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lfunc_lfunctions • Show schema
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{'Lhash': '610803179309379549596598014012', 'a10': [1.056570960785646, -0.2298429438132142], 'a2': [-0.9898214418809327, -0.14231483827328514], 'a3': [0.0, 0.0], 'a4': [0.9594929736144974, 0.28173255684142967], 'a5': [-1.013106530477337, 0.37786919945981257], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.9096319953545183, -0.41541501300188644], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [0.3494641795990983, -0.9369497249997617]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.863', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '1431945710952371827408297848239', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9898214418809327, 0.14231483827328514]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.013106530477337, 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['0.48183874894186913989365443862836', '1.84152247081335107840735668282369', '2.95079645231560273556145398705886', '3.93817664257677161002679417596773', '4.88434261240657152271601540319938', '5.77364320687451359255742614410968', '6.85927461966472648188527875912083', '7.17770661876938779591502857720362', '8.257296395573057903005368490360782', '8.454121040557250902671355357846347'], 'prelabel': '2-3204-1068.863-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.4190246851224172, 'root_number': '0.25165649466653155326606796081897 - 0.96781661935108036038067478395120*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20951234256120857', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48183874894186913989365443863', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84152247081335107840735668282', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95079645231560273556145398706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.863', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/863/1'], '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': '2-3204-1068.863-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.863-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.2095123425612086, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48183874894186913989365443863', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '610803179309379549596598014012', 'Lhash_array': ['610803179309379549596598014012'], 'label': '2-3204-1068.863-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/863/1'}