Properties

Label 8008.2.a.u.1.7
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.54918\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.54918 q^{3} -0.356949 q^{5} -1.00000 q^{7} -0.600028 q^{9} +O(q^{10})\) \(q+1.54918 q^{3} -0.356949 q^{5} -1.00000 q^{7} -0.600028 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.552981 q^{15} -6.04878 q^{17} +8.48928 q^{19} -1.54918 q^{21} +7.98257 q^{23} -4.87259 q^{25} -5.57711 q^{27} +5.31591 q^{29} -9.77065 q^{31} -1.54918 q^{33} +0.356949 q^{35} +10.5368 q^{37} -1.54918 q^{39} +8.72233 q^{41} -7.46133 q^{43} +0.214180 q^{45} +1.45382 q^{47} +1.00000 q^{49} -9.37067 q^{51} -1.71369 q^{53} +0.356949 q^{55} +13.1515 q^{57} -0.781383 q^{59} -5.31139 q^{61} +0.600028 q^{63} +0.356949 q^{65} -6.19727 q^{67} +12.3665 q^{69} -7.65289 q^{71} -2.44764 q^{73} -7.54854 q^{75} +1.00000 q^{77} -11.8586 q^{79} -6.83988 q^{81} -5.43355 q^{83} +2.15911 q^{85} +8.23533 q^{87} +9.25740 q^{89} +1.00000 q^{91} -15.1365 q^{93} -3.03024 q^{95} +3.82384 q^{97} +0.600028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.54918 0.894422 0.447211 0.894429i \(-0.352417\pi\)
0.447211 + 0.894429i \(0.352417\pi\)
\(4\) 0 0
\(5\) −0.356949 −0.159633 −0.0798163 0.996810i \(-0.525433\pi\)
−0.0798163 + 0.996810i \(0.525433\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.600028 −0.200009
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.552981 −0.142779
\(16\) 0 0
\(17\) −6.04878 −1.46704 −0.733522 0.679665i \(-0.762125\pi\)
−0.733522 + 0.679665i \(0.762125\pi\)
\(18\) 0 0
\(19\) 8.48928 1.94757 0.973787 0.227462i \(-0.0730427\pi\)
0.973787 + 0.227462i \(0.0730427\pi\)
\(20\) 0 0
\(21\) −1.54918 −0.338060
\(22\) 0 0
\(23\) 7.98257 1.66448 0.832241 0.554414i \(-0.187058\pi\)
0.832241 + 0.554414i \(0.187058\pi\)
\(24\) 0 0
\(25\) −4.87259 −0.974517
\(26\) 0 0
\(27\) −5.57711 −1.07331
\(28\) 0 0
\(29\) 5.31591 0.987140 0.493570 0.869706i \(-0.335692\pi\)
0.493570 + 0.869706i \(0.335692\pi\)
\(30\) 0 0
\(31\) −9.77065 −1.75486 −0.877430 0.479705i \(-0.840744\pi\)
−0.877430 + 0.479705i \(0.840744\pi\)
\(32\) 0 0
\(33\) −1.54918 −0.269678
\(34\) 0 0
\(35\) 0.356949 0.0603355
\(36\) 0 0
\(37\) 10.5368 1.73225 0.866123 0.499832i \(-0.166605\pi\)
0.866123 + 0.499832i \(0.166605\pi\)
\(38\) 0 0
\(39\) −1.54918 −0.248068
\(40\) 0 0
\(41\) 8.72233 1.36220 0.681099 0.732191i \(-0.261502\pi\)
0.681099 + 0.732191i \(0.261502\pi\)
\(42\) 0 0
\(43\) −7.46133 −1.13784 −0.568921 0.822392i \(-0.692639\pi\)
−0.568921 + 0.822392i \(0.692639\pi\)
\(44\) 0 0
\(45\) 0.214180 0.0319280
\(46\) 0 0
\(47\) 1.45382 0.212062 0.106031 0.994363i \(-0.466186\pi\)
0.106031 + 0.994363i \(0.466186\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −9.37067 −1.31216
\(52\) 0 0
\(53\) −1.71369 −0.235393 −0.117696 0.993050i \(-0.537551\pi\)
−0.117696 + 0.993050i \(0.537551\pi\)
\(54\) 0 0
\(55\) 0.356949 0.0481311
\(56\) 0 0
\(57\) 13.1515 1.74195
\(58\) 0 0
\(59\) −0.781383 −0.101727 −0.0508637 0.998706i \(-0.516197\pi\)
−0.0508637 + 0.998706i \(0.516197\pi\)
\(60\) 0 0
\(61\) −5.31139 −0.680053 −0.340027 0.940416i \(-0.610436\pi\)
−0.340027 + 0.940416i \(0.610436\pi\)
\(62\) 0 0
\(63\) 0.600028 0.0755964
\(64\) 0 0
\(65\) 0.356949 0.0442741
\(66\) 0 0
\(67\) −6.19727 −0.757117 −0.378559 0.925577i \(-0.623580\pi\)
−0.378559 + 0.925577i \(0.623580\pi\)
\(68\) 0 0
\(69\) 12.3665 1.48875
\(70\) 0 0
\(71\) −7.65289 −0.908231 −0.454115 0.890943i \(-0.650045\pi\)
−0.454115 + 0.890943i \(0.650045\pi\)
\(72\) 0 0
\(73\) −2.44764 −0.286475 −0.143237 0.989688i \(-0.545751\pi\)
−0.143237 + 0.989688i \(0.545751\pi\)
\(74\) 0 0
\(75\) −7.54854 −0.871630
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −11.8586 −1.33420 −0.667100 0.744968i \(-0.732465\pi\)
−0.667100 + 0.744968i \(0.732465\pi\)
\(80\) 0 0
\(81\) −6.83988 −0.759987
\(82\) 0 0
\(83\) −5.43355 −0.596409 −0.298205 0.954502i \(-0.596388\pi\)
−0.298205 + 0.954502i \(0.596388\pi\)
\(84\) 0 0
\(85\) 2.15911 0.234188
\(86\) 0 0
\(87\) 8.23533 0.882920
\(88\) 0 0
\(89\) 9.25740 0.981282 0.490641 0.871362i \(-0.336763\pi\)
0.490641 + 0.871362i \(0.336763\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −15.1365 −1.56958
\(94\) 0 0
\(95\) −3.03024 −0.310896
\(96\) 0 0
\(97\) 3.82384 0.388252 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(98\) 0 0
\(99\) 0.600028 0.0603051
\(100\) 0 0
\(101\) −6.64381 −0.661084 −0.330542 0.943791i \(-0.607232\pi\)
−0.330542 + 0.943791i \(0.607232\pi\)
\(102\) 0 0
\(103\) −9.22802 −0.909263 −0.454632 0.890680i \(-0.650229\pi\)
−0.454632 + 0.890680i \(0.650229\pi\)
\(104\) 0 0
\(105\) 0.552981 0.0539654
\(106\) 0 0
\(107\) −11.0799 −1.07114 −0.535569 0.844492i \(-0.679903\pi\)
−0.535569 + 0.844492i \(0.679903\pi\)
\(108\) 0 0
\(109\) −17.6595 −1.69147 −0.845736 0.533602i \(-0.820838\pi\)
−0.845736 + 0.533602i \(0.820838\pi\)
\(110\) 0 0
\(111\) 16.3235 1.54936
\(112\) 0 0
\(113\) −2.20701 −0.207618 −0.103809 0.994597i \(-0.533103\pi\)
−0.103809 + 0.994597i \(0.533103\pi\)
\(114\) 0 0
\(115\) −2.84938 −0.265706
\(116\) 0 0
\(117\) 0.600028 0.0554726
\(118\) 0 0
\(119\) 6.04878 0.554491
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 13.5125 1.21838
\(124\) 0 0
\(125\) 3.52401 0.315197
\(126\) 0 0
\(127\) 6.04203 0.536144 0.268072 0.963399i \(-0.413614\pi\)
0.268072 + 0.963399i \(0.413614\pi\)
\(128\) 0 0
\(129\) −11.5590 −1.01771
\(130\) 0 0
\(131\) −21.7877 −1.90360 −0.951799 0.306724i \(-0.900767\pi\)
−0.951799 + 0.306724i \(0.900767\pi\)
\(132\) 0 0
\(133\) −8.48928 −0.736114
\(134\) 0 0
\(135\) 1.99075 0.171336
\(136\) 0 0
\(137\) −18.9167 −1.61616 −0.808081 0.589071i \(-0.799494\pi\)
−0.808081 + 0.589071i \(0.799494\pi\)
\(138\) 0 0
\(139\) 22.9664 1.94798 0.973991 0.226588i \(-0.0727572\pi\)
0.973991 + 0.226588i \(0.0727572\pi\)
\(140\) 0 0
\(141\) 2.25224 0.189673
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −1.89751 −0.157580
\(146\) 0 0
\(147\) 1.54918 0.127775
\(148\) 0 0
\(149\) −9.37265 −0.767837 −0.383919 0.923367i \(-0.625426\pi\)
−0.383919 + 0.923367i \(0.625426\pi\)
\(150\) 0 0
\(151\) 1.64898 0.134192 0.0670961 0.997747i \(-0.478627\pi\)
0.0670961 + 0.997747i \(0.478627\pi\)
\(152\) 0 0
\(153\) 3.62944 0.293423
\(154\) 0 0
\(155\) 3.48763 0.280133
\(156\) 0 0
\(157\) −14.7041 −1.17352 −0.586759 0.809761i \(-0.699597\pi\)
−0.586759 + 0.809761i \(0.699597\pi\)
\(158\) 0 0
\(159\) −2.65482 −0.210541
\(160\) 0 0
\(161\) −7.98257 −0.629115
\(162\) 0 0
\(163\) −14.5583 −1.14029 −0.570147 0.821543i \(-0.693114\pi\)
−0.570147 + 0.821543i \(0.693114\pi\)
\(164\) 0 0
\(165\) 0.552981 0.0430495
\(166\) 0 0
\(167\) −1.80194 −0.139438 −0.0697192 0.997567i \(-0.522210\pi\)
−0.0697192 + 0.997567i \(0.522210\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.09381 −0.389533
\(172\) 0 0
\(173\) 13.4645 1.02369 0.511845 0.859078i \(-0.328962\pi\)
0.511845 + 0.859078i \(0.328962\pi\)
\(174\) 0 0
\(175\) 4.87259 0.368333
\(176\) 0 0
\(177\) −1.21051 −0.0909872
\(178\) 0 0
\(179\) 8.43106 0.630167 0.315083 0.949064i \(-0.397968\pi\)
0.315083 + 0.949064i \(0.397968\pi\)
\(180\) 0 0
\(181\) −22.4436 −1.66822 −0.834109 0.551599i \(-0.814018\pi\)
−0.834109 + 0.551599i \(0.814018\pi\)
\(182\) 0 0
\(183\) −8.22832 −0.608255
\(184\) 0 0
\(185\) −3.76112 −0.276523
\(186\) 0 0
\(187\) 6.04878 0.442331
\(188\) 0 0
\(189\) 5.57711 0.405675
\(190\) 0 0
\(191\) −8.38303 −0.606574 −0.303287 0.952899i \(-0.598084\pi\)
−0.303287 + 0.952899i \(0.598084\pi\)
\(192\) 0 0
\(193\) −8.19008 −0.589535 −0.294767 0.955569i \(-0.595242\pi\)
−0.294767 + 0.955569i \(0.595242\pi\)
\(194\) 0 0
\(195\) 0.552981 0.0395998
\(196\) 0 0
\(197\) −12.1023 −0.862252 −0.431126 0.902292i \(-0.641884\pi\)
−0.431126 + 0.902292i \(0.641884\pi\)
\(198\) 0 0
\(199\) 24.8646 1.76261 0.881303 0.472551i \(-0.156667\pi\)
0.881303 + 0.472551i \(0.156667\pi\)
\(200\) 0 0
\(201\) −9.60072 −0.677182
\(202\) 0 0
\(203\) −5.31591 −0.373104
\(204\) 0 0
\(205\) −3.11343 −0.217451
\(206\) 0 0
\(207\) −4.78977 −0.332912
\(208\) 0 0
\(209\) −8.48928 −0.587216
\(210\) 0 0
\(211\) −25.7697 −1.77406 −0.887030 0.461713i \(-0.847235\pi\)
−0.887030 + 0.461713i \(0.847235\pi\)
\(212\) 0 0
\(213\) −11.8557 −0.812341
\(214\) 0 0
\(215\) 2.66332 0.181637
\(216\) 0 0
\(217\) 9.77065 0.663275
\(218\) 0 0
\(219\) −3.79185 −0.256229
\(220\) 0 0
\(221\) 6.04878 0.406885
\(222\) 0 0
\(223\) 7.74588 0.518703 0.259351 0.965783i \(-0.416491\pi\)
0.259351 + 0.965783i \(0.416491\pi\)
\(224\) 0 0
\(225\) 2.92369 0.194913
\(226\) 0 0
\(227\) −7.51314 −0.498665 −0.249332 0.968418i \(-0.580211\pi\)
−0.249332 + 0.968418i \(0.580211\pi\)
\(228\) 0 0
\(229\) −21.0839 −1.39326 −0.696630 0.717430i \(-0.745318\pi\)
−0.696630 + 0.717430i \(0.745318\pi\)
\(230\) 0 0
\(231\) 1.54918 0.101929
\(232\) 0 0
\(233\) 23.3809 1.53173 0.765866 0.643001i \(-0.222311\pi\)
0.765866 + 0.643001i \(0.222311\pi\)
\(234\) 0 0
\(235\) −0.518941 −0.0338520
\(236\) 0 0
\(237\) −18.3712 −1.19334
\(238\) 0 0
\(239\) 5.42839 0.351133 0.175567 0.984468i \(-0.443824\pi\)
0.175567 + 0.984468i \(0.443824\pi\)
\(240\) 0 0
\(241\) −17.9194 −1.15429 −0.577145 0.816641i \(-0.695833\pi\)
−0.577145 + 0.816641i \(0.695833\pi\)
\(242\) 0 0
\(243\) 6.13508 0.393566
\(244\) 0 0
\(245\) −0.356949 −0.0228047
\(246\) 0 0
\(247\) −8.48928 −0.540160
\(248\) 0 0
\(249\) −8.41757 −0.533442
\(250\) 0 0
\(251\) 4.32837 0.273204 0.136602 0.990626i \(-0.456382\pi\)
0.136602 + 0.990626i \(0.456382\pi\)
\(252\) 0 0
\(253\) −7.98257 −0.501860
\(254\) 0 0
\(255\) 3.34486 0.209463
\(256\) 0 0
\(257\) −11.9892 −0.747866 −0.373933 0.927456i \(-0.621991\pi\)
−0.373933 + 0.927456i \(0.621991\pi\)
\(258\) 0 0
\(259\) −10.5368 −0.654727
\(260\) 0 0
\(261\) −3.18970 −0.197437
\(262\) 0 0
\(263\) −7.00402 −0.431886 −0.215943 0.976406i \(-0.569283\pi\)
−0.215943 + 0.976406i \(0.569283\pi\)
\(264\) 0 0
\(265\) 0.611699 0.0375764
\(266\) 0 0
\(267\) 14.3414 0.877680
\(268\) 0 0
\(269\) −13.2468 −0.807672 −0.403836 0.914831i \(-0.632323\pi\)
−0.403836 + 0.914831i \(0.632323\pi\)
\(270\) 0 0
\(271\) 20.5661 1.24930 0.624650 0.780905i \(-0.285242\pi\)
0.624650 + 0.780905i \(0.285242\pi\)
\(272\) 0 0
\(273\) 1.54918 0.0937609
\(274\) 0 0
\(275\) 4.87259 0.293828
\(276\) 0 0
\(277\) 9.45404 0.568038 0.284019 0.958819i \(-0.408332\pi\)
0.284019 + 0.958819i \(0.408332\pi\)
\(278\) 0 0
\(279\) 5.86266 0.350988
\(280\) 0 0
\(281\) 0.798874 0.0476568 0.0238284 0.999716i \(-0.492414\pi\)
0.0238284 + 0.999716i \(0.492414\pi\)
\(282\) 0 0
\(283\) 15.4553 0.918719 0.459360 0.888250i \(-0.348079\pi\)
0.459360 + 0.888250i \(0.348079\pi\)
\(284\) 0 0
\(285\) −4.69441 −0.278073
\(286\) 0 0
\(287\) −8.72233 −0.514863
\(288\) 0 0
\(289\) 19.5877 1.15222
\(290\) 0 0
\(291\) 5.92384 0.347261
\(292\) 0 0
\(293\) −24.5721 −1.43552 −0.717759 0.696292i \(-0.754832\pi\)
−0.717759 + 0.696292i \(0.754832\pi\)
\(294\) 0 0
\(295\) 0.278914 0.0162390
\(296\) 0 0
\(297\) 5.57711 0.323617
\(298\) 0 0
\(299\) −7.98257 −0.461644
\(300\) 0 0
\(301\) 7.46133 0.430064
\(302\) 0 0
\(303\) −10.2925 −0.591288
\(304\) 0 0
\(305\) 1.89590 0.108559
\(306\) 0 0
\(307\) −2.47883 −0.141474 −0.0707371 0.997495i \(-0.522535\pi\)
−0.0707371 + 0.997495i \(0.522535\pi\)
\(308\) 0 0
\(309\) −14.2959 −0.813265
\(310\) 0 0
\(311\) −30.8260 −1.74798 −0.873992 0.485941i \(-0.838477\pi\)
−0.873992 + 0.485941i \(0.838477\pi\)
\(312\) 0 0
\(313\) 22.2593 1.25817 0.629086 0.777336i \(-0.283429\pi\)
0.629086 + 0.777336i \(0.283429\pi\)
\(314\) 0 0
\(315\) −0.214180 −0.0120677
\(316\) 0 0
\(317\) 2.10203 0.118062 0.0590310 0.998256i \(-0.481199\pi\)
0.0590310 + 0.998256i \(0.481199\pi\)
\(318\) 0 0
\(319\) −5.31591 −0.297634
\(320\) 0 0
\(321\) −17.1649 −0.958049
\(322\) 0 0
\(323\) −51.3498 −2.85718
\(324\) 0 0
\(325\) 4.87259 0.270283
\(326\) 0 0
\(327\) −27.3578 −1.51289
\(328\) 0 0
\(329\) −1.45382 −0.0801519
\(330\) 0 0
\(331\) 30.4137 1.67169 0.835845 0.548966i \(-0.184978\pi\)
0.835845 + 0.548966i \(0.184978\pi\)
\(332\) 0 0
\(333\) −6.32240 −0.346465
\(334\) 0 0
\(335\) 2.21211 0.120861
\(336\) 0 0
\(337\) 5.11263 0.278503 0.139251 0.990257i \(-0.455530\pi\)
0.139251 + 0.990257i \(0.455530\pi\)
\(338\) 0 0
\(339\) −3.41907 −0.185698
\(340\) 0 0
\(341\) 9.77065 0.529110
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −4.41421 −0.237653
\(346\) 0 0
\(347\) 34.2330 1.83773 0.918863 0.394576i \(-0.129109\pi\)
0.918863 + 0.394576i \(0.129109\pi\)
\(348\) 0 0
\(349\) 33.2630 1.78053 0.890263 0.455446i \(-0.150520\pi\)
0.890263 + 0.455446i \(0.150520\pi\)
\(350\) 0 0
\(351\) 5.57711 0.297684
\(352\) 0 0
\(353\) −18.7880 −0.999987 −0.499993 0.866029i \(-0.666664\pi\)
−0.499993 + 0.866029i \(0.666664\pi\)
\(354\) 0 0
\(355\) 2.73169 0.144983
\(356\) 0 0
\(357\) 9.37067 0.495949
\(358\) 0 0
\(359\) 2.76999 0.146195 0.0730973 0.997325i \(-0.476712\pi\)
0.0730973 + 0.997325i \(0.476712\pi\)
\(360\) 0 0
\(361\) 53.0678 2.79304
\(362\) 0 0
\(363\) 1.54918 0.0813111
\(364\) 0 0
\(365\) 0.873685 0.0457308
\(366\) 0 0
\(367\) 21.6481 1.13002 0.565012 0.825083i \(-0.308872\pi\)
0.565012 + 0.825083i \(0.308872\pi\)
\(368\) 0 0
\(369\) −5.23364 −0.272453
\(370\) 0 0
\(371\) 1.71369 0.0889702
\(372\) 0 0
\(373\) 8.47631 0.438887 0.219443 0.975625i \(-0.429576\pi\)
0.219443 + 0.975625i \(0.429576\pi\)
\(374\) 0 0
\(375\) 5.45935 0.281920
\(376\) 0 0
\(377\) −5.31591 −0.273783
\(378\) 0 0
\(379\) 12.1315 0.623152 0.311576 0.950221i \(-0.399143\pi\)
0.311576 + 0.950221i \(0.399143\pi\)
\(380\) 0 0
\(381\) 9.36022 0.479539
\(382\) 0 0
\(383\) −29.1500 −1.48950 −0.744748 0.667346i \(-0.767430\pi\)
−0.744748 + 0.667346i \(0.767430\pi\)
\(384\) 0 0
\(385\) −0.356949 −0.0181918
\(386\) 0 0
\(387\) 4.47701 0.227579
\(388\) 0 0
\(389\) −8.15489 −0.413469 −0.206735 0.978397i \(-0.566284\pi\)
−0.206735 + 0.978397i \(0.566284\pi\)
\(390\) 0 0
\(391\) −48.2848 −2.44187
\(392\) 0 0
\(393\) −33.7531 −1.70262
\(394\) 0 0
\(395\) 4.23293 0.212982
\(396\) 0 0
\(397\) −29.6320 −1.48719 −0.743595 0.668631i \(-0.766881\pi\)
−0.743595 + 0.668631i \(0.766881\pi\)
\(398\) 0 0
\(399\) −13.1515 −0.658396
\(400\) 0 0
\(401\) 21.0032 1.04885 0.524424 0.851457i \(-0.324281\pi\)
0.524424 + 0.851457i \(0.324281\pi\)
\(402\) 0 0
\(403\) 9.77065 0.486711
\(404\) 0 0
\(405\) 2.44149 0.121319
\(406\) 0 0
\(407\) −10.5368 −0.522292
\(408\) 0 0
\(409\) −9.66645 −0.477975 −0.238988 0.971023i \(-0.576816\pi\)
−0.238988 + 0.971023i \(0.576816\pi\)
\(410\) 0 0
\(411\) −29.3054 −1.44553
\(412\) 0 0
\(413\) 0.781383 0.0384493
\(414\) 0 0
\(415\) 1.93950 0.0952064
\(416\) 0 0
\(417\) 35.5791 1.74232
\(418\) 0 0
\(419\) −14.0140 −0.684628 −0.342314 0.939586i \(-0.611211\pi\)
−0.342314 + 0.939586i \(0.611211\pi\)
\(420\) 0 0
\(421\) −9.94209 −0.484548 −0.242274 0.970208i \(-0.577893\pi\)
−0.242274 + 0.970208i \(0.577893\pi\)
\(422\) 0 0
\(423\) −0.872335 −0.0424144
\(424\) 0 0
\(425\) 29.4732 1.42966
\(426\) 0 0
\(427\) 5.31139 0.257036
\(428\) 0 0
\(429\) 1.54918 0.0747953
\(430\) 0 0
\(431\) −6.12683 −0.295119 −0.147559 0.989053i \(-0.547142\pi\)
−0.147559 + 0.989053i \(0.547142\pi\)
\(432\) 0 0
\(433\) 22.4768 1.08017 0.540083 0.841612i \(-0.318393\pi\)
0.540083 + 0.841612i \(0.318393\pi\)
\(434\) 0 0
\(435\) −2.93960 −0.140943
\(436\) 0 0
\(437\) 67.7663 3.24170
\(438\) 0 0
\(439\) 25.1531 1.20049 0.600247 0.799815i \(-0.295069\pi\)
0.600247 + 0.799815i \(0.295069\pi\)
\(440\) 0 0
\(441\) −0.600028 −0.0285728
\(442\) 0 0
\(443\) 14.5891 0.693147 0.346574 0.938023i \(-0.387345\pi\)
0.346574 + 0.938023i \(0.387345\pi\)
\(444\) 0 0
\(445\) −3.30442 −0.156645
\(446\) 0 0
\(447\) −14.5200 −0.686771
\(448\) 0 0
\(449\) −16.3003 −0.769257 −0.384629 0.923071i \(-0.625670\pi\)
−0.384629 + 0.923071i \(0.625670\pi\)
\(450\) 0 0
\(451\) −8.72233 −0.410718
\(452\) 0 0
\(453\) 2.55458 0.120024
\(454\) 0 0
\(455\) −0.356949 −0.0167341
\(456\) 0 0
\(457\) 3.10112 0.145064 0.0725321 0.997366i \(-0.476892\pi\)
0.0725321 + 0.997366i \(0.476892\pi\)
\(458\) 0 0
\(459\) 33.7347 1.57460
\(460\) 0 0
\(461\) 26.5437 1.23626 0.618131 0.786075i \(-0.287890\pi\)
0.618131 + 0.786075i \(0.287890\pi\)
\(462\) 0 0
\(463\) −15.2201 −0.707340 −0.353670 0.935370i \(-0.615066\pi\)
−0.353670 + 0.935370i \(0.615066\pi\)
\(464\) 0 0
\(465\) 5.40298 0.250557
\(466\) 0 0
\(467\) 14.6005 0.675631 0.337815 0.941212i \(-0.390312\pi\)
0.337815 + 0.941212i \(0.390312\pi\)
\(468\) 0 0
\(469\) 6.19727 0.286163
\(470\) 0 0
\(471\) −22.7794 −1.04962
\(472\) 0 0
\(473\) 7.46133 0.343072
\(474\) 0 0
\(475\) −41.3647 −1.89794
\(476\) 0 0
\(477\) 1.02826 0.0470808
\(478\) 0 0
\(479\) 22.2842 1.01819 0.509095 0.860711i \(-0.329980\pi\)
0.509095 + 0.860711i \(0.329980\pi\)
\(480\) 0 0
\(481\) −10.5368 −0.480438
\(482\) 0 0
\(483\) −12.3665 −0.562694
\(484\) 0 0
\(485\) −1.36492 −0.0619778
\(486\) 0 0
\(487\) −36.2685 −1.64348 −0.821742 0.569860i \(-0.806997\pi\)
−0.821742 + 0.569860i \(0.806997\pi\)
\(488\) 0 0
\(489\) −22.5535 −1.01990
\(490\) 0 0
\(491\) 5.21894 0.235528 0.117764 0.993042i \(-0.462427\pi\)
0.117764 + 0.993042i \(0.462427\pi\)
\(492\) 0 0
\(493\) −32.1548 −1.44818
\(494\) 0 0
\(495\) −0.214180 −0.00962666
\(496\) 0 0
\(497\) 7.65289 0.343279
\(498\) 0 0
\(499\) 16.5188 0.739482 0.369741 0.929135i \(-0.379446\pi\)
0.369741 + 0.929135i \(0.379446\pi\)
\(500\) 0 0
\(501\) −2.79154 −0.124717
\(502\) 0 0
\(503\) −35.4935 −1.58258 −0.791288 0.611444i \(-0.790589\pi\)
−0.791288 + 0.611444i \(0.790589\pi\)
\(504\) 0 0
\(505\) 2.37151 0.105531
\(506\) 0 0
\(507\) 1.54918 0.0688017
\(508\) 0 0
\(509\) −43.8652 −1.94429 −0.972146 0.234376i \(-0.924695\pi\)
−0.972146 + 0.234376i \(0.924695\pi\)
\(510\) 0 0
\(511\) 2.44764 0.108277
\(512\) 0 0
\(513\) −47.3456 −2.09036
\(514\) 0 0
\(515\) 3.29394 0.145148
\(516\) 0 0
\(517\) −1.45382 −0.0639391
\(518\) 0 0
\(519\) 20.8591 0.915611
\(520\) 0 0
\(521\) −11.9666 −0.524264 −0.262132 0.965032i \(-0.584426\pi\)
−0.262132 + 0.965032i \(0.584426\pi\)
\(522\) 0 0
\(523\) 15.6990 0.686470 0.343235 0.939249i \(-0.388477\pi\)
0.343235 + 0.939249i \(0.388477\pi\)
\(524\) 0 0
\(525\) 7.54854 0.329445
\(526\) 0 0
\(527\) 59.1005 2.57446
\(528\) 0 0
\(529\) 40.7215 1.77050
\(530\) 0 0
\(531\) 0.468852 0.0203464
\(532\) 0 0
\(533\) −8.72233 −0.377806
\(534\) 0 0
\(535\) 3.95498 0.170988
\(536\) 0 0
\(537\) 13.0613 0.563635
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 26.7880 1.15171 0.575854 0.817553i \(-0.304670\pi\)
0.575854 + 0.817553i \(0.304670\pi\)
\(542\) 0 0
\(543\) −34.7692 −1.49209
\(544\) 0 0
\(545\) 6.30354 0.270014
\(546\) 0 0
\(547\) −9.09563 −0.388901 −0.194450 0.980912i \(-0.562292\pi\)
−0.194450 + 0.980912i \(0.562292\pi\)
\(548\) 0 0
\(549\) 3.18698 0.136017
\(550\) 0 0
\(551\) 45.1283 1.92253
\(552\) 0 0
\(553\) 11.8586 0.504280
\(554\) 0 0
\(555\) −5.82667 −0.247328
\(556\) 0 0
\(557\) −13.5695 −0.574958 −0.287479 0.957787i \(-0.592817\pi\)
−0.287479 + 0.957787i \(0.592817\pi\)
\(558\) 0 0
\(559\) 7.46133 0.315581
\(560\) 0 0
\(561\) 9.37067 0.395630
\(562\) 0 0
\(563\) −6.20690 −0.261590 −0.130795 0.991409i \(-0.541753\pi\)
−0.130795 + 0.991409i \(0.541753\pi\)
\(564\) 0 0
\(565\) 0.787791 0.0331426
\(566\) 0 0
\(567\) 6.83988 0.287248
\(568\) 0 0
\(569\) −29.4433 −1.23433 −0.617164 0.786834i \(-0.711719\pi\)
−0.617164 + 0.786834i \(0.711719\pi\)
\(570\) 0 0
\(571\) 29.8202 1.24794 0.623968 0.781450i \(-0.285519\pi\)
0.623968 + 0.781450i \(0.285519\pi\)
\(572\) 0 0
\(573\) −12.9869 −0.542533
\(574\) 0 0
\(575\) −38.8958 −1.62207
\(576\) 0 0
\(577\) 12.5995 0.524524 0.262262 0.964997i \(-0.415531\pi\)
0.262262 + 0.964997i \(0.415531\pi\)
\(578\) 0 0
\(579\) −12.6879 −0.527293
\(580\) 0 0
\(581\) 5.43355 0.225422
\(582\) 0 0
\(583\) 1.71369 0.0709736
\(584\) 0 0
\(585\) −0.214180 −0.00885524
\(586\) 0 0
\(587\) 31.3278 1.29303 0.646517 0.762899i \(-0.276225\pi\)
0.646517 + 0.762899i \(0.276225\pi\)
\(588\) 0 0
\(589\) −82.9457 −3.41772
\(590\) 0 0
\(591\) −18.7487 −0.771217
\(592\) 0 0
\(593\) 14.1972 0.583010 0.291505 0.956569i \(-0.405844\pi\)
0.291505 + 0.956569i \(0.405844\pi\)
\(594\) 0 0
\(595\) −2.15911 −0.0885148
\(596\) 0 0
\(597\) 38.5199 1.57651
\(598\) 0 0
\(599\) −35.9027 −1.46694 −0.733472 0.679720i \(-0.762101\pi\)
−0.733472 + 0.679720i \(0.762101\pi\)
\(600\) 0 0
\(601\) 6.89109 0.281094 0.140547 0.990074i \(-0.455114\pi\)
0.140547 + 0.990074i \(0.455114\pi\)
\(602\) 0 0
\(603\) 3.71854 0.151431
\(604\) 0 0
\(605\) −0.356949 −0.0145121
\(606\) 0 0
\(607\) −19.0947 −0.775032 −0.387516 0.921863i \(-0.626667\pi\)
−0.387516 + 0.921863i \(0.626667\pi\)
\(608\) 0 0
\(609\) −8.23533 −0.333712
\(610\) 0 0
\(611\) −1.45382 −0.0588154
\(612\) 0 0
\(613\) 11.4928 0.464189 0.232095 0.972693i \(-0.425442\pi\)
0.232095 + 0.972693i \(0.425442\pi\)
\(614\) 0 0
\(615\) −4.82328 −0.194493
\(616\) 0 0
\(617\) −32.1261 −1.29335 −0.646674 0.762767i \(-0.723841\pi\)
−0.646674 + 0.762767i \(0.723841\pi\)
\(618\) 0 0
\(619\) 24.8651 0.999411 0.499706 0.866195i \(-0.333442\pi\)
0.499706 + 0.866195i \(0.333442\pi\)
\(620\) 0 0
\(621\) −44.5197 −1.78651
\(622\) 0 0
\(623\) −9.25740 −0.370890
\(624\) 0 0
\(625\) 23.1050 0.924202
\(626\) 0 0
\(627\) −13.1515 −0.525219
\(628\) 0 0
\(629\) −63.7350 −2.54128
\(630\) 0 0
\(631\) 14.4588 0.575595 0.287797 0.957691i \(-0.407077\pi\)
0.287797 + 0.957691i \(0.407077\pi\)
\(632\) 0 0
\(633\) −39.9220 −1.58676
\(634\) 0 0
\(635\) −2.15670 −0.0855860
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 4.59195 0.181655
\(640\) 0 0
\(641\) −46.4826 −1.83595 −0.917976 0.396637i \(-0.870177\pi\)
−0.917976 + 0.396637i \(0.870177\pi\)
\(642\) 0 0
\(643\) −22.9147 −0.903666 −0.451833 0.892102i \(-0.649230\pi\)
−0.451833 + 0.892102i \(0.649230\pi\)
\(644\) 0 0
\(645\) 4.12597 0.162460
\(646\) 0 0
\(647\) 9.93310 0.390511 0.195255 0.980752i \(-0.437446\pi\)
0.195255 + 0.980752i \(0.437446\pi\)
\(648\) 0 0
\(649\) 0.781383 0.0306720
\(650\) 0 0
\(651\) 15.1365 0.593247
\(652\) 0 0
\(653\) 23.8734 0.934238 0.467119 0.884195i \(-0.345292\pi\)
0.467119 + 0.884195i \(0.345292\pi\)
\(654\) 0 0
\(655\) 7.77710 0.303876
\(656\) 0 0
\(657\) 1.46865 0.0572977
\(658\) 0 0
\(659\) 26.9548 1.05001 0.525004 0.851100i \(-0.324064\pi\)
0.525004 + 0.851100i \(0.324064\pi\)
\(660\) 0 0
\(661\) −22.9740 −0.893586 −0.446793 0.894637i \(-0.647434\pi\)
−0.446793 + 0.894637i \(0.647434\pi\)
\(662\) 0 0
\(663\) 9.37067 0.363927
\(664\) 0 0
\(665\) 3.03024 0.117508
\(666\) 0 0
\(667\) 42.4347 1.64308
\(668\) 0 0
\(669\) 11.9998 0.463939
\(670\) 0 0
\(671\) 5.31139 0.205044
\(672\) 0 0
\(673\) −6.05070 −0.233237 −0.116619 0.993177i \(-0.537206\pi\)
−0.116619 + 0.993177i \(0.537206\pi\)
\(674\) 0 0
\(675\) 27.1749 1.04596
\(676\) 0 0
\(677\) 29.1842 1.12164 0.560820 0.827938i \(-0.310486\pi\)
0.560820 + 0.827938i \(0.310486\pi\)
\(678\) 0 0
\(679\) −3.82384 −0.146746
\(680\) 0 0
\(681\) −11.6392 −0.446017
\(682\) 0 0
\(683\) −28.6520 −1.09634 −0.548169 0.836367i \(-0.684675\pi\)
−0.548169 + 0.836367i \(0.684675\pi\)
\(684\) 0 0
\(685\) 6.75230 0.257992
\(686\) 0 0
\(687\) −32.6628 −1.24616
\(688\) 0 0
\(689\) 1.71369 0.0652862
\(690\) 0 0
\(691\) −13.0755 −0.497416 −0.248708 0.968579i \(-0.580006\pi\)
−0.248708 + 0.968579i \(0.580006\pi\)
\(692\) 0 0
\(693\) −0.600028 −0.0227932
\(694\) 0 0
\(695\) −8.19783 −0.310961
\(696\) 0 0
\(697\) −52.7594 −1.99841
\(698\) 0 0
\(699\) 36.2213 1.37001
\(700\) 0 0
\(701\) 9.91478 0.374476 0.187238 0.982315i \(-0.440046\pi\)
0.187238 + 0.982315i \(0.440046\pi\)
\(702\) 0 0
\(703\) 89.4501 3.37368
\(704\) 0 0
\(705\) −0.803936 −0.0302780
\(706\) 0 0
\(707\) 6.64381 0.249866
\(708\) 0 0
\(709\) −37.4122 −1.40504 −0.702522 0.711662i \(-0.747943\pi\)
−0.702522 + 0.711662i \(0.747943\pi\)
\(710\) 0 0
\(711\) 7.11551 0.266853
\(712\) 0 0
\(713\) −77.9949 −2.92093
\(714\) 0 0
\(715\) −0.356949 −0.0133492
\(716\) 0 0
\(717\) 8.40957 0.314061
\(718\) 0 0
\(719\) 26.1404 0.974872 0.487436 0.873159i \(-0.337932\pi\)
0.487436 + 0.873159i \(0.337932\pi\)
\(720\) 0 0
\(721\) 9.22802 0.343669
\(722\) 0 0
\(723\) −27.7605 −1.03242
\(724\) 0 0
\(725\) −25.9023 −0.961985
\(726\) 0 0
\(727\) 19.2363 0.713435 0.356717 0.934212i \(-0.383896\pi\)
0.356717 + 0.934212i \(0.383896\pi\)
\(728\) 0 0
\(729\) 30.0240 1.11200
\(730\) 0 0
\(731\) 45.1319 1.66926
\(732\) 0 0
\(733\) −17.8790 −0.660378 −0.330189 0.943915i \(-0.607112\pi\)
−0.330189 + 0.943915i \(0.607112\pi\)
\(734\) 0 0
\(735\) −0.552981 −0.0203970
\(736\) 0 0
\(737\) 6.19727 0.228279
\(738\) 0 0
\(739\) 20.4069 0.750681 0.375341 0.926887i \(-0.377526\pi\)
0.375341 + 0.926887i \(0.377526\pi\)
\(740\) 0 0
\(741\) −13.1515 −0.483131
\(742\) 0 0
\(743\) −20.3952 −0.748226 −0.374113 0.927383i \(-0.622053\pi\)
−0.374113 + 0.927383i \(0.622053\pi\)
\(744\) 0 0
\(745\) 3.34556 0.122572
\(746\) 0 0
\(747\) 3.26028 0.119287
\(748\) 0 0
\(749\) 11.0799 0.404852
\(750\) 0 0
\(751\) 35.5747 1.29814 0.649070 0.760728i \(-0.275158\pi\)
0.649070 + 0.760728i \(0.275158\pi\)
\(752\) 0 0
\(753\) 6.70544 0.244360
\(754\) 0 0
\(755\) −0.588603 −0.0214215
\(756\) 0 0
\(757\) −7.55291 −0.274515 −0.137258 0.990535i \(-0.543829\pi\)
−0.137258 + 0.990535i \(0.543829\pi\)
\(758\) 0 0
\(759\) −12.3665 −0.448875
\(760\) 0 0
\(761\) 29.6862 1.07612 0.538062 0.842906i \(-0.319157\pi\)
0.538062 + 0.842906i \(0.319157\pi\)
\(762\) 0 0
\(763\) 17.6595 0.639316
\(764\) 0 0
\(765\) −1.29553 −0.0468398
\(766\) 0 0
\(767\) 0.781383 0.0282141
\(768\) 0 0
\(769\) 49.3335 1.77901 0.889506 0.456924i \(-0.151049\pi\)
0.889506 + 0.456924i \(0.151049\pi\)
\(770\) 0 0
\(771\) −18.5735 −0.668907
\(772\) 0 0
\(773\) −50.8325 −1.82832 −0.914160 0.405354i \(-0.867148\pi\)
−0.914160 + 0.405354i \(0.867148\pi\)
\(774\) 0 0
\(775\) 47.6083 1.71014
\(776\) 0 0
\(777\) −16.3235 −0.585602
\(778\) 0 0
\(779\) 74.0463 2.65298
\(780\) 0 0
\(781\) 7.65289 0.273842
\(782\) 0 0
\(783\) −29.6474 −1.05951
\(784\) 0 0
\(785\) 5.24864 0.187332
\(786\) 0 0
\(787\) 48.7664 1.73833 0.869167 0.494518i \(-0.164655\pi\)
0.869167 + 0.494518i \(0.164655\pi\)
\(788\) 0 0
\(789\) −10.8505 −0.386289
\(790\) 0 0
\(791\) 2.20701 0.0784723
\(792\) 0 0
\(793\) 5.31139 0.188613
\(794\) 0 0
\(795\) 0.947635 0.0336092
\(796\) 0 0
\(797\) 24.3353 0.861999 0.431000 0.902352i \(-0.358161\pi\)
0.431000 + 0.902352i \(0.358161\pi\)
\(798\) 0 0
\(799\) −8.79385 −0.311104
\(800\) 0 0
\(801\) −5.55470 −0.196266
\(802\) 0 0
\(803\) 2.44764 0.0863754
\(804\) 0 0
\(805\) 2.84938 0.100427
\(806\) 0 0
\(807\) −20.5218 −0.722400
\(808\) 0 0
\(809\) 41.2803 1.45134 0.725668 0.688045i \(-0.241531\pi\)
0.725668 + 0.688045i \(0.241531\pi\)
\(810\) 0 0
\(811\) 19.5033 0.684855 0.342428 0.939544i \(-0.388751\pi\)
0.342428 + 0.939544i \(0.388751\pi\)
\(812\) 0 0
\(813\) 31.8606 1.11740
\(814\) 0 0
\(815\) 5.19658 0.182028
\(816\) 0 0
\(817\) −63.3413 −2.21603
\(818\) 0 0
\(819\) −0.600028 −0.0209667
\(820\) 0 0
\(821\) 17.3464 0.605392 0.302696 0.953087i \(-0.402113\pi\)
0.302696 + 0.953087i \(0.402113\pi\)
\(822\) 0 0
\(823\) −29.1458 −1.01596 −0.507980 0.861369i \(-0.669608\pi\)
−0.507980 + 0.861369i \(0.669608\pi\)
\(824\) 0 0
\(825\) 7.54854 0.262806
\(826\) 0 0
\(827\) 22.7663 0.791661 0.395830 0.918324i \(-0.370457\pi\)
0.395830 + 0.918324i \(0.370457\pi\)
\(828\) 0 0
\(829\) 17.2238 0.598206 0.299103 0.954221i \(-0.403313\pi\)
0.299103 + 0.954221i \(0.403313\pi\)
\(830\) 0 0
\(831\) 14.6460 0.508066
\(832\) 0 0
\(833\) −6.04878 −0.209578
\(834\) 0 0
\(835\) 0.643202 0.0222589
\(836\) 0 0
\(837\) 54.4919 1.88352
\(838\) 0 0
\(839\) 30.2951 1.04590 0.522952 0.852362i \(-0.324831\pi\)
0.522952 + 0.852362i \(0.324831\pi\)
\(840\) 0 0
\(841\) −0.741062 −0.0255539
\(842\) 0 0
\(843\) 1.23760 0.0426253
\(844\) 0 0
\(845\) −0.356949 −0.0122794
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 23.9430 0.821723
\(850\) 0 0
\(851\) 84.1111 2.88329
\(852\) 0 0
\(853\) 33.4519 1.14537 0.572686 0.819775i \(-0.305901\pi\)
0.572686 + 0.819775i \(0.305901\pi\)
\(854\) 0 0
\(855\) 1.81823 0.0621822
\(856\) 0 0
\(857\) 4.70378 0.160678 0.0803391 0.996768i \(-0.474400\pi\)
0.0803391 + 0.996768i \(0.474400\pi\)
\(858\) 0 0
\(859\) −31.7030 −1.08169 −0.540846 0.841122i \(-0.681896\pi\)
−0.540846 + 0.841122i \(0.681896\pi\)
\(860\) 0 0
\(861\) −13.5125 −0.460505
\(862\) 0 0
\(863\) 7.32286 0.249273 0.124636 0.992202i \(-0.460224\pi\)
0.124636 + 0.992202i \(0.460224\pi\)
\(864\) 0 0
\(865\) −4.80616 −0.163414
\(866\) 0 0
\(867\) 30.3450 1.03057
\(868\) 0 0
\(869\) 11.8586 0.402277
\(870\) 0 0
\(871\) 6.19727 0.209987
\(872\) 0 0
\(873\) −2.29441 −0.0776541
\(874\) 0 0
\(875\) −3.52401 −0.119133
\(876\) 0 0
\(877\) −42.9628 −1.45075 −0.725375 0.688354i \(-0.758334\pi\)
−0.725375 + 0.688354i \(0.758334\pi\)
\(878\) 0 0
\(879\) −38.0667 −1.28396
\(880\) 0 0
\(881\) 3.65959 0.123295 0.0616474 0.998098i \(-0.480365\pi\)
0.0616474 + 0.998098i \(0.480365\pi\)
\(882\) 0 0
\(883\) −22.2488 −0.748731 −0.374366 0.927281i \(-0.622140\pi\)
−0.374366 + 0.927281i \(0.622140\pi\)
\(884\) 0 0
\(885\) 0.432089 0.0145245
\(886\) 0 0
\(887\) −17.2501 −0.579202 −0.289601 0.957147i \(-0.593523\pi\)
−0.289601 + 0.957147i \(0.593523\pi\)
\(888\) 0 0
\(889\) −6.04203 −0.202643
\(890\) 0 0
\(891\) 6.83988 0.229145
\(892\) 0 0
\(893\) 12.3419 0.413006
\(894\) 0 0
\(895\) −3.00946 −0.100595
\(896\) 0 0
\(897\) −12.3665 −0.412905
\(898\) 0 0
\(899\) −51.9399 −1.73229
\(900\) 0 0
\(901\) 10.3657 0.345332
\(902\) 0 0
\(903\) 11.5590 0.384659
\(904\) 0 0
\(905\) 8.01122 0.266302
\(906\) 0 0
\(907\) −10.7320 −0.356349 −0.178175 0.983999i \(-0.557019\pi\)
−0.178175 + 0.983999i \(0.557019\pi\)
\(908\) 0 0
\(909\) 3.98648 0.132223
\(910\) 0 0
\(911\) 17.3482 0.574771 0.287386 0.957815i \(-0.407214\pi\)
0.287386 + 0.957815i \(0.407214\pi\)
\(912\) 0 0
\(913\) 5.43355 0.179824
\(914\) 0 0
\(915\) 2.93709 0.0970973
\(916\) 0 0
\(917\) 21.7877 0.719492
\(918\) 0 0
\(919\) −42.9821 −1.41785 −0.708924 0.705285i \(-0.750819\pi\)
−0.708924 + 0.705285i \(0.750819\pi\)
\(920\) 0 0
\(921\) −3.84016 −0.126538
\(922\) 0 0
\(923\) 7.65289 0.251898
\(924\) 0 0
\(925\) −51.3417 −1.68810
\(926\) 0 0
\(927\) 5.53707 0.181861
\(928\) 0 0
\(929\) −48.4507 −1.58962 −0.794808 0.606861i \(-0.792428\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(930\) 0 0
\(931\) 8.48928 0.278225
\(932\) 0 0
\(933\) −47.7552 −1.56343
\(934\) 0 0
\(935\) −2.15911 −0.0706104
\(936\) 0 0
\(937\) −33.0939 −1.08113 −0.540565 0.841302i \(-0.681789\pi\)
−0.540565 + 0.841302i \(0.681789\pi\)
\(938\) 0 0
\(939\) 34.4838 1.12534
\(940\) 0 0
\(941\) 13.8501 0.451499 0.225750 0.974185i \(-0.427517\pi\)
0.225750 + 0.974185i \(0.427517\pi\)
\(942\) 0 0
\(943\) 69.6266 2.26735
\(944\) 0 0
\(945\) −1.99075 −0.0647590
\(946\) 0 0
\(947\) −0.457427 −0.0148644 −0.00743219 0.999972i \(-0.502366\pi\)
−0.00743219 + 0.999972i \(0.502366\pi\)
\(948\) 0 0
\(949\) 2.44764 0.0794539
\(950\) 0 0
\(951\) 3.25644 0.105597
\(952\) 0 0
\(953\) −33.5821 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(954\) 0 0
\(955\) 2.99232 0.0968291
\(956\) 0 0
\(957\) −8.23533 −0.266210
\(958\) 0 0
\(959\) 18.9167 0.610852
\(960\) 0 0
\(961\) 64.4655 2.07953
\(962\) 0 0
\(963\) 6.64827 0.214238
\(964\) 0 0
\(965\) 2.92345 0.0941090
\(966\) 0 0
\(967\) −51.2960 −1.64957 −0.824784 0.565448i \(-0.808703\pi\)
−0.824784 + 0.565448i \(0.808703\pi\)
\(968\) 0 0
\(969\) −79.5503 −2.55552
\(970\) 0 0
\(971\) −57.5395 −1.84653 −0.923265 0.384163i \(-0.874490\pi\)
−0.923265 + 0.384163i \(0.874490\pi\)
\(972\) 0 0
\(973\) −22.9664 −0.736268
\(974\) 0 0
\(975\) 7.54854 0.241747
\(976\) 0 0
\(977\) 3.89398 0.124579 0.0622897 0.998058i \(-0.480160\pi\)
0.0622897 + 0.998058i \(0.480160\pi\)
\(978\) 0 0
\(979\) −9.25740 −0.295868
\(980\) 0 0
\(981\) 10.5962 0.338310
\(982\) 0 0
\(983\) 22.9979 0.733519 0.366760 0.930316i \(-0.380467\pi\)
0.366760 + 0.930316i \(0.380467\pi\)
\(984\) 0 0
\(985\) 4.31991 0.137644
\(986\) 0 0
\(987\) −2.25224 −0.0716896
\(988\) 0 0
\(989\) −59.5606 −1.89392
\(990\) 0 0
\(991\) −30.3704 −0.964749 −0.482375 0.875965i \(-0.660226\pi\)
−0.482375 + 0.875965i \(0.660226\pi\)
\(992\) 0 0
\(993\) 47.1165 1.49520
\(994\) 0 0
\(995\) −8.87541 −0.281370
\(996\) 0 0
\(997\) 3.31661 0.105038 0.0525190 0.998620i \(-0.483275\pi\)
0.0525190 + 0.998620i \(0.483275\pi\)
\(998\) 0 0
\(999\) −58.7651 −1.85924
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 \(a_p\))