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lfunc_lfunctions • Show schema
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{'Lhash': '1883283787158213671840065243098', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.52594900053381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '4950.1', 'coefficient_field': '1.1.1.1', 'conductor': 4950, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1, 4, 7], [1, 1], [1, 0, 13], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 0, 29], [1, 8, 31], [1, 4, 37], [1, -4, 41], [1, 8, 43], [1, 12, 47], [1, -2, 53], [1, 12, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, 4, 73], [1, 4, 79], [1, 12, 83], [1, 16, 89], [1, 16, 97], [1, 0, 101], [1, -4, 103], [1, 12, 107], [1, 14, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [1], [[[1, 4, 7], 1]], [[[1, 1], 1]], [[[1, 0, 13], 1]], [[[1, 2, 17], 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2.473373642361965, 2.5176847740911312, 2.4577083440143137, 2.2978341001979143, 2.0473370006283367, 1.7198177571709246, 1.332426535386166, 0.9049121423874035, 0.45854812718543864], 'positive_zeros': ['1.48564895312568376525360123882537', '2.81738706083250408786678249491440', '3.24113841118841835121981805378953', '4.00790890036147446033281252921499', '5.14397056712661196206888550988103', '5.54317531553370379113419407133030', '6.53668170022004700395203828966771', '6.95357732142672684665681057726189', '7.65503445966005832377121014513048'], 'prelabel': '2-4950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.286966597695092, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2141818771590134706, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48564895312568376525360123883', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81738706083250408786678249491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24113841118841835121981805379', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.52594900053381, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 4950, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -4, 1, 0, 0, -1, 0, 0, -4, 0, 1, -2, 0, 8, 0, 0, -1, 4, 0, 0, 0, 0, -4, 0, 0, -8, 1, 0, -2, 0, 0, -4, 8, 0, 0, 4, 0, -8, -1, 0, 4, -12, 0, 9, 0, 0, 0, 2, 0, 0, -4, 0, 0, -12, 0, 2, -8, 0, 1, 0, 0, 8, -2, 0, 0, 8, 0, -4, -4, 0, 8, 4, 0, -4, 0, 0, 4, -12, 0, 0, -8, 0, -1, -16, 0, 0, 4, 0, -12, 0, 0, -16, 9, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, -8, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 4, 37], 'euler41': [1, -4, 41], 'euler43': [1, 8, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, 4, 73], 'euler79': [1, 4, 79], 'euler83': [1, 12, 83], 'euler89': [1, 16, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, 1, 0], [1, 0, 13], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 0, 29], [1, 8, 31], [1, 4, 37], [1, -4, 41], [1, 8, 43], [1, 12, 47], [1, -2, 53], [1, 12, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, 4, 73], [1, 4, 79], [1, 12, 83], [1, 16, 89], [1, 16, 97]], 'index': 65, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4950/w', 'ModularForm/GL2/Q/holomorphic/4950/2/a/w/1/1', 'ModularForm/GL2/Q/holomorphic/4950/2/a/w'], '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': '2-4950-1.1-c1-0-65', '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': '2-4950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.286966597695092, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2141818771590134706, 'z1': {'__RealLiteral__': 0, 'data': '1.48564895312568376525360123883', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20381140
{'Lhash': '1883283787158213671840065243098', 'Lhash_array': ['1883283787158213671840065243098'], 'factors': ['2-4950-1.1-c1-0-65'], 'label': '2-4950-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4950/2/a/w'}
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id: 24568246
{'Lhash': '1883283787158213671840065243098', 'Lhash_array': ['1883283787158213671840065243098'], 'factors': ['2-4950-1.1-c1-0-65'], 'label': '2-4950-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4950/2/a/w/1/1'}
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id: 88059
{'Lhash': '2141818771590134706', 'Lhash_array': ['2141818771590134706'], 'factors': ['2-4950-1.1-c1-0-65'], 'label': '2-4950-1.1-c1-0-65', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4950/w'}