Formats: - HTML - YAML - JSON - 2026-09-27T03:11:33.336439
  • nf_fields • Show schema
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 0, 0, 0, 0, 0, 0, 0, -102, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'disc_abs': 5385144351531158470656, 'disc_rad': 6, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [100, 28], 'galois_label': '16T45', 'galt': 45, 'grd': 22.813915798899377, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 14, 'label': '16.4.5385144351531158470656.14', 'local_algs': ['2.1.16.50h1.489', '3.2.8.14a1.2'], 'maxp': 3, 'minimal_sibling': [12, 0, 0, 0, -6, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 6, 'ramps': [2, 3], 'rd': 22.813915798899377, 'regulator': {'__RealLiteral__': 0, 'data': '66414.75672882414', 'prec': 54}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1], 'subfields': ['-6.0.1', '-3.0.1', '-2.0.1', '-3.0.0.0.1', '1.-2.0.-2.1', '1.0.-4.0.1', '-2.16.-16.4.-8.8.2.-4.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[2, 8]]], [11, [[4, 4]]], [13, [[2, 8]]], [17, [[8, 2]]], [19, [[2, 8]]], [23, [[2, 6], [1, 4]]], [29, [[8, 2]]], [31, [[2, 8]]], [37, [[4, 4]]], [41, [[8, 2]]], [43, [[2, 8]]], [47, [[2, 6], [1, 4]]], [53, [[8, 2]]], [59, [[4, 4]]]], 'label': '16.4.5385144351531158470656.14', 'res': {'gal': ['81,0,0,0,1620,0,0,0,10962,0,0,0,3240,0,0,0,-405,0,0,0,-216,0,0,0,66,0,0,0,-12,0,0,0,1'], 'sib': ['108,0,0,0,-18,0,0,0,1', '12,0,0,0,-6,0,0,0,1', '81,0,-324,0,594,0,-576,0,363,0,-168,0,60,0,-12,0,1', '9,0,-36,0,144,0,-360,0,447,0,-264,0,78,0,-12,0,1', '9,0,36,0,972,0,-1584,0,1059,0,-384,0,84,0,-12,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( -\\frac{1}{36} a^{12} - \\frac{1}{72} a^{10} + \\frac{35}{12} a^{4} + \\frac{41}{24} a^{2} + \\frac{1}{2} \\)', '\\( \\frac{7}{144} a^{14} + \\frac{1}{48} a^{12} + \\frac{1}{48} a^{10} - \\frac{1}{144} a^{8} - \\frac{239}{48} a^{6} - \\frac{33}{16} a^{4} - \\frac{33}{16} a^{2} - \\frac{7}{48} \\)', '\\( \\frac{1}{24} a^{12} - \\frac{1}{72} a^{8} - \\frac{33}{8} a^{4} + \\frac{17}{24} \\)', '\\( \\frac{7}{144} a^{14} + \\frac{1}{48} a^{12} + \\frac{1}{48} a^{10} + \\frac{1}{48} a^{8} - \\frac{239}{48} a^{6} - \\frac{33}{16} a^{4} - \\frac{33}{16} a^{2} - \\frac{25}{16} \\)', '\\( \\frac{1}{36} a^{8} - \\frac{29}{12} \\)', '\\( -\\frac{7}{144} a^{13} + \\frac{1}{144} a^{12} - \\frac{1}{72} a^{11} - \\frac{1}{72} a^{10} - \\frac{1}{144} a^{9} - \\frac{1}{144} a^{8} + \\frac{239}{48} a^{5} - \\frac{41}{48} a^{4} + \\frac{29}{24} a^{3} + \\frac{29}{24} a^{2} - \\frac{7}{48} a + \\frac{41}{48} \\)', '\\( \\frac{17}{144} a^{15} - \\frac{7}{144} a^{14} + \\frac{5}{72} a^{13} - \\frac{1}{36} a^{12} + \\frac{1}{48} a^{11} - \\frac{1}{144} a^{10} + \\frac{1}{72} a^{9} - \\frac{1}{72} a^{8} - \\frac{577}{48} a^{7} + \\frac{239}{48} a^{6} - \\frac{169}{24} a^{5} + \\frac{35}{12} a^{4} - \\frac{33}{16} a^{3} + \\frac{41}{48} a^{2} - \\frac{17}{24} a + \\frac{41}{24} \\)', '\\( -\\frac{7}{144} a^{15} - \\frac{7}{144} a^{14} + \\frac{7}{144} a^{13} + \\frac{1}{144} a^{12} - \\frac{1}{144} a^{11} - \\frac{1}{144} a^{10} + \\frac{1}{48} a^{9} + \\frac{1}{144} a^{8} + \\frac{239}{48} a^{7} + \\frac{239}{48} a^{6} - \\frac{239}{48} a^{5} - \\frac{41}{48} a^{4} + \\frac{17}{48} a^{3} + \\frac{17}{48} a^{2} - \\frac{33}{16} a + \\frac{31}{48} \\)', '\\( -\\frac{17}{144} a^{15} + \\frac{7}{144} a^{14} + \\frac{1}{48} a^{13} - \\frac{7}{144} a^{12} + \\frac{7}{144} a^{11} - \\frac{1}{48} a^{10} + \\frac{1}{144} a^{9} + \\frac{1}{144} a^{8} + \\frac{577}{48} a^{7} - \\frac{239}{48} a^{6} - \\frac{33}{16} a^{5} + \\frac{239}{48} a^{4} - \\frac{239}{48} a^{3} + \\frac{33}{16} a^{2} + \\frac{7}{48} a - \\frac{65}{48} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/72*a^8 - 1/2*a^6 - 1/2*a^2 + 7/24', '1/72*a^9 - 1/2*a^7 - 1/2*a^3 + 7/24*a', '1/72*a^10 - 1/2*a^4 + 7/24*a^2 - 1/2', '1/72*a^11 - 1/2*a^5 + 7/24*a^3 - 1/2*a', '1/72*a^12 - 1/2*a^6 + 7/24*a^4 - 1/2*a^2', '1/144*a^13 - 1/144*a^12 - 1/144*a^9 - 1/144*a^8 - 1/2*a^6 - 17/48*a^5 + 17/48*a^4 - 1/2*a^3 + 17/48*a + 17/48', '1/144*a^14 - 1/144*a^12 - 1/144*a^10 - 1/144*a^8 + 7/48*a^6 - 7/48*a^4 + 17/48*a^2 + 17/48', '1/144*a^15 - 1/144*a^12 - 1/144*a^11 - 1/144*a^8 - 17/48*a^7 - 1/2*a^6 - 1/2*a^5 + 17/48*a^4 + 17/48*a^3 + 17/48']}