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nf_fields • Show schema
{'class_group': [7], 'class_number': 7, 'cm': False, 'coeffs': [4408, 70035, 49126, 9338, -406, -203, 0, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 3429038075724121, 'disc_rad': 203, 'disc_sign': 1, 'frobs': [[2, [[3, 2], [1, 1]]], [3, [[3, 2], [1, 1]]], [5, [[3, 2], [1, 1]]], [7, [0]], [11, [[3, 2], [1, 1]]], [13, [[7, 1]]], [17, [[3, 2], [1, 1]]], [19, [[3, 2], [1, 1]]], [23, [[3, 2], [1, 1]]], [29, [0]], [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': [26, 18], 'galois_label': '7T3', 'galt': 3, 'grd': 199.4324650301191, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.7.3429038075724121.1', 'local_algs': ['7.7.8.3', '29.7.6.3'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [7, 29], 'rd': 165.695353395, 'regulator': {'__RealLiteral__': 0, 'data': '165602.32598', 'prec': 40}, 'res': {'gal': ['-56000,1234800,352800,-91295281,-12627006,271187952,-25644220,-286617366,64582490,126945343,-28735854,-30067919,5030662,4037019,-367108,-288967,11116,10486,-112,-175,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2379}{22342} a^{6} - \\frac{4488}{11171} a^{5} - \\frac{225472}{11171} a^{4} + \\frac{360813}{11171} a^{3} + \\frac{19692165}{22342} a^{2} + \\frac{44249325}{22342} a + \\frac{1430505}{11171} \\)', '\\( \\frac{8401}{11171} a^{6} - \\frac{31035}{11171} a^{5} - \\frac{1590167}{11171} a^{4} + \\frac{2461316}{11171} a^{3} + \\frac{69244917}{11171} a^{2} + \\frac{157090793}{11171} a + \\frac{12886737}{11171} \\)', '\\( \\frac{879}{22342} a^{6} - \\frac{3077}{22342} a^{5} - \\frac{166433}{22342} a^{4} + \\frac{122101}{11171} a^{3} + \\frac{3594593}{11171} a^{2} + \\frac{16286347}{22342} a + \\frac{510375}{11171} \\)', '\\( \\frac{10059}{22342} a^{6} - \\frac{36051}{22342} a^{5} - \\frac{954267}{11171} a^{4} + \\frac{2783095}{22342} a^{3} + \\frac{41731498}{11171} a^{2} + \\frac{95803555}{11171} a + \\frac{7106745}{11171} \\)', '\\( \\frac{1139}{11171} a^{6} - \\frac{5369}{22342} a^{5} - \\frac{410495}{22342} a^{4} + \\frac{163561}{11171} a^{3} + \\frac{16188241}{22342} a^{2} + \\frac{19128590}{11171} a + \\frac{1949665}{11171} \\)', '\\( \\frac{37721}{11171} a^{6} - \\frac{280319}{22342} a^{5} - \\frac{14267517}{22342} a^{4} + \\frac{11211876}{11171} a^{3} + \\frac{620541613}{22342} a^{2} + \\frac{697725171}{11171} a + \\frac{44670795}{11171} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^3 - 1/2*a', '1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a', '1/22342*a^6 - 2469/22342*a^5 - 1804/11171*a^4 + 4459/22342*a^3 + 1751/11171*a^2 + 2179/11171*a + 390/11171']}
Number field data - 7.7.3429038075724121.1