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lfunc_lfunctions • Show schema
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{'Lhash': '3992089432301762849722681863698', 'a10': [-7.5235038746748515, 0.0], 'a2': [0.0, -1.4142135623730951], 'a3': [-0.06105167110739089, -2.9993787179105933], 'a4': [-2.0, 0.0], 'a5': [0.0, -5.3199206080658525], 'a6': [-4.241762061562387, 0.08634010128561383], 'a7': [-5.799593760097217, 0.0], 'a8': [0.0, 2.8284271247461903], 'a9': [-8.99254538690999, 0.3662341660247706], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.645801358354511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [0.06105167110739089, 2.9993787179105933]]], [59, [[1.0, 0], [0, 7.681145747868608]]]], 'bad_primes': [2, 3, 59], 'central_character': '354.119', 'coefficient_field': 'CDF', 'conductor': 354, 'conductor_radical': 354, 'conjugate': '191347305339884346107920893593', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [0.06105167110739089, 2.9993787179105933]], 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-1.2306932508440833, -0.5701224998354348, 0.18938945369035196, 0.7471354827964508], 'positive_zeros': ['3.14920328328880376752570898056522', '3.62990353775936348596123478981672', '5.37244957857904215995400642182775', '6.04638085014474741783047494976320', '7.07162227768136559217597609403806', '8.265051553584879386348743143112054', '9.207049082001235484714528725986077', '10.05695583835761787012545007775271', '10.84507674681781605304964720849512', '11.63921857728500779386050928113199'], 'prelabel': '2-354-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1057690445933854, 'root_angle': -0.5064782307009831, 'root_number': '-0.020350557035796957 - 0.9997929059701978*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25323911535', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.14920328328880376752570898057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.62990353775936348596123478982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.37244957857904215995400642183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.645801358354511, 'bad_primes': [2, 3, 59], 'central_character': '3.2', 'conductor': 354, 'conductor_radical': 354, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/354/3/b/a/119/10'], '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': '2-354-3.2-c2-0-39', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-354-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1057690445933854, 'root_angle': -0.25323911535049154, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.14920328328880376752570898057', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3992089432301762849722681863698', 'Lhash_array': ['3992089432301762849722681863698'], 'label': '2-354-3.2-c2-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/354/3/b/a/119/10'}