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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-32, -28, -56, 0, -28, 7, 0, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 39846304512, 'disc_rad': 42, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1], [3, 1]]], [7, [0]], [11, [[4, 1], [3, 1]]], [13, [[7, 1]]], [17, [[3, 1], [2, 1], [1, 2]]], [19, [[7, 1]]], [23, [[3, 1], [2, 1], [1, 2]]], [29, [[5, 1], [2, 1]]], [31, [[5, 1], [1, 2]]], [37, [[7, 1]]], [41, [[4, 1], [3, 1]]], [43, [[7, 1]]], [47, [[5, 1], [2, 1]]], [53, [[4, 1], [3, 1]]], [59, [[3, 1], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [10920, 2520, 6240], 'galois_label': '7T7', 'galt': 7, 'grd': 86.51753627157204, 'index': 4, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '7.1.39846304512.3', 'local_algs': ['2.1.0.1', '2.1.0.1', '2.1.0.1', '2.4.8.8', '3.1.0.1', '3.6.3.2', '7.7.8.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 7], 'rd': 32.6844476444, 'regulator': {'__RealLiteral__': 0, 'data': '4481.27430614', 'prec': 44}, 'res': {'sib': ['-19872,119448,-1260,-244692,24360,393582,-336553,98913,-101731,133063,-93065,58849,-36841,20545,-9671,4263,-1645,553,-147,35,-7,1', '1728,1008,-1820,-1176,1764,3024,1666,72,-266,-84,7,0,-7,0,1', '1048576,7340032,9175040,-4128768,-630784,-1835008,-6322176,8663040,-19059712,16739072,6112064,-314944,2777600,-3738112,-928016,8917328,-18229456,15053808,-12049660,11676532,-7418068,3459008,-1875937,1035139,-435498,133686,-46193,30191,-14424,3388,-651,217,-42,14,-7,1', '4005072,27128304,81801216,9339120,-564346440,-1372895832,-126140336,5887003448,14919055956,19397799372,14107893408,2603184164,-6108584832,-8398161604,-4937669416,-420074620,4208304114,4972699942,5059236700,2823475886,2377354511,411000513,684763968,-175389865,166845714,-120202229,50651335,-40076540,15993431,-9451869,3940090,-1729329,735728,-259231,105595,-33302,11389,-3437,868,-231,42,-7,1', '40891968,-164197440,344765184,-498738240,548766400,-483831040,336004928,-164034112,36347120,22716304,-32309760,19894672,-5999392,-1093232,2575472,-1694208,559564,14756,-112784,60900,-16996,-416,2396,-716,273,-245,56,35,-16,-1,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{25} a^{6} + \\frac{1}{50} a^{5} + \\frac{1}{25} a^{4} - \\frac{1}{10} a^{3} - \\frac{4}{5} a^{2} - \\frac{16}{25} a - \\frac{11}{25} \\)', '\\( \\frac{27}{100} a^{6} + \\frac{81}{100} a^{5} + \\frac{57}{100} a^{4} - \\frac{207}{20} a^{3} + \\frac{11}{5} a^{2} - \\frac{951}{50} a - \\frac{153}{25} \\)', '\\( \\frac{7557}{100} a^{6} + \\frac{17491}{100} a^{5} + \\frac{98507}{100} a^{4} + \\frac{8839}{20} a^{3} + \\frac{9133}{5} a^{2} + \\frac{33119}{50} a + \\frac{16837}{25} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2', '1/2*a^4 - 1/2*a^2', '1/20*a^5 - 1/5*a^4 - 1/20*a^3 + 1/10*a^2 + 3/10*a - 2/5', '1/100*a^6 - 1/50*a^5 + 11/100*a^4 - 1/2*a^2 + 11/25*a - 4/25']}
Number field data - 7.1.39846304512.3