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lfunc_lfunctions • Show schema
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{'Lhash': '652058641542790093313960088507', 'a10': [3.699628148275318, -2.8594462550255966e-61], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.6439960694802112, -0.5452310735216923], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.849814074137659, 3.203971960962407], 'a6': [-1.2941819953425522, -1.1511268231307836], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [2.405446152932766, -1.7927154836562764], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-1.6439960694802112, 0.5452310735216923]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.589', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '2353228194815048467522137999943', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.6439960694802112, 0.5452310735216923]], 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'8.901880395101820761111309970970987', '9.565350476708772800949829846263656'], 'prelabel': '2-882-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.4260899436273932, 'root_number': '0.23011445269620096 - 0.973163572407192*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.213044971814', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51438357022462864683837619678', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22877211727421014800527144491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88565878420189518526940675817', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '9.4', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/f/l/589/3'], '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': '2-882-9.4-c1-0-8', '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': '2-882-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.2130449718136966, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51438357022462864683837619678', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '652058641542790093313960088507', 'Lhash_array': ['652058641542790093313960088507'], 'label': '2-882-9.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/f/l/589/3'}