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lfunc_lfunctions • Show schema
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{'Lhash': '3804376446548503317954832844886', 'a10': [-1.7867530576926702, -3.0947470765027503], 'a2': [0.766044443118978, -0.6427876096865394], 'a3': [-1.078556044724167, -1.3552552742524047], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.6205328248182957, -3.5192165278680214], 'a6': [-1.6973631629051107, -0.3449033099475255], 'a7': [-0.6703487880250416, -2.5594203449987183], 'a8': [-0.5, -0.8660254037844386], 'a9': [-0.6734337167779206, 2.9234375363784797], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, 0.6427876096865394]]], [3, [[1.0, 0], [1.078556044724167, 1.3552552742524047]]], [7, [[1.0, 0], [0.6703487880250416, 2.5594203449987183]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.67', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1133406583325276724627009814706', 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.00112384742574856071489338162', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47007420372313535142892967989', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33129495148294699943813205890', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '189.67', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/v/b/67/4'], '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': '2-378-189.67-c1-0-23', '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': '2-378-189.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.44466433953338924, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.00112384742574856071489338162', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3804376446548503317954832844886', 'Lhash_array': ['3804376446548503317954832844886'], 'label': '2-378-189.67-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/v/b/67/4'}