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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 8, -4, 0, -2, 0, 4, -4, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 708837376, 'disc_rad': 26, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 1], [2, 1]]], [5, [[6, 1], [2, 1]]], [7, [[3, 2], [1, 2]]], [11, [[4, 2]]], [13, [0]], [17, [[3, 2], [1, 2]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[6, 1], [2, 1]]], [41, [[4, 2]]], [43, [[6, 1], [2, 1]]], [47, [[3, 2], [1, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [132, 24], 'galois_label': '8T24', 'galt': 24, 'grd': 24.255161140409015, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.4.708837376.1', 'local_algs': ['2.1.8.22d1.22', '13.2.1.0a1.1', '13.2.1.0a1.1', '13.2.2.2a1.2'], 'minimal_sibling': [-2, 0, -1, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 2, 'ramps': [2, 13], 'rd': 12.7737474703, 'regulator': {'__RealLiteral__': 0, 'data': '42.9351678954', 'prec': 44}, 'res': {'sib': ['-2,0,-1,0,0,0,1', '4,10,14,8,2,-1,1', '-2,-8,-8,4,11,8,-10,-20,-18,-8,-2,0,1', '-2,8,4,24,-138,0,-176,980,-759,1572,-1064,1636,438,1252,-32,348,-92,-12,-76,-12,0,-4,0,0,1', '14,-48,82,-48,19,-4,4,-4,1', '16,-96,236,-300,182,16,-120,100,-34,-8,14,-6,1', '16,0,-80,0,172,0,376,0,-420,0,28,0,703,0,-762,0,543,0,-184,0,25,0,-2,0,1', '16,0,80,0,276,0,496,0,1004,0,1472,0,1304,0,744,0,312,0,108,0,33,0,8,0,1', '169,0,-468,0,688,0,-588,0,358,0,-124,0,32,0,-4,0,1', '368,176,44,-408,-138,8,128,32,-2,-16,-2,0,1', '4,-8,14,4,-12,16,3,-22,11,12,-5,-2,1', '4,0,-32,0,36,0,-28,0,17,0,-6,0,1', '4,0,8,0,20,0,12,0,25,0,-8,0,1', '64,0,-528,0,2774,0,-7058,0,9929,0,-8184,0,4120,0,-1148,0,238,0,-8,0,10,0,-2,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '1.-4.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{37}{79} a^{7} - \\frac{133}{79} a^{6} + \\frac{77}{79} a^{5} + \\frac{91}{79} a^{4} - \\frac{67}{79} a^{3} - \\frac{72}{79} a^{2} - \\frac{111}{79} a + \\frac{251}{79} \\)', '\\( \\frac{11}{79} a^{7} - \\frac{31}{79} a^{6} - \\frac{7}{79} a^{5} + \\frac{42}{79} a^{4} - \\frac{37}{79} a^{3} + \\frac{64}{79} a^{2} - \\frac{33}{79} a + \\frac{49}{79} \\)', '\\( a - 1 \\)', '\\( \\frac{36}{79} a^{7} - \\frac{123}{79} a^{6} + \\frac{92}{79} a^{5} + \\frac{1}{79} a^{4} - \\frac{78}{79} a^{3} - \\frac{6}{79} a^{2} - \\frac{108}{79} a + \\frac{225}{79} \\)', '\\( \\frac{11}{79} a^{7} - \\frac{31}{79} a^{6} - \\frac{7}{79} a^{5} + \\frac{42}{79} a^{4} + \\frac{42}{79} a^{3} - \\frac{94}{79} a^{2} - \\frac{112}{79} a + \\frac{49}{79} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/79*a^7 - 10/79*a^6 - 15/79*a^5 + 11/79*a^4 + 11/79*a^3 + 13/79*a^2 - 3/79*a + 26/79']}
Number field data - 8.4.708837376.1