Properties

Label 189.2.u.a.142.4
Level $189$
Weight $2$
Character 189.142
Analytic conductor $1.509$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(4,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.u (of order \(9\), 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 142.4
Character \(\chi\) \(=\) 189.142
Dual form 189.2.u.a.4.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.324131 + 1.83824i) q^{2} +(0.743955 + 1.56414i) q^{3} +(-1.39467 - 0.507617i) q^{4} +(1.37479 + 0.500384i) q^{5} +(-3.11640 + 0.860580i) q^{6} +(-2.42382 - 1.06071i) q^{7} +(-0.481419 + 0.833843i) q^{8} +(-1.89306 + 2.32730i) q^{9} +(-1.36544 + 2.36501i) q^{10} +(4.29056 - 1.56163i) q^{11} +(-0.243586 - 2.55910i) q^{12} +(0.925783 + 0.336957i) q^{13} +(2.73547 - 4.11174i) q^{14} +(0.240115 + 2.52263i) q^{15} +(-3.65064 - 3.06325i) q^{16} +(0.620234 - 1.07428i) q^{17} +(-3.66453 - 4.23424i) q^{18} +(-0.718027 - 1.24366i) q^{19} +(-1.66338 - 1.39574i) q^{20} +(-0.144117 - 4.58031i) q^{21} +(1.47995 + 8.39323i) q^{22} +(0.165636 + 0.939366i) q^{23} +(-1.66240 - 0.132665i) q^{24} +(-2.19055 - 1.83809i) q^{25} +(-0.919482 + 1.59259i) q^{26} +(-5.04857 - 1.22960i) q^{27} +(2.84199 + 2.70971i) q^{28} +(5.18835 - 1.88840i) q^{29} +(-4.71503 - 0.376275i) q^{30} +(6.28413 + 2.28724i) q^{31} +(5.33911 - 4.48005i) q^{32} +(5.63460 + 5.54924i) q^{33} +(1.77374 + 1.48834i) q^{34} +(-2.80149 - 2.67110i) q^{35} +(3.82157 - 2.28486i) q^{36} -2.88764 q^{37} +(2.51887 - 0.916795i) q^{38} +(0.161693 + 1.69873i) q^{39} +(-1.07909 + 0.905468i) q^{40} +(11.1576 + 4.06104i) q^{41} +(8.46640 + 1.21970i) q^{42} +(0.559660 - 3.17399i) q^{43} -6.77661 q^{44} +(-3.76711 + 2.25230i) q^{45} -1.78046 q^{46} +(-10.6381 + 3.87197i) q^{47} +(2.07544 - 7.98904i) q^{48} +(4.74979 + 5.14193i) q^{49} +(4.08886 - 3.43096i) q^{50} +(2.14175 + 0.170918i) q^{51} +(-1.12011 - 0.939887i) q^{52} +(2.32509 + 4.02717i) q^{53} +(3.89670 - 8.88191i) q^{54} +6.68005 q^{55} +(2.05134 - 1.51044i) q^{56} +(1.41108 - 2.04832i) q^{57} +(1.78963 + 10.1495i) q^{58} +(-4.83431 + 4.05647i) q^{59} +(0.945652 - 3.64012i) q^{60} +(-4.93482 + 1.79613i) q^{61} +(-6.24136 + 10.8104i) q^{62} +(7.05702 - 3.63296i) q^{63} +(1.73924 + 3.01245i) q^{64} +(1.10415 + 0.926495i) q^{65} +(-12.0272 + 8.55904i) q^{66} +(-2.28146 - 12.9388i) q^{67} +(-1.41034 + 1.18342i) q^{68} +(-1.34607 + 0.957924i) q^{69} +(5.81816 - 4.28402i) q^{70} +(-5.80593 - 10.0562i) q^{71} +(-1.02924 - 2.69892i) q^{72} +9.93018 q^{73} +(0.935973 - 5.30816i) q^{74} +(1.24535 - 4.79377i) q^{75} +(0.370105 + 2.09897i) q^{76} +(-12.0560 - 0.765911i) q^{77} +(-3.17508 - 0.253382i) q^{78} +(2.45710 - 13.9349i) q^{79} +(-3.48608 - 6.03807i) q^{80} +(-1.83264 - 8.81144i) q^{81} +(-11.0817 + 19.1940i) q^{82} +(-7.82112 + 2.84665i) q^{83} +(-2.12405 + 6.46116i) q^{84} +(1.39025 - 1.16656i) q^{85} +(5.65314 + 2.05757i) q^{86} +(6.81363 + 6.71041i) q^{87} +(-0.763399 + 4.32945i) q^{88} +(0.307487 + 0.532584i) q^{89} +(-2.91922 - 7.65489i) q^{90} +(-1.88652 - 1.79871i) q^{91} +(0.245832 - 1.39418i) q^{92} +(1.09756 + 11.5309i) q^{93} +(-3.66944 - 20.8104i) q^{94} +(-0.364832 - 2.06907i) q^{95} +(10.9795 + 5.01816i) q^{96} +(-0.991251 + 5.62167i) q^{97} +(-10.9916 + 7.06459i) q^{98} +(-4.48790 + 12.9417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.324131 + 1.83824i −0.229195 + 1.29983i 0.625306 + 0.780380i \(0.284974\pi\)
−0.854501 + 0.519450i \(0.826137\pi\)
\(3\) 0.743955 + 1.56414i 0.429523 + 0.903056i
\(4\) −1.39467 0.507617i −0.697333 0.253809i
\(5\) 1.37479 + 0.500384i 0.614827 + 0.223779i 0.630614 0.776097i \(-0.282803\pi\)
−0.0157870 + 0.999875i \(0.505025\pi\)
\(6\) −3.11640 + 0.860580i −1.27226 + 0.351330i
\(7\) −2.42382 1.06071i −0.916117 0.400910i
\(8\) −0.481419 + 0.833843i −0.170207 + 0.294808i
\(9\) −1.89306 + 2.32730i −0.631020 + 0.775766i
\(10\) −1.36544 + 2.36501i −0.431789 + 0.747881i
\(11\) 4.29056 1.56163i 1.29365 0.470851i 0.398727 0.917069i \(-0.369452\pi\)
0.894924 + 0.446219i \(0.147230\pi\)
\(12\) −0.243586 2.55910i −0.0703172 0.738748i
\(13\) 0.925783 + 0.336957i 0.256766 + 0.0934552i 0.467196 0.884154i \(-0.345264\pi\)
−0.210430 + 0.977609i \(0.567486\pi\)
\(14\) 2.73547 4.11174i 0.731084 1.09891i
\(15\) 0.240115 + 2.52263i 0.0619974 + 0.651341i
\(16\) −3.65064 3.06325i −0.912661 0.765813i
\(17\) 0.620234 1.07428i 0.150429 0.260550i −0.780956 0.624586i \(-0.785268\pi\)
0.931385 + 0.364035i \(0.118601\pi\)
\(18\) −3.66453 4.23424i −0.863737 0.998021i
\(19\) −0.718027 1.24366i −0.164727 0.285315i 0.771832 0.635827i \(-0.219341\pi\)
−0.936558 + 0.350512i \(0.886008\pi\)
\(20\) −1.66338 1.39574i −0.371942 0.312097i
\(21\) −0.144117 4.58031i −0.0314488 0.999505i
\(22\) 1.47995 + 8.39323i 0.315527 + 1.78944i
\(23\) 0.165636 + 0.939366i 0.0345374 + 0.195871i 0.997195 0.0748517i \(-0.0238483\pi\)
−0.962657 + 0.270723i \(0.912737\pi\)
\(24\) −1.66240 0.132665i −0.339336 0.0270801i
\(25\) −2.19055 1.83809i −0.438109 0.367617i
\(26\) −0.919482 + 1.59259i −0.180325 + 0.312333i
\(27\) −5.04857 1.22960i −0.971598 0.236638i
\(28\) 2.84199 + 2.70971i 0.537085 + 0.512087i
\(29\) 5.18835 1.88840i 0.963452 0.350668i 0.188067 0.982156i \(-0.439778\pi\)
0.775385 + 0.631488i \(0.217556\pi\)
\(30\) −4.71503 0.376275i −0.860842 0.0686981i
\(31\) 6.28413 + 2.28724i 1.12866 + 0.410800i 0.837807 0.545967i \(-0.183837\pi\)
0.290857 + 0.956767i \(0.406060\pi\)
\(32\) 5.33911 4.48005i 0.943831 0.791968i
\(33\) 5.63460 + 5.54924i 0.980857 + 0.965999i
\(34\) 1.77374 + 1.48834i 0.304194 + 0.255249i
\(35\) −2.80149 2.67110i −0.473538 0.451498i
\(36\) 3.82157 2.28486i 0.636928 0.380809i
\(37\) −2.88764 −0.474725 −0.237363 0.971421i \(-0.576283\pi\)
−0.237363 + 0.971421i \(0.576283\pi\)
\(38\) 2.51887 0.916795i 0.408615 0.148724i
\(39\) 0.161693 + 1.69873i 0.0258916 + 0.272015i
\(40\) −1.07909 + 0.905468i −0.170620 + 0.143167i
\(41\) 11.1576 + 4.06104i 1.74253 + 0.634227i 0.999390 0.0349137i \(-0.0111156\pi\)
0.743135 + 0.669141i \(0.233338\pi\)
\(42\) 8.46640 + 1.21970i 1.30639 + 0.188204i
\(43\) 0.559660 3.17399i 0.0853473 0.484029i −0.911934 0.410337i \(-0.865411\pi\)
0.997281 0.0736913i \(-0.0234780\pi\)
\(44\) −6.77661 −1.02161
\(45\) −3.76711 + 2.25230i −0.561568 + 0.335753i
\(46\) −1.78046 −0.262515
\(47\) −10.6381 + 3.87197i −1.55173 + 0.564785i −0.968823 0.247753i \(-0.920308\pi\)
−0.582909 + 0.812537i \(0.698086\pi\)
\(48\) 2.07544 7.98904i 0.299564 1.15312i
\(49\) 4.74979 + 5.14193i 0.678542 + 0.734562i
\(50\) 4.08886 3.43096i 0.578252 0.485211i
\(51\) 2.14175 + 0.170918i 0.299904 + 0.0239334i
\(52\) −1.12011 0.939887i −0.155332 0.130339i
\(53\) 2.32509 + 4.02717i 0.319376 + 0.553175i 0.980358 0.197227i \(-0.0631935\pi\)
−0.660982 + 0.750402i \(0.729860\pi\)
\(54\) 3.89670 8.88191i 0.530274 1.20868i
\(55\) 6.68005 0.900738
\(56\) 2.05134 1.51044i 0.274122 0.201841i
\(57\) 1.41108 2.04832i 0.186902 0.271307i
\(58\) 1.78963 + 10.1495i 0.234990 + 1.33269i
\(59\) −4.83431 + 4.05647i −0.629374 + 0.528108i −0.900734 0.434370i \(-0.856971\pi\)
0.271360 + 0.962478i \(0.412527\pi\)
\(60\) 0.945652 3.64012i 0.122083 0.469938i
\(61\) −4.93482 + 1.79613i −0.631839 + 0.229970i −0.638031 0.770010i \(-0.720251\pi\)
0.00619278 + 0.999981i \(0.498029\pi\)
\(62\) −6.24136 + 10.8104i −0.792654 + 1.37292i
\(63\) 7.05702 3.63296i 0.889101 0.457710i
\(64\) 1.73924 + 3.01245i 0.217405 + 0.376557i
\(65\) 1.10415 + 0.926495i 0.136953 + 0.114918i
\(66\) −12.0272 + 8.55904i −1.48044 + 1.05354i
\(67\) −2.28146 12.9388i −0.278725 1.58073i −0.726875 0.686770i \(-0.759028\pi\)
0.448150 0.893958i \(-0.352083\pi\)
\(68\) −1.41034 + 1.18342i −0.171029 + 0.143510i
\(69\) −1.34607 + 0.957924i −0.162048 + 0.115320i
\(70\) 5.81816 4.28402i 0.695403 0.512038i
\(71\) −5.80593 10.0562i −0.689037 1.19345i −0.972150 0.234360i \(-0.924701\pi\)
0.283113 0.959087i \(-0.408633\pi\)
\(72\) −1.02924 2.69892i −0.121298 0.318071i
\(73\) 9.93018 1.16224 0.581120 0.813818i \(-0.302615\pi\)
0.581120 + 0.813818i \(0.302615\pi\)
\(74\) 0.935973 5.30816i 0.108805 0.617062i
\(75\) 1.24535 4.79377i 0.143801 0.553537i
\(76\) 0.370105 + 2.09897i 0.0424540 + 0.240769i
\(77\) −12.0560 0.765911i −1.37391 0.0872837i
\(78\) −3.17508 0.253382i −0.359508 0.0286899i
\(79\) 2.45710 13.9349i 0.276445 1.56780i −0.457887 0.889010i \(-0.651394\pi\)
0.734333 0.678790i \(-0.237495\pi\)
\(80\) −3.48608 6.03807i −0.389756 0.675077i
\(81\) −1.83264 8.81144i −0.203626 0.979049i
\(82\) −11.0817 + 19.1940i −1.22377 + 2.11962i
\(83\) −7.82112 + 2.84665i −0.858479 + 0.312461i −0.733493 0.679697i \(-0.762111\pi\)
−0.124987 + 0.992158i \(0.539889\pi\)
\(84\) −2.12405 + 6.46116i −0.231753 + 0.704970i
\(85\) 1.39025 1.16656i 0.150793 0.126531i
\(86\) 5.65314 + 2.05757i 0.609594 + 0.221874i
\(87\) 6.81363 + 6.71041i 0.730497 + 0.719431i
\(88\) −0.763399 + 4.32945i −0.0813786 + 0.461521i
\(89\) 0.307487 + 0.532584i 0.0325936 + 0.0564538i 0.881862 0.471507i \(-0.156290\pi\)
−0.849268 + 0.527961i \(0.822957\pi\)
\(90\) −2.91922 7.65489i −0.307713 0.806896i
\(91\) −1.88652 1.79871i −0.197761 0.188556i
\(92\) 0.245832 1.39418i 0.0256298 0.145354i
\(93\) 1.09756 + 11.5309i 0.113811 + 1.19569i
\(94\) −3.66944 20.8104i −0.378474 2.14643i
\(95\) −0.364832 2.06907i −0.0374310 0.212282i
\(96\) 10.9795 + 5.01816i 1.12059 + 0.512164i
\(97\) −0.991251 + 5.62167i −0.100646 + 0.570794i 0.892224 + 0.451593i \(0.149144\pi\)
−0.992870 + 0.119200i \(0.961967\pi\)
\(98\) −10.9916 + 7.06459i −1.11032 + 0.713631i
\(99\) −4.48790 + 12.9417i −0.451050 + 1.30069i
\(100\) 2.12204 + 3.67548i 0.212204 + 0.367548i
\(101\) −2.05653 + 11.6632i −0.204632 + 1.16053i 0.693385 + 0.720567i \(0.256119\pi\)
−0.898017 + 0.439960i \(0.854993\pi\)
\(102\) −1.00839 + 3.88163i −0.0998458 + 0.384339i
\(103\) −12.0593 4.38923i −1.18824 0.432484i −0.329134 0.944283i \(-0.606757\pi\)
−0.859105 + 0.511800i \(0.828979\pi\)
\(104\) −0.726659 + 0.609740i −0.0712548 + 0.0597899i
\(105\) 2.09378 6.36910i 0.204332 0.621560i
\(106\) −8.15653 + 2.96873i −0.792232 + 0.288349i
\(107\) 5.52411 9.56804i 0.534036 0.924977i −0.465173 0.885220i \(-0.654008\pi\)
0.999209 0.0397577i \(-0.0126586\pi\)
\(108\) 6.41691 + 4.27763i 0.617467 + 0.411615i
\(109\) −9.52408 16.4962i −0.912242 1.58005i −0.810890 0.585198i \(-0.801017\pi\)
−0.101352 0.994851i \(-0.532317\pi\)
\(110\) −2.16521 + 12.2795i −0.206445 + 1.17081i
\(111\) −2.14827 4.51667i −0.203905 0.428703i
\(112\) 5.59928 + 11.2970i 0.529082 + 1.06747i
\(113\) 1.36095 + 7.71833i 0.128027 + 0.726080i 0.979464 + 0.201621i \(0.0646210\pi\)
−0.851436 + 0.524458i \(0.824268\pi\)
\(114\) 3.30792 + 3.25781i 0.309815 + 0.305122i
\(115\) −0.242329 + 1.37432i −0.0225973 + 0.128156i
\(116\) −8.19460 −0.760850
\(117\) −2.53676 + 1.51669i −0.234524 + 0.140218i
\(118\) −5.88980 10.2014i −0.542200 0.939119i
\(119\) −2.64283 + 1.94596i −0.242268 + 0.178386i
\(120\) −2.21908 1.01423i −0.202573 0.0925858i
\(121\) 7.54368 6.32990i 0.685789 0.575445i
\(122\) −1.70218 9.65354i −0.154108 0.873990i
\(123\) 1.94873 + 20.4733i 0.175711 + 1.84601i
\(124\) −7.60323 6.37987i −0.682790 0.572929i
\(125\) −5.74937 9.95820i −0.514239 0.890688i
\(126\) 4.39085 + 14.1500i 0.391168 + 1.26058i
\(127\) −6.35187 + 11.0018i −0.563637 + 0.976249i 0.433538 + 0.901136i \(0.357265\pi\)
−0.997175 + 0.0751132i \(0.976068\pi\)
\(128\) 6.99744 2.54686i 0.618492 0.225113i
\(129\) 5.38092 1.48592i 0.473764 0.130828i
\(130\) −2.06101 + 1.72939i −0.180762 + 0.151677i
\(131\) −1.45783 8.26775i −0.127371 0.722357i −0.979871 0.199630i \(-0.936026\pi\)
0.852500 0.522727i \(-0.175085\pi\)
\(132\) −5.04149 10.5996i −0.438806 0.922573i
\(133\) 0.421207 + 3.77602i 0.0365233 + 0.327423i
\(134\) 24.5241 2.11856
\(135\) −6.32547 4.21668i −0.544410 0.362914i
\(136\) 0.597185 + 1.03436i 0.0512082 + 0.0886953i
\(137\) −1.77965 1.49330i −0.152046 0.127581i 0.563592 0.826054i \(-0.309419\pi\)
−0.715637 + 0.698472i \(0.753864\pi\)
\(138\) −1.32459 2.78489i −0.112756 0.237066i
\(139\) 16.4618 13.8131i 1.39627 1.17161i 0.433546 0.901131i \(-0.357262\pi\)
0.962726 0.270480i \(-0.0871824\pi\)
\(140\) 2.55125 + 5.14738i 0.215620 + 0.435033i
\(141\) −13.9706 13.7590i −1.17654 1.15871i
\(142\) 20.3675 7.41316i 1.70920 0.622098i
\(143\) 4.49833 0.376169
\(144\) 14.0400 2.69721i 1.17000 0.224768i
\(145\) 8.07784 0.670828
\(146\) −3.21868 + 18.2540i −0.266380 + 1.51071i
\(147\) −4.50906 + 11.2547i −0.371901 + 0.928272i
\(148\) 4.02730 + 1.46582i 0.331042 + 0.120489i
\(149\) 3.36481 2.82341i 0.275656 0.231303i −0.494470 0.869195i \(-0.664638\pi\)
0.770126 + 0.637892i \(0.220193\pi\)
\(150\) 8.40843 + 3.84306i 0.686545 + 0.313785i
\(151\) −13.9287 + 5.06965i −1.13351 + 0.412562i −0.839564 0.543261i \(-0.817189\pi\)
−0.293942 + 0.955823i \(0.594967\pi\)
\(152\) 1.38269 0.112151
\(153\) 1.32602 + 3.47714i 0.107203 + 0.281110i
\(154\) 5.31564 21.9135i 0.428346 1.76584i
\(155\) 7.49490 + 6.28896i 0.602005 + 0.505142i
\(156\) 0.636799 2.45125i 0.0509847 0.196257i
\(157\) 0.289738 0.243119i 0.0231236 0.0194030i −0.631153 0.775659i \(-0.717418\pi\)
0.654276 + 0.756256i \(0.272973\pi\)
\(158\) 24.8192 + 9.03346i 1.97451 + 0.718664i
\(159\) −4.56930 + 6.63280i −0.362369 + 0.526015i
\(160\) 9.58193 3.48754i 0.757518 0.275714i
\(161\) 0.594923 2.45254i 0.0468865 0.193288i
\(162\) 16.7915 0.512764i 1.31927 0.0402866i
\(163\) −2.58086 + 4.47018i −0.202148 + 0.350131i −0.949220 0.314612i \(-0.898126\pi\)
0.747072 + 0.664743i \(0.231459\pi\)
\(164\) −13.4997 11.3276i −1.05415 0.884536i
\(165\) 4.96966 + 10.4485i 0.386887 + 0.813417i
\(166\) −2.69776 15.2998i −0.209387 1.18749i
\(167\) −1.88838 10.7095i −0.146127 0.828727i −0.966455 0.256834i \(-0.917321\pi\)
0.820329 0.571893i \(-0.193791\pi\)
\(168\) 3.88864 + 2.08488i 0.300015 + 0.160852i
\(169\) −9.21504 7.73234i −0.708850 0.594795i
\(170\) 1.69378 + 2.93372i 0.129907 + 0.225006i
\(171\) 4.25363 + 0.683260i 0.325284 + 0.0522502i
\(172\) −2.39171 + 4.14256i −0.182366 + 0.315868i
\(173\) 9.27634 + 7.78377i 0.705267 + 0.591789i 0.923267 0.384160i \(-0.125509\pi\)
−0.218000 + 0.975949i \(0.569953\pi\)
\(174\) −14.5438 + 10.3500i −1.10256 + 0.784632i
\(175\) 3.35981 + 6.77872i 0.253978 + 0.512423i
\(176\) −20.4470 7.44209i −1.54125 0.560969i
\(177\) −9.94140 4.54371i −0.747241 0.341526i
\(178\) −1.07868 + 0.392608i −0.0808505 + 0.0294272i
\(179\) −6.18889 + 10.7195i −0.462579 + 0.801211i −0.999089 0.0426837i \(-0.986409\pi\)
0.536510 + 0.843894i \(0.319743\pi\)
\(180\) 6.39718 1.22896i 0.476817 0.0916009i
\(181\) −7.93495 + 13.7437i −0.589800 + 1.02156i 0.404458 + 0.914557i \(0.367460\pi\)
−0.994258 + 0.107007i \(0.965873\pi\)
\(182\) 3.91793 2.88485i 0.290416 0.213839i
\(183\) −6.48067 6.38250i −0.479065 0.471808i
\(184\) −0.863024 0.314115i −0.0636230 0.0231569i
\(185\) −3.96991 1.44493i −0.291874 0.106233i
\(186\) −21.5522 1.71994i −1.58028 0.126112i
\(187\) 0.983521 5.57783i 0.0719222 0.407891i
\(188\) 16.8021 1.22542
\(189\) 10.9326 + 8.33540i 0.795227 + 0.606311i
\(190\) 3.92168 0.284509
\(191\) −2.63991 + 14.9717i −0.191017 + 1.08331i 0.726960 + 0.686680i \(0.240932\pi\)
−0.917977 + 0.396633i \(0.870179\pi\)
\(192\) −3.41798 + 4.96155i −0.246671 + 0.358069i
\(193\) 17.6672 + 6.43032i 1.27171 + 0.462865i 0.887682 0.460456i \(-0.152314\pi\)
0.384028 + 0.923321i \(0.374536\pi\)
\(194\) −10.0127 3.64431i −0.718867 0.261646i
\(195\) −0.627726 + 2.41632i −0.0449524 + 0.173036i
\(196\) −4.01425 9.58236i −0.286732 0.684454i
\(197\) 0.130567 0.226149i 0.00930255 0.0161125i −0.861337 0.508035i \(-0.830372\pi\)
0.870639 + 0.491922i \(0.163706\pi\)
\(198\) −22.3352 12.4446i −1.58729 0.884400i
\(199\) 0.818784 1.41818i 0.0580421 0.100532i −0.835544 0.549423i \(-0.814848\pi\)
0.893586 + 0.448891i \(0.148181\pi\)
\(200\) 2.58725 0.941681i 0.182946 0.0665869i
\(201\) 18.5408 13.1944i 1.30777 0.930663i
\(202\) −20.7731 7.56077i −1.46159 0.531974i
\(203\) −14.5787 0.926177i −1.02322 0.0650049i
\(204\) −2.90026 1.32556i −0.203059 0.0928078i
\(205\) 13.3073 + 11.1662i 0.929425 + 0.779880i
\(206\) 11.9772 20.7452i 0.834493 1.44538i
\(207\) −2.49974 1.39279i −0.173744 0.0968059i
\(208\) −2.34752 4.06602i −0.162771 0.281928i
\(209\) −5.02288 4.21469i −0.347440 0.291536i
\(210\) 11.0292 + 5.91329i 0.761091 + 0.408056i
\(211\) 1.10692 + 6.27765i 0.0762034 + 0.432171i 0.998910 + 0.0466690i \(0.0148606\pi\)
−0.922707 + 0.385502i \(0.874028\pi\)
\(212\) −1.19846 6.79682i −0.0823108 0.466808i
\(213\) 11.4099 16.5626i 0.781792 1.13485i
\(214\) 15.7978 + 13.2559i 1.07991 + 0.906156i
\(215\) 2.35763 4.08354i 0.160789 0.278495i
\(216\) 3.45578 3.61776i 0.235136 0.246157i
\(217\) −12.8055 12.2095i −0.869294 0.828834i
\(218\) 33.4110 12.1606i 2.26288 0.823619i
\(219\) 7.38761 + 15.5322i 0.499209 + 1.04957i
\(220\) −9.31645 3.39091i −0.628115 0.228615i
\(221\) 0.936188 0.785555i 0.0629748 0.0528421i
\(222\) 8.99903 2.48505i 0.603975 0.166785i
\(223\) 4.42813 + 3.71564i 0.296529 + 0.248818i 0.778898 0.627151i \(-0.215779\pi\)
−0.482369 + 0.875968i \(0.660223\pi\)
\(224\) −17.6931 + 5.19558i −1.18217 + 0.347144i
\(225\) 8.42461 1.61844i 0.561641 0.107896i
\(226\) −14.6292 −0.973123
\(227\) −12.0490 + 4.38547i −0.799718 + 0.291074i −0.709370 0.704837i \(-0.751020\pi\)
−0.0903484 + 0.995910i \(0.528798\pi\)
\(228\) −3.00774 + 2.14044i −0.199193 + 0.141754i
\(229\) −4.48966 + 3.76727i −0.296685 + 0.248948i −0.778963 0.627070i \(-0.784254\pi\)
0.482278 + 0.876018i \(0.339810\pi\)
\(230\) −2.44777 0.890917i −0.161401 0.0587453i
\(231\) −7.77111 19.4270i −0.511301 1.27820i
\(232\) −0.923139 + 5.23538i −0.0606070 + 0.343720i
\(233\) 0.971513 0.0636459 0.0318230 0.999494i \(-0.489869\pi\)
0.0318230 + 0.999494i \(0.489869\pi\)
\(234\) −1.96580 5.15478i −0.128508 0.336978i
\(235\) −16.5627 −1.08043
\(236\) 8.80139 3.20345i 0.572922 0.208527i
\(237\) 23.6241 6.52370i 1.53455 0.423760i
\(238\) −2.72052 5.48889i −0.176345 0.355792i
\(239\) −18.1999 + 15.2715i −1.17726 + 0.987834i −0.177262 + 0.984164i \(0.556724\pi\)
−0.999993 + 0.00367051i \(0.998832\pi\)
\(240\) 6.85089 9.94477i 0.442223 0.641932i
\(241\) −0.219263 0.183983i −0.0141239 0.0118514i 0.635698 0.771938i \(-0.280712\pi\)
−0.649822 + 0.760086i \(0.725157\pi\)
\(242\) 9.19071 + 15.9188i 0.590801 + 1.02330i
\(243\) 12.4189 9.42182i 0.796674 0.604410i
\(244\) 7.79417 0.498971
\(245\) 3.95705 + 9.44582i 0.252807 + 0.603472i
\(246\) −38.2664 3.05378i −2.43977 0.194702i
\(247\) −0.245677 1.39330i −0.0156320 0.0886537i
\(248\) −4.93250 + 4.13886i −0.313214 + 0.262818i
\(249\) −10.2711 10.1155i −0.650906 0.641046i
\(250\) 20.1691 7.34094i 1.27560 0.464282i
\(251\) 3.91719 6.78477i 0.247251 0.428251i −0.715511 0.698601i \(-0.753806\pi\)
0.962762 + 0.270350i \(0.0871395\pi\)
\(252\) −11.6864 + 1.48451i −0.736171 + 0.0935151i
\(253\) 2.17762 + 3.77174i 0.136906 + 0.237127i
\(254\) −18.1650 15.2423i −1.13977 0.956384i
\(255\) 2.85894 + 1.30667i 0.179033 + 0.0818271i
\(256\) 3.62171 + 20.5397i 0.226357 + 1.28373i
\(257\) −7.40124 + 6.21038i −0.461677 + 0.387393i −0.843748 0.536740i \(-0.819656\pi\)
0.382071 + 0.924133i \(0.375211\pi\)
\(258\) 0.987350 + 10.3730i 0.0614697 + 0.645797i
\(259\) 6.99912 + 3.06295i 0.434904 + 0.190322i
\(260\) −1.06962 1.85264i −0.0663351 0.114896i
\(261\) −5.42698 + 15.6497i −0.335922 + 0.968692i
\(262\) 15.6706 0.968134
\(263\) 3.18277 18.0504i 0.196258 1.11304i −0.714358 0.699781i \(-0.753281\pi\)
0.910616 0.413254i \(-0.135608\pi\)
\(264\) −7.33980 + 2.02686i −0.451733 + 0.124744i
\(265\) 1.18139 + 6.69998i 0.0725720 + 0.411576i
\(266\) −7.07774 0.449647i −0.433964 0.0275696i
\(267\) −0.604278 + 0.877171i −0.0369812 + 0.0536820i
\(268\) −3.38609 + 19.2035i −0.206838 + 1.17304i
\(269\) 2.28434 + 3.95659i 0.139279 + 0.241238i 0.927224 0.374508i \(-0.122188\pi\)
−0.787945 + 0.615745i \(0.788855\pi\)
\(270\) 9.80154 10.2610i 0.596503 0.624462i
\(271\) −6.60709 + 11.4438i −0.401352 + 0.695162i −0.993889 0.110381i \(-0.964793\pi\)
0.592537 + 0.805543i \(0.298126\pi\)
\(272\) −5.55504 + 2.02187i −0.336824 + 0.122594i
\(273\) 1.40995 4.28893i 0.0853340 0.259578i
\(274\) 3.32188 2.78739i 0.200682 0.168392i
\(275\) −12.2691 4.46558i −0.739853 0.269285i
\(276\) 2.36358 0.652694i 0.142271 0.0392876i
\(277\) −5.27455 + 29.9135i −0.316917 + 1.79733i 0.244345 + 0.969688i \(0.421427\pi\)
−0.561262 + 0.827638i \(0.689684\pi\)
\(278\) 20.0560 + 34.7379i 1.20288 + 2.08344i
\(279\) −17.2193 + 10.2952i −1.03089 + 0.616356i
\(280\) 3.57597 1.05009i 0.213705 0.0627546i
\(281\) 3.38213 19.1810i 0.201761 1.14424i −0.700695 0.713461i \(-0.747127\pi\)
0.902456 0.430782i \(-0.141762\pi\)
\(282\) 29.8205 21.2216i 1.77579 1.26373i
\(283\) 1.33894 + 7.59351i 0.0795917 + 0.451387i 0.998393 + 0.0566670i \(0.0180473\pi\)
−0.918801 + 0.394720i \(0.870842\pi\)
\(284\) 2.99265 + 16.9722i 0.177581 + 1.00711i
\(285\) 2.96489 2.10994i 0.175625 0.124982i
\(286\) −1.45805 + 8.26899i −0.0862161 + 0.488956i
\(287\) −22.7364 21.6782i −1.34209 1.27962i
\(288\) 0.319141 + 20.9067i 0.0188056 + 1.23194i
\(289\) 7.73062 + 13.3898i 0.454742 + 0.787637i
\(290\) −2.61828 + 14.8490i −0.153750 + 0.871962i
\(291\) −9.53051 + 2.63181i −0.558689 + 0.154280i
\(292\) −13.8493 5.04073i −0.810469 0.294987i
\(293\) 10.4784 8.79240i 0.612153 0.513657i −0.283173 0.959069i \(-0.591387\pi\)
0.895326 + 0.445411i \(0.146943\pi\)
\(294\) −19.2273 11.9367i −1.12136 0.696163i
\(295\) −8.67599 + 3.15780i −0.505135 + 0.183854i
\(296\) 1.39017 2.40784i 0.0808017 0.139953i
\(297\) −23.5814 + 2.60834i −1.36833 + 0.151351i
\(298\) 4.09946 + 7.10047i 0.237475 + 0.411319i
\(299\) −0.163184 + 0.925461i −0.00943716 + 0.0535208i
\(300\) −4.17026 + 6.05355i −0.240770 + 0.349502i
\(301\) −4.72319 + 7.09954i −0.272240 + 0.409211i
\(302\) −4.80448 27.2476i −0.276467 1.56792i
\(303\) −19.7728 + 5.46017i −1.13592 + 0.313679i
\(304\) −1.18838 + 6.73965i −0.0681584 + 0.386546i
\(305\) −7.68311 −0.439934
\(306\) −6.82161 + 1.31049i −0.389966 + 0.0749159i
\(307\) 8.70668 + 15.0804i 0.496916 + 0.860684i 0.999994 0.00355714i \(-0.00113228\pi\)
−0.503077 + 0.864241i \(0.667799\pi\)
\(308\) 16.4253 + 7.18801i 0.935917 + 0.409575i
\(309\) −2.10622 22.1278i −0.119819 1.25881i
\(310\) −13.9899 + 11.7389i −0.794575 + 0.666727i
\(311\) 5.19029 + 29.4356i 0.294315 + 1.66914i 0.669975 + 0.742383i \(0.266305\pi\)
−0.375661 + 0.926757i \(0.622584\pi\)
\(312\) −1.49432 0.682977i −0.0845992 0.0386660i
\(313\) 2.42961 + 2.03869i 0.137330 + 0.115233i 0.708865 0.705344i \(-0.249208\pi\)
−0.571535 + 0.820578i \(0.693652\pi\)
\(314\) 0.352998 + 0.611410i 0.0199208 + 0.0345039i
\(315\) 11.5198 1.46335i 0.649069 0.0824507i
\(316\) −10.5004 + 18.1873i −0.590696 + 1.02311i
\(317\) 6.27590 2.28424i 0.352489 0.128296i −0.159706 0.987165i \(-0.551055\pi\)
0.512195 + 0.858869i \(0.328832\pi\)
\(318\) −10.7116 10.5493i −0.600677 0.591578i
\(319\) 19.3119 16.2046i 1.08126 0.907284i
\(320\) 0.883715 + 5.01180i 0.0494012 + 0.280168i
\(321\) 19.0754 + 1.52228i 1.06469 + 0.0849656i
\(322\) 4.31552 + 1.88855i 0.240495 + 0.105245i
\(323\) −1.78138 −0.0991186
\(324\) −1.91692 + 13.2193i −0.106495 + 0.734406i
\(325\) −1.40861 2.43979i −0.0781358 0.135335i
\(326\) −7.38070 6.19315i −0.408779 0.343007i
\(327\) 18.7169 27.1694i 1.03504 1.50247i
\(328\) −8.75776 + 7.34863i −0.483566 + 0.405760i
\(329\) 29.8920 + 1.89903i 1.64800 + 0.104697i
\(330\) −20.8177 + 5.74872i −1.14598 + 0.316457i
\(331\) −4.68844 + 1.70645i −0.257700 + 0.0937951i −0.467640 0.883919i \(-0.654895\pi\)
0.209940 + 0.977714i \(0.432673\pi\)
\(332\) 12.3529 0.677952
\(333\) 5.46648 6.72040i 0.299561 0.368276i
\(334\) 20.2987 1.11070
\(335\) 3.33784 18.9298i 0.182366 1.03425i
\(336\) −13.5045 + 17.1625i −0.736732 + 0.936293i
\(337\) 13.6802 + 4.97920i 0.745209 + 0.271234i 0.686588 0.727046i \(-0.259107\pi\)
0.0586210 + 0.998280i \(0.481330\pi\)
\(338\) 17.2007 14.4331i 0.935597 0.785059i
\(339\) −11.0601 + 7.87081i −0.600700 + 0.427484i
\(340\) −2.53109 + 0.921243i −0.137268 + 0.0499614i
\(341\) 30.5343 1.65352
\(342\) −2.63473 + 7.59772i −0.142470 + 0.410838i
\(343\) −6.05855 17.5013i −0.327131 0.944979i
\(344\) 2.37718 + 1.99469i 0.128169 + 0.107546i
\(345\) −2.32991 + 0.643394i −0.125438 + 0.0346392i
\(346\) −17.3152 + 14.5291i −0.930868 + 0.781091i
\(347\) 8.17009 + 2.97367i 0.438593 + 0.159635i 0.551873 0.833928i \(-0.313913\pi\)
−0.113280 + 0.993563i \(0.536136\pi\)
\(348\) −6.09642 12.8175i −0.326802 0.687090i
\(349\) −10.4169 + 3.79143i −0.557602 + 0.202950i −0.605421 0.795906i \(-0.706995\pi\)
0.0478190 + 0.998856i \(0.484773\pi\)
\(350\) −13.5499 + 3.97894i −0.724273 + 0.212683i
\(351\) −4.25956 2.83950i −0.227358 0.151561i
\(352\) 15.9116 27.5596i 0.848090 1.46893i
\(353\) −17.7388 14.8846i −0.944140 0.792228i 0.0341608 0.999416i \(-0.489124\pi\)
−0.978301 + 0.207189i \(0.933569\pi\)
\(354\) 11.5747 16.8019i 0.615189 0.893010i
\(355\) −2.95001 16.7304i −0.156570 0.887955i
\(356\) −0.158494 0.898863i −0.00840015 0.0476396i
\(357\) −5.00991 2.68604i −0.265152 0.142160i
\(358\) −17.6989 14.8511i −0.935416 0.784907i
\(359\) 1.03966 + 1.80074i 0.0548710 + 0.0950394i 0.892156 0.451727i \(-0.149192\pi\)
−0.837285 + 0.546766i \(0.815859\pi\)
\(360\) −0.0645020 4.22548i −0.00339955 0.222702i
\(361\) 8.46888 14.6685i 0.445730 0.772027i
\(362\) −22.6923 19.0411i −1.19268 1.00078i
\(363\) 15.5130 + 7.09020i 0.814221 + 0.372139i
\(364\) 1.71801 + 3.46623i 0.0900480 + 0.181680i
\(365\) 13.6520 + 4.96891i 0.714576 + 0.260085i
\(366\) 13.8331 9.84425i 0.723069 0.514567i
\(367\) 14.3862 5.23615i 0.750954 0.273325i 0.0619470 0.998079i \(-0.480269\pi\)
0.689007 + 0.724754i \(0.258047\pi\)
\(368\) 2.27284 3.93668i 0.118480 0.205213i
\(369\) −30.5733 + 18.2793i −1.59158 + 0.951582i
\(370\) 3.94289 6.82929i 0.204981 0.355038i
\(371\) −1.36394 12.2274i −0.0708121 0.634814i
\(372\) 4.32254 16.6388i 0.224113 0.862684i
\(373\) −28.8193 10.4894i −1.49221 0.543119i −0.538177 0.842832i \(-0.680887\pi\)
−0.954029 + 0.299713i \(0.903109\pi\)
\(374\) 9.93457 + 3.61589i 0.513704 + 0.186973i
\(375\) 11.2987 16.4013i 0.583464 0.846957i
\(376\) 1.89280 10.7346i 0.0976135 0.553594i
\(377\) 5.43960 0.280153
\(378\) −18.8660 + 17.3949i −0.970363 + 0.894696i
\(379\) 33.1265 1.70159 0.850797 0.525495i \(-0.176120\pi\)
0.850797 + 0.525495i \(0.176120\pi\)
\(380\) −0.541474 + 3.07085i −0.0277770 + 0.157531i
\(381\) −21.9338 1.75039i −1.12370 0.0896752i
\(382\) −26.6658 9.70556i −1.36434 0.496580i
\(383\) 11.1640 + 4.06336i 0.570453 + 0.207628i 0.611110 0.791545i \(-0.290723\pi\)
−0.0406578 + 0.999173i \(0.512945\pi\)
\(384\) 9.18943 + 9.05022i 0.468946 + 0.461842i
\(385\) −16.1912 7.08559i −0.825182 0.361115i
\(386\) −17.5469 + 30.3922i −0.893115 + 1.54692i
\(387\) 6.32735 + 7.31105i 0.321637 + 0.371642i
\(388\) 4.23612 7.33718i 0.215056 0.372489i
\(389\) −21.4924 + 7.82259i −1.08971 + 0.396621i −0.823512 0.567298i \(-0.807989\pi\)
−0.266195 + 0.963919i \(0.585766\pi\)
\(390\) −4.23830 1.93711i −0.214615 0.0980895i
\(391\) 1.11187 + 0.404689i 0.0562298 + 0.0204660i
\(392\) −6.57421 + 1.48516i −0.332048 + 0.0750117i
\(393\) 11.8474 8.43108i 0.597620 0.425292i
\(394\) 0.373395 + 0.313316i 0.0188114 + 0.0157846i
\(395\) 10.3508 17.9281i 0.520806 0.902063i
\(396\) 12.8285 15.7712i 0.644658 0.792532i
\(397\) −11.1473 19.3077i −0.559466 0.969023i −0.997541 0.0700851i \(-0.977673\pi\)
0.438075 0.898938i \(-0.355660\pi\)
\(398\) 2.34155 + 1.96479i 0.117371 + 0.0984862i
\(399\) −5.59286 + 3.46802i −0.279993 + 0.173618i
\(400\) 2.36638 + 13.4204i 0.118319 + 0.671020i
\(401\) 0.878529 + 4.98238i 0.0438716 + 0.248808i 0.998854 0.0478529i \(-0.0152379\pi\)
−0.954983 + 0.296661i \(0.904127\pi\)
\(402\) 18.2448 + 38.3591i 0.909970 + 1.91318i
\(403\) 5.04704 + 4.23497i 0.251411 + 0.210959i
\(404\) 8.78859 15.2223i 0.437249 0.757337i
\(405\) 1.88960 13.0309i 0.0938952 0.647513i
\(406\) 6.42792 26.4988i 0.319013 1.31511i
\(407\) −12.3896 + 4.50944i −0.614129 + 0.223525i
\(408\) −1.17360 + 1.70360i −0.0581017 + 0.0843405i
\(409\) −21.3726 7.77898i −1.05681 0.384646i −0.245578 0.969377i \(-0.578978\pi\)
−0.811227 + 0.584731i \(0.801200\pi\)
\(410\) −24.8394 + 20.8427i −1.22673 + 1.02935i
\(411\) 1.01175 3.89456i 0.0499061 0.192105i
\(412\) 14.5907 + 12.2430i 0.718831 + 0.603171i
\(413\) 16.0202 4.70435i 0.788304 0.231486i
\(414\) 3.37053 4.14367i 0.165652 0.203650i
\(415\) −12.1769 −0.597738
\(416\) 6.45245 2.34850i 0.316357 0.115145i
\(417\) 33.8524 + 15.4722i 1.65776 + 0.757678i
\(418\) 9.37567 7.86712i 0.458579 0.384793i
\(419\) 28.5404 + 10.3878i 1.39429 + 0.507480i 0.926478 0.376349i \(-0.122821\pi\)
0.467811 + 0.883829i \(0.345043\pi\)
\(420\) −6.15320 + 7.81993i −0.300245 + 0.381574i
\(421\) 5.43779 30.8393i 0.265022 1.50301i −0.503951 0.863732i \(-0.668121\pi\)
0.768973 0.639281i \(-0.220768\pi\)
\(422\) −11.8986 −0.579214
\(423\) 11.1274 32.0880i 0.541034 1.56017i
\(424\) −4.47737 −0.217440
\(425\) −3.33327 + 1.21321i −0.161687 + 0.0588493i
\(426\) 26.7477 + 26.3425i 1.29593 + 1.27630i
\(427\) 13.8663 + 0.880919i 0.671036 + 0.0426307i
\(428\) −12.5612 + 10.5401i −0.607168 + 0.509475i
\(429\) 3.34655 + 7.03601i 0.161573 + 0.339702i
\(430\) 6.74233 + 5.65748i 0.325144 + 0.272828i
\(431\) −5.25777 9.10673i −0.253258 0.438656i 0.711163 0.703027i \(-0.248169\pi\)
−0.964421 + 0.264372i \(0.914835\pi\)
\(432\) 14.6639 + 19.9539i 0.705519 + 0.960033i
\(433\) −6.33812 −0.304591 −0.152295 0.988335i \(-0.548667\pi\)
−0.152295 + 0.988335i \(0.548667\pi\)
\(434\) 26.5946 19.5821i 1.27658 0.939970i
\(435\) 6.00955 + 12.6349i 0.288136 + 0.605796i
\(436\) 4.90917 + 27.8413i 0.235107 + 1.33336i
\(437\) 1.04932 0.880484i 0.0501958 0.0421193i
\(438\) −30.9464 + 8.54572i −1.47868 + 0.408330i
\(439\) −19.0176 + 6.92183i −0.907659 + 0.330361i −0.753318 0.657657i \(-0.771548\pi\)
−0.154341 + 0.988018i \(0.549326\pi\)
\(440\) −3.21591 + 5.57011i −0.153312 + 0.265545i
\(441\) −20.9585 + 1.32020i −0.998022 + 0.0628665i
\(442\) 1.14059 + 1.97556i 0.0542523 + 0.0939677i
\(443\) 6.80079 + 5.70654i 0.323115 + 0.271126i 0.789888 0.613252i \(-0.210139\pi\)
−0.466772 + 0.884377i \(0.654583\pi\)
\(444\) 0.703388 + 7.38975i 0.0333813 + 0.350702i
\(445\) 0.156235 + 0.886055i 0.00740627 + 0.0420030i
\(446\) −8.26552 + 6.93559i −0.391384 + 0.328410i
\(447\) 6.91948 + 3.16254i 0.327280 + 0.149583i
\(448\) −1.02027 9.14647i −0.0482032 0.432130i
\(449\) 6.01834 + 10.4241i 0.284023 + 0.491943i 0.972372 0.233437i \(-0.0749974\pi\)
−0.688349 + 0.725380i \(0.741664\pi\)
\(450\) 0.244408 + 16.0110i 0.0115215 + 0.754767i
\(451\) 54.2142 2.55285
\(452\) 2.01989 11.4553i 0.0950075 0.538814i
\(453\) −18.2920 18.0149i −0.859433 0.846414i
\(454\) −4.15608 23.5703i −0.195055 1.10621i
\(455\) −1.69353 3.41684i −0.0793937 0.160184i
\(456\) 1.02866 + 2.16272i 0.0481713 + 0.101278i
\(457\) −0.558880 + 3.16957i −0.0261433 + 0.148266i −0.995085 0.0990224i \(-0.968428\pi\)
0.968942 + 0.247289i \(0.0795396\pi\)
\(458\) −5.46990 9.47414i −0.255591 0.442697i
\(459\) −4.45223 + 4.66092i −0.207812 + 0.217553i
\(460\) 1.03560 1.79370i 0.0482849 0.0836319i
\(461\) 32.0957 11.6819i 1.49485 0.544080i 0.540126 0.841584i \(-0.318377\pi\)
0.954720 + 0.297505i \(0.0961544\pi\)
\(462\) 38.2303 7.98825i 1.77863 0.371647i
\(463\) 8.38189 7.03324i 0.389539 0.326862i −0.426894 0.904302i \(-0.640392\pi\)
0.816434 + 0.577439i \(0.195948\pi\)
\(464\) −24.7255 8.99933i −1.14785 0.417784i
\(465\) −4.26095 + 16.4018i −0.197597 + 0.760614i
\(466\) −0.314897 + 1.78587i −0.0145873 + 0.0827288i
\(467\) 20.7032 + 35.8590i 0.958031 + 1.65936i 0.727275 + 0.686346i \(0.240786\pi\)
0.230755 + 0.973012i \(0.425880\pi\)
\(468\) 4.30784 0.827575i 0.199130 0.0382547i
\(469\) −8.19447 + 33.7813i −0.378385 + 1.55988i
\(470\) 5.36849 30.4462i 0.247630 1.40438i
\(471\) 0.595825 + 0.272321i 0.0274541 + 0.0125479i
\(472\) −1.05513 5.98392i −0.0485662 0.275432i
\(473\) −2.55536 14.4922i −0.117496 0.666350i
\(474\) 4.33481 + 45.5412i 0.199104 + 2.09178i
\(475\) −0.713082 + 4.04409i −0.0327184 + 0.185555i
\(476\) 4.67367 1.37243i 0.214217 0.0629051i
\(477\) −13.7740 2.21251i −0.630667 0.101304i
\(478\) −22.1736 38.4057i −1.01420 1.75664i
\(479\) 1.44178 8.17673i 0.0658765 0.373604i −0.933990 0.357298i \(-0.883698\pi\)
0.999867 0.0163066i \(-0.00519078\pi\)
\(480\) 12.5835 + 12.3929i 0.574357 + 0.565656i
\(481\) −2.67333 0.973012i −0.121893 0.0443655i
\(482\) 0.409274 0.343422i 0.0186419 0.0156424i
\(483\) 4.27872 0.894041i 0.194688 0.0406803i
\(484\) −13.7341 + 4.99880i −0.624277 + 0.227218i
\(485\) −4.17576 + 7.23263i −0.189612 + 0.328417i
\(486\) 13.2942 + 25.8828i 0.603036 + 1.17407i
\(487\) 11.9736 + 20.7388i 0.542574 + 0.939766i 0.998755 + 0.0498789i \(0.0158835\pi\)
−0.456181 + 0.889887i \(0.650783\pi\)
\(488\) 0.878029 4.97955i 0.0397465 0.225414i
\(489\) −8.91202 0.711209i −0.403015 0.0321620i
\(490\) −18.6463 + 4.21231i −0.842352 + 0.190293i
\(491\) 6.82562 + 38.7100i 0.308036 + 1.74696i 0.608859 + 0.793278i \(0.291627\pi\)
−0.300823 + 0.953680i \(0.597261\pi\)
\(492\) 7.67475 29.5426i 0.346005 1.33188i
\(493\) 1.18932 6.74498i 0.0535643 0.303778i
\(494\) 2.64085 0.118817
\(495\) −12.6457 + 15.5465i −0.568384 + 0.698762i
\(496\) −15.9347 27.5998i −0.715491 1.23927i
\(497\) 3.40586 + 30.5327i 0.152774 + 1.36958i
\(498\) 21.9239 15.6020i 0.982435 0.699142i
\(499\) −4.79773 + 4.02577i −0.214776 + 0.180218i −0.743828 0.668371i \(-0.766992\pi\)
0.529052 + 0.848589i \(0.322548\pi\)
\(500\) 2.96350 + 16.8068i 0.132532 + 0.751625i
\(501\) 15.3463 10.9211i 0.685622 0.487918i
\(502\) 11.2023 + 9.39988i 0.499985 + 0.419537i
\(503\) −1.54894 2.68284i −0.0690637 0.119622i 0.829426 0.558617i \(-0.188668\pi\)
−0.898489 + 0.438995i \(0.855335\pi\)
\(504\) −0.368068 + 7.63343i −0.0163950 + 0.340020i
\(505\) −8.66337 + 15.0054i −0.385515 + 0.667731i
\(506\) −7.63918 + 2.78044i −0.339603 + 0.123605i
\(507\) 5.23887 20.1661i 0.232667 0.895609i
\(508\) 14.4434 12.1195i 0.640824 0.537715i
\(509\) −0.840121 4.76457i −0.0372377 0.211186i 0.960512 0.278240i \(-0.0897510\pi\)
−0.997749 + 0.0670543i \(0.978640\pi\)
\(510\) −3.32864 + 4.83187i −0.147395 + 0.213959i
\(511\) −24.0690 10.5330i −1.06475 0.465954i
\(512\) −24.0378 −1.06233
\(513\) 2.09580 + 7.16159i 0.0925318 + 0.316192i
\(514\) −9.01718 15.6182i −0.397731 0.688890i
\(515\) −14.3828 12.0686i −0.633781 0.531805i
\(516\) −8.25887 0.659085i −0.363577 0.0290146i
\(517\) −39.5970 + 33.2258i −1.74147 + 1.46127i
\(518\) −7.89904 + 11.8732i −0.347064 + 0.521680i
\(519\) −5.27372 + 20.3003i −0.231491 + 0.891082i
\(520\) −1.30411 + 0.474658i −0.0571891 + 0.0208151i
\(521\) −30.4398 −1.33359 −0.666796 0.745240i \(-0.732335\pi\)
−0.666796 + 0.745240i \(0.732335\pi\)
\(522\) −27.0088 15.0486i −1.18214 0.658660i
\(523\) 33.7422 1.47545 0.737723 0.675104i \(-0.235901\pi\)
0.737723 + 0.675104i \(0.235901\pi\)
\(524\) −2.16367 + 12.2708i −0.0945203 + 0.536051i
\(525\) −8.10331 + 10.2983i −0.353657 + 0.449454i
\(526\) 32.1493 + 11.7014i 1.40177 + 0.510204i
\(527\) 6.35476 5.33228i 0.276818 0.232278i
\(528\) −3.57117 37.5185i −0.155415 1.63278i
\(529\) 20.7580 7.55528i 0.902520 0.328490i
\(530\) −12.6991 −0.551612
\(531\) −0.288967 18.9300i −0.0125401 0.821494i
\(532\) 1.32933 5.48010i 0.0576338 0.237593i
\(533\) 8.96113 + 7.51928i 0.388149 + 0.325696i
\(534\) −1.41658 1.39512i −0.0613015 0.0603729i
\(535\) 12.3822 10.3899i 0.535330 0.449195i
\(536\) 11.8873 + 4.32662i 0.513452 + 0.186881i
\(537\) −21.3710 1.70548i −0.922226 0.0735967i
\(538\) −8.01357 + 2.91670i −0.345490 + 0.125748i
\(539\) 28.4091 + 14.6443i 1.22367 + 0.630775i
\(540\) 6.68147 + 9.09179i 0.287525 + 0.391248i
\(541\) 7.87553 13.6408i 0.338596 0.586465i −0.645573 0.763698i \(-0.723382\pi\)
0.984169 + 0.177234i \(0.0567148\pi\)
\(542\) −18.8949 15.8547i −0.811604 0.681017i
\(543\) −27.4004 2.18664i −1.17586 0.0938377i
\(544\) −1.50131 8.51437i −0.0643683 0.365050i
\(545\) −4.83922 27.4446i −0.207289 1.17560i
\(546\) 7.42706 + 3.98199i 0.317849 + 0.170414i
\(547\) −16.6514 13.9722i −0.711963 0.597408i 0.213186 0.977012i \(-0.431616\pi\)
−0.925149 + 0.379603i \(0.876060\pi\)
\(548\) 1.72399 + 2.98604i 0.0736452 + 0.127557i
\(549\) 5.16179 14.8850i 0.220300 0.635275i
\(550\) 12.1856 21.1060i 0.519595 0.899964i
\(551\) −6.07390 5.09661i −0.258757 0.217123i
\(552\) −0.150732 1.58358i −0.00641556 0.0674015i
\(553\) −20.7364 + 31.1694i −0.881803 + 1.32546i
\(554\) −53.2784 19.3918i −2.26358 0.823877i
\(555\) −0.693366 7.28446i −0.0294317 0.309208i
\(556\) −29.9705 + 10.9084i −1.27103 + 0.462618i
\(557\) −12.3971 + 21.4723i −0.525280 + 0.909811i 0.474287 + 0.880370i \(0.342706\pi\)
−0.999567 + 0.0294409i \(0.990627\pi\)
\(558\) −13.3436 34.9902i −0.564882 1.48125i
\(559\) 1.58762 2.74984i 0.0671493 0.116306i
\(560\) 2.04499 + 18.3329i 0.0864168 + 0.774707i
\(561\) 9.45619 2.61129i 0.399241 0.110249i
\(562\) 34.1630 + 12.4343i 1.44108 + 0.524509i
\(563\) −17.9677 6.53971i −0.757248 0.275616i −0.0655957 0.997846i \(-0.520895\pi\)
−0.691652 + 0.722230i \(0.743117\pi\)
\(564\) 12.5000 + 26.2809i 0.526347 + 1.10663i
\(565\) −1.99111 + 11.2921i −0.0837665 + 0.475063i
\(566\) −14.3927 −0.604968
\(567\) −4.90439 + 23.3012i −0.205965 + 0.978559i
\(568\) 11.1803 0.469117
\(569\) −3.50374 + 19.8707i −0.146884 + 0.833022i 0.818951 + 0.573864i \(0.194556\pi\)
−0.965835 + 0.259158i \(0.916555\pi\)
\(570\) 2.91756 + 6.13406i 0.122203 + 0.256927i
\(571\) −1.27023 0.462325i −0.0531574 0.0193477i 0.315305 0.948991i \(-0.397893\pi\)
−0.368462 + 0.929643i \(0.620116\pi\)
\(572\) −6.27367 2.28343i −0.262315 0.0954750i
\(573\) −25.3818 + 7.00907i −1.06034 + 0.292808i
\(574\) 47.2192 34.7684i 1.97089 1.45120i
\(575\) 1.36380 2.36218i 0.0568746 0.0985096i
\(576\) −10.3034 1.65503i −0.429307 0.0689595i
\(577\) −6.07544 + 10.5230i −0.252924 + 0.438077i −0.964330 0.264705i \(-0.914726\pi\)
0.711406 + 0.702782i \(0.248059\pi\)
\(578\) −27.1194 + 9.87065i −1.12802 + 0.410565i
\(579\) 3.08566 + 32.4178i 0.128236 + 1.34724i
\(580\) −11.2659 4.10045i −0.467791 0.170262i
\(581\) 21.9764 + 1.39616i 0.911737 + 0.0579223i
\(582\) −1.74876 18.3724i −0.0724885 0.761560i
\(583\) 16.2649 + 13.6479i 0.673623 + 0.565237i
\(584\) −4.78058 + 8.28021i −0.197822 + 0.342638i
\(585\) −4.24646 + 0.815783i −0.175570 + 0.0337285i
\(586\) 12.7661 + 22.1116i 0.527365 + 0.913422i
\(587\) −36.1996 30.3750i −1.49412 1.25371i −0.889282 0.457360i \(-0.848795\pi\)
−0.604834 0.796352i \(-0.706761\pi\)
\(588\) 12.0017 13.4077i 0.494943 0.552924i
\(589\) −1.66763 9.45762i −0.0687136 0.389694i
\(590\) −2.99263 16.9721i −0.123205 0.698728i
\(591\) 0.450865 + 0.0359806i 0.0185461 + 0.00148004i
\(592\) 10.5417 + 8.84557i 0.433263 + 0.363551i
\(593\) 5.30960 9.19649i 0.218039 0.377655i −0.736169 0.676797i \(-0.763367\pi\)
0.954208 + 0.299143i \(0.0967006\pi\)
\(594\) 2.84871 44.1936i 0.116884 1.81328i
\(595\) −4.60708 + 1.35287i −0.188872 + 0.0554623i
\(596\) −6.12600 + 2.22968i −0.250931 + 0.0913314i
\(597\) 2.82736 + 0.225633i 0.115716 + 0.00923454i
\(598\) −1.64832 0.599941i −0.0674050 0.0245334i
\(599\) 7.85627 6.59219i 0.320999 0.269350i −0.468022 0.883717i \(-0.655033\pi\)
0.789020 + 0.614367i \(0.210589\pi\)
\(600\) 3.39771 + 3.34624i 0.138711 + 0.136610i
\(601\) −19.1642 16.0807i −0.781724 0.655945i 0.161958 0.986798i \(-0.448219\pi\)
−0.943682 + 0.330853i \(0.892664\pi\)
\(602\) −11.5197 10.9835i −0.469508 0.447655i
\(603\) 34.4314 + 19.1843i 1.40216 + 0.781246i
\(604\) 21.9994 0.895143
\(605\) 13.5384 4.92757i 0.550414 0.200334i
\(606\) −3.62812 38.1168i −0.147382 1.54839i
\(607\) 0.503454 0.422448i 0.0204346 0.0171466i −0.632513 0.774550i \(-0.717977\pi\)
0.652948 + 0.757403i \(0.273532\pi\)
\(608\) −9.40528 3.42324i −0.381434 0.138831i
\(609\) −9.39720 23.4921i −0.380794 0.951947i
\(610\) 2.49033 14.1234i 0.100831 0.571839i
\(611\) −11.1533 −0.451214
\(612\) −0.0843020 5.52257i −0.00340770 0.223237i
\(613\) −27.7448 −1.12060 −0.560301 0.828289i \(-0.689314\pi\)
−0.560301 + 0.828289i \(0.689314\pi\)
\(614\) −30.5435 + 11.1169i −1.23263 + 0.448642i
\(615\) −7.56540 + 29.1217i −0.305066 + 1.17430i
\(616\) 6.44263 9.68406i 0.259581 0.390182i
\(617\) 12.7820 10.7253i 0.514582 0.431786i −0.348156 0.937437i \(-0.613192\pi\)
0.862738 + 0.505651i \(0.168748\pi\)
\(618\) 41.3589 + 3.30057i 1.66370 + 0.132769i
\(619\) −7.28444 6.11237i −0.292787 0.245677i 0.484548 0.874765i \(-0.338984\pi\)
−0.777334 + 0.629088i \(0.783429\pi\)
\(620\) −7.26050 12.5755i −0.291589 0.505046i
\(621\) 0.318826 4.94612i 0.0127941 0.198481i
\(622\) −55.7920 −2.23705
\(623\) −0.180377 1.61704i −0.00722667 0.0647854i
\(624\) 4.61337 6.69678i 0.184683 0.268086i
\(625\) −0.438492 2.48681i −0.0175397 0.0994725i
\(626\) −4.53510 + 3.80540i −0.181259 + 0.152094i
\(627\) 2.85557 10.9920i 0.114041 0.438979i
\(628\) −0.527500 + 0.191994i −0.0210495 + 0.00766141i
\(629\) −1.79101 + 3.10213i −0.0714124 + 0.123690i
\(630\) −1.04394 + 21.6505i −0.0415916 + 0.862577i
\(631\) −22.9465 39.7445i −0.913486 1.58220i −0.809103 0.587667i \(-0.800047\pi\)
−0.104383 0.994537i \(-0.533287\pi\)
\(632\) 10.4366 + 8.75737i 0.415147 + 0.348349i
\(633\) −8.99561 + 6.40166i −0.357544 + 0.254443i
\(634\) 2.16476 + 12.2770i 0.0859737 + 0.487581i
\(635\) −14.2376 + 11.9468i −0.565003 + 0.474094i
\(636\) 9.73957 6.93109i 0.386199 0.274836i
\(637\) 2.66467 + 6.36079i 0.105578 + 0.252024i
\(638\) 23.5283 + 40.7523i 0.931495 + 1.61340i
\(639\) 34.3947 + 5.52480i 1.36063 + 0.218558i
\(640\) 10.8945 0.430641
\(641\) −4.98155 + 28.2518i −0.196759 + 1.11588i 0.713132 + 0.701030i \(0.247276\pi\)
−0.909891 + 0.414847i \(0.863835\pi\)
\(642\) −8.98125 + 34.5717i −0.354462 + 1.36444i
\(643\) 0.172431 + 0.977906i 0.00680002 + 0.0385648i 0.988019 0.154332i \(-0.0493227\pi\)
−0.981219 + 0.192897i \(0.938212\pi\)
\(644\) −2.07467 + 3.11849i −0.0817536 + 0.122886i
\(645\) 8.14119 + 0.649694i 0.320559 + 0.0255817i
\(646\) 0.577400 3.27460i 0.0227175 0.128837i
\(647\) 8.87356 + 15.3695i 0.348856 + 0.604236i 0.986046 0.166470i \(-0.0532370\pi\)
−0.637191 + 0.770706i \(0.719904\pi\)
\(648\) 8.22962 + 2.71386i 0.323290 + 0.106611i
\(649\) −14.4072 + 24.9540i −0.565531 + 0.979528i
\(650\) 4.94148 1.79855i 0.193821 0.0705451i
\(651\) 9.57061 29.1129i 0.375102 1.14102i
\(652\) 5.86857 4.92432i 0.229831 0.192851i
\(653\) 17.1213 + 6.23165i 0.670008 + 0.243863i 0.654552 0.756017i \(-0.272857\pi\)
0.0154569 + 0.999881i \(0.495080\pi\)
\(654\) 43.8771 + 43.2124i 1.71573 + 1.68974i
\(655\) 2.13284 12.0959i 0.0833370 0.472627i
\(656\) −28.2925 49.0040i −1.10463 1.91328i
\(657\) −18.7984 + 23.1105i −0.733397 + 0.901627i
\(658\) −13.1798 + 54.3330i −0.513800 + 2.11812i
\(659\) −0.516836 + 2.93112i −0.0201331 + 0.114180i −0.993218 0.116266i \(-0.962907\pi\)
0.973085 + 0.230446i \(0.0740186\pi\)
\(660\) −1.62717 17.0949i −0.0633373 0.665418i
\(661\) 4.25035 + 24.1049i 0.165320 + 0.937574i 0.948734 + 0.316075i \(0.102365\pi\)
−0.783415 + 0.621499i \(0.786524\pi\)
\(662\) −1.61720 9.17158i −0.0628541 0.356463i
\(663\) 1.92520 + 0.879910i 0.0747685 + 0.0341729i
\(664\) 1.39158 7.89202i 0.0540036 0.306270i
\(665\) −1.31039 + 5.40202i −0.0508147 + 0.209481i
\(666\) 10.5818 + 12.2270i 0.410038 + 0.473785i
\(667\) 2.63328 + 4.56097i 0.101961 + 0.176602i
\(668\) −2.80268 + 15.8948i −0.108439 + 0.614987i
\(669\) −2.51745 + 9.69048i −0.0973302 + 0.374656i
\(670\) 33.7156 + 12.2715i 1.30255 + 0.474089i
\(671\) −18.3682 + 15.4128i −0.709097 + 0.595003i
\(672\) −21.2895 23.8091i −0.821259 0.918458i
\(673\) 23.3965 8.51562i 0.901868 0.328253i 0.150867 0.988554i \(-0.451794\pi\)
0.751001 + 0.660301i \(0.229571\pi\)
\(674\) −13.5871 + 23.5336i −0.523356 + 0.906480i
\(675\) 8.79901 + 11.9732i 0.338674 + 0.460849i
\(676\) 8.92685 + 15.4618i 0.343340 + 0.594683i
\(677\) 1.53657 8.71430i 0.0590550 0.334918i −0.940938 0.338578i \(-0.890054\pi\)
0.999993 + 0.00366049i \(0.00116517\pi\)
\(678\) −10.8835 22.8822i −0.417978 0.878785i
\(679\) 8.36556 12.5745i 0.321041 0.482564i
\(680\) 0.303432 + 1.72085i 0.0116361 + 0.0659916i
\(681\) −15.8234 15.5837i −0.606353 0.597168i
\(682\) −9.89709 + 56.1292i −0.378979 + 2.14930i
\(683\) 6.28032 0.240310 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(684\) −5.58557 3.11214i −0.213570 0.118996i
\(685\) −1.69943 2.94349i −0.0649317 0.112465i
\(686\) 34.1352 5.46435i 1.30329 0.208630i
\(687\) −9.23264 4.21977i −0.352247 0.160994i
\(688\) −11.7658 + 9.87272i −0.448569 + 0.376394i
\(689\) 0.795542 + 4.51174i 0.0303077 + 0.171884i
\(690\) −0.427516 4.49146i −0.0162753 0.170987i
\(691\) −8.61563 7.22938i −0.327754 0.275018i 0.464030 0.885820i \(-0.346403\pi\)
−0.791784 + 0.610801i \(0.790847\pi\)
\(692\) −8.98622 15.5646i −0.341605 0.591677i
\(693\) 24.6052 26.6079i 0.934674 1.01075i
\(694\) −8.11448 + 14.0547i −0.308022 + 0.533509i
\(695\) 29.5435 10.7529i 1.12065 0.407882i
\(696\) −8.87564 + 2.45097i −0.336430 + 0.0929038i
\(697\) 11.2830 9.46757i 0.427374 0.358610i
\(698\) −3.59312 20.3776i −0.136001 0.771302i
\(699\) 0.722762 + 1.51958i 0.0273374 + 0.0574758i
\(700\) −1.24482 11.1596i −0.0470499 0.421791i
\(701\) 11.0400 0.416976 0.208488 0.978025i \(-0.433146\pi\)
0.208488 + 0.978025i \(0.433146\pi\)
\(702\) 6.60033 6.90970i 0.249113 0.260790i
\(703\) 2.07340 + 3.59124i 0.0781999 + 0.135446i
\(704\) 12.1667 + 10.2090i 0.458549 + 0.384768i
\(705\) −12.3219 25.9064i −0.464071 0.975692i
\(706\) 33.1111 27.7835i 1.24615 1.04565i
\(707\) 17.3559 26.0880i 0.652735 0.981140i
\(708\) 11.5585 + 11.3834i 0.434394 + 0.427814i
\(709\) 17.8195 6.48575i 0.669224 0.243577i 0.0150100 0.999887i \(-0.495222\pi\)
0.654214 + 0.756310i \(0.273000\pi\)
\(710\) 31.7105 1.19008
\(711\) 27.7793 + 32.0980i 1.04180 + 1.20377i
\(712\) −0.592121 −0.0221907
\(713\) −1.10768 + 6.28195i −0.0414828 + 0.235261i
\(714\) 6.56145 8.33876i 0.245556 0.312070i
\(715\) 6.18428 + 2.25089i 0.231279 + 0.0841786i
\(716\) 14.0728 11.8085i 0.525926 0.441304i
\(717\) −37.4267 17.1059i −1.39773 0.638830i
\(718\) −3.64717 + 1.32746i −0.136111 + 0.0495404i
\(719\) 3.54116 0.132063 0.0660316 0.997818i \(-0.478966\pi\)
0.0660316 + 0.997818i \(0.478966\pi\)
\(720\) 20.6518 + 3.31728i 0.769646 + 0.123628i
\(721\) 24.5739 + 23.4301i 0.915179 + 0.872583i
\(722\) 24.2192 + 20.3223i 0.901345 + 0.756318i
\(723\) 0.124654 0.479832i 0.00463592 0.0178452i
\(724\) 18.0432 15.1400i 0.670569 0.562674i
\(725\) −14.8364 5.40000i −0.551009 0.200551i
\(726\) −18.0617 + 26.2184i −0.670333 + 0.973057i
\(727\) 34.1662 12.4355i 1.26715 0.461206i 0.380990 0.924579i \(-0.375583\pi\)
0.886163 + 0.463373i \(0.153361\pi\)
\(728\) 2.40805 0.707124i 0.0892481 0.0262078i
\(729\) 23.9761 + 12.4155i 0.888005 + 0.459833i
\(730\) −13.5590 + 23.4850i −0.501843 + 0.869217i
\(731\) −3.06262 2.56985i −0.113275 0.0950492i
\(732\) 5.79851 + 12.1912i 0.214319 + 0.450598i
\(733\) −3.73447 21.1792i −0.137936 0.782272i −0.972770 0.231771i \(-0.925548\pi\)
0.834835 0.550501i \(-0.185563\pi\)
\(734\) 4.96227 + 28.1425i 0.183161 + 1.03876i
\(735\) −11.8307 + 13.2166i −0.436382 + 0.487503i
\(736\) 5.09275 + 4.27333i 0.187721 + 0.157517i
\(737\) −29.9945 51.9519i −1.10486 1.91367i
\(738\) −23.6919 62.1258i −0.872112 2.28688i
\(739\) −3.59765 + 6.23131i −0.132342 + 0.229223i −0.924579 0.380991i \(-0.875583\pi\)
0.792237 + 0.610213i \(0.208916\pi\)
\(740\) 4.80323 + 4.03039i 0.176570 + 0.148160i
\(741\) 1.99655 1.42083i 0.0733450 0.0521954i
\(742\) 22.9189 + 1.45603i 0.841380 + 0.0534525i
\(743\) −5.28136 1.92226i −0.193754 0.0705207i 0.243321 0.969946i \(-0.421763\pi\)
−0.437075 + 0.899425i \(0.643985\pi\)
\(744\) −10.1433 4.63599i −0.371872 0.169964i
\(745\) 6.03872 2.19791i 0.221242 0.0805253i
\(746\) 28.6232 49.5768i 1.04797 1.81513i
\(747\) 8.18084 23.5910i 0.299321 0.863149i
\(748\) −4.20308 + 7.27996i −0.153680 + 0.266182i
\(749\) −23.5383 + 17.3317i −0.860072 + 0.633287i
\(750\) 26.4871 + 26.0859i 0.967173 + 0.952522i
\(751\) −40.3558 14.6883i −1.47260 0.535984i −0.523797 0.851843i \(-0.675485\pi\)
−0.948806 + 0.315860i \(0.897707\pi\)
\(752\) 50.6969 + 18.4522i 1.84873 + 0.672881i
\(753\) 13.5265 + 1.07946i 0.492935 + 0.0393378i
\(754\) −1.76314 + 9.99926i −0.0642098 + 0.364152i
\(755\) −21.6859 −0.789232
\(756\) −11.0161 17.1747i −0.400652 0.624637i
\(757\) −18.7190 −0.680354 −0.340177 0.940361i \(-0.610487\pi\)
−0.340177 + 0.940361i \(0.610487\pi\)
\(758\) −10.7373 + 60.8943i −0.389997 + 2.21178i
\(759\) −4.27948 + 6.21210i −0.155335 + 0.225485i
\(760\) 1.90091 + 0.691876i 0.0689533 + 0.0250970i
\(761\) 11.7685 + 4.28340i 0.426609 + 0.155273i 0.546397 0.837526i \(-0.315999\pi\)
−0.119787 + 0.992800i \(0.538221\pi\)
\(762\) 10.3270 39.7521i 0.374109 1.44007i
\(763\) 5.58699 + 50.0861i 0.202263 + 1.81324i
\(764\) 11.2817 19.5404i 0.408157 0.706948i
\(765\) 0.0831008 + 5.44388i 0.00300452 + 0.196824i
\(766\) −11.0880 + 19.2050i −0.400626 + 0.693904i
\(767\) −5.84238 + 2.12645i −0.210956 + 0.0767818i
\(768\) −29.4326 + 20.9455i −1.06206 + 0.755806i
\(769\) 18.4388 + 6.71117i 0.664920 + 0.242011i 0.652359 0.757910i \(-0.273779\pi\)
0.0125608 + 0.999921i \(0.496002\pi\)
\(770\) 18.2731 27.4667i 0.658516 0.989830i
\(771\) −15.2201 6.95633i −0.548138 0.250526i
\(772\) −21.3757 17.9363i −0.769327 0.645542i
\(773\) −5.39853 + 9.35052i −0.194171 + 0.336315i −0.946629 0.322326i \(-0.895535\pi\)
0.752457 + 0.658641i \(0.228868\pi\)
\(774\) −15.4903 + 9.26143i −0.556788 + 0.332895i
\(775\) −9.56154 16.5611i −0.343461 0.594891i
\(776\) −4.21038 3.53293i −0.151144 0.126825i
\(777\) 0.416157 + 13.2263i 0.0149295 + 0.474490i
\(778\) −7.41343 42.0436i −0.265784 1.50734i
\(779\) −2.96092 16.7922i −0.106086 0.601643i
\(780\) 2.10203 3.05132i 0.0752649 0.109255i
\(781\) −40.6147 34.0798i −1.45331 1.21947i
\(782\) −1.10431 + 1.91271i −0.0394899 + 0.0683985i
\(783\) −28.5157 + 3.15413i −1.01907 + 0.112719i
\(784\) −1.58876 33.3212i −0.0567415 1.19004i
\(785\) 0.519984 0.189259i 0.0185590 0.00675493i
\(786\) 11.6582 + 24.5110i 0.415835 + 0.874279i
\(787\) −39.4055 14.3424i −1.40465 0.511252i −0.475097 0.879933i \(-0.657587\pi\)
−0.929556 + 0.368681i \(0.879809\pi\)
\(788\) −0.296895 + 0.249125i −0.0105765 + 0.00887471i
\(789\) 30.6012 8.45039i 1.08943 0.300842i
\(790\) 29.6012 + 24.8383i 1.05316 + 0.883708i
\(791\) 4.88821 20.1514i 0.173805 0.716502i
\(792\) −8.63076 9.97257i −0.306681 0.354360i
\(793\) −5.17379 −0.183727
\(794\) 39.1052 14.2331i 1.38779 0.505115i
\(795\) −9.60079 + 6.83233i −0.340505 + 0.242318i
\(796\) −1.86182 + 1.56225i −0.0659905 + 0.0553726i
\(797\) −12.2053 4.44238i −0.432335 0.157357i 0.116680 0.993170i \(-0.462775\pi\)
−0.549015 + 0.835812i \(0.684997\pi\)
\(798\) −4.56222 11.4051i −0.161501 0.403736i
\(799\) −2.43857 + 13.8298i −0.0862705 + 0.489265i
\(800\) −19.9303 −0.704642
\(801\) −1.82157 0.292599i −0.0643621 0.0103385i
\(802\) −9.44356 −0.333464
\(803\) 42.6060 15.5073i 1.50353 0.547241i
\(804\) −32.5560 + 8.99020i −1.14816 + 0.317060i
\(805\) 2.04511 3.07406i 0.0720808 0.108346i
\(806\) −9.42078 + 7.90497i −0.331833 + 0.278441i
\(807\) −4.48921 + 6.51655i −0.158028 + 0.229393i
\(808\) −8.73519 7.32969i −0.307303 0.257858i
\(809\) −14.8787 25.7707i −0.523109 0.906051i −0.999638 0.0268927i \(-0.991439\pi\)
0.476529 0.879159i \(-0.341895\pi\)
\(810\) 23.3415 + 7.69727i 0.820136 + 0.270454i
\(811\) 38.9051 1.36614 0.683072 0.730351i \(-0.260643\pi\)
0.683072 + 0.730351i \(0.260643\pi\)
\(812\) 19.8622 + 8.69209i 0.697028 + 0.305033i
\(813\) −22.8151 1.82072i −0.800160 0.0638554i
\(814\) −4.27357 24.2366i −0.149789 0.849493i
\(815\) −5.78496 + 4.85415i −0.202638 + 0.170034i
\(816\) −7.29518 7.18467i −0.255382 0.251514i
\(817\) −4.34921 + 1.58298i −0.152160 + 0.0553816i
\(818\) 21.2271 36.7664i 0.742188 1.28551i
\(819\) 7.75743 0.985419i 0.271066 0.0344333i
\(820\) −12.8912 22.3281i −0.450179 0.779733i
\(821\) 30.4574 + 25.5568i 1.06297 + 0.891939i 0.994397 0.105707i \(-0.0337104\pi\)
0.0685747 + 0.997646i \(0.478155\pi\)
\(822\) 6.83119 + 3.12219i 0.238265 + 0.108899i
\(823\) −6.77095 38.3999i −0.236020 1.33854i −0.840454 0.541883i \(-0.817712\pi\)
0.604434 0.796655i \(-0.293399\pi\)
\(824\) 9.46551 7.94251i 0.329747 0.276690i
\(825\) −2.14286 22.5127i −0.0746048 0.783793i
\(826\) 3.45506 + 30.9738i 0.120217 + 1.07772i
\(827\) 15.3937 + 26.6626i 0.535290 + 0.927150i 0.999149 + 0.0412408i \(0.0131311\pi\)
−0.463859 + 0.885909i \(0.653536\pi\)
\(828\) 2.77930 + 3.21140i 0.0965875 + 0.111604i
\(829\) −25.5293 −0.886669 −0.443335 0.896356i \(-0.646205\pi\)
−0.443335 + 0.896356i \(0.646205\pi\)
\(830\) 3.94689 22.3839i 0.136999 0.776958i
\(831\) −50.7129 + 14.0042i −1.75921 + 0.485799i
\(832\) 0.595091 + 3.37493i 0.0206311 + 0.117005i
\(833\) 8.46984 1.91339i 0.293463 0.0662951i
\(834\) −39.4142 + 57.2138i −1.36480 + 1.98115i
\(835\) 2.76274 15.6683i 0.0956087 0.542224i
\(836\) 4.86579 + 8.42779i 0.168287 + 0.291481i
\(837\) −28.9135 19.2743i −0.999397 0.666217i
\(838\) −28.3461 + 49.0969i −0.979201 + 1.69603i
\(839\) −15.4625 + 5.62791i −0.533826 + 0.194297i −0.594846 0.803840i \(-0.702787\pi\)
0.0610197 + 0.998137i \(0.480565\pi\)
\(840\) 4.30284 + 4.81209i 0.148462 + 0.166033i
\(841\) 1.13760 0.954559i 0.0392275 0.0329158i
\(842\) 54.9273 + 19.9919i 1.89292 + 0.688966i
\(843\) 32.5179 8.97969i 1.11998 0.309277i
\(844\) 1.64286 9.31712i 0.0565495 0.320708i
\(845\) −8.79965 15.2414i −0.302717 0.524322i
\(846\) 55.3786 + 30.8556i 1.90396 + 1.06084i
\(847\) −24.9987 + 7.34088i −0.858965 + 0.252236i
\(848\) 3.84818 21.8241i 0.132147 0.749443i
\(849\) −10.8812 + 7.74352i −0.373441 + 0.265757i
\(850\) −1.14975 6.52057i −0.0394362 0.223654i
\(851\) −0.478296 2.71255i −0.0163958 0.0929851i
\(852\) −24.3204 + 17.3075i −0.833205 + 0.592944i
\(853\) −1.40699 + 7.97942i −0.0481743 + 0.273210i −0.999374 0.0353643i \(-0.988741\pi\)
0.951200 + 0.308575i \(0.0998519\pi\)
\(854\) −6.11382 + 25.2039i −0.209211 + 0.862461i
\(855\) 5.50598 + 3.06779i 0.188301 + 0.104916i
\(856\) 5.31883 + 9.21248i 0.181794 + 0.314876i
\(857\) −1.18534 + 6.72238i −0.0404903 + 0.229632i −0.998337 0.0576480i \(-0.981640\pi\)
0.957847 + 0.287280i \(0.0927510\pi\)
\(858\) −14.0186 + 3.87117i −0.478586 + 0.132160i
\(859\) 42.9069 + 15.6168i 1.46397 + 0.532840i 0.946455 0.322837i \(-0.104636\pi\)
0.517511 + 0.855677i \(0.326859\pi\)
\(860\) −5.36099 + 4.49840i −0.182808 + 0.153394i
\(861\) 16.9928 51.6906i 0.579113 1.76161i
\(862\) 18.4445 6.71326i 0.628223 0.228655i
\(863\) 0.791478 1.37088i 0.0269422 0.0466653i −0.852240 0.523151i \(-0.824756\pi\)
0.879182 + 0.476486i \(0.158090\pi\)
\(864\) −32.4636 + 16.0528i −1.10443 + 0.546129i
\(865\) 8.85818 + 15.3428i 0.301187 + 0.521672i
\(866\) 2.05438 11.6510i 0.0698107 0.395916i
\(867\) −15.1923 + 22.0532i −0.515958 + 0.748966i
\(868\) 11.6617 + 23.5285i 0.395823 + 0.798608i
\(869\) −11.2189 63.6256i −0.380575 2.15835i
\(870\) −25.1738 + 6.95163i −0.853470 + 0.235682i
\(871\) 2.24769 12.7473i 0.0761601 0.431926i
\(872\) 18.3403 0.621081
\(873\) −11.2068 12.9491i −0.379293 0.438261i
\(874\) 1.27842 + 2.21429i 0.0432433 + 0.0748995i
\(875\) 3.37268 + 30.2353i 0.114017 + 1.02214i
\(876\) −2.41885 25.4123i −0.0817254 0.858602i
\(877\) 17.0243 14.2851i 0.574869 0.482372i −0.308389 0.951260i \(-0.599790\pi\)
0.883257 + 0.468888i \(0.155345\pi\)
\(878\) −6.55978 37.2024i −0.221382 1.25552i
\(879\) 21.5480 + 9.84848i 0.726795 + 0.332181i
\(880\) −24.3865 20.4627i −0.822068 0.689797i
\(881\) 12.8210 + 22.2065i 0.431949 + 0.748158i 0.997041 0.0768702i \(-0.0244927\pi\)
−0.565092 + 0.825028i \(0.691159\pi\)
\(882\) 4.36645 38.9545i 0.147026 1.31167i
\(883\) −17.2315 + 29.8458i −0.579886 + 1.00439i 0.415606 + 0.909545i \(0.363569\pi\)
−0.995492 + 0.0948467i \(0.969764\pi\)
\(884\) −1.70443 + 0.620362i −0.0573262 + 0.0208650i
\(885\) −11.3938 11.2212i −0.382998 0.377196i
\(886\) −12.6943 + 10.6518i −0.426474 + 0.357854i
\(887\) 2.16361 + 12.2704i 0.0726469 + 0.412001i 0.999345 + 0.0361938i \(0.0115234\pi\)
−0.926698 + 0.375807i \(0.877366\pi\)
\(888\) 4.80041 + 0.383089i 0.161091 + 0.0128556i
\(889\) 27.0655 19.9288i 0.907746 0.668390i
\(890\) −1.67942 −0.0562943
\(891\) −21.6233 34.9441i −0.724407 1.17067i
\(892\) −4.28964 7.42988i −0.143628 0.248771i
\(893\) 12.4539 + 10.4500i 0.416753 + 0.349697i
\(894\) −8.05631 + 11.6946i −0.269443 + 0.391125i
\(895\) −13.8723 + 11.6402i −0.463700 + 0.389090i
\(896\) −19.6620 1.24912i −0.656861 0.0417302i
\(897\) −1.56895 + 0.433260i −0.0523858 + 0.0144661i
\(898\) −21.1127 + 7.68438i −0.704538 + 0.256431i
\(899\) 36.9235 1.23147
\(900\) −12.5711 2.01929i −0.419036 0.0673096i
\(901\) 5.76840 0.192173
\(902\) −17.5725 + 99.6585i −0.585100 + 3.31827i
\(903\) −14.6185 2.10599i −0.486473 0.0700830i
\(904\) −7.09106 2.58094i −0.235845 0.0858407i
\(905\) −17.7861 + 14.9243i −0.591229 + 0.496100i
\(906\) 39.0447 27.7858i 1.29717 0.923123i
\(907\) −19.0510 + 6.93399i −0.632577 + 0.230239i −0.638353 0.769744i \(-0.720384\pi\)
0.00577554 + 0.999983i \(0.498162\pi\)
\(908\) 19.0304 0.631547
\(909\) −23.2505 26.8652i −0.771171 0.891063i
\(910\) 6.82988 2.00560i 0.226408 0.0664850i
\(911\) −16.6560 13.9761i −0.551838 0.463047i 0.323725 0.946151i \(-0.395065\pi\)
−0.875563 + 0.483104i \(0.839509\pi\)
\(912\) −11.4259 + 3.15520i −0.378348 + 0.104479i
\(913\) −29.1115 + 24.4275i −0.963451 + 0.808431i
\(914\) −5.64526 2.05471i −0.186729 0.0679637i
\(915\) −5.71589 12.0175i −0.188962 0.397285i
\(916\) 8.17391 2.97506i 0.270073 0.0982987i
\(917\) −5.23617 + 21.5859i −0.172913 + 0.712828i
\(918\) −7.12477 9.69500i −0.235152 0.319983i
\(919\) −8.04117 + 13.9277i −0.265254 + 0.459433i −0.967630 0.252373i \(-0.918789\pi\)
0.702376 + 0.711806i \(0.252122\pi\)
\(920\) −1.02930 0.863688i −0.0339351 0.0284749i
\(921\) −17.1105 + 24.8376i −0.563809 + 0.818427i
\(922\) 11.0709 + 62.7860i 0.364599 + 2.06775i
\(923\) −1.98653 11.2662i −0.0653874 0.370831i
\(924\) 0.976622 + 31.0390i 0.0321285 + 1.02111i
\(925\) 6.32551 + 5.30773i 0.207981 + 0.174517i
\(926\) 10.2119 + 17.6876i 0.335585 + 0.581250i
\(927\) 33.0441 19.7565i 1.08531 0.648890i
\(928\) 19.2410 33.3265i 0.631618 1.09399i
\(929\) −34.8423 29.2361i −1.14314 0.959206i −0.143601 0.989636i \(-0.545868\pi\)
−0.999537 + 0.0304292i \(0.990313\pi\)
\(930\) −28.7692 13.1489i −0.943380 0.431171i
\(931\) 2.98433 9.59917i 0.0978075 0.314600i
\(932\) −1.35494 0.493157i −0.0443824 0.0161539i
\(933\) −42.1800 + 30.0171i −1.38091 + 0.982716i
\(934\) −72.6279 + 26.4344i −2.37646 + 0.864960i
\(935\) 4.14320 7.17623i 0.135497 0.234688i
\(936\) −0.0434354 2.84543i −0.00141973 0.0930057i
\(937\) 19.6409 34.0190i 0.641639 1.11135i −0.343428 0.939179i \(-0.611588\pi\)
0.985067 0.172172i \(-0.0550784\pi\)
\(938\) −59.4420 26.0129i −1.94085 0.849352i
\(939\) −1.38127 + 5.31694i −0.0450759 + 0.173512i
\(940\) 23.0995 + 8.40753i 0.753423 + 0.274223i
\(941\) 34.2173 + 12.4541i 1.11545 + 0.405991i 0.832990 0.553288i \(-0.186627\pi\)
0.282461 + 0.959279i \(0.408849\pi\)
\(942\) −0.693715 + 1.00700i −0.0226025 + 0.0328098i
\(943\) −1.96670 + 11.1537i −0.0640447 + 0.363216i
\(944\) 30.0744 0.978837
\(945\) 10.8591 + 16.9300i 0.353248 + 0.550732i
\(946\) 27.4683 0.893071
\(947\) 2.93396 16.6393i 0.0953410 0.540705i −0.899301 0.437329i \(-0.855924\pi\)
0.994642 0.103376i \(-0.0329645\pi\)
\(948\) −36.2593 2.89361i −1.17765 0.0939802i
\(949\) 9.19319 + 3.34605i 0.298424 + 0.108617i
\(950\) −7.20286 2.62163i −0.233691 0.0850567i
\(951\) 8.24185 + 8.11700i 0.267260 + 0.263212i
\(952\) −0.350319 3.14053i −0.0113539 0.101785i
\(953\) −10.9661 + 18.9938i −0.355226 + 0.615270i −0.987157 0.159755i \(-0.948930\pi\)
0.631930 + 0.775025i \(0.282263\pi\)
\(954\) 8.53168 24.6027i 0.276223 0.796541i
\(955\) −11.1209 + 19.2620i −0.359865 + 0.623304i
\(956\) 33.1349 12.0601i 1.07166 0.390052i
\(957\) 39.7135 + 18.1510i 1.28375 + 0.586738i
\(958\) 14.5634 + 5.30066i 0.470523 + 0.171257i
\(959\) 2.72958 + 5.50718i 0.0881429 + 0.177836i
\(960\) −7.18170 + 5.11081i −0.231788 + 0.164951i
\(961\) 10.5115 + 8.82019i 0.339081 + 0.284522i
\(962\) 2.65513 4.59883i 0.0856049 0.148272i
\(963\) 11.8102 + 30.9691i 0.380579 + 0.997967i
\(964\) 0.212405 + 0.367897i 0.00684111 + 0.0118492i
\(965\) 21.0711 + 17.6808i 0.678303 + 0.569164i
\(966\) 0.256595 + 8.15508i 0.00825579 + 0.262385i
\(967\) 2.64027 + 14.9737i 0.0849053 + 0.481522i 0.997377 + 0.0723820i \(0.0230601\pi\)
−0.912472 + 0.409140i \(0.865829\pi\)
\(968\) 1.64647 + 9.33758i 0.0529195 + 0.300121i
\(969\) −1.32527 2.78632i −0.0425737 0.0895096i
\(970\) −11.9418 10.0204i −0.383428 0.321734i
\(971\) −12.0551 + 20.8800i −0.386866 + 0.670072i −0.992026 0.126032i \(-0.959776\pi\)
0.605160 + 0.796104i \(0.293109\pi\)
\(972\) −22.1029 + 6.83624i −0.708952 + 0.219272i
\(973\) −54.5521 + 16.0193i −1.74886 + 0.513554i
\(974\) −42.0039 + 15.2882i −1.34589 + 0.489864i
\(975\) 2.76822 4.01836i 0.0886541 0.128691i
\(976\) 23.5172 + 8.55958i 0.752769 + 0.273985i
\(977\) 22.0256 18.4817i 0.704662 0.591282i −0.218434 0.975852i \(-0.570095\pi\)
0.923096 + 0.384570i \(0.125650\pi\)
\(978\) 4.19603 16.1519i 0.134174 0.516480i
\(979\) 2.15099 + 1.80490i 0.0687460 + 0.0576848i
\(980\) −0.723903 15.1824i −0.0231242 0.484985i
\(981\) 56.4212 + 9.06292i 1.80139 + 0.289357i
\(982\) −73.3705 −2.34135
\(983\) −4.51817 + 1.64448i −0.144107 + 0.0524508i −0.413067 0.910701i \(-0.635542\pi\)
0.268960 + 0.963151i \(0.413320\pi\)
\(984\) −18.0097 8.23130i −0.574127 0.262404i
\(985\) 0.292665 0.245575i 0.00932509 0.00782468i
\(986\) 12.0134 + 4.37251i 0.382583 + 0.139249i
\(987\) 19.2679 + 48.1680i 0.613305 + 1.53320i
\(988\) −0.364627 + 2.06790i −0.0116003 + 0.0657887i
\(989\) 3.07424 0.0977551
\(990\) −24.4792 28.2850i −0.778001 0.898955i
\(991\) 52.7537 1.67578 0.837888 0.545842i \(-0.183790\pi\)
0.837888 + 0.545842i \(0.183790\pi\)
\(992\) 43.7986 15.9414i 1.39061 0.506140i
\(993\) −6.15712 6.06385i −0.195390 0.192430i
\(994\) −57.2303 3.63582i −1.81523 0.115321i
\(995\) 1.83529 1.53999i 0.0581827 0.0488211i
\(996\) 9.18998 + 19.3216i 0.291196 + 0.612228i
\(997\) 39.3451 + 33.0144i 1.24607 + 1.04558i 0.997024 + 0.0770861i \(0.0245616\pi\)
0.249046 + 0.968492i \(0.419883\pi\)
\(998\) −5.84523 10.1242i −0.185028 0.320477i
\(999\) 14.5785 + 3.55066i 0.461242 + 0.112338i
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 189.2.u.a.142.4 yes 132
3.2 odd 2 567.2.u.a.100.19 132
7.4 even 3 189.2.w.a.88.4 yes 132
21.11 odd 6 567.2.w.a.424.19 132
27.4 even 9 189.2.w.a.58.4 yes 132
27.23 odd 18 567.2.w.a.226.19 132
189.4 even 9 inner 189.2.u.a.4.4 132
189.158 odd 18 567.2.u.a.550.19 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.u.a.4.4 132 189.4 even 9 inner
189.2.u.a.142.4 yes 132 1.1 even 1 trivial
189.2.w.a.58.4 yes 132 27.4 even 9
189.2.w.a.88.4 yes 132 7.4 even 3
567.2.u.a.100.19 132 3.2 odd 2
567.2.u.a.550.19 132 189.158 odd 18
567.2.w.a.226.19 132 27.23 odd 18
567.2.w.a.424.19 132 21.11 odd 6