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lfunc_lfunctions • Show schema
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{'Lhash': '1689651229767805264884506820897', 'a10': [1.9761837174904149, -1.1409502012612462], 'a2': [0.0, -1.0], 'a3': [-0.8909154428157607, 1.4853517003566519], 'a4': [-1.0, 0.0], 'a5': [1.1409502012612462, 1.9761837174904149], 'a6': [1.4853517003566519, 0.8909154428157607], 'a7': [1.4233714300707312, 2.230249710695733], 'a8': [0.0, 1.0], 'a9': [-1.4125393475047938, -2.646645535720779], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0061150654681332, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0.8909154428157607, -1.4853517003566519]]], [7, [[1.0, 0], [-1.4233714300707312, -2.230249710695733]]]], 'bad_primes': [2, 3, 7], 'central_character': '126.5', 'coefficient_field': 'CDF', 'conductor': 126, 'conductor_radical': 42, 'conjugate': '3146839985947578615832773830878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0.8909154428157607, -1.4853517003566519]], [[1.0, 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'10.28927291094765305729893036960713', '11.17461374748683766714677680624095', '12.86941844469528458343671913798056', '13.07690848733152196642238407447990'], 'prelabel': '2-126-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.00305287271815, 'root_angle': -0.18540826162828036, 'root_number': '0.8351025019653856 - 0.5500943657329651*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0927041308141', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33289979862242666992768682035', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.34428361106753044321314579809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.69011459079965489777860593833', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0061150654681332, 'bad_primes': [2, 3, 7], 'central_character': '63.5', 'conductor': 126, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/126/2/l/a/5/1'], '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': '2-126-63.5-c1-0-1', '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': '2-126-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.00305287271815, 'root_angle': -0.09270413081414018, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33289979862242666992768682035', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1689651229767805264884506820897', 'Lhash_array': ['1689651229767805264884506820897'], 'label': '2-126-63.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/126/2/l/a/5/1'}