Properties

Label 252.4.t.a.89.5
Level $252$
Weight $4$
Character 252.89
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + 14344616 x^{9} - 18123280 x^{8} - 273588032 x^{7} + 1239640536 x^{6} - 1407381792 x^{5} - 1961185792 x^{4} + 4297169408 x^{3} + 2991779296 x^{2} - 11217342336 x + 7375227456\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.5
Root \(5.70754 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.89
Dual form 252.4.t.a.17.5

$q$-expansion

\(f(q)\) \(=\) \(q+(3.41226 - 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +O(q^{10})\) \(q+(3.41226 - 5.91021i) q^{5} +(-14.9386 - 10.9471i) q^{7} +(-50.5303 + 29.1737i) q^{11} +38.5535i q^{13} +(16.1260 + 27.9310i) q^{17} +(107.846 + 62.2650i) q^{19} +(-174.217 - 100.584i) q^{23} +(39.2130 + 67.9188i) q^{25} +104.357i q^{29} +(-240.747 + 138.995i) q^{31} +(-115.674 + 50.9356i) q^{35} +(23.8286 - 41.2724i) q^{37} -387.272 q^{41} +272.528 q^{43} +(-81.5941 + 141.325i) q^{47} +(103.321 + 327.068i) q^{49} +(-313.867 + 181.211i) q^{53} +398.193i q^{55} +(-105.853 - 183.342i) q^{59} +(-202.919 - 117.155i) q^{61} +(227.859 + 131.555i) q^{65} +(-262.131 - 454.024i) q^{67} -348.689i q^{71} +(465.143 - 268.550i) q^{73} +(1074.22 + 117.348i) q^{77} +(-362.792 + 628.374i) q^{79} -392.121 q^{83} +220.104 q^{85} +(430.015 - 744.807i) q^{89} +(422.050 - 575.934i) q^{91} +(735.998 - 424.929i) q^{95} -978.030i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{7} + O(q^{10}) \) \( 16q - 4q^{7} - 72q^{19} - 212q^{25} - 708q^{31} + 76q^{37} + 1408q^{43} + 400q^{49} - 1632q^{61} - 1528q^{67} - 2700q^{73} - 364q^{79} + 7392q^{85} + 2472q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) 3.41226 5.91021i 0.305202 0.528625i −0.672104 0.740456i \(-0.734609\pi\)
0.977306 + 0.211831i \(0.0679427\pi\)
\(6\) 0 0
\(7\) −14.9386 10.9471i −0.806607 0.591089i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −50.5303 + 29.1737i −1.38504 + 0.799654i −0.992751 0.120187i \(-0.961651\pi\)
−0.392290 + 0.919841i \(0.628317\pi\)
\(12\) 0 0
\(13\) 38.5535i 0.822525i 0.911517 + 0.411262i \(0.134912\pi\)
−0.911517 + 0.411262i \(0.865088\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16.1260 + 27.9310i 0.230066 + 0.398486i 0.957827 0.287345i \(-0.0927725\pi\)
−0.727761 + 0.685830i \(0.759439\pi\)
\(18\) 0 0
\(19\) 107.846 + 62.2650i 1.30219 + 0.751819i 0.980779 0.195121i \(-0.0625100\pi\)
0.321410 + 0.946940i \(0.395843\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −174.217 100.584i −1.57942 0.911880i −0.994940 0.100475i \(-0.967964\pi\)
−0.584484 0.811405i \(-0.698703\pi\)
\(24\) 0 0
\(25\) 39.2130 + 67.9188i 0.313704 + 0.543351i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 104.357i 0.668226i 0.942533 + 0.334113i \(0.108437\pi\)
−0.942533 + 0.334113i \(0.891563\pi\)
\(30\) 0 0
\(31\) −240.747 + 138.995i −1.39482 + 0.805299i −0.993844 0.110790i \(-0.964662\pi\)
−0.400975 + 0.916089i \(0.631329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −115.674 + 50.9356i −0.558642 + 0.245991i
\(36\) 0 0
\(37\) 23.8286 41.2724i 0.105876 0.183382i −0.808220 0.588881i \(-0.799569\pi\)
0.914096 + 0.405499i \(0.132902\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −387.272 −1.47516 −0.737582 0.675258i \(-0.764032\pi\)
−0.737582 + 0.675258i \(0.764032\pi\)
\(42\) 0 0
\(43\) 272.528 0.966515 0.483257 0.875478i \(-0.339454\pi\)
0.483257 + 0.875478i \(0.339454\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −81.5941 + 141.325i −0.253228 + 0.438604i −0.964413 0.264401i \(-0.914826\pi\)
0.711185 + 0.703005i \(0.248159\pi\)
\(48\) 0 0
\(49\) 103.321 + 327.068i 0.301229 + 0.953552i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −313.867 + 181.211i −0.813452 + 0.469646i −0.848153 0.529751i \(-0.822285\pi\)
0.0347015 + 0.999398i \(0.488952\pi\)
\(54\) 0 0
\(55\) 398.193i 0.976224i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −105.853 183.342i −0.233573 0.404561i 0.725284 0.688450i \(-0.241709\pi\)
−0.958857 + 0.283889i \(0.908375\pi\)
\(60\) 0 0
\(61\) −202.919 117.155i −0.425919 0.245905i 0.271687 0.962386i \(-0.412418\pi\)
−0.697607 + 0.716481i \(0.745752\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 227.859 + 131.555i 0.434807 + 0.251036i
\(66\) 0 0
\(67\) −262.131 454.024i −0.477976 0.827879i 0.521705 0.853126i \(-0.325296\pi\)
−0.999681 + 0.0252470i \(0.991963\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 348.689i 0.582842i −0.956595 0.291421i \(-0.905872\pi\)
0.956595 0.291421i \(-0.0941280\pi\)
\(72\) 0 0
\(73\) 465.143 268.550i 0.745765 0.430567i −0.0783969 0.996922i \(-0.524980\pi\)
0.824162 + 0.566355i \(0.191647\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1074.22 + 117.348i 1.58985 + 0.173676i
\(78\) 0 0
\(79\) −362.792 + 628.374i −0.516675 + 0.894907i 0.483138 + 0.875544i \(0.339497\pi\)
−0.999813 + 0.0193623i \(0.993836\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −392.121 −0.518565 −0.259283 0.965801i \(-0.583486\pi\)
−0.259283 + 0.965801i \(0.583486\pi\)
\(84\) 0 0
\(85\) 220.104 0.280866
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 430.015 744.807i 0.512151 0.887072i −0.487750 0.872984i \(-0.662182\pi\)
0.999901 0.0140882i \(-0.00448456\pi\)
\(90\) 0 0
\(91\) 422.050 575.934i 0.486185 0.663454i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 735.998 424.929i 0.794861 0.458913i
\(96\) 0 0
\(97\) 978.030i 1.02375i −0.859059 0.511876i \(-0.828951\pi\)
0.859059 0.511876i \(-0.171049\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 224.150 + 388.240i 0.220830 + 0.382488i 0.955060 0.296412i \(-0.0957902\pi\)
−0.734230 + 0.678900i \(0.762457\pi\)
\(102\) 0 0
\(103\) −1137.56 656.773i −1.08823 0.628289i −0.155124 0.987895i \(-0.549578\pi\)
−0.933104 + 0.359606i \(0.882911\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 161.506 + 93.2455i 0.145919 + 0.0842466i 0.571182 0.820823i \(-0.306485\pi\)
−0.425263 + 0.905070i \(0.639818\pi\)
\(108\) 0 0
\(109\) −61.5811 106.662i −0.0541137 0.0937277i 0.837700 0.546131i \(-0.183900\pi\)
−0.891813 + 0.452404i \(0.850567\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2267.03i 1.88729i 0.330956 + 0.943646i \(0.392629\pi\)
−0.330956 + 0.943646i \(0.607371\pi\)
\(114\) 0 0
\(115\) −1188.95 + 686.439i −0.964086 + 0.556615i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 64.8649 593.781i 0.0499677 0.457410i
\(120\) 0 0
\(121\) 1036.71 1795.63i 0.778894 1.34908i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1388.28 0.993376
\(126\) 0 0
\(127\) 839.285 0.586413 0.293207 0.956049i \(-0.405278\pi\)
0.293207 + 0.956049i \(0.405278\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1185.33 2053.06i 0.790559 1.36929i −0.135063 0.990837i \(-0.543124\pi\)
0.925621 0.378451i \(-0.123543\pi\)
\(132\) 0 0
\(133\) −929.444 2110.75i −0.605963 1.37613i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2656.64 1533.81i 1.65673 0.956513i 0.682520 0.730866i \(-0.260884\pi\)
0.974209 0.225647i \(-0.0724495\pi\)
\(138\) 0 0
\(139\) 2191.44i 1.33723i 0.743608 + 0.668616i \(0.233113\pi\)
−0.743608 + 0.668616i \(0.766887\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1124.75 1948.12i −0.657735 1.13923i
\(144\) 0 0
\(145\) 616.770 + 356.092i 0.353241 + 0.203944i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −398.867 230.286i −0.219305 0.126616i 0.386323 0.922363i \(-0.373745\pi\)
−0.605628 + 0.795748i \(0.707078\pi\)
\(150\) 0 0
\(151\) −317.552 550.017i −0.171139 0.296422i 0.767679 0.640834i \(-0.221412\pi\)
−0.938818 + 0.344412i \(0.888078\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1897.15i 0.983115i
\(156\) 0 0
\(157\) 479.721 276.967i 0.243859 0.140792i −0.373090 0.927795i \(-0.621702\pi\)
0.616949 + 0.787003i \(0.288368\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1501.44 + 3409.76i 0.734971 + 1.66911i
\(162\) 0 0
\(163\) −687.621 + 1190.99i −0.330421 + 0.572306i −0.982594 0.185764i \(-0.940524\pi\)
0.652173 + 0.758070i \(0.273857\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3999.79 −1.85337 −0.926685 0.375839i \(-0.877355\pi\)
−0.926685 + 0.375839i \(0.877355\pi\)
\(168\) 0 0
\(169\) 710.626 0.323453
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 225.948 391.354i 0.0992979 0.171989i −0.812096 0.583523i \(-0.801674\pi\)
0.911394 + 0.411534i \(0.135007\pi\)
\(174\) 0 0
\(175\) 157.730 1443.88i 0.0681329 0.623697i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1959.62 + 1131.39i −0.818262 + 0.472424i −0.849817 0.527078i \(-0.823287\pi\)
0.0315548 + 0.999502i \(0.489954\pi\)
\(180\) 0 0
\(181\) 3035.53i 1.24657i 0.781994 + 0.623286i \(0.214203\pi\)
−0.781994 + 0.623286i \(0.785797\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −162.619 281.664i −0.0646270 0.111937i
\(186\) 0 0
\(187\) −1629.70 940.907i −0.637302 0.367946i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1676.68 968.031i −0.635184 0.366724i 0.147573 0.989051i \(-0.452854\pi\)
−0.782757 + 0.622327i \(0.786187\pi\)
\(192\) 0 0
\(193\) 1062.00 + 1839.43i 0.396084 + 0.686038i 0.993239 0.116088i \(-0.0370356\pi\)
−0.597155 + 0.802126i \(0.703702\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2122.77i 0.767720i 0.923391 + 0.383860i \(0.125406\pi\)
−0.923391 + 0.383860i \(0.874594\pi\)
\(198\) 0 0
\(199\) 1035.18 597.659i 0.368752 0.212899i −0.304161 0.952621i \(-0.598376\pi\)
0.672913 + 0.739722i \(0.265043\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1142.40 1558.94i 0.394981 0.538995i
\(204\) 0 0
\(205\) −1321.47 + 2288.86i −0.450223 + 0.779809i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7265.99 −2.40478
\(210\) 0 0
\(211\) 188.402 0.0614698 0.0307349 0.999528i \(-0.490215\pi\)
0.0307349 + 0.999528i \(0.490215\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 929.937 1610.70i 0.294982 0.510924i
\(216\) 0 0
\(217\) 5118.01 + 559.093i 1.60107 + 0.174902i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1076.84 + 621.712i −0.327764 + 0.189235i
\(222\) 0 0
\(223\) 2802.67i 0.841618i 0.907149 + 0.420809i \(0.138254\pi\)
−0.907149 + 0.420809i \(0.861746\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −812.590 1407.45i −0.237593 0.411522i 0.722430 0.691444i \(-0.243025\pi\)
−0.960023 + 0.279921i \(0.909692\pi\)
\(228\) 0 0
\(229\) −5733.12 3310.02i −1.65439 0.955163i −0.975236 0.221167i \(-0.929013\pi\)
−0.679154 0.733996i \(-0.737653\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1356.99 + 783.461i 0.381543 + 0.220284i 0.678490 0.734610i \(-0.262635\pi\)
−0.296946 + 0.954894i \(0.595968\pi\)
\(234\) 0 0
\(235\) 556.841 + 964.477i 0.154571 + 0.267726i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5211.23i 1.41040i 0.709006 + 0.705202i \(0.249144\pi\)
−0.709006 + 0.705202i \(0.750856\pi\)
\(240\) 0 0
\(241\) −3449.81 + 1991.75i −0.922082 + 0.532364i −0.884299 0.466922i \(-0.845363\pi\)
−0.0377833 + 0.999286i \(0.512030\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2285.60 + 505.391i 0.596007 + 0.131789i
\(246\) 0 0
\(247\) −2400.53 + 4157.85i −0.618390 + 1.07108i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7086.26 −1.78199 −0.890997 0.454009i \(-0.849993\pi\)
−0.890997 + 0.454009i \(0.849993\pi\)
\(252\) 0 0
\(253\) 11737.6 2.91676
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1221.82 + 2116.25i −0.296556 + 0.513651i −0.975346 0.220682i \(-0.929172\pi\)
0.678789 + 0.734333i \(0.262505\pi\)
\(258\) 0 0
\(259\) −807.779 + 355.696i −0.193795 + 0.0853354i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2167.27 1251.27i 0.508135 0.293372i −0.223932 0.974605i \(-0.571889\pi\)
0.732067 + 0.681233i \(0.238556\pi\)
\(264\) 0 0
\(265\) 2473.36i 0.573348i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4160.18 7205.64i −0.942939 1.63322i −0.759825 0.650127i \(-0.774716\pi\)
−0.183114 0.983092i \(-0.558618\pi\)
\(270\) 0 0
\(271\) 5816.51 + 3358.16i 1.30379 + 0.752745i 0.981052 0.193742i \(-0.0620626\pi\)
0.322740 + 0.946488i \(0.395396\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3962.88 2287.97i −0.868985 0.501709i
\(276\) 0 0
\(277\) −3335.48 5777.22i −0.723500 1.25314i −0.959589 0.281407i \(-0.909199\pi\)
0.236089 0.971732i \(-0.424134\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5065.50i 1.07538i 0.843142 + 0.537692i \(0.180704\pi\)
−0.843142 + 0.537692i \(0.819296\pi\)
\(282\) 0 0
\(283\) −2227.91 + 1286.28i −0.467969 + 0.270182i −0.715389 0.698726i \(-0.753751\pi\)
0.247420 + 0.968908i \(0.420417\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5785.29 + 4239.51i 1.18988 + 0.871952i
\(288\) 0 0
\(289\) 1936.41 3353.96i 0.394139 0.682670i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5796.55 1.15576 0.577881 0.816121i \(-0.303880\pi\)
0.577881 + 0.816121i \(0.303880\pi\)
\(294\) 0 0
\(295\) −1444.79 −0.285148
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3877.87 6716.67i 0.750044 1.29911i
\(300\) 0 0
\(301\) −4071.18 2983.39i −0.779597 0.571296i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1384.82 + 799.528i −0.259983 + 0.150101i
\(306\) 0 0
\(307\) 753.054i 0.139997i 0.997547 + 0.0699985i \(0.0222994\pi\)
−0.997547 + 0.0699985i \(0.977701\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2694.45 + 4666.93i 0.491281 + 0.850924i 0.999950 0.0100384i \(-0.00319538\pi\)
−0.508668 + 0.860963i \(0.669862\pi\)
\(312\) 0 0
\(313\) −6116.48 3531.35i −1.10455 0.637712i −0.167138 0.985934i \(-0.553452\pi\)
−0.937412 + 0.348221i \(0.886786\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2126.55 1227.77i −0.376780 0.217534i 0.299636 0.954053i \(-0.403135\pi\)
−0.676416 + 0.736520i \(0.736468\pi\)
\(318\) 0 0
\(319\) −3044.47 5273.17i −0.534350 0.925521i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4016.33i 0.691872i
\(324\) 0 0
\(325\) −2618.51 + 1511.80i −0.446919 + 0.258029i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2766.00 1217.98i 0.463510 0.204101i
\(330\) 0 0
\(331\) 4255.12 7370.09i 0.706594 1.22386i −0.259519 0.965738i \(-0.583564\pi\)
0.966113 0.258119i \(-0.0831028\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3577.84 −0.583517
\(336\) 0 0
\(337\) 1803.01 0.291443 0.145722 0.989326i \(-0.453450\pi\)
0.145722 + 0.989326i \(0.453450\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8110.00 14046.9i 1.28792 2.23075i
\(342\) 0 0
\(343\) 2036.98 6017.00i 0.320661 0.947194i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7237.09 4178.34i 1.11962 0.646412i 0.178314 0.983974i \(-0.442936\pi\)
0.941303 + 0.337562i \(0.109602\pi\)
\(348\) 0 0
\(349\) 4977.74i 0.763474i 0.924271 + 0.381737i \(0.124674\pi\)
−0.924271 + 0.381737i \(0.875326\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3820.07 + 6616.56i 0.575983 + 0.997631i 0.995934 + 0.0900846i \(0.0287137\pi\)
−0.419952 + 0.907547i \(0.637953\pi\)
\(354\) 0 0
\(355\) −2060.82 1189.82i −0.308105 0.177884i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3601.64 + 2079.40i 0.529490 + 0.305701i 0.740809 0.671716i \(-0.234442\pi\)
−0.211319 + 0.977417i \(0.567776\pi\)
\(360\) 0 0
\(361\) 4324.35 + 7490.00i 0.630464 + 1.09200i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3665.45i 0.525640i
\(366\) 0 0
\(367\) −1885.57 + 1088.64i −0.268191 + 0.154840i −0.628065 0.778161i \(-0.716153\pi\)
0.359874 + 0.933001i \(0.382820\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6672.46 + 728.902i 0.933738 + 0.102002i
\(372\) 0 0
\(373\) 190.136 329.324i 0.0263937 0.0457152i −0.852527 0.522683i \(-0.824931\pi\)
0.878921 + 0.476968i \(0.158264\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4023.32 −0.549632
\(378\) 0 0
\(379\) 6918.48 0.937673 0.468837 0.883285i \(-0.344673\pi\)
0.468837 + 0.883285i \(0.344673\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 63.4117 109.832i 0.00846002 0.0146532i −0.861764 0.507309i \(-0.830640\pi\)
0.870224 + 0.492656i \(0.163974\pi\)
\(384\) 0 0
\(385\) 4359.06 5948.43i 0.577035 0.787429i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1278.19 737.963i 0.166598 0.0961856i −0.414383 0.910103i \(-0.636002\pi\)
0.580981 + 0.813917i \(0.302669\pi\)
\(390\) 0 0
\(391\) 6488.06i 0.839170i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2475.88 + 4288.35i 0.315380 + 0.546254i
\(396\) 0 0
\(397\) 751.551 + 433.908i 0.0950107 + 0.0548545i 0.546753 0.837294i \(-0.315864\pi\)
−0.451742 + 0.892149i \(0.649197\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −603.832 348.623i −0.0751968 0.0434149i 0.461930 0.886916i \(-0.347157\pi\)
−0.537127 + 0.843501i \(0.680490\pi\)
\(402\) 0 0
\(403\) −5358.75 9281.63i −0.662378 1.14727i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2780.68i 0.338656i
\(408\) 0 0
\(409\) −5359.98 + 3094.59i −0.648005 + 0.374126i −0.787692 0.616070i \(-0.788724\pi\)
0.139686 + 0.990196i \(0.455391\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −425.780 + 3897.65i −0.0507295 + 0.464384i
\(414\) 0 0
\(415\) −1338.02 + 2317.52i −0.158267 + 0.274127i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1443.53 0.168308 0.0841538 0.996453i \(-0.473181\pi\)
0.0841538 + 0.996453i \(0.473181\pi\)
\(420\) 0 0
\(421\) −15750.0 −1.82330 −0.911648 0.410971i \(-0.865190\pi\)
−0.911648 + 0.410971i \(0.865190\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1264.69 + 2190.51i −0.144345 + 0.250013i
\(426\) 0 0
\(427\) 1748.80 + 3971.50i 0.198198 + 0.450104i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9792.23 5653.55i 1.09437 0.631837i 0.159637 0.987176i \(-0.448968\pi\)
0.934738 + 0.355339i \(0.115634\pi\)
\(432\) 0 0
\(433\) 2318.26i 0.257295i 0.991690 + 0.128647i \(0.0410635\pi\)
−0.991690 + 0.128647i \(0.958936\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12525.7 21695.2i −1.37114 2.37488i
\(438\) 0 0
\(439\) −6678.84 3856.03i −0.726113 0.419222i 0.0908855 0.995861i \(-0.471030\pi\)
−0.816998 + 0.576640i \(0.804364\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11158.1 + 6442.15i 1.19670 + 0.690916i 0.959818 0.280623i \(-0.0905410\pi\)
0.236883 + 0.971538i \(0.423874\pi\)
\(444\) 0 0
\(445\) −2934.64 5082.95i −0.312619 0.541472i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 319.989i 0.0336330i 0.999859 + 0.0168165i \(0.00535311\pi\)
−0.999859 + 0.0168165i \(0.994647\pi\)
\(450\) 0 0
\(451\) 19569.0 11298.1i 2.04316 1.17962i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1963.75 4459.64i −0.202334 0.459497i
\(456\) 0 0
\(457\) −3897.48 + 6750.64i −0.398942 + 0.690988i −0.993596 0.112994i \(-0.963956\pi\)
0.594653 + 0.803982i \(0.297289\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4610.97 −0.465844 −0.232922 0.972495i \(-0.574829\pi\)
−0.232922 + 0.972495i \(0.574829\pi\)
\(462\) 0 0
\(463\) 15203.3 1.52604 0.763022 0.646373i \(-0.223715\pi\)
0.763022 + 0.646373i \(0.223715\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8060.07 + 13960.4i −0.798663 + 1.38332i 0.121824 + 0.992552i \(0.461126\pi\)
−0.920487 + 0.390773i \(0.872208\pi\)
\(468\) 0 0
\(469\) −1054.39 + 9652.05i −0.103811 + 0.950299i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −13770.9 + 7950.65i −1.33866 + 0.772878i
\(474\) 0 0
\(475\) 9766.37i 0.943393i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3361.99 5823.14i −0.320696 0.555461i 0.659936 0.751322i \(-0.270583\pi\)
−0.980632 + 0.195861i \(0.937250\pi\)
\(480\) 0 0
\(481\) 1591.20 + 918.678i 0.150836 + 0.0870854i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5780.36 3337.29i −0.541181 0.312451i
\(486\) 0 0
\(487\) 5029.52 + 8711.38i 0.467986 + 0.810575i 0.999331 0.0365803i \(-0.0116465\pi\)
−0.531345 + 0.847156i \(0.678313\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18097.6i 1.66340i 0.555222 + 0.831702i \(0.312633\pi\)
−0.555222 + 0.831702i \(0.687367\pi\)
\(492\) 0 0
\(493\) −2914.78 + 1682.85i −0.266278 + 0.153736i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3817.14 + 5208.91i −0.344511 + 0.470124i
\(498\) 0 0
\(499\) −5594.25 + 9689.53i −0.501870 + 0.869264i 0.498128 + 0.867104i \(0.334021\pi\)
−0.999998 + 0.00216055i \(0.999312\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2912.13 −0.258142 −0.129071 0.991635i \(-0.541200\pi\)
−0.129071 + 0.991635i \(0.541200\pi\)
\(504\) 0 0
\(505\) 3059.44 0.269591
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2400.48 4157.75i 0.209036 0.362061i −0.742375 0.669984i \(-0.766301\pi\)
0.951411 + 0.307924i \(0.0996341\pi\)
\(510\) 0 0
\(511\) −9888.41 1080.21i −0.856042 0.0935144i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7763.33 + 4482.16i −0.664258 + 0.383510i
\(516\) 0 0
\(517\) 9521.61i 0.809980i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3256.63 + 5640.65i 0.273849 + 0.474321i 0.969844 0.243726i \(-0.0783697\pi\)
−0.695995 + 0.718047i \(0.745036\pi\)
\(522\) 0 0
\(523\) −3856.61 2226.62i −0.322443 0.186163i 0.330038 0.943968i \(-0.392939\pi\)
−0.652481 + 0.757805i \(0.726272\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7764.54 4482.86i −0.641800 0.370543i
\(528\) 0 0
\(529\) 14150.9 + 24510.0i 1.16305 + 2.01447i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14930.7i 1.21336i
\(534\) 0 0
\(535\) 1102.20 636.356i 0.0890697 0.0514244i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −14762.7 13512.6i −1.17973 1.07983i
\(540\) 0 0
\(541\) −3885.32 + 6729.58i −0.308767 + 0.534800i −0.978093 0.208169i \(-0.933250\pi\)
0.669326 + 0.742969i \(0.266583\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −840.523 −0.0660624
\(546\) 0 0
\(547\) −4095.62 −0.320139 −0.160069 0.987106i \(-0.551172\pi\)
−0.160069 + 0.987106i \(0.551172\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6497.77 + 11254.5i −0.502385 + 0.870156i
\(552\) 0 0
\(553\) 12298.5 5415.48i 0.945722 0.416437i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −219.268 + 126.594i −0.0166799 + 0.00963012i −0.508317 0.861170i \(-0.669732\pi\)
0.491637 + 0.870800i \(0.336399\pi\)
\(558\) 0 0
\(559\) 10506.9i 0.794982i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10252.3 + 17757.6i 0.767469 + 1.32929i 0.938931 + 0.344104i \(0.111817\pi\)
−0.171463 + 0.985191i \(0.554849\pi\)
\(564\) 0 0
\(565\) 13398.6 + 7735.69i 0.997670 + 0.576005i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11746.8 6782.03i −0.865470 0.499679i 0.000370481 1.00000i \(-0.499882\pi\)
−0.865840 + 0.500321i \(0.833215\pi\)
\(570\) 0 0
\(571\) 2350.96 + 4071.98i 0.172302 + 0.298436i 0.939224 0.343304i \(-0.111546\pi\)
−0.766922 + 0.641740i \(0.778213\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 15776.8i 1.14424i
\(576\) 0 0
\(577\) −3418.50 + 1973.67i −0.246644 + 0.142400i −0.618227 0.786000i \(-0.712149\pi\)
0.371582 + 0.928400i \(0.378815\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5857.73 + 4292.60i 0.418278 + 0.306518i
\(582\) 0 0
\(583\) 10573.2 18313.3i 0.751110 1.30096i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12531.1 0.881116 0.440558 0.897724i \(-0.354781\pi\)
0.440558 + 0.897724i \(0.354781\pi\)
\(588\) 0 0
\(589\) −34618.1 −2.42176
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6475.41 + 11215.7i −0.448420 + 0.776686i −0.998283 0.0585683i \(-0.981346\pi\)
0.549863 + 0.835255i \(0.314680\pi\)
\(594\) 0 0
\(595\) −3288.04 2409.50i −0.226548 0.166017i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 121.786 70.3130i 0.00830722 0.00479618i −0.495841 0.868414i \(-0.665140\pi\)
0.504148 + 0.863617i \(0.331807\pi\)
\(600\) 0 0
\(601\) 19220.3i 1.30451i −0.758000 0.652255i \(-0.773823\pi\)
0.758000 0.652255i \(-0.226177\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7075.03 12254.3i −0.475440 0.823486i
\(606\) 0 0
\(607\) 14750.7 + 8516.30i 0.986344 + 0.569466i 0.904180 0.427152i \(-0.140483\pi\)
0.0821649 + 0.996619i \(0.473817\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5448.58 3145.74i −0.360763 0.208287i
\(612\) 0 0
\(613\) −3246.99 5623.95i −0.213939 0.370553i 0.739005 0.673700i \(-0.235296\pi\)
−0.952944 + 0.303147i \(0.901963\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12338.5i 0.805074i 0.915404 + 0.402537i \(0.131871\pi\)
−0.915404 + 0.402537i \(0.868129\pi\)
\(618\) 0 0
\(619\) −8967.52 + 5177.40i −0.582286 + 0.336183i −0.762041 0.647528i \(-0.775803\pi\)
0.179755 + 0.983711i \(0.442469\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14577.3 + 6418.93i −0.937442 + 0.412791i
\(624\) 0 0
\(625\) −164.430 + 284.802i −0.0105235 + 0.0182273i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1537.04 0.0974336
\(630\) 0 0
\(631\) −4917.41 −0.310236 −0.155118 0.987896i \(-0.549576\pi\)
−0.155118 + 0.987896i \(0.549576\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2863.86 4960.35i 0.178974 0.309993i
\(636\) 0 0
\(637\) −12609.6 + 3983.40i −0.784320 + 0.247768i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −14808.6 + 8549.73i −0.912486 + 0.526824i −0.881230 0.472688i \(-0.843284\pi\)
−0.0312556 + 0.999511i \(0.509951\pi\)
\(642\) 0 0
\(643\) 14631.4i 0.897365i 0.893691 + 0.448683i \(0.148107\pi\)
−0.893691 + 0.448683i \(0.851893\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14808.8 + 25649.5i 0.899833 + 1.55856i 0.827706 + 0.561161i \(0.189645\pi\)
0.0721269 + 0.997395i \(0.477021\pi\)
\(648\) 0 0
\(649\) 10697.5 + 6176.22i 0.647018 + 0.373556i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24397.1 + 14085.7i 1.46207 + 0.844127i 0.999107 0.0422510i \(-0.0134529\pi\)
0.462963 + 0.886378i \(0.346786\pi\)
\(654\) 0 0
\(655\) −8089.34 14011.2i −0.482560 0.835818i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 25287.9i 1.49480i −0.664372 0.747402i \(-0.731301\pi\)
0.664372 0.747402i \(-0.268699\pi\)
\(660\) 0 0
\(661\) 8541.36 4931.35i 0.502603 0.290178i −0.227185 0.973852i \(-0.572952\pi\)
0.729788 + 0.683674i \(0.239619\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −15646.5 1709.23i −0.912399 0.0996708i
\(666\) 0 0
\(667\) 10496.6 18180.7i 0.609342 1.05541i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 13671.4 0.786555
\(672\) 0 0
\(673\) 21145.6 1.21115 0.605574 0.795789i \(-0.292943\pi\)
0.605574 + 0.795789i \(0.292943\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12062.4 20892.7i 0.684779 1.18607i −0.288727 0.957412i \(-0.593232\pi\)
0.973506 0.228661i \(-0.0734348\pi\)
\(678\) 0 0
\(679\) −10706.6 + 14610.4i −0.605128 + 0.825765i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26779.8 15461.4i 1.50030 0.866197i 0.500296 0.865854i \(-0.333224\pi\)
1.00000 0.000342338i \(-0.000108969\pi\)
\(684\) 0 0
\(685\) 20935.1i 1.16772i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6986.33 12100.7i −0.386296 0.669084i
\(690\) 0 0
\(691\) 10946.4 + 6319.92i 0.602636 + 0.347932i 0.770078 0.637950i \(-0.220217\pi\)
−0.167442 + 0.985882i \(0.553551\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12951.9 + 7477.76i 0.706895 + 0.408126i
\(696\) 0 0
\(697\) −6245.13 10816.9i −0.339385 0.587832i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24051.5i 1.29588i −0.761690 0.647942i \(-0.775630\pi\)
0.761690 0.647942i \(-0.224370\pi\)
\(702\) 0 0
\(703\) 5139.65 2967.38i 0.275741 0.159199i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 901.621 8253.55i 0.0479617 0.439048i
\(708\) 0 0
\(709\) 5438.14 9419.14i 0.288059 0.498932i −0.685288 0.728273i \(-0.740323\pi\)
0.973346 + 0.229340i \(0.0736568\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 55922.8 2.93735
\(714\) 0 0
\(715\) −15351.7 −0.802968
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10456.8 + 18111.7i −0.542381 + 0.939431i 0.456386 + 0.889782i \(0.349144\pi\)
−0.998767 + 0.0496490i \(0.984190\pi\)
\(720\) 0 0
\(721\) 9803.80 + 22264.3i 0.506398 + 1.15002i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7087.78 + 4092.13i −0.363081 + 0.209625i
\(726\) 0 0
\(727\) 22897.9i 1.16814i −0.811704 0.584068i \(-0.801460\pi\)
0.811704 0.584068i \(-0.198540\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4394.77 + 7611.97i 0.222362 + 0.385142i
\(732\) 0 0
\(733\) −26899.9 15530.7i −1.35549 0.782590i −0.366474 0.930428i \(-0.619435\pi\)
−0.989012 + 0.147838i \(0.952769\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 26491.1 + 15294.7i 1.32403 + 0.764431i
\(738\) 0 0
\(739\) −10170.9 17616.5i −0.506281 0.876904i −0.999974 0.00726747i \(-0.997687\pi\)
0.493693 0.869636i \(-0.335647\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 31458.9i 1.55332i −0.629921 0.776660i \(-0.716913\pi\)
0.629921 0.776660i \(-0.283087\pi\)
\(744\) 0 0
\(745\) −2722.08 + 1571.59i −0.133865 + 0.0772868i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1391.90 3160.98i −0.0679023 0.154205i
\(750\) 0 0
\(751\) −9653.81 + 16720.9i −0.469071 + 0.812456i −0.999375 0.0353523i \(-0.988745\pi\)
0.530303 + 0.847808i \(0.322078\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4334.29 −0.208928
\(756\) 0 0
\(757\) −18791.2 −0.902216 −0.451108 0.892469i \(-0.648971\pi\)
−0.451108 + 0.892469i \(0.648971\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13249.7 + 22949.2i −0.631145 + 1.09318i 0.356172 + 0.934420i \(0.384082\pi\)
−0.987318 + 0.158756i \(0.949252\pi\)
\(762\) 0 0
\(763\) −247.703 + 2267.50i −0.0117529 + 0.107587i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7068.48 4080.99i 0.332761 0.192120i
\(768\) 0 0
\(769\) 29077.1i 1.36352i −0.731575 0.681761i \(-0.761215\pi\)
0.731575 0.681761i \(-0.238785\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14605.3 + 25297.2i 0.679582 + 1.17707i 0.975107 + 0.221735i \(0.0711721\pi\)
−0.295525 + 0.955335i \(0.595495\pi\)
\(774\) 0 0
\(775\) −18880.8 10900.8i −0.875119 0.505250i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −41765.8 24113.5i −1.92094 1.10906i
\(780\) 0 0
\(781\) 10172.5 + 17619.4i 0.466072 + 0.807260i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3780.33i 0.171880i
\(786\) 0 0
\(787\) 29887.2 17255.4i 1.35370 0.781561i 0.364937 0.931032i \(-0.381090\pi\)
0.988766 + 0.149471i \(0.0477571\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24817.4 33866.1i 1.11556 1.52230i
\(792\) 0 0
\(793\) 4516.74 7823.23i 0.202263 0.350329i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 40125.5 1.78333 0.891667 0.452692i \(-0.149536\pi\)
0.891667 + 0.452692i \(0.149536\pi\)
\(798\) 0 0
\(799\) −5263.13 −0.233037
\(800\) 0 0
\(801\) 0 0
\(802\) 0