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lfunc_lfunctions • Show schema
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{'Lhash': '1994406184859839842725239374630', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.70839068204551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, -1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '7728.1', 'coefficient_field': '1.1.1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, -1], [1, -5, 11], [1, 6, 13], [1, -4, 17], [1, 7, 19], [1, -1], [1, -2, 29], [1, 10, 31], [1, 2, 37], [1, 7, 41], [1, 8, 43], [1, 9, 47], [1, -11, 53], [1, 3, 59], [1, 11, 61], [1, 8, 67], [1, 0, 71], [1, -8, 73], [1, 10, 79], [1, -14, 83], [1, 10, 89], [1, -10, 97], [1, 19, 101], [1, -3, 103], [1, 4, 107], [1, -4, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, -1], 1]], [[[1, -5, 11], 1]], [[[1, 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-1.185392507301303, -1.4058008723509907, -1.5049407038018792, -1.4864217720873854, -1.360553405102637, -1.143688341964369, -0.8572259616585581, -0.5263299911805233], 'positive_zeros': ['1.57330906836691786812748087214733', '2.07619581738186788228273092936781', '3.19521790940355524934143527745488', '3.88714816749374542194421076546376', '4.60329477227147321605608920862432', '5.31797773349142158270635479696304', '6.25309718519970647700320378976305', '6.95647997768904725125540842260728', '7.48584937198436003006659823474782'], 'prelabel': '2-7728-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.855468839098371, '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': 1492663695997635187, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57330906836691786812748087215', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07619581738186788228273092937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19521790940355524934143527745', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.70839068204551, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 5, 0, -6, 0, 0, 0, 4, 0, -7, 0, 1, 0, 1, 0, -5, 0, 1, 0, 2, 0, -10, 0, 5, 0, 0, 0, -2, 0, -6, 0, -7, 0, -8, 0, 0, 0, -9, 0, 1, 0, 4, 0, 11, 0, 0, 0, -7, 0, -3, 0, -11, 0, 1, 0, 0, 0, -8, 0, 1, 0, 0, 0, 8, 0, -5, 0, 5, 0, -10, 0, 1, 0, 14, 0, 0, 0, 2, 0, -10, 0, -6, 0, -10, 0, 0, 0, 10, 0, 5, 0], 'euler11': [1, -5, 11], 'euler13': [1, 6, 13], 'euler17': [1, -4, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, 7, 41], 'euler43': [1, 8, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 5], 'euler53': [1, -11, 53], 'euler59': [1, 3, 59], 'euler61': [1, 11, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -8, 73], 'euler79': [1, 10, 79], 'euler83': [1, -14, 83], 'euler89': [1, 10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, -1, 0], [1, -5, 11], [1, 6, 13], [1, -4, 17], [1, 7, 19], [1, -1, 0], [1, -2, 29], [1, 10, 31], [1, 2, 37], [1, 7, 41], [1, 8, 43], [1, 9, 47], [1, -11, 53], [1, 3, 59], [1, 11, 61], [1, 8, 67], [1, 0, 71], [1, -8, 73], [1, 10, 79], [1, -14, 83], [1, 10, 89], [1, -10, 97]], 'index': 126, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7728/r', 'ModularForm/GL2/Q/holomorphic/7728/2/a/r/1/1', 'ModularForm/GL2/Q/holomorphic/7728/2/a/r'], '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': '2-7728-1.1-c1-0-126', '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': '2-7728-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1492663695997635187, 'z1': {'__RealLiteral__': 0, 'data': '1.57330906836691786812748087215', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22163876
{'Lhash': '1994406184859839842725239374630', 'Lhash_array': ['1994406184859839842725239374630'], 'label': '2-7728-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/r'}
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id: 24580875
{'Lhash': '1994406184859839842725239374630', 'Lhash_array': ['1994406184859839842725239374630'], 'label': '2-7728-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/r/1/1'}
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id: 39549
{'Lhash': '1492663695997635187', 'Lhash_array': ['1492663695997635187'], 'label': '2-7728-1.1-c1-0-126', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7728/r'}