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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 11, -20, 30, -45, 84, -164, 276, -377, 419, -386, 299, -195, 107, -49, 18, -5, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 33019305672452059136, 'disc_rad': 946, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[9, 2]]], [5, [[9, 2]]], [7, [[6, 1], [2, 6]]], [11, [0]], [13, [[6, 1], [2, 6]]], [17, [[6, 3]]], [19, [[6, 3]]], [23, [[9, 2]]], [29, [[6, 1], [2, 6]]], [31, [[9, 2]]], [37, [[9, 2]]], [41, [[2, 9]]], [43, [0]], [47, [[3, 4], [1, 6]]], [53, [[3, 4], [1, 6]]], [59, [[3, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [108, 81, 108], 'galois_label': '18T86', 'galt': 86, 'grd': 64.61925947014737, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.0.33019305672452059136.1', 'local_algs': ['2.18.12.1', '11.6.3.2', '11.6.3.2', '11.6.3.2', '43.2.0.1', '43.2.0.1', '43.2.0.1', '43.2.0.1', '43.2.0.1', '43.2.0.1', '43.6.4.1'], 'minimal_sibling': [-1, 0, 3, -5, 1, 2, -2, 1, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 9, 'ramps': [2, 11, 43], 'rd': 12.144398136, 'regulator': {'__RealLiteral__': 0, 'data': '134.134877065', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 3, 1, 1], 'subfields': ['3.-1.1', '1.1.-1.1', '1.-1.2.-3.2.-1.1', '-1.0.3.-5.1.2.-2.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7459}{6349} a^{17} - \\frac{30112}{6349} a^{16} + \\frac{103641}{6349} a^{15} - \\frac{259513}{6349} a^{14} + \\frac{524297}{6349} a^{13} - \\frac{888533}{6349} a^{12} + \\frac{1241690}{6349} a^{11} - \\frac{206110}{907} a^{10} + \\frac{1374992}{6349} a^{9} - \\frac{1027940}{6349} a^{8} + \\frac{584518}{6349} a^{7} - \\frac{256204}{6349} a^{6} + \\frac{118460}{6349} a^{5} - \\frac{15821}{907} a^{4} + \\frac{100304}{6349} a^{3} - \\frac{46327}{6349} a^{2} + \\frac{2150}{907} a + \\frac{1720}{6349} \\)', '\\( \\frac{11020}{6349} a^{17} - \\frac{50252}{6349} a^{16} + \\frac{171139}{6349} a^{15} - \\frac{441904}{6349} a^{14} + \\frac{907825}{6349} a^{13} - \\frac{1551229}{6349} a^{12} + \\frac{2208018}{6349} a^{11} - \\frac{370003}{907} a^{10} + \\frac{2491739}{6349} a^{9} - \\frac{1895560}{6349} a^{8} + \\frac{1072304}{6349} a^{7} - \\frac{449892}{6349} a^{6} + \\frac{196486}{6349} a^{5} - \\frac{22082}{907} a^{4} + \\frac{141327}{6349} a^{3} - \\frac{76360}{6349} a^{2} + \\frac{2821}{907} a - \\frac{827}{6349} \\)', '\\( \\frac{1520}{6349} a^{17} - \\frac{11091}{6349} a^{16} + \\frac{40682}{6349} a^{15} - \\frac{118969}{6349} a^{14} + \\frac{268836}{6349} a^{13} - \\frac{501638}{6349} a^{12} + \\frac{781386}{6349} a^{11} - \\frac{144581}{907} a^{10} + \\frac{1080610}{6349} a^{9} - \\frac{936202}{6349} a^{8} + \\frac{624079}{6349} a^{7} - \\frac{309884}{6349} a^{6} + \\frac{127153}{6349} a^{5} - \\frac{11459}{907} a^{4} + \\frac{81013}{6349} a^{3} - \\frac{56289}{6349} a^{2} + \\frac{2985}{907} a - \\frac{6682}{6349} \\)', '\\( a \\)', '\\( \\frac{12521}{6349} a^{17} - \\frac{54776}{6349} a^{16} + \\frac{187345}{6349} a^{15} - \\frac{481690}{6349} a^{14} + \\frac{989497}{6349} a^{13} - \\frac{1702322}{6349} a^{12} + \\frac{2442670}{6349} a^{11} - \\frac{416442}{907} a^{10} + \\frac{2892990}{6349} a^{9} - \\frac{2319917}{6349} a^{8} + \\frac{1467240}{6349} a^{7} - \\frac{761934}{6349} a^{6} + \\frac{388476}{6349} a^{5} - \\frac{35858}{907} a^{4} + \\frac{181408}{6349} a^{3} - \\frac{95518}{6349} a^{2} + \\frac{4805}{907} a - \\frac{2505}{6349} \\)', '\\( \\frac{1633}{6349} a^{17} - \\frac{13390}{6349} a^{16} + \\frac{51250}{6349} a^{15} - \\frac{150816}{6349} a^{14} + \\frac{350758}{6349} a^{13} - \\frac{660038}{6349} a^{12} + \\frac{1043638}{6349} a^{11} - \\frac{196336}{907} a^{10} + \\frac{1486707}{6349} a^{9} - \\frac{1318431}{6349} a^{8} + \\frac{914230}{6349} a^{7} - \\frac{477829}{6349} a^{6} + \\frac{223065}{6349} a^{5} - \\frac{20163}{907} a^{4} + \\frac{115602}{6349} a^{3} - \\frac{76626}{6349} a^{2} + \\frac{3735}{907} a - \\frac{3361}{6349} \\)', '\\( \\frac{2273}{907} a^{17} - \\frac{9515}{907} a^{16} + \\frac{32147}{907} a^{15} - \\frac{81041}{907} a^{14} + \\frac{163210}{907} a^{13} - \\frac{275355}{907} a^{12} + \\frac{385397}{907} a^{11} - \\frac{446239}{907} a^{10} + \\frac{425865}{907} a^{9} - \\frac{322429}{907} a^{8} + \\frac{186938}{907} a^{7} - \\frac{86686}{907} a^{6} + \\frac{43886}{907} a^{5} - \\frac{32134}{907} a^{4} + \\frac{26313}{907} a^{3} - \\frac{14639}{907} a^{2} + \\frac{5537}{907} a - \\frac{637}{907} \\)', '\\( \\frac{8816}{6349} a^{17} - \\frac{44011}{6349} a^{16} + \\frac{157228}{6349} a^{15} - \\frac{424632}{6349} a^{14} + \\frac{916730}{6349} a^{13} - \\frac{1648589}{6349} a^{12} + \\frac{2480042}{6349} a^{11} - \\frac{446383}{907} a^{10} + \\frac{3270810}{6349} a^{9} - \\frac{2792597}{6349} a^{8} + \\frac{1881302}{6349} a^{7} - \\frac{985925}{6349} a^{6} + \\frac{447973}{6349} a^{5} - \\frac{37801}{907} a^{4} + \\frac{218455}{6349} a^{3} - \\frac{143625}{6349} a^{2} + \\frac{8243}{907} a - \\frac{10820}{6349} \\)'], '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', 'a^15', 'a^16', '1/6349*a^17 + 991/6349*a^16 + 2959/6349*a^15 + 1179/6349*a^14 - 174/6349*a^13 - 2076/6349*a^12 + 2377/6349*a^11 - 153/907*a^10 + 335/6349*a^9 + 3135/6349*a^8 - 972/6349*a^7 + 3121/6349*a^6 - 2410/6349*a^5 - 69/907*a^4 + 1486/6349*a^3 + 719/6349*a^2 - 186/907*a - 1600/6349']}