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lfunc_lfunctions • Show schema
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{'Lhash': '3454792947579131424336500792648', 'a10': [0.0, 0.0], 'a2': [0.4501294201851612, -1.3406653218024887], 'a3': [0.0, -1.0], 'a4': [-1.594767010167541, -1.2069458079306137], 'a5': [0.0, 0.0], 'a6': [-1.3406653218024887, -0.4501294201851612], 'a7': [-2.6426489071648906, 0.0], 'a8': [-2.335961939604599, 1.594767010167541], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.4501294201851612, 1.3406653218024887]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.301', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '360194228580205558409270477683', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4501294201851612, 1.3406653218024887]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6426489071648906, 0], [7.0, 0]], [[1.0, 0], [0, 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'4.01800411772319870696005235265889', '4.67938071288689578034888146540379', '5.89934040240097214639981962155012', '6.72665972837522423557202747024147', '7.42594845241027896663923377770728', '8.900995494827857685119987846098512', '9.172777691871051603627047364100401', '10.10072985281646554590310143751946', '11.26444153145257290644283589539002'], 'prelabel': '2-600-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.6906747242308352, 'root_number': '-0.5638352836510322 - 0.8258872640440462*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.345337362115', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72535109197844120118420219990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.01800411772319870696005235266', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67938071288689578034888146540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/k/f/301/7'], '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': '2-600-8.5-c1-0-37', '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': '2-600-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.3453373621154176, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72535109197844120118420219990', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3454792947579131424336500792648', 'Lhash_array': ['3454792947579131424336500792648'], 'label': '2-600-8.5-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/k/f/301/7'}