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lfunc_lfunctions • Show schema
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{'Lhash': '182944970437589285025556340921', 'a10': [-0.8412535328311812, -0.5406408174555976], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [-0.41541501300188644, 0.9096319953545183], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [-0.9594929736144974, -0.28173255684142967], 'a7': [-0.30682331268104057, 0.1971833699456219], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [-0.6548607339452851, -0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [3, [[1.0, 0], [0.41541501300188644, -0.9096319953545183]]], [5, [[1.0, 0], [0.6548607339452851, -0.7557495743542583]]], [23, [[1.0, 0], [-4.55055442167521, -1.5140853527368243]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.601', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '3135909632979852849408193267876', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [0.30682331268104057, -0.1971833699456219], [2.907905091013205, -6.367423967481629]], [[1.0, 0], [0.3383580656849865, -2.3533320384008447], [-10.554422709759471, -3.0990581252557265]], [[1.0, 0], [2.1893698257016756, 1.4070225515682975], [5.400395169024524, 11.82521593960874]], [[1.0, 0], [5.183710772244322, 1.522074814460933], [14.30131005813008, 9.190893896745159]], [[1.0, 0], [4.824486575344519, -1.4165970733466422], [15.983817123792441, -10.272175531656353]], [[1.0, 0], [-4.55055442167521, -1.5140853527368243]], [[1.0, 0], [0.3473927154846368, 0.10200370472008975], [24.396352452104253, 15.67858370621233]], [[1.0, 0], [2.2348072240731636, 4.8935452278830684], [-20.300682752303835, 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[32.817786027149026, 71.86092763300695]], [[1.0, 0], [-0.5203479348542284, -0.6005135289040822], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [5.166297128194734, -11.312612732397213], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [4.792764726756273, -5.5311453481173185], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-7.640434977652911, -8.81753200784371], [-14.373798665601798, 99.9719656299742]], [[1.0, 0], [1.530823668283332, -10.647112479557254], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-3.47104350016297, -7.600525080207528], [-70.07009853214551, 80.86520445590564]], [[1.0, 0], [12.433904063466413, 3.6509236436877495], [91.69663507859875, 58.929849102660135]], [[1.0, 0], [0.5669090655638708, 3.942939158700066], [-108.4227060184382, 31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-690-23.3-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/690/2/m/e/601/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.2878571523830425, 0.037105215371129555, -0.19630215577914636, -0.4148838846624678, -0.6175624365392357, -0.7994030245445366, -0.9520855135690109, -1.0649366566664, -1.1263486743335014, -1.1254408176383197, -1.0538346526811153, -0.9074007268016154, -0.6878059541091861, -0.4036651219222804, -0.07109163025588358, 0.2865374418686903, 0.639733006289763, 0.9550054476138844, 1.197862257668319, 1.3364838894828406, 1.3457346252763682, 1.2110494749631127, 0.931663938028452, 0.5226413807077256, 0.015218008578017111, -0.5448658432302302, -1.1011529522809895, -1.592195249805541, -1.9587291083141514, -2.1515189011656672, -2.1388640600856297, -1.9126563444954223, -1.491918541981495, -0.9229728068070295, -0.2757707248788944, 0.3635663730971282, 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'root_analytic_conductor': 2.3472702740563025, 'root_angle': 0.659403037753086, 'root_number': '-0.4801093916134109 + 0.8772086251768164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.329701518877', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14431813498502792761097024116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77524850491333608379608414878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00350209828709948829567057353', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.3', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/e/601/1'], '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': '2-690-23.3-c1-0-0', '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': '2-690-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': 0.329701518876543, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14431813498502792761097024116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '182944970437589285025556340921', 'Lhash_array': ['182944970437589285025556340921'], 'label': '2-690-23.3-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/e/601/1'}