Properties

Label 729.2.g.d.109.4
Level $729$
Weight $2$
Character 729.109
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 109.4
Character \(\chi\) \(=\) 729.109
Dual form 729.2.g.d.622.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.217727 - 0.230777i) q^{2} +(0.110437 - 1.89612i) q^{4} +(-2.10697 + 0.246269i) q^{5} +(-2.27300 - 1.14154i) q^{7} +(-0.947719 + 0.795231i) q^{8} +O(q^{10})\) \(q+(-0.217727 - 0.230777i) q^{2} +(0.110437 - 1.89612i) q^{4} +(-2.10697 + 0.246269i) q^{5} +(-2.27300 - 1.14154i) q^{7} +(-0.947719 + 0.795231i) q^{8} +(0.515577 + 0.432621i) q^{10} +(-1.21202 - 2.80978i) q^{11} +(5.37024 + 1.27277i) q^{13} +(0.231451 + 0.773099i) q^{14} +(-3.38312 - 0.395430i) q^{16} +(-0.745021 + 4.22522i) q^{17} +(-0.0105922 - 0.0600713i) q^{19} +(0.234271 + 4.02227i) q^{20} +(-0.384543 + 0.891471i) q^{22} +(-3.82550 + 1.92124i) q^{23} +(-0.486554 + 0.115315i) q^{25} +(-0.875520 - 1.51644i) q^{26} +(-2.41553 + 4.18381i) q^{28} +(-3.06272 + 10.2302i) q^{29} +(-3.85453 - 2.53516i) q^{31} +(2.12290 + 2.85155i) q^{32} +(1.13730 - 0.748011i) q^{34} +(5.07026 + 1.84542i) q^{35} +(-3.30730 + 1.20376i) q^{37} +(-0.0115569 + 0.0155236i) q^{38} +(1.80097 - 1.90892i) q^{40} +(-1.72935 + 1.83301i) q^{41} +(-0.463275 + 0.622287i) q^{43} +(-5.46154 + 1.98784i) q^{44} +(1.27629 + 0.464532i) q^{46} +(3.79858 - 2.49837i) q^{47} +(-0.316716 - 0.425424i) q^{49} +(0.132548 + 0.0871782i) q^{50} +(3.00640 - 10.0421i) q^{52} +(0.986349 - 1.70841i) q^{53} +(3.24565 + 5.62164i) q^{55} +(3.06195 - 0.725696i) q^{56} +(3.02773 - 1.52058i) q^{58} +(2.85708 - 6.62346i) q^{59} +(0.679073 + 11.6592i) q^{61} +(0.254177 + 1.44151i) q^{62} +(-0.987085 + 5.59804i) q^{64} +(-11.6284 - 1.35916i) q^{65} +(0.347884 + 1.16201i) q^{67} +(7.92927 + 1.87927i) q^{68} +(-0.678050 - 1.57190i) q^{70} +(-10.9300 - 9.17137i) q^{71} +(7.44218 - 6.24473i) q^{73} +(0.997887 + 0.501157i) q^{74} +(-0.115072 + 0.0134500i) q^{76} +(-0.452562 + 7.77019i) q^{77} +(-1.10564 - 1.17191i) q^{79} +7.22552 q^{80} +0.799542 q^{82} +(-2.26614 - 2.40196i) q^{83} +(0.529193 - 9.08589i) q^{85} +(0.244477 - 0.0285753i) q^{86} +(3.38308 + 1.69905i) q^{88} +(-10.7606 + 9.02919i) q^{89} +(-10.7536 - 9.02336i) q^{91} +(3.22043 + 7.46579i) q^{92} +(-1.40362 - 0.332664i) q^{94} +(0.0371112 + 0.123960i) q^{95} +(-6.97567 - 0.815339i) q^{97} +(-0.0292204 + 0.165717i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.217727 0.230777i −0.153956 0.163184i 0.645805 0.763503i \(-0.276522\pi\)
−0.799761 + 0.600319i \(0.795040\pi\)
\(3\) 0 0
\(4\) 0.110437 1.89612i 0.0552183 0.948062i
\(5\) −2.10697 + 0.246269i −0.942265 + 0.110135i −0.573334 0.819322i \(-0.694350\pi\)
−0.368931 + 0.929457i \(0.620276\pi\)
\(6\) 0 0
\(7\) −2.27300 1.14154i −0.859112 0.431462i −0.0360069 0.999352i \(-0.511464\pi\)
−0.823105 + 0.567889i \(0.807760\pi\)
\(8\) −0.947719 + 0.795231i −0.335069 + 0.281157i
\(9\) 0 0
\(10\) 0.515577 + 0.432621i 0.163040 + 0.136807i
\(11\) −1.21202 2.80978i −0.365438 0.847181i −0.997392 0.0721747i \(-0.977006\pi\)
0.631954 0.775006i \(-0.282253\pi\)
\(12\) 0 0
\(13\) 5.37024 + 1.27277i 1.48944 + 0.353003i 0.893147 0.449766i \(-0.148492\pi\)
0.596291 + 0.802769i \(0.296641\pi\)
\(14\) 0.231451 + 0.773099i 0.0618578 + 0.206620i
\(15\) 0 0
\(16\) −3.38312 0.395430i −0.845781 0.0988576i
\(17\) −0.745021 + 4.22522i −0.180694 + 1.02477i 0.750670 + 0.660678i \(0.229731\pi\)
−0.931364 + 0.364090i \(0.881380\pi\)
\(18\) 0 0
\(19\) −0.0105922 0.0600713i −0.00243002 0.0137813i 0.983569 0.180535i \(-0.0577828\pi\)
−0.985999 + 0.166753i \(0.946672\pi\)
\(20\) 0.234271 + 4.02227i 0.0523845 + 0.899407i
\(21\) 0 0
\(22\) −0.384543 + 0.891471i −0.0819849 + 0.190062i
\(23\) −3.82550 + 1.92124i −0.797671 + 0.400606i −0.800457 0.599390i \(-0.795410\pi\)
0.00278538 + 0.999996i \(0.499113\pi\)
\(24\) 0 0
\(25\) −0.486554 + 0.115315i −0.0973108 + 0.0230631i
\(26\) −0.875520 1.51644i −0.171704 0.297399i
\(27\) 0 0
\(28\) −2.41553 + 4.18381i −0.456491 + 0.790666i
\(29\) −3.06272 + 10.2302i −0.568733 + 1.89970i −0.159755 + 0.987157i \(0.551070\pi\)
−0.408979 + 0.912544i \(0.634115\pi\)
\(30\) 0 0
\(31\) −3.85453 2.53516i −0.692294 0.455329i 0.153982 0.988074i \(-0.450790\pi\)
−0.846276 + 0.532745i \(0.821161\pi\)
\(32\) 2.12290 + 2.85155i 0.375280 + 0.504088i
\(33\) 0 0
\(34\) 1.13730 0.748011i 0.195045 0.128283i
\(35\) 5.07026 + 1.84542i 0.857030 + 0.311933i
\(36\) 0 0
\(37\) −3.30730 + 1.20376i −0.543716 + 0.197896i −0.599252 0.800560i \(-0.704535\pi\)
0.0555362 + 0.998457i \(0.482313\pi\)
\(38\) −0.0115569 + 0.0155236i −0.00187477 + 0.00251826i
\(39\) 0 0
\(40\) 1.80097 1.90892i 0.284759 0.301827i
\(41\) −1.72935 + 1.83301i −0.270080 + 0.286268i −0.848191 0.529690i \(-0.822308\pi\)
0.578112 + 0.815958i \(0.303790\pi\)
\(42\) 0 0
\(43\) −0.463275 + 0.622287i −0.0706488 + 0.0948978i −0.836043 0.548664i \(-0.815137\pi\)
0.765394 + 0.643562i \(0.222544\pi\)
\(44\) −5.46154 + 1.98784i −0.823359 + 0.299678i
\(45\) 0 0
\(46\) 1.27629 + 0.464532i 0.188179 + 0.0684915i
\(47\) 3.79858 2.49837i 0.554080 0.364424i −0.241379 0.970431i \(-0.577600\pi\)
0.795460 + 0.606007i \(0.207229\pi\)
\(48\) 0 0
\(49\) −0.316716 0.425424i −0.0452452 0.0607748i
\(50\) 0.132548 + 0.0871782i 0.0187451 + 0.0123289i
\(51\) 0 0
\(52\) 3.00640 10.0421i 0.416913 1.39259i
\(53\) 0.986349 1.70841i 0.135485 0.234668i −0.790297 0.612724i \(-0.790074\pi\)
0.925783 + 0.378056i \(0.123407\pi\)
\(54\) 0 0
\(55\) 3.24565 + 5.62164i 0.437644 + 0.758021i
\(56\) 3.06195 0.725696i 0.409170 0.0969752i
\(57\) 0 0
\(58\) 3.02773 1.52058i 0.397561 0.199662i
\(59\) 2.85708 6.62346i 0.371960 0.862301i −0.624717 0.780851i \(-0.714786\pi\)
0.996677 0.0814496i \(-0.0259550\pi\)
\(60\) 0 0
\(61\) 0.679073 + 11.6592i 0.0869464 + 1.49281i 0.706419 + 0.707794i \(0.250309\pi\)
−0.619473 + 0.785018i \(0.712654\pi\)
\(62\) 0.254177 + 1.44151i 0.0322805 + 0.183072i
\(63\) 0 0
\(64\) −0.987085 + 5.59804i −0.123386 + 0.699755i
\(65\) −11.6284 1.35916i −1.44232 0.168583i
\(66\) 0 0
\(67\) 0.347884 + 1.16201i 0.0425008 + 0.141963i 0.976607 0.215034i \(-0.0689861\pi\)
−0.934106 + 0.356996i \(0.883801\pi\)
\(68\) 7.92927 + 1.87927i 0.961565 + 0.227895i
\(69\) 0 0
\(70\) −0.678050 1.57190i −0.0810425 0.187878i
\(71\) −10.9300 9.17137i −1.29715 1.08844i −0.990629 0.136579i \(-0.956389\pi\)
−0.306525 0.951863i \(-0.599166\pi\)
\(72\) 0 0
\(73\) 7.44218 6.24473i 0.871042 0.730891i −0.0932755 0.995640i \(-0.529734\pi\)
0.964317 + 0.264750i \(0.0852893\pi\)
\(74\) 0.997887 + 0.501157i 0.116002 + 0.0582584i
\(75\) 0 0
\(76\) −0.115072 + 0.0134500i −0.0131997 + 0.00154282i
\(77\) −0.452562 + 7.77019i −0.0515742 + 0.885496i
\(78\) 0 0
\(79\) −1.10564 1.17191i −0.124395 0.131851i 0.662183 0.749342i \(-0.269630\pi\)
−0.786577 + 0.617492i \(0.788149\pi\)
\(80\) 7.22552 0.807838
\(81\) 0 0
\(82\) 0.799542 0.0882947
\(83\) −2.26614 2.40196i −0.248741 0.263650i 0.590958 0.806702i \(-0.298750\pi\)
−0.839699 + 0.543053i \(0.817268\pi\)
\(84\) 0 0
\(85\) 0.529193 9.08589i 0.0573990 0.985503i
\(86\) 0.244477 0.0285753i 0.0263626 0.00308135i
\(87\) 0 0
\(88\) 3.38308 + 1.69905i 0.360637 + 0.181119i
\(89\) −10.7606 + 9.02919i −1.14062 + 0.957092i −0.999459 0.0328946i \(-0.989527\pi\)
−0.141159 + 0.989987i \(0.545083\pi\)
\(90\) 0 0
\(91\) −10.7536 9.02336i −1.12729 0.945905i
\(92\) 3.22043 + 7.46579i 0.335753 + 0.778363i
\(93\) 0 0
\(94\) −1.40362 0.332664i −0.144772 0.0343117i
\(95\) 0.0371112 + 0.123960i 0.00380752 + 0.0127180i
\(96\) 0 0
\(97\) −6.97567 0.815339i −0.708272 0.0827851i −0.245673 0.969353i \(-0.579009\pi\)
−0.462599 + 0.886568i \(0.653083\pi\)
\(98\) −0.0292204 + 0.165717i −0.00295170 + 0.0167399i
\(99\) 0 0
\(100\) 0.164919 + 0.935301i 0.0164919 + 0.0935301i
\(101\) −0.631091 10.8354i −0.0627959 1.07816i −0.871642 0.490143i \(-0.836944\pi\)
0.808846 0.588021i \(-0.200093\pi\)
\(102\) 0 0
\(103\) −4.92595 + 11.4196i −0.485368 + 1.12521i 0.482986 + 0.875628i \(0.339552\pi\)
−0.968354 + 0.249582i \(0.919707\pi\)
\(104\) −6.10163 + 3.06435i −0.598314 + 0.300485i
\(105\) 0 0
\(106\) −0.609016 + 0.144339i −0.0591528 + 0.0140195i
\(107\) −2.48915 4.31134i −0.240636 0.416793i 0.720260 0.693704i \(-0.244023\pi\)
−0.960896 + 0.276911i \(0.910689\pi\)
\(108\) 0 0
\(109\) −0.180626 + 0.312853i −0.0173008 + 0.0299659i −0.874546 0.484942i \(-0.838841\pi\)
0.857245 + 0.514908i \(0.172174\pi\)
\(110\) 0.590678 1.97300i 0.0563190 0.188119i
\(111\) 0 0
\(112\) 7.23843 + 4.76079i 0.683967 + 0.449852i
\(113\) −11.7891 15.8355i −1.10902 1.48968i −0.852200 0.523216i \(-0.824732\pi\)
−0.256822 0.966459i \(-0.582675\pi\)
\(114\) 0 0
\(115\) 7.58706 4.99009i 0.707497 0.465328i
\(116\) 19.0595 + 6.93709i 1.76963 + 0.644092i
\(117\) 0 0
\(118\) −2.15060 + 0.782756i −0.197979 + 0.0720585i
\(119\) 6.51670 8.75344i 0.597385 0.802427i
\(120\) 0 0
\(121\) 1.12279 1.19008i 0.102072 0.108189i
\(122\) 2.54283 2.69524i 0.230217 0.244016i
\(123\) 0 0
\(124\) −5.23266 + 7.02869i −0.469907 + 0.631195i
\(125\) 10.9637 3.99045i 0.980620 0.356916i
\(126\) 0 0
\(127\) 13.5556 + 4.93382i 1.20286 + 0.437806i 0.864222 0.503111i \(-0.167811\pi\)
0.338639 + 0.940916i \(0.390033\pi\)
\(128\) 7.44714 4.89806i 0.658240 0.432932i
\(129\) 0 0
\(130\) 2.21815 + 2.97949i 0.194544 + 0.261318i
\(131\) −2.55224 1.67864i −0.222990 0.146663i 0.433099 0.901346i \(-0.357420\pi\)
−0.656089 + 0.754683i \(0.727791\pi\)
\(132\) 0 0
\(133\) −0.0444979 + 0.148633i −0.00385846 + 0.0128881i
\(134\) 0.192422 0.333285i 0.0166228 0.0287915i
\(135\) 0 0
\(136\) −2.65396 4.59679i −0.227575 0.394171i
\(137\) 2.53477 0.600750i 0.216560 0.0513256i −0.120904 0.992664i \(-0.538579\pi\)
0.337463 + 0.941339i \(0.390431\pi\)
\(138\) 0 0
\(139\) −16.9648 + 8.52003i −1.43893 + 0.722660i −0.985665 0.168714i \(-0.946038\pi\)
−0.453269 + 0.891374i \(0.649742\pi\)
\(140\) 4.05909 9.41004i 0.343056 0.795293i
\(141\) 0 0
\(142\) 0.263216 + 4.51925i 0.0220886 + 0.379247i
\(143\) −2.93264 16.6318i −0.245240 1.39082i
\(144\) 0 0
\(145\) 3.93367 22.3090i 0.326674 1.85266i
\(146\) −3.06150 0.357838i −0.253372 0.0296149i
\(147\) 0 0
\(148\) 1.91723 + 6.40398i 0.157595 + 0.526404i
\(149\) 3.98717 + 0.944978i 0.326642 + 0.0774156i 0.390665 0.920533i \(-0.372245\pi\)
−0.0640232 + 0.997948i \(0.520393\pi\)
\(150\) 0 0
\(151\) 3.93753 + 9.12821i 0.320431 + 0.742843i 0.999958 + 0.00919237i \(0.00292606\pi\)
−0.679526 + 0.733651i \(0.737815\pi\)
\(152\) 0.0578090 + 0.0485075i 0.00468893 + 0.00393448i
\(153\) 0 0
\(154\) 1.89172 1.58734i 0.152439 0.127911i
\(155\) 8.74570 + 4.39226i 0.702472 + 0.352795i
\(156\) 0 0
\(157\) −11.4715 + 1.34082i −0.915523 + 0.107009i −0.560790 0.827958i \(-0.689502\pi\)
−0.354733 + 0.934968i \(0.615428\pi\)
\(158\) −0.0297224 + 0.510314i −0.00236459 + 0.0405984i
\(159\) 0 0
\(160\) −5.17514 5.48533i −0.409131 0.433653i
\(161\) 10.8885 0.858135
\(162\) 0 0
\(163\) −14.1333 −1.10700 −0.553502 0.832848i \(-0.686709\pi\)
−0.553502 + 0.832848i \(0.686709\pi\)
\(164\) 3.28462 + 3.48150i 0.256486 + 0.271859i
\(165\) 0 0
\(166\) −0.0609193 + 1.04594i −0.00472825 + 0.0811810i
\(167\) 6.65820 0.778232i 0.515227 0.0602214i 0.145493 0.989359i \(-0.453523\pi\)
0.369733 + 0.929138i \(0.379449\pi\)
\(168\) 0 0
\(169\) 15.6023 + 7.83578i 1.20018 + 0.602753i
\(170\) −2.21203 + 1.85612i −0.169655 + 0.142358i
\(171\) 0 0
\(172\) 1.12877 + 0.947150i 0.0860679 + 0.0722195i
\(173\) −5.85754 13.5793i −0.445340 1.03242i −0.982045 0.188645i \(-0.939590\pi\)
0.536705 0.843770i \(-0.319669\pi\)
\(174\) 0 0
\(175\) 1.23757 + 0.293310i 0.0935517 + 0.0221722i
\(176\) 2.98934 + 9.98511i 0.225330 + 0.752656i
\(177\) 0 0
\(178\) 4.42659 + 0.517395i 0.331787 + 0.0387804i
\(179\) −0.110050 + 0.624125i −0.00822552 + 0.0466493i −0.988644 0.150275i \(-0.951984\pi\)
0.980419 + 0.196924i \(0.0630953\pi\)
\(180\) 0 0
\(181\) −2.42311 13.7421i −0.180108 1.02145i −0.932081 0.362251i \(-0.882008\pi\)
0.751972 0.659195i \(-0.229103\pi\)
\(182\) 0.258968 + 4.44631i 0.0191960 + 0.329583i
\(183\) 0 0
\(184\) 2.09767 4.86295i 0.154642 0.358501i
\(185\) 6.67192 3.35077i 0.490529 0.246353i
\(186\) 0 0
\(187\) 12.7749 3.02771i 0.934195 0.221408i
\(188\) −4.31771 7.47849i −0.314901 0.545425i
\(189\) 0 0
\(190\) 0.0205270 0.0355538i 0.00148918 0.00257934i
\(191\) −2.43589 + 8.13645i −0.176255 + 0.588733i 0.823515 + 0.567294i \(0.192010\pi\)
−0.999770 + 0.0214386i \(0.993175\pi\)
\(192\) 0 0
\(193\) −11.0711 7.28156i −0.796914 0.524138i 0.0845336 0.996421i \(-0.473060\pi\)
−0.881447 + 0.472282i \(0.843430\pi\)
\(194\) 1.33063 + 1.78735i 0.0955336 + 0.128324i
\(195\) 0 0
\(196\) −0.841633 + 0.553551i −0.0601167 + 0.0395394i
\(197\) 7.09307 + 2.58167i 0.505360 + 0.183936i 0.582103 0.813115i \(-0.302230\pi\)
−0.0767431 + 0.997051i \(0.524452\pi\)
\(198\) 0 0
\(199\) 1.98595 0.722827i 0.140780 0.0512399i −0.270669 0.962672i \(-0.587245\pi\)
0.411449 + 0.911433i \(0.365023\pi\)
\(200\) 0.369414 0.496209i 0.0261215 0.0350873i
\(201\) 0 0
\(202\) −2.36316 + 2.50480i −0.166271 + 0.176237i
\(203\) 18.6398 19.7570i 1.30825 1.38667i
\(204\) 0 0
\(205\) 3.19228 4.28798i 0.222958 0.299485i
\(206\) 3.70790 1.34957i 0.258342 0.0940287i
\(207\) 0 0
\(208\) −17.6649 6.42950i −1.22484 0.445805i
\(209\) −0.155949 + 0.102569i −0.0107872 + 0.00709488i
\(210\) 0 0
\(211\) 0.392021 + 0.526575i 0.0269878 + 0.0362509i 0.815412 0.578881i \(-0.196510\pi\)
−0.788424 + 0.615132i \(0.789103\pi\)
\(212\) −3.13042 2.05891i −0.214998 0.141407i
\(213\) 0 0
\(214\) −0.453003 + 1.51313i −0.0309666 + 0.103436i
\(215\) 0.822857 1.42523i 0.0561184 0.0971998i
\(216\) 0 0
\(217\) 5.86733 + 10.1625i 0.398301 + 0.689877i
\(218\) 0.111526 0.0264323i 0.00755352 0.00179022i
\(219\) 0 0
\(220\) 11.0178 5.53333i 0.742817 0.373057i
\(221\) −9.37868 + 21.7422i −0.630878 + 1.46254i
\(222\) 0 0
\(223\) −1.30890 22.4729i −0.0876503 1.50490i −0.699904 0.714237i \(-0.746774\pi\)
0.612254 0.790661i \(-0.290263\pi\)
\(224\) −1.57018 8.90495i −0.104912 0.594987i
\(225\) 0 0
\(226\) −1.08766 + 6.16845i −0.0723503 + 0.410319i
\(227\) 13.3179 + 1.55664i 0.883942 + 0.103318i 0.545937 0.837826i \(-0.316174\pi\)
0.338005 + 0.941144i \(0.390248\pi\)
\(228\) 0 0
\(229\) −1.78489 5.96194i −0.117949 0.393976i 0.878543 0.477663i \(-0.158516\pi\)
−0.996492 + 0.0836862i \(0.973331\pi\)
\(230\) −2.80351 0.664443i −0.184858 0.0438121i
\(231\) 0 0
\(232\) −5.23277 12.1309i −0.343548 0.796434i
\(233\) −9.49107 7.96396i −0.621781 0.521736i 0.276582 0.960990i \(-0.410798\pi\)
−0.898363 + 0.439254i \(0.855243\pi\)
\(234\) 0 0
\(235\) −7.38822 + 6.19946i −0.481955 + 0.404408i
\(236\) −12.2434 6.14885i −0.796975 0.400256i
\(237\) 0 0
\(238\) −3.43895 + 0.401956i −0.222914 + 0.0260549i
\(239\) 0.571683 9.81542i 0.0369791 0.634907i −0.928000 0.372580i \(-0.878473\pi\)
0.964979 0.262327i \(-0.0844897\pi\)
\(240\) 0 0
\(241\) 11.8975 + 12.6106i 0.766384 + 0.812320i 0.986605 0.163130i \(-0.0521591\pi\)
−0.220220 + 0.975450i \(0.570678\pi\)
\(242\) −0.519105 −0.0333693
\(243\) 0 0
\(244\) 22.1823 1.42008
\(245\) 0.772080 + 0.818357i 0.0493264 + 0.0522829i
\(246\) 0 0
\(247\) 0.0195744 0.336079i 0.00124549 0.0213842i
\(248\) 5.66905 0.662617i 0.359985 0.0420762i
\(249\) 0 0
\(250\) −3.30799 1.66133i −0.209216 0.105072i
\(251\) −19.1764 + 16.0909i −1.21040 + 1.01565i −0.211132 + 0.977458i \(0.567715\pi\)
−0.999270 + 0.0381908i \(0.987841\pi\)
\(252\) 0 0
\(253\) 10.0348 + 8.42023i 0.630885 + 0.529375i
\(254\) −1.81280 4.20253i −0.113745 0.263690i
\(255\) 0 0
\(256\) 8.31055 + 1.96964i 0.519409 + 0.123102i
\(257\) −0.691327 2.30919i −0.0431238 0.144044i 0.933716 0.358013i \(-0.116546\pi\)
−0.976840 + 0.213970i \(0.931361\pi\)
\(258\) 0 0
\(259\) 8.89161 + 1.03928i 0.552498 + 0.0645777i
\(260\) −3.86134 + 21.8987i −0.239470 + 1.35810i
\(261\) 0 0
\(262\) 0.168301 + 0.954483i 0.0103977 + 0.0589682i
\(263\) 0.228089 + 3.91614i 0.0140646 + 0.241480i 0.998012 + 0.0630218i \(0.0200737\pi\)
−0.983948 + 0.178458i \(0.942889\pi\)
\(264\) 0 0
\(265\) −1.65748 + 3.84247i −0.101818 + 0.236041i
\(266\) 0.0439895 0.0220924i 0.00269717 0.00135457i
\(267\) 0 0
\(268\) 2.24174 0.531302i 0.136936 0.0324545i
\(269\) −5.54513 9.60445i −0.338093 0.585594i 0.645981 0.763353i \(-0.276448\pi\)
−0.984074 + 0.177760i \(0.943115\pi\)
\(270\) 0 0
\(271\) −0.397309 + 0.688159i −0.0241348 + 0.0418027i −0.877841 0.478953i \(-0.841016\pi\)
0.853706 + 0.520756i \(0.174350\pi\)
\(272\) 4.19128 13.9998i 0.254134 0.848865i
\(273\) 0 0
\(274\) −0.690526 0.454166i −0.0417162 0.0274372i
\(275\) 0.913725 + 1.22735i 0.0550997 + 0.0740117i
\(276\) 0 0
\(277\) −24.3861 + 16.0390i −1.46522 + 0.963688i −0.468436 + 0.883497i \(0.655182\pi\)
−0.996780 + 0.0801905i \(0.974447\pi\)
\(278\) 5.65991 + 2.06004i 0.339459 + 0.123553i
\(279\) 0 0
\(280\) −6.27272 + 2.28308i −0.374867 + 0.136440i
\(281\) −16.4750 + 22.1297i −0.982814 + 1.32015i −0.0356623 + 0.999364i \(0.511354\pi\)
−0.947152 + 0.320785i \(0.896053\pi\)
\(282\) 0 0
\(283\) 3.50574 3.71587i 0.208395 0.220886i −0.614743 0.788728i \(-0.710740\pi\)
0.823137 + 0.567842i \(0.192222\pi\)
\(284\) −18.5971 + 19.7118i −1.10354 + 1.16968i
\(285\) 0 0
\(286\) −3.19973 + 4.29798i −0.189204 + 0.254145i
\(287\) 6.02327 2.19229i 0.355542 0.129407i
\(288\) 0 0
\(289\) −1.32268 0.481415i −0.0778046 0.0283185i
\(290\) −6.00486 + 3.94946i −0.352618 + 0.231920i
\(291\) 0 0
\(292\) −11.0189 14.8009i −0.644832 0.866160i
\(293\) 1.95792 + 1.28775i 0.114383 + 0.0752310i 0.605412 0.795913i \(-0.293009\pi\)
−0.491028 + 0.871144i \(0.663379\pi\)
\(294\) 0 0
\(295\) −4.38863 + 14.6590i −0.255516 + 0.853482i
\(296\) 2.17712 3.77089i 0.126543 0.219178i
\(297\) 0 0
\(298\) −0.650036 1.12590i −0.0376556 0.0652214i
\(299\) −22.9891 + 5.44853i −1.32950 + 0.315096i
\(300\) 0 0
\(301\) 1.76339 0.885607i 0.101640 0.0510456i
\(302\) 1.24928 2.89615i 0.0718878 0.166655i
\(303\) 0 0
\(304\) 0.0120807 + 0.207417i 0.000692874 + 0.0118962i
\(305\) −4.30210 24.3984i −0.246337 1.39705i
\(306\) 0 0
\(307\) −2.80743 + 15.9217i −0.160228 + 0.908700i 0.793620 + 0.608413i \(0.208194\pi\)
−0.953849 + 0.300287i \(0.902918\pi\)
\(308\) 14.6833 + 1.71623i 0.836657 + 0.0977911i
\(309\) 0 0
\(310\) −0.890543 2.97462i −0.0505794 0.168947i
\(311\) −20.6275 4.88881i −1.16968 0.277219i −0.400527 0.916285i \(-0.631173\pi\)
−0.769152 + 0.639066i \(0.779321\pi\)
\(312\) 0 0
\(313\) −2.14335 4.96885i −0.121149 0.280856i 0.846840 0.531848i \(-0.178502\pi\)
−0.967989 + 0.250992i \(0.919243\pi\)
\(314\) 2.80708 + 2.35542i 0.158413 + 0.132924i
\(315\) 0 0
\(316\) −2.34420 + 1.96701i −0.131871 + 0.110653i
\(317\) 7.79902 + 3.91682i 0.438037 + 0.219990i 0.654130 0.756382i \(-0.273035\pi\)
−0.216093 + 0.976373i \(0.569331\pi\)
\(318\) 0 0
\(319\) 32.4567 3.79364i 1.81723 0.212403i
\(320\) 0.701133 12.0380i 0.0391945 0.672944i
\(321\) 0 0
\(322\) −2.37072 2.51282i −0.132115 0.140034i
\(323\) 0.261706 0.0145617
\(324\) 0 0
\(325\) −2.75968 −0.153080
\(326\) 3.07719 + 3.26163i 0.170430 + 0.180645i
\(327\) 0 0
\(328\) 0.181277 3.11241i 0.0100094 0.171854i
\(329\) −11.4862 + 1.34254i −0.633252 + 0.0740166i
\(330\) 0 0
\(331\) −17.5604 8.81917i −0.965207 0.484745i −0.104878 0.994485i \(-0.533445\pi\)
−0.860329 + 0.509740i \(0.829742\pi\)
\(332\) −4.80468 + 4.03161i −0.263691 + 0.221263i
\(333\) 0 0
\(334\) −1.62927 1.36712i −0.0891495 0.0748053i
\(335\) −1.01915 2.36265i −0.0556821 0.129086i
\(336\) 0 0
\(337\) −7.14751 1.69399i −0.389350 0.0922776i 0.0312784 0.999511i \(-0.490042\pi\)
−0.420628 + 0.907233i \(0.638190\pi\)
\(338\) −1.58873 5.30672i −0.0864154 0.288647i
\(339\) 0 0
\(340\) −17.1695 2.00683i −0.931148 0.108836i
\(341\) −2.45148 + 13.9030i −0.132755 + 0.752892i
\(342\) 0 0
\(343\) 3.32603 + 18.8629i 0.179589 + 1.01850i
\(344\) −0.0558067 0.958164i −0.00300889 0.0516607i
\(345\) 0 0
\(346\) −1.85845 + 4.30836i −0.0999107 + 0.231619i
\(347\) 16.2806 8.17644i 0.873990 0.438934i 0.0455174 0.998964i \(-0.485506\pi\)
0.828473 + 0.560029i \(0.189210\pi\)
\(348\) 0 0
\(349\) −15.6760 + 3.71527i −0.839116 + 0.198874i −0.627635 0.778508i \(-0.715977\pi\)
−0.211481 + 0.977382i \(0.567829\pi\)
\(350\) −0.201764 0.349465i −0.0107847 0.0186797i
\(351\) 0 0
\(352\) 5.43923 9.42103i 0.289912 0.502142i
\(353\) 4.92839 16.4620i 0.262312 0.876183i −0.720795 0.693149i \(-0.756223\pi\)
0.983107 0.183034i \(-0.0585919\pi\)
\(354\) 0 0
\(355\) 25.2878 + 16.6321i 1.34214 + 0.882739i
\(356\) 15.9321 + 21.4005i 0.844400 + 1.13423i
\(357\) 0 0
\(358\) 0.167994 0.110492i 0.00887878 0.00583967i
\(359\) 26.7193 + 9.72505i 1.41019 + 0.513268i 0.931187 0.364543i \(-0.118775\pi\)
0.479007 + 0.877811i \(0.340997\pi\)
\(360\) 0 0
\(361\) 17.8507 6.49711i 0.939509 0.341953i
\(362\) −2.64379 + 3.55123i −0.138955 + 0.186649i
\(363\) 0 0
\(364\) −18.2970 + 19.3937i −0.959023 + 1.01651i
\(365\) −14.1426 + 14.9902i −0.740256 + 0.784625i
\(366\) 0 0
\(367\) 6.19676 8.32370i 0.323468 0.434494i −0.610409 0.792086i \(-0.708995\pi\)
0.933878 + 0.357593i \(0.116402\pi\)
\(368\) 13.7018 4.98706i 0.714258 0.259969i
\(369\) 0 0
\(370\) −2.22594 0.810174i −0.115721 0.0421190i
\(371\) −4.19218 + 2.75724i −0.217647 + 0.143149i
\(372\) 0 0
\(373\) 8.89318 + 11.9456i 0.460472 + 0.618521i 0.970344 0.241730i \(-0.0777147\pi\)
−0.509872 + 0.860250i \(0.670307\pi\)
\(374\) −3.48017 2.28895i −0.179955 0.118359i
\(375\) 0 0
\(376\) −1.61321 + 5.38850i −0.0831950 + 0.277891i
\(377\) −29.4683 + 51.0405i −1.51769 + 2.62872i
\(378\) 0 0
\(379\) −5.81217 10.0670i −0.298551 0.517106i 0.677253 0.735750i \(-0.263170\pi\)
−0.975805 + 0.218644i \(0.929837\pi\)
\(380\) 0.239142 0.0566776i 0.0122677 0.00290750i
\(381\) 0 0
\(382\) 2.40807 1.20938i 0.123207 0.0618771i
\(383\) −11.2946 + 26.1838i −0.577127 + 1.33793i 0.340408 + 0.940278i \(0.389435\pi\)
−0.917535 + 0.397654i \(0.869824\pi\)
\(384\) 0 0
\(385\) −0.960026 16.4830i −0.0489274 0.840052i
\(386\) 0.730054 + 4.14034i 0.0371588 + 0.210738i
\(387\) 0 0
\(388\) −2.31635 + 13.1367i −0.117595 + 0.666915i
\(389\) −3.04961 0.356448i −0.154621 0.0180726i 0.0384301 0.999261i \(-0.487764\pi\)
−0.193051 + 0.981189i \(0.561838\pi\)
\(390\) 0 0
\(391\) −5.26758 17.5949i −0.266393 0.889814i
\(392\) 0.638468 + 0.151320i 0.0322475 + 0.00764280i
\(393\) 0 0
\(394\) −0.948562 2.19901i −0.0477879 0.110785i
\(395\) 2.61816 + 2.19690i 0.131734 + 0.110538i
\(396\) 0 0
\(397\) −8.05095 + 6.75555i −0.404065 + 0.339051i −0.822063 0.569397i \(-0.807177\pi\)
0.417997 + 0.908448i \(0.362732\pi\)
\(398\) −0.599207 0.300933i −0.0300355 0.0150844i
\(399\) 0 0
\(400\) 1.69167 0.197728i 0.0845836 0.00988640i
\(401\) −1.54074 + 26.4534i −0.0769407 + 1.32102i 0.710092 + 0.704109i \(0.248653\pi\)
−0.787033 + 0.616912i \(0.788384\pi\)
\(402\) 0 0
\(403\) −17.4731 18.5204i −0.870395 0.922565i
\(404\) −20.6150 −1.02563
\(405\) 0 0
\(406\) −8.61783 −0.427696
\(407\) 7.39081 + 7.83380i 0.366349 + 0.388307i
\(408\) 0 0
\(409\) −1.53226 + 26.3079i −0.0757654 + 1.30084i 0.719463 + 0.694531i \(0.244388\pi\)
−0.795228 + 0.606311i \(0.792649\pi\)
\(410\) −1.68461 + 0.196903i −0.0831970 + 0.00972434i
\(411\) 0 0
\(412\) 21.1090 + 10.6014i 1.03997 + 0.522291i
\(413\) −14.0551 + 11.7936i −0.691605 + 0.580326i
\(414\) 0 0
\(415\) 5.36621 + 4.50278i 0.263417 + 0.221033i
\(416\) 7.77112 + 18.0155i 0.381011 + 0.883282i
\(417\) 0 0
\(418\) 0.0576250 + 0.0136574i 0.00281853 + 0.000668004i
\(419\) −2.24612 7.50255i −0.109730 0.366523i 0.885432 0.464768i \(-0.153862\pi\)
−0.995162 + 0.0982448i \(0.968677\pi\)
\(420\) 0 0
\(421\) 31.6365 + 3.69777i 1.54187 + 0.180218i 0.844131 0.536136i \(-0.180117\pi\)
0.697736 + 0.716355i \(0.254191\pi\)
\(422\) 0.0361680 0.205119i 0.00176063 0.00998504i
\(423\) 0 0
\(424\) 0.423796 + 2.40347i 0.0205813 + 0.116723i
\(425\) −0.124740 2.14171i −0.00605080 0.103888i
\(426\) 0 0
\(427\) 11.7660 27.2766i 0.569395 1.32001i
\(428\) −8.44973 + 4.24361i −0.408433 + 0.205123i
\(429\) 0 0
\(430\) −0.508068 + 0.120414i −0.0245012 + 0.00580690i
\(431\) 16.6567 + 28.8502i 0.802324 + 1.38967i 0.918083 + 0.396389i \(0.129737\pi\)
−0.115759 + 0.993277i \(0.536930\pi\)
\(432\) 0 0
\(433\) 2.75793 4.77688i 0.132538 0.229562i −0.792116 0.610370i \(-0.791021\pi\)
0.924654 + 0.380808i \(0.124354\pi\)
\(434\) 1.06780 3.56670i 0.0512560 0.171207i
\(435\) 0 0
\(436\) 0.573261 + 0.377040i 0.0274542 + 0.0180569i
\(437\) 0.155932 + 0.209453i 0.00745922 + 0.0100195i
\(438\) 0 0
\(439\) 2.76551 1.81890i 0.131990 0.0868114i −0.481797 0.876283i \(-0.660016\pi\)
0.613787 + 0.789472i \(0.289645\pi\)
\(440\) −7.54647 2.74669i −0.359764 0.130943i
\(441\) 0 0
\(442\) 7.05960 2.56948i 0.335791 0.122218i
\(443\) 10.2627 13.7852i 0.487595 0.654954i −0.488432 0.872602i \(-0.662431\pi\)
0.976027 + 0.217648i \(0.0698385\pi\)
\(444\) 0 0
\(445\) 20.4486 21.6742i 0.969355 1.02746i
\(446\) −4.90125 + 5.19502i −0.232081 + 0.245991i
\(447\) 0 0
\(448\) 8.63404 11.5975i 0.407920 0.547931i
\(449\) 16.5392 6.01977i 0.780532 0.284090i 0.0791375 0.996864i \(-0.474783\pi\)
0.701394 + 0.712773i \(0.252561\pi\)
\(450\) 0 0
\(451\) 7.24636 + 2.63746i 0.341218 + 0.124193i
\(452\) −31.3279 + 20.6047i −1.47354 + 0.969164i
\(453\) 0 0
\(454\) −2.54043 3.41239i −0.119228 0.160152i
\(455\) 24.8797 + 16.3636i 1.16638 + 0.767140i
\(456\) 0 0
\(457\) −5.12647 + 17.1236i −0.239806 + 0.801009i 0.750350 + 0.661041i \(0.229885\pi\)
−0.990156 + 0.139968i \(0.955300\pi\)
\(458\) −0.987261 + 1.70999i −0.0461317 + 0.0799024i
\(459\) 0 0
\(460\) −8.62394 14.9371i −0.402093 0.696446i
\(461\) −4.89168 + 1.15935i −0.227828 + 0.0539963i −0.342944 0.939356i \(-0.611424\pi\)
0.115116 + 0.993352i \(0.463276\pi\)
\(462\) 0 0
\(463\) 15.3751 7.72167i 0.714542 0.358857i −0.0541001 0.998536i \(-0.517229\pi\)
0.768642 + 0.639679i \(0.220933\pi\)
\(464\) 14.4069 33.3989i 0.668823 1.55051i
\(465\) 0 0
\(466\) 0.228564 + 3.92429i 0.0105880 + 0.181789i
\(467\) −6.50441 36.8883i −0.300988 1.70699i −0.641812 0.766862i \(-0.721817\pi\)
0.340824 0.940127i \(-0.389294\pi\)
\(468\) 0 0
\(469\) 0.535748 3.03838i 0.0247385 0.140299i
\(470\) 3.03931 + 0.355244i 0.140193 + 0.0163862i
\(471\) 0 0
\(472\) 2.55947 + 8.54921i 0.117809 + 0.393510i
\(473\) 2.30999 + 0.547477i 0.106213 + 0.0251730i
\(474\) 0 0
\(475\) 0.0120808 + 0.0280065i 0.000554306 + 0.00128503i
\(476\) −15.8779 13.3232i −0.727764 0.610666i
\(477\) 0 0
\(478\) −2.38964 + 2.00515i −0.109300 + 0.0917134i
\(479\) −3.05867 1.53612i −0.139754 0.0701872i 0.377548 0.925990i \(-0.376767\pi\)
−0.517302 + 0.855803i \(0.673064\pi\)
\(480\) 0 0
\(481\) −19.2931 + 2.25504i −0.879689 + 0.102821i
\(482\) 0.319834 5.49133i 0.0145680 0.250123i
\(483\) 0 0
\(484\) −2.13255 2.26037i −0.0969341 0.102744i
\(485\) 14.8983 0.676498
\(486\) 0 0
\(487\) −5.43342 −0.246212 −0.123106 0.992394i \(-0.539285\pi\)
−0.123106 + 0.992394i \(0.539285\pi\)
\(488\) −9.91535 10.5097i −0.448847 0.475750i
\(489\) 0 0
\(490\) 0.0207554 0.356357i 0.000937634 0.0160986i
\(491\) −3.94699 + 0.461337i −0.178125 + 0.0208199i −0.204688 0.978827i \(-0.565618\pi\)
0.0265626 + 0.999647i \(0.491544\pi\)
\(492\) 0 0
\(493\) −40.9431 20.5624i −1.84398 0.926084i
\(494\) −0.0818212 + 0.0686561i −0.00368131 + 0.00308898i
\(495\) 0 0
\(496\) 12.0379 + 10.1010i 0.540516 + 0.453547i
\(497\) 14.3744 + 33.3236i 0.644779 + 1.49477i
\(498\) 0 0
\(499\) −20.8781 4.94820i −0.934632 0.221512i −0.265037 0.964238i \(-0.585384\pi\)
−0.669595 + 0.742727i \(0.733532\pi\)
\(500\) −6.35559 21.2292i −0.284231 0.949397i
\(501\) 0 0
\(502\) 7.88862 + 0.922048i 0.352086 + 0.0411530i
\(503\) 4.28340 24.2924i 0.190987 1.08314i −0.727031 0.686605i \(-0.759100\pi\)
0.918018 0.396538i \(-0.129789\pi\)
\(504\) 0 0
\(505\) 3.99812 + 22.6745i 0.177914 + 1.00900i
\(506\) −0.241659 4.14912i −0.0107430 0.184451i
\(507\) 0 0
\(508\) 10.8522 25.1581i 0.481487 1.11621i
\(509\) −6.56544 + 3.29729i −0.291008 + 0.146150i −0.588314 0.808633i \(-0.700208\pi\)
0.297306 + 0.954782i \(0.403912\pi\)
\(510\) 0 0
\(511\) −24.0447 + 5.69869i −1.06367 + 0.252095i
\(512\) −10.2684 17.7854i −0.453804 0.786011i
\(513\) 0 0
\(514\) −0.382388 + 0.662316i −0.0168664 + 0.0292135i
\(515\) 7.56652 25.2739i 0.333421 1.11370i
\(516\) 0 0
\(517\) −11.6238 7.64511i −0.511215 0.336232i
\(518\) −1.69610 2.27826i −0.0745224 0.100101i
\(519\) 0 0
\(520\) 12.1013 7.95914i 0.530676 0.349031i
\(521\) −25.5909 9.31432i −1.12116 0.408068i −0.286082 0.958205i \(-0.592353\pi\)
−0.835074 + 0.550137i \(0.814575\pi\)
\(522\) 0 0
\(523\) −14.3006 + 5.20499i −0.625321 + 0.227598i −0.635193 0.772353i \(-0.719080\pi\)
0.00987267 + 0.999951i \(0.496857\pi\)
\(524\) −3.46476 + 4.65399i −0.151359 + 0.203310i
\(525\) 0 0
\(526\) 0.854094 0.905286i 0.0372403 0.0394724i
\(527\) 13.5833 14.3975i 0.591699 0.627165i
\(528\) 0 0
\(529\) −2.79137 + 3.74946i −0.121364 + 0.163020i
\(530\) 1.24763 0.454101i 0.0541936 0.0197249i
\(531\) 0 0
\(532\) 0.276913 + 0.100788i 0.0120057 + 0.00436972i
\(533\) −11.6200 + 7.64262i −0.503320 + 0.331039i
\(534\) 0 0
\(535\) 6.30632 + 8.47086i 0.272646 + 0.366227i
\(536\) −1.25377 0.824615i −0.0541544 0.0356179i
\(537\) 0 0
\(538\) −1.00916 + 3.37084i −0.0435081 + 0.145327i
\(539\) −0.811481 + 1.40553i −0.0349530 + 0.0605403i
\(540\) 0 0
\(541\) −8.31159 14.3961i −0.357343 0.618937i 0.630173 0.776455i \(-0.282984\pi\)
−0.987516 + 0.157518i \(0.949651\pi\)
\(542\) 0.245316 0.0581409i 0.0105372 0.00249737i
\(543\) 0 0
\(544\) −13.6300 + 6.84527i −0.584383 + 0.293488i
\(545\) 0.303527 0.703655i 0.0130017 0.0301413i
\(546\) 0 0
\(547\) −0.656042 11.2638i −0.0280503 0.481605i −0.982856 0.184375i \(-0.940974\pi\)
0.954806 0.297231i \(-0.0960630\pi\)
\(548\) −0.859166 4.87257i −0.0367018 0.208146i
\(549\) 0 0
\(550\) 0.0843006 0.478093i 0.00359459 0.0203859i
\(551\) 0.646983 + 0.0756214i 0.0275624 + 0.00322158i
\(552\) 0 0
\(553\) 1.17533 + 3.92589i 0.0499803 + 0.166946i
\(554\) 9.01092 + 2.13563i 0.382837 + 0.0907341i
\(555\) 0 0
\(556\) 14.2815 + 33.1082i 0.605671 + 1.40410i
\(557\) 22.3339 + 18.7404i 0.946318 + 0.794055i 0.978674 0.205421i \(-0.0658565\pi\)
−0.0323557 + 0.999476i \(0.510301\pi\)
\(558\) 0 0
\(559\) −3.27993 + 2.75219i −0.138726 + 0.116405i
\(560\) −16.4236 8.24823i −0.694023 0.348551i
\(561\) 0 0
\(562\) 8.69407 1.01619i 0.366737 0.0428655i
\(563\) 1.24814 21.4297i 0.0526028 0.903154i −0.864034 0.503433i \(-0.832070\pi\)
0.916637 0.399721i \(-0.130893\pi\)
\(564\) 0 0
\(565\) 28.7390 + 30.4615i 1.20906 + 1.28153i
\(566\) −1.62083 −0.0681286
\(567\) 0 0
\(568\) 17.6519 0.740659
\(569\) 1.83992 + 1.95021i 0.0771336 + 0.0817569i 0.764791 0.644279i \(-0.222842\pi\)
−0.687657 + 0.726035i \(0.741361\pi\)
\(570\) 0 0
\(571\) 0.165178 2.83600i 0.00691248 0.118683i −0.993087 0.117383i \(-0.962549\pi\)
0.999999 0.00129937i \(-0.000413604\pi\)
\(572\) −31.8599 + 3.72388i −1.33213 + 0.155703i
\(573\) 0 0
\(574\) −1.81736 0.912711i −0.0758550 0.0380958i
\(575\) 1.63976 1.37592i 0.0683828 0.0573800i
\(576\) 0 0
\(577\) 4.53692 + 3.80692i 0.188874 + 0.158484i 0.732322 0.680959i \(-0.238437\pi\)
−0.543447 + 0.839443i \(0.682881\pi\)
\(578\) 0.176883 + 0.410061i 0.00735736 + 0.0170563i
\(579\) 0 0
\(580\) −41.8662 9.92246i −1.73840 0.412008i
\(581\) 2.40898 + 8.04654i 0.0999412 + 0.333827i
\(582\) 0 0
\(583\) −5.99572 0.700800i −0.248318 0.0290242i
\(584\) −2.08710 + 11.8365i −0.0863646 + 0.489798i
\(585\) 0 0
\(586\) −0.129110 0.732221i −0.00533350 0.0302478i
\(587\) 0.655164 + 11.2487i 0.0270415 + 0.464285i 0.984463 + 0.175592i \(0.0561838\pi\)
−0.957422 + 0.288694i \(0.906779\pi\)
\(588\) 0 0
\(589\) −0.111463 + 0.258400i −0.00459274 + 0.0106472i
\(590\) 4.33849 2.17887i 0.178613 0.0897027i
\(591\) 0 0
\(592\) 11.6650 2.76465i 0.479428 0.113627i
\(593\) 4.74627 + 8.22078i 0.194906 + 0.337587i 0.946870 0.321617i \(-0.104226\pi\)
−0.751964 + 0.659205i \(0.770893\pi\)
\(594\) 0 0
\(595\) −11.5748 + 20.0481i −0.474519 + 0.821892i
\(596\) 2.23212 7.45582i 0.0914314 0.305402i
\(597\) 0 0
\(598\) 6.26275 + 4.11907i 0.256103 + 0.168441i
\(599\) 14.8996 + 20.0136i 0.608780 + 0.817733i 0.994484 0.104889i \(-0.0334488\pi\)
−0.385704 + 0.922623i \(0.626041\pi\)
\(600\) 0 0
\(601\) 9.59732 6.31226i 0.391483 0.257482i −0.338474 0.940976i \(-0.609911\pi\)
0.729957 + 0.683494i \(0.239540\pi\)
\(602\) −0.588315 0.214129i −0.0239779 0.00872725i
\(603\) 0 0
\(604\) 17.7431 6.45795i 0.721955 0.262770i
\(605\) −2.07260 + 2.78398i −0.0842630 + 0.113185i
\(606\) 0 0
\(607\) −27.3496 + 28.9889i −1.11009 + 1.17662i −0.127303 + 0.991864i \(0.540632\pi\)
−0.982784 + 0.184759i \(0.940849\pi\)
\(608\) 0.148810 0.157730i 0.00603505 0.00639678i
\(609\) 0 0
\(610\) −4.69391 + 6.30501i −0.190051 + 0.255283i
\(611\) 23.5792 8.58211i 0.953911 0.347195i
\(612\) 0 0
\(613\) −16.9065 6.15347i −0.682848 0.248536i −0.0227782 0.999741i \(-0.507251\pi\)
−0.660070 + 0.751204i \(0.729473\pi\)
\(614\) 4.28562 2.81869i 0.172953 0.113753i
\(615\) 0 0
\(616\) −5.75019 7.72385i −0.231682 0.311203i
\(617\) −15.3291 10.0821i −0.617124 0.405889i 0.202098 0.979365i \(-0.435224\pi\)
−0.819222 + 0.573476i \(0.805594\pi\)
\(618\) 0 0
\(619\) 12.8881 43.0492i 0.518016 1.73029i −0.152409 0.988317i \(-0.548703\pi\)
0.670425 0.741977i \(-0.266112\pi\)
\(620\) 9.29411 16.0979i 0.373260 0.646506i
\(621\) 0 0
\(622\) 3.36294 + 5.82478i 0.134842 + 0.233553i
\(623\) 34.7659 8.23968i 1.39287 0.330116i
\(624\) 0 0
\(625\) −19.8832 + 9.98569i −0.795326 + 0.399428i
\(626\) −0.680030 + 1.57649i −0.0271795 + 0.0630091i
\(627\) 0 0
\(628\) 1.27549 + 21.8994i 0.0508978 + 0.873881i
\(629\) −2.62214 14.8709i −0.104552 0.592941i
\(630\) 0 0
\(631\) 5.90645 33.4972i 0.235132 1.33350i −0.607203 0.794547i \(-0.707708\pi\)
0.842335 0.538954i \(-0.181180\pi\)
\(632\) 1.97978 + 0.231403i 0.0787515 + 0.00920473i
\(633\) 0 0
\(634\) −0.794146 2.65263i −0.0315396 0.105349i
\(635\) −29.7762 7.05709i −1.18163 0.280052i
\(636\) 0 0
\(637\) −1.15938 2.68774i −0.0459362 0.106492i
\(638\) −7.94218 6.66428i −0.314434 0.263841i
\(639\) 0 0
\(640\) −14.4847 + 12.1541i −0.572556 + 0.480432i
\(641\) −0.281153 0.141200i −0.0111049 0.00557707i 0.443238 0.896404i \(-0.353830\pi\)
−0.454343 + 0.890827i \(0.650126\pi\)
\(642\) 0 0
\(643\) 32.9098 3.84660i 1.29783 0.151695i 0.561027 0.827797i \(-0.310406\pi\)
0.736808 + 0.676102i \(0.236332\pi\)
\(644\) 1.20249 20.6460i 0.0473848 0.813565i
\(645\) 0 0
\(646\) −0.0569804 0.0603957i −0.00224187 0.00237624i
\(647\) 14.0510 0.552403 0.276201 0.961100i \(-0.410924\pi\)
0.276201 + 0.961100i \(0.410924\pi\)
\(648\) 0 0
\(649\) −22.0733 −0.866453
\(650\) 0.600857 + 0.636871i 0.0235675 + 0.0249801i
\(651\) 0 0
\(652\) −1.56083 + 26.7984i −0.0611268 + 1.04951i
\(653\) 44.6094 5.21409i 1.74570 0.204043i 0.817451 0.575999i \(-0.195387\pi\)
0.928251 + 0.371955i \(0.121313\pi\)
\(654\) 0 0
\(655\) 5.79089 + 2.90830i 0.226269 + 0.113637i
\(656\) 6.57544 5.51745i 0.256728 0.215420i
\(657\) 0 0
\(658\) 2.81067 + 2.35843i 0.109571 + 0.0919413i
\(659\) −13.2766 30.7786i −0.517182 1.19896i −0.954107 0.299465i \(-0.903192\pi\)
0.436925 0.899498i \(-0.356067\pi\)
\(660\) 0 0
\(661\) 15.7899 + 3.74227i 0.614156 + 0.145558i 0.525909 0.850541i \(-0.323725\pi\)
0.0882470 + 0.996099i \(0.471874\pi\)
\(662\) 1.78811 + 5.97271i 0.0694969 + 0.232136i
\(663\) 0 0
\(664\) 4.05778 + 0.474286i 0.157472 + 0.0184059i
\(665\) 0.0571518 0.324124i 0.00221625 0.0125690i
\(666\) 0 0
\(667\) −7.93821 45.0198i −0.307369 1.74317i
\(668\) −0.740315 12.7107i −0.0286436 0.491792i
\(669\) 0 0
\(670\) −0.323350 + 0.749610i −0.0124921 + 0.0289599i
\(671\) 31.9368 16.0393i 1.23291 0.619190i
\(672\) 0 0
\(673\) 1.91409 0.453649i 0.0737829 0.0174869i −0.193559 0.981089i \(-0.562003\pi\)
0.267342 + 0.963602i \(0.413855\pi\)
\(674\) 1.16527 + 2.01831i 0.0448846 + 0.0777424i
\(675\) 0 0
\(676\) 16.5807 28.7186i 0.637719 1.10456i
\(677\) −5.88502 + 19.6573i −0.226180 + 0.755493i 0.767280 + 0.641312i \(0.221609\pi\)
−0.993460 + 0.114181i \(0.963576\pi\)
\(678\) 0 0
\(679\) 14.9249 + 9.81628i 0.572766 + 0.376714i
\(680\) 6.72385 + 9.03170i 0.257848 + 0.346350i
\(681\) 0 0
\(682\) 3.74226 2.46132i 0.143298 0.0942489i
\(683\) 20.1405 + 7.33055i 0.770656 + 0.280496i 0.697271 0.716808i \(-0.254398\pi\)
0.0733852 + 0.997304i \(0.476620\pi\)
\(684\) 0 0
\(685\) −5.19273 + 1.89000i −0.198404 + 0.0722131i
\(686\) 3.62895 4.87452i 0.138554 0.186110i
\(687\) 0 0
\(688\) 1.81339 1.92208i 0.0691348 0.0732786i
\(689\) 7.47134 7.91916i 0.284636 0.301696i
\(690\) 0 0
\(691\) 16.5776 22.2675i 0.630640 0.847096i −0.365862 0.930669i \(-0.619226\pi\)
0.996502 + 0.0835728i \(0.0266331\pi\)
\(692\) −26.3949 + 9.60696i −1.00338 + 0.365202i
\(693\) 0 0
\(694\) −5.43167 1.97696i −0.206183 0.0750446i
\(695\) 33.6460 22.1293i 1.27627 0.839414i
\(696\) 0 0
\(697\) −6.45646 8.67253i −0.244556 0.328495i
\(698\) 4.27048 + 2.80874i 0.161640 + 0.106312i
\(699\) 0 0
\(700\) 0.692825 2.31420i 0.0261863 0.0874685i
\(701\) −0.354873 + 0.614659i −0.0134034 + 0.0232153i −0.872649 0.488347i \(-0.837600\pi\)
0.859246 + 0.511563i \(0.170933\pi\)
\(702\) 0 0
\(703\) 0.107343 + 0.185923i 0.00404851 + 0.00701223i
\(704\) 16.9256 4.01145i 0.637909 0.151187i
\(705\) 0 0
\(706\) −4.87209 + 2.44686i −0.183364 + 0.0920886i
\(707\) −10.9346 + 25.3493i −0.411238 + 0.953357i
\(708\) 0 0
\(709\) 1.17399 + 20.1566i 0.0440900 + 0.756996i 0.945819 + 0.324694i \(0.105261\pi\)
−0.901729 + 0.432302i \(0.857702\pi\)
\(710\) −1.66754 9.45710i −0.0625817 0.354919i
\(711\) 0 0
\(712\) 3.01771 17.1143i 0.113093 0.641385i
\(713\) 19.6161 + 2.29280i 0.734630 + 0.0858659i
\(714\) 0 0
\(715\) 10.2749 + 34.3205i 0.384259 + 1.28351i
\(716\) 1.17126 + 0.277595i 0.0437722 + 0.0103742i
\(717\) 0 0
\(718\) −3.57320 8.28361i −0.133351 0.309142i
\(719\) 12.8502 + 10.7826i 0.479231 + 0.402123i 0.850148 0.526543i \(-0.176512\pi\)
−0.370917 + 0.928666i \(0.620957\pi\)
\(720\) 0 0
\(721\) 24.2326 20.3336i 0.902471 0.757263i
\(722\) −5.38595 2.70493i −0.200444 0.100667i
\(723\) 0 0
\(724\) −26.3244 + 3.07688i −0.978339 + 0.114351i
\(725\) 0.310479 5.33072i 0.0115309 0.197978i
\(726\) 0 0
\(727\) 15.2361 + 16.1493i 0.565075 + 0.598945i 0.945402 0.325908i \(-0.105670\pi\)
−0.380327 + 0.924852i \(0.624188\pi\)
\(728\) 17.3671 0.643666
\(729\) 0 0
\(730\) 6.53862 0.242005
\(731\) −2.28415 2.42106i −0.0844823 0.0895461i
\(732\) 0 0
\(733\) −0.226456 + 3.88810i −0.00836434 + 0.143610i 0.991540 + 0.129799i \(0.0414333\pi\)
−0.999905 + 0.0138108i \(0.995604\pi\)
\(734\) −3.27012 + 0.382222i −0.120702 + 0.0141081i
\(735\) 0 0
\(736\) −13.5997 6.83001i −0.501290 0.251757i
\(737\) 2.84336 2.38586i 0.104737 0.0878844i
\(738\) 0 0
\(739\) −15.2233 12.7738i −0.559997 0.469894i 0.318312 0.947986i \(-0.396884\pi\)
−0.878310 + 0.478092i \(0.841328\pi\)
\(740\) −5.61664 13.0208i −0.206472 0.478655i
\(741\) 0 0
\(742\) 1.54906 + 0.367134i 0.0568678 + 0.0134779i
\(743\) −1.78348 5.95723i −0.0654294 0.218549i 0.919022 0.394206i \(-0.128980\pi\)
−0.984452 + 0.175657i \(0.943795\pi\)
\(744\) 0 0
\(745\) −8.63357 1.00912i −0.316310 0.0369713i
\(746\) 0.820489 4.65322i 0.0300402 0.170367i
\(747\) 0 0
\(748\) −4.33010 24.5572i −0.158324 0.897901i
\(749\) 0.736262 + 12.6411i 0.0269024 + 0.461897i
\(750\) 0 0
\(751\) −6.38259 + 14.7965i −0.232904 + 0.539933i −0.994085 0.108608i \(-0.965361\pi\)
0.761181 + 0.648540i \(0.224620\pi\)
\(752\) −13.8390 + 6.95021i −0.504657 + 0.253448i
\(753\) 0 0
\(754\) 18.1950 4.31230i 0.662623 0.157045i
\(755\) −10.5442 18.2632i −0.383744 0.664665i
\(756\) 0 0
\(757\) 17.7618 30.7643i 0.645563 1.11815i −0.338608 0.940928i \(-0.609956\pi\)
0.984171 0.177221i \(-0.0567106\pi\)
\(758\) −1.05776 + 3.53317i −0.0384196 + 0.128330i
\(759\) 0 0
\(760\) −0.133748 0.0879672i −0.00485154 0.00319091i
\(761\) −12.1544 16.3261i −0.440595 0.591822i 0.525248 0.850949i \(-0.323973\pi\)
−0.965843 + 0.259127i \(0.916565\pi\)
\(762\) 0 0
\(763\) 0.767697 0.504922i 0.0277925 0.0182794i
\(764\) 15.1587 + 5.51732i 0.548423 + 0.199610i
\(765\) 0 0
\(766\) 8.50177 3.09439i 0.307181 0.111805i
\(767\) 23.7734 31.9332i 0.858406 1.15304i
\(768\) 0 0
\(769\) 12.7783 13.5442i 0.460797 0.488416i −0.454755 0.890617i \(-0.650273\pi\)
0.915552 + 0.402201i \(0.131755\pi\)
\(770\) −3.59488 + 3.81035i −0.129550 + 0.137315i
\(771\) 0 0
\(772\) −15.0294 + 20.1880i −0.540920 + 0.726582i
\(773\) 3.69733 1.34572i 0.132984 0.0484021i −0.274671 0.961538i \(-0.588569\pi\)
0.407655 + 0.913136i \(0.366347\pi\)
\(774\) 0 0
\(775\) 2.16778 + 0.789007i 0.0778689 + 0.0283420i
\(776\) 7.25936 4.77456i 0.260596 0.171397i
\(777\) 0 0
\(778\) 0.581721 + 0.781387i 0.0208557 + 0.0280141i
\(779\) 0.128429 + 0.0844689i 0.00460144 + 0.00302641i
\(780\) 0 0
\(781\) −12.5221 + 41.8268i −0.448077 + 1.49668i
\(782\) −2.91361 + 5.04653i −0.104191 + 0.180463i
\(783\) 0 0
\(784\) 0.903265 + 1.56450i 0.0322595 + 0.0558750i
\(785\) 23.8398 5.65014i 0.850880 0.201662i
\(786\) 0 0
\(787\) 6.59214 3.31070i 0.234984 0.118014i −0.327411 0.944882i \(-0.606176\pi\)
0.562395 + 0.826868i \(0.309880\pi\)
\(788\) 5.67849 13.1642i 0.202288 0.468956i
\(789\) 0 0
\(790\) −0.0630505 1.08254i −0.00224324 0.0385149i
\(791\) 8.71966 + 49.4517i 0.310035 + 1.75830i
\(792\) 0 0
\(793\) −11.1927 + 63.4772i −0.397466 + 2.25414i
\(794\) 3.31193 + 0.387109i 0.117536 + 0.0137380i
\(795\) 0 0
\(796\) −1.15125 3.84544i −0.0408049 0.136298i
\(797\) 14.5445 + 3.44711i 0.515192 + 0.122103i 0.479984 0.877277i \(-0.340642\pi\)
0.0352081 + 0.999380i \(0.488791\pi\)
\(798\) 0 0
\(799\) 7.72613 + 17.9112i 0.273331 + 0.633652i
\(800\) −1.36173 1.14263i −0.0481446 0.0403981i
\(801\) 0 0
\(802\) 6.44030 5.40405i 0.227415 0.190824i
\(803\) −26.5664 13.3422i −0.937508 0.470834i
\(804\) 0 0
\(805\) −22.9418 + 2.68151i −0.808591 + 0.0945107i
\(806\) −0.469719 + 8.06476i −0.0165451 + 0.284069i
\(807\) 0 0
\(808\) 9.21475 + 9.76707i 0.324174 + 0.343604i
\(809\) −28.6228 −1.00633 −0.503163 0.864192i \(-0.667830\pi\)
−0.503163 + 0.864192i \(0.667830\pi\)
\(810\) 0 0
\(811\) 15.2720 0.536273 0.268136 0.963381i \(-0.413592\pi\)
0.268136 + 0.963381i \(0.413592\pi\)
\(812\) −35.4032 37.5252i −1.24241 1.31688i
\(813\) 0 0
\(814\) 0.198683 3.41126i 0.00696384 0.119564i
\(815\) 29.7784 3.48059i 1.04309 0.121920i
\(816\) 0 0
\(817\) 0.0422887 + 0.0212382i 0.00147949 + 0.000743030i
\(818\) 6.40487 5.37433i 0.223941 0.187909i
\(819\) 0 0
\(820\) −7.77799 6.52651i −0.271619 0.227915i
\(821\) −1.23281 2.85798i −0.0430254 0.0997441i 0.895348 0.445367i \(-0.146927\pi\)
−0.938373 + 0.345623i \(0.887668\pi\)
\(822\) 0 0
\(823\) 37.4863 + 8.88442i 1.30669 + 0.309691i 0.824244 0.566234i \(-0.191600\pi\)
0.482446 + 0.875926i \(0.339748\pi\)
\(824\) −4.41283 14.7399i −0.153728 0.513488i
\(825\) 0 0
\(826\) 5.78186 + 0.675803i 0.201177 + 0.0235142i
\(827\) −1.37656 + 7.80687i −0.0478677 + 0.271471i −0.999343 0.0362552i \(-0.988457\pi\)
0.951475 + 0.307727i \(0.0995682\pi\)
\(828\) 0 0
\(829\) 5.51283 + 31.2648i 0.191469 + 1.08587i 0.917359 + 0.398061i \(0.130317\pi\)
−0.725890 + 0.687811i \(0.758572\pi\)
\(830\) −0.129229 2.21877i −0.00448560 0.0770148i
\(831\) 0 0
\(832\) −12.4259 + 28.8065i −0.430791 + 0.998686i
\(833\) 2.03347 1.02125i 0.0704556 0.0353841i
\(834\) 0 0
\(835\) −13.8370 + 3.27942i −0.478848 + 0.113489i
\(836\) 0.177262 + 0.307026i 0.00613073 + 0.0106187i
\(837\) 0 0
\(838\) −1.24238 + 2.15186i −0.0429172 + 0.0743347i
\(839\) −12.9827 + 43.3653i −0.448214 + 1.49714i 0.373713 + 0.927544i \(0.378084\pi\)
−0.821927 + 0.569593i \(0.807101\pi\)
\(840\) 0 0
\(841\) −71.0476 46.7288i −2.44992 1.61134i
\(842\) −6.03475 8.10608i −0.207971 0.279354i
\(843\) 0 0
\(844\) 1.04175 0.685167i 0.0358584 0.0235844i
\(845\) −34.8033 12.6674i −1.19727 0.435771i
\(846\) 0 0
\(847\) −3.91062 + 1.42335i −0.134370 + 0.0489069i
\(848\) −4.01250 + 5.38972i −0.137790 + 0.185084i
\(849\) 0 0
\(850\) −0.467098 + 0.495095i −0.0160213 + 0.0169816i
\(851\) 10.3393 10.9591i 0.354428 0.375672i
\(852\) 0 0
\(853\) 27.8462 37.4040i 0.953437 1.28069i −0.00635570 0.999980i \(-0.502023\pi\)
0.959793 0.280709i \(-0.0905695\pi\)
\(854\) −8.85657 + 3.22353i −0.303066 + 0.110307i
\(855\) 0 0
\(856\) 5.78753 + 2.10649i 0.197814 + 0.0719983i
\(857\) 5.70365 3.75135i 0.194833 0.128144i −0.448344 0.893861i \(-0.647986\pi\)
0.643177 + 0.765717i \(0.277616\pi\)
\(858\) 0 0
\(859\) 6.56110 + 8.81309i 0.223862 + 0.300699i 0.899837 0.436225i \(-0.143685\pi\)
−0.675976 + 0.736924i \(0.736278\pi\)
\(860\) −2.61154 1.71764i −0.0890527 0.0585709i
\(861\) 0 0
\(862\) 3.03136 10.1254i 0.103249 0.344874i
\(863\) 27.8142 48.1756i 0.946807 1.63992i 0.194715 0.980860i \(-0.437622\pi\)
0.752092 0.659058i \(-0.229045\pi\)
\(864\) 0 0
\(865\) 15.6858 + 27.1686i 0.533334 + 0.923761i
\(866\) −1.70287 + 0.403587i −0.0578659 + 0.0137145i
\(867\) 0 0
\(868\) 19.9174 10.0029i 0.676039 0.339520i
\(869\) −1.95276 + 4.52700i −0.0662427 + 0.153568i
\(870\) 0 0
\(871\) 0.389245 + 6.68307i 0.0131891 + 0.226447i
\(872\) −0.0776079 0.440136i −0.00262814 0.0149049i
\(873\) 0 0
\(874\) 0.0143863 0.0815889i 0.000486625 0.00275979i
\(875\) −29.4756 3.44521i −0.996458 0.116469i
\(876\) 0 0
\(877\) −7.07646 23.6370i −0.238955 0.798166i −0.990383 0.138351i \(-0.955820\pi\)
0.751428 0.659815i \(-0.229365\pi\)
\(878\) −1.02189 0.242191i −0.0344870 0.00817356i
\(879\) 0 0
\(880\) −8.75748 20.3021i −0.295215 0.684384i
\(881\) −13.2241 11.0964i −0.445532 0.373846i 0.392243 0.919862i \(-0.371699\pi\)
−0.837775 + 0.546016i \(0.816144\pi\)
\(882\) 0 0
\(883\) −24.0818 + 20.2071i −0.810419 + 0.680022i −0.950708 0.310089i \(-0.899641\pi\)
0.140289 + 0.990111i \(0.455197\pi\)
\(884\) 40.1902 + 20.1843i 1.35174 + 0.678871i
\(885\) 0 0
\(886\) −5.41577 + 0.633012i −0.181946 + 0.0212665i
\(887\) −2.57144 + 44.1499i −0.0863405 + 1.48241i 0.625586 + 0.780155i \(0.284860\pi\)
−0.711927 + 0.702254i \(0.752177\pi\)
\(888\) 0 0
\(889\) −25.1796 26.6888i −0.844495 0.895113i
\(890\) −9.45412 −0.316903
\(891\) 0 0
\(892\) −42.7560 −1.43158
\(893\) −0.190316 0.201723i −0.00636867 0.00675039i
\(894\) 0 0
\(895\) 0.0781692 1.34211i 0.00261291 0.0448619i
\(896\) −22.5187 + 2.63205i −0.752296 + 0.0879307i
\(897\) 0 0
\(898\) −4.99025 2.50620i −0.166527 0.0836328i
\(899\) 37.7406 31.6681i 1.25872 1.05619i
\(900\) 0 0
\(901\) 6.48355 + 5.44034i 0.215998 + 0.181244i
\(902\) −0.969062 2.24654i −0.0322662 0.0748016i
\(903\) 0 0
\(904\) 23.7656 + 5.63254i 0.790431 + 0.187336i
\(905\) 8.48969 + 28.3575i 0.282207 + 0.942636i
\(906\) 0 0
\(907\) −14.6813 1.71600i −0.487486 0.0569790i −0.131200 0.991356i \(-0.541883\pi\)
−0.356286 + 0.934377i \(0.615957\pi\)
\(908\) 4.42237 25.0805i 0.146762 0.832327i
\(909\) 0 0
\(910\) −1.64063 9.30447i −0.0543863 0.308440i
\(911\) 2.25338 + 38.6890i 0.0746577 + 1.28182i 0.802738 + 0.596332i \(0.203376\pi\)
−0.728081 + 0.685492i \(0.759587\pi\)
\(912\) 0 0
\(913\) −4.00239 + 9.27857i −0.132460 + 0.307076i
\(914\) 5.06791 2.54520i 0.167631 0.0841877i
\(915\) 0 0
\(916\) −11.5017 + 2.72595i −0.380027 + 0.0900680i
\(917\) 3.88500 + 6.72903i 0.128294 + 0.222212i
\(918\) 0 0
\(919\) −20.8939 + 36.1894i −0.689228 + 1.19378i 0.282860 + 0.959161i \(0.408717\pi\)
−0.972088 + 0.234616i \(0.924617\pi\)
\(920\) −3.22213 + 10.7627i −0.106231 + 0.354835i
\(921\) 0 0
\(922\) 1.33260 + 0.876466i 0.0438869 + 0.0288649i
\(923\) −47.0238 63.1639i −1.54781 2.07906i
\(924\) 0 0
\(925\) 1.47037 0.967075i 0.0483453 0.0317972i
\(926\) −5.12956 1.86701i −0.168568 0.0613536i
\(927\) 0 0
\(928\) −35.6738 + 12.9842i −1.17105 + 0.426227i
\(929\) −15.8991 + 21.3562i −0.521633 + 0.700675i −0.982388 0.186853i \(-0.940171\pi\)
0.460755 + 0.887527i \(0.347579\pi\)
\(930\) 0 0
\(931\) −0.0222011 + 0.0235317i −0.000727610 + 0.000771222i
\(932\) −16.1488 + 17.1167i −0.528972 + 0.560677i
\(933\) 0 0
\(934\) −7.09680 + 9.53265i −0.232214 + 0.311918i
\(935\) −26.1707 + 9.52537i −0.855875 + 0.311513i
\(936\) 0 0
\(937\) 10.5874 + 3.85350i 0.345875 + 0.125888i 0.509116 0.860698i \(-0.329972\pi\)
−0.163241 + 0.986586i \(0.552195\pi\)
\(938\) −0.817834 + 0.537898i −0.0267032 + 0.0175630i
\(939\) 0 0
\(940\) 10.9390 + 14.6936i 0.356791 + 0.479254i
\(941\) −14.7963 9.73168i −0.482346 0.317244i 0.284944 0.958544i \(-0.408025\pi\)
−0.767290 + 0.641300i \(0.778395\pi\)
\(942\) 0 0
\(943\) 3.09399 10.3347i 0.100754 0.336543i
\(944\) −12.2850 + 21.2782i −0.399842 + 0.692546i
\(945\) 0 0
\(946\) −0.376601 0.652293i −0.0122444 0.0212079i
\(947\) −57.8204 + 13.7037i −1.87891 + 0.445310i −0.999525 0.0308032i \(-0.990193\pi\)
−0.879384 + 0.476113i \(0.842045\pi\)
\(948\) 0 0
\(949\) 47.9144 24.0635i 1.55537 0.781135i
\(950\) 0.00383293 0.00888574i 0.000124357 0.000288292i
\(951\) 0 0
\(952\) 0.785009 + 13.4781i 0.0254423 + 0.436827i
\(953\) 9.46496 + 53.6784i 0.306600 + 1.73881i 0.615876 + 0.787843i \(0.288802\pi\)
−0.309277 + 0.950972i \(0.600087\pi\)
\(954\) 0 0
\(955\) 3.12859 17.7431i 0.101239 0.574155i
\(956\) −18.5481 2.16796i −0.599889 0.0701169i
\(957\) 0 0
\(958\) 0.311453 + 1.04033i 0.0100626 + 0.0336114i
\(959\) −6.44729 1.52804i −0.208194 0.0493429i
\(960\) 0 0
\(961\) −3.84814 8.92099i −0.124133 0.287774i
\(962\) 4.72103 + 3.96142i 0.152212 + 0.127721i
\(963\) 0 0
\(964\) 25.2252 21.1664i 0.812448 0.681725i
\(965\) 25.1197 + 12.6156i 0.808630 + 0.406109i
\(966\) 0 0
\(967\) −28.1479 + 3.29002i −0.905175 + 0.105800i −0.555927 0.831231i \(-0.687637\pi\)
−0.349247 + 0.937031i \(0.613563\pi\)
\(968\) −0.117695 + 2.02074i −0.00378285 + 0.0649491i
\(969\) 0 0
\(970\) −3.24376 3.43819i −0.104151 0.110394i
\(971\) −34.6038 −1.11049 −0.555244 0.831687i \(-0.687375\pi\)
−0.555244 + 0.831687i \(0.687375\pi\)
\(972\) 0 0
\(973\) 48.2868 1.54801
\(974\) 1.18300 + 1.25391i 0.0379058 + 0.0401778i
\(975\) 0 0
\(976\) 2.31303 39.7132i 0.0740382 1.27119i
\(977\) 13.1806 1.54060i 0.421686 0.0492880i 0.0973958 0.995246i \(-0.468949\pi\)
0.324290 + 0.945958i \(0.394875\pi\)
\(978\) 0 0
\(979\) 38.4121 + 19.2913i 1.22766 + 0.616552i
\(980\) 1.63697 1.37358i 0.0522912 0.0438775i
\(981\) 0 0
\(982\) 0.965832 + 0.810430i 0.0308209 + 0.0258618i
\(983\) 14.2596 + 33.0575i 0.454811 + 1.05437i 0.979201 + 0.202892i \(0.0650341\pi\)
−0.524390 + 0.851478i \(0.675707\pi\)
\(984\) 0 0
\(985\) −15.5807 3.69268i −0.496441 0.117659i
\(986\) 4.16908 + 13.9257i 0.132771 + 0.443485i
\(987\) 0 0
\(988\) −0.635085 0.0742308i −0.0202048 0.00236160i
\(989\) 0.576698 3.27062i 0.0183379 0.104000i
\(990\) 0 0
\(991\) 9.06181 + 51.3921i 0.287858 + 1.63252i 0.694895 + 0.719111i \(0.255451\pi\)
−0.407037 + 0.913412i \(0.633438\pi\)
\(992\) −0.953635 16.3733i −0.0302780 0.519852i
\(993\) 0 0
\(994\) 4.56062 10.5727i 0.144654 0.335346i
\(995\) −4.00633 + 2.01205i −0.127009 + 0.0637864i
\(996\) 0 0
\(997\) 17.5636 4.16265i 0.556245 0.131833i 0.0571279 0.998367i \(-0.481806\pi\)
0.499118 + 0.866534i \(0.333658\pi\)
\(998\) 3.40379 + 5.89554i 0.107745 + 0.186620i
\(999\) 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.d.109.4 144
3.2 odd 2 729.2.g.a.109.5 144
9.2 odd 6 729.2.g.b.352.5 144
9.4 even 3 81.2.g.a.76.5 yes 144
9.5 odd 6 243.2.g.a.118.4 144
9.7 even 3 729.2.g.c.352.4 144
81.11 odd 54 729.2.g.a.622.5 144
81.16 even 27 729.2.g.c.379.4 144
81.31 even 27 6561.2.a.c.1.42 72
81.38 odd 54 243.2.g.a.208.4 144
81.43 even 27 81.2.g.a.16.5 144
81.50 odd 54 6561.2.a.d.1.31 72
81.65 odd 54 729.2.g.b.379.5 144
81.70 even 27 inner 729.2.g.d.622.4 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.16.5 144 81.43 even 27
81.2.g.a.76.5 yes 144 9.4 even 3
243.2.g.a.118.4 144 9.5 odd 6
243.2.g.a.208.4 144 81.38 odd 54
729.2.g.a.109.5 144 3.2 odd 2
729.2.g.a.622.5 144 81.11 odd 54
729.2.g.b.352.5 144 9.2 odd 6
729.2.g.b.379.5 144 81.65 odd 54
729.2.g.c.352.4 144 9.7 even 3
729.2.g.c.379.4 144 81.16 even 27
729.2.g.d.109.4 144 1.1 even 1 trivial
729.2.g.d.622.4 144 81.70 even 27 inner
6561.2.a.c.1.42 72 81.31 even 27
6561.2.a.d.1.31 72 81.50 odd 54