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lfunc_lfunctions • Show schema
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{'Lhash': '1628100338101569171506646168492', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.527342128550434, 1.6229921874986268], 'a4': [0.0, 0.0], 'a5': [1.5573288843046114, -1.1314656645384404], 'a6': [0.0, 0.0], 'a7': [-0.06639518169797974, -0.20434335765963194], 'a8': [0.0, 0.0], 'a9': [0.07103706298736662, 0.051611447324917396], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.56744299561724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.4198541015480302, 2.997334537604576]]], [13, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 11, 13], 'central_character': '572.521', 'coefficient_field': 'CDF', 'conductor': 572, 'conductor_radical': 286, 'conjugate': '1666485749351022824309465946465', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.527342128550434, -1.6229921874986268], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], 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'data': '3.90942873444309187116003853432', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.56744299561724, 'bad_primes': [2, 11, 13], 'central_character': '11.4', 'conductor': 572, 'conductor_radical': 286, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/572/2/n/b/521/2'], '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': '2-572-11.4-c1-0-5', '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': '2-572-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1371576908635546, 'root_angle': -0.08337491479689407, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28434470650543923367010660226', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1628100338101569171506646168492', 'Lhash_array': ['1628100338101569171506646168492'], 'label': '2-572-11.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/572/2/n/b/521/2'}