Properties

Label 668.2.e.a.9.12
Level $668$
Weight $2$
Character 668.9
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 9.12
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.214009 + 1.60599i) q^{3} +(-2.48108 - 1.09715i) q^{5} +(1.06258 - 2.28498i) q^{7} +(0.361919 - 0.0982005i) q^{9} +O(q^{10})\) \(q+(0.214009 + 1.60599i) q^{3} +(-2.48108 - 1.09715i) q^{5} +(1.06258 - 2.28498i) q^{7} +(0.361919 - 0.0982005i) q^{9} +(-3.72532 + 4.77647i) q^{11} +(-1.08338 + 2.11634i) q^{13} +(1.23104 - 4.21938i) q^{15} +(-6.88280 - 0.522032i) q^{17} +(-1.76173 + 2.65017i) q^{19} +(3.89705 + 1.21748i) q^{21} +(-4.28650 - 1.70466i) q^{23} +(1.58765 + 1.74546i) q^{25} +(2.11644 + 5.04193i) q^{27} +(-2.36493 + 0.940486i) q^{29} +(5.54645 - 1.28173i) q^{31} +(-8.46820 - 4.96061i) q^{33} +(-5.14332 + 4.50340i) q^{35} +(-9.30865 - 2.52574i) q^{37} +(-3.63066 - 1.28697i) q^{39} +(2.19421 - 1.07133i) q^{41} +(-0.440626 + 4.64258i) q^{43} +(-1.00569 - 0.153438i) q^{45} +(-0.142072 - 7.50609i) q^{47} +(0.418722 + 0.496887i) q^{49} +(-0.634606 - 11.1654i) q^{51} +(-0.00584961 - 0.0340106i) q^{53} +(14.4833 - 7.76354i) q^{55} +(-4.63316 - 2.26216i) q^{57} +(-4.88556 + 0.370550i) q^{59} +(1.70898 - 1.74164i) q^{61} +(0.160182 - 0.931324i) q^{63} +(5.00989 - 4.06217i) q^{65} +(6.72221 - 2.97262i) q^{67} +(1.82031 - 7.24888i) q^{69} +(-3.54590 + 0.404382i) q^{71} +(-7.19162 + 5.39324i) q^{73} +(-2.46342 + 2.92328i) q^{75} +(6.95568 + 13.5877i) q^{77} +(-1.77841 + 4.73079i) q^{79} +(-6.67362 + 3.90936i) q^{81} +(6.30040 - 8.74114i) q^{83} +(16.5040 + 8.84670i) q^{85} +(-2.01653 - 3.59677i) q^{87} +(3.16420 + 10.8453i) q^{89} +(3.68461 + 4.72427i) q^{91} +(3.24543 + 8.63323i) q^{93} +(7.27864 - 4.64238i) q^{95} +(1.96802 + 0.454789i) q^{97} +(-0.879213 + 2.09452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{11}{83}\right)\) \(1\)

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
\(3\) 0.214009 + 1.60599i 0.123558 + 0.927217i 0.937918 + 0.346857i \(0.112751\pi\)
−0.814360 + 0.580360i \(0.802912\pi\)
\(4\) 0 0
\(5\) −2.48108 1.09715i −1.10957 0.490662i −0.233264 0.972413i \(-0.574941\pi\)
−0.876308 + 0.481751i \(0.840001\pi\)
\(6\) 0 0
\(7\) 1.06258 2.28498i 0.401618 0.863641i −0.596518 0.802600i \(-0.703449\pi\)
0.998135 0.0610413i \(-0.0194421\pi\)
\(8\) 0 0
\(9\) 0.361919 0.0982005i 0.120640 0.0327335i
\(10\) 0 0
\(11\) −3.72532 + 4.77647i −1.12323 + 1.44016i −0.240268 + 0.970707i \(0.577235\pi\)
−0.882958 + 0.469452i \(0.844451\pi\)
\(12\) 0 0
\(13\) −1.08338 + 2.11634i −0.300475 + 0.586966i −0.990611 0.136714i \(-0.956346\pi\)
0.690136 + 0.723680i \(0.257551\pi\)
\(14\) 0 0
\(15\) 1.23104 4.21938i 0.317854 1.08944i
\(16\) 0 0
\(17\) −6.88280 0.522032i −1.66932 0.126611i −0.793284 0.608851i \(-0.791631\pi\)
−0.876039 + 0.482240i \(0.839823\pi\)
\(18\) 0 0
\(19\) −1.76173 + 2.65017i −0.404169 + 0.607990i −0.977399 0.211405i \(-0.932196\pi\)
0.573230 + 0.819395i \(0.305690\pi\)
\(20\) 0 0
\(21\) 3.89705 + 1.21748i 0.850406 + 0.265677i
\(22\) 0 0
\(23\) −4.28650 1.70466i −0.893797 0.355446i −0.122910 0.992418i \(-0.539223\pi\)
−0.770887 + 0.636972i \(0.780187\pi\)
\(24\) 0 0
\(25\) 1.58765 + 1.74546i 0.317529 + 0.349093i
\(26\) 0 0
\(27\) 2.11644 + 5.04193i 0.407309 + 0.970321i
\(28\) 0 0
\(29\) −2.36493 + 0.940486i −0.439157 + 0.174644i −0.578645 0.815580i \(-0.696418\pi\)
0.139488 + 0.990224i \(0.455454\pi\)
\(30\) 0 0
\(31\) 5.54645 1.28173i 0.996173 0.230205i 0.304575 0.952488i \(-0.401486\pi\)
0.691598 + 0.722283i \(0.256907\pi\)
\(32\) 0 0
\(33\) −8.46820 4.96061i −1.47412 0.863531i
\(34\) 0 0
\(35\) −5.14332 + 4.50340i −0.869380 + 0.761214i
\(36\) 0 0
\(37\) −9.30865 2.52574i −1.53033 0.415229i −0.605576 0.795788i \(-0.707057\pi\)
−0.924757 + 0.380558i \(0.875732\pi\)
\(38\) 0 0
\(39\) −3.63066 1.28697i −0.581371 0.206081i
\(40\) 0 0
\(41\) 2.19421 1.07133i 0.342678 0.167314i −0.259361 0.965780i \(-0.583512\pi\)
0.602039 + 0.798467i \(0.294355\pi\)
\(42\) 0 0
\(43\) −0.440626 + 4.64258i −0.0671948 + 0.707986i 0.896866 + 0.442303i \(0.145838\pi\)
−0.964060 + 0.265683i \(0.914403\pi\)
\(44\) 0 0
\(45\) −1.00569 0.153438i −0.149920 0.0228732i
\(46\) 0 0
\(47\) −0.142072 7.50609i −0.0207233 1.09488i −0.846994 0.531602i \(-0.821590\pi\)
0.826271 0.563273i \(-0.190458\pi\)
\(48\) 0 0
\(49\) 0.418722 + 0.496887i 0.0598174 + 0.0709839i
\(50\) 0 0
\(51\) −0.634606 11.1654i −0.0888627 1.56347i
\(52\) 0 0
\(53\) −0.00584961 0.0340106i −0.000803506 0.00467172i 0.985125 0.171840i \(-0.0549713\pi\)
−0.985928 + 0.167169i \(0.946538\pi\)
\(54\) 0 0
\(55\) 14.4833 7.76354i 1.95293 1.04684i
\(56\) 0 0
\(57\) −4.63316 2.26216i −0.613677 0.299630i
\(58\) 0 0
\(59\) −4.88556 + 0.370550i −0.636045 + 0.0482415i −0.389702 0.920941i \(-0.627422\pi\)
−0.246343 + 0.969183i \(0.579229\pi\)
\(60\) 0 0
\(61\) 1.70898 1.74164i 0.218813 0.222994i −0.595598 0.803283i \(-0.703085\pi\)
0.814410 + 0.580289i \(0.197061\pi\)
\(62\) 0 0
\(63\) 0.160182 0.931324i 0.0201810 0.117336i
\(64\) 0 0
\(65\) 5.00989 4.06217i 0.621401 0.503850i
\(66\) 0 0
\(67\) 6.72221 2.97262i 0.821249 0.363163i 0.0492497 0.998786i \(-0.484317\pi\)
0.772000 + 0.635623i \(0.219257\pi\)
\(68\) 0 0
\(69\) 1.82031 7.24888i 0.219139 0.872662i
\(70\) 0 0
\(71\) −3.54590 + 0.404382i −0.420821 + 0.0479913i −0.321148 0.947029i \(-0.604069\pi\)
−0.0996728 + 0.995020i \(0.531780\pi\)
\(72\) 0 0
\(73\) −7.19162 + 5.39324i −0.841715 + 0.631231i −0.931099 0.364766i \(-0.881149\pi\)
0.0893836 + 0.995997i \(0.471510\pi\)
\(74\) 0 0
\(75\) −2.46342 + 2.92328i −0.284451 + 0.337552i
\(76\) 0 0
\(77\) 6.95568 + 13.5877i 0.792673 + 1.54846i
\(78\) 0 0
\(79\) −1.77841 + 4.73079i −0.200087 + 0.532255i −0.997460 0.0712319i \(-0.977307\pi\)
0.797373 + 0.603487i \(0.206223\pi\)
\(80\) 0 0
\(81\) −6.67362 + 3.90936i −0.741513 + 0.434373i
\(82\) 0 0
\(83\) 6.30040 8.74114i 0.691559 0.959465i −0.308408 0.951254i \(-0.599796\pi\)
0.999966 0.00821078i \(-0.00261360\pi\)
\(84\) 0 0
\(85\) 16.5040 + 8.84670i 1.79011 + 0.959559i
\(86\) 0 0
\(87\) −2.01653 3.59677i −0.216194 0.385615i
\(88\) 0 0
\(89\) 3.16420 + 10.8453i 0.335404 + 1.14960i 0.936573 + 0.350473i \(0.113979\pi\)
−0.601168 + 0.799122i \(0.705298\pi\)
\(90\) 0 0
\(91\) 3.68461 + 4.72427i 0.386252 + 0.495239i
\(92\) 0 0
\(93\) 3.24543 + 8.63323i 0.336536 + 0.895225i
\(94\) 0 0
\(95\) 7.27864 4.64238i 0.746772 0.476299i
\(96\) 0 0
\(97\) 1.96802 + 0.454789i 0.199822 + 0.0461768i 0.323880 0.946098i \(-0.395013\pi\)
−0.124058 + 0.992275i \(0.539591\pi\)
\(98\) 0 0
\(99\) −0.879213 + 2.09452i −0.0883642 + 0.210508i
\(100\) 0 0
\(101\) 0.482908 + 5.08808i 0.0480512 + 0.506283i 0.986830 + 0.161762i \(0.0517176\pi\)
−0.938779 + 0.344521i \(0.888041\pi\)
\(102\) 0 0
\(103\) −4.01477 + 2.77984i −0.395587 + 0.273905i −0.750336 0.661056i \(-0.770108\pi\)
0.354749 + 0.934962i \(0.384566\pi\)
\(104\) 0 0
\(105\) −8.33313 7.29634i −0.813230 0.712050i
\(106\) 0 0
\(107\) 9.13177 + 6.32285i 0.882802 + 0.611253i 0.921663 0.387991i \(-0.126831\pi\)
−0.0388614 + 0.999245i \(0.512373\pi\)
\(108\) 0 0
\(109\) −1.34991 0.860988i −0.129298 0.0824677i 0.471511 0.881860i \(-0.343709\pi\)
−0.600809 + 0.799393i \(0.705155\pi\)
\(110\) 0 0
\(111\) 2.06417 15.4901i 0.195922 1.47026i
\(112\) 0 0
\(113\) −9.46933 + 15.4854i −0.890800 + 1.45675i −0.00120328 + 0.999999i \(0.500383\pi\)
−0.889597 + 0.456747i \(0.849015\pi\)
\(114\) 0 0
\(115\) 8.76488 + 8.93235i 0.817329 + 0.832946i
\(116\) 0 0
\(117\) −0.184270 + 0.872331i −0.0170357 + 0.0806470i
\(118\) 0 0
\(119\) −8.50636 + 15.1724i −0.779777 + 1.39085i
\(120\) 0 0
\(121\) −6.25754 24.9190i −0.568867 2.26536i
\(122\) 0 0
\(123\) 2.19012 + 3.29460i 0.197477 + 0.297064i
\(124\) 0 0
\(125\) 2.26507 + 6.79570i 0.202594 + 0.607826i
\(126\) 0 0
\(127\) 13.6576 + 1.55754i 1.21192 + 0.138210i 0.695754 0.718280i \(-0.255071\pi\)
0.516164 + 0.856490i \(0.327360\pi\)
\(128\) 0 0
\(129\) −7.55021 + 0.285916i −0.664759 + 0.0251735i
\(130\) 0 0
\(131\) 0.864954 15.2182i 0.0755714 1.32962i −0.707069 0.707145i \(-0.749983\pi\)
0.782640 0.622475i \(-0.213873\pi\)
\(132\) 0 0
\(133\) 4.18360 + 6.84153i 0.362764 + 0.593236i
\(134\) 0 0
\(135\) 0.280724 14.8315i 0.0241608 1.27649i
\(136\) 0 0
\(137\) −7.37705 + 2.61497i −0.630264 + 0.223412i −0.630009 0.776588i \(-0.716949\pi\)
−0.000255055 1.00000i \(0.500081\pi\)
\(138\) 0 0
\(139\) −16.2418 15.3449i −1.37761 1.30154i −0.908185 0.418569i \(-0.862532\pi\)
−0.469430 0.882970i \(-0.655541\pi\)
\(140\) 0 0
\(141\) 12.0243 1.83454i 1.01263 0.154496i
\(142\) 0 0
\(143\) −6.07269 13.0587i −0.507824 1.09203i
\(144\) 0 0
\(145\) 6.89944 + 0.261272i 0.572967 + 0.0216975i
\(146\) 0 0
\(147\) −0.708385 + 0.778800i −0.0584266 + 0.0642344i
\(148\) 0 0
\(149\) 14.1145 + 11.4445i 1.15631 + 0.937568i 0.998752 0.0499423i \(-0.0159038\pi\)
0.157555 + 0.987510i \(0.449639\pi\)
\(150\) 0 0
\(151\) 14.3091 + 10.7309i 1.16446 + 0.873268i 0.993703 0.112045i \(-0.0357402\pi\)
0.170757 + 0.985313i \(0.445379\pi\)
\(152\) 0 0
\(153\) −2.54228 + 0.486961i −0.205531 + 0.0393684i
\(154\) 0 0
\(155\) −15.1674 2.90525i −1.21828 0.233355i
\(156\) 0 0
\(157\) −0.147707 0.699246i −0.0117883 0.0558059i 0.972117 0.234496i \(-0.0753441\pi\)
−0.983905 + 0.178690i \(0.942814\pi\)
\(158\) 0 0
\(159\) 0.0533687 0.0166730i 0.00423241 0.00132225i
\(160\) 0 0
\(161\) −8.44986 + 7.98323i −0.665942 + 0.629167i
\(162\) 0 0
\(163\) 1.22694 3.68109i 0.0961015 0.288325i −0.889622 0.456698i \(-0.849032\pi\)
0.985723 + 0.168373i \(0.0538513\pi\)
\(164\) 0 0
\(165\) 15.5677 + 21.5986i 1.21195 + 1.68145i
\(166\) 0 0
\(167\) 7.14397 10.7686i 0.552817 0.833303i
\(168\) 0 0
\(169\) 4.29617 + 5.96048i 0.330475 + 0.458499i
\(170\) 0 0
\(171\) −0.377356 + 1.13215i −0.0288572 + 0.0865776i
\(172\) 0 0
\(173\) −0.699585 + 0.660952i −0.0531885 + 0.0502512i −0.712886 0.701280i \(-0.752612\pi\)
0.659697 + 0.751531i \(0.270684\pi\)
\(174\) 0 0
\(175\) 5.67535 1.77304i 0.429016 0.134030i
\(176\) 0 0
\(177\) −1.64065 7.76684i −0.123319 0.583791i
\(178\) 0 0
\(179\) −4.23323 0.810853i −0.316406 0.0606060i 0.0274650 0.999623i \(-0.491257\pi\)
−0.343871 + 0.939017i \(0.611738\pi\)
\(180\) 0 0
\(181\) −14.0005 + 2.68173i −1.04065 + 0.199331i −0.679880 0.733323i \(-0.737968\pi\)
−0.360771 + 0.932655i \(0.617486\pi\)
\(182\) 0 0
\(183\) 3.16278 + 2.37188i 0.233800 + 0.175334i
\(184\) 0 0
\(185\) 20.3244 + 16.4796i 1.49428 + 1.21160i
\(186\) 0 0
\(187\) 28.1341 30.9307i 2.05737 2.26188i
\(188\) 0 0
\(189\) 13.7696 + 0.521436i 1.00159 + 0.0379289i
\(190\) 0 0
\(191\) 11.3609 + 24.4306i 0.822048 + 1.76774i 0.613447 + 0.789736i \(0.289782\pi\)
0.208600 + 0.978001i \(0.433109\pi\)
\(192\) 0 0
\(193\) 0.779247 0.118889i 0.0560915 0.00855785i −0.122718 0.992442i \(-0.539161\pi\)
0.178809 + 0.983884i \(0.442775\pi\)
\(194\) 0 0
\(195\) 7.59596 + 7.17648i 0.543958 + 0.513919i
\(196\) 0 0
\(197\) 19.4342 6.88893i 1.38463 0.490816i 0.465599 0.884996i \(-0.345839\pi\)
0.919033 + 0.394180i \(0.128971\pi\)
\(198\) 0 0
\(199\) 0.381402 20.1507i 0.0270369 1.42844i −0.686145 0.727465i \(-0.740698\pi\)
0.713182 0.700979i \(-0.247253\pi\)
\(200\) 0 0
\(201\) 6.21261 + 10.1596i 0.438204 + 0.716604i
\(202\) 0 0
\(203\) −0.363936 + 6.40316i −0.0255433 + 0.449414i
\(204\) 0 0
\(205\) −6.61942 + 0.250668i −0.462320 + 0.0175074i
\(206\) 0 0
\(207\) −1.71877 0.196012i −0.119462 0.0136237i
\(208\) 0 0
\(209\) −6.09542 18.2876i −0.421629 1.26498i
\(210\) 0 0
\(211\) −5.05209 7.59984i −0.347800 0.523194i 0.616728 0.787177i \(-0.288458\pi\)
−0.964528 + 0.263982i \(0.914964\pi\)
\(212\) 0 0
\(213\) −1.40829 5.60813i −0.0964944 0.384263i
\(214\) 0 0
\(215\) 6.18685 11.0352i 0.421940 0.752592i
\(216\) 0 0
\(217\) 2.96483 14.0355i 0.201266 0.952790i
\(218\) 0 0
\(219\) −10.2005 10.3954i −0.689289 0.702459i
\(220\) 0 0
\(221\) 8.56146 14.0008i 0.575906 0.941793i
\(222\) 0 0
\(223\) −2.18249 + 16.3780i −0.146150 + 1.09675i 0.752658 + 0.658411i \(0.228771\pi\)
−0.898809 + 0.438341i \(0.855566\pi\)
\(224\) 0 0
\(225\) 0.746005 + 0.475809i 0.0497337 + 0.0317206i
\(226\) 0 0
\(227\) −17.6102 12.1933i −1.16883 0.809300i −0.184018 0.982923i \(-0.558910\pi\)
−0.984812 + 0.173623i \(0.944453\pi\)
\(228\) 0 0
\(229\) −17.8014 15.5866i −1.17635 1.02999i −0.998948 0.0458494i \(-0.985401\pi\)
−0.177398 0.984139i \(-0.556768\pi\)
\(230\) 0 0
\(231\) −20.3330 + 14.0786i −1.33781 + 0.926305i
\(232\) 0 0
\(233\) −2.58581 27.2450i −0.169402 1.78488i −0.525864 0.850569i \(-0.676258\pi\)
0.356462 0.934310i \(-0.383983\pi\)
\(234\) 0 0
\(235\) −7.88285 + 18.7791i −0.514220 + 1.22501i
\(236\) 0 0
\(237\) −7.97818 1.84368i −0.518239 0.119760i
\(238\) 0 0
\(239\) −12.4918 + 7.96741i −0.808029 + 0.515369i −0.875996 0.482319i \(-0.839795\pi\)
0.0679665 + 0.997688i \(0.478349\pi\)
\(240\) 0 0
\(241\) 5.52755 + 14.7039i 0.356061 + 0.947164i 0.985434 + 0.170060i \(0.0543962\pi\)
−0.629373 + 0.777104i \(0.716688\pi\)
\(242\) 0 0
\(243\) 2.38208 + 3.05421i 0.152810 + 0.195928i
\(244\) 0 0
\(245\) −0.493720 1.69222i −0.0315426 0.108112i
\(246\) 0 0
\(247\) −3.70003 6.59955i −0.235427 0.419919i
\(248\) 0 0
\(249\) 15.3865 + 8.24767i 0.975080 + 0.522675i
\(250\) 0 0
\(251\) 9.17667 12.7317i 0.579226 0.803615i −0.415124 0.909765i \(-0.636262\pi\)
0.994350 + 0.106149i \(0.0338522\pi\)
\(252\) 0 0
\(253\) 24.1108 14.1239i 1.51583 0.887964i
\(254\) 0 0
\(255\) −10.6757 + 28.3985i −0.668536 + 1.77838i
\(256\) 0 0
\(257\) −4.31179 8.42292i −0.268962 0.525408i 0.716016 0.698083i \(-0.245964\pi\)
−0.984979 + 0.172676i \(0.944759\pi\)
\(258\) 0 0
\(259\) −15.6625 + 18.5863i −0.973218 + 1.15489i
\(260\) 0 0
\(261\) −0.763557 + 0.572617i −0.0472630 + 0.0354441i
\(262\) 0 0
\(263\) −4.36912 + 0.498264i −0.269411 + 0.0307243i −0.246967 0.969024i \(-0.579434\pi\)
−0.0224443 + 0.999748i \(0.507145\pi\)
\(264\) 0 0
\(265\) −0.0228015 + 0.0908009i −0.00140069 + 0.00557786i
\(266\) 0 0
\(267\) −16.7402 + 7.40265i −1.02448 + 0.453035i
\(268\) 0 0
\(269\) −5.44463 + 4.41467i −0.331965 + 0.269167i −0.781246 0.624224i \(-0.785415\pi\)
0.449280 + 0.893391i \(0.351680\pi\)
\(270\) 0 0
\(271\) −1.01412 + 5.89626i −0.0616034 + 0.358172i 0.938320 + 0.345769i \(0.112382\pi\)
−0.999923 + 0.0124032i \(0.996052\pi\)
\(272\) 0 0
\(273\) −6.79858 + 6.92848i −0.411469 + 0.419331i
\(274\) 0 0
\(275\) −14.2516 + 1.08093i −0.859406 + 0.0651825i
\(276\) 0 0
\(277\) −6.41221 3.13078i −0.385272 0.188111i 0.235913 0.971774i \(-0.424192\pi\)
−0.621185 + 0.783664i \(0.713349\pi\)
\(278\) 0 0
\(279\) 1.88150 1.00855i 0.112643 0.0603801i
\(280\) 0 0
\(281\) −2.29681 13.3541i −0.137016 0.796636i −0.969958 0.243274i \(-0.921778\pi\)
0.832941 0.553362i \(-0.186655\pi\)
\(282\) 0 0
\(283\) 0.508397 + 8.94485i 0.0302211 + 0.531716i 0.977451 + 0.211162i \(0.0677247\pi\)
−0.947230 + 0.320555i \(0.896131\pi\)
\(284\) 0 0
\(285\) 9.01331 + 10.6959i 0.533902 + 0.633569i
\(286\) 0 0
\(287\) −0.116444 6.15209i −0.00687346 0.363147i
\(288\) 0 0
\(289\) 30.2948 + 4.62207i 1.78205 + 0.271887i
\(290\) 0 0
\(291\) −0.309210 + 3.25794i −0.0181262 + 0.190984i
\(292\) 0 0
\(293\) −17.7457 + 8.66440i −1.03672 + 0.506180i −0.876752 0.480943i \(-0.840294\pi\)
−0.159964 + 0.987123i \(0.551138\pi\)
\(294\) 0 0
\(295\) 12.5280 + 4.44085i 0.729409 + 0.258556i
\(296\) 0 0
\(297\) −31.9671 8.67371i −1.85492 0.503300i
\(298\) 0 0
\(299\) 8.25153 7.22489i 0.477198 0.417826i
\(300\) 0 0
\(301\) 10.1400 + 5.93993i 0.584459 + 0.342372i
\(302\) 0 0
\(303\) −8.06804 + 1.86444i −0.463497 + 0.107109i
\(304\) 0 0
\(305\) −6.15096 + 2.44612i −0.352203 + 0.140064i
\(306\) 0 0
\(307\) −2.89830 6.90454i −0.165415 0.394063i 0.818054 0.575142i \(-0.195053\pi\)
−0.983469 + 0.181079i \(0.942041\pi\)
\(308\) 0 0
\(309\) −5.32358 5.85276i −0.302848 0.332952i
\(310\) 0 0
\(311\) 9.14114 + 3.63525i 0.518346 + 0.206136i 0.614040 0.789275i \(-0.289543\pi\)
−0.0956941 + 0.995411i \(0.530507\pi\)
\(312\) 0 0
\(313\) −16.2325 5.07123i −0.917517 0.286643i −0.197261 0.980351i \(-0.563205\pi\)
−0.720256 + 0.693708i \(0.755976\pi\)
\(314\) 0 0
\(315\) −1.41923 + 2.13494i −0.0799646 + 0.120291i
\(316\) 0 0
\(317\) −15.0343 1.14029i −0.844409 0.0640450i −0.353690 0.935363i \(-0.615073\pi\)
−0.490719 + 0.871318i \(0.663266\pi\)
\(318\) 0 0
\(319\) 4.31792 14.7996i 0.241757 0.828620i
\(320\) 0 0
\(321\) −8.20014 + 16.0187i −0.457687 + 0.894074i
\(322\) 0 0
\(323\) 13.5091 17.3209i 0.751667 0.963760i
\(324\) 0 0
\(325\) −5.41401 + 1.46900i −0.300315 + 0.0814853i
\(326\) 0 0
\(327\) 1.09384 2.35220i 0.0604895 0.130077i
\(328\) 0 0
\(329\) −17.3022 7.65119i −0.953902 0.421824i
\(330\) 0 0
\(331\) 3.40563 + 25.5568i 0.187190 + 1.40473i 0.793050 + 0.609157i \(0.208492\pi\)
−0.605860 + 0.795572i \(0.707171\pi\)
\(332\) 0 0
\(333\) −3.61701 −0.198211
\(334\) 0 0
\(335\) −19.9398 −1.08943
\(336\) 0 0
\(337\) 2.84072 + 21.3176i 0.154744 + 1.16124i 0.880760 + 0.473563i \(0.157033\pi\)
−0.726016 + 0.687678i \(0.758630\pi\)
\(338\) 0 0
\(339\) −26.8959 11.8936i −1.46079 0.645972i
\(340\) 0 0
\(341\) −14.5402 + 31.2673i −0.787395 + 1.69322i
\(342\) 0 0
\(343\) 18.6045 5.04801i 1.00455 0.272567i
\(344\) 0 0
\(345\) −12.4695 + 15.9879i −0.671333 + 0.860759i
\(346\) 0 0
\(347\) −16.4571 + 32.1484i −0.883466 + 1.72582i −0.223218 + 0.974768i \(0.571656\pi\)
−0.660247 + 0.751048i \(0.729549\pi\)
\(348\) 0 0
\(349\) 0.252530 0.865545i 0.0135176 0.0463316i −0.952938 0.303166i \(-0.901956\pi\)
0.966456 + 0.256834i \(0.0826794\pi\)
\(350\) 0 0
\(351\) −12.9633 0.983217i −0.691932 0.0524802i
\(352\) 0 0
\(353\) 9.62238 14.4749i 0.512147 0.770422i −0.482261 0.876028i \(-0.660184\pi\)
0.994408 + 0.105606i \(0.0336782\pi\)
\(354\) 0 0
\(355\) 9.24133 + 2.88710i 0.490479 + 0.153231i
\(356\) 0 0
\(357\) −26.1870 10.4141i −1.38597 0.551171i
\(358\) 0 0
\(359\) −9.14268 10.0515i −0.482532 0.530497i 0.449303 0.893379i \(-0.351672\pi\)
−0.931835 + 0.362882i \(0.881793\pi\)
\(360\) 0 0
\(361\) 3.43427 + 8.18135i 0.180751 + 0.430598i
\(362\) 0 0
\(363\) 38.6804 15.3824i 2.03019 0.807368i
\(364\) 0 0
\(365\) 23.7602 5.49074i 1.24367 0.287398i
\(366\) 0 0
\(367\) −11.6127 6.80262i −0.606177 0.355094i 0.170156 0.985417i \(-0.445573\pi\)
−0.776333 + 0.630324i \(0.782922\pi\)
\(368\) 0 0
\(369\) 0.688921 0.603207i 0.0358638 0.0314017i
\(370\) 0 0
\(371\) −0.0839292 0.0227727i −0.00435739 0.00118230i
\(372\) 0 0
\(373\) −33.2637 11.7911i −1.72233 0.610521i −0.725365 0.688365i \(-0.758329\pi\)
−0.996966 + 0.0778439i \(0.975196\pi\)
\(374\) 0 0
\(375\) −10.4291 + 5.09202i −0.538554 + 0.262951i
\(376\) 0 0
\(377\) 0.571726 6.02389i 0.0294454 0.310246i
\(378\) 0 0
\(379\) 17.8107 + 2.71737i 0.914874 + 0.139582i 0.591143 0.806567i \(-0.298677\pi\)
0.323732 + 0.946149i \(0.395063\pi\)
\(380\) 0 0
\(381\) 0.421464 + 22.2673i 0.0215923 + 1.14079i
\(382\) 0 0
\(383\) 17.2352 + 20.4527i 0.880680 + 1.04508i 0.998644 + 0.0520645i \(0.0165801\pi\)
−0.117964 + 0.993018i \(0.537637\pi\)
\(384\) 0 0
\(385\) −2.34984 41.3435i −0.119759 2.10706i
\(386\) 0 0
\(387\) 0.296432 + 1.72351i 0.0150685 + 0.0876108i
\(388\) 0 0
\(389\) −32.3289 + 17.3293i −1.63914 + 0.878632i −0.645787 + 0.763518i \(0.723471\pi\)
−0.993352 + 0.115115i \(0.963276\pi\)
\(390\) 0 0
\(391\) 28.6132 + 13.9705i 1.44703 + 0.706519i
\(392\) 0 0
\(393\) 24.6253 1.86773i 1.24218 0.0942146i
\(394\) 0 0
\(395\) 9.60279 9.78627i 0.483169 0.492401i
\(396\) 0 0
\(397\) 4.92179 28.6161i 0.247018 1.43620i −0.551473 0.834193i \(-0.685934\pi\)
0.798491 0.602007i \(-0.205632\pi\)
\(398\) 0 0
\(399\) −10.0921 + 8.18296i −0.505236 + 0.409660i
\(400\) 0 0
\(401\) −31.1165 + 13.7600i −1.55388 + 0.687141i −0.990304 0.138920i \(-0.955637\pi\)
−0.563581 + 0.826061i \(0.690577\pi\)
\(402\) 0 0
\(403\) −3.29633 + 13.1268i −0.164202 + 0.653891i
\(404\) 0 0
\(405\) 20.8470 2.37743i 1.03589 0.118135i
\(406\) 0 0
\(407\) 46.7418 35.0533i 2.31691 1.73753i
\(408\) 0 0
\(409\) −10.4887 + 12.4467i −0.518634 + 0.615451i −0.959358 0.282192i \(-0.908939\pi\)
0.440724 + 0.897643i \(0.354722\pi\)
\(410\) 0 0
\(411\) −5.77836 11.2878i −0.285026 0.556787i
\(412\) 0 0
\(413\) −4.34460 + 11.5571i −0.213784 + 0.568690i
\(414\) 0 0
\(415\) −25.2222 + 14.7750i −1.23811 + 0.725274i
\(416\) 0 0
\(417\) 21.1678 29.3681i 1.03659 1.43816i
\(418\) 0 0
\(419\) 14.1810 + 7.60146i 0.692785 + 0.371355i 0.780815 0.624762i \(-0.214804\pi\)
−0.0880301 + 0.996118i \(0.528057\pi\)
\(420\) 0 0
\(421\) 11.2155 + 20.0046i 0.546611 + 0.974963i 0.996637 + 0.0819469i \(0.0261138\pi\)
−0.450025 + 0.893016i \(0.648585\pi\)
\(422\) 0 0
\(423\) −0.788520 2.70265i −0.0383392 0.131407i
\(424\) 0 0
\(425\) −10.0163 12.8425i −0.485860 0.622952i
\(426\) 0 0
\(427\) −2.16367 5.75562i −0.104707 0.278534i
\(428\) 0 0
\(429\) 19.6726 12.5474i 0.949801 0.605792i
\(430\) 0 0
\(431\) 18.9190 + 4.37199i 0.911297 + 0.210591i 0.654666 0.755918i \(-0.272809\pi\)
0.256631 + 0.966510i \(0.417388\pi\)
\(432\) 0 0
\(433\) −7.21812 + 17.1955i −0.346881 + 0.826364i 0.650861 + 0.759197i \(0.274408\pi\)
−0.997742 + 0.0671670i \(0.978604\pi\)
\(434\) 0 0
\(435\) 1.05695 + 11.1363i 0.0506767 + 0.533946i
\(436\) 0 0
\(437\) 12.0693 8.35680i 0.577352 0.399760i
\(438\) 0 0
\(439\) −3.27831 2.87043i −0.156465 0.136998i 0.576949 0.816780i \(-0.304243\pi\)
−0.733414 + 0.679782i \(0.762074\pi\)
\(440\) 0 0
\(441\) 0.200338 + 0.138714i 0.00953991 + 0.00660545i
\(442\) 0 0
\(443\) −14.3613 9.15978i −0.682326 0.435194i 0.150588 0.988597i \(-0.451883\pi\)
−0.832914 + 0.553403i \(0.813329\pi\)
\(444\) 0 0
\(445\) 4.04830 30.3796i 0.191908 1.44013i
\(446\) 0 0
\(447\) −15.3590 + 25.1170i −0.726457 + 1.18799i
\(448\) 0 0
\(449\) 14.5405 + 14.8183i 0.686207 + 0.699318i 0.965358 0.260929i \(-0.0840289\pi\)
−0.279151 + 0.960247i \(0.590053\pi\)
\(450\) 0 0
\(451\) −3.05696 + 14.4716i −0.143946 + 0.681441i
\(452\) 0 0
\(453\) −14.1714 + 25.2768i −0.665830 + 1.18761i
\(454\) 0 0
\(455\) −3.95856 15.7639i −0.185580 0.739023i
\(456\) 0 0
\(457\) −21.7363 32.6979i −1.01678 1.52954i −0.838010 0.545654i \(-0.816281\pi\)
−0.178773 0.983890i \(-0.557213\pi\)
\(458\) 0 0
\(459\) −11.9350 35.8075i −0.557077 1.67135i
\(460\) 0 0
\(461\) −32.0302 3.65279i −1.49179 0.170127i −0.671046 0.741416i \(-0.734155\pi\)
−0.820749 + 0.571289i \(0.806444\pi\)
\(462\) 0 0
\(463\) −10.7432 + 0.406828i −0.499277 + 0.0189069i −0.286280 0.958146i \(-0.592419\pi\)
−0.212997 + 0.977053i \(0.568322\pi\)
\(464\) 0 0
\(465\) 1.41981 24.9805i 0.0658422 1.15844i
\(466\) 0 0
\(467\) 19.8490 + 32.4596i 0.918504 + 1.50205i 0.863972 + 0.503540i \(0.167969\pi\)
0.0545322 + 0.998512i \(0.482633\pi\)
\(468\) 0 0
\(469\) 0.350514 18.5188i 0.0161853 0.855118i
\(470\) 0 0
\(471\) 1.09137 0.386862i 0.0502876 0.0178256i
\(472\) 0 0
\(473\) −20.5336 19.3997i −0.944138 0.892000i
\(474\) 0 0
\(475\) −7.42277 + 1.13249i −0.340580 + 0.0519622i
\(476\) 0 0
\(477\) −0.00545695 0.0117347i −0.000249856 0.000537293i
\(478\) 0 0
\(479\) −14.8401 0.561975i −0.678063 0.0256773i −0.303434 0.952852i \(-0.598133\pi\)
−0.374628 + 0.927175i \(0.622230\pi\)
\(480\) 0 0
\(481\) 15.4301 16.9639i 0.703552 0.773488i
\(482\) 0 0
\(483\) −14.6293 11.8619i −0.665657 0.539734i
\(484\) 0 0
\(485\) −4.38384 3.28759i −0.199060 0.149282i
\(486\) 0 0
\(487\) 17.4530 3.34304i 0.790872 0.151488i 0.223233 0.974765i \(-0.428339\pi\)
0.567639 + 0.823278i \(0.307857\pi\)
\(488\) 0 0
\(489\) 6.17435 + 1.18267i 0.279214 + 0.0534820i
\(490\) 0 0
\(491\) 7.15094 + 33.8525i 0.322717 + 1.52774i 0.772739 + 0.634723i \(0.218886\pi\)
−0.450022 + 0.893017i \(0.648584\pi\)
\(492\) 0 0
\(493\) 16.7683 5.23861i 0.755206 0.235935i
\(494\) 0 0
\(495\) 4.47941 4.23205i 0.201335 0.190216i
\(496\) 0 0
\(497\) −2.84380 + 8.53200i −0.127562 + 0.382713i
\(498\) 0 0
\(499\) 7.14305 + 9.91024i 0.319767 + 0.443643i 0.940203 0.340614i \(-0.110635\pi\)
−0.620436 + 0.784257i \(0.713044\pi\)
\(500\) 0 0
\(501\) 18.8232 + 9.16854i 0.840958 + 0.409620i
\(502\) 0 0
\(503\) −20.0889 27.8712i −0.895719 1.24272i −0.969413 0.245435i \(-0.921069\pi\)
0.0736943 0.997281i \(-0.476521\pi\)
\(504\) 0 0
\(505\) 4.38427 13.1538i 0.195098 0.585334i
\(506\) 0 0
\(507\) −8.65304 + 8.17519i −0.384295 + 0.363073i
\(508\) 0 0
\(509\) 5.31294 1.65982i 0.235492 0.0735703i −0.178174 0.983999i \(-0.557019\pi\)
0.413666 + 0.910429i \(0.364248\pi\)
\(510\) 0 0
\(511\) 4.68177 + 22.1635i 0.207109 + 0.980454i
\(512\) 0 0
\(513\) −17.0906 3.27361i −0.754567 0.144533i
\(514\) 0 0
\(515\) 13.0109 2.49217i 0.573328 0.109818i
\(516\) 0 0
\(517\) 36.3818 + 27.2840i 1.60007 + 1.19995i
\(518\) 0 0
\(519\) −1.21120 0.982074i −0.0531657 0.0431083i
\(520\) 0 0
\(521\) 21.6662 23.8199i 0.949214 1.04357i −0.0497818 0.998760i \(-0.515853\pi\)
0.998996 0.0448089i \(-0.0142679\pi\)
\(522\) 0 0
\(523\) 7.99025 + 0.302580i 0.349389 + 0.0132309i 0.211953 0.977280i \(-0.432017\pi\)
0.137436 + 0.990511i \(0.456114\pi\)
\(524\) 0 0
\(525\) 4.06207 + 8.73509i 0.177283 + 0.381231i
\(526\) 0 0
\(527\) −38.8442 + 5.92645i −1.69208 + 0.258160i
\(528\) 0 0
\(529\) −1.25029 1.18125i −0.0543605 0.0513586i
\(530\) 0 0
\(531\) −1.73179 + 0.613873i −0.0751532 + 0.0266398i
\(532\) 0 0
\(533\) −0.109862 + 5.80434i −0.00475864 + 0.251414i
\(534\) 0 0
\(535\) −15.7195 25.7065i −0.679613 1.11139i
\(536\) 0 0
\(537\) 0.396269 6.97204i 0.0171003 0.300866i
\(538\) 0 0
\(539\) −3.93324 + 0.148946i −0.169417 + 0.00641557i
\(540\) 0 0
\(541\) 26.9246 + 3.07054i 1.15758 + 0.132013i 0.670886 0.741560i \(-0.265914\pi\)
0.486693 + 0.873573i \(0.338203\pi\)
\(542\) 0 0
\(543\) −7.30307 21.9108i −0.313405 0.940280i
\(544\) 0 0
\(545\) 2.40461 + 3.61724i 0.103002 + 0.154946i
\(546\) 0 0
\(547\) 2.83915 + 11.3062i 0.121393 + 0.483416i 0.999983 + 0.00583881i \(0.00185856\pi\)
−0.878590 + 0.477578i \(0.841515\pi\)
\(548\) 0 0
\(549\) 0.447484 0.798154i 0.0190982 0.0340644i
\(550\) 0 0
\(551\) 1.67392 7.92434i 0.0713116 0.337588i
\(552\) 0 0
\(553\) 8.92005 + 9.09048i 0.379319 + 0.386567i
\(554\) 0 0
\(555\) −22.1164 + 36.1675i −0.938789 + 1.53522i
\(556\) 0 0
\(557\) 2.07692 15.5858i 0.0880018 0.660390i −0.890624 0.454741i \(-0.849732\pi\)
0.978626 0.205649i \(-0.0659307\pi\)
\(558\) 0 0
\(559\) −9.34789 5.96217i −0.395374 0.252173i
\(560\) 0 0
\(561\) 55.6953 + 38.5635i 2.35146 + 1.62815i
\(562\) 0 0
\(563\) −10.9665 9.60210i −0.462184 0.404680i 0.395816 0.918330i \(-0.370462\pi\)
−0.858000 + 0.513650i \(0.828293\pi\)
\(564\) 0 0
\(565\) 40.4841 28.0312i 1.70318 1.17928i
\(566\) 0 0
\(567\) 1.84154 + 19.4031i 0.0773375 + 0.814853i
\(568\) 0 0
\(569\) −7.40360 + 17.6374i −0.310375 + 0.739397i 0.689511 + 0.724275i \(0.257826\pi\)
−0.999886 + 0.0151216i \(0.995186\pi\)
\(570\) 0 0
\(571\) 8.77794 + 2.02849i 0.367345 + 0.0848897i 0.404792 0.914409i \(-0.367344\pi\)
−0.0374465 + 0.999299i \(0.511922\pi\)
\(572\) 0 0
\(573\) −36.8039 + 23.4739i −1.53750 + 0.980635i
\(574\) 0 0
\(575\) −3.83003 10.1883i −0.159723 0.424883i
\(576\) 0 0
\(577\) −22.2818 28.5689i −0.927604 1.18934i −0.981629 0.190800i \(-0.938892\pi\)
0.0540253 0.998540i \(-0.482795\pi\)
\(578\) 0 0
\(579\) 0.357701 + 1.22602i 0.0148656 + 0.0509516i
\(580\) 0 0
\(581\) −13.2787 23.6845i −0.550892 0.982597i
\(582\) 0 0
\(583\) 0.184242 + 0.0987599i 0.00763053 + 0.00409022i
\(584\) 0 0
\(585\) 1.41427 1.96215i 0.0584729 0.0811250i
\(586\) 0 0
\(587\) 12.5194 7.33380i 0.516733 0.302698i −0.223895 0.974613i \(-0.571877\pi\)
0.740628 + 0.671915i \(0.234528\pi\)
\(588\) 0 0
\(589\) −6.37456 + 16.9571i −0.262659 + 0.698705i
\(590\) 0 0
\(591\) 15.2226 + 29.7369i 0.626176 + 1.22321i
\(592\) 0 0
\(593\) 13.5203 16.0442i 0.555212 0.658857i −0.412488 0.910963i \(-0.635340\pi\)
0.967700 + 0.252106i \(0.0811232\pi\)
\(594\) 0 0
\(595\) 37.7514 28.3110i 1.54766 1.16064i
\(596\) 0 0
\(597\) 32.4434 3.69991i 1.32782 0.151427i
\(598\) 0 0
\(599\) −2.62214 + 10.4420i −0.107138 + 0.426648i −0.999706 0.0242657i \(-0.992275\pi\)
0.892568 + 0.450914i \(0.148902\pi\)
\(600\) 0 0
\(601\) −26.3081 + 11.6336i −1.07313 + 0.474546i −0.864078 0.503358i \(-0.832098\pi\)
−0.209050 + 0.977905i \(0.567037\pi\)
\(602\) 0 0
\(603\) 2.14099 1.73597i 0.0871877 0.0706943i
\(604\) 0 0
\(605\) −11.8145 + 68.6914i −0.480328 + 2.79270i
\(606\) 0 0
\(607\) −25.7082 + 26.1994i −1.04346 + 1.06340i −0.0455411 + 0.998962i \(0.514501\pi\)
−0.997922 + 0.0644374i \(0.979475\pi\)
\(608\) 0 0
\(609\) −10.3613 + 0.785861i −0.419860 + 0.0318447i
\(610\) 0 0
\(611\) 16.0393 + 7.83125i 0.648882 + 0.316819i
\(612\) 0 0
\(613\) 2.26383 1.21349i 0.0914353 0.0490123i −0.426086 0.904683i \(-0.640108\pi\)
0.517521 + 0.855670i \(0.326855\pi\)
\(614\) 0 0
\(615\) −1.81919 10.5771i −0.0733567 0.426508i
\(616\) 0 0
\(617\) 1.55992 + 27.4455i 0.0627999 + 1.10492i 0.863007 + 0.505192i \(0.168578\pi\)
−0.800207 + 0.599724i \(0.795277\pi\)
\(618\) 0 0
\(619\) 2.05121 + 2.43413i 0.0824452 + 0.0978358i 0.804347 0.594159i \(-0.202515\pi\)
−0.721902 + 0.691995i \(0.756732\pi\)
\(620\) 0 0
\(621\) −0.477353 25.2201i −0.0191555 1.01205i
\(622\) 0 0
\(623\) 28.1434 + 4.29383i 1.12754 + 0.172029i
\(624\) 0 0
\(625\) 2.95080 31.0905i 0.118032 1.24362i
\(626\) 0 0
\(627\) 28.0651 13.7029i 1.12081 0.547241i
\(628\) 0 0
\(629\) 62.7510 + 22.2436i 2.50205 + 0.886910i
\(630\) 0 0
\(631\) −0.882918 0.239565i −0.0351484 0.00953691i 0.244247 0.969713i \(-0.421459\pi\)
−0.279395 + 0.960176i \(0.590134\pi\)
\(632\) 0 0
\(633\) 11.1240 9.74002i 0.442141 0.387131i
\(634\) 0 0
\(635\) −32.1768 18.8489i −1.27690 0.747996i
\(636\) 0 0
\(637\) −1.50522 + 0.347840i −0.0596388 + 0.0137819i
\(638\) 0 0
\(639\) −1.24362 + 0.494563i −0.0491968 + 0.0195646i
\(640\) 0 0
\(641\) 13.2919 + 31.6649i 0.524998 + 1.25069i 0.940095 + 0.340911i \(0.110736\pi\)
−0.415097 + 0.909777i \(0.636252\pi\)
\(642\) 0 0
\(643\) −1.78864 1.96643i −0.0705369 0.0775486i 0.703473 0.710722i \(-0.251632\pi\)
−0.774010 + 0.633173i \(0.781752\pi\)
\(644\) 0 0
\(645\) 19.0464 + 7.57437i 0.749950 + 0.298241i
\(646\) 0 0
\(647\) 28.4653 + 8.89288i 1.11909 + 0.349615i 0.801130 0.598491i \(-0.204233\pi\)
0.317956 + 0.948106i \(0.397004\pi\)
\(648\) 0 0
\(649\) 16.4303 24.7161i 0.644947 0.970192i
\(650\) 0 0
\(651\) 23.1753 + 1.75775i 0.908312 + 0.0688918i
\(652\) 0 0
\(653\) 4.51237 15.4661i 0.176583 0.605236i −0.822739 0.568419i \(-0.807555\pi\)
0.999322 0.0368170i \(-0.0117219\pi\)
\(654\) 0 0
\(655\) −18.8427 + 36.8086i −0.736246 + 1.43823i
\(656\) 0 0
\(657\) −2.07317 + 2.65814i −0.0808819 + 0.103704i
\(658\) 0 0
\(659\) −22.8751 + 6.20675i −0.891086 + 0.241781i −0.677833 0.735216i \(-0.737081\pi\)
−0.213253 + 0.976997i \(0.568406\pi\)
\(660\) 0 0
\(661\) 9.18287 19.7469i 0.357172 0.768066i −0.642826 0.766013i \(-0.722238\pi\)
0.999998 0.00205334i \(-0.000653598\pi\)
\(662\) 0 0
\(663\) 24.3173 + 10.7533i 0.944405 + 0.417624i
\(664\) 0 0
\(665\) −2.87362 21.5644i −0.111434 0.836233i
\(666\) 0 0
\(667\) 11.7405 0.454593
\(668\) 0 0
\(669\) −26.7699 −1.03499
\(670\) 0 0
\(671\) 1.95236 + 14.6510i 0.0753700 + 0.565597i
\(672\) 0 0
\(673\) 35.2318 + 15.5798i 1.35809 + 0.600558i 0.949961 0.312367i \(-0.101122\pi\)
0.408127 + 0.912925i \(0.366182\pi\)
\(674\) 0 0
\(675\) −5.44036 + 11.6990i −0.209399 + 0.450294i
\(676\) 0 0
\(677\) −11.8603 + 3.21810i −0.455829 + 0.123681i −0.482372 0.875966i \(-0.660225\pi\)
0.0265430 + 0.999648i \(0.491550\pi\)
\(678\) 0 0
\(679\) 3.13036 4.01364i 0.120132 0.154029i
\(680\) 0 0
\(681\) 15.8136 30.8912i 0.605978 1.18375i
\(682\) 0 0
\(683\) −1.05765 + 3.62508i −0.0404698 + 0.138710i −0.977703 0.209994i \(-0.932655\pi\)
0.937233 + 0.348704i \(0.113378\pi\)
\(684\) 0 0
\(685\) 21.1721 + 1.60582i 0.808943 + 0.0613551i
\(686\) 0 0
\(687\) 21.2221 31.9244i 0.809675 1.21799i
\(688\) 0 0
\(689\) 0.0783152 + 0.0244666i 0.00298357 + 0.000932102i
\(690\) 0 0
\(691\) −16.2511 6.46276i −0.618222 0.245855i 0.0393750 0.999225i \(-0.487463\pi\)
−0.657597 + 0.753370i \(0.728427\pi\)
\(692\) 0 0
\(693\) 3.85171 + 4.23458i 0.146314 + 0.160859i
\(694\) 0 0
\(695\) 23.4616 + 55.8918i 0.889948 + 2.12010i
\(696\) 0 0
\(697\) −15.6616 + 6.22829i −0.593224 + 0.235913i
\(698\) 0 0
\(699\) 43.2017 9.98347i 1.63404 0.377610i
\(700\) 0 0
\(701\) −26.7708 15.6821i −1.01112 0.592306i −0.0959546 0.995386i \(-0.530590\pi\)
−0.915165 + 0.403080i \(0.867940\pi\)
\(702\) 0 0
\(703\) 23.0930 20.2198i 0.870968 0.762604i
\(704\) 0 0
\(705\) −31.8460 8.64085i −1.19939 0.325433i
\(706\) 0 0
\(707\) 12.1393 + 4.30306i 0.456545 + 0.161833i
\(708\) 0 0
\(709\) 4.70652 2.29797i 0.176757 0.0863022i −0.348244 0.937404i \(-0.613222\pi\)
0.525000 + 0.851102i \(0.324065\pi\)
\(710\) 0 0
\(711\) −0.179076 + 1.88680i −0.00671588 + 0.0707607i
\(712\) 0 0
\(713\) −25.9598 3.96068i −0.972202 0.148328i
\(714\) 0 0
\(715\) 0.739356 + 39.0625i 0.0276503 + 1.46085i
\(716\) 0 0
\(717\) −15.4689 18.3566i −0.577698 0.685540i
\(718\) 0 0
\(719\) −0.954054 16.7858i −0.0355802 0.626006i −0.965846 0.259118i \(-0.916568\pi\)
0.930265 0.366887i \(-0.119577\pi\)
\(720\) 0 0
\(721\) 2.08585 + 12.1275i 0.0776812 + 0.451651i
\(722\) 0 0
\(723\) −22.4314 + 12.0240i −0.834232 + 0.447176i
\(724\) 0 0
\(725\) −5.39626 2.63474i −0.200412 0.0978518i
\(726\) 0 0
\(727\) −39.4791 + 2.99433i −1.46420 + 0.111054i −0.783446 0.621459i \(-0.786540\pi\)
−0.680753 + 0.732513i \(0.738347\pi\)
\(728\) 0 0
\(729\) −20.6463 + 21.0408i −0.764678 + 0.779288i
\(730\) 0 0
\(731\) 5.45631 31.7239i 0.201809 1.17335i
\(732\) 0 0
\(733\) −8.34290 + 6.76466i −0.308152 + 0.249859i −0.771372 0.636385i \(-0.780429\pi\)
0.463220 + 0.886243i \(0.346694\pi\)
\(734\) 0 0
\(735\) 2.61202 1.15506i 0.0963459 0.0426050i
\(736\) 0 0
\(737\) −10.8438 + 43.1824i −0.399436 + 1.59064i
\(738\) 0 0
\(739\) −33.4343 + 3.81291i −1.22990 + 0.140260i −0.703946 0.710253i \(-0.748580\pi\)
−0.525953 + 0.850514i \(0.676291\pi\)
\(740\) 0 0
\(741\) 9.80695 7.35456i 0.360267 0.270177i
\(742\) 0 0
\(743\) 11.6236 13.7934i 0.426427 0.506031i −0.508407 0.861117i \(-0.669765\pi\)
0.934834 + 0.355086i \(0.115548\pi\)
\(744\) 0 0
\(745\) −22.4629 43.8805i −0.822978 1.60766i
\(746\) 0 0
\(747\) 1.42185 3.78229i 0.0520228 0.138387i
\(748\) 0 0
\(749\) 24.1508 14.1474i 0.882452 0.516934i
\(750\) 0 0
\(751\) −10.9987 + 15.2596i −0.401349 + 0.556830i −0.962638 0.270790i \(-0.912715\pi\)
0.561289 + 0.827620i \(0.310305\pi\)
\(752\) 0 0
\(753\) 22.4108 + 12.0129i 0.816694 + 0.437775i
\(754\) 0 0
\(755\) −23.7286 42.3235i −0.863573 1.54031i
\(756\) 0 0
\(757\) −8.74964 29.9893i −0.318011 1.08998i −0.949284 0.314419i \(-0.898190\pi\)
0.631273 0.775560i \(-0.282533\pi\)
\(758\) 0 0
\(759\) 27.8428 + 35.6990i 1.01063 + 1.29579i
\(760\) 0 0
\(761\) −3.97238 10.5670i −0.143999 0.383054i 0.844241 0.535963i \(-0.180051\pi\)
−0.988240 + 0.152909i \(0.951136\pi\)
\(762\) 0 0
\(763\) −3.40173 + 2.16966i −0.123151 + 0.0785469i
\(764\) 0 0
\(765\) 6.84187 + 1.58109i 0.247368 + 0.0571643i
\(766\) 0 0
\(767\) 4.50869 10.7409i 0.162799 0.387832i
\(768\) 0 0
\(769\) −1.74395 18.3749i −0.0628886 0.662614i −0.970224 0.242208i \(-0.922128\pi\)
0.907336 0.420407i \(-0.138113\pi\)
\(770\) 0 0
\(771\) 12.6043 8.72727i 0.453934 0.314305i
\(772\) 0 0
\(773\) 30.7589 + 26.9319i 1.10632 + 0.968674i 0.999672 0.0256228i \(-0.00815689\pi\)
0.106648 + 0.994297i \(0.465988\pi\)
\(774\) 0 0
\(775\) 11.0430 + 7.64620i 0.396677 + 0.274660i
\(776\) 0 0
\(777\) −33.2012 21.1761i −1.19109 0.759687i
\(778\) 0 0
\(779\) −1.02640 + 7.70241i −0.0367747 + 0.275967i
\(780\) 0 0
\(781\) 11.2781 18.4433i 0.403562 0.659954i
\(782\) 0 0
\(783\) −9.74711 9.93334i −0.348333 0.354989i
\(784\) 0 0
\(785\) −0.400707 + 1.89694i −0.0143018 + 0.0677048i
\(786\) 0 0
\(787\) −1.47864 + 2.63737i −0.0527078 + 0.0940122i −0.897351 0.441317i \(-0.854511\pi\)
0.844643 + 0.535329i \(0.179813\pi\)
\(788\) 0 0
\(789\) −1.73524 6.91012i −0.0617761 0.246007i
\(790\) 0 0
\(791\) 25.3220 + 38.0917i 0.900345 + 1.35439i
\(792\) 0 0
\(793\) 1.83441 + 5.50363i 0.0651420 + 0.195440i
\(794\) 0 0
\(795\) −0.150705 0.0171867i −0.00534495 0.000609550i
\(796\) 0 0