Properties

Label 252.4.t.a.17.5
Level $252$
Weight $4$
Character 252.17
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 17.5
Root \(5.70754 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.17
Dual form 252.4.t.a.89.5

$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

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

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 0.977306 0.211831i \(-0.0679427\pi\)
−0.672104 + 0.740456i \(0.734609\pi\)
\(6\) 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 −0.392290 0.919841i \(-0.628317\pi\)
−0.992751 + 0.120187i \(0.961651\pi\)
\(12\) 0 0
\(13\) 38.5535i 0.822525i −0.911517 0.411262i \(-0.865088\pi\)
0.911517 0.411262i \(-0.134912\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16.1260 27.9310i 0.230066 0.398486i −0.727761 0.685830i \(-0.759439\pi\)
0.957827 + 0.287345i \(0.0927725\pi\)
\(18\) 0 0
\(19\) 107.846 62.2650i 1.30219 0.751819i 0.321410 0.946940i \(-0.395843\pi\)
0.980779 + 0.195121i \(0.0625100\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −174.217 + 100.584i −1.57942 + 0.911880i −0.584484 + 0.811405i \(0.698703\pi\)
−0.994940 + 0.100475i \(0.967964\pi\)
\(24\) 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 \(-0.891563\pi\)
0.942533 0.334113i \(-0.108437\pi\)
\(30\) 0 0
\(31\) −240.747 138.995i −1.39482 0.805299i −0.400975 0.916089i \(-0.631329\pi\)
−0.993844 + 0.110790i \(0.964662\pi\)
\(32\) 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 0.914096 0.405499i \(-0.132902\pi\)
−0.808220 + 0.588881i \(0.799569\pi\)
\(38\) 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 0.711185 0.703005i \(-0.248159\pi\)
−0.964413 + 0.264401i \(0.914826\pi\)
\(48\) 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 0.0347015 0.999398i \(-0.488952\pi\)
−0.848153 + 0.529751i \(0.822285\pi\)
\(54\) 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 −0.958857 0.283889i \(-0.908375\pi\)
0.725284 + 0.688450i \(0.241709\pi\)
\(60\) 0 0
\(61\) −202.919 + 117.155i −0.425919 + 0.245905i −0.697607 0.716481i \(-0.745752\pi\)
0.271687 + 0.962386i \(0.412418\pi\)
\(62\) 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 −0.999681 0.0252470i \(-0.991963\pi\)
0.521705 + 0.853126i \(0.325296\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 348.689i 0.582842i 0.956595 + 0.291421i \(0.0941280\pi\)
−0.956595 + 0.291421i \(0.905872\pi\)
\(72\) 0 0
\(73\) 465.143 + 268.550i 0.745765 + 0.430567i 0.824162 0.566355i \(-0.191647\pi\)
−0.0783969 + 0.996922i \(0.524980\pi\)
\(74\) 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 −0.999813 0.0193623i \(-0.993836\pi\)
0.483138 0.875544i \(-0.339497\pi\)
\(80\) 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 0.999901 + 0.0140882i \(0.00448456\pi\)
−0.487750 + 0.872984i \(0.662182\pi\)
\(90\) 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 \(0.171049\pi\)
−0.859059 + 0.511876i \(0.828951\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 224.150 388.240i 0.220830 0.382488i −0.734230 0.678900i \(-0.762457\pi\)
0.955060 + 0.296412i \(0.0957902\pi\)
\(102\) 0 0
\(103\) −1137.56 + 656.773i −1.08823 + 0.628289i −0.933104 0.359606i \(-0.882911\pi\)
−0.155124 + 0.987895i \(0.549578\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 161.506 93.2455i 0.145919 0.0842466i −0.425263 0.905070i \(-0.639818\pi\)
0.571182 + 0.820823i \(0.306485\pi\)
\(108\) 0 0
\(109\) −61.5811 + 106.662i −0.0541137 + 0.0937277i −0.891813 0.452404i \(-0.850567\pi\)
0.837700 + 0.546131i \(0.183900\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2267.03i 1.88729i −0.330956 0.943646i \(-0.607371\pi\)
0.330956 0.943646i \(-0.392629\pi\)
\(114\) 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 0.925621 + 0.378451i \(0.123543\pi\)
−0.135063 + 0.990837i \(0.543124\pi\)
\(132\) 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 0.974209 + 0.225647i \(0.0724495\pi\)
0.682520 + 0.730866i \(0.260884\pi\)
\(138\) 0 0
\(139\) 2191.44i 1.33723i −0.743608 0.668616i \(-0.766887\pi\)
0.743608 0.668616i \(-0.233113\pi\)
\(140\) 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 −0.605628 0.795748i \(-0.707078\pi\)
0.386323 + 0.922363i \(0.373745\pi\)
\(150\) 0 0
\(151\) −317.552 + 550.017i −0.171139 + 0.296422i −0.938818 0.344412i \(-0.888078\pi\)
0.767679 + 0.640834i \(0.221412\pi\)
\(152\) 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 0.616949 0.787003i \(-0.288368\pi\)
−0.373090 + 0.927795i \(0.621702\pi\)
\(158\) 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 0.652173 0.758070i \(-0.273857\pi\)
−0.982594 + 0.185764i \(0.940524\pi\)
\(164\) 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 0.911394 0.411534i \(-0.135007\pi\)
−0.812096 + 0.583523i \(0.801674\pi\)
\(174\) 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 0.0315548 0.999502i \(-0.489954\pi\)
−0.849817 + 0.527078i \(0.823287\pi\)
\(180\) 0 0
\(181\) 3035.53i 1.24657i −0.781994 0.623286i \(-0.785797\pi\)
0.781994 0.623286i \(-0.214203\pi\)
\(182\) 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 −0.782757 0.622327i \(-0.786187\pi\)
0.147573 + 0.989051i \(0.452854\pi\)
\(192\) 0 0
\(193\) 1062.00 1839.43i 0.396084 0.686038i −0.597155 0.802126i \(-0.703702\pi\)
0.993239 + 0.116088i \(0.0370356\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2122.77i 0.767720i −0.923391 0.383860i \(-0.874594\pi\)
0.923391 0.383860i \(-0.125406\pi\)
\(198\) 0 0
\(199\) 1035.18 + 597.659i 0.368752 + 0.212899i 0.672913 0.739722i \(-0.265043\pi\)
−0.304161 + 0.952621i \(0.598376\pi\)
\(200\) 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 \(-0.861746\pi\)
0.907149 0.420809i \(-0.138254\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −812.590 + 1407.45i −0.237593 + 0.411522i −0.960023 0.279921i \(-0.909692\pi\)
0.722430 + 0.691444i \(0.243025\pi\)
\(228\) 0 0
\(229\) −5733.12 + 3310.02i −1.65439 + 0.955163i −0.679154 + 0.733996i \(0.737653\pi\)
−0.975236 + 0.221167i \(0.929013\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1356.99 783.461i 0.381543 0.220284i −0.296946 0.954894i \(-0.595968\pi\)
0.678490 + 0.734610i \(0.262635\pi\)
\(234\) 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 \(-0.750856\pi\)
0.709006 0.705202i \(-0.249144\pi\)
\(240\) 0 0
\(241\) −3449.81 1991.75i −0.922082 0.532364i −0.0377833 0.999286i \(-0.512030\pi\)
−0.884299 + 0.466922i \(0.845363\pi\)
\(242\) 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 0.678789 0.734333i \(-0.262505\pi\)
−0.975346 + 0.220682i \(0.929172\pi\)
\(258\) 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 0.732067 0.681233i \(-0.238556\pi\)
−0.223932 + 0.974605i \(0.571889\pi\)
\(264\) 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 −0.183114 + 0.983092i \(0.558618\pi\)
−0.759825 + 0.650127i \(0.774716\pi\)
\(270\) 0 0
\(271\) 5816.51 3358.16i 1.30379 0.752745i 0.322740 0.946488i \(-0.395396\pi\)
0.981052 + 0.193742i \(0.0620626\pi\)
\(272\) 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 0.236089 + 0.971732i \(0.424134\pi\)
−0.959589 + 0.281407i \(0.909199\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5065.50i 1.07538i −0.843142 0.537692i \(-0.819296\pi\)
0.843142 0.537692i \(-0.180704\pi\)
\(282\) 0 0
\(283\) −2227.91 1286.28i −0.467969 0.270182i 0.247420 0.968908i \(-0.420417\pi\)
−0.715389 + 0.698726i \(0.753751\pi\)
\(284\) 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 \(-0.977701\pi\)
0.997547 0.0699985i \(-0.0222994\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2694.45 4666.93i 0.491281 0.850924i −0.508668 0.860963i \(-0.669862\pi\)
0.999950 + 0.0100384i \(0.00319538\pi\)
\(312\) 0 0
\(313\) −6116.48 + 3531.35i −1.10455 + 0.637712i −0.937412 0.348221i \(-0.886786\pi\)
−0.167138 + 0.985934i \(0.553452\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2126.55 + 1227.77i −0.376780 + 0.217534i −0.676416 0.736520i \(-0.736468\pi\)
0.299636 + 0.954053i \(0.403135\pi\)
\(318\) 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 0.966113 + 0.258119i \(0.0831028\pi\)
−0.259519 + 0.965738i \(0.583564\pi\)
\(332\) 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 0.941303 0.337562i \(-0.109602\pi\)
0.178314 + 0.983974i \(0.442936\pi\)
\(348\) 0 0
\(349\) 4977.74i 0.763474i −0.924271 0.381737i \(-0.875326\pi\)
0.924271 0.381737i \(-0.124674\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3820.07 6616.56i 0.575983 0.997631i −0.419952 0.907547i \(-0.637953\pi\)
0.995934 0.0900846i \(-0.0287137\pi\)
\(354\) 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 −0.211319 0.977417i \(-0.567776\pi\)
0.740809 + 0.671716i \(0.234442\pi\)
\(360\) 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 0.359874 0.933001i \(-0.382820\pi\)
−0.628065 + 0.778161i \(0.716153\pi\)
\(368\) 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 0.878921 0.476968i \(-0.158264\pi\)
−0.852527 + 0.522683i \(0.824931\pi\)
\(374\) 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 0.870224 0.492656i \(-0.163974\pi\)
−0.861764 + 0.507309i \(0.830640\pi\)
\(384\) 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 0.580981 0.813917i \(-0.302669\pi\)
−0.414383 + 0.910103i \(0.636002\pi\)
\(390\) 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 −0.451742 0.892149i \(-0.649197\pi\)
0.546753 + 0.837294i \(0.315864\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −603.832 + 348.623i −0.0751968 + 0.0434149i −0.537127 0.843501i \(-0.680490\pi\)
0.461930 + 0.886916i \(0.347157\pi\)
\(402\) 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 0.139686 0.990196i \(-0.455391\pi\)
−0.787692 + 0.616070i \(0.788724\pi\)
\(410\) 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 0.934738 0.355339i \(-0.115634\pi\)
0.159637 + 0.987176i \(0.448968\pi\)
\(432\) 0 0
\(433\) 2318.26i 0.257295i −0.991690 0.128647i \(-0.958936\pi\)
0.991690 0.128647i \(-0.0410635\pi\)
\(434\) 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 −0.816998 0.576640i \(-0.804364\pi\)
0.0908855 + 0.995861i \(0.471030\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11158.1 6442.15i 1.19670 0.690916i 0.236883 0.971538i \(-0.423874\pi\)
0.959818 + 0.280623i \(0.0905410\pi\)
\(444\) 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 \(-0.994647\pi\)
0.999859 0.0168165i \(-0.00535311\pi\)
\(450\) 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 0.594653 0.803982i \(-0.297289\pi\)
−0.993596 + 0.112994i \(0.963956\pi\)
\(458\) 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 −0.920487 0.390773i \(-0.872208\pi\)
0.121824 0.992552i \(-0.461126\pi\)
\(468\) 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 −0.980632 0.195861i \(-0.937250\pi\)
0.659936 + 0.751322i \(0.270583\pi\)
\(480\) 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 −0.531345 0.847156i \(-0.678313\pi\)
0.999331 + 0.0365803i \(0.0116465\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18097.6i 1.66340i −0.555222 0.831702i \(-0.687367\pi\)
0.555222 0.831702i \(-0.312633\pi\)
\(492\) 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 −0.999998 0.00216055i \(-0.999312\pi\)
0.498128 0.867104i \(-0.334021\pi\)
\(500\) 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 0.951411 0.307924i \(-0.0996341\pi\)
−0.742375 + 0.669984i \(0.766301\pi\)
\(510\) 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 −0.695995 0.718047i \(-0.745036\pi\)
0.969844 + 0.243726i \(0.0783697\pi\)
\(522\) 0 0
\(523\) −3856.61 + 2226.62i −0.322443 + 0.186163i −0.652481 0.757805i \(-0.726272\pi\)
0.330038 + 0.943968i \(0.392939\pi\)
\(524\) 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 0.669326 0.742969i \(-0.266583\pi\)
−0.978093 + 0.208169i \(0.933250\pi\)
\(542\) 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 0.491637 0.870800i \(-0.336399\pi\)
−0.508317 + 0.861170i \(0.669732\pi\)
\(558\) 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 −0.171463 0.985191i \(-0.554849\pi\)
0.938931 0.344104i \(-0.111817\pi\)
\(564\) 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 −0.865840 0.500321i \(-0.833215\pi\)
0.000370481 1.00000i \(0.499882\pi\)
\(570\) 0 0
\(571\) 2350.96 4071.98i 0.172302 0.298436i −0.766922 0.641740i \(-0.778213\pi\)
0.939224 + 0.343304i \(0.111546\pi\)
\(572\) 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 0.371582 0.928400i \(-0.378815\pi\)
−0.618227 + 0.786000i \(0.712149\pi\)
\(578\) 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 0.549863 0.835255i \(-0.314680\pi\)
−0.998283 + 0.0585683i \(0.981346\pi\)
\(594\) 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 0.504148 0.863617i \(-0.331807\pi\)
−0.495841 + 0.868414i \(0.665140\pi\)
\(600\) 0 0
\(601\) 19220.3i 1.30451i 0.758000 + 0.652255i \(0.226177\pi\)
−0.758000 + 0.652255i \(0.773823\pi\)
\(602\) 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 0.0821649 0.996619i \(-0.473817\pi\)
0.904180 + 0.427152i \(0.140483\pi\)
\(608\) 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 −0.952944 0.303147i \(-0.901963\pi\)
0.739005 + 0.673700i \(0.235296\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12338.5i 0.805074i −0.915404 0.402537i \(-0.868129\pi\)
0.915404 0.402537i \(-0.131871\pi\)
\(618\) 0 0
\(619\) −8967.52 5177.40i −0.582286 0.336183i 0.179755 0.983711i \(-0.442469\pi\)
−0.762041 + 0.647528i \(0.775803\pi\)
\(620\) 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 −0.0312556 0.999511i \(-0.509951\pi\)
−0.881230 + 0.472688i \(0.843284\pi\)
\(642\) 0 0
\(643\) 14631.4i 0.897365i −0.893691 0.448683i \(-0.851893\pi\)
0.893691 0.448683i \(-0.148107\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14808.8 25649.5i 0.899833 1.55856i 0.0721269 0.997395i \(-0.477021\pi\)
0.827706 0.561161i \(-0.189645\pi\)
\(648\) 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 0.462963 0.886378i \(-0.346786\pi\)
0.999107 + 0.0422510i \(0.0134529\pi\)
\(654\) 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 \(0.268699\pi\)
−0.664372 + 0.747402i \(0.731301\pi\)
\(660\) 0 0
\(661\) 8541.36 + 4931.35i 0.502603 + 0.290178i 0.729788 0.683674i \(-0.239619\pi\)
−0.227185 + 0.973852i \(0.572952\pi\)
\(662\) 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 0.973506 + 0.228661i \(0.0734348\pi\)
−0.288727 + 0.957412i \(0.593232\pi\)
\(678\) 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 1.00000 0.000342338i \(0.000108969\pi\)
0.500296 + 0.865854i \(0.333224\pi\)
\(684\) 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 −0.167442 0.985882i \(-0.553551\pi\)
0.770078 + 0.637950i \(0.220217\pi\)
\(692\) 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 \(0.224370\pi\)
−0.761690 + 0.647942i \(0.775630\pi\)
\(702\) 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 0.973346 0.229340i \(-0.0736568\pi\)
−0.685288 + 0.728273i \(0.740323\pi\)
\(710\) 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 −0.998767 0.0496490i \(-0.984190\pi\)
0.456386 0.889782i \(-0.349144\pi\)
\(720\) 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 \(0.198540\pi\)
−0.811704 + 0.584068i \(0.801460\pi\)
\(728\) 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 −0.989012 0.147838i \(-0.952769\pi\)
−0.366474 + 0.930428i \(0.619435\pi\)
\(734\) 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 0.493693 + 0.869636i \(0.335647\pi\)
−0.999974 + 0.00726747i \(0.997687\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 31458.9i 1.55332i 0.629921 + 0.776660i \(0.283087\pi\)
−0.629921 + 0.776660i \(0.716913\pi\)
\(744\) 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 0.530303 0.847808i \(-0.322078\pi\)
−0.999375 + 0.0353523i \(0.988745\pi\)
\(752\) 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 −0.987318 0.158756i \(-0.949252\pi\)
0.356172 0.934420i \(-0.384082\pi\)
\(762\) 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 \(0.238785\pi\)
−0.731575 + 0.681761i \(0.761215\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14605.3 25297.2i 0.679582 1.17707i −0.295525 0.955335i \(-0.595495\pi\)
0.975107 0.221735i \(-0.0711721\pi\)
\(774\) 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 0.988766 0.149471i \(-0.0477571\pi\)
0.364937 + 0.931032i \(0.381090\pi\)
\(788\) 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
\(802\)