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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 0, 0, 0, 0, 27, 0, 0, -53, 0, 0, 36, 0, 0, -9, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 2954312706550833698643, 'disc_rad': 3, 'disc_sign': -1, 'frobs': [[2, [[18, 1]]], [3, [0]], [5, [[18, 1]]], [7, [[9, 2]]], [11, [[18, 1]]], [13, [[9, 2]]], [17, [[6, 3]]], [19, [[3, 3], [1, 9]]], [23, [[18, 1]]], [29, [[18, 1]]], [31, [[9, 2]]], [37, [[3, 3], [1, 9]]], [41, [[18, 1]]], [43, [[9, 2]]], [47, [[18, 1]]], [53, [[2, 9]]], [59, [[18, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [147], 'galois_label': '18T16', 'galt': 16, 'grd': 19.898946404249138, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '18.0.2954312706550833698643.2', 'local_algs': ['m3.18.1.45'], 'monogenic': 0, 'num_ram': 1, 'r2': 9, 'ramps': [3], 'rd': 15.5884572681, 'regulator': {'__RealLiteral__': 0, 'data': '23143.3269777', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['1.-1.1', '-1.-3.0.1', '1.0.0.-1.0.0.1'], 'torsion_gen': '\\( \\frac{350}{2071} a^{15} - \\frac{2935}{2071} a^{12} + \\frac{10945}{2071} a^{9} - \\frac{13158}{2071} a^{6} + \\frac{6811}{2071} a^{3} - \\frac{1822}{2071} \\)', 'torsion_order': 18, 'units': ['\\( \\frac{350}{2071} a^{16} - \\frac{2935}{2071} a^{13} + \\frac{10945}{2071} a^{10} - \\frac{13158}{2071} a^{7} + \\frac{6811}{2071} a^{4} - \\frac{3893}{2071} a \\)', '\\( \\frac{6}{109} a^{16} - \\frac{69}{109} a^{13} + \\frac{334}{109} a^{10} - \\frac{717}{109} a^{7} + \\frac{483}{109} a^{4} + \\frac{46}{109} a \\)', '\\( \\frac{6}{109} a^{17} - \\frac{604}{2071} a^{16} - \\frac{75}{2071} a^{15} - \\frac{69}{109} a^{14} + \\frac{5420}{2071} a^{13} + \\frac{481}{2071} a^{12} + \\frac{334}{109} a^{11} - \\frac{21669}{2071} a^{10} - \\frac{1014}{2071} a^{9} - \\frac{717}{109} a^{8} + \\frac{31630}{2071} a^{7} - \\frac{2210}{2071} a^{6} + \\frac{483}{109} a^{5} - \\frac{15813}{2071} a^{4} + \\frac{3718}{2071} a^{3} + \\frac{46}{109} a^{2} + \\frac{20}{2071} a - \\frac{793}{2071} \\)', '\\( \\frac{975}{2071} a^{17} + \\frac{726}{2071} a^{16} + \\frac{451}{2071} a^{15} - \\frac{8324}{2071} a^{14} - \\frac{5733}{2071} a^{13} - \\frac{3279}{2071} a^{12} + \\frac{31821}{2071} a^{11} + \\frac{19922}{2071} a^{10} + \\frac{9991}{2071} a^{9} - \\frac{41684}{2071} a^{8} - \\frac{17542}{2071} a^{7} - \\frac{2174}{2071} a^{6} + \\frac{24151}{2071} a^{5} + \\frac{4270}{2071} a^{4} - \\frac{6259}{2071} a^{3} - \\frac{6259}{2071} a^{2} - \\frac{1519}{2071} a - \\frac{975}{2071} \\)', '\\( \\frac{544}{2071} a^{17} + \\frac{1418}{2071} a^{16} + \\frac{275}{2071} a^{15} - \\frac{4621}{2071} a^{14} - \\frac{12601}{2071} a^{13} - \\frac{2454}{2071} a^{12} + \\frac{17130}{2071} a^{11} + \\frac{49905}{2071} a^{10} + \\frac{9931}{2071} a^{9} - \\frac{18901}{2071} a^{8} - \\frac{71569}{2071} a^{7} - \\frac{15368}{2071} a^{6} - \\frac{680}{2071} a^{5} + \\frac{36541}{2071} a^{4} + \\frac{10529}{2071} a^{3} + \\frac{10529}{2071} a^{2} + \\frac{1352}{2071} a - \\frac{544}{2071} \\)', '\\( \\frac{653}{2071} a^{17} - \\frac{303}{2071} a^{16} - \\frac{425}{2071} a^{15} - \\frac{6038}{2071} a^{14} + \\frac{3103}{2071} a^{13} + \\frac{3416}{2071} a^{12} + \\frac{24651}{2071} a^{11} - \\frac{13706}{2071} a^{10} - \\frac{11959}{2071} a^{9} - \\frac{38194}{2071} a^{8} + \\frac{25036}{2071} a^{7} + \\frac{10948}{2071} a^{6} + \\frac{19376}{2071} a^{5} - \\frac{12565}{2071} a^{4} - \\frac{1022}{2071} a^{3} - \\frac{1352}{2071} a^{2} - \\frac{2541}{2071} a + \\frac{1029}{2071} \\)', '\\( \\frac{140}{2071} a^{15} - \\frac{1174}{2071} a^{12} + \\frac{4378}{2071} a^{9} - \\frac{4849}{2071} a^{6} - \\frac{175}{2071} a^{3} - a^{2} - a + \\frac{928}{2071} \\)', '\\( \\frac{6}{109} a^{17} - \\frac{6}{109} a^{16} + \\frac{140}{2071} a^{15} - \\frac{69}{109} a^{14} + \\frac{69}{109} a^{13} - \\frac{1174}{2071} a^{12} + \\frac{334}{109} a^{11} - \\frac{334}{109} a^{10} + \\frac{4378}{2071} a^{9} - \\frac{717}{109} a^{8} + \\frac{717}{109} a^{7} - \\frac{4849}{2071} a^{6} + \\frac{483}{109} a^{5} - \\frac{483}{109} a^{4} - \\frac{175}{2071} a^{3} + \\frac{46}{109} a^{2} + \\frac{63}{109} a + \\frac{928}{2071} \\)'], 'used_grh': False, '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', '1/2071*a^15 - 393/2071*a^12 - 235/2071*a^9 - 937/2071*a^6 - 519/2071*a^3 + 480/2071', '1/2071*a^16 - 393/2071*a^13 - 235/2071*a^10 - 937/2071*a^7 - 519/2071*a^4 + 480/2071*a', '1/2071*a^17 - 393/2071*a^14 - 235/2071*a^11 - 937/2071*a^8 - 519/2071*a^5 + 480/2071*a^2']}
Number field data - 18.0.2954312706550833698643.2