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lfunc_lfunctions • Show schema
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{'Lhash': '2093586689947442386787708049794', 'a10': [-4981.4212547401785, -12692.454358275005], 'a2': [-4.883031111299861, -21.393957151883384], 'a3': [-49.8210482401751, -46.227177205822066], 'a4': [27.438650583338706, -13.213757695264311], 'a5': [614.4099028955278, -92.60739234658952], 'a6': [-745.7045198395314, 1291.5981157958222], 'a7': [2279.676692176871, 3948.515855680896], 'a8': [-7421.836307958762, -9306.688362805284], 'a9': [-1125.727496730209, -15021.789488760402], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-12001130.987352246, -18935824.961201366]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '958992031071857828093999455812', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.883031111299861, 21.393957151883384], [-461.2960603660386, 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'-0.9021331857000443 + 0.43145766334449237*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42899971461083436', 'prec': 64}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65154869139060117780796045622094', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '4.00220871563950595360509831015334', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.74327070824930807825646191636682', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/10'], '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': '2-43-43.10-c9-0-19', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.42899971461083436, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65154869139060117780796045622094', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2093586689947442386787708049794', 'Lhash_array': ['2093586689947442386787708049794'], 'label': '2-43-43.10-c9-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/10'}