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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, -2, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2358310656, 'disc_rad': 18424302, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[7, 1], [1, 1]]], [7, [[8, 1]]], [11, [[8, 1]]], [13, [0]], [17, [[4, 1], [2, 1], [1, 2]]], [19, [[8, 1]]], [23, [[6, 1], [2, 1]]], [29, [[5, 1], [2, 1], [1, 1]]], [31, [[6, 1], [1, 2]]], [37, [[6, 1], [1, 2]]], [41, [[6, 1], [2, 1]]], [43, [[7, 1], [1, 1]]], [47, [[7, 1], [1, 1]]], [53, [[5, 1], [3, 1]]], [59, [[4, 1], [3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [44640, 20160, 20160, 20160], 'galois_label': '8T50', 'galt': 50, 'grd': 6538.283286871174, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.2358310656.1', 'local_algs': ['2.8.8.13', '3.2.1.1', '3.6.0.1', '13.1.0.1', '13.2.1.1', '13.5.0.1', 'm236209.2.1.1', 'm236209.1.3.0', 'm236209.1.3.0'], 'monogenic': 1, 'num_ram': 4, 'r2': 3, 'ramps': [2, 3, 13, 236209], 'rd': 14.844826519, 'regulator': {'__RealLiteral__': 0, 'data': '79.3019753896', 'prec': 44}, 'res': {'sib': ['-128,0,0,0,-64,-64,-64,-64,96,64,32,0,48,64,48,0,-24,-16,0,0,-12,-12,0,0,2,0,0,0,1', '1384,-12832,33960,15872,-209120,232224,602144,-486636,-143184,1561988,-900720,-3257920,1664320,3588900,-1597656,-2358276,1511248,739700,-1598776,304496,1304504,-535260,-713868,337304,261542,-128532,-64792,32240,10762,-5376,-1152,576,72,-36,-2,1', '483951511907897344,2003415893264386048,3322780145942829056,3031025177442318336,1943038587328210432,1039828044780407040,471033619510400256,138431126801535360,-5114074805575728,-27138235754836232,-11345078681858048,-833664708303872,951499728542464,331825372453120,-1182323741184,-23578733302464,-3789599960868,737994611072,261537374912,-4823186464,-9498901232,-446021912,220595380,17572018,-3493440,-315456,38352,2976,-276,-12,1', '9327198619670788772433208332467888530,-2194869748571740216267603175363786,1150115808889128065100015621066296,-36233354960647635944553546488,8459455449601345930467565932,594546909489722196249668,-86892463481431349253760,21000335822847964436,-6046847642785884969,-1497696489305302,52510967432384,1880760812,-544582830,-28196,4832,-8,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a^{7} - a^{6} + a^{5} + a^{3} - 3 \\)', '\\( a^{6} - a^{5} + a^{4} + a - 1 \\)', '\\( a^{7} - a^{6} + a^{5} - a^{3} + a^{2} - 2 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7']}
Number field data - 8.2.2358310656.1