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lfunc_lfunctions • Show schema
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{'Lhash': '1376679621894617769905784093405', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.14231483827328514, -0.9898214418809327], 'a4': [0.0, 0.0], 'a5': [2.63475165844199, 0.7736328892318669], 'a6': [0.0, 0.0], 'a7': [-2.501928760800074, 2.887379709954202], 'a8': [0.0, 0.0], 'a9': [-0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.4077421915746795, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.14231483827328514, 0.9898214418809327]]], [23, [[1.0, 0], [-2.3005277445340813, -4.208036608280509]]]], 'bad_primes': [2, 3, 23], 'central_character': '552.25', 'coefficient_field': 'CDF', 'conductor': 552, 'conductor_radical': 138, 'conjugate': '2070065776809436782143455242529', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [-2.63475165844199, -0.7736328892318669], 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08600873272710843730542392335', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91508136226414420948826718898', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06325686215418404547758992113', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.4077421915746795, 'bad_primes': [2, 3, 23], 'central_character': '23.2', 'conductor': 552, 'conductor_radical': 138, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/552/2/q/a/25/3'], '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': '2-552-23.2-c1-0-4', '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': '2-552-23.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0994623577417815, 'root_angle': -0.06334200767847906, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08600873272710843730542392335', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1376679621894617769905784093405', 'Lhash_array': ['1376679621894617769905784093405'], 'label': '2-552-23.2-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/552/2/q/a/25/3'}