# Properties

 Label 600.2.d.g.349.8 Level 600 Weight 2 Character 600.349 Analytic conductor 4.791 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$600 = 2^{3} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 600.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.79102412128$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.214798336.3 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 349.8 Root $$-0.565036 - 1.29643i$$ of $$x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16$$ Character $$\chi$$ $$=$$ 600.349 Dual form 600.2.d.g.349.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.796431 + 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 + 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} -4.72294i q^{7} +(-2.75787 + 0.627801i) q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+(0.796431 + 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 + 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} -4.72294i q^{7} +(-2.75787 + 0.627801i) q^{8} +1.00000 q^{9} -3.93012i q^{11} +(0.731395 - 1.86147i) q^{12} +3.46733 q^{13} +(5.51937 - 3.76149i) q^{14} +(-2.93012 - 2.72294i) q^{16} -3.51575i q^{17} +(0.796431 + 1.16863i) q^{18} +5.44133i q^{19} +4.72294i q^{21} +(4.59286 - 3.13007i) q^{22} -7.11585i q^{23} +(2.75787 - 0.627801i) q^{24} +(2.76149 + 4.05203i) q^{26} -1.00000 q^{27} +(8.79159 + 3.45433i) q^{28} +3.66998i q^{29} +5.23414 q^{31} +(0.848464 - 5.59286i) q^{32} +3.93012i q^{33} +(4.10861 - 2.80005i) q^{34} +(-0.731395 + 1.86147i) q^{36} -0.414376 q^{37} +(-6.35890 + 4.33364i) q^{38} -3.46733 q^{39} +3.00454 q^{41} +(-5.51937 + 3.76149i) q^{42} -5.34450 q^{43} +(7.31580 + 2.87447i) q^{44} +(8.31580 - 5.66728i) q^{46} +0.925579i q^{47} +(2.93012 + 2.72294i) q^{48} -15.3061 q^{49} +3.51575i q^{51} +(-2.53599 + 6.45433i) q^{52} +0.233196 q^{53} +(-0.796431 - 1.16863i) q^{54} +(2.96506 + 13.0253i) q^{56} -5.44133i q^{57} +(-4.28885 + 2.92288i) q^{58} -14.3805i q^{59} -0.118290i q^{61} +(4.16863 + 6.11677i) q^{62} -4.72294i q^{63} +(7.21173 - 3.46279i) q^{64} +(-4.59286 + 3.13007i) q^{66} +13.4504 q^{67} +(6.54445 + 2.57140i) q^{68} +7.11585i q^{69} +2.19027 q^{71} +(-2.75787 + 0.627801i) q^{72} -0.563219i q^{73} +(-0.330022 - 0.484253i) q^{74} +(-10.1289 - 3.97976i) q^{76} -18.5617 q^{77} +(-2.76149 - 4.05203i) q^{78} +10.2746 q^{79} +1.00000 q^{81} +(2.39291 + 3.51120i) q^{82} -11.3490 q^{83} +(-8.79159 - 3.45433i) q^{84} +(-4.25653 - 6.24575i) q^{86} -3.66998i q^{87} +(2.46733 + 10.8388i) q^{88} -8.88265 q^{89} -16.3760i q^{91} +(13.2459 + 5.20449i) q^{92} -5.23414 q^{93} +(-1.08166 + 0.737160i) q^{94} +(-0.848464 + 5.59286i) q^{96} -7.27462i q^{97} +(-12.1903 - 17.8872i) q^{98} -3.93012i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + O(q^{10})$$ $$8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + 4q^{12} + 6q^{14} + 8q^{16} - 2q^{18} + 20q^{22} + 8q^{24} - 2q^{26} - 8q^{27} + 24q^{28} + 8q^{31} - 12q^{32} - 12q^{34} - 4q^{36} + 14q^{38} - 6q^{42} - 8q^{43} + 12q^{44} + 20q^{46} - 8q^{48} + 24q^{52} + 8q^{53} + 2q^{54} + 8q^{56} - 20q^{58} + 26q^{62} + 32q^{64} - 20q^{66} + 24q^{67} + 36q^{68} - 40q^{71} - 8q^{72} - 8q^{74} - 20q^{76} - 24q^{77} + 2q^{78} + 16q^{79} + 8q^{81} - 16q^{82} - 32q^{83} - 24q^{84} - 18q^{86} - 8q^{88} + 28q^{92} - 8q^{93} + 4q^{94} + 12q^{96} - 40q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$$.

 $$n$$ $$151$$ $$301$$ $$401$$ $$577$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.796431 + 1.16863i 0.563162 + 0.826347i
$$3$$ −1.00000 −0.577350
$$4$$ −0.731395 + 1.86147i −0.365697 + 0.930734i
$$5$$ 0 0
$$6$$ −0.796431 1.16863i −0.325142 0.477091i
$$7$$ 4.72294i 1.78510i −0.450947 0.892551i $$-0.648914\pi$$
0.450947 0.892551i $$-0.351086\pi$$
$$8$$ −2.75787 + 0.627801i −0.975056 + 0.221961i
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.93012i 1.18498i −0.805579 0.592488i $$-0.798146\pi$$
0.805579 0.592488i $$-0.201854\pi$$
$$12$$ 0.731395 1.86147i 0.211135 0.537359i
$$13$$ 3.46733 0.961665 0.480833 0.876812i $$-0.340334\pi$$
0.480833 + 0.876812i $$0.340334\pi$$
$$14$$ 5.51937 3.76149i 1.47511 1.00530i
$$15$$ 0 0
$$16$$ −2.93012 2.72294i −0.732531 0.680734i
$$17$$ 3.51575i 0.852694i −0.904560 0.426347i $$-0.859800\pi$$
0.904560 0.426347i $$-0.140200\pi$$
$$18$$ 0.796431 + 1.16863i 0.187721 + 0.275449i
$$19$$ 5.44133i 1.24833i 0.781294 + 0.624163i $$0.214560\pi$$
−0.781294 + 0.624163i $$0.785440\pi$$
$$20$$ 0 0
$$21$$ 4.72294i 1.03063i
$$22$$ 4.59286 3.13007i 0.979202 0.667334i
$$23$$ 7.11585i 1.48376i −0.670534 0.741878i $$-0.733935\pi$$
0.670534 0.741878i $$-0.266065\pi$$
$$24$$ 2.75787 0.627801i 0.562949 0.128149i
$$25$$ 0 0
$$26$$ 2.76149 + 4.05203i 0.541573 + 0.794669i
$$27$$ −1.00000 −0.192450
$$28$$ 8.79159 + 3.45433i 1.66145 + 0.652807i
$$29$$ 3.66998i 0.681498i 0.940154 + 0.340749i $$0.110681\pi$$
−0.940154 + 0.340749i $$0.889319\pi$$
$$30$$ 0 0
$$31$$ 5.23414 0.940079 0.470039 0.882645i $$-0.344240\pi$$
0.470039 + 0.882645i $$0.344240\pi$$
$$32$$ 0.848464 5.59286i 0.149989 0.988688i
$$33$$ 3.93012i 0.684147i
$$34$$ 4.10861 2.80005i 0.704621 0.480205i
$$35$$ 0 0
$$36$$ −0.731395 + 1.86147i −0.121899 + 0.310245i
$$37$$ −0.414376 −0.0681231 −0.0340615 0.999420i $$-0.510844\pi$$
−0.0340615 + 0.999420i $$0.510844\pi$$
$$38$$ −6.35890 + 4.33364i −1.03155 + 0.703010i
$$39$$ −3.46733 −0.555218
$$40$$ 0 0
$$41$$ 3.00454 0.469231 0.234616 0.972088i $$-0.424617\pi$$
0.234616 + 0.972088i $$0.424617\pi$$
$$42$$ −5.51937 + 3.76149i −0.851657 + 0.580411i
$$43$$ −5.34450 −0.815029 −0.407514 0.913199i $$-0.633604\pi$$
−0.407514 + 0.913199i $$0.633604\pi$$
$$44$$ 7.31580 + 2.87447i 1.10290 + 0.433343i
$$45$$ 0 0
$$46$$ 8.31580 5.66728i 1.22610 0.835595i
$$47$$ 0.925579i 0.135010i 0.997719 + 0.0675048i $$0.0215038\pi$$
−0.997719 + 0.0675048i $$0.978496\pi$$
$$48$$ 2.93012 + 2.72294i 0.422927 + 0.393022i
$$49$$ −15.3061 −2.18659
$$50$$ 0 0
$$51$$ 3.51575i 0.492303i
$$52$$ −2.53599 + 6.45433i −0.351679 + 0.895055i
$$53$$ 0.233196 0.0320320 0.0160160 0.999872i $$-0.494902\pi$$
0.0160160 + 0.999872i $$0.494902\pi$$
$$54$$ −0.796431 1.16863i −0.108381 0.159030i
$$55$$ 0 0
$$56$$ 2.96506 + 13.0253i 0.396223 + 1.74057i
$$57$$ 5.44133i 0.720721i
$$58$$ −4.28885 + 2.92288i −0.563153 + 0.383794i
$$59$$ 14.3805i 1.87219i −0.351752 0.936093i $$-0.614414\pi$$
0.351752 0.936093i $$-0.385586\pi$$
$$60$$ 0 0
$$61$$ 0.118290i 0.0151454i −0.999971 0.00757271i $$-0.997590\pi$$
0.999971 0.00757271i $$-0.00241049\pi$$
$$62$$ 4.16863 + 6.11677i 0.529417 + 0.776831i
$$63$$ 4.72294i 0.595034i
$$64$$ 7.21173 3.46279i 0.901467 0.432849i
$$65$$ 0 0
$$66$$ −4.59286 + 3.13007i −0.565342 + 0.385285i
$$67$$ 13.4504 1.64323 0.821615 0.570043i $$-0.193073\pi$$
0.821615 + 0.570043i $$0.193073\pi$$
$$68$$ 6.54445 + 2.57140i 0.793631 + 0.311828i
$$69$$ 7.11585i 0.856647i
$$70$$ 0 0
$$71$$ 2.19027 0.259937 0.129969 0.991518i $$-0.458512\pi$$
0.129969 + 0.991518i $$0.458512\pi$$
$$72$$ −2.75787 + 0.627801i −0.325019 + 0.0739870i
$$73$$ 0.563219i 0.0659197i −0.999457 0.0329599i $$-0.989507\pi$$
0.999457 0.0329599i $$-0.0104934\pi$$
$$74$$ −0.330022 0.484253i −0.0383643 0.0562933i
$$75$$ 0 0
$$76$$ −10.1289 3.97976i −1.16186 0.456509i
$$77$$ −18.5617 −2.11530
$$78$$ −2.76149 4.05203i −0.312678 0.458802i
$$79$$ 10.2746 1.15599 0.577993 0.816042i $$-0.303836\pi$$
0.577993 + 0.816042i $$0.303836\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 2.39291 + 3.51120i 0.264253 + 0.387747i
$$83$$ −11.3490 −1.24572 −0.622860 0.782334i $$-0.714029\pi$$
−0.622860 + 0.782334i $$0.714029\pi$$
$$84$$ −8.79159 3.45433i −0.959241 0.376898i
$$85$$ 0 0
$$86$$ −4.25653 6.24575i −0.458993 0.673496i
$$87$$ 3.66998i 0.393463i
$$88$$ 2.46733 + 10.8388i 0.263019 + 1.15542i
$$89$$ −8.88265 −0.941559 −0.470780 0.882251i $$-0.656027\pi$$
−0.470780 + 0.882251i $$0.656027\pi$$
$$90$$ 0 0
$$91$$ 16.3760i 1.71667i
$$92$$ 13.2459 + 5.20449i 1.38098 + 0.542606i
$$93$$ −5.23414 −0.542755
$$94$$ −1.08166 + 0.737160i −0.111565 + 0.0760322i
$$95$$ 0 0
$$96$$ −0.848464 + 5.59286i −0.0865960 + 0.570819i
$$97$$ 7.27462i 0.738626i −0.929305 0.369313i $$-0.879593\pi$$
0.929305 0.369313i $$-0.120407\pi$$
$$98$$ −12.1903 17.8872i −1.23140 1.80688i
$$99$$ 3.93012i 0.394992i
$$100$$ 0 0
$$101$$ 4.23320i 0.421219i 0.977570 + 0.210609i $$0.0675448\pi$$
−0.977570 + 0.210609i $$0.932455\pi$$
$$102$$ −4.10861 + 2.80005i −0.406813 + 0.277246i
$$103$$ 0.0429270i 0.00422972i 0.999998 + 0.00211486i $$0.000673181\pi$$
−0.999998 + 0.00211486i $$0.999327\pi$$
$$104$$ −9.56247 + 2.17679i −0.937677 + 0.213452i
$$105$$ 0 0
$$106$$ 0.185725 + 0.272520i 0.0180392 + 0.0264695i
$$107$$ −15.4728 −1.49581 −0.747907 0.663804i $$-0.768941\pi$$
−0.747907 + 0.663804i $$0.768941\pi$$
$$108$$ 0.731395 1.86147i 0.0703785 0.179120i
$$109$$ 12.9561i 1.24097i 0.784217 + 0.620486i $$0.213065\pi$$
−0.784217 + 0.620486i $$0.786935\pi$$
$$110$$ 0 0
$$111$$ 0.414376 0.0393309
$$112$$ −12.8602 + 13.8388i −1.21518 + 1.30764i
$$113$$ 3.86025i 0.363141i 0.983378 + 0.181571i $$0.0581181\pi$$
−0.983378 + 0.181571i $$0.941882\pi$$
$$114$$ 6.35890 4.33364i 0.595566 0.405883i
$$115$$ 0 0
$$116$$ −6.83154 2.68420i −0.634293 0.249222i
$$117$$ 3.46733 0.320555
$$118$$ 16.8055 11.4531i 1.54708 1.05434i
$$119$$ −16.6046 −1.52215
$$120$$ 0 0
$$121$$ −4.44587 −0.404170
$$122$$ 0.138237 0.0942095i 0.0125154 0.00852933i
$$123$$ −3.00454 −0.270911
$$124$$ −3.82822 + 9.74318i −0.343784 + 0.874963i
$$125$$ 0 0
$$126$$ 5.51937 3.76149i 0.491704 0.335100i
$$127$$ 18.3805i 1.63101i 0.578751 + 0.815505i $$0.303540\pi$$
−0.578751 + 0.815505i $$0.696460\pi$$
$$128$$ 9.79037 + 5.66998i 0.865355 + 0.501160i
$$129$$ 5.34450 0.470557
$$130$$ 0 0
$$131$$ 3.41892i 0.298713i −0.988783 0.149356i $$-0.952280\pi$$
0.988783 0.149356i $$-0.0477201\pi$$
$$132$$ −7.31580 2.87447i −0.636758 0.250191i
$$133$$ 25.6990 2.22839
$$134$$ 10.7123 + 15.7186i 0.925404 + 1.35788i
$$135$$ 0 0
$$136$$ 2.20719 + 9.69599i 0.189265 + 0.831424i
$$137$$ 16.3714i 1.39871i 0.714776 + 0.699354i $$0.246529\pi$$
−0.714776 + 0.699354i $$0.753471\pi$$
$$138$$ −8.31580 + 5.66728i −0.707888 + 0.482431i
$$139$$ 1.95707i 0.165997i 0.996550 + 0.0829984i $$0.0264496\pi$$
−0.996550 + 0.0829984i $$0.973550\pi$$
$$140$$ 0 0
$$141$$ 0.925579i 0.0779478i
$$142$$ 1.74440 + 2.55962i 0.146387 + 0.214798i
$$143$$ 13.6271i 1.13955i
$$144$$ −2.93012 2.72294i −0.244177 0.226911i
$$145$$ 0 0
$$146$$ 0.658194 0.448565i 0.0544726 0.0371235i
$$147$$ 15.3061 1.26243
$$148$$ 0.303073 0.771348i 0.0249124 0.0634044i
$$149$$ 12.0968i 0.991011i −0.868605 0.495505i $$-0.834983\pi$$
0.868605 0.495505i $$-0.165017\pi$$
$$150$$ 0 0
$$151$$ −4.87178 −0.396460 −0.198230 0.980156i $$-0.563519\pi$$
−0.198230 + 0.980156i $$0.563519\pi$$
$$152$$ −3.41607 15.0065i −0.277080 1.21719i
$$153$$ 3.51575i 0.284231i
$$154$$ −14.7831 21.6918i −1.19126 1.74797i
$$155$$ 0 0
$$156$$ 2.53599 6.45433i 0.203042 0.516760i
$$157$$ 21.6561 1.72835 0.864173 0.503195i $$-0.167842\pi$$
0.864173 + 0.503195i $$0.167842\pi$$
$$158$$ 8.18303 + 12.0072i 0.651007 + 0.955245i
$$159$$ −0.233196 −0.0184937
$$160$$ 0 0
$$161$$ −33.6077 −2.64866
$$162$$ 0.796431 + 1.16863i 0.0625735 + 0.0918163i
$$163$$ −16.2362 −1.27172 −0.635860 0.771804i $$-0.719355\pi$$
−0.635860 + 0.771804i $$0.719355\pi$$
$$164$$ −2.19751 + 5.59286i −0.171597 + 0.436729i
$$165$$ 0 0
$$166$$ −9.03873 13.2628i −0.701542 1.02940i
$$167$$ 6.69238i 0.517872i 0.965894 + 0.258936i $$0.0833719\pi$$
−0.965894 + 0.258936i $$0.916628\pi$$
$$168$$ −2.96506 13.0253i −0.228759 1.00492i
$$169$$ −0.977595 −0.0751996
$$170$$ 0 0
$$171$$ 5.44133i 0.416109i
$$172$$ 3.90894 9.94861i 0.298054 0.758575i
$$173$$ 22.4220 1.70471 0.852355 0.522963i $$-0.175173\pi$$
0.852355 + 0.522963i $$0.175173\pi$$
$$174$$ 4.28885 2.92288i 0.325137 0.221583i
$$175$$ 0 0
$$176$$ −10.7015 + 11.5157i −0.806654 + 0.868032i
$$177$$ 14.3805i 1.08091i
$$178$$ −7.07442 10.3805i −0.530250 0.778054i
$$179$$ 0.148842i 0.0111250i 0.999985 + 0.00556249i $$0.00177060\pi$$
−0.999985 + 0.00556249i $$0.998229\pi$$
$$180$$ 0 0
$$181$$ 10.3929i 0.772499i 0.922394 + 0.386250i $$0.126230\pi$$
−0.922394 + 0.386250i $$0.873770\pi$$
$$182$$ 19.1375 13.0424i 1.41856 0.966763i
$$183$$ 0.118290i 0.00874422i
$$184$$ 4.46733 + 19.6246i 0.329336 + 1.44675i
$$185$$ 0 0
$$186$$ −4.16863 6.11677i −0.305659 0.448504i
$$187$$ −13.8173 −1.01042
$$188$$ −1.72294 0.676964i −0.125658 0.0493726i
$$189$$ 4.72294i 0.343543i
$$190$$ 0 0
$$191$$ 6.23320 0.451018 0.225509 0.974241i $$-0.427595\pi$$
0.225509 + 0.974241i $$0.427595\pi$$
$$192$$ −7.21173 + 3.46279i −0.520462 + 0.249905i
$$193$$ 0.391971i 0.0282147i −0.999900 0.0141074i $$-0.995509\pi$$
0.999900 0.0141074i $$-0.00449066\pi$$
$$194$$ 8.50135 5.79374i 0.610361 0.415966i
$$195$$ 0 0
$$196$$ 11.1948 28.4918i 0.799630 2.03513i
$$197$$ −5.96616 −0.425071 −0.212536 0.977153i $$-0.568172\pi$$
−0.212536 + 0.977153i $$0.568172\pi$$
$$198$$ 4.59286 3.13007i 0.326401 0.222445i
$$199$$ 17.9322 1.27118 0.635591 0.772026i $$-0.280757\pi$$
0.635591 + 0.772026i $$0.280757\pi$$
$$200$$ 0 0
$$201$$ −13.4504 −0.948719
$$202$$ −4.94704 + 3.37145i −0.348073 + 0.237214i
$$203$$ 17.3331 1.21654
$$204$$ −6.54445 2.57140i −0.458203 0.180034i
$$205$$ 0 0
$$206$$ −0.0501658 + 0.0341884i −0.00349521 + 0.00238202i
$$207$$ 7.11585i 0.494586i
$$208$$ −10.1597 9.44133i −0.704450 0.654638i
$$209$$ 21.3851 1.47924
$$210$$ 0 0
$$211$$ 6.51575i 0.448563i 0.974524 + 0.224281i $$0.0720034\pi$$
−0.974524 + 0.224281i $$0.927997\pi$$
$$212$$ −0.170558 + 0.434087i −0.0117140 + 0.0298132i
$$213$$ −2.19027 −0.150075
$$214$$ −12.3230 18.0820i −0.842385 1.23606i
$$215$$ 0 0
$$216$$ 2.75787 0.627801i 0.187650 0.0427164i
$$217$$ 24.7205i 1.67814i
$$218$$ −15.1409 + 10.3187i −1.02547 + 0.698868i
$$219$$ 0.563219i 0.0380588i
$$220$$ 0 0
$$221$$ 12.1903i 0.820006i
$$222$$ 0.330022 + 0.484253i 0.0221496 + 0.0325009i
$$223$$ 3.14640i 0.210699i 0.994435 + 0.105349i $$0.0335961\pi$$
−0.994435 + 0.105349i $$0.966404\pi$$
$$224$$ −26.4147 4.00724i −1.76491 0.267745i
$$225$$ 0 0
$$226$$ −4.51120 + 3.07442i −0.300081 + 0.204507i
$$227$$ 3.92103 0.260248 0.130124 0.991498i $$-0.458462\pi$$
0.130124 + 0.991498i $$0.458462\pi$$
$$228$$ 10.1289 + 3.97976i 0.670800 + 0.263566i
$$229$$ 25.6899i 1.69764i −0.528683 0.848820i $$-0.677314\pi$$
0.528683 0.848820i $$-0.322686\pi$$
$$230$$ 0 0
$$231$$ 18.5617 1.22127
$$232$$ −2.30401 10.1213i −0.151266 0.664498i
$$233$$ 25.7565i 1.68737i 0.536841 + 0.843683i $$0.319617\pi$$
−0.536841 + 0.843683i $$0.680383\pi$$
$$234$$ 2.76149 + 4.05203i 0.180524 + 0.264890i
$$235$$ 0 0
$$236$$ 26.7689 + 10.5179i 1.74251 + 0.684654i
$$237$$ −10.2746 −0.667409
$$238$$ −13.2245 19.4047i −0.857214 1.25782i
$$239$$ 15.8727 1.02672 0.513360 0.858173i $$-0.328400\pi$$
0.513360 + 0.858173i $$0.328400\pi$$
$$240$$ 0 0
$$241$$ 28.1664 1.81436 0.907178 0.420748i $$-0.138232\pi$$
0.907178 + 0.420748i $$0.138232\pi$$
$$242$$ −3.54083 5.19558i −0.227613 0.333985i
$$243$$ −1.00000 −0.0641500
$$244$$ 0.220192 + 0.0865164i 0.0140964 + 0.00553864i
$$245$$ 0 0
$$246$$ −2.39291 3.51120i −0.152567 0.223866i
$$247$$ 18.8669i 1.20047i
$$248$$ −14.4351 + 3.28600i −0.916629 + 0.208661i
$$249$$ 11.3490 0.719216
$$250$$ 0 0
$$251$$ 4.66004i 0.294139i −0.989126 0.147070i $$-0.953016\pi$$
0.989126 0.147070i $$-0.0469842\pi$$
$$252$$ 8.79159 + 3.45433i 0.553818 + 0.217602i
$$253$$ −27.9662 −1.75822
$$254$$ −21.4801 + 14.6388i −1.34778 + 0.918522i
$$255$$ 0 0
$$256$$ 1.17125 + 15.9571i 0.0732029 + 0.997317i
$$257$$ 3.33996i 0.208341i 0.994559 + 0.104170i $$0.0332187\pi$$
−0.994559 + 0.104170i $$0.966781\pi$$
$$258$$ 4.25653 + 6.24575i 0.265000 + 0.388843i
$$259$$ 1.95707i 0.121607i
$$260$$ 0 0
$$261$$ 3.66998i 0.227166i
$$262$$ 3.99546 2.72294i 0.246840 0.168224i
$$263$$ 27.5932i 1.70147i 0.525595 + 0.850735i $$0.323843\pi$$
−0.525595 + 0.850735i $$0.676157\pi$$
$$264$$ −2.46733 10.8388i −0.151854 0.667081i
$$265$$ 0 0
$$266$$ 20.4675 + 30.0327i 1.25494 + 1.84142i
$$267$$ 8.88265 0.543609
$$268$$ −9.83756 + 25.0375i −0.600925 + 1.52941i
$$269$$ 21.8727i 1.33360i 0.745235 + 0.666802i $$0.232337\pi$$
−0.745235 + 0.666802i $$0.767663\pi$$
$$270$$ 0 0
$$271$$ −8.78583 −0.533701 −0.266850 0.963738i $$-0.585983\pi$$
−0.266850 + 0.963738i $$0.585983\pi$$
$$272$$ −9.57315 + 10.3016i −0.580458 + 0.624625i
$$273$$ 16.3760i 0.991120i
$$274$$ −19.1322 + 13.0387i −1.15582 + 0.787699i
$$275$$ 0 0
$$276$$ −13.2459 5.20449i −0.797311 0.313274i
$$277$$ 10.3838 0.623904 0.311952 0.950098i $$-0.399017\pi$$
0.311952 + 0.950098i $$0.399017\pi$$
$$278$$ −2.28710 + 1.55867i −0.137171 + 0.0934831i
$$279$$ 5.23414 0.313360
$$280$$ 0 0
$$281$$ 17.0584 1.01762 0.508811 0.860878i $$-0.330085\pi$$
0.508811 + 0.860878i $$0.330085\pi$$
$$282$$ 1.08166 0.737160i 0.0644119 0.0438972i
$$283$$ −3.54724 −0.210862 −0.105431 0.994427i $$-0.533622\pi$$
−0.105431 + 0.994427i $$0.533622\pi$$
$$284$$ −1.60195 + 4.07712i −0.0950583 + 0.241932i
$$285$$ 0 0
$$286$$ 15.9250 10.8530i 0.941664 0.641752i
$$287$$ 14.1903i 0.837625i
$$288$$ 0.848464 5.59286i 0.0499962 0.329563i
$$289$$ 4.63952 0.272913
$$290$$ 0 0
$$291$$ 7.27462i 0.426446i
$$292$$ 1.04841 + 0.411935i 0.0613537 + 0.0241067i
$$293$$ 5.72538 0.334480 0.167240 0.985916i $$-0.446515\pi$$
0.167240 + 0.985916i $$0.446515\pi$$
$$294$$ 12.1903 + 17.8872i 0.710951 + 1.04320i
$$295$$ 0 0
$$296$$ 1.14280 0.260146i 0.0664238 0.0151207i
$$297$$ 3.93012i 0.228049i
$$298$$ 14.1367 9.63429i 0.818918 0.558099i
$$299$$ 24.6730i 1.42688i
$$300$$ 0 0
$$301$$ 25.2417i 1.45491i
$$302$$ −3.88004 5.69331i −0.223271 0.327613i
$$303$$ 4.23320i 0.243191i
$$304$$ 14.8164 15.9438i 0.849778 0.914437i
$$305$$ 0 0
$$306$$ 4.10861 2.80005i 0.234874 0.160068i
$$307$$ −12.3760 −0.706335 −0.353168 0.935560i $$-0.614895\pi$$
−0.353168 + 0.935560i $$0.614895\pi$$
$$308$$ 13.5759 34.5520i 0.773561 1.96879i
$$309$$ 0.0429270i 0.00244203i
$$310$$ 0 0
$$311$$ −18.2746 −1.03626 −0.518129 0.855302i $$-0.673371\pi$$
−0.518129 + 0.855302i $$0.673371\pi$$
$$312$$ 9.56247 2.17679i 0.541368 0.123237i
$$313$$ 12.7114i 0.718491i −0.933243 0.359246i $$-0.883034\pi$$
0.933243 0.359246i $$-0.116966\pi$$
$$314$$ 17.2476 + 25.3080i 0.973338 + 1.42821i
$$315$$ 0 0
$$316$$ −7.51481 + 19.1259i −0.422741 + 1.07591i
$$317$$ −15.8602 −0.890800 −0.445400 0.895332i $$-0.646939\pi$$
−0.445400 + 0.895332i $$0.646939\pi$$
$$318$$ −0.185725 0.272520i −0.0104149 0.0152822i
$$319$$ 14.4235 0.807559
$$320$$ 0 0
$$321$$ 15.4728 0.863609
$$322$$ −26.7662 39.2750i −1.49162 2.18871i
$$323$$ 19.1303 1.06444
$$324$$ −0.731395 + 1.86147i −0.0406330 + 0.103415i
$$325$$ 0 0
$$326$$ −12.9310 18.9742i −0.716185 1.05088i
$$327$$ 12.9561i 0.716476i
$$328$$ −8.28615 + 1.88625i −0.457526 + 0.104151i
$$329$$ 4.37145 0.241006
$$330$$ 0 0
$$331$$ 23.0315i 1.26593i 0.774182 + 0.632963i $$0.218161\pi$$
−0.774182 + 0.632963i $$0.781839\pi$$
$$332$$ 8.30063 21.1259i 0.455556 1.15943i
$$333$$ −0.414376 −0.0227077
$$334$$ −7.82092 + 5.33002i −0.427942 + 0.291646i
$$335$$ 0 0
$$336$$ 12.8602 13.8388i 0.701584 0.754968i
$$337$$ 0.860247i 0.0468606i 0.999725 + 0.0234303i $$0.00745878\pi$$
−0.999725 + 0.0234303i $$0.992541\pi$$
$$338$$ −0.778587 1.14245i −0.0423496 0.0621409i
$$339$$ 3.86025i 0.209660i
$$340$$ 0 0
$$341$$ 20.5708i 1.11397i
$$342$$ −6.35890 + 4.33364i −0.343850 + 0.234337i
$$343$$ 39.2293i 2.11818i
$$344$$ 14.7395 3.35528i 0.794698 0.180905i
$$345$$ 0 0
$$346$$ 17.8576 + 26.2030i 0.960028 + 1.40868i
$$347$$ 32.2856 1.73318 0.866591 0.499019i $$-0.166306\pi$$
0.866591 + 0.499019i $$0.166306\pi$$
$$348$$ 6.83154 + 2.68420i 0.366209 + 0.143888i
$$349$$ 0.742899i 0.0397665i −0.999802 0.0198832i $$-0.993671\pi$$
0.999802 0.0198832i $$-0.00632945\pi$$
$$350$$ 0 0
$$351$$ −3.46733 −0.185073
$$352$$ −21.9806 3.33457i −1.17157 0.177733i
$$353$$ 32.6392i 1.73721i −0.495506 0.868604i $$-0.665018\pi$$
0.495506 0.868604i $$-0.334982\pi$$
$$354$$ −16.8055 + 11.4531i −0.893204 + 0.608726i
$$355$$ 0 0
$$356$$ 6.49672 16.5348i 0.344326 0.876341i
$$357$$ 16.6046 0.878811
$$358$$ −0.173941 + 0.118542i −0.00919309 + 0.00626517i
$$359$$ 2.71056 0.143058 0.0715290 0.997439i $$-0.477212\pi$$
0.0715290 + 0.997439i $$0.477212\pi$$
$$360$$ 0 0
$$361$$ −10.6080 −0.558317
$$362$$ −12.1455 + 8.27724i −0.638352 + 0.435042i
$$363$$ 4.44587 0.233348
$$364$$ 30.4834 + 11.9773i 1.59776 + 0.627782i
$$365$$ 0 0
$$366$$ −0.138237 + 0.0942095i −0.00722575 + 0.00492441i
$$367$$ 0.680008i 0.0354961i −0.999842 0.0177481i $$-0.994350\pi$$
0.999842 0.0177481i $$-0.00564968\pi$$
$$368$$ −19.3760 + 20.8503i −1.01004 + 1.08690i
$$369$$ 3.00454 0.156410
$$370$$ 0 0
$$371$$ 1.10137i 0.0571803i
$$372$$ 3.82822 9.74318i 0.198484 0.505160i
$$373$$ −3.47642 −0.180002 −0.0900012 0.995942i $$-0.528687\pi$$
−0.0900012 + 0.995942i $$0.528687\pi$$
$$374$$ −11.0045 16.1473i −0.569031 0.834959i
$$375$$ 0 0
$$376$$ −0.581079 2.55263i −0.0299669 0.131642i
$$377$$ 12.7250i 0.655373i
$$378$$ −5.51937 + 3.76149i −0.283886 + 0.193470i
$$379$$ 23.0650i 1.18477i 0.805655 + 0.592385i $$0.201813\pi$$
−0.805655 + 0.592385i $$0.798187\pi$$
$$380$$ 0 0
$$381$$ 18.3805i 0.941664i
$$382$$ 4.96431 + 7.28430i 0.253996 + 0.372697i
$$383$$ 9.81544i 0.501545i −0.968046 0.250773i $$-0.919315\pi$$
0.968046 0.250773i $$-0.0806847\pi$$
$$384$$ −9.79037 5.66998i −0.499613 0.289345i
$$385$$ 0 0
$$386$$ 0.458070 0.312178i 0.0233151 0.0158895i
$$387$$ −5.34450 −0.271676
$$388$$ 13.5415 + 5.32062i 0.687464 + 0.270114i
$$389$$ 9.86175i 0.500010i −0.968244 0.250005i $$-0.919568\pi$$
0.968244 0.250005i $$-0.0804323\pi$$
$$390$$ 0 0
$$391$$ −25.0175 −1.26519
$$392$$ 42.2123 9.60919i 2.13204 0.485337i
$$393$$ 3.41892i 0.172462i
$$394$$ −4.75164 6.97224i −0.239384 0.351256i
$$395$$ 0 0
$$396$$ 7.31580 + 2.87447i 0.367633 + 0.144448i
$$397$$ −12.7783 −0.641326 −0.320663 0.947193i $$-0.603906\pi$$
−0.320663 + 0.947193i $$0.603906\pi$$
$$398$$ 14.2818 + 20.9561i 0.715881 + 1.05044i
$$399$$ −25.6990 −1.28656
$$400$$ 0 0
$$401$$ 3.17325 0.158465 0.0792323 0.996856i $$-0.474753\pi$$
0.0792323 + 0.996856i $$0.474753\pi$$
$$402$$ −10.7123 15.7186i −0.534282 0.783971i
$$403$$ 18.1485 0.904041
$$404$$ −7.87996 3.09614i −0.392043 0.154039i
$$405$$ 0 0
$$406$$ 13.8046 + 20.2560i 0.685111 + 1.00529i
$$407$$ 1.62855i 0.0807243i
$$408$$ −2.20719 9.69599i −0.109272 0.480023i
$$409$$ −12.1125 −0.598923 −0.299461 0.954108i $$-0.596807\pi$$
−0.299461 + 0.954108i $$0.596807\pi$$
$$410$$ 0 0
$$411$$ 16.3714i 0.807544i
$$412$$ −0.0799071 0.0313965i −0.00393674 0.00154680i
$$413$$ −67.9184 −3.34204
$$414$$ 8.31580 5.66728i 0.408699 0.278532i
$$415$$ 0 0
$$416$$ 2.94191 19.3923i 0.144239 0.950787i
$$417$$ 1.95707i 0.0958383i
$$418$$ 17.0317 + 24.9913i 0.833050 + 1.22236i
$$419$$ 4.24767i 0.207512i 0.994603 + 0.103756i $$0.0330862\pi$$
−0.994603 + 0.103756i $$0.966914\pi$$
$$420$$ 0 0
$$421$$ 3.77928i 0.184191i 0.995750 + 0.0920953i $$0.0293564\pi$$
−0.995750 + 0.0920953i $$0.970644\pi$$
$$422$$ −7.61450 + 5.18934i −0.370668 + 0.252613i
$$423$$ 0.925579i 0.0450032i
$$424$$ −0.643126 + 0.146401i −0.0312329 + 0.00710985i
$$425$$ 0 0
$$426$$ −1.74440 2.55962i −0.0845164 0.124014i
$$427$$ −0.558674 −0.0270361
$$428$$ 11.3167 28.8022i 0.547015 1.39220i
$$429$$ 13.6271i 0.657920i
$$430$$ 0 0
$$431$$ 25.6271 1.23441 0.617206 0.786802i $$-0.288265\pi$$
0.617206 + 0.786802i $$0.288265\pi$$
$$432$$ 2.93012 + 2.72294i 0.140976 + 0.131007i
$$433$$ 2.03149i 0.0976274i −0.998808 0.0488137i $$-0.984456\pi$$
0.998808 0.0488137i $$-0.0155441\pi$$
$$434$$ 28.8891 19.6882i 1.38672 0.945063i
$$435$$ 0 0
$$436$$ −24.1174 9.47605i −1.15501 0.453820i
$$437$$ 38.7196 1.85221
$$438$$ −0.658194 + 0.448565i −0.0314497 + 0.0214333i
$$439$$ 22.4864 1.07322 0.536608 0.843832i $$-0.319706\pi$$
0.536608 + 0.843832i $$0.319706\pi$$
$$440$$ 0 0
$$441$$ −15.3061 −0.728863
$$442$$ 14.2459 9.70871i 0.677609 0.461796i
$$443$$ −3.39385 −0.161247 −0.0806234 0.996745i $$-0.525691\pi$$
−0.0806234 + 0.996745i $$0.525691\pi$$
$$444$$ −0.303073 + 0.771348i −0.0143832 + 0.0366066i
$$445$$ 0 0
$$446$$ −3.67698 + 2.50589i −0.174110 + 0.118657i
$$447$$ 12.0968i 0.572160i
$$448$$ −16.3545 34.0605i −0.772679 1.60921i
$$449$$ 2.17780 0.102777 0.0513883 0.998679i $$-0.483635\pi$$
0.0513883 + 0.998679i $$0.483635\pi$$
$$450$$ 0 0
$$451$$ 11.8082i 0.556028i
$$452$$ −7.18572 2.82336i −0.337988 0.132800i
$$453$$ 4.87178 0.228896
$$454$$ 3.12283 + 4.58224i 0.146562 + 0.215055i
$$455$$ 0 0
$$456$$ 3.41607 + 15.0065i 0.159972 + 0.702743i
$$457$$ 3.57653i 0.167303i 0.996495 + 0.0836516i $$0.0266583\pi$$
−0.996495 + 0.0836516i $$0.973342\pi$$
$$458$$ 30.0221 20.4603i 1.40284 0.956046i
$$459$$ 3.51575i 0.164101i
$$460$$ 0 0
$$461$$ 13.1158i 0.610866i −0.952214 0.305433i $$-0.901199\pi$$
0.952214 0.305433i $$-0.0988012\pi$$
$$462$$ 14.7831 + 21.6918i 0.687774 + 1.00919i
$$463$$ 3.21417i 0.149375i −0.997207 0.0746877i $$-0.976204\pi$$
0.997207 0.0746877i $$-0.0237960\pi$$
$$464$$ 9.99311 10.7535i 0.463919 0.499218i
$$465$$ 0 0
$$466$$ −30.0999 + 20.5133i −1.39435 + 0.950261i
$$467$$ −30.3016 −1.40219 −0.701095 0.713068i $$-0.747305\pi$$
−0.701095 + 0.713068i $$0.747305\pi$$
$$468$$ −2.53599 + 6.45433i −0.117226 + 0.298352i
$$469$$ 63.5254i 2.93333i
$$470$$ 0 0
$$471$$ −21.6561 −0.997861
$$472$$ 9.02811 + 39.6597i 0.415552 + 1.82549i
$$473$$ 21.0045i 0.965790i
$$474$$ −8.18303 12.0072i −0.375859 0.551511i
$$475$$ 0 0
$$476$$ 12.1446 30.9090i 0.556645 1.41671i
$$477$$ 0.233196 0.0106773
$$478$$ 12.6415 + 18.5493i 0.578210 + 0.848427i
$$479$$ −35.0896 −1.60328 −0.801642 0.597804i $$-0.796040\pi$$
−0.801642 + 0.597804i $$0.796040\pi$$
$$480$$ 0 0
$$481$$ −1.43678 −0.0655116
$$482$$ 22.4326 + 32.9161i 1.02178 + 1.49929i
$$483$$ 33.6077 1.52920
$$484$$ 3.25169 8.27584i 0.147804 0.376175i
$$485$$ 0 0
$$486$$ −0.796431 1.16863i −0.0361269 0.0530102i
$$487$$ 36.9117i 1.67263i −0.548250 0.836315i $$-0.684706\pi$$
0.548250 0.836315i $$-0.315294\pi$$
$$488$$ 0.0742623 + 0.326228i 0.00336169 + 0.0147676i
$$489$$ 16.2362 0.734228
$$490$$ 0 0
$$491$$ 20.9867i 0.947116i 0.880763 + 0.473558i $$0.157031\pi$$
−0.880763 + 0.473558i $$0.842969\pi$$
$$492$$ 2.19751 5.59286i 0.0990713 0.252146i
$$493$$ 12.9027 0.581109
$$494$$ −22.0484 + 15.0262i −0.992006 + 0.676060i
$$495$$ 0 0
$$496$$ −15.3367 14.2522i −0.688637 0.639943i
$$497$$ 10.3445i 0.464014i
$$498$$ 9.03873 + 13.2628i 0.405035 + 0.594322i
$$499$$ 15.9906i 0.715836i 0.933753 + 0.357918i $$0.116513\pi$$
−0.933753 + 0.357918i $$0.883487\pi$$
$$500$$ 0 0
$$501$$ 6.69238i 0.298994i
$$502$$ 5.44587 3.71140i 0.243061 0.165648i
$$503$$ 37.6023i 1.67660i −0.545206 0.838302i $$-0.683549\pi$$
0.545206 0.838302i $$-0.316451\pi$$
$$504$$ 2.96506 + 13.0253i 0.132074 + 0.580191i
$$505$$ 0 0
$$506$$ −22.2731 32.6821i −0.990161 1.45290i
$$507$$ 0.977595 0.0434165
$$508$$ −34.2148 13.4434i −1.51804 0.596456i
$$509$$ 12.8579i 0.569917i −0.958540 0.284958i $$-0.908020\pi$$
0.958540 0.284958i $$-0.0919797\pi$$
$$510$$ 0 0
$$511$$ −2.66004 −0.117673
$$512$$ −17.7151 + 14.0775i −0.782904 + 0.622142i
$$513$$ 5.44133i 0.240240i
$$514$$ −3.90317 + 2.66004i −0.172162 + 0.117330i
$$515$$ 0 0
$$516$$ −3.90894 + 9.94861i −0.172081 + 0.437963i
$$517$$ 3.63764 0.159983
$$518$$ −2.28710 + 1.55867i −0.100489 + 0.0684842i
$$519$$ −22.4220 −0.984215
$$520$$ 0 0
$$521$$ 37.0015 1.62107 0.810534 0.585692i $$-0.199177\pi$$
0.810534 + 0.585692i $$0.199177\pi$$
$$522$$ −4.28885 + 2.92288i −0.187718 + 0.127931i
$$523$$ −17.4952 −0.765013 −0.382506 0.923953i $$-0.624939\pi$$
−0.382506 + 0.923953i $$0.624939\pi$$
$$524$$ 6.36421 + 2.50058i 0.278022 + 0.109238i
$$525$$ 0 0
$$526$$ −32.2463 + 21.9761i −1.40600 + 0.958203i
$$527$$ 18.4019i 0.801600i
$$528$$ 10.7015 11.5157i 0.465722 0.501159i
$$529$$ −27.6353 −1.20153
$$530$$ 0 0
$$531$$ 14.3805i 0.624062i
$$532$$ −18.7961 + 47.8379i −0.814916 + 2.07404i
$$533$$ 10.4178 0.451243
$$534$$ 7.07442 + 10.3805i 0.306140 + 0.449210i
$$535$$ 0 0
$$536$$ −37.0945 + 8.44418i −1.60224 + 0.364733i
$$537$$ 0.148842i 0.00642301i
$$538$$ −25.5611 + 17.4201i −1.10202 + 0.751035i
$$539$$ 60.1549i 2.59106i
$$540$$ 0 0
$$541$$ 38.1225i 1.63901i −0.573069 0.819507i $$-0.694247\pi$$
0.573069 0.819507i $$-0.305753\pi$$
$$542$$ −6.99731 10.2674i −0.300560 0.441022i
$$543$$ 10.3929i 0.446003i
$$544$$ −19.6631 2.98298i −0.843048 0.127894i
$$545$$ 0 0
$$546$$ −19.1375 + 13.0424i −0.819009 + 0.558161i
$$547$$ −35.7406 −1.52816 −0.764078 0.645124i $$-0.776806\pi$$
−0.764078 + 0.645124i $$0.776806\pi$$
$$548$$ −30.4749 11.9740i −1.30182 0.511504i
$$549$$ 0.118290i 0.00504848i
$$550$$ 0 0
$$551$$ −19.9695 −0.850731
$$552$$ −4.46733 19.6246i −0.190142 0.835279i
$$553$$ 48.5264i 2.06355i
$$554$$ 8.27000 + 12.1349i 0.351359 + 0.515561i
$$555$$ 0 0
$$556$$ −3.64303 1.43139i −0.154499 0.0607046i
$$557$$ 2.65516 0.112503 0.0562514 0.998417i $$-0.482085\pi$$
0.0562514 + 0.998417i $$0.482085\pi$$
$$558$$ 4.16863 + 6.11677i 0.176472 + 0.258944i
$$559$$ −18.5312 −0.783785
$$560$$ 0 0
$$561$$ 13.8173 0.583368
$$562$$ 13.5859 + 19.9350i 0.573086 + 0.840908i
$$563$$ 20.3107 0.855992 0.427996 0.903781i $$-0.359220\pi$$
0.427996 + 0.903781i $$0.359220\pi$$
$$564$$ 1.72294 + 0.676964i 0.0725487 + 0.0285053i
$$565$$ 0 0
$$566$$ −2.82513 4.14541i −0.118749 0.174245i
$$567$$ 4.72294i 0.198345i
$$568$$ −6.04049 + 1.37505i −0.253453 + 0.0576959i
$$569$$ 28.4274 1.19174 0.595868 0.803082i $$-0.296808\pi$$
0.595868 + 0.803082i $$0.296808\pi$$
$$570$$ 0 0
$$571$$ 16.1485i 0.675794i 0.941183 + 0.337897i $$0.109716\pi$$
−0.941183 + 0.337897i $$0.890284\pi$$
$$572$$ 25.3663 + 9.96675i 1.06062 + 0.416731i
$$573$$ −6.23320 −0.260396
$$574$$ 16.5832 11.3016i 0.692169 0.471719i
$$575$$ 0 0
$$576$$ 7.21173 3.46279i 0.300489 0.144283i
$$577$$ 30.3600i 1.26390i 0.775008 + 0.631952i $$0.217746\pi$$
−0.775008 + 0.631952i $$0.782254\pi$$
$$578$$ 3.69506 + 5.42189i 0.153694 + 0.225521i
$$579$$ 0.391971i 0.0162898i
$$580$$ 0 0
$$581$$ 53.6008i 2.22374i
$$582$$ −8.50135 + 5.79374i −0.352392 + 0.240158i
$$583$$ 0.916490i 0.0379571i
$$584$$ 0.353589 + 1.55329i 0.0146316 + 0.0642754i
$$585$$ 0 0
$$586$$ 4.55987 + 6.69085i 0.188366 + 0.276396i
$$587$$ −2.74070 −0.113121 −0.0565604 0.998399i $$-0.518013\pi$$
−0.0565604 + 0.998399i $$0.518013\pi$$
$$588$$ −11.1948 + 28.4918i −0.461666 + 1.17498i
$$589$$ 28.4807i 1.17352i
$$590$$ 0 0
$$591$$ 5.96616 0.245415
$$592$$ 1.21417 + 1.12832i 0.0499022 + 0.0463737i
$$593$$ 22.2586i 0.914053i −0.889453 0.457027i $$-0.848914\pi$$
0.889453 0.457027i $$-0.151086\pi$$
$$594$$ −4.59286 + 3.13007i −0.188447 + 0.128428i
$$595$$ 0 0
$$596$$ 22.5179 + 8.84755i 0.922367 + 0.362410i
$$597$$ −17.9322 −0.733917
$$598$$ 28.8336 19.6504i 1.17910 0.803563i
$$599$$ −48.4526 −1.97972 −0.989860 0.142046i $$-0.954632\pi$$
−0.989860 + 0.142046i $$0.954632\pi$$
$$600$$ 0 0
$$601$$ 5.26553 0.214786 0.107393 0.994217i $$-0.465750\pi$$
0.107393 + 0.994217i $$0.465750\pi$$
$$602$$ −29.4983 + 20.1033i −1.20226 + 0.819349i
$$603$$ 13.4504 0.547743
$$604$$ 3.56319 9.06866i 0.144984 0.368998i
$$605$$ 0 0
$$606$$ 4.94704 3.37145i 0.200960 0.136956i
$$607$$ 7.38288i 0.299662i 0.988712 + 0.149831i $$0.0478730\pi$$
−0.988712 + 0.149831i $$0.952127\pi$$
$$608$$ 30.4326 + 4.61677i 1.23420 + 0.187235i
$$609$$ −17.3331 −0.702371
$$610$$ 0 0
$$611$$ 3.20929i 0.129834i
$$612$$ 6.54445 + 2.57140i 0.264544 + 0.103943i
$$613$$ −2.64607 −0.106874 −0.0534369 0.998571i $$-0.517018\pi$$
−0.0534369 + 0.998571i $$0.517018\pi$$
$$614$$ −9.85663 14.4630i −0.397781 0.583678i
$$615$$ 0 0
$$616$$ 51.1909 11.6531i 2.06254 0.469515i
$$617$$ 21.0136i 0.845977i 0.906135 + 0.422989i $$0.139019\pi$$
−0.906135 + 0.422989i $$0.860981\pi$$
$$618$$ 0.0501658 0.0341884i 0.00201796 0.00137526i
$$619$$ 24.0874i 0.968154i 0.875025 + 0.484077i $$0.160845\pi$$
−0.875025 + 0.484077i $$0.839155\pi$$
$$620$$ 0 0
$$621$$ 7.11585i 0.285549i
$$622$$ −14.5545 21.3563i −0.583581 0.856309i
$$623$$ 41.9522i 1.68078i
$$624$$ 10.1597 + 9.44133i 0.406714 + 0.377956i
$$625$$ 0 0
$$626$$ 14.8549 10.1238i 0.593723 0.404627i
$$627$$ −21.3851 −0.854038
$$628$$ −15.8392 + 40.3121i −0.632051 + 1.60863i
$$629$$ 1.45684i 0.0580881i
$$630$$ 0 0
$$631$$ 25.2094 1.00357 0.501785 0.864992i $$-0.332677\pi$$
0.501785 + 0.864992i $$0.332677\pi$$
$$632$$ −28.3361 + 6.45042i −1.12715 + 0.256584i
$$633$$ 6.51575i 0.258978i
$$634$$ −12.6316 18.5348i −0.501665 0.736110i
$$635$$ 0 0
$$636$$ 0.170558 0.434087i 0.00676308 0.0172127i
$$637$$ −53.0714 −2.10277
$$638$$ 11.4873 + 16.8557i 0.454786 + 0.667324i
$$639$$ 2.19027 0.0866457
$$640$$ 0 0
$$641$$ −18.4755 −0.729738 −0.364869 0.931059i $$-0.618886\pi$$
−0.364869 + 0.931059i $$0.618886\pi$$
$$642$$ 12.3230 + 18.0820i 0.486351 + 0.713640i
$$643$$ −0.636984 −0.0251202 −0.0125601 0.999921i $$-0.503998\pi$$
−0.0125601 + 0.999921i $$0.503998\pi$$
$$644$$ 24.5805 62.5596i 0.968607 2.46519i
$$645$$ 0 0
$$646$$ 15.2360 + 22.3563i 0.599452 + 0.879596i
$$647$$ 32.0182i 1.25876i 0.777096 + 0.629382i $$0.216692\pi$$
−0.777096 + 0.629382i $$0.783308\pi$$
$$648$$ −2.75787 + 0.627801i −0.108340 + 0.0246623i
$$649$$ −56.5173 −2.21850
$$650$$ 0 0
$$651$$ 24.7205i 0.968873i
$$652$$ 11.8751 30.2232i 0.465065 1.18363i
$$653$$ −25.9769 −1.01656 −0.508278 0.861193i $$-0.669718\pi$$
−0.508278 + 0.861193i $$0.669718\pi$$
$$654$$ 15.1409 10.3187i 0.592057 0.403492i
$$655$$ 0 0
$$656$$ −8.80369 8.18118i −0.343726 0.319421i
$$657$$ 0.563219i 0.0219732i
$$658$$ 3.48156 + 5.10861i 0.135725 + 0.199154i
$$659$$ 21.3422i 0.831372i −0.909508 0.415686i $$-0.863541\pi$$
0.909508 0.415686i $$-0.136459\pi$$
$$660$$ 0 0
$$661$$ 14.8397i 0.577198i −0.957450 0.288599i $$-0.906810\pi$$
0.957450 0.288599i $$-0.0931895\pi$$
$$662$$ −26.9153 + 18.3430i −1.04609 + 0.712921i
$$663$$ 12.1903i 0.473431i
$$664$$ 31.2992 7.12494i 1.21465 0.276501i
$$665$$ 0 0
$$666$$ −0.330022 0.484253i −0.0127881 0.0187644i
$$667$$ 26.1150 1.01118
$$668$$ −12.4577 4.89477i −0.482001 0.189384i
$$669$$ 3.14640i 0.121647i
$$670$$ 0 0
$$671$$ −0.464893 −0.0179470
$$672$$ 26.4147 + 4.00724i 1.01897 + 0.154583i
$$673$$ 18.1167i 0.698347i −0.937058 0.349174i $$-0.886462\pi$$
0.937058 0.349174i $$-0.113538\pi$$
$$674$$ −1.00531 + 0.685127i −0.0387231 + 0.0263901i
$$675$$ 0 0
$$676$$ 0.715008 1.81976i 0.0275003 0.0699908i
$$677$$ 30.5617 1.17458 0.587291 0.809376i $$-0.300194\pi$$
0.587291 + 0.809376i $$0.300194\pi$$
$$678$$ 4.51120 3.07442i 0.173252 0.118072i
$$679$$ −34.3576 −1.31852
$$680$$ 0 0
$$681$$ −3.92103 −0.150254
$$682$$ 24.0397 16.3832i 0.920527 0.627346i
$$683$$ −22.2027 −0.849564 −0.424782 0.905296i $$-0.639649\pi$$
−0.424782 + 0.905296i $$0.639649\pi$$
$$684$$ −10.1289 3.97976i −0.387286 0.152170i
$$685$$ 0 0
$$686$$ −45.8445 + 31.2434i −1.75035 + 1.19288i
$$687$$ 25.6899i 0.980132i
$$688$$ 15.6600 + 14.5527i 0.597034 + 0.554818i
$$689$$ 0.808569 0.0308040
$$690$$ 0 0
$$691$$ 12.6890i 0.482712i 0.970437 + 0.241356i $$0.0775922\pi$$
−0.970437 + 0.241356i $$0.922408\pi$$
$$692$$ −16.3993 + 41.7378i −0.623408 + 1.58663i
$$693$$ −18.5617 −0.705101
$$694$$ 25.7133 + 37.7299i 0.976062 + 1.43221i
$$695$$ 0 0
$$696$$ 2.30401 + 10.1213i 0.0873334 + 0.383648i
$$697$$ 10.5632i 0.400110i
$$698$$ 0.868174 0.591668i 0.0328609 0.0223950i
$$699$$ 25.7565i 0.974202i
$$700$$ 0 0
$$701$$ 34.9241i 1.31906i −0.751676 0.659532i $$-0.770754\pi$$
0.751676 0.659532i $$-0.229246\pi$$
$$702$$ −2.76149 4.05203i −0.104226 0.152934i
$$703$$ 2.25476i 0.0850398i
$$704$$ −13.6092 28.3430i −0.512916 1.06822i
$$705$$ 0 0
$$706$$ 38.1431 25.9949i 1.43554 0.978330i
$$707$$ 19.9931 0.751918
$$708$$ −26.7689 10.5179i −1.00604 0.395285i
$$709$$ 5.65610i 0.212419i 0.994344 + 0.106210i $$0.0338715\pi$$
−0.994344 + 0.106210i $$0.966129\pi$$
$$710$$ 0 0
$$711$$ 10.2746 0.385328
$$712$$ 24.4972 5.57653i 0.918073 0.208989i
$$713$$ 37.2453i 1.39485i
$$714$$ 13.2245 + 19.4047i 0.494913 + 0.726203i
$$715$$ 0 0
$$716$$ −0.277065 0.108862i −0.0103544 0.00406838i
$$717$$ −15.8727 −0.592778
$$718$$ 2.15878 + 3.16764i 0.0805648 + 0.118215i
$$719$$ 20.0844 0.749020 0.374510 0.927223i $$-0.377811\pi$$
0.374510 + 0.927223i $$0.377811\pi$$
$$720$$ 0 0
$$721$$ 0.202741 0.00755048
$$722$$ −8.44856 12.3969i −0.314423 0.461364i
$$723$$ −28.1664 −1.04752
$$724$$ −19.3461 7.60132i −0.718991 0.282501i
$$725$$ 0 0
$$726$$ 3.54083 + 5.19558i 0.131413 + 0.192826i
$$727$$ 13.0424i 0.483715i 0.970312 + 0.241857i $$0.0777566\pi$$
−0.970312 + 0.241857i $$0.922243\pi$$
$$728$$ 10.2809 + 45.1629i 0.381034 + 1.67385i
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 18.7899i 0.694970i
$$732$$ −0.220192 0.0865164i −0.00813854 0.00319774i
$$733$$ −34.8917 −1.28876 −0.644378 0.764707i $$-0.722884\pi$$
−0.644378 + 0.764707i $$0.722884\pi$$
$$734$$ 0.794678 0.541580i 0.0293321 0.0199901i
$$735$$ 0 0
$$736$$ −39.7980 6.03754i −1.46697 0.222547i
$$737$$ 52.8618i 1.94719i
$$738$$ 2.39291 + 3.51120i 0.0880843 + 0.129249i
$$739$$ 41.5040i 1.52675i −0.645957 0.763374i $$-0.723541\pi$$
0.645957 0.763374i $$-0.276459\pi$$
$$740$$ 0 0
$$741$$ 18.8669i 0.693093i
$$742$$ 1.28710 0.877166i 0.0472508 0.0322018i
$$743$$ 7.63764i 0.280198i −0.990138 0.140099i $$-0.955258\pi$$
0.990138 0.140099i $$-0.0447421\pi$$
$$744$$ 14.4351 3.28600i 0.529216 0.120470i
$$745$$ 0 0
$$746$$ −2.76873 4.06265i −0.101370 0.148744i
$$747$$ −11.3490 −0.415240
$$748$$ 10.1059 25.7205i 0.369509 0.940434i
$$749$$ 73.0771i 2.67018i
$$750$$ 0 0
$$751$$ −19.4029 −0.708023 −0.354012 0.935241i $$-0.615183\pi$$
−0.354012 + 0.935241i $$0.615183\pi$$
$$752$$ 2.52029 2.71206i 0.0919056 0.0988987i
$$753$$ 4.66004i 0.169821i
$$754$$ −14.8709 + 10.1346i −0.541565 + 0.369081i
$$755$$ 0 0
$$756$$ −8.79159 3.45433i −0.319747 0.125633i
$$757$$ 43.7959 1.59179 0.795894 0.605436i $$-0.207001\pi$$
0.795894 + 0.605436i $$0.207001\pi$$
$$758$$ −26.9545 + 18.3697i −0.979030 + 0.667217i
$$759$$ 27.9662 1.01511
$$760$$ 0 0
$$761$$ 9.95519 0.360875 0.180438 0.983586i $$-0.442249\pi$$
0.180438 + 0.983586i $$0.442249\pi$$
$$762$$ 21.4801 14.6388i 0.778140 0.530309i
$$763$$ 61.1910 2.21526
$$764$$ −4.55893 + 11.6029i −0.164936 + 0.419778i
$$765$$ 0 0
$$766$$ 11.4706 7.81732i 0.414450 0.282451i
$$767$$ 49.8621i 1.80042i
$$768$$ −1.17125 15.9571i −0.0422637 0.575801i
$$769$$ 17.9008 0.645520 0.322760 0.946481i $$-0.395389\pi$$
0.322760 + 0.946481i $$0.395389\pi$$
$$770$$ 0 0
$$771$$ 3.33996i 0.120286i
$$772$$ 0.729642 + 0.286686i 0.0262604 + 0.0103180i
$$773$$ 20.8182 0.748777 0.374389 0.927272i $$-0.377853\pi$$
0.374389 + 0.927272i $$0.377853\pi$$
$$774$$ −4.25653 6.24575i −0.152998 0.224499i
$$775$$ 0 0
$$776$$ 4.56701 + 20.0625i 0.163946 + 0.720201i
$$777$$ 1.95707i 0.0702096i
$$778$$ 11.5247 7.85420i 0.413182 0.281587i
$$779$$ 16.3487i 0.585753i
$$780$$ 0 0
$$781$$ 8.60803i 0.308019i
$$782$$ −19.9247 29.2362i −0.712507 1.04549i
$$783$$ 3.66998i 0.131154i
$$784$$ 44.8488 + 41.6776i 1.60174 + 1.48848i
$$785$$ 0 0
$$786$$ −3.99546 + 2.72294i −0.142513 + 0.0971239i
$$787$$ −27.2047 −0.969744 −0.484872 0.874585i $$-0.661134\pi$$
−0.484872 + 0.874585i $$0.661134\pi$$