-
nf_fields • Show schema
Hide schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-1, -1, 8, 22, 0, 10, -6, 4, -1, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 78066229248, 'disc_rad': 42, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 1], [3, 1]]], [7, [0]], [11, [[6, 1], [3, 1]]], [13, [[6, 1], [3, 1]]], [17, [[2, 4], [1, 1]]], [19, [[6, 1], [3, 1]]], [23, [[2, 4], [1, 1]]], [29, [[6, 1], [3, 1]]], [31, [[3, 3]]], [37, [[6, 1], [3, 1]]], [41, [[2, 4], [1, 1]]], [43, [[6, 1], [3, 1]]], [47, [[2, 4], [1, 1]]], [53, [[6, 1], [3, 1]]], [59, [[6, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [66, 18, 24], 'galois_label': '9T8', 'galt': 8, 'grd': 22.58643281430495, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '9.1.78066229248.1', 'local_algs': ['2.3.2.1', '2.6.11.5', '3.1.0.1', '3.2.1.1', '3.2.1.2', '3.4.2.1', '7.9.6.1'], 'minimal_sibling': [1, 2, -3, 0, 3, -2, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 7], 'rd': 16.2283247223, 'regulator': {'__RealLiteral__': 0, 'data': '142.481756164', 'prec': 44}, 'res': {'sib': ['-8,0,-32,0,80,0,428,0,-408,0,60,0,50,0,-16,0,-2,0,1', '1,1,9,36,86,166,506,-158,-181,299,-3,-74,40,-4,0,8,-3,-1,1', '1,2,-3,0,3,-2,1', '1,2,7,-6,6,-14,15,-10,12,-6,1,-2,1', '6,12,34,-8,94,-40,55,112,-210,248,-153,-16,180,-212,175,-88,34,-8,1']}, 'subfield_mults': [1, 1], 'subfields': ['-6.-2.-1.1', '1.5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{1}{102} a^{8} + \\frac{7}{102} a^{7} + \\frac{3}{34} a^{6} + \\frac{5}{34} a^{5} - \\frac{23}{102} a^{4} + \\frac{71}{102} a^{3} + \\frac{29}{102} a^{2} + \\frac{131}{34} a + \\frac{16}{51} \\)', '\\( \\frac{1}{2} a^{8} - \\frac{5}{6} a^{7} + \\frac{5}{2} a^{6} - \\frac{9}{2} a^{5} + \\frac{15}{2} a^{4} - \\frac{23}{6} a^{3} + \\frac{73}{6} a^{2} - \\frac{11}{6} a - \\frac{2}{3} \\)', '\\( \\frac{41}{102} a^{8} - \\frac{19}{102} a^{7} + \\frac{55}{34} a^{6} - \\frac{67}{34} a^{5} + \\frac{383}{102} a^{4} + \\frac{55}{102} a^{3} + \\frac{1087}{102} a^{2} + \\frac{271}{34} a + \\frac{95}{51} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/6*a^7 - 1/2*a^5 + 1/6*a^3 - 1/3*a^2 + 1/6*a + 1/3', '1/102*a^8 + 7/102*a^7 + 3/34*a^6 + 5/34*a^5 - 23/102*a^4 - 31/102*a^3 + 29/102*a^2 - 5/34*a + 16/51']}