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lfunc_lfunctions • Show schema
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{'Lhash': '1147315582199182047185711275334', 'a10': [-0.4210666143089474, 0.0], 'a2': [-0.23912327825655447, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9428200577958383, 0.0], 'a5': [1.7608767217434456, 0.0], 'a6': [0.0, 0.0], 'a7': [3.181943336052393, 0.0], 'a8': [0.9428200577958384, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.83018685014203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 19], 'central_character': '9747.1', 'coefficient_field': 'CDF', 'conductor': 9747, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.23912327825655447, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7608767217434456, 0], [5.0, 0]], [[1.0, 0], [-3.181943336052393, 0], [7.0, 0]], [[1.0, 0], [0.18194333605239288, 0], [11.0, 0]], [[1.0, 0], [-3.181943336052393, 0], [13.0, 0]], [[1.0, 0], [-7.842133228617895, 0], [17.0, 0]], [[1.0, 0], 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'4.09034719415614529365769555217301', '5.14845364568032009931596537240284', '5.57239079968392182041047314711810', '5.94347332473036330614507793320715', '7.33634167899986426216560260685780', '7.66524688504165734274949270394180'], 'prelabel': '2-9747-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.822141851622089, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.905072408747818928201522592086', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.46807731065605480305266196089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.47227296976484530290445415120', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 77.83018685014203, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 9747, 'conductor_radical': 57, 'degree': 2, 'index': 212, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9747/2/a/x/1/2'], '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': '2-9747-1.1-c1-0-212', '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': '2-9747-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.822141851622089, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.905072408747818928201522592086', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1147315582199182047185711275334', 'Lhash_array': ['1147315582199182047185711275334'], 'label': '2-9747-1.1-c1-0-212', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9747/2/a/x/1/2'}