Properties

Label 729.2.g.b.55.8
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.8
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.b.676.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.964822 - 2.23671i) q^{2} +(-2.69950 - 2.86130i) q^{4} +(0.171598 + 2.94623i) q^{5} +(2.22815 + 0.528081i) q^{7} +(-4.42639 + 1.61107i) q^{8} +O(q^{10})\) \(q+(0.964822 - 2.23671i) q^{2} +(-2.69950 - 2.86130i) q^{4} +(0.171598 + 2.94623i) q^{5} +(2.22815 + 0.528081i) q^{7} +(-4.42639 + 1.61107i) q^{8} +(6.75541 + 2.45877i) q^{10} +(1.97872 + 1.30142i) q^{11} +(-0.609623 - 0.0712547i) q^{13} +(3.33093 - 4.47422i) q^{14} +(-0.209720 + 3.60075i) q^{16} +(5.54151 - 4.64988i) q^{17} +(-3.45309 - 2.89749i) q^{19} +(7.96681 - 8.44433i) q^{20} +(4.82002 - 3.17018i) q^{22} +(7.28714 - 1.72708i) q^{23} +(-3.68461 + 0.430669i) q^{25} +(-0.747554 + 1.29480i) q^{26} +(-4.50389 - 7.80096i) q^{28} +(1.29693 + 1.74208i) q^{29} +(-0.890466 + 2.97436i) q^{31} +(-0.567355 - 0.284936i) q^{32} +(-5.05386 - 16.8811i) q^{34} +(-1.17350 + 6.65525i) q^{35} +(0.740274 + 4.19830i) q^{37} +(-9.81244 + 4.92800i) q^{38} +(-5.50614 - 12.7647i) q^{40} +(2.55020 + 5.91203i) q^{41} +(-3.63470 + 1.82541i) q^{43} +(-1.61778 - 9.17491i) q^{44} +(3.16781 - 17.9655i) q^{46} +(-0.248155 - 0.828895i) q^{47} +(-1.56965 - 0.788307i) q^{49} +(-2.59171 + 8.65691i) q^{50} +(1.44180 + 1.93667i) q^{52} +(1.55323 + 2.69028i) q^{53} +(-3.49475 + 6.05308i) q^{55} +(-10.7134 + 1.25222i) q^{56} +(5.14783 - 1.22006i) q^{58} +(0.512703 - 0.337210i) q^{59} +(3.75166 - 3.97653i) q^{61} +(5.79364 + 4.86144i) q^{62} +(-6.71074 + 5.63098i) q^{64} +(0.105322 - 1.80831i) q^{65} +(0.168582 - 0.226445i) q^{67} +(-28.2640 - 3.30359i) q^{68} +(13.7536 + 9.04591i) q^{70} +(-7.71930 - 2.80960i) q^{71} +(-14.3245 + 5.21369i) q^{73} +(10.1046 + 2.39484i) q^{74} +(1.03103 + 17.7021i) q^{76} +(3.72163 + 3.94469i) q^{77} +(2.95265 - 6.84501i) q^{79} -10.6446 q^{80} +15.6840 q^{82} +(2.16942 - 5.02929i) q^{83} +(14.6505 + 15.5286i) q^{85} +(0.576083 + 9.89096i) q^{86} +(-10.8553 - 2.57274i) q^{88} +(-8.64084 + 3.14501i) q^{89} +(-1.32070 - 0.480697i) q^{91} +(-24.6133 - 16.1885i) q^{92} +(-2.09342 - 0.244686i) q^{94} +(7.94410 - 10.6708i) q^{95} +(0.0995190 - 1.70867i) q^{97} +(-3.27764 + 2.75027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.964822 2.23671i 0.682232 1.58159i −0.125535 0.992089i \(-0.540065\pi\)
0.807767 0.589502i \(-0.200676\pi\)
\(3\) 0 0
\(4\) −2.69950 2.86130i −1.34975 1.43065i
\(5\) 0.171598 + 2.94623i 0.0767410 + 1.31759i 0.788442 + 0.615109i \(0.210888\pi\)
−0.711701 + 0.702483i \(0.752075\pi\)
\(6\) 0 0
\(7\) 2.22815 + 0.528081i 0.842161 + 0.199596i 0.628985 0.777418i \(-0.283471\pi\)
0.213177 + 0.977014i \(0.431619\pi\)
\(8\) −4.42639 + 1.61107i −1.56496 + 0.569600i
\(9\) 0 0
\(10\) 6.75541 + 2.45877i 2.13625 + 0.777531i
\(11\) 1.97872 + 1.30142i 0.596606 + 0.392394i 0.811593 0.584223i \(-0.198601\pi\)
−0.214987 + 0.976617i \(0.568971\pi\)
\(12\) 0 0
\(13\) −0.609623 0.0712547i −0.169079 0.0197625i 0.0311321 0.999515i \(-0.490089\pi\)
−0.200211 + 0.979753i \(0.564163\pi\)
\(14\) 3.33093 4.47422i 0.890229 1.19578i
\(15\) 0 0
\(16\) −0.209720 + 3.60075i −0.0524300 + 0.900188i
\(17\) 5.54151 4.64988i 1.34401 1.12776i 0.363439 0.931618i \(-0.381602\pi\)
0.980575 0.196144i \(-0.0628421\pi\)
\(18\) 0 0
\(19\) −3.45309 2.89749i −0.792193 0.664729i 0.154094 0.988056i \(-0.450754\pi\)
−0.946287 + 0.323327i \(0.895199\pi\)
\(20\) 7.96681 8.44433i 1.78143 1.88821i
\(21\) 0 0
\(22\) 4.82002 3.17018i 1.02763 0.675884i
\(23\) 7.28714 1.72708i 1.51947 0.360122i 0.615648 0.788021i \(-0.288894\pi\)
0.903826 + 0.427899i \(0.140746\pi\)
\(24\) 0 0
\(25\) −3.68461 + 0.430669i −0.736922 + 0.0861338i
\(26\) −0.747554 + 1.29480i −0.146607 + 0.253931i
\(27\) 0 0
\(28\) −4.50389 7.80096i −0.851155 1.47424i
\(29\) 1.29693 + 1.74208i 0.240834 + 0.323496i 0.906063 0.423143i \(-0.139073\pi\)
−0.665229 + 0.746640i \(0.731666\pi\)
\(30\) 0 0
\(31\) −0.890466 + 2.97436i −0.159932 + 0.534212i −0.999965 0.00832388i \(-0.997350\pi\)
0.840033 + 0.542535i \(0.182536\pi\)
\(32\) −0.567355 0.284936i −0.100295 0.0503701i
\(33\) 0 0
\(34\) −5.05386 16.8811i −0.866729 2.89508i
\(35\) −1.17350 + 6.65525i −0.198358 + 1.12494i
\(36\) 0 0
\(37\) 0.740274 + 4.19830i 0.121700 + 0.690197i 0.983213 + 0.182461i \(0.0584063\pi\)
−0.861513 + 0.507736i \(0.830483\pi\)
\(38\) −9.81244 + 4.92800i −1.59179 + 0.799426i
\(39\) 0 0
\(40\) −5.50614 12.7647i −0.870598 2.01827i
\(41\) 2.55020 + 5.91203i 0.398275 + 0.923305i 0.992861 + 0.119273i \(0.0380564\pi\)
−0.594587 + 0.804031i \(0.702684\pi\)
\(42\) 0 0
\(43\) −3.63470 + 1.82541i −0.554286 + 0.278373i −0.703814 0.710385i \(-0.748521\pi\)
0.149527 + 0.988758i \(0.452225\pi\)
\(44\) −1.61778 9.17491i −0.243890 1.38317i
\(45\) 0 0
\(46\) 3.16781 17.9655i 0.467068 2.64887i
\(47\) −0.248155 0.828895i −0.0361971 0.120907i 0.937982 0.346685i \(-0.112693\pi\)
−0.974179 + 0.225778i \(0.927508\pi\)
\(48\) 0 0
\(49\) −1.56965 0.788307i −0.224235 0.112615i
\(50\) −2.59171 + 8.65691i −0.366523 + 1.22427i
\(51\) 0 0
\(52\) 1.44180 + 1.93667i 0.199941 + 0.268568i
\(53\) 1.55323 + 2.69028i 0.213353 + 0.369538i 0.952762 0.303718i \(-0.0982282\pi\)
−0.739409 + 0.673257i \(0.764895\pi\)
\(54\) 0 0
\(55\) −3.49475 + 6.05308i −0.471231 + 0.816197i
\(56\) −10.7134 + 1.25222i −1.43164 + 0.167335i
\(57\) 0 0
\(58\) 5.14783 1.22006i 0.675943 0.160202i
\(59\) 0.512703 0.337210i 0.0667483 0.0439010i −0.515696 0.856771i \(-0.672467\pi\)
0.582445 + 0.812870i \(0.302096\pi\)
\(60\) 0 0
\(61\) 3.75166 3.97653i 0.480351 0.509142i −0.441195 0.897411i \(-0.645445\pi\)
0.921546 + 0.388269i \(0.126927\pi\)
\(62\) 5.79364 + 4.86144i 0.735793 + 0.617404i
\(63\) 0 0
\(64\) −6.71074 + 5.63098i −0.838842 + 0.703872i
\(65\) 0.105322 1.80831i 0.0130636 0.224294i
\(66\) 0 0
\(67\) 0.168582 0.226445i 0.0205956 0.0276647i −0.791706 0.610902i \(-0.790807\pi\)
0.812302 + 0.583237i \(0.198214\pi\)
\(68\) −28.2640 3.30359i −3.42752 0.400619i
\(69\) 0 0
\(70\) 13.7536 + 9.04591i 1.64387 + 1.08119i
\(71\) −7.71930 2.80960i −0.916113 0.333438i −0.159422 0.987211i \(-0.550963\pi\)
−0.756691 + 0.653773i \(0.773185\pi\)
\(72\) 0 0
\(73\) −14.3245 + 5.21369i −1.67656 + 0.610216i −0.992831 0.119525i \(-0.961863\pi\)
−0.683724 + 0.729741i \(0.739641\pi\)
\(74\) 10.1046 + 2.39484i 1.17464 + 0.278394i
\(75\) 0 0
\(76\) 1.03103 + 17.7021i 0.118267 + 2.03057i
\(77\) 3.72163 + 3.94469i 0.424119 + 0.449539i
\(78\) 0 0
\(79\) 2.95265 6.84501i 0.332199 0.770123i −0.667476 0.744631i \(-0.732625\pi\)
0.999675 0.0254922i \(-0.00811529\pi\)
\(80\) −10.6446 −1.19010
\(81\) 0 0
\(82\) 15.6840 1.73201
\(83\) 2.16942 5.02929i 0.238125 0.552036i −0.756686 0.653779i \(-0.773183\pi\)
0.994811 + 0.101743i \(0.0324419\pi\)
\(84\) 0 0
\(85\) 14.6505 + 15.5286i 1.58907 + 1.68432i
\(86\) 0.576083 + 9.89096i 0.0621206 + 1.06657i
\(87\) 0 0
\(88\) −10.8553 2.57274i −1.15717 0.274255i
\(89\) −8.64084 + 3.14501i −0.915927 + 0.333370i −0.756617 0.653858i \(-0.773149\pi\)
−0.159310 + 0.987229i \(0.550927\pi\)
\(90\) 0 0
\(91\) −1.32070 0.480697i −0.138447 0.0503907i
\(92\) −24.6133 16.1885i −2.56612 1.68776i
\(93\) 0 0
\(94\) −2.09342 0.244686i −0.215920 0.0252374i
\(95\) 7.94410 10.6708i 0.815048 1.09480i
\(96\) 0 0
\(97\) 0.0995190 1.70867i 0.0101046 0.173490i −0.989480 0.144670i \(-0.953788\pi\)
0.999585 0.0288199i \(-0.00917493\pi\)
\(98\) −3.27764 + 2.75027i −0.331092 + 0.277819i
\(99\) 0 0
\(100\) 11.1789 + 9.38019i 1.11789 + 0.938019i
\(101\) −5.81634 + 6.16496i −0.578747 + 0.613436i −0.948916 0.315528i \(-0.897818\pi\)
0.370169 + 0.928964i \(0.379300\pi\)
\(102\) 0 0
\(103\) 1.51566 0.996863i 0.149342 0.0982238i −0.472639 0.881256i \(-0.656698\pi\)
0.621981 + 0.783032i \(0.286328\pi\)
\(104\) 2.81322 0.666746i 0.275859 0.0653798i
\(105\) 0 0
\(106\) 7.51596 0.878490i 0.730015 0.0853265i
\(107\) −2.26668 + 3.92601i −0.219129 + 0.379542i −0.954542 0.298077i \(-0.903655\pi\)
0.735413 + 0.677619i \(0.236988\pi\)
\(108\) 0 0
\(109\) −6.62630 11.4771i −0.634684 1.09931i −0.986582 0.163267i \(-0.947797\pi\)
0.351898 0.936039i \(-0.385537\pi\)
\(110\) 10.1672 + 13.6569i 0.969401 + 1.30213i
\(111\) 0 0
\(112\) −2.36878 + 7.91226i −0.223828 + 0.747639i
\(113\) 3.83584 + 1.92643i 0.360845 + 0.181223i 0.619979 0.784618i \(-0.287141\pi\)
−0.259134 + 0.965841i \(0.583437\pi\)
\(114\) 0 0
\(115\) 6.33884 + 21.1732i 0.591100 + 1.97441i
\(116\) 1.48355 8.41365i 0.137745 0.781188i
\(117\) 0 0
\(118\) −0.259574 1.47211i −0.0238957 0.135519i
\(119\) 14.8028 7.43426i 1.35697 0.681498i
\(120\) 0 0
\(121\) −2.13525 4.95007i −0.194114 0.450006i
\(122\) −5.27465 12.2280i −0.477544 1.10707i
\(123\) 0 0
\(124\) 10.9144 5.48140i 0.980139 0.492244i
\(125\) 0.661249 + 3.75013i 0.0591439 + 0.335422i
\(126\) 0 0
\(127\) −1.02230 + 5.79777i −0.0907147 + 0.514469i 0.905262 + 0.424854i \(0.139675\pi\)
−0.995977 + 0.0896144i \(0.971437\pi\)
\(128\) 5.75601 + 19.2264i 0.508764 + 1.69939i
\(129\) 0 0
\(130\) −3.94305 1.98028i −0.345829 0.173682i
\(131\) −3.74549 + 12.5108i −0.327245 + 1.09307i 0.623169 + 0.782087i \(0.285845\pi\)
−0.950414 + 0.310987i \(0.899340\pi\)
\(132\) 0 0
\(133\) −6.16389 8.27954i −0.534477 0.717927i
\(134\) −0.343840 0.595549i −0.0297033 0.0514476i
\(135\) 0 0
\(136\) −17.0376 + 29.5099i −1.46096 + 2.53046i
\(137\) 4.49660 0.525577i 0.384170 0.0449030i 0.0781838 0.996939i \(-0.475088\pi\)
0.305986 + 0.952036i \(0.401014\pi\)
\(138\) 0 0
\(139\) −4.66352 + 1.10527i −0.395555 + 0.0937482i −0.423579 0.905859i \(-0.639226\pi\)
0.0280246 + 0.999607i \(0.491078\pi\)
\(140\) 22.2105 14.6081i 1.87713 1.23461i
\(141\) 0 0
\(142\) −13.7320 + 14.5551i −1.15236 + 1.22143i
\(143\) −1.11354 0.934372i −0.0931189 0.0781361i
\(144\) 0 0
\(145\) −4.91001 + 4.11999i −0.407754 + 0.342146i
\(146\) −2.15908 + 37.0700i −0.178687 + 3.06793i
\(147\) 0 0
\(148\) 10.0142 13.4515i 0.823166 1.10570i
\(149\) −9.74923 1.13952i −0.798688 0.0933532i −0.293048 0.956098i \(-0.594669\pi\)
−0.505640 + 0.862745i \(0.668744\pi\)
\(150\) 0 0
\(151\) −11.1565 7.33774i −0.907902 0.597137i 0.00736985 0.999973i \(-0.497654\pi\)
−0.915272 + 0.402836i \(0.868024\pi\)
\(152\) 19.9528 + 7.26221i 1.61838 + 0.589043i
\(153\) 0 0
\(154\) 12.4138 4.51826i 1.00033 0.364092i
\(155\) −8.91595 2.11312i −0.716146 0.169730i
\(156\) 0 0
\(157\) 0.174383 + 2.99403i 0.0139172 + 0.238950i 0.998092 + 0.0617480i \(0.0196675\pi\)
−0.984175 + 0.177202i \(0.943295\pi\)
\(158\) −12.4615 13.2084i −0.991384 1.05081i
\(159\) 0 0
\(160\) 0.742130 1.72045i 0.0586705 0.136014i
\(161\) 17.1489 1.35152
\(162\) 0 0
\(163\) 17.7302 1.38874 0.694370 0.719618i \(-0.255683\pi\)
0.694370 + 0.719618i \(0.255683\pi\)
\(164\) 10.0318 23.2564i 0.783355 1.81602i
\(165\) 0 0
\(166\) −9.15595 9.70474i −0.710639 0.753234i
\(167\) −1.27868 21.9542i −0.0989476 1.69886i −0.573958 0.818885i \(-0.694593\pi\)
0.475011 0.879980i \(-0.342444\pi\)
\(168\) 0 0
\(169\) −12.2830 2.91113i −0.944848 0.223933i
\(170\) 48.8682 17.7866i 3.74802 1.36417i
\(171\) 0 0
\(172\) 15.0349 + 5.47227i 1.14640 + 0.417256i
\(173\) 9.04414 + 5.94843i 0.687614 + 0.452251i 0.844634 0.535345i \(-0.179818\pi\)
−0.157020 + 0.987595i \(0.550189\pi\)
\(174\) 0 0
\(175\) −8.43729 0.986177i −0.637799 0.0745480i
\(176\) −5.10108 + 6.85194i −0.384509 + 0.516485i
\(177\) 0 0
\(178\) −1.30240 + 22.3614i −0.0976193 + 1.67606i
\(179\) 6.84973 5.74761i 0.511973 0.429596i −0.349850 0.936806i \(-0.613767\pi\)
0.861823 + 0.507210i \(0.169323\pi\)
\(180\) 0 0
\(181\) 3.31310 + 2.78002i 0.246261 + 0.206637i 0.757560 0.652765i \(-0.226391\pi\)
−0.511299 + 0.859403i \(0.670836\pi\)
\(182\) −2.34942 + 2.49024i −0.174151 + 0.184589i
\(183\) 0 0
\(184\) −29.4732 + 19.3849i −2.17280 + 1.42907i
\(185\) −12.2421 + 2.90144i −0.900059 + 0.213318i
\(186\) 0 0
\(187\) 17.0166 1.98895i 1.24437 0.145447i
\(188\) −1.70182 + 2.94765i −0.124118 + 0.214979i
\(189\) 0 0
\(190\) −16.2028 28.0640i −1.17547 2.03598i
\(191\) −12.6673 17.0151i −0.916570 1.23117i −0.972540 0.232735i \(-0.925233\pi\)
0.0559700 0.998432i \(-0.482175\pi\)
\(192\) 0 0
\(193\) 5.20688 17.3922i 0.374799 1.25192i −0.537804 0.843070i \(-0.680746\pi\)
0.912603 0.408847i \(-0.134069\pi\)
\(194\) −3.72579 1.87116i −0.267496 0.134342i
\(195\) 0 0
\(196\) 1.98168 + 6.61927i 0.141548 + 0.472805i
\(197\) −1.23957 + 7.02994i −0.0883155 + 0.500862i 0.908276 + 0.418371i \(0.137399\pi\)
−0.996592 + 0.0824914i \(0.973712\pi\)
\(198\) 0 0
\(199\) −0.634860 3.60047i −0.0450040 0.255231i 0.954002 0.299799i \(-0.0969197\pi\)
−0.999006 + 0.0445688i \(0.985809\pi\)
\(200\) 15.6157 7.84248i 1.10419 0.554547i
\(201\) 0 0
\(202\) 8.17748 + 18.9575i 0.575366 + 1.33385i
\(203\) 1.96980 + 4.56650i 0.138253 + 0.320505i
\(204\) 0 0
\(205\) −16.9806 + 8.52797i −1.18597 + 0.595619i
\(206\) −0.767353 4.35187i −0.0534640 0.303209i
\(207\) 0 0
\(208\) 0.384421 2.18016i 0.0266548 0.151167i
\(209\) −3.06184 10.2272i −0.211792 0.707433i
\(210\) 0 0
\(211\) −15.9532 8.01201i −1.09827 0.551570i −0.195066 0.980790i \(-0.562492\pi\)
−0.903200 + 0.429220i \(0.858788\pi\)
\(212\) 3.50475 11.7067i 0.240707 0.804018i
\(213\) 0 0
\(214\) 6.59440 + 8.85781i 0.450784 + 0.605508i
\(215\) −6.00179 10.3954i −0.409319 0.708961i
\(216\) 0 0
\(217\) −3.55480 + 6.15709i −0.241315 + 0.417970i
\(218\) −32.0641 + 3.74775i −2.17165 + 0.253830i
\(219\) 0 0
\(220\) 26.7537 6.34075i 1.80374 0.427493i
\(221\) −3.70956 + 2.43982i −0.249532 + 0.164120i
\(222\) 0 0
\(223\) 9.68032 10.2605i 0.648242 0.687096i −0.317008 0.948423i \(-0.602678\pi\)
0.965251 + 0.261326i \(0.0841598\pi\)
\(224\) −1.11368 0.934490i −0.0744110 0.0624383i
\(225\) 0 0
\(226\) 8.00976 6.72099i 0.532801 0.447073i
\(227\) −0.334510 + 5.74332i −0.0222022 + 0.381197i 0.968843 + 0.247674i \(0.0796662\pi\)
−0.991046 + 0.133523i \(0.957371\pi\)
\(228\) 0 0
\(229\) −14.6753 + 19.7124i −0.969772 + 1.30263i −0.0167077 + 0.999860i \(0.505318\pi\)
−0.953064 + 0.302769i \(0.902089\pi\)
\(230\) 53.4741 + 6.25023i 3.52598 + 0.412128i
\(231\) 0 0
\(232\) −8.54733 5.62167i −0.561160 0.369081i
\(233\) −11.9802 4.36045i −0.784852 0.285663i −0.0816576 0.996660i \(-0.526021\pi\)
−0.703194 + 0.710998i \(0.748244\pi\)
\(234\) 0 0
\(235\) 2.39953 0.873357i 0.156528 0.0569715i
\(236\) −2.34890 0.556700i −0.152900 0.0362381i
\(237\) 0 0
\(238\) −2.34618 40.2824i −0.152080 2.61112i
\(239\) 16.7115 + 17.7132i 1.08098 + 1.14577i 0.988680 + 0.150038i \(0.0479396\pi\)
0.0922975 + 0.995731i \(0.470579\pi\)
\(240\) 0 0
\(241\) −11.5147 + 26.6940i −0.741725 + 1.71951i −0.0484641 + 0.998825i \(0.515433\pi\)
−0.693261 + 0.720687i \(0.743827\pi\)
\(242\) −13.1320 −0.844157
\(243\) 0 0
\(244\) −21.5057 −1.37676
\(245\) 2.05318 4.75981i 0.131173 0.304093i
\(246\) 0 0
\(247\) 1.89862 + 2.01242i 0.120807 + 0.128047i
\(248\) −0.850370 14.6003i −0.0539985 0.927119i
\(249\) 0 0
\(250\) 9.02593 + 2.13918i 0.570850 + 0.135294i
\(251\) −22.4049 + 8.15471i −1.41418 + 0.514721i −0.932355 0.361545i \(-0.882249\pi\)
−0.481828 + 0.876266i \(0.660027\pi\)
\(252\) 0 0
\(253\) 16.6669 + 6.06625i 1.04784 + 0.381382i
\(254\) 11.9816 + 7.88040i 0.751791 + 0.494460i
\(255\) 0 0
\(256\) 31.1554 + 3.64154i 1.94721 + 0.227596i
\(257\) −7.24789 + 9.73561i −0.452111 + 0.607291i −0.968485 0.249073i \(-0.919874\pi\)
0.516374 + 0.856363i \(0.327282\pi\)
\(258\) 0 0
\(259\) −0.567604 + 9.74538i −0.0352692 + 0.605548i
\(260\) −5.45845 + 4.58018i −0.338519 + 0.284051i
\(261\) 0 0
\(262\) 24.3693 + 20.4483i 1.50554 + 1.26330i
\(263\) 5.49109 5.82022i 0.338595 0.358890i −0.535594 0.844476i \(-0.679912\pi\)
0.874189 + 0.485586i \(0.161394\pi\)
\(264\) 0 0
\(265\) −7.65964 + 5.03782i −0.470528 + 0.309471i
\(266\) −24.4660 + 5.79854i −1.50011 + 0.355531i
\(267\) 0 0
\(268\) −1.10302 + 0.128924i −0.0673774 + 0.00787529i
\(269\) 11.2578 19.4990i 0.686397 1.18887i −0.286598 0.958051i \(-0.592524\pi\)
0.972995 0.230824i \(-0.0741422\pi\)
\(270\) 0 0
\(271\) 15.1514 + 26.2430i 0.920381 + 1.59415i 0.798826 + 0.601562i \(0.205455\pi\)
0.121555 + 0.992585i \(0.461212\pi\)
\(272\) 15.5809 + 20.9288i 0.944731 + 1.26899i
\(273\) 0 0
\(274\) 3.16285 10.5647i 0.191075 0.638234i
\(275\) −7.85129 3.94307i −0.473451 0.237776i
\(276\) 0 0
\(277\) 1.26874 + 4.23789i 0.0762312 + 0.254630i 0.987607 0.156944i \(-0.0501643\pi\)
−0.911376 + 0.411574i \(0.864979\pi\)
\(278\) −2.02729 + 11.4973i −0.121589 + 0.689564i
\(279\) 0 0
\(280\) −5.52773 31.3493i −0.330345 1.87348i
\(281\) −5.06519 + 2.54383i −0.302164 + 0.151752i −0.593421 0.804893i \(-0.702223\pi\)
0.291257 + 0.956645i \(0.405927\pi\)
\(282\) 0 0
\(283\) 11.4164 + 26.4661i 0.678632 + 1.57324i 0.812968 + 0.582309i \(0.197851\pi\)
−0.134336 + 0.990936i \(0.542890\pi\)
\(284\) 12.7991 + 29.6718i 0.759490 + 1.76069i
\(285\) 0 0
\(286\) −3.16428 + 1.58916i −0.187108 + 0.0939692i
\(287\) 2.56020 + 14.5196i 0.151124 + 0.857065i
\(288\) 0 0
\(289\) 6.13495 34.7930i 0.360879 2.04665i
\(290\) 4.47793 + 14.9573i 0.262953 + 0.878324i
\(291\) 0 0
\(292\) 53.5869 + 26.9123i 3.13594 + 1.57493i
\(293\) 0.620892 2.07392i 0.0362729 0.121160i −0.937936 0.346809i \(-0.887265\pi\)
0.974209 + 0.225649i \(0.0724503\pi\)
\(294\) 0 0
\(295\) 1.08148 + 1.45267i 0.0629660 + 0.0845780i
\(296\) −10.0405 17.3907i −0.583593 1.01081i
\(297\) 0 0
\(298\) −11.9550 + 20.7067i −0.692537 + 1.19951i
\(299\) −4.56548 + 0.533627i −0.264028 + 0.0308605i
\(300\) 0 0
\(301\) −9.06262 + 2.14788i −0.522361 + 0.123802i
\(302\) −27.1764 + 17.8742i −1.56383 + 1.02854i
\(303\) 0 0
\(304\) 11.1573 11.8261i 0.639915 0.678271i
\(305\) 12.3595 + 10.3709i 0.707704 + 0.593835i
\(306\) 0 0
\(307\) 3.63465 3.04984i 0.207441 0.174063i −0.533148 0.846022i \(-0.678991\pi\)
0.740589 + 0.671959i \(0.234547\pi\)
\(308\) 1.24043 21.2974i 0.0706801 1.21353i
\(309\) 0 0
\(310\) −13.3287 + 17.9036i −0.757021 + 1.01686i
\(311\) 23.4449 + 2.74032i 1.32944 + 0.155389i 0.750981 0.660323i \(-0.229581\pi\)
0.578458 + 0.815713i \(0.303655\pi\)
\(312\) 0 0
\(313\) −19.7427 12.9850i −1.11592 0.733955i −0.148955 0.988844i \(-0.547591\pi\)
−0.966970 + 0.254889i \(0.917961\pi\)
\(314\) 6.86503 + 2.49867i 0.387416 + 0.141008i
\(315\) 0 0
\(316\) −27.5563 + 10.0297i −1.55016 + 0.564213i
\(317\) −33.1557 7.85805i −1.86221 0.441352i −0.864129 0.503270i \(-0.832130\pi\)
−0.998081 + 0.0619179i \(0.980278\pi\)
\(318\) 0 0
\(319\) 0.299076 + 5.13494i 0.0167451 + 0.287502i
\(320\) −17.7417 18.8051i −0.991790 1.05124i
\(321\) 0 0
\(322\) 16.5456 38.3571i 0.922051 2.13756i
\(323\) −32.6083 −1.81437
\(324\) 0 0
\(325\) 2.27691 0.126300
\(326\) 17.1065 39.6574i 0.947443 2.19642i
\(327\) 0 0
\(328\) −20.8129 22.0604i −1.14920 1.21808i
\(329\) −0.115202 1.97795i −0.00635131 0.109048i
\(330\) 0 0
\(331\) 25.2281 + 5.97918i 1.38666 + 0.328645i 0.855140 0.518398i \(-0.173471\pi\)
0.531524 + 0.847043i \(0.321619\pi\)
\(332\) −20.2467 + 7.36919i −1.11118 + 0.404437i
\(333\) 0 0
\(334\) −50.3388 18.3218i −2.75441 1.00252i
\(335\) 0.696087 + 0.457824i 0.0380313 + 0.0250136i
\(336\) 0 0
\(337\) −22.0017 2.57162i −1.19851 0.140085i −0.506670 0.862140i \(-0.669124\pi\)
−0.691836 + 0.722055i \(0.743198\pi\)
\(338\) −18.3623 + 24.6648i −0.998776 + 1.34159i
\(339\) 0 0
\(340\) 4.88307 83.8391i 0.264822 4.54681i
\(341\) −5.63289 + 4.72656i −0.305038 + 0.255957i
\(342\) 0 0
\(343\) −15.3601 12.8887i −0.829369 0.695923i
\(344\) 13.1477 13.9357i 0.708877 0.751365i
\(345\) 0 0
\(346\) 22.0309 14.4899i 1.18439 0.778984i
\(347\) −1.74506 + 0.413587i −0.0936797 + 0.0222025i −0.277188 0.960816i \(-0.589403\pi\)
0.183509 + 0.983018i \(0.441254\pi\)
\(348\) 0 0
\(349\) −0.174688 + 0.0204181i −0.00935083 + 0.00109295i −0.120767 0.992681i \(-0.538535\pi\)
0.111416 + 0.993774i \(0.464461\pi\)
\(350\) −10.3463 + 17.9203i −0.553031 + 0.957878i
\(351\) 0 0
\(352\) −0.751813 1.30218i −0.0400718 0.0694064i
\(353\) 18.1618 + 24.3956i 0.966656 + 1.29844i 0.954404 + 0.298520i \(0.0964928\pi\)
0.0122526 + 0.999925i \(0.496100\pi\)
\(354\) 0 0
\(355\) 6.95309 23.2249i 0.369032 1.23265i
\(356\) 32.3247 + 16.2341i 1.71321 + 0.860406i
\(357\) 0 0
\(358\) −6.24695 20.8663i −0.330161 1.10282i
\(359\) 1.11991 6.35130i 0.0591064 0.335209i −0.940887 0.338719i \(-0.890006\pi\)
0.999994 + 0.00351034i \(0.00111738\pi\)
\(360\) 0 0
\(361\) 0.229085 + 1.29920i 0.0120571 + 0.0683792i
\(362\) 9.41464 4.72821i 0.494823 0.248509i
\(363\) 0 0
\(364\) 2.18982 + 5.07657i 0.114778 + 0.266085i
\(365\) −17.8188 41.3085i −0.932677 2.16219i
\(366\) 0 0
\(367\) 16.4470 8.26000i 0.858527 0.431169i 0.0356343 0.999365i \(-0.488655\pi\)
0.822893 + 0.568196i \(0.192359\pi\)
\(368\) 4.69054 + 26.6014i 0.244512 + 1.38669i
\(369\) 0 0
\(370\) −5.32180 + 30.1814i −0.276667 + 1.56906i
\(371\) 2.04015 + 6.81458i 0.105919 + 0.353795i
\(372\) 0 0
\(373\) −28.8505 14.4893i −1.49382 0.750227i −0.500517 0.865727i \(-0.666857\pi\)
−0.993307 + 0.115500i \(0.963153\pi\)
\(374\) 11.9693 39.9801i 0.618915 2.06732i
\(375\) 0 0
\(376\) 2.43384 + 3.26921i 0.125516 + 0.168597i
\(377\) −0.666508 1.15442i −0.0343269 0.0594559i
\(378\) 0 0
\(379\) 11.0163 19.0808i 0.565870 0.980116i −0.431098 0.902305i \(-0.641874\pi\)
0.996968 0.0778111i \(-0.0247931\pi\)
\(380\) −51.9774 + 6.07529i −2.66639 + 0.311656i
\(381\) 0 0
\(382\) −50.2794 + 11.9164i −2.57252 + 0.609698i
\(383\) −11.8857 + 7.81734i −0.607330 + 0.399447i −0.815593 0.578626i \(-0.803589\pi\)
0.208263 + 0.978073i \(0.433219\pi\)
\(384\) 0 0
\(385\) −10.9833 + 11.6417i −0.559762 + 0.593313i
\(386\) −33.8775 28.4266i −1.72432 1.44688i
\(387\) 0 0
\(388\) −5.15768 + 4.32781i −0.261842 + 0.219711i
\(389\) 0.713209 12.2453i 0.0361612 0.620863i −0.930735 0.365694i \(-0.880832\pi\)
0.966896 0.255169i \(-0.0821312\pi\)
\(390\) 0 0
\(391\) 32.3511 43.4550i 1.63606 2.19761i
\(392\) 8.21788 + 0.960533i 0.415066 + 0.0485142i
\(393\) 0 0
\(394\) 14.5280 + 9.55519i 0.731908 + 0.481383i
\(395\) 20.6736 + 7.52457i 1.04020 + 0.378602i
\(396\) 0 0
\(397\) −9.12859 + 3.32254i −0.458151 + 0.166753i −0.560777 0.827967i \(-0.689498\pi\)
0.102626 + 0.994720i \(0.467275\pi\)
\(398\) −8.66573 2.05382i −0.434374 0.102948i
\(399\) 0 0
\(400\) −0.777996 13.3577i −0.0388998 0.667884i
\(401\) 0.802397 + 0.850491i 0.0400698 + 0.0424715i 0.747098 0.664713i \(-0.231446\pi\)
−0.707029 + 0.707185i \(0.749965\pi\)
\(402\) 0 0
\(403\) 0.754786 1.74979i 0.0375986 0.0871633i
\(404\) 33.3410 1.65878
\(405\) 0 0
\(406\) 12.1144 0.601229
\(407\) −3.99898 + 9.27068i −0.198222 + 0.459530i
\(408\) 0 0
\(409\) 18.8448 + 19.9743i 0.931816 + 0.987668i 0.999950 0.0100086i \(-0.00318588\pi\)
−0.0681336 + 0.997676i \(0.521704\pi\)
\(410\) 2.69134 + 46.2086i 0.132916 + 2.28208i
\(411\) 0 0
\(412\) −6.94384 1.64572i −0.342098 0.0810788i
\(413\) 1.32045 0.480606i 0.0649753 0.0236491i
\(414\) 0 0
\(415\) 15.1897 + 5.52860i 0.745633 + 0.271388i
\(416\) 0.325570 + 0.214131i 0.0159624 + 0.0104986i
\(417\) 0 0
\(418\) −25.8295 3.01903i −1.26336 0.147666i
\(419\) −14.6886 + 19.7303i −0.717587 + 0.963886i 0.282403 + 0.959296i \(0.408869\pi\)
−0.999989 + 0.00459033i \(0.998539\pi\)
\(420\) 0 0
\(421\) 0.715310 12.2814i 0.0348621 0.598559i −0.934961 0.354750i \(-0.884566\pi\)
0.969823 0.243809i \(-0.0783970\pi\)
\(422\) −33.3126 + 27.9526i −1.62163 + 1.36071i
\(423\) 0 0
\(424\) −11.2094 9.40584i −0.544379 0.456788i
\(425\) −18.4157 + 19.5196i −0.893295 + 0.946837i
\(426\) 0 0
\(427\) 10.4592 6.87912i 0.506156 0.332904i
\(428\) 17.3524 4.11260i 0.838761 0.198790i
\(429\) 0 0
\(430\) −29.0421 + 3.39454i −1.40054 + 0.163699i
\(431\) −3.97831 + 6.89064i −0.191628 + 0.331910i −0.945790 0.324779i \(-0.894710\pi\)
0.754162 + 0.656689i \(0.228044\pi\)
\(432\) 0 0
\(433\) −5.95735 10.3184i −0.286292 0.495872i 0.686630 0.727007i \(-0.259089\pi\)
−0.972922 + 0.231135i \(0.925756\pi\)
\(434\) 10.3419 + 13.8915i 0.496425 + 0.666815i
\(435\) 0 0
\(436\) −14.9517 + 49.9422i −0.716058 + 2.39180i
\(437\) −30.1674 15.1506i −1.44310 0.724752i
\(438\) 0 0
\(439\) −1.98064 6.61580i −0.0945308 0.315755i 0.897625 0.440759i \(-0.145291\pi\)
−0.992156 + 0.125004i \(0.960106\pi\)
\(440\) 5.71714 32.4235i 0.272554 1.54573i
\(441\) 0 0
\(442\) 1.87809 + 10.6512i 0.0893318 + 0.506626i
\(443\) −6.47445 + 3.25159i −0.307610 + 0.154488i −0.595907 0.803053i \(-0.703207\pi\)
0.288297 + 0.957541i \(0.406911\pi\)
\(444\) 0 0
\(445\) −10.7487 24.9182i −0.509535 1.18124i
\(446\) −13.6100 31.5516i −0.644454 1.49401i
\(447\) 0 0
\(448\) −17.9261 + 9.00284i −0.846930 + 0.425344i
\(449\) −5.97095 33.8630i −0.281787 1.59809i −0.716542 0.697543i \(-0.754276\pi\)
0.434756 0.900548i \(-0.356835\pi\)
\(450\) 0 0
\(451\) −2.64793 + 15.0172i −0.124686 + 0.707130i
\(452\) −4.84274 16.1759i −0.227783 0.760850i
\(453\) 0 0
\(454\) 12.5234 + 6.28948i 0.587752 + 0.295180i
\(455\) 1.18961 3.97358i 0.0557698 0.186284i
\(456\) 0 0
\(457\) 9.94490 + 13.3583i 0.465203 + 0.624876i 0.971374 0.237557i \(-0.0763468\pi\)
−0.506170 + 0.862433i \(0.668939\pi\)
\(458\) 29.9317 + 51.8433i 1.39862 + 2.42248i
\(459\) 0 0
\(460\) 43.4712 75.2944i 2.02686 3.51062i
\(461\) 13.6903 1.60016i 0.637619 0.0745270i 0.208860 0.977946i \(-0.433025\pi\)
0.428760 + 0.903419i \(0.358951\pi\)
\(462\) 0 0
\(463\) 11.9128 2.82340i 0.553637 0.131214i 0.0557317 0.998446i \(-0.482251\pi\)
0.497905 + 0.867231i \(0.334103\pi\)
\(464\) −6.54479 + 4.30458i −0.303834 + 0.199835i
\(465\) 0 0
\(466\) −21.3119 + 22.5893i −0.987253 + 1.04643i
\(467\) 11.7925 + 9.89507i 0.545691 + 0.457889i 0.873479 0.486862i \(-0.161859\pi\)
−0.327788 + 0.944751i \(0.606303\pi\)
\(468\) 0 0
\(469\) 0.495208 0.415529i 0.0228666 0.0191873i
\(470\) 0.361672 6.20968i 0.0166827 0.286431i
\(471\) 0 0
\(472\) −1.72615 + 2.31862i −0.0794526 + 0.106723i
\(473\) −9.56769 1.11830i −0.439923 0.0514196i
\(474\) 0 0
\(475\) 13.9711 + 9.18896i 0.641040 + 0.421619i
\(476\) −61.2319 22.2866i −2.80656 1.02150i
\(477\) 0 0
\(478\) 55.7428 20.2887i 2.54962 0.927985i
\(479\) 14.7420 + 3.49392i 0.673579 + 0.159641i 0.553151 0.833081i \(-0.313425\pi\)
0.120428 + 0.992722i \(0.461573\pi\)
\(480\) 0 0
\(481\) −0.152139 2.61213i −0.00693696 0.119103i
\(482\) 48.5971 + 51.5099i 2.21354 + 2.34621i
\(483\) 0 0
\(484\) −8.39953 + 19.4723i −0.381797 + 0.885105i
\(485\) 5.05122 0.229364
\(486\) 0 0
\(487\) −9.74343 −0.441517 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(488\) −10.1998 + 23.6458i −0.461724 + 1.07040i
\(489\) 0 0
\(490\) −8.66535 9.18473i −0.391460 0.414924i
\(491\) −1.11256 19.1020i −0.0502093 0.862060i −0.925567 0.378584i \(-0.876411\pi\)
0.875358 0.483476i \(-0.160626\pi\)
\(492\) 0 0
\(493\) 15.2874 + 3.62319i 0.688511 + 0.163180i
\(494\) 6.33304 2.30504i 0.284937 0.103709i
\(495\) 0 0
\(496\) −10.5232 3.83013i −0.472506 0.171978i
\(497\) −15.7161 10.3366i −0.704962 0.463661i
\(498\) 0 0
\(499\) 25.9471 + 3.03278i 1.16155 + 0.135766i 0.674953 0.737861i \(-0.264164\pi\)
0.486597 + 0.873627i \(0.338238\pi\)
\(500\) 8.94521 12.0155i 0.400042 0.537350i
\(501\) 0 0
\(502\) −3.37701 + 57.9810i −0.150723 + 2.58782i
\(503\) −0.849443 + 0.712768i −0.0378748 + 0.0317807i −0.661529 0.749920i \(-0.730092\pi\)
0.623654 + 0.781701i \(0.285648\pi\)
\(504\) 0 0
\(505\) −19.1614 16.0784i −0.852673 0.715477i
\(506\) 29.6490 31.4261i 1.31806 1.39706i
\(507\) 0 0
\(508\) 19.3489 12.7259i 0.858467 0.564623i
\(509\) 16.5171 3.91463i 0.732109 0.173513i 0.152379 0.988322i \(-0.451306\pi\)
0.579729 + 0.814809i \(0.303158\pi\)
\(510\) 0 0
\(511\) −34.6704 + 4.05238i −1.53373 + 0.179267i
\(512\) 18.1349 31.4106i 0.801458 1.38817i
\(513\) 0 0
\(514\) 14.7828 + 25.6045i 0.652041 + 1.12937i
\(515\) 3.19707 + 4.29441i 0.140880 + 0.189234i
\(516\) 0 0
\(517\) 0.587715 1.96310i 0.0258477 0.0863372i
\(518\) 21.2499 + 10.6721i 0.933668 + 0.468906i
\(519\) 0 0
\(520\) 2.44713 + 8.17398i 0.107314 + 0.358453i
\(521\) 5.42618 30.7734i 0.237725 1.34821i −0.599072 0.800695i \(-0.704464\pi\)
0.836798 0.547512i \(-0.184425\pi\)
\(522\) 0 0
\(523\) −2.23807 12.6927i −0.0978638 0.555013i −0.993832 0.110895i \(-0.964628\pi\)
0.895968 0.444118i \(-0.146483\pi\)
\(524\) 45.9082 23.0559i 2.00551 1.00720i
\(525\) 0 0
\(526\) −7.72021 17.8974i −0.336617 0.780366i
\(527\) 8.89591 + 20.6230i 0.387512 + 0.898354i
\(528\) 0 0
\(529\) 29.5661 14.8487i 1.28548 0.645594i
\(530\) 3.87796 + 21.9930i 0.168448 + 0.955314i
\(531\) 0 0
\(532\) −7.05085 + 39.9874i −0.305693 + 1.73367i
\(533\) −1.13340 3.78583i −0.0490931 0.163982i
\(534\) 0 0
\(535\) −11.9559 6.00447i −0.516898 0.259596i
\(536\) −0.381390 + 1.27393i −0.0164736 + 0.0550255i
\(537\) 0 0
\(538\) −32.7518 43.9934i −1.41203 1.89669i
\(539\) −2.07997 3.60261i −0.0895907 0.155176i
\(540\) 0 0
\(541\) −3.97103 + 6.87802i −0.170728 + 0.295709i −0.938675 0.344804i \(-0.887945\pi\)
0.767947 + 0.640514i \(0.221279\pi\)
\(542\) 73.3162 8.56944i 3.14920 0.368089i
\(543\) 0 0
\(544\) −4.46893 + 1.05915i −0.191604 + 0.0454109i
\(545\) 32.6770 21.4920i 1.39973 0.920617i
\(546\) 0 0
\(547\) 7.43375 7.87931i 0.317844 0.336895i −0.548678 0.836034i \(-0.684869\pi\)
0.866522 + 0.499139i \(0.166350\pi\)
\(548\) −13.6424 11.4473i −0.582774 0.489005i
\(549\) 0 0
\(550\) −16.3946 + 13.7567i −0.699067 + 0.586587i
\(551\) 0.569235 9.77340i 0.0242502 0.416361i
\(552\) 0 0
\(553\) 10.1937 13.6925i 0.433478 0.582263i
\(554\) 10.7030 + 1.25100i 0.454728 + 0.0531501i
\(555\) 0 0
\(556\) 15.7517 + 10.3601i 0.668020 + 0.439364i
\(557\) −1.66135 0.604682i −0.0703937 0.0256212i 0.306583 0.951844i \(-0.400814\pi\)
−0.376977 + 0.926223i \(0.623036\pi\)
\(558\) 0 0
\(559\) 2.34587 0.853825i 0.0992196 0.0361130i
\(560\) −23.7178 5.62122i −1.00226 0.237540i
\(561\) 0 0
\(562\) 0.802809 + 13.7837i 0.0338644 + 0.581430i
\(563\) −5.25025 5.56494i −0.221272 0.234534i 0.607223 0.794532i \(-0.292284\pi\)
−0.828494 + 0.559997i \(0.810802\pi\)
\(564\) 0 0
\(565\) −5.01748 + 11.6318i −0.211087 + 0.489354i
\(566\) 70.2116 2.95121
\(567\) 0 0
\(568\) 38.6951 1.62361
\(569\) −7.88133 + 18.2710i −0.330402 + 0.765959i 0.669333 + 0.742962i \(0.266580\pi\)
−0.999736 + 0.0229964i \(0.992679\pi\)
\(570\) 0 0
\(571\) 31.6143 + 33.5092i 1.32302 + 1.40232i 0.855028 + 0.518582i \(0.173540\pi\)
0.467990 + 0.883734i \(0.344978\pi\)
\(572\) 0.332483 + 5.70851i 0.0139018 + 0.238685i
\(573\) 0 0
\(574\) 34.9463 + 8.28242i 1.45863 + 0.345701i
\(575\) −26.1065 + 9.50198i −1.08872 + 0.396260i
\(576\) 0 0
\(577\) −24.3829 8.87465i −1.01507 0.369457i −0.219695 0.975569i \(-0.570506\pi\)
−0.795379 + 0.606112i \(0.792728\pi\)
\(578\) −71.9027 47.2912i −2.99076 1.96705i
\(579\) 0 0
\(580\) 25.0431 + 2.92712i 1.03986 + 0.121542i
\(581\) 7.48967 10.0604i 0.310724 0.417375i
\(582\) 0 0
\(583\) −0.427782 + 7.34472i −0.0177169 + 0.304187i
\(584\) 55.0061 46.1556i 2.27617 1.90993i
\(585\) 0 0
\(586\) −4.03971 3.38972i −0.166879 0.140028i
\(587\) 14.4213 15.2857i 0.595231 0.630908i −0.357794 0.933801i \(-0.616471\pi\)
0.953025 + 0.302893i \(0.0979523\pi\)
\(588\) 0 0
\(589\) 11.6930 7.69063i 0.481803 0.316887i
\(590\) 4.29264 1.01737i 0.176725 0.0418846i
\(591\) 0 0
\(592\) −15.2723 + 1.78508i −0.627688 + 0.0733662i
\(593\) 12.9024 22.3476i 0.529837 0.917705i −0.469557 0.882902i \(-0.655586\pi\)
0.999394 0.0348027i \(-0.0110803\pi\)
\(594\) 0 0
\(595\) 24.4432 + 42.3368i 1.00207 + 1.73564i
\(596\) 23.0575 + 30.9716i 0.944472 + 1.26865i
\(597\) 0 0
\(598\) −3.21130 + 10.7265i −0.131320 + 0.438639i
\(599\) 24.5346 + 12.3217i 1.00246 + 0.503453i 0.872785 0.488105i \(-0.162312\pi\)
0.129671 + 0.991557i \(0.458608\pi\)
\(600\) 0 0
\(601\) −0.109405 0.365437i −0.00446271 0.0149065i 0.955729 0.294248i \(-0.0950691\pi\)
−0.960192 + 0.279341i \(0.909884\pi\)
\(602\) −3.93963 + 22.3428i −0.160567 + 0.910623i
\(603\) 0 0
\(604\) 9.12145 + 51.7303i 0.371146 + 2.10488i
\(605\) 14.2176 7.14036i 0.578028 0.290297i
\(606\) 0 0
\(607\) 2.44005 + 5.65667i 0.0990386 + 0.229597i 0.960531 0.278173i \(-0.0897290\pi\)
−0.861492 + 0.507771i \(0.830470\pi\)
\(608\) 1.13353 + 2.62781i 0.0459706 + 0.106572i
\(609\) 0 0
\(610\) 35.1214 17.6386i 1.42202 0.714166i
\(611\) 0.0922182 + 0.522996i 0.00373075 + 0.0211581i
\(612\) 0 0
\(613\) −4.86771 + 27.6062i −0.196605 + 1.11500i 0.713509 + 0.700646i \(0.247105\pi\)
−0.910114 + 0.414357i \(0.864006\pi\)
\(614\) −3.31480 11.0722i −0.133775 0.446838i
\(615\) 0 0
\(616\) −22.8285 11.4649i −0.919788 0.461935i
\(617\) −4.27981 + 14.2956i −0.172299 + 0.575518i 0.827600 + 0.561318i \(0.189705\pi\)
−0.999899 + 0.0142003i \(0.995480\pi\)
\(618\) 0 0
\(619\) −2.49285 3.34848i −0.100196 0.134587i 0.749197 0.662347i \(-0.230439\pi\)
−0.849394 + 0.527760i \(0.823032\pi\)
\(620\) 18.0223 + 31.2156i 0.723794 + 1.25365i
\(621\) 0 0
\(622\) 28.7494 49.7955i 1.15275 1.99662i
\(623\) −20.9139 + 2.44448i −0.837898 + 0.0979362i
\(624\) 0 0
\(625\) −28.9837 + 6.86927i −1.15935 + 0.274771i
\(626\) −48.0919 + 31.6305i −1.92214 + 1.26421i
\(627\) 0 0
\(628\) 8.09609 8.58135i 0.323069 0.342433i
\(629\) 23.6239 + 19.8228i 0.941945 + 0.790386i
\(630\) 0 0
\(631\) 24.5789 20.6241i 0.978470 0.821034i −0.00538805 0.999985i \(-0.501715\pi\)
0.983858 + 0.178952i \(0.0572706\pi\)
\(632\) −2.04175 + 35.0556i −0.0812166 + 1.39444i
\(633\) 0 0
\(634\) −49.5655 + 66.5780i −1.96850 + 2.64415i
\(635\) −17.2570 2.01705i −0.684821 0.0800441i
\(636\) 0 0
\(637\) 0.900723 + 0.592415i 0.0356879 + 0.0234723i
\(638\) 11.7739 + 4.28536i 0.466134 + 0.169659i
\(639\) 0 0
\(640\) −55.6576 + 20.2577i −2.20006 + 0.800757i
\(641\) 38.3438 + 9.08765i 1.51449 + 0.358941i 0.902069 0.431591i \(-0.142048\pi\)
0.612421 + 0.790532i \(0.290196\pi\)
\(642\) 0 0
\(643\) 1.65969 + 28.4958i 0.0654519 + 1.12376i 0.857897 + 0.513822i \(0.171771\pi\)
−0.792445 + 0.609943i \(0.791192\pi\)
\(644\) −46.2934 49.0681i −1.82422 1.93356i
\(645\) 0 0
\(646\) −31.4612 + 72.9353i −1.23782 + 2.86960i
\(647\) −3.61582 −0.142153 −0.0710764 0.997471i \(-0.522643\pi\)
−0.0710764 + 0.997471i \(0.522643\pi\)
\(648\) 0 0
\(649\) 1.45335 0.0570489
\(650\) 2.19681 5.09278i 0.0861661 0.199755i
\(651\) 0 0
\(652\) −47.8628 50.7316i −1.87445 1.98680i
\(653\) 0.689989 + 11.8467i 0.0270014 + 0.463595i 0.984525 + 0.175242i \(0.0560708\pi\)
−0.957524 + 0.288353i \(0.906892\pi\)
\(654\) 0 0
\(655\) −37.5024 8.88823i −1.46534 0.347292i
\(656\) −21.8226 + 7.94277i −0.852029 + 0.310113i
\(657\) 0 0
\(658\) −4.53524 1.65069i −0.176802 0.0643507i
\(659\) −2.19931 1.44651i −0.0856730 0.0563481i 0.505950 0.862563i \(-0.331142\pi\)
−0.591623 + 0.806215i \(0.701512\pi\)
\(660\) 0 0
\(661\) −25.6714 3.00056i −0.998503 0.116708i −0.398890 0.916999i \(-0.630605\pi\)
−0.599613 + 0.800290i \(0.704679\pi\)
\(662\) 37.7143 50.6591i 1.46581 1.96892i
\(663\) 0 0
\(664\) −1.50016 + 25.7567i −0.0582173 + 0.999553i
\(665\) 23.3357 19.5810i 0.904919 0.759317i
\(666\) 0 0
\(667\) 12.4596 + 10.4549i 0.482439 + 0.404815i
\(668\) −59.3657 + 62.9240i −2.29693 + 2.43460i
\(669\) 0 0
\(670\) 1.69562 1.11523i 0.0655075 0.0430849i
\(671\) 12.5986 2.98593i 0.486365 0.115271i
\(672\) 0 0
\(673\) −1.19536 + 0.139717i −0.0460776 + 0.00538570i −0.139100 0.990278i \(-0.544421\pi\)
0.0930229 + 0.995664i \(0.470347\pi\)
\(674\) −26.9796 + 46.7301i −1.03922 + 1.79998i
\(675\) 0 0
\(676\) 24.8284 + 43.0040i 0.954938 + 1.65400i
\(677\) 23.4105 + 31.4457i 0.899737 + 1.20856i 0.977362 + 0.211574i \(0.0678590\pi\)
−0.0776247 + 0.996983i \(0.524734\pi\)
\(678\) 0 0
\(679\) 1.12406 3.75463i 0.0431375 0.144089i
\(680\) −89.8666 45.1327i −3.44623 1.73076i
\(681\) 0 0
\(682\) 5.13719 + 17.1594i 0.196713 + 0.657068i
\(683\) −1.15437 + 6.54674i −0.0441706 + 0.250504i −0.998896 0.0469860i \(-0.985038\pi\)
0.954725 + 0.297490i \(0.0961495\pi\)
\(684\) 0 0
\(685\) 2.32008 + 13.1578i 0.0886455 + 0.502734i
\(686\) −43.6480 + 21.9209i −1.66649 + 0.836942i
\(687\) 0 0
\(688\) −5.81059 13.4705i −0.221527 0.513557i
\(689\) −0.755192 1.75073i −0.0287705 0.0666976i
\(690\) 0 0
\(691\) −10.1591 + 5.10207i −0.386469 + 0.194092i −0.631416 0.775445i \(-0.717526\pi\)
0.244947 + 0.969536i \(0.421229\pi\)
\(692\) −7.39441 41.9358i −0.281093 1.59416i
\(693\) 0 0
\(694\) −0.758598 + 4.30222i −0.0287960 + 0.163310i
\(695\) −4.05664 13.5501i −0.153877 0.513985i
\(696\) 0 0
\(697\) 41.6222 + 20.9035i 1.57655 + 0.791776i
\(698\) −0.122873 + 0.410425i −0.00465082 + 0.0155348i
\(699\) 0 0
\(700\) 19.9547 + 26.8038i 0.754217 + 1.01309i
\(701\) 14.2748 + 24.7247i 0.539152 + 0.933838i 0.998950 + 0.0458147i \(0.0145884\pi\)
−0.459798 + 0.888023i \(0.652078\pi\)
\(702\) 0 0
\(703\) 9.60829 16.6421i 0.362384 0.627667i
\(704\) −20.6070 + 2.40861i −0.776654 + 0.0907778i
\(705\) 0 0
\(706\) 72.0887 17.0853i 2.71309 0.643015i
\(707\) −16.2153 + 10.6650i −0.609838 + 0.401097i
\(708\) 0 0
\(709\) 29.9559 31.7514i 1.12502 1.19245i 0.145870 0.989304i \(-0.453402\pi\)
0.979148 0.203146i \(-0.0651166\pi\)
\(710\) −45.2389 37.9599i −1.69779 1.42461i
\(711\) 0 0
\(712\) 33.1808 27.8420i 1.24350 1.04342i
\(713\) −1.35198 + 23.2125i −0.0506319 + 0.869316i
\(714\) 0 0
\(715\) 2.56179 3.44108i 0.0958054 0.128689i
\(716\) −34.9365 4.08349i −1.30564 0.152607i
\(717\) 0 0
\(718\) −13.1255 8.63278i −0.489839 0.322173i
\(719\) 28.1797 + 10.2566i 1.05093 + 0.382506i 0.809012 0.587792i \(-0.200002\pi\)
0.241914 + 0.970298i \(0.422225\pi\)
\(720\) 0 0
\(721\) 3.90353 1.42077i 0.145375 0.0529122i
\(722\) 3.12697 + 0.741105i 0.116374 + 0.0275811i
\(723\) 0 0
\(724\) −0.989230 16.9844i −0.0367645 0.631221i
\(725\) −5.52894 5.86034i −0.205340 0.217647i
\(726\) 0 0
\(727\) 15.8758 36.8042i 0.588800 1.36499i −0.319865 0.947463i \(-0.603637\pi\)
0.908664 0.417528i \(-0.137103\pi\)
\(728\) 6.62038 0.245368
\(729\) 0 0
\(730\) −109.587 −4.05600
\(731\) −11.6538 + 27.0165i −0.431030 + 0.999240i
\(732\) 0 0
\(733\) −18.8469 19.9765i −0.696125 0.737849i 0.278808 0.960347i \(-0.410061\pi\)
−0.974933 + 0.222497i \(0.928579\pi\)
\(734\) −2.60678 44.7566i −0.0962178 1.65200i
\(735\) 0 0
\(736\) −4.62651 1.09650i −0.170535 0.0404176i
\(737\) 0.628278 0.228675i 0.0231429 0.00842334i
\(738\) 0 0
\(739\) −29.1919 10.6250i −1.07384 0.390846i −0.256229 0.966616i \(-0.582480\pi\)
−0.817612 + 0.575770i \(0.804702\pi\)
\(740\) 41.3495 + 27.1960i 1.52004 + 0.999744i
\(741\) 0 0
\(742\) 17.2106 + 2.01163i 0.631821 + 0.0738493i
\(743\) 3.86766 5.19517i 0.141891 0.190592i −0.725497 0.688226i \(-0.758390\pi\)
0.867388 + 0.497633i \(0.165797\pi\)
\(744\) 0 0
\(745\) 1.68434 28.9190i 0.0617094 1.05951i
\(746\) −60.2439 + 50.5507i −2.20569 + 1.85079i
\(747\) 0 0
\(748\) −51.6272 43.3204i −1.88768 1.58395i
\(749\) −7.12377 + 7.55075i −0.260297 + 0.275898i
\(750\) 0 0
\(751\) 6.19254 4.07290i 0.225969 0.148622i −0.431477 0.902124i \(-0.642007\pi\)
0.657446 + 0.753502i \(0.271637\pi\)
\(752\) 3.03669 0.719708i 0.110737 0.0262450i
\(753\) 0 0
\(754\) −3.22517 + 0.376969i −0.117454 + 0.0137284i
\(755\) 19.7042 34.1287i 0.717109 1.24207i
\(756\) 0 0
\(757\) −22.2841 38.5972i −0.809930 1.40284i −0.912912 0.408157i \(-0.866172\pi\)
0.102981 0.994683i \(-0.467162\pi\)
\(758\) −32.0495 43.0499i −1.16409 1.56364i
\(759\) 0 0
\(760\) −17.9723 + 60.0315i −0.651922 + 2.17757i
\(761\) 17.8901 + 8.98475i 0.648516 + 0.325697i 0.742470 0.669880i \(-0.233654\pi\)
−0.0939538 + 0.995577i \(0.529951\pi\)
\(762\) 0 0
\(763\) −8.70355 29.0719i −0.315090 1.05247i
\(764\) −14.4900 + 82.1770i −0.524231 + 2.97306i
\(765\) 0 0
\(766\) 6.01753 + 34.1271i 0.217422 + 1.23306i
\(767\) −0.336584 + 0.169039i −0.0121533 + 0.00610363i
\(768\) 0 0
\(769\) −1.97582 4.58046i −0.0712499 0.165176i 0.878870 0.477062i \(-0.158298\pi\)
−0.950119 + 0.311887i \(0.899039\pi\)
\(770\) 15.4420 + 35.7986i 0.556492 + 1.29009i
\(771\) 0 0
\(772\) −63.8202 + 32.0517i −2.29694 + 1.15357i
\(773\) 4.06522 + 23.0550i 0.146216 + 0.829232i 0.966383 + 0.257108i \(0.0827695\pi\)
−0.820167 + 0.572124i \(0.806119\pi\)
\(774\) 0 0
\(775\) 2.00005 11.3429i 0.0718440 0.407448i
\(776\) 2.31229 + 7.72358i 0.0830063 + 0.277260i
\(777\) 0 0
\(778\) −26.7011 13.4098i −0.957281 0.480765i
\(779\) 8.32396 27.8040i 0.298237 0.996180i
\(780\) 0 0
\(781\) −11.6179 15.6055i −0.415720 0.558408i
\(782\) −65.9832 114.286i −2.35955 4.08687i
\(783\) 0 0
\(784\) 3.16768 5.48659i 0.113132 0.195950i
\(785\) −8.79117 + 1.02754i −0.313770 + 0.0366745i
\(786\) 0 0
\(787\) −48.5708 + 11.5115i −1.73136 + 0.410340i −0.970984 0.239143i \(-0.923134\pi\)
−0.760376 + 0.649483i \(0.774985\pi\)
\(788\) 23.4610 15.4305i 0.835763 0.549690i
\(789\) 0 0
\(790\) 36.7766 38.9809i 1.30845 1.38688i
\(791\) 7.52951 + 6.31801i 0.267719 + 0.224642i
\(792\) 0 0
\(793\) −2.57045 + 2.15686i −0.0912792 + 0.0765923i
\(794\) −1.37592 + 23.6236i −0.0488296 + 0.838372i
\(795\) 0 0
\(796\) −8.58823 + 11.5360i −0.304402 + 0.408882i
\(797\) −39.9343 4.66765i −1.41454 0.165337i −0.625764 0.780012i \(-0.715213\pi\)
−0.788780 + 0.614676i \(0.789287\pi\)
\(798\) 0 0
\(799\) −5.22942 3.43944i −0.185003 0.121679i
\(800\) 2.21319 + 0.805537i 0.0782482 + 0.0284800i
\(801\) 0 0
\(802\) 2.67647 0.974155i 0.0945094 0.0343986i
\(803\) −35.1294 8.32581i −1.23969 0.293812i
\(804\) 0 0
\(805\) 2.94272 + 50.5245i 0.103717 + 1.78075i
\(806\) −3.18554 3.37647i −0.112206 0.118931i
\(807\) 0 0
\(808\) 15.8132 36.6590i 0.556305 1.28966i
\(809\) −44.4490 −1.56274 −0.781371 0.624066i \(-0.785479\pi\)
−0.781371 + 0.624066i \(0.785479\pi\)
\(810\) 0 0
\(811\) −38.6494 −1.35716 −0.678582 0.734524i \(-0.737405\pi\)
−0.678582 + 0.734524i \(0.737405\pi\)
\(812\) 7.74867 17.9634i 0.271925 0.630393i
\(813\) 0 0
\(814\) 16.8775 + 17.8891i 0.591556 + 0.627013i
\(815\) 3.04248 + 52.2373i 0.106573 + 1.82979i
\(816\) 0 0
\(817\) 17.8400 + 4.22817i 0.624144 + 0.147925i
\(818\) 62.8587 22.8787i 2.19780 0.799934i
\(819\) 0 0
\(820\) 70.2401 + 25.5653i 2.45289 + 0.892780i
\(821\) 36.1767 + 23.7938i 1.26257 + 0.830408i 0.991240 0.132076i \(-0.0421644\pi\)
0.271335 + 0.962485i \(0.412535\pi\)
\(822\) 0 0
\(823\) 29.9006 + 3.49488i 1.04227 + 0.121824i 0.619965 0.784629i \(-0.287147\pi\)
0.422306 + 0.906453i \(0.361221\pi\)
\(824\) −5.10286 + 6.85433i −0.177767 + 0.238782i
\(825\) 0 0
\(826\) 0.199027 3.41717i 0.00692505 0.118898i
\(827\) 12.5660 10.5441i 0.436963 0.366655i −0.397609 0.917555i \(-0.630160\pi\)
0.834571 + 0.550900i \(0.185715\pi\)
\(828\) 0 0
\(829\) 22.2396 + 18.6612i 0.772413 + 0.648132i 0.941326 0.337500i \(-0.109581\pi\)
−0.168913 + 0.985631i \(0.554026\pi\)
\(830\) 27.0212 28.6408i 0.937920 0.994137i
\(831\) 0 0
\(832\) 4.49225 2.95460i 0.155741 0.102432i
\(833\) −12.3638 + 2.93026i −0.428379 + 0.101528i
\(834\) 0 0
\(835\) 64.4625 7.53459i 2.23082 0.260745i
\(836\) −20.9978 + 36.3693i −0.726224 + 1.25786i
\(837\) 0 0
\(838\) 29.9589 + 51.8904i 1.03491 + 1.79252i
\(839\) −21.2010 28.4779i −0.731940 0.983166i −0.999806 0.0197096i \(-0.993726\pi\)
0.267866 0.963456i \(-0.413682\pi\)
\(840\) 0 0
\(841\) 6.96448 23.2630i 0.240154 0.802172i
\(842\) −26.7798 13.4493i −0.922891 0.463493i
\(843\) 0 0
\(844\) 20.1409 + 67.2754i 0.693280 + 2.31572i
\(845\) 6.46910 36.6881i 0.222544 1.26211i
\(846\) 0 0
\(847\) −2.14362 12.1571i −0.0736557 0.417722i
\(848\) −10.0128 + 5.02860i −0.343840 + 0.172683i
\(849\) 0 0
\(850\) 25.8916 + 60.0235i 0.888076 + 2.05879i
\(851\) 12.6453 + 29.3151i 0.433476 + 1.00491i
\(852\) 0 0
\(853\) −0.860025 + 0.431921i −0.0294467 + 0.0147887i −0.463462 0.886117i \(-0.653393\pi\)
0.434015 + 0.900906i \(0.357097\pi\)
\(854\) −5.29532 30.0313i −0.181202 1.02765i
\(855\) 0 0
\(856\) 3.70813 21.0298i 0.126741 0.718785i
\(857\) 0.162781 + 0.543725i 0.00556048 + 0.0185733i 0.960725 0.277503i \(-0.0895069\pi\)
−0.955164 + 0.296076i \(0.904322\pi\)
\(858\) 0 0
\(859\) 17.9700 + 9.02486i 0.613128 + 0.307924i 0.728128 0.685441i \(-0.240391\pi\)
−0.115000 + 0.993365i \(0.536687\pi\)
\(860\) −13.5426 + 45.2353i −0.461798 + 1.54251i
\(861\) 0 0
\(862\) 11.5740 + 15.5466i 0.394211 + 0.529518i
\(863\) 18.8153 + 32.5891i 0.640481 + 1.10935i 0.985326 + 0.170686i \(0.0545982\pi\)
−0.344845 + 0.938660i \(0.612068\pi\)
\(864\) 0 0
\(865\) −15.9735 + 27.6668i −0.543114 + 0.940700i
\(866\) −28.8271 + 3.36941i −0.979585 + 0.114497i
\(867\) 0 0
\(868\) 27.2135 6.44971i 0.923685 0.218917i
\(869\) 14.7507 9.70170i 0.500384 0.329108i
\(870\) 0 0
\(871\) −0.118907 + 0.126034i −0.00402901 + 0.00427050i
\(872\) 47.8210 + 40.1266i 1.61942 + 1.35886i
\(873\) 0 0
\(874\) −62.9936 + 52.8579i −2.13079 + 1.78795i
\(875\) −0.507011 + 8.70504i −0.0171401 + 0.294284i
\(876\) 0 0
\(877\) 16.3657 21.9830i 0.552632 0.742313i −0.434771 0.900541i \(-0.643171\pi\)
0.987403 + 0.158228i \(0.0505780\pi\)
\(878\) −16.7086 1.95295i −0.563887 0.0659090i
\(879\) 0 0
\(880\) −21.0627 13.8532i −0.710024 0.466990i
\(881\) 31.5862 + 11.4964i 1.06417 + 0.387324i 0.813992 0.580877i \(-0.197290\pi\)
0.250174 + 0.968201i \(0.419512\pi\)
\(882\) 0 0
\(883\) 40.4061 14.7066i 1.35977 0.494917i 0.443789 0.896131i \(-0.353634\pi\)
0.915984 + 0.401214i \(0.131412\pi\)
\(884\) 16.9950 + 4.02789i 0.571604 + 0.135473i
\(885\) 0 0
\(886\) 1.02617 + 17.6187i 0.0344748 + 0.591910i
\(887\) −21.2743 22.5495i −0.714322 0.757137i 0.263934 0.964541i \(-0.414980\pi\)
−0.978255 + 0.207404i \(0.933498\pi\)
\(888\) 0 0
\(889\) −5.33953 + 12.3784i −0.179082 + 0.415159i
\(890\) −66.1052 −2.21585
\(891\) 0 0
\(892\) −55.4905 −1.85796
\(893\) −1.54481 + 3.58127i −0.0516951 + 0.119843i
\(894\) 0 0
\(895\) 18.1091 + 19.1946i 0.605322 + 0.641604i
\(896\) 2.67215 + 45.8790i 0.0892701 + 1.53271i
\(897\) 0 0
\(898\) −81.5025 19.3164i −2.71977 0.644598i
\(899\) −6.33645 + 2.30628i −0.211333 + 0.0769188i
\(900\) 0 0
\(901\) 21.1167 + 7.68587i 0.703501 + 0.256053i
\(902\) 31.0342 + 20.4115i 1.03333 + 0.679629i
\(903\) 0 0
\(904\) −20.0825 2.34731i −0.667934 0.0780703i
\(905\) −7.62204 + 10.2382i −0.253365 + 0.340329i
\(906\) 0 0
\(907\) 0.227537 3.90667i 0.00755526 0.129719i −0.992421 0.122881i \(-0.960787\pi\)
0.999977 0.00683739i \(-0.00217643\pi\)
\(908\) 17.3364 14.5469i 0.575328 0.482757i
\(909\) 0 0
\(910\) −7.73997 6.49461i −0.256577 0.215294i
\(911\) 26.7414 28.3443i 0.885983 0.939087i −0.112528 0.993649i \(-0.535895\pi\)
0.998510 + 0.0545616i \(0.0173761\pi\)
\(912\) 0 0
\(913\) 10.8379 7.12821i 0.358683 0.235909i
\(914\) 39.4737 9.35545i 1.30568 0.309451i
\(915\) 0 0
\(916\) 96.0190 11.2230i 3.17256 0.370819i
\(917\) −14.9522 + 25.8980i −0.493766 + 0.855228i
\(918\) 0 0
\(919\) 10.6253 + 18.4036i 0.350497 + 0.607078i 0.986337 0.164743i \(-0.0526794\pi\)
−0.635840 + 0.771821i \(0.719346\pi\)
\(920\) −62.1697 83.5084i −2.04968 2.75319i
\(921\) 0 0
\(922\) 9.62957 32.1650i 0.317133 1.05930i
\(923\) 4.50567 + 2.26283i 0.148306 + 0.0744820i
\(924\) 0 0
\(925\) −4.53570 15.1503i −0.149133 0.498139i
\(926\) 5.17866 29.3696i 0.170181 0.965146i
\(927\) 0 0
\(928\) −0.239438 1.35792i −0.00785994 0.0445759i
\(929\) −14.6055 + 7.33516i −0.479191 + 0.240659i −0.671963 0.740585i \(-0.734549\pi\)
0.192772 + 0.981244i \(0.438252\pi\)
\(930\) 0 0
\(931\) 3.13603 + 7.27012i 0.102779 + 0.238269i
\(932\) 19.8641 + 46.0501i 0.650670 + 1.50842i
\(933\) 0 0
\(934\) 33.5100 16.8294i 1.09648 0.550674i
\(935\) 8.77991 + 49.7934i 0.287134 + 1.62842i
\(936\) 0 0
\(937\) −3.94626 + 22.3803i −0.128919 + 0.731134i 0.849984 + 0.526808i \(0.176611\pi\)
−0.978903 + 0.204326i \(0.934500\pi\)
\(938\) −0.451629 1.50855i −0.0147462 0.0492558i
\(939\) 0 0
\(940\) −8.97646 4.50815i −0.292780 0.147040i
\(941\) −3.75885 + 12.5554i −0.122535 + 0.409295i −0.997143 0.0755352i \(-0.975933\pi\)
0.874608 + 0.484830i \(0.161119\pi\)
\(942\) 0 0
\(943\) 28.7943 + 38.6774i 0.937671 + 1.25951i
\(944\) 1.10669 + 1.91684i 0.0360196 + 0.0623877i
\(945\) 0 0
\(946\) −11.7324 + 20.3212i −0.381454 + 0.660698i
\(947\) 21.4807 2.51073i 0.698029 0.0815879i 0.240325 0.970692i \(-0.422746\pi\)
0.457704 + 0.889105i \(0.348672\pi\)
\(948\) 0 0
\(949\) 9.10404 2.15770i 0.295530 0.0700418i
\(950\) 34.0327 22.3836i 1.10417 0.726221i
\(951\) 0 0
\(952\) −53.5459 + 56.7554i −1.73543 + 1.83945i
\(953\) −16.8450 14.1347i −0.545665 0.457867i 0.327805 0.944745i \(-0.393691\pi\)
−0.873470 + 0.486878i \(0.838135\pi\)
\(954\) 0 0
\(955\) 47.9566 40.2403i 1.55184 1.30215i
\(956\) 5.57001 95.6333i 0.180147 3.09300i
\(957\) 0 0
\(958\) 22.0383 29.6025i 0.712024 0.956415i
\(959\) 10.2966 + 1.20350i 0.332496 + 0.0388632i
\(960\) 0 0
\(961\) 17.8462 + 11.7376i 0.575684 + 0.378633i
\(962\) −5.98936 2.17995i −0.193105 0.0702844i
\(963\) 0 0
\(964\) 107.463 39.1135i 3.46116 1.25976i
\(965\) 52.1348 + 12.3562i 1.67828 + 0.397759i
\(966\) 0 0
\(967\) −1.38226 23.7325i −0.0444505 0.763185i −0.944725 0.327863i \(-0.893672\pi\)
0.900275 0.435322i \(-0.143366\pi\)
\(968\) 17.4264 + 18.4709i 0.560105 + 0.593676i
\(969\) 0 0
\(970\) 4.87352 11.2981i 0.156479 0.362760i
\(971\) 16.4980 0.529445 0.264723 0.964325i \(-0.414720\pi\)
0.264723 + 0.964325i \(0.414720\pi\)
\(972\) 0 0
\(973\) −10.9747 −0.351833
\(974\) −9.40067 + 21.7932i −0.301217 + 0.698299i
\(975\) 0 0
\(976\) 13.5317 + 14.3428i 0.433139 + 0.459100i
\(977\) −0.357579 6.13940i −0.0114400 0.196417i −0.999186 0.0403456i \(-0.987154\pi\)
0.987746 0.156071i \(-0.0498829\pi\)
\(978\) 0 0
\(979\) −21.1908 5.02231i −0.677260 0.160514i
\(980\) −19.1618 + 6.97433i −0.612101 + 0.222787i
\(981\) 0 0
\(982\) −43.7990 15.9415i −1.39768 0.508714i
\(983\) 9.73833 + 6.40500i 0.310604 + 0.204288i 0.695234 0.718783i \(-0.255301\pi\)
−0.384630 + 0.923071i \(0.625671\pi\)
\(984\) 0 0
\(985\) −20.9245 2.44572i −0.666710 0.0779272i
\(986\) 22.8536 30.6978i 0.727808 0.977616i
\(987\) 0 0
\(988\) 0.632818 10.8651i 0.0201326 0.345664i
\(989\) −23.3339 + 19.5795i −0.741976 + 0.622592i
\(990\) 0 0
\(991\) −20.9608 17.5882i −0.665840 0.558706i 0.245991 0.969272i \(-0.420887\pi\)
−0.911831 + 0.410566i \(0.865331\pi\)
\(992\) 1.35271 1.43379i 0.0429487 0.0455230i
\(993\) 0 0
\(994\) −38.2832 + 25.1793i −1.21427 + 0.798638i
\(995\) 10.4989 2.48828i 0.332836 0.0788836i
\(996\) 0 0
\(997\) −54.2532 + 6.34129i −1.71822 + 0.200831i −0.917369 0.398037i \(-0.869691\pi\)
−0.800848 + 0.598868i \(0.795617\pi\)
\(998\) 31.8177 55.1099i 1.00717 1.74447i
\(999\) 0 0
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 729.2.g.b.55.8 144
3.2 odd 2 729.2.g.c.55.1 144
9.2 odd 6 729.2.g.d.298.8 144
9.4 even 3 243.2.g.a.100.8 144
9.5 odd 6 81.2.g.a.7.1 144
9.7 even 3 729.2.g.a.298.1 144
81.4 even 27 243.2.g.a.226.8 144
81.23 odd 54 729.2.g.d.433.8 144
81.29 odd 54 6561.2.a.c.1.8 72
81.31 even 27 inner 729.2.g.b.676.8 144
81.50 odd 54 729.2.g.c.676.1 144
81.52 even 27 6561.2.a.d.1.65 72
81.58 even 27 729.2.g.a.433.1 144
81.77 odd 54 81.2.g.a.58.1 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.1 144 9.5 odd 6
81.2.g.a.58.1 yes 144 81.77 odd 54
243.2.g.a.100.8 144 9.4 even 3
243.2.g.a.226.8 144 81.4 even 27
729.2.g.a.298.1 144 9.7 even 3
729.2.g.a.433.1 144 81.58 even 27
729.2.g.b.55.8 144 1.1 even 1 trivial
729.2.g.b.676.8 144 81.31 even 27 inner
729.2.g.c.55.1 144 3.2 odd 2
729.2.g.c.676.1 144 81.50 odd 54
729.2.g.d.298.8 144 9.2 odd 6
729.2.g.d.433.8 144 81.23 odd 54
6561.2.a.c.1.8 72 81.29 odd 54
6561.2.a.d.1.65 72 81.52 even 27