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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -4, 3, -3, 3, 0, -2, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 175748049, 'disc_rad': 1473, 'disc_sign': 1, 'frobs': [[2, [[7, 1]]], [3, [0]], [5, [[3, 2], [1, 1]]], [7, [[4, 1], [2, 1], [1, 1]]], [11, [[3, 2], [1, 1]]], [13, [[7, 1]]], [17, [[7, 1]]], [19, [[4, 1], [2, 1], [1, 1]]], [23, [[7, 1]]], [29, [[7, 1]]], [31, [[4, 1], [2, 1], [1, 1]]], [37, [[7, 1]]], [41, [[7, 1]]], [43, [[3, 2], [1, 1]]], [47, [[7, 1]]], [53, [[3, 2], [1, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [196, 84], 'galois_label': '7T5', 'galt': 5, 'grd': 79.83295592165204, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.3.175748049.1', 'local_algs': ['3.1.0.1', '3.3.3.1', '3.3.3.1', 'm491.1.1.0', 'm491.1.2.0', 'm491.2.1.1', 'm491.2.1.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 2, 'ramps': [3, 491], 'rd': 15.0605732182, 'regulator': {'__RealLiteral__': 0, 'data': '70.8696950957', 'prec': 44}, 'res': {'ae': ['3,-15,-6,4,5,0,-1,1'], 'sib': ['415,-1046,1303,-335,91,52,-11,-2,1', '-3645,2916,1458,-1188,-2889,-198,1557,864,-21,-162,-6,-22,6,0,1', '1,-3,15,-55,-93,1092,-1704,-1257,-759,-1455,204,-834,57,-303,-12,-3,-3,12,-1,-3,0,1', '1935,576,-1716,-1008,777,1116,-1164,342,362,-537,297,-120,30,-6,1', '1569537,5298372,17305731,117146898,-183660858,98589960,-368000010,710470035,-1016077608,1233219060,-1359447165,1381078674,-1277633160,724585383,324813618,-1383422889,1837282824,-1457273307,564134256,201520188,-481811304,345672583,-101038725,-38260998,53268110,-19964253,-2564376,5772756,-1689435,-620685,665271,-159963,-52752,43962,-6585,-4005,1917,36,-240,59,6,-6,1', '19239588,-6803712,44313345,-35355021,48754434,-57958683,46559536,-45397248,34412595,-22782830,15326244,-8429643,4096322,-1890747,744060,-232313,56610,-15132,3833,-69,-168,46,-9,-3,1', '462444547761,-2728106317980,1976151856878,-3193082614188,6488711644923,-12120205765305,17306399310949,-18738482071962,17341667681484,-15529157960157,13780593402882,-11323324509411,8336576679597,-5936644762068,4593905810898,-3846839588280,3112456175694,-2250082604253,1430581852710,-810989920740,418250107638,-198649897371,87109528755,-35298036744,13382430289,-4895926278,1783463055,-642547638,213513906,-57201891,8460459,1841088,-1837689,681741,-121878,-18060,24174,-11364,3726,-909,159,-18,1', '59049,295245,2302911,6530382,11687328,28659906,55918431,56835027,35645427,20801772,-15898923,-62825058,-66732795,-43670502,-17022447,8714529,17507340,14523534,4576275,-4895139,-1905684,2763800,2238885,-137631,-1193464,-305667,-81495,-132318,10125,-726,71424,36012,-17331,-3906,84,-1929,729,261,-114,19,6,-6,1', '6561,-32805,83106,-153090,207765,-196830,117450,21951,-166185,238167,-237294,158238,-43502,-42092,95331,-101783,77767,-49782,23872,-8435,1806,526,-539,249,-80,1,3,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{4} - a^{3} - a^{2} + 3 a \\)', '\\( \\frac{1}{3} a^{6} + 2 a - \\frac{1}{3} \\)', '\\( a^{6} - 2 a^{5} - a^{4} + 5 a^{3} - 2 a^{2} - 2 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3']}
Number field data - 7.3.175748049.1