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lfunc_lfunctions • Show schema
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{'Lhash': '1543049981359777382535697559169', 'a10': [1.6033388367821997, -0.8280427782657742], 'a2': [-1.2565354726761266, 0.6489365191654597], 'a3': [0, 0], 'a4': [1.157762788186834, -1.6308235116927425], 'a5': [-1.275999660692, 0], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [-0.3964690792500939, 2.8005021459014423], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.0733807856176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.2565354726761266, -0.6489365191654597]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1512.323', 'coefficient_field': 'CDF', 'conductor': 1512, 'conductor_radical': 42, 'conjugate': '227127537468311101697433669979', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2565354726761266, -0.6489365191654597]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.275999660692, 0], [5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -6.5740053354641095], 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'positive_zeros': ['1.21725180509673937880650008002963', '2.51557109610896399236196000509377', '3.80322100972509194637271000613941', '4.09244339021460077247390985514441', '5.98928380501168004361263107575366', '6.43813851124861679796642696549170', '7.61941658605275658947370607737822', '8.310957007901385308816100637437440', '8.685501310562847644995137303843412', '9.709650123563649156877224879110393'], 'prelabel': '2-1512-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.474677076451508, 'root_angle': 0.5447658688505621, 'root_number': '-0.140172987234264058476243315341818140396028229156159658 + 0.990127029047193946614388250484123676401558844833739312*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27238293442528105', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21725180509673937880650008003', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51557109610896399236196000509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80322100972509194637271000614', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.0733807856176, 'bad_primes': [2, 3, 7], 'central_character': '24.11', 'conductor': 1512, 'conductor_radical': 42, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1512/2/j/d/323/8'], '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': '2-1512-24.11-c1-0-56', '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': '2-1512-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.474677076451508, 'root_angle': 0.27238293442528105, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21725180509673937880650008003', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1543049981359777382535697559169', 'Lhash_array': ['1543049981359777382535697559169'], 'label': '2-1512-24.11-c1-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1512/2/j/d/323/8'}