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lfunc_lfunctions • Show schema
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{'Lhash': '311902738042793590684068238051', 'a10': [-2.22943057488747, 0.0], 'a2': [-2.2167764974570088, 0.0], 'a3': [-2.5917796393647126, 0.0], 'a4': [2.9140980396777625, 0.0], 'a5': [1.0057083235251627, 0.0], 'a6': [5.745396191131296, 0.0], 'a7': [-1.8209593966877031, 0.0], 'a8': [-2.0263510507291884, 0.0], 'a9': [3.717321699025479, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.833625618948815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '5239.1', 'coefficient_field': 'CDF', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2167764974570088, 0], [2.0, 0]], [[1.0, 0], [2.5917796393647126, 0], [3.0, 0]], [[1.0, 0], [-1.0057083235251627, 0], [5.0, 0]], [[1.0, 0], [1.8209593966877031, 0], [7.0, 0]], [[1.0, 0], [2.7355836751042557, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'3.62564482059638851171649433049418', '4.90954734418192680864858929084789', '5.44040402172472041871510984922977', '6.35511628733672379043796007485621', '6.71023692475335425481751710791587', '7.49760054823191164389749170829305', '8.226589698882379197341452822951245'], 'prelabel': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24604787627335026792293288491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48260718034285220702445510520', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.36332041273623034655983968621', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.833625618948815, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5239/2/a/l/1/2'], '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': '2-5239-1.1-c1-0-17', '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': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24604787627335026792293288491', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '311902738042793590684068238051', 'Lhash_array': ['311902738042793590684068238051'], 'label': '2-5239-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5239/2/a/l/1/2'}