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lfunc_lfunctions • Show schema
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{'Lhash': '446315341946647060368336198888', 'a10': [-0.3108705700343962, 0.43211436147153803], 'a2': [-0.21747882916164557, 0.09682781319007919], 'a3': [-1.50542112470954, 0.8565671236267849], 'a4': [-1.300339796991369, 1.4441736520690664], 'a5': [1.9312388659641095, -1.1270831569097552], 'a6': [0.24445770216574056, -0.3320518505804859], 'a7': [-1.5805023452088676, 2.7375103633835236], 'a8': [0.29008950495069147, -0.8928036936940622], 'a9': [1.5325855254434724, -2.5789884852789], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.50542112470954, -0.8565671236267849]]], [5, [[1.0, 0], [-1.9312388659641095, 1.1270831569097552]]]], 'bad_primes': [3, 5], 'central_character': '225.16', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3398428024272202688150460642085', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'-0.9803227345076654 - 0.19740145948653323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46837487657', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35208072466205742126433678311', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39384758763461818534447864439', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70872597963532370109891305183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.16', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/16/13'], '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': '2-15e2-225.16-c1-0-2', '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': '2-15e2-225.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.46837487657028626, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35208072466205742126433678311', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '446315341946647060368336198888', 'Lhash_array': ['446315341946647060368336198888'], 'label': '2-15e2-225.16-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/16/13'}