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lfunc_lfunctions • Show schema
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{'Lhash': '3454549669961992614000790715689', 'a10': [0.21058929932171938, -0.6481272196277275], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [0.6497576383445145, 1.9997483866867847], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.6814812879391342, 0.0], 'a6': [2.102659886582573, 4.07697232738257e-61], 'a7': [-2.2841411745217073, -1.6595257032581354], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-1.1497576383445145, 0.835347821156297], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.49507249253193863, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [31, [[1.0, 0], [-4.025478678178071, 3.8464946914734894]]]], 'bad_primes': [2, 31], 'central_character': '62.39', 'coefficient_field': 'CDF', 'conductor': 62, 'conductor_radical': 62, 'conjugate': '3980854369027415641250502336128', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.0226122912749', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72515917977716506852677048302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.31825142155208792642946489868', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.67326917599417497162834425540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.49507249253193863, 'bad_primes': [2, 31], 'central_character': '31.8', 'conductor': 62, 'conductor_radical': 62, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/62/2/d/a/39/2'], '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': '2-62-31.8-c1-0-1', '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': '2-62-31.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7036138802865807, 'root_angle': 0.02261229127488281, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72515917977716506852677048302', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3454549669961992614000790715689', 'Lhash_array': ['3454549669961992614000790715689'], 'factors': ['2-62-31.8-c1-0-1'], 'label': '2-62-31.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/62/2/d/a/39/2'}