# Properties

 Label 729.2.i.a.685.3 Level $729$ Weight $2$ Character 729.685 Analytic conductor $5.821$ Analytic rank $0$ Dimension $1404$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.i (of order $$81$$, degree $$54$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.82109430735$$ Analytic rank: $$0$$ Dimension: $$1404$$ Relative dimension: $$26$$ over $$\Q(\zeta_{81})$$ Twist minimal: no (minimal twist has level 243) Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

## Embedding invariants

 Embedding label 685.3 Character $$\chi$$ $$=$$ 729.685 Dual form 729.2.i.a.613.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +O(q^{10})$$ $$q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +(-6.28508 - 1.48959i) q^{10} +(-0.475940 - 3.48450i) q^{11} +(3.06939 - 4.47529i) q^{13} +(-4.36224 - 1.98288i) q^{14} +(0.657389 + 1.24802i) q^{16} +(-6.06937 + 3.04815i) q^{17} +(-0.238916 - 4.10203i) q^{19} +(8.49249 + 4.68596i) q^{20} +(-1.11941 + 8.19555i) q^{22} +(3.06012 - 7.92590i) q^{23} +(2.53425 - 0.196978i) q^{25} +(-9.77754 + 8.20433i) q^{26} +(5.51215 + 4.62524i) q^{28} +(3.45486 + 2.46939i) q^{29} +(-3.03787 + 3.48101i) q^{31} +(0.823198 + 3.80030i) q^{32} +(15.6749 - 3.07845i) q^{34} +(5.55714 + 0.649536i) q^{35} +(-1.71554 - 2.30438i) q^{37} +(-2.04598 + 9.44528i) q^{38} +(-7.06426 - 6.92858i) q^{40} +(-0.270732 + 1.05105i) q^{41} +(2.62829 + 2.38505i) q^{43} +(4.91979 - 11.4054i) q^{44} +(-11.9330 + 16.0288i) q^{46} +(1.07362 + 1.23024i) q^{47} +(-2.71330 - 0.869985i) q^{49} +(-5.86647 - 1.15214i) q^{50} +(17.4487 - 7.93139i) q^{52} +(-0.605884 + 3.43614i) q^{53} +(-1.67712 - 9.51143i) q^{55} +(-4.15187 - 6.05357i) q^{56} +(-6.27065 - 7.77439i) q^{58} +(5.85044 - 2.39017i) q^{59} +(-1.49488 + 0.902167i) q^{61} +(9.07897 - 5.97134i) q^{62} +(0.695806 - 11.9465i) q^{64} +(7.94643 - 12.6079i) q^{65} +(-3.44909 + 2.46526i) q^{67} +(-23.9159 - 1.85889i) q^{68} +(-12.1819 - 4.97687i) q^{70} +(-3.29550 - 11.0077i) q^{71} +(4.93945 - 1.17067i) q^{73} +(2.43370 + 6.30344i) q^{74} +(6.76348 - 12.8402i) q^{76} +(0.138937 - 7.16358i) q^{77} +(2.80526 - 2.75138i) q^{79} +(1.93690 + 3.35480i) q^{80} +(1.27638 - 2.21075i) q^{82} +(3.48933 + 13.5464i) q^{83} +(-16.3309 + 9.01101i) q^{85} +(-4.45097 - 7.06194i) q^{86} +(-7.95527 + 9.86299i) q^{88} +(1.52261 - 5.08586i) q^{89} +(7.58704 - 8.04179i) q^{91} +(23.7178 - 18.3827i) q^{92} +(-1.65671 - 3.46471i) q^{94} +(-1.09244 - 11.2313i) q^{95} +(-8.20755 - 0.318490i) q^{97} +(5.59919 + 3.68265i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10})$$ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 $$1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100})$$ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{7}{81}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.26585 0.630742i −1.60220 0.446002i −0.652146 0.758094i $$-0.726131\pi$$
−0.950052 + 0.312091i $$0.898970\pi$$
$$3$$ 0 0
$$4$$ 3.02391 + 1.82494i 1.51195 + 0.912468i
$$5$$ 2.74419 0.106487i 1.22724 0.0476224i 0.583015 0.812461i $$-0.301873\pi$$
0.644222 + 0.764839i $$0.277181\pi$$
$$6$$ 0 0
$$7$$ 2.01284 + 0.314803i 0.760783 + 0.118984i 0.522998 0.852334i $$-0.324813\pi$$
0.237785 + 0.971318i $$0.423579\pi$$
$$8$$ −2.47257 2.62077i −0.874185 0.926582i
$$9$$ 0 0
$$10$$ −6.28508 1.48959i −1.98752 0.471050i
$$11$$ −0.475940 3.48450i −0.143501 1.05062i −0.911832 0.410563i $$-0.865332\pi$$
0.768331 0.640053i $$-0.221088\pi$$
$$12$$ 0 0
$$13$$ 3.06939 4.47529i 0.851297 1.24122i −0.117427 0.993081i $$-0.537465\pi$$
0.968724 0.248140i $$-0.0798192\pi$$
$$14$$ −4.36224 1.98288i −1.16586 0.529947i
$$15$$ 0 0
$$16$$ 0.657389 + 1.24802i 0.164347 + 0.312006i
$$17$$ −6.06937 + 3.04815i −1.47204 + 0.739286i −0.990548 0.137165i $$-0.956201\pi$$
−0.481491 + 0.876451i $$0.659905\pi$$
$$18$$ 0 0
$$19$$ −0.238916 4.10203i −0.0548111 0.941070i −0.907869 0.419254i $$-0.862292\pi$$
0.853058 0.521816i $$-0.174745\pi$$
$$20$$ 8.49249 + 4.68596i 1.89898 + 1.04781i
$$21$$ 0 0
$$22$$ −1.11941 + 8.19555i −0.238659 + 1.74730i
$$23$$ 3.06012 7.92590i 0.638079 1.65267i −0.113912 0.993491i $$-0.536338\pi$$
0.751990 0.659174i $$-0.229094\pi$$
$$24$$ 0 0
$$25$$ 2.53425 0.196978i 0.506850 0.0393955i
$$26$$ −9.77754 + 8.20433i −1.91753 + 1.60900i
$$27$$ 0 0
$$28$$ 5.51215 + 4.62524i 1.04170 + 0.874089i
$$29$$ 3.45486 + 2.46939i 0.641552 + 0.458554i 0.855159 0.518366i $$-0.173459\pi$$
−0.213607 + 0.976920i $$0.568521\pi$$
$$30$$ 0 0
$$31$$ −3.03787 + 3.48101i −0.545617 + 0.625208i −0.958334 0.285652i $$-0.907790\pi$$
0.412716 + 0.910860i $$0.364580\pi$$
$$32$$ 0.823198 + 3.80030i 0.145522 + 0.671805i
$$33$$ 0 0
$$34$$ 15.6749 3.07845i 2.68822 0.527949i
$$35$$ 5.55714 + 0.649536i 0.939328 + 0.109792i
$$36$$ 0 0
$$37$$ −1.71554 2.30438i −0.282034 0.378837i 0.638420 0.769688i $$-0.279588\pi$$
−0.920454 + 0.390851i $$0.872181\pi$$
$$38$$ −2.04598 + 9.44528i −0.331901 + 1.53223i
$$39$$ 0 0
$$40$$ −7.06426 6.92858i −1.11696 1.09550i
$$41$$ −0.270732 + 1.05105i −0.0422813 + 0.164146i −0.986046 0.166471i $$-0.946763\pi$$
0.943765 + 0.330617i $$0.107257\pi$$
$$42$$ 0 0
$$43$$ 2.62829 + 2.38505i 0.400811 + 0.363717i 0.847338 0.531053i $$-0.178204\pi$$
−0.446527 + 0.894770i $$0.647339\pi$$
$$44$$ 4.91979 11.4054i 0.741686 1.71942i
$$45$$ 0 0
$$46$$ −11.9330 + 16.0288i −1.75942 + 2.36331i
$$47$$ 1.07362 + 1.23024i 0.156604 + 0.179448i 0.826376 0.563118i $$-0.190398\pi$$
−0.669772 + 0.742567i $$0.733608\pi$$
$$48$$ 0 0
$$49$$ −2.71330 0.869985i −0.387614 0.124284i
$$50$$ −5.86647 1.15214i −0.829645 0.162937i
$$51$$ 0 0
$$52$$ 17.4487 7.93139i 2.41970 1.09989i
$$53$$ −0.605884 + 3.43614i −0.0832246 + 0.471990i 0.914501 + 0.404584i $$0.132584\pi$$
−0.997726 + 0.0674066i $$0.978528\pi$$
$$54$$ 0 0
$$55$$ −1.67712 9.51143i −0.226143 1.28252i
$$56$$ −4.15187 6.05357i −0.554816 0.808942i
$$57$$ 0 0
$$58$$ −6.27065 7.77439i −0.823377 1.02083i
$$59$$ 5.85044 2.39017i 0.761662 0.311173i 0.0361170 0.999348i $$-0.488501\pi$$
0.725545 + 0.688174i $$0.241588\pi$$
$$60$$ 0 0
$$61$$ −1.49488 + 0.902167i −0.191400 + 0.115511i −0.609161 0.793046i $$-0.708494\pi$$
0.417761 + 0.908557i $$0.362815\pi$$
$$62$$ 9.07897 5.97134i 1.15303 0.758360i
$$63$$ 0 0
$$64$$ 0.695806 11.9465i 0.0869757 1.49332i
$$65$$ 7.94643 12.6079i 0.985633 1.56381i
$$66$$ 0 0
$$67$$ −3.44909 + 2.46526i −0.421374 + 0.301180i −0.772341 0.635208i $$-0.780914\pi$$
0.350968 + 0.936388i $$0.385853\pi$$
$$68$$ −23.9159 1.85889i −2.90023 0.225424i
$$69$$ 0 0
$$70$$ −12.1819 4.97687i −1.45602 0.594850i
$$71$$ −3.29550 11.0077i −0.391103 1.30638i −0.896329 0.443389i $$-0.853776\pi$$
0.505226 0.862987i $$-0.331409\pi$$
$$72$$ 0 0
$$73$$ 4.93945 1.17067i 0.578119 0.137017i 0.0688543 0.997627i $$-0.478066\pi$$
0.509264 + 0.860610i $$0.329918\pi$$
$$74$$ 2.43370 + 6.30344i 0.282912 + 0.732760i
$$75$$ 0 0
$$76$$ 6.76348 12.8402i 0.775825 1.47287i
$$77$$ 0.138937 7.16358i 0.0158334 0.816365i
$$78$$ 0 0
$$79$$ 2.80526 2.75138i 0.315617 0.309555i −0.525089 0.851048i $$-0.675968\pi$$
0.840705 + 0.541493i $$0.182141\pi$$
$$80$$ 1.93690 + 3.35480i 0.216552 + 0.375078i
$$81$$ 0 0
$$82$$ 1.27638 2.21075i 0.140952 0.244137i
$$83$$ 3.48933 + 13.5464i 0.383004 + 1.48691i 0.812027 + 0.583620i $$0.198364\pi$$
−0.429023 + 0.903294i $$0.641142\pi$$
$$84$$ 0 0
$$85$$ −16.3309 + 9.01101i −1.77133 + 0.977381i
$$86$$ −4.45097 7.06194i −0.479960 0.761508i
$$87$$ 0 0
$$88$$ −7.95527 + 9.86299i −0.848035 + 1.05140i
$$89$$ 1.52261 5.08586i 0.161396 0.539100i −0.838588 0.544766i $$-0.816618\pi$$
0.999984 + 0.00566589i $$0.00180352\pi$$
$$90$$ 0 0
$$91$$ 7.58704 8.04179i 0.795338 0.843009i
$$92$$ 23.7178 18.3827i 2.47275 1.91653i
$$93$$ 0 0
$$94$$ −1.65671 3.46471i −0.170876 0.357358i
$$95$$ −1.09244 11.2313i −0.112082 1.15231i
$$96$$ 0 0
$$97$$ −8.20755 0.318490i −0.833351 0.0323378i −0.381432 0.924397i $$-0.624569\pi$$
−0.451919 + 0.892059i $$0.649260\pi$$
$$98$$ 5.59919 + 3.68265i 0.565604 + 0.372004i
$$99$$ 0 0
$$100$$ 8.02281 + 4.02921i 0.802281 + 0.402921i
$$101$$ −0.303406 15.6435i −0.0301900 1.55659i −0.642695 0.766122i $$-0.722184\pi$$
0.612505 0.790467i $$-0.290162\pi$$
$$102$$ 0 0
$$103$$ 6.82645 + 5.29090i 0.672630 + 0.521327i 0.890692 0.454607i $$-0.150220\pi$$
−0.218062 + 0.975935i $$0.569974\pi$$
$$104$$ −19.3180 + 3.02128i −1.89428 + 0.296261i
$$105$$ 0 0
$$106$$ 3.54016 7.40362i 0.343851 0.719103i
$$107$$ 9.60541 + 3.49608i 0.928590 + 0.337979i 0.761650 0.647988i $$-0.224389\pi$$
0.166939 + 0.985967i $$0.446612\pi$$
$$108$$ 0 0
$$109$$ −11.9146 + 4.33655i −1.14121 + 0.415367i −0.842350 0.538930i $$-0.818829\pi$$
−0.298860 + 0.954297i $$0.596606\pi$$
$$110$$ −2.19916 + 22.6093i −0.209681 + 2.15571i
$$111$$ 0 0
$$112$$ 0.930340 + 2.71902i 0.0879089 + 0.256923i
$$113$$ −0.898174 + 0.815050i −0.0844931 + 0.0766734i −0.713160 0.701001i $$-0.752737\pi$$
0.628667 + 0.777675i $$0.283601\pi$$
$$114$$ 0 0
$$115$$ 7.55353 22.0760i 0.704370 2.05860i
$$116$$ 5.94071 + 13.7721i 0.551581 + 1.27871i
$$117$$ 0 0
$$118$$ −14.7638 + 1.72564i −1.35912 + 0.158858i
$$119$$ −13.1763 + 4.22480i −1.20787 + 0.387287i
$$120$$ 0 0
$$121$$ −1.31814 + 0.366928i −0.119831 + 0.0333571i
$$122$$ 3.95622 1.10129i 0.358179 0.0997060i
$$123$$ 0 0
$$124$$ −15.5389 + 4.98233i −1.39543 + 0.447427i
$$125$$ −6.70493 + 0.783694i −0.599707 + 0.0700957i
$$126$$ 0 0
$$127$$ 4.68643 + 10.8644i 0.415853 + 0.964056i 0.989444 + 0.144914i $$0.0462906\pi$$
−0.573591 + 0.819142i $$0.694450\pi$$
$$128$$ −6.59413 + 19.2721i −0.582844 + 1.70343i
$$129$$ 0 0
$$130$$ −25.9577 + 23.5554i −2.27664 + 2.06594i
$$131$$ 6.73353 + 19.6795i 0.588311 + 1.71940i 0.689262 + 0.724512i $$0.257935\pi$$
−0.100951 + 0.994891i $$0.532189\pi$$
$$132$$ 0 0
$$133$$ 0.810430 8.33195i 0.0702732 0.722472i
$$134$$ 9.37007 3.41043i 0.809451 0.294616i
$$135$$ 0 0
$$136$$ 22.9955 + 8.36966i 1.97184 + 0.717692i
$$137$$ −2.07853 + 4.34688i −0.177581 + 0.371379i −0.971641 0.236460i $$-0.924013\pi$$
0.794060 + 0.607839i $$0.207963\pi$$
$$138$$ 0 0
$$139$$ 18.6595 2.91829i 1.58268 0.247526i 0.698825 0.715293i $$-0.253707\pi$$
0.883852 + 0.467766i $$0.154941\pi$$
$$140$$ 15.6189 + 12.1056i 1.32004 + 1.02311i
$$141$$ 0 0
$$142$$ 0.524061 + 27.0205i 0.0439782 + 2.26751i
$$143$$ −17.0550 8.56533i −1.42621 0.716269i
$$144$$ 0 0
$$145$$ 9.74375 + 6.40856i 0.809174 + 0.532202i
$$146$$ −11.9304 0.462955i −0.987370 0.0383145i
$$147$$ 0 0
$$148$$ −0.982305 10.0990i −0.0807449 0.830131i
$$149$$ −1.88833 3.94910i −0.154698 0.323523i 0.810198 0.586156i $$-0.199360\pi$$
−0.964896 + 0.262634i $$0.915409\pi$$
$$150$$ 0 0
$$151$$ 1.50440 1.16600i 0.122426 0.0948876i −0.549547 0.835463i $$-0.685200\pi$$
0.671974 + 0.740575i $$0.265447\pi$$
$$152$$ −10.1597 + 10.7687i −0.824063 + 0.873456i
$$153$$ 0 0
$$154$$ −4.83318 + 16.1440i −0.389469 + 1.30092i
$$155$$ −7.96579 + 9.87603i −0.639828 + 0.793262i
$$156$$ 0 0
$$157$$ 9.21069 + 14.6138i 0.735093 + 1.16630i 0.980430 + 0.196867i $$0.0630766\pi$$
−0.245337 + 0.969438i $$0.578899\pi$$
$$158$$ −8.09172 + 4.46482i −0.643742 + 0.355202i
$$159$$ 0 0
$$160$$ 2.66369 + 10.3411i 0.210583 + 0.817534i
$$161$$ 8.65463 14.9903i 0.682081 1.18140i
$$162$$ 0 0
$$163$$ 5.52274 + 9.56566i 0.432574 + 0.749240i 0.997094 0.0761790i $$-0.0242720\pi$$
−0.564520 + 0.825419i $$0.690939\pi$$
$$164$$ −2.73676 + 2.68420i −0.213705 + 0.209601i
$$165$$ 0 0
$$166$$ 0.637999 32.8950i 0.0495183 2.55315i
$$167$$ 11.0801 21.0351i 0.857406 1.62775i 0.0816955 0.996657i $$-0.473967\pi$$
0.775711 0.631088i $$-0.217392\pi$$
$$168$$ 0 0
$$169$$ −5.92470 15.3453i −0.455746 1.18041i
$$170$$ 42.6870 10.1170i 3.27394 0.775939i
$$171$$ 0 0
$$172$$ 3.59515 + 12.0086i 0.274127 + 0.915649i
$$173$$ 17.4511 + 7.12957i 1.32678 + 0.542051i 0.927173 0.374634i $$-0.122232\pi$$
0.399611 + 0.916685i $$0.369145\pi$$
$$174$$ 0 0
$$175$$ 5.16306 + 0.401305i 0.390290 + 0.0303358i
$$176$$ 4.03586 2.88466i 0.304214 0.217439i
$$177$$ 0 0
$$178$$ −6.65787 + 10.5634i −0.499028 + 0.791763i
$$179$$ −0.312381 + 5.36337i −0.0233484 + 0.400877i 0.966305 + 0.257399i $$0.0828656\pi$$
−0.989654 + 0.143478i $$0.954171\pi$$
$$180$$ 0 0
$$181$$ −9.95648 + 6.54848i −0.740059 + 0.486745i −0.862706 0.505706i $$-0.831232\pi$$
0.122647 + 0.992450i $$0.460862\pi$$
$$182$$ −22.2634 + 13.4360i −1.65027 + 0.995945i
$$183$$ 0 0
$$184$$ −28.3383 + 11.5775i −2.08913 + 0.853503i
$$185$$ −4.95316 6.14095i −0.364163 0.451492i
$$186$$ 0 0
$$187$$ 13.5100 + 19.6980i 0.987945 + 1.44046i
$$188$$ 1.00143 + 5.67941i 0.0730370 + 0.414214i
$$189$$ 0 0
$$190$$ −4.60874 + 26.1375i −0.334353 + 1.89621i
$$191$$ −7.06783 + 3.21272i −0.511410 + 0.232465i −0.652857 0.757481i $$-0.726430\pi$$
0.141446 + 0.989946i $$0.454825\pi$$
$$192$$ 0 0
$$193$$ 20.0324 + 3.93424i 1.44197 + 0.283193i 0.851706 0.524020i $$-0.175568\pi$$
0.590261 + 0.807213i $$0.299025\pi$$
$$194$$ 18.3962 + 5.89850i 1.32077 + 0.423488i
$$195$$ 0 0
$$196$$ −6.61710 7.58235i −0.472650 0.541597i
$$197$$ −3.23175 + 4.34100i −0.230253 + 0.309283i −0.902202 0.431314i $$-0.858050\pi$$
0.671949 + 0.740597i $$0.265457\pi$$
$$198$$ 0 0
$$199$$ 7.85817 18.2173i 0.557051 1.29139i −0.374314 0.927302i $$-0.622122\pi$$
0.931365 0.364087i $$-0.118619\pi$$
$$200$$ −6.78234 6.15465i −0.479584 0.435199i
$$201$$ 0 0
$$202$$ −9.17956 + 35.6373i −0.645872 + 2.50743i
$$203$$ 6.17673 + 6.05809i 0.433521 + 0.425195i
$$204$$ 0 0
$$205$$ −0.631017 + 2.91310i −0.0440721 + 0.203460i
$$206$$ −12.1305 16.2941i −0.845173 1.13526i
$$207$$ 0 0
$$208$$ 7.60305 + 0.888669i 0.527177 + 0.0616181i
$$209$$ −14.1798 + 2.78482i −0.980838 + 0.192630i
$$210$$ 0 0
$$211$$ −0.789332 3.64396i −0.0543399 0.250861i 0.942082 0.335383i $$-0.108866\pi$$
−0.996422 + 0.0845228i $$0.973063\pi$$
$$212$$ −8.10288 + 9.28487i −0.556508 + 0.637687i
$$213$$ 0 0
$$214$$ −19.5593 13.9801i −1.33705 0.955663i
$$215$$ 7.46650 + 6.26514i 0.509211 + 0.427279i
$$216$$ 0 0
$$217$$ −7.21058 + 6.05040i −0.489486 + 0.410728i
$$218$$ 29.7319 2.31095i 2.01370 0.156517i
$$219$$ 0 0
$$220$$ 12.2863 31.8223i 0.828342 2.14546i
$$221$$ −4.98794 + 36.5182i −0.335525 + 2.45648i
$$222$$ 0 0
$$223$$ 5.27169 + 2.90880i 0.353019 + 0.194787i 0.649703 0.760188i $$-0.274893\pi$$
−0.296684 + 0.954976i $$0.595881\pi$$
$$224$$ 0.460621 + 7.90856i 0.0307765 + 0.528413i
$$225$$ 0 0
$$226$$ 2.54921 1.28026i 0.169571 0.0851619i
$$227$$ 5.09961 + 9.68138i 0.338473 + 0.642576i 0.993602 0.112942i $$-0.0360274\pi$$
−0.655128 + 0.755518i $$0.727385\pi$$
$$228$$ 0 0
$$229$$ −18.3623 8.34671i −1.21342 0.551566i −0.298191 0.954506i $$-0.596383\pi$$
−0.915226 + 0.402940i $$0.867988\pi$$
$$230$$ −31.0394 + 45.2566i −2.04668 + 2.98413i
$$231$$ 0 0
$$232$$ −2.07069 15.1601i −0.135947 0.995311i
$$233$$ −12.4860 2.95923i −0.817984 0.193866i −0.199737 0.979850i $$-0.564009\pi$$
−0.618247 + 0.785984i $$0.712157\pi$$
$$234$$ 0 0
$$235$$ 3.07723 + 3.26167i 0.200736 + 0.212768i
$$236$$ 22.0531 + 3.44904i 1.43553 + 0.224513i
$$237$$ 0 0
$$238$$ 32.5202 1.26193i 2.10797 0.0817989i
$$239$$ −6.27719 3.78831i −0.406038 0.245045i 0.298944 0.954271i $$-0.403366\pi$$
−0.704982 + 0.709226i $$0.749045\pi$$
$$240$$ 0 0
$$241$$ 1.28930 + 0.358902i 0.0830513 + 0.0231189i 0.309449 0.950916i $$-0.399855\pi$$
−0.226398 + 0.974035i $$0.572695\pi$$
$$242$$ 3.21814 0.206870
$$243$$ 0 0
$$244$$ −6.16679 −0.394788
$$245$$ −7.53844 2.09847i −0.481613 0.134066i
$$246$$ 0 0
$$247$$ −19.0911 11.5215i −1.21474 0.733097i
$$248$$ 16.6343 0.645485i 1.05628 0.0409884i
$$249$$ 0 0
$$250$$ 15.6867 + 2.45335i 0.992112 + 0.155164i
$$251$$ −12.4919 13.2406i −0.788481 0.835741i 0.201122 0.979566i $$-0.435541\pi$$
−0.989603 + 0.143826i $$0.954060\pi$$
$$252$$ 0 0
$$253$$ −29.0742 6.89072i −1.82788 0.433216i
$$254$$ −3.76613 27.5729i −0.236308 1.73008i
$$255$$ 0 0
$$256$$ 13.5600 19.7710i 0.847503 1.23569i
$$257$$ 10.3642 + 4.71110i 0.646499 + 0.293870i 0.710095 0.704106i $$-0.248652\pi$$
−0.0635957 + 0.997976i $$0.520257\pi$$
$$258$$ 0 0
$$259$$ −2.72770 5.17840i −0.169491 0.321770i
$$260$$ 47.0378 23.6233i 2.91716 1.46505i
$$261$$ 0 0
$$262$$ −2.84448 48.8378i −0.175733 3.01721i
$$263$$ 4.60701 + 2.54204i 0.284080 + 0.156749i 0.618753 0.785585i $$-0.287638\pi$$
−0.334673 + 0.942334i $$0.608626\pi$$
$$264$$ 0 0
$$265$$ −1.29676 + 9.49393i −0.0796591 + 0.583207i
$$266$$ −7.09163 + 18.3678i −0.434816 + 1.12620i
$$267$$ 0 0
$$268$$ −14.9287 + 1.16035i −0.911914 + 0.0708795i
$$269$$ −18.8875 + 15.8485i −1.15159 + 0.966301i −0.999756 0.0221041i $$-0.992963\pi$$
−0.151837 + 0.988405i $$0.548519\pi$$
$$270$$ 0 0
$$271$$ 3.39725 + 2.85063i 0.206368 + 0.173163i 0.740114 0.672482i $$-0.234772\pi$$
−0.533746 + 0.845645i $$0.679216\pi$$
$$272$$ −7.79411 5.57089i −0.472587 0.337785i
$$273$$ 0 0
$$274$$ 7.45139 8.53835i 0.450155 0.515821i
$$275$$ −1.89252 8.73685i −0.114123 0.526852i
$$276$$ 0 0
$$277$$ −1.56079 + 0.306529i −0.0937788 + 0.0184176i −0.239382 0.970926i $$-0.576945\pi$$
0.145603 + 0.989343i $$0.453488\pi$$
$$278$$ −44.1203 5.15692i −2.64616 0.309292i
$$279$$ 0 0
$$280$$ −12.0381 16.1700i −0.719415 0.966342i
$$281$$ −1.83332 + 8.46357i −0.109367 + 0.504894i 0.889484 + 0.456967i $$0.151064\pi$$
−0.998851 + 0.0479275i $$0.984738\pi$$
$$282$$ 0 0
$$283$$ −11.6567 11.4328i −0.692920 0.679611i 0.265779 0.964034i $$-0.414371\pi$$
−0.958699 + 0.284423i $$0.908198\pi$$
$$284$$ 10.1231 39.3004i 0.600697 2.33205i
$$285$$ 0 0
$$286$$ 33.2415 + 30.1651i 1.96561 + 1.78370i
$$287$$ −0.875814 + 2.03036i −0.0516977 + 0.119849i
$$288$$ 0 0
$$289$$ 17.3944 23.3647i 1.02320 1.37439i
$$290$$ −18.0357 20.6666i −1.05909 1.21359i
$$291$$ 0 0
$$292$$ 17.0728 + 5.47418i 0.999112 + 0.320352i
$$293$$ 12.6452 + 2.48344i 0.738741 + 0.145084i 0.547908 0.836538i $$-0.315424\pi$$
0.190833 + 0.981622i $$0.438881\pi$$
$$294$$ 0 0
$$295$$ 15.8002 7.18206i 0.919922 0.418156i
$$296$$ −1.79744 + 10.1938i −0.104474 + 0.592501i
$$297$$ 0 0
$$298$$ 1.78780 + 10.1391i 0.103564 + 0.587343i
$$299$$ −26.0780 38.0226i −1.50813 2.19891i
$$300$$ 0 0
$$301$$ 4.53952 + 5.62812i 0.261654 + 0.324400i
$$302$$ −4.14419 + 1.69309i −0.238471 + 0.0974262i
$$303$$ 0 0
$$304$$ 4.96237 2.99480i 0.284611 0.171764i
$$305$$ −4.00617 + 2.63490i −0.229393 + 0.150874i
$$306$$ 0 0
$$307$$ −1.03115 + 17.7042i −0.0588510 + 1.01043i 0.831606 + 0.555366i $$0.187422\pi$$
−0.890457 + 0.455067i $$0.849615\pi$$
$$308$$ 13.4932 21.4084i 0.768847 1.21986i
$$309$$ 0 0
$$310$$ 24.2785 17.3532i 1.37893 0.985598i
$$311$$ 25.0480 + 1.94689i 1.42034 + 0.110398i 0.764561 0.644552i $$-0.222956\pi$$
0.655783 + 0.754950i $$0.272339\pi$$
$$312$$ 0 0
$$313$$ 1.63062 + 0.666182i 0.0921681 + 0.0376548i 0.423815 0.905749i $$-0.360691\pi$$
−0.331647 + 0.943404i $$0.607604\pi$$
$$314$$ −11.6525 38.9221i −0.657590 2.19650i
$$315$$ 0 0
$$316$$ 13.5039 3.20049i 0.759656 0.180042i
$$317$$ −9.20980 23.8540i −0.517274 1.33977i −0.907886 0.419217i $$-0.862305\pi$$
0.390612 0.920555i $$-0.372263\pi$$
$$318$$ 0 0
$$319$$ 6.96027 13.2138i 0.389700 0.739828i
$$320$$ 0.637272 32.8576i 0.0356246 1.83679i
$$321$$ 0 0
$$322$$ −29.0651 + 28.5068i −1.61973 + 1.58862i
$$323$$ 13.9537 + 24.1685i 0.776404 + 1.34477i
$$324$$ 0 0
$$325$$ 6.89709 11.9461i 0.382581 0.662650i
$$326$$ −6.48022 25.1578i −0.358906 1.39336i
$$327$$ 0 0
$$328$$ 3.42396 1.88926i 0.189056 0.104317i
$$329$$ 1.77375 + 2.81425i 0.0977902 + 0.155155i
$$330$$ 0 0
$$331$$ 5.41705 6.71609i 0.297748 0.369150i −0.607290 0.794480i $$-0.707743\pi$$
0.905038 + 0.425331i $$0.139842\pi$$
$$332$$ −14.1700 + 47.3309i −0.777677 + 2.59762i
$$333$$ 0 0
$$334$$ −38.3737 + 40.6737i −2.09971 + 2.22557i
$$335$$ −9.20243 + 7.13242i −0.502782 + 0.389686i
$$336$$ 0 0
$$337$$ 11.3603 + 23.7580i 0.618834 + 1.29418i 0.938050 + 0.346499i $$0.112630\pi$$
−0.319217 + 0.947682i $$0.603420\pi$$
$$338$$ 3.74551 + 38.5072i 0.203729 + 2.09452i
$$339$$ 0 0
$$340$$ −65.8276 2.55441i −3.57000 0.138532i
$$341$$ 13.5754 + 8.92870i 0.735150 + 0.483516i
$$342$$ 0 0
$$343$$ −17.9318 9.00570i −0.968228 0.486262i
$$344$$ −0.247971 12.7853i −0.0133697 0.689340i
$$345$$ 0 0
$$346$$ −35.0447 27.1617i −1.88401 1.46022i
$$347$$ 16.6880 2.60996i 0.895861 0.140110i 0.310205 0.950670i $$-0.399602\pi$$
0.585656 + 0.810559i $$0.300837\pi$$
$$348$$ 0 0
$$349$$ −4.02871 + 8.42534i −0.215652 + 0.450998i −0.981357 0.192194i $$-0.938440\pi$$
0.765705 + 0.643192i $$0.222390\pi$$
$$350$$ −11.4456 4.16586i −0.611793 0.222674i
$$351$$ 0 0
$$352$$ 12.8504 4.67715i 0.684927 0.249293i
$$353$$ −1.68470 + 17.3202i −0.0896675 + 0.921863i 0.837306 + 0.546735i $$0.184129\pi$$
−0.926973 + 0.375128i $$0.877599\pi$$
$$354$$ 0 0
$$355$$ −10.2156 29.8563i −0.542189 1.58461i
$$356$$ 13.8856 12.6005i 0.735935 0.667826i
$$357$$ 0 0
$$358$$ 4.09071 11.9556i 0.216201 0.631871i
$$359$$ −8.26195 19.1533i −0.436049 1.01088i −0.984610 0.174765i $$-0.944084\pi$$
0.548561 0.836110i $$-0.315176\pi$$
$$360$$ 0 0
$$361$$ 2.10197 0.245685i 0.110630 0.0129308i
$$362$$ 26.6903 8.55790i 1.40281 0.449793i
$$363$$ 0 0
$$364$$ 37.6183 10.4718i 1.97173 0.548869i
$$365$$ 13.4301 3.73852i 0.702964 0.195683i
$$366$$ 0 0
$$367$$ −20.2383 + 6.48916i −1.05643 + 0.338731i −0.782262 0.622950i $$-0.785934\pi$$
−0.274170 + 0.961681i $$0.588403\pi$$
$$368$$ 11.9034 1.39131i 0.620508 0.0725269i
$$369$$ 0 0
$$370$$ 7.34975 + 17.0386i 0.382096 + 0.885797i
$$371$$ −2.30126 + 6.72568i −0.119475 + 0.349180i
$$372$$ 0 0
$$373$$ −10.5117 + 9.53883i −0.544274 + 0.493902i −0.897125 0.441778i $$-0.854348\pi$$
0.352851 + 0.935680i $$0.385212\pi$$
$$374$$ −18.1872 53.1540i −0.940436 2.74853i
$$375$$ 0 0
$$376$$ 0.569557 5.85556i 0.0293727 0.301978i
$$377$$ 21.6556 7.88198i 1.11532 0.405943i
$$378$$ 0 0
$$379$$ 17.8430 + 6.49434i 0.916536 + 0.333592i 0.756859 0.653578i $$-0.226733\pi$$
0.159676 + 0.987169i $$0.448955\pi$$
$$380$$ 17.1929 35.9560i 0.881979 1.84450i
$$381$$ 0 0
$$382$$ 18.0410 2.82157i 0.923060 0.144364i
$$383$$ 2.89576 + 2.24438i 0.147966 + 0.114683i 0.683894 0.729581i $$-0.260285\pi$$
−0.535928 + 0.844264i $$0.680038\pi$$
$$384$$ 0 0
$$385$$ −0.381557 19.6730i −0.0194459 1.00263i
$$386$$ −42.9090 21.5497i −2.18401 1.09685i
$$387$$ 0 0
$$388$$ −24.2376 15.9413i −1.23048 0.809299i
$$389$$ 14.8910 + 0.577838i 0.755003 + 0.0292976i 0.413403 0.910548i $$-0.364340\pi$$
0.341600 + 0.939846i $$0.389031\pi$$
$$390$$ 0 0
$$391$$ 5.58638 + 57.4330i 0.282515 + 2.90451i
$$392$$ 4.42879 + 9.26203i 0.223688 + 0.467803i
$$393$$ 0 0
$$394$$ 10.0607 7.79764i 0.506851 0.392839i
$$395$$ 7.40517 7.84903i 0.372595 0.394927i
$$396$$ 0 0
$$397$$ 4.94007 16.5010i 0.247935 0.828160i −0.739909 0.672707i $$-0.765131\pi$$
0.987843 0.155453i $$-0.0496836\pi$$
$$398$$ −29.2959 + 36.3212i −1.46847 + 1.82062i
$$399$$ 0 0
$$400$$ 1.91182 + 3.03331i 0.0955911 + 0.151666i
$$401$$ −17.0499 + 9.40772i −0.851430 + 0.469799i −0.847876 0.530194i $$-0.822119\pi$$
−0.00355411 + 0.999994i $$0.501131\pi$$
$$402$$ 0 0
$$403$$ 6.25411 + 24.2799i 0.311539 + 1.20947i
$$404$$ 27.6310 47.8582i 1.37469 2.38104i
$$405$$ 0 0
$$406$$ −10.1744 17.6226i −0.504949 0.874597i
$$407$$ −7.21310 + 7.07456i −0.357540 + 0.350673i
$$408$$ 0 0
$$409$$ −0.655222 + 33.7831i −0.0323986 + 1.67047i 0.533355 + 0.845892i $$0.320931\pi$$
−0.565754 + 0.824574i $$0.691415\pi$$
$$410$$ 3.26720 6.20263i 0.161356 0.306326i
$$411$$ 0 0
$$412$$ 10.9870 + 28.4570i 0.541290 + 1.40198i
$$413$$ 12.5284 2.96930i 0.616485 0.146110i
$$414$$ 0 0
$$415$$ 11.0179 + 36.8023i 0.540847 + 1.80656i
$$416$$ 19.5342 + 7.98059i 0.957742 + 0.391280i
$$417$$ 0 0
$$418$$ 33.8858 + 2.63381i 1.65741 + 0.128824i
$$419$$ 3.72897 2.66531i 0.182172 0.130209i −0.486750 0.873541i $$-0.661818\pi$$
0.668922 + 0.743333i $$0.266756\pi$$
$$420$$ 0 0
$$421$$ 7.16781 11.3725i 0.349338 0.554262i −0.624638 0.780915i $$-0.714753\pi$$
0.973976 + 0.226652i $$0.0727781\pi$$
$$422$$ −0.509894 + 8.75454i −0.0248212 + 0.426164i
$$423$$ 0 0
$$424$$ 10.5034 6.90821i 0.510091 0.335492i
$$425$$ −14.7809 + 8.92032i −0.716979 + 0.432699i
$$426$$ 0 0
$$427$$ −3.29297 + 1.34533i −0.159358 + 0.0651049i
$$428$$ 22.6657 + 28.1011i 1.09559 + 1.35832i
$$429$$ 0 0
$$430$$ −12.9663 18.9053i −0.625290 0.911694i
$$431$$ 2.10249 + 11.9238i 0.101273 + 0.574350i 0.992643 + 0.121074i $$0.0386338\pi$$
−0.891370 + 0.453276i $$0.850255\pi$$
$$432$$ 0 0
$$433$$ −6.29503 + 35.7009i −0.302520 + 1.71568i 0.332435 + 0.943126i $$0.392130\pi$$
−0.634955 + 0.772549i $$0.718981\pi$$
$$434$$ 20.1543 9.16127i 0.967439 0.439755i
$$435$$ 0 0
$$436$$ −43.9425 8.63003i −2.10446 0.413303i
$$437$$ −33.2434 10.6591i −1.59025 0.509892i
$$438$$ 0 0
$$439$$ 0.118936 + 0.136286i 0.00567652 + 0.00650457i 0.756267 0.654263i $$-0.227021\pi$$
−0.750591 + 0.660768i $$0.770231\pi$$
$$440$$ −20.7805 + 27.9130i −0.990670 + 1.33070i
$$441$$ 0 0
$$442$$ 34.3355 79.5986i 1.63317 3.78612i
$$443$$ −22.1281 20.0802i −1.05134 0.954038i −0.0523323 0.998630i $$-0.516666\pi$$
−0.999005 + 0.0445917i $$0.985801\pi$$
$$444$$ 0 0
$$445$$ 3.63674 14.1187i 0.172398 0.669290i
$$446$$ −10.1102 9.91598i −0.478730 0.469535i
$$447$$ 0 0
$$448$$ 5.16135 23.8274i 0.243851 1.12574i
$$449$$ 10.4161 + 13.9913i 0.491567 + 0.660289i 0.976814 0.214088i $$-0.0686779\pi$$
−0.485248 + 0.874377i $$0.661271\pi$$
$$450$$ 0 0
$$451$$ 3.79122 + 0.443131i 0.178522 + 0.0208662i
$$452$$ −4.20341 + 0.825522i −0.197712 + 0.0388293i
$$453$$ 0 0
$$454$$ −5.44850 25.1531i −0.255711 1.18049i
$$455$$ 19.9639 22.8761i 0.935922 1.07245i
$$456$$ 0 0
$$457$$ −14.6293 10.4564i −0.684331 0.489131i 0.185396 0.982664i $$-0.440643\pi$$
−0.869727 + 0.493533i $$0.835705\pi$$
$$458$$ 36.3417 + 30.4943i 1.69814 + 1.42490i
$$459$$ 0 0
$$460$$ 63.1285 52.9711i 2.94338 2.46979i
$$461$$ −23.8883 + 1.85674i −1.11259 + 0.0864772i −0.620602 0.784126i $$-0.713112\pi$$
−0.491986 + 0.870603i $$0.663729\pi$$
$$462$$ 0 0
$$463$$ −9.39527 + 24.3344i −0.436635 + 1.13091i 0.523660 + 0.851927i $$0.324566\pi$$
−0.960295 + 0.278986i $$0.910002\pi$$
$$464$$ −0.810663 + 5.93510i −0.0376341 + 0.275530i
$$465$$ 0 0
$$466$$ 26.4249 + 14.5806i 1.22411 + 0.675434i
$$467$$ −0.0830352 1.42566i −0.00384241 0.0659716i 0.995842 0.0910989i $$-0.0290379\pi$$
−0.999684 + 0.0251273i $$0.992001\pi$$
$$468$$ 0 0
$$469$$ −7.71855 + 3.87640i −0.356410 + 0.178996i
$$470$$ −4.91526 9.33139i −0.226724 0.430425i
$$471$$ 0 0
$$472$$ −20.7297 9.42280i −0.954161 0.433720i
$$473$$ 7.05979 10.2934i 0.324609 0.473292i
$$474$$ 0 0
$$475$$ −1.41348 10.3485i −0.0648549 0.474822i
$$476$$ −47.5538 11.2704i −2.17962 0.516580i
$$477$$ 0 0
$$478$$ 11.8337 + 12.5430i 0.541262 + 0.573705i
$$479$$ 19.5312 + 3.05463i 0.892405 + 0.139570i 0.584065 0.811707i $$-0.301461\pi$$
0.308340 + 0.951276i $$0.400227\pi$$
$$480$$ 0 0
$$481$$ −15.5784 + 0.604514i −0.710315 + 0.0275635i
$$482$$ −2.69499 1.62644i −0.122754 0.0740822i
$$483$$ 0 0
$$484$$ −4.65554 1.29596i −0.211616 0.0589072i
$$485$$ −22.5570 −1.02426
$$486$$ 0 0
$$487$$ −10.6963 −0.484697 −0.242349 0.970189i $$-0.577918\pi$$
−0.242349 + 0.970189i $$0.577918\pi$$
$$488$$ 6.06057 + 1.68708i 0.274349 + 0.0763704i
$$489$$ 0 0
$$490$$ 15.7574 + 9.50963i 0.711846 + 0.429601i
$$491$$ −20.1197 + 0.780736i −0.907989 + 0.0352341i −0.488537 0.872543i $$-0.662469\pi$$
−0.419452 + 0.907777i $$0.637778\pi$$
$$492$$ 0 0
$$493$$ −28.4959 4.45668i −1.28339 0.200719i
$$494$$ 35.9904 + 38.1476i 1.61929 + 1.71634i
$$495$$ 0 0
$$496$$ −6.34144 1.50295i −0.284739 0.0674844i
$$497$$ −3.16805 23.1942i −0.142107 1.04040i
$$498$$ 0 0
$$499$$ −14.7346 + 21.4836i −0.659611 + 0.961736i 0.340161 + 0.940367i $$0.389519\pi$$
−0.999772 + 0.0213690i $$0.993198\pi$$
$$500$$ −21.7053 9.86625i −0.970689 0.441232i
$$501$$ 0 0
$$502$$ 19.9533 + 37.8804i 0.890560 + 1.69069i
$$503$$ −30.6455 + 15.3907i −1.36641 + 0.686239i −0.972499 0.232907i $$-0.925176\pi$$
−0.393916 + 0.919147i $$0.628880\pi$$
$$504$$ 0 0
$$505$$ −2.49843 42.8964i −0.111179 1.90887i
$$506$$ 61.5316 + 33.9517i 2.73541 + 1.50934i
$$507$$ 0 0
$$508$$ −5.65545 + 41.4052i −0.250920 + 1.83706i
$$509$$ −7.69506 + 19.9307i −0.341077 + 0.883413i 0.651147 + 0.758952i $$0.274288\pi$$
−0.992224 + 0.124461i $$0.960280\pi$$
$$510$$ 0 0
$$511$$ 10.3109 0.801424i 0.456126 0.0354529i
$$512$$ −11.9884 + 10.0594i −0.529816 + 0.444569i
$$513$$ 0 0
$$514$$ −20.5122 17.2118i −0.904753 0.759178i
$$515$$ 19.2964 + 13.7923i 0.850303 + 0.607760i
$$516$$ 0 0
$$517$$ 3.77578 4.32656i 0.166058 0.190282i
$$518$$ 2.91431 + 13.4540i 0.128048 + 0.591133i
$$519$$ 0 0
$$520$$ −52.6904 + 10.3481i −2.31063 + 0.453792i
$$521$$ −4.35729 0.509294i −0.190896 0.0223126i 0.0201075 0.999798i $$-0.493599\pi$$
−0.211004 + 0.977485i $$0.567673\pi$$
$$522$$ 0 0
$$523$$ 8.15494 + 10.9540i 0.356590 + 0.478984i 0.943831 0.330428i $$-0.107193\pi$$
−0.587241 + 0.809412i $$0.699786\pi$$
$$524$$ −15.5522 + 71.7971i −0.679403 + 3.13647i
$$525$$ 0 0
$$526$$ −8.83542 8.66572i −0.385243 0.377843i
$$527$$ 7.82730 30.3874i 0.340963 1.32370i
$$528$$ 0 0
$$529$$ −36.4231 33.0522i −1.58361 1.43705i
$$530$$ 8.92648 20.6939i 0.387741 0.898886i
$$531$$ 0 0
$$532$$ 17.6559 23.7160i 0.765482 1.02822i
$$533$$ 3.87275 + 4.43768i 0.167748 + 0.192217i
$$534$$ 0 0
$$535$$ 26.7313 + 8.57105i 1.15570 + 0.370559i
$$536$$ 14.9890 + 2.94374i 0.647426 + 0.127150i
$$537$$ 0 0
$$538$$ 52.7926 23.9972i 2.27605 1.03459i
$$539$$ −1.74009 + 9.86855i −0.0749511 + 0.425069i
$$540$$ 0 0
$$541$$ 5.30788 + 30.1025i 0.228204 + 1.29421i 0.856465 + 0.516205i $$0.172656\pi$$
−0.628261 + 0.778003i $$0.716233\pi$$
$$542$$ −5.89964 8.60189i −0.253411 0.369483i
$$543$$ 0 0
$$544$$ −16.5802 20.5562i −0.710871 0.881341i
$$545$$ −32.2340 + 13.1691i −1.38075 + 0.564100i
$$546$$ 0 0
$$547$$ −4.06531 + 2.45343i −0.173820 + 0.104901i −0.600940 0.799294i $$-0.705207\pi$$
0.427120 + 0.904195i $$0.359528\pi$$
$$548$$ −14.2180 + 9.35136i −0.607365 + 0.399470i
$$549$$ 0 0
$$550$$ −1.22253 + 20.9901i −0.0521290 + 0.895020i
$$551$$ 9.30408 14.7619i 0.396367 0.628879i
$$552$$ 0 0
$$553$$ 6.51269 4.65499i 0.276948 0.197950i
$$554$$ 3.72986 + 0.289907i 0.158466 + 0.0123170i
$$555$$ 0 0
$$556$$ 61.7502 + 25.2277i 2.61879 + 1.06989i
$$557$$ 9.92217 + 33.1423i 0.420416 + 1.40429i 0.861928 + 0.507031i $$0.169257\pi$$
−0.441512 + 0.897255i $$0.645558\pi$$
$$558$$ 0 0
$$559$$ 18.7410 4.44171i 0.792662 0.187864i
$$560$$ 2.84257 + 7.36243i 0.120120 + 0.311120i
$$561$$ 0 0
$$562$$ 9.49237 18.0208i 0.400411 0.760162i
$$563$$ −0.0965944 + 4.98038i −0.00407097 + 0.209898i 0.992253 + 0.124233i $$0.0396471\pi$$
−0.996324 + 0.0856648i $$0.972699\pi$$
$$564$$ 0 0
$$565$$ −2.37796 + 2.33229i −0.100042 + 0.0981202i
$$566$$ 19.2012 + 33.2575i 0.807087 + 1.39792i
$$567$$ 0 0
$$568$$ −20.7004 + 35.8541i −0.868568 + 1.50440i
$$569$$ 2.12779 + 8.26060i 0.0892018 + 0.346303i 0.997385 0.0722701i $$-0.0230244\pi$$
−0.908183 + 0.418573i $$0.862531\pi$$
$$570$$ 0 0
$$571$$ 2.71811 1.49979i 0.113749 0.0627642i −0.425218 0.905091i $$-0.639802\pi$$
0.538967 + 0.842327i $$0.318815\pi$$
$$572$$ −35.9415 57.0250i −1.50279 2.38434i
$$573$$ 0 0
$$574$$ 3.26510 4.04809i 0.136283 0.168964i
$$575$$ 6.19388 20.6890i 0.258303 0.862791i
$$576$$ 0 0
$$577$$ 22.2585 23.5926i 0.926633 0.982173i −0.0732528 0.997313i $$-0.523338\pi$$
0.999885 + 0.0151403i $$0.00481949\pi$$
$$578$$ −54.1501 + 41.9695i −2.25235 + 1.74570i
$$579$$ 0 0
$$580$$ 17.7689 + 37.1606i 0.737815 + 1.54301i
$$581$$ 2.75903 + 28.3653i 0.114464 + 1.17679i
$$582$$ 0 0
$$583$$ 12.2616 + 0.475806i 0.507823 + 0.0197059i
$$584$$ −15.2812 10.0506i −0.632340 0.415896i
$$585$$ 0 0
$$586$$ −27.0858 13.6030i −1.11890 0.561934i
$$587$$ −0.577092 29.7547i −0.0238191 1.22811i −0.800935 0.598751i $$-0.795664\pi$$
0.777116 0.629357i $$-0.216682\pi$$
$$588$$ 0 0
$$589$$ 15.0050 + 11.6298i 0.618270 + 0.479196i
$$590$$ −40.3309 + 6.30763i −1.66039 + 0.259681i
$$591$$ 0 0
$$592$$ 1.74813 3.65591i 0.0718479 0.150257i
$$593$$ −17.3860 6.32799i −0.713958 0.259860i −0.0405995 0.999176i $$-0.512927\pi$$
−0.673359 + 0.739316i $$0.735149\pi$$
$$594$$ 0 0
$$595$$ −35.7082 + 12.9967i −1.46389 + 0.532814i
$$596$$ 1.49673 15.3878i 0.0613086 0.630308i
$$597$$ 0 0
$$598$$ 35.1063 + 102.602i 1.43560 + 4.19571i
$$599$$ 1.99940 1.81436i 0.0816934 0.0741328i −0.630138 0.776483i $$-0.717002\pi$$
0.711832 + 0.702350i $$0.247866\pi$$
$$600$$ 0 0
$$601$$ −7.48402 + 21.8729i −0.305280 + 0.892214i 0.681737 + 0.731597i $$0.261225\pi$$
−0.987017 + 0.160616i $$0.948652\pi$$
$$602$$ −6.73598 15.6157i −0.274538 0.636450i
$$603$$ 0 0
$$604$$ 6.67704 0.780434i 0.271685 0.0317554i
$$605$$ −3.57814 + 1.14728i −0.145472 + 0.0466437i
$$606$$ 0 0
$$607$$ −12.6817 + 3.53019i −0.514734 + 0.143286i −0.515793 0.856714i $$-0.672502\pi$$
0.00105883 + 0.999999i $$0.499663\pi$$
$$608$$ 15.3923 4.28474i 0.624240 0.173769i
$$609$$ 0 0
$$610$$ 10.7393 3.44343i 0.434822 0.139420i
$$611$$ 8.80103 1.02869i 0.356052 0.0416165i
$$612$$ 0 0
$$613$$ −9.96575 23.1032i −0.402513 0.933130i −0.992103 0.125427i $$-0.959970\pi$$
0.589590 0.807703i $$-0.299289\pi$$
$$614$$ 13.5032 39.4647i 0.544947 1.59267i
$$615$$ 0 0
$$616$$ −19.1176 + 17.3483i −0.770271 + 0.698983i
$$617$$ 0.271197 + 0.792604i 0.0109180 + 0.0319090i 0.951473 0.307733i $$-0.0995705\pi$$
−0.940555 + 0.339642i $$0.889694\pi$$
$$618$$ 0 0
$$619$$ 4.15235 42.6899i 0.166897 1.71585i −0.421121 0.907004i $$-0.638363\pi$$
0.588018 0.808848i $$-0.299908\pi$$
$$620$$ −42.1109 + 15.3271i −1.69122 + 0.615552i
$$621$$ 0 0
$$622$$ −55.5271 20.2102i −2.22643 0.810356i
$$623$$ 4.66581 9.75772i 0.186932 0.390935i
$$624$$ 0 0
$$625$$ −30.8729 + 4.82844i −1.23492 + 0.193138i
$$626$$ −3.27455 2.53797i −0.130877 0.101438i
$$627$$ 0 0
$$628$$ 1.18308 + 60.9995i 0.0472102 + 2.43415i
$$629$$ 17.4364 + 8.75688i 0.695234 + 0.349160i
$$630$$ 0 0
$$631$$ −18.0503 11.8718i −0.718569 0.472610i 0.136820 0.990596i $$-0.456312\pi$$
−0.855389 + 0.517985i $$0.826682\pi$$
$$632$$ −14.1469 0.548966i −0.562735 0.0218367i
$$633$$ 0 0
$$634$$ 5.82231 + 59.8585i 0.231233 + 2.37729i
$$635$$ 14.0173 + 29.3148i 0.556261 + 1.16332i
$$636$$ 0 0
$$637$$ −12.2216 + 9.47247i −0.484238 + 0.375313i
$$638$$ −24.1054 + 25.5502i −0.954342 + 1.01154i
$$639$$ 0 0
$$640$$ −16.0433 + 53.5883i −0.634167 + 2.11826i
$$641$$ −11.0097 + 13.6498i −0.434855 + 0.539136i −0.947623 0.319392i $$-0.896521\pi$$
0.512768 + 0.858527i $$0.328620\pi$$
$$642$$ 0 0
$$643$$ −3.65641 5.80128i −0.144195 0.228780i 0.766120 0.642698i $$-0.222185\pi$$
−0.910314 + 0.413917i $$0.864160\pi$$
$$644$$ 53.5271 29.5350i 2.10926 1.16384i
$$645$$ 0 0
$$646$$ −16.3729 63.5634i −0.644182 2.50087i
$$647$$ −14.7935 + 25.6232i −0.581594 + 1.00735i 0.413697 + 0.910415i $$0.364237\pi$$
−0.995291 + 0.0969356i $$0.969096\pi$$
$$648$$ 0 0
$$649$$ −11.1130 19.2483i −0.436223 0.755561i
$$650$$ −23.1627 + 22.7178i −0.908515 + 0.891065i
$$651$$ 0 0
$$652$$ −0.756488 + 39.0043i −0.0296263 + 1.52753i
$$653$$ 21.2827 40.4042i 0.832856 1.58114i 0.0191813 0.999816i $$-0.493894\pi$$
0.813674 0.581321i $$-0.197464\pi$$
$$654$$ 0 0
$$655$$ 20.5737 + 53.2871i 0.803879 + 2.08210i
$$656$$ −1.48971 + 0.353067i −0.0581633 + 0.0137850i
$$657$$ 0 0
$$658$$ −2.24399 7.49545i −0.0874799 0.292203i
$$659$$ 14.1933 + 5.79858i 0.552891 + 0.225881i 0.637388 0.770543i $$-0.280015\pi$$
−0.0844974 + 0.996424i $$0.526928\pi$$
$$660$$ 0 0
$$661$$ 47.6557 + 3.70409i 1.85359 + 0.144072i 0.955359 0.295448i $$-0.0954691\pi$$
0.898232 + 0.439521i $$0.144852\pi$$
$$662$$ −16.5103 + 11.8009i −0.641693 + 0.458654i
$$663$$ 0 0
$$664$$ 26.8744 42.6392i 1.04293 1.65472i
$$665$$ 1.33673 22.9507i 0.0518361 0.889991i
$$666$$ 0 0
$$667$$ 30.1444 19.8263i 1.16720 0.767677i
$$668$$ 71.8930 43.3877i 2.78162 1.67872i
$$669$$ 0 0
$$670$$ 25.3500 10.3566i 0.979358 0.400112i
$$671$$ 3.85508 + 4.77954i 0.148824 + 0.184512i
$$672$$ 0 0
$$673$$ 22.4286 + 32.7017i 0.864560 + 1.26056i 0.964104 + 0.265526i $$0.0855456\pi$$
−0.0995438 + 0.995033i $$0.531738\pi$$
$$674$$ −10.7555 60.9975i −0.414286 2.34953i
$$675$$ 0 0
$$676$$ 10.0886 57.2151i 0.388022 2.20058i
$$677$$ −10.1875 + 4.63077i −0.391536 + 0.177975i −0.599897 0.800077i $$-0.704792\pi$$
0.208361 + 0.978052i $$0.433187\pi$$
$$678$$ 0 0
$$679$$ −16.4202 3.22483i −0.630151 0.123758i
$$680$$ 63.9950 + 20.5192i 2.45410 + 0.786875i
$$681$$ 0 0
$$682$$ −25.1282 28.7937i −0.962207 1.10257i
$$683$$ −20.0015 + 26.8667i −0.765338 + 1.02803i 0.233117 + 0.972449i $$0.425108\pi$$
−0.998454 + 0.0555783i $$0.982300\pi$$
$$684$$ 0 0
$$685$$ −5.24099 + 12.1500i −0.200248 + 0.464226i
$$686$$ 34.9505 + 31.7159i 1.33442 + 1.21092i
$$687$$ 0 0
$$688$$ −1.24878 + 4.84808i −0.0476094 + 0.184831i
$$689$$ 13.5180 + 13.2584i 0.514996 + 0.505104i
$$690$$ 0 0
$$691$$ 1.91763 8.85275i 0.0729500 0.336774i −0.926244 0.376925i $$-0.876981\pi$$
0.999194 + 0.0401508i $$0.0127838\pi$$
$$692$$ 39.7595 + 53.4063i 1.51143 + 2.03020i
$$693$$ 0 0
$$694$$ −39.4588 4.61208i −1.49784 0.175072i
$$695$$ 50.8943 9.99532i 1.93053 0.379144i
$$696$$ 0 0
$$697$$ −1.56058 7.20443i −0.0591111 0.272887i
$$698$$ 14.4427 16.5495i 0.546663 0.626407i
$$699$$ 0 0
$$700$$ 14.8802 + 10.6358i 0.562420 + 0.401994i
$$701$$ −0.828040 0.694808i −0.0312746 0.0262425i 0.627016 0.779006i $$-0.284276\pi$$
−0.658291 + 0.752764i $$0.728720\pi$$
$$702$$ 0 0
$$703$$ −9.04275 + 7.58777i −0.341054 + 0.286178i
$$704$$ −41.9588 + 3.26130i −1.58138 + 0.122915i
$$705$$ 0 0
$$706$$ 14.7419 38.1824i 0.554818 1.43701i
$$707$$ 4.31392 31.5835i 0.162242 1.18782i
$$708$$ 0 0
$$709$$ −3.19359 1.76215i −0.119938 0.0661788i 0.422009 0.906592i $$-0.361325\pi$$
−0.541947 + 0.840413i $$0.682313\pi$$
$$710$$ 4.31545 + 74.0933i 0.161956 + 2.78067i
$$711$$ 0 0
$$712$$ −17.0936 + 8.58474i −0.640611 + 0.321727i
$$713$$ 18.2939 + 34.7302i 0.685113 + 1.30065i
$$714$$ 0 0
$$715$$ −47.7141 21.6887i −1.78441 0.811113i
$$716$$ −10.7324 + 15.6483i −0.401089 + 0.584803i
$$717$$ 0 0
$$718$$ 6.63950 + 48.6098i 0.247784 + 1.81410i
$$719$$ 28.9896 + 6.87067i 1.08113 + 0.256233i 0.732320 0.680961i $$-0.238438\pi$$
0.348810 + 0.937193i $$0.386586\pi$$
$$720$$ 0 0
$$721$$ 12.0750 + 12.7987i 0.449696 + 0.476649i
$$722$$ −4.91771 0.769116i −0.183018 0.0286235i
$$723$$ 0 0
$$724$$ −42.0580 + 1.63204i −1.56307 + 0.0606544i
$$725$$ 9.24191 + 5.57752i 0.343236 + 0.207144i
$$726$$ 0 0
$$727$$ −7.64608 2.12843i −0.283577 0.0789391i 0.123463 0.992349i $$-0.460600\pi$$
−0.407041 + 0.913410i $$0.633439\pi$$
$$728$$ −39.8352 −1.47639
$$729$$ 0 0
$$730$$ −32.7886 −1.21356
$$731$$ −23.2221 6.46431i −0.858900 0.239091i
$$732$$ 0 0
$$733$$ −3.99533 2.41119i −0.147571 0.0890595i 0.440992 0.897511i $$-0.354627\pi$$
−0.588562 + 0.808452i $$0.700306\pi$$
$$734$$ 49.9500 1.93829i 1.84369 0.0715435i
$$735$$ 0 0
$$736$$ 32.6399 + 5.10479i 1.20312 + 0.188165i
$$737$$ 10.2318 + 10.8450i 0.376892 + 0.399482i
$$738$$ 0 0
$$739$$ 34.8218 + 8.25291i 1.28094 + 0.303588i 0.814085 0.580746i $$-0.197239\pi$$
0.466855 + 0.884334i $$0.345387\pi$$
$$740$$ −3.77104 27.6089i −0.138626 1.01492i
$$741$$ 0 0
$$742$$ 9.45647 13.7879i 0.347158 0.506169i
$$743$$ −7.32151 3.32804i −0.268600 0.122094i 0.274983 0.961449i $$-0.411328\pi$$
−0.543583 + 0.839355i $$0.682933\pi$$
$$744$$ 0 0
$$745$$ −5.60244 10.6360i −0.205258 0.389672i
$$746$$ 29.8344 14.9834i 1.09232 0.548581i
$$747$$ 0 0
$$748$$ 4.90524 + 84.2197i 0.179353 + 3.07938i
$$749$$ 18.2336 + 10.0609i 0.666241 + 0.367616i
$$750$$ 0 0
$$751$$ 4.73356 34.6558i 0.172730 1.26461i −0.676444 0.736494i $$-0.736480\pi$$
0.849174 0.528113i $$-0.177100\pi$$
$$752$$ −0.829574 + 2.14865i −0.0302515 + 0.0783532i
$$753$$ 0 0
$$754$$ −54.0397 + 4.20030i −1.96801 + 0.152966i
$$755$$ 4.00419 3.35991i 0.145727 0.122280i
$$756$$ 0 0
$$757$$ −20.1696 16.9243i −0.733076 0.615123i 0.197893 0.980224i $$-0.436590\pi$$
−0.930968 + 0.365100i $$0.881035\pi$$
$$758$$ −36.3334 25.9696i −1.31969 0.943257i
$$759$$ 0 0
$$760$$ −26.7335 + 30.6332i −0.969725 + 1.11118i
$$761$$ 5.66582 + 26.1563i 0.205386 + 0.948166i 0.957343 + 0.288954i $$0.0933076\pi$$
−0.751957 + 0.659212i $$0.770890\pi$$
$$762$$ 0 0
$$763$$ −25.3473 + 4.97806i −0.917635 + 0.180218i
$$764$$ −27.2355 3.18337i −0.985345 0.115170i
$$765$$ 0 0
$$766$$ −5.14573 6.91191i −0.185923 0.249737i
$$767$$ 7.26062 33.5188i 0.262166 1.21029i
$$768$$ 0 0
$$769$$ −33.2820 32.6428i −1.20018 1.17713i −0.979427 0.201798i $$-0.935322\pi$$
−0.220752 0.975330i $$-0.570851\pi$$
$$770$$ −11.5440 + 44.8167i −0.416018 + 1.61508i
$$771$$ 0 0
$$772$$ 53.3965 + 48.4547i 1.92178 + 1.74392i
$$773$$ −0.117392 + 0.272145i −0.00422229 + 0.00978837i −0.920314 0.391180i $$-0.872067\pi$$
0.916092 + 0.400968i $$0.131326\pi$$
$$774$$ 0 0
$$775$$ −7.01304 + 9.42015i −0.251916 + 0.338382i
$$776$$ 19.4590 + 22.2976i 0.698539 + 0.800437i
$$777$$ 0 0
$$778$$ −33.3763 10.7017i −1.19660 0.383674i
$$779$$ 4.37611 + 0.859439i 0.156790 + 0.0307926i
$$780$$ 0 0
$$781$$ −36.7879 + 16.7222i −1.31638 + 0.598366i
$$782$$ 23.5675 133.658i 0.842773 4.77960i
$$783$$ 0 0
$$784$$ −0.697934 3.95818i −0.0249262 0.141364i
$$785$$ 26.8320 + 39.1220i 0.957676 + 1.39633i
$$786$$ 0 0
$$787$$ −21.2654