Properties

Label 945.2.cs.b.104.19
Level $945$
Weight $2$
Character 945.104
Analytic conductor $7.546$
Analytic rank $0$
Dimension $816$
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] = [945,2,Mod(104,945)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(945, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11, 9, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("945.104");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.cs (of order \(18\), degree \(6\), 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: \(7.54586299101\)
Analytic rank: \(0\)
Dimension: \(816\)
Relative dimension: \(136\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 104.19
Character \(\chi\) \(=\) 945.104
Dual form 945.2.cs.b.209.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96750 - 0.716110i) q^{2} +(-1.00171 + 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(-1.23328 + 1.86521i) q^{5} +(2.98272 - 2.06275i) q^{6} +(-2.38678 + 1.14161i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +O(q^{10})\) \(q+(-1.96750 - 0.716110i) q^{2} +(-1.00171 + 1.41301i) q^{3} +(1.82614 + 1.53231i) q^{4} +(-1.23328 + 1.86521i) q^{5} +(2.98272 - 2.06275i) q^{6} +(-2.38678 + 1.14161i) q^{7} +(-0.401851 - 0.696026i) q^{8} +(-0.993173 - 2.83083i) q^{9} +(3.76217 - 2.78664i) q^{10} +(-4.44627 + 0.783998i) q^{11} +(-3.99442 + 1.04542i) q^{12} +(-3.46319 + 1.26050i) q^{13} +(5.51350 - 0.536918i) q^{14} +(-1.40017 - 3.61103i) q^{15} +(-0.535695 - 3.03808i) q^{16} +(-1.90720 - 1.10112i) q^{17} +(-0.0731236 + 6.28087i) q^{18} +(4.91222 - 2.83607i) q^{19} +(-5.11023 + 1.51637i) q^{20} +(0.777748 - 4.51609i) q^{21} +(9.30946 + 1.64151i) q^{22} +(-5.48722 - 4.60432i) q^{23} +(1.38602 + 0.129395i) q^{24} +(-1.95804 - 4.60066i) q^{25} +7.71647 q^{26} +(4.99485 + 1.43230i) q^{27} +(-6.10790 - 1.57255i) q^{28} +(-2.81698 + 7.73958i) q^{29} +(0.168946 + 8.10736i) q^{30} +(-4.05814 + 4.83631i) q^{31} +(-1.40074 + 7.94401i) q^{32} +(3.34606 - 7.06795i) q^{33} +(2.96388 + 3.53222i) q^{34} +(0.814221 - 5.85978i) q^{35} +(2.52405 - 6.69134i) q^{36} +(1.79890 + 1.03859i) q^{37} +(-11.6957 + 2.06227i) q^{38} +(1.68800 - 6.15616i) q^{39} +(1.79383 + 0.108857i) q^{40} +(-6.31954 + 2.30012i) q^{41} +(-4.76424 + 8.32845i) q^{42} +(4.69546 - 0.827937i) q^{43} +(-9.32084 - 5.38139i) q^{44} +(6.50496 + 1.63873i) q^{45} +(7.49887 + 12.9884i) q^{46} +(6.25944 + 7.45971i) q^{47} +(4.82943 + 2.28632i) q^{48} +(4.39345 - 5.44955i) q^{49} +(0.557859 + 10.4540i) q^{50} +(3.46634 - 1.59188i) q^{51} +(-8.25574 - 3.00484i) q^{52} +2.90976 q^{53} +(-8.80166 - 6.39491i) q^{54} +(4.02118 - 9.26014i) q^{55} +(1.75372 + 1.20250i) q^{56} +(-0.913211 + 9.78191i) q^{57} +(11.0848 - 13.2103i) q^{58} +(-1.44006 + 8.16701i) q^{59} +(2.97631 - 8.73974i) q^{60} +(-0.318741 - 0.379861i) q^{61} +(11.4477 - 6.60934i) q^{62} +(5.60219 + 5.62276i) q^{63} +(5.35979 - 9.28344i) q^{64} +(1.91999 - 8.01414i) q^{65} +(-11.6448 + 11.5100i) q^{66} +(2.04359 + 5.61471i) q^{67} +(-1.79555 - 4.93323i) q^{68} +(12.0025 - 3.14130i) q^{69} +(-5.79822 + 10.9460i) q^{70} +(-6.10717 - 3.52597i) q^{71} +(-1.57122 + 1.82885i) q^{72} +(0.632890 + 1.09620i) q^{73} +(-2.79558 - 3.33164i) q^{74} +(8.46214 + 1.84178i) q^{75} +(13.3161 + 2.34799i) q^{76} +(9.71726 - 6.94715i) q^{77} +(-7.72963 + 10.9034i) q^{78} +(8.96547 + 3.26316i) q^{79} +(6.32733 + 2.74762i) q^{80} +(-7.02722 + 5.62301i) q^{81} +14.0808 q^{82} +(-0.743273 + 2.04213i) q^{83} +(8.34034 - 7.05526i) q^{84} +(4.40594 - 2.19934i) q^{85} +(-9.83120 - 1.73351i) q^{86} +(-8.11430 - 11.7332i) q^{87} +(2.33242 + 2.77967i) q^{88} +(-5.99817 - 10.3891i) q^{89} +(-11.6250 - 7.88246i) q^{90} +(6.82688 - 6.96215i) q^{91} +(-2.96516 - 16.8163i) q^{92} +(-2.76867 - 10.5787i) q^{93} +(-6.97345 - 19.1594i) q^{94} +(-0.768264 + 12.6600i) q^{95} +(-9.82180 - 9.93682i) q^{96} +(-2.37599 - 13.4749i) q^{97} +(-12.5466 + 7.57578i) q^{98} +(6.63528 + 11.8080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).

\(n\) \(136\) \(596\) \(757\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96750 0.716110i −1.39123 0.506366i −0.465667 0.884960i \(-0.654186\pi\)
−0.925563 + 0.378594i \(0.876408\pi\)
\(3\) −1.00171 + 1.41301i −0.578335 + 0.815799i
\(4\) 1.82614 + 1.53231i 0.913069 + 0.766156i
\(5\) −1.23328 + 1.86521i −0.551540 + 0.834149i
\(6\) 2.98272 2.06275i 1.21769 0.842115i
\(7\) −2.38678 + 1.14161i −0.902118 + 0.431488i
\(8\) −0.401851 0.696026i −0.142076 0.246082i
\(9\) −0.993173 2.83083i −0.331058 0.943611i
\(10\) 3.76217 2.78664i 1.18970 0.881212i
\(11\) −4.44627 + 0.783998i −1.34060 + 0.236384i −0.797519 0.603294i \(-0.793854\pi\)
−0.543084 + 0.839679i \(0.682743\pi\)
\(12\) −3.99442 + 1.04542i −1.15309 + 0.301787i
\(13\) −3.46319 + 1.26050i −0.960516 + 0.349599i −0.774236 0.632897i \(-0.781866\pi\)
−0.186280 + 0.982497i \(0.559643\pi\)
\(14\) 5.51350 0.536918i 1.47355 0.143497i
\(15\) −1.40017 3.61103i −0.361524 0.932363i
\(16\) −0.535695 3.03808i −0.133924 0.759520i
\(17\) −1.90720 1.10112i −0.462564 0.267061i 0.250558 0.968102i \(-0.419386\pi\)
−0.713122 + 0.701040i \(0.752719\pi\)
\(18\) −0.0731236 + 6.28087i −0.0172354 + 1.48042i
\(19\) 4.91222 2.83607i 1.12694 0.650639i 0.183777 0.982968i \(-0.441168\pi\)
0.943164 + 0.332329i \(0.107834\pi\)
\(20\) −5.11023 + 1.51637i −1.14268 + 0.339070i
\(21\) 0.777748 4.51609i 0.169718 0.985493i
\(22\) 9.30946 + 1.64151i 1.98478 + 0.349971i
\(23\) −5.48722 4.60432i −1.14416 0.960067i −0.144596 0.989491i \(-0.546188\pi\)
−0.999567 + 0.0294235i \(0.990633\pi\)
\(24\) 1.38602 + 0.129395i 0.282921 + 0.0264127i
\(25\) −1.95804 4.60066i −0.391608 0.920132i
\(26\) 7.71647 1.51332
\(27\) 4.99485 + 1.43230i 0.961259 + 0.275646i
\(28\) −6.10790 1.57255i −1.15428 0.297185i
\(29\) −2.81698 + 7.73958i −0.523100 + 1.43720i 0.343952 + 0.938987i \(0.388234\pi\)
−0.867052 + 0.498217i \(0.833988\pi\)
\(30\) 0.168946 + 8.10736i 0.0308452 + 1.48019i
\(31\) −4.05814 + 4.83631i −0.728864 + 0.868626i −0.995460 0.0951822i \(-0.969657\pi\)
0.266596 + 0.963808i \(0.414101\pi\)
\(32\) −1.40074 + 7.94401i −0.247619 + 1.40432i
\(33\) 3.34606 7.06795i 0.582475 1.23037i
\(34\) 2.96388 + 3.53222i 0.508302 + 0.605770i
\(35\) 0.814221 5.85978i 0.137628 0.990484i
\(36\) 2.52405 6.69134i 0.420674 1.11522i
\(37\) 1.79890 + 1.03859i 0.295737 + 0.170744i 0.640526 0.767936i \(-0.278716\pi\)
−0.344789 + 0.938680i \(0.612050\pi\)
\(38\) −11.6957 + 2.06227i −1.89730 + 0.334544i
\(39\) 1.68800 6.15616i 0.270297 0.985774i
\(40\) 1.79383 + 0.108857i 0.283630 + 0.0172119i
\(41\) −6.31954 + 2.30012i −0.986946 + 0.359219i −0.784537 0.620082i \(-0.787099\pi\)
−0.202409 + 0.979301i \(0.564877\pi\)
\(42\) −4.76424 + 8.32845i −0.735138 + 1.28511i
\(43\) 4.69546 0.827937i 0.716051 0.126259i 0.196259 0.980552i \(-0.437121\pi\)
0.519792 + 0.854293i \(0.326009\pi\)
\(44\) −9.32084 5.38139i −1.40517 0.811275i
\(45\) 6.50496 + 1.63873i 0.969703 + 0.244287i
\(46\) 7.49887 + 12.9884i 1.10565 + 1.91504i
\(47\) 6.25944 + 7.45971i 0.913034 + 1.08811i 0.995801 + 0.0915423i \(0.0291797\pi\)
−0.0827675 + 0.996569i \(0.526376\pi\)
\(48\) 4.82943 + 2.28632i 0.697069 + 0.330002i
\(49\) 4.39345 5.44955i 0.627635 0.778507i
\(50\) 0.557859 + 10.4540i 0.0788932 + 1.47841i
\(51\) 3.46634 1.59188i 0.485385 0.222908i
\(52\) −8.25574 3.00484i −1.14487 0.416697i
\(53\) 2.90976 0.399686 0.199843 0.979828i \(-0.435957\pi\)
0.199843 + 0.979828i \(0.435957\pi\)
\(54\) −8.80166 6.39491i −1.19775 0.870237i
\(55\) 4.02118 9.26014i 0.542215 1.24864i
\(56\) 1.75372 + 1.20250i 0.234351 + 0.160691i
\(57\) −0.913211 + 9.78191i −0.120958 + 1.29564i
\(58\) 11.0848 13.2103i 1.45550 1.73460i
\(59\) −1.44006 + 8.16701i −0.187480 + 1.06325i 0.735246 + 0.677800i \(0.237066\pi\)
−0.922727 + 0.385455i \(0.874045\pi\)
\(60\) 2.97631 8.73974i 0.384240 1.12830i
\(61\) −0.318741 0.379861i −0.0408106 0.0486362i 0.745253 0.666782i \(-0.232329\pi\)
−0.786064 + 0.618146i \(0.787884\pi\)
\(62\) 11.4477 6.60934i 1.45386 0.839387i
\(63\) 5.60219 + 5.62276i 0.705810 + 0.708401i
\(64\) 5.35979 9.28344i 0.669974 1.16043i
\(65\) 1.91999 8.01414i 0.238145 0.994031i
\(66\) −11.6448 + 11.5100i −1.43338 + 1.41678i
\(67\) 2.04359 + 5.61471i 0.249664 + 0.685946i 0.999699 + 0.0245475i \(0.00781449\pi\)
−0.750035 + 0.661398i \(0.769963\pi\)
\(68\) −1.79555 4.93323i −0.217742 0.598242i
\(69\) 12.0025 3.14130i 1.44493 0.378168i
\(70\) −5.79822 + 10.9460i −0.693020 + 1.30830i
\(71\) −6.10717 3.52597i −0.724787 0.418456i 0.0917247 0.995784i \(-0.470762\pi\)
−0.816512 + 0.577328i \(0.804095\pi\)
\(72\) −1.57122 + 1.82885i −0.185171 + 0.215531i
\(73\) 0.632890 + 1.09620i 0.0740742 + 0.128300i 0.900683 0.434476i \(-0.143067\pi\)
−0.826609 + 0.562776i \(0.809733\pi\)
\(74\) −2.79558 3.33164i −0.324979 0.387295i
\(75\) 8.46214 + 1.84178i 0.977124 + 0.212671i
\(76\) 13.3161 + 2.34799i 1.52747 + 0.269333i
\(77\) 9.71726 6.94715i 1.10738 0.791701i
\(78\) −7.72963 + 10.9034i −0.875208 + 1.23457i
\(79\) 8.96547 + 3.26316i 1.00869 + 0.367135i 0.792931 0.609311i \(-0.208554\pi\)
0.215763 + 0.976446i \(0.430776\pi\)
\(80\) 6.32733 + 2.74762i 0.707417 + 0.307193i
\(81\) −7.02722 + 5.62301i −0.780802 + 0.624779i
\(82\) 14.0808 1.55497
\(83\) −0.743273 + 2.04213i −0.0815848 + 0.224152i −0.973777 0.227503i \(-0.926944\pi\)
0.892193 + 0.451655i \(0.149166\pi\)
\(84\) 8.34034 7.05526i 0.910006 0.769792i
\(85\) 4.40594 2.19934i 0.477891 0.238552i
\(86\) −9.83120 1.73351i −1.06013 0.186929i
\(87\) −8.11430 11.7332i −0.869944 1.25793i
\(88\) 2.33242 + 2.77967i 0.248637 + 0.296314i
\(89\) −5.99817 10.3891i −0.635805 1.10125i −0.986344 0.164699i \(-0.947335\pi\)
0.350539 0.936548i \(-0.385999\pi\)
\(90\) −11.6250 7.88246i −1.22538 0.830885i
\(91\) 6.82688 6.96215i 0.715651 0.729832i
\(92\) −2.96516 16.8163i −0.309139 1.75322i
\(93\) −2.76867 10.5787i −0.287097 1.09696i
\(94\) −6.97345 19.1594i −0.719257 1.97614i
\(95\) −0.768264 + 12.6600i −0.0788223 + 1.29889i
\(96\) −9.82180 9.93682i −1.00243 1.01417i
\(97\) −2.37599 13.4749i −0.241245 1.36817i −0.829054 0.559169i \(-0.811120\pi\)
0.587809 0.809000i \(-0.299991\pi\)
\(98\) −12.5466 + 7.57578i −1.26739 + 0.765269i
\(99\) 6.63528 + 11.8080i 0.666871 + 1.18675i
\(100\) 3.47399 11.4018i 0.347399 1.14018i
\(101\) 12.6510 10.6155i 1.25882 1.05628i 0.263019 0.964791i \(-0.415282\pi\)
0.995806 0.0914885i \(-0.0291625\pi\)
\(102\) −7.95998 + 0.649743i −0.788156 + 0.0643341i
\(103\) −1.18283 + 6.70816i −0.116548 + 0.660975i 0.869425 + 0.494066i \(0.164490\pi\)
−0.985972 + 0.166909i \(0.946621\pi\)
\(104\) 2.26902 + 1.90394i 0.222496 + 0.186696i
\(105\) 7.46430 + 7.02027i 0.728441 + 0.685109i
\(106\) −5.72493 2.08371i −0.556055 0.202387i
\(107\) 1.61281 0.155916 0.0779579 0.996957i \(-0.475160\pi\)
0.0779579 + 0.996957i \(0.475160\pi\)
\(108\) 6.92655 + 10.2692i 0.666508 + 0.988159i
\(109\) −11.0718 −1.06048 −0.530241 0.847847i \(-0.677899\pi\)
−0.530241 + 0.847847i \(0.677899\pi\)
\(110\) −14.5429 + 15.3397i −1.38661 + 1.46258i
\(111\) −3.26951 + 1.50149i −0.310328 + 0.142515i
\(112\) 4.74689 + 6.63968i 0.448539 + 0.627390i
\(113\) 1.99228 11.2988i 0.187418 1.06290i −0.735391 0.677643i \(-0.763001\pi\)
0.922809 0.385258i \(-0.125888\pi\)
\(114\) 8.80166 18.5919i 0.824351 1.74129i
\(115\) 15.3553 4.55641i 1.43189 0.424887i
\(116\) −17.0036 + 9.81706i −1.57875 + 0.911491i
\(117\) 7.00780 + 8.55182i 0.647872 + 0.790616i
\(118\) 8.68180 15.0373i 0.799225 1.38430i
\(119\) 5.80912 + 0.450857i 0.532521 + 0.0413300i
\(120\) −1.95071 + 2.42565i −0.178074 + 0.221431i
\(121\) 8.81808 3.20952i 0.801644 0.291775i
\(122\) 0.355100 + 0.975628i 0.0321492 + 0.0883292i
\(123\) 3.08023 11.2336i 0.277735 1.01290i
\(124\) −14.8215 + 2.61342i −1.33101 + 0.234692i
\(125\) 10.9960 + 2.02174i 0.983514 + 0.180830i
\(126\) −6.99578 15.0745i −0.623234 1.34295i
\(127\) −7.94667 + 4.58801i −0.705153 + 0.407120i −0.809264 0.587446i \(-0.800134\pi\)
0.104111 + 0.994566i \(0.466800\pi\)
\(128\) −4.83465 + 4.05675i −0.427327 + 0.358570i
\(129\) −3.53359 + 7.46407i −0.311115 + 0.657174i
\(130\) −9.51657 + 14.3929i −0.834658 + 1.26234i
\(131\) 7.10311 + 5.96022i 0.620602 + 0.520747i 0.897993 0.440010i \(-0.145025\pi\)
−0.277391 + 0.960757i \(0.589470\pi\)
\(132\) 16.9407 7.77984i 1.47450 0.677148i
\(133\) −8.48670 + 12.3769i −0.735890 + 1.07322i
\(134\) 12.5104i 1.08073i
\(135\) −8.83159 + 7.55003i −0.760102 + 0.649803i
\(136\) 1.76995i 0.151772i
\(137\) 18.3118 + 6.66493i 1.56448 + 0.569424i 0.971757 0.235983i \(-0.0758311\pi\)
0.592722 + 0.805407i \(0.298053\pi\)
\(138\) −25.8644 2.41463i −2.20172 0.205547i
\(139\) 4.02795 4.80032i 0.341646 0.407158i −0.567675 0.823253i \(-0.692157\pi\)
0.909321 + 0.416095i \(0.136602\pi\)
\(140\) 10.4659 9.45313i 0.884530 0.798936i
\(141\) −16.8107 + 1.37220i −1.41572 + 0.115560i
\(142\) 9.49084 + 11.3107i 0.796454 + 0.949177i
\(143\) 14.4101 8.31966i 1.20503 0.695725i
\(144\) −8.06825 + 4.53380i −0.672355 + 0.377817i
\(145\) −10.9619 14.7993i −0.910332 1.22902i
\(146\) −0.460210 2.60998i −0.0380873 0.216004i
\(147\) 3.29931 + 11.6668i 0.272123 + 0.962263i
\(148\) 1.69359 + 4.65309i 0.139212 + 0.382482i
\(149\) −5.26471 14.4647i −0.431302 1.18499i −0.945014 0.327029i \(-0.893953\pi\)
0.513713 0.857962i \(-0.328270\pi\)
\(150\) −15.3303 9.68352i −1.25171 0.790656i
\(151\) 1.40527 + 7.96969i 0.114359 + 0.648564i 0.987065 + 0.160318i \(0.0512520\pi\)
−0.872706 + 0.488246i \(0.837637\pi\)
\(152\) −3.94796 2.27935i −0.320222 0.184880i
\(153\) −1.22291 + 6.49256i −0.0988667 + 0.524893i
\(154\) −24.0936 + 6.70986i −1.94152 + 0.540696i
\(155\) −4.01592 13.5338i −0.322566 1.08706i
\(156\) 12.5157 8.65544i 1.00206 0.692990i
\(157\) −0.754737 + 4.28032i −0.0602345 + 0.341607i −1.00000 0.000212988i \(-0.999932\pi\)
0.939765 + 0.341820i \(0.111043\pi\)
\(158\) −15.3027 12.8405i −1.21742 1.02154i
\(159\) −2.91472 + 4.11150i −0.231152 + 0.326063i
\(160\) −13.0898 12.4099i −1.03484 0.981087i
\(161\) 18.3531 + 4.72524i 1.44643 + 0.372401i
\(162\) 17.8527 6.03099i 1.40264 0.473839i
\(163\) 7.67621i 0.601247i −0.953743 0.300624i \(-0.902805\pi\)
0.953743 0.300624i \(-0.0971948\pi\)
\(164\) −15.0649 5.48316i −1.17637 0.428163i
\(165\) 9.05660 + 14.9579i 0.705055 + 1.16447i
\(166\) 2.92477 3.48561i 0.227006 0.270536i
\(167\) −8.58297 1.51341i −0.664170 0.117111i −0.168608 0.985683i \(-0.553927\pi\)
−0.495563 + 0.868572i \(0.665038\pi\)
\(168\) −3.45586 + 1.27346i −0.266625 + 0.0982498i
\(169\) 0.446254 0.374451i 0.0343272 0.0288039i
\(170\) −10.2436 + 1.17206i −0.785651 + 0.0898929i
\(171\) −12.9071 11.0890i −0.987032 0.847994i
\(172\) 9.84322 + 5.68299i 0.750539 + 0.433324i
\(173\) −15.4779 + 2.72917i −1.17676 + 0.207495i −0.727630 0.685970i \(-0.759378\pi\)
−0.449132 + 0.893465i \(0.648267\pi\)
\(174\) 7.56259 + 28.8957i 0.573319 + 2.19058i
\(175\) 9.92558 + 8.74545i 0.750303 + 0.661094i
\(176\) 4.76370 + 13.0882i 0.359077 + 0.986557i
\(177\) −10.0975 10.2158i −0.758976 0.767864i
\(178\) 4.36162 + 24.7360i 0.326917 + 1.85404i
\(179\) 21.0864 + 12.1743i 1.57607 + 0.909947i 0.995399 + 0.0958117i \(0.0305447\pi\)
0.580675 + 0.814135i \(0.302789\pi\)
\(180\) 9.36792 + 12.9602i 0.698244 + 0.965995i
\(181\) −2.40999 + 1.39141i −0.179133 + 0.103423i −0.586885 0.809670i \(-0.699646\pi\)
0.407752 + 0.913093i \(0.366313\pi\)
\(182\) −18.4175 + 8.80921i −1.36520 + 0.652982i
\(183\) 0.856030 0.0698744i 0.0632796 0.00516527i
\(184\) −0.999684 + 5.66949i −0.0736977 + 0.417960i
\(185\) −4.15575 + 2.07445i −0.305537 + 0.152517i
\(186\) −2.12820 + 22.7963i −0.156047 + 1.67150i
\(187\) 9.34321 + 3.40065i 0.683243 + 0.248680i
\(188\) 23.2139i 1.69305i
\(189\) −13.5567 + 2.28359i −0.986108 + 0.166107i
\(190\) 10.5775 24.3584i 0.767374 1.76714i
\(191\) −0.575587 + 1.58141i −0.0416480 + 0.114427i −0.958773 0.284172i \(-0.908281\pi\)
0.917125 + 0.398599i \(0.130503\pi\)
\(192\) 7.74862 + 16.8727i 0.559208 + 1.21768i
\(193\) 7.11343 8.47746i 0.512036 0.610221i −0.446642 0.894713i \(-0.647380\pi\)
0.958679 + 0.284492i \(0.0918248\pi\)
\(194\) −4.97476 + 28.2133i −0.357167 + 2.02559i
\(195\) 9.40076 + 10.7408i 0.673203 + 0.769161i
\(196\) 16.3735 3.21950i 1.16953 0.229965i
\(197\) −4.17651 7.23392i −0.297564 0.515396i 0.678014 0.735049i \(-0.262841\pi\)
−0.975578 + 0.219653i \(0.929507\pi\)
\(198\) −4.59906 27.9838i −0.326841 1.98872i
\(199\) 7.22720 + 4.17262i 0.512322 + 0.295790i 0.733788 0.679379i \(-0.237751\pi\)
−0.221465 + 0.975168i \(0.571084\pi\)
\(200\) −2.41534 + 3.21162i −0.170790 + 0.227096i
\(201\) −9.98069 2.73668i −0.703984 0.193031i
\(202\) −32.4927 + 11.8264i −2.28618 + 0.832101i
\(203\) −2.11209 21.6886i −0.148239 1.52224i
\(204\) 8.76929 + 2.40452i 0.613973 + 0.168350i
\(205\) 3.50354 14.6240i 0.244698 1.02138i
\(206\) 7.13099 12.3512i 0.496840 0.860552i
\(207\) −7.58430 + 20.1063i −0.527146 + 1.39748i
\(208\) 5.68471 + 9.84620i 0.394164 + 0.682711i
\(209\) −19.6176 + 16.4611i −1.35698 + 1.13864i
\(210\) −9.65869 19.1576i −0.666513 1.32200i
\(211\) 1.31065 7.43306i 0.0902288 0.511713i −0.905877 0.423542i \(-0.860787\pi\)
0.996105 0.0881712i \(-0.0281022\pi\)
\(212\) 5.31362 + 4.45865i 0.364941 + 0.306222i
\(213\) 11.0998 5.09748i 0.760546 0.349273i
\(214\) −3.17319 1.15495i −0.216915 0.0789505i
\(215\) −4.24654 + 9.77912i −0.289612 + 0.666930i
\(216\) −1.01027 4.05211i −0.0687398 0.275711i
\(217\) 4.16472 16.1760i 0.282719 1.09810i
\(218\) 21.7837 + 7.92860i 1.47538 + 0.536993i
\(219\) −2.18290 0.203790i −0.147507 0.0137708i
\(220\) 21.5326 10.7486i 1.45173 0.724670i
\(221\) 7.99296 + 1.40937i 0.537664 + 0.0948047i
\(222\) 7.50797 0.612847i 0.503902 0.0411316i
\(223\) −18.6222 + 15.6259i −1.24703 + 1.04639i −0.250093 + 0.968222i \(0.580461\pi\)
−0.996941 + 0.0781635i \(0.975094\pi\)
\(224\) −5.72570 20.5597i −0.382565 1.37370i
\(225\) −11.0790 + 10.1121i −0.738601 + 0.674142i
\(226\) −12.0110 + 20.8036i −0.798959 + 1.38384i
\(227\) −11.8463 + 2.08883i −0.786268 + 0.138640i −0.552346 0.833615i \(-0.686267\pi\)
−0.233922 + 0.972255i \(0.575156\pi\)
\(228\) −16.6566 + 16.4638i −1.10311 + 1.09034i
\(229\) 0.436253 + 1.19860i 0.0288284 + 0.0792054i 0.953272 0.302114i \(-0.0976922\pi\)
−0.924444 + 0.381319i \(0.875470\pi\)
\(230\) −33.4744 2.03137i −2.20724 0.133945i
\(231\) 0.0825299 + 20.6895i 0.00543007 + 1.36127i
\(232\) 6.51895 1.14947i 0.427990 0.0754662i
\(233\) 8.77621 15.2008i 0.574949 0.995841i −0.421098 0.907015i \(-0.638355\pi\)
0.996047 0.0888257i \(-0.0283114\pi\)
\(234\) −7.66379 21.8440i −0.500997 1.42799i
\(235\) −21.6336 + 2.47528i −1.41122 + 0.161470i
\(236\) −15.1442 + 12.7075i −0.985802 + 0.827186i
\(237\) −13.5916 + 9.39954i −0.882871 + 0.610566i
\(238\) −11.1066 5.04703i −0.719931 0.327150i
\(239\) −3.48022 + 4.14756i −0.225116 + 0.268283i −0.866766 0.498714i \(-0.833806\pi\)
0.641650 + 0.766998i \(0.278250\pi\)
\(240\) −10.2205 + 6.18825i −0.659732 + 0.399450i
\(241\) −9.89061 + 27.1742i −0.637110 + 1.75045i 0.0235067 + 0.999724i \(0.492517\pi\)
−0.660617 + 0.750723i \(0.729705\pi\)
\(242\) −19.6479 −1.26302
\(243\) −0.906146 15.5621i −0.0581293 0.998309i
\(244\) 1.18209i 0.0756755i
\(245\) 4.74623 + 14.9155i 0.303225 + 0.952919i
\(246\) −14.1048 + 19.8963i −0.899291 + 1.26854i
\(247\) −13.4371 + 16.0137i −0.854982 + 1.01893i
\(248\) 4.99696 + 0.881099i 0.317307 + 0.0559498i
\(249\) −2.14100 3.09586i −0.135680 0.196192i
\(250\) −20.1869 11.8521i −1.27673 0.749594i
\(251\) −8.93455 15.4751i −0.563944 0.976780i −0.997147 0.0754833i \(-0.975950\pi\)
0.433203 0.901296i \(-0.357383\pi\)
\(252\) 1.61456 + 18.8522i 0.101708 + 1.18758i
\(253\) 28.0074 + 16.1701i 1.76081 + 1.01661i
\(254\) 18.9206 3.33620i 1.18718 0.209332i
\(255\) −1.30577 + 8.42871i −0.0817704 + 0.527826i
\(256\) −7.72900 + 2.81312i −0.483062 + 0.175820i
\(257\) −2.61908 7.19585i −0.163374 0.448865i 0.830811 0.556555i \(-0.187877\pi\)
−0.994185 + 0.107690i \(0.965655\pi\)
\(258\) 12.2974 12.1551i 0.765604 0.756742i
\(259\) −5.47925 0.425255i −0.340464 0.0264241i
\(260\) 15.7863 11.6929i 0.979026 0.725163i
\(261\) 24.7072 + 0.287648i 1.52934 + 0.0178050i
\(262\) −9.70717 16.8133i −0.599711 1.03873i
\(263\) 8.78731 7.37343i 0.541849 0.454665i −0.330321 0.943869i \(-0.607157\pi\)
0.872170 + 0.489203i \(0.162712\pi\)
\(264\) −6.26409 + 0.511314i −0.385528 + 0.0314692i
\(265\) −3.58854 + 5.42732i −0.220443 + 0.333397i
\(266\) 25.5608 18.2741i 1.56723 1.12046i
\(267\) 20.6883 + 1.93140i 1.26610 + 0.118200i
\(268\) −4.87161 + 13.3846i −0.297581 + 0.817597i
\(269\) −12.4690 −0.760248 −0.380124 0.924935i \(-0.624119\pi\)
−0.380124 + 0.924935i \(0.624119\pi\)
\(270\) 22.7828 8.53026i 1.38652 0.519135i
\(271\) 17.0770i 1.03735i 0.854970 + 0.518677i \(0.173575\pi\)
−0.854970 + 0.518677i \(0.826425\pi\)
\(272\) −2.32362 + 6.38409i −0.140890 + 0.387092i
\(273\) 2.99904 + 16.6204i 0.181510 + 1.00592i
\(274\) −31.2555 26.2265i −1.88821 1.58440i
\(275\) 12.3129 + 18.9207i 0.742496 + 1.14096i
\(276\) 26.7317 + 12.6551i 1.60906 + 0.761750i
\(277\) 2.63866 + 3.14464i 0.158542 + 0.188943i 0.839468 0.543409i \(-0.182867\pi\)
−0.680926 + 0.732352i \(0.738422\pi\)
\(278\) −11.3625 + 6.56016i −0.681479 + 0.393452i
\(279\) 17.7212 + 6.68463i 1.06094 + 0.400198i
\(280\) −4.40575 + 1.78804i −0.263294 + 0.106856i
\(281\) 27.8803 4.91605i 1.66320 0.293267i 0.738582 0.674164i \(-0.235496\pi\)
0.924618 + 0.380897i \(0.124385\pi\)
\(282\) 34.0577 + 9.33855i 2.02811 + 0.556102i
\(283\) −2.02830 + 0.738240i −0.120570 + 0.0438838i −0.401600 0.915815i \(-0.631546\pi\)
0.281031 + 0.959699i \(0.409324\pi\)
\(284\) −5.74964 15.7970i −0.341178 0.937380i
\(285\) −17.1191 13.7672i −1.01405 0.815496i
\(286\) −34.3095 + 6.04970i −2.02877 + 0.357726i
\(287\) 12.4575 12.7044i 0.735344 0.749914i
\(288\) 23.8793 3.92450i 1.40710 0.231254i
\(289\) −6.07506 10.5223i −0.357356 0.618960i
\(290\) 10.9694 + 36.9675i 0.644148 + 2.17081i
\(291\) 21.4201 + 10.1406i 1.25567 + 0.594452i
\(292\) −0.523972 + 2.97159i −0.0306631 + 0.173899i
\(293\) 13.2899 15.8383i 0.776405 0.925283i −0.222360 0.974965i \(-0.571376\pi\)
0.998765 + 0.0496814i \(0.0158206\pi\)
\(294\) 1.86334 25.3171i 0.108672 1.47652i
\(295\) −13.4572 12.7582i −0.783510 0.742814i
\(296\) 1.66944i 0.0970342i
\(297\) −23.3314 2.45245i −1.35382 0.142305i
\(298\) 32.2293i 1.86699i
\(299\) 24.8070 + 9.02901i 1.43463 + 0.522161i
\(300\) 12.6309 + 16.3300i 0.729243 + 0.942812i
\(301\) −10.2619 + 7.33650i −0.591484 + 0.422869i
\(302\) 2.94231 16.6867i 0.169311 0.960209i
\(303\) 2.32713 + 28.5096i 0.133690 + 1.63783i
\(304\) −11.2477 13.4044i −0.645098 0.768798i
\(305\) 1.10162 0.126045i 0.0630785 0.00721733i
\(306\) 7.05547 11.8984i 0.403334 0.680184i
\(307\) −2.89678 + 5.01737i −0.165328 + 0.286356i −0.936772 0.349941i \(-0.886202\pi\)
0.771444 + 0.636297i \(0.219535\pi\)
\(308\) 28.3903 + 2.20342i 1.61769 + 0.125552i
\(309\) −8.29382 8.39094i −0.471819 0.477344i
\(310\) −1.79041 + 29.5036i −0.101688 + 1.67569i
\(311\) 12.4442 4.52931i 0.705645 0.256834i 0.0358257 0.999358i \(-0.488594\pi\)
0.669819 + 0.742524i \(0.266372\pi\)
\(312\) −4.96317 + 1.29896i −0.280984 + 0.0735392i
\(313\) −4.72350 26.7883i −0.266988 1.51417i −0.763313 0.646029i \(-0.776429\pi\)
0.496325 0.868137i \(-0.334682\pi\)
\(314\) 4.55012 7.88105i 0.256778 0.444753i
\(315\) −17.3967 + 3.51485i −0.980194 + 0.198040i
\(316\) 11.3720 + 19.6969i 0.639725 + 1.10804i
\(317\) −19.2423 + 16.1462i −1.08076 + 0.906862i −0.995983 0.0895379i \(-0.971461\pi\)
−0.0847731 + 0.996400i \(0.527017\pi\)
\(318\) 8.67899 6.00211i 0.486693 0.336581i
\(319\) 6.45724 36.6208i 0.361536 2.05037i
\(320\) 10.7055 + 21.4462i 0.598453 + 1.19888i
\(321\) −1.61556 + 2.27890i −0.0901716 + 0.127196i
\(322\) −32.7259 22.4397i −1.82374 1.25052i
\(323\) −12.4914 −0.695043
\(324\) −21.4489 0.499495i −1.19160 0.0277497i
\(325\) 12.5802 + 13.4649i 0.697824 + 0.746896i
\(326\) −5.49701 + 15.1029i −0.304451 + 0.836473i
\(327\) 11.0906 15.6445i 0.613314 0.865141i
\(328\) 4.14046 + 3.47426i 0.228618 + 0.191834i
\(329\) −23.4560 10.6589i −1.29317 0.587642i
\(330\) −7.10733 35.9151i −0.391246 1.97706i
\(331\) 8.38165 7.03304i 0.460697 0.386571i −0.382690 0.923877i \(-0.625002\pi\)
0.843387 + 0.537306i \(0.180558\pi\)
\(332\) −4.48649 + 2.59028i −0.246228 + 0.142160i
\(333\) 1.15347 6.12388i 0.0632097 0.335587i
\(334\) 15.8032 + 9.12398i 0.864713 + 0.499242i
\(335\) −12.9929 3.11278i −0.709880 0.170069i
\(336\) −14.1369 + 0.0563916i −0.771231 + 0.00307641i
\(337\) 3.38123 + 9.28985i 0.184187 + 0.506050i 0.997080 0.0763631i \(-0.0243308\pi\)
−0.812893 + 0.582413i \(0.802109\pi\)
\(338\) −1.14615 + 0.417165i −0.0623424 + 0.0226908i
\(339\) 13.9696 + 14.1332i 0.758724 + 0.767609i
\(340\) 11.4159 + 2.73497i 0.619116 + 0.148325i
\(341\) 14.2520 24.6851i 0.771787 1.33677i
\(342\) 17.4538 + 31.0604i 0.943793 + 1.67955i
\(343\) −4.26493 + 18.0225i −0.230284 + 0.973123i
\(344\) −2.46314 2.93546i −0.132804 0.158269i
\(345\) −8.94326 + 26.2613i −0.481489 + 1.41386i
\(346\) 32.4071 + 5.71424i 1.74221 + 0.307199i
\(347\) −19.5786 16.4284i −1.05103 0.881921i −0.0578309 0.998326i \(-0.518418\pi\)
−0.993202 + 0.116405i \(0.962863\pi\)
\(348\) 3.16108 33.8601i 0.169452 1.81509i
\(349\) 6.51740 17.9064i 0.348868 0.958508i −0.633859 0.773448i \(-0.718530\pi\)
0.982727 0.185059i \(-0.0592477\pi\)
\(350\) −13.2658 24.3144i −0.709089 1.29966i
\(351\) −19.1035 + 1.33567i −1.01967 + 0.0712928i
\(352\) 36.4194i 1.94116i
\(353\) −5.80576 + 15.9512i −0.309009 + 0.848996i 0.683841 + 0.729631i \(0.260308\pi\)
−0.992850 + 0.119365i \(0.961914\pi\)
\(354\) 12.5512 + 27.3304i 0.667090 + 1.45259i
\(355\) 14.1085 7.04266i 0.748804 0.373785i
\(356\) 4.96591 28.1631i 0.263193 1.49264i
\(357\) −6.45609 + 7.75670i −0.341693 + 0.410528i
\(358\) −32.7694 39.0530i −1.73192 2.06402i
\(359\) 28.1244 16.2376i 1.48435 0.856989i 0.484507 0.874787i \(-0.338999\pi\)
0.999842 + 0.0177981i \(0.00566560\pi\)
\(360\) −1.47343 5.18615i −0.0776564 0.273334i
\(361\) 6.58660 11.4083i 0.346663 0.600439i
\(362\) 5.73805 1.01177i 0.301585 0.0531776i
\(363\) −4.29805 + 15.6750i −0.225589 + 0.822724i
\(364\) 23.1350 2.25294i 1.21260 0.118086i
\(365\) −2.82517 0.171444i −0.147876 0.00897377i
\(366\) −1.73427 0.475534i −0.0906519 0.0248566i
\(367\) −2.19754 12.4629i −0.114711 0.650556i −0.986893 0.161375i \(-0.948407\pi\)
0.872183 0.489180i \(-0.162704\pi\)
\(368\) −11.0488 + 19.1371i −0.575959 + 0.997591i
\(369\) 12.7877 + 15.6051i 0.665699 + 0.812371i
\(370\) 9.66195 1.10550i 0.502301 0.0574724i
\(371\) −6.94495 + 3.32181i −0.360564 + 0.172460i
\(372\) 11.1540 23.5607i 0.578306 1.22157i
\(373\) −10.5128 1.85370i −0.544334 0.0959807i −0.105282 0.994442i \(-0.533574\pi\)
−0.439052 + 0.898462i \(0.644686\pi\)
\(374\) −15.9475 13.3815i −0.824625 0.691943i
\(375\) −13.8715 + 13.5123i −0.716322 + 0.697770i
\(376\) 2.67679 7.35442i 0.138045 0.379275i
\(377\) 30.3544i 1.56333i
\(378\) 28.3081 + 5.21517i 1.45601 + 0.268239i
\(379\) −18.0645 −0.927910 −0.463955 0.885859i \(-0.653570\pi\)
−0.463955 + 0.885859i \(0.653570\pi\)
\(380\) −20.8020 + 21.9417i −1.06712 + 1.12559i
\(381\) 1.47733 15.8245i 0.0756860 0.810715i
\(382\) 2.26493 2.69924i 0.115884 0.138105i
\(383\) −1.57647 0.277975i −0.0805540 0.0142038i 0.133226 0.991086i \(-0.457466\pi\)
−0.213780 + 0.976882i \(0.568578\pi\)
\(384\) −0.889322 10.8951i −0.0453830 0.555986i
\(385\) 0.973809 + 26.6925i 0.0496299 + 1.36038i
\(386\) −20.0664 + 11.5854i −1.02136 + 0.589680i
\(387\) −7.00716 12.4698i −0.356194 0.633875i
\(388\) 16.3089 28.2478i 0.827957 1.43406i
\(389\) 4.32725 0.763010i 0.219400 0.0386861i −0.0628675 0.998022i \(-0.520025\pi\)
0.282267 + 0.959336i \(0.408913\pi\)
\(390\) −10.8044 27.8644i −0.547102 1.41097i
\(391\) 5.39529 + 14.8235i 0.272852 + 0.749654i
\(392\) −5.55854 0.868046i −0.280749 0.0438430i
\(393\) −15.5371 + 4.06636i −0.783741 + 0.205121i
\(394\) 3.03698 + 17.2235i 0.153001 + 0.867710i
\(395\) −17.1434 + 12.6981i −0.862580 + 0.638912i
\(396\) −5.97661 + 31.7304i −0.300336 + 1.59451i
\(397\) 10.1088 + 17.5090i 0.507348 + 0.878752i 0.999964 + 0.00850506i \(0.00270728\pi\)
−0.492616 + 0.870247i \(0.663959\pi\)
\(398\) −11.2314 13.3851i −0.562980 0.670934i
\(399\) −8.98750 24.3898i −0.449938 1.22102i
\(400\) −12.9283 + 8.41324i −0.646413 + 0.420662i
\(401\) 15.3228 18.2610i 0.765186 0.911913i −0.232978 0.972482i \(-0.574847\pi\)
0.998164 + 0.0605693i \(0.0192916\pi\)
\(402\) 17.6772 + 12.5317i 0.881659 + 0.625024i
\(403\) 7.95796 21.8643i 0.396414 1.08914i
\(404\) 39.3688 1.95867
\(405\) −1.82159 20.0420i −0.0905154 0.995895i
\(406\) −11.3759 + 44.1847i −0.564576 + 2.19285i
\(407\) −8.81265 3.20754i −0.436827 0.158992i
\(408\) −2.50094 1.77296i −0.123815 0.0877748i
\(409\) 12.2108 14.5523i 0.603787 0.719565i −0.374406 0.927265i \(-0.622153\pi\)
0.978193 + 0.207700i \(0.0665977\pi\)
\(410\) −17.3656 + 26.2637i −0.857625 + 1.29707i
\(411\) −27.7606 + 19.1983i −1.36933 + 0.946984i
\(412\) −12.4390 + 10.4376i −0.612826 + 0.514222i
\(413\) −5.88644 21.1369i −0.289653 1.04008i
\(414\) 29.3204 34.1278i 1.44102 1.67729i
\(415\) −2.89234 3.90487i −0.141979 0.191683i
\(416\) −5.16237 29.2772i −0.253106 1.43544i
\(417\) 2.74806 + 10.5000i 0.134573 + 0.514188i
\(418\) 50.3855 18.3388i 2.46444 0.896982i
\(419\) 4.06130 1.47819i 0.198407 0.0722144i −0.240905 0.970549i \(-0.577444\pi\)
0.439313 + 0.898334i \(0.355222\pi\)
\(420\) 2.87359 + 24.2576i 0.140217 + 1.18365i
\(421\) −5.27236 29.9011i −0.256959 1.45729i −0.790993 0.611825i \(-0.790436\pi\)
0.534034 0.845463i \(-0.320675\pi\)
\(422\) −7.90159 + 13.6859i −0.384643 + 0.666222i
\(423\) 14.9005 25.1282i 0.724486 1.22178i
\(424\) −1.16929 2.02526i −0.0567856 0.0983556i
\(425\) −1.33151 + 10.9304i −0.0645879 + 0.530203i
\(426\) −25.4892 + 2.08058i −1.23495 + 0.100805i
\(427\) 1.19442 + 0.542766i 0.0578019 + 0.0262663i
\(428\) 2.94521 + 2.47132i 0.142362 + 0.119456i
\(429\) −2.67892 + 28.6954i −0.129339 + 1.38542i
\(430\) 15.3580 16.1994i 0.740628 0.781204i
\(431\) 8.71009i 0.419551i 0.977750 + 0.209775i \(0.0672732\pi\)
−0.977750 + 0.209775i \(0.932727\pi\)
\(432\) 1.67572 15.9420i 0.0806233 0.767011i
\(433\) −4.19676 −0.201683 −0.100842 0.994902i \(-0.532154\pi\)
−0.100842 + 0.994902i \(0.532154\pi\)
\(434\) −19.7779 + 28.8439i −0.949368 + 1.38455i
\(435\) 31.8921 0.664586i 1.52911 0.0318645i
\(436\) −20.2186 16.9654i −0.968294 0.812495i
\(437\) −40.0126 7.05530i −1.91406 0.337501i
\(438\) 4.14892 + 1.96415i 0.198243 + 0.0938509i
\(439\) −13.4488 16.0277i −0.641878 0.764960i 0.342788 0.939413i \(-0.388629\pi\)
−0.984666 + 0.174453i \(0.944184\pi\)
\(440\) −8.06121 + 0.922350i −0.384303 + 0.0439713i
\(441\) −19.7902 7.02476i −0.942391 0.334513i
\(442\) −14.7168 8.49677i −0.700009 0.404150i
\(443\) −2.89508 16.4188i −0.137549 0.780080i −0.973051 0.230592i \(-0.925934\pi\)
0.835501 0.549488i \(-0.185177\pi\)
\(444\) −8.27132 2.26798i −0.392540 0.107633i
\(445\) 26.7754 + 1.62485i 1.26928 + 0.0770252i
\(446\) 47.8289 17.4083i 2.26476 0.824307i
\(447\) 25.7123 + 7.05027i 1.21615 + 0.333466i
\(448\) −2.19458 + 28.2763i −0.103684 + 1.33593i
\(449\) −32.8568 18.9699i −1.55061 0.895245i −0.998092 0.0617431i \(-0.980334\pi\)
−0.552517 0.833502i \(-0.686333\pi\)
\(450\) 29.0393 11.9618i 1.36893 0.563884i
\(451\) 26.2951 15.1815i 1.23819 0.714869i
\(452\) 20.9515 17.5804i 0.985474 0.826911i
\(453\) −12.6689 5.99762i −0.595236 0.281793i
\(454\) 24.8034 + 4.37351i 1.16408 + 0.205259i
\(455\) 4.56644 + 21.3199i 0.214078 + 0.999491i
\(456\) 7.17543 3.29525i 0.336020 0.154314i
\(457\) −6.45144 + 17.7252i −0.301786 + 0.829149i 0.692404 + 0.721510i \(0.256551\pi\)
−0.994190 + 0.107640i \(0.965671\pi\)
\(458\) 2.67064i 0.124791i
\(459\) −7.94904 8.23162i −0.371029 0.384219i
\(460\) 35.0228 + 15.2085i 1.63295 + 0.709100i
\(461\) −5.36766 1.95367i −0.249997 0.0909915i 0.213982 0.976838i \(-0.431357\pi\)
−0.463979 + 0.885846i \(0.653579\pi\)
\(462\) 14.6536 40.7657i 0.681748 1.89659i
\(463\) 18.4686 22.0100i 0.858308 1.02289i −0.141151 0.989988i \(-0.545080\pi\)
0.999459 0.0329035i \(-0.0104754\pi\)
\(464\) 25.0225 + 4.41214i 1.16164 + 0.204829i
\(465\) 23.1461 + 7.88239i 1.07338 + 0.365537i
\(466\) −28.1526 + 23.6229i −1.30415 + 1.09431i
\(467\) −14.3300 + 8.27343i −0.663113 + 0.382848i −0.793462 0.608620i \(-0.791724\pi\)
0.130349 + 0.991468i \(0.458390\pi\)
\(468\) −0.306831 + 26.3549i −0.0141833 + 1.21826i
\(469\) −11.2874 11.0681i −0.521204 0.511077i
\(470\) 44.3366 + 10.6219i 2.04510 + 0.489953i
\(471\) −5.29210 5.35407i −0.243847 0.246703i
\(472\) 6.26314 2.27960i 0.288284 0.104927i
\(473\) −20.2282 + 7.36247i −0.930094 + 0.338527i
\(474\) 33.4726 8.76045i 1.53745 0.402381i
\(475\) −22.6661 17.0463i −1.03999 0.782138i
\(476\) 9.91740 + 9.72471i 0.454563 + 0.445731i
\(477\) −2.88989 8.23703i −0.132319 0.377148i
\(478\) 9.81742 5.66809i 0.449038 0.259252i
\(479\) −8.40305 + 7.05099i −0.383945 + 0.322168i −0.814249 0.580516i \(-0.802851\pi\)
0.430304 + 0.902684i \(0.358406\pi\)
\(480\) 30.6473 6.06488i 1.39885 0.276823i
\(481\) −7.53907 1.32934i −0.343752 0.0606128i
\(482\) 38.9195 46.3824i 1.77273 2.11266i
\(483\) −25.0612 + 21.1998i −1.14032 + 0.964624i
\(484\) 21.0210 + 7.65103i 0.955501 + 0.347774i
\(485\) 28.0638 + 12.1866i 1.27431 + 0.553365i
\(486\) −9.36134 + 31.2673i −0.424639 + 1.41831i
\(487\) 12.6066i 0.571259i 0.958340 + 0.285630i \(0.0922027\pi\)
−0.958340 + 0.285630i \(0.907797\pi\)
\(488\) −0.136307 + 0.374499i −0.00617031 + 0.0169528i
\(489\) 10.8465 + 7.68930i 0.490497 + 0.347722i
\(490\) 1.34299 32.7451i 0.0606699 1.47927i
\(491\) 33.0592 + 5.82924i 1.49194 + 0.263070i 0.859339 0.511406i \(-0.170875\pi\)
0.632603 + 0.774476i \(0.281986\pi\)
\(492\) 22.8383 15.7942i 1.02963 0.712059i
\(493\) 13.8948 11.6591i 0.625789 0.525099i
\(494\) 37.9050 21.8845i 1.70543 0.984628i
\(495\) −30.2076 2.18636i −1.35773 0.0982696i
\(496\) 16.8670 + 9.73817i 0.757351 + 0.437257i
\(497\) 18.6018 + 1.44372i 0.834403 + 0.0647596i
\(498\) 1.99543 + 7.62428i 0.0894172 + 0.341652i
\(499\) −3.61055 + 1.31413i −0.161630 + 0.0588286i −0.421568 0.906797i \(-0.638520\pi\)
0.259938 + 0.965625i \(0.416298\pi\)
\(500\) 16.9823 + 20.5413i 0.759473 + 0.918636i
\(501\) 10.7361 10.6118i 0.479652 0.474100i
\(502\) 6.49682 + 36.8453i 0.289967 + 1.64449i
\(503\) 18.6458 + 10.7652i 0.831376 + 0.479995i 0.854324 0.519741i \(-0.173972\pi\)
−0.0229475 + 0.999737i \(0.507305\pi\)
\(504\) 1.66234 6.15878i 0.0740464 0.274334i
\(505\) 4.19786 + 36.6887i 0.186802 + 1.63263i
\(506\) −43.5250 51.8710i −1.93492 2.30595i
\(507\) 0.0820872 + 1.00565i 0.00364562 + 0.0446624i
\(508\) −21.5420 3.79843i −0.955771 0.168528i
\(509\) −5.32142 4.46520i −0.235868 0.197917i 0.517191 0.855870i \(-0.326978\pi\)
−0.753058 + 0.657954i \(0.771422\pi\)
\(510\) 8.60498 15.6484i 0.381035 0.692922i
\(511\) −2.76200 1.89387i −0.122184 0.0837798i
\(512\) 29.8437 1.31892
\(513\) 28.5979 7.12997i 1.26263 0.314796i
\(514\) 16.0334i 0.707201i
\(515\) −11.0534 10.4793i −0.487070 0.461772i
\(516\) −17.8901 + 8.21586i −0.787568 + 0.361683i
\(517\) −33.6796 28.2605i −1.48123 1.24290i
\(518\) 10.4759 + 4.76043i 0.460283 + 0.209161i
\(519\) 11.6480 24.6042i 0.511288 1.08000i
\(520\) −6.34959 + 1.88413i −0.278448 + 0.0826244i
\(521\) −7.63869 13.2306i −0.334657 0.579643i 0.648762 0.760991i \(-0.275287\pi\)
−0.983419 + 0.181349i \(0.941954\pi\)
\(522\) −48.4053 18.2590i −2.11864 0.799176i
\(523\) 11.4024 19.7495i 0.498592 0.863587i −0.501407 0.865212i \(-0.667184\pi\)
0.999999 + 0.00162509i \(0.000517283\pi\)
\(524\) 3.83835 + 21.7684i 0.167679 + 0.950956i
\(525\) −22.2999 + 5.26455i −0.973246 + 0.229764i
\(526\) −22.5692 + 8.21451i −0.984064 + 0.358170i
\(527\) 13.0650 4.75529i 0.569123 0.207144i
\(528\) −23.2655 6.37934i −1.01250 0.277625i
\(529\) 4.91586 + 27.8792i 0.213733 + 1.21214i
\(530\) 10.9470 8.10843i 0.475507 0.352208i
\(531\) 24.5497 4.03467i 1.06537 0.175090i
\(532\) −34.4632 + 9.59771i −1.49417 + 0.416113i
\(533\) 18.9865 15.9315i 0.822395 0.690072i
\(534\) −39.3211 18.6151i −1.70159 0.805556i
\(535\) −1.98904 + 3.00823i −0.0859937 + 0.130057i
\(536\) 3.08676 3.67866i 0.133328 0.158894i
\(537\) −38.3247 + 17.6002i −1.65383 + 0.759507i
\(538\) 24.5327 + 8.92917i 1.05768 + 0.384964i
\(539\) −15.2620 + 27.6747i −0.657382 + 1.19203i
\(540\) −27.6967 + 0.254646i −1.19188 + 0.0109582i
\(541\) 34.3030 1.47480 0.737400 0.675457i \(-0.236054\pi\)
0.737400 + 0.675457i \(0.236054\pi\)
\(542\) 12.2290 33.5989i 0.525281 1.44320i
\(543\) 0.448032 4.79912i 0.0192269 0.205950i
\(544\) 11.4188 13.6084i 0.489578 0.583456i
\(545\) 13.6546 20.6512i 0.584898 0.884600i
\(546\) 6.00147 34.8483i 0.256839 1.49137i
\(547\) −5.91721 7.05186i −0.253002 0.301516i 0.624563 0.780975i \(-0.285277\pi\)
−0.877564 + 0.479459i \(0.840833\pi\)
\(548\) 23.2270 + 40.2304i 0.992210 + 1.71856i
\(549\) −0.758757 + 1.27957i −0.0323830 + 0.0546107i
\(550\) −10.6763 46.0438i −0.455238 1.96331i
\(551\) 8.11240 + 46.0077i 0.345600 + 1.95999i
\(552\) −7.00964 7.09172i −0.298350 0.301844i
\(553\) −25.1239 + 2.44662i −1.06838 + 0.104041i
\(554\) −2.93965 8.07663i −0.124894 0.343143i
\(555\) 1.23162 7.95008i 0.0522794 0.337462i
\(556\) 14.7112 2.59398i 0.623893 0.110009i
\(557\) 16.6747 28.8815i 0.706531 1.22375i −0.259605 0.965715i \(-0.583592\pi\)
0.966136 0.258033i \(-0.0830744\pi\)
\(558\) −30.0795 25.8423i −1.27337 1.09399i
\(559\) −15.2177 + 8.78593i −0.643639 + 0.371605i
\(560\) −18.2387 + 0.665391i −0.770724 + 0.0281179i
\(561\) −14.1643 + 9.79556i −0.598016 + 0.413569i
\(562\) −58.3748 10.2931i −2.46239 0.434186i
\(563\) −16.6369 + 19.8271i −0.701163 + 0.835614i −0.992658 0.120959i \(-0.961403\pi\)
0.291494 + 0.956573i \(0.405848\pi\)
\(564\) −32.8014 23.2535i −1.38119 0.979148i
\(565\) 18.6176 + 17.6506i 0.783249 + 0.742567i
\(566\) 4.51933 0.189962
\(567\) 10.3531 21.4432i 0.434791 0.900531i
\(568\) 5.66766i 0.237810i
\(569\) −15.3291 + 42.1163i −0.642628 + 1.76561i 0.000682401 1.00000i \(0.499783\pi\)
−0.643310 + 0.765606i \(0.722439\pi\)
\(570\) 23.8230 + 39.3460i 0.997834 + 1.64802i
\(571\) −2.04055 1.71223i −0.0853944 0.0716544i 0.599091 0.800681i \(-0.295529\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(572\) 39.0631 + 6.88788i 1.63331 + 0.287997i
\(573\) −1.65798 2.39742i −0.0692629 0.100154i
\(574\) −33.6078 + 16.0748i −1.40276 + 0.670950i
\(575\) −10.4387 + 34.2603i −0.435325 + 1.42875i
\(576\) −31.6030 5.95262i −1.31679 0.248026i
\(577\) −14.5617 + 25.2217i −0.606213 + 1.04999i 0.385646 + 0.922647i \(0.373979\pi\)
−0.991859 + 0.127345i \(0.959355\pi\)
\(578\) 4.41752 + 25.0530i 0.183745 + 1.04207i
\(579\) 4.85314 + 18.5432i 0.201690 + 0.770631i
\(580\) 2.65935 43.8226i 0.110423 1.81963i
\(581\) −0.557284 5.72264i −0.0231200 0.237415i
\(582\) −34.8823 35.2908i −1.44592 1.46285i
\(583\) −12.9376 + 2.28124i −0.535820 + 0.0944794i
\(584\) 0.508654 0.881015i 0.0210483 0.0364567i
\(585\) −24.5935 + 2.52427i −1.01682 + 0.104366i
\(586\) −37.4898 + 21.6447i −1.54869 + 0.894136i
\(587\) 9.87308 + 11.7663i 0.407506 + 0.485647i 0.930293 0.366817i \(-0.119552\pi\)
−0.522787 + 0.852463i \(0.675108\pi\)
\(588\) −11.8522 + 26.3608i −0.488777 + 1.08710i
\(589\) −6.21838 + 35.2662i −0.256224 + 1.45312i
\(590\) 17.3407 + 34.7386i 0.713906 + 1.43017i
\(591\) 14.4052 + 1.34483i 0.592551 + 0.0553189i
\(592\) 2.19167 6.02157i 0.0900771 0.247485i
\(593\) 34.6784i 1.42407i 0.702143 + 0.712036i \(0.252227\pi\)
−0.702143 + 0.712036i \(0.747773\pi\)
\(594\) 44.1482 + 21.5330i 1.81142 + 0.883511i
\(595\) −8.00522 + 10.2792i −0.328182 + 0.421407i
\(596\) 12.5503 34.4816i 0.514080 1.41242i
\(597\) −13.1355 + 6.03233i −0.537599 + 0.246887i
\(598\) −42.3419 35.5291i −1.73149 1.45289i
\(599\) −14.1986 2.50360i −0.580140 0.102294i −0.124125 0.992267i \(-0.539613\pi\)
−0.456015 + 0.889972i \(0.650724\pi\)
\(600\) −2.11859 6.62999i −0.0864910 0.270668i
\(601\) −21.0441 25.0794i −0.858407 1.02301i −0.999455 0.0330066i \(-0.989492\pi\)
0.141048 0.990003i \(-0.454953\pi\)
\(602\) 25.4439 7.08591i 1.03702 0.288800i
\(603\) 13.8647 11.3614i 0.564613 0.462673i
\(604\) −9.64583 + 16.7071i −0.392483 + 0.679801i
\(605\) −4.88873 + 20.4058i −0.198755 + 0.829615i
\(606\) 15.8374 57.7589i 0.643349 2.34630i
\(607\) −1.55390 + 0.565575i −0.0630710 + 0.0229560i −0.373363 0.927685i \(-0.621795\pi\)
0.310292 + 0.950641i \(0.399573\pi\)
\(608\) 15.6490 + 42.9953i 0.634652 + 1.74369i
\(609\) 32.7618 + 18.7412i 1.32757 + 0.759431i
\(610\) −2.25769 0.540886i −0.0914113 0.0218998i
\(611\) −31.0806 17.9444i −1.25739 0.725952i
\(612\) −12.1818 + 9.98244i −0.492422 + 0.403516i
\(613\) 0.0468704 0.0270606i 0.00189308 0.00109297i −0.499053 0.866571i \(-0.666319\pi\)
0.500946 + 0.865478i \(0.332985\pi\)
\(614\) 9.29238 7.79724i 0.375010 0.314671i
\(615\) 17.1543 + 19.5995i 0.691727 + 0.790326i
\(616\) −8.74028 3.97175i −0.352156 0.160026i
\(617\) 14.6348 + 12.2801i 0.589175 + 0.494377i 0.887946 0.459948i \(-0.152132\pi\)
−0.298770 + 0.954325i \(0.596576\pi\)
\(618\) 10.3092 + 22.4484i 0.414698 + 0.903009i
\(619\) 12.2042 33.5306i 0.490526 1.34771i −0.409673 0.912232i \(-0.634357\pi\)
0.900200 0.435478i \(-0.143421\pi\)
\(620\) 13.4044 30.8683i 0.538334 1.23970i
\(621\) −20.8130 30.8572i −0.835199 1.23826i
\(622\) −27.7274 −1.11177
\(623\) 26.1767 + 17.9490i 1.04875 + 0.719113i
\(624\) −19.6072 1.83047i −0.784914 0.0732774i
\(625\) −17.3322 + 18.0166i −0.693286 + 0.720663i
\(626\) −9.88991 + 56.0885i −0.395280 + 2.24175i
\(627\) −3.60861 44.2090i −0.144114 1.76554i
\(628\) −7.93704 + 6.65997i −0.316723 + 0.265762i
\(629\) −2.28724 3.96161i −0.0911982 0.157960i
\(630\) 36.7450 + 5.54250i 1.46396 + 0.220819i
\(631\) −4.85472 + 8.40861i −0.193263 + 0.334742i −0.946330 0.323203i \(-0.895240\pi\)
0.753067 + 0.657944i \(0.228574\pi\)
\(632\) −1.33153 7.55150i −0.0529656 0.300383i
\(633\) 9.19008 + 9.29769i 0.365273 + 0.369550i
\(634\) 49.4217 17.9880i 1.96279 0.714395i
\(635\) 1.24285 20.4805i 0.0493209 0.812745i
\(636\) −11.6228 + 3.04192i −0.460873 + 0.120620i
\(637\) −8.34619 + 24.4108i −0.330688 + 0.967190i
\(638\) −38.9291 + 67.4272i −1.54122 + 2.66947i
\(639\) −3.91597 + 20.7903i −0.154913 + 0.822450i
\(640\) −1.60423 14.0208i −0.0634129 0.554220i
\(641\) −29.7726 35.4815i −1.17595 1.40144i −0.897517 0.440980i \(-0.854631\pi\)
−0.278428 0.960457i \(-0.589813\pi\)
\(642\) 4.81055 3.32682i 0.189857 0.131299i
\(643\) 3.12370 17.7154i 0.123187 0.698626i −0.859182 0.511670i \(-0.829027\pi\)
0.982368 0.186955i \(-0.0598620\pi\)
\(644\) 26.2748 + 36.7517i 1.03537 + 1.44822i
\(645\) −9.56417 15.7962i −0.376589 0.621974i
\(646\) 24.5769 + 8.94525i 0.966964 + 0.351946i
\(647\) 2.57630i 0.101285i 0.998717 + 0.0506424i \(0.0161269\pi\)
−0.998717 + 0.0506424i \(0.983873\pi\)
\(648\) 6.73765 + 2.63151i 0.264680 + 0.103376i
\(649\) 37.4418i 1.46972i
\(650\) −15.1092 35.5009i −0.592630 1.39246i
\(651\) 18.6850 + 22.0884i 0.732323 + 0.865712i
\(652\) 11.7624 14.0178i 0.460649 0.548981i
\(653\) 6.21509 35.2475i 0.243215 1.37934i −0.581386 0.813628i \(-0.697489\pi\)
0.824601 0.565714i \(-0.191399\pi\)
\(654\) −33.0240 + 22.8383i −1.29134 + 0.893049i
\(655\) −19.8772 + 5.89820i −0.776667 + 0.230462i
\(656\) 10.3733 + 17.9671i 0.405010 + 0.701497i
\(657\) 2.47458 2.88032i 0.0965426 0.112372i
\(658\) 38.5167 + 37.7683i 1.50154 + 1.47236i
\(659\) 18.6704 3.29210i 0.727297 0.128242i 0.202273 0.979329i \(-0.435167\pi\)
0.525024 + 0.851087i \(0.324056\pi\)
\(660\) −6.38154 + 41.1927i −0.248401 + 1.60342i
\(661\) −1.71768 4.71928i −0.0668099 0.183559i 0.901795 0.432164i \(-0.142250\pi\)
−0.968605 + 0.248606i \(0.920028\pi\)
\(662\) −21.5273 + 7.83529i −0.836682 + 0.304527i
\(663\) −9.99804 + 9.88232i −0.388292 + 0.383797i
\(664\) 1.72006 0.303292i 0.0667511 0.0117700i
\(665\) −12.6191 31.0937i −0.489349 1.20576i
\(666\) −6.65482 + 11.2227i −0.257869 + 0.434871i
\(667\) 51.0929 29.4985i 1.97832 1.14219i
\(668\) −13.3547 15.9155i −0.516708 0.615789i
\(669\) −3.42550 41.9658i −0.132438 1.62249i
\(670\) 23.3345 + 15.4288i 0.901489 + 0.596065i
\(671\) 1.71502 + 1.43907i 0.0662076 + 0.0555548i
\(672\) 34.7865 + 12.5043i 1.34192 + 0.482365i
\(673\) −10.9530 + 30.0930i −0.422205 + 1.16000i 0.528237 + 0.849097i \(0.322853\pi\)
−0.950442 + 0.310902i \(0.899369\pi\)
\(674\) 20.6991i 0.797298i
\(675\) −3.19059 25.7841i −0.122806 0.992431i
\(676\) 1.38870 0.0534114
\(677\) −1.82703 + 5.01973i −0.0702185 + 0.192924i −0.969838 0.243751i \(-0.921622\pi\)
0.899619 + 0.436675i \(0.143844\pi\)
\(678\) −17.3642 37.8107i −0.666868 1.45211i
\(679\) 21.0541 + 29.4492i 0.807980 + 1.13016i
\(680\) −3.30133 2.18284i −0.126600 0.0837081i
\(681\) 8.91500 18.8313i 0.341623 0.721617i
\(682\) −45.7179 + 38.3619i −1.75063 + 1.46895i
\(683\) 25.1727 + 43.6004i 0.963207 + 1.66832i 0.714358 + 0.699781i \(0.246719\pi\)
0.248849 + 0.968542i \(0.419948\pi\)
\(684\) −6.57845 40.0277i −0.251533 1.53050i
\(685\) −35.0150 + 25.9356i −1.33786 + 0.990948i
\(686\) 21.2973 32.4050i 0.813135 1.23723i
\(687\) −2.13062 0.584211i −0.0812882 0.0222890i
\(688\) −5.03068 13.8217i −0.191793 0.526946i
\(689\) −10.0770 + 3.66774i −0.383905 + 0.139730i
\(690\) 36.4018 45.2647i 1.38579 1.72320i
\(691\) 36.5482 6.44444i 1.39036 0.245158i 0.572183 0.820126i \(-0.306097\pi\)
0.818176 + 0.574968i \(0.194985\pi\)
\(692\) −32.4467 18.7331i −1.23344 0.712126i
\(693\) −29.3171 20.6082i −1.11367 0.782841i
\(694\) 26.7562 + 46.3432i 1.01565 + 1.75916i
\(695\) 3.98603 + 13.4331i 0.151199 + 0.509547i
\(696\) −4.90587 + 10.3627i −0.185956 + 0.392799i
\(697\) 14.5853 + 2.57179i 0.552459 + 0.0974135i
\(698\) −25.6459 + 30.5636i −0.970712 + 1.15685i
\(699\) 12.6877 + 27.6276i 0.479893 + 1.04497i
\(700\) 4.72473 + 31.1795i 0.178578 + 1.17847i
\(701\) 4.36553i 0.164884i 0.996596 + 0.0824419i \(0.0262719\pi\)
−0.996596 + 0.0824419i \(0.973728\pi\)
\(702\) 38.5426 + 11.0523i 1.45470 + 0.417142i
\(703\) 11.7821 0.444371
\(704\) −16.5529 + 45.4788i −0.623862 + 1.71405i
\(705\) 18.1729 33.0479i 0.684431 1.24466i
\(706\) 22.8456 27.2263i 0.859806 1.02468i
\(707\) −18.0765 + 39.7794i −0.679837 + 1.49606i
\(708\) −2.78573 34.1280i −0.104694 1.28261i
\(709\) 2.58861 2.17210i 0.0972174 0.0815751i −0.592884 0.805288i \(-0.702011\pi\)
0.690101 + 0.723713i \(0.257566\pi\)
\(710\) −32.8018 + 3.75313i −1.23103 + 0.140852i
\(711\) 0.333209 28.6206i 0.0124963 1.07336i
\(712\) −4.82074 + 8.34977i −0.180665 + 0.312921i
\(713\) 44.5358 7.85286i 1.66788 0.294092i
\(714\) 18.2570 10.6380i 0.683250 0.398117i
\(715\) −2.25371 + 37.1383i −0.0842841 + 1.38889i
\(716\) 19.8520 + 54.5429i 0.741904 + 2.03836i
\(717\) −2.37438 9.07220i −0.0886727 0.338808i
\(718\) −66.9626 + 11.8073i −2.49902 + 0.440645i
\(719\) −15.1075 + 26.1669i −0.563413 + 0.975860i 0.433782 + 0.901018i \(0.357179\pi\)
−0.997195 + 0.0748424i \(0.976155\pi\)
\(720\) 1.49391 20.6405i 0.0556747 0.769225i
\(721\) −4.83495 17.3612i −0.180063 0.646566i
\(722\) −21.1287 + 17.7291i −0.786330 + 0.659809i
\(723\) −28.4899 41.1961i −1.05955 1.53210i
\(724\) −6.53305 1.15195i −0.242799 0.0428120i
\(725\) 41.1229 2.19446i 1.52727 0.0815003i
\(726\) 19.6814 27.7626i 0.730446 1.03037i
\(727\) −9.33068 3.39609i −0.346056 0.125954i 0.163144 0.986602i \(-0.447836\pi\)
−0.509200 + 0.860648i \(0.670059\pi\)
\(728\) −7.58922 1.95394i −0.281275 0.0724178i
\(729\) 22.8970 + 14.3082i 0.848038 + 0.529935i
\(730\) 5.43574 + 2.36045i 0.201186 + 0.0873641i
\(731\) −9.86684 3.59124i −0.364938 0.132827i
\(732\) 1.67030 + 1.18410i 0.0617360 + 0.0437658i
\(733\) −15.4420 12.9574i −0.570363 0.478592i 0.311403 0.950278i \(-0.399201\pi\)
−0.881766 + 0.471686i \(0.843646\pi\)
\(734\) −4.60113 + 26.0943i −0.169831 + 0.963158i
\(735\) −25.8301 8.23453i −0.952756 0.303735i
\(736\) 44.2629 37.1410i 1.63155 1.36904i
\(737\) −13.4883 23.3624i −0.496847 0.860564i
\(738\) −13.9847 39.8604i −0.514783 1.46728i
\(739\) −3.19346 + 5.53123i −0.117473 + 0.203470i −0.918766 0.394803i \(-0.870813\pi\)
0.801292 + 0.598273i \(0.204146\pi\)
\(740\) −10.7677 2.57966i −0.395828 0.0948303i
\(741\) −9.16745 35.0277i −0.336775 1.28677i
\(742\) 16.0429 1.56230i 0.588955 0.0573538i
\(743\) 17.5737 6.39631i 0.644717 0.234658i 0.00109279 0.999999i \(-0.499652\pi\)
0.643624 + 0.765342i \(0.277430\pi\)
\(744\) −6.25048 + 6.17813i −0.229154 + 0.226501i
\(745\) 33.4725 + 8.01918i 1.22634 + 0.293800i
\(746\) 19.3565 + 11.1755i 0.708692 + 0.409164i
\(747\) 6.51911 + 0.0758973i 0.238522 + 0.00277694i
\(748\) 11.8511 + 20.5268i 0.433320 + 0.750533i
\(749\) −3.84941 + 1.84120i −0.140655 + 0.0672759i
\(750\) 36.9684 16.6518i 1.34990 0.608038i
\(751\) −7.00662 + 39.7365i −0.255675 + 1.45001i 0.538659 + 0.842524i \(0.318931\pi\)
−0.794334 + 0.607482i \(0.792180\pi\)
\(752\) 19.3101 23.0128i 0.704165 0.839191i
\(753\) 30.8162 + 2.87691i 1.12300 + 0.104841i
\(754\) −21.7371 + 59.7222i −0.791619 + 2.17496i
\(755\) −16.5983 7.20773i −0.604072 0.262316i
\(756\) −28.2557 16.6030i −1.02765 0.603846i
\(757\) 27.5160i 1.00009i 0.866000 + 0.500044i \(0.166683\pi\)
−0.866000 + 0.500044i \(0.833317\pi\)
\(758\) 35.5418 + 12.9362i 1.29094 + 0.469862i
\(759\) −50.9037 + 23.3770i −1.84769 + 0.848532i
\(760\) 9.12042 4.55270i 0.330832 0.165144i
\(761\) 6.08100 34.4870i 0.220436 1.25015i −0.650785 0.759262i \(-0.725560\pi\)
0.871221 0.490892i \(-0.163329\pi\)
\(762\) −14.2387 + 30.0768i −0.515815 + 1.08957i
\(763\) 26.4259 12.6397i 0.956681 0.457586i
\(764\) −3.47432 + 2.00590i −0.125696 + 0.0725708i
\(765\) −10.6018 10.2881i −0.383310 0.371969i
\(766\) 2.90264 + 1.67584i 0.104877 + 0.0605506i
\(767\) −5.30729 30.0991i −0.191635 1.08682i
\(768\) 3.76722 13.7390i 0.135938 0.495765i
\(769\) 15.8244 + 43.4773i 0.570644 + 1.56783i 0.803490 + 0.595318i \(0.202974\pi\)
−0.232847 + 0.972513i \(0.574804\pi\)
\(770\) 17.1988 53.2148i 0.619803 1.91773i
\(771\) 12.7913 + 3.50735i 0.460669 + 0.126314i
\(772\) 25.9802 4.58102i 0.935049 0.164874i
\(773\) −15.4782 8.93634i −0.556712 0.321418i 0.195113 0.980781i \(-0.437493\pi\)
−0.751825 + 0.659363i \(0.770826\pi\)
\(774\) 4.85682 + 29.5521i 0.174575 + 1.06223i
\(775\) 30.1962 + 9.20045i 1.08468 + 0.330490i
\(776\) −8.42408 + 7.06864i −0.302407 + 0.253749i
\(777\) 6.08948 7.31623i 0.218459 0.262468i
\(778\) −9.06024 1.59756i −0.324825 0.0572755i
\(779\) −24.5197 + 29.2214i −0.878508 + 1.04696i
\(780\) 0.708908 + 34.0190i 0.0253830 + 1.21808i
\(781\) 29.9185 + 10.8894i 1.07057 + 0.389655i
\(782\) 33.0287i 1.18110i
\(783\) −25.1558 + 34.6233i −0.898994 + 1.23734i
\(784\) −18.9097 10.4283i −0.675347 0.372441i
\(785\) −7.05291 6.68658i −0.251729 0.238654i
\(786\) 33.4811 + 3.12570i 1.19423 + 0.111490i
\(787\) 5.71659 + 4.79679i 0.203774 + 0.170987i 0.738964 0.673745i \(-0.235315\pi\)
−0.535190 + 0.844732i \(0.679760\pi\)
\(788\) 3.45775 19.6099i 0.123177 0.698572i
\(789\) 1.61640 + 19.8025i 0.0575455 + 0.704989i
\(790\) 42.8229 12.7069i 1.52357 0.452092i
\(791\) 8.14369 + 29.2422i 0.289556 + 1.03973i
\(792\) 5.55228 9.36338i 0.197292 0.332713i
\(793\) 1.58267 + 0.913757i 0.0562024 + 0.0324485i
\(794\) −7.35071 41.6879i −0.260867 1.47945i
\(795\) −4.07417 10.5072i −0.144496 0.372652i
\(796\) 6.80410 + 18.6941i 0.241165 + 0.662595i
\(797\) −4.32804 11.8912i −0.153307 0.421207i 0.839135 0.543923i \(-0.183062\pi\)
−0.992442 + 0.122716i \(0.960840\pi\)
\(798\) 0.217091 + 54.4229i 0.00768494 + 1.92655i
\(799\) −3.72395 21.1196i −0.131744 0.747157i
\(800\) 39.2904 9.11035i 1.38913 0.322100i
\(801\) −23.4527 + 27.2980i −0.828660 + 0.964529i
\(802\) −43.2245 + 24.9557i −1.52631 + 0.881216i
\(803\) −3.67342 4.37781i −0.129632 0.154490i
\(804\) −14.0327 20.2911i −0.494894 0.715612i
\(805\) −31.4481 + 28.4050i −1.10840 + 1.00114i
\(806\) −31.3145 + 37.3192i −1.10301 + 1.31451i
\(807\) 12.4903 17.6188i 0.439678 0.620210i
\(808\) −12.4725 4.53961i −0.438780 0.159703i
\(809\) 18.8468i 0.662618i 0.943522 + 0.331309i \(0.107490\pi\)
−0.943522 + 0.331309i \(0.892510\pi\)
\(810\) −10.7683 + 40.7370i −0.378360 + 1.43135i
\(811\) 31.0285i 1.08956i 0.838579 + 0.544779i \(0.183387\pi\)
−0.838579 + 0.544779i \(0.816613\pi\)
\(812\) 29.3767 42.8427i 1.03092 1.50349i
\(813\) −24.1299 17.1061i −0.846273 0.599938i
\(814\) 15.0419 + 12.6217i 0.527219 + 0.442389i
\(815\) 14.3178 + 9.46692i 0.501530 + 0.331612i
\(816\) −6.69318 9.67826i −0.234308 0.338807i
\(817\) 20.7171 17.3837i 0.724798 0.608178i
\(818\) −34.4458 + 19.8873i −1.20437 + 0.695343i
\(819\) −26.4889 12.4111i −0.925599 0.433680i
\(820\) 28.8065 21.3369i 1.00597 0.745117i
\(821\) 4.74489 0.836651i 0.165598 0.0291993i −0.0902345 0.995921i \(-0.528762\pi\)
0.255832 + 0.966721i \(0.417651\pi\)
\(822\) 68.3669 17.8930i 2.38457 0.624090i
\(823\) −6.86958 18.8740i −0.239458 0.657906i −0.999963 0.00857426i \(-0.997271\pi\)
0.760505 0.649332i \(-0.224952\pi\)
\(824\) 5.14437 1.87240i 0.179213 0.0652281i
\(825\) −39.0690 1.55477i −1.36021 0.0541300i
\(826\) −3.55478 + 45.8020i −0.123687 + 1.59366i
\(827\) −20.4523 + 35.4245i −0.711197 + 1.23183i 0.253211 + 0.967411i \(0.418513\pi\)
−0.964408 + 0.264418i \(0.914820\pi\)
\(828\) −44.6591 + 25.0953i −1.55201 + 0.872122i
\(829\) −4.07579 + 2.35316i −0.141558 + 0.0817285i −0.569106 0.822264i \(-0.692711\pi\)
0.427548 + 0.903992i \(0.359377\pi\)
\(830\) 2.89434 + 9.75406i 0.100464 + 0.338568i
\(831\) −7.08655 + 0.578448i −0.245830 + 0.0200661i
\(832\) −6.86023 + 38.9063i −0.237836 + 1.34883i
\(833\) −14.3798 + 5.55566i −0.498231 + 0.192492i
\(834\) 2.11236 22.6267i 0.0731451 0.783497i
\(835\) 13.4080 14.1426i 0.464004 0.489425i
\(836\) −61.0480 −2.11139
\(837\) −27.1969 + 18.3441i −0.940061 + 0.634066i
\(838\) −9.04914 −0.312597
\(839\) 3.64095 + 1.32520i 0.125700 + 0.0457509i 0.404104 0.914713i \(-0.367583\pi\)
−0.278405 + 0.960464i \(0.589806\pi\)
\(840\) 1.88676 8.01644i 0.0650993 0.276594i
\(841\) −29.7505 24.9636i −1.02588 0.860815i
\(842\) −11.0391 + 62.6058i −0.380432 + 2.15754i
\(843\) −20.9814 + 44.3195i −0.722639 + 1.52644i
\(844\) 13.7832 11.5655i 0.474437 0.398100i
\(845\) 0.148076 + 1.29416i 0.00509396 + 0.0445205i
\(846\) −47.3112 + 38.7693i −1.62659 + 1.33292i
\(847\) −17.3828 + 17.7272i −0.597280 + 0.609115i
\(848\) −1.55874 8.84007i −0.0535275 0.303569i
\(849\) 0.988619 3.60550i 0.0339293 0.123740i
\(850\) 10.4471 20.5520i 0.358334 0.704929i
\(851\) −5.08892 13.9817i −0.174446 0.479286i
\(852\) 28.0807 + 7.69967i 0.962029 + 0.263786i
\(853\) −1.91732 10.8736i −0.0656477 0.372307i −0.999878 0.0156356i \(-0.995023\pi\)
0.934230 0.356671i \(-0.116088\pi\)
\(854\) −1.96133 1.92322i −0.0671154 0.0658114i
\(855\) 36.6014 10.3987i 1.25174 0.355630i
\(856\) −0.648107 1.12255i −0.0221518 0.0383681i
\(857\) 18.2665 + 21.7692i 0.623973 + 0.743622i 0.981748 0.190186i \(-0.0609091\pi\)
−0.357775 + 0.933808i \(0.616465\pi\)
\(858\) 25.8198 54.5396i 0.881473 1.86195i
\(859\) −27.4050 4.83224i −0.935047 0.164874i −0.314691 0.949194i \(-0.601901\pi\)
−0.620356 + 0.784320i \(0.713012\pi\)
\(860\) −22.7394 + 11.3510i −0.775408 + 0.387066i
\(861\) 5.47257 + 30.3286i 0.186505 + 1.03359i
\(862\) 6.23739 17.1371i 0.212446 0.583691i
\(863\) −22.1229 −0.753074 −0.376537 0.926402i \(-0.622885\pi\)
−0.376537 + 0.926402i \(0.622885\pi\)
\(864\) −18.3747 + 37.6728i −0.625120 + 1.28166i
\(865\) 13.9981 32.2354i 0.475949 1.09604i
\(866\) 8.25711 + 3.00534i 0.280588 + 0.102126i
\(867\) 20.9535 + 1.95616i 0.711619 + 0.0664347i
\(868\) 32.3921 23.1580i 1.09946 0.786034i
\(869\) −42.4213 7.48001i −1.43904 0.253742i
\(870\) −63.2235 21.5307i −2.14348 0.729958i
\(871\) −14.1547 16.8689i −0.479612 0.571580i
\(872\) 4.44920 + 7.70623i 0.150669 + 0.260966i
\(873\) −35.7854 + 20.1089i −1.21115 + 0.680584i
\(874\) 73.6722 + 42.5347i 2.49200 + 1.43876i
\(875\) −28.5531 + 7.72774i −0.965272 + 0.261245i
\(876\) −3.67401 3.71704i −0.124133 0.125587i
\(877\) −5.67982 15.6052i −0.191794 0.526949i 0.806103 0.591776i \(-0.201573\pi\)
−0.997897 + 0.0648263i \(0.979351\pi\)
\(878\) 14.9829 + 41.1653i 0.505649 + 1.38926i
\(879\) 9.06704 + 34.6440i 0.305824 + 1.16851i
\(880\) −30.2872 7.25604i −1.02098 0.244601i
\(881\) 7.35278 12.7354i 0.247721 0.429066i −0.715172 0.698949i \(-0.753652\pi\)
0.962893 + 0.269883i \(0.0869849\pi\)
\(882\) 33.9067 + 27.9932i 1.14170 + 0.942579i
\(883\) 18.8685 10.8938i 0.634977 0.366604i −0.147700 0.989032i \(-0.547187\pi\)
0.782677 + 0.622428i \(0.213854\pi\)
\(884\) 12.4366 + 14.8214i 0.418290 + 0.498498i
\(885\) 31.5076 6.23513i 1.05912 0.209592i
\(886\) −6.06161 + 34.3771i −0.203644 + 1.15492i
\(887\) 2.87146 3.42207i 0.0964142 0.114902i −0.715680 0.698428i \(-0.753883\pi\)
0.812094 + 0.583526i \(0.198328\pi\)
\(888\) 2.35893 + 1.67229i 0.0791604 + 0.0561183i
\(889\) 13.7292 20.0226i 0.460464 0.671536i
\(890\) −51.5169 22.3710i −1.72685 0.749878i
\(891\) 26.8365 30.5108i 0.899057 1.02215i
\(892\) −57.9504 −1.94032
\(893\) 51.9040 + 18.8915i 1.73690 + 0.632181i
\(894\) −45.5402 32.2842i −1.52309 1.07975i
\(895\) −48.7131 + 24.3164i −1.62830 + 0.812809i
\(896\) 6.90802 15.2019i 0.230781 0.507859i
\(897\) −37.6074 + 26.0080i −1.25567 + 0.868383i
\(898\) 51.0611 + 60.8523i 1.70393 + 2.03067i
\(899\) −25.9993 45.0321i −0.867125 1.50190i
\(900\) −35.7268 + 1.48964i −1.19089 + 0.0496546i
\(901\) −5.54949 3.20400i −0.184880 0.106741i
\(902\) −62.6072 + 11.0393i −2.08459 + 0.367570i
\(903\) −0.0871552 21.8491i −0.00290034 0.727092i
\(904\) −8.66485 + 3.15375i −0.288189 + 0.104892i
\(905\) 0.376919 6.21115i 0.0125292 0.206466i
\(906\) 20.6310 + 20.8726i 0.685420 + 0.693446i
\(907\) 35.9614 6.34096i 1.19408 0.210548i 0.458941 0.888467i \(-0.348229\pi\)
0.735137 + 0.677919i \(0.237118\pi\)
\(908\) −24.8338 14.3378i −0.824137 0.475816i
\(909\) −42.6153 25.2699i −1.41346 0.838151i
\(910\) 6.28291 45.2168i 0.208276 1.49892i
\(911\) −15.7057 18.7173i −0.520353 0.620133i 0.440311 0.897845i \(-0.354868\pi\)
−0.960664 + 0.277712i \(0.910424\pi\)
\(912\) 30.2074 2.46571i 1.00027 0.0816480i
\(913\) 1.70377 9.66257i 0.0563866 0.319785i
\(914\) 25.3864 30.2543i 0.839707 1.00072i
\(915\) −0.925394 + 1.68285i −0.0305926 + 0.0556334i
\(916\) −1.03996 + 2.85728i −0.0343614 + 0.0944071i
\(917\) −23.7578 6.11675i −0.784553 0.201993i
\(918\) 9.74495 + 21.8881i 0.321631 + 0.722414i
\(919\) 7.21074 0.237860 0.118930 0.992903i \(-0.462054\pi\)
0.118930 + 0.992903i \(0.462054\pi\)
\(920\) −9.34192 8.85669i −0.307994 0.291997i
\(921\) −4.18785 9.11909i −0.137994 0.300484i
\(922\) 9.16182 + 7.68768i 0.301728 + 0.253180i
\(923\) 25.5948 + 4.51305i 0.842462 + 0.148549i
\(924\) −31.5521 + 37.9084i −1.03799 + 1.24710i
\(925\) 1.25590 10.3097i 0.0412939 0.338982i
\(926\) −52.0985 + 30.0791i −1.71206 + 0.988459i
\(927\) 20.1644 3.31397i 0.662287 0.108845i
\(928\) −57.5375 33.2193i −1.88876 1.09048i
\(929\) −8.22788 46.6626i −0.269948 1.53095i −0.754565 0.656225i \(-0.772152\pi\)
0.484617 0.874726i \(-0.338959\pi\)
\(930\) −39.8953 32.0837i −1.30822 1.05207i
\(931\) 6.12626 39.2295i 0.200780 1.28570i
\(932\) 39.3190 14.3110i 1.28794 0.468771i
\(933\) −6.06546 + 22.1207i −0.198574 + 0.724200i
\(934\) 34.1189 6.01608i 1.11640 0.196852i
\(935\) −17.8657 + 13.2331i −0.584272 + 0.432769i
\(936\) 3.13619 8.31416i 0.102510 0.271757i
\(937\) −7.66648 13.2787i −0.250453 0.433797i 0.713198 0.700963i \(-0.247246\pi\)
−0.963651 + 0.267166i \(0.913913\pi\)
\(938\) 14.2820 + 29.8595i 0.466322 + 0.974946i
\(939\) 42.5836 + 20.1597i 1.38966 + 0.657886i
\(940\) −43.2989 28.6292i −1.41225 0.933782i
\(941\) 2.32465 + 1.95061i 0.0757814 + 0.0635881i 0.679892 0.733313i \(-0.262027\pi\)
−0.604110 + 0.796901i \(0.706471\pi\)
\(942\) 6.57808 + 14.3238i 0.214325 + 0.466696i
\(943\) 45.2672 + 16.4759i 1.47410 + 0.536529i
\(944\) 25.5835 0.832671
\(945\) 12.4599 28.1025i 0.405320 0.914175i
\(946\) 45.0713 1.46539
\(947\) −17.5905 6.40240i −0.571613 0.208050i 0.0400102 0.999199i \(-0.487261\pi\)
−0.611623 + 0.791149i \(0.709483\pi\)
\(948\) −39.2232 3.66177i −1.27391 0.118929i
\(949\) −3.57357 2.99858i −0.116003 0.0973381i
\(950\) 32.3885 + 49.7700i 1.05082 + 1.61475i
\(951\) −3.53958 43.3633i −0.114779 1.40615i
\(952\) −2.02059 4.22447i −0.0654877 0.136916i
\(953\) −12.5736 21.7781i −0.407298 0.705461i 0.587288 0.809378i \(-0.300196\pi\)
−0.994586 + 0.103917i \(0.966862\pi\)
\(954\) −0.212772 + 18.2758i −0.00688874 + 0.591701i
\(955\) −2.23981 3.02392i −0.0724786 0.0978516i
\(956\) −12.7107 + 2.24124i −0.411094 + 0.0724869i
\(957\) 45.2772 + 45.8074i 1.46360 + 1.48074i
\(958\) 21.5822 7.85530i 0.697291 0.253793i
\(959\) −51.3149 + 4.99717i −1.65705 + 0.161367i
\(960\) −41.0274 6.35593i −1.32415 0.205137i
\(961\) −1.53824 8.72380i −0.0496207 0.281413i
\(962\) 13.8811 + 8.01428i 0.447546 + 0.258391i
\(963\) −1.60179 4.56558i −0.0516171 0.147124i
\(964\) −59.7010 + 34.4684i −1.92284 + 1.11015i
\(965\) 7.03942 + 23.7232i 0.226607 + 0.763675i
\(966\) 64.4892 23.7639i 2.07491 0.764591i
\(967\) 16.6675 + 2.93893i 0.535991 + 0.0945097i 0.435090 0.900387i \(-0.356716\pi\)
0.100901 + 0.994897i \(0.467828\pi\)
\(968\) −5.77746 4.84786i −0.185695 0.155816i
\(969\) 12.5127 17.6505i 0.401967 0.567015i
\(970\) −46.4885 44.0739i −1.49266 1.41513i
\(971\) −5.47368 −0.175659 −0.0878294 0.996136i \(-0.527993\pi\)
−0.0878294 + 0.996136i \(0.527993\pi\)
\(972\) 22.1912 29.8070i 0.711784 0.956061i
\(973\) −4.13373 + 16.0557i −0.132521 + 0.514721i
\(974\) 9.02771 24.8034i 0.289266 0.794753i
\(975\) −31.6276 + 4.28807i −1.01289 + 0.137328i
\(976\) −0.983299 + 1.17185i −0.0314746 + 0.0375100i
\(977\) 9.52464 54.0169i 0.304720 1.72815i −0.320099 0.947384i \(-0.603716\pi\)
0.624819 0.780770i \(-0.285173\pi\)
\(978\) −15.8341 22.8960i −0.506320 0.732133i
\(979\) 34.8146 + 41.4904i 1.11268 + 1.32604i
\(980\) −14.1880 + 34.5105i −0.453219 + 1.10240i
\(981\) 10.9962 + 31.3423i 0.351081 + 1.00068i
\(982\) −60.8695 35.1430i −1.94243 1.12146i
\(983\) 39.3717 6.94230i 1.25576 0.221425i 0.494104 0.869403i \(-0.335496\pi\)
0.761659 + 0.647978i \(0.224385\pi\)
\(984\) −9.05666 + 2.37031i −0.288716 + 0.0755627i
\(985\) 18.6436 + 1.13138i 0.594035 + 0.0360486i
\(986\) −35.6871 + 12.9890i −1.13651 + 0.413655i
\(987\) 38.5570 22.4665i 1.22728 0.715115i
\(988\) −49.0760 + 8.65342i −1.56131 + 0.275302i
\(989\) −29.5771 17.0763i −0.940497 0.542996i
\(990\) 57.8677 + 25.9336i 1.83916 + 0.824225i
\(991\) −12.1277 21.0058i −0.385249 0.667271i 0.606555 0.795042i \(-0.292551\pi\)
−0.991804 + 0.127771i \(0.959218\pi\)
\(992\) −32.7352 39.0123i −1.03934 1.23864i
\(993\) 1.54178 + 18.8883i 0.0489270 + 0.599404i
\(994\) −35.5650 16.1614i −1.12805 0.512609i
\(995\) −16.6960 + 8.33425i −0.529299 + 0.264214i
\(996\) 0.834066 8.93414i 0.0264284 0.283089i
\(997\) 46.0475 + 16.7599i 1.45834 + 0.530792i 0.944908 0.327337i \(-0.106151\pi\)
0.513433 + 0.858130i \(0.328374\pi\)
\(998\) 8.04480 0.254654
\(999\) 7.49765 + 7.76419i 0.237215 + 0.245648i
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 945.2.cs.b.104.19 816
5.4 even 2 inner 945.2.cs.b.104.118 yes 816
7.6 odd 2 inner 945.2.cs.b.104.20 yes 816
27.20 odd 18 inner 945.2.cs.b.209.117 yes 816
35.34 odd 2 inner 945.2.cs.b.104.117 yes 816
135.74 odd 18 inner 945.2.cs.b.209.20 yes 816
189.20 even 18 inner 945.2.cs.b.209.118 yes 816
945.209 even 18 inner 945.2.cs.b.209.19 yes 816
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
945.2.cs.b.104.19 816 1.1 even 1 trivial
945.2.cs.b.104.20 yes 816 7.6 odd 2 inner
945.2.cs.b.104.117 yes 816 35.34 odd 2 inner
945.2.cs.b.104.118 yes 816 5.4 even 2 inner
945.2.cs.b.209.19 yes 816 945.209 even 18 inner
945.2.cs.b.209.20 yes 816 135.74 odd 18 inner
945.2.cs.b.209.117 yes 816 27.20 odd 18 inner
945.2.cs.b.209.118 yes 816 189.20 even 18 inner