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lfunc_lfunctions • Show schema
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{'Lhash': '332304117283601125052250362174,1241746600042672651220752238858,1439985916369865335879980745471,2329870528998600040787767329095', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.934894292685584, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1, 0, 1]], [5, [1]], [19, [1, -2, 3, -2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': '1.1.1.1', 'conductor': 208513600000000, 'conductor_radical': 190, 'degree': 8, 'euler_factors': [[1, 0, -1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 4, 10, 16, 19, 16, 10, 4, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, -2, 0, 3, 0, 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'1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 1315237546020506647, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26214172676901085807433587199', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.979565346964776444200058671677', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.13594859349304017073477690312', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.934894292685584, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 208513600000000, 'conductor_radical': 190, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0], 'euler11': [1, 4, 10, 16, 19, 16, 10, 4, 1], 'euler13': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler17': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler19': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler29': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler3': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler31': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler37': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler41': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler43': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler47': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler59': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler61': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler67': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler7': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler71': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler73': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler79': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler83': [1, 0, -2, 0, 3, 0, -2, 0, 1], 'euler89': [1, -4, 10, -16, 19, -16, 10, -4, 1], 'euler97': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 4, 10, 16, 19, 16, 10, 4, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -2, 0, 1], [1, -4, 10, -16, 19, -16, 10, -4, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/bn/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '8-3800e4-1.1-c0e4-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-3800e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3771154809983837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 1315237546020506647, 'z1': {'__RealLiteral__': 0, 'data': '0.26214172676901085807433587199', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '332304117283601125052250362174,1241746600042672651220752238858,1439985916369865335879980745471,2329870528998600040787767329095', 'Lhash_array': ['332304117283601125052250362174', '1241746600042672651220752238858', '1439985916369865335879980745471', '2329870528998600040787767329095'], 'label': '8-3800e4-1.1-c0e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/bn/b'}