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lfunc_lfunctions • Show schema
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{'Lhash': '2777396315578826577843256029538', 'a10': [-1.1133407984528387, -1.928362829059618], 'a2': [1.032088886237956, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.03208888623795607, -0.18198511713310117], 'a5': [-1.5530334192387472, -0.565257937423568], 'a6': [0.0, 0.0], 'a7': [0.41874808778511735, -2.3748384172554164], 'a8': [1.4717815070238645, -2.5492003478056238], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.406', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '615978441315000260831465314253', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.032088886237956, -0.8660254037844386], [0.3472963553338607, 1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5530334192387472, 0.565257937423568], [3.83022221559489, 3.2139380484326967]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93002952876166923136851428472', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.16', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/c/406/1'], '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': '2-3e6-27.16-c1-0-30', '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': '2-3e6-27.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.25925925925925924, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19097937166501610708544338159', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2777396315578826577843256029538', 'Lhash_array': ['2777396315578826577843256029538'], 'label': '2-3e6-27.16-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/c/406/1'}