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lfunc_lfunctions • Show schema
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{'Lhash': '527563790409526353336722551175', 'a10': [-2.0, 1.0], 'a2': [1.0, 0], 'a3': [0, -1.0], 'a4': [1.0, 0], 'a5': [-2.0, 1.0], 'a6': [0, -1.0], 'a7': [0, 3.0], 'a8': [1.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.863394624362128, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [2.0, -1.0]]], [37, [[1.0, 0], [6.0, 1.0]]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '1110.739', 'coefficient_field': 'CDF', 'conductor': 1110, 'conductor_radical': 1110, 'conjugate': '2404318826321360087573975970468', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [2.0, -1.0]], [[1.0, 0], [0, -3.0], [-7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [7.0, 0], [17.0, 0]], [[1.0, 0], [0, -4.0], [-19.0, 0]], [[1.0, 0], [6.0, 0], [23.0, 0]], [[1.0, 0], [0, -9.0], 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-0.5950151609391798, 'root_number': '-0.2940858488375230993519986458823219060106757937366003315 - 0.9557790087219500728939955991175461945346963296439510774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2975075804695899', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41617444926428710550282091252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38792154522695698696898176337', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84664529118434080072232867263', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.863394624362128, 'bad_primes': [2, 3, 5, 37], 'central_character': '185.184', 'conductor': 1110, 'conductor_radical': 1110, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1110/2/e/b/739/1'], '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': '2-1110-185.184-c1-0-6', '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': '2-1110-185.184-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': -0.2975075804695899, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41617444926428710550282091252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '527563790409526353336722551175', 'Lhash_array': ['527563790409526353336722551175'], 'label': '2-1110-185.184-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1110/2/e/b/739/1'}