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lfunc_lfunctions • Show schema
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{'Lhash': '396233207190115092192645902340', 'a10': [868.9856155311203, 0.0], 'a2': [-8.717797887081348, 0.0], 'a3': [0.0, 0.0], 'a4': [44.0, 0.0], 'a5': [-99.67948635501689, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-104.61357464497617, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [8.717797887081348, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [99.67948635501689, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [374.8653091444979, 0], [161051.0, 0]], [[1.0, 0], [-868.9856155311203, 0], [371293.0, 0]], [[1.0, 0], [-1096.4743499051858, 0], [1419857.0, 0]], [[1.0, 0], [868.9856155311203, 0], [2476099.0, 0]], [[1.0, 0], 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'3.29261813417647266645000541962718', '4.24142733142983482289497017072778', '5.82922022001886276778251643061174', '7.26956299575436218335375215301059', '7.74462590608702901226574664591926', '8.434675646195359268099417963972685', '9.147601277011634480392056367543158', '10.55386834660206064227043275040961'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31257288650261891516641592546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62074843303436833791400965166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29261813417647266645000541963', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/y/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': '2-21e2-1.1-c5-0-5', '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': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31257288650261891516641592546', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '396233207190115092192645902340', 'Lhash_array': ['396233207190115092192645902340'], 'label': '2-21e2-1.1-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/y/1/1'}