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lfunc_lfunctions • Show schema
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{'Lhash': '1482840954988315252299870652431', 'a10': [-1.4161839548925634, -0.9101261643013665], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [-0.9096319953545183, -0.41541501300188644], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [1.1024063827480979, -1.2722447863195647], 'a6': [-0.28173255684142967, 0.9594929736144974], 'a7': [1.3295489912301883, 2.2874220161393017], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.713548835255689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, 0.9898214418809327]]], [3, [[1.0, 0], [0.9096319953545183, 0.41541501300188644]]], [7, [[1.0, 0], [-1.3295489912301883, -2.2874220161393017]]], [23, [[1.0, 0], [-4.418561288680052, 1.8644881705653369]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.181', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'conjugate': '1102377302720105817786027208347', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [-1.1024063827480979, 1.2722447863195647], [-0.7115741913664257, -4.949107209404664]], [[1.0, 0], [-1.3295489912301883, -2.2874220161393017]], [[1.0, 0], [3.2857195309671483, 0.4724151487084205], [10.554422709759471, 3.0990581252557265]], [[1.0, 0], [-0.6971508537373264, 1.0847879029610397], [-5.400395169024524, -11.82521593960874]], [[1.0, 0], [-0.7115755626274892, -0.20893743691495478], [14.30131005813008, 9.190893896745159]], [[1.0, 0], [-6.490149755723704, 1.9056799114179486], [15.983817123792441, -10.272175531656353]], [[1.0, 0], [-4.418561288680052, 1.8644881705653369]], [[1.0, 0], [5.768511271215465, 1.6937877340424365], [24.396352452104253, 15.67858370621233]], [[1.0, 0], [-8.464808751760081, 3.865748627608924], [20.300682752303835, 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[-32.817786027149026, -71.86092763300695]], [[1.0, 0], [5.212524560592741, 6.015574020213315], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [2.5485617583779527, -5.5805718257636245], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [4.561113307171965, -5.263805358598222], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-3.509845078392184, 3.041298072888821], [14.373798665601798, -99.9719656299742]], [[1.0, 0], [1.4671337236520765, -10.204139184621077], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-1.5347335638728858, 0.7008893339797357], [70.07009853214551, -80.86520445590564]], [[1.0, 0], [5.012492314390534, -17.070981110150285], [-91.69663507859875, -58.929849102660135]], [[1.0, 0], [-19.04466679171129, 2.738209701014971], [108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-966-161.20-c1-0-19', '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/966/2/s/a/181/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3481618483735143, 1.4394120789309597, 1.5029568019679511, 1.5305155503887247, 1.5097343025483205, 1.425627899677711, 1.2626757532289774, 1.0072644584163022, 0.6502335251742005, 0.18931281442834913, -0.3687733205980452, -1.0067934826104565, -1.6963662740931063, -2.3984467250088386, -3.0651330506879133, -3.6428630966760385, -4.076903015820118, -4.316835341143476, -4.322554486061404, -4.070105692671593, -3.556591894240376, -2.8033527267643663, -1.8567136714531407, -0.7858197835205597, 0.32260205836713374, 1.3722964578866204, 2.267648289433707, 2.9248560994056945, 3.28269403339543, 3.31131410570942, 3.017631662761289, 2.4461713960949036, 1.6748109066406087, 0.8055831214651238, -0.04851109584197223, -0.778998745855937, -1.2975212797950726, 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False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': 0.47366927497238565, 'root_number': '0.08262610654745489 + 0.9965806171689316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.236834637486', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16975525805087199095499858102', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96342718604491587637809674799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24254014945413635363760413703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.713548835255689, 'bad_primes': [2, 3, 7, 23], 'central_character': '161.20', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/2/s/a/181/6'], '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': '2-966-161.20-c1-0-19', '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': '2-966-161.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.777327642763037, 'root_angle': 0.23683463748619282, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16975525805087199095499858102', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1482840954988315252299870652431', 'Lhash_array': ['1482840954988315252299870652431'], 'label': '2-966-161.20-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/2/s/a/181/6'}