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lfunc_lfunctions • Show schema
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{'Lhash': '1359593156063431374584288002869', 'a10': [1.7057370639048863, -1.4312833412080066], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [-0.9396926207859084, 0.3420201433256687], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [-0.38665920154716127, 2.1928533001223154], 'a6': [0.9396926207859084, 0.3420201433256687], 'a7': [1.3263518223330697, 2.297308744992445], 'a8': [0.5, -0.8660254037844386], 'a9': [0.766044443118978, -0.6427876096865394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [3, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [19, [[1.0, 0], [4.298133329356934, 0.7252929636161356]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.73', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2992185390356859769758126699335', 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'data': '-0.142472211933', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07252988782449084960696443483', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.26451998751676803319155536322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.57526400348734760616258660642', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '19.16', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/i/a/73/1'], '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': '2-114-19.16-c1-0-0', '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': '2-114-19.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.1424722119326779, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07252988782449084960696443483', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359593156063431374584288002869', 'Lhash_array': ['1359593156063431374584288002869'], 'label': '2-114-19.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/i/a/73/1'}