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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 4, 0, -12, 0, 0, -18, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 17, 'dirichlet_group': [], 'disc_abs': 44542611246065932779454464, 'disc_rad': 1359332618593320702498, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[10, 1], [6, 1], [1, 1]]], [7, [[11, 1], [6, 1]]], [11, [[17, 1]]], [13, [[9, 1], [6, 1], [2, 1]]], [17, [[8, 2], [1, 1]]], [19, [[6, 1], [5, 1], [4, 1], [1, 2]]], [23, [[13, 1], [3, 1], [1, 1]]], [29, [[8, 1], [6, 1], [3, 1]]], [31, [[11, 1], [4, 1], [1, 2]]], [37, [[13, 1], [2, 2]]], [41, [[8, 1], [7, 1], [2, 1]]], [43, [[9, 1], [4, 1], [3, 1], [1, 1]]], [47, [[8, 2], [1, 1]]], [53, [[11, 1], [5, 1], [1, 1]]], [59, [[8, 1], [6, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_label': '17T10', 'galt': 10, 'index': 1, 'inessentialp': [], 'is_galois': False, 'iso_number': 1, 'label': '17.1.44542611246065932779454464.1', 'local_algs': ['2.17.16.1', '3.2.1.2', '3.3.0.1', '3.5.0.1', '3.7.0.1', 'm271.2.1.1', 'm271.1.4.0', 'm271.1.11.0', 'm835997920414096373.1.1.0', 'm835997920414096373.2.1.1', 'm835997920414096373.1.14.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 8, 'ramps': [2, 3, 271, 835997920414096373], 'rd': 32.2664740609, 'regulator': {'__RealLiteral__': 0, 'data': '1877308.99113', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{59048}{472383} a^{16} + \\frac{26122}{472383} a^{15} + \\frac{13124}{472383} a^{14} - \\frac{54674}{472383} a^{13} - \\frac{26203}{472383} a^{12} + \\frac{65608}{472383} a^{11} + \\frac{53216}{472383} a^{10} + \\frac{26230}{472383} a^{9} - \\frac{109348}{157461} a^{8} - \\frac{52406}{157461} a^{7} - \\frac{26245}{157461} a^{6} - \\frac{247856}{157461} a^{5} - \\frac{104272}{157461} a^{4} - \\frac{104987}{157461} a^{3} - \\frac{4536}{52487} a^{2} + \\frac{84}{52487} a - \\frac{26257}{472383} \\)', '\\( \\frac{25474}{157461} a^{16} + \\frac{13136}{157461} a^{15} - \\frac{66338}{157461} a^{14} - \\frac{25987}{157461} a^{13} + \\frac{13117}{157461} a^{12} + \\frac{57104}{157461} a^{11} + \\frac{26158}{157461} a^{10} - \\frac{21868}{157461} a^{9} - \\frac{51974}{52487} a^{8} - \\frac{26253}{52487} a^{7} + \\frac{114208}{52487} a^{6} - \\frac{100528}{52487} a^{5} - \\frac{122552}{52487} a^{4} + \\frac{289976}{52487} a^{3} + \\frac{54083}{52487} a^{2} - \\frac{81676}{52487} a + \\frac{30619}{157461} \\)', '\\( \\frac{59048}{472383} a^{16} + \\frac{26122}{472383} a^{15} + \\frac{13124}{472383} a^{14} - \\frac{54674}{472383} a^{13} - \\frac{26203}{472383} a^{12} + \\frac{65608}{472383} a^{11} + \\frac{53216}{472383} a^{10} + \\frac{26230}{472383} a^{9} - \\frac{109348}{157461} a^{8} - \\frac{52406}{157461} a^{7} - \\frac{26245}{157461} a^{6} - \\frac{247856}{157461} a^{5} - \\frac{104272}{157461} a^{4} - \\frac{104987}{157461} a^{3} + \\frac{47951}{52487} a^{2} + \\frac{52571}{52487} a - \\frac{26257}{472383} \\)', '\\( \\frac{8748}{52487} a^{16} - \\frac{162}{52487} a^{15} + \\frac{3}{52487} a^{14} - \\frac{2916}{52487} a^{13} + \\frac{54}{52487} a^{12} - \\frac{1}{52487} a^{11} + \\frac{972}{52487} a^{10} - \\frac{18}{52487} a^{9} - \\frac{17496}{52487} a^{8} + \\frac{324}{52487} a^{7} - \\frac{6}{52487} a^{6} - \\frac{151632}{52487} a^{5} + \\frac{55295}{52487} a^{4} - \\frac{52}{52487} a^{3} - \\frac{54432}{52487} a^{2} + \\frac{53495}{52487} a + \\frac{52469}{52487} \\)', '\\( \\frac{2}{3} a^{16} + \\frac{1}{3} a^{15} - \\frac{1}{3} a^{14} - \\frac{2}{3} a^{13} - \\frac{1}{3} a^{12} + \\frac{1}{3} a^{11} + \\frac{2}{3} a^{10} + \\frac{1}{3} a^{9} - 3 a^{8} - 2 a^{7} + a^{6} - 9 a^{5} - 4 a^{4} + 5 a^{3} + a^{2} + \\frac{5}{3} \\)', '\\( \\frac{26248}{472383} a^{16} - \\frac{109348}{472383} a^{15} - \\frac{52406}{472383} a^{14} + \\frac{131216}{472383} a^{13} + \\frac{106432}{472383} a^{12} + \\frac{52460}{472383} a^{11} - \\frac{183704}{472383} a^{10} - \\frac{105460}{472383} a^{9} - \\frac{52490}{157461} a^{8} + \\frac{212864}{157461} a^{7} + \\frac{104920}{157461} a^{6} - \\frac{367435}{157461} a^{5} + \\frac{445168}{157461} a^{4} + \\frac{209480}{157461} a^{3} - \\frac{163296}{52487} a^{2} + \\frac{3024}{52487} a + \\frac{576871}{472383} \\)', '\\( \\frac{95540}{157461} a^{16} - \\frac{15377}{157461} a^{15} + \\frac{40136}{157461} a^{14} - \\frac{14351}{157461} a^{13} - \\frac{12370}{157461} a^{12} + \\frac{4117}{157461} a^{11} - \\frac{12712}{157461} a^{10} + \\frac{21619}{157461} a^{9} - \\frac{133676}{52487} a^{8} + \\frac{27747}{52487} a^{7} - \\frac{44253}{52487} a^{6} - \\frac{546177}{52487} a^{5} + \\frac{135500}{52487} a^{4} - \\frac{226065}{52487} a^{3} - \\frac{305075}{52487} a^{2} + \\frac{86324}{52487} a - \\frac{188329}{157461} \\)', '\\( \\frac{1589914}{472383} a^{16} + \\frac{923099}{472383} a^{15} + \\frac{380446}{472383} a^{14} + \\frac{134864}{472383} a^{13} + \\frac{24718}{472383} a^{12} - \\frac{39337}{472383} a^{11} - \\frac{79946}{472383} a^{10} - \\frac{25735}{472383} a^{9} - \\frac{2092187}{157461} a^{8} - \\frac{1210252}{157461} a^{7} - \\frac{551057}{157461} a^{6} - \\frac{9699376}{157461} a^{5} - \\frac{5590064}{157461} a^{4} - \\frac{2273947}{157461} a^{3} - \\frac{2348520}{52487} a^{2} - \\frac{1262852}{52487} a + \\frac{2388667}{472383} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', '1/472383*a^16 + 208976/472383*a^15 + 104992/472383*a^14 + 34991/472383*a^13 - 209624/472383*a^12 + 52481/472383*a^11 - 46655/472383*a^10 + 209840/472383*a^9 + 69982/157461*a^8 + 53135/157461*a^7 - 52499/157461*a^6 + 64145/157461*a^5 - 46871/157461*a^4 - 52591/157461*a^3 + 16199/52487*a^2 + 672/52487*a - 210056/472383']}
Number field data - 17.1.44542611246065932779454464.1