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lfunc_lfunctions • Show schema
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{'Lhash': '634887065866550176349489150635', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, 2.0], 'a6': [0, 0], 'a7': [1.0, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.92757612664035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '5376.2689', 'coefficient_field': 'CDF', 'conductor': 5376, 'conductor_radical': 42, 'conjugate': '1527855045853923978611687271382', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -2.0], [-5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -4.0], [-11.0, 0]], [[1.0, 0], [0, 6.0], [-13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [0, -4.0], [-19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [0, 2.0], [-29.0, 0]], [[1.0, 0], [-8.0, 0], [31.0, 0]], [[1.0, 0], [0, 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'-0.70710678118654752440084436210484903928483593768847403659 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50083758549259891800268889200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39131758895307238553349666187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.33602292609139606580468359735', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.92757612664035, 'bad_primes': [2, 3, 7], 'central_character': '8.5', 'conductor': 5376, 'conductor_radical': 42, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5376/2/c/s/2689/2'], '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': '2-5376-8.5-c1-0-23', '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': '2-5376-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.551913928512825, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50083758549259891800268889200', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '634887065866550176349489150635', 'Lhash_array': ['634887065866550176349489150635'], 'label': '2-5376-8.5-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5376/2/c/s/2689/2'}