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lfunc_lfunctions • Show schema
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{'Lhash': '136666749238482379426814830480', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [-0.8478504765076886, -2.069093900596511], 'a6': [0, 0], 'a7': [0, -3.6731261266690045], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.09986161255473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0.8478504765076886, 2.069093900596511]]], [67, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '4020.1609', 'coefficient_field': 'CDF', 'conductor': 4020, 'conductor_radical': 2010, 'conjugate': '1236650873316052478238478984400', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0.8478504765076886, 2.069093900596511]], [[1.0, 0], [0, 3.6731261266690045], [-7.0, 0]], [[1.0, 0], [3.985898336179872, 0], [11.0, 0]], [[1.0, 0], [0, -1.2492051918908957], [-13.0, 0]], 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'positive_zeros': ['0.10781105551788223565013949916351', '1.90556505200146854873133157274575', '2.72042003759165761755195923227832', '3.15407530465865373570542536035584', '4.50266433654314162932632246815606', '5.46125972702817438234072336722602', '5.97940113051864612984352919683654', '6.80092031827859918570551505597883', '7.47180590948857050130842186422331', '8.305565595554742800596317513831629'], 'prelabel': '2-4020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.6237905340340267, 'root_number': '-0.3791702600453560794054479611749717283504484488279556289 - 0.9253269227127983263456656858782158654405816838943011107*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31189526701701337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10781105551788223565013949916', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90556505200146854873133157275', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72042003759165761755195923228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.09986161255473, 'bad_primes': [2, 3, 5, 67], 'central_character': '5.4', 'conductor': 4020, 'conductor_radical': 2010, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4020/2/g/c/1609/26'], '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': '2-4020-5.4-c1-0-3', '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': '2-4020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.31189526701701337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10781105551788223565013949916', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '136666749238482379426814830480', 'Lhash_array': ['136666749238482379426814830480'], 'label': '2-4020-5.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4020/2/g/c/1609/26'}