Properties

Label 729.2.g.d.55.6
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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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 55.6
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.d.676.6

$q$-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 −0.740987 0.671520i \(-0.765642\pi\)
0.996942 + 0.0781494i \(0.0249011\pi\)
\(3\) 0 0
\(4\) 0.799333 + 0.847243i 0.399666 + 0.423621i
\(5\) 0.221432 + 3.80183i 0.0990272 + 1.70023i 0.572889 + 0.819633i \(0.305822\pi\)
−0.473862 + 0.880599i \(0.657141\pi\)
\(6\) 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 0.841328 0.540525i \(-0.181774\pi\)
−0.163086 + 0.986612i \(0.552145\pi\)
\(12\) 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 −0.722914 0.690938i \(-0.757198\pi\)
0.554909 + 0.831911i \(0.312753\pi\)
\(18\) 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 0.185090 0.982722i \(-0.440742\pi\)
0.606447 + 0.795124i \(0.292594\pi\)
\(24\) 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 0.989883 0.141884i \(-0.0453161\pi\)
−0.419825 + 0.907605i \(0.637909\pi\)
\(30\) 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 \(-0.958470\pi\)
0.585778 0.810472i \(-0.300789\pi\)
\(42\) 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 \(0.0131706\pi\)
−0.812042 + 0.583598i \(0.801644\pi\)
\(48\) 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 0.999483 0.0321487i \(-0.0102350\pi\)
−0.527583 + 0.849503i \(0.676902\pi\)
\(54\) 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 −0.510460 0.859901i \(-0.670525\pi\)
0.587392 + 0.809302i \(0.300155\pi\)
\(60\) 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 −0.267328 0.963606i \(-0.586141\pi\)
−0.824179 + 0.566330i \(0.808363\pi\)
\(72\) 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 \(0.259756\pi\)
−0.999999 + 0.00156176i \(0.999503\pi\)
\(84\) 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 0.0569608 0.998376i \(-0.481859\pi\)
0.685378 + 0.728187i \(0.259637\pi\)
\(90\) 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 −0.237222 0.971455i \(-0.576237\pi\)
0.983605 + 0.180336i \(0.0577185\pi\)
\(102\) 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 −0.792349 0.610067i \(-0.791142\pi\)
0.924509 + 0.381161i \(0.124476\pi\)
\(108\) 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 0.798079 0.602553i \(-0.205850\pi\)
−0.00674204 + 0.999977i \(0.502146\pi\)
\(114\) 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 −0.970490 0.241142i \(-0.922478\pi\)
0.943342 + 0.331821i \(0.107663\pi\)
\(132\) 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 −0.0848115 0.996397i \(-0.527029\pi\)
0.147260 + 0.989098i \(0.452955\pi\)
\(138\) 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 −0.372887 0.927877i \(-0.621632\pi\)
−0.576819 + 0.816872i \(0.695706\pi\)
\(150\) 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 \(-0.881080\pi\)
0.882355 0.470585i \(-0.155957\pi\)
\(168\) 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 0.862106 0.506728i \(-0.169145\pi\)
−0.123823 + 0.992304i \(0.539516\pi\)
\(174\) 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 −0.561303 0.827611i \(-0.689700\pi\)
0.717568 + 0.696488i \(0.245255\pi\)
\(180\) 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 0.745435 0.666578i \(-0.232242\pi\)
−0.852368 + 0.522942i \(0.824834\pi\)
\(192\) 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 \(-0.597969\pi\)
0.610621 0.791923i \(-0.290920\pi\)
\(198\) 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 \(-0.944130\pi\)
0.998250 0.0591321i \(-0.0188333\pi\)
\(228\) 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 0.827952 0.560799i \(-0.189506\pi\)
0.273773 + 0.961794i \(0.411728\pi\)
\(234\) 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 0.719077 0.694930i \(-0.244565\pi\)
−0.735565 + 0.677454i \(0.763083\pi\)
\(240\) 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 −0.492366 0.870388i \(-0.663868\pi\)
0.182300 + 0.983243i \(0.441646\pi\)
\(252\) 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 −0.858768 0.512364i \(-0.828770\pi\)
0.737137 + 0.675743i \(0.236177\pi\)
\(258\) 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 −0.756344 0.654175i \(-0.773016\pi\)
0.697045 + 0.717027i \(0.254498\pi\)
\(264\) 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 −0.979593 0.200993i \(-0.935583\pi\)
0.663861 + 0.747856i \(0.268917\pi\)
\(270\) 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 −0.856841 0.515581i \(-0.827576\pi\)
−0.0981105 + 0.995176i \(0.531280\pi\)
\(282\) 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 \(-0.587126\pi\)
0.754893 0.655848i \(-0.227689\pi\)
\(294\) 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 0.505303 0.862942i \(-0.331381\pi\)
0.292674 + 0.956212i \(0.405455\pi\)
\(312\) 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 0.835736 0.549132i \(-0.185041\pi\)
0.500391 + 0.865800i \(0.333190\pi\)
\(318\) 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 −0.721496 0.692418i \(-0.756545\pi\)
−0.333996 + 0.942575i \(0.608397\pi\)
\(348\) 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 0.999696 0.0246374i \(-0.00784313\pi\)
−0.310319 + 0.950633i \(0.600436\pi\)
\(354\) 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 \(0.395315\pi\)
−0.627193 + 0.778864i \(0.715796\pi\)
\(360\) 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 −0.816137 0.577859i \(-0.803889\pi\)
0.207344 + 0.978268i \(0.433518\pi\)
\(384\) 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 \(-0.804897\pi\)
0.879217 0.476421i \(-0.158066\pi\)
\(390\) 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 0.563378 0.826199i \(-0.309501\pi\)
−0.857559 + 0.514386i \(0.828020\pi\)
\(402\) 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 \(0.488715\pi\)
−0.967554 + 0.252666i \(0.918693\pi\)
\(420\) 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 \(-0.529864\pi\)
0.909058 0.416669i \(-0.136802\pi\)
\(432\) 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 −0.857402 0.514648i \(-0.827923\pi\)
−0.0991939 + 0.995068i \(0.531626\pi\)
\(444\) 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 \(0.120144\pi\)
−0.747497 + 0.664265i \(0.768745\pi\)
\(450\) 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 −0.662846 0.748755i \(-0.730652\pi\)
−0.472305 + 0.881435i \(0.656578\pi\)
\(462\) 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 0.705595 0.708615i \(-0.250680\pi\)
−0.575324 + 0.817925i \(0.695124\pi\)
\(468\) 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 0.163838 0.986487i \(-0.447613\pi\)
−0.296324 + 0.955088i \(0.595761\pi\)
\(480\) 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 \(0.0593550\pi\)
−0.954498 + 0.298217i \(0.903608\pi\)
\(492\) 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 −0.979652 0.200705i \(-0.935677\pi\)
0.0275408 + 0.999621i \(0.491232\pi\)
\(504\) 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 0.679984 0.733227i \(-0.261987\pi\)
0.936728 + 0.350059i \(0.113839\pi\)
\(510\) 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 \(-0.605391\pi\)
0.628918 0.777472i \(-0.283498\pi\)
\(522\) 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 0.294224 0.955736i \(-0.404939\pi\)
−0.388947 + 0.921260i \(0.627161\pi\)
\(558\) 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 \(0.0269137\pi\)
0.0263710 + 0.999652i \(0.491605\pi\)
\(564\) 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 \(0.365821\pi\)
−0.944485 + 0.328554i \(0.893439\pi\)
\(570\) 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 −0.596395 0.802691i \(-0.703401\pi\)
0.836010 + 0.548714i \(0.184882\pi\)
\(588\) 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 −0.897298 0.441426i \(-0.854473\pi\)
0.830935 + 0.556370i \(0.187806\pi\)
\(594\) 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 0.460044 0.887896i \(-0.347834\pi\)
−0.437483 + 0.899227i \(0.644130\pi\)
\(600\) 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 \(-0.792735\pi\)
0.997595 0.0693101i \(-0.0220798\pi\)
\(618\) 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 −0.360964 0.932580i \(-0.617552\pi\)
−0.741111 + 0.671383i \(0.765701\pi\)
\(642\) 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 \(-0.699417\pi\)
−0.586303 + 0.810092i \(0.699417\pi\)
\(648\) 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 \(0.142838\pi\)
−0.844537 + 0.535497i \(0.820124\pi\)
\(654\) 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 0.232142 0.972682i \(-0.425427\pi\)
−0.801186 + 0.598416i \(0.795797\pi\)
\(660\) 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 0.500733 0.865602i \(-0.333064\pi\)
−0.972849 + 0.231439i \(0.925656\pi\)
\(678\) 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 \(-0.859315\pi\)
0.995687 0.0927760i \(-0.0295741\pi\)
\(684\) 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 0.998268 0.0588360i \(-0.0187389\pi\)
−0.550087 + 0.835107i \(0.685406\pi\)
\(702\) 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 0.736439 0.676504i \(-0.236506\pi\)
0.129296 + 0.991606i \(0.458728\pi\)
\(720\) 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 −0.994953 0.100340i \(-0.968007\pi\)
0.381481 + 0.924377i \(0.375414\pi\)
\(744\) 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 −0.268083 0.963396i \(-0.586390\pi\)
−0.932850 + 0.360265i \(0.882686\pi\)
\(762\) 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 \(-0.777339\pi\)
0.498807 0.866713i \(-0.333772\pi\)
\(774\) 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