Properties

Label 1008.4.bt.d.17.17
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.17
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.17

$q$-expansion

\(f(q)\) \(=\) \(q+(3.34783 + 5.79860i) q^{5} +(12.7404 - 13.4418i) q^{7} +O(q^{10})\) \(q+(3.34783 + 5.79860i) q^{5} +(12.7404 - 13.4418i) q^{7} +(28.2958 + 16.3366i) q^{11} -67.9019i q^{13} +(15.3179 - 26.5313i) q^{17} +(21.8820 - 12.6336i) q^{19} +(-68.6216 + 39.6187i) q^{23} +(40.0841 - 69.4277i) q^{25} -109.668i q^{29} +(-238.527 - 137.714i) q^{31} +(120.596 + 28.8753i) q^{35} +(160.221 + 277.511i) q^{37} +184.846 q^{41} -364.766 q^{43} +(25.7730 + 44.6402i) q^{47} +(-18.3666 - 342.508i) q^{49} +(-532.671 - 307.538i) q^{53} +218.769i q^{55} +(207.843 - 359.995i) q^{59} +(411.761 - 237.730i) q^{61} +(393.736 - 227.324i) q^{65} +(-142.188 + 246.277i) q^{67} +965.404i q^{71} +(225.387 + 130.127i) q^{73} +(580.093 - 172.214i) q^{77} +(-219.163 - 379.602i) q^{79} +76.4726 q^{83} +205.126 q^{85} +(-356.559 - 617.579i) q^{89} +(-912.728 - 865.095i) q^{91} +(146.514 + 84.5900i) q^{95} -410.607i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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
\(5\) 3.34783 + 5.79860i 0.299439 + 0.518643i 0.976008 0.217736i \(-0.0698673\pi\)
−0.676569 + 0.736379i \(0.736534\pi\)
\(6\) 0 0
\(7\) 12.7404 13.4418i 0.687915 0.725792i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 28.2958 + 16.3366i 0.775593 + 0.447789i 0.834866 0.550453i \(-0.185545\pi\)
−0.0592734 + 0.998242i \(0.518878\pi\)
\(12\) 0 0
\(13\) 67.9019i 1.44866i −0.689452 0.724331i \(-0.742149\pi\)
0.689452 0.724331i \(-0.257851\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 15.3179 26.5313i 0.218537 0.378517i −0.735824 0.677173i \(-0.763205\pi\)
0.954361 + 0.298656i \(0.0965383\pi\)
\(18\) 0 0
\(19\) 21.8820 12.6336i 0.264215 0.152544i −0.362041 0.932162i \(-0.617920\pi\)
0.626256 + 0.779618i \(0.284587\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −68.6216 + 39.6187i −0.622113 + 0.359177i −0.777691 0.628647i \(-0.783609\pi\)
0.155578 + 0.987824i \(0.450276\pi\)
\(24\) 0 0
\(25\) 40.0841 69.4277i 0.320673 0.555422i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 109.668i 0.702236i −0.936331 0.351118i \(-0.885802\pi\)
0.936331 0.351118i \(-0.114198\pi\)
\(30\) 0 0
\(31\) −238.527 137.714i −1.38196 0.797875i −0.389568 0.920998i \(-0.627376\pi\)
−0.992391 + 0.123123i \(0.960709\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 120.596 + 28.8753i 0.582415 + 0.139452i
\(36\) 0 0
\(37\) 160.221 + 277.511i 0.711898 + 1.23304i 0.964144 + 0.265380i \(0.0854975\pi\)
−0.252246 + 0.967663i \(0.581169\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 184.846 0.704100 0.352050 0.935981i \(-0.385485\pi\)
0.352050 + 0.935981i \(0.385485\pi\)
\(42\) 0 0
\(43\) −364.766 −1.29363 −0.646817 0.762645i \(-0.723900\pi\)
−0.646817 + 0.762645i \(0.723900\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 25.7730 + 44.6402i 0.0799868 + 0.138541i 0.903244 0.429127i \(-0.141179\pi\)
−0.823257 + 0.567669i \(0.807846\pi\)
\(48\) 0 0
\(49\) −18.3666 342.508i −0.0535471 0.998565i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −532.671 307.538i −1.38053 0.797048i −0.388306 0.921531i \(-0.626940\pi\)
−0.992222 + 0.124483i \(0.960273\pi\)
\(54\) 0 0
\(55\) 218.769i 0.536341i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 207.843 359.995i 0.458625 0.794362i −0.540263 0.841496i \(-0.681675\pi\)
0.998889 + 0.0471340i \(0.0150088\pi\)
\(60\) 0 0
\(61\) 411.761 237.730i 0.864271 0.498987i −0.00116918 0.999999i \(-0.500372\pi\)
0.865440 + 0.501012i \(0.167039\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 393.736 227.324i 0.751338 0.433785i
\(66\) 0 0
\(67\) −142.188 + 246.277i −0.259269 + 0.449068i −0.966046 0.258369i \(-0.916815\pi\)
0.706777 + 0.707436i \(0.250148\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 965.404i 1.61370i 0.590759 + 0.806848i \(0.298828\pi\)
−0.590759 + 0.806848i \(0.701172\pi\)
\(72\) 0 0
\(73\) 225.387 + 130.127i 0.361364 + 0.208633i 0.669679 0.742651i \(-0.266432\pi\)
−0.308315 + 0.951284i \(0.599765\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 580.093 172.214i 0.858543 0.254878i
\(78\) 0 0
\(79\) −219.163 379.602i −0.312124 0.540615i 0.666698 0.745328i \(-0.267707\pi\)
−0.978822 + 0.204713i \(0.934374\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 76.4726 0.101132 0.0505660 0.998721i \(-0.483897\pi\)
0.0505660 + 0.998721i \(0.483897\pi\)
\(84\) 0 0
\(85\) 205.126 0.261753
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −356.559 617.579i −0.424665 0.735542i 0.571724 0.820446i \(-0.306275\pi\)
−0.996389 + 0.0849045i \(0.972941\pi\)
\(90\) 0 0
\(91\) −912.728 865.095i −1.05143 0.996556i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 146.514 + 84.5900i 0.158232 + 0.0913553i
\(96\) 0 0
\(97\) 410.607i 0.429803i −0.976636 0.214901i \(-0.931057\pi\)
0.976636 0.214901i \(-0.0689430\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 953.656 1651.78i 0.939527 1.62731i 0.173173 0.984891i \(-0.444598\pi\)
0.766355 0.642418i \(-0.222069\pi\)
\(102\) 0 0
\(103\) −1177.37 + 679.756i −1.12631 + 0.650276i −0.943004 0.332780i \(-0.892013\pi\)
−0.183306 + 0.983056i \(0.558680\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1555.77 898.226i 1.40563 0.811540i 0.410666 0.911786i \(-0.365296\pi\)
0.994963 + 0.100246i \(0.0319629\pi\)
\(108\) 0 0
\(109\) 42.0727 72.8720i 0.0369709 0.0640355i −0.846948 0.531676i \(-0.821562\pi\)
0.883919 + 0.467640i \(0.154896\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 117.441i 0.0977688i −0.998804 0.0488844i \(-0.984433\pi\)
0.998804 0.0488844i \(-0.0155666\pi\)
\(114\) 0 0
\(115\) −459.466 265.273i −0.372569 0.215103i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −161.475 543.918i −0.124390 0.418999i
\(120\) 0 0
\(121\) −131.730 228.163i −0.0989707 0.171422i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1373.74 0.982965
\(126\) 0 0
\(127\) 510.925 0.356986 0.178493 0.983941i \(-0.442878\pi\)
0.178493 + 0.983941i \(0.442878\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 991.274 + 1716.94i 0.661130 + 1.14511i 0.980319 + 0.197419i \(0.0632560\pi\)
−0.319189 + 0.947691i \(0.603411\pi\)
\(132\) 0 0
\(133\) 108.966 455.091i 0.0710416 0.296702i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 857.943 + 495.334i 0.535029 + 0.308899i 0.743062 0.669223i \(-0.233373\pi\)
−0.208033 + 0.978122i \(0.566706\pi\)
\(138\) 0 0
\(139\) 369.921i 0.225729i −0.993610 0.112864i \(-0.963997\pi\)
0.993610 0.112864i \(-0.0360026\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1109.29 1921.34i 0.648694 1.12357i
\(144\) 0 0
\(145\) 635.922 367.149i 0.364210 0.210277i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1054.73 608.947i 0.579910 0.334811i −0.181188 0.983449i \(-0.557994\pi\)
0.761098 + 0.648637i \(0.224661\pi\)
\(150\) 0 0
\(151\) 764.206 1323.64i 0.411856 0.713355i −0.583237 0.812302i \(-0.698214\pi\)
0.995093 + 0.0989470i \(0.0315474\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1844.17i 0.955658i
\(156\) 0 0
\(157\) −2610.74 1507.31i −1.32713 0.766220i −0.342277 0.939599i \(-0.611198\pi\)
−0.984855 + 0.173379i \(0.944531\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −341.715 + 1427.16i −0.167273 + 0.698607i
\(162\) 0 0
\(163\) −822.212 1424.11i −0.395096 0.684326i 0.598018 0.801483i \(-0.295955\pi\)
−0.993113 + 0.117157i \(0.962622\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2783.64 1.28985 0.644923 0.764248i \(-0.276889\pi\)
0.644923 + 0.764248i \(0.276889\pi\)
\(168\) 0 0
\(169\) −2413.67 −1.09862
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 64.1081 + 111.038i 0.0281737 + 0.0487983i 0.879768 0.475402i \(-0.157698\pi\)
−0.851595 + 0.524201i \(0.824364\pi\)
\(174\) 0 0
\(175\) −422.551 1423.34i −0.182525 0.614825i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1676.79 968.093i −0.700161 0.404238i 0.107246 0.994233i \(-0.465797\pi\)
−0.807408 + 0.589994i \(0.799130\pi\)
\(180\) 0 0
\(181\) 1596.97i 0.655810i −0.944711 0.327905i \(-0.893657\pi\)
0.944711 0.327905i \(-0.106343\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1072.79 + 1858.12i −0.426340 + 0.738442i
\(186\) 0 0
\(187\) 866.863 500.484i 0.338991 0.195717i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −715.285 + 412.970i −0.270975 + 0.156448i −0.629331 0.777138i \(-0.716671\pi\)
0.358356 + 0.933585i \(0.383338\pi\)
\(192\) 0 0
\(193\) 927.072 1605.74i 0.345762 0.598878i −0.639730 0.768600i \(-0.720954\pi\)
0.985492 + 0.169722i \(0.0542870\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2938.42i 1.06271i −0.847150 0.531355i \(-0.821683\pi\)
0.847150 0.531355i \(-0.178317\pi\)
\(198\) 0 0
\(199\) 2850.16 + 1645.54i 1.01529 + 0.586178i 0.912736 0.408550i \(-0.133965\pi\)
0.102554 + 0.994727i \(0.467299\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1474.14 1397.21i −0.509677 0.483078i
\(204\) 0 0
\(205\) 618.833 + 1071.85i 0.210835 + 0.365177i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 825.560 0.273230
\(210\) 0 0
\(211\) 1133.21 0.369733 0.184867 0.982764i \(-0.440815\pi\)
0.184867 + 0.982764i \(0.440815\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1221.17 2115.13i −0.387364 0.670934i
\(216\) 0 0
\(217\) −4890.05 + 1451.72i −1.52976 + 0.454145i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1801.53 1040.11i −0.548343 0.316586i
\(222\) 0 0
\(223\) 1631.23i 0.489845i −0.969543 0.244922i \(-0.921238\pi\)
0.969543 0.244922i \(-0.0787624\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −584.886 + 1013.05i −0.171014 + 0.296205i −0.938775 0.344532i \(-0.888038\pi\)
0.767760 + 0.640737i \(0.221371\pi\)
\(228\) 0 0
\(229\) −4457.87 + 2573.75i −1.28640 + 0.742701i −0.978009 0.208561i \(-0.933122\pi\)
−0.308386 + 0.951261i \(0.599789\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3811.38 2200.50i 1.07164 0.618710i 0.143009 0.989721i \(-0.454322\pi\)
0.928629 + 0.371011i \(0.120989\pi\)
\(234\) 0 0
\(235\) −172.567 + 298.895i −0.0479023 + 0.0829692i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5998.62i 1.62351i −0.583998 0.811755i \(-0.698513\pi\)
0.583998 0.811755i \(-0.301487\pi\)
\(240\) 0 0
\(241\) 796.548 + 459.887i 0.212905 + 0.122921i 0.602661 0.797997i \(-0.294107\pi\)
−0.389756 + 0.920918i \(0.627441\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1924.58 1253.16i 0.501865 0.326781i
\(246\) 0 0
\(247\) −857.845 1485.83i −0.220985 0.382758i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 701.991 0.176531 0.0882655 0.996097i \(-0.471868\pi\)
0.0882655 + 0.996097i \(0.471868\pi\)
\(252\) 0 0
\(253\) −2588.94 −0.643341
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2170.80 + 3759.94i 0.526891 + 0.912602i 0.999509 + 0.0313343i \(0.00997565\pi\)
−0.472618 + 0.881267i \(0.656691\pi\)
\(258\) 0 0
\(259\) 5771.54 + 1381.92i 1.38466 + 0.331539i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3606.74 + 2082.35i 0.845632 + 0.488226i 0.859175 0.511683i \(-0.170978\pi\)
−0.0135429 + 0.999908i \(0.504311\pi\)
\(264\) 0 0
\(265\) 4118.33i 0.954668i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4219.12 + 7307.74i −0.956299 + 1.65636i −0.224933 + 0.974374i \(0.572216\pi\)
−0.731366 + 0.681985i \(0.761117\pi\)
\(270\) 0 0
\(271\) −4544.68 + 2623.87i −1.01871 + 0.588150i −0.913729 0.406324i \(-0.866810\pi\)
−0.104977 + 0.994475i \(0.533477\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2268.43 1309.68i 0.497423 0.287187i
\(276\) 0 0
\(277\) 198.173 343.245i 0.0429857 0.0744534i −0.843732 0.536765i \(-0.819646\pi\)
0.886718 + 0.462311i \(0.152980\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5244.36i 1.11335i 0.830729 + 0.556677i \(0.187924\pi\)
−0.830729 + 0.556677i \(0.812076\pi\)
\(282\) 0 0
\(283\) 4113.33 + 2374.83i 0.864000 + 0.498830i 0.865350 0.501169i \(-0.167096\pi\)
−0.00134996 + 0.999999i \(0.500430\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2355.01 2484.67i 0.484361 0.511030i
\(288\) 0 0
\(289\) 1987.23 + 3441.98i 0.404483 + 0.700586i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3597.22 −0.717242 −0.358621 0.933483i \(-0.616753\pi\)
−0.358621 + 0.933483i \(0.616753\pi\)
\(294\) 0 0
\(295\) 2783.29 0.549320
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2690.19 + 4659.54i 0.520326 + 0.901231i
\(300\) 0 0
\(301\) −4647.25 + 4903.13i −0.889910 + 0.938909i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2757.00 + 1591.76i 0.517592 + 0.298832i
\(306\) 0 0
\(307\) 27.5911i 0.00512933i −0.999997 0.00256467i \(-0.999184\pi\)
0.999997 0.00256467i \(-0.000816359\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −621.896 + 1077.15i −0.113391 + 0.196398i −0.917135 0.398576i \(-0.869504\pi\)
0.803745 + 0.594974i \(0.202838\pi\)
\(312\) 0 0
\(313\) 7541.55 4354.12i 1.36190 0.786292i 0.372021 0.928224i \(-0.378665\pi\)
0.989876 + 0.141933i \(0.0453317\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7799.09 4502.81i 1.38183 0.797801i 0.389455 0.921046i \(-0.372663\pi\)
0.992376 + 0.123245i \(0.0393301\pi\)
\(318\) 0 0
\(319\) 1791.60 3103.15i 0.314453 0.544649i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 774.077i 0.133346i
\(324\) 0 0
\(325\) −4714.28 2721.79i −0.804619 0.464547i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 928.404 + 222.295i 0.155576 + 0.0372508i
\(330\) 0 0
\(331\) −1194.18 2068.38i −0.198302 0.343470i 0.749676 0.661805i \(-0.230209\pi\)
−0.947978 + 0.318336i \(0.896876\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1904.08 −0.310541
\(336\) 0 0
\(337\) 11637.2 1.88106 0.940531 0.339707i \(-0.110328\pi\)
0.940531 + 0.339707i \(0.110328\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4499.55 7793.45i −0.714558 1.23765i
\(342\) 0 0
\(343\) −4837.94 4116.79i −0.761586 0.648064i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2539.63 1466.26i −0.392895 0.226838i 0.290519 0.956869i \(-0.406172\pi\)
−0.683414 + 0.730031i \(0.739506\pi\)
\(348\) 0 0
\(349\) 63.0106i 0.00966442i 0.999988 + 0.00483221i \(0.00153815\pi\)
−0.999988 + 0.00483221i \(0.998462\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −386.737 + 669.848i −0.0583114 + 0.100998i −0.893708 0.448650i \(-0.851905\pi\)
0.835396 + 0.549648i \(0.185238\pi\)
\(354\) 0 0
\(355\) −5598.00 + 3232.00i −0.836932 + 0.483203i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10567.3 + 6101.03i −1.55354 + 0.896936i −0.555689 + 0.831390i \(0.687546\pi\)
−0.997850 + 0.0655458i \(0.979121\pi\)
\(360\) 0 0
\(361\) −3110.29 + 5387.17i −0.453460 + 0.785417i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1742.57i 0.249892i
\(366\) 0 0
\(367\) 4835.15 + 2791.58i 0.687719 + 0.397055i 0.802757 0.596306i \(-0.203366\pi\)
−0.115038 + 0.993361i \(0.536699\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −10920.3 + 3241.94i −1.52818 + 0.453674i
\(372\) 0 0
\(373\) 1656.22 + 2868.66i 0.229909 + 0.398213i 0.957781 0.287499i \(-0.0928240\pi\)
−0.727872 + 0.685713i \(0.759491\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7446.67 −1.01730
\(378\) 0 0
\(379\) 1118.64 0.151611 0.0758057 0.997123i \(-0.475847\pi\)
0.0758057 + 0.997123i \(0.475847\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4388.43 + 7600.98i 0.585479 + 1.01408i 0.994816 + 0.101695i \(0.0324267\pi\)
−0.409337 + 0.912383i \(0.634240\pi\)
\(384\) 0 0
\(385\) 2940.65 + 2787.19i 0.389272 + 0.368957i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8285.22 4783.47i −1.07989 0.623475i −0.149023 0.988834i \(-0.547613\pi\)
−0.930867 + 0.365359i \(0.880946\pi\)
\(390\) 0 0
\(391\) 2427.49i 0.313973i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1467.44 2541.68i 0.186924 0.323762i
\(396\) 0 0
\(397\) 8470.20 4890.27i 1.07080 0.618226i 0.142399 0.989809i \(-0.454518\pi\)
0.928399 + 0.371584i \(0.121185\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10450.1 + 6033.35i −1.30137 + 0.751349i −0.980640 0.195820i \(-0.937263\pi\)
−0.320735 + 0.947169i \(0.603930\pi\)
\(402\) 0 0
\(403\) −9351.03 + 16196.5i −1.15585 + 2.00199i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10469.9i 1.27512i
\(408\) 0 0
\(409\) 6194.67 + 3576.49i 0.748916 + 0.432387i 0.825302 0.564691i \(-0.191005\pi\)
−0.0763859 + 0.997078i \(0.524338\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2191.00 7380.26i −0.261046 0.879319i
\(414\) 0 0
\(415\) 256.017 + 443.434i 0.0302828 + 0.0524514i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5703.45 0.664992 0.332496 0.943105i \(-0.392109\pi\)
0.332496 + 0.943105i \(0.392109\pi\)
\(420\) 0 0
\(421\) −10027.7 −1.16086 −0.580428 0.814312i \(-0.697115\pi\)
−0.580428 + 0.814312i \(0.697115\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1228.01 2126.97i −0.140158 0.242760i
\(426\) 0 0
\(427\) 2050.44 8563.59i 0.232384 0.970541i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12128.8 7002.59i −1.35551 0.782605i −0.366497 0.930419i \(-0.619443\pi\)
−0.989015 + 0.147814i \(0.952776\pi\)
\(432\) 0 0
\(433\) 3410.83i 0.378554i −0.981924 0.189277i \(-0.939386\pi\)
0.981924 0.189277i \(-0.0606145\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1001.05 + 1733.87i −0.109581 + 0.189800i
\(438\) 0 0
\(439\) −11009.7 + 6356.44i −1.19695 + 0.691062i −0.959875 0.280428i \(-0.909524\pi\)
−0.237080 + 0.971490i \(0.576190\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10853.8 + 6266.44i −1.16406 + 0.672071i −0.952274 0.305245i \(-0.901262\pi\)
−0.211787 + 0.977316i \(0.567928\pi\)
\(444\) 0 0
\(445\) 2387.40 4135.09i 0.254322 0.440499i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10884.1i 1.14399i 0.820258 + 0.571993i \(0.193830\pi\)
−0.820258 + 0.571993i \(0.806170\pi\)
\(450\) 0 0
\(451\) 5230.38 + 3019.76i 0.546095 + 0.315288i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1960.69 8188.73i 0.202019 0.843722i
\(456\) 0 0
\(457\) 9222.57 + 15974.0i 0.944012 + 1.63508i 0.757717 + 0.652583i \(0.226315\pi\)
0.186295 + 0.982494i \(0.440352\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4657.01 0.470496 0.235248 0.971935i \(-0.424410\pi\)
0.235248 + 0.971935i \(0.424410\pi\)
\(462\) 0 0
\(463\) 5088.08 0.510720 0.255360 0.966846i \(-0.417806\pi\)
0.255360 + 0.966846i \(0.417806\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7950.04 + 13769.9i 0.787760 + 1.36444i 0.927336 + 0.374229i \(0.122092\pi\)
−0.139577 + 0.990211i \(0.544574\pi\)
\(468\) 0 0
\(469\) 1498.89 + 5048.93i 0.147574 + 0.497096i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10321.4 5959.04i −1.00333 0.579275i
\(474\) 0 0
\(475\) 2025.62i 0.195667i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9702.00 + 16804.4i −0.925461 + 1.60295i −0.134643 + 0.990894i \(0.542989\pi\)
−0.790818 + 0.612051i \(0.790345\pi\)
\(480\) 0 0
\(481\) 18843.6 10879.3i 1.78626 1.03130i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2380.95 1374.64i 0.222914 0.128700i
\(486\) 0 0
\(487\) −6123.60 + 10606.4i −0.569788 + 0.986903i 0.426798 + 0.904347i \(0.359642\pi\)
−0.996586 + 0.0825556i \(0.973692\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7773.35i 0.714473i 0.934014 + 0.357237i \(0.116281\pi\)
−0.934014 + 0.357237i \(0.883719\pi\)
\(492\) 0 0
\(493\) −2909.64 1679.88i −0.265808 0.153464i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12976.8 + 12299.6i 1.17121 + 1.11008i
\(498\) 0 0
\(499\) −9518.91 16487.2i −0.853958 1.47910i −0.877609 0.479378i \(-0.840862\pi\)
0.0236507 0.999720i \(-0.492471\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14323.9 1.26973 0.634863 0.772624i \(-0.281056\pi\)
0.634863 + 0.772624i \(0.281056\pi\)
\(504\) 0 0
\(505\) 12770.7 1.12532
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4294.66 7438.57i −0.373983 0.647758i 0.616191 0.787597i \(-0.288675\pi\)
−0.990174 + 0.139839i \(0.955342\pi\)
\(510\) 0 0
\(511\) 4620.66 1371.75i 0.400012 0.118753i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7883.28 4551.41i −0.674522 0.389435i
\(516\) 0 0
\(517\) 1684.17i 0.143269i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11308.3 + 19586.6i −0.950917 + 1.64704i −0.207471 + 0.978241i \(0.566523\pi\)
−0.743447 + 0.668795i \(0.766810\pi\)
\(522\) 0 0
\(523\) −122.551 + 70.7547i −0.0102462 + 0.00591566i −0.505114 0.863052i \(-0.668550\pi\)
0.494868 + 0.868968i \(0.335216\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7307.45 + 4218.96i −0.604018 + 0.348730i
\(528\) 0 0
\(529\) −2944.22 + 5099.53i −0.241984 + 0.419128i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12551.4i 1.02000i
\(534\) 0 0
\(535\) 10416.9 + 6014.21i 0.841799 + 0.486013i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5075.72 9991.60i 0.405615 0.798458i
\(540\) 0 0
\(541\) 4655.90 + 8064.25i 0.370005 + 0.640867i 0.989566 0.144081i \(-0.0460227\pi\)
−0.619561 + 0.784949i \(0.712689\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 563.408 0.0442821
\(546\) 0 0
\(547\) −11888.7 −0.929294 −0.464647 0.885496i \(-0.653819\pi\)
−0.464647 + 0.885496i \(0.653819\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1385.50 2399.76i −0.107122 0.185541i
\(552\) 0 0
\(553\) −7894.77 1890.30i −0.607088 0.145360i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18409.4 10628.7i −1.40042 0.808530i −0.405980 0.913882i \(-0.633070\pi\)
−0.994435 + 0.105352i \(0.966403\pi\)
\(558\) 0 0
\(559\) 24768.3i 1.87404i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4661.33 8073.66i 0.348937 0.604377i −0.637124 0.770762i \(-0.719876\pi\)
0.986061 + 0.166385i \(0.0532093\pi\)
\(564\) 0 0
\(565\) 680.991 393.170i 0.0507071 0.0292758i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14734.2 8506.79i 1.08557 0.626754i 0.153176 0.988199i \(-0.451050\pi\)
0.932394 + 0.361445i \(0.117716\pi\)
\(570\) 0 0
\(571\) 1134.69 1965.34i 0.0831617 0.144040i −0.821445 0.570288i \(-0.806832\pi\)
0.904606 + 0.426248i \(0.140165\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6352.32i 0.460713i
\(576\) 0 0
\(577\) 2687.93 + 1551.88i 0.193934 + 0.111968i 0.593823 0.804596i \(-0.297618\pi\)
−0.399889 + 0.916564i \(0.630951\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 974.288 1027.93i 0.0695702 0.0734008i
\(582\) 0 0
\(583\) −10048.2 17404.1i −0.713818 1.23637i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12544.8 −0.882075 −0.441038 0.897489i \(-0.645389\pi\)
−0.441038 + 0.897489i \(0.645389\pi\)
\(588\) 0 0
\(589\) −6959.27 −0.486845
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2644.32 + 4580.09i 0.183118 + 0.317170i 0.942941 0.332960i \(-0.108048\pi\)
−0.759823 + 0.650131i \(0.774714\pi\)
\(594\) 0 0
\(595\) 2613.38 2757.27i 0.180064 0.189978i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5058.01 + 2920.24i 0.345016 + 0.199195i 0.662488 0.749073i \(-0.269501\pi\)
−0.317472 + 0.948268i \(0.602834\pi\)
\(600\) 0 0
\(601\) 10801.2i 0.733098i −0.930399 0.366549i \(-0.880539\pi\)
0.930399 0.366549i \(-0.119461\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 882.018 1527.70i 0.0592713 0.102661i
\(606\) 0 0
\(607\) 21239.7 12262.8i 1.42025 0.819984i 0.423934 0.905693i \(-0.360649\pi\)
0.996320 + 0.0857094i \(0.0273157\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3031.15 1750.04i 0.200699 0.115874i
\(612\) 0 0
\(613\) −8223.34 + 14243.2i −0.541823 + 0.938465i 0.456976 + 0.889479i \(0.348932\pi\)
−0.998799 + 0.0489865i \(0.984401\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 23852.4i 1.55634i 0.628055 + 0.778169i \(0.283851\pi\)
−0.628055 + 0.778169i \(0.716149\pi\)
\(618\) 0 0
\(619\) 14617.4 + 8439.34i 0.949147 + 0.547990i 0.892816 0.450422i \(-0.148726\pi\)
0.0563309 + 0.998412i \(0.482060\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12844.1 3075.36i −0.825983 0.197771i
\(624\) 0 0
\(625\) −411.490 712.722i −0.0263354 0.0456142i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9816.99 0.622304
\(630\) 0 0
\(631\) 19613.0 1.23737 0.618686 0.785638i \(-0.287665\pi\)
0.618686 + 0.785638i \(0.287665\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1710.49 + 2962.65i 0.106895 + 0.185148i
\(636\) 0 0
\(637\) −23257.0 + 1247.13i −1.44658 + 0.0775716i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7437.62 + 4294.11i 0.458297 + 0.264598i 0.711328 0.702860i \(-0.248094\pi\)
−0.253031 + 0.967458i \(0.581427\pi\)
\(642\) 0 0
\(643\) 11966.4i 0.733920i 0.930237 + 0.366960i \(0.119601\pi\)
−0.930237 + 0.366960i \(0.880399\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3663.93 6346.11i 0.222634 0.385613i −0.732973 0.680257i \(-0.761868\pi\)
0.955607 + 0.294645i \(0.0952013\pi\)
\(648\) 0 0
\(649\) 11762.2 6790.91i 0.711412 0.410734i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3124.09 1803.69i 0.187221 0.108092i −0.403460 0.914997i \(-0.632193\pi\)
0.590681 + 0.806905i \(0.298859\pi\)
\(654\) 0 0
\(655\) −6637.22 + 11496.0i −0.395936 + 0.685780i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3244.57i 0.191792i −0.995391 0.0958958i \(-0.969428\pi\)
0.995391 0.0958958i \(-0.0305716\pi\)
\(660\) 0 0
\(661\) −12548.2 7244.69i −0.738377 0.426302i 0.0831019 0.996541i \(-0.473517\pi\)
−0.821479 + 0.570239i \(0.806851\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3003.69 891.715i 0.175155 0.0519989i
\(666\) 0 0
\(667\) 4344.90 + 7525.60i 0.252227 + 0.436870i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15534.8 0.893763
\(672\) 0 0
\(673\) −27609.5 −1.58138 −0.790688 0.612219i \(-0.790277\pi\)
−0.790688 + 0.612219i \(0.790277\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7610.03 13181.0i −0.432019 0.748279i 0.565028 0.825072i \(-0.308865\pi\)
−0.997047 + 0.0767925i \(0.975532\pi\)
\(678\) 0 0
\(679\) −5519.32 5231.28i −0.311947 0.295668i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14491.6 + 8366.71i 0.811866 + 0.468731i 0.847603 0.530630i \(-0.178045\pi\)
−0.0357376 + 0.999361i \(0.511378\pi\)
\(684\) 0 0
\(685\) 6633.16i 0.369986i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −20882.4 + 36169.4i −1.15465 + 1.99992i
\(690\) 0 0
\(691\) −3981.41 + 2298.67i −0.219190 + 0.126549i −0.605575 0.795788i \(-0.707057\pi\)
0.386385 + 0.922337i \(0.373724\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2145.03 1238.43i 0.117073 0.0675920i
\(696\) 0 0
\(697\) 2831.45 4904.21i 0.153872 0.266514i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7621.26i 0.410629i 0.978696 + 0.205315i \(0.0658217\pi\)
−0.978696 + 0.205315i \(0.934178\pi\)
\(702\) 0 0
\(703\) 7011.93 + 4048.34i 0.376188 + 0.217192i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10053.1 33863.2i −0.534773 1.80135i
\(708\) 0 0
\(709\) 3850.25 + 6668.83i 0.203948 + 0.353249i 0.949797 0.312867i \(-0.101289\pi\)
−0.745849 + 0.666115i \(0.767956\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 21824.2 1.14631
\(714\) 0 0
\(715\) 14854.8 0.776977
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5049.89 8746.67i −0.261932 0.453680i 0.704823 0.709383i \(-0.251026\pi\)
−0.966755 + 0.255703i \(0.917693\pi\)
\(720\) 0 0
\(721\) −5862.96 + 24486.4i −0.302841 + 1.26480i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7614.00 4395.95i −0.390037 0.225188i
\(726\) 0 0
\(727\) 23945.7i 1.22159i −0.791789 0.610795i \(-0.790850\pi\)
0.791789 0.610795i \(-0.209150\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5587.43 + 9677.71i −0.282707 + 0.489662i
\(732\) 0 0
\(733\) 18035.8 10413.0i 0.908822 0.524708i 0.0287698 0.999586i \(-0.490841\pi\)
0.880052 + 0.474878i \(0.157508\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8046.67 + 4645.75i −0.402175 + 0.232196i
\(738\) 0 0
\(739\) 7648.41 13247.4i 0.380719 0.659424i −0.610446 0.792058i \(-0.709010\pi\)
0.991165 + 0.132633i \(0.0423433\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27249.8i 1.34549i −0.739875 0.672744i \(-0.765115\pi\)
0.739875 0.672744i \(-0.234885\pi\)
\(744\) 0 0
\(745\) 7062.08 + 4077.29i 0.347295 + 0.200511i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7747.28 32356.2i 0.377943 1.57846i
\(750\) 0 0
\(751\) −19864.5 34406.4i −0.965203 1.67178i −0.709069 0.705139i \(-0.750884\pi\)
−0.256134 0.966641i \(-0.582449\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10233.7 0.493302
\(756\) 0 0
\(757\) −24557.2 −1.17906 −0.589530 0.807747i \(-0.700687\pi\)
−0.589530 + 0.807747i \(0.700687\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9686.45 + 16777.4i 0.461411 + 0.799187i 0.999032 0.0440000i \(-0.0140102\pi\)
−0.537621 + 0.843187i \(0.680677\pi\)
\(762\) 0 0
\(763\) −443.514 1493.95i −0.0210436 0.0708842i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24444.4 14113.0i −1.15076 0.664393i
\(768\) 0 0
\(769\) 39937.6i 1.87280i −0.350930 0.936402i \(-0.614134\pi\)
0.350930 0.936402i \(-0.385866\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8058.12 + 13957.1i −0.374942 + 0.649419i −0.990318 0.138815i \(-0.955671\pi\)
0.615376 + 0.788234i \(0.289004\pi\)
\(774\) 0 0
\(775\) −19122.3 + 11040.3i −0.886314 + 0.511714i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4044.80 2335.27i 0.186034 0.107407i
\(780\) 0 0
\(781\) −15771.4 + 27316.9i −0.722594 + 1.25157i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20184.9i 0.917744i
\(786\) 0 0
\(787\) 19040.0 + 10992.8i 0.862394 + 0.497903i 0.864813 0.502094i \(-0.167437\pi\)
−0.00241936 + 0.999997i \(0.500770\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1578.62 1496.23i −0.0709598 0.0672566i
\(792\) 0 0
\(793\) −16142.3 27959.3i −0.722864 1.25204i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2291.42 0.101840 0.0509198 0.998703i \(-0.483785\pi\)
0.0509198 + 0.998703i \(0.483785\pi\)
\(798\) 0 0
\(799\) 1579.15 0.0699202
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4251.67 + 7364.12i 0.186847 + </