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nf_fields • Show schema
{'class_group': [14], 'class_number': 14, 'cm': False, 'coeffs': [32400, 18360, 5544, 3114, 651, -231, -26, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 259403074940025, 'disc_rad': 1065, 'disc_sign': 1, 'frobs': [[2, [[2, 4]]], [3, [0]], [5, [0]], [7, [[2, 4]]], [11, [[2, 4]]], [13, [[2, 4]]], [17, [[4, 2]]], [19, [[1, 8]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[4, 2]]], [37, [[2, 2], [1, 4]]], [41, [[2, 4]]], [43, [[2, 2], [1, 4]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 8, 12], 'galois_label': '8T9', 'galt': 9, 'grd': 94.73040435062453, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '8.0.259403074940025.3', 'local_algs': ['3.1.2.1a1.1', '3.1.2.1a1.1', '3.2.2.2a1.2', '5.2.1.0a1.1', '5.2.1.0a1.1', '5.2.2.2a1.2', '71.2.4.6a1.2'], 'maximal_cm_subfield': [324, -18, -17, -1, 1], 'monogenic': -1, 'narrow_class_group': [14], 'narrow_class_number': 14, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 71], 'rd': 63.350039496, 'regulator': {'__RealLiteral__': 0, 'data': '10525.9475375', 'prec': 44}, 'res': {'gal': ['312111936,-75858336,149859168,-43510248,44991976,-14143074,7919193,-2129006,897467,-197564,72131,-12806,4275,-378,113,-4,1'], 'sib': ['53404,-53170,31067,-7946,1400,-304,50,-2,1', '549081,26676,28713,-4296,2038,-2,-33,-2,1', '57600,0,-38640,0,1369,0,-19,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1], 'subfields': ['18.-1.1', '1.-1.1', '-53.-1.1', '608.-36.37.-2.1', '180.102.27.-1.1', '324.-18.-17.-1.1'], 'torsion_gen': '\\( -\\frac{25747}{358197120} a^{7} + \\frac{54097}{358197120} a^{6} + \\frac{118553}{89549280} a^{5} + \\frac{1835519}{119399040} a^{4} - \\frac{6904849}{119399040} a^{3} - \\frac{33379}{310935} a^{2} - \\frac{2331119}{4974960} a - \\frac{155385}{331664} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{2213}{14924880} a^{7} - \\frac{8131}{14924880} a^{6} - \\frac{17819}{3731220} a^{5} - \\frac{271739}{14924880} a^{4} + \\frac{1037827}{4974960} a^{3} + \\frac{40136}{103645} a^{2} - \\frac{297319}{207290} a - \\frac{137225}{41458} \\)', '\\( \\frac{12796009}{358197120} a^{7} - \\frac{43751971}{358197120} a^{6} - \\frac{95881979}{89549280} a^{5} + \\frac{525145073}{39799680} a^{4} + \\frac{5584427107}{119399040} a^{3} + \\frac{26995897}{310935} a^{2} + \\frac{1233841973}{4974960} a + \\frac{125670555}{331664} \\)', '\\( \\frac{195228446489}{358197120} a^{7} - \\frac{491765544659}{358197120} a^{6} - \\frac{224001517199}{17909856} a^{5} - \\frac{2502264707321}{23879808} a^{4} + \\frac{61764362424979}{119399040} a^{3} + \\frac{309903219016}{310935} a^{2} + \\frac{282888232003}{331664} a + \\frac{3191437668091}{331664} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/6*a^4 + 1/3*a^3 - 1/3*a^2 - 1/2*a', '1/180*a^5 - 1/45*a^4 + 13/45*a^3 + 23/60*a^2 - 7/15*a', '1/180*a^6 + 1/30*a^4 + 37/180*a^3 + 2/5*a^2 - 11/30*a', '1/358197120*a^7 - 672811/358197120*a^6 + 18425/17909856*a^5 + 212917/7959936*a^4 + 4392019/13266560*a^3 + 49583/103645*a^2 - 350095/994992*a - 8045/331664']}
Number field data - 8.0.259403074940025.3