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lfunc_lfunctions • Show schema
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{'Lhash': '2683176024697237334093718721821', 'a10': [0.46685380827412126, -0.39955771665492273], 'a2': [0.27480860511947053, 0.0], 'a3': [1.670948939803949, -1.670948939803949], 'a4': [-1.924480230552291, 0.0], 'a5': [1.6988325677471445, -1.4539490729601376], 'a6': [0.4591911473733814, -0.4591911473733814], 'a7': [0.0, 0.38610362483552135], 'a8': [-1.0784809379770133, 0.0], 'a9': [0.0, -2.5841407188638827], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.6988325677471445, 1.4539490729601376]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.577', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '957899888896832554977670662411', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.27480860511947053, 0], [2.0, 0]], [[1.0, 0], [-1.670948939803949, 1.670948939803949], [0, -3.0]], [[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11665266770997857182875952248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26167525571816232988289820609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04826169490676460524484980448', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.57', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/k/e/577/5'], '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': '2-845-65.57-c1-0-57', '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': '2-845-65.57-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.34602480978082784, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11665266770997857182875952248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2683176024697237334093718721821', 'Lhash_array': ['2683176024697237334093718721821'], 'factors': ['2-845-65.57-c1-0-57'], 'label': '2-845-65.57-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/k/e/577/5'}