Properties

Label 400.2.y.c.369.1
Level $400$
Weight $2$
Character 400.369
Analytic conductor $3.194$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.y (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 369.1
Root \(1.17421 - 0.0566033i\) of defining polynomial
Character \(\chi\) \(=\) 400.369
Dual form 400.2.y.c.129.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +O(q^{10})\) \(q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +(-0.618034 - 1.90211i) q^{11} +(-3.20892 - 1.04264i) q^{13} +(-1.74248 + 4.59680i) q^{15} +(-1.70135 + 2.34171i) q^{17} +(2.09089 + 1.51912i) q^{19} +(1.76510 - 1.28242i) q^{21} +(-4.32696 + 1.40591i) q^{23} +(-1.99532 + 4.58462i) q^{25} +(-2.43930 + 0.792578i) q^{27} +(-4.35599 + 3.16481i) q^{29} +(0.110461 + 0.0802548i) q^{31} +(-2.58448 + 3.55723i) q^{33} +(1.85599 - 1.21638i) q^{35} +(2.04392 + 0.664110i) q^{37} +(2.29224 + 7.05479i) q^{39} +(2.66780 - 8.21064i) q^{41} -4.64398i q^{43} +(3.95536 - 1.07763i) q^{45} +(-5.83453 - 8.03054i) q^{47} +6.01515 q^{49} +6.36356 q^{51} +(-4.44672 - 6.12038i) q^{53} +(-2.79981 + 3.48727i) q^{55} -5.68196i q^{57} +(1.51967 - 4.67706i) q^{59} +(-0.855890 - 2.63416i) q^{61} +(-1.73038 - 0.562235i) q^{63} +(1.98322 + 7.27931i) q^{65} +(1.28477 - 1.76833i) q^{67} +(8.09205 + 5.87922i) q^{69} +(7.80098 - 5.66774i) q^{71} +(-0.737953 + 0.239775i) q^{73} +(10.7327 - 2.37552i) q^{75} +(1.88765 - 0.613336i) q^{77} +(-12.8236 + 9.31689i) q^{79} +(9.01153 + 6.54726i) q^{81} +(1.04103 - 1.43285i) q^{83} +(6.46482 + 0.311640i) q^{85} +(11.2580 + 3.65794i) q^{87} +(-4.48322 - 13.7979i) q^{89} +(1.03472 - 3.18453i) q^{91} -0.300177i q^{93} +(0.278260 - 5.77237i) q^{95} +(-10.0095 - 13.7768i) q^{97} +3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\)

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
\(3\) −1.29224 1.77862i −0.746076 1.02689i −0.998246 0.0592022i \(-0.981144\pi\)
0.252170 0.967683i \(-0.418856\pi\)
\(4\) 0 0
\(5\) −1.22570 1.87020i −0.548150 0.836380i
\(6\) 0 0
\(7\) 0.992398i 0.375091i 0.982256 + 0.187546i \(0.0600533\pi\)
−0.982256 + 0.187546i \(0.939947\pi\)
\(8\) 0 0
\(9\) −0.566541 + 1.74363i −0.188847 + 0.581211i
\(10\) 0 0
\(11\) −0.618034 1.90211i −0.186344 0.573509i 0.813625 0.581390i \(-0.197491\pi\)
−0.999969 + 0.00788181i \(0.997491\pi\)
\(12\) 0 0
\(13\) −3.20892 1.04264i −0.889995 0.289177i −0.171894 0.985115i \(-0.554989\pi\)
−0.718101 + 0.695938i \(0.754989\pi\)
\(14\) 0 0
\(15\) −1.74248 + 4.59680i −0.449905 + 1.18689i
\(16\) 0 0
\(17\) −1.70135 + 2.34171i −0.412638 + 0.567948i −0.963859 0.266411i \(-0.914162\pi\)
0.551221 + 0.834359i \(0.314162\pi\)
\(18\) 0 0
\(19\) 2.09089 + 1.51912i 0.479683 + 0.348510i 0.801203 0.598393i \(-0.204194\pi\)
−0.321520 + 0.946903i \(0.604194\pi\)
\(20\) 0 0
\(21\) 1.76510 1.28242i 0.385176 0.279847i
\(22\) 0 0
\(23\) −4.32696 + 1.40591i −0.902233 + 0.293153i −0.723158 0.690682i \(-0.757310\pi\)
−0.179075 + 0.983835i \(0.557310\pi\)
\(24\) 0 0
\(25\) −1.99532 + 4.58462i −0.399064 + 0.916923i
\(26\) 0 0
\(27\) −2.43930 + 0.792578i −0.469444 + 0.152532i
\(28\) 0 0
\(29\) −4.35599 + 3.16481i −0.808886 + 0.587690i −0.913508 0.406822i \(-0.866637\pi\)
0.104621 + 0.994512i \(0.466637\pi\)
\(30\) 0 0
\(31\) 0.110461 + 0.0802548i 0.0198394 + 0.0144142i 0.597661 0.801749i \(-0.296097\pi\)
−0.577821 + 0.816163i \(0.696097\pi\)
\(32\) 0 0
\(33\) −2.58448 + 3.55723i −0.449901 + 0.619235i
\(34\) 0 0
\(35\) 1.85599 1.21638i 0.313719 0.205606i
\(36\) 0 0
\(37\) 2.04392 + 0.664110i 0.336018 + 0.109179i 0.472166 0.881510i \(-0.343472\pi\)
−0.136148 + 0.990689i \(0.543472\pi\)
\(38\) 0 0
\(39\) 2.29224 + 7.05479i 0.367052 + 1.12967i
\(40\) 0 0
\(41\) 2.66780 8.21064i 0.416640 1.28229i −0.494135 0.869385i \(-0.664515\pi\)
0.910776 0.412902i \(-0.135485\pi\)
\(42\) 0 0
\(43\) 4.64398i 0.708200i −0.935208 0.354100i \(-0.884787\pi\)
0.935208 0.354100i \(-0.115213\pi\)
\(44\) 0 0
\(45\) 3.95536 1.07763i 0.589630 0.160643i
\(46\) 0 0
\(47\) −5.83453 8.03054i −0.851054 1.17137i −0.983630 0.180202i \(-0.942325\pi\)
0.132576 0.991173i \(-0.457675\pi\)
\(48\) 0 0
\(49\) 6.01515 0.859306
\(50\) 0 0
\(51\) 6.36356 0.891077
\(52\) 0 0
\(53\) −4.44672 6.12038i −0.610804 0.840699i 0.385839 0.922566i \(-0.373912\pi\)
−0.996643 + 0.0818665i \(0.973912\pi\)
\(54\) 0 0
\(55\) −2.79981 + 3.48727i −0.377527 + 0.470223i
\(56\) 0 0
\(57\) 5.68196i 0.752594i
\(58\) 0 0
\(59\) 1.51967 4.67706i 0.197844 0.608901i −0.802088 0.597206i \(-0.796277\pi\)
0.999932 0.0116948i \(-0.00372266\pi\)
\(60\) 0 0
\(61\) −0.855890 2.63416i −0.109585 0.337269i 0.881194 0.472755i \(-0.156740\pi\)
−0.990779 + 0.135486i \(0.956740\pi\)
\(62\) 0 0
\(63\) −1.73038 0.562235i −0.218007 0.0708349i
\(64\) 0 0
\(65\) 1.98322 + 7.27931i 0.245989 + 0.902887i
\(66\) 0 0
\(67\) 1.28477 1.76833i 0.156959 0.216036i −0.723294 0.690540i \(-0.757373\pi\)
0.880253 + 0.474505i \(0.157373\pi\)
\(68\) 0 0
\(69\) 8.09205 + 5.87922i 0.974169 + 0.707775i
\(70\) 0 0
\(71\) 7.80098 5.66774i 0.925806 0.672637i −0.0191565 0.999816i \(-0.506098\pi\)
0.944962 + 0.327179i \(0.106098\pi\)
\(72\) 0 0
\(73\) −0.737953 + 0.239775i −0.0863708 + 0.0280636i −0.351884 0.936044i \(-0.614459\pi\)
0.265513 + 0.964107i \(0.414459\pi\)
\(74\) 0 0
\(75\) 10.7327 2.37552i 1.23931 0.274301i
\(76\) 0 0
\(77\) 1.88765 0.613336i 0.215118 0.0698961i
\(78\) 0 0
\(79\) −12.8236 + 9.31689i −1.44277 + 1.04823i −0.455313 + 0.890332i \(0.650473\pi\)
−0.987455 + 0.157900i \(0.949527\pi\)
\(80\) 0 0
\(81\) 9.01153 + 6.54726i 1.00128 + 0.727474i
\(82\) 0 0
\(83\) 1.04103 1.43285i 0.114268 0.157276i −0.748052 0.663640i \(-0.769011\pi\)
0.862320 + 0.506364i \(0.169011\pi\)
\(84\) 0 0
\(85\) 6.46482 + 0.311640i 0.701208 + 0.0338021i
\(86\) 0 0
\(87\) 11.2580 + 3.65794i 1.20698 + 0.392172i
\(88\) 0 0
\(89\) −4.48322 13.7979i −0.475221 1.46258i −0.845660 0.533722i \(-0.820793\pi\)
0.370439 0.928857i \(-0.379207\pi\)
\(90\) 0 0
\(91\) 1.03472 3.18453i 0.108468 0.333830i
\(92\) 0 0
\(93\) 0.300177i 0.0311269i
\(94\) 0 0
\(95\) 0.278260 5.77237i 0.0285489 0.592233i
\(96\) 0 0
\(97\) −10.0095 13.7768i −1.01631 1.39883i −0.914761 0.403995i \(-0.867621\pi\)
−0.101545 0.994831i \(-0.532379\pi\)
\(98\) 0 0
\(99\) 3.66673 0.368520
\(100\) 0 0
\(101\) −2.54716 −0.253452 −0.126726 0.991938i \(-0.540447\pi\)
−0.126726 + 0.991938i \(0.540447\pi\)
\(102\) 0 0
\(103\) 5.97509 + 8.22400i 0.588743 + 0.810335i 0.994620 0.103593i \(-0.0330338\pi\)
−0.405877 + 0.913928i \(0.633034\pi\)
\(104\) 0 0
\(105\) −4.56186 1.72923i −0.445192 0.168756i
\(106\) 0 0
\(107\) 4.81720i 0.465697i −0.972513 0.232848i \(-0.925195\pi\)
0.972513 0.232848i \(-0.0748046\pi\)
\(108\) 0 0
\(109\) −5.02903 + 15.4778i −0.481694 + 1.48250i 0.355019 + 0.934859i \(0.384474\pi\)
−0.836713 + 0.547642i \(0.815526\pi\)
\(110\) 0 0
\(111\) −1.46004 4.49354i −0.138581 0.426508i
\(112\) 0 0
\(113\) 6.42633 + 2.08804i 0.604538 + 0.196426i 0.595264 0.803531i \(-0.297048\pi\)
0.00927487 + 0.999957i \(0.497048\pi\)
\(114\) 0 0
\(115\) 7.93290 + 6.36906i 0.739746 + 0.593918i
\(116\) 0 0
\(117\) 3.63597 5.00449i 0.336146 0.462665i
\(118\) 0 0
\(119\) −2.32391 1.68842i −0.213032 0.154777i
\(120\) 0 0
\(121\) 5.66312 4.11450i 0.514829 0.374045i
\(122\) 0 0
\(123\) −18.0510 + 5.86513i −1.62761 + 0.528841i
\(124\) 0 0
\(125\) 11.0198 1.88771i 0.985643 0.168842i
\(126\) 0 0
\(127\) 1.41785 0.460687i 0.125814 0.0408793i −0.245433 0.969413i \(-0.578930\pi\)
0.371247 + 0.928534i \(0.378930\pi\)
\(128\) 0 0
\(129\) −8.25985 + 6.00114i −0.727240 + 0.528370i
\(130\) 0 0
\(131\) 11.4190 + 8.29640i 0.997684 + 0.724860i 0.961590 0.274489i \(-0.0885086\pi\)
0.0360934 + 0.999348i \(0.488509\pi\)
\(132\) 0 0
\(133\) −1.50757 + 2.07500i −0.130723 + 0.179925i
\(134\) 0 0
\(135\) 4.47214 + 3.59053i 0.384900 + 0.309024i
\(136\) 0 0
\(137\) 0.655703 + 0.213051i 0.0560205 + 0.0182022i 0.336893 0.941543i \(-0.390624\pi\)
−0.280873 + 0.959745i \(0.590624\pi\)
\(138\) 0 0
\(139\) −5.12099 15.7608i −0.434356 1.33681i −0.893745 0.448576i \(-0.851931\pi\)
0.459388 0.888236i \(-0.348069\pi\)
\(140\) 0 0
\(141\) −6.74364 + 20.7548i −0.567917 + 1.74787i
\(142\) 0 0
\(143\) 6.74812i 0.564307i
\(144\) 0 0
\(145\) 11.2580 + 4.26747i 0.934923 + 0.354394i
\(146\) 0 0
\(147\) −7.77302 10.6986i −0.641108 0.882409i
\(148\) 0 0
\(149\) −3.21156 −0.263101 −0.131551 0.991309i \(-0.541996\pi\)
−0.131551 + 0.991309i \(0.541996\pi\)
\(150\) 0 0
\(151\) −17.6863 −1.43929 −0.719647 0.694340i \(-0.755696\pi\)
−0.719647 + 0.694340i \(0.755696\pi\)
\(152\) 0 0
\(153\) −3.11920 4.29321i −0.252172 0.347085i
\(154\) 0 0
\(155\) 0.0147004 0.304953i 0.00118077 0.0244944i
\(156\) 0 0
\(157\) 1.65512i 0.132093i −0.997817 0.0660465i \(-0.978961\pi\)
0.997817 0.0660465i \(-0.0210386\pi\)
\(158\) 0 0
\(159\) −5.13959 + 15.8180i −0.407596 + 1.25445i
\(160\) 0 0
\(161\) −1.39523 4.29407i −0.109959 0.338420i
\(162\) 0 0
\(163\) −0.849231 0.275932i −0.0665169 0.0216127i 0.275570 0.961281i \(-0.411134\pi\)
−0.342086 + 0.939668i \(0.611134\pi\)
\(164\) 0 0
\(165\) 9.82055 + 0.473405i 0.764529 + 0.0368545i
\(166\) 0 0
\(167\) 3.05388 4.20331i 0.236317 0.325262i −0.674344 0.738417i \(-0.735573\pi\)
0.910660 + 0.413156i \(0.135573\pi\)
\(168\) 0 0
\(169\) −1.30713 0.949687i −0.100549 0.0730529i
\(170\) 0 0
\(171\) −3.83337 + 2.78510i −0.293145 + 0.212982i
\(172\) 0 0
\(173\) 5.48250 1.78137i 0.416827 0.135435i −0.0930924 0.995657i \(-0.529675\pi\)
0.509919 + 0.860222i \(0.329675\pi\)
\(174\) 0 0
\(175\) −4.54977 1.98015i −0.343930 0.149685i
\(176\) 0 0
\(177\) −10.2825 + 3.34098i −0.772878 + 0.251123i
\(178\) 0 0
\(179\) −7.01326 + 5.09543i −0.524196 + 0.380850i −0.818182 0.574959i \(-0.805018\pi\)
0.293986 + 0.955810i \(0.405018\pi\)
\(180\) 0 0
\(181\) −11.5616 8.39996i −0.859363 0.624364i 0.0683483 0.997662i \(-0.478227\pi\)
−0.927712 + 0.373297i \(0.878227\pi\)
\(182\) 0 0
\(183\) −3.57914 + 4.92627i −0.264578 + 0.364160i
\(184\) 0 0
\(185\) −1.26321 4.63655i −0.0928732 0.340886i
\(186\) 0 0
\(187\) 5.50569 + 1.78891i 0.402616 + 0.130818i
\(188\) 0 0
\(189\) −0.786553 2.42076i −0.0572133 0.176084i
\(190\) 0 0
\(191\) 0.391326 1.20438i 0.0283154 0.0871458i −0.935900 0.352265i \(-0.885411\pi\)
0.964216 + 0.265120i \(0.0854114\pi\)
\(192\) 0 0
\(193\) 21.1730i 1.52406i 0.647540 + 0.762031i \(0.275798\pi\)
−0.647540 + 0.762031i \(0.724202\pi\)
\(194\) 0 0
\(195\) 10.3843 12.9340i 0.743635 0.926224i
\(196\) 0 0
\(197\) −7.17176 9.87108i −0.510967 0.703285i 0.473115 0.881001i \(-0.343129\pi\)
−0.984082 + 0.177715i \(0.943129\pi\)
\(198\) 0 0
\(199\) 10.4065 0.737695 0.368848 0.929490i \(-0.379752\pi\)
0.368848 + 0.929490i \(0.379752\pi\)
\(200\) 0 0
\(201\) −4.80540 −0.338947
\(202\) 0 0
\(203\) −3.14075 4.32287i −0.220438 0.303406i
\(204\) 0 0
\(205\) −18.6255 + 5.07446i −1.30086 + 0.354415i
\(206\) 0 0
\(207\) 8.34114i 0.579749i
\(208\) 0 0
\(209\) 1.59730 4.91598i 0.110487 0.340045i
\(210\) 0 0
\(211\) 2.67537 + 8.23395i 0.184180 + 0.566848i 0.999933 0.0115520i \(-0.00367718\pi\)
−0.815753 + 0.578400i \(0.803677\pi\)
\(212\) 0 0
\(213\) −20.1615 6.55086i −1.38144 0.448858i
\(214\) 0 0
\(215\) −8.68518 + 5.69212i −0.592324 + 0.388199i
\(216\) 0 0
\(217\) −0.0796448 + 0.109622i −0.00540664 + 0.00744160i
\(218\) 0 0
\(219\) 1.38008 + 1.00269i 0.0932573 + 0.0677554i
\(220\) 0 0
\(221\) 7.90107 5.74046i 0.531484 0.386145i
\(222\) 0 0
\(223\) 26.9562 8.75859i 1.80512 0.586518i 0.805139 0.593086i \(-0.202091\pi\)
0.999978 + 0.00656747i \(0.00209051\pi\)
\(224\) 0 0
\(225\) −6.86346 6.07648i −0.457564 0.405099i
\(226\) 0 0
\(227\) −21.1529 + 6.87299i −1.40397 + 0.456176i −0.910471 0.413572i \(-0.864281\pi\)
−0.493495 + 0.869749i \(0.664281\pi\)
\(228\) 0 0
\(229\) 2.00280 1.45512i 0.132348 0.0961568i −0.519641 0.854384i \(-0.673934\pi\)
0.651990 + 0.758228i \(0.273934\pi\)
\(230\) 0 0
\(231\) −3.53019 2.56484i −0.232270 0.168754i
\(232\) 0 0
\(233\) 3.50088 4.81854i 0.229350 0.315673i −0.678796 0.734327i \(-0.737498\pi\)
0.908146 + 0.418654i \(0.137498\pi\)
\(234\) 0 0
\(235\) −7.86736 + 20.7548i −0.513210 + 1.35389i
\(236\) 0 0
\(237\) 33.1424 + 10.7686i 2.15283 + 0.699496i
\(238\) 0 0
\(239\) −2.17314 6.68823i −0.140569 0.432626i 0.855846 0.517231i \(-0.173037\pi\)
−0.996415 + 0.0846050i \(0.973037\pi\)
\(240\) 0 0
\(241\) 0.364567 1.12202i 0.0234838 0.0722758i −0.938628 0.344932i \(-0.887902\pi\)
0.962112 + 0.272656i \(0.0879021\pi\)
\(242\) 0 0
\(243\) 16.7942i 1.07735i
\(244\) 0 0
\(245\) −7.37276 11.2495i −0.471029 0.718707i
\(246\) 0 0
\(247\) −5.12561 7.05479i −0.326135 0.448886i
\(248\) 0 0
\(249\) −3.89375 −0.246757
\(250\) 0 0
\(251\) −4.60867 −0.290897 −0.145448 0.989366i \(-0.546462\pi\)
−0.145448 + 0.989366i \(0.546462\pi\)
\(252\) 0 0
\(253\) 5.34841 + 7.36146i 0.336252 + 0.462811i
\(254\) 0 0
\(255\) −7.79981 11.9011i −0.488443 0.745279i
\(256\) 0 0
\(257\) 9.75542i 0.608526i 0.952588 + 0.304263i \(0.0984102\pi\)
−0.952588 + 0.304263i \(0.901590\pi\)
\(258\) 0 0
\(259\) −0.659062 + 2.02838i −0.0409521 + 0.126038i
\(260\) 0 0
\(261\) −3.05043 9.38824i −0.188817 0.581118i
\(262\) 0 0
\(263\) −0.947088 0.307728i −0.0584000 0.0189753i 0.279671 0.960096i \(-0.409775\pi\)
−0.338071 + 0.941121i \(0.609775\pi\)
\(264\) 0 0
\(265\) −5.99602 + 15.8180i −0.368333 + 0.971693i
\(266\) 0 0
\(267\) −18.7479 + 25.8042i −1.14735 + 1.57919i
\(268\) 0 0
\(269\) −2.66048 1.93295i −0.162212 0.117854i 0.503718 0.863868i \(-0.331965\pi\)
−0.665930 + 0.746014i \(0.731965\pi\)
\(270\) 0 0
\(271\) 9.82960 7.14162i 0.597105 0.433823i −0.247745 0.968825i \(-0.579689\pi\)
0.844850 + 0.535003i \(0.179689\pi\)
\(272\) 0 0
\(273\) −7.00116 + 2.27482i −0.423730 + 0.137678i
\(274\) 0 0
\(275\) 9.95363 + 0.961876i 0.600227 + 0.0580033i
\(276\) 0 0
\(277\) −11.2858 + 3.66697i −0.678096 + 0.220327i −0.627762 0.778406i \(-0.716029\pi\)
−0.0503346 + 0.998732i \(0.516029\pi\)
\(278\) 0 0
\(279\) −0.202516 + 0.147136i −0.0121243 + 0.00880883i
\(280\) 0 0
\(281\) 19.9355 + 14.4840i 1.18925 + 0.864041i 0.993185 0.116549i \(-0.0371833\pi\)
0.196066 + 0.980591i \(0.437183\pi\)
\(282\) 0 0
\(283\) 1.97697 2.72107i 0.117519 0.161751i −0.746205 0.665716i \(-0.768126\pi\)
0.863724 + 0.503965i \(0.168126\pi\)
\(284\) 0 0
\(285\) −10.6264 + 6.96438i −0.629455 + 0.412534i
\(286\) 0 0
\(287\) 8.14823 + 2.64752i 0.480975 + 0.156278i
\(288\) 0 0
\(289\) 2.66428 + 8.19982i 0.156723 + 0.482342i
\(290\) 0 0
\(291\) −11.5691 + 35.6060i −0.678192 + 2.08726i
\(292\) 0 0
\(293\) 8.96340i 0.523647i −0.965116 0.261824i \(-0.915676\pi\)
0.965116 0.261824i \(-0.0843239\pi\)
\(294\) 0 0
\(295\) −10.6097 + 2.89058i −0.617721 + 0.168296i
\(296\) 0 0
\(297\) 3.01515 + 4.14999i 0.174956 + 0.240807i
\(298\) 0 0
\(299\) 15.3507 0.887756
\(300\) 0 0
\(301\) 4.60867 0.265640
\(302\) 0 0
\(303\) 3.29155 + 4.53042i 0.189094 + 0.260266i
\(304\) 0 0
\(305\) −3.87735 + 4.82937i −0.222016 + 0.276529i
\(306\) 0 0
\(307\) 9.48133i 0.541128i 0.962702 + 0.270564i \(0.0872102\pi\)
−0.962702 + 0.270564i \(0.912790\pi\)
\(308\) 0 0
\(309\) 6.90610 21.2548i 0.392874 1.20914i
\(310\) 0 0
\(311\) −9.06409 27.8964i −0.513978 1.58186i −0.785135 0.619325i \(-0.787406\pi\)
0.271157 0.962535i \(-0.412594\pi\)
\(312\) 0 0
\(313\) 17.9655 + 5.83735i 1.01547 + 0.329947i 0.769031 0.639212i \(-0.220739\pi\)
0.246440 + 0.969158i \(0.420739\pi\)
\(314\) 0 0
\(315\) 1.06943 + 3.92529i 0.0602558 + 0.221165i
\(316\) 0 0
\(317\) −13.3952 + 18.4369i −0.752351 + 1.03552i 0.245461 + 0.969406i \(0.421061\pi\)
−0.997812 + 0.0661157i \(0.978939\pi\)
\(318\) 0 0
\(319\) 8.71197 + 6.32962i 0.487777 + 0.354391i
\(320\) 0 0
\(321\) −8.56796 + 6.22499i −0.478217 + 0.347445i
\(322\) 0 0
\(323\) −7.11468 + 2.31170i −0.395871 + 0.128626i
\(324\) 0 0
\(325\) 11.1829 12.6313i 0.620318 0.700657i
\(326\) 0 0
\(327\) 34.0277 11.0563i 1.88174 0.611414i
\(328\) 0 0
\(329\) 7.96950 5.79018i 0.439373 0.319223i
\(330\) 0 0
\(331\) 2.39711 + 1.74160i 0.131757 + 0.0957272i 0.651712 0.758467i \(-0.274051\pi\)
−0.519955 + 0.854194i \(0.674051\pi\)
\(332\) 0 0
\(333\) −2.31593 + 3.18760i −0.126912 + 0.174680i
\(334\) 0 0
\(335\) −4.88187 0.235333i −0.266725 0.0128576i
\(336\) 0 0
\(337\) 17.8916 + 5.81332i 0.974615 + 0.316672i 0.752678 0.658389i \(-0.228762\pi\)
0.221937 + 0.975061i \(0.428762\pi\)
\(338\) 0 0
\(339\) −4.59054 14.1282i −0.249324 0.767340i
\(340\) 0 0
\(341\) 0.0843849 0.259710i 0.00456970 0.0140641i
\(342\) 0 0
\(343\) 12.9162i 0.697410i
\(344\) 0 0
\(345\) 1.07691 22.3399i 0.0579788 1.20274i
\(346\) 0 0
\(347\) 13.3652 + 18.3956i 0.717480 + 0.987526i 0.999604 + 0.0281483i \(0.00896108\pi\)
−0.282124 + 0.959378i \(0.591039\pi\)
\(348\) 0 0
\(349\) −1.93849 −0.103765 −0.0518824 0.998653i \(-0.516522\pi\)
−0.0518824 + 0.998653i \(0.516522\pi\)
\(350\) 0 0
\(351\) 8.65392 0.461912
\(352\) 0 0
\(353\) −3.08555 4.24689i −0.164227 0.226039i 0.718970 0.695041i \(-0.244614\pi\)
−0.883197 + 0.469002i \(0.844614\pi\)
\(354\) 0 0
\(355\) −20.1615 7.64246i −1.07006 0.405620i
\(356\) 0 0
\(357\) 6.31519i 0.334235i
\(358\) 0 0
\(359\) 6.98184 21.4879i 0.368488 1.13409i −0.579281 0.815128i \(-0.696666\pi\)
0.947768 0.318960i \(-0.103334\pi\)
\(360\) 0 0
\(361\) −3.80723 11.7174i −0.200380 0.616708i
\(362\) 0 0
\(363\) −14.6362 4.75560i −0.768203 0.249604i
\(364\) 0 0
\(365\) 1.35294 + 1.08623i 0.0708160 + 0.0568558i
\(366\) 0 0
\(367\) −4.29008 + 5.90479i −0.223940 + 0.308228i −0.906173 0.422908i \(-0.861009\pi\)
0.682232 + 0.731136i \(0.261009\pi\)
\(368\) 0 0
\(369\) 12.8049 + 9.30333i 0.666598 + 0.484312i
\(370\) 0 0
\(371\) 6.07386 4.41292i 0.315339 0.229107i
\(372\) 0 0
\(373\) 21.2156 6.89335i 1.09850 0.356924i 0.296975 0.954885i \(-0.404022\pi\)
0.801525 + 0.597961i \(0.204022\pi\)
\(374\) 0 0
\(375\) −17.5978 17.1607i −0.908746 0.886173i
\(376\) 0 0
\(377\) 17.2778 5.61390i 0.889852 0.289130i
\(378\) 0 0
\(379\) 26.6544 19.3655i 1.36914 0.994740i 0.371339 0.928497i \(-0.378899\pi\)
0.997804 0.0662429i \(-0.0211012\pi\)
\(380\) 0 0
\(381\) −2.65159 1.92649i −0.135845 0.0986971i
\(382\) 0 0
\(383\) 12.1673 16.7468i 0.621719 0.855722i −0.375758 0.926718i \(-0.622618\pi\)
0.997477 + 0.0709955i \(0.0226176\pi\)
\(384\) 0 0
\(385\) −3.46076 2.77853i −0.176377 0.141607i
\(386\) 0 0
\(387\) 8.09739 + 2.63100i 0.411614 + 0.133741i
\(388\) 0 0
\(389\) 0.353657 + 1.08844i 0.0179311 + 0.0551863i 0.959622 0.281294i \(-0.0907635\pi\)
−0.941691 + 0.336480i \(0.890764\pi\)
\(390\) 0 0
\(391\) 4.06943 12.5244i 0.205800 0.633388i
\(392\) 0 0
\(393\) 31.0310i 1.56531i
\(394\) 0 0
\(395\) 33.1424 + 12.5630i 1.66757 + 0.632114i
\(396\) 0 0
\(397\) −2.75385 3.79035i −0.138212 0.190232i 0.734300 0.678825i \(-0.237510\pi\)
−0.872512 + 0.488593i \(0.837510\pi\)
\(398\) 0 0
\(399\) 5.63877 0.282292
\(400\) 0 0
\(401\) −24.0851 −1.20275 −0.601376 0.798966i \(-0.705381\pi\)
−0.601376 + 0.798966i \(0.705381\pi\)
\(402\) 0 0
\(403\) −0.270785 0.372703i −0.0134888 0.0185657i
\(404\) 0 0
\(405\) 1.19928 24.8784i 0.0595925 1.23622i
\(406\) 0 0
\(407\) 4.29821i 0.213054i
\(408\) 0 0
\(409\) 0.586930 1.80638i 0.0290218 0.0893199i −0.935496 0.353336i \(-0.885047\pi\)
0.964518 + 0.264016i \(0.0850472\pi\)
\(410\) 0 0
\(411\) −0.468391 1.44156i −0.0231040 0.0711068i
\(412\) 0 0
\(413\) 4.64151 + 1.50812i 0.228394 + 0.0742096i
\(414\) 0 0
\(415\) −3.95571 0.190687i −0.194178 0.00936047i
\(416\) 0 0
\(417\) −21.4148 + 29.4750i −1.04869 + 1.44340i
\(418\) 0 0
\(419\) 1.88344 + 1.36840i 0.0920120 + 0.0668507i 0.632840 0.774283i \(-0.281889\pi\)
−0.540828 + 0.841133i \(0.681889\pi\)
\(420\) 0 0
\(421\) 19.3760 14.0775i 0.944329 0.686095i −0.00513010 0.999987i \(-0.501633\pi\)
0.949459 + 0.313892i \(0.101633\pi\)
\(422\) 0 0
\(423\) 17.3078 5.62366i 0.841536 0.273431i
\(424\) 0 0
\(425\) −7.34110 12.4725i −0.356095 0.605005i
\(426\) 0 0
\(427\) 2.61413 0.849384i 0.126507 0.0411045i
\(428\) 0 0
\(429\) 12.0023 8.72020i 0.579478 0.421015i
\(430\) 0 0
\(431\) 0.964563 + 0.700796i 0.0464614 + 0.0337562i 0.610774 0.791805i \(-0.290859\pi\)
−0.564312 + 0.825561i \(0.690859\pi\)
\(432\) 0 0
\(433\) 15.0554 20.7220i 0.723518 0.995837i −0.275882 0.961192i \(-0.588970\pi\)
0.999400 0.0346454i \(-0.0110302\pi\)
\(434\) 0 0
\(435\) −6.95781 25.5382i −0.333601 1.22446i
\(436\) 0 0
\(437\) −11.1829 3.63356i −0.534953 0.173817i
\(438\) 0 0
\(439\) 5.98693 + 18.4259i 0.285741 + 0.879420i 0.986176 + 0.165703i \(0.0529894\pi\)
−0.700435 + 0.713716i \(0.747011\pi\)
\(440\) 0 0
\(441\) −3.40783 + 10.4882i −0.162277 + 0.499439i
\(442\) 0 0
\(443\) 2.46263i 0.117003i 0.998287 + 0.0585016i \(0.0186323\pi\)
−0.998287 + 0.0585016i \(0.981368\pi\)
\(444\) 0 0
\(445\) −20.3099 + 25.2967i −0.962780 + 1.19918i
\(446\) 0 0
\(447\) 4.15011 + 5.71214i 0.196294 + 0.270175i
\(448\) 0 0
\(449\) 14.3585 0.677618 0.338809 0.940855i \(-0.389976\pi\)
0.338809 + 0.940855i \(0.389976\pi\)
\(450\) 0 0
\(451\) −17.2664 −0.813041
\(452\) 0 0
\(453\) 22.8550 + 31.4572i 1.07382 + 1.47799i
\(454\) 0 0
\(455\) −7.22397 + 1.96815i −0.338665 + 0.0922682i
\(456\) 0 0
\(457\) 25.1964i 1.17864i −0.807901 0.589319i \(-0.799396\pi\)
0.807901 0.589319i \(-0.200604\pi\)
\(458\) 0 0
\(459\) 2.29413 7.06059i 0.107081 0.329560i
\(460\) 0 0
\(461\) 8.90758 + 27.4147i 0.414867 + 1.27683i 0.912370 + 0.409367i \(0.134251\pi\)
−0.497502 + 0.867463i \(0.665749\pi\)
\(462\) 0 0
\(463\) 30.3193 + 9.85134i 1.40906 + 0.457831i 0.912108 0.409949i \(-0.134453\pi\)
0.496949 + 0.867780i \(0.334453\pi\)
\(464\) 0 0
\(465\) −0.561392 + 0.367927i −0.0260339 + 0.0170622i
\(466\) 0 0
\(467\) −25.3333 + 34.8683i −1.17229 + 1.61351i −0.525706 + 0.850666i \(0.676199\pi\)
−0.646580 + 0.762847i \(0.723801\pi\)
\(468\) 0 0
\(469\) 1.75489 + 1.27500i 0.0810331 + 0.0588740i
\(470\) 0 0
\(471\) −2.94383 + 2.13882i −0.135644 + 0.0985514i
\(472\) 0 0
\(473\) −8.83337 + 2.87013i −0.406159 + 0.131969i
\(474\) 0 0
\(475\) −11.1366 + 6.55479i −0.510981 + 0.300755i
\(476\) 0 0
\(477\) 13.1910 4.28600i 0.603973 0.196243i
\(478\) 0 0
\(479\) −17.0107 + 12.3590i −0.777237 + 0.564696i −0.904148 0.427218i \(-0.859494\pi\)
0.126912 + 0.991914i \(0.459494\pi\)
\(480\) 0 0
\(481\) −5.86635 4.26216i −0.267483 0.194338i
\(482\) 0 0
\(483\) −5.83453 + 8.03054i −0.265480 + 0.365402i
\(484\) 0 0
\(485\) −13.4969 + 35.6060i −0.612862 + 1.61678i
\(486\) 0 0
\(487\) 26.5525 + 8.62744i 1.20321 + 0.390947i 0.840941 0.541127i \(-0.182002\pi\)
0.362269 + 0.932073i \(0.382002\pi\)
\(488\) 0 0
\(489\) 0.606634 + 1.86703i 0.0274329 + 0.0844299i
\(490\) 0 0
\(491\) −4.62322 + 14.2288i −0.208643 + 0.642137i 0.790901 + 0.611944i \(0.209612\pi\)
−0.999544 + 0.0301930i \(0.990388\pi\)
\(492\) 0 0
\(493\) 15.5849i 0.701909i
\(494\) 0 0
\(495\) −4.49431 6.85753i −0.202004 0.308223i
\(496\) 0 0
\(497\) 5.62466 + 7.74168i 0.252300 + 0.347262i
\(498\) 0 0
\(499\) −44.3253 −1.98427 −0.992137 0.125160i \(-0.960056\pi\)
−0.992137 + 0.125160i \(0.960056\pi\)
\(500\) 0 0
\(501\) −11.4224 −0.510316
\(502\) 0 0
\(503\) −13.8842 19.1100i −0.619066 0.852071i 0.378219 0.925716i \(-0.376537\pi\)
−0.997284 + 0.0736453i \(0.976537\pi\)
\(504\) 0 0
\(505\) 3.12205 + 4.76371i 0.138930 + 0.211982i
\(506\) 0 0
\(507\) 3.55211i 0.157755i
\(508\) 0 0
\(509\) 8.25552 25.4079i 0.365920 1.12618i −0.583484 0.812125i \(-0.698311\pi\)
0.949403 0.314060i \(-0.101689\pi\)
\(510\) 0 0
\(511\) −0.237953 0.732343i −0.0105264 0.0323970i
\(512\) 0 0
\(513\) −6.30434 2.04840i −0.278343 0.0904392i
\(514\) 0 0
\(515\) 8.05689 21.2548i 0.355029 0.936598i
\(516\) 0 0
\(517\) −11.6691 + 16.0611i −0.513205 + 0.706366i
\(518\) 0 0
\(519\) −10.2531 7.44931i −0.450061 0.326988i
\(520\) 0 0
\(521\) −26.4607 + 19.2249i −1.15927 + 0.842256i −0.989685 0.143260i \(-0.954241\pi\)
−0.169581 + 0.985516i \(0.554241\pi\)
\(522\) 0 0
\(523\) 0.224417 0.0729175i 0.00981307 0.00318846i −0.304106 0.952638i \(-0.598358\pi\)
0.313919 + 0.949450i \(0.398358\pi\)
\(524\) 0 0
\(525\) 2.35746 + 10.6511i 0.102888 + 0.464853i
\(526\) 0 0
\(527\) −0.375867 + 0.122127i −0.0163730 + 0.00531992i
\(528\) 0 0
\(529\) −1.86142 + 1.35240i −0.0809313 + 0.0588001i
\(530\) 0 0
\(531\) 7.29413 + 5.29949i 0.316538 + 0.229978i
\(532\) 0 0
\(533\) −17.1215 + 23.5658i −0.741616 + 1.02075i
\(534\) 0 0
\(535\) −9.00915 + 5.90445i −0.389499 + 0.255271i
\(536\) 0 0
\(537\) 18.1256 + 5.88938i 0.782179 + 0.254145i
\(538\) 0 0
\(539\) −3.71756 11.4415i −0.160127 0.492820i
\(540\) 0 0
\(541\) −10.3698 + 31.9148i −0.445830 + 1.37213i 0.435740 + 0.900073i \(0.356487\pi\)
−0.881570 + 0.472053i \(0.843513\pi\)
\(542\) 0 0
\(543\) 31.4183i 1.34829i
\(544\) 0 0
\(545\) 35.1106 9.56578i 1.50397 0.409753i
\(546\) 0 0
\(547\) −22.6371 31.1573i −0.967892 1.33219i −0.943105 0.332496i \(-0.892109\pi\)
−0.0247869 0.999693i \(-0.507891\pi\)
\(548\) 0 0
\(549\) 5.07790 0.216720
\(550\) 0 0
\(551\) −13.9156 −0.592825
\(552\) 0 0
\(553\) −9.24607 12.7261i −0.393183 0.541170i
\(554\) 0 0
\(555\) −6.61426 + 8.23830i −0.280760 + 0.349697i
\(556\) 0 0
\(557\) 4.33445i 0.183657i −0.995775 0.0918283i \(-0.970729\pi\)
0.995775 0.0918283i \(-0.0292711\pi\)
\(558\) 0 0
\(559\) −4.84201 + 14.9022i −0.204795 + 0.630294i
\(560\) 0 0
\(561\) −3.93290 12.1042i −0.166047 0.511040i
\(562\) 0 0
\(563\) 33.1936 + 10.7853i 1.39894 + 0.454544i 0.908849 0.417125i \(-0.136962\pi\)
0.490094 + 0.871669i \(0.336962\pi\)
\(564\) 0 0
\(565\) −3.97169 14.5779i −0.167090 0.613295i
\(566\) 0 0
\(567\) −6.49749 + 8.94303i −0.272869 + 0.375572i
\(568\) 0 0
\(569\) −33.9501 24.6662i −1.42326 1.03406i −0.991223 0.132204i \(-0.957795\pi\)
−0.432038 0.901855i \(-0.642205\pi\)
\(570\) 0 0
\(571\) −11.1913 + 8.13093i −0.468340 + 0.340269i −0.796794 0.604251i \(-0.793472\pi\)
0.328454 + 0.944520i \(0.393472\pi\)
\(572\) 0 0
\(573\) −2.64782 + 0.860328i −0.110614 + 0.0359407i
\(574\) 0 0
\(575\) 2.18809 22.6427i 0.0912497 0.944265i
\(576\) 0 0
\(577\) 12.1538 3.94902i 0.505970 0.164400i −0.0448986 0.998992i \(-0.514296\pi\)
0.550869 + 0.834592i \(0.314296\pi\)
\(578\) 0 0
\(579\) 37.6586 27.3606i 1.56504 1.13707i
\(580\) 0 0
\(581\) 1.42196 + 1.03311i 0.0589928 + 0.0428608i
\(582\) 0 0
\(583\) −8.89344 + 12.2408i −0.368329 + 0.506961i
\(584\) 0 0
\(585\) −13.8160 0.666009i −0.571222 0.0275361i
\(586\) 0 0
\(587\) 11.5905 + 3.76597i 0.478390 + 0.155438i 0.538279 0.842767i \(-0.319075\pi\)
−0.0598889 + 0.998205i \(0.519075\pi\)
\(588\) 0 0
\(589\) 0.109046 + 0.335608i 0.00449315 + 0.0138285i
\(590\) 0 0
\(591\) −8.28923 + 25.5116i −0.340973 + 1.04941i
\(592\) 0 0
\(593\) 31.2580i 1.28361i 0.766866 + 0.641807i \(0.221815\pi\)
−0.766866 + 0.641807i \(0.778185\pi\)
\(594\) 0 0
\(595\) −0.309271 + 6.41567i −0.0126789 + 0.263017i
\(596\) 0 0
\(597\) −13.4477 18.5091i −0.550376 0.757528i
\(598\) 0 0
\(599\) −33.3707 −1.36349 −0.681746 0.731589i \(-0.738779\pi\)
−0.681746 + 0.731589i \(0.738779\pi\)
\(600\) 0 0
\(601\) −46.8052 −1.90922 −0.954611 0.297854i \(-0.903729\pi\)
−0.954611 + 0.297854i \(0.903729\pi\)
\(602\) 0 0
\(603\) 2.35544 + 3.24199i 0.0959211 + 0.132024i
\(604\) 0 0
\(605\) −14.6362 5.54805i −0.595047 0.225560i
\(606\) 0 0
\(607\) 30.7401i 1.24770i −0.781543 0.623851i \(-0.785567\pi\)
0.781543 0.623851i \(-0.214433\pi\)
\(608\) 0 0
\(609\) −3.63013 + 11.1724i −0.147100 + 0.452728i
\(610\) 0 0
\(611\) 10.3496 + 31.8527i 0.418699 + 1.28862i
\(612\) 0 0
\(613\) 36.4154 + 11.8321i 1.47081 + 0.477894i 0.931352 0.364121i \(-0.118631\pi\)
0.539454 + 0.842015i \(0.318631\pi\)
\(614\) 0 0
\(615\) 33.0941 + 26.5702i 1.33448 + 1.07141i
\(616\) 0 0
\(617\) 0.249989 0.344080i 0.0100642 0.0138521i −0.803955 0.594690i \(-0.797275\pi\)
0.814019 + 0.580838i \(0.197275\pi\)
\(618\) 0 0
\(619\) −6.07691 4.41513i −0.244252 0.177459i 0.458924 0.888476i \(-0.348235\pi\)
−0.703175 + 0.711016i \(0.748235\pi\)
\(620\) 0 0
\(621\) 9.44047 6.85890i 0.378833 0.275238i
\(622\) 0 0
\(623\) 13.6931 4.44914i 0.548601 0.178251i
\(624\) 0 0
\(625\) −17.0374 18.2955i −0.681496 0.731822i
\(626\) 0 0
\(627\) −10.8077 + 3.51165i −0.431619 + 0.140242i
\(628\) 0 0
\(629\) −5.03258 + 3.65638i −0.200662 + 0.145789i
\(630\) 0 0
\(631\) −9.11889 6.62526i −0.363017 0.263747i 0.391292 0.920266i \(-0.372028\pi\)
−0.754309 + 0.656519i \(0.772028\pi\)
\(632\) 0 0
\(633\) 11.1878 15.3987i 0.444676 0.612044i
\(634\) 0 0
\(635\) −2.59943 2.08700i −0.103155 0.0828201i
\(636\) 0 0
\(637\) −19.3021 6.27165i −0.764779 0.248492i
\(638\) 0 0
\(639\) 5.46290 + 16.8131i 0.216109 + 0.665115i
\(640\) 0 0
\(641\) 8.05994 24.8060i 0.318349 0.979776i −0.656006 0.754756i \(-0.727755\pi\)
0.974354 0.225020i \(-0.0722448\pi\)
\(642\) 0 0
\(643\) 31.9492i 1.25995i −0.776614 0.629977i \(-0.783064\pi\)
0.776614 0.629977i \(-0.216936\pi\)
\(644\) 0 0
\(645\) 21.3474 + 8.09201i 0.840555 + 0.318623i
\(646\) 0 0
\(647\) −4.34628 5.98214i −0.170870 0.235182i 0.714990 0.699134i \(-0.246431\pi\)
−0.885860 + 0.463952i \(0.846431\pi\)
\(648\) 0 0
\(649\) −9.83550 −0.386077
\(650\) 0 0
\(651\) 0.297895 0.0116754
\(652\) 0 0
\(653\) 10.9829 + 15.1167i 0.429796 + 0.591563i 0.967906 0.251311i \(-0.0808618\pi\)
−0.538111 + 0.842874i \(0.680862\pi\)
\(654\) 0 0
\(655\) 1.51967 31.5248i 0.0593784 1.23177i
\(656\) 0 0
\(657\) 1.42256i 0.0554994i
\(658\) 0 0
\(659\) 3.02885 9.32184i 0.117987 0.363128i −0.874571 0.484897i \(-0.838857\pi\)
0.992558 + 0.121770i \(0.0388570\pi\)
\(660\) 0 0
\(661\) −8.70145 26.7803i −0.338447 1.04163i −0.964999 0.262253i \(-0.915534\pi\)
0.626552 0.779380i \(-0.284466\pi\)
\(662\) 0 0
\(663\) −20.4202 6.63492i −0.793054 0.257679i
\(664\) 0 0
\(665\) 5.72850 + 0.276145i 0.222142 + 0.0107085i
\(666\) 0 0
\(667\) 14.3987 19.8181i 0.557521 0.767361i
\(668\) 0 0
\(669\) −50.4120 36.6265i −1.94904 1.41606i
\(670\) 0 0
\(671\) −4.48150 + 3.25600i −0.173006 + 0.125696i
\(672\) 0 0
\(673\) −37.1153 + 12.0595i −1.43069 + 0.464859i −0.918981 0.394301i \(-0.870987\pi\)
−0.511707 + 0.859160i \(0.670987\pi\)
\(674\) 0 0
\(675\) 1.23353 12.7647i 0.0474785 0.491314i
\(676\) 0 0
\(677\) −4.78888 + 1.55600i −0.184052 + 0.0598020i −0.399593 0.916693i \(-0.630848\pi\)
0.215541 + 0.976495i \(0.430848\pi\)
\(678\) 0 0
\(679\) 13.6721 9.93337i 0.524687 0.381208i
\(680\) 0 0
\(681\) 39.5590 + 28.7413i 1.51591 + 1.10137i
\(682\) 0 0
\(683\) −17.8282 + 24.5384i −0.682178 + 0.938937i −0.999957 0.00922734i \(-0.997063\pi\)
0.317780 + 0.948165i \(0.397063\pi\)
\(684\) 0 0
\(685\) −0.405247 1.48743i −0.0154837 0.0568320i
\(686\) 0 0
\(687\) −5.17619 1.68185i −0.197484 0.0641664i
\(688\) 0 0
\(689\) 7.88781 + 24.2762i 0.300502 + 0.924849i
\(690\) 0 0
\(691\) 6.56134 20.1937i 0.249605 0.768205i −0.745240 0.666796i \(-0.767665\pi\)
0.994845 0.101409i \(-0.0323349\pi\)
\(692\) 0 0
\(693\) 3.63886i 0.138229i
\(694\) 0 0
\(695\) −23.1991 + 28.8953i −0.879991 + 1.09606i
\(696\) 0 0
\(697\) 14.6881 + 20.2164i 0.556350 + 0.765751i
\(698\) 0 0
\(699\) −13.0943 −0.495273
\(700\) 0 0
\(701\) 32.7698 1.23770 0.618849 0.785510i \(-0.287599\pi\)
0.618849 + 0.785510i \(0.287599\pi\)
\(702\) 0 0
\(703\) 3.26475 + 4.49354i 0.123132 + 0.169477i
\(704\) 0 0
\(705\) 47.0814 12.8272i 1.77319 0.483099i
\(706\) 0 0
\(707\) 2.52780i 0.0950676i
\(708\) 0 0
\(709\) −6.13273 + 18.8746i −0.230320 + 0.708851i 0.767388 + 0.641183i \(0.221556\pi\)
−0.997708 + 0.0676683i \(0.978444\pi\)
\(710\) 0 0
\(711\) −8.98015 27.6381i −0.336782 1.03651i
\(712\) 0 0
\(713\) −0.590793 0.191960i −0.0221254 0.00718897i
\(714\) 0 0
\(715\) 12.6204 8.27117i 0.471975 0.309324i
\(716\) 0 0
\(717\) −9.08759 + 12.5080i −0.339382 + 0.467120i
\(718\) 0 0
\(719\) −19.5945 14.2362i −0.730751 0.530922i 0.159050 0.987271i \(-0.449157\pi\)
−0.889801 + 0.456349i \(0.849157\pi\)
\(720\) 0 0
\(721\) −8.16149 + 5.92967i −0.303950 + 0.220832i
\(722\) 0 0
\(723\) −2.46676 + 0.801498i −0.0917397 + 0.0298080i
\(724\) 0 0
\(725\) −5.81785 26.2853i −0.216069 0.976213i
\(726\) 0 0
\(727\) −5.57804 + 1.81242i −0.206878 + 0.0672188i −0.410623 0.911805i \(-0.634689\pi\)
0.203745 + 0.979024i \(0.434689\pi\)
\(728\) 0 0
\(729\) −2.83585 + 2.06037i −0.105032 + 0.0763099i
\(730\) 0 0
\(731\) 10.8748 + 7.90103i 0.402220 + 0.292230i
\(732\) 0 0
\(733\) 20.2795 27.9123i 0.749039 1.03096i −0.249008 0.968501i \(-0.580105\pi\)
0.998047 0.0624625i \(-0.0198954\pi\)
\(734\) 0 0
\(735\) −10.4812 + 27.6504i −0.386607 + 1.01990i
\(736\) 0 0
\(737\) −4.15759 1.35088i −0.153147 0.0497604i
\(738\) 0 0
\(739\) 12.2282 + 37.6345i 0.449821 + 1.38441i 0.877109 + 0.480291i \(0.159469\pi\)
−0.427288 + 0.904116i \(0.640531\pi\)
\(740\) 0 0
\(741\) −5.92426 + 18.2330i −0.217633 + 0.669805i
\(742\) 0 0
\(743\) 29.7058i 1.08980i 0.838501 + 0.544900i \(0.183433\pi\)
−0.838501 + 0.544900i \(0.816567\pi\)
\(744\) 0 0
\(745\) 3.93641 + 6.00627i 0.144219 + 0.220053i
\(746\) 0 0
\(747\) 1.90858 + 2.62694i 0.0698314 + 0.0961147i
\(748\) 0 0
\(749\) 4.78058 0.174679
\(750\) 0 0
\(751\) −26.8870 −0.981122 −0.490561 0.871407i \(-0.663208\pi\)
−0.490561 + 0.871407i \(0.663208\pi\)
\(752\) 0 0
\(753\) 5.95552 + 8.19707i 0.217031 + 0.298718i
\(754\) 0 0
\(755\) 21.6781 + 33.0771i 0.788949 + 1.20380i
\(756\) 0 0
\(757\) 44.6792i 1.62389i −0.583731 0.811947i \(-0.698408\pi\)
0.583731 0.811947i \(-0.301592\pi\)
\(758\) 0 0
\(759\) 6.18178 19.0256i 0.224384 0.690584i
\(760\) 0 0
\(761\) 6.27550 + 19.3140i 0.227487 + 0.700132i 0.998030 + 0.0627441i \(0.0199852\pi\)
−0.770543 + 0.637388i \(0.780015\pi\)
\(762\) 0 0
\(763\) −15.3601 4.99080i −0.556073 0.180679i
\(764\) 0 0
\(765\) −4.20597 + 11.0957i −0.152067 + 0.401167i
\(766\) 0 0
\(767\) −9.75300 + 13.4239i −0.352160 + 0.484707i
\(768\) 0 0
\(769\) 21.0811 + 15.3163i 0.760205 + 0.552321i 0.898973 0.438004i \(-0.144314\pi\)
−0.138768 + 0.990325i \(0.544314\pi\)
\(770\) 0 0
\(771\) 17.3511 12.6063i 0.624886 0.454007i
\(772\) 0 0
\(773\) −13.0585 + 4.24295i −0.469680 + 0.152608i −0.534288 0.845302i \(-0.679420\pi\)
0.0646079 + 0.997911i \(0.479420\pi\)
\(774\) 0 0
\(775\) −0.588343 + 0.346289i −0.0211339 + 0.0124391i
\(776\) 0 0
\(777\) 4.45938 1.44894i 0.159979 0.0519805i
\(778\) 0 0
\(779\) 18.0510 13.1148i 0.646745 0.469888i
\(780\) 0 0
\(781\) −15.6020 11.3355i −0.558282 0.405616i
\(782\) 0 0
\(783\) 8.11722 11.1724i 0.290086 0.399269i
\(784\) 0 0
\(785\) −3.09541 + 2.02868i −0.110480 + 0.0724068i
\(786\) 0 0
\(787\) −18.7035 6.07714i −0.666708 0.216627i −0.0439412 0.999034i \(-0.513991\pi\)
−0.622767 + 0.782408i \(0.713991\pi\)
\(788\) 0 0
\(789\) 0.676537 + 2.08217i 0.0240853 + 0.0741271i
\(790\) 0 0
\(791\) −2.07217 + 6.37748i −0.0736779 + 0.226757i
\(792\) 0 0
\(793\)