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lfunc_lfunctions • Show schema
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{'Lhash': '792575766207063799298915599437', 'a10': [0.09133037128687506, 0.0], 'a2': [0.02965868558671278, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.9991203623692686, 0.0], 'a5': [3.0793802719224845, 0.0], 'a6': [-0.02965868558671278, 0.0], 'a7': [-1.0, 0.0], 'a8': [-0.11860865345093101, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.29610221907549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [127, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '2667.1', 'coefficient_field': 'CDF', 'conductor': 2667, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.02965868558671278, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.0793802719224845, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.208873048227513, 0], [11.0, 0]], [[1.0, 0], [6.436166714645726, 0], [13.0, 0]], [[1.0, 0], [0.9781076089413621, 0], 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['0.62523203638634136712268818242204', '2.18245555956808545319297098119846', '2.96240661689041571512463288255579', '4.43499761356964604601261555507690', '5.10949882534811626996101075040404', '5.52321555787388106201273825325373', '6.39991400907715229389802680570063', '7.29330302509586434973378647412813', '8.110494920039174504989109589914320', '9.108642898165902457508221854894502'], 'prelabel': '2-2667-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.614770007169966, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62523203638634136712268818242', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18245555956808545319297098120', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96240661689041571512463288256', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.29610221907549, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 2667, 'conductor_radical': 2667, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2667/2/a/o/1/7'], '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': '2-2667-1.1-c1-0-13', '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': '2-2667-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.614770007169966, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62523203638634136712268818242', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '792575766207063799298915599437', 'Lhash_array': ['792575766207063799298915599437'], 'label': '2-2667-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2667/2/a/o/1/7'}