Properties

Label 8008.2.a.v.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.983398\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.983398 q^{3} -1.20732 q^{5} -1.00000 q^{7} -2.03293 q^{9} +O(q^{10})\) \(q-0.983398 q^{3} -1.20732 q^{5} -1.00000 q^{7} -2.03293 q^{9} +1.00000 q^{11} -1.00000 q^{13} +1.18728 q^{15} +3.10486 q^{17} -6.13942 q^{19} +0.983398 q^{21} +9.39792 q^{23} -3.54237 q^{25} +4.94937 q^{27} -2.82165 q^{29} +0.543253 q^{31} -0.983398 q^{33} +1.20732 q^{35} -0.252569 q^{37} +0.983398 q^{39} +0.665720 q^{41} -0.327119 q^{43} +2.45440 q^{45} +9.39792 q^{47} +1.00000 q^{49} -3.05332 q^{51} +8.35464 q^{53} -1.20732 q^{55} +6.03749 q^{57} +8.49766 q^{59} -4.81738 q^{61} +2.03293 q^{63} +1.20732 q^{65} -13.9821 q^{67} -9.24189 q^{69} -9.69998 q^{71} +14.8876 q^{73} +3.48356 q^{75} -1.00000 q^{77} +4.53081 q^{79} +1.23159 q^{81} -9.44676 q^{83} -3.74857 q^{85} +2.77480 q^{87} -3.56230 q^{89} +1.00000 q^{91} -0.534234 q^{93} +7.41225 q^{95} +15.7191 q^{97} -2.03293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) −0.983398 −0.567765 −0.283882 0.958859i \(-0.591623\pi\)
−0.283882 + 0.958859i \(0.591623\pi\)
\(4\) 0 0
\(5\) −1.20732 −0.539931 −0.269965 0.962870i \(-0.587012\pi\)
−0.269965 + 0.962870i \(0.587012\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.03293 −0.677643
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.18728 0.306554
\(16\) 0 0
\(17\) 3.10486 0.753040 0.376520 0.926408i \(-0.377121\pi\)
0.376520 + 0.926408i \(0.377121\pi\)
\(18\) 0 0
\(19\) −6.13942 −1.40848 −0.704240 0.709962i \(-0.748712\pi\)
−0.704240 + 0.709962i \(0.748712\pi\)
\(20\) 0 0
\(21\) 0.983398 0.214595
\(22\) 0 0
\(23\) 9.39792 1.95960 0.979800 0.199978i \(-0.0640870\pi\)
0.979800 + 0.199978i \(0.0640870\pi\)
\(24\) 0 0
\(25\) −3.54237 −0.708475
\(26\) 0 0
\(27\) 4.94937 0.952507
\(28\) 0 0
\(29\) −2.82165 −0.523967 −0.261984 0.965072i \(-0.584377\pi\)
−0.261984 + 0.965072i \(0.584377\pi\)
\(30\) 0 0
\(31\) 0.543253 0.0975711 0.0487855 0.998809i \(-0.484465\pi\)
0.0487855 + 0.998809i \(0.484465\pi\)
\(32\) 0 0
\(33\) −0.983398 −0.171188
\(34\) 0 0
\(35\) 1.20732 0.204075
\(36\) 0 0
\(37\) −0.252569 −0.0415221 −0.0207611 0.999784i \(-0.506609\pi\)
−0.0207611 + 0.999784i \(0.506609\pi\)
\(38\) 0 0
\(39\) 0.983398 0.157470
\(40\) 0 0
\(41\) 0.665720 0.103968 0.0519840 0.998648i \(-0.483446\pi\)
0.0519840 + 0.998648i \(0.483446\pi\)
\(42\) 0 0
\(43\) −0.327119 −0.0498852 −0.0249426 0.999689i \(-0.507940\pi\)
−0.0249426 + 0.999689i \(0.507940\pi\)
\(44\) 0 0
\(45\) 2.45440 0.365880
\(46\) 0 0
\(47\) 9.39792 1.37083 0.685413 0.728154i \(-0.259621\pi\)
0.685413 + 0.728154i \(0.259621\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.05332 −0.427550
\(52\) 0 0
\(53\) 8.35464 1.14760 0.573799 0.818996i \(-0.305469\pi\)
0.573799 + 0.818996i \(0.305469\pi\)
\(54\) 0 0
\(55\) −1.20732 −0.162795
\(56\) 0 0
\(57\) 6.03749 0.799685
\(58\) 0 0
\(59\) 8.49766 1.10630 0.553150 0.833081i \(-0.313426\pi\)
0.553150 + 0.833081i \(0.313426\pi\)
\(60\) 0 0
\(61\) −4.81738 −0.616802 −0.308401 0.951256i \(-0.599794\pi\)
−0.308401 + 0.951256i \(0.599794\pi\)
\(62\) 0 0
\(63\) 2.03293 0.256125
\(64\) 0 0
\(65\) 1.20732 0.149750
\(66\) 0 0
\(67\) −13.9821 −1.70819 −0.854095 0.520117i \(-0.825888\pi\)
−0.854095 + 0.520117i \(0.825888\pi\)
\(68\) 0 0
\(69\) −9.24189 −1.11259
\(70\) 0 0
\(71\) −9.69998 −1.15118 −0.575588 0.817740i \(-0.695227\pi\)
−0.575588 + 0.817740i \(0.695227\pi\)
\(72\) 0 0
\(73\) 14.8876 1.74246 0.871232 0.490872i \(-0.163322\pi\)
0.871232 + 0.490872i \(0.163322\pi\)
\(74\) 0 0
\(75\) 3.48356 0.402247
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 4.53081 0.509756 0.254878 0.966973i \(-0.417965\pi\)
0.254878 + 0.966973i \(0.417965\pi\)
\(80\) 0 0
\(81\) 1.23159 0.136843
\(82\) 0 0
\(83\) −9.44676 −1.03692 −0.518458 0.855103i \(-0.673494\pi\)
−0.518458 + 0.855103i \(0.673494\pi\)
\(84\) 0 0
\(85\) −3.74857 −0.406589
\(86\) 0 0
\(87\) 2.77480 0.297490
\(88\) 0 0
\(89\) −3.56230 −0.377603 −0.188801 0.982015i \(-0.560460\pi\)
−0.188801 + 0.982015i \(0.560460\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −0.534234 −0.0553974
\(94\) 0 0
\(95\) 7.41225 0.760481
\(96\) 0 0
\(97\) 15.7191 1.59603 0.798015 0.602637i \(-0.205883\pi\)
0.798015 + 0.602637i \(0.205883\pi\)
\(98\) 0 0
\(99\) −2.03293 −0.204317
\(100\) 0 0
\(101\) −14.8431 −1.47694 −0.738470 0.674286i \(-0.764451\pi\)
−0.738470 + 0.674286i \(0.764451\pi\)
\(102\) 0 0
\(103\) −8.48994 −0.836538 −0.418269 0.908323i \(-0.637363\pi\)
−0.418269 + 0.908323i \(0.637363\pi\)
\(104\) 0 0
\(105\) −1.18728 −0.115866
\(106\) 0 0
\(107\) 6.85572 0.662768 0.331384 0.943496i \(-0.392485\pi\)
0.331384 + 0.943496i \(0.392485\pi\)
\(108\) 0 0
\(109\) −12.1174 −1.16064 −0.580320 0.814389i \(-0.697072\pi\)
−0.580320 + 0.814389i \(0.697072\pi\)
\(110\) 0 0
\(111\) 0.248376 0.0235748
\(112\) 0 0
\(113\) 12.0522 1.13377 0.566886 0.823796i \(-0.308148\pi\)
0.566886 + 0.823796i \(0.308148\pi\)
\(114\) 0 0
\(115\) −11.3463 −1.05805
\(116\) 0 0
\(117\) 2.03293 0.187944
\(118\) 0 0
\(119\) −3.10486 −0.284622
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −0.654667 −0.0590294
\(124\) 0 0
\(125\) 10.3134 0.922458
\(126\) 0 0
\(127\) −14.3558 −1.27387 −0.636936 0.770917i \(-0.719798\pi\)
−0.636936 + 0.770917i \(0.719798\pi\)
\(128\) 0 0
\(129\) 0.321689 0.0283231
\(130\) 0 0
\(131\) 6.34706 0.554545 0.277272 0.960791i \(-0.410570\pi\)
0.277272 + 0.960791i \(0.410570\pi\)
\(132\) 0 0
\(133\) 6.13942 0.532355
\(134\) 0 0
\(135\) −5.97548 −0.514288
\(136\) 0 0
\(137\) 11.3083 0.966131 0.483066 0.875584i \(-0.339523\pi\)
0.483066 + 0.875584i \(0.339523\pi\)
\(138\) 0 0
\(139\) 9.20021 0.780352 0.390176 0.920740i \(-0.372414\pi\)
0.390176 + 0.920740i \(0.372414\pi\)
\(140\) 0 0
\(141\) −9.24189 −0.778307
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 3.40664 0.282906
\(146\) 0 0
\(147\) −0.983398 −0.0811093
\(148\) 0 0
\(149\) 7.01224 0.574465 0.287232 0.957861i \(-0.407265\pi\)
0.287232 + 0.957861i \(0.407265\pi\)
\(150\) 0 0
\(151\) −15.2909 −1.24436 −0.622178 0.782876i \(-0.713752\pi\)
−0.622178 + 0.782876i \(0.713752\pi\)
\(152\) 0 0
\(153\) −6.31197 −0.510292
\(154\) 0 0
\(155\) −0.655881 −0.0526816
\(156\) 0 0
\(157\) 10.4837 0.836690 0.418345 0.908288i \(-0.362610\pi\)
0.418345 + 0.908288i \(0.362610\pi\)
\(158\) 0 0
\(159\) −8.21593 −0.651566
\(160\) 0 0
\(161\) −9.39792 −0.740660
\(162\) 0 0
\(163\) −4.19699 −0.328734 −0.164367 0.986399i \(-0.552558\pi\)
−0.164367 + 0.986399i \(0.552558\pi\)
\(164\) 0 0
\(165\) 1.18728 0.0924294
\(166\) 0 0
\(167\) −19.8468 −1.53579 −0.767896 0.640575i \(-0.778696\pi\)
−0.767896 + 0.640575i \(0.778696\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 12.4810 0.954446
\(172\) 0 0
\(173\) 8.42778 0.640752 0.320376 0.947290i \(-0.396191\pi\)
0.320376 + 0.947290i \(0.396191\pi\)
\(174\) 0 0
\(175\) 3.54237 0.267778
\(176\) 0 0
\(177\) −8.35658 −0.628119
\(178\) 0 0
\(179\) 3.90430 0.291821 0.145911 0.989298i \(-0.453389\pi\)
0.145911 + 0.989298i \(0.453389\pi\)
\(180\) 0 0
\(181\) −10.2429 −0.761347 −0.380674 0.924709i \(-0.624308\pi\)
−0.380674 + 0.924709i \(0.624308\pi\)
\(182\) 0 0
\(183\) 4.73740 0.350198
\(184\) 0 0
\(185\) 0.304932 0.0224191
\(186\) 0 0
\(187\) 3.10486 0.227050
\(188\) 0 0
\(189\) −4.94937 −0.360014
\(190\) 0 0
\(191\) 16.8254 1.21745 0.608723 0.793383i \(-0.291682\pi\)
0.608723 + 0.793383i \(0.291682\pi\)
\(192\) 0 0
\(193\) −24.8726 −1.79037 −0.895186 0.445693i \(-0.852957\pi\)
−0.895186 + 0.445693i \(0.852957\pi\)
\(194\) 0 0
\(195\) −1.18728 −0.0850227
\(196\) 0 0
\(197\) 2.51647 0.179291 0.0896456 0.995974i \(-0.471427\pi\)
0.0896456 + 0.995974i \(0.471427\pi\)
\(198\) 0 0
\(199\) −13.2409 −0.938624 −0.469312 0.883032i \(-0.655498\pi\)
−0.469312 + 0.883032i \(0.655498\pi\)
\(200\) 0 0
\(201\) 13.7500 0.969850
\(202\) 0 0
\(203\) 2.82165 0.198041
\(204\) 0 0
\(205\) −0.803738 −0.0561355
\(206\) 0 0
\(207\) −19.1053 −1.32791
\(208\) 0 0
\(209\) −6.13942 −0.424672
\(210\) 0 0
\(211\) −24.5369 −1.68919 −0.844595 0.535406i \(-0.820159\pi\)
−0.844595 + 0.535406i \(0.820159\pi\)
\(212\) 0 0
\(213\) 9.53894 0.653597
\(214\) 0 0
\(215\) 0.394938 0.0269346
\(216\) 0 0
\(217\) −0.543253 −0.0368784
\(218\) 0 0
\(219\) −14.6404 −0.989310
\(220\) 0 0
\(221\) −3.10486 −0.208856
\(222\) 0 0
\(223\) −4.25717 −0.285081 −0.142541 0.989789i \(-0.545527\pi\)
−0.142541 + 0.989789i \(0.545527\pi\)
\(224\) 0 0
\(225\) 7.20140 0.480093
\(226\) 0 0
\(227\) 11.9967 0.796246 0.398123 0.917332i \(-0.369662\pi\)
0.398123 + 0.917332i \(0.369662\pi\)
\(228\) 0 0
\(229\) 6.48496 0.428538 0.214269 0.976775i \(-0.431263\pi\)
0.214269 + 0.976775i \(0.431263\pi\)
\(230\) 0 0
\(231\) 0.983398 0.0647028
\(232\) 0 0
\(233\) −16.4755 −1.07934 −0.539672 0.841875i \(-0.681452\pi\)
−0.539672 + 0.841875i \(0.681452\pi\)
\(234\) 0 0
\(235\) −11.3463 −0.740151
\(236\) 0 0
\(237\) −4.45559 −0.289422
\(238\) 0 0
\(239\) −24.0623 −1.55646 −0.778232 0.627977i \(-0.783883\pi\)
−0.778232 + 0.627977i \(0.783883\pi\)
\(240\) 0 0
\(241\) −22.5115 −1.45009 −0.725046 0.688701i \(-0.758181\pi\)
−0.725046 + 0.688701i \(0.758181\pi\)
\(242\) 0 0
\(243\) −16.0593 −1.03020
\(244\) 0 0
\(245\) −1.20732 −0.0771329
\(246\) 0 0
\(247\) 6.13942 0.390642
\(248\) 0 0
\(249\) 9.28993 0.588725
\(250\) 0 0
\(251\) 14.3686 0.906936 0.453468 0.891273i \(-0.350187\pi\)
0.453468 + 0.891273i \(0.350187\pi\)
\(252\) 0 0
\(253\) 9.39792 0.590842
\(254\) 0 0
\(255\) 3.68633 0.230847
\(256\) 0 0
\(257\) −8.26987 −0.515860 −0.257930 0.966164i \(-0.583040\pi\)
−0.257930 + 0.966164i \(0.583040\pi\)
\(258\) 0 0
\(259\) 0.252569 0.0156939
\(260\) 0 0
\(261\) 5.73621 0.355063
\(262\) 0 0
\(263\) 11.7923 0.727145 0.363572 0.931566i \(-0.381557\pi\)
0.363572 + 0.931566i \(0.381557\pi\)
\(264\) 0 0
\(265\) −10.0867 −0.619623
\(266\) 0 0
\(267\) 3.50315 0.214390
\(268\) 0 0
\(269\) −29.4401 −1.79500 −0.897499 0.441017i \(-0.854618\pi\)
−0.897499 + 0.441017i \(0.854618\pi\)
\(270\) 0 0
\(271\) 31.6383 1.92189 0.960946 0.276737i \(-0.0892531\pi\)
0.960946 + 0.276737i \(0.0892531\pi\)
\(272\) 0 0
\(273\) −0.983398 −0.0595179
\(274\) 0 0
\(275\) −3.54237 −0.213613
\(276\) 0 0
\(277\) −24.4158 −1.46700 −0.733501 0.679688i \(-0.762115\pi\)
−0.733501 + 0.679688i \(0.762115\pi\)
\(278\) 0 0
\(279\) −1.10439 −0.0661184
\(280\) 0 0
\(281\) −15.5560 −0.927990 −0.463995 0.885838i \(-0.653585\pi\)
−0.463995 + 0.885838i \(0.653585\pi\)
\(282\) 0 0
\(283\) −1.37089 −0.0814909 −0.0407454 0.999170i \(-0.512973\pi\)
−0.0407454 + 0.999170i \(0.512973\pi\)
\(284\) 0 0
\(285\) −7.28919 −0.431774
\(286\) 0 0
\(287\) −0.665720 −0.0392962
\(288\) 0 0
\(289\) −7.35982 −0.432930
\(290\) 0 0
\(291\) −15.4581 −0.906170
\(292\) 0 0
\(293\) 4.61245 0.269462 0.134731 0.990882i \(-0.456983\pi\)
0.134731 + 0.990882i \(0.456983\pi\)
\(294\) 0 0
\(295\) −10.2594 −0.597326
\(296\) 0 0
\(297\) 4.94937 0.287192
\(298\) 0 0
\(299\) −9.39792 −0.543495
\(300\) 0 0
\(301\) 0.327119 0.0188549
\(302\) 0 0
\(303\) 14.5966 0.838555
\(304\) 0 0
\(305\) 5.81612 0.333030
\(306\) 0 0
\(307\) −10.8025 −0.616534 −0.308267 0.951300i \(-0.599749\pi\)
−0.308267 + 0.951300i \(0.599749\pi\)
\(308\) 0 0
\(309\) 8.34898 0.474957
\(310\) 0 0
\(311\) −2.10376 −0.119293 −0.0596466 0.998220i \(-0.518997\pi\)
−0.0596466 + 0.998220i \(0.518997\pi\)
\(312\) 0 0
\(313\) 30.8507 1.74379 0.871893 0.489696i \(-0.162892\pi\)
0.871893 + 0.489696i \(0.162892\pi\)
\(314\) 0 0
\(315\) −2.45440 −0.138290
\(316\) 0 0
\(317\) −0.515547 −0.0289560 −0.0144780 0.999895i \(-0.504609\pi\)
−0.0144780 + 0.999895i \(0.504609\pi\)
\(318\) 0 0
\(319\) −2.82165 −0.157982
\(320\) 0 0
\(321\) −6.74190 −0.376296
\(322\) 0 0
\(323\) −19.0621 −1.06064
\(324\) 0 0
\(325\) 3.54237 0.196496
\(326\) 0 0
\(327\) 11.9163 0.658970
\(328\) 0 0
\(329\) −9.39792 −0.518124
\(330\) 0 0
\(331\) −27.5435 −1.51393 −0.756963 0.653458i \(-0.773318\pi\)
−0.756963 + 0.653458i \(0.773318\pi\)
\(332\) 0 0
\(333\) 0.513455 0.0281372
\(334\) 0 0
\(335\) 16.8809 0.922304
\(336\) 0 0
\(337\) 29.4616 1.60487 0.802437 0.596737i \(-0.203537\pi\)
0.802437 + 0.596737i \(0.203537\pi\)
\(338\) 0 0
\(339\) −11.8521 −0.643716
\(340\) 0 0
\(341\) 0.543253 0.0294188
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 11.1579 0.600723
\(346\) 0 0
\(347\) −10.1374 −0.544205 −0.272102 0.962268i \(-0.587719\pi\)
−0.272102 + 0.962268i \(0.587719\pi\)
\(348\) 0 0
\(349\) −24.7739 −1.32612 −0.663058 0.748568i \(-0.730742\pi\)
−0.663058 + 0.748568i \(0.730742\pi\)
\(350\) 0 0
\(351\) −4.94937 −0.264178
\(352\) 0 0
\(353\) 28.7554 1.53050 0.765248 0.643736i \(-0.222616\pi\)
0.765248 + 0.643736i \(0.222616\pi\)
\(354\) 0 0
\(355\) 11.7110 0.621555
\(356\) 0 0
\(357\) 3.05332 0.161599
\(358\) 0 0
\(359\) −27.2941 −1.44053 −0.720265 0.693699i \(-0.755980\pi\)
−0.720265 + 0.693699i \(0.755980\pi\)
\(360\) 0 0
\(361\) 18.6925 0.983814
\(362\) 0 0
\(363\) −0.983398 −0.0516150
\(364\) 0 0
\(365\) −17.9741 −0.940810
\(366\) 0 0
\(367\) 18.1081 0.945234 0.472617 0.881268i \(-0.343309\pi\)
0.472617 + 0.881268i \(0.343309\pi\)
\(368\) 0 0
\(369\) −1.35336 −0.0704532
\(370\) 0 0
\(371\) −8.35464 −0.433751
\(372\) 0 0
\(373\) 35.1752 1.82130 0.910652 0.413174i \(-0.135580\pi\)
0.910652 + 0.413174i \(0.135580\pi\)
\(374\) 0 0
\(375\) −10.1422 −0.523739
\(376\) 0 0
\(377\) 2.82165 0.145322
\(378\) 0 0
\(379\) −28.6829 −1.47334 −0.736670 0.676252i \(-0.763603\pi\)
−0.736670 + 0.676252i \(0.763603\pi\)
\(380\) 0 0
\(381\) 14.1175 0.723260
\(382\) 0 0
\(383\) −12.4746 −0.637421 −0.318710 0.947852i \(-0.603250\pi\)
−0.318710 + 0.947852i \(0.603250\pi\)
\(384\) 0 0
\(385\) 1.20732 0.0615308
\(386\) 0 0
\(387\) 0.665011 0.0338044
\(388\) 0 0
\(389\) 33.5399 1.70054 0.850270 0.526348i \(-0.176439\pi\)
0.850270 + 0.526348i \(0.176439\pi\)
\(390\) 0 0
\(391\) 29.1793 1.47566
\(392\) 0 0
\(393\) −6.24168 −0.314851
\(394\) 0 0
\(395\) −5.47015 −0.275233
\(396\) 0 0
\(397\) −6.10662 −0.306482 −0.153241 0.988189i \(-0.548971\pi\)
−0.153241 + 0.988189i \(0.548971\pi\)
\(398\) 0 0
\(399\) −6.03749 −0.302253
\(400\) 0 0
\(401\) −5.60807 −0.280054 −0.140027 0.990148i \(-0.544719\pi\)
−0.140027 + 0.990148i \(0.544719\pi\)
\(402\) 0 0
\(403\) −0.543253 −0.0270614
\(404\) 0 0
\(405\) −1.48692 −0.0738858
\(406\) 0 0
\(407\) −0.252569 −0.0125194
\(408\) 0 0
\(409\) −25.2843 −1.25023 −0.625115 0.780533i \(-0.714948\pi\)
−0.625115 + 0.780533i \(0.714948\pi\)
\(410\) 0 0
\(411\) −11.1205 −0.548535
\(412\) 0 0
\(413\) −8.49766 −0.418142
\(414\) 0 0
\(415\) 11.4053 0.559863
\(416\) 0 0
\(417\) −9.04747 −0.443056
\(418\) 0 0
\(419\) −14.7084 −0.718553 −0.359276 0.933231i \(-0.616976\pi\)
−0.359276 + 0.933231i \(0.616976\pi\)
\(420\) 0 0
\(421\) −2.64194 −0.128760 −0.0643801 0.997925i \(-0.520507\pi\)
−0.0643801 + 0.997925i \(0.520507\pi\)
\(422\) 0 0
\(423\) −19.1053 −0.928931
\(424\) 0 0
\(425\) −10.9986 −0.533510
\(426\) 0 0
\(427\) 4.81738 0.233129
\(428\) 0 0
\(429\) 0.983398 0.0474789
\(430\) 0 0
\(431\) 17.4640 0.841213 0.420606 0.907243i \(-0.361817\pi\)
0.420606 + 0.907243i \(0.361817\pi\)
\(432\) 0 0
\(433\) 3.23544 0.155486 0.0777428 0.996973i \(-0.475229\pi\)
0.0777428 + 0.996973i \(0.475229\pi\)
\(434\) 0 0
\(435\) −3.35008 −0.160624
\(436\) 0 0
\(437\) −57.6977 −2.76006
\(438\) 0 0
\(439\) −20.5487 −0.980738 −0.490369 0.871515i \(-0.663138\pi\)
−0.490369 + 0.871515i \(0.663138\pi\)
\(440\) 0 0
\(441\) −2.03293 −0.0968061
\(442\) 0 0
\(443\) −9.59221 −0.455739 −0.227870 0.973692i \(-0.573176\pi\)
−0.227870 + 0.973692i \(0.573176\pi\)
\(444\) 0 0
\(445\) 4.30084 0.203879
\(446\) 0 0
\(447\) −6.89582 −0.326161
\(448\) 0 0
\(449\) −21.4237 −1.01105 −0.505524 0.862812i \(-0.668701\pi\)
−0.505524 + 0.862812i \(0.668701\pi\)
\(450\) 0 0
\(451\) 0.665720 0.0313475
\(452\) 0 0
\(453\) 15.0370 0.706502
\(454\) 0 0
\(455\) −1.20732 −0.0566001
\(456\) 0 0
\(457\) −8.89787 −0.416225 −0.208112 0.978105i \(-0.566732\pi\)
−0.208112 + 0.978105i \(0.566732\pi\)
\(458\) 0 0
\(459\) 15.3671 0.717276
\(460\) 0 0
\(461\) 27.3690 1.27470 0.637352 0.770573i \(-0.280030\pi\)
0.637352 + 0.770573i \(0.280030\pi\)
\(462\) 0 0
\(463\) −39.9067 −1.85462 −0.927311 0.374293i \(-0.877886\pi\)
−0.927311 + 0.374293i \(0.877886\pi\)
\(464\) 0 0
\(465\) 0.644992 0.0299108
\(466\) 0 0
\(467\) −32.7796 −1.51686 −0.758430 0.651755i \(-0.774033\pi\)
−0.758430 + 0.651755i \(0.774033\pi\)
\(468\) 0 0
\(469\) 13.9821 0.645635
\(470\) 0 0
\(471\) −10.3096 −0.475043
\(472\) 0 0
\(473\) −0.327119 −0.0150410
\(474\) 0 0
\(475\) 21.7481 0.997872
\(476\) 0 0
\(477\) −16.9844 −0.777661
\(478\) 0 0
\(479\) 13.1936 0.602831 0.301416 0.953493i \(-0.402541\pi\)
0.301416 + 0.953493i \(0.402541\pi\)
\(480\) 0 0
\(481\) 0.252569 0.0115162
\(482\) 0 0
\(483\) 9.24189 0.420520
\(484\) 0 0
\(485\) −18.9780 −0.861746
\(486\) 0 0
\(487\) −13.3460 −0.604766 −0.302383 0.953187i \(-0.597782\pi\)
−0.302383 + 0.953187i \(0.597782\pi\)
\(488\) 0 0
\(489\) 4.12731 0.186644
\(490\) 0 0
\(491\) −25.8482 −1.16651 −0.583257 0.812288i \(-0.698222\pi\)
−0.583257 + 0.812288i \(0.698222\pi\)
\(492\) 0 0
\(493\) −8.76084 −0.394568
\(494\) 0 0
\(495\) 2.45440 0.110317
\(496\) 0 0
\(497\) 9.69998 0.435103
\(498\) 0 0
\(499\) −13.5125 −0.604901 −0.302451 0.953165i \(-0.597805\pi\)
−0.302451 + 0.953165i \(0.597805\pi\)
\(500\) 0 0
\(501\) 19.5173 0.871969
\(502\) 0 0
\(503\) −5.23981 −0.233632 −0.116816 0.993154i \(-0.537269\pi\)
−0.116816 + 0.993154i \(0.537269\pi\)
\(504\) 0 0
\(505\) 17.9203 0.797445
\(506\) 0 0
\(507\) −0.983398 −0.0436742
\(508\) 0 0
\(509\) −9.99253 −0.442911 −0.221456 0.975170i \(-0.571081\pi\)
−0.221456 + 0.975170i \(0.571081\pi\)
\(510\) 0 0
\(511\) −14.8876 −0.658589
\(512\) 0 0
\(513\) −30.3863 −1.34159
\(514\) 0 0
\(515\) 10.2501 0.451673
\(516\) 0 0
\(517\) 9.39792 0.413320
\(518\) 0 0
\(519\) −8.28786 −0.363797
\(520\) 0 0
\(521\) 16.7804 0.735161 0.367580 0.929992i \(-0.380186\pi\)
0.367580 + 0.929992i \(0.380186\pi\)
\(522\) 0 0
\(523\) −8.57181 −0.374819 −0.187409 0.982282i \(-0.560009\pi\)
−0.187409 + 0.982282i \(0.560009\pi\)
\(524\) 0 0
\(525\) −3.48356 −0.152035
\(526\) 0 0
\(527\) 1.68673 0.0734750
\(528\) 0 0
\(529\) 65.3208 2.84004
\(530\) 0 0
\(531\) −17.2751 −0.749677
\(532\) 0 0
\(533\) −0.665720 −0.0288355
\(534\) 0 0
\(535\) −8.27706 −0.357848
\(536\) 0 0
\(537\) −3.83948 −0.165686
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 44.0296 1.89298 0.946491 0.322730i \(-0.104601\pi\)
0.946491 + 0.322730i \(0.104601\pi\)
\(542\) 0 0
\(543\) 10.0728 0.432266
\(544\) 0 0
\(545\) 14.6296 0.626665
\(546\) 0 0
\(547\) 14.6835 0.627820 0.313910 0.949453i \(-0.398361\pi\)
0.313910 + 0.949453i \(0.398361\pi\)
\(548\) 0 0
\(549\) 9.79338 0.417971
\(550\) 0 0
\(551\) 17.3233 0.737997
\(552\) 0 0
\(553\) −4.53081 −0.192670
\(554\) 0 0
\(555\) −0.299870 −0.0127288
\(556\) 0 0
\(557\) 11.6989 0.495698 0.247849 0.968799i \(-0.420276\pi\)
0.247849 + 0.968799i \(0.420276\pi\)
\(558\) 0 0
\(559\) 0.327119 0.0138357
\(560\) 0 0
\(561\) −3.05332 −0.128911
\(562\) 0 0
\(563\) −32.0608 −1.35120 −0.675600 0.737269i \(-0.736115\pi\)
−0.675600 + 0.737269i \(0.736115\pi\)
\(564\) 0 0
\(565\) −14.5508 −0.612158
\(566\) 0 0
\(567\) −1.23159 −0.0517218
\(568\) 0 0
\(569\) −21.0792 −0.883688 −0.441844 0.897092i \(-0.645675\pi\)
−0.441844 + 0.897092i \(0.645675\pi\)
\(570\) 0 0
\(571\) −35.6616 −1.49239 −0.746195 0.665728i \(-0.768121\pi\)
−0.746195 + 0.665728i \(0.768121\pi\)
\(572\) 0 0
\(573\) −16.5461 −0.691223
\(574\) 0 0
\(575\) −33.2909 −1.38833
\(576\) 0 0
\(577\) −33.4537 −1.39270 −0.696349 0.717703i \(-0.745193\pi\)
−0.696349 + 0.717703i \(0.745193\pi\)
\(578\) 0 0
\(579\) 24.4597 1.01651
\(580\) 0 0
\(581\) 9.44676 0.391918
\(582\) 0 0
\(583\) 8.35464 0.346014
\(584\) 0 0
\(585\) −2.45440 −0.101477
\(586\) 0 0
\(587\) −35.7131 −1.47404 −0.737019 0.675872i \(-0.763767\pi\)
−0.737019 + 0.675872i \(0.763767\pi\)
\(588\) 0 0
\(589\) −3.33526 −0.137427
\(590\) 0 0
\(591\) −2.47469 −0.101795
\(592\) 0 0
\(593\) 43.0926 1.76960 0.884801 0.465968i \(-0.154294\pi\)
0.884801 + 0.465968i \(0.154294\pi\)
\(594\) 0 0
\(595\) 3.74857 0.153676
\(596\) 0 0
\(597\) 13.0211 0.532918
\(598\) 0 0
\(599\) −16.1346 −0.659242 −0.329621 0.944113i \(-0.606921\pi\)
−0.329621 + 0.944113i \(0.606921\pi\)
\(600\) 0 0
\(601\) −8.22210 −0.335386 −0.167693 0.985839i \(-0.553632\pi\)
−0.167693 + 0.985839i \(0.553632\pi\)
\(602\) 0 0
\(603\) 28.4247 1.15754
\(604\) 0 0
\(605\) −1.20732 −0.0490846
\(606\) 0 0
\(607\) 29.3796 1.19248 0.596240 0.802806i \(-0.296660\pi\)
0.596240 + 0.802806i \(0.296660\pi\)
\(608\) 0 0
\(609\) −2.77480 −0.112441
\(610\) 0 0
\(611\) −9.39792 −0.380199
\(612\) 0 0
\(613\) 18.7971 0.759209 0.379605 0.925149i \(-0.376060\pi\)
0.379605 + 0.925149i \(0.376060\pi\)
\(614\) 0 0
\(615\) 0.790394 0.0318718
\(616\) 0 0
\(617\) 1.83888 0.0740307 0.0370153 0.999315i \(-0.488215\pi\)
0.0370153 + 0.999315i \(0.488215\pi\)
\(618\) 0 0
\(619\) −38.9980 −1.56746 −0.783731 0.621100i \(-0.786686\pi\)
−0.783731 + 0.621100i \(0.786686\pi\)
\(620\) 0 0
\(621\) 46.5138 1.86653
\(622\) 0 0
\(623\) 3.56230 0.142720
\(624\) 0 0
\(625\) 5.26029 0.210412
\(626\) 0 0
\(627\) 6.03749 0.241114
\(628\) 0 0
\(629\) −0.784193 −0.0312678
\(630\) 0 0
\(631\) 32.9847 1.31310 0.656550 0.754282i \(-0.272015\pi\)
0.656550 + 0.754282i \(0.272015\pi\)
\(632\) 0 0
\(633\) 24.1295 0.959063
\(634\) 0 0
\(635\) 17.3321 0.687803
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 19.7194 0.780086
\(640\) 0 0
\(641\) −38.5731 −1.52354 −0.761772 0.647845i \(-0.775671\pi\)
−0.761772 + 0.647845i \(0.775671\pi\)
\(642\) 0 0
\(643\) 39.4676 1.55645 0.778225 0.627985i \(-0.216120\pi\)
0.778225 + 0.627985i \(0.216120\pi\)
\(644\) 0 0
\(645\) −0.388381 −0.0152925
\(646\) 0 0
\(647\) −26.7325 −1.05096 −0.525482 0.850805i \(-0.676115\pi\)
−0.525482 + 0.850805i \(0.676115\pi\)
\(648\) 0 0
\(649\) 8.49766 0.333562
\(650\) 0 0
\(651\) 0.534234 0.0209383
\(652\) 0 0
\(653\) −41.8212 −1.63659 −0.818295 0.574799i \(-0.805080\pi\)
−0.818295 + 0.574799i \(0.805080\pi\)
\(654\) 0 0
\(655\) −7.66294 −0.299416
\(656\) 0 0
\(657\) −30.2655 −1.18077
\(658\) 0 0
\(659\) 5.87697 0.228934 0.114467 0.993427i \(-0.463484\pi\)
0.114467 + 0.993427i \(0.463484\pi\)
\(660\) 0 0
\(661\) 22.3236 0.868286 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(662\) 0 0
\(663\) 3.05332 0.118581
\(664\) 0 0
\(665\) −7.41225 −0.287435
\(666\) 0 0
\(667\) −26.5176 −1.02677
\(668\) 0 0
\(669\) 4.18649 0.161859
\(670\) 0 0
\(671\) −4.81738 −0.185973
\(672\) 0 0
\(673\) −21.3322 −0.822296 −0.411148 0.911569i \(-0.634872\pi\)
−0.411148 + 0.911569i \(0.634872\pi\)
\(674\) 0 0
\(675\) −17.5325 −0.674827
\(676\) 0 0
\(677\) −8.83707 −0.339636 −0.169818 0.985475i \(-0.554318\pi\)
−0.169818 + 0.985475i \(0.554318\pi\)
\(678\) 0 0
\(679\) −15.7191 −0.603243
\(680\) 0 0
\(681\) −11.7975 −0.452081
\(682\) 0 0
\(683\) −15.2393 −0.583116 −0.291558 0.956553i \(-0.594174\pi\)
−0.291558 + 0.956553i \(0.594174\pi\)
\(684\) 0 0
\(685\) −13.6527 −0.521644
\(686\) 0 0
\(687\) −6.37729 −0.243309
\(688\) 0 0
\(689\) −8.35464 −0.318286
\(690\) 0 0
\(691\) 13.9709 0.531479 0.265739 0.964045i \(-0.414384\pi\)
0.265739 + 0.964045i \(0.414384\pi\)
\(692\) 0 0
\(693\) 2.03293 0.0772246
\(694\) 0 0
\(695\) −11.1076 −0.421336
\(696\) 0 0
\(697\) 2.06697 0.0782921
\(698\) 0 0
\(699\) 16.2019 0.612814
\(700\) 0 0
\(701\) 50.6077 1.91143 0.955714 0.294297i \(-0.0950854\pi\)
0.955714 + 0.294297i \(0.0950854\pi\)
\(702\) 0 0
\(703\) 1.55063 0.0584831
\(704\) 0 0
\(705\) 11.1579 0.420232
\(706\) 0 0
\(707\) 14.8431 0.558231
\(708\) 0 0
\(709\) 15.5674 0.584645 0.292322 0.956320i \(-0.405572\pi\)
0.292322 + 0.956320i \(0.405572\pi\)
\(710\) 0 0
\(711\) −9.21082 −0.345433
\(712\) 0 0
\(713\) 5.10544 0.191200
\(714\) 0 0
\(715\) 1.20732 0.0451513
\(716\) 0 0
\(717\) 23.6628 0.883705
\(718\) 0 0
\(719\) 17.9502 0.669429 0.334715 0.942320i \(-0.391360\pi\)
0.334715 + 0.942320i \(0.391360\pi\)
\(720\) 0 0
\(721\) 8.48994 0.316182
\(722\) 0 0
\(723\) 22.1377 0.823311
\(724\) 0 0
\(725\) 9.99534 0.371218
\(726\) 0 0
\(727\) −32.7618 −1.21507 −0.607534 0.794293i \(-0.707841\pi\)
−0.607534 + 0.794293i \(0.707841\pi\)
\(728\) 0 0
\(729\) 12.0979 0.448069
\(730\) 0 0
\(731\) −1.01566 −0.0375656
\(732\) 0 0
\(733\) 23.1389 0.854655 0.427327 0.904097i \(-0.359455\pi\)
0.427327 + 0.904097i \(0.359455\pi\)
\(734\) 0 0
\(735\) 1.18728 0.0437934
\(736\) 0 0
\(737\) −13.9821 −0.515039
\(738\) 0 0
\(739\) −42.5508 −1.56526 −0.782628 0.622490i \(-0.786121\pi\)
−0.782628 + 0.622490i \(0.786121\pi\)
\(740\) 0 0
\(741\) −6.03749 −0.221793
\(742\) 0 0
\(743\) −5.48758 −0.201320 −0.100660 0.994921i \(-0.532095\pi\)
−0.100660 + 0.994921i \(0.532095\pi\)
\(744\) 0 0
\(745\) −8.46602 −0.310171
\(746\) 0 0
\(747\) 19.2046 0.702660
\(748\) 0 0
\(749\) −6.85572 −0.250503
\(750\) 0 0
\(751\) −4.99964 −0.182440 −0.0912198 0.995831i \(-0.529077\pi\)
−0.0912198 + 0.995831i \(0.529077\pi\)
\(752\) 0 0
\(753\) −14.1300 −0.514926
\(754\) 0 0
\(755\) 18.4610 0.671866
\(756\) 0 0
\(757\) −0.999819 −0.0363391 −0.0181695 0.999835i \(-0.505784\pi\)
−0.0181695 + 0.999835i \(0.505784\pi\)
\(758\) 0 0
\(759\) −9.24189 −0.335459
\(760\) 0 0
\(761\) 26.7254 0.968794 0.484397 0.874848i \(-0.339039\pi\)
0.484397 + 0.874848i \(0.339039\pi\)
\(762\) 0 0
\(763\) 12.1174 0.438680
\(764\) 0 0
\(765\) 7.62058 0.275523
\(766\) 0 0
\(767\) −8.49766 −0.306833
\(768\) 0 0
\(769\) 3.38079 0.121915 0.0609573 0.998140i \(-0.480585\pi\)
0.0609573 + 0.998140i \(0.480585\pi\)
\(770\) 0 0
\(771\) 8.13257 0.292887
\(772\) 0 0
\(773\) −36.7123 −1.32045 −0.660224 0.751069i \(-0.729539\pi\)
−0.660224 + 0.751069i \(0.729539\pi\)
\(774\) 0 0
\(775\) −1.92440 −0.0691267
\(776\) 0 0
\(777\) −0.248376 −0.00891044
\(778\) 0 0
\(779\) −4.08713 −0.146437
\(780\) 0 0
\(781\) −9.69998 −0.347093
\(782\) 0 0
\(783\) −13.9654 −0.499082
\(784\) 0 0
\(785\) −12.6572 −0.451754
\(786\) 0 0
\(787\) −40.2828 −1.43593 −0.717964 0.696080i \(-0.754926\pi\)
−0.717964 + 0.696080i \(0.754926\pi\)
\(788\) 0 0
\(789\) −11.5965 −0.412847
\(790\) 0 0
\(791\) −12.0522 −0.428526
\(792\) 0 0
\(793\) 4.81738 0.171070
\(794\) 0 0
\(795\) 9.91927 0.351800
\(796\) 0 0
\(797\) 1.20483 0.0426773 0.0213387 0.999772i \(-0.493207\pi\)
0.0213387 + 0.999772i \(0.493207\pi\)
\(798\) 0 0
\(799\) 29.1793 1.03229
\(800\) 0 0
\(801\) 7.24190 0.255880
\(802\) 0 0
\(803\) 14.8876 0.525373
\(804\) 0 0
\(805\) 11.3463 0.399905
\(806\) 0 0
\(807\) 28.9514 1.01914
\(808\) 0 0
\(809\) −21.4406 −0.753811 −0.376906 0.926252i \(-0.623012\pi\)
−0.376906 + 0.926252i \(0.623012\pi\)
\(810\) 0 0
\(811\) 18.4290 0.647130 0.323565 0.946206i \(-0.395119\pi\)
0.323565 + 0.946206i \(0.395119\pi\)
\(812\) 0 0
\(813\) −31.1131 −1.09118
\(814\) 0 0
\(815\) 5.06712 0.177493
\(816\) 0 0
\(817\) 2.00832 0.0702623
\(818\) 0 0
\(819\) −2.03293 −0.0710363
\(820\) 0 0
\(821\) −43.9270 −1.53306 −0.766531 0.642208i \(-0.778019\pi\)
−0.766531 + 0.642208i \(0.778019\pi\)
\(822\) 0 0
\(823\) 28.0795 0.978791 0.489396 0.872062i \(-0.337217\pi\)
0.489396 + 0.872062i \(0.337217\pi\)
\(824\) 0 0
\(825\) 3.48356 0.121282
\(826\) 0 0
\(827\) 2.92863 0.101838 0.0509192 0.998703i \(-0.483785\pi\)
0.0509192 + 0.998703i \(0.483785\pi\)
\(828\) 0 0
\(829\) −34.8137 −1.20913 −0.604565 0.796556i \(-0.706653\pi\)
−0.604565 + 0.796556i \(0.706653\pi\)
\(830\) 0 0
\(831\) 24.0104 0.832913
\(832\) 0 0
\(833\) 3.10486 0.107577
\(834\) 0 0
\(835\) 23.9615 0.829221
\(836\) 0 0
\(837\) 2.68876 0.0929371
\(838\) 0 0
\(839\) −37.5674 −1.29697 −0.648486 0.761227i \(-0.724597\pi\)
−0.648486 + 0.761227i \(0.724597\pi\)
\(840\) 0 0
\(841\) −21.0383 −0.725458
\(842\) 0 0
\(843\) 15.2977 0.526880
\(844\) 0 0
\(845\) −1.20732 −0.0415331
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 1.34813 0.0462677
\(850\) 0 0
\(851\) −2.37362 −0.0813668
\(852\) 0 0
\(853\) 48.4415 1.65861 0.829303 0.558800i \(-0.188738\pi\)
0.829303 + 0.558800i \(0.188738\pi\)
\(854\) 0 0
\(855\) −15.0686 −0.515335
\(856\) 0 0
\(857\) −1.95212 −0.0666831 −0.0333416 0.999444i \(-0.510615\pi\)
−0.0333416 + 0.999444i \(0.510615\pi\)
\(858\) 0 0
\(859\) −49.5046 −1.68908 −0.844538 0.535495i \(-0.820125\pi\)
−0.844538 + 0.535495i \(0.820125\pi\)
\(860\) 0 0
\(861\) 0.654667 0.0223110
\(862\) 0 0
\(863\) 41.5788 1.41536 0.707679 0.706534i \(-0.249742\pi\)
0.707679 + 0.706534i \(0.249742\pi\)
\(864\) 0 0
\(865\) −10.1750 −0.345962
\(866\) 0 0
\(867\) 7.23763 0.245803
\(868\) 0 0
\(869\) 4.53081 0.153697
\(870\) 0 0
\(871\) 13.9821 0.473767
\(872\) 0 0
\(873\) −31.9558 −1.08154
\(874\) 0 0
\(875\) −10.3134 −0.348656
\(876\) 0 0
\(877\) −25.2456 −0.852483 −0.426241 0.904609i \(-0.640163\pi\)
−0.426241 + 0.904609i \(0.640163\pi\)
\(878\) 0 0
\(879\) −4.53588 −0.152991
\(880\) 0 0
\(881\) −43.3232 −1.45960 −0.729798 0.683662i \(-0.760386\pi\)
−0.729798 + 0.683662i \(0.760386\pi\)
\(882\) 0 0
\(883\) 13.0166 0.438044 0.219022 0.975720i \(-0.429713\pi\)
0.219022 + 0.975720i \(0.429713\pi\)
\(884\) 0 0
\(885\) 10.0891 0.339140
\(886\) 0 0
\(887\) 32.2842 1.08400 0.541998 0.840380i \(-0.317668\pi\)
0.541998 + 0.840380i \(0.317668\pi\)
\(888\) 0 0
\(889\) 14.3558 0.481478
\(890\) 0 0
\(891\) 1.23159 0.0412597
\(892\) 0 0
\(893\) −57.6977 −1.93078
\(894\) 0 0
\(895\) −4.71375 −0.157563
\(896\) 0 0
\(897\) 9.24189 0.308578
\(898\) 0 0
\(899\) −1.53287 −0.0511240
\(900\) 0 0
\(901\) 25.9400 0.864187
\(902\) 0 0
\(903\) −0.321689 −0.0107051
\(904\) 0 0
\(905\) 12.3665 0.411075
\(906\) 0 0
\(907\) 18.3936 0.610749 0.305375 0.952232i \(-0.401218\pi\)
0.305375 + 0.952232i \(0.401218\pi\)
\(908\) 0 0
\(909\) 30.1749 1.00084
\(910\) 0 0
\(911\) 42.5622 1.41015 0.705074 0.709134i \(-0.250914\pi\)
0.705074 + 0.709134i \(0.250914\pi\)
\(912\) 0 0
\(913\) −9.44676 −0.312642
\(914\) 0 0
\(915\) −5.71956 −0.189083
\(916\) 0 0
\(917\) −6.34706 −0.209598
\(918\) 0 0
\(919\) 41.0242 1.35326 0.676631 0.736322i \(-0.263439\pi\)
0.676631 + 0.736322i \(0.263439\pi\)
\(920\) 0 0
\(921\) 10.6232 0.350046
\(922\) 0 0
\(923\) 9.69998 0.319279
\(924\) 0 0
\(925\) 0.894695 0.0294174
\(926\) 0 0
\(927\) 17.2594 0.566874
\(928\) 0 0
\(929\) 9.64229 0.316353 0.158177 0.987411i \(-0.449438\pi\)
0.158177 + 0.987411i \(0.449438\pi\)
\(930\) 0 0
\(931\) −6.13942 −0.201211
\(932\) 0 0
\(933\) 2.06883 0.0677305
\(934\) 0 0
\(935\) −3.74857 −0.122591
\(936\) 0 0
\(937\) 56.0178 1.83002 0.915012 0.403427i \(-0.132181\pi\)
0.915012 + 0.403427i \(0.132181\pi\)
\(938\) 0 0
\(939\) −30.3385 −0.990061
\(940\) 0 0
\(941\) −13.8445 −0.451317 −0.225658 0.974207i \(-0.572453\pi\)
−0.225658 + 0.974207i \(0.572453\pi\)
\(942\) 0 0
\(943\) 6.25638 0.203736
\(944\) 0 0
\(945\) 5.97548 0.194382
\(946\) 0 0
\(947\) −27.8060 −0.903574 −0.451787 0.892126i \(-0.649213\pi\)
−0.451787 + 0.892126i \(0.649213\pi\)
\(948\) 0 0
\(949\) −14.8876 −0.483273
\(950\) 0 0
\(951\) 0.506987 0.0164402
\(952\) 0 0
\(953\) 9.93118 0.321702 0.160851 0.986979i \(-0.448576\pi\)
0.160851 + 0.986979i \(0.448576\pi\)
\(954\) 0 0
\(955\) −20.3137 −0.657336
\(956\) 0 0
\(957\) 2.77480 0.0896967
\(958\) 0 0
\(959\) −11.3083 −0.365163
\(960\) 0 0
\(961\) −30.7049 −0.990480
\(962\) 0 0
\(963\) −13.9372 −0.449120
\(964\) 0 0
\(965\) 30.0293 0.966677
\(966\) 0 0
\(967\) −16.4626 −0.529401 −0.264701 0.964331i \(-0.585273\pi\)
−0.264701 + 0.964331i \(0.585273\pi\)
\(968\) 0 0
\(969\) 18.7456 0.602195
\(970\) 0 0
\(971\) 1.35918 0.0436182 0.0218091 0.999762i \(-0.493057\pi\)
0.0218091 + 0.999762i \(0.493057\pi\)
\(972\) 0 0
\(973\) −9.20021 −0.294945
\(974\) 0 0
\(975\) −3.48356 −0.111563
\(976\) 0 0
\(977\) −28.3576 −0.907241 −0.453620 0.891195i \(-0.649868\pi\)
−0.453620 + 0.891195i \(0.649868\pi\)
\(978\) 0 0
\(979\) −3.56230 −0.113852
\(980\) 0 0
\(981\) 24.6339 0.786499
\(982\) 0 0
\(983\) 50.9697 1.62568 0.812841 0.582485i \(-0.197920\pi\)
0.812841 + 0.582485i \(0.197920\pi\)
\(984\) 0 0
\(985\) −3.03819 −0.0968048
\(986\) 0 0
\(987\) 9.24189 0.294173
\(988\) 0 0
\(989\) −3.07424 −0.0977552
\(990\) 0 0
\(991\) −58.9843 −1.87370 −0.936848 0.349736i \(-0.886271\pi\)
−0.936848 + 0.349736i \(0.886271\pi\)
\(992\) 0 0
\(993\) 27.0862 0.859554
\(994\) 0 0
\(995\) 15.9860 0.506792
\(996\) 0 0
\(997\) −32.0535 −1.01515 −0.507573 0.861609i \(-0.669457\pi\)
−0.507573 + 0.861609i \(0.669457\pi\)
\(998\) 0 0
\(999\) −1.25006 −0.0395501
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 \(a_p\))