Properties

Label 648.4.i.m.433.1
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 433.1
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.4.i.m.217.1

$q$-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 \(0.565176\pi\)
−0.746269 + 0.665644i \(0.768157\pi\)
\(6\) 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 0.859092 0.511822i \(-0.171029\pi\)
−0.872797 + 0.488084i \(0.837696\pi\)
\(12\) 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 \(-0.743039\pi\)
−0.691474 + 0.722401i \(0.743039\pi\)
\(18\) 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 −0.809352 0.587324i \(-0.800181\pi\)
0.913313 + 0.407257i \(0.133515\pi\)
\(24\) 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 0.996652 0.0817555i \(-0.0260527\pi\)
−0.569129 + 0.822249i \(0.692719\pi\)
\(30\) 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 −0.881163 0.472812i \(-0.843239\pi\)
0.850049 + 0.526704i \(0.176572\pi\)
\(42\) 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 0.992561 0.121752i \(-0.0388513\pi\)
−0.601721 + 0.798707i \(0.705518\pi\)
\(48\) 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 \(-0.561444\pi\)
−0.191836 + 0.981427i \(0.561444\pi\)
\(54\) 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 −0.822559 0.568680i \(-0.807454\pi\)
0.903771 + 0.428017i \(0.140788\pi\)
\(60\) 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 \(-0.300689\pi\)
0.586033 + 0.810287i \(0.300689\pi\)
\(72\) 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 0.808079 0.589074i \(-0.200507\pi\)
−0.914192 + 0.405281i \(0.867174\pi\)
\(84\) 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 \(-0.417533\pi\)
0.256190 + 0.966626i \(0.417533\pi\)
\(90\) 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 0.999837 0.0180698i \(-0.00575212\pi\)
−0.515567 + 0.856849i \(0.672419\pi\)
\(102\) 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 \(-0.539224\pi\)
−0.122914 + 0.992417i \(0.539224\pi\)
\(108\) 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 \(-0.534510\pi\)
0.915043 0.403356i \(-0.132156\pi\)
\(114\) 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 \(-0.451252\pi\)
0.779616 0.626258i \(-0.215414\pi\)
\(132\) 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 0.992890 0.119035i \(-0.0379801\pi\)
−0.599532 + 0.800351i \(0.704647\pi\)
\(138\) 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 −0.997631 0.0687929i \(-0.978085\pi\)
0.558392 + 0.829577i \(0.311419\pi\)
\(150\) 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 −0.999844 0.0176906i \(-0.994369\pi\)
0.515242 + 0.857045i \(0.327702\pi\)
\(168\) 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 \(-0.944510\pi\)
0.342213 0.939622i \(-0.388824\pi\)
\(174\) 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 \(-0.515418\pi\)
−0.0484191 + 0.998827i \(0.515418\pi\)
\(180\) 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 \(0.127931\pi\)
−0.121391 + 0.992605i \(0.538736\pi\)
\(192\) 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 \(-0.691527\pi\)
−0.566044 + 0.824375i \(0.691527\pi\)
\(198\) 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 0.664559 0.747236i \(-0.268619\pi\)
−0.979405 + 0.201907i \(0.935286\pi\)
\(228\) 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 \(-0.689539\pi\)
−0.560886 + 0.827893i \(0.689539\pi\)
\(234\) 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 \(-0.552625\pi\)
0.936504 0.350656i \(-0.114041\pi\)
\(240\) 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 \(-0.302577\pi\)
0.581217 + 0.813749i \(0.302577\pi\)
\(252\) 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 \(-0.630377\pi\)
0.993508 0.113761i \(-0.0362899\pi\)
\(258\) 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 \(-0.992725\pi\)
0.480079 0.877225i \(-0.340608\pi\)
\(264\) 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 \(-0.331544\pi\)
0.504860 + 0.863201i \(0.331544\pi\)
\(270\) 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 0.942580 0.333980i \(-0.108392\pi\)
−0.760525 + 0.649308i \(0.775059\pi\)
\(282\) 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 −0.937722 0.347386i \(-0.887069\pi\)
0.769707 + 0.638398i \(0.220403\pi\)
\(294\) 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 −0.958738 0.284290i \(-0.908242\pi\)
0.725571 + 0.688147i \(0.241576\pi\)
\(312\) 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 \(0.0723570\pi\)
−0.291967 + 0.956428i \(0.594310\pi\)
\(318\) 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 \(0.375749\pi\)
−0.991135 + 0.132858i \(0.957585\pi\)
\(348\) 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 \(-0.941973\pi\)
0.334714 0.942320i \(-0.391360\pi\)
\(354\) 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 \(-0.591955\pi\)
−0.284884 + 0.958562i \(0.591955\pi\)
\(360\) 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 \(0.458757\pi\)
−0.923369 + 0.383914i \(0.874576\pi\)
\(384\) 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 \(-0.855728\pi\)
0.0702954 0.997526i \(-0.477606\pi\)
\(390\) 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 −0.675600 0.737269i \(-0.736115\pi\)
0.976293 + 0.216452i \(0.0694485\pi\)
\(402\) 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 −0.999702 0.0244030i \(-0.992232\pi\)
0.520985 + 0.853566i \(0.325565\pi\)
\(420\) 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 \(-0.284606\pi\)
0.626207 + 0.779657i \(0.284606\pi\)
\(432\) 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 0.773494 0.633803i \(-0.218507\pi\)
−0.935637 + 0.352964i \(0.885174\pi\)
\(444\) 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 \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(450\) 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 \(0.0459745\pi\)
−0.370145 + 0.928974i \(0.620692\pi\)
\(462\) 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 \(-0.300757\pi\)
0.585860 + 0.810412i \(0.300757\pi\)
\(468\) 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 0.903795 0.427965i \(-0.140769\pi\)
−0.822526 + 0.568727i \(0.807436\pi\)
\(480\) 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 \(0.546350\pi\)
−0.784311 + 0.620368i \(0.786983\pi\)
\(492\) 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 \(-0.292154\pi\)
0.607546 + 0.794285i \(0.292154\pi\)
\(504\) 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 \(0.347205\pi\)
−0.999051 + 0.0435650i \(0.986128\pi\)
\(510\) 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 \(-0.481029\pi\)
0.0595649 + 0.998224i \(0.481029\pi\)
\(522\) 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 \(-0.313623\pi\)
0.552634 + 0.833424i \(0.313623\pi\)
\(558\) 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 −0.608467 0.793579i \(-0.708215\pi\)
0.991493 + 0.130158i \(0.0415484\pi\)
\(564\) 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 0.860081 0.510157i \(-0.170413\pi\)
−0.871850 + 0.489774i \(0.837079\pi\)
\(570\) 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 \(0.149233\pi\)
−0.0547416 + 0.998501i \(0.517434\pi\)
\(588\) 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 \(-0.692441\pi\)
−0.568408 + 0.822747i \(0.692441\pi\)
\(594\) 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 −0.772450 0.635075i \(-0.780969\pi\)
0.936216 + 0.351424i \(0.114302\pi\)
\(600\) 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 −0.860407 0.509607i \(-0.829791\pi\)
0.871536 + 0.490331i \(0.163124\pi\)
\(618\) 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 0.677437 0.735581i \(-0.263091\pi\)
−0.975750 + 0.218887i \(0.929757\pi\)
\(642\) 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 \(-0.579300\pi\)
−0.246559 + 0.969128i \(0.579300\pi\)
\(648\) 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 −0.810091 0.586304i \(-0.800582\pi\)
0.912800 + 0.408407i \(0.133916\pi\)
\(654\) 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 0.994718 0.102644i \(-0.0327302\pi\)
−0.586251 + 0.810129i \(0.699397\pi\)
\(660\) 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 0.703403 0.710792i \(-0.251663\pi\)
−0.967265 + 0.253769i \(0.918330\pi\)
\(678\) 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 \(-0.373427\pi\)
0.387243 + 0.921978i \(0.373427\pi\)
\(684\) 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 \(-0.503949\pi\)
−0.0124064 + 0.999923i \(0.503949\pi\)
\(702\) 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 \(-0.368101\pi\)
0.402617 + 0.915368i \(0.368101\pi\)
\(720\) 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 \(0.457865\pi\)
−0.924441 + 0.381325i \(0.875468\pi\)
\(744\) 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 −0.999307 0.0372327i \(-0.988146\pi\)
0.531898 + 0.846809i \(0.321479\pi\)
\(762\) 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 \(-0.675722\pi\)
−0.524430 + 0.851454i \(0.675722\pi\)
\(774\) 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 −0.843044 0.537845i \(-0.819239\pi\)
0.887309 + 0.461175i \(0.152572\pi\)
\(798\) 0 0
\(799\) −12207.5 21143.9i −0.540511 0.936193i
\(800\)