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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [961, 868, 58, -239, -65, 31, -2, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 136744453125, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[8, 1]]], [3, [0]], [5, [0]], [7, [0]], [11, [[4, 2]]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [[4, 2]]], [23, [[8, 1]]], [29, [[2, 2], [1, 4]]], [31, [[1, 8]]], [37, [[8, 1]]], [41, [[4, 2]]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[8, 1]]], [59, [[2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 14, 8], 'galois_label': '8T7', 'galt': 7, 'grd': 24.659752579382083, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.4.136744453125.1', 'local_algs': ['3.8.6.3', '5.8.7.1', '7.8.4.2'], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [3, 5, 7], 'rd': 24.6597525794, 'regulator': {'__RealLiteral__': 0, 'data': '165.382367822', 'prec': 44}, 'res': {'gal': ['7921,-93450,780201,-476065,610382,-277215,223233,-82410,49455,-14680,6972,-1680,657,-125,39,-5,1']}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.4.-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{385}{161913} a^{7} - \\frac{1607}{161913} a^{6} + \\frac{1462}{161913} a^{5} + \\frac{391}{5223} a^{4} - \\frac{17032}{53971} a^{3} - \\frac{2239}{161913} a^{2} + \\frac{144532}{161913} a + \\frac{8327}{5223} \\)', '\\( \\frac{9473}{4695477} a^{7} + \\frac{1010}{161913} a^{6} - \\frac{21643}{4695477} a^{5} + \\frac{6419}{151467} a^{4} + \\frac{1212542}{4695477} a^{3} - \\frac{110968}{161913} a^{2} - \\frac{350450}{161913} a + \\frac{10163}{50489} \\)', '\\( \\frac{47065}{4695477} a^{7} - \\frac{969}{53971} a^{6} + \\frac{113539}{4695477} a^{5} + \\frac{41965}{151467} a^{4} - \\frac{2595217}{4695477} a^{3} - \\frac{184838}{161913} a^{2} - \\frac{120979}{161913} a + \\frac{208135}{151467} \\)', '\\( \\frac{14806}{1565159} a^{7} - \\frac{10328}{161913} a^{6} + \\frac{199633}{1565159} a^{5} - \\frac{2423}{50489} a^{4} - \\frac{4949755}{4695477} a^{3} - \\frac{5681}{53971} a^{2} + \\frac{233034}{53971} a + \\frac{1024319}{151467} \\)', '\\( \\frac{309698}{4695477} a^{7} - \\frac{37223}{161913} a^{6} + \\frac{1093199}{4695477} a^{5} + \\frac{252061}{151467} a^{4} - \\frac{31564286}{4695477} a^{3} - \\frac{824047}{161913} a^{2} + \\frac{551113}{53971} a + \\frac{1990345}{50489} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a^3 - 1/3*a + 1/3', '1/3*a^5 - 1/3*a^3 - 1/3*a^2 + 1/3', '1/3*a^6 + 1/3*a^3 + 1/3', '1/4695477*a^7 - 4009/53971*a^6 + 10188/1565159*a^5 + 1672/50489*a^4 - 1291091/4695477*a^3 - 26677/53971*a^2 - 77219/161913*a + 68816/151467']}
Number field data - 8.4.136744453125.1