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lfunc_lfunctions • Show schema
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{'Lhash': '501073360072107317488354137323', 'a10': [2.961537630038956, -4.364944804382019], 'a2': [-1.6680362190143936, -1.6680362190143936], 'a3': [0.0, 0.0], 'a4': [0.0, 3.5646896558876686], 'a5': [0.4206764692352742, 2.1961400930340815], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [2.609959017537799, -2.609959017537799], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.545862991011, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.4206764692352742, -2.1961400930340815]]], [7, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 7], 'central_character': '945.323', 'coefficient_field': 'CDF', 'conductor': 945, 'conductor_radical': 105, 'conjugate': '2068329116194854118330113274557', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6680362190143936, 1.6680362190143936], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39527718440861657168424295576', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66788738494377180221472923606', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62901801616905630392651842049', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.545862991011, 'bad_primes': [3, 5, 7], 'central_character': '15.8', 'conductor': 945, 'conductor_radical': 105, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/945/2/m/a/323/4'], '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': '2-945-15.8-c1-0-2', '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': '2-945-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.746973423790445, 'root_angle': -0.192017581282121, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39527718440861657168424295576', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '501073360072107317488354137323', 'Lhash_array': ['501073360072107317488354137323'], 'label': '2-945-15.8-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/945/2/m/a/323/4'}