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lfunc_lfunctions • Show schema
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{'Lhash': '2055346517352042856842254361053', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-11.0, 2.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.440305600918503, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [11.0, -2.0]]]], 'bad_primes': [2, 5], 'central_character': '160.129', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '774708954618688414570094254725', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-27.0, 0]], [[1.0, 0], [11.0, -2.0]], [[1.0, 0], [0, 0], [-343.0, 0]], [[1.0, 0], [0, 0], [1331.0, 0]], [[1.0, 0], [0, 92.0], [-2197.0, 0]], [[1.0, 0], [0, 104.0], [-4913.0, 0]], [[1.0, 0], [0, 0], [6859.0, 0]], [[1.0, 0], [0, 0], [-12167.0, 0]], [[1.0, 0], [130.0, 0], [24389.0, 0]], [[1.0, 0], [0, 0], [29791.0, 0]], 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0.22137542647564992, 'root_number': '0.17888543819998307 + 0.9838699100999074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.221375426476', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62138251422118657619404990248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81647198083376130530739013199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58320432736613966477524676957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.440305600918503, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/4/c/a/129/2'], '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': '2-160-5.4-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-160-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': 0.22137542647564992, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62138251422118657619404990248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2055346517352042856842254361053', 'Lhash_array': ['2055346517352042856842254361053'], 'factors': ['2-160-5.4-c3-0-11'], 'label': '2-160-5.4-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/4/c/a/129/2'}