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lfunc_lfunctions • Show schema
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{'Lhash': '748360919148366766556619347978', 'a10': [27.031852930309064, 0.0], 'a2': [1.0812741172123626, 0.0], 'a3': [-9.0, 0.0], 'a4': [-30.830846283446625, 0.0], 'a5': [25.0, 0.0], 'a6': [-9.731467054911263, 0.0], 'a7': [-139.5079775171979, 0.0], 'a8': [-67.9373678488394, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0812741172123626, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [139.5079775171979, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [646.3312427219229, 0], [371293.0, 0]], [[1.0, 0], [1378.3172140704316, 0], [1419857.0, 0]], [[1.0, 0], 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-1.0305437513309705], 'positive_zeros': ['0.59035267211140903457833964201979', '2.77608166455904849518776534731441', '4.31994535398646703916880005375695', '5.37990289158597660332594887223383', '6.39119191606861073606589229219396', '7.66609064906276933676167276478176', '9.334602781076864785980735753348770', '9.638418718604824914349084907357104', '10.85372426454698831054354432579678', '12.20927243792349202160507831687481'], 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59035267211140903457833964202', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77608166455904849518776534731', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31994535398646703916880005376', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/a/d/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': '2-165-1.1-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59035267211140903457833964202', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '748360919148366766556619347978', 'Lhash_array': ['748360919148366766556619347978'], 'label': '2-165-1.1-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/a/d/1/2'}