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lfunc_lfunctions • Show schema
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{'Lhash': '2993592313679869318775282916899', 'a10': [0.6472334315798023, -0.9686532834920916], 'a2': [0.9238795325112867, -0.3826834323650898], 'a3': [0.037040851374611446, -0.18621693493754812], 'a4': [0.7071067811865476, -0.7071067811865476], 'a5': [0.9686532834920916, -0.6472334315798023], 'a6': [-0.037040851374611446, -0.18621693493754812], 'a7': [-1.5937145511849695, -2.111888711400601], 'a8': [0.3826834323650898, -0.9238795325112867], 'a9': [2.738333875346881, 1.1342550294743545], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.900439568106474, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [7, [[1.0, 0], [1.5937145511849695, 2.111888711400601]]], [17, [[1.0, 0], [-4.0873739392689625, -0.5416403609268076]]]], 'bad_primes': [2, 7, 17], 'central_character': '238.139', 'coefficient_field': 'CDF', 'conductor': 238, 'conductor_radical': 238, 'conjugate': 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47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36152794243216483300386475212', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.68802286432273861516505126328', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10850418426119743730155424403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.900439568106474, 'bad_primes': [2, 7, 17], 'central_character': '119.20', 'conductor': 238, 'conductor_radical': 238, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/238/2/p/b/139/4'], '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': '2-238-119.20-c1-0-9', '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': '2-238-119.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3785643140987198, 'root_angle': 0.13843984323295602, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36152794243216483300386475212', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2993592313679869318775282916899', 'Lhash_array': ['2993592313679869318775282916899'], 'label': '2-238-119.20-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/238/2/p/b/139/4'}