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lfunc_lfunctions • Show schema
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{'Lhash': '685273417775459303194592268638', 'a10': [0.8632912658024403, 0.0], 'a2': [-2.7562770486696615, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.40293683097686, 0.0], 'a5': [-0.31320917692911693, 0.0], 'a6': [0.0, 0.0], 'a7': [28.565959650550873, 0.0], 'a8': [23.1608219286425, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.7562770486696615, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.31320917692911693, 0], [125.0, 0]], [[1.0, 0], [-28.565959650550873, 0], [343.0, 0]], [[1.0, 0], [63.21728982154525, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [98.82703466108072, 0], [4913.0, 0]], [[1.0, 0], [14.48972274459418, 0], 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'1.76765274860768698619404287873433', '2.59924426086718583736948297907687', '4.40225964069154970726104231966537', '4.75126237305562480039273117922361', '5.74035659858340926880361001630611', '7.08188912355695665698204681016272', '7.80172569296715166805641611266090', '8.380625010876465931197625968468948', '8.792040024361805965521131670661688'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54058540867024542797197543457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76765274860768698619404287873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59924426086718583736948297908', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bc/1/3'], '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': '2-39e2-1.1-c3-0-35', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54058540867024542797197543457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '685273417775459303194592268638', 'Lhash_array': ['685273417775459303194592268638'], 'label': '2-39e2-1.1-c3-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bc/1/3'}