Properties

Label 804.2.s.b.5.5
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 5.5
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.53236 - 0.807386i) q^{3} +(-3.45254 + 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(1.69626 + 2.47441i) q^{9} +O(q^{10})\) \(q+(-1.53236 - 0.807386i) q^{3} +(-3.45254 + 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(1.69626 + 2.47441i) q^{9} +(0.843418 - 0.247650i) q^{11} +(2.49538 + 3.88288i) q^{13} +(6.10903 + 1.23409i) q^{15} +(-6.49699 - 0.934126i) q^{17} +(-1.01843 - 1.17533i) q^{19} +(0.335791 + 0.860967i) q^{21} +(1.87132 - 0.854604i) q^{23} +(6.68605 - 4.29687i) q^{25} +(-0.601471 - 5.16122i) q^{27} -3.54360i q^{29} +(2.94854 - 4.58802i) q^{31} +(-1.49237 - 0.301475i) q^{33} +(1.74637 + 0.797540i) q^{35} +6.30938 q^{37} +(-0.688832 - 7.96470i) q^{39} +(1.58851 - 11.0483i) q^{41} +(4.21011 + 0.605322i) q^{43} +(-8.36484 - 6.82341i) q^{45} +(8.24517 - 3.76544i) q^{47} +(-0.955691 - 6.64697i) q^{49} +(9.20153 + 6.67700i) q^{51} +(0.880650 + 6.12505i) q^{53} +(-2.66088 + 1.71004i) q^{55} +(0.611657 + 2.62330i) q^{57} +(-0.431424 + 0.671308i) q^{59} +(-1.65734 + 5.64439i) q^{61} +(0.180579 - 1.59043i) q^{63} +(-12.5517 - 10.8761i) q^{65} +(4.80367 + 6.62757i) q^{67} +(-3.55753 - 0.201317i) q^{69} +(3.24010 - 0.465856i) q^{71} +(-4.50675 - 1.32330i) q^{73} +(-13.7147 + 1.18612i) q^{75} +(-0.426619 - 0.194830i) q^{77} +(-1.15200 - 1.79255i) q^{79} +(-3.24543 + 8.39447i) q^{81} +(0.393211 + 1.33915i) q^{83} +(23.3781 - 3.36126i) q^{85} +(-2.86105 + 5.43007i) q^{87} +(-0.163010 - 0.0744440i) q^{89} +(0.350470 - 2.43757i) q^{91} +(-8.22254 + 4.64989i) q^{93} +(4.70767 + 3.02544i) q^{95} -3.07848i q^{97} +(2.04344 + 1.66689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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
\(3\) −1.53236 0.807386i −0.884709 0.466144i
\(4\) 0 0
\(5\) −3.45254 + 1.01376i −1.54402 + 0.453366i −0.939308 0.343076i \(-0.888531\pi\)
−0.604715 + 0.796442i \(0.706713\pi\)
\(6\) 0 0
\(7\) −0.403229 0.349400i −0.152406 0.132061i 0.575320 0.817928i \(-0.304877\pi\)
−0.727726 + 0.685868i \(0.759423\pi\)
\(8\) 0 0
\(9\) 1.69626 + 2.47441i 0.565419 + 0.824804i
\(10\) 0 0
\(11\) 0.843418 0.247650i 0.254300 0.0746692i −0.152098 0.988365i \(-0.548603\pi\)
0.406398 + 0.913696i \(0.366785\pi\)
\(12\) 0 0
\(13\) 2.49538 + 3.88288i 0.692093 + 1.07692i 0.992397 + 0.123074i \(0.0392753\pi\)
−0.300305 + 0.953843i \(0.597088\pi\)
\(14\) 0 0
\(15\) 6.10903 + 1.23409i 1.57734 + 0.318641i
\(16\) 0 0
\(17\) −6.49699 0.934126i −1.57575 0.226559i −0.701729 0.712444i \(-0.747588\pi\)
−0.874023 + 0.485885i \(0.838497\pi\)
\(18\) 0 0
\(19\) −1.01843 1.17533i −0.233644 0.269640i 0.626805 0.779176i \(-0.284362\pi\)
−0.860449 + 0.509537i \(0.829817\pi\)
\(20\) 0 0
\(21\) 0.335791 + 0.860967i 0.0732757 + 0.187879i
\(22\) 0 0
\(23\) 1.87132 0.854604i 0.390198 0.178197i −0.210649 0.977562i \(-0.567558\pi\)
0.600846 + 0.799365i \(0.294830\pi\)
\(24\) 0 0
\(25\) 6.68605 4.29687i 1.33721 0.859373i
\(26\) 0 0
\(27\) −0.601471 5.16122i −0.115753 0.993278i
\(28\) 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 −0.468664 0.883377i \(-0.655264\pi\)
0.998238 + 0.0593434i \(0.0189007\pi\)
\(32\) 0 0
\(33\) −1.49237 0.301475i −0.259788 0.0524800i
\(34\) 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
\(39\) −0.688832 7.96470i −0.110301 1.27537i
\(40\) 0 0
\(41\) 1.58851 11.0483i 0.248084 1.72546i −0.361182 0.932495i \(-0.617627\pi\)
0.609266 0.792966i \(-0.291464\pi\)
\(42\) 0 0
\(43\) 4.21011 + 0.605322i 0.642035 + 0.0923107i 0.455640 0.890164i \(-0.349410\pi\)
0.186395 + 0.982475i \(0.440320\pi\)
\(44\) 0 0
\(45\) −8.36484 6.82341i −1.24696 1.01717i
\(46\) 0 0
\(47\) 8.24517 3.76544i 1.20268 0.549246i 0.289649 0.957133i \(-0.406462\pi\)
0.913032 + 0.407887i \(0.133734\pi\)
\(48\) 0 0
\(49\) −0.955691 6.64697i −0.136527 0.949568i
\(50\) 0 0
\(51\) 9.20153 + 6.67700i 1.28847 + 0.934966i
\(52\) 0 0
\(53\) 0.880650 + 6.12505i 0.120967 + 0.841341i 0.956465 + 0.291848i \(0.0942700\pi\)
−0.835498 + 0.549493i \(0.814821\pi\)
\(54\) 0 0
\(55\) −2.66088 + 1.71004i −0.358792 + 0.230582i
\(56\) 0 0
\(57\) 0.611657 + 2.62330i 0.0810160 + 0.347465i
\(58\) 0 0
\(59\) −0.431424 + 0.671308i −0.0561666 + 0.0873969i −0.868201 0.496212i \(-0.834724\pi\)
0.812035 + 0.583609i \(0.198360\pi\)
\(60\) 0 0
\(61\) −1.65734 + 5.64439i −0.212201 + 0.722689i 0.782751 + 0.622335i \(0.213816\pi\)
−0.994952 + 0.100354i \(0.968002\pi\)
\(62\) 0 0
\(63\) 0.180579 1.59043i 0.0227509 0.200375i
\(64\) 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
\(69\) −3.55753 0.201317i −0.428277 0.0242357i
\(70\) 0 0
\(71\) 3.24010 0.465856i 0.384529 0.0552869i 0.0526601 0.998612i \(-0.483230\pi\)
0.331869 + 0.943326i \(0.392321\pi\)
\(72\) 0 0
\(73\) −4.50675 1.32330i −0.527475 0.154881i 0.00714274 0.999974i \(-0.497726\pi\)
−0.534618 + 0.845094i \(0.679545\pi\)
\(74\) 0 0
\(75\) −13.7147 + 1.18612i −1.58363 + 0.136962i
\(76\) 0 0
\(77\) −0.426619 0.194830i −0.0486178 0.0222030i
\(78\) 0 0
\(79\) −1.15200 1.79255i −0.129610 0.201678i 0.770383 0.637582i \(-0.220065\pi\)
−0.899993 + 0.435904i \(0.856429\pi\)
\(80\) 0 0
\(81\) −3.24543 + 8.39447i −0.360603 + 0.932719i
\(82\) 0 0
\(83\) 0.393211 + 1.33915i 0.0431605 + 0.146991i 0.978254 0.207409i \(-0.0665031\pi\)
−0.935094 + 0.354400i \(0.884685\pi\)
\(84\) 0 0
\(85\) 23.3781 3.36126i 2.53571 0.364580i
\(86\) 0 0
\(87\) −2.86105 + 5.43007i −0.306737 + 0.582165i
\(88\) 0 0
\(89\) −0.163010 0.0744440i −0.0172790 0.00789105i 0.406757 0.913536i \(-0.366660\pi\)
−0.424036 + 0.905645i \(0.639387\pi\)
\(90\) 0 0
\(91\) 0.350470 2.43757i 0.0367392 0.255527i
\(92\) 0 0
\(93\) −8.22254 + 4.64989i −0.852637 + 0.482171i
\(94\) 0 0
\(95\) 4.70767 + 3.02544i 0.482997 + 0.310403i
\(96\) 0 0
\(97\) 3.07848i 0.312572i −0.987712 0.156286i \(-0.950048\pi\)
0.987712 0.156286i \(-0.0499522\pi\)
\(98\) 0 0
\(99\) 2.04344 + 1.66689i 0.205374 + 0.167528i
\(100\) 0 0
\(101\) −2.92667 3.37755i −0.291214 0.336079i 0.591224 0.806507i \(-0.298645\pi\)
−0.882438 + 0.470428i \(0.844099\pi\)
\(102\) 0 0
\(103\) 1.49986 + 0.963903i 0.147786 + 0.0949762i 0.612444 0.790514i \(-0.290186\pi\)
−0.464658 + 0.885490i \(0.653823\pi\)
\(104\) 0 0
\(105\) −2.03214 2.63211i −0.198317 0.256868i
\(106\) 0 0
\(107\) −1.95591 + 6.66122i −0.189085 + 0.643965i 0.809313 + 0.587378i \(0.199840\pi\)
−0.998398 + 0.0565865i \(0.981978\pi\)
\(108\) 0 0
\(109\) −10.3159 16.0519i −0.988088 1.53750i −0.835709 0.549173i \(-0.814943\pi\)
−0.152380 0.988322i \(-0.548694\pi\)
\(110\) 0 0
\(111\) −9.66824 5.09410i −0.917669 0.483511i
\(112\) 0 0
\(113\) 14.7239 + 4.32334i 1.38511 + 0.406705i 0.887545 0.460721i \(-0.152409\pi\)
0.497566 + 0.867426i \(0.334227\pi\)
\(114\) 0 0
\(115\) −5.59445 + 4.84762i −0.521685 + 0.452043i
\(116\) 0 0
\(117\) −5.37505 + 12.7609i −0.496923 + 1.17975i
\(118\) 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
\(123\) −11.3544 + 15.6475i −1.02380 + 1.41089i
\(124\) 0 0
\(125\) −6.94597 + 8.01608i −0.621266 + 0.716980i
\(126\) 0 0
\(127\) 12.7273 14.6881i 1.12937 1.30336i 0.181971 0.983304i \(-0.441752\pi\)
0.947398 0.320058i \(-0.103702\pi\)
\(128\) 0 0
\(129\) −5.96267 4.32675i −0.524984 0.380949i
\(130\) 0 0
\(131\) 11.7755 5.37767i 1.02883 0.469849i 0.171806 0.985131i \(-0.445040\pi\)
0.857021 + 0.515281i \(0.172313\pi\)
\(132\) 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 0.922318 + 0.386432i \(0.126293\pi\)
−0.311944 + 0.950101i \(0.600980\pi\)
\(138\) 0 0
\(139\) 5.06115 + 17.2367i 0.429281 + 1.46200i 0.836145 + 0.548509i \(0.184804\pi\)
−0.406864 + 0.913489i \(0.633378\pi\)
\(140\) 0 0
\(141\) −15.6747 0.887017i −1.32005 0.0747003i
\(142\) 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
\(147\) −3.90221 + 10.9572i −0.321849 + 0.903732i
\(148\) 0 0
\(149\) 5.57355 4.82951i 0.456603 0.395649i −0.395965 0.918266i \(-0.629590\pi\)
0.852568 + 0.522617i \(0.175044\pi\)
\(150\) 0 0
\(151\) 2.82914 19.6771i 0.230232 1.60130i −0.466869 0.884327i \(-0.654618\pi\)
0.697101 0.716973i \(-0.254473\pi\)
\(152\) 0 0
\(153\) −8.70915 17.6607i −0.704093 1.42779i
\(154\) 0 0
\(155\) −5.52882 + 18.8294i −0.444086 + 1.51242i
\(156\) 0 0
\(157\) −5.31680 11.6422i −0.424327 0.929146i −0.994213 0.107423i \(-0.965740\pi\)
0.569886 0.821723i \(-0.306987\pi\)
\(158\) 0 0
\(159\) 3.59581 10.0968i 0.285166 0.800729i
\(160\) 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
\(165\) 5.45808 0.472046i 0.424911 0.0367487i
\(166\) 0 0
\(167\) 16.9979 14.7288i 1.31534 1.13975i 0.335042 0.942203i \(-0.391250\pi\)
0.980294 0.197542i \(-0.0632959\pi\)
\(168\) 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 \(-0.900751\pi\)
0.674434 + 0.738335i \(0.264388\pi\)
\(174\) 0 0
\(175\) −4.19733 0.603485i −0.317289 0.0456192i
\(176\) 0 0
\(177\) 1.20310 0.680361i 0.0904306 0.0511391i
\(178\) 0 0
\(179\) −7.58099 + 16.6001i −0.566630 + 1.24075i 0.381942 + 0.924186i \(0.375255\pi\)
−0.948572 + 0.316560i \(0.897472\pi\)
\(180\) 0 0
\(181\) −7.25678 15.8901i −0.539392 1.18110i −0.961562 0.274587i \(-0.911459\pi\)
0.422170 0.906517i \(-0.361269\pi\)
\(182\) 0 0
\(183\) 7.09684 7.31112i 0.524614 0.540453i
\(184\) 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
\(189\) −1.56080 + 2.29131i −0.113531 + 0.166668i
\(190\) 0 0
\(191\) −4.54526 + 9.95273i −0.328883 + 0.720154i −0.999771 0.0214049i \(-0.993186\pi\)
0.670887 + 0.741559i \(0.265913\pi\)
\(192\) 0 0
\(193\) −10.0851 6.48129i −0.725941 0.466534i 0.124758 0.992187i \(-0.460185\pi\)
−0.850699 + 0.525653i \(0.823821\pi\)
\(194\) 0 0
\(195\) 10.4525 + 26.8001i 0.748519 + 1.91920i
\(196\) 0 0
\(197\) 1.10270 + 7.66945i 0.0785642 + 0.546426i 0.990650 + 0.136427i \(0.0435619\pi\)
−0.912086 + 0.409999i \(0.865529\pi\)
\(198\) 0 0
\(199\) 0.317248 0.366124i 0.0224891 0.0259538i −0.744394 0.667741i \(-0.767261\pi\)
0.766883 + 0.641787i \(0.221807\pi\)
\(200\) 0 0
\(201\) −2.00995 14.0342i −0.141771 0.989900i
\(202\) 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
\(207\) 5.28888 + 3.18079i 0.367603 + 0.221080i
\(208\) 0 0
\(209\) −1.15003 0.739082i −0.0795495 0.0511234i
\(210\) 0 0
\(211\) 4.84812 10.6159i 0.333758 0.730828i −0.666129 0.745836i \(-0.732050\pi\)
0.999887 + 0.0150079i \(0.00477734\pi\)
\(212\) 0 0
\(213\) −5.34112 1.90215i −0.365968 0.130333i
\(214\) 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
\(219\) 5.83755 + 5.66646i 0.394465 + 0.382904i
\(220\) 0 0
\(221\) −12.5853 27.5580i −0.846581 1.85375i
\(222\) 0 0
\(223\) −11.2385 + 24.6088i −0.752584 + 1.64793i 0.00908061 + 0.999959i \(0.497110\pi\)
−0.761665 + 0.647971i \(0.775618\pi\)
\(224\) 0 0
\(225\) 21.9735 + 9.25546i 1.46490 + 0.617031i
\(226\) 0 0
\(227\) −10.3756 1.49178i −0.688652 0.0990132i −0.210899 0.977508i \(-0.567639\pi\)
−0.477752 + 0.878495i \(0.658548\pi\)
\(228\) 0 0
\(229\) 3.49616 5.44013i 0.231033 0.359494i −0.706310 0.707903i \(-0.749641\pi\)
0.937343 + 0.348409i \(0.113278\pi\)
\(230\) 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 \(-0.803726\pi\)
0.971294 + 0.237883i \(0.0764534\pi\)
\(234\) 0 0
\(235\) −24.6495 + 21.3589i −1.60796 + 1.39330i
\(236\) 0 0
\(237\) 0.318003 + 3.67694i 0.0206565 + 0.238843i
\(238\) 0 0
\(239\) −3.72434 −0.240907 −0.120454 0.992719i \(-0.538435\pi\)
−0.120454 + 0.992719i \(0.538435\pi\)
\(240\) 0 0
\(241\) 1.00745 + 0.295814i 0.0648955 + 0.0190550i 0.314019 0.949417i \(-0.398324\pi\)
−0.249124 + 0.968472i \(0.580143\pi\)
\(242\) 0 0
\(243\) 11.7507 10.2430i 0.753811 0.657092i
\(244\) 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
\(249\) 0.478673 2.36954i 0.0303347 0.150164i
\(250\) 0 0
\(251\) 1.48784 10.3481i 0.0939115 0.653169i −0.887437 0.460930i \(-0.847516\pi\)
0.981348 0.192239i \(-0.0615749\pi\)
\(252\) 0 0
\(253\) 1.36666 1.18422i 0.0859214 0.0744513i
\(254\) 0 0
\(255\) −38.5375 13.7245i −2.41331 0.859460i
\(256\) 0 0
\(257\) −4.05802 13.8203i −0.253132 0.862089i −0.983787 0.179342i \(-0.942603\pi\)
0.730655 0.682747i \(-0.239215\pi\)
\(258\) 0 0
\(259\) −2.54412 2.20450i −0.158084 0.136981i
\(260\) 0 0
\(261\) 8.76832 6.01085i 0.542745 0.372062i
\(262\) 0 0
\(263\) −6.35551 21.6449i −0.391898 1.33468i −0.885357 0.464912i \(-0.846086\pi\)
0.493460 0.869769i \(-0.335732\pi\)
\(264\) 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 0.700168 0.713978i \(-0.253108\pi\)
0.998101 0.0615959i \(-0.0196190\pi\)
\(272\) 0 0
\(273\) −2.50511 + 3.45228i −0.151616 + 0.208941i
\(274\) 0 0
\(275\) 4.57502 5.27985i 0.275884 0.318387i
\(276\) 0 0
\(277\) 3.85148 4.44485i 0.231413 0.267065i −0.628153 0.778090i \(-0.716189\pi\)
0.859566 + 0.511025i \(0.170734\pi\)
\(278\) 0 0
\(279\) 16.3541 0.486553i 0.979097 0.0291292i
\(280\) 0 0
\(281\) −4.93616 + 3.17228i −0.294467 + 0.189242i −0.679530 0.733648i \(-0.737816\pi\)
0.385063 + 0.922890i \(0.374180\pi\)
\(282\) 0 0
\(283\) −17.6010 20.3126i −1.04627 1.20746i −0.977742 0.209813i \(-0.932715\pi\)
−0.0685298 0.997649i \(-0.521831\pi\)
\(284\) 0 0
\(285\) −4.77116 8.43697i −0.282619 0.499763i
\(286\) 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
\(291\) −2.48552 + 4.71734i −0.145704 + 0.276535i
\(292\) 0 0
\(293\) 3.40318 + 5.29545i 0.198816 + 0.309364i 0.926319 0.376741i \(-0.122955\pi\)
−0.727503 + 0.686105i \(0.759319\pi\)
\(294\) 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
\(303\) 1.75772 + 7.53858i 0.100978 + 0.433080i
\(304\) 0 0
\(305\) 21.1676i 1.21205i
\(306\) 0 0
\(307\) −25.9210 16.6584i −1.47939 0.950747i −0.997208 0.0746775i \(-0.976207\pi\)
−0.482184 0.876070i \(-0.660156\pi\)
\(308\) 0 0
\(309\) −1.52009 2.68801i −0.0864748 0.152916i
\(310\) 0 0
\(311\) 3.85323 26.7998i 0.218497 1.51968i −0.525094 0.851044i \(-0.675970\pi\)
0.743591 0.668635i \(-0.233121\pi\)
\(312\) 0 0
\(313\) 0.0443396 + 0.0202492i 0.00250622 + 0.00114455i 0.416668 0.909059i \(-0.363198\pi\)
−0.414162 + 0.910203i \(0.635925\pi\)
\(314\) 0 0
\(315\) 0.988847 + 5.67407i 0.0557152 + 0.319698i
\(316\) 0 0
\(317\) 24.3438 3.50011i 1.36728 0.196586i 0.580725 0.814100i \(-0.302769\pi\)
0.786560 + 0.617514i \(0.211860\pi\)
\(318\) 0 0
\(319\) −0.877571 2.98873i −0.0491346 0.167337i
\(320\) 0 0
\(321\) 8.37534 8.62822i 0.467466 0.481580i
\(322\) 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
\(327\) 2.84765 + 32.9263i 0.157475 + 1.82083i
\(328\) 0 0
\(329\) −4.64033 1.36252i −0.255830 0.0751184i
\(330\) 0 0
\(331\) −28.6734 + 4.12262i −1.57603 + 0.226600i −0.874137 0.485679i \(-0.838572\pi\)
−0.701897 + 0.712278i \(0.747663\pi\)
\(332\) 0 0
\(333\) 10.7023 + 15.6120i 0.586484 + 0.855532i
\(334\) 0 0
\(335\) −23.3036 18.0122i −1.27321 0.984112i
\(336\) 0 0
\(337\) 18.6056 + 16.1218i 1.01351 + 0.878213i 0.992583 0.121568i \(-0.0387924\pi\)
0.0209282 + 0.999781i \(0.493338\pi\)
\(338\) 0 0
\(339\) −19.0718 18.5128i −1.03584 1.00548i
\(340\) 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
\(345\) 12.4866 2.91142i 0.672257 0.156746i
\(346\) 0 0
\(347\) 10.9803 7.05658i 0.589451 0.378817i −0.211651 0.977345i \(-0.567884\pi\)
0.801102 + 0.598528i \(0.204248\pi\)
\(348\) 0 0
\(349\) 3.55366 + 24.7162i 0.190223 + 1.32303i 0.831417 + 0.555650i \(0.187530\pi\)
−0.641194 + 0.767379i \(0.721561\pi\)
\(350\) 0 0
\(351\) 18.5395 15.2146i 0.989566 0.812097i
\(352\) 0 0
\(353\) 5.20707 + 36.2159i 0.277144 + 1.92758i 0.364084 + 0.931366i \(0.381382\pi\)
−0.0869396 + 0.996214i \(0.527709\pi\)
\(354\) 0 0
\(355\) −10.7143 + 4.89305i −0.568656 + 0.259696i
\(356\) 0 0
\(357\) −1.37738 5.90737i −0.0728988 0.312651i
\(358\) 0 0
\(359\) −12.3469 1.77521i −0.651643 0.0936921i −0.191438 0.981505i \(-0.561315\pi\)
−0.460205 + 0.887813i \(0.652224\pi\)
\(360\) 0 0
\(361\) 2.35978 16.4126i 0.124199 0.863822i
\(362\) 0 0
\(363\) 17.6484 1.52633i 0.926298 0.0801115i
\(364\) 0 0
\(365\) 16.9012 0.884651
\(366\) 0 0
\(367\) 29.9811 + 13.6919i 1.56500 + 0.714712i 0.994317 0.106459i \(-0.0339512\pi\)
0.570683 + 0.821170i \(0.306678\pi\)
\(368\) 0 0
\(369\) 30.0327 14.8102i 1.56344 0.770988i
\(370\) 0 0
\(371\) 1.78499 2.77750i 0.0926720 0.144200i
\(372\) 0 0
\(373\) 34.5460i 1.78872i −0.447344 0.894362i \(-0.647630\pi\)
0.447344 0.894362i \(-0.352370\pi\)
\(374\) 0 0
\(375\) 17.1158 6.67544i 0.883856 0.344718i
\(376\) 0 0
\(377\) 13.7594 8.84261i 0.708644 0.455418i
\(378\) 0 0
\(379\) −6.63231 + 3.02887i −0.340679 + 0.155583i −0.578406 0.815749i \(-0.696325\pi\)
0.237727 + 0.971332i \(0.423598\pi\)
\(380\) 0 0
\(381\) −31.3619 + 12.2316i −1.60672 + 0.626646i
\(382\) 0 0
\(383\) 7.80832 + 9.01128i 0.398986 + 0.460455i 0.919321 0.393507i \(-0.128738\pi\)
−0.520335 + 0.853962i \(0.674193\pi\)
\(384\) 0 0
\(385\) 1.67043 + 0.240172i 0.0851330 + 0.0122403i
\(386\) 0 0
\(387\) 5.64360 + 11.4443i 0.286881 + 0.581747i
\(388\) 0 0
\(389\) 4.09382 + 6.37010i 0.207565 + 0.322977i 0.929391 0.369098i \(-0.120333\pi\)
−0.721826 + 0.692075i \(0.756697\pi\)
\(390\) 0 0
\(391\) −12.9563 + 3.80430i −0.655227 + 0.192392i
\(392\) 0 0
\(393\) −22.3861 1.26681i −1.12923 0.0639020i
\(394\) 0 0
\(395\) 5.79454 + 5.02100i 0.291555 + 0.252634i
\(396\) 0 0
\(397\) −19.8773 + 5.83650i −0.997612 + 0.292925i −0.739476 0.673183i \(-0.764927\pi\)
−0.258136 + 0.966108i \(0.583108\pi\)
\(398\) 0 0
\(399\) 0.669942 1.27150i 0.0335391 0.0636548i
\(400\) 0 0
\(401\) −32.6440 −1.63016 −0.815082 0.579346i \(-0.803308\pi\)
−0.815082 + 0.579346i \(0.803308\pi\)
\(402\) 0 0
\(403\) 25.1725 1.25393
\(404\) 0 0
\(405\) 2.69501 32.2723i 0.133916 1.60362i
\(406\) 0 0
\(407\) 5.32144 1.56252i 0.263774 0.0774511i
\(408\) 0 0
\(409\) −1.77856 1.54113i −0.0879442 0.0762041i 0.609779 0.792571i \(-0.291258\pi\)
−0.697723 + 0.716367i \(0.745804\pi\)
\(410\) 0 0
\(411\) 1.68295 29.7400i 0.0830140 1.46696i
\(412\) 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
\(417\) 6.16116 30.4991i 0.301713 1.49355i
\(418\) 0 0
\(419\) 26.2060 + 3.76786i 1.28025 + 0.184072i 0.748673 0.662939i \(-0.230691\pi\)
0.531575 + 0.847011i \(0.321600\pi\)
\(420\) 0 0
\(421\) 12.7519 + 14.7165i 0.621490 + 0.717238i 0.975989 0.217818i \(-0.0698940\pi\)
−0.354499 + 0.935056i \(0.615349\pi\)
\(422\) 0 0
\(423\) 23.3032 + 14.0148i 1.13304 + 0.681422i
\(424\) 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
\(429\) −2.55343 6.54698i −0.123281 0.316091i
\(430\) 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 0.341944 + 0.939720i \(0.388915\pi\)
−0.996848 + 0.0793307i \(0.974722\pi\)
\(434\) 0 0
\(435\) 4.37312 21.6479i 0.209675 1.03794i
\(436\) 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
\(441\) 14.8263 13.6397i 0.706012 0.649512i
\(442\) 0 0
\(443\) 3.46305 24.0860i 0.164534 1.14436i −0.725418 0.688309i \(-0.758353\pi\)
0.889952 0.456054i \(-0.150737\pi\)
\(444\) 0 0
\(445\) 0.638265 + 0.0917687i 0.0302567 + 0.00435025i
\(446\) 0 0
\(447\) −12.4400 + 2.90054i −0.588390 + 0.137191i
\(448\) 0 0
\(449\) 18.5737 8.48232i 0.876547 0.400306i 0.0742564 0.997239i \(-0.476342\pi\)
0.802291 + 0.596934i \(0.203614\pi\)
\(450\) 0 0
\(451\) −1.39634 9.71176i −0.0657511 0.457309i
\(452\) 0 0
\(453\) −20.2223 + 27.8682i −0.950125 + 1.30936i
\(454\) 0 0
\(455\) 1.26109 + 8.77111i 0.0591210 + 0.411196i
\(456\) 0 0
\(457\) −11.6428 + 7.48240i −0.544629 + 0.350012i −0.783847 0.620954i \(-0.786745\pi\)
0.239218 + 0.970966i \(0.423109\pi\)
\(458\) 0 0
\(459\) −0.913482 + 34.0943i −0.0426377 + 1.59138i
\(460\) 0 0
\(461\) 9.65928 15.0301i 0.449877 0.700023i −0.540045 0.841636i \(-0.681593\pi\)
0.989922 + 0.141613i \(0.0452290\pi\)
\(462\) 0 0
\(463\) −4.26786 + 14.5350i −0.198344 + 0.675498i 0.798911 + 0.601450i \(0.205410\pi\)
−0.997255 + 0.0740482i \(0.976408\pi\)
\(464\) 0 0
\(465\) 23.6748 24.3896i 1.09789 1.13104i
\(466\) 0 0
\(467\) −12.3289 10.6831i −0.570516 0.494355i 0.321163 0.947024i \(-0.395926\pi\)
−0.891678 + 0.452669i \(0.850472\pi\)
\(468\) 0 0
\(469\) 0.378694 4.35083i 0.0174865 0.200903i
\(470\) 0 0
\(471\) −1.25247 + 22.1327i −0.0577107 + 1.01982i
\(472\) 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
\(477\) −13.6621 + 12.5687i −0.625544 + 0.575483i
\(478\) 0 0
\(479\) −5.69939 2.60282i −0.260412 0.118926i 0.280931 0.959728i \(-0.409357\pi\)
−0.541343 + 0.840802i \(0.682084\pi\)
\(480\) 0 0
\(481\) 15.7443 + 24.4986i 0.717877 + 1.11704i
\(482\) 0 0
\(483\) 1.36416 + 1.32418i 0.0620714 + 0.0602522i
\(484\) 0 0
\(485\) 3.12083 + 10.6286i 0.141709 + 0.482618i
\(486\) 0 0
\(487\) −5.71344 + 0.821468i −0.258901 + 0.0372243i −0.270543 0.962708i \(-0.587203\pi\)
0.0116422 + 0.999932i \(0.496294\pi\)
\(488\) 0 0
\(489\) −20.2027 10.6446i −0.913599 0.481366i
\(490\) 0 0
\(491\) −18.9804 8.66806i −0.856574 0.391184i −0.0617992 0.998089i \(-0.519684\pi\)
−0.794775 + 0.606904i \(0.792411\pi\)
\(492\) 0 0
\(493\) −3.31017 + 23.0227i −0.149082 + 1.03689i
\(494\) 0 0
\(495\) −8.74487 3.68343i −0.393053 0.165558i
\(496\) 0 0
\(497\) −1.46927 0.944243i −0.0659058 0.0423551i
\(498\) 0 0
\(499\) 8.03703i 0.359787i −0.983686 0.179893i \(-0.942425\pi\)
0.983686 0.179893i \(-0.0575753\pi\)
\(500\) 0 0
\(501\) −37.9387 + 8.84591i −1.69498 + 0.395206i
\(502\) 0 0
\(503\) −0.626975 0.723568i −0.0279554 0.0322623i 0.741600 0.670843i \(-0.234067\pi\)
−0.769555 + 0.638580i \(0.779522\pi\)
\(504\) 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 −0.577493 0.816396i \(-0.695969\pi\)
0.927195 0.374579i \(-0.122213\pi\)
\(510\) 0 0
\(511\) 1.35489 + 2.10825i 0.0599368 + 0.0932635i
\(512\) 0 0
\(513\) −5.45360 + 5.96328i −0.240782 + 0.263285i
\(514\) 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
\(519\) 10.1730 5.75288i 0.446544 0.252523i
\(520\) 0 0
\(521\) −21.7553 25.1070i −0.953119 1.09996i −0.994904 0.100831i \(-0.967850\pi\)
0.0417847 0.999127i \(-0.486696\pi\)
\(522\) 0 0
\(523\) −3.23105 + 2.07647i −0.141284 + 0.0907977i −0.609373 0.792883i \(-0.708579\pi\)
0.468089 + 0.883681i \(0.344943\pi\)
\(524\) 0 0
\(525\) 5.94458 + 4.31362i 0.259443 + 0.188262i
\(526\) 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
\(531\) −2.39290 + 0.0711912i −0.103843 + 0.00308944i
\(532\) 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 0.997221 + 0.0745062i \(0.0237381\pi\)
−0.798634 + 0.601817i \(0.794444\pi\)
\(542\) 0 0
\(543\) −1.70946 + 30.2084i −0.0733601 + 1.29637i
\(544\) 0 0
\(545\) 51.8889 + 44.9620i 2.22268 + 1.92596i
\(546\) 0 0
\(547\) −8.24133 28.0674i −0.352374 1.20007i −0.924907 0.380193i \(-0.875858\pi\)
0.572533 0.819881i \(-0.305961\pi\)
\(548\) 0 0
\(549\) −16.7778 + 5.47338i −0.716059 + 0.233598i
\(550\) 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
\(555\) 38.5442 + 7.78634i 1.63611 + 0.330512i
\(556\) 0 0
\(557\) 6.62330 22.5569i 0.280638 0.955765i −0.691700 0.722185i \(-0.743138\pi\)
0.972338 0.233580i \(-0.0750441\pi\)
\(558\) 0 0
\(559\) 8.15541 + 17.8578i 0.344937 + 0.755306i
\(560\) 0 0
\(561\) 9.41429 + 3.35274i 0.397472 + 0.141553i
\(562\) 0 0
\(563\) 26.7894 + 7.86607i 1.12904 + 0.331515i 0.792329 0.610094i \(-0.208868\pi\)
0.336708 + 0.941609i \(0.390686\pi\)
\(564\) 0 0
\(565\) −55.2178 −2.32303
\(566\) 0 0
\(567\) 4.24168 2.25094i 0.178134 0.0945307i
\(568\) 0 0
\(569\) 27.6340 23.9450i 1.15848 1.00382i 0.158612 0.987341i \(-0.449298\pi\)
0.999864 0.0164839i \(-0.00524723\pi\)
\(570\) 0 0
\(571\) 14.5299 31.8160i 0.608057 1.33146i −0.315838 0.948813i \(-0.602285\pi\)
0.923895 0.382646i \(-0.124987\pi\)
\(572\) 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 −0.103214 0.994659i \(-0.532913\pi\)
−0.379261 + 0.925290i \(0.623822\pi\)
\(578\) 0 0
\(579\) 10.2211 + 18.0742i 0.424774 + 0.751140i
\(580\) 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
\(585\) 5.62106 49.5067i 0.232402 2.04685i
\(586\) 0 0
\(587\) −12.3037 + 3.61268i −0.507826 + 0.149111i −0.525602 0.850731i \(-0.676160\pi\)
0.0177754 + 0.999842i \(0.494342\pi\)
\(588\) 0 0
\(589\) −8.39534 + 1.20707i −0.345924 + 0.0497364i
\(590\) 0 0
\(591\) 4.50247 12.6427i 0.185207 0.520050i
\(592\) 0 0
\(593\) −11.9991 + 26.2744i −0.492744 + 1.07896i 0.486016 + 0.873950i \(0.338450\pi\)
−0.978760 + 0.205009i \(0.934278\pi\)
\(594\) 0 0
\(595\) −10.6011 6.81294i −0.434604 0.279303i
\(596\) 0 0
\(597\) −0.781741 + 0.304892i −0.0319945 + 0.0124784i
\(598\) 0 0
\(599\) −4.51941 31.4332i −0.184658 1.28432i −0.845571 0.533862i \(-0.820740\pi\)
0.660913 0.750462i \(-0.270169\pi\)
\(600\) 0 0
\(601\) −16.0531 + 18.5263i −0.654820 + 0.755703i −0.981922 0.189287i \(-0.939382\pi\)
0.327102 + 0.944989i \(0.393928\pi\)
\(602\) 0 0
\(603\) −8.25109 + 23.1283i −0.336010 + 0.941858i
\(604\) 0 0
\(605\) 24.0995 27.8123i 0.979783 1.13073i
\(606\) 0 0
\(607\) −4.93516 34.3248i −0.200312 1.39320i −0.803360 0.595494i \(-0.796956\pi\)
0.603048 0.797705i \(-0.293953\pi\)
\(608\) 0 0
\(609\) 3.05092 1.18991i 0.123630 0.0482176i
\(610\) 0 0
\(611\) 35.1956 + 22.6188i 1.42386 + 0.915059i
\(612\) 0 0
\(613\) −1.27604 + 2.79414i −0.0515388 + 0.112854i −0.933650 0.358188i \(-0.883395\pi\)
0.882111 + 0.471042i \(0.156122\pi\)
\(614\) 0 0
\(615\) 23.3389 65.5342i 0.941116 2.64260i
\(616\) 0 0
\(617\) −39.1417 + 5.62773i −1.57578 + 0.226564i −0.874036 0.485861i \(-0.838506\pi\)
−0.701749 + 0.712424i \(0.747597\pi\)
\(618\) 0 0
\(619\) 6.65459 1.95396i 0.267471 0.0785364i −0.145247 0.989395i \(-0.546398\pi\)
0.412718 + 0.910859i \(0.364580\pi\)
\(620\) 0 0
\(621\) −5.53635 9.14429i −0.222166 0.366948i
\(622\) 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
\(627\) 1.16554 + 2.06106i 0.0465473 + 0.0823108i
\(628\) 0 0
\(629\) −40.9920 5.89376i −1.63446 0.234999i
\(630\) 0 0
\(631\) 2.95415 4.59675i 0.117603 0.182994i −0.777462 0.628931i \(-0.783493\pi\)
0.895065 + 0.445937i \(0.147129\pi\)
\(632\) 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
\(639\) 6.64875 + 7.22712i 0.263021 + 0.285901i
\(640\) 0 0
\(641\) 1.86830 0.0737935 0.0368968 0.999319i \(-0.488253\pi\)
0.0368968 + 0.999319i \(0.488253\pi\)
\(642\) 0 0
\(643\) −21.5122 6.31654i −0.848357 0.249100i −0.171472 0.985189i \(-0.554852\pi\)
−0.676885 + 0.736089i \(0.736671\pi\)
\(644\) 0 0
\(645\) 24.9726 + 8.89358i 0.983296 + 0.350184i
\(646\) 0 0
\(647\) 7.18251 + 15.7275i 0.282374 + 0.618312i 0.996671 0.0815305i \(-0.0259808\pi\)
−0.714297 + 0.699842i \(0.753254\pi\)
\(648\) 0 0
\(649\) −0.197621 + 0.673035i −0.00775730 + 0.0264190i
\(650\) 0 0
\(651\) 4.94023 + 0.997981i 0.193623 + 0.0391140i
\(652\) 0 0
\(653\) −1.42691 + 9.92438i −0.0558393 + 0.388371i 0.942667 + 0.333735i \(0.108309\pi\)
−0.998506 + 0.0546361i \(0.982600\pi\)
\(654\) 0 0
\(655\) −35.2036 + 30.5041i −1.37552 + 1.19189i
\(656\) 0 0
\(657\) −4.37021 13.3962i −0.170498 0.522636i
\(658\) 0 0
\(659\) 4.69024 + 15.9735i 0.182706 + 0.622239i 0.999005 + 0.0446089i \(0.0142042\pi\)
−0.816299 + 0.577630i \(0.803978\pi\)
\(660\) 0 0
\(661\) 5.32675 + 4.61565i 0.207187 + 0.179528i 0.752273 0.658852i \(-0.228958\pi\)
−0.545086 + 0.838380i \(0.683503\pi\)
\(662\) 0 0
\(663\) −2.96470 + 52.3901i −0.115139 + 2.03466i
\(664\) 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 −0.624527 0.781003i \(-0.714708\pi\)
0.181265 + 0.983434i \(0.441981\pi\)
\(674\) 0 0
\(675\) −26.1986 31.9238i −1.00838 1.22875i
\(676\) 0 0
\(677\) −19.7763 + 22.8231i −0.760065 + 0.877162i −0.995503 0.0947271i \(-0.969802\pi\)
0.235438 + 0.971889i \(0.424348\pi\)
\(678\) 0 0
\(679\) −1.07562 + 1.24133i −0.0412785 + 0.0476379i
\(680\) 0 0
\(681\) 14.6947 + 10.6630i 0.563102 + 0.408609i
\(682\) 0 0
\(683\) 7.04095 4.52494i 0.269415 0.173142i −0.398957 0.916969i \(-0.630628\pi\)
0.668372 + 0.743827i \(0.266991\pi\)
\(684\) 0 0
\(685\) −40.5247 46.7680i −1.54837 1.78691i
\(686\) 0 0
\(687\) −9.74966 + 5.51349i −0.371973 + 0.210353i
\(688\) 0 0
\(689\) −21.5853 + 18.7038i −0.822334 + 0.712557i
\(690\) 0 0
\(691\) 15.4212 + 4.52806i 0.586648 + 0.172255i 0.561569 0.827430i \(-0.310198\pi\)
0.0250794 + 0.999685i \(0.492016\pi\)
\(692\) 0 0
\(693\) −0.241565 1.38611i −0.00917628 0.0526541i
\(694\) 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 \(-0.110307\pi\)
0.0817670 + 0.996651i \(0.473944\pi\)
\(702\) 0 0
\(703\) −6.42567 7.41562i −0.242349 0.279685i
\(704\) 0 0
\(705\) 55.0168 12.8279i 2.07205 0.483127i
\(706\) 0 0
\(707\) 2.38450i 0.0896785i
\(708\) 0 0
\(709\) 15.4091 + 9.90282i 0.578700 + 0.371908i 0.797005 0.603973i \(-0.206416\pi\)
−0.218305 + 0.975881i \(0.570053\pi\)
\(710\) 0 0
\(711\) 2.48142 5.89115i 0.0930604 0.220936i
\(712\) 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
\(717\) 5.70703 + 3.00698i 0.213133 + 0.112298i
\(718\) 0 0
\(719\) 13.1317 1.88805i 0.489729 0.0704125i 0.106973 0.994262i \(-0.465884\pi\)
0.382756 + 0.923849i \(0.374975\pi\)
\(720\) 0 0
\(721\) −0.268000 0.912725i −0.00998085 0.0339917i
\(722\) 0 0
\(723\) −1.30494 1.26669i −0.0485312 0.0471088i
\(724\) 0 0
\(725\) −15.2264 23.6927i −0.565493 0.879924i
\(726\) 0 0
\(727\) 27.4715 + 12.5458i 1.01886 + 0.465298i 0.853587 0.520950i \(-0.174422\pi\)
0.165274 + 0.986248i \(0.447149\pi\)
\(728\) 0 0
\(729\) −26.2765 + 6.20865i −0.973202 + 0.229950i
\(730\) 0 0
\(731\) −26.7876 7.86554i −0.990774 0.290918i
\(732\) 0 0
\(733\) 21.1843 3.04584i 0.782460 0.112501i 0.260504 0.965473i \(-0.416111\pi\)
0.521957 + 0.852972i \(0.325202\pi\)
\(734\) 0 0
\(735\) 2.36462 41.7859i 0.0872205 1.54130i
\(736\) 0 0
\(737\) 5.69282 + 4.40019i 0.209698 + 0.162083i
\(738\) 0 0
\(739\) 28.5238 + 24.7160i 1.04927 + 0.909194i 0.995997 0.0893860i \(-0.0284905\pi\)
0.0532690 + 0.998580i \(0.483036\pi\)
\(740\) 0 0
\(741\) −8.65965 + 8.92111i −0.318120 + 0.327725i
\(742\) 0 0
\(743\) −14.6368 + 49.8485i −0.536973 + 1.82876i 0.0222593 + 0.999752i \(0.492914\pi\)
−0.559233 + 0.829011i \(0.688904\pi\)
\(744\) 0 0
\(745\) −14.3469 + 22.3243i −0.525632 + 0.817899i
\(746\) 0 0
\(747\) −2.64663 + 3.24452i −0.0968352 + 0.118711i
\(748\) 0 0
\(749\) 3.11611 2.00260i 0.113860 0.0731735i
\(750\) 0 0
\(751\) −5.71140 39.7236i −0.208412 1.44954i −0.778341 0.627842i \(-0.783938\pi\)
0.569929 0.821694i \(-0.306971\pi\)
\(752\) 0 0
\(753\) −10.6348 + 14.6558i −0.387555 + 0.534088i
\(754\) 0 0
\(755\) 10.1801 + 70.8040i 0.370491 + 2.57682i
\(756\) 0 0
\(757\) −5.39167 + 2.46229i −0.195964 + 0.0894936i −0.510980 0.859593i \(-0.670717\pi\)
0.315016 + 0.949086i \(0.397990\pi\)
\(758\) 0 0
\(759\) −3.05034 + 0.711228i −0.110720 + 0.0258159i
\(760\) 0 0
\(761\) −14.3473 2.06283i −0.520090 0.0747777i −0.122729 0.992440i \(-0.539165\pi\)
−0.397361 + 0.917663i \(0.630074\pi\)
\(762\) 0 0
\(763\) −1.44885 + 10.0770i −0.0524520 + 0.364811i
\(764\) 0 0
\(765\) 47.9724 + 52.1455i 1.73444 + 1.88532i
\(766\) 0 0
\(767\) −3.68318 −0.132992
\(768\) 0 0
\(769\) 0.524680 + 0.239613i 0.0189204 + 0.00864067i 0.424853 0.905262i \(-0.360326\pi\)
−0.405932 + 0.913903i \(0.633053\pi\)
\(770\) 0 0
\(771\) −4.94000 + 24.4541i −0.177910 + 0.880694i
\(772\) 0 0
\(773\) −22.0997 + 34.3878i −0.794872 + 1.23684i 0.172881 + 0.984943i \(0.444692\pi\)
−0.967753 + 0.251902i \(0.918944\pi\)
\(774\) 0 0
\(775\) 43.3453i 1.55701i
\(776\) 0 0