Properties

Label 2268.2.i.n.2053.6
Level $2268$
Weight $2$
Character 2268.2053
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 9 x^{14} + 31 x^{12} - 282 x^{10} + 1695 x^{8} - 3318 x^{6} + 4606 x^{4} - 4116 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2053.6
Root \(-1.04556 - 0.339889i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.n.865.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.515559 + 0.892975i) q^{5} +(-2.63118 - 0.277320i) q^{7} +O(q^{10})\) \(q+(0.515559 + 0.892975i) q^{5} +(-2.63118 - 0.277320i) q^{7} +(-0.792879 + 1.37331i) q^{11} +(-2.52415 + 4.37196i) q^{13} +(2.58242 + 4.47288i) q^{17} +(-0.392975 + 0.680652i) q^{19} +(-2.93289 - 5.07991i) q^{23} +(1.96840 - 3.40936i) q^{25} +(-4.44511 - 7.69915i) q^{29} -1.15085 q^{31} +(-1.10889 - 2.49255i) q^{35} +(4.07991 - 7.06661i) q^{37} +(3.87206 - 6.70660i) q^{41} +(1.26628 + 2.19326i) q^{43} -8.49189 q^{47} +(6.84619 + 1.45935i) q^{49} +(-2.41270 - 4.17892i) q^{53} -1.63510 q^{55} -3.87245 q^{59} -9.64407 q^{61} -5.20540 q^{65} -1.67444 q^{67} -14.2795 q^{71} +(3.04382 + 5.27205i) q^{73} +(2.46705 - 3.39353i) q^{77} -8.31066 q^{79} +(-7.12095 - 12.3339i) q^{83} +(-2.66278 + 4.61207i) q^{85} +(-6.69272 + 11.5921i) q^{89} +(7.85392 - 10.8034i) q^{91} -0.810407 q^{95} +(-2.67500 - 4.63323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7} + O(q^{10}) \) \( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) 0.515559 + 0.892975i 0.230565 + 0.399350i 0.957975 0.286853i \(-0.0926092\pi\)
−0.727409 + 0.686204i \(0.759276\pi\)
\(6\) 0 0
\(7\) −2.63118 0.277320i −0.994492 0.104817i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.792879 + 1.37331i −0.239062 + 0.414067i −0.960445 0.278468i \(-0.910173\pi\)
0.721383 + 0.692536i \(0.243507\pi\)
\(12\) 0 0
\(13\) −2.52415 + 4.37196i −0.700074 + 1.21256i 0.268366 + 0.963317i \(0.413516\pi\)
−0.968440 + 0.249246i \(0.919817\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.58242 + 4.47288i 0.626329 + 1.08483i 0.988282 + 0.152637i \(0.0487765\pi\)
−0.361954 + 0.932196i \(0.617890\pi\)
\(18\) 0 0
\(19\) −0.392975 + 0.680652i −0.0901546 + 0.156152i −0.907576 0.419888i \(-0.862069\pi\)
0.817421 + 0.576040i \(0.195403\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.93289 5.07991i −0.611549 1.05923i −0.990980 0.134014i \(-0.957213\pi\)
0.379431 0.925220i \(-0.376120\pi\)
\(24\) 0 0
\(25\) 1.96840 3.40936i 0.393679 0.681873i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.44511 7.69915i −0.825435 1.42970i −0.901586 0.432600i \(-0.857596\pi\)
0.0761506 0.997096i \(-0.475737\pi\)
\(30\) 0 0
\(31\) −1.15085 −0.206698 −0.103349 0.994645i \(-0.532956\pi\)
−0.103349 + 0.994645i \(0.532956\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.10889 2.49255i −0.187436 0.421318i
\(36\) 0 0
\(37\) 4.07991 7.06661i 0.670732 1.16174i −0.306964 0.951721i \(-0.599313\pi\)
0.977697 0.210022i \(-0.0673535\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.87206 6.70660i 0.604714 1.04739i −0.387383 0.921919i \(-0.626621\pi\)
0.992097 0.125476i \(-0.0400458\pi\)
\(42\) 0 0
\(43\) 1.26628 + 2.19326i 0.193106 + 0.334470i 0.946278 0.323354i \(-0.104811\pi\)
−0.753172 + 0.657824i \(0.771477\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.49189 −1.23867 −0.619335 0.785127i \(-0.712598\pi\)
−0.619335 + 0.785127i \(0.712598\pi\)
\(48\) 0 0
\(49\) 6.84619 + 1.45935i 0.978027 + 0.208479i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.41270 4.17892i −0.331410 0.574019i 0.651378 0.758753i \(-0.274191\pi\)
−0.982789 + 0.184734i \(0.940858\pi\)
\(54\) 0 0
\(55\) −1.63510 −0.220477
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.87245 −0.504150 −0.252075 0.967708i \(-0.581113\pi\)
−0.252075 + 0.967708i \(0.581113\pi\)
\(60\) 0 0
\(61\) −9.64407 −1.23480 −0.617398 0.786651i \(-0.711813\pi\)
−0.617398 + 0.786651i \(0.711813\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.20540 −0.645650
\(66\) 0 0
\(67\) −1.67444 −0.204565 −0.102283 0.994755i \(-0.532615\pi\)
−0.102283 + 0.994755i \(0.532615\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.2795 −1.69467 −0.847333 0.531062i \(-0.821793\pi\)
−0.847333 + 0.531062i \(0.821793\pi\)
\(72\) 0 0
\(73\) 3.04382 + 5.27205i 0.356252 + 0.617047i 0.987331 0.158671i \(-0.0507211\pi\)
−0.631079 + 0.775718i \(0.717388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.46705 3.39353i 0.281146 0.386729i
\(78\) 0 0
\(79\) −8.31066 −0.935022 −0.467511 0.883987i \(-0.654849\pi\)
−0.467511 + 0.883987i \(0.654849\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.12095 12.3339i −0.781626 1.35382i −0.930994 0.365034i \(-0.881057\pi\)
0.149368 0.988782i \(-0.452276\pi\)
\(84\) 0 0
\(85\) −2.66278 + 4.61207i −0.288819 + 0.500249i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.69272 + 11.5921i −0.709426 + 1.22876i 0.255644 + 0.966771i \(0.417713\pi\)
−0.965070 + 0.261992i \(0.915621\pi\)
\(90\) 0 0
\(91\) 7.85392 10.8034i 0.823315 1.13250i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.810407 −0.0831460
\(96\) 0 0
\(97\) −2.67500 4.63323i −0.271605 0.470433i 0.697668 0.716421i \(-0.254221\pi\)
−0.969273 + 0.245988i \(0.920888\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.59038 + 2.75462i −0.158249 + 0.274095i −0.934237 0.356652i \(-0.883918\pi\)
0.775988 + 0.630747i \(0.217251\pi\)
\(102\) 0 0
\(103\) 5.70660 + 9.88412i 0.562288 + 0.973911i 0.997296 + 0.0734850i \(0.0234121\pi\)
−0.435008 + 0.900426i \(0.643255\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.311386 0.539337i 0.0301028 0.0521396i −0.850582 0.525843i \(-0.823750\pi\)
0.880684 + 0.473704i \(0.157083\pi\)
\(108\) 0 0
\(109\) 0.971921 + 1.68342i 0.0930932 + 0.161242i 0.908811 0.417208i \(-0.136991\pi\)
−0.815718 + 0.578450i \(0.803658\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.79416 3.10758i 0.168781 0.292337i −0.769211 0.638995i \(-0.779350\pi\)
0.937991 + 0.346658i \(0.112684\pi\)
\(114\) 0 0
\(115\) 3.02415 5.23798i 0.282004 0.488445i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.55438 12.4851i −0.509170 1.14451i
\(120\) 0 0
\(121\) 4.24269 + 7.34855i 0.385699 + 0.668050i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.21489 0.824205
\(126\) 0 0
\(127\) 11.6202 1.03113 0.515563 0.856852i \(-0.327583\pi\)
0.515563 + 0.856852i \(0.327583\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.07898 7.06501i −0.356382 0.617272i 0.630971 0.775806i \(-0.282657\pi\)
−0.987354 + 0.158534i \(0.949323\pi\)
\(132\) 0 0
\(133\) 1.22274 1.68194i 0.106025 0.145842i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.28181 + 12.6125i −0.622127 + 1.07756i 0.366962 + 0.930236i \(0.380398\pi\)
−0.989089 + 0.147320i \(0.952935\pi\)
\(138\) 0 0
\(139\) 5.91713 10.2488i 0.501884 0.869289i −0.498113 0.867112i \(-0.665974\pi\)
0.999998 0.00217698i \(-0.000692954\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00269 6.93287i −0.334722 0.579756i
\(144\) 0 0
\(145\) 4.58343 7.93873i 0.380633 0.659276i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.02477 12.1673i −0.575492 0.996781i −0.995988 0.0894868i \(-0.971477\pi\)
0.420496 0.907294i \(-0.361856\pi\)
\(150\) 0 0
\(151\) −1.24269 + 2.15240i −0.101128 + 0.175159i −0.912150 0.409857i \(-0.865579\pi\)
0.811021 + 0.585016i \(0.198912\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.593329 1.02768i −0.0476573 0.0825449i
\(156\) 0 0
\(157\) −3.03934 −0.242565 −0.121283 0.992618i \(-0.538701\pi\)
−0.121283 + 0.992618i \(0.538701\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.30818 + 14.1795i 0.497154 + 1.11750i
\(162\) 0 0
\(163\) −8.75883 + 15.1707i −0.686045 + 1.18826i 0.287063 + 0.957912i \(0.407321\pi\)
−0.973107 + 0.230352i \(0.926012\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.2738 21.2588i 0.949775 1.64506i 0.203877 0.978996i \(-0.434646\pi\)
0.745897 0.666061i \(-0.232021\pi\)
\(168\) 0 0
\(169\) −6.24269 10.8126i −0.480207 0.831742i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.0689138 0.00523942 0.00261971 0.999997i \(-0.499166\pi\)
0.00261971 + 0.999997i \(0.499166\pi\)
\(174\) 0 0
\(175\) −6.12469 + 8.42477i −0.462983 + 0.636853i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.96086 6.86041i −0.296049 0.512771i 0.679180 0.733972i \(-0.262336\pi\)
−0.975228 + 0.221201i \(0.929002\pi\)
\(180\) 0 0
\(181\) 3.59688 0.267354 0.133677 0.991025i \(-0.457322\pi\)
0.133677 + 0.991025i \(0.457322\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.41373 0.618590
\(186\) 0 0
\(187\) −8.19018 −0.598925
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −16.0492 −1.16128 −0.580638 0.814162i \(-0.697197\pi\)
−0.580638 + 0.814162i \(0.697197\pi\)
\(192\) 0 0
\(193\) −21.5730 −1.55286 −0.776430 0.630204i \(-0.782971\pi\)
−0.776430 + 0.630204i \(0.782971\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 20.4441 1.45659 0.728293 0.685266i \(-0.240314\pi\)
0.728293 + 0.685266i \(0.240314\pi\)
\(198\) 0 0
\(199\) −6.50056 11.2593i −0.460812 0.798150i 0.538189 0.842824i \(-0.319109\pi\)
−0.999002 + 0.0446737i \(0.985775\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.56074 + 21.4905i 0.671032 + 1.50834i
\(204\) 0 0
\(205\) 7.98510 0.557703
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.623163 1.07935i −0.0431051 0.0746602i
\(210\) 0 0
\(211\) −2.11924 + 3.67064i −0.145895 + 0.252697i −0.929706 0.368302i \(-0.879939\pi\)
0.783812 + 0.620999i \(0.213273\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.30569 + 2.26151i −0.0890470 + 0.154234i
\(216\) 0 0
\(217\) 3.02808 + 0.319152i 0.205559 + 0.0216655i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −26.0737 −1.75391
\(222\) 0 0
\(223\) 5.83329 + 10.1036i 0.390626 + 0.676584i 0.992532 0.121982i \(-0.0389252\pi\)
−0.601906 + 0.798567i \(0.705592\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.08989 3.61980i 0.138711 0.240255i −0.788298 0.615294i \(-0.789037\pi\)
0.927009 + 0.375039i \(0.122371\pi\)
\(228\) 0 0
\(229\) 4.19086 + 7.25878i 0.276940 + 0.479674i 0.970623 0.240607i \(-0.0773464\pi\)
−0.693683 + 0.720280i \(0.744013\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.499512 + 0.865180i −0.0327241 + 0.0566798i −0.881924 0.471392i \(-0.843752\pi\)
0.849200 + 0.528072i \(0.177085\pi\)
\(234\) 0 0
\(235\) −4.37807 7.58305i −0.285594 0.494663i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.15412 + 10.6593i −0.398077 + 0.689490i −0.993489 0.113931i \(-0.963656\pi\)
0.595411 + 0.803421i \(0.296989\pi\)
\(240\) 0 0
\(241\) −3.23916 + 5.61039i −0.208653 + 0.361397i −0.951290 0.308296i \(-0.900241\pi\)
0.742638 + 0.669694i \(0.233575\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.22645 + 6.86586i 0.142243 + 0.438643i
\(246\) 0 0
\(247\) −1.98386 3.43614i −0.126230 0.218636i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.2236 −0.771544 −0.385772 0.922594i \(-0.626065\pi\)
−0.385772 + 0.922594i \(0.626065\pi\)
\(252\) 0 0
\(253\) 9.30169 0.584792
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.96355 + 13.7933i 0.496753 + 0.860401i 0.999993 0.00374541i \(-0.00119220\pi\)
−0.503240 + 0.864147i \(0.667859\pi\)
\(258\) 0 0
\(259\) −12.6947 + 17.4621i −0.788808 + 1.08504i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.5305 19.9714i 0.711002 1.23149i −0.253480 0.967341i \(-0.581575\pi\)
0.964481 0.264150i \(-0.0850916\pi\)
\(264\) 0 0
\(265\) 2.48778 4.30897i 0.152823 0.264698i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.51107 9.54546i −0.336016 0.581997i 0.647663 0.761927i \(-0.275746\pi\)
−0.983679 + 0.179930i \(0.942413\pi\)
\(270\) 0 0
\(271\) 2.74213 4.74951i 0.166572 0.288512i −0.770640 0.637271i \(-0.780063\pi\)
0.937213 + 0.348759i \(0.113397\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.12140 + 5.40643i 0.188228 + 0.326020i
\(276\) 0 0
\(277\) 15.0331 26.0381i 0.903253 1.56448i 0.0800068 0.996794i \(-0.474506\pi\)
0.823246 0.567685i \(-0.192161\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.90908 + 10.2348i 0.352506 + 0.610559i 0.986688 0.162625i \(-0.0519961\pi\)
−0.634182 + 0.773184i \(0.718663\pi\)
\(282\) 0 0
\(283\) 21.1210 1.25552 0.627758 0.778409i \(-0.283973\pi\)
0.627758 + 0.778409i \(0.283973\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0479 + 16.5725i −0.711167 + 0.978241i
\(288\) 0 0
\(289\) −4.83778 + 8.37928i −0.284575 + 0.492899i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.15098 10.6538i 0.359344 0.622402i −0.628507 0.777804i \(-0.716334\pi\)
0.987851 + 0.155401i \(0.0496671\pi\)
\(294\) 0 0
\(295\) −1.99648 3.45800i −0.116239 0.201332i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 29.6122 1.71252
\(300\) 0 0
\(301\) −2.72358 6.12203i −0.156984 0.352868i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.97209 8.61191i −0.284701 0.493117i
\(306\) 0 0
\(307\) −33.5033 −1.91213 −0.956067 0.293147i \(-0.905297\pi\)
−0.956067 + 0.293147i \(0.905297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −29.6114 −1.67911 −0.839555 0.543275i \(-0.817184\pi\)
−0.839555 + 0.543275i \(0.817184\pi\)
\(312\) 0 0
\(313\) −11.7149 −0.662165 −0.331082 0.943602i \(-0.607414\pi\)
−0.331082 + 0.943602i \(0.607414\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.16168 −0.121412 −0.0607061 0.998156i \(-0.519335\pi\)
−0.0607061 + 0.998156i \(0.519335\pi\)
\(318\) 0 0
\(319\) 14.0977 0.789321
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.05930 −0.225866
\(324\) 0 0
\(325\) 9.93707 + 17.2115i 0.551209 + 0.954723i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 22.3437 + 2.35497i 1.23185 + 0.129834i
\(330\) 0 0
\(331\) 31.2003 1.71492 0.857461 0.514549i \(-0.172041\pi\)
0.857461 + 0.514549i \(0.172041\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.863273 1.49523i −0.0471656 0.0816933i
\(336\) 0 0
\(337\) −1.94425 + 3.36753i −0.105910 + 0.183441i −0.914110 0.405467i \(-0.867109\pi\)
0.808200 + 0.588908i \(0.200442\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.912481 1.58046i 0.0494136 0.0855869i
\(342\) 0 0
\(343\) −17.6088 5.73840i −0.950787 0.309845i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.7566 −0.899543 −0.449771 0.893144i \(-0.648495\pi\)
−0.449771 + 0.893144i \(0.648495\pi\)
\(348\) 0 0
\(349\) 15.9097 + 27.5564i 0.851625 + 1.47506i 0.879741 + 0.475454i \(0.157716\pi\)
−0.0281152 + 0.999605i \(0.508951\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.66867 6.35431i 0.195263 0.338206i −0.751723 0.659478i \(-0.770777\pi\)
0.946987 + 0.321272i \(0.104111\pi\)
\(354\) 0 0
\(355\) −7.36193 12.7512i −0.390731 0.676765i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.16644 12.4126i 0.378230 0.655114i −0.612574 0.790413i \(-0.709866\pi\)
0.990805 + 0.135299i \(0.0431994\pi\)
\(360\) 0 0
\(361\) 9.19114 + 15.9195i 0.483744 + 0.837870i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.13854 + 5.43611i −0.164279 + 0.284539i
\(366\) 0 0
\(367\) −12.7865 + 22.1469i −0.667450 + 1.15606i 0.311165 + 0.950356i \(0.399281\pi\)
−0.978615 + 0.205702i \(0.934052\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.18935 + 11.6646i 0.269418 + 0.605595i
\(372\) 0 0
\(373\) −15.5734 26.9739i −0.806361 1.39666i −0.915368 0.402617i \(-0.868101\pi\)
0.109008 0.994041i \(-0.465233\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 44.8805 2.31146
\(378\) 0 0
\(379\) −6.72979 −0.345686 −0.172843 0.984949i \(-0.555295\pi\)
−0.172843 + 0.984949i \(0.555295\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.7673 + 32.5060i 0.958967 + 1.66098i 0.725018 + 0.688730i \(0.241832\pi\)
0.233949 + 0.972249i \(0.424835\pi\)
\(384\) 0 0
\(385\) 4.30225 + 0.453446i 0.219263 + 0.0231098i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −15.3213 + 26.5372i −0.776819 + 1.34549i 0.156947 + 0.987607i \(0.449835\pi\)
−0.933766 + 0.357883i \(0.883499\pi\)
\(390\) 0 0
\(391\) 15.1479 26.2369i 0.766061 1.32686i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.28464 7.42121i −0.215583 0.373401i
\(396\) 0 0
\(397\) −2.65885 + 4.60527i −0.133444 + 0.231132i −0.925002 0.379962i \(-0.875937\pi\)
0.791558 + 0.611094i \(0.209270\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.328399 + 0.568803i 0.0163994 + 0.0284047i 0.874109 0.485730i \(-0.161446\pi\)
−0.857709 + 0.514135i \(0.828113\pi\)
\(402\) 0 0
\(403\) 2.90491 5.03145i 0.144704 0.250634i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.46974 + 11.2059i 0.320693 + 0.555457i
\(408\) 0 0
\(409\) −31.5988 −1.56246 −0.781230 0.624243i \(-0.785407\pi\)
−0.781230 + 0.624243i \(0.785407\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.1891 + 1.07391i 0.501373 + 0.0528435i
\(414\) 0 0
\(415\) 7.34254 12.7177i 0.360431 0.624285i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.4424 18.0868i 0.510146 0.883598i −0.489785 0.871843i \(-0.662925\pi\)
0.999931 0.0117550i \(-0.00374180\pi\)
\(420\) 0 0
\(421\) −6.79788 11.7743i −0.331309 0.573843i 0.651460 0.758683i \(-0.274157\pi\)
−0.982769 + 0.184840i \(0.940823\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 20.3329 0.986291
\(426\) 0 0
\(427\) 25.3753 + 2.67449i 1.22799 + 0.129428i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.9416 24.1475i −0.671541 1.16314i −0.977467 0.211088i \(-0.932299\pi\)
0.305926 0.952055i \(-0.401034\pi\)
\(432\) 0 0
\(433\) −22.7059 −1.09118 −0.545589 0.838053i \(-0.683694\pi\)
−0.545589 + 0.838053i \(0.683694\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.61020 0.220536
\(438\) 0 0
\(439\) 31.9016 1.52258 0.761290 0.648411i \(-0.224566\pi\)
0.761290 + 0.648411i \(0.224566\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 35.1257 1.66887 0.834436 0.551104i \(-0.185793\pi\)
0.834436 + 0.551104i \(0.185793\pi\)
\(444\) 0 0
\(445\) −13.8020 −0.654276
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.0966532 0.00456135 0.00228067 0.999997i \(-0.499274\pi\)
0.00228067 + 0.999997i \(0.499274\pi\)
\(450\) 0 0
\(451\) 6.14014 + 10.6350i 0.289128 + 0.500785i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.6963 + 1.44356i 0.642094 + 0.0676751i
\(456\) 0 0
\(457\) −17.0185 −0.796092 −0.398046 0.917365i \(-0.630312\pi\)
−0.398046 + 0.917365i \(0.630312\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.08817 + 14.0091i 0.376704 + 0.652470i 0.990580 0.136932i \(-0.0437242\pi\)
−0.613877 + 0.789402i \(0.710391\pi\)
\(462\) 0 0
\(463\) 6.24297 10.8131i 0.290135 0.502529i −0.683706 0.729757i \(-0.739633\pi\)
0.973842 + 0.227228i \(0.0729663\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.72717 + 11.6518i −0.311296 + 0.539181i −0.978643 0.205566i \(-0.934097\pi\)
0.667347 + 0.744747i \(0.267430\pi\)
\(468\) 0 0
\(469\) 4.40575 + 0.464355i 0.203439 + 0.0214419i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.01603 −0.184657
\(474\) 0 0
\(475\) 1.54706 + 2.67959i 0.0709840 + 0.122948i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.98107 + 12.0916i −0.318973 + 0.552478i −0.980274 0.197643i \(-0.936671\pi\)
0.661301 + 0.750121i \(0.270005\pi\)
\(480\) 0 0
\(481\) 20.5966 + 35.6744i 0.939124 + 1.62661i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.75824 4.77741i 0.125245 0.216931i
\(486\) 0 0
\(487\) 14.4858 + 25.0901i 0.656413 + 1.13694i 0.981538 + 0.191270i \(0.0612605\pi\)
−0.325124 + 0.945671i \(0.605406\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −20.8775 + 36.1609i −0.942189 + 1.63192i −0.180906 + 0.983500i \(0.557903\pi\)
−0.761283 + 0.648419i \(0.775430\pi\)
\(492\) 0 0
\(493\) 22.9583 39.7649i 1.03399 1.79092i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 37.5719 + 3.95999i 1.68533 + 0.177630i
\(498\) 0 0
\(499\) −10.7230 18.5728i −0.480028 0.831433i 0.519709 0.854343i \(-0.326040\pi\)
−0.999738 + 0.0229099i \(0.992707\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 28.3098 1.26227 0.631135 0.775673i \(-0.282589\pi\)
0.631135 + 0.775673i \(0.282589\pi\)
\(504\) 0 0
\(505\) −3.27974 −0.145947
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.8142 + 27.3910i 0.700951 + 1.21408i 0.968133 + 0.250437i \(0.0805743\pi\)
−0.267182 + 0.963646i \(0.586092\pi\)
\(510\) 0 0
\(511\) −6.54679 14.7158i −0.289613 0.650989i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.88418 + 10.1917i −0.259288 + 0.449100i
\(516\) 0 0
\(517\) 6.73304 11.6620i 0.296119 0.512893i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.0364 + 26.0439i 0.658759 + 1.14100i 0.980937 + 0.194325i \(0.0622515\pi\)
−0.322179 + 0.946679i \(0.604415\pi\)
\(522\) 0 0
\(523\) 7.73793 13.4025i 0.338356 0.586050i −0.645768 0.763534i \(-0.723463\pi\)
0.984124 + 0.177484i \(0.0567959\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.97197 5.14760i −0.129461 0.224233i
\(528\) 0 0
\(529\) −5.70363 + 9.87898i −0.247984 + 0.429521i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19.5473 + 33.8570i 0.846689 + 1.46651i
\(534\) 0 0
\(535\) 0.642152 0.0277626
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7.43234 + 8.24482i −0.320133 + 0.355130i
\(540\) 0 0
\(541\) −8.11884 + 14.0622i −0.349056 + 0.604583i −0.986082 0.166259i \(-0.946831\pi\)
0.637026 + 0.770842i \(0.280164\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.00217 + 1.73580i −0.0429281 + 0.0743536i
\(546\) 0 0
\(547\) 19.4541 + 33.6954i 0.831795 + 1.44071i 0.896613 + 0.442815i \(0.146020\pi\)
−0.0648180 + 0.997897i \(0.520647\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.98726 0.297667
\(552\) 0 0
\(553\) 21.8668 + 2.30471i 0.929872 + 0.0980062i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.86210 + 4.95730i 0.121271 + 0.210048i 0.920269 0.391286i \(-0.127970\pi\)
−0.798998 + 0.601334i \(0.794636\pi\)
\(558\) 0 0
\(559\) −12.7851 −0.540754
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.94667 0.208477 0.104239 0.994552i \(-0.466759\pi\)
0.104239 + 0.994552i \(0.466759\pi\)
\(564\) 0 0
\(565\) 3.69999 0.155660
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.2194 0.679954 0.339977 0.940434i \(-0.389581\pi\)
0.339977 + 0.940434i \(0.389581\pi\)
\(570\) 0 0
\(571\) −36.6058 −1.53191 −0.765954 0.642896i \(-0.777733\pi\)
−0.765954 + 0.642896i \(0.777733\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −23.0923 −0.963017
\(576\) 0 0
\(577\) −18.2684 31.6417i −0.760522 1.31726i −0.942582 0.333975i \(-0.891610\pi\)
0.182060 0.983287i \(-0.441723\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 15.3161 + 34.4273i 0.635418 + 1.42829i
\(582\) 0 0
\(583\) 7.65192 0.316910
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.9237 20.6525i −0.492144 0.852419i 0.507815 0.861466i \(-0.330453\pi\)
−0.999959 + 0.00904721i \(0.997120\pi\)
\(588\) 0 0
\(589\) 0.452253 0.783325i 0.0186348 0.0322764i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.54751 + 11.3406i −0.268874 + 0.465704i −0.968571 0.248736i \(-0.919985\pi\)
0.699697 + 0.714439i \(0.253318\pi\)
\(594\) 0 0
\(595\) 8.28526 11.3967i 0.339663 0.467220i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.1539 −1.51807 −0.759034 0.651051i \(-0.774328\pi\)
−0.759034 + 0.651051i \(0.774328\pi\)
\(600\) 0 0
\(601\) 8.53133 + 14.7767i 0.348000 + 0.602754i 0.985894 0.167370i \(-0.0535275\pi\)
−0.637894 + 0.770124i \(0.720194\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.37471 + 7.57722i −0.177857 + 0.308058i
\(606\) 0 0
\(607\) −11.5973 20.0871i −0.470719 0.815310i 0.528720 0.848796i \(-0.322672\pi\)
−0.999439 + 0.0334867i \(0.989339\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.4348 37.1262i 0.867160 1.50197i
\(612\) 0 0
\(613\) 22.2875 + 38.6030i 0.900182 + 1.55916i 0.827257 + 0.561824i \(0.189900\pi\)
0.0729255 + 0.997337i \(0.476766\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.12703 + 5.41618i −0.125890 + 0.218047i −0.922080 0.386999i \(-0.873512\pi\)
0.796191 + 0.605046i \(0.206845\pi\)
\(618\) 0 0
\(619\) 0.770208 1.33404i 0.0309573 0.0536196i −0.850132 0.526570i \(-0.823478\pi\)
0.881089 + 0.472951i \(0.156811\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 20.8244 28.6449i 0.834314 1.14763i
\(624\) 0 0
\(625\) −5.09116 8.81816i −0.203647 0.352726i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 42.1441 1.68040
\(630\) 0 0
\(631\) −44.5148 −1.77210 −0.886052 0.463585i \(-0.846563\pi\)
−0.886052 + 0.463585i \(0.846563\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.99090 + 10.3765i 0.237742 + 0.411781i
\(636\) 0 0
\(637\) −23.6611 + 26.2476i −0.937485 + 1.03997i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.87520 + 3.24794i −0.0740660 + 0.128286i −0.900680 0.434484i \(-0.856931\pi\)
0.826614 + 0.562770i \(0.190264\pi\)
\(642\) 0 0
\(643\) −0.818392 + 1.41750i −0.0322742 + 0.0559006i −0.881711 0.471789i \(-0.843608\pi\)
0.849437 + 0.527690i \(0.176942\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.0748 17.4501i −0.396082 0.686034i 0.597157 0.802125i \(-0.296297\pi\)
−0.993239 + 0.116091i \(0.962964\pi\)
\(648\) 0 0
\(649\) 3.07038 5.31806i 0.120523 0.208752i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21.4570 37.1646i −0.839677 1.45436i −0.890165 0.455638i \(-0.849411\pi\)
0.0504888 0.998725i \(-0.483922\pi\)
\(654\) 0 0
\(655\) 4.20591 7.28486i 0.164339 0.284643i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.8526 18.7973i −0.422758 0.732238i 0.573450 0.819240i \(-0.305605\pi\)
−0.996208 + 0.0870025i \(0.972271\pi\)
\(660\) 0 0
\(661\) −25.3815 −0.987225 −0.493613 0.869682i \(-0.664324\pi\)
−0.493613 + 0.869682i \(0.664324\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.13232 + 0.224742i 0.0826880 + 0.00871511i
\(666\) 0 0
\(667\) −26.0740 + 45.1614i −1.00959 + 1.74866i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.64658 13.2443i 0.295193 0.511289i
\(672\) 0 0
\(673\) 7.88676 + 13.6603i 0.304012 + 0.526565i 0.977041 0.213052i \(-0.0683403\pi\)
−0.673029 + 0.739616i \(0.735007\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.6506 −0.409336 −0.204668 0.978831i \(-0.565612\pi\)
−0.204668 + 0.978831i \(0.565612\pi\)
\(678\) 0 0
\(679\) 5.75351 + 12.9327i 0.220799 + 0.496311i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −14.3656 24.8819i −0.549683 0.952078i −0.998296 0.0583524i \(-0.981415\pi\)
0.448613 0.893726i \(-0.351918\pi\)
\(684\) 0 0
\(685\) −15.0168 −0.573763
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.3601 0.928046
\(690\) 0 0
\(691\) −39.2272 −1.49227 −0.746136 0.665794i \(-0.768093\pi\)
−0.746136 + 0.665794i \(0.768093\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.2025 0.462868
\(696\) 0 0
\(697\) 39.9971 1.51500
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.1643 −1.29037 −0.645184 0.764028i \(-0.723219\pi\)
−0.645184 + 0.764028i \(0.723219\pi\)
\(702\) 0 0
\(703\) 3.20660 + 5.55399i 0.120939 + 0.209473i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.94848 6.80685i 0.186107 0.255998i
\(708\) 0 0
\(709\) 19.7070 0.740113 0.370057 0.929009i \(-0.379338\pi\)
0.370057 + 0.929009i \(0.379338\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.37530 + 5.84619i 0.126406 + 0.218941i
\(714\) 0 0
\(715\) 4.12725 7.14861i 0.154350 0.267343i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.87829 + 10.1815i −0.219223 + 0.379705i −0.954571 0.297985i \(-0.903686\pi\)
0.735348 + 0.677690i \(0.237019\pi\)
\(720\) 0 0
\(721\) −12.2740 27.5894i −0.457108 1.02748i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −34.9989 −1.29983
\(726\) 0 0
\(727\) 22.8161 + 39.5186i 0.846202 + 1.46567i 0.884573 + 0.466402i \(0.154450\pi\)
−0.0383705 + 0.999264i \(0.512217\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.54014 + 11.3279i −0.241896 + 0.418976i
\(732\) 0 0
\(733\) −19.4901 33.7579i −0.719885 1.24688i −0.961045 0.276392i \(-0.910861\pi\)
0.241160 0.970485i \(-0.422472\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.32763 2.29952i 0.0489038 0.0847039i
\(738\) 0 0
\(739\) −11.7719 20.3895i −0.433036 0.750040i 0.564097 0.825708i \(-0.309224\pi\)
−0.997133 + 0.0756686i \(0.975891\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.09612 + 7.09469i −0.150272 + 0.260279i −0.931327 0.364183i \(-0.881348\pi\)
0.781055 + 0.624462i \(0.214682\pi\)
\(744\) 0 0
\(745\) 7.24337 12.5459i 0.265377 0.459646i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.968881 + 1.33274i −0.0354021 + 0.0486971i
\(750\) 0 0
\(751\) 14.0936 + 24.4109i 0.514284 + 0.890766i 0.999863 + 0.0165733i \(0.00527570\pi\)
−0.485578 + 0.874193i \(0.661391\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.56271 −0.0932667
\(756\) 0 0
\(757\) 7.42352 0.269812 0.134906 0.990858i \(-0.456927\pi\)
0.134906 + 0.990858i \(0.456927\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.3534 + 26.5928i 0.556559 + 0.963988i 0.997780 + 0.0665900i \(0.0212120\pi\)
−0.441222 + 0.897398i \(0.645455\pi\)
\(762\) 0 0
\(763\) −2.09045 4.69890i −0.0756795 0.170112i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.77465 16.9302i 0.352942 0.611314i
\(768\) 0 0
\(769\) 20.0973 34.8095i 0.724727 1.25526i −0.234360 0.972150i \(-0.575299\pi\)
0.959086 0.283113i \(-0.0913673\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.69611 + 2.93775i 0.0610050 + 0.105664i 0.894915 0.446237i \(-0.147236\pi\)
−0.833910 + 0.551901i \(0.813903\pi\)
\(774\) 0 0
\(775\) −2.26532 + 3.92365i −0.0813727 + 0.140942i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.04324 + 5.27105i 0.109035 + 0.188855i
\(780\) 0 0
\(781\) 11.3219 19.6101i 0.405130 0.701706i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.56696 2.71405i −0.0559271 0.0968686i
\(786\) 0 0
\(787\) 10.8331 0.386160 0.193080 0.981183i \(-0.438152\pi\)
0.193080 + 0.981183i \(0.438152\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.58256 + 7.67904i −0.198493 + 0.273035i
\(792\) 0 0
\(793\) 24.3431 42.1635i 0.864449 1.49727i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.4982 40.7001i 0.832350 1.44167i −0.0638193 0.997961i \(-0.520328\pi\)
0.896170 0.443712i \(-0.146339\pi\)
\(798\) 0 0
\(799\) −21.9296 37.9832i −0.775814 1.34375i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9.65352 −0.340665
\(804\) 0 0