Properties

Label 504.4.s.j.289.2
Level $504$
Weight $4$
Character 504.289
Analytic conductor $29.737$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(29.7369626429\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(-2.57353i\) of defining polynomial
Character \(\chi\) \(=\) 504.289
Dual form 504.4.s.j.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0642956 - 0.111363i) q^{5} +(-0.866259 + 18.5000i) q^{7} +O(q^{10})\) \(q+(0.0642956 - 0.111363i) q^{5} +(-0.866259 + 18.5000i) q^{7} +(27.0033 + 46.7711i) q^{11} -50.2350 q^{13} +(-65.7436 - 113.871i) q^{17} +(-45.7547 + 79.2495i) q^{19} +(89.7436 - 155.441i) q^{23} +(62.4917 + 108.239i) q^{25} +69.8961 q^{29} +(-163.423 - 283.058i) q^{31} +(2.00452 + 1.28594i) q^{35} +(-150.849 + 261.278i) q^{37} -296.048 q^{41} -144.302 q^{43} +(-180.043 + 311.843i) q^{47} +(-341.499 - 32.0516i) q^{49} +(0.917567 + 1.58927i) q^{53} +6.94477 q^{55} +(-26.6193 - 46.1060i) q^{59} +(54.0605 - 93.6356i) q^{61} +(-3.22989 + 5.59433i) q^{65} +(-421.004 - 729.199i) q^{67} +241.111 q^{71} +(103.492 + 179.253i) q^{73} +(-888.656 + 459.045i) q^{77} +(-279.981 + 484.942i) q^{79} -986.652 q^{83} -16.9081 q^{85} +(-221.683 + 383.966i) q^{89} +(43.5165 - 929.348i) q^{91} +(5.88365 + 10.1908i) q^{95} -740.815 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + 18q^{7} + O(q^{10}) \) \( 8q + 4q^{5} + 18q^{7} + 14q^{11} + 44q^{13} + 96q^{17} + 26q^{19} + 96q^{23} - 110q^{25} + 152q^{29} - 238q^{31} - 152q^{35} - 562q^{37} - 856q^{41} - 516q^{43} - 80q^{47} + 156q^{49} + 2952q^{55} + 262q^{59} + 276q^{61} + 2196q^{65} - 150q^{67} + 1696q^{71} + 218q^{73} + 764q^{77} - 1762q^{79} - 6900q^{83} + 2904q^{85} - 344q^{89} - 2806q^{91} + 2004q^{95} - 1244q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(5\) 0.0642956 0.111363i 0.00575077 0.00996063i −0.863136 0.504972i \(-0.831503\pi\)
0.868886 + 0.495011i \(0.164836\pi\)
\(6\) 0 0
\(7\) −0.866259 + 18.5000i −0.0467736 + 0.998906i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 27.0033 + 46.7711i 0.740163 + 1.28200i 0.952421 + 0.304787i \(0.0985852\pi\)
−0.212257 + 0.977214i \(0.568081\pi\)
\(12\) 0 0
\(13\) −50.2350 −1.07175 −0.535873 0.844299i \(-0.680017\pi\)
−0.535873 + 0.844299i \(0.680017\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −65.7436 113.871i −0.937951 1.62458i −0.769285 0.638906i \(-0.779387\pi\)
−0.168666 0.985673i \(-0.553946\pi\)
\(18\) 0 0
\(19\) −45.7547 + 79.2495i −0.552466 + 0.956899i 0.445630 + 0.895217i \(0.352980\pi\)
−0.998096 + 0.0616814i \(0.980354\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 89.7436 155.441i 0.813602 1.40920i −0.0967260 0.995311i \(-0.530837\pi\)
0.910328 0.413888i \(-0.135830\pi\)
\(24\) 0 0
\(25\) 62.4917 + 108.239i 0.499934 + 0.865911i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 69.8961 0.447565 0.223782 0.974639i \(-0.428159\pi\)
0.223782 + 0.974639i \(0.428159\pi\)
\(30\) 0 0
\(31\) −163.423 283.058i −0.946829 1.63996i −0.752046 0.659110i \(-0.770933\pi\)
−0.194783 0.980846i \(-0.562400\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00452 + 1.28594i 0.00968074 + 0.00621037i
\(36\) 0 0
\(37\) −150.849 + 261.278i −0.670254 + 1.16091i 0.307578 + 0.951523i \(0.400481\pi\)
−0.977832 + 0.209391i \(0.932852\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −296.048 −1.12768 −0.563840 0.825884i \(-0.690676\pi\)
−0.563840 + 0.825884i \(0.690676\pi\)
\(42\) 0 0
\(43\) −144.302 −0.511764 −0.255882 0.966708i \(-0.582366\pi\)
−0.255882 + 0.966708i \(0.582366\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −180.043 + 311.843i −0.558764 + 0.967808i 0.438836 + 0.898567i \(0.355391\pi\)
−0.997600 + 0.0692409i \(0.977942\pi\)
\(48\) 0 0
\(49\) −341.499 32.0516i −0.995624 0.0934448i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.917567 + 1.58927i 0.00237807 + 0.00411893i 0.867212 0.497939i \(-0.165910\pi\)
−0.864834 + 0.502058i \(0.832576\pi\)
\(54\) 0 0
\(55\) 6.94477 0.0170260
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −26.6193 46.1060i −0.0587379 0.101737i 0.835161 0.550005i \(-0.185374\pi\)
−0.893899 + 0.448268i \(0.852041\pi\)
\(60\) 0 0
\(61\) 54.0605 93.6356i 0.113471 0.196538i −0.803696 0.595040i \(-0.797136\pi\)
0.917168 + 0.398502i \(0.130470\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.22989 + 5.59433i −0.00616336 + 0.0106753i
\(66\) 0 0
\(67\) −421.004 729.199i −0.767668 1.32964i −0.938824 0.344396i \(-0.888084\pi\)
0.171156 0.985244i \(-0.445250\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 241.111 0.403023 0.201511 0.979486i \(-0.435415\pi\)
0.201511 + 0.979486i \(0.435415\pi\)
\(72\) 0 0
\(73\) 103.492 + 179.253i 0.165929 + 0.287397i 0.936985 0.349370i \(-0.113605\pi\)
−0.771056 + 0.636767i \(0.780271\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −888.656 + 459.045i −1.31522 + 0.679390i
\(78\) 0 0
\(79\) −279.981 + 484.942i −0.398738 + 0.690635i −0.993571 0.113215i \(-0.963885\pi\)
0.594832 + 0.803850i \(0.297219\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −986.652 −1.30481 −0.652404 0.757871i \(-0.726240\pi\)
−0.652404 + 0.757871i \(0.726240\pi\)
\(84\) 0 0
\(85\) −16.9081 −0.0215758
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −221.683 + 383.966i −0.264026 + 0.457307i −0.967308 0.253604i \(-0.918384\pi\)
0.703282 + 0.710911i \(0.251717\pi\)
\(90\) 0 0
\(91\) 43.5165 929.348i 0.0501294 1.07057i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.88365 + 10.1908i 0.00635421 + 0.0110058i
\(96\) 0 0
\(97\) −740.815 −0.775447 −0.387723 0.921776i \(-0.626738\pi\)
−0.387723 + 0.921776i \(0.626738\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 371.888 + 644.130i 0.366379 + 0.634587i 0.988996 0.147939i \(-0.0472640\pi\)
−0.622617 + 0.782526i \(0.713931\pi\)
\(102\) 0 0
\(103\) −52.3253 + 90.6300i −0.0500559 + 0.0866994i −0.889968 0.456024i \(-0.849273\pi\)
0.839912 + 0.542723i \(0.182607\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 256.850 444.878i 0.232062 0.401943i −0.726353 0.687322i \(-0.758786\pi\)
0.958415 + 0.285379i \(0.0921194\pi\)
\(108\) 0 0
\(109\) −487.519 844.408i −0.428402 0.742015i 0.568329 0.822801i \(-0.307590\pi\)
−0.996731 + 0.0807868i \(0.974257\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1926.07 −1.60345 −0.801723 0.597696i \(-0.796083\pi\)
−0.801723 + 0.597696i \(0.796083\pi\)
\(114\) 0 0
\(115\) −11.5402 19.9883i −0.00935767 0.0162080i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2163.57 1117.61i 1.66667 0.860937i
\(120\) 0 0
\(121\) −792.855 + 1373.27i −0.595684 + 1.03175i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 32.1457 0.0230016
\(126\) 0 0
\(127\) −1125.95 −0.786709 −0.393355 0.919387i \(-0.628686\pi\)
−0.393355 + 0.919387i \(0.628686\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 746.621 1293.19i 0.497959 0.862490i −0.502038 0.864845i \(-0.667416\pi\)
0.999997 + 0.00235541i \(0.000749751\pi\)
\(132\) 0 0
\(133\) −1426.48 915.112i −0.930010 0.596619i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 730.386 + 1265.07i 0.455483 + 0.788919i 0.998716 0.0506627i \(-0.0161334\pi\)
−0.543233 + 0.839582i \(0.682800\pi\)
\(138\) 0 0
\(139\) 2225.85 1.35823 0.679116 0.734031i \(-0.262363\pi\)
0.679116 + 0.734031i \(0.262363\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1356.51 2349.55i −0.793267 1.37398i
\(144\) 0 0
\(145\) 4.49401 7.78385i 0.00257384 0.00445803i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 197.340 341.804i 0.108502 0.187930i −0.806662 0.591013i \(-0.798728\pi\)
0.915163 + 0.403083i \(0.132061\pi\)
\(150\) 0 0
\(151\) 1562.10 + 2705.64i 0.841867 + 1.45816i 0.888314 + 0.459236i \(0.151877\pi\)
−0.0464473 + 0.998921i \(0.514790\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −42.0296 −0.0217800
\(156\) 0 0
\(157\) 1800.35 + 3118.30i 0.915183 + 1.58514i 0.806633 + 0.591053i \(0.201288\pi\)
0.108551 + 0.994091i \(0.465379\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2797.91 + 1794.91i 1.36960 + 0.878624i
\(162\) 0 0
\(163\) −987.012 + 1709.55i −0.474287 + 0.821489i −0.999567 0.0294409i \(-0.990627\pi\)
0.525280 + 0.850930i \(0.323961\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1067.09 −0.494453 −0.247227 0.968958i \(-0.579519\pi\)
−0.247227 + 0.968958i \(0.579519\pi\)
\(168\) 0 0
\(169\) 326.559 0.148638
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −137.327 + 237.858i −0.0603515 + 0.104532i −0.894623 0.446823i \(-0.852555\pi\)
0.834271 + 0.551355i \(0.185889\pi\)
\(174\) 0 0
\(175\) −2056.55 + 1062.33i −0.888347 + 0.458885i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 277.166 + 480.066i 0.115734 + 0.200457i 0.918073 0.396412i \(-0.129745\pi\)
−0.802339 + 0.596869i \(0.796411\pi\)
\(180\) 0 0
\(181\) −685.436 −0.281481 −0.140741 0.990047i \(-0.544948\pi\)
−0.140741 + 0.990047i \(0.544948\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 19.3978 + 33.5980i 0.00770895 + 0.0133523i
\(186\) 0 0
\(187\) 3550.59 6149.80i 1.38847 2.40491i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2449.44 4242.55i 0.927932 1.60722i 0.141155 0.989988i \(-0.454918\pi\)
0.786777 0.617237i \(-0.211748\pi\)
\(192\) 0 0
\(193\) −1570.13 2719.55i −0.585598 1.01429i −0.994801 0.101842i \(-0.967526\pi\)
0.409202 0.912444i \(-0.365807\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 227.412 0.0822460 0.0411230 0.999154i \(-0.486906\pi\)
0.0411230 + 0.999154i \(0.486906\pi\)
\(198\) 0 0
\(199\) 607.250 + 1051.79i 0.216316 + 0.374670i 0.953679 0.300827i \(-0.0972626\pi\)
−0.737363 + 0.675497i \(0.763929\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −60.5481 + 1293.08i −0.0209342 + 0.447075i
\(204\) 0 0
\(205\) −19.0345 + 32.9688i −0.00648502 + 0.0112324i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4942.11 −1.63566
\(210\) 0 0
\(211\) 5116.07 1.66922 0.834608 0.550844i \(-0.185694\pi\)
0.834608 + 0.550844i \(0.185694\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.27799 + 16.0699i −0.00294304 + 0.00509749i
\(216\) 0 0
\(217\) 5378.13 2778.13i 1.68245 0.869087i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3302.63 + 5720.33i 1.00524 + 1.74114i
\(222\) 0 0
\(223\) 119.384 0.0358499 0.0179250 0.999839i \(-0.494294\pi\)
0.0179250 + 0.999839i \(0.494294\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 996.000 + 1725.12i 0.291220 + 0.504407i 0.974098 0.226124i \(-0.0726056\pi\)
−0.682879 + 0.730532i \(0.739272\pi\)
\(228\) 0 0
\(229\) −351.738 + 609.228i −0.101500 + 0.175803i −0.912303 0.409516i \(-0.865698\pi\)
0.810803 + 0.585319i \(0.199031\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 480.892 832.929i 0.135211 0.234193i −0.790467 0.612505i \(-0.790162\pi\)
0.925678 + 0.378312i \(0.123495\pi\)
\(234\) 0 0
\(235\) 23.1519 + 40.1003i 0.00642665 + 0.0111313i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4464.71 1.20836 0.604179 0.796848i \(-0.293501\pi\)
0.604179 + 0.796848i \(0.293501\pi\)
\(240\) 0 0
\(241\) 217.656 + 376.991i 0.0581761 + 0.100764i 0.893647 0.448771i \(-0.148138\pi\)
−0.835471 + 0.549535i \(0.814805\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −25.5262 + 35.9697i −0.00665638 + 0.00937966i
\(246\) 0 0
\(247\) 2298.49 3981.10i 0.592103 1.02555i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −863.003 −0.217021 −0.108510 0.994095i \(-0.534608\pi\)
−0.108510 + 0.994095i \(0.534608\pi\)
\(252\) 0 0
\(253\) 9693.49 2.40879
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −268.346 + 464.790i −0.0651322 + 0.112812i −0.896753 0.442532i \(-0.854080\pi\)
0.831620 + 0.555344i \(0.187414\pi\)
\(258\) 0 0
\(259\) −4702.96 3017.03i −1.12829 0.723820i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 185.954 + 322.082i 0.0435986 + 0.0755149i 0.887001 0.461767i \(-0.152784\pi\)
−0.843403 + 0.537282i \(0.819451\pi\)
\(264\) 0 0
\(265\) 0.235982 5.47029e−5
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2252.80 3901.97i −0.510616 0.884414i −0.999924 0.0123024i \(-0.996084\pi\)
0.489308 0.872111i \(-0.337249\pi\)
\(270\) 0 0
\(271\) 198.058 343.046i 0.0443954 0.0768951i −0.842974 0.537955i \(-0.819197\pi\)
0.887369 + 0.461059i \(0.152531\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3374.96 + 5845.61i −0.740066 + 1.28183i
\(276\) 0 0
\(277\) 3254.37 + 5636.73i 0.705907 + 1.22267i 0.966363 + 0.257181i \(0.0827935\pi\)
−0.260457 + 0.965486i \(0.583873\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2785.80 −0.591413 −0.295707 0.955279i \(-0.595555\pi\)
−0.295707 + 0.955279i \(0.595555\pi\)
\(282\) 0 0
\(283\) −0.305923 0.529874i −6.42588e−5 0.000111299i 0.865993 0.500056i \(-0.166687\pi\)
−0.866058 + 0.499944i \(0.833354\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 256.454 5476.88i 0.0527456 1.12645i
\(288\) 0 0
\(289\) −6187.95 + 10717.8i −1.25950 + 2.18153i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4145.98 0.826657 0.413329 0.910582i \(-0.364366\pi\)
0.413329 + 0.910582i \(0.364366\pi\)
\(294\) 0 0
\(295\) −6.84601 −0.00135115
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4508.27 + 7808.56i −0.871974 + 1.51030i
\(300\) 0 0
\(301\) 125.003 2669.59i 0.0239371 0.511204i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.95171 12.0407i −0.00130509 0.00226049i
\(306\) 0 0
\(307\) 1960.53 0.364473 0.182236 0.983255i \(-0.441666\pi\)
0.182236 + 0.983255i \(0.441666\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2603.78 + 4509.89i 0.474749 + 0.822290i 0.999582 0.0289155i \(-0.00920538\pi\)
−0.524833 + 0.851206i \(0.675872\pi\)
\(312\) 0 0
\(313\) 1995.86 3456.92i 0.360423 0.624271i −0.627607 0.778530i \(-0.715966\pi\)
0.988030 + 0.154259i \(0.0492990\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 902.519 1563.21i 0.159907 0.276967i −0.774928 0.632050i \(-0.782214\pi\)
0.934835 + 0.355083i \(0.115547\pi\)
\(318\) 0 0
\(319\) 1887.43 + 3269.12i 0.331271 + 0.573779i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12032.3 2.07274
\(324\) 0 0
\(325\) −3139.27 5437.38i −0.535802 0.928036i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5613.13 3600.92i −0.940614 0.603421i
\(330\) 0 0
\(331\) −3453.09 + 5980.93i −0.573411 + 0.993177i 0.422801 + 0.906222i \(0.361047\pi\)
−0.996212 + 0.0869547i \(0.972286\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −108.275 −0.0176587
\(336\) 0 0
\(337\) −6081.36 −0.983006 −0.491503 0.870876i \(-0.663552\pi\)
−0.491503 + 0.870876i \(0.663552\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8825.94 15287.0i 1.40162 2.42767i
\(342\) 0 0
\(343\) 888.780 6289.97i 0.139911 0.990164i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3893.51 6743.75i −0.602347 1.04330i −0.992465 0.122531i \(-0.960899\pi\)
0.390117 0.920765i \(-0.372434\pi\)
\(348\) 0 0
\(349\) −1928.25 −0.295751 −0.147875 0.989006i \(-0.547243\pi\)
−0.147875 + 0.989006i \(0.547243\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1702.14 2948.18i −0.256645 0.444521i 0.708696 0.705514i \(-0.249284\pi\)
−0.965341 + 0.260992i \(0.915950\pi\)
\(354\) 0 0
\(355\) 15.5024 26.8509i 0.00231769 0.00401436i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2208.53 3825.28i 0.324684 0.562369i −0.656764 0.754096i \(-0.728075\pi\)
0.981448 + 0.191727i \(0.0614088\pi\)
\(360\) 0 0
\(361\) −757.484 1312.00i −0.110436 0.191282i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 26.6162 0.00381687
\(366\) 0 0
\(367\) 2538.33 + 4396.51i 0.361034 + 0.625329i 0.988131 0.153612i \(-0.0490905\pi\)
−0.627097 + 0.778941i \(0.715757\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −30.1964 + 15.5983i −0.00422566 + 0.00218281i
\(372\) 0 0
\(373\) 3438.32 5955.35i 0.477291 0.826692i −0.522370 0.852719i \(-0.674952\pi\)
0.999661 + 0.0260264i \(0.00828540\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3511.23 −0.479676
\(378\) 0 0
\(379\) −9285.61 −1.25850 −0.629248 0.777205i \(-0.716637\pi\)
−0.629248 + 0.777205i \(0.716637\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3840.83 + 6652.51i −0.512420 + 0.887538i 0.487476 + 0.873136i \(0.337918\pi\)
−0.999896 + 0.0144017i \(0.995416\pi\)
\(384\) 0 0
\(385\) −6.01597 + 128.478i −0.000796369 + 0.0170074i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4313.86 + 7471.83i 0.562266 + 0.973873i 0.997298 + 0.0734585i \(0.0234036\pi\)
−0.435032 + 0.900415i \(0.643263\pi\)
\(390\) 0 0
\(391\) −23600.3 −3.05247
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 36.0031 + 62.3592i 0.00458611 + 0.00794337i
\(396\) 0 0
\(397\) −2867.81 + 4967.19i −0.362547 + 0.627949i −0.988379 0.152008i \(-0.951426\pi\)
0.625832 + 0.779957i \(0.284759\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3608.89 + 6250.79i −0.449425 + 0.778427i −0.998349 0.0574453i \(-0.981705\pi\)
0.548923 + 0.835873i \(0.315038\pi\)
\(402\) 0 0
\(403\) 8209.58 + 14219.4i 1.01476 + 1.75762i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16293.7 −1.98439
\(408\) 0 0
\(409\) 5401.46 + 9355.60i 0.653019 + 1.13106i 0.982386 + 0.186861i \(0.0598313\pi\)
−0.329367 + 0.944202i \(0.606835\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 876.019 452.517i 0.104373 0.0539150i
\(414\) 0 0
\(415\) −63.4373 + 109.877i −0.00750365 + 0.0129967i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13257.1 −1.54571 −0.772856 0.634582i \(-0.781172\pi\)
−0.772856 + 0.634582i \(0.781172\pi\)
\(420\) 0 0
\(421\) −6252.11 −0.723774 −0.361887 0.932222i \(-0.617867\pi\)
−0.361887 + 0.932222i \(0.617867\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8216.87 14232.0i 0.937827 1.62436i
\(426\) 0 0
\(427\) 1685.43 + 1081.23i 0.191015 + 0.122540i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2474.54 + 4286.03i 0.276553 + 0.479004i 0.970526 0.240997i \(-0.0774745\pi\)
−0.693973 + 0.720001i \(0.744141\pi\)
\(432\) 0 0
\(433\) −16602.8 −1.84267 −0.921337 0.388764i \(-0.872902\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8212.38 + 14224.3i 0.898974 + 1.55707i
\(438\) 0 0
\(439\) 2354.19 4077.57i 0.255944 0.443307i −0.709208 0.705000i \(-0.750947\pi\)
0.965151 + 0.261692i \(0.0842805\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −850.218 + 1472.62i −0.0911852 + 0.157937i −0.908010 0.418948i \(-0.862399\pi\)
0.816825 + 0.576886i \(0.195732\pi\)
\(444\) 0 0
\(445\) 28.5065 + 49.3746i 0.00303671 + 0.00525973i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10050.2 −1.05635 −0.528173 0.849137i \(-0.677123\pi\)
−0.528173 + 0.849137i \(0.677123\pi\)
\(450\) 0 0
\(451\) −7994.26 13846.5i −0.834667 1.44569i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −100.697 64.5991i −0.0103753 0.00665594i
\(456\) 0 0
\(457\) 5495.95 9519.27i 0.562560 0.974382i −0.434712 0.900569i \(-0.643150\pi\)
0.997272 0.0738128i \(-0.0235167\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 548.440 0.0554086 0.0277043 0.999616i \(-0.491180\pi\)
0.0277043 + 0.999616i \(0.491180\pi\)
\(462\) 0 0
\(463\) 4028.04 0.404317 0.202159 0.979353i \(-0.435204\pi\)
0.202159 + 0.979353i \(0.435204\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1035.35 1793.27i 0.102591 0.177693i −0.810160 0.586208i \(-0.800620\pi\)
0.912751 + 0.408515i \(0.133953\pi\)
\(468\) 0 0
\(469\) 13854.9 7156.88i 1.36409 0.704636i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3896.63 6749.16i −0.378789 0.656082i
\(474\) 0 0
\(475\) −11437.2 −1.10479
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −89.3926 154.832i −0.00852704 0.0147693i 0.861730 0.507366i \(-0.169381\pi\)
−0.870257 + 0.492597i \(0.836048\pi\)
\(480\) 0 0
\(481\) 7577.89 13125.3i 0.718341 1.24420i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −47.6311 + 82.4995i −0.00445942 + 0.00772393i
\(486\) 0 0
\(487\) 8298.48 + 14373.4i 0.772156 + 1.33741i 0.936379 + 0.350991i \(0.114155\pi\)
−0.164223 + 0.986423i \(0.552512\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4547.22 0.417949 0.208975 0.977921i \(-0.432987\pi\)
0.208975 + 0.977921i \(0.432987\pi\)
\(492\) 0 0
\(493\) −4595.22 7959.16i −0.419794 0.727105i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −208.864 + 4460.55i −0.0188508 + 0.402581i
\(498\) 0 0
\(499\) −512.984 + 888.515i −0.0460207 + 0.0797102i −0.888118 0.459615i \(-0.847987\pi\)
0.842097 + 0.539325i \(0.181321\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6745.26 −0.597925 −0.298962 0.954265i \(-0.596641\pi\)
−0.298962 + 0.954265i \(0.596641\pi\)
\(504\) 0 0
\(505\) 95.6431 0.00842785
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3000.51 + 5197.03i −0.261287 + 0.452563i −0.966584 0.256349i \(-0.917480\pi\)
0.705297 + 0.708912i \(0.250814\pi\)
\(510\) 0 0
\(511\) −3405.83 + 1759.32i −0.294843 + 0.152304i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.72856 + 11.6542i 0.000575720 + 0.000997177i
\(516\) 0 0
\(517\) −19447.0 −1.65431
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2347.61 + 4066.17i 0.197410 + 0.341924i 0.947688 0.319199i \(-0.103414\pi\)
−0.750278 + 0.661122i \(0.770080\pi\)
\(522\) 0 0
\(523\) −385.884 + 668.370i −0.0322629 + 0.0558810i −0.881706 0.471799i \(-0.843605\pi\)
0.849443 + 0.527680i \(0.176938\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21488.1 + 37218.5i −1.77616 + 3.07640i
\(528\) 0 0
\(529\) −10024.3 17362.7i −0.823895 1.42703i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14872.0 1.20859
\(534\) 0 0
\(535\) −33.0286 57.2073i −0.00266907 0.00462297i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7722.52 16837.8i −0.617129 1.34556i
\(540\) 0 0
\(541\) −1692.83 + 2932.07i −0.134529 + 0.233012i −0.925418 0.378949i \(-0.876286\pi\)
0.790888 + 0.611961i \(0.209619\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −125.381 −0.00985457
\(546\) 0 0
\(547\) 4988.75 0.389952 0.194976 0.980808i \(-0.437537\pi\)
0.194976 + 0.980808i \(0.437537\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3198.08 + 5539.23i −0.247264 + 0.428274i
\(552\) 0 0
\(553\) −8728.88 5599.73i −0.671229 0.430606i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10103.6 17500.0i −0.768591 1.33124i −0.938327 0.345749i \(-0.887625\pi\)
0.169736 0.985490i \(-0.445709\pi\)
\(558\) 0 0
\(559\) 7249.02 0.548481
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5845.20 10124.2i −0.437559 0.757875i 0.559941 0.828532i \(-0.310824\pi\)
−0.997501 + 0.0706574i \(0.977490\pi\)
\(564\) 0 0
\(565\) −123.838 + 214.493i −0.00922104 + 0.0159713i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8964.45 + 15526.9i −0.660473 + 1.14397i 0.320018 + 0.947411i \(0.396311\pi\)
−0.980491 + 0.196562i \(0.937022\pi\)
\(570\) 0 0
\(571\) 7836.84 + 13573.8i 0.574364 + 0.994827i 0.996110 + 0.0881136i \(0.0280838\pi\)
−0.421747 + 0.906714i \(0.638583\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22432.9 1.62699
\(576\) 0 0
\(577\) 6826.50 + 11823.8i 0.492532 + 0.853090i 0.999963 0.00860205i \(-0.00273815\pi\)
−0.507431 + 0.861692i \(0.669405\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 854.696 18253.0i 0.0610306 1.30338i
\(582\) 0 0
\(583\) −49.5547 + 85.8312i −0.00352032 + 0.00609737i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18021.5 1.26717 0.633583 0.773675i \(-0.281583\pi\)
0.633583 + 0.773675i \(0.281583\pi\)
\(588\) 0 0
\(589\) 29909.6 2.09236
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10568.7 18305.5i 0.731877 1.26765i −0.224204 0.974542i \(-0.571978\pi\)
0.956080 0.293105i \(-0.0946886\pi\)
\(594\) 0 0
\(595\) 14.6468 312.800i 0.00100918 0.0215522i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4684.80 + 8114.30i 0.319559 + 0.553492i 0.980396 0.197037i \(-0.0631321\pi\)
−0.660837 + 0.750529i \(0.729799\pi\)
\(600\) 0 0
\(601\) −22750.0 −1.54408 −0.772040 0.635573i \(-0.780764\pi\)
−0.772040 + 0.635573i \(0.780764\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 101.954 + 176.590i 0.00685128 + 0.0118668i
\(606\) 0 0
\(607\) 2986.82 5173.33i 0.199722 0.345929i −0.748716 0.662891i \(-0.769329\pi\)
0.948438 + 0.316962i \(0.102663\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9044.45 15665.4i 0.598853 1.03724i
\(612\) 0 0
\(613\) 11673.7 + 20219.4i 0.769162 + 1.33223i 0.938018 + 0.346586i \(0.112659\pi\)
−0.168856 + 0.985641i \(0.554007\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28199.1 −1.83996 −0.919979 0.391968i \(-0.871794\pi\)
−0.919979 + 0.391968i \(0.871794\pi\)
\(618\) 0 0
\(619\) 1487.78 + 2576.91i 0.0966057 + 0.167326i 0.910278 0.413998i \(-0.135868\pi\)
−0.813672 + 0.581324i \(0.802535\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6911.33 4433.75i −0.444457 0.285127i
\(624\) 0 0
\(625\) −7809.40 + 13526.3i −0.499802 + 0.865682i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 39669.4 2.51466
\(630\) 0 0
\(631\) −2631.33 −0.166009 −0.0830044 0.996549i \(-0.526452\pi\)
−0.0830044 + 0.996549i \(0.526452\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −72.3937 + 125.390i −0.00452418 + 0.00783611i
\(636\) 0 0
\(637\) 17155.2 + 1610.11i 1.06706 + 0.100149i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7247.12 + 12552.4i 0.446559 + 0.773462i 0.998159 0.0606460i \(-0.0193161\pi\)
−0.551601 + 0.834108i \(0.685983\pi\)
\(642\) 0 0
\(643\) −15176.0 −0.930767 −0.465383 0.885109i \(-0.654084\pi\)
−0.465383 + 0.885109i \(0.654084\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3784.59 6555.10i −0.229965 0.398312i 0.727832 0.685755i \(-0.240528\pi\)
−0.957798 + 0.287443i \(0.907195\pi\)
\(648\) 0 0
\(649\) 1437.62 2490.02i 0.0869513 0.150604i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6966.75 + 12066.8i −0.417504 + 0.723138i −0.995688 0.0927688i \(-0.970428\pi\)
0.578184 + 0.815906i \(0.303762\pi\)
\(654\) 0 0
\(655\) −96.0089 166.292i −0.00572729 0.00991996i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17015.5 1.00581 0.502904 0.864342i \(-0.332265\pi\)
0.502904 + 0.864342i \(0.332265\pi\)
\(660\) 0 0
\(661\) 8267.70 + 14320.1i 0.486500 + 0.842642i 0.999880 0.0155194i \(-0.00494019\pi\)
−0.513380 + 0.858161i \(0.671607\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −193.626 + 100.020i −0.0112910 + 0.00583247i
\(666\) 0 0
\(667\) 6272.73 10864.7i 0.364140 0.630708i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5839.25 0.335949
\(672\) 0 0
\(673\) 4571.05 0.261814 0.130907 0.991395i \(-0.458211\pi\)
0.130907 + 0.991395i \(0.458211\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13142.3 22763.1i 0.746083 1.29225i −0.203604 0.979053i \(-0.565265\pi\)
0.949687 0.313201i \(-0.101401\pi\)
\(678\) 0 0
\(679\) 641.737 13705.1i 0.0362704 0.774598i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3398.61 + 5886.57i 0.190402 + 0.329785i 0.945383 0.325961i \(-0.105688\pi\)
−0.754982 + 0.655746i \(0.772354\pi\)
\(684\) 0 0
\(685\) 187.842 0.0104775
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −46.0940 79.8372i −0.00254868 0.00441445i
\(690\) 0 0
\(691\) −13879.3 + 24039.7i −0.764103 + 1.32346i 0.176617 + 0.984280i \(0.443485\pi\)
−0.940720 + 0.339185i \(0.889849\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 143.112 247.878i 0.00781088 0.0135288i
\(696\) 0 0
\(697\) 19463.2 + 33711.3i 1.05771 + 1.83200i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21638.3 1.16586 0.582929 0.812523i \(-0.301907\pi\)
0.582929 + 0.812523i \(0.301907\pi\)
\(702\) 0 0
\(703\) −13804.1 23909.4i −0.740584 1.28273i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12238.5 + 6321.95i −0.651029 + 0.336296i
\(708\) 0 0
\(709\) 8144.36 14106.4i 0.431408 0.747220i −0.565587 0.824688i \(-0.691350\pi\)
0.996995 + 0.0774687i \(0.0246838\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −58664.8 −3.08137
\(714\) 0 0
\(715\) −348.871 −0.0182476
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1695.87 + 2937.33i −0.0879628 + 0.152356i −0.906650 0.421884i \(-0.861369\pi\)
0.818687 + 0.574240i \(0.194702\pi\)
\(720\) 0 0
\(721\) −1631.33 1046.53i −0.0842632 0.0540564i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4367.93 + 7565.48i 0.223753 + 0.387551i
\(726\) 0 0
\(727\) 23158.7 1.18144 0.590722 0.806875i \(-0.298843\pi\)
0.590722 + 0.806875i \(0.298843\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9486.94 + 16431.9i 0.480010 + 0.831402i
\(732\) 0 0
\(733\) 13814.6 23927.6i 0.696116 1.20571i −0.273686 0.961819i \(-0.588243\pi\)
0.969803 0.243890i \(-0.0784236\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22737.0 39381.6i 1.13640 1.96830i
\(738\) 0 0
\(739\) 4730.82 + 8194.03i 0.235489 + 0.407879i 0.959415 0.281999i \(-0.0909976\pi\)
−0.723926 + 0.689878i \(0.757664\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14316.9 0.706913 0.353457 0.935451i \(-0.385006\pi\)
0.353457 + 0.935451i \(0.385006\pi\)
\(744\) 0 0
\(745\) −25.3762 43.9529i −0.00124794 0.00216149i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8007.73 + 5137.10i 0.390649 + 0.250608i
\(750\) 0 0
\(751\) 3743.03 6483.13i 0.181871 0.315010i −0.760647 0.649166i \(-0.775118\pi\)
0.942518 + 0.334156i \(0.108451\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 401.744 0.0193655
\(756\) 0 0
\(757\) −17416.8 −0.836227 −0.418114 0.908395i \(-0.637309\pi\)
−0.418114 + 0.908395i \(0.637309\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16615.5 + 28778.9i −0.791474 + 1.37087i 0.133580 + 0.991038i \(0.457353\pi\)
−0.925054 + 0.379835i \(0.875981\pi\)
\(762\) 0 0
\(763\) 16043.9 8287.62i 0.761240 0.393227i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1337.22 + 2316.13i 0.0629521 + 0.109036i
\(768\) 0 0
\(769\) 13714.2 0.643103 0.321552 0.946892i \(-0.395796\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7604.65 + 13171.6i 0.353842 + 0.612873i 0.986919 0.161216i \(-0.0515416\pi\)
−0.633077 + 0.774089i \(0.718208\pi\)
\(774\) 0 0
\(775\) 20425.2 35377.5i 0.946704 1.63974i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 13545.6 23461.6i 0.623004 1.07907i
\(780\) 0 0
\(781\) 6510.79 + 11277.0i 0.298303 + 0.516675i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 463.019 0.0210520
\(786\) 0 0
\(787\) 6610.74 + 11450.1i 0.299425 + 0.518619i 0.976004 0.217750i \(-0.0698719\pi\)
−0.676580 + 0.736369i \(0.736539\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1668.47 35632.3i 0.0749989 1.60169i
\(792\) 0 0
\(793\) −2715.73 + 4703.79i −0.121612 + 0.210639i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13373.9 −0.594387 −0.297194 0.954817i \(-0.596051\pi\)
−0.297194 + 0.954817i \(0.596051\pi\)
\(798\) 0 0
\(799\) 47346.6 2.09637
\(800\) 0 0
\(801\) 0 0