Properties

Label 4003.2.a.b.1.18
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} +O(q^{10})\) \(q-2.37503 q^{2} -2.00580 q^{3} +3.64079 q^{4} +0.380635 q^{5} +4.76385 q^{6} +3.69515 q^{7} -3.89692 q^{8} +1.02324 q^{9} -0.904022 q^{10} -5.88580 q^{11} -7.30269 q^{12} +3.92815 q^{13} -8.77610 q^{14} -0.763479 q^{15} +1.97375 q^{16} +7.17930 q^{17} -2.43023 q^{18} -2.89072 q^{19} +1.38581 q^{20} -7.41173 q^{21} +13.9790 q^{22} -2.31289 q^{23} +7.81645 q^{24} -4.85512 q^{25} -9.32949 q^{26} +3.96499 q^{27} +13.4532 q^{28} +2.31156 q^{29} +1.81329 q^{30} +7.04153 q^{31} +3.10613 q^{32} +11.8058 q^{33} -17.0511 q^{34} +1.40650 q^{35} +3.72540 q^{36} -1.79441 q^{37} +6.86556 q^{38} -7.87909 q^{39} -1.48331 q^{40} -10.3212 q^{41} +17.6031 q^{42} -0.380637 q^{43} -21.4289 q^{44} +0.389482 q^{45} +5.49320 q^{46} -0.614354 q^{47} -3.95895 q^{48} +6.65412 q^{49} +11.5311 q^{50} -14.4002 q^{51} +14.3016 q^{52} -13.7636 q^{53} -9.41698 q^{54} -2.24035 q^{55} -14.3997 q^{56} +5.79822 q^{57} -5.49004 q^{58} +3.52453 q^{59} -2.77966 q^{60} -10.4148 q^{61} -16.7239 q^{62} +3.78103 q^{63} -11.3246 q^{64} +1.49519 q^{65} -28.0391 q^{66} -4.27333 q^{67} +26.1383 q^{68} +4.63920 q^{69} -3.34049 q^{70} +3.16932 q^{71} -3.98749 q^{72} +15.9931 q^{73} +4.26179 q^{74} +9.73840 q^{75} -10.5245 q^{76} -21.7489 q^{77} +18.7131 q^{78} -0.687068 q^{79} +0.751278 q^{80} -11.0227 q^{81} +24.5133 q^{82} +1.33334 q^{83} -26.9845 q^{84} +2.73269 q^{85} +0.904025 q^{86} -4.63654 q^{87} +22.9365 q^{88} -15.9201 q^{89} -0.925032 q^{90} +14.5151 q^{91} -8.42074 q^{92} -14.1239 q^{93} +1.45911 q^{94} -1.10031 q^{95} -6.23027 q^{96} -6.95578 q^{97} -15.8038 q^{98} -6.02260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37503 −1.67940 −0.839701 0.543049i \(-0.817270\pi\)
−0.839701 + 0.543049i \(0.817270\pi\)
\(3\) −2.00580 −1.15805 −0.579025 0.815310i \(-0.696567\pi\)
−0.579025 + 0.815310i \(0.696567\pi\)
\(4\) 3.64079 1.82039
\(5\) 0.380635 0.170225 0.0851127 0.996371i \(-0.472875\pi\)
0.0851127 + 0.996371i \(0.472875\pi\)
\(6\) 4.76385 1.94483
\(7\) 3.69515 1.39663 0.698317 0.715788i \(-0.253932\pi\)
0.698317 + 0.715788i \(0.253932\pi\)
\(8\) −3.89692 −1.37777
\(9\) 1.02324 0.341080
\(10\) −0.904022 −0.285877
\(11\) −5.88580 −1.77464 −0.887318 0.461157i \(-0.847434\pi\)
−0.887318 + 0.461157i \(0.847434\pi\)
\(12\) −7.30269 −2.10811
\(13\) 3.92815 1.08947 0.544737 0.838607i \(-0.316630\pi\)
0.544737 + 0.838607i \(0.316630\pi\)
\(14\) −8.77610 −2.34551
\(15\) −0.763479 −0.197129
\(16\) 1.97375 0.493437
\(17\) 7.17930 1.74124 0.870618 0.491960i \(-0.163719\pi\)
0.870618 + 0.491960i \(0.163719\pi\)
\(18\) −2.43023 −0.572811
\(19\) −2.89072 −0.663177 −0.331589 0.943424i \(-0.607585\pi\)
−0.331589 + 0.943424i \(0.607585\pi\)
\(20\) 1.38581 0.309877
\(21\) −7.41173 −1.61737
\(22\) 13.9790 2.98033
\(23\) −2.31289 −0.482271 −0.241136 0.970491i \(-0.577520\pi\)
−0.241136 + 0.970491i \(0.577520\pi\)
\(24\) 7.81645 1.59553
\(25\) −4.85512 −0.971023
\(26\) −9.32949 −1.82966
\(27\) 3.96499 0.763062
\(28\) 13.4532 2.54242
\(29\) 2.31156 0.429247 0.214623 0.976697i \(-0.431148\pi\)
0.214623 + 0.976697i \(0.431148\pi\)
\(30\) 1.81329 0.331060
\(31\) 7.04153 1.26470 0.632348 0.774684i \(-0.282091\pi\)
0.632348 + 0.774684i \(0.282091\pi\)
\(32\) 3.10613 0.549091
\(33\) 11.8058 2.05512
\(34\) −17.0511 −2.92424
\(35\) 1.40650 0.237743
\(36\) 3.72540 0.620900
\(37\) −1.79441 −0.295000 −0.147500 0.989062i \(-0.547123\pi\)
−0.147500 + 0.989062i \(0.547123\pi\)
\(38\) 6.86556 1.11374
\(39\) −7.87909 −1.26166
\(40\) −1.48331 −0.234531
\(41\) −10.3212 −1.61191 −0.805954 0.591978i \(-0.798347\pi\)
−0.805954 + 0.591978i \(0.798347\pi\)
\(42\) 17.6031 2.71622
\(43\) −0.380637 −0.0580465 −0.0290233 0.999579i \(-0.509240\pi\)
−0.0290233 + 0.999579i \(0.509240\pi\)
\(44\) −21.4289 −3.23054
\(45\) 0.389482 0.0580605
\(46\) 5.49320 0.809928
\(47\) −0.614354 −0.0896128 −0.0448064 0.998996i \(-0.514267\pi\)
−0.0448064 + 0.998996i \(0.514267\pi\)
\(48\) −3.95895 −0.571425
\(49\) 6.65412 0.950588
\(50\) 11.5311 1.63074
\(51\) −14.4002 −2.01644
\(52\) 14.3016 1.98327
\(53\) −13.7636 −1.89057 −0.945285 0.326245i \(-0.894216\pi\)
−0.945285 + 0.326245i \(0.894216\pi\)
\(54\) −9.41698 −1.28149
\(55\) −2.24035 −0.302088
\(56\) −14.3997 −1.92424
\(57\) 5.79822 0.767992
\(58\) −5.49004 −0.720878
\(59\) 3.52453 0.458855 0.229428 0.973326i \(-0.426315\pi\)
0.229428 + 0.973326i \(0.426315\pi\)
\(60\) −2.77966 −0.358853
\(61\) −10.4148 −1.33348 −0.666738 0.745292i \(-0.732310\pi\)
−0.666738 + 0.745292i \(0.732310\pi\)
\(62\) −16.7239 −2.12393
\(63\) 3.78103 0.476365
\(64\) −11.3246 −1.41558
\(65\) 1.49519 0.185456
\(66\) −28.0391 −3.45137
\(67\) −4.27333 −0.522071 −0.261035 0.965329i \(-0.584064\pi\)
−0.261035 + 0.965329i \(0.584064\pi\)
\(68\) 26.1383 3.16973
\(69\) 4.63920 0.558494
\(70\) −3.34049 −0.399265
\(71\) 3.16932 0.376130 0.188065 0.982157i \(-0.439779\pi\)
0.188065 + 0.982157i \(0.439779\pi\)
\(72\) −3.98749 −0.469930
\(73\) 15.9931 1.87185 0.935923 0.352204i \(-0.114568\pi\)
0.935923 + 0.352204i \(0.114568\pi\)
\(74\) 4.26179 0.495424
\(75\) 9.73840 1.12449
\(76\) −10.5245 −1.20724
\(77\) −21.7489 −2.47852
\(78\) 18.7131 2.11884
\(79\) −0.687068 −0.0773012 −0.0386506 0.999253i \(-0.512306\pi\)
−0.0386506 + 0.999253i \(0.512306\pi\)
\(80\) 0.751278 0.0839954
\(81\) −11.0227 −1.22474
\(82\) 24.5133 2.70704
\(83\) 1.33334 0.146353 0.0731765 0.997319i \(-0.476686\pi\)
0.0731765 + 0.997319i \(0.476686\pi\)
\(84\) −26.9845 −2.94425
\(85\) 2.73269 0.296402
\(86\) 0.904025 0.0974835
\(87\) −4.63654 −0.497089
\(88\) 22.9365 2.44504
\(89\) −15.9201 −1.68753 −0.843764 0.536715i \(-0.819665\pi\)
−0.843764 + 0.536715i \(0.819665\pi\)
\(90\) −0.925032 −0.0975070
\(91\) 14.5151 1.52160
\(92\) −8.42074 −0.877923
\(93\) −14.1239 −1.46458
\(94\) 1.45911 0.150496
\(95\) −1.10031 −0.112890
\(96\) −6.23027 −0.635874
\(97\) −6.95578 −0.706253 −0.353126 0.935576i \(-0.614881\pi\)
−0.353126 + 0.935576i \(0.614881\pi\)
\(98\) −15.8038 −1.59642
\(99\) −6.02260 −0.605294
\(100\) −17.6764 −1.76764
\(101\) −4.82265 −0.479872 −0.239936 0.970789i \(-0.577126\pi\)
−0.239936 + 0.970789i \(0.577126\pi\)
\(102\) 34.2011 3.38641
\(103\) −3.19513 −0.314825 −0.157413 0.987533i \(-0.550315\pi\)
−0.157413 + 0.987533i \(0.550315\pi\)
\(104\) −15.3077 −1.50104
\(105\) −2.82117 −0.275318
\(106\) 32.6889 3.17503
\(107\) −12.9431 −1.25125 −0.625626 0.780123i \(-0.715156\pi\)
−0.625626 + 0.780123i \(0.715156\pi\)
\(108\) 14.4357 1.38907
\(109\) −8.90516 −0.852960 −0.426480 0.904497i \(-0.640246\pi\)
−0.426480 + 0.904497i \(0.640246\pi\)
\(110\) 5.32090 0.507328
\(111\) 3.59924 0.341625
\(112\) 7.29329 0.689151
\(113\) 12.0402 1.13264 0.566322 0.824184i \(-0.308366\pi\)
0.566322 + 0.824184i \(0.308366\pi\)
\(114\) −13.7710 −1.28977
\(115\) −0.880368 −0.0820948
\(116\) 8.41591 0.781397
\(117\) 4.01945 0.371598
\(118\) −8.37088 −0.770602
\(119\) 26.5286 2.43187
\(120\) 2.97522 0.271599
\(121\) 23.6427 2.14934
\(122\) 24.7355 2.23944
\(123\) 20.7024 1.86667
\(124\) 25.6367 2.30224
\(125\) −3.75121 −0.335518
\(126\) −8.98007 −0.800008
\(127\) 17.9513 1.59292 0.796460 0.604691i \(-0.206703\pi\)
0.796460 + 0.604691i \(0.206703\pi\)
\(128\) 20.6842 1.82824
\(129\) 0.763481 0.0672208
\(130\) −3.55114 −0.311455
\(131\) 10.1338 0.885391 0.442695 0.896672i \(-0.354022\pi\)
0.442695 + 0.896672i \(0.354022\pi\)
\(132\) 42.9822 3.74112
\(133\) −10.6816 −0.926216
\(134\) 10.1493 0.876767
\(135\) 1.50921 0.129892
\(136\) −27.9772 −2.39902
\(137\) −6.00931 −0.513410 −0.256705 0.966490i \(-0.582637\pi\)
−0.256705 + 0.966490i \(0.582637\pi\)
\(138\) −11.0183 −0.937937
\(139\) 18.4916 1.56843 0.784217 0.620487i \(-0.213065\pi\)
0.784217 + 0.620487i \(0.213065\pi\)
\(140\) 5.12078 0.432785
\(141\) 1.23227 0.103776
\(142\) −7.52725 −0.631673
\(143\) −23.1203 −1.93342
\(144\) 2.01962 0.168302
\(145\) 0.879863 0.0730686
\(146\) −37.9841 −3.14358
\(147\) −13.3468 −1.10083
\(148\) −6.53308 −0.537016
\(149\) −14.7721 −1.21018 −0.605091 0.796156i \(-0.706863\pi\)
−0.605091 + 0.796156i \(0.706863\pi\)
\(150\) −23.1290 −1.88848
\(151\) 18.8468 1.53373 0.766864 0.641810i \(-0.221816\pi\)
0.766864 + 0.641810i \(0.221816\pi\)
\(152\) 11.2649 0.913705
\(153\) 7.34615 0.593901
\(154\) 51.6544 4.16243
\(155\) 2.68026 0.215283
\(156\) −28.6861 −2.29673
\(157\) −4.58648 −0.366041 −0.183021 0.983109i \(-0.558588\pi\)
−0.183021 + 0.983109i \(0.558588\pi\)
\(158\) 1.63181 0.129820
\(159\) 27.6070 2.18938
\(160\) 1.18230 0.0934691
\(161\) −8.54648 −0.673557
\(162\) 26.1793 2.05684
\(163\) 19.5549 1.53166 0.765831 0.643042i \(-0.222328\pi\)
0.765831 + 0.643042i \(0.222328\pi\)
\(164\) −37.5774 −2.93431
\(165\) 4.49369 0.349833
\(166\) −3.16673 −0.245786
\(167\) −4.74414 −0.367112 −0.183556 0.983009i \(-0.558761\pi\)
−0.183556 + 0.983009i \(0.558761\pi\)
\(168\) 28.8829 2.22837
\(169\) 2.43038 0.186952
\(170\) −6.49024 −0.497779
\(171\) −2.95791 −0.226197
\(172\) −1.38582 −0.105667
\(173\) −3.22129 −0.244910 −0.122455 0.992474i \(-0.539077\pi\)
−0.122455 + 0.992474i \(0.539077\pi\)
\(174\) 11.0119 0.834813
\(175\) −17.9404 −1.35616
\(176\) −11.6171 −0.875671
\(177\) −7.06951 −0.531377
\(178\) 37.8108 2.83404
\(179\) −7.86653 −0.587972 −0.293986 0.955810i \(-0.594982\pi\)
−0.293986 + 0.955810i \(0.594982\pi\)
\(180\) 1.41802 0.105693
\(181\) −11.0914 −0.824419 −0.412210 0.911089i \(-0.635243\pi\)
−0.412210 + 0.911089i \(0.635243\pi\)
\(182\) −34.4739 −2.55537
\(183\) 20.8900 1.54423
\(184\) 9.01315 0.664459
\(185\) −0.683018 −0.0502165
\(186\) 33.5448 2.45962
\(187\) −42.2559 −3.09006
\(188\) −2.23673 −0.163130
\(189\) 14.6512 1.06572
\(190\) 2.61328 0.189587
\(191\) 15.5546 1.12549 0.562745 0.826631i \(-0.309745\pi\)
0.562745 + 0.826631i \(0.309745\pi\)
\(192\) 22.7150 1.63931
\(193\) 2.87185 0.206720 0.103360 0.994644i \(-0.467041\pi\)
0.103360 + 0.994644i \(0.467041\pi\)
\(194\) 16.5202 1.18608
\(195\) −2.99906 −0.214767
\(196\) 24.2262 1.73044
\(197\) −19.2917 −1.37448 −0.687240 0.726431i \(-0.741178\pi\)
−0.687240 + 0.726431i \(0.741178\pi\)
\(198\) 14.3039 1.01653
\(199\) 6.06776 0.430132 0.215066 0.976600i \(-0.431003\pi\)
0.215066 + 0.976600i \(0.431003\pi\)
\(200\) 18.9200 1.33785
\(201\) 8.57146 0.604584
\(202\) 11.4540 0.805898
\(203\) 8.54157 0.599501
\(204\) −52.4282 −3.67071
\(205\) −3.92863 −0.274388
\(206\) 7.58853 0.528718
\(207\) −2.36665 −0.164493
\(208\) 7.75318 0.537586
\(209\) 17.0142 1.17690
\(210\) 6.70037 0.462369
\(211\) 7.93815 0.546485 0.273242 0.961945i \(-0.411904\pi\)
0.273242 + 0.961945i \(0.411904\pi\)
\(212\) −50.1102 −3.44158
\(213\) −6.35704 −0.435577
\(214\) 30.7402 2.10136
\(215\) −0.144884 −0.00988099
\(216\) −15.4512 −1.05132
\(217\) 26.0195 1.76632
\(218\) 21.1501 1.43246
\(219\) −32.0789 −2.16769
\(220\) −8.15662 −0.549919
\(221\) 28.2014 1.89703
\(222\) −8.54832 −0.573725
\(223\) 18.1382 1.21462 0.607311 0.794464i \(-0.292248\pi\)
0.607311 + 0.794464i \(0.292248\pi\)
\(224\) 11.4776 0.766879
\(225\) −4.96796 −0.331197
\(226\) −28.5958 −1.90216
\(227\) 13.3964 0.889148 0.444574 0.895742i \(-0.353355\pi\)
0.444574 + 0.895742i \(0.353355\pi\)
\(228\) 21.1101 1.39805
\(229\) 2.08349 0.137681 0.0688406 0.997628i \(-0.478070\pi\)
0.0688406 + 0.997628i \(0.478070\pi\)
\(230\) 2.09090 0.137870
\(231\) 43.6240 2.87025
\(232\) −9.00798 −0.591403
\(233\) −8.57263 −0.561611 −0.280806 0.959765i \(-0.590602\pi\)
−0.280806 + 0.959765i \(0.590602\pi\)
\(234\) −9.54632 −0.624063
\(235\) −0.233845 −0.0152544
\(236\) 12.8321 0.835296
\(237\) 1.37812 0.0895187
\(238\) −63.0062 −4.08409
\(239\) −12.5476 −0.811636 −0.405818 0.913954i \(-0.633013\pi\)
−0.405818 + 0.913954i \(0.633013\pi\)
\(240\) −1.50691 −0.0972709
\(241\) −16.1622 −1.04110 −0.520548 0.853832i \(-0.674272\pi\)
−0.520548 + 0.853832i \(0.674272\pi\)
\(242\) −56.1522 −3.60960
\(243\) 10.2144 0.655254
\(244\) −37.9180 −2.42745
\(245\) 2.53279 0.161814
\(246\) −49.1688 −3.13489
\(247\) −11.3552 −0.722514
\(248\) −27.4403 −1.74246
\(249\) −2.67442 −0.169484
\(250\) 8.90924 0.563470
\(251\) 12.4636 0.786695 0.393348 0.919390i \(-0.371317\pi\)
0.393348 + 0.919390i \(0.371317\pi\)
\(252\) 13.7659 0.867171
\(253\) 13.6132 0.855856
\(254\) −42.6350 −2.67515
\(255\) −5.48124 −0.343249
\(256\) −26.4763 −1.65477
\(257\) −10.7138 −0.668311 −0.334155 0.942518i \(-0.608451\pi\)
−0.334155 + 0.942518i \(0.608451\pi\)
\(258\) −1.81329 −0.112891
\(259\) −6.63063 −0.412007
\(260\) 5.44368 0.337603
\(261\) 2.36529 0.146408
\(262\) −24.0680 −1.48693
\(263\) −11.1142 −0.685333 −0.342666 0.939457i \(-0.611330\pi\)
−0.342666 + 0.939457i \(0.611330\pi\)
\(264\) −46.0061 −2.83148
\(265\) −5.23890 −0.321823
\(266\) 25.3693 1.55549
\(267\) 31.9326 1.95424
\(268\) −15.5583 −0.950374
\(269\) −6.00551 −0.366163 −0.183081 0.983098i \(-0.558607\pi\)
−0.183081 + 0.983098i \(0.558607\pi\)
\(270\) −3.58443 −0.218142
\(271\) −21.0775 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(272\) 14.1701 0.859190
\(273\) −29.1144 −1.76208
\(274\) 14.2723 0.862221
\(275\) 28.5763 1.72321
\(276\) 16.8903 1.01668
\(277\) −1.28704 −0.0773304 −0.0386652 0.999252i \(-0.512311\pi\)
−0.0386652 + 0.999252i \(0.512311\pi\)
\(278\) −43.9181 −2.63403
\(279\) 7.20519 0.431363
\(280\) −5.48103 −0.327554
\(281\) 28.1334 1.67830 0.839150 0.543900i \(-0.183053\pi\)
0.839150 + 0.543900i \(0.183053\pi\)
\(282\) −2.92669 −0.174282
\(283\) −13.5533 −0.805660 −0.402830 0.915275i \(-0.631973\pi\)
−0.402830 + 0.915275i \(0.631973\pi\)
\(284\) 11.5388 0.684703
\(285\) 2.20701 0.130732
\(286\) 54.9116 3.24699
\(287\) −38.1385 −2.25125
\(288\) 3.17832 0.187284
\(289\) 34.5423 2.03190
\(290\) −2.08970 −0.122712
\(291\) 13.9519 0.817876
\(292\) 58.2273 3.40750
\(293\) −32.1762 −1.87975 −0.939877 0.341514i \(-0.889060\pi\)
−0.939877 + 0.341514i \(0.889060\pi\)
\(294\) 31.6992 1.84873
\(295\) 1.34156 0.0781088
\(296\) 6.99269 0.406442
\(297\) −23.3371 −1.35416
\(298\) 35.0844 2.03238
\(299\) −9.08539 −0.525422
\(300\) 35.4554 2.04702
\(301\) −1.40651 −0.0810698
\(302\) −44.7617 −2.57575
\(303\) 9.67328 0.555716
\(304\) −5.70555 −0.327236
\(305\) −3.96423 −0.226991
\(306\) −17.4474 −0.997399
\(307\) −20.1560 −1.15037 −0.575183 0.818025i \(-0.695069\pi\)
−0.575183 + 0.818025i \(0.695069\pi\)
\(308\) −79.1831 −4.51188
\(309\) 6.40879 0.364583
\(310\) −6.36570 −0.361547
\(311\) −15.0129 −0.851305 −0.425652 0.904887i \(-0.639955\pi\)
−0.425652 + 0.904887i \(0.639955\pi\)
\(312\) 30.7042 1.73828
\(313\) −3.96499 −0.224115 −0.112057 0.993702i \(-0.535744\pi\)
−0.112057 + 0.993702i \(0.535744\pi\)
\(314\) 10.8931 0.614731
\(315\) 1.43919 0.0810893
\(316\) −2.50147 −0.140719
\(317\) −1.50386 −0.0844654 −0.0422327 0.999108i \(-0.513447\pi\)
−0.0422327 + 0.999108i \(0.513447\pi\)
\(318\) −65.5675 −3.67684
\(319\) −13.6054 −0.761757
\(320\) −4.31056 −0.240968
\(321\) 25.9612 1.44901
\(322\) 20.2982 1.13117
\(323\) −20.7534 −1.15475
\(324\) −40.1313 −2.22952
\(325\) −19.0716 −1.05790
\(326\) −46.4437 −2.57228
\(327\) 17.8620 0.987770
\(328\) 40.2211 2.22084
\(329\) −2.27013 −0.125156
\(330\) −10.6727 −0.587511
\(331\) −5.91314 −0.325016 −0.162508 0.986707i \(-0.551958\pi\)
−0.162508 + 0.986707i \(0.551958\pi\)
\(332\) 4.85440 0.266420
\(333\) −1.83612 −0.100619
\(334\) 11.2675 0.616529
\(335\) −1.62658 −0.0888697
\(336\) −14.6289 −0.798071
\(337\) −27.3405 −1.48933 −0.744667 0.667436i \(-0.767392\pi\)
−0.744667 + 0.667436i \(0.767392\pi\)
\(338\) −5.77223 −0.313968
\(339\) −24.1502 −1.31166
\(340\) 9.94916 0.539569
\(341\) −41.4451 −2.24438
\(342\) 7.02513 0.379875
\(343\) −1.27809 −0.0690101
\(344\) 1.48331 0.0799747
\(345\) 1.76584 0.0950699
\(346\) 7.65066 0.411302
\(347\) 34.5288 1.85360 0.926802 0.375551i \(-0.122546\pi\)
0.926802 + 0.375551i \(0.122546\pi\)
\(348\) −16.8806 −0.904897
\(349\) −27.4704 −1.47045 −0.735227 0.677821i \(-0.762925\pi\)
−0.735227 + 0.677821i \(0.762925\pi\)
\(350\) 42.6090 2.27755
\(351\) 15.5751 0.831336
\(352\) −18.2820 −0.974436
\(353\) 25.7140 1.36862 0.684310 0.729192i \(-0.260104\pi\)
0.684310 + 0.729192i \(0.260104\pi\)
\(354\) 16.7903 0.892396
\(355\) 1.20636 0.0640268
\(356\) −57.9617 −3.07196
\(357\) −53.2111 −2.81623
\(358\) 18.6833 0.987442
\(359\) −16.4347 −0.867392 −0.433696 0.901059i \(-0.642791\pi\)
−0.433696 + 0.901059i \(0.642791\pi\)
\(360\) −1.51778 −0.0799940
\(361\) −10.6437 −0.560196
\(362\) 26.3425 1.38453
\(363\) −47.4226 −2.48904
\(364\) 52.8464 2.76990
\(365\) 6.08753 0.318636
\(366\) −49.6144 −2.59339
\(367\) −34.7485 −1.81385 −0.906927 0.421287i \(-0.861579\pi\)
−0.906927 + 0.421287i \(0.861579\pi\)
\(368\) −4.56506 −0.237970
\(369\) −10.5611 −0.549790
\(370\) 1.62219 0.0843336
\(371\) −50.8584 −2.64044
\(372\) −51.4222 −2.66611
\(373\) 10.8726 0.562964 0.281482 0.959567i \(-0.409174\pi\)
0.281482 + 0.959567i \(0.409174\pi\)
\(374\) 100.359 5.18946
\(375\) 7.52418 0.388547
\(376\) 2.39409 0.123466
\(377\) 9.08017 0.467653
\(378\) −34.7971 −1.78977
\(379\) 1.96246 0.100805 0.0504025 0.998729i \(-0.483950\pi\)
0.0504025 + 0.998729i \(0.483950\pi\)
\(380\) −4.00600 −0.205503
\(381\) −36.0068 −1.84468
\(382\) −36.9426 −1.89015
\(383\) 5.22298 0.266882 0.133441 0.991057i \(-0.457397\pi\)
0.133441 + 0.991057i \(0.457397\pi\)
\(384\) −41.4883 −2.11719
\(385\) −8.27841 −0.421907
\(386\) −6.82074 −0.347166
\(387\) −0.389483 −0.0197985
\(388\) −25.3245 −1.28566
\(389\) 31.9841 1.62166 0.810828 0.585284i \(-0.199017\pi\)
0.810828 + 0.585284i \(0.199017\pi\)
\(390\) 7.12287 0.360681
\(391\) −16.6049 −0.839748
\(392\) −25.9306 −1.30969
\(393\) −20.3263 −1.02533
\(394\) 45.8185 2.30830
\(395\) −0.261522 −0.0131586
\(396\) −21.9270 −1.10187
\(397\) −7.56001 −0.379426 −0.189713 0.981840i \(-0.560756\pi\)
−0.189713 + 0.981840i \(0.560756\pi\)
\(398\) −14.4111 −0.722365
\(399\) 21.4253 1.07260
\(400\) −9.58277 −0.479139
\(401\) 0.217122 0.0108425 0.00542127 0.999985i \(-0.498274\pi\)
0.00542127 + 0.999985i \(0.498274\pi\)
\(402\) −20.3575 −1.01534
\(403\) 27.6602 1.37785
\(404\) −17.5582 −0.873555
\(405\) −4.19563 −0.208483
\(406\) −20.2865 −1.00680
\(407\) 10.5616 0.523518
\(408\) 56.1166 2.77819
\(409\) 28.2700 1.39786 0.698931 0.715190i \(-0.253660\pi\)
0.698931 + 0.715190i \(0.253660\pi\)
\(410\) 9.33063 0.460807
\(411\) 12.0535 0.594554
\(412\) −11.6328 −0.573105
\(413\) 13.0237 0.640853
\(414\) 5.62086 0.276250
\(415\) 0.507516 0.0249130
\(416\) 12.2013 0.598220
\(417\) −37.0904 −1.81632
\(418\) −40.4094 −1.97649
\(419\) −15.1265 −0.738977 −0.369488 0.929235i \(-0.620467\pi\)
−0.369488 + 0.929235i \(0.620467\pi\)
\(420\) −10.2713 −0.501187
\(421\) 28.5594 1.39190 0.695951 0.718089i \(-0.254983\pi\)
0.695951 + 0.718089i \(0.254983\pi\)
\(422\) −18.8534 −0.917768
\(423\) −0.628633 −0.0305652
\(424\) 53.6355 2.60477
\(425\) −34.8563 −1.69078
\(426\) 15.0982 0.731509
\(427\) −38.4842 −1.86238
\(428\) −47.1229 −2.27777
\(429\) 46.3748 2.23900
\(430\) 0.344104 0.0165942
\(431\) 3.70488 0.178458 0.0892288 0.996011i \(-0.471560\pi\)
0.0892288 + 0.996011i \(0.471560\pi\)
\(432\) 7.82588 0.376523
\(433\) −2.36927 −0.113860 −0.0569298 0.998378i \(-0.518131\pi\)
−0.0569298 + 0.998378i \(0.518131\pi\)
\(434\) −61.7972 −2.96636
\(435\) −1.76483 −0.0846171
\(436\) −32.4218 −1.55272
\(437\) 6.68593 0.319831
\(438\) 76.1885 3.64043
\(439\) −31.7571 −1.51568 −0.757842 0.652439i \(-0.773746\pi\)
−0.757842 + 0.652439i \(0.773746\pi\)
\(440\) 8.73045 0.416208
\(441\) 6.80877 0.324227
\(442\) −66.9792 −3.18588
\(443\) 7.81652 0.371374 0.185687 0.982609i \(-0.440549\pi\)
0.185687 + 0.982609i \(0.440549\pi\)
\(444\) 13.1041 0.621891
\(445\) −6.05975 −0.287260
\(446\) −43.0788 −2.03984
\(447\) 29.6300 1.40145
\(448\) −41.8462 −1.97705
\(449\) 8.42855 0.397768 0.198884 0.980023i \(-0.436268\pi\)
0.198884 + 0.980023i \(0.436268\pi\)
\(450\) 11.7991 0.556213
\(451\) 60.7488 2.86055
\(452\) 43.8357 2.06186
\(453\) −37.8029 −1.77613
\(454\) −31.8168 −1.49324
\(455\) 5.52496 0.259014
\(456\) −22.5952 −1.05812
\(457\) 5.75154 0.269045 0.134523 0.990911i \(-0.457050\pi\)
0.134523 + 0.990911i \(0.457050\pi\)
\(458\) −4.94837 −0.231222
\(459\) 28.4658 1.32867
\(460\) −3.20523 −0.149445
\(461\) 18.8788 0.879275 0.439638 0.898175i \(-0.355107\pi\)
0.439638 + 0.898175i \(0.355107\pi\)
\(462\) −103.609 −4.82030
\(463\) −26.3522 −1.22469 −0.612345 0.790591i \(-0.709774\pi\)
−0.612345 + 0.790591i \(0.709774\pi\)
\(464\) 4.56244 0.211806
\(465\) −5.37606 −0.249309
\(466\) 20.3603 0.943172
\(467\) −5.34430 −0.247305 −0.123652 0.992326i \(-0.539461\pi\)
−0.123652 + 0.992326i \(0.539461\pi\)
\(468\) 14.6339 0.676454
\(469\) −15.7906 −0.729142
\(470\) 0.555390 0.0256182
\(471\) 9.19958 0.423894
\(472\) −13.7348 −0.632196
\(473\) 2.24035 0.103011
\(474\) −3.27309 −0.150338
\(475\) 14.0348 0.643960
\(476\) 96.5848 4.42696
\(477\) −14.0834 −0.644836
\(478\) 29.8010 1.36306
\(479\) −8.53830 −0.390125 −0.195062 0.980791i \(-0.562491\pi\)
−0.195062 + 0.980791i \(0.562491\pi\)
\(480\) −2.37146 −0.108242
\(481\) −7.04873 −0.321395
\(482\) 38.3857 1.74842
\(483\) 17.1425 0.780013
\(484\) 86.0780 3.91263
\(485\) −2.64762 −0.120222
\(486\) −24.2595 −1.10043
\(487\) −18.1447 −0.822214 −0.411107 0.911587i \(-0.634858\pi\)
−0.411107 + 0.911587i \(0.634858\pi\)
\(488\) 40.5856 1.83722
\(489\) −39.2233 −1.77374
\(490\) −6.01547 −0.271751
\(491\) −11.7271 −0.529237 −0.264619 0.964353i \(-0.585246\pi\)
−0.264619 + 0.964353i \(0.585246\pi\)
\(492\) 75.3729 3.39807
\(493\) 16.5954 0.747419
\(494\) 26.9690 1.21339
\(495\) −2.29241 −0.103036
\(496\) 13.8982 0.624048
\(497\) 11.7111 0.525316
\(498\) 6.35183 0.284632
\(499\) 5.05800 0.226427 0.113214 0.993571i \(-0.463886\pi\)
0.113214 + 0.993571i \(0.463886\pi\)
\(500\) −13.6573 −0.610775
\(501\) 9.51580 0.425135
\(502\) −29.6015 −1.32118
\(503\) 6.50916 0.290229 0.145114 0.989415i \(-0.453645\pi\)
0.145114 + 0.989415i \(0.453645\pi\)
\(504\) −14.7344 −0.656321
\(505\) −1.83567 −0.0816863
\(506\) −32.3319 −1.43733
\(507\) −4.87486 −0.216500
\(508\) 65.3568 2.89974
\(509\) −18.8379 −0.834973 −0.417487 0.908683i \(-0.637089\pi\)
−0.417487 + 0.908683i \(0.637089\pi\)
\(510\) 13.0181 0.576453
\(511\) 59.0967 2.61429
\(512\) 21.5138 0.950783
\(513\) −11.4617 −0.506045
\(514\) 25.4457 1.12236
\(515\) −1.21618 −0.0535912
\(516\) 2.77967 0.122368
\(517\) 3.61597 0.159030
\(518\) 15.7480 0.691926
\(519\) 6.46126 0.283618
\(520\) −5.82665 −0.255516
\(521\) −16.2888 −0.713625 −0.356813 0.934176i \(-0.616137\pi\)
−0.356813 + 0.934176i \(0.616137\pi\)
\(522\) −5.61764 −0.245877
\(523\) 0.970548 0.0424391 0.0212196 0.999775i \(-0.493245\pi\)
0.0212196 + 0.999775i \(0.493245\pi\)
\(524\) 36.8948 1.61176
\(525\) 35.9848 1.57051
\(526\) 26.3967 1.15095
\(527\) 50.5533 2.20213
\(528\) 23.3016 1.01407
\(529\) −17.6505 −0.767414
\(530\) 12.4426 0.540470
\(531\) 3.60645 0.156506
\(532\) −38.8896 −1.68608
\(533\) −40.5434 −1.75613
\(534\) −75.8409 −3.28196
\(535\) −4.92658 −0.212995
\(536\) 16.6528 0.719293
\(537\) 15.7787 0.680901
\(538\) 14.2633 0.614935
\(539\) −39.1648 −1.68695
\(540\) 5.49472 0.236455
\(541\) −30.0294 −1.29106 −0.645532 0.763733i \(-0.723364\pi\)
−0.645532 + 0.763733i \(0.723364\pi\)
\(542\) 50.0598 2.15025
\(543\) 22.2472 0.954719
\(544\) 22.2998 0.956096
\(545\) −3.38962 −0.145195
\(546\) 69.1477 2.95925
\(547\) −36.1310 −1.54485 −0.772425 0.635105i \(-0.780957\pi\)
−0.772425 + 0.635105i \(0.780957\pi\)
\(548\) −21.8786 −0.934607
\(549\) −10.6568 −0.454823
\(550\) −67.8696 −2.89397
\(551\) −6.68209 −0.284666
\(552\) −18.0786 −0.769476
\(553\) −2.53882 −0.107962
\(554\) 3.05675 0.129869
\(555\) 1.37000 0.0581532
\(556\) 67.3238 2.85516
\(557\) −5.65590 −0.239648 −0.119824 0.992795i \(-0.538233\pi\)
−0.119824 + 0.992795i \(0.538233\pi\)
\(558\) −17.1126 −0.724432
\(559\) −1.49520 −0.0632401
\(560\) 2.77608 0.117311
\(561\) 84.7570 3.57845
\(562\) −66.8178 −2.81854
\(563\) −23.4781 −0.989483 −0.494742 0.869040i \(-0.664737\pi\)
−0.494742 + 0.869040i \(0.664737\pi\)
\(564\) 4.48644 0.188913
\(565\) 4.58291 0.192805
\(566\) 32.1896 1.35303
\(567\) −40.7305 −1.71052
\(568\) −12.3506 −0.518220
\(569\) −35.4718 −1.48705 −0.743527 0.668706i \(-0.766848\pi\)
−0.743527 + 0.668706i \(0.766848\pi\)
\(570\) −5.24171 −0.219551
\(571\) 4.91958 0.205878 0.102939 0.994688i \(-0.467175\pi\)
0.102939 + 0.994688i \(0.467175\pi\)
\(572\) −84.1762 −3.51958
\(573\) −31.1994 −1.30337
\(574\) 90.5803 3.78075
\(575\) 11.2294 0.468297
\(576\) −11.5878 −0.482827
\(577\) −12.4617 −0.518786 −0.259393 0.965772i \(-0.583522\pi\)
−0.259393 + 0.965772i \(0.583522\pi\)
\(578\) −82.0392 −3.41238
\(579\) −5.76036 −0.239392
\(580\) 3.20339 0.133014
\(581\) 4.92689 0.204402
\(582\) −33.1363 −1.37354
\(583\) 81.0096 3.35508
\(584\) −62.3237 −2.57897
\(585\) 1.52994 0.0632554
\(586\) 76.4196 3.15686
\(587\) 14.9059 0.615233 0.307617 0.951510i \(-0.400469\pi\)
0.307617 + 0.951510i \(0.400469\pi\)
\(588\) −48.5930 −2.00394
\(589\) −20.3551 −0.838718
\(590\) −3.18625 −0.131176
\(591\) 38.6954 1.59172
\(592\) −3.54172 −0.145564
\(593\) 15.4188 0.633174 0.316587 0.948564i \(-0.397463\pi\)
0.316587 + 0.948564i \(0.397463\pi\)
\(594\) 55.4265 2.27418
\(595\) 10.0977 0.413966
\(596\) −53.7822 −2.20301
\(597\) −12.1707 −0.498114
\(598\) 21.5781 0.882394
\(599\) 18.7977 0.768055 0.384028 0.923322i \(-0.374537\pi\)
0.384028 + 0.923322i \(0.374537\pi\)
\(600\) −37.9498 −1.54929
\(601\) −39.1535 −1.59711 −0.798553 0.601925i \(-0.794401\pi\)
−0.798553 + 0.601925i \(0.794401\pi\)
\(602\) 3.34050 0.136149
\(603\) −4.37265 −0.178068
\(604\) 68.6170 2.79199
\(605\) 8.99924 0.365871
\(606\) −22.9744 −0.933270
\(607\) −27.3324 −1.10939 −0.554694 0.832055i \(-0.687165\pi\)
−0.554694 + 0.832055i \(0.687165\pi\)
\(608\) −8.97894 −0.364144
\(609\) −17.1327 −0.694252
\(610\) 9.41519 0.381210
\(611\) −2.41328 −0.0976308
\(612\) 26.7458 1.08113
\(613\) 46.8361 1.89169 0.945847 0.324613i \(-0.105234\pi\)
0.945847 + 0.324613i \(0.105234\pi\)
\(614\) 47.8713 1.93193
\(615\) 7.88006 0.317755
\(616\) 84.7538 3.41483
\(617\) 3.40628 0.137132 0.0685658 0.997647i \(-0.478158\pi\)
0.0685658 + 0.997647i \(0.478158\pi\)
\(618\) −15.2211 −0.612282
\(619\) 19.2512 0.773771 0.386885 0.922128i \(-0.373551\pi\)
0.386885 + 0.922128i \(0.373551\pi\)
\(620\) 9.75824 0.391900
\(621\) −9.17058 −0.368003
\(622\) 35.6562 1.42968
\(623\) −58.8271 −2.35686
\(624\) −15.5513 −0.622552
\(625\) 22.8477 0.913910
\(626\) 9.41699 0.376378
\(627\) −34.1272 −1.36291
\(628\) −16.6984 −0.666339
\(629\) −12.8826 −0.513664
\(630\) −3.41813 −0.136182
\(631\) −22.0229 −0.876719 −0.438359 0.898800i \(-0.644440\pi\)
−0.438359 + 0.898800i \(0.644440\pi\)
\(632\) 2.67745 0.106503
\(633\) −15.9224 −0.632857
\(634\) 3.57173 0.141851
\(635\) 6.83290 0.271155
\(636\) 100.511 3.98552
\(637\) 26.1384 1.03564
\(638\) 32.3133 1.27930
\(639\) 3.24298 0.128290
\(640\) 7.87313 0.311213
\(641\) 42.4663 1.67732 0.838659 0.544657i \(-0.183340\pi\)
0.838659 + 0.544657i \(0.183340\pi\)
\(642\) −61.6587 −2.43348
\(643\) −28.4350 −1.12137 −0.560684 0.828030i \(-0.689462\pi\)
−0.560684 + 0.828030i \(0.689462\pi\)
\(644\) −31.1159 −1.22614
\(645\) 0.290608 0.0114427
\(646\) 49.2899 1.93929
\(647\) −35.4993 −1.39562 −0.697811 0.716282i \(-0.745842\pi\)
−0.697811 + 0.716282i \(0.745842\pi\)
\(648\) 42.9546 1.68742
\(649\) −20.7447 −0.814301
\(650\) 45.2958 1.77665
\(651\) −52.1900 −2.04549
\(652\) 71.1954 2.78823
\(653\) 6.46573 0.253024 0.126512 0.991965i \(-0.459622\pi\)
0.126512 + 0.991965i \(0.459622\pi\)
\(654\) −42.4228 −1.65886
\(655\) 3.85727 0.150716
\(656\) −20.3715 −0.795375
\(657\) 16.3648 0.638450
\(658\) 5.39164 0.210188
\(659\) −27.0816 −1.05495 −0.527475 0.849570i \(-0.676861\pi\)
−0.527475 + 0.849570i \(0.676861\pi\)
\(660\) 16.3606 0.636834
\(661\) 32.3165 1.25696 0.628482 0.777824i \(-0.283677\pi\)
0.628482 + 0.777824i \(0.283677\pi\)
\(662\) 14.0439 0.545832
\(663\) −56.5664 −2.19686
\(664\) −5.19592 −0.201641
\(665\) −4.06581 −0.157665
\(666\) 4.36084 0.168979
\(667\) −5.34640 −0.207013
\(668\) −17.2724 −0.668289
\(669\) −36.3816 −1.40659
\(670\) 3.86319 0.149248
\(671\) 61.2994 2.36644
\(672\) −23.0218 −0.888084
\(673\) −4.43995 −0.171148 −0.0855738 0.996332i \(-0.527272\pi\)
−0.0855738 + 0.996332i \(0.527272\pi\)
\(674\) 64.9347 2.50119
\(675\) −19.2505 −0.740951
\(676\) 8.84849 0.340326
\(677\) 31.8338 1.22347 0.611735 0.791063i \(-0.290472\pi\)
0.611735 + 0.791063i \(0.290472\pi\)
\(678\) 57.3575 2.20280
\(679\) −25.7026 −0.986377
\(680\) −10.6491 −0.408374
\(681\) −26.8705 −1.02968
\(682\) 98.4335 3.76921
\(683\) −29.9231 −1.14497 −0.572487 0.819914i \(-0.694021\pi\)
−0.572487 + 0.819914i \(0.694021\pi\)
\(684\) −10.7691 −0.411767
\(685\) −2.28735 −0.0873953
\(686\) 3.03550 0.115896
\(687\) −4.17908 −0.159442
\(688\) −0.751280 −0.0286423
\(689\) −54.0654 −2.05973
\(690\) −4.19394 −0.159661
\(691\) −44.5569 −1.69503 −0.847513 0.530775i \(-0.821901\pi\)
−0.847513 + 0.530775i \(0.821901\pi\)
\(692\) −11.7280 −0.445832
\(693\) −22.2544 −0.845374
\(694\) −82.0071 −3.11295
\(695\) 7.03854 0.266987
\(696\) 18.0682 0.684874
\(697\) −74.0993 −2.80671
\(698\) 65.2430 2.46948
\(699\) 17.1950 0.650374
\(700\) −65.3171 −2.46875
\(701\) −28.4049 −1.07284 −0.536420 0.843951i \(-0.680224\pi\)
−0.536420 + 0.843951i \(0.680224\pi\)
\(702\) −36.9913 −1.39615
\(703\) 5.18715 0.195637
\(704\) 66.6546 2.51214
\(705\) 0.469047 0.0176653
\(706\) −61.0717 −2.29846
\(707\) −17.8204 −0.670206
\(708\) −25.7386 −0.967315
\(709\) −46.0109 −1.72798 −0.863989 0.503511i \(-0.832041\pi\)
−0.863989 + 0.503511i \(0.832041\pi\)
\(710\) −2.86514 −0.107527
\(711\) −0.703036 −0.0263659
\(712\) 62.0394 2.32502
\(713\) −16.2863 −0.609927
\(714\) 126.378 4.72958
\(715\) −8.80042 −0.329117
\(716\) −28.6404 −1.07034
\(717\) 25.1680 0.939916
\(718\) 39.0330 1.45670
\(719\) 13.5356 0.504794 0.252397 0.967624i \(-0.418781\pi\)
0.252397 + 0.967624i \(0.418781\pi\)
\(720\) 0.768739 0.0286492
\(721\) −11.8065 −0.439696
\(722\) 25.2792 0.940795
\(723\) 32.4181 1.20564
\(724\) −40.3815 −1.50077
\(725\) −11.2229 −0.416808
\(726\) 112.630 4.18010
\(727\) 46.0232 1.70691 0.853453 0.521169i \(-0.174504\pi\)
0.853453 + 0.521169i \(0.174504\pi\)
\(728\) −56.5642 −2.09641
\(729\) 12.5801 0.465928
\(730\) −14.4581 −0.535118
\(731\) −2.73270 −0.101073
\(732\) 76.0560 2.81111
\(733\) −26.8089 −0.990210 −0.495105 0.868833i \(-0.664870\pi\)
−0.495105 + 0.868833i \(0.664870\pi\)
\(734\) 82.5288 3.04619
\(735\) −5.08028 −0.187389
\(736\) −7.18413 −0.264811
\(737\) 25.1520 0.926486
\(738\) 25.0830 0.923319
\(739\) −30.0325 −1.10476 −0.552381 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(740\) −2.48672 −0.0914137
\(741\) 22.7763 0.836707
\(742\) 120.790 4.43435
\(743\) 42.5036 1.55931 0.779653 0.626211i \(-0.215395\pi\)
0.779653 + 0.626211i \(0.215395\pi\)
\(744\) 55.0398 2.01786
\(745\) −5.62280 −0.206004
\(746\) −25.8229 −0.945443
\(747\) 1.36433 0.0499182
\(748\) −153.845 −5.62512
\(749\) −47.8265 −1.74754
\(750\) −17.8702 −0.652526
\(751\) 1.51702 0.0553568 0.0276784 0.999617i \(-0.491189\pi\)
0.0276784 + 0.999617i \(0.491189\pi\)
\(752\) −1.21258 −0.0442183
\(753\) −24.9995 −0.911033
\(754\) −21.5657 −0.785377
\(755\) 7.17374 0.261079
\(756\) 53.3419 1.94003
\(757\) −20.9129 −0.760093 −0.380046 0.924967i \(-0.624092\pi\)
−0.380046 + 0.924967i \(0.624092\pi\)
\(758\) −4.66091 −0.169292
\(759\) −27.3054 −0.991125
\(760\) 4.28782 0.155536
\(761\) −11.5739 −0.419555 −0.209778 0.977749i \(-0.567274\pi\)
−0.209778 + 0.977749i \(0.567274\pi\)
\(762\) 85.5173 3.09796
\(763\) −32.9059 −1.19127
\(764\) 56.6309 2.04883
\(765\) 2.79621 0.101097
\(766\) −12.4048 −0.448202
\(767\) 13.8449 0.499910
\(768\) 53.1062 1.91631
\(769\) 18.2768 0.659078 0.329539 0.944142i \(-0.393107\pi\)
0.329539 + 0.944142i \(0.393107\pi\)
\(770\) 19.6615 0.708551
\(771\) 21.4898 0.773938
\(772\) 10.4558 0.376312
\(773\) −6.03388 −0.217024 −0.108512 0.994095i \(-0.534609\pi\)
−0.108512 + 0.994095i \(0.534609\pi\)
\(774\) 0.925035 0.0332497
\(775\) −34.1875 −1.22805
\(776\) 27.1061 0.973053
\(777\) 13.2997 0.477125
\(778\) −75.9633 −2.72341
\(779\) 29.8359 1.06898
\(780\) −10.9189 −0.390961
\(781\) −18.6540 −0.667493
\(782\) 39.4373 1.41027
\(783\) 9.16532 0.327542
\(784\) 13.1335 0.469055
\(785\) −1.74578 −0.0623095
\(786\) 48.2757 1.72194
\(787\) 47.1506 1.68074 0.840368 0.542016i \(-0.182339\pi\)
0.840368 + 0.542016i \(0.182339\pi\)
\(788\) −70.2371 −2.50209
\(789\) 22.2929 0.793650
\(790\) 0.621125 0.0220986
\(791\) 44.4902 1.58189
\(792\) 23.4696 0.833955
\(793\) −40.9109 −1.45279
\(794\) 17.9553 0.637209
\(795\) 10.5082 0.372687
\(796\) 22.0914 0.783009
\(797\) −2.01393 −0.0713370 −0.0356685 0.999364i \(-0.511356\pi\)
−0.0356685 + 0.999364i \(0.511356\pi\)
\(798\) −50.8857 −1.80133
\(799\) −4.41063 −0.156037
\(800\) −15.0806 −0.533180
\(801\) −16.2901 −0.575582
\(802\) −0.515671 −0.0182090
\(803\) −94.1320 −3.32185
\(804\) 31.2069 1.10058
\(805\) −3.25309 −0.114656
\(806\) −65.6939 −2.31397
\(807\) 12.0459 0.424035
\(808\) 18.7935 0.661153
\(809\) −14.9044 −0.524011 −0.262005 0.965066i \(-0.584384\pi\)
−0.262005 + 0.965066i \(0.584384\pi\)
\(810\) 9.96476 0.350126
\(811\) 25.5094 0.895755 0.447877 0.894095i \(-0.352180\pi\)
0.447877 + 0.894095i \(0.352180\pi\)
\(812\) 31.0980 1.09133
\(813\) 42.2773 1.48273
\(814\) −25.0841 −0.879197
\(815\) 7.44330 0.260728
\(816\) −28.4224 −0.994985
\(817\) 1.10031 0.0384951
\(818\) −67.1422 −2.34757
\(819\) 14.8525 0.518987
\(820\) −14.3033 −0.499493
\(821\) −33.6747 −1.17525 −0.587627 0.809132i \(-0.699938\pi\)
−0.587627 + 0.809132i \(0.699938\pi\)
\(822\) −28.6274 −0.998496
\(823\) −27.2548 −0.950044 −0.475022 0.879974i \(-0.657560\pi\)
−0.475022 + 0.879974i \(0.657560\pi\)
\(824\) 12.4511 0.433756
\(825\) −57.3183 −1.99557
\(826\) −30.9317 −1.07625
\(827\) −35.5275 −1.23541 −0.617706 0.786409i \(-0.711938\pi\)
−0.617706 + 0.786409i \(0.711938\pi\)
\(828\) −8.61645 −0.299442
\(829\) −3.82252 −0.132762 −0.0663808 0.997794i \(-0.521145\pi\)
−0.0663808 + 0.997794i \(0.521145\pi\)
\(830\) −1.20537 −0.0418389
\(831\) 2.58154 0.0895525
\(832\) −44.4849 −1.54224
\(833\) 47.7719 1.65520
\(834\) 88.0909 3.05034
\(835\) −1.80579 −0.0624918
\(836\) 61.9451 2.14242
\(837\) 27.9196 0.965042
\(838\) 35.9259 1.24104
\(839\) −34.3715 −1.18664 −0.593318 0.804968i \(-0.702182\pi\)
−0.593318 + 0.804968i \(0.702182\pi\)
\(840\) 10.9939 0.379325
\(841\) −23.6567 −0.815747
\(842\) −67.8297 −2.33756
\(843\) −56.4301 −1.94356
\(844\) 28.9011 0.994817
\(845\) 0.925088 0.0318240
\(846\) 1.49302 0.0513312
\(847\) 87.3632 3.00184
\(848\) −27.1658 −0.932877
\(849\) 27.1852 0.932995
\(850\) 82.7850 2.83950
\(851\) 4.15029 0.142270
\(852\) −23.1446 −0.792921
\(853\) −3.79283 −0.129864 −0.0649320 0.997890i \(-0.520683\pi\)
−0.0649320 + 0.997890i \(0.520683\pi\)
\(854\) 91.4012 3.12768
\(855\) −1.12588 −0.0385044
\(856\) 50.4380 1.72394
\(857\) 31.5703 1.07842 0.539211 0.842171i \(-0.318722\pi\)
0.539211 + 0.842171i \(0.318722\pi\)
\(858\) −110.142 −3.76018
\(859\) −25.6617 −0.875565 −0.437783 0.899081i \(-0.644236\pi\)
−0.437783 + 0.899081i \(0.644236\pi\)
\(860\) −0.527491 −0.0179873
\(861\) 76.4983 2.60706
\(862\) −8.79920 −0.299702
\(863\) 23.5739 0.802463 0.401232 0.915977i \(-0.368582\pi\)
0.401232 + 0.915977i \(0.368582\pi\)
\(864\) 12.3157 0.418990
\(865\) −1.22614 −0.0416899
\(866\) 5.62708 0.191216
\(867\) −69.2850 −2.35304
\(868\) 94.7314 3.21539
\(869\) 4.04395 0.137182
\(870\) 4.19153 0.142106
\(871\) −16.7863 −0.568782
\(872\) 34.7027 1.17518
\(873\) −7.11744 −0.240889
\(874\) −15.8793 −0.537125
\(875\) −13.8613 −0.468596
\(876\) −116.792 −3.94605
\(877\) 22.1962 0.749512 0.374756 0.927124i \(-0.377727\pi\)
0.374756 + 0.927124i \(0.377727\pi\)
\(878\) 75.4242 2.54544
\(879\) 64.5391 2.17685
\(880\) −4.42187 −0.149061
\(881\) 30.3799 1.02352 0.511762 0.859127i \(-0.328993\pi\)
0.511762 + 0.859127i \(0.328993\pi\)
\(882\) −16.1711 −0.544508
\(883\) −18.2820 −0.615239 −0.307620 0.951509i \(-0.599532\pi\)
−0.307620 + 0.951509i \(0.599532\pi\)
\(884\) 102.675 3.45334
\(885\) −2.69091 −0.0904539
\(886\) −18.5645 −0.623687
\(887\) −47.2954 −1.58803 −0.794013 0.607901i \(-0.792012\pi\)
−0.794013 + 0.607901i \(0.792012\pi\)
\(888\) −14.0259 −0.470680
\(889\) 66.3327 2.22473
\(890\) 14.3921 0.482425
\(891\) 64.8775 2.17348
\(892\) 66.0373 2.21109
\(893\) 1.77593 0.0594292
\(894\) −70.3723 −2.35360
\(895\) −2.99428 −0.100088
\(896\) 76.4311 2.55338
\(897\) 18.2235 0.608465
\(898\) −20.0181 −0.668013
\(899\) 16.2769 0.542867
\(900\) −18.0873 −0.602909
\(901\) −98.8127 −3.29193
\(902\) −144.281 −4.80402
\(903\) 2.82118 0.0938829
\(904\) −46.9196 −1.56052
\(905\) −4.22179 −0.140337
\(906\) 89.7831 2.98284
\(907\) 54.8948 1.82275 0.911376 0.411574i \(-0.135021\pi\)
0.911376 + 0.411574i \(0.135021\pi\)
\(908\) 48.7733 1.61860
\(909\) −4.93474 −0.163675
\(910\) −13.1220 −0.434989
\(911\) 3.34925 0.110966 0.0554829 0.998460i \(-0.482330\pi\)
0.0554829 + 0.998460i \(0.482330\pi\)
\(912\) 11.4442 0.378956
\(913\) −7.84778 −0.259724
\(914\) −13.6601 −0.451836
\(915\) 7.95147 0.262867
\(916\) 7.58556 0.250634
\(917\) 37.4457 1.23657
\(918\) −67.6073 −2.23137
\(919\) −4.45987 −0.147118 −0.0735588 0.997291i \(-0.523436\pi\)
−0.0735588 + 0.997291i \(0.523436\pi\)
\(920\) 3.43073 0.113108
\(921\) 40.4290 1.33218
\(922\) −44.8379 −1.47666
\(923\) 12.4496 0.409783
\(924\) 158.826 5.22498
\(925\) 8.71209 0.286452
\(926\) 62.5873 2.05675
\(927\) −3.26938 −0.107381
\(928\) 7.18001 0.235695
\(929\) −41.8654 −1.37356 −0.686779 0.726866i \(-0.740976\pi\)
−0.686779 + 0.726866i \(0.740976\pi\)
\(930\) 12.7683 0.418690
\(931\) −19.2352 −0.630408
\(932\) −31.2111 −1.02235
\(933\) 30.1129 0.985854
\(934\) 12.6929 0.415324
\(935\) −16.0841 −0.526007
\(936\) −15.6635 −0.511976
\(937\) −30.1671 −0.985516 −0.492758 0.870166i \(-0.664011\pi\)
−0.492758 + 0.870166i \(0.664011\pi\)
\(938\) 37.5032 1.22452
\(939\) 7.95299 0.259536
\(940\) −0.851380 −0.0277689
\(941\) −27.5051 −0.896641 −0.448321 0.893873i \(-0.647978\pi\)
−0.448321 + 0.893873i \(0.647978\pi\)
\(942\) −21.8493 −0.711889
\(943\) 23.8719 0.777377
\(944\) 6.95654 0.226416
\(945\) 5.57677 0.181412
\(946\) −5.32091 −0.172998
\(947\) −41.3422 −1.34344 −0.671721 0.740804i \(-0.734445\pi\)
−0.671721 + 0.740804i \(0.734445\pi\)
\(948\) 5.01745 0.162959
\(949\) 62.8232 2.03933
\(950\) −33.3331 −1.08147
\(951\) 3.01645 0.0978152
\(952\) −103.380 −3.35056
\(953\) −10.6417 −0.344720 −0.172360 0.985034i \(-0.555139\pi\)
−0.172360 + 0.985034i \(0.555139\pi\)
\(954\) 33.4486 1.08294
\(955\) 5.92062 0.191587
\(956\) −45.6831 −1.47750
\(957\) 27.2898 0.882152
\(958\) 20.2787 0.655176
\(959\) −22.2053 −0.717046
\(960\) 8.64613 0.279053
\(961\) 18.5832 0.599457
\(962\) 16.7410 0.539751
\(963\) −13.2439 −0.426778
\(964\) −58.8430 −1.89520
\(965\) 1.09313 0.0351890
\(966\) −40.7141 −1.30995
\(967\) −19.8862 −0.639497 −0.319749 0.947502i \(-0.603598\pi\)
−0.319749 + 0.947502i \(0.603598\pi\)
\(968\) −92.1337 −2.96129
\(969\) 41.6271 1.33726
\(970\) 6.28818 0.201901
\(971\) 8.81261 0.282810 0.141405 0.989952i \(-0.454838\pi\)
0.141405 + 0.989952i \(0.454838\pi\)
\(972\) 37.1884 1.19282
\(973\) 68.3290 2.19053
\(974\) 43.0942 1.38083
\(975\) 38.2539 1.22511
\(976\) −20.5561 −0.657986
\(977\) 22.4435 0.718031 0.359015 0.933332i \(-0.383113\pi\)
0.359015 + 0.933332i \(0.383113\pi\)
\(978\) 93.1568 2.97883
\(979\) 93.7026 2.99475
\(980\) 9.22135 0.294565
\(981\) −9.11213 −0.290928
\(982\) 27.8523 0.888802
\(983\) 46.5258 1.48394 0.741971 0.670432i \(-0.233891\pi\)
0.741971 + 0.670432i \(0.233891\pi\)
\(984\) −80.6755 −2.57184
\(985\) −7.34312 −0.233971
\(986\) −39.4146 −1.25522
\(987\) 4.55343 0.144937
\(988\) −41.3418 −1.31526
\(989\) 0.880371 0.0279942
\(990\) 5.44456 0.173039
\(991\) −6.35525 −0.201881 −0.100941 0.994892i \(-0.532185\pi\)
−0.100941 + 0.994892i \(0.532185\pi\)
\(992\) 21.8719 0.694433
\(993\) 11.8606 0.376385
\(994\) −27.8143 −0.882216
\(995\) 2.30960 0.0732193
\(996\) −9.73697 −0.308528
\(997\) −26.0743 −0.825780 −0.412890 0.910781i \(-0.635481\pi\)
−0.412890 + 0.910781i \(0.635481\pi\)
\(998\) −12.0129 −0.380262
\(999\) −7.11483 −0.225103
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))