Properties

Label 252.4.k.f.37.2
Level $252$
Weight $4$
Character 252.37
Analytic conductor $14.868$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \(x^{4} - x^{3} + 49 x^{2} + 48 x + 2304\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(-3.22311 + 5.58259i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.4.k.f.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +O(q^{10})\) \(q+(6.22311 - 10.7787i) q^{5} +(15.3924 + 10.2992i) q^{7} +(-25.5618 - 44.2743i) q^{11} +37.2311 q^{13} +(11.1076 + 19.2389i) q^{17} +(-27.1693 + 47.0587i) q^{19} +(88.4622 - 153.221i) q^{23} +(-14.9542 - 25.9015i) q^{25} -61.0916 q^{29} +(-159.962 - 277.063i) q^{31} +(206.801 - 101.818i) q^{35} +(157.540 - 272.867i) q^{37} +206.032 q^{41} +339.661 q^{43} +(71.0320 - 123.031i) q^{47} +(130.855 + 317.058i) q^{49} +(155.008 + 268.482i) q^{53} -636.295 q^{55} +(-140.825 - 243.916i) q^{59} +(271.924 - 470.987i) q^{61} +(231.693 - 401.305i) q^{65} +(239.680 + 415.137i) q^{67} -1105.63 q^{71} +(-119.675 - 207.283i) q^{73} +(62.5298 - 944.754i) q^{77} +(-580.333 + 1005.17i) q^{79} +2.93158 q^{83} +276.494 q^{85} +(-639.371 + 1107.42i) q^{89} +(573.078 + 383.449i) q^{91} +(338.156 + 585.703i) q^{95} +79.0596 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 11q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 11q^{5} + 6q^{7} - 5q^{11} + 10q^{13} + 100q^{17} - 67q^{19} + 76q^{23} + 93q^{25} - 550q^{29} - 362q^{31} + 466q^{35} + 5q^{37} + 324q^{41} + 1442q^{43} - 216q^{47} + 190q^{49} + 495q^{53} - 1406q^{55} + 173q^{59} + 532q^{61} + 510q^{65} - 111q^{67} - 3200q^{71} - 1215q^{73} + 653q^{77} - 1460q^{79} + 2818q^{83} + 328q^{85} - 1974q^{89} + 1945q^{91} + 658q^{95} + 1122q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 6.22311 10.7787i 0.556612 0.964080i −0.441164 0.897426i \(-0.645434\pi\)
0.997776 0.0666538i \(-0.0212323\pi\)
\(6\) 0 0
\(7\) 15.3924 + 10.2992i 0.831114 + 0.556102i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −25.5618 44.2743i −0.700651 1.21356i −0.968238 0.250030i \(-0.919559\pi\)
0.267587 0.963534i \(-0.413774\pi\)
\(12\) 0 0
\(13\) 37.2311 0.794312 0.397156 0.917751i \(-0.369997\pi\)
0.397156 + 0.917751i \(0.369997\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 11.1076 + 19.2389i 0.158469 + 0.274477i 0.934317 0.356444i \(-0.116011\pi\)
−0.775848 + 0.630920i \(0.782677\pi\)
\(18\) 0 0
\(19\) −27.1693 + 47.0587i −0.328056 + 0.568210i −0.982126 0.188224i \(-0.939727\pi\)
0.654070 + 0.756434i \(0.273060\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 88.4622 153.221i 0.801985 1.38908i −0.116323 0.993211i \(-0.537111\pi\)
0.918308 0.395867i \(-0.129556\pi\)
\(24\) 0 0
\(25\) −14.9542 25.9015i −0.119634 0.207212i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −61.0916 −0.391187 −0.195593 0.980685i \(-0.562663\pi\)
−0.195593 + 0.980685i \(0.562663\pi\)
\(30\) 0 0
\(31\) −159.962 277.063i −0.926776 1.60522i −0.788679 0.614805i \(-0.789235\pi\)
−0.138097 0.990419i \(-0.544099\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 206.801 101.818i 0.998735 0.491727i
\(36\) 0 0
\(37\) 157.540 272.867i 0.699984 1.21241i −0.268487 0.963283i \(-0.586524\pi\)
0.968471 0.249125i \(-0.0801430\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 206.032 0.784800 0.392400 0.919795i \(-0.371645\pi\)
0.392400 + 0.919795i \(0.371645\pi\)
\(42\) 0 0
\(43\) 339.661 1.20460 0.602301 0.798269i \(-0.294251\pi\)
0.602301 + 0.798269i \(0.294251\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 71.0320 123.031i 0.220449 0.381828i −0.734496 0.678613i \(-0.762581\pi\)
0.954944 + 0.296785i \(0.0959146\pi\)
\(48\) 0 0
\(49\) 130.855 + 317.058i 0.381500 + 0.924369i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 155.008 + 268.482i 0.401736 + 0.695826i 0.993936 0.109965i \(-0.0350738\pi\)
−0.592200 + 0.805791i \(0.701740\pi\)
\(54\) 0 0
\(55\) −636.295 −1.55996
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −140.825 243.916i −0.310743 0.538223i 0.667780 0.744358i \(-0.267245\pi\)
−0.978523 + 0.206136i \(0.933911\pi\)
\(60\) 0 0
\(61\) 271.924 470.987i 0.570760 0.988585i −0.425728 0.904851i \(-0.639982\pi\)
0.996488 0.0837341i \(-0.0266846\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 231.693 401.305i 0.442123 0.765780i
\(66\) 0 0
\(67\) 239.680 + 415.137i 0.437038 + 0.756971i 0.997459 0.0712360i \(-0.0226943\pi\)
−0.560422 + 0.828207i \(0.689361\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1105.63 −1.84809 −0.924046 0.382280i \(-0.875139\pi\)
−0.924046 + 0.382280i \(0.875139\pi\)
\(72\) 0 0
\(73\) −119.675 207.283i −0.191876 0.332338i 0.753996 0.656879i \(-0.228124\pi\)
−0.945872 + 0.324541i \(0.894790\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 62.5298 944.754i 0.0925445 1.39824i
\(78\) 0 0
\(79\) −580.333 + 1005.17i −0.826488 + 1.43152i 0.0742888 + 0.997237i \(0.476331\pi\)
−0.900777 + 0.434282i \(0.857002\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.93158 0.00387690 0.00193845 0.999998i \(-0.499383\pi\)
0.00193845 + 0.999998i \(0.499383\pi\)
\(84\) 0 0
\(85\) 276.494 0.352824
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −639.371 + 1107.42i −0.761496 + 1.31895i 0.180583 + 0.983560i \(0.442202\pi\)
−0.942079 + 0.335390i \(0.891132\pi\)
\(90\) 0 0
\(91\) 573.078 + 383.449i 0.660163 + 0.441719i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 338.156 + 585.703i 0.365200 + 0.632545i
\(96\) 0 0
\(97\) 79.0596 0.0827555 0.0413777 0.999144i \(-0.486825\pi\)
0.0413777 + 0.999144i \(0.486825\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 686.052 + 1188.28i 0.675889 + 1.17067i 0.976208 + 0.216835i \(0.0695734\pi\)
−0.300319 + 0.953839i \(0.597093\pi\)
\(102\) 0 0
\(103\) −129.265 + 223.894i −0.123659 + 0.214184i −0.921208 0.389070i \(-0.872796\pi\)
0.797549 + 0.603254i \(0.206130\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −631.184 + 1093.24i −0.570270 + 0.987736i 0.426268 + 0.904597i \(0.359828\pi\)
−0.996538 + 0.0831393i \(0.973505\pi\)
\(108\) 0 0
\(109\) −138.416 239.744i −0.121632 0.210673i 0.798779 0.601624i \(-0.205479\pi\)
−0.920411 + 0.390951i \(0.872146\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −52.9156 −0.0440520 −0.0220260 0.999757i \(-0.507012\pi\)
−0.0220260 + 0.999757i \(0.507012\pi\)
\(114\) 0 0
\(115\) −1101.02 1907.02i −0.892789 1.54636i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −27.1715 + 410.531i −0.0209312 + 0.316247i
\(120\) 0 0
\(121\) −641.309 + 1110.78i −0.481825 + 0.834545i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1183.53 0.846866
\(126\) 0 0
\(127\) 443.700 0.310016 0.155008 0.987913i \(-0.450460\pi\)
0.155008 + 0.987913i \(0.450460\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1076.74 + 1864.97i −0.718133 + 1.24384i 0.243606 + 0.969874i \(0.421670\pi\)
−0.961739 + 0.273968i \(0.911664\pi\)
\(132\) 0 0
\(133\) −902.867 + 444.527i −0.588635 + 0.289815i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 131.554 + 227.858i 0.0820394 + 0.142096i 0.904126 0.427266i \(-0.140523\pi\)
−0.822086 + 0.569363i \(0.807190\pi\)
\(138\) 0 0
\(139\) 1165.77 0.711360 0.355680 0.934608i \(-0.384249\pi\)
0.355680 + 0.934608i \(0.384249\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −951.693 1648.38i −0.556536 0.963948i
\(144\) 0 0
\(145\) −380.180 + 658.490i −0.217739 + 0.377135i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −882.597 + 1528.70i −0.485270 + 0.840512i −0.999857 0.0169263i \(-0.994612\pi\)
0.514587 + 0.857438i \(0.327945\pi\)
\(150\) 0 0
\(151\) −1346.16 2331.61i −0.725488 1.25658i −0.958773 0.284173i \(-0.908281\pi\)
0.233285 0.972408i \(-0.425052\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3981.85 −2.06342
\(156\) 0 0
\(157\) 970.691 + 1681.29i 0.493437 + 0.854657i 0.999971 0.00756226i \(-0.00240716\pi\)
−0.506535 + 0.862220i \(0.669074\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2939.70 1447.36i 1.43901 0.708497i
\(162\) 0 0
\(163\) −1051.42 + 1821.11i −0.505236 + 0.875094i 0.494746 + 0.869038i \(0.335261\pi\)
−0.999982 + 0.00605658i \(0.998072\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2344.22 1.08623 0.543116 0.839658i \(-0.317244\pi\)
0.543116 + 0.839658i \(0.317244\pi\)
\(168\) 0 0
\(169\) −810.844 −0.369069
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1735.32 3005.67i 0.762626 1.32091i −0.178867 0.983873i \(-0.557243\pi\)
0.941493 0.337033i \(-0.109424\pi\)
\(174\) 0 0
\(175\) 36.5813 552.703i 0.0158017 0.238745i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −477.885 827.722i −0.199547 0.345625i 0.748835 0.662757i \(-0.230614\pi\)
−0.948381 + 0.317132i \(0.897280\pi\)
\(180\) 0 0
\(181\) 4220.26 1.73309 0.866546 0.499098i \(-0.166335\pi\)
0.866546 + 0.499098i \(0.166335\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1960.78 3396.17i −0.779239 1.34968i
\(186\) 0 0
\(187\) 567.858 983.558i 0.222063 0.384625i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1759.02 + 3046.71i −0.666377 + 1.15420i 0.312534 + 0.949907i \(0.398822\pi\)
−0.978910 + 0.204291i \(0.934511\pi\)
\(192\) 0 0
\(193\) 2508.84 + 4345.43i 0.935699 + 1.62068i 0.773382 + 0.633940i \(0.218563\pi\)
0.162317 + 0.986739i \(0.448103\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2838.14 1.02644 0.513221 0.858257i \(-0.328452\pi\)
0.513221 + 0.858257i \(0.328452\pi\)
\(198\) 0 0
\(199\) −177.451 307.354i −0.0632118 0.109486i 0.832688 0.553743i \(-0.186801\pi\)
−0.895899 + 0.444257i \(0.853468\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −940.348 629.192i −0.325121 0.217540i
\(204\) 0 0
\(205\) 1282.16 2220.77i 0.436829 0.756610i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2777.99 0.919413
\(210\) 0 0
\(211\) 752.672 0.245574 0.122787 0.992433i \(-0.460817\pi\)
0.122787 + 0.992433i \(0.460817\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2113.75 3661.12i 0.670496 1.16133i
\(216\) 0 0
\(217\) 391.303 5912.15i 0.122412 1.84951i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 413.547 + 716.284i 0.125874 + 0.218020i
\(222\) 0 0
\(223\) −3077.75 −0.924221 −0.462111 0.886822i \(-0.652908\pi\)
−0.462111 + 0.886822i \(0.652908\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3108.72 5384.46i −0.908955 1.57436i −0.815518 0.578731i \(-0.803548\pi\)
−0.0934368 0.995625i \(-0.529785\pi\)
\(228\) 0 0
\(229\) −251.627 + 435.831i −0.0726113 + 0.125766i −0.900045 0.435797i \(-0.856467\pi\)
0.827434 + 0.561563i \(0.189800\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −134.170 + 232.389i −0.0377243 + 0.0653404i −0.884271 0.466974i \(-0.845344\pi\)
0.846547 + 0.532314i \(0.178678\pi\)
\(234\) 0 0
\(235\) −884.080 1531.27i −0.245409 0.425060i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5189.77 1.40459 0.702297 0.711884i \(-0.252158\pi\)
0.702297 + 0.711884i \(0.252158\pi\)
\(240\) 0 0
\(241\) −3085.47 5344.19i −0.824699 1.42842i −0.902149 0.431425i \(-0.858011\pi\)
0.0774495 0.996996i \(-0.475322\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4231.82 + 562.641i 1.10351 + 0.146718i
\(246\) 0 0
\(247\) −1011.54 + 1752.05i −0.260579 + 0.451336i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1891.91 −0.475763 −0.237882 0.971294i \(-0.576453\pi\)
−0.237882 + 0.971294i \(0.576453\pi\)
\(252\) 0 0
\(253\) −9045.01 −2.24765
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3269.97 + 5663.75i −0.793676 + 1.37469i 0.130000 + 0.991514i \(0.458502\pi\)
−0.923676 + 0.383174i \(0.874831\pi\)
\(258\) 0 0
\(259\) 5235.23 2577.56i 1.25599 0.618386i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2687.95 + 4655.67i 0.630214 + 1.09156i 0.987508 + 0.157570i \(0.0503661\pi\)
−0.357294 + 0.933992i \(0.616301\pi\)
\(264\) 0 0
\(265\) 3858.53 0.894443
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1619.44 2804.95i −0.367060 0.635766i 0.622045 0.782982i \(-0.286302\pi\)
−0.989104 + 0.147216i \(0.952969\pi\)
\(270\) 0 0
\(271\) −678.729 + 1175.59i −0.152140 + 0.263514i −0.932014 0.362423i \(-0.881950\pi\)
0.779874 + 0.625936i \(0.215283\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −764.513 + 1324.18i −0.167643 + 0.290366i
\(276\) 0 0
\(277\) 1280.82 + 2218.44i 0.277823 + 0.481203i 0.970843 0.239715i \(-0.0770539\pi\)
−0.693021 + 0.720918i \(0.743721\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1786.17 −0.379196 −0.189598 0.981862i \(-0.560718\pi\)
−0.189598 + 0.981862i \(0.560718\pi\)
\(282\) 0 0
\(283\) 3694.14 + 6398.44i 0.775950 + 1.34398i 0.934259 + 0.356595i \(0.116063\pi\)
−0.158309 + 0.987390i \(0.550604\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3171.34 + 2121.96i 0.652258 + 0.436429i
\(288\) 0 0
\(289\) 2209.74 3827.39i 0.449775 0.779033i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −492.981 −0.0982945 −0.0491472 0.998792i \(-0.515650\pi\)
−0.0491472 + 0.998792i \(0.515650\pi\)
\(294\) 0 0
\(295\) −3505.48 −0.691853
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3293.55 5704.59i 0.637026 1.10336i
\(300\) 0 0
\(301\) 5228.22 + 3498.23i 1.00116 + 0.669882i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3384.43 5862.01i −0.635384 1.10052i
\(306\) 0 0
\(307\) −988.810 −0.183825 −0.0919126 0.995767i \(-0.529298\pi\)
−0.0919126 + 0.995767i \(0.529298\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4798.28 8310.87i −0.874874 1.51533i −0.856897 0.515487i \(-0.827611\pi\)
−0.0179763 0.999838i \(-0.505722\pi\)
\(312\) 0 0
\(313\) −482.856 + 836.332i −0.0871970 + 0.151030i −0.906325 0.422581i \(-0.861124\pi\)
0.819128 + 0.573610i \(0.194458\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4492.99 + 7782.08i −0.796061 + 1.37882i 0.126103 + 0.992017i \(0.459753\pi\)
−0.922163 + 0.386801i \(0.873580\pi\)
\(318\) 0 0
\(319\) 1561.61 + 2704.79i 0.274086 + 0.474730i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1207.14 −0.207947
\(324\) 0 0
\(325\) −556.762 964.340i −0.0950265 0.164591i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2360.47 1162.18i 0.395553 0.194751i
\(330\) 0 0
\(331\) 1903.65 3297.22i 0.316115 0.547527i −0.663559 0.748124i \(-0.730955\pi\)
0.979674 + 0.200597i \(0.0642882\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5966.21 0.973041
\(336\) 0 0
\(337\) −1649.82 −0.266681 −0.133340 0.991070i \(-0.542570\pi\)
−0.133340 + 0.991070i \(0.542570\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8177.84 + 14164.4i −1.29869 + 2.24940i
\(342\) 0 0
\(343\) −1251.26 + 6228.00i −0.196973 + 0.980409i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2855.00 + 4945.00i 0.441684 + 0.765019i 0.997815 0.0660760i \(-0.0210480\pi\)
−0.556131 + 0.831095i \(0.687715\pi\)
\(348\) 0 0
\(349\) −447.244 −0.0685973 −0.0342986 0.999412i \(-0.510920\pi\)
−0.0342986 + 0.999412i \(0.510920\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5322.85 9219.45i −0.802569 1.39009i −0.917920 0.396765i \(-0.870133\pi\)
0.115352 0.993325i \(-0.463201\pi\)
\(354\) 0 0
\(355\) −6880.48 + 11917.3i −1.02867 + 1.78171i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4548.73 + 7878.64i −0.668727 + 1.15827i 0.309533 + 0.950889i \(0.399827\pi\)
−0.978260 + 0.207381i \(0.933506\pi\)
\(360\) 0 0
\(361\) 1953.15 + 3382.96i 0.284758 + 0.493215i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2979.01 −0.427201
\(366\) 0 0
\(367\) −2643.91 4579.39i −0.376052 0.651341i 0.614432 0.788970i \(-0.289385\pi\)
−0.990484 + 0.137629i \(0.956052\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −379.184 + 5729.04i −0.0530627 + 0.801717i
\(372\) 0 0
\(373\) −2947.51 + 5105.23i −0.409159 + 0.708683i −0.994796 0.101890i \(-0.967511\pi\)
0.585637 + 0.810573i \(0.300844\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2274.51 −0.310724
\(378\) 0 0
\(379\) 3842.41 0.520769 0.260384 0.965505i \(-0.416151\pi\)
0.260384 + 0.965505i \(0.416151\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2506.87 4342.02i 0.334452 0.579287i −0.648928 0.760850i \(-0.724782\pi\)
0.983379 + 0.181563i \(0.0581156\pi\)
\(384\) 0 0
\(385\) −9794.14 6553.30i −1.29651 0.867499i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5591.24 + 9684.31i 0.728758 + 1.26225i 0.957408 + 0.288738i \(0.0932355\pi\)
−0.228650 + 0.973509i \(0.573431\pi\)
\(390\) 0 0
\(391\) 3930.40 0.508360
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7222.95 + 12510.5i 0.920066 + 1.59360i
\(396\) 0 0
\(397\) 1703.40 2950.37i 0.215343 0.372985i −0.738036 0.674762i \(-0.764246\pi\)
0.953379 + 0.301777i \(0.0975798\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 41.5201 71.9149i 0.00517061 0.00895575i −0.863429 0.504471i \(-0.831687\pi\)
0.868599 + 0.495515i \(0.165021\pi\)
\(402\) 0 0
\(403\) −5955.57 10315.4i −0.736149 1.27505i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16108.0 −1.96178
\(408\) 0 0
\(409\) −1228.10 2127.13i −0.148473 0.257164i 0.782190 0.623040i \(-0.214103\pi\)
−0.930663 + 0.365876i \(0.880769\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 344.489 5204.84i 0.0410440 0.620129i
\(414\) 0 0
\(415\) 18.2435 31.5987i 0.00215793 0.00373764i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3437.96 0.400848 0.200424 0.979709i \(-0.435768\pi\)
0.200424 + 0.979709i \(0.435768\pi\)
\(420\) 0 0
\(421\) −5347.62 −0.619067 −0.309533 0.950889i \(-0.600173\pi\)
−0.309533 + 0.950889i \(0.600173\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 332.210 575.404i 0.0379166 0.0656734i
\(426\) 0 0
\(427\) 9036.35 4449.05i 1.02412 0.504226i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 425.821 + 737.544i 0.0475895 + 0.0824275i 0.888839 0.458220i \(-0.151513\pi\)
−0.841249 + 0.540647i \(0.818179\pi\)
\(432\) 0 0
\(433\) −3433.42 −0.381061 −0.190531 0.981681i \(-0.561021\pi\)
−0.190531 + 0.981681i \(0.561021\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4806.92 + 8325.83i 0.526192 + 0.911392i
\(438\) 0 0
\(439\) 4869.20 8433.70i 0.529371 0.916898i −0.470042 0.882644i \(-0.655761\pi\)
0.999413 0.0342540i \(-0.0109055\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4967.48 8603.93i 0.532759 0.922765i −0.466509 0.884516i \(-0.654489\pi\)
0.999268 0.0382491i \(-0.0121780\pi\)
\(444\) 0 0
\(445\) 7957.75 + 13783.2i 0.847716 + 1.46829i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7557.33 0.794327 0.397163 0.917748i \(-0.369995\pi\)
0.397163 + 0.917748i \(0.369995\pi\)
\(450\) 0 0
\(451\) −5266.54 9121.92i −0.549871 0.952405i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7699.43 3790.81i 0.793307 0.390585i
\(456\) 0 0
\(457\) −7005.92 + 12134.6i −0.717118 + 1.24209i 0.245018 + 0.969518i \(0.421206\pi\)
−0.962137 + 0.272567i \(0.912127\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1669.61 0.168680 0.0843399 0.996437i \(-0.473122\pi\)
0.0843399 + 0.996437i \(0.473122\pi\)
\(462\) 0 0
\(463\) 14785.4 1.48409 0.742046 0.670349i \(-0.233856\pi\)
0.742046 + 0.670349i \(0.233856\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2301.58 3986.46i 0.228061 0.395014i −0.729172 0.684330i \(-0.760095\pi\)
0.957233 + 0.289317i \(0.0934280\pi\)
\(468\) 0 0
\(469\) −586.309 + 8858.47i −0.0577255 + 0.872167i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8682.35 15038.3i −0.844006 1.46186i
\(474\) 0 0
\(475\) 1625.18 0.156987
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1738.68 + 3011.47i 0.165850 + 0.287261i 0.936957 0.349445i \(-0.113630\pi\)
−0.771107 + 0.636706i \(0.780297\pi\)
\(480\) 0 0
\(481\) 5865.39 10159.2i 0.556006 0.963030i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 491.996 852.163i 0.0460627 0.0797829i
\(486\) 0 0
\(487\) −2172.08 3762.16i −0.202108 0.350061i 0.747100 0.664712i \(-0.231446\pi\)
−0.949207 + 0.314651i \(0.898112\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4982.89 −0.457993 −0.228997 0.973427i \(-0.573544\pi\)
−0.228997 + 0.973427i \(0.573544\pi\)
\(492\) 0 0
\(493\) −678.578 1175.33i −0.0619911 0.107372i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −17018.4 11387.1i −1.53598 1.02773i
\(498\) 0 0
\(499\) −7663.08 + 13272.8i −0.687468 + 1.19073i 0.285187 + 0.958472i \(0.407944\pi\)
−0.972654 + 0.232257i \(0.925389\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1516.04 0.134387 0.0671936 0.997740i \(-0.478595\pi\)
0.0671936 + 0.997740i \(0.478595\pi\)
\(504\) 0 0
\(505\) 17077.5 1.50483
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1326.82 2298.12i 0.115541 0.200122i −0.802455 0.596713i \(-0.796473\pi\)
0.917996 + 0.396590i \(0.129807\pi\)
\(510\) 0 0
\(511\) 292.752 4423.15i 0.0253436 0.382913i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1608.86 + 2786.64i 0.137660 + 0.238435i
\(516\) 0 0
\(517\) −7262.82 −0.617830
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6566.06 11372.8i −0.552139 0.956333i −0.998120 0.0612905i \(-0.980478\pi\)
0.445981 0.895042i \(-0.352855\pi\)
\(522\) 0 0
\(523\) 1543.17 2672.85i 0.129021 0.223471i −0.794276 0.607557i \(-0.792150\pi\)
0.923298 + 0.384085i \(0.125483\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3553.58 6154.98i 0.293731 0.508757i
\(528\) 0 0
\(529\) −9567.63 16571.6i −0.786359 1.36201i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7670.80 0.623376
\(534\) 0 0
\(535\) 7855.86 + 13606.7i 0.634838 + 1.09957i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10692.7 13898.1i 0.854482 1.11064i
\(540\) 0 0
\(541\) −463.047 + 802.022i −0.0367985 + 0.0637368i −0.883838 0.467793i \(-0.845049\pi\)
0.847040 + 0.531530i \(0.178383\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3445.52 −0.270807
\(546\) 0 0
\(547\) 592.871 0.0463425 0.0231712 0.999732i \(-0.492624\pi\)
0.0231712 + 0.999732i \(0.492624\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1659.82 2874.89i 0.128331 0.222276i
\(552\) 0 0
\(553\) −19285.1 + 9495.02i −1.48298 + 0.730144i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6122.67 10604.8i −0.465756 0.806713i 0.533480 0.845813i \(-0.320884\pi\)
−0.999235 + 0.0391003i \(0.987551\pi\)
\(558\) 0 0
\(559\) 12646.0 0.956829
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7297.31 + 12639.3i 0.546261 + 0.946152i 0.998526 + 0.0542682i \(0.0172826\pi\)
−0.452266 + 0.891883i \(0.649384\pi\)
\(564\) 0 0
\(565\) −329.300 + 570.364i −0.0245199 + 0.0424697i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11455.6 19841.7i 0.844015 1.46188i −0.0424590 0.999098i \(-0.513519\pi\)
0.886474 0.462779i \(-0.153147\pi\)
\(570\) 0 0
\(571\) −2952.32 5113.57i −0.216376 0.374774i 0.737321 0.675542i \(-0.236090\pi\)
−0.953697 + 0.300768i \(0.902757\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5291.53 −0.383778
\(576\) 0 0
\(577\) −4756.61 8238.68i −0.343189 0.594421i 0.641834 0.766844i \(-0.278174\pi\)
−0.985023 + 0.172423i \(0.944840\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 45.1242 + 30.1928i 0.00322214 + 0.00215595i
\(582\) 0 0
\(583\) 7924.56 13725.7i 0.562953 0.975064i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22790.6 1.60250 0.801252 0.598327i \(-0.204167\pi\)
0.801252 + 0.598327i \(0.204167\pi\)
\(588\) 0 0
\(589\) 17384.3 1.21614
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9131.39 + 15816.0i −0.632346 + 1.09526i 0.354724 + 0.934971i \(0.384575\pi\)
−0.987071 + 0.160285i \(0.948759\pi\)
\(594\) 0 0
\(595\) 4255.92 + 2847.66i 0.293237 + 0.196206i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3479.05 + 6025.88i 0.237312 + 0.411037i 0.959942 0.280198i \(-0.0904003\pi\)
−0.722630 + 0.691235i \(0.757067\pi\)
\(600\) 0 0
\(601\) 2305.39 0.156471 0.0782353 0.996935i \(-0.475071\pi\)
0.0782353 + 0.996935i \(0.475071\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7981.87 + 13825.0i 0.536379 + 0.929036i
\(606\) 0 0
\(607\) 8089.62 14011.6i 0.540935 0.936927i −0.457916 0.888996i \(-0.651404\pi\)
0.998851 0.0479312i \(-0.0152628\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2644.60 4580.58i 0.175105 0.303291i
\(612\) 0 0
\(613\) −10270.4 17788.8i −0.676699 1.17208i −0.975969 0.217908i \(-0.930077\pi\)
0.299271 0.954168i \(-0.403257\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6918.19 −0.451403 −0.225702 0.974196i \(-0.572467\pi\)
−0.225702 + 0.974196i \(0.572467\pi\)
\(618\) 0 0
\(619\) 4040.81 + 6998.89i 0.262381 + 0.454457i 0.966874 0.255254i \(-0.0821589\pi\)
−0.704493 + 0.709711i \(0.748826\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21247.0 + 10461.0i −1.36636 + 0.672728i
\(624\) 0 0
\(625\) 9234.52 15994.7i 0.591009 1.02366i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6999.54 0.443704
\(630\) 0 0
\(631\) −27293.3 −1.72191 −0.860957 0.508677i \(-0.830135\pi\)
−0.860957 + 0.508677i \(0.830135\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2761.20 4782.53i 0.172559 0.298880i
\(636\) 0 0
\(637\) 4871.86 + 11804.4i 0.303030 + 0.734237i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9627.82 + 16675.9i 0.593254 + 1.02755i 0.993791 + 0.111266i \(0.0354905\pi\)
−0.400536 + 0.916281i \(0.631176\pi\)
\(642\) 0 0
\(643\) −19996.4 −1.22641 −0.613204 0.789925i \(-0.710120\pi\)
−0.613204 + 0.789925i \(0.710120\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3532.10 + 6117.77i 0.214623 + 0.371738i 0.953156 0.302479i \(-0.0978144\pi\)
−0.738533 + 0.674218i \(0.764481\pi\)
\(648\) 0 0
\(649\) −7199.47 + 12469.8i −0.435445 + 0.754213i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6910.53 + 11969.4i −0.414134 + 0.717302i −0.995337 0.0964570i \(-0.969249\pi\)
0.581203 + 0.813759i \(0.302582\pi\)
\(654\) 0 0
\(655\) 13401.4 + 23211.9i 0.799443 + 1.38468i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7802.80 0.461235 0.230617 0.973044i \(-0.425925\pi\)
0.230617 + 0.973044i \(0.425925\pi\)
\(660\) 0 0
\(661\) −7908.65 13698.2i −0.465372 0.806048i 0.533846 0.845581i \(-0.320746\pi\)
−0.999218 + 0.0395338i \(0.987413\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −827.204 + 12498.1i −0.0482370 + 0.728806i
\(666\) 0 0
\(667\) −5404.29 + 9360.51i −0.313726 + 0.543389i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −27803.5 −1.59962
\(672\) 0 0
\(673\) 2943.30 0.168582 0.0842911 0.996441i \(-0.473137\pi\)
0.0842911 + 0.996441i \(0.473137\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1585.74 + 2746.58i −0.0900220 + 0.155923i −0.907520 0.420009i \(-0.862027\pi\)
0.817498 + 0.575931i \(0.195360\pi\)
\(678\) 0 0
\(679\) 1216.92 + 814.247i 0.0687792 + 0.0460205i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12226.6 21177.1i −0.684975 1.18641i −0.973445 0.228923i \(-0.926480\pi\)
0.288470 0.957489i \(-0.406854\pi\)
\(684\) 0 0
\(685\) 3274.70 0.182656
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5771.12 + 9995.87i 0.319103 + 0.552703i
\(690\) 0 0
\(691\) −4297.95 + 7444.26i −0.236616 + 0.409831i −0.959741 0.280886i \(-0.909372\pi\)
0.723125 + 0.690717i \(0.242705\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7254.69 12565.5i 0.395951 0.685808i
\(696\) 0 0
\(697\) 2288.51 + 3963.82i 0.124367 + 0.215409i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21476.1 1.15712 0.578561 0.815639i \(-0.303615\pi\)
0.578561 + 0.815639i \(0.303615\pi\)
\(702\) 0 0
\(703\) 8560.51 + 14827.2i 0.459269 + 0.795477i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1678.24 + 25356.3i −0.0892738 + 1.34883i
\(708\) 0 0
\(709\) 6769.46 11725.0i 0.358579 0.621077i −0.629145 0.777288i \(-0.716595\pi\)
0.987724 + 0.156211i \(0.0499281\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −56602.5 −2.97304
\(714\) 0 0
\(715\) −23690.0 −1.23910
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6941.84 12023.6i 0.360065 0.623652i −0.627906 0.778289i \(-0.716088\pi\)
0.987971 + 0.154638i \(0.0494210\pi\)
\(720\) 0 0
\(721\) −4295.63 + 2114.95i −0.221883 + 0.109244i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 913.577 + 1582.36i 0.0467992 + 0.0810585i
\(726\) 0 0
\(727\) −18292.9 −0.933215 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3772.81 + 6534.69i 0.190892 + 0.330635i
\(732\) 0 0
\(733\) −7122.92 + 12337.3i −0.358924 + 0.621674i −0.987781 0.155846i \(-0.950190\pi\)
0.628857 + 0.777521i \(0.283523\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12253.3 21223.3i 0.612422 1.06075i
\(738\) 0 0
\(739\) 681.947 + 1181.17i 0.0339456 + 0.0587956i 0.882499 0.470314i \(-0.155859\pi\)
−0.848553 + 0.529110i \(0.822526\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21789.4 −1.07588 −0.537938 0.842984i \(-0.680797\pi\)
−0.537938 + 0.842984i \(0.680797\pi\)
\(744\) 0 0
\(745\) 10985.0 + 19026.6i 0.540214 + 0.935678i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −20974.9 + 10327.0i −1.02324 + 0.503793i
\(750\) 0 0
\(751\) 1059.78 1835.59i 0.0514937 0.0891898i −0.839130 0.543932i \(-0.816935\pi\)
0.890623 + 0.454742i \(0.150268\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −33509.1 −1.61526
\(756\) 0 0
\(757\) 28202.4 1.35408 0.677038 0.735948i \(-0.263263\pi\)
0.677038 + 0.735948i \(0.263263\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5573.52 9653.62i 0.265493 0.459847i −0.702200 0.711980i \(-0.747799\pi\)
0.967693 + 0.252133i \(0.0811321\pi\)
\(762\) 0 0
\(763\) 338.597 5115.82i 0.0160656 0.242733i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5243.07 9081.26i −0.246827 0.427517i
\(768\) 0 0
\(769\) −4109.29 −0.192698 −0.0963491 0.995348i \(-0.530717\pi\)
−0.0963491 + 0.995348i \(0.530717\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6945.68 + 12030.3i 0.323181 + 0.559766i 0.981143 0.193286i \(-0.0619144\pi\)
−0.657962 + 0.753052i \(0.728581\pi\)
\(774\) 0 0
\(775\) −4784.22 + 8286.51i −0.221747 + 0.384078i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5597.75 + 9695.59i −0.257459 + 0.445931i
\(780\) 0 0
\(781\) 28262.0 + 48951.2i 1.29487 + 2.24278i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 24162.9 1.09861
\(786\) 0 0
\(787\) 4671.18 + 8090.71i 0.211575 + 0.366458i 0.952208 0.305452i \(-0.0988074\pi\)
−0.740633 + 0.671910i \(0.765474\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −814.500 544.986i −0.0366123 0.0244974i
\(792\) 0 0
\(793\) 10124.0 17535.4i 0.453361 0.785245i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24324.3 1.08107 0.540534 0.841322i \(-0.318222\pi\)
0.540534 + 0.841322i \(0.318222\pi\)
\(798\) 0 0
\(799\) 3155.97 0.139737
\(800\) 0 0