Properties

Label 729.2.i.a.685.8
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.8
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16160 - 0.323353i) q^{2} +(-0.467580 - 0.282186i) q^{4} +(1.06011 - 0.0411373i) q^{5} +(-5.09437 - 0.796745i) q^{7} +(2.10679 + 2.23306i) q^{8} +O(q^{10})\) \(q+(-1.16160 - 0.323353i) q^{2} +(-0.467580 - 0.282186i) q^{4} +(1.06011 - 0.0411373i) q^{5} +(-5.09437 - 0.796745i) q^{7} +(2.10679 + 2.23306i) q^{8} +(-1.24473 - 0.295006i) q^{10} +(-0.460015 - 3.36790i) q^{11} +(1.07510 - 1.56753i) q^{13} +(5.65998 + 2.57278i) q^{14} +(-1.21613 - 2.30876i) q^{16} +(1.45551 - 0.730985i) q^{17} +(0.362880 + 6.23041i) q^{19} +(-0.507297 - 0.279915i) q^{20} +(-0.554669 + 4.06090i) q^{22} +(-1.67377 + 4.33516i) q^{23} +(-3.86281 + 0.300242i) q^{25} +(-1.75569 + 1.47320i) q^{26} +(2.15720 + 1.81010i) q^{28} +(5.05124 + 3.61041i) q^{29} +(-3.36645 + 3.85752i) q^{31} +(-0.633769 - 2.92581i) q^{32} +(-1.92708 + 0.378467i) q^{34} +(-5.43339 - 0.635072i) q^{35} +(-3.97044 - 5.33323i) q^{37} +(1.59310 - 7.35458i) q^{38} +(2.32530 + 2.28064i) q^{40} +(-1.40191 + 5.44257i) q^{41} +(3.72490 + 3.38017i) q^{43} +(-0.735282 + 1.70458i) q^{44} +(3.34603 - 4.49450i) q^{46} +(3.71155 + 4.25297i) q^{47} +(18.6520 + 5.98054i) q^{49} +(4.58412 + 0.900292i) q^{50} +(-0.945028 + 0.429568i) q^{52} +(0.178958 - 1.01492i) q^{53} +(-0.626215 - 3.55144i) q^{55} +(-8.95356 - 13.0546i) q^{56} +(-4.70007 - 5.82717i) q^{58} +(-7.85300 + 3.20830i) q^{59} +(-4.86498 + 2.93603i) q^{61} +(5.15780 - 3.39234i) q^{62} +(-0.513337 + 8.81366i) q^{64} +(1.07524 - 1.70599i) q^{65} +(-2.72787 + 1.94976i) q^{67} +(-0.886842 - 0.0689308i) q^{68} +(6.10606 + 2.49460i) q^{70} +(4.36535 + 14.5813i) q^{71} +(3.76584 - 0.892520i) q^{73} +(2.88754 + 7.47892i) q^{74} +(1.58846 - 3.01562i) q^{76} +(-0.339875 + 17.5239i) q^{77} +(-9.19140 + 9.01486i) q^{79} +(-1.38421 - 2.39753i) q^{80} +(3.38833 - 5.86876i) q^{82} +(1.47505 + 5.72648i) q^{83} +(1.51294 - 0.834803i) q^{85} +(-3.23385 - 5.13086i) q^{86} +(6.55159 - 8.12269i) q^{88} +(0.365741 - 1.22166i) q^{89} +(-6.72585 + 7.12899i) q^{91} +(2.00594 - 1.55472i) q^{92} +(-2.93612 - 6.14038i) q^{94} +(0.640997 + 6.59002i) q^{95} +(-11.0068 - 0.427113i) q^{97} +(-19.7324 - 12.9782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16160 0.323353i −0.821374 0.228645i −0.168103 0.985769i \(-0.553764\pi\)
−0.653271 + 0.757124i \(0.726604\pi\)
\(3\) 0 0
\(4\) −0.467580 0.282186i −0.233790 0.141093i
\(5\) 1.06011 0.0411373i 0.474098 0.0183971i 0.199380 0.979922i \(-0.436107\pi\)
0.274717 + 0.961525i \(0.411416\pi\)
\(6\) 0 0
\(7\) −5.09437 0.796745i −1.92549 0.301141i −0.928038 0.372485i \(-0.878506\pi\)
−0.997452 + 0.0713435i \(0.977271\pi\)
\(8\) 2.10679 + 2.23306i 0.744861 + 0.789507i
\(9\) 0 0
\(10\) −1.24473 0.295006i −0.393618 0.0932892i
\(11\) −0.460015 3.36790i −0.138700 1.01546i −0.920170 0.391519i \(-0.871950\pi\)
0.781470 0.623942i \(-0.214470\pi\)
\(12\) 0 0
\(13\) 1.07510 1.56753i 0.298178 0.434754i −0.646421 0.762981i \(-0.723735\pi\)
0.944599 + 0.328227i \(0.106451\pi\)
\(14\) 5.65998 + 2.57278i 1.51269 + 0.687603i
\(15\) 0 0
\(16\) −1.21613 2.30876i −0.304032 0.577191i
\(17\) 1.45551 0.730985i 0.353013 0.177290i −0.263451 0.964673i \(-0.584861\pi\)
0.616464 + 0.787383i \(0.288564\pi\)
\(18\) 0 0
\(19\) 0.362880 + 6.23041i 0.0832504 + 1.42935i 0.738659 + 0.674080i \(0.235460\pi\)
−0.655408 + 0.755275i \(0.727503\pi\)
\(20\) −0.507297 0.279915i −0.113435 0.0625909i
\(21\) 0 0
\(22\) −0.554669 + 4.06090i −0.118256 + 0.865786i
\(23\) −1.67377 + 4.33516i −0.349004 + 0.903944i 0.641582 + 0.767055i \(0.278278\pi\)
−0.990586 + 0.136890i \(0.956289\pi\)
\(24\) 0 0
\(25\) −3.86281 + 0.300242i −0.772563 + 0.0600483i
\(26\) −1.75569 + 1.47320i −0.344320 + 0.288919i
\(27\) 0 0
\(28\) 2.15720 + 1.81010i 0.407672 + 0.342077i
\(29\) 5.05124 + 3.61041i 0.937991 + 0.670436i 0.944140 0.329546i \(-0.106896\pi\)
−0.00614886 + 0.999981i \(0.501957\pi\)
\(30\) 0 0
\(31\) −3.36645 + 3.85752i −0.604632 + 0.692831i −0.971391 0.237485i \(-0.923677\pi\)
0.366760 + 0.930316i \(0.380467\pi\)
\(32\) −0.633769 2.92581i −0.112036 0.517214i
\(33\) 0 0
\(34\) −1.92708 + 0.378467i −0.330492 + 0.0649066i
\(35\) −5.43339 0.635072i −0.918411 0.107347i
\(36\) 0 0
\(37\) −3.97044 5.33323i −0.652737 0.876778i 0.345358 0.938471i \(-0.387757\pi\)
−0.998095 + 0.0616933i \(0.980350\pi\)
\(38\) 1.59310 7.35458i 0.258435 1.19307i
\(39\) 0 0
\(40\) 2.32530 + 2.28064i 0.367662 + 0.360600i
\(41\) −1.40191 + 5.44257i −0.218942 + 0.849986i 0.760678 + 0.649129i \(0.224867\pi\)
−0.979621 + 0.200857i \(0.935627\pi\)
\(42\) 0 0
\(43\) 3.72490 + 3.38017i 0.568042 + 0.515471i 0.904639 0.426178i \(-0.140140\pi\)
−0.336597 + 0.941649i \(0.609276\pi\)
\(44\) −0.735282 + 1.70458i −0.110848 + 0.256974i
\(45\) 0 0
\(46\) 3.34603 4.49450i 0.493346 0.662678i
\(47\) 3.71155 + 4.25297i 0.541386 + 0.620359i 0.957318 0.289036i \(-0.0933348\pi\)
−0.415932 + 0.909396i \(0.636545\pi\)
\(48\) 0 0
\(49\) 18.6520 + 5.98054i 2.66458 + 0.854363i
\(50\) 4.58412 + 0.900292i 0.648293 + 0.127321i
\(51\) 0 0
\(52\) −0.945028 + 0.429568i −0.131052 + 0.0595704i
\(53\) 0.178958 1.01492i 0.0245817 0.139410i −0.970047 0.242918i \(-0.921896\pi\)
0.994629 + 0.103508i \(0.0330066\pi\)
\(54\) 0 0
\(55\) −0.626215 3.55144i −0.0844388 0.478876i
\(56\) −8.95356 13.0546i −1.19647 1.74450i
\(57\) 0 0
\(58\) −4.70007 5.82717i −0.617149 0.765145i
\(59\) −7.85300 + 3.20830i −1.02237 + 0.417686i −0.826496 0.562943i \(-0.809669\pi\)
−0.195878 + 0.980628i \(0.562756\pi\)
\(60\) 0 0
\(61\) −4.86498 + 2.93603i −0.622897 + 0.375920i −0.792748 0.609550i \(-0.791350\pi\)
0.169851 + 0.985470i \(0.445671\pi\)
\(62\) 5.15780 3.39234i 0.655041 0.430827i
\(63\) 0 0
\(64\) −0.513337 + 8.81366i −0.0641672 + 1.10171i
\(65\) 1.07524 1.70599i 0.133367 0.211601i
\(66\) 0 0
\(67\) −2.72787 + 1.94976i −0.333262 + 0.238201i −0.735795 0.677204i \(-0.763191\pi\)
0.402533 + 0.915405i \(0.368130\pi\)
\(68\) −0.886842 0.0689308i −0.107545 0.00835909i
\(69\) 0 0
\(70\) 6.10606 + 2.49460i 0.729814 + 0.298162i
\(71\) 4.36535 + 14.5813i 0.518072 + 1.73048i 0.670258 + 0.742128i \(0.266184\pi\)
−0.152186 + 0.988352i \(0.548631\pi\)
\(72\) 0 0
\(73\) 3.76584 0.892520i 0.440758 0.104462i −0.00424423 0.999991i \(-0.501351\pi\)
0.445002 + 0.895529i \(0.353203\pi\)
\(74\) 2.88754 + 7.47892i 0.335670 + 0.869407i
\(75\) 0 0
\(76\) 1.58846 3.01562i 0.182209 0.345915i
\(77\) −0.339875 + 17.5239i −0.0387323 + 1.99703i
\(78\) 0 0
\(79\) −9.19140 + 9.01486i −1.03411 + 1.01425i −0.0342236 + 0.999414i \(0.510896\pi\)
−0.999890 + 0.0148372i \(0.995277\pi\)
\(80\) −1.38421 2.39753i −0.154760 0.268052i
\(81\) 0 0
\(82\) 3.38833 5.86876i 0.374179 0.648097i
\(83\) 1.47505 + 5.72648i 0.161907 + 0.628563i 0.996927 + 0.0783423i \(0.0249627\pi\)
−0.835019 + 0.550221i \(0.814543\pi\)
\(84\) 0 0
\(85\) 1.51294 0.834803i 0.164101 0.0905471i
\(86\) −3.23385 5.13086i −0.348715 0.553275i
\(87\) 0 0
\(88\) 6.55159 8.12269i 0.698402 0.865882i
\(89\) 0.365741 1.22166i 0.0387684 0.129496i −0.936415 0.350895i \(-0.885877\pi\)
0.975183 + 0.221400i \(0.0710625\pi\)
\(90\) 0 0
\(91\) −6.72585 + 7.12899i −0.705061 + 0.747321i
\(92\) 2.00594 1.55472i 0.209134 0.162091i
\(93\) 0 0
\(94\) −2.93612 6.14038i −0.302838 0.633332i
\(95\) 0.640997 + 6.59002i 0.0657649 + 0.676122i
\(96\) 0 0
\(97\) −11.0068 0.427113i −1.11757 0.0433668i −0.526639 0.850089i \(-0.676548\pi\)
−0.590931 + 0.806722i \(0.701239\pi\)
\(98\) −19.7324 12.9782i −1.99327 1.31099i
\(99\) 0 0
\(100\) 1.89090 + 0.949646i 0.189090 + 0.0949646i
\(101\) −0.287246 14.8103i −0.0285821 1.47368i −0.690078 0.723735i \(-0.742424\pi\)
0.661496 0.749949i \(-0.269922\pi\)
\(102\) 0 0
\(103\) 2.72646 + 2.11317i 0.268646 + 0.208217i 0.738013 0.674787i \(-0.235764\pi\)
−0.469366 + 0.883004i \(0.655518\pi\)
\(104\) 5.76538 0.901690i 0.565342 0.0884179i
\(105\) 0 0
\(106\) −0.536054 + 1.12106i −0.0520662 + 0.108887i
\(107\) 8.41522 + 3.06289i 0.813530 + 0.296101i 0.715081 0.699041i \(-0.246390\pi\)
0.0984490 + 0.995142i \(0.468612\pi\)
\(108\) 0 0
\(109\) 4.22664 1.53837i 0.404839 0.147349i −0.131571 0.991307i \(-0.542002\pi\)
0.536410 + 0.843957i \(0.319780\pi\)
\(110\) −0.420959 + 4.32783i −0.0401368 + 0.412643i
\(111\) 0 0
\(112\) 4.35591 + 12.7306i 0.411595 + 1.20293i
\(113\) 7.72128 7.00669i 0.726357 0.659134i −0.222466 0.974940i \(-0.571411\pi\)
0.948824 + 0.315806i \(0.102275\pi\)
\(114\) 0 0
\(115\) −1.59605 + 4.66462i −0.148832 + 0.434978i
\(116\) −1.34305 3.11354i −0.124699 0.289085i
\(117\) 0 0
\(118\) 10.1594 1.18747i 0.935253 0.109315i
\(119\) −7.99731 + 2.56424i −0.733113 + 0.235063i
\(120\) 0 0
\(121\) −0.534079 + 0.148671i −0.0485526 + 0.0135155i
\(122\) 6.60053 1.83738i 0.597584 0.166349i
\(123\) 0 0
\(124\) 2.66262 0.853736i 0.239111 0.0766678i
\(125\) −9.35137 + 1.09302i −0.836412 + 0.0977625i
\(126\) 0 0
\(127\) −5.19008 12.0320i −0.460545 1.06766i −0.977363 0.211568i \(-0.932143\pi\)
0.516818 0.856095i \(-0.327116\pi\)
\(128\) 1.50792 4.40705i 0.133282 0.389532i
\(129\) 0 0
\(130\) −1.80063 + 1.63399i −0.157926 + 0.143310i
\(131\) −1.15372 3.37189i −0.100801 0.294603i 0.884211 0.467088i \(-0.154697\pi\)
−0.985012 + 0.172485i \(0.944820\pi\)
\(132\) 0 0
\(133\) 3.11540 32.0291i 0.270140 2.77728i
\(134\) 3.79915 1.38278i 0.328196 0.119454i
\(135\) 0 0
\(136\) 4.69878 + 1.71022i 0.402917 + 0.146650i
\(137\) 0.519553 1.08655i 0.0443884 0.0928305i −0.878778 0.477230i \(-0.841641\pi\)
0.923167 + 0.384400i \(0.125591\pi\)
\(138\) 0 0
\(139\) −8.10344 + 1.26735i −0.687325 + 0.107496i −0.488532 0.872546i \(-0.662467\pi\)
−0.198793 + 0.980042i \(0.563702\pi\)
\(140\) 2.36134 + 1.83018i 0.199570 + 0.154678i
\(141\) 0 0
\(142\) −0.355881 18.3491i −0.0298649 1.53983i
\(143\) −5.77384 2.89973i −0.482833 0.242488i
\(144\) 0 0
\(145\) 5.50341 + 3.61965i 0.457033 + 0.300596i
\(146\) −4.66299 0.180945i −0.385912 0.0149751i
\(147\) 0 0
\(148\) 0.351537 + 3.61412i 0.0288962 + 0.297079i
\(149\) 3.06646 + 6.41296i 0.251214 + 0.525370i 0.988685 0.150010i \(-0.0479305\pi\)
−0.737470 + 0.675380i \(0.763980\pi\)
\(150\) 0 0
\(151\) −9.14505 + 7.08795i −0.744214 + 0.576809i −0.912572 0.408917i \(-0.865907\pi\)
0.168358 + 0.985726i \(0.446154\pi\)
\(152\) −13.1484 + 13.9365i −1.06648 + 1.13040i
\(153\) 0 0
\(154\) 6.06119 20.2458i 0.488424 1.63145i
\(155\) −3.41013 + 4.22790i −0.273908 + 0.339593i
\(156\) 0 0
\(157\) 1.20350 + 1.90948i 0.0960496 + 0.152393i 0.890573 0.454841i \(-0.150304\pi\)
−0.794523 + 0.607234i \(0.792279\pi\)
\(158\) 13.5917 7.49958i 1.08130 0.596635i
\(159\) 0 0
\(160\) −0.792228 3.07562i −0.0626311 0.243149i
\(161\) 11.9808 20.7514i 0.944219 1.63544i
\(162\) 0 0
\(163\) −7.52478 13.0333i −0.589386 1.02085i −0.994313 0.106498i \(-0.966036\pi\)
0.404927 0.914349i \(-0.367297\pi\)
\(164\) 2.19133 2.14924i 0.171114 0.167827i
\(165\) 0 0
\(166\) 0.138264 7.12884i 0.0107313 0.553305i
\(167\) 8.96893 17.0271i 0.694037 1.31760i −0.243565 0.969885i \(-0.578317\pi\)
0.937602 0.347712i \(-0.113041\pi\)
\(168\) 0 0
\(169\) 3.38100 + 8.75700i 0.260077 + 0.673616i
\(170\) −2.02736 + 0.480493i −0.155492 + 0.0368522i
\(171\) 0 0
\(172\) −0.787855 2.63162i −0.0600733 0.200659i
\(173\) −20.4774 8.36595i −1.55687 0.636052i −0.573753 0.819028i \(-0.694513\pi\)
−0.983117 + 0.182977i \(0.941427\pi\)
\(174\) 0 0
\(175\) 19.9178 + 1.54813i 1.50565 + 0.117028i
\(176\) −7.21625 + 5.15787i −0.543946 + 0.388789i
\(177\) 0 0
\(178\) −0.819871 + 1.30081i −0.0614519 + 0.0975001i
\(179\) −0.179928 + 3.08924i −0.0134484 + 0.230901i 0.984886 + 0.173205i \(0.0554124\pi\)
−0.998334 + 0.0576958i \(0.981625\pi\)
\(180\) 0 0
\(181\) −5.12498 + 3.37075i −0.380936 + 0.250546i −0.725507 0.688214i \(-0.758395\pi\)
0.344571 + 0.938760i \(0.388024\pi\)
\(182\) 10.1179 6.10619i 0.749990 0.452621i
\(183\) 0 0
\(184\) −13.2070 + 5.39564i −0.973630 + 0.397772i
\(185\) −4.42852 5.49050i −0.325591 0.403670i
\(186\) 0 0
\(187\) −3.13144 4.56575i −0.228994 0.333881i
\(188\) −0.535321 3.03595i −0.0390423 0.221420i
\(189\) 0 0
\(190\) 1.38632 7.86223i 0.100574 0.570386i
\(191\) 11.5320 5.24192i 0.834423 0.379292i 0.0494159 0.998778i \(-0.484264\pi\)
0.785007 + 0.619486i \(0.212659\pi\)
\(192\) 0 0
\(193\) −6.38554 1.25408i −0.459641 0.0902706i −0.0424686 0.999098i \(-0.513522\pi\)
−0.417173 + 0.908827i \(0.636979\pi\)
\(194\) 12.6474 + 4.05521i 0.908027 + 0.291147i
\(195\) 0 0
\(196\) −7.03371 8.05974i −0.502408 0.575695i
\(197\) −14.2567 + 19.1501i −1.01575 + 1.36439i −0.0859583 + 0.996299i \(0.527395\pi\)
−0.929791 + 0.368089i \(0.880012\pi\)
\(198\) 0 0
\(199\) −4.51175 + 10.4594i −0.319829 + 0.741448i 0.680136 + 0.733086i \(0.261921\pi\)
−0.999965 + 0.00836158i \(0.997338\pi\)
\(200\) −8.80858 7.99336i −0.622861 0.565216i
\(201\) 0 0
\(202\) −4.45530 + 17.2965i −0.313474 + 1.21698i
\(203\) −22.8563 22.4173i −1.60420 1.57338i
\(204\) 0 0
\(205\) −1.26230 + 5.82742i −0.0881627 + 0.407004i
\(206\) −2.48376 3.33626i −0.173051 0.232448i
\(207\) 0 0
\(208\) −4.92650 0.575826i −0.341592 0.0399263i
\(209\) 20.8165 4.08823i 1.43991 0.282789i
\(210\) 0 0
\(211\) −1.86515 8.61049i −0.128402 0.592771i −0.995511 0.0946511i \(-0.969826\pi\)
0.867108 0.498120i \(-0.165976\pi\)
\(212\) −0.370074 + 0.424057i −0.0254168 + 0.0291244i
\(213\) 0 0
\(214\) −8.78471 6.27894i −0.600511 0.429219i
\(215\) 4.08788 + 3.43013i 0.278791 + 0.233933i
\(216\) 0 0
\(217\) 20.2234 16.9694i 1.37285 1.15196i
\(218\) −5.40709 + 0.420273i −0.366215 + 0.0284644i
\(219\) 0 0
\(220\) −0.709362 + 1.83729i −0.0478252 + 0.123870i
\(221\) 0.418974 3.06743i 0.0281832 0.206338i
\(222\) 0 0
\(223\) 2.24629 + 1.23945i 0.150423 + 0.0829998i 0.556538 0.830822i \(-0.312129\pi\)
−0.406115 + 0.913822i \(0.633117\pi\)
\(224\) 0.897535 + 15.4101i 0.0599691 + 1.02963i
\(225\) 0 0
\(226\) −11.2347 + 5.64226i −0.747319 + 0.375318i
\(227\) −3.75983 7.13785i −0.249548 0.473756i 0.727688 0.685908i \(-0.240595\pi\)
−0.977237 + 0.212152i \(0.931953\pi\)
\(228\) 0 0
\(229\) −14.2020 6.45559i −0.938493 0.426597i −0.114644 0.993407i \(-0.536573\pi\)
−0.823849 + 0.566809i \(0.808178\pi\)
\(230\) 3.36229 4.90233i 0.221703 0.323250i
\(231\) 0 0
\(232\) 2.57961 + 18.8861i 0.169360 + 1.23993i
\(233\) −17.0958 4.05179i −1.11999 0.265441i −0.371396 0.928475i \(-0.621121\pi\)
−0.748590 + 0.663033i \(0.769269\pi\)
\(234\) 0 0
\(235\) 4.10963 + 4.35595i 0.268083 + 0.284151i
\(236\) 4.57725 + 0.715869i 0.297954 + 0.0465991i
\(237\) 0 0
\(238\) 10.1188 0.392656i 0.655906 0.0254521i
\(239\) −25.8298 15.5884i −1.67079 1.00833i −0.948520 0.316717i \(-0.897419\pi\)
−0.722271 0.691610i \(-0.756902\pi\)
\(240\) 0 0
\(241\) 23.9987 + 6.68049i 1.54589 + 0.430328i 0.933011 0.359848i \(-0.117171\pi\)
0.612880 + 0.790176i \(0.290011\pi\)
\(242\) 0.668458 0.0429701
\(243\) 0 0
\(244\) 3.10328 0.198667
\(245\) 20.0193 + 5.57276i 1.27899 + 0.356031i
\(246\) 0 0
\(247\) 10.1565 + 6.12946i 0.646241 + 0.390008i
\(248\) −15.7065 + 0.609483i −0.997362 + 0.0387022i
\(249\) 0 0
\(250\) 11.2160 + 1.75414i 0.709360 + 0.110942i
\(251\) 0.741629 + 0.786080i 0.0468112 + 0.0496170i 0.750356 0.661034i \(-0.229882\pi\)
−0.703545 + 0.710651i \(0.748401\pi\)
\(252\) 0 0
\(253\) 15.3704 + 3.64284i 0.966327 + 0.229024i
\(254\) 2.13822 + 15.6545i 0.134164 + 0.982252i
\(255\) 0 0
\(256\) 6.81040 9.92981i 0.425650 0.620613i
\(257\) 26.9900 + 12.2684i 1.68359 + 0.765284i 0.999351 + 0.0360236i \(0.0114692\pi\)
0.684236 + 0.729261i \(0.260136\pi\)
\(258\) 0 0
\(259\) 15.9777 + 30.3329i 0.992804 + 1.88479i
\(260\) −0.984167 + 0.494267i −0.0610355 + 0.0306532i
\(261\) 0 0
\(262\) 0.249855 + 4.28984i 0.0154361 + 0.265027i
\(263\) −1.97083 1.08746i −0.121527 0.0670556i 0.421184 0.906975i \(-0.361614\pi\)
−0.542711 + 0.839919i \(0.682602\pi\)
\(264\) 0 0
\(265\) 0.147965 1.08329i 0.00908940 0.0665462i
\(266\) −13.9756 + 36.1976i −0.856897 + 2.21942i
\(267\) 0 0
\(268\) 1.82569 0.141904i 0.111522 0.00866818i
\(269\) −0.644714 + 0.540979i −0.0393089 + 0.0329841i −0.662230 0.749300i \(-0.730390\pi\)
0.622922 + 0.782284i \(0.285946\pi\)
\(270\) 0 0
\(271\) 9.20330 + 7.72248i 0.559060 + 0.469107i 0.877995 0.478669i \(-0.158881\pi\)
−0.318935 + 0.947777i \(0.603325\pi\)
\(272\) −3.45776 2.47146i −0.209657 0.149854i
\(273\) 0 0
\(274\) −0.954852 + 1.09414i −0.0576847 + 0.0660994i
\(275\) 2.78814 + 12.8715i 0.168131 + 0.776179i
\(276\) 0 0
\(277\) −4.09682 + 0.804590i −0.246154 + 0.0483431i −0.314267 0.949334i \(-0.601759\pi\)
0.0681132 + 0.997678i \(0.478302\pi\)
\(278\) 9.82274 + 1.14811i 0.589129 + 0.0688593i
\(279\) 0 0
\(280\) −10.0288 13.4711i −0.599338 0.805050i
\(281\) −4.53332 + 20.9281i −0.270435 + 1.24847i 0.616789 + 0.787128i \(0.288433\pi\)
−0.887224 + 0.461339i \(0.847369\pi\)
\(282\) 0 0
\(283\) −23.1447 22.7002i −1.37581 1.34938i −0.875240 0.483689i \(-0.839297\pi\)
−0.500570 0.865696i \(-0.666876\pi\)
\(284\) 2.07349 8.04977i 0.123039 0.477666i
\(285\) 0 0
\(286\) 5.76925 + 5.23531i 0.341143 + 0.309570i
\(287\) 11.4782 26.6095i 0.677537 1.57071i
\(288\) 0 0
\(289\) −8.56752 + 11.5082i −0.503972 + 0.676952i
\(290\) −5.22233 5.98412i −0.306666 0.351400i
\(291\) 0 0
\(292\) −2.01269 0.645343i −0.117784 0.0377658i
\(293\) −19.7446 3.87772i −1.15349 0.226539i −0.420837 0.907136i \(-0.638264\pi\)
−0.732658 + 0.680597i \(0.761720\pi\)
\(294\) 0 0
\(295\) −8.19310 + 3.72422i −0.477021 + 0.216833i
\(296\) 3.54456 20.1022i 0.206024 1.16842i
\(297\) 0 0
\(298\) −1.48835 8.44083i −0.0862176 0.488964i
\(299\) 4.99603 + 7.28439i 0.288928 + 0.421267i
\(300\) 0 0
\(301\) −16.2829 20.1876i −0.938530 1.16360i
\(302\) 12.9148 5.27627i 0.743163 0.303615i
\(303\) 0 0
\(304\) 13.9432 8.41479i 0.799700 0.482621i
\(305\) −5.03666 + 3.31266i −0.288398 + 0.189682i
\(306\) 0 0
\(307\) −0.362404 + 6.22224i −0.0206835 + 0.355122i 0.972049 + 0.234779i \(0.0754365\pi\)
−0.992732 + 0.120343i \(0.961601\pi\)
\(308\) 5.10391 8.09790i 0.290822 0.461421i
\(309\) 0 0
\(310\) 5.32831 3.80844i 0.302627 0.216305i
\(311\) −4.81001 0.373864i −0.272751 0.0211999i −0.0596114 0.998222i \(-0.518986\pi\)
−0.213139 + 0.977022i \(0.568369\pi\)
\(312\) 0 0
\(313\) 5.44938 + 2.22632i 0.308017 + 0.125839i 0.526938 0.849904i \(-0.323340\pi\)
−0.218921 + 0.975743i \(0.570254\pi\)
\(314\) −0.780546 2.60720i −0.0440487 0.147133i
\(315\) 0 0
\(316\) 6.84159 1.62149i 0.384870 0.0912158i
\(317\) 8.09352 + 20.9628i 0.454578 + 1.17739i 0.950969 + 0.309287i \(0.100090\pi\)
−0.496391 + 0.868099i \(0.665342\pi\)
\(318\) 0 0
\(319\) 9.83586 18.6729i 0.550702 1.04548i
\(320\) −0.181626 + 9.36461i −0.0101532 + 0.523498i
\(321\) 0 0
\(322\) −20.6269 + 20.2307i −1.14949 + 1.12741i
\(323\) 5.08251 + 8.80317i 0.282799 + 0.489822i
\(324\) 0 0
\(325\) −3.68226 + 6.37786i −0.204255 + 0.353780i
\(326\) 4.52642 + 17.5726i 0.250695 + 0.973258i
\(327\) 0 0
\(328\) −15.1071 + 8.33576i −0.834152 + 0.460265i
\(329\) −15.5195 24.6234i −0.855617 1.35753i
\(330\) 0 0
\(331\) 11.1587 13.8346i 0.613335 0.760417i −0.372518 0.928025i \(-0.621506\pi\)
0.985854 + 0.167608i \(0.0536044\pi\)
\(332\) 0.926232 3.09383i 0.0508336 0.169796i
\(333\) 0 0
\(334\) −15.9241 + 16.8785i −0.871326 + 0.923551i
\(335\) −2.81164 + 2.17919i −0.153617 + 0.119062i
\(336\) 0 0
\(337\) 5.22008 + 10.9169i 0.284356 + 0.594680i 0.993938 0.109943i \(-0.0350669\pi\)
−0.709582 + 0.704623i \(0.751116\pi\)
\(338\) −1.09576 11.2654i −0.0596014 0.612756i
\(339\) 0 0
\(340\) −0.942990 0.0365923i −0.0511408 0.00198450i
\(341\) 14.5404 + 9.56335i 0.787405 + 0.517885i
\(342\) 0 0
\(343\) −58.0006 29.1290i −3.13174 1.57282i
\(344\) 0.299444 + 15.4392i 0.0161449 + 0.832428i
\(345\) 0 0
\(346\) 21.0814 + 16.3393i 1.13334 + 0.878407i
\(347\) 19.4445 3.04107i 1.04384 0.163253i 0.390720 0.920510i \(-0.372226\pi\)
0.653117 + 0.757257i \(0.273461\pi\)
\(348\) 0 0
\(349\) 6.78638 14.1925i 0.363267 0.759708i −0.636668 0.771138i \(-0.719688\pi\)
0.999935 + 0.0114302i \(0.00363841\pi\)
\(350\) −22.6359 8.23879i −1.20994 0.440382i
\(351\) 0 0
\(352\) −9.56228 + 3.48039i −0.509671 + 0.185505i
\(353\) −2.46228 + 25.3144i −0.131054 + 1.34735i 0.667133 + 0.744939i \(0.267521\pi\)
−0.798186 + 0.602411i \(0.794207\pi\)
\(354\) 0 0
\(355\) 5.22761 + 15.2783i 0.277453 + 0.810886i
\(356\) −0.515749 + 0.468017i −0.0273346 + 0.0248048i
\(357\) 0 0
\(358\) 1.20792 3.53028i 0.0638406 0.186581i
\(359\) 6.23837 + 14.4622i 0.329248 + 0.763284i 0.999771 + 0.0213946i \(0.00681064\pi\)
−0.670523 + 0.741889i \(0.733930\pi\)
\(360\) 0 0
\(361\) −19.8148 + 2.31602i −1.04289 + 0.121896i
\(362\) 7.04311 2.25828i 0.370177 0.118693i
\(363\) 0 0
\(364\) 5.15658 1.43543i 0.270278 0.0752371i
\(365\) 3.95551 1.10109i 0.207041 0.0576337i
\(366\) 0 0
\(367\) −2.44722 + 0.784668i −0.127744 + 0.0409593i −0.368510 0.929624i \(-0.620132\pi\)
0.240767 + 0.970583i \(0.422601\pi\)
\(368\) 12.0444 1.40779i 0.627857 0.0733859i
\(369\) 0 0
\(370\) 3.36879 + 7.80973i 0.175135 + 0.406009i
\(371\) −1.72031 + 5.02779i −0.0893140 + 0.261030i
\(372\) 0 0
\(373\) −7.28041 + 6.60662i −0.376965 + 0.342078i −0.838360 0.545117i \(-0.816485\pi\)
0.461394 + 0.887195i \(0.347349\pi\)
\(374\) 2.16113 + 6.31613i 0.111749 + 0.326599i
\(375\) 0 0
\(376\) −1.67770 + 17.2482i −0.0865206 + 0.889510i
\(377\) 11.0900 4.03642i 0.571163 0.207886i
\(378\) 0 0
\(379\) 10.4634 + 3.80836i 0.537467 + 0.195622i 0.596470 0.802636i \(-0.296570\pi\)
−0.0590021 + 0.998258i \(0.518792\pi\)
\(380\) 1.55990 3.26225i 0.0800210 0.167350i
\(381\) 0 0
\(382\) −15.0905 + 2.36011i −0.772097 + 0.120754i
\(383\) 6.69339 + 5.18777i 0.342016 + 0.265083i 0.769099 0.639130i \(-0.220705\pi\)
−0.427082 + 0.904213i \(0.640459\pi\)
\(384\) 0 0
\(385\) 0.360577 + 18.5913i 0.0183767 + 0.947499i
\(386\) 7.01193 + 3.52152i 0.356898 + 0.179241i
\(387\) 0 0
\(388\) 5.02603 + 3.30567i 0.255158 + 0.167820i
\(389\) 6.02911 + 0.233957i 0.305688 + 0.0118621i 0.191163 0.981558i \(-0.438774\pi\)
0.114525 + 0.993420i \(0.463465\pi\)
\(390\) 0 0
\(391\) 0.732754 + 7.53337i 0.0370570 + 0.380979i
\(392\) 25.9410 + 54.2509i 1.31022 + 2.74009i
\(393\) 0 0
\(394\) 22.7528 17.6348i 1.14627 0.888426i
\(395\) −9.37309 + 9.93490i −0.471611 + 0.499879i
\(396\) 0 0
\(397\) −1.66994 + 5.57798i −0.0838117 + 0.279951i −0.989614 0.143750i \(-0.954084\pi\)
0.905802 + 0.423701i \(0.139269\pi\)
\(398\) 8.62292 10.6907i 0.432228 0.535879i
\(399\) 0 0
\(400\) 5.39087 + 8.55319i 0.269543 + 0.427660i
\(401\) 23.0942 12.7428i 1.15327 0.636346i 0.213091 0.977032i \(-0.431647\pi\)
0.940177 + 0.340686i \(0.110659\pi\)
\(402\) 0 0
\(403\) 2.42752 + 9.42420i 0.120923 + 0.469453i
\(404\) −4.04496 + 7.00608i −0.201244 + 0.348566i
\(405\) 0 0
\(406\) 19.3011 + 33.4305i 0.957898 + 1.65913i
\(407\) −16.1353 + 15.8254i −0.799799 + 0.784437i
\(408\) 0 0
\(409\) −0.0306793 + 1.58182i −0.00151699 + 0.0782158i 0.998288 + 0.0584844i \(0.0186268\pi\)
−0.999805 + 0.0197314i \(0.993719\pi\)
\(410\) 3.35060 6.36095i 0.165474 0.314145i
\(411\) 0 0
\(412\) −0.678534 1.75745i −0.0334290 0.0865832i
\(413\) 42.5623 10.0874i 2.09435 0.496371i
\(414\) 0 0
\(415\) 1.79929 + 6.01005i 0.0883237 + 0.295022i
\(416\) −5.26764 2.15207i −0.258267 0.105514i
\(417\) 0 0
\(418\) −25.5023 1.98220i −1.24736 0.0969525i
\(419\) −5.16049 + 3.68849i −0.252106 + 0.180195i −0.700523 0.713630i \(-0.747050\pi\)
0.448417 + 0.893825i \(0.351988\pi\)
\(420\) 0 0
\(421\) −17.9804 + 28.5279i −0.876312 + 1.39036i 0.0439385 + 0.999034i \(0.486009\pi\)
−0.920251 + 0.391330i \(0.872015\pi\)
\(422\) −0.617673 + 10.6050i −0.0300679 + 0.516245i
\(423\) 0 0
\(424\) 2.64341 1.73860i 0.128375 0.0844337i
\(425\) −5.40289 + 3.26066i −0.262079 + 0.158165i
\(426\) 0 0
\(427\) 27.1233 11.0811i 1.31259 0.536251i
\(428\) −3.07049 3.80681i −0.148418 0.184009i
\(429\) 0 0
\(430\) −3.63932 5.30626i −0.175504 0.255891i
\(431\) 2.82320 + 16.0112i 0.135989 + 0.771232i 0.974166 + 0.225833i \(0.0725105\pi\)
−0.838177 + 0.545398i \(0.816378\pi\)
\(432\) 0 0
\(433\) −5.81911 + 33.0018i −0.279649 + 1.58597i 0.444148 + 0.895953i \(0.353506\pi\)
−0.723797 + 0.690013i \(0.757605\pi\)
\(434\) −28.9786 + 13.1724i −1.39102 + 0.632294i
\(435\) 0 0
\(436\) −2.41040 0.473387i −0.115437 0.0226711i
\(437\) −27.6172 8.85511i −1.32111 0.423597i
\(438\) 0 0
\(439\) −16.7094 19.1469i −0.797497 0.913830i 0.200329 0.979729i \(-0.435799\pi\)
−0.997826 + 0.0658984i \(0.979009\pi\)
\(440\) 6.61129 8.88050i 0.315181 0.423361i
\(441\) 0 0
\(442\) −1.47854 + 3.42765i −0.0703271 + 0.163037i
\(443\) 16.6859 + 15.1416i 0.792770 + 0.719400i 0.964021 0.265827i \(-0.0856450\pi\)
−0.171251 + 0.985227i \(0.554781\pi\)
\(444\) 0 0
\(445\) 0.337471 1.31014i 0.0159977 0.0621068i
\(446\) −2.20851 2.16609i −0.104576 0.102567i
\(447\) 0 0
\(448\) 9.63737 44.4910i 0.455323 2.10200i
\(449\) 4.67513 + 6.27979i 0.220633 + 0.296362i 0.898634 0.438700i \(-0.144561\pi\)
−0.678001 + 0.735061i \(0.737153\pi\)
\(450\) 0 0
\(451\) 18.9749 + 2.21785i 0.893495 + 0.104435i
\(452\) −5.58751 + 1.09735i −0.262815 + 0.0516151i
\(453\) 0 0
\(454\) 2.05936 + 9.50707i 0.0966506 + 0.446189i
\(455\) −6.83691 + 7.83423i −0.320519 + 0.367274i
\(456\) 0 0
\(457\) −6.08976 4.35270i −0.284867 0.203611i 0.430077 0.902792i \(-0.358486\pi\)
−0.714944 + 0.699181i \(0.753548\pi\)
\(458\) 14.4096 + 12.0911i 0.673314 + 0.564978i
\(459\) 0 0
\(460\) 2.06257 1.73070i 0.0961680 0.0806945i
\(461\) −7.70894 + 0.599186i −0.359041 + 0.0279069i −0.255746 0.966744i \(-0.582321\pi\)
−0.103295 + 0.994651i \(0.532938\pi\)
\(462\) 0 0
\(463\) −6.90361 + 17.8808i −0.320838 + 0.830991i 0.674827 + 0.737976i \(0.264218\pi\)
−0.995665 + 0.0930150i \(0.970350\pi\)
\(464\) 2.19262 16.0528i 0.101790 0.745234i
\(465\) 0 0
\(466\) 18.5483 + 10.2345i 0.859235 + 0.474106i
\(467\) 0.340683 + 5.84931i 0.0157649 + 0.270674i 0.996975 + 0.0777288i \(0.0247668\pi\)
−0.981210 + 0.192945i \(0.938196\pi\)
\(468\) 0 0
\(469\) 15.4502 7.75940i 0.713425 0.358296i
\(470\) −3.36523 6.38873i −0.155226 0.294690i
\(471\) 0 0
\(472\) −23.7089 10.7770i −1.09129 0.496053i
\(473\) 9.67057 14.1000i 0.444653 0.648321i
\(474\) 0 0
\(475\) −3.27237 23.9580i −0.150147 1.09927i
\(476\) 4.46298 + 1.05775i 0.204560 + 0.0484817i
\(477\) 0 0
\(478\) 24.9633 + 26.4596i 1.14180 + 1.21023i
\(479\) 6.74496 + 1.05489i 0.308185 + 0.0481993i 0.306720 0.951800i \(-0.400768\pi\)
0.00146464 + 0.999999i \(0.499534\pi\)
\(480\) 0 0
\(481\) −12.6286 + 0.490047i −0.575814 + 0.0223442i
\(482\) −25.7167 15.5201i −1.17136 0.706921i
\(483\) 0 0
\(484\) 0.291678 + 0.0811940i 0.0132581 + 0.00369064i
\(485\) −11.6860 −0.530635
\(486\) 0 0
\(487\) −6.34053 −0.287317 −0.143658 0.989627i \(-0.545887\pi\)
−0.143658 + 0.989627i \(0.545887\pi\)
\(488\) −16.8058 4.67822i −0.760764 0.211773i
\(489\) 0 0
\(490\) −21.4525 12.9466i −0.969123 0.584869i
\(491\) −6.50680 + 0.252494i −0.293648 + 0.0113949i −0.185178 0.982705i \(-0.559286\pi\)
−0.108469 + 0.994100i \(0.534595\pi\)
\(492\) 0 0
\(493\) 9.99128 + 1.56261i 0.449985 + 0.0703763i
\(494\) −9.81576 10.4041i −0.441632 0.468103i
\(495\) 0 0
\(496\) 13.0001 + 3.08109i 0.583723 + 0.138345i
\(497\) −10.6211 77.7605i −0.476423 3.48804i
\(498\) 0 0
\(499\) 14.8258 21.6166i 0.663695 0.967690i −0.335972 0.941872i \(-0.609065\pi\)
0.999667 0.0258185i \(-0.00821919\pi\)
\(500\) 4.68095 + 2.12775i 0.209339 + 0.0951560i
\(501\) 0 0
\(502\) −0.607293 1.15292i −0.0271048 0.0514572i
\(503\) 14.6872 7.37621i 0.654872 0.328889i −0.0901510 0.995928i \(-0.528735\pi\)
0.745023 + 0.667039i \(0.232439\pi\)
\(504\) 0 0
\(505\) −0.913771 15.6888i −0.0406623 0.698144i
\(506\) −16.6763 9.20158i −0.741351 0.409060i
\(507\) 0 0
\(508\) −0.968473 + 7.09048i −0.0429690 + 0.314589i
\(509\) −14.0786 + 36.4646i −0.624024 + 1.61626i 0.154030 + 0.988066i \(0.450775\pi\)
−0.778054 + 0.628197i \(0.783793\pi\)
\(510\) 0 0
\(511\) −19.8957 + 1.54641i −0.880133 + 0.0684094i
\(512\) −18.2581 + 15.3204i −0.806901 + 0.677070i
\(513\) 0 0
\(514\) −27.3844 22.9783i −1.20788 1.01353i
\(515\) 2.97729 + 2.12804i 0.131195 + 0.0937727i
\(516\) 0 0
\(517\) 12.6162 14.4566i 0.554861 0.635800i
\(518\) −8.75142 40.4010i −0.384515 1.77512i
\(519\) 0 0
\(520\) 6.07487 1.19307i 0.266401 0.0523194i
\(521\) 3.64138 + 0.425617i 0.159532 + 0.0186466i 0.195484 0.980707i \(-0.437372\pi\)
−0.0359520 + 0.999354i \(0.511446\pi\)
\(522\) 0 0
\(523\) −10.0993 13.5657i −0.441611 0.593187i 0.524469 0.851430i \(-0.324264\pi\)
−0.966080 + 0.258243i \(0.916856\pi\)
\(524\) −0.412041 + 1.90219i −0.0180001 + 0.0830977i
\(525\) 0 0
\(526\) 1.93768 + 1.90046i 0.0844869 + 0.0828642i
\(527\) −2.08011 + 8.07548i −0.0906110 + 0.351774i
\(528\) 0 0
\(529\) 1.04036 + 0.944078i 0.0452331 + 0.0410469i
\(530\) −0.522162 + 1.21051i −0.0226813 + 0.0525811i
\(531\) 0 0
\(532\) −10.4949 + 14.0971i −0.455011 + 0.611186i
\(533\) 7.02418 + 8.04882i 0.304251 + 0.348633i
\(534\) 0 0
\(535\) 9.04710 + 2.90084i 0.391140 + 0.125414i
\(536\) −10.1010 1.98377i −0.436296 0.0856857i
\(537\) 0 0
\(538\) 0.923826 0.419930i 0.0398290 0.0181045i
\(539\) 11.5617 65.5694i 0.497996 2.82428i
\(540\) 0 0
\(541\) −0.384823 2.18244i −0.0165448 0.0938304i 0.975417 0.220366i \(-0.0707252\pi\)
−0.991962 + 0.126536i \(0.959614\pi\)
\(542\) −8.19344 11.9463i −0.351939 0.513139i
\(543\) 0 0
\(544\) −3.06118 3.79526i −0.131247 0.162721i
\(545\) 4.41744 1.80472i 0.189222 0.0773058i
\(546\) 0 0
\(547\) 14.5518 8.78204i 0.622189 0.375493i −0.170289 0.985394i \(-0.554470\pi\)
0.792477 + 0.609901i \(0.208791\pi\)
\(548\) −0.549543 + 0.361440i −0.0234753 + 0.0154400i
\(549\) 0 0
\(550\) 0.923334 15.8530i 0.0393711 0.675975i
\(551\) −20.6613 + 32.7814i −0.880202 + 1.39654i
\(552\) 0 0
\(553\) 54.0069 38.6018i 2.29661 1.64152i
\(554\) 5.01903 + 0.390110i 0.213238 + 0.0165742i
\(555\) 0 0
\(556\) 4.14664 + 1.69409i 0.175857 + 0.0718454i
\(557\) −10.9744 36.6570i −0.464999 1.55321i −0.793421 0.608674i \(-0.791702\pi\)
0.328421 0.944531i \(-0.393483\pi\)
\(558\) 0 0
\(559\) 9.30313 2.20488i 0.393481 0.0932566i
\(560\) 5.14147 + 13.3167i 0.217267 + 0.562735i
\(561\) 0 0
\(562\) 12.0331 22.8442i 0.507584 0.963625i
\(563\) 0.315087 16.2458i 0.0132793 0.684678i −0.932737 0.360558i \(-0.882586\pi\)
0.946016 0.324120i \(-0.105068\pi\)
\(564\) 0 0
\(565\) 7.89721 7.74553i 0.332238 0.325857i
\(566\) 19.5447 + 33.8524i 0.821524 + 1.42292i
\(567\) 0 0
\(568\) −23.3641 + 40.4678i −0.980335 + 1.69799i
\(569\) −0.763520 2.96417i −0.0320084 0.124264i 0.950390 0.311059i \(-0.100684\pi\)
−0.982399 + 0.186795i \(0.940190\pi\)
\(570\) 0 0
\(571\) −8.86951 + 4.89399i −0.371178 + 0.204807i −0.657724 0.753259i \(-0.728481\pi\)
0.286546 + 0.958066i \(0.407493\pi\)
\(572\) 1.88147 + 2.98516i 0.0786682 + 0.124816i
\(573\) 0 0
\(574\) −21.9373 + 27.1980i −0.915646 + 1.13522i
\(575\) 5.16385 17.2485i 0.215347 0.719311i
\(576\) 0 0
\(577\) −9.33936 + 9.89915i −0.388803 + 0.412107i −0.891979 0.452077i \(-0.850683\pi\)
0.503176 + 0.864184i \(0.332165\pi\)
\(578\) 13.6732 10.5975i 0.568731 0.440800i
\(579\) 0 0
\(580\) −1.55187 3.24546i −0.0644380 0.134761i
\(581\) −2.95189 30.3481i −0.122465 1.25905i
\(582\) 0 0
\(583\) −3.50048 0.135834i −0.144975 0.00562569i
\(584\) 9.92687 + 6.52901i 0.410777 + 0.270172i
\(585\) 0 0
\(586\) 21.6815 + 10.8888i 0.895653 + 0.449814i
\(587\) −0.162155 8.36069i −0.00669287 0.345083i −0.988158 0.153441i \(-0.950964\pi\)
0.981465 0.191642i \(-0.0613812\pi\)
\(588\) 0 0
\(589\) −25.2556 19.5745i −1.04064 0.806555i
\(590\) 10.7213 1.67679i 0.441390 0.0690322i
\(591\) 0 0
\(592\) −7.48460 + 15.6527i −0.307615 + 0.643322i
\(593\) 5.39978 + 1.96536i 0.221742 + 0.0807076i 0.450502 0.892775i \(-0.351245\pi\)
−0.228760 + 0.973483i \(0.573467\pi\)
\(594\) 0 0
\(595\) −8.37258 + 3.04737i −0.343242 + 0.124930i
\(596\) 0.375832 3.86389i 0.0153947 0.158271i
\(597\) 0 0
\(598\) −3.44795 10.0770i −0.140997 0.412080i
\(599\) −29.3321 + 26.6174i −1.19848 + 1.08756i −0.204397 + 0.978888i \(0.565523\pi\)
−0.994078 + 0.108670i \(0.965341\pi\)
\(600\) 0 0
\(601\) 8.29052 24.2300i 0.338177 0.988361i −0.637746 0.770247i \(-0.720133\pi\)
0.975923 0.218114i \(-0.0699905\pi\)
\(602\) 12.3865 + 28.7150i 0.504834 + 1.17034i
\(603\) 0 0
\(604\) 6.27617 0.733579i 0.255374 0.0298489i
\(605\) −0.560069 + 0.179579i −0.0227700 + 0.00730092i
\(606\) 0 0
\(607\) −12.9788 + 3.61291i −0.526795 + 0.146643i −0.521352 0.853342i \(-0.674572\pi\)
−0.00544317 + 0.999985i \(0.501733\pi\)
\(608\) 17.9990 5.01036i 0.729955 0.203197i
\(609\) 0 0
\(610\) 6.92173 2.21936i 0.280253 0.0898594i
\(611\) 10.6569 1.24562i 0.431133 0.0503922i
\(612\) 0 0
\(613\) −16.0179 37.1337i −0.646958 1.49982i −0.853345 0.521347i \(-0.825430\pi\)
0.206387 0.978470i \(-0.433829\pi\)
\(614\) 2.43295 7.11056i 0.0981857 0.286959i
\(615\) 0 0
\(616\) −39.8479 + 36.1601i −1.60552 + 1.45693i
\(617\) −7.48936 21.8885i −0.301510 0.881197i −0.988054 0.154108i \(-0.950750\pi\)
0.686544 0.727088i \(-0.259127\pi\)
\(618\) 0 0
\(619\) −2.28747 + 23.5173i −0.0919412 + 0.945238i 0.829963 + 0.557819i \(0.188362\pi\)
−0.921904 + 0.387419i \(0.873367\pi\)
\(620\) 2.78757 1.01459i 0.111951 0.0407470i
\(621\) 0 0
\(622\) 5.46641 + 1.98961i 0.219183 + 0.0797761i
\(623\) −2.83657 + 5.93218i −0.113645 + 0.237668i
\(624\) 0 0
\(625\) 9.27110 1.44997i 0.370844 0.0579989i
\(626\) −5.61010 4.34816i −0.224225 0.173787i
\(627\) 0 0
\(628\) −0.0239033 1.23245i −0.000953845 0.0491800i
\(629\) −9.67753 4.86024i −0.385868 0.193790i
\(630\) 0 0
\(631\) −21.2288 13.9624i −0.845106 0.555835i 0.0514956 0.998673i \(-0.483601\pi\)
−0.896601 + 0.442838i \(0.853972\pi\)
\(632\) −39.4951 1.53259i −1.57103 0.0609631i
\(633\) 0 0
\(634\) −2.62305 26.9674i −0.104175 1.07101i
\(635\) −5.99704 12.5417i −0.237985 0.497704i
\(636\) 0 0
\(637\) 29.4274 22.8080i 1.16596 0.903684i
\(638\) −17.4633 + 18.5100i −0.691377 + 0.732817i
\(639\) 0 0
\(640\) 1.41727 4.73401i 0.0560225 0.187128i
\(641\) 7.15307 8.86842i 0.282529 0.350281i −0.617140 0.786853i \(-0.711709\pi\)
0.899669 + 0.436572i \(0.143808\pi\)
\(642\) 0 0
\(643\) −17.9682 28.5085i −0.708597 1.12426i −0.986517 0.163661i \(-0.947670\pi\)
0.277920 0.960604i \(-0.410355\pi\)
\(644\) −11.4577 + 6.32211i −0.451498 + 0.249126i
\(645\) 0 0
\(646\) −3.05731 11.8692i −0.120288 0.466987i
\(647\) 11.2173 19.4288i 0.440996 0.763827i −0.556768 0.830668i \(-0.687959\pi\)
0.997764 + 0.0668412i \(0.0212921\pi\)
\(648\) 0 0
\(649\) 14.4178 + 24.9723i 0.565946 + 0.980248i
\(650\) 6.33960 6.21784i 0.248660 0.243884i
\(651\) 0 0
\(652\) −0.159378 + 8.21751i −0.00624174 + 0.321822i
\(653\) −1.25416 + 2.38097i −0.0490791 + 0.0931744i −0.908074 0.418810i \(-0.862447\pi\)
0.858995 + 0.511984i \(0.171089\pi\)
\(654\) 0 0
\(655\) −1.36179 3.52713i −0.0532095 0.137816i
\(656\) 14.2705 3.38217i 0.557170 0.132052i
\(657\) 0 0
\(658\) 10.0654 + 33.6207i 0.392389 + 1.31067i
\(659\) 28.1555 + 11.5028i 1.09678 + 0.448085i 0.853088 0.521768i \(-0.174727\pi\)
0.243694 + 0.969852i \(0.421641\pi\)
\(660\) 0 0
\(661\) 27.7954 + 2.16043i 1.08112 + 0.0840310i 0.605672 0.795715i \(-0.292904\pi\)
0.475445 + 0.879746i \(0.342287\pi\)
\(662\) −17.4353 + 12.4620i −0.677643 + 0.484350i
\(663\) 0 0
\(664\) −9.67999 + 15.3584i −0.375657 + 0.596020i
\(665\) 1.98509 34.0827i 0.0769786 1.32167i
\(666\) 0 0
\(667\) −24.1063 + 15.8550i −0.933399 + 0.613906i
\(668\) −8.99851 + 5.43063i −0.348163 + 0.210117i
\(669\) 0 0
\(670\) 3.97065 1.62219i 0.153400 0.0626706i
\(671\) 12.1262 + 15.0342i 0.468128 + 0.580388i
\(672\) 0 0
\(673\) 13.5610 + 19.7725i 0.522739 + 0.762172i 0.992712 0.120509i \(-0.0384525\pi\)
−0.469973 + 0.882681i \(0.655736\pi\)
\(674\) −2.53363 14.3689i −0.0975918 0.553471i
\(675\) 0 0
\(676\) 0.890218 5.04868i 0.0342391 0.194180i
\(677\) −6.37018 + 2.89560i −0.244826 + 0.111287i −0.532466 0.846452i \(-0.678734\pi\)
0.287640 + 0.957739i \(0.407129\pi\)
\(678\) 0 0
\(679\) 55.7323 + 10.9455i 2.13881 + 0.420048i
\(680\) 5.05160 + 1.61973i 0.193720 + 0.0621139i
\(681\) 0 0
\(682\) −13.7977 15.8104i −0.528342 0.605413i
\(683\) 2.16077 2.90242i 0.0826797 0.111058i −0.758859 0.651255i \(-0.774243\pi\)
0.841539 + 0.540197i \(0.181650\pi\)
\(684\) 0 0
\(685\) 0.506088 1.17324i 0.0193366 0.0448273i
\(686\) 57.9545 + 52.5909i 2.21271 + 2.00793i
\(687\) 0 0
\(688\) 3.27405 12.7106i 0.124822 0.484589i
\(689\) −1.39852 1.37166i −0.0532793 0.0522560i
\(690\) 0 0
\(691\) −2.94684 + 13.6041i −0.112103 + 0.517526i 0.886404 + 0.462912i \(0.153195\pi\)
−0.998508 + 0.0546140i \(0.982607\pi\)
\(692\) 7.21409 + 9.69021i 0.274239 + 0.368366i
\(693\) 0 0
\(694\) −23.5701 2.75495i −0.894708 0.104576i
\(695\) −8.53844 + 1.67689i −0.323881 + 0.0636082i
\(696\) 0 0
\(697\) 1.93793 + 8.94649i 0.0734044 + 0.338873i
\(698\) −12.4722 + 14.2916i −0.472081 + 0.540945i
\(699\) 0 0
\(700\) −8.87632 6.34441i −0.335493 0.239796i
\(701\) −5.06239 4.24785i −0.191204 0.160439i 0.542160 0.840275i \(-0.317606\pi\)
−0.733364 + 0.679836i \(0.762051\pi\)
\(702\) 0 0
\(703\) 31.7874 26.6728i 1.19889 1.00598i
\(704\) 29.9197 2.32554i 1.12764 0.0876472i
\(705\) 0 0
\(706\) 11.0457 28.6090i 0.415709 1.07671i
\(707\) −10.3367 + 75.6782i −0.388752 + 2.84617i
\(708\) 0 0
\(709\) 38.9652 + 21.5001i 1.46337 + 0.807452i 0.997020 0.0771498i \(-0.0245820\pi\)
0.466348 + 0.884602i \(0.345570\pi\)
\(710\) −1.13211 19.4376i −0.0424873 0.729479i
\(711\) 0 0
\(712\) 3.49858 1.75705i 0.131115 0.0658483i
\(713\) −11.0883 21.0507i −0.415261 0.788354i
\(714\) 0 0
\(715\) −6.24022 2.83653i −0.233371 0.106080i
\(716\) 0.955873 1.39370i 0.0357227 0.0520849i
\(717\) 0 0
\(718\) −2.57009 18.8164i −0.0959150 0.702222i
\(719\) 30.9948 + 7.34591i 1.15591 + 0.273956i 0.763484 0.645827i \(-0.223487\pi\)
0.392428 + 0.919783i \(0.371635\pi\)
\(720\) 0 0
\(721\) −12.2060 12.9376i −0.454573 0.481820i
\(722\) 23.7658 + 3.71690i 0.884470 + 0.138329i
\(723\) 0 0
\(724\) 3.34752 0.129899i 0.124410 0.00482766i
\(725\) −20.5960 12.4297i −0.764915 0.461629i
\(726\) 0 0
\(727\) −39.2686 10.9312i −1.45639 0.405414i −0.552622 0.833432i \(-0.686373\pi\)
−0.903770 + 0.428018i \(0.859212\pi\)
\(728\) −30.0894 −1.11519
\(729\) 0 0
\(730\) −4.95075 −0.183235
\(731\) 7.89249 + 2.19702i 0.291914 + 0.0812599i
\(732\) 0 0
\(733\) 16.3376 + 9.85977i 0.603442 + 0.364179i 0.785272 0.619151i \(-0.212523\pi\)
−0.181830 + 0.983330i \(0.558202\pi\)
\(734\) 3.09641 0.120155i 0.114290 0.00443499i
\(735\) 0 0
\(736\) 13.7446 + 2.14962i 0.506634 + 0.0792361i
\(737\) 7.82147 + 8.29028i 0.288108 + 0.305376i
\(738\) 0 0
\(739\) 22.3767 + 5.30337i 0.823139 + 0.195087i 0.620540 0.784174i \(-0.286913\pi\)
0.202598 + 0.979262i \(0.435061\pi\)
\(740\) 0.521345 + 3.81692i 0.0191650 + 0.140313i
\(741\) 0 0
\(742\) 3.62406 5.28401i 0.133043 0.193982i
\(743\) −46.9575 21.3448i −1.72270 0.783065i −0.995298 0.0968566i \(-0.969121\pi\)
−0.727405 0.686208i \(-0.759274\pi\)
\(744\) 0 0
\(745\) 3.51461 + 6.67232i 0.128765 + 0.244455i
\(746\) 10.5932 5.32010i 0.387844 0.194783i
\(747\) 0 0
\(748\) 0.175808 + 3.01851i 0.00642818 + 0.110368i
\(749\) −40.4299 22.3083i −1.47728 0.815127i
\(750\) 0 0
\(751\) −1.74081 + 12.7450i −0.0635232 + 0.465072i 0.931365 + 0.364087i \(0.118619\pi\)
−0.994888 + 0.100985i \(0.967801\pi\)
\(752\) 5.30537 13.7413i 0.193467 0.501092i
\(753\) 0 0
\(754\) −14.1873 + 1.10272i −0.516670 + 0.0401588i
\(755\) −9.40323 + 7.89024i −0.342218 + 0.287155i
\(756\) 0 0
\(757\) 18.9418 + 15.8941i 0.688451 + 0.577679i 0.918462 0.395509i \(-0.129432\pi\)
−0.230011 + 0.973188i \(0.573876\pi\)
\(758\) −10.9228 7.80714i −0.396734 0.283568i
\(759\) 0 0
\(760\) −13.3655 + 15.3152i −0.484817 + 0.555539i
\(761\) 6.04458 + 27.9049i 0.219116 + 1.01155i 0.945843 + 0.324625i \(0.105238\pi\)
−0.726727 + 0.686926i \(0.758960\pi\)
\(762\) 0 0
\(763\) −22.7577 + 4.46948i −0.823886 + 0.161806i
\(764\) −6.87132 0.803142i −0.248596 0.0290566i
\(765\) 0 0
\(766\) −6.09755 8.19043i −0.220313 0.295932i
\(767\) −3.41362 + 15.7590i −0.123259 + 0.569026i
\(768\) 0 0
\(769\) −32.6653 32.0379i −1.17794 1.15532i −0.984717 0.174160i \(-0.944279\pi\)
−0.193223 0.981155i \(-0.561894\pi\)
\(770\) 5.59270 21.7122i 0.201547 0.782453i
\(771\) 0 0
\(772\) 2.63187 + 2.38830i 0.0947231 + 0.0859567i
\(773\) 3.46808 8.03991i 0.124738 0.289175i −0.844392 0.535726i \(-0.820038\pi\)
0.969130 + 0.246551i \(0.0792972\pi\)
\(774\) 0 0
\(775\) 11.8458 15.9116i 0.425513 0.571563i
\(776\) −22.2352 25.4787i −0.798196 0.914631i
\(777\) 0 0
\(778\) −6.92775 2.22129i −0.248372 0.0796372i
\(779\) −34.4182 6.75951i −1.23316 0.242185i
\(780\) 0 0
\(781\) 47.1002 21.4097i 1.68538 0.766099i
\(782\) 1.58477 8.98769i 0.0566714 0.321399i
\(783\) 0 0
\(784\) −8.87564 50.3363i −0.316987 1.79772i
\(785\) 1.35440 + 1.97476i 0.0483405 + 0.0704822i
\(786\) 0 0