Properties

Label 4004.2.a.j.1.9
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.69862\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.69862 q^{3} -3.84237 q^{5} -1.00000 q^{7} -0.114675 q^{9} +O(q^{10})\) \(q+1.69862 q^{3} -3.84237 q^{5} -1.00000 q^{7} -0.114675 q^{9} -1.00000 q^{11} -1.00000 q^{13} -6.52674 q^{15} -3.95435 q^{17} -0.644451 q^{19} -1.69862 q^{21} +9.08955 q^{23} +9.76379 q^{25} -5.29066 q^{27} +5.91006 q^{29} -1.51833 q^{31} -1.69862 q^{33} +3.84237 q^{35} -4.94012 q^{37} -1.69862 q^{39} -4.71529 q^{41} +6.12792 q^{43} +0.440624 q^{45} -11.9510 q^{47} +1.00000 q^{49} -6.71695 q^{51} +3.05783 q^{53} +3.84237 q^{55} -1.09468 q^{57} +2.39174 q^{59} -7.58904 q^{61} +0.114675 q^{63} +3.84237 q^{65} +13.4609 q^{67} +15.4397 q^{69} +8.90183 q^{71} +14.4086 q^{73} +16.5850 q^{75} +1.00000 q^{77} +16.1673 q^{79} -8.64282 q^{81} +8.07356 q^{83} +15.1941 q^{85} +10.0390 q^{87} -3.46837 q^{89} +1.00000 q^{91} -2.57907 q^{93} +2.47622 q^{95} +10.7099 q^{97} +0.114675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 1.69862 0.980701 0.490351 0.871525i \(-0.336869\pi\)
0.490351 + 0.871525i \(0.336869\pi\)
\(4\) 0 0
\(5\) −3.84237 −1.71836 −0.859180 0.511674i \(-0.829026\pi\)
−0.859180 + 0.511674i \(0.829026\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.114675 −0.0382250
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −6.52674 −1.68520
\(16\) 0 0
\(17\) −3.95435 −0.959070 −0.479535 0.877523i \(-0.659195\pi\)
−0.479535 + 0.877523i \(0.659195\pi\)
\(18\) 0 0
\(19\) −0.644451 −0.147847 −0.0739236 0.997264i \(-0.523552\pi\)
−0.0739236 + 0.997264i \(0.523552\pi\)
\(20\) 0 0
\(21\) −1.69862 −0.370670
\(22\) 0 0
\(23\) 9.08955 1.89530 0.947651 0.319309i \(-0.103451\pi\)
0.947651 + 0.319309i \(0.103451\pi\)
\(24\) 0 0
\(25\) 9.76379 1.95276
\(26\) 0 0
\(27\) −5.29066 −1.01819
\(28\) 0 0
\(29\) 5.91006 1.09747 0.548736 0.835996i \(-0.315109\pi\)
0.548736 + 0.835996i \(0.315109\pi\)
\(30\) 0 0
\(31\) −1.51833 −0.272699 −0.136350 0.990661i \(-0.543537\pi\)
−0.136350 + 0.990661i \(0.543537\pi\)
\(32\) 0 0
\(33\) −1.69862 −0.295693
\(34\) 0 0
\(35\) 3.84237 0.649479
\(36\) 0 0
\(37\) −4.94012 −0.812150 −0.406075 0.913840i \(-0.633103\pi\)
−0.406075 + 0.913840i \(0.633103\pi\)
\(38\) 0 0
\(39\) −1.69862 −0.271998
\(40\) 0 0
\(41\) −4.71529 −0.736405 −0.368202 0.929746i \(-0.620027\pi\)
−0.368202 + 0.929746i \(0.620027\pi\)
\(42\) 0 0
\(43\) 6.12792 0.934499 0.467249 0.884126i \(-0.345245\pi\)
0.467249 + 0.884126i \(0.345245\pi\)
\(44\) 0 0
\(45\) 0.440624 0.0656843
\(46\) 0 0
\(47\) −11.9510 −1.74324 −0.871619 0.490184i \(-0.836930\pi\)
−0.871619 + 0.490184i \(0.836930\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −6.71695 −0.940561
\(52\) 0 0
\(53\) 3.05783 0.420025 0.210012 0.977699i \(-0.432650\pi\)
0.210012 + 0.977699i \(0.432650\pi\)
\(54\) 0 0
\(55\) 3.84237 0.518105
\(56\) 0 0
\(57\) −1.09468 −0.144994
\(58\) 0 0
\(59\) 2.39174 0.311378 0.155689 0.987806i \(-0.450240\pi\)
0.155689 + 0.987806i \(0.450240\pi\)
\(60\) 0 0
\(61\) −7.58904 −0.971677 −0.485838 0.874049i \(-0.661486\pi\)
−0.485838 + 0.874049i \(0.661486\pi\)
\(62\) 0 0
\(63\) 0.114675 0.0144477
\(64\) 0 0
\(65\) 3.84237 0.476587
\(66\) 0 0
\(67\) 13.4609 1.64451 0.822255 0.569119i \(-0.192716\pi\)
0.822255 + 0.569119i \(0.192716\pi\)
\(68\) 0 0
\(69\) 15.4397 1.85872
\(70\) 0 0
\(71\) 8.90183 1.05645 0.528227 0.849104i \(-0.322857\pi\)
0.528227 + 0.849104i \(0.322857\pi\)
\(72\) 0 0
\(73\) 14.4086 1.68640 0.843202 0.537597i \(-0.180668\pi\)
0.843202 + 0.537597i \(0.180668\pi\)
\(74\) 0 0
\(75\) 16.5850 1.91507
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 16.1673 1.81896 0.909480 0.415747i \(-0.136480\pi\)
0.909480 + 0.415747i \(0.136480\pi\)
\(80\) 0 0
\(81\) −8.64282 −0.960314
\(82\) 0 0
\(83\) 8.07356 0.886188 0.443094 0.896475i \(-0.353881\pi\)
0.443094 + 0.896475i \(0.353881\pi\)
\(84\) 0 0
\(85\) 15.1941 1.64803
\(86\) 0 0
\(87\) 10.0390 1.07629
\(88\) 0 0
\(89\) −3.46837 −0.367647 −0.183823 0.982959i \(-0.558847\pi\)
−0.183823 + 0.982959i \(0.558847\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −2.57907 −0.267437
\(94\) 0 0
\(95\) 2.47622 0.254055
\(96\) 0 0
\(97\) 10.7099 1.08742 0.543711 0.839272i \(-0.317019\pi\)
0.543711 + 0.839272i \(0.317019\pi\)
\(98\) 0 0
\(99\) 0.114675 0.0115253
\(100\) 0 0
\(101\) −5.92179 −0.589240 −0.294620 0.955614i \(-0.595193\pi\)
−0.294620 + 0.955614i \(0.595193\pi\)
\(102\) 0 0
\(103\) −11.8342 −1.16606 −0.583028 0.812452i \(-0.698132\pi\)
−0.583028 + 0.812452i \(0.698132\pi\)
\(104\) 0 0
\(105\) 6.52674 0.636945
\(106\) 0 0
\(107\) 8.00613 0.773982 0.386991 0.922084i \(-0.373515\pi\)
0.386991 + 0.922084i \(0.373515\pi\)
\(108\) 0 0
\(109\) −5.05604 −0.484281 −0.242140 0.970241i \(-0.577849\pi\)
−0.242140 + 0.970241i \(0.577849\pi\)
\(110\) 0 0
\(111\) −8.39140 −0.796476
\(112\) 0 0
\(113\) −4.89270 −0.460267 −0.230133 0.973159i \(-0.573916\pi\)
−0.230133 + 0.973159i \(0.573916\pi\)
\(114\) 0 0
\(115\) −34.9254 −3.25681
\(116\) 0 0
\(117\) 0.114675 0.0106017
\(118\) 0 0
\(119\) 3.95435 0.362494
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −8.00951 −0.722193
\(124\) 0 0
\(125\) −18.3043 −1.63718
\(126\) 0 0
\(127\) 1.58091 0.140283 0.0701416 0.997537i \(-0.477655\pi\)
0.0701416 + 0.997537i \(0.477655\pi\)
\(128\) 0 0
\(129\) 10.4090 0.916464
\(130\) 0 0
\(131\) 19.5796 1.71068 0.855340 0.518067i \(-0.173348\pi\)
0.855340 + 0.518067i \(0.173348\pi\)
\(132\) 0 0
\(133\) 0.644451 0.0558810
\(134\) 0 0
\(135\) 20.3287 1.74961
\(136\) 0 0
\(137\) 9.95843 0.850806 0.425403 0.905004i \(-0.360132\pi\)
0.425403 + 0.905004i \(0.360132\pi\)
\(138\) 0 0
\(139\) 22.8376 1.93706 0.968530 0.248896i \(-0.0800678\pi\)
0.968530 + 0.248896i \(0.0800678\pi\)
\(140\) 0 0
\(141\) −20.3003 −1.70960
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −22.7086 −1.88585
\(146\) 0 0
\(147\) 1.69862 0.140100
\(148\) 0 0
\(149\) −2.54032 −0.208111 −0.104055 0.994571i \(-0.533182\pi\)
−0.104055 + 0.994571i \(0.533182\pi\)
\(150\) 0 0
\(151\) −6.29694 −0.512438 −0.256219 0.966619i \(-0.582477\pi\)
−0.256219 + 0.966619i \(0.582477\pi\)
\(152\) 0 0
\(153\) 0.453465 0.0366605
\(154\) 0 0
\(155\) 5.83397 0.468596
\(156\) 0 0
\(157\) 20.9627 1.67301 0.836503 0.547962i \(-0.184596\pi\)
0.836503 + 0.547962i \(0.184596\pi\)
\(158\) 0 0
\(159\) 5.19410 0.411919
\(160\) 0 0
\(161\) −9.08955 −0.716357
\(162\) 0 0
\(163\) −2.15810 −0.169035 −0.0845176 0.996422i \(-0.526935\pi\)
−0.0845176 + 0.996422i \(0.526935\pi\)
\(164\) 0 0
\(165\) 6.52674 0.508106
\(166\) 0 0
\(167\) 14.1307 1.09347 0.546734 0.837307i \(-0.315871\pi\)
0.546734 + 0.837307i \(0.315871\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.0739025 0.00565147
\(172\) 0 0
\(173\) −6.10180 −0.463911 −0.231956 0.972726i \(-0.574512\pi\)
−0.231956 + 0.972726i \(0.574512\pi\)
\(174\) 0 0
\(175\) −9.76379 −0.738074
\(176\) 0 0
\(177\) 4.06266 0.305369
\(178\) 0 0
\(179\) 23.4714 1.75433 0.877167 0.480185i \(-0.159431\pi\)
0.877167 + 0.480185i \(0.159431\pi\)
\(180\) 0 0
\(181\) −7.97598 −0.592850 −0.296425 0.955056i \(-0.595794\pi\)
−0.296425 + 0.955056i \(0.595794\pi\)
\(182\) 0 0
\(183\) −12.8909 −0.952924
\(184\) 0 0
\(185\) 18.9817 1.39557
\(186\) 0 0
\(187\) 3.95435 0.289170
\(188\) 0 0
\(189\) 5.29066 0.384839
\(190\) 0 0
\(191\) −19.9334 −1.44233 −0.721164 0.692764i \(-0.756393\pi\)
−0.721164 + 0.692764i \(0.756393\pi\)
\(192\) 0 0
\(193\) −9.84685 −0.708791 −0.354396 0.935096i \(-0.615313\pi\)
−0.354396 + 0.935096i \(0.615313\pi\)
\(194\) 0 0
\(195\) 6.52674 0.467390
\(196\) 0 0
\(197\) −19.7165 −1.40474 −0.702372 0.711811i \(-0.747875\pi\)
−0.702372 + 0.711811i \(0.747875\pi\)
\(198\) 0 0
\(199\) 16.2245 1.15013 0.575063 0.818109i \(-0.304978\pi\)
0.575063 + 0.818109i \(0.304978\pi\)
\(200\) 0 0
\(201\) 22.8650 1.61277
\(202\) 0 0
\(203\) −5.91006 −0.414805
\(204\) 0 0
\(205\) 18.1179 1.26541
\(206\) 0 0
\(207\) −1.04234 −0.0724479
\(208\) 0 0
\(209\) 0.644451 0.0445776
\(210\) 0 0
\(211\) −3.97045 −0.273337 −0.136669 0.990617i \(-0.543640\pi\)
−0.136669 + 0.990617i \(0.543640\pi\)
\(212\) 0 0
\(213\) 15.1209 1.03606
\(214\) 0 0
\(215\) −23.5457 −1.60580
\(216\) 0 0
\(217\) 1.51833 0.103071
\(218\) 0 0
\(219\) 24.4749 1.65386
\(220\) 0 0
\(221\) 3.95435 0.265998
\(222\) 0 0
\(223\) 21.3421 1.42917 0.714586 0.699548i \(-0.246615\pi\)
0.714586 + 0.699548i \(0.246615\pi\)
\(224\) 0 0
\(225\) −1.11966 −0.0746443
\(226\) 0 0
\(227\) −21.5761 −1.43205 −0.716027 0.698072i \(-0.754041\pi\)
−0.716027 + 0.698072i \(0.754041\pi\)
\(228\) 0 0
\(229\) 16.4871 1.08950 0.544748 0.838600i \(-0.316625\pi\)
0.544748 + 0.838600i \(0.316625\pi\)
\(230\) 0 0
\(231\) 1.69862 0.111761
\(232\) 0 0
\(233\) −24.2029 −1.58558 −0.792792 0.609493i \(-0.791373\pi\)
−0.792792 + 0.609493i \(0.791373\pi\)
\(234\) 0 0
\(235\) 45.9203 2.99551
\(236\) 0 0
\(237\) 27.4621 1.78386
\(238\) 0 0
\(239\) −27.1848 −1.75844 −0.879219 0.476418i \(-0.841935\pi\)
−0.879219 + 0.476418i \(0.841935\pi\)
\(240\) 0 0
\(241\) 16.0746 1.03545 0.517727 0.855546i \(-0.326778\pi\)
0.517727 + 0.855546i \(0.326778\pi\)
\(242\) 0 0
\(243\) 1.19108 0.0764076
\(244\) 0 0
\(245\) −3.84237 −0.245480
\(246\) 0 0
\(247\) 0.644451 0.0410055
\(248\) 0 0
\(249\) 13.7139 0.869086
\(250\) 0 0
\(251\) −15.7228 −0.992415 −0.496208 0.868204i \(-0.665275\pi\)
−0.496208 + 0.868204i \(0.665275\pi\)
\(252\) 0 0
\(253\) −9.08955 −0.571455
\(254\) 0 0
\(255\) 25.8090 1.61622
\(256\) 0 0
\(257\) −9.92503 −0.619107 −0.309553 0.950882i \(-0.600180\pi\)
−0.309553 + 0.950882i \(0.600180\pi\)
\(258\) 0 0
\(259\) 4.94012 0.306964
\(260\) 0 0
\(261\) −0.677737 −0.0419509
\(262\) 0 0
\(263\) 15.6730 0.966437 0.483218 0.875500i \(-0.339468\pi\)
0.483218 + 0.875500i \(0.339468\pi\)
\(264\) 0 0
\(265\) −11.7493 −0.721753
\(266\) 0 0
\(267\) −5.89147 −0.360552
\(268\) 0 0
\(269\) 7.74980 0.472514 0.236257 0.971691i \(-0.424079\pi\)
0.236257 + 0.971691i \(0.424079\pi\)
\(270\) 0 0
\(271\) −5.74990 −0.349282 −0.174641 0.984632i \(-0.555876\pi\)
−0.174641 + 0.984632i \(0.555876\pi\)
\(272\) 0 0
\(273\) 1.69862 0.102805
\(274\) 0 0
\(275\) −9.76379 −0.588779
\(276\) 0 0
\(277\) −2.86436 −0.172102 −0.0860512 0.996291i \(-0.527425\pi\)
−0.0860512 + 0.996291i \(0.527425\pi\)
\(278\) 0 0
\(279\) 0.174114 0.0104239
\(280\) 0 0
\(281\) 1.90503 0.113645 0.0568223 0.998384i \(-0.481903\pi\)
0.0568223 + 0.998384i \(0.481903\pi\)
\(282\) 0 0
\(283\) 8.36551 0.497278 0.248639 0.968596i \(-0.420017\pi\)
0.248639 + 0.968596i \(0.420017\pi\)
\(284\) 0 0
\(285\) 4.20617 0.249152
\(286\) 0 0
\(287\) 4.71529 0.278335
\(288\) 0 0
\(289\) −1.36315 −0.0801854
\(290\) 0 0
\(291\) 18.1920 1.06644
\(292\) 0 0
\(293\) −16.9454 −0.989961 −0.494981 0.868904i \(-0.664825\pi\)
−0.494981 + 0.868904i \(0.664825\pi\)
\(294\) 0 0
\(295\) −9.18994 −0.535059
\(296\) 0 0
\(297\) 5.29066 0.306995
\(298\) 0 0
\(299\) −9.08955 −0.525662
\(300\) 0 0
\(301\) −6.12792 −0.353207
\(302\) 0 0
\(303\) −10.0589 −0.577869
\(304\) 0 0
\(305\) 29.1599 1.66969
\(306\) 0 0
\(307\) 20.2064 1.15324 0.576619 0.817013i \(-0.304372\pi\)
0.576619 + 0.817013i \(0.304372\pi\)
\(308\) 0 0
\(309\) −20.1018 −1.14355
\(310\) 0 0
\(311\) −15.0387 −0.852767 −0.426384 0.904542i \(-0.640213\pi\)
−0.426384 + 0.904542i \(0.640213\pi\)
\(312\) 0 0
\(313\) −18.3600 −1.03777 −0.518883 0.854845i \(-0.673652\pi\)
−0.518883 + 0.854845i \(0.673652\pi\)
\(314\) 0 0
\(315\) −0.440624 −0.0248263
\(316\) 0 0
\(317\) −19.3785 −1.08841 −0.544203 0.838953i \(-0.683168\pi\)
−0.544203 + 0.838953i \(0.683168\pi\)
\(318\) 0 0
\(319\) −5.91006 −0.330900
\(320\) 0 0
\(321\) 13.5994 0.759045
\(322\) 0 0
\(323\) 2.54838 0.141796
\(324\) 0 0
\(325\) −9.76379 −0.541598
\(326\) 0 0
\(327\) −8.58831 −0.474935
\(328\) 0 0
\(329\) 11.9510 0.658882
\(330\) 0 0
\(331\) 33.1575 1.82250 0.911251 0.411851i \(-0.135118\pi\)
0.911251 + 0.411851i \(0.135118\pi\)
\(332\) 0 0
\(333\) 0.566508 0.0310444
\(334\) 0 0
\(335\) −51.7217 −2.82586
\(336\) 0 0
\(337\) −13.2109 −0.719643 −0.359822 0.933021i \(-0.617162\pi\)
−0.359822 + 0.933021i \(0.617162\pi\)
\(338\) 0 0
\(339\) −8.31086 −0.451384
\(340\) 0 0
\(341\) 1.51833 0.0822220
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −59.3251 −3.19396
\(346\) 0 0
\(347\) 33.2100 1.78280 0.891402 0.453213i \(-0.149722\pi\)
0.891402 + 0.453213i \(0.149722\pi\)
\(348\) 0 0
\(349\) −29.6881 −1.58917 −0.794584 0.607154i \(-0.792311\pi\)
−0.794584 + 0.607154i \(0.792311\pi\)
\(350\) 0 0
\(351\) 5.29066 0.282395
\(352\) 0 0
\(353\) −19.8351 −1.05572 −0.527859 0.849332i \(-0.677005\pi\)
−0.527859 + 0.849332i \(0.677005\pi\)
\(354\) 0 0
\(355\) −34.2041 −1.81537
\(356\) 0 0
\(357\) 6.71695 0.355499
\(358\) 0 0
\(359\) 27.3063 1.44117 0.720585 0.693367i \(-0.243874\pi\)
0.720585 + 0.693367i \(0.243874\pi\)
\(360\) 0 0
\(361\) −18.5847 −0.978141
\(362\) 0 0
\(363\) 1.69862 0.0891547
\(364\) 0 0
\(365\) −55.3633 −2.89785
\(366\) 0 0
\(367\) −30.2744 −1.58031 −0.790155 0.612907i \(-0.790000\pi\)
−0.790155 + 0.612907i \(0.790000\pi\)
\(368\) 0 0
\(369\) 0.540726 0.0281491
\(370\) 0 0
\(371\) −3.05783 −0.158754
\(372\) 0 0
\(373\) 13.9451 0.722050 0.361025 0.932556i \(-0.382427\pi\)
0.361025 + 0.932556i \(0.382427\pi\)
\(374\) 0 0
\(375\) −31.0921 −1.60559
\(376\) 0 0
\(377\) −5.91006 −0.304384
\(378\) 0 0
\(379\) −11.1449 −0.572474 −0.286237 0.958159i \(-0.592404\pi\)
−0.286237 + 0.958159i \(0.592404\pi\)
\(380\) 0 0
\(381\) 2.68537 0.137576
\(382\) 0 0
\(383\) 19.8868 1.01617 0.508083 0.861308i \(-0.330354\pi\)
0.508083 + 0.861308i \(0.330354\pi\)
\(384\) 0 0
\(385\) −3.84237 −0.195825
\(386\) 0 0
\(387\) −0.702719 −0.0357212
\(388\) 0 0
\(389\) 18.6695 0.946582 0.473291 0.880906i \(-0.343066\pi\)
0.473291 + 0.880906i \(0.343066\pi\)
\(390\) 0 0
\(391\) −35.9432 −1.81773
\(392\) 0 0
\(393\) 33.2584 1.67767
\(394\) 0 0
\(395\) −62.1206 −3.12563
\(396\) 0 0
\(397\) 26.3387 1.32190 0.660950 0.750430i \(-0.270153\pi\)
0.660950 + 0.750430i \(0.270153\pi\)
\(398\) 0 0
\(399\) 1.09468 0.0548026
\(400\) 0 0
\(401\) −2.38231 −0.118967 −0.0594835 0.998229i \(-0.518945\pi\)
−0.0594835 + 0.998229i \(0.518945\pi\)
\(402\) 0 0
\(403\) 1.51833 0.0756332
\(404\) 0 0
\(405\) 33.2089 1.65016
\(406\) 0 0
\(407\) 4.94012 0.244872
\(408\) 0 0
\(409\) 19.6750 0.972864 0.486432 0.873718i \(-0.338298\pi\)
0.486432 + 0.873718i \(0.338298\pi\)
\(410\) 0 0
\(411\) 16.9156 0.834386
\(412\) 0 0
\(413\) −2.39174 −0.117690
\(414\) 0 0
\(415\) −31.0216 −1.52279
\(416\) 0 0
\(417\) 38.7925 1.89968
\(418\) 0 0
\(419\) −37.5432 −1.83411 −0.917053 0.398766i \(-0.869439\pi\)
−0.917053 + 0.398766i \(0.869439\pi\)
\(420\) 0 0
\(421\) 15.3135 0.746334 0.373167 0.927764i \(-0.378272\pi\)
0.373167 + 0.927764i \(0.378272\pi\)
\(422\) 0 0
\(423\) 1.37049 0.0666353
\(424\) 0 0
\(425\) −38.6094 −1.87283
\(426\) 0 0
\(427\) 7.58904 0.367259
\(428\) 0 0
\(429\) 1.69862 0.0820104
\(430\) 0 0
\(431\) 36.3218 1.74956 0.874779 0.484522i \(-0.161006\pi\)
0.874779 + 0.484522i \(0.161006\pi\)
\(432\) 0 0
\(433\) 29.6305 1.42395 0.711977 0.702203i \(-0.247800\pi\)
0.711977 + 0.702203i \(0.247800\pi\)
\(434\) 0 0
\(435\) −38.5735 −1.84946
\(436\) 0 0
\(437\) −5.85777 −0.280215
\(438\) 0 0
\(439\) −2.44318 −0.116607 −0.0583034 0.998299i \(-0.518569\pi\)
−0.0583034 + 0.998299i \(0.518569\pi\)
\(440\) 0 0
\(441\) −0.114675 −0.00546072
\(442\) 0 0
\(443\) 1.65000 0.0783939 0.0391969 0.999232i \(-0.487520\pi\)
0.0391969 + 0.999232i \(0.487520\pi\)
\(444\) 0 0
\(445\) 13.3268 0.631750
\(446\) 0 0
\(447\) −4.31504 −0.204095
\(448\) 0 0
\(449\) −17.8922 −0.844387 −0.422194 0.906506i \(-0.638740\pi\)
−0.422194 + 0.906506i \(0.638740\pi\)
\(450\) 0 0
\(451\) 4.71529 0.222034
\(452\) 0 0
\(453\) −10.6961 −0.502548
\(454\) 0 0
\(455\) −3.84237 −0.180133
\(456\) 0 0
\(457\) 23.1950 1.08502 0.542508 0.840051i \(-0.317475\pi\)
0.542508 + 0.840051i \(0.317475\pi\)
\(458\) 0 0
\(459\) 20.9211 0.976514
\(460\) 0 0
\(461\) −5.97389 −0.278232 −0.139116 0.990276i \(-0.544426\pi\)
−0.139116 + 0.990276i \(0.544426\pi\)
\(462\) 0 0
\(463\) −19.8461 −0.922326 −0.461163 0.887316i \(-0.652568\pi\)
−0.461163 + 0.887316i \(0.652568\pi\)
\(464\) 0 0
\(465\) 9.90972 0.459552
\(466\) 0 0
\(467\) −4.16050 −0.192525 −0.0962624 0.995356i \(-0.530689\pi\)
−0.0962624 + 0.995356i \(0.530689\pi\)
\(468\) 0 0
\(469\) −13.4609 −0.621567
\(470\) 0 0
\(471\) 35.6078 1.64072
\(472\) 0 0
\(473\) −6.12792 −0.281762
\(474\) 0 0
\(475\) −6.29229 −0.288710
\(476\) 0 0
\(477\) −0.350656 −0.0160555
\(478\) 0 0
\(479\) −6.39739 −0.292304 −0.146152 0.989262i \(-0.546689\pi\)
−0.146152 + 0.989262i \(0.546689\pi\)
\(480\) 0 0
\(481\) 4.94012 0.225250
\(482\) 0 0
\(483\) −15.4397 −0.702532
\(484\) 0 0
\(485\) −41.1512 −1.86858
\(486\) 0 0
\(487\) −20.7555 −0.940520 −0.470260 0.882528i \(-0.655840\pi\)
−0.470260 + 0.882528i \(0.655840\pi\)
\(488\) 0 0
\(489\) −3.66580 −0.165773
\(490\) 0 0
\(491\) −13.1498 −0.593444 −0.296722 0.954964i \(-0.595894\pi\)
−0.296722 + 0.954964i \(0.595894\pi\)
\(492\) 0 0
\(493\) −23.3704 −1.05255
\(494\) 0 0
\(495\) −0.440624 −0.0198046
\(496\) 0 0
\(497\) −8.90183 −0.399302
\(498\) 0 0
\(499\) −25.3975 −1.13695 −0.568474 0.822701i \(-0.692466\pi\)
−0.568474 + 0.822701i \(0.692466\pi\)
\(500\) 0 0
\(501\) 24.0028 1.07236
\(502\) 0 0
\(503\) 35.6641 1.59018 0.795092 0.606489i \(-0.207423\pi\)
0.795092 + 0.606489i \(0.207423\pi\)
\(504\) 0 0
\(505\) 22.7537 1.01253
\(506\) 0 0
\(507\) 1.69862 0.0754386
\(508\) 0 0
\(509\) −21.3928 −0.948219 −0.474110 0.880466i \(-0.657230\pi\)
−0.474110 + 0.880466i \(0.657230\pi\)
\(510\) 0 0
\(511\) −14.4086 −0.637401
\(512\) 0 0
\(513\) 3.40958 0.150536
\(514\) 0 0
\(515\) 45.4712 2.00370
\(516\) 0 0
\(517\) 11.9510 0.525606
\(518\) 0 0
\(519\) −10.3647 −0.454958
\(520\) 0 0
\(521\) 34.5101 1.51191 0.755957 0.654621i \(-0.227172\pi\)
0.755957 + 0.654621i \(0.227172\pi\)
\(522\) 0 0
\(523\) 30.9307 1.35250 0.676252 0.736670i \(-0.263603\pi\)
0.676252 + 0.736670i \(0.263603\pi\)
\(524\) 0 0
\(525\) −16.5850 −0.723830
\(526\) 0 0
\(527\) 6.00399 0.261538
\(528\) 0 0
\(529\) 59.6199 2.59217
\(530\) 0 0
\(531\) −0.274273 −0.0119024
\(532\) 0 0
\(533\) 4.71529 0.204242
\(534\) 0 0
\(535\) −30.7625 −1.32998
\(536\) 0 0
\(537\) 39.8691 1.72048
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 8.24004 0.354267 0.177133 0.984187i \(-0.443318\pi\)
0.177133 + 0.984187i \(0.443318\pi\)
\(542\) 0 0
\(543\) −13.5482 −0.581408
\(544\) 0 0
\(545\) 19.4272 0.832168
\(546\) 0 0
\(547\) −0.780352 −0.0333654 −0.0166827 0.999861i \(-0.505311\pi\)
−0.0166827 + 0.999861i \(0.505311\pi\)
\(548\) 0 0
\(549\) 0.870273 0.0371424
\(550\) 0 0
\(551\) −3.80875 −0.162258
\(552\) 0 0
\(553\) −16.1673 −0.687503
\(554\) 0 0
\(555\) 32.2429 1.36863
\(556\) 0 0
\(557\) −16.4952 −0.698923 −0.349461 0.936951i \(-0.613635\pi\)
−0.349461 + 0.936951i \(0.613635\pi\)
\(558\) 0 0
\(559\) −6.12792 −0.259183
\(560\) 0 0
\(561\) 6.71695 0.283590
\(562\) 0 0
\(563\) 1.33174 0.0561260 0.0280630 0.999606i \(-0.491066\pi\)
0.0280630 + 0.999606i \(0.491066\pi\)
\(564\) 0 0
\(565\) 18.7996 0.790903
\(566\) 0 0
\(567\) 8.64282 0.362965
\(568\) 0 0
\(569\) −24.4028 −1.02302 −0.511509 0.859278i \(-0.670913\pi\)
−0.511509 + 0.859278i \(0.670913\pi\)
\(570\) 0 0
\(571\) 18.2551 0.763952 0.381976 0.924172i \(-0.375244\pi\)
0.381976 + 0.924172i \(0.375244\pi\)
\(572\) 0 0
\(573\) −33.8593 −1.41449
\(574\) 0 0
\(575\) 88.7485 3.70107
\(576\) 0 0
\(577\) 24.4256 1.01685 0.508426 0.861106i \(-0.330227\pi\)
0.508426 + 0.861106i \(0.330227\pi\)
\(578\) 0 0
\(579\) −16.7261 −0.695113
\(580\) 0 0
\(581\) −8.07356 −0.334948
\(582\) 0 0
\(583\) −3.05783 −0.126642
\(584\) 0 0
\(585\) −0.440624 −0.0182176
\(586\) 0 0
\(587\) −10.0589 −0.415175 −0.207588 0.978216i \(-0.566561\pi\)
−0.207588 + 0.978216i \(0.566561\pi\)
\(588\) 0 0
\(589\) 0.978487 0.0403179
\(590\) 0 0
\(591\) −33.4909 −1.37763
\(592\) 0 0
\(593\) −5.35178 −0.219771 −0.109886 0.993944i \(-0.535048\pi\)
−0.109886 + 0.993944i \(0.535048\pi\)
\(594\) 0 0
\(595\) −15.1941 −0.622895
\(596\) 0 0
\(597\) 27.5594 1.12793
\(598\) 0 0
\(599\) −38.9731 −1.59240 −0.796199 0.605035i \(-0.793159\pi\)
−0.796199 + 0.605035i \(0.793159\pi\)
\(600\) 0 0
\(601\) 11.3094 0.461320 0.230660 0.973034i \(-0.425912\pi\)
0.230660 + 0.973034i \(0.425912\pi\)
\(602\) 0 0
\(603\) −1.54363 −0.0628615
\(604\) 0 0
\(605\) −3.84237 −0.156214
\(606\) 0 0
\(607\) −15.0931 −0.612611 −0.306306 0.951933i \(-0.599093\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(608\) 0 0
\(609\) −10.0390 −0.406800
\(610\) 0 0
\(611\) 11.9510 0.483487
\(612\) 0 0
\(613\) −35.7707 −1.44477 −0.722383 0.691493i \(-0.756953\pi\)
−0.722383 + 0.691493i \(0.756953\pi\)
\(614\) 0 0
\(615\) 30.7755 1.24099
\(616\) 0 0
\(617\) −33.9746 −1.36777 −0.683883 0.729592i \(-0.739710\pi\)
−0.683883 + 0.729592i \(0.739710\pi\)
\(618\) 0 0
\(619\) 30.3408 1.21950 0.609749 0.792594i \(-0.291270\pi\)
0.609749 + 0.792594i \(0.291270\pi\)
\(620\) 0 0
\(621\) −48.0897 −1.92977
\(622\) 0 0
\(623\) 3.46837 0.138958
\(624\) 0 0
\(625\) 21.5127 0.860509
\(626\) 0 0
\(627\) 1.09468 0.0437173
\(628\) 0 0
\(629\) 19.5349 0.778908
\(630\) 0 0
\(631\) −15.2634 −0.607627 −0.303814 0.952731i \(-0.598260\pi\)
−0.303814 + 0.952731i \(0.598260\pi\)
\(632\) 0 0
\(633\) −6.74431 −0.268062
\(634\) 0 0
\(635\) −6.07444 −0.241057
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −1.02082 −0.0403829
\(640\) 0 0
\(641\) 27.0881 1.06992 0.534958 0.844879i \(-0.320327\pi\)
0.534958 + 0.844879i \(0.320327\pi\)
\(642\) 0 0
\(643\) 11.7248 0.462380 0.231190 0.972909i \(-0.425738\pi\)
0.231190 + 0.972909i \(0.425738\pi\)
\(644\) 0 0
\(645\) −39.9953 −1.57481
\(646\) 0 0
\(647\) −14.9856 −0.589143 −0.294571 0.955629i \(-0.595177\pi\)
−0.294571 + 0.955629i \(0.595177\pi\)
\(648\) 0 0
\(649\) −2.39174 −0.0938839
\(650\) 0 0
\(651\) 2.57907 0.101082
\(652\) 0 0
\(653\) 7.88481 0.308556 0.154278 0.988027i \(-0.450695\pi\)
0.154278 + 0.988027i \(0.450695\pi\)
\(654\) 0 0
\(655\) −75.2322 −2.93956
\(656\) 0 0
\(657\) −1.65231 −0.0644628
\(658\) 0 0
\(659\) 46.0052 1.79211 0.896054 0.443946i \(-0.146422\pi\)
0.896054 + 0.443946i \(0.146422\pi\)
\(660\) 0 0
\(661\) 44.3021 1.72315 0.861576 0.507629i \(-0.169478\pi\)
0.861576 + 0.507629i \(0.169478\pi\)
\(662\) 0 0
\(663\) 6.71695 0.260865
\(664\) 0 0
\(665\) −2.47622 −0.0960237
\(666\) 0 0
\(667\) 53.7198 2.08004
\(668\) 0 0
\(669\) 36.2522 1.40159
\(670\) 0 0
\(671\) 7.58904 0.292971
\(672\) 0 0
\(673\) 41.2852 1.59143 0.795714 0.605672i \(-0.207096\pi\)
0.795714 + 0.605672i \(0.207096\pi\)
\(674\) 0 0
\(675\) −51.6569 −1.98828
\(676\) 0 0
\(677\) 12.5689 0.483061 0.241531 0.970393i \(-0.422351\pi\)
0.241531 + 0.970393i \(0.422351\pi\)
\(678\) 0 0
\(679\) −10.7099 −0.411007
\(680\) 0 0
\(681\) −36.6497 −1.40442
\(682\) 0 0
\(683\) −6.20600 −0.237466 −0.118733 0.992926i \(-0.537883\pi\)
−0.118733 + 0.992926i \(0.537883\pi\)
\(684\) 0 0
\(685\) −38.2639 −1.46199
\(686\) 0 0
\(687\) 28.0053 1.06847
\(688\) 0 0
\(689\) −3.05783 −0.116494
\(690\) 0 0
\(691\) −19.7028 −0.749529 −0.374765 0.927120i \(-0.622276\pi\)
−0.374765 + 0.927120i \(0.622276\pi\)
\(692\) 0 0
\(693\) −0.114675 −0.00435615
\(694\) 0 0
\(695\) −87.7505 −3.32857
\(696\) 0 0
\(697\) 18.6459 0.706263
\(698\) 0 0
\(699\) −41.1116 −1.55498
\(700\) 0 0
\(701\) 14.4217 0.544700 0.272350 0.962198i \(-0.412199\pi\)
0.272350 + 0.962198i \(0.412199\pi\)
\(702\) 0 0
\(703\) 3.18366 0.120074
\(704\) 0 0
\(705\) 78.0013 2.93770
\(706\) 0 0
\(707\) 5.92179 0.222712
\(708\) 0 0
\(709\) 43.3911 1.62959 0.814794 0.579750i \(-0.196850\pi\)
0.814794 + 0.579750i \(0.196850\pi\)
\(710\) 0 0
\(711\) −1.85398 −0.0695298
\(712\) 0 0
\(713\) −13.8009 −0.516848
\(714\) 0 0
\(715\) −3.84237 −0.143696
\(716\) 0 0
\(717\) −46.1767 −1.72450
\(718\) 0 0
\(719\) −35.9937 −1.34234 −0.671169 0.741305i \(-0.734207\pi\)
−0.671169 + 0.741305i \(0.734207\pi\)
\(720\) 0 0
\(721\) 11.8342 0.440727
\(722\) 0 0
\(723\) 27.3046 1.01547
\(724\) 0 0
\(725\) 57.7047 2.14310
\(726\) 0 0
\(727\) −23.9224 −0.887234 −0.443617 0.896216i \(-0.646305\pi\)
−0.443617 + 0.896216i \(0.646305\pi\)
\(728\) 0 0
\(729\) 27.9517 1.03525
\(730\) 0 0
\(731\) −24.2319 −0.896249
\(732\) 0 0
\(733\) 4.47363 0.165237 0.0826187 0.996581i \(-0.473672\pi\)
0.0826187 + 0.996581i \(0.473672\pi\)
\(734\) 0 0
\(735\) −6.52674 −0.240742
\(736\) 0 0
\(737\) −13.4609 −0.495839
\(738\) 0 0
\(739\) −47.9236 −1.76290 −0.881449 0.472279i \(-0.843431\pi\)
−0.881449 + 0.472279i \(0.843431\pi\)
\(740\) 0 0
\(741\) 1.09468 0.0402141
\(742\) 0 0
\(743\) 28.4625 1.04419 0.522093 0.852888i \(-0.325151\pi\)
0.522093 + 0.852888i \(0.325151\pi\)
\(744\) 0 0
\(745\) 9.76083 0.357609
\(746\) 0 0
\(747\) −0.925836 −0.0338746
\(748\) 0 0
\(749\) −8.00613 −0.292538
\(750\) 0 0
\(751\) −21.7806 −0.794785 −0.397392 0.917649i \(-0.630085\pi\)
−0.397392 + 0.917649i \(0.630085\pi\)
\(752\) 0 0
\(753\) −26.7072 −0.973263
\(754\) 0 0
\(755\) 24.1952 0.880552
\(756\) 0 0
\(757\) 4.44815 0.161671 0.0808353 0.996727i \(-0.474241\pi\)
0.0808353 + 0.996727i \(0.474241\pi\)
\(758\) 0 0
\(759\) −15.4397 −0.560427
\(760\) 0 0
\(761\) 13.3140 0.482632 0.241316 0.970447i \(-0.422421\pi\)
0.241316 + 0.970447i \(0.422421\pi\)
\(762\) 0 0
\(763\) 5.05604 0.183041
\(764\) 0 0
\(765\) −1.74238 −0.0629958
\(766\) 0 0
\(767\) −2.39174 −0.0863606
\(768\) 0 0
\(769\) 45.2259 1.63089 0.815444 0.578836i \(-0.196493\pi\)
0.815444 + 0.578836i \(0.196493\pi\)
\(770\) 0 0
\(771\) −16.8589 −0.607159
\(772\) 0 0
\(773\) 42.0325 1.51180 0.755902 0.654684i \(-0.227198\pi\)
0.755902 + 0.654684i \(0.227198\pi\)
\(774\) 0 0
\(775\) −14.8246 −0.532516
\(776\) 0 0
\(777\) 8.39140 0.301040
\(778\) 0 0
\(779\) 3.03878 0.108875
\(780\) 0 0
\(781\) −8.90183 −0.318533
\(782\) 0 0
\(783\) −31.2682 −1.11743
\(784\) 0 0
\(785\) −80.5464 −2.87483
\(786\) 0 0
\(787\) 22.2808 0.794223 0.397112 0.917770i \(-0.370013\pi\)
0.397112 + 0.917770i \(0.370013\pi\)
\(788\) 0 0
\(789\) 26.6225 0.947786
\(790\) 0 0
\(791\) 4.89270 0.173964
\(792\) 0 0
\(793\) 7.58904 0.269495
\(794\) 0 0
\(795\) −19.9576 −0.707824
\(796\) 0 0
\(797\) −14.3429 −0.508051 −0.254026 0.967197i \(-0.581755\pi\)
−0.254026 + 0.967197i \(0.581755\pi\)
\(798\) 0 0
\(799\) 47.2585 1.67189
\(800\) 0 0
\(801\) 0.397736 0.0140533
\(802\) 0 0
\(803\) −14.4086 −0.508470
\(804\) 0 0
\(805\) 34.9254 1.23096
\(806\) 0 0
\(807\) 13.1640 0.463395
\(808\) 0 0
\(809\) 34.0331 1.19654 0.598270 0.801295i \(-0.295855\pi\)
0.598270 + 0.801295i \(0.295855\pi\)
\(810\) 0 0
\(811\) 47.3269 1.66187 0.830935 0.556369i \(-0.187806\pi\)
0.830935 + 0.556369i \(0.187806\pi\)
\(812\) 0 0
\(813\) −9.76692 −0.342541
\(814\) 0 0
\(815\) 8.29220 0.290463
\(816\) 0 0
\(817\) −3.94915 −0.138163
\(818\) 0 0
\(819\) −0.114675 −0.00400707
\(820\) 0 0
\(821\) 33.5230 1.16996 0.584981 0.811047i \(-0.301102\pi\)
0.584981 + 0.811047i \(0.301102\pi\)
\(822\) 0 0
\(823\) 56.1962 1.95888 0.979439 0.201743i \(-0.0646604\pi\)
0.979439 + 0.201743i \(0.0646604\pi\)
\(824\) 0 0
\(825\) −16.5850 −0.577416
\(826\) 0 0
\(827\) 2.98192 0.103691 0.0518457 0.998655i \(-0.483490\pi\)
0.0518457 + 0.998655i \(0.483490\pi\)
\(828\) 0 0
\(829\) 24.3752 0.846585 0.423293 0.905993i \(-0.360874\pi\)
0.423293 + 0.905993i \(0.360874\pi\)
\(830\) 0 0
\(831\) −4.86546 −0.168781
\(832\) 0 0
\(833\) −3.95435 −0.137010
\(834\) 0 0
\(835\) −54.2954 −1.87897
\(836\) 0 0
\(837\) 8.03295 0.277659
\(838\) 0 0
\(839\) −21.2830 −0.734770 −0.367385 0.930069i \(-0.619747\pi\)
−0.367385 + 0.930069i \(0.619747\pi\)
\(840\) 0 0
\(841\) 5.92885 0.204443
\(842\) 0 0
\(843\) 3.23593 0.111451
\(844\) 0 0
\(845\) −3.84237 −0.132181
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 14.2099 0.487681
\(850\) 0 0
\(851\) −44.9034 −1.53927
\(852\) 0 0
\(853\) 11.2026 0.383570 0.191785 0.981437i \(-0.438572\pi\)
0.191785 + 0.981437i \(0.438572\pi\)
\(854\) 0 0
\(855\) −0.283961 −0.00971125
\(856\) 0 0
\(857\) −4.01908 −0.137289 −0.0686445 0.997641i \(-0.521867\pi\)
−0.0686445 + 0.997641i \(0.521867\pi\)
\(858\) 0 0
\(859\) −27.9123 −0.952355 −0.476178 0.879349i \(-0.657978\pi\)
−0.476178 + 0.879349i \(0.657978\pi\)
\(860\) 0 0
\(861\) 8.00951 0.272963
\(862\) 0 0
\(863\) 1.05187 0.0358059 0.0179030 0.999840i \(-0.494301\pi\)
0.0179030 + 0.999840i \(0.494301\pi\)
\(864\) 0 0
\(865\) 23.4454 0.797166
\(866\) 0 0
\(867\) −2.31548 −0.0786379
\(868\) 0 0
\(869\) −16.1673 −0.548437
\(870\) 0 0
\(871\) −13.4609 −0.456105
\(872\) 0 0
\(873\) −1.22815 −0.0415667
\(874\) 0 0
\(875\) 18.3043 0.618797
\(876\) 0 0
\(877\) 2.06181 0.0696224 0.0348112 0.999394i \(-0.488917\pi\)
0.0348112 + 0.999394i \(0.488917\pi\)
\(878\) 0 0
\(879\) −28.7839 −0.970856
\(880\) 0 0
\(881\) −13.6430 −0.459644 −0.229822 0.973233i \(-0.573814\pi\)
−0.229822 + 0.973233i \(0.573814\pi\)
\(882\) 0 0
\(883\) 14.3678 0.483517 0.241758 0.970336i \(-0.422276\pi\)
0.241758 + 0.970336i \(0.422276\pi\)
\(884\) 0 0
\(885\) −15.6103 −0.524733
\(886\) 0 0
\(887\) 15.8604 0.532539 0.266270 0.963899i \(-0.414209\pi\)
0.266270 + 0.963899i \(0.414209\pi\)
\(888\) 0 0
\(889\) −1.58091 −0.0530221
\(890\) 0 0
\(891\) 8.64282 0.289546
\(892\) 0 0
\(893\) 7.70186 0.257733
\(894\) 0 0
\(895\) −90.1857 −3.01458
\(896\) 0 0
\(897\) −15.4397 −0.515517
\(898\) 0 0
\(899\) −8.97340 −0.299280
\(900\) 0 0
\(901\) −12.0917 −0.402833
\(902\) 0 0
\(903\) −10.4090 −0.346391
\(904\) 0 0
\(905\) 30.6466 1.01873
\(906\) 0 0
\(907\) −5.65489 −0.187768 −0.0938838 0.995583i \(-0.529928\pi\)
−0.0938838 + 0.995583i \(0.529928\pi\)
\(908\) 0 0
\(909\) 0.679082 0.0225237
\(910\) 0 0
\(911\) −13.5578 −0.449189 −0.224594 0.974452i \(-0.572106\pi\)
−0.224594 + 0.974452i \(0.572106\pi\)
\(912\) 0 0
\(913\) −8.07356 −0.267196
\(914\) 0 0
\(915\) 49.5317 1.63747
\(916\) 0 0
\(917\) −19.5796 −0.646576
\(918\) 0 0
\(919\) −55.8746 −1.84313 −0.921566 0.388222i \(-0.873089\pi\)
−0.921566 + 0.388222i \(0.873089\pi\)
\(920\) 0 0
\(921\) 34.3230 1.13098
\(922\) 0 0
\(923\) −8.90183 −0.293007
\(924\) 0 0
\(925\) −48.2343 −1.58593
\(926\) 0 0
\(927\) 1.35708 0.0445725
\(928\) 0 0
\(929\) 32.4785 1.06558 0.532792 0.846246i \(-0.321143\pi\)
0.532792 + 0.846246i \(0.321143\pi\)
\(930\) 0 0
\(931\) −0.644451 −0.0211210
\(932\) 0 0
\(933\) −25.5451 −0.836310
\(934\) 0 0
\(935\) −15.1941 −0.496899
\(936\) 0 0
\(937\) 34.7046 1.13375 0.566875 0.823804i \(-0.308152\pi\)
0.566875 + 0.823804i \(0.308152\pi\)
\(938\) 0 0
\(939\) −31.1867 −1.01774
\(940\) 0 0
\(941\) 11.3037 0.368489 0.184245 0.982880i \(-0.441016\pi\)
0.184245 + 0.982880i \(0.441016\pi\)
\(942\) 0 0
\(943\) −42.8599 −1.39571
\(944\) 0 0
\(945\) −20.3287 −0.661292
\(946\) 0 0
\(947\) 9.92651 0.322568 0.161284 0.986908i \(-0.448436\pi\)
0.161284 + 0.986908i \(0.448436\pi\)
\(948\) 0 0
\(949\) −14.4086 −0.467724
\(950\) 0 0
\(951\) −32.9168 −1.06740
\(952\) 0 0
\(953\) 11.9685 0.387699 0.193850 0.981031i \(-0.437903\pi\)
0.193850 + 0.981031i \(0.437903\pi\)
\(954\) 0 0
\(955\) 76.5914 2.47844
\(956\) 0 0
\(957\) −10.0390 −0.324514
\(958\) 0 0
\(959\) −9.95843 −0.321574
\(960\) 0 0
\(961\) −28.6947 −0.925635
\(962\) 0 0
\(963\) −0.918103 −0.0295855
\(964\) 0 0
\(965\) 37.8352 1.21796
\(966\) 0 0
\(967\) −17.4649 −0.561633 −0.280816 0.959762i \(-0.590605\pi\)
−0.280816 + 0.959762i \(0.590605\pi\)
\(968\) 0 0
\(969\) 4.32875 0.139059
\(970\) 0 0
\(971\) 48.2923 1.54977 0.774887 0.632100i \(-0.217807\pi\)
0.774887 + 0.632100i \(0.217807\pi\)
\(972\) 0 0
\(973\) −22.8376 −0.732140
\(974\) 0 0
\(975\) −16.5850 −0.531146
\(976\) 0 0
\(977\) −5.92048 −0.189413 −0.0947064 0.995505i \(-0.530191\pi\)
−0.0947064 + 0.995505i \(0.530191\pi\)
\(978\) 0 0
\(979\) 3.46837 0.110850
\(980\) 0 0
\(981\) 0.579802 0.0185116
\(982\) 0 0
\(983\) −11.4494 −0.365180 −0.182590 0.983189i \(-0.558448\pi\)
−0.182590 + 0.983189i \(0.558448\pi\)
\(984\) 0 0
\(985\) 75.7581 2.41385
\(986\) 0 0
\(987\) 20.3003 0.646166
\(988\) 0 0
\(989\) 55.7000 1.77116
\(990\) 0 0
\(991\) 11.5659 0.367402 0.183701 0.982982i \(-0.441192\pi\)
0.183701 + 0.982982i \(0.441192\pi\)
\(992\) 0 0
\(993\) 56.3222 1.78733
\(994\) 0 0
\(995\) −62.3406 −1.97633
\(996\) 0 0
\(997\) −25.5600 −0.809494 −0.404747 0.914429i \(-0.632640\pi\)
−0.404747 + 0.914429i \(0.632640\pi\)
\(998\) 0 0
\(999\) 26.1365 0.826922
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 \(a_p\))