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lfunc_lfunctions • Show schema
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{'Lhash': '3359047523966920042580757190649', 'a10': [-3.0791966589786424, 0.7201027255432156], 'a2': [1.39193335542393, -0.25004306440747254], 'a3': [1.0185566515121856, 1.4009076870587456], 'a4': [1.8749569318834411, -0.6960865632823502], 'a5': [-2.2330466148626473, 0.11620161724550729], 'a6': [1.7680502286528723, 1.6952871110701355], 'a7': [-2.2904106208671786, -2.2904106208671786], 'a8': [2.43576347609589, -1.4377260825752818], 'a9': [-0.925084695320568, 2.853807685616473], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.39193335542393, 0.25004306440747254]]], [3, [[1.0, 0], [-1.0185566515121856, -1.4009076870587456]]], [5, [[1.0, 0], [2.2330466148626473, -0.11620161724550729]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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0.9788793716568784, 'root_angle': -0.0625975754934426, 'root_number': '0.9807254308568771 - 0.1953909651713528*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0312987877467', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.64982127043694289258862022966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77338372295083905536486703812', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.64412936629592742128139491280', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/77/15'], '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': '2-120-120.77-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': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.0312987877467213, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.64982127043694289258862022966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3359047523966920042580757190649', 'Lhash_array': ['3359047523966920042580757190649'], 'label': '2-120-120.77-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/15'}