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lfunc_lfunctions • Show schema
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{'Lhash': '2631750354830171720402060560353', 'a10': [-0.6453287760160725, -3.095731055961677], 'a2': [-1.3065629648763766, -0.541196100146197], 'a3': [0.541196100146197, -1.6453287760160726], 'a4': [1.4142135623730951, 1.4142135623730951], 'a5': [1.2592801267497653, 1.8477590650225735], 'a6': [-1.5975522982247616, 1.856832424974527], 'a7': [3.2906575520321453, 0.0], 'a8': [-1.082392200292394, -2.613125929752753], 'a9': [-2.414213562373095, -1.7808910340764283], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3065629648763766, 0.541196100146197]]], [3, [[1.0, 0], [-0.541196100146197, 1.6453287760160726]]], [5, [[1.0, 0], [-1.2592801267497653, -1.8477590650225735]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '2200771542242463391730622593247', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3065629648763766, 0.541196100146197]], [[1.0, 0], [-0.541196100146197, 1.6453287760160726]], [[1.0, 0], [-1.2592801267497653, -1.8477590650225735]], [[1.0, 0], [-3.2906575520321453, 0], [7.0, 0]], [[1.0, 0], [0, 2.5185602534995306], [-11.0, 0]], [[1.0, 0], [4.653692539209309, 0], [13.0, 0]], [[1.0, 0], [-3.695518130045147, 0], [17.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [19.0, 0]], [[1.0, 0], [0, -2.613125929752753], [-23.0, 0]], [[1.0, 0], [6.080342321652387, 0], [29.0, 0]], [[1.0, 0], [0, -1.17157287525381], [-31.0, 0]], [[1.0, 0], [1.9276225648549818, 0], [37.0, 0]], [[1.0, 0], [0, -8.598902575151918], [-41.0, 0]], [[1.0, 0], [0, 6.016727526386472], [-43.0, 0]], [[1.0, 0], [0, 2.613125929752753], [-47.0, 0]], [[1.0, 0], [0, -4.592201188381077], [-53.0, 0]], [[1.0, 0], [0, -2.5185602534995306], [-59.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-61.0, 0]], [[1.0, 0], [0, -3.2906575520321453], [-67.0, 0]], [[1.0, 0], [7.123564136305713, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/m/b/59/1'], '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': '2-120-120.59-c1-0-8', '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': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.14286781244126442, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07608496722704828197574997567', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2631750354830171720402060560353', 'Lhash_array': ['2631750354830171720402060560353'], 'label': '2-120-120.59-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/m/b/59/1'}