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lfunc_lfunctions • Show schema
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{'Lhash': '1873052094170612171755350564296', 'a10': [0.0, 0.0], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [0.44918062442533513, -0.9835683711044663], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [0.0, 0.0], 'a6': [1.0374821311956879, 0.3046322396692123], 'a7': [-0.4740170175128286, 0.3046322396692123], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [-0.1107827733326741, -0.1278501358411696], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7805376797580158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [17, [[1.0, 0], [0.9594929736144974, 0.28173255684142967]]], [23, [[1.0, 0], [-0.28173255684142967, 0.9594929736144974]]]], 'bad_primes': [2, 17, 23], 'central_character': '1564.1291', 'coefficient_field': 'CDF', 'conductor': 1564, 'conductor_radical': 782, 'conjugate': '1401534612062795882463682356281', 'degree': 2, 'euler_factors': 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'positive_zeros': ['1.47757757053354096717780731021021', '2.78684303005574373109668417927609', '3.81741173015340650330442972494959', '4.12970100311591750543200497551351', '5.15337525903470894022007596105844', '6.18623495364147884312945981204728', '7.32880484111456381307867287268355', '8.407430904011505150926703260399063', '9.152487704757588671168986520272379', '9.781838316021002097215219715869200'], 'prelabel': '2-1564-1564.1291-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8834804354132669, 'root_angle': -0.0337482633672272, 'root_number': '0.99438479329865057609463618176967 - 0.10582477430356262438257827244780*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.016874131683613597', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47757757053354096717780731021', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78684303005574373109668417928', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81741173015340650330442972495', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7805376797580158, 'bad_primes': [2, 17, 23], 'central_character': '1564.1291', 'conductor': 1564, 'conductor_radical': 782, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1564/1/w/c/1291/2'], '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': '2-1564-1564.1291-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1564-1564.1291-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8834804354132669, 'root_angle': -0.0168741316836136, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47757757053354096717780731021', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1873052094170612171755350564296', 'Lhash_array': ['1873052094170612171755350564296'], 'label': '2-1564-1564.1291-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1564/1/w/c/1291/2'}