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lfunc_lfunctions • Show schema
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{'Lhash': '978738050480283907459198398220', 'a10': [-2.23606797749979, -3.0776835371752536], 'a2': [-0.8312538755549068, -1.1441228056353685], 'a3': [0.0, 0.0], 'a4': [-0.6180339887498949, 1.902113032590307], 'a5': [2.6899940478558295, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 4.151634374255492], 'a8': [2.6899940478558295, -0.8740320488976422], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.473997629191848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8312538755549068, 1.1441228056353685]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.53159113644255, 0.7265425280053609]]]], 'bad_primes': [2, 3, 13], 'central_character': '936.181', 'coefficient_field': 'CDF', 'conductor': 936, 'conductor_radical': 78, 'conjugate': '1945304454017945083394604393253', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8312538755549068, 1.1441228056353685]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6899940478558295, 0], [5.0, 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-4.424523230534982, -3.7462037908294192], 'positive_zeros': ['0.77208818447612511145700257560631', '2.08149480793782563679378734611011', '3.83019144736018986309873651287678', '4.98513632046713885797941520910351', '5.87371637289237688525466787039342', '6.54371062261716312455608168517678', '7.59496763038452666709878050196526', '8.086830691919261055208023288990619', '9.252017449179354124684384462917728', '9.967484107616127292985106391267427'], 'prelabel': '2-936-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7338613039420725, 'root_angle': -0.16458376200909924, 'root_number': '0.8692786582298057 - 0.4943223789655783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0822918810045', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77208818447612511145700257561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08149480793782563679378734611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83019144736018986309873651288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.473997629191848, 'bad_primes': [2, 3, 13], 'central_character': '104.77', 'conductor': 936, 'conductor_radical': 78, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/936/2/m/h/181/6'], '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': '2-936-104.77-c1-0-20', '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': '2-936-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7338613039420725, 'root_angle': -0.08229188100454962, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77208818447612511145700257561', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '978738050480283907459198398220', 'Lhash_array': ['978738050480283907459198398220'], 'label': '2-936-104.77-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/936/2/m/h/181/6'}