Properties

Label 729.2.g.a.55.3
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.3
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.a.676.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +O(q^{10})\) \(q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +(3.27047 + 1.19035i) q^{10} +(-2.24948 - 1.47950i) q^{11} +(-4.57632 - 0.534895i) q^{13} +(0.396347 - 0.532387i) q^{14} +(0.0182372 - 0.313121i) q^{16} +(0.692702 - 0.581246i) q^{17} +(-1.12072 - 0.940396i) q^{19} +(3.04408 - 3.22654i) q^{20} +(2.05578 - 1.35211i) q^{22} +(-3.79608 + 0.899688i) q^{23} +(-9.43871 + 1.10323i) q^{25} +(2.10537 - 3.64661i) q^{26} +(-0.422971 - 0.732607i) q^{28} +(-3.06986 - 4.12353i) q^{29} +(-2.86446 + 9.56797i) q^{31} +(-4.91313 - 2.46747i) q^{32} +(0.237013 + 0.791679i) q^{34} +(-0.480274 + 2.72377i) q^{35} +(-0.348559 - 1.97678i) q^{37} +(1.19481 - 0.600055i) q^{38} +(4.36268 + 10.1138i) q^{40} +(2.59790 + 6.02260i) q^{41} +(6.51223 - 3.27057i) q^{43} +(-0.544580 - 3.08847i) q^{44} +(0.619111 - 3.51115i) q^{46} +(-1.28270 - 4.28453i) q^{47} +(-5.78408 - 2.90488i) q^{49} +(2.49080 - 8.31986i) q^{50} +(-3.20482 - 4.30482i) q^{52} +(-3.43548 - 5.95043i) q^{53} +(-5.12672 + 8.87974i) q^{55} +(2.08634 - 0.243858i) q^{56} +(4.57148 - 1.08346i) q^{58} +(-0.590929 + 0.388660i) q^{59} +(1.83608 - 1.94613i) q^{61} +(-6.99212 - 5.86709i) q^{62} +(4.32956 - 3.63293i) q^{64} +(-1.02024 + 17.5169i) q^{65} +(8.91352 - 11.9729i) q^{67} +(1.04616 + 0.122278i) q^{68} +(-2.11181 - 1.38896i) q^{70} +(9.19719 + 3.34750i) q^{71} +(15.0748 - 5.48678i) q^{73} +(1.78499 + 0.423050i) q^{74} +(-0.0990843 - 1.70121i) q^{76} +(1.34186 + 1.42229i) q^{77} +(1.89166 - 4.38536i) q^{79} -1.19447 q^{80} -5.99425 q^{82} +(2.86882 - 6.65067i) q^{83} +(-2.36319 - 2.50483i) q^{85} +(0.387238 + 6.64862i) q^{86} +(7.57733 + 1.79586i) q^{88} +(-7.00321 + 2.54896i) q^{89} +(3.14441 + 1.14447i) q^{91} +(-3.79659 - 2.49705i) q^{92} +(4.05968 + 0.474509i) q^{94} +(-3.32707 + 4.46903i) q^{95} +(0.258735 - 4.44232i) q^{97} +(4.53133 - 3.80223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.361975 + 0.839152i −0.255955 + 0.593370i −0.996942 0.0781494i \(-0.975099\pi\)
0.740987 + 0.671520i \(0.234358\pi\)
\(3\) 0 0
\(4\) 0.799333 + 0.847243i 0.399666 + 0.423621i
\(5\) −0.221432 3.80183i −0.0990272 1.70023i −0.572889 0.819633i \(-0.694178\pi\)
0.473862 0.880599i \(-0.342859\pi\)
\(6\) 0 0
\(7\) −0.706680 0.167486i −0.267100 0.0633039i 0.0948834 0.995488i \(-0.469752\pi\)
−0.361983 + 0.932185i \(0.617900\pi\)
\(8\) −2.71786 + 0.989221i −0.960910 + 0.349743i
\(9\) 0 0
\(10\) 3.27047 + 1.19035i 1.03421 + 0.376423i
\(11\) −2.24948 1.47950i −0.678243 0.446087i 0.163086 0.986612i \(-0.447855\pi\)
−0.841328 + 0.540525i \(0.818226\pi\)
\(12\) 0 0
\(13\) −4.57632 0.534895i −1.26924 0.148353i −0.545317 0.838230i \(-0.683591\pi\)
−0.723927 + 0.689877i \(0.757665\pi\)
\(14\) 0.396347 0.532387i 0.105928 0.142286i
\(15\) 0 0
\(16\) 0.0182372 0.313121i 0.00455931 0.0782803i
\(17\) 0.692702 0.581246i 0.168005 0.140973i −0.554909 0.831911i \(-0.687247\pi\)
0.722914 + 0.690938i \(0.242802\pi\)
\(18\) 0 0
\(19\) −1.12072 0.940396i −0.257111 0.215742i 0.505116 0.863051i \(-0.331450\pi\)
−0.762227 + 0.647310i \(0.775894\pi\)
\(20\) 3.04408 3.22654i 0.680677 0.721475i
\(21\) 0 0
\(22\) 2.05578 1.35211i 0.438294 0.288271i
\(23\) −3.79608 + 0.899688i −0.791538 + 0.187598i −0.606447 0.795124i \(-0.707406\pi\)
−0.185090 + 0.982722i \(0.559258\pi\)
\(24\) 0 0
\(25\) −9.43871 + 1.10323i −1.88774 + 0.220645i
\(26\) 2.10537 3.64661i 0.412898 0.715160i
\(27\) 0 0
\(28\) −0.422971 0.732607i −0.0799340 0.138450i
\(29\) −3.06986 4.12353i −0.570058 0.765721i 0.419825 0.907605i \(-0.362091\pi\)
−0.989883 + 0.141884i \(0.954684\pi\)
\(30\) 0 0
\(31\) −2.86446 + 9.56797i −0.514473 + 1.71846i 0.166402 + 0.986058i \(0.446785\pi\)
−0.680874 + 0.732400i \(0.738400\pi\)
\(32\) −4.91313 2.46747i −0.868528 0.436191i
\(33\) 0 0
\(34\) 0.237013 + 0.791679i 0.0406474 + 0.135772i
\(35\) −0.480274 + 2.72377i −0.0811811 + 0.460401i
\(36\) 0 0
\(37\) −0.348559 1.97678i −0.0573028 0.324980i 0.942659 0.333758i \(-0.108317\pi\)
−0.999961 + 0.00877810i \(0.997206\pi\)
\(38\) 1.19481 0.600055i 0.193824 0.0973418i
\(39\) 0 0
\(40\) 4.36268 + 10.1138i 0.689800 + 1.59914i
\(41\) 2.59790 + 6.02260i 0.405723 + 0.940572i 0.991501 + 0.130100i \(0.0415299\pi\)
−0.585778 + 0.810472i \(0.699211\pi\)
\(42\) 0 0
\(43\) 6.51223 3.27057i 0.993106 0.498757i 0.123416 0.992355i \(-0.460615\pi\)
0.869690 + 0.493598i \(0.164319\pi\)
\(44\) −0.544580 3.08847i −0.0820986 0.465604i
\(45\) 0 0
\(46\) 0.619111 3.51115i 0.0912830 0.517692i
\(47\) −1.28270 4.28453i −0.187102 0.624963i −0.999144 0.0413648i \(-0.986829\pi\)
0.812042 0.583598i \(-0.198356\pi\)
\(48\) 0 0
\(49\) −5.78408 2.90488i −0.826298 0.414982i
\(50\) 2.49080 8.31986i 0.352253 1.17661i
\(51\) 0 0
\(52\) −3.20482 4.30482i −0.444428 0.596971i
\(53\) −3.43548 5.95043i −0.471900 0.817355i 0.527583 0.849503i \(-0.323098\pi\)
−0.999483 + 0.0321487i \(0.989765\pi\)
\(54\) 0 0
\(55\) −5.12672 + 8.87974i −0.691287 + 1.19734i
\(56\) 2.08634 0.243858i 0.278799 0.0325870i
\(57\) 0 0
\(58\) 4.57148 1.08346i 0.600265 0.142265i
\(59\) −0.590929 + 0.388660i −0.0769324 + 0.0505992i −0.587392 0.809302i \(-0.699845\pi\)
0.510460 + 0.859901i \(0.329475\pi\)
\(60\) 0 0
\(61\) 1.83608 1.94613i 0.235086 0.249177i −0.599081 0.800688i \(-0.704467\pi\)
0.834167 + 0.551512i \(0.185949\pi\)
\(62\) −6.99212 5.86709i −0.888000 0.745121i
\(63\) 0 0
\(64\) 4.32956 3.63293i 0.541195 0.454116i
\(65\) −1.02024 + 17.5169i −0.126545 + 2.17270i
\(66\) 0 0
\(67\) 8.91352 11.9729i 1.08896 1.46273i 0.215073 0.976598i \(-0.431001\pi\)
0.873887 0.486129i \(-0.161591\pi\)
\(68\) 1.04616 + 0.122278i 0.126865 + 0.0148284i
\(69\) 0 0
\(70\) −2.11181 1.38896i −0.252409 0.166012i
\(71\) 9.19719 + 3.34750i 1.09151 + 0.397276i 0.824179 0.566330i \(-0.191637\pi\)
0.267328 + 0.963606i \(0.413859\pi\)
\(72\) 0 0
\(73\) 15.0748 5.48678i 1.76437 0.642179i 0.764376 0.644771i \(-0.223047\pi\)
0.999997 + 0.00259223i \(0.000825133\pi\)
\(74\) 1.78499 + 0.423050i 0.207501 + 0.0491785i
\(75\) 0 0
\(76\) −0.0990843 1.70121i −0.0113658 0.195142i
\(77\) 1.34186 + 1.42229i 0.152920 + 0.162085i
\(78\) 0 0
\(79\) 1.89166 4.38536i 0.212828 0.493391i −0.778042 0.628213i \(-0.783787\pi\)
0.990870 + 0.134821i \(0.0430461\pi\)
\(80\) −1.19447 −0.133546
\(81\) 0 0
\(82\) −5.99425 −0.661954
\(83\) 2.86882 6.65067i 0.314894 0.730006i −0.685105 0.728444i \(-0.740244\pi\)
0.999999 0.00156176i \(-0.000497123\pi\)
\(84\) 0 0
\(85\) −2.36319 2.50483i −0.256324 0.271687i
\(86\) 0.387238 + 6.64862i 0.0417569 + 0.716939i
\(87\) 0 0
\(88\) 7.57733 + 1.79586i 0.807746 + 0.191439i
\(89\) −7.00321 + 2.54896i −0.742339 + 0.270189i −0.685378 0.728187i \(-0.740363\pi\)
−0.0569608 + 0.998376i \(0.518141\pi\)
\(90\) 0 0
\(91\) 3.14441 + 1.14447i 0.329624 + 0.119973i
\(92\) −3.79659 2.49705i −0.395821 0.260336i
\(93\) 0 0
\(94\) 4.05968 + 0.474509i 0.418724 + 0.0489418i
\(95\) −3.32707 + 4.46903i −0.341350 + 0.458512i
\(96\) 0 0
\(97\) 0.258735 4.44232i 0.0262706 0.451049i −0.959366 0.282166i \(-0.908947\pi\)
0.985636 0.168883i \(-0.0540159\pi\)
\(98\) 4.53133 3.80223i 0.457733 0.384084i
\(99\) 0 0
\(100\) −8.47937 7.11504i −0.847937 0.711504i
\(101\) −7.50105 + 7.95065i −0.746383 + 0.791119i −0.983605 0.180336i \(-0.942282\pi\)
0.237222 + 0.971455i \(0.423763\pi\)
\(102\) 0 0
\(103\) −4.04794 + 2.66237i −0.398856 + 0.262332i −0.733053 0.680172i \(-0.761905\pi\)
0.334197 + 0.942503i \(0.391535\pi\)
\(104\) 12.9669 3.07322i 1.27151 0.301354i
\(105\) 0 0
\(106\) 6.23688 0.728986i 0.605779 0.0708054i
\(107\) −1.36707 + 2.36783i −0.132159 + 0.228906i −0.924509 0.381161i \(-0.875524\pi\)
0.792349 + 0.610067i \(0.208858\pi\)
\(108\) 0 0
\(109\) 1.70034 + 2.94507i 0.162863 + 0.282087i 0.935894 0.352281i \(-0.114594\pi\)
−0.773031 + 0.634368i \(0.781261\pi\)
\(110\) −5.59571 7.51635i −0.533530 0.716655i
\(111\) 0 0
\(112\) −0.0653315 + 0.218222i −0.00617324 + 0.0206201i
\(113\) −8.41203 4.22468i −0.791337 0.397424i 0.00674204 0.999977i \(-0.497854\pi\)
−0.798079 + 0.602553i \(0.794150\pi\)
\(114\) 0 0
\(115\) 4.26104 + 14.2328i 0.397344 + 1.32722i
\(116\) 1.03980 5.89699i 0.0965428 0.547521i
\(117\) 0 0
\(118\) −0.112244 0.636565i −0.0103329 0.0586005i
\(119\) −0.586870 + 0.294737i −0.0537983 + 0.0270185i
\(120\) 0 0
\(121\) −1.48567 3.44416i −0.135061 0.313106i
\(122\) 0.968487 + 2.24520i 0.0876827 + 0.203271i
\(123\) 0 0
\(124\) −10.3961 + 5.22109i −0.933593 + 0.468868i
\(125\) 2.97782 + 16.8880i 0.266344 + 1.51051i
\(126\) 0 0
\(127\) −1.36769 + 7.75655i −0.121363 + 0.688283i 0.862039 + 0.506842i \(0.169187\pi\)
−0.983402 + 0.181441i \(0.941924\pi\)
\(128\) −1.67226 5.58574i −0.147808 0.493714i
\(129\) 0 0
\(130\) −14.3300 7.19680i −1.25683 0.631201i
\(131\) 0.310717 1.03787i 0.0271475 0.0906789i −0.943342 0.331821i \(-0.892337\pi\)
0.970490 + 0.241142i \(0.0775221\pi\)
\(132\) 0 0
\(133\) 0.634488 + 0.852265i 0.0550171 + 0.0739008i
\(134\) 6.82065 + 11.8137i 0.589214 + 1.02055i
\(135\) 0 0
\(136\) −1.30769 + 2.26498i −0.112133 + 0.194221i
\(137\) −0.730936 + 0.0854341i −0.0624481 + 0.00729913i −0.147260 0.989098i \(-0.547045\pi\)
0.0848115 + 0.996397i \(0.472971\pi\)
\(138\) 0 0
\(139\) −4.09766 + 0.971163i −0.347559 + 0.0823730i −0.400688 0.916215i \(-0.631229\pi\)
0.0531287 + 0.998588i \(0.483081\pi\)
\(140\) −2.69159 + 1.77029i −0.227481 + 0.149617i
\(141\) 0 0
\(142\) −6.13822 + 6.50613i −0.515108 + 0.545983i
\(143\) 9.50295 + 7.97392i 0.794676 + 0.666813i
\(144\) 0 0
\(145\) −14.9972 + 12.5842i −1.24545 + 1.04506i
\(146\) −0.852458 + 14.6361i −0.0705499 + 1.21130i
\(147\) 0 0
\(148\) 1.39620 1.87542i 0.114767 0.154158i
\(149\) 11.5926 + 1.35499i 0.949706 + 0.111005i 0.576819 0.816872i \(-0.304294\pi\)
0.372887 + 0.927877i \(0.378368\pi\)
\(150\) 0 0
\(151\) 4.00498 + 2.63412i 0.325920 + 0.214361i 0.701915 0.712261i \(-0.252329\pi\)
−0.375995 + 0.926622i \(0.622699\pi\)
\(152\) 3.97623 + 1.44723i 0.322515 + 0.117386i
\(153\) 0 0
\(154\) −1.67924 + 0.611194i −0.135317 + 0.0492514i
\(155\) 37.0101 + 8.77156i 2.97272 + 0.704549i
\(156\) 0 0
\(157\) −0.543531 9.33207i −0.0433785 0.744780i −0.947942 0.318442i \(-0.896840\pi\)
0.904564 0.426338i \(-0.140197\pi\)
\(158\) 2.99525 + 3.17478i 0.238289 + 0.252572i
\(159\) 0 0
\(160\) −8.29298 + 19.2253i −0.655618 + 1.51989i
\(161\) 2.83330 0.223295
\(162\) 0 0
\(163\) −7.79498 −0.610550 −0.305275 0.952264i \(-0.598748\pi\)
−0.305275 + 0.952264i \(0.598748\pi\)
\(164\) −3.02602 + 7.01511i −0.236293 + 0.547788i
\(165\) 0 0
\(166\) 4.54249 + 4.81475i 0.352565 + 0.373697i
\(167\) 0.628896 + 10.7977i 0.0486654 + 0.835553i 0.931020 + 0.364968i \(0.118920\pi\)
−0.882355 + 0.470585i \(0.844043\pi\)
\(168\) 0 0
\(169\) 8.00703 + 1.89770i 0.615925 + 0.145977i
\(170\) 2.95735 1.07639i 0.226818 0.0825551i
\(171\) 0 0
\(172\) 7.97640 + 2.90317i 0.608195 + 0.221365i
\(173\) −9.71059 6.38676i −0.738282 0.485576i 0.123823 0.992304i \(-0.460484\pi\)
−0.862106 + 0.506728i \(0.830855\pi\)
\(174\) 0 0
\(175\) 6.85493 + 0.801226i 0.518184 + 0.0605670i
\(176\) −0.504289 + 0.677377i −0.0380122 + 0.0510592i
\(177\) 0 0
\(178\) 0.396021 6.79942i 0.0296831 0.509638i
\(179\) −2.09069 + 1.75429i −0.156265 + 0.131122i −0.717568 0.696488i \(-0.754745\pi\)
0.561303 + 0.827611i \(0.310300\pi\)
\(180\) 0 0
\(181\) −11.5914 9.72633i −0.861581 0.722953i 0.100727 0.994914i \(-0.467883\pi\)
−0.962308 + 0.271962i \(0.912328\pi\)
\(182\) −2.09858 + 2.22437i −0.155557 + 0.164881i
\(183\) 0 0
\(184\) 9.42724 6.20039i 0.694985 0.457099i
\(185\) −7.43820 + 1.76288i −0.546867 + 0.129610i
\(186\) 0 0
\(187\) −2.41817 + 0.282644i −0.176834 + 0.0206690i
\(188\) 2.60473 4.51153i 0.189970 0.329037i
\(189\) 0 0
\(190\) −2.54588 4.40959i −0.184697 0.319905i
\(191\) 1.47784 + 1.98509i 0.106933 + 0.143636i 0.852368 0.522942i \(-0.175166\pi\)
−0.745435 + 0.666578i \(0.767758\pi\)
\(192\) 0 0
\(193\) 1.13748 3.79946i 0.0818778 0.273491i −0.907241 0.420612i \(-0.861815\pi\)
0.989119 + 0.147121i \(0.0470006\pi\)
\(194\) 3.63412 + 1.82513i 0.260915 + 0.131036i
\(195\) 0 0
\(196\) −2.16227 7.22248i −0.154448 0.515892i
\(197\) −4.31848 + 24.4913i −0.307679 + 1.74493i 0.302942 + 0.953009i \(0.402031\pi\)
−0.610621 + 0.791923i \(0.709080\pi\)
\(198\) 0 0
\(199\) 2.00332 + 11.3614i 0.142011 + 0.805386i 0.969718 + 0.244226i \(0.0785338\pi\)
−0.827707 + 0.561160i \(0.810355\pi\)
\(200\) 24.5618 12.3354i 1.73678 0.872245i
\(201\) 0 0
\(202\) −3.95661 9.17246i −0.278386 0.645372i
\(203\) 1.47877 + 3.42818i 0.103789 + 0.240611i
\(204\) 0 0
\(205\) 22.3217 11.2104i 1.55901 0.782966i
\(206\) −0.768884 4.36056i −0.0535707 0.303814i
\(207\) 0 0
\(208\) −0.250947 + 1.42319i −0.0174000 + 0.0986804i
\(209\) 1.12971 + 3.77351i 0.0781440 + 0.261019i
\(210\) 0 0
\(211\) 18.9771 + 9.53064i 1.30643 + 0.656116i 0.959483 0.281767i \(-0.0909205\pi\)
0.346952 + 0.937883i \(0.387217\pi\)
\(212\) 2.29537 7.66706i 0.157647 0.526576i
\(213\) 0 0
\(214\) −1.49212 2.00427i −0.101999 0.137009i
\(215\) −13.8762 24.0342i −0.946346 1.63912i
\(216\) 0 0
\(217\) 3.62676 6.28174i 0.246201 0.426432i
\(218\) −3.08684 + 0.360800i −0.209068 + 0.0244365i
\(219\) 0 0
\(220\) −11.6213 + 2.75429i −0.783505 + 0.185694i
\(221\) −3.48093 + 2.28945i −0.234153 + 0.154005i
\(222\) 0 0
\(223\) −1.53505 + 1.62706i −0.102795 + 0.108956i −0.776728 0.629836i \(-0.783122\pi\)
0.673933 + 0.738792i \(0.264604\pi\)
\(224\) 3.05875 + 2.56659i 0.204371 + 0.171488i
\(225\) 0 0
\(226\) 6.59009 5.52974i 0.438366 0.367833i
\(227\) −0.205125 + 3.52186i −0.0136146 + 0.233754i 0.984636 + 0.174622i \(0.0558704\pi\)
−0.998250 + 0.0591321i \(0.981167\pi\)
\(228\) 0 0
\(229\) −6.30941 + 8.47500i −0.416937 + 0.560044i −0.960126 0.279566i \(-0.909809\pi\)
0.543189 + 0.839610i \(0.317217\pi\)
\(230\) −13.4859 1.57628i −0.889235 0.103937i
\(231\) 0 0
\(232\) 12.4225 + 8.17043i 0.815579 + 0.536415i
\(233\) −16.8171 6.12092i −1.10172 0.400995i −0.273773 0.961794i \(-0.588272\pi\)
−0.827952 + 0.560799i \(0.810494\pi\)
\(234\) 0 0
\(235\) −16.0050 + 5.82536i −1.04405 + 0.380005i
\(236\) −0.801638 0.189992i −0.0521822 0.0123674i
\(237\) 0 0
\(238\) −0.0348971 0.599160i −0.00226204 0.0388378i
\(239\) 0.254893 + 0.270171i 0.0164877 + 0.0174759i 0.735565 0.677454i \(-0.236917\pi\)
−0.719077 + 0.694930i \(0.755435\pi\)
\(240\) 0 0
\(241\) 2.49079 5.77431i 0.160446 0.371956i −0.818962 0.573848i \(-0.805450\pi\)
0.979408 + 0.201892i \(0.0647091\pi\)
\(242\) 3.42795 0.220357
\(243\) 0 0
\(244\) 3.11649 0.199513
\(245\) −9.76307 + 22.6334i −0.623740 + 1.44599i
\(246\) 0 0
\(247\) 4.62577 + 4.90302i 0.294330 + 0.311972i
\(248\) −1.67962 28.8380i −0.106656 1.83122i
\(249\) 0 0
\(250\) −15.2495 3.61420i −0.964465 0.228582i
\(251\) 4.91237 1.78796i 0.310066 0.112855i −0.182300 0.983243i \(-0.558354\pi\)
0.492366 + 0.870388i \(0.336132\pi\)
\(252\) 0 0
\(253\) 9.87029 + 3.59249i 0.620540 + 0.225858i
\(254\) −6.01386 3.95538i −0.377343 0.248182i
\(255\) 0 0
\(256\) 16.5198 + 1.93089i 1.03249 + 0.120681i
\(257\) 1.94989 2.61916i 0.121631 0.163379i −0.737137 0.675743i \(-0.763823\pi\)
0.858768 + 0.512364i \(0.171230\pi\)
\(258\) 0 0
\(259\) −0.0847632 + 1.45533i −0.00526693 + 0.0904297i
\(260\) −15.6565 + 13.1374i −0.970978 + 0.814747i
\(261\) 0 0
\(262\) 0.758457 + 0.636421i 0.0468576 + 0.0393182i
\(263\) 0.961659 1.01930i 0.0592984 0.0628527i −0.697045 0.717027i \(-0.745502\pi\)
0.756344 + 0.654175i \(0.226984\pi\)
\(264\) 0 0
\(265\) −21.8618 + 14.3787i −1.34296 + 0.883280i
\(266\) −0.944849 + 0.223933i −0.0579324 + 0.0137302i
\(267\) 0 0
\(268\) 17.2689 2.01844i 1.05486 0.123296i
\(269\) 5.17838 8.96922i 0.315732 0.546863i −0.663861 0.747856i \(-0.731083\pi\)
0.979593 + 0.200993i \(0.0644168\pi\)
\(270\) 0 0
\(271\) −9.29809 16.1048i −0.564819 0.978295i −0.997067 0.0765398i \(-0.975613\pi\)
0.432248 0.901755i \(-0.357721\pi\)
\(272\) −0.169368 0.227500i −0.0102694 0.0137942i
\(273\) 0 0
\(274\) 0.192888 0.644292i 0.0116528 0.0389231i
\(275\) 22.8644 + 11.4829i 1.37877 + 0.692447i
\(276\) 0 0
\(277\) −2.93650 9.80858i −0.176437 0.589341i −0.999763 0.0217719i \(-0.993069\pi\)
0.823326 0.567569i \(-0.192116\pi\)
\(278\) 0.668297 3.79010i 0.0400818 0.227315i
\(279\) 0 0
\(280\) −1.38909 7.87793i −0.0830141 0.470796i
\(281\) 16.0079 8.03947i 0.954951 0.479595i 0.0981105 0.995176i \(-0.468720\pi\)
0.856841 + 0.515581i \(0.172424\pi\)
\(282\) 0 0
\(283\) −10.5546 24.4683i −0.627404 1.45449i −0.874271 0.485437i \(-0.838660\pi\)
0.246867 0.969049i \(-0.420599\pi\)
\(284\) 4.51547 + 10.4680i 0.267944 + 0.621163i
\(285\) 0 0
\(286\) −10.1312 + 5.08806i −0.599068 + 0.300863i
\(287\) −0.827179 4.69117i −0.0488268 0.276911i
\(288\) 0 0
\(289\) −2.81003 + 15.9365i −0.165296 + 0.937439i
\(290\) −5.13141 17.1401i −0.301327 1.00650i
\(291\) 0 0
\(292\) 16.6984 + 8.38626i 0.977201 + 0.490769i
\(293\) −8.29474 + 27.7063i −0.484584 + 1.61862i 0.270309 + 0.962774i \(0.412874\pi\)
−0.754893 + 0.655848i \(0.772311\pi\)
\(294\) 0 0
\(295\) 1.60847 + 2.16055i 0.0936488 + 0.125792i
\(296\) 2.90281 + 5.02781i 0.168722 + 0.292235i
\(297\) 0 0
\(298\) −5.33328 + 9.23752i −0.308949 + 0.535115i
\(299\) 17.8533 2.08675i 1.03248 0.120680i
\(300\) 0 0
\(301\) −5.14984 + 1.22053i −0.296832 + 0.0703505i
\(302\) −3.66013 + 2.40730i −0.210617 + 0.138525i
\(303\) 0 0
\(304\) −0.314897 + 0.333771i −0.0180606 + 0.0191431i
\(305\) −7.80544 6.54955i −0.446938 0.375026i
\(306\) 0 0
\(307\) 2.94847 2.47406i 0.168278 0.141202i −0.554759 0.832011i \(-0.687190\pi\)
0.723038 + 0.690809i \(0.242745\pi\)
\(308\) −0.132432 + 2.27377i −0.00754601 + 0.129560i
\(309\) 0 0
\(310\) −20.7574 + 27.8820i −1.17894 + 1.58359i
\(311\) −14.0725 1.64484i −0.797977 0.0932701i −0.292674 0.956212i \(-0.594545\pi\)
−0.505303 + 0.862942i \(0.668619\pi\)
\(312\) 0 0
\(313\) −17.3980 11.4428i −0.983391 0.646786i −0.0474241 0.998875i \(-0.515101\pi\)
−0.935967 + 0.352089i \(0.885472\pi\)
\(314\) 8.02777 + 2.92187i 0.453033 + 0.164891i
\(315\) 0 0
\(316\) 5.22753 1.90266i 0.294071 0.107033i
\(317\) −23.7891 5.63811i −1.33613 0.316668i −0.500391 0.865800i \(-0.666810\pi\)
−0.835736 + 0.549132i \(0.814959\pi\)
\(318\) 0 0
\(319\) 0.804786 + 13.8176i 0.0450594 + 0.773640i
\(320\) −14.7705 15.6558i −0.825696 0.875186i
\(321\) 0 0
\(322\) −1.02558 + 2.37757i −0.0571536 + 0.132497i
\(323\) −1.32293 −0.0736096
\(324\) 0 0
\(325\) 43.7847 2.42874
\(326\) 2.82159 6.54117i 0.156273 0.362282i
\(327\) 0 0
\(328\) −13.0184 13.7987i −0.718822 0.761906i
\(329\) 0.188862 + 3.24263i 0.0104123 + 0.178772i
\(330\) 0 0
\(331\) −6.56661 1.55632i −0.360934 0.0855429i 0.0461480 0.998935i \(-0.485305\pi\)
−0.407082 + 0.913392i \(0.633454\pi\)
\(332\) 7.92788 2.88551i 0.435099 0.158363i
\(333\) 0 0
\(334\) −9.28858 3.38077i −0.508249 0.184987i
\(335\) −47.4928 31.2365i −2.59481 1.70663i
\(336\) 0 0
\(337\) 4.23038 + 0.494461i 0.230444 + 0.0269350i 0.230531 0.973065i \(-0.425954\pi\)
−8.72681e−5 1.00000i \(0.500028\pi\)
\(338\) −4.49080 + 6.03220i −0.244268 + 0.328108i
\(339\) 0 0
\(340\) 0.233229 4.00439i 0.0126486 0.217168i
\(341\) 20.5994 17.2849i 1.11552 0.936032i
\(342\) 0 0
\(343\) 7.49539 + 6.28938i 0.404713 + 0.339594i
\(344\) −14.4640 + 15.3310i −0.779849 + 0.826592i
\(345\) 0 0
\(346\) 8.87445 5.83682i 0.477093 0.313789i
\(347\) 19.6616 4.65989i 1.05549 0.250156i 0.333996 0.942575i \(-0.391603\pi\)
0.721496 + 0.692418i \(0.243455\pi\)
\(348\) 0 0
\(349\) −22.8564 + 2.67153i −1.22348 + 0.143004i −0.703199 0.710993i \(-0.748246\pi\)
−0.520278 + 0.853997i \(0.674172\pi\)
\(350\) −3.15366 + 5.46231i −0.168570 + 0.291973i
\(351\) 0 0
\(352\) 7.40135 + 12.8195i 0.394493 + 0.683282i
\(353\) −12.9522 17.3979i −0.689378 0.925995i 0.310319 0.950633i \(-0.399564\pi\)
−0.999696 + 0.0246374i \(0.992157\pi\)
\(354\) 0 0
\(355\) 10.6901 35.7074i 0.567372 1.89515i
\(356\) −7.75749 3.89596i −0.411146 0.206485i
\(357\) 0 0
\(358\) −0.715344 2.38942i −0.0378071 0.126285i
\(359\) 5.76399 32.6892i 0.304212 1.72527i −0.322981 0.946405i \(-0.604685\pi\)
0.627193 0.778864i \(-0.284204\pi\)
\(360\) 0 0
\(361\) −2.92765 16.6035i −0.154087 0.873869i
\(362\) 12.3577 6.20625i 0.649505 0.326193i
\(363\) 0 0
\(364\) 1.54378 + 3.57889i 0.0809162 + 0.187585i
\(365\) −24.1979 56.0969i −1.26657 2.93625i
\(366\) 0 0
\(367\) −18.5041 + 9.29311i −0.965906 + 0.485096i −0.860565 0.509340i \(-0.829890\pi\)
−0.105341 + 0.994436i \(0.533593\pi\)
\(368\) 0.212481 + 1.20504i 0.0110764 + 0.0628172i
\(369\) 0 0
\(370\) 1.21311 6.87990i 0.0630667 0.357669i
\(371\) 1.43117 + 4.78045i 0.0743028 + 0.248189i
\(372\) 0 0
\(373\) −3.59966 1.80782i −0.186383 0.0936052i 0.353161 0.935563i \(-0.385107\pi\)
−0.539544 + 0.841958i \(0.681403\pi\)
\(374\) 0.638137 2.13152i 0.0329973 0.110219i
\(375\) 0 0
\(376\) 7.72457 + 10.3759i 0.398364 + 0.535096i
\(377\) 11.8430 + 20.5127i 0.609945 + 1.05646i
\(378\) 0 0
\(379\) 17.2610 29.8970i 0.886640 1.53570i 0.0428169 0.999083i \(-0.486367\pi\)
0.843823 0.536622i \(-0.180300\pi\)
\(380\) −6.44578 + 0.753404i −0.330662 + 0.0386488i
\(381\) 0 0
\(382\) −2.20073 + 0.521583i −0.112599 + 0.0266865i
\(383\) 11.9143 7.83617i 0.608793 0.400410i −0.207344 0.978268i \(-0.566482\pi\)
0.816137 + 0.577859i \(0.196111\pi\)
\(384\) 0 0
\(385\) 5.11019 5.41648i 0.260439 0.276050i
\(386\) 2.77658 + 2.32983i 0.141324 + 0.118585i
\(387\) 0 0
\(388\) 3.97054 3.33168i 0.201573 0.169140i
\(389\) −1.20812 + 20.7426i −0.0612541 + 1.05169i 0.817963 + 0.575271i \(0.195103\pi\)
−0.879217 + 0.476421i \(0.841934\pi\)
\(390\) 0 0
\(391\) −2.10661 + 2.82967i −0.106536 + 0.143103i
\(392\) 18.5939 + 2.17332i 0.939134 + 0.109769i
\(393\) 0 0
\(394\) −18.9887 12.4891i −0.956639 0.629191i
\(395\) −17.0913 6.22071i −0.859955 0.312998i
\(396\) 0 0
\(397\) 21.4426 7.80446i 1.07617 0.391695i 0.257691 0.966227i \(-0.417038\pi\)
0.818482 + 0.574533i \(0.194816\pi\)
\(398\) −10.2591 2.43144i −0.514241 0.121877i
\(399\) 0 0
\(400\) 0.173308 + 2.97558i 0.00866540 + 0.148779i
\(401\) 5.89097 + 6.24406i 0.294181 + 0.311814i 0.857559 0.514386i \(-0.171980\pi\)
−0.563378 + 0.826199i \(0.690499\pi\)
\(402\) 0 0
\(403\) 18.2266 42.2539i 0.907930 2.10482i
\(404\) −12.7320 −0.633439
\(405\) 0 0
\(406\) −3.41204 −0.169337
\(407\) −2.14057 + 4.96241i −0.106104 + 0.245977i
\(408\) 0 0
\(409\) 19.3500 + 20.5098i 0.956798 + 1.01415i 0.999886 + 0.0150751i \(0.00479872\pi\)
−0.0430887 + 0.999071i \(0.513720\pi\)
\(410\) 1.32732 + 22.7891i 0.0655515 + 1.12548i
\(411\) 0 0
\(412\) −5.49133 1.30147i −0.270538 0.0641188i
\(413\) 0.482693 0.175686i 0.0237518 0.00864494i
\(414\) 0 0
\(415\) −25.9200 9.43411i −1.27236 0.463102i
\(416\) 21.1642 + 13.9199i 1.03766 + 0.682481i
\(417\) 0 0
\(418\) −3.57548 0.417913i −0.174882 0.0204408i
\(419\) 19.0798 25.6286i 0.932108 1.25204i −0.0354460 0.999372i \(-0.511285\pi\)
0.967554 0.252666i \(-0.0813074\pi\)
\(420\) 0 0
\(421\) −1.62148 + 27.8397i −0.0790260 + 1.35682i 0.692865 + 0.721068i \(0.256348\pi\)
−0.771891 + 0.635755i \(0.780689\pi\)
\(422\) −14.8669 + 12.4748i −0.723708 + 0.607263i
\(423\) 0 0
\(424\) 15.2235 + 12.7740i 0.739317 + 0.620361i
\(425\) −5.89697 + 6.25042i −0.286045 + 0.303190i
\(426\) 0 0
\(427\) −1.62347 + 1.06778i −0.0785654 + 0.0516733i
\(428\) −3.09886 + 0.734444i −0.149789 + 0.0355007i
\(429\) 0 0
\(430\) 25.1912 2.94443i 1.21483 0.141993i
\(431\) −16.9276 + 29.3195i −0.815375 + 1.41227i 0.0936837 + 0.995602i \(0.470136\pi\)
−0.909058 + 0.416669i \(0.863198\pi\)
\(432\) 0 0
\(433\) 4.23939 + 7.34284i 0.203732 + 0.352874i 0.949728 0.313076i \(-0.101360\pi\)
−0.745996 + 0.665950i \(0.768026\pi\)
\(434\) 3.95854 + 5.31724i 0.190016 + 0.255236i
\(435\) 0 0
\(436\) −1.13606 + 3.79469i −0.0544072 + 0.181733i
\(437\) 5.10041 + 2.56152i 0.243986 + 0.122534i
\(438\) 0 0
\(439\) 6.37737 + 21.3019i 0.304375 + 1.01668i 0.964180 + 0.265247i \(0.0854535\pi\)
−0.659805 + 0.751437i \(0.729361\pi\)
\(440\) 5.14970 29.2054i 0.245502 1.39231i
\(441\) 0 0
\(442\) −0.661183 3.74976i −0.0314493 0.178358i
\(443\) 20.1340 10.1117i 0.956596 0.480420i 0.0991939 0.995068i \(-0.468374\pi\)
0.857402 + 0.514648i \(0.172077\pi\)
\(444\) 0 0
\(445\) 11.2415 + 26.0606i 0.532896 + 1.23539i
\(446\) −0.809702 1.87710i −0.0383405 0.0888832i
\(447\) 0 0
\(448\) −3.66808 + 1.84218i −0.173300 + 0.0870348i
\(449\) −3.85889 21.8849i −0.182112 1.03281i −0.929610 0.368546i \(-0.879856\pi\)
0.747497 0.664265i \(-0.231255\pi\)
\(450\) 0 0
\(451\) 3.06655 17.3913i 0.144398 0.818924i
\(452\) −3.14468 10.5040i −0.147913 0.494064i
\(453\) 0 0
\(454\) −2.88113 1.44696i −0.135218 0.0679091i
\(455\) 3.65482 12.2079i 0.171341 0.572317i
\(456\) 0 0
\(457\) −1.38320 1.85796i −0.0647032 0.0869115i 0.768594 0.639737i \(-0.220957\pi\)
−0.833297 + 0.552826i \(0.813549\pi\)
\(458\) −4.82797 8.36229i −0.225596 0.390744i
\(459\) 0 0
\(460\) −8.65270 + 14.9869i −0.403434 + 0.698768i
\(461\) 24.3727 2.84876i 1.13515 0.132680i 0.472305 0.881435i \(-0.343422\pi\)
0.662846 + 0.748755i \(0.269348\pi\)
\(462\) 0 0
\(463\) 26.5407 6.29025i 1.23345 0.292333i 0.438345 0.898807i \(-0.355565\pi\)
0.795103 + 0.606474i \(0.207417\pi\)
\(464\) −1.34715 + 0.886036i −0.0625399 + 0.0411332i
\(465\) 0 0
\(466\) 11.2238 11.8965i 0.519931 0.551094i
\(467\) −2.81518 2.36222i −0.130271 0.109310i 0.575324 0.817925i \(-0.304876\pi\)
−0.705595 + 0.708615i \(0.749320\pi\)
\(468\) 0 0
\(469\) −8.30431 + 6.96815i −0.383458 + 0.321759i
\(470\) 0.905062 15.5393i 0.0417474 0.716775i
\(471\) 0 0
\(472\) 1.22159 1.64088i 0.0562284 0.0755278i
\(473\) −19.4879 2.27781i −0.896056 0.104734i
\(474\) 0 0
\(475\) 11.6156 + 7.63972i 0.532962 + 0.350535i
\(476\) −0.718818 0.261628i −0.0329470 0.0119917i
\(477\) 0 0
\(478\) −0.318980 + 0.116099i −0.0145898 + 0.00531025i
\(479\) 2.89958 + 0.687214i 0.132485 + 0.0313996i 0.296324 0.955088i \(-0.404239\pi\)
−0.163838 + 0.986487i \(0.552387\pi\)
\(480\) 0 0
\(481\) 0.537750 + 9.23281i 0.0245193 + 0.420980i
\(482\) 3.94392 + 4.18031i 0.179641 + 0.190408i
\(483\) 0 0
\(484\) 1.73050 4.01175i 0.0786591 0.182352i
\(485\) −16.9462 −0.769489
\(486\) 0 0
\(487\) −19.3605 −0.877310 −0.438655 0.898656i \(-0.644545\pi\)
−0.438655 + 0.898656i \(0.644545\pi\)
\(488\) −3.06506 + 7.10562i −0.138749 + 0.321656i
\(489\) 0 0
\(490\) −15.4588 16.3854i −0.698359 0.740218i
\(491\) −0.624138 10.7160i −0.0281669 0.483608i −0.982665 0.185390i \(-0.940645\pi\)
0.954498 0.298217i \(-0.0963920\pi\)
\(492\) 0 0
\(493\) −4.52328 1.07204i −0.203718 0.0482821i
\(494\) −5.78880 + 2.10695i −0.260450 + 0.0947961i
\(495\) 0 0
\(496\) 2.94370 + 1.07142i 0.132176 + 0.0481081i
\(497\) −5.93882 3.90602i −0.266392 0.175209i
\(498\) 0 0
\(499\) −30.4517 3.55929i −1.36320 0.159336i −0.597159 0.802123i \(-0.703704\pi\)
−0.766045 + 0.642787i \(0.777778\pi\)
\(500\) −11.9280 + 16.0221i −0.533436 + 0.716529i
\(501\) 0 0
\(502\) −0.277787 + 4.76942i −0.0123982 + 0.212870i
\(503\) 21.3536 17.9178i 0.952111 0.798916i −0.0275408 0.999621i \(-0.508768\pi\)
0.979652 + 0.200705i \(0.0643232\pi\)
\(504\) 0 0
\(505\) 31.8880 + 26.7572i 1.41900 + 1.19068i
\(506\) −6.58744 + 6.98228i −0.292848 + 0.310400i
\(507\) 0 0
\(508\) −7.66492 + 5.04130i −0.340076 + 0.223671i
\(509\) −36.4747 + 8.64466i −1.61671 + 0.383168i −0.936728 0.350059i \(-0.886161\pi\)
−0.679984 + 0.733227i \(0.738013\pi\)
\(510\) 0 0
\(511\) −11.5720 + 1.35258i −0.511916 + 0.0598345i
\(512\) −1.76939 + 3.06468i −0.0781968 + 0.135441i
\(513\) 0 0
\(514\) 1.49206 + 2.58432i 0.0658120 + 0.113990i
\(515\) 11.0182 + 14.8001i 0.485522 + 0.652169i
\(516\) 0 0
\(517\) −3.45357 + 11.5357i −0.151888 + 0.507340i
\(518\) −1.19056 0.597922i −0.0523102 0.0262712i
\(519\) 0 0
\(520\) −14.5552 48.6177i −0.638287 2.13203i
\(521\) −6.93526 + 39.3318i −0.303839 + 1.72316i 0.325079 + 0.945687i \(0.394609\pi\)
−0.628918 + 0.777472i \(0.716502\pi\)
\(522\) 0 0
\(523\) 1.17678 + 6.67383i 0.0514568 + 0.291826i 0.999667 0.0258185i \(-0.00821918\pi\)
−0.948210 + 0.317645i \(0.897108\pi\)
\(524\) 1.12769 0.566348i 0.0492634 0.0247410i
\(525\) 0 0
\(526\) 0.507251 + 1.17594i 0.0221172 + 0.0512734i
\(527\) 3.57713 + 8.29271i 0.155822 + 0.361236i
\(528\) 0 0
\(529\) −6.95276 + 3.49181i −0.302294 + 0.151818i
\(530\) −4.15253 23.5502i −0.180374 1.02295i
\(531\) 0 0
\(532\) −0.214909 + 1.21881i −0.00931748 + 0.0528421i
\(533\) −8.66735 28.9510i −0.375425 1.25401i
\(534\) 0 0
\(535\) 9.30479 + 4.67304i 0.402281 + 0.202033i
\(536\) −12.3818 + 41.3583i −0.534814 + 1.78640i
\(537\) 0 0
\(538\) 5.65210 + 7.59209i 0.243679 + 0.327318i
\(539\) 8.71338 + 15.0920i 0.375312 + 0.650059i
\(540\) 0 0
\(541\) 10.2033 17.6727i 0.438676 0.759809i −0.558912 0.829227i \(-0.688781\pi\)
0.997588 + 0.0694179i \(0.0221142\pi\)
\(542\) 16.8800 1.97299i 0.725059 0.0847473i
\(543\) 0 0
\(544\) −4.83754 + 1.14652i −0.207408 + 0.0491566i
\(545\) 10.8202 7.11654i 0.463485 0.304839i
\(546\) 0 0
\(547\) −2.46158 + 2.60912i −0.105249 + 0.111558i −0.777856 0.628442i \(-0.783693\pi\)
0.672607 + 0.740000i \(0.265174\pi\)
\(548\) −0.656644 0.550990i −0.0280505 0.0235371i
\(549\) 0 0
\(550\) −17.9123 + 15.0302i −0.763782 + 0.640889i
\(551\) −0.437303 + 7.50821i −0.0186297 + 0.319860i
\(552\) 0 0
\(553\) −2.07129 + 2.78222i −0.0880800 + 0.118312i
\(554\) 9.29384 + 1.08629i 0.394857 + 0.0461522i
\(555\) 0 0
\(556\) −4.09820 2.69543i −0.173803 0.114312i
\(557\) 2.23552 + 0.813664i 0.0947221 + 0.0344760i 0.388947 0.921260i \(-0.372839\pi\)
−0.294224 + 0.955736i \(0.595061\pi\)
\(558\) 0 0
\(559\) −31.5515 + 11.4838i −1.33449 + 0.485713i
\(560\) 0.844111 + 0.200058i 0.0356702 + 0.00845399i
\(561\) 0 0
\(562\) 0.951880 + 16.3432i 0.0401527 + 0.689394i
\(563\) −24.2686 25.7232i −1.02280 1.08410i −0.996428 0.0844510i \(-0.973086\pi\)
−0.0263710 0.999652i \(-0.508395\pi\)
\(564\) 0 0
\(565\) −14.1988 + 32.9166i −0.597349 + 1.38481i
\(566\) 24.3531 1.02364
\(567\) 0 0
\(568\) −28.3081 −1.18778
\(569\) 12.7694 29.6028i 0.535322 1.24102i −0.409163 0.912461i \(-0.634179\pi\)
0.944485 0.328554i \(-0.106561\pi\)
\(570\) 0 0
\(571\) −2.04866 2.17145i −0.0857336 0.0908723i 0.683086 0.730338i \(-0.260637\pi\)
−0.768820 + 0.639465i \(0.779156\pi\)
\(572\) 0.840167 + 14.4251i 0.0351292 + 0.603145i
\(573\) 0 0
\(574\) 4.23602 + 1.00396i 0.176808 + 0.0419043i
\(575\) 34.8376 12.6798i 1.45283 0.528786i
\(576\) 0 0
\(577\) −31.1151 11.3250i −1.29534 0.471464i −0.399862 0.916575i \(-0.630942\pi\)
−0.895475 + 0.445111i \(0.853164\pi\)
\(578\) −12.3560 8.12665i −0.513940 0.338024i
\(579\) 0 0
\(580\) −22.6496 2.64736i −0.940474 0.109926i
\(581\) −3.14124 + 4.21941i −0.130320 + 0.175051i
\(582\) 0 0
\(583\) −1.07565 + 18.4682i −0.0445488 + 0.764873i
\(584\) −35.5436 + 29.8246i −1.47081 + 1.23415i
\(585\) 0 0
\(586\) −20.2474 16.9896i −0.836411 0.701832i
\(587\) −5.80543 + 6.15339i −0.239616 + 0.253978i −0.836010 0.548714i \(-0.815118\pi\)
0.596395 + 0.802691i \(0.296599\pi\)
\(588\) 0 0
\(589\) 12.2079 8.02929i 0.503020 0.330841i
\(590\) −2.39526 + 0.567687i −0.0986112 + 0.0233713i
\(591\) 0 0
\(592\) −0.625328 + 0.0730904i −0.0257008 + 0.00300400i
\(593\) 1.61604 2.79907i 0.0663629 0.114944i −0.830935 0.556370i \(-0.812194\pi\)
0.897298 + 0.441426i \(0.145527\pi\)
\(594\) 0 0
\(595\) 1.25049 + 2.16592i 0.0512652 + 0.0887939i
\(596\) 8.11837 + 10.9049i 0.332541 + 0.446681i
\(597\) 0 0
\(598\) −4.71135 + 15.7370i −0.192662 + 0.643534i
\(599\) −0.552166 0.277308i −0.0225609 0.0113305i 0.437483 0.899227i \(-0.355870\pi\)
−0.460044 + 0.887896i \(0.652166\pi\)
\(600\) 0 0
\(601\) −5.21882 17.4321i −0.212880 0.711068i −0.996013 0.0892137i \(-0.971565\pi\)
0.783133 0.621855i \(-0.213621\pi\)
\(602\) 0.839899 4.76331i 0.0342317 0.194138i
\(603\) 0 0
\(604\) 0.969573 + 5.49872i 0.0394514 + 0.223740i
\(605\) −12.7652 + 6.41090i −0.518977 + 0.260640i
\(606\) 0 0
\(607\) −2.86882 6.65067i −0.116442 0.269942i 0.850021 0.526748i \(-0.176589\pi\)
−0.966463 + 0.256806i \(0.917330\pi\)
\(608\) 3.18585 + 7.38564i 0.129203 + 0.299527i
\(609\) 0 0
\(610\) 8.32144 4.17919i 0.336925 0.169210i
\(611\) 3.57829 + 20.2935i 0.144762 + 0.820988i
\(612\) 0 0
\(613\) −6.98532 + 39.6157i −0.282134 + 1.60006i 0.433211 + 0.901293i \(0.357381\pi\)
−0.715345 + 0.698771i \(0.753731\pi\)
\(614\) 1.00884 + 3.36977i 0.0407136 + 0.135993i
\(615\) 0 0
\(616\) −5.05397 2.53820i −0.203630 0.102267i
\(617\) −5.02262 + 16.7767i −0.202203 + 0.675405i 0.795392 + 0.606095i \(0.207265\pi\)
−0.997595 + 0.0693101i \(0.977920\pi\)
\(618\) 0 0
\(619\) 6.13883 + 8.24588i 0.246740 + 0.331430i 0.908189 0.418561i \(-0.137465\pi\)
−0.661448 + 0.749991i \(0.730058\pi\)
\(620\) 22.1517 + 38.3680i 0.889636 + 1.54089i
\(621\) 0 0
\(622\) 6.47415 11.2136i 0.259590 0.449623i
\(623\) 5.37595 0.628359i 0.215383 0.0251747i
\(624\) 0 0
\(625\) 17.3120 4.10302i 0.692481 0.164121i
\(626\) 15.8999 10.4575i 0.635488 0.417967i
\(627\) 0 0
\(628\) 7.47207 7.91993i 0.298168 0.316039i
\(629\) −1.39044 1.16672i −0.0554405 0.0465201i
\(630\) 0 0
\(631\) 22.0848 18.5313i 0.879182 0.737721i −0.0868288 0.996223i \(-0.527673\pi\)
0.966011 + 0.258502i \(0.0832289\pi\)
\(632\) −0.803180 + 13.7901i −0.0319488 + 0.548540i
\(633\) 0 0
\(634\) 13.3423 17.9218i 0.529890 0.711765i
\(635\) 29.7920 + 3.48218i 1.18226 + 0.138186i
\(636\) 0 0
\(637\) 24.9160 + 16.3875i 0.987209 + 0.649297i
\(638\) −11.8864 4.32630i −0.470588 0.171280i
\(639\) 0 0
\(640\) −20.8658 + 7.59452i −0.824792 + 0.300200i
\(641\) 27.9023 + 6.61297i 1.10207 + 0.261197i 0.741111 0.671383i \(-0.234299\pi\)
0.360964 + 0.932580i \(0.382448\pi\)
\(642\) 0 0
\(643\) −1.12427 19.3030i −0.0443369 0.761235i −0.945071 0.326864i \(-0.894008\pi\)
0.900734 0.434370i \(-0.143029\pi\)
\(644\) 2.26475 + 2.40049i 0.0892437 + 0.0945928i
\(645\) 0 0
\(646\) 0.478866 1.11014i 0.0188407 0.0436778i
\(647\) 29.8266 1.17261 0.586303 0.810092i \(-0.300583\pi\)
0.586303 + 0.810092i \(0.300583\pi\)
\(648\) 0 0
\(649\) 1.90430 0.0747505
\(650\) −15.8490 + 36.7420i −0.621648 + 1.44114i
\(651\) 0 0
\(652\) −6.23078 6.60424i −0.244016 0.258642i
\(653\) −1.44269 24.7701i −0.0564569 0.969328i −0.900994 0.433831i \(-0.857162\pi\)
0.844537 0.535497i \(-0.179876\pi\)
\(654\) 0 0
\(655\) −4.01460 0.951478i −0.156863 0.0371773i
\(656\) 1.93318 0.703621i 0.0754781 0.0274718i
\(657\) 0 0
\(658\) −2.78942 1.01527i −0.108743 0.0395792i
\(659\) 14.6079 + 9.60779i 0.569044 + 0.374266i 0.801186 0.598416i \(-0.204203\pi\)
−0.232142 + 0.972682i \(0.574573\pi\)
\(660\) 0 0
\(661\) −37.3153 4.36154i −1.45140 0.169644i −0.646435 0.762969i \(-0.723741\pi\)
−0.804963 + 0.593324i \(0.797815\pi\)
\(662\) 3.68294 4.94704i 0.143141 0.192272i
\(663\) 0 0
\(664\) −1.21807 + 20.9135i −0.0472704 + 0.811602i
\(665\) 3.09967 2.60094i 0.120200 0.100860i
\(666\) 0 0
\(667\) 15.3633 + 12.8913i 0.594870 + 0.499155i
\(668\) −8.64560 + 9.16380i −0.334508 + 0.354558i
\(669\) 0 0
\(670\) 43.4034 28.5469i 1.67682 1.10286i
\(671\) −7.00954 + 1.66129i −0.270600 + 0.0641334i
\(672\) 0 0
\(673\) 26.3408 3.07880i 1.01536 0.118679i 0.407900 0.913027i \(-0.366261\pi\)
0.607464 + 0.794348i \(0.292187\pi\)
\(674\) −1.94622 + 3.37095i −0.0749656 + 0.129844i
\(675\) 0 0
\(676\) 4.79246 + 8.30079i 0.184326 + 0.319261i
\(677\) 12.2841 + 16.5004i 0.472116 + 0.634162i 0.972849 0.231439i \(-0.0743435\pi\)
−0.500733 + 0.865602i \(0.666936\pi\)
\(678\) 0 0
\(679\) −0.926871 + 3.09596i −0.0355700 + 0.118812i
\(680\) 8.90065 + 4.47007i 0.341324 + 0.171420i
\(681\) 0 0
\(682\) 7.04823 + 23.5427i 0.269891 + 0.901498i
\(683\) −2.39856 + 13.6029i −0.0917785 + 0.520502i 0.903908 + 0.427726i \(0.140685\pi\)
−0.995687 + 0.0927760i \(0.970426\pi\)
\(684\) 0 0
\(685\) 0.486659 + 2.75998i 0.0185943 + 0.105453i
\(686\) −7.99089 + 4.01317i −0.305093 + 0.153224i
\(687\) 0 0
\(688\) −0.905319 2.09877i −0.0345150 0.0800147i
\(689\) 12.5390 + 29.0687i 0.477699 + 1.10743i
\(690\) 0 0
\(691\) −5.67005 + 2.84760i −0.215699 + 0.108328i −0.553368 0.832937i \(-0.686658\pi\)
0.337669 + 0.941265i \(0.390361\pi\)
\(692\) −2.35086 13.3324i −0.0893662 0.506821i
\(693\) 0 0
\(694\) −3.20666 + 18.1859i −0.121723 + 0.690326i
\(695\) 4.59955 + 15.3636i 0.174471 + 0.582774i
\(696\) 0 0
\(697\) 5.30018 + 2.66185i 0.200759 + 0.100825i
\(698\) 6.03163 20.1471i 0.228301 0.762577i
\(699\) 0 0
\(700\) 4.80054 + 6.44824i 0.181443 + 0.243720i
\(701\) −11.8662 20.5529i −0.448180 0.776271i 0.550087 0.835107i \(-0.314594\pi\)
−0.998268 + 0.0588360i \(0.981261\pi\)
\(702\) 0 0
\(703\) −1.46832 + 2.54320i −0.0553786 + 0.0959186i
\(704\) −15.1142 + 1.76659i −0.569637 + 0.0665810i
\(705\) 0 0
\(706\) 19.2878 4.57130i 0.725908 0.172043i
\(707\) 6.63247 4.36225i 0.249440 0.164059i
\(708\) 0 0
\(709\) 0.00970556 0.0102873i 0.000364500 0.000386348i −0.727191 0.686435i \(-0.759175\pi\)
0.727556 + 0.686048i \(0.240656\pi\)
\(710\) 26.0944 + 21.8958i 0.979307 + 0.821736i
\(711\) 0 0
\(712\) 16.5123 13.8555i 0.618824 0.519255i
\(713\) 2.26555 38.8979i 0.0848454 1.45674i
\(714\) 0 0
\(715\) 28.2113 37.8943i 1.05504 1.41717i
\(716\) −3.15747 0.369055i −0.118000 0.0137922i
\(717\) 0 0
\(718\) 25.3448 + 16.6695i 0.945859 + 0.622101i
\(719\) −23.2140 8.44919i −0.865735 0.315102i −0.129296 0.991606i \(-0.541272\pi\)
−0.736439 + 0.676504i \(0.763494\pi\)
\(720\) 0 0
\(721\) 3.30651 1.20347i 0.123141 0.0448197i
\(722\) 14.9926 + 3.55331i 0.557967 + 0.132241i
\(723\) 0 0
\(724\) −1.02481 17.5953i −0.0380867 0.653924i
\(725\) 33.5247 + 35.5341i 1.24508 + 1.31970i
\(726\) 0 0
\(727\) −16.2048 + 37.5669i −0.601003 + 1.39328i 0.297674 + 0.954668i \(0.403789\pi\)
−0.898676 + 0.438613i \(0.855470\pi\)
\(728\) −9.67821 −0.358698
\(729\) 0 0
\(730\) 55.8329 2.06647
\(731\) 2.61003 6.05074i 0.0965355 0.223795i
\(732\) 0 0
\(733\) −10.2665 10.8819i −0.379203 0.401932i 0.509458 0.860495i \(-0.329846\pi\)
−0.888662 + 0.458563i \(0.848364\pi\)
\(734\) −1.10031 18.8916i −0.0406133 0.697303i
\(735\) 0 0
\(736\) 20.8706 + 4.94642i 0.769301 + 0.182328i
\(737\) −37.7648 + 13.7452i −1.39108 + 0.506313i
\(738\) 0 0
\(739\) −12.3654 4.50063i −0.454868 0.165558i 0.104418 0.994534i \(-0.466702\pi\)
−0.559285 + 0.828975i \(0.688924\pi\)
\(740\) −7.43918 4.89283i −0.273470 0.179864i
\(741\) 0 0
\(742\) −4.52958 0.529431i −0.166286 0.0194360i
\(743\) 16.7221 22.4616i 0.613473 0.824037i −0.381481 0.924377i \(-0.624586\pi\)
0.994953 + 0.100340i \(0.0319931\pi\)
\(744\) 0 0
\(745\) 2.58445 44.3733i 0.0946870 1.62571i
\(746\) 2.82002 2.36628i 0.103248 0.0866355i
\(747\) 0 0
\(748\) −2.17239 1.82285i −0.0794305 0.0666501i
\(749\) 1.36266 1.44433i 0.0497904 0.0527747i
\(750\) 0 0
\(751\) 6.38696 4.20077i 0.233063 0.153288i −0.427606 0.903965i \(-0.640643\pi\)
0.660669 + 0.750677i \(0.270273\pi\)
\(752\) −1.36497 + 0.323504i −0.0497754 + 0.0117970i
\(753\) 0 0
\(754\) −21.5001 + 2.51300i −0.782988 + 0.0915182i
\(755\) 9.12764 15.8095i 0.332189 0.575368i
\(756\) 0 0
\(757\) −16.9101 29.2892i −0.614608 1.06453i −0.990453 0.137850i \(-0.955981\pi\)
0.375845 0.926683i \(-0.377353\pi\)
\(758\) 18.8401 + 25.3066i 0.684302 + 0.919177i
\(759\) 0 0
\(760\) 4.62166 15.4374i 0.167645 0.559974i
\(761\) 33.1292 + 16.6381i 1.20093 + 0.603131i 0.932850 0.360265i \(-0.117314\pi\)
0.268083 + 0.963396i \(0.413610\pi\)
\(762\) 0 0
\(763\) −0.708337 2.36601i −0.0256435 0.0856553i
\(764\) −0.500564 + 2.83884i −0.0181098 + 0.102706i
\(765\) 0 0
\(766\) 2.26306 + 12.8344i 0.0817675 + 0.463727i
\(767\) 2.91217 1.46255i 0.105152 0.0528096i
\(768\) 0 0
\(769\) 18.4305 + 42.7267i 0.664622 + 1.54077i 0.831942 + 0.554863i \(0.187229\pi\)
−0.167320 + 0.985903i \(0.553511\pi\)
\(770\) 2.69549 + 6.24886i 0.0971389 + 0.225193i
\(771\) 0 0
\(772\) 4.12829 2.07331i 0.148580 0.0746199i
\(773\) 7.40534 + 41.9978i 0.266352 + 1.51056i 0.765158 + 0.643842i \(0.222661\pi\)
−0.498807 + 0.866713i \(0.666228\pi\)
\(774\) 0 0
\(775\) 16.4812 93.4695i 0.592022 3.35752i
\(776\) 3.69123 + 12.3296i 0.132507 + 0.442605i
\(777\) 0 0
\(778\) −16.9689 8.52210i −0.608364 0.305532i
\(779\) 2.75212 9.19270i 0.0986048 0.329363i
\(780\) 0 0
\(781\) −15.7362 21.1374i −0.563086 0.756356i
\(782\) −1.61198 2.79204i −0.0576445 0.0998431i
\(783\) 0