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lfunc_lfunctions • Show schema
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{'Lhash': '2593791086342884385781923348008', 'a10': [0, 19.26092193186506], 'a2': [0, -2.2151665788958805], 'a3': [0, 0], 'a4': [-0.90696297225728, 0], 'a5': [-8.69502190732103, 0], 'a6': [0, 0], 'a7': [0, -6.671891093309577], 'a8': [0, -6.851592251143124], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.604', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '170395516871032347347699882620', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.2151665788958805], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [8.69502190732103, 0], [25.0, 0]], [[1.0, 0], [0, 6.671891093309577], [-49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 11.154668092650569], [-169.0, 0]], [[1.0, 0], [0, 7.826871924964006], [-289.0, 0]], [[1.0, 0], [0, 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'3.44544398132813238477289388097513', '4.38590736273279198902419264259239', '5.36117466907122709289593135941804', '6.26811579781848671314267517971482', '7.15443771263763496962666214168037', '7.72029686750817018612415559389805', '8.595088866161590533483793379277138', '8.917473006070644449954297669526376', '10.40659970407582733888965723197022'], 'prelabel': '2-33e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.37843599448277054, 'root_number': '0.3726885178854784635996786094663660342775287066825589093 - 0.9279565014785582067483702708483166827891438365472320070*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1892179972413853', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04614038432663936773178679458', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44544398132813238477289388098', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38590736273279198902419264259', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '11.10', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 84, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/c/m/604/5'], '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': '2-33e2-11.10-c2-0-84', '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': '2-33e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.18921799724138527, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04614038432663936773178679458', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2593791086342884385781923348008', 'Lhash_array': ['2593791086342884385781923348008'], 'label': '2-33e2-11.10-c2-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/c/m/604/5'}