Properties

Label 1008.4.bt.d.17.18
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
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: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.18
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.18

$q$-expansion

\(f(q)\) \(=\) \(q+(5.00025 + 8.66069i) q^{5} +(-1.56940 + 18.4536i) q^{7} +O(q^{10})\) \(q+(5.00025 + 8.66069i) q^{5} +(-1.56940 + 18.4536i) q^{7} +(8.94164 + 5.16246i) q^{11} -52.4866i q^{13} +(-0.584477 + 1.01234i) q^{17} +(86.7124 - 50.0634i) q^{19} +(90.1373 - 52.0408i) q^{23} +(12.4950 - 21.6419i) q^{25} -187.555i q^{29} +(107.524 + 62.0789i) q^{31} +(-167.669 + 78.6808i) q^{35} +(16.0459 + 27.7922i) q^{37} +415.597 q^{41} +193.264 q^{43} +(196.466 + 340.289i) q^{47} +(-338.074 - 57.9222i) q^{49} +(74.7758 + 43.1718i) q^{53} +103.254i q^{55} +(-102.286 + 177.165i) q^{59} +(-183.527 + 105.959i) q^{61} +(454.570 - 262.446i) q^{65} +(-364.857 + 631.951i) q^{67} +315.022i q^{71} +(-899.220 - 519.165i) q^{73} +(-109.299 + 156.904i) q^{77} +(607.787 + 1052.72i) q^{79} -333.797 q^{83} -11.6901 q^{85} +(168.355 + 291.599i) q^{89} +(968.568 + 82.3723i) q^{91} +(867.167 + 500.659i) q^{95} +893.179i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

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
\(5\) 5.00025 + 8.66069i 0.447236 + 0.774636i 0.998205 0.0598902i \(-0.0190751\pi\)
−0.550969 + 0.834526i \(0.685742\pi\)
\(6\) 0 0
\(7\) −1.56940 + 18.4536i −0.0847395 + 0.996403i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 8.94164 + 5.16246i 0.245092 + 0.141504i 0.617515 0.786559i \(-0.288140\pi\)
−0.372423 + 0.928063i \(0.621473\pi\)
\(12\) 0 0
\(13\) 52.4866i 1.11978i −0.828567 0.559891i \(-0.810843\pi\)
0.828567 0.559891i \(-0.189157\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.584477 + 1.01234i −0.00833862 + 0.0144429i −0.870165 0.492761i \(-0.835988\pi\)
0.861826 + 0.507204i \(0.169321\pi\)
\(18\) 0 0
\(19\) 86.7124 50.0634i 1.04701 0.604491i 0.125199 0.992132i \(-0.460043\pi\)
0.921811 + 0.387640i \(0.126710\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 90.1373 52.0408i 0.817171 0.471794i −0.0322689 0.999479i \(-0.510273\pi\)
0.849440 + 0.527685i \(0.176940\pi\)
\(24\) 0 0
\(25\) 12.4950 21.6419i 0.0999598 0.173135i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 187.555i 1.20097i −0.799636 0.600485i \(-0.794974\pi\)
0.799636 0.600485i \(-0.205026\pi\)
\(30\) 0 0
\(31\) 107.524 + 62.0789i 0.622963 + 0.359668i 0.778022 0.628238i \(-0.216223\pi\)
−0.155059 + 0.987905i \(0.549557\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −167.669 + 78.6808i −0.809748 + 0.379985i
\(36\) 0 0
\(37\) 16.0459 + 27.7922i 0.0712952 + 0.123487i 0.899469 0.436984i \(-0.143953\pi\)
−0.828174 + 0.560471i \(0.810620\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 415.597 1.58306 0.791528 0.611133i \(-0.209286\pi\)
0.791528 + 0.611133i \(0.209286\pi\)
\(42\) 0 0
\(43\) 193.264 0.685407 0.342703 0.939444i \(-0.388657\pi\)
0.342703 + 0.939444i \(0.388657\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 196.466 + 340.289i 0.609735 + 1.05609i 0.991284 + 0.131743i \(0.0420573\pi\)
−0.381549 + 0.924348i \(0.624609\pi\)
\(48\) 0 0
\(49\) −338.074 57.9222i −0.985638 0.168869i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 74.7758 + 43.1718i 0.193797 + 0.111889i 0.593759 0.804643i \(-0.297643\pi\)
−0.399962 + 0.916532i \(0.630977\pi\)
\(54\) 0 0
\(55\) 103.254i 0.253142i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −102.286 + 177.165i −0.225704 + 0.390931i −0.956531 0.291632i \(-0.905802\pi\)
0.730826 + 0.682564i \(0.239135\pi\)
\(60\) 0 0
\(61\) −183.527 + 105.959i −0.385217 + 0.222405i −0.680086 0.733133i \(-0.738057\pi\)
0.294869 + 0.955538i \(0.404724\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 454.570 262.446i 0.867422 0.500806i
\(66\) 0 0
\(67\) −364.857 + 631.951i −0.665290 + 1.15232i 0.313917 + 0.949450i \(0.398359\pi\)
−0.979207 + 0.202865i \(0.934975\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 315.022i 0.526566i 0.964719 + 0.263283i \(0.0848053\pi\)
−0.964719 + 0.263283i \(0.915195\pi\)
\(72\) 0 0
\(73\) −899.220 519.165i −1.44172 0.832379i −0.443758 0.896147i \(-0.646355\pi\)
−0.997965 + 0.0637680i \(0.979688\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −109.299 + 156.904i −0.161764 + 0.232219i
\(78\) 0 0
\(79\) 607.787 + 1052.72i 0.865587 + 1.49924i 0.866463 + 0.499241i \(0.166388\pi\)
−0.000876764 1.00000i \(0.500279\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −333.797 −0.441434 −0.220717 0.975338i \(-0.570840\pi\)
−0.220717 + 0.975338i \(0.570840\pi\)
\(84\) 0 0
\(85\) −11.6901 −0.0149173
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 168.355 + 291.599i 0.200512 + 0.347297i 0.948693 0.316197i \(-0.102406\pi\)
−0.748182 + 0.663494i \(0.769073\pi\)
\(90\) 0 0
\(91\) 968.568 + 82.3723i 1.11575 + 0.0948897i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 867.167 + 500.659i 0.936521 + 0.540701i
\(96\) 0 0
\(97\) 893.179i 0.934934i 0.884011 + 0.467467i \(0.154833\pi\)
−0.884011 + 0.467467i \(0.845167\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 463.543 802.881i 0.456676 0.790986i −0.542107 0.840310i \(-0.682373\pi\)
0.998783 + 0.0493234i \(0.0157065\pi\)
\(102\) 0 0
\(103\) −487.361 + 281.378i −0.466224 + 0.269175i −0.714658 0.699474i \(-0.753418\pi\)
0.248434 + 0.968649i \(0.420084\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1290.34 744.979i 1.16581 0.673082i 0.213123 0.977025i \(-0.431637\pi\)
0.952690 + 0.303943i \(0.0983033\pi\)
\(108\) 0 0
\(109\) −726.305 + 1258.00i −0.638233 + 1.10545i 0.347587 + 0.937648i \(0.387001\pi\)
−0.985820 + 0.167804i \(0.946332\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1761.48i 1.46642i −0.680001 0.733211i \(-0.738021\pi\)
0.680001 0.733211i \(-0.261979\pi\)
\(114\) 0 0
\(115\) 901.419 + 520.434i 0.730937 + 0.422007i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −17.7642 12.3745i −0.0136844 0.00953251i
\(120\) 0 0
\(121\) −612.198 1060.36i −0.459953 0.796663i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1499.97 1.07329
\(126\) 0 0
\(127\) −68.3256 −0.0477395 −0.0238697 0.999715i \(-0.507599\pi\)
−0.0238697 + 0.999715i \(0.507599\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −242.249 419.588i −0.161568 0.279844i 0.773863 0.633353i \(-0.218322\pi\)
−0.935431 + 0.353509i \(0.884988\pi\)
\(132\) 0 0
\(133\) 787.766 + 1678.73i 0.513594 + 1.09447i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1247.91 + 720.479i 0.778217 + 0.449304i 0.835798 0.549037i \(-0.185005\pi\)
−0.0575809 + 0.998341i \(0.518339\pi\)
\(138\) 0 0
\(139\) 1445.47i 0.882035i 0.897499 + 0.441017i \(0.145382\pi\)
−0.897499 + 0.441017i \(0.854618\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 270.960 469.316i 0.158453 0.274449i
\(144\) 0 0
\(145\) 1624.36 937.824i 0.930314 0.537117i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 846.151 488.526i 0.465231 0.268601i −0.249010 0.968501i \(-0.580105\pi\)
0.714241 + 0.699900i \(0.246772\pi\)
\(150\) 0 0
\(151\) −667.146 + 1155.53i −0.359547 + 0.622753i −0.987885 0.155187i \(-0.950402\pi\)
0.628338 + 0.777940i \(0.283735\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1241.64i 0.643425i
\(156\) 0 0
\(157\) 1296.09 + 748.295i 0.658846 + 0.380385i 0.791837 0.610732i \(-0.209125\pi\)
−0.132991 + 0.991117i \(0.542458\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 818.881 + 1745.04i 0.400850 + 0.854211i
\(162\) 0 0
\(163\) −1894.73 3281.76i −0.910469 1.57698i −0.813403 0.581700i \(-0.802388\pi\)
−0.0970652 0.995278i \(-0.530946\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1202.66 0.557273 0.278637 0.960397i \(-0.410117\pi\)
0.278637 + 0.960397i \(0.410117\pi\)
\(168\) 0 0
\(169\) −557.839 −0.253910
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 765.529 + 1325.94i 0.336428 + 0.582711i 0.983758 0.179499i \(-0.0574477\pi\)
−0.647330 + 0.762210i \(0.724114\pi\)
\(174\) 0 0
\(175\) 379.763 + 264.543i 0.164042 + 0.114272i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1595.31 + 921.053i 0.666141 + 0.384596i 0.794613 0.607117i \(-0.207674\pi\)
−0.128472 + 0.991713i \(0.541007\pi\)
\(180\) 0 0
\(181\) 325.049i 0.133485i 0.997770 + 0.0667423i \(0.0212605\pi\)
−0.997770 + 0.0667423i \(0.978739\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −160.467 + 277.936i −0.0637716 + 0.110456i
\(186\) 0 0
\(187\) −10.4524 + 6.03468i −0.00408745 + 0.00235989i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3045.91 1758.56i 1.15390 0.666203i 0.204063 0.978958i \(-0.434585\pi\)
0.949834 + 0.312755i \(0.101252\pi\)
\(192\) 0 0
\(193\) −502.491 + 870.339i −0.187410 + 0.324603i −0.944386 0.328839i \(-0.893343\pi\)
0.756976 + 0.653442i \(0.226676\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2808.91i 1.01587i 0.861395 + 0.507935i \(0.169591\pi\)
−0.861395 + 0.507935i \(0.830409\pi\)
\(198\) 0 0
\(199\) 210.249 + 121.387i 0.0748954 + 0.0432409i 0.536980 0.843595i \(-0.319565\pi\)
−0.462085 + 0.886836i \(0.652898\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3461.08 + 294.349i 1.19665 + 0.101770i
\(204\) 0 0
\(205\) 2078.09 + 3599.35i 0.707999 + 1.22629i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1033.80 0.342151
\(210\) 0 0
\(211\) −2238.46 −0.730342 −0.365171 0.930940i \(-0.618989\pi\)
−0.365171 + 0.930940i \(0.618989\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 966.369 + 1673.80i 0.306539 + 0.530941i
\(216\) 0 0
\(217\) −1314.33 + 1886.78i −0.411164 + 0.590244i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 53.1345 + 30.6772i 0.0161729 + 0.00933743i
\(222\) 0 0
\(223\) 724.158i 0.217458i −0.994071 0.108729i \(-0.965322\pi\)
0.994071 0.108729i \(-0.0346781\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1234.34 2137.94i 0.360908 0.625111i −0.627202 0.778856i \(-0.715800\pi\)
0.988111 + 0.153745i \(0.0491335\pi\)
\(228\) 0 0
\(229\) 3595.98 2076.14i 1.03768 0.599106i 0.118507 0.992953i \(-0.462189\pi\)
0.919176 + 0.393847i \(0.128856\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5140.63 + 2967.94i −1.44538 + 0.834492i −0.998201 0.0599522i \(-0.980905\pi\)
−0.447180 + 0.894444i \(0.647572\pi\)
\(234\) 0 0
\(235\) −1964.76 + 3403.06i −0.545391 + 0.944644i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4306.49i 1.16554i −0.812638 0.582769i \(-0.801969\pi\)
0.812638 0.582769i \(-0.198031\pi\)
\(240\) 0 0
\(241\) 674.728 + 389.554i 0.180345 + 0.104122i 0.587455 0.809257i \(-0.300130\pi\)
−0.407110 + 0.913379i \(0.633463\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1188.81 3217.58i −0.310001 0.839035i
\(246\) 0 0
\(247\) −2627.66 4551.23i −0.676898 1.17242i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 804.927 0.202416 0.101208 0.994865i \(-0.467729\pi\)
0.101208 + 0.994865i \(0.467729\pi\)
\(252\) 0 0
\(253\) 1074.63 0.267042
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2967.92 + 5140.59i 0.720365 + 1.24771i 0.960854 + 0.277057i \(0.0893589\pi\)
−0.240489 + 0.970652i \(0.577308\pi\)
\(258\) 0 0
\(259\) −538.050 + 252.487i −0.129084 + 0.0605745i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6468.89 3734.82i −1.51669 0.875660i −0.999808 0.0196026i \(-0.993760\pi\)
−0.516880 0.856058i \(-0.672907\pi\)
\(264\) 0 0
\(265\) 863.480i 0.200163i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3714.97 6434.52i 0.842029 1.45844i −0.0461472 0.998935i \(-0.514694\pi\)
0.888176 0.459503i \(-0.151972\pi\)
\(270\) 0 0
\(271\) −1076.21 + 621.349i −0.241236 + 0.139278i −0.615745 0.787946i \(-0.711145\pi\)
0.374509 + 0.927223i \(0.377811\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 223.451 129.010i 0.0489986 0.0282894i
\(276\) 0 0
\(277\) −339.471 + 587.980i −0.0736347 + 0.127539i −0.900492 0.434873i \(-0.856793\pi\)
0.826857 + 0.562412i \(0.190127\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2157.54i 0.458036i 0.973422 + 0.229018i \(0.0735515\pi\)
−0.973422 + 0.229018i \(0.926449\pi\)
\(282\) 0 0
\(283\) 843.962 + 487.262i 0.177273 + 0.102349i 0.586011 0.810303i \(-0.300698\pi\)
−0.408738 + 0.912652i \(0.634031\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −652.236 + 7669.27i −0.134147 + 1.57736i
\(288\) 0 0
\(289\) 2455.82 + 4253.60i 0.499861 + 0.865785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6457.16 −1.28748 −0.643740 0.765245i \(-0.722618\pi\)
−0.643740 + 0.765245i \(0.722618\pi\)
\(294\) 0 0
\(295\) −2045.83 −0.403773
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2731.44 4731.00i −0.528306 0.915053i
\(300\) 0 0
\(301\) −303.308 + 3566.43i −0.0580810 + 0.682942i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1835.36 1059.65i −0.344566 0.198935i
\(306\) 0 0
\(307\) 4133.66i 0.768471i 0.923235 + 0.384235i \(0.125535\pi\)
−0.923235 + 0.384235i \(0.874465\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1222.12 2116.77i 0.222829 0.385952i −0.732837 0.680405i \(-0.761804\pi\)
0.955666 + 0.294453i \(0.0951374\pi\)
\(312\) 0 0
\(313\) 3072.40 1773.85i 0.554831 0.320332i −0.196237 0.980556i \(-0.562872\pi\)
0.751068 + 0.660225i \(0.229539\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6357.24 3670.36i 1.12637 0.650308i 0.183348 0.983048i \(-0.441306\pi\)
0.943019 + 0.332740i \(0.107973\pi\)
\(318\) 0 0
\(319\) 968.247 1677.05i 0.169942 0.294348i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 117.044i 0.0201625i
\(324\) 0 0
\(325\) −1135.91 655.818i −0.193874 0.111933i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6587.91 + 3091.47i −1.10396 + 0.518049i
\(330\) 0 0
\(331\) −2815.66 4876.87i −0.467561 0.809840i 0.531752 0.846900i \(-0.321534\pi\)
−0.999313 + 0.0370602i \(0.988201\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7297.51 −1.19017
\(336\) 0 0
\(337\) −9281.97 −1.50036 −0.750180 0.661234i \(-0.770033\pi\)
−0.750180 + 0.661234i \(0.770033\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 640.960 + 1110.17i 0.101789 + 0.176303i
\(342\) 0 0
\(343\) 1599.45 6147.79i 0.251784 0.967783i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4441.01 + 2564.02i 0.687049 + 0.396668i 0.802506 0.596644i \(-0.203500\pi\)
−0.115456 + 0.993313i \(0.536833\pi\)
\(348\) 0 0
\(349\) 11096.5i 1.70196i −0.525199 0.850980i \(-0.676009\pi\)
0.525199 0.850980i \(-0.323991\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 401.521 695.454i 0.0605405 0.104859i −0.834167 0.551512i \(-0.814051\pi\)
0.894707 + 0.446653i \(0.147384\pi\)
\(354\) 0 0
\(355\) −2728.30 + 1575.19i −0.407897 + 0.235499i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1596.45 921.712i 0.234701 0.135504i −0.378038 0.925790i \(-0.623401\pi\)
0.612739 + 0.790286i \(0.290068\pi\)
\(360\) 0 0
\(361\) 1583.19 2742.16i 0.230819 0.399791i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10383.8i 1.48908i
\(366\) 0 0
\(367\) 10118.6 + 5841.98i 1.43920 + 0.830924i 0.997794 0.0663827i \(-0.0211458\pi\)
0.441408 + 0.897307i \(0.354479\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −914.030 + 1312.13i −0.127909 + 0.183619i
\(372\) 0 0
\(373\) 541.327 + 937.606i 0.0751444 + 0.130154i 0.901149 0.433509i \(-0.142725\pi\)
−0.826005 + 0.563663i \(0.809392\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9844.13 −1.34482
\(378\) 0 0
\(379\) 13929.3 1.88786 0.943929 0.330148i \(-0.107099\pi\)
0.943929 + 0.330148i \(0.107099\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1693.36 2932.98i −0.225918 0.391301i 0.730677 0.682724i \(-0.239205\pi\)
−0.956594 + 0.291423i \(0.905871\pi\)
\(384\) 0 0
\(385\) −1905.42 162.047i −0.252232 0.0214511i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6652.61 + 3840.89i 0.867097 + 0.500619i 0.866382 0.499381i \(-0.166439\pi\)
0.000714618 1.00000i \(0.499773\pi\)
\(390\) 0 0
\(391\) 121.667i 0.0157364i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6078.17 + 10527.7i −0.774243 + 1.34103i
\(396\) 0 0
\(397\) 8528.01 4923.65i 1.07811 0.622446i 0.147722 0.989029i \(-0.452806\pi\)
0.930385 + 0.366583i \(0.119472\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11009.5 + 6356.33i −1.37104 + 0.791571i −0.991059 0.133423i \(-0.957403\pi\)
−0.379982 + 0.924994i \(0.624070\pi\)
\(402\) 0 0
\(403\) 3258.31 5643.55i 0.402749 0.697582i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 331.344i 0.0403541i
\(408\) 0 0
\(409\) −13544.0 7819.64i −1.63743 0.945370i −0.981714 0.190362i \(-0.939034\pi\)
−0.655715 0.755009i \(-0.727633\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3108.82 2165.60i −0.370399 0.258020i
\(414\) 0 0
\(415\) −1669.07 2890.91i −0.197425 0.341950i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10568.3 −1.23221 −0.616105 0.787664i \(-0.711290\pi\)
−0.616105 + 0.787664i \(0.711290\pi\)
\(420\) 0 0
\(421\) −3890.36 −0.450367 −0.225184 0.974316i \(-0.572298\pi\)
−0.225184 + 0.974316i \(0.572298\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 14.6061 + 25.2984i 0.00166705 + 0.00288742i
\(426\) 0 0
\(427\) −1667.31 3553.04i −0.188962 0.402678i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2554.42 + 1474.79i 0.285480 + 0.164822i 0.635902 0.771770i \(-0.280628\pi\)
−0.350422 + 0.936592i \(0.613962\pi\)
\(432\) 0 0
\(433\) 14292.9i 1.58632i −0.609017 0.793158i \(-0.708436\pi\)
0.609017 0.793158i \(-0.291564\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5210.68 9025.17i 0.570391 0.987946i
\(438\) 0 0
\(439\) −10289.2 + 5940.50i −1.11863 + 0.645842i −0.941051 0.338265i \(-0.890160\pi\)
−0.177580 + 0.984106i \(0.556827\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8000.43 + 4619.05i −0.858040 + 0.495390i −0.863356 0.504596i \(-0.831641\pi\)
0.00531517 + 0.999986i \(0.498308\pi\)
\(444\) 0 0
\(445\) −1683.63 + 2916.14i −0.179352 + 0.310647i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5478.22i 0.575798i 0.957661 + 0.287899i \(0.0929568\pi\)
−0.957661 + 0.287899i \(0.907043\pi\)
\(450\) 0 0
\(451\) 3716.12 + 2145.50i 0.387994 + 0.224008i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4129.68 + 8800.35i 0.425500 + 0.906740i
\(456\) 0 0
\(457\) −4423.49 7661.71i −0.452784 0.784244i 0.545774 0.837932i \(-0.316236\pi\)
−0.998558 + 0.0536880i \(0.982902\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15927.8 1.60917 0.804587 0.593834i \(-0.202386\pi\)
0.804587 + 0.593834i \(0.202386\pi\)
\(462\) 0 0
\(463\) 10491.3 1.05307 0.526535 0.850153i \(-0.323491\pi\)
0.526535 + 0.850153i \(0.323491\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7862.95 13619.0i −0.779130 1.34949i −0.932444 0.361316i \(-0.882328\pi\)
0.153313 0.988178i \(-0.451006\pi\)
\(468\) 0 0
\(469\) −11089.2 7724.73i −1.09179 0.760543i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1728.10 + 997.718i 0.167987 + 0.0969876i
\(474\) 0 0
\(475\) 2502.16i 0.241699i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8758.87 + 15170.8i −0.835496 + 1.44712i 0.0581291 + 0.998309i \(0.481487\pi\)
−0.893626 + 0.448813i \(0.851847\pi\)
\(480\) 0 0
\(481\) 1458.72 842.192i 0.138278 0.0798350i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7735.54 + 4466.12i −0.724233 + 0.418136i
\(486\) 0 0
\(487\) −7026.77 + 12170.7i −0.653826 + 1.13246i 0.328360 + 0.944553i \(0.393504\pi\)
−0.982187 + 0.187908i \(0.939829\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9854.09i 0.905720i 0.891582 + 0.452860i \(0.149596\pi\)
−0.891582 + 0.452860i \(0.850404\pi\)
\(492\) 0 0
\(493\) 189.871 + 109.622i 0.0173455 + 0.0100144i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5813.30 494.394i −0.524672 0.0446209i
\(498\) 0 0
\(499\) −6290.14 10894.8i −0.564300 0.977396i −0.997114 0.0759128i \(-0.975813\pi\)
0.432815 0.901483i \(-0.357520\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2545.29 −0.225624 −0.112812 0.993616i \(-0.535986\pi\)
−0.112812 + 0.993616i \(0.535986\pi\)
\(504\) 0 0
\(505\) 9271.33 0.816968
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7388.51 12797.3i −0.643399 1.11440i −0.984669 0.174434i \(-0.944190\pi\)
0.341270 0.939965i \(-0.389143\pi\)
\(510\) 0 0
\(511\) 10991.7 15779.1i 0.951556 1.36600i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4873.85 2813.92i −0.417025 0.240769i
\(516\) 0 0
\(517\) 4056.99i 0.345119i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −25.4037 + 44.0005i −0.00213619 + 0.00369999i −0.867092 0.498149i \(-0.834013\pi\)
0.864955 + 0.501849i \(0.167347\pi\)
\(522\) 0 0
\(523\) 12714.2 7340.56i 1.06301 0.613729i 0.136746 0.990606i \(-0.456335\pi\)
0.926263 + 0.376877i \(0.123002\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −125.690 + 72.5674i −0.0103893 + 0.00599827i
\(528\) 0 0
\(529\) −667.006 + 1155.29i −0.0548209 + 0.0949526i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 21813.2i 1.77268i
\(534\) 0 0
\(535\) 12904.1 + 7450.16i 1.04279 + 0.602053i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2723.92 2263.21i −0.217676 0.180860i
\(540\) 0 0
\(541\) 8294.42 + 14366.4i 0.659159 + 1.14170i 0.980834 + 0.194846i \(0.0624208\pi\)
−0.321675 + 0.946850i \(0.604246\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −14526.8 −1.14176
\(546\) 0 0
\(547\) −2029.96 −0.158674 −0.0793371 0.996848i \(-0.525280\pi\)
−0.0793371 + 0.996848i \(0.525280\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9389.66 16263.4i −0.725976 1.25743i
\(552\) 0 0
\(553\) −20380.3 + 9563.75i −1.56720 + 0.735428i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2597.94 + 1499.92i 0.197627 + 0.114100i 0.595548 0.803320i \(-0.296935\pi\)
−0.397921 + 0.917420i \(0.630268\pi\)
\(558\) 0 0
\(559\) 10143.8i 0.767506i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8333.02 14433.2i 0.623792 1.08044i −0.364981 0.931015i \(-0.618925\pi\)
0.988773 0.149424i \(-0.0477420\pi\)
\(564\) 0 0
\(565\) 15255.6 8807.82i 1.13594 0.655837i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16427.3 + 9484.30i −1.21031 + 0.698774i −0.962827 0.270118i \(-0.912937\pi\)
−0.247485 + 0.968892i \(0.579604\pi\)
\(570\) 0 0
\(571\) −7667.11 + 13279.8i −0.561924 + 0.973281i 0.435405 + 0.900235i \(0.356605\pi\)
−0.997329 + 0.0730460i \(0.976728\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2601.00i 0.188642i
\(576\) 0 0
\(577\) −10576.2 6106.20i −0.763076 0.440562i 0.0673231 0.997731i \(-0.478554\pi\)
−0.830399 + 0.557169i \(0.811887\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 523.861 6159.78i 0.0374069 0.439846i
\(582\) 0 0
\(583\) 445.746 + 772.054i 0.0316653 + 0.0548460i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23173.7 −1.62944 −0.814718 0.579857i \(-0.803108\pi\)
−0.814718 + 0.579857i \(0.803108\pi\)
\(588\) 0 0
\(589\) 12431.5 0.869664
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1894.64 3281.61i −0.131203 0.227251i 0.792937 0.609303i \(-0.208551\pi\)
−0.924141 + 0.382052i \(0.875217\pi\)
\(594\) 0 0
\(595\) 18.3465 215.726i 0.00126409 0.0148637i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13663.6 + 7888.67i 0.932018 + 0.538101i 0.887449 0.460906i \(-0.152475\pi\)
0.0445687 + 0.999006i \(0.485809\pi\)
\(600\) 0 0
\(601\) 23750.2i 1.61197i −0.591939 0.805983i \(-0.701638\pi\)
0.591939 0.805983i \(-0.298362\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6122.29 10604.1i 0.411416 0.712593i
\(606\) 0 0
\(607\) −21418.8 + 12366.1i −1.43223 + 0.826897i −0.997290 0.0735641i \(-0.976563\pi\)
−0.434937 + 0.900461i \(0.643229\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17860.6 10311.8i 1.18259 0.682769i
\(612\) 0 0
\(613\) 4659.04 8069.69i 0.306977 0.531700i −0.670723 0.741708i \(-0.734016\pi\)
0.977700 + 0.210009i \(0.0673492\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16544.3i 1.07949i 0.841828 + 0.539746i \(0.181480\pi\)
−0.841828 + 0.539746i \(0.818520\pi\)
\(618\) 0 0
\(619\) 8835.49 + 5101.18i 0.573713 + 0.331234i 0.758631 0.651520i \(-0.225869\pi\)
−0.184918 + 0.982754i \(0.559202\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5645.28 + 2649.12i −0.363039 + 0.170361i
\(624\) 0 0
\(625\) 5938.38 + 10285.6i 0.380056 + 0.658277i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −37.5137 −0.00237801
\(630\) 0 0
\(631\) −14729.3 −0.929259 −0.464630 0.885505i \(-0.653813\pi\)
−0.464630 + 0.885505i \(0.653813\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −341.645 591.746i −0.0213508 0.0369807i
\(636\) 0 0
\(637\) −3040.14 + 17744.3i −0.189097 + 1.10370i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25503.6 + 14724.5i 1.57150 + 0.907304i 0.995986 + 0.0895107i \(0.0285303\pi\)
0.575511 + 0.817794i \(0.304803\pi\)
\(642\) 0 0
\(643\) 4194.07i 0.257228i 0.991695 + 0.128614i \(0.0410529\pi\)
−0.991695 + 0.128614i \(0.958947\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10732.4 18589.0i 0.652137 1.12953i −0.330466 0.943818i \(-0.607206\pi\)
0.982603 0.185717i \(-0.0594608\pi\)
\(648\) 0 0
\(649\) −1829.22 + 1056.10i −0.110636 + 0.0638760i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28232.5 + 16300.1i −1.69192 + 0.976832i −0.738956 + 0.673753i \(0.764681\pi\)
−0.952966 + 0.303078i \(0.901986\pi\)
\(654\) 0 0
\(655\) 2422.61 4196.09i 0.144518 0.250313i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5931.69i 0.350631i 0.984512 + 0.175315i \(0.0560945\pi\)
−0.984512 + 0.175315i \(0.943905\pi\)
\(660\) 0 0
\(661\) 16409.5 + 9474.01i 0.965589 + 0.557483i 0.897889 0.440223i \(-0.145100\pi\)
0.0677004 + 0.997706i \(0.478434\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10599.9 + 15216.7i −0.618116 + 0.887334i
\(666\) 0 0
\(667\) −9760.53 16905.7i −0.566611 0.981398i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2188.05 −0.125885
\(672\) 0 0
\(673\) −19463.2 −1.11479 −0.557394 0.830248i \(-0.688199\pi\)
−0.557394 + 0.830248i \(0.688199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7010.82 + 12143.1i 0.398003 + 0.689361i 0.993479 0.114012i \(-0.0363701\pi\)
−0.595477 + 0.803373i \(0.703037\pi\)
\(678\) 0 0
\(679\) −16482.4 1401.75i −0.931571 0.0792258i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24229.0 + 13988.6i 1.35739 + 0.783688i 0.989271 0.146091i \(-0.0466693\pi\)
0.368117 + 0.929780i \(0.380003\pi\)
\(684\) 0 0
\(685\) 14410.3i 0.803780i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2265.94 3924.72i 0.125291 0.217010i
\(690\) 0 0
\(691\) −22352.5 + 12905.2i −1.23058 + 0.710475i −0.967151 0.254203i \(-0.918187\pi\)
−0.263429 + 0.964679i \(0.584853\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12518.7 + 7227.69i −0.683255 + 0.394478i
\(696\) 0 0
\(697\) −242.907 + 420.727i −0.0132005 + 0.0228639i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15653.8i 0.843420i −0.906731 0.421710i \(-0.861430\pi\)
0.906731 0.421710i \(-0.138570\pi\)
\(702\) 0 0
\(703\) 2782.75 + 1606.62i 0.149293 + 0.0861946i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 14088.6 + 9814.10i 0.749443 + 0.522061i
\(708\) 0 0
\(709\) 16769.6 + 29045.8i 0.888286 + 1.53856i 0.841900 + 0.539633i \(0.181437\pi\)
0.0463856 + 0.998924i \(0.485230\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12922.5 0.678756
\(714\) 0 0
\(715\) 5419.47 0.283464
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6620.60 11467.2i −0.343403 0.594791i 0.641659 0.766990i \(-0.278246\pi\)
−0.985062 + 0.172198i \(0.944913\pi\)
\(720\) 0 0
\(721\) −4427.58 9435.18i −0.228699 0.487357i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4059.06 2343.50i −0.207931 0.120049i
\(726\) 0 0
\(727\) 33618.0i 1.71502i −0.514464 0.857512i \(-0.672009\pi\)
0.514464 0.857512i \(-0.327991\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −112.958 + 195.650i −0.00571535 + 0.00989927i
\(732\) 0 0
\(733\) 3921.55 2264.11i 0.197607 0.114088i −0.397932 0.917415i \(-0.630272\pi\)
0.595539 + 0.803327i \(0.296939\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6524.85 + 3767.12i −0.326114 + 0.188282i
\(738\) 0 0
\(739\) 8723.03 15108.7i 0.434211 0.752075i −0.563020 0.826443i \(-0.690361\pi\)
0.997231 + 0.0743682i \(0.0236940\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5516.23i 0.272370i 0.990683 + 0.136185i \(0.0434842\pi\)
−0.990683 + 0.136185i \(0.956516\pi\)
\(744\) 0 0
\(745\) 8461.94 + 4885.50i 0.416136 + 0.240256i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 11722.5 + 24980.7i 0.571871 + 1.21866i
\(750\) 0 0
\(751\) 1743.07 + 3019.09i 0.0846947 + 0.146695i 0.905261 0.424856i \(-0.139675\pi\)
−0.820566 + 0.571551i \(0.806342\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13343.6 −0.643209
\(756\) 0 0
\(757\) 28650.9 1.37561 0.687805 0.725896i \(-0.258575\pi\)
0.687805 + 0.725896i \(0.258575\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9804.44 + 16981.8i 0.467031 + 0.808922i 0.999291 0.0376594i \(-0.0119902\pi\)
−0.532259 + 0.846581i \(0.678657\pi\)
\(762\) 0 0
\(763\) −22074.8 15377.3i −1.04739 0.729613i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9298.80 + 5368.66i 0.437758 + 0.252739i
\(768\) 0 0
\(769\) 6180.49i 0.289823i −0.989445 0.144912i \(-0.953710\pi\)
0.989445 0.144912i \(-0.0462898\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18600.6 32217.2i 0.865483 1.49906i −0.00108453 0.999999i \(-0.500345\pi\)
0.866567 0.499060i \(-0.166321\pi\)
\(774\) 0 0
\(775\) 2687.01 1551.35i 0.124542 0.0719046i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 36037.4 20806.2i 1.65747 0.956943i
\(780\) 0 0
\(781\) −1626.29 + 2816.81i −0.0745110 + 0.129057i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14966.7i 0.680488i
\(786\) 0 0
\(787\) 4876.40 + 2815.39i 0.220870 + 0.127519i 0.606353 0.795196i \(-0.292632\pi\)
−0.385483 + 0.922715i \(0.625965\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 32505.6 + 2764.45i 1.46115 + 0.124264i
\(792\) 0 0
\(793\) 5561.45 + 9632.71i 0.249045 + 0.431359i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 482.766 0.0214560 0.0107280 0.999942i \(-0.496585\pi\)
0.0107280 + 0.999942i \(0.496585\pi\)
\(798\) 0 0
\(799\) −459.320 −0.0203374
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5360.34 9284.38i −0.235569 0.408018i