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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [823, -4245, -4982, 264, 1125, 66, -62, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 151939915084881, 'disc_rad': 231, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [0]], [11, [0]], [13, [[4, 2]]], [17, [[2, 4]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[1, 8]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 59.252814612259755, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.8.151939915084881.1', 'local_algs': ['3.8.6.1', '7.8.6.1', '11.8.6.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 0, 'ramps': [3, 7, 11], 'rd': 59.2528146123, 'regulator': {'__RealLiteral__': 0, 'data': '17804.5169355', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-8.-1.1', '-5.-1.1', '-19.-1.1', '-17.37.-16.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2771541}{1176549949} a^{7} - \\frac{16553179}{1176549949} a^{6} - \\frac{1647377}{17560447} a^{5} + \\frac{445604385}{1176549949} a^{4} + \\frac{1329149119}{1176549949} a^{3} - \\frac{2001340842}{1176549949} a^{2} - \\frac{3233178638}{1176549949} a + \\frac{2176949433}{1176549949} \\)', '\\( \\frac{2693101}{1176549949} a^{7} - \\frac{14848940}{1176549949} a^{6} - \\frac{1946134}{17560447} a^{5} + \\frac{500451975}{1176549949} a^{4} + \\frac{1920269502}{1176549949} a^{3} - \\frac{4241339349}{1176549949} a^{2} - \\frac{6558418569}{1176549949} a + \\frac{8851520168}{1176549949} \\)', '\\( \\frac{3959654}{1176549949} a^{7} - \\frac{27322543}{1176549949} a^{6} - \\frac{1779362}{17560447} a^{5} + \\frac{662845719}{1176549949} a^{4} + \\frac{1035178530}{1176549949} a^{3} - \\frac{2581305324}{1176549949} a^{2} - \\frac{3026890050}{1176549949} a + \\frac{177640211}{1176549949} \\)', '\\( \\frac{13503205}{2353099898} a^{7} - \\frac{93962991}{2353099898} a^{6} - \\frac{6923015}{35120894} a^{5} + \\frac{1307546494}{1176549949} a^{4} + \\frac{2735552794}{1176549949} a^{3} - \\frac{14948424319}{2353099898} a^{2} - \\frac{21578417989}{2353099898} a + \\frac{4235520517}{2353099898} \\)', '\\( \\frac{10722247}{2353099898} a^{7} - \\frac{47611471}{2353099898} a^{6} - \\frac{8117281}{35120894} a^{5} + \\frac{573333521}{1176549949} a^{4} + \\frac{4363722758}{1176549949} a^{3} - \\frac{683271385}{2353099898} a^{2} - \\frac{37023523589}{2353099898} a - \\frac{32773732173}{2353099898} \\)', '\\( \\frac{1304995}{1176549949} a^{7} - \\frac{5179165}{1176549949} a^{6} - \\frac{1223016}{17560447} a^{5} + \\frac{163412763}{1176549949} a^{4} + \\frac{1702899392}{1176549949} a^{3} - \\frac{615930422}{1176549949} a^{2} - \\frac{11668686655}{1176549949} a - \\frac{11165147376}{1176549949} \\)', '\\( \\frac{4552052}{1176549949} a^{7} - \\frac{22524123}{1176549949} a^{6} - \\frac{3574695}{17560447} a^{5} + \\frac{721703225}{1176549949} a^{4} + \\frac{3967168669}{1176549949} a^{3} - \\frac{4584395722}{1176549949} a^{2} - \\frac{15912081091}{1176549949} a + \\frac{1951985211}{1176549949} \\)'], '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^3 - 1/2*a^2 - 1/2', '1/2353099898*a^7 + 407547641/2353099898*a^6 + 14549161/35120894*a^5 - 521753154/1176549949*a^4 - 402984125/1176549949*a^3 - 698086745/2353099898*a^2 - 219533267/2353099898*a - 199951589/2353099898']}
Number field data - 8.8.151939915084881.1