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lfunc_lfunctions • Show schema
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{'Lhash': '1611337562394070396811006679526', 'a10': [2.879385241571817, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.3472963553338606, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.879385241571817, 0.0], 'a6': [-1.3472963553338606, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-1.1847925309040954, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.3472963553338606, 0], [3.0, 0]], [[1.0, 0], [2.879385241571817, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.6527036446661393, 0], [11.0, 0]], [[1.0, 0], [-1.532088886237956, 0], [13.0, 0]], [[1.0, 0], [-5.638155724715451, 0], [17.0, 0]], [[1.0, 0], [0, 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'5.67212422220794682046227082178757', '6.83139639748571341907716405260657', '7.38929306430245737405458067309621', '8.211826329426982325368248771048744'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27112120808680496365448716562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39334166901707793521730267709', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47484667335726850016520009413', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 114, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/s/1/2'], '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': '2-5054-1.1-c1-0-114', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27112120808680496365448716562', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1611337562394070396811006679526', 'Lhash_array': ['1611337562394070396811006679526'], 'label': '2-5054-1.1-c1-0-114', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/s/1/2'}