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lfunc_lfunctions • Show schema
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{'Lhash': '6387847998045424977639905589110', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': -2, 'a5': 3, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [1, -1]]], 'bad_primes': [19], 'central_character': '19.1', 'coefficient_field': '1.1.1.1', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, -3, 5], [1, 1, 7], [1, -3, 11], [1, 4, 13], [1, 3, 17], [1, -1], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 1, 43], [1, 3, 47], [1, -12, 53], [1, 6, 59], [1, 1, 61], [1, 4, 67], [1, -6, 71], [1, 7, 73], [1, -8, 79], [1, -12, 83], [1, -12, 89], [1, -8, 97], [1, -6, 101], [1, -14, 103], [1, 18, 107], [1, 16, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 2, 3], 1]], [[[1, -3, 5], 1]], [[[1, 1, 7], 1]], [[[1, -3, 11], 1]], [[[1, 4, 13], 1]], [[[1, 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0.5531567828147579, 1.2833753818954463, 1.2104642574431557, 0.6140379854610066, -0.12217982847406526, -0.6532404066414016, -0.7903876001451643], 'positive_zeros': ['5.03912355415234199771433602491991', '6.39084306102520193435942181608554', '9.180168549070062598241568188032870', '10.24320445923116880350231460909254', '12.06296001644352266090310246809029', '13.35149180731186594820148200229738', '14.50114185013199863152077458509748', '16.70224717326536251258127220714807', '17.42643155985520821799903376960673', '18.12139870347555292446209785145167'], 'prelabel': '2-19-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.3895070780363725, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 409437620317032020, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.03912355415234199771433602492', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.39084306102520193435942181609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.180168549070062598241568188033', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'bad_primes': [19], 'central_character': '1.1', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, -2, 3, 0, -1, 0, 1, 0, 3, 4, -4, 0, -6, 4, -3, 0, 1, -6, 2, 0, 0, 0, 4, 0, 4, 2, 6, 0, -4, 0, -6, 0, -3, -2, 2, 0, 8, 0, -6, 0, -1, -6, 3, 0, -3, -8, -6, 0, 6, 8, 12, 0, 9, 0, -2, 0, -6, 12, -1, 0, -1, -8, -12, 0, -4, 6, 0, 0, 6, 0, -7, 0, -8, -2, -3, 0, 8, 12, -11, 0, 12, -4, -9, 0, -12, 0, 12, 0, 4, 0, 8, 0, 3, 0, 8, 0, 3, -8], 'euler11': [1, -3, 11], 'euler13': [1, 4, 13], 'euler17': [1, 3, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 2], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 1, 43], 'euler47': [1, 3, 47], 'euler5': [1, -3, 5], 'euler53': [1, -12, 53], 'euler59': [1, 6, 59], 'euler61': [1, 1, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 7], 'euler71': [1, -6, 71], 'euler73': [1, 7, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -12, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, -3, 5], [1, 1, 7], [1, -3, 11], [1, 4, 13], [1, 3, 17], [1, -1, 0], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 1, 43], [1, 3, 47], [1, -12, 53], [1, 6, 59], [1, 1, 61], [1, 4, 67], [1, -6, 71], [1, 7, 73], [1, -8, 79], [1, -12, 83], [1, -12, 89], [1, -8, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/19/a', 'ModularForm/GL2/Q/holomorphic/19/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/19/2/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': '2-19-1.1-c1-0-0', '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': '2-19-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.3895070780363725, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 409437620317032020, 'z1': {'__RealLiteral__': 0, 'data': '5.03912355415234199771433602492', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955499
{'Lhash': '6387847998045424977639905589110', 'Lhash_array': ['6387847998045424977639905589110'], 'label': '2-19-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/2/a/a'}
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id: 24545852
{'Lhash': '6387847998045424977639905589110', 'Lhash_array': ['6387847998045424977639905589110'], 'label': '2-19-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/2/a/a/1/1'}
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id: 21868
{'Lhash': '409437620317032020', 'Lhash_array': ['409437620317032020'], 'label': '2-19-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/19/a'}