Properties

Label 1008.4.bt.a.593.2
Level $1008$
Weight $4$
Character 1008.593
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 593.2
Root \(4.21355 - 2.43270i\) of defining polynomial
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.a.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.38217 + 11.0542i) q^{5} +(-2.53897 + 18.3454i) q^{7} +O(q^{10})\) \(q+(-6.38217 + 11.0542i) q^{5} +(-2.53897 + 18.3454i) q^{7} +(-46.8633 + 27.0565i) q^{11} -8.85528i q^{13} +(34.4587 + 59.6841i) q^{17} +(141.898 + 81.9246i) q^{19} +(81.3807 + 46.9852i) q^{23} +(-18.9642 - 32.8469i) q^{25} +119.620i q^{29} +(-85.6311 + 49.4391i) q^{31} +(-186.590 - 145.150i) q^{35} +(-47.0949 + 81.5708i) q^{37} -259.347 q^{41} -5.01418 q^{43} +(28.6747 - 49.6660i) q^{47} +(-330.107 - 93.1568i) q^{49} +(-407.058 + 235.015i) q^{53} -690.718i q^{55} +(-112.979 - 195.685i) q^{59} +(370.650 + 213.995i) q^{61} +(97.8884 + 56.5159i) q^{65} +(81.9267 + 141.901i) q^{67} -79.8529i q^{71} +(666.447 - 384.774i) q^{73} +(-377.379 - 928.422i) q^{77} +(267.408 - 463.165i) q^{79} +438.520 q^{83} -879.684 q^{85} +(-12.8242 + 22.2121i) q^{89} +(162.454 + 22.4833i) q^{91} +(-1811.23 + 1045.71i) q^{95} -1381.00i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 56q^{7} + O(q^{10}) \) \( 16q - 56q^{7} + 612q^{19} - 20q^{25} - 1128q^{31} - 1196q^{37} - 328q^{43} + 784q^{49} - 1632q^{61} - 308q^{67} + 4068q^{73} + 2176q^{79} - 4608q^{85} - 924q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −6.38217 + 11.0542i −0.570839 + 0.988721i 0.425642 + 0.904892i \(0.360048\pi\)
−0.996480 + 0.0838295i \(0.973285\pi\)
\(6\) 0 0
\(7\) −2.53897 + 18.3454i −0.137091 + 0.990558i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −46.8633 + 27.0565i −1.28453 + 0.741623i −0.977673 0.210133i \(-0.932610\pi\)
−0.306856 + 0.951756i \(0.599277\pi\)
\(12\) 0 0
\(13\) 8.85528i 0.188924i −0.995528 0.0944620i \(-0.969887\pi\)
0.995528 0.0944620i \(-0.0301131\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 34.4587 + 59.6841i 0.491615 + 0.851502i 0.999953 0.00965543i \(-0.00307347\pi\)
−0.508339 + 0.861157i \(0.669740\pi\)
\(18\) 0 0
\(19\) 141.898 + 81.9246i 1.71334 + 0.989199i 0.929960 + 0.367660i \(0.119841\pi\)
0.783383 + 0.621540i \(0.213492\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 81.3807 + 46.9852i 0.737785 + 0.425960i 0.821263 0.570549i \(-0.193270\pi\)
−0.0834783 + 0.996510i \(0.526603\pi\)
\(24\) 0 0
\(25\) −18.9642 32.8469i −0.151713 0.262775i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 119.620i 0.765961i 0.923756 + 0.382981i \(0.125102\pi\)
−0.923756 + 0.382981i \(0.874898\pi\)
\(30\) 0 0
\(31\) −85.6311 + 49.4391i −0.496123 + 0.286437i −0.727111 0.686520i \(-0.759137\pi\)
0.230988 + 0.972957i \(0.425804\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −186.590 145.150i −0.901129 0.700994i
\(36\) 0 0
\(37\) −47.0949 + 81.5708i −0.209253 + 0.362437i −0.951479 0.307712i \(-0.900437\pi\)
0.742227 + 0.670149i \(0.233770\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −259.347 −0.987883 −0.493941 0.869495i \(-0.664444\pi\)
−0.493941 + 0.869495i \(0.664444\pi\)
\(42\) 0 0
\(43\) −5.01418 −0.0177827 −0.00889133 0.999960i \(-0.502830\pi\)
−0.00889133 + 0.999960i \(0.502830\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 28.6747 49.6660i 0.0889921 0.154139i −0.818093 0.575086i \(-0.804969\pi\)
0.907085 + 0.420947i \(0.138302\pi\)
\(48\) 0 0
\(49\) −330.107 93.1568i −0.962412 0.271594i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −407.058 + 235.015i −1.05497 + 0.609090i −0.924038 0.382301i \(-0.875132\pi\)
−0.130937 + 0.991391i \(0.541798\pi\)
\(54\) 0 0
\(55\) 690.718i 1.69339i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −112.979 195.685i −0.249299 0.431798i 0.714033 0.700112i \(-0.246867\pi\)
−0.963331 + 0.268314i \(0.913533\pi\)
\(60\) 0 0
\(61\) 370.650 + 213.995i 0.777982 + 0.449168i 0.835715 0.549164i \(-0.185054\pi\)
−0.0577325 + 0.998332i \(0.518387\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 97.8884 + 56.5159i 0.186793 + 0.107845i
\(66\) 0 0
\(67\) 81.9267 + 141.901i 0.149387 + 0.258746i 0.931001 0.365016i \(-0.118937\pi\)
−0.781614 + 0.623762i \(0.785603\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 79.8529i 0.133476i −0.997771 0.0667380i \(-0.978741\pi\)
0.997771 0.0667380i \(-0.0212592\pi\)
\(72\) 0 0
\(73\) 666.447 384.774i 1.06852 0.616909i 0.140741 0.990046i \(-0.455051\pi\)
0.927776 + 0.373138i \(0.121718\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −377.379 928.422i −0.558523 1.37407i
\(78\) 0 0
\(79\) 267.408 463.165i 0.380833 0.659622i −0.610349 0.792133i \(-0.708971\pi\)
0.991182 + 0.132511i \(0.0423040\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 438.520 0.579926 0.289963 0.957038i \(-0.406357\pi\)
0.289963 + 0.957038i \(0.406357\pi\)
\(84\) 0 0
\(85\) −879.684 −1.12253
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.8242 + 22.2121i −0.0152737 + 0.0264548i −0.873561 0.486714i \(-0.838195\pi\)
0.858288 + 0.513169i \(0.171529\pi\)
\(90\) 0 0
\(91\) 162.454 + 22.4833i 0.187140 + 0.0258999i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1811.23 + 1045.71i −1.95608 + 1.12935i
\(96\) 0 0
\(97\) 1381.00i 1.44555i −0.691081 0.722777i \(-0.742865\pi\)
0.691081 0.722777i \(-0.257135\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 356.808 + 618.009i 0.351522 + 0.608854i 0.986516 0.163663i \(-0.0523309\pi\)
−0.634994 + 0.772517i \(0.718998\pi\)
\(102\) 0 0
\(103\) −1552.42 896.288i −1.48509 0.857416i −0.485232 0.874385i \(-0.661265\pi\)
−0.999856 + 0.0169695i \(0.994598\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −19.5366 11.2794i −0.0176511 0.0101909i 0.491148 0.871076i \(-0.336577\pi\)
−0.508800 + 0.860885i \(0.669911\pi\)
\(108\) 0 0
\(109\) −476.210 824.820i −0.418465 0.724802i 0.577320 0.816518i \(-0.304098\pi\)
−0.995785 + 0.0917154i \(0.970765\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 120.145i 0.100020i −0.998749 0.0500102i \(-0.984075\pi\)
0.998749 0.0500102i \(-0.0159254\pi\)
\(114\) 0 0
\(115\) −1038.77 + 599.735i −0.842312 + 0.486309i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1182.42 + 480.622i −0.910859 + 0.370240i
\(120\) 0 0
\(121\) 798.612 1383.24i 0.600009 1.03925i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1111.41 −0.795262
\(126\) 0 0
\(127\) −884.302 −0.617867 −0.308934 0.951084i \(-0.599972\pi\)
−0.308934 + 0.951084i \(0.599972\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −803.439 + 1391.60i −0.535853 + 0.928125i 0.463268 + 0.886218i \(0.346677\pi\)
−0.999122 + 0.0419070i \(0.986657\pi\)
\(132\) 0 0
\(133\) −1863.21 + 2395.16i −1.21474 + 1.56156i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 615.297 355.242i 0.383711 0.221535i −0.295721 0.955274i \(-0.595560\pi\)
0.679431 + 0.733739i \(0.262227\pi\)
\(138\) 0 0
\(139\) 1531.91i 0.934782i −0.884051 0.467391i \(-0.845194\pi\)
0.884051 0.467391i \(-0.154806\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 239.593 + 414.987i 0.140110 + 0.242678i
\(144\) 0 0
\(145\) −1322.31 763.435i −0.757322 0.437240i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2079.39 1200.54i −1.14329 0.660079i −0.196046 0.980595i \(-0.562810\pi\)
−0.947243 + 0.320516i \(0.896144\pi\)
\(150\) 0 0
\(151\) 1233.99 + 2137.33i 0.665035 + 1.15188i 0.979276 + 0.202532i \(0.0649169\pi\)
−0.314240 + 0.949343i \(0.601750\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1262.12i 0.654036i
\(156\) 0 0
\(157\) 2109.74 1218.06i 1.07246 0.619184i 0.143606 0.989635i \(-0.454130\pi\)
0.928852 + 0.370451i \(0.120797\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1068.59 + 1373.67i −0.523083 + 0.672424i
\(162\) 0 0
\(163\) 1638.50 2837.97i 0.787347 1.36372i −0.140240 0.990118i \(-0.544787\pi\)
0.927587 0.373607i \(-0.121879\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −365.585 −0.169400 −0.0847000 0.996406i \(-0.526993\pi\)
−0.0847000 + 0.996406i \(0.526993\pi\)
\(168\) 0 0
\(169\) 2118.58 0.964308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1046.47 + 1812.53i −0.459892 + 0.796557i −0.998955 0.0457089i \(-0.985445\pi\)
0.539062 + 0.842266i \(0.318779\pi\)
\(174\) 0 0
\(175\) 650.739 264.508i 0.281093 0.114257i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1524.01 + 879.890i −0.636370 + 0.367408i −0.783215 0.621751i \(-0.786422\pi\)
0.146845 + 0.989160i \(0.453088\pi\)
\(180\) 0 0
\(181\) 3197.54i 1.31310i 0.754282 + 0.656551i \(0.227985\pi\)
−0.754282 + 0.656551i \(0.772015\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −601.135 1041.20i −0.238899 0.413786i
\(186\) 0 0
\(187\) −3229.69 1864.66i −1.26299 0.729186i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −475.772 274.687i −0.180239 0.104061i 0.407166 0.913354i \(-0.366517\pi\)
−0.587405 + 0.809293i \(0.699850\pi\)
\(192\) 0 0
\(193\) 352.238 + 610.094i 0.131371 + 0.227542i 0.924205 0.381896i \(-0.124729\pi\)
−0.792834 + 0.609437i \(0.791395\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5317.81i 1.92324i 0.274384 + 0.961620i \(0.411526\pi\)
−0.274384 + 0.961620i \(0.588474\pi\)
\(198\) 0 0
\(199\) 2155.80 1244.65i 0.767942 0.443371i −0.0641982 0.997937i \(-0.520449\pi\)
0.832140 + 0.554566i \(0.187116\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2194.48 303.711i −0.758729 0.105007i
\(204\) 0 0
\(205\) 1655.20 2866.88i 0.563922 0.976741i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8866.38 −2.93445
\(210\) 0 0
\(211\) 3454.31 1.12704 0.563519 0.826103i \(-0.309447\pi\)
0.563519 + 0.826103i \(0.309447\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 32.0013 55.4279i 0.0101510 0.0175821i
\(216\) 0 0
\(217\) −689.566 1696.46i −0.215718 0.530706i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 528.520 305.141i 0.160869 0.0928778i
\(222\) 0 0
\(223\) 3896.38i 1.17005i 0.811016 + 0.585024i \(0.198915\pi\)
−0.811016 + 0.585024i \(0.801085\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −302.747 524.374i −0.0885201 0.153321i 0.818366 0.574698i \(-0.194880\pi\)
−0.906886 + 0.421377i \(0.861547\pi\)
\(228\) 0 0
\(229\) −1912.98 1104.46i −0.552023 0.318711i 0.197914 0.980219i \(-0.436583\pi\)
−0.749938 + 0.661509i \(0.769917\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2065.77 + 1192.67i 0.580829 + 0.335342i 0.761463 0.648209i \(-0.224482\pi\)
−0.180634 + 0.983550i \(0.557815\pi\)
\(234\) 0 0
\(235\) 366.013 + 633.953i 0.101600 + 0.175977i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3017.95i 0.816798i −0.912803 0.408399i \(-0.866087\pi\)
0.912803 0.408399i \(-0.133913\pi\)
\(240\) 0 0
\(241\) −2178.48 + 1257.75i −0.582275 + 0.336176i −0.762037 0.647534i \(-0.775800\pi\)
0.179762 + 0.983710i \(0.442467\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3136.58 3054.54i 0.817913 0.796521i
\(246\) 0 0
\(247\) 725.465 1256.54i 0.186883 0.323692i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1306.11 −0.328451 −0.164226 0.986423i \(-0.552512\pi\)
−0.164226 + 0.986423i \(0.552512\pi\)
\(252\) 0 0
\(253\) −5085.03 −1.26361
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3735.91 6470.79i 0.906770 1.57057i 0.0882460 0.996099i \(-0.471874\pi\)
0.818524 0.574473i \(-0.194793\pi\)
\(258\) 0 0
\(259\) −1376.88 1071.08i −0.330328 0.256964i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1330.77 768.318i 0.312010 0.180139i −0.335816 0.941928i \(-0.609012\pi\)
0.647825 + 0.761789i \(0.275679\pi\)
\(264\) 0 0
\(265\) 5999.62i 1.39077i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1958.09 + 3391.52i 0.443818 + 0.768715i 0.997969 0.0637010i \(-0.0202904\pi\)
−0.554151 + 0.832416i \(0.686957\pi\)
\(270\) 0 0
\(271\) −3117.42 1799.84i −0.698780 0.403441i 0.108113 0.994139i \(-0.465519\pi\)
−0.806893 + 0.590698i \(0.798853\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1777.45 + 1026.21i 0.389760 + 0.225028i
\(276\) 0 0
\(277\) −142.040 246.021i −0.0308100 0.0533645i 0.850209 0.526445i \(-0.176475\pi\)
−0.881019 + 0.473080i \(0.843142\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 321.256i 0.0682011i −0.999418 0.0341006i \(-0.989143\pi\)
0.999418 0.0341006i \(-0.0108566\pi\)
\(282\) 0 0
\(283\) −5891.40 + 3401.40i −1.23748 + 0.714460i −0.968579 0.248707i \(-0.919994\pi\)
−0.268903 + 0.963167i \(0.586661\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 658.474 4757.82i 0.135430 0.978556i
\(288\) 0 0
\(289\) 81.7017 141.511i 0.0166297 0.0288035i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3180.05 0.634063 0.317031 0.948415i \(-0.397314\pi\)
0.317031 + 0.948415i \(0.397314\pi\)
\(294\) 0 0
\(295\) 2884.20 0.569237
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 416.067 720.649i 0.0804741 0.139385i
\(300\) 0 0
\(301\) 12.7308 91.9871i 0.00243785 0.0176148i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4731.11 + 2731.51i −0.888204 + 0.512805i
\(306\) 0 0
\(307\) 2976.39i 0.553328i 0.960967 + 0.276664i \(0.0892289\pi\)
−0.960967 + 0.276664i \(0.910771\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2340.89 + 4054.55i 0.426817 + 0.739268i 0.996588 0.0825352i \(-0.0263017\pi\)
−0.569772 + 0.821803i \(0.692968\pi\)
\(312\) 0 0
\(313\) −850.477 491.023i −0.153584 0.0886718i 0.421238 0.906950i \(-0.361596\pi\)
−0.574823 + 0.818278i \(0.694929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4269.80 + 2465.17i 0.756516 + 0.436775i 0.828044 0.560664i \(-0.189454\pi\)
−0.0715272 + 0.997439i \(0.522787\pi\)
\(318\) 0 0
\(319\) −3236.50 5605.79i −0.568055 0.983899i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11292.0i 1.94522i
\(324\) 0 0
\(325\) −290.868 + 167.933i −0.0496445 + 0.0286623i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 838.338 + 652.148i 0.140483 + 0.109283i
\(330\) 0 0
\(331\) −2017.25 + 3493.99i −0.334980 + 0.580202i −0.983481 0.181012i \(-0.942063\pi\)
0.648501 + 0.761214i \(0.275396\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2091.48 −0.341104
\(336\) 0 0
\(337\) 2771.62 0.448011 0.224006 0.974588i \(-0.428087\pi\)
0.224006 + 0.974588i \(0.428087\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2675.30 4633.76i 0.424856 0.735872i
\(342\) 0 0
\(343\) 2547.13 5819.43i 0.400968 0.916092i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3743.15 2161.11i 0.579085 0.334335i −0.181685 0.983357i \(-0.558155\pi\)
0.760770 + 0.649022i \(0.224822\pi\)
\(348\) 0 0
\(349\) 1331.65i 0.204245i 0.994772 + 0.102122i \(0.0325634\pi\)
−0.994772 + 0.102122i \(0.967437\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5674.26 9828.10i −0.855553 1.48186i −0.876131 0.482073i \(-0.839884\pi\)
0.0205782 0.999788i \(-0.493449\pi\)
\(354\) 0 0
\(355\) 882.713 + 509.634i 0.131970 + 0.0761932i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7247.49 + 4184.34i 1.06548 + 0.615156i 0.926943 0.375201i \(-0.122426\pi\)
0.138538 + 0.990357i \(0.455760\pi\)
\(360\) 0 0
\(361\) 9993.77 + 17309.7i 1.45703 + 2.52365i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9822.76i 1.40862i
\(366\) 0 0
\(367\) −2351.31 + 1357.53i −0.334434 + 0.193086i −0.657808 0.753186i \(-0.728516\pi\)
0.323374 + 0.946271i \(0.395183\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3277.93 8064.33i −0.458711 1.12851i
\(372\) 0 0
\(373\) −3048.56 + 5280.25i −0.423186 + 0.732979i −0.996249 0.0865320i \(-0.972422\pi\)
0.573063 + 0.819511i \(0.305755\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1059.27 0.144708
\(378\) 0 0
\(379\) 9922.24 1.34478 0.672389 0.740198i \(-0.265268\pi\)
0.672389 + 0.740198i \(0.265268\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 609.532 1055.74i 0.0813202 0.140851i −0.822497 0.568769i \(-0.807420\pi\)
0.903817 + 0.427919i \(0.140753\pi\)
\(384\) 0 0
\(385\) 12671.5 + 1753.71i 1.67740 + 0.232149i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11374.6 6567.15i 1.48256 0.855958i 0.482759 0.875753i \(-0.339635\pi\)
0.999804 + 0.0197949i \(0.00630133\pi\)
\(390\) 0 0
\(391\) 6476.19i 0.837634i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3413.29 + 5911.99i 0.434788 + 0.753075i
\(396\) 0 0
\(397\) 2697.68 + 1557.51i 0.341040 + 0.196900i 0.660732 0.750622i \(-0.270246\pi\)
−0.319692 + 0.947522i \(0.603579\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9724.47 5614.42i −1.21101 0.699179i −0.248034 0.968751i \(-0.579784\pi\)
−0.962980 + 0.269572i \(0.913118\pi\)
\(402\) 0 0
\(403\) 437.797 + 758.287i 0.0541147 + 0.0937295i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5096.90i 0.620747i
\(408\) 0 0
\(409\) −10739.4 + 6200.41i −1.29836 + 0.749610i −0.980121 0.198399i \(-0.936426\pi\)
−0.318242 + 0.948010i \(0.603092\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3876.78 1575.81i 0.461898 0.187749i
\(414\) 0 0
\(415\) −2798.71 + 4847.51i −0.331044 + 0.573385i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8260.19 0.963095 0.481547 0.876420i \(-0.340075\pi\)
0.481547 + 0.876420i \(0.340075\pi\)
\(420\) 0 0
\(421\) 5571.81 0.645020 0.322510 0.946566i \(-0.395473\pi\)
0.322510 + 0.946566i \(0.395473\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1306.96 2263.72i 0.149169 0.258368i
\(426\) 0 0
\(427\) −4866.89 + 6256.40i −0.551582 + 0.709060i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6094.88 3518.88i 0.681160 0.393268i −0.119132 0.992878i \(-0.538011\pi\)
0.800292 + 0.599611i \(0.204678\pi\)
\(432\) 0 0
\(433\) 9212.26i 1.02243i −0.859452 0.511216i \(-0.829195\pi\)
0.859452 0.511216i \(-0.170805\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7698.48 + 13334.2i 0.842719 + 1.45963i
\(438\) 0 0
\(439\) 7345.30 + 4240.81i 0.798570 + 0.461054i 0.842971 0.537959i \(-0.180805\pi\)
−0.0444012 + 0.999014i \(0.514138\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11305.9 6527.49i −1.21255 0.700068i −0.249239 0.968442i \(-0.580180\pi\)
−0.963315 + 0.268374i \(0.913514\pi\)
\(444\) 0 0
\(445\) −163.692 283.523i −0.0174376 0.0302029i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14114.0i 1.48348i −0.670689 0.741738i \(-0.734002\pi\)
0.670689 0.741738i \(-0.265998\pi\)
\(450\) 0 0
\(451\) 12153.9 7017.03i 1.26896 0.732637i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1285.34 + 1652.31i −0.132435 + 0.170245i
\(456\) 0 0
\(457\) 4486.87 7771.49i 0.459271 0.795481i −0.539651 0.841889i \(-0.681444\pi\)
0.998923 + 0.0464073i \(0.0147772\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 955.010 0.0964842 0.0482421 0.998836i \(-0.484638\pi\)
0.0482421 + 0.998836i \(0.484638\pi\)
\(462\) 0 0
\(463\) −12004.5 −1.20496 −0.602479 0.798135i \(-0.705820\pi\)
−0.602479 + 0.798135i \(0.705820\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2532.46 + 4386.34i −0.250938 + 0.434638i −0.963784 0.266683i \(-0.914072\pi\)
0.712846 + 0.701320i \(0.247406\pi\)
\(468\) 0 0
\(469\) −2811.24 + 1142.69i −0.276783 + 0.112505i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 234.981 135.666i 0.0228423 0.0131880i
\(474\) 0 0
\(475\) 6214.52i 0.600299i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7606.85 + 13175.5i 0.725607 + 1.25679i 0.958724 + 0.284340i \(0.0917744\pi\)
−0.233116 + 0.972449i \(0.574892\pi\)
\(480\) 0 0
\(481\) 722.332 + 417.038i 0.0684730 + 0.0395329i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15265.9 + 8813.75i 1.42925 + 0.825179i
\(486\) 0 0
\(487\) 7905.92 + 13693.5i 0.735629 + 1.27415i 0.954447 + 0.298382i \(0.0964468\pi\)
−0.218817 + 0.975766i \(0.570220\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18064.2i 1.66034i −0.557512 0.830169i \(-0.688244\pi\)
0.557512 0.830169i \(-0.311756\pi\)
\(492\) 0 0
\(493\) −7139.42 + 4121.94i −0.652217 + 0.376558i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1464.93 + 202.744i 0.132216 + 0.0182984i
\(498\) 0 0
\(499\) −5262.33 + 9114.62i −0.472092 + 0.817688i −0.999490 0.0319305i \(-0.989834\pi\)
0.527398 + 0.849619i \(0.323168\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7790.82 −0.690607 −0.345304 0.938491i \(-0.612224\pi\)
−0.345304 + 0.938491i \(0.612224\pi\)
\(504\) 0 0
\(505\) −9108.83 −0.802649
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5098.24 + 8830.41i −0.443960 + 0.768961i −0.997979 0.0635430i \(-0.979760\pi\)
0.554019 + 0.832504i \(0.313093\pi\)
\(510\) 0 0
\(511\) 5366.74 + 13203.2i 0.464600 + 1.14300i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 19815.6 11440.5i 1.69549 0.978892i
\(516\) 0 0
\(517\) 3103.35i 0.263994i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −963.789 1669.33i −0.0810449 0.140374i 0.822654 0.568542i \(-0.192492\pi\)
−0.903699 + 0.428168i \(0.859159\pi\)
\(522\) 0 0
\(523\) 6716.70 + 3877.89i 0.561569 + 0.324222i 0.753775 0.657133i \(-0.228231\pi\)
−0.192206 + 0.981355i \(0.561564\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5901.47 3407.21i −0.487803 0.281633i
\(528\) 0 0
\(529\) −1668.28 2889.55i −0.137115 0.237491i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2296.59i 0.186635i
\(534\) 0 0
\(535\) 249.371 143.975i 0.0201519 0.0116347i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 17990.4 4565.93i 1.43767 0.364876i
\(540\) 0 0
\(541\) −8380.42 + 14515.3i −0.665993 + 1.15353i 0.313022 + 0.949746i \(0.398659\pi\)
−0.979015 + 0.203788i \(0.934675\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12157.0 0.955503
\(546\) 0 0
\(547\) −5869.79 −0.458819 −0.229410 0.973330i \(-0.573680\pi\)
−0.229410 + 0.973330i \(0.573680\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9799.82 + 16973.8i −0.757688 + 1.31235i
\(552\) 0 0
\(553\) 7818.00 + 6081.67i 0.601185 + 0.467666i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18756.5 10829.1i 1.42682 0.823774i 0.429951 0.902852i \(-0.358531\pi\)
0.996868 + 0.0790779i \(0.0251976\pi\)
\(558\) 0 0
\(559\) 44.4019i 0.00335957i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4795.36 + 8305.80i 0.358970 + 0.621755i 0.987789 0.155797i \(-0.0497946\pi\)
−0.628819 + 0.777552i \(0.716461\pi\)
\(564\) 0 0
\(565\) 1328.11 + 766.787i 0.0988923 + 0.0570955i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14405.5 8317.01i −1.06135 0.612772i −0.135546 0.990771i \(-0.543279\pi\)
−0.925806 + 0.377999i \(0.876612\pi\)
\(570\) 0 0
\(571\) 3165.51 + 5482.83i 0.232001 + 0.401838i 0.958397 0.285439i \(-0.0921394\pi\)
−0.726396 + 0.687277i \(0.758806\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3564.14i 0.258495i
\(576\) 0 0
\(577\) 8431.94 4868.18i 0.608364 0.351239i −0.163961 0.986467i \(-0.552427\pi\)
0.772325 + 0.635228i \(0.219094\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1113.39 + 8044.83i −0.0795028 + 0.574450i
\(582\) 0 0
\(583\) 12717.4 22027.1i 0.903430 1.56479i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10940.3 0.769255 0.384628 0.923072i \(-0.374330\pi\)
0.384628 + 0.923072i \(0.374330\pi\)
\(588\) 0 0
\(589\) −16201.1 −1.13337
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12430.4 + 21530.0i −0.860799 + 1.49095i 0.0103608 + 0.999946i \(0.496702\pi\)
−0.871159 + 0.491000i \(0.836631\pi\)
\(594\) 0 0
\(595\) 2233.49 16138.2i 0.153889 1.11193i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20207.8 11667.0i 1.37841 0.795825i 0.386442 0.922314i \(-0.373704\pi\)
0.991968 + 0.126488i \(0.0403706\pi\)
\(600\) 0 0
\(601\) 13012.4i 0.883175i −0.897218 0.441587i \(-0.854416\pi\)
0.897218 0.441587i \(-0.145584\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10193.8 + 17656.1i 0.685017 + 1.18648i
\(606\) 0 0
\(607\) −7355.69 4246.81i −0.491859 0.283975i 0.233486 0.972360i \(-0.424987\pi\)
−0.725345 + 0.688385i \(0.758320\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −439.806 253.922i −0.0291205 0.0168127i
\(612\) 0 0
\(613\) 4569.79 + 7915.11i 0.301097 + 0.521514i 0.976385 0.216040i \(-0.0693140\pi\)
−0.675288 + 0.737554i \(0.735981\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7360.91i 0.480290i −0.970737 0.240145i \(-0.922805\pi\)
0.970737 0.240145i \(-0.0771950\pi\)
\(618\) 0 0
\(619\) −19878.5 + 11476.9i −1.29077 + 0.745225i −0.978790 0.204864i \(-0.934325\pi\)
−0.311978 + 0.950089i \(0.600991\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −374.930 291.660i −0.0241112 0.0187562i
\(624\) 0 0
\(625\) 9463.74 16391.7i 0.605679 1.04907i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6491.31 −0.411487
\(630\) 0 0
\(631\) −21126.0 −1.33282 −0.666412 0.745584i \(-0.732171\pi\)
−0.666412 + 0.745584i \(0.732171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5643.77 9775.29i 0.352703 0.610899i
\(636\) 0 0
\(637\) −824.929 + 2923.19i −0.0513106 + 0.181823i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15447.5 8918.61i 0.951855 0.549554i 0.0581985 0.998305i \(-0.481464\pi\)
0.893657 + 0.448751i \(0.148131\pi\)
\(642\) 0 0
\(643\) 25449.0i 1.56082i −0.625266 0.780412i \(-0.715009\pi\)
0.625266 0.780412i \(-0.284991\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −13149.2 22775.1i −0.798993 1.38390i −0.920273 0.391277i \(-0.872033\pi\)
0.121280 0.992618i \(-0.461300\pi\)
\(648\) 0 0
\(649\) 10589.1 + 6113.64i 0.640462 + 0.369771i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8203.79 4736.46i −0.491637 0.283847i 0.233616 0.972329i \(-0.424944\pi\)
−0.725253 + 0.688482i \(0.758277\pi\)
\(654\) 0 0
\(655\) −10255.4 17762.8i −0.611771 1.05962i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22384.5i 1.32318i 0.749865 + 0.661591i \(0.230118\pi\)
−0.749865 + 0.661591i \(0.769882\pi\)
\(660\) 0 0
\(661\) −19857.3 + 11464.6i −1.16847 + 0.674618i −0.953320 0.301962i \(-0.902359\pi\)
−0.215153 + 0.976580i \(0.569025\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −14585.4 35882.7i −0.850521 2.09244i
\(666\) 0 0
\(667\) −5620.37 + 9734.77i −0.326269 + 0.565115i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −23159.9 −1.33245
\(672\) 0 0
\(673\) −4873.86 −0.279158 −0.139579 0.990211i \(-0.544575\pi\)
−0.139579 + 0.990211i \(0.544575\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8123.71 + 14070.7i −0.461181 + 0.798789i −0.999020 0.0442583i \(-0.985908\pi\)
0.537839 + 0.843048i \(0.319241\pi\)
\(678\) 0 0
\(679\) 25334.9 + 3506.30i 1.43191 + 0.198173i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18786.2 + 10846.2i −1.05247 + 0.607641i −0.923339 0.383987i \(-0.874551\pi\)
−0.129127 + 0.991628i \(0.541217\pi\)
\(684\) 0 0
\(685\) 9068.85i 0.505844i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2081.12 + 3604.61i 0.115072 + 0.199310i
\(690\) 0 0
\(691\) 19499.9 + 11258.3i 1.07353 + 0.619803i 0.929144 0.369718i \(-0.120546\pi\)
0.144387 + 0.989521i \(0.453879\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16934.1 + 9776.90i 0.924239 + 0.533610i
\(696\) 0 0
\(697\) −8936.75 15478.9i −0.485658 0.841184i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 33929.0i 1.82807i −0.405631 0.914037i \(-0.632948\pi\)
0.405631 0.914037i \(-0.367052\pi\)
\(702\) 0 0
\(703\) −13365.3 + 7716.46i −0.717044 + 0.413986i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12243.6 + 4976.68i −0.651296 + 0.264734i
\(708\) 0 0
\(709\) −9593.62 + 16616.6i −0.508175 + 0.880185i 0.491780 + 0.870719i \(0.336346\pi\)
−0.999955 + 0.00946553i \(0.996987\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9291.63 −0.488043
\(714\) 0 0
\(715\) −6116.49 −0.319922
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6883.43 11922.4i 0.357036 0.618404i −0.630429 0.776247i \(-0.717121\pi\)
0.987464 + 0.157844i \(0.0504542\pi\)
\(720\) 0 0
\(721\) 20384.3 26204.0i 1.05291 1.35352i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3929.15 2268.49i 0.201276 0.116207i
\(726\) 0 0
\(727\) 12226.1i 0.623717i −0.950129 0.311858i \(-0.899049\pi\)
0.950129 0.311858i \(-0.100951\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −172.782 299.267i −0.00874222 0.0151420i
\(732\) 0 0
\(733\) 2256.76 + 1302.94i 0.113718 + 0.0656553i 0.555780 0.831329i \(-0.312420\pi\)
−0.442062 + 0.896984i \(0.645753\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7678.71 4433.30i −0.383784 0.221578i
\(738\) 0 0
\(739\) 16871.7 + 29222.7i 0.839833 + 1.45463i 0.890034 + 0.455894i \(0.150680\pi\)
−0.0502016 + 0.998739i \(0.515986\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14586.9i 0.720244i 0.932905 + 0.360122i \(0.117265\pi\)
−0.932905 + 0.360122i \(0.882735\pi\)
\(744\) 0 0
\(745\) 26542.0 15324.0i 1.30527 0.753597i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 256.528 329.768i 0.0125145 0.0160874i
\(750\) 0 0
\(751\) −3757.62 + 6508.39i −0.182580 + 0.316238i −0.942758 0.333477i \(-0.891778\pi\)
0.760178 + 0.649714i \(0.225111\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −31502.0 −1.51851
\(756\) 0 0
\(757\) 23917.4 1.14834 0.574169 0.818737i \(-0.305325\pi\)
0.574169 + 0.818737i \(0.305325\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6099.27 10564.2i 0.290537 0.503224i −0.683400 0.730044i \(-0.739500\pi\)
0.973937 + 0.226820i \(0.0728328\pi\)
\(762\) 0 0
\(763\) 16340.7 6642.07i 0.775327 0.315150i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1732.85 + 1000.46i −0.0815769 + 0.0470985i
\(768\) 0 0
\(769\) 2013.08i 0.0943999i 0.998885 + 0.0471999i \(0.0150298\pi\)
−0.998885 + 0.0471999i \(0.984970\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15139.1 + 26221.7i 0.704418 + 1.22009i 0.966901 + 0.255152i \(0.0821254\pi\)
−0.262483 + 0.964937i \(0.584541\pi\)
\(774\) 0 0
\(775\) 3247.85 + 1875.14i 0.150537 + 0.0869125i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −36800.7 21246.9i −1.69258 0.977213i
\(780\) 0 0
\(781\) 2160.54 + 3742.17i 0.0989888 + 0.171454i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 31095.5i 1.41382i
\(786\) 0 0
\(787\) −24839.3 + 14341.0i −1.12507 + 0.649557i −0.942689 0.333671i \(-0.891712\pi\)
−0.182377 + 0.983229i \(0.558379\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2204.11 + 305.045i 0.0990761 + 0.0137119i
\(792\) 0 0
\(793\) 1894.99 3282.21i 0.0848586 0.146979i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27108.9 −1.20483 −0.602413 0.798184i \(-0.705794\pi\)
−0.602413 + 0.798184i \(0.705794\pi\)
\(798\) 0 0
\(799\) 3952.36 0.174999