Properties

Label 504.4.s.j.361.3
Level $504$
Weight $4$
Character 504.361
Analytic conductor $29.737$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(29.7369626429\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Root \(-8.34231i\) of defining polynomial
Character \(\chi\) \(=\) 504.361
Dual form 504.4.s.j.289.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.363171 + 0.629031i) q^{5} +(-18.1420 - 3.72380i) q^{7} +O(q^{10})\) \(q+(0.363171 + 0.629031i) q^{5} +(-18.1420 - 3.72380i) q^{7} +(-32.2447 + 55.8495i) q^{11} +71.8475 q^{13} +(24.4517 - 42.3515i) q^{17} +(-17.1984 - 29.7885i) q^{19} +(-0.451675 - 0.782324i) q^{23} +(62.2362 - 107.796i) q^{25} -226.686 q^{29} +(137.898 - 238.846i) q^{31} +(-4.24627 - 12.7643i) q^{35} +(-147.605 - 255.658i) q^{37} -186.604 q^{41} -455.317 q^{43} +(141.167 + 244.509i) q^{47} +(315.267 + 135.115i) q^{49} +(178.107 - 308.491i) q^{53} -46.8414 q^{55} +(364.685 - 631.653i) q^{59} +(-137.176 - 237.596i) q^{61} +(26.0929 + 45.1943i) q^{65} +(-96.6361 + 167.379i) q^{67} -40.5277 q^{71} +(103.236 - 178.810i) q^{73} +(792.958 - 893.151i) q^{77} +(-468.870 - 812.107i) q^{79} -911.607 q^{83} +35.5206 q^{85} +(-474.988 - 822.703i) q^{89} +(-1303.46 - 267.546i) q^{91} +(12.4919 - 21.6367i) q^{95} +39.4687 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + 18q^{7} + O(q^{10}) \) \( 8q + 4q^{5} + 18q^{7} + 14q^{11} + 44q^{13} + 96q^{17} + 26q^{19} + 96q^{23} - 110q^{25} + 152q^{29} - 238q^{31} - 152q^{35} - 562q^{37} - 856q^{41} - 516q^{43} - 80q^{47} + 156q^{49} + 2952q^{55} + 262q^{59} + 276q^{61} + 2196q^{65} - 150q^{67} + 1696q^{71} + 218q^{73} + 764q^{77} - 1762q^{79} - 6900q^{83} + 2904q^{85} - 344q^{89} - 2806q^{91} + 2004q^{95} - 1244q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(5\) 0.363171 + 0.629031i 0.0324830 + 0.0562622i 0.881810 0.471605i \(-0.156325\pi\)
−0.849327 + 0.527867i \(0.822992\pi\)
\(6\) 0 0
\(7\) −18.1420 3.72380i −0.979578 0.201066i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −32.2447 + 55.8495i −0.883832 + 1.53084i −0.0367856 + 0.999323i \(0.511712\pi\)
−0.847046 + 0.531519i \(0.821621\pi\)
\(12\) 0 0
\(13\) 71.8475 1.53284 0.766420 0.642340i \(-0.222036\pi\)
0.766420 + 0.642340i \(0.222036\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 24.4517 42.3515i 0.348847 0.604221i −0.637198 0.770700i \(-0.719907\pi\)
0.986045 + 0.166479i \(0.0532399\pi\)
\(18\) 0 0
\(19\) −17.1984 29.7885i −0.207663 0.359682i 0.743315 0.668941i \(-0.233252\pi\)
−0.950978 + 0.309259i \(0.899919\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.451675 0.782324i −0.00409482 0.00709243i 0.863971 0.503542i \(-0.167970\pi\)
−0.868066 + 0.496450i \(0.834637\pi\)
\(24\) 0 0
\(25\) 62.2362 107.796i 0.497890 0.862370i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −226.686 −1.45154 −0.725769 0.687939i \(-0.758516\pi\)
−0.725769 + 0.687939i \(0.758516\pi\)
\(30\) 0 0
\(31\) 137.898 238.846i 0.798940 1.38380i −0.121367 0.992608i \(-0.538728\pi\)
0.920307 0.391197i \(-0.127939\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.24627 12.7643i −0.0205072 0.0616444i
\(36\) 0 0
\(37\) −147.605 255.658i −0.655839 1.13595i −0.981683 0.190522i \(-0.938982\pi\)
0.325844 0.945423i \(-0.394352\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −186.604 −0.710798 −0.355399 0.934715i \(-0.615655\pi\)
−0.355399 + 0.934715i \(0.615655\pi\)
\(42\) 0 0
\(43\) −455.317 −1.61477 −0.807386 0.590023i \(-0.799119\pi\)
−0.807386 + 0.590023i \(0.799119\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 141.167 + 244.509i 0.438114 + 0.758835i 0.997544 0.0700420i \(-0.0223133\pi\)
−0.559430 + 0.828877i \(0.688980\pi\)
\(48\) 0 0
\(49\) 315.267 + 135.115i 0.919145 + 0.393920i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 178.107 308.491i 0.461602 0.799518i −0.537439 0.843303i \(-0.680608\pi\)
0.999041 + 0.0437844i \(0.0139415\pi\)
\(54\) 0 0
\(55\) −46.8414 −0.114838
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 364.685 631.653i 0.804711 1.39380i −0.111776 0.993733i \(-0.535654\pi\)
0.916486 0.400066i \(-0.131013\pi\)
\(60\) 0 0
\(61\) −137.176 237.596i −0.287928 0.498706i 0.685387 0.728179i \(-0.259633\pi\)
−0.973315 + 0.229473i \(0.926300\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 26.0929 + 45.1943i 0.0497912 + 0.0862409i
\(66\) 0 0
\(67\) −96.6361 + 167.379i −0.176209 + 0.305202i −0.940579 0.339575i \(-0.889717\pi\)
0.764370 + 0.644778i \(0.223050\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −40.5277 −0.0677429 −0.0338715 0.999426i \(-0.510784\pi\)
−0.0338715 + 0.999426i \(0.510784\pi\)
\(72\) 0 0
\(73\) 103.236 178.810i 0.165519 0.286687i −0.771320 0.636447i \(-0.780403\pi\)
0.936839 + 0.349760i \(0.113737\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 792.958 893.151i 1.17358 1.32187i
\(78\) 0 0
\(79\) −468.870 812.107i −0.667747 1.15657i −0.978533 0.206092i \(-0.933925\pi\)
0.310785 0.950480i \(-0.399408\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −911.607 −1.20556 −0.602782 0.797906i \(-0.705941\pi\)
−0.602782 + 0.797906i \(0.705941\pi\)
\(84\) 0 0
\(85\) 35.5206 0.0453264
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −474.988 822.703i −0.565715 0.979846i −0.996983 0.0776226i \(-0.975267\pi\)
0.431268 0.902224i \(-0.358066\pi\)
\(90\) 0 0
\(91\) −1303.46 267.546i −1.50154 0.308203i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.4919 21.6367i 0.0134910 0.0233671i
\(96\) 0 0
\(97\) 39.4687 0.0413138 0.0206569 0.999787i \(-0.493424\pi\)
0.0206569 + 0.999787i \(0.493424\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −158.437 + 274.421i −0.156090 + 0.270356i −0.933455 0.358694i \(-0.883222\pi\)
0.777365 + 0.629049i \(0.216556\pi\)
\(102\) 0 0
\(103\) 161.317 + 279.409i 0.154321 + 0.267291i 0.932811 0.360365i \(-0.117348\pi\)
−0.778491 + 0.627656i \(0.784014\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 340.726 + 590.154i 0.307843 + 0.533200i 0.977890 0.209119i \(-0.0670595\pi\)
−0.670047 + 0.742318i \(0.733726\pi\)
\(108\) 0 0
\(109\) 227.984 394.879i 0.200338 0.346996i −0.748299 0.663361i \(-0.769129\pi\)
0.948637 + 0.316365i \(0.102463\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 796.025 0.662688 0.331344 0.943510i \(-0.392498\pi\)
0.331344 + 0.943510i \(0.392498\pi\)
\(114\) 0 0
\(115\) 0.328071 0.568235i 0.000266024 0.000460767i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −601.312 + 677.290i −0.463212 + 0.521740i
\(120\) 0 0
\(121\) −1413.95 2449.03i −1.06232 1.83999i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 181.202 0.129658
\(126\) 0 0
\(127\) 2333.92 1.63072 0.815362 0.578952i \(-0.196538\pi\)
0.815362 + 0.578952i \(0.196538\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −943.489 1634.17i −0.629259 1.08991i −0.987701 0.156357i \(-0.950025\pi\)
0.358441 0.933552i \(-0.383308\pi\)
\(132\) 0 0
\(133\) 201.088 + 604.468i 0.131102 + 0.394091i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1473.63 2552.40i 0.918983 1.59173i 0.118021 0.993011i \(-0.462345\pi\)
0.800963 0.598714i \(-0.204322\pi\)
\(138\) 0 0
\(139\) 955.433 0.583013 0.291506 0.956569i \(-0.405844\pi\)
0.291506 + 0.956569i \(0.405844\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2316.70 + 4012.65i −1.35477 + 2.34654i
\(144\) 0 0
\(145\) −82.3259 142.593i −0.0471503 0.0816667i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1091.87 + 1891.17i 0.600332 + 1.03981i 0.992771 + 0.120027i \(0.0382981\pi\)
−0.392439 + 0.919778i \(0.628369\pi\)
\(150\) 0 0
\(151\) −202.360 + 350.497i −0.109058 + 0.188894i −0.915389 0.402570i \(-0.868117\pi\)
0.806331 + 0.591465i \(0.201450\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 200.322 0.103808
\(156\) 0 0
\(157\) 464.791 805.042i 0.236270 0.409231i −0.723371 0.690459i \(-0.757408\pi\)
0.959641 + 0.281228i \(0.0907418\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.28108 + 15.8749i 0.00258514 + 0.00777092i
\(162\) 0 0
\(163\) 712.840 + 1234.68i 0.342540 + 0.593296i 0.984904 0.173104i \(-0.0553796\pi\)
−0.642364 + 0.766400i \(0.722046\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4185.15 −1.93926 −0.969631 0.244572i \(-0.921353\pi\)
−0.969631 + 0.244572i \(0.921353\pi\)
\(168\) 0 0
\(169\) 2965.07 1.34960
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1117.78 + 1936.05i 0.491231 + 0.850837i 0.999949 0.0100961i \(-0.00321376\pi\)
−0.508718 + 0.860933i \(0.669880\pi\)
\(174\) 0 0
\(175\) −1530.50 + 1723.89i −0.661115 + 0.744650i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −470.740 + 815.345i −0.196563 + 0.340457i −0.947412 0.320017i \(-0.896311\pi\)
0.750849 + 0.660474i \(0.229645\pi\)
\(180\) 0 0
\(181\) −467.540 −0.192000 −0.0960000 0.995381i \(-0.530605\pi\)
−0.0960000 + 0.995381i \(0.530605\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 107.211 185.696i 0.0426072 0.0737979i
\(186\) 0 0
\(187\) 1576.88 + 2731.23i 0.616645 + 1.06806i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 137.701 + 238.506i 0.0521660 + 0.0903542i 0.890929 0.454142i \(-0.150054\pi\)
−0.838763 + 0.544496i \(0.816721\pi\)
\(192\) 0 0
\(193\) −820.148 + 1420.54i −0.305884 + 0.529806i −0.977458 0.211131i \(-0.932285\pi\)
0.671574 + 0.740937i \(0.265619\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1303.88 −0.471560 −0.235780 0.971806i \(-0.575764\pi\)
−0.235780 + 0.971806i \(0.575764\pi\)
\(198\) 0 0
\(199\) 663.678 1149.52i 0.236417 0.409485i −0.723267 0.690569i \(-0.757360\pi\)
0.959683 + 0.281083i \(0.0906937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4112.55 + 844.135i 1.42189 + 0.291855i
\(204\) 0 0
\(205\) −67.7693 117.380i −0.0230889 0.0399911i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2218.23 0.734155
\(210\) 0 0
\(211\) −4753.28 −1.55085 −0.775426 0.631439i \(-0.782465\pi\)
−0.775426 + 0.631439i \(0.782465\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −165.358 286.408i −0.0524527 0.0908507i
\(216\) 0 0
\(217\) −3391.16 + 3819.64i −1.06086 + 1.19490i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1756.79 3042.85i 0.534727 0.926174i
\(222\) 0 0
\(223\) 513.149 0.154094 0.0770470 0.997027i \(-0.475451\pi\)
0.0770470 + 0.997027i \(0.475451\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1654.67 2865.97i 0.483808 0.837980i −0.516019 0.856577i \(-0.672587\pi\)
0.999827 + 0.0185972i \(0.00592001\pi\)
\(228\) 0 0
\(229\) 2954.73 + 5117.75i 0.852639 + 1.47681i 0.878819 + 0.477156i \(0.158332\pi\)
−0.0261800 + 0.999657i \(0.508334\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −176.786 306.202i −0.0497065 0.0860943i 0.840102 0.542429i \(-0.182495\pi\)
−0.889808 + 0.456335i \(0.849162\pi\)
\(234\) 0 0
\(235\) −102.536 + 177.597i −0.0284625 + 0.0492985i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1652.55 0.447259 0.223629 0.974674i \(-0.428209\pi\)
0.223629 + 0.974674i \(0.428209\pi\)
\(240\) 0 0
\(241\) 1553.47 2690.69i 0.415220 0.719182i −0.580232 0.814451i \(-0.697038\pi\)
0.995452 + 0.0952696i \(0.0303713\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 29.5044 + 247.382i 0.00769374 + 0.0645088i
\(246\) 0 0
\(247\) −1235.66 2140.23i −0.318313 0.551335i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1771.77 −0.445551 −0.222776 0.974870i \(-0.571512\pi\)
−0.222776 + 0.974870i \(0.571512\pi\)
\(252\) 0 0
\(253\) 58.2566 0.0144765
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 739.063 + 1280.09i 0.179383 + 0.310701i 0.941669 0.336539i \(-0.109257\pi\)
−0.762286 + 0.647240i \(0.775923\pi\)
\(258\) 0 0
\(259\) 1725.82 + 5187.81i 0.414044 + 1.24461i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −715.987 + 1240.13i −0.167869 + 0.290758i −0.937671 0.347525i \(-0.887022\pi\)
0.769801 + 0.638284i \(0.220355\pi\)
\(264\) 0 0
\(265\) 258.734 0.0599769
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 142.699 247.162i 0.0323439 0.0560213i −0.849400 0.527749i \(-0.823036\pi\)
0.881744 + 0.471728i \(0.156369\pi\)
\(270\) 0 0
\(271\) 2624.66 + 4546.05i 0.588328 + 1.01901i 0.994452 + 0.105196i \(0.0335470\pi\)
−0.406123 + 0.913818i \(0.633120\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4013.58 + 6951.72i 0.880102 + 1.52438i
\(276\) 0 0
\(277\) −3573.93 + 6190.24i −0.775224 + 1.34273i 0.159445 + 0.987207i \(0.449029\pi\)
−0.934669 + 0.355520i \(0.884304\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4228.36 −0.897661 −0.448831 0.893617i \(-0.648159\pi\)
−0.448831 + 0.893617i \(0.648159\pi\)
\(282\) 0 0
\(283\) −4171.19 + 7224.71i −0.876154 + 1.51754i −0.0206255 + 0.999787i \(0.506566\pi\)
−0.855528 + 0.517756i \(0.826768\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3385.38 + 694.878i 0.696282 + 0.142918i
\(288\) 0 0
\(289\) 1260.73 + 2183.65i 0.256611 + 0.444464i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5038.84 −1.00468 −0.502342 0.864669i \(-0.667528\pi\)
−0.502342 + 0.864669i \(0.667528\pi\)
\(294\) 0 0
\(295\) 529.772 0.104558
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −32.4517 56.2081i −0.00627670 0.0108716i
\(300\) 0 0
\(301\) 8260.38 + 1695.51i 1.58180 + 0.324677i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 99.6369 172.576i 0.0187055 0.0323990i
\(306\) 0 0
\(307\) −4869.67 −0.905300 −0.452650 0.891688i \(-0.649521\pi\)
−0.452650 + 0.891688i \(0.649521\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −726.421 + 1258.20i −0.132449 + 0.229408i −0.924620 0.380891i \(-0.875617\pi\)
0.792171 + 0.610299i \(0.208951\pi\)
\(312\) 0 0
\(313\) −2848.14 4933.12i −0.514333 0.890850i −0.999862 0.0166299i \(-0.994706\pi\)
0.485529 0.874221i \(-0.338627\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1735.73 3006.38i −0.307535 0.532666i 0.670288 0.742101i \(-0.266171\pi\)
−0.977822 + 0.209435i \(0.932837\pi\)
\(318\) 0 0
\(319\) 7309.44 12660.3i 1.28291 2.22207i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1682.12 −0.289770
\(324\) 0 0
\(325\) 4471.52 7744.90i 0.763185 1.32188i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1650.56 4961.56i −0.276590 0.831428i
\(330\) 0 0
\(331\) −3127.19 5416.45i −0.519293 0.899441i −0.999749 0.0224223i \(-0.992862\pi\)
0.480456 0.877019i \(-0.340471\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −140.382 −0.0228951
\(336\) 0 0
\(337\) 8006.96 1.29426 0.647132 0.762378i \(-0.275968\pi\)
0.647132 + 0.762378i \(0.275968\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8892.94 + 15403.0i 1.41226 + 2.44610i
\(342\) 0 0
\(343\) −5216.44 3625.25i −0.821169 0.570685i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3817.80 6612.62i 0.590634 1.02301i −0.403513 0.914974i \(-0.632211\pi\)
0.994147 0.108034i \(-0.0344556\pi\)
\(348\) 0 0
\(349\) −10358.0 −1.58869 −0.794345 0.607468i \(-0.792185\pi\)
−0.794345 + 0.607468i \(0.792185\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1692.12 2930.83i 0.255134 0.441905i −0.709798 0.704405i \(-0.751214\pi\)
0.964932 + 0.262500i \(0.0845471\pi\)
\(354\) 0 0
\(355\) −14.7185 25.4931i −0.00220049 0.00381137i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4097.31 7096.74i −0.602361 1.04332i −0.992463 0.122548i \(-0.960894\pi\)
0.390102 0.920772i \(-0.372440\pi\)
\(360\) 0 0
\(361\) 2837.93 4915.44i 0.413752 0.716640i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 149.970 0.0215062
\(366\) 0 0
\(367\) −402.755 + 697.592i −0.0572851 + 0.0992208i −0.893246 0.449569i \(-0.851578\pi\)
0.835961 + 0.548789i \(0.184911\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4379.99 + 4933.41i −0.612931 + 0.690377i
\(372\) 0 0
\(373\) −3952.86 6846.55i −0.548716 0.950404i −0.998363 0.0571977i \(-0.981783\pi\)
0.449647 0.893206i \(-0.351550\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16286.8 −2.22497
\(378\) 0 0
\(379\) 3324.24 0.450540 0.225270 0.974296i \(-0.427674\pi\)
0.225270 + 0.974296i \(0.427674\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4235.38 7335.90i −0.565060 0.978712i −0.997044 0.0768310i \(-0.975520\pi\)
0.431984 0.901881i \(-0.357814\pi\)
\(384\) 0 0
\(385\) 849.798 + 174.428i 0.112493 + 0.0230901i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3954.20 + 6848.88i −0.515388 + 0.892678i 0.484452 + 0.874818i \(0.339019\pi\)
−0.999840 + 0.0178606i \(0.994314\pi\)
\(390\) 0 0
\(391\) −44.1769 −0.00571386
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 340.560 589.868i 0.0433809 0.0751379i
\(396\) 0 0
\(397\) 4890.79 + 8471.10i 0.618292 + 1.07091i 0.989797 + 0.142482i \(0.0455083\pi\)
−0.371506 + 0.928431i \(0.621158\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −397.827 689.056i −0.0495424 0.0858100i 0.840191 0.542291i \(-0.182443\pi\)
−0.889733 + 0.456481i \(0.849110\pi\)
\(402\) 0 0
\(403\) 9907.60 17160.5i 1.22465 2.12115i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 19037.9 2.31860
\(408\) 0 0
\(409\) −4292.36 + 7434.59i −0.518933 + 0.898818i 0.480825 + 0.876817i \(0.340337\pi\)
−0.999758 + 0.0220017i \(0.992996\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8968.27 + 10101.4i −1.06852 + 1.20353i
\(414\) 0 0
\(415\) −331.069 573.428i −0.0391603 0.0678277i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7447.09 0.868292 0.434146 0.900843i \(-0.357050\pi\)
0.434146 + 0.900843i \(0.357050\pi\)
\(420\) 0 0
\(421\) −4446.76 −0.514779 −0.257390 0.966308i \(-0.582862\pi\)
−0.257390 + 0.966308i \(0.582862\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3043.56 5271.60i −0.347375 0.601671i
\(426\) 0 0
\(427\) 1603.89 + 4821.30i 0.181775 + 0.546414i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4481.85 + 7762.79i −0.500889 + 0.867565i 0.499110 + 0.866538i \(0.333660\pi\)
−0.999999 + 0.00102683i \(0.999673\pi\)
\(432\) 0 0
\(433\) −16173.6 −1.79504 −0.897520 0.440973i \(-0.854633\pi\)
−0.897520 + 0.440973i \(0.854633\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.5362 + 26.9095i −0.00170068 + 0.00294567i
\(438\) 0 0
\(439\) 3149.21 + 5454.60i 0.342378 + 0.593015i 0.984874 0.173274i \(-0.0554345\pi\)
−0.642496 + 0.766289i \(0.722101\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8392.35 14536.0i −0.900074 1.55897i −0.827397 0.561618i \(-0.810179\pi\)
−0.0726770 0.997356i \(-0.523154\pi\)
\(444\) 0 0
\(445\) 345.004 597.564i 0.0367522 0.0636567i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2733.88 −0.287349 −0.143674 0.989625i \(-0.545892\pi\)
−0.143674 + 0.989625i \(0.545892\pi\)
\(450\) 0 0
\(451\) 6017.01 10421.8i 0.628226 1.08812i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −305.084 917.081i −0.0314342 0.0944910i
\(456\) 0 0
\(457\) −4614.60 7992.72i −0.472345 0.818126i 0.527154 0.849770i \(-0.323259\pi\)
−0.999499 + 0.0316437i \(0.989926\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19726.7 1.99298 0.996491 0.0837048i \(-0.0266753\pi\)
0.996491 + 0.0837048i \(0.0266753\pi\)
\(462\) 0 0
\(463\) 368.924 0.0370310 0.0185155 0.999829i \(-0.494106\pi\)
0.0185155 + 0.999829i \(0.494106\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6654.78 11526.4i −0.659414 1.14214i −0.980768 0.195179i \(-0.937471\pi\)
0.321353 0.946959i \(-0.395862\pi\)
\(468\) 0 0
\(469\) 2376.46 2676.73i 0.233976 0.263540i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 14681.6 25429.2i 1.42719 2.47196i
\(474\) 0 0
\(475\) −4281.46 −0.413572
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5781.39 10013.7i 0.551479 0.955189i −0.446689 0.894689i \(-0.647397\pi\)
0.998168 0.0605002i \(-0.0192696\pi\)
\(480\) 0 0
\(481\) −10605.0 18368.4i −1.00530 1.74122i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.3339 + 24.8270i 0.00134200 + 0.00232440i
\(486\) 0 0
\(487\) −1314.06 + 2276.02i −0.122271 + 0.211779i −0.920663 0.390359i \(-0.872351\pi\)
0.798392 + 0.602138i \(0.205684\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12319.9 1.13236 0.566181 0.824281i \(-0.308420\pi\)
0.566181 + 0.824281i \(0.308420\pi\)
\(492\) 0 0
\(493\) −5542.86 + 9600.51i −0.506365 + 0.877049i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 735.254 + 150.917i 0.0663595 + 0.0136208i
\(498\) 0 0
\(499\) 1652.90 + 2862.91i 0.148285 + 0.256837i 0.930594 0.366054i \(-0.119291\pi\)
−0.782309 + 0.622891i \(0.785958\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3072.72 0.272377 0.136189 0.990683i \(-0.456515\pi\)
0.136189 + 0.990683i \(0.456515\pi\)
\(504\) 0 0
\(505\) −230.159 −0.0202811
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6784.91 + 11751.8i 0.590836 + 1.02336i 0.994120 + 0.108284i \(0.0345355\pi\)
−0.403284 + 0.915075i \(0.632131\pi\)
\(510\) 0 0
\(511\) −2538.77 + 2859.55i −0.219782 + 0.247552i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −117.171 + 202.947i −0.0100256 + 0.0173648i
\(516\) 0 0
\(517\) −18207.6 −1.54888
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5366.68 + 9295.36i −0.451283 + 0.781645i −0.998466 0.0553681i \(-0.982367\pi\)
0.547183 + 0.837013i \(0.315700\pi\)
\(522\) 0 0
\(523\) −4174.07 7229.71i −0.348986 0.604461i 0.637084 0.770794i \(-0.280140\pi\)
−0.986070 + 0.166334i \(0.946807\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6743.65 11680.3i −0.557416 0.965473i
\(528\) 0 0
\(529\) 6083.09 10536.2i 0.499966 0.865967i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13407.1 −1.08954
\(534\) 0 0
\(535\) −247.483 + 428.654i −0.0199993 + 0.0346399i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −17711.8 + 13250.7i −1.41540 + 1.05891i
\(540\) 0 0
\(541\) 11553.6 + 20011.5i 0.918170 + 1.59032i 0.802192 + 0.597066i \(0.203667\pi\)
0.115978 + 0.993252i \(0.463000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 331.188 0.0260304
\(546\) 0 0
\(547\) 13935.2 1.08926 0.544630 0.838676i \(-0.316670\pi\)
0.544630 + 0.838676i \(0.316670\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3898.65 + 6752.65i 0.301430 + 0.522092i
\(552\) 0 0
\(553\) 5482.13 + 16479.3i 0.421562 + 1.26721i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7523.76 + 13031.5i −0.572337 + 0.991317i 0.423988 + 0.905668i \(0.360630\pi\)
−0.996325 + 0.0856492i \(0.972704\pi\)
\(558\) 0 0
\(559\) −32713.4 −2.47519
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7721.08 13373.3i 0.577983 1.00110i −0.417727 0.908572i \(-0.637173\pi\)
0.995710 0.0925239i \(-0.0294934\pi\)
\(564\) 0 0
\(565\) 289.093 + 500.724i 0.0215261 + 0.0372843i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6681.06 11571.9i −0.492240 0.852585i 0.507720 0.861522i \(-0.330489\pi\)
−0.999960 + 0.00893696i \(0.997155\pi\)
\(570\) 0 0
\(571\) 11092.6 19213.0i 0.812981 1.40812i −0.0977876 0.995207i \(-0.531177\pi\)
0.910769 0.412917i \(-0.135490\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −112.442 −0.00815507
\(576\) 0 0
\(577\) 9475.68 16412.4i 0.683671 1.18415i −0.290182 0.956971i \(-0.593716\pi\)
0.973853 0.227181i \(-0.0729508\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16538.4 + 3394.64i 1.18094 + 0.242399i
\(582\) 0 0
\(583\) 11486.0 + 19894.4i 0.815957 + 1.41328i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19579.5 −1.37672 −0.688359 0.725371i \(-0.741668\pi\)
−0.688359 + 0.725371i \(0.741668\pi\)
\(588\) 0 0
\(589\) −9486.48 −0.663640
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2806.51 + 4861.01i 0.194350 + 0.336624i 0.946687 0.322154i \(-0.104407\pi\)
−0.752337 + 0.658778i \(0.771074\pi\)
\(594\) 0 0
\(595\) −644.415 132.272i −0.0444007 0.00911362i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 10962.8 18988.0i 0.747790 1.29521i −0.201090 0.979573i \(-0.564448\pi\)
0.948880 0.315637i \(-0.102218\pi\)
\(600\) 0 0
\(601\) −2067.51 −0.140326 −0.0701628 0.997536i \(-0.522352\pi\)
−0.0701628 + 0.997536i \(0.522352\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1027.01 1778.83i 0.0690146 0.119537i
\(606\) 0 0
\(607\) 5083.61 + 8805.07i 0.339930 + 0.588775i 0.984419 0.175838i \(-0.0562634\pi\)
−0.644490 + 0.764613i \(0.722930\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10142.5 + 17567.3i 0.671558 + 1.16317i
\(612\) 0 0
\(613\) 9093.05 15749.6i 0.599127 1.03772i −0.393824 0.919186i \(-0.628848\pi\)
0.992950 0.118532i \(-0.0378188\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6584.41 −0.429625 −0.214812 0.976655i \(-0.568914\pi\)
−0.214812 + 0.976655i \(0.568914\pi\)
\(618\) 0 0
\(619\) 3889.86 6737.43i 0.252579 0.437480i −0.711656 0.702528i \(-0.752054\pi\)
0.964235 + 0.265048i \(0.0853878\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5553.66 + 16694.3i 0.357147 + 1.07358i
\(624\) 0 0
\(625\) −7713.72 13360.6i −0.493678 0.855075i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14436.7 −0.915150
\(630\) 0 0
\(631\) 3787.78 0.238969 0.119484 0.992836i \(-0.461876\pi\)
0.119484 + 0.992836i \(0.461876\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 847.612 + 1468.11i 0.0529708 + 0.0917481i
\(636\) 0 0
\(637\) 22651.1 + 9707.66i 1.40890 + 0.603817i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9965.44 + 17260.6i −0.614058 + 1.06358i 0.376491 + 0.926420i \(0.377131\pi\)
−0.990549 + 0.137159i \(0.956203\pi\)
\(642\) 0 0
\(643\) 3185.18 0.195352 0.0976759 0.995218i \(-0.468859\pi\)
0.0976759 + 0.995218i \(0.468859\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8471.50 + 14673.1i −0.514759 + 0.891589i 0.485094 + 0.874462i \(0.338785\pi\)
−0.999853 + 0.0171270i \(0.994548\pi\)
\(648\) 0 0
\(649\) 23518.3 + 40734.9i 1.42246 + 2.46377i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10039.4 17388.7i −0.601640 1.04207i −0.992573 0.121652i \(-0.961181\pi\)
0.390932 0.920419i \(-0.372153\pi\)
\(654\) 0 0
\(655\) 685.295 1186.97i 0.0408805 0.0708070i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9442.46 0.558158 0.279079 0.960268i \(-0.409971\pi\)
0.279079 + 0.960268i \(0.409971\pi\)
\(660\) 0 0
\(661\) −380.995 + 659.902i −0.0224190 + 0.0388309i −0.877017 0.480459i \(-0.840470\pi\)
0.854598 + 0.519290i \(0.173803\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −307.200 + 346.016i −0.0179138 + 0.0201773i
\(666\) 0 0
\(667\) 102.389 + 177.342i 0.00594378 + 0.0102949i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17692.8 1.01792
\(672\) 0 0
\(673\) −16111.6 −0.922818 −0.461409 0.887188i \(-0.652656\pi\)
−0.461409 + 0.887188i \(0.652656\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15620.7 + 27055.9i 0.886786 + 1.53596i 0.843653 + 0.536889i \(0.180401\pi\)
0.0431329 + 0.999069i \(0.486266\pi\)
\(678\) 0 0
\(679\) −716.042 146.974i −0.0404700 0.00830682i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −15056.8 + 26079.1i −0.843530 + 1.46104i 0.0433614 + 0.999059i \(0.486193\pi\)
−0.886892 + 0.461978i \(0.847140\pi\)
\(684\) 0 0
\(685\) 2140.72 0.119405
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12796.6 22164.3i 0.707562 1.22553i
\(690\) 0 0
\(691\) 4875.43 + 8444.49i 0.268408 + 0.464896i 0.968451 0.249204i \(-0.0801691\pi\)
−0.700043 + 0.714101i \(0.746836\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 346.986 + 600.997i 0.0189380 + 0.0328016i
\(696\) 0 0
\(697\) −4562.79 + 7902.99i −0.247960 + 0.429479i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −11851.6 −0.638559 −0.319280 0.947661i \(-0.603441\pi\)
−0.319280 + 0.947661i \(0.603441\pi\)
\(702\) 0 0
\(703\) −5077.13 + 8793.85i −0.272386 + 0.471787i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3896.26 4388.57i 0.207262 0.233450i
\(708\) 0 0
\(709\) −661.196 1145.22i −0.0350236 0.0606627i 0.847982 0.530025i \(-0.177817\pi\)
−0.883006 + 0.469362i \(0.844484\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −249.140 −0.0130861
\(714\) 0 0
\(715\) −3365.44 −0.176028
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3650.78 + 6323.33i 0.189362 + 0.327984i 0.945038 0.326962i \(-0.106025\pi\)
−0.755676 + 0.654946i \(0.772691\pi\)
\(720\) 0 0
\(721\) −1886.15 5669.76i −0.0974257 0.292861i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −14108.1 + 24435.9i −0.722705 + 1.25176i
\(726\) 0 0
\(727\) −6088.72 −0.310616 −0.155308 0.987866i \(-0.549637\pi\)
−0.155308 + 0.987866i \(0.549637\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11133.3 + 19283.4i −0.563309 + 0.975680i
\(732\) 0 0
\(733\) 13289.2 + 23017.6i 0.669644 + 1.15986i 0.978004 + 0.208587i \(0.0668865\pi\)
−0.308360 + 0.951270i \(0.599780\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6232.01 10794.2i −0.311478 0.539495i
\(738\) 0 0
\(739\) −12609.9 + 21841.0i −0.627689 + 1.08719i 0.360325 + 0.932827i \(0.382666\pi\)
−0.988014 + 0.154363i \(0.950668\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2634.28 −0.130071 −0.0650353 0.997883i \(-0.520716\pi\)
−0.0650353 + 0.997883i \(0.520716\pi\)
\(744\) 0 0
\(745\) −793.071 + 1373.64i −0.0390012 + 0.0675520i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3983.84 11975.4i −0.194347 0.584207i
\(750\) 0 0
\(751\) −2883.64 4994.62i −0.140114 0.242685i 0.787425 0.616410i \(-0.211414\pi\)
−0.927539 + 0.373725i \(0.878080\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −293.965 −0.0141702
\(756\) 0 0
\(757\) 33378.7 1.60260 0.801302 0.598260i \(-0.204141\pi\)
0.801302 + 0.598260i \(0.204141\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1813.04 + 3140.28i 0.0863637 + 0.149586i 0.905971 0.423339i \(-0.139142\pi\)
−0.819608 + 0.572925i \(0.805809\pi\)
\(762\) 0 0
\(763\) −5606.54 + 6314.95i −0.266016 + 0.299628i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26201.7 45382.7i 1.23349 2.13647i
\(768\) 0 0
\(769\) 3426.15 0.160663 0.0803316 0.996768i \(-0.474402\pi\)
0.0803316 + 0.996768i \(0.474402\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6554.09 11352.0i 0.304960 0.528207i −0.672292 0.740286i \(-0.734690\pi\)
0.977252 + 0.212079i \(0.0680235\pi\)
\(774\) 0 0
\(775\) −17164.4 29729.7i −0.795568 1.37796i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3209.30 + 5558.67i 0.147606 + 0.255661i
\(780\) 0 0
\(781\) 1306.80 2263.45i 0.0598734 0.103704i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 675.194 0.0306990
\(786\) 0 0
\(787\) −19659.9 + 34051.9i −0.890468 + 1.54234i −0.0511538 + 0.998691i \(0.516290\pi\)
−0.839315 + 0.543646i \(0.817043\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14441.5 2964.24i −0.649154 0.133244i
\(792\) 0 0
\(793\) −9855.77 17070.7i −0.441348 0.764437i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14597.8 0.648785 0.324393 0.945923i \(-0.394840\pi\)
0.324393 + 0.945923i \(0.394840\pi\)
\(798\) 0 0
\(799\) 13807.1 0.611339
\(800\) 0 0
\(801\) 0 0