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lfunc_lfunctions • Show schema
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{'Lhash': '3165983256321265925051526526802', 'a10': [0.0, 1.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.2928932188134525, -1.7071067811865475], 'a4': [0.0, -1.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [-1.0, -1.4142135623730951], 'a7': [2.0, -2.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [-2.8284271247461903, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-0.2928932188134525, 1.7071067811865475]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [13, [[1.0, 0], [-3.5355339059327378, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.281', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1331725916296362799607476465083', 'degree': 2, 'euler_factors': 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'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49752041749616048376467577338', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88605592448865906594288773242', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89159059447817598370733025184', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '39.8', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/p/e/281/2'], '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': '2-390-39.8-c1-0-14', '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': '2-390-39.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.3552516015395985, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49752041749616048376467577338', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3165983256321265925051526526802', 'Lhash_array': ['3165983256321265925051526526802'], 'label': '2-390-39.8-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/p/e/281/2'}