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lfunc_lfunctions • Show schema
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{'Lhash': '1156636220821786130044896052805', 'a10': [0.0, 0.0], 'a2': [-2.662018113121885, 0.0], 'a3': [0.0, 0.0], 'a4': [5.086340434589, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.4683064458391053, 0.0], 'a8': [-8.215894140136388, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.91585113697024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '5625.1', 'coefficient_field': 'CDF', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.662018113121885, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4683064458391053, 0], [7.0, 0]], [[1.0, 0], [3.4324841539981925, 0], [11.0, 0]], [[1.0, 0], [-5.704374423338895, 0], [13.0, 0]], [[1.0, 0], [-1.8915520722455774, 0], [17.0, 0]], [[1.0, 0], [-2.4683064458391053, 0], [19.0, 0]], [[1.0, 0], 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'4.59835275883113257795201434556291', '5.49441198113124862367775488758240', '6.21277637928280832267622817111886', '7.12037098265556745357804225201606', '7.71449665175950713507805937962996', '8.201590931792182726896065261342560'], 'prelabel': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.912425096168884309632086098525', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.35929699446451392608734575075', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.51142708551713243934303710408', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.91585113697024, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5625/2/a/bb/1/1'], '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': '2-75e2-1.1-c1-0-76', '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': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.912425096168884309632086098525', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1156636220821786130044896052805', 'Lhash_array': ['1156636220821786130044896052805'], 'label': '2-75e2-1.1-c1-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5625/2/a/bb/1/1'}