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lfunc_lfunctions • Show schema
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{'Lhash': '2173616991872217993226271845380', 'a10': [0.585786437626905, 0.0], 'a2': [1.0, 0.0], 'a3': [2.414213562373095, 0.0], 'a4': [1.0, 0.0], 'a5': [0.585786437626905, 0.0], 'a6': [2.414213562373095, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [2.8284271247461903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.414213562373095, 0], [3.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [3.65685424949238, 0], [17.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [19.0, 0]], 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'6.45956538376357479745880691367484', '7.43859449054564588581994481337438', '8.353574591729780356308186853498530', '8.866034767022388039937337483764422', '9.818711379786306205475740730765262'], 'prelabel': '2-1078-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71468146781209054614105011130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62167723068659257429210932383', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68887207499182716285174986087', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/a/x/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': '2-1078-1.1-c1-0-23', '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': '2-1078-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71468146781209054614105011130', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2173616991872217993226271845380', 'Lhash_array': ['2173616991872217993226271845380'], 'label': '2-1078-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/a/x/1/2'}