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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-1376, -2352, -1992, -1020, -44, 72, -14, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 99714188227072, 'disc_rad': 82, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [[4, 1], [2, 2]]], [7, [[4, 1], [2, 2]]], [11, [[4, 2]]], [13, [[2, 4]]], [17, [[8, 1]]], [19, [[4, 2]]], [23, [[4, 1], [2, 1], [1, 2]]], [29, [[2, 4]]], [31, [[4, 1], [2, 1], [1, 2]]], [37, [[4, 1], [1, 4]]], [41, [0]], [43, [[2, 3], [1, 2]]], [47, [[4, 1], [2, 2]]], [53, [[4, 2]]], [59, [[4, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [256, 112], 'galois_label': '8T35', 'galt': 35, 'grd': 103.09696152933505, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.4.99714188227072.1', 'local_algs': ['2.1.1.0a1.1', '2.1.1.0a1.1', '2.1.2.3a1.1', '2.1.2.3a1.1', '2.1.2.3a1.3', '41.1.8.7a1.7'], 'monogenic': -1, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 2, 'r2': 2, 'ramps': [2, 41], 'rd': 56.214016881, 'regulator': {'__RealLiteral__': 0, 'data': '108013.947264', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-10.-1.1', '-86.-59.-15.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{4143}{440336} a^{7} - \\frac{14231}{440336} a^{6} - \\frac{11671}{110084} a^{5} + \\frac{64817}{110084} a^{4} - \\frac{121261}{110084} a^{3} - \\frac{731329}{110084} a^{2} - \\frac{211994}{27521} a - \\frac{254790}{27521} \\)', '\\( \\frac{671}{440336} a^{7} - \\frac{1893}{440336} a^{6} - \\frac{1719}{55042} a^{5} + \\frac{22065}{220168} a^{4} + \\frac{13787}{110084} a^{3} - \\frac{78311}{55042} a^{2} - \\frac{97494}{27521} a - \\frac{73171}{27521} \\)', '\\( \\frac{3387}{440336} a^{7} - \\frac{25305}{440336} a^{6} + \\frac{1137}{27521} a^{5} + \\frac{187665}{220168} a^{4} - \\frac{352861}{110084} a^{3} - \\frac{167821}{55042} a^{2} + \\frac{392654}{27521} a + \\frac{394435}{27521} \\)', '\\( \\frac{96125}{27521} a^{7} - \\frac{6381449}{440336} a^{6} - \\frac{14216749}{440336} a^{5} + \\frac{31787937}{110084} a^{4} - \\frac{106801377}{220168} a^{3} - \\frac{331235061}{110084} a^{2} - \\frac{96159027}{27521} a - \\frac{114442279}{27521} \\)', '\\( \\frac{234505}{440336} a^{7} - \\frac{1207321}{440336} a^{6} - \\frac{37334}{27521} a^{5} + \\frac{1135896}{27521} a^{4} - \\frac{12399613}{110084} a^{3} - \\frac{31587745}{110084} a^{2} - \\frac{11443128}{27521} a - \\frac{9242514}{27521} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2', '1/4*a^4 - 1/4*a^3 - 1/2*a^2 - 1/2*a', '1/16*a^5 - 1/16*a^4 - 1/8*a^3 - 3/8*a^2 - 1/2*a - 1/2', '1/32*a^6 - 1/32*a^5 - 1/16*a^4 - 3/16*a^3 + 1/4*a^2 - 1/4*a', '1/880672*a^7 - 495/880672*a^6 + 11679/440336*a^5 + 16689/220168*a^4 - 18631/110084*a^3 - 106421/220168*a^2 - 12049/27521*a + 22039/55042']}
Number field data - 8.4.99714188227072.1