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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [171, -189, 69, 27, -7, -7, -1, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 139012099200, 'disc_rad': 390, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[7, 1]]], [11, [[5, 1], [2, 1]]], [13, [0]], [17, [[7, 1]]], [19, [[3, 1], [2, 1], [1, 2]]], [23, [[4, 1], [2, 1], [1, 1]]], [29, [[4, 1], [1, 3]]], [31, [[4, 1], [2, 1], [1, 1]]], [37, [[6, 1], [1, 1]]], [41, [[2, 2], [1, 3]]], [43, [[4, 1], [3, 1]]], [47, [[3, 1], [2, 2]]], [53, [[6, 1], [1, 1]]], [59, [[4, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [10920, 2520, 3360, 4320], 'galois_label': '7T7', 'galt': 7, 'grd': 204.91836176274478, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.3.139012099200.1', 'local_algs': ['2.1.2.2a1.1', '2.1.2.3a1.2', '2.1.3.2a1.1', '3.3.1.0a1.1', '3.2.2.2a1.1', '5.1.1.0a1.1', '5.3.1.0a1.1', '5.1.3.2a1.1', '13.1.7.6a1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 4, 'r2': 2, 'ramps': [2, 3, 5, 13], 'rd': 39.0719113926, 'regulator': {'__RealLiteral__': 0, 'data': '7099.99680901', 'prec': 44}, 'res': {'sib': ['-11618128080000,0,100152839826000,0,-201154457579400,0,99906503103264,0,72037395516424,0,-81511429118080,0,-1226528170322,0,14926665922268,0,-2893018403938,0,-603563143527,0,176214210744,0,17911981202,0,-5151527160,0,-419098625,0,74226022,0,6627864,0,-706290,0,-74713,0,4940,0,986,0,52,0,1', '-236918292500,-577188090000,333515527500,-51333948000,-1810271618000,1269139538000,-350624841900,-1265727286000,609223804775,672341199220,544240392865,-524329008480,-573417062424,-281367731256,-292985224888,175646827104,-94292873388,151004278088,-62136542204,45255477296,-29818060224,10777828456,-5441655392,1834490272,158349466,-522692160,537337846,-404855104,249109512,-143321576,75746200,-35796064,15460936,-6143896,2202232,-703088,198720,-48600,9932,-1648,215,-20,1', '-311739088896,0,551297021952,0,-3006983458304,0,-1618471745280,0,-3928668288384,0,-5766185689792,0,-1797334070432,0,691839646576,0,373308236920,0,-18516144796,0,-27092903264,0,-685108348,0,1075442452,0,51117864,0,-26761462,0,-1503771,0,410600,0,26203,0,-3458,0,-253,0,12,0,1', '-4465280,-5126080,16577440,-29497872,32088348,-23711698,12204792,-5112810,1685676,-259112,-129910,79771,-20024,10823,-9526,3482,90,-486,144,-3,-6,1', '-512,0,7936,0,-9554,0,4260,0,-656,0,5,0,-4,0,1', '129873175968,-723525790144,1510542433520,-674400727944,-2966194802384,5518960465156,-1632889282024,-4905527178720,5144053798284,249907184772,-3130188606400,1303815146270,846892888792,-851231021116,42935212580,222333575628,-74781268136,-30153153484,23120792880,-2797794,-3977666810,908065722,354696520,-178944857,-6708074,17774074,-1933634,-1031643,242082,29936,-14408,183,450,-40,-6,1', '26241625408288,71320523999104,77643677382336,31823336974240,-27934345441424,-40272828520448,-6598066883528,12490345988176,5640808832920,-1649128792128,-1450278832324,5357198596,209062592987,33827633158,-18691284527,-6465457056,985863042,722718572,-10204396,-56927964,-3300914,3088220,312668,-63672,-23160,-3648,1690,168,-43,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{40} a^{6} - \\frac{2}{15} a^{5} - \\frac{1}{24} a^{4} + \\frac{47}{60} a^{3} - \\frac{113}{120} a^{2} + \\frac{1}{4} a + \\frac{21}{40} \\)', '\\( \\frac{19}{30} a^{6} - \\frac{13}{30} a^{5} - \\frac{29}{6} a^{4} - \\frac{74}{15} a^{3} + \\frac{217}{10} a^{2} + \\frac{119}{2} a - \\frac{1177}{10} \\)', '\\( \\frac{113}{240} a^{6} + \\frac{1}{60} a^{5} - \\frac{175}{48} a^{4} - \\frac{883}{120} a^{3} + \\frac{639}{80} a^{2} + \\frac{389}{8} a - \\frac{3229}{80} \\)', '\\( \\frac{1}{24} a^{6} + \\frac{1}{6} a^{5} - \\frac{13}{8} a^{4} + \\frac{3}{4} a^{3} + \\frac{13}{24} a^{2} + \\frac{105}{4} a - \\frac{345}{8} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^4 - 1/2', '1/12*a^5 - 1/12*a^4 + 1/6*a^3 - 1/3*a^2 - 1/4*a - 1/4', '1/240*a^6 + 1/30*a^5 - 11/48*a^4 - 11/120*a^3 + 23/80*a^2 - 1/8*a - 33/80']}
Number field data - 7.3.139012099200.1