Properties

Label 8008.2.a.n.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.763644\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.763644 q^{3} +1.55421 q^{5} -1.00000 q^{7} -2.41685 q^{9} +O(q^{10})\) \(q+0.763644 q^{3} +1.55421 q^{5} -1.00000 q^{7} -2.41685 q^{9} +1.00000 q^{11} -1.00000 q^{13} +1.18686 q^{15} +3.61102 q^{17} +1.02809 q^{19} -0.763644 q^{21} +4.55145 q^{23} -2.58443 q^{25} -4.13654 q^{27} -4.78553 q^{29} +2.84863 q^{31} +0.763644 q^{33} -1.55421 q^{35} +1.27046 q^{37} -0.763644 q^{39} +3.11068 q^{41} +8.35432 q^{43} -3.75629 q^{45} +9.30529 q^{47} +1.00000 q^{49} +2.75753 q^{51} +1.24483 q^{53} +1.55421 q^{55} +0.785092 q^{57} -2.95515 q^{59} -6.44819 q^{61} +2.41685 q^{63} -1.55421 q^{65} -6.51850 q^{67} +3.47569 q^{69} -10.4003 q^{71} +6.95921 q^{73} -1.97358 q^{75} -1.00000 q^{77} +2.23287 q^{79} +4.09170 q^{81} -10.5278 q^{83} +5.61229 q^{85} -3.65444 q^{87} +12.4084 q^{89} +1.00000 q^{91} +2.17534 q^{93} +1.59786 q^{95} +1.06194 q^{97} -2.41685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) 0.763644 0.440890 0.220445 0.975399i \(-0.429249\pi\)
0.220445 + 0.975399i \(0.429249\pi\)
\(4\) 0 0
\(5\) 1.55421 0.695064 0.347532 0.937668i \(-0.387020\pi\)
0.347532 + 0.937668i \(0.387020\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.41685 −0.805616
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.18686 0.306447
\(16\) 0 0
\(17\) 3.61102 0.875801 0.437900 0.899024i \(-0.355722\pi\)
0.437900 + 0.899024i \(0.355722\pi\)
\(18\) 0 0
\(19\) 1.02809 0.235859 0.117930 0.993022i \(-0.462374\pi\)
0.117930 + 0.993022i \(0.462374\pi\)
\(20\) 0 0
\(21\) −0.763644 −0.166641
\(22\) 0 0
\(23\) 4.55145 0.949043 0.474522 0.880244i \(-0.342621\pi\)
0.474522 + 0.880244i \(0.342621\pi\)
\(24\) 0 0
\(25\) −2.58443 −0.516885
\(26\) 0 0
\(27\) −4.13654 −0.796078
\(28\) 0 0
\(29\) −4.78553 −0.888651 −0.444325 0.895865i \(-0.646557\pi\)
−0.444325 + 0.895865i \(0.646557\pi\)
\(30\) 0 0
\(31\) 2.84863 0.511630 0.255815 0.966726i \(-0.417656\pi\)
0.255815 + 0.966726i \(0.417656\pi\)
\(32\) 0 0
\(33\) 0.763644 0.132933
\(34\) 0 0
\(35\) −1.55421 −0.262710
\(36\) 0 0
\(37\) 1.27046 0.208862 0.104431 0.994532i \(-0.466698\pi\)
0.104431 + 0.994532i \(0.466698\pi\)
\(38\) 0 0
\(39\) −0.763644 −0.122281
\(40\) 0 0
\(41\) 3.11068 0.485806 0.242903 0.970051i \(-0.421900\pi\)
0.242903 + 0.970051i \(0.421900\pi\)
\(42\) 0 0
\(43\) 8.35432 1.27402 0.637011 0.770855i \(-0.280171\pi\)
0.637011 + 0.770855i \(0.280171\pi\)
\(44\) 0 0
\(45\) −3.75629 −0.559955
\(46\) 0 0
\(47\) 9.30529 1.35732 0.678658 0.734455i \(-0.262562\pi\)
0.678658 + 0.734455i \(0.262562\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 2.75753 0.386132
\(52\) 0 0
\(53\) 1.24483 0.170990 0.0854950 0.996339i \(-0.472753\pi\)
0.0854950 + 0.996339i \(0.472753\pi\)
\(54\) 0 0
\(55\) 1.55421 0.209570
\(56\) 0 0
\(57\) 0.785092 0.103988
\(58\) 0 0
\(59\) −2.95515 −0.384728 −0.192364 0.981324i \(-0.561615\pi\)
−0.192364 + 0.981324i \(0.561615\pi\)
\(60\) 0 0
\(61\) −6.44819 −0.825606 −0.412803 0.910820i \(-0.635450\pi\)
−0.412803 + 0.910820i \(0.635450\pi\)
\(62\) 0 0
\(63\) 2.41685 0.304494
\(64\) 0 0
\(65\) −1.55421 −0.192776
\(66\) 0 0
\(67\) −6.51850 −0.796362 −0.398181 0.917307i \(-0.630358\pi\)
−0.398181 + 0.917307i \(0.630358\pi\)
\(68\) 0 0
\(69\) 3.47569 0.418424
\(70\) 0 0
\(71\) −10.4003 −1.23429 −0.617146 0.786849i \(-0.711711\pi\)
−0.617146 + 0.786849i \(0.711711\pi\)
\(72\) 0 0
\(73\) 6.95921 0.814514 0.407257 0.913314i \(-0.366485\pi\)
0.407257 + 0.913314i \(0.366485\pi\)
\(74\) 0 0
\(75\) −1.97358 −0.227890
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 2.23287 0.251217 0.125609 0.992080i \(-0.459912\pi\)
0.125609 + 0.992080i \(0.459912\pi\)
\(80\) 0 0
\(81\) 4.09170 0.454633
\(82\) 0 0
\(83\) −10.5278 −1.15558 −0.577788 0.816187i \(-0.696084\pi\)
−0.577788 + 0.816187i \(0.696084\pi\)
\(84\) 0 0
\(85\) 5.61229 0.608738
\(86\) 0 0
\(87\) −3.65444 −0.391797
\(88\) 0 0
\(89\) 12.4084 1.31529 0.657646 0.753327i \(-0.271552\pi\)
0.657646 + 0.753327i \(0.271552\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 2.17534 0.225572
\(94\) 0 0
\(95\) 1.59786 0.163937
\(96\) 0 0
\(97\) 1.06194 0.107824 0.0539120 0.998546i \(-0.482831\pi\)
0.0539120 + 0.998546i \(0.482831\pi\)
\(98\) 0 0
\(99\) −2.41685 −0.242902
\(100\) 0 0
\(101\) 9.07986 0.903480 0.451740 0.892150i \(-0.350804\pi\)
0.451740 + 0.892150i \(0.350804\pi\)
\(102\) 0 0
\(103\) 14.1645 1.39567 0.697837 0.716257i \(-0.254146\pi\)
0.697837 + 0.716257i \(0.254146\pi\)
\(104\) 0 0
\(105\) −1.18686 −0.115826
\(106\) 0 0
\(107\) 0.191694 0.0185317 0.00926586 0.999957i \(-0.497051\pi\)
0.00926586 + 0.999957i \(0.497051\pi\)
\(108\) 0 0
\(109\) 15.3709 1.47226 0.736131 0.676839i \(-0.236651\pi\)
0.736131 + 0.676839i \(0.236651\pi\)
\(110\) 0 0
\(111\) 0.970177 0.0920851
\(112\) 0 0
\(113\) 16.4325 1.54584 0.772921 0.634503i \(-0.218795\pi\)
0.772921 + 0.634503i \(0.218795\pi\)
\(114\) 0 0
\(115\) 7.07392 0.659646
\(116\) 0 0
\(117\) 2.41685 0.223438
\(118\) 0 0
\(119\) −3.61102 −0.331022
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 2.37545 0.214187
\(124\) 0 0
\(125\) −11.7878 −1.05433
\(126\) 0 0
\(127\) −4.82092 −0.427788 −0.213894 0.976857i \(-0.568615\pi\)
−0.213894 + 0.976857i \(0.568615\pi\)
\(128\) 0 0
\(129\) 6.37973 0.561704
\(130\) 0 0
\(131\) 3.95281 0.345358 0.172679 0.984978i \(-0.444758\pi\)
0.172679 + 0.984978i \(0.444758\pi\)
\(132\) 0 0
\(133\) −1.02809 −0.0891464
\(134\) 0 0
\(135\) −6.42906 −0.553326
\(136\) 0 0
\(137\) −13.4629 −1.15021 −0.575105 0.818080i \(-0.695039\pi\)
−0.575105 + 0.818080i \(0.695039\pi\)
\(138\) 0 0
\(139\) 8.51502 0.722234 0.361117 0.932520i \(-0.382395\pi\)
0.361117 + 0.932520i \(0.382395\pi\)
\(140\) 0 0
\(141\) 7.10593 0.598427
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −7.43773 −0.617669
\(146\) 0 0
\(147\) 0.763644 0.0629843
\(148\) 0 0
\(149\) 12.1535 0.995653 0.497826 0.867277i \(-0.334132\pi\)
0.497826 + 0.867277i \(0.334132\pi\)
\(150\) 0 0
\(151\) −8.43997 −0.686835 −0.343417 0.939183i \(-0.611585\pi\)
−0.343417 + 0.939183i \(0.611585\pi\)
\(152\) 0 0
\(153\) −8.72728 −0.705559
\(154\) 0 0
\(155\) 4.42738 0.355616
\(156\) 0 0
\(157\) −11.7574 −0.938346 −0.469173 0.883106i \(-0.655448\pi\)
−0.469173 + 0.883106i \(0.655448\pi\)
\(158\) 0 0
\(159\) 0.950604 0.0753878
\(160\) 0 0
\(161\) −4.55145 −0.358705
\(162\) 0 0
\(163\) −12.4942 −0.978620 −0.489310 0.872110i \(-0.662751\pi\)
−0.489310 + 0.872110i \(0.662751\pi\)
\(164\) 0 0
\(165\) 1.18686 0.0923973
\(166\) 0 0
\(167\) 24.4830 1.89455 0.947277 0.320415i \(-0.103822\pi\)
0.947277 + 0.320415i \(0.103822\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.48473 −0.190012
\(172\) 0 0
\(173\) −19.8952 −1.51261 −0.756303 0.654221i \(-0.772997\pi\)
−0.756303 + 0.654221i \(0.772997\pi\)
\(174\) 0 0
\(175\) 2.58443 0.195364
\(176\) 0 0
\(177\) −2.25668 −0.169623
\(178\) 0 0
\(179\) −8.89979 −0.665202 −0.332601 0.943068i \(-0.607926\pi\)
−0.332601 + 0.943068i \(0.607926\pi\)
\(180\) 0 0
\(181\) 18.7538 1.39396 0.696980 0.717090i \(-0.254526\pi\)
0.696980 + 0.717090i \(0.254526\pi\)
\(182\) 0 0
\(183\) −4.92412 −0.364002
\(184\) 0 0
\(185\) 1.97456 0.145172
\(186\) 0 0
\(187\) 3.61102 0.264064
\(188\) 0 0
\(189\) 4.13654 0.300889
\(190\) 0 0
\(191\) −12.1866 −0.881794 −0.440897 0.897558i \(-0.645340\pi\)
−0.440897 + 0.897558i \(0.645340\pi\)
\(192\) 0 0
\(193\) 14.7549 1.06208 0.531042 0.847346i \(-0.321801\pi\)
0.531042 + 0.847346i \(0.321801\pi\)
\(194\) 0 0
\(195\) −1.18686 −0.0849931
\(196\) 0 0
\(197\) 11.1653 0.795496 0.397748 0.917495i \(-0.369792\pi\)
0.397748 + 0.917495i \(0.369792\pi\)
\(198\) 0 0
\(199\) 26.7758 1.89808 0.949042 0.315149i \(-0.102055\pi\)
0.949042 + 0.315149i \(0.102055\pi\)
\(200\) 0 0
\(201\) −4.97782 −0.351108
\(202\) 0 0
\(203\) 4.78553 0.335878
\(204\) 0 0
\(205\) 4.83465 0.337666
\(206\) 0 0
\(207\) −11.0002 −0.764565
\(208\) 0 0
\(209\) 1.02809 0.0711142
\(210\) 0 0
\(211\) 20.7307 1.42716 0.713582 0.700572i \(-0.247072\pi\)
0.713582 + 0.700572i \(0.247072\pi\)
\(212\) 0 0
\(213\) −7.94214 −0.544187
\(214\) 0 0
\(215\) 12.9844 0.885528
\(216\) 0 0
\(217\) −2.84863 −0.193378
\(218\) 0 0
\(219\) 5.31436 0.359111
\(220\) 0 0
\(221\) −3.61102 −0.242903
\(222\) 0 0
\(223\) −5.70228 −0.381853 −0.190926 0.981604i \(-0.561149\pi\)
−0.190926 + 0.981604i \(0.561149\pi\)
\(224\) 0 0
\(225\) 6.24617 0.416411
\(226\) 0 0
\(227\) −9.36092 −0.621306 −0.310653 0.950523i \(-0.600548\pi\)
−0.310653 + 0.950523i \(0.600548\pi\)
\(228\) 0 0
\(229\) 21.4426 1.41697 0.708483 0.705728i \(-0.249380\pi\)
0.708483 + 0.705728i \(0.249380\pi\)
\(230\) 0 0
\(231\) −0.763644 −0.0502441
\(232\) 0 0
\(233\) 19.6958 1.29031 0.645157 0.764050i \(-0.276792\pi\)
0.645157 + 0.764050i \(0.276792\pi\)
\(234\) 0 0
\(235\) 14.4624 0.943422
\(236\) 0 0
\(237\) 1.70511 0.110759
\(238\) 0 0
\(239\) −1.59704 −0.103304 −0.0516520 0.998665i \(-0.516449\pi\)
−0.0516520 + 0.998665i \(0.516449\pi\)
\(240\) 0 0
\(241\) 19.0106 1.22458 0.612290 0.790634i \(-0.290249\pi\)
0.612290 + 0.790634i \(0.290249\pi\)
\(242\) 0 0
\(243\) 15.5342 0.996521
\(244\) 0 0
\(245\) 1.55421 0.0992949
\(246\) 0 0
\(247\) −1.02809 −0.0654155
\(248\) 0 0
\(249\) −8.03949 −0.509482
\(250\) 0 0
\(251\) 5.42958 0.342712 0.171356 0.985209i \(-0.445185\pi\)
0.171356 + 0.985209i \(0.445185\pi\)
\(252\) 0 0
\(253\) 4.55145 0.286147
\(254\) 0 0
\(255\) 4.28579 0.268387
\(256\) 0 0
\(257\) 14.7935 0.922791 0.461396 0.887194i \(-0.347349\pi\)
0.461396 + 0.887194i \(0.347349\pi\)
\(258\) 0 0
\(259\) −1.27046 −0.0789424
\(260\) 0 0
\(261\) 11.5659 0.715911
\(262\) 0 0
\(263\) −7.19227 −0.443494 −0.221747 0.975104i \(-0.571176\pi\)
−0.221747 + 0.975104i \(0.571176\pi\)
\(264\) 0 0
\(265\) 1.93472 0.118849
\(266\) 0 0
\(267\) 9.47563 0.579899
\(268\) 0 0
\(269\) 23.6556 1.44231 0.721155 0.692774i \(-0.243612\pi\)
0.721155 + 0.692774i \(0.243612\pi\)
\(270\) 0 0
\(271\) −16.2942 −0.989805 −0.494902 0.868949i \(-0.664796\pi\)
−0.494902 + 0.868949i \(0.664796\pi\)
\(272\) 0 0
\(273\) 0.763644 0.0462178
\(274\) 0 0
\(275\) −2.58443 −0.155847
\(276\) 0 0
\(277\) 4.65531 0.279710 0.139855 0.990172i \(-0.455336\pi\)
0.139855 + 0.990172i \(0.455336\pi\)
\(278\) 0 0
\(279\) −6.88471 −0.412177
\(280\) 0 0
\(281\) 11.1294 0.663922 0.331961 0.943293i \(-0.392290\pi\)
0.331961 + 0.943293i \(0.392290\pi\)
\(282\) 0 0
\(283\) 3.69259 0.219502 0.109751 0.993959i \(-0.464995\pi\)
0.109751 + 0.993959i \(0.464995\pi\)
\(284\) 0 0
\(285\) 1.22020 0.0722783
\(286\) 0 0
\(287\) −3.11068 −0.183617
\(288\) 0 0
\(289\) −3.96054 −0.232973
\(290\) 0 0
\(291\) 0.810946 0.0475385
\(292\) 0 0
\(293\) −13.8153 −0.807098 −0.403549 0.914958i \(-0.632223\pi\)
−0.403549 + 0.914958i \(0.632223\pi\)
\(294\) 0 0
\(295\) −4.59293 −0.267411
\(296\) 0 0
\(297\) −4.13654 −0.240027
\(298\) 0 0
\(299\) −4.55145 −0.263217
\(300\) 0 0
\(301\) −8.35432 −0.481535
\(302\) 0 0
\(303\) 6.93378 0.398335
\(304\) 0 0
\(305\) −10.0218 −0.573849
\(306\) 0 0
\(307\) −15.6569 −0.893589 −0.446794 0.894637i \(-0.647434\pi\)
−0.446794 + 0.894637i \(0.647434\pi\)
\(308\) 0 0
\(309\) 10.8167 0.615339
\(310\) 0 0
\(311\) −16.1559 −0.916119 −0.458059 0.888922i \(-0.651455\pi\)
−0.458059 + 0.888922i \(0.651455\pi\)
\(312\) 0 0
\(313\) 16.5609 0.936077 0.468038 0.883708i \(-0.344961\pi\)
0.468038 + 0.883708i \(0.344961\pi\)
\(314\) 0 0
\(315\) 3.75629 0.211643
\(316\) 0 0
\(317\) 27.6460 1.55275 0.776376 0.630270i \(-0.217056\pi\)
0.776376 + 0.630270i \(0.217056\pi\)
\(318\) 0 0
\(319\) −4.78553 −0.267938
\(320\) 0 0
\(321\) 0.146386 0.00817046
\(322\) 0 0
\(323\) 3.71244 0.206566
\(324\) 0 0
\(325\) 2.58443 0.143358
\(326\) 0 0
\(327\) 11.7379 0.649106
\(328\) 0 0
\(329\) −9.30529 −0.513017
\(330\) 0 0
\(331\) 10.7209 0.589274 0.294637 0.955609i \(-0.404801\pi\)
0.294637 + 0.955609i \(0.404801\pi\)
\(332\) 0 0
\(333\) −3.07050 −0.168262
\(334\) 0 0
\(335\) −10.1311 −0.553523
\(336\) 0 0
\(337\) −9.30889 −0.507088 −0.253544 0.967324i \(-0.581596\pi\)
−0.253544 + 0.967324i \(0.581596\pi\)
\(338\) 0 0
\(339\) 12.5486 0.681546
\(340\) 0 0
\(341\) 2.84863 0.154262
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 5.40196 0.290832
\(346\) 0 0
\(347\) −28.1924 −1.51345 −0.756724 0.653734i \(-0.773201\pi\)
−0.756724 + 0.653734i \(0.773201\pi\)
\(348\) 0 0
\(349\) 19.8050 1.06014 0.530068 0.847955i \(-0.322166\pi\)
0.530068 + 0.847955i \(0.322166\pi\)
\(350\) 0 0
\(351\) 4.13654 0.220792
\(352\) 0 0
\(353\) −21.9753 −1.16963 −0.584813 0.811168i \(-0.698832\pi\)
−0.584813 + 0.811168i \(0.698832\pi\)
\(354\) 0 0
\(355\) −16.1643 −0.857912
\(356\) 0 0
\(357\) −2.75753 −0.145944
\(358\) 0 0
\(359\) 20.8772 1.10186 0.550928 0.834553i \(-0.314274\pi\)
0.550928 + 0.834553i \(0.314274\pi\)
\(360\) 0 0
\(361\) −17.9430 −0.944370
\(362\) 0 0
\(363\) 0.763644 0.0400809
\(364\) 0 0
\(365\) 10.8161 0.566140
\(366\) 0 0
\(367\) 7.25726 0.378826 0.189413 0.981898i \(-0.439342\pi\)
0.189413 + 0.981898i \(0.439342\pi\)
\(368\) 0 0
\(369\) −7.51803 −0.391373
\(370\) 0 0
\(371\) −1.24483 −0.0646281
\(372\) 0 0
\(373\) −9.05017 −0.468600 −0.234300 0.972164i \(-0.575280\pi\)
−0.234300 + 0.972164i \(0.575280\pi\)
\(374\) 0 0
\(375\) −9.00169 −0.464845
\(376\) 0 0
\(377\) 4.78553 0.246467
\(378\) 0 0
\(379\) −7.92065 −0.406856 −0.203428 0.979090i \(-0.565208\pi\)
−0.203428 + 0.979090i \(0.565208\pi\)
\(380\) 0 0
\(381\) −3.68147 −0.188607
\(382\) 0 0
\(383\) −33.8448 −1.72939 −0.864695 0.502298i \(-0.832488\pi\)
−0.864695 + 0.502298i \(0.832488\pi\)
\(384\) 0 0
\(385\) −1.55421 −0.0792099
\(386\) 0 0
\(387\) −20.1911 −1.02637
\(388\) 0 0
\(389\) −23.1083 −1.17164 −0.585818 0.810443i \(-0.699227\pi\)
−0.585818 + 0.810443i \(0.699227\pi\)
\(390\) 0 0
\(391\) 16.4354 0.831173
\(392\) 0 0
\(393\) 3.01854 0.152265
\(394\) 0 0
\(395\) 3.47035 0.174612
\(396\) 0 0
\(397\) 13.7326 0.689217 0.344609 0.938746i \(-0.388012\pi\)
0.344609 + 0.938746i \(0.388012\pi\)
\(398\) 0 0
\(399\) −0.785092 −0.0393038
\(400\) 0 0
\(401\) −38.2794 −1.91158 −0.955790 0.294051i \(-0.904997\pi\)
−0.955790 + 0.294051i \(0.904997\pi\)
\(402\) 0 0
\(403\) −2.84863 −0.141901
\(404\) 0 0
\(405\) 6.35936 0.315999
\(406\) 0 0
\(407\) 1.27046 0.0629742
\(408\) 0 0
\(409\) 37.5213 1.85531 0.927655 0.373439i \(-0.121821\pi\)
0.927655 + 0.373439i \(0.121821\pi\)
\(410\) 0 0
\(411\) −10.2808 −0.507116
\(412\) 0 0
\(413\) 2.95515 0.145414
\(414\) 0 0
\(415\) −16.3624 −0.803200
\(416\) 0 0
\(417\) 6.50244 0.318426
\(418\) 0 0
\(419\) 26.8698 1.31267 0.656337 0.754468i \(-0.272105\pi\)
0.656337 + 0.754468i \(0.272105\pi\)
\(420\) 0 0
\(421\) −15.8231 −0.771170 −0.385585 0.922672i \(-0.626000\pi\)
−0.385585 + 0.922672i \(0.626000\pi\)
\(422\) 0 0
\(423\) −22.4895 −1.09347
\(424\) 0 0
\(425\) −9.33242 −0.452689
\(426\) 0 0
\(427\) 6.44819 0.312050
\(428\) 0 0
\(429\) −0.763644 −0.0368691
\(430\) 0 0
\(431\) 30.3780 1.46325 0.731627 0.681705i \(-0.238761\pi\)
0.731627 + 0.681705i \(0.238761\pi\)
\(432\) 0 0
\(433\) −10.2984 −0.494911 −0.247456 0.968899i \(-0.579594\pi\)
−0.247456 + 0.968899i \(0.579594\pi\)
\(434\) 0 0
\(435\) −5.67978 −0.272324
\(436\) 0 0
\(437\) 4.67928 0.223841
\(438\) 0 0
\(439\) −0.227077 −0.0108378 −0.00541889 0.999985i \(-0.501725\pi\)
−0.00541889 + 0.999985i \(0.501725\pi\)
\(440\) 0 0
\(441\) −2.41685 −0.115088
\(442\) 0 0
\(443\) 2.57932 0.122547 0.0612737 0.998121i \(-0.480484\pi\)
0.0612737 + 0.998121i \(0.480484\pi\)
\(444\) 0 0
\(445\) 19.2853 0.914212
\(446\) 0 0
\(447\) 9.28094 0.438973
\(448\) 0 0
\(449\) 21.8040 1.02899 0.514497 0.857492i \(-0.327979\pi\)
0.514497 + 0.857492i \(0.327979\pi\)
\(450\) 0 0
\(451\) 3.11068 0.146476
\(452\) 0 0
\(453\) −6.44513 −0.302819
\(454\) 0 0
\(455\) 1.55421 0.0728625
\(456\) 0 0
\(457\) −29.0371 −1.35830 −0.679149 0.734000i \(-0.737651\pi\)
−0.679149 + 0.734000i \(0.737651\pi\)
\(458\) 0 0
\(459\) −14.9371 −0.697206
\(460\) 0 0
\(461\) −34.2576 −1.59553 −0.797767 0.602966i \(-0.793985\pi\)
−0.797767 + 0.602966i \(0.793985\pi\)
\(462\) 0 0
\(463\) −25.4791 −1.18412 −0.592058 0.805895i \(-0.701684\pi\)
−0.592058 + 0.805895i \(0.701684\pi\)
\(464\) 0 0
\(465\) 3.38094 0.156787
\(466\) 0 0
\(467\) −26.5467 −1.22843 −0.614216 0.789138i \(-0.710528\pi\)
−0.614216 + 0.789138i \(0.710528\pi\)
\(468\) 0 0
\(469\) 6.51850 0.300997
\(470\) 0 0
\(471\) −8.97850 −0.413707
\(472\) 0 0
\(473\) 8.35432 0.384132
\(474\) 0 0
\(475\) −2.65701 −0.121912
\(476\) 0 0
\(477\) −3.00855 −0.137752
\(478\) 0 0
\(479\) 22.3747 1.02233 0.511164 0.859483i \(-0.329215\pi\)
0.511164 + 0.859483i \(0.329215\pi\)
\(480\) 0 0
\(481\) −1.27046 −0.0579279
\(482\) 0 0
\(483\) −3.47569 −0.158149
\(484\) 0 0
\(485\) 1.65048 0.0749446
\(486\) 0 0
\(487\) −3.34573 −0.151610 −0.0758048 0.997123i \(-0.524153\pi\)
−0.0758048 + 0.997123i \(0.524153\pi\)
\(488\) 0 0
\(489\) −9.54111 −0.431464
\(490\) 0 0
\(491\) 9.58951 0.432768 0.216384 0.976308i \(-0.430574\pi\)
0.216384 + 0.976308i \(0.430574\pi\)
\(492\) 0 0
\(493\) −17.2806 −0.778281
\(494\) 0 0
\(495\) −3.75629 −0.168833
\(496\) 0 0
\(497\) 10.4003 0.466518
\(498\) 0 0
\(499\) 4.05910 0.181710 0.0908552 0.995864i \(-0.471040\pi\)
0.0908552 + 0.995864i \(0.471040\pi\)
\(500\) 0 0
\(501\) 18.6963 0.835290
\(502\) 0 0
\(503\) 25.3910 1.13213 0.566065 0.824361i \(-0.308465\pi\)
0.566065 + 0.824361i \(0.308465\pi\)
\(504\) 0 0
\(505\) 14.1120 0.627977
\(506\) 0 0
\(507\) 0.763644 0.0339146
\(508\) 0 0
\(509\) −10.4880 −0.464873 −0.232436 0.972612i \(-0.574670\pi\)
−0.232436 + 0.972612i \(0.574670\pi\)
\(510\) 0 0
\(511\) −6.95921 −0.307858
\(512\) 0 0
\(513\) −4.25272 −0.187762
\(514\) 0 0
\(515\) 22.0147 0.970083
\(516\) 0 0
\(517\) 9.30529 0.409246
\(518\) 0 0
\(519\) −15.1929 −0.666893
\(520\) 0 0
\(521\) −3.86958 −0.169529 −0.0847646 0.996401i \(-0.527014\pi\)
−0.0847646 + 0.996401i \(0.527014\pi\)
\(522\) 0 0
\(523\) −13.4579 −0.588472 −0.294236 0.955733i \(-0.595065\pi\)
−0.294236 + 0.955733i \(0.595065\pi\)
\(524\) 0 0
\(525\) 1.97358 0.0861342
\(526\) 0 0
\(527\) 10.2865 0.448086
\(528\) 0 0
\(529\) −2.28428 −0.0993165
\(530\) 0 0
\(531\) 7.14215 0.309943
\(532\) 0 0
\(533\) −3.11068 −0.134738
\(534\) 0 0
\(535\) 0.297933 0.0128807
\(536\) 0 0
\(537\) −6.79627 −0.293281
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −12.4446 −0.535037 −0.267518 0.963553i \(-0.586204\pi\)
−0.267518 + 0.963553i \(0.586204\pi\)
\(542\) 0 0
\(543\) 14.3212 0.614583
\(544\) 0 0
\(545\) 23.8896 1.02332
\(546\) 0 0
\(547\) 21.0611 0.900507 0.450254 0.892901i \(-0.351334\pi\)
0.450254 + 0.892901i \(0.351334\pi\)
\(548\) 0 0
\(549\) 15.5843 0.665121
\(550\) 0 0
\(551\) −4.91994 −0.209596
\(552\) 0 0
\(553\) −2.23287 −0.0949511
\(554\) 0 0
\(555\) 1.50786 0.0640051
\(556\) 0 0
\(557\) 3.47725 0.147336 0.0736679 0.997283i \(-0.476530\pi\)
0.0736679 + 0.997283i \(0.476530\pi\)
\(558\) 0 0
\(559\) −8.35432 −0.353350
\(560\) 0 0
\(561\) 2.75753 0.116423
\(562\) 0 0
\(563\) 10.5980 0.446652 0.223326 0.974744i \(-0.428309\pi\)
0.223326 + 0.974744i \(0.428309\pi\)
\(564\) 0 0
\(565\) 25.5396 1.07446
\(566\) 0 0
\(567\) −4.09170 −0.171835
\(568\) 0 0
\(569\) −2.94541 −0.123478 −0.0617390 0.998092i \(-0.519665\pi\)
−0.0617390 + 0.998092i \(0.519665\pi\)
\(570\) 0 0
\(571\) 10.7824 0.451230 0.225615 0.974217i \(-0.427561\pi\)
0.225615 + 0.974217i \(0.427561\pi\)
\(572\) 0 0
\(573\) −9.30626 −0.388774
\(574\) 0 0
\(575\) −11.7629 −0.490547
\(576\) 0 0
\(577\) 14.0827 0.586271 0.293135 0.956071i \(-0.405301\pi\)
0.293135 + 0.956071i \(0.405301\pi\)
\(578\) 0 0
\(579\) 11.2675 0.468262
\(580\) 0 0
\(581\) 10.5278 0.436767
\(582\) 0 0
\(583\) 1.24483 0.0515554
\(584\) 0 0
\(585\) 3.75629 0.155304
\(586\) 0 0
\(587\) 2.60754 0.107625 0.0538123 0.998551i \(-0.482863\pi\)
0.0538123 + 0.998551i \(0.482863\pi\)
\(588\) 0 0
\(589\) 2.92864 0.120673
\(590\) 0 0
\(591\) 8.52633 0.350726
\(592\) 0 0
\(593\) −9.05565 −0.371871 −0.185936 0.982562i \(-0.559532\pi\)
−0.185936 + 0.982562i \(0.559532\pi\)
\(594\) 0 0
\(595\) −5.61229 −0.230081
\(596\) 0 0
\(597\) 20.4472 0.836847
\(598\) 0 0
\(599\) −44.1995 −1.80594 −0.902971 0.429702i \(-0.858619\pi\)
−0.902971 + 0.429702i \(0.858619\pi\)
\(600\) 0 0
\(601\) −36.4066 −1.48506 −0.742528 0.669815i \(-0.766373\pi\)
−0.742528 + 0.669815i \(0.766373\pi\)
\(602\) 0 0
\(603\) 15.7542 0.641562
\(604\) 0 0
\(605\) 1.55421 0.0631877
\(606\) 0 0
\(607\) −27.3187 −1.10883 −0.554417 0.832239i \(-0.687059\pi\)
−0.554417 + 0.832239i \(0.687059\pi\)
\(608\) 0 0
\(609\) 3.65444 0.148085
\(610\) 0 0
\(611\) −9.30529 −0.376452
\(612\) 0 0
\(613\) 28.6930 1.15890 0.579449 0.815008i \(-0.303268\pi\)
0.579449 + 0.815008i \(0.303268\pi\)
\(614\) 0 0
\(615\) 3.69195 0.148874
\(616\) 0 0
\(617\) 46.4942 1.87178 0.935892 0.352286i \(-0.114596\pi\)
0.935892 + 0.352286i \(0.114596\pi\)
\(618\) 0 0
\(619\) −22.6265 −0.909434 −0.454717 0.890636i \(-0.650260\pi\)
−0.454717 + 0.890636i \(0.650260\pi\)
\(620\) 0 0
\(621\) −18.8273 −0.755513
\(622\) 0 0
\(623\) −12.4084 −0.497133
\(624\) 0 0
\(625\) −5.39860 −0.215944
\(626\) 0 0
\(627\) 0.785092 0.0313535
\(628\) 0 0
\(629\) 4.58765 0.182921
\(630\) 0 0
\(631\) −1.70304 −0.0677970 −0.0338985 0.999425i \(-0.510792\pi\)
−0.0338985 + 0.999425i \(0.510792\pi\)
\(632\) 0 0
\(633\) 15.8309 0.629222
\(634\) 0 0
\(635\) −7.49273 −0.297340
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 25.1360 0.994365
\(640\) 0 0
\(641\) −18.3537 −0.724928 −0.362464 0.931998i \(-0.618064\pi\)
−0.362464 + 0.931998i \(0.618064\pi\)
\(642\) 0 0
\(643\) 11.0360 0.435219 0.217609 0.976036i \(-0.430174\pi\)
0.217609 + 0.976036i \(0.430174\pi\)
\(644\) 0 0
\(645\) 9.91545 0.390420
\(646\) 0 0
\(647\) 18.3081 0.719767 0.359884 0.932997i \(-0.382816\pi\)
0.359884 + 0.932997i \(0.382816\pi\)
\(648\) 0 0
\(649\) −2.95515 −0.116000
\(650\) 0 0
\(651\) −2.17534 −0.0852584
\(652\) 0 0
\(653\) −1.10285 −0.0431577 −0.0215789 0.999767i \(-0.506869\pi\)
−0.0215789 + 0.999767i \(0.506869\pi\)
\(654\) 0 0
\(655\) 6.14349 0.240046
\(656\) 0 0
\(657\) −16.8194 −0.656186
\(658\) 0 0
\(659\) −33.9239 −1.32149 −0.660743 0.750612i \(-0.729759\pi\)
−0.660743 + 0.750612i \(0.729759\pi\)
\(660\) 0 0
\(661\) 24.5526 0.954986 0.477493 0.878636i \(-0.341546\pi\)
0.477493 + 0.878636i \(0.341546\pi\)
\(662\) 0 0
\(663\) −2.75753 −0.107094
\(664\) 0 0
\(665\) −1.59786 −0.0619625
\(666\) 0 0
\(667\) −21.7811 −0.843368
\(668\) 0 0
\(669\) −4.35451 −0.168355
\(670\) 0 0
\(671\) −6.44819 −0.248930
\(672\) 0 0
\(673\) −14.1038 −0.543660 −0.271830 0.962345i \(-0.587629\pi\)
−0.271830 + 0.962345i \(0.587629\pi\)
\(674\) 0 0
\(675\) 10.6906 0.411481
\(676\) 0 0
\(677\) 31.2490 1.20100 0.600498 0.799626i \(-0.294969\pi\)
0.600498 + 0.799626i \(0.294969\pi\)
\(678\) 0 0
\(679\) −1.06194 −0.0407536
\(680\) 0 0
\(681\) −7.14841 −0.273928
\(682\) 0 0
\(683\) −50.8580 −1.94603 −0.973013 0.230749i \(-0.925882\pi\)
−0.973013 + 0.230749i \(0.925882\pi\)
\(684\) 0 0
\(685\) −20.9241 −0.799469
\(686\) 0 0
\(687\) 16.3745 0.624726
\(688\) 0 0
\(689\) −1.24483 −0.0474241
\(690\) 0 0
\(691\) 8.29206 0.315445 0.157722 0.987484i \(-0.449585\pi\)
0.157722 + 0.987484i \(0.449585\pi\)
\(692\) 0 0
\(693\) 2.41685 0.0918085
\(694\) 0 0
\(695\) 13.2341 0.501999
\(696\) 0 0
\(697\) 11.2327 0.425469
\(698\) 0 0
\(699\) 15.0406 0.568886
\(700\) 0 0
\(701\) 22.1036 0.834840 0.417420 0.908714i \(-0.362934\pi\)
0.417420 + 0.908714i \(0.362934\pi\)
\(702\) 0 0
\(703\) 1.30614 0.0492620
\(704\) 0 0
\(705\) 11.0441 0.415945
\(706\) 0 0
\(707\) −9.07986 −0.341483
\(708\) 0 0
\(709\) −0.389720 −0.0146362 −0.00731811 0.999973i \(-0.502329\pi\)
−0.00731811 + 0.999973i \(0.502329\pi\)
\(710\) 0 0
\(711\) −5.39650 −0.202384
\(712\) 0 0
\(713\) 12.9654 0.485559
\(714\) 0 0
\(715\) −1.55421 −0.0581242
\(716\) 0 0
\(717\) −1.21957 −0.0455457
\(718\) 0 0
\(719\) −12.7073 −0.473904 −0.236952 0.971521i \(-0.576148\pi\)
−0.236952 + 0.971521i \(0.576148\pi\)
\(720\) 0 0
\(721\) −14.1645 −0.527515
\(722\) 0 0
\(723\) 14.5173 0.539905
\(724\) 0 0
\(725\) 12.3679 0.459331
\(726\) 0 0
\(727\) −4.87754 −0.180898 −0.0904489 0.995901i \(-0.528830\pi\)
−0.0904489 + 0.995901i \(0.528830\pi\)
\(728\) 0 0
\(729\) −0.412464 −0.0152765
\(730\) 0 0
\(731\) 30.1676 1.11579
\(732\) 0 0
\(733\) 21.9663 0.811345 0.405672 0.914019i \(-0.367037\pi\)
0.405672 + 0.914019i \(0.367037\pi\)
\(734\) 0 0
\(735\) 1.18686 0.0437781
\(736\) 0 0
\(737\) −6.51850 −0.240112
\(738\) 0 0
\(739\) 24.9920 0.919346 0.459673 0.888088i \(-0.347967\pi\)
0.459673 + 0.888088i \(0.347967\pi\)
\(740\) 0 0
\(741\) −0.785092 −0.0288411
\(742\) 0 0
\(743\) −8.97156 −0.329135 −0.164567 0.986366i \(-0.552623\pi\)
−0.164567 + 0.986366i \(0.552623\pi\)
\(744\) 0 0
\(745\) 18.8891 0.692043
\(746\) 0 0
\(747\) 25.4441 0.930951
\(748\) 0 0
\(749\) −0.191694 −0.00700434
\(750\) 0 0
\(751\) 9.35304 0.341297 0.170649 0.985332i \(-0.445414\pi\)
0.170649 + 0.985332i \(0.445414\pi\)
\(752\) 0 0
\(753\) 4.14626 0.151098
\(754\) 0 0
\(755\) −13.1175 −0.477394
\(756\) 0 0
\(757\) 42.1416 1.53166 0.765832 0.643041i \(-0.222328\pi\)
0.765832 + 0.643041i \(0.222328\pi\)
\(758\) 0 0
\(759\) 3.47569 0.126160
\(760\) 0 0
\(761\) −39.7772 −1.44192 −0.720962 0.692975i \(-0.756300\pi\)
−0.720962 + 0.692975i \(0.756300\pi\)
\(762\) 0 0
\(763\) −15.3709 −0.556463
\(764\) 0 0
\(765\) −13.5640 −0.490409
\(766\) 0 0
\(767\) 2.95515 0.106704
\(768\) 0 0
\(769\) −5.61322 −0.202418 −0.101209 0.994865i \(-0.532271\pi\)
−0.101209 + 0.994865i \(0.532271\pi\)
\(770\) 0 0
\(771\) 11.2969 0.406850
\(772\) 0 0
\(773\) 41.2364 1.48317 0.741584 0.670860i \(-0.234075\pi\)
0.741584 + 0.670860i \(0.234075\pi\)
\(774\) 0 0
\(775\) −7.36209 −0.264454
\(776\) 0 0
\(777\) −0.970177 −0.0348049
\(778\) 0 0
\(779\) 3.19804 0.114582
\(780\) 0 0
\(781\) −10.4003 −0.372153
\(782\) 0 0
\(783\) 19.7956 0.707435
\(784\) 0 0
\(785\) −18.2735 −0.652211
\(786\) 0 0
\(787\) −9.08239 −0.323752 −0.161876 0.986811i \(-0.551755\pi\)
−0.161876 + 0.986811i \(0.551755\pi\)
\(788\) 0 0
\(789\) −5.49233 −0.195532
\(790\) 0 0
\(791\) −16.4325 −0.584273
\(792\) 0 0
\(793\) 6.44819 0.228982
\(794\) 0 0
\(795\) 1.47744 0.0523994
\(796\) 0 0
\(797\) −37.5216 −1.32908 −0.664542 0.747251i \(-0.731373\pi\)
−0.664542 + 0.747251i \(0.731373\pi\)
\(798\) 0 0
\(799\) 33.6016 1.18874
\(800\) 0 0
\(801\) −29.9893 −1.05962
\(802\) 0 0
\(803\) 6.95921 0.245585
\(804\) 0 0
\(805\) −7.07392 −0.249323
\(806\) 0 0
\(807\) 18.0645 0.635900
\(808\) 0 0
\(809\) −2.22629 −0.0782721 −0.0391360 0.999234i \(-0.512461\pi\)
−0.0391360 + 0.999234i \(0.512461\pi\)
\(810\) 0 0
\(811\) −9.05440 −0.317943 −0.158971 0.987283i \(-0.550818\pi\)
−0.158971 + 0.987283i \(0.550818\pi\)
\(812\) 0 0
\(813\) −12.4430 −0.436395
\(814\) 0 0
\(815\) −19.4186 −0.680204
\(816\) 0 0
\(817\) 8.58896 0.300490
\(818\) 0 0
\(819\) −2.41685 −0.0844515
\(820\) 0 0
\(821\) 29.2651 1.02136 0.510679 0.859771i \(-0.329394\pi\)
0.510679 + 0.859771i \(0.329394\pi\)
\(822\) 0 0
\(823\) 51.6067 1.79890 0.899448 0.437027i \(-0.143969\pi\)
0.899448 + 0.437027i \(0.143969\pi\)
\(824\) 0 0
\(825\) −1.97358 −0.0687113
\(826\) 0 0
\(827\) −17.6269 −0.612947 −0.306474 0.951879i \(-0.599149\pi\)
−0.306474 + 0.951879i \(0.599149\pi\)
\(828\) 0 0
\(829\) 35.5997 1.23643 0.618215 0.786009i \(-0.287856\pi\)
0.618215 + 0.786009i \(0.287856\pi\)
\(830\) 0 0
\(831\) 3.55500 0.123321
\(832\) 0 0
\(833\) 3.61102 0.125114
\(834\) 0 0
\(835\) 38.0518 1.31684
\(836\) 0 0
\(837\) −11.7835 −0.407297
\(838\) 0 0
\(839\) −35.6882 −1.23209 −0.616047 0.787709i \(-0.711267\pi\)
−0.616047 + 0.787709i \(0.711267\pi\)
\(840\) 0 0
\(841\) −6.09870 −0.210300
\(842\) 0 0
\(843\) 8.49887 0.292717
\(844\) 0 0
\(845\) 1.55421 0.0534665
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 2.81982 0.0967761
\(850\) 0 0
\(851\) 5.78243 0.198219
\(852\) 0 0
\(853\) 22.2507 0.761849 0.380925 0.924606i \(-0.375606\pi\)
0.380925 + 0.924606i \(0.375606\pi\)
\(854\) 0 0
\(855\) −3.86179 −0.132070
\(856\) 0 0
\(857\) 18.0586 0.616870 0.308435 0.951245i \(-0.400195\pi\)
0.308435 + 0.951245i \(0.400195\pi\)
\(858\) 0 0
\(859\) −36.3958 −1.24181 −0.620905 0.783886i \(-0.713235\pi\)
−0.620905 + 0.783886i \(0.713235\pi\)
\(860\) 0 0
\(861\) −2.37545 −0.0809551
\(862\) 0 0
\(863\) −30.2661 −1.03027 −0.515136 0.857109i \(-0.672258\pi\)
−0.515136 + 0.857109i \(0.672258\pi\)
\(864\) 0 0
\(865\) −30.9214 −1.05136
\(866\) 0 0
\(867\) −3.02444 −0.102716
\(868\) 0 0
\(869\) 2.23287 0.0757448
\(870\) 0 0
\(871\) 6.51850 0.220871
\(872\) 0 0
\(873\) −2.56655 −0.0868647
\(874\) 0 0
\(875\) 11.7878 0.398500
\(876\) 0 0
\(877\) −36.1400 −1.22036 −0.610181 0.792262i \(-0.708903\pi\)
−0.610181 + 0.792262i \(0.708903\pi\)
\(878\) 0 0
\(879\) −10.5500 −0.355841
\(880\) 0 0
\(881\) 0.936792 0.0315613 0.0157807 0.999875i \(-0.494977\pi\)
0.0157807 + 0.999875i \(0.494977\pi\)
\(882\) 0 0
\(883\) −37.9589 −1.27742 −0.638710 0.769447i \(-0.720532\pi\)
−0.638710 + 0.769447i \(0.720532\pi\)
\(884\) 0 0
\(885\) −3.50736 −0.117899
\(886\) 0 0
\(887\) 51.3329 1.72359 0.861796 0.507256i \(-0.169340\pi\)
0.861796 + 0.507256i \(0.169340\pi\)
\(888\) 0 0
\(889\) 4.82092 0.161689
\(890\) 0 0
\(891\) 4.09170 0.137077
\(892\) 0 0
\(893\) 9.56664 0.320135
\(894\) 0 0
\(895\) −13.8322 −0.462358
\(896\) 0 0
\(897\) −3.47569 −0.116050
\(898\) 0 0
\(899\) −13.6322 −0.454660
\(900\) 0 0
\(901\) 4.49509 0.149753
\(902\) 0 0
\(903\) −6.37973 −0.212304
\(904\) 0 0
\(905\) 29.1474 0.968892
\(906\) 0 0
\(907\) −27.3418 −0.907870 −0.453935 0.891035i \(-0.649980\pi\)
−0.453935 + 0.891035i \(0.649980\pi\)
\(908\) 0 0
\(909\) −21.9446 −0.727858
\(910\) 0 0
\(911\) 47.8164 1.58423 0.792114 0.610373i \(-0.208980\pi\)
0.792114 + 0.610373i \(0.208980\pi\)
\(912\) 0 0
\(913\) −10.5278 −0.348419
\(914\) 0 0
\(915\) −7.65313 −0.253005
\(916\) 0 0
\(917\) −3.95281 −0.130533
\(918\) 0 0
\(919\) −42.2920 −1.39509 −0.697543 0.716543i \(-0.745723\pi\)
−0.697543 + 0.716543i \(0.745723\pi\)
\(920\) 0 0
\(921\) −11.9563 −0.393974
\(922\) 0 0
\(923\) 10.4003 0.342331
\(924\) 0 0
\(925\) −3.28340 −0.107958
\(926\) 0 0
\(927\) −34.2335 −1.12438
\(928\) 0 0
\(929\) 25.2483 0.828369 0.414184 0.910193i \(-0.364067\pi\)
0.414184 + 0.910193i \(0.364067\pi\)
\(930\) 0 0
\(931\) 1.02809 0.0336942
\(932\) 0 0
\(933\) −12.3374 −0.403908
\(934\) 0 0
\(935\) 5.61229 0.183541
\(936\) 0 0
\(937\) −17.5207 −0.572377 −0.286189 0.958173i \(-0.592388\pi\)
−0.286189 + 0.958173i \(0.592388\pi\)
\(938\) 0 0
\(939\) 12.6466 0.412707
\(940\) 0 0
\(941\) 16.8160 0.548186 0.274093 0.961703i \(-0.411622\pi\)
0.274093 + 0.961703i \(0.411622\pi\)
\(942\) 0 0
\(943\) 14.1581 0.461051
\(944\) 0 0
\(945\) 6.42906 0.209137
\(946\) 0 0
\(947\) 56.9736 1.85139 0.925697 0.378266i \(-0.123479\pi\)
0.925697 + 0.378266i \(0.123479\pi\)
\(948\) 0 0
\(949\) −6.95921 −0.225906
\(950\) 0 0
\(951\) 21.1117 0.684593
\(952\) 0 0
\(953\) 27.2538 0.882836 0.441418 0.897302i \(-0.354476\pi\)
0.441418 + 0.897302i \(0.354476\pi\)
\(954\) 0 0
\(955\) −18.9406 −0.612904
\(956\) 0 0
\(957\) −3.65444 −0.118131
\(958\) 0 0
\(959\) 13.4629 0.434738
\(960\) 0 0
\(961\) −22.8853 −0.738235
\(962\) 0 0
\(963\) −0.463294 −0.0149295
\(964\) 0 0
\(965\) 22.9323 0.738216
\(966\) 0 0
\(967\) −3.65503 −0.117538 −0.0587689 0.998272i \(-0.518717\pi\)
−0.0587689 + 0.998272i \(0.518717\pi\)
\(968\) 0 0
\(969\) 2.83498 0.0910727
\(970\) 0 0
\(971\) −19.8780 −0.637917 −0.318958 0.947769i \(-0.603333\pi\)
−0.318958 + 0.947769i \(0.603333\pi\)
\(972\) 0 0
\(973\) −8.51502 −0.272979
\(974\) 0 0
\(975\) 1.97358 0.0632052
\(976\) 0 0
\(977\) 23.8678 0.763599 0.381799 0.924245i \(-0.375304\pi\)
0.381799 + 0.924245i \(0.375304\pi\)
\(978\) 0 0
\(979\) 12.4084 0.396575
\(980\) 0 0
\(981\) −37.1491 −1.18608
\(982\) 0 0
\(983\) −28.0856 −0.895791 −0.447895 0.894086i \(-0.647826\pi\)
−0.447895 + 0.894086i \(0.647826\pi\)
\(984\) 0 0
\(985\) 17.3533 0.552921
\(986\) 0 0
\(987\) −7.10593 −0.226184
\(988\) 0 0
\(989\) 38.0243 1.20910
\(990\) 0 0
\(991\) 5.18594 0.164737 0.0823684 0.996602i \(-0.473752\pi\)
0.0823684 + 0.996602i \(0.473752\pi\)
\(992\) 0 0
\(993\) 8.18696 0.259805
\(994\) 0 0
\(995\) 41.6152 1.31929
\(996\) 0 0
\(997\) −18.3344 −0.580656 −0.290328 0.956927i \(-0.593764\pi\)
−0.290328 + 0.956927i \(0.593764\pi\)
\(998\) 0 0
\(999\) −5.25530 −0.166270
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 \(a_p\))