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lfunc_lfunctions • Show schema
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{'Lhash': '3147986252870820173511532804763', 'a10': [0.7385505385030223, -4.18852824188106], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [2.4065836281914748, -2.019363434812747], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [-3.9966471311890808, -1.4546605926182354], 'a6': [2.4065836281914748, 2.019363434812747], 'a7': [0.39451595908752163, -0.683321685536352], 'a8': [-0.5, -0.8660254037844386], 'a9': [1.192871544619717, -6.765110704141096], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-4.070307545290476, -1.5596783279738884]]]], 'bad_primes': [2, 11, 19], 'central_character': '418.199', 'coefficient_field': 'CDF', 'conductor': 418, 'conductor_radical': 418, 'conjugate': '1067610833445124287423076899988', 'degree': 2, 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'0.22239015884', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48332328506297617532684705811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53677369334722652535150365955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98204049327876803633126707921', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'bad_primes': [2, 11, 19], 'central_character': '19.9', 'conductor': 418, 'conductor_radical': 418, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/j/d/199/5'], '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': '2-418-19.9-c1-0-16', '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': '2-418-19.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': 0.22239015884041632, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48332328506297617532684705811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3147986252870820173511532804763', 'Lhash_array': ['3147986252870820173511532804763'], 'label': '2-418-19.9-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/j/d/199/5'}