Properties

Label 2268.2.i.n.2053.3
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: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
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 2053.3
Root \(1.04556 + 0.339889i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.n.865.3

$q$-expansion

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

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 0.727409 0.686204i \(-0.240724\pi\)
−0.957975 + 0.286853i \(0.907391\pi\)
\(6\) 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 −0.721383 0.692536i \(-0.756493\pi\)
0.960445 + 0.278468i \(0.0898268\pi\)
\(12\) 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 \(-0.951223\pi\)
0.361954 0.932196i \(-0.382110\pi\)
\(18\) 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 \(0.0427866\pi\)
−0.379431 + 0.925220i \(0.623880\pi\)
\(24\) 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 \(0.142404\pi\)
−0.0761506 + 0.997096i \(0.524263\pi\)
\(30\) 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 \(0.373379\pi\)
−0.992097 + 0.125476i \(0.959954\pi\)
\(42\) 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 \(-0.287402\pi\)
0.619335 + 0.785127i \(0.287402\pi\)
\(48\) 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 0.982789 0.184734i \(-0.0591423\pi\)
−0.651378 + 0.758753i \(0.725809\pi\)
\(54\) 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 \(-0.418887\pi\)
0.252075 + 0.967708i \(0.418887\pi\)
\(60\) 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 \(-0.178207\pi\)
0.847333 + 0.531062i \(0.178207\pi\)
\(72\) 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 \(0.118943\pi\)
−0.149368 + 0.988782i \(0.547724\pi\)
\(84\) 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 \(-0.582287\pi\)
0.965070 0.261992i \(-0.0843793\pi\)
\(90\) 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 −0.775988 0.630747i \(-0.782749\pi\)
0.934237 + 0.356652i \(0.116082\pi\)
\(102\) 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 −0.880684 0.473704i \(-0.842917\pi\)
0.850582 + 0.525843i \(0.176250\pi\)
\(108\) 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 −0.937991 0.346658i \(-0.887316\pi\)
0.769211 + 0.638995i \(0.220650\pi\)
\(114\) 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 0.987354 0.158534i \(-0.0506767\pi\)
−0.630971 + 0.775806i \(0.717343\pi\)
\(132\) 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 \(-0.619602\pi\)
0.989089 0.147320i \(-0.0470647\pi\)
\(138\) 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 \(0.0285227\pi\)
−0.420496 + 0.907294i \(0.638144\pi\)
\(150\) 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 \(0.565354\pi\)
−0.745897 + 0.666061i \(0.767979\pi\)
\(168\) 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 \(-0.500834\pi\)
−0.00261971 + 0.999997i \(0.500834\pi\)
\(174\) 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 0.975228 0.221201i \(-0.0709976\pi\)
−0.679180 + 0.733972i \(0.737664\pi\)
\(180\) 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 \(-0.302803\pi\)
0.580638 + 0.814162i \(0.302803\pi\)
\(192\) 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 \(-0.759686\pi\)
−0.728293 + 0.685266i \(0.759686\pi\)
\(198\) 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 −0.927009 0.375039i \(-0.877629\pi\)
0.788298 + 0.615294i \(0.210963\pi\)
\(228\) 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 −0.849200 0.528072i \(-0.822915\pi\)
0.881924 + 0.471392i \(0.156248\pi\)
\(234\) 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 −0.595411 0.803421i \(-0.703011\pi\)
0.993489 + 0.113931i \(0.0363443\pi\)
\(240\) 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 \(-0.373935\pi\)
0.385772 + 0.922594i \(0.373935\pi\)
\(252\) 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 0.503240 0.864147i \(-0.332141\pi\)
−0.999993 + 0.00374541i \(0.998808\pi\)
\(258\) 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 \(0.418425\pi\)
−0.964481 + 0.264150i \(0.914908\pi\)
\(264\) 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 0.983679 0.179930i \(-0.0575871\pi\)
−0.647663 + 0.761927i \(0.724254\pi\)
\(270\) 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 0.634182 0.773184i \(-0.281337\pi\)
−0.986688 + 0.162625i \(0.948004\pi\)
\(282\) 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 −0.987851 0.155401i \(-0.950333\pi\)
0.628507 + 0.777804i \(0.283666\pi\)
\(294\) 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 \(-0.182816\pi\)
0.839555 + 0.543275i \(0.182816\pi\)
\(312\) 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 \(-0.480665\pi\)
0.0607061 + 0.998156i \(0.480665\pi\)
\(318\) 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 \(-0.351505\pi\)
0.449771 + 0.893144i \(0.351505\pi\)
\(348\) 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 −0.946987 0.321272i \(-0.895889\pi\)
0.751723 + 0.659478i \(0.229223\pi\)
\(354\) 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 −0.990805 0.135299i \(-0.956801\pi\)
0.612574 + 0.790413i \(0.290134\pi\)
\(360\) 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 \(-0.758168\pi\)
−0.233949 0.972249i \(-0.575165\pi\)
\(384\) 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 \(-0.550165\pi\)
0.933766 0.357883i \(-0.116501\pi\)
\(390\) 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 0.857709 0.514135i \(-0.171887\pi\)
−0.874109 + 0.485730i \(0.838554\pi\)
\(402\) 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 \(0.337075\pi\)
−0.999931 + 0.0117550i \(0.996258\pi\)
\(420\) 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 \(0.0677006\pi\)
−0.305926 + 0.952055i \(0.598966\pi\)
\(432\) 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 \(-0.814207\pi\)
−0.834436 + 0.551104i \(0.814207\pi\)
\(444\) 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 \(-0.500726\pi\)
−0.00228067 + 0.999997i \(0.500726\pi\)
\(450\) 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 0.613877 0.789402i \(-0.289609\pi\)
−0.990580 + 0.136932i \(0.956276\pi\)
\(462\) 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 −0.667347 0.744747i \(-0.732570\pi\)
0.978643 + 0.205566i \(0.0659035\pi\)
\(468\) 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 −0.661301 0.750121i \(-0.729995\pi\)
0.980274 + 0.197643i \(0.0633287\pi\)
\(480\) 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 \(-0.442097\pi\)
0.761283 0.648419i \(-0.224570\pi\)
\(492\) 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 \(-0.717411\pi\)
−0.631135 + 0.775673i \(0.717411\pi\)
\(504\) 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 \(-0.919426\pi\)
0.267182 0.963646i \(-0.413908\pi\)
\(510\) 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 \(-0.937749\pi\)
0.322179 0.946679i \(-0.395585\pi\)
\(522\) 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 0.798998 0.601334i \(-0.205364\pi\)
−0.920269 + 0.391286i \(0.872030\pi\)
\(558\) 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 \(-0.533241\pi\)
−0.104239 + 0.994552i \(0.533241\pi\)
\(564\) 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 \(-0.610419\pi\)
−0.339977 + 0.940434i \(0.610419\pi\)
\(570\) 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 0.999959 0.00904721i \(-0.00287986\pi\)
−0.507815 + 0.861466i \(0.669547\pi\)
\(588\) 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 −0.699697 0.714439i \(-0.746682\pi\)
0.968571 + 0.248736i \(0.0800151\pi\)
\(594\) 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 \(-0.225672\pi\)
0.759034 + 0.651051i \(0.225672\pi\)
\(600\) 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 −0.796191 0.605046i \(-0.793155\pi\)
0.922080 + 0.386999i \(0.126488\pi\)
\(618\) 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 −0.826614 0.562770i \(-0.809736\pi\)
0.900680 + 0.434484i \(0.143069\pi\)
\(642\) 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 0.993239 0.116091i \(-0.0370363\pi\)
−0.597157 + 0.802125i \(0.703703\pi\)
\(648\) 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 \(0.150589\pi\)
−0.0504888 + 0.998725i \(0.516078\pi\)
\(654\) 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 0.996208 0.0870025i \(-0.0277288\pi\)
−0.573450 + 0.819240i \(0.694395\pi\)
\(660\) 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 \(-0.434388\pi\)
0.204668 + 0.978831i \(0.434388\pi\)
\(678\) 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 \(0.0185847\pi\)
−0.448613 + 0.893726i \(0.648082\pi\)
\(684\) 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 \(-0.276781\pi\)
0.645184 + 0.764028i \(0.276781\pi\)
\(702\) 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 −0.735348 0.677690i \(-0.762981\pi\)
0.954571 + 0.297985i \(0.0963144\pi\)
\(720\) 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 −0.781055 0.624462i \(-0.785318\pi\)
0.931327 + 0.364183i \(0.118652\pi\)
\(744\) 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 \(-0.978788\pi\)
0.441222 0.897398i \(-0.354545\pi\)
\(762\) 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 0.833910 0.551901i \(-0.186097\pi\)
−0.894915 + 0.446237i \(0.852764\pi\)
\(774\) 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 \(0.479672\pi\)
−0.896170 + 0.443712i \(0.853661\pi\)
\(798\) 0 0
\(799\) −21.9296 37.9832i −0.775814 1.34375i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0