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lfunc_lfunctions • Show schema
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{'Lhash': '3879623010951305784178718552535', 'a10': [-0.8412535328311812, -0.5406408174555976], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [1.3092401686557755, -2.8668360789532445], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [0.6548607339452851, -0.7557495743542583], 'a6': [-3.0239801241689155, -0.8879206785750453], 'a7': [-0.4930598929188544, 0.31687035258574364], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [-4.540057082530356, -5.2395051799716414], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, 0.9898214418809327]]], [5, [[1.0, 0], [-0.6548607339452851, 0.7557495743542583]]], [23, [[1.0, 0], [1.2999412601439049, -4.616292096496438]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.141', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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1.355197124587213, 'root_angle': 0.7808974852248268, 'root_number': '-0.7723074156635424 + 0.6352489714364756*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.390448742612', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.06048292033531447780619307370', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.01962342838275411488109641280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29730185043216789137664766675', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '23.3', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/g/d/141/3'], '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': '2-230-23.3-c1-0-7', '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': '2-230-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.3904487426124134, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.06048292033531447780619307370', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3879623010951305784178718552535', 'Lhash_array': ['3879623010951305784178718552535'], 'label': '2-230-23.3-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/g/d/141/3'}