Properties

Label 1008.4.bt.a.17.3
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.3
Root \(-0.648633 - 0.374489i\) of defining polynomial
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.a.593.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.42768 - 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +O(q^{10})\) \(q+(-5.42768 - 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +(44.9131 + 25.9306i) q^{11} +32.1880i q^{13} +(-40.7324 + 70.5506i) q^{17} +(0.0420661 - 0.0242869i) q^{19} +(-77.3322 + 44.6478i) q^{23} +(3.58060 - 6.20178i) q^{25} +175.246i q^{29} +(-186.238 - 107.524i) q^{31} +(-129.458 - 153.816i) q^{35} +(-32.2729 - 55.8983i) q^{37} -411.485 q^{41} +234.771 q^{43} +(316.076 + 547.460i) q^{47} +(321.963 - 118.274i) q^{49} +(-230.049 - 132.819i) q^{53} -562.971i q^{55} +(175.530 - 304.026i) q^{59} +(-673.827 + 389.034i) q^{61} +(302.600 - 174.706i) q^{65} +(-98.0043 + 169.748i) q^{67} +142.632i q^{71} +(676.261 + 390.439i) q^{73} +(903.046 + 327.157i) q^{77} +(644.525 + 1116.35i) q^{79} -235.123 q^{83} +884.330 q^{85} +(335.390 + 580.913i) q^{89} +(104.392 + 586.919i) q^{91} +(-0.456642 - 0.263642i) q^{95} -655.891i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 56q^{7} + O(q^{10}) \) \( 16q - 56q^{7} + 612q^{19} - 20q^{25} - 1128q^{31} - 1196q^{37} - 328q^{43} + 784q^{49} - 1632q^{61} - 308q^{67} + 4068q^{73} + 2176q^{79} - 4608q^{85} - 924q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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
\(5\) −5.42768 9.40102i −0.485466 0.840852i 0.514394 0.857554i \(-0.328017\pi\)
−0.999861 + 0.0167014i \(0.994684\pi\)
\(6\) 0 0
\(7\) 18.2341 3.24321i 0.984548 0.175117i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 44.9131 + 25.9306i 1.23107 + 0.710760i 0.967254 0.253812i \(-0.0816845\pi\)
0.263819 + 0.964572i \(0.415018\pi\)
\(12\) 0 0
\(13\) 32.1880i 0.686719i 0.939204 + 0.343360i \(0.111565\pi\)
−0.939204 + 0.343360i \(0.888435\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −40.7324 + 70.5506i −0.581121 + 1.00653i 0.414225 + 0.910174i \(0.364053\pi\)
−0.995347 + 0.0963575i \(0.969281\pi\)
\(18\) 0 0
\(19\) 0.0420661 0.0242869i 0.000507927 0.000293252i −0.499746 0.866172i \(-0.666573\pi\)
0.500254 + 0.865879i \(0.333240\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −77.3322 + 44.6478i −0.701082 + 0.404770i −0.807750 0.589525i \(-0.799315\pi\)
0.106668 + 0.994295i \(0.465982\pi\)
\(24\) 0 0
\(25\) 3.58060 6.20178i 0.0286448 0.0496142i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 175.246i 1.12215i 0.827766 + 0.561074i \(0.189612\pi\)
−0.827766 + 0.561074i \(0.810388\pi\)
\(30\) 0 0
\(31\) −186.238 107.524i −1.07901 0.622966i −0.148380 0.988930i \(-0.547406\pi\)
−0.930629 + 0.365964i \(0.880739\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −129.458 153.816i −0.625212 0.742846i
\(36\) 0 0
\(37\) −32.2729 55.8983i −0.143395 0.248368i 0.785378 0.619017i \(-0.212469\pi\)
−0.928773 + 0.370649i \(0.879135\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −411.485 −1.56740 −0.783698 0.621142i \(-0.786669\pi\)
−0.783698 + 0.621142i \(0.786669\pi\)
\(42\) 0 0
\(43\) 234.771 0.832611 0.416305 0.909225i \(-0.363325\pi\)
0.416305 + 0.909225i \(0.363325\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 316.076 + 547.460i 0.980946 + 1.69905i 0.658726 + 0.752382i \(0.271095\pi\)
0.322219 + 0.946665i \(0.395571\pi\)
\(48\) 0 0
\(49\) 321.963 118.274i 0.938668 0.344822i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −230.049 132.819i −0.596220 0.344228i 0.171333 0.985213i \(-0.445193\pi\)
−0.767553 + 0.640985i \(0.778526\pi\)
\(54\) 0 0
\(55\) 562.971i 1.38020i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 175.530 304.026i 0.387322 0.670862i −0.604766 0.796403i \(-0.706733\pi\)
0.992088 + 0.125541i \(0.0400667\pi\)
\(60\) 0 0
\(61\) −673.827 + 389.034i −1.41434 + 0.816569i −0.995793 0.0916261i \(-0.970794\pi\)
−0.418546 + 0.908196i \(0.637460\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 302.600 174.706i 0.577430 0.333379i
\(66\) 0 0
\(67\) −98.0043 + 169.748i −0.178703 + 0.309523i −0.941437 0.337190i \(-0.890524\pi\)
0.762733 + 0.646713i \(0.223857\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 142.632i 0.238412i 0.992870 + 0.119206i \(0.0380349\pi\)
−0.992870 + 0.119206i \(0.961965\pi\)
\(72\) 0 0
\(73\) 676.261 + 390.439i 1.08425 + 0.625993i 0.932040 0.362355i \(-0.118027\pi\)
0.152211 + 0.988348i \(0.451361\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 903.046 + 327.157i 1.33652 + 0.484196i
\(78\) 0 0
\(79\) 644.525 + 1116.35i 0.917908 + 1.58986i 0.802588 + 0.596534i \(0.203456\pi\)
0.115320 + 0.993328i \(0.463211\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −235.123 −0.310940 −0.155470 0.987841i \(-0.549689\pi\)
−0.155470 + 0.987841i \(0.549689\pi\)
\(84\) 0 0
\(85\) 884.330 1.12846
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 335.390 + 580.913i 0.399453 + 0.691872i 0.993658 0.112441i \(-0.0358669\pi\)
−0.594206 + 0.804313i \(0.702534\pi\)
\(90\) 0 0
\(91\) 104.392 + 586.919i 0.120256 + 0.676108i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.456642 0.263642i −0.000493163 0.000284728i
\(96\) 0 0
\(97\) 655.891i 0.686553i −0.939234 0.343276i \(-0.888463\pi\)
0.939234 0.343276i \(-0.111537\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −581.618 + 1007.39i −0.573002 + 0.992468i 0.423254 + 0.906011i \(0.360888\pi\)
−0.996256 + 0.0864572i \(0.972445\pi\)
\(102\) 0 0
\(103\) −22.8802 + 13.2099i −0.0218879 + 0.0126370i −0.510904 0.859638i \(-0.670689\pi\)
0.489016 + 0.872275i \(0.337356\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1270.53 + 733.538i −1.14791 + 0.662746i −0.948377 0.317145i \(-0.897276\pi\)
−0.199532 + 0.979891i \(0.563942\pi\)
\(108\) 0 0
\(109\) 67.5343 116.973i 0.0593450 0.102789i −0.834827 0.550513i \(-0.814432\pi\)
0.894172 + 0.447724i \(0.147765\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 288.471i 0.240151i −0.992765 0.120076i \(-0.961686\pi\)
0.992765 0.120076i \(-0.0383137\pi\)
\(114\) 0 0
\(115\) 839.469 + 484.668i 0.680703 + 0.393004i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −513.908 + 1418.53i −0.395881 + 1.09274i
\(120\) 0 0
\(121\) 679.288 + 1176.56i 0.510359 + 0.883969i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1434.66 −1.02656
\(126\) 0 0
\(127\) 2269.80 1.58592 0.792961 0.609273i \(-0.208539\pi\)
0.792961 + 0.609273i \(0.208539\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 194.846 + 337.483i 0.129952 + 0.225084i 0.923658 0.383218i \(-0.125184\pi\)
−0.793706 + 0.608302i \(0.791851\pi\)
\(132\) 0 0
\(133\) 0.688269 0.579277i 0.000448725 0.000377667i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1271.93 + 734.347i 0.793197 + 0.457953i 0.841087 0.540900i \(-0.181916\pi\)
−0.0478898 + 0.998853i \(0.515250\pi\)
\(138\) 0 0
\(139\) 624.712i 0.381204i −0.981667 0.190602i \(-0.938956\pi\)
0.981667 0.190602i \(-0.0610440\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −834.654 + 1445.66i −0.488093 + 0.845401i
\(144\) 0 0
\(145\) 1647.49 951.177i 0.943561 0.544765i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1387.25 + 800.930i −0.762739 + 0.440367i −0.830278 0.557349i \(-0.811818\pi\)
0.0675396 + 0.997717i \(0.478485\pi\)
\(150\) 0 0
\(151\) 202.188 350.200i 0.108966 0.188734i −0.806386 0.591390i \(-0.798579\pi\)
0.915351 + 0.402656i \(0.131913\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2334.43i 1.20972i
\(156\) 0 0
\(157\) −2088.91 1206.04i −1.06187 0.613071i −0.135921 0.990720i \(-0.543399\pi\)
−0.925949 + 0.377649i \(0.876733\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1265.28 + 1064.92i −0.619367 + 0.521287i
\(162\) 0 0
\(163\) −472.684 818.712i −0.227138 0.393414i 0.729821 0.683638i \(-0.239603\pi\)
−0.956959 + 0.290224i \(0.906270\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1271.18 −0.589022 −0.294511 0.955648i \(-0.595157\pi\)
−0.294511 + 0.955648i \(0.595157\pi\)
\(168\) 0 0
\(169\) 1160.93 0.528417
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2217.49 + 3840.81i 0.974525 + 1.68793i 0.681493 + 0.731825i \(0.261331\pi\)
0.293032 + 0.956103i \(0.405336\pi\)
\(174\) 0 0
\(175\) 45.1752 124.696i 0.0195139 0.0538637i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −941.835 543.769i −0.393274 0.227057i 0.290304 0.956935i \(-0.406244\pi\)
−0.683578 + 0.729878i \(0.739577\pi\)
\(180\) 0 0
\(181\) 2916.08i 1.19752i 0.800930 + 0.598758i \(0.204339\pi\)
−0.800930 + 0.598758i \(0.795661\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −350.334 + 606.796i −0.139227 + 0.241149i
\(186\) 0 0
\(187\) −3658.84 + 2112.43i −1.43081 + 0.826076i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3948.97 2279.94i 1.49601 0.863719i 0.496017 0.868313i \(-0.334796\pi\)
0.999989 + 0.00459364i \(0.00146221\pi\)
\(192\) 0 0
\(193\) 1878.60 3253.83i 0.700645 1.21355i −0.267595 0.963531i \(-0.586229\pi\)
0.968240 0.250022i \(-0.0804378\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2014.34i 0.728507i −0.931300 0.364253i \(-0.881324\pi\)
0.931300 0.364253i \(-0.118676\pi\)
\(198\) 0 0
\(199\) −10.8355 6.25590i −0.00385986 0.00222849i 0.498069 0.867137i \(-0.334043\pi\)
−0.501929 + 0.864909i \(0.667376\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 568.358 + 3195.44i 0.196507 + 1.10481i
\(204\) 0 0
\(205\) 2233.41 + 3868.38i 0.760918 + 1.31795i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.51909 0.000833727
\(210\) 0 0
\(211\) 2915.84 0.951349 0.475675 0.879621i \(-0.342204\pi\)
0.475675 + 0.879621i \(0.342204\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1274.26 2207.09i −0.404205 0.700103i
\(216\) 0 0
\(217\) −3744.60 1356.60i −1.17143 0.424387i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2270.88 1311.10i −0.691205 0.399067i
\(222\) 0 0
\(223\) 1097.87i 0.329681i 0.986320 + 0.164841i \(0.0527110\pi\)
−0.986320 + 0.164841i \(0.947289\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −250.297 + 433.527i −0.0731841 + 0.126759i −0.900295 0.435280i \(-0.856649\pi\)
0.827111 + 0.562039i \(0.189983\pi\)
\(228\) 0 0
\(229\) −981.664 + 566.764i −0.283276 + 0.163549i −0.634906 0.772590i \(-0.718961\pi\)
0.351630 + 0.936139i \(0.385628\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2975.12 + 1717.68i −0.836508 + 0.482958i −0.856076 0.516850i \(-0.827104\pi\)
0.0195676 + 0.999809i \(0.493771\pi\)
\(234\) 0 0
\(235\) 3431.12 5942.87i 0.952432 1.64966i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2213.97i 0.599203i 0.954064 + 0.299602i \(0.0968537\pi\)
−0.954064 + 0.299602i \(0.903146\pi\)
\(240\) 0 0
\(241\) 5154.55 + 2975.98i 1.37773 + 0.795435i 0.991886 0.127128i \(-0.0405760\pi\)
0.385847 + 0.922563i \(0.373909\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2859.41 2384.83i −0.745636 0.621882i
\(246\) 0 0
\(247\) 0.781746 + 1.35402i 0.000201382 + 0.000348803i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4889.86 1.22966 0.614831 0.788659i \(-0.289224\pi\)
0.614831 + 0.788659i \(0.289224\pi\)
\(252\) 0 0
\(253\) −4630.97 −1.15078
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1598.21 + 2768.18i 0.387913 + 0.671884i 0.992169 0.124906i \(-0.0398629\pi\)
−0.604256 + 0.796790i \(0.706530\pi\)
\(258\) 0 0
\(259\) −769.756 914.586i −0.184673 0.219419i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 648.189 + 374.232i 0.151973 + 0.0877419i 0.574058 0.818814i \(-0.305368\pi\)
−0.422085 + 0.906556i \(0.638702\pi\)
\(264\) 0 0
\(265\) 2883.59i 0.668444i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 649.628 1125.19i 0.147244 0.255033i −0.782964 0.622067i \(-0.786293\pi\)
0.930208 + 0.367033i \(0.119627\pi\)
\(270\) 0 0
\(271\) −72.3660 + 41.7806i −0.0162211 + 0.00936527i −0.508089 0.861305i \(-0.669648\pi\)
0.491868 + 0.870670i \(0.336314\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 321.631 185.694i 0.0705276 0.0407191i
\(276\) 0 0
\(277\) 2320.93 4019.97i 0.503434 0.871973i −0.496558 0.868003i \(-0.665403\pi\)
0.999992 0.00396948i \(-0.00126353\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 179.289i 0.0380622i 0.999819 + 0.0190311i \(0.00605816\pi\)
−0.999819 + 0.0190311i \(0.993942\pi\)
\(282\) 0 0
\(283\) 3506.14 + 2024.27i 0.736461 + 0.425196i 0.820781 0.571243i \(-0.193539\pi\)
−0.0843205 + 0.996439i \(0.526872\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7503.06 + 1334.53i −1.54318 + 0.274477i
\(288\) 0 0
\(289\) −861.761 1492.61i −0.175404 0.303809i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3389.52 −0.675828 −0.337914 0.941177i \(-0.609721\pi\)
−0.337914 + 0.941177i \(0.609721\pi\)
\(294\) 0 0
\(295\) −3810.88 −0.752128
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1437.12 2489.17i −0.277963 0.481446i
\(300\) 0 0
\(301\) 4280.84 761.412i 0.819745 0.145804i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7314.63 + 4223.11i 1.37323 + 0.792834i
\(306\) 0 0
\(307\) 2014.64i 0.374534i 0.982309 + 0.187267i \(0.0599629\pi\)
−0.982309 + 0.187267i \(0.940037\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2922.01 5061.07i 0.532772 0.922788i −0.466496 0.884524i \(-0.654484\pi\)
0.999268 0.0382648i \(-0.0121830\pi\)
\(312\) 0 0
\(313\) 2121.29 1224.73i 0.383074 0.221168i −0.296081 0.955163i \(-0.595680\pi\)
0.679155 + 0.733995i \(0.262346\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5303.24 3061.83i 0.939621 0.542490i 0.0497796 0.998760i \(-0.484148\pi\)
0.889842 + 0.456270i \(0.150815\pi\)
\(318\) 0 0
\(319\) −4544.22 + 7870.82i −0.797578 + 1.38145i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.95705i 0.000681660i
\(324\) 0 0
\(325\) 199.623 + 115.252i 0.0340710 + 0.0196709i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7538.88 + 8957.33i 1.26332 + 1.50101i
\(330\) 0 0
\(331\) 3798.52 + 6579.23i 0.630772 + 1.09253i 0.987394 + 0.158280i \(0.0505949\pi\)
−0.356622 + 0.934249i \(0.616072\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2127.74 0.347018
\(336\) 0 0
\(337\) −3863.22 −0.624460 −0.312230 0.950007i \(-0.601076\pi\)
−0.312230 + 0.950007i \(0.601076\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5576.34 9658.50i −0.885559 1.53383i
\(342\) 0 0
\(343\) 5487.11 3200.81i 0.863779 0.503870i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1579.98 + 912.204i 0.244432 + 0.141123i 0.617212 0.786797i \(-0.288262\pi\)
−0.372780 + 0.927920i \(0.621595\pi\)
\(348\) 0 0
\(349\) 1537.52i 0.235822i 0.993024 + 0.117911i \(0.0376197\pi\)
−0.993024 + 0.117911i \(0.962380\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2963.66 5133.22i 0.446855 0.773976i −0.551324 0.834291i \(-0.685877\pi\)
0.998179 + 0.0603149i \(0.0192105\pi\)
\(354\) 0 0
\(355\) 1340.88 774.159i 0.200469 0.115741i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4191.12 + 2419.74i −0.616153 + 0.355736i −0.775370 0.631508i \(-0.782436\pi\)
0.159217 + 0.987244i \(0.449103\pi\)
\(360\) 0 0
\(361\) −3429.50 + 5940.07i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8476.72i 1.21559i
\(366\) 0 0
\(367\) −9967.21 5754.57i −1.41767 0.818491i −0.421575 0.906794i \(-0.638522\pi\)
−0.996094 + 0.0883026i \(0.971856\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4625.49 1675.73i −0.647287 0.234501i
\(372\) 0 0
\(373\) −93.7487 162.378i −0.0130137 0.0225405i 0.859445 0.511228i \(-0.170809\pi\)
−0.872459 + 0.488687i \(0.837476\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5640.81 −0.770601
\(378\) 0 0
\(379\) −3515.82 −0.476506 −0.238253 0.971203i \(-0.576575\pi\)
−0.238253 + 0.971203i \(0.576575\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1014.69 + 1757.49i 0.135374 + 0.234474i 0.925740 0.378160i \(-0.123443\pi\)
−0.790366 + 0.612634i \(0.790110\pi\)
\(384\) 0 0
\(385\) −1825.83 10265.3i −0.241696 1.35887i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5577.15 3219.97i −0.726923 0.419689i 0.0903727 0.995908i \(-0.471194\pi\)
−0.817295 + 0.576219i \(0.804528\pi\)
\(390\) 0 0
\(391\) 7274.45i 0.940882i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6996.55 12118.4i 0.891227 1.54365i
\(396\) 0 0
\(397\) −8369.80 + 4832.31i −1.05811 + 0.610898i −0.924908 0.380191i \(-0.875858\pi\)
−0.133199 + 0.991089i \(0.542525\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10186.9 5881.40i 1.26860 0.732426i 0.293876 0.955843i \(-0.405055\pi\)
0.974723 + 0.223417i \(0.0717212\pi\)
\(402\) 0 0
\(403\) 3461.00 5994.62i 0.427803 0.740976i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3347.42i 0.407679i
\(408\) 0 0
\(409\) −4565.71 2636.01i −0.551980 0.318686i 0.197940 0.980214i \(-0.436575\pi\)
−0.749920 + 0.661528i \(0.769908\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2214.60 6112.92i 0.263858 0.728322i
\(414\) 0 0
\(415\) 1276.17 + 2210.39i 0.150951 + 0.261455i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5103.18 −0.595003 −0.297502 0.954721i \(-0.596153\pi\)
−0.297502 + 0.954721i \(0.596153\pi\)
\(420\) 0 0
\(421\) −8395.31 −0.971882 −0.485941 0.873992i \(-0.661523\pi\)
−0.485941 + 0.873992i \(0.661523\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 291.693 + 505.227i 0.0332922 + 0.0576638i
\(426\) 0 0
\(427\) −11024.9 + 9279.04i −1.24949 + 1.05163i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1808.68 + 1044.24i 0.202137 + 0.116704i 0.597652 0.801756i \(-0.296100\pi\)
−0.395515 + 0.918460i \(0.629434\pi\)
\(432\) 0 0
\(433\) 11495.3i 1.27582i −0.770111 0.637910i \(-0.779799\pi\)
0.770111 0.637910i \(-0.220201\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.16871 + 3.75631i −0.000237399 + 0.000411187i
\(438\) 0 0
\(439\) −3682.95 + 2126.35i −0.400404 + 0.231173i −0.686658 0.726980i \(-0.740923\pi\)
0.286254 + 0.958154i \(0.407590\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2862.03 + 1652.40i −0.306951 + 0.177218i −0.645561 0.763708i \(-0.723377\pi\)
0.338610 + 0.940927i \(0.390043\pi\)
\(444\) 0 0
\(445\) 3640.78 6306.02i 0.387842 0.671761i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6952.63i 0.730768i 0.930857 + 0.365384i \(0.119062\pi\)
−0.930857 + 0.365384i \(0.880938\pi\)
\(450\) 0 0
\(451\) −18481.1 10670.0i −1.92958 1.11404i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4951.02 4167.00i 0.510127 0.429345i
\(456\) 0 0
\(457\) −4870.57 8436.08i −0.498546 0.863508i 0.501452 0.865185i \(-0.332799\pi\)
−0.999999 + 0.00167767i \(0.999466\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5563.15 −0.562043 −0.281021 0.959702i \(-0.590673\pi\)
−0.281021 + 0.959702i \(0.590673\pi\)
\(462\) 0 0
\(463\) −4114.02 −0.412948 −0.206474 0.978452i \(-0.566199\pi\)
−0.206474 + 0.978452i \(0.566199\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3030.79 5249.49i −0.300318 0.520166i 0.675890 0.737002i \(-0.263759\pi\)
−0.976208 + 0.216837i \(0.930426\pi\)
\(468\) 0 0
\(469\) −1236.49 + 3413.05i −0.121739 + 0.336034i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 10544.3 + 6087.75i 1.02500 + 0.591787i
\(474\) 0 0
\(475\) 0.347846i 3.36005e-5i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4123.33 7141.82i 0.393319 0.681248i −0.599566 0.800325i \(-0.704660\pi\)
0.992885 + 0.119077i \(0.0379935\pi\)
\(480\) 0 0
\(481\) 1799.25 1038.80i 0.170559 0.0984724i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6166.04 + 3559.96i −0.577290 + 0.333298i
\(486\) 0 0
\(487\) 5872.08 10170.7i 0.546385 0.946366i −0.452134 0.891950i \(-0.649337\pi\)
0.998518 0.0544159i \(-0.0173297\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6008.34i 0.552246i −0.961122 0.276123i \(-0.910950\pi\)
0.961122 0.276123i \(-0.0890497\pi\)
\(492\) 0 0
\(493\) −12363.7 7138.18i −1.12948 0.652104i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 462.584 + 2600.76i 0.0417500 + 0.234728i
\(498\) 0 0
\(499\) −6824.93 11821.1i −0.612276 1.06049i −0.990856 0.134925i \(-0.956921\pi\)
0.378580 0.925569i \(-0.376413\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4862.69 −0.431047 −0.215524 0.976499i \(-0.569146\pi\)
−0.215524 + 0.976499i \(0.569146\pi\)
\(504\) 0 0
\(505\) 12627.4 1.11269
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8861.33 15348.3i −0.771653 1.33654i −0.936656 0.350250i \(-0.886097\pi\)
0.165003 0.986293i \(-0.447237\pi\)
\(510\) 0 0
\(511\) 13597.3 + 4926.05i 1.17712 + 0.426449i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 248.373 + 143.398i 0.0212517 + 0.0122697i
\(516\) 0 0
\(517\) 32784.1i 2.78887i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6877.95 11913.0i 0.578366 1.00176i −0.417301 0.908768i \(-0.637024\pi\)
0.995667 0.0929909i \(-0.0296427\pi\)
\(522\) 0 0
\(523\) −1136.17 + 655.971i −0.0949932 + 0.0548443i −0.546744 0.837300i \(-0.684133\pi\)
0.451751 + 0.892144i \(0.350800\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15171.8 8759.46i 1.25407 0.724038i
\(528\) 0 0
\(529\) −2096.65 + 3631.50i −0.172323 + 0.298472i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13244.9i 1.07636i
\(534\) 0 0
\(535\) 13792.0 + 7962.82i 1.11454 + 0.643482i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 17527.3 + 3036.65i 1.40065 + 0.242667i
\(540\) 0 0
\(541\) −597.954 1035.69i −0.0475195 0.0823061i 0.841287 0.540588i \(-0.181798\pi\)
−0.888807 + 0.458282i \(0.848465\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1466.22 −0.115240
\(546\) 0 0
\(547\) 6178.59 0.482957 0.241478 0.970406i \(-0.422368\pi\)
0.241478 + 0.970406i \(0.422368\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.25617 + 7.37189i 0.000329072 + 0.000569970i
\(552\) 0 0
\(553\) 15372.9 + 18265.3i 1.18214 + 1.40455i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2906.56 1678.10i −0.221104 0.127654i 0.385357 0.922767i \(-0.374078\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(558\) 0 0
\(559\) 7556.82i 0.571770i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1792.64 + 3104.94i −0.134193 + 0.232429i −0.925289 0.379263i \(-0.876178\pi\)
0.791096 + 0.611692i \(0.209511\pi\)
\(564\) 0 0
\(565\) −2711.92 + 1565.73i −0.201932 + 0.116585i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15835.9 + 9142.84i −1.16674 + 0.673617i −0.952910 0.303254i \(-0.901927\pi\)
−0.213829 + 0.976871i \(0.568593\pi\)
\(570\) 0 0
\(571\) −8181.51 + 14170.8i −0.599624 + 1.03858i 0.393252 + 0.919431i \(0.371350\pi\)
−0.992876 + 0.119149i \(0.961983\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 639.463i 0.0463782i
\(576\) 0 0
\(577\) −6678.26 3855.69i −0.481836 0.278188i 0.239345 0.970935i \(-0.423067\pi\)
−0.721181 + 0.692746i \(0.756401\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4287.24 + 762.552i −0.306136 + 0.0544509i
\(582\) 0 0
\(583\) −6888.14 11930.6i −0.489327 0.847539i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4182.21 0.294069 0.147034 0.989131i \(-0.453027\pi\)
0.147034 + 0.989131i \(0.453027\pi\)
\(588\) 0 0
\(589\) −10.4457 −0.000730744
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8094.65 + 14020.4i 0.560552 + 0.970905i 0.997448 + 0.0713932i \(0.0227445\pi\)
−0.436896 + 0.899512i \(0.643922\pi\)
\(594\) 0 0
\(595\) 16124.9 2868.07i 1.11102 0.197612i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11065.5 + 6388.67i 0.754798 + 0.435783i 0.827425 0.561576i \(-0.189805\pi\)
−0.0726267 + 0.997359i \(0.523138\pi\)
\(600\) 0 0
\(601\) 24022.7i 1.63046i −0.579137 0.815231i \(-0.696610\pi\)
0.579137 0.815231i \(-0.303390\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7373.92 12772.0i 0.495525 0.858274i
\(606\) 0 0
\(607\) −8371.72 + 4833.42i −0.559798 + 0.323200i −0.753065 0.657947i \(-0.771425\pi\)
0.193266 + 0.981146i \(0.438092\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17621.7 + 10173.9i −1.16677 + 0.673634i
\(612\) 0 0
\(613\) −7192.73 + 12458.2i −0.473918 + 0.820850i −0.999554 0.0298593i \(-0.990494\pi\)
0.525636 + 0.850710i \(0.323827\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7712.69i 0.503244i −0.967826 0.251622i \(-0.919036\pi\)
0.967826 0.251622i \(-0.0809639\pi\)
\(618\) 0 0
\(619\) −12398.9 7158.52i −0.805096 0.464822i 0.0401539 0.999194i \(-0.487215\pi\)
−0.845250 + 0.534371i \(0.820549\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7999.55 + 9504.67i 0.514439 + 0.611230i
\(624\) 0 0
\(625\) 7339.28 + 12712.0i 0.469714 + 0.813569i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5258.21 0.333320
\(630\) 0 0
\(631\) −4971.96 −0.313678 −0.156839 0.987624i \(-0.550130\pi\)
−0.156839 + 0.987624i \(0.550130\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12319.7 21338.4i −0.769911 1.33353i
\(636\) 0 0
\(637\) 3807.00 + 10363.4i 0.236796 + 0.644601i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25481.7 + 14711.9i 1.57015 + 0.906529i 0.996149 + 0.0876763i \(0.0279441\pi\)
0.574004 + 0.818852i \(0.305389\pi\)
\(642\) 0 0
\(643\) 31273.9i 1.91807i 0.283283 + 0.959036i \(0.408576\pi\)
−0.283283 + 0.959036i \(0.591424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4005.82 6938.29i 0.243408 0.421595i −0.718275 0.695760i \(-0.755068\pi\)
0.961683 + 0.274164i \(0.0884012\pi\)
\(648\) 0 0
\(649\) 15767.2 9103.17i 0.953644 0.550586i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13372.0 + 7720.32i −0.801357 + 0.462664i −0.843945 0.536429i \(-0.819773\pi\)
0.0425886 + 0.999093i \(0.486440\pi\)
\(654\) 0 0
\(655\) 2115.12 3663.50i 0.126175 0.218542i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 31288.9i 1.84953i −0.380537 0.924766i \(-0.624261\pi\)
0.380537 0.924766i \(-0.375739\pi\)
\(660\) 0 0
\(661\) −26263.2 15163.1i −1.54541 0.892246i −0.998483 0.0550690i \(-0.982462\pi\)
−0.546932 0.837177i \(-0.684205\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.18150 3.32629i −0.000535403 0.000193967i
\(666\) 0 0
\(667\) −7824.33 13552.1i −0.454212 0.786718i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −40351.5 −2.32154
\(672\) 0 0
\(673\) 12067.9 0.691207 0.345604 0.938381i \(-0.387674\pi\)
0.345604 + 0.938381i \(0.387674\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3272.41 5667.98i −0.185774 0.321770i 0.758063 0.652181i \(-0.226146\pi\)
−0.943837 + 0.330411i \(0.892813\pi\)
\(678\) 0 0
\(679\) −2127.19 11959.6i −0.120227 0.675944i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 27267.1 + 15742.7i 1.52759 + 0.881956i 0.999462 + 0.0327927i \(0.0104401\pi\)
0.528130 + 0.849163i \(0.322893\pi\)
\(684\) 0 0
\(685\) 15943.2i 0.889282i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4275.18 7404.82i 0.236388 0.409436i
\(690\) 0 0
\(691\) 8690.83 5017.66i 0.478459 0.276238i −0.241315 0.970447i \(-0.577579\pi\)
0.719774 + 0.694209i \(0.244245\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5872.93 + 3390.74i −0.320537 + 0.185062i
\(696\) 0 0
\(697\) 16760.8 29030.6i 0.910847 1.57763i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 768.196i 0.0413900i 0.999786 + 0.0206950i \(0.00658789\pi\)
−0.999786 + 0.0206950i \(0.993412\pi\)
\(702\) 0 0
\(703\) −2.71519 1.56761i −0.000145669 8.41019e-5i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7338.09 + 20255.2i −0.390350 + 1.07747i
\(708\) 0 0
\(709\) −6984.30 12097.2i −0.369959 0.640787i 0.619600 0.784918i \(-0.287295\pi\)
−0.989559 + 0.144130i \(0.953962\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19202.9 1.00863
\(714\) 0 0
\(715\) 18120.9 0.947810
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5984.78 10365.9i −0.310424 0.537669i 0.668031 0.744134i \(-0.267138\pi\)
−0.978454 + 0.206465i \(0.933804\pi\)
\(720\) 0 0
\(721\) −374.357 + 315.075i −0.0193367 + 0.0162746i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1086.83 + 627.484i 0.0556745 + 0.0321437i
\(726\) 0 0
\(727\) 12223.3i 0.623575i −0.950152 0.311787i \(-0.899072\pi\)
0.950152 0.311787i \(-0.100928\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −9562.80 + 16563.3i −0.483848 + 0.838049i
\(732\) 0 0
\(733\) −20598.5 + 11892.5i −1.03796 + 0.599264i −0.919253 0.393666i \(-0.871207\pi\)
−0.118702 + 0.992930i \(0.537873\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8803.34 + 5082.61i −0.439994 + 0.254030i
\(738\) 0 0
\(739\) 5739.04 9940.31i 0.285675 0.494804i −0.687097 0.726565i \(-0.741115\pi\)
0.972773 + 0.231761i \(0.0744488\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18604.0i 0.918593i 0.888283 + 0.459297i \(0.151899\pi\)
−0.888283 + 0.459297i \(0.848101\pi\)
\(744\) 0 0
\(745\) 15059.1 + 8694.38i 0.740568 + 0.427567i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −20787.8 + 17496.0i −1.01411 + 0.853523i
\(750\) 0 0
\(751\) 15506.2 + 26857.6i 0.753436 + 1.30499i 0.946148 + 0.323734i \(0.104938\pi\)
−0.192713 + 0.981255i \(0.561728\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4389.64 −0.211597
\(756\) 0 0
\(757\) −19065.9 −0.915407 −0.457703 0.889105i \(-0.651328\pi\)
−0.457703 + 0.889105i \(0.651328\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7339.58 12712.5i −0.349618 0.605556i 0.636563 0.771224i \(-0.280355\pi\)
−0.986182 + 0.165668i \(0.947022\pi\)
\(762\) 0 0
\(763\) 852.058 2351.92i 0.0404280 0.111593i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9786.01 + 5649.95i 0.460694 + 0.265982i
\(768\) 0 0
\(769\) 29972.5i 1.40551i 0.711434 + 0.702753i \(0.248046\pi\)
−0.711434 + 0.702753i \(0.751954\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11343.9 19648.2i 0.527828 0.914225i −0.471646 0.881788i \(-0.656340\pi\)
0.999474 0.0324367i \(-0.0103267\pi\)
\(774\) 0 0
\(775\) −1333.68 + 770.003i −0.0618159 + 0.0356894i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −17.3096 + 9.99369i −0.000796123 + 0.000459642i
\(780\) 0 0
\(781\) −3698.52 + 6406.02i −0.169454 + 0.293503i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 26183.9i 1.19050i
\(786\) 0 0
\(787\) 18132.8 + 10469.0i 0.821301 + 0.474178i 0.850865 0.525385i \(-0.176079\pi\)
−0.0295639 + 0.999563i \(0.509412\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −935.573 5260.01i −0.0420545 0.236440i
\(792\) 0 0
\(793\) −12522.2 21689.2i −0.560754 0.971254i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27393.4 −1.21747 −0.608735 0.793373i \(-0.708323\pi\)
−0.608735 + 0.793373i \(0.708323\pi\)
\(798\) 0 0
\(799\) −51498.2 −2.28019