '1/102497430912*a^7 + 11004950591/102497430912*a^6 + 273689981/12812178864*a^5 - 2209408315/25624357728*a^4 + 3949753381/25624357728*a^3 + 955479019/3203044716*a^2 - 17929435073/102497430912*a - 34555326703/102497430912']}
Number field data - 8.0.698538609674161.2