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lfunc_lfunctions • Show schema
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{'Lhash': '891892229806300995825470713990', 'a10': [0.0, 0.0], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [-1.224744871391589, -1.224744871391589], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [0.8660254037844386, -1.5], 'a7': [-1.224744871391589, 0.32816939922353555], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [1.224744871391589, 1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.407', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '1983244917460055536639883207660', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [1.224744871391589, 1.224744871391589]], 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[-29.5, 51.09549882328188]], [[1.0, 0], [-2.0, 3.4641016151377544], [-30.5, -52.827549630850754]], [[1.0, 0], [3.2259468780907405, -12.039397651552846], [-58.023702053557386, -33.5]], [[1.0, 0], [0, 10.732050807568877], [-71.0, 0]], [[1.0, 0], [-3.6742346141747673, 3.6742346141747673], [0, -73.0]], [[1.0, 0], [8.660254037844387, 5.0], [39.5, 68.41600689897065]], [[1.0, 0], [-6.572012093041972, 1.760965332978169], [71.88010851410841, -41.5]], [[1.0, 0], [-8.660254037844387, 0], [89.0, 0]], [[1.0, 0], [-14.160717995112488, 3.7943529510352585], [84.00446416709055, -48.5]], [[1.0, 0], [9.294228634059948, 5.366025403784438], [50.5, 87.4685657822283]], [[1.0, 0], [-10.038195644853696, -2.6897264165041608], [89.20061658979718, 51.5]], [[1.0, 0], [0.568406072944518, -0.568406072944518], [0, -107.0]], [[1.0, 0], [0, -12.196152422706632], [-109.0, 0]], [[1.0, 0], [1.9132692811965983, -7.14041816598649], [-97.86087062764156, -56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 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'10.89480220630815091341822652826511'], 'prelabel': '2-450-45.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': -0.505272193861407, 'root_number': '-0.016562328205795968 - 0.9998628352351154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.252636096931', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70357891176458529021146494111', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86562912005665874930117973554', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00982937557795730917977902309', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.593268090957619, 'bad_primes': [2, 3, 5], 'central_character': '45.2', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/2/p/c/407/2'], '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': '2-450-45.2-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': '2-450-45.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': -0.2526360969307035, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70357891176458529021146494111', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '891892229806300995825470713990', 'Lhash_array': ['891892229806300995825470713990'], 'label': '2-450-45.2-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/p/c/407/2'}