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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, 0, 8, 0, 24, 0, -52, 0, -21, 0, 78, 0, -13, 0, -48, 0, 36, 0, -10, 0, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 1082081291410568717705150464, 'disc_rad': 178, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1], [4, 2]]], [5, [[5, 4]]], [7, [[6, 2], [4, 1], [2, 2]]], [11, [[8, 2], [4, 1]]], [13, [[5, 4]]], [17, [[10, 2]]], [19, [[4, 1], [3, 4], [2, 2]]], [23, [[16, 1], [2, 2]]], [29, [[6, 2], [4, 1], [2, 1], [1, 2]]], [31, [[8, 1], [6, 2]]], [37, [[8, 1], [4, 2], [2, 1], [1, 2]]], [41, [[10, 2]]], [43, [[6, 1], [3, 2], [2, 4]]], [47, [[8, 2], [2, 1], [1, 2]]], [53, [[5, 4]]], [59, [[8, 1], [4, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_label': '20T965', 'galt': 965, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '20.10.1082081291410568717705150464.1', 'local_algs': ['2.8.14.3', '2.12.24.35', '89.8.0.1', '89.12.8.1'], 'minimal_sibling': [1, 0, -2, 0, -21, 0, 22, 0, 108, 0, 74, 0, -2, 0, -4, 0, 10, 0, 6, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 89], 'rd': 22.4756879837, 'regulator': {'__RealLiteral__': 0, 'data': '2261786.67414', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['2.-6.3.0.-1.1', '-1.0.2.0.8.0.3.0.-5.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{2} a^{18} - \\frac{27}{2} a^{16} + 41 a^{14} - 35 a^{12} - \\frac{89}{2} a^{10} + \\frac{137}{2} a^{8} + \\frac{47}{2} a^{6} - \\frac{97}{2} a^{4} - a^{2} + 8 \\)', '\\( \\frac{3}{2} a^{19} - \\frac{53}{4} a^{17} + \\frac{77}{2} a^{15} - \\frac{53}{2} a^{13} - \\frac{107}{2} a^{11} + \\frac{245}{4} a^{9} + 38 a^{7} - \\frac{177}{4} a^{5} - 10 a^{3} + \\frac{15}{2} a \\)', '\\( a^{2} - 1 \\)', '\\( \\frac{7}{4} a^{18} - \\frac{31}{2} a^{16} + \\frac{91}{2} a^{14} - 34 a^{12} - \\frac{223}{4} a^{10} + \\frac{139}{2} a^{8} + \\frac{135}{4} a^{6} - 46 a^{4} - \\frac{9}{2} a^{2} + 7 \\)', '\\( a^{19} - \\frac{39}{4} a^{17} + \\frac{67}{2} a^{15} - \\frac{79}{2} a^{13} - 21 a^{11} + \\frac{259}{4} a^{9} + \\frac{5}{2} a^{7} - \\frac{175}{4} a^{5} + 4 a^{3} + \\frac{11}{2} a \\)', '\\( \\frac{3}{2} a^{19} - \\frac{59}{4} a^{17} + \\frac{103}{2} a^{15} - \\frac{127}{2} a^{13} - \\frac{55}{2} a^{11} + \\frac{415}{4} a^{9} - 8 a^{7} - \\frac{275}{4} a^{5} + 14 a^{3} + \\frac{15}{2} a \\)', '\\( \\frac{3}{8} a^{18} - \\frac{1}{4} a^{17} - 4 a^{16} + 2 a^{15} + \\frac{61}{4} a^{14} - 5 a^{13} - 21 a^{12} + 2 a^{11} - \\frac{59}{8} a^{10} + \\frac{29}{4} a^{9} + \\frac{71}{2} a^{8} - 5 a^{7} - \\frac{13}{8} a^{6} - \\frac{19}{4} a^{5} - \\frac{101}{4} a^{4} + \\frac{7}{2} a^{3} + \\frac{9}{4} a^{2} + a + \\frac{7}{2} \\)', '\\( \\frac{1}{4} a^{19} + \\frac{5}{8} a^{18} - \\frac{9}{4} a^{17} - \\frac{23}{4} a^{16} + 7 a^{15} + \\frac{73}{4} a^{14} - 7 a^{13} - \\frac{35}{2} a^{12} - \\frac{21}{4} a^{11} - \\frac{157}{8} a^{10} + \\frac{49}{4} a^{9} + \\frac{153}{4} a^{8} - \\frac{1}{4} a^{7} + \\frac{65}{8} a^{6} - \\frac{33}{4} a^{5} - \\frac{59}{2} a^{4} + \\frac{5}{2} a^{3} - \\frac{1}{4} a^{2} + 2 a + 6 \\)', '\\( \\frac{5}{8} a^{18} + \\frac{1}{2} a^{17} - \\frac{21}{4} a^{16} - 4 a^{15} + \\frac{57}{4} a^{14} + \\frac{19}{2} a^{13} - \\frac{17}{2} a^{12} - a^{11} - \\frac{141}{8} a^{10} - \\frac{37}{2} a^{9} + \\frac{63}{4} a^{8} + 6 a^{7} + \\frac{81}{8} a^{6} + 15 a^{5} - 7 a^{4} - 2 a^{3} - \\frac{5}{4} a^{2} - \\frac{5}{2} a \\)', '\\( \\frac{5}{8} a^{19} - \\frac{1}{4} a^{18} - \\frac{23}{4} a^{17} + \\frac{5}{2} a^{16} + \\frac{73}{4} a^{15} - 9 a^{14} - \\frac{37}{2} a^{13} + 12 a^{12} - \\frac{109}{8} a^{11} + \\frac{13}{4} a^{10} + \\frac{117}{4} a^{9} - \\frac{39}{2} a^{8} + \\frac{33}{8} a^{7} + \\frac{21}{4} a^{6} - \\frac{37}{2} a^{5} + 12 a^{4} + \\frac{7}{4} a^{3} - 4 a^{2} + 2 a - 1 \\)', '\\( \\frac{5}{4} a^{19} - \\frac{5}{8} a^{18} - \\frac{45}{4} a^{17} + \\frac{25}{4} a^{16} + 34 a^{15} - \\frac{89}{4} a^{14} - 28 a^{13} + \\frac{55}{2} a^{12} - \\frac{157}{4} a^{11} + \\frac{125}{8} a^{10} + \\frac{225}{4} a^{9} - \\frac{207}{4} a^{8} + \\frac{91}{4} a^{7} - \\frac{17}{8} a^{6} - \\frac{149}{4} a^{5} + 40 a^{4} - \\frac{7}{2} a^{3} - \\frac{3}{4} a^{2} + 5 a - 7 \\)', '\\( \\frac{7}{8} a^{19} - \\frac{7}{8} a^{18} - 8 a^{17} + \\frac{15}{2} a^{16} + \\frac{99}{4} a^{15} - \\frac{83}{4} a^{14} - \\frac{43}{2} a^{13} + 12 a^{12} - \\frac{231}{8} a^{11} + \\frac{239}{8} a^{10} + \\frac{93}{2} a^{9} - 28 a^{8} + \\frac{107}{8} a^{7} - \\frac{155}{8} a^{6} - \\frac{127}{4} a^{5} + \\frac{63}{4} a^{4} + \\frac{3}{4} a^{3} + \\frac{17}{4} a^{2} + 4 a - \\frac{5}{2} \\)', '\\( \\frac{5}{4} a^{19} - \\frac{1}{4} a^{18} - \\frac{23}{2} a^{17} + \\frac{7}{4} a^{16} + 36 a^{15} - 3 a^{14} - 33 a^{13} - \\frac{5}{2} a^{12} - \\frac{149}{4} a^{11} + \\frac{25}{4} a^{10} + \\frac{127}{2} a^{9} + \\frac{25}{4} a^{8} + \\frac{71}{4} a^{7} - \\frac{23}{4} a^{6} - 41 a^{5} - \\frac{27}{4} a^{4} - 2 a^{3} + \\frac{1}{2} a^{2} + 5 a + \\frac{1}{2} \\)', '\\( \\frac{9}{8} a^{19} - \\frac{43}{4} a^{17} - \\frac{1}{4} a^{16} + \\frac{143}{4} a^{15} + 2 a^{14} - \\frac{77}{2} a^{13} - \\frac{9}{2} a^{12} - \\frac{241}{8} a^{11} - a^{10} + \\frac{289}{4} a^{9} + \\frac{45}{4} a^{8} + \\frac{65}{8} a^{7} - a^{6} - \\frac{107}{2} a^{5} - \\frac{45}{4} a^{4} + \\frac{13}{4} a^{3} + \\frac{1}{2} a^{2} + 10 a + \\frac{7}{2} \\)'], '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', '1/4*a^16 - 1/2*a^15 - 1/2*a^14 - 1/2*a^12 - 1/4*a^8 - 1/2*a^7 - 1/2*a^6 + 1/4*a^4 - 1/2*a^3 - 1/2', '1/4*a^17 - 1/2*a^15 - 1/2*a^13 - 1/4*a^9 - 1/2*a^7 + 1/4*a^5 - 1/2*a', '1/8*a^18 - 1/2*a^15 - 1/4*a^14 - 1/2*a^13 - 1/8*a^10 - 1/2*a^8 - 1/2*a^7 + 1/8*a^6 - 1/2*a^5 + 1/4*a^4 - 1/2*a^3 - 1/4*a^2 - 1/2*a - 1/2', '1/8*a^19 - 1/4*a^15 - 1/2*a^14 - 1/8*a^11 - 1/2*a^9 + 1/8*a^7 - 1/2*a^6 + 1/4*a^5 - 1/4*a^3 - 1/2*a^2 - 1/2*a']}
Number field data - 20.10.1082081291410568717705150464.1