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lfunc_lfunctions • Show schema
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{'Lhash': '1400900523296006229144467929398', 'a10': [0.0, 0.0], 'a2': [0.6548607339452851, 0.7557495743542583], 'a3': [0.0, 0.0], 'a4': [-0.14231483827328514, 0.9898214418809327], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9594929736144974, -0.28173255684142967], 'a8': [-0.8412535328311812, 0.5406408174555976], '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], [-0.6548607339452851, -0.7557495743542583]]], [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': '2623909753728757149709187957038', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6548607339452851, -0.7557495743542583]], [[1.0, 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'positive_zeros': ['1.10511565493187661066442799508341', '2.57329590643575108802434121288037', '3.29939206678765687445343778385178', '4.53615753650304592545942639643238', '5.23213293574460777776795869211468', '6.06468253649586397966999265250700', '6.94221075645050418876759412864386', '8.375901835732327923689223706936174', '8.714046498514682020354844191684359', '9.838585806163045499098017201755051'], 'prelabel': '2-1288-1288.1189-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.801745431088514, 'root_angle': -0.5871605346267698, 'root_number': '-0.27041387383750361057809892075324 - 0.96274416998296836236488590178234*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2935802673133849', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10511565493187661066442799508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57329590643575108802434121288', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29939206678765687445343778385', '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': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1288/1/bi/d/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-c0-0-1', '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': '2-1288-1288.1189-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.801745431088514, 'root_angle': -0.2935802673133849, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10511565493187661066442799508', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1400900523296006229144467929398', 'Lhash_array': ['1400900523296006229144467929398'], 'label': '2-1288-1288.1189-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1288/1/bi/d/1189/1'}