Properties

Label 8004.2.a.j.1.8
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.434018\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.434018 q^{5}\) \(-2.25969 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.434018 q^{5}\) \(-2.25969 q^{7}\) \(+1.00000 q^{9}\) \(+3.49169 q^{11}\) \(+5.02170 q^{13}\) \(-0.434018 q^{15}\) \(-0.922556 q^{17}\) \(+5.87027 q^{19}\) \(-2.25969 q^{21}\) \(+1.00000 q^{23}\) \(-4.81163 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+9.57575 q^{31}\) \(+3.49169 q^{33}\) \(+0.980749 q^{35}\) \(+2.89227 q^{37}\) \(+5.02170 q^{39}\) \(-5.70503 q^{41}\) \(+4.57680 q^{43}\) \(-0.434018 q^{45}\) \(-1.28633 q^{47}\) \(-1.89378 q^{49}\) \(-0.922556 q^{51}\) \(-9.88390 q^{53}\) \(-1.51546 q^{55}\) \(+5.87027 q^{57}\) \(-0.268728 q^{59}\) \(-4.59157 q^{61}\) \(-2.25969 q^{63}\) \(-2.17951 q^{65}\) \(+12.9610 q^{67}\) \(+1.00000 q^{69}\) \(-1.25321 q^{71}\) \(-2.10581 q^{73}\) \(-4.81163 q^{75}\) \(-7.89016 q^{77}\) \(-9.21562 q^{79}\) \(+1.00000 q^{81}\) \(+3.24748 q^{83}\) \(+0.400406 q^{85}\) \(-1.00000 q^{87}\) \(+8.36608 q^{89}\) \(-11.3475 q^{91}\) \(+9.57575 q^{93}\) \(-2.54781 q^{95}\) \(+0.502057 q^{97}\) \(+3.49169 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −0.434018 −0.194099 −0.0970495 0.995280i \(-0.530941\pi\)
−0.0970495 + 0.995280i \(0.530941\pi\)
\(6\) 0 0
\(7\) −2.25969 −0.854084 −0.427042 0.904232i \(-0.640444\pi\)
−0.427042 + 0.904232i \(0.640444\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.49169 1.05278 0.526392 0.850242i \(-0.323544\pi\)
0.526392 + 0.850242i \(0.323544\pi\)
\(12\) 0 0
\(13\) 5.02170 1.39277 0.696384 0.717669i \(-0.254791\pi\)
0.696384 + 0.717669i \(0.254791\pi\)
\(14\) 0 0
\(15\) −0.434018 −0.112063
\(16\) 0 0
\(17\) −0.922556 −0.223753 −0.111876 0.993722i \(-0.535686\pi\)
−0.111876 + 0.993722i \(0.535686\pi\)
\(18\) 0 0
\(19\) 5.87027 1.34673 0.673367 0.739309i \(-0.264848\pi\)
0.673367 + 0.739309i \(0.264848\pi\)
\(20\) 0 0
\(21\) −2.25969 −0.493106
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.81163 −0.962326
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 9.57575 1.71986 0.859928 0.510416i \(-0.170508\pi\)
0.859928 + 0.510416i \(0.170508\pi\)
\(32\) 0 0
\(33\) 3.49169 0.607826
\(34\) 0 0
\(35\) 0.980749 0.165777
\(36\) 0 0
\(37\) 2.89227 0.475487 0.237743 0.971328i \(-0.423592\pi\)
0.237743 + 0.971328i \(0.423592\pi\)
\(38\) 0 0
\(39\) 5.02170 0.804115
\(40\) 0 0
\(41\) −5.70503 −0.890975 −0.445488 0.895288i \(-0.646970\pi\)
−0.445488 + 0.895288i \(0.646970\pi\)
\(42\) 0 0
\(43\) 4.57680 0.697956 0.348978 0.937131i \(-0.386529\pi\)
0.348978 + 0.937131i \(0.386529\pi\)
\(44\) 0 0
\(45\) −0.434018 −0.0646996
\(46\) 0 0
\(47\) −1.28633 −0.187631 −0.0938155 0.995590i \(-0.529906\pi\)
−0.0938155 + 0.995590i \(0.529906\pi\)
\(48\) 0 0
\(49\) −1.89378 −0.270541
\(50\) 0 0
\(51\) −0.922556 −0.129184
\(52\) 0 0
\(53\) −9.88390 −1.35766 −0.678829 0.734296i \(-0.737512\pi\)
−0.678829 + 0.734296i \(0.737512\pi\)
\(54\) 0 0
\(55\) −1.51546 −0.204344
\(56\) 0 0
\(57\) 5.87027 0.777537
\(58\) 0 0
\(59\) −0.268728 −0.0349855 −0.0174927 0.999847i \(-0.505568\pi\)
−0.0174927 + 0.999847i \(0.505568\pi\)
\(60\) 0 0
\(61\) −4.59157 −0.587890 −0.293945 0.955822i \(-0.594968\pi\)
−0.293945 + 0.955822i \(0.594968\pi\)
\(62\) 0 0
\(63\) −2.25969 −0.284695
\(64\) 0 0
\(65\) −2.17951 −0.270335
\(66\) 0 0
\(67\) 12.9610 1.58344 0.791719 0.610886i \(-0.209187\pi\)
0.791719 + 0.610886i \(0.209187\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −1.25321 −0.148728 −0.0743640 0.997231i \(-0.523693\pi\)
−0.0743640 + 0.997231i \(0.523693\pi\)
\(72\) 0 0
\(73\) −2.10581 −0.246466 −0.123233 0.992378i \(-0.539326\pi\)
−0.123233 + 0.992378i \(0.539326\pi\)
\(74\) 0 0
\(75\) −4.81163 −0.555599
\(76\) 0 0
\(77\) −7.89016 −0.899167
\(78\) 0 0
\(79\) −9.21562 −1.03684 −0.518419 0.855127i \(-0.673479\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.24748 0.356457 0.178228 0.983989i \(-0.442963\pi\)
0.178228 + 0.983989i \(0.442963\pi\)
\(84\) 0 0
\(85\) 0.400406 0.0434301
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 8.36608 0.886803 0.443401 0.896323i \(-0.353772\pi\)
0.443401 + 0.896323i \(0.353772\pi\)
\(90\) 0 0
\(91\) −11.3475 −1.18954
\(92\) 0 0
\(93\) 9.57575 0.992959
\(94\) 0 0
\(95\) −2.54781 −0.261399
\(96\) 0 0
\(97\) 0.502057 0.0509761 0.0254881 0.999675i \(-0.491886\pi\)
0.0254881 + 0.999675i \(0.491886\pi\)
\(98\) 0 0
\(99\) 3.49169 0.350928
\(100\) 0 0
\(101\) 9.47938 0.943234 0.471617 0.881803i \(-0.343670\pi\)
0.471617 + 0.881803i \(0.343670\pi\)
\(102\) 0 0
\(103\) 7.20742 0.710168 0.355084 0.934834i \(-0.384452\pi\)
0.355084 + 0.934834i \(0.384452\pi\)
\(104\) 0 0
\(105\) 0.980749 0.0957113
\(106\) 0 0
\(107\) 8.72557 0.843532 0.421766 0.906705i \(-0.361410\pi\)
0.421766 + 0.906705i \(0.361410\pi\)
\(108\) 0 0
\(109\) −12.9076 −1.23633 −0.618164 0.786049i \(-0.712123\pi\)
−0.618164 + 0.786049i \(0.712123\pi\)
\(110\) 0 0
\(111\) 2.89227 0.274522
\(112\) 0 0
\(113\) 18.2048 1.71256 0.856281 0.516510i \(-0.172769\pi\)
0.856281 + 0.516510i \(0.172769\pi\)
\(114\) 0 0
\(115\) −0.434018 −0.0404724
\(116\) 0 0
\(117\) 5.02170 0.464256
\(118\) 0 0
\(119\) 2.08469 0.191104
\(120\) 0 0
\(121\) 1.19192 0.108356
\(122\) 0 0
\(123\) −5.70503 −0.514405
\(124\) 0 0
\(125\) 4.25843 0.380885
\(126\) 0 0
\(127\) −6.38726 −0.566777 −0.283389 0.959005i \(-0.591459\pi\)
−0.283389 + 0.959005i \(0.591459\pi\)
\(128\) 0 0
\(129\) 4.57680 0.402965
\(130\) 0 0
\(131\) −3.83334 −0.334920 −0.167460 0.985879i \(-0.553557\pi\)
−0.167460 + 0.985879i \(0.553557\pi\)
\(132\) 0 0
\(133\) −13.2650 −1.15022
\(134\) 0 0
\(135\) −0.434018 −0.0373544
\(136\) 0 0
\(137\) 10.7808 0.921069 0.460535 0.887642i \(-0.347658\pi\)
0.460535 + 0.887642i \(0.347658\pi\)
\(138\) 0 0
\(139\) 7.97508 0.676438 0.338219 0.941067i \(-0.390176\pi\)
0.338219 + 0.941067i \(0.390176\pi\)
\(140\) 0 0
\(141\) −1.28633 −0.108329
\(142\) 0 0
\(143\) 17.5342 1.46629
\(144\) 0 0
\(145\) 0.434018 0.0360433
\(146\) 0 0
\(147\) −1.89378 −0.156197
\(148\) 0 0
\(149\) −13.6244 −1.11616 −0.558078 0.829788i \(-0.688461\pi\)
−0.558078 + 0.829788i \(0.688461\pi\)
\(150\) 0 0
\(151\) −0.216471 −0.0176161 −0.00880807 0.999961i \(-0.502804\pi\)
−0.00880807 + 0.999961i \(0.502804\pi\)
\(152\) 0 0
\(153\) −0.922556 −0.0745842
\(154\) 0 0
\(155\) −4.15605 −0.333822
\(156\) 0 0
\(157\) 2.63225 0.210076 0.105038 0.994468i \(-0.466504\pi\)
0.105038 + 0.994468i \(0.466504\pi\)
\(158\) 0 0
\(159\) −9.88390 −0.783844
\(160\) 0 0
\(161\) −2.25969 −0.178089
\(162\) 0 0
\(163\) −16.0811 −1.25957 −0.629786 0.776769i \(-0.716857\pi\)
−0.629786 + 0.776769i \(0.716857\pi\)
\(164\) 0 0
\(165\) −1.51546 −0.117978
\(166\) 0 0
\(167\) −2.56463 −0.198457 −0.0992285 0.995065i \(-0.531637\pi\)
−0.0992285 + 0.995065i \(0.531637\pi\)
\(168\) 0 0
\(169\) 12.2174 0.939804
\(170\) 0 0
\(171\) 5.87027 0.448911
\(172\) 0 0
\(173\) −6.88517 −0.523470 −0.261735 0.965140i \(-0.584295\pi\)
−0.261735 + 0.965140i \(0.584295\pi\)
\(174\) 0 0
\(175\) 10.8728 0.821907
\(176\) 0 0
\(177\) −0.268728 −0.0201989
\(178\) 0 0
\(179\) −5.43773 −0.406435 −0.203217 0.979134i \(-0.565140\pi\)
−0.203217 + 0.979134i \(0.565140\pi\)
\(180\) 0 0
\(181\) 21.5095 1.59878 0.799392 0.600809i \(-0.205155\pi\)
0.799392 + 0.600809i \(0.205155\pi\)
\(182\) 0 0
\(183\) −4.59157 −0.339418
\(184\) 0 0
\(185\) −1.25530 −0.0922915
\(186\) 0 0
\(187\) −3.22128 −0.235563
\(188\) 0 0
\(189\) −2.25969 −0.164369
\(190\) 0 0
\(191\) −22.6965 −1.64226 −0.821132 0.570738i \(-0.806657\pi\)
−0.821132 + 0.570738i \(0.806657\pi\)
\(192\) 0 0
\(193\) 22.6343 1.62925 0.814627 0.579985i \(-0.196942\pi\)
0.814627 + 0.579985i \(0.196942\pi\)
\(194\) 0 0
\(195\) −2.17951 −0.156078
\(196\) 0 0
\(197\) 10.3349 0.736332 0.368166 0.929760i \(-0.379986\pi\)
0.368166 + 0.929760i \(0.379986\pi\)
\(198\) 0 0
\(199\) 1.80944 0.128268 0.0641339 0.997941i \(-0.479572\pi\)
0.0641339 + 0.997941i \(0.479572\pi\)
\(200\) 0 0
\(201\) 12.9610 0.914198
\(202\) 0 0
\(203\) 2.25969 0.158599
\(204\) 0 0
\(205\) 2.47609 0.172937
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 20.4972 1.41782
\(210\) 0 0
\(211\) −9.37416 −0.645343 −0.322672 0.946511i \(-0.604581\pi\)
−0.322672 + 0.946511i \(0.604581\pi\)
\(212\) 0 0
\(213\) −1.25321 −0.0858682
\(214\) 0 0
\(215\) −1.98642 −0.135472
\(216\) 0 0
\(217\) −21.6383 −1.46890
\(218\) 0 0
\(219\) −2.10581 −0.142297
\(220\) 0 0
\(221\) −4.63280 −0.311636
\(222\) 0 0
\(223\) 7.80672 0.522776 0.261388 0.965234i \(-0.415820\pi\)
0.261388 + 0.965234i \(0.415820\pi\)
\(224\) 0 0
\(225\) −4.81163 −0.320775
\(226\) 0 0
\(227\) 1.27849 0.0848562 0.0424281 0.999100i \(-0.486491\pi\)
0.0424281 + 0.999100i \(0.486491\pi\)
\(228\) 0 0
\(229\) 23.8626 1.57689 0.788443 0.615108i \(-0.210888\pi\)
0.788443 + 0.615108i \(0.210888\pi\)
\(230\) 0 0
\(231\) −7.89016 −0.519134
\(232\) 0 0
\(233\) 10.8170 0.708648 0.354324 0.935123i \(-0.384711\pi\)
0.354324 + 0.935123i \(0.384711\pi\)
\(234\) 0 0
\(235\) 0.558292 0.0364190
\(236\) 0 0
\(237\) −9.21562 −0.598619
\(238\) 0 0
\(239\) 25.8482 1.67198 0.835992 0.548742i \(-0.184893\pi\)
0.835992 + 0.548742i \(0.184893\pi\)
\(240\) 0 0
\(241\) −3.80834 −0.245317 −0.122658 0.992449i \(-0.539142\pi\)
−0.122658 + 0.992449i \(0.539142\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.821937 0.0525116
\(246\) 0 0
\(247\) 29.4787 1.87569
\(248\) 0 0
\(249\) 3.24748 0.205800
\(250\) 0 0
\(251\) −27.6031 −1.74229 −0.871147 0.491023i \(-0.836623\pi\)
−0.871147 + 0.491023i \(0.836623\pi\)
\(252\) 0 0
\(253\) 3.49169 0.219521
\(254\) 0 0
\(255\) 0.400406 0.0250744
\(256\) 0 0
\(257\) 9.90359 0.617769 0.308885 0.951100i \(-0.400044\pi\)
0.308885 + 0.951100i \(0.400044\pi\)
\(258\) 0 0
\(259\) −6.53565 −0.406106
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −22.5105 −1.38805 −0.694027 0.719949i \(-0.744165\pi\)
−0.694027 + 0.719949i \(0.744165\pi\)
\(264\) 0 0
\(265\) 4.28980 0.263520
\(266\) 0 0
\(267\) 8.36608 0.511996
\(268\) 0 0
\(269\) 20.7434 1.26475 0.632373 0.774664i \(-0.282081\pi\)
0.632373 + 0.774664i \(0.282081\pi\)
\(270\) 0 0
\(271\) 20.7623 1.26122 0.630611 0.776099i \(-0.282805\pi\)
0.630611 + 0.776099i \(0.282805\pi\)
\(272\) 0 0
\(273\) −11.3475 −0.686782
\(274\) 0 0
\(275\) −16.8007 −1.01312
\(276\) 0 0
\(277\) 22.1310 1.32973 0.664863 0.746966i \(-0.268490\pi\)
0.664863 + 0.746966i \(0.268490\pi\)
\(278\) 0 0
\(279\) 9.57575 0.573285
\(280\) 0 0
\(281\) 19.5397 1.16564 0.582821 0.812600i \(-0.301949\pi\)
0.582821 + 0.812600i \(0.301949\pi\)
\(282\) 0 0
\(283\) −14.4356 −0.858109 −0.429054 0.903279i \(-0.641153\pi\)
−0.429054 + 0.903279i \(0.641153\pi\)
\(284\) 0 0
\(285\) −2.54781 −0.150919
\(286\) 0 0
\(287\) 12.8916 0.760968
\(288\) 0 0
\(289\) −16.1489 −0.949935
\(290\) 0 0
\(291\) 0.502057 0.0294311
\(292\) 0 0
\(293\) −6.35213 −0.371095 −0.185548 0.982635i \(-0.559406\pi\)
−0.185548 + 0.982635i \(0.559406\pi\)
\(294\) 0 0
\(295\) 0.116633 0.00679064
\(296\) 0 0
\(297\) 3.49169 0.202609
\(298\) 0 0
\(299\) 5.02170 0.290412
\(300\) 0 0
\(301\) −10.3422 −0.596113
\(302\) 0 0
\(303\) 9.47938 0.544576
\(304\) 0 0
\(305\) 1.99282 0.114109
\(306\) 0 0
\(307\) 13.6533 0.779232 0.389616 0.920977i \(-0.372608\pi\)
0.389616 + 0.920977i \(0.372608\pi\)
\(308\) 0 0
\(309\) 7.20742 0.410016
\(310\) 0 0
\(311\) 30.0516 1.70407 0.852034 0.523486i \(-0.175369\pi\)
0.852034 + 0.523486i \(0.175369\pi\)
\(312\) 0 0
\(313\) 18.8442 1.06513 0.532567 0.846388i \(-0.321227\pi\)
0.532567 + 0.846388i \(0.321227\pi\)
\(314\) 0 0
\(315\) 0.980749 0.0552589
\(316\) 0 0
\(317\) 13.1249 0.737166 0.368583 0.929595i \(-0.379843\pi\)
0.368583 + 0.929595i \(0.379843\pi\)
\(318\) 0 0
\(319\) −3.49169 −0.195497
\(320\) 0 0
\(321\) 8.72557 0.487014
\(322\) 0 0
\(323\) −5.41565 −0.301335
\(324\) 0 0
\(325\) −24.1625 −1.34030
\(326\) 0 0
\(327\) −12.9076 −0.713794
\(328\) 0 0
\(329\) 2.90672 0.160253
\(330\) 0 0
\(331\) 30.6848 1.68659 0.843293 0.537454i \(-0.180614\pi\)
0.843293 + 0.537454i \(0.180614\pi\)
\(332\) 0 0
\(333\) 2.89227 0.158496
\(334\) 0 0
\(335\) −5.62531 −0.307343
\(336\) 0 0
\(337\) −15.9484 −0.868767 −0.434384 0.900728i \(-0.643034\pi\)
−0.434384 + 0.900728i \(0.643034\pi\)
\(338\) 0 0
\(339\) 18.2048 0.988748
\(340\) 0 0
\(341\) 33.4356 1.81064
\(342\) 0 0
\(343\) 20.0972 1.08515
\(344\) 0 0
\(345\) −0.434018 −0.0233668
\(346\) 0 0
\(347\) −2.32704 −0.124922 −0.0624610 0.998047i \(-0.519895\pi\)
−0.0624610 + 0.998047i \(0.519895\pi\)
\(348\) 0 0
\(349\) 30.6041 1.63820 0.819101 0.573649i \(-0.194473\pi\)
0.819101 + 0.573649i \(0.194473\pi\)
\(350\) 0 0
\(351\) 5.02170 0.268038
\(352\) 0 0
\(353\) 11.1607 0.594025 0.297013 0.954874i \(-0.404010\pi\)
0.297013 + 0.954874i \(0.404010\pi\)
\(354\) 0 0
\(355\) 0.543914 0.0288680
\(356\) 0 0
\(357\) 2.08469 0.110334
\(358\) 0 0
\(359\) 19.9648 1.05370 0.526851 0.849957i \(-0.323372\pi\)
0.526851 + 0.849957i \(0.323372\pi\)
\(360\) 0 0
\(361\) 15.4601 0.813690
\(362\) 0 0
\(363\) 1.19192 0.0625595
\(364\) 0 0
\(365\) 0.913959 0.0478388
\(366\) 0 0
\(367\) −31.2584 −1.63168 −0.815839 0.578280i \(-0.803724\pi\)
−0.815839 + 0.578280i \(0.803724\pi\)
\(368\) 0 0
\(369\) −5.70503 −0.296992
\(370\) 0 0
\(371\) 22.3346 1.15955
\(372\) 0 0
\(373\) −3.08153 −0.159556 −0.0797778 0.996813i \(-0.525421\pi\)
−0.0797778 + 0.996813i \(0.525421\pi\)
\(374\) 0 0
\(375\) 4.25843 0.219904
\(376\) 0 0
\(377\) −5.02170 −0.258631
\(378\) 0 0
\(379\) 15.6639 0.804600 0.402300 0.915508i \(-0.368211\pi\)
0.402300 + 0.915508i \(0.368211\pi\)
\(380\) 0 0
\(381\) −6.38726 −0.327229
\(382\) 0 0
\(383\) −31.6604 −1.61777 −0.808886 0.587965i \(-0.799929\pi\)
−0.808886 + 0.587965i \(0.799929\pi\)
\(384\) 0 0
\(385\) 3.42447 0.174527
\(386\) 0 0
\(387\) 4.57680 0.232652
\(388\) 0 0
\(389\) −14.6235 −0.741439 −0.370719 0.928745i \(-0.620889\pi\)
−0.370719 + 0.928745i \(0.620889\pi\)
\(390\) 0 0
\(391\) −0.922556 −0.0466556
\(392\) 0 0
\(393\) −3.83334 −0.193366
\(394\) 0 0
\(395\) 3.99975 0.201249
\(396\) 0 0
\(397\) −10.6325 −0.533628 −0.266814 0.963748i \(-0.585971\pi\)
−0.266814 + 0.963748i \(0.585971\pi\)
\(398\) 0 0
\(399\) −13.2650 −0.664082
\(400\) 0 0
\(401\) −10.3394 −0.516326 −0.258163 0.966101i \(-0.583117\pi\)
−0.258163 + 0.966101i \(0.583117\pi\)
\(402\) 0 0
\(403\) 48.0865 2.39536
\(404\) 0 0
\(405\) −0.434018 −0.0215665
\(406\) 0 0
\(407\) 10.0989 0.500585
\(408\) 0 0
\(409\) 31.1147 1.53852 0.769262 0.638933i \(-0.220624\pi\)
0.769262 + 0.638933i \(0.220624\pi\)
\(410\) 0 0
\(411\) 10.7808 0.531780
\(412\) 0 0
\(413\) 0.607244 0.0298805
\(414\) 0 0
\(415\) −1.40946 −0.0691879
\(416\) 0 0
\(417\) 7.97508 0.390541
\(418\) 0 0
\(419\) −1.74209 −0.0851067 −0.0425534 0.999094i \(-0.513549\pi\)
−0.0425534 + 0.999094i \(0.513549\pi\)
\(420\) 0 0
\(421\) −9.80160 −0.477701 −0.238850 0.971056i \(-0.576771\pi\)
−0.238850 + 0.971056i \(0.576771\pi\)
\(422\) 0 0
\(423\) −1.28633 −0.0625437
\(424\) 0 0
\(425\) 4.43899 0.215323
\(426\) 0 0
\(427\) 10.3755 0.502107
\(428\) 0 0
\(429\) 17.5342 0.846560
\(430\) 0 0
\(431\) 2.75416 0.132663 0.0663316 0.997798i \(-0.478870\pi\)
0.0663316 + 0.997798i \(0.478870\pi\)
\(432\) 0 0
\(433\) −7.90262 −0.379776 −0.189888 0.981806i \(-0.560812\pi\)
−0.189888 + 0.981806i \(0.560812\pi\)
\(434\) 0 0
\(435\) 0.434018 0.0208096
\(436\) 0 0
\(437\) 5.87027 0.280813
\(438\) 0 0
\(439\) 16.8389 0.803679 0.401839 0.915710i \(-0.368371\pi\)
0.401839 + 0.915710i \(0.368371\pi\)
\(440\) 0 0
\(441\) −1.89378 −0.0901802
\(442\) 0 0
\(443\) −26.6857 −1.26788 −0.633938 0.773384i \(-0.718562\pi\)
−0.633938 + 0.773384i \(0.718562\pi\)
\(444\) 0 0
\(445\) −3.63103 −0.172127
\(446\) 0 0
\(447\) −13.6244 −0.644413
\(448\) 0 0
\(449\) −8.79784 −0.415196 −0.207598 0.978214i \(-0.566565\pi\)
−0.207598 + 0.978214i \(0.566565\pi\)
\(450\) 0 0
\(451\) −19.9202 −0.938005
\(452\) 0 0
\(453\) −0.216471 −0.0101707
\(454\) 0 0
\(455\) 4.92502 0.230889
\(456\) 0 0
\(457\) 35.9992 1.68397 0.841986 0.539500i \(-0.181387\pi\)
0.841986 + 0.539500i \(0.181387\pi\)
\(458\) 0 0
\(459\) −0.922556 −0.0430612
\(460\) 0 0
\(461\) −41.4402 −1.93006 −0.965031 0.262134i \(-0.915574\pi\)
−0.965031 + 0.262134i \(0.915574\pi\)
\(462\) 0 0
\(463\) −0.188109 −0.00874218 −0.00437109 0.999990i \(-0.501391\pi\)
−0.00437109 + 0.999990i \(0.501391\pi\)
\(464\) 0 0
\(465\) −4.15605 −0.192732
\(466\) 0 0
\(467\) −31.3961 −1.45284 −0.726420 0.687251i \(-0.758817\pi\)
−0.726420 + 0.687251i \(0.758817\pi\)
\(468\) 0 0
\(469\) −29.2879 −1.35239
\(470\) 0 0
\(471\) 2.63225 0.121288
\(472\) 0 0
\(473\) 15.9808 0.734797
\(474\) 0 0
\(475\) −28.2456 −1.29600
\(476\) 0 0
\(477\) −9.88390 −0.452553
\(478\) 0 0
\(479\) −36.6453 −1.67437 −0.837183 0.546922i \(-0.815799\pi\)
−0.837183 + 0.546922i \(0.815799\pi\)
\(480\) 0 0
\(481\) 14.5241 0.662243
\(482\) 0 0
\(483\) −2.25969 −0.102820
\(484\) 0 0
\(485\) −0.217902 −0.00989441
\(486\) 0 0
\(487\) −22.4622 −1.01786 −0.508929 0.860808i \(-0.669958\pi\)
−0.508929 + 0.860808i \(0.669958\pi\)
\(488\) 0 0
\(489\) −16.0811 −0.727214
\(490\) 0 0
\(491\) −21.7683 −0.982388 −0.491194 0.871050i \(-0.663439\pi\)
−0.491194 + 0.871050i \(0.663439\pi\)
\(492\) 0 0
\(493\) 0.922556 0.0415498
\(494\) 0 0
\(495\) −1.51546 −0.0681148
\(496\) 0 0
\(497\) 2.83186 0.127026
\(498\) 0 0
\(499\) 18.1913 0.814356 0.407178 0.913349i \(-0.366513\pi\)
0.407178 + 0.913349i \(0.366513\pi\)
\(500\) 0 0
\(501\) −2.56463 −0.114579
\(502\) 0 0
\(503\) 19.5579 0.872044 0.436022 0.899936i \(-0.356387\pi\)
0.436022 + 0.899936i \(0.356387\pi\)
\(504\) 0 0
\(505\) −4.11423 −0.183081
\(506\) 0 0
\(507\) 12.2174 0.542596
\(508\) 0 0
\(509\) 25.2850 1.12074 0.560369 0.828243i \(-0.310659\pi\)
0.560369 + 0.828243i \(0.310659\pi\)
\(510\) 0 0
\(511\) 4.75848 0.210503
\(512\) 0 0
\(513\) 5.87027 0.259179
\(514\) 0 0
\(515\) −3.12815 −0.137843
\(516\) 0 0
\(517\) −4.49148 −0.197535
\(518\) 0 0
\(519\) −6.88517 −0.302225
\(520\) 0 0
\(521\) −3.75838 −0.164658 −0.0823289 0.996605i \(-0.526236\pi\)
−0.0823289 + 0.996605i \(0.526236\pi\)
\(522\) 0 0
\(523\) −37.4445 −1.63734 −0.818668 0.574268i \(-0.805287\pi\)
−0.818668 + 0.574268i \(0.805287\pi\)
\(524\) 0 0
\(525\) 10.8728 0.474528
\(526\) 0 0
\(527\) −8.83416 −0.384822
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −0.268728 −0.0116618
\(532\) 0 0
\(533\) −28.6489 −1.24092
\(534\) 0 0
\(535\) −3.78706 −0.163729
\(536\) 0 0
\(537\) −5.43773 −0.234655
\(538\) 0 0
\(539\) −6.61251 −0.284821
\(540\) 0 0
\(541\) −36.7346 −1.57934 −0.789671 0.613530i \(-0.789749\pi\)
−0.789671 + 0.613530i \(0.789749\pi\)
\(542\) 0 0
\(543\) 21.5095 0.923059
\(544\) 0 0
\(545\) 5.60215 0.239970
\(546\) 0 0
\(547\) −6.53085 −0.279239 −0.139620 0.990205i \(-0.544588\pi\)
−0.139620 + 0.990205i \(0.544588\pi\)
\(548\) 0 0
\(549\) −4.59157 −0.195963
\(550\) 0 0
\(551\) −5.87027 −0.250082
\(552\) 0 0
\(553\) 20.8245 0.885547
\(554\) 0 0
\(555\) −1.25530 −0.0532845
\(556\) 0 0
\(557\) −27.6425 −1.17125 −0.585625 0.810582i \(-0.699151\pi\)
−0.585625 + 0.810582i \(0.699151\pi\)
\(558\) 0 0
\(559\) 22.9833 0.972090
\(560\) 0 0
\(561\) −3.22128 −0.136003
\(562\) 0 0
\(563\) −11.6355 −0.490376 −0.245188 0.969476i \(-0.578850\pi\)
−0.245188 + 0.969476i \(0.578850\pi\)
\(564\) 0 0
\(565\) −7.90121 −0.332407
\(566\) 0 0
\(567\) −2.25969 −0.0948982
\(568\) 0 0
\(569\) 26.2384 1.09997 0.549986 0.835174i \(-0.314633\pi\)
0.549986 + 0.835174i \(0.314633\pi\)
\(570\) 0 0
\(571\) −8.60075 −0.359930 −0.179965 0.983673i \(-0.557598\pi\)
−0.179965 + 0.983673i \(0.557598\pi\)
\(572\) 0 0
\(573\) −22.6965 −0.948162
\(574\) 0 0
\(575\) −4.81163 −0.200659
\(576\) 0 0
\(577\) 7.96052 0.331401 0.165700 0.986176i \(-0.447012\pi\)
0.165700 + 0.986176i \(0.447012\pi\)
\(578\) 0 0
\(579\) 22.6343 0.940650
\(580\) 0 0
\(581\) −7.33830 −0.304444
\(582\) 0 0
\(583\) −34.5116 −1.42932
\(584\) 0 0
\(585\) −2.17951 −0.0901116
\(586\) 0 0
\(587\) 22.4480 0.926527 0.463264 0.886221i \(-0.346678\pi\)
0.463264 + 0.886221i \(0.346678\pi\)
\(588\) 0 0
\(589\) 56.2123 2.31619
\(590\) 0 0
\(591\) 10.3349 0.425122
\(592\) 0 0
\(593\) 21.2147 0.871185 0.435593 0.900144i \(-0.356539\pi\)
0.435593 + 0.900144i \(0.356539\pi\)
\(594\) 0 0
\(595\) −0.904795 −0.0370930
\(596\) 0 0
\(597\) 1.80944 0.0740554
\(598\) 0 0
\(599\) −10.2582 −0.419139 −0.209570 0.977794i \(-0.567206\pi\)
−0.209570 + 0.977794i \(0.567206\pi\)
\(600\) 0 0
\(601\) −26.8975 −1.09717 −0.548586 0.836094i \(-0.684833\pi\)
−0.548586 + 0.836094i \(0.684833\pi\)
\(602\) 0 0
\(603\) 12.9610 0.527812
\(604\) 0 0
\(605\) −0.517315 −0.0210318
\(606\) 0 0
\(607\) 19.4719 0.790339 0.395170 0.918608i \(-0.370686\pi\)
0.395170 + 0.918608i \(0.370686\pi\)
\(608\) 0 0
\(609\) 2.25969 0.0915674
\(610\) 0 0
\(611\) −6.45958 −0.261327
\(612\) 0 0
\(613\) −35.4825 −1.43313 −0.716563 0.697523i \(-0.754286\pi\)
−0.716563 + 0.697523i \(0.754286\pi\)
\(614\) 0 0
\(615\) 2.47609 0.0998454
\(616\) 0 0
\(617\) −19.6980 −0.793012 −0.396506 0.918032i \(-0.629777\pi\)
−0.396506 + 0.918032i \(0.629777\pi\)
\(618\) 0 0
\(619\) 32.3551 1.30046 0.650230 0.759737i \(-0.274672\pi\)
0.650230 + 0.759737i \(0.274672\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −18.9048 −0.757404
\(624\) 0 0
\(625\) 22.2099 0.888396
\(626\) 0 0
\(627\) 20.4972 0.818579
\(628\) 0 0
\(629\) −2.66828 −0.106391
\(630\) 0 0
\(631\) 44.7436 1.78121 0.890607 0.454773i \(-0.150280\pi\)
0.890607 + 0.454773i \(0.150280\pi\)
\(632\) 0 0
\(633\) −9.37416 −0.372589
\(634\) 0 0
\(635\) 2.77219 0.110011
\(636\) 0 0
\(637\) −9.51001 −0.376800
\(638\) 0 0
\(639\) −1.25321 −0.0495760
\(640\) 0 0
\(641\) 4.62045 0.182497 0.0912483 0.995828i \(-0.470914\pi\)
0.0912483 + 0.995828i \(0.470914\pi\)
\(642\) 0 0
\(643\) 16.8433 0.664234 0.332117 0.943238i \(-0.392237\pi\)
0.332117 + 0.943238i \(0.392237\pi\)
\(644\) 0 0
\(645\) −1.98642 −0.0782150
\(646\) 0 0
\(647\) −26.5057 −1.04205 −0.521023 0.853542i \(-0.674450\pi\)
−0.521023 + 0.853542i \(0.674450\pi\)
\(648\) 0 0
\(649\) −0.938317 −0.0368322
\(650\) 0 0
\(651\) −21.6383 −0.848070
\(652\) 0 0
\(653\) 17.9743 0.703388 0.351694 0.936115i \(-0.385606\pi\)
0.351694 + 0.936115i \(0.385606\pi\)
\(654\) 0 0
\(655\) 1.66374 0.0650077
\(656\) 0 0
\(657\) −2.10581 −0.0821554
\(658\) 0 0
\(659\) −5.15635 −0.200863 −0.100431 0.994944i \(-0.532022\pi\)
−0.100431 + 0.994944i \(0.532022\pi\)
\(660\) 0 0
\(661\) −1.14690 −0.0446092 −0.0223046 0.999751i \(-0.507100\pi\)
−0.0223046 + 0.999751i \(0.507100\pi\)
\(662\) 0 0
\(663\) −4.63280 −0.179923
\(664\) 0 0
\(665\) 5.75726 0.223257
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 7.80672 0.301825
\(670\) 0 0
\(671\) −16.0323 −0.618922
\(672\) 0 0
\(673\) −42.0563 −1.62115 −0.810576 0.585634i \(-0.800846\pi\)
−0.810576 + 0.585634i \(0.800846\pi\)
\(674\) 0 0
\(675\) −4.81163 −0.185200
\(676\) 0 0
\(677\) −18.5900 −0.714472 −0.357236 0.934014i \(-0.616281\pi\)
−0.357236 + 0.934014i \(0.616281\pi\)
\(678\) 0 0
\(679\) −1.13449 −0.0435379
\(680\) 0 0
\(681\) 1.27849 0.0489918
\(682\) 0 0
\(683\) −26.1459 −1.00044 −0.500222 0.865897i \(-0.666748\pi\)
−0.500222 + 0.865897i \(0.666748\pi\)
\(684\) 0 0
\(685\) −4.67908 −0.178779
\(686\) 0 0
\(687\) 23.8626 0.910415
\(688\) 0 0
\(689\) −49.6340 −1.89090
\(690\) 0 0
\(691\) 9.14832 0.348018 0.174009 0.984744i \(-0.444328\pi\)
0.174009 + 0.984744i \(0.444328\pi\)
\(692\) 0 0
\(693\) −7.89016 −0.299722
\(694\) 0 0
\(695\) −3.46133 −0.131296
\(696\) 0 0
\(697\) 5.26320 0.199358
\(698\) 0 0
\(699\) 10.8170 0.409138
\(700\) 0 0
\(701\) −45.3203 −1.71172 −0.855862 0.517204i \(-0.826973\pi\)
−0.855862 + 0.517204i \(0.826973\pi\)
\(702\) 0 0
\(703\) 16.9784 0.640354
\(704\) 0 0
\(705\) 0.558292 0.0210265
\(706\) 0 0
\(707\) −21.4205 −0.805601
\(708\) 0 0
\(709\) 21.9814 0.825530 0.412765 0.910837i \(-0.364563\pi\)
0.412765 + 0.910837i \(0.364563\pi\)
\(710\) 0 0
\(711\) −9.21562 −0.345613
\(712\) 0 0
\(713\) 9.57575 0.358615
\(714\) 0 0
\(715\) −7.61018 −0.284604
\(716\) 0 0
\(717\) 25.8482 0.965320
\(718\) 0 0
\(719\) 15.1433 0.564748 0.282374 0.959304i \(-0.408878\pi\)
0.282374 + 0.959304i \(0.408878\pi\)
\(720\) 0 0
\(721\) −16.2866 −0.606543
\(722\) 0 0
\(723\) −3.80834 −0.141634
\(724\) 0 0
\(725\) 4.81163 0.178699
\(726\) 0 0
\(727\) 15.3237 0.568324 0.284162 0.958776i \(-0.408285\pi\)
0.284162 + 0.958776i \(0.408285\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.22235 −0.156169
\(732\) 0 0
\(733\) −15.1025 −0.557825 −0.278912 0.960317i \(-0.589974\pi\)
−0.278912 + 0.960317i \(0.589974\pi\)
\(734\) 0 0
\(735\) 0.821937 0.0303176
\(736\) 0 0
\(737\) 45.2558 1.66702
\(738\) 0 0
\(739\) 43.2234 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(740\) 0 0
\(741\) 29.4787 1.08293
\(742\) 0 0
\(743\) −3.71900 −0.136437 −0.0682185 0.997670i \(-0.521732\pi\)
−0.0682185 + 0.997670i \(0.521732\pi\)
\(744\) 0 0
\(745\) 5.91325 0.216645
\(746\) 0 0
\(747\) 3.24748 0.118819
\(748\) 0 0
\(749\) −19.7171 −0.720448
\(750\) 0 0
\(751\) −7.61239 −0.277780 −0.138890 0.990308i \(-0.544353\pi\)
−0.138890 + 0.990308i \(0.544353\pi\)
\(752\) 0 0
\(753\) −27.6031 −1.00591
\(754\) 0 0
\(755\) 0.0939523 0.00341927
\(756\) 0 0
\(757\) 27.1191 0.985660 0.492830 0.870126i \(-0.335962\pi\)
0.492830 + 0.870126i \(0.335962\pi\)
\(758\) 0 0
\(759\) 3.49169 0.126740
\(760\) 0 0
\(761\) 16.1490 0.585400 0.292700 0.956204i \(-0.405446\pi\)
0.292700 + 0.956204i \(0.405446\pi\)
\(762\) 0 0
\(763\) 29.1673 1.05593
\(764\) 0 0
\(765\) 0.400406 0.0144767
\(766\) 0 0
\(767\) −1.34947 −0.0487266
\(768\) 0 0
\(769\) −54.4394 −1.96314 −0.981568 0.191111i \(-0.938791\pi\)
−0.981568 + 0.191111i \(0.938791\pi\)
\(770\) 0 0
\(771\) 9.90359 0.356669
\(772\) 0 0
\(773\) −35.7818 −1.28698 −0.643492 0.765453i \(-0.722515\pi\)
−0.643492 + 0.765453i \(0.722515\pi\)
\(774\) 0 0
\(775\) −46.0750 −1.65506
\(776\) 0 0
\(777\) −6.53565 −0.234465
\(778\) 0 0
\(779\) −33.4901 −1.19991
\(780\) 0 0
\(781\) −4.37581 −0.156579
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −1.14244 −0.0407756
\(786\) 0 0
\(787\) 45.1538 1.60956 0.804780 0.593573i \(-0.202283\pi\)
0.804780 + 0.593573i \(0.202283\pi\)
\(788\) 0 0
\(789\) −22.5105 −0.801393
\(790\) 0 0
\(791\) −41.1372 −1.46267
\(792\) 0 0
\(793\) −23.0575 −0.818794
\(794\) 0 0
\(795\) 4.28980 0.152143
\(796\) 0 0
\(797\) 33.1561 1.17445 0.587225 0.809424i \(-0.300220\pi\)
0.587225 + 0.809424i \(0.300220\pi\)
\(798\) 0 0
\(799\) 1.18671 0.0419829
\(800\) 0 0
\(801\) 8.36608 0.295601
\(802\) 0 0
\(803\) −7.35283 −0.259476
\(804\) 0 0
\(805\) 0.980749 0.0345668
\(806\) 0 0
\(807\) 20.7434 0.730201
\(808\) 0 0
\(809\) 52.4675 1.84466 0.922329 0.386405i \(-0.126283\pi\)
0.922329 + 0.386405i \(0.126283\pi\)
\(810\) 0 0
\(811\) −7.74967 −0.272128 −0.136064 0.990700i \(-0.543445\pi\)
−0.136064 + 0.990700i \(0.543445\pi\)
\(812\) 0 0
\(813\) 20.7623 0.728166
\(814\) 0 0
\(815\) 6.97951 0.244482
\(816\) 0 0
\(817\) 26.8671 0.939960
\(818\) 0 0
\(819\) −11.3475 −0.396514
\(820\) 0 0
\(821\) −21.4881 −0.749940 −0.374970 0.927037i \(-0.622347\pi\)
−0.374970 + 0.927037i \(0.622347\pi\)
\(822\) 0 0
\(823\) −36.5549 −1.27422 −0.637112 0.770772i \(-0.719871\pi\)
−0.637112 + 0.770772i \(0.719871\pi\)
\(824\) 0 0
\(825\) −16.8007 −0.584926
\(826\) 0 0
\(827\) −33.0011 −1.14756 −0.573781 0.819009i \(-0.694524\pi\)
−0.573781 + 0.819009i \(0.694524\pi\)
\(828\) 0 0
\(829\) −4.66918 −0.162167 −0.0810837 0.996707i \(-0.525838\pi\)
−0.0810837 + 0.996707i \(0.525838\pi\)
\(830\) 0 0
\(831\) 22.1310 0.767717
\(832\) 0 0
\(833\) 1.74712 0.0605342
\(834\) 0 0
\(835\) 1.11310 0.0385203
\(836\) 0 0
\(837\) 9.57575 0.330986
\(838\) 0 0
\(839\) 36.5811 1.26292 0.631459 0.775409i \(-0.282456\pi\)
0.631459 + 0.775409i \(0.282456\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 19.5397 0.672984
\(844\) 0 0
\(845\) −5.30260 −0.182415
\(846\) 0 0
\(847\) −2.69337 −0.0925453
\(848\) 0 0
\(849\) −14.4356 −0.495429
\(850\) 0 0
\(851\) 2.89227 0.0991458
\(852\) 0 0
\(853\) −54.0770 −1.85156 −0.925780 0.378062i \(-0.876591\pi\)
−0.925780 + 0.378062i \(0.876591\pi\)
\(854\) 0 0
\(855\) −2.54781 −0.0871331
\(856\) 0 0
\(857\) 25.5237 0.871874 0.435937 0.899977i \(-0.356417\pi\)
0.435937 + 0.899977i \(0.356417\pi\)
\(858\) 0 0
\(859\) 33.6725 1.14889 0.574446 0.818542i \(-0.305218\pi\)
0.574446 + 0.818542i \(0.305218\pi\)
\(860\) 0 0
\(861\) 12.8916 0.439345
\(862\) 0 0
\(863\) −50.3410 −1.71363 −0.856814 0.515626i \(-0.827559\pi\)
−0.856814 + 0.515626i \(0.827559\pi\)
\(864\) 0 0
\(865\) 2.98829 0.101605
\(866\) 0 0
\(867\) −16.1489 −0.548445
\(868\) 0 0
\(869\) −32.1781 −1.09157
\(870\) 0 0
\(871\) 65.0862 2.20536
\(872\) 0 0
\(873\) 0.502057 0.0169920
\(874\) 0 0
\(875\) −9.62274 −0.325308
\(876\) 0 0
\(877\) 15.2179 0.513873 0.256936 0.966428i \(-0.417287\pi\)
0.256936 + 0.966428i \(0.417287\pi\)
\(878\) 0 0
\(879\) −6.35213 −0.214252
\(880\) 0 0
\(881\) 39.4235 1.32821 0.664105 0.747639i \(-0.268813\pi\)
0.664105 + 0.747639i \(0.268813\pi\)
\(882\) 0 0
\(883\) −30.1861 −1.01584 −0.507921 0.861404i \(-0.669586\pi\)
−0.507921 + 0.861404i \(0.669586\pi\)
\(884\) 0 0
\(885\) 0.116633 0.00392058
\(886\) 0 0
\(887\) −19.3380 −0.649305 −0.324653 0.945833i \(-0.605247\pi\)
−0.324653 + 0.945833i \(0.605247\pi\)
\(888\) 0 0
\(889\) 14.4332 0.484075
\(890\) 0 0
\(891\) 3.49169 0.116976
\(892\) 0 0
\(893\) −7.55113 −0.252689
\(894\) 0 0
\(895\) 2.36007 0.0788885
\(896\) 0 0
\(897\) 5.02170 0.167670
\(898\) 0 0
\(899\) −9.57575 −0.319369
\(900\) 0 0
\(901\) 9.11845 0.303780
\(902\) 0 0
\(903\) −10.3422 −0.344166
\(904\) 0 0
\(905\) −9.33550 −0.310322
\(906\) 0 0
\(907\) −36.4290 −1.20960 −0.604802 0.796376i \(-0.706748\pi\)
−0.604802 + 0.796376i \(0.706748\pi\)
\(908\) 0 0
\(909\) 9.47938 0.314411
\(910\) 0 0
\(911\) −45.6790 −1.51341 −0.756707 0.653754i \(-0.773193\pi\)
−0.756707 + 0.653754i \(0.773193\pi\)
\(912\) 0 0
\(913\) 11.3392 0.375272
\(914\) 0 0
\(915\) 1.99282 0.0658807
\(916\) 0 0
\(917\) 8.66217 0.286050
\(918\) 0 0
\(919\) 29.1818 0.962617 0.481309 0.876551i \(-0.340162\pi\)
0.481309 + 0.876551i \(0.340162\pi\)
\(920\) 0 0
\(921\) 13.6533 0.449890
\(922\) 0 0
\(923\) −6.29322 −0.207144
\(924\) 0 0
\(925\) −13.9165 −0.457573
\(926\) 0 0
\(927\) 7.20742 0.236723
\(928\) 0 0
\(929\) 32.7941 1.07594 0.537971 0.842964i \(-0.319191\pi\)
0.537971 + 0.842964i \(0.319191\pi\)
\(930\) 0 0
\(931\) −11.1170 −0.364346
\(932\) 0 0
\(933\) 30.0516 0.983844
\(934\) 0 0
\(935\) 1.39810 0.0457226
\(936\) 0 0
\(937\) 15.6579 0.511521 0.255760 0.966740i \(-0.417674\pi\)
0.255760 + 0.966740i \(0.417674\pi\)
\(938\) 0 0
\(939\) 18.8442 0.614956
\(940\) 0 0
\(941\) −54.5724 −1.77901 −0.889504 0.456927i \(-0.848950\pi\)
−0.889504 + 0.456927i \(0.848950\pi\)
\(942\) 0 0
\(943\) −5.70503 −0.185781
\(944\) 0 0
\(945\) 0.980749 0.0319038
\(946\) 0 0
\(947\) −9.79570 −0.318318 −0.159159 0.987253i \(-0.550878\pi\)
−0.159159 + 0.987253i \(0.550878\pi\)
\(948\) 0 0
\(949\) −10.5747 −0.343270
\(950\) 0 0
\(951\) 13.1249 0.425603
\(952\) 0 0
\(953\) 19.2918 0.624924 0.312462 0.949930i \(-0.398846\pi\)
0.312462 + 0.949930i \(0.398846\pi\)
\(954\) 0 0
\(955\) 9.85072 0.318762
\(956\) 0 0
\(957\) −3.49169 −0.112870
\(958\) 0 0
\(959\) −24.3614 −0.786670
\(960\) 0 0
\(961\) 60.6950 1.95790
\(962\) 0 0
\(963\) 8.72557 0.281177
\(964\) 0 0
\(965\) −9.82371 −0.316236
\(966\) 0 0
\(967\) 12.0831 0.388565 0.194282 0.980946i \(-0.437762\pi\)
0.194282 + 0.980946i \(0.437762\pi\)
\(968\) 0 0
\(969\) −5.41565 −0.173976
\(970\) 0 0
\(971\) 13.7988 0.442825 0.221412 0.975180i \(-0.428933\pi\)
0.221412 + 0.975180i \(0.428933\pi\)
\(972\) 0 0
\(973\) −18.0212 −0.577734
\(974\) 0 0
\(975\) −24.1625 −0.773821
\(976\) 0 0
\(977\) −36.4835 −1.16721 −0.583605 0.812038i \(-0.698358\pi\)
−0.583605 + 0.812038i \(0.698358\pi\)
\(978\) 0 0
\(979\) 29.2118 0.933613
\(980\) 0 0
\(981\) −12.9076 −0.412109
\(982\) 0 0
\(983\) 1.07110 0.0341627 0.0170814 0.999854i \(-0.494563\pi\)
0.0170814 + 0.999854i \(0.494563\pi\)
\(984\) 0 0
\(985\) −4.48554 −0.142921
\(986\) 0 0
\(987\) 2.90672 0.0925219
\(988\) 0 0
\(989\) 4.57680 0.145534
\(990\) 0 0
\(991\) 14.9592 0.475196 0.237598 0.971364i \(-0.423640\pi\)
0.237598 + 0.971364i \(0.423640\pi\)
\(992\) 0 0
\(993\) 30.6848 0.973751
\(994\) 0 0
\(995\) −0.785330 −0.0248966
\(996\) 0 0
\(997\) 34.3969 1.08936 0.544680 0.838644i \(-0.316651\pi\)
0.544680 + 0.838644i \(0.316651\pi\)
\(998\) 0 0
\(999\) 2.89227 0.0915075
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 \(a_p\))