Properties

Label 729.2.g.a.28.1
Level $729$
Weight $2$
Character 729.28
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 28.1
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.a.703.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.23012 + 1.46677i) q^{2} +(2.02985 - 4.70573i) q^{4} +(1.24595 - 1.32063i) q^{5} +(2.56492 + 0.299797i) q^{7} +(1.44840 + 8.21430i) q^{8} +O(q^{10})\) \(q+(-2.23012 + 1.46677i) q^{2} +(2.02985 - 4.70573i) q^{4} +(1.24595 - 1.32063i) q^{5} +(2.56492 + 0.299797i) q^{7} +(1.44840 + 8.21430i) q^{8} +(-0.841551 + 4.77267i) q^{10} +(-1.04979 + 3.50653i) q^{11} +(-0.0220064 + 0.377836i) q^{13} +(-6.15982 + 3.09358i) q^{14} +(-8.24485 - 8.73903i) q^{16} +(-2.13907 + 0.778557i) q^{17} +(-1.32149 - 0.480985i) q^{19} +(-3.68542 - 8.54376i) q^{20} +(-2.80213 - 9.35978i) q^{22} +(3.51611 - 0.410974i) q^{23} +(0.0990536 + 1.70069i) q^{25} +(-0.505123 - 0.874898i) q^{26} +(6.61718 - 11.4613i) q^{28} +(5.90521 + 2.96571i) q^{29} +(5.83658 + 7.83989i) q^{31} +(14.9728 + 3.54862i) q^{32} +(3.62841 - 4.87381i) q^{34} +(3.59167 - 3.01377i) q^{35} +(-0.463728 - 0.389114i) q^{37} +(3.65259 - 0.865679i) q^{38} +(12.6526 + 8.32178i) q^{40} +(-2.79880 - 1.84080i) q^{41} +(2.59620 - 0.615311i) q^{43} +(14.3699 + 12.0578i) q^{44} +(-7.23854 + 6.07386i) q^{46} +(-0.0900157 + 0.120912i) q^{47} +(-0.322362 - 0.0764011i) q^{49} +(-2.71542 - 3.64744i) q^{50} +(1.73333 + 0.870509i) q^{52} +(6.72572 - 11.6493i) q^{53} +(3.32284 + 5.75532i) q^{55} +(1.25242 + 21.5033i) q^{56} +(-17.5193 + 2.04772i) q^{58} +(-1.21847 - 4.06996i) q^{59} +(2.95087 + 6.84088i) q^{61} +(-24.5156 - 8.92296i) q^{62} +(-16.0163 + 5.82946i) q^{64} +(0.471561 + 0.499826i) q^{65} +(9.01808 - 4.52905i) q^{67} +(-0.678316 + 11.6462i) q^{68} +(-3.58935 + 11.9892i) q^{70} +(0.305263 - 1.73123i) q^{71} +(0.930968 + 5.27978i) q^{73} +(1.60491 + 0.187587i) q^{74} +(-4.94583 + 5.24227i) q^{76} +(-3.74387 + 8.67926i) q^{77} +(-3.55048 + 2.33519i) q^{79} -21.8136 q^{80} +8.94171 q^{82} +(2.17613 - 1.43126i) q^{83} +(-1.63698 + 3.79495i) q^{85} +(-4.88732 + 5.18025i) q^{86} +(-30.3242 - 3.54439i) q^{88} +(0.553979 + 3.14177i) q^{89} +(-0.169719 + 0.962523i) q^{91} +(5.20326 - 17.3801i) q^{92} +(0.0233953 - 0.401681i) q^{94} +(-2.28171 + 1.14592i) q^{95} +(-10.5487 - 11.1810i) q^{97} +(0.830968 - 0.302448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23012 + 1.46677i −1.57693 + 1.03717i −0.606720 + 0.794916i \(0.707515\pi\)
−0.970214 + 0.242249i \(0.922115\pi\)
\(3\) 0 0
\(4\) 2.02985 4.70573i 1.01493 2.35287i
\(5\) 1.24595 1.32063i 0.557204 0.590602i −0.386131 0.922444i \(-0.626189\pi\)
0.943335 + 0.331842i \(0.107670\pi\)
\(6\) 0 0
\(7\) 2.56492 + 0.299797i 0.969450 + 0.113312i 0.586054 0.810272i \(-0.300681\pi\)
0.383396 + 0.923584i \(0.374755\pi\)
\(8\) 1.44840 + 8.21430i 0.512088 + 2.90419i
\(9\) 0 0
\(10\) −0.841551 + 4.77267i −0.266122 + 1.50925i
\(11\) −1.04979 + 3.50653i −0.316522 + 1.05726i 0.640673 + 0.767814i \(0.278656\pi\)
−0.957195 + 0.289444i \(0.906530\pi\)
\(12\) 0 0
\(13\) −0.0220064 + 0.377836i −0.00610349 + 0.104793i −0.999984 0.00566826i \(-0.998196\pi\)
0.993880 + 0.110461i \(0.0352328\pi\)
\(14\) −6.15982 + 3.09358i −1.64628 + 0.826794i
\(15\) 0 0
\(16\) −8.24485 8.73903i −2.06121 2.18476i
\(17\) −2.13907 + 0.778557i −0.518800 + 0.188828i −0.588131 0.808766i \(-0.700136\pi\)
0.0693304 + 0.997594i \(0.477914\pi\)
\(18\) 0 0
\(19\) −1.32149 0.480985i −0.303172 0.110345i 0.185955 0.982558i \(-0.440462\pi\)
−0.489127 + 0.872213i \(0.662684\pi\)
\(20\) −3.68542 8.54376i −0.824085 1.91044i
\(21\) 0 0
\(22\) −2.80213 9.35978i −0.597417 1.99551i
\(23\) 3.51611 0.410974i 0.733160 0.0856941i 0.258683 0.965962i \(-0.416711\pi\)
0.474476 + 0.880268i \(0.342637\pi\)
\(24\) 0 0
\(25\) 0.0990536 + 1.70069i 0.0198107 + 0.340137i
\(26\) −0.505123 0.874898i −0.0990627 0.171582i
\(27\) 0 0
\(28\) 6.61718 11.4613i 1.25053 2.16598i
\(29\) 5.90521 + 2.96571i 1.09657 + 0.550718i 0.902683 0.430306i \(-0.141594\pi\)
0.193887 + 0.981024i \(0.437891\pi\)
\(30\) 0 0
\(31\) 5.83658 + 7.83989i 1.04828 + 1.40809i 0.908491 + 0.417905i \(0.137235\pi\)
0.139790 + 0.990181i \(0.455357\pi\)
\(32\) 14.9728 + 3.54862i 2.64684 + 0.627313i
\(33\) 0 0
\(34\) 3.62841 4.87381i 0.622268 0.835851i
\(35\) 3.59167 3.01377i 0.607104 0.509421i
\(36\) 0 0
\(37\) −0.463728 0.389114i −0.0762364 0.0639699i 0.603873 0.797080i \(-0.293623\pi\)
−0.680110 + 0.733111i \(0.738068\pi\)
\(38\) 3.65259 0.865679i 0.592528 0.140432i
\(39\) 0 0
\(40\) 12.6526 + 8.32178i 2.00056 + 1.31579i
\(41\) −2.79880 1.84080i −0.437099 0.287485i 0.311826 0.950139i \(-0.399059\pi\)
−0.748925 + 0.662654i \(0.769430\pi\)
\(42\) 0 0
\(43\) 2.59620 0.615311i 0.395917 0.0938340i −0.0278346 0.999613i \(-0.508861\pi\)
0.423751 + 0.905779i \(0.360713\pi\)
\(44\) 14.3699 + 12.0578i 2.16634 + 1.81778i
\(45\) 0 0
\(46\) −7.23854 + 6.07386i −1.06726 + 0.895542i
\(47\) −0.0900157 + 0.120912i −0.0131301 + 0.0176368i −0.808640 0.588304i \(-0.799796\pi\)
0.795510 + 0.605941i \(0.207203\pi\)
\(48\) 0 0
\(49\) −0.322362 0.0764011i −0.0460516 0.0109144i
\(50\) −2.71542 3.64744i −0.384019 0.515826i
\(51\) 0 0
\(52\) 1.73333 + 0.870509i 0.240369 + 0.120718i
\(53\) 6.72572 11.6493i 0.923849 1.60015i 0.130448 0.991455i \(-0.458358\pi\)
0.793401 0.608699i \(-0.208308\pi\)
\(54\) 0 0
\(55\) 3.32284 + 5.75532i 0.448051 + 0.776047i
\(56\) 1.25242 + 21.5033i 0.167362 + 2.87350i
\(57\) 0 0
\(58\) −17.5193 + 2.04772i −2.30040 + 0.268879i
\(59\) −1.21847 4.06996i −0.158631 0.529864i 0.841312 0.540550i \(-0.181784\pi\)
−0.999943 + 0.0106860i \(0.996598\pi\)
\(60\) 0 0
\(61\) 2.95087 + 6.84088i 0.377820 + 0.875885i 0.995958 + 0.0898159i \(0.0286279\pi\)
−0.618138 + 0.786069i \(0.712113\pi\)
\(62\) −24.5156 8.92296i −3.11349 1.13322i
\(63\) 0 0
\(64\) −16.0163 + 5.82946i −2.00204 + 0.728682i
\(65\) 0.471561 + 0.499826i 0.0584900 + 0.0619957i
\(66\) 0 0
\(67\) 9.01808 4.52905i 1.10173 0.553311i 0.197480 0.980307i \(-0.436724\pi\)
0.904254 + 0.426996i \(0.140428\pi\)
\(68\) −0.678316 + 11.6462i −0.0822579 + 1.41231i
\(69\) 0 0
\(70\) −3.58935 + 11.9892i −0.429009 + 1.43299i
\(71\) 0.305263 1.73123i 0.0362281 0.205460i −0.961321 0.275431i \(-0.911180\pi\)
0.997549 + 0.0699711i \(0.0222907\pi\)
\(72\) 0 0
\(73\) 0.930968 + 5.27978i 0.108962 + 0.617951i 0.989564 + 0.144095i \(0.0460272\pi\)
−0.880602 + 0.473856i \(0.842862\pi\)
\(74\) 1.60491 + 0.187587i 0.186567 + 0.0218066i
\(75\) 0 0
\(76\) −4.94583 + 5.24227i −0.567325 + 0.601330i
\(77\) −3.74387 + 8.67926i −0.426653 + 0.989093i
\(78\) 0 0
\(79\) −3.55048 + 2.33519i −0.399460 + 0.262729i −0.733306 0.679898i \(-0.762024\pi\)
0.333846 + 0.942628i \(0.391653\pi\)
\(80\) −21.8136 −2.43884
\(81\) 0 0
\(82\) 8.94171 0.987446
\(83\) 2.17613 1.43126i 0.238861 0.157102i −0.424435 0.905458i \(-0.639527\pi\)
0.663296 + 0.748357i \(0.269157\pi\)
\(84\) 0 0
\(85\) −1.63698 + 3.79495i −0.177556 + 0.411620i
\(86\) −4.88732 + 5.18025i −0.527013 + 0.558601i
\(87\) 0 0
\(88\) −30.3242 3.54439i −3.23257 0.377833i
\(89\) 0.553979 + 3.14177i 0.0587216 + 0.333027i 0.999989 0.00463450i \(-0.00147521\pi\)
−0.941268 + 0.337661i \(0.890364\pi\)
\(90\) 0 0
\(91\) −0.169719 + 0.962523i −0.0177914 + 0.100900i
\(92\) 5.20326 17.3801i 0.542477 1.81200i
\(93\) 0 0
\(94\) 0.0233953 0.401681i 0.00241304 0.0414302i
\(95\) −2.28171 + 1.14592i −0.234099 + 0.117569i
\(96\) 0 0
\(97\) −10.5487 11.1810i −1.07106 1.13526i −0.990360 0.138520i \(-0.955765\pi\)
−0.0807017 0.996738i \(-0.525716\pi\)
\(98\) 0.830968 0.302448i 0.0839405 0.0305518i
\(99\) 0 0
\(100\) 8.20403 + 2.98602i 0.820403 + 0.298602i
\(101\) 5.16679 + 11.9780i 0.514115 + 1.19185i 0.955622 + 0.294594i \(0.0951846\pi\)
−0.441508 + 0.897258i \(0.645556\pi\)
\(102\) 0 0
\(103\) 3.93516 + 13.1443i 0.387742 + 1.29515i 0.899839 + 0.436222i \(0.143684\pi\)
−0.512097 + 0.858928i \(0.671131\pi\)
\(104\) −3.13553 + 0.366491i −0.307464 + 0.0359374i
\(105\) 0 0
\(106\) 2.08770 + 35.8445i 0.202776 + 3.48152i
\(107\) 1.15268 + 1.99650i 0.111434 + 0.193009i 0.916349 0.400381i \(-0.131122\pi\)
−0.804915 + 0.593390i \(0.797789\pi\)
\(108\) 0 0
\(109\) −4.62468 + 8.01018i −0.442964 + 0.767236i −0.997908 0.0646518i \(-0.979406\pi\)
0.554944 + 0.831888i \(0.312740\pi\)
\(110\) −15.8521 7.96121i −1.51144 0.759072i
\(111\) 0 0
\(112\) −18.5275 24.8867i −1.75068 2.35157i
\(113\) −9.24278 2.19058i −0.869487 0.206072i −0.228425 0.973561i \(-0.573358\pi\)
−0.641062 + 0.767489i \(0.721506\pi\)
\(114\) 0 0
\(115\) 3.83814 5.15552i 0.357908 0.480754i
\(116\) 25.9425 21.7684i 2.40870 2.02114i
\(117\) 0 0
\(118\) 8.68704 + 7.28929i 0.799706 + 0.671033i
\(119\) −5.71996 + 1.35565i −0.524347 + 0.124273i
\(120\) 0 0
\(121\) −2.00333 1.31761i −0.182121 0.119783i
\(122\) −16.6148 10.9277i −1.50424 0.989351i
\(123\) 0 0
\(124\) 48.7398 11.5516i 4.37697 1.03736i
\(125\) 9.32357 + 7.82340i 0.833925 + 0.699746i
\(126\) 0 0
\(127\) 9.69030 8.13112i 0.859875 0.721521i −0.102066 0.994778i \(-0.532545\pi\)
0.961941 + 0.273257i \(0.0881009\pi\)
\(128\) 8.79016 11.8072i 0.776948 1.04362i
\(129\) 0 0
\(130\) −1.78477 0.422998i −0.156535 0.0370994i
\(131\) 8.88502 + 11.9347i 0.776288 + 1.04274i 0.997715 + 0.0675591i \(0.0215211\pi\)
−0.221427 + 0.975177i \(0.571071\pi\)
\(132\) 0 0
\(133\) −3.24533 1.62987i −0.281406 0.141328i
\(134\) −13.4683 + 23.3278i −1.16349 + 2.01522i
\(135\) 0 0
\(136\) −9.49354 16.4433i −0.814064 1.41000i
\(137\) −0.944711 16.2201i −0.0807121 1.38577i −0.759054 0.651027i \(-0.774338\pi\)
0.678342 0.734746i \(-0.262699\pi\)
\(138\) 0 0
\(139\) 16.3959 1.91640i 1.39068 0.162547i 0.612441 0.790516i \(-0.290188\pi\)
0.778238 + 0.627969i \(0.216114\pi\)
\(140\) −6.89143 23.0190i −0.582432 1.94546i
\(141\) 0 0
\(142\) 1.85855 + 4.30861i 0.155966 + 0.361570i
\(143\) −1.30179 0.473813i −0.108861 0.0396223i
\(144\) 0 0
\(145\) 11.2742 4.10346i 0.936268 0.340774i
\(146\) −9.82041 10.4090i −0.812743 0.861457i
\(147\) 0 0
\(148\) −2.77237 + 1.39233i −0.227887 + 0.114449i
\(149\) −0.198127 + 3.40171i −0.0162312 + 0.278679i 0.980421 + 0.196915i \(0.0630923\pi\)
−0.996652 + 0.0817637i \(0.973945\pi\)
\(150\) 0 0
\(151\) 2.47827 8.27799i 0.201678 0.673653i −0.795984 0.605318i \(-0.793046\pi\)
0.997662 0.0683353i \(-0.0217688\pi\)
\(152\) 2.03690 11.5518i 0.165214 0.936976i
\(153\) 0 0
\(154\) −4.38123 24.8472i −0.353050 2.00224i
\(155\) 17.6256 + 2.06014i 1.41572 + 0.165474i
\(156\) 0 0
\(157\) −2.66576 + 2.82554i −0.212751 + 0.225503i −0.824957 0.565195i \(-0.808801\pi\)
0.612206 + 0.790698i \(0.290282\pi\)
\(158\) 4.49281 10.4155i 0.357429 0.828613i
\(159\) 0 0
\(160\) 23.3417 15.3521i 1.84532 1.21369i
\(161\) 9.14176 0.720472
\(162\) 0 0
\(163\) −23.8379 −1.86713 −0.933564 0.358412i \(-0.883318\pi\)
−0.933564 + 0.358412i \(0.883318\pi\)
\(164\) −14.3435 + 9.43385i −1.12004 + 0.736660i
\(165\) 0 0
\(166\) −2.75369 + 6.38378i −0.213728 + 0.495477i
\(167\) 8.77585 9.30186i 0.679096 0.719799i −0.292548 0.956251i \(-0.594503\pi\)
0.971643 + 0.236452i \(0.0759845\pi\)
\(168\) 0 0
\(169\) 12.7698 + 1.49258i 0.982294 + 0.114814i
\(170\) −1.91566 10.8643i −0.146925 0.833252i
\(171\) 0 0
\(172\) 2.37442 13.4660i 0.181048 1.02677i
\(173\) −1.46229 + 4.88437i −0.111176 + 0.371352i −0.995411 0.0956887i \(-0.969495\pi\)
0.884236 + 0.467041i \(0.154680\pi\)
\(174\) 0 0
\(175\) −0.255795 + 4.39182i −0.0193362 + 0.331991i
\(176\) 39.2990 19.7367i 2.96227 1.48771i
\(177\) 0 0
\(178\) −5.84370 6.19397i −0.438004 0.464257i
\(179\) −1.10838 + 0.403418i −0.0828444 + 0.0301529i −0.383110 0.923703i \(-0.625147\pi\)
0.300266 + 0.953856i \(0.402925\pi\)
\(180\) 0 0
\(181\) −10.7631 3.91744i −0.800013 0.291181i −0.0905211 0.995895i \(-0.528853\pi\)
−0.709492 + 0.704714i \(0.751075\pi\)
\(182\) −1.03331 2.39548i −0.0765940 0.177565i
\(183\) 0 0
\(184\) 8.46861 + 28.2871i 0.624314 + 2.08535i
\(185\) −1.09165 + 0.127596i −0.0802600 + 0.00938105i
\(186\) 0 0
\(187\) −0.484470 8.31803i −0.0354279 0.608274i
\(188\) 0.386261 + 0.669024i 0.0281710 + 0.0487936i
\(189\) 0 0
\(190\) 3.40769 5.90229i 0.247220 0.428197i
\(191\) 13.7471 + 6.90406i 0.994706 + 0.499560i 0.870221 0.492661i \(-0.163976\pi\)
0.124485 + 0.992222i \(0.460272\pi\)
\(192\) 0 0
\(193\) −10.4188 13.9948i −0.749958 1.00737i −0.999242 0.0389382i \(-0.987602\pi\)
0.249283 0.968431i \(-0.419805\pi\)
\(194\) 39.9249 + 9.46238i 2.86644 + 0.679360i
\(195\) 0 0
\(196\) −1.01387 + 1.36186i −0.0724193 + 0.0972760i
\(197\) −7.01270 + 5.88435i −0.499634 + 0.419243i −0.857464 0.514544i \(-0.827961\pi\)
0.357830 + 0.933787i \(0.383517\pi\)
\(198\) 0 0
\(199\) −17.7580 14.9007i −1.25883 1.05629i −0.995805 0.0914967i \(-0.970835\pi\)
−0.263026 0.964789i \(-0.584721\pi\)
\(200\) −13.8265 + 3.27693i −0.977679 + 0.231714i
\(201\) 0 0
\(202\) −29.0915 19.1338i −2.04687 1.34625i
\(203\) 14.2573 + 9.37717i 1.00067 + 0.658148i
\(204\) 0 0
\(205\) −5.91817 + 1.40263i −0.413343 + 0.0979640i
\(206\) −28.0556 23.5415i −1.95473 1.64021i
\(207\) 0 0
\(208\) 3.48336 2.92289i 0.241527 0.202666i
\(209\) 3.07387 4.12893i 0.212624 0.285604i
\(210\) 0 0
\(211\) −25.1316 5.95630i −1.73013 0.410048i −0.759478 0.650534i \(-0.774545\pi\)
−0.970653 + 0.240485i \(0.922693\pi\)
\(212\) −41.1662 55.2958i −2.82731 3.79773i
\(213\) 0 0
\(214\) −5.49903 2.76172i −0.375906 0.188787i
\(215\) 2.42213 4.19525i 0.165188 0.286114i
\(216\) 0 0
\(217\) 12.6200 + 21.8585i 0.856702 + 1.48385i
\(218\) −1.43553 24.6470i −0.0972261 1.66931i
\(219\) 0 0
\(220\) 33.8279 3.95391i 2.28067 0.266573i
\(221\) −0.247094 0.825350i −0.0166213 0.0555191i
\(222\) 0 0
\(223\) 1.61565 + 3.74549i 0.108192 + 0.250816i 0.963708 0.266960i \(-0.0860192\pi\)
−0.855516 + 0.517776i \(0.826760\pi\)
\(224\) 37.3402 + 13.5907i 2.49490 + 0.908069i
\(225\) 0 0
\(226\) 23.8256 8.67180i 1.58485 0.576840i
\(227\) −14.6081 15.4837i −0.969576 1.02769i −0.999604 0.0281412i \(-0.991041\pi\)
0.0300282 0.999549i \(-0.490440\pi\)
\(228\) 0 0
\(229\) 10.8317 5.43987i 0.715777 0.359477i −0.0533473 0.998576i \(-0.516989\pi\)
0.769124 + 0.639099i \(0.220693\pi\)
\(230\) −0.997540 + 17.1271i −0.0657758 + 1.12933i
\(231\) 0 0
\(232\) −15.8081 + 52.8027i −1.03785 + 3.46667i
\(233\) −4.18661 + 23.7435i −0.274274 + 1.55549i 0.466984 + 0.884266i \(0.345341\pi\)
−0.741258 + 0.671220i \(0.765771\pi\)
\(234\) 0 0
\(235\) 0.0475249 + 0.269527i 0.00310018 + 0.0175820i
\(236\) −21.6254 2.52765i −1.40770 0.164536i
\(237\) 0 0
\(238\) 10.7678 11.4132i 0.697970 0.739805i
\(239\) 9.40236 21.7971i 0.608188 1.40994i −0.284242 0.958753i \(-0.591742\pi\)
0.892430 0.451186i \(-0.148999\pi\)
\(240\) 0 0
\(241\) 10.5898 6.96500i 0.682146 0.448655i −0.160561 0.987026i \(-0.551330\pi\)
0.842708 + 0.538371i \(0.180960\pi\)
\(242\) 6.40031 0.411428
\(243\) 0 0
\(244\) 38.1812 2.44430
\(245\) −0.502542 + 0.330527i −0.0321062 + 0.0211166i
\(246\) 0 0
\(247\) 0.210815 0.488724i 0.0134138 0.0310967i
\(248\) −55.9455 + 59.2988i −3.55254 + 3.76548i
\(249\) 0 0
\(250\) −32.2678 3.77157i −2.04080 0.238535i
\(251\) −2.35563 13.3595i −0.148686 0.843242i −0.964333 0.264692i \(-0.914730\pi\)
0.815647 0.578550i \(-0.196381\pi\)
\(252\) 0 0
\(253\) −2.25007 + 12.7608i −0.141461 + 0.802263i
\(254\) −9.68401 + 32.3469i −0.607629 + 2.02962i
\(255\) 0 0
\(256\) −0.302516 + 5.19400i −0.0189073 + 0.324625i
\(257\) −2.50132 + 1.25621i −0.156028 + 0.0783603i −0.525100 0.851041i \(-0.675972\pi\)
0.369072 + 0.929401i \(0.379676\pi\)
\(258\) 0 0
\(259\) −1.07277 1.13707i −0.0666588 0.0706542i
\(260\) 3.30925 1.20447i 0.205231 0.0746979i
\(261\) 0 0
\(262\) −37.3201 13.5834i −2.30564 0.839186i
\(263\) 0.588361 + 1.36397i 0.0362799 + 0.0841063i 0.935393 0.353611i \(-0.115046\pi\)
−0.899113 + 0.437717i \(0.855787\pi\)
\(264\) 0 0
\(265\) −7.00447 23.3966i −0.430281 1.43724i
\(266\) 9.62814 1.12537i 0.590339 0.0690007i
\(267\) 0 0
\(268\) −3.00710 51.6300i −0.183688 3.15380i
\(269\) 4.56187 + 7.90140i 0.278142 + 0.481757i 0.970923 0.239392i \(-0.0769480\pi\)
−0.692781 + 0.721148i \(0.743615\pi\)
\(270\) 0 0
\(271\) −2.94843 + 5.10683i −0.179105 + 0.310218i −0.941574 0.336806i \(-0.890653\pi\)
0.762470 + 0.647024i \(0.223987\pi\)
\(272\) 24.4401 + 12.2743i 1.48190 + 0.744238i
\(273\) 0 0
\(274\) 25.8980 + 34.7870i 1.56455 + 2.10156i
\(275\) −6.06749 1.43802i −0.365883 0.0867159i
\(276\) 0 0
\(277\) −2.95581 + 3.97034i −0.177597 + 0.238555i −0.882004 0.471242i \(-0.843806\pi\)
0.704407 + 0.709797i \(0.251213\pi\)
\(278\) −33.7538 + 28.3228i −2.02442 + 1.69869i
\(279\) 0 0
\(280\) 29.9582 + 25.1379i 1.79035 + 1.50228i
\(281\) −13.2418 + 3.13837i −0.789942 + 0.187220i −0.605733 0.795668i \(-0.707120\pi\)
−0.184208 + 0.982887i \(0.558972\pi\)
\(282\) 0 0
\(283\) 9.88030 + 6.49838i 0.587323 + 0.386289i 0.808108 0.589034i \(-0.200492\pi\)
−0.220785 + 0.975322i \(0.570862\pi\)
\(284\) −7.52708 4.95064i −0.446650 0.293766i
\(285\) 0 0
\(286\) 3.59813 0.852772i 0.212762 0.0504255i
\(287\) −6.62685 5.56058i −0.391170 0.328231i
\(288\) 0 0
\(289\) −9.05329 + 7.59661i −0.532547 + 0.446860i
\(290\) −19.1239 + 25.6878i −1.12299 + 1.50844i
\(291\) 0 0
\(292\) 26.7350 + 6.33630i 1.56454 + 0.370804i
\(293\) 9.72118 + 13.0578i 0.567918 + 0.762846i 0.989592 0.143902i \(-0.0459649\pi\)
−0.421674 + 0.906747i \(0.638557\pi\)
\(294\) 0 0
\(295\) −6.89304 3.46181i −0.401328 0.201555i
\(296\) 2.52464 4.37280i 0.146741 0.254164i
\(297\) 0 0
\(298\) −4.54769 7.87683i −0.263440 0.456292i
\(299\) 0.0779038 + 1.33756i 0.00450529 + 0.0773529i
\(300\) 0 0
\(301\) 6.84352 0.799893i 0.394454 0.0461051i
\(302\) 6.61510 + 22.0960i 0.380656 + 1.27148i
\(303\) 0 0
\(304\) 6.69218 + 15.5142i 0.383823 + 0.889802i
\(305\) 12.7109 + 4.62638i 0.727822 + 0.264906i
\(306\) 0 0
\(307\) 23.4445 8.53312i 1.33805 0.487011i 0.428853 0.903374i \(-0.358918\pi\)
0.909198 + 0.416364i \(0.136696\pi\)
\(308\) 33.2427 + 35.2353i 1.89418 + 2.00772i
\(309\) 0 0
\(310\) −42.3290 + 21.2584i −2.40413 + 1.20740i
\(311\) 0.482249 8.27990i 0.0273459 0.469510i −0.956641 0.291269i \(-0.905922\pi\)
0.983987 0.178241i \(-0.0570406\pi\)
\(312\) 0 0
\(313\) −1.58728 + 5.30188i −0.0897183 + 0.299680i −0.991058 0.133433i \(-0.957400\pi\)
0.901340 + 0.433113i \(0.142585\pi\)
\(314\) 1.80054 10.2114i 0.101610 0.576261i
\(315\) 0 0
\(316\) 3.78181 + 21.4477i 0.212743 + 1.20653i
\(317\) −21.9438 2.56486i −1.23249 0.144057i −0.525196 0.850981i \(-0.676008\pi\)
−0.707289 + 0.706924i \(0.750082\pi\)
\(318\) 0 0
\(319\) −16.5985 + 17.5934i −0.929340 + 0.985043i
\(320\) −12.2569 + 28.4147i −0.685183 + 1.58843i
\(321\) 0 0
\(322\) −20.3872 + 13.4089i −1.13614 + 0.747248i
\(323\) 3.20124 0.178122
\(324\) 0 0
\(325\) −0.644760 −0.0357648
\(326\) 53.1614 34.9648i 2.94434 1.93652i
\(327\) 0 0
\(328\) 11.0671 25.6564i 0.611079 1.41664i
\(329\) −0.267132 + 0.283144i −0.0147275 + 0.0156102i
\(330\) 0 0
\(331\) −2.84377 0.332389i −0.156308 0.0182698i 0.0375791 0.999294i \(-0.488035\pi\)
−0.193887 + 0.981024i \(0.562109\pi\)
\(332\) −2.31791 13.1455i −0.127212 0.721455i
\(333\) 0 0
\(334\) −5.92749 + 33.6165i −0.324338 + 1.83941i
\(335\) 5.25486 17.5525i 0.287104 0.958993i
\(336\) 0 0
\(337\) 0.939940 16.1381i 0.0512018 0.879101i −0.870733 0.491756i \(-0.836355\pi\)
0.921935 0.387345i \(-0.126608\pi\)
\(338\) −30.6675 + 15.4018i −1.66809 + 0.837748i
\(339\) 0 0
\(340\) 14.5352 + 15.4064i 0.788281 + 0.835529i
\(341\) −33.6180 + 12.2359i −1.82052 + 0.662613i
\(342\) 0 0
\(343\) −17.7905 6.47520i −0.960595 0.349628i
\(344\) 8.81469 + 20.4348i 0.475256 + 1.10177i
\(345\) 0 0
\(346\) −3.90320 13.0376i −0.209837 0.700905i
\(347\) 14.6404 1.71122i 0.785939 0.0918631i 0.286349 0.958125i \(-0.407558\pi\)
0.499590 + 0.866262i \(0.333484\pi\)
\(348\) 0 0
\(349\) 0.143834 + 2.46953i 0.00769924 + 0.132191i 0.999967 + 0.00807818i \(0.00257139\pi\)
−0.992268 + 0.124113i \(0.960392\pi\)
\(350\) −5.87136 10.1695i −0.313837 0.543582i
\(351\) 0 0
\(352\) −28.1616 + 48.7773i −1.50102 + 2.59984i
\(353\) −13.9985 7.03032i −0.745066 0.374186i 0.0354092 0.999373i \(-0.488727\pi\)
−0.780475 + 0.625187i \(0.785023\pi\)
\(354\) 0 0
\(355\) −1.90597 2.56016i −0.101158 0.135879i
\(356\) 15.9088 + 3.77046i 0.843166 + 0.199834i
\(357\) 0 0
\(358\) 1.88010 2.52542i 0.0993665 0.133472i
\(359\) 0.180567 0.151513i 0.00952994 0.00799657i −0.638010 0.770028i \(-0.720242\pi\)
0.647540 + 0.762031i \(0.275798\pi\)
\(360\) 0 0
\(361\) −13.0398 10.9417i −0.686307 0.575880i
\(362\) 29.7490 7.05063i 1.56357 0.370573i
\(363\) 0 0
\(364\) 4.18487 + 2.75243i 0.219347 + 0.144267i
\(365\) 8.13255 + 5.34886i 0.425677 + 0.279972i
\(366\) 0 0
\(367\) −9.37480 + 2.22187i −0.489361 + 0.115981i −0.467886 0.883789i \(-0.654984\pi\)
−0.0214745 + 0.999769i \(0.506836\pi\)
\(368\) −32.5813 27.3390i −1.69842 1.42514i
\(369\) 0 0
\(370\) 2.24737 1.88576i 0.116835 0.0980362i
\(371\) 20.7434 27.8632i 1.07694 1.44659i
\(372\) 0 0
\(373\) −0.0585838 0.0138846i −0.00303336 0.000718918i 0.229099 0.973403i \(-0.426422\pi\)
−0.232132 + 0.972684i \(0.574570\pi\)
\(374\) 13.2811 + 17.8396i 0.686749 + 0.922463i
\(375\) 0 0
\(376\) −1.12359 0.564287i −0.0579446 0.0291009i
\(377\) −1.25050 + 2.16594i −0.0644042 + 0.111551i
\(378\) 0 0
\(379\) −1.23614 2.14105i −0.0634961 0.109979i 0.832530 0.553980i \(-0.186892\pi\)
−0.896026 + 0.444002i \(0.853558\pi\)
\(380\) 0.760843 + 13.0632i 0.0390304 + 0.670127i
\(381\) 0 0
\(382\) −40.7844 + 4.76701i −2.08671 + 0.243902i
\(383\) −7.91287 26.4308i −0.404329 1.35055i −0.881684 0.471841i \(-0.843590\pi\)
0.477355 0.878711i \(-0.341596\pi\)
\(384\) 0 0
\(385\) 6.79739 + 15.7581i 0.346427 + 0.803109i
\(386\) 43.7623 + 15.9282i 2.22744 + 0.810723i
\(387\) 0 0
\(388\) −74.0272 + 26.9437i −3.75816 + 1.36786i
\(389\) 7.41631 + 7.86083i 0.376022 + 0.398560i 0.887554 0.460705i \(-0.152403\pi\)
−0.511532 + 0.859264i \(0.670922\pi\)
\(390\) 0 0
\(391\) −7.20123 + 3.61659i −0.364182 + 0.182899i
\(392\) 0.160672 2.75863i 0.00811517 0.139332i
\(393\) 0 0
\(394\) 7.00815 23.4089i 0.353065 1.17932i
\(395\) −1.33980 + 7.59837i −0.0674126 + 0.382316i
\(396\) 0 0
\(397\) −3.32712 18.8690i −0.166983 0.947010i −0.946996 0.321246i \(-0.895898\pi\)
0.780012 0.625764i \(-0.215213\pi\)
\(398\) 61.4585 + 7.18347i 3.08064 + 0.360075i
\(399\) 0 0
\(400\) 14.0457 14.8875i 0.702283 0.744376i
\(401\) −12.4792 + 28.9301i −0.623182 + 1.44470i 0.255271 + 0.966870i \(0.417835\pi\)
−0.878453 + 0.477829i \(0.841424\pi\)
\(402\) 0 0
\(403\) −3.09064 + 2.03274i −0.153956 + 0.101258i
\(404\) 66.8529 3.32606
\(405\) 0 0
\(406\) −45.5497 −2.26059
\(407\) 1.85125 1.21759i 0.0917633 0.0603537i
\(408\) 0 0
\(409\) −0.362689 + 0.840808i −0.0179338 + 0.0415753i −0.926948 0.375191i \(-0.877577\pi\)
0.909014 + 0.416766i \(0.136837\pi\)
\(410\) 11.1409 11.8086i 0.550209 0.583187i
\(411\) 0 0
\(412\) 69.8415 + 8.16330i 3.44084 + 0.402177i
\(413\) −1.90511 10.8044i −0.0937444 0.531651i
\(414\) 0 0
\(415\) 0.821178 4.65713i 0.0403100 0.228609i
\(416\) −1.67029 + 5.57917i −0.0818929 + 0.273541i
\(417\) 0 0
\(418\) −0.798906 + 13.7167i −0.0390758 + 0.670905i
\(419\) 10.9019 5.47513i 0.532591 0.267477i −0.162114 0.986772i \(-0.551831\pi\)
0.694705 + 0.719295i \(0.255535\pi\)
\(420\) 0 0
\(421\) −21.5036 22.7925i −1.04802 1.11084i −0.993672 0.112318i \(-0.964172\pi\)
−0.0543513 0.998522i \(-0.517309\pi\)
\(422\) 64.7830 23.5791i 3.15359 1.14781i
\(423\) 0 0
\(424\) 105.432 + 38.3743i 5.12025 + 1.86362i
\(425\) −1.53596 3.56076i −0.0745052 0.172722i
\(426\) 0 0
\(427\) 5.51788 + 18.4310i 0.267029 + 0.891938i
\(428\) 11.7348 1.37160i 0.567221 0.0662987i
\(429\) 0 0
\(430\) 0.751842 + 12.9086i 0.0362570 + 0.622509i
\(431\) −6.90324 11.9568i −0.332518 0.575937i 0.650487 0.759517i \(-0.274565\pi\)
−0.983005 + 0.183580i \(0.941231\pi\)
\(432\) 0 0
\(433\) 12.1413 21.0293i 0.583472 1.01060i −0.411592 0.911368i \(-0.635027\pi\)
0.995064 0.0992354i \(-0.0316397\pi\)
\(434\) −60.2056 30.2364i −2.88996 1.45139i
\(435\) 0 0
\(436\) 28.3063 + 38.0220i 1.35563 + 1.82092i
\(437\) −4.84419 1.14809i −0.231729 0.0549208i
\(438\) 0 0
\(439\) 7.58958 10.1946i 0.362231 0.486561i −0.583225 0.812311i \(-0.698209\pi\)
0.945456 + 0.325750i \(0.105617\pi\)
\(440\) −42.4631 + 35.6308i −2.02435 + 1.69863i
\(441\) 0 0
\(442\) 1.76165 + 1.47820i 0.0837932 + 0.0703108i
\(443\) −24.8296 + 5.88473i −1.17969 + 0.279592i −0.773260 0.634090i \(-0.781375\pi\)
−0.406431 + 0.913681i \(0.633227\pi\)
\(444\) 0 0
\(445\) 4.83933 + 3.18288i 0.229406 + 0.150883i
\(446\) −9.09687 5.98310i −0.430749 0.283308i
\(447\) 0 0
\(448\) −42.8282 + 10.1505i −2.02344 + 0.479565i
\(449\) −2.45881 2.06318i −0.116038 0.0973677i 0.582922 0.812528i \(-0.301909\pi\)
−0.698960 + 0.715160i \(0.746354\pi\)
\(450\) 0 0
\(451\) 9.39297 7.88164i 0.442298 0.371132i
\(452\) −29.0698 + 39.0475i −1.36733 + 1.83664i
\(453\) 0 0
\(454\) 55.2890 + 13.1037i 2.59484 + 0.614989i
\(455\) 1.05967 + 1.42339i 0.0496782 + 0.0667294i
\(456\) 0 0
\(457\) −1.90624 0.957349i −0.0891701 0.0447829i 0.403655 0.914911i \(-0.367740\pi\)
−0.492825 + 0.870128i \(0.664036\pi\)
\(458\) −16.1769 + 28.0192i −0.755896 + 1.30925i
\(459\) 0 0
\(460\) −16.4696 28.5262i −0.767899 1.33004i
\(461\) 1.33368 + 22.8984i 0.0621157 + 1.06648i 0.875020 + 0.484087i \(0.160848\pi\)
−0.812904 + 0.582398i \(0.802115\pi\)
\(462\) 0 0
\(463\) −28.7556 + 3.36105i −1.33639 + 0.156201i −0.754088 0.656774i \(-0.771921\pi\)
−0.582298 + 0.812975i \(0.697846\pi\)
\(464\) −22.7701 76.0576i −1.05708 3.53088i
\(465\) 0 0
\(466\) −25.4896 59.0916i −1.18078 2.73737i
\(467\) 1.96329 + 0.714577i 0.0908500 + 0.0330667i 0.387045 0.922061i \(-0.373496\pi\)
−0.296195 + 0.955127i \(0.595718\pi\)
\(468\) 0 0
\(469\) 24.4885 8.91307i 1.13077 0.411567i
\(470\) −0.501321 0.531369i −0.0231242 0.0245102i
\(471\) 0 0
\(472\) 31.6671 15.9038i 1.45759 0.732031i
\(473\) −0.567849 + 9.74959i −0.0261097 + 0.448287i
\(474\) 0 0
\(475\) 0.687105 2.29509i 0.0315265 0.105306i
\(476\) −5.23133 + 29.6684i −0.239778 + 1.35985i
\(477\) 0 0
\(478\) 11.0030 + 62.4013i 0.503267 + 2.85417i
\(479\) −21.5915 2.52368i −0.986540 0.115310i −0.392505 0.919750i \(-0.628392\pi\)
−0.594034 + 0.804440i \(0.702466\pi\)
\(480\) 0 0
\(481\) 0.157226 0.166650i 0.00716890 0.00759859i
\(482\) −13.4004 + 31.0656i −0.610370 + 1.41500i
\(483\) 0 0
\(484\) −10.2668 + 6.75258i −0.466673 + 0.306936i
\(485\) −27.9091 −1.26729
\(486\) 0 0
\(487\) −3.65843 −0.165779 −0.0828896 0.996559i \(-0.526415\pi\)
−0.0828896 + 0.996559i \(0.526415\pi\)
\(488\) −51.9190 + 34.1477i −2.35026 + 1.54579i
\(489\) 0 0
\(490\) 0.635921 1.47423i 0.0287280 0.0665990i
\(491\) −11.9181 + 12.6324i −0.537855 + 0.570093i −0.938122 0.346306i \(-0.887436\pi\)
0.400267 + 0.916399i \(0.368917\pi\)
\(492\) 0 0
\(493\) −14.9406 1.74631i −0.672892 0.0786498i
\(494\) 0.246704 + 1.39913i 0.0110998 + 0.0629498i
\(495\) 0 0
\(496\) 20.3913 115.645i 0.915596 5.19260i
\(497\) 1.30199 4.34896i 0.0584024 0.195078i
\(498\) 0 0
\(499\) 0.983696 16.8894i 0.0440363 0.756074i −0.901945 0.431852i \(-0.857860\pi\)
0.945981 0.324222i \(-0.105103\pi\)
\(500\) 55.7403 27.9938i 2.49278 1.25192i
\(501\) 0 0
\(502\) 24.8487 + 26.3380i 1.10905 + 1.17552i
\(503\) 27.0776 9.85546i 1.20733 0.439433i 0.341555 0.939862i \(-0.389047\pi\)
0.865778 + 0.500429i \(0.166824\pi\)
\(504\) 0 0
\(505\) 22.2559 + 8.10050i 0.990377 + 0.360468i
\(506\) −13.6992 31.7584i −0.609006 1.41183i
\(507\) 0 0
\(508\) −18.5930 62.1049i −0.824931 2.75546i
\(509\) −11.8969 + 1.39055i −0.527322 + 0.0616351i −0.375589 0.926786i \(-0.622560\pi\)
−0.151733 + 0.988421i \(0.548485\pi\)
\(510\) 0 0
\(511\) 0.805001 + 13.8213i 0.0356111 + 0.611420i
\(512\) 7.77620 + 13.4688i 0.343663 + 0.595241i
\(513\) 0 0
\(514\) 3.73567 6.47037i 0.164773 0.285396i
\(515\) 22.2617 + 11.1803i 0.980969 + 0.492661i
\(516\) 0 0
\(517\) −0.329484 0.442574i −0.0144907 0.0194644i
\(518\) 4.06024 + 0.962294i 0.178397 + 0.0422808i
\(519\) 0 0
\(520\) −3.42271 + 4.59749i −0.150096 + 0.201613i
\(521\) −2.74519 + 2.30349i −0.120269 + 0.100918i −0.700939 0.713222i \(-0.747235\pi\)
0.580669 + 0.814139i \(0.302791\pi\)
\(522\) 0 0
\(523\) −20.6502 17.3276i −0.902971 0.757683i 0.0677978 0.997699i \(-0.478403\pi\)
−0.970769 + 0.240016i \(0.922847\pi\)
\(524\) 74.1966 17.5849i 3.24129 0.768201i
\(525\) 0 0
\(526\) −3.31276 2.17884i −0.144443 0.0950018i
\(527\) −18.5887 12.2260i −0.809735 0.532571i
\(528\) 0 0
\(529\) −10.1859 + 2.41410i −0.442865 + 0.104961i
\(530\) 49.9383 + 41.9032i 2.16918 + 1.82016i
\(531\) 0 0
\(532\) −14.2573 + 11.9633i −0.618132 + 0.518674i
\(533\) 0.757113 1.01698i 0.0327942 0.0440502i
\(534\) 0 0
\(535\) 4.07281 + 0.965273i 0.176083 + 0.0417324i
\(536\) 50.2648 + 67.5173i 2.17111 + 2.91630i
\(537\) 0 0
\(538\) −21.7631 10.9298i −0.938273 0.471219i
\(539\) 0.606313 1.05017i 0.0261158 0.0452338i
\(540\) 0 0
\(541\) 8.33503 + 14.4367i 0.358351 + 0.620682i 0.987685 0.156453i \(-0.0500058\pi\)
−0.629335 + 0.777134i \(0.716672\pi\)
\(542\) −0.915210 15.7135i −0.0393116 0.674954i
\(543\) 0 0
\(544\) −34.7906 + 4.06644i −1.49164 + 0.174347i
\(545\) 4.81635 + 16.0877i 0.206310 + 0.689122i
\(546\) 0 0
\(547\) −15.3370 35.5553i −0.655765 1.52023i −0.842997 0.537918i \(-0.819211\pi\)
0.187232 0.982316i \(-0.440048\pi\)
\(548\) −78.2449 28.4788i −3.34246 1.21655i
\(549\) 0 0
\(550\) 15.6405 5.69267i 0.666912 0.242736i
\(551\) −6.37724 6.75948i −0.271680 0.287964i
\(552\) 0 0
\(553\) −9.80679 + 4.92516i −0.417027 + 0.209439i
\(554\) 0.768221 13.1898i 0.0326386 0.560383i
\(555\) 0 0
\(556\) 24.2632 81.0446i 1.02899 3.43706i
\(557\) −3.42298 + 19.4127i −0.145036 + 0.822542i 0.822302 + 0.569052i \(0.192690\pi\)
−0.967338 + 0.253490i \(0.918421\pi\)
\(558\) 0 0
\(559\) 0.175353 + 0.994479i 0.00741666 + 0.0420620i
\(560\) −55.9502 6.53965i −2.36433 0.276350i
\(561\) 0 0
\(562\) 24.9276 26.4217i 1.05151 1.11453i
\(563\) −0.290922 + 0.674433i −0.0122609 + 0.0284240i −0.924237 0.381820i \(-0.875297\pi\)
0.911976 + 0.410244i \(0.134557\pi\)
\(564\) 0 0
\(565\) −14.4089 + 9.47690i −0.606188 + 0.398696i
\(566\) −31.5659 −1.32681
\(567\) 0 0
\(568\) 14.6630 0.615246
\(569\) −17.1901 + 11.3061i −0.720647 + 0.473977i −0.856102 0.516806i \(-0.827121\pi\)
0.135455 + 0.990784i \(0.456750\pi\)
\(570\) 0 0
\(571\) 0.929249 2.15424i 0.0388878 0.0901521i −0.897665 0.440678i \(-0.854738\pi\)
0.936553 + 0.350526i \(0.113997\pi\)
\(572\) −4.87208 + 5.16411i −0.203712 + 0.215922i
\(573\) 0 0
\(574\) 22.9348 + 2.68069i 0.957280 + 0.111890i
\(575\) 1.04722 + 5.93909i 0.0436721 + 0.247677i
\(576\) 0 0
\(577\) −5.62981 + 31.9282i −0.234372 + 1.32919i 0.609561 + 0.792739i \(0.291346\pi\)
−0.843932 + 0.536449i \(0.819765\pi\)
\(578\) 9.04742 30.2205i 0.376323 1.25701i
\(579\) 0 0
\(580\) 3.57513 61.3826i 0.148449 2.54877i
\(581\) 6.01069 3.01868i 0.249366 0.125236i
\(582\) 0 0
\(583\) 33.7880 + 35.8132i 1.39936 + 1.48323i
\(584\) −42.0213 + 15.2945i −1.73885 + 0.632891i
\(585\) 0 0
\(586\) −40.8323 14.8617i −1.68677 0.613932i
\(587\) 7.34958 + 17.0382i 0.303350 + 0.703244i 0.999898 0.0142660i \(-0.00454116\pi\)
−0.696549 + 0.717510i \(0.745282\pi\)
\(588\) 0 0
\(589\) −3.94215 13.1677i −0.162433 0.542565i
\(590\) 20.4500 2.39026i 0.841913 0.0984055i
\(591\) 0 0
\(592\) 0.422889 + 7.26072i 0.0173806 + 0.298414i
\(593\) −20.4339 35.3926i −0.839120 1.45340i −0.890631 0.454727i \(-0.849737\pi\)
0.0515108 0.998672i \(-0.483596\pi\)
\(594\) 0 0
\(595\) −5.33644 + 9.24299i −0.218773 + 0.378926i
\(596\) 15.6054 + 7.83730i 0.639220 + 0.321028i
\(597\) 0 0
\(598\) −2.13563 2.86865i −0.0873323 0.117308i
\(599\) −8.88883 2.10669i −0.363188 0.0860771i 0.0449704 0.998988i \(-0.485681\pi\)
−0.408158 + 0.912911i \(0.633829\pi\)
\(600\) 0 0
\(601\) −22.1512 + 29.7542i −0.903565 + 1.21370i 0.0727514 + 0.997350i \(0.476822\pi\)
−0.976316 + 0.216348i \(0.930585\pi\)
\(602\) −14.0886 + 11.8218i −0.574209 + 0.481819i
\(603\) 0 0
\(604\) −33.9235 28.4652i −1.38033 1.15823i
\(605\) −4.23612 + 1.00398i −0.172223 + 0.0408175i
\(606\) 0 0
\(607\) 27.9450 + 18.3797i 1.13425 + 0.746009i 0.970645 0.240516i \(-0.0773167\pi\)
0.163607 + 0.986526i \(0.447687\pi\)
\(608\) −18.0796 11.8912i −0.733226 0.482251i
\(609\) 0 0
\(610\) −35.1326 + 8.32658i −1.42248 + 0.337133i
\(611\) −0.0437040 0.0366720i −0.00176807 0.00148359i
\(612\) 0 0
\(613\) 35.2558 29.5831i 1.42397 1.19485i 0.474794 0.880097i \(-0.342522\pi\)
0.949173 0.314754i \(-0.101922\pi\)
\(614\) −39.7680 + 53.4177i −1.60491 + 2.15576i
\(615\) 0 0
\(616\) −76.7167 18.1822i −3.09100 0.732581i
\(617\) −25.3857 34.0989i −1.02199 1.37277i −0.926059 0.377380i \(-0.876825\pi\)
−0.0959295 0.995388i \(-0.530582\pi\)
\(618\) 0 0
\(619\) 37.5931 + 18.8800i 1.51099 + 0.758850i 0.995200 0.0978633i \(-0.0312008\pi\)
0.515794 + 0.856713i \(0.327497\pi\)
\(620\) 45.4719 78.7597i 1.82620 3.16307i
\(621\) 0 0
\(622\) 11.0693 + 19.1725i 0.443837 + 0.768749i
\(623\) 0.479021 + 8.22448i 0.0191916 + 0.329507i
\(624\) 0 0
\(625\) 13.4882 1.57654i 0.539528 0.0630618i
\(626\) −4.23683 14.1520i −0.169338 0.565628i
\(627\) 0 0
\(628\) 7.88513 + 18.2798i 0.314651 + 0.729443i
\(629\) 1.29489 + 0.471303i 0.0516308 + 0.0187921i
\(630\) 0 0
\(631\) −1.25540 + 0.456928i −0.0499766 + 0.0181900i −0.366888 0.930265i \(-0.619577\pi\)
0.316911 + 0.948455i \(0.397354\pi\)
\(632\) −24.3245 25.7824i −0.967576 1.02557i
\(633\) 0 0
\(634\) 52.6993 26.4666i 2.09296 1.05112i
\(635\) 1.33542 22.9282i 0.0529943 0.909878i
\(636\) 0 0
\(637\) 0.0359611 0.120118i 0.00142483 0.00475927i
\(638\) 11.2112 63.5818i 0.443855 2.51723i
\(639\) 0 0
\(640\) −4.64087 26.3197i −0.183446 1.04038i
\(641\) −9.56344 1.11781i −0.377733 0.0441507i −0.0748919 0.997192i \(-0.523861\pi\)
−0.302841 + 0.953041i \(0.597935\pi\)
\(642\) 0 0
\(643\) 12.6003 13.3556i 0.496909 0.526692i −0.429573 0.903032i \(-0.641336\pi\)
0.926482 + 0.376340i \(0.122817\pi\)
\(644\) 18.5564 43.0187i 0.731226 1.69517i
\(645\) 0 0
\(646\) −7.13916 + 4.69550i −0.280886 + 0.184742i
\(647\) 24.2705 0.954170 0.477085 0.878857i \(-0.341693\pi\)
0.477085 + 0.878857i \(0.341693\pi\)
\(648\) 0 0
\(649\) 15.5506 0.610413
\(650\) 1.43789 0.945717i 0.0563988 0.0370941i
\(651\) 0 0
\(652\) −48.3874 + 112.175i −1.89500 + 4.39310i
\(653\) 29.2055 30.9560i 1.14290 1.21140i 0.168712 0.985665i \(-0.446039\pi\)
0.974188 0.225738i \(-0.0724794\pi\)
\(654\) 0 0
\(655\) 26.8315 + 3.13615i 1.04839 + 0.122540i
\(656\) 6.98888 + 39.6359i 0.272870 + 1.54752i
\(657\) 0 0
\(658\) 0.180430 1.02327i 0.00703388 0.0398911i
\(659\) 0.540877 1.80666i 0.0210696 0.0703773i −0.946808 0.321798i \(-0.895713\pi\)
0.967878 + 0.251421i \(0.0808979\pi\)
\(660\) 0 0
\(661\) −2.44763 + 42.0242i −0.0952019 + 1.63455i 0.525704 + 0.850668i \(0.323802\pi\)
−0.620906 + 0.783885i \(0.713235\pi\)
\(662\) 6.82949 3.42990i 0.265436 0.133307i
\(663\) 0 0
\(664\) 14.9087 + 15.8023i 0.578571 + 0.613250i
\(665\) −6.19596 + 2.25514i −0.240269 + 0.0874507i
\(666\) 0 0
\(667\) 21.9822 + 8.00086i 0.851154 + 0.309795i
\(668\) −25.9584 60.1782i −1.00436 2.32837i
\(669\) 0 0
\(670\) 14.0265 + 46.8518i 0.541891 + 1.81004i
\(671\) −27.0855 + 3.16585i −1.04563 + 0.122216i
\(672\) 0 0
\(673\) −0.626161 10.7508i −0.0241367 0.414412i −0.988636 0.150327i \(-0.951967\pi\)
0.964500 0.264085i \(-0.0850698\pi\)
\(674\) 21.5748 + 37.3687i 0.831031 + 1.43939i
\(675\) 0 0
\(676\) 32.9446 57.0616i 1.26710 2.19468i
\(677\) 9.37345 + 4.70752i 0.360251 + 0.180925i 0.619713 0.784828i \(-0.287249\pi\)
−0.259462 + 0.965753i \(0.583545\pi\)
\(678\) 0 0
\(679\) −23.7047 31.8409i −0.909701 1.22194i
\(680\) −33.5439 7.95004i −1.28635 0.304870i
\(681\) 0 0
\(682\) 57.0248 76.5976i 2.18359 2.93307i
\(683\) 18.5237 15.5432i 0.708789 0.594745i −0.215470 0.976510i \(-0.569128\pi\)
0.924259 + 0.381766i \(0.124684\pi\)
\(684\) 0 0
\(685\) −22.5977 18.9617i −0.863413 0.724490i
\(686\) 49.1725 11.6541i 1.87742 0.444956i
\(687\) 0 0
\(688\) −26.7825 17.6151i −1.02107 0.671570i
\(689\) 4.25351 + 2.79758i 0.162046 + 0.106579i
\(690\) 0 0
\(691\) −8.33265 + 1.97488i −0.316989 + 0.0751278i −0.386031 0.922486i \(-0.626154\pi\)
0.0690415 + 0.997614i \(0.478006\pi\)
\(692\) 20.0163 + 16.7957i 0.760907 + 0.638476i
\(693\) 0 0
\(694\) −30.1399 + 25.2904i −1.14410 + 0.960011i
\(695\) 17.8975 24.0405i 0.678891 0.911910i
\(696\) 0 0
\(697\) 7.42000 + 1.75857i 0.281053 + 0.0666107i
\(698\) −3.94301 5.29638i −0.149245 0.200471i
\(699\) 0 0
\(700\) 20.1475 + 10.1185i 0.761504 + 0.382442i
\(701\) 1.21019 2.09612i 0.0457084 0.0791693i −0.842266 0.539062i \(-0.818779\pi\)
0.887974 + 0.459893i \(0.152112\pi\)
\(702\) 0 0
\(703\) 0.425656 + 0.737258i 0.0160539 + 0.0278062i
\(704\) −3.62747 62.2813i −0.136716 2.34732i
\(705\) 0 0
\(706\) 41.5303 4.85419i 1.56301 0.182690i
\(707\) 9.66147 + 32.2715i 0.363357 + 1.21370i
\(708\) 0 0
\(709\) 19.7152 + 45.7050i 0.740420 + 1.71649i 0.696613 + 0.717447i \(0.254689\pi\)
0.0438071 + 0.999040i \(0.486051\pi\)
\(710\) 8.00572 + 2.91384i 0.300449 + 0.109355i
\(711\) 0 0
\(712\) −25.0051 + 9.10110i −0.937104 + 0.341078i
\(713\) 23.7441 + 25.1672i 0.889222 + 0.942520i
\(714\) 0 0
\(715\) −2.24769 + 1.12883i −0.0840589 + 0.0422160i
\(716\) −0.351477 + 6.03463i −0.0131353 + 0.225525i
\(717\) 0 0
\(718\) −0.180450 + 0.602743i −0.00673432 + 0.0224942i
\(719\) 9.09244 51.5658i 0.339091 1.92308i −0.0432647 0.999064i \(-0.513776\pi\)
0.382355 0.924015i \(-0.375113\pi\)
\(720\) 0 0
\(721\) 6.15275 + 34.8940i 0.229140 + 1.29952i
\(722\) 45.1295 + 5.27488i 1.67954 + 0.196311i
\(723\) 0 0
\(724\) −40.2819 + 42.6963i −1.49706 + 1.58680i
\(725\) −4.45880 + 10.3367i −0.165596 + 0.383894i
\(726\) 0 0
\(727\) 29.4097 19.3431i 1.09075 0.717396i 0.129085 0.991634i \(-0.458796\pi\)
0.961662 + 0.274238i \(0.0884256\pi\)
\(728\) −8.15228 −0.302143
\(729\) 0 0
\(730\) −25.9821 −0.961642
\(731\) −5.07439 + 3.33748i −0.187683 + 0.123441i
\(732\) 0 0
\(733\) 9.42379 21.8468i 0.348076 0.806930i −0.650787 0.759260i \(-0.725561\pi\)
0.998863 0.0476702i \(-0.0151797\pi\)
\(734\) 17.6480 18.7057i 0.651398 0.690442i
\(735\) 0 0
\(736\) 54.1044 + 6.32390i 1.99431 + 0.233102i
\(737\) 6.41419 + 36.3767i 0.236270 + 1.33995i
\(738\) 0 0
\(739\) −7.56827 + 42.9218i −0.278403 + 1.57890i 0.449536 + 0.893262i \(0.351589\pi\)
−0.727939 + 0.685642i \(0.759522\pi\)
\(740\) −1.61547 + 5.39603i −0.0593857 + 0.198362i
\(741\) 0 0
\(742\) −5.39125 + 92.5642i −0.197919 + 3.39814i
\(743\) −9.08770 + 4.56402i −0.333396 + 0.167438i −0.607619 0.794228i \(-0.707875\pi\)
0.274224 + 0.961666i \(0.411579\pi\)
\(744\) 0 0
\(745\) 4.24553 + 4.50000i 0.155544 + 0.164867i
\(746\) 0.151015 0.0549648i 0.00552904 0.00201240i
\(747\) 0 0
\(748\) −40.1258 14.6046i −1.46714 0.533997i
\(749\) 2.35799 + 5.46644i 0.0861591 + 0.199739i
\(750\) 0 0
\(751\) 4.79574 + 16.0189i 0.174999 + 0.584537i 0.999817 + 0.0191386i \(0.00609236\pi\)
−0.824818 + 0.565398i \(0.808722\pi\)
\(752\) 1.79882 0.210252i 0.0655962 0.00766709i
\(753\) 0 0
\(754\) −0.388163 6.66450i −0.0141361 0.242707i
\(755\) −7.84433 13.5868i −0.285485 0.494474i
\(756\) 0 0
\(757\) 20.3289 35.2107i 0.738867 1.27975i −0.214139 0.976803i \(-0.568695\pi\)
0.953006 0.302951i \(-0.0979720\pi\)
\(758\) 5.89718 + 2.96167i 0.214195 + 0.107573i
\(759\) 0 0
\(760\) −12.7178 17.0829i −0.461322 0.619663i
\(761\) −13.2491 3.14009i −0.480278 0.113828i −0.0166566 0.999861i \(-0.505302\pi\)
−0.463622 + 0.886033i \(0.653450\pi\)
\(762\) 0 0
\(763\) −14.2634 + 19.1590i −0.516369 + 0.693603i
\(764\) 60.3933 50.6760i 2.18495 1.83339i
\(765\) 0 0
\(766\) 56.4147 + 47.3375i 2.03835 + 1.71037i
\(767\) 1.56459 0.370815i 0.0564941 0.0133894i
\(768\) 0 0
\(769\) −37.5321 24.6852i −1.35344 0.890172i −0.354449 0.935075i \(-0.615332\pi\)
−0.998991 + 0.0449035i \(0.985702\pi\)
\(770\) −38.2726 25.1723i −1.37925 0.907146i
\(771\) 0 0
\(772\) −87.0044 + 20.6204i −3.13136 + 0.742145i
\(773\) −17.8408 14.9702i −0.641688 0.538440i 0.262848 0.964837i \(-0.415338\pi\)
−0.904536 + 0.426397i \(0.859783\pi\)
\(774\) 0 0
\(775\) −12.7551 + 10.7028i −0.458175 + 0.384454i
\(776\) 76.5653 102.845i 2.74853 3.69192i
\(777\) 0 0
\(778\) −28.0693 6.65255i −1.00633 0.238506i
\(779\) 2.81321 + 3.77879i 0.100794 + 0.135389i
\(780\) 0 0
\(781\) 5.75016 + 2.88784i 0.205757 + 0.103335i
\(782\) 10.7549 18.6280i 0.384594 0.666137i
\(783\) 0 0
\(784\) 1.99015 + 3.44704i 0.0710768 + 0.123109i
\(785\) 0.410088 + 7.04094i 0.0146367 + 0.251302i
\(786\) 0 0
\(787\) −2.96226 + 0.346239i −0.105593 + 0.0123421i −0.168725 0.985663i \(-0.553965\pi\)
0.0631322 + 0.998005i \(0.479891\pi\)
\(788\) 13.4554 + 44.9442i 0.479330 + 1.60107i
\(789\) 0 0
\(790\) −8.15718 18.9105i −0.290220 0.672804i
\(791\) −23.0503 8.38962i −0.819574 0.298300i
\(792\) 0 0
\(793\) −2.64967 + 0.964401i −0.0940925 + 0.0342469i
\(794\) 35.0965 + 37.2001i 1.24553 + 1.32018i
\(795\) 0 0
\(796\) −106.165 + 53.3181i −3.76292 + 1.88981i
\(797\) −1.39283 + 23.9140i −0.0493366 + 0.847076i 0.879342 + 0.476191i \(0.157983\pi\)
−0.928679 + 0.370885i \(0.879054\pi\)
\(798\) 0 0
\(799\) 0.0984128 0.328722i 0.00348159 0.0116293i
\(800\) −4.55197 + 25.8155i −0.160937 + 0.912716i
\(801\) 0 0
\(802\) −14.6037 82.8217i −0.515675 2.92454i
\(803\) −19.4910 2.27817i −0.687823 0.0803950i
\(804\) 0 0
\(805\) 11.3901 12.0728i 0.401450 0.425512i
\(806\) 3.91092 9.06653i 0.137756 0.319355i
\(807\) 0 0
\(808\) −90.9070 + 59.7905i −3.19810 + 2.10342i
\(809\) −36.1049 −1.26938 −0.634691 0.772766i \(-0.718872\pi\)
−0.634691 + 0.772766i \(0.718872\pi\)
\(810\) 0 0
\(811\) −41.1368 −1.44451 −0.722255 0.691627i \(-0.756894\pi\)
−0.722255 + 0.691627i \(0.756894\pi\)
\(812\) 73.0667 48.0567i 2.56414 1.68646i
\(813\) 0 0
\(814\) −2.34259 + 5.43074i −0.0821079 + 0.190347i
\(815\) −29.7007 + 31.4809i −1.04037 + 1.10273i
\(816\) 0 0
\(817\) −3.72682 0.435603i −0.130385 0.0152398i
\(818\) −0.424434 2.40709i −0.0148400 0.0841618i
\(819\) 0 0
\(820\) −5.41261 + 30.6964i −0.189017 + 1.07197i
\(821\) −11.9792 + 40.0134i −0.418078 + 1.39648i 0.446862 + 0.894603i \(0.352541\pi\)
−0.864940 + 0.501875i \(0.832644\pi\)
\(822\) 0 0
\(823\) −1.08254 + 18.5865i −0.0377349 + 0.647884i 0.925421 + 0.378940i \(0.123711\pi\)
−0.963156 + 0.268943i \(0.913326\pi\)
\(824\) −102.272 + 51.3629i −3.56281 + 1.78931i
\(825\) 0 0
\(826\) 20.0963 + 21.3008i 0.699239 + 0.741150i
\(827\) −4.62778 + 1.68437i −0.160924 + 0.0585714i −0.421226 0.906956i \(-0.638400\pi\)
0.260302 + 0.965527i \(0.416178\pi\)
\(828\) 0 0
\(829\) 8.59129 + 3.12697i 0.298388 + 0.108604i 0.486876 0.873471i \(-0.338136\pi\)
−0.188488 + 0.982076i \(0.560359\pi\)
\(830\) 4.99963 + 11.5904i 0.173540 + 0.402310i
\(831\) 0 0
\(832\) −1.85012 6.17982i −0.0641413 0.214247i
\(833\) 0.749036 0.0875498i 0.0259526 0.00303342i
\(834\) 0 0
\(835\) −1.35004 23.1792i −0.0467199 0.802150i
\(836\) −13.1901 22.8460i −0.456190 0.790144i
\(837\) 0 0
\(838\) −16.2817 + 28.2008i −0.562443 + 0.974180i
\(839\) −32.3604 16.2520i −1.11721 0.561081i −0.208292 0.978067i \(-0.566790\pi\)
−0.908913 + 0.416985i \(0.863087\pi\)
\(840\) 0 0
\(841\) 8.75847 + 11.7647i 0.302016 + 0.405678i
\(842\) 81.3872 + 19.2891i 2.80479 + 0.664747i
\(843\) 0 0
\(844\) −79.0422 + 106.172i −2.72075 + 3.65460i
\(845\) 17.8816 15.0045i 0.615147 0.516170i
\(846\) 0 0
\(847\) −4.74338 3.98017i −0.162984 0.136760i
\(848\) −157.256 + 37.2704i −5.40020 + 1.27987i
\(849\) 0 0
\(850\) 8.64822 + 5.68802i 0.296631 + 0.195098i
\(851\) −1.79043 1.17759i −0.0613753 0.0403672i
\(852\) 0 0
\(853\) 1.80399 0.427554i 0.0617675 0.0146392i −0.199616 0.979874i \(-0.563969\pi\)
0.261383 + 0.965235i \(0.415821\pi\)
\(854\) −39.3396 33.0099i −1.34617 1.12957i
\(855\) 0 0
\(856\) −14.7303 + 12.3602i −0.503472 + 0.422463i
\(857\) −0.604769 + 0.812346i −0.0206585 + 0.0277492i −0.812332 0.583195i \(-0.801802\pi\)
0.791674 + 0.610944i \(0.209210\pi\)
\(858\) 0 0
\(859\) 5.71885 + 1.35539i 0.195125 + 0.0462454i 0.327016 0.945019i \(-0.393957\pi\)
−0.131891 + 0.991264i \(0.542105\pi\)
\(860\) −14.8252 19.9136i −0.505534 0.679049i
\(861\) 0 0
\(862\) 32.9329 + 16.5395i 1.12170 + 0.563339i
\(863\) −13.5850 + 23.5299i −0.462438 + 0.800966i −0.999082 0.0428431i \(-0.986358\pi\)
0.536644 + 0.843809i \(0.319692\pi\)
\(864\) 0 0
\(865\) 4.62850 + 8.01680i 0.157374 + 0.272579i
\(866\) 3.76872 + 64.7064i 0.128066 + 2.19881i
\(867\) 0 0
\(868\) 128.477 15.0168i 4.36080 0.509704i
\(869\) −4.46116 14.9013i −0.151335 0.505493i
\(870\) 0 0
\(871\) 1.51278 + 3.50702i 0.0512587 + 0.118831i
\(872\) −72.4964 26.3865i −2.45504 0.893561i
\(873\) 0 0
\(874\) 12.4871 4.54494i 0.422383 0.153735i
\(875\) 21.5688 + 22.8616i 0.729159 + 0.772863i
\(876\) 0 0
\(877\) 5.41496 2.71950i 0.182850 0.0918309i −0.355019 0.934859i \(-0.615526\pi\)
0.537869 + 0.843028i \(0.319229\pi\)
\(878\) −1.97255 + 33.8673i −0.0665703 + 1.14297i
\(879\) 0 0
\(880\) 22.8996 76.4901i 0.771946 2.57848i
\(881\) 4.80252 27.2365i 0.161801 0.917620i −0.790500 0.612461i \(-0.790179\pi\)
0.952302 0.305158i \(-0.0987094\pi\)
\(882\) 0 0
\(883\) 8.01388 + 45.4489i 0.269688 + 1.52948i 0.755344 + 0.655329i \(0.227470\pi\)
−0.485656 + 0.874150i \(0.661419\pi\)
\(884\) −4.38544 0.512585i −0.147498 0.0172401i
\(885\) 0 0
\(886\) 46.7415 49.5431i 1.57031 1.66443i
\(887\) 4.18762 9.70799i 0.140606 0.325962i −0.833333 0.552772i \(-0.813570\pi\)
0.973939 + 0.226809i \(0.0728294\pi\)
\(888\) 0 0
\(889\) 27.2925 17.9506i 0.915363 0.602044i
\(890\) −15.4608 −0.518249
\(891\) 0 0
\(892\) 20.9048 0.699944
\(893\) 0.177112 0.116488i 0.00592683 0.00389814i
\(894\) 0 0
\(895\) −0.848220 + 1.96639i −0.0283529 + 0.0657293i
\(896\) 26.0859 27.6494i 0.871467 0.923701i
\(897\) 0 0
\(898\) 8.50966 + 0.994636i 0.283971 + 0.0331914i
\(899\) 11.2154 + 63.6058i 0.374055 + 2.12137i
\(900\) 0 0
\(901\) −5.31714 + 30.1550i −0.177140 + 1.00461i
\(902\) −9.38688 + 31.3544i −0.312549 + 1.04399i
\(903\) 0 0
\(904\) 4.60681 79.0958i 0.153220 2.63069i
\(905\) −18.5837 + 9.33307i −0.617742 + 0.310242i
\(906\) 0 0
\(907\) 4.53694 + 4.80888i 0.150647 + 0.159676i 0.798302 0.602257i \(-0.205732\pi\)
−0.647655 + 0.761933i \(0.724250\pi\)
\(908\) −102.515 + 37.3123i −3.40207 + 1.23825i
\(909\) 0 0
\(910\) −4.45098 1.62002i −0.147549 0.0537033i
\(911\) 3.63484 + 8.42650i 0.120428 + 0.279182i 0.967757 0.251885i \(-0.0810504\pi\)
−0.847330 + 0.531067i \(0.821791\pi\)
\(912\) 0 0
\(913\) 2.73430 + 9.13318i 0.0904920 + 0.302264i
\(914\) 5.65536 0.661017i 0.187063 0.0218645i
\(915\) 0 0
\(916\) −3.61185 62.0131i −0.119339 2.04897i
\(917\) 19.2114 + 33.2752i 0.634417 + 1.09884i
\(918\) 0 0
\(919\) 7.47487 12.9469i 0.246573 0.427077i −0.716000 0.698101i \(-0.754029\pi\)
0.962573 + 0.271023i \(0.0873621\pi\)
\(920\) 47.9081 + 24.0604i 1.57948 + 0.793247i
\(921\) 0 0
\(922\) −36.5610 49.1100i −1.20407 1.61735i
\(923\) 0.647404 + 0.153438i 0.0213096 + 0.00505046i
\(924\) 0 0
\(925\) 0.615826 0.827198i 0.0202482 0.0271981i
\(926\) 59.1986 49.6735i 1.94539 1.63237i
\(927\) 0 0
\(928\) 77.8933 + 65.3603i 2.55697 + 2.14556i
\(929\) 22.5487 5.34414i 0.739799 0.175336i 0.156597 0.987663i \(-0.449948\pi\)
0.583202 + 0.812327i \(0.301799\pi\)
\(930\) 0 0
\(931\) 0.389251 + 0.256015i 0.0127572 + 0.00839054i
\(932\) 103.232 + 67.8968i 3.38148 + 2.22404i
\(933\) 0 0
\(934\) −5.42649 + 1.28610i −0.177560 + 0.0420825i
\(935\) −11.5886 9.72401i −0.378988 0.318009i
\(936\) 0 0
\(937\) 18.9849 15.9303i 0.620211 0.520419i −0.277659 0.960680i \(-0.589558\pi\)
0.897870 + 0.440261i \(0.145114\pi\)
\(938\) −41.5388 + 55.7963i −1.35629 + 1.82181i
\(939\) 0 0
\(940\) 1.36479 + 0.323461i 0.0445145 + 0.0105501i
\(941\) −25.0739 33.6802i −0.817387 1.09794i −0.993529 0.113577i \(-0.963769\pi\)
0.176142 0.984365i \(-0.443638\pi\)
\(942\) 0 0
\(943\) −10.5974 5.32222i −0.345099 0.173315i
\(944\) −25.5214 + 44.2044i −0.830652 + 1.43873i
\(945\) 0 0
\(946\) −13.0341 22.5757i −0.423774 0.733999i
\(947\) −0.314003 5.39122i −0.0102037 0.175191i −0.999560 0.0296750i \(-0.990553\pi\)
0.989356 0.145516i \(-0.0464843\pi\)
\(948\) 0 0
\(949\) −2.01538 + 0.235564i −0.0654220 + 0.00764673i
\(950\) 1.83405 + 6.12615i 0.0595044 + 0.198759i
\(951\) 0 0
\(952\) −19.4206 45.0219i −0.629424 1.45917i
\(953\) 25.1832 + 9.16594i 0.815765 + 0.296914i 0.716003 0.698097i \(-0.245970\pi\)
0.0997617 + 0.995011i \(0.468192\pi\)
\(954\) 0 0
\(955\) 26.2458 9.55270i 0.849295 0.309118i
\(956\) −83.4860 88.4899i −2.70013 2.86197i
\(957\) 0 0
\(958\) 51.8533 26.0417i 1.67530 0.841369i
\(959\) 2.43961 41.8864i 0.0787790 1.35258i
\(960\) 0 0
\(961\) −18.5073 + 61.8187i −0.597010 + 1.99415i
\(962\) −0.106196 + 0.602265i −0.00342388 + 0.0194178i
\(963\) 0 0
\(964\) −11.2797 63.9705i −0.363295 2.06035i
\(965\) −31.4631 3.67751i −1.01283 0.118383i
\(966\) 0 0
\(967\) −17.2608 + 18.2954i −0.555070 + 0.588340i −0.942769 0.333446i \(-0.891788\pi\)
0.387699 + 0.921786i \(0.373270\pi\)
\(968\) 7.92164 18.3644i 0.254611 0.590255i
\(969\) 0 0
\(970\) 62.2406 40.9363i 1.99842 1.31438i
\(971\) 42.8042 1.37365 0.686826 0.726822i \(-0.259003\pi\)
0.686826 + 0.726822i \(0.259003\pi\)
\(972\) 0 0
\(973\) 42.6287 1.36661
\(974\) 8.15874 5.36609i 0.261423 0.171941i
\(975\) 0 0
\(976\) 35.4532 82.1897i 1.13483 2.63083i
\(977\) −18.2696 + 19.3647i −0.584497 + 0.619530i −0.950365 0.311136i \(-0.899290\pi\)
0.365869 + 0.930667i \(0.380772\pi\)
\(978\) 0 0
\(979\) −11.5983 1.35564i −0.370682 0.0433265i
\(980\) 0.535285 + 3.03575i 0.0170990 + 0.0969735i
\(981\) 0 0
\(982\) 8.04984 45.6529i 0.256881 1.45684i
\(983\) 17.0243 56.8651i 0.542990 1.81371i −0.0372995 0.999304i \(-0.511876\pi\)
0.580290 0.814410i \(-0.302939\pi\)
\(984\) 0 0
\(985\) −0.966416 + 16.5927i −0.0307926 + 0.528688i
\(986\) 35.8808 18.0200i 1.14268 0.573875i
\(987\) 0 0
\(988\) −1.87188 1.98408i −0.0595524 0.0631219i
\(989\) 8.87564 3.23047i 0.282229 0.102723i
\(990\) 0 0
\(991\) 17.0810 + 6.21699i 0.542597 + 0.197489i 0.598754 0.800933i \(-0.295663\pi\)
−0.0561572 + 0.998422i \(0.517885\pi\)
\(992\) 59.5692 + 138.097i 1.89132 + 4.38458i
\(993\) 0 0
\(994\) 3.47534 + 11.6084i 0.110231 + 0.368197i
\(995\) −41.8038 + 4.88616i −1.32527 + 0.154902i
\(996\) 0 0
\(997\) −0.563902 9.68183i −0.0178590 0.306626i −0.995395 0.0958582i \(-0.969440\pi\)
0.977536 0.210768i \(-0.0675966\pi\)
\(998\) 22.5792 + 39.1083i 0.714731 + 1.23795i
\(999\) 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.a.28.1 144
3.2 odd 2 729.2.g.d.28.8 144
9.2 odd 6 729.2.g.c.271.1 144
9.4 even 3 243.2.g.a.91.1 144
9.5 odd 6 81.2.g.a.40.8 144
9.7 even 3 729.2.g.b.271.8 144
81.2 odd 54 729.2.g.c.460.1 144
81.25 even 27 243.2.g.a.235.1 144
81.29 odd 54 729.2.g.d.703.8 144
81.32 odd 54 6561.2.a.c.1.3 72
81.49 even 27 6561.2.a.d.1.70 72
81.52 even 27 inner 729.2.g.a.703.1 144
81.56 odd 54 81.2.g.a.79.8 yes 144
81.79 even 27 729.2.g.b.460.8 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.40.8 144 9.5 odd 6
81.2.g.a.79.8 yes 144 81.56 odd 54
243.2.g.a.91.1 144 9.4 even 3
243.2.g.a.235.1 144 81.25 even 27
729.2.g.a.28.1 144 1.1 even 1 trivial
729.2.g.a.703.1 144 81.52 even 27 inner
729.2.g.b.271.8 144 9.7 even 3
729.2.g.b.460.8 144 81.79 even 27
729.2.g.c.271.1 144 9.2 odd 6
729.2.g.c.460.1 144 81.2 odd 54
729.2.g.d.28.8 144 3.2 odd 2
729.2.g.d.703.8 144 81.29 odd 54
6561.2.a.c.1.3 72 81.32 odd 54
6561.2.a.d.1.70 72 81.49 even 27