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lfunc_lfunctions • Show schema
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{'Lhash': '1306673835695448035341008535447', 'a10': [9.637947471857387, 0.0], 'a2': [2.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [4.818973735928694, 0.0], 'a6': [-6.0, 0.0], 'a7': [7.0, 0.0], 'a8': [8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.99584506554546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [-7.0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-4.818973735928694, 0], [125.0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [-43.03488152244518, 0], [1331.0, 0]], [[1.0, 0], [-48.68446235871474, 0], [2197.0, 0]], [[1.0, 0], [24.77352364154779, 0], [4913.0, 0]], [[1.0, 0], [-63.24788561055646, 0], [6859.0, 0]], 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'4.29702838143686037608451591319900', '5.40972937367743305560591128242213', '6.06603659364882314503565473841301', '6.79993553985949136435972669349197', '7.77986730190477973009711503547267', '8.907455920075984879001147103696667', '9.688798591399700340350621645264536'], 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03078390485532278505089932112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01949348780647044692893375241', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55719272965556093408953065427', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.99584506554546, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/4/a/f/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': '2-966-1.1-c3-0-30', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03078390485532278505089932112', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1306673835695448035341008535447', 'Lhash_array': ['1306673835695448035341008535447'], 'label': '2-966-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/f/1/2'}