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lfunc_lfunctions • Show schema
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{'Lhash': '1728995811274292747444886590029', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -0.9364263849242712], 'a4': [0.0, 0.0], 'a5': [0.0, 3.335132025215443], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [2.1231056256176606, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '224.113', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '2513462651894000014485442457793', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.9364263849242712], [-3.0, 0]], [[1.0, 0], [0, -3.335132025215443], [-5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -4.271558410139714], [-11.0, 0]], [[1.0, 0], [0, 3.335132025215443], [-13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [0, 0.9364263849242712], [-19.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-224-8.5-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/224/2/b/b/113/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3073985097384617, 1.2691526540804483, 1.2330211850214348, 1.1939147288410528, 1.1452267258232462, 1.079548471637046, 0.9893580146509696, 0.8676360359680579, 0.708418853542077, 0.5073150614989259, 0.26199983286604367, -0.02732196249934066, -0.3575140462573481, -0.7222136404723712, -1.1116956159320472, -1.5129482880846177, -1.9100055980886543, -2.2845655063137795, -2.616902773753155, -2.8870569448238648, -3.076245023470508, -3.168415592932789, -3.1518302351319867, -3.020532855017807, -2.775551905656497, -2.4256782988471124, -1.9876759752242017, 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'10.18412109204969958804887701260051', '11.27269946673338102420603771210686', '12.19585775275808448895316825889417'], 'prelabel': '2-224-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': -0.1393867418664765, 'root_number': '0.9056456821522995 - 0.42403525608007675*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0696933709332', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36393720080517626578335742800', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72924650051081452777375767085', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77508113317440899125380030023', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '8.5', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/b/b/113/2'], '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': '2-224-8.5-c1-0-2', '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': '2-224-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': -0.06969337093323826, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36393720080517626578335742800', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728995811274292747444886590029', 'Lhash_array': ['1728995811274292747444886590029'], 'label': '2-224-8.5-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/b/b/113/2'}