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nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-296, -432, 216, 420, 144, 0, -36, -18, 0, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 74310349154112, 'disc_rad': 222, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 1], [3, 1]]], [7, [[9, 1]]], [11, [[9, 1]]], [13, [[6, 1], [3, 1]]], [17, [[3, 2], [2, 1], [1, 1]]], [19, [[2, 3], [1, 3]]], [23, [[6, 1], [3, 1]]], [29, [[6, 1], [3, 1]]], [31, [[6, 1], [3, 1]]], [37, [0]], [41, [[9, 1]]], [43, [[6, 1], [3, 1]]], [47, [[9, 1]]], [53, [[2, 2], [1, 5]]], [59, [[6, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [432, 1584, 324], 'galois_label': '9T28', 'galt': 28, 'grd': 141.6067404717884, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.5.74310349154112.1', 'local_algs': ['2.9.6.1', '3.9.22.6', '37.1.0.1', '37.1.0.1', '37.2.0.1', '37.2.1.2', '37.3.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 37], 'rd': 34.7718422118, 'regulator': {'__RealLiteral__': 0, 'data': '1539.48699795', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{12015}{7278772} a^{8} + \\frac{23649}{3639386} a^{7} - \\frac{284971}{7278772} a^{6} - \\frac{574533}{3639386} a^{5} - \\frac{262077}{3639386} a^{4} + \\frac{1009719}{3639386} a^{3} + \\frac{1875024}{1819693} a^{2} + \\frac{2971653}{1819693} a - \\frac{1460872}{1819693} \\)', '\\( \\frac{15687}{7278772} a^{8} - \\frac{42729}{3639386} a^{7} - \\frac{118533}{7278772} a^{6} + \\frac{158580}{1819693} a^{5} + \\frac{154005}{1819693} a^{4} + \\frac{366776}{1819693} a^{3} - \\frac{385749}{1819693} a^{2} - \\frac{2707854}{1819693} a + \\frac{1830186}{1819693} \\)', '\\( \\frac{69771}{7278772} a^{8} - \\frac{78375}{7278772} a^{7} - \\frac{1080519}{7278772} a^{6} - \\frac{312585}{1819693} a^{5} + \\frac{43951}{1819693} a^{4} + \\frac{1666108}{1819693} a^{3} + \\frac{3940701}{1819693} a^{2} - \\frac{2636221}{1819693} a - \\frac{2991024}{1819693} \\)', '\\( \\frac{44220}{1819693} a^{8} - \\frac{64461}{1819693} a^{7} - \\frac{2888957}{7278772} a^{6} - \\frac{466960}{1819693} a^{5} + \\frac{885635}{1819693} a^{4} + \\frac{4897036}{1819693} a^{3} + \\frac{10449165}{1819693} a^{2} - \\frac{6229331}{1819693} a - \\frac{8334610}{1819693} \\)', '\\( \\frac{360061}{7278772} a^{8} - \\frac{339039}{3639386} a^{7} - \\frac{5515109}{7278772} a^{6} - \\frac{608179}{1819693} a^{5} + \\frac{4703647}{3639386} a^{4} + \\frac{21777883}{3639386} a^{3} + \\frac{18682529}{1819693} a^{2} - \\frac{22310015}{1819693} a - \\frac{21623892}{1819693} \\)', '\\( \\frac{13335}{7278772} a^{8} - \\frac{36105}{7278772} a^{7} - \\frac{129993}{7278772} a^{6} - \\frac{146949}{3639386} a^{5} + \\frac{49897}{3639386} a^{4} + \\frac{1897597}{3639386} a^{3} + \\frac{2346817}{1819693} a^{2} - \\frac{211768}{1819693} a - \\frac{3179806}{1819693} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/2*a^4', '1/2*a^5', '1/4*a^6', '1/4*a^7', '1/7278772*a^8 + 814663/7278772*a^7 - 201929/1819693*a^6 - 198350/1819693*a^5 + 332350/1819693*a^4 + 433539/3639386*a^3 - 745441/1819693*a^2 - 695825/1819693*a + 602505/1819693']}
Number field data - 9.5.74310349154112.1