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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-96360, -74536, 0, 6776, 0, -154, 0, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 32027016613996096, 'disc_rad': 154, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 2], [1, 1]]], [5, [[3, 2], [1, 1]]], [7, [0]], [11, [0]], [13, [[7, 1]]], [17, [[3, 2], [1, 1]]], [19, [[3, 2], [1, 1]]], [23, [[3, 2], [1, 1]]], [29, [[7, 1]]], [31, [[3, 2], [1, 1]]], [37, [[3, 2], [1, 1]]], [41, [[7, 1]]], [43, [[7, 1]]], [47, [[3, 2], [1, 1]]], [53, [[3, 2], [1, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 32, 18], 'galois_label': '7T3', 'galt': 3, 'grd': 274.42043856096353, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 4, 'label': '7.7.32027016613996096.4', 'local_algs': ['2.7.6.1', '7.7.10.3', '11.7.6.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 0, 'ramps': [2, 7, 11], 'rd': 227.997941756, 'regulator': {'__RealLiteral__': 0, 'data': '2396810.65353', 'prec': 44}, 'res': {'gal': ['805565125,-121575388550,-359725843575,-104842778481,339974339453,184714810784,-113898240232,-81302376703,15925250054,16279999729,-737532649,-1718052693,-31781988,100699536,4224345,-3286052,-136780,56987,1638,-441,-7,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{452} a^{6} - \\frac{11}{452} a^{5} - \\frac{37}{226} a^{4} + \\frac{253}{113} a^{3} + \\frac{115}{113} a^{2} - \\frac{3201}{113} a - \\frac{4463}{113} \\)', '\\( \\frac{1}{226} a^{6} + \\frac{11}{452} a^{5} - \\frac{1}{2} a^{4} - \\frac{627}{226} a^{3} + \\frac{1153}{113} a^{2} + \\frac{6512}{113} a + \\frac{6751}{113} \\)', '\\( \\frac{12}{113} a^{6} - \\frac{41}{226} a^{5} - \\frac{3619}{226} a^{4} + \\frac{3093}{113} a^{3} + \\frac{75600}{113} a^{2} - \\frac{129842}{113} a - \\frac{661823}{113} \\)', '\\( \\frac{1}{226} a^{6} - \\frac{13}{226} a^{5} - \\frac{145}{226} a^{4} + \\frac{1451}{226} a^{3} + \\frac{3546}{113} a^{2} - \\frac{17744}{113} a - \\frac{51851}{113} \\)', '\\( \\frac{139}{226} a^{6} - \\frac{2393}{452} a^{5} - \\frac{11119}{226} a^{4} + \\frac{47869}{113} a^{3} + \\frac{59302}{113} a^{2} - \\frac{511740}{113} a - \\frac{777851}{113} \\)', '\\( \\frac{53}{452} a^{6} + \\frac{122}{113} a^{5} - \\frac{907}{113} a^{4} - \\frac{16009}{226} a^{3} + \\frac{14776}{113} a^{2} + \\frac{112821}{113} a + \\frac{119287}{113} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/226*a^4 - 19/226*a^3 - 44/113*a^2 - 51/113*a + 32/113', '1/452*a^5 - 55/226*a^3 - 48/113*a^2 + 40/113*a - 35/113', '1/452*a^6 - 11/226*a^3 - 7/113*a^2 - 15/113*a - 48/113']}
Number field data - 7.7.32027016613996096.4