Properties

Label 552.2.bf.a.5.15
Level $552$
Weight $2$
Character 552.5
Analytic conductor $4.408$
Analytic rank $0$
Dimension $920$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(5,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.bf (of order \(22\), degree \(10\), 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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(920\)
Relative dimension: \(92\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.15
Character \(\chi\) \(=\) 552.5
Dual form 552.2.bf.a.221.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24635 - 0.668282i) q^{2} +(-0.580308 + 1.63194i) q^{3} +(1.10680 + 1.66583i) q^{4} +(-0.920190 - 0.132303i) q^{5} +(1.81387 - 1.64617i) q^{6} +(-0.322471 + 0.147268i) q^{7} +(-0.266214 - 2.81587i) q^{8} +(-2.32649 - 1.89406i) q^{9} +O(q^{10})\) \(q+(-1.24635 - 0.668282i) q^{2} +(-0.580308 + 1.63194i) q^{3} +(1.10680 + 1.66583i) q^{4} +(-0.920190 - 0.132303i) q^{5} +(1.81387 - 1.64617i) q^{6} +(-0.322471 + 0.147268i) q^{7} +(-0.266214 - 2.81587i) q^{8} +(-2.32649 - 1.89406i) q^{9} +(1.05847 + 0.779843i) q^{10} +(0.0901905 + 0.307161i) q^{11} +(-3.36083 + 0.839535i) q^{12} +(-2.16222 - 0.987452i) q^{13} +(0.500330 + 0.0319542i) q^{14} +(0.749905 - 1.42492i) q^{15} +(-1.55000 + 3.68748i) q^{16} +(-1.75516 + 1.12798i) q^{17} +(1.63386 + 3.91542i) q^{18} +(-0.0845676 - 0.0543483i) q^{19} +(-0.798068 - 1.67932i) q^{20} +(-0.0532001 - 0.611716i) q^{21} +(0.0928608 - 0.443104i) q^{22} +(1.23653 - 4.63368i) q^{23} +(4.74983 + 1.19963i) q^{24} +(-3.96822 - 1.16517i) q^{25} +(2.03499 + 2.67569i) q^{26} +(4.44108 - 2.69756i) q^{27} +(-0.602234 - 0.374188i) q^{28} +(2.99108 - 1.92225i) q^{29} +(-1.88690 + 1.27481i) q^{30} +(0.0401171 + 0.0462976i) q^{31} +(4.39613 - 3.56007i) q^{32} +(-0.553607 - 0.0310618i) q^{33} +(2.94136 - 0.232911i) q^{34} +(0.316219 - 0.0928502i) q^{35} +(0.580241 - 5.97188i) q^{36} +(-1.13015 - 7.86034i) q^{37} +(0.0690812 + 0.124252i) q^{38} +(2.86622 - 2.95559i) q^{39} +(-0.127582 + 2.62636i) q^{40} +(-1.26210 - 0.181463i) q^{41} +(-0.342493 + 0.797967i) q^{42} +(6.23713 - 7.19803i) q^{43} +(-0.411856 + 0.490207i) q^{44} +(1.89022 + 2.05070i) q^{45} +(-4.63776 + 4.94885i) q^{46} -9.44900i q^{47} +(-5.11828 - 4.66939i) q^{48} +(-4.50173 + 5.19527i) q^{49} +(4.16714 + 4.10411i) q^{50} +(-0.822258 - 3.51890i) q^{51} +(-0.748206 - 4.69480i) q^{52} +(-0.326207 + 0.148974i) q^{53} +(-7.33789 + 0.394216i) q^{54} +(-0.0423540 - 0.294578i) q^{55} +(0.500533 + 0.868833i) q^{56} +(0.137769 - 0.106471i) q^{57} +(-5.01255 + 0.396918i) q^{58} +(-2.31548 + 5.07020i) q^{59} +(3.20367 - 0.327883i) q^{60} +(-5.63485 - 6.50296i) q^{61} +(-0.0190602 - 0.0845128i) q^{62} +(1.02916 + 0.268164i) q^{63} +(-7.85826 + 1.49925i) q^{64} +(1.85901 + 1.19471i) q^{65} +(0.669233 + 0.408680i) q^{66} +(-3.74302 - 1.09905i) q^{67} +(-3.82163 - 1.67537i) q^{68} +(6.84434 + 4.70691i) q^{69} +(-0.456170 - 0.0955992i) q^{70} +(2.34896 - 7.99984i) q^{71} +(-4.71409 + 7.05531i) q^{72} +(0.748775 + 0.481208i) q^{73} +(-3.84437 + 10.5520i) q^{74} +(4.20429 - 5.79976i) q^{75} +(-0.00306398 - 0.201028i) q^{76} +(-0.0743187 - 0.0857683i) q^{77} +(-5.54749 + 1.76827i) q^{78} +(0.311167 + 0.142105i) q^{79} +(1.91416 - 3.18811i) q^{80} +(1.82507 + 8.81301i) q^{81} +(1.45176 + 1.06961i) q^{82} +(-3.39721 + 0.488445i) q^{83} +(0.960135 - 0.765668i) q^{84} +(1.76432 - 0.805737i) q^{85} +(-12.5840 + 4.80313i) q^{86} +(1.40126 + 5.99677i) q^{87} +(0.840915 - 0.335735i) q^{88} +(-7.83239 + 9.03906i) q^{89} +(-0.985436 - 3.81909i) q^{90} +0.842673 q^{91} +(9.08753 - 3.06869i) q^{92} +(-0.0988354 + 0.0386020i) q^{93} +(-6.31460 + 11.7768i) q^{94} +(0.0706278 + 0.0611993i) q^{95} +(3.25872 + 9.24017i) q^{96} +(-13.2196 - 1.90069i) q^{97} +(9.08265 - 3.46672i) q^{98} +(0.371954 - 0.885431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24635 0.668282i −0.881305 0.472547i
\(3\) −0.580308 + 1.63194i −0.335041 + 0.942204i
\(4\) 1.10680 + 1.66583i 0.553399 + 0.832917i
\(5\) −0.920190 0.132303i −0.411521 0.0591678i −0.0665547 0.997783i \(-0.521201\pi\)
−0.344967 + 0.938615i \(0.612110\pi\)
\(6\) 1.81387 1.64617i 0.740509 0.672047i
\(7\) −0.322471 + 0.147268i −0.121883 + 0.0556619i −0.475423 0.879757i \(-0.657705\pi\)
0.353540 + 0.935419i \(0.384978\pi\)
\(8\) −0.266214 2.81587i −0.0941209 0.995561i
\(9\) −2.32649 1.89406i −0.775495 0.631353i
\(10\) 1.05847 + 0.779843i 0.334716 + 0.246608i
\(11\) 0.0901905 + 0.307161i 0.0271935 + 0.0926124i 0.971972 0.235098i \(-0.0755411\pi\)
−0.944778 + 0.327710i \(0.893723\pi\)
\(12\) −3.36083 + 0.839535i −0.970188 + 0.242353i
\(13\) −2.16222 0.987452i −0.599691 0.273870i 0.0923513 0.995726i \(-0.470562\pi\)
−0.692043 + 0.721857i \(0.743289\pi\)
\(14\) 0.500330 + 0.0319542i 0.133719 + 0.00854012i
\(15\) 0.749905 1.42492i 0.193625 0.367913i
\(16\) −1.55000 + 3.68748i −0.387500 + 0.921870i
\(17\) −1.75516 + 1.12798i −0.425690 + 0.273574i −0.735895 0.677095i \(-0.763238\pi\)
0.310206 + 0.950670i \(0.399602\pi\)
\(18\) 1.63386 + 3.91542i 0.385104 + 0.922873i
\(19\) −0.0845676 0.0543483i −0.0194011 0.0124684i 0.530904 0.847432i \(-0.321852\pi\)
−0.550305 + 0.834963i \(0.685489\pi\)
\(20\) −0.798068 1.67932i −0.178453 0.375506i
\(21\) −0.0532001 0.611716i −0.0116092 0.133487i
\(22\) 0.0928608 0.443104i 0.0197980 0.0944700i
\(23\) 1.23653 4.63368i 0.257835 0.966189i
\(24\) 4.74983 + 1.19963i 0.969555 + 0.244873i
\(25\) −3.96822 1.16517i −0.793644 0.233035i
\(26\) 2.03499 + 2.67569i 0.399095 + 0.524745i
\(27\) 4.44108 2.69756i 0.854686 0.519145i
\(28\) −0.602234 0.374188i −0.113811 0.0707148i
\(29\) 2.99108 1.92225i 0.555429 0.356953i −0.232617 0.972568i \(-0.574729\pi\)
0.788047 + 0.615616i \(0.211093\pi\)
\(30\) −1.88690 + 1.27481i −0.344499 + 0.232747i
\(31\) 0.0401171 + 0.0462976i 0.00720525 + 0.00831530i 0.759341 0.650693i \(-0.225522\pi\)
−0.752136 + 0.659008i \(0.770976\pi\)
\(32\) 4.39613 3.56007i 0.777133 0.629337i
\(33\) −0.553607 0.0310618i −0.0963707 0.00540717i
\(34\) 2.94136 0.232911i 0.504439 0.0399440i
\(35\) 0.316219 0.0928502i 0.0534507 0.0156945i
\(36\) 0.580241 5.97188i 0.0967069 0.995313i
\(37\) −1.13015 7.86034i −0.185795 1.29223i −0.842751 0.538303i \(-0.819065\pi\)
0.656956 0.753929i \(-0.271844\pi\)
\(38\) 0.0690812 + 0.124252i 0.0112064 + 0.0201564i
\(39\) 2.86622 2.95559i 0.458962 0.473274i
\(40\) −0.127582 + 2.62636i −0.0201724 + 0.415263i
\(41\) −1.26210 0.181463i −0.197107 0.0283397i 0.0430542 0.999073i \(-0.486291\pi\)
−0.240161 + 0.970733i \(0.577200\pi\)
\(42\) −0.342493 + 0.797967i −0.0528478 + 0.123129i
\(43\) 6.23713 7.19803i 0.951153 1.09769i −0.0439688 0.999033i \(-0.514000\pi\)
0.995122 0.0986559i \(-0.0314543\pi\)
\(44\) −0.411856 + 0.490207i −0.0620896 + 0.0739015i
\(45\) 1.89022 + 2.05070i 0.281777 + 0.305700i
\(46\) −4.63776 + 4.94885i −0.683801 + 0.729669i
\(47\) 9.44900i 1.37828i −0.724629 0.689139i \(-0.757989\pi\)
0.724629 0.689139i \(-0.242011\pi\)
\(48\) −5.11828 4.66939i −0.738761 0.673968i
\(49\) −4.50173 + 5.19527i −0.643104 + 0.742181i
\(50\) 4.16714 + 4.10411i 0.589323 + 0.580409i
\(51\) −0.822258 3.51890i −0.115139 0.492745i
\(52\) −0.748206 4.69480i −0.103758 0.651052i
\(53\) −0.326207 + 0.148974i −0.0448079 + 0.0204631i −0.437693 0.899125i \(-0.644204\pi\)
0.392885 + 0.919588i \(0.371477\pi\)
\(54\) −7.33789 + 0.394216i −0.998560 + 0.0536460i
\(55\) −0.0423540 0.294578i −0.00571101 0.0397210i
\(56\) 0.500533 + 0.868833i 0.0668865 + 0.116103i
\(57\) 0.137769 0.106471i 0.0182479 0.0141024i
\(58\) −5.01255 + 0.396918i −0.658180 + 0.0521179i
\(59\) −2.31548 + 5.07020i −0.301450 + 0.660084i −0.998370 0.0570646i \(-0.981826\pi\)
0.696920 + 0.717149i \(0.254553\pi\)
\(60\) 3.20367 0.327883i 0.413593 0.0423295i
\(61\) −5.63485 6.50296i −0.721468 0.832619i 0.270015 0.962856i \(-0.412971\pi\)
−0.991483 + 0.130238i \(0.958426\pi\)
\(62\) −0.0190602 0.0845128i −0.00242065 0.0107331i
\(63\) 1.02916 + 0.268164i 0.129662 + 0.0337855i
\(64\) −7.85826 + 1.49925i −0.982283 + 0.187406i
\(65\) 1.85901 + 1.19471i 0.230581 + 0.148186i
\(66\) 0.669233 + 0.408680i 0.0823768 + 0.0503050i
\(67\) −3.74302 1.09905i −0.457282 0.134270i 0.0449755 0.998988i \(-0.485679\pi\)
−0.502258 + 0.864718i \(0.667497\pi\)
\(68\) −3.82163 1.67537i −0.463441 0.203169i
\(69\) 6.84434 + 4.70691i 0.823962 + 0.566646i
\(70\) −0.456170 0.0955992i −0.0545228 0.0114263i
\(71\) 2.34896 7.99984i 0.278771 0.949406i −0.694451 0.719540i \(-0.744353\pi\)
0.973222 0.229867i \(-0.0738290\pi\)
\(72\) −4.71409 + 7.05531i −0.555560 + 0.831476i
\(73\) 0.748775 + 0.481208i 0.0876375 + 0.0563212i 0.583726 0.811951i \(-0.301594\pi\)
−0.496088 + 0.868272i \(0.665231\pi\)
\(74\) −3.84437 + 10.5520i −0.446898 + 1.22665i
\(75\) 4.20429 5.79976i 0.485470 0.669698i
\(76\) −0.00306398 0.201028i −0.000351462 0.0230595i
\(77\) −0.0743187 0.0857683i −0.00846940 0.00977421i
\(78\) −5.54749 + 1.76827i −0.628130 + 0.200217i
\(79\) 0.311167 + 0.142105i 0.0350090 + 0.0159881i 0.432843 0.901470i \(-0.357511\pi\)
−0.397834 + 0.917458i \(0.630238\pi\)
\(80\) 1.91416 3.18811i 0.214010 0.356441i
\(81\) 1.82507 + 8.81301i 0.202786 + 0.979223i
\(82\) 1.45176 + 1.06961i 0.160320 + 0.118118i
\(83\) −3.39721 + 0.488445i −0.372892 + 0.0536138i −0.326213 0.945296i \(-0.605773\pi\)
−0.0466788 + 0.998910i \(0.514864\pi\)
\(84\) 0.960135 0.765668i 0.104759 0.0835412i
\(85\) 1.76432 0.805737i 0.191367 0.0873945i
\(86\) −12.5840 + 4.80313i −1.35697 + 0.517935i
\(87\) 1.40126 + 5.99677i 0.150231 + 0.642921i
\(88\) 0.840915 0.335735i 0.0896418 0.0357895i
\(89\) −7.83239 + 9.03906i −0.830231 + 0.958138i −0.999624 0.0274106i \(-0.991274\pi\)
0.169393 + 0.985549i \(0.445819\pi\)
\(90\) −0.985436 3.81909i −0.103874 0.402568i
\(91\) 0.842673 0.0883361
\(92\) 9.08753 3.06869i 0.947440 0.319933i
\(93\) −0.0988354 + 0.0386020i −0.0102488 + 0.00400284i
\(94\) −6.31460 + 11.7768i −0.651301 + 1.21468i
\(95\) 0.0706278 + 0.0611993i 0.00724626 + 0.00627892i
\(96\) 3.25872 + 9.24017i 0.332592 + 0.943071i
\(97\) −13.2196 1.90069i −1.34224 0.192985i −0.566515 0.824052i \(-0.691709\pi\)
−0.775729 + 0.631066i \(0.782618\pi\)
\(98\) 9.08265 3.46672i 0.917486 0.350192i
\(99\) 0.371954 0.885431i 0.0373828 0.0889892i
\(100\) −2.45103 7.90000i −0.245103 0.790000i
\(101\) −0.627578 4.36490i −0.0624463 0.434324i −0.996929 0.0783144i \(-0.975046\pi\)
0.934482 0.356009i \(-0.115863\pi\)
\(102\) −1.32680 + 4.93530i −0.131372 + 0.488668i
\(103\) 2.81418 + 9.58421i 0.277289 + 0.944360i 0.973913 + 0.226923i \(0.0728667\pi\)
−0.696623 + 0.717437i \(0.745315\pi\)
\(104\) −2.20492 + 6.35140i −0.216211 + 0.622806i
\(105\) −0.0319778 + 0.569933i −0.00312072 + 0.0556198i
\(106\) 0.506125 + 0.0323243i 0.0491593 + 0.00313962i
\(107\) 5.88028 5.09529i 0.568468 0.492580i −0.322547 0.946553i \(-0.604539\pi\)
0.891015 + 0.453973i \(0.149994\pi\)
\(108\) 9.40905 + 4.41245i 0.905387 + 0.424588i
\(109\) −0.596822 + 0.383555i −0.0571652 + 0.0367379i −0.568911 0.822399i \(-0.692635\pi\)
0.511746 + 0.859137i \(0.328999\pi\)
\(110\) −0.144074 + 0.395454i −0.0137369 + 0.0377050i
\(111\) 13.4835 + 2.71708i 1.27979 + 0.257894i
\(112\) −0.0432159 1.41737i −0.00408352 0.133929i
\(113\) 0.259715 + 0.0762591i 0.0244319 + 0.00717385i 0.293926 0.955828i \(-0.405038\pi\)
−0.269494 + 0.963002i \(0.586856\pi\)
\(114\) −0.242861 + 0.0406321i −0.0227460 + 0.00380554i
\(115\) −1.75089 + 4.10027i −0.163272 + 0.382352i
\(116\) 6.51266 + 2.85510i 0.604686 + 0.265089i
\(117\) 3.16008 + 6.39266i 0.292149 + 0.591002i
\(118\) 6.27424 4.77187i 0.577591 0.439286i
\(119\) 0.399876 0.622218i 0.0366565 0.0570387i
\(120\) −4.21203 1.73230i −0.384504 0.158137i
\(121\) 9.16758 5.89164i 0.833416 0.535604i
\(122\) 2.67720 + 11.8707i 0.242382 + 1.07472i
\(123\) 1.02854 1.95437i 0.0927406 0.176220i
\(124\) −0.0327226 + 0.118070i −0.00293858 + 0.0106030i
\(125\) 7.72556 + 3.52815i 0.690995 + 0.315567i
\(126\) −1.10349 1.02200i −0.0983064 0.0910466i
\(127\) 2.09253 0.614422i 0.185682 0.0545211i −0.187570 0.982251i \(-0.560061\pi\)
0.373252 + 0.927730i \(0.378243\pi\)
\(128\) 10.7961 + 3.38294i 0.954249 + 0.299013i
\(129\) 8.12733 + 14.3557i 0.715571 + 1.26395i
\(130\) −1.51858 2.73138i −0.133188 0.239557i
\(131\) −3.76405 8.24213i −0.328867 0.720118i 0.670903 0.741545i \(-0.265906\pi\)
−0.999770 + 0.0214265i \(0.993179\pi\)
\(132\) −0.560987 0.956597i −0.0488277 0.0832610i
\(133\) 0.0352744 + 0.00507169i 0.00305868 + 0.000439771i
\(134\) 3.93065 + 3.87120i 0.339557 + 0.334421i
\(135\) −4.44353 + 1.89469i −0.382438 + 0.163069i
\(136\) 3.64348 + 4.64203i 0.312426 + 0.398051i
\(137\) −12.4739 −1.06571 −0.532857 0.846205i \(-0.678882\pi\)
−0.532857 + 0.846205i \(0.678882\pi\)
\(138\) −5.38492 10.4404i −0.458395 0.888748i
\(139\) 9.29929i 0.788756i 0.918948 + 0.394378i \(0.129040\pi\)
−0.918948 + 0.394378i \(0.870960\pi\)
\(140\) 0.504663 + 0.424001i 0.0426518 + 0.0358346i
\(141\) 15.4202 + 5.48333i 1.29862 + 0.461780i
\(142\) −8.27379 + 8.40086i −0.694321 + 0.704985i
\(143\) 0.108295 0.753207i 0.00905607 0.0629863i
\(144\) 10.5904 5.64307i 0.882530 0.470256i
\(145\) −3.00668 + 1.37310i −0.249691 + 0.114030i
\(146\) −0.611656 1.10015i −0.0506210 0.0910490i
\(147\) −5.86600 10.3614i −0.483820 0.854596i
\(148\) 11.8432 10.5824i 0.973503 0.869871i
\(149\) 5.34702 + 18.2103i 0.438045 + 1.49184i 0.822535 + 0.568714i \(0.192559\pi\)
−0.384490 + 0.923129i \(0.625623\pi\)
\(150\) −9.11591 + 4.41890i −0.744311 + 0.360801i
\(151\) −3.69476 + 8.09039i −0.300675 + 0.658387i −0.998313 0.0580639i \(-0.981507\pi\)
0.697638 + 0.716451i \(0.254235\pi\)
\(152\) −0.130525 + 0.252600i −0.0105870 + 0.0204885i
\(153\) 6.21982 + 0.700168i 0.502842 + 0.0566052i
\(154\) 0.0353099 + 0.156564i 0.00284535 + 0.0126162i
\(155\) −0.0307900 0.0479102i −0.00247311 0.00384824i
\(156\) 8.09585 + 1.50340i 0.648187 + 0.120368i
\(157\) 0.177692 + 0.114196i 0.0141814 + 0.00911382i 0.547712 0.836667i \(-0.315499\pi\)
−0.533531 + 0.845781i \(0.679135\pi\)
\(158\) −0.292858 0.385061i −0.0232985 0.0306338i
\(159\) −0.0538163 0.618802i −0.00426791 0.0490742i
\(160\) −4.51628 + 2.69431i −0.357043 + 0.213004i
\(161\) 0.283645 + 1.67633i 0.0223544 + 0.132113i
\(162\) 3.61490 12.2038i 0.284013 0.958820i
\(163\) −3.35221 + 11.4166i −0.262566 + 0.894217i 0.717670 + 0.696383i \(0.245209\pi\)
−0.980236 + 0.197833i \(0.936610\pi\)
\(164\) −1.09460 2.30329i −0.0854741 0.179857i
\(165\) 0.505314 + 0.101827i 0.0393386 + 0.00792721i
\(166\) 4.56055 + 1.66152i 0.353967 + 0.128959i
\(167\) −4.07581 6.34209i −0.315396 0.490766i 0.646973 0.762513i \(-0.276035\pi\)
−0.962369 + 0.271748i \(0.912398\pi\)
\(168\) −1.70835 + 0.312652i −0.131802 + 0.0241216i
\(169\) −4.81306 5.55457i −0.370236 0.427275i
\(170\) −2.73743 0.174829i −0.209951 0.0134088i
\(171\) 0.0938064 + 0.286617i 0.00717355 + 0.0219181i
\(172\) 18.8939 + 2.42326i 1.44065 + 0.184772i
\(173\) −16.8652 + 4.95208i −1.28224 + 0.376499i −0.850727 0.525608i \(-0.823838\pi\)
−0.431512 + 0.902107i \(0.642020\pi\)
\(174\) 2.26107 8.41053i 0.171411 0.637601i
\(175\) 1.45123 0.208655i 0.109703 0.0157729i
\(176\) −1.27244 0.143524i −0.0959140 0.0108185i
\(177\) −6.93059 6.72102i −0.520935 0.505183i
\(178\) 15.8026 6.03162i 1.18445 0.452089i
\(179\) −2.10280 + 14.6253i −0.157170 + 1.09314i 0.746646 + 0.665222i \(0.231663\pi\)
−0.903816 + 0.427921i \(0.859246\pi\)
\(180\) −1.32403 + 5.41849i −0.0986874 + 0.403870i
\(181\) 3.03080 3.49772i 0.225277 0.259984i −0.631847 0.775093i \(-0.717703\pi\)
0.857125 + 0.515109i \(0.172249\pi\)
\(182\) −1.05027 0.563143i −0.0778511 0.0417430i
\(183\) 13.8824 5.42204i 1.02622 0.400809i
\(184\) −13.3770 2.24836i −0.986168 0.165752i
\(185\) 7.38253i 0.542774i
\(186\) 0.148981 + 0.0179382i 0.0109238 + 0.00131529i
\(187\) −0.504769 0.437385i −0.0369123 0.0319847i
\(188\) 15.7405 10.4581i 1.14799 0.762737i
\(189\) −1.03486 + 1.52391i −0.0752748 + 0.110848i
\(190\) −0.0471288 0.123475i −0.00341908 0.00895784i
\(191\) −3.39636 7.43700i −0.245752 0.538122i 0.746052 0.665887i \(-0.231947\pi\)
−0.991804 + 0.127765i \(0.959220\pi\)
\(192\) 2.11352 13.6943i 0.152530 0.988299i
\(193\) −0.458314 3.18764i −0.0329902 0.229452i 0.966655 0.256081i \(-0.0824315\pi\)
−0.999645 + 0.0266298i \(0.991522\pi\)
\(194\) 15.2061 + 11.2033i 1.09173 + 0.804352i
\(195\) −3.02850 + 2.34050i −0.216875 + 0.167606i
\(196\) −13.6369 1.74902i −0.974068 0.124930i
\(197\) −6.31144 + 13.8201i −0.449672 + 0.984644i 0.540050 + 0.841633i \(0.318405\pi\)
−0.989721 + 0.143010i \(0.954322\pi\)
\(198\) −1.05530 + 0.854990i −0.0749972 + 0.0607615i
\(199\) 20.0270 17.3535i 1.41967 1.23015i 0.485063 0.874479i \(-0.338796\pi\)
0.934610 0.355675i \(-0.115749\pi\)
\(200\) −2.22459 + 11.4842i −0.157302 + 0.812054i
\(201\) 3.96569 5.47061i 0.279718 0.385867i
\(202\) −2.13480 + 5.85961i −0.150204 + 0.412281i
\(203\) −0.681451 + 1.06036i −0.0478285 + 0.0744226i
\(204\) 4.95183 5.26446i 0.346698 0.368586i
\(205\) 1.13736 + 0.333960i 0.0794369 + 0.0233248i
\(206\) 2.89750 13.8260i 0.201878 0.963302i
\(207\) −11.6532 + 8.43812i −0.809956 + 0.586490i
\(208\) 6.99265 6.44258i 0.484853 0.446713i
\(209\) 0.00906646 0.0308775i 0.000627140 0.00213584i
\(210\) 0.420732 0.688968i 0.0290333 0.0475433i
\(211\) −6.71529 + 10.4492i −0.462299 + 0.719352i −0.991637 0.129060i \(-0.958804\pi\)
0.529337 + 0.848411i \(0.322441\pi\)
\(212\) −0.609210 0.378522i −0.0418407 0.0259970i
\(213\) 11.6922 + 8.47575i 0.801134 + 0.580749i
\(214\) −10.7340 + 2.42085i −0.733761 + 0.165486i
\(215\) −6.69166 + 5.79836i −0.456367 + 0.395445i
\(216\) −8.77825 11.7874i −0.597284 0.802030i
\(217\) −0.0197548 0.00902169i −0.00134104 0.000612432i
\(218\) 1.00017 0.0791987i 0.0677404 0.00536402i
\(219\) −1.21983 + 0.942710i −0.0824282 + 0.0637024i
\(220\) 0.443841 0.396593i 0.0299238 0.0267383i
\(221\) 4.90887 0.705789i 0.330206 0.0474765i
\(222\) −14.9894 12.3972i −1.00602 0.832047i
\(223\) −4.04126 8.84912i −0.270623 0.592581i 0.724713 0.689051i \(-0.241972\pi\)
−0.995336 + 0.0964696i \(0.969245\pi\)
\(224\) −0.893342 + 1.79543i −0.0596889 + 0.119962i
\(225\) 7.02510 + 10.2268i 0.468340 + 0.681787i
\(226\) −0.272734 0.268608i −0.0181420 0.0178676i
\(227\) −17.5913 15.2430i −1.16758 1.01171i −0.999664 0.0259084i \(-0.991752\pi\)
−0.167912 0.985802i \(-0.553702\pi\)
\(228\) 0.329845 + 0.111658i 0.0218445 + 0.00739473i
\(229\) −15.5298 −1.02624 −0.513119 0.858317i \(-0.671510\pi\)
−0.513119 + 0.858317i \(0.671510\pi\)
\(230\) 4.92237 3.94029i 0.324572 0.259815i
\(231\) 0.183097 0.0715119i 0.0120469 0.00470514i
\(232\) −6.20907 7.91076i −0.407646 0.519367i
\(233\) −17.1456 14.8567i −1.12324 0.973296i −0.123425 0.992354i \(-0.539388\pi\)
−0.999818 + 0.0190580i \(0.993933\pi\)
\(234\) 0.333532 10.0793i 0.0218037 0.658907i
\(235\) −1.25013 + 8.69487i −0.0815497 + 0.567191i
\(236\) −11.0089 + 1.75448i −0.716617 + 0.114207i
\(237\) −0.412480 + 0.425342i −0.0267935 + 0.0276290i
\(238\) −0.914204 + 0.508275i −0.0592591 + 0.0329466i
\(239\) −14.8841 + 2.14001i −0.962770 + 0.138425i −0.605736 0.795666i \(-0.707121\pi\)
−0.357034 + 0.934091i \(0.616212\pi\)
\(240\) 4.09202 + 4.97389i 0.264138 + 0.321063i
\(241\) 6.34645 + 21.6140i 0.408810 + 1.39228i 0.864720 + 0.502254i \(0.167496\pi\)
−0.455909 + 0.890026i \(0.650686\pi\)
\(242\) −15.3633 + 1.21654i −0.987592 + 0.0782024i
\(243\) −15.4414 2.13585i −0.990569 0.137015i
\(244\) 4.59621 16.5842i 0.294242 1.06169i
\(245\) 4.82979 4.18504i 0.308564 0.267372i
\(246\) −2.58800 + 1.74848i −0.165005 + 0.111479i
\(247\) 0.129187 + 0.201019i 0.00821999 + 0.0127906i
\(248\) 0.119688 0.125290i 0.00760022 0.00795590i
\(249\) 1.17431 5.82751i 0.0744190 0.369303i
\(250\) −7.27099 9.56018i −0.459858 0.604639i
\(251\) −1.89361 + 6.44904i −0.119523 + 0.407060i −0.997420 0.0717914i \(-0.977128\pi\)
0.877896 + 0.478851i \(0.158947\pi\)
\(252\) 0.692353 + 2.01121i 0.0436142 + 0.126694i
\(253\) 1.53481 0.0381001i 0.0964925 0.00239533i
\(254\) −3.01864 0.632613i −0.189406 0.0396937i
\(255\) 0.291071 + 3.34685i 0.0182275 + 0.209588i
\(256\) −11.1950 11.4312i −0.699687 0.714449i
\(257\) 2.82934 4.40254i 0.176490 0.274623i −0.741727 0.670702i \(-0.765993\pi\)
0.918216 + 0.396079i \(0.129629\pi\)
\(258\) −0.535855 23.3237i −0.0333609 1.45207i
\(259\) 1.52201 + 2.36830i 0.0945733 + 0.147159i
\(260\) 0.0673539 + 4.41910i 0.00417711 + 0.274061i
\(261\) −10.5996 1.19320i −0.656096 0.0738571i
\(262\) −0.816726 + 12.7881i −0.0504575 + 0.790049i
\(263\) 6.71392 14.7014i 0.413998 0.906530i −0.581659 0.813433i \(-0.697596\pi\)
0.995657 0.0930970i \(-0.0296767\pi\)
\(264\) 0.0599119 + 1.56716i 0.00368732 + 0.0964518i
\(265\) 0.319882 0.0939257i 0.0196502 0.00576981i
\(266\) −0.0405750 0.0298944i −0.00248781 0.00183294i
\(267\) −10.2060 18.0275i −0.624600 1.10326i
\(268\) −2.31193 7.45167i −0.141224 0.455183i
\(269\) −9.05469 19.8270i −0.552074 1.20887i −0.955807 0.293996i \(-0.905015\pi\)
0.403733 0.914877i \(-0.367713\pi\)
\(270\) 6.80440 + 0.608073i 0.414103 + 0.0370062i
\(271\) −2.87994 + 20.0304i −0.174944 + 1.21676i 0.693310 + 0.720639i \(0.256152\pi\)
−0.868254 + 0.496120i \(0.834758\pi\)
\(272\) −1.43888 8.22049i −0.0872449 0.498441i
\(273\) −0.489010 + 1.37520i −0.0295962 + 0.0832306i
\(274\) 15.5469 + 8.33607i 0.939220 + 0.503600i
\(275\) 1.32397i 0.0798383i
\(276\) −0.265635 + 16.6111i −0.0159893 + 0.999872i
\(277\) 16.6215i 0.998690i −0.866403 0.499345i \(-0.833574\pi\)
0.866403 0.499345i \(-0.166426\pi\)
\(278\) 6.21455 11.5902i 0.372724 0.695135i
\(279\) −0.00564140 0.183695i −0.000337742 0.0109975i
\(280\) −0.345636 0.865713i −0.0206557 0.0517362i
\(281\) 3.63417 25.2762i 0.216796 1.50785i −0.532962 0.846139i \(-0.678921\pi\)
0.749758 0.661712i \(-0.230170\pi\)
\(282\) −15.5547 17.1392i −0.926267 1.02063i
\(283\) 12.9937 + 28.4523i 0.772398 + 1.69132i 0.721301 + 0.692622i \(0.243545\pi\)
0.0510976 + 0.998694i \(0.483728\pi\)
\(284\) 15.9262 4.94122i 0.945048 0.293207i
\(285\) −0.140860 + 0.0797462i −0.00834381 + 0.00472376i
\(286\) −0.638329 + 0.866391i −0.0377452 + 0.0512308i
\(287\) 0.433714 0.127350i 0.0256014 0.00751723i
\(288\) −16.9705 0.0440875i −0.999997 0.00259788i
\(289\) −5.25378 + 11.5042i −0.309046 + 0.676716i
\(290\) 4.66501 + 0.297937i 0.273939 + 0.0174954i
\(291\) 10.7732 20.4706i 0.631538 1.20001i
\(292\) 0.0271289 + 1.77993i 0.00158760 + 0.104163i
\(293\) −12.1148 18.8511i −0.707757 1.10129i −0.989879 0.141913i \(-0.954675\pi\)
0.282122 0.959379i \(-0.408962\pi\)
\(294\) 0.386760 + 16.8341i 0.0225563 + 0.981787i
\(295\) 2.80149 4.35920i 0.163109 0.253802i
\(296\) −21.8328 + 5.27488i −1.26901 + 0.306596i
\(297\) 1.22913 + 1.12083i 0.0713211 + 0.0650372i
\(298\) 5.50533 26.2698i 0.318915 1.52177i
\(299\) −7.24919 + 8.79801i −0.419231 + 0.508802i
\(300\) 14.3147 + 0.584493i 0.826461 + 0.0337457i
\(301\) −0.951257 + 3.23968i −0.0548295 + 0.186732i
\(302\) 10.0116 7.61435i 0.576105 0.438157i
\(303\) 7.48746 + 1.50881i 0.430143 + 0.0866791i
\(304\) 0.331488 0.227601i 0.0190121 0.0130538i
\(305\) 4.32476 + 6.72946i 0.247635 + 0.385328i
\(306\) −7.28418 5.02925i −0.416409 0.287503i
\(307\) −6.47536 + 5.61093i −0.369568 + 0.320233i −0.819769 0.572695i \(-0.805898\pi\)
0.450200 + 0.892928i \(0.351353\pi\)
\(308\) 0.0606200 0.218731i 0.00345415 0.0124633i
\(309\) −17.2740 0.969211i −0.982683 0.0551365i
\(310\) 0.00635772 + 0.0802895i 0.000361094 + 0.00456014i
\(311\) 5.73628 + 19.5360i 0.325275 + 1.10778i 0.946111 + 0.323843i \(0.104975\pi\)
−0.620836 + 0.783940i \(0.713207\pi\)
\(312\) −9.08560 7.28408i −0.514371 0.412380i
\(313\) 25.9251 3.72747i 1.46537 0.210689i 0.636999 0.770865i \(-0.280176\pi\)
0.828374 + 0.560176i \(0.189266\pi\)
\(314\) −0.145152 0.261077i −0.00819142 0.0147334i
\(315\) −0.911542 0.382923i −0.0513596 0.0215752i
\(316\) 0.107675 + 0.675634i 0.00605720 + 0.0380074i
\(317\) −1.59902 + 11.1214i −0.0898099 + 0.624642i 0.894351 + 0.447365i \(0.147638\pi\)
−0.984161 + 0.177276i \(0.943271\pi\)
\(318\) −0.346460 + 0.807211i −0.0194285 + 0.0452661i
\(319\) 0.860206 + 0.745373i 0.0481623 + 0.0417329i
\(320\) 7.42944 0.339919i 0.415319 0.0190021i
\(321\) 4.90286 + 12.5531i 0.273651 + 0.700647i
\(322\) 0.766739 2.27886i 0.0427287 0.126996i
\(323\) 0.209734 0.0116699
\(324\) −12.6610 + 12.7945i −0.703390 + 0.710804i
\(325\) 7.42960 + 6.43779i 0.412120 + 0.357104i
\(326\) 11.8076 11.9889i 0.653960 0.664003i
\(327\) −0.279599 1.19656i −0.0154619 0.0661700i
\(328\) −0.174987 + 3.60222i −0.00966202 + 0.198899i
\(329\) 1.39153 + 3.04703i 0.0767177 + 0.167988i
\(330\) −0.561751 0.464605i −0.0309234 0.0255757i
\(331\) 31.4747 4.52539i 1.73001 0.248738i 0.795824 0.605528i \(-0.207038\pi\)
0.934184 + 0.356790i \(0.116129\pi\)
\(332\) −4.57369 5.11858i −0.251014 0.280918i
\(333\) −12.2587 + 20.4275i −0.671772 + 1.11942i
\(334\) 0.841599 + 10.6283i 0.0460503 + 0.581554i
\(335\) 3.29888 + 1.50655i 0.180237 + 0.0823115i
\(336\) 2.33815 + 0.751985i 0.127556 + 0.0410242i
\(337\) 14.4986 12.5631i 0.789791 0.684357i −0.163456 0.986551i \(-0.552264\pi\)
0.953247 + 0.302193i \(0.0977188\pi\)
\(338\) 2.28676 + 10.1395i 0.124383 + 0.551513i
\(339\) −0.275165 + 0.379586i −0.0149449 + 0.0206163i
\(340\) 3.29497 + 2.04727i 0.178695 + 0.111029i
\(341\) −0.0106026 + 0.0164980i −0.000574164 + 0.000893417i
\(342\) 0.0746250 0.419915i 0.00403526 0.0227064i
\(343\) 1.38572 4.71931i 0.0748216 0.254819i
\(344\) −21.9291 15.6467i −1.18234 0.843615i
\(345\) −5.67535 5.23678i −0.305551 0.281939i
\(346\) 24.3294 + 5.09869i 1.30796 + 0.274107i
\(347\) 11.9355 + 3.50457i 0.640730 + 0.188135i 0.585930 0.810362i \(-0.300729\pi\)
0.0548007 + 0.998497i \(0.482548\pi\)
\(348\) −8.43871 + 8.97147i −0.452362 + 0.480921i
\(349\) −3.56518 + 5.54753i −0.190840 + 0.296952i −0.923467 0.383677i \(-0.874657\pi\)
0.732627 + 0.680630i \(0.238294\pi\)
\(350\) −1.94819 0.709773i −0.104135 0.0379389i
\(351\) −12.2663 + 1.44735i −0.654726 + 0.0772541i
\(352\) 1.49000 + 1.02923i 0.0794173 + 0.0548583i
\(353\) 19.1379 16.5831i 1.01861 0.882627i 0.0254798 0.999675i \(-0.491889\pi\)
0.993126 + 0.117048i \(0.0373432\pi\)
\(354\) 4.14644 + 13.0084i 0.220381 + 0.691387i
\(355\) −3.21990 + 7.05059i −0.170894 + 0.374207i
\(356\) −23.7264 3.04305i −1.25750 0.161281i
\(357\) 0.783375 + 1.01365i 0.0414606 + 0.0536482i
\(358\) 12.3946 16.8230i 0.655077 0.889123i
\(359\) 1.58193 + 11.0026i 0.0834912 + 0.580694i 0.988025 + 0.154292i \(0.0493098\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(360\) 5.27129 5.86853i 0.277822 0.309299i
\(361\) −7.88869 17.2738i −0.415194 0.909148i
\(362\) −6.11491 + 2.33398i −0.321393 + 0.122671i
\(363\) 4.29482 + 18.3799i 0.225419 + 0.964697i
\(364\) 0.932668 + 1.40375i 0.0488851 + 0.0735766i
\(365\) −0.625349 0.541868i −0.0327323 0.0283627i
\(366\) −20.9259 2.51960i −1.09381 0.131701i
\(367\) 24.9875i 1.30434i −0.758073 0.652169i \(-0.773859\pi\)
0.758073 0.652169i \(-0.226141\pi\)
\(368\) 15.1700 + 11.7419i 0.790789 + 0.612088i
\(369\) 2.59256 + 2.81266i 0.134963 + 0.146421i
\(370\) 4.93361 9.20124i 0.256486 0.478350i
\(371\) 0.0832533 0.0960794i 0.00432229 0.00498819i
\(372\) −0.173695 0.121919i −0.00900568 0.00632119i
\(373\) −0.750236 + 5.21800i −0.0388457 + 0.270178i −0.999983 0.00589420i \(-0.998124\pi\)
0.961137 + 0.276072i \(0.0890329\pi\)
\(374\) 0.336824 + 0.882464i 0.0174168 + 0.0456311i
\(375\) −10.2409 + 10.5603i −0.528840 + 0.545331i
\(376\) −26.6072 + 2.51546i −1.37216 + 0.129725i
\(377\) −8.36549 + 1.20278i −0.430845 + 0.0619461i
\(378\) 2.30820 1.20776i 0.118721 0.0621203i
\(379\) 34.3575 10.0883i 1.76483 0.518199i 0.771776 0.635895i \(-0.219369\pi\)
0.993050 + 0.117696i \(0.0375507\pi\)
\(380\) −0.0237772 + 0.185389i −0.00121975 + 0.00951027i
\(381\) −0.211608 + 3.77144i −0.0108410 + 0.193217i
\(382\) −0.736944 + 11.5389i −0.0377054 + 0.590380i
\(383\) 9.61537 + 11.0967i 0.491323 + 0.567016i 0.946219 0.323528i \(-0.104869\pi\)
−0.454896 + 0.890545i \(0.650324\pi\)
\(384\) −11.7858 + 15.6555i −0.601443 + 0.798915i
\(385\) 0.0570398 + 0.0887557i 0.00290702 + 0.00452341i
\(386\) −1.55903 + 4.27922i −0.0793523 + 0.217806i
\(387\) −28.1441 + 4.93261i −1.43064 + 0.250739i
\(388\) −11.4652 24.1253i −0.582055 1.22477i
\(389\) 3.08056 10.4914i 0.156190 0.531936i −0.843798 0.536660i \(-0.819686\pi\)
0.999989 + 0.00472459i \(0.00150389\pi\)
\(390\) 5.33869 0.893194i 0.270335 0.0452286i
\(391\) 3.05636 + 9.52765i 0.154567 + 0.481834i
\(392\) 15.8276 + 11.2932i 0.799416 + 0.570394i
\(393\) 15.6350 1.35976i 0.788682 0.0685906i
\(394\) 17.1020 13.0070i 0.861588 0.655281i
\(395\) −0.267531 0.171932i −0.0134610 0.00865084i
\(396\) 1.88666 0.360379i 0.0948081 0.0181097i
\(397\) −1.71971 2.67592i −0.0863098 0.134301i 0.795414 0.606066i \(-0.207253\pi\)
−0.881724 + 0.471765i \(0.843617\pi\)
\(398\) −36.5577 + 8.24489i −1.83247 + 0.413279i
\(399\) −0.0287467 + 0.0546227i −0.00143914 + 0.00273455i
\(400\) 10.4473 12.8267i 0.522365 0.641335i
\(401\) 12.0123 26.3033i 0.599867 1.31352i −0.329426 0.944181i \(-0.606855\pi\)
0.929293 0.369343i \(-0.120417\pi\)
\(402\) −8.59857 + 4.16812i −0.428858 + 0.207887i
\(403\) −0.0410253 0.139719i −0.00204361 0.00695991i
\(404\) 6.57659 5.87650i 0.327198 0.292367i
\(405\) −0.513420 8.35110i −0.0255121 0.414970i
\(406\) 1.55795 0.866181i 0.0773197 0.0429878i
\(407\) 2.31246 1.05606i 0.114624 0.0523472i
\(408\) −9.68988 + 3.25215i −0.479721 + 0.161006i
\(409\) −0.668664 + 4.65066i −0.0330633 + 0.229960i −0.999652 0.0263712i \(-0.991605\pi\)
0.966589 + 0.256332i \(0.0825139\pi\)
\(410\) −1.19438 1.17631i −0.0589861 0.0580939i
\(411\) 7.23869 20.3567i 0.357058 1.00412i
\(412\) −12.8510 + 15.2957i −0.633122 + 0.753567i
\(413\) 1.97599i 0.0972321i
\(414\) 20.1631 2.72923i 0.990963 0.134134i
\(415\) 3.19070 0.156625
\(416\) −13.0208 + 3.35668i −0.638396 + 0.164575i
\(417\) −15.1759 5.39645i −0.743168 0.264265i
\(418\) −0.0319349 + 0.0324254i −0.00156199 + 0.00158598i
\(419\) 30.2562 + 4.35018i 1.47811 + 0.212520i 0.833725 0.552179i \(-0.186204\pi\)
0.644387 + 0.764700i \(0.277113\pi\)
\(420\) −0.984806 + 0.577530i −0.0480536 + 0.0281806i
\(421\) −4.94332 10.8244i −0.240923 0.527547i 0.750087 0.661339i \(-0.230012\pi\)
−0.991009 + 0.133792i \(0.957284\pi\)
\(422\) 15.3526 8.53568i 0.747355 0.415510i
\(423\) −17.8970 + 21.9830i −0.870181 + 1.06885i
\(424\) 0.506331 + 0.878897i 0.0245896 + 0.0426830i
\(425\) 8.27917 2.43098i 0.401599 0.117920i
\(426\) −8.90839 18.3775i −0.431613 0.890391i
\(427\) 2.77475 + 1.26719i 0.134280 + 0.0613235i
\(428\) 14.9962 + 4.15611i 0.724868 + 0.200893i
\(429\) 1.16635 + 0.613823i 0.0563118 + 0.0296357i
\(430\) 12.2151 2.75489i 0.589065 0.132852i
\(431\) −12.3191 + 7.91699i −0.593389 + 0.381348i −0.802596 0.596523i \(-0.796548\pi\)
0.209206 + 0.977872i \(0.432912\pi\)
\(432\) 3.06351 + 20.5576i 0.147393 + 0.989078i
\(433\) 4.66609 7.26058i 0.224238 0.348921i −0.710846 0.703348i \(-0.751688\pi\)
0.935084 + 0.354427i \(0.115324\pi\)
\(434\) 0.0185924 + 0.0244460i 0.000892463 + 0.00117344i
\(435\) −0.496030 5.70356i −0.0237828 0.273465i
\(436\) −1.29950 0.569690i −0.0622347 0.0272832i
\(437\) −0.356403 + 0.324656i −0.0170491 + 0.0155304i
\(438\) 2.15033 0.359763i 0.102747 0.0171901i
\(439\) −7.70419 2.26215i −0.367701 0.107967i 0.0926618 0.995698i \(-0.470462\pi\)
−0.460363 + 0.887731i \(0.652281\pi\)
\(440\) −0.818220 + 0.197684i −0.0390071 + 0.00942423i
\(441\) 20.3134 3.56018i 0.967302 0.169532i
\(442\) −6.58985 2.40085i −0.313447 0.114197i
\(443\) −14.6184 + 9.39471i −0.694543 + 0.446356i −0.839698 0.543053i \(-0.817268\pi\)
0.145155 + 0.989409i \(0.453632\pi\)
\(444\) 10.3973 + 25.4685i 0.493432 + 1.20868i
\(445\) 8.40318 7.28139i 0.398349 0.345171i
\(446\) −0.876874 + 13.7298i −0.0415212 + 0.650127i
\(447\) −32.8211 1.84153i −1.55238 0.0871012i
\(448\) 2.31327 1.64073i 0.109292 0.0775173i
\(449\) 6.60463 + 22.4933i 0.311692 + 1.06153i 0.955169 + 0.296060i \(0.0956729\pi\)
−0.643477 + 0.765465i \(0.722509\pi\)
\(450\) −1.92136 17.4410i −0.0905737 0.822176i
\(451\) −0.0580913 0.404034i −0.00273541 0.0190252i
\(452\) 0.160416 + 0.517044i 0.00754535 + 0.0243197i
\(453\) −11.0590 10.7246i −0.519596 0.503884i
\(454\) 11.7384 + 30.7541i 0.550910 + 1.44336i
\(455\) −0.775419 0.111488i −0.0363522 0.00522665i
\(456\) −0.336484 0.359595i −0.0157573 0.0168396i
\(457\) 2.24874 + 1.94854i 0.105192 + 0.0911490i 0.705869 0.708343i \(-0.250557\pi\)
−0.600677 + 0.799492i \(0.705102\pi\)
\(458\) 19.3556 + 10.3783i 0.904429 + 0.484946i
\(459\) −4.75204 + 9.74408i −0.221806 + 0.454815i
\(460\) −8.76824 + 1.62147i −0.408822 + 0.0756012i
\(461\) −20.9722 −0.976771 −0.488385 0.872628i \(-0.662414\pi\)
−0.488385 + 0.872628i \(0.662414\pi\)
\(462\) −0.275994 0.0332312i −0.0128404 0.00154606i
\(463\) 13.2307 15.2691i 0.614885 0.709615i −0.359843 0.933013i \(-0.617170\pi\)
0.974727 + 0.223398i \(0.0717151\pi\)
\(464\) 2.45208 + 14.0090i 0.113835 + 0.650353i
\(465\) 0.0960545 0.0224449i 0.00445442 0.00104086i
\(466\) 11.4410 + 29.9748i 0.529992 + 1.38856i
\(467\) 29.4667 13.4570i 1.36356 0.622716i 0.406778 0.913527i \(-0.366652\pi\)
0.956780 + 0.290811i \(0.0939251\pi\)
\(468\) −7.15155 + 12.3395i −0.330580 + 0.570395i
\(469\) 1.36887 0.196814i 0.0632085 0.00908802i
\(470\) 7.36874 10.0014i 0.339895 0.461332i
\(471\) −0.289478 + 0.223715i −0.0133384 + 0.0103082i
\(472\) 14.8934 + 5.17034i 0.685527 + 0.237984i
\(473\) 2.77348 + 1.26661i 0.127525 + 0.0582386i
\(474\) 0.798345 0.254474i 0.0366692 0.0116884i
\(475\) 0.272258 + 0.314202i 0.0124920 + 0.0144166i
\(476\) 1.47909 0.0225437i 0.0677941 0.00103329i
\(477\) 1.04108 + 0.271270i 0.0476678 + 0.0124206i
\(478\) 19.9809 + 7.27956i 0.913907 + 0.332959i
\(479\) 21.0854 + 13.5508i 0.963416 + 0.619150i 0.924941 0.380110i \(-0.124114\pi\)
0.0384745 + 0.999260i \(0.487750\pi\)
\(480\) −1.77614 8.93385i −0.0810693 0.407772i
\(481\) −5.31809 + 18.1117i −0.242484 + 0.825824i
\(482\) 6.53434 31.1799i 0.297631 1.42021i
\(483\) −2.90028 0.509894i −0.131967 0.0232010i
\(484\) 19.9611 + 8.75080i 0.907325 + 0.397764i
\(485\) 11.9130 + 3.49798i 0.540943 + 0.158835i
\(486\) 17.8182 + 12.9813i 0.808248 + 0.588842i
\(487\) −21.4495 13.7848i −0.971971 0.624648i −0.0446849 0.999001i \(-0.514228\pi\)
−0.927286 + 0.374353i \(0.877865\pi\)
\(488\) −16.8114 + 17.5982i −0.761017 + 0.796632i
\(489\) −16.6859 12.0958i −0.754564 0.546990i
\(490\) −8.81642 + 1.98837i −0.398285 + 0.0898256i
\(491\) 7.49428 + 8.64886i 0.338212 + 0.390318i 0.899223 0.437491i \(-0.144133\pi\)
−0.561011 + 0.827809i \(0.689587\pi\)
\(492\) 4.39405 0.449712i 0.198099 0.0202746i
\(493\) −3.08158 + 6.74772i −0.138787 + 0.303902i
\(494\) −0.0266754 0.336875i −0.00120018 0.0151567i
\(495\) −0.459414 + 0.765554i −0.0206491 + 0.0344091i
\(496\) −0.232903 + 0.0761697i −0.0104577 + 0.00342012i
\(497\) 0.420644 + 2.92564i 0.0188685 + 0.131233i
\(498\) −5.35803 + 6.47837i −0.240099 + 0.290302i
\(499\) −22.4491 + 10.2522i −1.00496 + 0.458950i −0.848762 0.528776i \(-0.822651\pi\)
−0.156198 + 0.987726i \(0.549924\pi\)
\(500\) 2.67333 + 16.7744i 0.119555 + 0.750176i
\(501\) 12.7152 2.97114i 0.568072 0.132741i
\(502\) 6.66989 6.77232i 0.297692 0.302263i
\(503\) −25.4556 + 29.3773i −1.13501 + 1.30987i −0.190387 + 0.981709i \(0.560974\pi\)
−0.944622 + 0.328161i \(0.893571\pi\)
\(504\) 0.481138 2.96937i 0.0214316 0.132266i
\(505\) 4.09957i 0.182428i
\(506\) −1.93838 0.978199i −0.0861713 0.0434862i
\(507\) 11.8578 4.63129i 0.526624 0.205683i
\(508\) 3.33953 + 2.80576i 0.148168 + 0.124486i
\(509\) 23.5211 27.1448i 1.04255 1.20317i 0.0638367 0.997960i \(-0.479666\pi\)
0.978718 0.205212i \(-0.0657882\pi\)
\(510\) 1.87386 4.36587i 0.0829760 0.193324i
\(511\) −0.312325 0.0449055i −0.0138164 0.00198650i
\(512\) 6.31367 + 21.7287i 0.279027 + 0.960283i
\(513\) −0.522179 0.0132392i −0.0230548 0.000584524i
\(514\) −6.46851 + 3.59633i −0.285314 + 0.158627i
\(515\) −1.32155 9.19162i −0.0582347 0.405031i
\(516\) −14.9189 + 29.4276i −0.656769 + 1.29548i
\(517\) 2.90236 0.852210i 0.127646 0.0374802i
\(518\) −0.314275 3.96887i −0.0138084 0.174382i
\(519\) 1.70551 30.3968i 0.0748635 1.33427i
\(520\) 2.86926 5.55277i 0.125825 0.243505i
\(521\) 9.99111 + 11.5304i 0.437719 + 0.505154i 0.931153 0.364629i \(-0.118804\pi\)
−0.493434 + 0.869783i \(0.664259\pi\)
\(522\) 12.4134 + 8.57064i 0.543320 + 0.375127i
\(523\) 11.4379 7.35072i 0.500146 0.321425i −0.266128 0.963938i \(-0.585745\pi\)
0.766275 + 0.642513i \(0.222108\pi\)
\(524\) 9.56397 15.3927i 0.417804 0.672431i
\(525\) −0.501646 + 2.48941i −0.0218936 + 0.108647i
\(526\) −18.1926 + 13.8364i −0.793237 + 0.603296i
\(527\) −0.122635 0.0360088i −0.00534205 0.00156857i
\(528\) 0.972631 1.99327i 0.0423284 0.0867459i
\(529\) −19.9420 11.4594i −0.867043 0.498234i
\(530\) −0.461455 0.0967066i −0.0200443 0.00420067i
\(531\) 14.9902 7.41009i 0.650520 0.321570i
\(532\) 0.0305930 + 0.0643745i 0.00132637 + 0.00279099i
\(533\) 2.54975 + 1.63862i 0.110442 + 0.0709767i
\(534\) 0.672910 + 29.2891i 0.0291197 + 1.26746i
\(535\) −6.08510 + 3.91065i −0.263082 + 0.169072i
\(536\) −2.09834 + 10.8324i −0.0906344 + 0.467890i
\(537\) −22.6473 11.9188i −0.977305 0.514334i
\(538\) −1.96469 + 30.7625i −0.0847038 + 1.32627i
\(539\) −2.00179 0.914189i −0.0862234 0.0393769i
\(540\) −8.07433 5.30514i −0.347464 0.228297i
\(541\) −11.4927 39.1406i −0.494111 1.68279i −0.708233 0.705979i \(-0.750507\pi\)
0.214122 0.976807i \(-0.431311\pi\)
\(542\) 16.9754 23.0403i 0.729155 0.989668i
\(543\) 3.94930 + 6.97585i 0.169481 + 0.299362i
\(544\) −3.70026 + 11.2072i −0.158647 + 0.480506i
\(545\) 0.599935 0.273981i 0.0256984 0.0117361i
\(546\) 1.52850 1.38718i 0.0654137 0.0593660i
\(547\) −5.70053 0.819613i −0.243737 0.0350441i 0.0193634 0.999813i \(-0.493836\pi\)
−0.263101 + 0.964768i \(0.584745\pi\)
\(548\) −13.8060 20.7794i −0.589765 0.887652i
\(549\) 0.792390 + 25.8018i 0.0338184 + 1.10119i
\(550\) −0.884785 + 1.65013i −0.0377274 + 0.0703619i
\(551\) −0.357419 −0.0152266
\(552\) 11.4320 20.5258i 0.486578 0.873637i
\(553\) −0.121270 −0.00515692
\(554\) −11.1079 + 20.7163i −0.471928 + 0.880151i
\(555\) −12.0479 4.28414i −0.511404 0.181852i
\(556\) −15.4911 + 10.2924i −0.656968 + 0.436496i
\(557\) 28.2719 + 4.06489i 1.19792 + 0.172235i 0.712262 0.701914i \(-0.247671\pi\)
0.485658 + 0.874149i \(0.338580\pi\)
\(558\) −0.115729 + 0.232719i −0.00489920 + 0.00985178i
\(559\) −20.5937 + 9.40484i −0.871022 + 0.397782i
\(560\) −0.147756 + 1.30997i −0.00624383 + 0.0553562i
\(561\) 1.00671 0.569937i 0.0425033 0.0240628i
\(562\) −21.4211 + 29.0744i −0.903594 + 1.22643i
\(563\) −5.25898 17.9104i −0.221640 0.754835i −0.992966 0.118396i \(-0.962225\pi\)
0.771327 0.636439i \(-0.219593\pi\)
\(564\) 7.93277 + 31.7565i 0.334030 + 1.33719i
\(565\) −0.228897 0.104534i −0.00962978 0.00439777i
\(566\) 2.81939 44.1452i 0.118508 1.85556i
\(567\) −1.88640 2.57317i −0.0792215 0.108063i
\(568\) −23.1518 4.48471i −0.971430 0.188174i
\(569\) −3.79661 + 2.43993i −0.159162 + 0.102287i −0.617797 0.786337i \(-0.711975\pi\)
0.458635 + 0.888625i \(0.348338\pi\)
\(570\) 0.228854 0.00525786i 0.00958564 0.000220228i
\(571\) −9.59828 6.16844i −0.401675 0.258141i 0.324170 0.945999i \(-0.394915\pi\)
−0.725846 + 0.687858i \(0.758551\pi\)
\(572\) 1.37458 0.653246i 0.0574740 0.0273136i
\(573\) 14.1077 1.22693i 0.589358 0.0512556i
\(574\) −0.625668 0.131120i −0.0261149 0.00547286i
\(575\) −10.3059 + 16.9467i −0.429785 + 0.706726i
\(576\) 21.1218 + 11.3960i 0.880075 + 0.474835i
\(577\) −18.1792 5.33791i −0.756812 0.222220i −0.119508 0.992833i \(-0.538132\pi\)
−0.637303 + 0.770613i \(0.719950\pi\)
\(578\) 14.2361 10.8273i 0.592144 0.450355i
\(579\) 5.46802 + 1.10187i 0.227243 + 0.0457922i
\(580\) −5.61514 3.48888i −0.233156 0.144868i
\(581\) 1.02357 0.657809i 0.0424649 0.0272905i
\(582\) −27.1074 + 18.3141i −1.12364 + 0.759143i
\(583\) −0.0751796 0.0867618i −0.00311362 0.00359331i
\(584\) 1.15569 2.23656i 0.0478227 0.0925494i
\(585\) −2.06210 6.30055i −0.0852573 0.260496i
\(586\) 2.50155 + 31.5913i 0.103338 + 1.30502i
\(587\) 13.5980 3.99274i 0.561251 0.164798i 0.0112118 0.999937i \(-0.496431\pi\)
0.550039 + 0.835139i \(0.314613\pi\)
\(588\) 10.7679 21.2398i 0.444062 0.875913i
\(589\) −0.000876412 0.00609558i −3.61119e−5 0.000251164i
\(590\) −6.40482 + 3.56092i −0.263682 + 0.146601i
\(591\) −18.8911 18.3199i −0.777076 0.753578i
\(592\) 30.7366 + 8.01614i 1.26327 + 0.329461i
\(593\) −4.13142 0.594009i −0.169657 0.0243930i 0.0569627 0.998376i \(-0.481858\pi\)
−0.226620 + 0.973983i \(0.572767\pi\)
\(594\) −0.782895 2.21836i −0.0321226 0.0910202i
\(595\) −0.450283 + 0.519654i −0.0184598 + 0.0213037i
\(596\) −24.4172 + 29.0623i −1.00017 + 1.19044i
\(597\) 16.6981 + 42.7532i 0.683407 + 1.74977i
\(598\) 14.9146 6.12093i 0.609904 0.250304i
\(599\) 25.0261i 1.02254i 0.859421 + 0.511269i \(0.170824\pi\)
−0.859421 + 0.511269i \(0.829176\pi\)
\(600\) −17.4506 10.2948i −0.712418 0.420282i
\(601\) −17.4304 + 20.1158i −0.711002 + 0.820541i −0.990195 0.139695i \(-0.955388\pi\)
0.279192 + 0.960235i \(0.409933\pi\)
\(602\) 3.35063 3.40208i 0.136561 0.138659i
\(603\) 6.62641 + 9.64643i 0.269848 + 0.392833i
\(604\) −17.5666 + 2.79957i −0.714774 + 0.113913i
\(605\) −9.21539 + 4.20853i −0.374659 + 0.171101i
\(606\) −8.32371 6.88425i −0.338128 0.279654i
\(607\) 4.42198 + 30.7555i 0.179483 + 1.24833i 0.857964 + 0.513711i \(0.171729\pi\)
−0.678481 + 0.734618i \(0.737361\pi\)
\(608\) −0.565254 + 0.0621443i −0.0229241 + 0.00252028i
\(609\) −1.33500 1.72743i −0.0540967 0.0699988i
\(610\) −0.893004 11.2775i −0.0361567 0.456611i
\(611\) −9.33043 + 20.4308i −0.377469 + 0.826542i
\(612\) 5.71771 + 11.1361i 0.231125 + 0.450151i
\(613\) −21.1251 24.3797i −0.853235 0.984685i 0.146755 0.989173i \(-0.453117\pi\)
−0.999990 + 0.00448754i \(0.998572\pi\)
\(614\) 11.8203 2.66584i 0.477028 0.107584i
\(615\) −1.20502 + 1.66231i −0.0485913 + 0.0670310i
\(616\) −0.221728 + 0.232104i −0.00893367 + 0.00935176i
\(617\) 17.6640 + 11.3519i 0.711125 + 0.457012i 0.845539 0.533913i \(-0.179279\pi\)
−0.134415 + 0.990925i \(0.542915\pi\)
\(618\) 20.8818 + 12.7519i 0.839989 + 0.512956i
\(619\) 22.2986 + 6.54746i 0.896256 + 0.263165i 0.697245 0.716833i \(-0.254409\pi\)
0.199011 + 0.979997i \(0.436227\pi\)
\(620\) 0.0457321 0.104318i 0.00183665 0.00418951i
\(621\) −7.00808 23.9142i −0.281225 0.959642i
\(622\) 5.90611 28.1822i 0.236814 1.13000i
\(623\) 1.19456 4.06829i 0.0478590 0.162993i
\(624\) 6.45605 + 15.1503i 0.258449 + 0.606497i
\(625\) 10.7539 + 6.91109i 0.430154 + 0.276443i
\(626\) −34.8028 12.6795i −1.39100 0.506776i
\(627\) 0.0451291 + 0.0327144i 0.00180228 + 0.00130649i
\(628\) 0.00643799 + 0.422397i 0.000256904 + 0.0168555i
\(629\) 10.8499 + 12.5214i 0.432612 + 0.499261i
\(630\) 0.880203 + 1.08642i 0.0350681 + 0.0432842i
\(631\) −30.4525 13.9072i −1.21229 0.553636i −0.296402 0.955063i \(-0.595787\pi\)
−0.915891 + 0.401427i \(0.868514\pi\)
\(632\) 0.317313 0.914036i 0.0126220 0.0363584i
\(633\) −13.1556 17.0227i −0.522887 0.676592i
\(634\) 9.42520 12.7926i 0.374323 0.508061i
\(635\) −2.00681 + 0.288536i −0.0796379 + 0.0114502i
\(636\) 0.971257 0.774537i 0.0385128 0.0307124i
\(637\) 14.8638 6.78806i 0.588925 0.268953i
\(638\) −0.574002 1.50386i −0.0227249 0.0595383i
\(639\) −20.6170 + 14.1624i −0.815596 + 0.560257i
\(640\) −9.48688 4.54131i −0.375002 0.179511i
\(641\) 15.5727 17.9718i 0.615083 0.709843i −0.359683 0.933075i \(-0.617115\pi\)
0.974766 + 0.223231i \(0.0716605\pi\)
\(642\) 2.27834 18.9221i 0.0899187 0.746797i
\(643\) −38.2407 −1.50807 −0.754033 0.656837i \(-0.771894\pi\)
−0.754033 + 0.656837i \(0.771894\pi\)
\(644\) −2.47855 + 2.32786i −0.0976684 + 0.0917306i
\(645\) −5.57937 14.2853i −0.219688 0.562481i
\(646\) −0.261402 0.140161i −0.0102847 0.00551457i
\(647\) −0.135678 0.117566i −0.00533407 0.00462200i 0.652190 0.758056i \(-0.273851\pi\)
−0.657524 + 0.753434i \(0.728396\pi\)
\(648\) 24.3304 7.48531i 0.955790 0.294051i
\(649\) −1.76620 0.253941i −0.0693294 0.00996807i
\(650\) −4.95766 12.9888i −0.194455 0.509464i
\(651\) 0.0261867 0.0270033i 0.00102634 0.00105834i
\(652\) −22.7284 + 7.05162i −0.890111 + 0.276163i
\(653\) −0.321229 2.23420i −0.0125707 0.0874309i 0.982570 0.185891i \(-0.0595173\pi\)
−0.995141 + 0.0984605i \(0.968608\pi\)
\(654\) −0.451161 + 1.67819i −0.0176418 + 0.0656224i
\(655\) 2.37318 + 8.08232i 0.0927279 + 0.315802i
\(656\) 2.62539 4.37270i 0.102504 0.170725i
\(657\) −0.830576 2.53775i −0.0324039 0.0990070i
\(658\) 0.301935 4.72762i 0.0117707 0.184302i
\(659\) 18.0165 15.6114i 0.701822 0.608132i −0.229077 0.973408i \(-0.573571\pi\)
0.930899 + 0.365276i \(0.119025\pi\)
\(660\) 0.389654 + 0.954471i 0.0151672 + 0.0371527i
\(661\) 37.6995 24.2280i 1.46634 0.942361i 0.468064 0.883694i \(-0.344952\pi\)
0.998278 0.0586663i \(-0.0186848\pi\)
\(662\) −42.2529 15.3938i −1.64221 0.598297i
\(663\) −1.69685 + 8.42058i −0.0659001 + 0.327028i
\(664\) 2.27978 + 9.43608i 0.0884728 + 0.366191i
\(665\) −0.0317881 0.00933383i −0.00123269 0.000361950i
\(666\) 28.9300 17.2677i 1.12102 0.669109i
\(667\) −5.20852 16.2366i −0.201675 0.628684i
\(668\) 6.05376 13.8090i 0.234227 0.534287i
\(669\) 16.7864 1.45989i 0.649001 0.0564428i
\(670\) −3.10477 4.08227i −0.119948 0.157712i
\(671\) 1.48924 2.31731i 0.0574916 0.0894587i
\(672\) −2.41162 2.49978i −0.0930304 0.0964312i
\(673\) 13.1136 8.42757i 0.505490 0.324859i −0.262919 0.964818i \(-0.584685\pi\)
0.768409 + 0.639959i \(0.221049\pi\)
\(674\) −26.4661 + 5.96893i −1.01944 + 0.229915i
\(675\) −20.7663 + 5.52987i −0.799295 + 0.212845i
\(676\) 3.92591 14.1655i 0.150996 0.544829i
\(677\) −3.89904 1.78063i −0.149852 0.0684352i 0.339077 0.940759i \(-0.389885\pi\)
−0.488929 + 0.872323i \(0.662612\pi\)
\(678\) 0.596624 0.289211i 0.0229132 0.0111071i
\(679\) 4.54284 1.33390i 0.174338 0.0511903i
\(680\) −2.73854 4.75359i −0.105018 0.182292i
\(681\) 35.0840 19.8624i 1.34442 0.761130i
\(682\) 0.0242399 0.0134768i 0.000928196 0.000516054i
\(683\) −10.3763 22.7209i −0.397037 0.869390i −0.997562 0.0697842i \(-0.977769\pi\)
0.600525 0.799606i \(-0.294958\pi\)
\(684\) −0.373631 + 0.473492i −0.0142861 + 0.0181044i
\(685\) 11.4783 + 1.65033i 0.438564 + 0.0630560i
\(686\) −4.88093 + 4.95589i −0.186355 + 0.189217i
\(687\) 9.01207 25.3438i 0.343832 0.966925i
\(688\) 16.8750 + 34.1562i 0.643354 + 1.30219i
\(689\) 0.852434 0.0324752
\(690\) 3.57385 + 10.3196i 0.136054 + 0.392861i
\(691\) 26.7672i 1.01827i −0.860686 0.509135i \(-0.829965\pi\)
0.860686 0.509135i \(-0.170035\pi\)
\(692\) −26.9157 22.6137i −1.02318 0.859644i
\(693\) 0.0104509 + 0.340303i 0.000396998 + 0.0129270i
\(694\) −12.5338 12.3442i −0.475776 0.468580i
\(695\) 1.23033 8.55711i 0.0466690 0.324590i
\(696\) 16.5131 5.54218i 0.625927 0.210076i
\(697\) 2.41988 1.10512i 0.0916594 0.0418594i
\(698\) 8.15080 4.53164i 0.308512 0.171525i
\(699\) 34.1950 19.3591i 1.29338 0.732230i
\(700\) 1.95380 + 2.18657i 0.0738467 + 0.0826445i
\(701\) 12.3827 + 42.1718i 0.467690 + 1.59281i 0.768980 + 0.639273i \(0.220765\pi\)
−0.301290 + 0.953533i \(0.597417\pi\)
\(702\) 16.2554 + 6.39343i 0.613520 + 0.241304i
\(703\) −0.331622 + 0.726152i −0.0125074 + 0.0273873i
\(704\) −1.16925 2.27853i −0.0440678 0.0858753i
\(705\) −13.4641 7.08585i −0.507087 0.266869i
\(706\) −34.9347 + 7.87886i −1.31479 + 0.296525i
\(707\) 0.845184 + 1.31513i 0.0317864 + 0.0494606i
\(708\) 3.52533 18.9840i 0.132490 0.713463i
\(709\) −32.5114 20.8938i −1.22099 0.784683i −0.238526 0.971136i \(-0.576664\pi\)
−0.982464 + 0.186453i \(0.940301\pi\)
\(710\) 8.72492 6.63573i 0.327440 0.249035i
\(711\) −0.454769 0.919974i −0.0170552 0.0345017i
\(712\) 27.5379 + 19.6487i 1.03203 + 0.736365i
\(713\) 0.264134 0.128641i 0.00989191 0.00481766i
\(714\) −0.298956 1.78689i −0.0111882 0.0668725i
\(715\) −0.199304 + 0.678765i −0.00745353 + 0.0253844i
\(716\) −26.6906 + 12.6843i −0.997475 + 0.474034i
\(717\) 5.14497 25.5318i 0.192142 0.953504i
\(718\) 5.38118 14.7703i 0.200824 0.551222i
\(719\) 12.3642 + 19.2391i 0.461108 + 0.717498i 0.991479 0.130268i \(-0.0415838\pi\)
−0.530371 + 0.847766i \(0.677947\pi\)
\(720\) −10.4917 + 3.79156i −0.391004 + 0.141303i
\(721\) −2.31894 2.67619i −0.0863617 0.0996667i
\(722\) −1.71169 + 26.8012i −0.0637025 + 0.997436i
\(723\) −38.9558 2.18573i −1.44878 0.0812883i
\(724\) 9.18110 + 1.17753i 0.341213 + 0.0437625i
\(725\) −14.1090 + 4.14278i −0.523996 + 0.153859i
\(726\) 6.93013 25.7781i 0.257201 0.956714i
\(727\) −14.1504 + 2.03451i −0.524808 + 0.0754559i −0.399627 0.916678i \(-0.630860\pi\)
−0.125181 + 0.992134i \(0.539951\pi\)
\(728\) −0.224331 2.37286i −0.00831427 0.0879440i
\(729\) 12.4464 23.9601i 0.460977 0.887412i
\(730\) 0.417286 + 1.09327i 0.0154444 + 0.0404637i
\(731\) −2.82798 + 19.6690i −0.104597 + 0.727486i
\(732\) 24.3972 + 17.1247i 0.901748 + 0.632947i
\(733\) −23.7641 + 27.4252i −0.877748 + 1.01297i 0.122043 + 0.992525i \(0.461055\pi\)
−0.999791 + 0.0204499i \(0.993490\pi\)
\(734\) −16.6987 + 31.1433i −0.616362 + 1.14952i
\(735\) 4.02698 + 10.3106i 0.148538 + 0.380311i
\(736\) −11.0603 24.7724i −0.407686 0.913122i
\(737\) 1.24883i 0.0460013i
\(738\) −1.35159 5.23813i −0.0497527 0.192818i
\(739\) −24.4370 21.1748i −0.898929 0.778927i 0.0769962 0.997031i \(-0.475467\pi\)
−0.975925 + 0.218105i \(0.930013\pi\)
\(740\) −12.2981 + 8.17096i −0.452086 + 0.300370i
\(741\) −0.403021 + 0.0941734i −0.0148053 + 0.00345955i
\(742\) −0.167971 + 0.0641122i −0.00616642 + 0.00235363i
\(743\) −14.9039 32.6350i −0.546772 1.19726i −0.958273 0.285855i \(-0.907723\pi\)
0.411501 0.911409i \(-0.365005\pi\)
\(744\) 0.135010 + 0.268031i 0.00494970 + 0.00982651i
\(745\) −2.51099 17.4643i −0.0919956 0.639844i
\(746\) 4.42216 6.00211i 0.161907 0.219753i
\(747\) 8.82871 + 5.29816i 0.323025 + 0.193850i
\(748\) 0.169933 1.32496i 0.00621337 0.0484452i
\(749\) −1.14585 + 2.50906i −0.0418684 + 0.0916790i
\(750\) 19.8211 6.31800i 0.723764 0.230701i
\(751\) 29.5968 25.6458i 1.08000 0.935829i 0.0818547 0.996644i \(-0.473916\pi\)
0.998149 + 0.0608157i \(0.0193702\pi\)
\(752\) 34.8430 + 14.6460i 1.27059 + 0.534083i
\(753\) −9.42560 6.83269i −0.343488 0.248997i
\(754\) 11.2302 + 4.09143i 0.408978 + 0.149001i
\(755\) 4.47026 6.95587i 0.162690 0.253150i
\(756\) −3.68396 0.0372384i −0.133984 0.00135435i
\(757\) 41.3624 + 12.1451i 1.50334 + 0.441421i 0.926771 0.375627i \(-0.122573\pi\)
0.576570 + 0.817048i \(0.304391\pi\)
\(758\) −49.5634 10.3869i −1.80022 0.377271i
\(759\) −0.828484 + 2.52683i −0.0300720 + 0.0917181i
\(760\) 0.153527 0.215171i 0.00556902 0.00780507i
\(761\) 8.11093 27.6233i 0.294021 1.00134i −0.671497 0.741007i \(-0.734348\pi\)
0.965518 0.260337i \(-0.0838335\pi\)
\(762\) 2.78413 4.55914i 0.100858 0.165160i
\(763\) 0.135973 0.211578i 0.00492255 0.00765963i
\(764\) 8.62971 13.8890i 0.312212 0.502487i
\(765\) −5.63078 1.46719i −0.203581 0.0530464i
\(766\) −4.56841 20.2562i −0.165063 0.731888i
\(767\) 10.0132 8.67645i 0.361554 0.313289i
\(768\) 25.1516 11.6360i 0.907580 0.419878i
\(769\) 23.2590 + 10.6220i 0.838741 + 0.383040i 0.788003 0.615672i \(-0.211115\pi\)
0.0507386 + 0.998712i \(0.483842\pi\)
\(770\) −0.0117779 0.148740i −0.000424448 0.00536021i
\(771\) 5.54282 + 7.17216i 0.199620 + 0.258299i
\(772\) 4.80282 4.29155i 0.172857 0.154456i
\(773\) 6.00471 0.863347i 0.215974 0.0310524i −0.0334782 0.999439i \(-0.510658\pi\)
0.249453 + 0.968387i \(0.419749\pi\)
\(774\) 38.3739 + 12.6604i 1.37932 + 0.455069i
\(775\) −0.105249 0.230463i −0.00378065 0.00827846i
\(776\) −1.83286 + 37.7306i −0.0657957 + 1.35445i
\(777\) −4.74817 + 1.10950i −0.170340 + 0.0398031i
\(778\) −10.8507 + 11.0173i −0.389016 + 0.394990i
\(779\) 0.0968706 + 0.0839389i 0.00347075 + 0.00300742i
\(780\) −7.25081 2.45452i −0.259621 0.0878859i
\(781\) 2.66909 0.0955075
\(782\) 2.55785 13.9173i 0.0914685 0.497683i
\(783\) 8.09824 16.6055i 0.289407 0.593431i
\(784\) −12.1798 24.6527i −0.434992 0.880453i
\(785\) −0.148402 0.128591i −0.00529670 0.00458961i
\(786\) −20.3955 8.75387i −0.727482 0.312240i
\(787\) −5.75148 + 40.0024i −0.205018 + 1.42593i 0.584095 + 0.811685i \(0.301450\pi\)
−0.789113 + 0.614248i \(0.789460\pi\)
\(788\) −30.0075 + 4.78227i −1.06897 + 0.170361i
\(789\) 20.0958 + 19.4881i 0.715429 + 0.693795i
\(790\) 0.218540 + 0.393075i 0.00777530 + 0.0139850i
\(791\) −0.0949809 + 0.0136562i −0.00337713 + 0.000485558i
\(792\) −2.59228 0.811660i −0.0921126 0.0288411i
\(793\) 5.76241 + 19.6250i 0.204629 + 0.696903i
\(794\) 0.355097 + 4.48440i 0.0126019 + 0.159145i
\(795\) −0.0323483 + 0.576535i −0.00114727 + 0.0204476i
\(796\) 51.0737 + 14.1548i 1.81026 + 0.501704i
\(797\) −6.04550 + 5.23846i −0.214143 + 0.185556i −0.755327 0.655349i \(-0.772522\pi\)
0.541184 + 0.840904i \(0.317976\pi\)
\(798\) 0.0723319 0.0488683i 0.00256052 0.00172992i
\(799\) 10.6582 + 16.5845i 0.377061 + 0.586719i
\(800\) −21.5929 + 9.00487i −0.763424 + 0.318370i
\(801\) 35.3425 6.19422i 1.24876 0.218862i
\(802\) −32.5496 + 24.7556i −1.14937 + 0.874151i
\(803\) −0.0802759 + 0.273395i −0.00283287 + 0.00964789i
\(804\) 13.5023 + 0.551322i 0.476191 + 0.0194436i
\(805\) −0.0392236 1.58007i −0.00138245 0.0556901i
\(806\) −0.0422399 + 0.201556i −0.00148784 + 0.00709951i
\(807\) 37.6111 3.27098i 1.32397 0.115144i
\(808\) −12.1239 + 2.92918i −0.426518 + 0.103048i
\(809\) −24.1758 + 37.6183i −0.849977 + 1.32259i 0.0950078 + 0.995477i \(0.469712\pi\)
−0.944985 + 0.327114i \(0.893924\pi\)
\(810\) −4.94099 + 10.7515i −0.173609 + 0.377771i
\(811\) −5.34983 8.32449i −0.187858 0.292312i 0.734531 0.678575i \(-0.237402\pi\)
−0.922389 + 0.386263i \(0.873766\pi\)
\(812\) −2.52061 + 0.0384180i −0.0884560 + 0.00134821i
\(813\) −31.0172 16.3237i −1.08782 0.572497i
\(814\) −3.58789 0.229145i −0.125756 0.00803154i
\(815\) 4.59513 10.0619i 0.160960 0.352454i
\(816\) 14.2504 + 2.42224i 0.498863 + 0.0847955i
\(817\) −0.918659 + 0.269743i −0.0321398 + 0.00943710i
\(818\) 3.94135 5.34951i 0.137806 0.187041i
\(819\) −1.96047 1.59607i −0.0685042 0.0557713i
\(820\) 0.702509 + 2.26428i 0.0245327 + 0.0790722i
\(821\) −18.2061 39.8657i −0.635396 1.39132i −0.903774 0.428009i \(-0.859215\pi\)
0.268378 0.963314i \(-0.413512\pi\)
\(822\) −22.6260 + 20.5341i −0.789171 + 0.716210i
\(823\) −3.71550 + 25.8419i −0.129514 + 0.900792i 0.816657 + 0.577124i \(0.195825\pi\)
−0.946171 + 0.323668i \(0.895084\pi\)
\(824\) 26.2387 10.4758i 0.914070 0.364942i
\(825\) 2.16064 + 0.768309i 0.0752239 + 0.0267491i
\(826\) −1.32052 + 2.46278i −0.0459467 + 0.0856912i
\(827\) 15.2004i 0.528570i 0.964445 + 0.264285i \(0.0851360\pi\)
−0.964445 + 0.264285i \(0.914864\pi\)
\(828\) −26.9543 10.0731i −0.936726 0.350063i
\(829\) 19.3885i 0.673390i −0.941614 0.336695i \(-0.890691\pi\)
0.941614 0.336695i \(-0.109309\pi\)
\(830\) −3.97674 2.13229i −0.138035 0.0740128i
\(831\) 27.1254 + 9.64560i 0.940969 + 0.334602i
\(832\) 18.4717 + 4.51795i 0.640391 + 0.156632i
\(833\) 2.04113 14.1964i 0.0707210 0.491876i
\(834\) 15.3082 + 16.8677i 0.530081 + 0.584081i
\(835\) 2.91144 + 6.37517i 0.100755 + 0.220622i
\(836\) 0.0614716 0.0190720i 0.00212604 0.000659617i
\(837\) 0.303054 + 0.0973932i 0.0104751 + 0.00336640i
\(838\) −34.8028 25.6416i −1.20224 0.885773i
\(839\) −0.239080 + 0.0702003i −0.00825396 + 0.00242358i −0.285857 0.958272i \(-0.592278\pi\)
0.277603 + 0.960696i \(0.410460\pi\)
\(840\) 1.61337 0.0616786i 0.0556666 0.00212811i
\(841\) −6.79553 + 14.8801i −0.234329 + 0.513108i
\(842\) −1.07260 + 16.7945i −0.0369644 + 0.578777i
\(843\) 39.1404 + 20.5987i 1.34807 + 0.709458i
\(844\) −24.8391 + 0.378586i −0.854996 + 0.0130315i
\(845\) 3.69404 + 5.74804i 0.127079 + 0.197739i
\(846\) 36.9968 15.4383i 1.27198 0.530780i
\(847\) −2.08863 + 3.24997i −0.0717662 + 0.111670i
\(848\) −0.0437165 1.43379i −0.00150123 0.0492365i
\(849\) −53.9730 + 4.69396i −1.85235 + 0.161096i
\(850\) −11.9434 2.50296i −0.409654 0.0858507i
\(851\) −37.8198 4.48282i −1.29644 0.153669i
\(852\) −1.17832 + 28.8581i −0.0403687 + 0.988664i
\(853\) −14.1979 + 48.3537i −0.486128 + 1.65560i 0.242090 + 0.970254i \(0.422167\pi\)
−0.728218 + 0.685346i \(0.759651\pi\)
\(854\) −2.61148 3.43368i −0.0893631 0.117498i
\(855\) −0.0483993 0.276153i −0.00165522 0.00944422i
\(856\) −15.9131 15.2017i −0.543898 0.519582i
\(857\) 22.3260 + 34.7400i 0.762643 + 1.18670i 0.977682 + 0.210090i \(0.0673757\pi\)
−0.215039 + 0.976605i \(0.568988\pi\)
\(858\) −1.04347 1.54449i −0.0356236 0.0527280i
\(859\) 2.92720 2.53643i 0.0998748 0.0865420i −0.603492 0.797369i \(-0.706225\pi\)
0.703367 + 0.710827i \(0.251679\pi\)
\(860\) −17.0654 4.72959i −0.581926 0.161278i
\(861\) −0.0438597 + 0.781700i −0.00149473 + 0.0266403i
\(862\) 20.6447 1.63475i 0.703162 0.0556798i
\(863\) −4.76960 16.2438i −0.162359 0.552945i −0.999978 0.00668882i \(-0.997871\pi\)
0.837618 0.546256i \(-0.183947\pi\)
\(864\) 9.92007 27.6693i 0.337488 0.941330i
\(865\) 16.1744 2.32552i 0.549945 0.0790702i
\(866\) −10.6677 + 5.93099i −0.362504 + 0.201543i
\(867\) −15.7254 15.2498i −0.534062 0.517912i
\(868\) −0.00683587 0.0428933i −0.000232024 0.00145589i
\(869\) −0.0155848 + 0.108395i −0.000528678 + 0.00367704i
\(870\) −3.19336 + 7.44014i −0.108265 + 0.252244i
\(871\) 7.00796 + 6.07243i 0.237456 + 0.205757i
\(872\) 1.23892 + 1.57847i 0.0419552 + 0.0534537i
\(873\) 27.1551 + 29.4606i 0.919061 + 0.997089i
\(874\) 0.661166 0.166458i 0.0223643 0.00563053i
\(875\) −3.01085 −0.101785
\(876\) −2.92050 0.988637i −0.0986744 0.0334029i
\(877\) 20.5876 + 17.8392i 0.695193 + 0.602388i 0.929081 0.369875i \(-0.120600\pi\)
−0.233888 + 0.972263i \(0.575145\pi\)
\(878\) 8.09039 + 7.96802i 0.273037 + 0.268908i
\(879\) 37.7942 8.83133i 1.27477 0.297874i
\(880\) 1.15190 + 0.300417i 0.0388306 + 0.0101271i
\(881\) −7.44316 16.2982i −0.250766 0.549102i 0.741826 0.670592i \(-0.233960\pi\)
−0.992593 + 0.121491i \(0.961233\pi\)
\(882\) −27.6968 9.13782i −0.932601 0.307686i
\(883\) −10.8004 + 1.55287i −0.363464 + 0.0522582i −0.321627 0.946866i \(-0.604230\pi\)
−0.0418362 + 0.999124i \(0.513321\pi\)
\(884\) 6.60885 + 7.39619i 0.222280 + 0.248761i
\(885\) 5.48825 + 7.10155i 0.184485 + 0.238716i
\(886\) 24.4981 1.93988i 0.823029 0.0651715i
\(887\) 34.7324 + 15.8618i 1.16620 + 0.532586i 0.901938 0.431865i \(-0.142144\pi\)
0.264263 + 0.964451i \(0.414871\pi\)
\(888\) 4.06146 38.6910i 0.136294 1.29839i
\(889\) −0.584296 + 0.506295i −0.0195966 + 0.0169806i
\(890\) −15.3394 + 3.45950i −0.514177 + 0.115963i
\(891\) −2.54241 + 1.35544i −0.0851738 + 0.0454089i
\(892\) 10.2683 16.5262i 0.343808 0.553339i
\(893\) −0.513537 + 0.799080i −0.0171849 + 0.0267402i
\(894\) 39.6760 + 24.2289i 1.32696 + 0.810337i
\(895\) 3.86994 13.1798i 0.129358 0.440552i
\(896\) −3.97963 + 0.499014i −0.132950 + 0.0166709i
\(897\) −10.1511 16.9358i −0.338936 0.565471i
\(898\) 6.80018 32.4484i 0.226925 1.08282i
\(899\) 0.208989 + 0.0613647i 0.00697017 + 0.00204663i
\(900\) −9.26081 + 23.0216i −0.308694 + 0.767388i
\(901\) 0.404508 0.629426i 0.0134761 0.0209692i
\(902\) −0.197606 + 0.542390i −0.00657957 + 0.0180596i
\(903\) −4.73496 3.43241i −0.157570 0.114224i
\(904\) 0.145596 0.751624i 0.00484245 0.0249986i
\(905\) −3.25167 + 2.81759i −0.108089 + 0.0936597i
\(906\) 6.61636 + 20.7571i 0.219814 + 0.689609i
\(907\) 13.1859 28.8731i 0.437831 0.958716i −0.554160 0.832410i \(-0.686961\pi\)
0.991991 0.126306i \(-0.0403122\pi\)
\(908\) 5.92221 46.1750i 0.196536 1.53237i
\(909\) −6.80733 + 11.3435i −0.225785 + 0.376242i
\(910\) 0.891940 + 0.657153i 0.0295675 + 0.0217844i
\(911\) −3.01202 20.9490i −0.0997925 0.694072i −0.976887 0.213755i \(-0.931431\pi\)
0.877095 0.480317i \(-0.159478\pi\)
\(912\) 0.179068 + 0.673049i 0.00592952 + 0.0222869i
\(913\) −0.456427 0.999436i −0.0151055 0.0330765i
\(914\) −1.50055 3.93137i −0.0496337 0.130038i
\(915\) −13.4918 + 3.15261i −0.446025 + 0.104222i
\(916\) −17.1883 25.8701i −0.567919 0.854771i
\(917\) 2.42760 + 2.10353i 0.0801664 + 0.0694645i
\(918\) 12.4345 8.96887i 0.410401 0.296017i
\(919\) 4.75166i 0.156743i 0.996924 + 0.0783714i \(0.0249720\pi\)
−0.996924 + 0.0783714i \(0.975028\pi\)
\(920\) 12.0119 + 3.83874i 0.396022 + 0.126560i
\(921\) −5.39903 13.8235i −0.177904 0.455500i
\(922\) 26.1387 + 14.0153i 0.860833 + 0.461570i
\(923\) −12.9784 + 14.9779i −0.427190 + 0.493004i
\(924\) 0.321778 + 0.225860i 0.0105857 + 0.00743023i
\(925\) −4.67400 + 32.5084i −0.153680 + 1.06887i
\(926\) −26.6942 + 10.1888i −0.877227 + 0.334825i
\(927\) 11.6059 27.6278i 0.381189 0.907415i
\(928\) 6.30582 19.0989i 0.206999 0.626952i
\(929\) 7.80994 1.12290i 0.256236 0.0368411i −0.0129998 0.999915i \(-0.504138\pi\)
0.269236 + 0.963074i \(0.413229\pi\)
\(930\) −0.134717 0.0362172i −0.00441756 0.00118761i
\(931\) 0.663054 0.194690i 0.0217307 0.00638072i
\(932\) 5.77215 45.0050i 0.189073 1.47419i
\(933\) −35.2104 1.97559i −1.15274 0.0646779i
\(934\) −45.7191 2.91991i −1.49597 0.0955423i
\(935\) 0.406615 + 0.469259i 0.0132977 + 0.0153464i
\(936\) 17.1597 10.6002i 0.560881 0.346478i
\(937\) −0.0458357 0.0713218i −0.00149739 0.00232998i 0.840504 0.541805i \(-0.182259\pi\)
−0.842001 + 0.539475i \(0.818623\pi\)
\(938\) −1.83762 0.669492i −0.0600005 0.0218597i
\(939\) −8.96152 + 44.4714i −0.292448 + 1.45127i
\(940\) −15.8679 + 7.54094i −0.517552 + 0.245958i
\(941\) −3.08024 + 10.4903i −0.100413 + 0.341975i −0.994341 0.106235i \(-0.966120\pi\)
0.893928 + 0.448210i \(0.147938\pi\)
\(942\) 0.510296 0.0853755i 0.0166264 0.00278168i
\(943\) −2.40147 + 5.62378i −0.0782025 + 0.183136i
\(944\) −15.1073 16.3971i −0.491699 0.533680i
\(945\) 1.15388 1.26537i 0.0375358 0.0411626i
\(946\) −2.61029 3.43211i −0.0848678 0.111587i
\(947\) −36.5357 23.4801i −1.18725 0.763001i −0.210547 0.977584i \(-0.567524\pi\)
−0.976706 + 0.214583i \(0.931161\pi\)
\(948\) −1.16508 0.216356i −0.0378401 0.00702691i
\(949\) −1.14384 1.77986i −0.0371308 0.0577766i
\(950\) −0.129354 0.573552i −0.00419679 0.0186085i
\(951\) −17.2216 9.06336i −0.558450 0.293900i
\(952\) −1.85854 0.960355i −0.0602356 0.0311253i
\(953\) −23.5507 + 51.5688i −0.762882 + 1.67048i −0.0211559 + 0.999776i \(0.506735\pi\)
−0.741726 + 0.670703i \(0.765993\pi\)
\(954\) −1.11627 1.03383i −0.0361406 0.0334716i
\(955\) 2.14136 + 7.29280i 0.0692928 + 0.235989i
\(956\) −20.0385 22.4258i −0.648092 0.725303i
\(957\) −1.71559 + 0.971263i −0.0554572 + 0.0313965i
\(958\) −17.2241 30.9800i −0.556486 1.00092i
\(959\) 4.02246 1.83700i 0.129892 0.0593198i
\(960\) −3.75664 + 12.3217i −0.121245 + 0.397681i
\(961\) 4.41123 30.6808i 0.142298 0.989702i
\(962\) 18.7320 19.0197i 0.603943 0.613218i
\(963\) −23.3312 + 0.716516i −0.751837 + 0.0230894i
\(964\) −28.9811 + 34.4944i −0.933418 + 1.11099i
\(965\) 2.99387i 0.0963762i
\(966\) 3.27402 + 2.57371i 0.105340 + 0.0828079i
\(967\) 52.2375 1.67985 0.839923 0.542706i \(-0.182600\pi\)
0.839923 + 0.542706i \(0.182600\pi\)
\(968\) −19.0306 24.2463i −0.611668 0.779305i
\(969\) −0.121710 + 0.342274i −0.00390989 + 0.0109954i
\(970\) −12.5102 12.3210i −0.401679 0.395604i
\(971\) 42.7192 + 6.14210i 1.37093 + 0.197109i 0.788130 0.615509i \(-0.211050\pi\)
0.582796 + 0.812618i \(0.301959\pi\)
\(972\) −13.5326 28.0868i −0.434058 0.900885i
\(973\) −1.36949 2.99875i −0.0439037 0.0961356i
\(974\) 17.5216 + 31.5151i 0.561428 + 1.00981i
\(975\) −14.8176 + 8.38880i −0.474542 + 0.268657i
\(976\) 32.7135 10.6988i 1.04713 0.342460i
\(977\) −3.73721 + 1.09734i −0.119564 + 0.0351072i −0.340967 0.940075i \(-0.610755\pi\)
0.221403 + 0.975182i \(0.428936\pi\)
\(978\) 12.7132 + 26.2265i 0.406523 + 0.838632i
\(979\) −3.48285 1.59056i −0.111312 0.0508346i
\(980\) 12.3172 + 3.41364i 0.393458 + 0.109045i
\(981\) 2.11497 + 0.238084i 0.0675259 + 0.00760143i
\(982\) −3.56065 15.7878i −0.113625 0.503810i
\(983\) 22.1570 14.2394i 0.706699 0.454168i −0.137288 0.990531i \(-0.543839\pi\)
0.843987 + 0.536363i \(0.180202\pi\)
\(984\) −5.77707 2.37596i −0.184166 0.0757430i
\(985\) 7.63617 11.8821i 0.243309 0.378596i
\(986\) 8.35013 6.35069i 0.265922 0.202247i
\(987\) −5.78010 + 0.502687i −0.183983 + 0.0160007i
\(988\) −0.191881 + 0.437692i −0.00610453 + 0.0139248i
\(989\) −25.6410 37.8014i −0.815335 1.20202i
\(990\) 1.08420 0.647133i 0.0344581 0.0205672i
\(991\) −9.29965 2.73062i −0.295413 0.0867411i 0.130668 0.991426i \(-0.458288\pi\)
−0.426081 + 0.904685i \(0.640106\pi\)
\(992\) 0.341182 + 0.0607106i 0.0108326 + 0.00192756i
\(993\) −10.8799 + 53.9912i −0.345262 + 1.71336i
\(994\) 1.43089 3.92750i 0.0453849 0.124573i
\(995\) −20.7245 + 13.3188i −0.657011 + 0.422235i
\(996\) 11.0074 4.49366i 0.348782 0.142387i
\(997\) −29.4893 + 25.5526i −0.933934 + 0.809259i −0.981863 0.189592i \(-0.939283\pi\)
0.0479288 + 0.998851i \(0.484738\pi\)
\(998\) 34.8309 + 2.22452i 1.10255 + 0.0704159i
\(999\) −26.2228 31.8598i −0.829652 1.00800i
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 552.2.bf.a.5.15 yes 920
3.2 odd 2 inner 552.2.bf.a.5.78 yes 920
8.5 even 2 inner 552.2.bf.a.5.89 yes 920
23.14 odd 22 inner 552.2.bf.a.221.4 yes 920
24.5 odd 2 inner 552.2.bf.a.5.4 920
69.14 even 22 inner 552.2.bf.a.221.89 yes 920
184.37 odd 22 inner 552.2.bf.a.221.78 yes 920
552.221 even 22 inner 552.2.bf.a.221.15 yes 920
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.bf.a.5.4 920 24.5 odd 2 inner
552.2.bf.a.5.15 yes 920 1.1 even 1 trivial
552.2.bf.a.5.78 yes 920 3.2 odd 2 inner
552.2.bf.a.5.89 yes 920 8.5 even 2 inner
552.2.bf.a.221.4 yes 920 23.14 odd 22 inner
552.2.bf.a.221.15 yes 920 552.221 even 22 inner
552.2.bf.a.221.78 yes 920 184.37 odd 22 inner
552.2.bf.a.221.89 yes 920 69.14 even 22 inner