Properties

Label 504.4.s.j.361.2
Level $504$
Weight $4$
Character 504.361
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 361.2
Root \(2.57353i\) of defining polynomial
Character \(\chi\) \(=\) 504.361
Dual form 504.4.s.j.289.2

$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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 0.868886 0.495011i \(-0.164836\pi\)
−0.863136 + 0.504972i \(0.831503\pi\)
\(6\) 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 −0.212257 0.977214i \(-0.568081\pi\)
0.952421 0.304787i \(-0.0985852\pi\)
\(12\) 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 −0.168666 + 0.985673i \(0.553946\pi\)
−0.769285 + 0.638906i \(0.779387\pi\)
\(18\) 0 0
\(19\) −45.7547 79.2495i −0.552466 0.956899i −0.998096 0.0616814i \(-0.980354\pi\)
0.445630 0.895217i \(-0.352980\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 89.7436 + 155.441i 0.813602 + 1.40920i 0.910328 + 0.413888i \(0.135830\pi\)
−0.0967260 + 0.995311i \(0.530837\pi\)
\(24\) 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 −0.194783 + 0.980846i \(0.562400\pi\)
−0.752046 + 0.659110i \(0.770933\pi\)
\(32\) 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 −0.977832 0.209391i \(-0.932852\pi\)
0.307578 0.951523i \(-0.400481\pi\)
\(38\) 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 −0.997600 0.0692409i \(-0.977942\pi\)
0.438836 0.898567i \(-0.355391\pi\)
\(48\) 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 −0.864834 0.502058i \(-0.832576\pi\)
0.867212 + 0.497939i \(0.165910\pi\)
\(54\) 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 −0.893899 0.448268i \(-0.852041\pi\)
0.835161 + 0.550005i \(0.185374\pi\)
\(60\) 0 0
\(61\) 54.0605 + 93.6356i 0.113471 + 0.196538i 0.917168 0.398502i \(-0.130470\pi\)
−0.803696 + 0.595040i \(0.797136\pi\)
\(62\) 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 0.171156 + 0.985244i \(0.445250\pi\)
−0.938824 + 0.344396i \(0.888084\pi\)
\(68\) 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 −0.771056 0.636767i \(-0.780271\pi\)
0.936985 + 0.349370i \(0.113605\pi\)
\(74\) 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 0.594832 0.803850i \(-0.297219\pi\)
−0.993571 + 0.113215i \(0.963885\pi\)
\(80\) 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 0.703282 0.710911i \(-0.251717\pi\)
−0.967308 + 0.253604i \(0.918384\pi\)
\(90\) 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 −0.622617 0.782526i \(-0.713931\pi\)
0.988996 + 0.147939i \(0.0472640\pi\)
\(102\) 0 0
\(103\) −52.3253 90.6300i −0.0500559 0.0866994i 0.839912 0.542723i \(-0.182607\pi\)
−0.889968 + 0.456024i \(0.849273\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 256.850 + 444.878i 0.232062 + 0.401943i 0.958415 0.285379i \(-0.0921194\pi\)
−0.726353 + 0.687322i \(0.758786\pi\)
\(108\) 0 0
\(109\) −487.519 + 844.408i −0.428402 + 0.742015i −0.996731 0.0807868i \(-0.974257\pi\)
0.568329 + 0.822801i \(0.307590\pi\)
\(110\) 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 0.999997 0.00235541i \(-0.000749751\pi\)
−0.502038 + 0.864845i \(0.667416\pi\)
\(132\) 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 −0.543233 0.839582i \(-0.682800\pi\)
0.998716 + 0.0506627i \(0.0161334\pi\)
\(138\) 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 0.915163 0.403083i \(-0.132061\pi\)
−0.806662 + 0.591013i \(0.798728\pi\)
\(150\) 0 0
\(151\) 1562.10 2705.64i 0.841867 1.45816i −0.0464473 0.998921i \(-0.514790\pi\)
0.888314 0.459236i \(-0.151877\pi\)
\(152\) 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 0.108551 0.994091i \(-0.465379\pi\)
0.806633 0.591053i \(-0.201288\pi\)
\(158\) 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 0.525280 0.850930i \(-0.323961\pi\)
−0.999567 + 0.0294409i \(0.990627\pi\)
\(164\) 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 0.834271 0.551355i \(-0.185889\pi\)
−0.894623 + 0.446823i \(0.852555\pi\)
\(174\) 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 −0.802339 0.596869i \(-0.796411\pi\)
0.918073 + 0.396412i \(0.129745\pi\)
\(180\) 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 0.786777 + 0.617237i \(0.211748\pi\)
0.141155 + 0.989988i \(0.454918\pi\)
\(192\) 0 0
\(193\) −1570.13 + 2719.55i −0.585598 + 1.01429i 0.409202 + 0.912444i \(0.365807\pi\)
−0.994801 + 0.101842i \(0.967526\pi\)
\(194\) 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 −0.737363 0.675497i \(-0.763929\pi\)
0.953679 + 0.300827i \(0.0972626\pi\)
\(200\) 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 −0.682879 0.730532i \(-0.739272\pi\)
0.974098 + 0.226124i \(0.0726056\pi\)
\(228\) 0 0
\(229\) −351.738 609.228i −0.101500 0.175803i 0.810803 0.585319i \(-0.199031\pi\)
−0.912303 + 0.409516i \(0.865698\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 480.892 + 832.929i 0.135211 + 0.234193i 0.925678 0.378312i \(-0.123495\pi\)
−0.790467 + 0.612505i \(0.790162\pi\)
\(234\) 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 −0.835471 0.549535i \(-0.814805\pi\)
0.893647 + 0.448771i \(0.148138\pi\)
\(242\) 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 0.831620 0.555344i \(-0.187414\pi\)
−0.896753 + 0.442532i \(0.854080\pi\)
\(258\) 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 −0.843403 0.537282i \(-0.819451\pi\)
0.887001 + 0.461767i \(0.152784\pi\)
\(264\) 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 0.489308 + 0.872111i \(0.337249\pi\)
−0.999924 + 0.0123024i \(0.996084\pi\)
\(270\) 0 0
\(271\) 198.058 + 343.046i 0.0443954 + 0.0768951i 0.887369 0.461059i \(-0.152531\pi\)
−0.842974 + 0.537955i \(0.819197\pi\)
\(272\) 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 −0.260457 0.965486i \(-0.583873\pi\)
0.966363 0.257181i \(-0.0827935\pi\)
\(278\) 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 −0.866058 0.499944i \(-0.833354\pi\)
0.865993 + 0.500056i \(0.166687\pi\)
\(284\) 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 −0.524833 0.851206i \(-0.675872\pi\)
0.999582 + 0.0289155i \(0.00920538\pi\)
\(312\) 0 0
\(313\) 1995.86 + 3456.92i 0.360423 + 0.624271i 0.988030 0.154259i \(-0.0492990\pi\)
−0.627607 + 0.778530i \(0.715966\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 902.519 + 1563.21i 0.159907 + 0.276967i 0.934835 0.355083i \(-0.115547\pi\)
−0.774928 + 0.632050i \(0.782214\pi\)
\(318\) 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 −0.996212 0.0869547i \(-0.972286\pi\)
0.422801 0.906222i \(-0.361047\pi\)
\(332\) 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 0.390117 + 0.920765i \(0.372434\pi\)
−0.992465 + 0.122531i \(0.960899\pi\)
\(348\) 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 −0.965341 0.260992i \(-0.915950\pi\)
0.708696 + 0.705514i \(0.249284\pi\)
\(354\) 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 0.981448 0.191727i \(-0.0614088\pi\)
−0.656764 + 0.754096i \(0.728075\pi\)
\(360\) 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 −0.627097 0.778941i \(-0.715757\pi\)
0.988131 + 0.153612i \(0.0490905\pi\)
\(368\) 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 0.999661 0.0260264i \(-0.00828540\pi\)
−0.522370 + 0.852719i \(0.674952\pi\)
\(374\) 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 −0.999896 0.0144017i \(-0.995416\pi\)
0.487476 0.873136i \(-0.337918\pi\)
\(384\) 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 −0.435032 0.900415i \(-0.643263\pi\)
0.997298 0.0734585i \(-0.0234036\pi\)
\(390\) 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 0.625832 0.779957i \(-0.284759\pi\)
−0.988379 + 0.152008i \(0.951426\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3608.89 6250.79i −0.449425 0.778427i 0.548923 0.835873i \(-0.315038\pi\)
−0.998349 + 0.0574453i \(0.981705\pi\)
\(402\) 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 −0.329367 0.944202i \(-0.606835\pi\)
0.982386 0.186861i \(-0.0598313\pi\)
\(410\) 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 −0.693973 0.720001i \(-0.744141\pi\)
0.970526 + 0.240997i \(0.0774745\pi\)
\(432\) 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 0.965151 0.261692i \(-0.0842805\pi\)
−0.709208 + 0.705000i \(0.750947\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −850.218 1472.62i −0.0911852 0.157937i 0.816825 0.576886i \(-0.195732\pi\)
−0.908010 + 0.418948i \(0.862399\pi\)
\(444\) 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 0.997272 + 0.0738128i \(0.0235167\pi\)
−0.434712 + 0.900569i \(0.643150\pi\)
\(458\) 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 0.912751 0.408515i \(-0.133953\pi\)
−0.810160 + 0.586208i \(0.800620\pi\)
\(468\) 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 −0.870257 0.492597i \(-0.836048\pi\)
0.861730 + 0.507366i \(0.169381\pi\)
\(480\) 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 −0.164223 0.986423i \(-0.552512\pi\)
0.936379 0.350991i \(-0.114155\pi\)
\(488\) 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 0.842097 0.539325i \(-0.181321\pi\)
−0.888118 + 0.459615i \(0.847987\pi\)
\(500\) 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 0.705297 0.708912i \(-0.250814\pi\)
−0.966584 + 0.256349i \(0.917480\pi\)
\(510\) 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 −0.750278 0.661122i \(-0.770080\pi\)
0.947688 + 0.319199i \(0.103414\pi\)
\(522\) 0 0
\(523\) −385.884 668.370i −0.0322629 0.0558810i 0.849443 0.527680i \(-0.176938\pi\)
−0.881706 + 0.471799i \(0.843605\pi\)
\(524\) 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 0.790888 0.611961i \(-0.209619\pi\)
−0.925418 + 0.378949i \(0.876286\pi\)
\(542\) 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 0.169736 + 0.985490i \(0.445709\pi\)
−0.938327 + 0.345749i \(0.887625\pi\)
\(558\) 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 −0.997501 0.0706574i \(-0.977490\pi\)
0.559941 + 0.828532i \(0.310824\pi\)
\(564\) 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 −0.980491 0.196562i \(-0.937022\pi\)
0.320018 0.947411i \(-0.396311\pi\)
\(570\) 0 0
\(571\) 7836.84 13573.8i 0.574364 0.994827i −0.421747 0.906714i \(-0.638583\pi\)
0.996110 0.0881136i \(-0.0280838\pi\)
\(572\) 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 −0.507431 0.861692i \(-0.669405\pi\)
0.999963 + 0.00860205i \(0.00273815\pi\)
\(578\) 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 0.956080 + 0.293105i \(0.0946886\pi\)
−0.224204 + 0.974542i \(0.571978\pi\)
\(594\) 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 −0.660837 0.750529i \(-0.729799\pi\)
0.980396 + 0.197037i \(0.0631321\pi\)
\(600\) 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 0.948438 0.316962i \(-0.102663\pi\)
−0.748716 + 0.662891i \(0.769329\pi\)
\(608\) 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 −0.168856 0.985641i \(-0.554007\pi\)
0.938018 0.346586i \(-0.112659\pi\)
\(614\) 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 −0.813672 0.581324i \(-0.802535\pi\)
0.910278 + 0.413998i \(0.135868\pi\)
\(620\) 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 −0.551601 0.834108i \(-0.685983\pi\)
0.998159 + 0.0606460i \(0.0193161\pi\)
\(642\) 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 −0.957798 0.287443i \(-0.907195\pi\)
0.727832 + 0.685755i \(0.240528\pi\)
\(648\) 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 0.578184 0.815906i \(-0.303762\pi\)
−0.995688 + 0.0927688i \(0.970428\pi\)
\(654\) 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 −0.513380 0.858161i \(-0.671607\pi\)
0.999880 + 0.0155194i \(0.00494019\pi\)
\(662\) 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 0.949687 + 0.313201i \(0.101401\pi\)
−0.203604 + 0.979053i \(0.565265\pi\)
\(678\) 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 −0.754982 0.655746i \(-0.772354\pi\)
0.945383 + 0.325961i \(0.105688\pi\)
\(684\) 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 −0.940720 0.339185i \(-0.889849\pi\)
0.176617 0.984280i \(-0.443485\pi\)
\(692\) 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 0.996995 0.0774687i \(-0.0246838\pi\)
−0.565587 + 0.824688i \(0.691350\pi\)
\(710\) 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 0.818687 0.574240i \(-0.194702\pi\)
−0.906650 + 0.421884i \(0.861369\pi\)
\(720\) 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 0.969803 + 0.243890i \(0.0784236\pi\)
−0.273686 + 0.961819i \(0.588243\pi\)
\(734\) 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 −0.723926 0.689878i \(-0.757664\pi\)
0.959415 + 0.281999i \(0.0909976\pi\)
\(740\) 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 0.942518 0.334156i \(-0.108451\pi\)
−0.760647 + 0.649166i \(0.775118\pi\)
\(752\) 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 −0.925054 0.379835i \(-0.875981\pi\)
0.133580 0.991038i \(-0.457353\pi\)
\(762\) 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 −0.633077 0.774089i \(-0.718208\pi\)
0.986919 + 0.161216i \(0.0515416\pi\)
\(774\) 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 −0.676580 0.736369i \(-0.736539\pi\)
0.976004 + 0.217750i \(0.0698719\pi\)
\(788\) 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