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lfunc_lfunctions • Show schema
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{'Lhash': '2728349489443914985139180169487', 'a10': [-0.8916013418728299, -0.5147662747401099], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [1.0969910277687343, -1.3403770682143499], 'a4': [0.0, 1.0], 'a5': [0.9944520785481724, -0.26646263135843423], 'a6': [-1.7234795089173827, 0.17209991964523813], 'a7': [0.33916263766757815, -0.09087835486583704], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.593221369989792, -2.940763235316205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.0969910277687343, 1.3403770682143499]]], [13, [[1.0, 0], [-0.024174628096638038, -3.6054702311011235]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.149', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '1731191046977272761462185099436', 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'5.16559157811899310211207644119433', '6.36851845575163992153159333232841', '7.65668289946992788389127027697694', '8.572130313288803638289759967351559', '9.475514618008991854409688840423368', '10.22444611187654467036514583266837', '11.02448551524699784409956814022365', '12.48929785841482736790763546122865'], 'prelabel': '2-234-117.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.2372871812853261, 'root_number': '0.079792082529485 + 0.9968115286078948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237287181285', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15228824800201216837612273747', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89841582326666725855230575125', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16559157811899310211207644119', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.32', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/y/a/149/5'], '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': '2-234-117.32-c1-0-12', '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': '2-234-117.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.2372871812853261, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15228824800201216837612273747', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2728349489443914985139180169487', 'Lhash_array': ['2728349489443914985139180169487'], 'factors': ['2-234-117.32-c1-0-12'], 'label': '2-234-117.32-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/y/a/149/5'}