Properties

Label 648.4.i.s.433.2
Level $648$
Weight $4$
Character 648.433
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 433.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.4.i.s.217.2

$q$-expansion

\(f(q)\) \(=\) \(q+(10.6168 - 18.3889i) q^{5} +(-14.6168 - 25.3171i) q^{7} +O(q^{10})\) \(q+(10.6168 - 18.3889i) q^{5} +(-14.6168 - 25.3171i) q^{7} +(0.500000 + 0.866025i) q^{11} +(26.4674 - 45.8428i) q^{13} +96.9348 q^{17} +126.467 q^{19} +(-11.4674 + 19.8621i) q^{23} +(-162.935 - 282.211i) q^{25} +(-66.7663 - 115.643i) q^{29} +(-50.9158 + 88.1887i) q^{31} -620.739 q^{35} +105.065 q^{37} +(8.16844 - 14.1482i) q^{41} +(100.636 + 174.306i) q^{43} +(-125.935 - 218.125i) q^{47} +(-255.804 + 443.066i) q^{49} +148.038 q^{53} +21.2337 q^{55} +(-36.8043 + 63.7468i) q^{59} +(303.739 + 526.091i) q^{61} +(-562.000 - 973.413i) q^{65} +(-380.973 + 659.864i) q^{67} -701.196 q^{71} -287.000 q^{73} +(14.6168 - 25.3171i) q^{77} +(64.2610 + 111.303i) q^{79} +(80.2390 + 138.978i) q^{83} +(1029.14 - 1782.52i) q^{85} -430.206 q^{89} -1547.48 q^{91} +(1342.68 - 2325.60i) q^{95} +(15.5652 + 26.9598i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{5} - 24q^{7} + O(q^{10}) \) \( 4q + 8q^{5} - 24q^{7} + 2q^{11} - 32q^{13} + 112q^{17} + 368q^{19} + 92q^{23} - 376q^{25} - 336q^{29} - 376q^{31} - 1380q^{35} + 696q^{37} - 312q^{41} - 80q^{43} - 228q^{47} - 196q^{49} - 304q^{53} + 16q^{55} + 680q^{59} + 112q^{61} - 2248q^{65} - 352q^{67} - 3632q^{71} - 1148q^{73} + 24q^{77} + 1360q^{79} - 782q^{83} + 2600q^{85} - 480q^{89} - 3984q^{91} + 1924q^{95} + 338q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 10.6168 18.3889i 0.949599 1.64475i 0.203330 0.979110i \(-0.434824\pi\)
0.746269 0.665644i \(-0.231843\pi\)
\(6\) 0 0
\(7\) −14.6168 25.3171i −0.789235 1.36700i −0.926436 0.376453i \(-0.877144\pi\)
0.137201 0.990543i \(-0.456190\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.0137051 + 0.0237379i 0.872797 0.488084i \(-0.162304\pi\)
−0.859092 + 0.511822i \(0.828971\pi\)
\(12\) 0 0
\(13\) 26.4674 45.8428i 0.564671 0.978040i −0.432409 0.901678i \(-0.642336\pi\)
0.997080 0.0763620i \(-0.0243305\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 96.9348 1.38295 0.691474 0.722401i \(-0.256961\pi\)
0.691474 + 0.722401i \(0.256961\pi\)
\(18\) 0 0
\(19\) 126.467 1.52703 0.763516 0.645789i \(-0.223471\pi\)
0.763516 + 0.645789i \(0.223471\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −11.4674 + 19.8621i −0.103961 + 0.180066i −0.913313 0.407257i \(-0.866485\pi\)
0.809352 + 0.587324i \(0.199819\pi\)
\(24\) 0 0
\(25\) −162.935 282.211i −1.30348 2.25769i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −66.7663 115.643i −0.427524 0.740493i 0.569129 0.822249i \(-0.307281\pi\)
−0.996652 + 0.0817555i \(0.973947\pi\)
\(30\) 0 0
\(31\) −50.9158 + 88.1887i −0.294992 + 0.510941i −0.974983 0.222280i \(-0.928650\pi\)
0.679991 + 0.733220i \(0.261984\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −620.739 −2.99783
\(36\) 0 0
\(37\) 105.065 0.466828 0.233414 0.972378i \(-0.425010\pi\)
0.233414 + 0.972378i \(0.425010\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.16844 14.1482i 0.0311145 0.0538920i −0.850049 0.526704i \(-0.823428\pi\)
0.881163 + 0.472812i \(0.156761\pi\)
\(42\) 0 0
\(43\) 100.636 + 174.306i 0.356903 + 0.618174i 0.987442 0.157984i \(-0.0504994\pi\)
−0.630539 + 0.776158i \(0.717166\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −125.935 218.125i −0.390840 0.676954i 0.601721 0.798707i \(-0.294482\pi\)
−0.992561 + 0.121752i \(0.961149\pi\)
\(48\) 0 0
\(49\) −255.804 + 443.066i −0.745785 + 1.29174i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 148.038 0.383671 0.191836 0.981427i \(-0.438556\pi\)
0.191836 + 0.981427i \(0.438556\pi\)
\(54\) 0 0
\(55\) 21.2337 0.0520573
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −36.8043 + 63.7468i −0.0812120 + 0.140663i −0.903771 0.428017i \(-0.859212\pi\)
0.822559 + 0.568680i \(0.192546\pi\)
\(60\) 0 0
\(61\) 303.739 + 526.091i 0.637538 + 1.10425i 0.985971 + 0.166914i \(0.0533803\pi\)
−0.348434 + 0.937333i \(0.613286\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −562.000 973.413i −1.07242 1.85749i
\(66\) 0 0
\(67\) −380.973 + 659.864i −0.694675 + 1.20321i 0.275615 + 0.961268i \(0.411118\pi\)
−0.970290 + 0.241944i \(0.922215\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −701.196 −1.17207 −0.586033 0.810287i \(-0.699311\pi\)
−0.586033 + 0.810287i \(0.699311\pi\)
\(72\) 0 0
\(73\) −287.000 −0.460148 −0.230074 0.973173i \(-0.573897\pi\)
−0.230074 + 0.973173i \(0.573897\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 14.6168 25.3171i 0.0216330 0.0374695i
\(78\) 0 0
\(79\) 64.2610 + 111.303i 0.0915181 + 0.158514i 0.908150 0.418645i \(-0.137495\pi\)
−0.816632 + 0.577159i \(0.804161\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 80.2390 + 138.978i 0.106113 + 0.183793i 0.914192 0.405281i \(-0.132826\pi\)
−0.808079 + 0.589074i \(0.799493\pi\)
\(84\) 0 0
\(85\) 1029.14 1782.52i 1.31325 2.27461i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −430.206 −0.512380 −0.256190 0.966626i \(-0.582467\pi\)
−0.256190 + 0.966626i \(0.582467\pi\)
\(90\) 0 0
\(91\) −1547.48 −1.78263
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1342.68 2325.60i 1.45007 2.51159i
\(96\) 0 0
\(97\) 15.5652 + 26.9598i 0.0162929 + 0.0282201i 0.874057 0.485824i \(-0.161480\pi\)
−0.857764 + 0.514044i \(0.828147\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −491.552 851.392i −0.484269 0.838779i 0.515567 0.856849i \(-0.327581\pi\)
−0.999837 + 0.0180698i \(0.994248\pi\)
\(102\) 0 0
\(103\) 476.076 824.588i 0.455429 0.788826i −0.543284 0.839549i \(-0.682819\pi\)
0.998713 + 0.0507234i \(0.0161527\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 272.087 0.245828 0.122914 0.992417i \(-0.460776\pi\)
0.122914 + 0.992417i \(0.460776\pi\)
\(108\) 0 0
\(109\) 1355.76 1.19136 0.595680 0.803222i \(-0.296883\pi\)
0.595680 + 0.803222i \(0.296883\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −969.179 + 1678.67i −0.806838 + 1.39748i 0.108205 + 0.994129i \(0.465490\pi\)
−0.915043 + 0.403356i \(0.867844\pi\)
\(114\) 0 0
\(115\) 243.495 + 421.745i 0.197443 + 0.341982i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1416.88 2454.11i −1.09147 1.89049i
\(120\) 0 0
\(121\) 665.000 1151.81i 0.499624 0.865375i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4265.20 −3.05193
\(126\) 0 0
\(127\) 232.375 0.162362 0.0811808 0.996699i \(-0.474131\pi\)
0.0811808 + 0.996699i \(0.474131\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1397.65 + 2420.80i −0.932163 + 1.61455i −0.152548 + 0.988296i \(0.548748\pi\)
−0.779616 + 0.626258i \(0.784586\pi\)
\(132\) 0 0
\(133\) −1848.55 3201.79i −1.20519 2.08745i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −630.766 1092.52i −0.393358 0.681315i 0.599532 0.800351i \(-0.295353\pi\)
−0.992890 + 0.119035i \(0.962020\pi\)
\(138\) 0 0
\(139\) 153.684 266.189i 0.0937794 0.162431i −0.815319 0.579012i \(-0.803438\pi\)
0.909099 + 0.416581i \(0.136772\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 52.9348 0.0309554
\(144\) 0 0
\(145\) −2835.39 −1.62391
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 798.878 1383.70i 0.439239 0.760784i −0.558392 0.829577i \(-0.688581\pi\)
0.997631 + 0.0687929i \(0.0219148\pi\)
\(150\) 0 0
\(151\) 1707.70 + 2957.83i 0.920337 + 1.59407i 0.798893 + 0.601473i \(0.205419\pi\)
0.121444 + 0.992598i \(0.461248\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1081.13 + 1872.57i 0.560248 + 0.970378i
\(156\) 0 0
\(157\) −238.413 + 412.943i −0.121194 + 0.209914i −0.920239 0.391358i \(-0.872006\pi\)
0.799045 + 0.601271i \(0.205339\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 670.467 0.328200
\(162\) 0 0
\(163\) 3304.04 1.58768 0.793842 0.608124i \(-0.208078\pi\)
0.793842 + 0.608124i \(0.208078\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1045.83 1811.42i 0.484601 0.839354i −0.515242 0.857045i \(-0.672298\pi\)
0.999844 + 0.0176906i \(0.00563138\pi\)
\(168\) 0 0
\(169\) −302.544 524.022i −0.137708 0.238517i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1462.28 + 2532.74i 0.642631 + 1.11307i 0.984843 + 0.173446i \(0.0554903\pi\)
−0.342213 + 0.939622i \(0.611176\pi\)
\(174\) 0 0
\(175\) −4763.18 + 8250.08i −2.05750 + 3.56370i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 231.913 0.0968381 0.0484191 0.998827i \(-0.484582\pi\)
0.0484191 + 0.998827i \(0.484582\pi\)
\(180\) 0 0
\(181\) 2291.74 0.941125 0.470562 0.882367i \(-0.344051\pi\)
0.470562 + 0.882367i \(0.344051\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1115.46 1932.04i 0.443299 0.767817i
\(186\) 0 0
\(187\) 48.4674 + 83.9480i 0.0189534 + 0.0328282i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2108.90 3652.72i −0.798925 1.38378i −0.920316 0.391175i \(-0.872069\pi\)
0.121391 0.992605i \(-0.461264\pi\)
\(192\) 0 0
\(193\) 594.174 1029.14i 0.221604 0.383829i −0.733691 0.679483i \(-0.762204\pi\)
0.955295 + 0.295654i \(0.0955375\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3130.25 1.13209 0.566044 0.824375i \(-0.308473\pi\)
0.566044 + 0.824375i \(0.308473\pi\)
\(198\) 0 0
\(199\) −659.146 −0.234802 −0.117401 0.993085i \(-0.537456\pi\)
−0.117401 + 0.993085i \(0.537456\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1951.83 + 3380.66i −0.674834 + 1.16885i
\(204\) 0 0
\(205\) −173.446 300.417i −0.0590927 0.102352i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 63.2337 + 109.524i 0.0209281 + 0.0362485i
\(210\) 0 0
\(211\) −1806.97 + 3129.77i −0.589560 + 1.02115i 0.404730 + 0.914436i \(0.367365\pi\)
−0.994290 + 0.106711i \(0.965968\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4273.74 1.35566
\(216\) 0 0
\(217\) 2976.91 0.931272
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2565.61 4443.76i 0.780912 1.35258i
\(222\) 0 0
\(223\) 1027.07 + 1778.93i 0.308419 + 0.534197i 0.978017 0.208527i \(-0.0668669\pi\)
−0.669598 + 0.742724i \(0.733534\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1076.80 + 1865.08i 0.314846 + 0.545329i 0.979405 0.201907i \(-0.0647138\pi\)
−0.664559 + 0.747236i \(0.731381\pi\)
\(228\) 0 0
\(229\) 909.935 1576.05i 0.262577 0.454797i −0.704349 0.709854i \(-0.748761\pi\)
0.966926 + 0.255057i \(0.0820942\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3989.68 1.12177 0.560886 0.827893i \(-0.310461\pi\)
0.560886 + 0.827893i \(0.310461\pi\)
\(234\) 0 0
\(235\) −5348.12 −1.48457
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2852.16 + 4940.09i −0.771929 + 1.33702i 0.164575 + 0.986365i \(0.447375\pi\)
−0.936504 + 0.350656i \(0.885959\pi\)
\(240\) 0 0
\(241\) −3111.98 5390.10i −0.831785 1.44069i −0.896622 0.442797i \(-0.853986\pi\)
0.0648372 0.997896i \(-0.479347\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5431.67 + 9407.92i 1.41639 + 2.45327i
\(246\) 0 0
\(247\) 3347.26 5797.62i 0.862271 1.49350i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4622.52 −1.16243 −0.581217 0.813749i \(-0.697423\pi\)
−0.581217 + 0.813749i \(0.697423\pi\)
\(252\) 0 0
\(253\) −22.9348 −0.00569919
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2452.54 + 4247.93i −0.595274 + 1.03104i 0.398234 + 0.917284i \(0.369623\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(258\) 0 0
\(259\) −1535.72 2659.95i −0.368437 0.638151i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2216.42 + 3838.96i 0.519660 + 0.900077i 0.999739 + 0.0228519i \(0.00727463\pi\)
−0.480079 + 0.877225i \(0.659392\pi\)
\(264\) 0 0
\(265\) 1571.70 2722.26i 0.364334 0.631045i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4454.81 −1.00972 −0.504860 0.863201i \(-0.668456\pi\)
−0.504860 + 0.863201i \(0.668456\pi\)
\(270\) 0 0
\(271\) 3256.23 0.729897 0.364948 0.931028i \(-0.381087\pi\)
0.364948 + 0.931028i \(0.381087\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 162.935 282.211i 0.0357285 0.0618836i
\(276\) 0 0
\(277\) 1710.80 + 2963.20i 0.371091 + 0.642749i 0.989734 0.142924i \(-0.0456504\pi\)
−0.618642 + 0.785673i \(0.712317\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −857.554 1485.33i −0.182055 0.315328i 0.760525 0.649308i \(-0.224941\pi\)
−0.942580 + 0.333980i \(0.891608\pi\)
\(282\) 0 0
\(283\) 2243.80 3886.37i 0.471307 0.816328i −0.528154 0.849149i \(-0.677116\pi\)
0.999461 + 0.0328205i \(0.0104490\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −477.587 −0.0982268
\(288\) 0 0
\(289\) 4483.35 0.912548
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 842.657 1459.52i 0.168016 0.291011i −0.769707 0.638398i \(-0.779597\pi\)
0.937722 + 0.347386i \(0.112931\pi\)
\(294\) 0 0
\(295\) 781.490 + 1353.58i 0.154238 + 0.267147i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 607.023 + 1051.39i 0.117408 + 0.203357i
\(300\) 0 0
\(301\) 2941.96 5095.62i 0.563361 0.975769i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12899.0 2.42162
\(306\) 0 0
\(307\) −8079.07 −1.50194 −0.750972 0.660334i \(-0.770415\pi\)
−0.750972 + 0.660334i \(0.770415\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1278.81 2214.97i 0.233167 0.403857i −0.725571 0.688147i \(-0.758424\pi\)
0.958738 + 0.284290i \(0.0917578\pi\)
\(312\) 0 0
\(313\) 2040.72 + 3534.63i 0.368524 + 0.638303i 0.989335 0.145658i \(-0.0465298\pi\)
−0.620811 + 0.783961i \(0.713196\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3850.96 6670.06i −0.682308 1.18179i −0.974275 0.225364i \(-0.927643\pi\)
0.291967 0.956428i \(-0.405690\pi\)
\(318\) 0 0
\(319\) 66.7663 115.643i 0.0117185 0.0202970i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12259.1 2.11181
\(324\) 0 0
\(325\) −17249.8 −2.94415
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3681.54 + 6376.61i −0.616929 + 1.06855i
\(330\) 0 0
\(331\) 178.657 + 309.443i 0.0296673 + 0.0513853i 0.880478 0.474087i \(-0.157222\pi\)
−0.850811 + 0.525473i \(0.823889\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8089.46 + 14011.3i 1.31933 + 2.28514i
\(336\) 0 0
\(337\) 3329.54 5766.94i 0.538195 0.932181i −0.460806 0.887501i \(-0.652440\pi\)
0.999001 0.0446806i \(-0.0142270\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −101.832 −0.0161715
\(342\) 0 0
\(343\) 4929.05 0.775929
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3947.02 6836.44i 0.610626 1.05763i −0.380509 0.924777i \(-0.624251\pi\)
0.991135 0.132858i \(-0.0424154\pi\)
\(348\) 0 0
\(349\) 627.228 + 1086.39i 0.0962027 + 0.166628i 0.910110 0.414367i \(-0.135997\pi\)
−0.813907 + 0.580995i \(0.802664\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4302.46 + 7452.08i 0.648716 + 1.12361i 0.983430 + 0.181290i \(0.0580271\pi\)
−0.334714 + 0.942320i \(0.608640\pi\)
\(354\) 0 0
\(355\) −7444.49 + 12894.2i −1.11299 + 1.92776i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3875.61 0.569768 0.284884 0.958562i \(-0.408045\pi\)
0.284884 + 0.958562i \(0.408045\pi\)
\(360\) 0 0
\(361\) 9135.00 1.33183
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3047.03 + 5277.62i −0.436956 + 0.756831i
\(366\) 0 0
\(367\) 5945.05 + 10297.1i 0.845583 + 1.46459i 0.885114 + 0.465375i \(0.154081\pi\)
−0.0395301 + 0.999218i \(0.512586\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2163.85 3747.89i −0.302807 0.524477i
\(372\) 0 0
\(373\) −6192.25 + 10725.3i −0.859578 + 1.48883i 0.0127544 + 0.999919i \(0.495940\pi\)
−0.872332 + 0.488914i \(0.837393\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7068.52 −0.965642
\(378\) 0 0
\(379\) 2062.80 0.279576 0.139788 0.990181i \(-0.455358\pi\)
0.139788 + 0.990181i \(0.455358\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5952.62 10310.2i 0.794164 1.37553i −0.129205 0.991618i \(-0.541243\pi\)
0.923369 0.383914i \(-0.125424\pi\)
\(384\) 0 0
\(385\) −310.370 537.576i −0.0410854 0.0711621i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6358.29 + 11012.9i 0.828735 + 1.43541i 0.899031 + 0.437886i \(0.144272\pi\)
−0.0702954 + 0.997526i \(0.522394\pi\)
\(390\) 0 0
\(391\) −1111.59 + 1925.33i −0.143773 + 0.249023i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2729.00 0.347622
\(396\) 0 0
\(397\) −4531.59 −0.572881 −0.286441 0.958098i \(-0.592472\pi\)
−0.286441 + 0.958098i \(0.592472\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2414.58 + 4182.17i −0.300694 + 0.520817i −0.976293 0.216452i \(-0.930552\pi\)
0.675600 + 0.737269i \(0.263885\pi\)
\(402\) 0 0
\(403\) 2695.21 + 4668.25i 0.333147 + 0.577027i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 52.5326 + 90.9892i 0.00639790 + 0.0110815i
\(408\) 0 0
\(409\) −5742.46 + 9946.23i −0.694245 + 1.20247i 0.276190 + 0.961103i \(0.410928\pi\)
−0.970435 + 0.241364i \(0.922405\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2151.85 0.256381
\(414\) 0 0
\(415\) 3407.54 0.403059
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4105.82 7111.50i 0.478718 0.829163i −0.520985 0.853566i \(-0.674435\pi\)
0.999702 + 0.0244030i \(0.00776848\pi\)
\(420\) 0 0
\(421\) −4894.06 8476.77i −0.566561 0.981312i −0.996903 0.0786460i \(-0.974940\pi\)
0.430342 0.902666i \(-0.358393\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −15794.0 27356.1i −1.80264 3.12227i
\(426\) 0 0
\(427\) 8879.41 15379.6i 1.00633 1.74302i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11206.3 −1.25241 −0.626207 0.779657i \(-0.715394\pi\)
−0.626207 + 0.779657i \(0.715394\pi\)
\(432\) 0 0
\(433\) 719.306 0.0798329 0.0399165 0.999203i \(-0.487291\pi\)
0.0399165 + 0.999203i \(0.487291\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1450.25 + 2511.90i −0.158752 + 0.274967i
\(438\) 0 0
\(439\) −4397.50 7616.70i −0.478090 0.828075i 0.521595 0.853193i \(-0.325337\pi\)
−0.999684 + 0.0251179i \(0.992004\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1511.83 + 2618.56i 0.162142 + 0.280839i 0.935637 0.352964i \(-0.114826\pi\)
−0.773494 + 0.633803i \(0.781493\pi\)
\(444\) 0 0
\(445\) −4567.43 + 7911.03i −0.486555 + 0.842739i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3137.67 −0.329790 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(450\) 0 0
\(451\) 16.3369 0.00170571
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −16429.3 + 28456.4i −1.69279 + 2.93200i
\(456\) 0 0
\(457\) 4507.87 + 7807.86i 0.461421 + 0.799204i 0.999032 0.0439888i \(-0.0140066\pi\)
−0.537611 + 0.843193i \(0.680673\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6131.30 10619.7i −0.619442 1.07291i −0.989588 0.143932i \(-0.954025\pi\)
0.370145 0.928974i \(-0.379308\pi\)
\(462\) 0 0
\(463\) −1736.15 + 3007.10i −0.174267 + 0.301840i −0.939907 0.341429i \(-0.889089\pi\)
0.765640 + 0.643269i \(0.222422\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11825.0 −1.17172 −0.585860 0.810412i \(-0.699243\pi\)
−0.585860 + 0.810412i \(0.699243\pi\)
\(468\) 0 0
\(469\) 22274.5 2.19305
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −100.636 + 174.306i −0.00978275 + 0.0169442i
\(474\) 0 0
\(475\) −20605.9 35690.5i −1.99045 3.44756i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −851.980 1475.67i −0.0812692 0.140762i 0.822526 0.568727i \(-0.192564\pi\)
−0.903795 + 0.427965i \(0.859231\pi\)
\(480\) 0 0
\(481\) 2780.80 4816.49i 0.263604 0.456576i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 661.015 0.0618869
\(486\) 0 0
\(487\) 7721.95 0.718512 0.359256 0.933239i \(-0.383031\pi\)
0.359256 + 0.933239i \(0.383031\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10111.8 17514.2i 0.929410 1.60979i 0.145099 0.989417i \(-0.453650\pi\)
0.784311 0.620368i \(-0.213017\pi\)
\(492\) 0 0
\(493\) −6471.98 11209.8i −0.591244 1.02406i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10249.3 + 17752.3i 0.925035 + 1.60221i
\(498\) 0 0
\(499\) 6851.20 11866.6i 0.614633 1.06458i −0.375816 0.926694i \(-0.622638\pi\)
0.990449 0.137881i \(-0.0440291\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13707.6 −1.21509 −0.607546 0.794285i \(-0.707846\pi\)
−0.607546 + 0.794285i \(0.707846\pi\)
\(504\) 0 0
\(505\) −20874.9 −1.83945
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6169.59 10686.0i 0.537254 0.930551i −0.461797 0.886986i \(-0.652795\pi\)
0.999051 0.0435650i \(-0.0138716\pi\)
\(510\) 0 0
\(511\) 4195.03 + 7266.01i 0.363165 + 0.629020i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10108.8 17509.0i −0.864950 1.49814i
\(516\) 0 0
\(517\) 125.935 218.125i 0.0107130 0.0185554i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1416.70 −0.119130 −0.0595649 0.998224i \(-0.518971\pi\)
−0.0595649 + 0.998224i \(0.518971\pi\)
\(522\) 0 0
\(523\) 6696.15 0.559851 0.279925 0.960022i \(-0.409690\pi\)
0.279925 + 0.960022i \(0.409690\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4935.51 + 8548.55i −0.407958 + 0.706605i
\(528\) 0 0
\(529\) 5820.50 + 10081.4i 0.478384 + 0.828585i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −432.394 748.929i −0.0351390 0.0608625i
\(534\) 0 0
\(535\) 2888.70 5003.38i 0.233438 0.404327i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −511.609 −0.0408841
\(540\) 0 0
\(541\) 7105.69 0.564691 0.282345 0.959313i \(-0.408888\pi\)
0.282345 + 0.959313i \(0.408888\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14393.9 24931.0i 1.13132 1.95950i
\(546\) 0 0
\(547\) −6014.01 10416.6i −0.470092 0.814224i 0.529323 0.848420i \(-0.322446\pi\)
−0.999415 + 0.0341968i \(0.989113\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8443.76 14625.0i −0.652843 1.13076i
\(552\) 0 0
\(553\) 1878.59 3253.81i 0.144459 0.250210i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14529.5 −1.10527 −0.552634 0.833424i \(-0.686377\pi\)
−0.552634 + 0.833424i \(0.686377\pi\)
\(558\) 0 0
\(559\) 10654.3 0.806131
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5116.72 + 8862.42i −0.383027 + 0.663422i −0.991493 0.130158i \(-0.958452\pi\)
0.608467 + 0.793579i \(0.291785\pi\)
\(564\) 0 0
\(565\) 20579.2 + 35644.3i 1.53235 + 2.65410i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 159.730 + 276.660i 0.0117684 + 0.0203835i 0.871850 0.489774i \(-0.162921\pi\)
−0.860081 + 0.510157i \(0.829587\pi\)
\(570\) 0 0
\(571\) 3396.98 5883.74i 0.248965 0.431221i −0.714274 0.699866i \(-0.753243\pi\)
0.963239 + 0.268646i \(0.0865761\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7473.74 0.542046
\(576\) 0 0
\(577\) −11145.6 −0.804156 −0.402078 0.915605i \(-0.631712\pi\)
−0.402078 + 0.915605i \(0.631712\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2345.68 4062.84i 0.167496 0.290112i
\(582\) 0 0
\(583\) 74.0190 + 128.205i 0.00525824 + 0.00910753i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11908.8 20626.6i −0.837356 1.45034i −0.892098 0.451843i \(-0.850767\pi\)
0.0547416 0.998501i \(-0.482566\pi\)
\(588\) 0 0
\(589\) −6439.19 + 11153.0i −0.450462 + 0.780223i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16416.2 1.13682 0.568408 0.822747i \(-0.307559\pi\)
0.568408 + 0.822747i \(0.307559\pi\)
\(594\) 0 0
\(595\) −60171.2 −4.14585
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2400.85 + 4158.39i −0.163766 + 0.283652i −0.936216 0.351424i \(-0.885698\pi\)
0.772450 + 0.635075i \(0.219031\pi\)
\(600\) 0 0
\(601\) −2262.11 3918.08i −0.153533 0.265927i 0.778991 0.627035i \(-0.215732\pi\)
−0.932524 + 0.361108i \(0.882398\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14120.4 24457.3i −0.948886 1.64352i
\(606\) 0 0
\(607\) 7489.15 12971.6i 0.500783 0.867382i −0.499216 0.866477i \(-0.666379\pi\)
1.00000 0.000904500i \(-0.000287911\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13332.6 −0.882784
\(612\) 0 0
\(613\) 11651.6 0.767709 0.383854 0.923394i \(-0.374596\pi\)
0.383854 + 0.923394i \(0.374596\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −170.560 + 295.418i −0.0111288 + 0.0192757i −0.871536 0.490331i \(-0.836876\pi\)
0.860407 + 0.509607i \(0.170209\pi\)
\(618\) 0 0
\(619\) −9207.57 15948.0i −0.597873 1.03555i −0.993135 0.116978i \(-0.962679\pi\)
0.395262 0.918569i \(-0.370654\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6288.26 + 10891.6i 0.404388 + 0.700421i
\(624\) 0 0
\(625\) −24916.1 + 43156.0i −1.59463 + 2.76198i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10184.5 0.645599
\(630\) 0 0
\(631\) 13557.6 0.855341 0.427671 0.903935i \(-0.359334\pi\)
0.427671 + 0.903935i \(0.359334\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2467.09 4273.12i 0.154179 0.267045i
\(636\) 0 0
\(637\) 13540.9 + 23453.6i 0.842247 + 1.45881i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4841.27 + 8385.33i 0.298313 + 0.516694i 0.975750 0.218887i \(-0.0702427\pi\)
−0.677437 + 0.735581i \(0.736909\pi\)
\(642\) 0 0
\(643\) 1629.75 2822.81i 0.0999551 0.173127i −0.811711 0.584060i \(-0.801463\pi\)
0.911666 + 0.410932i \(0.134797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8115.35 0.493118 0.246559 0.969128i \(-0.420700\pi\)
0.246559 + 0.969128i \(0.420700\pi\)
\(648\) 0 0
\(649\) −73.6085 −0.00445206
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1713.87 + 2968.51i −0.102709 + 0.177897i −0.912800 0.408407i \(-0.866084\pi\)
0.810091 + 0.586304i \(0.199418\pi\)
\(654\) 0 0
\(655\) 29677.3 + 51402.6i 1.77036 + 3.06636i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6910.11 11968.7i −0.408467 0.707485i 0.586251 0.810129i \(-0.300603\pi\)
−0.994718 + 0.102644i \(0.967270\pi\)
\(660\) 0 0
\(661\) 11359.8 19675.8i 0.668451 1.15779i −0.309886 0.950774i \(-0.600291\pi\)
0.978337 0.207018i \(-0.0663759\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −78503.2 −4.57778
\(666\) 0 0
\(667\) 3062.54 0.177784
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −303.739 + 526.091i −0.0174750 + 0.0302676i
\(672\) 0 0
\(673\) 2566.59 + 4445.46i 0.147005 + 0.254621i 0.930119 0.367257i \(-0.119703\pi\)
−0.783114 + 0.621878i \(0.786370\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4647.94 + 8050.46i 0.263862 + 0.457023i 0.967265 0.253769i \(-0.0816702\pi\)
−0.703403 + 0.710792i \(0.748337\pi\)
\(678\) 0 0
\(679\) 455.030 788.134i 0.0257179 0.0445447i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13824.3 −0.774486 −0.387243 0.921978i \(-0.626573\pi\)
−0.387243 + 0.921978i \(0.626573\pi\)
\(684\) 0 0
\(685\) −26787.0 −1.49413
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3918.18 6786.48i 0.216648 0.375246i
\(690\) 0 0
\(691\) 5507.61 + 9539.47i 0.303212 + 0.525179i 0.976862 0.213872i \(-0.0686076\pi\)
−0.673650 + 0.739051i \(0.735274\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3263.29 5652.18i −0.178106 0.308488i
\(696\) 0 0
\(697\) 791.806 1371.45i 0.0430298 0.0745298i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 460.523 0.0248127 0.0124064 0.999923i \(-0.496051\pi\)
0.0124064 + 0.999923i \(0.496051\pi\)
\(702\) 0 0
\(703\) 13287.3 0.712861
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14369.9 + 24889.3i −0.764405 + 1.32399i
\(708\) 0 0
\(709\) −13222.5 22902.1i −0.700398 1.21313i −0.968327 0.249686i \(-0.919672\pi\)
0.267929 0.963439i \(-0.413661\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1167.74 2022.59i −0.0613355 0.106236i
\(714\) 0 0
\(715\) 562.000 973.413i 0.0293953 0.0509141i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −15524.4 −0.805235 −0.402617 0.915368i \(-0.631899\pi\)
−0.402617 + 0.915368i \(0.631899\pi\)
\(720\) 0 0
\(721\) −27834.9 −1.43776
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −21757.1 + 37684.4i −1.11454 + 1.93043i
\(726\) 0 0
\(727\) −9467.02 16397.4i −0.482961 0.836513i 0.516848 0.856077i \(-0.327105\pi\)
−0.999809 + 0.0195647i \(0.993772\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9755.11 + 16896.3i 0.493578 + 0.854903i
\(732\) 0 0
\(733\) 8389.96 14531.8i 0.422770 0.732259i −0.573439 0.819248i \(-0.694391\pi\)
0.996209 + 0.0869891i \(0.0277245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −761.945 −0.0380823
\(738\) 0 0
\(739\) 30309.0 1.50871 0.754353 0.656469i \(-0.227951\pi\)
0.754353 + 0.656469i \(0.227951\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16049.4 27798.4i 0.792458 1.37258i −0.131983 0.991252i \(-0.542135\pi\)
0.924441 0.381325i \(-0.124532\pi\)
\(744\) 0 0
\(745\) −16963.1 29381.0i −0.834202 1.44488i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3977.05 6888.45i −0.194016 0.336046i
\(750\) 0 0
\(751\) −4717.04 + 8170.15i −0.229197 + 0.396981i −0.957570 0.288199i \(-0.906943\pi\)
0.728373 + 0.685181i \(0.240277\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 72521.7 3.49581
\(756\) 0 0
\(757\) 1280.65 0.0614876 0.0307438 0.999527i \(-0.490212\pi\)
0.0307438 + 0.999527i \(0.490212\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9812.37 16995.5i 0.467409 0.809576i −0.531898 0.846809i \(-0.678521\pi\)
0.999307 + 0.0372327i \(0.0118543\pi\)
\(762\) 0 0
\(763\) −19816.9 34323.9i −0.940264 1.62858i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1948.22 + 3374.42i 0.0917162 + 0.158857i
\(768\) 0 0
\(769\) −8822.44 + 15280.9i −0.413713 + 0.716572i −0.995292 0.0969179i \(-0.969102\pi\)
0.581580 + 0.813490i \(0.302435\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22541.7 1.04886 0.524430 0.851454i \(-0.324278\pi\)
0.524430 + 0.851454i \(0.324278\pi\)
\(774\) 0 0
\(775\) 33183.8 1.53806
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1033.04 1789.28i 0.0475129 0.0822947i
\(780\) 0 0
\(781\) −350.598 607.253i −0.0160632 0.0278223i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5062.38 + 8768.30i 0.230171 + 0.398668i
\(786\) 0 0
\(787\) 19843.9 34370.7i 0.898804 1.55677i 0.0697798 0.997562i \(-0.477770\pi\)
0.829025 0.559212i \(-0.188896\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 56665.4 2.54714
\(792\) 0 0
\(793\) 32156.7 1.44000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −995.984 + 1725.09i −0.0442654 + 0.0766700i −0.887309 0.461175i \(-0.847428\pi\)
0.843044 + 0.537845i \(0.180761\pi\)
\(798\) 0 0
\(799\) −12207.5 21143.9i −0.540511 0.936193i
\(800\) 0