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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [56, -56, 0, 28, 12, 4, -8, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 567647723776, 'disc_rad': 434, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[7, 1], [1, 1]]], [5, [[7, 1], [1, 1]]], [7, [0]], [11, [[6, 1], [2, 1]]], [13, [[6, 1], [2, 1]]], [17, [[3, 2], [1, 2]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[3, 2], [1, 2]]], [31, [0]], [37, [[3, 2], [1, 2]]], [41, [[3, 2], [1, 2]]], [43, [[7, 1], [1, 1]]], [47, [[3, 2], [1, 2]]], [53, [[7, 1], [1, 1]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1488, 1008, 672], 'galois_label': '8T48', 'galt': 48, 'grd': 51.616385159869715, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '8.4.567647723776.3', 'local_algs': ['2.8.8.13', '7.1.0.1', '7.1.0.1', '7.2.1.2', '7.4.3.2', '31.8.4.1'], 'minimal_sibling': [8, -16, 16, 4, -8, 4, 2, -2, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [2, 7, 31], 'rd': 29.4618397253, 'regulator': {'__RealLiteral__': 0, 'data': '3004.84581333', 'prec': 44}, 'res': {'sib': ['-13,8,4,440,-393,506,4940,-17768,45981,-86966,124864,-140830,126753,-100402,74476,-53966,40233,-29066,19710,-12200,6661,-3222,1354,-514,171,-52,16,-4,1', '-14,98,-98,-308,440,258,-514,-40,250,-54,-56,32,2,-4,1', '-19208,134456,10976,-765576,-1023512,-686000,5256328,5981920,955696,683256,-10728032,7075992,-5107816,-9823128,10959316,9080224,-21679300,16281024,-3739008,-339616,-2977160,7028284,-6467556,2439172,230488,-390576,-303608,324532,72190,-235102,116258,26072,-54628,22932,3112,-6376,1782,214,-280,66,6,-4,1', '1099,-1582,-7746,22376,-17831,-1854,10472,-16026,32283,-40654,20046,7214,-9465,960,-1604,8592,-8971,3970,-1050,552,-297,-154,144,74,-107,34,6,-6,1', '2,2,18,-76,104,-146,172,-160,112,-78,52,-32,16,-6,1', '6724,0,180,0,-23324,0,-10836,0,35580,0,-11892,0,-18980,0,16667,0,3051,0,-765,0,1651,0,-355,0,81,0,-7,0,1', '8,-16,16,4,-8,4,2,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{6}{17} a^{7} - \\frac{16}{17} a^{6} - \\frac{26}{17} a^{5} + \\frac{9}{34} a^{4} + \\frac{35}{17} a^{3} + \\frac{190}{17} a^{2} - \\frac{53}{17} a + \\frac{11}{17} \\)', '\\( \\frac{63}{68} a^{7} - \\frac{253}{68} a^{6} - \\frac{9}{34} a^{5} + \\frac{183}{34} a^{4} + \\frac{26}{17} a^{3} + \\frac{367}{17} a^{2} - \\frac{783}{17} a + \\frac{507}{17} \\)', '\\( \\frac{6}{17} a^{7} - \\frac{115}{68} a^{6} + \\frac{8}{17} a^{5} + \\frac{111}{34} a^{4} + \\frac{53}{34} a^{3} + \\frac{139}{17} a^{2} - \\frac{393}{17} a + \\frac{215}{17} \\)', '\\( \\frac{21}{34} a^{7} - \\frac{73}{34} a^{6} - \\frac{20}{17} a^{5} + \\frac{44}{17} a^{4} + \\frac{63}{34} a^{3} + \\frac{256}{17} a^{2} - \\frac{403}{17} a + \\frac{151}{17} \\)', '\\( \\frac{1}{68} a^{7} + \\frac{3}{68} a^{6} - \\frac{5}{34} a^{5} - \\frac{23}{34} a^{4} - \\frac{12}{17} a^{3} + \\frac{32}{17} a^{2} + \\frac{58}{17} a - \\frac{13}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/2*a^4', '1/2*a^5', '1/4*a^6', '1/68*a^7 + 3/68*a^6 - 5/34*a^5 - 3/17*a^4 - 7/34*a^3 - 2/17*a^2 + 7/17*a + 4/17']}
Number field data - 8.4.567647723776.3