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lfunc_lfunctions • Show schema
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{'Lhash': '1188875285941554164695739091077', 'a10': [-3.2057370639048863, 1.1667928701453092], 'a2': [2.379385241571817, 0.8660254037844386], 'a3': [-0.5, 0.41954981558864], 'a4': [3.379385241571817, 2.8356409098088546], 'a5': [-1.032088886237956, 0.8660254037844386], 'a6': [-1.5530334192387472, 0.565257937423568], 'a7': [0.0, 0.0], 'a8': [3.053033419238747, 5.288008999327243], 'a9': [-0.4469665807612529, 2.5348734434479843], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.434072428181207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.298133329356934, 2.849967814166494]]]], 'bad_primes': [7, 19], 'central_character': '931.557', 'coefficient_field': 'CDF', 'conductor': 931, 'conductor_radical': 133, 'conjugate': '3017868522959957485507703458201', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.379385241571817, -0.8660254037844386], [1.532088886237956, 1.2855752193730787]], [[1.0, 0], 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'data': '2.55742850845518141558566547189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43858584966076556311096519681', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.434072428181207, 'bad_primes': [7, 19], 'central_character': '133.25', 'conductor': 931, 'conductor_radical': 133, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/931/2/x/a/557/1'], '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': '2-931-133.25-c1-0-29', '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': '2-931-133.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': -0.353402405428276, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937857234262743668823727715256', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1188875285941554164695739091077', 'Lhash_array': ['1188875285941554164695739091077'], 'label': '2-931-133.25-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/931/2/x/a/557/1'}