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lfunc_lfunctions • Show schema
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{'Lhash': '3087873881472645099353699198335', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, -2.6457513110645907], 'a4': [0.0, 0.0], 'a5': [5.656854249492381, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-5.0, -7.483314773547883], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6158105378588505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.4142135623730951, 2.6457513110645907]]]], 'bad_primes': [2, 3], 'central_character': '96.17', 'coefficient_field': 'CDF', 'conductor': 96, 'conductor_radical': 6, 'conjugate': '2089301929821638766780319256962', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 2.6457513110645907]], [[1.0, 0], [-5.656854249492381, 0], [25.0, 0]], [[1.0, 0], [4.0, 0], [49.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [121.0, 0]], [[1.0, 0], [0, 10.583005244258363], [-169.0, 0]], [[1.0, 0], [0, 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'9.460062704500694166646597056455152', '10.35110355161242870528211232295987', '11.61132569964307705971719558369748', '13.08766582892914806156478698202699', '14.04785314880408570935374111271135'], 'prelabel': '2-96-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6173467586942667, 'root_angle': 0.271279537537173, 'root_number': '0.6582912447176388 + 0.7527633340752602*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.135639768769', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43590298534683012724796529922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13646676666139680601719786919', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61974447412954744232155675306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6158105378588505, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 96, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/96/3/h/c/17/3'], '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': '2-96-24.5-c2-0-4', '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': '2-96-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6173467586942667, 'root_angle': 0.1356397687685865, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43590298534683012724796529922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3087873881472645099353699198335', 'Lhash_array': ['3087873881472645099353699198335'], 'label': '2-96-24.5-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/96/3/h/c/17/3'}