Properties

Label 2736.2.s.x.577.2
Level $2736$
Weight $2$
Character 2736.577
Analytic conductor $21.847$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 577.2
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 2736.577
Dual form 2736.2.s.x.1873.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.347296 + 0.601535i) q^{5} -0.305407 q^{7} +O(q^{10})\) \(q+(0.347296 + 0.601535i) q^{5} -0.305407 q^{7} +4.82295 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-3.75877 - 6.51038i) q^{17} +(-3.06418 + 3.10013i) q^{19} +(-0.347296 + 0.601535i) q^{23} +(2.25877 - 3.91231i) q^{25} +(5.06418 - 8.77141i) q^{29} +1.82295 q^{31} +(-0.106067 - 0.183713i) q^{35} +6.51754 q^{37} +(2.69459 + 4.66717i) q^{41} +(1.84730 + 3.19961i) q^{43} +(3.00000 - 5.19615i) q^{47} -6.90673 q^{49} +(2.71688 - 4.70578i) q^{53} +(1.67499 + 2.90117i) q^{55} +(2.04189 + 3.53666i) q^{59} +(-0.194593 + 0.337044i) q^{61} -0.694593 q^{65} +(-3.91147 + 6.77487i) q^{67} +(-5.45336 - 9.44550i) q^{71} +(2.19459 + 3.80115i) q^{73} -1.47296 q^{77} +(7.21688 + 12.5000i) q^{79} +0.739170 q^{83} +(2.61081 - 4.52206i) q^{85} +(-0.411474 + 0.712694i) q^{89} +(0.152704 - 0.264490i) q^{91} +(-2.92902 - 0.766546i) q^{95} +(-5.45336 - 9.44550i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{7} - 12 q^{11} - 3 q^{13} - 9 q^{25} + 12 q^{29} - 30 q^{31} + 24 q^{35} - 6 q^{37} + 12 q^{41} + 9 q^{43} + 18 q^{47} + 12 q^{49} + 6 q^{59} + 3 q^{61} - 3 q^{67} - 6 q^{71} + 9 q^{73} + 12 q^{77} + 27 q^{79} - 24 q^{83} + 24 q^{85} + 18 q^{89} + 3 q^{91} + 48 q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(5\) 0.347296 + 0.601535i 0.155316 + 0.269015i 0.933174 0.359425i \(-0.117027\pi\)
−0.777858 + 0.628440i \(0.783694\pi\)
\(6\) 0 0
\(7\) −0.305407 −0.115433 −0.0577166 0.998333i \(-0.518382\pi\)
−0.0577166 + 0.998333i \(0.518382\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.82295 1.45417 0.727087 0.686546i \(-0.240874\pi\)
0.727087 + 0.686546i \(0.240874\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.75877 6.51038i −0.911636 1.57900i −0.811754 0.584000i \(-0.801487\pi\)
−0.0998822 0.994999i \(-0.531847\pi\)
\(18\) 0 0
\(19\) −3.06418 + 3.10013i −0.702971 + 0.711219i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.347296 + 0.601535i −0.0724163 + 0.125429i −0.899960 0.435973i \(-0.856404\pi\)
0.827544 + 0.561402i \(0.189738\pi\)
\(24\) 0 0
\(25\) 2.25877 3.91231i 0.451754 0.782461i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.06418 8.77141i 0.940394 1.62881i 0.175674 0.984448i \(-0.443790\pi\)
0.764721 0.644362i \(-0.222877\pi\)
\(30\) 0 0
\(31\) 1.82295 0.327411 0.163706 0.986509i \(-0.447655\pi\)
0.163706 + 0.986509i \(0.447655\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.106067 0.183713i −0.0179286 0.0310532i
\(36\) 0 0
\(37\) 6.51754 1.07148 0.535739 0.844384i \(-0.320033\pi\)
0.535739 + 0.844384i \(0.320033\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.69459 + 4.66717i 0.420825 + 0.728890i 0.996020 0.0891261i \(-0.0284074\pi\)
−0.575196 + 0.818016i \(0.695074\pi\)
\(42\) 0 0
\(43\) 1.84730 + 3.19961i 0.281710 + 0.487936i 0.971806 0.235782i \(-0.0757650\pi\)
−0.690096 + 0.723718i \(0.742432\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −6.90673 −0.986675
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.71688 4.70578i 0.373192 0.646388i −0.616862 0.787071i \(-0.711596\pi\)
0.990055 + 0.140683i \(0.0449298\pi\)
\(54\) 0 0
\(55\) 1.67499 + 2.90117i 0.225856 + 0.391194i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.04189 + 3.53666i 0.265831 + 0.460433i 0.967781 0.251793i \(-0.0810202\pi\)
−0.701950 + 0.712226i \(0.747687\pi\)
\(60\) 0 0
\(61\) −0.194593 + 0.337044i −0.0249150 + 0.0431541i −0.878214 0.478268i \(-0.841265\pi\)
0.853299 + 0.521422i \(0.174598\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.694593 −0.0861536
\(66\) 0 0
\(67\) −3.91147 + 6.77487i −0.477863 + 0.827682i −0.999678 0.0253761i \(-0.991922\pi\)
0.521815 + 0.853058i \(0.325255\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.45336 9.44550i −0.647195 1.12097i −0.983790 0.179325i \(-0.942609\pi\)
0.336595 0.941650i \(-0.390725\pi\)
\(72\) 0 0
\(73\) 2.19459 + 3.80115i 0.256858 + 0.444890i 0.965398 0.260779i \(-0.0839795\pi\)
−0.708541 + 0.705670i \(0.750646\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.47296 −0.167860
\(78\) 0 0
\(79\) 7.21688 + 12.5000i 0.811963 + 1.40636i 0.911489 + 0.411326i \(0.134934\pi\)
−0.0995259 + 0.995035i \(0.531733\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.739170 0.0811345 0.0405672 0.999177i \(-0.487084\pi\)
0.0405672 + 0.999177i \(0.487084\pi\)
\(84\) 0 0
\(85\) 2.61081 4.52206i 0.283183 0.490487i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.411474 + 0.712694i −0.0436162 + 0.0755454i −0.887009 0.461751i \(-0.847221\pi\)
0.843393 + 0.537297i \(0.180555\pi\)
\(90\) 0 0
\(91\) 0.152704 0.264490i 0.0160077 0.0277261i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.92902 0.766546i −0.300511 0.0786459i
\(96\) 0 0
\(97\) −5.45336 9.44550i −0.553705 0.959045i −0.998003 0.0631663i \(-0.979880\pi\)
0.444298 0.895879i \(-0.353453\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.75877 8.24243i 0.473515 0.820153i −0.526025 0.850469i \(-0.676318\pi\)
0.999540 + 0.0303164i \(0.00965150\pi\)
\(102\) 0 0
\(103\) 2.30541 0.227159 0.113579 0.993529i \(-0.463768\pi\)
0.113579 + 0.993529i \(0.463768\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.51754 0.920095 0.460048 0.887894i \(-0.347832\pi\)
0.460048 + 0.887894i \(0.347832\pi\)
\(108\) 0 0
\(109\) −6.75877 11.7065i −0.647373 1.12128i −0.983748 0.179555i \(-0.942534\pi\)
0.336375 0.941728i \(-0.390799\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 21.0797 1.98301 0.991504 0.130078i \(-0.0415228\pi\)
0.991504 + 0.130078i \(0.0415228\pi\)
\(114\) 0 0
\(115\) −0.482459 −0.0449895
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.14796 + 1.98832i 0.105233 + 0.182269i
\(120\) 0 0
\(121\) 12.2608 1.11462
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.61081 0.591289
\(126\) 0 0
\(127\) 4.69459 8.13127i 0.416578 0.721534i −0.579015 0.815317i \(-0.696563\pi\)
0.995593 + 0.0937831i \(0.0298960\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.06418 + 7.03936i 0.355089 + 0.615032i 0.987133 0.159900i \(-0.0511173\pi\)
−0.632044 + 0.774932i \(0.717784\pi\)
\(132\) 0 0
\(133\) 0.935822 0.946803i 0.0811461 0.0820982i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.67499 + 4.63322i −0.228540 + 0.395843i −0.957376 0.288846i \(-0.906729\pi\)
0.728836 + 0.684689i \(0.240062\pi\)
\(138\) 0 0
\(139\) 6.97565 12.0822i 0.591667 1.02480i −0.402341 0.915490i \(-0.631803\pi\)
0.994008 0.109308i \(-0.0348633\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.41147 + 4.17680i −0.201658 + 0.349281i
\(144\) 0 0
\(145\) 7.03508 0.584232
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.34730 + 9.26179i 0.438068 + 0.758755i 0.997540 0.0700934i \(-0.0223297\pi\)
−0.559473 + 0.828849i \(0.688996\pi\)
\(150\) 0 0
\(151\) 17.6459 1.43600 0.718001 0.696042i \(-0.245057\pi\)
0.718001 + 0.696042i \(0.245057\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.633103 + 1.09657i 0.0508521 + 0.0880784i
\(156\) 0 0
\(157\) −7.95336 13.7756i −0.634747 1.09941i −0.986569 0.163348i \(-0.947771\pi\)
0.351821 0.936067i \(-0.385563\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.106067 0.183713i 0.00835924 0.0144786i
\(162\) 0 0
\(163\) 2.17705 0.170520 0.0852599 0.996359i \(-0.472828\pi\)
0.0852599 + 0.996359i \(0.472828\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.47565 9.48411i 0.423719 0.733902i −0.572581 0.819848i \(-0.694058\pi\)
0.996300 + 0.0859458i \(0.0273912\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.06418 8.77141i −0.385022 0.666878i 0.606750 0.794893i \(-0.292473\pi\)
−0.991772 + 0.128015i \(0.959140\pi\)
\(174\) 0 0
\(175\) −0.689845 + 1.19485i −0.0521474 + 0.0903219i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.69459 0.649864 0.324932 0.945737i \(-0.394659\pi\)
0.324932 + 0.945737i \(0.394659\pi\)
\(180\) 0 0
\(181\) −3.93582 + 6.81704i −0.292547 + 0.506707i −0.974411 0.224772i \(-0.927836\pi\)
0.681864 + 0.731479i \(0.261170\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.26352 + 3.92053i 0.166417 + 0.288243i
\(186\) 0 0
\(187\) −18.1284 31.3992i −1.32568 2.29614i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.8580 1.00273 0.501366 0.865235i \(-0.332831\pi\)
0.501366 + 0.865235i \(0.332831\pi\)
\(192\) 0 0
\(193\) −1.04664 1.81283i −0.0753386 0.130490i 0.825895 0.563824i \(-0.190670\pi\)
−0.901233 + 0.433334i \(0.857337\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.0446 −1.00063 −0.500317 0.865842i \(-0.666783\pi\)
−0.500317 + 0.865842i \(0.666783\pi\)
\(198\) 0 0
\(199\) −10.9953 + 19.0443i −0.779433 + 1.35002i 0.152836 + 0.988252i \(0.451159\pi\)
−0.932269 + 0.361766i \(0.882174\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.54664 + 2.67885i −0.108553 + 0.188019i
\(204\) 0 0
\(205\) −1.87164 + 3.24178i −0.130721 + 0.226416i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −14.7784 + 14.9518i −1.02224 + 1.03424i
\(210\) 0 0
\(211\) −7.97565 13.8142i −0.549067 0.951011i −0.998339 0.0576162i \(-0.981650\pi\)
0.449272 0.893395i \(-0.351683\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.28312 + 2.22243i −0.0875080 + 0.151568i
\(216\) 0 0
\(217\) −0.556742 −0.0377941
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.51754 0.505685
\(222\) 0 0
\(223\) −13.2520 22.9531i −0.887417 1.53705i −0.842918 0.538042i \(-0.819164\pi\)
−0.0444991 0.999009i \(-0.514169\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.65539 0.176245 0.0881223 0.996110i \(-0.471913\pi\)
0.0881223 + 0.996110i \(0.471913\pi\)
\(228\) 0 0
\(229\) 21.2567 1.40468 0.702342 0.711840i \(-0.252138\pi\)
0.702342 + 0.711840i \(0.252138\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.75877 + 11.7065i 0.442782 + 0.766921i 0.997895 0.0648544i \(-0.0206583\pi\)
−0.555113 + 0.831775i \(0.687325\pi\)
\(234\) 0 0
\(235\) 4.16756 0.271861
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −24.4688 −1.58276 −0.791379 0.611326i \(-0.790636\pi\)
−0.791379 + 0.611326i \(0.790636\pi\)
\(240\) 0 0
\(241\) −5.93376 + 10.2776i −0.382227 + 0.662037i −0.991380 0.131016i \(-0.958176\pi\)
0.609153 + 0.793053i \(0.291510\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.39868 4.15464i −0.153246 0.265430i
\(246\) 0 0
\(247\) −1.15270 4.20372i −0.0733448 0.267476i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.69459 + 6.39922i −0.233201 + 0.403915i −0.958748 0.284257i \(-0.908253\pi\)
0.725548 + 0.688172i \(0.241587\pi\)
\(252\) 0 0
\(253\) −1.67499 + 2.90117i −0.105306 + 0.182395i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.67230 4.62857i 0.166694 0.288722i −0.770562 0.637365i \(-0.780024\pi\)
0.937255 + 0.348643i \(0.113358\pi\)
\(258\) 0 0
\(259\) −1.99050 −0.123684
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0642 + 20.8958i 0.743909 + 1.28849i 0.950703 + 0.310104i \(0.100364\pi\)
−0.206794 + 0.978385i \(0.566303\pi\)
\(264\) 0 0
\(265\) 3.77425 0.231850
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.80066 3.11883i −0.109788 0.190159i 0.805896 0.592057i \(-0.201684\pi\)
−0.915684 + 0.401898i \(0.868351\pi\)
\(270\) 0 0
\(271\) 9.38919 + 16.2625i 0.570352 + 0.987879i 0.996530 + 0.0832396i \(0.0265267\pi\)
−0.426177 + 0.904640i \(0.640140\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.8939 18.8688i 0.656929 1.13783i
\(276\) 0 0
\(277\) 20.1284 1.20940 0.604698 0.796455i \(-0.293294\pi\)
0.604698 + 0.796455i \(0.293294\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.17024 + 12.4192i −0.427741 + 0.740869i −0.996672 0.0815162i \(-0.974024\pi\)
0.568931 + 0.822385i \(0.307357\pi\)
\(282\) 0 0
\(283\) 3.38919 + 5.87024i 0.201466 + 0.348950i 0.949001 0.315273i \(-0.102096\pi\)
−0.747535 + 0.664223i \(0.768763\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.822948 1.42539i −0.0485771 0.0841380i
\(288\) 0 0
\(289\) −19.7567 + 34.2196i −1.16216 + 2.01292i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −16.7784 −0.980203 −0.490101 0.871665i \(-0.663040\pi\)
−0.490101 + 0.871665i \(0.663040\pi\)
\(294\) 0 0
\(295\) −1.41828 + 2.45654i −0.0825755 + 0.143025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.347296 0.601535i −0.0200847 0.0347877i
\(300\) 0 0
\(301\) −0.564178 0.977185i −0.0325187 0.0563240i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.270325 −0.0154788
\(306\) 0 0
\(307\) −8.58172 14.8640i −0.489785 0.848332i 0.510146 0.860088i \(-0.329591\pi\)
−0.999931 + 0.0117559i \(0.996258\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.1729 −0.690264 −0.345132 0.938554i \(-0.612166\pi\)
−0.345132 + 0.938554i \(0.612166\pi\)
\(312\) 0 0
\(313\) −1.85204 + 3.20783i −0.104684 + 0.181318i −0.913609 0.406594i \(-0.866716\pi\)
0.808925 + 0.587912i \(0.200050\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.7811 20.4054i 0.661690 1.14608i −0.318481 0.947929i \(-0.603173\pi\)
0.980171 0.198152i \(-0.0634939\pi\)
\(318\) 0 0
\(319\) 24.4243 42.3041i 1.36750 2.36857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 31.7006 + 8.29628i 1.76387 + 0.461618i
\(324\) 0 0
\(325\) 2.25877 + 3.91231i 0.125294 + 0.217016i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.916222 + 1.58694i −0.0505129 + 0.0874910i
\(330\) 0 0
\(331\) 4.30541 0.236647 0.118323 0.992975i \(-0.462248\pi\)
0.118323 + 0.992975i \(0.462248\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.43376 −0.296878
\(336\) 0 0
\(337\) −9.77631 16.9331i −0.532550 0.922403i −0.999278 0.0380021i \(-0.987901\pi\)
0.466728 0.884401i \(-0.345433\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.79199 0.476113
\(342\) 0 0
\(343\) 4.24722 0.229328
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.8452 29.1768i −0.904300 1.56629i −0.821855 0.569697i \(-0.807060\pi\)
−0.0824452 0.996596i \(-0.526273\pi\)
\(348\) 0 0
\(349\) 12.5567 0.672147 0.336073 0.941836i \(-0.390901\pi\)
0.336073 + 0.941836i \(0.390901\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.65951 0.301225 0.150613 0.988593i \(-0.451875\pi\)
0.150613 + 0.988593i \(0.451875\pi\)
\(354\) 0 0
\(355\) 3.78787 6.56078i 0.201039 0.348210i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.3892 19.7266i −0.601098 1.04113i −0.992655 0.120979i \(-0.961397\pi\)
0.391557 0.920154i \(-0.371937\pi\)
\(360\) 0 0
\(361\) −0.221629 18.9987i −0.0116647 0.999932i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.52435 + 2.64025i −0.0797880 + 0.138197i
\(366\) 0 0
\(367\) −13.5574 + 23.4821i −0.707689 + 1.22575i 0.258023 + 0.966139i \(0.416929\pi\)
−0.965712 + 0.259615i \(0.916404\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.829755 + 1.43718i −0.0430788 + 0.0746146i
\(372\) 0 0
\(373\) −13.9418 −0.721879 −0.360940 0.932589i \(-0.617544\pi\)
−0.360940 + 0.932589i \(0.617544\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.06418 + 8.77141i 0.260818 + 0.451751i
\(378\) 0 0
\(379\) −1.08378 −0.0556699 −0.0278350 0.999613i \(-0.508861\pi\)
−0.0278350 + 0.999613i \(0.508861\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.5398 28.6478i −0.845146 1.46384i −0.885495 0.464650i \(-0.846180\pi\)
0.0403487 0.999186i \(-0.487153\pi\)
\(384\) 0 0
\(385\) −0.511555 0.886039i −0.0260713 0.0451567i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.41147 + 2.44474i −0.0715646 + 0.123953i −0.899587 0.436741i \(-0.856133\pi\)
0.828023 + 0.560695i \(0.189466\pi\)
\(390\) 0 0
\(391\) 5.22163 0.264069
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.01279 + 8.68241i −0.252221 + 0.436860i
\(396\) 0 0
\(397\) 14.7567 + 25.5594i 0.740618 + 1.28279i 0.952214 + 0.305431i \(0.0988005\pi\)
−0.211596 + 0.977357i \(0.567866\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.1506 + 19.3135i 0.556837 + 0.964469i 0.997758 + 0.0669236i \(0.0213184\pi\)
−0.440922 + 0.897546i \(0.645348\pi\)
\(402\) 0 0
\(403\) −0.911474 + 1.57872i −0.0454038 + 0.0786416i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 31.4338 1.55811
\(408\) 0 0
\(409\) −14.8871 + 25.7853i −0.736121 + 1.27500i 0.218109 + 0.975924i \(0.430011\pi\)
−0.954230 + 0.299075i \(0.903322\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.623608 1.08012i −0.0306857 0.0531493i
\(414\) 0 0
\(415\) 0.256711 + 0.444637i 0.0126015 + 0.0218264i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −40.1147 −1.95973 −0.979867 0.199653i \(-0.936019\pi\)
−0.979867 + 0.199653i \(0.936019\pi\)
\(420\) 0 0
\(421\) −17.0155 29.4717i −0.829284 1.43636i −0.898601 0.438767i \(-0.855415\pi\)
0.0693170 0.997595i \(-0.477918\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −33.9608 −1.64734
\(426\) 0 0
\(427\) 0.0594300 0.102936i 0.00287602 0.00498141i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.12836 + 8.88257i −0.247024 + 0.427858i −0.962699 0.270575i \(-0.912786\pi\)
0.715675 + 0.698434i \(0.246119\pi\)
\(432\) 0 0
\(433\) −15.9979 + 27.7092i −0.768812 + 1.33162i 0.169396 + 0.985548i \(0.445818\pi\)
−0.938208 + 0.346073i \(0.887515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.800660 2.91987i −0.0383007 0.139677i
\(438\) 0 0
\(439\) 6.05943 + 10.4952i 0.289201 + 0.500911i 0.973619 0.228179i \(-0.0732771\pi\)
−0.684418 + 0.729089i \(0.739944\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.45336 + 4.24935i −0.116563 + 0.201893i −0.918403 0.395645i \(-0.870521\pi\)
0.801841 + 0.597538i \(0.203854\pi\)
\(444\) 0 0
\(445\) −0.571614 −0.0270971
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.12836 0.289215 0.144607 0.989489i \(-0.453808\pi\)
0.144607 + 0.989489i \(0.453808\pi\)
\(450\) 0 0
\(451\) 12.9959 + 22.5095i 0.611952 + 1.05993i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.212134 0.00994498
\(456\) 0 0
\(457\) 29.9959 1.40315 0.701574 0.712597i \(-0.252481\pi\)
0.701574 + 0.712597i \(0.252481\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.53983 14.7914i −0.397740 0.688905i 0.595707 0.803202i \(-0.296872\pi\)
−0.993447 + 0.114297i \(0.963539\pi\)
\(462\) 0 0
\(463\) −28.3756 −1.31872 −0.659362 0.751825i \(-0.729174\pi\)
−0.659362 + 0.751825i \(0.729174\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.61081 0.305912 0.152956 0.988233i \(-0.451121\pi\)
0.152956 + 0.988233i \(0.451121\pi\)
\(468\) 0 0
\(469\) 1.19459 2.06910i 0.0551612 0.0955419i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.90941 + 15.4316i 0.409655 + 0.709544i
\(474\) 0 0
\(475\) 5.20739 + 18.9905i 0.238931 + 0.871343i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.45336 + 9.44550i −0.249171 + 0.431576i −0.963296 0.268442i \(-0.913491\pi\)
0.714125 + 0.700018i \(0.246825\pi\)
\(480\) 0 0
\(481\) −3.25877 + 5.64436i −0.148587 + 0.257360i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.78787 6.56078i 0.171998 0.297910i
\(486\) 0 0
\(487\) −11.8324 −0.536179 −0.268090 0.963394i \(-0.586392\pi\)
−0.268090 + 0.963394i \(0.586392\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.45336 + 12.9096i 0.336366 + 0.582602i 0.983746 0.179565i \(-0.0574689\pi\)
−0.647381 + 0.762167i \(0.724136\pi\)
\(492\) 0 0
\(493\) −76.1403 −3.42919
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.66550 + 2.88473i 0.0747077 + 0.129398i
\(498\) 0 0
\(499\) 19.9115 + 34.4877i 0.891360 + 1.54388i 0.838246 + 0.545292i \(0.183581\pi\)
0.0531141 + 0.998588i \(0.483085\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.06418 8.77141i 0.225801 0.391098i −0.730759 0.682636i \(-0.760834\pi\)
0.956559 + 0.291538i \(0.0941669\pi\)
\(504\) 0 0
\(505\) 6.61081 0.294177
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12.5175 21.6810i 0.554830 0.960994i −0.443086 0.896479i \(-0.646117\pi\)
0.997917 0.0645153i \(-0.0205501\pi\)
\(510\) 0 0
\(511\) −0.670245 1.16090i −0.0296499 0.0513551i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.800660 + 1.38678i 0.0352813 + 0.0611090i
\(516\) 0 0
\(517\) 14.4688 25.0608i 0.636339 1.10217i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −23.9162 −1.04779 −0.523894 0.851783i \(-0.675521\pi\)
−0.523894 + 0.851783i \(0.675521\pi\)
\(522\) 0 0
\(523\) −18.4290 + 31.9200i −0.805845 + 1.39576i 0.109875 + 0.993945i \(0.464955\pi\)
−0.915719 + 0.401818i \(0.868378\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.85204 11.8681i −0.298480 0.516982i
\(528\) 0 0
\(529\) 11.2588 + 19.5008i 0.489512 + 0.847859i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.38919 −0.233432
\(534\) 0 0
\(535\) 3.30541 + 5.72513i 0.142905 + 0.247519i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −33.3108 −1.43480
\(540\) 0 0
\(541\) −11.2101 + 19.4164i −0.481959 + 0.834777i −0.999786 0.0207084i \(-0.993408\pi\)
0.517827 + 0.855485i \(0.326741\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.69459 8.13127i 0.201094 0.348305i
\(546\) 0 0
\(547\) −3.18779 + 5.52141i −0.136300 + 0.236078i −0.926093 0.377295i \(-0.876854\pi\)
0.789793 + 0.613373i \(0.210188\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11.6750 + 42.5768i 0.497371 + 1.81383i
\(552\) 0 0
\(553\) −2.20409 3.81759i −0.0937274 0.162341i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.97090 + 15.5381i −0.380109 + 0.658369i −0.991078 0.133286i \(-0.957447\pi\)
0.610968 + 0.791655i \(0.290780\pi\)
\(558\) 0 0
\(559\) −3.69459 −0.156265
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −17.5175 −0.738276 −0.369138 0.929375i \(-0.620347\pi\)
−0.369138 + 0.929375i \(0.620347\pi\)
\(564\) 0 0
\(565\) 7.32089 + 12.6802i 0.307992 + 0.533458i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12.6810 −0.531614 −0.265807 0.964026i \(-0.585638\pi\)
−0.265807 + 0.964026i \(0.585638\pi\)
\(570\) 0 0
\(571\) −39.0256 −1.63317 −0.816585 0.577225i \(-0.804135\pi\)
−0.816585 + 0.577225i \(0.804135\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.56893 + 2.71746i 0.0654287 + 0.113326i
\(576\) 0 0
\(577\) 28.2959 1.17797 0.588987 0.808142i \(-0.299527\pi\)
0.588987 + 0.808142i \(0.299527\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.225748 −0.00936560
\(582\) 0 0
\(583\) 13.1034 22.6957i 0.542686 0.939961i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.8648 22.2826i −0.530989 0.919699i −0.999346 0.0361602i \(-0.988487\pi\)
0.468357 0.883539i \(-0.344846\pi\)
\(588\) 0 0
\(589\) −5.58584 + 5.65138i −0.230160 + 0.232861i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.49525 + 11.2501i −0.266728 + 0.461987i −0.968015 0.250893i \(-0.919276\pi\)
0.701287 + 0.712879i \(0.252609\pi\)
\(594\) 0 0
\(595\) −0.797362 + 1.38107i −0.0326886 + 0.0566184i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.18984 8.98908i 0.212051 0.367284i −0.740305 0.672271i \(-0.765319\pi\)
0.952356 + 0.304987i \(0.0986523\pi\)
\(600\) 0 0
\(601\) −7.29591 −0.297606 −0.148803 0.988867i \(-0.547542\pi\)
−0.148803 + 0.988867i \(0.547542\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.25814 + 7.37532i 0.173118 + 0.299849i
\(606\) 0 0
\(607\) −39.1147 −1.58762 −0.793809 0.608167i \(-0.791905\pi\)
−0.793809 + 0.608167i \(0.791905\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 0 0
\(613\) −20.3209 35.1968i −0.820753 1.42159i −0.905122 0.425151i \(-0.860221\pi\)
0.0843693 0.996435i \(-0.473112\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.38238 + 14.5187i −0.337462 + 0.584501i −0.983955 0.178419i \(-0.942902\pi\)
0.646493 + 0.762920i \(0.276235\pi\)
\(618\) 0 0
\(619\) 14.0797 0.565909 0.282955 0.959133i \(-0.408685\pi\)
0.282955 + 0.959133i \(0.408685\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.125667 0.217662i 0.00503475 0.00872044i
\(624\) 0 0
\(625\) −8.99794 15.5849i −0.359918 0.623396i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.4979 42.4317i −0.976797 1.69186i
\(630\) 0 0
\(631\) 10.4486 18.0975i 0.415953 0.720451i −0.579575 0.814919i \(-0.696781\pi\)
0.995528 + 0.0944674i \(0.0301148\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.52166 0.258804
\(636\) 0 0
\(637\) 3.45336 5.98140i 0.136827 0.236992i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.69459 + 2.93512i 0.0669324 + 0.115930i 0.897550 0.440914i \(-0.145345\pi\)
−0.830617 + 0.556844i \(0.812012\pi\)
\(642\) 0 0
\(643\) −8.82770 15.2900i −0.348130 0.602979i 0.637787 0.770213i \(-0.279850\pi\)
−0.985917 + 0.167233i \(0.946517\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.6500 −0.654580 −0.327290 0.944924i \(-0.606135\pi\)
−0.327290 + 0.944924i \(0.606135\pi\)
\(648\) 0 0
\(649\) 9.84793 + 17.0571i 0.386565 + 0.669550i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 35.5877 1.39265 0.696327 0.717724i \(-0.254816\pi\)
0.696327 + 0.717724i \(0.254816\pi\)
\(654\) 0 0
\(655\) −2.82295 + 4.88949i −0.110302 + 0.191048i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.4561 + 35.4309i −0.796855 + 1.38019i 0.124800 + 0.992182i \(0.460171\pi\)
−0.921655 + 0.388011i \(0.873162\pi\)
\(660\) 0 0
\(661\) 0.645897 1.11873i 0.0251225 0.0435134i −0.853191 0.521599i \(-0.825336\pi\)
0.878313 + 0.478085i \(0.158669\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.894543 + 0.234109i 0.0346889 + 0.00907834i
\(666\) 0 0
\(667\) 3.51754 + 6.09256i 0.136200 + 0.235905i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.938511 + 1.62555i −0.0362308 + 0.0627536i
\(672\) 0 0
\(673\) 7.99588 0.308219 0.154109 0.988054i \(-0.450749\pi\)
0.154109 + 0.988054i \(0.450749\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −46.7701 −1.79752 −0.898761 0.438439i \(-0.855532\pi\)
−0.898761 + 0.438439i \(0.855532\pi\)
\(678\) 0 0
\(679\) 1.66550 + 2.88473i 0.0639159 + 0.110706i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.69047 −0.217740 −0.108870 0.994056i \(-0.534723\pi\)
−0.108870 + 0.994056i \(0.534723\pi\)
\(684\) 0 0
\(685\) −3.71606 −0.141983
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.71688 + 4.70578i 0.103505 + 0.179276i
\(690\) 0 0
\(691\) 28.8485 1.09745 0.548725 0.836003i \(-0.315113\pi\)
0.548725 + 0.836003i \(0.315113\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.69047 0.367581
\(696\) 0 0
\(697\) 20.2567 35.0857i 0.767278 1.32896i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −22.7716 39.4415i −0.860070 1.48969i −0.871860 0.489755i \(-0.837086\pi\)
0.0117902 0.999930i \(-0.496247\pi\)
\(702\) 0 0
\(703\) −19.9709 + 20.2052i −0.753217 + 0.762055i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.45336 + 2.51730i −0.0546593 + 0.0946728i
\(708\) 0 0
\(709\) 15.1013 26.1563i 0.567142 0.982319i −0.429705 0.902969i \(-0.641382\pi\)
0.996847 0.0793493i \(-0.0252842\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.633103 + 1.09657i −0.0237099 + 0.0410668i
\(714\) 0 0
\(715\) −3.34998 −0.125282
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.0770 + 31.3102i 0.674157 + 1.16767i 0.976714 + 0.214543i \(0.0688263\pi\)
−0.302557 + 0.953131i \(0.597840\pi\)
\(720\) 0 0
\(721\) −0.704088 −0.0262216
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −22.8776 39.6252i −0.849654 1.47164i
\(726\) 0 0
\(727\) −3.65064 6.32310i −0.135395 0.234511i 0.790353 0.612651i \(-0.209897\pi\)
−0.925748 + 0.378140i \(0.876564\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 13.8871 24.0532i 0.513634 0.889640i
\(732\) 0 0
\(733\) 51.4986 1.90214 0.951071 0.308972i \(-0.0999849\pi\)
0.951071 + 0.308972i \(0.0999849\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.8648 + 32.6749i −0.694895 + 1.20359i
\(738\) 0 0
\(739\) 16.3452 + 28.3108i 0.601269 + 1.04143i 0.992629 + 0.121191i \(0.0386714\pi\)
−0.391360 + 0.920238i \(0.627995\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22.7965 + 39.4848i 0.836324 + 1.44856i 0.892948 + 0.450160i \(0.148633\pi\)
−0.0566239 + 0.998396i \(0.518034\pi\)
\(744\) 0 0
\(745\) −3.71419 + 6.43317i −0.136078 + 0.235693i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.90673 −0.106209
\(750\) 0 0
\(751\) −9.15270 + 15.8529i −0.333987 + 0.578482i −0.983290 0.182048i \(-0.941727\pi\)
0.649303 + 0.760530i \(0.275061\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.12836 + 10.6146i 0.223034 + 0.386306i
\(756\) 0 0
\(757\) 15.7121 + 27.2142i 0.571067 + 0.989117i 0.996457 + 0.0841071i \(0.0268038\pi\)
−0.425390 + 0.905010i \(0.639863\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.5580 −1.39773 −0.698863 0.715255i \(-0.746310\pi\)
−0.698863 + 0.715255i \(0.746310\pi\)
\(762\) 0 0
\(763\) 2.06418 + 3.57526i 0.0747283 + 0.129433i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.08378 −0.147457
\(768\) 0 0
\(769\) −7.37164 + 12.7681i −0.265828 + 0.460428i −0.967780 0.251796i \(-0.918979\pi\)
0.701952 + 0.712224i \(0.252312\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.95130 + 3.37976i −0.0701835 + 0.121561i −0.898982 0.437986i \(-0.855692\pi\)
0.828798 + 0.559548i \(0.189025\pi\)
\(774\) 0 0
\(775\) 4.11762 7.13193i 0.147909 0.256186i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −22.7256 5.94745i −0.814228 0.213090i
\(780\) 0 0
\(781\) −26.3013 45.5552i −0.941134 1.63009i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.52435 9.56845i 0.197172 0.341513i
\(786\) 0 0
\(787\) 10.7879 0.384546 0.192273 0.981341i \(-0.438414\pi\)
0.192273 + 0.981341i \(0.438414\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.43788 −0.228905
\(792\) 0 0
\(793\) −0.194593 0.337044i −0.00691019 0.0119688i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.5526 1.71982 0.859911 0.510444i \(-0.170519\pi\)
0.859911 + 0.510444i \(0.170519\pi\)
\(798\) 0 0
\(799\) −45.1052 −1.59571
\(800\) 0 0
\(801\) 0 0
\(802\)