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lfunc_lfunctions • Show schema
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{'Lhash': '1506780681483885204006919104748', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-18.54219969115419, 0.0], 'a6': [0.0, 0.0], 'a7': [9.326693273197067, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [18.54219969115419, 0], [125.0, 0]], [[1.0, 0], [-9.326693273197067, 0], [343.0, 0]], [[1.0, 0], [39.737785928702515, 0], [1331.0, 0]], [[1.0, 0], [-32.95329234665964, 0], [2197.0, 0]], [[1.0, 0], [-90.59981160053101, 0], [4913.0, 0]], [[1.0, 0], [-72.59981160053101, 0], [6859.0, 0]], [[1.0, 0], [-45.34661345360586, 0], [12167.0, 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'5.75003461029218146942210396830517', '7.21522431960868665290002735993138', '7.70353582395919625639268348945339', '8.361679690073748069119438934249654', '9.545926400828767969814625644480577'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18864037236491074372327602677', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08474330877103364898518681223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96262756695492195544689232680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/q/1/1'], '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': '2-768-1.1-c3-0-23', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18864037236491074372327602677', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1506780681483885204006919104748', 'Lhash_array': ['1506780681483885204006919104748'], 'label': '2-768-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/q/1/1'}