# Properties

 Label 1170.2.bj.c.829.5 Level $1170$ Weight $2$ Character 1170.829 Analytic conductor $9.342$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.bj (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197$$ x^12 - 2*x^11 - 8*x^10 + 34*x^9 + 8*x^8 - 134*x^7 + 98*x^6 + 154*x^5 + 104*x^4 + 190*x^3 - 1196*x^2 - 338*x + 2197 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 829.5 Root $$2.00607 - 1.30680i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.829 Dual form 1170.2.bj.c.199.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.26873 + 1.84128i) q^{5} +(2.17283 - 3.76344i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.26873 + 1.84128i) q^{5} +(2.17283 - 3.76344i) q^{7} +1.00000 q^{8} +(0.960230 - 2.01940i) q^{10} +(2.04055 - 1.17811i) q^{11} +(3.18419 - 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.60564 + 1.50437i) q^{17} +(0.585872 + 0.338254i) q^{19} +(-2.22896 + 0.178114i) q^{20} +(-2.04055 - 1.17811i) q^{22} +(-5.58405 + 3.22396i) q^{23} +(-1.78064 + 4.67219i) q^{25} +(-3.05692 - 1.91187i) q^{26} +(2.17283 + 3.76344i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00874i q^{34} +(9.68629 - 0.774021i) q^{35} +(-3.74165 - 6.48073i) q^{37} -0.676507i q^{38} +(1.26873 + 1.84128i) q^{40} +(2.60564 - 1.50437i) q^{41} +(5.91710 + 3.41624i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} +5.61529 q^{47} +(-5.94234 - 10.2924i) q^{49} +(4.93655 - 0.794019i) q^{50} +(-0.127265 + 3.60330i) q^{52} -9.43400i q^{53} +(4.75816 + 2.26252i) q^{55} +(2.17283 - 3.76344i) q^{56} +(-4.82620 + 8.35922i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(6.16171 - 3.55746i) q^{62} +1.00000 q^{64} +(7.15429 + 3.71700i) q^{65} +(2.91329 + 5.04596i) q^{67} +(-2.60564 + 1.50437i) q^{68} +(-5.51347 - 8.00157i) q^{70} +(-2.52520 - 1.45793i) q^{71} +7.67804 q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} -10.2393i q^{77} -3.74519 q^{79} +(0.960230 - 2.01940i) q^{80} +(-2.60564 - 1.50437i) q^{82} +10.3557 q^{83} +(0.535898 + 6.70637i) q^{85} -6.83247i q^{86} +(2.04055 - 1.17811i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} -6.44791i q^{92} +(-2.80764 - 4.86298i) q^{94} +(0.120495 + 1.50791i) q^{95} +(8.17066 - 14.1520i) q^{97} +(-5.94234 + 10.2924i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10})$$ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 $$12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100})$$ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 1.26873 + 1.84128i 0.567394 + 0.823446i
$$6$$ 0 0
$$7$$ 2.17283 3.76344i 0.821251 1.42245i −0.0835003 0.996508i $$-0.526610\pi$$
0.904751 0.425940i $$-0.140057\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0.960230 2.01940i 0.303651 0.638589i
$$11$$ 2.04055 1.17811i 0.615250 0.355215i −0.159767 0.987155i $$-0.551074\pi$$
0.775017 + 0.631940i $$0.217741\pi$$
$$12$$ 0 0
$$13$$ 3.18419 1.69144i 0.883134 0.469120i
$$14$$ −4.34565 −1.16142
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.60564 + 1.50437i 0.631962 + 0.364863i 0.781511 0.623891i $$-0.214449\pi$$
−0.149550 + 0.988754i $$0.547782\pi$$
$$18$$ 0 0
$$19$$ 0.585872 + 0.338254i 0.134408 + 0.0776007i 0.565696 0.824614i $$-0.308607\pi$$
−0.431288 + 0.902214i $$0.641941\pi$$
$$20$$ −2.22896 + 0.178114i −0.498411 + 0.0398275i
$$21$$ 0 0
$$22$$ −2.04055 1.17811i −0.435047 0.251175i
$$23$$ −5.58405 + 3.22396i −1.16436 + 0.672241i −0.952344 0.305026i $$-0.901335\pi$$
−0.212012 + 0.977267i $$0.568002\pi$$
$$24$$ 0 0
$$25$$ −1.78064 + 4.67219i −0.356127 + 0.934438i
$$26$$ −3.05692 1.91187i −0.599511 0.374948i
$$27$$ 0 0
$$28$$ 2.17283 + 3.76344i 0.410625 + 0.711224i
$$29$$ −4.82620 8.35922i −0.896202 1.55227i −0.832310 0.554311i $$-0.812982\pi$$
−0.0638921 0.997957i $$-0.520351\pi$$
$$30$$ 0 0
$$31$$ 7.11493i 1.27788i 0.769257 + 0.638939i $$0.220626\pi$$
−0.769257 + 0.638939i $$0.779374\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 3.00874i 0.515995i
$$35$$ 9.68629 0.774021i 1.63728 0.130833i
$$36$$ 0 0
$$37$$ −3.74165 6.48073i −0.615123 1.06542i −0.990363 0.138497i $$-0.955773\pi$$
0.375240 0.926928i $$-0.377560\pi$$
$$38$$ 0.676507i 0.109744i
$$39$$ 0 0
$$40$$ 1.26873 + 1.84128i 0.200604 + 0.291132i
$$41$$ 2.60564 1.50437i 0.406933 0.234943i −0.282538 0.959256i $$-0.591176\pi$$
0.689471 + 0.724313i $$0.257843\pi$$
$$42$$ 0 0
$$43$$ 5.91710 + 3.41624i 0.902349 + 0.520971i 0.877961 0.478731i $$-0.158903\pi$$
0.0243872 + 0.999703i $$0.492237\pi$$
$$44$$ 2.35623i 0.355215i
$$45$$ 0 0
$$46$$ 5.58405 + 3.22396i 0.823324 + 0.475346i
$$47$$ 5.61529 0.819074 0.409537 0.912294i $$-0.365690\pi$$
0.409537 + 0.912294i $$0.365690\pi$$
$$48$$ 0 0
$$49$$ −5.94234 10.2924i −0.848906 1.47035i
$$50$$ 4.93655 0.794019i 0.698134 0.112291i
$$51$$ 0 0
$$52$$ −0.127265 + 3.60330i −0.0176485 + 0.499688i
$$53$$ 9.43400i 1.29586i −0.761700 0.647930i $$-0.775635\pi$$
0.761700 0.647930i $$-0.224365\pi$$
$$54$$ 0 0
$$55$$ 4.75816 + 2.26252i 0.641590 + 0.305078i
$$56$$ 2.17283 3.76344i 0.290356 0.502911i
$$57$$ 0 0
$$58$$ −4.82620 + 8.35922i −0.633711 + 1.09762i
$$59$$ 4.56364 + 2.63482i 0.594135 + 0.343024i 0.766731 0.641969i $$-0.221882\pi$$
−0.172596 + 0.984993i $$0.555215\pi$$
$$60$$ 0 0
$$61$$ 2.15646 3.73509i 0.276106 0.478230i −0.694307 0.719679i $$-0.744289\pi$$
0.970414 + 0.241449i $$0.0776225\pi$$
$$62$$ 6.16171 3.55746i 0.782538 0.451798i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 7.15429 + 3.71700i 0.887381 + 0.461037i
$$66$$ 0 0
$$67$$ 2.91329 + 5.04596i 0.355915 + 0.616463i 0.987274 0.159028i $$-0.0508360\pi$$
−0.631359 + 0.775490i $$0.717503\pi$$
$$68$$ −2.60564 + 1.50437i −0.315981 + 0.182432i
$$69$$ 0 0
$$70$$ −5.51347 8.00157i −0.658986 0.956370i
$$71$$ −2.52520 1.45793i −0.299686 0.173024i 0.342616 0.939476i $$-0.388687\pi$$
−0.642302 + 0.766452i $$0.722020\pi$$
$$72$$ 0 0
$$73$$ 7.67804 0.898647 0.449323 0.893369i $$-0.351665\pi$$
0.449323 + 0.893369i $$0.351665\pi$$
$$74$$ −3.74165 + 6.48073i −0.434958 + 0.753369i
$$75$$ 0 0
$$76$$ −0.585872 + 0.338254i −0.0672042 + 0.0388004i
$$77$$ 10.2393i 1.16688i
$$78$$ 0 0
$$79$$ −3.74519 −0.421367 −0.210683 0.977554i $$-0.567569\pi$$
−0.210683 + 0.977554i $$0.567569\pi$$
$$80$$ 0.960230 2.01940i 0.107357 0.225775i
$$81$$ 0 0
$$82$$ −2.60564 1.50437i −0.287745 0.166130i
$$83$$ 10.3557 1.13668 0.568341 0.822793i $$-0.307585\pi$$
0.568341 + 0.822793i $$0.307585\pi$$
$$84$$ 0 0
$$85$$ 0.535898 + 6.70637i 0.0581263 + 0.727408i
$$86$$ 6.83247i 0.736765i
$$87$$ 0 0
$$88$$ 2.04055 1.17811i 0.217524 0.125587i
$$89$$ −4.15208 + 2.39720i −0.440119 + 0.254103i −0.703648 0.710549i $$-0.748447\pi$$
0.263529 + 0.964651i $$0.415114\pi$$
$$90$$ 0 0
$$91$$ 0.553049 15.6587i 0.0579753 1.64148i
$$92$$ 6.44791i 0.672241i
$$93$$ 0 0
$$94$$ −2.80764 4.86298i −0.289586 0.501578i
$$95$$ 0.120495 + 1.50791i 0.0123626 + 0.154708i
$$96$$ 0 0
$$97$$ 8.17066 14.1520i 0.829605 1.43692i −0.0687436 0.997634i $$-0.521899\pi$$
0.898349 0.439283i $$-0.144768\pi$$
$$98$$ −5.94234 + 10.2924i −0.600267 + 1.03969i
$$99$$ 0 0
$$100$$ −3.15592 3.87817i −0.315592 0.387817i
$$101$$ 6.11911 + 10.5986i 0.608875 + 1.05460i 0.991426 + 0.130668i $$0.0417121\pi$$
−0.382552 + 0.923934i $$0.624955\pi$$
$$102$$ 0 0
$$103$$ 3.75144i 0.369640i 0.982772 + 0.184820i $$0.0591702\pi$$
−0.982772 + 0.184820i $$0.940830\pi$$
$$104$$ 3.18419 1.69144i 0.312235 0.165859i
$$105$$ 0 0
$$106$$ −8.17008 + 4.71700i −0.793549 + 0.458156i
$$107$$ 14.3904 8.30831i 1.39117 0.803194i 0.397728 0.917503i $$-0.369799\pi$$
0.993445 + 0.114309i $$0.0364654\pi$$
$$108$$ 0 0
$$109$$ 11.1116i 1.06430i 0.846652 + 0.532148i $$0.178615\pi$$
−0.846652 + 0.532148i $$0.821385\pi$$
$$110$$ −0.419677 5.25194i −0.0400146 0.500753i
$$111$$ 0 0
$$112$$ −4.34565 −0.410625
$$113$$ −13.5620 7.83002i −1.27581 0.736587i −0.299731 0.954024i $$-0.596897\pi$$
−0.976074 + 0.217437i $$0.930230\pi$$
$$114$$ 0 0
$$115$$ −13.0209 6.19148i −1.21420 0.577358i
$$116$$ 9.65239 0.896202
$$117$$ 0 0
$$118$$ 5.26964i 0.485109i
$$119$$ 11.3232 6.53747i 1.03800 0.599288i
$$120$$ 0 0
$$121$$ −2.72410 + 4.71827i −0.247645 + 0.428934i
$$122$$ −4.31292 −0.390473
$$123$$ 0 0
$$124$$ −6.16171 3.55746i −0.553338 0.319470i
$$125$$ −10.8620 + 2.64911i −0.971523 + 0.236943i
$$126$$ 0 0
$$127$$ −11.7820 + 6.80236i −1.04549 + 0.603611i −0.921382 0.388658i $$-0.872939\pi$$
−0.124103 + 0.992269i $$0.539605\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −0.358130 8.05430i −0.0314101 0.706409i
$$131$$ −10.2122 −0.892246 −0.446123 0.894972i $$-0.647196\pi$$
−0.446123 + 0.894972i $$0.647196\pi$$
$$132$$ 0 0
$$133$$ 2.54600 1.46993i 0.220766 0.127459i
$$134$$ 2.91329 5.04596i 0.251670 0.435905i
$$135$$ 0 0
$$136$$ 2.60564 + 1.50437i 0.223432 + 0.128999i
$$137$$ −6.20689 + 10.7506i −0.530290 + 0.918489i 0.469085 + 0.883153i $$0.344584\pi$$
−0.999375 + 0.0353365i $$0.988750\pi$$
$$138$$ 0 0
$$139$$ −7.80915 + 13.5258i −0.662363 + 1.14725i 0.317630 + 0.948215i $$0.397113\pi$$
−0.979993 + 0.199032i $$0.936220\pi$$
$$140$$ −4.17283 + 8.77559i −0.352668 + 0.741673i
$$141$$ 0 0
$$142$$ 2.91585i 0.244693i
$$143$$ 4.50479 7.20280i 0.376710 0.602329i
$$144$$ 0 0
$$145$$ 9.26852 19.4920i 0.769709 1.61872i
$$146$$ −3.83902 6.64938i −0.317720 0.550307i
$$147$$ 0 0
$$148$$ 7.48330 0.615123
$$149$$ −16.9104 9.76324i −1.38536 0.799836i −0.392569 0.919722i $$-0.628414\pi$$
−0.992788 + 0.119886i $$0.961747\pi$$
$$150$$ 0 0
$$151$$ 11.5027i 0.936079i −0.883707 0.468040i $$-0.844960\pi$$
0.883707 0.468040i $$-0.155040\pi$$
$$152$$ 0.585872 + 0.338254i 0.0475205 + 0.0274360i
$$153$$ 0 0
$$154$$ −8.86753 + 5.11967i −0.714566 + 0.412555i
$$155$$ −13.1006 + 9.02694i −1.05226 + 0.725061i
$$156$$ 0 0
$$157$$ 4.47595i 0.357220i 0.983920 + 0.178610i $$0.0571600\pi$$
−0.983920 + 0.178610i $$0.942840\pi$$
$$158$$ 1.87260 + 3.24343i 0.148976 + 0.258033i
$$159$$ 0 0
$$160$$ −2.22896 + 0.178114i −0.176215 + 0.0140811i
$$161$$ 28.0204i 2.20831i
$$162$$ 0 0
$$163$$ −3.87774 + 6.71645i −0.303728 + 0.526073i −0.976977 0.213343i $$-0.931565\pi$$
0.673249 + 0.739416i $$0.264898\pi$$
$$164$$ 3.00874i 0.234943i
$$165$$ 0 0
$$166$$ −5.17783 8.96827i −0.401878 0.696073i
$$167$$ 0.339021 + 0.587202i 0.0262342 + 0.0454390i 0.878844 0.477108i $$-0.158315\pi$$
−0.852610 + 0.522547i $$0.824982\pi$$
$$168$$ 0 0
$$169$$ 7.27808 10.7717i 0.559852 0.828593i
$$170$$ 5.53994 3.81729i 0.424894 0.292772i
$$171$$ 0 0
$$172$$ −5.91710 + 3.41624i −0.451174 + 0.260486i
$$173$$ 0.625226 + 0.360974i 0.0475350 + 0.0274444i 0.523579 0.851977i $$-0.324596\pi$$
−0.476044 + 0.879421i $$0.657930\pi$$
$$174$$ 0 0
$$175$$ 13.7145 + 16.8532i 1.03672 + 1.27398i
$$176$$ −2.04055 1.17811i −0.153812 0.0888037i
$$177$$ 0 0
$$178$$ 4.15208 + 2.39720i 0.311211 + 0.179678i
$$179$$ −3.18673 5.51958i −0.238187 0.412553i 0.722007 0.691886i $$-0.243220\pi$$
−0.960194 + 0.279333i $$0.909887\pi$$
$$180$$ 0 0
$$181$$ 22.0214 1.63683 0.818417 0.574624i $$-0.194852\pi$$
0.818417 + 0.574624i $$0.194852\pi$$
$$182$$ −13.8374 + 7.35040i −1.02569 + 0.544848i
$$183$$ 0 0
$$184$$ −5.58405 + 3.22396i −0.411662 + 0.237673i
$$185$$ 7.18569 15.1117i 0.528302 1.11104i
$$186$$ 0 0
$$187$$ 7.08928 0.518419
$$188$$ −2.80764 + 4.86298i −0.204768 + 0.354669i
$$189$$ 0 0
$$190$$ 1.24564 0.858307i 0.0903682 0.0622681i
$$191$$ 0.293441 0.508255i 0.0212326 0.0367760i −0.855214 0.518275i $$-0.826574\pi$$
0.876446 + 0.481499i $$0.159908\pi$$
$$192$$ 0 0
$$193$$ −11.3135 19.5955i −0.814363 1.41052i −0.909784 0.415081i $$-0.863753\pi$$
0.0954215 0.995437i $$-0.469580\pi$$
$$194$$ −16.3413 −1.17324
$$195$$ 0 0
$$196$$ 11.8847 0.848906
$$197$$ −0.823770 1.42681i −0.0586912 0.101656i 0.835187 0.549966i $$-0.185359\pi$$
−0.893878 + 0.448310i $$0.852026\pi$$
$$198$$ 0 0
$$199$$ −5.13665 + 8.89694i −0.364127 + 0.630687i −0.988636 0.150331i $$-0.951966\pi$$
0.624508 + 0.781018i $$0.285299\pi$$
$$200$$ −1.78064 + 4.67219i −0.125910 + 0.330374i
$$201$$ 0 0
$$202$$ 6.11911 10.5986i 0.430539 0.745716i
$$203$$ −41.9459 −2.94403
$$204$$ 0 0
$$205$$ 6.07583 + 2.88908i 0.424355 + 0.201782i
$$206$$ 3.24884 1.87572i 0.226357 0.130688i
$$207$$ 0 0
$$208$$ −3.05692 1.91187i −0.211959 0.132564i
$$209$$ 1.59401 0.110260
$$210$$ 0 0
$$211$$ 12.1905 + 21.1145i 0.839226 + 1.45358i 0.890543 + 0.454900i $$0.150325\pi$$
−0.0513166 + 0.998682i $$0.516342\pi$$
$$212$$ 8.17008 + 4.71700i 0.561124 + 0.323965i
$$213$$ 0 0
$$214$$ −14.3904 8.30831i −0.983708 0.567944i
$$215$$ 1.21696 + 15.2293i 0.0829959 + 1.03863i
$$216$$ 0 0
$$217$$ 26.7766 + 15.4595i 1.81772 + 1.04946i
$$218$$ 9.62290 5.55578i 0.651745 0.376285i
$$219$$ 0 0
$$220$$ −4.33848 + 2.98942i −0.292500 + 0.201547i
$$221$$ 10.8414 + 0.382907i 0.729272 + 0.0257571i
$$222$$ 0 0
$$223$$ −2.31792 4.01476i −0.155220 0.268848i 0.777919 0.628364i $$-0.216275\pi$$
−0.933139 + 0.359516i $$0.882942\pi$$
$$224$$ 2.17283 + 3.76344i 0.145178 + 0.251456i
$$225$$ 0 0
$$226$$ 15.6600i 1.04169i
$$227$$ −8.89213 + 15.4016i −0.590192 + 1.02224i 0.404015 + 0.914753i $$0.367615\pi$$
−0.994206 + 0.107489i $$0.965719\pi$$
$$228$$ 0 0
$$229$$ 15.3361i 1.01344i 0.862111 + 0.506720i $$0.169142\pi$$
−0.862111 + 0.506720i $$0.830858\pi$$
$$230$$ 1.14846 + 14.3722i 0.0757274 + 0.947672i
$$231$$ 0 0
$$232$$ −4.82620 8.35922i −0.316855 0.548809i
$$233$$ 7.75548i 0.508079i 0.967194 + 0.254039i $$0.0817593\pi$$
−0.967194 + 0.254039i $$0.918241\pi$$
$$234$$ 0 0
$$235$$ 7.12430 + 10.3393i 0.464738 + 0.674463i
$$236$$ −4.56364 + 2.63482i −0.297068 + 0.171512i
$$237$$ 0 0
$$238$$ −11.3232 6.53747i −0.733975 0.423761i
$$239$$ 18.6409i 1.20578i 0.797824 + 0.602890i $$0.205984\pi$$
−0.797824 + 0.602890i $$0.794016\pi$$
$$240$$ 0 0
$$241$$ −2.65884 1.53508i −0.171271 0.0988833i 0.411914 0.911223i $$-0.364860\pi$$
−0.583185 + 0.812339i $$0.698194\pi$$
$$242$$ 5.44819 0.350223
$$243$$ 0 0
$$244$$ 2.15646 + 3.73509i 0.138053 + 0.239115i
$$245$$ 11.4120 23.9999i 0.729088 1.53330i
$$246$$ 0 0
$$247$$ 2.43766 + 0.0860957i 0.155105 + 0.00547814i
$$248$$ 7.11493i 0.451798i
$$249$$ 0 0
$$250$$ 7.72518 + 8.08218i 0.488583 + 0.511162i
$$251$$ 3.56404 6.17309i 0.224960 0.389642i −0.731347 0.682005i $$-0.761108\pi$$
0.956307 + 0.292363i $$0.0944415\pi$$
$$252$$ 0 0
$$253$$ −7.59637 + 13.1573i −0.477580 + 0.827193i
$$254$$ 11.7820 + 6.80236i 0.739270 + 0.426818i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 12.3353 7.12178i 0.769454 0.444244i −0.0632261 0.997999i $$-0.520139\pi$$
0.832680 + 0.553755i $$0.186806\pi$$
$$258$$ 0 0
$$259$$ −32.5198 −2.02068
$$260$$ −6.79616 + 4.33730i −0.421480 + 0.268988i
$$261$$ 0 0
$$262$$ 5.10611 + 8.84404i 0.315457 + 0.546387i
$$263$$ 13.3385 7.70101i 0.822490 0.474865i −0.0287845 0.999586i $$-0.509164\pi$$
0.851274 + 0.524721i $$0.175830\pi$$
$$264$$ 0 0
$$265$$ 17.3707 11.9692i 1.06707 0.735264i
$$266$$ −2.54600 1.46993i −0.156105 0.0901273i
$$267$$ 0 0
$$268$$ −5.82658 −0.355915
$$269$$ −13.3134 + 23.0595i −0.811732 + 1.40596i 0.0999185 + 0.994996i $$0.468142\pi$$
−0.911651 + 0.410966i $$0.865192\pi$$
$$270$$ 0 0
$$271$$ −6.66899 + 3.85034i −0.405112 + 0.233892i −0.688687 0.725058i $$-0.741813\pi$$
0.283575 + 0.958950i $$0.408479\pi$$
$$272$$ 3.00874i 0.182432i
$$273$$ 0 0
$$274$$ 12.4138 0.749943
$$275$$ 1.87089 + 11.6316i 0.112819 + 0.701414i
$$276$$ 0 0
$$277$$ −12.3861 7.15114i −0.744211 0.429671i 0.0793871 0.996844i $$-0.474704\pi$$
−0.823599 + 0.567173i $$0.808037\pi$$
$$278$$ 15.6183 0.936723
$$279$$ 0 0
$$280$$ 9.68629 0.774021i 0.578867 0.0462566i
$$281$$ 7.96746i 0.475299i 0.971351 + 0.237649i $$0.0763769\pi$$
−0.971351 + 0.237649i $$0.923623\pi$$
$$282$$ 0 0
$$283$$ 12.7095 7.33785i 0.755503 0.436190i −0.0721756 0.997392i $$-0.522994\pi$$
0.827679 + 0.561202i $$0.189661\pi$$
$$284$$ 2.52520 1.45793i 0.149843 0.0865120i
$$285$$ 0 0
$$286$$ −8.49021 0.299865i −0.502036 0.0177314i
$$287$$ 13.0749i 0.771789i
$$288$$ 0 0
$$289$$ −3.97374 6.88273i −0.233750 0.404866i
$$290$$ −21.5148 + 1.71923i −1.26339 + 0.100956i
$$291$$ 0 0
$$292$$ −3.83902 + 6.64938i −0.224662 + 0.389125i
$$293$$ −3.43198 + 5.94436i −0.200498 + 0.347273i −0.948689 0.316210i $$-0.897589\pi$$
0.748191 + 0.663484i $$0.230923\pi$$
$$294$$ 0 0
$$295$$ 0.938596 + 11.7458i 0.0546472 + 0.683868i
$$296$$ −3.74165 6.48073i −0.217479 0.376685i
$$297$$ 0 0
$$298$$ 19.5265i 1.13114i
$$299$$ −12.3275 + 19.7108i −0.712921 + 1.13990i
$$300$$ 0 0
$$301$$ 25.7136 14.8458i 1.48211 0.855696i
$$302$$ −9.96166 + 5.75137i −0.573229 + 0.330954i
$$303$$ 0 0
$$304$$ 0.676507i 0.0388004i
$$305$$ 9.61333 0.768190i 0.550458 0.0439865i
$$306$$ 0 0
$$307$$ −10.9917 −0.627328 −0.313664 0.949534i $$-0.601557\pi$$
−0.313664 + 0.949534i $$0.601557\pi$$
$$308$$ 8.86753 + 5.11967i 0.505275 + 0.291720i
$$309$$ 0 0
$$310$$ 14.3678 + 6.83197i 0.816039 + 0.388030i
$$311$$ 13.9044 0.788446 0.394223 0.919015i $$-0.371014\pi$$
0.394223 + 0.919015i $$0.371014\pi$$
$$312$$ 0 0
$$313$$ 14.1734i 0.801130i −0.916268 0.400565i $$-0.868814\pi$$
0.916268 0.400565i $$-0.131186\pi$$
$$314$$ 3.87629 2.23798i 0.218752 0.126296i
$$315$$ 0 0
$$316$$ 1.87260 3.24343i 0.105342 0.182457i
$$317$$ −3.20808 −0.180184 −0.0900920 0.995933i $$-0.528716\pi$$
−0.0900920 + 0.995933i $$0.528716\pi$$
$$318$$ 0 0
$$319$$ −19.6962 11.3716i −1.10278 0.636688i
$$320$$ 1.26873 + 1.84128i 0.0709243 + 0.102931i
$$321$$ 0 0
$$322$$ 24.2664 14.0102i 1.35231 0.780757i
$$323$$ 1.01772 + 1.76274i 0.0566273 + 0.0980813i
$$324$$ 0 0
$$325$$ 2.23284 + 17.8889i 0.123856 + 0.992300i
$$326$$ 7.75548 0.429537
$$327$$ 0 0
$$328$$ 2.60564 1.50437i 0.143873 0.0830649i
$$329$$ 12.2010 21.1328i 0.672665 1.16509i
$$330$$ 0 0
$$331$$ −22.3066 12.8787i −1.22608 0.707878i −0.259873 0.965643i $$-0.583681\pi$$
−0.966208 + 0.257765i $$0.917014\pi$$
$$332$$ −5.17783 + 8.96827i −0.284170 + 0.492198i
$$333$$ 0 0
$$334$$ 0.339021 0.587202i 0.0185504 0.0321302i
$$335$$ −5.59485 + 11.7662i −0.305680 + 0.642854i
$$336$$ 0 0
$$337$$ 0.772078i 0.0420578i −0.999779 0.0210289i $$-0.993306\pi$$
0.999779 0.0210289i $$-0.00669420\pi$$
$$338$$ −12.9676 0.917149i −0.705345 0.0498863i
$$339$$ 0 0
$$340$$ −6.07583 2.88908i −0.329508 0.156682i
$$341$$ 8.38219 + 14.5184i 0.453921 + 0.786215i
$$342$$ 0 0
$$343$$ −21.2271 −1.14616
$$344$$ 5.91710 + 3.41624i 0.319028 + 0.184191i
$$345$$ 0 0
$$346$$ 0.721948i 0.0388122i
$$347$$ 21.7856 + 12.5779i 1.16951 + 0.675218i 0.953565 0.301188i $$-0.0973830\pi$$
0.215946 + 0.976405i $$0.430716\pi$$
$$348$$ 0 0
$$349$$ −23.6602 + 13.6602i −1.26650 + 0.731214i −0.974324 0.225151i $$-0.927713\pi$$
−0.292176 + 0.956365i $$0.594379\pi$$
$$350$$ 7.73802 20.3037i 0.413614 1.08528i
$$351$$ 0 0
$$352$$ 2.35623i 0.125587i
$$353$$ 3.75948 + 6.51161i 0.200097 + 0.346578i 0.948559 0.316599i $$-0.102541\pi$$
−0.748462 + 0.663177i $$0.769208\pi$$
$$354$$ 0 0
$$355$$ −0.519354 6.49932i −0.0275644 0.344948i
$$356$$ 4.79440i 0.254103i
$$357$$ 0 0
$$358$$ −3.18673 + 5.51958i −0.168424 + 0.291719i
$$359$$ 10.8402i 0.572124i −0.958211 0.286062i $$-0.907654\pi$$
0.958211 0.286062i $$-0.0923463\pi$$
$$360$$ 0 0
$$361$$ −9.27117 16.0581i −0.487956 0.845165i
$$362$$ −11.0107 19.0711i −0.578708 1.00235i
$$363$$ 0 0
$$364$$ 13.2843 + 8.30831i 0.696287 + 0.435474i
$$365$$ 9.74138 + 14.1374i 0.509887 + 0.739987i
$$366$$ 0 0
$$367$$ −6.50838 + 3.75761i −0.339735 + 0.196146i −0.660155 0.751130i $$-0.729509\pi$$
0.320420 + 0.947276i $$0.396176\pi$$
$$368$$ 5.58405 + 3.22396i 0.291089 + 0.168060i
$$369$$ 0 0
$$370$$ −16.6800 + 1.33288i −0.867151 + 0.0692931i
$$371$$ −35.5043 20.4984i −1.84329 1.06423i
$$372$$ 0 0
$$373$$ −19.8135 11.4393i −1.02590 0.592305i −0.110095 0.993921i $$-0.535115\pi$$
−0.915808 + 0.401616i $$0.868449\pi$$
$$374$$ −3.54464 6.13949i −0.183289 0.317466i
$$375$$ 0 0
$$376$$ 5.61529 0.289586
$$377$$ −29.5066 18.4541i −1.51967 0.950434i
$$378$$ 0 0
$$379$$ −22.6152 + 13.0569i −1.16166 + 0.670687i −0.951702 0.307022i $$-0.900667\pi$$
−0.209962 + 0.977710i $$0.567334\pi$$
$$380$$ −1.36614 0.649603i −0.0700813 0.0333239i
$$381$$ 0 0
$$382$$ −0.586882 −0.0300275
$$383$$ 6.84652 11.8585i 0.349841 0.605942i −0.636380 0.771376i $$-0.719569\pi$$
0.986221 + 0.165434i $$0.0529024\pi$$
$$384$$ 0 0
$$385$$ 18.8535 12.9910i 0.960864 0.662082i
$$386$$ −11.3135 + 19.5955i −0.575842 + 0.997387i
$$387$$ 0 0
$$388$$ 8.17066 + 14.1520i 0.414802 + 0.718459i
$$389$$ −24.9403 −1.26452 −0.632261 0.774755i $$-0.717873\pi$$
−0.632261 + 0.774755i $$0.717873\pi$$
$$390$$ 0 0
$$391$$ −19.4001 −0.981104
$$392$$ −5.94234 10.2924i −0.300134 0.519847i
$$393$$ 0 0
$$394$$ −0.823770 + 1.42681i −0.0415009 + 0.0718817i
$$395$$ −4.75165 6.89595i −0.239081 0.346973i
$$396$$ 0 0
$$397$$ −14.5517 + 25.2043i −0.730328 + 1.26497i 0.226415 + 0.974031i $$0.427300\pi$$
−0.956743 + 0.290934i $$0.906034\pi$$
$$398$$ 10.2733 0.514954
$$399$$ 0 0
$$400$$ 4.93655 0.794019i 0.246828 0.0397009i
$$401$$ 14.4596 8.34823i 0.722076 0.416891i −0.0934404 0.995625i $$-0.529786\pi$$
0.815516 + 0.578734i $$0.196453\pi$$
$$402$$ 0 0
$$403$$ 12.0345 + 22.6552i 0.599479 + 1.12854i
$$404$$ −12.2382 −0.608875
$$405$$ 0 0
$$406$$ 20.9730 + 36.3262i 1.04087 + 1.80284i
$$407$$ −15.2701 8.81618i −0.756909 0.437002i
$$408$$ 0 0
$$409$$ 21.3140 + 12.3056i 1.05391 + 0.608475i 0.923741 0.383017i $$-0.125115\pi$$
0.130168 + 0.991492i $$0.458448\pi$$
$$410$$ −0.535898 6.70637i −0.0264661 0.331204i
$$411$$ 0 0
$$412$$ −3.24884 1.87572i −0.160059 0.0924100i
$$413$$ 19.8320 11.4500i 0.975868 0.563418i
$$414$$ 0 0
$$415$$ 13.1386 + 19.0677i 0.644947 + 0.935996i
$$416$$ −0.127265 + 3.60330i −0.00623968 + 0.176667i
$$417$$ 0 0
$$418$$ −0.797003 1.38045i −0.0389827 0.0675200i
$$419$$ 13.5527 + 23.4739i 0.662091 + 1.14678i 0.980065 + 0.198676i $$0.0636643\pi$$
−0.317974 + 0.948099i $$0.603002\pi$$
$$420$$ 0 0
$$421$$ 32.9996i 1.60830i 0.594425 + 0.804151i $$0.297380\pi$$
−0.594425 + 0.804151i $$0.702620\pi$$
$$422$$ 12.1905 21.1145i 0.593422 1.02784i
$$423$$ 0 0
$$424$$ 9.43400i 0.458156i
$$425$$ −11.6684 + 9.49533i −0.566000 + 0.460591i
$$426$$ 0 0
$$427$$ −9.37121 16.2314i −0.453505 0.785493i
$$428$$ 16.6166i 0.803194i
$$429$$ 0 0
$$430$$ 12.5805 8.66858i 0.606686 0.418036i
$$431$$ −7.45678 + 4.30517i −0.359180 + 0.207373i −0.668721 0.743513i $$-0.733158\pi$$
0.309541 + 0.950886i $$0.399825\pi$$
$$432$$ 0 0
$$433$$ 2.99201 + 1.72744i 0.143787 + 0.0830155i 0.570168 0.821528i $$-0.306878\pi$$
−0.426381 + 0.904544i $$0.640212\pi$$
$$434$$ 30.9190i 1.48416i
$$435$$ 0 0
$$436$$ −9.62290 5.55578i −0.460853 0.266074i
$$437$$ −4.36206 −0.208666
$$438$$ 0 0
$$439$$ −12.1229 20.9974i −0.578593 1.00215i −0.995641 0.0932675i $$-0.970269\pi$$
0.417049 0.908884i $$-0.363064\pi$$
$$440$$ 4.75816 + 2.26252i 0.226836 + 0.107861i
$$441$$ 0 0
$$442$$ −5.08909 9.58038i −0.242064 0.455692i
$$443$$ 13.1629i 0.625390i 0.949854 + 0.312695i $$0.101232\pi$$
−0.949854 + 0.312695i $$0.898768\pi$$
$$444$$ 0 0
$$445$$ −9.68180 4.60373i −0.458961 0.218238i
$$446$$ −2.31792 + 4.01476i −0.109757 + 0.190104i
$$447$$ 0 0
$$448$$ 2.17283 3.76344i 0.102656 0.177806i
$$449$$ −2.17774 1.25732i −0.102774 0.0593365i 0.447732 0.894168i $$-0.352232\pi$$
−0.550506 + 0.834831i $$0.685565\pi$$
$$450$$ 0 0
$$451$$ 3.54464 6.13949i 0.166910 0.289097i
$$452$$ 13.5620 7.83002i 0.637903 0.368293i
$$453$$ 0 0
$$454$$ 17.7843 0.834657
$$455$$ 29.5338 18.8484i 1.38456 0.883626i
$$456$$ 0 0
$$457$$ −5.38493 9.32698i −0.251897 0.436298i 0.712151 0.702026i $$-0.247721\pi$$
−0.964048 + 0.265728i $$0.914388\pi$$
$$458$$ 13.2815 7.66806i 0.620602 0.358305i
$$459$$ 0 0
$$460$$ 11.8724 8.18068i 0.553554 0.381426i
$$461$$ −10.2984 5.94576i −0.479642 0.276922i 0.240625 0.970618i $$-0.422648\pi$$
−0.720267 + 0.693697i $$0.755981\pi$$
$$462$$ 0 0
$$463$$ −29.9462 −1.39172 −0.695860 0.718178i $$-0.744976\pi$$
−0.695860 + 0.718178i $$0.744976\pi$$
$$464$$ −4.82620 + 8.35922i −0.224051 + 0.388067i
$$465$$ 0 0
$$466$$ 6.71645 3.87774i 0.311133 0.179633i
$$467$$ 21.8940i 1.01313i 0.862201 + 0.506566i $$0.169085\pi$$
−0.862201 + 0.506566i $$0.830915\pi$$
$$468$$ 0 0
$$469$$ 25.3203 1.16918
$$470$$ 5.39197 11.3395i 0.248713 0.523051i
$$471$$ 0 0
$$472$$ 4.56364 + 2.63482i 0.210059 + 0.121277i
$$473$$ 16.0989 0.740227
$$474$$ 0 0
$$475$$ −2.62361 + 2.13500i −0.120379 + 0.0979605i
$$476$$ 13.0749i 0.599288i
$$477$$ 0 0
$$478$$ 16.1435 9.32045i 0.738386 0.426307i
$$479$$ 7.90106 4.56168i 0.361009 0.208429i −0.308514 0.951220i $$-0.599832\pi$$
0.669523 + 0.742791i $$0.266498\pi$$
$$480$$ 0 0
$$481$$ −22.8758 14.3071i −1.04305 0.652346i
$$482$$ 3.07016i 0.139842i
$$483$$ 0 0
$$484$$ −2.72410 4.71827i −0.123823 0.214467i
$$485$$ 36.4242 2.91062i 1.65394 0.132164i
$$486$$ 0 0
$$487$$ 10.8587 18.8079i 0.492056 0.852265i −0.507902 0.861415i $$-0.669579\pi$$
0.999958 + 0.00914916i $$0.00291231\pi$$
$$488$$ 2.15646 3.73509i 0.0976183 0.169080i
$$489$$ 0 0
$$490$$ −26.4905 + 2.11683i −1.19672 + 0.0956285i
$$491$$ −16.5438 28.6548i −0.746613 1.29317i −0.949437 0.313957i $$-0.898345\pi$$
0.202824 0.979215i $$-0.434988\pi$$
$$492$$ 0 0
$$493$$ 29.0415i 1.30796i
$$494$$ −1.14427 2.15412i −0.0514831 0.0969187i
$$495$$ 0 0
$$496$$ 6.16171 3.55746i 0.276669 0.159735i
$$497$$ −10.9736 + 6.33564i −0.492235 + 0.284192i
$$498$$ 0 0
$$499$$ 10.4889i 0.469546i −0.972050 0.234773i $$-0.924565\pi$$
0.972050 0.234773i $$-0.0754347\pi$$
$$500$$ 3.13679 10.7313i 0.140281 0.479918i
$$501$$ 0 0
$$502$$ −7.12807 −0.318142
$$503$$ 7.14818 + 4.12700i 0.318722 + 0.184014i 0.650823 0.759230i $$-0.274424\pi$$
−0.332101 + 0.943244i $$0.607757\pi$$
$$504$$ 0 0
$$505$$ −11.7515 + 24.7138i −0.522936 + 1.09975i
$$506$$ 15.1927 0.675400
$$507$$ 0 0
$$508$$ 13.6047i 0.603611i
$$509$$ −5.84526 + 3.37476i −0.259087 + 0.149584i −0.623918 0.781490i $$-0.714460\pi$$
0.364831 + 0.931074i $$0.381127\pi$$
$$510$$ 0 0
$$511$$ 16.6830 28.8959i 0.738014 1.27828i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −12.3353 7.12178i −0.544086 0.314128i
$$515$$ −6.90745 + 4.75957i −0.304379 + 0.209732i
$$516$$ 0 0
$$517$$ 11.4583 6.61545i 0.503935 0.290947i
$$518$$ 16.2599 + 28.1630i 0.714419 + 1.23741i
$$519$$ 0 0
$$520$$ 7.15429 + 3.71700i 0.313737 + 0.163001i
$$521$$ 30.4048 1.33206 0.666029 0.745926i $$-0.267993\pi$$
0.666029 + 0.745926i $$0.267993\pi$$
$$522$$ 0 0
$$523$$ −2.72235 + 1.57175i −0.119040 + 0.0687279i −0.558338 0.829614i $$-0.688561\pi$$
0.439298 + 0.898342i $$0.355227\pi$$
$$524$$ 5.10611 8.84404i 0.223062 0.386354i
$$525$$ 0 0
$$526$$ −13.3385 7.70101i −0.581588 0.335780i
$$527$$ −10.7035 + 18.5390i −0.466251 + 0.807570i
$$528$$ 0 0
$$529$$ 9.28778 16.0869i 0.403816 0.699431i
$$530$$ −19.0510 9.05881i −0.827522 0.393490i
$$531$$ 0 0
$$532$$ 2.93986i 0.127459i
$$533$$ 5.75231 9.19748i 0.249160 0.398387i
$$534$$ 0 0
$$535$$ 33.5555 + 15.9558i 1.45073 + 0.689828i
$$536$$ 2.91329 + 5.04596i 0.125835 + 0.217952i
$$537$$ 0 0
$$538$$ 26.6268 1.14796
$$539$$ −24.2513 14.0015i −1.04458 0.603088i
$$540$$ 0 0
$$541$$ 17.6144i 0.757301i 0.925540 + 0.378650i $$0.123612\pi$$
−0.925540 + 0.378650i $$0.876388\pi$$
$$542$$ 6.66899 + 3.85034i 0.286458 + 0.165386i
$$543$$ 0 0
$$544$$ −2.60564 + 1.50437i −0.111716 + 0.0644993i
$$545$$ −20.4595 + 14.0976i −0.876390 + 0.603875i
$$546$$ 0 0
$$547$$ 40.8067i 1.74477i 0.488820 + 0.872385i $$0.337428\pi$$
−0.488820 + 0.872385i $$0.662572\pi$$
$$548$$ −6.20689 10.7506i −0.265145 0.459245i
$$549$$ 0 0
$$550$$ 9.13785 7.43606i 0.389639 0.317075i
$$551$$ 6.52991i 0.278184i
$$552$$ 0 0
$$553$$ −8.13765 + 14.0948i −0.346048 + 0.599373i
$$554$$ 14.3023i 0.607646i
$$555$$ 0 0
$$556$$ −7.80915 13.5258i −0.331182 0.573623i
$$557$$ 12.6109 + 21.8427i 0.534340 + 0.925504i 0.999195 + 0.0401170i $$0.0127731\pi$$
−0.464855 + 0.885387i $$0.653894\pi$$
$$558$$ 0 0
$$559$$ 24.6195 + 0.869535i 1.04129 + 0.0367774i
$$560$$ −5.51347 8.00157i −0.232987 0.338128i
$$561$$ 0 0
$$562$$ 6.90002 3.98373i 0.291060 0.168043i
$$563$$ −31.5356 18.2071i −1.32907 0.767337i −0.343912 0.939002i $$-0.611752\pi$$
−0.985155 + 0.171664i $$0.945086\pi$$
$$564$$ 0 0
$$565$$ −2.78927 34.9057i −0.117346 1.46849i
$$566$$ −12.7095 7.33785i −0.534222 0.308433i
$$567$$ 0 0
$$568$$ −2.52520 1.45793i −0.105955 0.0611732i
$$569$$ 13.6768 + 23.6888i 0.573360 + 0.993088i 0.996218 + 0.0868922i $$0.0276936\pi$$
−0.422858 + 0.906196i $$0.638973\pi$$
$$570$$ 0 0
$$571$$ 45.7020 1.91257 0.956285 0.292438i $$-0.0944664\pi$$
0.956285 + 0.292438i $$0.0944664\pi$$
$$572$$ 3.98541 + 7.50267i 0.166638 + 0.313702i
$$573$$ 0 0
$$574$$ −11.3232 + 6.53747i −0.472622 + 0.272869i
$$575$$ −5.11976 31.8304i −0.213509 1.32742i
$$576$$ 0 0
$$577$$ −31.1697 −1.29761 −0.648806 0.760954i $$-0.724731\pi$$
−0.648806 + 0.760954i $$0.724731\pi$$
$$578$$ −3.97374 + 6.88273i −0.165286 + 0.286284i
$$579$$ 0 0
$$580$$ 12.2463 + 17.7728i 0.508500 + 0.737974i
$$581$$ 22.5011 38.9730i 0.933501 1.61687i
$$582$$ 0 0
$$583$$ −11.1143 19.2506i −0.460308 0.797278i
$$584$$ 7.67804 0.317720
$$585$$ 0 0
$$586$$ 6.86396 0.283547
$$587$$ 7.61411 + 13.1880i 0.314268 + 0.544328i 0.979282 0.202503i $$-0.0649076\pi$$
−0.665014 + 0.746831i $$0.731574\pi$$
$$588$$ 0 0
$$589$$ −2.40665 + 4.16844i −0.0991643 + 0.171758i
$$590$$ 9.70288 6.68576i 0.399461 0.275248i
$$591$$ 0 0
$$592$$ −3.74165 + 6.48073i −0.153781 + 0.266356i
$$593$$ −15.1921 −0.623865 −0.311933 0.950104i $$-0.600976\pi$$
−0.311933 + 0.950104i $$0.600976\pi$$
$$594$$ 0 0
$$595$$ 26.4035 + 12.5549i 1.08244 + 0.514703i
$$596$$ 16.9104 9.76324i 0.692678 0.399918i
$$597$$ 0 0
$$598$$ 23.2338 + 0.820594i 0.950100 + 0.0335566i
$$599$$ −4.34655 −0.177595 −0.0887975 0.996050i $$-0.528302\pi$$
−0.0887975 + 0.996050i $$0.528302\pi$$
$$600$$ 0 0
$$601$$ −5.14622 8.91351i −0.209918 0.363590i 0.741770 0.670654i $$-0.233987\pi$$
−0.951689 + 0.307065i $$0.900653\pi$$
$$602$$ −25.7136 14.8458i −1.04801 0.605069i
$$603$$ 0 0
$$604$$ 9.96166 + 5.75137i 0.405334 + 0.234020i
$$605$$ −12.1438 + 0.970399i −0.493716 + 0.0394523i
$$606$$ 0 0
$$607$$ 37.6094 + 21.7138i 1.52652 + 0.881335i 0.999504 + 0.0314772i $$0.0100212\pi$$
0.527012 + 0.849858i $$0.323312\pi$$
$$608$$ −0.585872 + 0.338254i −0.0237603 + 0.0137180i
$$609$$ 0 0
$$610$$ −5.47194 7.94129i −0.221552 0.321534i
$$611$$ 17.8801 9.49791i 0.723352 0.384244i
$$612$$ 0 0
$$613$$ −16.3258 28.2771i −0.659392 1.14210i −0.980773 0.195150i $$-0.937481\pi$$
0.321382 0.946950i $$-0.395853\pi$$
$$614$$ 5.49584 + 9.51907i 0.221794 + 0.384159i
$$615$$ 0 0
$$616$$ 10.2393i 0.412555i
$$617$$ −4.83488 + 8.37426i −0.194645 + 0.337135i −0.946784 0.321869i $$-0.895689\pi$$
0.752139 + 0.659004i $$0.229022\pi$$
$$618$$ 0 0
$$619$$ 5.20064i 0.209031i −0.994523 0.104516i $$-0.966671\pi$$
0.994523 0.104516i $$-0.0333292\pi$$
$$620$$ −1.26727 15.8589i −0.0508947 0.636909i
$$621$$ 0 0
$$622$$ −6.95220 12.0416i −0.278758 0.482823i
$$623$$ 20.8348i 0.834729i
$$624$$ 0 0
$$625$$ −18.6587 16.6389i −0.746347 0.665557i
$$626$$ −12.2746 + 7.08672i −0.490590 + 0.283242i
$$627$$ 0 0
$$628$$ −3.87629 2.23798i −0.154681 0.0893050i
$$629$$ 22.5153i 0.897743i
$$630$$ 0 0
$$631$$ −6.86811 3.96531i −0.273415 0.157856i 0.357023 0.934095i $$-0.383792\pi$$
−0.630439 + 0.776239i $$0.717125\pi$$
$$632$$ −3.74519 −0.148976
$$633$$ 0 0
$$634$$ 1.60404 + 2.77828i 0.0637046 + 0.110340i
$$635$$ −27.4733 13.0637i −1.09024 0.518415i
$$636$$ 0 0
$$637$$ −36.3305 22.7219i −1.43947 0.900276i
$$638$$ 22.7432i 0.900413i
$$639$$ 0 0
$$640$$ 0.960230 2.01940i 0.0379564 0.0798236i
$$641$$ 1.69937 2.94340i 0.0671212 0.116257i −0.830512 0.557001i $$-0.811952\pi$$
0.897633 + 0.440744i $$0.145285\pi$$
$$642$$ 0 0
$$643$$ −4.69916 + 8.13918i −0.185317 + 0.320978i −0.943683 0.330851i $$-0.892664\pi$$
0.758367 + 0.651828i $$0.225998\pi$$
$$644$$ −24.2664 14.0102i −0.956228 0.552079i
$$645$$ 0 0
$$646$$ 1.01772 1.76274i 0.0400415 0.0693540i
$$647$$ −34.6972 + 20.0324i −1.36409 + 0.787555i −0.990165 0.139905i $$-0.955320\pi$$
−0.373921 + 0.927461i $$0.621987\pi$$
$$648$$ 0 0
$$649$$ 12.4165 0.487389
$$650$$ 14.3759 10.8782i 0.563868 0.426677i
$$651$$ 0 0
$$652$$ −3.87774 6.71645i −0.151864 0.263036i
$$653$$ 27.1900 15.6981i 1.06403 0.614316i 0.137483 0.990504i $$-0.456099\pi$$
0.926543 + 0.376189i $$0.122766\pi$$
$$654$$ 0 0
$$655$$ −12.9566 18.8036i −0.506255 0.734717i
$$656$$ −2.60564 1.50437i −0.101733 0.0587358i
$$657$$ 0 0
$$658$$ −24.4021 −0.951292
$$659$$ −9.48950 + 16.4363i −0.369659 + 0.640268i −0.989512 0.144450i $$-0.953859\pi$$
0.619853 + 0.784718i $$0.287192\pi$$
$$660$$ 0 0
$$661$$ 11.4484 6.60972i 0.445290 0.257088i −0.260549 0.965461i $$-0.583904\pi$$
0.705839 + 0.708372i $$0.250570\pi$$
$$662$$ 25.7574i 1.00109i
$$663$$ 0 0
$$664$$ 10.3557 0.401878
$$665$$ 5.93675 + 2.82295i 0.230217 + 0.109469i
$$666$$ 0 0
$$667$$ 53.8995 + 31.1189i 2.08700 + 1.20493i
$$668$$ −0.678042 −0.0262342
$$669$$ 0 0
$$670$$ 12.9872 1.03779i 0.501740 0.0400935i
$$671$$ 10.1622i 0.392308i
$$672$$ 0 0
$$673$$ −7.44817 + 4.30020i −0.287106 + 0.165761i −0.636636 0.771164i $$-0.719675\pi$$
0.349530 + 0.936925i $$0.386341\pi$$
$$674$$ −0.668639 + 0.386039i −0.0257550 + 0.0148697i
$$675$$ 0 0
$$676$$ 5.68953 + 11.6889i 0.218828 + 0.449571i
$$677$$ 25.8539i 0.993646i −0.867852 0.496823i $$-0.834500\pi$$
0.867852 0.496823i $$-0.165500\pi$$
$$678$$ 0 0
$$679$$ −35.5068 61.4997i −1.36263 2.36014i
$$680$$ 0.535898 + 6.70637i 0.0205508 + 0.257177i
$$681$$ 0 0
$$682$$ 8.38219 14.5184i 0.320971 0.555938i
$$683$$ 10.4524 18.1041i 0.399950 0.692734i −0.593769 0.804636i $$-0.702361\pi$$
0.993719 + 0.111901i $$0.0356941\pi$$
$$684$$ 0 0
$$685$$ −27.6698 + 2.21107i −1.05721 + 0.0844805i
$$686$$ 10.6136 + 18.3832i 0.405228 + 0.701875i
$$687$$ 0 0
$$688$$ 6.83247i 0.260486i
$$689$$ −15.9570 30.0396i −0.607914 1.14442i
$$690$$ 0 0
$$691$$ −42.3440 + 24.4473i −1.61084 + 0.930019i −0.621665 + 0.783283i $$0.713543\pi$$
−0.989176 + 0.146736i $$0.953123\pi$$
$$692$$ −0.625226 + 0.360974i −0.0237675 + 0.0137222i
$$693$$ 0 0
$$694$$ 25.1558i 0.954902i
$$695$$ −34.8126 + 2.78184i −1.32052 + 0.105521i
$$696$$ 0 0
$$697$$ 9.05251 0.342888
$$698$$ 23.6602 + 13.6602i 0.895551 + 0.517046i
$$699$$ 0 0
$$700$$ −21.4525 + 3.45053i −0.810829 + 0.130418i
$$701$$ −31.9805 −1.20789 −0.603944 0.797027i $$-0.706405\pi$$
−0.603944 + 0.797027i $$0.706405\pi$$
$$702$$ 0 0
$$703$$ 5.06250i 0.190936i
$$704$$ 2.04055 1.17811i 0.0769062 0.0444018i
$$705$$ 0 0
$$706$$ 3.75948 6.51161i 0.141490 0.245068i
$$707$$ 53.1831 2.00016
$$708$$ 0 0
$$709$$ −5.42026 3.12939i −0.203562 0.117527i 0.394754 0.918787i $$-0.370830\pi$$
−0.598316 + 0.801260i $$0.704163\pi$$
$$710$$ −5.36890 + 3.69944i −0.201491 + 0.138837i
$$711$$ 0 0
$$712$$ −4.15208 + 2.39720i −0.155606 + 0.0898389i
$$713$$ −22.9382 39.7301i −0.859043 1.48791i
$$714$$ 0 0
$$715$$ 18.9778 0.843835i 0.709728 0.0315577i
$$716$$ 6.37346 0.238187
$$717$$ 0 0
$$718$$ −9.38789 + 5.42010i −0.350353 + 0.202276i
$$719$$ 9.52308 16.4945i 0.355151 0.615140i −0.631993 0.774974i $$-0.717763\pi$$
0.987144 + 0.159835i $$0.0510961\pi$$
$$720$$ 0 0
$$721$$ 14.1183 + 8.15122i 0.525794 + 0.303567i
$$722$$ −9.27117 + 16.0581i −0.345037 + 0.597622i
$$723$$ 0 0
$$724$$ −11.0107 + 19.0711i −0.409209 + 0.708770i
$$725$$ 47.6495 7.66418i 1.76966 0.284640i
$$726$$ 0 0
$$727$$ 28.2602i 1.04811i −0.851684 0.524056i $$-0.824418\pi$$
0.851684 0.524056i $$-0.175582\pi$$
$$728$$ 0.553049 15.6587i 0.0204974 0.580350i
$$729$$ 0 0
$$730$$ 7.37269 15.5050i 0.272875 0.573866i
$$731$$ 10.2786 + 17.8030i 0.380166 + 0.658468i
$$732$$ 0 0
$$733$$ 5.28165 0.195082 0.0975410 0.995232i $$-0.468902\pi$$
0.0975410 + 0.995232i $$0.468902\pi$$
$$734$$ 6.50838 + 3.75761i 0.240229 + 0.138696i
$$735$$ 0 0
$$736$$ 6.44791i 0.237673i
$$737$$ 11.8894 + 6.86437i 0.437953 + 0.252852i
$$738$$ 0 0
$$739$$ 34.5736 19.9611i 1.27181 0.734280i 0.296482 0.955038i $$-0.404187\pi$$
0.975329 + 0.220758i $$0.0708533\pi$$
$$740$$ 9.49430 + 13.7789i 0.349018 + 0.506521i
$$741$$ 0 0
$$742$$ 40.9969i 1.50504i
$$743$$ −9.28543 16.0828i −0.340650 0.590022i 0.643904 0.765106i $$-0.277314\pi$$
−0.984553 + 0.175084i $$0.943980\pi$$
$$744$$ 0 0
$$745$$ −3.47794 43.5238i −0.127422 1.59459i
$$746$$ 22.8786i 0.837646i
$$747$$ 0 0
$$748$$ −3.54464 + 6.13949i −0.129605 + 0.224482i
$$749$$ 72.2100i 2.63850i
$$750$$ 0 0
$$751$$ 15.1001 + 26.1541i 0.551010 + 0.954377i 0.998202 + 0.0599394i $$0.0190907\pi$$
−0.447192 + 0.894438i $$0.647576\pi$$
$$752$$ −2.80764 4.86298i −0.102384 0.177335i
$$753$$ 0 0
$$754$$ −1.22841 + 34.7805i −0.0447361 + 1.26663i
$$755$$ 21.1798 14.5939i 0.770811 0.531126i
$$756$$ 0 0
$$757$$ 4.85341 2.80211i 0.176400 0.101845i −0.409200 0.912445i $$-0.634192\pi$$
0.585600 + 0.810600i $$0.300859\pi$$
$$758$$ 22.6152 + 13.0569i 0.821421 + 0.474247i
$$759$$ 0 0
$$760$$ 0.120495 + 1.50791i 0.00437083 + 0.0546976i
$$761$$ 5.77640 + 3.33501i 0.209394 + 0.120894i 0.601030 0.799227i $$-0.294757\pi$$
−0.391635 + 0.920120i $$0.628091\pi$$
$$762$$ 0 0
$$763$$ 41.8178 + 24.1435i 1.51391 + 0.874053i
$$764$$ 0.293441 + 0.508255i 0.0106163 + 0.0183880i
$$765$$ 0 0
$$766$$ −13.6930 −0.494750
$$767$$ 18.9881 + 0.670640i 0.685621 + 0.0242154i
$$768$$ 0 0
$$769$$ 6.03234 3.48277i 0.217532 0.125592i −0.387275 0.921964i $$-0.626584\pi$$
0.604807 + 0.796372i $$0.293250\pi$$
$$770$$ −20.6773 9.83213i −0.745158 0.354325i
$$771$$ 0 0
$$772$$ 22.6270 0.814363
$$773$$ −10.6748 + 18.4893i −0.383945 + 0.665013i −0.991622 0.129172i $$-0.958768\pi$$
0.607677 + 0.794184i $$0.292102\pi$$
$$774$$ 0 0
$$775$$ −33.2423 12.6691i −1.19410 0.455087i
$$776$$ 8.17066 14.1520i 0.293310 0.508027i
$$777$$ 0 0
$$778$$ 12.4701 + 21.5989i 0.447076 + 0.774359i
$$779$$ 2.03543 0.0729270
$$780$$ 0 0
$$781$$ −6.87041 −0.245843
$$782$$ 9.70004 + 16.8010i 0.346873 + 0.600801i
$$783$$ 0 0
$$784$$ −5.94234 + 10.2924i −0.212226 + 0.367587i
$$785$$ −8.24149 + 5.67879i −0.294151 + 0.202685i
$$786$$ 0 0