Properties

Label 804.2.s.b.161.10
Level 804
Weight 2
Character 804.161
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 161.10
Character \(\chi\) = 804.161
Dual form 804.2.s.b.5.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.393301 - 1.68681i) q^{3} +(3.45254 + 1.01376i) q^{5} +(-0.403229 + 0.349400i) q^{7} +(-2.69063 + 1.32685i) q^{9} +O(q^{10})\) \(q+(-0.393301 - 1.68681i) q^{3} +(3.45254 + 1.01376i) q^{5} +(-0.403229 + 0.349400i) q^{7} +(-2.69063 + 1.32685i) q^{9} +(-0.843418 - 0.247650i) q^{11} +(2.49538 - 3.88288i) q^{13} +(0.352124 - 6.22247i) q^{15} +(6.49699 - 0.934126i) q^{17} +(-1.01843 + 1.17533i) q^{19} +(0.747960 + 0.542749i) q^{21} +(-1.87132 - 0.854604i) q^{23} +(6.68605 + 4.29687i) q^{25} +(3.29636 + 4.01672i) q^{27} -3.54360i q^{29} +(2.94854 + 4.58802i) q^{31} +(-0.0860200 + 1.52008i) q^{33} +(-1.74637 + 0.797540i) q^{35} +6.30938 q^{37} +(-7.53110 - 2.68207i) q^{39} +(-1.58851 - 11.0483i) q^{41} +(4.21011 - 0.605322i) q^{43} +(-10.6346 + 1.85334i) q^{45} +(-8.24517 - 3.76544i) q^{47} +(-0.955691 + 6.64697i) q^{49} +(-4.13096 - 10.5918i) q^{51} +(-0.880650 + 6.12505i) q^{53} +(-2.66088 - 1.71004i) q^{55} +(2.38311 + 1.25564i) q^{57} +(0.431424 + 0.671308i) q^{59} +(-1.65734 - 5.64439i) q^{61} +(0.621339 - 1.47513i) q^{63} +(12.5517 - 10.8761i) q^{65} +(4.80367 - 6.62757i) q^{67} +(-0.705558 + 3.49267i) q^{69} +(-3.24010 - 0.465856i) q^{71} +(-4.50675 + 1.32330i) q^{73} +(4.61835 - 12.9680i) q^{75} +(0.426619 - 0.194830i) q^{77} +(-1.15200 + 1.79255i) q^{79} +(5.47896 - 7.14010i) q^{81} +(-0.393211 + 1.33915i) q^{83} +(23.3781 + 3.36126i) q^{85} +(-5.97736 + 1.39370i) q^{87} +(0.163010 - 0.0744440i) q^{89} +(0.350470 + 2.43757i) q^{91} +(6.57944 - 6.77810i) q^{93} +(-4.70767 + 3.02544i) q^{95} +3.07848i q^{97} +(2.59792 - 0.452751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{17}{22}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.393301 1.68681i −0.227073 0.973878i
\(4\) 0 0
\(5\) 3.45254 + 1.01376i 1.54402 + 0.453366i 0.939308 0.343076i \(-0.111469\pi\)
0.604715 + 0.796442i \(0.293287\pi\)
\(6\) 0 0
\(7\) −0.403229 + 0.349400i −0.152406 + 0.132061i −0.727726 0.685868i \(-0.759423\pi\)
0.575320 + 0.817928i \(0.304877\pi\)
\(8\) 0 0
\(9\) −2.69063 + 1.32685i −0.896876 + 0.442282i
\(10\) 0 0
\(11\) −0.843418 0.247650i −0.254300 0.0746692i 0.152098 0.988365i \(-0.451397\pi\)
−0.406398 + 0.913696i \(0.633215\pi\)
\(12\) 0 0
\(13\) 2.49538 3.88288i 0.692093 1.07692i −0.300305 0.953843i \(-0.597088\pi\)
0.992397 0.123074i \(-0.0392753\pi\)
\(14\) 0 0
\(15\) 0.352124 6.22247i 0.0909179 1.60664i
\(16\) 0 0
\(17\) 6.49699 0.934126i 1.57575 0.226559i 0.701729 0.712444i \(-0.252412\pi\)
0.874023 + 0.485885i \(0.161503\pi\)
\(18\) 0 0
\(19\) −1.01843 + 1.17533i −0.233644 + 0.269640i −0.860449 0.509537i \(-0.829817\pi\)
0.626805 + 0.779176i \(0.284362\pi\)
\(20\) 0 0
\(21\) 0.747960 + 0.542749i 0.163218 + 0.118438i
\(22\) 0 0
\(23\) −1.87132 0.854604i −0.390198 0.178197i 0.210649 0.977562i \(-0.432442\pi\)
−0.600846 + 0.799365i \(0.705170\pi\)
\(24\) 0 0
\(25\) 6.68605 + 4.29687i 1.33721 + 0.859373i
\(26\) 0 0
\(27\) 3.29636 + 4.01672i 0.634384 + 0.773018i
\(28\) 0 0
\(29\) 3.54360i 0.658030i −0.944325 0.329015i \(-0.893283\pi\)
0.944325 0.329015i \(-0.106717\pi\)
\(30\) 0 0
\(31\) 2.94854 + 4.58802i 0.529574 + 0.824033i 0.998238 0.0593434i \(-0.0189007\pi\)
−0.468664 + 0.883377i \(0.655264\pi\)
\(32\) 0 0
\(33\) −0.0860200 + 1.52008i −0.0149742 + 0.264613i
\(34\) 0 0
\(35\) −1.74637 + 0.797540i −0.295190 + 0.134809i
\(36\) 0 0
\(37\) 6.30938 1.03726 0.518628 0.855000i \(-0.326443\pi\)
0.518628 + 0.855000i \(0.326443\pi\)
\(38\) 0 0
\(39\) −7.53110 2.68207i −1.20594 0.429475i
\(40\) 0 0
\(41\) −1.58851 11.0483i −0.248084 1.72546i −0.609266 0.792966i \(-0.708536\pi\)
0.361182 0.932495i \(-0.382373\pi\)
\(42\) 0 0
\(43\) 4.21011 0.605322i 0.642035 0.0923107i 0.186395 0.982475i \(-0.440320\pi\)
0.455640 + 0.890164i \(0.349410\pi\)
\(44\) 0 0
\(45\) −10.6346 + 1.85334i −1.58531 + 0.276280i
\(46\) 0 0
\(47\) −8.24517 3.76544i −1.20268 0.549246i −0.289649 0.957133i \(-0.593538\pi\)
−0.913032 + 0.407887i \(0.866266\pi\)
\(48\) 0 0
\(49\) −0.955691 + 6.64697i −0.136527 + 0.949568i
\(50\) 0 0
\(51\) −4.13096 10.5918i −0.578451 1.48314i
\(52\) 0 0
\(53\) −0.880650 + 6.12505i −0.120967 + 0.841341i 0.835498 + 0.549493i \(0.185179\pi\)
−0.956465 + 0.291848i \(0.905730\pi\)
\(54\) 0 0
\(55\) −2.66088 1.71004i −0.358792 0.230582i
\(56\) 0 0
\(57\) 2.38311 + 1.25564i 0.315650 + 0.166313i
\(58\) 0 0
\(59\) 0.431424 + 0.671308i 0.0561666 + 0.0873969i 0.868201 0.496212i \(-0.165276\pi\)
−0.812035 + 0.583609i \(0.801640\pi\)
\(60\) 0 0
\(61\) −1.65734 5.64439i −0.212201 0.722689i −0.994952 0.100354i \(-0.968002\pi\)
0.782751 0.622335i \(-0.213816\pi\)
\(62\) 0 0
\(63\) 0.621339 1.47513i 0.0782814 0.185849i
\(64\) 0 0
\(65\) 12.5517 10.8761i 1.55684 1.34901i
\(66\) 0 0
\(67\) 4.80367 6.62757i 0.586862 0.809687i
\(68\) 0 0
\(69\) −0.705558 + 3.49267i −0.0849392 + 0.420468i
\(70\) 0 0
\(71\) −3.24010 0.465856i −0.384529 0.0552869i −0.0526601 0.998612i \(-0.516770\pi\)
−0.331869 + 0.943326i \(0.607679\pi\)
\(72\) 0 0
\(73\) −4.50675 + 1.32330i −0.527475 + 0.154881i −0.534618 0.845094i \(-0.679545\pi\)
0.00714274 + 0.999974i \(0.497726\pi\)
\(74\) 0 0
\(75\) 4.61835 12.9680i 0.533281 1.49742i
\(76\) 0 0
\(77\) 0.426619 0.194830i 0.0486178 0.0222030i
\(78\) 0 0
\(79\) −1.15200 + 1.79255i −0.129610 + 0.201678i −0.899993 0.435904i \(-0.856429\pi\)
0.770383 + 0.637582i \(0.220065\pi\)
\(80\) 0 0
\(81\) 5.47896 7.14010i 0.608774 0.793344i
\(82\) 0 0
\(83\) −0.393211 + 1.33915i −0.0431605 + 0.146991i −0.978254 0.207409i \(-0.933497\pi\)
0.935094 + 0.354400i \(0.115315\pi\)
\(84\) 0 0
\(85\) 23.3781 + 3.36126i 2.53571 + 0.364580i
\(86\) 0 0
\(87\) −5.97736 + 1.39370i −0.640841 + 0.149420i
\(88\) 0 0
\(89\) 0.163010 0.0744440i 0.0172790 0.00789105i −0.406757 0.913536i \(-0.633340\pi\)
0.424036 + 0.905645i \(0.360613\pi\)
\(90\) 0 0
\(91\) 0.350470 + 2.43757i 0.0367392 + 0.255527i
\(92\) 0 0
\(93\) 6.57944 6.77810i 0.682256 0.702856i
\(94\) 0 0
\(95\) −4.70767 + 3.02544i −0.482997 + 0.310403i
\(96\) 0 0
\(97\) 3.07848i 0.312572i 0.987712 + 0.156286i \(0.0499522\pi\)
−0.987712 + 0.156286i \(0.950048\pi\)
\(98\) 0 0
\(99\) 2.59792 0.452751i 0.261100 0.0455032i
\(100\) 0 0
\(101\) 2.92667 3.37755i 0.291214 0.336079i −0.591224 0.806507i \(-0.701355\pi\)
0.882438 + 0.470428i \(0.155901\pi\)
\(102\) 0 0
\(103\) 1.49986 0.963903i 0.147786 0.0949762i −0.464658 0.885490i \(-0.653823\pi\)
0.612444 + 0.790514i \(0.290186\pi\)
\(104\) 0 0
\(105\) 2.03214 + 2.63211i 0.198317 + 0.256868i
\(106\) 0 0
\(107\) 1.95591 + 6.66122i 0.189085 + 0.643965i 0.998398 + 0.0565865i \(0.0180217\pi\)
−0.809313 + 0.587378i \(0.800160\pi\)
\(108\) 0 0
\(109\) −10.3159 + 16.0519i −0.988088 + 1.53750i −0.152380 + 0.988322i \(0.548694\pi\)
−0.835709 + 0.549173i \(0.814943\pi\)
\(110\) 0 0
\(111\) −2.48149 10.6427i −0.235532 1.01016i
\(112\) 0 0
\(113\) −14.7239 + 4.32334i −1.38511 + 0.406705i −0.887545 0.460721i \(-0.847591\pi\)
−0.497566 + 0.867426i \(0.665773\pi\)
\(114\) 0 0
\(115\) −5.59445 4.84762i −0.521685 0.452043i
\(116\) 0 0
\(117\) −1.56215 + 13.7584i −0.144421 + 1.27196i
\(118\) 0 0
\(119\) −2.29339 + 2.64671i −0.210235 + 0.242624i
\(120\) 0 0
\(121\) −8.60377 5.52930i −0.782161 0.502664i
\(122\) 0 0
\(123\) −18.0116 + 7.02484i −1.62406 + 0.633408i
\(124\) 0 0
\(125\) 6.94597 + 8.01608i 0.621266 + 0.716980i
\(126\) 0 0
\(127\) 12.7273 + 14.6881i 1.12937 + 1.30336i 0.947398 + 0.320058i \(0.103702\pi\)
0.181971 + 0.983304i \(0.441752\pi\)
\(128\) 0 0
\(129\) −2.67690 6.86356i −0.235688 0.604303i
\(130\) 0 0
\(131\) −11.7755 5.37767i −1.02883 0.469849i −0.171806 0.985131i \(-0.554960\pi\)
−0.857021 + 0.515281i \(0.827687\pi\)
\(132\) 0 0
\(133\) 0.829767i 0.0719500i
\(134\) 0 0
\(135\) 7.30883 + 17.2096i 0.629044 + 1.48116i
\(136\) 0 0
\(137\) −7.14425 + 15.6437i −0.610374 + 1.33653i 0.311944 + 0.950101i \(0.399020\pi\)
−0.922318 + 0.386432i \(0.873707\pi\)
\(138\) 0 0
\(139\) 5.06115 17.2367i 0.429281 1.46200i −0.406864 0.913489i \(-0.633378\pi\)
0.836145 0.548509i \(-0.184804\pi\)
\(140\) 0 0
\(141\) −3.10874 + 15.3889i −0.261803 + 1.29598i
\(142\) 0 0
\(143\) −3.06624 + 2.65691i −0.256412 + 0.222182i
\(144\) 0 0
\(145\) 3.59235 12.2344i 0.298328 1.01601i
\(146\) 0 0
\(147\) 11.5880 1.00220i 0.955765 0.0826599i
\(148\) 0 0
\(149\) −5.57355 4.82951i −0.456603 0.395649i 0.395965 0.918266i \(-0.370410\pi\)
−0.852568 + 0.522617i \(0.824956\pi\)
\(150\) 0 0
\(151\) 2.82914 + 19.6771i 0.230232 + 1.60130i 0.697101 + 0.716973i \(0.254473\pi\)
−0.466869 + 0.884327i \(0.654618\pi\)
\(152\) 0 0
\(153\) −16.2415 + 11.1339i −1.31305 + 0.900122i
\(154\) 0 0
\(155\) 5.52882 + 18.8294i 0.444086 + 1.51242i
\(156\) 0 0
\(157\) −5.31680 + 11.6422i −0.424327 + 0.929146i 0.569886 + 0.821723i \(0.306987\pi\)
−0.994213 + 0.107423i \(0.965740\pi\)
\(158\) 0 0
\(159\) 10.6781 0.923505i 0.846831 0.0732387i
\(160\) 0 0
\(161\) 1.05317 0.309238i 0.0830014 0.0243714i
\(162\) 0 0
\(163\) 13.1841 1.03266 0.516328 0.856391i \(-0.327299\pi\)
0.516328 + 0.856391i \(0.327299\pi\)
\(164\) 0 0
\(165\) −1.83798 + 5.16094i −0.143087 + 0.401779i
\(166\) 0 0
\(167\) −16.9979 14.7288i −1.31534 1.13975i −0.980294 0.197542i \(-0.936704\pi\)
−0.335042 0.942203i \(-0.608750\pi\)
\(168\) 0 0
\(169\) −3.44947 7.55328i −0.265344 0.581022i
\(170\) 0 0
\(171\) 1.18074 4.51368i 0.0902931 0.345170i
\(172\) 0 0
\(173\) 3.64796 + 5.67634i 0.277349 + 0.431564i 0.951783 0.306771i \(-0.0992487\pi\)
−0.674434 + 0.738335i \(0.735612\pi\)
\(174\) 0 0
\(175\) −4.19733 + 0.603485i −0.317289 + 0.0456192i
\(176\) 0 0
\(177\) 0.962688 0.991754i 0.0723600 0.0745448i
\(178\) 0 0
\(179\) 7.58099 + 16.6001i 0.566630 + 1.24075i 0.948572 + 0.316560i \(0.102528\pi\)
−0.381942 + 0.924186i \(0.624745\pi\)
\(180\) 0 0
\(181\) −7.25678 + 15.8901i −0.539392 + 1.18110i 0.422170 + 0.906517i \(0.361269\pi\)
−0.961562 + 0.274587i \(0.911459\pi\)
\(182\) 0 0
\(183\) −8.86915 + 5.01556i −0.655626 + 0.370761i
\(184\) 0 0
\(185\) 21.7834 + 6.39618i 1.60155 + 0.470256i
\(186\) 0 0
\(187\) −5.71101 0.821120i −0.417631 0.0600462i
\(188\) 0 0
\(189\) −2.73263 0.467910i −0.198769 0.0340354i
\(190\) 0 0
\(191\) 4.54526 + 9.95273i 0.328883 + 0.720154i 0.999771 0.0214049i \(-0.00681392\pi\)
−0.670887 + 0.741559i \(0.734087\pi\)
\(192\) 0 0
\(193\) −10.0851 + 6.48129i −0.725941 + 0.466534i −0.850699 0.525653i \(-0.823821\pi\)
0.124758 + 0.992187i \(0.460185\pi\)
\(194\) 0 0
\(195\) −23.2824 16.8947i −1.66729 1.20985i
\(196\) 0 0
\(197\) −1.10270 + 7.66945i −0.0785642 + 0.546426i 0.912086 + 0.409999i \(0.134471\pi\)
−0.990650 + 0.136427i \(0.956438\pi\)
\(198\) 0 0
\(199\) 0.317248 + 0.366124i 0.0224891 + 0.0259538i 0.766883 0.641787i \(-0.221807\pi\)
−0.744394 + 0.667741i \(0.767261\pi\)
\(200\) 0 0
\(201\) −13.0687 5.49623i −0.921797 0.387674i
\(202\) 0 0
\(203\) 1.23813 + 1.42888i 0.0868999 + 0.100288i
\(204\) 0 0
\(205\) 5.71593 39.7552i 0.399218 2.77662i
\(206\) 0 0
\(207\) 6.16896 0.183533i 0.428772 0.0127564i
\(208\) 0 0
\(209\) 1.15003 0.739082i 0.0795495 0.0511234i
\(210\) 0 0
\(211\) 4.84812 + 10.6159i 0.333758 + 0.730828i 0.999887 0.0150079i \(-0.00477734\pi\)
−0.666129 + 0.745836i \(0.732050\pi\)
\(212\) 0 0
\(213\) 0.488526 + 5.64864i 0.0334732 + 0.387038i
\(214\) 0 0
\(215\) 15.1492 + 2.17813i 1.03317 + 0.148547i
\(216\) 0 0
\(217\) −2.79199 0.819803i −0.189533 0.0556518i
\(218\) 0 0
\(219\) 4.00466 + 7.08156i 0.270610 + 0.478527i
\(220\) 0 0
\(221\) 12.5853 27.5580i 0.846581 1.85375i
\(222\) 0 0
\(223\) −11.2385 24.6088i −0.752584 1.64793i −0.761665 0.647971i \(-0.775618\pi\)
0.00908061 0.999959i \(-0.497110\pi\)
\(224\) 0 0
\(225\) −23.6910 2.68991i −1.57940 0.179327i
\(226\) 0 0
\(227\) 10.3756 1.49178i 0.688652 0.0990132i 0.210899 0.977508i \(-0.432361\pi\)
0.477752 + 0.878495i \(0.341452\pi\)
\(228\) 0 0
\(229\) 3.49616 + 5.44013i 0.231033 + 0.359494i 0.937343 0.348409i \(-0.113278\pi\)
−0.706310 + 0.707903i \(0.749641\pi\)
\(230\) 0 0
\(231\) −0.496431 0.642997i −0.0326628 0.0423061i
\(232\) 0 0
\(233\) −2.37287 5.19586i −0.155452 0.340392i 0.815842 0.578275i \(-0.196274\pi\)
−0.971294 + 0.237883i \(0.923547\pi\)
\(234\) 0 0
\(235\) −24.6495 21.3589i −1.60796 1.39330i
\(236\) 0 0
\(237\) 3.47677 + 1.23819i 0.225840 + 0.0804292i
\(238\) 0 0
\(239\) 3.72434 0.240907 0.120454 0.992719i \(-0.461565\pi\)
0.120454 + 0.992719i \(0.461565\pi\)
\(240\) 0 0
\(241\) 1.00745 0.295814i 0.0648955 0.0190550i −0.249124 0.968472i \(-0.580143\pi\)
0.314019 + 0.949417i \(0.398324\pi\)
\(242\) 0 0
\(243\) −14.1988 6.43374i −0.910856 0.412724i
\(244\) 0 0
\(245\) −10.0380 + 21.9801i −0.641303 + 1.40426i
\(246\) 0 0
\(247\) 2.02231 + 6.88734i 0.128676 + 0.438231i
\(248\) 0 0
\(249\) 2.41354 + 0.136580i 0.152952 + 0.00865541i
\(250\) 0 0
\(251\) −1.48784 10.3481i −0.0939115 0.653169i −0.981348 0.192239i \(-0.938425\pi\)
0.887437 0.460930i \(-0.152484\pi\)
\(252\) 0 0
\(253\) 1.36666 + 1.18422i 0.0859214 + 0.0744513i
\(254\) 0 0
\(255\) −3.52483 40.7563i −0.220734 2.55226i
\(256\) 0 0
\(257\) 4.05802 13.8203i 0.253132 0.862089i −0.730655 0.682747i \(-0.760785\pi\)
0.983787 0.179342i \(-0.0573968\pi\)
\(258\) 0 0
\(259\) −2.54412 + 2.20450i −0.158084 + 0.136981i
\(260\) 0 0
\(261\) 4.70181 + 9.53451i 0.291035 + 0.590171i
\(262\) 0 0
\(263\) 6.35551 21.6449i 0.391898 1.33468i −0.493460 0.869769i \(-0.664268\pi\)
0.885357 0.464912i \(-0.153914\pi\)
\(264\) 0 0
\(265\) −9.24979 + 20.2542i −0.568210 + 1.24421i
\(266\) 0 0
\(267\) −0.189684 0.245687i −0.0116085 0.0150358i
\(268\) 0 0
\(269\) 23.7751i 1.44960i 0.688962 + 0.724798i \(0.258067\pi\)
−0.688962 + 0.724798i \(0.741933\pi\)
\(270\) 0 0
\(271\) 27.9570 + 12.7676i 1.69827 + 0.775574i 0.998101 + 0.0615959i \(0.0196190\pi\)
0.700168 + 0.713978i \(0.253108\pi\)
\(272\) 0 0
\(273\) 3.97387 1.54988i 0.240510 0.0938027i
\(274\) 0 0
\(275\) −4.57502 5.27985i −0.275884 0.318387i
\(276\) 0 0
\(277\) 3.85148 + 4.44485i 0.231413 + 0.267065i 0.859566 0.511025i \(-0.170734\pi\)
−0.628153 + 0.778090i \(0.716189\pi\)
\(278\) 0 0
\(279\) −14.0210 8.43240i −0.839417 0.504835i
\(280\) 0 0
\(281\) 4.93616 + 3.17228i 0.294467 + 0.189242i 0.679530 0.733648i \(-0.262184\pi\)
−0.385063 + 0.922890i \(0.625820\pi\)
\(282\) 0 0
\(283\) −17.6010 + 20.3126i −1.04627 + 1.20746i −0.0685298 + 0.997649i \(0.521831\pi\)
−0.977742 + 0.209813i \(0.932715\pi\)
\(284\) 0 0
\(285\) 6.95486 + 6.75102i 0.411970 + 0.399896i
\(286\) 0 0
\(287\) 4.50082 + 3.89998i 0.265675 + 0.230209i
\(288\) 0 0
\(289\) 25.0269 7.34856i 1.47217 0.432268i
\(290\) 0 0
\(291\) 5.19279 1.21077i 0.304407 0.0709765i
\(292\) 0 0
\(293\) −3.40318 + 5.29545i −0.198816 + 0.309364i −0.926319 0.376741i \(-0.877045\pi\)
0.727503 + 0.686105i \(0.240681\pi\)
\(294\) 0 0
\(295\) 0.808964 + 2.75508i 0.0470997 + 0.160407i
\(296\) 0 0
\(297\) −1.78547 4.20411i −0.103603 0.243947i
\(298\) 0 0
\(299\) −7.98798 + 5.13356i −0.461957 + 0.296881i
\(300\) 0 0
\(301\) −1.48614 + 1.71509i −0.0856595 + 0.0988563i
\(302\) 0 0
\(303\) −6.84834 3.60832i −0.393427 0.207293i
\(304\) 0 0
\(305\) 21.1676i 1.21205i
\(306\) 0 0
\(307\) −25.9210 + 16.6584i −1.47939 + 0.950747i −0.482184 + 0.876070i \(0.660156\pi\)
−0.997208 + 0.0746775i \(0.976207\pi\)
\(308\) 0 0
\(309\) −2.21581 2.15087i −0.126053 0.122359i
\(310\) 0 0
\(311\) −3.85323 26.7998i −0.218497 1.51968i −0.743591 0.668635i \(-0.766879\pi\)
0.525094 0.851044i \(-0.324030\pi\)
\(312\) 0 0
\(313\) 0.0443396 0.0202492i 0.00250622 0.00114455i −0.414162 0.910203i \(-0.635925\pi\)
0.416668 + 0.909059i \(0.363198\pi\)
\(314\) 0 0
\(315\) 3.64062 4.46305i 0.205126 0.251464i
\(316\) 0 0
\(317\) −24.3438 3.50011i −1.36728 0.196586i −0.580725 0.814100i \(-0.697231\pi\)
−0.786560 + 0.617514i \(0.788140\pi\)
\(318\) 0 0
\(319\) −0.877571 + 2.98873i −0.0491346 + 0.167337i
\(320\) 0 0
\(321\) 10.4669 5.91911i 0.584207 0.330372i
\(322\) 0 0
\(323\) −5.51883 + 8.58747i −0.307076 + 0.477819i
\(324\) 0 0
\(325\) 33.3684 15.2389i 1.85095 0.845299i
\(326\) 0 0
\(327\) 31.1337 + 11.0878i 1.72170 + 0.613154i
\(328\) 0 0
\(329\) 4.64033 1.36252i 0.255830 0.0751184i
\(330\) 0 0
\(331\) −28.6734 4.12262i −1.57603 0.226600i −0.701897 0.712278i \(-0.747663\pi\)
−0.874137 + 0.485679i \(0.838572\pi\)
\(332\) 0 0
\(333\) −16.9762 + 8.37157i −0.930290 + 0.458759i
\(334\) 0 0
\(335\) 23.3036 18.0122i 1.27321 0.984112i
\(336\) 0 0
\(337\) 18.6056 16.1218i 1.01351 0.878213i 0.0209282 0.999781i \(-0.493338\pi\)
0.992583 + 0.121568i \(0.0387924\pi\)
\(338\) 0 0
\(339\) 13.0836 + 23.1360i 0.710602 + 1.25658i
\(340\) 0 0
\(341\) −1.35063 4.59983i −0.0731408 0.249095i
\(342\) 0 0
\(343\) −3.95629 6.15611i −0.213620 0.332399i
\(344\) 0 0
\(345\) −5.97669 + 11.3433i −0.321774 + 0.610704i
\(346\) 0 0
\(347\) −10.9803 7.05658i −0.589451 0.378817i 0.211651 0.977345i \(-0.432116\pi\)
−0.801102 + 0.598528i \(0.795752\pi\)
\(348\) 0 0
\(349\) 3.55366 24.7162i 0.190223 1.32303i −0.641194 0.767379i \(-0.721561\pi\)
0.831417 0.555650i \(-0.187530\pi\)
\(350\) 0 0
\(351\) 23.8221 2.77614i 1.27153 0.148180i
\(352\) 0 0
\(353\) −5.20707 + 36.2159i −0.277144 + 1.92758i 0.0869396 + 0.996214i \(0.472291\pi\)
−0.364084 + 0.931366i \(0.618618\pi\)
\(354\) 0 0
\(355\) −10.7143 4.89305i −0.568656 0.259696i
\(356\) 0 0
\(357\) 5.36648 + 2.82755i 0.284024 + 0.149650i
\(358\) 0 0
\(359\) 12.3469 1.77521i 0.651643 0.0936921i 0.191438 0.981505i \(-0.438685\pi\)
0.460205 + 0.887813i \(0.347776\pi\)
\(360\) 0 0
\(361\) 2.35978 + 16.4126i 0.124199 + 0.863822i
\(362\) 0 0
\(363\) −5.94299 + 16.6876i −0.311926 + 0.875870i
\(364\) 0 0
\(365\) −16.9012 −0.884651
\(366\) 0 0
\(367\) 29.9811 13.6919i 1.56500 0.714712i 0.570683 0.821170i \(-0.306678\pi\)
0.994317 + 0.106459i \(0.0339512\pi\)
\(368\) 0 0
\(369\) 18.9335 + 27.6193i 0.985641 + 1.43780i
\(370\) 0 0
\(371\) −1.78499 2.77750i −0.0926720 0.144200i
\(372\) 0 0
\(373\) 34.5460i 1.78872i 0.447344 + 0.894362i \(0.352370\pi\)
−0.447344 + 0.894362i \(0.647630\pi\)
\(374\) 0 0
\(375\) 10.7897 14.8692i 0.557178 0.767844i
\(376\) 0 0
\(377\) −13.7594 8.84261i −0.708644 0.455418i
\(378\) 0 0
\(379\) −6.63231 3.02887i −0.340679 0.155583i 0.237727 0.971332i \(-0.423598\pi\)
−0.578406 + 0.815749i \(0.696325\pi\)
\(380\) 0 0
\(381\) 19.7704 27.2454i 1.01287 1.39583i
\(382\) 0 0
\(383\) −7.80832 + 9.01128i −0.398986 + 0.460455i −0.919321 0.393507i \(-0.871262\pi\)
0.520335 + 0.853962i \(0.325807\pi\)
\(384\) 0 0
\(385\) 1.67043 0.240172i 0.0851330 0.0122403i
\(386\) 0 0
\(387\) −10.5247 + 7.21486i −0.534999 + 0.366752i
\(388\) 0 0
\(389\) −4.09382 + 6.37010i −0.207565 + 0.322977i −0.929391 0.369098i \(-0.879667\pi\)
0.721826 + 0.692075i \(0.243303\pi\)
\(390\) 0 0
\(391\) −12.9563 3.80430i −0.655227 0.192392i
\(392\) 0 0
\(393\) −4.43979 + 21.9780i −0.223958 + 1.10864i
\(394\) 0 0
\(395\) −5.79454 + 5.02100i −0.291555 + 0.252634i
\(396\) 0 0
\(397\) −19.8773 5.83650i −0.997612 0.292925i −0.258136 0.966108i \(-0.583108\pi\)
−0.739476 + 0.673183i \(0.764927\pi\)
\(398\) 0 0
\(399\) −1.39966 + 0.326349i −0.0700705 + 0.0163379i
\(400\) 0 0
\(401\) 32.6440 1.63016 0.815082 0.579346i \(-0.196692\pi\)
0.815082 + 0.579346i \(0.196692\pi\)
\(402\) 0 0
\(403\) 25.1725 1.25393
\(404\) 0 0
\(405\) 26.1547 19.0971i 1.29964 0.948944i
\(406\) 0 0
\(407\) −5.32144 1.56252i −0.263774 0.0774511i
\(408\) 0 0
\(409\) −1.77856 + 1.54113i −0.0879442 + 0.0762041i −0.697723 0.716367i \(-0.745804\pi\)
0.609779 + 0.792571i \(0.291258\pi\)
\(410\) 0 0
\(411\) 29.1978 + 5.89826i 1.44022 + 0.290940i
\(412\) 0 0
\(413\) −0.408517 0.119952i −0.0201018 0.00590243i
\(414\) 0 0
\(415\) −2.71515 + 4.22486i −0.133282 + 0.207390i
\(416\) 0 0
\(417\) −31.0655 1.75797i −1.52128 0.0860880i
\(418\) 0 0
\(419\) −26.2060 + 3.76786i −1.28025 + 0.184072i −0.748673 0.662939i \(-0.769309\pi\)
−0.531575 + 0.847011i \(0.678400\pi\)
\(420\) 0 0
\(421\) 12.7519 14.7165i 0.621490 0.717238i −0.354499 0.935056i \(-0.615349\pi\)
0.975989 + 0.217818i \(0.0698940\pi\)
\(422\) 0 0
\(423\) 27.1808 0.808658i 1.32158 0.0393183i
\(424\) 0 0
\(425\) 47.4530 + 21.6711i 2.30181 + 1.05120i
\(426\) 0 0
\(427\) 2.64043 + 1.69690i 0.127780 + 0.0821189i
\(428\) 0 0
\(429\) 5.68765 + 4.12718i 0.274602 + 0.199262i
\(430\) 0 0
\(431\) 26.5469i 1.27872i −0.768908 0.639360i \(-0.779199\pi\)
0.768908 0.639360i \(-0.220801\pi\)
\(432\) 0 0
\(433\) −13.6277 21.2051i −0.654904 1.01905i −0.996848 0.0793307i \(-0.974722\pi\)
0.341944 0.939720i \(-0.388915\pi\)
\(434\) 0 0
\(435\) −22.0500 1.24778i −1.05721 0.0598267i
\(436\) 0 0
\(437\) 2.91026 1.32907i 0.139216 0.0635780i
\(438\) 0 0
\(439\) −9.69798 −0.462859 −0.231430 0.972852i \(-0.574340\pi\)
−0.231430 + 0.972852i \(0.574340\pi\)
\(440\) 0 0
\(441\) −6.24810 19.1526i −0.297529 0.912028i
\(442\) 0 0
\(443\) −3.46305 24.0860i −0.164534 1.14436i −0.889952 0.456054i \(-0.849263\pi\)
0.725418 0.688309i \(-0.241647\pi\)
\(444\) 0 0
\(445\) 0.638265 0.0917687i 0.0302567 0.00435025i
\(446\) 0 0
\(447\) −5.95436 + 11.3009i −0.281632 + 0.534516i
\(448\) 0 0
\(449\) −18.5737 8.48232i −0.876547 0.400306i −0.0742564 0.997239i \(-0.523658\pi\)
−0.802291 + 0.596934i \(0.796386\pi\)
\(450\) 0 0
\(451\) −1.39634 + 9.71176i −0.0657511 + 0.457309i
\(452\) 0 0
\(453\) 32.0787 12.5112i 1.50719 0.587829i
\(454\) 0 0
\(455\) −1.26109 + 8.77111i −0.0591210 + 0.411196i
\(456\) 0 0
\(457\) −11.6428 7.48240i −0.544629 0.350012i 0.239218 0.970966i \(-0.423109\pi\)
−0.783847 + 0.620954i \(0.786745\pi\)
\(458\) 0 0
\(459\) 25.1685 + 23.0174i 1.17477 + 1.07436i
\(460\) 0 0
\(461\) −9.65928 15.0301i −0.449877 0.700023i 0.540045 0.841636i \(-0.318407\pi\)
−0.989922 + 0.141613i \(0.954771\pi\)
\(462\) 0 0
\(463\) −4.26786 14.5350i −0.198344 0.675498i −0.997255 0.0740482i \(-0.976408\pi\)
0.798911 0.601450i \(-0.205410\pi\)
\(464\) 0 0
\(465\) 29.5871 16.7317i 1.37207 0.775913i
\(466\) 0 0
\(467\) 12.3289 10.6831i 0.570516 0.494355i −0.321163 0.947024i \(-0.604074\pi\)
0.891678 + 0.452669i \(0.149528\pi\)
\(468\) 0 0
\(469\) 0.378694 + 4.35083i 0.0174865 + 0.200903i
\(470\) 0 0
\(471\) 21.7292 + 4.38953i 1.00123 + 0.202259i
\(472\) 0 0
\(473\) −3.70079 0.532093i −0.170162 0.0244657i
\(474\) 0 0
\(475\) −11.8595 + 3.48227i −0.544153 + 0.159778i
\(476\) 0 0
\(477\) −5.75750 17.6487i −0.263618 0.808080i
\(478\) 0 0
\(479\) 5.69939 2.60282i 0.260412 0.118926i −0.280931 0.959728i \(-0.590643\pi\)
0.541343 + 0.840802i \(0.317916\pi\)
\(480\) 0 0
\(481\) 15.7443 24.4986i 0.717877 1.11704i
\(482\) 0 0
\(483\) −0.935838 1.65487i −0.0425821 0.0752991i
\(484\) 0 0
\(485\) −3.12083 + 10.6286i −0.141709 + 0.482618i
\(486\) 0 0
\(487\) −5.71344 0.821468i −0.258901 0.0372243i 0.0116422 0.999932i \(-0.496294\pi\)
−0.270543 + 0.962708i \(0.587203\pi\)
\(488\) 0 0
\(489\) −5.18531 22.2389i −0.234488 1.00568i
\(490\) 0 0
\(491\) 18.9804 8.66806i 0.856574 0.391184i 0.0617992 0.998089i \(-0.480316\pi\)
0.794775 + 0.606904i \(0.207589\pi\)
\(492\) 0 0
\(493\) −3.31017 23.0227i −0.149082 1.03689i
\(494\) 0 0
\(495\) 9.42839 + 1.07051i 0.423775 + 0.0481160i
\(496\) 0 0
\(497\) 1.46927 0.944243i 0.0659058 0.0423551i
\(498\) 0 0
\(499\) 8.03703i 0.359787i 0.983686 + 0.179893i \(0.0575753\pi\)
−0.983686 + 0.179893i \(0.942425\pi\)
\(500\) 0 0
\(501\) −18.1593 + 34.4650i −0.811296 + 1.53978i
\(502\) 0 0
\(503\) 0.626975 0.723568i 0.0279554 0.0322623i −0.741600 0.670843i \(-0.765933\pi\)
0.769555 + 0.638580i \(0.220478\pi\)
\(504\) 0 0
\(505\) 13.5284 8.69420i 0.602008 0.386887i
\(506\) 0 0
\(507\) −11.3842 + 8.78930i −0.505592 + 0.390346i
\(508\) 0 0
\(509\) −7.88963 26.8696i −0.349702 1.19097i −0.927195 0.374579i \(-0.877787\pi\)
0.577493 0.816396i \(-0.304031\pi\)
\(510\) 0 0
\(511\) 1.35489 2.10825i 0.0599368 0.0932635i
\(512\) 0 0
\(513\) −8.07809 0.216435i −0.356657 0.00955584i
\(514\) 0 0
\(515\) 6.15550 1.80742i 0.271244 0.0796443i
\(516\) 0 0
\(517\) 6.02161 + 5.21775i 0.264830 + 0.229477i
\(518\) 0 0
\(519\) 8.14013 8.38591i 0.357312 0.368101i
\(520\) 0 0
\(521\) 21.7553 25.1070i 0.953119 1.09996i −0.0417847 0.999127i \(-0.513304\pi\)
0.994904 0.100831i \(-0.0321502\pi\)
\(522\) 0 0
\(523\) −3.23105 2.07647i −0.141284 0.0907977i 0.468089 0.883681i \(-0.344943\pi\)
−0.609373 + 0.792883i \(0.708579\pi\)
\(524\) 0 0
\(525\) 2.66878 + 6.84273i 0.116475 + 0.298641i
\(526\) 0 0
\(527\) 23.4425 + 27.0540i 1.02117 + 1.17849i
\(528\) 0 0
\(529\) −12.2903 14.1838i −0.534361 0.616685i
\(530\) 0 0
\(531\) −2.05152 1.23381i −0.0890285 0.0535427i
\(532\) 0 0
\(533\) −46.8633 21.4018i −2.02988 0.927013i
\(534\) 0 0
\(535\) 24.9809i 1.08002i
\(536\) 0 0
\(537\) 25.0195 19.3165i 1.07967 0.833568i
\(538\) 0 0
\(539\) 2.45217 5.36950i 0.105622 0.231281i
\(540\) 0 0
\(541\) 4.61900 15.7309i 0.198586 0.676323i −0.798634 0.601817i \(-0.794444\pi\)
0.997221 0.0745062i \(-0.0237381\pi\)
\(542\) 0 0
\(543\) 29.6577 + 5.99117i 1.27273 + 0.257106i
\(544\) 0 0
\(545\) −51.8889 + 44.9620i −2.22268 + 1.92596i
\(546\) 0 0
\(547\) −8.24133 + 28.0674i −0.352374 + 1.20007i 0.572533 + 0.819881i \(0.305961\pi\)
−0.924907 + 0.380193i \(0.875858\pi\)
\(548\) 0 0
\(549\) 11.9485 + 12.9879i 0.509950 + 0.554310i
\(550\) 0 0
\(551\) 4.16491 + 3.60891i 0.177431 + 0.153745i
\(552\) 0 0
\(553\) −0.161796 1.12532i −0.00688027 0.0478534i
\(554\) 0 0
\(555\) 2.22168 39.2600i 0.0943051 1.66649i
\(556\) 0 0
\(557\) −6.62330 22.5569i −0.280638 0.955765i −0.972338 0.233580i \(-0.924956\pi\)
0.691700 0.722185i \(-0.256862\pi\)
\(558\) 0 0
\(559\) 8.15541 17.8578i 0.344937 0.755306i
\(560\) 0 0
\(561\) 0.861079 + 9.95632i 0.0363548 + 0.420356i
\(562\) 0 0
\(563\) −26.7894 + 7.86607i −1.12904 + 0.331515i −0.792329 0.610094i \(-0.791132\pi\)
−0.336708 + 0.941609i \(0.609314\pi\)
\(564\) 0 0
\(565\) −55.2178 −2.32303
\(566\) 0 0
\(567\) 0.285472 + 4.79344i 0.0119887 + 0.201306i
\(568\) 0 0
\(569\) −27.6340 23.9450i −1.15848 1.00382i −0.999864 0.0164839i \(-0.994753\pi\)
−0.158612 0.987341i \(-0.550702\pi\)
\(570\) 0 0
\(571\) 14.5299 + 31.8160i 0.608057 + 1.33146i 0.923895 + 0.382646i \(0.124987\pi\)
−0.315838 + 0.948813i \(0.602285\pi\)
\(572\) 0 0
\(573\) 15.0007 11.5814i 0.626662 0.483820i
\(574\) 0 0
\(575\) −8.83964 13.7547i −0.368638 0.573612i
\(576\) 0 0
\(577\) −11.5894 + 1.66631i −0.482475 + 0.0693694i −0.379261 0.925290i \(-0.623822\pi\)
−0.103214 + 0.994659i \(0.532913\pi\)
\(578\) 0 0
\(579\) 14.8992 + 14.4625i 0.619188 + 0.601041i
\(580\) 0 0
\(581\) −0.309346 0.677374i −0.0128338 0.0281022i
\(582\) 0 0
\(583\) 2.25962 4.94789i 0.0935840 0.204920i
\(584\) 0 0
\(585\) −19.3410 + 45.9177i −0.799652 + 1.89846i
\(586\) 0 0
\(587\) 12.3037 + 3.61268i 0.507826 + 0.149111i 0.525602 0.850731i \(-0.323840\pi\)
−0.0177754 + 0.999842i \(0.505658\pi\)
\(588\) 0 0
\(589\) −8.39534 1.20707i −0.345924 0.0497364i
\(590\) 0 0
\(591\) 13.3706 1.15636i 0.549992 0.0475664i
\(592\) 0 0
\(593\) 11.9991 + 26.2744i 0.492744 + 1.07896i 0.978760 + 0.205009i \(0.0657223\pi\)
−0.486016 + 0.873950i \(0.661550\pi\)
\(594\) 0 0
\(595\) −10.6011 + 6.81294i −0.434604 + 0.279303i
\(596\) 0 0
\(597\) 0.492806 0.679133i 0.0201692 0.0277951i
\(598\) 0 0
\(599\) 4.51941 31.4332i 0.184658 1.28432i −0.660913 0.750462i \(-0.729831\pi\)
0.845571 0.533862i \(-0.179260\pi\)
\(600\) 0 0
\(601\) −16.0531 18.5263i −0.654820 0.755703i 0.327102 0.944989i \(-0.393928\pi\)
−0.981922 + 0.189287i \(0.939382\pi\)
\(602\) 0 0
\(603\) −4.13113 + 24.2061i −0.168232 + 0.985747i
\(604\) 0 0
\(605\) −24.0995 27.8123i −0.979783 1.13073i
\(606\) 0 0
\(607\) −4.93516 + 34.3248i −0.200312 + 1.39320i 0.603048 + 0.797705i \(0.293953\pi\)
−0.803360 + 0.595494i \(0.796956\pi\)
\(608\) 0 0
\(609\) 1.92329 2.65047i 0.0779355 0.107402i
\(610\) 0 0
\(611\) −35.1956 + 22.6188i −1.42386 + 0.915059i
\(612\) 0 0
\(613\) −1.27604 2.79414i −0.0515388 0.112854i 0.882111 0.471042i \(-0.156122\pi\)
−0.933650 + 0.358188i \(0.883395\pi\)
\(614\) 0 0
\(615\) −69.3074 + 5.99409i −2.79474 + 0.241705i
\(616\) 0 0
\(617\) 39.1417 + 5.62773i 1.57578 + 0.226564i 0.874036 0.485861i \(-0.161494\pi\)
0.701749 + 0.712424i \(0.252403\pi\)
\(618\) 0 0
\(619\) 6.65459 + 1.95396i 0.267471 + 0.0785364i 0.412718 0.910859i \(-0.364580\pi\)
−0.145247 + 0.989395i \(0.546398\pi\)
\(620\) 0 0
\(621\) −2.73584 10.3337i −0.109786 0.414675i
\(622\) 0 0
\(623\) −0.0397195 + 0.0869735i −0.00159133 + 0.00348452i
\(624\) 0 0
\(625\) −0.653146 1.43019i −0.0261259 0.0572076i
\(626\) 0 0
\(627\) −1.69900 1.64920i −0.0678514 0.0658628i
\(628\) 0 0
\(629\) 40.9920 5.89376i 1.63446 0.234999i
\(630\) 0 0
\(631\) 2.95415 + 4.59675i 0.117603 + 0.182994i 0.895065 0.445937i \(-0.147129\pi\)
−0.777462 + 0.628931i \(0.783493\pi\)
\(632\) 0 0
\(633\) 16.0002 12.3531i 0.635950 0.490991i
\(634\) 0 0
\(635\) 29.0515 + 63.6138i 1.15287 + 2.52444i
\(636\) 0 0
\(637\) 23.4246 + 20.2975i 0.928116 + 0.804218i
\(638\) 0 0
\(639\) 9.33601 3.04566i 0.369327 0.120485i
\(640\) 0 0
\(641\) −1.86830 −0.0737935 −0.0368968 0.999319i \(-0.511747\pi\)
−0.0368968 + 0.999319i \(0.511747\pi\)
\(642\) 0 0
\(643\) −21.5122 + 6.31654i −0.848357 + 0.249100i −0.676885 0.736089i \(-0.736671\pi\)
−0.171472 + 0.985189i \(0.554852\pi\)
\(644\) 0 0
\(645\) −2.28412 26.4104i −0.0899372 1.03991i
\(646\) 0 0
\(647\) −7.18251 + 15.7275i −0.282374 + 0.618312i −0.996671 0.0815305i \(-0.974019\pi\)
0.714297 + 0.699842i \(0.246746\pi\)
\(648\) 0 0
\(649\) −0.197621 0.673035i −0.00775730 0.0264190i
\(650\) 0 0
\(651\) −0.284755 + 5.03198i −0.0111604 + 0.197219i
\(652\) 0 0
\(653\) 1.42691 + 9.92438i 0.0558393 + 0.388371i 0.998506 + 0.0546361i \(0.0173999\pi\)
−0.942667 + 0.333735i \(0.891691\pi\)
\(654\) 0 0
\(655\) −35.2036 30.5041i −1.37552 1.19189i
\(656\) 0 0
\(657\) 10.3702 9.54028i 0.404579 0.372202i
\(658\) 0 0
\(659\) −4.69024 + 15.9735i −0.182706 + 0.622239i 0.816299 + 0.577630i \(0.196022\pi\)
−0.999005 + 0.0446089i \(0.985796\pi\)
\(660\) 0 0
\(661\) 5.32675 4.61565i 0.207187 0.179528i −0.545086 0.838380i \(-0.683503\pi\)
0.752273 + 0.658852i \(0.228958\pi\)
\(662\) 0 0
\(663\) −51.4349 10.3904i −1.99757 0.403530i
\(664\) 0 0
\(665\) 0.841182 2.86480i 0.0326197 0.111092i
\(666\) 0 0
\(667\) −3.02837 + 6.63121i −0.117259 + 0.256762i
\(668\) 0 0
\(669\) −37.0902 + 28.6358i −1.43399 + 1.10712i
\(670\) 0 0
\(671\) 5.17102i 0.199625i
\(672\) 0 0
\(673\) −11.4992 5.25151i −0.443262 0.202431i 0.181265 0.983434i \(-0.441981\pi\)
−0.624527 + 0.781003i \(0.714708\pi\)
\(674\) 0 0
\(675\) 4.78033 + 41.0200i 0.183995 + 1.57886i
\(676\) 0 0
\(677\) 19.7763 + 22.8231i 0.760065 + 0.877162i 0.995503 0.0947271i \(-0.0301979\pi\)
−0.235438 + 0.971889i \(0.575652\pi\)
\(678\) 0 0
\(679\) −1.07562 1.24133i −0.0412785 0.0476379i
\(680\) 0 0
\(681\) −6.59708 16.9149i −0.252801 0.648179i
\(682\) 0 0
\(683\) −7.04095 4.52494i −0.269415 0.173142i 0.398957 0.916969i \(-0.369372\pi\)
−0.668372 + 0.743827i \(0.733009\pi\)
\(684\) 0 0
\(685\) −40.5247 + 46.7680i −1.54837 + 1.78691i
\(686\) 0 0
\(687\) 7.80140 8.03696i 0.297642 0.306629i
\(688\) 0 0
\(689\) 21.5853 + 18.7038i 0.822334 + 0.712557i
\(690\) 0 0
\(691\) 15.4212 4.52806i 0.586648 0.172255i 0.0250794 0.999685i \(-0.492016\pi\)
0.561569 + 0.827430i \(0.310198\pi\)
\(692\) 0 0
\(693\) −0.889364 + 1.09027i −0.0337841 + 0.0414161i
\(694\) 0 0
\(695\) 34.9476 54.3796i 1.32564 2.06274i
\(696\) 0 0
\(697\) −20.6411 70.2971i −0.781837 2.66269i
\(698\) 0 0
\(699\) −7.83115 + 6.04611i −0.296201 + 0.228685i
\(700\) 0 0
\(701\) −27.0674 + 17.3951i −1.02232 + 0.657005i −0.940553 0.339646i \(-0.889693\pi\)
−0.0817670 + 0.996651i \(0.526056\pi\)
\(702\) 0 0
\(703\) −6.42567 + 7.41562i −0.242349 + 0.279685i
\(704\) 0 0
\(705\) −26.3337 + 49.9794i −0.991784 + 1.88233i
\(706\) 0 0
\(707\) 2.38450i 0.0896785i
\(708\) 0 0
\(709\) 15.4091 9.90282i 0.578700 0.371908i −0.218305 0.975881i \(-0.570053\pi\)
0.797005 + 0.603973i \(0.206416\pi\)
\(710\) 0 0
\(711\) 0.721172 6.35162i 0.0270461 0.238204i
\(712\) 0 0
\(713\) −1.59673 11.1055i −0.0597980 0.415904i
\(714\) 0 0
\(715\) −13.2798 + 6.06467i −0.496635 + 0.226806i
\(716\) 0 0
\(717\) −1.46479 6.28223i −0.0547034 0.234614i
\(718\) 0 0
\(719\) −13.1317 1.88805i −0.489729 0.0704125i −0.106973 0.994262i \(-0.534116\pi\)
−0.382756 + 0.923849i \(0.625025\pi\)
\(720\) 0 0
\(721\) −0.268000 + 0.912725i −0.00998085 + 0.0339917i
\(722\) 0 0
\(723\) −0.895211 1.58303i −0.0332933 0.0588734i
\(724\) 0 0
\(725\) 15.2264 23.6927i 0.565493 0.879924i
\(726\) 0 0
\(727\) 27.4715 12.5458i 1.01886 0.465298i 0.165274 0.986248i \(-0.447149\pi\)
0.853587 + 0.520950i \(0.174422\pi\)
\(728\) 0 0
\(729\) −5.26805 + 26.4811i −0.195113 + 0.980781i
\(730\) 0 0
\(731\) 26.7876 7.86554i 0.990774 0.290918i
\(732\) 0 0
\(733\) 21.1843 + 3.04584i 0.782460 + 0.112501i 0.521957 0.852972i \(-0.325202\pi\)
0.260504 + 0.965473i \(0.416111\pi\)
\(734\) 0 0
\(735\) 41.0241 + 8.28732i 1.51320 + 0.305682i
\(736\) 0 0
\(737\) −5.69282 + 4.40019i −0.209698 + 0.162083i
\(738\) 0 0
\(739\) 28.5238 24.7160i 1.04927 0.909194i 0.0532690 0.998580i \(-0.483036\pi\)
0.995997 + 0.0893860i \(0.0284905\pi\)
\(740\) 0 0
\(741\) 10.8222 6.12004i 0.397565 0.224825i
\(742\) 0 0
\(743\) 14.6368 + 49.8485i 0.536973 + 1.82876i 0.559233 + 0.829011i \(0.311096\pi\)
−0.0222593 + 0.999752i \(0.507086\pi\)
\(744\) 0 0
\(745\) −14.3469 22.3243i −0.525632 0.817899i
\(746\) 0 0
\(747\) −0.718866 4.12490i −0.0263019 0.150922i
\(748\) 0 0
\(749\) −3.11611 2.00260i −0.113860 0.0731735i
\(750\) 0 0
\(751\) −5.71140 + 39.7236i −0.208412 + 1.44954i 0.569929 + 0.821694i \(0.306971\pi\)
−0.778341 + 0.627842i \(0.783938\pi\)
\(752\) 0 0
\(753\) −16.8701 + 6.57963i −0.614782 + 0.239775i
\(754\) 0 0
\(755\) −10.1801 + 70.8040i −0.370491 + 2.57682i
\(756\) 0 0
\(757\) −5.39167 2.46229i −0.195964 0.0894936i 0.315016 0.949086i \(-0.397990\pi\)
−0.510980 + 0.859593i \(0.670717\pi\)
\(758\) 0 0
\(759\) 1.46004 2.77105i 0.0529961 0.100583i
\(760\) 0 0
\(761\) 14.3473 2.06283i 0.520090 0.0747777i 0.122729 0.992440i \(-0.460835\pi\)
0.397361 + 0.917663i \(0.369926\pi\)
\(762\) 0 0
\(763\) −1.44885 10.0770i −0.0524520 0.364811i
\(764\) 0 0
\(765\) −67.3616 + 21.9752i −2.43546 + 0.794515i
\(766\) 0 0
\(767\) 3.68318 0.132992
\(768\) 0 0
\(769\) 0.524680 0.239613i 0.0189204 0.00864067i −0.405932 0.913903i \(-0.633053\pi\)
0.424853 + 0.905262i \(0.360326\pi\)
\(770\) 0 0
\(771\) −24.9083 1.40953i −0.897049 0.0507631i
\(772\) 0 0
\(773\) 22.0997 + 34.3878i 0.794872 + 1.23684i 0.967753 + 0.251902i \(0.0810561\pi\)
−0.172881 + 0.984943i \(0.555308\pi\)
\(774\) 0 0
\(775\) 43.3453i 1.55701i
\(776\) 0 <