Properties

Label 1008.4.bt.d.17.2
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 17.2
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.74197 - 16.8736i) q^{5} +(18.4446 - 1.67197i) q^{7} +O(q^{10})\) \(q+(-9.74197 - 16.8736i) q^{5} +(18.4446 - 1.67197i) q^{7} +(15.1087 + 8.72302i) q^{11} -16.5278i q^{13} +(68.6466 - 118.899i) q^{17} +(20.6975 - 11.9497i) q^{19} +(108.910 - 62.8794i) q^{23} +(-127.312 + 220.511i) q^{25} +105.188i q^{29} +(95.0849 + 54.8973i) q^{31} +(-207.899 - 294.939i) q^{35} +(58.5919 + 101.484i) q^{37} +348.056 q^{41} +141.953 q^{43} +(-172.830 - 299.351i) q^{47} +(337.409 - 61.6778i) q^{49} +(149.292 + 86.1937i) q^{53} -339.918i q^{55} +(297.569 - 515.404i) q^{59} +(-561.746 + 324.324i) q^{61} +(-278.884 + 161.014i) q^{65} +(64.9996 - 112.583i) q^{67} +908.671i q^{71} +(-44.8988 - 25.9223i) q^{73} +(293.259 + 135.632i) q^{77} +(-474.917 - 822.580i) q^{79} -1302.27 q^{83} -2675.01 q^{85} +(-210.570 - 364.719i) q^{89} +(-27.6341 - 304.850i) q^{91} +(-403.269 - 232.827i) q^{95} -553.292i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

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
\(5\) −9.74197 16.8736i −0.871348 1.50922i −0.860603 0.509277i \(-0.829913\pi\)
−0.0107451 0.999942i \(-0.503420\pi\)
\(6\) 0 0
\(7\) 18.4446 1.67197i 0.995917 0.0902780i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 15.1087 + 8.72302i 0.414132 + 0.239099i 0.692563 0.721357i \(-0.256481\pi\)
−0.278432 + 0.960456i \(0.589815\pi\)
\(12\) 0 0
\(13\) 16.5278i 0.352615i −0.984335 0.176308i \(-0.943585\pi\)
0.984335 0.176308i \(-0.0564154\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 68.6466 118.899i 0.979368 1.69632i 0.314674 0.949200i \(-0.398105\pi\)
0.664694 0.747115i \(-0.268562\pi\)
\(18\) 0 0
\(19\) 20.6975 11.9497i 0.249912 0.144287i −0.369812 0.929107i \(-0.620578\pi\)
0.619724 + 0.784820i \(0.287244\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 108.910 62.8794i 0.987365 0.570055i 0.0828792 0.996560i \(-0.473588\pi\)
0.904486 + 0.426504i \(0.140255\pi\)
\(24\) 0 0
\(25\) −127.312 + 220.511i −1.01849 + 1.76408i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 105.188i 0.673548i 0.941586 + 0.336774i \(0.109336\pi\)
−0.941586 + 0.336774i \(0.890664\pi\)
\(30\) 0 0
\(31\) 95.0849 + 54.8973i 0.550895 + 0.318060i 0.749483 0.662024i \(-0.230302\pi\)
−0.198588 + 0.980083i \(0.563635\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −207.899 294.939i −1.00404 1.42439i
\(36\) 0 0
\(37\) 58.5919 + 101.484i 0.260336 + 0.450916i 0.966331 0.257301i \(-0.0828332\pi\)
−0.705995 + 0.708217i \(0.749500\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 348.056 1.32579 0.662893 0.748714i \(-0.269328\pi\)
0.662893 + 0.748714i \(0.269328\pi\)
\(42\) 0 0
\(43\) 141.953 0.503432 0.251716 0.967801i \(-0.419005\pi\)
0.251716 + 0.967801i \(0.419005\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −172.830 299.351i −0.536381 0.929040i −0.999095 0.0425319i \(-0.986458\pi\)
0.462714 0.886508i \(-0.346876\pi\)
\(48\) 0 0
\(49\) 337.409 61.6778i 0.983700 0.179819i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 149.292 + 86.1937i 0.386921 + 0.223389i 0.680825 0.732446i \(-0.261621\pi\)
−0.293904 + 0.955835i \(0.594955\pi\)
\(54\) 0 0
\(55\) 339.918i 0.833354i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 297.569 515.404i 0.656613 1.13729i −0.324874 0.945757i \(-0.605322\pi\)
0.981487 0.191530i \(-0.0613448\pi\)
\(60\) 0 0
\(61\) −561.746 + 324.324i −1.17909 + 0.680746i −0.955803 0.294008i \(-0.905011\pi\)
−0.223283 + 0.974754i \(0.571677\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −278.884 + 161.014i −0.532174 + 0.307251i
\(66\) 0 0
\(67\) 64.9996 112.583i 0.118522 0.205286i −0.800660 0.599119i \(-0.795518\pi\)
0.919182 + 0.393833i \(0.128851\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 908.671i 1.51886i 0.650586 + 0.759432i \(0.274523\pi\)
−0.650586 + 0.759432i \(0.725477\pi\)
\(72\) 0 0
\(73\) −44.8988 25.9223i −0.0719864 0.0415614i 0.463575 0.886058i \(-0.346567\pi\)
−0.535561 + 0.844496i \(0.679900\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 293.259 + 135.632i 0.434026 + 0.200736i
\(78\) 0 0
\(79\) −474.917 822.580i −0.676358 1.17149i −0.976070 0.217457i \(-0.930224\pi\)
0.299712 0.954030i \(-0.403109\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1302.27 −1.72220 −0.861100 0.508436i \(-0.830224\pi\)
−0.861100 + 0.508436i \(0.830224\pi\)
\(84\) 0 0
\(85\) −2675.01 −3.41348
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −210.570 364.719i −0.250791 0.434383i 0.712953 0.701212i \(-0.247357\pi\)
−0.963744 + 0.266829i \(0.914024\pi\)
\(90\) 0 0
\(91\) −27.6341 304.850i −0.0318334 0.351175i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −403.269 232.827i −0.435521 0.251448i
\(96\) 0 0
\(97\) 553.292i 0.579158i −0.957154 0.289579i \(-0.906485\pi\)
0.957154 0.289579i \(-0.0935153\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −115.951 + 200.833i −0.114233 + 0.197858i −0.917473 0.397798i \(-0.869774\pi\)
0.803240 + 0.595656i \(0.203108\pi\)
\(102\) 0 0
\(103\) 1674.49 966.766i 1.60187 0.924837i 0.610751 0.791823i \(-0.290868\pi\)
0.991114 0.133015i \(-0.0424657\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 769.974 444.544i 0.695665 0.401642i −0.110066 0.993924i \(-0.535106\pi\)
0.805731 + 0.592282i \(0.201773\pi\)
\(108\) 0 0
\(109\) −961.155 + 1664.77i −0.844605 + 1.46290i 0.0413585 + 0.999144i \(0.486831\pi\)
−0.885964 + 0.463755i \(0.846502\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2070.45i 1.72365i −0.507210 0.861823i \(-0.669323\pi\)
0.507210 0.861823i \(-0.330677\pi\)
\(114\) 0 0
\(115\) −2122.00 1225.14i −1.72068 0.993433i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1067.37 2307.83i 0.822229 1.77780i
\(120\) 0 0
\(121\) −513.318 889.092i −0.385663 0.667988i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2525.58 1.80716
\(126\) 0 0
\(127\) −1508.37 −1.05391 −0.526955 0.849893i \(-0.676666\pi\)
−0.526955 + 0.849893i \(0.676666\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1067.52 1848.99i −0.711979 1.23318i −0.964113 0.265491i \(-0.914466\pi\)
0.252134 0.967692i \(-0.418868\pi\)
\(132\) 0 0
\(133\) 361.778 255.014i 0.235866 0.166259i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −494.811 285.679i −0.308574 0.178155i 0.337714 0.941249i \(-0.390346\pi\)
−0.646288 + 0.763094i \(0.723680\pi\)
\(138\) 0 0
\(139\) 3003.94i 1.83302i 0.400006 + 0.916512i \(0.369008\pi\)
−0.400006 + 0.916512i \(0.630992\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 144.173 249.714i 0.0843100 0.146029i
\(144\) 0 0
\(145\) 1774.89 1024.74i 1.01653 0.586894i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1433.52 + 827.646i −0.788180 + 0.455056i −0.839322 0.543635i \(-0.817047\pi\)
0.0511412 + 0.998691i \(0.483714\pi\)
\(150\) 0 0
\(151\) −396.703 + 687.109i −0.213796 + 0.370306i −0.952899 0.303286i \(-0.901916\pi\)
0.739103 + 0.673592i \(0.235250\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2139.23i 1.10856i
\(156\) 0 0
\(157\) −621.514 358.831i −0.315938 0.182407i 0.333643 0.942700i \(-0.391722\pi\)
−0.649580 + 0.760293i \(0.725055\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1903.68 1341.88i 0.931869 0.656865i
\(162\) 0 0
\(163\) −1038.88 1799.39i −0.499211 0.864659i 0.500788 0.865570i \(-0.333043\pi\)
−1.00000 0.000910600i \(0.999710\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1017.38 0.471420 0.235710 0.971823i \(-0.424258\pi\)
0.235710 + 0.971823i \(0.424258\pi\)
\(168\) 0 0
\(169\) 1923.83 0.875662
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1498.46 2595.42i −0.658533 1.14061i −0.980996 0.194030i \(-0.937844\pi\)
0.322463 0.946582i \(-0.395489\pi\)
\(174\) 0 0
\(175\) −1979.53 + 4280.10i −0.855078 + 1.84883i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3473.51 + 2005.43i 1.45040 + 0.837391i 0.998504 0.0546769i \(-0.0174129\pi\)
0.451900 + 0.892068i \(0.350746\pi\)
\(180\) 0 0
\(181\) 2885.89i 1.18512i 0.805527 + 0.592559i \(0.201882\pi\)
−0.805527 + 0.592559i \(0.798118\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1141.60 1977.31i 0.453687 0.785809i
\(186\) 0 0
\(187\) 2074.33 1197.61i 0.811175 0.468332i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1169.89 675.436i 0.443195 0.255879i −0.261757 0.965134i \(-0.584302\pi\)
0.704952 + 0.709255i \(0.250969\pi\)
\(192\) 0 0
\(193\) −315.843 + 547.055i −0.117797 + 0.204031i −0.918894 0.394504i \(-0.870917\pi\)
0.801097 + 0.598534i \(0.204250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2350.91i 0.850232i −0.905139 0.425116i \(-0.860233\pi\)
0.905139 0.425116i \(-0.139767\pi\)
\(198\) 0 0
\(199\) 970.169 + 560.127i 0.345595 + 0.199530i 0.662744 0.748846i \(-0.269392\pi\)
−0.317148 + 0.948376i \(0.602725\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 175.871 + 1940.15i 0.0608066 + 0.670797i
\(204\) 0 0
\(205\) −3390.75 5872.95i −1.15522 2.00090i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 416.950 0.137996
\(210\) 0 0
\(211\) 396.657 0.129417 0.0647085 0.997904i \(-0.479388\pi\)
0.0647085 + 0.997904i \(0.479388\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1382.90 2395.25i −0.438664 0.759789i
\(216\) 0 0
\(217\) 1845.59 + 853.581i 0.577360 + 0.267027i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1965.15 1134.58i −0.598147 0.345340i
\(222\) 0 0
\(223\) 2574.52i 0.773106i −0.922267 0.386553i \(-0.873666\pi\)
0.922267 0.386553i \(-0.126334\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1165.21 + 2018.20i −0.340694 + 0.590100i −0.984562 0.175037i \(-0.943995\pi\)
0.643868 + 0.765137i \(0.277329\pi\)
\(228\) 0 0
\(229\) 1211.86 699.668i 0.349703 0.201901i −0.314852 0.949141i \(-0.601955\pi\)
0.664554 + 0.747240i \(0.268621\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1950.66 + 1126.21i −0.548463 + 0.316655i −0.748502 0.663133i \(-0.769227\pi\)
0.200039 + 0.979788i \(0.435893\pi\)
\(234\) 0 0
\(235\) −3367.42 + 5832.54i −0.934749 + 1.61903i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3423.46i 0.926549i 0.886215 + 0.463275i \(0.153326\pi\)
−0.886215 + 0.463275i \(0.846674\pi\)
\(240\) 0 0
\(241\) 1997.78 + 1153.42i 0.533977 + 0.308292i 0.742635 0.669697i \(-0.233576\pi\)
−0.208657 + 0.977989i \(0.566909\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4327.75 5092.43i −1.12853 1.32793i
\(246\) 0 0
\(247\) −197.503 342.085i −0.0508778 0.0881229i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7897.26 1.98594 0.992970 0.118368i \(-0.0377662\pi\)
0.992970 + 0.118368i \(0.0377662\pi\)
\(252\) 0 0
\(253\) 2194.00 0.545199
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 217.517 + 376.750i 0.0527950 + 0.0914437i 0.891215 0.453581i \(-0.149854\pi\)
−0.838420 + 0.545025i \(0.816520\pi\)
\(258\) 0 0
\(259\) 1250.38 + 1773.87i 0.299981 + 0.425572i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5144.46 2970.16i −1.20616 0.696379i −0.244245 0.969714i \(-0.578540\pi\)
−0.961919 + 0.273335i \(0.911873\pi\)
\(264\) 0 0
\(265\) 3358.78i 0.778598i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 915.170 1585.12i 0.207431 0.359281i −0.743474 0.668765i \(-0.766823\pi\)
0.950905 + 0.309484i \(0.100156\pi\)
\(270\) 0 0
\(271\) −2605.49 + 1504.28i −0.584030 + 0.337190i −0.762733 0.646713i \(-0.776143\pi\)
0.178703 + 0.983903i \(0.442810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3847.04 + 2221.09i −0.843582 + 0.487042i
\(276\) 0 0
\(277\) 147.124 254.826i 0.0319127 0.0552744i −0.849628 0.527383i \(-0.823173\pi\)
0.881541 + 0.472108i \(0.156507\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8000.78i 1.69853i 0.527967 + 0.849265i \(0.322954\pi\)
−0.527967 + 0.849265i \(0.677046\pi\)
\(282\) 0 0
\(283\) −7523.20 4343.52i −1.58024 0.912352i −0.994823 0.101619i \(-0.967598\pi\)
−0.585416 0.810733i \(-0.699069\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6419.77 581.940i 1.32037 0.119689i
\(288\) 0 0
\(289\) −6968.22 12069.3i −1.41832 2.45661i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4055.18 −0.808554 −0.404277 0.914637i \(-0.632477\pi\)
−0.404277 + 0.914637i \(0.632477\pi\)
\(294\) 0 0
\(295\) −11595.6 −2.28855
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1039.26 1800.05i −0.201010 0.348160i
\(300\) 0 0
\(301\) 2618.26 237.341i 0.501376 0.0454488i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 10945.0 + 6319.11i 2.05479 + 1.18633i
\(306\) 0 0
\(307\) 4591.37i 0.853562i −0.904355 0.426781i \(-0.859648\pi\)
0.904355 0.426781i \(-0.140352\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2849.94 + 4936.24i −0.519631 + 0.900028i 0.480108 + 0.877209i \(0.340597\pi\)
−0.999740 + 0.0228187i \(0.992736\pi\)
\(312\) 0 0
\(313\) −3909.34 + 2257.06i −0.705971 + 0.407593i −0.809568 0.587027i \(-0.800298\pi\)
0.103596 + 0.994619i \(0.466965\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1819.78 + 1050.65i −0.322427 + 0.186153i −0.652474 0.757811i \(-0.726269\pi\)
0.330047 + 0.943965i \(0.392935\pi\)
\(318\) 0 0
\(319\) −917.555 + 1589.25i −0.161045 + 0.278937i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3281.23i 0.565240i
\(324\) 0 0
\(325\) 3644.56 + 2104.19i 0.622043 + 0.359137i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3688.30 5232.46i −0.618063 0.876822i
\(330\) 0 0
\(331\) 3111.81 + 5389.81i 0.516739 + 0.895018i 0.999811 + 0.0194375i \(0.00618755\pi\)
−0.483072 + 0.875581i \(0.660479\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2532.89 −0.413095
\(336\) 0 0
\(337\) 1599.77 0.258591 0.129295 0.991606i \(-0.458728\pi\)
0.129295 + 0.991606i \(0.458728\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 957.741 + 1658.86i 0.152096 + 0.263437i
\(342\) 0 0
\(343\) 6120.26 1701.76i 0.963449 0.267891i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2237.47 1291.80i −0.346149 0.199849i 0.316839 0.948479i \(-0.397379\pi\)
−0.662988 + 0.748630i \(0.730712\pi\)
\(348\) 0 0
\(349\) 6406.75i 0.982652i 0.870976 + 0.491326i \(0.163488\pi\)
−0.870976 + 0.491326i \(0.836512\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3536.88 + 6126.05i −0.533283 + 0.923673i 0.465961 + 0.884805i \(0.345709\pi\)
−0.999244 + 0.0388682i \(0.987625\pi\)
\(354\) 0 0
\(355\) 15332.5 8852.24i 2.29230 1.32346i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1355.38 + 782.532i −0.199260 + 0.115043i −0.596310 0.802754i \(-0.703367\pi\)
0.397050 + 0.917797i \(0.370034\pi\)
\(360\) 0 0
\(361\) −3143.91 + 5445.41i −0.458363 + 0.793907i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1010.14i 0.144858i
\(366\) 0 0
\(367\) 8459.40 + 4884.03i 1.20321 + 0.694672i 0.961267 0.275620i \(-0.0888830\pi\)
0.241940 + 0.970291i \(0.422216\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2897.75 + 1340.20i 0.405508 + 0.187546i
\(372\) 0 0
\(373\) 3840.66 + 6652.21i 0.533141 + 0.923427i 0.999251 + 0.0387005i \(0.0123218\pi\)
−0.466110 + 0.884727i \(0.654345\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1738.53 0.237503
\(378\) 0 0
\(379\) 6320.25 0.856595 0.428297 0.903638i \(-0.359114\pi\)
0.428297 + 0.903638i \(0.359114\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 91.9525 + 159.266i 0.0122678 + 0.0212484i 0.872094 0.489338i \(-0.162762\pi\)
−0.859826 + 0.510587i \(0.829428\pi\)
\(384\) 0 0
\(385\) −568.333 6269.65i −0.0752336 0.829951i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9127.81 5269.94i −1.18971 0.686881i −0.231471 0.972842i \(-0.574354\pi\)
−0.958241 + 0.285961i \(0.907687\pi\)
\(390\) 0 0
\(391\) 17265.9i 2.23318i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9253.24 + 16027.1i −1.17869 + 2.04154i
\(396\) 0 0
\(397\) −4797.29 + 2769.72i −0.606471 + 0.350146i −0.771583 0.636129i \(-0.780535\pi\)
0.165112 + 0.986275i \(0.447201\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3816.52 2203.47i 0.475282 0.274404i −0.243166 0.969985i \(-0.578186\pi\)
0.718448 + 0.695580i \(0.244853\pi\)
\(402\) 0 0
\(403\) 907.334 1571.55i 0.112153 0.194254i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2044.39i 0.248985i
\(408\) 0 0
\(409\) 8336.94 + 4813.33i 1.00791 + 0.581917i 0.910579 0.413335i \(-0.135636\pi\)
0.0973306 + 0.995252i \(0.468970\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4626.81 10004.0i 0.551260 1.19192i
\(414\) 0 0
\(415\) 12686.7 + 21973.9i 1.50063 + 2.59918i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3095.82 −0.360957 −0.180478 0.983579i \(-0.557765\pi\)
−0.180478 + 0.983579i \(0.557765\pi\)
\(420\) 0 0
\(421\) 4652.51 0.538598 0.269299 0.963057i \(-0.413208\pi\)
0.269299 + 0.963057i \(0.413208\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 17479.1 + 30274.6i 1.99496 + 3.45538i
\(426\) 0 0
\(427\) −9818.94 + 6921.27i −1.11281 + 0.784411i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6562.34 + 3788.77i 0.733404 + 0.423431i 0.819666 0.572842i \(-0.194159\pi\)
−0.0862625 + 0.996272i \(0.527492\pi\)
\(432\) 0 0
\(433\) 10028.8i 1.11305i 0.830829 + 0.556527i \(0.187867\pi\)
−0.830829 + 0.556527i \(0.812133\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1502.78 2602.90i 0.164503 0.284928i
\(438\) 0 0
\(439\) 12522.8 7230.07i 1.36146 0.786042i 0.371646 0.928375i \(-0.378794\pi\)
0.989819 + 0.142333i \(0.0454603\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12101.9 6987.05i 1.29792 0.749356i 0.317878 0.948132i \(-0.397030\pi\)
0.980045 + 0.198775i \(0.0636963\pi\)
\(444\) 0 0
\(445\) −4102.74 + 7106.15i −0.437053 + 0.756998i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12850.1i 1.35064i 0.737527 + 0.675318i \(0.235993\pi\)
−0.737527 + 0.675318i \(0.764007\pi\)
\(450\) 0 0
\(451\) 5258.68 + 3036.10i 0.549050 + 0.316994i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4874.70 + 3436.12i −0.502263 + 0.354040i
\(456\) 0 0
\(457\) 4530.38 + 7846.86i 0.463725 + 0.803196i 0.999143 0.0413917i \(-0.0131792\pi\)
−0.535418 + 0.844587i \(0.679846\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3390.73 −0.342564 −0.171282 0.985222i \(-0.554791\pi\)
−0.171282 + 0.985222i \(0.554791\pi\)
\(462\) 0 0
\(463\) −707.176 −0.0709833 −0.0354916 0.999370i \(-0.511300\pi\)
−0.0354916 + 0.999370i \(0.511300\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2360.37 4088.28i −0.233886 0.405103i 0.725062 0.688683i \(-0.241811\pi\)
−0.958948 + 0.283581i \(0.908478\pi\)
\(468\) 0 0
\(469\) 1010.66 2185.22i 0.0995050 0.215147i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2144.72 + 1238.26i 0.208487 + 0.120370i
\(474\) 0 0
\(475\) 6085.36i 0.587822i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2300.35 3984.32i 0.219427 0.380059i −0.735206 0.677844i \(-0.762915\pi\)
0.954633 + 0.297785i \(0.0962479\pi\)
\(480\) 0 0
\(481\) 1677.31 968.398i 0.159000 0.0917986i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9336.02 + 5390.15i −0.874076 + 0.504648i
\(486\) 0 0
\(487\) 8189.27 14184.2i 0.761994 1.31981i −0.179827 0.983698i \(-0.557554\pi\)
0.941821 0.336115i \(-0.109113\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4293.59i 0.394637i 0.980339 + 0.197319i \(0.0632234\pi\)
−0.980339 + 0.197319i \(0.936777\pi\)
\(492\) 0 0
\(493\) 12506.8 + 7220.79i 1.14255 + 0.659651i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1519.27 + 16760.1i 0.137120 + 1.51266i
\(498\) 0 0
\(499\) −2603.39 4509.21i −0.233555 0.404529i 0.725297 0.688436i \(-0.241702\pi\)
−0.958852 + 0.283907i \(0.908369\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16409.4 −1.45459 −0.727295 0.686325i \(-0.759223\pi\)
−0.727295 + 0.686325i \(0.759223\pi\)
\(504\) 0 0
\(505\) 4518.37 0.398148
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 992.966 + 1719.87i 0.0864685 + 0.149768i 0.906016 0.423243i \(-0.139108\pi\)
−0.819548 + 0.573011i \(0.805775\pi\)
\(510\) 0 0
\(511\) −871.483 403.058i −0.0754445 0.0348929i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −32625.6 18836.4i −2.79156 1.61171i
\(516\) 0 0
\(517\) 6030.42i 0.512993i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1336.56 + 2315.00i −0.112391 + 0.194668i −0.916734 0.399498i \(-0.869184\pi\)
0.804343 + 0.594166i \(0.202518\pi\)
\(522\) 0 0
\(523\) 1236.34 713.801i 0.103368 0.0596794i −0.447425 0.894322i \(-0.647659\pi\)
0.550793 + 0.834642i \(0.314325\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13054.5 7537.03i 1.07906 0.622995i
\(528\) 0 0
\(529\) 1824.15 3159.52i 0.149926 0.259679i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5752.62i 0.467493i
\(534\) 0 0
\(535\) −15002.1 8661.47i −1.21233 0.699941i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5635.83 + 2011.35i 0.450376 + 0.160733i
\(540\) 0 0
\(541\) −10091.7 17479.3i −0.801985 1.38908i −0.918308 0.395868i \(-0.870444\pi\)
0.116322 0.993211i \(-0.462889\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 37454.2 2.94378
\(546\) 0 0
\(547\) 21275.8 1.66305 0.831524 0.555488i \(-0.187469\pi\)
0.831524 + 0.555488i \(0.187469\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1256.96 + 2177.13i 0.0971842 + 0.168328i
\(552\) 0 0
\(553\) −10135.0 14378.1i −0.779356 1.10564i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15295.5 8830.84i −1.16354 0.671768i −0.211388 0.977402i \(-0.567798\pi\)
−0.952149 + 0.305634i \(0.901132\pi\)
\(558\) 0 0
\(559\) 2346.17i 0.177518i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7447.80 + 12900.0i −0.557527 + 0.965665i 0.440175 + 0.897912i \(0.354916\pi\)
−0.997702 + 0.0677527i \(0.978417\pi\)
\(564\) 0 0
\(565\) −34936.0 + 20170.3i −2.60136 + 1.50189i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11813.4 + 6820.47i −0.870375 + 0.502511i −0.867473 0.497485i \(-0.834257\pi\)
−0.00290206 + 0.999996i \(0.500924\pi\)
\(570\) 0 0
\(571\) 7222.20 12509.2i 0.529317 0.916803i −0.470099 0.882614i \(-0.655782\pi\)
0.999415 0.0341895i \(-0.0108850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 32021.2i 2.32239i
\(576\) 0 0
\(577\) 19780.9 + 11420.5i 1.42719 + 0.823989i 0.996898 0.0787009i \(-0.0250772\pi\)
0.430292 + 0.902690i \(0.358411\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −24019.9 + 2177.36i −1.71517 + 0.155477i
\(582\) 0 0
\(583\) 1503.74 + 2604.55i 0.106824 + 0.185025i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21564.8 1.51631 0.758156 0.652073i \(-0.226100\pi\)
0.758156 + 0.652073i \(0.226100\pi\)
\(588\) 0 0
\(589\) 2624.03 0.183567
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4857.29 8413.08i −0.336366 0.582603i 0.647380 0.762167i \(-0.275865\pi\)
−0.983746 + 0.179564i \(0.942531\pi\)
\(594\) 0 0
\(595\) −49339.6 + 4472.55i −3.39954 + 0.308162i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5905.86 + 3409.75i 0.402849 + 0.232585i 0.687713 0.725983i \(-0.258615\pi\)
−0.284863 + 0.958568i \(0.591948\pi\)
\(600\) 0 0
\(601\) 23101.9i 1.56796i −0.620783 0.783982i \(-0.713185\pi\)
0.620783 0.783982i \(-0.286815\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10001.4 + 17323.0i −0.672094 + 1.16410i
\(606\) 0 0
\(607\) −734.613 + 424.129i −0.0491219 + 0.0283606i −0.524360 0.851497i \(-0.675695\pi\)
0.475238 + 0.879857i \(0.342362\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4947.63 + 2856.52i −0.327594 + 0.189136i
\(612\) 0 0
\(613\) −7859.10 + 13612.4i −0.517824 + 0.896897i 0.481962 + 0.876192i \(0.339924\pi\)
−0.999786 + 0.0207049i \(0.993409\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24534.6i 1.60086i −0.599429 0.800428i \(-0.704606\pi\)
0.599429 0.800428i \(-0.295394\pi\)
\(618\) 0 0
\(619\) −1330.23 768.007i −0.0863754 0.0498689i 0.456190 0.889882i \(-0.349214\pi\)
−0.542566 + 0.840013i \(0.682547\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4493.69 6375.03i −0.288982 0.409968i
\(624\) 0 0
\(625\) −8690.12 15051.7i −0.556168 0.963311i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16088.5 1.01986
\(630\) 0 0
\(631\) 14860.1 0.937515 0.468758 0.883327i \(-0.344702\pi\)
0.468758 + 0.883327i \(0.344702\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14694.5 + 25451.7i 0.918322 + 1.59058i
\(636\) 0 0
\(637\) −1019.40 5576.64i −0.0634069 0.346868i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17466.3 10084.2i −1.07625 0.621373i −0.146368 0.989230i \(-0.546758\pi\)
−0.929882 + 0.367857i \(0.880092\pi\)
\(642\) 0 0
\(643\) 3124.44i 0.191627i 0.995399 + 0.0958133i \(0.0305452\pi\)
−0.995399 + 0.0958133i \(0.969455\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10143.8 + 17569.5i −0.616372 + 1.06759i 0.373770 + 0.927521i \(0.378065\pi\)
−0.990142 + 0.140066i \(0.955268\pi\)
\(648\) 0 0
\(649\) 8991.77 5191.40i 0.543848 0.313991i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2651.27 + 1530.71i −0.158885 + 0.0917325i −0.577335 0.816508i \(-0.695907\pi\)
0.418449 + 0.908240i \(0.362574\pi\)
\(654\) 0 0
\(655\) −20799.4 + 36025.6i −1.24076 + 2.14906i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3017.77i 0.178385i −0.996014 0.0891924i \(-0.971571\pi\)
0.996014 0.0891924i \(-0.0284286\pi\)
\(660\) 0 0
\(661\) −4671.67 2697.19i −0.274897 0.158712i 0.356214 0.934404i \(-0.384067\pi\)
−0.631111 + 0.775693i \(0.717401\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7827.43 3620.16i −0.456443 0.211104i
\(666\) 0 0
\(667\) 6614.15 + 11456.0i 0.383959 + 0.665037i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −11316.4 −0.651063
\(672\) 0 0
\(673\) 21062.8 1.20641 0.603204 0.797587i \(-0.293890\pi\)
0.603204 + 0.797587i \(0.293890\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13505.8 + 23392.7i 0.766718 + 1.32800i 0.939333 + 0.343006i \(0.111445\pi\)
−0.172615 + 0.984989i \(0.555222\pi\)
\(678\) 0 0
\(679\) −925.089 10205.3i −0.0522852 0.576793i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12369.6 7141.59i −0.692986 0.400095i 0.111744 0.993737i \(-0.464356\pi\)
−0.804730 + 0.593642i \(0.797690\pi\)
\(684\) 0 0
\(685\) 11132.3i 0.620940i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1424.60 2467.47i 0.0787704 0.136434i
\(690\) 0 0
\(691\) −2246.31 + 1296.91i −0.123666 + 0.0713989i −0.560557 0.828116i \(-0.689413\pi\)
0.436891 + 0.899515i \(0.356080\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 50687.1 29264.2i 2.76644 1.59720i
\(696\) 0 0
\(697\) 23892.9 41383.7i 1.29843 2.24895i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30185.3i 1.62637i −0.582009 0.813183i \(-0.697733\pi\)
0.582009 0.813183i \(-0.302267\pi\)
\(702\) 0 0
\(703\) 2425.41 + 1400.31i 0.130123 + 0.0751263i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1802.89 + 3898.16i −0.0959047 + 0.207363i
\(708\) 0 0
\(709\) 15514.3 + 26871.5i 0.821793 + 1.42339i 0.904345 + 0.426801i \(0.140360\pi\)
−0.0825520 + 0.996587i \(0.526307\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13807.7 0.725246
\(714\) 0 0
\(715\) −5618.10 −0.293853
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5323.93 9221.32i −0.276146 0.478299i 0.694277 0.719707i \(-0.255724\pi\)
−0.970424 + 0.241408i \(0.922391\pi\)
\(720\) 0 0
\(721\) 29268.9 20631.3i 1.51183 1.06567i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −23195.0 13391.6i −1.18819 0.686005i
\(726\) 0 0
\(727\) 11374.6i 0.580278i −0.956985 0.290139i \(-0.906299\pi\)
0.956985 0.290139i \(-0.0937015\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9744.57 16878.1i 0.493045 0.853979i
\(732\) 0 0
\(733\) −19102.2 + 11028.7i −0.962559 + 0.555734i −0.896960 0.442113i \(-0.854229\pi\)
−0.0655991 + 0.997846i \(0.520896\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1964.12 1133.99i 0.0981673 0.0566769i
\(738\) 0 0
\(739\) 13160.9 22795.4i 0.655119 1.13470i −0.326745 0.945113i \(-0.605952\pi\)
0.981864 0.189587i \(-0.0607149\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4269.63i 0.210818i −0.994429 0.105409i \(-0.966385\pi\)
0.994429 0.105409i \(-0.0336151\pi\)
\(744\) 0 0
\(745\) 27930.7 + 16125.8i 1.37356 + 0.793025i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 13458.6 9486.83i 0.656565 0.462806i
\(750\) 0 0
\(751\) 14942.7 + 25881.5i 0.726054 + 1.25756i 0.958539 + 0.284963i \(0.0919813\pi\)
−0.232484 + 0.972600i \(0.574685\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15458.7 0.745163
\(756\) 0 0
\(757\) −12658.2 −0.607756 −0.303878 0.952711i \(-0.598281\pi\)
−0.303878 + 0.952711i \(0.598281\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13590.3 + 23539.0i 0.647367 + 1.12127i 0.983749 + 0.179548i \(0.0574634\pi\)
−0.336382 + 0.941726i \(0.609203\pi\)
\(762\) 0 0
\(763\) −14944.7 + 32313.1i −0.709089 + 1.53317i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8518.52 4918.17i −0.401025 0.231532i
\(768\) 0 0
\(769\) 21028.3i 0.986087i −0.870005 0.493044i \(-0.835884\pi\)
0.870005 0.493044i \(-0.164116\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7220.65 12506.5i 0.335975 0.581926i −0.647697 0.761898i \(-0.724268\pi\)
0.983672 + 0.179972i \(0.0576009\pi\)
\(774\) 0 0
\(775\) −24210.9 + 13978.2i −1.12217 + 0.647884i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7203.90 4159.17i 0.331330 0.191294i
\(780\) 0 0
\(781\) −7926.36 + 13728.9i −0.363159 + 0.629010i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 13982.9i 0.635759i
\(786\) 0 0
\(787\) 17907.5 + 10338.9i 0.811098 + 0.468288i 0.847337 0.531055i \(-0.178204\pi\)
−0.0362388 + 0.999343i \(0.511538\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3461.74 38188.8i −0.155607 1.71661i
\(792\) 0 0
\(793\) 5360.38 + 9284.45i 0.240041 + 0.415764i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21175.0 −0.941099 −0.470550 0.882374i \(-0.655944\pi\)
−0.470550 + 0.882374i \(0.655944\pi\)
\(798\) 0 0
\(799\) −47456.9 −2.10126
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −452.242 783.306i −0.0198746