Properties

Label 164.2.o.b.111.2
Level $164$
Weight $2$
Character 164.111
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), 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: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 111.2
Character \(\chi\) \(=\) 164.111
Dual form 164.2.o.b.99.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39799 - 0.213623i) q^{2} +(-1.12890 - 0.467604i) q^{3} +(1.90873 + 0.597285i) q^{4} +(-0.906832 + 0.462054i) q^{5} +(1.47829 + 0.894863i) q^{6} +(1.47692 + 2.41011i) q^{7} +(-2.54078 - 1.24274i) q^{8} +(-1.06557 - 1.06557i) q^{9} +O(q^{10})\) \(q+(-1.39799 - 0.213623i) q^{2} +(-1.12890 - 0.467604i) q^{3} +(1.90873 + 0.597285i) q^{4} +(-0.906832 + 0.462054i) q^{5} +(1.47829 + 0.894863i) q^{6} +(1.47692 + 2.41011i) q^{7} +(-2.54078 - 1.24274i) q^{8} +(-1.06557 - 1.06557i) q^{9} +(1.36644 - 0.452225i) q^{10} +(5.44266 + 0.428347i) q^{11} +(-1.87547 - 1.56680i) q^{12} +(1.37654 + 5.73369i) q^{13} +(-1.54985 - 3.68480i) q^{14} +(1.23978 - 0.0975727i) q^{15} +(3.28650 + 2.28011i) q^{16} +(5.06768 - 4.32821i) q^{17} +(1.26202 + 1.71728i) q^{18} +(3.80095 + 0.912526i) q^{19} +(-2.00687 + 0.340300i) q^{20} +(-0.540309 - 3.41138i) q^{21} +(-7.51726 - 1.76150i) q^{22} +(-4.52941 + 3.29081i) q^{23} +(2.28717 + 2.59101i) q^{24} +(-2.33008 + 3.20707i) q^{25} +(-0.699530 - 8.30968i) q^{26} +(2.10746 + 5.08787i) q^{27} +(1.37951 + 5.48238i) q^{28} +(1.13345 + 0.968059i) q^{29} +(-1.75404 - 0.128440i) q^{30} +(-2.34282 - 7.21046i) q^{31} +(-4.10740 - 3.88964i) q^{32} +(-5.94391 - 3.02857i) q^{33} +(-8.00916 + 4.96820i) q^{34} +(-2.45291 - 1.50315i) q^{35} +(-1.39743 - 2.67032i) q^{36} +(0.577596 - 1.77766i) q^{37} +(-5.11873 - 2.08767i) q^{38} +(1.12713 - 7.11642i) q^{39} +(2.87828 - 0.0470189i) q^{40} +(-6.40312 + 0.00937645i) q^{41} +(0.0265951 + 4.88448i) q^{42} +(0.547861 + 0.0867727i) q^{43} +(10.1327 + 4.06842i) q^{44} +(1.45864 + 0.473940i) q^{45} +(7.03505 - 3.63292i) q^{46} +(-1.86886 + 3.04969i) q^{47} +(-2.64393 - 4.11079i) q^{48} +(-0.449404 + 0.882006i) q^{49} +(3.94252 - 3.98569i) q^{50} +(-7.74478 + 2.51643i) q^{51} +(-0.797207 + 11.7662i) q^{52} +(-4.02561 + 4.71338i) q^{53} +(-1.85932 - 7.56297i) q^{54} +(-5.13350 + 2.12637i) q^{55} +(-0.757376 - 7.95899i) q^{56} +(-3.86417 - 2.80749i) q^{57} +(-1.37775 - 1.59546i) q^{58} +(0.796244 + 1.09594i) q^{59} +(2.42468 + 0.554261i) q^{60} +(8.44013 - 1.33679i) q^{61} +(1.73491 + 10.5806i) q^{62} +(0.994377 - 4.14188i) q^{63} +(4.91117 + 6.31509i) q^{64} +(-3.89756 - 4.56346i) q^{65} +(7.66253 + 5.50366i) q^{66} +(-0.660735 - 8.39544i) q^{67} +(12.2580 - 5.23454i) q^{68} +(6.65204 - 1.59701i) q^{69} +(3.10803 + 2.62538i) q^{70} +(-0.307788 + 3.91082i) q^{71} +(1.38315 + 4.03160i) q^{72} +(2.33419 - 2.33419i) q^{73} +(-1.18722 + 2.36175i) q^{74} +(4.13006 - 2.53090i) q^{75} +(6.70994 + 4.01201i) q^{76} +(7.00599 + 13.7500i) q^{77} +(-3.09594 + 9.70787i) q^{78} +(2.36361 - 5.70626i) q^{79} +(-4.03384 - 0.549136i) q^{80} -2.20832i q^{81} +(8.95347 + 1.35475i) q^{82} -1.36416i q^{83} +(1.00626 - 6.83411i) q^{84} +(-2.59567 + 6.26650i) q^{85} +(-0.747366 - 0.238343i) q^{86} +(-0.826881 - 1.62285i) q^{87} +(-13.2963 - 7.85218i) q^{88} +(12.4288 - 7.61637i) q^{89} +(-1.93791 - 0.974161i) q^{90} +(-11.7858 + 11.7858i) q^{91} +(-10.6110 + 3.57592i) q^{92} +(-0.726840 + 9.23538i) q^{93} +(3.26412 - 3.86420i) q^{94} +(-3.86845 + 0.928734i) q^{95} +(2.81802 + 6.31164i) q^{96} +(-0.242507 - 3.08135i) q^{97} +(0.816678 - 1.13703i) q^{98} +(-5.34309 - 6.25595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{40}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39799 0.213623i −0.988525 0.151054i
\(3\) −1.12890 0.467604i −0.651769 0.269972i 0.0322014 0.999481i \(-0.489748\pi\)
−0.683970 + 0.729510i \(0.739748\pi\)
\(4\) 1.90873 + 0.597285i 0.954365 + 0.298642i
\(5\) −0.906832 + 0.462054i −0.405548 + 0.206637i −0.644851 0.764308i \(-0.723081\pi\)
0.239304 + 0.970945i \(0.423081\pi\)
\(6\) 1.47829 + 0.894863i 0.603510 + 0.365326i
\(7\) 1.47692 + 2.41011i 0.558222 + 0.910935i 0.999905 + 0.0137641i \(0.00438139\pi\)
−0.441684 + 0.897171i \(0.645619\pi\)
\(8\) −2.54078 1.24274i −0.898303 0.439377i
\(9\) −1.06557 1.06557i −0.355189 0.355189i
\(10\) 1.36644 0.452225i 0.432107 0.143006i
\(11\) 5.44266 + 0.428347i 1.64102 + 0.129151i 0.865075 0.501643i \(-0.167271\pi\)
0.775950 + 0.630794i \(0.217271\pi\)
\(12\) −1.87547 1.56680i −0.541401 0.452297i
\(13\) 1.37654 + 5.73369i 0.381783 + 1.59024i 0.750613 + 0.660742i \(0.229758\pi\)
−0.368830 + 0.929497i \(0.620242\pi\)
\(14\) −1.54985 3.68480i −0.414216 0.984804i
\(15\) 1.23978 0.0975727i 0.320109 0.0251931i
\(16\) 3.28650 + 2.28011i 0.821626 + 0.570028i
\(17\) 5.06768 4.32821i 1.22909 1.04975i 0.232066 0.972700i \(-0.425451\pi\)
0.997028 0.0770453i \(-0.0245486\pi\)
\(18\) 1.26202 + 1.71728i 0.297460 + 0.404766i
\(19\) 3.80095 + 0.912526i 0.871997 + 0.209348i 0.644661 0.764469i \(-0.276999\pi\)
0.227336 + 0.973816i \(0.426999\pi\)
\(20\) −2.00687 + 0.340300i −0.448751 + 0.0760933i
\(21\) −0.540309 3.41138i −0.117905 0.744423i
\(22\) −7.51726 1.76150i −1.60269 0.375554i
\(23\) −4.52941 + 3.29081i −0.944448 + 0.686182i −0.949487 0.313806i \(-0.898396\pi\)
0.00503926 + 0.999987i \(0.498396\pi\)
\(24\) 2.28717 + 2.59101i 0.466867 + 0.528888i
\(25\) −2.33008 + 3.20707i −0.466015 + 0.641415i
\(26\) −0.699530 8.30968i −0.137189 1.62966i
\(27\) 2.10746 + 5.08787i 0.405582 + 0.979161i
\(28\) 1.37951 + 5.48238i 0.260704 + 1.03607i
\(29\) 1.13345 + 0.968059i 0.210477 + 0.179764i 0.748437 0.663206i \(-0.230805\pi\)
−0.537960 + 0.842970i \(0.680805\pi\)
\(30\) −1.75404 0.128440i −0.320242 0.0234499i
\(31\) −2.34282 7.21046i −0.420783 1.29504i −0.906975 0.421185i \(-0.861614\pi\)
0.486191 0.873852i \(-0.338386\pi\)
\(32\) −4.10740 3.88964i −0.726093 0.687597i
\(33\) −5.94391 3.02857i −1.03470 0.527207i
\(34\) −8.00916 + 4.96820i −1.37356 + 0.852040i
\(35\) −2.45291 1.50315i −0.414618 0.254078i
\(36\) −1.39743 2.67032i −0.232905 0.445054i
\(37\) 0.577596 1.77766i 0.0949563 0.292245i −0.892286 0.451471i \(-0.850900\pi\)
0.987242 + 0.159225i \(0.0508996\pi\)
\(38\) −5.11873 2.08767i −0.830368 0.338665i
\(39\) 1.12713 7.11642i 0.180485 1.13954i
\(40\) 2.87828 0.0470189i 0.455096 0.00743434i
\(41\) −6.40312 + 0.00937645i −0.999999 + 0.00146436i
\(42\) 0.0265951 + 4.88448i 0.00410372 + 0.753691i
\(43\) 0.547861 + 0.0867727i 0.0835481 + 0.0132327i 0.198069 0.980188i \(-0.436533\pi\)
−0.114520 + 0.993421i \(0.536533\pi\)
\(44\) 10.1327 + 4.06842i 1.52757 + 0.613337i
\(45\) 1.45864 + 0.473940i 0.217441 + 0.0706508i
\(46\) 7.03505 3.63292i 1.03726 0.535645i
\(47\) −1.86886 + 3.04969i −0.272601 + 0.444844i −0.959419 0.281986i \(-0.909007\pi\)
0.686818 + 0.726829i \(0.259007\pi\)
\(48\) −2.64393 4.11079i −0.381619 0.593342i
\(49\) −0.449404 + 0.882006i −0.0642006 + 0.126001i
\(50\) 3.94252 3.98569i 0.557556 0.563661i
\(51\) −7.74478 + 2.51643i −1.08449 + 0.352371i
\(52\) −0.797207 + 11.7662i −0.110553 + 1.63169i
\(53\) −4.02561 + 4.71338i −0.552960 + 0.647433i −0.964539 0.263941i \(-0.914977\pi\)
0.411579 + 0.911374i \(0.364977\pi\)
\(54\) −1.85932 7.56297i −0.253021 1.02919i
\(55\) −5.13350 + 2.12637i −0.692201 + 0.286719i
\(56\) −0.757376 7.95899i −0.101209 1.06357i
\(57\) −3.86417 2.80749i −0.511822 0.371861i
\(58\) −1.37775 1.59546i −0.180907 0.209495i
\(59\) 0.796244 + 1.09594i 0.103662 + 0.142679i 0.857697 0.514156i \(-0.171895\pi\)
−0.754034 + 0.656835i \(0.771895\pi\)
\(60\) 2.42468 + 0.554261i 0.313025 + 0.0715547i
\(61\) 8.44013 1.33679i 1.08065 0.171158i 0.409374 0.912367i \(-0.365747\pi\)
0.671274 + 0.741209i \(0.265747\pi\)
\(62\) 1.73491 + 10.5806i 0.220334 + 1.34374i
\(63\) 0.994377 4.14188i 0.125280 0.521828i
\(64\) 4.91117 + 6.31509i 0.613896 + 0.789387i
\(65\) −3.89756 4.56346i −0.483433 0.566027i
\(66\) 7.66253 + 5.50366i 0.943192 + 0.677454i
\(67\) −0.660735 8.39544i −0.0807217 1.02567i −0.895256 0.445551i \(-0.853008\pi\)
0.814535 0.580115i \(-0.196992\pi\)
\(68\) 12.2580 5.23454i 1.48650 0.634781i
\(69\) 6.65204 1.59701i 0.800811 0.192258i
\(70\) 3.10803 + 2.62538i 0.371481 + 0.313793i
\(71\) −0.307788 + 3.91082i −0.0365277 + 0.464129i 0.951267 + 0.308368i \(0.0997829\pi\)
−0.987795 + 0.155761i \(0.950217\pi\)
\(72\) 1.38315 + 4.03160i 0.163005 + 0.475129i
\(73\) 2.33419 2.33419i 0.273196 0.273196i −0.557189 0.830385i \(-0.688120\pi\)
0.830385 + 0.557189i \(0.188120\pi\)
\(74\) −1.18722 + 2.36175i −0.138012 + 0.274548i
\(75\) 4.13006 2.53090i 0.476898 0.292243i
\(76\) 6.70994 + 4.01201i 0.769683 + 0.460209i
\(77\) 7.00599 + 13.7500i 0.798407 + 1.56696i
\(78\) −3.09594 + 9.70787i −0.350547 + 1.09920i
\(79\) 2.36361 5.70626i 0.265927 0.642004i −0.733357 0.679844i \(-0.762048\pi\)
0.999284 + 0.0378394i \(0.0120475\pi\)
\(80\) −4.03384 0.549136i −0.450997 0.0613952i
\(81\) 2.20832i 0.245369i
\(82\) 8.95347 + 1.35475i 0.988746 + 0.149607i
\(83\) 1.36416i 0.149737i −0.997193 0.0748683i \(-0.976146\pi\)
0.997193 0.0748683i \(-0.0238536\pi\)
\(84\) 1.00626 6.83411i 0.109792 0.745663i
\(85\) −2.59567 + 6.26650i −0.281540 + 0.679698i
\(86\) −0.747366 0.238343i −0.0805905 0.0257012i
\(87\) −0.826881 1.62285i −0.0886510 0.173987i
\(88\) −13.2963 7.85218i −1.41739 0.837045i
\(89\) 12.4288 7.61637i 1.31745 0.807334i 0.326975 0.945033i \(-0.393971\pi\)
0.990474 + 0.137699i \(0.0439708\pi\)
\(90\) −1.93791 0.974161i −0.204274 0.102686i
\(91\) −11.7858 + 11.7858i −1.23549 + 1.23549i
\(92\) −10.6110 + 3.57592i −1.10627 + 0.372816i
\(93\) −0.726840 + 9.23538i −0.0753698 + 0.957665i
\(94\) 3.26412 3.86420i 0.336668 0.398562i
\(95\) −3.86845 + 0.928734i −0.396895 + 0.0952861i
\(96\) 2.81802 + 6.31164i 0.287613 + 0.644179i
\(97\) −0.242507 3.08135i −0.0246229 0.312864i −0.996879 0.0789446i \(-0.974845\pi\)
0.972256 0.233919i \(-0.0751550\pi\)
\(98\) 0.816678 1.13703i 0.0824969 0.114857i
\(99\) −5.34309 6.25595i −0.537000 0.628747i
\(100\) −6.36302 + 4.72972i −0.636302 + 0.472972i
\(101\) 1.43265 5.96744i 0.142554 0.593782i −0.854660 0.519189i \(-0.826234\pi\)
0.997214 0.0745933i \(-0.0237659\pi\)
\(102\) 11.3647 1.86347i 1.12527 0.184511i
\(103\) −1.10695 + 0.175323i −0.109071 + 0.0172751i −0.210731 0.977544i \(-0.567584\pi\)
0.101660 + 0.994819i \(0.467584\pi\)
\(104\) 3.62803 16.2788i 0.355757 1.59626i
\(105\) 2.06621 + 2.84389i 0.201641 + 0.277535i
\(106\) 6.63463 5.72928i 0.644412 0.556477i
\(107\) −3.17002 2.30316i −0.306458 0.222655i 0.423917 0.905701i \(-0.360655\pi\)
−0.730375 + 0.683046i \(0.760655\pi\)
\(108\) 0.983675 + 10.9701i 0.0946542 + 1.05560i
\(109\) −13.8245 + 5.72631i −1.32415 + 0.548481i −0.928981 0.370128i \(-0.879314\pi\)
−0.395169 + 0.918609i \(0.629314\pi\)
\(110\) 7.63080 1.87599i 0.727568 0.178869i
\(111\) −1.48329 + 1.73671i −0.140787 + 0.164841i
\(112\) −0.641424 + 11.2884i −0.0606089 + 1.06665i
\(113\) −11.5983 + 3.76851i −1.09108 + 0.354512i −0.798662 0.601780i \(-0.794458\pi\)
−0.292414 + 0.956292i \(0.594458\pi\)
\(114\) 4.80232 + 4.75030i 0.449778 + 0.444907i
\(115\) 2.58688 5.07705i 0.241228 0.473437i
\(116\) 1.58525 + 2.52476i 0.147186 + 0.234418i
\(117\) 4.64283 7.57641i 0.429230 0.700440i
\(118\) −0.879021 1.70220i −0.0809204 0.156700i
\(119\) 17.9160 + 5.82126i 1.64236 + 0.533634i
\(120\) −3.27127 1.29282i −0.298624 0.118017i
\(121\) 18.5745 + 2.94192i 1.68859 + 0.267447i
\(122\) −12.0848 + 0.0657994i −1.09410 + 0.00595719i
\(123\) 7.23284 + 2.98354i 0.652164 + 0.269017i
\(124\) −0.165115 15.1622i −0.0148278 1.36160i
\(125\) 1.42721 9.01105i 0.127654 0.805973i
\(126\) −2.27493 + 5.57787i −0.202667 + 0.496916i
\(127\) 3.85927 11.8776i 0.342455 1.05397i −0.620478 0.784224i \(-0.713061\pi\)
0.962932 0.269743i \(-0.0869387\pi\)
\(128\) −5.51670 9.87755i −0.487612 0.873061i
\(129\) −0.577904 0.354140i −0.0508816 0.0311803i
\(130\) 4.47388 + 7.21226i 0.392385 + 0.632557i
\(131\) −7.42436 3.78290i −0.648669 0.330513i 0.0985100 0.995136i \(-0.468592\pi\)
−0.747179 + 0.664623i \(0.768592\pi\)
\(132\) −9.53640 9.33093i −0.830037 0.812154i
\(133\) 3.41439 + 10.5084i 0.296065 + 0.911195i
\(134\) −0.869762 + 11.8779i −0.0751360 + 1.02609i
\(135\) −4.26198 3.64008i −0.366813 0.313288i
\(136\) −18.2548 + 4.69921i −1.56533 + 0.402954i
\(137\) −4.24185 10.2407i −0.362406 0.874924i −0.994947 0.100398i \(-0.967988\pi\)
0.632542 0.774526i \(-0.282012\pi\)
\(138\) −9.64062 + 0.811572i −0.820664 + 0.0690856i
\(139\) −3.43733 + 4.73108i −0.291551 + 0.401285i −0.929517 0.368779i \(-0.879776\pi\)
0.637966 + 0.770064i \(0.279776\pi\)
\(140\) −3.78414 4.33419i −0.319819 0.366306i
\(141\) 3.53580 2.56891i 0.297768 0.216341i
\(142\) 1.26573 5.40152i 0.106217 0.453286i
\(143\) 5.03602 + 31.7962i 0.421133 + 2.65893i
\(144\) −1.07238 5.93159i −0.0893647 0.494299i
\(145\) −1.47515 0.354151i −0.122504 0.0294106i
\(146\) −3.76180 + 2.76453i −0.311329 + 0.228794i
\(147\) 0.919761 0.785550i 0.0758606 0.0647911i
\(148\) 2.16424 3.04808i 0.177900 0.250551i
\(149\) −14.2165 + 1.11886i −1.16466 + 0.0916606i −0.646011 0.763328i \(-0.723564\pi\)
−0.518647 + 0.854989i \(0.673564\pi\)
\(150\) −6.31442 + 2.65589i −0.515570 + 0.216853i
\(151\) 0.497557 + 2.07247i 0.0404906 + 0.168656i 0.988952 0.148238i \(-0.0473602\pi\)
−0.948461 + 0.316894i \(0.897360\pi\)
\(152\) −8.52335 7.04214i −0.691335 0.571193i
\(153\) −10.0119 0.787957i −0.809418 0.0637026i
\(154\) −6.85695 20.7190i −0.552549 1.66958i
\(155\) 5.45617 + 5.45617i 0.438250 + 0.438250i
\(156\) 6.40191 12.9101i 0.512563 1.03364i
\(157\) −1.23688 2.01841i −0.0987140 0.161087i 0.799470 0.600705i \(-0.205114\pi\)
−0.898184 + 0.439619i \(0.855114\pi\)
\(158\) −4.52328 + 7.47235i −0.359853 + 0.594468i
\(159\) 6.74849 3.43853i 0.535190 0.272693i
\(160\) 5.52194 + 1.62941i 0.436548 + 0.128816i
\(161\) −14.6208 6.05612i −1.15228 0.477289i
\(162\) −0.471749 + 3.08721i −0.0370641 + 0.242554i
\(163\) 4.47340 0.350384 0.175192 0.984534i \(-0.443945\pi\)
0.175192 + 0.984534i \(0.443945\pi\)
\(164\) −12.2274 3.80659i −0.954801 0.297244i
\(165\) 6.78949 0.528561
\(166\) −0.291417 + 1.90708i −0.0226184 + 0.148018i
\(167\) 13.6855 + 5.66873i 1.05902 + 0.438659i 0.843103 0.537753i \(-0.180727\pi\)
0.215915 + 0.976412i \(0.430727\pi\)
\(168\) −2.86666 + 9.33903i −0.221168 + 0.720522i
\(169\) −19.3972 + 9.88339i −1.49210 + 0.760261i
\(170\) 4.96738 8.20599i 0.380981 0.629370i
\(171\) −3.07780 5.02251i −0.235365 0.384081i
\(172\) 0.993891 + 0.492855i 0.0757835 + 0.0375798i
\(173\) −4.59958 4.59958i −0.349699 0.349699i 0.510298 0.859998i \(-0.329535\pi\)
−0.859998 + 0.510298i \(0.829535\pi\)
\(174\) 0.809291 + 2.44536i 0.0613522 + 0.185382i
\(175\) −11.1707 0.879155i −0.844427 0.0664579i
\(176\) 16.9106 + 13.8176i 1.27469 + 1.04154i
\(177\) −0.386413 1.60953i −0.0290446 0.120979i
\(178\) −19.0023 + 7.99250i −1.42428 + 0.599063i
\(179\) 9.33343 0.734557i 0.697613 0.0549033i 0.275307 0.961356i \(-0.411221\pi\)
0.422306 + 0.906453i \(0.361221\pi\)
\(180\) 2.50107 + 1.77585i 0.186419 + 0.132364i
\(181\) 10.8703 9.28415i 0.807986 0.690085i −0.146215 0.989253i \(-0.546709\pi\)
0.954201 + 0.299168i \(0.0967090\pi\)
\(182\) 18.9941 13.9586i 1.40793 1.03468i
\(183\) −10.1531 2.43755i −0.750541 0.180189i
\(184\) 15.5979 2.73234i 1.14989 0.201431i
\(185\) 0.297591 + 1.87892i 0.0218794 + 0.138141i
\(186\) 2.98901 12.7557i 0.219165 0.935291i
\(187\) 29.4357 21.3863i 2.15255 1.56392i
\(188\) −5.38868 + 4.70481i −0.393010 + 0.343133i
\(189\) −9.14976 + 12.5936i −0.665547 + 0.916047i
\(190\) 5.60644 0.471965i 0.406734 0.0342399i
\(191\) 5.25896 + 12.6963i 0.380525 + 0.918669i 0.991864 + 0.127300i \(0.0406311\pi\)
−0.611339 + 0.791369i \(0.709369\pi\)
\(192\) −2.59124 9.42557i −0.187007 0.680232i
\(193\) −12.4327 10.6185i −0.894923 0.764337i 0.0776385 0.996982i \(-0.475262\pi\)
−0.972562 + 0.232645i \(0.925262\pi\)
\(194\) −0.319226 + 4.35949i −0.0229191 + 0.312993i
\(195\) 2.26605 + 6.97419i 0.162275 + 0.499432i
\(196\) −1.38460 + 1.41509i −0.0989000 + 0.101078i
\(197\) 7.72424 + 3.93570i 0.550329 + 0.280407i 0.706964 0.707250i \(-0.250064\pi\)
−0.156634 + 0.987657i \(0.550064\pi\)
\(198\) 6.13314 + 9.88714i 0.435864 + 0.702648i
\(199\) 4.00709 + 2.45555i 0.284055 + 0.174069i 0.657226 0.753693i \(-0.271730\pi\)
−0.373171 + 0.927763i \(0.621730\pi\)
\(200\) 9.90580 5.25280i 0.700446 0.371429i
\(201\) −3.17984 + 9.78655i −0.224289 + 0.690290i
\(202\) −3.27761 + 8.03634i −0.230612 + 0.565435i
\(203\) −0.659114 + 4.16148i −0.0462607 + 0.292079i
\(204\) −16.2857 + 0.177351i −1.14023 + 0.0124171i
\(205\) 5.80222 2.96709i 0.405244 0.207230i
\(206\) 1.58495 0.00862977i 0.110429 0.000601265i
\(207\) 8.33297 + 1.31981i 0.579181 + 0.0917333i
\(208\) −8.54945 + 21.9824i −0.592798 + 1.52421i
\(209\) 20.2964 + 6.59470i 1.40393 + 0.456165i
\(210\) −2.28101 4.41711i −0.157405 0.304810i
\(211\) −13.1292 + 21.4250i −0.903854 + 1.47496i −0.0240003 + 0.999712i \(0.507640\pi\)
−0.879854 + 0.475244i \(0.842360\pi\)
\(212\) −10.4990 + 6.59214i −0.721076 + 0.452750i
\(213\) 2.17618 4.27099i 0.149109 0.292643i
\(214\) 3.93964 + 3.89697i 0.269308 + 0.266392i
\(215\) −0.536912 + 0.174453i −0.0366171 + 0.0118976i
\(216\) 0.968310 15.5462i 0.0658851 1.05779i
\(217\) 13.9178 16.2957i 0.944805 1.10622i
\(218\) 20.5498 5.05206i 1.39181 0.342168i
\(219\) −3.72653 + 1.54358i −0.251816 + 0.104306i
\(220\) −11.0685 + 0.992497i −0.746239 + 0.0669141i
\(221\) 31.7925 + 23.0986i 2.13859 + 1.55378i
\(222\) 2.44462 2.11103i 0.164072 0.141683i
\(223\) −16.7244 23.0192i −1.11995 1.54148i −0.805880 0.592079i \(-0.798307\pi\)
−0.314070 0.949400i \(-0.601693\pi\)
\(224\) 3.30816 15.6439i 0.221036 1.04525i
\(225\) 5.90020 0.934500i 0.393347 0.0623000i
\(226\) 17.0193 2.79066i 1.13211 0.185632i
\(227\) −2.51074 + 10.4580i −0.166644 + 0.694121i 0.825002 + 0.565130i \(0.191174\pi\)
−0.991646 + 0.128991i \(0.958826\pi\)
\(228\) −5.69880 7.66675i −0.377412 0.507743i
\(229\) 4.53311 + 5.30759i 0.299556 + 0.350736i 0.889686 0.456573i \(-0.150923\pi\)
−0.590129 + 0.807309i \(0.700923\pi\)
\(230\) −4.70100 + 6.54502i −0.309975 + 0.431566i
\(231\) −1.47947 18.7984i −0.0973418 1.23684i
\(232\) −1.67681 3.86822i −0.110088 0.253961i
\(233\) 11.0506 2.65300i 0.723946 0.173804i 0.145305 0.989387i \(-0.453584\pi\)
0.578640 + 0.815583i \(0.303584\pi\)
\(234\) −8.10911 + 9.59991i −0.530109 + 0.627565i
\(235\) 0.285614 3.62907i 0.0186314 0.236735i
\(236\) 0.865230 + 2.56743i 0.0563217 + 0.167126i
\(237\) −5.33654 + 5.33654i −0.346646 + 0.346646i
\(238\) −23.8028 11.9653i −1.54290 0.775596i
\(239\) −3.30830 + 2.02733i −0.213996 + 0.131137i −0.625366 0.780331i \(-0.715050\pi\)
0.411370 + 0.911468i \(0.365050\pi\)
\(240\) 4.29701 + 2.50616i 0.277371 + 0.161772i
\(241\) −8.44434 16.5730i −0.543948 1.06756i −0.985397 0.170272i \(-0.945536\pi\)
0.441449 0.897286i \(-0.354464\pi\)
\(242\) −25.3385 8.08071i −1.62882 0.519448i
\(243\) 5.28977 12.7706i 0.339339 0.819237i
\(244\) 16.9084 + 2.48960i 1.08245 + 0.159380i
\(245\) 1.00748i 0.0643655i
\(246\) −9.47406 5.71605i −0.604044 0.364442i
\(247\) 23.0496i 1.46661i
\(248\) −3.00816 + 21.2318i −0.191018 + 1.34822i
\(249\) −0.637890 + 1.54000i −0.0404246 + 0.0975936i
\(250\) −3.92019 + 12.2924i −0.247935 + 0.777442i
\(251\) −3.04158 5.96944i −0.191983 0.376788i 0.774870 0.632120i \(-0.217815\pi\)
−0.966853 + 0.255332i \(0.917815\pi\)
\(252\) 4.37188 7.31180i 0.275403 0.460600i
\(253\) −26.0617 + 15.9706i −1.63848 + 1.00406i
\(254\) −7.93253 + 15.7803i −0.497732 + 0.990144i
\(255\) 5.86049 5.86049i 0.366998 0.366998i
\(256\) 5.60219 + 14.9872i 0.350137 + 0.936698i
\(257\) 0.0236599 0.300627i 0.00147586 0.0187526i −0.996135 0.0878319i \(-0.972006\pi\)
0.997611 + 0.0690793i \(0.0220062\pi\)
\(258\) 0.732249 + 0.618536i 0.0455878 + 0.0385084i
\(259\) 5.13741 1.23338i 0.319223 0.0766387i
\(260\) −4.71371 11.0384i −0.292332 0.684570i
\(261\) −0.176237 2.23930i −0.0109088 0.138609i
\(262\) 9.57104 + 6.87446i 0.591301 + 0.424705i
\(263\) −14.5572 17.0443i −0.897637 1.05100i −0.998426 0.0560899i \(-0.982137\pi\)
0.100789 0.994908i \(-0.467863\pi\)
\(264\) 11.3384 + 15.0817i 0.697833 + 0.928215i
\(265\) 1.47271 6.13429i 0.0904680 0.376827i
\(266\) −2.52843 15.4200i −0.155028 0.945461i
\(267\) −17.5923 + 2.78634i −1.07663 + 0.170521i
\(268\) 3.75330 16.4193i 0.229269 1.00297i
\(269\) −1.58745 2.18493i −0.0967884 0.133218i 0.757876 0.652399i \(-0.226237\pi\)
−0.854664 + 0.519181i \(0.826237\pi\)
\(270\) 5.18059 + 5.99924i 0.315281 + 0.365102i
\(271\) 1.41012 + 1.02451i 0.0856588 + 0.0622347i 0.629790 0.776765i \(-0.283141\pi\)
−0.544132 + 0.839000i \(0.683141\pi\)
\(272\) 26.5238 2.66980i 1.60824 0.161880i
\(273\) 18.8160 7.79385i 1.13880 0.471705i
\(274\) 3.74239 + 15.2226i 0.226086 + 0.919628i
\(275\) −14.0556 + 16.4569i −0.847582 + 0.992391i
\(276\) 13.6508 + 0.924893i 0.821683 + 0.0556720i
\(277\) 6.90537 2.24369i 0.414903 0.134810i −0.0941244 0.995560i \(-0.530005\pi\)
0.509028 + 0.860750i \(0.330005\pi\)
\(278\) 5.81601 5.87969i 0.348821 0.352641i
\(279\) −5.18679 + 10.1797i −0.310525 + 0.609440i
\(280\) 4.36430 + 6.86752i 0.260817 + 0.410413i
\(281\) −16.8454 + 27.4893i −1.00492 + 1.63987i −0.268578 + 0.963258i \(0.586554\pi\)
−0.736337 + 0.676615i \(0.763446\pi\)
\(282\) −5.49177 + 2.83597i −0.327030 + 0.168879i
\(283\) 6.52964 + 2.12161i 0.388147 + 0.126117i 0.496588 0.867986i \(-0.334586\pi\)
−0.108441 + 0.994103i \(0.534586\pi\)
\(284\) −2.92336 + 7.28086i −0.173469 + 0.432040i
\(285\) 4.80137 + 0.760462i 0.284408 + 0.0450459i
\(286\) −0.247883 45.5264i −0.0146576 2.69203i
\(287\) −9.47946 15.4184i −0.559555 0.910117i
\(288\) 0.232042 + 8.52137i 0.0136732 + 0.502127i
\(289\) 4.28862 27.0773i 0.252272 1.59278i
\(290\) 1.98658 + 0.810224i 0.116656 + 0.0475780i
\(291\) −1.16709 + 3.59192i −0.0684158 + 0.210562i
\(292\) 5.84951 3.06116i 0.342317 0.179141i
\(293\) −9.65090 5.91408i −0.563812 0.345504i 0.211208 0.977441i \(-0.432260\pi\)
−0.775020 + 0.631937i \(0.782260\pi\)
\(294\) −1.45362 + 0.901706i −0.0847771 + 0.0525885i
\(295\) −1.22844 0.625922i −0.0715226 0.0364426i
\(296\) −3.67672 + 3.79884i −0.213705 + 0.220803i
\(297\) 9.29085 + 28.5943i 0.539110 + 1.65921i
\(298\) 20.1134 + 1.47282i 1.16514 + 0.0853179i
\(299\) −25.1034 21.4403i −1.45177 1.23993i
\(300\) 9.39484 2.36399i 0.542411 0.136485i
\(301\) 0.600013 + 1.44856i 0.0345842 + 0.0834936i
\(302\) −0.252849 3.00358i −0.0145498 0.172837i
\(303\) −4.40772 + 6.06670i −0.253217 + 0.348523i
\(304\) 10.4112 + 11.6656i 0.597121 + 0.669068i
\(305\) −7.03611 + 5.11204i −0.402887 + 0.292714i
\(306\) 13.8282 + 3.24034i 0.790508 + 0.185238i
\(307\) −1.27461 8.04760i −0.0727461 0.459301i −0.996992 0.0775033i \(-0.975305\pi\)
0.924246 0.381798i \(-0.124695\pi\)
\(308\) 5.15987 + 30.4297i 0.294011 + 1.73389i
\(309\) 1.33161 + 0.319692i 0.0757527 + 0.0181866i
\(310\) −6.46208 8.79321i −0.367022 0.499421i
\(311\) 11.5688 9.88072i 0.656009 0.560284i −0.257916 0.966167i \(-0.583036\pi\)
0.913925 + 0.405883i \(0.133036\pi\)
\(312\) −11.7077 + 16.6805i −0.662817 + 0.944350i
\(313\) 4.19940 0.330500i 0.237364 0.0186809i 0.0407808 0.999168i \(-0.487015\pi\)
0.196583 + 0.980487i \(0.437015\pi\)
\(314\) 1.29797 + 3.08594i 0.0732485 + 0.174149i
\(315\) 1.01204 + 4.21544i 0.0570219 + 0.237513i
\(316\) 7.91976 9.47996i 0.445521 0.533290i
\(317\) 6.22376 + 0.489820i 0.349561 + 0.0275110i 0.252024 0.967721i \(-0.418904\pi\)
0.0975366 + 0.995232i \(0.468904\pi\)
\(318\) −10.1689 + 3.36538i −0.570241 + 0.188721i
\(319\) 5.75433 + 5.75433i 0.322181 + 0.322181i
\(320\) −7.37152 3.45750i −0.412080 0.193280i
\(321\) 2.50166 + 4.08235i 0.139629 + 0.227854i
\(322\) 19.1459 + 11.5897i 1.06696 + 0.645869i
\(323\) 23.2116 11.8269i 1.29153 0.658066i
\(324\) 1.31900 4.21510i 0.0732777 0.234172i
\(325\) −21.5958 8.94527i −1.19792 0.496195i
\(326\) −6.25375 0.955622i −0.346363 0.0529270i
\(327\) 18.2841 1.01111
\(328\) 16.2806 + 7.93362i 0.898945 + 0.438061i
\(329\) −10.1102 −0.557395
\(330\) −9.49161 1.45039i −0.522496 0.0798415i
\(331\) −29.5740 12.2500i −1.62554 0.673319i −0.630815 0.775933i \(-0.717279\pi\)
−0.994721 + 0.102614i \(0.967279\pi\)
\(332\) 0.814795 2.60382i 0.0447177 0.142903i
\(333\) −2.50968 + 1.27875i −0.137530 + 0.0700748i
\(334\) −17.9212 10.8484i −0.980604 0.593595i
\(335\) 4.47832 + 7.30796i 0.244677 + 0.399276i
\(336\) 6.00259 12.4435i 0.327468 0.678846i
\(337\) −11.3377 11.3377i −0.617603 0.617603i 0.327313 0.944916i \(-0.393857\pi\)
−0.944916 + 0.327313i \(0.893857\pi\)
\(338\) 29.2284 9.67314i 1.58982 0.526149i
\(339\) 14.8554 + 1.16915i 0.806837 + 0.0634995i
\(340\) −8.69732 + 10.4107i −0.471678 + 0.564600i
\(341\) −9.66261 40.2477i −0.523260 2.17953i
\(342\) 3.22980 + 7.67890i 0.174647 + 0.415227i
\(343\) 16.9360 1.33289i 0.914460 0.0719695i
\(344\) −1.28416 0.901322i −0.0692373 0.0485960i
\(345\) −5.29437 + 4.52182i −0.285040 + 0.243447i
\(346\) 5.44757 + 7.41272i 0.292863 + 0.398510i
\(347\) 18.6436 + 4.47594i 1.00084 + 0.240281i 0.700578 0.713576i \(-0.252925\pi\)
0.300263 + 0.953856i \(0.402925\pi\)
\(348\) −0.608992 3.59146i −0.0326454 0.192522i
\(349\) 0.501141 + 3.16408i 0.0268255 + 0.169369i 0.997464 0.0711737i \(-0.0226745\pi\)
−0.970638 + 0.240543i \(0.922674\pi\)
\(350\) 15.4287 + 3.61537i 0.824699 + 0.193250i
\(351\) −26.2713 + 19.0872i −1.40226 + 1.01880i
\(352\) −20.6891 22.9294i −1.10273 1.22214i
\(353\) −3.64615 + 5.01850i −0.194065 + 0.267108i −0.894950 0.446167i \(-0.852789\pi\)
0.700885 + 0.713275i \(0.252789\pi\)
\(354\) 0.196368 + 2.33264i 0.0104368 + 0.123979i
\(355\) −1.52790 3.68867i −0.0810924 0.195774i
\(356\) 28.2723 7.11407i 1.49843 0.377045i
\(357\) −17.5033 14.9492i −0.926371 0.791196i
\(358\) −13.2049 0.966937i −0.697902 0.0511042i
\(359\) −2.17051 6.68013i −0.114555 0.352564i 0.877299 0.479944i \(-0.159343\pi\)
−0.991854 + 0.127380i \(0.959343\pi\)
\(360\) −3.11710 3.01689i −0.164286 0.159004i
\(361\) −3.31464 1.68890i −0.174455 0.0888892i
\(362\) −17.1799 + 10.6569i −0.902955 + 0.560117i
\(363\) −19.5931 12.0067i −1.02837 0.630186i
\(364\) −29.5353 + 15.4564i −1.54807 + 0.810136i
\(365\) −1.03820 + 3.19524i −0.0543416 + 0.167246i
\(366\) 13.6732 + 5.57660i 0.714710 + 0.291494i
\(367\) 3.71575 23.4603i 0.193961 1.22462i −0.678007 0.735056i \(-0.737156\pi\)
0.871968 0.489564i \(-0.162844\pi\)
\(368\) −22.3893 + 0.487696i −1.16713 + 0.0254229i
\(369\) 6.83294 + 6.81295i 0.355708 + 0.354668i
\(370\) −0.0146481 2.69027i −0.000761517 0.139861i
\(371\) −17.3052 2.74088i −0.898443 0.142299i
\(372\) −6.90350 + 17.1937i −0.357930 + 0.891453i
\(373\) −1.84959 0.600968i −0.0957682 0.0311170i 0.260741 0.965409i \(-0.416033\pi\)
−0.356509 + 0.934292i \(0.616033\pi\)
\(374\) −45.7193 + 23.6096i −2.36409 + 1.22082i
\(375\) −5.82478 + 9.50518i −0.300790 + 0.490845i
\(376\) 8.53835 5.42611i 0.440332 0.279830i
\(377\) −3.99031 + 7.83143i −0.205512 + 0.403339i
\(378\) 15.4815 15.6510i 0.796283 0.805002i
\(379\) −23.8054 + 7.73484i −1.22280 + 0.397312i −0.848101 0.529834i \(-0.822254\pi\)
−0.374700 + 0.927146i \(0.622254\pi\)
\(380\) −7.93855 0.537866i −0.407239 0.0275920i
\(381\) −9.91074 + 11.6040i −0.507742 + 0.594490i
\(382\) −4.63974 18.8726i −0.237390 0.965607i
\(383\) −10.2887 + 4.26172i −0.525728 + 0.217764i −0.629731 0.776813i \(-0.716835\pi\)
0.104003 + 0.994577i \(0.466835\pi\)
\(384\) 1.60900 + 13.7304i 0.0821088 + 0.700675i
\(385\) −12.7065 9.23182i −0.647584 0.470497i
\(386\) 15.1123 + 17.5004i 0.769198 + 0.890748i
\(387\) −0.491320 0.676244i −0.0249752 0.0343754i
\(388\) 1.37756 6.02631i 0.0699351 0.305940i
\(389\) 8.63099 1.36701i 0.437609 0.0693104i 0.0662567 0.997803i \(-0.478894\pi\)
0.371352 + 0.928492i \(0.378894\pi\)
\(390\) −1.67806 10.2339i −0.0849718 0.518214i
\(391\) −8.71031 + 36.2810i −0.440499 + 1.83481i
\(392\) 2.23795 1.68249i 0.113033 0.0849786i
\(393\) 6.61244 + 7.74217i 0.333553 + 0.390541i
\(394\) −9.95763 7.15213i −0.501658 0.360319i
\(395\) 0.493203 + 6.26673i 0.0248157 + 0.315314i
\(396\) −6.46193 15.1323i −0.324724 0.760425i
\(397\) 29.0273 6.96884i 1.45684 0.349756i 0.573776 0.819012i \(-0.305478\pi\)
0.883062 + 0.469256i \(0.155478\pi\)
\(398\) −5.07730 4.28883i −0.254502 0.214980i
\(399\) 1.05929 13.4595i 0.0530306 0.673818i
\(400\) −14.9703 + 5.22723i −0.748514 + 0.261361i
\(401\) 13.9830 13.9830i 0.698277 0.698277i −0.265762 0.964039i \(-0.585623\pi\)
0.964039 + 0.265762i \(0.0856234\pi\)
\(402\) 6.53601 13.0022i 0.325986 0.648489i
\(403\) 38.1176 23.3585i 1.89877 1.16357i
\(404\) 6.29881 10.5345i 0.313377 0.524112i
\(405\) 1.02036 + 2.00258i 0.0507023 + 0.0995089i
\(406\) 1.81042 5.67689i 0.0898497 0.281739i
\(407\) 3.90512 9.42779i 0.193569 0.467318i
\(408\) 22.8051 + 3.23108i 1.12902 + 0.159962i
\(409\) 15.7412i 0.778353i 0.921163 + 0.389176i \(0.127240\pi\)
−0.921163 + 0.389176i \(0.872760\pi\)
\(410\) −8.74526 + 2.90846i −0.431898 + 0.143639i
\(411\) 13.5442i 0.668088i
\(412\) −2.21758 0.326518i −0.109252 0.0160864i
\(413\) −1.46534 + 3.53764i −0.0721046 + 0.174076i
\(414\) −11.3674 3.62519i −0.558679 0.178169i
\(415\) 0.630318 + 1.23707i 0.0309411 + 0.0607253i
\(416\) 16.6480 28.9048i 0.816234 1.41717i
\(417\) 6.09267 3.73359i 0.298359 0.182835i
\(418\) −26.9653 13.5551i −1.31892 0.663000i
\(419\) −13.2926 + 13.2926i −0.649385 + 0.649385i −0.952844 0.303459i \(-0.901858\pi\)
0.303459 + 0.952844i \(0.401858\pi\)
\(420\) 2.24522 + 6.66234i 0.109556 + 0.325089i
\(421\) −1.35727 + 17.2458i −0.0661495 + 0.840509i 0.870933 + 0.491401i \(0.163515\pi\)
−0.937083 + 0.349107i \(0.886485\pi\)
\(422\) 22.9314 27.1471i 1.11628 1.32150i
\(423\) 5.24104 1.25826i 0.254828 0.0611788i
\(424\) 16.0857 6.97288i 0.781192 0.338633i
\(425\) 2.07281 + 26.3375i 0.100546 + 1.27756i
\(426\) −3.95465 + 5.50590i −0.191603 + 0.266762i
\(427\) 15.6872 + 18.3673i 0.759155 + 0.888856i
\(428\) −4.67508 6.28951i −0.225979 0.304015i
\(429\) 9.18288 38.2495i 0.443354 1.84670i
\(430\) 0.787862 0.129186i 0.0379941 0.00622992i
\(431\) −3.93121 + 0.622643i −0.189360 + 0.0299916i −0.250394 0.968144i \(-0.580560\pi\)
0.0610342 + 0.998136i \(0.480560\pi\)
\(432\) −4.67472 + 21.5265i −0.224912 + 1.03570i
\(433\) 8.22399 + 11.3193i 0.395220 + 0.543973i 0.959536 0.281585i \(-0.0908602\pi\)
−0.564317 + 0.825559i \(0.690860\pi\)
\(434\) −22.9381 + 19.8080i −1.10106 + 0.950814i
\(435\) 1.49968 + 1.08958i 0.0719044 + 0.0522416i
\(436\) −29.8075 + 2.67280i −1.42752 + 0.128004i
\(437\) −20.2190 + 8.37499i −0.967206 + 0.400630i
\(438\) 5.53939 1.36183i 0.264682 0.0650708i
\(439\) 9.04238 10.5873i 0.431569 0.505302i −0.501422 0.865203i \(-0.667189\pi\)
0.932991 + 0.359901i \(0.117189\pi\)
\(440\) 15.6856 + 0.976994i 0.747784 + 0.0465764i
\(441\) 1.41871 0.460965i 0.0675574 0.0219507i
\(442\) −39.5110 39.0831i −1.87935 1.85899i
\(443\) 0.750591 1.47312i 0.0356616 0.0699899i −0.872488 0.488635i \(-0.837495\pi\)
0.908150 + 0.418645i \(0.137495\pi\)
\(444\) −3.86850 + 2.42896i −0.183591 + 0.115273i
\(445\) −7.75165 + 12.6495i −0.367463 + 0.599646i
\(446\) 18.4631 + 35.7532i 0.874252 + 1.69296i
\(447\) 16.5721 + 5.38460i 0.783834 + 0.254683i
\(448\) −7.96667 + 21.1633i −0.376390 + 0.999872i
\(449\) 27.5311 + 4.36050i 1.29927 + 0.205785i 0.767472 0.641083i \(-0.221515\pi\)
0.531803 + 0.846868i \(0.321515\pi\)
\(450\) −8.44803 + 0.0459980i −0.398244 + 0.00216837i
\(451\) −34.8540 2.69172i −1.64121 0.126748i
\(452\) −24.3889 + 0.265594i −1.14716 + 0.0124925i
\(453\) 0.407408 2.57227i 0.0191417 0.120856i
\(454\) 5.74405 14.0838i 0.269582 0.660984i
\(455\) 5.24205 16.1334i 0.245751 0.756345i
\(456\) 6.32904 + 11.9354i 0.296385 + 0.558926i
\(457\) 1.05472 + 0.646336i 0.0493379 + 0.0302343i 0.546949 0.837166i \(-0.315789\pi\)
−0.497611 + 0.867400i \(0.665789\pi\)
\(458\) −5.20340 8.38832i −0.243139 0.391960i
\(459\) 32.7013 + 16.6622i 1.52637 + 0.777723i
\(460\) 7.97010 8.14560i 0.371608 0.379791i
\(461\) −5.90451 18.1722i −0.275000 0.846364i −0.989219 0.146442i \(-0.953218\pi\)
0.714219 0.699922i \(-0.246782\pi\)
\(462\) −1.94750 + 26.5960i −0.0906060 + 1.23736i
\(463\) 19.4565 + 16.6174i 0.904218 + 0.772275i 0.974297 0.225266i \(-0.0723252\pi\)
−0.0700792 + 0.997541i \(0.522325\pi\)
\(464\) 1.51781 + 5.76592i 0.0704625 + 0.267676i
\(465\) −3.60812 8.71078i −0.167323 0.403953i
\(466\) −16.0153 + 1.34821i −0.741893 + 0.0624545i
\(467\) 10.4027 14.3181i 0.481379 0.662562i −0.497390 0.867527i \(-0.665708\pi\)
0.978769 + 0.204965i \(0.0657081\pi\)
\(468\) 13.3872 11.6882i 0.618823 0.540289i
\(469\) 19.2581 13.9918i 0.889254 0.646081i
\(470\) −1.17454 + 5.01238i −0.0541774 + 0.231204i
\(471\) 0.452496 + 2.85695i 0.0208499 + 0.131641i
\(472\) −0.661116 3.77407i −0.0304303 0.173715i
\(473\) 2.94466 + 0.706949i 0.135395 + 0.0325056i
\(474\) 8.60043 6.32041i 0.395031 0.290306i
\(475\) −11.7830 + 10.0637i −0.540643 + 0.461752i
\(476\) 30.7199 + 21.8122i 1.40804 + 0.999759i
\(477\) 9.31197 0.732868i 0.426366 0.0335557i
\(478\) 5.05804 2.12745i 0.231349 0.0973072i
\(479\) −7.74777 32.2718i −0.354005 1.47454i −0.810990 0.585061i \(-0.801071\pi\)
0.456985 0.889474i \(-0.348929\pi\)
\(480\) −5.47179 4.42152i −0.249752 0.201814i
\(481\) 10.9876 + 0.864745i 0.500993 + 0.0394290i
\(482\) 8.26470 + 24.9727i 0.376447 + 1.13747i
\(483\) 13.6735 + 13.6735i 0.622165 + 0.622165i
\(484\) 33.6966 + 16.7096i 1.53166 + 0.759528i
\(485\) 1.64366 + 2.68221i 0.0746349 + 0.121793i
\(486\) −10.1231 + 16.7232i −0.459194 + 0.758578i
\(487\) −14.8775 + 7.58048i −0.674165 + 0.343504i −0.757331 0.653031i \(-0.773497\pi\)
0.0831656 + 0.996536i \(0.473497\pi\)
\(488\) −23.1058 7.09245i −1.04595 0.321060i
\(489\) −5.05001 2.09178i −0.228369 0.0945936i
\(490\) −0.215221 + 1.40844i −0.00972270 + 0.0636270i
\(491\) 37.1251 1.67543 0.837715 0.546107i \(-0.183891\pi\)
0.837715 + 0.546107i \(0.183891\pi\)
\(492\) 12.0235 + 10.0148i 0.542062 + 0.451504i
\(493\) 9.93394 0.447402
\(494\) 4.92392 32.2230i 0.221538 1.44978i
\(495\) 7.73587 + 3.20430i 0.347701 + 0.144023i
\(496\) 8.74096 29.0391i 0.392481 1.30389i
\(497\) −9.88008 + 5.03415i −0.443182 + 0.225812i
\(498\) 1.22074 2.01663i 0.0547027 0.0903675i
\(499\) 14.9056 + 24.3238i 0.667268 + 1.08888i 0.989819 + 0.142330i \(0.0454595\pi\)
−0.322551 + 0.946552i \(0.604540\pi\)
\(500\) 8.10632 16.3472i 0.362526 0.731070i
\(501\) −12.7988 12.7988i −0.571809 0.571809i
\(502\) 2.97688 + 8.99495i 0.132865 + 0.401464i
\(503\) −7.58066 0.596611i −0.338005 0.0266016i −0.0916790 0.995789i \(-0.529223\pi\)
−0.246326 + 0.969187i \(0.579223\pi\)
\(504\) −7.67380 + 9.28787i −0.341818 + 0.413714i
\(505\) 1.45810 + 6.07342i 0.0648846 + 0.270264i
\(506\) 39.8456 16.7593i 1.77135 0.745043i
\(507\) 26.5190 2.08709i 1.17775 0.0926910i
\(508\) 14.4606 20.3661i 0.641586 0.903598i
\(509\) −4.82145 + 4.11791i −0.213707 + 0.182523i −0.749857 0.661599i \(-0.769878\pi\)
0.536150 + 0.844122i \(0.319878\pi\)
\(510\) −9.44482 + 6.94094i −0.418224 + 0.307350i
\(511\) 9.07304 + 2.17825i 0.401368 + 0.0963599i
\(512\) −4.63018 22.1486i −0.204627 0.978840i
\(513\) 3.36754 + 21.2618i 0.148681 + 0.938732i
\(514\) −0.0972971 + 0.415218i −0.00429159 + 0.0183145i
\(515\) 0.922806 0.670458i 0.0406637 0.0295439i
\(516\) −0.891540 1.02113i −0.0392478 0.0449527i
\(517\) −11.4779 + 15.7979i −0.504797 + 0.694793i
\(518\) −7.44551 + 0.626782i −0.327137 + 0.0275392i
\(519\) 3.04167 + 7.34323i 0.133514 + 0.322332i
\(520\) 4.23165 + 16.4384i 0.185570 + 0.720873i
\(521\) 28.7941 + 24.5925i 1.26149 + 1.07742i 0.993481 + 0.114002i \(0.0363669\pi\)
0.268013 + 0.963415i \(0.413633\pi\)
\(522\) −0.231990 + 3.16816i −0.0101539 + 0.138666i
\(523\) 12.9967 + 39.9997i 0.568305 + 1.74906i 0.657921 + 0.753087i \(0.271436\pi\)
−0.0896165 + 0.995976i \(0.528564\pi\)
\(524\) −11.9116 11.6550i −0.520362 0.509151i
\(525\) 12.1995 + 6.21595i 0.532430 + 0.271286i
\(526\) 16.7097 + 26.9375i 0.728579 + 1.17453i
\(527\) −43.0811 26.4001i −1.87664 1.15001i
\(528\) −12.6292 23.5062i −0.549615 1.02298i
\(529\) 2.57875 7.93659i 0.112120 0.345069i
\(530\) −3.36926 + 8.26105i −0.146351 + 0.358837i
\(531\) 0.319342 2.01624i 0.0138582 0.0874975i
\(532\) 0.240637 + 22.0971i 0.0104329 + 0.958030i
\(533\) −8.86789 36.7006i −0.384111 1.58968i
\(534\) 25.1890 0.137150i 1.09003 0.00593504i
\(535\) 3.93886 + 0.623854i 0.170292 + 0.0269716i
\(536\) −8.75460 + 22.1521i −0.378141 + 0.956826i
\(537\) −10.8800 3.53511i −0.469505 0.152551i
\(538\) 1.75248 + 3.39362i 0.0755546 + 0.146309i
\(539\) −2.82376 + 4.60796i −0.121628 + 0.198479i
\(540\) −5.96082 9.49355i −0.256513 0.408537i
\(541\) −13.2552 + 26.0148i −0.569887 + 1.11847i 0.408707 + 0.912666i \(0.365980\pi\)
−0.978594 + 0.205800i \(0.934020\pi\)
\(542\) −1.75247 1.73349i −0.0752751 0.0744598i
\(543\) −16.6128 + 5.39783i −0.712923 + 0.231643i
\(544\) −37.6502 1.93375i −1.61424 0.0829090i
\(545\) 9.89066 11.5805i 0.423669 0.496053i
\(546\) −27.9695 + 6.87615i −1.19698 + 0.294272i
\(547\) 23.7913 9.85467i 1.01724 0.421355i 0.189150 0.981948i \(-0.439427\pi\)
0.828091 + 0.560593i \(0.189427\pi\)
\(548\) −1.97991 22.0804i −0.0845778 0.943227i
\(549\) −10.4180 7.56908i −0.444627 0.323041i
\(550\) 23.1651 20.0040i 0.987762 0.852973i
\(551\) 3.42481 + 4.71384i 0.145902 + 0.200816i
\(552\) −18.8861 4.20912i −0.803845 0.179152i
\(553\) 17.2436 2.73111i 0.733270 0.116139i
\(554\) −10.1329 + 1.66150i −0.430506 + 0.0705904i
\(555\) 0.542640 2.26026i 0.0230338 0.0959427i
\(556\) −9.38675 + 6.97730i −0.398087 + 0.295903i
\(557\) −5.77222 6.75840i −0.244577 0.286363i 0.624516 0.781012i \(-0.285296\pi\)
−0.869092 + 0.494650i \(0.835296\pi\)
\(558\) 9.42568 13.1230i 0.399021 0.555541i
\(559\) 0.256624 + 3.26071i 0.0108540 + 0.137913i
\(560\) −4.63416 10.5330i −0.195829 0.445101i
\(561\) −43.2302 + 10.3786i −1.82518 + 0.438187i
\(562\) 29.4220 34.8310i 1.24109 1.46926i
\(563\) −0.315504 + 4.00885i −0.0132969 + 0.168953i 0.986683 + 0.162653i \(0.0520052\pi\)
−0.999980 + 0.00629960i \(0.997995\pi\)
\(564\) 8.28325 2.79147i 0.348788 0.117542i
\(565\) 8.77644 8.77644i 0.369228 0.369228i
\(566\) −8.67512 4.36086i −0.364642 0.183301i
\(567\) 5.32230 3.26151i 0.223516 0.136971i
\(568\) 5.64218 9.55405i 0.236740 0.400879i
\(569\) 2.20147 + 4.32063i 0.0922905 + 0.181130i 0.932537 0.361074i \(-0.117590\pi\)
−0.840247 + 0.542204i \(0.817590\pi\)
\(570\) −6.54979 2.08880i −0.274341 0.0874901i
\(571\) 15.6952 37.8917i 0.656825 1.58572i −0.145855 0.989306i \(-0.546593\pi\)
0.802680 0.596410i \(-0.203407\pi\)
\(572\) −9.37896 + 63.6983i −0.392154 + 2.66336i
\(573\) 16.7919i 0.701491i
\(574\) 9.95844 + 23.5797i 0.415657 + 0.984197i
\(575\) 22.1940i 0.925554i
\(576\) 1.49597 11.9623i 0.0623321 0.498430i
\(577\) −11.8371 + 28.5773i −0.492785 + 1.18969i 0.460512 + 0.887653i \(0.347666\pi\)
−0.953297 + 0.302034i \(0.902334\pi\)
\(578\) −11.7798 + 36.9375i −0.489974 + 1.53640i
\(579\) 9.06994 + 17.8008i 0.376934 + 0.739775i
\(580\) −2.60413 1.55706i −0.108130 0.0646534i
\(581\) 3.28778 2.01476i 0.136400 0.0835862i
\(582\) 2.39889 4.77214i 0.0994371 0.197812i
\(583\) −23.9290 + 23.9290i −0.991038 + 0.991038i
\(584\) −8.83147 + 3.02987i −0.365449 + 0.125377i
\(585\) −0.709557 + 9.01577i −0.0293366 + 0.372756i
\(586\) 12.2284 + 10.3295i 0.505152 + 0.426706i
\(587\) 1.42885 0.343035i 0.0589748 0.0141586i −0.203851 0.979002i \(-0.565346\pi\)
0.262825 + 0.964843i \(0.415346\pi\)
\(588\) 2.22477 0.950044i 0.0917481 0.0391792i
\(589\) −2.32520 29.5445i −0.0958082 1.21736i
\(590\) 1.58363 + 1.13745i 0.0651971 + 0.0468282i
\(591\) −6.87952 8.05489i −0.282986 0.331334i
\(592\) 5.95153 4.52530i 0.244606 0.185989i
\(593\) −1.56458 + 6.51696i −0.0642497 + 0.267619i −0.995244 0.0974147i \(-0.968943\pi\)
0.930994 + 0.365034i \(0.118943\pi\)
\(594\) −6.88007 41.9591i −0.282293 1.72160i
\(595\) −18.9365 + 2.99925i −0.776322 + 0.122957i
\(596\) −27.8037 6.35567i −1.13888 0.260338i
\(597\) −3.37537 4.64580i −0.138145 0.190140i
\(598\) 30.5140 + 35.3359i 1.24781 + 1.44499i
\(599\) −28.8635 20.9706i −1.17933 0.856835i −0.187236 0.982315i \(-0.559953\pi\)
−0.992096 + 0.125480i \(0.959953\pi\)
\(600\) −13.6389 + 1.29787i −0.556804 + 0.0529853i
\(601\) 20.5544 8.51389i 0.838430 0.347289i 0.0781955 0.996938i \(-0.475084\pi\)
0.760234 + 0.649649i \(0.225084\pi\)
\(602\) −0.529364 2.15324i −0.0215753 0.0877597i
\(603\) −8.24184 + 9.64995i −0.335634 + 0.392976i
\(604\) −0.288155 + 4.25298i −0.0117249 + 0.173051i
\(605\) −18.2033 + 5.91461i −0.740070 + 0.240463i
\(606\) 7.45792 7.53958i 0.302957 0.306274i
\(607\) −12.8383 + 25.1966i −0.521091 + 1.02270i 0.469122 + 0.883134i \(0.344571\pi\)
−0.990213 + 0.139566i \(0.955429\pi\)
\(608\) −12.0626 18.5324i −0.489203 0.751588i
\(609\) 2.69000 4.38968i 0.109004 0.177879i
\(610\) 10.9284 5.64348i 0.442480 0.228498i
\(611\) −20.0585 6.51742i −0.811482 0.263666i
\(612\) −18.6395 7.48398i −0.753456 0.302522i
\(613\) −38.9074 6.16232i −1.57145 0.248894i −0.690939 0.722913i \(-0.742803\pi\)
−0.880515 + 0.474019i \(0.842803\pi\)
\(614\) 0.0627392 + 11.5227i 0.00253195 + 0.465019i
\(615\) −7.93753 + 0.636394i −0.320072 + 0.0256619i
\(616\) −0.712934 43.6425i −0.0287249 1.75841i
\(617\) −5.17938 + 32.7013i −0.208514 + 1.31651i 0.632106 + 0.774882i \(0.282191\pi\)
−0.840620 + 0.541625i \(0.817809\pi\)
\(618\) −1.79328 0.731387i −0.0721363 0.0294207i
\(619\) 7.10767 21.8751i 0.285681 0.879236i −0.700512 0.713640i \(-0.747045\pi\)
0.986194 0.165596i \(-0.0529548\pi\)
\(620\) 7.15547 + 13.6732i 0.287370 + 0.549130i
\(621\) −26.2888 16.1098i −1.05493 0.646464i
\(622\) −18.2838 + 11.3417i −0.733115 + 0.454762i
\(623\) 36.7125 + 18.7060i 1.47086 + 0.749439i
\(624\) 19.9305 20.8181i 0.797860 0.833393i
\(625\) −3.25562 10.0198i −0.130225 0.400790i
\(626\) −5.94130 0.435055i −0.237462 0.0173883i
\(627\) −19.8288 16.9354i −0.791887 0.676335i
\(628\) −1.15531 4.59137i −0.0461019 0.183216i
\(629\) −4.76701 11.5086i −0.190073 0.458877i
\(630\) −0.514299 6.10933i −0.0204902 0.243401i
\(631\) −10.0247 + 13.7979i −0.399078 + 0.549284i −0.960512 0.278238i \(-0.910250\pi\)
0.561434 + 0.827521i \(0.310250\pi\)
\(632\) −13.0968 + 11.5610i −0.520965 + 0.459872i
\(633\) 24.8400 18.0473i 0.987300 0.717316i
\(634\) −8.59609 2.01430i −0.341394 0.0799981i
\(635\) 1.98839 + 12.5542i 0.0789067 + 0.498197i
\(636\) 14.9348 2.53245i 0.592205 0.100418i
\(637\) −5.67577 1.36263i −0.224882 0.0539894i
\(638\) −6.81522 9.27373i −0.269817 0.367151i
\(639\) 4.49521 3.83927i 0.177828 0.151879i
\(640\) 9.56668 + 6.40827i 0.378156 + 0.253309i
\(641\) 16.4218 1.29242i 0.648623 0.0510477i 0.250120 0.968215i \(-0.419530\pi\)
0.398503 + 0.917167i \(0.369530\pi\)
\(642\) −2.62521 6.24148i −0.103609 0.246331i
\(643\) −6.57355 27.3808i −0.259236 1.07979i −0.938329 0.345743i \(-0.887627\pi\)
0.679094 0.734052i \(-0.262373\pi\)
\(644\) −24.2899 20.2923i −0.957155 0.799627i
\(645\) 0.687693 + 0.0541226i 0.0270779 + 0.00213108i
\(646\) −34.9760 + 11.5753i −1.37611 + 0.455424i
\(647\) 22.9661 + 22.9661i 0.902891 + 0.902891i 0.995685 0.0927947i \(-0.0295800\pi\)
−0.0927947 + 0.995685i \(0.529580\pi\)
\(648\) −2.74438 + 5.61088i −0.107810 + 0.220416i
\(649\) 3.86425 + 6.30588i 0.151685 + 0.247528i
\(650\) 28.2797 + 17.1187i 1.10922 + 0.671452i
\(651\) −23.3317 + 11.8881i −0.914443 + 0.465932i
\(652\) 8.53851 + 2.67189i 0.334394 + 0.104639i
\(653\) 28.8241 + 11.9393i 1.12797 + 0.467222i 0.867091 0.498149i \(-0.165987\pi\)
0.260882 + 0.965371i \(0.415987\pi\)
\(654\) −25.5609 3.90591i −0.999512 0.152733i
\(655\) 8.48055 0.331362
\(656\) −21.0652 14.5690i −0.822459 0.568824i
\(657\) −4.97446 −0.194072
\(658\) 14.1340 + 2.15978i 0.550999 + 0.0841970i
\(659\) −8.95101 3.70763i −0.348682 0.144429i 0.201467 0.979495i \(-0.435429\pi\)
−0.550149 + 0.835067i \(0.685429\pi\)
\(660\) 12.9593 + 4.05526i 0.504440 + 0.157851i
\(661\) 24.4706 12.4684i 0.951795 0.484964i 0.0920877 0.995751i \(-0.470646\pi\)
0.859707 + 0.510787i \(0.170646\pi\)
\(662\) 38.7272 + 23.4430i 1.50518 + 0.911138i
\(663\) −25.0894 40.9422i −0.974392 1.59006i
\(664\) −1.69531 + 3.46605i −0.0657907 + 0.134509i
\(665\) −7.95173 7.95173i −0.308355 0.308355i
\(666\) 3.78167 1.25154i 0.146537 0.0484963i
\(667\) −8.31957 0.654764i −0.322135 0.0253526i
\(668\) 22.7361 + 18.9942i 0.879687 + 0.734909i
\(669\) 8.11627 + 33.8067i 0.313793 + 1.30704i
\(670\) −4.69948 11.1731i −0.181557 0.431654i
\(671\) 46.5094 3.66037i 1.79548 0.141307i
\(672\) −11.0497 + 16.1135i −0.426253 + 0.621591i
\(673\) 13.0713 11.1639i 0.503860 0.430337i −0.360839 0.932628i \(-0.617509\pi\)
0.864699 + 0.502291i \(0.167509\pi\)
\(674\) 13.4279 + 18.2719i 0.517225 + 0.703808i
\(675\) −21.2277 5.09633i −0.817056 0.196158i
\(676\) −42.9273 + 7.27905i −1.65105 + 0.279963i
\(677\) 0.397260 + 2.50820i 0.0152680 + 0.0963981i 0.994146 0.108049i \(-0.0344604\pi\)
−0.978878 + 0.204447i \(0.934460\pi\)
\(678\) −20.5180 4.80792i −0.787987 0.184647i
\(679\) 7.06822 5.13536i 0.271253 0.197077i
\(680\) 14.3827 12.6961i 0.551551 0.486872i
\(681\) 7.72457 10.6320i 0.296006 0.407418i
\(682\) 4.91036 + 58.3298i 0.188027 + 2.23357i
\(683\) −14.9592 36.1146i −0.572396 1.38189i −0.899510 0.436901i \(-0.856076\pi\)
0.327114 0.944985i \(-0.393924\pi\)
\(684\) −2.87482 11.4249i −0.109922 0.436844i
\(685\) 8.57841 + 7.32666i 0.327764 + 0.279937i
\(686\) −23.9611 1.75456i −0.914838 0.0669895i
\(687\) −2.63556 8.11143i −0.100553 0.309470i
\(688\) 1.60270 + 1.53436i 0.0611022 + 0.0584970i
\(689\) −32.5665 16.5934i −1.24068 0.632160i
\(690\) 8.36743 5.19044i 0.318543 0.197597i
\(691\) −0.230824 0.141449i −0.00878095 0.00538098i 0.518101 0.855319i \(-0.326639\pi\)
−0.526882 + 0.849938i \(0.676639\pi\)
\(692\) −6.03209 11.5266i −0.229306 0.438176i
\(693\) 7.18622 22.1169i 0.272982 0.840152i
\(694\) −25.1074 10.2400i −0.953062 0.388705i
\(695\) 0.931068 5.87853i 0.0353174 0.222985i
\(696\) 0.0841439 + 5.15090i 0.00318947 + 0.195245i
\(697\) −32.4084 + 27.7616i −1.22756 + 1.05154i
\(698\) −0.0246672 4.53040i −0.000933668 0.171478i
\(699\) −13.7155 2.17232i −0.518768 0.0821647i
\(700\) −20.7968 8.35017i −0.786045 0.315607i
\(701\) −2.97243 0.965800i −0.112267 0.0364778i 0.252345 0.967637i \(-0.418798\pi\)
−0.364612 + 0.931160i \(0.618798\pi\)
\(702\) 40.8043 21.0715i 1.54006 0.795291i
\(703\) 3.81757 6.22971i 0.143982 0.234958i
\(704\) 24.0248 + 36.4746i 0.905469 + 1.37469i
\(705\) −2.01940 + 3.96329i −0.0760550 + 0.149266i
\(706\) 6.16934 6.23689i 0.232186 0.234728i
\(707\) 16.4981 5.36055i 0.620474 0.201604i
\(708\) 0.223787 3.30295i 0.00841043 0.124132i
\(709\) −23.8381 + 27.9108i −0.895259 + 1.04821i 0.103305 + 0.994650i \(0.467058\pi\)
−0.998564 + 0.0535640i \(0.982942\pi\)
\(710\) 1.34799 + 5.48311i 0.0505893 + 0.205777i
\(711\) −8.59898 + 3.56181i −0.322487 + 0.133578i
\(712\) −41.0441 + 3.90575i −1.53819 + 0.146374i
\(713\) 34.3399 + 24.9494i 1.28604 + 0.934362i
\(714\) 21.2758 + 24.6379i 0.796228 + 0.922049i
\(715\) −19.2584 26.5069i −0.720222 0.991301i
\(716\) 18.2537 + 4.17264i 0.682174 + 0.155939i
\(717\) 4.68272 0.741669i 0.174879 0.0276982i
\(718\) 1.60731 + 9.80240i 0.0599841 + 0.365822i
\(719\) −11.5267 + 48.0122i −0.429874 + 1.79055i 0.164513 + 0.986375i \(0.447395\pi\)
−0.594387 + 0.804179i \(0.702605\pi\)
\(720\) 3.71318 + 4.88346i 0.138382 + 0.181996i
\(721\) −2.05742 2.40892i −0.0766222 0.0897130i
\(722\) 4.27304 + 3.06914i 0.159026 + 0.114221i
\(723\) 1.78320 + 22.6578i 0.0663181 + 0.842651i
\(724\) 26.2938 11.2282i 0.977202 0.417294i
\(725\) −5.74567 + 1.37941i −0.213389 + 0.0512301i
\(726\) 24.8260 + 20.9707i 0.921378 + 0.778295i
\(727\) 1.21844 15.4818i 0.0451895 0.574187i −0.932089 0.362229i \(-0.882016\pi\)
0.977279 0.211958i \(-0.0679841\pi\)
\(728\) 44.5918 15.2984i 1.65268 0.566997i
\(729\) −16.6278 + 16.6278i −0.615843 + 0.615843i
\(730\) 2.13396 4.24511i 0.0789814 0.157119i
\(731\) 3.15196 1.93152i 0.116579 0.0714399i
\(732\) −17.9237 10.7169i −0.662478 0.396109i
\(733\) −3.23601 6.35103i −0.119525 0.234581i 0.823490 0.567330i \(-0.192024\pi\)
−0.943015 + 0.332749i \(0.892024\pi\)
\(734\) −10.2062 + 32.0034i −0.376719 + 1.18127i
\(735\) −0.471102 + 1.13734i −0.0173769 + 0.0419514i
\(736\) 31.4042 + 4.10109i 1.15757 + 0.151168i
\(737\) 45.9766i 1.69357i
\(738\) −8.09694 10.9841i −0.298053 0.404330i
\(739\) 32.1492i 1.18263i 0.806441 + 0.591315i \(0.201391\pi\)
−0.806441 + 0.591315i \(0.798609\pi\)
\(740\) −0.554227 + 3.76409i −0.0203738 + 0.138371i
\(741\) 10.7781 26.0206i 0.395943 0.955890i
\(742\) 23.6070 + 7.52851i 0.866639 + 0.276380i
\(743\) −0.108777 0.213487i −0.00399065 0.00783209i 0.889003 0.457902i \(-0.151399\pi\)
−0.892993 + 0.450070i \(0.851399\pi\)
\(744\) 13.3240 22.5618i 0.488480 0.827157i
\(745\) 12.3750 7.58339i 0.453384 0.277834i
\(746\) 2.45732 + 1.23526i 0.0899689 + 0.0452261i
\(747\) −1.45361 + 1.45361i −0.0531847 + 0.0531847i
\(748\) 68.9584 23.2391i 2.52137 0.849707i
\(749\) 0.868998 11.0417i 0.0317525 0.403454i
\(750\) 10.1735 12.0438i 0.371483 0.439777i
\(751\) 8.87043 2.12960i 0.323687 0.0777103i −0.0683457 0.997662i \(-0.521772\pi\)
0.392032 + 0.919951i \(0.371772\pi\)
\(752\) −13.0956 + 5.76163i −0.477549 + 0.210105i
\(753\) 0.642296 + 8.16114i 0.0234066 + 0.297408i
\(754\) 7.25137 10.0958i 0.264079 0.367667i
\(755\) −1.40880 1.64949i −0.0512713 0.0600310i
\(756\) −24.9864 + 18.5727i −0.908746 + 0.675483i
\(757\) −6.98607 + 29.0991i −0.253913 + 1.05762i 0.689047 + 0.724717i \(0.258029\pi\)
−0.942960 + 0.332907i \(0.891971\pi\)
\(758\) 34.9320 5.72782i 1.26879 0.208044i
\(759\) 36.8889 5.84263i 1.33898 0.212074i
\(760\) 10.9831 + 2.44779i 0.398398 + 0.0887906i
\(761\) −4.54632 6.25748i −0.164804 0.226833i 0.718625 0.695397i \(-0.244772\pi\)
−0.883430 + 0.468564i \(0.844772\pi\)
\(762\) 16.3340 14.1050i 0.591717 0.510972i
\(763\) −34.2187 24.8613i −1.23880 0.900040i
\(764\) 2.45466 + 27.3748i 0.0888065 + 0.990386i
\(765\) 9.44323 3.91151i 0.341421 0.141421i
\(766\) 15.2939 3.75992i 0.552590 0.135851i
\(767\) −5.18770 + 6.07401i −0.187317 + 0.219320i
\(768\) 0.683771 19.5386i 0.0246735 0.705038i
\(769\) 18.7296 6.08562i 0.675407 0.219453i 0.0488235 0.998807i \(-0.484453\pi\)
0.626583 + 0.779354i \(0.284453\pi\)
\(770\) 15.7914 + 15.6204i 0.569083 + 0.562919i
\(771\) −0.167284 + 0.328314i −0.00602459 + 0.0118239i
\(772\) −17.3883 27.6937i −0.625820 0.996718i
\(773\) 17.8883 29.1911i 0.643398 1.04993i −0.350169 0.936687i \(-0.613876\pi\)
0.993567 0.113244i \(-0.0361241\pi\)
\(774\) 0.542397 + 1.05034i 0.0194961 + 0.0377536i
\(775\) 28.5834 + 9.28733i 1.02675 + 0.333611i
\(776\) −3.21317 + 8.13042i −0.115346 + 0.291865i
\(777\) −6.37634 1.00991i −0.228750 0.0362304i
\(778\) −12.3580 + 0.0672873i −0.443057 + 0.00241237i
\(779\) −24.3465 5.80737i −0.872302 0.208071i
\(780\) 0.159705 + 14.6653i 0.00571835 + 0.525103i
\(781\) −3.35038 + 21.1534i −0.119886 + 0.756930i
\(782\) 19.9274 48.8597i 0.712601 1.74722i
\(783\) −2.53665 + 7.80700i −0.0906524 + 0.278999i
\(784\) −3.48804 + 1.87402i −0.124573 + 0.0669294i
\(785\) 2.05426 + 1.25885i 0.0733197 + 0.0449304i
\(786\) −7.59019 12.2360i −0.270733 0.436444i
\(787\) −17.2723 8.80068i −0.615691 0.313710i 0.118187 0.992991i \(-0.462292\pi\)
−0.733878 + 0.679281i \(0.762292\pi\)
\(788\) 12.3928 + 12.1258i 0.441474 + 0.431962i
\(789\) 8.46361 + 26.0483i 0.301312 + 0.927344i
\(790\) 0.649229 8.86617i 0.0230985 0.315444i
\(791\) −26.2122 22.3873i −0.931999 0.796003i
\(792\) 5.80108 + 22.5351i 0.206132 + 0.800750i
\(793\) 19.2829 + 46.5530i 0.684755 + 1.65314i
\(794\) −42.0685 + 3.54143i −1.49295 + 0.125681i
\(795\) −4.53096 + 6.23634i −0.160697 + 0.221180i
\(796\) 6.18180 + 7.08035i 0.219108 + 0.250957i
\(797\) −36.8726 + 26.7895i −1.30609 + 0.948933i −0.999995 0.00306705i \(-0.999024\pi\)
−0.306099 + 0.952000i \(0.599024\pi\)
\(798\) −4.35613 + 18.5899i −0.154205 + 0.658075i
\(799\) 3.72895 + 23.5437i 0.131921 + 0.832916i
\(800\) 22.0449 4.10959i 0.779405 0.145296i
\(801\) −21.3594 5.12795i −0.754699 0.181187i
\(802\) −22.5351 + 16.5609i −0.795742 + 0.584787i
\(803\) 13.7040 11.7044i 0.483605 0.413038i
\(804\) −11.9148 + 16.7806i −0.420203 + 0.591806i
\(805\) 16.0568 1.26370i 0.565929 0.0445396i
\(806\) −58.2778 + 24.5120i −2.05275 + 0.863399i
\(807\) 0.770380 + 3.20886i 0.0271186 + 0.112957i
\(808\) −11.0561 + 13.3815i −0.388951 + 0.470761i
\(809\) −15.0923 1.18779i −0.530618 0.0417605i −0.189679 0.981846i \(-0.560745\pi\)
−0.340939 + 0.940086i \(0.610745\pi\)
\(810\) −0.998659 3.01755i −0.0350893 0.106026i
\(811\) 1.28504 + 1.28504i 0.0451239 + 0.0451239i 0.729309 0.684185i \(-0.239842\pi\)
−0.684185 + 0.729309i \(0.739842\pi\)
\(812\) −3.74366 + 7.54947i −0.131377 + 0.264934i
\(813\) −1.11281 1.81595i −0.0390281 0.0636881i
\(814\) −7.47329 + 12.3457i −0.261939 + 0.432716i
\(815\) −4.05662 + 2.06695i −0.142097 + 0.0724021i
\(816\) −31.1910 9.38870i −1.09190 0.328670i
\(817\) 2.00321 + 0.829756i 0.0700834 + 0.0290295i
\(818\) 3.36269 22.0060i 0.117574 0.769421i
\(819\) 25.1170 0.877661
\(820\) 12.8471 2.19780i 0.448639 0.0767503i
\(821\) −4.08752 −0.142656 −0.0713278 0.997453i \(-0.522724\pi\)
−0.0713278 + 0.997453i \(0.522724\pi\)
\(822\) 2.89336 18.9346i 0.100918 0.660422i
\(823\) −34.5766 14.3221i −1.20526 0.499236i −0.312567 0.949896i \(-0.601189\pi\)
−0.892696 + 0.450659i \(0.851189\pi\)
\(824\) 3.03040 + 0.930194i 0.105569 + 0.0324049i
\(825\) 23.5626 12.0058i 0.820345 0.417987i
\(826\) 2.80424 4.63254i 0.0975722 0.161187i
\(827\) −12.1105 19.7625i −0.421122 0.687208i 0.569780 0.821797i \(-0.307029\pi\)
−0.990901 + 0.134589i \(0.957029\pi\)
\(828\) 15.1171 + 7.49632i 0.525355 + 0.260515i
\(829\) 25.9686 + 25.9686i 0.901926 + 0.901926i 0.995603 0.0936763i \(-0.0298619\pi\)
−0.0936763 + 0.995603i \(0.529862\pi\)
\(830\) −0.616909 1.86405i −0.0214132 0.0647023i
\(831\) −8.84460 0.696085i −0.306816 0.0241469i
\(832\) −29.4484 + 36.8521i −1.02094 + 1.27762i
\(833\) 1.54007 + 6.41484i 0.0533602 + 0.222261i
\(834\) −9.31505 + 3.91798i −0.322554 + 0.135668i
\(835\) −15.0297 + 1.18287i −0.520125 + 0.0409347i
\(836\) 34.8014 + 24.7102i 1.20363 + 0.854621i
\(837\) 31.7485 27.1158i 1.09739 0.937258i
\(838\) 21.4225 15.7432i 0.740027 0.543841i
\(839\) −48.1591 11.5620i −1.66264 0.399164i −0.710224 0.703976i \(-0.751406\pi\)
−0.952413 + 0.304812i \(0.901406\pi\)
\(840\) −1.71556 9.79349i −0.0591924 0.337907i
\(841\) −4.18903 26.4485i −0.144449 0.912016i
\(842\) 5.58155 23.8194i 0.192353 0.820872i
\(843\) 31.8709 23.1555i 1.09769 0.797519i
\(844\) −37.8570 + 33.0526i −1.30309 + 1.13772i
\(845\) 13.0234 17.9251i 0.448018 0.616644i
\(846\) −7.59569 + 0.639425i −0.261145 + 0.0219839i
\(847\) 20.3427 + 49.1116i 0.698983 + 1.68749i
\(848\) −23.9772 + 6.31171i −0.823380 + 0.216745i
\(849\) −6.37922 5.44836i −0.218934 0.186987i
\(850\) 2.72855 37.2623i 0.0935884 1.27808i
\(851\) 3.23377 + 9.95251i 0.110852 + 0.341168i
\(852\) 6.70473 6.85237i 0.229700 0.234758i
\(853\) −25.9549 13.2247i −0.888677 0.452804i −0.0508292 0.998707i \(-0.516186\pi\)
−0.837848 + 0.545904i \(0.816186\pi\)
\(854\) −18.0067 29.0284i −0.616178 0.993331i
\(855\) 5.11172 + 3.13247i 0.174817 + 0.107128i
\(856\) 5.19211 + 9.79136i 0.177463 + 0.334662i
\(857\) −3.50414 + 10.7846i −0.119699 + 0.368396i −0.992898 0.118968i \(-0.962041\pi\)
0.873199 + 0.487364i \(0.162041\pi\)
\(858\) −21.0085 + 51.5105i −0.717219 + 1.75854i
\(859\) 0.209762 1.32438i 0.00715697 0.0451873i −0.983851 0.178987i \(-0.942718\pi\)
0.991008 + 0.133800i \(0.0427179\pi\)
\(860\) −1.12902 + 0.0122950i −0.0384992 + 0.000419255i
\(861\) 3.49165 + 21.8384i 0.118995 + 0.744250i
\(862\) 5.62879 0.0306478i 0.191717 0.00104387i
\(863\) 43.7611 + 6.93108i 1.48965 + 0.235937i 0.847561 0.530697i \(-0.178070\pi\)
0.642084 + 0.766634i \(0.278070\pi\)
\(864\) 11.1338 29.0952i 0.378778 0.989838i
\(865\) 6.29629 + 2.04579i 0.214080 + 0.0695589i
\(866\) −9.07895 17.5811i −0.308515 0.597431i
\(867\) −17.5029 + 28.5621i −0.594429 + 0.970020i
\(868\) 36.2986 22.7912i 1.23205 0.773583i
\(869\) 15.3086 30.0448i 0.519309 1.01920i
\(870\) −1.86378 1.84359i −0.0631880 0.0625036i
\(871\) 47.2273 15.3451i 1.60024 0.519948i
\(872\) 42.2415 + 2.63105i 1.43048 + 0.0890985i
\(873\) −3.02497 + 3.54179i −0.102380 + 0.119871i
\(874\) 30.0550 7.38886i 1.01662 0.249932i
\(875\) 23.8255 9.86883i 0.805448 0.333627i
\(876\) −8.03491 + 0.720478i −0.271474 + 0.0243427i
\(877\) −44.3128 32.1951i −1.49634 1.08715i −0.971812 0.235758i \(-0.924243\pi\)
−0.524525 0.851395i \(-0.675757\pi\)
\(878\) −14.9028 + 12.8692i −0.502945 + 0.434314i
\(879\) 8.12942 + 11.1892i 0.274199 + 0.377402i
\(880\) −21.7196 4.71664i −0.732168 0.158998i
\(881\) −11.7169 + 1.85578i −0.394754 + 0.0625228i −0.350656 0.936504i \(-0.614041\pi\)
−0.0440978 + 0.999027i \(0.514041\pi\)
\(882\) −2.08180 + 0.341355i −0.0700979 + 0.0114940i
\(883\) −10.1860 + 42.4279i −0.342788 + 1.42781i 0.488788 + 0.872402i \(0.337439\pi\)
−0.831576 + 0.555411i \(0.812561\pi\)
\(884\) 46.8868 + 63.0781i 1.57697 + 2.12155i
\(885\) 1.09410 + 1.28103i 0.0367778 + 0.0430612i
\(886\) −1.36401 + 1.89905i −0.0458247 + 0.0638000i
\(887\) −2.83633 36.0390i −0.0952347 1.21007i −0.839941 0.542678i \(-0.817410\pi\)
0.744706 0.667393i \(-0.232590\pi\)
\(888\) 5.92700 2.56925i 0.198897 0.0862184i
\(889\) 34.3261 8.24097i 1.15126 0.276393i
\(890\) 13.5389 16.0279i 0.453826 0.537258i
\(891\) 0.945929 12.0192i 0.0316898 0.402657i
\(892\) −18.1734 53.9267i −0.608490 1.80560i
\(893\) −9.88634 + 9.88634i −0.330834 + 0.330834i
\(894\) −22.0173 11.0678i −0.736368 0.370162i
\(895\) −8.12444 + 4.97867i −0.271570 + 0.166418i
\(896\) 15.6583 27.8841i 0.523106 0.931544i
\(897\) 18.3136 + 35.9424i 0.611472 + 1.20008i
\(898\) −37.5566 11.9772i −1.25328 0.399685i
\(899\) 4.32468 10.4407i 0.144236 0.348217i
\(900\) 11.8201 + 1.74039i 0.394002 + 0.0580130i
\(901\) 41.3096i 1.37622i
\(902\) 48.1504 + 11.2086i 1.60323 + 0.373206i
\(903\) 1.91584i 0.0637553i
\(904\) 34.1521 + 4.83873i 1.13588 + 0.160934i
\(905\) −5.56779 + 13.4418i −0.185080 + 0.446822i
\(906\) −1.11905 + 3.50897i −0.0371778 + 0.116578i
\(907\) 19.9743 + 39.2018i 0.663236 + 1.30167i 0.940144 + 0.340778i \(0.110691\pi\)
−0.276907 + 0.960897i \(0.589309\pi\)
\(908\) −11.0387 + 18.4619i −0.366333 + 0.612678i
\(909\) −7.88529 + 4.83211i −0.261538 + 0.160271i
\(910\) −10.7748 + 21.4344i −0.357181 + 0.710544i
\(911\) 12.2607 12.2607i 0.406216 0.406216i −0.474201 0.880417i \(-0.657263\pi\)
0.880417 + 0.474201i \(0.157263\pi\)
\(912\) −6.29824 18.0376i −0.208555 0.597283i
\(913\) 0.584336 7.42469i 0.0193387 0.245721i
\(914\) −1.33642 1.12888i −0.0442048 0.0373401i
\(915\) 10.3335 2.48084i 0.341614 0.0820142i
\(916\) 5.48234 + 12.8383i 0.181142 + 0.424190i
\(917\) −1.84796 23.4805i −0.0610249 0.775395i
\(918\) −42.1566 30.2792i −1.39137 0.999363i
\(919\) −23.2820 27.2598i −0.768004 0.899217i 0.229243 0.973369i \(-0.426375\pi\)
−0.997247 + 0.0741523i \(0.976375\pi\)
\(920\) −12.8822 + 9.68484i −0.424713 + 0.319300i
\(921\) −2.32419 + 9.68093i −0.0765845 + 0.318997i
\(922\) 4.37241 + 26.6658i 0.143998 + 0.878193i
\(923\) −22.8471 + 3.61863i −0.752022 + 0.119109i
\(924\) 8.40410 36.7648i 0.276474 1.20947i
\(925\) 4.35524 + 5.99448i 0.143199 + 0.197097i
\(926\) −23.6500 27.3872i −0.777187 0.900000i
\(927\) 1.36634 + 0.992707i 0.0448766 + 0.0326048i
\(928\) −0.890141 8.38492i −0.0292203 0.275248i
\(929\) −12.8165 + 5.30875i −0.420494 + 0.174175i −0.582890 0.812551i \(-0.698078\pi\)
0.162395 + 0.986726i \(0.448078\pi\)
\(930\) 3.18328 + 12.9483i 0.104384 + 0.424592i
\(931\) −2.51301 + 2.94236i −0.0823607 + 0.0964320i
\(932\) 22.6771 + 1.53646i 0.742814 + 0.0503284i
\(933\) −17.6803 + 5.74468i −0.578827 + 0.188072i
\(934\) −17.6015 + 17.7942i −0.575939 + 0.582245i
\(935\) −16.8116 + 32.9946i −0.549798 + 1.07904i
\(936\) −21.2120 + 13.4802i −0.693335 + 0.440613i
\(937\) 26.1176 42.6201i 0.853226 1.39234i −0.0656718 0.997841i \(-0.520919\pi\)
0.918897 0.394496i \(-0.129081\pi\)
\(938\) −29.9115 + 15.4464i −0.976644 + 0.504342i
\(939\) −4.89523 1.59056i −0.159750 0.0519058i
\(940\) 2.71275 6.75633i 0.0884801 0.220367i
\(941\) 6.95395 + 1.10140i 0.226692 + 0.0359045i 0.268747 0.963211i \(-0.413390\pi\)
−0.0420548 + 0.999115i \(0.513390\pi\)
\(942\) −0.0222728 4.09064i −0.000725687 0.133280i
\(943\) 28.9715 21.1139i 0.943442 0.687564i
\(944\) 0.118003 + 5.41732i 0.00384067 + 0.176319i
\(945\) 2.47839 15.6479i 0.0806220 0.509027i
\(946\) −3.96557 1.61735i −0.128932 0.0525847i
\(947\) −14.3484 + 44.1599i −0.466261 + 1.43500i 0.391130 + 0.920336i \(0.372084\pi\)
−0.857390 + 0.514667i \(0.827916\pi\)
\(948\) −13.3735 + 6.99859i −0.434350 + 0.227304i
\(949\) 16.5966 + 10.1704i 0.538749 + 0.330146i
\(950\) 18.6223 11.5517i 0.604189 0.374787i
\(951\) −6.79694 3.46321i −0.220406 0.112302i
\(952\) −38.2863 37.0556i −1.24087 1.20098i
\(953\) −14.6011 44.9375i −0.472976 1.45567i −0.848668 0.528925i \(-0.822595\pi\)
0.375693 0.926744i \(-0.377405\pi\)
\(954\) −13.1746 0.964714i −0.426542 0.0312338i
\(955\) −10.6353 9.08344i −0.344152 0.293933i
\(956\) −7.52554 + 1.89363i −0.243393 + 0.0612443i
\(957\) −3.80530 9.18680i −0.123008 0.296967i
\(958\) 3.93727 + 46.7706i 0.127207 + 1.51109i
\(959\) 18.4164 25.3480i 0.594697 0.818530i
\(960\) 6.70494 + 7.35012i 0.216401 + 0.237224i
\(961\) −21.4224 + 15.5643i −0.691047 + 0.502075i
\(962\) −15.1758 3.55611i −0.489288 0.114654i
\(963\) 0.923704 + 5.83204i 0.0297659 + 0.187935i
\(964\) −6.21920 36.6770i −0.200307 1.18129i
\(965\) 16.1807 + 3.88463i 0.520874 + 0.125051i
\(966\) −16.1944 22.0363i −0.521045 0.709006i
\(967\) 4.47217 3.81960i 0.143815 0.122830i −0.574630 0.818413i \(-0.694854\pi\)
0.718445 + 0.695583i \(0.244854\pi\)
\(968\) −43.5378 30.5582i −1.39936 0.982177i
\(969\) −31.7338 + 2.49750i −1.01944 + 0.0802314i
\(970\) −1.72483 4.10082i −0.0553811 0.131669i
\(971\) 6.66976 + 27.7816i 0.214043 + 0.891553i 0.971190 + 0.238308i \(0.0765928\pi\)
−0.757147 + 0.653245i \(0.773407\pi\)
\(972\) 17.7244 21.2162i 0.568512 0.680510i
\(973\) −16.4791 1.29693i −0.528295 0.0415777i
\(974\) 22.4179 7.41922i 0.718317 0.237727i
\(975\) 20.1966 + 20.1966i 0.646808 + 0.646808i
\(976\) 30.7865 + 14.8511i 0.985453 + 0.475372i
\(977\) 7.89289 + 12.8800i 0.252516 + 0.412068i 0.953630 0.300980i \(-0.0973138\pi\)
−0.701115 + 0.713049i \(0.747314\pi\)
\(978\) 6.61298 + 4.00308i 0.211460 + 0.128004i
\(979\) 70.9082 36.1295i 2.26623 1.15470i
\(980\) 0.601752 1.92301i 0.0192223 0.0614282i
\(981\) 20.8327 + 8.62919i 0.665137 + 0.275509i
\(982\) −51.9003 7.93078i −1.65621 0.253081i
\(983\) 33.9174 1.08180 0.540899 0.841088i \(-0.318084\pi\)
0.540899 + 0.841088i \(0.318084\pi\)
\(984\) −14.6693 16.5691i −0.467641 0.528204i
\(985\) −8.82309 −0.281127
\(986\) −13.8875 2.12212i −0.442268 0.0675821i
\(987\) 11.4134 + 4.72759i 0.363293 + 0.150481i
\(988\) −13.7671 + 43.9954i −0.437991 + 1.39968i
\(989\) −2.76704 + 1.40988i −0.0879868 + 0.0448315i
\(990\) −10.1301 6.13213i −0.321956 0.194892i
\(991\) 1.44515 + 2.35828i 0.0459068 + 0.0749131i 0.874770 0.484538i \(-0.161012\pi\)
−0.828864 + 0.559451i \(0.811012\pi\)
\(992\) −18.4232 + 38.7290i −0.584936 + 1.22965i
\(993\) 27.6579 + 27.6579i 0.877697 + 0.877697i
\(994\) 14.8876 4.92706i 0.472207 0.156277i
\(995\) −4.76835 0.375278i −0.151167 0.0118971i
\(996\) −2.13738 + 2.55845i −0.0677254 + 0.0810675i
\(997\) −0.754270 3.14176i −0.0238880 0.0995005i 0.959152 0.282890i \(-0.0912931\pi\)
−0.983040 + 0.183389i \(0.941293\pi\)
\(998\) −15.6417 37.1885i −0.495131 1.17718i
\(999\) 10.2618 0.807618i 0.324668 0.0255519i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 164.2.o.b.111.2 yes 288
4.3 odd 2 inner 164.2.o.b.111.18 yes 288
41.17 odd 40 inner 164.2.o.b.99.18 yes 288
164.99 even 40 inner 164.2.o.b.99.2 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.99.2 288 164.99 even 40 inner
164.2.o.b.99.18 yes 288 41.17 odd 40 inner
164.2.o.b.111.2 yes 288 1.1 even 1 trivial
164.2.o.b.111.18 yes 288 4.3 odd 2 inner