# Properties

 Label 729.2.e.m.82.1 Level $729$ Weight $2$ Character 729.82 Analytic conductor $5.821$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.e (of order $$9$$, degree $$6$$, 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: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: $$\Q(\zeta_{36})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - x^{6} + 1$$ x^12 - x^6 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 82.1 Root $$-0.642788 + 0.766044i$$ of defining polynomial Character $$\chi$$ $$=$$ 729.82 Dual form 729.2.e.m.649.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.342020 - 1.93969i) q^{2} +(-1.76604 + 0.642788i) q^{4} +(2.83564 + 2.37939i) q^{5} +(2.20574 + 0.802823i) q^{7} +(-0.118782 - 0.205737i) q^{8} +O(q^{10})$$ $$q+(-0.342020 - 1.93969i) q^{2} +(-1.76604 + 0.642788i) q^{4} +(2.83564 + 2.37939i) q^{5} +(2.20574 + 0.802823i) q^{7} +(-0.118782 - 0.205737i) q^{8} +(3.64543 - 6.31407i) q^{10} +(-1.66885 + 1.40033i) q^{11} +(-0.819078 + 4.64522i) q^{13} +(0.802823 - 4.55303i) q^{14} +(-3.23783 + 2.71686i) q^{16} +(1.46756 - 2.54189i) q^{17} +(3.11334 + 5.39246i) q^{19} +(-6.53731 - 2.37939i) q^{20} +(3.28699 + 2.75811i) q^{22} +(-0.487728 + 0.177519i) q^{23} +(1.51114 + 8.57013i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(-0.606511 - 3.43969i) q^{29} +(4.04576 - 1.47254i) q^{31} +(6.01330 + 5.04576i) q^{32} +(-5.43242 - 1.97724i) q^{34} +(4.34445 + 7.52481i) q^{35} +(-1.20574 + 2.08840i) q^{37} +(9.39490 - 7.88326i) q^{38} +(0.152704 - 0.866025i) q^{40} +(0.433877 - 2.46064i) q^{41} +(0.815207 - 0.684040i) q^{43} +(2.04715 - 3.54576i) q^{44} +(0.511144 + 0.885328i) q^{46} +(0.223238 + 0.0812519i) q^{47} +(-1.14156 - 0.957882i) q^{49} +(16.1066 - 5.86231i) q^{50} +(-1.53936 - 8.73016i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(-0.0968323 - 0.549163i) q^{56} +(-6.46451 + 2.35289i) q^{58} +(-10.1977 - 8.55690i) q^{59} +(3.45336 + 1.25692i) q^{61} +(-4.24000 - 7.34389i) q^{62} +(3.50387 - 6.06888i) q^{64} +(-13.3754 + 11.2233i) q^{65} +(2.48293 - 14.0814i) q^{67} +(-0.957882 + 5.43242i) q^{68} +(13.1099 - 11.0005i) q^{70} +(-0.601535 + 1.04189i) q^{71} +(2.34002 + 4.05304i) q^{73} +(4.46324 + 1.62449i) q^{74} +(-8.96451 - 7.52211i) q^{76} +(-4.80526 + 1.74897i) q^{77} +(-2.22281 - 12.6062i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(-1.96291 - 11.1322i) q^{83} +(10.2096 - 3.71599i) q^{85} +(-1.60565 - 1.34730i) q^{86} +(0.486329 + 0.177009i) q^{88} +(-0.349643 - 0.605600i) q^{89} +(-5.53596 + 9.58856i) q^{91} +(0.747243 - 0.627011i) q^{92} +(0.0812519 - 0.460802i) q^{94} +(-4.00243 + 22.6989i) q^{95} +(-5.42855 + 4.55509i) q^{97} +(-1.46756 + 2.54189i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 12 q^{4} + 6 q^{7}+O(q^{10})$$ 12 * q - 12 * q^4 + 6 * q^7 $$12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100})$$ 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{4}{9}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.342020 1.93969i −0.241845 1.37157i −0.827708 0.561160i $$-0.810355\pi$$
0.585863 0.810410i $$-0.300756\pi$$
$$3$$ 0 0
$$4$$ −1.76604 + 0.642788i −0.883022 + 0.321394i
$$5$$ 2.83564 + 2.37939i 1.26814 + 1.06409i 0.994765 + 0.102185i $$0.0325834\pi$$
0.273372 + 0.961908i $$0.411861\pi$$
$$6$$ 0 0
$$7$$ 2.20574 + 0.802823i 0.833690 + 0.303438i 0.723373 0.690458i $$-0.242591\pi$$
0.110318 + 0.993896i $$0.464813\pi$$
$$8$$ −0.118782 0.205737i −0.0419959 0.0727390i
$$9$$ 0 0
$$10$$ 3.64543 6.31407i 1.15279 1.99668i
$$11$$ −1.66885 + 1.40033i −0.503177 + 0.422215i −0.858720 0.512444i $$-0.828740\pi$$
0.355544 + 0.934660i $$0.384296\pi$$
$$12$$ 0 0
$$13$$ −0.819078 + 4.64522i −0.227171 + 1.28835i 0.631319 + 0.775523i $$0.282514\pi$$
−0.858490 + 0.512829i $$0.828597\pi$$
$$14$$ 0.802823 4.55303i 0.214563 1.21685i
$$15$$ 0 0
$$16$$ −3.23783 + 2.71686i −0.809456 + 0.679215i
$$17$$ 1.46756 2.54189i 0.355936 0.616499i −0.631342 0.775505i $$-0.717496\pi$$
0.987278 + 0.159006i $$0.0508289\pi$$
$$18$$ 0 0
$$19$$ 3.11334 + 5.39246i 0.714249 + 1.23712i 0.963248 + 0.268612i $$0.0865651\pi$$
−0.248999 + 0.968504i $$0.580102\pi$$
$$20$$ −6.53731 2.37939i −1.46179 0.532047i
$$21$$ 0 0
$$22$$ 3.28699 + 2.75811i 0.700788 + 0.588031i
$$23$$ −0.487728 + 0.177519i −0.101698 + 0.0370152i −0.392368 0.919808i $$-0.628344\pi$$
0.290670 + 0.956823i $$0.406122\pi$$
$$24$$ 0 0
$$25$$ 1.51114 + 8.57013i 0.302229 + 1.71403i
$$26$$ 9.29044 1.82201
$$27$$ 0 0
$$28$$ −4.41147 −0.833690
$$29$$ −0.606511 3.43969i −0.112626 0.638735i −0.987898 0.155104i $$-0.950429\pi$$
0.875272 0.483631i $$-0.160682\pi$$
$$30$$ 0 0
$$31$$ 4.04576 1.47254i 0.726640 0.264475i 0.0478980 0.998852i $$-0.484748\pi$$
0.678742 + 0.734377i $$0.262526\pi$$
$$32$$ 6.01330 + 5.04576i 1.06301 + 0.891973i
$$33$$ 0 0
$$34$$ −5.43242 1.97724i −0.931652 0.339094i
$$35$$ 4.34445 + 7.52481i 0.734347 + 1.27193i
$$36$$ 0 0
$$37$$ −1.20574 + 2.08840i −0.198222 + 0.343330i −0.947952 0.318413i $$-0.896850\pi$$
0.749730 + 0.661744i $$0.230183\pi$$
$$38$$ 9.39490 7.88326i 1.52405 1.27883i
$$39$$ 0 0
$$40$$ 0.152704 0.866025i 0.0241446 0.136931i
$$41$$ 0.433877 2.46064i 0.0677602 0.384287i −0.932001 0.362454i $$-0.881939\pi$$
0.999762 0.0218325i $$-0.00695005\pi$$
$$42$$ 0 0
$$43$$ 0.815207 0.684040i 0.124318 0.104315i −0.578509 0.815676i $$-0.696365\pi$$
0.702827 + 0.711361i $$0.251921\pi$$
$$44$$ 2.04715 3.54576i 0.308619 0.534543i
$$45$$ 0 0
$$46$$ 0.511144 + 0.885328i 0.0753641 + 0.130534i
$$47$$ 0.223238 + 0.0812519i 0.0325626 + 0.0118518i 0.358250 0.933626i $$-0.383374\pi$$
−0.325688 + 0.945477i $$0.605596\pi$$
$$48$$ 0 0
$$49$$ −1.14156 0.957882i −0.163080 0.136840i
$$50$$ 16.1066 5.86231i 2.27781 0.829056i
$$51$$ 0 0
$$52$$ −1.53936 8.73016i −0.213471 1.21066i
$$53$$ 4.66717 0.641085 0.320543 0.947234i $$-0.396135\pi$$
0.320543 + 0.947234i $$0.396135\pi$$
$$54$$ 0 0
$$55$$ −8.06418 −1.08737
$$56$$ −0.0968323 0.549163i −0.0129398 0.0733850i
$$57$$ 0 0
$$58$$ −6.46451 + 2.35289i −0.848831 + 0.308949i
$$59$$ −10.1977 8.55690i −1.32763 1.11401i −0.984625 0.174680i $$-0.944111\pi$$
−0.343005 0.939334i $$-0.611445\pi$$
$$60$$ 0 0
$$61$$ 3.45336 + 1.25692i 0.442158 + 0.160932i 0.553499 0.832850i $$-0.313292\pi$$
−0.111341 + 0.993782i $$0.535515\pi$$
$$62$$ −4.24000 7.34389i −0.538480 0.932675i
$$63$$ 0 0
$$64$$ 3.50387 6.06888i 0.437984 0.758610i
$$65$$ −13.3754 + 11.2233i −1.65901 + 1.39208i
$$66$$ 0 0
$$67$$ 2.48293 14.0814i 0.303338 1.72031i −0.327890 0.944716i $$-0.606338\pi$$
0.631228 0.775598i $$-0.282551\pi$$
$$68$$ −0.957882 + 5.43242i −0.116160 + 0.658778i
$$69$$ 0 0
$$70$$ 13.1099 11.0005i 1.56694 1.31482i
$$71$$ −0.601535 + 1.04189i −0.0713891 + 0.123649i −0.899510 0.436900i $$-0.856077\pi$$
0.828121 + 0.560549i $$0.189410\pi$$
$$72$$ 0 0
$$73$$ 2.34002 + 4.05304i 0.273879 + 0.474372i 0.969852 0.243696i $$-0.0783599\pi$$
−0.695973 + 0.718068i $$0.745027\pi$$
$$74$$ 4.46324 + 1.62449i 0.518841 + 0.188843i
$$75$$ 0 0
$$76$$ −8.96451 7.52211i −1.02830 0.862846i
$$77$$ −4.80526 + 1.74897i −0.547610 + 0.199314i
$$78$$ 0 0
$$79$$ −2.22281 12.6062i −0.250086 1.41831i −0.808379 0.588663i $$-0.799655\pi$$
0.558293 0.829644i $$-0.311457\pi$$
$$80$$ −15.6458 −1.74925
$$81$$ 0 0
$$82$$ −4.92127 −0.543464
$$83$$ −1.96291 11.1322i −0.215458 1.22192i −0.880111 0.474768i $$-0.842532\pi$$
0.664653 0.747152i $$-0.268579\pi$$
$$84$$ 0 0
$$85$$ 10.2096 3.71599i 1.10739 0.403056i
$$86$$ −1.60565 1.34730i −0.173141 0.145283i
$$87$$ 0 0
$$88$$ 0.486329 + 0.177009i 0.0518429 + 0.0188693i
$$89$$ −0.349643 0.605600i −0.0370621 0.0641935i 0.846899 0.531753i $$-0.178467\pi$$
−0.883961 + 0.467560i $$0.845133\pi$$
$$90$$ 0 0
$$91$$ −5.53596 + 9.58856i −0.580326 + 1.00515i
$$92$$ 0.747243 0.627011i 0.0779055 0.0653705i
$$93$$ 0 0
$$94$$ 0.0812519 0.460802i 0.00838049 0.0475281i
$$95$$ −4.00243 + 22.6989i −0.410641 + 2.32886i
$$96$$ 0 0
$$97$$ −5.42855 + 4.55509i −0.551186 + 0.462500i −0.875342 0.483504i $$-0.839364\pi$$
0.324157 + 0.946003i $$0.394919\pi$$
$$98$$ −1.46756 + 2.54189i −0.148246 + 0.256770i
$$99$$ 0 0
$$100$$ −8.17752 14.1639i −0.817752 1.41639i
$$101$$ −4.39506 1.59967i −0.437325 0.159173i 0.113969 0.993484i $$-0.463643\pi$$
−0.551294 + 0.834311i $$0.685866\pi$$
$$102$$ 0 0
$$103$$ −10.4363 8.75709i −1.02832 0.862861i −0.0376683 0.999290i $$-0.511993\pi$$
−0.990650 + 0.136429i $$0.956437\pi$$
$$104$$ 1.05299 0.383256i 0.103254 0.0375813i
$$105$$ 0 0
$$106$$ −1.59627 9.05288i −0.155043 0.879293i
$$107$$ 11.6340 1.12470 0.562350 0.826900i $$-0.309898\pi$$
0.562350 + 0.826900i $$0.309898\pi$$
$$108$$ 0 0
$$109$$ 14.6040 1.39881 0.699405 0.714725i $$-0.253448\pi$$
0.699405 + 0.714725i $$0.253448\pi$$
$$110$$ 2.75811 + 15.6420i 0.262976 + 1.49141i
$$111$$ 0 0
$$112$$ −9.32295 + 3.39328i −0.880936 + 0.320634i
$$113$$ 3.59721 + 3.01842i 0.338397 + 0.283949i 0.796111 0.605151i $$-0.206887\pi$$
−0.457714 + 0.889100i $$0.651332\pi$$
$$114$$ 0 0
$$115$$ −1.80541 0.657115i −0.168355 0.0612762i
$$116$$ 3.28212 + 5.68479i 0.304737 + 0.527820i
$$117$$ 0 0
$$118$$ −13.1099 + 22.7071i −1.20687 + 2.09036i
$$119$$ 5.27774 4.42855i 0.483809 0.405964i
$$120$$ 0 0
$$121$$ −1.08600 + 6.15901i −0.0987272 + 0.559910i
$$122$$ 1.25692 7.12836i 0.113796 0.645371i
$$123$$ 0 0
$$124$$ −6.19846 + 5.20113i −0.556638 + 0.467075i
$$125$$ −6.85240 + 11.8687i −0.612897 + 1.06157i
$$126$$ 0 0
$$127$$ −3.04576 5.27541i −0.270267 0.468117i 0.698663 0.715451i $$-0.253779\pi$$
−0.968930 + 0.247334i $$0.920445\pi$$
$$128$$ 1.78265 + 0.648833i 0.157566 + 0.0573493i
$$129$$ 0 0
$$130$$ 26.3444 + 22.1055i 2.31055 + 1.93878i
$$131$$ −9.72432 + 3.53936i −0.849618 + 0.309236i −0.729884 0.683571i $$-0.760426\pi$$
−0.119733 + 0.992806i $$0.538204\pi$$
$$132$$ 0 0
$$133$$ 2.53802 + 14.3938i 0.220074 + 1.24810i
$$134$$ −28.1627 −2.43289
$$135$$ 0 0
$$136$$ −0.697281 −0.0597914
$$137$$ 3.31402 + 18.7947i 0.283136 + 1.60574i 0.711870 + 0.702311i $$0.247849\pi$$
−0.428734 + 0.903431i $$0.641040\pi$$
$$138$$ 0 0
$$139$$ 21.8983 7.97032i 1.85739 0.676034i 0.876517 0.481371i $$-0.159861\pi$$
0.980870 0.194662i $$-0.0623610\pi$$
$$140$$ −12.5094 10.4966i −1.05723 0.887124i
$$141$$ 0 0
$$142$$ 2.22668 + 0.810446i 0.186859 + 0.0680111i
$$143$$ −5.13793 8.89915i −0.429655 0.744184i
$$144$$ 0 0
$$145$$ 6.46451 11.1969i 0.536848 0.929848i
$$146$$ 7.06131 5.92514i 0.584398 0.490368i
$$147$$ 0 0
$$148$$ 0.786989 4.46324i 0.0646901 0.366876i
$$149$$ 2.69258 15.2704i 0.220585 1.25100i −0.650363 0.759623i $$-0.725383\pi$$
0.870948 0.491375i $$-0.163506\pi$$
$$150$$ 0 0
$$151$$ −4.52094 + 3.79352i −0.367909 + 0.308713i −0.807934 0.589273i $$-0.799414\pi$$
0.440025 + 0.897986i $$0.354970\pi$$
$$152$$ 0.739620 1.28106i 0.0599911 0.103908i
$$153$$ 0 0
$$154$$ 5.03596 + 8.72254i 0.405809 + 0.702882i
$$155$$ 14.9761 + 5.45084i 1.20291 + 0.437822i
$$156$$ 0 0
$$157$$ −0.928548 0.779145i −0.0741062 0.0621825i 0.604982 0.796239i $$-0.293180\pi$$
−0.679088 + 0.734057i $$0.737625\pi$$
$$158$$ −23.6919 + 8.62314i −1.88483 + 0.686020i
$$159$$ 0 0
$$160$$ 5.04576 + 28.6159i 0.398902 + 2.26229i
$$161$$ −1.21832 −0.0960168
$$162$$ 0 0
$$163$$ 2.77332 0.217223 0.108612 0.994084i $$-0.465360\pi$$
0.108612 + 0.994084i $$0.465360\pi$$
$$164$$ 0.815422 + 4.62449i 0.0636737 + 0.361112i
$$165$$ 0 0
$$166$$ −20.9217 + 7.61489i −1.62384 + 0.591030i
$$167$$ −2.93247 2.46064i −0.226922 0.190410i 0.522237 0.852800i $$-0.325098\pi$$
−0.749159 + 0.662390i $$0.769542\pi$$
$$168$$ 0 0
$$169$$ −8.69119 3.16333i −0.668553 0.243333i
$$170$$ −10.6998 18.5326i −0.820635 1.42138i
$$171$$ 0 0
$$172$$ −1.00000 + 1.73205i −0.0762493 + 0.132068i
$$173$$ −5.38484 + 4.51842i −0.409402 + 0.343529i −0.824114 0.566424i $$-0.808327\pi$$
0.414712 + 0.909953i $$0.363882\pi$$
$$174$$ 0 0
$$175$$ −3.54710 + 20.1166i −0.268136 + 1.52067i
$$176$$ 1.59894 9.06805i 0.120525 0.683530i
$$177$$ 0 0
$$178$$ −1.05509 + 0.885328i −0.0790825 + 0.0663581i
$$179$$ 7.19269 12.4581i 0.537607 0.931163i −0.461425 0.887179i $$-0.652662\pi$$
0.999032 0.0439838i $$-0.0140050\pi$$
$$180$$ 0 0
$$181$$ −6.60014 11.4318i −0.490584 0.849717i 0.509357 0.860555i $$-0.329883\pi$$
−0.999941 + 0.0108384i $$0.996550\pi$$
$$182$$ 20.4923 + 7.45858i 1.51899 + 0.552867i
$$183$$ 0 0
$$184$$ 0.0944557 + 0.0792577i 0.00696336 + 0.00584296i
$$185$$ −8.38814 + 3.05303i −0.616708 + 0.224463i
$$186$$ 0 0
$$187$$ 1.11035 + 6.29710i 0.0811967 + 0.460489i
$$188$$ −0.446476 −0.0325626
$$189$$ 0 0
$$190$$ 45.3979 3.29351
$$191$$ 2.33094 + 13.2194i 0.168661 + 0.956523i 0.945209 + 0.326465i $$0.105858\pi$$
−0.776548 + 0.630058i $$0.783031\pi$$
$$192$$ 0 0
$$193$$ −14.1001 + 5.13203i −1.01495 + 0.369412i −0.795332 0.606174i $$-0.792703\pi$$
−0.219618 + 0.975586i $$0.570481\pi$$
$$194$$ 10.6922 + 8.97178i 0.767652 + 0.644136i
$$195$$ 0 0
$$196$$ 2.63176 + 0.957882i 0.187983 + 0.0684201i
$$197$$ 11.1606 + 19.3307i 0.795158 + 1.37725i 0.922739 + 0.385426i $$0.125946\pi$$
−0.127580 + 0.991828i $$0.540721\pi$$
$$198$$ 0 0
$$199$$ 4.55051 7.88171i 0.322577 0.558720i −0.658442 0.752631i $$-0.728784\pi$$
0.981019 + 0.193912i $$0.0621176\pi$$
$$200$$ 1.58370 1.32888i 0.111984 0.0939659i
$$201$$ 0 0
$$202$$ −1.59967 + 9.07218i −0.112552 + 0.638316i
$$203$$ 1.42366 8.07398i 0.0999214 0.566682i
$$204$$ 0 0
$$205$$ 7.08512 5.94512i 0.494846 0.415225i
$$206$$ −13.4166 + 23.2383i −0.934781 + 1.61909i
$$207$$ 0 0
$$208$$ −9.96838 17.2657i −0.691183 1.19716i
$$209$$ −12.7469 4.63950i −0.881723 0.320921i
$$210$$ 0 0
$$211$$ −4.57919 3.84240i −0.315245 0.264522i 0.471411 0.881914i $$-0.343745\pi$$
−0.786656 + 0.617392i $$0.788189\pi$$
$$212$$ −8.24243 + 3.00000i −0.566093 + 0.206041i
$$213$$ 0 0
$$214$$ −3.97906 22.5663i −0.272003 1.54260i
$$215$$ 3.93923 0.268653
$$216$$ 0 0
$$217$$ 10.1061 0.686045
$$218$$ −4.99486 28.3273i −0.338295 1.91857i
$$219$$ 0 0
$$220$$ 14.2417 5.18355i 0.960175 0.349475i
$$221$$ 10.6056 + 8.89915i 0.713409 + 0.598621i
$$222$$ 0 0
$$223$$ 8.36484 + 3.04455i 0.560151 + 0.203878i 0.606551 0.795045i $$-0.292553\pi$$
−0.0463999 + 0.998923i $$0.514775\pi$$
$$224$$ 9.21291 + 15.9572i 0.615564 + 1.06619i
$$225$$ 0 0
$$226$$ 4.62449 8.00984i 0.307616 0.532807i
$$227$$ −8.17253 + 6.85756i −0.542430 + 0.455152i −0.872368 0.488850i $$-0.837417\pi$$
0.329938 + 0.944003i $$0.392972\pi$$
$$228$$ 0 0
$$229$$ −1.43629 + 8.14560i −0.0949127 + 0.538276i 0.899861 + 0.436176i $$0.143667\pi$$
−0.994774 + 0.102101i $$0.967444\pi$$
$$230$$ −0.657115 + 3.72668i −0.0433288 + 0.245730i
$$231$$ 0 0
$$232$$ −0.635630 + 0.533356i −0.0417311 + 0.0350166i
$$233$$ −6.36965 + 11.0326i −0.417290 + 0.722767i −0.995666 0.0930034i $$-0.970353\pi$$
0.578376 + 0.815770i $$0.303687\pi$$
$$234$$ 0 0
$$235$$ 0.439693 + 0.761570i 0.0286824 + 0.0496793i
$$236$$ 23.5099 + 8.55690i 1.53036 + 0.557007i
$$237$$ 0 0
$$238$$ −10.3951 8.72254i −0.673815 0.565398i
$$239$$ −14.1100 + 5.13563i −0.912702 + 0.332196i −0.755331 0.655343i $$-0.772524\pi$$
−0.157371 + 0.987540i $$0.550302\pi$$
$$240$$ 0 0
$$241$$ 0.138156 + 0.783520i 0.00889939 + 0.0504710i 0.988934 0.148356i $$-0.0473980\pi$$
−0.980035 + 0.198827i $$0.936287\pi$$
$$242$$ 12.3180 0.791832
$$243$$ 0 0
$$244$$ −6.90673 −0.442158
$$245$$ −0.957882 5.43242i −0.0611968 0.347064i
$$246$$ 0 0
$$247$$ −27.5993 + 10.0453i −1.75610 + 0.639168i
$$248$$ −0.783520 0.657451i −0.0497536 0.0417482i
$$249$$ 0 0
$$250$$ 25.3653 + 9.23222i 1.60424 + 0.583897i
$$251$$ −4.15749 7.20099i −0.262419 0.454522i 0.704465 0.709738i $$-0.251187\pi$$
−0.966884 + 0.255216i $$0.917853\pi$$
$$252$$ 0 0
$$253$$ 0.565360 0.979232i 0.0355439 0.0615638i
$$254$$ −9.19096 + 7.71213i −0.576692 + 0.483902i
$$255$$ 0 0
$$256$$ 3.08260 17.4823i 0.192662 1.09264i
$$257$$ −4.44891 + 25.2310i −0.277515 + 1.57387i 0.453341 + 0.891337i $$0.350232\pi$$
−0.730857 + 0.682531i $$0.760879\pi$$
$$258$$ 0 0
$$259$$ −4.33615 + 3.63846i −0.269435 + 0.226083i
$$260$$ 16.4073 28.4183i 1.01754 1.76243i
$$261$$ 0 0
$$262$$ 10.1912 + 17.6517i 0.629614 + 1.09052i
$$263$$ −26.3725 9.59879i −1.62620 0.591887i −0.641648 0.767000i $$-0.721749\pi$$
−0.984548 + 0.175113i $$0.943971\pi$$
$$264$$ 0 0
$$265$$ 13.2344 + 11.1050i 0.812984 + 0.682175i
$$266$$ 27.0515 9.84595i 1.65864 0.603694i
$$267$$ 0 0
$$268$$ 4.66637 + 26.4643i 0.285044 + 1.61657i
$$269$$ −30.1710 −1.83956 −0.919778 0.392439i $$-0.871631\pi$$
−0.919778 + 0.392439i $$0.871631\pi$$
$$270$$ 0 0
$$271$$ −19.0000 −1.15417 −0.577084 0.816685i $$-0.695809\pi$$
−0.577084 + 0.816685i $$0.695809\pi$$
$$272$$ 2.15425 + 12.2173i 0.130620 + 0.740786i
$$273$$ 0 0
$$274$$ 35.3225 12.8564i 2.13391 0.776681i
$$275$$ −14.5229 12.1861i −0.875762 0.734852i
$$276$$ 0 0
$$277$$ −19.8478 7.22400i −1.19254 0.434048i −0.331923 0.943306i $$-0.607697\pi$$
−0.860613 + 0.509259i $$0.829920\pi$$
$$278$$ −22.9496 39.7499i −1.37643 2.38404i
$$279$$ 0 0
$$280$$ 1.03209 1.78763i 0.0616791 0.106831i
$$281$$ −1.33851 + 1.12314i −0.0798487 + 0.0670010i −0.681838 0.731503i $$-0.738819\pi$$
0.601990 + 0.798504i $$0.294375\pi$$
$$282$$ 0 0
$$283$$ −1.26558 + 7.17745i −0.0752308 + 0.426655i 0.923809 + 0.382853i $$0.125058\pi$$
−0.999040 + 0.0438023i $$0.986053\pi$$
$$284$$ 0.392624 2.22668i 0.0232980 0.132129i
$$285$$ 0 0
$$286$$ −15.5043 + 13.0097i −0.916791 + 0.769279i
$$287$$ 2.93247 5.07919i 0.173098 0.299815i
$$288$$ 0 0
$$289$$ 4.19253 + 7.26168i 0.246620 + 0.427158i
$$290$$ −23.9294 8.70961i −1.40519 0.511446i
$$291$$ 0 0
$$292$$ −6.73783 5.65371i −0.394301 0.330858i
$$293$$ 14.4251 5.25031i 0.842725 0.306727i 0.115654 0.993290i $$-0.463104\pi$$
0.727070 + 0.686563i $$0.240881\pi$$
$$294$$ 0 0
$$295$$ −8.55690 48.5286i −0.498202 2.82545i
$$296$$ 0.572881 0.0332980
$$297$$ 0 0
$$298$$ −30.5408 −1.76918
$$299$$ −0.425126 2.41101i −0.0245857 0.139432i
$$300$$ 0 0
$$301$$ 2.34730 0.854346i 0.135296 0.0492437i
$$302$$ 8.90452 + 7.47178i 0.512398 + 0.429953i
$$303$$ 0 0
$$304$$ −24.7310 9.00135i −1.41842 0.516263i
$$305$$ 6.80180 + 11.7811i 0.389470 + 0.674581i
$$306$$ 0 0
$$307$$ −8.38191 + 14.5179i −0.478381 + 0.828580i −0.999693 0.0247861i $$-0.992110\pi$$
0.521312 + 0.853366i $$0.325443\pi$$
$$308$$ 7.36208 6.17752i 0.419493 0.351997i
$$309$$ 0 0
$$310$$ 5.45084 30.9132i 0.309587 1.75575i
$$311$$ 2.78239 15.7797i 0.157775 0.894786i −0.798430 0.602088i $$-0.794336\pi$$
0.956205 0.292698i $$-0.0945531\pi$$
$$312$$ 0 0
$$313$$ 26.3562 22.1155i 1.48974 1.25004i 0.594788 0.803883i $$-0.297236\pi$$
0.894954 0.446159i $$-0.147208\pi$$
$$314$$ −1.19372 + 2.06758i −0.0673654 + 0.116680i
$$315$$ 0 0
$$316$$ 12.0287 + 20.8343i 0.676666 + 1.17202i
$$317$$ −15.3274 5.57873i −0.860874 0.313332i −0.126408 0.991978i $$-0.540345\pi$$
−0.734466 + 0.678646i $$0.762567\pi$$
$$318$$ 0 0
$$319$$ 5.82888 + 4.89101i 0.326355 + 0.273844i
$$320$$ 24.3759 8.87211i 1.36266 0.495966i
$$321$$ 0 0
$$322$$ 0.416689 + 2.36316i 0.0232212 + 0.131694i
$$323$$ 18.2761 1.01691
$$324$$ 0 0
$$325$$ −41.0479 −2.27693
$$326$$ −0.948531 5.37939i −0.0525343 0.297937i
$$327$$ 0 0
$$328$$ −0.557781 + 0.203016i −0.0307983 + 0.0112097i
$$329$$ 0.427173 + 0.358441i 0.0235508 + 0.0197615i
$$330$$ 0 0
$$331$$ 29.6755 + 10.8010i 1.63111 + 0.593676i 0.985453 0.169951i $$-0.0543609\pi$$
0.645658 + 0.763627i $$0.276583\pi$$
$$332$$ 10.6222 + 18.3983i 0.582972 + 1.00974i
$$333$$ 0 0
$$334$$ −3.76991 + 6.52968i −0.206281 + 0.357288i
$$335$$ 40.5457 34.0219i 2.21525 1.85881i
$$336$$ 0 0
$$337$$ 1.04277 5.91382i 0.0568031 0.322146i −0.943144 0.332383i $$-0.892147\pi$$
0.999948 + 0.0102366i $$0.00325846\pi$$
$$338$$ −3.16333 + 17.9402i −0.172063 + 0.975816i
$$339$$ 0 0
$$340$$ −15.6420 + 13.1252i −0.848308 + 0.711815i
$$341$$ −4.68972 + 8.12284i −0.253963 + 0.439876i
$$342$$ 0 0
$$343$$ −9.96451 17.2590i −0.538033 0.931900i
$$344$$ −0.237565 0.0864665i −0.0128086 0.00466196i
$$345$$ 0 0
$$346$$ 10.6061 + 8.89955i 0.570186 + 0.478443i
$$347$$ 21.6415 7.87686i 1.16178 0.422852i 0.312045 0.950067i $$-0.398986\pi$$
0.849732 + 0.527216i $$0.176764\pi$$
$$348$$ 0 0
$$349$$ −2.00846 11.3905i −0.107510 0.609721i −0.990188 0.139742i $$-0.955373\pi$$
0.882678 0.469979i $$-0.155738\pi$$
$$350$$ 40.2332 2.15056
$$351$$ 0 0
$$352$$ −17.1010 −0.911487
$$353$$ 0.370674 + 2.10220i 0.0197290 + 0.111889i 0.993082 0.117423i $$-0.0374635\pi$$
−0.973353 + 0.229312i $$0.926352\pi$$
$$354$$ 0 0
$$355$$ −4.18479 + 1.52314i −0.222106 + 0.0808399i
$$356$$ 1.00676 + 0.844770i 0.0533581 + 0.0447727i
$$357$$ 0 0
$$358$$ −26.6250 9.69069i −1.40717 0.512169i
$$359$$ 12.1118 + 20.9782i 0.639234 + 1.10719i 0.985601 + 0.169087i $$0.0540818\pi$$
−0.346367 + 0.938099i $$0.612585\pi$$
$$360$$ 0 0
$$361$$ −9.88578 + 17.1227i −0.520304 + 0.901193i
$$362$$ −19.9167 + 16.7121i −1.04680 + 0.878370i
$$363$$ 0 0
$$364$$ 3.61334 20.4923i 0.189391 1.07409i
$$365$$ −3.00827 + 17.0608i −0.157460 + 0.893002i
$$366$$ 0 0
$$367$$ −2.17159 + 1.82218i −0.113356 + 0.0951170i −0.697704 0.716386i $$-0.745795\pi$$
0.584348 + 0.811503i $$0.301350\pi$$
$$368$$ 1.09689 1.89986i 0.0571792 0.0990372i
$$369$$ 0 0
$$370$$ 8.79086 + 15.2262i 0.457015 + 0.791573i
$$371$$ 10.2946 + 3.74691i 0.534467 + 0.194530i
$$372$$ 0 0
$$373$$ −22.0876 18.5337i −1.14366 0.959641i −0.144103 0.989563i $$-0.546030\pi$$
−0.999552 + 0.0299222i $$0.990474\pi$$
$$374$$ 11.8347 4.30747i 0.611956 0.222734i
$$375$$ 0 0
$$376$$ −0.00980018 0.0555796i −0.000505406 0.00286630i
$$377$$ 16.4749 0.848501
$$378$$ 0 0
$$379$$ 32.1985 1.65393 0.826963 0.562256i $$-0.190066\pi$$
0.826963 + 0.562256i $$0.190066\pi$$
$$380$$ −7.52211 42.6600i −0.385876 2.18841i
$$381$$ 0 0
$$382$$ 24.8444 9.04261i 1.27115 0.462660i
$$383$$ −0.514973 0.432114i −0.0263139 0.0220800i 0.629536 0.776971i $$-0.283245\pi$$
−0.655850 + 0.754891i $$0.727690\pi$$
$$384$$ 0 0
$$385$$ −17.7875 6.47410i −0.906533 0.329951i
$$386$$ 14.7771 + 25.5947i 0.752134 + 1.30273i
$$387$$ 0 0
$$388$$ 6.65910 11.5339i 0.338065 0.585545i
$$389$$ 3.26281 2.73783i 0.165431 0.138813i −0.556314 0.830972i $$-0.687785\pi$$
0.721745 + 0.692159i $$0.243340\pi$$
$$390$$ 0 0
$$391$$ −0.264538 + 1.50027i −0.0133783 + 0.0758719i
$$392$$ −0.0614747 + 0.348641i −0.00310494 + 0.0176090i
$$393$$ 0 0
$$394$$ 33.6785 28.2596i 1.69670 1.42370i
$$395$$ 23.6919 41.0355i 1.19207 2.06472i
$$396$$ 0 0
$$397$$ 4.43242 + 7.67717i 0.222457 + 0.385306i 0.955553 0.294818i $$-0.0952591\pi$$
−0.733097 + 0.680124i $$0.761926\pi$$
$$398$$ −16.8445 6.13088i −0.844336 0.307313i
$$399$$ 0 0
$$400$$ −28.1766 23.6430i −1.40883 1.18215i
$$401$$ 34.8475 12.6834i 1.74020 0.633381i 0.740930 0.671582i $$-0.234385\pi$$
0.999270 + 0.0382006i $$0.0121626\pi$$
$$402$$ 0 0
$$403$$ 3.52646 + 19.9996i 0.175666 + 0.996250i
$$404$$ 8.79012 0.437325
$$405$$ 0 0
$$406$$ −16.1480 −0.801410
$$407$$ −0.912254 5.17365i −0.0452187 0.256448i
$$408$$ 0 0
$$409$$ 3.18479 1.15917i 0.157478 0.0573173i −0.262078 0.965047i $$-0.584408\pi$$
0.419556 + 0.907729i $$0.362186\pi$$
$$410$$ −13.9550 11.7096i −0.689187 0.578296i
$$411$$ 0 0
$$412$$ 24.0599 + 8.75709i 1.18535 + 0.431431i
$$413$$ −15.6238 27.0612i −0.768798 1.33160i
$$414$$ 0 0
$$415$$ 20.9217 36.2375i 1.02701 1.77883i
$$416$$ −28.3640 + 23.8002i −1.39066 + 1.16690i
$$417$$ 0 0
$$418$$ −4.63950 + 26.3119i −0.226925 + 1.28696i
$$419$$ 3.58694 20.3425i 0.175233 0.993799i −0.762641 0.646823i $$-0.776097\pi$$
0.937874 0.346976i $$-0.112791\pi$$
$$420$$ 0 0
$$421$$ 21.0915 17.6979i 1.02794 0.862542i 0.0373336 0.999303i $$-0.488114\pi$$
0.990604 + 0.136761i $$0.0436691\pi$$
$$422$$ −5.88690 + 10.1964i −0.286570 + 0.496353i
$$423$$ 0 0
$$424$$ −0.554378 0.960210i −0.0269230 0.0466319i
$$425$$ 24.0020 + 8.73601i 1.16427 + 0.423759i
$$426$$ 0 0
$$427$$ 6.60813 + 5.54488i 0.319790 + 0.268335i
$$428$$ −20.5461 + 7.47818i −0.993134 + 0.361471i
$$429$$ 0 0
$$430$$ −1.34730 7.64090i −0.0649724 0.368477i
$$431$$ 2.58110 0.124327 0.0621636 0.998066i $$-0.480200\pi$$
0.0621636 + 0.998066i $$0.480200\pi$$
$$432$$ 0 0
$$433$$ −27.0137 −1.29820 −0.649098 0.760704i $$-0.724854\pi$$
−0.649098 + 0.760704i $$0.724854\pi$$
$$434$$ −3.45648 19.6027i −0.165916 0.940958i
$$435$$ 0 0
$$436$$ −25.7913 + 9.38728i −1.23518 + 0.449569i
$$437$$ −2.47573 2.07738i −0.118430 0.0993746i
$$438$$ 0 0
$$439$$ −11.0039 4.00508i −0.525186 0.191152i 0.0658015 0.997833i $$-0.479040\pi$$
−0.590988 + 0.806681i $$0.701262\pi$$
$$440$$ 0.957882 + 1.65910i 0.0456652 + 0.0790945i
$$441$$ 0 0
$$442$$ 13.6343 23.6153i 0.648517 1.12326i
$$443$$ −1.59397 + 1.33750i −0.0757316 + 0.0635464i −0.679868 0.733335i $$-0.737963\pi$$
0.604136 + 0.796881i $$0.293518\pi$$
$$444$$ 0 0
$$445$$ 0.449493 2.54920i 0.0213080 0.120844i
$$446$$ 3.04455 17.2665i 0.144164 0.817593i
$$447$$ 0 0
$$448$$ 12.6009 10.5734i 0.595334 0.499545i
$$449$$ 5.27541 9.13728i 0.248962 0.431215i −0.714276 0.699864i $$-0.753244\pi$$
0.963238 + 0.268649i $$0.0865772\pi$$
$$450$$ 0 0
$$451$$ 2.72163 + 4.71400i 0.128157 + 0.221974i
$$452$$ −8.29304 3.01842i −0.390072 0.141974i
$$453$$ 0 0
$$454$$ 16.0967 + 13.5068i 0.755457 + 0.633904i
$$455$$ −38.5129 + 14.0175i −1.80551 + 0.657152i
$$456$$ 0 0
$$457$$ −1.37346 7.78925i −0.0642475 0.364366i −0.999934 0.0115320i $$-0.996329\pi$$
0.935686 0.352834i $$-0.114782\pi$$
$$458$$ 16.2912 0.761238
$$459$$ 0 0
$$460$$ 3.61081 0.168355
$$461$$ 6.78839 + 38.4989i 0.316167 + 1.79307i 0.565600 + 0.824679i $$0.308644\pi$$
−0.249434 + 0.968392i $$0.580244\pi$$
$$462$$ 0 0
$$463$$ −22.2640 + 8.10343i −1.03470 + 0.376598i −0.802867 0.596158i $$-0.796693\pi$$
−0.231828 + 0.972757i $$0.574471\pi$$
$$464$$ 11.3089 + 9.48932i 0.525004 + 0.440531i
$$465$$ 0 0
$$466$$ 23.5783 + 8.58180i 1.09224 + 0.397544i
$$467$$ −17.3576 30.0642i −0.803214 1.39121i −0.917490 0.397758i $$-0.869788\pi$$
0.114277 0.993449i $$-0.463545\pi$$
$$468$$ 0 0
$$469$$ 16.7815 29.0665i 0.774899 1.34216i
$$470$$ 1.32683 1.11334i 0.0612020 0.0513546i
$$471$$ 0 0
$$472$$ −0.549163 + 3.11446i −0.0252773 + 0.143355i
$$473$$ −0.402575 + 2.28312i −0.0185104 + 0.104978i
$$474$$ 0 0
$$475$$ −41.5094 + 34.8305i −1.90458 + 1.59813i
$$476$$ −6.47410 + 11.2135i −0.296740 + 0.513969i
$$477$$ 0 0
$$478$$ 14.7875 + 25.6126i 0.676362 + 1.17149i
$$479$$ −6.09083 2.21688i −0.278297 0.101292i 0.199101 0.979979i $$-0.436198\pi$$
−0.477398 + 0.878687i $$0.658420\pi$$
$$480$$ 0 0
$$481$$ −8.71348 7.31148i −0.397300 0.333375i
$$482$$ 1.47254 0.535959i 0.0670722 0.0244123i
$$483$$ 0 0
$$484$$ −2.04101 11.5752i −0.0927733 0.526143i
$$485$$ −26.2317 −1.19112
$$486$$ 0 0
$$487$$ 19.9828 0.905505 0.452753 0.891636i $$-0.350442\pi$$
0.452753 + 0.891636i $$0.350442\pi$$
$$488$$ −0.151603 0.859785i −0.00686276 0.0389206i
$$489$$ 0 0
$$490$$ −10.2096 + 3.71599i −0.461223 + 0.167871i
$$491$$ 20.0911 + 16.8584i 0.906699 + 0.760811i 0.971488 0.237088i $$-0.0761930\pi$$
−0.0647892 + 0.997899i $$0.520637\pi$$
$$492$$ 0 0
$$493$$ −9.63341 3.50627i −0.433867 0.157915i
$$494$$ 28.9243 + 50.0984i 1.30137 + 2.25403i
$$495$$ 0 0
$$496$$ −9.09879 + 15.7596i −0.408548 + 0.707626i
$$497$$ −2.16328 + 1.81521i −0.0970364 + 0.0814232i
$$498$$ 0 0
$$499$$ 1.09698 6.22129i 0.0491077 0.278503i −0.950359 0.311155i $$-0.899284\pi$$
0.999467 + 0.0326518i $$0.0103952\pi$$
$$500$$ 4.47259 25.3653i 0.200020 1.13437i
$$501$$ 0 0
$$502$$ −12.5458 + 10.5271i −0.559945 + 0.469849i
$$503$$ −10.9131 + 18.9020i −0.486589 + 0.842798i −0.999881 0.0154166i $$-0.995093\pi$$
0.513292 + 0.858214i $$0.328426\pi$$
$$504$$ 0 0
$$505$$ −8.65657 14.9936i −0.385212 0.667208i
$$506$$ −2.09277 0.761707i −0.0930351 0.0338620i
$$507$$ 0 0
$$508$$ 8.76991 + 7.35883i 0.389102 + 0.326495i
$$509$$ 27.3386 9.95043i 1.21176 0.441045i 0.344447 0.938806i $$-0.388067\pi$$
0.867314 + 0.497761i $$0.165844\pi$$
$$510$$ 0 0
$$511$$ 1.90760 + 10.8186i 0.0843874 + 0.478585i
$$512$$ −31.1704 −1.37755
$$513$$ 0 0
$$514$$ 50.4620 2.22579
$$515$$ −8.75709 49.6639i −0.385883 2.18845i
$$516$$ 0 0
$$517$$ −0.486329 + 0.177009i −0.0213887 + 0.00778487i
$$518$$ 8.54055 + 7.16637i 0.375250 + 0.314872i
$$519$$ 0 0
$$520$$ 3.89780 + 1.41868i 0.170930 + 0.0622134i
$$521$$ −6.84743 11.8601i −0.299991 0.519600i 0.676142 0.736771i $$-0.263650\pi$$
−0.976134 + 0.217171i $$0.930317\pi$$
$$522$$ 0 0
$$523$$ −6.57532 + 11.3888i −0.287519 + 0.497997i −0.973217 0.229889i $$-0.926164\pi$$
0.685698 + 0.727886i $$0.259497\pi$$
$$524$$ 14.8985 12.5013i 0.650845 0.546124i
$$525$$ 0 0
$$526$$ −9.59879 + 54.4375i −0.418527 + 2.37359i
$$527$$ 2.19437 12.4449i 0.0955884 0.542109i
$$528$$ 0 0
$$529$$ −17.4127 + 14.6110i −0.757072 + 0.635259i
$$530$$ 17.0138 29.4688i 0.739034 1.28004i
$$531$$ 0 0
$$532$$ −13.7344 23.7887i −0.595463 1.03137i
$$533$$ 11.0748 + 4.03091i 0.479704 + 0.174598i
$$534$$ 0 0
$$535$$ 32.9898 + 27.6817i 1.42627 + 1.19679i
$$536$$ −3.19199 + 1.16179i −0.137873 + 0.0501816i
$$537$$ 0 0
$$538$$ 10.3191 + 58.5224i 0.444887 + 2.52308i
$$539$$ 3.24644 0.139834
$$540$$ 0 0
$$541$$ 6.26083 0.269174 0.134587 0.990902i $$-0.457029\pi$$
0.134587 + 0.990902i $$0.457029\pi$$
$$542$$ 6.49838 + 36.8542i 0.279129 + 1.58302i
$$543$$ 0 0
$$544$$ 21.6506 7.88019i 0.928264 0.337860i
$$545$$ 41.4117 + 34.7486i 1.77388 + 1.48846i
$$546$$ 0 0
$$547$$ 29.4859 + 10.7320i 1.26073 + 0.458867i 0.884013 0.467463i $$-0.154832\pi$$
0.376714 + 0.926330i $$0.377054\pi$$
$$548$$ −17.9337 31.0621i −0.766091 1.32691i
$$549$$ 0 0
$$550$$ −18.6702 + 32.3378i −0.796102 + 1.37889i
$$551$$ 16.6601 13.9795i 0.709746 0.595548i
$$552$$ 0 0
$$553$$ 5.21760 29.5905i 0.221875 1.25831i
$$554$$ −7.22400 + 40.9693i −0.306918 + 1.74062i
$$555$$ 0 0
$$556$$ −33.5501 + 28.1519i −1.42284 + 1.19391i
$$557$$ −21.7196 + 37.6195i −0.920290 + 1.59399i −0.121324 + 0.992613i $$0.538714\pi$$
−0.798966 + 0.601376i $$0.794619\pi$$
$$558$$ 0 0
$$559$$ 2.50980 + 4.34710i 0.106153 + 0.183863i
$$560$$ −34.5104 12.5608i −1.45833 0.530790i
$$561$$ 0 0
$$562$$ 2.63634 + 2.21216i 0.111207 + 0.0933142i
$$563$$ −30.0867 + 10.9507i −1.26800 + 0.461516i −0.886447 0.462829i $$-0.846834\pi$$
−0.381557 + 0.924345i $$0.624612\pi$$
$$564$$ 0 0
$$565$$ 3.01842 + 17.1183i 0.126986 + 0.720172i
$$566$$ 14.3549 0.603381
$$567$$ 0 0
$$568$$ 0.285807 0.0119922
$$569$$ 1.17594 + 6.66906i 0.0492978 + 0.279582i 0.999485 0.0320990i $$-0.0102192\pi$$
−0.950187 + 0.311681i $$0.899108\pi$$
$$570$$ 0 0
$$571$$ 19.8773 7.23475i 0.831840 0.302765i 0.109226 0.994017i $$-0.465163\pi$$
0.722614 + 0.691252i $$0.242940\pi$$
$$572$$ 14.7941 + 12.4137i 0.618571 + 0.519043i
$$573$$ 0 0
$$574$$ −10.8550 3.95091i −0.453080 0.164908i
$$575$$ −2.25838 3.91164i −0.0941811 0.163127i
$$576$$ 0 0
$$577$$ −5.95811 + 10.3198i −0.248039 + 0.429617i −0.962982 0.269567i $$-0.913120\pi$$
0.714942 + 0.699183i $$0.246453\pi$$
$$578$$ 12.6515 10.6159i 0.526233 0.441562i
$$579$$ 0 0
$$580$$ −4.21941 + 23.9294i −0.175201 + 0.993616i
$$581$$ 4.60754 26.1306i 0.191153 1.08408i
$$582$$ 0 0
$$583$$ −7.78880 + 6.53558i −0.322579 + 0.270676i
$$584$$ 0.555907 0.962859i 0.0230036 0.0398434i
$$585$$ 0 0
$$586$$ −15.1177 26.1846i −0.624506 1.08168i
$$587$$ −0.122030 0.0444153i −0.00503672 0.00183322i 0.339501 0.940606i $$-0.389742\pi$$
−0.344537 + 0.938773i $$0.611964\pi$$
$$588$$ 0 0
$$589$$ 20.5364 + 17.2321i 0.846189 + 0.710037i
$$590$$ −91.2040 + 33.1955i −3.75481 + 1.36664i
$$591$$ 0 0
$$592$$ −1.76991 10.0377i −0.0727431 0.412546i
$$593$$ −26.2622 −1.07846 −0.539230 0.842158i $$-0.681285\pi$$
−0.539230 + 0.842158i $$0.681285\pi$$
$$594$$ 0 0
$$595$$ 25.5030 1.04552
$$596$$ 5.06040 + 28.6989i 0.207282 + 1.17555i
$$597$$ 0 0
$$598$$ −4.53121 + 1.64923i −0.185295 + 0.0674419i
$$599$$ −21.1391 17.7378i −0.863721 0.724748i 0.0990454 0.995083i $$-0.468421\pi$$
−0.962766 + 0.270335i $$0.912866\pi$$
$$600$$ 0 0
$$601$$ −1.25237 0.455827i −0.0510854 0.0185936i 0.316351 0.948642i $$-0.397542\pi$$
−0.367436 + 0.930049i $$0.619764\pi$$
$$602$$ −2.45999 4.26083i −0.100262 0.173658i
$$603$$ 0 0
$$604$$ 5.54576 9.60554i 0.225654 0.390844i
$$605$$ −17.7342 + 14.8807i −0.720996 + 0.604988i
$$606$$ 0 0
$$607$$ −2.18180 + 12.3736i −0.0885565 + 0.502229i 0.907976 + 0.419023i $$0.137627\pi$$
−0.996532 + 0.0832064i $$0.973484\pi$$
$$608$$ −8.48762 + 48.1357i −0.344218 + 1.95216i
$$609$$ 0 0
$$610$$ 20.5253 17.2228i 0.831044 0.697329i
$$611$$ −0.560282 + 0.970437i −0.0226666 + 0.0392597i
$$612$$ 0 0
$$613$$ 6.99912 + 12.1228i 0.282692 + 0.489637i 0.972047 0.234787i $$-0.0754393\pi$$
−0.689355 + 0.724424i $$0.742106\pi$$
$$614$$ 31.0270 + 11.2929i 1.25215 + 0.455745i
$$615$$ 0 0
$$616$$ 0.930608 + 0.780873i 0.0374953 + 0.0314623i
$$617$$ 22.5965 8.22446i 0.909702 0.331104i 0.155568 0.987825i $$-0.450279\pi$$
0.754134 + 0.656721i $$0.228057\pi$$
$$618$$ 0 0
$$619$$ 1.19325 + 6.76725i 0.0479607 + 0.271999i 0.999352 0.0359850i $$-0.0114569\pi$$
−0.951392 + 0.307984i $$0.900346\pi$$
$$620$$ −29.9521 −1.20291
$$621$$ 0 0
$$622$$ −31.5594 −1.26542
$$623$$ −0.285032 1.61650i −0.0114196 0.0647635i
$$624$$ 0 0
$$625$$ −6.78359 + 2.46902i −0.271343 + 0.0987609i
$$626$$ −51.9116 43.5590i −2.07481 1.74097i
$$627$$ 0 0
$$628$$ 2.14068 + 0.779145i 0.0854225 + 0.0310913i
$$629$$ 3.53898 + 6.12970i 0.141109 + 0.244407i
$$630$$ 0 0
$$631$$ 17.6887 30.6377i 0.704175 1.21967i −0.262814 0.964847i $$-0.584651\pi$$
0.966989 0.254820i $$-0.0820161\pi$$
$$632$$ −2.32953 + 1.95471i −0.0926637 + 0.0777541i
$$633$$ 0 0
$$634$$ −5.57873 + 31.6385i −0.221560 + 1.25653i
$$635$$ 3.91555 22.2062i 0.155384 0.881226i
$$636$$ 0 0
$$637$$ 5.38460 4.51822i 0.213346 0.179018i
$$638$$ 7.49346 12.9791i 0.296669 0.513846i
$$639$$ 0 0
$$640$$ 3.51114 + 6.08148i 0.138790 + 0.240392i
$$641$$ −18.0174 6.55778i −0.711643 0.259017i −0.0392691 0.999229i $$-0.512503\pi$$
−0.672374 + 0.740212i $$0.734725\pi$$
$$642$$ 0 0
$$643$$ 14.8432 + 12.4549i 0.585358 + 0.491173i 0.886702 0.462342i $$-0.152991\pi$$
−0.301344 + 0.953516i $$0.597435\pi$$
$$644$$ 2.15160 0.783119i 0.0847849 0.0308592i
$$645$$ 0 0
$$646$$ −6.25078 35.4499i −0.245934 1.39476i
$$647$$ −8.77141 −0.344840 −0.172420 0.985024i $$-0.555159\pi$$
−0.172420 + 0.985024i $$0.555159\pi$$
$$648$$ 0 0
$$649$$ 29.0009 1.13839
$$650$$ 14.0392 + 79.6203i 0.550663 + 3.12296i
$$651$$ 0 0
$$652$$ −4.89780 + 1.78265i −0.191813 + 0.0698141i
$$653$$ −25.1334 21.0895i −0.983547 0.825294i 0.00107333 0.999999i $$-0.499658\pi$$
−0.984621 + 0.174705i $$0.944103\pi$$
$$654$$ 0 0
$$655$$ −35.9962 13.1015i −1.40649 0.511920i
$$656$$ 5.28039 + 9.14590i 0.206164 + 0.357087i
$$657$$ 0 0
$$658$$ 0.549163 0.951178i 0.0214086 0.0370808i
$$659$$ −14.2880 + 11.9890i −0.556580 + 0.467026i −0.877162 0.480195i $$-0.840566\pi$$
0.320582 + 0.947221i $$0.396121\pi$$
$$660$$ 0 0
$$661$$ 6.32207 35.8542i 0.245900 1.39457i −0.572493 0.819910i $$-0.694024\pi$$
0.818393 0.574659i $$-0.194865\pi$$
$$662$$ 10.8010 61.2554i 0.419792 2.38076i
$$663$$ 0 0
$$664$$ −2.05715 + 1.72616i −0.0798330 + 0.0669878i
$$665$$ −27.0515 + 46.8546i −1.04901 + 1.81694i
$$666$$ 0 0
$$667$$ 0.906422 + 1.56997i 0.0350968 + 0.0607894i
$$668$$ 6.76055 + 2.46064i 0.261573 + 0.0952049i
$$669$$ 0 0
$$670$$ −79.8594 67.0100i −3.08524 2.58882i
$$671$$ −7.52324 + 2.73824i −0.290432 + 0.105708i
$$672$$ 0 0
$$673$$ 6.84002 + 38.7917i 0.263663 + 1.49531i 0.772814 + 0.634632i $$0.218849\pi$$
−0.509151 + 0.860677i $$0.670040\pi$$
$$674$$ −11.8276 −0.455584
$$675$$ 0 0
$$676$$ 17.3824 0.668553
$$677$$ −5.50038 31.1942i −0.211397 1.19889i −0.887051 0.461671i $$-0.847250\pi$$
0.675654 0.737218i $$-0.263861\pi$$
$$678$$ 0 0
$$679$$ −15.6309 + 5.68918i −0.599858 + 0.218331i
$$680$$ −1.97724 1.65910i −0.0758236 0.0636236i
$$681$$ 0 0
$$682$$ 17.3598 + 6.31844i 0.664741 + 0.241946i
$$683$$ −14.5328 25.1716i −0.556083 0.963164i −0.997818 0.0660187i $$-0.978970\pi$$
0.441735 0.897145i $$-0.354363\pi$$
$$684$$ 0 0
$$685$$ −35.3225 + 61.1804i −1.34960 + 2.33758i
$$686$$ −30.0692 + 25.2310i −1.14805 + 0.963325i
$$687$$ 0 0
$$688$$ −0.781059 + 4.42961i −0.0297776 + 0.168877i
$$689$$ −3.82278 + 21.6800i −0.145636 + 0.825944i
$$690$$ 0 0
$$691$$ 4.10401 3.44367i 0.156124 0.131003i −0.561380 0.827558i $$-0.689729\pi$$
0.717503 + 0.696555i $$0.245285\pi$$
$$692$$ 6.60549 11.4410i 0.251103 0.434923i
$$693$$ 0 0
$$694$$ −22.6805 39.2838i −0.860940 1.49119i
$$695$$ 81.0601 + 29.5035i 3.07478 + 1.11913i
$$696$$ 0 0
$$697$$ −5.61793 4.71400i −0.212794 0.178555i
$$698$$ −21.4072 + 7.79157i −0.810274 + 0.294915i
$$699$$ 0 0
$$700$$ −6.66637 37.8069i −0.251965 1.42897i
$$701$$ 25.6536 0.968922 0.484461 0.874813i $$-0.339016\pi$$
0.484461 + 0.874813i $$0.339016\pi$$
$$702$$ 0 0
$$703$$ −15.0155 −0.566320
$$704$$ 2.65101 + 15.0346i 0.0999136 + 0.566638i
$$705$$ 0 0
$$706$$ 3.95084 1.43799i 0.148692 0.0541194i
$$707$$ −8.41009 7.05690i −0.316294 0.265402i
$$708$$ 0 0
$$709$$ 4.40760 + 1.60424i 0.165531 + 0.0602484i 0.423456 0.905916i $$-0.360817\pi$$
−0.257925 + 0.966165i $$0.583039\pi$$
$$710$$ 4.38571 + 7.59627i 0.164593 + 0.285083i
$$711$$ 0 0
$$712$$ −0.0830629 + 0.143869i −0.00311291 + 0.00539173i
$$713$$ −1.71183 + 1.43639i −0.0641085 + 0.0537934i
$$714$$ 0 0
$$715$$ 6.60519 37.4599i 0.247020 1.40092i
$$716$$ −4.69470 + 26.6250i −0.175449 + 0.995021i
$$717$$ 0 0
$$718$$ 36.5488 30.6680i 1.36399 1.14452i
$$719$$ 19.5335 33.8330i 0.728476 1.26176i −0.229052 0.973414i $$-0.573562\pi$$
0.957527 0.288343i $$-0.0931042\pi$$
$$720$$ 0 0
$$721$$ −15.9893 27.6943i −0.595473 1.03139i
$$722$$ 36.5939 + 13.3191i 1.36188 + 0.495685i
$$723$$ 0 0
$$724$$ 19.0043 + 15.9465i 0.706291 + 0.592648i
$$725$$ 28.5621 10.3957i 1.06077 0.386088i
$$726$$ 0 0
$$727$$ −1.87980 10.6609i −0.0697178 0.395389i −0.999620 0.0275812i $$-0.991220\pi$$
0.929902 0.367808i $$-0.119892\pi$$
$$728$$ 2.63030 0.0974853
$$729$$ 0 0
$$730$$ 34.1215 1.26290
$$731$$ −0.542388 3.07604i −0.0200610 0.113771i
$$732$$ 0 0
$$733$$ 3.20661 1.16711i 0.118439 0.0431083i −0.282121 0.959379i $$-0.591038\pi$$
0.400560 + 0.916271i $$0.368816\pi$$
$$734$$ 4.27719 + 3.58899i 0.157874 + 0.132472i
$$735$$ 0 0
$$736$$ −3.82857 1.39349i −0.141123 0.0513646i
$$737$$ 15.5749 + 26.9766i 0.573710 + 0.993695i
$$738$$ 0 0
$$739$$ −13.1505 + 22.7773i −0.483748 + 0.837877i −0.999826 0.0186653i $$-0.994058\pi$$
0.516077 + 0.856542i $$0.327392\pi$$
$$740$$ 12.8514 10.7836i 0.472426 0.396412i
$$741$$ 0 0
$$742$$ 3.74691 21.2498i 0.137553 0.780104i
$$743$$ −5.02606 + 28.5042i −0.184388 + 1.04572i 0.742351 + 0.670011i $$0.233711\pi$$
−0.926739 + 0.375706i $$0.877400\pi$$
$$744$$ 0 0
$$745$$ 43.9693 36.8946i 1.61091 1.35171i
$$746$$ −28.3953 + 49.1822i −1.03963 + 1.80069i
$$747$$ 0 0
$$748$$ −6.00862 10.4072i −0.219697 0.380526i
$$749$$ 25.6615 + 9.34002i 0.937651 + 0.341277i
$$750$$ 0 0
$$751$$ −14.8983 12.5011i −0.543646 0.456173i 0.329137 0.944282i $$-0.393242\pi$$
−0.872782 + 0.488109i $$0.837687\pi$$
$$752$$ −0.943555 + 0.343426i −0.0344079 + 0.0125235i
$$753$$ 0 0
$$754$$ −5.63475 31.9563i −0.205206 1.16378i
$$755$$ −21.8460 −0.795058
$$756$$ 0 0
$$757$$ 6.59627 0.239745 0.119873 0.992789i $$-0.461751\pi$$
0.119873 + 0.992789i $$0.461751\pi$$
$$758$$ −11.0125 62.4552i −0.399994 2.26848i
$$759$$ 0 0
$$760$$ 5.14543 1.87278i 0.186644 0.0679330i
$$761$$ −7.91301 6.63980i −0.286846 0.240693i 0.487998 0.872845i $$-0.337727\pi$$
−0.774844 + 0.632152i $$0.782172\pi$$
$$762$$ 0 0
$$763$$ 32.2126 + 11.7244i 1.16617 + 0.424453i
$$764$$ −12.6138 21.8478i −0.456352 0.790424i
$$765$$ 0 0
$$766$$ −0.662037 + 1.14668i −0.0239204 + 0.0414313i
$$767$$ 48.1014 40.3619i 1.73684 1.45738i
$$768$$ 0 0
$$769$$ 7.78968 44.1775i 0.280903 1.59308i −0.438660 0.898653i $$-0.644547\pi$$
0.719563 0.694427i $$-0.244342\pi$$
$$770$$ −6.47410 + 36.7165i −0.233311 + 1.32317i
$$771$$ 0 0
$$772$$ 21.6027 18.1268i 0.777497 0.652397i
$$773$$ 21.4677 37.1832i 0.772141 1.33739i −0.164247 0.986419i $$-0.552519\pi$$
0.936388 0.350968i $$-0.114147\pi$$
$$774$$ 0 0
$$775$$ 18.7335 + 32.4475i 0.672929 + 1.16555i
$$776$$ 1.58197 + 0.575789i 0.0567893 + 0.0206696i
$$777$$ 0 0
$$778$$ −6.42649 5.39246i −0.230401 0.193329i
$$779$$ 14.6197 5.32114i 0.523805 0.190650i
$$780$$ 0 0