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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1832, -2244, 3528, -1063, -654, 314, 40, -25, -2, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 44869371487471, 'disc_rad': 6107, 'disc_sign': -1, 'frobs': [[2, [[3, 3]]], [3, [[6, 1], [3, 1]]], [5, [[3, 3]]], [7, [[3, 3]]], [11, [[2, 3], [1, 3]]], [13, [[2, 3], [1, 3]]], [17, [[2, 3], [1, 3]]], [19, [[3, 3]]], [23, [[6, 1], [3, 1]]], [29, [[6, 1], [3, 1]]], [31, [0]], [37, [[6, 1], [3, 1]]], [41, [[3, 3]]], [43, [[6, 1], [3, 1]]], [47, [[3, 3]]], [53, [[6, 1], [3, 1]]], [59, [[3, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [27, 36], 'galois_label': '9T12', 'galt': 12, 'grd': 188.50592172874553, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.3.44869371487471.1', 'local_algs': ['31.3.1.0a1.1', '31.3.2.3a1.2', '197.3.1.0a1.1', '197.2.3.4a1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 3, 'ramps': [31, 197], 'rd': 32.8763300542, 'regulator': {'__RealLiteral__': 0, 'data': '3111.74669351', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{779}{7809828} a^{8} - \\frac{7431}{6508190} a^{7} - \\frac{211531}{39049140} a^{6} + \\frac{152553}{6508190} a^{5} + \\frac{977954}{9762285} a^{4} - \\frac{301139}{1301638} a^{3} - \\frac{20648323}{39049140} a^{2} + \\frac{603540}{650819} a - \\frac{564566}{3254095} \\)', '\\( \\frac{15638}{9762285} a^{8} + \\frac{21519}{6508190} a^{7} - \\frac{137563}{3904914} a^{6} - \\frac{433887}{6508190} a^{5} + \\frac{1212347}{3254095} a^{4} + \\frac{197059}{650819} a^{3} - \\frac{11231097}{6508190} a^{2} + \\frac{4819641}{3254095} a + \\frac{10423637}{9762285} \\)', '\\( \\frac{526531}{214770270} a^{8} - \\frac{824371}{107385135} a^{7} - \\frac{457167}{14318018} a^{6} + \\frac{12418711}{107385135} a^{5} + \\frac{5437607}{19524570} a^{4} - \\frac{389985841}{214770270} a^{3} + \\frac{596713969}{214770270} a^{2} - \\frac{214084861}{214770270} a - \\frac{23601430}{21477027} \\)', '\\( \\frac{1465787}{33041580} a^{8} - \\frac{1828249}{16520790} a^{7} - \\frac{52824757}{33041580} a^{6} + \\frac{5403367}{16520790} a^{5} + \\frac{9634401}{500630} a^{4} - \\frac{6555275}{1652079} a^{3} - \\frac{666693671}{11013860} a^{2} + \\frac{789529688}{8260395} a + \\frac{257480816}{8260395} \\)', '\\( \\frac{486341}{429540540} a^{8} + \\frac{762101}{71590090} a^{7} - \\frac{58163987}{429540540} a^{6} + \\frac{8795004}{35795045} a^{5} + \\frac{19066207}{19524570} a^{4} - \\frac{243003411}{71590090} a^{3} + \\frac{292881763}{429540540} a^{2} + \\frac{558977609}{71590090} a - \\frac{351120152}{35795045} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^3 - 1/2*a', '1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a', '1/30*a^6 - 1/5*a^5 - 1/30*a^4 - 3/10*a^3 - 7/30*a^2 + 2/5*a - 2/15', '1/30*a^7 - 7/30*a^5 + 7/15*a^3 - 7/30*a + 1/5', '1/429540540*a^8 + 338941/107385135*a^7 - 1820529/143180180*a^6 - 49793969/214770270*a^5 - 421669/9762285*a^4 - 30866026/107385135*a^3 + 6098863/429540540*a^2 + 16487329/214770270*a - 21626674/107385135']}
Number field data - 9.3.44869371487471.1