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lfunc_lfunctions • Show schema
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{'Lhash': '1869676602834887971414594280680', 'a10': [0, 0], 'a2': [0, 0], 'a3': [46767.80425259953, 0], 'a4': [0, 0], 'a5': [-1953125.0, 0], 'a6': [0, 0], 'a7': [32584728.483728576, 0], 'a8': [0, 0], 'a9': [1024966047.6094669, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 183.0533572451046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '9.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1953125.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '80.1', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-46767.80425259953, 0], [1162261467.0, 0]], [[1.0, 0], [1953125.0, 0]], [[1.0, 0], [-32584728.483728576, 0], [11398895185373144, 0]], [[1.0, 0], [3593365576.6986623, 0], [61159090448414550000, 0]], [[1.0, 0], [-7050846220.595316, 0], [1461920290375446000000, 0]], [[1.0, 0], [-480091272665.193, 0], [239072435685151320000000, 0]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 13.5297212552626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c19-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47491477738287589223233694723', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52616095608242940157219779386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46900395800610637582189254618', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 183.0533572451046, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/20/a/e/1/3'], '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': '2-80-1.1-c19-0-34', 'motivic_weight': 19, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [19], 'order_of_vanishing': 1, 'prelabel': '2-80-1.1-c19-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.5297212552626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c19-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47491477738287589223233694723', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1869676602834887971414594280680', 'Lhash_array': ['1869676602834887971414594280680'], 'label': '2-80-1.1-c19-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/20/a/e/1/3'}