# Properties

 Label 729.2.g.d.55.6 Level $729$ Weight $2$ Character 729.55 Analytic conductor $5.821$ Analytic rank $0$ Dimension $144$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.g (of order $$27$$, degree $$18$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.82109430735$$ Analytic rank: $$0$$ Dimension: $$144$$ Relative dimension: $$8$$ over $$\Q(\zeta_{27})$$ Twist minimal: no (minimal twist has level 81) Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

## Embedding invariants

 Embedding label 55.6 Character $$\chi$$ $$=$$ 729.55 Dual form 729.2.g.d.676.6

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.361975 - 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(0.221432 + 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(2.71786 - 0.989221i) q^{8} +O(q^{10})$$ $$q+(0.361975 - 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(0.221432 + 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(2.71786 - 0.989221i) q^{8} +(3.27047 + 1.19035i) q^{10} +(2.24948 + 1.47950i) q^{11} +(-4.57632 - 0.534895i) q^{13} +(-0.396347 + 0.532387i) q^{14} +(0.0182372 - 0.313121i) q^{16} +(-0.692702 + 0.581246i) q^{17} +(-1.12072 - 0.940396i) q^{19} +(-3.04408 + 3.22654i) q^{20} +(2.05578 - 1.35211i) q^{22} +(3.79608 - 0.899688i) q^{23} +(-9.43871 + 1.10323i) q^{25} +(-2.10537 + 3.64661i) q^{26} +(-0.422971 - 0.732607i) q^{28} +(3.06986 + 4.12353i) q^{29} +(-2.86446 + 9.56797i) q^{31} +(4.91313 + 2.46747i) q^{32} +(0.237013 + 0.791679i) q^{34} +(0.480274 - 2.72377i) q^{35} +(-0.348559 - 1.97678i) q^{37} +(-1.19481 + 0.600055i) q^{38} +(4.36268 + 10.1138i) q^{40} +(-2.59790 - 6.02260i) q^{41} +(6.51223 - 3.27057i) q^{43} +(0.544580 + 3.08847i) q^{44} +(0.619111 - 3.51115i) q^{46} +(1.28270 + 4.28453i) q^{47} +(-5.78408 - 2.90488i) q^{49} +(-2.49080 + 8.31986i) q^{50} +(-3.20482 - 4.30482i) q^{52} +(3.43548 + 5.95043i) q^{53} +(-5.12672 + 8.87974i) q^{55} +(-2.08634 + 0.243858i) q^{56} +(4.57148 - 1.08346i) q^{58} +(0.590929 - 0.388660i) q^{59} +(1.83608 - 1.94613i) q^{61} +(6.99212 + 5.86709i) q^{62} +(4.32956 - 3.63293i) q^{64} +(1.02024 - 17.5169i) q^{65} +(8.91352 - 11.9729i) q^{67} +(-1.04616 - 0.122278i) q^{68} +(-2.11181 - 1.38896i) q^{70} +(-9.19719 - 3.34750i) q^{71} +(15.0748 - 5.48678i) q^{73} +(-1.78499 - 0.423050i) q^{74} +(-0.0990843 - 1.70121i) q^{76} +(-1.34186 - 1.42229i) q^{77} +(1.89166 - 4.38536i) q^{79} +1.19447 q^{80} -5.99425 q^{82} +(-2.86882 + 6.65067i) q^{83} +(-2.36319 - 2.50483i) q^{85} +(-0.387238 - 6.64862i) q^{86} +(7.57733 + 1.79586i) q^{88} +(7.00321 - 2.54896i) q^{89} +(3.14441 + 1.14447i) q^{91} +(3.79659 + 2.49705i) q^{92} +(4.05968 + 0.474509i) q^{94} +(3.32707 - 4.46903i) q^{95} +(0.258735 - 4.44232i) q^{97} +(-4.53133 + 3.80223i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10})$$ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100})$$ 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

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.361975 0.839152i 0.255955 0.593370i −0.740987 0.671520i $$-0.765642\pi$$
0.996942 + 0.0781494i $$0.0249011\pi$$
$$3$$ 0 0
$$4$$ 0.799333 + 0.847243i 0.399666 + 0.423621i
$$5$$ 0.221432 + 3.80183i 0.0990272 + 1.70023i 0.572889 + 0.819633i $$0.305822\pi$$
−0.473862 + 0.880599i $$0.657141\pi$$
$$6$$ 0 0
$$7$$ −0.706680 0.167486i −0.267100 0.0633039i 0.0948834 0.995488i $$-0.469752\pi$$
−0.361983 + 0.932185i $$0.617900\pi$$
$$8$$ 2.71786 0.989221i 0.960910 0.349743i
$$9$$ 0 0
$$10$$ 3.27047 + 1.19035i 1.03421 + 0.376423i
$$11$$ 2.24948 + 1.47950i 0.678243 + 0.446087i 0.841328 0.540525i $$-0.181774\pi$$
−0.163086 + 0.986612i $$0.552145\pi$$
$$12$$ 0 0
$$13$$ −4.57632 0.534895i −1.26924 0.148353i −0.545317 0.838230i $$-0.683591\pi$$
−0.723927 + 0.689877i $$0.757665\pi$$
$$14$$ −0.396347 + 0.532387i −0.105928 + 0.142286i
$$15$$ 0 0
$$16$$ 0.0182372 0.313121i 0.00455931 0.0782803i
$$17$$ −0.692702 + 0.581246i −0.168005 + 0.140973i −0.722914 0.690938i $$-0.757198\pi$$
0.554909 + 0.831911i $$0.312753\pi$$
$$18$$ 0 0
$$19$$ −1.12072 0.940396i −0.257111 0.215742i 0.505116 0.863051i $$-0.331450\pi$$
−0.762227 + 0.647310i $$0.775894\pi$$
$$20$$ −3.04408 + 3.22654i −0.680677 + 0.721475i
$$21$$ 0 0
$$22$$ 2.05578 1.35211i 0.438294 0.288271i
$$23$$ 3.79608 0.899688i 0.791538 0.187598i 0.185090 0.982722i $$-0.440742\pi$$
0.606447 + 0.795124i $$0.292594\pi$$
$$24$$ 0 0
$$25$$ −9.43871 + 1.10323i −1.88774 + 0.220645i
$$26$$ −2.10537 + 3.64661i −0.412898 + 0.715160i
$$27$$ 0 0
$$28$$ −0.422971 0.732607i −0.0799340 0.138450i
$$29$$ 3.06986 + 4.12353i 0.570058 + 0.765721i 0.989883 0.141884i $$-0.0453161\pi$$
−0.419825 + 0.907605i $$0.637909\pi$$
$$30$$ 0 0
$$31$$ −2.86446 + 9.56797i −0.514473 + 1.71846i 0.166402 + 0.986058i $$0.446785\pi$$
−0.680874 + 0.732400i $$0.738400\pi$$
$$32$$ 4.91313 + 2.46747i 0.868528 + 0.436191i
$$33$$ 0 0
$$34$$ 0.237013 + 0.791679i 0.0406474 + 0.135772i
$$35$$ 0.480274 2.72377i 0.0811811 0.460401i
$$36$$ 0 0
$$37$$ −0.348559 1.97678i −0.0573028 0.324980i 0.942659 0.333758i $$-0.108317\pi$$
−0.999961 + 0.00877810i $$0.997206\pi$$
$$38$$ −1.19481 + 0.600055i −0.193824 + 0.0973418i
$$39$$ 0 0
$$40$$ 4.36268 + 10.1138i 0.689800 + 1.59914i
$$41$$ −2.59790 6.02260i −0.405723 0.940572i −0.991501 0.130100i $$-0.958470\pi$$
0.585778 0.810472i $$-0.300789\pi$$
$$42$$ 0 0
$$43$$ 6.51223 3.27057i 0.993106 0.498757i 0.123416 0.992355i $$-0.460615\pi$$
0.869690 + 0.493598i $$0.164319\pi$$
$$44$$ 0.544580 + 3.08847i 0.0820986 + 0.465604i
$$45$$ 0 0
$$46$$ 0.619111 3.51115i 0.0912830 0.517692i
$$47$$ 1.28270 + 4.28453i 0.187102 + 0.624963i 0.999144 + 0.0413648i $$0.0131706\pi$$
−0.812042 + 0.583598i $$0.801644\pi$$
$$48$$ 0 0
$$49$$ −5.78408 2.90488i −0.826298 0.414982i
$$50$$ −2.49080 + 8.31986i −0.352253 + 1.17661i
$$51$$ 0 0
$$52$$ −3.20482 4.30482i −0.444428 0.596971i
$$53$$ 3.43548 + 5.95043i 0.471900 + 0.817355i 0.999483 0.0321487i $$-0.0102350\pi$$
−0.527583 + 0.849503i $$0.676902\pi$$
$$54$$ 0 0
$$55$$ −5.12672 + 8.87974i −0.691287 + 1.19734i
$$56$$ −2.08634 + 0.243858i −0.278799 + 0.0325870i
$$57$$ 0 0
$$58$$ 4.57148 1.08346i 0.600265 0.142265i
$$59$$ 0.590929 0.388660i 0.0769324 0.0505992i −0.510460 0.859901i $$-0.670525\pi$$
0.587392 + 0.809302i $$0.300155\pi$$
$$60$$ 0 0
$$61$$ 1.83608 1.94613i 0.235086 0.249177i −0.599081 0.800688i $$-0.704467\pi$$
0.834167 + 0.551512i $$0.185949\pi$$
$$62$$ 6.99212 + 5.86709i 0.888000 + 0.745121i
$$63$$ 0 0
$$64$$ 4.32956 3.63293i 0.541195 0.454116i
$$65$$ 1.02024 17.5169i 0.126545 2.17270i
$$66$$ 0 0
$$67$$ 8.91352 11.9729i 1.08896 1.46273i 0.215073 0.976598i $$-0.431001\pi$$
0.873887 0.486129i $$-0.161591\pi$$
$$68$$ −1.04616 0.122278i −0.126865 0.0148284i
$$69$$ 0 0
$$70$$ −2.11181 1.38896i −0.252409 0.166012i
$$71$$ −9.19719 3.34750i −1.09151 0.397276i −0.267328 0.963606i $$-0.586141\pi$$
−0.824179 + 0.566330i $$0.808363\pi$$
$$72$$ 0 0
$$73$$ 15.0748 5.48678i 1.76437 0.642179i 0.764376 0.644771i $$-0.223047\pi$$
0.999997 + 0.00259223i $$0.000825133\pi$$
$$74$$ −1.78499 0.423050i −0.207501 0.0491785i
$$75$$ 0 0
$$76$$ −0.0990843 1.70121i −0.0113658 0.195142i
$$77$$ −1.34186 1.42229i −0.152920 0.162085i
$$78$$ 0 0
$$79$$ 1.89166 4.38536i 0.212828 0.493391i −0.778042 0.628213i $$-0.783787\pi$$
0.990870 + 0.134821i $$0.0430461\pi$$
$$80$$ 1.19447 0.133546
$$81$$ 0 0
$$82$$ −5.99425 −0.661954
$$83$$ −2.86882 + 6.65067i −0.314894 + 0.730006i 0.685105 + 0.728444i $$0.259756\pi$$
−0.999999 + 0.00156176i $$0.999503\pi$$
$$84$$ 0 0
$$85$$ −2.36319 2.50483i −0.256324 0.271687i
$$86$$ −0.387238 6.64862i −0.0417569 0.716939i
$$87$$ 0 0
$$88$$ 7.57733 + 1.79586i 0.807746 + 0.191439i
$$89$$ 7.00321 2.54896i 0.742339 0.270189i 0.0569608 0.998376i $$-0.481859\pi$$
0.685378 + 0.728187i $$0.259637\pi$$
$$90$$ 0 0
$$91$$ 3.14441 + 1.14447i 0.329624 + 0.119973i
$$92$$ 3.79659 + 2.49705i 0.395821 + 0.260336i
$$93$$ 0 0
$$94$$ 4.05968 + 0.474509i 0.418724 + 0.0489418i
$$95$$ 3.32707 4.46903i 0.341350 0.458512i
$$96$$ 0 0
$$97$$ 0.258735 4.44232i 0.0262706 0.451049i −0.959366 0.282166i $$-0.908947\pi$$
0.985636 0.168883i $$-0.0540159\pi$$
$$98$$ −4.53133 + 3.80223i −0.457733 + 0.384084i
$$99$$ 0 0
$$100$$ −8.47937 7.11504i −0.847937 0.711504i
$$101$$ 7.50105 7.95065i 0.746383 0.791119i −0.237222 0.971455i $$-0.576237\pi$$
0.983605 + 0.180336i $$0.0577185\pi$$
$$102$$ 0 0
$$103$$ −4.04794 + 2.66237i −0.398856 + 0.262332i −0.733053 0.680172i $$-0.761905\pi$$
0.334197 + 0.942503i $$0.391535\pi$$
$$104$$ −12.9669 + 3.07322i −1.27151 + 0.301354i
$$105$$ 0 0
$$106$$ 6.23688 0.728986i 0.605779 0.0708054i
$$107$$ 1.36707 2.36783i 0.132159 0.228906i −0.792349 0.610067i $$-0.791142\pi$$
0.924509 + 0.381161i $$0.124476\pi$$
$$108$$ 0 0
$$109$$ 1.70034 + 2.94507i 0.162863 + 0.282087i 0.935894 0.352281i $$-0.114594\pi$$
−0.773031 + 0.634368i $$0.781261\pi$$
$$110$$ 5.59571 + 7.51635i 0.533530 + 0.716655i
$$111$$ 0 0
$$112$$ −0.0653315 + 0.218222i −0.00617324 + 0.0206201i
$$113$$ 8.41203 + 4.22468i 0.791337 + 0.397424i 0.798079 0.602553i $$-0.205850\pi$$
−0.00674204 + 0.999977i $$0.502146\pi$$
$$114$$ 0 0
$$115$$ 4.26104 + 14.2328i 0.397344 + 1.32722i
$$116$$ −1.03980 + 5.89699i −0.0965428 + 0.547521i
$$117$$ 0 0
$$118$$ −0.112244 0.636565i −0.0103329 0.0586005i
$$119$$ 0.586870 0.294737i 0.0537983 0.0270185i
$$120$$ 0 0
$$121$$ −1.48567 3.44416i −0.135061 0.313106i
$$122$$ −0.968487 2.24520i −0.0876827 0.203271i
$$123$$ 0 0
$$124$$ −10.3961 + 5.22109i −0.933593 + 0.468868i
$$125$$ −2.97782 16.8880i −0.266344 1.51051i
$$126$$ 0 0
$$127$$ −1.36769 + 7.75655i −0.121363 + 0.688283i 0.862039 + 0.506842i $$0.169187\pi$$
−0.983402 + 0.181441i $$0.941924\pi$$
$$128$$ 1.67226 + 5.58574i 0.147808 + 0.493714i
$$129$$ 0 0
$$130$$ −14.3300 7.19680i −1.25683 0.631201i
$$131$$ −0.310717 + 1.03787i −0.0271475 + 0.0906789i −0.970490 0.241142i $$-0.922478\pi$$
0.943342 + 0.331821i $$0.107663\pi$$
$$132$$ 0 0
$$133$$ 0.634488 + 0.852265i 0.0550171 + 0.0739008i
$$134$$ −6.82065 11.8137i −0.589214 1.02055i
$$135$$ 0 0
$$136$$ −1.30769 + 2.26498i −0.112133 + 0.194221i
$$137$$ 0.730936 0.0854341i 0.0624481 0.00729913i −0.0848115 0.996397i $$-0.527029\pi$$
0.147260 + 0.989098i $$0.452955\pi$$
$$138$$ 0 0
$$139$$ −4.09766 + 0.971163i −0.347559 + 0.0823730i −0.400688 0.916215i $$-0.631229\pi$$
0.0531287 + 0.998588i $$0.483081\pi$$
$$140$$ 2.69159 1.77029i 0.227481 0.149617i
$$141$$ 0 0
$$142$$ −6.13822 + 6.50613i −0.515108 + 0.545983i
$$143$$ −9.50295 7.97392i −0.794676 0.666813i
$$144$$ 0 0
$$145$$ −14.9972 + 12.5842i −1.24545 + 1.04506i
$$146$$ 0.852458 14.6361i 0.0705499 1.21130i
$$147$$ 0 0
$$148$$ 1.39620 1.87542i 0.114767 0.154158i
$$149$$ −11.5926 1.35499i −0.949706 0.111005i −0.372887 0.927877i $$-0.621632\pi$$
−0.576819 + 0.816872i $$0.695706\pi$$
$$150$$ 0 0
$$151$$ 4.00498 + 2.63412i 0.325920 + 0.214361i 0.701915 0.712261i $$-0.252329\pi$$
−0.375995 + 0.926622i $$0.622699\pi$$
$$152$$ −3.97623 1.44723i −0.322515 0.117386i
$$153$$ 0 0
$$154$$ −1.67924 + 0.611194i −0.135317 + 0.0492514i
$$155$$ −37.0101 8.77156i −2.97272 0.704549i
$$156$$ 0 0
$$157$$ −0.543531 9.33207i −0.0433785 0.744780i −0.947942 0.318442i $$-0.896840\pi$$
0.904564 0.426338i $$-0.140197\pi$$
$$158$$ −2.99525 3.17478i −0.238289 0.252572i
$$159$$ 0 0
$$160$$ −8.29298 + 19.2253i −0.655618 + 1.51989i
$$161$$ −2.83330 −0.223295
$$162$$ 0 0
$$163$$ −7.79498 −0.610550 −0.305275 0.952264i $$-0.598748\pi$$
−0.305275 + 0.952264i $$0.598748\pi$$
$$164$$ 3.02602 7.01511i 0.236293 0.547788i
$$165$$ 0 0
$$166$$ 4.54249 + 4.81475i 0.352565 + 0.373697i
$$167$$ −0.628896 10.7977i −0.0486654 0.835553i −0.931020 0.364968i $$-0.881080\pi$$
0.882355 0.470585i $$-0.155957\pi$$
$$168$$ 0 0
$$169$$ 8.00703 + 1.89770i 0.615925 + 0.145977i
$$170$$ −2.95735 + 1.07639i −0.226818 + 0.0825551i
$$171$$ 0 0
$$172$$ 7.97640 + 2.90317i 0.608195 + 0.221365i
$$173$$ 9.71059 + 6.38676i 0.738282 + 0.485576i 0.862106 0.506728i $$-0.169145\pi$$
−0.123823 + 0.992304i $$0.539516\pi$$
$$174$$ 0 0
$$175$$ 6.85493 + 0.801226i 0.518184 + 0.0605670i
$$176$$ 0.504289 0.677377i 0.0380122 0.0510592i
$$177$$ 0 0
$$178$$ 0.396021 6.79942i 0.0296831 0.509638i
$$179$$ 2.09069 1.75429i 0.156265 0.131122i −0.561303 0.827611i $$-0.689700\pi$$
0.717568 + 0.696488i $$0.245255\pi$$
$$180$$ 0 0
$$181$$ −11.5914 9.72633i −0.861581 0.722953i 0.100727 0.994914i $$-0.467883\pi$$
−0.962308 + 0.271962i $$0.912328\pi$$
$$182$$ 2.09858 2.22437i 0.155557 0.164881i
$$183$$ 0 0
$$184$$ 9.42724 6.20039i 0.694985 0.457099i
$$185$$ 7.43820 1.76288i 0.546867 0.129610i
$$186$$ 0 0
$$187$$ −2.41817 + 0.282644i −0.176834 + 0.0206690i
$$188$$ −2.60473 + 4.51153i −0.189970 + 0.329037i
$$189$$ 0 0
$$190$$ −2.54588 4.40959i −0.184697 0.319905i
$$191$$ −1.47784 1.98509i −0.106933 0.143636i 0.745435 0.666578i $$-0.232242\pi$$
−0.852368 + 0.522942i $$0.824834\pi$$
$$192$$ 0 0
$$193$$ 1.13748 3.79946i 0.0818778 0.273491i −0.907241 0.420612i $$-0.861815\pi$$
0.989119 + 0.147121i $$0.0470006\pi$$
$$194$$ −3.63412 1.82513i −0.260915 0.131036i
$$195$$ 0 0
$$196$$ −2.16227 7.22248i −0.154448 0.515892i
$$197$$ 4.31848 24.4913i 0.307679 1.74493i −0.302942 0.953009i $$-0.597969\pi$$
0.610621 0.791923i $$-0.290920\pi$$
$$198$$ 0 0
$$199$$ 2.00332 + 11.3614i 0.142011 + 0.805386i 0.969718 + 0.244226i $$0.0785338\pi$$
−0.827707 + 0.561160i $$0.810355\pi$$
$$200$$ −24.5618 + 12.3354i −1.73678 + 0.872245i
$$201$$ 0 0
$$202$$ −3.95661 9.17246i −0.278386 0.645372i
$$203$$ −1.47877 3.42818i −0.103789 0.240611i
$$204$$ 0 0
$$205$$ 22.3217 11.2104i 1.55901 0.782966i
$$206$$ 0.768884 + 4.36056i 0.0535707 + 0.303814i
$$207$$ 0 0
$$208$$ −0.250947 + 1.42319i −0.0174000 + 0.0986804i
$$209$$ −1.12971 3.77351i −0.0781440 0.261019i
$$210$$ 0 0
$$211$$ 18.9771 + 9.53064i 1.30643 + 0.656116i 0.959483 0.281767i $$-0.0909205\pi$$
0.346952 + 0.937883i $$0.387217\pi$$
$$212$$ −2.29537 + 7.66706i −0.157647 + 0.526576i
$$213$$ 0 0
$$214$$ −1.49212 2.00427i −0.101999 0.137009i
$$215$$ 13.8762 + 24.0342i 0.946346 + 1.63912i
$$216$$ 0 0
$$217$$ 3.62676 6.28174i 0.246201 0.426432i
$$218$$ 3.08684 0.360800i 0.209068 0.0244365i
$$219$$ 0 0
$$220$$ −11.6213 + 2.75429i −0.783505 + 0.185694i
$$221$$ 3.48093 2.28945i 0.234153 0.154005i
$$222$$ 0 0
$$223$$ −1.53505 + 1.62706i −0.102795 + 0.108956i −0.776728 0.629836i $$-0.783122\pi$$
0.673933 + 0.738792i $$0.264604\pi$$
$$224$$ −3.05875 2.56659i −0.204371 0.171488i
$$225$$ 0 0
$$226$$ 6.59009 5.52974i 0.438366 0.367833i
$$227$$ 0.205125 3.52186i 0.0136146 0.233754i −0.984636 0.174622i $$-0.944130\pi$$
0.998250 0.0591321i $$-0.0188333\pi$$
$$228$$ 0 0
$$229$$ −6.30941 + 8.47500i −0.416937 + 0.560044i −0.960126 0.279566i $$-0.909809\pi$$
0.543189 + 0.839610i $$0.317217\pi$$
$$230$$ 13.4859 + 1.57628i 0.889235 + 0.103937i
$$231$$ 0 0
$$232$$ 12.4225 + 8.17043i 0.815579 + 0.536415i
$$233$$ 16.8171 + 6.12092i 1.10172 + 0.400995i 0.827952 0.560799i $$-0.189506\pi$$
0.273773 + 0.961794i $$0.411728\pi$$
$$234$$ 0 0
$$235$$ −16.0050 + 5.82536i −1.04405 + 0.380005i
$$236$$ 0.801638 + 0.189992i 0.0521822 + 0.0123674i
$$237$$ 0 0
$$238$$ −0.0348971 0.599160i −0.00226204 0.0388378i
$$239$$ −0.254893 0.270171i −0.0164877 0.0174759i 0.719077 0.694930i $$-0.244565\pi$$
−0.735565 + 0.677454i $$0.763083\pi$$
$$240$$ 0 0
$$241$$ 2.49079 5.77431i 0.160446 0.371956i −0.818962 0.573848i $$-0.805450\pi$$
0.979408 + 0.201892i $$0.0647091\pi$$
$$242$$ −3.42795 −0.220357
$$243$$ 0 0
$$244$$ 3.11649 0.199513
$$245$$ 9.76307 22.6334i 0.623740 1.44599i
$$246$$ 0 0
$$247$$ 4.62577 + 4.90302i 0.294330 + 0.311972i
$$248$$ 1.67962 + 28.8380i 0.106656 + 1.83122i
$$249$$ 0 0
$$250$$ −15.2495 3.61420i −0.964465 0.228582i
$$251$$ −4.91237 + 1.78796i −0.310066 + 0.112855i −0.492366 0.870388i $$-0.663868\pi$$
0.182300 + 0.983243i $$0.441646\pi$$
$$252$$ 0 0
$$253$$ 9.87029 + 3.59249i 0.620540 + 0.225858i
$$254$$ 6.01386 + 3.95538i 0.377343 + 0.248182i
$$255$$ 0 0
$$256$$ 16.5198 + 1.93089i 1.03249 + 0.120681i
$$257$$ −1.94989 + 2.61916i −0.121631 + 0.163379i −0.858768 0.512364i $$-0.828770\pi$$
0.737137 + 0.675743i $$0.236177\pi$$
$$258$$ 0 0
$$259$$ −0.0847632 + 1.45533i −0.00526693 + 0.0904297i
$$260$$ 15.6565 13.1374i 0.970978 0.814747i
$$261$$ 0 0
$$262$$ 0.758457 + 0.636421i 0.0468576 + 0.0393182i
$$263$$ −0.961659 + 1.01930i −0.0592984 + 0.0628527i −0.756344 0.654175i $$-0.773016\pi$$
0.697045 + 0.717027i $$0.254498\pi$$
$$264$$ 0 0
$$265$$ −21.8618 + 14.3787i −1.34296 + 0.883280i
$$266$$ 0.944849 0.223933i 0.0579324 0.0137302i
$$267$$ 0 0
$$268$$ 17.2689 2.01844i 1.05486 0.123296i
$$269$$ −5.17838 + 8.96922i −0.315732 + 0.546863i −0.979593 0.200993i $$-0.935583\pi$$
0.663861 + 0.747856i $$0.268917\pi$$
$$270$$ 0 0
$$271$$ −9.29809 16.1048i −0.564819 0.978295i −0.997067 0.0765398i $$-0.975613\pi$$
0.432248 0.901755i $$-0.357721\pi$$
$$272$$ 0.169368 + 0.227500i 0.0102694 + 0.0137942i
$$273$$ 0 0
$$274$$ 0.192888 0.644292i 0.0116528 0.0389231i
$$275$$ −22.8644 11.4829i −1.37877 0.692447i
$$276$$ 0 0
$$277$$ −2.93650 9.80858i −0.176437 0.589341i −0.999763 0.0217719i $$-0.993069\pi$$
0.823326 0.567569i $$-0.192116\pi$$
$$278$$ −0.668297 + 3.79010i −0.0400818 + 0.227315i
$$279$$ 0 0
$$280$$ −1.38909 7.87793i −0.0830141 0.470796i
$$281$$ −16.0079 + 8.03947i −0.954951 + 0.479595i −0.856841 0.515581i $$-0.827576\pi$$
−0.0981105 + 0.995176i $$0.531280\pi$$
$$282$$ 0 0
$$283$$ −10.5546 24.4683i −0.627404 1.45449i −0.874271 0.485437i $$-0.838660\pi$$
0.246867 0.969049i $$-0.420599\pi$$
$$284$$ −4.51547 10.4680i −0.267944 0.621163i
$$285$$ 0 0
$$286$$ −10.1312 + 5.08806i −0.599068 + 0.300863i
$$287$$ 0.827179 + 4.69117i 0.0488268 + 0.276911i
$$288$$ 0 0
$$289$$ −2.81003 + 15.9365i −0.165296 + 0.937439i
$$290$$ 5.13141 + 17.1401i 0.301327 + 1.00650i
$$291$$ 0 0
$$292$$ 16.6984 + 8.38626i 0.977201 + 0.490769i
$$293$$ 8.29474 27.7063i 0.484584 1.61862i −0.270309 0.962774i $$-0.587126\pi$$
0.754893 0.655848i $$-0.227689\pi$$
$$294$$ 0 0
$$295$$ 1.60847 + 2.16055i 0.0936488 + 0.125792i
$$296$$ −2.90281 5.02781i −0.168722 0.292235i
$$297$$ 0 0
$$298$$ −5.33328 + 9.23752i −0.308949 + 0.535115i
$$299$$ −17.8533 + 2.08675i −1.03248 + 0.120680i
$$300$$ 0 0
$$301$$ −5.14984 + 1.22053i −0.296832 + 0.0703505i
$$302$$ 3.66013 2.40730i 0.210617 0.138525i
$$303$$ 0 0
$$304$$ −0.314897 + 0.333771i −0.0180606 + 0.0191431i
$$305$$ 7.80544 + 6.54955i 0.446938 + 0.375026i
$$306$$ 0 0
$$307$$ 2.94847 2.47406i 0.168278 0.141202i −0.554759 0.832011i $$-0.687190\pi$$
0.723038 + 0.690809i $$0.242745\pi$$
$$308$$ 0.132432 2.27377i 0.00754601 0.129560i
$$309$$ 0 0
$$310$$ −20.7574 + 27.8820i −1.17894 + 1.58359i
$$311$$ 14.0725 + 1.64484i 0.797977 + 0.0932701i 0.505303 0.862942i $$-0.331381\pi$$
0.292674 + 0.956212i $$0.405455\pi$$
$$312$$ 0 0
$$313$$ −17.3980 11.4428i −0.983391 0.646786i −0.0474241 0.998875i $$-0.515101\pi$$
−0.935967 + 0.352089i $$0.885472\pi$$
$$314$$ −8.02777 2.92187i −0.453033 0.164891i
$$315$$ 0 0
$$316$$ 5.22753 1.90266i 0.294071 0.107033i
$$317$$ 23.7891 + 5.63811i 1.33613 + 0.316668i 0.835736 0.549132i $$-0.185041\pi$$
0.500391 + 0.865800i $$0.333190\pi$$
$$318$$ 0 0
$$319$$ 0.804786 + 13.8176i 0.0450594 + 0.773640i
$$320$$ 14.7705 + 15.6558i 0.825696 + 0.875186i
$$321$$ 0 0
$$322$$ −1.02558 + 2.37757i −0.0571536 + 0.132497i
$$323$$ 1.32293 0.0736096
$$324$$ 0 0
$$325$$ 43.7847 2.42874
$$326$$ −2.82159 + 6.54117i −0.156273 + 0.362282i
$$327$$ 0 0
$$328$$ −13.0184 13.7987i −0.718822 0.761906i
$$329$$ −0.188862 3.24263i −0.0104123 0.178772i
$$330$$ 0 0
$$331$$ −6.56661 1.55632i −0.360934 0.0855429i 0.0461480 0.998935i $$-0.485305\pi$$
−0.407082 + 0.913392i $$0.633454\pi$$
$$332$$ −7.92788 + 2.88551i −0.435099 + 0.158363i
$$333$$ 0 0
$$334$$ −9.28858 3.38077i −0.508249 0.184987i
$$335$$ 47.4928 + 31.2365i 2.59481 + 1.70663i
$$336$$ 0 0
$$337$$ 4.23038 + 0.494461i 0.230444 + 0.0269350i 0.230531 0.973065i $$-0.425954\pi$$
−8.72681e−5 1.00000i $$0.500028\pi$$
$$338$$ 4.49080 6.03220i 0.244268 0.328108i
$$339$$ 0 0
$$340$$ 0.233229 4.00439i 0.0126486 0.217168i
$$341$$ −20.5994 + 17.2849i −1.11552 + 0.936032i
$$342$$ 0 0
$$343$$ 7.49539 + 6.28938i 0.404713 + 0.339594i
$$344$$ 14.4640 15.3310i 0.779849 0.826592i
$$345$$ 0 0
$$346$$ 8.87445 5.83682i 0.477093 0.313789i
$$347$$ −19.6616 + 4.65989i −1.05549 + 0.250156i −0.721496 0.692418i $$-0.756545\pi$$
−0.333996 + 0.942575i $$0.608397\pi$$
$$348$$ 0 0
$$349$$ −22.8564 + 2.67153i −1.22348 + 0.143004i −0.703199 0.710993i $$-0.748246\pi$$
−0.520278 + 0.853997i $$0.674172\pi$$
$$350$$ 3.15366 5.46231i 0.168570 0.291973i
$$351$$ 0 0
$$352$$ 7.40135 + 12.8195i 0.394493 + 0.683282i
$$353$$ 12.9522 + 17.3979i 0.689378 + 0.925995i 0.999696 0.0246374i $$-0.00784313\pi$$
−0.310319 + 0.950633i $$0.600436\pi$$
$$354$$ 0 0
$$355$$ 10.6901 35.7074i 0.567372 1.89515i
$$356$$ 7.75749 + 3.89596i 0.411146 + 0.206485i
$$357$$ 0 0
$$358$$ −0.715344 2.38942i −0.0378071 0.126285i
$$359$$ −5.76399 + 32.6892i −0.304212 + 1.72527i 0.322981 + 0.946405i $$0.395315\pi$$
−0.627193 + 0.778864i $$0.715796\pi$$
$$360$$ 0 0
$$361$$ −2.92765 16.6035i −0.154087 0.873869i
$$362$$ −12.3577 + 6.20625i −0.649505 + 0.326193i
$$363$$ 0 0
$$364$$ 1.54378 + 3.57889i 0.0809162 + 0.187585i
$$365$$ 24.1979 + 56.0969i 1.26657 + 2.93625i
$$366$$ 0 0
$$367$$ −18.5041 + 9.29311i −0.965906 + 0.485096i −0.860565 0.509340i $$-0.829890\pi$$
−0.105341 + 0.994436i $$0.533593\pi$$
$$368$$ −0.212481 1.20504i −0.0110764 0.0628172i
$$369$$ 0 0
$$370$$ 1.21311 6.87990i 0.0630667 0.357669i
$$371$$ −1.43117 4.78045i −0.0743028 0.248189i
$$372$$ 0 0
$$373$$ −3.59966 1.80782i −0.186383 0.0936052i 0.353161 0.935563i $$-0.385107\pi$$
−0.539544 + 0.841958i $$0.681403\pi$$
$$374$$ −0.638137 + 2.13152i −0.0329973 + 0.110219i
$$375$$ 0 0
$$376$$ 7.72457 + 10.3759i 0.398364 + 0.535096i
$$377$$ −11.8430 20.5127i −0.609945 1.05646i
$$378$$ 0 0
$$379$$ 17.2610 29.8970i 0.886640 1.53570i 0.0428169 0.999083i $$-0.486367\pi$$
0.843823 0.536622i $$-0.180300\pi$$
$$380$$ 6.44578 0.753404i 0.330662 0.0386488i
$$381$$ 0 0
$$382$$ −2.20073 + 0.521583i −0.112599 + 0.0266865i
$$383$$ −11.9143 + 7.83617i −0.608793 + 0.400410i −0.816137 0.577859i $$-0.803889\pi$$
0.207344 + 0.978268i $$0.433518\pi$$
$$384$$ 0 0
$$385$$ 5.11019 5.41648i 0.260439 0.276050i
$$386$$ −2.77658 2.32983i −0.141324 0.118585i
$$387$$ 0 0
$$388$$ 3.97054 3.33168i 0.201573 0.169140i
$$389$$ 1.20812 20.7426i 0.0612541 1.05169i −0.817963 0.575271i $$-0.804897\pi$$
0.879217 0.476421i $$-0.158066\pi$$
$$390$$ 0 0
$$391$$ −2.10661 + 2.82967i −0.106536 + 0.143103i
$$392$$ −18.5939 2.17332i −0.939134 0.109769i
$$393$$ 0 0
$$394$$ −18.9887 12.4891i −0.956639 0.629191i
$$395$$ 17.0913 + 6.22071i 0.859955 + 0.312998i
$$396$$ 0 0
$$397$$ 21.4426 7.80446i 1.07617 0.391695i 0.257691 0.966227i $$-0.417038\pi$$
0.818482 + 0.574533i $$0.194816\pi$$
$$398$$ 10.2591 + 2.43144i 0.514241 + 0.121877i
$$399$$ 0 0
$$400$$ 0.173308 + 2.97558i 0.00866540 + 0.148779i
$$401$$ −5.89097 6.24406i −0.294181 0.311814i 0.563378 0.826199i $$-0.309501\pi$$
−0.857559 + 0.514386i $$0.828020\pi$$
$$402$$ 0 0
$$403$$ 18.2266 42.2539i 0.907930 2.10482i
$$404$$ 12.7320 0.633439
$$405$$ 0 0
$$406$$ −3.41204 −0.169337
$$407$$ 2.14057 4.96241i 0.106104 0.245977i
$$408$$ 0 0
$$409$$ 19.3500 + 20.5098i 0.956798 + 1.01415i 0.999886 + 0.0150751i $$0.00479872\pi$$
−0.0430887 + 0.999071i $$0.513720\pi$$
$$410$$ −1.32732 22.7891i −0.0655515 1.12548i
$$411$$ 0 0
$$412$$ −5.49133 1.30147i −0.270538 0.0641188i
$$413$$ −0.482693 + 0.175686i −0.0237518 + 0.00864494i
$$414$$ 0 0
$$415$$ −25.9200 9.43411i −1.27236 0.463102i
$$416$$ −21.1642 13.9199i −1.03766 0.682481i
$$417$$ 0 0
$$418$$ −3.57548 0.417913i −0.174882 0.0204408i
$$419$$ −19.0798 + 25.6286i −0.932108 + 1.25204i 0.0354460 + 0.999372i $$0.488715\pi$$
−0.967554 + 0.252666i $$0.918693\pi$$
$$420$$ 0 0
$$421$$ −1.62148 + 27.8397i −0.0790260 + 1.35682i 0.692865 + 0.721068i $$0.256348\pi$$
−0.771891 + 0.635755i $$0.780689\pi$$
$$422$$ 14.8669 12.4748i 0.723708 0.607263i
$$423$$ 0 0
$$424$$ 15.2235 + 12.7740i 0.739317 + 0.620361i
$$425$$ 5.89697 6.25042i 0.286045 0.303190i
$$426$$ 0 0
$$427$$ −1.62347 + 1.06778i −0.0785654 + 0.0516733i
$$428$$ 3.09886 0.734444i 0.149789 0.0355007i
$$429$$ 0 0
$$430$$ 25.1912 2.94443i 1.21483 0.141993i
$$431$$ 16.9276 29.3195i 0.815375 1.41227i −0.0936837 0.995602i $$-0.529864\pi$$
0.909058 0.416669i $$-0.136802\pi$$
$$432$$ 0 0
$$433$$ 4.23939 + 7.34284i 0.203732 + 0.352874i 0.949728 0.313076i $$-0.101360\pi$$
−0.745996 + 0.665950i $$0.768026\pi$$
$$434$$ −3.95854 5.31724i −0.190016 0.255236i
$$435$$ 0 0
$$436$$ −1.13606 + 3.79469i −0.0544072 + 0.181733i
$$437$$ −5.10041 2.56152i −0.243986 0.122534i
$$438$$ 0 0
$$439$$ 6.37737 + 21.3019i 0.304375 + 1.01668i 0.964180 + 0.265247i $$0.0854535\pi$$
−0.659805 + 0.751437i $$0.729361\pi$$
$$440$$ −5.14970 + 29.2054i −0.245502 + 1.39231i
$$441$$ 0 0
$$442$$ −0.661183 3.74976i −0.0314493 0.178358i
$$443$$ −20.1340 + 10.1117i −0.956596 + 0.480420i −0.857402 0.514648i $$-0.827923\pi$$
−0.0991939 + 0.995068i $$0.531626\pi$$
$$444$$ 0 0
$$445$$ 11.2415 + 26.0606i 0.532896 + 1.23539i
$$446$$ 0.809702 + 1.87710i 0.0383405 + 0.0888832i
$$447$$ 0 0
$$448$$ −3.66808 + 1.84218i −0.173300 + 0.0870348i
$$449$$ 3.85889 + 21.8849i 0.182112 + 1.03281i 0.929610 + 0.368546i $$0.120144\pi$$
−0.747497 + 0.664265i $$0.768745\pi$$
$$450$$ 0 0
$$451$$ 3.06655 17.3913i 0.144398 0.818924i
$$452$$ 3.14468 + 10.5040i 0.147913 + 0.494064i
$$453$$ 0 0
$$454$$ −2.88113 1.44696i −0.135218 0.0679091i
$$455$$ −3.65482 + 12.2079i −0.171341 + 0.572317i
$$456$$ 0 0
$$457$$ −1.38320 1.85796i −0.0647032 0.0869115i 0.768594 0.639737i $$-0.220957\pi$$
−0.833297 + 0.552826i $$0.813549\pi$$
$$458$$ 4.82797 + 8.36229i 0.225596 + 0.390744i
$$459$$ 0 0
$$460$$ −8.65270 + 14.9869i −0.403434 + 0.698768i
$$461$$ −24.3727 + 2.84876i −1.13515 + 0.132680i −0.662846 0.748755i $$-0.730652\pi$$
−0.472305 + 0.881435i $$0.656578\pi$$
$$462$$ 0 0
$$463$$ 26.5407 6.29025i 1.23345 0.292333i 0.438345 0.898807i $$-0.355565\pi$$
0.795103 + 0.606474i $$0.207417\pi$$
$$464$$ 1.34715 0.886036i 0.0625399 0.0411332i
$$465$$ 0 0
$$466$$ 11.2238 11.8965i 0.519931 0.551094i
$$467$$ 2.81518 + 2.36222i 0.130271 + 0.109310i 0.705595 0.708615i $$-0.250680\pi$$
−0.575324 + 0.817925i $$0.695124\pi$$
$$468$$ 0 0
$$469$$ −8.30431 + 6.96815i −0.383458 + 0.321759i
$$470$$ −0.905062 + 15.5393i −0.0417474 + 0.716775i
$$471$$ 0 0
$$472$$ 1.22159 1.64088i 0.0562284 0.0755278i
$$473$$ 19.4879 + 2.27781i 0.896056 + 0.104734i
$$474$$ 0 0
$$475$$ 11.6156 + 7.63972i 0.532962 + 0.350535i
$$476$$ 0.718818 + 0.261628i 0.0329470 + 0.0119917i
$$477$$ 0 0
$$478$$ −0.318980 + 0.116099i −0.0145898 + 0.00531025i
$$479$$ −2.89958 0.687214i −0.132485 0.0313996i 0.163838 0.986487i $$-0.447613\pi$$
−0.296324 + 0.955088i $$0.595761\pi$$
$$480$$ 0 0
$$481$$ 0.537750 + 9.23281i 0.0245193 + 0.420980i
$$482$$ −3.94392 4.18031i −0.179641 0.190408i
$$483$$ 0 0
$$484$$ 1.73050 4.01175i 0.0786591 0.182352i
$$485$$ 16.9462 0.769489
$$486$$ 0 0
$$487$$ −19.3605 −0.877310 −0.438655 0.898656i $$-0.644545\pi$$
−0.438655 + 0.898656i $$0.644545\pi$$
$$488$$ 3.06506 7.10562i 0.138749 0.321656i
$$489$$ 0 0
$$490$$ −15.4588 16.3854i −0.698359 0.740218i
$$491$$ 0.624138 + 10.7160i 0.0281669 + 0.483608i 0.982665 + 0.185390i $$0.0593550\pi$$
−0.954498 + 0.298217i $$0.903608\pi$$
$$492$$ 0 0
$$493$$ −4.52328 1.07204i −0.203718 0.0482821i
$$494$$ 5.78880 2.10695i 0.260450 0.0947961i
$$495$$ 0 0
$$496$$ 2.94370 + 1.07142i 0.132176 + 0.0481081i
$$497$$ 5.93882 + 3.90602i 0.266392 + 0.175209i
$$498$$ 0 0
$$499$$ −30.4517 3.55929i −1.36320 0.159336i −0.597159 0.802123i $$-0.703704\pi$$
−0.766045 + 0.642787i $$0.777778\pi$$
$$500$$ 11.9280 16.0221i 0.533436 0.716529i
$$501$$ 0 0
$$502$$ −0.277787 + 4.76942i −0.0123982 + 0.212870i
$$503$$ −21.3536 + 17.9178i −0.952111 + 0.798916i −0.979652 0.200705i $$-0.935677\pi$$
0.0275408 + 0.999621i $$0.491232\pi$$
$$504$$ 0 0
$$505$$ 31.8880 + 26.7572i 1.41900 + 1.19068i
$$506$$ 6.58744 6.98228i 0.292848 0.310400i
$$507$$ 0 0
$$508$$ −7.66492 + 5.04130i −0.340076 + 0.223671i
$$509$$ 36.4747 8.64466i 1.61671 0.383168i 0.679984 0.733227i $$-0.261987\pi$$
0.936728 + 0.350059i $$0.113839\pi$$
$$510$$ 0 0
$$511$$ −11.5720 + 1.35258i −0.511916 + 0.0598345i
$$512$$ 1.76939 3.06468i 0.0781968 0.135441i
$$513$$ 0 0
$$514$$ 1.49206 + 2.58432i 0.0658120 + 0.113990i
$$515$$ −11.0182 14.8001i −0.485522 0.652169i
$$516$$ 0 0
$$517$$ −3.45357 + 11.5357i −0.151888 + 0.507340i
$$518$$ 1.19056 + 0.597922i 0.0523102 + 0.0262712i
$$519$$ 0 0
$$520$$ −14.5552 48.6177i −0.638287 2.13203i
$$521$$ 6.93526 39.3318i 0.303839 1.72316i −0.325079 0.945687i $$-0.605391\pi$$
0.628918 0.777472i $$-0.283498\pi$$
$$522$$ 0 0
$$523$$ 1.17678 + 6.67383i 0.0514568 + 0.291826i 0.999667 0.0258185i $$-0.00821918\pi$$
−0.948210 + 0.317645i $$0.897108\pi$$
$$524$$ −1.12769 + 0.566348i −0.0492634 + 0.0247410i
$$525$$ 0 0
$$526$$ 0.507251 + 1.17594i 0.0221172 + 0.0512734i
$$527$$ −3.57713 8.29271i −0.155822 0.361236i
$$528$$ 0 0
$$529$$ −6.95276 + 3.49181i −0.302294 + 0.151818i
$$530$$ 4.15253 + 23.5502i 0.180374 + 1.02295i
$$531$$ 0 0
$$532$$ −0.214909 + 1.21881i −0.00931748 + 0.0528421i
$$533$$ 8.66735 + 28.9510i 0.375425 + 1.25401i
$$534$$ 0 0
$$535$$ 9.30479 + 4.67304i 0.402281 + 0.202033i
$$536$$ 12.3818 41.3583i 0.534814 1.78640i
$$537$$ 0 0
$$538$$ 5.65210 + 7.59209i 0.243679 + 0.327318i
$$539$$ −8.71338 15.0920i −0.375312 0.650059i
$$540$$ 0 0
$$541$$ 10.2033 17.6727i 0.438676 0.759809i −0.558912 0.829227i $$-0.688781\pi$$
0.997588 + 0.0694179i $$0.0221142\pi$$
$$542$$ −16.8800 + 1.97299i −0.725059 + 0.0847473i
$$543$$ 0 0
$$544$$ −4.83754 + 1.14652i −0.207408 + 0.0491566i
$$545$$ −10.8202 + 7.11654i −0.463485 + 0.304839i
$$546$$ 0 0
$$547$$ −2.46158 + 2.60912i −0.105249 + 0.111558i −0.777856 0.628442i $$-0.783693\pi$$
0.672607 + 0.740000i $$0.265174\pi$$
$$548$$ 0.656644 + 0.550990i 0.0280505 + 0.0235371i
$$549$$ 0 0
$$550$$ −17.9123 + 15.0302i −0.763782 + 0.640889i
$$551$$ 0.437303 7.50821i 0.0186297 0.319860i
$$552$$ 0 0
$$553$$ −2.07129 + 2.78222i −0.0880800 + 0.118312i
$$554$$ −9.29384 1.08629i −0.394857 0.0461522i
$$555$$ 0 0
$$556$$ −4.09820 2.69543i −0.173803 0.114312i
$$557$$ −2.23552 0.813664i −0.0947221 0.0344760i 0.294224 0.955736i $$-0.404939\pi$$
−0.388947 + 0.921260i $$0.627161\pi$$
$$558$$ 0 0
$$559$$ −31.5515 + 11.4838i −1.33449 + 0.485713i
$$560$$ −0.844111 0.200058i −0.0356702 0.00845399i
$$561$$ 0 0
$$562$$ 0.951880 + 16.3432i 0.0401527 + 0.689394i
$$563$$ 24.2686 + 25.7232i 1.02280 + 1.08410i 0.996428 + 0.0844510i $$0.0269137\pi$$
0.0263710 + 0.999652i $$0.491605\pi$$
$$564$$ 0 0
$$565$$ −14.1988 + 32.9166i −0.597349 + 1.38481i
$$566$$ −24.3531 −1.02364
$$567$$ 0 0
$$568$$ −28.3081 −1.18778
$$569$$ −12.7694 + 29.6028i −0.535322 + 1.24102i 0.409163 + 0.912461i $$0.365821\pi$$
−0.944485 + 0.328554i $$0.893439\pi$$
$$570$$ 0 0
$$571$$ −2.04866 2.17145i −0.0857336 0.0908723i 0.683086 0.730338i $$-0.260637\pi$$
−0.768820 + 0.639465i $$0.779156\pi$$
$$572$$ −0.840167 14.4251i −0.0351292 0.603145i
$$573$$ 0 0
$$574$$ 4.23602 + 1.00396i 0.176808 + 0.0419043i
$$575$$ −34.8376 + 12.6798i −1.45283 + 0.528786i
$$576$$ 0 0
$$577$$ −31.1151 11.3250i −1.29534 0.471464i −0.399862 0.916575i $$-0.630942\pi$$
−0.895475 + 0.445111i $$0.853164\pi$$
$$578$$ 12.3560 + 8.12665i 0.513940 + 0.338024i
$$579$$ 0 0
$$580$$ −22.6496 2.64736i −0.940474 0.109926i
$$581$$ 3.14124 4.21941i 0.130320 0.175051i
$$582$$ 0 0
$$583$$ −1.07565 + 18.4682i −0.0445488 + 0.764873i
$$584$$ 35.5436 29.8246i 1.47081 1.23415i
$$585$$ 0 0
$$586$$ −20.2474 16.9896i −0.836411 0.701832i
$$587$$ 5.80543 6.15339i 0.239616 0.253978i −0.596395 0.802691i $$-0.703401\pi$$
0.836010 + 0.548714i $$0.184882\pi$$
$$588$$ 0 0
$$589$$ 12.2079 8.02929i 0.503020 0.330841i
$$590$$ 2.39526 0.567687i 0.0986112 0.0233713i
$$591$$ 0 0
$$592$$ −0.625328 + 0.0730904i −0.0257008 + 0.00300400i
$$593$$ −1.61604 + 2.79907i −0.0663629 + 0.114944i −0.897298 0.441426i $$-0.854473\pi$$
0.830935 + 0.556370i $$0.187806\pi$$
$$594$$ 0 0
$$595$$ 1.25049 + 2.16592i 0.0512652 + 0.0887939i
$$596$$ −8.11837 10.9049i −0.332541 0.446681i
$$597$$ 0 0
$$598$$ −4.71135 + 15.7370i −0.192662 + 0.643534i
$$599$$ 0.552166 + 0.277308i 0.0225609 + 0.0113305i 0.460044 0.887896i $$-0.347834\pi$$
−0.437483 + 0.899227i $$0.644130\pi$$
$$600$$ 0 0
$$601$$ −5.21882 17.4321i −0.212880 0.711068i −0.996013 0.0892137i $$-0.971565\pi$$
0.783133 0.621855i $$-0.213621\pi$$
$$602$$ −0.839899 + 4.76331i −0.0342317 + 0.194138i
$$603$$ 0 0
$$604$$ 0.969573 + 5.49872i 0.0394514 + 0.223740i
$$605$$ 12.7652 6.41090i 0.518977 0.260640i
$$606$$ 0 0
$$607$$ −2.86882 6.65067i −0.116442 0.269942i 0.850021 0.526748i $$-0.176589\pi$$
−0.966463 + 0.256806i $$0.917330\pi$$
$$608$$ −3.18585 7.38564i −0.129203 0.299527i
$$609$$ 0 0
$$610$$ 8.32144 4.17919i 0.336925 0.169210i
$$611$$ −3.57829 20.2935i −0.144762 0.820988i
$$612$$ 0 0
$$613$$ −6.98532 + 39.6157i −0.282134 + 1.60006i 0.433211 + 0.901293i $$0.357381\pi$$
−0.715345 + 0.698771i $$0.753731\pi$$
$$614$$ −1.00884 3.36977i −0.0407136 0.135993i
$$615$$ 0 0
$$616$$ −5.05397 2.53820i −0.203630 0.102267i
$$617$$ 5.02262 16.7767i 0.202203 0.675405i −0.795392 0.606095i $$-0.792735\pi$$
0.997595 0.0693101i $$-0.0220798\pi$$
$$618$$ 0 0
$$619$$ 6.13883 + 8.24588i 0.246740 + 0.331430i 0.908189 0.418561i $$-0.137465\pi$$
−0.661448 + 0.749991i $$0.730058\pi$$
$$620$$ −22.1517 38.3680i −0.889636 1.54089i
$$621$$ 0 0
$$622$$ 6.47415 11.2136i 0.259590 0.449623i
$$623$$ −5.37595 + 0.628359i −0.215383 + 0.0251747i
$$624$$ 0 0
$$625$$ 17.3120 4.10302i 0.692481 0.164121i
$$626$$ −15.8999 + 10.4575i −0.635488 + 0.417967i
$$627$$ 0 0
$$628$$ 7.47207 7.91993i 0.298168 0.316039i
$$629$$ 1.39044 + 1.16672i 0.0554405 + 0.0465201i
$$630$$ 0 0
$$631$$ 22.0848 18.5313i 0.879182 0.737721i −0.0868288 0.996223i $$-0.527673\pi$$
0.966011 + 0.258502i $$0.0832289\pi$$
$$632$$ 0.803180 13.7901i 0.0319488 0.548540i
$$633$$ 0 0
$$634$$ 13.3423 17.9218i 0.529890 0.711765i
$$635$$ −29.7920 3.48218i −1.18226 0.138186i
$$636$$ 0 0
$$637$$ 24.9160 + 16.3875i 0.987209 + 0.649297i
$$638$$ 11.8864 + 4.32630i 0.470588 + 0.171280i
$$639$$ 0 0
$$640$$ −20.8658 + 7.59452i −0.824792 + 0.300200i
$$641$$ −27.9023 6.61297i −1.10207 0.261197i −0.360964 0.932580i $$-0.617552\pi$$
−0.741111 + 0.671383i $$0.765701\pi$$
$$642$$ 0 0
$$643$$ −1.12427 19.3030i −0.0443369 0.761235i −0.945071 0.326864i $$-0.894008\pi$$
0.900734 0.434370i $$-0.143029\pi$$
$$644$$ −2.26475 2.40049i −0.0892437 0.0945928i
$$645$$ 0 0
$$646$$ 0.478866 1.11014i 0.0188407 0.0436778i
$$647$$ −29.8266 −1.17261 −0.586303 0.810092i $$-0.699417\pi$$
−0.586303 + 0.810092i $$0.699417\pi$$
$$648$$ 0 0
$$649$$ 1.90430 0.0747505
$$650$$ 15.8490 36.7420i 0.621648 1.44114i
$$651$$ 0 0
$$652$$ −6.23078 6.60424i −0.244016 0.258642i
$$653$$ 1.44269 + 24.7701i 0.0564569 + 0.969328i 0.900994 + 0.433831i $$0.142838\pi$$
−0.844537 + 0.535497i $$0.820124\pi$$
$$654$$ 0 0
$$655$$ −4.01460 0.951478i −0.156863 0.0371773i
$$656$$ −1.93318 + 0.703621i −0.0754781 + 0.0274718i
$$657$$ 0 0
$$658$$ −2.78942 1.01527i −0.108743 0.0395792i
$$659$$ −14.6079 9.60779i −0.569044 0.374266i 0.232142 0.972682i $$-0.425427\pi$$
−0.801186 + 0.598416i $$0.795797\pi$$
$$660$$ 0 0
$$661$$ −37.3153 4.36154i −1.45140 0.169644i −0.646435 0.762969i $$-0.723741\pi$$
−0.804963 + 0.593324i $$0.797815\pi$$
$$662$$ −3.68294 + 4.94704i −0.143141 + 0.192272i
$$663$$ 0 0
$$664$$ −1.21807 + 20.9135i −0.0472704 + 0.811602i
$$665$$ −3.09967 + 2.60094i −0.120200 + 0.100860i
$$666$$ 0 0
$$667$$ 15.3633 + 12.8913i 0.594870 + 0.499155i
$$668$$ 8.64560 9.16380i 0.334508 0.354558i
$$669$$ 0 0
$$670$$ 43.4034 28.5469i 1.67682 1.10286i
$$671$$ 7.00954 1.66129i 0.270600 0.0641334i
$$672$$ 0 0
$$673$$ 26.3408 3.07880i 1.01536 0.118679i 0.407900 0.913027i $$-0.366261\pi$$
0.607464 + 0.794348i $$0.292187\pi$$
$$674$$ 1.94622 3.37095i 0.0749656 0.129844i
$$675$$ 0 0
$$676$$ 4.79246 + 8.30079i 0.184326 + 0.319261i
$$677$$ −12.2841 16.5004i −0.472116 0.634162i 0.500733 0.865602i $$-0.333064\pi$$
−0.972849 + 0.231439i $$0.925656\pi$$
$$678$$ 0 0
$$679$$ −0.926871 + 3.09596i −0.0355700 + 0.118812i
$$680$$ −8.90065 4.47007i −0.341324 0.171420i
$$681$$ 0 0
$$682$$ 7.04823 + 23.5427i 0.269891 + 0.901498i
$$683$$ 2.39856 13.6029i 0.0917785 0.520502i −0.903908 0.427726i $$-0.859315\pi$$
0.995687 0.0927760i $$-0.0295741\pi$$
$$684$$ 0 0
$$685$$ 0.486659 + 2.75998i 0.0185943 + 0.105453i
$$686$$ 7.99089 4.01317i 0.305093 0.153224i
$$687$$ 0 0
$$688$$ −0.905319 2.09877i −0.0345150 0.0800147i
$$689$$ −12.5390 29.0687i −0.477699 1.10743i
$$690$$ 0 0
$$691$$ −5.67005 + 2.84760i −0.215699 + 0.108328i −0.553368 0.832937i $$-0.686658\pi$$
0.337669 + 0.941265i $$0.390361\pi$$
$$692$$ 2.35086 + 13.3324i 0.0893662 + 0.506821i
$$693$$ 0 0
$$694$$ −3.20666 + 18.1859i −0.121723 + 0.690326i
$$695$$ −4.59955 15.3636i −0.174471 0.582774i
$$696$$ 0 0
$$697$$ 5.30018 + 2.66185i 0.200759 + 0.100825i
$$698$$ −6.03163 + 20.1471i −0.228301 + 0.762577i
$$699$$ 0 0
$$700$$ 4.80054 + 6.44824i 0.181443 + 0.243720i
$$701$$ 11.8662 + 20.5529i 0.448180 + 0.776271i 0.998268 0.0588360i $$-0.0187389\pi$$
−0.550087 + 0.835107i $$0.685406\pi$$
$$702$$ 0 0
$$703$$ −1.46832 + 2.54320i −0.0553786 + 0.0959186i
$$704$$ 15.1142 1.76659i 0.569637 0.0665810i
$$705$$ 0 0
$$706$$ 19.2878 4.57130i 0.725908 0.172043i
$$707$$ −6.63247 + 4.36225i −0.249440 + 0.164059i
$$708$$ 0 0
$$709$$ 0.00970556 0.0102873i 0.000364500 0.000386348i −0.727191 0.686435i $$-0.759175\pi$$
0.727556 + 0.686048i $$0.240656\pi$$
$$710$$ −26.0944 21.8958i −0.979307 0.821736i
$$711$$ 0 0
$$712$$ 16.5123 13.8555i 0.618824 0.519255i
$$713$$ −2.26555 + 38.8979i −0.0848454 + 1.45674i
$$714$$ 0 0
$$715$$ 28.2113 37.8943i 1.05504 1.41717i
$$716$$ 3.15747 + 0.369055i 0.118000 + 0.0137922i
$$717$$ 0 0
$$718$$ 25.3448 + 16.6695i 0.945859 + 0.622101i
$$719$$ 23.2140 + 8.44919i 0.865735 + 0.315102i 0.736439 0.676504i $$-0.236506\pi$$
0.129296 + 0.991606i $$0.458728\pi$$
$$720$$ 0 0
$$721$$ 3.30651 1.20347i 0.123141 0.0448197i
$$722$$ −14.9926 3.55331i −0.557967 0.132241i
$$723$$ 0 0
$$724$$ −1.02481 17.5953i −0.0380867 0.653924i
$$725$$ −33.5247 35.5341i −1.24508 1.31970i
$$726$$ 0 0
$$727$$ −16.2048 + 37.5669i −0.601003 + 1.39328i 0.297674 + 0.954668i $$0.403789\pi$$
−0.898676 + 0.438613i $$0.855470\pi$$
$$728$$ 9.67821 0.358698
$$729$$ 0 0
$$730$$ 55.8329 2.06647
$$731$$ −2.61003 + 6.05074i −0.0965355 + 0.223795i
$$732$$ 0 0
$$733$$ −10.2665 10.8819i −0.379203 0.401932i 0.509458 0.860495i $$-0.329846\pi$$
−0.888662 + 0.458563i $$0.848364\pi$$
$$734$$ 1.10031 + 18.8916i 0.0406133 + 0.697303i
$$735$$ 0 0
$$736$$ 20.8706 + 4.94642i 0.769301 + 0.182328i
$$737$$ 37.7648 13.7452i 1.39108 0.506313i
$$738$$ 0 0
$$739$$ −12.3654 4.50063i −0.454868 0.165558i 0.104418 0.994534i $$-0.466702\pi$$
−0.559285 + 0.828975i $$0.688924\pi$$
$$740$$ 7.43918 + 4.89283i 0.273470 + 0.179864i
$$741$$ 0 0
$$742$$ −4.52958 0.529431i −0.166286 0.0194360i
$$743$$ −16.7221 + 22.4616i −0.613473 + 0.824037i −0.994953 0.100340i $$-0.968007\pi$$
0.381481 + 0.924377i $$0.375414\pi$$
$$744$$ 0 0
$$745$$ 2.58445 44.3733i 0.0946870 1.62571i
$$746$$ −2.82002 + 2.36628i −0.103248 + 0.0866355i
$$747$$ 0 0
$$748$$ −2.17239 1.82285i −0.0794305 0.0666501i
$$749$$ −1.36266 + 1.44433i −0.0497904 + 0.0527747i
$$750$$ 0 0
$$751$$ 6.38696 4.20077i 0.233063 0.153288i −0.427606 0.903965i $$-0.640643\pi$$
0.660669 + 0.750677i $$0.270273\pi$$
$$752$$ 1.36497 0.323504i 0.0497754 0.0117970i
$$753$$ 0 0
$$754$$ −21.5001 + 2.51300i −0.782988 + 0.0915182i
$$755$$ −9.12764 + 15.8095i −0.332189 + 0.575368i
$$756$$ 0 0
$$757$$ −16.9101 29.2892i −0.614608 1.06453i −0.990453 0.137850i $$-0.955981\pi$$
0.375845 0.926683i $$-0.377353\pi$$
$$758$$ −18.8401 25.3066i −0.684302 0.919177i
$$759$$ 0 0
$$760$$ 4.62166 15.4374i 0.167645 0.559974i
$$761$$ −33.1292 16.6381i −1.20093 0.603131i −0.268083 0.963396i $$-0.586390\pi$$
−0.932850 + 0.360265i $$0.882686\pi$$
$$762$$ 0 0
$$763$$ −0.708337 2.36601i −0.0256435 0.0856553i
$$764$$ 0.500564 2.83884i 0.0181098 0.102706i
$$765$$ 0 0
$$766$$ 2.26306 + 12.8344i 0.0817675 + 0.463727i
$$767$$ −2.91217 + 1.46255i −0.105152 + 0.0528096i
$$768$$ 0 0
$$769$$ 18.4305 + 42.7267i 0.664622 + 1.54077i 0.831942 + 0.554863i $$0.187229\pi$$
−0.167320 + 0.985903i $$0.553511\pi$$
$$770$$ −2.69549 6.24886i −0.0971389 0.225193i
$$771$$ 0 0
$$772$$ 4.12829 2.07331i 0.148580 0.0746199i
$$773$$ −7.40534 41.9978i −0.266352 1.51056i −0.765158 0.643842i $$-0.777339\pi$$
0.498807 0.866713i $$-0.333772\pi$$
$$774$$ 0 0
$$775$$ 16.4812 93.4695i 0.592022 3.35752i
$$776$$ −3.69123 12.3296i −0.132507 0.442605i
$$777$$ 0 0
$$778$$ −16.9689 8.52210i −0.608364 0.305532i
$$779$$ −2.75212 + 9.19270i −0.0986048 + 0.329363i
$$780$$ 0 0
$$781$$ −15.7362 21.1374i −0.563086 0.756356i
$$782$$ 1.61198 + 2.79204i 0.0576445 + 0.0998431i
$$783$$ 0