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lfunc_lfunctions • Show schema
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{'Lhash': '188636991966357761680456816980', 'a10': [2.7744877600545865, -1.5173060565710805], 'a2': [0.3451181910744213, 1.3714566833077593], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [-1.7617868683790385, 0.9466292993601987], 'a5': [-0.5616966674997936, -2.164369851416256], 'a6': [-1.2138017340900857, -0.7257309076509699], 'a7': [-4.516144823129722, 0.0], 'a8': [-1.9062857762961294, -2.089515383789041], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.3451181910744213, -1.3714566833077593]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.5616966674997936, 2.164369851416256]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.109', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '4342583535216781097146275138258', 'degree': 2, 'euler_factors': 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1.384344483324411, 'root_angle': 0.7302900826039295, 'root_number': '-0.6619951828703056 + 0.7495080905877606*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.365145041302', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14880834824074971559494195170', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78644008064039313696558650836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39929404925038268261512875001', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '80.29', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/bl/a/109/13'], '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': '2-240-80.29-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': '2-240-80.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': 0.36514504130196473, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14880834824074971559494195170', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '188636991966357761680456816980', 'Lhash_array': ['188636991966357761680456816980'], 'label': '2-240-80.29-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/bl/a/109/13'}