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lfunc_lfunctions • Show schema
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{'Lhash': '1289336451459989264368464658103', 'a10': [-0.7071067811865476, 0.7071067811865476], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [1.4142135623730951, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.269', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'conjugate': '1994461874111765944242529662972', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476], [0, 1.0]], [[1.0, 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'5.21723281758893574486414839805139', '6.68243655666069059793955408898540', '7.88659554238131427615156143458009', '8.323644875006776803554879314842429', '9.154680313907273444776197842452181'], 'prelabel': '2-2160-240.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.038258362493308, 'root_angle': -0.625, 'root_number': '-0.38268343236508977172845998403043 - 0.92387953251128675612818318939698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3125', 'prec': 24}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01710712023317427930031504358', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16327285279202566813070696185', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75183510207255080940771329695', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872853, 'bad_primes': [2, 3, 5], 'central_character': '240.29', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/1/bn/a/269/2'], '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': '2-2160-240.29-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2160-240.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.038258362493308, 'root_angle': -0.3125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01710712023317427930031504358', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1289336451459989264368464658103', 'Lhash_array': ['1289336451459989264368464658103'], 'label': '2-2160-240.29-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/1/bn/a/269/2'}