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lfunc_lfunctions • Show schema
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{'Lhash': '665712461476621912233893593638', 'a10': [-0.7249320084358232, 6.617492960737587e-61], 'a2': [-1.0633901196225293, -1.0633901196225293], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.2615970930216342], 'a5': [0.3408589167130647, -0.3408589167130647], 'a6': [1.0633901196225293, 1.0633901196225293], 'a7': [-0.5931957941594672, 0.5931957941594672], 'a8': [-1.848600475203877, 1.848600475203877], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.42558224671293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.9602056258398928, -2.67536799420671]]], [13, [[1.0, 0], [-2.477360857374642, -2.619672342555072]]]], 'bad_primes': [3, 11, 13], 'central_character': '429.109', 'coefficient_field': 'CDF', 'conductor': 429, 'conductor_radical': 429, 'conjugate': '1759363376151073716602937323809', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0633901196225293, 1.0633901196225293], [0, 2.0]], 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{'__RealLiteral__': 0, 'data': '-0.0667111120998', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52515453497735591102369388273', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93486743470332520975707636217', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30736360814139222677783861333', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.42558224671293, 'bad_primes': [3, 11, 13], 'central_character': '143.109', 'conductor': 429, 'conductor_radical': 429, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/429/2/m/a/109/4'], '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': '2-429-143.109-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': '2-429-143.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': -0.0667111120998405, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52515453497735591102369388273', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '665712461476621912233893593638', 'Lhash_array': ['665712461476621912233893593638'], 'label': '2-429-143.109-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/429/2/m/a/109/4'}