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lfunc_lfunctions • Show schema
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{'Lhash': '1536158290889801978497609499737', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.7604492513125534, 0.0], 'a6': [0.0, 0.0], 'a7': [3.285421522963196, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.004041130129195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [167, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 167], 'central_character': '4008.1', 'coefficient_field': 'CDF', 'conductor': 4008, 'conductor_radical': 1002, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.7604492513125534, 0], [5.0, 0]], [[1.0, 0], [-3.285421522963196, 0], [7.0, 0]], [[1.0, 0], [3.5696061774648054, 0], [11.0, 0]], [[1.0, 0], [4.6790248632278475, 0], [13.0, 0]], [[1.0, 0], [-6.829984203911714, 0], [17.0, 0]], [[1.0, 0], [-3.929781635104492, 0], [19.0, 0]], [[1.0, 0], 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'3.49472255342800592748067931807', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.004041130129195, 'bad_primes': [2, 3, 167], 'central_character': '1.1', 'conductor': 4008, 'conductor_radical': 1002, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4008/2/a/j/1/3'], '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': '2-4008-1.1-c1-0-47', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4008-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.657211427030918, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21181521991409156129616521081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1536158290889801978497609499737', 'Lhash_array': ['1536158290889801978497609499737'], 'label': '2-4008-1.1-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4008/2/a/j/1/3'}