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lfunc_lfunctions • Show schema
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{'Lhash': '947583407180658725240766032089', 'a10': [0.0, 0.0], 'a2': [0.984807753012208, 0.17364817766693036], 'a3': [0.0, 0.0], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.6275953626987474, 0.9396926207859084], 'a8': [0.8660254037844386, 0.5], 'a9': [-0.17364817766693036, -0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.984807753012208, -0.17364817766693036]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1651', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '2175767772132428760256747902412', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.984807753012208, -0.17364817766693036]], [[1.0, 0], [0, 0], [0.17364817766693036, 0.984807753012208]], 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'6.99351047441964366713600417438389', '7.41910970068768186657221465644154', '8.406013416656313386893228889049731'], 'prelabel': '2-3800-152.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.24748445679042838, 'root_number': '0.015804966054588206236486223619355 - 0.99987509372321766744260676757934*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24748445679042838', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74751150436094506008877153765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44514766464527012564157558600', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97341384824334508680579613313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'bad_primes': [2, 5, 19], 'central_character': '152.131', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/cv/f/1651/2'], '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': '2-3800-152.131-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3800-152.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.24748445679042838, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74751150436094506008877153765', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '947583407180658725240766032089', 'Lhash_array': ['947583407180658725240766032089'], 'factors': ['2-3800-152.131-c0-0-1'], 'label': '2-3800-152.131-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/cv/f/1651/2'}