Properties

Label 8008.2.a.y.1.9
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-0.374242\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.374242 q^{3} +3.66821 q^{5} +1.00000 q^{7} -2.85994 q^{9} +O(q^{10})\) \(q+0.374242 q^{3} +3.66821 q^{5} +1.00000 q^{7} -2.85994 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.37280 q^{15} +1.83730 q^{17} -7.56300 q^{19} +0.374242 q^{21} -5.64869 q^{23} +8.45573 q^{25} -2.19303 q^{27} -3.73357 q^{29} +1.74855 q^{31} -0.374242 q^{33} +3.66821 q^{35} +5.77028 q^{37} -0.374242 q^{39} -12.4153 q^{41} +4.48406 q^{43} -10.4909 q^{45} -10.1674 q^{47} +1.00000 q^{49} +0.687595 q^{51} -0.412386 q^{53} -3.66821 q^{55} -2.83039 q^{57} -11.7860 q^{59} +5.17539 q^{61} -2.85994 q^{63} -3.66821 q^{65} -13.9379 q^{67} -2.11398 q^{69} +4.90321 q^{71} +14.5424 q^{73} +3.16449 q^{75} -1.00000 q^{77} +9.93053 q^{79} +7.75910 q^{81} +2.71855 q^{83} +6.73960 q^{85} -1.39726 q^{87} -17.7954 q^{89} -1.00000 q^{91} +0.654382 q^{93} -27.7426 q^{95} +10.2664 q^{97} +2.85994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.374242 0.216069 0.108034 0.994147i \(-0.465544\pi\)
0.108034 + 0.994147i \(0.465544\pi\)
\(4\) 0 0
\(5\) 3.66821 1.64047 0.820236 0.572026i \(-0.193842\pi\)
0.820236 + 0.572026i \(0.193842\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.85994 −0.953314
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.37280 0.354454
\(16\) 0 0
\(17\) 1.83730 0.445611 0.222805 0.974863i \(-0.428479\pi\)
0.222805 + 0.974863i \(0.428479\pi\)
\(18\) 0 0
\(19\) −7.56300 −1.73507 −0.867536 0.497375i \(-0.834297\pi\)
−0.867536 + 0.497375i \(0.834297\pi\)
\(20\) 0 0
\(21\) 0.374242 0.0816662
\(22\) 0 0
\(23\) −5.64869 −1.17783 −0.588917 0.808193i \(-0.700446\pi\)
−0.588917 + 0.808193i \(0.700446\pi\)
\(24\) 0 0
\(25\) 8.45573 1.69115
\(26\) 0 0
\(27\) −2.19303 −0.422050
\(28\) 0 0
\(29\) −3.73357 −0.693307 −0.346653 0.937993i \(-0.612682\pi\)
−0.346653 + 0.937993i \(0.612682\pi\)
\(30\) 0 0
\(31\) 1.74855 0.314050 0.157025 0.987595i \(-0.449810\pi\)
0.157025 + 0.987595i \(0.449810\pi\)
\(32\) 0 0
\(33\) −0.374242 −0.0651471
\(34\) 0 0
\(35\) 3.66821 0.620040
\(36\) 0 0
\(37\) 5.77028 0.948629 0.474314 0.880356i \(-0.342696\pi\)
0.474314 + 0.880356i \(0.342696\pi\)
\(38\) 0 0
\(39\) −0.374242 −0.0599266
\(40\) 0 0
\(41\) −12.4153 −1.93895 −0.969475 0.245190i \(-0.921150\pi\)
−0.969475 + 0.245190i \(0.921150\pi\)
\(42\) 0 0
\(43\) 4.48406 0.683813 0.341906 0.939734i \(-0.388927\pi\)
0.341906 + 0.939734i \(0.388927\pi\)
\(44\) 0 0
\(45\) −10.4909 −1.56388
\(46\) 0 0
\(47\) −10.1674 −1.48306 −0.741531 0.670918i \(-0.765900\pi\)
−0.741531 + 0.670918i \(0.765900\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0.687595 0.0962825
\(52\) 0 0
\(53\) −0.412386 −0.0566456 −0.0283228 0.999599i \(-0.509017\pi\)
−0.0283228 + 0.999599i \(0.509017\pi\)
\(54\) 0 0
\(55\) −3.66821 −0.494621
\(56\) 0 0
\(57\) −2.83039 −0.374894
\(58\) 0 0
\(59\) −11.7860 −1.53441 −0.767206 0.641401i \(-0.778353\pi\)
−0.767206 + 0.641401i \(0.778353\pi\)
\(60\) 0 0
\(61\) 5.17539 0.662640 0.331320 0.943518i \(-0.392506\pi\)
0.331320 + 0.943518i \(0.392506\pi\)
\(62\) 0 0
\(63\) −2.85994 −0.360319
\(64\) 0 0
\(65\) −3.66821 −0.454985
\(66\) 0 0
\(67\) −13.9379 −1.70279 −0.851393 0.524529i \(-0.824242\pi\)
−0.851393 + 0.524529i \(0.824242\pi\)
\(68\) 0 0
\(69\) −2.11398 −0.254493
\(70\) 0 0
\(71\) 4.90321 0.581904 0.290952 0.956738i \(-0.406028\pi\)
0.290952 + 0.956738i \(0.406028\pi\)
\(72\) 0 0
\(73\) 14.5424 1.70206 0.851032 0.525115i \(-0.175978\pi\)
0.851032 + 0.525115i \(0.175978\pi\)
\(74\) 0 0
\(75\) 3.16449 0.365403
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.93053 1.11727 0.558636 0.829413i \(-0.311325\pi\)
0.558636 + 0.829413i \(0.311325\pi\)
\(80\) 0 0
\(81\) 7.75910 0.862123
\(82\) 0 0
\(83\) 2.71855 0.298400 0.149200 0.988807i \(-0.452330\pi\)
0.149200 + 0.988807i \(0.452330\pi\)
\(84\) 0 0
\(85\) 6.73960 0.731012
\(86\) 0 0
\(87\) −1.39726 −0.149802
\(88\) 0 0
\(89\) −17.7954 −1.88631 −0.943157 0.332348i \(-0.892159\pi\)
−0.943157 + 0.332348i \(0.892159\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 0.654382 0.0678562
\(94\) 0 0
\(95\) −27.7426 −2.84634
\(96\) 0 0
\(97\) 10.2664 1.04239 0.521196 0.853437i \(-0.325486\pi\)
0.521196 + 0.853437i \(0.325486\pi\)
\(98\) 0 0
\(99\) 2.85994 0.287435
\(100\) 0 0
\(101\) −17.3328 −1.72468 −0.862338 0.506333i \(-0.831001\pi\)
−0.862338 + 0.506333i \(0.831001\pi\)
\(102\) 0 0
\(103\) 0.615058 0.0606035 0.0303017 0.999541i \(-0.490353\pi\)
0.0303017 + 0.999541i \(0.490353\pi\)
\(104\) 0 0
\(105\) 1.37280 0.133971
\(106\) 0 0
\(107\) 10.1390 0.980175 0.490088 0.871673i \(-0.336965\pi\)
0.490088 + 0.871673i \(0.336965\pi\)
\(108\) 0 0
\(109\) −12.9298 −1.23845 −0.619227 0.785212i \(-0.712554\pi\)
−0.619227 + 0.785212i \(0.712554\pi\)
\(110\) 0 0
\(111\) 2.15948 0.204969
\(112\) 0 0
\(113\) −5.48052 −0.515564 −0.257782 0.966203i \(-0.582992\pi\)
−0.257782 + 0.966203i \(0.582992\pi\)
\(114\) 0 0
\(115\) −20.7206 −1.93220
\(116\) 0 0
\(117\) 2.85994 0.264402
\(118\) 0 0
\(119\) 1.83730 0.168425
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −4.64634 −0.418946
\(124\) 0 0
\(125\) 12.6763 1.13381
\(126\) 0 0
\(127\) −0.347348 −0.0308221 −0.0154111 0.999881i \(-0.504906\pi\)
−0.0154111 + 0.999881i \(0.504906\pi\)
\(128\) 0 0
\(129\) 1.67812 0.147750
\(130\) 0 0
\(131\) 5.97212 0.521787 0.260893 0.965368i \(-0.415983\pi\)
0.260893 + 0.965368i \(0.415983\pi\)
\(132\) 0 0
\(133\) −7.56300 −0.655796
\(134\) 0 0
\(135\) −8.04450 −0.692361
\(136\) 0 0
\(137\) −6.72558 −0.574605 −0.287303 0.957840i \(-0.592759\pi\)
−0.287303 + 0.957840i \(0.592759\pi\)
\(138\) 0 0
\(139\) −12.2916 −1.04256 −0.521282 0.853385i \(-0.674546\pi\)
−0.521282 + 0.853385i \(0.674546\pi\)
\(140\) 0 0
\(141\) −3.80505 −0.320443
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −13.6955 −1.13735
\(146\) 0 0
\(147\) 0.374242 0.0308669
\(148\) 0 0
\(149\) −5.93356 −0.486096 −0.243048 0.970014i \(-0.578147\pi\)
−0.243048 + 0.970014i \(0.578147\pi\)
\(150\) 0 0
\(151\) −19.9900 −1.62676 −0.813381 0.581732i \(-0.802375\pi\)
−0.813381 + 0.581732i \(0.802375\pi\)
\(152\) 0 0
\(153\) −5.25458 −0.424807
\(154\) 0 0
\(155\) 6.41406 0.515189
\(156\) 0 0
\(157\) −8.42600 −0.672468 −0.336234 0.941778i \(-0.609153\pi\)
−0.336234 + 0.941778i \(0.609153\pi\)
\(158\) 0 0
\(159\) −0.154332 −0.0122393
\(160\) 0 0
\(161\) −5.64869 −0.445179
\(162\) 0 0
\(163\) −7.69740 −0.602907 −0.301454 0.953481i \(-0.597472\pi\)
−0.301454 + 0.953481i \(0.597472\pi\)
\(164\) 0 0
\(165\) −1.37280 −0.106872
\(166\) 0 0
\(167\) −17.1263 −1.32527 −0.662636 0.748941i \(-0.730562\pi\)
−0.662636 + 0.748941i \(0.730562\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 21.6298 1.65407
\(172\) 0 0
\(173\) −3.00911 −0.228778 −0.114389 0.993436i \(-0.536491\pi\)
−0.114389 + 0.993436i \(0.536491\pi\)
\(174\) 0 0
\(175\) 8.45573 0.639193
\(176\) 0 0
\(177\) −4.41083 −0.331538
\(178\) 0 0
\(179\) −13.9691 −1.04410 −0.522051 0.852914i \(-0.674833\pi\)
−0.522051 + 0.852914i \(0.674833\pi\)
\(180\) 0 0
\(181\) 4.00172 0.297445 0.148723 0.988879i \(-0.452484\pi\)
0.148723 + 0.988879i \(0.452484\pi\)
\(182\) 0 0
\(183\) 1.93685 0.143176
\(184\) 0 0
\(185\) 21.1666 1.55620
\(186\) 0 0
\(187\) −1.83730 −0.134357
\(188\) 0 0
\(189\) −2.19303 −0.159520
\(190\) 0 0
\(191\) 5.68270 0.411186 0.205593 0.978638i \(-0.434088\pi\)
0.205593 + 0.978638i \(0.434088\pi\)
\(192\) 0 0
\(193\) 3.69748 0.266151 0.133075 0.991106i \(-0.457515\pi\)
0.133075 + 0.991106i \(0.457515\pi\)
\(194\) 0 0
\(195\) −1.37280 −0.0983079
\(196\) 0 0
\(197\) 15.6567 1.11550 0.557748 0.830010i \(-0.311666\pi\)
0.557748 + 0.830010i \(0.311666\pi\)
\(198\) 0 0
\(199\) −10.7878 −0.764725 −0.382362 0.924012i \(-0.624889\pi\)
−0.382362 + 0.924012i \(0.624889\pi\)
\(200\) 0 0
\(201\) −5.21614 −0.367918
\(202\) 0 0
\(203\) −3.73357 −0.262045
\(204\) 0 0
\(205\) −45.5420 −3.18079
\(206\) 0 0
\(207\) 16.1549 1.12285
\(208\) 0 0
\(209\) 7.56300 0.523144
\(210\) 0 0
\(211\) 16.0456 1.10462 0.552312 0.833637i \(-0.313746\pi\)
0.552312 + 0.833637i \(0.313746\pi\)
\(212\) 0 0
\(213\) 1.83499 0.125731
\(214\) 0 0
\(215\) 16.4485 1.12178
\(216\) 0 0
\(217\) 1.74855 0.118700
\(218\) 0 0
\(219\) 5.44238 0.367762
\(220\) 0 0
\(221\) −1.83730 −0.123590
\(222\) 0 0
\(223\) 7.61843 0.510168 0.255084 0.966919i \(-0.417897\pi\)
0.255084 + 0.966919i \(0.417897\pi\)
\(224\) 0 0
\(225\) −24.1829 −1.61219
\(226\) 0 0
\(227\) 8.73535 0.579786 0.289893 0.957059i \(-0.406380\pi\)
0.289893 + 0.957059i \(0.406380\pi\)
\(228\) 0 0
\(229\) −6.25431 −0.413296 −0.206648 0.978415i \(-0.566256\pi\)
−0.206648 + 0.978415i \(0.566256\pi\)
\(230\) 0 0
\(231\) −0.374242 −0.0246233
\(232\) 0 0
\(233\) 28.0190 1.83558 0.917791 0.397063i \(-0.129971\pi\)
0.917791 + 0.397063i \(0.129971\pi\)
\(234\) 0 0
\(235\) −37.2960 −2.43292
\(236\) 0 0
\(237\) 3.71642 0.241407
\(238\) 0 0
\(239\) 10.4528 0.676135 0.338067 0.941122i \(-0.390227\pi\)
0.338067 + 0.941122i \(0.390227\pi\)
\(240\) 0 0
\(241\) 24.8323 1.59959 0.799793 0.600276i \(-0.204942\pi\)
0.799793 + 0.600276i \(0.204942\pi\)
\(242\) 0 0
\(243\) 9.48288 0.608327
\(244\) 0 0
\(245\) 3.66821 0.234353
\(246\) 0 0
\(247\) 7.56300 0.481222
\(248\) 0 0
\(249\) 1.01740 0.0644748
\(250\) 0 0
\(251\) 14.5513 0.918467 0.459233 0.888316i \(-0.348124\pi\)
0.459233 + 0.888316i \(0.348124\pi\)
\(252\) 0 0
\(253\) 5.64869 0.355130
\(254\) 0 0
\(255\) 2.52224 0.157949
\(256\) 0 0
\(257\) 3.41006 0.212714 0.106357 0.994328i \(-0.466081\pi\)
0.106357 + 0.994328i \(0.466081\pi\)
\(258\) 0 0
\(259\) 5.77028 0.358548
\(260\) 0 0
\(261\) 10.6778 0.660939
\(262\) 0 0
\(263\) 3.13868 0.193539 0.0967696 0.995307i \(-0.469149\pi\)
0.0967696 + 0.995307i \(0.469149\pi\)
\(264\) 0 0
\(265\) −1.51272 −0.0929255
\(266\) 0 0
\(267\) −6.65980 −0.407573
\(268\) 0 0
\(269\) 16.5827 1.01106 0.505531 0.862808i \(-0.331297\pi\)
0.505531 + 0.862808i \(0.331297\pi\)
\(270\) 0 0
\(271\) −19.3736 −1.17686 −0.588432 0.808546i \(-0.700255\pi\)
−0.588432 + 0.808546i \(0.700255\pi\)
\(272\) 0 0
\(273\) −0.374242 −0.0226501
\(274\) 0 0
\(275\) −8.45573 −0.509900
\(276\) 0 0
\(277\) 19.6335 1.17966 0.589831 0.807526i \(-0.299194\pi\)
0.589831 + 0.807526i \(0.299194\pi\)
\(278\) 0 0
\(279\) −5.00077 −0.299388
\(280\) 0 0
\(281\) −28.8706 −1.72228 −0.861138 0.508372i \(-0.830248\pi\)
−0.861138 + 0.508372i \(0.830248\pi\)
\(282\) 0 0
\(283\) 11.0960 0.659587 0.329793 0.944053i \(-0.393021\pi\)
0.329793 + 0.944053i \(0.393021\pi\)
\(284\) 0 0
\(285\) −10.3825 −0.615004
\(286\) 0 0
\(287\) −12.4153 −0.732854
\(288\) 0 0
\(289\) −13.6243 −0.801431
\(290\) 0 0
\(291\) 3.84210 0.225228
\(292\) 0 0
\(293\) 29.3282 1.71337 0.856685 0.515839i \(-0.172520\pi\)
0.856685 + 0.515839i \(0.172520\pi\)
\(294\) 0 0
\(295\) −43.2336 −2.51716
\(296\) 0 0
\(297\) 2.19303 0.127253
\(298\) 0 0
\(299\) 5.64869 0.326672
\(300\) 0 0
\(301\) 4.48406 0.258457
\(302\) 0 0
\(303\) −6.48665 −0.372648
\(304\) 0 0
\(305\) 18.9844 1.08704
\(306\) 0 0
\(307\) 0.588014 0.0335597 0.0167799 0.999859i \(-0.494659\pi\)
0.0167799 + 0.999859i \(0.494659\pi\)
\(308\) 0 0
\(309\) 0.230180 0.0130945
\(310\) 0 0
\(311\) −1.85579 −0.105232 −0.0526160 0.998615i \(-0.516756\pi\)
−0.0526160 + 0.998615i \(0.516756\pi\)
\(312\) 0 0
\(313\) 5.23568 0.295938 0.147969 0.988992i \(-0.452726\pi\)
0.147969 + 0.988992i \(0.452726\pi\)
\(314\) 0 0
\(315\) −10.4909 −0.591093
\(316\) 0 0
\(317\) −7.83296 −0.439943 −0.219971 0.975506i \(-0.570596\pi\)
−0.219971 + 0.975506i \(0.570596\pi\)
\(318\) 0 0
\(319\) 3.73357 0.209040
\(320\) 0 0
\(321\) 3.79444 0.211785
\(322\) 0 0
\(323\) −13.8955 −0.773167
\(324\) 0 0
\(325\) −8.45573 −0.469040
\(326\) 0 0
\(327\) −4.83888 −0.267591
\(328\) 0 0
\(329\) −10.1674 −0.560545
\(330\) 0 0
\(331\) −25.1488 −1.38230 −0.691152 0.722710i \(-0.742896\pi\)
−0.691152 + 0.722710i \(0.742896\pi\)
\(332\) 0 0
\(333\) −16.5027 −0.904341
\(334\) 0 0
\(335\) −51.1271 −2.79337
\(336\) 0 0
\(337\) −2.03102 −0.110636 −0.0553182 0.998469i \(-0.517617\pi\)
−0.0553182 + 0.998469i \(0.517617\pi\)
\(338\) 0 0
\(339\) −2.05104 −0.111397
\(340\) 0 0
\(341\) −1.74855 −0.0946895
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −7.75450 −0.417488
\(346\) 0 0
\(347\) −11.0112 −0.591113 −0.295557 0.955325i \(-0.595505\pi\)
−0.295557 + 0.955325i \(0.595505\pi\)
\(348\) 0 0
\(349\) −13.3381 −0.713970 −0.356985 0.934110i \(-0.616195\pi\)
−0.356985 + 0.934110i \(0.616195\pi\)
\(350\) 0 0
\(351\) 2.19303 0.117056
\(352\) 0 0
\(353\) 22.8646 1.21696 0.608479 0.793570i \(-0.291780\pi\)
0.608479 + 0.793570i \(0.291780\pi\)
\(354\) 0 0
\(355\) 17.9860 0.954597
\(356\) 0 0
\(357\) 0.687595 0.0363914
\(358\) 0 0
\(359\) 6.63030 0.349934 0.174967 0.984574i \(-0.444018\pi\)
0.174967 + 0.984574i \(0.444018\pi\)
\(360\) 0 0
\(361\) 38.1990 2.01047
\(362\) 0 0
\(363\) 0.374242 0.0196426
\(364\) 0 0
\(365\) 53.3446 2.79219
\(366\) 0 0
\(367\) −8.04286 −0.419834 −0.209917 0.977719i \(-0.567319\pi\)
−0.209917 + 0.977719i \(0.567319\pi\)
\(368\) 0 0
\(369\) 35.5072 1.84843
\(370\) 0 0
\(371\) −0.412386 −0.0214100
\(372\) 0 0
\(373\) −19.3644 −1.00265 −0.501324 0.865260i \(-0.667154\pi\)
−0.501324 + 0.865260i \(0.667154\pi\)
\(374\) 0 0
\(375\) 4.74401 0.244980
\(376\) 0 0
\(377\) 3.73357 0.192289
\(378\) 0 0
\(379\) −6.71205 −0.344775 −0.172387 0.985029i \(-0.555148\pi\)
−0.172387 + 0.985029i \(0.555148\pi\)
\(380\) 0 0
\(381\) −0.129992 −0.00665969
\(382\) 0 0
\(383\) −25.5152 −1.30377 −0.651883 0.758319i \(-0.726021\pi\)
−0.651883 + 0.758319i \(0.726021\pi\)
\(384\) 0 0
\(385\) −3.66821 −0.186949
\(386\) 0 0
\(387\) −12.8242 −0.651889
\(388\) 0 0
\(389\) −3.87362 −0.196400 −0.0982001 0.995167i \(-0.531309\pi\)
−0.0982001 + 0.995167i \(0.531309\pi\)
\(390\) 0 0
\(391\) −10.3784 −0.524856
\(392\) 0 0
\(393\) 2.23502 0.112742
\(394\) 0 0
\(395\) 36.4272 1.83285
\(396\) 0 0
\(397\) 22.8561 1.14712 0.573558 0.819165i \(-0.305563\pi\)
0.573558 + 0.819165i \(0.305563\pi\)
\(398\) 0 0
\(399\) −2.83039 −0.141697
\(400\) 0 0
\(401\) −16.1528 −0.806632 −0.403316 0.915061i \(-0.632142\pi\)
−0.403316 + 0.915061i \(0.632142\pi\)
\(402\) 0 0
\(403\) −1.74855 −0.0871017
\(404\) 0 0
\(405\) 28.4620 1.41429
\(406\) 0 0
\(407\) −5.77028 −0.286022
\(408\) 0 0
\(409\) 25.7234 1.27194 0.635970 0.771714i \(-0.280600\pi\)
0.635970 + 0.771714i \(0.280600\pi\)
\(410\) 0 0
\(411\) −2.51699 −0.124154
\(412\) 0 0
\(413\) −11.7860 −0.579953
\(414\) 0 0
\(415\) 9.97221 0.489516
\(416\) 0 0
\(417\) −4.60005 −0.225265
\(418\) 0 0
\(419\) −19.1677 −0.936403 −0.468202 0.883622i \(-0.655098\pi\)
−0.468202 + 0.883622i \(0.655098\pi\)
\(420\) 0 0
\(421\) −6.79107 −0.330977 −0.165488 0.986212i \(-0.552920\pi\)
−0.165488 + 0.986212i \(0.552920\pi\)
\(422\) 0 0
\(423\) 29.0781 1.41382
\(424\) 0 0
\(425\) 15.5357 0.753593
\(426\) 0 0
\(427\) 5.17539 0.250455
\(428\) 0 0
\(429\) 0.374242 0.0180686
\(430\) 0 0
\(431\) −2.17751 −0.104887 −0.0524435 0.998624i \(-0.516701\pi\)
−0.0524435 + 0.998624i \(0.516701\pi\)
\(432\) 0 0
\(433\) 28.8359 1.38576 0.692882 0.721051i \(-0.256341\pi\)
0.692882 + 0.721051i \(0.256341\pi\)
\(434\) 0 0
\(435\) −5.12543 −0.245745
\(436\) 0 0
\(437\) 42.7211 2.04363
\(438\) 0 0
\(439\) −18.0395 −0.860980 −0.430490 0.902595i \(-0.641659\pi\)
−0.430490 + 0.902595i \(0.641659\pi\)
\(440\) 0 0
\(441\) −2.85994 −0.136188
\(442\) 0 0
\(443\) −18.6299 −0.885135 −0.442567 0.896735i \(-0.645932\pi\)
−0.442567 + 0.896735i \(0.645932\pi\)
\(444\) 0 0
\(445\) −65.2773 −3.09444
\(446\) 0 0
\(447\) −2.22059 −0.105030
\(448\) 0 0
\(449\) 35.2493 1.66352 0.831760 0.555136i \(-0.187334\pi\)
0.831760 + 0.555136i \(0.187334\pi\)
\(450\) 0 0
\(451\) 12.4153 0.584615
\(452\) 0 0
\(453\) −7.48108 −0.351492
\(454\) 0 0
\(455\) −3.66821 −0.171968
\(456\) 0 0
\(457\) 19.7593 0.924301 0.462150 0.886802i \(-0.347078\pi\)
0.462150 + 0.886802i \(0.347078\pi\)
\(458\) 0 0
\(459\) −4.02927 −0.188070
\(460\) 0 0
\(461\) −18.6821 −0.870113 −0.435056 0.900403i \(-0.643272\pi\)
−0.435056 + 0.900403i \(0.643272\pi\)
\(462\) 0 0
\(463\) 33.6272 1.56279 0.781394 0.624038i \(-0.214509\pi\)
0.781394 + 0.624038i \(0.214509\pi\)
\(464\) 0 0
\(465\) 2.40041 0.111316
\(466\) 0 0
\(467\) −24.2611 −1.12267 −0.561335 0.827589i \(-0.689712\pi\)
−0.561335 + 0.827589i \(0.689712\pi\)
\(468\) 0 0
\(469\) −13.9379 −0.643593
\(470\) 0 0
\(471\) −3.15336 −0.145299
\(472\) 0 0
\(473\) −4.48406 −0.206177
\(474\) 0 0
\(475\) −63.9507 −2.93426
\(476\) 0 0
\(477\) 1.17940 0.0540011
\(478\) 0 0
\(479\) −17.2943 −0.790197 −0.395099 0.918639i \(-0.629290\pi\)
−0.395099 + 0.918639i \(0.629290\pi\)
\(480\) 0 0
\(481\) −5.77028 −0.263102
\(482\) 0 0
\(483\) −2.11398 −0.0961893
\(484\) 0 0
\(485\) 37.6591 1.71001
\(486\) 0 0
\(487\) −27.7873 −1.25916 −0.629581 0.776935i \(-0.716774\pi\)
−0.629581 + 0.776935i \(0.716774\pi\)
\(488\) 0 0
\(489\) −2.88069 −0.130269
\(490\) 0 0
\(491\) 31.5679 1.42464 0.712320 0.701855i \(-0.247645\pi\)
0.712320 + 0.701855i \(0.247645\pi\)
\(492\) 0 0
\(493\) −6.85969 −0.308945
\(494\) 0 0
\(495\) 10.4909 0.471529
\(496\) 0 0
\(497\) 4.90321 0.219939
\(498\) 0 0
\(499\) 12.5374 0.561252 0.280626 0.959817i \(-0.409458\pi\)
0.280626 + 0.959817i \(0.409458\pi\)
\(500\) 0 0
\(501\) −6.40937 −0.286350
\(502\) 0 0
\(503\) −24.3600 −1.08616 −0.543080 0.839681i \(-0.682742\pi\)
−0.543080 + 0.839681i \(0.682742\pi\)
\(504\) 0 0
\(505\) −63.5802 −2.82928
\(506\) 0 0
\(507\) 0.374242 0.0166207
\(508\) 0 0
\(509\) −29.3745 −1.30200 −0.651000 0.759078i \(-0.725650\pi\)
−0.651000 + 0.759078i \(0.725650\pi\)
\(510\) 0 0
\(511\) 14.5424 0.643319
\(512\) 0 0
\(513\) 16.5859 0.732287
\(514\) 0 0
\(515\) 2.25616 0.0994182
\(516\) 0 0
\(517\) 10.1674 0.447160
\(518\) 0 0
\(519\) −1.12613 −0.0494318
\(520\) 0 0
\(521\) −15.2997 −0.670293 −0.335146 0.942166i \(-0.608786\pi\)
−0.335146 + 0.942166i \(0.608786\pi\)
\(522\) 0 0
\(523\) 43.9372 1.92124 0.960620 0.277865i \(-0.0896267\pi\)
0.960620 + 0.277865i \(0.0896267\pi\)
\(524\) 0 0
\(525\) 3.16449 0.138110
\(526\) 0 0
\(527\) 3.21262 0.139944
\(528\) 0 0
\(529\) 8.90774 0.387293
\(530\) 0 0
\(531\) 33.7074 1.46278
\(532\) 0 0
\(533\) 12.4153 0.537768
\(534\) 0 0
\(535\) 37.1920 1.60795
\(536\) 0 0
\(537\) −5.22783 −0.225598
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 31.5557 1.35668 0.678342 0.734746i \(-0.262699\pi\)
0.678342 + 0.734746i \(0.262699\pi\)
\(542\) 0 0
\(543\) 1.49761 0.0642686
\(544\) 0 0
\(545\) −47.4293 −2.03165
\(546\) 0 0
\(547\) −10.9325 −0.467441 −0.233721 0.972304i \(-0.575090\pi\)
−0.233721 + 0.972304i \(0.575090\pi\)
\(548\) 0 0
\(549\) −14.8013 −0.631705
\(550\) 0 0
\(551\) 28.2370 1.20294
\(552\) 0 0
\(553\) 9.93053 0.422289
\(554\) 0 0
\(555\) 7.92142 0.336245
\(556\) 0 0
\(557\) 1.33827 0.0567044 0.0283522 0.999598i \(-0.490974\pi\)
0.0283522 + 0.999598i \(0.490974\pi\)
\(558\) 0 0
\(559\) −4.48406 −0.189656
\(560\) 0 0
\(561\) −0.687595 −0.0290303
\(562\) 0 0
\(563\) 29.9813 1.26356 0.631780 0.775148i \(-0.282325\pi\)
0.631780 + 0.775148i \(0.282325\pi\)
\(564\) 0 0
\(565\) −20.1037 −0.845768
\(566\) 0 0
\(567\) 7.75910 0.325852
\(568\) 0 0
\(569\) −24.2600 −1.01703 −0.508515 0.861053i \(-0.669805\pi\)
−0.508515 + 0.861053i \(0.669805\pi\)
\(570\) 0 0
\(571\) 13.0856 0.547614 0.273807 0.961785i \(-0.411717\pi\)
0.273807 + 0.961785i \(0.411717\pi\)
\(572\) 0 0
\(573\) 2.12670 0.0888444
\(574\) 0 0
\(575\) −47.7638 −1.99189
\(576\) 0 0
\(577\) −13.0671 −0.543991 −0.271995 0.962299i \(-0.587684\pi\)
−0.271995 + 0.962299i \(0.587684\pi\)
\(578\) 0 0
\(579\) 1.38375 0.0575068
\(580\) 0 0
\(581\) 2.71855 0.112785
\(582\) 0 0
\(583\) 0.412386 0.0170793
\(584\) 0 0
\(585\) 10.4909 0.433744
\(586\) 0 0
\(587\) −7.35049 −0.303387 −0.151694 0.988428i \(-0.548473\pi\)
−0.151694 + 0.988428i \(0.548473\pi\)
\(588\) 0 0
\(589\) −13.2243 −0.544899
\(590\) 0 0
\(591\) 5.85940 0.241024
\(592\) 0 0
\(593\) 40.6531 1.66942 0.834712 0.550686i \(-0.185634\pi\)
0.834712 + 0.550686i \(0.185634\pi\)
\(594\) 0 0
\(595\) 6.73960 0.276297
\(596\) 0 0
\(597\) −4.03723 −0.165233
\(598\) 0 0
\(599\) −7.16907 −0.292920 −0.146460 0.989217i \(-0.546788\pi\)
−0.146460 + 0.989217i \(0.546788\pi\)
\(600\) 0 0
\(601\) −20.1446 −0.821715 −0.410858 0.911700i \(-0.634771\pi\)
−0.410858 + 0.911700i \(0.634771\pi\)
\(602\) 0 0
\(603\) 39.8616 1.62329
\(604\) 0 0
\(605\) 3.66821 0.149134
\(606\) 0 0
\(607\) −46.0048 −1.86728 −0.933639 0.358216i \(-0.883385\pi\)
−0.933639 + 0.358216i \(0.883385\pi\)
\(608\) 0 0
\(609\) −1.39726 −0.0566197
\(610\) 0 0
\(611\) 10.1674 0.411328
\(612\) 0 0
\(613\) 3.33233 0.134592 0.0672958 0.997733i \(-0.478563\pi\)
0.0672958 + 0.997733i \(0.478563\pi\)
\(614\) 0 0
\(615\) −17.0437 −0.687269
\(616\) 0 0
\(617\) −29.4619 −1.18609 −0.593045 0.805169i \(-0.702075\pi\)
−0.593045 + 0.805169i \(0.702075\pi\)
\(618\) 0 0
\(619\) −6.10549 −0.245401 −0.122700 0.992444i \(-0.539155\pi\)
−0.122700 + 0.992444i \(0.539155\pi\)
\(620\) 0 0
\(621\) 12.3878 0.497105
\(622\) 0 0
\(623\) −17.7954 −0.712959
\(624\) 0 0
\(625\) 4.22072 0.168829
\(626\) 0 0
\(627\) 2.83039 0.113035
\(628\) 0 0
\(629\) 10.6017 0.422719
\(630\) 0 0
\(631\) −8.17489 −0.325437 −0.162719 0.986673i \(-0.552026\pi\)
−0.162719 + 0.986673i \(0.552026\pi\)
\(632\) 0 0
\(633\) 6.00493 0.238675
\(634\) 0 0
\(635\) −1.27414 −0.0505628
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −14.0229 −0.554738
\(640\) 0 0
\(641\) 5.11505 0.202032 0.101016 0.994885i \(-0.467791\pi\)
0.101016 + 0.994885i \(0.467791\pi\)
\(642\) 0 0
\(643\) 23.5056 0.926972 0.463486 0.886104i \(-0.346598\pi\)
0.463486 + 0.886104i \(0.346598\pi\)
\(644\) 0 0
\(645\) 6.15570 0.242380
\(646\) 0 0
\(647\) 45.7401 1.79823 0.899114 0.437715i \(-0.144212\pi\)
0.899114 + 0.437715i \(0.144212\pi\)
\(648\) 0 0
\(649\) 11.7860 0.462642
\(650\) 0 0
\(651\) 0.654382 0.0256472
\(652\) 0 0
\(653\) −8.04928 −0.314993 −0.157496 0.987520i \(-0.550342\pi\)
−0.157496 + 0.987520i \(0.550342\pi\)
\(654\) 0 0
\(655\) 21.9070 0.855976
\(656\) 0 0
\(657\) −41.5905 −1.62260
\(658\) 0 0
\(659\) 13.1745 0.513205 0.256603 0.966517i \(-0.417397\pi\)
0.256603 + 0.966517i \(0.417397\pi\)
\(660\) 0 0
\(661\) 20.0583 0.780176 0.390088 0.920778i \(-0.372445\pi\)
0.390088 + 0.920778i \(0.372445\pi\)
\(662\) 0 0
\(663\) −0.687595 −0.0267040
\(664\) 0 0
\(665\) −27.7426 −1.07581
\(666\) 0 0
\(667\) 21.0898 0.816600
\(668\) 0 0
\(669\) 2.85113 0.110231
\(670\) 0 0
\(671\) −5.17539 −0.199794
\(672\) 0 0
\(673\) −17.0122 −0.655771 −0.327886 0.944717i \(-0.606336\pi\)
−0.327886 + 0.944717i \(0.606336\pi\)
\(674\) 0 0
\(675\) −18.5437 −0.713748
\(676\) 0 0
\(677\) −7.83416 −0.301091 −0.150546 0.988603i \(-0.548103\pi\)
−0.150546 + 0.988603i \(0.548103\pi\)
\(678\) 0 0
\(679\) 10.2664 0.393987
\(680\) 0 0
\(681\) 3.26913 0.125273
\(682\) 0 0
\(683\) 37.9105 1.45060 0.725302 0.688431i \(-0.241700\pi\)
0.725302 + 0.688431i \(0.241700\pi\)
\(684\) 0 0
\(685\) −24.6708 −0.942623
\(686\) 0 0
\(687\) −2.34062 −0.0893004
\(688\) 0 0
\(689\) 0.412386 0.0157107
\(690\) 0 0
\(691\) −46.5888 −1.77232 −0.886162 0.463376i \(-0.846638\pi\)
−0.886162 + 0.463376i \(0.846638\pi\)
\(692\) 0 0
\(693\) 2.85994 0.108640
\(694\) 0 0
\(695\) −45.0883 −1.71030
\(696\) 0 0
\(697\) −22.8107 −0.864017
\(698\) 0 0
\(699\) 10.4859 0.396612
\(700\) 0 0
\(701\) −36.6628 −1.38474 −0.692368 0.721545i \(-0.743432\pi\)
−0.692368 + 0.721545i \(0.743432\pi\)
\(702\) 0 0
\(703\) −43.6407 −1.64594
\(704\) 0 0
\(705\) −13.9577 −0.525678
\(706\) 0 0
\(707\) −17.3328 −0.651866
\(708\) 0 0
\(709\) 22.5551 0.847076 0.423538 0.905878i \(-0.360788\pi\)
0.423538 + 0.905878i \(0.360788\pi\)
\(710\) 0 0
\(711\) −28.4008 −1.06511
\(712\) 0 0
\(713\) −9.87705 −0.369898
\(714\) 0 0
\(715\) 3.66821 0.137183
\(716\) 0 0
\(717\) 3.91187 0.146091
\(718\) 0 0
\(719\) 1.92314 0.0717210 0.0358605 0.999357i \(-0.488583\pi\)
0.0358605 + 0.999357i \(0.488583\pi\)
\(720\) 0 0
\(721\) 0.615058 0.0229060
\(722\) 0 0
\(723\) 9.29326 0.345620
\(724\) 0 0
\(725\) −31.5701 −1.17248
\(726\) 0 0
\(727\) −2.35686 −0.0874110 −0.0437055 0.999044i \(-0.513916\pi\)
−0.0437055 + 0.999044i \(0.513916\pi\)
\(728\) 0 0
\(729\) −19.7284 −0.730682
\(730\) 0 0
\(731\) 8.23857 0.304714
\(732\) 0 0
\(733\) 5.72337 0.211397 0.105699 0.994398i \(-0.466292\pi\)
0.105699 + 0.994398i \(0.466292\pi\)
\(734\) 0 0
\(735\) 1.37280 0.0506363
\(736\) 0 0
\(737\) 13.9379 0.513409
\(738\) 0 0
\(739\) 7.87657 0.289744 0.144872 0.989450i \(-0.453723\pi\)
0.144872 + 0.989450i \(0.453723\pi\)
\(740\) 0 0
\(741\) 2.83039 0.103977
\(742\) 0 0
\(743\) −4.34939 −0.159564 −0.0797818 0.996812i \(-0.525422\pi\)
−0.0797818 + 0.996812i \(0.525422\pi\)
\(744\) 0 0
\(745\) −21.7655 −0.797427
\(746\) 0 0
\(747\) −7.77490 −0.284469
\(748\) 0 0
\(749\) 10.1390 0.370471
\(750\) 0 0
\(751\) −47.0045 −1.71522 −0.857609 0.514303i \(-0.828051\pi\)
−0.857609 + 0.514303i \(0.828051\pi\)
\(752\) 0 0
\(753\) 5.44568 0.198452
\(754\) 0 0
\(755\) −73.3273 −2.66865
\(756\) 0 0
\(757\) −40.1138 −1.45796 −0.728981 0.684534i \(-0.760006\pi\)
−0.728981 + 0.684534i \(0.760006\pi\)
\(758\) 0 0
\(759\) 2.11398 0.0767325
\(760\) 0 0
\(761\) −44.7843 −1.62343 −0.811715 0.584054i \(-0.801465\pi\)
−0.811715 + 0.584054i \(0.801465\pi\)
\(762\) 0 0
\(763\) −12.9298 −0.468091
\(764\) 0 0
\(765\) −19.2749 −0.696884
\(766\) 0 0
\(767\) 11.7860 0.425569
\(768\) 0 0
\(769\) 5.96549 0.215121 0.107560 0.994199i \(-0.465696\pi\)
0.107560 + 0.994199i \(0.465696\pi\)
\(770\) 0 0
\(771\) 1.27619 0.0459608
\(772\) 0 0
\(773\) 35.1293 1.26351 0.631757 0.775166i \(-0.282334\pi\)
0.631757 + 0.775166i \(0.282334\pi\)
\(774\) 0 0
\(775\) 14.7853 0.531104
\(776\) 0 0
\(777\) 2.15948 0.0774709
\(778\) 0 0
\(779\) 93.8972 3.36422
\(780\) 0 0
\(781\) −4.90321 −0.175451
\(782\) 0 0
\(783\) 8.18785 0.292610
\(784\) 0 0
\(785\) −30.9083 −1.10316
\(786\) 0 0
\(787\) 40.3870 1.43964 0.719821 0.694160i \(-0.244224\pi\)
0.719821 + 0.694160i \(0.244224\pi\)
\(788\) 0 0
\(789\) 1.17462 0.0418177
\(790\) 0 0
\(791\) −5.48052 −0.194865
\(792\) 0 0
\(793\) −5.17539 −0.183783
\(794\) 0 0
\(795\) −0.566122 −0.0200783
\(796\) 0 0
\(797\) −23.3042 −0.825478 −0.412739 0.910849i \(-0.635428\pi\)
−0.412739 + 0.910849i \(0.635428\pi\)
\(798\) 0 0
\(799\) −18.6805 −0.660869
\(800\) 0 0
\(801\) 50.8940 1.79825
\(802\) 0 0
\(803\) −14.5424 −0.513191
\(804\) 0 0
\(805\) −20.7206 −0.730304
\(806\) 0 0
\(807\) 6.20592 0.218459
\(808\) 0 0
\(809\) 0.269364 0.00947033 0.00473516 0.999989i \(-0.498493\pi\)
0.00473516 + 0.999989i \(0.498493\pi\)
\(810\) 0 0
\(811\) −32.8329 −1.15292 −0.576459 0.817126i \(-0.695566\pi\)
−0.576459 + 0.817126i \(0.695566\pi\)
\(812\) 0 0
\(813\) −7.25042 −0.254283
\(814\) 0 0
\(815\) −28.2357 −0.989052
\(816\) 0 0
\(817\) −33.9130 −1.18646
\(818\) 0 0
\(819\) 2.85994 0.0999345
\(820\) 0 0
\(821\) 39.0940 1.36439 0.682195 0.731170i \(-0.261026\pi\)
0.682195 + 0.731170i \(0.261026\pi\)
\(822\) 0 0
\(823\) 38.6365 1.34678 0.673392 0.739285i \(-0.264836\pi\)
0.673392 + 0.739285i \(0.264836\pi\)
\(824\) 0 0
\(825\) −3.16449 −0.110173
\(826\) 0 0
\(827\) 2.02062 0.0702638 0.0351319 0.999383i \(-0.488815\pi\)
0.0351319 + 0.999383i \(0.488815\pi\)
\(828\) 0 0
\(829\) −21.6630 −0.752386 −0.376193 0.926541i \(-0.622767\pi\)
−0.376193 + 0.926541i \(0.622767\pi\)
\(830\) 0 0
\(831\) 7.34768 0.254888
\(832\) 0 0
\(833\) 1.83730 0.0636587
\(834\) 0 0
\(835\) −62.8228 −2.17407
\(836\) 0 0
\(837\) −3.83464 −0.132545
\(838\) 0 0
\(839\) −42.9752 −1.48367 −0.741835 0.670583i \(-0.766044\pi\)
−0.741835 + 0.670583i \(0.766044\pi\)
\(840\) 0 0
\(841\) −15.0605 −0.519326
\(842\) 0 0
\(843\) −10.8046 −0.372130
\(844\) 0 0
\(845\) 3.66821 0.126190
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 4.15257 0.142516
\(850\) 0 0
\(851\) −32.5946 −1.11733
\(852\) 0 0
\(853\) 24.4508 0.837178 0.418589 0.908176i \(-0.362525\pi\)
0.418589 + 0.908176i \(0.362525\pi\)
\(854\) 0 0
\(855\) 79.3424 2.71345
\(856\) 0 0
\(857\) −34.5716 −1.18094 −0.590471 0.807059i \(-0.701058\pi\)
−0.590471 + 0.807059i \(0.701058\pi\)
\(858\) 0 0
\(859\) −32.5539 −1.11073 −0.555363 0.831608i \(-0.687421\pi\)
−0.555363 + 0.831608i \(0.687421\pi\)
\(860\) 0 0
\(861\) −4.64634 −0.158347
\(862\) 0 0
\(863\) −26.7865 −0.911822 −0.455911 0.890025i \(-0.650686\pi\)
−0.455911 + 0.890025i \(0.650686\pi\)
\(864\) 0 0
\(865\) −11.0380 −0.375304
\(866\) 0 0
\(867\) −5.09879 −0.173164
\(868\) 0 0
\(869\) −9.93053 −0.336870
\(870\) 0 0
\(871\) 13.9379 0.472268
\(872\) 0 0
\(873\) −29.3612 −0.993727
\(874\) 0 0
\(875\) 12.6763 0.428538
\(876\) 0 0
\(877\) 25.9852 0.877458 0.438729 0.898619i \(-0.355429\pi\)
0.438729 + 0.898619i \(0.355429\pi\)
\(878\) 0 0
\(879\) 10.9758 0.370206
\(880\) 0 0
\(881\) 37.9108 1.27725 0.638623 0.769520i \(-0.279504\pi\)
0.638623 + 0.769520i \(0.279504\pi\)
\(882\) 0 0
\(883\) 25.5544 0.859974 0.429987 0.902835i \(-0.358518\pi\)
0.429987 + 0.902835i \(0.358518\pi\)
\(884\) 0 0
\(885\) −16.1798 −0.543879
\(886\) 0 0
\(887\) −36.8767 −1.23820 −0.619100 0.785312i \(-0.712502\pi\)
−0.619100 + 0.785312i \(0.712502\pi\)
\(888\) 0 0
\(889\) −0.347348 −0.0116497
\(890\) 0 0
\(891\) −7.75910 −0.259940
\(892\) 0 0
\(893\) 76.8958 2.57322
\(894\) 0 0
\(895\) −51.2416 −1.71282
\(896\) 0 0
\(897\) 2.11398 0.0705836
\(898\) 0 0
\(899\) −6.52835 −0.217733
\(900\) 0 0
\(901\) −0.757678 −0.0252419
\(902\) 0 0
\(903\) 1.67812 0.0558444
\(904\) 0 0
\(905\) 14.6791 0.487951
\(906\) 0 0
\(907\) −19.0484 −0.632493 −0.316246 0.948677i \(-0.602423\pi\)
−0.316246 + 0.948677i \(0.602423\pi\)
\(908\) 0 0
\(909\) 49.5708 1.64416
\(910\) 0 0
\(911\) 49.6121 1.64372 0.821862 0.569687i \(-0.192936\pi\)
0.821862 + 0.569687i \(0.192936\pi\)
\(912\) 0 0
\(913\) −2.71855 −0.0899709
\(914\) 0 0
\(915\) 7.10475 0.234876
\(916\) 0 0
\(917\) 5.97212 0.197217
\(918\) 0 0
\(919\) 4.79980 0.158331 0.0791654 0.996861i \(-0.474774\pi\)
0.0791654 + 0.996861i \(0.474774\pi\)
\(920\) 0 0
\(921\) 0.220059 0.00725120
\(922\) 0 0
\(923\) −4.90321 −0.161391
\(924\) 0 0
\(925\) 48.7920 1.60427
\(926\) 0 0
\(927\) −1.75903 −0.0577742
\(928\) 0 0
\(929\) 37.7339 1.23801 0.619004 0.785388i \(-0.287537\pi\)
0.619004 + 0.785388i \(0.287537\pi\)
\(930\) 0 0
\(931\) −7.56300 −0.247867
\(932\) 0 0
\(933\) −0.694513 −0.0227373
\(934\) 0 0
\(935\) −6.73960 −0.220408
\(936\) 0 0
\(937\) 56.2845 1.83874 0.919368 0.393399i \(-0.128701\pi\)
0.919368 + 0.393399i \(0.128701\pi\)
\(938\) 0 0
\(939\) 1.95941 0.0639429
\(940\) 0 0
\(941\) −33.0073 −1.07601 −0.538003 0.842943i \(-0.680821\pi\)
−0.538003 + 0.842943i \(0.680821\pi\)
\(942\) 0 0
\(943\) 70.1304 2.28376
\(944\) 0 0
\(945\) −8.04450 −0.261688
\(946\) 0 0
\(947\) 8.43995 0.274261 0.137131 0.990553i \(-0.456212\pi\)
0.137131 + 0.990553i \(0.456212\pi\)
\(948\) 0 0
\(949\) −14.5424 −0.472067
\(950\) 0 0
\(951\) −2.93142 −0.0950578
\(952\) 0 0
\(953\) 4.97118 0.161032 0.0805162 0.996753i \(-0.474343\pi\)
0.0805162 + 0.996753i \(0.474343\pi\)
\(954\) 0 0
\(955\) 20.8453 0.674539
\(956\) 0 0
\(957\) 1.39726 0.0451669
\(958\) 0 0
\(959\) −6.72558 −0.217180
\(960\) 0 0
\(961\) −27.9426 −0.901373
\(962\) 0 0
\(963\) −28.9970 −0.934415
\(964\) 0 0
\(965\) 13.5631 0.436613
\(966\) 0 0
\(967\) −5.35840 −0.172315 −0.0861573 0.996282i \(-0.527459\pi\)
−0.0861573 + 0.996282i \(0.527459\pi\)
\(968\) 0 0
\(969\) −5.20028 −0.167057
\(970\) 0 0
\(971\) 6.57700 0.211066 0.105533 0.994416i \(-0.466345\pi\)
0.105533 + 0.994416i \(0.466345\pi\)
\(972\) 0 0
\(973\) −12.2916 −0.394052
\(974\) 0 0
\(975\) −3.16449 −0.101345
\(976\) 0 0
\(977\) −19.3743 −0.619837 −0.309919 0.950763i \(-0.600302\pi\)
−0.309919 + 0.950763i \(0.600302\pi\)
\(978\) 0 0
\(979\) 17.7954 0.568745
\(980\) 0 0
\(981\) 36.9786 1.18064
\(982\) 0 0
\(983\) −17.8748 −0.570118 −0.285059 0.958510i \(-0.592013\pi\)
−0.285059 + 0.958510i \(0.592013\pi\)
\(984\) 0 0
\(985\) 57.4321 1.82994
\(986\) 0 0
\(987\) −3.80505 −0.121116
\(988\) 0 0
\(989\) −25.3291 −0.805418
\(990\) 0 0
\(991\) 37.7034 1.19769 0.598843 0.800866i \(-0.295627\pi\)
0.598843 + 0.800866i \(0.295627\pi\)
\(992\) 0 0
\(993\) −9.41173 −0.298672
\(994\) 0 0
\(995\) −39.5718 −1.25451
\(996\) 0 0
\(997\) 20.3448 0.644326 0.322163 0.946684i \(-0.395590\pi\)
0.322163 + 0.946684i \(0.395590\pi\)
\(998\) 0 0
\(999\) −12.6544 −0.400369
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 \(a_p\))