Properties

Label 324.4.i.a.37.8
Level $324$
Weight $4$
Character 324.37
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 37.8
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.8

$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{9}\right)\)

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 0.146903 0.989151i \(-0.453070\pi\)
0.748348 + 0.663306i \(0.230847\pi\)
\(6\) 0 0
\(7\) −2.90933 16.4997i −0.157089 0.890897i −0.956851 0.290580i \(-0.906152\pi\)
0.799762 0.600318i \(-0.204959\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.53602 1.28701i −0.0969227 0.0352770i 0.293104 0.956081i \(-0.405312\pi\)
−0.390026 + 0.920804i \(0.627534\pi\)
\(12\) 0 0
\(13\) −55.0460 46.1890i −1.17438 0.985426i −1.00000 0.000748193i \(-0.999762\pi\)
−0.174385 0.984678i \(-0.555794\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 14.0443 24.3254i 0.200367 0.347046i −0.748280 0.663383i \(-0.769120\pi\)
0.948647 + 0.316338i \(0.102453\pi\)
\(18\) 0 0
\(19\) 4.34509 + 7.52591i 0.0524648 + 0.0908717i 0.891065 0.453876i \(-0.149959\pi\)
−0.838600 + 0.544747i \(0.816626\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.21963 + 23.9307i −0.0382545 + 0.216952i −0.997942 0.0641155i \(-0.979577\pi\)
0.959688 + 0.281068i \(0.0906885\pi\)
\(24\) 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 −1.00000 0.000996932i \(-0.999683\pi\)
−0.172666 + 0.984980i \(0.555238\pi\)
\(30\) 0 0
\(31\) 45.3635 257.269i 0.262823 1.49055i −0.512339 0.858783i \(-0.671221\pi\)
0.775162 0.631762i \(-0.217668\pi\)
\(32\) 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 −0.733140 0.680078i \(-0.761946\pi\)
0.955535 + 0.294879i \(0.0952793\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −177.609 149.031i −0.676531 0.567677i 0.238459 0.971153i \(-0.423358\pi\)
−0.914991 + 0.403475i \(0.867802\pi\)
\(42\) 0 0
\(43\) 220.317 + 80.1887i 0.781348 + 0.284387i 0.701735 0.712438i \(-0.252409\pi\)
0.0796135 + 0.996826i \(0.474631\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −98.9672 561.271i −0.307146 1.74191i −0.613229 0.789905i \(-0.710130\pi\)
0.306083 0.952005i \(-0.400981\pi\)
\(48\) 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 0.254107 0.967176i \(-0.418218\pi\)
0.816346 + 0.577563i \(0.195996\pi\)
\(60\) 0 0
\(61\) −106.741 605.358i −0.224046 1.27063i −0.864501 0.502631i \(-0.832366\pi\)
0.640456 0.767995i \(-0.278746\pi\)
\(62\) 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 0.369528 0.929220i \(-0.379520\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −496.578 + 860.098i −0.830041 + 1.43767i 0.0679634 + 0.997688i \(0.478350\pi\)
−0.898005 + 0.439986i \(0.854983\pi\)
\(72\) 0 0
\(73\) −180.607 312.820i −0.289568 0.501546i 0.684139 0.729352i \(-0.260178\pi\)
−0.973707 + 0.227806i \(0.926845\pi\)
\(74\) 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 −0.547371 0.836890i \(-0.684371\pi\)
0.729126 + 0.684379i \(0.239927\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 718.475 602.872i 0.950156 0.797275i −0.0291680 0.999575i \(-0.509286\pi\)
0.979324 + 0.202299i \(0.0648413\pi\)
\(84\) 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 0.999778 0.0210490i \(-0.00670061\pi\)
−0.518118 + 0.855309i \(0.673367\pi\)
\(90\) 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 0.997842 + 0.0656621i \(0.0209160\pi\)
0.806598 + 0.591100i \(0.201306\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 104.411 + 592.143i 0.102864 + 0.583370i 0.992052 + 0.125829i \(0.0401589\pi\)
−0.889188 + 0.457542i \(0.848730\pi\)
\(102\) 0 0
\(103\) 61.8832 22.5237i 0.0591994 0.0215468i −0.312251 0.950000i \(-0.601083\pi\)
0.371450 + 0.928453i \(0.378861\pi\)
\(104\) 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 0.125462 0.992098i \(-0.459959\pi\)
0.733818 + 0.679346i \(0.237736\pi\)
\(114\) 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 0.955690 + 0.294376i \(0.0951118\pi\)
−0.222908 + 0.974840i \(0.571555\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 157.676 894.228i 0.105162 0.596405i −0.885993 0.463698i \(-0.846522\pi\)
0.991155 0.132707i \(-0.0423668\pi\)
\(132\) 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 −0.811185 0.584790i \(-0.801177\pi\)
0.435045 + 0.900409i \(0.356733\pi\)
\(138\) 0 0
\(139\) 175.366 994.552i 0.107010 0.606883i −0.883389 0.468641i \(-0.844744\pi\)
0.990398 0.138242i \(-0.0441452\pi\)
\(140\) 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 0.937352 + 0.348383i \(0.113269\pi\)
0.505859 + 0.862616i \(0.331175\pi\)
\(150\) 0 0
\(151\) 2253.91 + 820.356i 1.21471 + 0.442117i 0.868334 0.495980i \(-0.165191\pi\)
0.346372 + 0.938097i \(0.387413\pi\)
\(152\) 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 −0.714067 0.700077i \(-0.753149\pi\)
−0.0970061 + 0.995284i \(0.530927\pi\)
\(158\) 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 0.265284 0.964170i \(-0.414534\pi\)
0.822976 + 0.568076i \(0.192312\pi\)
\(168\) 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 0.0562317 0.998418i \(-0.482091\pi\)
−0.598695 + 0.800977i \(0.704314\pi\)
\(174\) 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 0.234554 + 0.972103i \(0.424637\pi\)
−0.959143 + 0.282922i \(0.908696\pi\)
\(180\) 0 0
\(181\) 1010.33 + 1749.94i 0.414901 + 0.718630i 0.995418 0.0956180i \(-0.0304827\pi\)
−0.580517 + 0.814248i \(0.697149\pi\)
\(182\) 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 −0.827178 0.561940i \(-0.810055\pi\)
0.409765 + 0.912191i \(0.365611\pi\)
\(192\) 0 0
\(193\) 165.021 935.881i 0.0615465 0.349048i −0.938447 0.345423i \(-0.887735\pi\)
0.999993 0.00362415i \(-0.00115361\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −630.410 1091.90i −0.227994 0.394898i 0.729219 0.684280i \(-0.239883\pi\)
−0.957214 + 0.289382i \(0.906550\pi\)
\(198\) 0 0
\(199\) 45.3986 78.6327i 0.0161720 0.0280107i −0.857826 0.513940i \(-0.828185\pi\)
0.873998 + 0.485929i \(0.161519\pi\)
\(200\) 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 0.264734 0.964322i \(-0.414716\pi\)
0.822652 + 0.568546i \(0.192494\pi\)
\(212\) 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 0.999591 0.0285993i \(-0.00910469\pi\)
−0.949090 + 0.315006i \(0.897994\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1558.12 + 567.109i 0.455577 + 0.165816i 0.559608 0.828758i \(-0.310952\pi\)
−0.104031 + 0.994574i \(0.533174\pi\)
\(228\) 0 0
\(229\) −3824.88 3209.45i −1.10373 0.926142i −0.106063 0.994359i \(-0.533825\pi\)
−0.997671 + 0.0682170i \(0.978269\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1892.72 + 3278.28i −0.532171 + 0.921748i 0.467123 + 0.884192i \(0.345290\pi\)
−0.999295 + 0.0375555i \(0.988043\pi\)
\(234\) 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 −0.922989 0.384826i \(-0.874262\pi\)
0.998944 0.0459369i \(-0.0146273\pi\)
\(240\) 0 0
\(241\) 4034.39 3385.25i 1.07833 0.904826i 0.0825491 0.996587i \(-0.473694\pi\)
0.995781 + 0.0917605i \(0.0292494\pi\)
\(242\) 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 −0.999994 0.00349620i \(-0.998887\pi\)
0.496969 0.867768i \(-0.334446\pi\)
\(252\) 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 −0.991859 0.127338i \(-0.959357\pi\)
−0.297638 0.954679i \(-0.596199\pi\)
\(258\) 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 −0.886644 0.462452i \(-0.846970\pi\)
0.675005 0.737813i \(-0.264141\pi\)
\(264\) 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 −0.900869 0.434090i \(-0.857070\pi\)
0.698073 0.716027i \(-0.254041\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3415.67 1243.20i −0.725131 0.263926i −0.0470287 0.998894i \(-0.514975\pi\)
−0.678102 + 0.734967i \(0.737197\pi\)
\(282\) 0 0
\(283\) 5021.18 + 4213.27i 1.05469 + 0.884993i 0.993579 0.113138i \(-0.0360902\pi\)
0.0611141 + 0.998131i \(0.480535\pi\)
\(284\) 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 −0.992373 0.123274i \(-0.960660\pi\)
0.974688 + 0.223571i \(0.0717716\pi\)
\(294\) 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 −0.761031 0.648715i \(-0.775307\pi\)
0.942319 + 0.334715i \(0.108640\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4843.13 4063.87i −0.883051 0.740968i 0.0837528 0.996487i \(-0.473309\pi\)
−0.966804 + 0.255518i \(0.917754\pi\)
\(312\) 0 0
\(313\) 472.116 + 171.836i 0.0852575 + 0.0310312i 0.384297 0.923210i \(-0.374444\pi\)
−0.299039 + 0.954241i \(0.596666\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1665.94 + 9448.01i 0.295169 + 1.67398i 0.666517 + 0.745490i \(0.267785\pi\)
−0.371348 + 0.928494i \(0.621104\pi\)
\(318\) 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 0.968804 + 0.247827i \(0.0797165\pi\)
−0.825616 + 0.564232i \(0.809172\pi\)
\(332\) 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 0.614016 0.789293i \(-0.289553\pi\)
−0.670679 + 0.741747i \(0.733997\pi\)
\(338\) 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 0.893382 + 0.449297i \(0.148325\pi\)
−0.993174 + 0.116646i \(0.962786\pi\)
\(348\) 0 0
\(349\) −2640.17 + 2215.37i −0.404943 + 0.339788i −0.822401 0.568909i \(-0.807366\pi\)
0.417457 + 0.908696i \(0.362921\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2239.14 1878.86i 0.337613 0.283291i −0.458181 0.888859i \(-0.651499\pi\)
0.795793 + 0.605569i \(0.207054\pi\)
\(354\) 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 −0.742727 0.669594i \(-0.766468\pi\)
−0.208522 0.978018i \(-0.566865\pi\)
\(360\) 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 −0.749620 0.661869i \(-0.769764\pi\)
−0.999683 + 0.0251747i \(0.991986\pi\)
\(368\) 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 0.335267 0.942123i \(-0.391174\pi\)
0.862414 + 0.506203i \(0.168951\pi\)
\(374\) 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 0.419583 0.907717i \(-0.362176\pi\)
0.904888 + 0.425649i \(0.139954\pi\)
\(384\) 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 0.883436 0.468552i \(-0.155224\pi\)
0.375571 + 0.926793i \(0.377446\pi\)
\(390\) 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 0.944875 0.327432i \(-0.106183\pi\)
−0.756002 + 0.654569i \(0.772850\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1287.47 + 7301.59i −0.160332 + 0.909287i 0.793416 + 0.608680i \(0.208300\pi\)
−0.953748 + 0.300607i \(0.902811\pi\)
\(402\) 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 −0.991926 0.126821i \(-0.959523\pi\)
0.975481 + 0.220086i \(0.0706337\pi\)
\(410\) 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 0.965664 0.259794i \(-0.0836547\pi\)
−0.0881616 + 0.996106i \(0.528099\pi\)
\(420\) 0 0
\(421\) 1020.41 + 371.400i 0.118128 + 0.0429951i 0.400408 0.916337i \(-0.368868\pi\)
−0.282280 + 0.959332i \(0.591091\pi\)
\(422\) 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 −0.910754 0.412950i \(-0.864498\pi\)
0.714591 0.699542i \(-0.246613\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12028.7 + 4378.09i 1.29007 + 0.469548i 0.893750 0.448565i \(-0.148065\pi\)
0.396321 + 0.918112i \(0.370287\pi\)
\(444\) 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 −0.980537 0.196336i \(-0.937096\pi\)
0.660300 + 0.751002i \(0.270429\pi\)
\(450\) 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 −0.878099 0.478478i \(-0.841189\pi\)
0.318729 + 0.947846i \(0.396744\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9715.80 + 8152.53i −0.981583 + 0.823646i −0.984328 0.176350i \(-0.943571\pi\)
0.00274406 + 0.999996i \(0.499127\pi\)
\(462\) 0 0
\(463\) −2328.16 + 13203.7i −0.233691 + 1.32533i 0.611663 + 0.791119i \(0.290501\pi\)
−0.845353 + 0.534208i \(0.820610\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 68.4431 + 118.547i 0.00678195 + 0.0117467i 0.869396 0.494115i \(-0.164508\pi\)
−0.862615 + 0.505862i \(0.831175\pi\)
\(468\) 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 0.942799 0.333362i \(-0.108183\pi\)
−0.999958 + 0.00919797i \(0.997072\pi\)
\(480\) 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 −0.825443 0.564485i \(-0.809075\pi\)
−0.269482 + 0.963005i \(0.586853\pi\)
\(492\) 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 0.999230 + 0.0392306i \(0.0124907\pi\)
0.212149 + 0.977237i \(0.431954\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3751.33 + 6497.50i −0.332532 + 0.575962i −0.983008 0.183565i \(-0.941236\pi\)
0.650476 + 0.759527i \(0.274570\pi\)
\(504\) 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 −0.0201923 0.999796i \(-0.506428\pi\)
0.360925 0.932595i \(-0.382461\pi\)
\(510\) 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 −0.865142 0.501527i \(-0.832772\pi\)
−0.00176401 0.999998i \(-0.500562\pi\)
\(522\) 0 0
\(523\) −3362.40 + 5823.85i −0.281123 + 0.486920i −0.971662 0.236376i \(-0.924040\pi\)
0.690538 + 0.723296i \(0.257374\pi\)
\(524\) 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 −0.995538 0.0943612i \(-0.969919\pi\)
0.903226 0.429165i \(-0.141192\pi\)
\(548\) 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 −0.293194 0.956053i \(-0.594718\pi\)
0.974563 0.224113i \(-0.0719484\pi\)
\(558\) 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 0.847992 + 0.530010i \(0.177812\pi\)
−0.978125 + 0.208016i \(0.933299\pi\)
\(564\) 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 −0.0971124 0.995273i \(-0.530961\pi\)
0.963290 + 0.268464i \(0.0865162\pi\)
\(570\) 0 0
\(571\) 661.504 3751.58i 0.0484818 0.274954i −0.950924 0.309425i \(-0.899864\pi\)
0.999406 + 0.0344710i \(0.0109746\pi\)
\(572\) 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 −0.711895 0.702286i \(-0.752163\pi\)
0.964145 + 0.265376i \(0.0854961\pi\)
\(578\) 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 0.971764 0.235954i \(-0.0758216\pi\)
−0.993861 + 0.110638i \(0.964711\pi\)
\(588\) 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 −0.297522 0.954715i \(-0.596160\pi\)
0.385764 + 0.922598i \(0.373938\pi\)
\(600\) 0 0
\(601\) −2569.25 14571.0i −0.174379 0.988955i −0.938858 0.344305i \(-0.888114\pi\)
0.764478 0.644649i \(-0.222997\pi\)
\(602\) 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 0.287894 0.957662i \(-0.407045\pi\)
−0.893121 + 0.449817i \(0.851489\pi\)
\(608\) 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 0.952498 0.304545i \(-0.0985042\pi\)
−0.739992 + 0.672615i \(0.765171\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2856.84 16201.9i 0.186405 1.05716i −0.737732 0.675094i \(-0.764103\pi\)
0.924137 0.382061i \(-0.124786\pi\)
\(618\) 0 0
\(619\) −13064.5 + 10962.4i −0.848316 + 0.711822i −0.959418 0.281987i \(-0.909006\pi\)
0.111102 + 0.993809i \(0.464562\pi\)
\(620\) 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 −0.537163 0.843479i \(-0.680504\pi\)
0.999055 + 0.0434573i \(0.0138373\pi\)
\(632\) 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 0.950610 0.310388i \(-0.100459\pi\)
−0.999440 + 0.0334585i \(0.989348\pi\)
\(642\) 0 0
\(643\) −4259.61 + 1550.37i −0.261248 + 0.0950865i −0.469324 0.883026i \(-0.655502\pi\)
0.208076 + 0.978113i \(0.433280\pi\)
\(644\) 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 −0.270397 0.962749i \(-0.587155\pi\)
0.411707 + 0.911316i \(0.364933\pi\)
\(654\) 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 −0.503196 0.864172i \(-0.667843\pi\)
−0.940950 + 0.338546i \(0.890065\pi\)
\(660\) 0 0
\(661\) −4539.92 3809.44i −0.267144 0.224161i 0.499369 0.866390i \(-0.333565\pi\)
−0.766513 + 0.642229i \(0.778010\pi\)
\(662\) 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 0.302649 0.953102i \(-0.402129\pi\)
0.991177 0.132547i \(-0.0423156\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16020.1 + 13442.5i −0.909459 + 0.763127i −0.972016 0.234915i \(-0.924519\pi\)
0.0625569 + 0.998041i \(0.480075\pi\)
\(678\) 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 0.712844 0.701323i \(-0.247407\pi\)
−0.963785 + 0.266680i \(0.914073\pi\)
\(684\) 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 −0.385677 0.922634i \(-0.626032\pi\)
−0.888503 + 0.458870i \(0.848254\pi\)
\(692\) 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 0.981146 + 0.193268i \(0.0619088\pi\)
−0.855874 + 0.517185i \(0.826980\pi\)
\(710\) 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 −0.994097 0.108495i \(-0.965397\pi\)
0.591008 + 0.806666i \(0.298730\pi\)
\(720\) 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 −0.634502 0.772921i \(-0.718795\pi\)
0.650998 + 0.759079i \(0.274351\pi\)
\(728\) 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 −0.579793 0.814764i \(-0.696867\pi\)
0.823493 0.567326i \(-0.192022\pi\)
\(734\) 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 −0.644105 0.764937i \(-0.722770\pi\)
0.984507 + 0.175343i \(0.0561033\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −25241.3 21180.0i −1.24632 1.04578i −0.997003 0.0773619i \(-0.975350\pi\)
−0.249314 0.968423i \(-0.580205\pi\)
\(744\) 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 0.0834654 0.996511i \(-0.473401\pi\)
0.704483 + 0.709721i \(0.251179\pi\)
\(752\) 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 0.0609065 0.998143i \(-0.480601\pi\)
0.688251 + 0.725472i \(0.258379\pi\)
\(762\) 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 −0.971148 0.238477i \(-0.923352\pi\)
−0.403492 0.914983i \(-0.632204\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9959.54 17250.4i 0.463415 0.802658i −0.535714 0.844400i \(-0.679957\pi\)
0.999128 + 0.0417417i \(0.0132907\pi\)
\(774\) 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 −0.999921 0.0125537i \(-0.996004\pi\)
0.943912 + 0.330197i \(0.107115\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9201.53