Properties

Label 2268.2.i.n.865.3
Level $2268$
Weight $2$
Character 2268.865
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 865.3
Root \(1.04556 - 0.339889i\) of defining polynomial
Character \(\chi\) \(=\) 2268.865
Dual form 2268.2.i.n.2053.3

$q$-expansion

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

Character values

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

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.907391\pi\)
0.727409 + 0.686204i \(0.240724\pi\)
\(6\) 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 \(-0.0898268\pi\)
−0.721383 + 0.692536i \(0.756493\pi\)
\(12\) 0 0
\(13\) −2.52415 4.37196i −0.700074 1.21256i −0.968440 0.249246i \(-0.919817\pi\)
0.268366 0.963317i \(-0.413516\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.58242 + 4.47288i −0.626329 + 1.08483i 0.361954 + 0.932196i \(0.382110\pi\)
−0.988282 + 0.152637i \(0.951223\pi\)
\(18\) 0 0
\(19\) −0.392975 0.680652i −0.0901546 0.156152i 0.817421 0.576040i \(-0.195403\pi\)
−0.907576 + 0.419888i \(0.862069\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.93289 5.07991i 0.611549 1.05923i −0.379431 0.925220i \(-0.623880\pi\)
0.990980 0.134014i \(-0.0427866\pi\)
\(24\) 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 −0.0761506 0.997096i \(-0.524263\pi\)
0.901586 0.432600i \(-0.142404\pi\)
\(30\) 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 0.977697 + 0.210022i \(0.0673535\pi\)
−0.306964 + 0.951721i \(0.599313\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.87206 6.70660i −0.604714 1.04739i −0.992097 0.125476i \(-0.959954\pi\)
0.387383 0.921919i \(-0.373379\pi\)
\(42\) 0 0
\(43\) 1.26628 2.19326i 0.193106 0.334470i −0.753172 0.657824i \(-0.771477\pi\)
0.946278 + 0.323354i \(0.104811\pi\)
\(44\) 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 −0.651378 0.758753i \(-0.725809\pi\)
0.982789 + 0.184734i \(0.0591423\pi\)
\(54\) 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 −0.631079 0.775718i \(-0.717388\pi\)
0.987331 + 0.158671i \(0.0507211\pi\)
\(74\) 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 −0.149368 0.988782i \(-0.547724\pi\)
0.930994 0.365034i \(-0.118943\pi\)
\(84\) 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 0.965070 + 0.261992i \(0.0843793\pi\)
−0.255644 + 0.966771i \(0.582287\pi\)
\(90\) 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 −0.969273 0.245988i \(-0.920888\pi\)
0.697668 + 0.716421i \(0.254221\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.59038 + 2.75462i 0.158249 + 0.274095i 0.934237 0.356652i \(-0.116082\pi\)
−0.775988 + 0.630747i \(0.782749\pi\)
\(102\) 0 0
\(103\) 5.70660 9.88412i 0.562288 0.973911i −0.435008 0.900426i \(-0.643255\pi\)
0.997296 0.0734850i \(-0.0234121\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.311386 0.539337i −0.0301028 0.0521396i 0.850582 0.525843i \(-0.176250\pi\)
−0.880684 + 0.473704i \(0.842917\pi\)
\(108\) 0 0
\(109\) 0.971921 1.68342i 0.0930932 0.161242i −0.815718 0.578450i \(-0.803658\pi\)
0.908811 + 0.417208i \(0.136991\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.79416 3.10758i −0.168781 0.292337i 0.769211 0.638995i \(-0.220650\pi\)
−0.937991 + 0.346658i \(0.887316\pi\)
\(114\) 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 \(-0.717343\pi\)
0.987354 + 0.158534i \(0.0506767\pi\)
\(132\) 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 0.989089 + 0.147320i \(0.0470647\pi\)
−0.366962 + 0.930236i \(0.619602\pi\)
\(138\) 0 0
\(139\) 5.91713 + 10.2488i 0.501884 + 0.869289i 0.999998 + 0.00217698i \(0.000692954\pi\)
−0.498113 + 0.867112i \(0.665974\pi\)
\(140\) 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 −0.420496 0.907294i \(-0.638144\pi\)
0.995988 0.0894868i \(-0.0285227\pi\)
\(150\) 0 0
\(151\) −1.24269 2.15240i −0.101128 0.175159i 0.811021 0.585016i \(-0.198912\pi\)
−0.912150 + 0.409857i \(0.865579\pi\)
\(152\) 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 −0.973107 0.230352i \(-0.926012\pi\)
0.287063 0.957912i \(-0.407321\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.2738 21.2588i −0.949775 1.64506i −0.745897 0.666061i \(-0.767979\pi\)
−0.203877 0.978996i \(-0.565354\pi\)
\(168\) 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 −0.679180 0.733972i \(-0.737664\pi\)
0.975228 + 0.221201i \(0.0709976\pi\)
\(180\) 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 −0.999002 0.0446737i \(-0.985775\pi\)
0.538189 + 0.842824i \(0.319109\pi\)
\(200\) 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 0.783812 0.620999i \(-0.213273\pi\)
−0.929706 + 0.368302i \(0.879939\pi\)
\(212\) 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 −0.601906 0.798567i \(-0.705592\pi\)
0.992532 + 0.121982i \(0.0389252\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.08989 3.61980i −0.138711 0.240255i 0.788298 0.615294i \(-0.210963\pi\)
−0.927009 + 0.375039i \(0.877629\pi\)
\(228\) 0 0
\(229\) 4.19086 7.25878i 0.276940 0.479674i −0.693683 0.720280i \(-0.744013\pi\)
0.970623 + 0.240607i \(0.0773464\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.499512 + 0.865180i 0.0327241 + 0.0566798i 0.881924 0.471392i \(-0.156248\pi\)
−0.849200 + 0.528072i \(0.822915\pi\)
\(234\) 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 \(-0.0363443\pi\)
−0.595411 + 0.803421i \(0.703011\pi\)
\(240\) 0 0
\(241\) −3.23916 5.61039i −0.208653 0.361397i 0.742638 0.669694i \(-0.233575\pi\)
−0.951290 + 0.308296i \(0.900241\pi\)
\(242\) 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 −0.999993 0.00374541i \(-0.998808\pi\)
0.503240 + 0.864147i \(0.332141\pi\)
\(258\) 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 −0.964481 0.264150i \(-0.914908\pi\)
0.253480 0.967341i \(-0.418425\pi\)
\(264\) 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 \(-0.724254\pi\)
0.983679 + 0.179930i \(0.0575871\pi\)
\(270\) 0 0
\(271\) 2.74213 + 4.74951i 0.166572 + 0.288512i 0.937213 0.348759i \(-0.113397\pi\)
−0.770640 + 0.637271i \(0.780063\pi\)
\(272\) 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 0.823246 + 0.567685i \(0.192161\pi\)
0.0800068 + 0.996794i \(0.474506\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.90908 + 10.2348i −0.352506 + 0.610559i −0.986688 0.162625i \(-0.948004\pi\)
0.634182 + 0.773184i \(0.281337\pi\)
\(282\) 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 \(-0.283666\pi\)
−0.987851 + 0.155401i \(0.950333\pi\)
\(294\) 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 0.808200 0.588908i \(-0.200442\pi\)
−0.914110 + 0.405467i \(0.867109\pi\)
\(338\) 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 −0.0281152 0.999605i \(-0.508951\pi\)
0.879741 0.475454i \(-0.157716\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.66867 6.35431i −0.195263 0.338206i 0.751723 0.659478i \(-0.229223\pi\)
−0.946987 + 0.321272i \(0.895889\pi\)
\(354\) 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 \(-0.290134\pi\)
−0.990805 + 0.135299i \(0.956801\pi\)
\(360\) 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 −0.978615 0.205702i \(-0.934052\pi\)
0.311165 0.950356i \(-0.399281\pi\)
\(368\) 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 0.109008 + 0.994041i \(0.465233\pi\)
−0.915368 + 0.402617i \(0.868101\pi\)
\(374\) 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 −0.233949 + 0.972249i \(0.575165\pi\)
−0.725018 + 0.688730i \(0.758168\pi\)
\(384\) 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 0.933766 + 0.357883i \(0.116501\pi\)
−0.156947 + 0.987607i \(0.550165\pi\)
\(390\) 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 0.791558 0.611094i \(-0.209270\pi\)
−0.925002 + 0.379962i \(0.875937\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.328399 + 0.568803i −0.0163994 + 0.0284047i −0.874109 0.485730i \(-0.838554\pi\)
0.857709 + 0.514135i \(0.171887\pi\)
\(402\) 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 −0.999931 0.0117550i \(-0.996258\pi\)
0.489785 0.871843i \(-0.337075\pi\)
\(420\) 0 0
\(421\) −6.79788 + 11.7743i −0.331309 + 0.573843i −0.982769 0.184840i \(-0.940823\pi\)
0.651460 + 0.758683i \(0.274157\pi\)
\(422\) 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 −0.305926 0.952055i \(-0.598966\pi\)
0.977467 0.211088i \(-0.0677006\pi\)
\(432\) 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 −0.990580 0.136932i \(-0.956276\pi\)
0.613877 + 0.789402i \(0.289609\pi\)
\(462\) 0 0
\(463\) 6.24297 + 10.8131i 0.290135 + 0.502529i 0.973842 0.227228i \(-0.0729663\pi\)
−0.683706 + 0.729757i \(0.739633\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.72717 + 11.6518i 0.311296 + 0.539181i 0.978643 0.205566i \(-0.0659035\pi\)
−0.667347 + 0.744747i \(0.732570\pi\)
\(468\) 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 \(-0.0633287\pi\)
−0.661301 + 0.750121i \(0.729995\pi\)
\(480\) 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 −0.325124 0.945671i \(-0.605406\pi\)
0.981538 0.191270i \(-0.0612605\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20.8775 + 36.1609i 0.942189 + 1.63192i 0.761283 + 0.648419i \(0.224570\pi\)
0.180906 + 0.983500i \(0.442097\pi\)
\(492\) 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 −0.999738 0.0229099i \(-0.992707\pi\)
0.519709 + 0.854343i \(0.326040\pi\)
\(500\) 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 0.267182 + 0.963646i \(0.413908\pi\)
−0.968133 + 0.250437i \(0.919426\pi\)
\(510\) 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 0.322179 + 0.946679i \(0.395585\pi\)
−0.980937 + 0.194325i \(0.937749\pi\)
\(522\) 0 0
\(523\) 7.73793 + 13.4025i 0.338356 + 0.586050i 0.984124 0.177484i \(-0.0567959\pi\)
−0.645768 + 0.763534i \(0.723463\pi\)
\(524\) 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 0.637026 0.770842i \(-0.280164\pi\)
−0.986082 + 0.166259i \(0.946831\pi\)
\(542\) 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 −0.0648180 0.997897i \(-0.520647\pi\)
0.896613 0.442815i \(-0.146020\pi\)
\(548\) 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 \(-0.872030\pi\)
0.798998 + 0.601334i \(0.205364\pi\)
\(558\) 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 0.182060 + 0.983287i \(0.441723\pi\)
−0.942582 + 0.333975i \(0.891610\pi\)
\(578\) 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 \(-0.669547\pi\)
0.999959 + 0.00904721i \(0.00287986\pi\)
\(588\) 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 \(-0.0800151\pi\)
−0.699697 + 0.714439i \(0.746682\pi\)
\(594\) 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 −0.637894 0.770124i \(-0.720194\pi\)
0.985894 + 0.167370i \(0.0535275\pi\)
\(602\) 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 −0.999439 0.0334867i \(-0.989339\pi\)
0.528720 + 0.848796i \(0.322672\pi\)
\(608\) 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 0.0729255 0.997337i \(-0.476766\pi\)
0.827257 0.561824i \(-0.189900\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.12703 + 5.41618i 0.125890 + 0.218047i 0.922080 0.386999i \(-0.126488\pi\)
−0.796191 + 0.605046i \(0.793155\pi\)
\(618\) 0 0
\(619\) 0.770208 + 1.33404i 0.0309573 + 0.0536196i 0.881089 0.472951i \(-0.156811\pi\)
−0.850132 + 0.526570i \(0.823478\pi\)
\(620\) 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 \(-0.143069\pi\)
−0.826614 + 0.562770i \(0.809736\pi\)
\(642\) 0 0
\(643\) −0.818392 1.41750i −0.0322742 0.0559006i 0.849437 0.527690i \(-0.176942\pi\)
−0.881711 + 0.471789i \(0.843608\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.0748 17.4501i 0.396082 0.686034i −0.597157 0.802125i \(-0.703703\pi\)
0.993239 + 0.116091i \(0.0370363\pi\)
\(648\) 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 −0.0504888 0.998725i \(-0.516078\pi\)
0.890165 0.455638i \(-0.150589\pi\)
\(654\) 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 \(-0.694395\pi\)
0.996208 + 0.0870025i \(0.0277288\pi\)
\(660\) 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 −0.673029 0.739616i \(-0.735007\pi\)
0.977041 + 0.213052i \(0.0683403\pi\)
\(674\) 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 −0.448613 0.893726i \(-0.648082\pi\)
0.998296 0.0583524i \(-0.0185847\pi\)
\(684\) 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 0.954571 0.297985i \(-0.0963144\pi\)
−0.735348 + 0.677690i \(0.762981\pi\)
\(720\) 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 −0.0383705 0.999264i \(-0.512217\pi\)
0.884573 0.466402i \(-0.154450\pi\)
\(728\) 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 0.241160 + 0.970485i \(0.422472\pi\)
−0.961045 + 0.276392i \(0.910861\pi\)
\(734\) 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 −0.997133 0.0756686i \(-0.975891\pi\)
0.564097 + 0.825708i \(0.309224\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.09612 + 7.09469i 0.150272 + 0.260279i 0.931327 0.364183i \(-0.118652\pi\)
−0.781055 + 0.624462i \(0.785318\pi\)
\(744\) 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 −0.485578 0.874193i \(-0.661391\pi\)
0.999863 0.0165733i \(-0.00527570\pi\)
\(752\) 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 0.441222 + 0.897398i \(0.354545\pi\)
−0.997780 + 0.0665900i \(0.978788\pi\)
\(762\) 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 0.959086 + 0.283113i \(0.0913673\pi\)
−0.234360 + 0.972150i \(0.575299\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.69611 + 2.93775i −0.0610050 + 0.105664i −0.894915 0.446237i \(-0.852764\pi\)
0.833910 + 0.551901i \(0.186097\pi\)
\(774\) 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 −0.896170 0.443712i \(-0.853661\pi\)
0.0638193 0.997961i \(-0.479672\pi\)
\(798\) 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