Properties

Label 8008.2.a.p.1.4
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
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: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.333725\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.333725 q^{3} +1.97301 q^{5} -1.00000 q^{7} -2.88863 q^{9} +O(q^{10})\) \(q-0.333725 q^{3} +1.97301 q^{5} -1.00000 q^{7} -2.88863 q^{9} +1.00000 q^{11} +1.00000 q^{13} -0.658443 q^{15} +3.01194 q^{17} +7.23548 q^{19} +0.333725 q^{21} -5.73685 q^{23} -1.10722 q^{25} +1.96518 q^{27} -5.03516 q^{29} -7.65880 q^{31} -0.333725 q^{33} -1.97301 q^{35} +2.20318 q^{37} -0.333725 q^{39} -7.09291 q^{41} +8.24968 q^{43} -5.69930 q^{45} -6.28197 q^{47} +1.00000 q^{49} -1.00516 q^{51} -13.7493 q^{53} +1.97301 q^{55} -2.41466 q^{57} -11.6777 q^{59} -6.71777 q^{61} +2.88863 q^{63} +1.97301 q^{65} -0.389294 q^{67} +1.91453 q^{69} +1.03512 q^{71} +16.0040 q^{73} +0.369507 q^{75} -1.00000 q^{77} +9.98212 q^{79} +8.01005 q^{81} +4.15167 q^{83} +5.94259 q^{85} +1.68036 q^{87} +2.98890 q^{89} -1.00000 q^{91} +2.55593 q^{93} +14.2757 q^{95} +1.28773 q^{97} -2.88863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) −0.333725 −0.192676 −0.0963381 0.995349i \(-0.530713\pi\)
−0.0963381 + 0.995349i \(0.530713\pi\)
\(4\) 0 0
\(5\) 1.97301 0.882358 0.441179 0.897419i \(-0.354560\pi\)
0.441179 + 0.897419i \(0.354560\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.88863 −0.962876
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −0.658443 −0.170009
\(16\) 0 0
\(17\) 3.01194 0.730502 0.365251 0.930909i \(-0.380983\pi\)
0.365251 + 0.930909i \(0.380983\pi\)
\(18\) 0 0
\(19\) 7.23548 1.65993 0.829967 0.557813i \(-0.188359\pi\)
0.829967 + 0.557813i \(0.188359\pi\)
\(20\) 0 0
\(21\) 0.333725 0.0728247
\(22\) 0 0
\(23\) −5.73685 −1.19622 −0.598108 0.801416i \(-0.704081\pi\)
−0.598108 + 0.801416i \(0.704081\pi\)
\(24\) 0 0
\(25\) −1.10722 −0.221444
\(26\) 0 0
\(27\) 1.96518 0.378199
\(28\) 0 0
\(29\) −5.03516 −0.935006 −0.467503 0.883992i \(-0.654846\pi\)
−0.467503 + 0.883992i \(0.654846\pi\)
\(30\) 0 0
\(31\) −7.65880 −1.37556 −0.687781 0.725918i \(-0.741415\pi\)
−0.687781 + 0.725918i \(0.741415\pi\)
\(32\) 0 0
\(33\) −0.333725 −0.0580940
\(34\) 0 0
\(35\) −1.97301 −0.333500
\(36\) 0 0
\(37\) 2.20318 0.362200 0.181100 0.983465i \(-0.442034\pi\)
0.181100 + 0.983465i \(0.442034\pi\)
\(38\) 0 0
\(39\) −0.333725 −0.0534387
\(40\) 0 0
\(41\) −7.09291 −1.10773 −0.553863 0.832607i \(-0.686847\pi\)
−0.553863 + 0.832607i \(0.686847\pi\)
\(42\) 0 0
\(43\) 8.24968 1.25806 0.629032 0.777379i \(-0.283451\pi\)
0.629032 + 0.777379i \(0.283451\pi\)
\(44\) 0 0
\(45\) −5.69930 −0.849601
\(46\) 0 0
\(47\) −6.28197 −0.916320 −0.458160 0.888870i \(-0.651491\pi\)
−0.458160 + 0.888870i \(0.651491\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.00516 −0.140750
\(52\) 0 0
\(53\) −13.7493 −1.88861 −0.944303 0.329078i \(-0.893262\pi\)
−0.944303 + 0.329078i \(0.893262\pi\)
\(54\) 0 0
\(55\) 1.97301 0.266041
\(56\) 0 0
\(57\) −2.41466 −0.319829
\(58\) 0 0
\(59\) −11.6777 −1.52030 −0.760152 0.649745i \(-0.774876\pi\)
−0.760152 + 0.649745i \(0.774876\pi\)
\(60\) 0 0
\(61\) −6.71777 −0.860122 −0.430061 0.902800i \(-0.641508\pi\)
−0.430061 + 0.902800i \(0.641508\pi\)
\(62\) 0 0
\(63\) 2.88863 0.363933
\(64\) 0 0
\(65\) 1.97301 0.244722
\(66\) 0 0
\(67\) −0.389294 −0.0475598 −0.0237799 0.999717i \(-0.507570\pi\)
−0.0237799 + 0.999717i \(0.507570\pi\)
\(68\) 0 0
\(69\) 1.91453 0.230482
\(70\) 0 0
\(71\) 1.03512 0.122846 0.0614230 0.998112i \(-0.480436\pi\)
0.0614230 + 0.998112i \(0.480436\pi\)
\(72\) 0 0
\(73\) 16.0040 1.87313 0.936563 0.350499i \(-0.113988\pi\)
0.936563 + 0.350499i \(0.113988\pi\)
\(74\) 0 0
\(75\) 0.369507 0.0426670
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.98212 1.12308 0.561538 0.827451i \(-0.310210\pi\)
0.561538 + 0.827451i \(0.310210\pi\)
\(80\) 0 0
\(81\) 8.01005 0.890006
\(82\) 0 0
\(83\) 4.15167 0.455706 0.227853 0.973696i \(-0.426830\pi\)
0.227853 + 0.973696i \(0.426830\pi\)
\(84\) 0 0
\(85\) 5.94259 0.644565
\(86\) 0 0
\(87\) 1.68036 0.180153
\(88\) 0 0
\(89\) 2.98890 0.316823 0.158412 0.987373i \(-0.449363\pi\)
0.158412 + 0.987373i \(0.449363\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 2.55593 0.265038
\(94\) 0 0
\(95\) 14.2757 1.46466
\(96\) 0 0
\(97\) 1.28773 0.130749 0.0653745 0.997861i \(-0.479176\pi\)
0.0653745 + 0.997861i \(0.479176\pi\)
\(98\) 0 0
\(99\) −2.88863 −0.290318
\(100\) 0 0
\(101\) −19.2561 −1.91605 −0.958024 0.286687i \(-0.907446\pi\)
−0.958024 + 0.286687i \(0.907446\pi\)
\(102\) 0 0
\(103\) 2.72365 0.268369 0.134185 0.990956i \(-0.457158\pi\)
0.134185 + 0.990956i \(0.457158\pi\)
\(104\) 0 0
\(105\) 0.658443 0.0642575
\(106\) 0 0
\(107\) 9.05980 0.875844 0.437922 0.899013i \(-0.355715\pi\)
0.437922 + 0.899013i \(0.355715\pi\)
\(108\) 0 0
\(109\) −3.35173 −0.321037 −0.160519 0.987033i \(-0.551317\pi\)
−0.160519 + 0.987033i \(0.551317\pi\)
\(110\) 0 0
\(111\) −0.735255 −0.0697873
\(112\) 0 0
\(113\) −6.41177 −0.603168 −0.301584 0.953440i \(-0.597515\pi\)
−0.301584 + 0.953440i \(0.597515\pi\)
\(114\) 0 0
\(115\) −11.3189 −1.05549
\(116\) 0 0
\(117\) −2.88863 −0.267054
\(118\) 0 0
\(119\) −3.01194 −0.276104
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 2.36708 0.213433
\(124\) 0 0
\(125\) −12.0496 −1.07775
\(126\) 0 0
\(127\) 8.47402 0.751948 0.375974 0.926630i \(-0.377308\pi\)
0.375974 + 0.926630i \(0.377308\pi\)
\(128\) 0 0
\(129\) −2.75312 −0.242399
\(130\) 0 0
\(131\) −2.86075 −0.249945 −0.124972 0.992160i \(-0.539884\pi\)
−0.124972 + 0.992160i \(0.539884\pi\)
\(132\) 0 0
\(133\) −7.23548 −0.627396
\(134\) 0 0
\(135\) 3.87733 0.333707
\(136\) 0 0
\(137\) 21.4412 1.83184 0.915922 0.401356i \(-0.131461\pi\)
0.915922 + 0.401356i \(0.131461\pi\)
\(138\) 0 0
\(139\) 1.37318 0.116472 0.0582359 0.998303i \(-0.481452\pi\)
0.0582359 + 0.998303i \(0.481452\pi\)
\(140\) 0 0
\(141\) 2.09645 0.176553
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −9.93444 −0.825010
\(146\) 0 0
\(147\) −0.333725 −0.0275252
\(148\) 0 0
\(149\) −21.4379 −1.75626 −0.878131 0.478419i \(-0.841210\pi\)
−0.878131 + 0.478419i \(0.841210\pi\)
\(150\) 0 0
\(151\) 7.30293 0.594304 0.297152 0.954830i \(-0.403963\pi\)
0.297152 + 0.954830i \(0.403963\pi\)
\(152\) 0 0
\(153\) −8.70037 −0.703383
\(154\) 0 0
\(155\) −15.1109 −1.21374
\(156\) 0 0
\(157\) −20.3412 −1.62340 −0.811701 0.584073i \(-0.801458\pi\)
−0.811701 + 0.584073i \(0.801458\pi\)
\(158\) 0 0
\(159\) 4.58847 0.363889
\(160\) 0 0
\(161\) 5.73685 0.452127
\(162\) 0 0
\(163\) −14.9727 −1.17275 −0.586377 0.810038i \(-0.699446\pi\)
−0.586377 + 0.810038i \(0.699446\pi\)
\(164\) 0 0
\(165\) −0.658443 −0.0512597
\(166\) 0 0
\(167\) −11.9193 −0.922346 −0.461173 0.887310i \(-0.652571\pi\)
−0.461173 + 0.887310i \(0.652571\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −20.9006 −1.59831
\(172\) 0 0
\(173\) 20.7129 1.57477 0.787385 0.616461i \(-0.211434\pi\)
0.787385 + 0.616461i \(0.211434\pi\)
\(174\) 0 0
\(175\) 1.10722 0.0836980
\(176\) 0 0
\(177\) 3.89713 0.292926
\(178\) 0 0
\(179\) 19.3446 1.44589 0.722943 0.690908i \(-0.242789\pi\)
0.722943 + 0.690908i \(0.242789\pi\)
\(180\) 0 0
\(181\) −9.53877 −0.709011 −0.354506 0.935054i \(-0.615351\pi\)
−0.354506 + 0.935054i \(0.615351\pi\)
\(182\) 0 0
\(183\) 2.24189 0.165725
\(184\) 0 0
\(185\) 4.34690 0.319590
\(186\) 0 0
\(187\) 3.01194 0.220255
\(188\) 0 0
\(189\) −1.96518 −0.142946
\(190\) 0 0
\(191\) −26.2877 −1.90211 −0.951054 0.309024i \(-0.899998\pi\)
−0.951054 + 0.309024i \(0.899998\pi\)
\(192\) 0 0
\(193\) −0.0136444 −0.000982144 0 −0.000491072 1.00000i \(-0.500156\pi\)
−0.000491072 1.00000i \(0.500156\pi\)
\(194\) 0 0
\(195\) −0.658443 −0.0471521
\(196\) 0 0
\(197\) −7.35999 −0.524377 −0.262189 0.965017i \(-0.584444\pi\)
−0.262189 + 0.965017i \(0.584444\pi\)
\(198\) 0 0
\(199\) −18.9107 −1.34054 −0.670271 0.742116i \(-0.733822\pi\)
−0.670271 + 0.742116i \(0.733822\pi\)
\(200\) 0 0
\(201\) 0.129917 0.00916364
\(202\) 0 0
\(203\) 5.03516 0.353399
\(204\) 0 0
\(205\) −13.9944 −0.977412
\(206\) 0 0
\(207\) 16.5716 1.15181
\(208\) 0 0
\(209\) 7.23548 0.500489
\(210\) 0 0
\(211\) 20.7642 1.42947 0.714735 0.699396i \(-0.246547\pi\)
0.714735 + 0.699396i \(0.246547\pi\)
\(212\) 0 0
\(213\) −0.345445 −0.0236695
\(214\) 0 0
\(215\) 16.2767 1.11006
\(216\) 0 0
\(217\) 7.65880 0.519913
\(218\) 0 0
\(219\) −5.34093 −0.360907
\(220\) 0 0
\(221\) 3.01194 0.202605
\(222\) 0 0
\(223\) 8.06011 0.539745 0.269872 0.962896i \(-0.413018\pi\)
0.269872 + 0.962896i \(0.413018\pi\)
\(224\) 0 0
\(225\) 3.19835 0.213223
\(226\) 0 0
\(227\) −8.28497 −0.549893 −0.274946 0.961460i \(-0.588660\pi\)
−0.274946 + 0.961460i \(0.588660\pi\)
\(228\) 0 0
\(229\) −12.3828 −0.818276 −0.409138 0.912473i \(-0.634171\pi\)
−0.409138 + 0.912473i \(0.634171\pi\)
\(230\) 0 0
\(231\) 0.333725 0.0219575
\(232\) 0 0
\(233\) −16.3046 −1.06815 −0.534076 0.845436i \(-0.679341\pi\)
−0.534076 + 0.845436i \(0.679341\pi\)
\(234\) 0 0
\(235\) −12.3944 −0.808522
\(236\) 0 0
\(237\) −3.33128 −0.216390
\(238\) 0 0
\(239\) −7.93137 −0.513038 −0.256519 0.966539i \(-0.582576\pi\)
−0.256519 + 0.966539i \(0.582576\pi\)
\(240\) 0 0
\(241\) 2.94072 0.189429 0.0947143 0.995504i \(-0.469806\pi\)
0.0947143 + 0.995504i \(0.469806\pi\)
\(242\) 0 0
\(243\) −8.56870 −0.549682
\(244\) 0 0
\(245\) 1.97301 0.126051
\(246\) 0 0
\(247\) 7.23548 0.460383
\(248\) 0 0
\(249\) −1.38552 −0.0878036
\(250\) 0 0
\(251\) 3.12181 0.197047 0.0985236 0.995135i \(-0.468588\pi\)
0.0985236 + 0.995135i \(0.468588\pi\)
\(252\) 0 0
\(253\) −5.73685 −0.360673
\(254\) 0 0
\(255\) −1.98319 −0.124192
\(256\) 0 0
\(257\) −13.9680 −0.871298 −0.435649 0.900117i \(-0.643481\pi\)
−0.435649 + 0.900117i \(0.643481\pi\)
\(258\) 0 0
\(259\) −2.20318 −0.136899
\(260\) 0 0
\(261\) 14.5447 0.900294
\(262\) 0 0
\(263\) 4.99827 0.308207 0.154103 0.988055i \(-0.450751\pi\)
0.154103 + 0.988055i \(0.450751\pi\)
\(264\) 0 0
\(265\) −27.1275 −1.66643
\(266\) 0 0
\(267\) −0.997471 −0.0610442
\(268\) 0 0
\(269\) 15.7699 0.961507 0.480753 0.876856i \(-0.340363\pi\)
0.480753 + 0.876856i \(0.340363\pi\)
\(270\) 0 0
\(271\) −16.8059 −1.02088 −0.510442 0.859912i \(-0.670518\pi\)
−0.510442 + 0.859912i \(0.670518\pi\)
\(272\) 0 0
\(273\) 0.333725 0.0201979
\(274\) 0 0
\(275\) −1.10722 −0.0667679
\(276\) 0 0
\(277\) −23.1821 −1.39288 −0.696438 0.717617i \(-0.745233\pi\)
−0.696438 + 0.717617i \(0.745233\pi\)
\(278\) 0 0
\(279\) 22.1234 1.32450
\(280\) 0 0
\(281\) −27.3623 −1.63230 −0.816148 0.577843i \(-0.803895\pi\)
−0.816148 + 0.577843i \(0.803895\pi\)
\(282\) 0 0
\(283\) −9.12121 −0.542199 −0.271100 0.962551i \(-0.587387\pi\)
−0.271100 + 0.962551i \(0.587387\pi\)
\(284\) 0 0
\(285\) −4.76415 −0.282204
\(286\) 0 0
\(287\) 7.09291 0.418681
\(288\) 0 0
\(289\) −7.92823 −0.466366
\(290\) 0 0
\(291\) −0.429747 −0.0251922
\(292\) 0 0
\(293\) −23.0401 −1.34602 −0.673008 0.739635i \(-0.734998\pi\)
−0.673008 + 0.739635i \(0.734998\pi\)
\(294\) 0 0
\(295\) −23.0402 −1.34145
\(296\) 0 0
\(297\) 1.96518 0.114031
\(298\) 0 0
\(299\) −5.73685 −0.331771
\(300\) 0 0
\(301\) −8.24968 −0.475504
\(302\) 0 0
\(303\) 6.42622 0.369177
\(304\) 0 0
\(305\) −13.2542 −0.758936
\(306\) 0 0
\(307\) −17.5530 −1.00181 −0.500903 0.865504i \(-0.666999\pi\)
−0.500903 + 0.865504i \(0.666999\pi\)
\(308\) 0 0
\(309\) −0.908950 −0.0517083
\(310\) 0 0
\(311\) 18.9725 1.07583 0.537916 0.842998i \(-0.319212\pi\)
0.537916 + 0.842998i \(0.319212\pi\)
\(312\) 0 0
\(313\) −29.3098 −1.65669 −0.828343 0.560221i \(-0.810716\pi\)
−0.828343 + 0.560221i \(0.810716\pi\)
\(314\) 0 0
\(315\) 5.69930 0.321119
\(316\) 0 0
\(317\) −12.8597 −0.722271 −0.361136 0.932513i \(-0.617611\pi\)
−0.361136 + 0.932513i \(0.617611\pi\)
\(318\) 0 0
\(319\) −5.03516 −0.281915
\(320\) 0 0
\(321\) −3.02348 −0.168754
\(322\) 0 0
\(323\) 21.7928 1.21259
\(324\) 0 0
\(325\) −1.10722 −0.0614175
\(326\) 0 0
\(327\) 1.11856 0.0618563
\(328\) 0 0
\(329\) 6.28197 0.346336
\(330\) 0 0
\(331\) 1.89233 0.104012 0.0520059 0.998647i \(-0.483439\pi\)
0.0520059 + 0.998647i \(0.483439\pi\)
\(332\) 0 0
\(333\) −6.36416 −0.348754
\(334\) 0 0
\(335\) −0.768082 −0.0419648
\(336\) 0 0
\(337\) −6.60409 −0.359748 −0.179874 0.983690i \(-0.557569\pi\)
−0.179874 + 0.983690i \(0.557569\pi\)
\(338\) 0 0
\(339\) 2.13977 0.116216
\(340\) 0 0
\(341\) −7.65880 −0.414747
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 3.77739 0.203368
\(346\) 0 0
\(347\) 17.2070 0.923718 0.461859 0.886953i \(-0.347183\pi\)
0.461859 + 0.886953i \(0.347183\pi\)
\(348\) 0 0
\(349\) 13.5809 0.726970 0.363485 0.931600i \(-0.381587\pi\)
0.363485 + 0.931600i \(0.381587\pi\)
\(350\) 0 0
\(351\) 1.96518 0.104894
\(352\) 0 0
\(353\) −35.7862 −1.90471 −0.952353 0.304998i \(-0.901344\pi\)
−0.952353 + 0.304998i \(0.901344\pi\)
\(354\) 0 0
\(355\) 2.04230 0.108394
\(356\) 0 0
\(357\) 1.00516 0.0531986
\(358\) 0 0
\(359\) 20.0878 1.06020 0.530098 0.847937i \(-0.322155\pi\)
0.530098 + 0.847937i \(0.322155\pi\)
\(360\) 0 0
\(361\) 33.3522 1.75538
\(362\) 0 0
\(363\) −0.333725 −0.0175160
\(364\) 0 0
\(365\) 31.5761 1.65277
\(366\) 0 0
\(367\) 6.45117 0.336748 0.168374 0.985723i \(-0.446148\pi\)
0.168374 + 0.985723i \(0.446148\pi\)
\(368\) 0 0
\(369\) 20.4888 1.06660
\(370\) 0 0
\(371\) 13.7493 0.713826
\(372\) 0 0
\(373\) 24.7860 1.28337 0.641686 0.766967i \(-0.278235\pi\)
0.641686 + 0.766967i \(0.278235\pi\)
\(374\) 0 0
\(375\) 4.02126 0.207657
\(376\) 0 0
\(377\) −5.03516 −0.259324
\(378\) 0 0
\(379\) −8.93159 −0.458785 −0.229392 0.973334i \(-0.573674\pi\)
−0.229392 + 0.973334i \(0.573674\pi\)
\(380\) 0 0
\(381\) −2.82799 −0.144882
\(382\) 0 0
\(383\) 13.9332 0.711952 0.355976 0.934495i \(-0.384148\pi\)
0.355976 + 0.934495i \(0.384148\pi\)
\(384\) 0 0
\(385\) −1.97301 −0.100554
\(386\) 0 0
\(387\) −23.8303 −1.21136
\(388\) 0 0
\(389\) −15.9822 −0.810331 −0.405166 0.914243i \(-0.632786\pi\)
−0.405166 + 0.914243i \(0.632786\pi\)
\(390\) 0 0
\(391\) −17.2790 −0.873839
\(392\) 0 0
\(393\) 0.954703 0.0481584
\(394\) 0 0
\(395\) 19.6949 0.990956
\(396\) 0 0
\(397\) 34.5270 1.73286 0.866431 0.499297i \(-0.166408\pi\)
0.866431 + 0.499297i \(0.166408\pi\)
\(398\) 0 0
\(399\) 2.41466 0.120884
\(400\) 0 0
\(401\) 13.5148 0.674896 0.337448 0.941344i \(-0.390436\pi\)
0.337448 + 0.941344i \(0.390436\pi\)
\(402\) 0 0
\(403\) −7.65880 −0.381512
\(404\) 0 0
\(405\) 15.8039 0.785304
\(406\) 0 0
\(407\) 2.20318 0.109207
\(408\) 0 0
\(409\) −23.4248 −1.15828 −0.579141 0.815227i \(-0.696612\pi\)
−0.579141 + 0.815227i \(0.696612\pi\)
\(410\) 0 0
\(411\) −7.15546 −0.352953
\(412\) 0 0
\(413\) 11.6777 0.574621
\(414\) 0 0
\(415\) 8.19131 0.402095
\(416\) 0 0
\(417\) −0.458265 −0.0224413
\(418\) 0 0
\(419\) 7.70241 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(420\) 0 0
\(421\) −12.2520 −0.597127 −0.298563 0.954390i \(-0.596507\pi\)
−0.298563 + 0.954390i \(0.596507\pi\)
\(422\) 0 0
\(423\) 18.1463 0.882302
\(424\) 0 0
\(425\) −3.33488 −0.161765
\(426\) 0 0
\(427\) 6.71777 0.325096
\(428\) 0 0
\(429\) −0.333725 −0.0161124
\(430\) 0 0
\(431\) −3.25226 −0.156656 −0.0783280 0.996928i \(-0.524958\pi\)
−0.0783280 + 0.996928i \(0.524958\pi\)
\(432\) 0 0
\(433\) 29.1913 1.40285 0.701423 0.712745i \(-0.252548\pi\)
0.701423 + 0.712745i \(0.252548\pi\)
\(434\) 0 0
\(435\) 3.31537 0.158960
\(436\) 0 0
\(437\) −41.5089 −1.98564
\(438\) 0 0
\(439\) 22.5808 1.07772 0.538861 0.842395i \(-0.318855\pi\)
0.538861 + 0.842395i \(0.318855\pi\)
\(440\) 0 0
\(441\) −2.88863 −0.137554
\(442\) 0 0
\(443\) 36.2552 1.72254 0.861268 0.508151i \(-0.169671\pi\)
0.861268 + 0.508151i \(0.169671\pi\)
\(444\) 0 0
\(445\) 5.89714 0.279551
\(446\) 0 0
\(447\) 7.15437 0.338390
\(448\) 0 0
\(449\) −27.5209 −1.29879 −0.649397 0.760450i \(-0.724979\pi\)
−0.649397 + 0.760450i \(0.724979\pi\)
\(450\) 0 0
\(451\) −7.09291 −0.333992
\(452\) 0 0
\(453\) −2.43717 −0.114508
\(454\) 0 0
\(455\) −1.97301 −0.0924963
\(456\) 0 0
\(457\) −20.0616 −0.938442 −0.469221 0.883081i \(-0.655465\pi\)
−0.469221 + 0.883081i \(0.655465\pi\)
\(458\) 0 0
\(459\) 5.91901 0.276275
\(460\) 0 0
\(461\) 25.6492 1.19460 0.597300 0.802018i \(-0.296240\pi\)
0.597300 + 0.802018i \(0.296240\pi\)
\(462\) 0 0
\(463\) −18.3062 −0.850763 −0.425381 0.905014i \(-0.639860\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(464\) 0 0
\(465\) 5.04289 0.233858
\(466\) 0 0
\(467\) −14.3676 −0.664851 −0.332426 0.943129i \(-0.607867\pi\)
−0.332426 + 0.943129i \(0.607867\pi\)
\(468\) 0 0
\(469\) 0.389294 0.0179759
\(470\) 0 0
\(471\) 6.78836 0.312791
\(472\) 0 0
\(473\) 8.24968 0.379321
\(474\) 0 0
\(475\) −8.01127 −0.367582
\(476\) 0 0
\(477\) 39.7165 1.81849
\(478\) 0 0
\(479\) 16.0193 0.731939 0.365970 0.930627i \(-0.380737\pi\)
0.365970 + 0.930627i \(0.380737\pi\)
\(480\) 0 0
\(481\) 2.20318 0.100456
\(482\) 0 0
\(483\) −1.91453 −0.0871141
\(484\) 0 0
\(485\) 2.54071 0.115367
\(486\) 0 0
\(487\) −8.68225 −0.393430 −0.196715 0.980461i \(-0.563027\pi\)
−0.196715 + 0.980461i \(0.563027\pi\)
\(488\) 0 0
\(489\) 4.99677 0.225962
\(490\) 0 0
\(491\) −12.1332 −0.547565 −0.273783 0.961792i \(-0.588275\pi\)
−0.273783 + 0.961792i \(0.588275\pi\)
\(492\) 0 0
\(493\) −15.1656 −0.683024
\(494\) 0 0
\(495\) −5.69930 −0.256164
\(496\) 0 0
\(497\) −1.03512 −0.0464315
\(498\) 0 0
\(499\) −33.0619 −1.48006 −0.740028 0.672576i \(-0.765188\pi\)
−0.740028 + 0.672576i \(0.765188\pi\)
\(500\) 0 0
\(501\) 3.97778 0.177714
\(502\) 0 0
\(503\) −34.5205 −1.53920 −0.769598 0.638529i \(-0.779543\pi\)
−0.769598 + 0.638529i \(0.779543\pi\)
\(504\) 0 0
\(505\) −37.9924 −1.69064
\(506\) 0 0
\(507\) −0.333725 −0.0148212
\(508\) 0 0
\(509\) 26.7308 1.18482 0.592411 0.805636i \(-0.298176\pi\)
0.592411 + 0.805636i \(0.298176\pi\)
\(510\) 0 0
\(511\) −16.0040 −0.707975
\(512\) 0 0
\(513\) 14.2190 0.627786
\(514\) 0 0
\(515\) 5.37380 0.236798
\(516\) 0 0
\(517\) −6.28197 −0.276281
\(518\) 0 0
\(519\) −6.91240 −0.303421
\(520\) 0 0
\(521\) −11.5034 −0.503973 −0.251987 0.967731i \(-0.581084\pi\)
−0.251987 + 0.967731i \(0.581084\pi\)
\(522\) 0 0
\(523\) 35.6213 1.55761 0.778805 0.627267i \(-0.215826\pi\)
0.778805 + 0.627267i \(0.215826\pi\)
\(524\) 0 0
\(525\) −0.369507 −0.0161266
\(526\) 0 0
\(527\) −23.0678 −1.00485
\(528\) 0 0
\(529\) 9.91144 0.430932
\(530\) 0 0
\(531\) 33.7325 1.46386
\(532\) 0 0
\(533\) −7.09291 −0.307228
\(534\) 0 0
\(535\) 17.8751 0.772808
\(536\) 0 0
\(537\) −6.45578 −0.278588
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 30.8895 1.32804 0.664021 0.747714i \(-0.268849\pi\)
0.664021 + 0.747714i \(0.268849\pi\)
\(542\) 0 0
\(543\) 3.18332 0.136609
\(544\) 0 0
\(545\) −6.61301 −0.283270
\(546\) 0 0
\(547\) −2.17472 −0.0929841 −0.0464921 0.998919i \(-0.514804\pi\)
−0.0464921 + 0.998919i \(0.514804\pi\)
\(548\) 0 0
\(549\) 19.4051 0.828191
\(550\) 0 0
\(551\) −36.4318 −1.55205
\(552\) 0 0
\(553\) −9.98212 −0.424483
\(554\) 0 0
\(555\) −1.45067 −0.0615774
\(556\) 0 0
\(557\) −27.2411 −1.15424 −0.577122 0.816658i \(-0.695824\pi\)
−0.577122 + 0.816658i \(0.695824\pi\)
\(558\) 0 0
\(559\) 8.24968 0.348924
\(560\) 0 0
\(561\) −1.00516 −0.0424378
\(562\) 0 0
\(563\) −16.2803 −0.686131 −0.343066 0.939311i \(-0.611465\pi\)
−0.343066 + 0.939311i \(0.611465\pi\)
\(564\) 0 0
\(565\) −12.6505 −0.532210
\(566\) 0 0
\(567\) −8.01005 −0.336391
\(568\) 0 0
\(569\) 7.80361 0.327144 0.163572 0.986531i \(-0.447698\pi\)
0.163572 + 0.986531i \(0.447698\pi\)
\(570\) 0 0
\(571\) −15.4786 −0.647760 −0.323880 0.946098i \(-0.604987\pi\)
−0.323880 + 0.946098i \(0.604987\pi\)
\(572\) 0 0
\(573\) 8.77285 0.366491
\(574\) 0 0
\(575\) 6.35195 0.264895
\(576\) 0 0
\(577\) 6.80388 0.283249 0.141625 0.989920i \(-0.454767\pi\)
0.141625 + 0.989920i \(0.454767\pi\)
\(578\) 0 0
\(579\) 0.00455347 0.000189236 0
\(580\) 0 0
\(581\) −4.15167 −0.172240
\(582\) 0 0
\(583\) −13.7493 −0.569436
\(584\) 0 0
\(585\) −5.69930 −0.235637
\(586\) 0 0
\(587\) −5.50993 −0.227419 −0.113710 0.993514i \(-0.536273\pi\)
−0.113710 + 0.993514i \(0.536273\pi\)
\(588\) 0 0
\(589\) −55.4151 −2.28334
\(590\) 0 0
\(591\) 2.45621 0.101035
\(592\) 0 0
\(593\) 2.55857 0.105068 0.0525339 0.998619i \(-0.483270\pi\)
0.0525339 + 0.998619i \(0.483270\pi\)
\(594\) 0 0
\(595\) −5.94259 −0.243623
\(596\) 0 0
\(597\) 6.31096 0.258290
\(598\) 0 0
\(599\) −6.57756 −0.268752 −0.134376 0.990930i \(-0.542903\pi\)
−0.134376 + 0.990930i \(0.542903\pi\)
\(600\) 0 0
\(601\) 26.7139 1.08968 0.544841 0.838540i \(-0.316590\pi\)
0.544841 + 0.838540i \(0.316590\pi\)
\(602\) 0 0
\(603\) 1.12453 0.0457942
\(604\) 0 0
\(605\) 1.97301 0.0802144
\(606\) 0 0
\(607\) 12.9126 0.524106 0.262053 0.965053i \(-0.415600\pi\)
0.262053 + 0.965053i \(0.415600\pi\)
\(608\) 0 0
\(609\) −1.68036 −0.0680915
\(610\) 0 0
\(611\) −6.28197 −0.254141
\(612\) 0 0
\(613\) −41.1308 −1.66126 −0.830630 0.556825i \(-0.812019\pi\)
−0.830630 + 0.556825i \(0.812019\pi\)
\(614\) 0 0
\(615\) 4.67028 0.188324
\(616\) 0 0
\(617\) −12.0996 −0.487112 −0.243556 0.969887i \(-0.578314\pi\)
−0.243556 + 0.969887i \(0.578314\pi\)
\(618\) 0 0
\(619\) −1.42334 −0.0572087 −0.0286043 0.999591i \(-0.509106\pi\)
−0.0286043 + 0.999591i \(0.509106\pi\)
\(620\) 0 0
\(621\) −11.2739 −0.452408
\(622\) 0 0
\(623\) −2.98890 −0.119748
\(624\) 0 0
\(625\) −18.2380 −0.729519
\(626\) 0 0
\(627\) −2.41466 −0.0964322
\(628\) 0 0
\(629\) 6.63584 0.264588
\(630\) 0 0
\(631\) 31.9088 1.27027 0.635135 0.772401i \(-0.280945\pi\)
0.635135 + 0.772401i \(0.280945\pi\)
\(632\) 0 0
\(633\) −6.92954 −0.275425
\(634\) 0 0
\(635\) 16.7194 0.663488
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −2.99008 −0.118286
\(640\) 0 0
\(641\) −46.8794 −1.85162 −0.925812 0.377984i \(-0.876617\pi\)
−0.925812 + 0.377984i \(0.876617\pi\)
\(642\) 0 0
\(643\) 4.36336 0.172074 0.0860370 0.996292i \(-0.472580\pi\)
0.0860370 + 0.996292i \(0.472580\pi\)
\(644\) 0 0
\(645\) −5.43195 −0.213883
\(646\) 0 0
\(647\) −6.75159 −0.265432 −0.132716 0.991154i \(-0.542370\pi\)
−0.132716 + 0.991154i \(0.542370\pi\)
\(648\) 0 0
\(649\) −11.6777 −0.458389
\(650\) 0 0
\(651\) −2.55593 −0.100175
\(652\) 0 0
\(653\) 28.8122 1.12751 0.563754 0.825943i \(-0.309357\pi\)
0.563754 + 0.825943i \(0.309357\pi\)
\(654\) 0 0
\(655\) −5.64430 −0.220541
\(656\) 0 0
\(657\) −46.2296 −1.80359
\(658\) 0 0
\(659\) −36.0871 −1.40575 −0.702876 0.711312i \(-0.748101\pi\)
−0.702876 + 0.711312i \(0.748101\pi\)
\(660\) 0 0
\(661\) −5.98285 −0.232706 −0.116353 0.993208i \(-0.537120\pi\)
−0.116353 + 0.993208i \(0.537120\pi\)
\(662\) 0 0
\(663\) −1.00516 −0.0390371
\(664\) 0 0
\(665\) −14.2757 −0.553588
\(666\) 0 0
\(667\) 28.8860 1.11847
\(668\) 0 0
\(669\) −2.68986 −0.103996
\(670\) 0 0
\(671\) −6.71777 −0.259337
\(672\) 0 0
\(673\) −5.18162 −0.199737 −0.0998683 0.995001i \(-0.531842\pi\)
−0.0998683 + 0.995001i \(0.531842\pi\)
\(674\) 0 0
\(675\) −2.17589 −0.0837500
\(676\) 0 0
\(677\) 19.6368 0.754704 0.377352 0.926070i \(-0.376835\pi\)
0.377352 + 0.926070i \(0.376835\pi\)
\(678\) 0 0
\(679\) −1.28773 −0.0494185
\(680\) 0 0
\(681\) 2.76490 0.105951
\(682\) 0 0
\(683\) −31.1124 −1.19048 −0.595241 0.803547i \(-0.702944\pi\)
−0.595241 + 0.803547i \(0.702944\pi\)
\(684\) 0 0
\(685\) 42.3037 1.61634
\(686\) 0 0
\(687\) 4.13244 0.157662
\(688\) 0 0
\(689\) −13.7493 −0.523805
\(690\) 0 0
\(691\) −19.6363 −0.747001 −0.373500 0.927630i \(-0.621843\pi\)
−0.373500 + 0.927630i \(0.621843\pi\)
\(692\) 0 0
\(693\) 2.88863 0.109730
\(694\) 0 0
\(695\) 2.70931 0.102770
\(696\) 0 0
\(697\) −21.3634 −0.809197
\(698\) 0 0
\(699\) 5.44126 0.205807
\(700\) 0 0
\(701\) 13.4620 0.508452 0.254226 0.967145i \(-0.418179\pi\)
0.254226 + 0.967145i \(0.418179\pi\)
\(702\) 0 0
\(703\) 15.9411 0.601228
\(704\) 0 0
\(705\) 4.13632 0.155783
\(706\) 0 0
\(707\) 19.2561 0.724198
\(708\) 0 0
\(709\) −30.9345 −1.16177 −0.580884 0.813986i \(-0.697293\pi\)
−0.580884 + 0.813986i \(0.697293\pi\)
\(710\) 0 0
\(711\) −28.8346 −1.08138
\(712\) 0 0
\(713\) 43.9374 1.64547
\(714\) 0 0
\(715\) 1.97301 0.0737865
\(716\) 0 0
\(717\) 2.64690 0.0988502
\(718\) 0 0
\(719\) 39.0701 1.45707 0.728534 0.685009i \(-0.240202\pi\)
0.728534 + 0.685009i \(0.240202\pi\)
\(720\) 0 0
\(721\) −2.72365 −0.101434
\(722\) 0 0
\(723\) −0.981392 −0.0364984
\(724\) 0 0
\(725\) 5.57503 0.207051
\(726\) 0 0
\(727\) −4.29250 −0.159200 −0.0795999 0.996827i \(-0.525364\pi\)
−0.0795999 + 0.996827i \(0.525364\pi\)
\(728\) 0 0
\(729\) −21.1706 −0.784095
\(730\) 0 0
\(731\) 24.8475 0.919019
\(732\) 0 0
\(733\) −0.420890 −0.0155459 −0.00777297 0.999970i \(-0.502474\pi\)
−0.00777297 + 0.999970i \(0.502474\pi\)
\(734\) 0 0
\(735\) −0.658443 −0.0242870
\(736\) 0 0
\(737\) −0.389294 −0.0143398
\(738\) 0 0
\(739\) 41.3074 1.51952 0.759759 0.650204i \(-0.225317\pi\)
0.759759 + 0.650204i \(0.225317\pi\)
\(740\) 0 0
\(741\) −2.41466 −0.0887047
\(742\) 0 0
\(743\) 39.3027 1.44188 0.720938 0.692999i \(-0.243711\pi\)
0.720938 + 0.692999i \(0.243711\pi\)
\(744\) 0 0
\(745\) −42.2973 −1.54965
\(746\) 0 0
\(747\) −11.9926 −0.438788
\(748\) 0 0
\(749\) −9.05980 −0.331038
\(750\) 0 0
\(751\) −13.9043 −0.507375 −0.253688 0.967286i \(-0.581643\pi\)
−0.253688 + 0.967286i \(0.581643\pi\)
\(752\) 0 0
\(753\) −1.04183 −0.0379663
\(754\) 0 0
\(755\) 14.4088 0.524389
\(756\) 0 0
\(757\) 1.48474 0.0539638 0.0269819 0.999636i \(-0.491410\pi\)
0.0269819 + 0.999636i \(0.491410\pi\)
\(758\) 0 0
\(759\) 1.91453 0.0694930
\(760\) 0 0
\(761\) 42.4869 1.54015 0.770075 0.637953i \(-0.220219\pi\)
0.770075 + 0.637953i \(0.220219\pi\)
\(762\) 0 0
\(763\) 3.35173 0.121341
\(764\) 0 0
\(765\) −17.1659 −0.620636
\(766\) 0 0
\(767\) −11.6777 −0.421657
\(768\) 0 0
\(769\) 42.3380 1.52675 0.763374 0.645956i \(-0.223541\pi\)
0.763374 + 0.645956i \(0.223541\pi\)
\(770\) 0 0
\(771\) 4.66146 0.167878
\(772\) 0 0
\(773\) −15.2131 −0.547177 −0.273589 0.961847i \(-0.588211\pi\)
−0.273589 + 0.961847i \(0.588211\pi\)
\(774\) 0 0
\(775\) 8.47998 0.304610
\(776\) 0 0
\(777\) 0.735255 0.0263771
\(778\) 0 0
\(779\) −51.3206 −1.83875
\(780\) 0 0
\(781\) 1.03512 0.0370395
\(782\) 0 0
\(783\) −9.89500 −0.353618
\(784\) 0 0
\(785\) −40.1334 −1.43242
\(786\) 0 0
\(787\) −52.9559 −1.88767 −0.943837 0.330412i \(-0.892812\pi\)
−0.943837 + 0.330412i \(0.892812\pi\)
\(788\) 0 0
\(789\) −1.66805 −0.0593840
\(790\) 0 0
\(791\) 6.41177 0.227976
\(792\) 0 0
\(793\) −6.71777 −0.238555
\(794\) 0 0
\(795\) 9.05311 0.321081
\(796\) 0 0
\(797\) 12.8354 0.454652 0.227326 0.973819i \(-0.427002\pi\)
0.227326 + 0.973819i \(0.427002\pi\)
\(798\) 0 0
\(799\) −18.9209 −0.669374
\(800\) 0 0
\(801\) −8.63383 −0.305061
\(802\) 0 0
\(803\) 16.0040 0.564769
\(804\) 0 0
\(805\) 11.3189 0.398938
\(806\) 0 0
\(807\) −5.26280 −0.185259
\(808\) 0 0
\(809\) −46.9610 −1.65106 −0.825531 0.564356i \(-0.809124\pi\)
−0.825531 + 0.564356i \(0.809124\pi\)
\(810\) 0 0
\(811\) −23.4840 −0.824635 −0.412317 0.911040i \(-0.635280\pi\)
−0.412317 + 0.911040i \(0.635280\pi\)
\(812\) 0 0
\(813\) 5.60854 0.196700
\(814\) 0 0
\(815\) −29.5414 −1.03479
\(816\) 0 0
\(817\) 59.6904 2.08830
\(818\) 0 0
\(819\) 2.88863 0.100937
\(820\) 0 0
\(821\) 25.5084 0.890250 0.445125 0.895468i \(-0.353159\pi\)
0.445125 + 0.895468i \(0.353159\pi\)
\(822\) 0 0
\(823\) −14.1797 −0.494272 −0.247136 0.968981i \(-0.579490\pi\)
−0.247136 + 0.968981i \(0.579490\pi\)
\(824\) 0 0
\(825\) 0.369507 0.0128646
\(826\) 0 0
\(827\) −49.7107 −1.72861 −0.864305 0.502969i \(-0.832241\pi\)
−0.864305 + 0.502969i \(0.832241\pi\)
\(828\) 0 0
\(829\) 30.0671 1.04427 0.522137 0.852861i \(-0.325135\pi\)
0.522137 + 0.852861i \(0.325135\pi\)
\(830\) 0 0
\(831\) 7.73643 0.268374
\(832\) 0 0
\(833\) 3.01194 0.104357
\(834\) 0 0
\(835\) −23.5170 −0.813839
\(836\) 0 0
\(837\) −15.0509 −0.520236
\(838\) 0 0
\(839\) −37.9182 −1.30908 −0.654541 0.756027i \(-0.727138\pi\)
−0.654541 + 0.756027i \(0.727138\pi\)
\(840\) 0 0
\(841\) −3.64717 −0.125764
\(842\) 0 0
\(843\) 9.13147 0.314504
\(844\) 0 0
\(845\) 1.97301 0.0678737
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 3.04397 0.104469
\(850\) 0 0
\(851\) −12.6393 −0.433270
\(852\) 0 0
\(853\) −44.3174 −1.51740 −0.758700 0.651440i \(-0.774165\pi\)
−0.758700 + 0.651440i \(0.774165\pi\)
\(854\) 0 0
\(855\) −41.2372 −1.41028
\(856\) 0 0
\(857\) −28.8189 −0.984435 −0.492218 0.870472i \(-0.663814\pi\)
−0.492218 + 0.870472i \(0.663814\pi\)
\(858\) 0 0
\(859\) 11.9287 0.407003 0.203501 0.979075i \(-0.434768\pi\)
0.203501 + 0.979075i \(0.434768\pi\)
\(860\) 0 0
\(861\) −2.36708 −0.0806699
\(862\) 0 0
\(863\) 14.9535 0.509022 0.254511 0.967070i \(-0.418085\pi\)
0.254511 + 0.967070i \(0.418085\pi\)
\(864\) 0 0
\(865\) 40.8668 1.38951
\(866\) 0 0
\(867\) 2.64585 0.0898576
\(868\) 0 0
\(869\) 9.98212 0.338620
\(870\) 0 0
\(871\) −0.389294 −0.0131907
\(872\) 0 0
\(873\) −3.71977 −0.125895
\(874\) 0 0
\(875\) 12.0496 0.407352
\(876\) 0 0
\(877\) −39.4530 −1.33223 −0.666116 0.745848i \(-0.732044\pi\)
−0.666116 + 0.745848i \(0.732044\pi\)
\(878\) 0 0
\(879\) 7.68905 0.259345
\(880\) 0 0
\(881\) 36.6337 1.23422 0.617110 0.786877i \(-0.288303\pi\)
0.617110 + 0.786877i \(0.288303\pi\)
\(882\) 0 0
\(883\) 47.3345 1.59293 0.796467 0.604682i \(-0.206700\pi\)
0.796467 + 0.604682i \(0.206700\pi\)
\(884\) 0 0
\(885\) 7.68909 0.258466
\(886\) 0 0
\(887\) −33.9341 −1.13940 −0.569698 0.821854i \(-0.692940\pi\)
−0.569698 + 0.821854i \(0.692940\pi\)
\(888\) 0 0
\(889\) −8.47402 −0.284210
\(890\) 0 0
\(891\) 8.01005 0.268347
\(892\) 0 0
\(893\) −45.4531 −1.52103
\(894\) 0 0
\(895\) 38.1672 1.27579
\(896\) 0 0
\(897\) 1.91453 0.0639243
\(898\) 0 0
\(899\) 38.5633 1.28616
\(900\) 0 0
\(901\) −41.4119 −1.37963
\(902\) 0 0
\(903\) 2.75312 0.0916182
\(904\) 0 0
\(905\) −18.8201 −0.625602
\(906\) 0 0
\(907\) 55.4136 1.83998 0.919989 0.391943i \(-0.128197\pi\)
0.919989 + 0.391943i \(0.128197\pi\)
\(908\) 0 0
\(909\) 55.6236 1.84492
\(910\) 0 0
\(911\) 31.7810 1.05295 0.526476 0.850190i \(-0.323513\pi\)
0.526476 + 0.850190i \(0.323513\pi\)
\(912\) 0 0
\(913\) 4.15167 0.137400
\(914\) 0 0
\(915\) 4.42327 0.146229
\(916\) 0 0
\(917\) 2.86075 0.0944703
\(918\) 0 0
\(919\) 11.4409 0.377399 0.188700 0.982035i \(-0.439573\pi\)
0.188700 + 0.982035i \(0.439573\pi\)
\(920\) 0 0
\(921\) 5.85789 0.193024
\(922\) 0 0
\(923\) 1.03512 0.0340714
\(924\) 0 0
\(925\) −2.43940 −0.0802071
\(926\) 0 0
\(927\) −7.86761 −0.258406
\(928\) 0 0
\(929\) 12.9478 0.424804 0.212402 0.977182i \(-0.431871\pi\)
0.212402 + 0.977182i \(0.431871\pi\)
\(930\) 0 0
\(931\) 7.23548 0.237133
\(932\) 0 0
\(933\) −6.33160 −0.207287
\(934\) 0 0
\(935\) 5.94259 0.194344
\(936\) 0 0
\(937\) 2.59120 0.0846507 0.0423253 0.999104i \(-0.486523\pi\)
0.0423253 + 0.999104i \(0.486523\pi\)
\(938\) 0 0
\(939\) 9.78140 0.319204
\(940\) 0 0
\(941\) 5.51308 0.179721 0.0898607 0.995954i \(-0.471358\pi\)
0.0898607 + 0.995954i \(0.471358\pi\)
\(942\) 0 0
\(943\) 40.6910 1.32508
\(944\) 0 0
\(945\) −3.87733 −0.126129
\(946\) 0 0
\(947\) 5.91068 0.192071 0.0960356 0.995378i \(-0.469384\pi\)
0.0960356 + 0.995378i \(0.469384\pi\)
\(948\) 0 0
\(949\) 16.0040 0.519512
\(950\) 0 0
\(951\) 4.29159 0.139164
\(952\) 0 0
\(953\) 39.7042 1.28615 0.643073 0.765805i \(-0.277659\pi\)
0.643073 + 0.765805i \(0.277659\pi\)
\(954\) 0 0
\(955\) −51.8659 −1.67834
\(956\) 0 0
\(957\) 1.68036 0.0543182
\(958\) 0 0
\(959\) −21.4412 −0.692372
\(960\) 0 0
\(961\) 27.6573 0.892170
\(962\) 0 0
\(963\) −26.1704 −0.843329
\(964\) 0 0
\(965\) −0.0269205 −0.000866603 0
\(966\) 0 0
\(967\) 38.3582 1.23352 0.616759 0.787152i \(-0.288445\pi\)
0.616759 + 0.787152i \(0.288445\pi\)
\(968\) 0 0
\(969\) −7.27281 −0.233636
\(970\) 0 0
\(971\) −23.9671 −0.769142 −0.384571 0.923095i \(-0.625651\pi\)
−0.384571 + 0.923095i \(0.625651\pi\)
\(972\) 0 0
\(973\) −1.37318 −0.0440222
\(974\) 0 0
\(975\) 0.369507 0.0118337
\(976\) 0 0
\(977\) 9.19563 0.294194 0.147097 0.989122i \(-0.453007\pi\)
0.147097 + 0.989122i \(0.453007\pi\)
\(978\) 0 0
\(979\) 2.98890 0.0955257
\(980\) 0 0
\(981\) 9.68190 0.309119
\(982\) 0 0
\(983\) 33.4086 1.06557 0.532784 0.846251i \(-0.321146\pi\)
0.532784 + 0.846251i \(0.321146\pi\)
\(984\) 0 0
\(985\) −14.5214 −0.462689
\(986\) 0 0
\(987\) −2.09645 −0.0667307
\(988\) 0 0
\(989\) −47.3272 −1.50492
\(990\) 0 0
\(991\) 7.27070 0.230961 0.115481 0.993310i \(-0.463159\pi\)
0.115481 + 0.993310i \(0.463159\pi\)
\(992\) 0 0
\(993\) −0.631517 −0.0200406
\(994\) 0 0
\(995\) −37.3110 −1.18284
\(996\) 0 0
\(997\) 0.815713 0.0258339 0.0129170 0.999917i \(-0.495888\pi\)
0.0129170 + 0.999917i \(0.495888\pi\)
\(998\) 0 0
\(999\) 4.32964 0.136984
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 \(a_p\))