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lfunc_lfunctions • Show schema
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{'Lhash': '844839696487227095103608540943', 'a10': [-1.600859781523404, -0.4937998457607181], 'a2': [-0.19252954911766765, 2.5691282886951523], 'a3': [1.5534122099816199, -0.7661008457638065], 'a4': [-4.5856908840399715, -0.6911816897434966], 'a5': [-0.14469666400800887, 0.6339575069763895], 'a6': [1.6691336024634362, 4.138412303081803], 'a7': [-1.1941238394565095, 2.3609464746244555], 'a8': [1.512039719302913, -6.624678858149061], 'a9': [1.8261789882399604, -2.380140815773486], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5534122099816199, 0.7661008457638065]]], [7, [[1.0, 0], [1.1941238394565095, -2.3609464746244555]]]], 'bad_primes': [3, 7], 'central_character': '441.4', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '3033745960334785805746092120603', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/2/z/a/4/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1213446775143348, 0.903843937354834, 0.6956065154793357, 0.49017175230689186, 0.28273593425506155, 0.0710829593667013, -0.143968556737685, -0.3585484370957507, -0.5660594753645157, -0.7577716776186738, -0.9236398921061878, -1.0533076529147318, -1.1372493748541896, -1.1679789098251048, -1.141223727148771, -1.0569388489751883, -0.9200201357105705, -0.7405781615991334, -0.5336556592732437, -0.31831507399621983, -0.11608711325634123, 0.05114797150068825, 0.1636849473214961, 0.2066748215084741, 0.17264070241148333, 0.06346219461730408, -0.10854034901815418, -0.32074194291701175, -0.5417861184698007, -0.7346563175863106, -0.8611110018209923, -0.887132017743654, -0.7888269301926819, -0.5580561353764418, -0.20695699447021076, 0.22946192313942645, 0.6933645423320575, 1.1072357727165598, 1.380251343725096, 1.4175583470116453, 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'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.8998483713091008, 'root_number': '-0.9509092064263804 + 0.30947000037734096*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.449924185655', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66646100773755883378809255824', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58287978026015853651309968429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17586028209969943228496387213', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '441.4', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/z/a/4/3'], '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': '2-21e2-441.4-c1-0-8', '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': '2-21e2-441.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.4499241856545504, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66646100773755883378809255824', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '844839696487227095103608540943', 'Lhash_array': ['844839696487227095103608540943'], 'label': '2-21e2-441.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/z/a/4/3'}