Properties

Label 324.4.i.a.289.8
Level $324$
Weight $4$
Character 324.289
Analytic conductor $19.117$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 289.8
Character \(\chi\) \(=\) 324.289
Dual form 324.4.i.a.37.8

$q$-expansion

\(f(q)\) \(=\) \(q+(10.0092 + 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +O(q^{10})\) \(q+(10.0092 + 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +(-3.53602 + 1.28701i) q^{11} +(-55.0460 + 46.1890i) q^{13} +(14.0443 + 24.3254i) q^{17} +(4.34509 - 7.52591i) q^{19} +(-4.21963 - 23.9307i) q^{23} +(-8.84313 - 7.42027i) q^{25} +(-183.135 - 153.668i) q^{29} +(45.3635 + 257.269i) q^{31} +(-89.2293 + 154.550i) q^{35} +(50.0527 + 86.6937i) q^{37} +(-177.609 + 149.031i) q^{41} +(220.317 - 80.1887i) q^{43} +(-98.9672 + 561.271i) q^{47} +(58.5403 + 21.3069i) q^{49} -368.316 q^{53} -40.0814 q^{55} +(485.116 + 176.568i) q^{59} +(-106.741 + 605.358i) q^{61} +(-719.236 + 261.780i) q^{65} +(-264.013 + 221.533i) q^{67} +(-496.578 - 860.098i) q^{71} +(-180.607 + 312.820i) q^{73} +(-10.9477 - 62.0874i) q^{77} +(127.623 + 107.088i) q^{79} +(718.475 + 602.872i) q^{83} +(51.9533 + 294.642i) q^{85} +(404.414 - 700.465i) q^{89} +(-601.956 - 1042.62i) q^{91} +(70.9082 - 59.4990i) q^{95} +(1723.85 - 627.431i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 10.0092 + 3.64305i 0.895251 + 0.325845i 0.748348 0.663306i \(-0.230847\pi\)
0.146903 + 0.989151i \(0.453070\pi\)
\(6\) 0 0
\(7\) −2.90933 + 16.4997i −0.157089 + 0.890897i 0.799762 + 0.600318i \(0.204959\pi\)
−0.956851 + 0.290580i \(0.906152\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.53602 + 1.28701i −0.0969227 + 0.0352770i −0.390026 0.920804i \(-0.627534\pi\)
0.293104 + 0.956081i \(0.405312\pi\)
\(12\) 0 0
\(13\) −55.0460 + 46.1890i −1.17438 + 0.985426i −0.174385 + 0.984678i \(0.555794\pi\)
−1.00000 0.000748193i \(0.999762\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 14.0443 + 24.3254i 0.200367 + 0.347046i 0.948647 0.316338i \(-0.102453\pi\)
−0.748280 + 0.663383i \(0.769120\pi\)
\(18\) 0 0
\(19\) 4.34509 7.52591i 0.0524648 0.0908717i −0.838600 0.544747i \(-0.816626\pi\)
0.891065 + 0.453876i \(0.149959\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.21963 23.9307i −0.0382545 0.216952i 0.959688 0.281068i \(-0.0906885\pi\)
−0.997942 + 0.0641155i \(0.979577\pi\)
\(24\) 0 0
\(25\) −8.84313 7.42027i −0.0707451 0.0593622i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −183.135 153.668i −1.17267 0.983983i −0.172666 0.984980i \(-0.555238\pi\)
−1.00000 0.000996932i \(0.999683\pi\)
\(30\) 0 0
\(31\) 45.3635 + 257.269i 0.262823 + 1.49055i 0.775162 + 0.631762i \(0.217668\pi\)
−0.512339 + 0.858783i \(0.671221\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −89.2293 + 154.550i −0.430928 + 0.746390i
\(36\) 0 0
\(37\) 50.0527 + 86.6937i 0.222395 + 0.385199i 0.955535 0.294879i \(-0.0952793\pi\)
−0.733140 + 0.680078i \(0.761946\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −177.609 + 149.031i −0.676531 + 0.567677i −0.914991 0.403475i \(-0.867802\pi\)
0.238459 + 0.971153i \(0.423358\pi\)
\(42\) 0 0
\(43\) 220.317 80.1887i 0.781348 0.284387i 0.0796135 0.996826i \(-0.474631\pi\)
0.701735 + 0.712438i \(0.252409\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −98.9672 + 561.271i −0.307146 + 1.74191i 0.306083 + 0.952005i \(0.400981\pi\)
−0.613229 + 0.789905i \(0.710130\pi\)
\(48\) 0 0
\(49\) 58.5403 + 21.3069i 0.170671 + 0.0621193i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −368.316 −0.954567 −0.477283 0.878749i \(-0.658378\pi\)
−0.477283 + 0.878749i \(0.658378\pi\)
\(54\) 0 0
\(55\) −40.0814 −0.0982649
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 485.116 + 176.568i 1.07045 + 0.389613i 0.816346 0.577563i \(-0.195996\pi\)
0.254107 + 0.967176i \(0.418218\pi\)
\(60\) 0 0
\(61\) −106.741 + 605.358i −0.224046 + 1.27063i 0.640456 + 0.767995i \(0.278746\pi\)
−0.864501 + 0.502631i \(0.832366\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −719.236 + 261.780i −1.37246 + 0.499536i
\(66\) 0 0
\(67\) −264.013 + 221.533i −0.481407 + 0.403949i −0.850935 0.525271i \(-0.823964\pi\)
0.369528 + 0.929220i \(0.379520\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −496.578 860.098i −0.830041 1.43767i −0.898005 0.439986i \(-0.854983\pi\)
0.0679634 0.997688i \(-0.478350\pi\)
\(72\) 0 0
\(73\) −180.607 + 312.820i −0.289568 + 0.501546i −0.973707 0.227806i \(-0.926845\pi\)
0.684139 + 0.729352i \(0.260178\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.9477 62.0874i −0.0162027 0.0918898i
\(78\) 0 0
\(79\) 127.623 + 107.088i 0.181756 + 0.152511i 0.729126 0.684379i \(-0.239927\pi\)
−0.547371 + 0.836890i \(0.684371\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 718.475 + 602.872i 0.950156 + 0.797275i 0.979324 0.202299i \(-0.0648413\pi\)
−0.0291680 + 0.999575i \(0.509286\pi\)
\(84\) 0 0
\(85\) 51.9533 + 294.642i 0.0662956 + 0.375981i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 404.414 700.465i 0.481660 0.834260i −0.518118 0.855309i \(-0.673367\pi\)
0.999778 + 0.0210490i \(0.00670061\pi\)
\(90\) 0 0
\(91\) −601.956 1042.62i −0.693430 1.20106i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 70.9082 59.4990i 0.0765792 0.0642576i
\(96\) 0 0
\(97\) 1723.85 627.431i 1.80444 0.656762i 0.806598 0.591100i \(-0.201306\pi\)
0.997842 0.0656621i \(-0.0209160\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 104.411 592.143i 0.102864 0.583370i −0.889188 0.457542i \(-0.848730\pi\)
0.992052 0.125829i \(-0.0401589\pi\)
\(102\) 0 0
\(103\) 61.8832 + 22.5237i 0.0591994 + 0.0215468i 0.371450 0.928453i \(-0.378861\pi\)
−0.312251 + 0.950000i \(0.601083\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1123.65 1.01520 0.507602 0.861591i \(-0.330532\pi\)
0.507602 + 0.861591i \(0.330532\pi\)
\(108\) 0 0
\(109\) −1790.18 −1.57310 −0.786550 0.617527i \(-0.788135\pi\)
−0.786550 + 0.617527i \(0.788135\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1032.17 + 375.680i 0.859281 + 0.312753i 0.733818 0.679346i \(-0.237736\pi\)
0.125462 + 0.992098i \(0.459959\pi\)
\(114\) 0 0
\(115\) 44.9457 254.900i 0.0364453 0.206692i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −442.220 + 160.955i −0.340657 + 0.123989i
\(120\) 0 0
\(121\) −1008.76 + 846.449i −0.757895 + 0.635949i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −727.204 1259.55i −0.520345 0.901264i
\(126\) 0 0
\(127\) 1048.77 1816.52i 0.732782 1.26922i −0.222908 0.974840i \(-0.571555\pi\)
0.955690 0.294376i \(-0.0951118\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 157.676 + 894.228i 0.105162 + 0.596405i 0.991155 + 0.132707i \(0.0423668\pi\)
−0.885993 + 0.463698i \(0.846522\pi\)
\(132\) 0 0
\(133\) 111.534 + 93.5878i 0.0727157 + 0.0610157i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −603.157 506.109i −0.376140 0.315619i 0.435045 0.900409i \(-0.356733\pi\)
−0.811185 + 0.584790i \(0.801177\pi\)
\(138\) 0 0
\(139\) 175.366 + 994.552i 0.107010 + 0.606883i 0.990398 + 0.138242i \(0.0441452\pi\)
−0.883389 + 0.468641i \(0.844744\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 135.198 234.170i 0.0790617 0.136939i
\(144\) 0 0
\(145\) −1273.21 2205.27i −0.729204 1.26302i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2624.88 2202.54i 1.44321 1.21100i 0.505859 0.862616i \(-0.331175\pi\)
0.937352 0.348383i \(-0.113269\pi\)
\(150\) 0 0
\(151\) 2253.91 820.356i 1.21471 0.442117i 0.346372 0.938097i \(-0.387413\pi\)
0.868334 + 0.495980i \(0.165191\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −483.193 + 2740.32i −0.250393 + 1.42005i
\(156\) 0 0
\(157\) −1595.55 580.732i −0.811073 0.295207i −0.0970061 0.995284i \(-0.530927\pi\)
−0.714067 + 0.700077i \(0.753149\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 407.125 0.199291
\(162\) 0 0
\(163\) 1962.35 0.942966 0.471483 0.881875i \(-0.343719\pi\)
0.471483 + 0.881875i \(0.343719\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2348.59 + 854.817i 1.08826 + 0.396094i 0.822976 0.568076i \(-0.192312\pi\)
0.265284 + 0.964170i \(0.414534\pi\)
\(168\) 0 0
\(169\) 515.125 2921.42i 0.234467 1.32973i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1234.35 + 449.268i −0.542463 + 0.197440i −0.598695 0.800977i \(-0.704314\pi\)
0.0562317 + 0.998418i \(0.482091\pi\)
\(174\) 0 0
\(175\) 148.159 124.321i 0.0639989 0.0537014i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1735.29 3005.61i −0.724589 1.25503i −0.959143 0.282922i \(-0.908696\pi\)
0.234554 0.972103i \(-0.424637\pi\)
\(180\) 0 0
\(181\) 1010.33 1749.94i 0.414901 0.718630i −0.580517 0.814248i \(-0.697149\pi\)
0.995418 + 0.0956180i \(0.0304827\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 185.157 + 1050.08i 0.0735841 + 0.417316i
\(186\) 0 0
\(187\) −80.9677 67.9400i −0.0316628 0.0265683i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1101.83 924.547i −0.417412 0.350251i 0.409765 0.912191i \(-0.365611\pi\)
−0.827178 + 0.561940i \(0.810055\pi\)
\(192\) 0 0
\(193\) 165.021 + 935.881i 0.0615465 + 0.349048i 0.999993 + 0.00362415i \(0.00115361\pi\)
−0.938447 + 0.345423i \(0.887735\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −630.410 + 1091.90i −0.227994 + 0.394898i −0.957214 0.289382i \(-0.906550\pi\)
0.729219 + 0.684280i \(0.239883\pi\)
\(198\) 0 0
\(199\) 45.3986 + 78.6327i 0.0161720 + 0.0280107i 0.873998 0.485929i \(-0.161519\pi\)
−0.857826 + 0.513940i \(0.828185\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3068.28 2574.59i 1.06084 0.890152i
\(204\) 0 0
\(205\) −2320.65 + 844.647i −0.790640 + 0.287769i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.67842 + 32.2039i −0.00187935 + 0.0106583i
\(210\) 0 0
\(211\) 3332.78 + 1213.03i 1.08739 + 0.395776i 0.822652 0.568546i \(-0.192494\pi\)
0.264734 + 0.964322i \(0.414716\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2497.33 0.792169
\(216\) 0 0
\(217\) −4376.83 −1.36921
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1896.65 690.323i −0.577295 0.210118i
\(222\) 0 0
\(223\) 168.174 953.762i 0.0505012 0.286406i −0.949090 0.315006i \(-0.897994\pi\)
0.999591 + 0.0285993i \(0.00910469\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1558.12 567.109i 0.455577 0.165816i −0.104031 0.994574i \(-0.533174\pi\)
0.559608 + 0.828758i \(0.310952\pi\)
\(228\) 0 0
\(229\) −3824.88 + 3209.45i −1.10373 + 0.926142i −0.997671 0.0682170i \(-0.978269\pi\)
−0.106063 + 0.994359i \(0.533825\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1892.72 3278.28i −0.532171 0.921748i −0.999295 0.0375555i \(-0.988043\pi\)
0.467123 0.884192i \(-0.345290\pi\)
\(234\) 0 0
\(235\) −3035.32 + 5257.33i −0.842565 + 1.45936i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 280.643 + 1591.60i 0.0759551 + 0.430763i 0.998944 + 0.0459369i \(0.0146273\pi\)
−0.922989 + 0.384826i \(0.874262\pi\)
\(240\) 0 0
\(241\) 4034.39 + 3385.25i 1.07833 + 0.904826i 0.995781 0.0917605i \(-0.0292494\pi\)
0.0825491 + 0.996587i \(0.473694\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 508.320 + 426.531i 0.132553 + 0.111225i
\(246\) 0 0
\(247\) 108.435 + 614.966i 0.0279335 + 0.158418i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2000.32 + 3464.66i −0.503025 + 0.871264i 0.496969 + 0.867768i \(0.334446\pi\)
−0.999994 + 0.00349620i \(0.998887\pi\)
\(252\) 0 0
\(253\) 45.7196 + 79.1887i 0.0113611 + 0.0196781i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5312.76 + 4457.93i −1.28950 + 1.08202i −0.297638 + 0.954679i \(0.596199\pi\)
−0.991859 + 0.127338i \(0.959357\pi\)
\(258\) 0 0
\(259\) −1576.04 + 573.630i −0.378109 + 0.137620i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −902.671 + 5119.30i −0.211639 + 1.20027i 0.675005 + 0.737813i \(0.264141\pi\)
−0.886644 + 0.462452i \(0.846970\pi\)
\(264\) 0 0
\(265\) −3686.55 1341.79i −0.854577 0.311041i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3202.65 0.725907 0.362953 0.931807i \(-0.381768\pi\)
0.362953 + 0.931807i \(0.381768\pi\)
\(270\) 0 0
\(271\) 2563.49 0.574616 0.287308 0.957838i \(-0.407240\pi\)
0.287308 + 0.957838i \(0.407240\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 40.8194 + 14.8570i 0.00895092 + 0.00325787i
\(276\) 0 0
\(277\) −934.933 + 5302.27i −0.202797 + 1.15012i 0.698073 + 0.716027i \(0.254041\pi\)
−0.900869 + 0.434090i \(0.857070\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3415.67 + 1243.20i −0.725131 + 0.263926i −0.678102 0.734967i \(-0.737197\pi\)
−0.0470287 + 0.998894i \(0.514975\pi\)
\(282\) 0 0
\(283\) 5021.18 4213.27i 1.05469 0.884993i 0.0611141 0.998131i \(-0.480535\pi\)
0.993579 + 0.113138i \(0.0360902\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1942.24 3364.06i −0.399466 0.691896i
\(288\) 0 0
\(289\) 2062.02 3571.52i 0.419706 0.726953i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −88.6969 503.025i −0.0176851 0.100297i 0.974688 0.223571i \(-0.0717716\pi\)
−0.992373 + 0.123274i \(0.960660\pi\)
\(294\) 0 0
\(295\) 4212.38 + 3534.61i 0.831371 + 0.697603i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1337.61 + 1122.39i 0.258716 + 0.217088i
\(300\) 0 0
\(301\) 682.111 + 3868.44i 0.130619 + 0.740775i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3273.75 + 5670.29i −0.614604 + 1.06452i
\(306\) 0 0
\(307\) 975.162 + 1689.03i 0.181288 + 0.314000i 0.942319 0.334715i \(-0.108640\pi\)
−0.761031 + 0.648715i \(0.775307\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4843.13 + 4063.87i −0.883051 + 0.740968i −0.966804 0.255518i \(-0.917754\pi\)
0.0837528 + 0.996487i \(0.473309\pi\)
\(312\) 0 0
\(313\) 472.116 171.836i 0.0852575 0.0310312i −0.299039 0.954241i \(-0.596666\pi\)
0.384297 + 0.923210i \(0.374444\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1665.94 9448.01i 0.295169 1.67398i −0.371348 0.928494i \(-0.621104\pi\)
0.666517 0.745490i \(-0.267785\pi\)
\(318\) 0 0
\(319\) 845.341 + 307.679i 0.148370 + 0.0540022i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 244.094 0.0420488
\(324\) 0 0
\(325\) 829.514 0.141579
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8972.84 3265.85i −1.50361 0.547271i
\(330\) 0 0
\(331\) 862.280 4890.23i 0.143188 0.812059i −0.825616 0.564232i \(-0.809172\pi\)
0.968804 0.247827i \(-0.0797165\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3449.62 + 1255.56i −0.562605 + 0.204771i
\(336\) 0 0
\(337\) −350.546 + 294.143i −0.0566632 + 0.0475460i −0.670679 0.741747i \(-0.733997\pi\)
0.614016 + 0.789293i \(0.289553\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −491.513 851.326i −0.0780555 0.135196i
\(342\) 0 0
\(343\) −3395.21 + 5880.68i −0.534473 + 0.925735i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −645.039 3658.20i −0.0997911 0.565943i −0.993174 0.116646i \(-0.962786\pi\)
0.893382 0.449297i \(-0.148325\pi\)
\(348\) 0 0
\(349\) −2640.17 2215.37i −0.404943 0.339788i 0.417457 0.908696i \(-0.362921\pi\)
−0.822401 + 0.568909i \(0.807366\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2239.14 + 1878.86i 0.337613 + 0.283291i 0.795793 0.605569i \(-0.207054\pi\)
−0.458181 + 0.888859i \(0.651499\pi\)
\(354\) 0 0
\(355\) −1836.97 10418.0i −0.274637 1.55754i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6470.47 + 11207.2i −0.951249 + 1.64761i −0.208522 + 0.978018i \(0.566865\pi\)
−0.742727 + 0.669594i \(0.766468\pi\)
\(360\) 0 0
\(361\) 3391.74 + 5874.67i 0.494495 + 0.856490i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2947.35 + 2473.12i −0.422662 + 0.354655i
\(366\) 0 0
\(367\) −12298.8 + 4476.41i −1.74930 + 0.636694i −0.999683 0.0251747i \(-0.991986\pi\)
−0.749620 + 0.661869i \(0.769764\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1071.55 6077.08i 0.149952 0.850421i
\(372\) 0 0
\(373\) 8627.89 + 3140.29i 1.19768 + 0.435920i 0.862414 0.506203i \(-0.168951\pi\)
0.335267 + 0.942123i \(0.391174\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 17178.6 2.34680
\(378\) 0 0
\(379\) 2260.05 0.306308 0.153154 0.988202i \(-0.451057\pi\)
0.153154 + 0.988202i \(0.451057\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9927.52 + 3613.32i 1.32447 + 0.482068i 0.904888 0.425649i \(-0.139954\pi\)
0.419583 + 0.907717i \(0.362176\pi\)
\(384\) 0 0
\(385\) 116.610 661.329i 0.0154364 0.0875440i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9659.45 3515.75i 1.25901 0.458241i 0.375571 0.926793i \(-0.377446\pi\)
0.883436 + 0.468552i \(0.155224\pi\)
\(390\) 0 0
\(391\) 522.862 438.733i 0.0676273 0.0567460i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 887.276 + 1536.81i 0.113022 + 0.195760i
\(396\) 0 0
\(397\) 1494.01 2587.71i 0.188873 0.327137i −0.756002 0.654569i \(-0.772850\pi\)
0.944875 + 0.327432i \(0.106183\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1287.47 7301.59i −0.160332 0.909287i −0.953748 0.300607i \(-0.902811\pi\)
0.793416 0.608680i \(-0.208300\pi\)
\(402\) 0 0
\(403\) −14380.1 12066.3i −1.77748 1.49148i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −288.562 242.133i −0.0351438 0.0294891i
\(408\) 0 0
\(409\) −136.025 771.437i −0.0164450 0.0932643i 0.975481 0.220086i \(-0.0706337\pi\)
−0.991926 + 0.126821i \(0.959523\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4324.67 + 7490.55i −0.515262 + 0.892460i
\(414\) 0 0
\(415\) 4995.07 + 8651.72i 0.590840 + 1.02336i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7526.09 6315.14i 0.877502 0.736312i −0.0881616 0.996106i \(-0.528099\pi\)
0.965664 + 0.259794i \(0.0836547\pi\)
\(420\) 0 0
\(421\) 1020.41 371.400i 0.118128 0.0429951i −0.282280 0.959332i \(-0.591091\pi\)
0.400408 + 0.916337i \(0.368868\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 56.3056 319.325i 0.00642641 0.0364460i
\(426\) 0 0
\(427\) −9677.65 3522.38i −1.09680 0.399203i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4258.28 0.475903 0.237951 0.971277i \(-0.423524\pi\)
0.237951 + 0.971277i \(0.423524\pi\)
\(432\) 0 0
\(433\) 7152.99 0.793882 0.396941 0.917844i \(-0.370072\pi\)
0.396941 + 0.917844i \(0.370072\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −198.435 72.2244i −0.0217218 0.00790609i
\(438\) 0 0
\(439\) −1804.32 + 10232.8i −0.196162 + 1.11249i 0.714591 + 0.699542i \(0.246613\pi\)
−0.910754 + 0.412950i \(0.864498\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12028.7 4378.09i 1.29007 0.469548i 0.396321 0.918112i \(-0.370287\pi\)
0.893750 + 0.448565i \(0.148065\pi\)
\(444\) 0 0
\(445\) 6599.69 5537.80i 0.703046 0.589926i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3046.78 5277.17i −0.320237 0.554666i 0.660300 0.751002i \(-0.270429\pi\)
−0.980537 + 0.196336i \(0.937096\pi\)
\(450\) 0 0
\(451\) 436.223 755.560i 0.0455453 0.0788868i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2226.79 12628.7i −0.229436 1.30120i
\(456\) 0 0
\(457\) −5464.80 4585.51i −0.559371 0.469368i 0.318729 0.947846i \(-0.396744\pi\)
−0.878099 + 0.478478i \(0.841189\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9715.80 8152.53i −0.981583 0.823646i 0.00274406 0.999996i \(-0.499127\pi\)
−0.984328 + 0.176350i \(0.943571\pi\)
\(462\) 0 0
\(463\) −2328.16 13203.7i −0.233691 1.32533i −0.845353 0.534208i \(-0.820610\pi\)
0.611663 0.791119i \(-0.290501\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 68.4431 118.547i 0.00678195 0.0117467i −0.862615 0.505862i \(-0.831175\pi\)
0.869396 + 0.494115i \(0.164508\pi\)
\(468\) 0 0
\(469\) −2887.12 5000.63i −0.284253 0.492341i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −675.840 + 567.097i −0.0656980 + 0.0551272i
\(474\) 0 0
\(475\) −94.2685 + 34.3109i −0.00910597 + 0.00331430i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −599.222 + 3398.35i −0.0571589 + 0.324164i −0.999958 0.00919797i \(-0.997072\pi\)
0.942799 + 0.333362i \(0.108183\pi\)
\(480\) 0 0
\(481\) −6759.50 2460.26i −0.640762 0.233218i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19540.2 1.82943
\(486\) 0 0
\(487\) 8808.83 0.819643 0.409821 0.912166i \(-0.365591\pi\)
0.409821 + 0.912166i \(0.365591\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11912.6 4335.83i −1.09493 0.398520i −0.269482 0.963005i \(-0.586853\pi\)
−0.825443 + 0.564485i \(0.809075\pi\)
\(492\) 0 0
\(493\) 1166.05 6612.99i 0.106524 0.604126i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15636.0 5691.05i 1.41121 0.513639i
\(498\) 0 0
\(499\) 13503.0 11330.4i 1.21138 1.01647i 0.212149 0.977237i \(-0.431954\pi\)
0.999230 0.0392306i \(-0.0124907\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3751.33 6497.50i −0.332532 0.575962i 0.650476 0.759527i \(-0.274570\pi\)
−0.983008 + 0.183565i \(0.941236\pi\)
\(504\) 0 0
\(505\) 3202.28 5546.51i 0.282177 0.488745i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3912.83 + 22190.7i 0.340733 + 1.93239i 0.360925 + 0.932595i \(0.382461\pi\)
−0.0201923 + 0.999796i \(0.506428\pi\)
\(510\) 0 0
\(511\) −4635.98 3890.05i −0.401338 0.336762i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 537.347 + 450.888i 0.0459774 + 0.0385796i
\(516\) 0 0
\(517\) −372.409 2112.04i −0.0316799 0.179666i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10309.3 + 17856.2i −0.866906 + 1.50153i −0.00176401 + 0.999998i \(0.500562\pi\)
−0.865142 + 0.501527i \(0.832772\pi\)
\(522\) 0 0
\(523\) −3362.40 5823.85i −0.281123 0.486920i 0.690538 0.723296i \(-0.257374\pi\)
−0.971662 + 0.236376i \(0.924040\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5621.08 + 4716.64i −0.464626 + 0.389868i
\(528\) 0 0
\(529\) 10878.4 3959.40i 0.894088 0.325421i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2893.02 16407.1i 0.235104 1.33334i
\(534\) 0 0
\(535\) 11246.8 + 4093.50i 0.908863 + 0.330799i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −234.422 −0.0187333
\(540\) 0 0
\(541\) −9213.40 −0.732190 −0.366095 0.930577i \(-0.619306\pi\)
−0.366095 + 0.930577i \(0.619306\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −17918.3 6521.71i −1.40832 0.512586i
\(546\) 0 0
\(547\) −1180.97 + 6697.60i −0.0923117 + 0.523526i 0.903226 + 0.429165i \(0.141192\pi\)
−0.995538 + 0.0943612i \(0.969919\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1952.23 + 710.554i −0.150940 + 0.0549376i
\(552\) 0 0
\(553\) −2138.22 + 1794.18i −0.164424 + 0.137968i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8957.05 + 15514.1i 0.681369 + 1.18017i 0.974563 + 0.224113i \(0.0719484\pi\)
−0.293194 + 0.956053i \(0.594718\pi\)
\(558\) 0 0
\(559\) −8423.70 + 14590.3i −0.637361 + 1.10394i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1738.41 9859.03i −0.130134 0.738026i −0.978125 0.208016i \(-0.933299\pi\)
0.847992 0.530010i \(-0.177812\pi\)
\(564\) 0 0
\(565\) 8962.62 + 7520.53i 0.667363 + 0.559984i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11756.4 + 9864.81i 0.866177 + 0.726809i 0.963290 0.268464i \(-0.0865162\pi\)
−0.0971124 + 0.995273i \(0.530961\pi\)
\(570\) 0 0
\(571\) 661.504 + 3751.58i 0.0484818 + 0.274954i 0.999406 0.0344710i \(-0.0109746\pi\)
−0.950924 + 0.309425i \(0.899864\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −140.258 + 242.933i −0.0101724 + 0.0176192i
\(576\) 0 0
\(577\) 3496.19 + 6055.58i 0.252250 + 0.436910i 0.964145 0.265376i \(-0.0854961\pi\)
−0.711895 + 0.702286i \(0.752163\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12037.5 + 10100.6i −0.859550 + 0.721248i
\(582\) 0 0
\(583\) 1302.37 474.024i 0.0925192 0.0336742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −314.256 + 1782.23i −0.0220966 + 0.125316i −0.993861 0.110638i \(-0.964711\pi\)
0.971764 + 0.235954i \(0.0758216\pi\)
\(588\) 0 0
\(589\) 2133.29 + 776.455i 0.149237 + 0.0543180i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 23574.5 1.63253 0.816265 0.577677i \(-0.196041\pi\)
0.816265 + 0.577677i \(0.196041\pi\)
\(594\) 0 0
\(595\) −5012.64 −0.345375
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1293.63 + 470.845i 0.0882412 + 0.0321172i 0.385764 0.922598i \(-0.373938\pi\)
−0.297522 + 0.954715i \(0.596160\pi\)
\(600\) 0 0
\(601\) −2569.25 + 14571.0i −0.174379 + 0.988955i 0.764478 + 0.644649i \(0.222997\pi\)
−0.938858 + 0.344305i \(0.888114\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13180.5 + 4797.32i −0.885727 + 0.322378i
\(606\) 0 0
\(607\) −9051.09 + 7594.77i −0.605226 + 0.507845i −0.893121 0.449817i \(-0.851489\pi\)
0.287894 + 0.957662i \(0.407045\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20476.8 35466.9i −1.35582 2.34834i
\(612\) 0 0
\(613\) 3225.23 5586.27i 0.212506 0.368071i −0.739992 0.672615i \(-0.765171\pi\)
0.952498 + 0.304545i \(0.0985042\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2856.84 + 16201.9i 0.186405 + 1.05716i 0.924137 + 0.382061i \(0.124786\pi\)
−0.737732 + 0.675094i \(0.764103\pi\)
\(618\) 0 0
\(619\) −13064.5 10962.4i −0.848316 0.711822i 0.111102 0.993809i \(-0.464562\pi\)
−0.959418 + 0.281987i \(0.909006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 10380.9 + 8710.57i 0.667576 + 0.560163i
\(624\) 0 0
\(625\) −2439.54 13835.3i −0.156131 0.885460i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1405.91 + 2435.10i −0.0891211 + 0.154362i
\(630\) 0 0
\(631\) 7321.24 + 12680.8i 0.461892 + 0.800021i 0.999055 0.0434573i \(-0.0138373\pi\)
−0.537163 + 0.843479i \(0.680504\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 17115.1 14361.2i 1.06959 0.897493i
\(636\) 0 0
\(637\) −4206.55 + 1531.06i −0.261648 + 0.0952321i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −792.456 + 4494.24i −0.0488301 + 0.276929i −0.999440 0.0334585i \(-0.989348\pi\)
0.950610 + 0.310388i \(0.100459\pi\)
\(642\) 0 0
\(643\) −4259.61 1550.37i −0.261248 0.0950865i 0.208076 0.978113i \(-0.433280\pi\)
−0.469324 + 0.883026i \(0.655502\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24993.3 −1.51868 −0.759342 0.650692i \(-0.774479\pi\)
−0.759342 + 0.650692i \(0.774479\pi\)
\(648\) 0 0
\(649\) −1942.62 −0.117496
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2358.00 + 858.241i 0.141310 + 0.0514327i 0.411707 0.911316i \(-0.364933\pi\)
−0.270397 + 0.962749i \(0.587155\pi\)
\(654\) 0 0
\(655\) −1679.50 + 9524.94i −0.100189 + 0.568199i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −24430.9 + 8892.11i −1.44415 + 0.525626i −0.940950 0.338546i \(-0.890065\pi\)
−0.503196 + 0.864172i \(0.667843\pi\)
\(660\) 0 0
\(661\) −4539.92 + 3809.44i −0.267144 + 0.224161i −0.766513 0.642229i \(-0.778010\pi\)
0.499369 + 0.866390i \(0.333565\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 775.418 + 1343.06i 0.0452171 + 0.0783184i
\(666\) 0 0
\(667\) −2904.63 + 5030.97i −0.168617 + 0.292054i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −401.661 2277.93i −0.0231087 0.131056i
\(672\) 0 0
\(673\) 22589.1 + 18954.5i 1.29383 + 1.08565i 0.991177 + 0.132547i \(0.0423156\pi\)
0.302649 + 0.953102i \(0.402129\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16020.1 13442.5i −0.909459 0.763127i 0.0625569 0.998041i \(-0.480075\pi\)
−0.972016 + 0.234915i \(0.924519\pi\)
\(678\) 0 0
\(679\) 5337.13 + 30268.4i 0.301650 + 1.71074i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4479.23 + 7758.25i −0.250941 + 0.434643i −0.963785 0.266680i \(-0.914073\pi\)
0.712844 + 0.701323i \(0.247407\pi\)
\(684\) 0 0
\(685\) −4193.34 7263.08i −0.233897 0.405121i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20274.3 17012.1i 1.12103 0.940655i
\(690\) 0 0
\(691\) −23144.5 + 8423.91i −1.27418 + 0.463764i −0.888503 0.458870i \(-0.848254\pi\)
−0.385677 + 0.922634i \(0.626032\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1867.93 + 10593.5i −0.101949 + 0.578182i
\(696\) 0 0
\(697\) −6119.62 2227.36i −0.332564 0.121044i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −13936.1 −0.750869 −0.375435 0.926849i \(-0.622507\pi\)
−0.375435 + 0.926849i \(0.622507\pi\)
\(702\) 0 0
\(703\) 869.932 0.0466716
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9466.38 + 3445.48i 0.503564 + 0.183282i
\(708\) 0 0
\(709\) 2364.96 13412.3i 0.125272 0.710453i −0.855874 0.517185i \(-0.826980\pi\)
0.981146 0.193268i \(-0.0619088\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5965.22 2171.16i 0.313323 0.114040i
\(714\) 0 0
\(715\) 2206.32 1851.32i 0.115401 0.0968328i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −7771.31 13460.3i −0.403089 0.698171i 0.591008 0.806666i \(-0.298730\pi\)
−0.994097 + 0.108495i \(0.965397\pi\)
\(720\) 0 0
\(721\) −551.671 + 955.523i −0.0284956 + 0.0493558i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 479.225 + 2717.82i 0.0245489 + 0.139224i
\(726\) 0 0
\(727\) 323.352 + 271.325i 0.0164958 + 0.0138417i 0.650998 0.759079i \(-0.274351\pi\)
−0.634502 + 0.772921i \(0.718795\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5044.81 + 4233.10i 0.255252 + 0.214182i
\(732\) 0 0
\(733\) 4836.28 + 27427.9i 0.243700 + 1.38209i 0.823493 + 0.567326i \(0.192022\pi\)
−0.579793 + 0.814764i \(0.696867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 648.440 1123.13i 0.0324092 0.0561344i
\(738\) 0 0
\(739\) 6838.48 + 11844.6i 0.340403 + 0.589595i 0.984507 0.175343i \(-0.0561033\pi\)
−0.644105 + 0.764937i \(0.722770\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −25241.3 + 21180.0i −1.24632 + 1.04578i −0.249314 + 0.968423i \(0.580205\pi\)
−0.997003 + 0.0773619i \(0.975350\pi\)
\(744\) 0 0
\(745\) 34296.9 12483.1i 1.68663 0.613885i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3269.06 + 18539.8i −0.159478 + 0.904443i
\(750\) 0 0
\(751\) 16216.5 + 5902.33i 0.787948 + 0.286790i 0.704483 0.709721i \(-0.251179\pi\)
0.0834654 + 0.996511i \(0.473401\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 25548.5 1.23153
\(756\) 0 0
\(757\) 11119.9 0.533897 0.266949 0.963711i \(-0.413985\pi\)
0.266949 + 0.963711i \(0.413985\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15727.2 + 5724.22i 0.749158 + 0.272671i 0.688251 0.725472i \(-0.258379\pi\)
0.0609065 + 0.998143i \(0.480601\pi\)
\(762\) 0 0
\(763\) 5208.22 29537.3i 0.247117 1.40147i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −34859.2 + 12687.7i −1.64106 + 0.597297i
\(768\) 0 0
\(769\) −29314.2 + 24597.6i −1.37464 + 1.15346i −0.403492 + 0.914983i \(0.632204\pi\)
−0.971148 + 0.238477i \(0.923352\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9959.54 + 17250.4i 0.463415 + 0.802658i 0.999128 0.0417417i \(-0.0132907\pi\)
−0.535714 + 0.844400i \(0.679957\pi\)
\(774\) 0 0
\(775\) 1507.85 2611.68i 0.0698886 0.121051i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 349.871 + 1984.22i 0.0160917 + 0.0912606i
\(780\) 0 0
\(781\) 2862.86 + 2402.22i 0.131167 + 0.110062i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −13854.5 11625.3i −0.629923 0.528568i
\(786\) 0 0
\(787\) −1236.57 7012.96i −0.0560090 0.317643i 0.943912 0.330197i \(-0.107115\pi\)
−0.999921 + 0.0125537i \(0.996004\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9201.53 + 15937.5i −0.413614 + 0.716401i