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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 3, 'Lhash': '144623944820733286,1411483842001532545', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.065437173337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '1663488.1', 'coefficient_field': '1.1.1.1', 'conductor': 1663488, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, 10, 47, 110, 121], [1, 0, 22, 0, 169], [1, 2, 35, 34, 289], [1, -2, 1], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 0, -38, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 0, 1681], [1, 22, 207, 946, 1849], [1, 0, 13, 0, 2209], [1, 0, 6, 0, 2809], [1, -8, 134, -472, 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3.9719418548914436, 3.9148275195370004, 3.528235368107629, 2.83095639088666], 'positive_zeros': ['1.36309445163470127656106423644838', '2.28209460163033114528392703875039', '2.43726074335480144289137857493346', '3.52150549884707699550976993427004', '3.57158847095535230984643484535904', '4.68719487779910370709247985619746', '4.90222652055451670072407703452164', '5.13767139935142260589740790897091', '5.74555815379121643011841017590763', '5.90641506250154868855227026944946', '6.60850791131037206491890289679578', '6.89246560599511419845030852503559', '7.65447158208167131181021939550157'], 'prelabel': '4-1663488-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.209175526634344, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1556107786822265831, 'z1': {'__RealLiteral__': 0, 'data': '1.36309445163470127656106423644838', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.28209460163033114528392703875039', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.43726074335480144289137857493346', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 106.065437173337, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 1663488, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, -10, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -9, 0, -4, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -5, 0, 4, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 26, 0, 18, 0, 0, 0, 0, 0, 5, 0, -8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, -30, 0], 'euler11': [1, 10, 47, 110, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 2, 35, 34, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -38, 0, 961], 'euler37': [1, 0, 74, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 22, 207, 946, 1849], 'euler47': [1, 0, 13, 0, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, 6, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 0, 97, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -26, 315, -1898, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 8, 182, 664, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, 10, 47, 110, 121], [1, 0, 22, 0, 169], [1, 2, 35, 34, 289], [1, -2, 1, 0, 0], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 0, -38, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 0, 1681], [1, 22, 207, 946, 1849], [1, 0, 13, 0, 2209], [1, 0, 6, 0, 2809], [1, -8, 134, -472, 3481], [1, 0, 97, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 78, 0, 5041], [1, -26, 315, -1898, 5329], [1, 0, 142, 0, 6241], [1, 8, 182, 664, 6889], [1, 12, 214, 1068, 7921], [1, -4, 198, -388, 9409]], 'index': 13, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/25992.5/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/25992.5/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1663488-1.1-c1e2-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1663488-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.209175526634344, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1556107786822265831, 'z1': {'__RealLiteral__': 0, 'data': '1.36309445163470127656106423644838', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9840252
{'Lhash': '144623944820733286,1411483842001532545', 'Lhash_array': ['144623944820733286', '1411483842001532545'], 'label': '4-1663488-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/25992.5/a'}
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id: 9839982
{'Lhash': '144623944820733286,1411483842001532545', 'Lhash_array': ['144623944820733286', '1411483842001532545'], 'label': '4-1663488-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/25992.5/a'}