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lfunc_lfunctions • Show schema
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{'Lhash': '1769239303275053206673387495965', 'a10': [1.962344604949007, -2.9363434004469418], 'a2': [0.7897122549992744, -1.3678217490185325], 'a3': [-0.9915300330538468, 0.26567967162798267], 'a4': [-0.2472908913920783, -0.4283203881400767], 'a5': [2.2312685786417075, 0.14642585142731512], 'a6': [-0.4196209851776019, 1.566046836604917], 'a7': [3.68058254210871, -2.124985321461101], 'a8': [2.3776944300690226, 0.0], 'a9': [-1.6855300928219061, 0.9731412528179424], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.2312685786417075, -0.14642585142731512]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.488', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '1922357133393574409523881407347', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7897122549992744, 1.3678217490185325], [-1.0, 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'6.58348516497234941462441068371321', '7.48964180938354976790491610592655', '8.619061690510316093855556357107966', '9.162124509377538903473198249841305', '10.50249822379784534542613178863925'], 'prelabel': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.2660684471996445, 'root_number': '0.6705260619104628 + 0.7418859752676594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1330342236', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39568371833415070916172878014', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68189279796298010384482048585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61917869577656733223626554066', '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': '65.33', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/o/d/488/3'], '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': '2-845-65.33-c1-0-40', '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': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.13303422359982225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39568371833415070916172878014', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1769239303275053206673387495965', 'Lhash_array': ['1769239303275053206673387495965'], 'label': '2-845-65.33-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/o/d/488/3'}