Properties

Label 819.2.et.c.145.9
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.9
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.74581 - 1.74581i) q^{2} -4.09571i q^{4} +(2.78539 - 0.746344i) q^{5} +(-2.58285 + 0.573466i) q^{7} +(-3.65872 - 3.65872i) q^{8} +O(q^{10})\) \(q+(1.74581 - 1.74581i) q^{2} -4.09571i q^{4} +(2.78539 - 0.746344i) q^{5} +(-2.58285 + 0.573466i) q^{7} +(-3.65872 - 3.65872i) q^{8} +(3.55979 - 6.16574i) q^{10} +(1.35345 - 0.362655i) q^{11} +(3.49837 - 0.872572i) q^{13} +(-3.50801 + 5.51034i) q^{14} -4.58344 q^{16} -7.55665 q^{17} +(1.78944 - 6.67828i) q^{19} +(-3.05681 - 11.4082i) q^{20} +(1.72974 - 2.99599i) q^{22} -2.27807i q^{23} +(2.87125 - 1.65772i) q^{25} +(4.58415 - 7.63085i) q^{26} +(2.34875 + 10.5786i) q^{28} +(3.75108 + 6.49707i) q^{29} +(-1.39265 + 5.19745i) q^{31} +(-0.684379 + 0.684379i) q^{32} +(-13.1925 + 13.1925i) q^{34} +(-6.76626 + 3.52502i) q^{35} +(1.61717 + 1.61717i) q^{37} +(-8.53499 - 14.7830i) q^{38} +(-12.9216 - 7.46031i) q^{40} +(-2.38652 + 8.90661i) q^{41} +(3.04772 + 1.75960i) q^{43} +(-1.48533 - 5.54333i) q^{44} +(-3.97708 - 3.97708i) q^{46} +(0.223361 + 0.833593i) q^{47} +(6.34227 - 2.96236i) q^{49} +(2.11860 - 7.90673i) q^{50} +(-3.57380 - 14.3283i) q^{52} +(0.886338 + 1.53518i) q^{53} +(3.49922 - 2.02027i) q^{55} +(11.5481 + 7.35179i) q^{56} +(17.8913 + 4.79397i) q^{58} +(-3.80628 + 3.80628i) q^{59} +(-3.62667 + 2.09386i) q^{61} +(6.64246 + 11.5051i) q^{62} -6.77728i q^{64} +(9.09310 - 5.04144i) q^{65} +(-1.44159 - 5.38010i) q^{67} +30.9499i q^{68} +(-5.65859 + 17.9666i) q^{70} +(1.75325 + 6.54321i) q^{71} +(8.10009 + 2.17041i) q^{73} +5.64656 q^{74} +(-27.3523 - 7.32903i) q^{76} +(-3.28779 + 1.71284i) q^{77} +(0.411935 - 0.713493i) q^{79} +(-12.7667 + 3.42082i) q^{80} +(11.3829 + 19.7157i) q^{82} +(-2.15380 - 2.15380i) q^{83} +(-21.0482 + 5.63986i) q^{85} +(8.39268 - 2.24881i) q^{86} +(-6.27874 - 3.62503i) q^{88} +(-1.81982 + 1.81982i) q^{89} +(-8.53540 + 4.25992i) q^{91} -9.33031 q^{92} +(1.84524 + 1.06535i) q^{94} -19.9372i q^{95} +(8.79336 - 2.35617i) q^{97} +(5.90070 - 16.2441i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.74581 1.74581i 1.23447 1.23447i 0.272248 0.962227i \(-0.412233\pi\)
0.962227 0.272248i \(-0.0877670\pi\)
\(3\) 0 0
\(4\) 4.09571i 2.04786i
\(5\) 2.78539 0.746344i 1.24567 0.333775i 0.425005 0.905191i \(-0.360272\pi\)
0.820661 + 0.571416i \(0.193606\pi\)
\(6\) 0 0
\(7\) −2.58285 + 0.573466i −0.976227 + 0.216750i
\(8\) −3.65872 3.65872i −1.29355 1.29355i
\(9\) 0 0
\(10\) 3.55979 6.16574i 1.12571 1.94978i
\(11\) 1.35345 0.362655i 0.408080 0.109345i −0.0489388 0.998802i \(-0.515584\pi\)
0.457019 + 0.889457i \(0.348917\pi\)
\(12\) 0 0
\(13\) 3.49837 0.872572i 0.970274 0.242008i
\(14\) −3.50801 + 5.51034i −0.937556 + 1.47270i
\(15\) 0 0
\(16\) −4.58344 −1.14586
\(17\) −7.55665 −1.83276 −0.916379 0.400312i \(-0.868902\pi\)
−0.916379 + 0.400312i \(0.868902\pi\)
\(18\) 0 0
\(19\) 1.78944 6.67828i 0.410526 1.53210i −0.383106 0.923704i \(-0.625146\pi\)
0.793632 0.608399i \(-0.208188\pi\)
\(20\) −3.05681 11.4082i −0.683523 2.55094i
\(21\) 0 0
\(22\) 1.72974 2.99599i 0.368781 0.638747i
\(23\) 2.27807i 0.475010i −0.971386 0.237505i \(-0.923670\pi\)
0.971386 0.237505i \(-0.0763296\pi\)
\(24\) 0 0
\(25\) 2.87125 1.65772i 0.574251 0.331544i
\(26\) 4.58415 7.63085i 0.899027 1.49653i
\(27\) 0 0
\(28\) 2.34875 + 10.5786i 0.443872 + 1.99917i
\(29\) 3.75108 + 6.49707i 0.696559 + 1.20647i 0.969652 + 0.244487i \(0.0786197\pi\)
−0.273094 + 0.961987i \(0.588047\pi\)
\(30\) 0 0
\(31\) −1.39265 + 5.19745i −0.250128 + 0.933490i 0.720608 + 0.693342i \(0.243863\pi\)
−0.970736 + 0.240148i \(0.922804\pi\)
\(32\) −0.684379 + 0.684379i −0.120982 + 0.120982i
\(33\) 0 0
\(34\) −13.1925 + 13.1925i −2.26249 + 2.26249i
\(35\) −6.76626 + 3.52502i −1.14371 + 0.595838i
\(36\) 0 0
\(37\) 1.61717 + 1.61717i 0.265862 + 0.265862i 0.827430 0.561569i \(-0.189802\pi\)
−0.561569 + 0.827430i \(0.689802\pi\)
\(38\) −8.53499 14.7830i −1.38456 2.39813i
\(39\) 0 0
\(40\) −12.9216 7.46031i −2.04309 1.17958i
\(41\) −2.38652 + 8.90661i −0.372712 + 1.39098i 0.483948 + 0.875097i \(0.339203\pi\)
−0.856659 + 0.515882i \(0.827464\pi\)
\(42\) 0 0
\(43\) 3.04772 + 1.75960i 0.464773 + 0.268337i 0.714049 0.700096i \(-0.246859\pi\)
−0.249276 + 0.968432i \(0.580193\pi\)
\(44\) −1.48533 5.54333i −0.223922 0.835689i
\(45\) 0 0
\(46\) −3.97708 3.97708i −0.586388 0.586388i
\(47\) 0.223361 + 0.833593i 0.0325805 + 0.121592i 0.980301 0.197510i \(-0.0632854\pi\)
−0.947720 + 0.319102i \(0.896619\pi\)
\(48\) 0 0
\(49\) 6.34227 2.96236i 0.906039 0.423194i
\(50\) 2.11860 7.90673i 0.299616 1.11818i
\(51\) 0 0
\(52\) −3.57380 14.3283i −0.495597 1.98698i
\(53\) 0.886338 + 1.53518i 0.121748 + 0.210873i 0.920457 0.390844i \(-0.127817\pi\)
−0.798709 + 0.601717i \(0.794483\pi\)
\(54\) 0 0
\(55\) 3.49922 2.02027i 0.471834 0.272414i
\(56\) 11.5481 + 7.35179i 1.54318 + 0.982424i
\(57\) 0 0
\(58\) 17.8913 + 4.79397i 2.34925 + 0.629479i
\(59\) −3.80628 + 3.80628i −0.495536 + 0.495536i −0.910045 0.414509i \(-0.863953\pi\)
0.414509 + 0.910045i \(0.363953\pi\)
\(60\) 0 0
\(61\) −3.62667 + 2.09386i −0.464347 + 0.268091i −0.713870 0.700278i \(-0.753059\pi\)
0.249523 + 0.968369i \(0.419726\pi\)
\(62\) 6.64246 + 11.5051i 0.843594 + 1.46115i
\(63\) 0 0
\(64\) 6.77728i 0.847160i
\(65\) 9.09310 5.04144i 1.12786 0.625314i
\(66\) 0 0
\(67\) −1.44159 5.38010i −0.176119 0.657283i −0.996358 0.0852636i \(-0.972827\pi\)
0.820240 0.572020i \(-0.193840\pi\)
\(68\) 30.9499i 3.75322i
\(69\) 0 0
\(70\) −5.65859 + 17.9666i −0.676330 + 2.14742i
\(71\) 1.75325 + 6.54321i 0.208072 + 0.776536i 0.988491 + 0.151279i \(0.0483391\pi\)
−0.780419 + 0.625257i \(0.784994\pi\)
\(72\) 0 0
\(73\) 8.10009 + 2.17041i 0.948043 + 0.254027i 0.699532 0.714601i \(-0.253392\pi\)
0.248512 + 0.968629i \(0.420059\pi\)
\(74\) 5.64656 0.656399
\(75\) 0 0
\(76\) −27.3523 7.32903i −3.13753 0.840698i
\(77\) −3.28779 + 1.71284i −0.374678 + 0.195196i
\(78\) 0 0
\(79\) 0.411935 0.713493i 0.0463463 0.0802742i −0.841922 0.539600i \(-0.818576\pi\)
0.888268 + 0.459326i \(0.151909\pi\)
\(80\) −12.7667 + 3.42082i −1.42736 + 0.382459i
\(81\) 0 0
\(82\) 11.3829 + 19.7157i 1.25703 + 2.17723i
\(83\) −2.15380 2.15380i −0.236410 0.236410i 0.578952 0.815362i \(-0.303462\pi\)
−0.815362 + 0.578952i \(0.803462\pi\)
\(84\) 0 0
\(85\) −21.0482 + 5.63986i −2.28300 + 0.611729i
\(86\) 8.39268 2.24881i 0.905006 0.242496i
\(87\) 0 0
\(88\) −6.27874 3.62503i −0.669316 0.386430i
\(89\) −1.81982 + 1.81982i −0.192901 + 0.192901i −0.796948 0.604047i \(-0.793554\pi\)
0.604047 + 0.796948i \(0.293554\pi\)
\(90\) 0 0
\(91\) −8.53540 + 4.25992i −0.894753 + 0.446561i
\(92\) −9.33031 −0.972752
\(93\) 0 0
\(94\) 1.84524 + 1.06535i 0.190322 + 0.109883i
\(95\) 19.9372i 2.04551i
\(96\) 0 0
\(97\) 8.79336 2.35617i 0.892830 0.239233i 0.216896 0.976195i \(-0.430407\pi\)
0.675934 + 0.736962i \(0.263740\pi\)
\(98\) 5.90070 16.2441i 0.596060 1.64090i
\(99\) 0 0
\(100\) −6.78954 11.7598i −0.678954 1.17598i
\(101\) −8.97642 + 15.5476i −0.893187 + 1.54704i −0.0571540 + 0.998365i \(0.518203\pi\)
−0.836033 + 0.548679i \(0.815131\pi\)
\(102\) 0 0
\(103\) 3.06226 5.30399i 0.301734 0.522618i −0.674795 0.738005i \(-0.735768\pi\)
0.976529 + 0.215387i \(0.0691014\pi\)
\(104\) −15.9921 9.60707i −1.56815 0.942051i
\(105\) 0 0
\(106\) 4.22752 + 1.13276i 0.410613 + 0.110023i
\(107\) 4.73397 0.457650 0.228825 0.973468i \(-0.426512\pi\)
0.228825 + 0.973468i \(0.426512\pi\)
\(108\) 0 0
\(109\) 17.0265 + 4.56224i 1.63084 + 0.436983i 0.954162 0.299291i \(-0.0967502\pi\)
0.676683 + 0.736275i \(0.263417\pi\)
\(110\) 2.58196 9.63599i 0.246180 0.918755i
\(111\) 0 0
\(112\) 11.8384 2.62844i 1.11862 0.248365i
\(113\) 6.86440 11.8895i 0.645748 1.11847i −0.338380 0.941010i \(-0.609879\pi\)
0.984128 0.177459i \(-0.0567879\pi\)
\(114\) 0 0
\(115\) −1.70022 6.34531i −0.158546 0.591703i
\(116\) 26.6101 15.3634i 2.47069 1.42645i
\(117\) 0 0
\(118\) 13.2901i 1.22345i
\(119\) 19.5177 4.33348i 1.78919 0.397250i
\(120\) 0 0
\(121\) −7.82598 + 4.51833i −0.711453 + 0.410757i
\(122\) −2.67600 + 9.98695i −0.242273 + 0.904176i
\(123\) 0 0
\(124\) 21.2873 + 5.70391i 1.91165 + 0.512226i
\(125\) −3.43490 + 3.43490i −0.307227 + 0.307227i
\(126\) 0 0
\(127\) −9.36268 + 5.40554i −0.830803 + 0.479665i −0.854128 0.520063i \(-0.825908\pi\)
0.0233243 + 0.999728i \(0.492575\pi\)
\(128\) −13.2006 13.2006i −1.16678 1.16678i
\(129\) 0 0
\(130\) 7.07344 24.6763i 0.620381 2.16425i
\(131\) −15.7531 9.09505i −1.37635 0.794638i −0.384635 0.923069i \(-0.625673\pi\)
−0.991719 + 0.128431i \(0.959006\pi\)
\(132\) 0 0
\(133\) −0.792097 + 18.2752i −0.0686835 + 1.58466i
\(134\) −11.9094 6.87588i −1.02881 0.593986i
\(135\) 0 0
\(136\) 27.6477 + 27.6477i 2.37077 + 2.37077i
\(137\) 6.88676 + 6.88676i 0.588376 + 0.588376i 0.937191 0.348815i \(-0.113416\pi\)
−0.348815 + 0.937191i \(0.613416\pi\)
\(138\) 0 0
\(139\) −13.6153 7.86079i −1.15483 0.666744i −0.204773 0.978809i \(-0.565646\pi\)
−0.950060 + 0.312066i \(0.898979\pi\)
\(140\) 14.4375 + 27.7127i 1.22019 + 2.34215i
\(141\) 0 0
\(142\) 14.4840 + 8.36236i 1.21547 + 0.701754i
\(143\) 4.41842 2.44968i 0.369487 0.204853i
\(144\) 0 0
\(145\) 15.2973 + 15.2973i 1.27037 + 1.27037i
\(146\) 17.9303 10.3521i 1.48393 0.856745i
\(147\) 0 0
\(148\) 6.62347 6.62347i 0.544446 0.544446i
\(149\) −12.4375 3.33261i −1.01892 0.273018i −0.289567 0.957158i \(-0.593511\pi\)
−0.729351 + 0.684140i \(0.760178\pi\)
\(150\) 0 0
\(151\) 0.904012 3.37382i 0.0735674 0.274557i −0.919337 0.393471i \(-0.871274\pi\)
0.992905 + 0.118913i \(0.0379410\pi\)
\(152\) −30.9810 + 17.8869i −2.51289 + 1.45082i
\(153\) 0 0
\(154\) −2.74956 + 8.73015i −0.221566 + 0.703496i
\(155\) 15.5163i 1.24630i
\(156\) 0 0
\(157\) 0.246511 0.142323i 0.0196737 0.0113586i −0.490131 0.871649i \(-0.663051\pi\)
0.509805 + 0.860290i \(0.329718\pi\)
\(158\) −0.526462 1.96478i −0.0418831 0.156310i
\(159\) 0 0
\(160\) −1.39548 + 2.41705i −0.110323 + 0.191084i
\(161\) 1.30639 + 5.88392i 0.102958 + 0.463718i
\(162\) 0 0
\(163\) 3.54792 13.2410i 0.277895 1.03712i −0.675982 0.736918i \(-0.736280\pi\)
0.953877 0.300199i \(-0.0970531\pi\)
\(164\) 36.4789 + 9.77450i 2.84853 + 0.763260i
\(165\) 0 0
\(166\) −7.52025 −0.583684
\(167\) 8.45838 + 2.26642i 0.654529 + 0.175381i 0.570776 0.821106i \(-0.306642\pi\)
0.0837535 + 0.996487i \(0.473309\pi\)
\(168\) 0 0
\(169\) 11.4772 6.10516i 0.882864 0.469628i
\(170\) −26.9001 + 46.5924i −2.06315 + 3.57347i
\(171\) 0 0
\(172\) 7.20683 12.4826i 0.549515 0.951789i
\(173\) 5.42128 + 9.38993i 0.412172 + 0.713903i 0.995127 0.0986015i \(-0.0314369\pi\)
−0.582955 + 0.812504i \(0.698104\pi\)
\(174\) 0 0
\(175\) −6.46539 + 5.92821i −0.488737 + 0.448131i
\(176\) −6.20344 + 1.66221i −0.467602 + 0.125294i
\(177\) 0 0
\(178\) 6.35414i 0.476263i
\(179\) 7.07802 + 4.08650i 0.529036 + 0.305439i 0.740624 0.671920i \(-0.234530\pi\)
−0.211588 + 0.977359i \(0.567863\pi\)
\(180\) 0 0
\(181\) 4.10394 0.305043 0.152522 0.988300i \(-0.451261\pi\)
0.152522 + 0.988300i \(0.451261\pi\)
\(182\) −7.46417 + 22.3382i −0.553281 + 1.65582i
\(183\) 0 0
\(184\) −8.33481 + 8.33481i −0.614450 + 0.614450i
\(185\) 5.71143 + 3.29749i 0.419912 + 0.242437i
\(186\) 0 0
\(187\) −10.2275 + 2.74046i −0.747911 + 0.200402i
\(188\) 3.41416 0.914821i 0.249003 0.0667201i
\(189\) 0 0
\(190\) −34.8065 34.8065i −2.52513 2.52513i
\(191\) −2.20939 3.82678i −0.159866 0.276896i 0.774954 0.632017i \(-0.217773\pi\)
−0.934820 + 0.355121i \(0.884440\pi\)
\(192\) 0 0
\(193\) 10.8992 2.92042i 0.784538 0.210216i 0.155754 0.987796i \(-0.450219\pi\)
0.628785 + 0.777580i \(0.283553\pi\)
\(194\) 11.2381 19.4650i 0.806849 1.39750i
\(195\) 0 0
\(196\) −12.1330 25.9761i −0.866640 1.85544i
\(197\) −4.66242 1.24929i −0.332183 0.0890083i 0.0888723 0.996043i \(-0.471674\pi\)
−0.421056 + 0.907035i \(0.638340\pi\)
\(198\) 0 0
\(199\) −11.5108 −0.815981 −0.407991 0.912986i \(-0.633770\pi\)
−0.407991 + 0.912986i \(0.633770\pi\)
\(200\) −16.5702 4.43998i −1.17169 0.313954i
\(201\) 0 0
\(202\) 11.4721 + 42.8143i 0.807171 + 3.01240i
\(203\) −13.4143 14.6299i −0.941503 1.02681i
\(204\) 0 0
\(205\) 26.5896i 1.85710i
\(206\) −3.91364 14.6059i −0.272676 1.01764i
\(207\) 0 0
\(208\) −16.0346 + 3.99938i −1.11180 + 0.277307i
\(209\) 9.68766i 0.670109i
\(210\) 0 0
\(211\) −1.96759 3.40797i −0.135454 0.234614i 0.790317 0.612699i \(-0.209916\pi\)
−0.925771 + 0.378085i \(0.876583\pi\)
\(212\) 6.28766 3.63018i 0.431839 0.249322i
\(213\) 0 0
\(214\) 8.26461 8.26461i 0.564957 0.564957i
\(215\) 9.80237 + 2.62654i 0.668516 + 0.179128i
\(216\) 0 0
\(217\) 0.616459 14.2229i 0.0418480 0.965514i
\(218\) 37.6899 21.7603i 2.55268 1.47379i
\(219\) 0 0
\(220\) −8.27446 14.3318i −0.557864 0.966249i
\(221\) −26.4360 + 6.59372i −1.77828 + 0.443542i
\(222\) 0 0
\(223\) 2.38797 8.91203i 0.159910 0.596794i −0.838724 0.544556i \(-0.816698\pi\)
0.998635 0.0522375i \(-0.0166353\pi\)
\(224\) 1.37518 2.16012i 0.0918833 0.144329i
\(225\) 0 0
\(226\) −8.77286 32.7408i −0.583562 2.17788i
\(227\) −4.15727 4.15727i −0.275928 0.275928i 0.555553 0.831481i \(-0.312507\pi\)
−0.831481 + 0.555553i \(0.812507\pi\)
\(228\) 0 0
\(229\) 0.564755 + 2.10769i 0.0373201 + 0.139280i 0.982072 0.188505i \(-0.0603643\pi\)
−0.944752 + 0.327786i \(0.893698\pi\)
\(230\) −14.0460 8.10945i −0.926164 0.534721i
\(231\) 0 0
\(232\) 10.0468 37.4951i 0.659603 2.46167i
\(233\) 10.5892 + 6.11367i 0.693720 + 0.400520i 0.805004 0.593269i \(-0.202163\pi\)
−0.111284 + 0.993789i \(0.535496\pi\)
\(234\) 0 0
\(235\) 1.24429 + 2.15518i 0.0811688 + 0.140588i
\(236\) 15.5894 + 15.5894i 1.01479 + 1.01479i
\(237\) 0 0
\(238\) 26.5088 41.6397i 1.71831 2.69910i
\(239\) −7.97620 + 7.97620i −0.515938 + 0.515938i −0.916340 0.400402i \(-0.868870\pi\)
0.400402 + 0.916340i \(0.368870\pi\)
\(240\) 0 0
\(241\) −9.09005 + 9.09005i −0.585542 + 0.585542i −0.936421 0.350879i \(-0.885883\pi\)
0.350879 + 0.936421i \(0.385883\pi\)
\(242\) −5.77453 + 21.5508i −0.371201 + 1.38534i
\(243\) 0 0
\(244\) 8.57584 + 14.8538i 0.549012 + 0.950916i
\(245\) 15.4548 12.9848i 0.987370 0.829571i
\(246\) 0 0
\(247\) 0.432850 24.9245i 0.0275416 1.58591i
\(248\) 24.1114 13.9207i 1.53107 0.883965i
\(249\) 0 0
\(250\) 11.9934i 0.758528i
\(251\) −13.1084 + 22.7045i −0.827397 + 1.43309i 0.0726757 + 0.997356i \(0.476846\pi\)
−0.900073 + 0.435739i \(0.856487\pi\)
\(252\) 0 0
\(253\) −0.826153 3.08324i −0.0519398 0.193842i
\(254\) −6.90841 + 25.7825i −0.433472 + 1.61774i
\(255\) 0 0
\(256\) −32.5370 −2.03356
\(257\) −6.43364 −0.401319 −0.200660 0.979661i \(-0.564309\pi\)
−0.200660 + 0.979661i \(0.564309\pi\)
\(258\) 0 0
\(259\) −5.10431 3.24953i −0.317167 0.201916i
\(260\) −20.6483 37.2427i −1.28055 2.30970i
\(261\) 0 0
\(262\) −43.3802 + 11.6237i −2.68003 + 0.718113i
\(263\) 7.50610 13.0010i 0.462846 0.801673i −0.536255 0.844056i \(-0.680162\pi\)
0.999101 + 0.0423827i \(0.0134949\pi\)
\(264\) 0 0
\(265\) 3.61457 + 3.61457i 0.222041 + 0.222041i
\(266\) 30.5222 + 33.2879i 1.87144 + 2.04101i
\(267\) 0 0
\(268\) −22.0353 + 5.90435i −1.34602 + 0.360665i
\(269\) 22.1690i 1.35167i −0.737054 0.675834i \(-0.763784\pi\)
0.737054 0.675834i \(-0.236216\pi\)
\(270\) 0 0
\(271\) −14.9017 + 14.9017i −0.905214 + 0.905214i −0.995881 0.0906673i \(-0.971100\pi\)
0.0906673 + 0.995881i \(0.471100\pi\)
\(272\) 34.6354 2.10008
\(273\) 0 0
\(274\) 24.0460 1.45267
\(275\) 3.28491 3.28491i 0.198088 0.198088i
\(276\) 0 0
\(277\) 9.86815i 0.592920i 0.955045 + 0.296460i \(0.0958061\pi\)
−0.955045 + 0.296460i \(0.904194\pi\)
\(278\) −37.4932 + 10.0463i −2.24869 + 0.602535i
\(279\) 0 0
\(280\) 37.6529 + 11.8588i 2.25019 + 0.708697i
\(281\) −21.3933 21.3933i −1.27622 1.27622i −0.942768 0.333449i \(-0.891788\pi\)
−0.333449 0.942768i \(-0.608212\pi\)
\(282\) 0 0
\(283\) 10.7440 18.6092i 0.638666 1.10620i −0.347060 0.937843i \(-0.612820\pi\)
0.985726 0.168359i \(-0.0538466\pi\)
\(284\) 26.7991 7.18080i 1.59023 0.426102i
\(285\) 0 0
\(286\) 3.43705 11.9904i 0.203237 0.709008i
\(287\) 1.05639 24.3731i 0.0623570 1.43870i
\(288\) 0 0
\(289\) 40.1030 2.35900
\(290\) 53.4123 3.13648
\(291\) 0 0
\(292\) 8.88938 33.1756i 0.520212 1.94146i
\(293\) 0.259901 + 0.969962i 0.0151836 + 0.0566658i 0.973102 0.230375i \(-0.0739952\pi\)
−0.957918 + 0.287041i \(0.907329\pi\)
\(294\) 0 0
\(295\) −7.76120 + 13.4428i −0.451874 + 0.782670i
\(296\) 11.8336i 0.687812i
\(297\) 0 0
\(298\) −27.5316 + 15.8954i −1.59486 + 0.920795i
\(299\) −1.98778 7.96953i −0.114956 0.460890i
\(300\) 0 0
\(301\) −8.88089 2.79703i −0.511886 0.161218i
\(302\) −4.31182 7.46828i −0.248117 0.429751i
\(303\) 0 0
\(304\) −8.20179 + 30.6095i −0.470405 + 1.75557i
\(305\) −8.53895 + 8.53895i −0.488939 + 0.488939i
\(306\) 0 0
\(307\) −4.86151 + 4.86151i −0.277461 + 0.277461i −0.832095 0.554634i \(-0.812858\pi\)
0.554634 + 0.832095i \(0.312858\pi\)
\(308\) 7.01531 + 13.4658i 0.399734 + 0.767287i
\(309\) 0 0
\(310\) 27.0886 + 27.0886i 1.53853 + 1.53853i
\(311\) −6.85636 11.8756i −0.388789 0.673402i 0.603498 0.797364i \(-0.293773\pi\)
−0.992287 + 0.123963i \(0.960440\pi\)
\(312\) 0 0
\(313\) −29.5010 17.0324i −1.66750 0.962730i −0.968981 0.247137i \(-0.920510\pi\)
−0.698517 0.715593i \(-0.746156\pi\)
\(314\) 0.181892 0.678830i 0.0102648 0.0383086i
\(315\) 0 0
\(316\) −2.92226 1.68717i −0.164390 0.0949106i
\(317\) 2.52285 + 9.41539i 0.141697 + 0.528821i 0.999880 + 0.0154772i \(0.00492673\pi\)
−0.858183 + 0.513344i \(0.828407\pi\)
\(318\) 0 0
\(319\) 7.43309 + 7.43309i 0.416173 + 0.416173i
\(320\) −5.05818 18.8774i −0.282761 1.05528i
\(321\) 0 0
\(322\) 12.5529 + 7.99149i 0.699547 + 0.445348i
\(323\) −13.5222 + 50.4655i −0.752394 + 2.80797i
\(324\) 0 0
\(325\) 8.59824 8.30470i 0.476945 0.460662i
\(326\) −16.9223 29.3103i −0.937241 1.62335i
\(327\) 0 0
\(328\) 41.3184 23.8552i 2.28143 1.31718i
\(329\) −1.05494 2.02496i −0.0581610 0.111640i
\(330\) 0 0
\(331\) −20.0124 5.36230i −1.09998 0.294739i −0.337223 0.941425i \(-0.609488\pi\)
−0.762756 + 0.646686i \(0.776154\pi\)
\(332\) −8.82134 + 8.82134i −0.484134 + 0.484134i
\(333\) 0 0
\(334\) 18.7235 10.8100i 1.02450 0.591497i
\(335\) −8.03080 13.9098i −0.438769 0.759971i
\(336\) 0 0
\(337\) 26.8744i 1.46394i 0.681336 + 0.731971i \(0.261399\pi\)
−0.681336 + 0.731971i \(0.738601\pi\)
\(338\) 9.37862 30.6956i 0.510130 1.66962i
\(339\) 0 0
\(340\) 23.0992 + 86.2076i 1.25273 + 4.67526i
\(341\) 7.53954i 0.408289i
\(342\) 0 0
\(343\) −14.6824 + 11.2884i −0.792773 + 0.609517i
\(344\) −4.71286 17.5886i −0.254101 0.948316i
\(345\) 0 0
\(346\) 25.8576 + 6.92851i 1.39011 + 0.372479i
\(347\) 6.16871 0.331154 0.165577 0.986197i \(-0.447051\pi\)
0.165577 + 0.986197i \(0.447051\pi\)
\(348\) 0 0
\(349\) −20.8536 5.58771i −1.11627 0.299103i −0.346896 0.937904i \(-0.612764\pi\)
−0.769372 + 0.638801i \(0.779431\pi\)
\(350\) −0.937801 + 21.6369i −0.0501276 + 1.15654i
\(351\) 0 0
\(352\) −0.678077 + 1.17446i −0.0361416 + 0.0625992i
\(353\) −12.7937 + 3.42805i −0.680938 + 0.182457i −0.582677 0.812704i \(-0.697995\pi\)
−0.0982609 + 0.995161i \(0.531328\pi\)
\(354\) 0 0
\(355\) 9.76696 + 16.9169i 0.518376 + 0.897854i
\(356\) 7.45348 + 7.45348i 0.395034 + 0.395034i
\(357\) 0 0
\(358\) 19.4911 5.22264i 1.03014 0.276025i
\(359\) −4.76941 + 1.27796i −0.251720 + 0.0674482i −0.382473 0.923967i \(-0.624927\pi\)
0.130753 + 0.991415i \(0.458261\pi\)
\(360\) 0 0
\(361\) −24.9429 14.4008i −1.31278 0.757936i
\(362\) 7.16470 7.16470i 0.376568 0.376568i
\(363\) 0 0
\(364\) 17.4474 + 34.9585i 0.914494 + 1.83233i
\(365\) 24.1818 1.26573
\(366\) 0 0
\(367\) 17.7483 + 10.2470i 0.926453 + 0.534888i 0.885688 0.464281i \(-0.153687\pi\)
0.0407648 + 0.999169i \(0.487021\pi\)
\(368\) 10.4414i 0.544295i
\(369\) 0 0
\(370\) 15.7279 4.21427i 0.817653 0.219090i
\(371\) −3.16966 3.45687i −0.164560 0.179472i
\(372\) 0 0
\(373\) −11.6214 20.1289i −0.601735 1.04224i −0.992558 0.121770i \(-0.961143\pi\)
0.390823 0.920466i \(-0.372190\pi\)
\(374\) −13.0710 + 22.6397i −0.675886 + 1.17067i
\(375\) 0 0
\(376\) 2.23267 3.86710i 0.115141 0.199430i
\(377\) 18.7918 + 19.4561i 0.967829 + 1.00204i
\(378\) 0 0
\(379\) −20.6487 5.53282i −1.06066 0.284202i −0.314007 0.949421i \(-0.601671\pi\)
−0.746648 + 0.665219i \(0.768338\pi\)
\(380\) −81.6569 −4.18891
\(381\) 0 0
\(382\) −10.5380 2.82365i −0.539171 0.144471i
\(383\) −2.74839 + 10.2571i −0.140436 + 0.524114i 0.859480 + 0.511169i \(0.170787\pi\)
−0.999916 + 0.0129453i \(0.995879\pi\)
\(384\) 0 0
\(385\) −7.87941 + 7.22476i −0.401572 + 0.368208i
\(386\) 13.9294 24.1264i 0.708986 1.22800i
\(387\) 0 0
\(388\) −9.65021 36.0151i −0.489915 1.82839i
\(389\) −14.3360 + 8.27689i −0.726864 + 0.419655i −0.817274 0.576250i \(-0.804516\pi\)
0.0904098 + 0.995905i \(0.471182\pi\)
\(390\) 0 0
\(391\) 17.2146i 0.870578i
\(392\) −34.0430 12.3662i −1.71943 0.624586i
\(393\) 0 0
\(394\) −10.3207 + 5.95867i −0.519951 + 0.300194i
\(395\) 0.614890 2.29480i 0.0309385 0.115464i
\(396\) 0 0
\(397\) −28.5741 7.65641i −1.43409 0.384264i −0.543632 0.839323i \(-0.682951\pi\)
−0.890461 + 0.455059i \(0.849618\pi\)
\(398\) −20.0957 + 20.0957i −1.00731 + 1.00731i
\(399\) 0 0
\(400\) −13.1602 + 7.59805i −0.658011 + 0.379903i
\(401\) −7.16742 7.16742i −0.357924 0.357924i 0.505123 0.863047i \(-0.331447\pi\)
−0.863047 + 0.505123i \(0.831447\pi\)
\(402\) 0 0
\(403\) −0.336871 + 19.3978i −0.0167807 + 0.966275i
\(404\) 63.6785 + 36.7648i 3.16813 + 1.82912i
\(405\) 0 0
\(406\) −48.9599 2.12205i −2.42984 0.105316i
\(407\) 2.77523 + 1.60228i 0.137563 + 0.0794222i
\(408\) 0 0
\(409\) −2.06212 2.06212i −0.101965 0.101965i 0.654284 0.756249i \(-0.272970\pi\)
−0.756249 + 0.654284i \(0.772970\pi\)
\(410\) 46.4204 + 46.4204i 2.29254 + 2.29254i
\(411\) 0 0
\(412\) −21.7236 12.5421i −1.07025 0.617907i
\(413\) 7.64830 12.0139i 0.376348 0.591163i
\(414\) 0 0
\(415\) −7.60664 4.39170i −0.373395 0.215580i
\(416\) −1.79704 + 2.99138i −0.0881073 + 0.146665i
\(417\) 0 0
\(418\) −16.9128 16.9128i −0.827233 0.827233i
\(419\) −8.98142 + 5.18542i −0.438771 + 0.253325i −0.703076 0.711115i \(-0.748191\pi\)
0.264305 + 0.964439i \(0.414857\pi\)
\(420\) 0 0
\(421\) 26.7368 26.7368i 1.30307 1.30307i 0.376762 0.926310i \(-0.377038\pi\)
0.926310 0.376762i \(-0.122962\pi\)
\(422\) −9.38470 2.51462i −0.456840 0.122410i
\(423\) 0 0
\(424\) 2.37394 8.85966i 0.115289 0.430263i
\(425\) −21.6971 + 12.5268i −1.05246 + 0.607640i
\(426\) 0 0
\(427\) 8.16640 7.48790i 0.395200 0.362365i
\(428\) 19.3890i 0.937201i
\(429\) 0 0
\(430\) 21.6985 12.5276i 1.04640 0.604137i
\(431\) 6.33146 + 23.6293i 0.304976 + 1.13818i 0.932966 + 0.359964i \(0.117211\pi\)
−0.627991 + 0.778221i \(0.716122\pi\)
\(432\) 0 0
\(433\) 8.76052 15.1737i 0.421004 0.729200i −0.575034 0.818129i \(-0.695011\pi\)
0.996038 + 0.0889293i \(0.0283445\pi\)
\(434\) −23.7543 25.9067i −1.14024 1.24356i
\(435\) 0 0
\(436\) 18.6856 69.7357i 0.894879 3.33974i
\(437\) −15.2136 4.07647i −0.727764 0.195004i
\(438\) 0 0
\(439\) 19.8929 0.949437 0.474719 0.880138i \(-0.342550\pi\)
0.474719 + 0.880138i \(0.342550\pi\)
\(440\) −20.1943 5.41104i −0.962724 0.257961i
\(441\) 0 0
\(442\) −34.6409 + 57.6636i −1.64770 + 2.74278i
\(443\) −7.68921 + 13.3181i −0.365325 + 0.632762i −0.988828 0.149059i \(-0.952376\pi\)
0.623503 + 0.781821i \(0.285709\pi\)
\(444\) 0 0
\(445\) −3.71071 + 6.42714i −0.175905 + 0.304676i
\(446\) −11.3898 19.7277i −0.539322 0.934132i
\(447\) 0 0
\(448\) 3.88654 + 17.5047i 0.183622 + 0.827021i
\(449\) 3.38883 0.908034i 0.159929 0.0428528i −0.177966 0.984037i \(-0.556952\pi\)
0.337895 + 0.941184i \(0.390285\pi\)
\(450\) 0 0
\(451\) 12.9201i 0.608385i
\(452\) −48.6959 28.1146i −2.29046 1.32240i
\(453\) 0 0
\(454\) −14.5156 −0.681252
\(455\) −20.5951 + 18.2359i −0.965512 + 0.854912i
\(456\) 0 0
\(457\) −21.5661 + 21.5661i −1.00882 + 1.00882i −0.00885742 + 0.999961i \(0.502819\pi\)
−0.999961 + 0.00885742i \(0.997181\pi\)
\(458\) 4.66559 + 2.69368i 0.218009 + 0.125867i
\(459\) 0 0
\(460\) −25.9886 + 6.96362i −1.21172 + 0.324680i
\(461\) 19.6958 5.27746i 0.917323 0.245796i 0.230882 0.972982i \(-0.425839\pi\)
0.686441 + 0.727186i \(0.259172\pi\)
\(462\) 0 0
\(463\) 7.72370 + 7.72370i 0.358951 + 0.358951i 0.863426 0.504475i \(-0.168314\pi\)
−0.504475 + 0.863426i \(0.668314\pi\)
\(464\) −17.1929 29.7789i −0.798158 1.38245i
\(465\) 0 0
\(466\) 29.1600 7.81340i 1.35081 0.361949i
\(467\) −17.0696 + 29.5655i −0.789888 + 1.36813i 0.136147 + 0.990689i \(0.456528\pi\)
−0.926035 + 0.377438i \(0.876805\pi\)
\(468\) 0 0
\(469\) 6.80872 + 13.0693i 0.314398 + 0.603484i
\(470\) 5.93484 + 1.59023i 0.273754 + 0.0733521i
\(471\) 0 0
\(472\) 27.8522 1.28200
\(473\) 4.76306 + 1.27626i 0.219006 + 0.0586824i
\(474\) 0 0
\(475\) −5.93278 22.1414i −0.272215 1.01592i
\(476\) −17.7487 79.9390i −0.813510 3.66400i
\(477\) 0 0
\(478\) 27.8499i 1.27382i
\(479\) −4.49601 16.7793i −0.205428 0.766668i −0.989319 0.145769i \(-0.953434\pi\)
0.783891 0.620899i \(-0.213232\pi\)
\(480\) 0 0
\(481\) 7.06857 + 4.24638i 0.322299 + 0.193618i
\(482\) 31.7390i 1.44567i
\(483\) 0 0
\(484\) 18.5058 + 32.0530i 0.841172 + 1.45695i
\(485\) 22.7344 13.1257i 1.03232 0.596009i
\(486\) 0 0
\(487\) 9.01723 9.01723i 0.408610 0.408610i −0.472644 0.881254i \(-0.656700\pi\)
0.881254 + 0.472644i \(0.156700\pi\)
\(488\) 20.9298 + 5.60812i 0.947447 + 0.253868i
\(489\) 0 0
\(490\) 4.31205 49.6502i 0.194799 2.24297i
\(491\) 16.0173 9.24760i 0.722851 0.417339i −0.0929498 0.995671i \(-0.529630\pi\)
0.815801 + 0.578332i \(0.196296\pi\)
\(492\) 0 0
\(493\) −28.3456 49.0961i −1.27662 2.21118i
\(494\) −42.7579 44.2692i −1.92377 1.99177i
\(495\) 0 0
\(496\) 6.38314 23.8222i 0.286612 1.06965i
\(497\) −8.28069 15.8947i −0.371440 0.712976i
\(498\) 0 0
\(499\) 9.65516 + 36.0336i 0.432224 + 1.61308i 0.747622 + 0.664124i \(0.231195\pi\)
−0.315398 + 0.948960i \(0.602138\pi\)
\(500\) 14.0684 + 14.0684i 0.629157 + 0.629157i
\(501\) 0 0
\(502\) 16.7529 + 62.5226i 0.747718 + 2.79052i
\(503\) −12.6061 7.27816i −0.562080 0.324517i 0.191900 0.981415i \(-0.438535\pi\)
−0.753980 + 0.656897i \(0.771868\pi\)
\(504\) 0 0
\(505\) −13.3990 + 50.0057i −0.596247 + 2.22522i
\(506\) −6.82507 3.94046i −0.303411 0.175175i
\(507\) 0 0
\(508\) 22.1396 + 38.3468i 0.982284 + 1.70137i
\(509\) −0.381529 0.381529i −0.0169110 0.0169110i 0.698601 0.715512i \(-0.253806\pi\)
−0.715512 + 0.698601i \(0.753806\pi\)
\(510\) 0 0
\(511\) −22.1660 0.960734i −0.980566 0.0425004i
\(512\) −30.4022 + 30.4022i −1.34360 + 1.34360i
\(513\) 0 0
\(514\) −11.2319 + 11.2319i −0.495419 + 0.495419i
\(515\) 4.57100 17.0592i 0.201422 0.751718i
\(516\) 0 0
\(517\) 0.604614 + 1.04722i 0.0265909 + 0.0460567i
\(518\) −14.5842 + 3.23811i −0.640794 + 0.142274i
\(519\) 0 0
\(520\) −51.7143 14.8239i −2.26782 0.650070i
\(521\) 30.2442 17.4615i 1.32502 0.765003i 0.340499 0.940245i \(-0.389404\pi\)
0.984525 + 0.175242i \(0.0560707\pi\)
\(522\) 0 0
\(523\) 21.0562i 0.920725i −0.887731 0.460362i \(-0.847719\pi\)
0.887731 0.460362i \(-0.152281\pi\)
\(524\) −37.2507 + 64.5201i −1.62730 + 2.81857i
\(525\) 0 0
\(526\) −9.59297 35.8014i −0.418273 1.56102i
\(527\) 10.5238 39.2754i 0.458424 1.71086i
\(528\) 0 0
\(529\) 17.8104 0.774366
\(530\) 12.6207 0.548209
\(531\) 0 0
\(532\) 74.8500 + 3.24420i 3.24516 + 0.140654i
\(533\) −0.577279 + 33.2411i −0.0250047 + 1.43983i
\(534\) 0 0
\(535\) 13.1860 3.53317i 0.570078 0.152752i
\(536\) −14.4099 + 24.9586i −0.622412 + 1.07805i
\(537\) 0 0
\(538\) −38.7029 38.7029i −1.66860 1.66860i
\(539\) 7.50962 6.30945i 0.323462 0.271767i
\(540\) 0 0
\(541\) −30.9919 + 8.30427i −1.33245 + 0.357028i −0.853627 0.520884i \(-0.825602\pi\)
−0.478821 + 0.877913i \(0.658936\pi\)
\(542\) 52.0311i 2.23493i
\(543\) 0 0
\(544\) 5.17161 5.17161i 0.221731 0.221731i
\(545\) 50.8305 2.17734
\(546\) 0 0
\(547\) 12.5039 0.534630 0.267315 0.963609i \(-0.413864\pi\)
0.267315 + 0.963609i \(0.413864\pi\)
\(548\) 28.2062 28.2062i 1.20491 1.20491i
\(549\) 0 0
\(550\) 11.4697i 0.489068i
\(551\) 50.1016 13.4247i 2.13440 0.571911i
\(552\) 0 0
\(553\) −0.654805 + 2.07908i −0.0278451 + 0.0884114i
\(554\) 17.2279 + 17.2279i 0.731944 + 0.731944i
\(555\) 0 0
\(556\) −32.1955 + 55.7643i −1.36540 + 2.36493i
\(557\) 30.4076 8.14769i 1.28841 0.345229i 0.451354 0.892345i \(-0.350941\pi\)
0.837057 + 0.547116i \(0.184274\pi\)
\(558\) 0 0
\(559\) 12.1974 + 3.49639i 0.515897 + 0.147882i
\(560\) 31.0127 16.1567i 1.31053 0.682746i
\(561\) 0 0
\(562\) −74.6973 −3.15092
\(563\) −3.71449 −0.156547 −0.0782736 0.996932i \(-0.524941\pi\)
−0.0782736 + 0.996932i \(0.524941\pi\)
\(564\) 0 0
\(565\) 10.2464 38.2401i 0.431069 1.60877i
\(566\) −13.7311 51.2452i −0.577161 2.15399i
\(567\) 0 0
\(568\) 17.5251 30.3544i 0.735337 1.27364i
\(569\) 28.7690i 1.20606i 0.797718 + 0.603030i \(0.206040\pi\)
−0.797718 + 0.603030i \(0.793960\pi\)
\(570\) 0 0
\(571\) 38.1385 22.0193i 1.59605 0.921478i 0.603808 0.797130i \(-0.293649\pi\)
0.992239 0.124348i \(-0.0396839\pi\)
\(572\) −10.0332 18.0966i −0.419509 0.756656i
\(573\) 0 0
\(574\) −40.7065 44.3951i −1.69906 1.85301i
\(575\) −3.77640 6.54091i −0.157487 0.272775i
\(576\) 0 0
\(577\) 5.37814 20.0715i 0.223895 0.835587i −0.758950 0.651149i \(-0.774287\pi\)
0.982844 0.184437i \(-0.0590462\pi\)
\(578\) 70.0123 70.0123i 2.91213 2.91213i
\(579\) 0 0
\(580\) 62.6533 62.6533i 2.60154 2.60154i
\(581\) 6.79808 + 4.32782i 0.282032 + 0.179548i
\(582\) 0 0
\(583\) 1.75635 + 1.75635i 0.0727407 + 0.0727407i
\(584\) −21.6950 37.5769i −0.897746 1.55494i
\(585\) 0 0
\(586\) 2.14711 + 1.23963i 0.0886962 + 0.0512088i
\(587\) 11.1326 41.5473i 0.459491 1.71484i −0.215049 0.976603i \(-0.568991\pi\)
0.674540 0.738239i \(-0.264342\pi\)
\(588\) 0 0
\(589\) 32.2180 + 18.6011i 1.32752 + 0.766444i
\(590\) 9.91899 + 37.0182i 0.408358 + 1.52401i
\(591\) 0 0
\(592\) −7.41221 7.41221i −0.304640 0.304640i
\(593\) 0.460561 + 1.71884i 0.0189130 + 0.0705842i 0.974737 0.223354i \(-0.0717006\pi\)
−0.955824 + 0.293938i \(0.905034\pi\)
\(594\) 0 0
\(595\) 51.1303 26.6374i 2.09614 1.09203i
\(596\) −13.6494 + 50.9403i −0.559102 + 2.08660i
\(597\) 0 0
\(598\) −17.3836 10.4430i −0.710867 0.427047i
\(599\) −8.48260 14.6923i −0.346590 0.600311i 0.639052 0.769164i \(-0.279327\pi\)
−0.985641 + 0.168853i \(0.945994\pi\)
\(600\) 0 0
\(601\) 30.5871 17.6595i 1.24767 0.720345i 0.277029 0.960862i \(-0.410650\pi\)
0.970645 + 0.240517i \(0.0773170\pi\)
\(602\) −20.3875 + 10.6213i −0.830931 + 0.432891i
\(603\) 0 0
\(604\) −13.8182 3.70257i −0.562254 0.150656i
\(605\) −18.4262 + 18.4262i −0.749131 + 0.749131i
\(606\) 0 0
\(607\) −17.5660 + 10.1417i −0.712980 + 0.411639i −0.812164 0.583430i \(-0.801710\pi\)
0.0991833 + 0.995069i \(0.468377\pi\)
\(608\) 3.34582 + 5.79513i 0.135691 + 0.235024i
\(609\) 0 0
\(610\) 29.8148i 1.20717i
\(611\) 1.50877 + 2.72132i 0.0610382 + 0.110093i
\(612\) 0 0
\(613\) −6.42633 23.9834i −0.259557 0.968680i −0.965498 0.260410i \(-0.916142\pi\)
0.705941 0.708270i \(-0.250524\pi\)
\(614\) 16.9745i 0.685037i
\(615\) 0 0
\(616\) 18.2959 + 5.76228i 0.737163 + 0.232169i
\(617\) −7.80877 29.1427i −0.314369 1.17324i −0.924575 0.380999i \(-0.875580\pi\)
0.610206 0.792243i \(-0.291087\pi\)
\(618\) 0 0
\(619\) −38.9926 10.4480i −1.56724 0.419942i −0.632296 0.774727i \(-0.717887\pi\)
−0.934948 + 0.354785i \(0.884554\pi\)
\(620\) 63.5505 2.55225
\(621\) 0 0
\(622\) −32.7024 8.76259i −1.31125 0.351348i
\(623\) 3.65674 5.74395i 0.146504 0.230127i
\(624\) 0 0
\(625\) −15.2925 + 26.4874i −0.611701 + 1.05950i
\(626\) −81.2387 + 21.7678i −3.24695 + 0.870018i
\(627\) 0 0
\(628\) −0.582914 1.00964i −0.0232608 0.0402889i
\(629\) −12.2204 12.2204i −0.487260 0.487260i
\(630\) 0 0
\(631\) 11.8790 3.18298i 0.472897 0.126712i −0.0144963 0.999895i \(-0.504614\pi\)
0.487393 + 0.873183i \(0.337948\pi\)
\(632\) −4.11762 + 1.10331i −0.163790 + 0.0438875i
\(633\) 0 0
\(634\) 20.8419 + 12.0331i 0.827738 + 0.477895i
\(635\) −22.0443 + 22.0443i −0.874803 + 0.874803i
\(636\) 0 0
\(637\) 19.6028 15.8975i 0.776690 0.629883i
\(638\) 25.9535 1.02751
\(639\) 0 0
\(640\) −46.6211 26.9167i −1.84286 1.06398i
\(641\) 10.9869i 0.433956i 0.976176 + 0.216978i \(0.0696200\pi\)
−0.976176 + 0.216978i \(0.930380\pi\)
\(642\) 0 0
\(643\) −5.20127 + 1.39368i −0.205118 + 0.0549612i −0.359915 0.932985i \(-0.617194\pi\)
0.154797 + 0.987946i \(0.450528\pi\)
\(644\) 24.0988 5.35061i 0.949627 0.210844i
\(645\) 0 0
\(646\) 64.4960 + 111.710i 2.53756 + 4.39518i
\(647\) 19.1619 33.1894i 0.753333 1.30481i −0.192866 0.981225i \(-0.561778\pi\)
0.946199 0.323586i \(-0.104888\pi\)
\(648\) 0 0
\(649\) −3.77124 + 6.53198i −0.148034 + 0.256402i
\(650\) 0.512472 29.5093i 0.0201008 1.15745i
\(651\) 0 0
\(652\) −54.2315 14.5313i −2.12387 0.569089i
\(653\) −7.74794 −0.303200 −0.151600 0.988442i \(-0.548443\pi\)
−0.151600 + 0.988442i \(0.548443\pi\)
\(654\) 0 0
\(655\) −50.6666 13.5761i −1.97971 0.530461i
\(656\) 10.9385 40.8229i 0.427075 1.59387i
\(657\) 0 0
\(658\) −5.37693 1.69346i −0.209615 0.0660180i
\(659\) −1.59593 + 2.76423i −0.0621686 + 0.107679i −0.895435 0.445193i \(-0.853135\pi\)
0.833266 + 0.552872i \(0.186468\pi\)
\(660\) 0 0
\(661\) 1.11096 + 4.14615i 0.0432113 + 0.161267i 0.984160 0.177282i \(-0.0567306\pi\)
−0.940949 + 0.338549i \(0.890064\pi\)
\(662\) −44.2994 + 25.5763i −1.72174 + 0.994049i
\(663\) 0 0
\(664\) 15.7603i 0.611617i
\(665\) 11.4333 + 51.4948i 0.443364 + 1.99688i
\(666\) 0 0
\(667\) 14.8008 8.54522i 0.573087 0.330872i
\(668\) 9.28259 34.6431i 0.359154 1.34038i
\(669\) 0 0
\(670\) −38.3041 10.2635i −1.47982 0.396515i
\(671\) −4.14915 + 4.14915i −0.160176 + 0.160176i
\(672\) 0 0
\(673\) 11.6256 6.71205i 0.448134 0.258731i −0.258908 0.965902i \(-0.583362\pi\)
0.707042 + 0.707172i \(0.250029\pi\)
\(674\) 46.9176 + 46.9176i 1.80720 + 1.80720i
\(675\) 0 0
\(676\) −25.0050 47.0075i −0.961731 1.80798i
\(677\) 19.3278 + 11.1589i 0.742830 + 0.428873i 0.823097 0.567901i \(-0.192244\pi\)
−0.0802677 + 0.996773i \(0.525578\pi\)
\(678\) 0 0
\(679\) −21.3608 + 11.1283i −0.819751 + 0.427067i
\(680\) 97.6443 + 56.3749i 3.74449 + 2.16188i
\(681\) 0 0
\(682\) 13.1626 + 13.1626i 0.504022 + 0.504022i
\(683\) 5.15641 + 5.15641i 0.197304 + 0.197304i 0.798843 0.601539i \(-0.205446\pi\)
−0.601539 + 0.798843i \(0.705446\pi\)
\(684\) 0 0
\(685\) 24.3222 + 14.0424i 0.929305 + 0.536534i
\(686\) −5.92518 + 45.3401i −0.226225 + 1.73109i
\(687\) 0 0
\(688\) −13.9690 8.06503i −0.532565 0.307476i
\(689\) 4.44030 + 4.59725i 0.169162 + 0.175141i
\(690\) 0 0
\(691\) 7.98871 + 7.98871i 0.303905 + 0.303905i 0.842539 0.538635i \(-0.181060\pi\)
−0.538635 + 0.842539i \(0.681060\pi\)
\(692\) 38.4584 22.2040i 1.46197 0.844069i
\(693\) 0 0
\(694\) 10.7694 10.7694i 0.408801 0.408801i
\(695\) −43.7908 11.7337i −1.66108 0.445085i
\(696\) 0 0
\(697\) 18.0341 67.3042i 0.683090 2.54933i
\(698\) −46.1615 + 26.6514i −1.74724 + 1.00877i
\(699\) 0 0
\(700\) 24.2803 + 26.4804i 0.917708 + 1.00086i
\(701\) 0.777837i 0.0293785i 0.999892 + 0.0146892i \(0.00467590\pi\)
−0.999892 + 0.0146892i \(0.995324\pi\)
\(702\) 0 0
\(703\) 13.6938 7.90610i 0.516470 0.298184i
\(704\) −2.45782 9.17270i −0.0926325 0.345709i
\(705\) 0 0
\(706\) −16.3506 + 28.3200i −0.615362 + 1.06584i
\(707\) 14.2688 45.3049i 0.536632 1.70387i
\(708\) 0 0
\(709\) 0.571859 2.13421i 0.0214766 0.0801518i −0.954356 0.298672i \(-0.903456\pi\)
0.975832 + 0.218520i \(0.0701230\pi\)
\(710\) 46.5849 + 12.4824i 1.74830 + 0.468456i
\(711\) 0 0
\(712\) 13.3165 0.499055
\(713\) 11.8402 + 3.17256i 0.443417 + 0.118813i
\(714\) 0 0
\(715\) 10.4787 10.1210i 0.391882 0.378504i
\(716\) 16.7371 28.9896i 0.625496 1.08339i
\(717\) 0 0
\(718\) −6.09542 + 10.5576i −0.227479 + 0.394005i
\(719\) 6.15320 + 10.6577i 0.229476 + 0.397463i 0.957653 0.287926i \(-0.0929656\pi\)
−0.728177 + 0.685389i \(0.759632\pi\)
\(720\) 0 0
\(721\) −4.86772 + 15.4555i −0.181283 + 0.575594i
\(722\) −68.6866 + 18.4045i −2.55625 + 0.684945i
\(723\) 0 0
\(724\) 16.8086i 0.624685i
\(725\) 21.5406 + 12.4365i 0.799999 + 0.461880i
\(726\) 0 0
\(727\) 46.3414 1.71871 0.859353 0.511383i \(-0.170867\pi\)
0.859353 + 0.511383i \(0.170867\pi\)
\(728\) 46.8145 + 15.6428i 1.73506 + 0.579759i
\(729\) 0 0
\(730\) 42.2168 42.2168i 1.56252 1.56252i
\(731\) −23.0306 13.2967i −0.851817 0.491797i
\(732\) 0 0
\(733\) 16.0476 4.29994i 0.592731 0.158822i 0.0500300 0.998748i \(-0.484068\pi\)
0.542701 + 0.839926i \(0.317402\pi\)
\(734\) 48.8744 13.0959i 1.80399 0.483377i
\(735\) 0 0
\(736\) 1.55906 + 1.55906i 0.0574678 + 0.0574678i
\(737\) −3.90224 6.75888i −0.143741 0.248966i
\(738\) 0 0
\(739\) −3.40979 + 0.913649i −0.125431 + 0.0336091i −0.320988 0.947083i \(-0.604015\pi\)
0.195557 + 0.980692i \(0.437348\pi\)
\(740\) 13.5056 23.3924i 0.496475 0.859920i
\(741\) 0 0
\(742\) −11.5687 0.501417i −0.424699 0.0184076i
\(743\) −42.9886 11.5188i −1.57710 0.422583i −0.639073 0.769146i \(-0.720682\pi\)
−0.938027 + 0.346563i \(0.887349\pi\)
\(744\) 0 0
\(745\) −37.1305 −1.36036
\(746\) −55.4301 14.8525i −2.02944 0.543787i
\(747\) 0 0
\(748\) 11.2241 + 41.8890i 0.410395 + 1.53161i
\(749\) −12.2271 + 2.71477i −0.446770 + 0.0991955i
\(750\) 0 0
\(751\) 52.0913i 1.90084i −0.310970 0.950420i \(-0.600654\pi\)
0.310970 0.950420i \(-0.399346\pi\)
\(752\) −1.02376 3.82072i −0.0373327 0.139327i
\(753\) 0 0
\(754\) 66.7736 + 1.15962i 2.43175 + 0.0422309i
\(755\) 10.0721i 0.366562i
\(756\) 0 0
\(757\) 23.5702 + 40.8248i 0.856674 + 1.48380i 0.875083 + 0.483973i \(0.160807\pi\)
−0.0184085 + 0.999831i \(0.505860\pi\)
\(758\) −45.7081 + 26.3896i −1.66019 + 0.958512i
\(759\) 0 0
\(760\) −72.9445 + 72.9445i −2.64598 + 2.64598i
\(761\) −29.1992 7.82391i −1.05847 0.283616i −0.312723 0.949844i \(-0.601241\pi\)
−0.745748 + 0.666228i \(0.767908\pi\)
\(762\) 0 0
\(763\) −46.5933 2.01948i −1.68679 0.0731101i
\(764\) −15.6734 + 9.04903i −0.567043 + 0.327382i
\(765\) 0 0
\(766\) 13.1088 + 22.7052i 0.473641 + 0.820371i
\(767\) −9.99455 + 16.6371i −0.360882 + 0.600729i
\(768\) 0 0
\(769\) 1.17278 4.37689i 0.0422916 0.157835i −0.941551 0.336871i \(-0.890631\pi\)
0.983842 + 0.179037i \(0.0572980\pi\)
\(770\) −1.14290 + 26.3690i −0.0411874 + 0.950273i
\(771\) 0 0
\(772\) −11.9612 44.6398i −0.430493 1.60662i
\(773\) 1.58168 + 1.58168i 0.0568893 + 0.0568893i 0.734979 0.678090i \(-0.237192\pi\)
−0.678090 + 0.734979i \(0.737192\pi\)
\(774\) 0 0
\(775\) 4.61726 + 17.2318i 0.165857 + 0.618986i
\(776\) −40.7930 23.5518i −1.46438 0.845462i
\(777\) 0 0
\(778\) −10.5781 + 39.4778i −0.379242 + 1.41535i
\(779\) 55.2104 + 31.8757i 1.97812 + 1.14207i
\(780\) 0 0
\(781\) 4.74586 + 8.22006i 0.169820 + 0.294137i
\(782\) 30.0534 + 30.0534i 1.07471 + 1.07471i
\(783\) 0 0
\(784\) −29.0694 + 13.5778i −1.03819 + 0.484921i
\(785\) 0.580407 0.580407i 0.0207156 0.0207156i
\(786\) 0 0
\(787\) −27.8371 + 27.8371i −0.992286 + 0.992286i −0.999970 0.00768427i \(-0.997554\pi\)
0.00768427 + 0.999970i \(0.497554\pi\)
\(788\) −5.11674 + 19.0959i −0.182276 + 0.680264i