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lfunc_lfunctions • Show schema
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{'Lhash': '624099597583539932785696452699', 'a10': [-0.9640976288892076, 1.112627975538148], 'a2': [-0.7951092923656297, 0.5109857147873158], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [-0.4597376399143046, 1.0066850105220606], 'a5': [1.4945619968383022, -0.438842997610593], 'a6': [0.8597370755821915, -0.3926287666387392], 'a7': [-0.27593851225579014, 2.6313224693020922], 'a8': [-0.41787722674848854, -2.906399951880762], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [7, [[1.0, 0], [0.27593851225579014, -2.6313224693020922]]], [23, [[1.0, 0], [3.242021411658386, 3.5340199725452273]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '2295586052814233485411579942370', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7951092923656297, -0.5109857147873158], [0.8308300260037729, -1.8192639907090367]], [[1.0, 0], [0.9898214418809327, 0.14231483827328514]], [[1.0, 0], [-1.4945619968383022, 0.438842997610593], [4.206267664155906, -2.703204087277988]], [[1.0, 0], [0.27593851225579014, -2.6313224693020922]], [[1.0, 0], [0.5725323049140886, -0.8908776559559585], [-4.569565143020751, -10.005951948899702]], [[1.0, 0], [-0.6238417090943091, -0.5405619180563134], [1.850092897552707, 12.867678744452126]], [[1.0, 0], [-2.424105426050564, -5.3080504715367045], [-11.132632477069846, 12.84774276402239]], [[1.0, 0], [0.16695044686529956, -0.3655704857896441], [-12.442353944960416, -14.359241912730907]], [[1.0, 0], [3.242021411658386, 3.5340199725452273]], [[1.0, 0], [0.9299655368203772, 2.0363404797433597], [-18.990961284413267, 21.91673765627349]], [[1.0, 0], [6.118045871359565, -0.8796421979670682], [29.744282182049417, 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[11.242872223589526, 78.19589390859369]], [[1.0, 0], [-4.408752690728867, -1.2945265908113048], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [-1.2577294979537919, 8.747700803834574], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [-4.810792078546363, 1.4125760062792443], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [-3.570347305393613, 12.159486256381648], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [1.109324878339171, 0.7129198103105916], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [13.32263958809491, -1.91550639148618], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [-7.365424790685471, 3.363676795465551], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [-3.8344649060119127, -5.966543857862958], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-483-161.34-c1-0-3', '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/483/2/r/a/34/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6271086394554116, 0.47474243261724425, 0.3193502563039441, 0.1580748901641158, -0.010559222034449912, -0.18562620312374606, -0.3631712111175229, -0.535984018551594, -0.6937455241118806, -0.8235246766529041, -0.9106160630592347, -0.9397065488797421, -0.8963376974627079, -0.7685933386767134, -0.5488961156424053, -0.235751440860228, 0.1647595806919775, 0.6379570229604846, 1.1602242323185443, 1.69953829638853, 2.2169883883915857, 2.6693078584031693, 3.0123282944010477, 3.2051328312069214, 3.2145567737346834, 3.0195742215433334, 2.6150390002613695, 2.0142344231178293, 1.2497422776243938, 0.3722725370039313, -0.552702657898169, -1.4504097232100261, -2.243941722254299, -2.8624670720485232, -3.249580769593859, -3.3707579578007447, -3.218851700830909, 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False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.8148052884354289, 'root_number': '-0.8354713653321559 - 0.5495339823068481*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.407402644218', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49232777349782050329963510547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95158315545756754142529190087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67553064674721680023749848349', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/13'], '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': '2-483-161.34-c1-0-3', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.40740264421771444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49232777349782050329963510547', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '624099597583539932785696452699', 'Lhash_array': ['624099597583539932785696452699'], 'label': '2-483-161.34-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/13'}