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lfunc_lfunctions • Show schema
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{'Lhash': '1346527418294476612412374410535', 'a10': [24.397542218270974, 0.0], 'a2': [1.150640649209096, 0.0], 'a3': [0.0, 0.0], 'a4': [-6.6760260963876705, 0.0], 'a5': [21.203441956479516, 0.0], 'a6': [0.0, 0.0], 'a7': [31.26679742391435, 0.0], 'a8': [-16.886832195357144, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.150640649209096, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-21.203441956479516, 0], [125.0, 0]], [[1.0, 0], [-31.26679742391435, 0], [343.0, 0]], [[1.0, 0], [-17.381130579207166, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [89.10709819929922, 0], [4913.0, 0]], [[1.0, 0], [-80.64662594611862, 0], 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'1.83837878524894448354377368803530', '2.92199567997045115831728419777843', '4.38007235485752507054225043220989', '5.02336735188402604402311066625635', '5.54819594394532261663123736119301', '6.43266019645422729658834170893728', '7.46112726171671319558696310325688', '8.689613990624009705390497193447832', '9.016980420972683753929066208346032'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06222283810069283272261601038', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83837878524894448354377368804', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92199567997045115831728419778', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bn/1/11'], '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': '2-39e2-1.1-c3-0-107', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06222283810069283272261601038', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1346527418294476612412374410535', 'Lhash_array': ['1346527418294476612412374410535'], 'label': '2-39e2-1.1-c3-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bn/1/11'}