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lfunc_lfunctions • Show schema
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{'Lhash': '927700833373090002389798673920', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.302775637731995], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 1.532088886237956], 'a8': [0, 0], 'a9': [-2.302775637731995, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.153532368300084, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 17], 'central_character': '5780.5201', 'coefficient_field': 'CDF', 'conductor': 5780, 'conductor_radical': 170, 'conjugate': '695594850018647508260745998722', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.302775637731995], [-3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.532088886237956], [-7.0, 0]], [[1.0, 0], [0, -2.4484173066328223], [-11.0, 0]], [[1.0, 0], [6.182160879303812, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.34589608276489925, 0], [19.0, 0]], [[1.0, 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'3.99593778532281431890572818747217', '4.45462429009808348939356083207566', '5.42893500431320514140006235586273', '5.62883532779518287794389279655520', '7.01025622796444784344242201226378', '7.53316308928049655043086178483472', '8.309193080517299212689390768079238'], 'prelabel': '2-5780-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.793639110837437, 'root_angle': 0.3651799316204712, 'root_number': '0.4109991022638095680428987392367467474879677975372042472 + 0.9116357484973604329049185952848247627397571954652668979*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1825899658102356', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73182691918898281799742053767', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17352207488376703431927761323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20568799675767873080319311155', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.153532368300084, 'bad_primes': [2, 5, 17], 'central_character': '17.16', 'conductor': 5780, 'conductor_radical': 170, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5780/2/c/g/5201/3'], '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': '2-5780-17.16-c1-0-39', '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': '2-5780-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.793639110837437, 'root_angle': 0.1825899658102356, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73182691918898281799742053767', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '927700833373090002389798673920', 'Lhash_array': ['927700833373090002389798673920'], 'label': '2-5780-17.16-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5780/2/c/g/5201/3'}