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lfunc_lfunctions • Show schema
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{'Lhash': '1337793775045005576987401585560', 'a10': [0.19170496466188894, -0.2212393230114264], 'a2': [0.227213642826444, -0.14602134172481865], 'a3': [0.9898214418809327, 0.14231483827328514], 'a4': [-0.8005262187564263, 1.7529079087416346], 'a5': [1.0399649554762533, -0.305361262655297], 'a6': [0.2456819391895057, -0.11219918217911905], 'a7': [-1.801099829293746, 1.9380504134098366], 'a8': [0.1509469385098482, 1.0498590177674907], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9898214418809327, -0.14231483827328514]]], [7, [[1.0, 0], [1.801099829293746, -1.9380504134098366]]], [23, [[1.0, 0], [0.2772899774666365, -4.787808503730758]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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-0.35501089962214066, 'root_number': '0.43990841918253315 - 0.8980426397072272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.177505449811', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05533320838103773268359733883', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68845310042261494810598392595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11590632582767566729608249224', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/20'], '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': '2-483-161.34-c1-0-13', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.17750544981107033, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05533320838103773268359733883', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1337793775045005576987401585560', 'Lhash_array': ['1337793775045005576987401585560'], 'label': '2-483-161.34-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/20'}