Properties

Label 8008.2.a.j.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 5
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: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.668973.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.16366\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.08441 q^{3} -0.239305 q^{5} +1.00000 q^{7} +6.51357 q^{9} +O(q^{10})\) \(q-3.08441 q^{3} -0.239305 q^{5} +1.00000 q^{7} +6.51357 q^{9} -1.00000 q^{11} -1.00000 q^{13} +0.738115 q^{15} +3.76069 q^{17} -6.06183 q^{19} -3.08441 q^{21} -0.585598 q^{23} -4.94273 q^{25} -10.8373 q^{27} -8.13147 q^{29} +10.9443 q^{31} +3.08441 q^{33} -0.239305 q^{35} +3.95055 q^{37} +3.08441 q^{39} +12.3960 q^{41} -9.90931 q^{43} -1.55873 q^{45} -4.96531 q^{47} +1.00000 q^{49} -11.5995 q^{51} +9.75288 q^{53} +0.239305 q^{55} +18.6971 q^{57} -7.12091 q^{59} +3.65371 q^{61} +6.51357 q^{63} +0.239305 q^{65} +9.25407 q^{67} +1.80622 q^{69} -1.55091 q^{71} +1.12994 q^{73} +15.2454 q^{75} -1.00000 q^{77} +8.56567 q^{79} +13.8859 q^{81} +2.51203 q^{83} -0.899954 q^{85} +25.0808 q^{87} -5.89301 q^{89} -1.00000 q^{91} -33.7566 q^{93} +1.45063 q^{95} +0.759157 q^{97} -6.51357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} - 5q^{11} - 5q^{13} - 5q^{15} + 19q^{17} - 5q^{19} + q^{21} + 5q^{23} + 12q^{25} - 11q^{27} - 17q^{29} + 4q^{31} - q^{33} - q^{35} + 10q^{37} - q^{39} + 10q^{41} - 25q^{43} + q^{45} + 3q^{47} + 5q^{49} - q^{51} + 22q^{53} + q^{55} + 16q^{57} + 21q^{59} + 26q^{61} + 6q^{63} + q^{65} + 28q^{67} + 16q^{69} + 28q^{71} - 4q^{73} - 5q^{77} - 11q^{79} + 5q^{81} + 33q^{85} + 31q^{87} - 37q^{89} - 5q^{91} - 49q^{93} + 29q^{95} + 18q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) −3.08441 −1.78078 −0.890392 0.455195i \(-0.849570\pi\)
−0.890392 + 0.455195i \(0.849570\pi\)
\(4\) 0 0
\(5\) −0.239305 −0.107021 −0.0535103 0.998567i \(-0.517041\pi\)
−0.0535103 + 0.998567i \(0.517041\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 6.51357 2.17119
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.738115 0.190580
\(16\) 0 0
\(17\) 3.76069 0.912102 0.456051 0.889954i \(-0.349263\pi\)
0.456051 + 0.889954i \(0.349263\pi\)
\(18\) 0 0
\(19\) −6.06183 −1.39068 −0.695339 0.718682i \(-0.744746\pi\)
−0.695339 + 0.718682i \(0.744746\pi\)
\(20\) 0 0
\(21\) −3.08441 −0.673073
\(22\) 0 0
\(23\) −0.585598 −0.122106 −0.0610528 0.998135i \(-0.519446\pi\)
−0.0610528 + 0.998135i \(0.519446\pi\)
\(24\) 0 0
\(25\) −4.94273 −0.988547
\(26\) 0 0
\(27\) −10.8373 −2.08564
\(28\) 0 0
\(29\) −8.13147 −1.50998 −0.754988 0.655738i \(-0.772358\pi\)
−0.754988 + 0.655738i \(0.772358\pi\)
\(30\) 0 0
\(31\) 10.9443 1.96565 0.982825 0.184542i \(-0.0590803\pi\)
0.982825 + 0.184542i \(0.0590803\pi\)
\(32\) 0 0
\(33\) 3.08441 0.536926
\(34\) 0 0
\(35\) −0.239305 −0.0404500
\(36\) 0 0
\(37\) 3.95055 0.649467 0.324733 0.945806i \(-0.394725\pi\)
0.324733 + 0.945806i \(0.394725\pi\)
\(38\) 0 0
\(39\) 3.08441 0.493900
\(40\) 0 0
\(41\) 12.3960 1.93593 0.967966 0.251081i \(-0.0807861\pi\)
0.967966 + 0.251081i \(0.0807861\pi\)
\(42\) 0 0
\(43\) −9.90931 −1.51116 −0.755578 0.655059i \(-0.772644\pi\)
−0.755578 + 0.655059i \(0.772644\pi\)
\(44\) 0 0
\(45\) −1.55873 −0.232362
\(46\) 0 0
\(47\) −4.96531 −0.724265 −0.362133 0.932127i \(-0.617951\pi\)
−0.362133 + 0.932127i \(0.617951\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −11.5995 −1.62426
\(52\) 0 0
\(53\) 9.75288 1.33966 0.669830 0.742514i \(-0.266367\pi\)
0.669830 + 0.742514i \(0.266367\pi\)
\(54\) 0 0
\(55\) 0.239305 0.0322679
\(56\) 0 0
\(57\) 18.6971 2.47650
\(58\) 0 0
\(59\) −7.12091 −0.927063 −0.463531 0.886080i \(-0.653418\pi\)
−0.463531 + 0.886080i \(0.653418\pi\)
\(60\) 0 0
\(61\) 3.65371 0.467809 0.233905 0.972260i \(-0.424850\pi\)
0.233905 + 0.972260i \(0.424850\pi\)
\(62\) 0 0
\(63\) 6.51357 0.820633
\(64\) 0 0
\(65\) 0.239305 0.0296821
\(66\) 0 0
\(67\) 9.25407 1.13056 0.565282 0.824898i \(-0.308767\pi\)
0.565282 + 0.824898i \(0.308767\pi\)
\(68\) 0 0
\(69\) 1.80622 0.217444
\(70\) 0 0
\(71\) −1.55091 −0.184059 −0.0920297 0.995756i \(-0.529335\pi\)
−0.0920297 + 0.995756i \(0.529335\pi\)
\(72\) 0 0
\(73\) 1.12994 0.132249 0.0661245 0.997811i \(-0.478937\pi\)
0.0661245 + 0.997811i \(0.478937\pi\)
\(74\) 0 0
\(75\) 15.2454 1.76039
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 8.56567 0.963713 0.481857 0.876250i \(-0.339963\pi\)
0.481857 + 0.876250i \(0.339963\pi\)
\(80\) 0 0
\(81\) 13.8859 1.54288
\(82\) 0 0
\(83\) 2.51203 0.275731 0.137866 0.990451i \(-0.455976\pi\)
0.137866 + 0.990451i \(0.455976\pi\)
\(84\) 0 0
\(85\) −0.899954 −0.0976137
\(86\) 0 0
\(87\) 25.0808 2.68894
\(88\) 0 0
\(89\) −5.89301 −0.624658 −0.312329 0.949974i \(-0.601109\pi\)
−0.312329 + 0.949974i \(0.601109\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −33.7566 −3.50040
\(94\) 0 0
\(95\) 1.45063 0.148831
\(96\) 0 0
\(97\) 0.759157 0.0770807 0.0385404 0.999257i \(-0.487729\pi\)
0.0385404 + 0.999257i \(0.487729\pi\)
\(98\) 0 0
\(99\) −6.51357 −0.654638
\(100\) 0 0
\(101\) −17.9462 −1.78571 −0.892856 0.450343i \(-0.851302\pi\)
−0.892856 + 0.450343i \(0.851302\pi\)
\(102\) 0 0
\(103\) −17.3229 −1.70687 −0.853437 0.521197i \(-0.825486\pi\)
−0.853437 + 0.521197i \(0.825486\pi\)
\(104\) 0 0
\(105\) 0.738115 0.0720326
\(106\) 0 0
\(107\) −8.22720 −0.795353 −0.397677 0.917526i \(-0.630183\pi\)
−0.397677 + 0.917526i \(0.630183\pi\)
\(108\) 0 0
\(109\) −16.6882 −1.59844 −0.799220 0.601038i \(-0.794754\pi\)
−0.799220 + 0.601038i \(0.794754\pi\)
\(110\) 0 0
\(111\) −12.1851 −1.15656
\(112\) 0 0
\(113\) 19.0018 1.78754 0.893770 0.448526i \(-0.148051\pi\)
0.893770 + 0.448526i \(0.148051\pi\)
\(114\) 0 0
\(115\) 0.140137 0.0130678
\(116\) 0 0
\(117\) −6.51357 −0.602180
\(118\) 0 0
\(119\) 3.76069 0.344742
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −38.2344 −3.44748
\(124\) 0 0
\(125\) 2.37935 0.212815
\(126\) 0 0
\(127\) −17.0640 −1.51419 −0.757093 0.653307i \(-0.773381\pi\)
−0.757093 + 0.653307i \(0.773381\pi\)
\(128\) 0 0
\(129\) 30.5644 2.69104
\(130\) 0 0
\(131\) 0.919785 0.0803620 0.0401810 0.999192i \(-0.487207\pi\)
0.0401810 + 0.999192i \(0.487207\pi\)
\(132\) 0 0
\(133\) −6.06183 −0.525627
\(134\) 0 0
\(135\) 2.59342 0.223206
\(136\) 0 0
\(137\) −17.0777 −1.45905 −0.729523 0.683956i \(-0.760258\pi\)
−0.729523 + 0.683956i \(0.760258\pi\)
\(138\) 0 0
\(139\) 10.6921 0.906893 0.453447 0.891283i \(-0.350194\pi\)
0.453447 + 0.891283i \(0.350194\pi\)
\(140\) 0 0
\(141\) 15.3151 1.28976
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.94590 0.161598
\(146\) 0 0
\(147\) −3.08441 −0.254398
\(148\) 0 0
\(149\) 11.7568 0.963154 0.481577 0.876404i \(-0.340064\pi\)
0.481577 + 0.876404i \(0.340064\pi\)
\(150\) 0 0
\(151\) −15.8260 −1.28790 −0.643949 0.765068i \(-0.722705\pi\)
−0.643949 + 0.765068i \(0.722705\pi\)
\(152\) 0 0
\(153\) 24.4956 1.98035
\(154\) 0 0
\(155\) −2.61902 −0.210365
\(156\) 0 0
\(157\) 23.0558 1.84005 0.920027 0.391854i \(-0.128166\pi\)
0.920027 + 0.391854i \(0.128166\pi\)
\(158\) 0 0
\(159\) −30.0818 −2.38565
\(160\) 0 0
\(161\) −0.585598 −0.0461516
\(162\) 0 0
\(163\) 14.8870 1.16604 0.583020 0.812458i \(-0.301871\pi\)
0.583020 + 0.812458i \(0.301871\pi\)
\(164\) 0 0
\(165\) −0.738115 −0.0574621
\(166\) 0 0
\(167\) 4.83272 0.373967 0.186984 0.982363i \(-0.440129\pi\)
0.186984 + 0.982363i \(0.440129\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −39.4841 −3.01943
\(172\) 0 0
\(173\) −0.201964 −0.0153550 −0.00767752 0.999971i \(-0.502444\pi\)
−0.00767752 + 0.999971i \(0.502444\pi\)
\(174\) 0 0
\(175\) −4.94273 −0.373635
\(176\) 0 0
\(177\) 21.9638 1.65090
\(178\) 0 0
\(179\) −17.6835 −1.32173 −0.660864 0.750506i \(-0.729810\pi\)
−0.660864 + 0.750506i \(0.729810\pi\)
\(180\) 0 0
\(181\) 18.3135 1.36123 0.680616 0.732640i \(-0.261712\pi\)
0.680616 + 0.732640i \(0.261712\pi\)
\(182\) 0 0
\(183\) −11.2695 −0.833067
\(184\) 0 0
\(185\) −0.945388 −0.0695063
\(186\) 0 0
\(187\) −3.76069 −0.275009
\(188\) 0 0
\(189\) −10.8373 −0.788296
\(190\) 0 0
\(191\) 9.08478 0.657351 0.328676 0.944443i \(-0.393398\pi\)
0.328676 + 0.944443i \(0.393398\pi\)
\(192\) 0 0
\(193\) −24.3788 −1.75482 −0.877412 0.479738i \(-0.840732\pi\)
−0.877412 + 0.479738i \(0.840732\pi\)
\(194\) 0 0
\(195\) −0.738115 −0.0528575
\(196\) 0 0
\(197\) 5.39448 0.384341 0.192170 0.981362i \(-0.438447\pi\)
0.192170 + 0.981362i \(0.438447\pi\)
\(198\) 0 0
\(199\) −0.417056 −0.0295643 −0.0147822 0.999891i \(-0.504705\pi\)
−0.0147822 + 0.999891i \(0.504705\pi\)
\(200\) 0 0
\(201\) −28.5433 −2.01329
\(202\) 0 0
\(203\) −8.13147 −0.570718
\(204\) 0 0
\(205\) −2.96643 −0.207184
\(206\) 0 0
\(207\) −3.81433 −0.265115
\(208\) 0 0
\(209\) 6.06183 0.419305
\(210\) 0 0
\(211\) 13.9629 0.961248 0.480624 0.876927i \(-0.340410\pi\)
0.480624 + 0.876927i \(0.340410\pi\)
\(212\) 0 0
\(213\) 4.78364 0.327770
\(214\) 0 0
\(215\) 2.37135 0.161725
\(216\) 0 0
\(217\) 10.9443 0.742946
\(218\) 0 0
\(219\) −3.48518 −0.235507
\(220\) 0 0
\(221\) −3.76069 −0.252972
\(222\) 0 0
\(223\) −14.5562 −0.974753 −0.487377 0.873192i \(-0.662046\pi\)
−0.487377 + 0.873192i \(0.662046\pi\)
\(224\) 0 0
\(225\) −32.1948 −2.14632
\(226\) 0 0
\(227\) −26.0029 −1.72587 −0.862936 0.505314i \(-0.831377\pi\)
−0.862936 + 0.505314i \(0.831377\pi\)
\(228\) 0 0
\(229\) −0.718664 −0.0474906 −0.0237453 0.999718i \(-0.507559\pi\)
−0.0237453 + 0.999718i \(0.507559\pi\)
\(230\) 0 0
\(231\) 3.08441 0.202939
\(232\) 0 0
\(233\) 10.0922 0.661161 0.330581 0.943778i \(-0.392755\pi\)
0.330581 + 0.943778i \(0.392755\pi\)
\(234\) 0 0
\(235\) 1.18822 0.0775113
\(236\) 0 0
\(237\) −26.4200 −1.71617
\(238\) 0 0
\(239\) −19.6127 −1.26864 −0.634321 0.773070i \(-0.718720\pi\)
−0.634321 + 0.773070i \(0.718720\pi\)
\(240\) 0 0
\(241\) 5.51320 0.355137 0.177568 0.984108i \(-0.443177\pi\)
0.177568 + 0.984108i \(0.443177\pi\)
\(242\) 0 0
\(243\) −10.3179 −0.661893
\(244\) 0 0
\(245\) −0.239305 −0.0152886
\(246\) 0 0
\(247\) 6.06183 0.385705
\(248\) 0 0
\(249\) −7.74813 −0.491018
\(250\) 0 0
\(251\) 13.2459 0.836072 0.418036 0.908430i \(-0.362719\pi\)
0.418036 + 0.908430i \(0.362719\pi\)
\(252\) 0 0
\(253\) 0.585598 0.0368162
\(254\) 0 0
\(255\) 2.77582 0.173829
\(256\) 0 0
\(257\) 30.2753 1.88852 0.944262 0.329196i \(-0.106778\pi\)
0.944262 + 0.329196i \(0.106778\pi\)
\(258\) 0 0
\(259\) 3.95055 0.245475
\(260\) 0 0
\(261\) −52.9649 −3.27845
\(262\) 0 0
\(263\) 0.123655 0.00762488 0.00381244 0.999993i \(-0.498786\pi\)
0.00381244 + 0.999993i \(0.498786\pi\)
\(264\) 0 0
\(265\) −2.33391 −0.143371
\(266\) 0 0
\(267\) 18.1765 1.11238
\(268\) 0 0
\(269\) 11.0766 0.675352 0.337676 0.941262i \(-0.390359\pi\)
0.337676 + 0.941262i \(0.390359\pi\)
\(270\) 0 0
\(271\) 22.5014 1.36686 0.683432 0.730014i \(-0.260487\pi\)
0.683432 + 0.730014i \(0.260487\pi\)
\(272\) 0 0
\(273\) 3.08441 0.186677
\(274\) 0 0
\(275\) 4.94273 0.298058
\(276\) 0 0
\(277\) −2.57386 −0.154648 −0.0773241 0.997006i \(-0.524638\pi\)
−0.0773241 + 0.997006i \(0.524638\pi\)
\(278\) 0 0
\(279\) 71.2863 4.26780
\(280\) 0 0
\(281\) −5.59178 −0.333578 −0.166789 0.985993i \(-0.553340\pi\)
−0.166789 + 0.985993i \(0.553340\pi\)
\(282\) 0 0
\(283\) 21.0842 1.25333 0.626664 0.779290i \(-0.284420\pi\)
0.626664 + 0.779290i \(0.284420\pi\)
\(284\) 0 0
\(285\) −4.47432 −0.265036
\(286\) 0 0
\(287\) 12.3960 0.731714
\(288\) 0 0
\(289\) −2.85717 −0.168069
\(290\) 0 0
\(291\) −2.34155 −0.137264
\(292\) 0 0
\(293\) 14.8727 0.868870 0.434435 0.900703i \(-0.356948\pi\)
0.434435 + 0.900703i \(0.356948\pi\)
\(294\) 0 0
\(295\) 1.70407 0.0992148
\(296\) 0 0
\(297\) 10.8373 0.628843
\(298\) 0 0
\(299\) 0.585598 0.0338660
\(300\) 0 0
\(301\) −9.90931 −0.571163
\(302\) 0 0
\(303\) 55.3533 3.17997
\(304\) 0 0
\(305\) −0.874351 −0.0500652
\(306\) 0 0
\(307\) 0.156067 0.00890724 0.00445362 0.999990i \(-0.498582\pi\)
0.00445362 + 0.999990i \(0.498582\pi\)
\(308\) 0 0
\(309\) 53.4308 3.03957
\(310\) 0 0
\(311\) −14.5146 −0.823049 −0.411525 0.911399i \(-0.635004\pi\)
−0.411525 + 0.911399i \(0.635004\pi\)
\(312\) 0 0
\(313\) 3.33890 0.188726 0.0943628 0.995538i \(-0.469919\pi\)
0.0943628 + 0.995538i \(0.469919\pi\)
\(314\) 0 0
\(315\) −1.55873 −0.0878245
\(316\) 0 0
\(317\) 9.19653 0.516528 0.258264 0.966074i \(-0.416850\pi\)
0.258264 + 0.966074i \(0.416850\pi\)
\(318\) 0 0
\(319\) 8.13147 0.455275
\(320\) 0 0
\(321\) 25.3760 1.41635
\(322\) 0 0
\(323\) −22.7967 −1.26844
\(324\) 0 0
\(325\) 4.94273 0.274173
\(326\) 0 0
\(327\) 51.4732 2.84648
\(328\) 0 0
\(329\) −4.96531 −0.273747
\(330\) 0 0
\(331\) −3.63695 −0.199905 −0.0999525 0.994992i \(-0.531869\pi\)
−0.0999525 + 0.994992i \(0.531869\pi\)
\(332\) 0 0
\(333\) 25.7322 1.41012
\(334\) 0 0
\(335\) −2.21455 −0.120994
\(336\) 0 0
\(337\) −23.2482 −1.26641 −0.633205 0.773984i \(-0.718261\pi\)
−0.633205 + 0.773984i \(0.718261\pi\)
\(338\) 0 0
\(339\) −58.6093 −3.18322
\(340\) 0 0
\(341\) −10.9443 −0.592666
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −0.432239 −0.0232709
\(346\) 0 0
\(347\) 26.7052 1.43361 0.716806 0.697272i \(-0.245603\pi\)
0.716806 + 0.697272i \(0.245603\pi\)
\(348\) 0 0
\(349\) −18.0921 −0.968448 −0.484224 0.874944i \(-0.660898\pi\)
−0.484224 + 0.874944i \(0.660898\pi\)
\(350\) 0 0
\(351\) 10.8373 0.578451
\(352\) 0 0
\(353\) 8.64743 0.460256 0.230128 0.973160i \(-0.426086\pi\)
0.230128 + 0.973160i \(0.426086\pi\)
\(354\) 0 0
\(355\) 0.371141 0.0196981
\(356\) 0 0
\(357\) −11.5995 −0.613911
\(358\) 0 0
\(359\) 1.58100 0.0834421 0.0417211 0.999129i \(-0.486716\pi\)
0.0417211 + 0.999129i \(0.486716\pi\)
\(360\) 0 0
\(361\) 17.7458 0.933987
\(362\) 0 0
\(363\) −3.08441 −0.161889
\(364\) 0 0
\(365\) −0.270400 −0.0141534
\(366\) 0 0
\(367\) 10.3396 0.539722 0.269861 0.962899i \(-0.413022\pi\)
0.269861 + 0.962899i \(0.413022\pi\)
\(368\) 0 0
\(369\) 80.7423 4.20328
\(370\) 0 0
\(371\) 9.75288 0.506344
\(372\) 0 0
\(373\) −2.41790 −0.125194 −0.0625970 0.998039i \(-0.519938\pi\)
−0.0625970 + 0.998039i \(0.519938\pi\)
\(374\) 0 0
\(375\) −7.33888 −0.378978
\(376\) 0 0
\(377\) 8.13147 0.418792
\(378\) 0 0
\(379\) 11.1875 0.574663 0.287332 0.957831i \(-0.407232\pi\)
0.287332 + 0.957831i \(0.407232\pi\)
\(380\) 0 0
\(381\) 52.6324 2.69644
\(382\) 0 0
\(383\) 11.8116 0.603546 0.301773 0.953380i \(-0.402422\pi\)
0.301773 + 0.953380i \(0.402422\pi\)
\(384\) 0 0
\(385\) 0.239305 0.0121961
\(386\) 0 0
\(387\) −64.5450 −3.28101
\(388\) 0 0
\(389\) −13.4022 −0.679519 −0.339759 0.940512i \(-0.610346\pi\)
−0.339759 + 0.940512i \(0.610346\pi\)
\(390\) 0 0
\(391\) −2.20226 −0.111373
\(392\) 0 0
\(393\) −2.83699 −0.143107
\(394\) 0 0
\(395\) −2.04981 −0.103137
\(396\) 0 0
\(397\) 35.3488 1.77410 0.887052 0.461670i \(-0.152750\pi\)
0.887052 + 0.461670i \(0.152750\pi\)
\(398\) 0 0
\(399\) 18.6971 0.936028
\(400\) 0 0
\(401\) −15.8356 −0.790790 −0.395395 0.918511i \(-0.629392\pi\)
−0.395395 + 0.918511i \(0.629392\pi\)
\(402\) 0 0
\(403\) −10.9443 −0.545173
\(404\) 0 0
\(405\) −3.32296 −0.165119
\(406\) 0 0
\(407\) −3.95055 −0.195822
\(408\) 0 0
\(409\) 9.58053 0.473727 0.236863 0.971543i \(-0.423881\pi\)
0.236863 + 0.971543i \(0.423881\pi\)
\(410\) 0 0
\(411\) 52.6746 2.59825
\(412\) 0 0
\(413\) −7.12091 −0.350397
\(414\) 0 0
\(415\) −0.601142 −0.0295089
\(416\) 0 0
\(417\) −32.9788 −1.61498
\(418\) 0 0
\(419\) 25.2866 1.23533 0.617665 0.786442i \(-0.288079\pi\)
0.617665 + 0.786442i \(0.288079\pi\)
\(420\) 0 0
\(421\) 3.85091 0.187682 0.0938409 0.995587i \(-0.470085\pi\)
0.0938409 + 0.995587i \(0.470085\pi\)
\(422\) 0 0
\(423\) −32.3419 −1.57252
\(424\) 0 0
\(425\) −18.5881 −0.901656
\(426\) 0 0
\(427\) 3.65371 0.176815
\(428\) 0 0
\(429\) −3.08441 −0.148917
\(430\) 0 0
\(431\) 4.80461 0.231430 0.115715 0.993282i \(-0.463084\pi\)
0.115715 + 0.993282i \(0.463084\pi\)
\(432\) 0 0
\(433\) 40.7174 1.95675 0.978376 0.206835i \(-0.0663164\pi\)
0.978376 + 0.206835i \(0.0663164\pi\)
\(434\) 0 0
\(435\) −6.00196 −0.287772
\(436\) 0 0
\(437\) 3.54979 0.169810
\(438\) 0 0
\(439\) −11.3669 −0.542513 −0.271257 0.962507i \(-0.587439\pi\)
−0.271257 + 0.962507i \(0.587439\pi\)
\(440\) 0 0
\(441\) 6.51357 0.310170
\(442\) 0 0
\(443\) −17.6240 −0.837342 −0.418671 0.908138i \(-0.637504\pi\)
−0.418671 + 0.908138i \(0.637504\pi\)
\(444\) 0 0
\(445\) 1.41023 0.0668512
\(446\) 0 0
\(447\) −36.2627 −1.71517
\(448\) 0 0
\(449\) 5.97663 0.282055 0.141027 0.990006i \(-0.454959\pi\)
0.141027 + 0.990006i \(0.454959\pi\)
\(450\) 0 0
\(451\) −12.3960 −0.583705
\(452\) 0 0
\(453\) 48.8137 2.29347
\(454\) 0 0
\(455\) 0.239305 0.0112188
\(456\) 0 0
\(457\) 1.75372 0.0820355 0.0410177 0.999158i \(-0.486940\pi\)
0.0410177 + 0.999158i \(0.486940\pi\)
\(458\) 0 0
\(459\) −40.7557 −1.90231
\(460\) 0 0
\(461\) 35.6034 1.65822 0.829109 0.559088i \(-0.188848\pi\)
0.829109 + 0.559088i \(0.188848\pi\)
\(462\) 0 0
\(463\) 13.1131 0.609417 0.304708 0.952446i \(-0.401441\pi\)
0.304708 + 0.952446i \(0.401441\pi\)
\(464\) 0 0
\(465\) 8.07813 0.374614
\(466\) 0 0
\(467\) 32.7788 1.51682 0.758411 0.651776i \(-0.225976\pi\)
0.758411 + 0.651776i \(0.225976\pi\)
\(468\) 0 0
\(469\) 9.25407 0.427313
\(470\) 0 0
\(471\) −71.1135 −3.27674
\(472\) 0 0
\(473\) 9.90931 0.455631
\(474\) 0 0
\(475\) 29.9620 1.37475
\(476\) 0 0
\(477\) 63.5260 2.90866
\(478\) 0 0
\(479\) 4.80860 0.219711 0.109855 0.993948i \(-0.464961\pi\)
0.109855 + 0.993948i \(0.464961\pi\)
\(480\) 0 0
\(481\) −3.95055 −0.180130
\(482\) 0 0
\(483\) 1.80622 0.0821860
\(484\) 0 0
\(485\) −0.181670 −0.00824922
\(486\) 0 0
\(487\) −18.1641 −0.823093 −0.411546 0.911389i \(-0.635011\pi\)
−0.411546 + 0.911389i \(0.635011\pi\)
\(488\) 0 0
\(489\) −45.9176 −2.07647
\(490\) 0 0
\(491\) 23.4791 1.05960 0.529799 0.848124i \(-0.322268\pi\)
0.529799 + 0.848124i \(0.322268\pi\)
\(492\) 0 0
\(493\) −30.5800 −1.37725
\(494\) 0 0
\(495\) 1.55873 0.0700597
\(496\) 0 0
\(497\) −1.55091 −0.0695679
\(498\) 0 0
\(499\) −12.8108 −0.573492 −0.286746 0.958007i \(-0.592574\pi\)
−0.286746 + 0.958007i \(0.592574\pi\)
\(500\) 0 0
\(501\) −14.9061 −0.665955
\(502\) 0 0
\(503\) 38.8430 1.73192 0.865961 0.500112i \(-0.166708\pi\)
0.865961 + 0.500112i \(0.166708\pi\)
\(504\) 0 0
\(505\) 4.29461 0.191108
\(506\) 0 0
\(507\) −3.08441 −0.136983
\(508\) 0 0
\(509\) 18.5986 0.824369 0.412185 0.911100i \(-0.364766\pi\)
0.412185 + 0.911100i \(0.364766\pi\)
\(510\) 0 0
\(511\) 1.12994 0.0499854
\(512\) 0 0
\(513\) 65.6937 2.90045
\(514\) 0 0
\(515\) 4.14545 0.182670
\(516\) 0 0
\(517\) 4.96531 0.218374
\(518\) 0 0
\(519\) 0.622939 0.0273440
\(520\) 0 0
\(521\) −12.9859 −0.568923 −0.284461 0.958688i \(-0.591815\pi\)
−0.284461 + 0.958688i \(0.591815\pi\)
\(522\) 0 0
\(523\) −37.1971 −1.62652 −0.813258 0.581904i \(-0.802308\pi\)
−0.813258 + 0.581904i \(0.802308\pi\)
\(524\) 0 0
\(525\) 15.2454 0.665364
\(526\) 0 0
\(527\) 41.1581 1.79287
\(528\) 0 0
\(529\) −22.6571 −0.985090
\(530\) 0 0
\(531\) −46.3825 −2.01283
\(532\) 0 0
\(533\) −12.3960 −0.536931
\(534\) 0 0
\(535\) 1.96881 0.0851191
\(536\) 0 0
\(537\) 54.5431 2.35371
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 2.99343 0.128697 0.0643487 0.997927i \(-0.479503\pi\)
0.0643487 + 0.997927i \(0.479503\pi\)
\(542\) 0 0
\(543\) −56.4863 −2.42406
\(544\) 0 0
\(545\) 3.99357 0.171066
\(546\) 0 0
\(547\) −0.986469 −0.0421784 −0.0210892 0.999778i \(-0.506713\pi\)
−0.0210892 + 0.999778i \(0.506713\pi\)
\(548\) 0 0
\(549\) 23.7987 1.01570
\(550\) 0 0
\(551\) 49.2916 2.09989
\(552\) 0 0
\(553\) 8.56567 0.364249
\(554\) 0 0
\(555\) 2.91596 0.123776
\(556\) 0 0
\(557\) −27.8975 −1.18205 −0.591027 0.806652i \(-0.701277\pi\)
−0.591027 + 0.806652i \(0.701277\pi\)
\(558\) 0 0
\(559\) 9.90931 0.419119
\(560\) 0 0
\(561\) 11.5995 0.489732
\(562\) 0 0
\(563\) 26.3621 1.11103 0.555515 0.831506i \(-0.312521\pi\)
0.555515 + 0.831506i \(0.312521\pi\)
\(564\) 0 0
\(565\) −4.54723 −0.191303
\(566\) 0 0
\(567\) 13.8859 0.583152
\(568\) 0 0
\(569\) −17.0711 −0.715657 −0.357828 0.933787i \(-0.616483\pi\)
−0.357828 + 0.933787i \(0.616483\pi\)
\(570\) 0 0
\(571\) −5.90345 −0.247052 −0.123526 0.992341i \(-0.539420\pi\)
−0.123526 + 0.992341i \(0.539420\pi\)
\(572\) 0 0
\(573\) −28.0212 −1.17060
\(574\) 0 0
\(575\) 2.89446 0.120707
\(576\) 0 0
\(577\) 8.10924 0.337592 0.168796 0.985651i \(-0.446012\pi\)
0.168796 + 0.985651i \(0.446012\pi\)
\(578\) 0 0
\(579\) 75.1941 3.12496
\(580\) 0 0
\(581\) 2.51203 0.104217
\(582\) 0 0
\(583\) −9.75288 −0.403923
\(584\) 0 0
\(585\) 1.55873 0.0644456
\(586\) 0 0
\(587\) 9.75194 0.402506 0.201253 0.979539i \(-0.435499\pi\)
0.201253 + 0.979539i \(0.435499\pi\)
\(588\) 0 0
\(589\) −66.3423 −2.73359
\(590\) 0 0
\(591\) −16.6388 −0.684427
\(592\) 0 0
\(593\) −1.53386 −0.0629883 −0.0314941 0.999504i \(-0.510027\pi\)
−0.0314941 + 0.999504i \(0.510027\pi\)
\(594\) 0 0
\(595\) −0.899954 −0.0368945
\(596\) 0 0
\(597\) 1.28637 0.0526477
\(598\) 0 0
\(599\) −6.82185 −0.278733 −0.139367 0.990241i \(-0.544507\pi\)
−0.139367 + 0.990241i \(0.544507\pi\)
\(600\) 0 0
\(601\) 13.7594 0.561257 0.280628 0.959817i \(-0.409457\pi\)
0.280628 + 0.959817i \(0.409457\pi\)
\(602\) 0 0
\(603\) 60.2770 2.45467
\(604\) 0 0
\(605\) −0.239305 −0.00972914
\(606\) 0 0
\(607\) −14.6714 −0.595495 −0.297748 0.954645i \(-0.596235\pi\)
−0.297748 + 0.954645i \(0.596235\pi\)
\(608\) 0 0
\(609\) 25.0808 1.01632
\(610\) 0 0
\(611\) 4.96531 0.200875
\(612\) 0 0
\(613\) 13.3896 0.540802 0.270401 0.962748i \(-0.412844\pi\)
0.270401 + 0.962748i \(0.412844\pi\)
\(614\) 0 0
\(615\) 9.14968 0.368951
\(616\) 0 0
\(617\) 3.40984 0.137275 0.0686375 0.997642i \(-0.478135\pi\)
0.0686375 + 0.997642i \(0.478135\pi\)
\(618\) 0 0
\(619\) 0.538205 0.0216323 0.0108161 0.999942i \(-0.496557\pi\)
0.0108161 + 0.999942i \(0.496557\pi\)
\(620\) 0 0
\(621\) 6.34629 0.254668
\(622\) 0 0
\(623\) −5.89301 −0.236099
\(624\) 0 0
\(625\) 24.1443 0.965771
\(626\) 0 0
\(627\) −18.6971 −0.746692
\(628\) 0 0
\(629\) 14.8568 0.592380
\(630\) 0 0
\(631\) 26.3648 1.04957 0.524784 0.851236i \(-0.324146\pi\)
0.524784 + 0.851236i \(0.324146\pi\)
\(632\) 0 0
\(633\) −43.0674 −1.71177
\(634\) 0 0
\(635\) 4.08350 0.162049
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −10.1020 −0.399628
\(640\) 0 0
\(641\) 5.68284 0.224459 0.112229 0.993682i \(-0.464201\pi\)
0.112229 + 0.993682i \(0.464201\pi\)
\(642\) 0 0
\(643\) 40.4740 1.59614 0.798069 0.602567i \(-0.205855\pi\)
0.798069 + 0.602567i \(0.205855\pi\)
\(644\) 0 0
\(645\) −7.31421 −0.287997
\(646\) 0 0
\(647\) −49.4134 −1.94264 −0.971320 0.237776i \(-0.923582\pi\)
−0.971320 + 0.237776i \(0.923582\pi\)
\(648\) 0 0
\(649\) 7.12091 0.279520
\(650\) 0 0
\(651\) −33.7566 −1.32303
\(652\) 0 0
\(653\) 44.9446 1.75882 0.879408 0.476068i \(-0.157938\pi\)
0.879408 + 0.476068i \(0.157938\pi\)
\(654\) 0 0
\(655\) −0.220109 −0.00860038
\(656\) 0 0
\(657\) 7.35992 0.287138
\(658\) 0 0
\(659\) 8.82285 0.343689 0.171845 0.985124i \(-0.445027\pi\)
0.171845 + 0.985124i \(0.445027\pi\)
\(660\) 0 0
\(661\) −49.7308 −1.93430 −0.967152 0.254198i \(-0.918188\pi\)
−0.967152 + 0.254198i \(0.918188\pi\)
\(662\) 0 0
\(663\) 11.5995 0.450488
\(664\) 0 0
\(665\) 1.45063 0.0562529
\(666\) 0 0
\(667\) 4.76178 0.184377
\(668\) 0 0
\(669\) 44.8972 1.73582
\(670\) 0 0
\(671\) −3.65371 −0.141050
\(672\) 0 0
\(673\) 37.2949 1.43761 0.718807 0.695210i \(-0.244689\pi\)
0.718807 + 0.695210i \(0.244689\pi\)
\(674\) 0 0
\(675\) 53.5658 2.06175
\(676\) 0 0
\(677\) 10.7454 0.412979 0.206489 0.978449i \(-0.433796\pi\)
0.206489 + 0.978449i \(0.433796\pi\)
\(678\) 0 0
\(679\) 0.759157 0.0291338
\(680\) 0 0
\(681\) 80.2035 3.07340
\(682\) 0 0
\(683\) 24.3394 0.931322 0.465661 0.884963i \(-0.345817\pi\)
0.465661 + 0.884963i \(0.345817\pi\)
\(684\) 0 0
\(685\) 4.08678 0.156148
\(686\) 0 0
\(687\) 2.21665 0.0845706
\(688\) 0 0
\(689\) −9.75288 −0.371555
\(690\) 0 0
\(691\) 21.5171 0.818550 0.409275 0.912411i \(-0.365782\pi\)
0.409275 + 0.912411i \(0.365782\pi\)
\(692\) 0 0
\(693\) −6.51357 −0.247430
\(694\) 0 0
\(695\) −2.55868 −0.0970562
\(696\) 0 0
\(697\) 46.6176 1.76577
\(698\) 0 0
\(699\) −31.1284 −1.17739
\(700\) 0 0
\(701\) 32.4519 1.22569 0.612845 0.790203i \(-0.290025\pi\)
0.612845 + 0.790203i \(0.290025\pi\)
\(702\) 0 0
\(703\) −23.9476 −0.903200
\(704\) 0 0
\(705\) −3.66497 −0.138031
\(706\) 0 0
\(707\) −17.9462 −0.674935
\(708\) 0 0
\(709\) 1.75027 0.0657329 0.0328665 0.999460i \(-0.489536\pi\)
0.0328665 + 0.999460i \(0.489536\pi\)
\(710\) 0 0
\(711\) 55.7931 2.09241
\(712\) 0 0
\(713\) −6.40894 −0.240017
\(714\) 0 0
\(715\) −0.239305 −0.00894950
\(716\) 0 0
\(717\) 60.4937 2.25918
\(718\) 0 0
\(719\) 45.7365 1.70568 0.852841 0.522170i \(-0.174878\pi\)
0.852841 + 0.522170i \(0.174878\pi\)
\(720\) 0 0
\(721\) −17.3229 −0.645137
\(722\) 0 0
\(723\) −17.0050 −0.632421
\(724\) 0 0
\(725\) 40.1917 1.49268
\(726\) 0 0
\(727\) −23.4193 −0.868575 −0.434288 0.900774i \(-0.643000\pi\)
−0.434288 + 0.900774i \(0.643000\pi\)
\(728\) 0 0
\(729\) −9.83309 −0.364189
\(730\) 0 0
\(731\) −37.2659 −1.37833
\(732\) 0 0
\(733\) −45.5250 −1.68150 −0.840752 0.541420i \(-0.817887\pi\)
−0.840752 + 0.541420i \(0.817887\pi\)
\(734\) 0 0
\(735\) 0.738115 0.0272258
\(736\) 0 0
\(737\) −9.25407 −0.340878
\(738\) 0 0
\(739\) 15.2693 0.561691 0.280846 0.959753i \(-0.409385\pi\)
0.280846 + 0.959753i \(0.409385\pi\)
\(740\) 0 0
\(741\) −18.6971 −0.686857
\(742\) 0 0
\(743\) 47.2611 1.73384 0.866921 0.498445i \(-0.166095\pi\)
0.866921 + 0.498445i \(0.166095\pi\)
\(744\) 0 0
\(745\) −2.81346 −0.103077
\(746\) 0 0
\(747\) 16.3623 0.598665
\(748\) 0 0
\(749\) −8.22720 −0.300615
\(750\) 0 0
\(751\) 35.9491 1.31180 0.655901 0.754847i \(-0.272289\pi\)
0.655901 + 0.754847i \(0.272289\pi\)
\(752\) 0 0
\(753\) −40.8557 −1.48886
\(754\) 0 0
\(755\) 3.78724 0.137832
\(756\) 0 0
\(757\) 42.3951 1.54088 0.770438 0.637515i \(-0.220038\pi\)
0.770438 + 0.637515i \(0.220038\pi\)
\(758\) 0 0
\(759\) −1.80622 −0.0655618
\(760\) 0 0
\(761\) −30.1286 −1.09216 −0.546080 0.837733i \(-0.683881\pi\)
−0.546080 + 0.837733i \(0.683881\pi\)
\(762\) 0 0
\(763\) −16.6882 −0.604154
\(764\) 0 0
\(765\) −5.86191 −0.211938
\(766\) 0 0
\(767\) 7.12091 0.257121
\(768\) 0 0
\(769\) 7.67122 0.276631 0.138316 0.990388i \(-0.455831\pi\)
0.138316 + 0.990388i \(0.455831\pi\)
\(770\) 0 0
\(771\) −93.3815 −3.36305
\(772\) 0 0
\(773\) 42.6322 1.53337 0.766686 0.642022i \(-0.221904\pi\)
0.766686 + 0.642022i \(0.221904\pi\)
\(774\) 0 0
\(775\) −54.0946 −1.94314
\(776\) 0 0
\(777\) −12.1851 −0.437139
\(778\) 0 0
\(779\) −75.1425 −2.69226
\(780\) 0 0
\(781\) 1.55091 0.0554960
\(782\) 0 0
\(783\) 88.1231 3.14926
\(784\) 0 0
\(785\) −5.51738 −0.196924
\(786\) 0 0
\(787\) 33.9665 1.21077 0.605387 0.795931i \(-0.293018\pi\)
0.605387 + 0.795931i \(0.293018\pi\)
\(788\) 0 0
\(789\) −0.381402 −0.0135783
\(790\) 0 0
\(791\) 19.0018 0.675627
\(792\) 0 0
\(793\) −3.65371 −0.129747
\(794\) 0 0
\(795\) 7.19874 0.255313
\(796\) 0 0
\(797\) 25.6048 0.906969 0.453484 0.891264i \(-0.350181\pi\)
0.453484 + 0.891264i \(0.350181\pi\)
\(798\) 0 0
\(799\) −18.6730 −0.660604
\(800\) 0 0
\(801\) −38.3845 −1.35625
\(802\) 0 0
\(803\) −1.12994 −0.0398746
\(804\) 0 0
\(805\) 0.140137 0.00493917
\(806\) 0 0
\(807\) −34.1647 −1.20265
\(808\) 0 0
\(809\) −24.0188 −0.844456 −0.422228 0.906490i \(-0.638752\pi\)
−0.422228 + 0.906490i \(0.638752\pi\)
\(810\) 0 0
\(811\) 27.5291 0.966678 0.483339 0.875433i \(-0.339424\pi\)
0.483339 + 0.875433i \(0.339424\pi\)
\(812\) 0 0
\(813\) −69.4035 −2.43409
\(814\) 0 0
\(815\) −3.56254 −0.124790
\(816\) 0 0
\(817\) 60.0685 2.10153
\(818\) 0 0
\(819\) −6.51357 −0.227603
\(820\) 0 0
\(821\) −46.9786 −1.63957 −0.819783 0.572675i \(-0.805906\pi\)
−0.819783 + 0.572675i \(0.805906\pi\)
\(822\) 0 0
\(823\) 1.81016 0.0630982 0.0315491 0.999502i \(-0.489956\pi\)
0.0315491 + 0.999502i \(0.489956\pi\)
\(824\) 0 0
\(825\) −15.2454 −0.530777
\(826\) 0 0
\(827\) 0.390795 0.0135893 0.00679464 0.999977i \(-0.497837\pi\)
0.00679464 + 0.999977i \(0.497837\pi\)
\(828\) 0 0
\(829\) −36.8716 −1.28060 −0.640302 0.768123i \(-0.721191\pi\)
−0.640302 + 0.768123i \(0.721191\pi\)
\(830\) 0 0
\(831\) 7.93883 0.275395
\(832\) 0 0
\(833\) 3.76069 0.130300
\(834\) 0 0
\(835\) −1.15650 −0.0400222
\(836\) 0 0
\(837\) −118.606 −4.09963
\(838\) 0 0
\(839\) 7.46618 0.257761 0.128881 0.991660i \(-0.458862\pi\)
0.128881 + 0.991660i \(0.458862\pi\)
\(840\) 0 0
\(841\) 37.1209 1.28003
\(842\) 0 0
\(843\) 17.2473 0.594030
\(844\) 0 0
\(845\) −0.239305 −0.00823235
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −65.0323 −2.23190
\(850\) 0 0
\(851\) −2.31344 −0.0793036
\(852\) 0 0
\(853\) −57.5071 −1.96900 −0.984502 0.175373i \(-0.943887\pi\)
−0.984502 + 0.175373i \(0.943887\pi\)
\(854\) 0 0
\(855\) 9.44876 0.323141
\(856\) 0 0
\(857\) 57.5651 1.96639 0.983193 0.182571i \(-0.0584420\pi\)
0.983193 + 0.182571i \(0.0584420\pi\)
\(858\) 0 0
\(859\) −29.6181 −1.01056 −0.505279 0.862956i \(-0.668610\pi\)
−0.505279 + 0.862956i \(0.668610\pi\)
\(860\) 0 0
\(861\) −38.2344 −1.30302
\(862\) 0 0
\(863\) 23.9466 0.815153 0.407576 0.913171i \(-0.366374\pi\)
0.407576 + 0.913171i \(0.366374\pi\)
\(864\) 0 0
\(865\) 0.0483310 0.00164330
\(866\) 0 0
\(867\) 8.81269 0.299295
\(868\) 0 0
\(869\) −8.56567 −0.290571
\(870\) 0 0
\(871\) −9.25407 −0.313562
\(872\) 0 0
\(873\) 4.94482 0.167357
\(874\) 0 0
\(875\) 2.37935 0.0804366
\(876\) 0 0
\(877\) −15.2847 −0.516127 −0.258064 0.966128i \(-0.583084\pi\)
−0.258064 + 0.966128i \(0.583084\pi\)
\(878\) 0 0
\(879\) −45.8734 −1.54727
\(880\) 0 0
\(881\) −39.5337 −1.33192 −0.665962 0.745986i \(-0.731979\pi\)
−0.665962 + 0.745986i \(0.731979\pi\)
\(882\) 0 0
\(883\) −27.9627 −0.941018 −0.470509 0.882395i \(-0.655930\pi\)
−0.470509 + 0.882395i \(0.655930\pi\)
\(884\) 0 0
\(885\) −5.25604 −0.176680
\(886\) 0 0
\(887\) 47.9469 1.60990 0.804950 0.593343i \(-0.202192\pi\)
0.804950 + 0.593343i \(0.202192\pi\)
\(888\) 0 0
\(889\) −17.0640 −0.572308
\(890\) 0 0
\(891\) −13.8859 −0.465195
\(892\) 0 0
\(893\) 30.0989 1.00722
\(894\) 0 0
\(895\) 4.23175 0.141452
\(896\) 0 0
\(897\) −1.80622 −0.0603080
\(898\) 0 0
\(899\) −88.9931 −2.96808
\(900\) 0 0
\(901\) 36.6776 1.22191
\(902\) 0 0
\(903\) 30.5644 1.01712
\(904\) 0 0
\(905\) −4.38252 −0.145680
\(906\) 0 0
\(907\) −30.7725 −1.02178 −0.510892 0.859645i \(-0.670685\pi\)
−0.510892 + 0.859645i \(0.670685\pi\)
\(908\) 0 0
\(909\) −116.894 −3.87712
\(910\) 0 0
\(911\) 3.13852 0.103984 0.0519919 0.998648i \(-0.483443\pi\)
0.0519919 + 0.998648i \(0.483443\pi\)
\(912\) 0 0
\(913\) −2.51203 −0.0831361
\(914\) 0 0
\(915\) 2.69685 0.0891553
\(916\) 0 0
\(917\) 0.919785 0.0303740
\(918\) 0 0
\(919\) −24.8000 −0.818078 −0.409039 0.912517i \(-0.634136\pi\)
−0.409039 + 0.912517i \(0.634136\pi\)
\(920\) 0 0
\(921\) −0.481376 −0.0158619
\(922\) 0 0
\(923\) 1.55091 0.0510489
\(924\) 0 0
\(925\) −19.5265 −0.642028
\(926\) 0 0
\(927\) −112.834 −3.70595
\(928\) 0 0
\(929\) 0.823768 0.0270270 0.0135135 0.999909i \(-0.495698\pi\)
0.0135135 + 0.999909i \(0.495698\pi\)
\(930\) 0 0
\(931\) −6.06183 −0.198668
\(932\) 0 0
\(933\) 44.7690 1.46567
\(934\) 0 0
\(935\) 0.899954 0.0294316
\(936\) 0 0
\(937\) 18.0829 0.590742 0.295371 0.955383i \(-0.404557\pi\)
0.295371 + 0.955383i \(0.404557\pi\)
\(938\) 0 0
\(939\) −10.2985 −0.336079
\(940\) 0 0
\(941\) 44.3134 1.44458 0.722288 0.691592i \(-0.243090\pi\)
0.722288 + 0.691592i \(0.243090\pi\)
\(942\) 0 0
\(943\) −7.25908 −0.236388
\(944\) 0 0
\(945\) 2.59342 0.0843639
\(946\) 0 0
\(947\) −26.3566 −0.856475 −0.428238 0.903666i \(-0.640865\pi\)
−0.428238 + 0.903666i \(0.640865\pi\)
\(948\) 0 0
\(949\) −1.12994 −0.0366793
\(950\) 0 0
\(951\) −28.3658 −0.919825
\(952\) 0 0
\(953\) 53.0224 1.71756 0.858782 0.512342i \(-0.171222\pi\)
0.858782 + 0.512342i \(0.171222\pi\)
\(954\) 0 0
\(955\) −2.17403 −0.0703501
\(956\) 0 0
\(957\) −25.0808 −0.810746
\(958\) 0 0
\(959\) −17.0777 −0.551468
\(960\) 0 0
\(961\) 88.7771 2.86378
\(962\) 0 0
\(963\) −53.5884 −1.72686
\(964\) 0 0
\(965\) 5.83397 0.187802
\(966\) 0 0
\(967\) 42.1398 1.35512 0.677562 0.735466i \(-0.263037\pi\)
0.677562 + 0.735466i \(0.263037\pi\)
\(968\) 0 0
\(969\) 70.3143 2.25882
\(970\) 0 0
\(971\) 36.6528 1.17624 0.588122 0.808772i \(-0.299867\pi\)
0.588122 + 0.808772i \(0.299867\pi\)
\(972\) 0 0
\(973\) 10.6921 0.342773
\(974\) 0 0
\(975\) −15.2454 −0.488244
\(976\) 0 0
\(977\) 19.7408 0.631563 0.315782 0.948832i \(-0.397733\pi\)
0.315782 + 0.948832i \(0.397733\pi\)
\(978\) 0 0
\(979\) 5.89301 0.188341
\(980\) 0 0
\(981\) −108.700 −3.47052
\(982\) 0 0
\(983\) −1.49645 −0.0477292 −0.0238646 0.999715i \(-0.507597\pi\)
−0.0238646 + 0.999715i \(0.507597\pi\)
\(984\) 0 0
\(985\) −1.29093 −0.0411323
\(986\) 0 0
\(987\) 15.3151 0.487483
\(988\) 0 0
\(989\) 5.80287 0.184521
\(990\) 0 0
\(991\) 49.3189 1.56667 0.783333 0.621602i \(-0.213518\pi\)
0.783333 + 0.621602i \(0.213518\pi\)
\(992\) 0 0
\(993\) 11.2178 0.355987
\(994\) 0 0
\(995\) 0.0998037 0.00316399
\(996\) 0 0
\(997\) −26.4510 −0.837713 −0.418857 0.908052i \(-0.637569\pi\)
−0.418857 + 0.908052i \(0.637569\pi\)
\(998\) 0 0
\(999\) −42.8133 −1.35455
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 \(a_p\))