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lfunc_lfunctions • Show schema
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{'Lhash': '1286186691915073528404940371168', 'a10': [0.5255394460172265, 0.0], 'a2': [-0.5255394460172265, 0.0], 'a3': [0.010382040406669754, 0.0], 'a4': [-1.7238082906799066, 0.0], 'a5': [-1.0, 0.0], 'a6': [-0.005456171763849684, 0.0], 'a7': [1.0, 0.0], 'a8': [1.9570081461582733, 0.0], 'a9': [-2.9998922132369943, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.00009722005626, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [229, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 7, 229], 'central_character': '8015.1', 'coefficient_field': 'CDF', 'conductor': 8015, 'conductor_radical': 8015, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5255394460172265, 0], [2.0, 0]], [[1.0, 0], [-0.010382040406669754, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.454897210761778, 0], [11.0, 0]], [[1.0, 0], [2.8617034428091115, 0], [13.0, 0]], [[1.0, 0], 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'4.71546263717416519483660560905917', '5.31706080574494915042207363407164', '5.96801096216017282396311832432324', '7.06010232360531328453321633686312', '7.63568488915483664921898410356498'], 'prelabel': '2-8015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.000006076251209, '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': '1.01462239806734352963575357624', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14153108605284536351932808715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24945998497930772997575595894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.00009722005626, 'bad_primes': [5, 7, 229], 'central_character': '1.1', 'conductor': 8015, 'conductor_radical': 8015, 'degree': 2, 'index': 281, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8015/2/a/j/1/22'], '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': '2-8015-1.1-c1-0-281', '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': '2-8015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.000006076251209, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01462239806734352963575357624', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286186691915073528404940371168', 'Lhash_array': ['1286186691915073528404940371168'], 'label': '2-8015-1.1-c1-0-281', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8015/2/a/j/1/22'}