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lfunc_lfunctions • Show schema
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{'Lhash': '1195499591028140296639689200310', 'a10': [0.0, 0.0], 'a2': [-1.4518153030021068, 0.0], 'a3': [-0.25705753998183967, 0.0], 'a4': [0.10776767403109935, 0.0], 'a5': [0.0, 0.0], 'a6': [0.3732000702977108, 0.0], 'a7': [-4.956231281007638, 0.0], 'a8': [2.747171847676921, 0.0], 'a9': [-2.9339214211384848, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.32632299548061, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [197, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 197], 'central_character': '4925.1', 'coefficient_field': 'CDF', 'conductor': 4925, 'conductor_radical': 985, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4518153030021068, 0], [2.0, 0]], [[1.0, 0], [0.25705753998183967, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.956231281007638, 0], [7.0, 0]], [[1.0, 0], [-4.281840852837459, 0], [11.0, 0]], [[1.0, 0], [0.0395948453077018, 0], [13.0, 0]], [[1.0, 0], [-2.3594233895577417, 0], 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6.271070322957685, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.943082889569808157856266105639', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26713238944527245523935240044', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38245898903025875422849534995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.32632299548061, 'bad_primes': [5, 197], 'central_character': '1.1', 'conductor': 4925, 'conductor_radical': 985, 'degree': 2, 'index': 134, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4925/2/a/r/1/14'], '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': '2-4925-1.1-c1-0-134', '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': '2-4925-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.271070322957685, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.943082889569808157856266105639', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1195499591028140296639689200310', 'Lhash_array': ['1195499591028140296639689200310'], 'factors': ['2-4925-1.1-c1-0-134'], 'label': '2-4925-1.1-c1-0-134', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4925/2/a/r/1/14'}