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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [1000, 0, 0, -300, 0, 0, 834, 0, 0, 475, 0, 0, 39, 0, 0, -15, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 3602271247127978904000000000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 3]]], [11, [[2, 9]]], [13, [[6, 3]]], [17, [[2, 8], [1, 2]]], [19, [[3, 6]]], [23, [[2, 8], [1, 2]]], [29, [[2, 9]]], [31, [[3, 6]]], [37, [[6, 3]]], [41, [[2, 9]]], [43, [[6, 3]]], [47, [[2, 8], [1, 2]]], [53, [[2, 8], [1, 2]]], [59, [[2, 9]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 74, 18], 'galois_label': '18T12', 'galt': 12, 'grd': 33.956342994275154, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '18.0.3602271247127978904000000000.3', 'local_algs': ['2.1.3.2a1.1', '2.1.3.2a1.1', '2.2.3.4a1.2', '2.2.3.4a1.2', '3.1.18.37c4.77', '5.1.2.1a1.2', '5.2.2.2a1.2', '5.2.2.2a1.2', '5.2.2.2a1.2', '5.2.2.2a1.2'], 'maximal_cm_subfield': [4, -1, 1], 'minimal_sibling': [-1, 0, 0, 12, 0, 0, 63, 0, 0, 112, 0, 0, 45, 0, 0, -12, 0, 0, 1], 'monogenic': -1, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 9, 'ramps': [2, 3, 5], 'rd': 33.9563429943, 'regulator': {'__RealLiteral__': 0, 'data': '5300270.93735502', 'prec': 54}, 'res': {'sib': ['-1,0,0,12,0,0,63,0,0,112,0,0,45,0,0,-12,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['4.-1.1', '-3.0.0.1', '-6.0.0.1', '-2.0.0.1', '-12.0.0.1', '24.0.0.-9.0.0.1', '4.12.18.5.-3.-3.1', '384.0.0.-36.0.0.1', '96.0.0.-18.0.0.1', '1.0.0.3.0.0.-3.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1093}{1252350} a^{16} - \\frac{14461}{1001880} a^{13} + \\frac{284683}{5009400} a^{10} + \\frac{63353}{200376} a^{7} + \\frac{1667873}{5009400} a^{4} - \\frac{53093}{100188} a \\)', '\\( \\frac{389}{404800} a^{17} + \\frac{27}{89056} a^{15} - \\frac{3307}{242880} a^{14} - \\frac{809}{267168} a^{12} + \\frac{10821}{404800} a^{11} - \\frac{965}{89056} a^{9} + \\frac{37297}{80960} a^{8} + \\frac{18283}{89056} a^{6} + \\frac{204241}{151800} a^{5} + \\frac{36775}{33396} a^{3} + \\frac{6313}{20240} a^{2} + \\frac{8883}{22264} \\)', '\\( \\frac{7499}{20037600} a^{16} - \\frac{103}{2003760} a^{15} - \\frac{25067}{4007520} a^{13} + \\frac{703}{400752} a^{12} + \\frac{453911}{20037600} a^{10} - \\frac{45307}{2003760} a^{9} + \\frac{148183}{801504} a^{7} + \\frac{35129}{400752} a^{6} - \\frac{474521}{5009400} a^{4} + \\frac{194047}{500940} a^{3} - \\frac{86327}{200376} a - \\frac{46549}{100188} \\)', '\\( \\frac{389}{404800} a^{17} - \\frac{39}{22264} a^{15} - \\frac{3307}{242880} a^{14} + \\frac{1787}{66792} a^{12} + \\frac{10821}{404800} a^{11} - \\frac{5095}{66792} a^{9} + \\frac{37297}{80960} a^{8} - \\frac{18369}{22264} a^{6} + \\frac{204241}{151800} a^{5} - \\frac{34675}{33396} a^{3} + \\frac{6313}{20240} a^{2} + \\frac{4409}{8349} \\)', '\\( \\frac{871}{404800} a^{17} - \\frac{44059}{20037600} a^{16} - \\frac{1}{125235} a^{15} - \\frac{6881}{242880} a^{14} + \\frac{132967}{4007520} a^{13} - \\frac{259}{50094} a^{12} + \\frac{26557}{1214400} a^{11} - \\frac{1760251}{20037600} a^{10} + \\frac{20527}{250470} a^{9} + \\frac{99059}{80960} a^{8} - \\frac{836771}{801504} a^{7} - \\frac{12383}{50094} a^{6} + \\frac{263437}{75900} a^{5} - \\frac{4642057}{2504700} a^{4} - \\frac{620683}{250470} a^{3} + \\frac{10343}{5520} a^{2} + \\frac{419149}{200376} a - \\frac{80869}{25047} \\)', '\\( \\frac{81809}{20037600} a^{16} + \\frac{119}{2003760} a^{15} - \\frac{227177}{4007520} a^{13} + \\frac{1369}{400752} a^{12} + \\frac{1877501}{20037600} a^{10} - \\frac{118909}{2003760} a^{9} + \\frac{1653229}{801504} a^{7} + \\frac{63935}{400752} a^{6} + \\frac{29515939}{5009400} a^{4} + \\frac{1047319}{500940} a^{3} + \\frac{589207}{200376} a + \\frac{570401}{100188} \\)', '\\( \\frac{1}{12650} a^{16} + \\frac{59}{30360} a^{13} - \\frac{7357}{151800} a^{10} + \\frac{459}{2024} a^{7} + \\frac{194633}{151800} a^{4} + \\frac{4247}{3036} a + 2 \\)', '\\( \\frac{135739}{6679200} a^{17} + \\frac{961}{139150} a^{16} - \\frac{8}{605} a^{15} - \\frac{457031}{1335840} a^{14} - \\frac{17057}{111320} a^{13} + \\frac{20}{121} a^{12} + \\frac{3049257}{2226400} a^{11} + \\frac{608391}{556600} a^{10} + \\frac{48}{605} a^{9} + \\frac{10658479}{1335840} a^{8} + \\frac{2765}{22264} a^{7} - \\frac{1088}{121} a^{6} - \\frac{85003}{834900} a^{5} - \\frac{6895979}{556600} a^{4} - \\frac{12352}{605} a^{3} - \\frac{3556803}{111320} a^{2} - \\frac{340149}{11132} a - \\frac{3298}{121} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/3*a^9 - 1/3', '1/3*a^10 - 1/3*a', '1/3*a^11 - 1/3*a^2', '1/132*a^12 + 17/132*a^9 + 13/44*a^6 - 1/132*a^3 + 23/66', '1/264*a^13 - 9/88*a^10 + 13/88*a^7 + 131/264*a^4 + 15/44*a', '1/3960*a^14 - 1/792*a^13 + 1/396*a^12 - 23/792*a^11 + 115/792*a^10 + 17/396*a^9 + 151/440*a^8 + 25/88*a^7 + 19/44*a^6 - 185/792*a^5 + 133/792*a^4 - 133/396*a^3 - 43/1980*a^2 + 43/396*a + 89/198', '1/4007520*a^15 + 2027/801504*a^12 - 475151/4007520*a^9 - 395699/801504*a^6 + 131533/500940*a^3 - 20579/200376', '1/20037600*a^16 + 2027/4007520*a^13 + 860689/20037600*a^10 + 81161/801504*a^7 + 632473/2504700*a^4 + 22601/200376*a', '1/40075200*a^17 + 1/2671680*a^14 + 1/792*a^13 - 1/396*a^12 + 2024489/40075200*a^11 - 115/792*a^10 - 17/396*a^9 - 2344811/8015040*a^8 - 25/88*a^7 - 19/44*a^6 - 117017/834900*a^5 - 133/792*a^4 + 133/396*a^3 + 156521/2003760*a^2 - 43/396*a - 89/198']}
Number field data - 18.0.3602271247127978904000000000.3