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lfunc_lfunctions • Show schema
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{'Lhash': '1999418992511627439426312031879', 'a10': [1.745046229802012, 0.39075893053328514], 'a2': [-1.1943472823575607, 0.7573206514582242], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.8529308617497815, -1.8090077238847753], 'a5': [-0.8941307071588769, -0.8941307071588769], 'a6': [-0.30902449426803114, 1.3800376306254796], 'a7': [0.0, 1.0], 'a8': [0.35130325117563366, 2.806525614654787], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.682973507915022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1943472823575607, -0.7573206514582242]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.85', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1310743458537415059220380625248', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1943472823575607, 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0.4692698512053104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0777414206416', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57726347634880584619816736734', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46710513114992282046816341573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85233278525033302193291860872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.682973507915022, 'bad_primes': [2, 3, 7], 'central_character': '16.5', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/w/a/85/3'], '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': '2-336-16.5-c1-0-12', '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': '2-336-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.07774142064163675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57726347634880584619816736734', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1999418992511627439426312031879', 'Lhash_array': ['1999418992511627439426312031879'], 'label': '2-336-16.5-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/w/a/85/3'}