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lfunc_lfunctions • Show schema
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{'Lhash': '1569647977428090287915493536406', 'a10': [0.0, 0.0], 'a2': [-0.8412535328311812, -0.5406408174555976], 'a3': [0.0, 0.0], 'a4': [0.41541501300188644, 0.9096319953545183], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9594929736144974, -0.28173255684142967], 'a8': [0.14231483827328514, -0.9898214418809327], 'a9': [-0.41541501300188644, 0.9096319953545183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6427957362713071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8412535328311812, 0.5406408174555976]]], [7, [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]]], [23, [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]]]], 'bad_primes': [2, 7, 23], 'central_character': '1288.1189', 'coefficient_field': 'CDF', 'conductor': 1288, 'conductor_radical': 322, 'conjugate': '1594781549519502464401473736654', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8412535328311812, 0.5406408174555976]], [[1.0, 0], 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'2.41511992798911031838341600001514', '3.97121273439975976229284932730490', '5.08231944681155929186289742051167', '5.88185190711044411879090857891889', '6.82476079979522188197818680070775', '7.43974032973640332974071274799042', '8.438243951336982497382739090419813', '9.107198945050977500669679480614718', '9.530175871973256455612044991042601'], 'prelabel': '2-1288-1288.1189-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.801745431088514, 'root_angle': 0.14011219264595753, 'root_number': '0.90467692456688735785005142874806 + 0.42609818370441148991463736983629*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07005609632297877', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23823392435225361029897719663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41511992798911031838341600002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97121273439975976229284932730', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6427957362713071, 'bad_primes': [2, 7, 23], 'central_character': '1288.1189', 'conductor': 1288, 'conductor_radical': 322, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1288/1/bi/c/1189/1'], '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': '2-1288-1288.1189-c0-0-2', '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': '2-1288-1288.1189-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.801745431088514, 'root_angle': 0.07005609632297877, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23823392435225361029897719663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1569647977428090287915493536406', 'Lhash_array': ['1569647977428090287915493536406'], 'label': '2-1288-1288.1189-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1288/1/bi/c/1189/1'}