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lfunc_lfunctions • Show schema
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{'Lhash': '1034392843627615370638219471474', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 0, 7], [1, -4, 11], [1, -1], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, -8, 31], [1, -6, 37], [1, 10, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, -12, 71], [1, 2, 73], [1, -8, 79], [1, 8, 83], [1, 2, 89], [1, -6, 97], [1, -2, 101], [1, -4, 103], [1, -12, 107], [1, 6, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 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1.3008976193970463, 0.9392099451542857, 0.5858279165901267, 0.25931218680405554, -0.024263887160732456, -0.2522435757198137, -0.41611287062458496, -0.5119801712553456, -0.5407800685867873, -0.5081872435855478, -0.424242996610859, -0.3027134956892905, -0.16021453878333486, -0.015151566328147887, 0.11346498184980988], 'positive_zeros': ['0.815992074978217174148687342211678', '1.50703669572845863680434335287364', '2.99583786789386571784697269859823', '3.62284880782181867823314174284659', '4.47680162456485182475114267126955', '5.15610259074422422063688994184375', '6.04040524925983557166863746843270', '6.52431635247964933864233169764675', '7.35636779219708892660325177777184', '7.947024942201543620404002077820415'], 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 833577681497972402, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.815992074978217174148687342212', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.50703669572845863680434335287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99583786789386571784697269860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.826650861278985, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 4, 0, 1, 0, 1, 0, 6, 0, 4, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 8, 0, -4, 0, 0, 0, 6, 0, -1, 0, -10, 0, -4, 0, -1, 0, 8, 0, -7, 0, -6, 0, 6, 0, -4, 0, -4, 0, -12, 0, -10, 0, 0, 0, -1, 0, -4, 0, 0, 0, 12, 0, -2, 0, -1, 0, 0, 0, 8, 0, 1, 0, -8, 0, -6, 0, -2, 0, -2, 0, 0, 0, -8, 0, -4, 0, 6, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -12, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 7], [1, -4, 11], [1, -1, 0], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, -8, 31], [1, -6, 37], [1, 10, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, -12, 71], [1, 2, 73], [1, -8, 79], [1, 8, 83], [1, 2, 89], [1, -6, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6240/e', 'ModularForm/GL2/Q/holomorphic/6240/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/6240/2/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6240-1.1-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 833577681497972402, 'z1': {'__RealLiteral__': 0, 'data': '0.815992074978217174148687342212', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21572011
{'Lhash': '1034392843627615370638219471474', 'Lhash_array': ['1034392843627615370638219471474'], 'label': '2-6240-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/e'}
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id: 24574080
{'Lhash': '1034392843627615370638219471474', 'Lhash_array': ['1034392843627615370638219471474'], 'label': '2-6240-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/e/1/1'}
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id: 38734
{'Lhash': '833577681497972402', 'Lhash_array': ['833577681497972402'], 'label': '2-6240-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6240/e'}