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lfunc_lfunctions • Show schema
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{'Lhash': '1963254277193421450573990808061', 'a10': [2.9223751199207655, 0.6926156267747194], 'a2': [1.367196714032556, 0.38058521707303833], 'a3': [0.0, 0.0], 'a4': [0.012047948346353875, 0.007270974079524207], 'a5': [2.1146518145721935, -0.08205812079318803], 'a6': [0.0, 0.0], 'a7': [1.6483094604772355, 0.25779089546472483], 'a8': [-1.9340961685981946, -2.0500221724739602], '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': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1834547772514610270086552230826', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.367196714032556, -0.38058521707303833], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1146518145721935, 0.08205812079318803], [4.98496470583896, 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{'__RealLiteral__': 0, 'data': '-0.0165057855352', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54873454628582567783102743406', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88564513541742550320533414536', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94454421320081145970255302576', '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': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/19'], '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': '2-3e6-243.103-c1-0-14', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.016505785535227635, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54873454628582567783102743406', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1963254277193421450573990808061', 'Lhash_array': ['1963254277193421450573990808061'], 'label': '2-3e6-243.103-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/19'}