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lfunc_lfunctions • Show schema
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{'Lhash': '474309709840733669763552692399', 'a10': [0.0, 0.0], 'a2': [-0.5483300702850246, 0.5483300702850246], 'a3': [-1.731761281836356, 0.031668008028629666], 'a4': [0.0, 1.39866826804244], 'a5': [0.0, 0.0], 'a6': [0.9322122643180881, -0.9669413064543386], 'a7': [1.3071053852842094, 1.3071053852842094], 'a8': [-1.863592010291194, -1.863592010291194], 'a9': [2.9979942745349972, -0.10968286035372744], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.994390075798016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.731761281836356, -0.031668008028629666]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '375.182', 'coefficient_field': 'CDF', 'conductor': 375, 'conductor_radical': 15, 'conjugate': '2738481151936371044322001245577', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5483300702850246, -0.5483300702850246], [0, -2.0]], [[1.0, 0], [1.731761281836356, -0.031668008028629666]], [[1.0, 0], 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'data': '0.497089923203', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37416438706007661388986098015', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86664501541885132731469763470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86375644412081998438374960946', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.994390075798016, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 375, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/375/2/e/c/182/5'], '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': '2-375-15.2-c1-0-1', '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': '2-375-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7304306041555138, 'root_angle': 0.49708992320311496, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37416438706007661388986098015', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '474309709840733669763552692399', 'Lhash_array': ['474309709840733669763552692399'], 'factors': ['2-375-15.2-c1-0-1'], 'label': '2-375-15.2-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/375/2/e/c/182/5'}