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lfunc_lfunctions • Show schema
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{'Lhash': '4727493349865116331967077008570', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': -2, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8064890604149323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[101, [1, 1]]], 'bad_primes': [101], 'central_character': '101.1', 'coefficient_field': '1.1.1.1', 'conductor': 101, 'conductor_radical': 101, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, 1, 5], [1, 2, 7], [1, 2, 11], [1, -1, 13], [1, -3, 17], [1, 5, 19], [1, -1, 23], [1, 4, 29], [1, 9, 31], [1, 2, 37], [1, -8, 41], [1, 8, 43], [1, -7, 47], [1, 2, 53], [1, 14, 59], [1, -4, 61], [1, -2, 67], [1, -13, 71], [1, -8, 73], [1, 9, 79], [1, 4, 83], [1, -14, 89], [1, -2, 97], [1, 1], [1, -16, 103], [1, -13, 107], [1, 0, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 2, 3], 1]], [[[1, 1, 5], 1]], [[[1, 2, 7], 1]], [[[1, 2, 11], 1]], [[[1, -1, 13], 1]], [[[1, -3, 17], 1]], [[[1, 5, 19], 1]], [[[1, -1, 23], 1]], [[[1, 4, 29], 1]], [[[1, 9, 31], 1]], [[[1, 2, 37], 1]], [[[1, -8, 41], 1]], [[[1, 8, 43], 1]], [[[1, -7, 47], 1]], [[[1, 2, 53], 1]], [[[1, 14, 59], 1]], [[[1, -4, 61], 1]], [[[1, -2, 67], 1]], [[[1, -13, 71], 1]], [[[1, -8, 73], 1]], [[[1, 9, 79], 1]], [[[1, 4, 83], 1]], [[[1, -14, 89], 1]], [[[1, -2, 97], 1]], [[[1, 1], 1]], [[[1, -16, 103], 1]], [[[1, -13, 107], 1]], [[[1, 0, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-101-1.1-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/101/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-1.5117802475569561e-120, 0.09528926259613564, 0.19522082594284818, 0.3040977140195333, 0.42560919044305995, 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1.960147708943245, 0.8527954442945013, 0.010175397934056758, -0.40132276034868625, -0.32164331177486205, 0.19087655605915493, 0.9748143441434176, 1.8048738489535097], 'positive_zeros': ['3.72933468340090913789145872057212', '5.17330498735283860298501426044468', '6.16055116457811093791815485098464', '7.74187934910278185224762610895640', '9.060317898736739853083259611177477', '10.24202176919572853588664276584628', '11.18987953654912073880974227562904', '12.46381898373739464831556120111151', '13.00508217019688623012513185043208'], 'prelabel': '2-101-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.898047359783955, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1800720059813796826, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.72933468340090913789145872057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.17330498735283860298501426044', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.16055116457811093791815485098', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8064890604149323, 'bad_primes': [101], 'central_character': '1.1', 'conductor': 101, 'conductor_radical': 101, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, -2, -1, 0, -2, 0, 1, 0, -2, 4, 1, 0, 2, 4, 3, 0, -5, 2, 4, 0, 1, 0, -4, 0, 4, 4, -4, 0, -9, 0, 4, 0, 2, -2, -2, 0, -2, 0, 8, 0, -8, 4, -1, 0, 7, -8, -3, 0, -6, -2, -2, 0, 2, 0, 10, 0, -14, -4, 4, 0, -2, -8, -1, 0, 2, -6, -2, 0, 13, 0, 8, 0, 8, 10, 4, 0, -9, -4, -11, 0, -4, -8, -3, 0, 8, 0, 14, 0, -2, -2, 18, 0, 5, 0, 2, 0, -2, 8], 'euler11': [1, 2, 11], 'euler13': [1, -1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 2], 'euler23': [1, -1, 23], 'euler29': [1, 4, 29], 'euler3': [1, 2, 3], 'euler31': [1, 9, 31], 'euler37': [1, 2, 37], 'euler41': [1, -8, 41], 'euler43': [1, 8, 43], 'euler47': [1, -7, 47], 'euler5': [1, 1, 5], 'euler53': [1, 2, 53], 'euler59': [1, 14, 59], 'euler61': [1, -4, 61], 'euler67': [1, -2, 67], 'euler7': [1, 2, 7], 'euler71': [1, -13, 71], 'euler73': [1, -8, 73], 'euler79': [1, 9, 79], 'euler83': [1, 4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, 1, 5], [1, 2, 7], [1, 2, 11], [1, -1, 13], [1, -3, 17], [1, 5, 19], [1, -1, 23], [1, 4, 29], [1, 9, 31], [1, 2, 37], [1, -8, 41], [1, 8, 43], [1, -7, 47], [1, 2, 53], [1, 14, 59], [1, -4, 61], [1, -2, 67], [1, -13, 71], [1, -8, 73], [1, 9, 79], [1, 4, 83], [1, -14, 89], [1, -2, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/101/a', 'ModularForm/GL2/Q/holomorphic/101/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/101/2/a/a'], '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': '2-101-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-101-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.898047359783955, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1800720059813796826, 'z1': {'__RealLiteral__': 0, 'data': '3.72933468340090913789145872057', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9964710
{'Lhash': '4727493349865116331967077008570', 'Lhash_array': ['4727493349865116331967077008570'], 'label': '2-101-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/101/2/a/a'}
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id: 24546699
{'Lhash': '4727493349865116331967077008570', 'Lhash_array': ['4727493349865116331967077008570'], 'label': '2-101-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/101/2/a/a/1/1'}
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id: 22147
{'Lhash': '1800720059813796826', 'Lhash_array': ['1800720059813796826'], 'label': '2-101-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/101/a'}