Properties

Label 804.2.s.b.5.9
Level 804
Weight 2
Character 804.5
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 5.9
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.496478 + 1.65937i) q^{3} +(0.583807 - 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(-2.50702 - 1.64768i) q^{9} +O(q^{10})\) \(q+(-0.496478 + 1.65937i) q^{3} +(0.583807 - 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(-2.50702 - 1.64768i) q^{9} +(-1.09908 + 0.322720i) q^{11} +(-1.75990 - 2.73846i) q^{13} +(-0.00539609 + 1.05386i) q^{15} +(-6.02227 - 0.865872i) q^{17} +(-3.63947 - 4.20017i) q^{19} +(1.87233 - 1.18977i) q^{21} +(8.45963 - 3.86338i) q^{23} +(-3.89482 + 2.50305i) q^{25} +(3.97879 - 3.34204i) q^{27} +1.03707i q^{29} +(-4.67082 + 7.26794i) q^{31} +(0.0101587 - 1.98401i) q^{33} +(-0.708870 - 0.323730i) q^{35} -7.68565 q^{37} +(5.41788 - 1.56074i) q^{39} +(0.975368 - 6.78383i) q^{41} +(6.37193 + 0.916145i) q^{43} +(-1.74606 - 0.532171i) q^{45} +(-1.82570 + 0.833771i) q^{47} +(-0.762752 - 5.30506i) q^{49} +(4.42673 - 9.56329i) q^{51} +(-0.719704 - 5.00565i) q^{53} +(-0.586331 + 0.376812i) q^{55} +(8.77655 - 3.95393i) q^{57} +(4.32558 - 6.73073i) q^{59} +(-2.70183 + 9.20160i) q^{61} +(1.04470 + 3.69758i) q^{63} +(-1.49687 - 1.29705i) q^{65} +(-6.99330 - 4.25368i) q^{67} +(2.21076 + 15.9557i) q^{69} +(12.4132 - 1.78475i) q^{71} +(-2.27484 - 0.667954i) q^{73} +(-2.21979 - 7.70566i) q^{75} +(1.33453 + 0.609459i) q^{77} +(-8.54411 - 13.2949i) q^{79} +(3.57029 + 8.26154i) q^{81} +(3.58147 + 12.1974i) q^{83} +(-3.66427 + 0.526843i) q^{85} +(-1.72088 - 0.514882i) q^{87} +(-1.31786 - 0.601845i) q^{89} +(-0.593340 + 4.12677i) q^{91} +(-9.74124 - 11.3590i) q^{93} +(-2.84474 - 1.82820i) q^{95} -10.2951i q^{97} +(3.28716 + 1.00187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) −0.496478 + 1.65937i −0.286642 + 0.958038i
\(4\) 0 0
\(5\) 0.583807 0.171421i 0.261086 0.0766618i −0.148570 0.988902i \(-0.547467\pi\)
0.409656 + 0.912240i \(0.365649\pi\)
\(6\) 0 0
\(7\) −0.967947 0.838730i −0.365849 0.317010i 0.452464 0.891783i \(-0.350545\pi\)
−0.818313 + 0.574772i \(0.805091\pi\)
\(8\) 0 0
\(9\) −2.50702 1.64768i −0.835673 0.549227i
\(10\) 0 0
\(11\) −1.09908 + 0.322720i −0.331386 + 0.0973037i −0.443193 0.896426i \(-0.646154\pi\)
0.111807 + 0.993730i \(0.464336\pi\)
\(12\) 0 0
\(13\) −1.75990 2.73846i −0.488109 0.759513i 0.506607 0.862177i \(-0.330900\pi\)
−0.994716 + 0.102664i \(0.967263\pi\)
\(14\) 0 0
\(15\) −0.00539609 + 1.05386i −0.00139326 + 0.272105i
\(16\) 0 0
\(17\) −6.02227 0.865872i −1.46062 0.210005i −0.634245 0.773132i \(-0.718689\pi\)
−0.826370 + 0.563127i \(0.809598\pi\)
\(18\) 0 0
\(19\) −3.63947 4.20017i −0.834951 0.963585i 0.164790 0.986329i \(-0.447305\pi\)
−0.999741 + 0.0227439i \(0.992760\pi\)
\(20\) 0 0
\(21\) 1.87233 1.18977i 0.408576 0.259629i
\(22\) 0 0
\(23\) 8.45963 3.86338i 1.76395 0.805571i 0.780323 0.625377i \(-0.215055\pi\)
0.983631 0.180194i \(-0.0576725\pi\)
\(24\) 0 0
\(25\) −3.89482 + 2.50305i −0.778965 + 0.500610i
\(26\) 0 0
\(27\) 3.97879 3.34204i 0.765719 0.643175i
\(28\) 0 0
\(29\) 1.03707i 0.192579i 0.995353 + 0.0962894i \(0.0306974\pi\)
−0.995353 + 0.0962894i \(0.969303\pi\)
\(30\) 0 0
\(31\) −4.67082 + 7.26794i −0.838904 + 1.30536i 0.111318 + 0.993785i \(0.464493\pi\)
−0.950222 + 0.311575i \(0.899143\pi\)
\(32\) 0 0
\(33\) 0.0101587 1.98401i 0.00176841 0.345371i
\(34\) 0 0
\(35\) −0.708870 0.323730i −0.119821 0.0547203i
\(36\) 0 0
\(37\) −7.68565 −1.26351 −0.631756 0.775167i \(-0.717666\pi\)
−0.631756 + 0.775167i \(0.717666\pi\)
\(38\) 0 0
\(39\) 5.41788 1.56074i 0.867555 0.249919i
\(40\) 0 0
\(41\) 0.975368 6.78383i 0.152327 1.05946i −0.759979 0.649947i \(-0.774791\pi\)
0.912306 0.409509i \(-0.134300\pi\)
\(42\) 0 0
\(43\) 6.37193 + 0.916145i 0.971710 + 0.139711i 0.609846 0.792520i \(-0.291231\pi\)
0.361864 + 0.932231i \(0.382140\pi\)
\(44\) 0 0
\(45\) −1.74606 0.532171i −0.260287 0.0793314i
\(46\) 0 0
\(47\) −1.82570 + 0.833771i −0.266306 + 0.121618i −0.544093 0.839025i \(-0.683126\pi\)
0.277787 + 0.960643i \(0.410399\pi\)
\(48\) 0 0
\(49\) −0.762752 5.30506i −0.108965 0.757865i
\(50\) 0 0
\(51\) 4.42673 9.56329i 0.619866 1.33913i
\(52\) 0 0
\(53\) −0.719704 5.00565i −0.0988589 0.687579i −0.977630 0.210334i \(-0.932545\pi\)
0.878771 0.477244i \(-0.158364\pi\)
\(54\) 0 0
\(55\) −0.586331 + 0.376812i −0.0790608 + 0.0508093i
\(56\) 0 0
\(57\) 8.77655 3.95393i 1.16248 0.523711i
\(58\) 0 0
\(59\) 4.32558 6.73073i 0.563142 0.876266i −0.436584 0.899663i \(-0.643812\pi\)
0.999726 + 0.0233972i \(0.00744825\pi\)
\(60\) 0 0
\(61\) −2.70183 + 9.20160i −0.345934 + 1.17814i 0.584410 + 0.811458i \(0.301326\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(62\) 0 0
\(63\) 1.04470 + 3.69758i 0.131620 + 0.465851i
\(64\) 0 0
\(65\) −1.49687 1.29705i −0.185664 0.160879i
\(66\) 0 0
\(67\) −6.99330 4.25368i −0.854367 0.519669i
\(68\) 0 0
\(69\) 2.21076 + 15.9557i 0.266145 + 1.92084i
\(70\) 0 0
\(71\) 12.4132 1.78475i 1.47318 0.211811i 0.641524 0.767103i \(-0.278302\pi\)
0.831656 + 0.555291i \(0.187393\pi\)
\(72\) 0 0
\(73\) −2.27484 0.667954i −0.266250 0.0781781i 0.145883 0.989302i \(-0.453398\pi\)
−0.412133 + 0.911124i \(0.635216\pi\)
\(74\) 0 0
\(75\) −2.21979 7.70566i −0.256320 0.889773i
\(76\) 0 0
\(77\) 1.33453 + 0.609459i 0.152084 + 0.0694542i
\(78\) 0 0
\(79\) −8.54411 13.2949i −0.961288 1.49579i −0.865817 0.500361i \(-0.833201\pi\)
−0.0954710 0.995432i \(-0.530436\pi\)
\(80\) 0 0
\(81\) 3.57029 + 8.26154i 0.396699 + 0.917949i
\(82\) 0 0
\(83\) 3.58147 + 12.1974i 0.393118 + 1.33884i 0.883950 + 0.467582i \(0.154875\pi\)
−0.490832 + 0.871254i \(0.663307\pi\)
\(84\) 0 0
\(85\) −3.66427 + 0.526843i −0.397446 + 0.0571441i
\(86\) 0 0
\(87\) −1.72088 0.514882i −0.184498 0.0552011i
\(88\) 0 0
\(89\) −1.31786 0.601845i −0.139692 0.0637954i 0.344342 0.938844i \(-0.388102\pi\)
−0.484035 + 0.875049i \(0.660829\pi\)
\(90\) 0 0
\(91\) −0.593340 + 4.12677i −0.0621989 + 0.432603i
\(92\) 0 0
\(93\) −9.74124 11.3590i −1.01012 1.17787i
\(94\) 0 0
\(95\) −2.84474 1.82820i −0.291864 0.187570i
\(96\) 0 0
\(97\) 10.2951i 1.04531i −0.852545 0.522654i \(-0.824942\pi\)
0.852545 0.522654i \(-0.175058\pi\)
\(98\) 0 0
\(99\) 3.28716 + 1.00187i 0.330372 + 0.100692i
\(100\) 0 0
\(101\) −11.0980 12.8078i −1.10430 1.27443i −0.958494 0.285113i \(-0.907969\pi\)
−0.145803 0.989314i \(-0.546577\pi\)
\(102\) 0 0
\(103\) 6.87710 + 4.41965i 0.677621 + 0.435481i 0.833666 0.552269i \(-0.186238\pi\)
−0.156045 + 0.987750i \(0.549874\pi\)
\(104\) 0 0
\(105\) 0.889126 1.01555i 0.0867698 0.0991078i
\(106\) 0 0
\(107\) −4.41018 + 15.0197i −0.426348 + 1.45201i 0.414158 + 0.910205i \(0.364076\pi\)
−0.840506 + 0.541802i \(0.817742\pi\)
\(108\) 0 0
\(109\) 4.47433 + 6.96219i 0.428563 + 0.666857i 0.986637 0.162934i \(-0.0520959\pi\)
−0.558074 + 0.829791i \(0.688460\pi\)
\(110\) 0 0
\(111\) 3.81575 12.7533i 0.362175 1.21049i
\(112\) 0 0
\(113\) 8.56513 + 2.51495i 0.805740 + 0.236587i 0.658565 0.752524i \(-0.271164\pi\)
0.147175 + 0.989110i \(0.452982\pi\)
\(114\) 0 0
\(115\) 4.27652 3.70563i 0.398788 0.345551i
\(116\) 0 0
\(117\) −0.100004 + 9.76514i −0.00924536 + 0.902788i
\(118\) 0 0
\(119\) 5.10300 + 5.88918i 0.467792 + 0.539860i
\(120\) 0 0
\(121\) −8.14995 + 5.23766i −0.740905 + 0.476151i
\(122\) 0 0
\(123\) 10.7726 + 4.98652i 0.971336 + 0.449619i
\(124\) 0 0
\(125\) −3.83701 + 4.42814i −0.343192 + 0.396065i
\(126\) 0 0
\(127\) −11.6912 + 13.4924i −1.03743 + 1.19725i −0.0574060 + 0.998351i \(0.518283\pi\)
−0.980019 + 0.198902i \(0.936262\pi\)
\(128\) 0 0
\(129\) −4.68375 + 10.1185i −0.412381 + 0.890888i
\(130\) 0 0
\(131\) −12.8076 + 5.84904i −1.11901 + 0.511033i −0.887041 0.461691i \(-0.847243\pi\)
−0.231966 + 0.972724i \(0.574516\pi\)
\(132\) 0 0
\(133\) 7.11807i 0.617215i
\(134\) 0 0
\(135\) 1.74995 2.63315i 0.150612 0.226626i
\(136\) 0 0
\(137\) 2.05122 + 4.49155i 0.175248 + 0.383739i 0.976790 0.214199i \(-0.0687141\pi\)
−0.801542 + 0.597938i \(0.795987\pi\)
\(138\) 0 0
\(139\) 4.82451 + 16.4308i 0.409210 + 1.39364i 0.864202 + 0.503145i \(0.167824\pi\)
−0.454992 + 0.890496i \(0.650358\pi\)
\(140\) 0 0
\(141\) −0.477113 3.44347i −0.0401802 0.289992i
\(142\) 0 0
\(143\) 2.81804 + 2.44184i 0.235656 + 0.204197i
\(144\) 0 0
\(145\) 0.177775 + 0.605447i 0.0147634 + 0.0502797i
\(146\) 0 0
\(147\) 9.18174 + 1.36816i 0.757297 + 0.112844i
\(148\) 0 0
\(149\) −7.26172 + 6.29231i −0.594903 + 0.515486i −0.899457 0.437009i \(-0.856038\pi\)
0.304554 + 0.952495i \(0.401492\pi\)
\(150\) 0 0
\(151\) 2.84904 19.8155i 0.231852 1.61256i −0.458231 0.888833i \(-0.651517\pi\)
0.690082 0.723731i \(-0.257574\pi\)
\(152\) 0 0
\(153\) 13.6713 + 12.0935i 1.10526 + 0.977705i
\(154\) 0 0
\(155\) −1.48098 + 5.04375i −0.118955 + 0.405123i
\(156\) 0 0
\(157\) −2.80627 6.14488i −0.223965 0.490414i 0.763976 0.645244i \(-0.223244\pi\)
−0.987941 + 0.154830i \(0.950517\pi\)
\(158\) 0 0
\(159\) 8.66354 + 1.29094i 0.687063 + 0.102378i
\(160\) 0 0
\(161\) −11.4288 3.35580i −0.900716 0.264474i
\(162\) 0 0
\(163\) 0.764311 0.0598654 0.0299327 0.999552i \(-0.490471\pi\)
0.0299327 + 0.999552i \(0.490471\pi\)
\(164\) 0 0
\(165\) −0.334170 1.16002i −0.0260151 0.0903073i
\(166\) 0 0
\(167\) −12.8888 + 11.1682i −0.997362 + 0.864219i −0.990742 0.135759i \(-0.956653\pi\)
−0.00661997 + 0.999978i \(0.502107\pi\)
\(168\) 0 0
\(169\) 0.998474 2.18635i 0.0768057 0.168181i
\(170\) 0 0
\(171\) 2.20367 + 16.5266i 0.168519 + 1.26382i
\(172\) 0 0
\(173\) −4.09433 + 6.37090i −0.311286 + 0.484371i −0.961282 0.275567i \(-0.911134\pi\)
0.649996 + 0.759938i \(0.274771\pi\)
\(174\) 0 0
\(175\) 5.86937 + 0.843887i 0.443682 + 0.0637919i
\(176\) 0 0
\(177\) 9.02122 + 10.5194i 0.678076 + 0.790686i
\(178\) 0 0
\(179\) 2.25923 4.94702i 0.168863 0.369758i −0.806214 0.591623i \(-0.798487\pi\)
0.975077 + 0.221865i \(0.0712145\pi\)
\(180\) 0 0
\(181\) −4.41394 9.66518i −0.328085 0.718407i 0.671662 0.740857i \(-0.265581\pi\)
−0.999748 + 0.0224503i \(0.992853\pi\)
\(182\) 0 0
\(183\) −13.9275 9.05174i −1.02955 0.669124i
\(184\) 0 0
\(185\) −4.48693 + 1.31748i −0.329886 + 0.0968632i
\(186\) 0 0
\(187\) 6.89841 0.991841i 0.504462 0.0725306i
\(188\) 0 0
\(189\) −6.65433 0.102224i −0.484031 0.00743570i
\(190\) 0 0
\(191\) 10.4922 22.9746i 0.759185 1.66238i 0.0100657 0.999949i \(-0.496796\pi\)
0.749120 0.662435i \(-0.230477\pi\)
\(192\) 0 0
\(193\) 13.0421 + 8.38163i 0.938789 + 0.603323i 0.918051 0.396462i \(-0.129762\pi\)
0.0207378 + 0.999785i \(0.493398\pi\)
\(194\) 0 0
\(195\) 2.89545 1.83991i 0.207347 0.131759i
\(196\) 0 0
\(197\) 2.51254 + 17.4751i 0.179011 + 1.24505i 0.859056 + 0.511881i \(0.171051\pi\)
−0.680045 + 0.733170i \(0.738040\pi\)
\(198\) 0 0
\(199\) −2.27947 + 2.63064i −0.161587 + 0.186481i −0.830769 0.556617i \(-0.812099\pi\)
0.669182 + 0.743098i \(0.266645\pi\)
\(200\) 0 0
\(201\) 10.5304 9.49261i 0.742760 0.669557i
\(202\) 0 0
\(203\) 0.869821 1.00383i 0.0610494 0.0704548i
\(204\) 0 0
\(205\) −0.593465 4.12764i −0.0414494 0.288287i
\(206\) 0 0
\(207\) −27.5741 4.25320i −1.91653 0.295618i
\(208\) 0 0
\(209\) 5.35555 + 3.44180i 0.370451 + 0.238075i
\(210\) 0 0
\(211\) 0.718721 1.57378i 0.0494788 0.108343i −0.883278 0.468849i \(-0.844669\pi\)
0.932757 + 0.360506i \(0.117396\pi\)
\(212\) 0 0
\(213\) −3.20133 + 21.4842i −0.219352 + 1.47208i
\(214\) 0 0
\(215\) 3.87702 0.557431i 0.264411 0.0380165i
\(216\) 0 0
\(217\) 10.6169 3.11742i 0.720725 0.211624i
\(218\) 0 0
\(219\) 2.23779 3.44318i 0.151216 0.232669i
\(220\) 0 0
\(221\) 8.22746 + 18.0156i 0.553439 + 1.21186i
\(222\) 0 0
\(223\) 1.72185 3.77033i 0.115304 0.252480i −0.843178 0.537635i \(-0.819318\pi\)
0.958481 + 0.285155i \(0.0920451\pi\)
\(224\) 0 0
\(225\) 13.8886 + 0.142232i 0.925908 + 0.00948214i
\(226\) 0 0
\(227\) 18.7033 + 2.68913i 1.24138 + 0.178484i 0.731548 0.681789i \(-0.238798\pi\)
0.509833 + 0.860273i \(0.329707\pi\)
\(228\) 0 0
\(229\) −5.93670 + 9.23768i −0.392308 + 0.610443i −0.980085 0.198580i \(-0.936367\pi\)
0.587777 + 0.809023i \(0.300003\pi\)
\(230\) 0 0
\(231\) −1.67388 + 1.91189i −0.110133 + 0.125793i
\(232\) 0 0
\(233\) −0.376373 + 0.824142i −0.0246570 + 0.0539913i −0.921560 0.388236i \(-0.873084\pi\)
0.896903 + 0.442228i \(0.145812\pi\)
\(234\) 0 0
\(235\) −0.922932 + 0.799725i −0.0602054 + 0.0521683i
\(236\) 0 0
\(237\) 26.3031 7.57722i 1.70857 0.492194i
\(238\) 0 0
\(239\) −4.03610 −0.261074 −0.130537 0.991443i \(-0.541670\pi\)
−0.130537 + 0.991443i \(0.541670\pi\)
\(240\) 0 0
\(241\) −4.39067 1.28922i −0.282828 0.0830458i 0.137242 0.990538i \(-0.456176\pi\)
−0.420070 + 0.907492i \(0.637994\pi\)
\(242\) 0 0
\(243\) −15.4815 + 1.82276i −0.993140 + 0.116930i
\(244\) 0 0
\(245\) −1.35470 2.96638i −0.0865485 0.189515i
\(246\) 0 0
\(247\) −5.09690 + 17.3584i −0.324308 + 1.10449i
\(248\) 0 0
\(249\) −22.0181 0.112740i −1.39534 0.00714458i
\(250\) 0 0
\(251\) 3.39552 23.6163i 0.214323 1.49065i −0.544173 0.838973i \(-0.683157\pi\)
0.758496 0.651677i \(-0.225934\pi\)
\(252\) 0 0
\(253\) −8.05104 + 6.97626i −0.506164 + 0.438594i
\(254\) 0 0
\(255\) 0.945003 6.34195i 0.0591784 0.397148i
\(256\) 0 0
\(257\) −5.18032 17.6425i −0.323139 1.10051i −0.947601 0.319456i \(-0.896500\pi\)
0.624462 0.781055i \(-0.285318\pi\)
\(258\) 0 0
\(259\) 7.43930 + 6.44619i 0.462255 + 0.400547i
\(260\) 0 0
\(261\) 1.70876 2.59995i 0.105769 0.160933i
\(262\) 0 0
\(263\) −2.34820 7.99724i −0.144796 0.493131i 0.854873 0.518837i \(-0.173635\pi\)
−0.999670 + 0.0257060i \(0.991817\pi\)
\(264\) 0 0
\(265\) −1.27824 2.79896i −0.0785217 0.171939i
\(266\) 0 0
\(267\) 1.65297 1.88801i 0.101160 0.115544i
\(268\) 0 0
\(269\) 11.6474i 0.710157i −0.934837 0.355078i \(-0.884454\pi\)
0.934837 0.355078i \(-0.115546\pi\)
\(270\) 0 0
\(271\) 9.86330 4.50442i 0.599153 0.273624i −0.0926633 0.995697i \(-0.529538\pi\)
0.691816 + 0.722073i \(0.256811\pi\)
\(272\) 0 0
\(273\) −6.55326 3.03342i −0.396621 0.183591i
\(274\) 0 0
\(275\) 3.47295 4.00800i 0.209427 0.241691i
\(276\) 0 0
\(277\) −1.64801 + 1.90191i −0.0990196 + 0.114275i −0.803096 0.595849i \(-0.796816\pi\)
0.704077 + 0.710124i \(0.251361\pi\)
\(278\) 0 0
\(279\) 23.6851 10.5248i 1.41799 0.630105i
\(280\) 0 0
\(281\) −7.41890 + 4.76784i −0.442574 + 0.284425i −0.742889 0.669415i \(-0.766545\pi\)
0.300314 + 0.953840i \(0.402908\pi\)
\(282\) 0 0
\(283\) −9.32066 10.7566i −0.554056 0.639415i 0.407767 0.913086i \(-0.366307\pi\)
−0.961823 + 0.273671i \(0.911762\pi\)
\(284\) 0 0
\(285\) 4.44602 3.81282i 0.263359 0.225852i
\(286\) 0 0
\(287\) −6.63391 + 5.74831i −0.391587 + 0.339312i
\(288\) 0 0
\(289\) 19.2066 + 5.63958i 1.12980 + 0.331740i
\(290\) 0 0
\(291\) 17.0834 + 5.11129i 1.00144 + 0.299629i
\(292\) 0 0
\(293\) 10.1776 + 15.8366i 0.594582 + 0.925187i 0.999939 + 0.0110287i \(0.00351062\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(294\) 0 0
\(295\) 1.37151 4.67094i 0.0798525 0.271953i
\(296\) 0 0
\(297\) −3.29448 + 4.95721i −0.191165 + 0.287646i
\(298\) 0 0
\(299\) −25.4679 16.3672i −1.47284 0.946539i
\(300\) 0 0
\(301\) −5.39929 6.23111i −0.311210 0.359155i
\(302\) 0 0
\(303\) 26.7629 12.0570i 1.53749 0.692654i
\(304\) 0 0
\(305\) 5.83511i 0.334117i
\(306\) 0 0
\(307\) −1.02503 0.658746i −0.0585015 0.0375966i 0.511063 0.859543i \(-0.329252\pi\)
−0.569565 + 0.821947i \(0.692888\pi\)
\(308\) 0 0
\(309\) −10.7482 + 9.21740i −0.611441 + 0.524360i
\(310\) 0 0
\(311\) 0.910675 6.33389i 0.0516397 0.359162i −0.947575 0.319534i \(-0.896474\pi\)
0.999215 0.0396278i \(-0.0126172\pi\)
\(312\) 0 0
\(313\) −18.0740 8.25412i −1.02160 0.466550i −0.167068 0.985945i \(-0.553430\pi\)
−0.854534 + 0.519395i \(0.826157\pi\)
\(314\) 0 0
\(315\) 1.24375 + 1.97959i 0.0700771 + 0.111537i
\(316\) 0 0
\(317\) 7.47147 1.07423i 0.419639 0.0603350i 0.0707391 0.997495i \(-0.477464\pi\)
0.348900 + 0.937160i \(0.386555\pi\)
\(318\) 0 0
\(319\) −0.334682 1.13982i −0.0187386 0.0638179i
\(320\) 0 0
\(321\) −22.7337 14.7751i −1.26887 0.824663i
\(322\) 0 0
\(323\) 18.2810 + 28.4459i 1.01718 + 1.58277i
\(324\) 0 0
\(325\) 13.7090 + 6.26070i 0.760440 + 0.347281i
\(326\) 0 0
\(327\) −13.7743 + 3.96799i −0.761718 + 0.219430i
\(328\) 0 0
\(329\) 2.46649 + 0.724228i 0.135982 + 0.0399280i
\(330\) 0 0
\(331\) 20.9135 3.00691i 1.14951 0.165275i 0.458891 0.888493i \(-0.348247\pi\)
0.690620 + 0.723218i \(0.257338\pi\)
\(332\) 0 0
\(333\) 19.2681 + 12.6635i 1.05588 + 0.693956i
\(334\) 0 0
\(335\) −4.81190 1.28453i −0.262902 0.0701812i
\(336\) 0 0
\(337\) −8.27804 7.17296i −0.450934 0.390736i 0.399572 0.916702i \(-0.369159\pi\)
−0.850506 + 0.525966i \(0.823704\pi\)
\(338\) 0 0
\(339\) −8.42563 + 12.9641i −0.457618 + 0.704114i
\(340\) 0 0
\(341\) 2.78811 9.49543i 0.150985 0.514206i
\(342\) 0 0
\(343\) −8.55829 + 13.3170i −0.462104 + 0.719048i
\(344\) 0 0
\(345\) 4.02581 + 8.93609i 0.216742 + 0.481103i
\(346\) 0 0
\(347\) −8.52778 + 5.48047i −0.457795 + 0.294207i −0.749141 0.662411i \(-0.769533\pi\)
0.291346 + 0.956618i \(0.405897\pi\)
\(348\) 0 0
\(349\) −3.83309 26.6597i −0.205181 1.42706i −0.788608 0.614897i \(-0.789198\pi\)
0.583427 0.812166i \(-0.301711\pi\)
\(350\) 0 0
\(351\) −16.1543 5.01412i −0.862255 0.267634i
\(352\) 0 0
\(353\) −4.00838 27.8789i −0.213344 1.48384i −0.761882 0.647716i \(-0.775724\pi\)
0.548537 0.836126i \(-0.315185\pi\)
\(354\) 0 0
\(355\) 6.94098 3.16984i 0.368389 0.168238i
\(356\) 0 0
\(357\) −12.3059 + 5.54392i −0.651295 + 0.293416i
\(358\) 0 0
\(359\) −13.9546 2.00637i −0.736496 0.105892i −0.236149 0.971717i \(-0.575885\pi\)
−0.500347 + 0.865825i \(0.666794\pi\)
\(360\) 0 0
\(361\) −1.69171 + 11.7661i −0.0890376 + 0.619270i
\(362\) 0 0
\(363\) −4.64494 16.1242i −0.243796 0.846300i
\(364\) 0 0
\(365\) −1.44257 −0.0755076
\(366\) 0 0
\(367\) 10.4511 + 4.77287i 0.545544 + 0.249142i 0.669070 0.743200i \(-0.266693\pi\)
−0.123526 + 0.992341i \(0.539420\pi\)
\(368\) 0 0
\(369\) −13.6229 + 15.4001i −0.709178 + 0.801697i
\(370\) 0 0
\(371\) −3.50175 + 5.44884i −0.181802 + 0.282890i
\(372\) 0 0
\(373\) 12.8632i 0.666030i −0.942922 0.333015i \(-0.891934\pi\)
0.942922 0.333015i \(-0.108066\pi\)
\(374\) 0 0
\(375\) −5.44294 8.56549i −0.281072 0.442320i
\(376\) 0 0
\(377\) 2.83997 1.82514i 0.146266 0.0939995i
\(378\) 0 0
\(379\) −16.1756 + 7.38714i −0.830884 + 0.379452i −0.785001 0.619495i \(-0.787337\pi\)
−0.0458831 + 0.998947i \(0.514610\pi\)
\(380\) 0 0
\(381\) −16.5844 26.0987i −0.849644 1.33708i
\(382\) 0 0
\(383\) −9.24502 10.6693i −0.472398 0.545177i 0.468679 0.883369i \(-0.344730\pi\)
−0.941077 + 0.338192i \(0.890185\pi\)
\(384\) 0 0
\(385\) 0.883580 + 0.127040i 0.0450314 + 0.00647454i
\(386\) 0 0
\(387\) −14.4650 12.7957i −0.735299 0.650442i
\(388\) 0 0
\(389\) 20.1160 + 31.3011i 1.01992 + 1.58703i 0.789322 + 0.613979i \(0.210432\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(390\) 0 0
\(391\) −54.2914 + 15.9414i −2.74563 + 0.806190i
\(392\) 0 0
\(393\) −3.34703 24.1565i −0.168835 1.21853i
\(394\) 0 0
\(395\) −7.26714 6.29701i −0.365649 0.316837i
\(396\) 0 0
\(397\) 0.849895 0.249552i 0.0426550 0.0125246i −0.260335 0.965518i \(-0.583833\pi\)
0.302990 + 0.952994i \(0.402015\pi\)
\(398\) 0 0
\(399\) −11.8115 3.53397i −0.591315 0.176920i
\(400\) 0 0
\(401\) 30.6446 1.53032 0.765160 0.643840i \(-0.222660\pi\)
0.765160 + 0.643840i \(0.222660\pi\)
\(402\) 0 0
\(403\) 28.1232 1.40091
\(404\) 0 0
\(405\) 3.50056 + 4.21112i 0.173944 + 0.209252i
\(406\) 0 0
\(407\) 8.44716 2.48031i 0.418710 0.122944i
\(408\) 0 0
\(409\) −3.99205 3.45913i −0.197394 0.171043i 0.550555 0.834799i \(-0.314416\pi\)
−0.747949 + 0.663756i \(0.768961\pi\)
\(410\) 0 0
\(411\) −8.47153 + 1.17378i −0.417870 + 0.0578984i
\(412\) 0 0
\(413\) −9.83219 + 2.88699i −0.483811 + 0.142060i
\(414\) 0 0
\(415\) 4.18178 + 6.50697i 0.205275 + 0.319415i
\(416\) 0 0
\(417\) −29.6600 0.151869i −1.45246 0.00743704i
\(418\) 0 0
\(419\) 31.2307 + 4.49030i 1.52572 + 0.219366i 0.853543 0.521023i \(-0.174449\pi\)
0.672179 + 0.740389i \(0.265359\pi\)
\(420\) 0 0
\(421\) −9.84377 11.3603i −0.479756 0.553668i 0.463343 0.886179i \(-0.346650\pi\)
−0.943099 + 0.332511i \(0.892104\pi\)
\(422\) 0 0
\(423\) 5.95086 + 0.917899i 0.289341 + 0.0446298i
\(424\) 0 0
\(425\) 25.6230 11.7016i 1.24290 0.567613i
\(426\) 0 0
\(427\) 10.3329 6.64055i 0.500044 0.321359i
\(428\) 0 0
\(429\) −5.45101 + 3.46384i −0.263177 + 0.167236i
\(430\) 0 0
\(431\) 34.5012i 1.66187i −0.556373 0.830933i \(-0.687808\pi\)
0.556373 0.830933i \(-0.312192\pi\)
\(432\) 0 0
\(433\) 8.95964 13.9415i 0.430573 0.669985i −0.556392 0.830920i \(-0.687815\pi\)
0.986965 + 0.160935i \(0.0514510\pi\)
\(434\) 0 0
\(435\) −1.09292 0.00559611i −0.0524016 0.000268313i
\(436\) 0 0
\(437\) −47.0154 21.4712i −2.24905 1.02711i
\(438\) 0 0
\(439\) −0.732575 −0.0349639 −0.0174819 0.999847i \(-0.505565\pi\)
−0.0174819 + 0.999847i \(0.505565\pi\)
\(440\) 0 0
\(441\) −6.82881 + 14.5567i −0.325182 + 0.693174i
\(442\) 0 0
\(443\) −5.09060 + 35.4059i −0.241862 + 1.68218i 0.400903 + 0.916120i \(0.368696\pi\)
−0.642765 + 0.766064i \(0.722213\pi\)
\(444\) 0 0
\(445\) −0.872542 0.125453i −0.0413624 0.00594702i
\(446\) 0 0
\(447\) −6.83599 15.1739i −0.323331 0.717699i
\(448\) 0 0
\(449\) −0.701077 + 0.320171i −0.0330859 + 0.0151098i −0.431889 0.901927i \(-0.642153\pi\)
0.398803 + 0.917036i \(0.369426\pi\)
\(450\) 0 0
\(451\) 1.11727 + 7.77076i 0.0526100 + 0.365911i
\(452\) 0 0
\(453\) 31.4668 + 14.5656i 1.47844 + 0.684351i
\(454\) 0 0
\(455\) 0.361020 + 2.51095i 0.0169249 + 0.117715i
\(456\) 0 0
\(457\) 22.2164 14.2776i 1.03924 0.667879i 0.0944416 0.995530i \(-0.469893\pi\)
0.944799 + 0.327651i \(0.106257\pi\)
\(458\) 0 0
\(459\) −26.8552 + 16.6815i −1.25349 + 0.778627i
\(460\) 0 0
\(461\) 13.8050 21.4810i 0.642964 1.00047i −0.354885 0.934910i \(-0.615480\pi\)
0.997849 0.0655610i \(-0.0208837\pi\)
\(462\) 0 0
\(463\) −2.08357 + 7.09599i −0.0968317 + 0.329779i −0.993635 0.112652i \(-0.964065\pi\)
0.896803 + 0.442431i \(0.145884\pi\)
\(464\) 0 0
\(465\) −7.63417 4.96160i −0.354026 0.230089i
\(466\) 0 0
\(467\) 8.29179 + 7.18487i 0.383698 + 0.332476i 0.825258 0.564755i \(-0.191029\pi\)
−0.441560 + 0.897232i \(0.645575\pi\)
\(468\) 0 0
\(469\) 3.20145 + 9.98283i 0.147829 + 0.460964i
\(470\) 0 0
\(471\) 11.5899 1.60585i 0.534033 0.0739935i
\(472\) 0 0
\(473\) −7.29893 + 1.04943i −0.335605 + 0.0482528i
\(474\) 0 0
\(475\) 24.6883 + 7.24914i 1.13278 + 0.332613i
\(476\) 0 0
\(477\) −6.44340 + 13.7351i −0.295023 + 0.628887i
\(478\) 0 0
\(479\) −26.7907 12.2349i −1.22410 0.559027i −0.304736 0.952437i \(-0.598568\pi\)
−0.919363 + 0.393409i \(0.871296\pi\)
\(480\) 0 0
\(481\) 13.5260 + 21.0469i 0.616732 + 0.959654i
\(482\) 0 0
\(483\) 11.2427 17.2985i 0.511559 0.787111i
\(484\) 0 0
\(485\) −1.76480 6.01034i −0.0801352 0.272916i
\(486\) 0 0
\(487\) −21.4636 + 3.08600i −0.972607 + 0.139840i −0.610258 0.792203i \(-0.708934\pi\)
−0.362349 + 0.932042i \(0.618025\pi\)
\(488\) 0 0
\(489\) −0.379463 + 1.26827i −0.0171599 + 0.0573533i
\(490\) 0 0
\(491\) 10.3451 + 4.72447i 0.466870 + 0.213212i 0.634938 0.772563i \(-0.281026\pi\)
−0.168068 + 0.985775i \(0.553753\pi\)
\(492\) 0 0
\(493\) 0.897968 6.24551i 0.0404425 0.281283i
\(494\) 0 0
\(495\) 2.09081 + 0.0214118i 0.0939748 + 0.000962387i
\(496\) 0 0
\(497\) −13.5123 8.68381i −0.606108 0.389522i
\(498\) 0 0
\(499\) 33.0070i 1.47760i −0.673927 0.738798i \(-0.735394\pi\)
0.673927 0.738798i \(-0.264606\pi\)
\(500\) 0 0
\(501\) −12.1331 26.9320i −0.542069 1.20323i
\(502\) 0 0
\(503\) 14.5907 + 16.8386i 0.650567 + 0.750795i 0.981206 0.192963i \(-0.0618097\pi\)
−0.330639 + 0.943757i \(0.607264\pi\)
\(504\) 0 0
\(505\) −8.67464 5.57485i −0.386017 0.248078i
\(506\) 0 0
\(507\) 3.13225 + 2.74231i 0.139108 + 0.121790i
\(508\) 0 0
\(509\) 0.629879 2.14517i 0.0279189 0.0950831i −0.944355 0.328928i \(-0.893313\pi\)
0.972274 + 0.233845i \(0.0751308\pi\)
\(510\) 0 0
\(511\) 1.64169 + 2.55453i 0.0726242 + 0.113006i
\(512\) 0 0
\(513\) −28.5178 4.54838i −1.25909 0.200816i
\(514\) 0 0
\(515\) 4.77252 + 1.40134i 0.210302 + 0.0617503i
\(516\) 0 0
\(517\) 1.73752 1.50557i 0.0764163 0.0662151i
\(518\) 0 0
\(519\) −8.53894 9.95702i −0.374818 0.437065i
\(520\) 0 0
\(521\) −12.0476 13.9037i −0.527817 0.609133i 0.427754 0.903895i \(-0.359305\pi\)
−0.955571 + 0.294762i \(0.904760\pi\)
\(522\) 0 0
\(523\) −5.28647 + 3.39741i −0.231161 + 0.148558i −0.651094 0.758997i \(-0.725690\pi\)
0.419933 + 0.907555i \(0.362053\pi\)
\(524\) 0 0
\(525\) −4.31433 + 9.32048i −0.188293 + 0.406779i
\(526\) 0 0
\(527\) 34.4220 39.7252i 1.49945 1.73046i
\(528\) 0 0
\(529\) 41.5778 47.9833i 1.80773 2.08623i
\(530\) 0 0
\(531\) −21.9344 + 9.74689i −0.951872 + 0.422979i
\(532\) 0 0
\(533\) −20.2938 + 9.26788i −0.879023 + 0.401436i
\(534\) 0 0
\(535\) 9.52458i 0.411784i
\(536\) 0 0
\(537\) 7.08729 + 6.20499i 0.305839 + 0.267765i
\(538\) 0 0
\(539\) 2.55037 + 5.58454i 0.109852 + 0.240543i
\(540\) 0 0
\(541\) −7.79124 26.5345i −0.334972 1.14081i −0.939020 0.343861i \(-0.888265\pi\)
0.604049 0.796947i \(-0.293553\pi\)
\(542\) 0 0
\(543\) 18.2295 2.52581i 0.782304 0.108393i
\(544\) 0 0
\(545\) 3.80561 + 3.29758i 0.163014 + 0.141253i
\(546\) 0 0
\(547\) 9.77075 + 33.2761i 0.417767 + 1.42278i 0.852737 + 0.522340i \(0.174941\pi\)
−0.434970 + 0.900445i \(0.643241\pi\)
\(548\) 0 0
\(549\) 21.9349 18.6168i 0.936157 0.794547i
\(550\) 0 0
\(551\) 4.35586 3.77437i 0.185566 0.160794i
\(552\) 0 0
\(553\) −2.88059 + 20.0350i −0.122495 + 0.851973i
\(554\) 0 0
\(555\) 0.0414724 8.09958i 0.00176041 0.343808i
\(556\) 0 0
\(557\) 3.66286 12.4745i 0.155200 0.528563i −0.844778 0.535116i \(-0.820268\pi\)
0.999979 + 0.00655314i \(0.00208594\pi\)
\(558\) 0 0
\(559\) −8.70515 19.0616i −0.368189 0.806220i
\(560\) 0 0
\(561\) −1.77908 + 11.9394i −0.0751126 + 0.504084i
\(562\) 0 0
\(563\) −7.56202 2.22041i −0.318701 0.0935791i 0.118469 0.992958i \(-0.462201\pi\)
−0.437171 + 0.899379i \(0.644019\pi\)
\(564\) 0 0
\(565\) 5.43150 0.228505
\(566\) 0 0
\(567\) 3.47335 10.9912i 0.145867 0.461589i
\(568\) 0 0
\(569\) −24.4567 + 21.1919i −1.02528 + 0.888409i −0.993810 0.111096i \(-0.964564\pi\)
−0.0314691 + 0.999505i \(0.510019\pi\)
\(570\) 0 0
\(571\) −11.7884 + 25.8130i −0.493330 + 1.08024i 0.485250 + 0.874376i \(0.338729\pi\)
−0.978580 + 0.205867i \(0.933999\pi\)
\(572\) 0 0
\(573\) 32.9143 + 28.8167i 1.37501 + 1.20384i
\(574\) 0 0
\(575\) −23.2785 + 36.2221i −0.970781 + 1.51056i
\(576\) 0 0
\(577\) −13.5436 1.94728i −0.563828 0.0810663i −0.145494 0.989359i \(-0.546477\pi\)
−0.418335 + 0.908293i \(0.637386\pi\)
\(578\) 0 0
\(579\) −20.3833 + 17.4803i −0.847102 + 0.726458i
\(580\) 0 0
\(581\) 6.76364 14.8103i 0.280603 0.614435i
\(582\) 0 0
\(583\) 2.40643 + 5.26936i 0.0996644 + 0.218234i
\(584\) 0 0
\(585\) 1.61557 + 5.71810i 0.0667955 + 0.236414i
\(586\) 0 0
\(587\) −15.3714 + 4.51344i −0.634444 + 0.186290i −0.583112 0.812392i \(-0.698165\pi\)
−0.0513323 + 0.998682i \(0.516347\pi\)
\(588\) 0 0
\(589\) 47.5258 6.83319i 1.95827 0.281556i
\(590\) 0 0
\(591\) −30.2451 4.50677i −1.24412 0.185384i
\(592\) 0 0
\(593\) 0.420135 0.919968i 0.0172529 0.0377786i −0.900809 0.434215i \(-0.857026\pi\)
0.918062 + 0.396436i \(0.129753\pi\)
\(594\) 0 0
\(595\) 3.98870 + 2.56338i 0.163521 + 0.105088i
\(596\) 0 0
\(597\) −3.23351 5.08854i −0.132339 0.208260i
\(598\) 0 0
\(599\) −1.01345 7.04867i −0.0414083 0.288001i −0.999995 0.00319963i \(-0.998982\pi\)
0.958587 0.284801i \(-0.0919276\pi\)
\(600\) 0 0
\(601\) 9.23676 10.6598i 0.376775 0.434822i −0.535415 0.844589i \(-0.679845\pi\)
0.912190 + 0.409767i \(0.134390\pi\)
\(602\) 0 0
\(603\) 10.5236 + 22.1868i 0.428555 + 0.903516i
\(604\) 0 0
\(605\) −3.86015 + 4.45485i −0.156937 + 0.181116i
\(606\) 0 0
\(607\) 2.12560 + 14.7839i 0.0862754 + 0.600059i 0.986392 + 0.164410i \(0.0525720\pi\)
−0.900117 + 0.435649i \(0.856519\pi\)
\(608\) 0 0
\(609\) 1.23387 + 1.94173i 0.0499991 + 0.0786830i
\(610\) 0 0
\(611\) 5.49631 + 3.53227i 0.222357 + 0.142900i
\(612\) 0 0
\(613\) −1.00616 + 2.20318i −0.0406384 + 0.0889857i −0.928862 0.370425i \(-0.879212\pi\)
0.888224 + 0.459411i \(0.151939\pi\)
\(614\) 0 0
\(615\) 7.14393 + 1.06450i 0.288071 + 0.0429250i
\(616\) 0 0
\(617\) 33.8862 4.87210i 1.36421 0.196144i 0.578976 0.815345i \(-0.303453\pi\)
0.785232 + 0.619201i \(0.212544\pi\)
\(618\) 0 0
\(619\) 18.7221 5.49730i 0.752504 0.220955i 0.117084 0.993122i \(-0.462645\pi\)
0.635420 + 0.772167i \(0.280827\pi\)
\(620\) 0 0
\(621\) 20.7475 43.6440i 0.832570 1.75137i
\(622\) 0 0
\(623\) 0.770829 + 1.68788i 0.0308826 + 0.0676235i
\(624\) 0 0
\(625\) 8.13542 17.8141i 0.325417 0.712563i
\(626\) 0 0
\(627\) −8.37014 + 7.17806i −0.334271 + 0.286664i
\(628\) 0 0
\(629\) 46.2851 + 6.65479i 1.84551 + 0.265344i
\(630\) 0 0
\(631\) 18.6285 28.9865i 0.741589 1.15394i −0.241427 0.970419i \(-0.577616\pi\)
0.983017 0.183517i \(-0.0587481\pi\)
\(632\) 0 0
\(633\) 2.25465 + 1.97397i 0.0896144 + 0.0784583i
\(634\) 0 0
\(635\) −4.51252 + 9.88104i −0.179074 + 0.392117i
\(636\) 0 0
\(637\) −13.1853 + 11.4252i −0.522422 + 0.452681i
\(638\) 0 0
\(639\) −34.0609 15.9786i −1.34743 0.632106i
\(640\) 0 0
\(641\) 39.9842 1.57928 0.789641 0.613570i \(-0.210267\pi\)
0.789641 + 0.613570i \(0.210267\pi\)
\(642\) 0 0
\(643\) 35.2776 + 10.3584i 1.39121 + 0.408497i 0.889658 0.456628i \(-0.150943\pi\)
0.501556 + 0.865125i \(0.332761\pi\)
\(644\) 0 0
\(645\) −0.999870 + 6.71016i −0.0393698 + 0.264212i
\(646\) 0 0
\(647\) −6.01849 13.1787i −0.236611 0.518106i 0.753659 0.657266i \(-0.228287\pi\)
−0.990270 + 0.139160i \(0.955560\pi\)
\(648\) 0 0
\(649\) −2.58203 + 8.79357i −0.101353 + 0.345178i
\(650\) 0 0
\(651\) −0.0981317 + 19.1652i −0.00384609 + 0.751142i
\(652\) 0 0
\(653\) −0.548182 + 3.81269i −0.0214520 + 0.149202i −0.997732 0.0673090i \(-0.978559\pi\)
0.976280 + 0.216511i \(0.0694678\pi\)
\(654\) 0 0
\(655\) −6.47452 + 5.61021i −0.252981 + 0.219209i
\(656\) 0 0
\(657\) 4.60250 + 5.42279i 0.179561 + 0.211563i
\(658\) 0 0
\(659\) 1.69144 + 5.76053i 0.0658893 + 0.224398i 0.985855 0.167601i \(-0.0536019\pi\)
−0.919966 + 0.391999i \(0.871784\pi\)
\(660\) 0 0
\(661\) −9.68627 8.39320i −0.376752 0.326458i 0.445815 0.895125i \(-0.352914\pi\)
−0.822568 + 0.568667i \(0.807459\pi\)
\(662\) 0 0
\(663\) −33.9793 + 4.70804i −1.31965 + 0.182845i
\(664\) 0 0
\(665\) 1.22019 + 4.15558i 0.0473168 + 0.161146i
\(666\) 0 0
\(667\) 4.00659 + 8.77321i 0.155136 + 0.339700i
\(668\) 0 0
\(669\) 5.40151 + 4.72907i 0.208834 + 0.182836i
\(670\) 0 0
\(671\) 10.9853i 0.424081i
\(672\) 0 0
\(673\) 32.8059 14.9819i 1.26457 0.577511i 0.333640 0.942701i \(-0.391723\pi\)
0.930933 + 0.365190i \(0.118996\pi\)
\(674\) 0 0
\(675\) −7.13141 + 22.9758i −0.274488 + 0.884337i
\(676\) 0 0
\(677\) 6.41707 7.40570i 0.246628 0.284624i −0.618915 0.785458i \(-0.712428\pi\)
0.865544 + 0.500834i \(0.166973\pi\)
\(678\) 0 0
\(679\) −8.63481 + 9.96510i −0.331373 + 0.382425i
\(680\) 0 0
\(681\) −13.7480 + 29.7006i −0.526826 + 1.13813i
\(682\) 0 0
\(683\) 13.6651 8.78203i 0.522881 0.336035i −0.252430 0.967615i \(-0.581230\pi\)
0.775311 + 0.631580i \(0.217593\pi\)
\(684\) 0 0
\(685\) 1.96746 + 2.27057i 0.0751729 + 0.0867542i
\(686\) 0 0
\(687\) −12.3813 14.4375i −0.472376 0.550824i
\(688\) 0 0
\(689\) −12.4412 + 10.7803i −0.473971 + 0.410698i
\(690\) 0 0
\(691\) −5.07491 1.49013i −0.193059 0.0566872i 0.183774 0.982969i \(-0.441169\pi\)
−0.376833 + 0.926281i \(0.622987\pi\)
\(692\) 0 0
\(693\) −2.34149 3.72680i −0.0889460 0.141569i
\(694\) 0 0
\(695\) 5.63317 + 8.76538i 0.213678 + 0.332490i
\(696\) 0 0
\(697\) −11.7479 + 40.0095i −0.444982 + 1.51547i
\(698\) 0 0
\(699\) −1.18070 1.03371i −0.0446580 0.0390985i
\(700\) 0 0
\(701\) −18.4569 11.8615i −0.697108 0.448004i 0.143499 0.989651i \(-0.454165\pi\)
−0.840606 + 0.541647i \(0.817801\pi\)
\(702\) 0 0
\(703\) 27.9717 + 32.2810i 1.05497 + 1.21750i
\(704\) 0 0
\(705\) −0.868825 1.92853i −0.0327218 0.0726327i
\(706\) 0 0
\(707\) 21.7056i 0.816322i
\(708\) 0 0
\(709\) −16.7714 10.7783i −0.629865 0.404789i 0.186395 0.982475i \(-0.440320\pi\)
−0.816259 + 0.577686i \(0.803956\pi\)
\(710\) 0 0
\(711\) −0.485506 + 47.4086i −0.0182079 + 1.77796i
\(712\) 0 0
\(713\) −11.4346 + 79.5292i −0.428228 + 2.97839i
\(714\) 0 0
\(715\) 2.06377 + 0.942492i 0.0771806 + 0.0352472i
\(716\) 0 0
\(717\) 2.00384 6.69739i 0.0748347 0.250119i
\(718\) 0 0
\(719\) −20.6253 + 2.96548i −0.769195 + 0.110594i −0.515730 0.856751i \(-0.672479\pi\)
−0.253465 + 0.967345i \(0.581570\pi\)
\(720\) 0 0
\(721\) −2.94978 10.0460i −0.109855 0.374133i
\(722\) 0 0
\(723\) 4.31916 6.64568i 0.160631 0.247156i
\(724\) 0 0
\(725\) −2.59583 4.03920i −0.0964069 0.150012i
\(726\) 0 0
\(727\) 14.7024 + 6.71435i 0.545281 + 0.249021i 0.668957 0.743301i \(-0.266741\pi\)
−0.123676 + 0.992323i \(0.539468\pi\)
\(728\) 0 0
\(729\) 4.66160 26.5945i 0.172652 0.984983i
\(730\) 0 0
\(731\) −37.5802 11.0345i −1.38995 0.408127i
\(732\) 0 0
\(733\) −6.02305 + 0.865984i −0.222467 + 0.0319859i −0.252647 0.967559i \(-0.581301\pi\)
0.0301801 + 0.999544i \(0.490392\pi\)
\(734\) 0 0
\(735\) 5.59489 0.775206i 0.206371 0.0285939i
\(736\) 0 0
\(737\) 9.05896 + 2.41827i 0.333691 + 0.0890780i
\(738\) 0 0
\(739\) 16.3473 + 14.1650i 0.601345 + 0.521068i 0.901476 0.432830i \(-0.142485\pi\)
−0.300131 + 0.953898i \(0.597030\pi\)
\(740\) 0 0
\(741\) −26.2736 17.0757i −0.965184 0.627292i
\(742\) 0 0
\(743\) −2.90477 + 9.89274i −0.106566 + 0.362929i −0.995460 0.0951835i \(-0.969656\pi\)
0.888894 + 0.458113i \(0.151474\pi\)
\(744\) 0 0
\(745\) −3.16080 + 4.91830i −0.115803 + 0.180193i
\(746\) 0 0
\(747\) 11.1186 36.4802i 0.406807 1.33474i
\(748\) 0 0
\(749\) 16.8663 10.8393i 0.616280 0.396059i
\(750\) 0 0
\(751\) 5.38440 + 37.4493i 0.196480 + 1.36654i 0.814400 + 0.580304i \(0.197066\pi\)
−0.617920 + 0.786241i \(0.712025\pi\)
\(752\) 0 0
\(753\) 37.5025 + 17.3594i 1.36667 + 0.632612i
\(754\) 0 0
\(755\) −1.73351 12.0568i −0.0630888 0.438792i
\(756\) 0 0
\(757\) −34.1999 + 15.6186i −1.24302 + 0.567667i −0.924837 0.380363i \(-0.875799\pi\)
−0.318180 + 0.948030i \(0.603072\pi\)
\(758\) 0 0
\(759\) −7.57904 16.8232i −0.275102 0.610644i
\(760\) 0 0
\(761\) −36.7723 5.28706i −1.33300 0.191656i −0.561281 0.827625i \(-0.689691\pi\)
−0.771714 + 0.635969i \(0.780600\pi\)
\(762\) 0 0
\(763\) 1.50849 10.4918i 0.0546110 0.379828i
\(764\) 0 0
\(765\) 10.0545 + 4.71675i 0.363520 + 0.170534i
\(766\) 0 0
\(767\) −26.0445 −0.940411
\(768\) 0 0
\(769\) −24.3703 11.1296i −0.878817 0.401342i −0.0756767 0.997132i \(-0.524112\pi\)
−0.803140 + 0.595790i \(0.796839\pi\)
\(770\) 0 0
\(771\) 31.8474 + 0.163069i 1.14696 + 0.00587278i
\(772\) 0 0
\(773\) −13.4086 + 20.8642i −0.482273 + 0.750432i −0.994078 0.108670i \(-0.965341\pi\)
0.511805 + 0.859102i \(0.328977\pi\)
\(774\) 0 0
\(775\) 39.9986i 1.43679i
\(776\) 0 0