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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, -8, -13, -1, 6, -2, -1, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 185868496, 'disc_rad': 23233562, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[7, 1]]], [5, [[7, 1]]], [7, [[7, 1]]], [11, [0]], [13, [[6, 1], [1, 1]]], [17, [[7, 1]]], [19, [[6, 1], [1, 1]]], [23, [[4, 1], [3, 1]]], [29, [[6, 1], [1, 1]]], [31, [[6, 1], [1, 1]]], [37, [[4, 1], [3, 1]]], [41, [[3, 2], [1, 1]]], [43, [[4, 1], [3, 1]]], [47, [[6, 1], [1, 1]]], [53, [[5, 1], [1, 2]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [4032, 2520, 2520], 'galois_label': '7T7', 'galt': 7, 'grd': 5934.264471899315, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.3.185868496.1', 'local_algs': ['2.1.0.1', '2.1.0.1', '2.5.4.1', '11.2.1.1', '11.5.0.1', 'm1056071.1.1.0', 'm1056071.2.1.1', 'm1056071.1.4.0'], 'monogenic': -1, 'num_ram': 3, 'r2': 2, 'ramps': [2, 11, 1056071], 'rd': 15.1815149683, 'regulator': {'__RealLiteral__': 0, 'data': '136.44614483095134', 'prec': 60}, 'res': {'sib': ['-14992,32188,46728,-123764,49808,4708,-30294,26822,-14186,-5262,11124,-4199,306,877,-1150,344,110,-140,48,5,-6,1', '-51635305583979211924418409279019,36151372819536007708301757108,17507634214177070597148432976,-6037398891553588387177566,-873540249335220057681776,9004705512001922304,23517937802230287273,-1112120153060490,-1132755150533869,-51458741856,1103187130,-26136,-97908,0,1', '-62243072,76547360,390887248,-760111936,1705908032,-939412224,-8837887344,17704159248,-25704745768,28152117280,6259758192,-5588387216,-90914210948,122939115572,-14214985992,-56061087780,22706524196,5396005836,2957193634,-9361168930,6303342596,-2801357222,1349108017,-862700196,133439468,401364436,-202414379,-102939732,87945884,9400624,-19883794,686860,3067756,-395012,-317592,62406,22484,-5870,-999,364,12,-12,1', '87608944,-426825232,1198939888,-1961162128,1844315056,-482751040,-1328059536,2649896176,-4111489424,4888795120,-3914587948,2561661852,-1473473864,481921960,174618088,-374828604,279396664,-131916888,44851544,-8165544,-3992921,4304247,-1935849,902535,-577749,269211,-73917,10635,4849,-6703,3153,-459,-163,85,-15,1', '9720617164690351214848,-7461528975191336300544,-5351732218155893217024,6625165628651221836544,-902897919648775213824,-1109076342156362523008,466992849774305684416,-41026379602470957952,-1984523064635118592,-2093534328072623616,328803701578758224,77052973391523552,-5909832194569488,208418430325152,-174169871965904,63314620071536,-759934137088,180662882784,-41555827552,4834745808,2580256012,-80684432,27176156,-4454672,876936,-30132,9104,-768,84,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{8} a^{6} - \\frac{3}{8} a^{5} + \\frac{1}{2} a^{4} + \\frac{3}{4} a^{3} - \\frac{13}{8} a^{2} - \\frac{3}{8} a - \\frac{1}{4} \\)', '\\( \\frac{1}{8} a^{6} - \\frac{3}{8} a^{5} + \\frac{1}{2} a^{4} - \\frac{1}{4} a^{3} - \\frac{5}{8} a^{2} - \\frac{3}{8} a - \\frac{1}{4} \\)', '\\( \\frac{1}{8} a^{6} - \\frac{3}{8} a^{5} + \\frac{1}{2} a^{4} - \\frac{1}{4} a^{3} - \\frac{5}{8} a^{2} + \\frac{13}{8} a - \\frac{9}{4} \\)', '\\( 2 a^{6} - 5 a^{5} + 3 a^{4} + 8 a^{3} - 13 a^{2} - 7 a - 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/16*a^6 + 5/16*a^5 - 1/4*a^4 - 1/8*a^3 + 3/16*a^2 + 5/16*a + 3/8']}
Number field data - 7.3.185868496.1