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lfunc_lfunctions • Show schema
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{'Lhash': '747352812111272809608708194678', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.2625739433950256], 'a6': [0, 0], 'a7': [0, 8.069627845140664], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.55060032897724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-5.611917934756467, -18.152310516668635]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.2735', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1607610760058814311974297596382', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.2625739433950256], [-25.0, 0]], [[1.0, 0], [0, -8.069627845140664], [-49.0, 0]], [[1.0, 0], [-8.70003987460792, 0], [121.0, 0]], [[1.0, 0], [0, -16.82363421212172], [-169.0, 0]], [[1.0, 0], [0, -4.746798291444056], [-289.0, 0]], [[1.0, 0], 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'1.21496734304584669963940636323009', '2.81569890763808671814084401482642', '3.50677967793021108709043229420902', '4.60530080787023970992678703348238', '5.07111294165582378060684601938924', '6.25611128478570837173251559797296', '6.95740125774457304025469496180113', '7.56694049632527490478951217453085', '8.442488819554968511692961003362803'], 'prelabel': '2-2736-228.227-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': -0.6246875637331001, 'root_number': '-0.38177641653761659342852632272590235867328798787752342497 - 0.92425470936084294926660573883588172160000041294863895416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31234378186655004', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58955741588156742357406300792', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.21496734304584669963940636323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81569890763808671814084401483', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.55060032897724, 'bad_primes': [2, 3, 19], 'central_character': '228.227', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/b/e/2735/4'], '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': '2-2736-228.227-c2-0-29', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2736-228.227-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': -0.31234378186655004, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58955741588156742357406300792', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '747352812111272809608708194678', 'Lhash_array': ['747352812111272809608708194678'], 'label': '2-2736-228.227-c2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/b/e/2735/4'}