Properties

Label 414.2.m.a.25.8
Level $414$
Weight $2$
Character 414.25
Analytic conductor $3.306$
Analytic rank $0$
Dimension $240$
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] = [414,2,Mod(13,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([22, 42]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.m (of order \(33\), degree \(20\), 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: \(3.30580664368\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 25.8
Character \(\chi\) \(=\) 414.25
Dual form 414.2.m.a.265.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.888835 - 0.458227i) q^{2} +(0.715945 + 1.57716i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.904639 + 3.72897i) q^{5} +(1.35905 + 1.07377i) q^{6} +(-0.0597010 - 0.172495i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-1.97485 + 2.25831i) q^{9} +O(q^{10})\) \(q+(0.888835 - 0.458227i) q^{2} +(0.715945 + 1.57716i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.904639 + 3.72897i) q^{5} +(1.35905 + 1.07377i) q^{6} +(-0.0597010 - 0.172495i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-1.97485 + 2.25831i) q^{9} +(2.51279 + 2.89991i) q^{10} +(-0.262786 - 5.51655i) q^{11} +(1.70000 + 0.331649i) q^{12} +(-0.752105 + 2.17306i) q^{13} +(-0.132106 - 0.125963i) q^{14} +(-5.23350 + 4.09649i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(-0.0745087 + 0.163151i) q^{17} +(-0.720494 + 2.91220i) q^{18} +(1.78293 + 3.90407i) q^{19} +(3.56227 + 1.42612i) q^{20} +(0.229309 - 0.217654i) q^{21} +(-2.76140 - 4.78289i) q^{22} +(0.209580 - 4.79125i) q^{23} +(1.66299 - 0.484205i) q^{24} +(-8.64268 + 4.45561i) q^{25} +(0.327258 + 2.27613i) q^{26} +(-4.97560 - 1.49781i) q^{27} +(-0.175140 - 0.0514257i) q^{28} +(0.919561 + 1.29134i) q^{29} +(-2.77460 + 6.03924i) q^{30} +(5.98311 - 2.39527i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(8.51233 - 4.36400i) q^{33} +(0.00853428 + 0.179157i) q^{34} +(0.589220 - 0.378669i) q^{35} +(0.694045 + 2.91861i) q^{36} +(8.67245 - 2.54646i) q^{37} +(3.37368 + 2.65309i) q^{38} +(-3.96573 + 0.369606i) q^{39} +(3.81976 - 0.364743i) q^{40} +(-1.39248 - 5.73988i) q^{41} +(0.104083 - 0.298534i) q^{42} +(1.11960 + 0.448219i) q^{43} +(-4.64608 - 2.98586i) q^{44} +(-10.2077 - 5.32119i) q^{45} +(-2.00920 - 4.35467i) q^{46} +(3.32763 - 5.76363i) q^{47} +(1.25625 - 1.19241i) q^{48} +(5.47618 - 4.30652i) q^{49} +(-5.64024 + 7.92061i) q^{50} +(-0.310659 - 0.000704600i) q^{51} +(1.33386 + 1.87315i) q^{52} +(-6.95356 + 8.02484i) q^{53} +(-5.10882 + 0.948639i) q^{54} +(20.3333 - 5.97041i) q^{55} +(-0.179235 + 0.0345448i) q^{56} +(-4.88085 + 5.60706i) q^{57} +(1.40907 + 0.726424i) q^{58} +(-1.80948 + 5.22815i) q^{59} +(0.301177 + 6.63928i) q^{60} +(-3.78466 - 2.97629i) q^{61} +(4.22042 - 4.87062i) q^{62} +(0.507447 + 0.205827i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-8.78368 - 0.838739i) q^{65} +(5.56636 - 7.77945i) q^{66} +(-0.525122 + 11.0237i) q^{67} +(0.0896799 + 0.155330i) q^{68} +(7.70660 - 3.09973i) q^{69} +(0.350203 - 0.606570i) q^{70} +(-8.71162 - 5.59862i) q^{71} +(1.95428 + 2.27614i) q^{72} +(-6.29065 - 13.7746i) q^{73} +(6.54152 - 6.23733i) q^{74} +(-13.2149 - 10.4409i) q^{75} +(4.21436 + 0.812251i) q^{76} +(-0.935887 + 0.374673i) q^{77} +(-3.35552 + 2.14572i) q^{78} +(7.03025 - 1.35497i) q^{79} +(3.22800 - 2.07451i) q^{80} +(-1.19996 - 8.91965i) q^{81} +(-3.86785 - 4.46374i) q^{82} +(-1.75630 + 7.23955i) q^{83} +(-0.0442841 - 0.313041i) q^{84} +(-0.675790 - 0.130248i) q^{85} +(1.20052 - 0.114636i) q^{86} +(-1.37829 + 2.37482i) q^{87} +(-5.49780 - 0.524976i) q^{88} +(0.259343 + 1.80377i) q^{89} +(-11.5113 - 0.0522173i) q^{90} +0.419743 q^{91} +(-3.78127 - 2.94992i) q^{92} +(8.06130 + 7.72141i) q^{93} +(0.316670 - 6.64773i) q^{94} +(-12.9453 + 10.1803i) q^{95} +(0.570209 - 1.63550i) q^{96} +(-11.2521 + 10.7289i) q^{97} +(2.89406 - 6.33712i) q^{98} +(12.9771 + 10.3009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.888835 0.458227i 0.628502 0.324015i
\(3\) 0.715945 + 1.57716i 0.413351 + 0.910572i
\(4\) 0.580057 0.814576i 0.290028 0.407288i
\(5\) 0.904639 + 3.72897i 0.404567 + 1.66765i 0.701439 + 0.712729i \(0.252541\pi\)
−0.296872 + 0.954917i \(0.595944\pi\)
\(6\) 1.35905 + 1.07377i 0.554831 + 0.438364i
\(7\) −0.0597010 0.172495i −0.0225649 0.0651969i 0.933156 0.359472i \(-0.117043\pi\)
−0.955721 + 0.294275i \(0.904922\pi\)
\(8\) 0.142315 0.989821i 0.0503159 0.349955i
\(9\) −1.97485 + 2.25831i −0.658282 + 0.752771i
\(10\) 2.51279 + 2.89991i 0.794613 + 0.917033i
\(11\) −0.262786 5.51655i −0.0792329 1.66330i −0.592872 0.805297i \(-0.702006\pi\)
0.513639 0.858006i \(-0.328297\pi\)
\(12\) 1.70000 + 0.331649i 0.490748 + 0.0957389i
\(13\) −0.752105 + 2.17306i −0.208596 + 0.602700i −0.999963 0.00864270i \(-0.997249\pi\)
0.791366 + 0.611342i \(0.209370\pi\)
\(14\) −0.132106 0.125963i −0.0353068 0.0336650i
\(15\) −5.23350 + 4.09649i −1.35128 + 1.05771i
\(16\) −0.327068 0.945001i −0.0817670 0.236250i
\(17\) −0.0745087 + 0.163151i −0.0180710 + 0.0395700i −0.918452 0.395532i \(-0.870560\pi\)
0.900381 + 0.435102i \(0.143288\pi\)
\(18\) −0.720494 + 2.91220i −0.169822 + 0.686411i
\(19\) 1.78293 + 3.90407i 0.409032 + 0.895655i 0.996274 + 0.0862436i \(0.0274863\pi\)
−0.587242 + 0.809411i \(0.699786\pi\)
\(20\) 3.56227 + 1.42612i 0.796548 + 0.318890i
\(21\) 0.229309 0.217654i 0.0500392 0.0474961i
\(22\) −2.76140 4.78289i −0.588733 1.01972i
\(23\) 0.209580 4.79125i 0.0437005 0.999045i
\(24\) 1.66299 0.484205i 0.339457 0.0988378i
\(25\) −8.64268 + 4.45561i −1.72854 + 0.891122i
\(26\) 0.327258 + 2.27613i 0.0641806 + 0.446386i
\(27\) −4.97560 1.49781i −0.957554 0.288255i
\(28\) −0.175140 0.0514257i −0.0330983 0.00971855i
\(29\) 0.919561 + 1.29134i 0.170758 + 0.239796i 0.891083 0.453841i \(-0.149947\pi\)
−0.720325 + 0.693637i \(0.756007\pi\)
\(30\) −2.77460 + 6.03924i −0.506570 + 1.10261i
\(31\) 5.98311 2.39527i 1.07460 0.430204i 0.234208 0.972187i \(-0.424750\pi\)
0.840390 + 0.541982i \(0.182326\pi\)
\(32\) −0.723734 0.690079i −0.127939 0.121990i
\(33\) 8.51233 4.36400i 1.48181 0.759675i
\(34\) 0.00853428 + 0.179157i 0.00146362 + 0.0307251i
\(35\) 0.589220 0.378669i 0.0995963 0.0640067i
\(36\) 0.694045 + 2.91861i 0.115674 + 0.486436i
\(37\) 8.67245 2.54646i 1.42574 0.418635i 0.524299 0.851534i \(-0.324327\pi\)
0.901443 + 0.432899i \(0.142509\pi\)
\(38\) 3.37368 + 2.65309i 0.547283 + 0.430388i
\(39\) −3.96573 + 0.369606i −0.635025 + 0.0591844i
\(40\) 3.81976 0.364743i 0.603957 0.0576709i
\(41\) −1.39248 5.73988i −0.217469 0.896419i −0.971014 0.239023i \(-0.923173\pi\)
0.753545 0.657396i \(-0.228342\pi\)
\(42\) 0.104083 0.298534i 0.0160603 0.0460648i
\(43\) 1.11960 + 0.448219i 0.170737 + 0.0683528i 0.455456 0.890258i \(-0.349476\pi\)
−0.284719 + 0.958611i \(0.591900\pi\)
\(44\) −4.64608 2.98586i −0.700423 0.450135i
\(45\) −10.2077 5.32119i −1.52168 0.793236i
\(46\) −2.00920 4.35467i −0.296240 0.642061i
\(47\) 3.32763 5.76363i 0.485385 0.840712i −0.514474 0.857506i \(-0.672013\pi\)
0.999859 + 0.0167942i \(0.00534601\pi\)
\(48\) 1.25625 1.19241i 0.181324 0.172109i
\(49\) 5.47618 4.30652i 0.782312 0.615217i
\(50\) −5.64024 + 7.92061i −0.797650 + 1.12014i
\(51\) −0.310659 0.000704600i −0.0435010 9.86637e-5i
\(52\) 1.33386 + 1.87315i 0.184973 + 0.259759i
\(53\) −6.95356 + 8.02484i −0.955145 + 1.10230i 0.0395281 + 0.999218i \(0.487415\pi\)
−0.994673 + 0.103078i \(0.967131\pi\)
\(54\) −5.10882 + 0.948639i −0.695223 + 0.129093i
\(55\) 20.3333 5.97041i 2.74175 0.805049i
\(56\) −0.179235 + 0.0345448i −0.0239513 + 0.00461624i
\(57\) −4.88085 + 5.60706i −0.646484 + 0.742673i
\(58\) 1.40907 + 0.726424i 0.185019 + 0.0953841i
\(59\) −1.80948 + 5.22815i −0.235574 + 0.680647i 0.763806 + 0.645446i \(0.223328\pi\)
−0.999380 + 0.0352014i \(0.988793\pi\)
\(60\) 0.301177 + 6.63928i 0.0388818 + 0.857128i
\(61\) −3.78466 2.97629i −0.484576 0.381074i 0.345774 0.938318i \(-0.387617\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(62\) 4.22042 4.87062i 0.535994 0.618570i
\(63\) 0.507447 + 0.205827i 0.0639324 + 0.0259318i
\(64\) −0.959493 0.281733i −0.119937 0.0352166i
\(65\) −8.78368 0.838739i −1.08948 0.104033i
\(66\) 5.56636 7.77945i 0.685171 0.957584i
\(67\) −0.525122 + 11.0237i −0.0641539 + 1.34676i 0.705689 + 0.708522i \(0.250638\pi\)
−0.769843 + 0.638234i \(0.779665\pi\)
\(68\) 0.0896799 + 0.155330i 0.0108753 + 0.0188365i
\(69\) 7.70660 3.09973i 0.927766 0.373164i
\(70\) 0.350203 0.606570i 0.0418573 0.0724990i
\(71\) −8.71162 5.59862i −1.03388 0.664434i −0.0904133 0.995904i \(-0.528819\pi\)
−0.943465 + 0.331471i \(0.892455\pi\)
\(72\) 1.95428 + 2.27614i 0.230314 + 0.268245i
\(73\) −6.29065 13.7746i −0.736265 1.61219i −0.789603 0.613618i \(-0.789713\pi\)
0.0533384 0.998576i \(-0.483014\pi\)
\(74\) 6.54152 6.23733i 0.760437 0.725075i
\(75\) −13.2149 10.4409i −1.52592 1.20561i
\(76\) 4.21436 + 0.812251i 0.483420 + 0.0931716i
\(77\) −0.935887 + 0.374673i −0.106654 + 0.0426979i
\(78\) −3.35552 + 2.14572i −0.379937 + 0.242955i
\(79\) 7.03025 1.35497i 0.790965 0.152446i 0.222260 0.974987i \(-0.428657\pi\)
0.568705 + 0.822541i \(0.307444\pi\)
\(80\) 3.22800 2.07451i 0.360902 0.231937i
\(81\) −1.19996 8.91965i −0.133329 0.991072i
\(82\) −3.86785 4.46374i −0.427133 0.492938i
\(83\) −1.75630 + 7.23955i −0.192779 + 0.794644i 0.790489 + 0.612476i \(0.209827\pi\)
−0.983267 + 0.182168i \(0.941689\pi\)
\(84\) −0.0442841 0.313041i −0.00483179 0.0341556i
\(85\) −0.675790 0.130248i −0.0732997 0.0141274i
\(86\) 1.20052 0.114636i 0.129456 0.0123615i
\(87\) −1.37829 + 2.37482i −0.147769 + 0.254608i
\(88\) −5.49780 0.524976i −0.586067 0.0559627i
\(89\) 0.259343 + 1.80377i 0.0274903 + 0.191199i 0.998939 0.0460498i \(-0.0146633\pi\)
−0.971449 + 0.237249i \(0.923754\pi\)
\(90\) −11.5113 0.0522173i −1.21340 0.00550418i
\(91\) 0.419743 0.0440011
\(92\) −3.78127 2.94992i −0.394225 0.307550i
\(93\) 8.06130 + 7.72141i 0.835918 + 0.800673i
\(94\) 0.316670 6.64773i 0.0326621 0.685661i
\(95\) −12.9453 + 10.1803i −1.32816 + 1.04447i
\(96\) 0.570209 1.63550i 0.0581967 0.166923i
\(97\) −11.2521 + 10.7289i −1.14248 + 1.08935i −0.147522 + 0.989059i \(0.547130\pi\)
−0.994958 + 0.100294i \(0.968022\pi\)
\(98\) 2.89406 6.33712i 0.292345 0.640145i
\(99\) 12.9771 + 10.3009i 1.30424 + 1.03528i
\(100\) −1.38381 + 9.62462i −0.138381 + 0.962462i
\(101\) 3.37721 13.9210i 0.336045 1.38520i −0.513686 0.857978i \(-0.671720\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(102\) −0.276448 + 0.141726i −0.0273724 + 0.0140330i
\(103\) 2.78602 + 1.43629i 0.274515 + 0.141522i 0.589987 0.807412i \(-0.299133\pi\)
−0.315472 + 0.948935i \(0.602163\pi\)
\(104\) 2.04391 + 1.05371i 0.200422 + 0.103325i
\(105\) 1.01907 + 0.658186i 0.0994509 + 0.0642324i
\(106\) −2.50338 + 10.3191i −0.243150 + 1.00228i
\(107\) 1.80582 12.5598i 0.174576 1.21420i −0.694490 0.719502i \(-0.744370\pi\)
0.869066 0.494697i \(-0.164721\pi\)
\(108\) −4.10621 + 3.18418i −0.395120 + 0.306398i
\(109\) −2.21633 + 4.85308i −0.212286 + 0.464841i −0.985581 0.169205i \(-0.945880\pi\)
0.773295 + 0.634046i \(0.218607\pi\)
\(110\) 15.3372 14.6240i 1.46234 1.39434i
\(111\) 10.2252 + 11.8547i 0.970529 + 1.12520i
\(112\) −0.143481 + 0.112835i −0.0135577 + 0.0106619i
\(113\) 0.488131 10.2471i 0.0459195 0.963969i −0.851927 0.523660i \(-0.824566\pi\)
0.897847 0.440308i \(-0.145131\pi\)
\(114\) −1.76897 + 7.22028i −0.165679 + 0.676242i
\(115\) 18.0560 3.55283i 1.68373 0.331303i
\(116\) 1.58529 0.147191
\(117\) −3.42217 5.98996i −0.316380 0.553772i
\(118\) 0.787347 + 5.47612i 0.0724812 + 0.504118i
\(119\) 0.0325910 + 0.00311206i 0.00298761 + 0.000285282i
\(120\) 3.30999 + 5.76322i 0.302160 + 0.526108i
\(121\) −19.4131 + 1.85373i −1.76483 + 0.168521i
\(122\) −4.72775 0.911199i −0.428030 0.0824961i
\(123\) 8.05576 6.30560i 0.726363 0.568557i
\(124\) 1.51941 6.26309i 0.136447 0.562442i
\(125\) −11.8694 13.6980i −1.06163 1.22519i
\(126\) 0.545353 0.0495796i 0.0485839 0.00441690i
\(127\) −12.7598 + 8.20022i −1.13225 + 0.727652i −0.966028 0.258437i \(-0.916793\pi\)
−0.166220 + 0.986089i \(0.553156\pi\)
\(128\) −0.981929 + 0.189251i −0.0867911 + 0.0167276i
\(129\) 0.0946579 + 2.08668i 0.00833417 + 0.183722i
\(130\) −8.19158 + 3.27941i −0.718449 + 0.287623i
\(131\) 5.31078 + 1.02357i 0.464005 + 0.0894297i 0.415896 0.909412i \(-0.363468\pi\)
0.0481096 + 0.998842i \(0.484680\pi\)
\(132\) 1.38282 9.46531i 0.120359 0.823849i
\(133\) 0.566989 0.540622i 0.0491641 0.0468779i
\(134\) 4.58459 + 10.0389i 0.396048 + 0.867225i
\(135\) 1.08419 19.9088i 0.0933124 1.71348i
\(136\) 0.150887 + 0.0969692i 0.0129385 + 0.00831504i
\(137\) −10.8174 + 18.7363i −0.924193 + 1.60075i −0.131339 + 0.991338i \(0.541928\pi\)
−0.792854 + 0.609412i \(0.791406\pi\)
\(138\) 5.42952 6.28652i 0.462192 0.535144i
\(139\) −0.373823 0.647480i −0.0317072 0.0549185i 0.849736 0.527208i \(-0.176761\pi\)
−0.881444 + 0.472289i \(0.843428\pi\)
\(140\) 0.0333267 0.699614i 0.00281662 0.0591281i
\(141\) 11.4726 + 1.12176i 0.966163 + 0.0944692i
\(142\) −10.3086 0.984355i −0.865081 0.0826052i
\(143\) 12.1855 + 3.57798i 1.01900 + 0.299205i
\(144\) 2.78002 + 1.12761i 0.231668 + 0.0939675i
\(145\) −3.98351 + 4.59721i −0.330812 + 0.381778i
\(146\) −11.9032 9.36081i −0.985119 0.774706i
\(147\) 10.7127 + 5.55357i 0.883568 + 0.458051i
\(148\) 2.95623 8.54146i 0.243000 0.702104i
\(149\) −8.89055 4.58340i −0.728342 0.375486i 0.0538291 0.998550i \(-0.482857\pi\)
−0.782171 + 0.623064i \(0.785888\pi\)
\(150\) −16.5301 3.22482i −1.34968 0.263306i
\(151\) 5.37726 1.03638i 0.437595 0.0843395i 0.0343043 0.999411i \(-0.489078\pi\)
0.403291 + 0.915072i \(0.367866\pi\)
\(152\) 4.11807 1.20917i 0.334019 0.0980770i
\(153\) −0.221304 0.490463i −0.0178913 0.0396516i
\(154\) −0.660165 + 0.761871i −0.0531976 + 0.0613933i
\(155\) 14.3445 + 20.1440i 1.15217 + 1.61800i
\(156\) −1.99928 + 3.44478i −0.160070 + 0.275803i
\(157\) −0.464952 + 0.652934i −0.0371072 + 0.0521098i −0.832713 0.553705i \(-0.813213\pi\)
0.795606 + 0.605815i \(0.207153\pi\)
\(158\) 5.62786 4.42579i 0.447728 0.352097i
\(159\) −17.6348 5.22152i −1.39853 0.414093i
\(160\) 1.91857 3.32306i 0.151676 0.262711i
\(161\) −0.838977 + 0.249891i −0.0661207 + 0.0196942i
\(162\) −5.15379 7.37824i −0.404920 0.579690i
\(163\) −3.80258 2.44377i −0.297841 0.191411i 0.383182 0.923673i \(-0.374828\pi\)
−0.681023 + 0.732262i \(0.738465\pi\)
\(164\) −5.48329 2.19518i −0.428173 0.171415i
\(165\) 23.9738 + 27.7944i 1.86636 + 2.16379i
\(166\) 1.75630 + 7.23955i 0.136315 + 0.561898i
\(167\) −5.65291 + 0.539787i −0.437435 + 0.0417700i −0.311451 0.950262i \(-0.600815\pi\)
−0.125984 + 0.992032i \(0.540209\pi\)
\(168\) −0.182805 0.257950i −0.0141037 0.0199013i
\(169\) 6.06214 + 4.76732i 0.466319 + 0.366717i
\(170\) −0.660349 + 0.193896i −0.0506465 + 0.0148711i
\(171\) −12.3376 3.68353i −0.943482 0.281686i
\(172\) 1.01454 0.652005i 0.0773579 0.0497149i
\(173\) −0.100396 2.10758i −0.00763298 0.160236i −0.999466 0.0326894i \(-0.989593\pi\)
0.991833 0.127547i \(-0.0407102\pi\)
\(174\) −0.136871 + 2.74240i −0.0103762 + 0.207901i
\(175\) 1.28455 + 1.22481i 0.0971025 + 0.0925870i
\(176\) −5.12720 + 2.05262i −0.386477 + 0.154722i
\(177\) −9.54110 + 0.889232i −0.717153 + 0.0668388i
\(178\) 1.05705 + 1.48442i 0.0792292 + 0.111262i
\(179\) −18.7833 5.51528i −1.40393 0.412231i −0.509899 0.860235i \(-0.670317\pi\)
−0.894032 + 0.448003i \(0.852135\pi\)
\(180\) −10.2556 + 5.22836i −0.764405 + 0.389699i
\(181\) 0.589379 + 4.09922i 0.0438082 + 0.304692i 0.999931 + 0.0117272i \(0.00373295\pi\)
−0.956123 + 0.292965i \(0.905358\pi\)
\(182\) 0.373083 0.192338i 0.0276547 0.0142570i
\(183\) 1.98447 8.09985i 0.146696 0.598758i
\(184\) −4.71266 0.889313i −0.347422 0.0655610i
\(185\) 17.3411 + 30.0357i 1.27494 + 2.20827i
\(186\) 10.7033 + 3.16917i 0.784806 + 0.232375i
\(187\) 0.919613 + 0.368157i 0.0672487 + 0.0269223i
\(188\) −2.76470 6.05384i −0.201636 0.441522i
\(189\) 0.0386829 + 0.947685i 0.00281377 + 0.0689339i
\(190\) −6.84134 + 14.9804i −0.496323 + 1.08679i
\(191\) −3.37255 9.74433i −0.244029 0.705075i −0.998795 0.0490809i \(-0.984371\pi\)
0.754766 0.655994i \(-0.227750\pi\)
\(192\) −0.242607 1.71498i −0.0175087 0.123768i
\(193\) 16.8073 + 16.0258i 1.20982 + 1.15356i 0.983768 + 0.179445i \(0.0574303\pi\)
0.226052 + 0.974115i \(0.427418\pi\)
\(194\) −5.08503 + 14.6922i −0.365084 + 1.05484i
\(195\) −4.96580 14.4537i −0.355608 1.03505i
\(196\) −0.331488 6.95879i −0.0236777 0.497056i
\(197\) −1.63112 1.88242i −0.116213 0.134117i 0.694662 0.719336i \(-0.255554\pi\)
−0.810875 + 0.585219i \(0.801008\pi\)
\(198\) 16.2546 + 3.20936i 1.15517 + 0.228079i
\(199\) 0.967781 6.73106i 0.0686042 0.477152i −0.926337 0.376695i \(-0.877060\pi\)
0.994941 0.100457i \(-0.0320305\pi\)
\(200\) 3.18028 + 9.18880i 0.224879 + 0.649747i
\(201\) −17.7620 + 7.06414i −1.25284 + 0.498266i
\(202\) −3.37721 13.9210i −0.237620 0.979481i
\(203\) 0.167851 0.235714i 0.0117808 0.0165439i
\(204\) −0.180774 + 0.252647i −0.0126567 + 0.0176888i
\(205\) 20.1442 10.3850i 1.40693 0.725323i
\(206\) 3.13446 0.218388
\(207\) 10.4063 + 9.93528i 0.723285 + 0.690550i
\(208\) 2.29954 0.159444
\(209\) 21.0685 10.8616i 1.45734 0.751309i
\(210\) 1.20738 + 0.118055i 0.0833173 + 0.00814657i
\(211\) −1.14668 + 1.61029i −0.0789407 + 0.110857i −0.852158 0.523284i \(-0.824707\pi\)
0.773218 + 0.634141i \(0.218646\pi\)
\(212\) 2.50338 + 10.3191i 0.171933 + 0.708716i
\(213\) 2.59286 17.7479i 0.177660 1.21607i
\(214\) −4.15014 11.9910i −0.283698 0.819691i
\(215\) −0.658566 + 4.58043i −0.0449138 + 0.312382i
\(216\) −2.19067 + 4.71179i −0.149056 + 0.320597i
\(217\) −0.770370 0.889054i −0.0522961 0.0603529i
\(218\) 0.253860 + 5.32917i 0.0171935 + 0.360937i
\(219\) 17.2209 19.7832i 1.16368 1.33682i
\(220\) 6.93114 20.0262i 0.467298 1.35017i
\(221\) −0.298500 0.284619i −0.0200793 0.0191456i
\(222\) 14.5206 + 5.85142i 0.974560 + 0.392722i
\(223\) 4.80335 + 13.8784i 0.321656 + 0.929364i 0.983687 + 0.179888i \(0.0575735\pi\)
−0.662031 + 0.749476i \(0.730305\pi\)
\(224\) −0.0758273 + 0.166039i −0.00506643 + 0.0110939i
\(225\) 7.00579 28.3170i 0.467053 1.88780i
\(226\) −4.26164 9.33169i −0.283480 0.620735i
\(227\) 25.4288 + 10.1801i 1.68777 + 0.675680i 0.998794 0.0491063i \(-0.0156373\pi\)
0.688974 + 0.724786i \(0.258062\pi\)
\(228\) 1.73620 + 7.22823i 0.114983 + 0.478702i
\(229\) 8.78484 + 15.2158i 0.580518 + 1.00549i 0.995418 + 0.0956201i \(0.0304834\pi\)
−0.414899 + 0.909867i \(0.636183\pi\)
\(230\) 14.4208 11.4316i 0.950882 0.753780i
\(231\) −1.26096 1.20780i −0.0829651 0.0794671i
\(232\) 1.40907 0.726424i 0.0925097 0.0476921i
\(233\) −0.355984 2.47592i −0.0233213 0.162203i 0.974833 0.222938i \(-0.0715647\pi\)
−0.998154 + 0.0607348i \(0.980656\pi\)
\(234\) −5.78650 3.75596i −0.378276 0.245535i
\(235\) 24.5027 + 7.19465i 1.59838 + 0.469327i
\(236\) 3.20912 + 4.50659i 0.208896 + 0.293354i
\(237\) 7.17027 + 10.1177i 0.465759 + 0.657217i
\(238\) 0.0303940 0.0121679i 0.00197015 0.000788730i
\(239\) −14.7389 14.0536i −0.953383 0.909049i 0.0425547 0.999094i \(-0.486450\pi\)
−0.995938 + 0.0900453i \(0.971299\pi\)
\(240\) 5.58290 + 3.60583i 0.360375 + 0.232755i
\(241\) 0.491657 + 10.3211i 0.0316704 + 0.664844i 0.957765 + 0.287552i \(0.0928415\pi\)
−0.926095 + 0.377291i \(0.876856\pi\)
\(242\) −16.4056 + 10.5433i −1.05459 + 0.677746i
\(243\) 13.2086 8.27850i 0.847330 0.531066i
\(244\) −4.61973 + 1.35647i −0.295748 + 0.0868394i
\(245\) 21.0128 + 16.5247i 1.34246 + 1.05572i
\(246\) 4.27085 9.29600i 0.272299 0.592691i
\(247\) −9.82474 + 0.938149i −0.625133 + 0.0596930i
\(248\) −1.51941 6.26309i −0.0964826 0.397707i
\(249\) −12.6753 + 2.41316i −0.803266 + 0.152928i
\(250\) −16.8267 6.73641i −1.06422 0.426048i
\(251\) 14.8312 + 9.53143i 0.936137 + 0.601618i 0.917297 0.398204i \(-0.130366\pi\)
0.0188397 + 0.999823i \(0.494003\pi\)
\(252\) 0.462010 0.293963i 0.0291039 0.0185179i
\(253\) −26.4863 + 0.102913i −1.66518 + 0.00647006i
\(254\) −7.58380 + 13.1355i −0.475850 + 0.824196i
\(255\) −0.278407 1.15908i −0.0174345 0.0725842i
\(256\) −0.786053 + 0.618159i −0.0491283 + 0.0386349i
\(257\) −2.21828 + 3.11514i −0.138373 + 0.194317i −0.877947 0.478757i \(-0.841087\pi\)
0.739575 + 0.673075i \(0.235027\pi\)
\(258\) 1.04031 + 1.81134i 0.0647668 + 0.112769i
\(259\) −0.957004 1.34392i −0.0594654 0.0835074i
\(260\) −5.77825 + 6.66845i −0.358352 + 0.413560i
\(261\) −4.73225 0.473546i −0.292919 0.0293118i
\(262\) 5.18944 1.52376i 0.320605 0.0941380i
\(263\) 3.25793 0.627914i 0.200892 0.0387188i −0.0878122 0.996137i \(-0.527988\pi\)
0.288705 + 0.957418i \(0.406775\pi\)
\(264\) −3.10815 9.04675i −0.191293 0.556789i
\(265\) −36.2148 18.6701i −2.22466 1.14689i
\(266\) 0.256232 0.740334i 0.0157106 0.0453928i
\(267\) −2.65916 + 1.70043i −0.162738 + 0.104064i
\(268\) 8.67502 + 6.82211i 0.529911 + 0.416727i
\(269\) −14.2264 + 16.4181i −0.867398 + 1.00103i 0.132553 + 0.991176i \(0.457682\pi\)
−0.999951 + 0.00985492i \(0.996863\pi\)
\(270\) −8.15909 18.1925i −0.496546 1.10716i
\(271\) −13.7911 4.04944i −0.837752 0.245986i −0.165408 0.986225i \(-0.552894\pi\)
−0.672344 + 0.740239i \(0.734712\pi\)
\(272\) 0.178548 + 0.0170492i 0.0108260 + 0.00103376i
\(273\) 0.300513 + 0.662001i 0.0181879 + 0.0400661i
\(274\) −1.02943 + 21.6103i −0.0621899 + 1.30553i
\(275\) 26.8508 + 46.5069i 1.61916 + 2.80447i
\(276\) 1.94530 8.07563i 0.117093 0.486096i
\(277\) 2.27998 3.94904i 0.136991 0.237275i −0.789365 0.613924i \(-0.789590\pi\)
0.926356 + 0.376649i \(0.122924\pi\)
\(278\) −0.628960 0.404208i −0.0377225 0.0242428i
\(279\) −6.40644 + 18.2420i −0.383543 + 1.09212i
\(280\) −0.290960 0.637113i −0.0173882 0.0380748i
\(281\) −5.92905 + 5.65334i −0.353698 + 0.337250i −0.846008 0.533169i \(-0.821001\pi\)
0.492311 + 0.870419i \(0.336152\pi\)
\(282\) 10.7112 4.25997i 0.637844 0.253677i
\(283\) −5.86211 1.12983i −0.348466 0.0671614i 0.0120149 0.999928i \(-0.496175\pi\)
−0.360481 + 0.932766i \(0.617388\pi\)
\(284\) −9.61373 + 3.84876i −0.570470 + 0.228382i
\(285\) −25.3240 13.1282i −1.50006 0.777647i
\(286\) 12.4704 2.40347i 0.737390 0.142120i
\(287\) −0.906967 + 0.582872i −0.0535365 + 0.0344059i
\(288\) 2.98768 0.271618i 0.176051 0.0160053i
\(289\) 11.1116 + 12.8234i 0.653622 + 0.754319i
\(290\) −1.43412 + 5.91152i −0.0842143 + 0.347136i
\(291\) −24.9770 10.0651i −1.46418 0.590025i
\(292\) −14.8694 2.86584i −0.870165 0.167711i
\(293\) 6.50767 0.621407i 0.380182 0.0363030i 0.0967842 0.995305i \(-0.469144\pi\)
0.283398 + 0.959002i \(0.408538\pi\)
\(294\) 12.0666 + 0.0273680i 0.703739 + 0.00159614i
\(295\) −21.1326 2.01791i −1.23038 0.117487i
\(296\) −1.28632 8.94657i −0.0747660 0.520009i
\(297\) −6.95526 + 27.8417i −0.403585 + 1.61554i
\(298\) −10.0025 −0.579427
\(299\) 10.2541 + 4.05895i 0.593008 + 0.234735i
\(300\) −16.1703 + 4.70821i −0.933591 + 0.271829i
\(301\) 0.0104744 0.219884i 0.000603732 0.0126739i
\(302\) 4.30460 3.38517i 0.247702 0.194795i
\(303\) 24.3736 4.64031i 1.40022 0.266579i
\(304\) 3.10621 2.96176i 0.178153 0.169869i
\(305\) 7.67474 16.8053i 0.439454 0.962271i
\(306\) −0.421446 0.334534i −0.0240924 0.0191240i
\(307\) 3.92876 27.3251i 0.224226 1.55953i −0.497573 0.867422i \(-0.665775\pi\)
0.721799 0.692103i \(-0.243316\pi\)
\(308\) −0.237668 + 0.979683i −0.0135424 + 0.0558226i
\(309\) −0.270623 + 5.42230i −0.0153952 + 0.308464i
\(310\) 21.9804 + 11.3317i 1.24840 + 0.643595i
\(311\) −4.93426 2.54379i −0.279796 0.144245i 0.312617 0.949879i \(-0.398794\pi\)
−0.592413 + 0.805634i \(0.701825\pi\)
\(312\) −0.198538 + 3.97796i −0.0112400 + 0.225208i
\(313\) −2.42723 + 10.0052i −0.137195 + 0.565525i 0.861168 + 0.508321i \(0.169734\pi\)
−0.998363 + 0.0572040i \(0.981781\pi\)
\(314\) −0.114074 + 0.793404i −0.00643758 + 0.0447744i
\(315\) −0.308466 + 2.07846i −0.0173801 + 0.117108i
\(316\) 2.97422 6.51264i 0.167313 0.366364i
\(317\) −7.76357 + 7.40255i −0.436046 + 0.415769i −0.876045 0.482229i \(-0.839827\pi\)
0.439999 + 0.897998i \(0.354979\pi\)
\(318\) −18.0671 + 3.43966i −1.01315 + 0.192887i
\(319\) 6.88211 5.41215i 0.385324 0.303022i
\(320\) 0.182578 3.83279i 0.0102064 0.214259i
\(321\) 21.1016 6.14404i 1.17778 0.342927i
\(322\) −0.631206 + 0.606553i −0.0351757 + 0.0338019i
\(323\) −0.769798 −0.0428327
\(324\) −7.96178 4.19644i −0.442321 0.233136i
\(325\) −3.18213 22.1322i −0.176513 1.22767i
\(326\) −4.49967 0.429666i −0.249214 0.0237970i
\(327\) −9.24084 0.0209589i −0.511019 0.00115903i
\(328\) −5.87963 + 0.561437i −0.324648 + 0.0310001i
\(329\) −1.19286 0.229905i −0.0657644 0.0126751i
\(330\) 34.0449 + 13.7192i 1.87411 + 0.755217i
\(331\) 1.24632 5.13742i 0.0685042 0.282378i −0.927248 0.374447i \(-0.877833\pi\)
0.995753 + 0.0920685i \(0.0293479\pi\)
\(332\) 4.87841 + 5.62999i 0.267738 + 0.308986i
\(333\) −11.3760 + 24.6140i −0.623403 + 1.34884i
\(334\) −4.77716 + 3.07009i −0.261394 + 0.167988i
\(335\) −41.5820 + 8.01427i −2.27187 + 0.437867i
\(336\) −0.280683 0.145509i −0.0153125 0.00793816i
\(337\) −33.9120 + 13.5763i −1.84731 + 0.739550i −0.886241 + 0.463224i \(0.846693\pi\)
−0.961064 + 0.276326i \(0.910883\pi\)
\(338\) 7.57276 + 1.45953i 0.411904 + 0.0793880i
\(339\) 16.5108 6.56652i 0.896744 0.356644i
\(340\) −0.498093 + 0.474931i −0.0270129 + 0.0257568i
\(341\) −14.7859 32.3767i −0.800703 1.75330i
\(342\) −12.6540 + 2.37938i −0.684250 + 0.128662i
\(343\) −2.14469 1.37831i −0.115802 0.0744215i
\(344\) 0.602993 1.04441i 0.0325112 0.0563110i
\(345\) 18.5305 + 25.9336i 0.997648 + 1.39622i
\(346\) −1.05498 1.82728i −0.0567162 0.0982354i
\(347\) −0.875876 + 18.3869i −0.0470195 + 0.987061i 0.844916 + 0.534899i \(0.179650\pi\)
−0.891936 + 0.452162i \(0.850653\pi\)
\(348\) 1.13498 + 2.50026i 0.0608415 + 0.134028i
\(349\) −25.6698 2.45117i −1.37407 0.131208i −0.618248 0.785983i \(-0.712157\pi\)
−0.755824 + 0.654775i \(0.772763\pi\)
\(350\) 1.70299 + 0.500043i 0.0910287 + 0.0267284i
\(351\) 6.99702 9.68577i 0.373473 0.516988i
\(352\) −3.61667 + 4.17386i −0.192769 + 0.222467i
\(353\) −7.16792 5.63691i −0.381510 0.300023i 0.408926 0.912568i \(-0.365903\pi\)
−0.790436 + 0.612545i \(0.790146\pi\)
\(354\) −8.07300 + 5.16237i −0.429075 + 0.274377i
\(355\) 12.9962 37.5501i 0.689767 1.99295i
\(356\) 1.61974 + 0.835036i 0.0858462 + 0.0442568i
\(357\) 0.0184251 + 0.0536291i 0.000975161 + 0.00283836i
\(358\) −19.2225 + 3.70484i −1.01594 + 0.195807i
\(359\) 27.6602 8.12176i 1.45985 0.428650i 0.547064 0.837091i \(-0.315746\pi\)
0.912785 + 0.408441i \(0.133927\pi\)
\(360\) −6.71973 + 9.34652i −0.354161 + 0.492605i
\(361\) 0.379433 0.437889i 0.0199702 0.0230468i
\(362\) 2.40223 + 3.37346i 0.126258 + 0.177305i
\(363\) −16.8223 29.2903i −0.882943 1.53734i
\(364\) 0.243475 0.341913i 0.0127616 0.0179211i
\(365\) 45.6743 35.9187i 2.39070 1.88007i
\(366\) −1.94770 8.10877i −0.101808 0.423852i
\(367\) 14.3500 24.8549i 0.749062 1.29741i −0.199211 0.979957i \(-0.563838\pi\)
0.948273 0.317457i \(-0.102829\pi\)
\(368\) −4.59628 + 1.36901i −0.239598 + 0.0713646i
\(369\) 15.7124 + 8.19073i 0.817954 + 0.426392i
\(370\) 29.1765 + 18.7506i 1.51682 + 0.974798i
\(371\) 1.79938 + 0.720362i 0.0934190 + 0.0373993i
\(372\) 10.9657 2.08768i 0.568545 0.108241i
\(373\) −2.61336 10.7724i −0.135315 0.557775i −0.998592 0.0530453i \(-0.983107\pi\)
0.863277 0.504730i \(-0.168408\pi\)
\(374\) 0.986084 0.0941596i 0.0509892 0.00486888i
\(375\) 13.1061 28.5269i 0.676795 1.47312i
\(376\) −5.23139 4.11401i −0.269789 0.212164i
\(377\) −3.49778 + 1.02704i −0.180145 + 0.0528952i
\(378\) 0.468637 + 0.824610i 0.0241041 + 0.0424134i
\(379\) −14.4877 + 9.31071i −0.744185 + 0.478259i −0.856974 0.515360i \(-0.827658\pi\)
0.112788 + 0.993619i \(0.464022\pi\)
\(380\) 0.783611 + 16.4500i 0.0401984 + 0.843868i
\(381\) −22.0683 14.2533i −1.13060 0.730218i
\(382\) −7.46275 7.11572i −0.381827 0.364072i
\(383\) −34.8678 + 13.9590i −1.78166 + 0.713269i −0.786214 + 0.617955i \(0.787961\pi\)
−0.995447 + 0.0953147i \(0.969614\pi\)
\(384\) −1.00149 1.41316i −0.0511068 0.0721151i
\(385\) −2.24378 3.15095i −0.114354 0.160587i
\(386\) 22.2824 + 6.54270i 1.13414 + 0.333015i
\(387\) −3.22325 + 1.64324i −0.163847 + 0.0835305i
\(388\) 2.21261 + 15.3891i 0.112328 + 0.781262i
\(389\) 3.22584 1.66304i 0.163557 0.0843194i −0.374505 0.927225i \(-0.622187\pi\)
0.538061 + 0.842906i \(0.319157\pi\)
\(390\) −11.0369 10.5715i −0.558873 0.535310i
\(391\) 0.766083 + 0.391183i 0.0387425 + 0.0197830i
\(392\) −3.48334 6.03332i −0.175935 0.304729i
\(393\) 2.18790 + 9.10875i 0.110365 + 0.459476i
\(394\) −2.31238 0.925736i −0.116496 0.0466379i
\(395\) 11.4125 + 24.9899i 0.574224 + 1.25738i
\(396\) 15.9183 4.59570i 0.799924 0.230943i
\(397\) 6.18354 13.5401i 0.310343 0.679556i −0.688618 0.725124i \(-0.741782\pi\)
0.998961 + 0.0455676i \(0.0145097\pi\)
\(398\) −2.22415 6.42627i −0.111487 0.322120i
\(399\) 1.25858 + 0.507174i 0.0630077 + 0.0253905i
\(400\) 7.03730 + 6.71005i 0.351865 + 0.335502i
\(401\) 1.13013 3.26528i 0.0564358 0.163061i −0.913259 0.407379i \(-0.866443\pi\)
0.969695 + 0.244318i \(0.0785641\pi\)
\(402\) −12.5505 + 14.4179i −0.625964 + 0.719099i
\(403\) 0.705162 + 14.8032i 0.0351266 + 0.737399i
\(404\) −9.38077 10.8260i −0.466711 0.538613i
\(405\) 32.1756 12.5437i 1.59882 0.623300i
\(406\) 0.0411816 0.286425i 0.00204381 0.0142150i
\(407\) −16.3267 47.1728i −0.809283 2.33827i
\(408\) −0.0449089 + 0.307397i −0.00222332 + 0.0152184i
\(409\) 0.872224 + 3.59536i 0.0431287 + 0.177779i 0.989302 0.145881i \(-0.0466017\pi\)
−0.946173 + 0.323660i \(0.895087\pi\)
\(410\) 13.1461 18.4612i 0.649242 0.911733i
\(411\) −37.2947 3.64659i −1.83961 0.179873i
\(412\) 2.78602 1.43629i 0.137257 0.0707611i
\(413\) 1.00986 0.0496918
\(414\) 13.8021 + 4.06241i 0.678334 + 0.199656i
\(415\) −28.5849 −1.40318
\(416\) 2.04391 1.05371i 0.100211 0.0516623i
\(417\) 0.753541 1.05314i 0.0369011 0.0515723i
\(418\) 13.7494 19.3083i 0.672503 0.944398i
\(419\) −5.48202 22.5972i −0.267814 1.10395i −0.933747 0.357934i \(-0.883481\pi\)
0.665933 0.746012i \(-0.268034\pi\)
\(420\) 1.12726 0.448323i 0.0550047 0.0218759i
\(421\) 2.52621 + 7.29901i 0.123120 + 0.355732i 0.989671 0.143356i \(-0.0457895\pi\)
−0.866551 + 0.499088i \(0.833668\pi\)
\(422\) −0.281334 + 1.95672i −0.0136951 + 0.0952516i
\(423\) 6.44452 + 18.8971i 0.313343 + 0.918810i
\(424\) 6.95356 + 8.02484i 0.337695 + 0.389721i
\(425\) −0.0829839 1.74205i −0.00402531 0.0845016i
\(426\) −5.82793 16.9631i −0.282364 0.821863i
\(427\) −0.287446 + 0.830520i −0.0139105 + 0.0401917i
\(428\) −9.18341 8.75636i −0.443897 0.423255i
\(429\) 3.08109 + 21.7800i 0.148756 + 1.05155i
\(430\) 1.51352 + 4.37302i 0.0729882 + 0.210886i
\(431\) 10.9357 23.9459i 0.526756 1.15344i −0.440061 0.897968i \(-0.645043\pi\)
0.966818 0.255468i \(-0.0822295\pi\)
\(432\) 0.211922 + 5.19183i 0.0101961 + 0.249792i
\(433\) 1.84539 + 4.04085i 0.0886840 + 0.194191i 0.948777 0.315946i \(-0.102322\pi\)
−0.860093 + 0.510137i \(0.829595\pi\)
\(434\) −1.09212 0.437219i −0.0524234 0.0209872i
\(435\) −10.1025 2.99127i −0.484378 0.143420i
\(436\) 2.66761 + 4.62043i 0.127755 + 0.221278i
\(437\) 19.0790 7.72424i 0.912674 0.369501i
\(438\) 6.24140 25.4751i 0.298226 1.21725i
\(439\) 31.0953 16.0308i 1.48410 0.765106i 0.489810 0.871829i \(-0.337066\pi\)
0.994289 + 0.106723i \(0.0340358\pi\)
\(440\) −3.01590 20.9760i −0.143777 0.999994i
\(441\) −1.08915 + 20.8716i −0.0518644 + 0.993888i
\(442\) −0.395737 0.116199i −0.0188233 0.00552702i
\(443\) 19.5275 + 27.4226i 0.927781 + 1.30289i 0.952926 + 0.303202i \(0.0980557\pi\)
−0.0251454 + 0.999684i \(0.508005\pi\)
\(444\) 15.5877 1.45278i 0.739760 0.0689458i
\(445\) −6.49160 + 2.59884i −0.307731 + 0.123197i
\(446\) 10.6288 + 10.1346i 0.503289 + 0.479886i
\(447\) 0.863593 17.3032i 0.0408466 0.818415i
\(448\) 0.00868531 + 0.182327i 0.000410342 + 0.00861415i
\(449\) −7.21227 + 4.63505i −0.340368 + 0.218741i −0.699647 0.714489i \(-0.746659\pi\)
0.359278 + 0.933230i \(0.383023\pi\)
\(450\) −6.74861 28.3794i −0.318133 1.33782i
\(451\) −31.2984 + 9.19005i −1.47379 + 0.432743i
\(452\) −8.06392 6.34154i −0.379295 0.298281i
\(453\) 5.48436 + 7.73879i 0.257677 + 0.363600i
\(454\) 27.2668 2.60366i 1.27969 0.122196i
\(455\) 0.379716 + 1.56521i 0.0178014 + 0.0733782i
\(456\) 4.85537 + 5.62914i 0.227373 + 0.263609i
\(457\) 1.97214 + 0.789524i 0.0922527 + 0.0369324i 0.417330 0.908755i \(-0.362966\pi\)
−0.325077 + 0.945688i \(0.605390\pi\)
\(458\) 14.7806 + 9.49888i 0.690650 + 0.443854i
\(459\) 0.615096 0.700175i 0.0287102 0.0326814i
\(460\) 7.57947 16.7688i 0.353395 0.781852i
\(461\) 18.5516 32.1323i 0.864033 1.49655i −0.00397159 0.999992i \(-0.501264\pi\)
0.868004 0.496557i \(-0.165402\pi\)
\(462\) −1.67423 0.495726i −0.0778923 0.0230633i
\(463\) −0.525970 + 0.413628i −0.0244439 + 0.0192229i −0.630306 0.776347i \(-0.717071\pi\)
0.605862 + 0.795570i \(0.292828\pi\)
\(464\) 0.919561 1.29134i 0.0426895 0.0599491i
\(465\) −21.5004 + 37.0454i −0.997056 + 1.71794i
\(466\) −1.45094 2.03757i −0.0672137 0.0943885i
\(467\) 2.50009 2.88526i 0.115690 0.133514i −0.694950 0.719058i \(-0.744574\pi\)
0.810641 + 0.585544i \(0.199119\pi\)
\(468\) −6.86433 0.686899i −0.317304 0.0317519i
\(469\) 1.93288 0.567543i 0.0892519 0.0262067i
\(470\) 25.0757 4.83294i 1.15665 0.222927i
\(471\) −1.36266 0.265838i −0.0627880 0.0122492i
\(472\) 4.91742 + 2.53511i 0.226343 + 0.116688i
\(473\) 2.17841 6.29411i 0.100163 0.289403i
\(474\) 11.0094 + 5.70739i 0.505679 + 0.262149i
\(475\) −32.8043 25.7976i −1.50516 1.18367i
\(476\) 0.0214396 0.0247427i 0.000982684 0.00113408i
\(477\) −4.39039 31.5511i −0.201022 1.44463i
\(478\) −19.5402 5.73752i −0.893748 0.262428i
\(479\) −3.97030 0.379118i −0.181408 0.0173224i 0.00395670 0.999992i \(-0.498741\pi\)
−0.185365 + 0.982670i \(0.559347\pi\)
\(480\) 6.61457 + 0.646757i 0.301912 + 0.0295203i
\(481\) −0.988968 + 20.7610i −0.0450930 + 0.946620i
\(482\) 5.16643 + 8.94851i 0.235324 + 0.407594i
\(483\) −0.994778 1.14429i −0.0452640 0.0520670i
\(484\) −9.75070 + 16.8887i −0.443214 + 0.767669i
\(485\) −50.1868 32.2531i −2.27886 1.46454i
\(486\) 7.94682 13.4107i 0.360475 0.608324i
\(487\) −6.71077 14.6945i −0.304094 0.665873i 0.694466 0.719526i \(-0.255641\pi\)
−0.998560 + 0.0536529i \(0.982914\pi\)
\(488\) −3.48461 + 3.32256i −0.157741 + 0.150405i
\(489\) 1.13177 7.74687i 0.0511805 0.350326i
\(490\) 26.2490 + 5.05908i 1.18581 + 0.228546i
\(491\) −38.4202 + 15.3811i −1.73388 + 0.694140i −0.733990 + 0.679160i \(0.762344\pi\)
−0.999888 + 0.0149804i \(0.995231\pi\)
\(492\) −0.463592 10.2196i −0.0209003 0.460737i
\(493\) −0.279200 + 0.0538113i −0.0125745 + 0.00242354i
\(494\) −8.30269 + 5.33582i −0.373556 + 0.240070i
\(495\) −26.6722 + 57.7097i −1.19882 + 2.59386i
\(496\) −4.22042 4.87062i −0.189502 0.218697i
\(497\) −0.445639 + 1.83695i −0.0199897 + 0.0823985i
\(498\) −10.1605 + 7.95307i −0.455303 + 0.356386i
\(499\) 0.820923 + 0.158220i 0.0367495 + 0.00708289i 0.207593 0.978215i \(-0.433437\pi\)
−0.170843 + 0.985298i \(0.554649\pi\)
\(500\) −18.0430 + 1.72290i −0.806907 + 0.0770503i
\(501\) −4.89850 8.52906i −0.218849 0.381050i
\(502\) 17.5500 + 1.67583i 0.783297 + 0.0747958i
\(503\) 4.25803 + 29.6153i 0.189856 + 1.32048i 0.832376 + 0.554211i \(0.186980\pi\)
−0.642520 + 0.766269i \(0.722111\pi\)
\(504\) 0.275949 0.472990i 0.0122918 0.0210687i
\(505\) 54.9663 2.44597
\(506\) −23.4948 + 12.2282i −1.04447 + 0.543609i
\(507\) −3.17866 + 12.9741i −0.141169 + 0.576200i
\(508\) −0.721703 + 15.1504i −0.0320204 + 0.672191i
\(509\) −19.8257 + 15.5911i −0.878760 + 0.691065i −0.951950 0.306253i \(-0.900925\pi\)
0.0731898 + 0.997318i \(0.476682\pi\)
\(510\) −0.778578 0.902655i −0.0344760 0.0399702i
\(511\) −2.00049 + 1.90746i −0.0884963 + 0.0843811i
\(512\) −0.415415 + 0.909632i −0.0183589 + 0.0402004i
\(513\) −3.02356 22.0956i −0.133493 0.975543i
\(514\) −0.544248 + 3.78533i −0.0240057 + 0.166964i
\(515\) −2.83556 + 11.6883i −0.124950 + 0.515049i
\(516\) 1.75467 + 1.13329i 0.0772449 + 0.0498902i
\(517\) −32.6698 16.8425i −1.43682 0.740731i
\(518\) −1.46644 0.756003i −0.0644317 0.0332169i
\(519\) 3.25210 1.66725i 0.142751 0.0731840i
\(520\) −2.08025 + 8.57491i −0.0912250 + 0.376035i
\(521\) −4.24504 + 29.5249i −0.185978 + 1.29351i 0.656314 + 0.754488i \(0.272115\pi\)
−0.842292 + 0.539021i \(0.818794\pi\)
\(522\) −4.42318 + 1.74754i −0.193597 + 0.0764876i
\(523\) −14.4158 + 31.5662i −0.630359 + 1.38029i 0.277380 + 0.960760i \(0.410534\pi\)
−0.907740 + 0.419534i \(0.862193\pi\)
\(524\) 3.91433 3.73231i 0.170998 0.163047i
\(525\) −1.01206 + 2.90283i −0.0441697 + 0.126690i
\(526\) 2.60803 2.05098i 0.113716 0.0894270i
\(527\) −0.0550014 + 1.15462i −0.00239590 + 0.0502961i
\(528\) −6.90809 6.61683i −0.300636 0.287961i
\(529\) −22.9122 2.00830i −0.996181 0.0873175i
\(530\) −40.7442 −1.76981
\(531\) −8.23336 14.4112i −0.357297 0.625392i
\(532\) −0.111492 0.775447i −0.00483381 0.0336199i
\(533\) 13.5204 + 1.29104i 0.585635 + 0.0559213i
\(534\) −1.58437 + 2.72989i −0.0685625 + 0.118134i
\(535\) 48.4687 4.62820i 2.09548 0.200094i
\(536\) 10.8367 + 2.08861i 0.468076 + 0.0902142i
\(537\) −4.74935 33.5729i −0.204950 1.44878i
\(538\) −5.12170 + 21.1119i −0.220812 + 0.910200i
\(539\) −25.1962 29.0779i −1.08528 1.25248i
\(540\) −15.5884 12.4314i −0.670816 0.534963i
\(541\) 12.2853 7.89527i 0.528186 0.339444i −0.249217 0.968448i \(-0.580173\pi\)
0.777403 + 0.629003i \(0.216537\pi\)
\(542\) −14.1136 + 2.72018i −0.606231 + 0.116842i
\(543\) −6.04315 + 3.86436i −0.259336 + 0.165835i
\(544\) 0.166512 0.0666613i 0.00713913 0.00285808i
\(545\) −20.1020 3.87434i −0.861074 0.165958i
\(546\) 0.570453 + 0.450707i 0.0244131 + 0.0192885i
\(547\) 2.59499 2.47432i 0.110954 0.105794i −0.632572 0.774502i \(-0.718001\pi\)
0.743526 + 0.668708i \(0.233152\pi\)
\(548\) 8.98742 + 19.6797i 0.383924 + 0.840676i
\(549\) 14.1955 2.66923i 0.605849 0.113920i
\(550\) 45.1766 + 29.0332i 1.92634 + 1.23798i
\(551\) −3.40198 + 5.89240i −0.144929 + 0.251025i
\(552\) −1.97141 8.06930i −0.0839090 0.343452i
\(553\) −0.653438 1.13179i −0.0277870 0.0481285i
\(554\) 0.216972 4.55480i 0.00921825 0.193515i
\(555\) −34.9557 + 48.8535i −1.48379 + 2.07372i
\(556\) −0.744260 0.0710682i −0.0315637 0.00301396i
\(557\) 22.9628 + 6.74248i 0.972964 + 0.285688i 0.729317 0.684176i \(-0.239838\pi\)
0.243647 + 0.969864i \(0.421656\pi\)
\(558\) 2.66472 + 19.1498i 0.112806 + 0.810674i
\(559\) −1.81606 + 2.09585i −0.0768114 + 0.0886450i
\(560\) −0.550557 0.432963i −0.0232653 0.0182960i
\(561\) 0.0777499 + 1.71395i 0.00328260 + 0.0723632i
\(562\) −2.67944 + 7.74174i −0.113025 + 0.326565i
\(563\) 41.3882 + 21.3371i 1.74430 + 0.899251i 0.960518 + 0.278218i \(0.0897439\pi\)
0.783785 + 0.621032i \(0.213286\pi\)
\(564\) 7.56849 8.69458i 0.318691 0.366108i
\(565\) 38.6528 7.44972i 1.62614 0.313412i
\(566\) −5.72817 + 1.68194i −0.240773 + 0.0706973i
\(567\) −1.46695 + 0.739499i −0.0616062 + 0.0310560i
\(568\) −6.78142 + 7.82618i −0.284542 + 0.328379i
\(569\) −3.39557 4.76840i −0.142350 0.199902i 0.737246 0.675625i \(-0.236126\pi\)
−0.879595 + 0.475723i \(0.842187\pi\)
\(570\) −28.5245 0.0646959i −1.19476 0.00270981i
\(571\) −12.4692 + 17.5105i −0.521819 + 0.732792i −0.988431 0.151670i \(-0.951535\pi\)
0.466612 + 0.884462i \(0.345474\pi\)
\(572\) 9.98280 7.85056i 0.417402 0.328248i
\(573\) 12.9538 12.2954i 0.541152 0.513649i
\(574\) −0.539057 + 0.933674i −0.0224998 + 0.0389708i
\(575\) 19.5366 + 42.3430i 0.814733 + 1.76583i
\(576\) 2.53109 1.61046i 0.105462 0.0671024i
\(577\) 15.5948 + 10.0221i 0.649219 + 0.417228i 0.823381 0.567489i \(-0.192085\pi\)
−0.174162 + 0.984717i \(0.555722\pi\)
\(578\) 15.7524 + 6.30631i 0.655213 + 0.262308i
\(579\) −13.2420 + 37.9814i −0.550320 + 1.57845i
\(580\) 1.43412 + 5.91152i 0.0595485 + 0.245462i
\(581\) 1.35364 0.129257i 0.0561583 0.00536247i
\(582\) −26.8125 + 2.49893i −1.11142 + 0.103584i
\(583\) 46.0967 + 36.2509i 1.90913 + 1.50136i
\(584\) −14.5296 + 4.26629i −0.601241 + 0.176540i
\(585\) 19.2405 18.1799i 0.795499 0.751647i
\(586\) 5.49950 3.53432i 0.227182 0.146001i
\(587\) −0.865332 18.1656i −0.0357161 0.749773i −0.943707 0.330783i \(-0.892687\pi\)
0.907991 0.418990i \(-0.137616\pi\)
\(588\) 10.7378 5.50492i 0.442818 0.227019i
\(589\) 20.0188 + 19.0879i 0.824859 + 0.786502i
\(590\) −19.7080 + 7.88990i −0.811366 + 0.324822i
\(591\) 1.80107 3.92025i 0.0740863 0.161257i
\(592\) −5.24289 7.36260i −0.215481 0.302601i
\(593\) 39.3011 + 11.5398i 1.61390 + 0.473885i 0.959371 0.282149i \(-0.0910473\pi\)
0.654532 + 0.756034i \(0.272866\pi\)
\(594\) 6.57574 + 27.9338i 0.269806 + 1.14614i
\(595\) 0.0178783 + 0.124346i 0.000732938 + 0.00509769i
\(596\) −8.89055 + 4.58340i −0.364171 + 0.187743i
\(597\) 11.3088 3.29273i 0.462839 0.134762i
\(598\) 10.9741 1.09094i 0.448764 0.0446120i
\(599\) −20.1698 34.9351i −0.824116 1.42741i −0.902593 0.430495i \(-0.858339\pi\)
0.0784772 0.996916i \(-0.474994\pi\)
\(600\) −12.2153 + 11.5945i −0.498687 + 0.473342i
\(601\) −3.59295 1.43840i −0.146559 0.0586736i 0.297223 0.954808i \(-0.403939\pi\)
−0.443783 + 0.896134i \(0.646364\pi\)
\(602\) −0.0914466 0.200240i −0.00372709 0.00816118i
\(603\) −23.8579 22.9560i −0.971568 0.934839i
\(604\) 2.27490 4.98135i 0.0925645 0.202688i
\(605\) −24.4743 70.7139i −0.995023 2.87493i
\(606\) 19.5378 15.2931i 0.793668 0.621239i
\(607\) 28.4715 + 27.1475i 1.15562 + 1.10188i 0.993350 + 0.115136i \(0.0367305\pi\)
0.162271 + 0.986746i \(0.448118\pi\)
\(608\) 1.40375 4.05587i 0.0569296 0.164487i
\(609\) 0.491930 + 0.0959693i 0.0199340 + 0.00388887i
\(610\) −0.879070 18.4539i −0.0355925 0.747179i
\(611\) 10.0220 + 11.5660i 0.405447 + 0.467911i
\(612\) −0.527888 0.104228i −0.0213386 0.00421316i
\(613\) 4.93449 34.3201i 0.199302 1.38618i −0.607014 0.794691i \(-0.707633\pi\)
0.806316 0.591485i \(-0.201458\pi\)
\(614\) −9.02907 26.0878i −0.364383 1.05282i
\(615\) 30.8009 + 24.3354i 1.24201 + 0.981298i
\(616\) 0.237668 + 0.979683i 0.00957594 + 0.0394725i
\(617\) 17.7752 24.9617i 0.715602 1.00492i −0.283344 0.959018i \(-0.591444\pi\)
0.998946 0.0459039i \(-0.0146168\pi\)
\(618\) 2.24410 + 4.94354i 0.0902710 + 0.198858i
\(619\) 15.1115 7.79053i 0.607383 0.313128i −0.126958 0.991908i \(-0.540521\pi\)
0.734341 + 0.678780i \(0.237491\pi\)
\(620\) 24.7294 0.993157
\(621\) −8.21919 + 23.5254i −0.329825 + 0.944042i
\(622\) −5.55138 −0.222590
\(623\) 0.295658 0.152422i 0.0118453 0.00610667i
\(624\) 1.64634 + 3.62673i 0.0659064 + 0.145185i
\(625\) 12.1408 17.0493i 0.485631 0.681973i
\(626\) 2.42723 + 10.0052i 0.0970115 + 0.399887i
\(627\) 32.2142 + 25.4520i 1.28651 + 1.01646i
\(628\) 0.262165 + 0.757477i 0.0104615 + 0.0302266i
\(629\) −0.230715 + 1.60465i −0.00919919 + 0.0639818i
\(630\) 0.678228 + 1.98875i 0.0270212 + 0.0792338i
\(631\) −21.0445 24.2866i −0.837767 0.966834i 0.162034 0.986785i \(-0.448195\pi\)
−0.999801 + 0.0199507i \(0.993649\pi\)
\(632\) −0.340669 7.15153i −0.0135511 0.284473i
\(633\) −3.36064 0.655618i −0.133573 0.0260585i
\(634\) −3.50849 + 10.1371i −0.139340 + 0.402597i
\(635\) −42.1214 40.1627i −1.67154 1.59381i
\(636\) −14.4825 + 11.3361i −0.574269 + 0.449506i
\(637\) 5.23967 + 15.1390i 0.207603 + 0.599831i
\(638\) 3.63707 7.96408i 0.143993 0.315301i
\(639\) 29.8475 8.61716i 1.18075 0.340889i
\(640\) −1.59400 3.49038i −0.0630085 0.137969i
\(641\) −12.0742 4.83379i −0.476903 0.190923i 0.120742 0.992684i \(-0.461473\pi\)
−0.597645 + 0.801761i \(0.703897\pi\)
\(642\) 15.9405 15.1304i 0.629121 0.597147i
\(643\) −7.29604 12.6371i −0.287728 0.498359i 0.685539 0.728036i \(-0.259566\pi\)
−0.973267 + 0.229677i \(0.926233\pi\)
\(644\) −0.283099 + 0.828362i −0.0111557 + 0.0326420i
\(645\) −7.69555 + 2.24067i −0.303012 + 0.0882263i
\(646\) −0.684224 + 0.352742i −0.0269204 + 0.0138784i
\(647\) 4.72696 + 32.8767i 0.185836 + 1.29252i 0.842649 + 0.538464i \(0.180995\pi\)
−0.656813 + 0.754054i \(0.728096\pi\)
\(648\) −8.99963 0.0816496i −0.353539 0.00320750i
\(649\) 29.3169 + 8.60821i 1.15079 + 0.337902i
\(650\) −12.9699 18.2137i −0.508723 0.714401i
\(651\) 0.850635 1.85151i 0.0333390 0.0725663i
\(652\) −4.19635 + 1.67997i −0.164342 + 0.0657925i
\(653\) 25.1452 + 23.9759i 0.984009 + 0.938251i 0.998098 0.0616501i \(-0.0196363\pi\)
−0.0140889 + 0.999901i \(0.504485\pi\)
\(654\) −8.22319 + 4.21577i −0.321552 + 0.164850i
\(655\) 0.987478 + 20.7297i 0.0385840 + 0.809977i
\(656\) −4.96876 + 3.19323i −0.193997 + 0.124675i
\(657\) 43.5304 + 12.9965i 1.69828 + 0.507040i
\(658\) −1.16560 + 0.342252i −0.0454400 + 0.0133424i
\(659\) 7.78579 + 6.12282i 0.303291 + 0.238511i 0.758192 0.652031i \(-0.226083\pi\)
−0.454901 + 0.890542i \(0.650325\pi\)
\(660\) 36.5468 3.40617i 1.42258 0.132585i
\(661\) −29.2787 + 2.79578i −1.13881 + 0.108743i −0.647375 0.762172i \(-0.724133\pi\)
−0.491434 + 0.870915i \(0.663527\pi\)
\(662\) −1.24632 5.13742i −0.0484398 0.199671i
\(663\) 0.235180 0.674553i 0.00913362 0.0261975i
\(664\) 6.91592 + 2.76872i 0.268390 + 0.107447i
\(665\) 2.52889 + 1.62522i 0.0980660 + 0.0630232i
\(666\) 1.16734 + 27.0906i 0.0452336 + 1.04974i
\(667\) 6.37987 4.13521i 0.247029 0.160116i
\(668\) −2.83931 + 4.91783i −0.109856 + 0.190276i
\(669\) −18.4494 + 17.5118i −0.713296 + 0.677045i
\(670\) −33.2872 + 26.1773i −1.28600 + 1.01132i
\(671\) −15.4243 + 21.6604i −0.595448 + 0.836190i
\(672\) −0.316157 0.000717070i −0.0121960 2.76616e-5i
\(673\) 2.07340 + 2.91169i 0.0799238 + 0.112237i 0.852602 0.522560i \(-0.175023\pi\)
−0.772679 + 0.634797i \(0.781084\pi\)
\(674\) −23.9212 + 27.6065i −0.921409 + 1.06336i
\(675\) 49.6761 9.22418i 1.91204 0.355039i
\(676\) 7.39973 2.17276i 0.284605 0.0835676i
\(677\) 0.112249 0.0216342i 0.00431407 0.000831470i −0.187094 0.982342i \(-0.559907\pi\)
0.191408 + 0.981511i \(0.438695\pi\)
\(678\) 11.6664 13.4022i 0.448047 0.514710i
\(679\) 2.52244 + 1.30041i 0.0968023 + 0.0499050i
\(680\) −0.225097 + 0.650375i −0.00863208 + 0.0249408i
\(681\) 2.14991 + 47.3936i 0.0823847 + 1.81613i
\(682\) −27.9781 22.0022i −1.07134 0.842509i
\(683\) 12.8805 14.8649i 0.492858 0.568788i −0.453769 0.891119i \(-0.649921\pi\)
0.946627 + 0.322331i \(0.104466\pi\)
\(684\) −10.1570 + 7.91328i −0.388364 + 0.302572i
\(685\) −79.6529 23.3882i −3.04338 0.893617i
\(686\) −2.53785 0.242335i −0.0968955 0.00925240i
\(687\) −17.7082 + 24.7487i −0.675611 + 0.944223i
\(688\) 0.0573831 1.20462i 0.00218771 0.0459257i
\(689\) −12.2087 21.1461i −0.465114 0.805601i
\(690\) 28.3540 + 14.5595i 1.07942 + 0.554271i
\(691\) 3.41794 5.92005i 0.130025 0.225209i −0.793661 0.608360i \(-0.791828\pi\)
0.923686 + 0.383151i \(0.125161\pi\)
\(692\) −1.77502 1.14073i −0.0674760 0.0433642i
\(693\) 1.00211 2.85345i 0.0380668 0.108394i
\(694\) 7.64686 + 16.7443i 0.290271 + 0.635604i
\(695\) 2.07626 1.97971i 0.0787570 0.0750947i
\(696\) 2.15450 + 1.70224i 0.0816660 + 0.0645232i
\(697\) 1.04022 + 0.200486i 0.0394012 + 0.00759396i
\(698\) −23.9394 + 9.58389i −0.906120 + 0.362756i
\(699\) 3.65005 2.33407i 0.138058 0.0882825i
\(700\) 1.74281 0.335899i 0.0658721 0.0126958i
\(701\) 28.4657 18.2938i 1.07513 0.690946i 0.121705 0.992566i \(-0.461164\pi\)
0.953428 + 0.301620i \(0.0975274\pi\)
\(702\) 1.78092 11.8153i 0.0672164 0.445939i
\(703\) 25.4039 + 29.3177i 0.958127 + 1.10574i
\(704\) −1.30205 + 5.36713i −0.0490729 + 0.202281i
\(705\) 6.19550 + 43.7956i 0.233336 + 1.64944i
\(706\) −8.95408 1.72576i −0.336991 0.0649497i
\(707\) −2.60293 + 0.248550i −0.0978932 + 0.00934767i
\(708\) −4.81004 + 8.28776i −0.180772 + 0.311473i
\(709\) 6.76372 + 0.645857i 0.254017 + 0.0242557i 0.221288 0.975209i \(-0.428974\pi\)
0.0327291 + 0.999464i \(0.489580\pi\)
\(710\) −5.65495 39.3311i −0.212227 1.47607i
\(711\) −10.8237 + 18.5524i −0.405921 + 0.695769i
\(712\) 1.82232 0.0682943
\(713\) −10.2224 29.1686i −0.382833 1.09237i
\(714\) 0.0409512 + 0.0392246i 0.00153256 + 0.00146794i
\(715\) −2.31872 + 48.6760i −0.0867154 + 1.82038i
\(716\) −15.3880 + 12.1013i −0.575077 + 0.452245i
\(717\) 11.6124 33.3072i 0.433673 1.24388i
\(718\) 20.8637 19.8935i 0.778628 0.742420i
\(719\) −4.16131 + 9.11200i −0.155191 + 0.339820i −0.971218 0.238193i \(-0.923445\pi\)
0.816027 + 0.578014i \(0.196172\pi\)
\(720\) −1.68991 + 11.3867i −0.0629793 + 0.424357i
\(721\) 0.0814248 0.566322i 0.00303242 0.0210909i
\(722\) 0.136601 0.563077i 0.00508377 0.0209556i
\(723\) −15.9261 + 8.16479i −0.592297 + 0.303652i
\(724\) 3.68100 + 1.89769i 0.136803 + 0.0705269i
\(725\) −13.7012 7.06345i −0.508849 0.262330i
\(726\) −28.3739 18.3259i −1.05305 0.680136i
\(727\) −4.43642 + 18.2872i −0.164538 + 0.678233i 0.828455 + 0.560056i \(0.189220\pi\)
−0.992992 + 0.118178i \(0.962295\pi\)
\(728\) 0.0597357 0.415471i 0.00221395 0.0153984i
\(729\) 22.5131 + 14.9050i 0.833819 + 0.552039i
\(730\) 24.1381 52.8550i 0.893389 1.95625i
\(731\) −0.156547 + 0.149268i −0.00579012 + 0.00552086i
\(732\) −5.44684 6.31487i −0.201321 0.233404i
\(733\) 11.8588 9.32590i 0.438017 0.344460i −0.374673 0.927157i \(-0.622245\pi\)
0.812689 + 0.582697i \(0.198003\pi\)
\(734\) 1.36560 28.6674i 0.0504051 1.05813i
\(735\) −11.0180 + 44.9713i −0.406404 + 1.65879i
\(736\) −3.45802 + 3.32296i −0.127464 + 0.122486i
\(737\) 60.9507 2.24515
\(738\) 17.7189 + 0.0803763i 0.652243 + 0.00295869i
\(739\) −2.63974 18.3598i −0.0971044 0.675376i −0.978989 0.203911i \(-0.934635\pi\)
0.881885 0.471465i \(-0.156275\pi\)
\(740\) 34.5252 + 3.29675i 1.26917 + 0.121191i
\(741\) −8.51358 14.8235i −0.312754 0.544555i
\(742\) 1.92944 0.184239i 0.0708319 0.00676363i
\(743\) 18.8136 + 3.62603i 0.690204 + 0.133026i 0.522280 0.852774i \(-0.325081\pi\)
0.167924 + 0.985800i \(0.446294\pi\)
\(744\) 8.79006 6.88037i 0.322259 0.252247i
\(745\) 9.04862 37.2989i 0.331516 1.36653i
\(746\) −7.25906 8.37741i −0.265773 0.306719i
\(747\) −12.8808 18.2633i −0.471283 0.668218i
\(748\) 0.833320 0.535542i 0.0304692 0.0195814i
\(749\) −2.27430 + 0.438336i −0.0831012 + 0.0160165i
\(750\) −1.42264 31.3613i −0.0519474 1.14515i
\(751\) 12.2475 4.90315i 0.446917 0.178919i −0.137277 0.990533i \(-0.543835\pi\)
0.584194 + 0.811614i \(0.301411\pi\)
\(752\) −6.53500 1.25952i −0.238307 0.0459299i
\(753\) −4.41424 + 30.2151i −0.160864 + 1.10110i
\(754\) −2.63833 + 2.51564i −0.0960823 + 0.0916143i
\(755\) 8.72911 + 19.1141i 0.317685 + 0.695633i
\(756\) 0.794399 + 0.518201i 0.0288920 + 0.0188468i
\(757\) −18.1995 11.6961i −0.661474 0.425103i 0.166369 0.986064i \(-0.446796\pi\)
−0.827843 + 0.560960i \(0.810432\pi\)
\(758\) −8.61081 + 14.9144i −0.312759 + 0.541714i
\(759\) −19.1250 41.6993i −0.694194 1.51359i
\(760\) 8.23434 + 14.2623i 0.298691 + 0.517348i
\(761\) 0.705390 14.8080i 0.0255704 0.536788i −0.949348 0.314226i \(-0.898255\pi\)
0.974919 0.222562i \(-0.0714420\pi\)
\(762\) −26.1464 2.55653i −0.947183 0.0926133i
\(763\) 0.969447 + 0.0925710i 0.0350964 + 0.00335130i
\(764\) −9.89377 2.90507i −0.357944 0.105102i
\(765\) 1.62872 1.26893i 0.0588866 0.0458781i
\(766\) −24.5954 + 28.3846i −0.888667 + 1.02558i
\(767\) −10.0002 7.86424i −0.361086 0.283961i
\(768\) −1.53770 0.797161i −0.0554871 0.0287651i
\(769\) −15.0067 + 43.3591i −0.541157 + 1.56357i 0.260307 + 0.965526i \(0.416176\pi\)
−0.801463 + 0.598044i \(0.795945\pi\)
\(770\) −3.43820 1.77252i −0.123904 0.0638771i
\(771\) −6.50124 1.26831i −0.234136 0.0456771i
\(772\) 22.8034 4.39500i 0.820713 0.158180i
\(773\) 22.8568 6.71135i 0.822100 0.241390i 0.156480 0.987681i \(-0.449985\pi\)
0.665620 + 0.746291i \(0.268167\pi\)
\(774\) −2.11197 + 2.93755i −0.0759131 + 0.105588i
\(775\) −41.0376 + 47.3600i −1.47412 + 1.70122i
\(776\) 9.01833 + 12.6645i 0.323739 + 0.454628i
\(777\) 1.43442 2.47152i 0.0514594 0.0886653i
\(778\) 2.10520 2.95633i 0.0754749 0.105990i
\(779\) 19.9262 15.6701i 0.713930 0.561441i
\(780\) −14.6541 4.33896i −0.524701 0.155360i
\(781\) −28.5958 + 49.5293i −1.02324 + 1.77230i
\(782\) 0.860172 0.00334221i 0.0307597 0.000119517i
\(783\) −2.64117 7.80253i −0.0943877 0.278840i
\(784\) −5.86075 3.76647i −0.209312 0.134517i
\(785\) −2.85538 1.14312i −0.101913 0.0407998i
\(786\) 6.11855 + 7.09363i 0.218242 + 0.253021i
\(787\) −12.3518 50.9149i −0.440295 1.81492i −0.567904 0.823095i \(-0.692245\pi\)
0.127609 0.991825i \(-0.459270\pi\)
\(788\) −2.47952 + 0.236765i −0.0883292 + 0.00843441i
\(789\) 3.32281 + 4.68871i 0.118295 + 0.166923i
\(790\) 21.5948 + 16.9824i 0.768310 + 0.604205i
\(791\) −1.79672 + 0.527564i −0.0638839 + 0.0187580i
\(792\) 12.0429 11.3790i 0.427925 0.404336i
\(793\) 9.31412 5.98582i 0.330754 0.212563i
\(794\) −0.708267 14.8684i −0.0251355 0.527658i
\(795\) 3.51777 70.4832i 0.124762 2.49978i
\(796\) −4.92160 4.69273i −0.174441 0.166329i
\(797\) 32.1803 12.8831i 1.13989 0.456341i 0.276564 0.960996i \(-0.410804\pi\)
0.863322 + 0.504654i \(0.168380\pi\)
\(798\) 1.35107 0.125920i 0.0478274 0.00445752i
\(799\) 0.692406 + 0.972349i 0.0244956 + 0.0343992i
\(800\) 9.32972 + 2.73945i 0.329855 + 0.0968543i
\(801\) −4.58565 2.97649i −0.162026 0.105169i
\(802\) −0.491744 3.42015i −0.0173641 0.120770i
\(803\) −74.3352 + 38.3225i −2.62323 + 1.35237i
\(804\) −4.54870 + 18.5661i −0.160420 + 0.654776i
\(805\) −1.69081 2.90246i −0.0595931 0.102298i
\(806\) 7.40998 + 12.8345i 0.261005 + 0.452075i
\(807\) −36.0793 10.6828i −1.27005 0.376051i
\(808\) −13.2987 5.32400i −0.467847 0.187298i
\(809\) −18.3632 40.2097i −0.645615 1.41370i −0.895341 0.445382i \(-0.853068\pi\)
0.249726 0.968317i \(-0.419659\pi\)
\(810\) 22.8509 25.8930i 0.802900 0.909786i
\(811\) 5.06177 11.0837i 0.177743 0.389203i −0.799701 0.600399i \(-0.795009\pi\)
0.977444 + 0.211196i \(0.0677358\pi\)
\(812\) −0.0946436 0.273455i −0.00332134 0.00959638i
\(813\) −3.48708 24.6500i −0.122297 0.864512i
\(814\) −36.1276 34.4476i −1.26627 1.20739i
\(815\) 5.67279 16.3904i 0.198709 0.574132i
\(816\) 0.100941 + 0.293804i 0.00353364 + 0.0102852i
\(817\) 0.246284 + 5.17013i 0.00861638 + 0.180880i
\(818\) 2.42275 + 2.79600i 0.0847095 + 0.0977600i
\(819\) −0.828929 + 0.947912i −0.0289651 + 0.0331227i
\(820\) 3.22536 22.4329i 0.112634 0.783390i
\(821\) 5.60783 + 16.2028i 0.195715 + 0.565480i 0.999569 0.0293454i \(-0.00934226\pi\)
−0.803855 + 0.594826i \(0.797221\pi\)
\(822\) −34.8198 + 13.8482i −1.21448 + 0.483012i
\(823\) 5.99697 + 24.7199i 0.209041 + 0.861680i 0.975609 + 0.219516i \(0.0704479\pi\)
−0.766567 + 0.642164i \(0.778037\pi\)
\(824\) 1.81817 2.55326i 0.0633389 0.0889470i
\(825\) −54.1250 + 75.6442i −1.88439 + 2.63359i
\(826\) 0.897596 0.462743i 0.0312314 0.0161009i
\(827\) 25.5474 0.888370 0.444185 0.895935i \(-0.353493\pi\)
0.444185 + 0.895935i \(0.353493\pi\)
\(828\) 14.1293 2.71366i 0.491026 0.0943062i
\(829\) 32.1267 1.11581 0.557903 0.829906i \(-0.311606\pi\)
0.557903 + 0.829906i \(0.311606\pi\)
\(830\) −25.4073 + 13.0984i −0.881899 + 0.454651i
\(831\) 7.86060 + 0.768591i 0.272681 + 0.0266621i
\(832\) 1.33386 1.87315i 0.0462434 0.0649397i
\(833\) 0.294591 + 1.21432i 0.0102070 + 0.0420737i
\(834\) 0.187199 1.28136i 0.00648216 0.0443698i
\(835\) −7.12669 20.5912i −0.246629 0.712588i
\(836\) 3.37335 23.4622i 0.116670 0.811457i
\(837\) −33.3572 + 2.95633i −1.15299 + 0.102186i
\(838\) −15.2273 17.5732i −0.526017 0.607056i
\(839\) 0.804419 + 16.8868i 0.0277716 + 0.582998i 0.969273 + 0.245988i \(0.0791125\pi\)
−0.941501 + 0.337010i \(0.890584\pi\)
\(840\) 0.796515 0.915026i 0.0274824 0.0315714i
\(841\) 8.66300 25.0301i 0.298724 0.863106i
\(842\) 5.58999 + 5.33004i 0.192644 + 0.183685i
\(843\) −13.1611 5.30357i −0.453291 0.182664i
\(844\) 0.646562 + 1.86812i 0.0222556 + 0.0643032i
\(845\) −12.2932 + 26.9183i −0.422897 + 0.926016i
\(846\) 14.3873 + 13.8434i 0.494645 + 0.475945i
\(847\) 1.47874 + 3.23799i 0.0508101 + 0.111259i
\(848\) 9.85777 + 3.94645i 0.338517 + 0.135522i
\(849\) −2.41503 10.0544i −0.0828836 0.345065i
\(850\) −0.872011 1.51037i −0.0299097 0.0518051i
\(851\) −10.3832 42.0855i −0.355930 1.44267i
\(852\) −12.9530 12.4069i −0.443762 0.425052i
\(853\) 41.3798 21.3328i 1.41682 0.730420i 0.431654 0.902039i \(-0.357930\pi\)
0.985163 + 0.171619i \(0.0548999\pi\)
\(854\) 0.125074 + 0.869911i 0.00427996 + 0.0297677i
\(855\) 2.57467 49.3389i 0.0880518 1.68735i
\(856\) −12.1749 3.57488i −0.416131 0.122187i
\(857\) 1.14790 + 1.61200i 0.0392116 + 0.0550649i 0.833716 0.552193i \(-0.186209\pi\)
−0.794505 + 0.607258i \(0.792269\pi\)
\(858\) 12.7188 + 17.9470i 0.434211 + 0.612701i
\(859\) −29.2889 + 11.7255i −0.999324 + 0.400069i −0.812902 0.582401i \(-0.802113\pi\)
−0.186422 + 0.982470i \(0.559689\pi\)
\(860\) 3.34910 + 3.19336i 0.114203 + 0.108893i
\(861\) −1.56862 1.01312i −0.0534584 0.0345272i
\(862\) −1.25259 26.2951i −0.0426633 0.895613i
\(863\) −21.9569 + 14.1108i −0.747421 + 0.480338i −0.858077 0.513521i \(-0.828341\pi\)
0.110657 + 0.993859i \(0.464705\pi\)
\(864\) 2.56740 + 4.51757i 0.0873446 + 0.153691i
\(865\) 7.76826 2.28097i 0.264129 0.0775552i
\(866\) 3.49188 + 2.74604i 0.118659 + 0.0933143i
\(867\) −12.2693 + 26.7055i −0.416687 + 0.906968i
\(868\) −1.17106 + 0.111823i −0.0397484 + 0.00379551i
\(869\) −9.32222 38.4267i −0.316234 1.30354i
\(870\) −10.3501 + 1.97049i −0.350902 + 0.0668058i
\(871\) −23.5602 9.43208i −0.798307 0.319594i
\(872\) 4.48827 + 2.88443i 0.151992 + 0.0976793i
\(873\) −2.00796 46.5987i −0.0679590 1.57713i
\(874\) 13.4187 15.6081i 0.453893 0.527952i
\(875\) −1.65422 + 2.86519i −0.0559228 + 0.0968612i
\(876\) −6.12578 25.5031i −0.206971 0.861671i
\(877\) −5.95959 + 4.68667i −0.201241 + 0.158258i −0.713694 0.700458i \(-0.752979\pi\)
0.512453 + 0.858715i \(0.328737\pi\)
\(878\) 20.2929 28.4974i 0.684853 0.961741i
\(879\) 5.63919 + 9.81872i 0.190205 + 0.331177i
\(880\) −12.2924 17.2623i −0.414377 0.581912i
\(881\) −21.3226 + 24.6076i −0.718377 + 0.829051i −0.991111 0.133038i \(-0.957527\pi\)
0.272734 + 0.962089i \(0.412072\pi\)
\(882\) 8.59586 + 19.0505i 0.289438 + 0.641465i
\(883\) 31.3951 9.21844i 1.05653 0.310225i 0.293077 0.956089i \(-0.405321\pi\)
0.763453 + 0.645864i \(0.223503\pi\)
\(884\) −0.404991 + 0.0780556i −0.0136213 + 0.00262529i
\(885\) −11.9472 34.7741i −0.401600 1.16892i
\(886\) 29.9225 + 15.4261i 1.00527 + 0.518251i
\(887\) 10.5294 30.4226i 0.353542 1.02149i −0.618317 0.785929i \(-0.712185\pi\)
0.971859 0.235564i \(-0.0756936\pi\)
\(888\) 13.1892 8.43398i 0.442601 0.283026i
\(889\) 2.17627 + 1.71144i 0.0729896 + 0.0573997i
\(890\) −4.57911 + 5.28457i −0.153492 + 0.177139i
\(891\) −48.8904 + 8.96361i −1.63789 + 0.300292i
\(892\) 14.0912 + 4.13755i 0.471808 + 0.138535i
\(893\) 28.4345 + 2.71517i 0.951526 + 0.0908597i
\(894\) −7.16121 15.7755i −0.239507 0.527610i
\(895\) 3.57420 75.0317i 0.119472 2.50803i
\(896\) 0.0912669 + 0.158079i 0.00304901 + 0.00528105i
\(897\) 0.939739 + 19.0783i 0.0313770 + 0.637004i
\(898\) −4.28662 + 7.42465i −0.143046 + 0.247764i
\(899\) 8.59495 + 5.52364i 0.286658 + 0.184224i
\(900\) −19.0026 22.1322i −0.633420 0.737741i
\(901\) −0.791162 1.73240i −0.0263574 0.0577147i
\(902\) −23.6080 + 22.5102i −0.786062 + 0.749508i
\(903\) 0.354290 0.140905i 0.0117900 0.00468902i
\(904\) −10.0734 1.94148i −0.335035 0.0645727i
\(905\) −14.7527 + 5.90609i −0.490396 + 0.196325i
\(906\) 8.42081 + 4.36543i 0.279763 + 0.145032i
\(907\) −1.22297 + 0.235708i −0.0406080 + 0.00782655i −0.209515 0.977805i \(-0.567188\pi\)
0.168907 + 0.985632i \(0.445976\pi\)
\(908\) 23.0426 14.8086i 0.764697 0.491441i
\(909\) 24.7686 + 35.1187i 0.821523 + 1.16481i
\(910\) 1.05473 + 1.21722i 0.0349638 + 0.0403504i
\(911\) 1.21418 5.00492i 0.0402276 0.165821i −0.948155 0.317810i \(-0.897053\pi\)
0.988382 + 0.151989i \(0.0485679\pi\)
\(912\) 6.89504 + 2.77852i 0.228318 + 0.0920060i
\(913\) 40.3989 + 7.78625i 1.33701 + 0.257687i
\(914\) 2.11469 0.201928i 0.0699476 0.00667919i
\(915\) 31.9993 + 0.0725770i 1.05787 + 0.00239932i
\(916\) 17.4901 + 1.67010i 0.577890 + 0.0551818i
\(917\) −0.140499 0.977190i −0.00463967 0.0322696i
\(918\) 0.225880 0.904193i 0.00745516 0.0298428i
\(919\) 24.0305 0.792694 0.396347 0.918101i \(-0.370278\pi\)
0.396347 + 0.918101i \(0.370278\pi\)
\(920\) −0.947028 18.3779i −0.0312226 0.605900i
\(921\) 45.9087 13.3670i 1.51274 0.440457i
\(922\) 1.76544 37.0611i 0.0581416 1.22054i
\(923\) 18.7182 14.7202i 0.616117 0.484520i
\(924\) −1.71527 + 0.326558i −0.0564283 + 0.0107430i
\(925\) −63.6071 + 60.6493i −2.09139 + 1.99414i
\(926\) −0.277966 + 0.608660i −0.00913453 + 0.0200018i
\(927\) −8.74557 + 3.45525i −0.287242 + 0.113485i
\(928\) 0.225611 1.56916i 0.00740604 0.0515101i
\(929\) −8.29060 + 34.1743i −0.272006 + 1.12122i 0.657806 + 0.753187i \(0.271485\pi\)
−0.929812 + 0.368036i \(0.880030\pi\)
\(930\) −2.13509 + 42.7793i −0.0700123 + 1.40279i
\(931\) 26.5766 + 13.7012i 0.871012 + 0.449038i
\(932\) −2.22332 1.14620i −0.0728272 0.0375450i
\(933\) 0.479295 9.60331i 0.0156914 0.314398i
\(934\) 0.900066 3.71012i 0.0294511 0.121399i
\(935\) −0.540931 + 3.76226i −0.0176903 + 0.123039i
\(936\) −6.41601 + 2.53488i −0.209714 + 0.0828550i
\(937\) −0.350899 + 0.768362i −0.0114634 + 0.0251013i −0.915277 0.402825i \(-0.868028\pi\)
0.903814 + 0.427926i \(0.140756\pi\)
\(938\) 1.45794 1.39015i 0.0476036 0.0453899i
\(939\) −17.5175 + 3.33503i −0.571661 + 0.108834i
\(940\) 20.0736 15.7860i 0.654727 0.514883i
\(941\) −2.37828 + 49.9263i −0.0775298 + 1.62755i 0.540463 + 0.841368i \(0.318249\pi\)
−0.617993 + 0.786183i \(0.712054\pi\)
\(942\) −1.33299 + 0.388120i −0.0434313 + 0.0126456i
\(943\) −27.7930 + 5.46876i −0.905066 + 0.178087i
\(944\) 5.53243 0.180065
\(945\) −3.49889 + 1.00156i −0.113819 + 0.0325807i
\(946\) −0.947877 6.59263i −0.0308181 0.214345i
\(947\) 17.3836 + 1.65993i 0.564891 + 0.0539405i 0.373595 0.927592i \(-0.378125\pi\)
0.191296 + 0.981532i \(0.438731\pi\)
\(948\) 12.4008 + 0.0281261i 0.402760 + 0.000913492i
\(949\) 34.6643 3.31004i 1.12525 0.107448i
\(950\) −40.9787 7.89800i −1.32953 0.256245i
\(951\) −17.2333 6.94455i −0.558827 0.225193i
\(952\) 0.00771856 0.0318164i 0.000250160 0.00103117i
\(953\) −3.27643 3.78120i −0.106134 0.122485i 0.700197 0.713950i \(-0.253095\pi\)
−0.806331 + 0.591465i \(0.798550\pi\)
\(954\) −18.3599 26.0320i −0.594424 0.842817i
\(955\) 33.2854 21.3912i 1.07709 0.692204i
\(956\) −19.9971 + 3.85413i −0.646753 + 0.124651i
\(957\) 13.4630 + 6.97937i 0.435198 + 0.225611i
\(958\) −3.70267 + 1.48233i −0.119628 + 0.0478918i
\(959\) 3.87772 + 0.747369i 0.125218 + 0.0241338i
\(960\) 6.17562 2.45611i 0.199317 0.0792706i
\(961\) 7.62448 7.26992i 0.245951 0.234514i
\(962\) 8.63421 + 18.9063i 0.278378 + 0.609563i
\(963\) 24.7977 + 28.8817i 0.799094 + 0.930701i
\(964\) 8.69255 + 5.58636i 0.279968 + 0.179925i
\(965\) −44.5551 + 77.1717i −1.43428 + 2.48424i
\(966\) −1.40854 0.561252i −0.0453190 0.0180580i
\(967\) −1.56835 2.71647i −0.0504349 0.0873557i 0.839706 0.543042i \(-0.182727\pi\)
−0.890141 + 0.455686i \(0.849394\pi\)
\(968\) −0.927914 + 19.4793i −0.0298243 + 0.626089i
\(969\) −0.551133 1.21409i −0.0177049 0.0390022i
\(970\) −59.3870 5.67077i −1.90680 0.182078i
\(971\) −40.8425 11.9924i −1.31070 0.384855i −0.449570 0.893245i \(-0.648423\pi\)
−0.861127 + 0.508390i \(0.830241\pi\)
\(972\) 0.918256 15.5614i 0.0294531 0.499132i
\(973\) −0.0893693 + 0.103138i −0.00286505 + 0.00330644i
\(974\) −12.6982 9.98597i −0.406876 0.319971i
\(975\) 32.6277 20.8641i 1.04492 0.668187i
\(976\) −1.57475 + 4.54995i −0.0504066 + 0.145640i
\(977\) 47.3095 + 24.3897i 1.51357 + 0.780297i 0.997107 0.0760151i \(-0.0242197\pi\)
0.516459 + 0.856312i \(0.327250\pi\)
\(978\) −2.54386 7.40430i −0.0813438 0.236763i
\(979\) 9.88245 1.90469i 0.315844 0.0608740i
\(980\) 25.6493 7.53130i 0.819335 0.240579i
\(981\) −6.58287 14.5893i −0.210175 0.465799i
\(982\) −27.1012 + 31.2764i −0.864833 + 0.998071i
\(983\) −10.0642 14.1332i −0.320999 0.450780i 0.622274 0.782800i \(-0.286209\pi\)
−0.943272 + 0.332020i \(0.892270\pi\)
\(984\) −5.09496 8.87114i −0.162421 0.282802i
\(985\) 5.54390 7.78532i 0.176643 0.248061i
\(986\) −0.223505 + 0.175766i −0.00711784 + 0.00559753i
\(987\) −0.491425 2.04592i −0.0156422 0.0651225i
\(988\) −4.93472 + 8.54718i −0.156994 + 0.271922i
\(989\) 2.38218 5.27034i 0.0757488 0.167587i
\(990\) 2.73694 + 63.5163i 0.0869857 + 2.01868i
\(991\) 0.391026 + 0.251297i 0.0124213 + 0.00798271i 0.546837 0.837239i \(-0.315832\pi\)
−0.534415 + 0.845222i \(0.679468\pi\)
\(992\) −5.98311 2.39527i −0.189964 0.0760501i
\(993\) 8.99482 1.71246i 0.285442 0.0543432i
\(994\) 0.445639 + 1.83695i 0.0141348 + 0.0582645i
\(995\) 25.9754 2.48035i 0.823477 0.0786325i
\(996\) −5.38670 + 11.7248i −0.170684 + 0.371514i
\(997\) −18.7180 14.7200i −0.592806 0.466188i 0.276125 0.961122i \(-0.410950\pi\)
−0.868930 + 0.494934i \(0.835192\pi\)
\(998\) 0.802166 0.235537i 0.0253921 0.00745580i
\(999\) −46.9647 0.319563i −1.48590 0.0101105i
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 414.2.m.a.25.8 240
9.4 even 3 inner 414.2.m.a.301.7 yes 240
23.12 even 11 inner 414.2.m.a.403.7 yes 240
207.58 even 33 inner 414.2.m.a.265.8 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.2.m.a.25.8 240 1.1 even 1 trivial
414.2.m.a.265.8 yes 240 207.58 even 33 inner
414.2.m.a.301.7 yes 240 9.4 even 3 inner
414.2.m.a.403.7 yes 240 23.12 even 11 inner