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lfunc_lfunctions • Show schema
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{'Lhash': '2003373275298128427671126545239', 'a10': [-2.0, 0.0], 'a2': [-0.6180339887498949, 0.0], 'a3': [0.38196601125010515, 0.0], 'a4': [-1.618033988749895, 0.0], 'a5': [3.23606797749979, 0.0], 'a6': [-0.2360679774997897, 0.0], 'a7': [1.618033988749895, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [-2.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6848434826490168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[211, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [211], 'central_character': '211.1', 'coefficient_field': 'CDF', 'conductor': 211, 'conductor_radical': 211, 'conjugate': '2003373275298128427671126545239', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6180339887498949, 0], [2.0, 0]], [[1.0, 0], [-0.38196601125010515, 0], [3.0, 0]], [[1.0, 0], [-3.23606797749979, 0], [5.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [-6.23606797749979, 0], [13.0, 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'7.64720430681378228300193610191680', '8.625227336884577484639808350635656', '9.250352518181498519287741720119778', '10.35441309180127155496159833846003', '11.00946118260807241438039653299203', '12.60765245875506820186987410091775'], 'prelabel': '2-211-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2980152089436459, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58038285544726488074611921013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41443173535724879756555829508', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35409419253810527228981723930', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6848434826490168, 'bad_primes': [211], 'central_character': '1.1', 'conductor': 211, 'conductor_radical': 211, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/211/2/a/a/1/1'], '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': '2-211-1.1-c1-0-4', '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': '2-211-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2980152089436459, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58038285544726488074611921013', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2003373275298128427671126545239', 'Lhash_array': ['2003373275298128427671126545239'], 'label': '2-211-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/211/2/a/a/1/1'}