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lfunc_lfunctions • Show schema
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{'Lhash': '570886308466297521966155904265', 'a10': [-2.0834243338320397, 0.0], 'a2': [-1.0, 0.0], 'a3': [-3.1152916420718855, 0.0], 'a4': [1.0, 0.0], 'a5': [2.0834243338320397, 0.0], 'a6': [3.1152916420718855, 0.0], 'a7': [-4.2929472670716535, 0.0], 'a8': [-1.0, 0.0], 'a9': [6.705042015162945, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.652043629638808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 23, 29], 'central_character': '1334.1', 'coefficient_field': 'CDF', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [3.1152916420718855, 0], [3.0, 0]], [[1.0, 0], [-2.0834243338320397, 0], [5.0, 0]], [[1.0, 0], [4.2929472670716535, 0], [7.0, 0]], [[1.0, 0], [5.593076092853003, 0], [11.0, 0]], [[1.0, 0], [2.4251496601080627, 0], [13.0, 0]], [[1.0, 0], 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'5.15390321805852139861913101977242', '5.45863353673738879717974083888507', '6.36997126313764636306507608393934', '6.93696788318870095858798091568461', '7.75378869437862979082424209618121', '9.266611889937116479669778964442267', '9.885991628494566802270458283504756'], 'prelabel': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45034989007500523889645252373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10196634266879139529369326590', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35098233686215685089388782659', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.652043629638808, 'bad_primes': [2, 23, 29], 'central_character': '1.1', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1334/2/a/j/1/2'], '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': '2-1334-1.1-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': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45034989007500523889645252373', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '570886308466297521966155904265', 'Lhash_array': ['570886308466297521966155904265'], 'label': '2-1334-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1334/2/a/j/1/2'}