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lfunc_lfunctions • Show schema
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{'Lhash': '3717157208475748115472251428413', 'a10': [-4.411474127809773, 0.0], 'a2': [1.0, 0.0], 'a3': [2.879385241571817, 0.0], 'a4': [1.0, 0.0], 'a5': [-4.411474127809773, 0.0], 'a6': [2.879385241571817, 0.0], 'a7': [-0.6945927106677214, 0.0], 'a8': [1.0, 0.0], 'a9': [5.2908593693815895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0699953870851577, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [67, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 67], 'central_character': '134.1', 'coefficient_field': 'CDF', 'conductor': 134, 'conductor_radical': 134, 'conjugate': '3717157208475748115472251428413', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.879385241571817, 0], [3.0, 0]], [[1.0, 0], [4.411474127809773, 0], [5.0, 0]], [[1.0, 0], [0.6945927106677214, 0], [7.0, 0]], [[1.0, 0], [5.596266658713868, 0], [11.0, 0]], [[1.0, 0], [0.16250382442976533, 0], [13.0, 0]], [[1.0, 0], 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'7.35884855139902712658880863107662', '7.73128921744132614398563094788856', '8.685743901035079225314272845137937', '10.19833252033824738945625497914589', '11.41234339634995860282874014626345', '12.56253973860395035539764903199028', '13.22488590432464789396231546972970'], 'prelabel': '2-134-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0344058135399075, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.93232000032698795456793095831', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59596559245939116333038332560', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92966724000788216658445541653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0699953870851577, 'bad_primes': [2, 67], 'central_character': '1.1', 'conductor': 134, 'conductor_radical': 134, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/134/2/a/b/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': '2-134-1.1-c1-0-5', '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': '2-134-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0344058135399075, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.93232000032698795456793095831', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3717157208475748115472251428413', 'Lhash_array': ['3717157208475748115472251428413'], 'label': '2-134-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/134/2/a/b/1/3'}