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lfunc_lfunctions • Show schema
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{'Lhash': '2857510682506554259897818865145', 'a10': [2.897365851500828, 1.9020431375859945], 'a2': [1.1694441434763396, -0.7952360626184468], 'a3': [1.2955793544611445, 0.5366465397483855], 'a4': [0.7351992094222193, -1.8599683122206527], 'a5': [0.937867115440829, 2.2642115098009827], 'a6': [1.9418683697707622, -0.40271327162583753], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [-0.6193394674581806, -2.759785974319135], 'a9': [-0.7307839884776021, -0.7307839884776021], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1694441434763396, 0.7952360626184468]]], [7, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 7], 'central_character': '224.29', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '3133826372979279608124420782651', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.39190230967230416, 0.38563616550275936], 'positive_zeros': ['2.25417846368083165681867285238347', '3.68298164016309748250272307555317', '5.07648885848302870701364080603472', '5.94090540311715409832129600421958', '7.38003262430693106905142500712925', '8.249628390533251956968130911127536', '8.951773670018705533335317744546269', '10.36932138603308859817712675631090', '11.70867105293060212863811618570668', '12.76943055913582738515416142734430'], 'prelabel': '2-224-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.11205075905601053, 'root_number': '0.9386788874839154 + 0.3447926133082885*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.056025379528', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25417846368083165681867285238', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.68298164016309748250272307555', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.07648885848302870701364080603', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '32.29', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/u/b/29/8'], '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': '2-224-32.29-c1-0-14', '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': '2-224-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.056025379528005265, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25417846368083165681867285238', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2857510682506554259897818865145', 'Lhash_array': ['2857510682506554259897818865145'], 'label': '2-224-32.29-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/u/b/29/8'}