# Properties

 Label 120.2.d.b.109.3 Level $120$ Weight $2$ Character 120.109 Analytic conductor $0.958$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.958204824255$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.839056.1 Defining polynomial: $$x^{6} + 6x^{4} + 8x^{2} + 1$$ x^6 + 6*x^4 + 8*x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 109.3 Root $$2.02852i$$ of defining polynomial Character $$\chi$$ $$=$$ 120.109 Dual form 120.2.d.b.109.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +(-1.67896 + 2.67975i) q^{10} -0.985939i q^{11} +(1.79387 + 0.884323i) q^{12} +4.94567 q^{13} +(-5.58774 - 1.30246i) q^{14} +(2.11491 + 0.726062i) q^{15} +(2.43594 + 3.17272i) q^{16} +4.52323i q^{17} +(0.321037 - 1.37729i) q^{18} -2.60492i q^{19} +(3.15180 + 3.17272i) q^{20} +4.05705i q^{21} +(-1.35793 - 0.316523i) q^{22} -3.53729i q^{23} +(1.79387 - 2.18678i) q^{24} +(3.94567 + 3.07111i) q^{25} +(1.58774 - 6.81163i) q^{26} -1.00000 q^{27} +(-3.58774 + 7.27782i) q^{28} -7.59434i q^{29} +(1.67896 - 2.67975i) q^{30} -3.28415 q^{31} +(5.15180 - 2.33645i) q^{32} +0.985939i q^{33} +(6.22982 + 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +(-1.79387 - 0.884323i) q^{36} -0.945668 q^{37} +(-3.58774 - 0.836276i) q^{38} -4.94567 q^{39} +(5.38161 - 3.32239i) q^{40} +0.568295 q^{41} +(5.58774 + 1.30246i) q^{42} +8.45963 q^{43} +(-0.871889 + 1.76865i) q^{44} +(-2.11491 - 0.726062i) q^{45} +(-4.87189 - 1.13560i) q^{46} +2.60492i q^{47} +(-2.43594 - 3.17272i) q^{48} -9.45963 q^{49} +(5.49652 - 4.44840i) q^{50} -4.52323i q^{51} +(-8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.321037 + 1.37729i) q^{54} +(-0.715853 + 2.08517i) q^{55} +(8.87189 + 7.27782i) q^{56} +2.60492i q^{57} +(-10.4596 - 2.43806i) q^{58} +9.10003i q^{59} +(-3.15180 - 3.17272i) q^{60} +11.0183i q^{61} +(-1.05433 + 4.52323i) q^{62} -4.05705i q^{63} +(-1.56406 - 7.84562i) q^{64} +(-10.4596 - 3.59086i) q^{65} +(1.35793 + 0.316523i) q^{66} -8.45963 q^{67} +(4.00000 - 8.11409i) q^{68} +3.53729i q^{69} +(10.8719 + 6.81163i) q^{70} +1.43171 q^{71} +(-1.79387 + 2.18678i) q^{72} -11.9507i q^{73} +(-0.303594 + 1.30246i) q^{74} +(-3.94567 - 3.07111i) q^{75} +(-2.30359 + 4.67289i) q^{76} -4.00000 q^{77} +(-1.58774 + 6.81163i) q^{78} +3.28415 q^{79} +(-2.84820 - 8.47866i) q^{80} +1.00000 q^{81} +(0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(3.58774 - 7.27782i) q^{84} +(3.28415 - 9.56622i) q^{85} +(2.71585 - 11.6514i) q^{86} +7.59434i q^{87} +(2.15604 + 1.76865i) q^{88} +12.3510 q^{89} +(-1.67896 + 2.67975i) q^{90} -20.0648i q^{91} +(-3.12811 + 6.34545i) q^{92} +3.28415 q^{93} +(3.58774 + 0.836276i) q^{94} +(-1.89134 + 5.50917i) q^{95} +(-5.15180 + 2.33645i) q^{96} -3.23797i q^{97} +(-3.03689 + 13.0287i) q^{98} -0.985939i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9}+O(q^{10})$$ 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9 $$6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28} + 11 q^{30} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} + q^{36} + 16 q^{37} + 2 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 10 q^{42} + 22 q^{44} - 2 q^{46} - q^{48} - 6 q^{49} - 15 q^{50} - 26 q^{52} - 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} - 12 q^{58} - 9 q^{60} - 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} + 24 q^{68} + 38 q^{70} + 16 q^{71} + q^{72} + 18 q^{74} - 2 q^{75} + 6 q^{76} - 24 q^{77} + 14 q^{78} + 16 q^{79} - 27 q^{80} + 6 q^{81} + 50 q^{82} + 16 q^{83} - 2 q^{84} + 16 q^{85} + 20 q^{86} - 18 q^{88} - 20 q^{89} - 11 q^{90} - 46 q^{92} + 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} - 21 q^{98}+O(q^{100})$$ 6 * q + q^2 - 6 * q^3 + q^4 - q^6 + q^8 + 6 * q^9 - 11 * q^10 - q^12 + 8 * q^13 - 10 * q^14 + q^16 + q^18 + 9 * q^20 - 10 * q^22 - q^24 + 2 * q^25 - 14 * q^26 - 6 * q^27 + 2 * q^28 + 11 * q^30 - 16 * q^31 + 21 * q^32 + 12 * q^34 + 4 * q^35 + q^36 + 16 * q^37 + 2 * q^38 - 8 * q^39 - 3 * q^40 - 4 * q^41 + 10 * q^42 + 22 * q^44 - 2 * q^46 - q^48 - 6 * q^49 - 15 * q^50 - 26 * q^52 - 24 * q^53 - q^54 - 8 * q^55 + 26 * q^56 - 12 * q^58 - 9 * q^60 - 28 * q^62 - 23 * q^64 - 12 * q^65 + 10 * q^66 + 24 * q^68 + 38 * q^70 + 16 * q^71 + q^72 + 18 * q^74 - 2 * q^75 + 6 * q^76 - 24 * q^77 + 14 * q^78 + 16 * q^79 - 27 * q^80 + 6 * q^81 + 50 * q^82 + 16 * q^83 - 2 * q^84 + 16 * q^85 + 20 * q^86 - 18 * q^88 - 20 * q^89 - 11 * q^90 - 46 * q^92 + 16 * q^93 - 2 * q^94 + 32 * q^95 - 21 * q^96 - 21 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$41$$ $$61$$ $$97$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.321037 1.37729i 0.227007 0.973893i
$$3$$ −1.00000 −0.577350
$$4$$ −1.79387 0.884323i −0.896935 0.442162i
$$5$$ −2.11491 0.726062i −0.945815 0.324705i
$$6$$ −0.321037 + 1.37729i −0.131063 + 0.562277i
$$7$$ 4.05705i 1.53342i −0.641994 0.766710i $$-0.721893\pi$$
0.641994 0.766710i $$-0.278107\pi$$
$$8$$ −1.79387 + 2.18678i −0.634229 + 0.773145i
$$9$$ 1.00000 0.333333
$$10$$ −1.67896 + 2.67975i −0.530935 + 0.847413i
$$11$$ 0.985939i 0.297272i −0.988892 0.148636i $$-0.952512\pi$$
0.988892 0.148636i $$-0.0474882\pi$$
$$12$$ 1.79387 + 0.884323i 0.517846 + 0.255282i
$$13$$ 4.94567 1.37168 0.685841 0.727752i $$-0.259435\pi$$
0.685841 + 0.727752i $$0.259435\pi$$
$$14$$ −5.58774 1.30246i −1.49339 0.348097i
$$15$$ 2.11491 + 0.726062i 0.546067 + 0.187468i
$$16$$ 2.43594 + 3.17272i 0.608986 + 0.793181i
$$17$$ 4.52323i 1.09704i 0.836136 + 0.548522i $$0.184809\pi$$
−0.836136 + 0.548522i $$0.815191\pi$$
$$18$$ 0.321037 1.37729i 0.0756691 0.324631i
$$19$$ 2.60492i 0.597610i −0.954314 0.298805i $$-0.903412\pi$$
0.954314 0.298805i $$-0.0965881\pi$$
$$20$$ 3.15180 + 3.17272i 0.704763 + 0.709443i
$$21$$ 4.05705i 0.885320i
$$22$$ −1.35793 0.316523i −0.289511 0.0674829i
$$23$$ 3.53729i 0.737577i −0.929513 0.368788i $$-0.879773\pi$$
0.929513 0.368788i $$-0.120227\pi$$
$$24$$ 1.79387 2.18678i 0.366172 0.446376i
$$25$$ 3.94567 + 3.07111i 0.789134 + 0.614222i
$$26$$ 1.58774 6.81163i 0.311382 1.33587i
$$27$$ −1.00000 −0.192450
$$28$$ −3.58774 + 7.27782i −0.678019 + 1.37538i
$$29$$ 7.59434i 1.41023i −0.709091 0.705117i $$-0.750895\pi$$
0.709091 0.705117i $$-0.249105\pi$$
$$30$$ 1.67896 2.67975i 0.306535 0.489254i
$$31$$ −3.28415 −0.589850 −0.294925 0.955520i $$-0.595295\pi$$
−0.294925 + 0.955520i $$0.595295\pi$$
$$32$$ 5.15180 2.33645i 0.910718 0.413029i
$$33$$ 0.985939i 0.171630i
$$34$$ 6.22982 + 1.45212i 1.06840 + 0.249037i
$$35$$ −2.94567 + 8.58028i −0.497909 + 1.45033i
$$36$$ −1.79387 0.884323i −0.298978 0.147387i
$$37$$ −0.945668 −0.155467 −0.0777334 0.996974i $$-0.524768\pi$$
−0.0777334 + 0.996974i $$0.524768\pi$$
$$38$$ −3.58774 0.836276i −0.582009 0.135662i
$$39$$ −4.94567 −0.791941
$$40$$ 5.38161 3.32239i 0.850908 0.525315i
$$41$$ 0.568295 0.0887527 0.0443763 0.999015i $$-0.485870\pi$$
0.0443763 + 0.999015i $$0.485870\pi$$
$$42$$ 5.58774 + 1.30246i 0.862207 + 0.200974i
$$43$$ 8.45963 1.29008 0.645041 0.764148i $$-0.276840\pi$$
0.645041 + 0.764148i $$0.276840\pi$$
$$44$$ −0.871889 + 1.76865i −0.131442 + 0.266634i
$$45$$ −2.11491 0.726062i −0.315272 0.108235i
$$46$$ −4.87189 1.13560i −0.718321 0.167435i
$$47$$ 2.60492i 0.379967i 0.981787 + 0.189984i $$0.0608435\pi$$
−0.981787 + 0.189984i $$0.939157\pi$$
$$48$$ −2.43594 3.17272i −0.351598 0.457943i
$$49$$ −9.45963 −1.35138
$$50$$ 5.49652 4.44840i 0.777325 0.629099i
$$51$$ 4.52323i 0.633379i
$$52$$ −8.87189 4.37357i −1.23031 0.606505i
$$53$$ 0.229815 0.0315675 0.0157838 0.999875i $$-0.494976\pi$$
0.0157838 + 0.999875i $$0.494976\pi$$
$$54$$ −0.321037 + 1.37729i −0.0436876 + 0.187426i
$$55$$ −0.715853 + 2.08517i −0.0965256 + 0.281164i
$$56$$ 8.87189 + 7.27782i 1.18556 + 0.972539i
$$57$$ 2.60492i 0.345030i
$$58$$ −10.4596 2.43806i −1.37342 0.320133i
$$59$$ 9.10003i 1.18472i 0.805672 + 0.592362i $$0.201804\pi$$
−0.805672 + 0.592362i $$0.798196\pi$$
$$60$$ −3.15180 3.17272i −0.406895 0.409597i
$$61$$ 11.0183i 1.41075i 0.708832 + 0.705377i $$0.249222\pi$$
−0.708832 + 0.705377i $$0.750778\pi$$
$$62$$ −1.05433 + 4.52323i −0.133900 + 0.574451i
$$63$$ 4.05705i 0.511140i
$$64$$ −1.56406 7.84562i −0.195507 0.980702i
$$65$$ −10.4596 3.59086i −1.29736 0.445392i
$$66$$ 1.35793 + 0.316523i 0.167149 + 0.0389612i
$$67$$ −8.45963 −1.03351 −0.516754 0.856134i $$-0.672860\pi$$
−0.516754 + 0.856134i $$0.672860\pi$$
$$68$$ 4.00000 8.11409i 0.485071 0.983978i
$$69$$ 3.53729i 0.425840i
$$70$$ 10.8719 + 6.81163i 1.29944 + 0.814146i
$$71$$ 1.43171 0.169912 0.0849561 0.996385i $$-0.472925\pi$$
0.0849561 + 0.996385i $$0.472925\pi$$
$$72$$ −1.79387 + 2.18678i −0.211410 + 0.257715i
$$73$$ 11.9507i 1.39873i −0.714767 0.699363i $$-0.753467\pi$$
0.714767 0.699363i $$-0.246533\pi$$
$$74$$ −0.303594 + 1.30246i −0.0352921 + 0.151408i
$$75$$ −3.94567 3.07111i −0.455606 0.354621i
$$76$$ −2.30359 + 4.67289i −0.264240 + 0.536018i
$$77$$ −4.00000 −0.455842
$$78$$ −1.58774 + 6.81163i −0.179776 + 0.771266i
$$79$$ 3.28415 0.369495 0.184748 0.982786i $$-0.440853\pi$$
0.184748 + 0.982786i $$0.440853\pi$$
$$80$$ −2.84820 8.47866i −0.318439 0.947943i
$$81$$ 1.00000 0.111111
$$82$$ 0.182443 0.782708i 0.0201475 0.0864356i
$$83$$ 9.89134 1.08572 0.542858 0.839825i $$-0.317342\pi$$
0.542858 + 0.839825i $$0.317342\pi$$
$$84$$ 3.58774 7.27782i 0.391455 0.794075i
$$85$$ 3.28415 9.56622i 0.356216 1.03760i
$$86$$ 2.71585 11.6514i 0.292858 1.25640i
$$87$$ 7.59434i 0.814199i
$$88$$ 2.15604 + 1.76865i 0.229834 + 0.188538i
$$89$$ 12.3510 1.30920 0.654600 0.755976i $$-0.272837\pi$$
0.654600 + 0.755976i $$0.272837\pi$$
$$90$$ −1.67896 + 2.67975i −0.176978 + 0.282471i
$$91$$ 20.0648i 2.10336i
$$92$$ −3.12811 + 6.34545i −0.326128 + 0.661559i
$$93$$ 3.28415 0.340550
$$94$$ 3.58774 + 0.836276i 0.370047 + 0.0862553i
$$95$$ −1.89134 + 5.50917i −0.194047 + 0.565229i
$$96$$ −5.15180 + 2.33645i −0.525803 + 0.238463i
$$97$$ 3.23797i 0.328766i −0.986397 0.164383i $$-0.947437\pi$$
0.986397 0.164383i $$-0.0525633\pi$$
$$98$$ −3.03689 + 13.0287i −0.306772 + 1.31610i
$$99$$ 0.985939i 0.0990906i
$$100$$ −4.36217 8.99842i −0.436217 0.899842i
$$101$$ 4.35637i 0.433475i 0.976230 + 0.216738i $$0.0695416\pi$$
−0.976230 + 0.216738i $$0.930458\pi$$
$$102$$ −6.22982 1.45212i −0.616844 0.143782i
$$103$$ 15.0754i 1.48542i 0.669612 + 0.742711i $$0.266460\pi$$
−0.669612 + 0.742711i $$0.733540\pi$$
$$104$$ −8.87189 + 10.8151i −0.869960 + 1.06051i
$$105$$ 2.94567 8.58028i 0.287468 0.837350i
$$106$$ 0.0737791 0.316523i 0.00716606 0.0307434i
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 1.79387 + 0.884323i 0.172615 + 0.0850941i
$$109$$ 4.17034i 0.399446i 0.979852 + 0.199723i $$0.0640042\pi$$
−0.979852 + 0.199723i $$0.935996\pi$$
$$110$$ 2.64207 + 1.65535i 0.251912 + 0.157832i
$$111$$ 0.945668 0.0897588
$$112$$ 12.8719 9.88274i 1.21628 0.933831i
$$113$$ 1.28526i 0.120907i 0.998171 + 0.0604537i $$0.0192548\pi$$
−0.998171 + 0.0604537i $$0.980745\pi$$
$$114$$ 3.58774 + 0.836276i 0.336023 + 0.0783244i
$$115$$ −2.56829 + 7.48105i −0.239495 + 0.697611i
$$116$$ −6.71585 + 13.6233i −0.623551 + 1.26489i
$$117$$ 4.94567 0.457227
$$118$$ 12.5334 + 2.92145i 1.15379 + 0.268941i
$$119$$ 18.3510 1.68223
$$120$$ −5.38161 + 3.32239i −0.491272 + 0.303291i
$$121$$ 10.0279 0.911630
$$122$$ 15.1755 + 3.53729i 1.37392 + 0.320252i
$$123$$ −0.568295 −0.0512414
$$124$$ 5.89134 + 2.90425i 0.529058 + 0.260809i
$$125$$ −6.11491 9.35991i −0.546934 0.837176i
$$126$$ −5.58774 1.30246i −0.497796 0.116032i
$$127$$ 1.15280i 0.102294i −0.998691 0.0511472i $$-0.983712\pi$$
0.998691 0.0511472i $$-0.0162878\pi$$
$$128$$ −11.3078 0.364570i −0.999481 0.0322237i
$$129$$ −8.45963 −0.744829
$$130$$ −8.30359 + 13.2532i −0.728273 + 1.16238i
$$131$$ 3.89019i 0.339887i −0.985454 0.169944i $$-0.945641\pi$$
0.985454 0.169944i $$-0.0543586\pi$$
$$132$$ 0.871889 1.76865i 0.0758882 0.153941i
$$133$$ −10.5683 −0.916387
$$134$$ −2.71585 + 11.6514i −0.234614 + 1.00653i
$$135$$ 2.11491 + 0.726062i 0.182022 + 0.0624895i
$$136$$ −9.89134 8.11409i −0.848175 0.695778i
$$137$$ 17.5135i 1.49628i −0.663544 0.748138i $$-0.730948\pi$$
0.663544 0.748138i $$-0.269052\pi$$
$$138$$ 4.87189 + 1.13560i 0.414723 + 0.0966688i
$$139$$ 16.8612i 1.43015i 0.699047 + 0.715076i $$0.253608\pi$$
−0.699047 + 0.715076i $$0.746392\pi$$
$$140$$ 12.8719 12.7870i 1.08787 1.08070i
$$141$$ 2.60492i 0.219374i
$$142$$ 0.459630 1.97188i 0.0385713 0.165476i
$$143$$ 4.87613i 0.407762i
$$144$$ 2.43594 + 3.17272i 0.202995 + 0.264394i
$$145$$ −5.51396 + 16.0613i −0.457910 + 1.33382i
$$146$$ −16.4596 3.83662i −1.36221 0.317521i
$$147$$ 9.45963 0.780217
$$148$$ 1.69641 + 0.836276i 0.139444 + 0.0687415i
$$149$$ 10.4986i 0.860078i −0.902810 0.430039i $$-0.858500\pi$$
0.902810 0.430039i $$-0.141500\pi$$
$$150$$ −5.49652 + 4.44840i −0.448789 + 0.363210i
$$151$$ 4.71585 0.383771 0.191885 0.981417i $$-0.438540\pi$$
0.191885 + 0.981417i $$0.438540\pi$$
$$152$$ 5.69641 + 4.67289i 0.462040 + 0.379022i
$$153$$ 4.52323i 0.365682i
$$154$$ −1.28415 + 5.50917i −0.103480 + 0.443942i
$$155$$ 6.94567 + 2.38449i 0.557889 + 0.191527i
$$156$$ 8.87189 + 4.37357i 0.710320 + 0.350166i
$$157$$ −8.94567 −0.713942 −0.356971 0.934115i $$-0.616191\pi$$
−0.356971 + 0.934115i $$0.616191\pi$$
$$158$$ 1.05433 4.52323i 0.0838782 0.359849i
$$159$$ −0.229815 −0.0182255
$$160$$ −12.5920 + 1.20085i −0.995483 + 0.0949352i
$$161$$ −14.3510 −1.13101
$$162$$ 0.321037 1.37729i 0.0252230 0.108210i
$$163$$ −15.7827 −1.23619 −0.618097 0.786102i $$-0.712096\pi$$
−0.618097 + 0.786102i $$0.712096\pi$$
$$164$$ −1.01945 0.502556i −0.0796054 0.0392430i
$$165$$ 0.715853 2.08517i 0.0557291 0.162330i
$$166$$ 3.17548 13.6233i 0.246465 1.05737i
$$167$$ 5.50917i 0.426312i 0.977018 + 0.213156i $$0.0683743\pi$$
−0.977018 + 0.213156i $$0.931626\pi$$
$$168$$ −8.87189 7.27782i −0.684481 0.561496i
$$169$$ 11.4596 0.881510
$$170$$ −12.1212 7.59434i −0.929650 0.582459i
$$171$$ 2.60492i 0.199203i
$$172$$ −15.1755 7.48105i −1.15712 0.570425i
$$173$$ 10.3385 0.786020 0.393010 0.919534i $$-0.371434\pi$$
0.393010 + 0.919534i $$0.371434\pi$$
$$174$$ 10.4596 + 2.43806i 0.792943 + 0.184829i
$$175$$ 12.4596 16.0078i 0.941860 1.21007i
$$176$$ 3.12811 2.40169i 0.235790 0.181034i
$$177$$ 9.10003i 0.684000i
$$178$$ 3.96511 17.0109i 0.297198 1.27502i
$$179$$ 16.1746i 1.20895i −0.796625 0.604474i $$-0.793383\pi$$
0.796625 0.604474i $$-0.206617\pi$$
$$180$$ 3.15180 + 3.17272i 0.234921 + 0.236481i
$$181$$ 8.11409i 0.603116i 0.953448 + 0.301558i $$0.0975067\pi$$
−0.953448 + 0.301558i $$0.902493\pi$$
$$182$$ −27.6351 6.44154i −2.04845 0.477479i
$$183$$ 11.0183i 0.814499i
$$184$$ 7.73530 + 6.34545i 0.570254 + 0.467793i
$$185$$ 2.00000 + 0.686614i 0.147043 + 0.0504808i
$$186$$ 1.05433 4.52323i 0.0773074 0.331659i
$$187$$ 4.45963 0.326120
$$188$$ 2.30359 4.67289i 0.168007 0.340806i
$$189$$ 4.05705i 0.295107i
$$190$$ 6.98055 + 4.37357i 0.506423 + 0.317292i
$$191$$ −24.9193 −1.80309 −0.901547 0.432681i $$-0.857568\pi$$
−0.901547 + 0.432681i $$0.857568\pi$$
$$192$$ 1.56406 + 7.84562i 0.112876 + 0.566209i
$$193$$ 1.03951i 0.0748254i −0.999300 0.0374127i $$-0.988088\pi$$
0.999300 0.0374127i $$-0.0119116\pi$$
$$194$$ −4.45963 1.03951i −0.320183 0.0746323i
$$195$$ 10.4596 + 3.59086i 0.749030 + 0.257147i
$$196$$ 16.9694 + 8.36537i 1.21210 + 0.597527i
$$197$$ 9.66152 0.688355 0.344177 0.938905i $$-0.388158\pi$$
0.344177 + 0.938905i $$0.388158\pi$$
$$198$$ −1.35793 0.316523i −0.0965036 0.0224943i
$$199$$ −23.0668 −1.63516 −0.817582 0.575813i $$-0.804686\pi$$
−0.817582 + 0.575813i $$0.804686\pi$$
$$200$$ −13.7939 + 3.11916i −0.975374 + 0.220558i
$$201$$ 8.45963 0.596696
$$202$$ 6.00000 + 1.39856i 0.422159 + 0.0984020i
$$203$$ −30.8106 −2.16248
$$204$$ −4.00000 + 8.11409i −0.280056 + 0.568100i
$$205$$ −1.20189 0.412617i −0.0839437 0.0288184i
$$206$$ 20.7632 + 4.83975i 1.44664 + 0.337202i
$$207$$ 3.53729i 0.245859i
$$208$$ 12.0474 + 15.6912i 0.835335 + 1.08799i
$$209$$ −2.56829 −0.177653
$$210$$ −10.8719 6.81163i −0.750232 0.470047i
$$211$$ 6.44154i 0.443454i 0.975109 + 0.221727i $$0.0711694\pi$$
−0.975109 + 0.221727i $$0.928831\pi$$
$$212$$ −0.412259 0.203231i −0.0283140 0.0139580i
$$213$$ −1.43171 −0.0980988
$$214$$ 1.28415 5.50917i 0.0877825 0.376599i
$$215$$ −17.8913 6.14222i −1.22018 0.418896i
$$216$$ 1.79387 2.18678i 0.122057 0.148792i
$$217$$ 13.3239i 0.904488i
$$218$$ 5.74378 + 1.33883i 0.389018 + 0.0906772i
$$219$$ 11.9507i 0.807554i
$$220$$ 3.12811 3.10748i 0.210897 0.209506i
$$221$$ 22.3704i 1.50480i
$$222$$ 0.303594 1.30246i 0.0203759 0.0874155i
$$223$$ 17.9796i 1.20401i 0.798494 + 0.602003i $$0.205630\pi$$
−0.798494 + 0.602003i $$0.794370\pi$$
$$224$$ −9.47908 20.9011i −0.633347 1.39651i
$$225$$ 3.94567 + 3.07111i 0.263045 + 0.204741i
$$226$$ 1.77018 + 0.412617i 0.117751 + 0.0274469i
$$227$$ 7.02792 0.466460 0.233230 0.972422i $$-0.425071\pi$$
0.233230 + 0.972422i $$0.425071\pi$$
$$228$$ 2.30359 4.67289i 0.152559 0.309470i
$$229$$ 4.17034i 0.275584i −0.990461 0.137792i $$-0.955999\pi$$
0.990461 0.137792i $$-0.0440005\pi$$
$$230$$ 9.47908 + 5.93899i 0.625032 + 0.391605i
$$231$$ 4.00000 0.263181
$$232$$ 16.6072 + 13.6233i 1.09032 + 0.894411i
$$233$$ 23.9894i 1.57160i 0.618483 + 0.785799i $$0.287748\pi$$
−0.618483 + 0.785799i $$0.712252\pi$$
$$234$$ 1.58774 6.81163i 0.103794 0.445290i
$$235$$ 1.89134 5.50917i 0.123377 0.359379i
$$236$$ 8.04737 16.3243i 0.523839 1.06262i
$$237$$ −3.28415 −0.213328
$$238$$ 5.89134 25.2747i 0.381879 1.63831i
$$239$$ 8.91926 0.576939 0.288469 0.957489i $$-0.406854\pi$$
0.288469 + 0.957489i $$0.406854\pi$$
$$240$$ 2.84820 + 8.47866i 0.183851 + 0.547295i
$$241$$ −16.3510 −1.05326 −0.526629 0.850095i $$-0.676544\pi$$
−0.526629 + 0.850095i $$0.676544\pi$$
$$242$$ 3.21933 13.8114i 0.206947 0.887830i
$$243$$ −1.00000 −0.0641500
$$244$$ 9.74378 19.7655i 0.623781 1.26536i
$$245$$ 20.0062 + 6.86828i 1.27815 + 0.438798i
$$246$$ −0.182443 + 0.782708i −0.0116322 + 0.0499036i
$$247$$ 12.8831i 0.819731i
$$248$$ 5.89134 7.18172i 0.374100 0.456040i
$$249$$ −9.89134 −0.626838
$$250$$ −14.8544 + 5.41714i −0.939478 + 0.342610i
$$251$$ 4.22391i 0.266611i −0.991075 0.133305i $$-0.957441\pi$$
0.991075 0.133305i $$-0.0425591\pi$$
$$252$$ −3.58774 + 7.27782i −0.226006 + 0.458459i
$$253$$ −3.48755 −0.219261
$$254$$ −1.58774 0.370091i −0.0996238 0.0232216i
$$255$$ −3.28415 + 9.56622i −0.205661 + 0.599060i
$$256$$ −4.13235 + 15.4572i −0.258272 + 0.966072i
$$257$$ 24.6952i 1.54044i 0.637777 + 0.770221i $$0.279854\pi$$
−0.637777 + 0.770221i $$0.720146\pi$$
$$258$$ −2.71585 + 11.6514i −0.169082 + 0.725384i
$$259$$ 3.83662i 0.238396i
$$260$$ 15.5877 + 15.6912i 0.966711 + 0.973129i
$$261$$ 7.59434i 0.470078i
$$262$$ −5.35793 1.24889i −0.331014 0.0771569i
$$263$$ 14.6628i 0.904145i −0.891981 0.452073i $$-0.850685\pi$$
0.891981 0.452073i $$-0.149315\pi$$
$$264$$ −2.15604 1.76865i −0.132695 0.108853i
$$265$$ −0.486038 0.166860i −0.0298571 0.0102501i
$$266$$ −3.39281 + 14.5556i −0.208027 + 0.892463i
$$267$$ −12.3510 −0.755867
$$268$$ 15.1755 + 7.48105i 0.926990 + 0.456978i
$$269$$ 11.5381i 0.703490i 0.936096 + 0.351745i $$0.114412\pi$$
−0.936096 + 0.351745i $$0.885588\pi$$
$$270$$ 1.67896 2.67975i 0.102178 0.163085i
$$271$$ 5.63511 0.342309 0.171154 0.985244i $$-0.445250\pi$$
0.171154 + 0.985244i $$0.445250\pi$$
$$272$$ −14.3510 + 11.0183i −0.870155 + 0.668085i
$$273$$ 20.0648i 1.21438i
$$274$$ −24.1212 5.62246i −1.45721 0.339665i
$$275$$ 3.02792 3.89019i 0.182591 0.234587i
$$276$$ 3.12811 6.34545i 0.188290 0.381951i
$$277$$ 17.4053 1.04578 0.522892 0.852399i $$-0.324853\pi$$
0.522892 + 0.852399i $$0.324853\pi$$
$$278$$ 23.2229 + 5.41308i 1.39281 + 0.324655i
$$279$$ −3.28415 −0.196617
$$280$$ −13.4791 21.8335i −0.805529 1.30480i
$$281$$ 21.7827 1.29945 0.649723 0.760171i $$-0.274885\pi$$
0.649723 + 0.760171i $$0.274885\pi$$
$$282$$ −3.58774 0.836276i −0.213647 0.0497995i
$$283$$ 21.5962 1.28376 0.641881 0.766804i $$-0.278154\pi$$
0.641881 + 0.766804i $$0.278154\pi$$
$$284$$ −2.56829 1.26609i −0.152400 0.0751287i
$$285$$ 1.89134 5.50917i 0.112033 0.326335i
$$286$$ −6.71585 1.56542i −0.397117 0.0925650i
$$287$$ 2.30560i 0.136095i
$$288$$ 5.15180 2.33645i 0.303573 0.137676i
$$289$$ −3.45963 −0.203508
$$290$$ 20.3510 + 12.7506i 1.19505 + 0.748742i
$$291$$ 3.23797i 0.189813i
$$292$$ −10.5683 + 21.4380i −0.618463 + 1.25457i
$$293$$ −32.0125 −1.87019 −0.935095 0.354398i $$-0.884686\pi$$
−0.935095 + 0.354398i $$0.884686\pi$$
$$294$$ 3.03689 13.0287i 0.177115 0.759848i
$$295$$ 6.60719 19.2457i 0.384685 1.12053i
$$296$$ 1.69641 2.06797i 0.0986016 0.120198i
$$297$$ 0.985939i 0.0572100i
$$298$$ −14.4596 3.37043i −0.837624 0.195244i
$$299$$ 17.4943i 1.01172i
$$300$$ 4.36217 + 8.99842i 0.251850 + 0.519524i
$$301$$ 34.3211i 1.97824i
$$302$$ 1.51396 6.49511i 0.0871187 0.373752i
$$303$$ 4.35637i 0.250267i
$$304$$ 8.26470 6.34545i 0.474013 0.363936i
$$305$$ 8.00000 23.3028i 0.458079 1.33431i
$$306$$ 6.22982 + 1.45212i 0.356135 + 0.0830124i
$$307$$ −1.13659 −0.0648686 −0.0324343 0.999474i $$-0.510326\pi$$
−0.0324343 + 0.999474i $$0.510326\pi$$
$$308$$ 7.17548 + 3.53729i 0.408861 + 0.201556i
$$309$$ 15.0754i 0.857609i
$$310$$ 5.51396 8.80071i 0.313172 0.499847i
$$311$$ 5.13659 0.291269 0.145635 0.989338i $$-0.453478\pi$$
0.145635 + 0.989338i $$0.453478\pi$$
$$312$$ 8.87189 10.8151i 0.502272 0.612285i
$$313$$ 23.0762i 1.30434i −0.758071 0.652172i $$-0.773858\pi$$
0.758071 0.652172i $$-0.226142\pi$$
$$314$$ −2.87189 + 12.3208i −0.162070 + 0.695303i
$$315$$ −2.94567 + 8.58028i −0.165970 + 0.483444i
$$316$$ −5.89134 2.90425i −0.331414 0.163377i
$$317$$ 1.66152 0.0933203 0.0466601 0.998911i $$-0.485142\pi$$
0.0466601 + 0.998911i $$0.485142\pi$$
$$318$$ −0.0737791 + 0.316523i −0.00413733 + 0.0177497i
$$319$$ −7.48755 −0.419223
$$320$$ −2.38857 + 17.7284i −0.133525 + 0.991045i
$$321$$ −4.00000 −0.223258
$$322$$ −4.60719 + 19.7655i −0.256749 + 1.10149i
$$323$$ 11.7827 0.655605
$$324$$ −1.79387 0.884323i −0.0996595 0.0491291i
$$325$$ 19.5140 + 15.1887i 1.08244 + 0.842516i
$$326$$ −5.06682 + 21.7374i −0.280625 + 1.20392i
$$327$$ 4.17034i 0.230620i
$$328$$ −1.01945 + 1.24274i −0.0562895 + 0.0686187i
$$329$$ 10.5683 0.582649
$$330$$ −2.64207 1.65535i −0.145441 0.0911243i
$$331$$ 25.9077i 1.42402i 0.702171 + 0.712008i $$0.252214\pi$$
−0.702171 + 0.712008i $$0.747786\pi$$
$$332$$ −17.7438 8.74714i −0.973816 0.480062i
$$333$$ −0.945668 −0.0518223
$$334$$ 7.58774 + 1.76865i 0.415183 + 0.0967760i
$$335$$ 17.8913 + 6.14222i 0.977508 + 0.335585i
$$336$$ −12.8719 + 9.88274i −0.702219 + 0.539148i
$$337$$ 8.00696i 0.436167i 0.975930 + 0.218083i $$0.0699805\pi$$
−0.975930 + 0.218083i $$0.930020\pi$$
$$338$$ 3.67896 15.7833i 0.200109 0.858496i
$$339$$ 1.28526i 0.0698060i
$$340$$ −14.3510 + 14.2563i −0.778290 + 0.773157i
$$341$$ 3.23797i 0.175346i
$$342$$ −3.58774 0.836276i −0.194003 0.0452206i
$$343$$ 9.97884i 0.538806i
$$344$$ −15.1755 + 18.4994i −0.818207 + 0.997420i
$$345$$ 2.56829 7.48105i 0.138272 0.402766i
$$346$$ 3.31903 14.2391i 0.178432 0.765499i
$$347$$ −23.0279 −1.23620 −0.618102 0.786098i $$-0.712098\pi$$
−0.618102 + 0.786098i $$0.712098\pi$$
$$348$$ 6.71585 13.6233i 0.360007 0.730284i
$$349$$ 21.4380i 1.14755i −0.819012 0.573776i $$-0.805478\pi$$
0.819012 0.573776i $$-0.194522\pi$$
$$350$$ −18.0474 22.2996i −0.964673 1.19197i
$$351$$ −4.94567 −0.263980
$$352$$ −2.30359 5.07936i −0.122782 0.270731i
$$353$$ 4.52323i 0.240747i 0.992729 + 0.120374i $$0.0384093\pi$$
−0.992729 + 0.120374i $$0.961591\pi$$
$$354$$ −12.5334 2.92145i −0.666143 0.155273i
$$355$$ −3.02792 1.03951i −0.160706 0.0551713i
$$356$$ −22.1560 10.9222i −1.17427 0.578878i
$$357$$ −18.3510 −0.971236
$$358$$ −22.2772 5.19265i −1.17739 0.274440i
$$359$$ −10.3510 −0.546303 −0.273152 0.961971i $$-0.588066\pi$$
−0.273152 + 0.961971i $$0.588066\pi$$
$$360$$ 5.38161 3.32239i 0.283636 0.175105i
$$361$$ 12.2144 0.642862
$$362$$ 11.1755 + 2.60492i 0.587370 + 0.136912i
$$363$$ −10.0279 −0.526330
$$364$$ −17.7438 + 35.9937i −0.930027 + 1.88658i
$$365$$ −8.67696 + 25.2747i −0.454173 + 1.32294i
$$366$$ −15.1755 3.53729i −0.793235 0.184897i
$$367$$ 0.485359i 0.0253355i −0.999920 0.0126678i $$-0.995968\pi$$
0.999920 0.0126678i $$-0.00403238\pi$$
$$368$$ 11.2229 8.61665i 0.585032 0.449174i
$$369$$ 0.568295 0.0295842
$$370$$ 1.58774 2.53416i 0.0825427 0.131745i
$$371$$ 0.932371i 0.0484063i
$$372$$ −5.89134 2.90425i −0.305452 0.150578i
$$373$$ −30.0823 −1.55760 −0.778800 0.627272i $$-0.784171\pi$$
−0.778800 + 0.627272i $$0.784171\pi$$
$$374$$ 1.43171 6.14222i 0.0740317 0.317606i
$$375$$ 6.11491 + 9.35991i 0.315772 + 0.483344i
$$376$$ −5.69641 4.67289i −0.293770 0.240986i
$$377$$ 37.5591i 1.93439i
$$378$$ 5.58774 + 1.30246i 0.287402 + 0.0669914i
$$379$$ 33.6881i 1.73044i −0.501392 0.865220i $$-0.667179\pi$$
0.501392 0.865220i $$-0.332821\pi$$
$$380$$ 8.26470 8.21019i 0.423970 0.421174i
$$381$$ 1.15280i 0.0590597i
$$382$$ −8.00000 + 34.3211i −0.409316 + 1.75602i
$$383$$ 5.17545i 0.264453i 0.991220 + 0.132227i $$0.0422127\pi$$
−0.991220 + 0.132227i $$0.957787\pi$$
$$384$$ 11.3078 + 0.364570i 0.577050 + 0.0186044i
$$385$$ 8.45963 + 2.90425i 0.431143 + 0.148014i
$$386$$ −1.43171 0.333720i −0.0728719 0.0169859i
$$387$$ 8.45963 0.430027
$$388$$ −2.86341 + 5.80850i −0.145368 + 0.294882i
$$389$$ 16.6408i 0.843722i 0.906660 + 0.421861i $$0.138623\pi$$
−0.906660 + 0.421861i $$0.861377\pi$$
$$390$$ 8.30359 13.2532i 0.420469 0.671101i
$$391$$ 16.0000 0.809155
$$392$$ 16.9694 20.6862i 0.857082 1.04481i
$$393$$ 3.89019i 0.196234i
$$394$$ 3.10170 13.3067i 0.156262 0.670384i
$$395$$ −6.94567 2.38449i −0.349474 0.119977i
$$396$$ −0.871889 + 1.76865i −0.0438141 + 0.0888778i
$$397$$ 20.4332 1.02551 0.512757 0.858534i $$-0.328624\pi$$
0.512757 + 0.858534i $$0.328624\pi$$
$$398$$ −7.40530 + 31.7698i −0.371194 + 1.59247i
$$399$$ 10.5683 0.529076
$$400$$ −0.132350 + 19.9996i −0.00661751 + 0.999978i
$$401$$ −4.56829 −0.228130 −0.114065 0.993473i $$-0.536387\pi$$
−0.114065 + 0.993473i $$0.536387\pi$$
$$402$$ 2.71585 11.6514i 0.135454 0.581118i
$$403$$ −16.2423 −0.809087
$$404$$ 3.85244 7.81477i 0.191666 0.388799i
$$405$$ −2.11491 0.726062i −0.105091 0.0360783i
$$406$$ −9.89134 + 42.4352i −0.490899 + 2.10602i
$$407$$ 0.932371i 0.0462159i
$$408$$ 9.89134 + 8.11409i 0.489694 + 0.401708i
$$409$$ −19.8913 −0.983563 −0.491782 0.870719i $$-0.663654\pi$$
−0.491782 + 0.870719i $$0.663654\pi$$
$$410$$ −0.954146 + 1.52289i −0.0471219 + 0.0752102i
$$411$$ 17.5135i 0.863875i
$$412$$ 13.3315 27.0433i 0.656797 1.33233i
$$413$$ 36.9193 1.81668
$$414$$ −4.87189 1.13560i −0.239440 0.0558118i
$$415$$ −20.9193 7.18172i −1.02689 0.352537i
$$416$$ 25.4791 11.5553i 1.24921 0.566545i
$$417$$ 16.8612i 0.825698i
$$418$$ −0.824517 + 3.53729i −0.0403284 + 0.173015i
$$419$$ 0.387288i 0.0189203i 0.999955 + 0.00946013i $$0.00301130\pi$$
−0.999955 + 0.00946013i $$0.996989\pi$$
$$420$$ −12.8719 + 12.7870i −0.628084 + 0.623941i
$$421$$ 12.0578i 0.587664i −0.955857 0.293832i $$-0.905069\pi$$
0.955857 0.293832i $$-0.0949306\pi$$
$$422$$ 8.87189 + 2.06797i 0.431877 + 0.100667i
$$423$$ 2.60492i 0.126656i
$$424$$ −0.412259 + 0.502556i −0.0200210 + 0.0244063i
$$425$$ −13.8913 + 17.8472i −0.673829 + 0.865715i
$$426$$ −0.459630 + 1.97188i −0.0222692 + 0.0955378i
$$427$$ 44.7019 2.16328
$$428$$ −7.17548 3.53729i −0.346840 0.170982i
$$429$$ 4.87613i 0.235422i
$$430$$ −14.2034 + 22.6697i −0.684949 + 1.09323i
$$431$$ 40.4068 1.94633 0.973164 0.230113i $$-0.0739096\pi$$
0.973164 + 0.230113i $$0.0739096\pi$$
$$432$$ −2.43594 3.17272i −0.117199 0.152648i
$$433$$ 36.1859i 1.73898i −0.493949 0.869491i $$-0.664447\pi$$
0.493949 0.869491i $$-0.335553\pi$$
$$434$$ 18.3510 + 4.27748i 0.880875 + 0.205325i
$$435$$ 5.51396 16.0613i 0.264374 0.770082i
$$436$$ 3.68793 7.48105i 0.176620 0.358277i
$$437$$ −9.21438 −0.440783
$$438$$ 16.4596 + 3.83662i 0.786472 + 0.183321i
$$439$$ 25.4178 1.21312 0.606562 0.795036i $$-0.292548\pi$$
0.606562 + 0.795036i $$0.292548\pi$$
$$440$$ −3.27567 5.30594i −0.156161 0.252951i
$$441$$ −9.45963 −0.450459
$$442$$ 30.8106 + 7.18172i 1.46551 + 0.341600i
$$443$$ −7.02792 −0.333907 −0.166953 0.985965i $$-0.553393\pi$$
−0.166953 + 0.985965i $$0.553393\pi$$
$$444$$ −1.69641 0.836276i −0.0805079 0.0396879i
$$445$$ −26.1212 8.96757i −1.23826 0.425103i
$$446$$ 24.7632 + 5.77213i 1.17257 + 0.273318i
$$447$$ 10.4986i 0.496566i
$$448$$ −31.8300 + 6.34545i −1.50383 + 0.299794i
$$449$$ 2.00000 0.0943858 0.0471929 0.998886i $$-0.484972\pi$$
0.0471929 + 0.998886i $$0.484972\pi$$
$$450$$ 5.49652 4.44840i 0.259108 0.209700i
$$451$$ 0.560304i 0.0263837i
$$452$$ 1.13659 2.30560i 0.0534607 0.108446i
$$453$$ −4.71585 −0.221570
$$454$$ 2.25622 9.67951i 0.105890 0.454282i
$$455$$ −14.5683 + 42.4352i −0.682972 + 1.98939i
$$456$$ −5.69641 4.67289i −0.266759 0.218828i
$$457$$ 25.2747i 1.18230i 0.806562 + 0.591149i $$0.201326\pi$$
−0.806562 + 0.591149i $$0.798674\pi$$
$$458$$ −5.74378 1.33883i −0.268389 0.0625595i
$$459$$ 4.52323i 0.211126i
$$460$$ 11.2229 11.1488i 0.523268 0.519817i
$$461$$ 41.0902i 1.91376i −0.290479 0.956881i $$-0.593815\pi$$
0.290479 0.956881i $$-0.406185\pi$$
$$462$$ 1.28415 5.50917i 0.0597439 0.256310i
$$463$$ 13.2106i 0.613951i 0.951717 + 0.306975i $$0.0993169\pi$$
−0.951717 + 0.306975i $$0.900683\pi$$
$$464$$ 24.0947 18.4994i 1.11857 0.858813i
$$465$$ −6.94567 2.38449i −0.322098 0.110578i
$$466$$ 33.0404 + 7.70148i 1.53057 + 0.356764i
$$467$$ −1.89134 −0.0875206 −0.0437603 0.999042i $$-0.513934\pi$$
−0.0437603 + 0.999042i $$0.513934\pi$$
$$468$$ −8.87189 4.37357i −0.410103 0.202168i
$$469$$ 34.3211i 1.58480i
$$470$$ −6.98055 4.37357i −0.321989 0.201738i
$$471$$ 8.94567 0.412195
$$472$$ −19.8998 16.3243i −0.915963 0.751386i
$$473$$ 8.34068i 0.383505i
$$474$$ −1.05433 + 4.52323i −0.0484271 + 0.207759i
$$475$$ 8.00000 10.2782i 0.367065 0.471594i
$$476$$ −32.9193 16.2282i −1.50885 0.743818i
$$477$$ 0.229815 0.0105225
$$478$$ 2.86341 12.2844i 0.130969 0.561877i
$$479$$ −31.4876 −1.43870 −0.719352 0.694646i $$-0.755561\pi$$
−0.719352 + 0.694646i $$0.755561\pi$$
$$480$$ 12.5920 1.20085i 0.574743 0.0548109i
$$481$$ −4.67696 −0.213251
$$482$$ −5.24926 + 22.5201i −0.239097 + 1.02576i
$$483$$ 14.3510 0.652992
$$484$$ −17.9888 8.86793i −0.817673 0.403088i
$$485$$ −2.35097 + 6.84800i −0.106752 + 0.310952i
$$486$$ −0.321037 + 1.37729i −0.0145625 + 0.0624753i
$$487$$ 12.9964i 0.588922i 0.955664 + 0.294461i $$0.0951401\pi$$
−0.955664 + 0.294461i $$0.904860\pi$$
$$488$$ −24.0947 19.7655i −1.09072 0.894741i
$$489$$ 15.7827 0.713717
$$490$$ 15.8824 25.3495i 0.717492 1.14517i
$$491$$ 14.9085i 0.672812i 0.941717 + 0.336406i $$0.109212\pi$$
−0.941717 + 0.336406i $$0.890788\pi$$
$$492$$ 1.01945 + 0.502556i 0.0459602 + 0.0226570i
$$493$$ 34.3510 1.54709
$$494$$ −17.7438 4.13594i −0.798330 0.186085i
$$495$$ −0.715853 + 2.08517i −0.0321752 + 0.0937214i
$$496$$ −8.00000 10.4197i −0.359211 0.467858i
$$497$$ 5.80850i 0.260547i
$$498$$ −3.17548 + 13.6233i −0.142297 + 0.610473i
$$499$$ 35.6599i 1.59636i 0.602420 + 0.798179i $$0.294203\pi$$
−0.602420 + 0.798179i $$0.705797\pi$$
$$500$$ 2.69217 + 22.1980i 0.120397 + 0.992726i
$$501$$ 5.50917i 0.246132i
$$502$$ −5.81756 1.35603i −0.259650 0.0605226i
$$503$$ 25.3090i 1.12847i 0.825613 + 0.564237i $$0.190830\pi$$
−0.825613 + 0.564237i $$0.809170\pi$$
$$504$$ 8.87189 + 7.27782i 0.395185 + 0.324180i
$$505$$ 3.16300 9.21332i 0.140751 0.409988i
$$506$$ −1.11963 + 4.80338i −0.0497738 + 0.213536i
$$507$$ −11.4596 −0.508940
$$508$$ −1.01945 + 2.06797i −0.0452306 + 0.0917514i
$$509$$ 13.7366i 0.608862i 0.952534 + 0.304431i $$0.0984663\pi$$
−0.952534 + 0.304431i $$0.901534\pi$$
$$510$$ 12.1212 + 7.59434i 0.536734 + 0.336283i
$$511$$ −48.4846 −2.14483
$$512$$ 19.9624 + 10.6538i 0.882221 + 0.470835i
$$513$$ 2.60492i 0.115010i
$$514$$ 34.0125 + 7.92806i 1.50023 + 0.349692i
$$515$$ 10.9457 31.8831i 0.482324 1.40494i
$$516$$ 15.1755 + 7.48105i 0.668063 + 0.329335i
$$517$$ 2.56829 0.112953
$$518$$ 5.28415 + 1.23170i 0.232172 + 0.0541176i
$$519$$ −10.3385 −0.453809
$$520$$ 26.6157 16.4314i 1.16717 0.720565i
$$521$$ −30.9193 −1.35460 −0.677299 0.735708i $$-0.736850\pi$$
−0.677299 + 0.735708i $$0.736850\pi$$
$$522$$ −10.4596 2.43806i −0.457806 0.106711i
$$523$$ 21.8385 0.954932 0.477466 0.878650i $$-0.341555\pi$$
0.477466 + 0.878650i $$0.341555\pi$$
$$524$$ −3.44018 + 6.97849i −0.150285 + 0.304857i
$$525$$ −12.4596 + 16.0078i −0.543783 + 0.698636i
$$526$$ −20.1949 4.70729i −0.880541 0.205248i
$$527$$ 14.8550i 0.647092i
$$528$$ −3.12811 + 2.40169i −0.136134 + 0.104520i
$$529$$ 10.4876 0.455981
$$530$$ −0.385851 + 0.615848i −0.0167603 + 0.0267507i
$$531$$ 9.10003i 0.394908i
$$532$$ 18.9582 + 9.34579i 0.821940 + 0.405191i
$$533$$ 2.81060 0.121740
$$534$$ −3.96511 + 17.0109i −0.171587 + 0.736133i
$$535$$ −8.45963 2.90425i −0.365742 0.125562i
$$536$$ 15.1755 18.4994i 0.655481 0.799052i
$$537$$ 16.1746i 0.697986i
$$538$$ 15.8913 + 3.70415i 0.685124 + 0.159697i
$$539$$ 9.32662i 0.401726i
$$540$$ −3.15180 3.17272i −0.135632 0.136532i
$$541$$ 24.3423i 1.04656i 0.852162 + 0.523278i $$0.175291\pi$$
−0.852162 + 0.523278i $$0.824709\pi$$
$$542$$ 1.80908 7.76120i 0.0777066 0.333372i
$$543$$ 8.11409i 0.348209i
$$544$$ 10.5683 + 23.3028i 0.453112 + 0.999098i
$$545$$ 3.02792 8.81988i 0.129702 0.377802i
$$546$$ 27.6351 + 6.44154i 1.18267 + 0.275673i
$$547$$ −33.3789 −1.42718 −0.713589 0.700564i $$-0.752932\pi$$
−0.713589 + 0.700564i $$0.752932\pi$$
$$548$$ −15.4876 + 31.4169i −0.661596 + 1.34206i
$$549$$ 11.0183i 0.470251i
$$550$$ −4.38585 5.41923i −0.187013 0.231077i
$$551$$ −19.7827 −0.842770
$$552$$ −7.73530 6.34545i −0.329236 0.270080i
$$553$$ 13.3239i 0.566592i
$$554$$ 5.58774 23.9722i 0.237400 1.01848i
$$555$$ −2.00000 0.686614i −0.0848953 0.0291451i
$$556$$ 14.9108 30.2469i 0.632358 1.28275i
$$557$$ −30.5808 −1.29575 −0.647875 0.761747i $$-0.724342\pi$$
−0.647875 + 0.761747i $$0.724342\pi$$
$$558$$ −1.05433 + 4.52323i −0.0446334 + 0.191484i
$$559$$ 41.8385 1.76958
$$560$$ −34.3983 + 11.5553i −1.45360 + 0.488300i
$$561$$ −4.45963 −0.188286
$$562$$ 6.99304 30.0011i 0.294984 1.26552i
$$563$$ 7.02792 0.296192 0.148096 0.988973i $$-0.452686\pi$$
0.148096 + 0.988973i $$0.452686\pi$$
$$564$$ −2.30359 + 4.67289i −0.0969988 + 0.196764i
$$565$$ 0.933181 2.71821i 0.0392592 0.114356i
$$566$$ 6.93318 29.7443i 0.291423 1.25025i
$$567$$ 4.05705i 0.170380i
$$568$$ −2.56829 + 3.13083i −0.107763 + 0.131367i
$$569$$ −24.3510 −1.02085 −0.510423 0.859924i $$-0.670511\pi$$
−0.510423 + 0.859924i $$0.670511\pi$$
$$570$$ −6.98055 4.37357i −0.292383 0.183189i
$$571$$ 20.0992i 0.841125i 0.907263 + 0.420563i $$0.138167\pi$$
−0.907263 + 0.420563i $$0.861833\pi$$
$$572$$ −4.31207 + 8.74714i −0.180297 + 0.365736i
$$573$$ 24.9193 1.04102
$$574$$ −3.17548 0.740182i −0.132542 0.0308946i
$$575$$ 10.8634 13.9570i 0.453036 0.582047i
$$576$$ −1.56406 7.84562i −0.0651690 0.326901i
$$577$$ 4.76899i 0.198536i −0.995061 0.0992678i $$-0.968350\pi$$
0.995061 0.0992678i $$-0.0316501\pi$$
$$578$$ −1.11067 + 4.76492i −0.0461977 + 0.198195i
$$579$$ 1.03951i 0.0432004i
$$580$$ 24.0947 23.9358i 1.00048 0.993881i
$$581$$ 40.1296i 1.66486i
$$582$$ 4.45963 + 1.03951i 0.184858 + 0.0430890i
$$583$$ 0.226584i 0.00938413i
$$584$$ 26.1336 + 21.4380i 1.08142 + 0.887112i
$$585$$ −10.4596 3.59086i −0.432452 0.148464i
$$586$$ −10.2772 + 44.0906i −0.424547 + 1.82136i
$$587$$ 8.21733 0.339165 0.169583 0.985516i $$-0.445758\pi$$
0.169583 + 0.985516i $$0.445758\pi$$
$$588$$ −16.9694 8.36537i −0.699804 0.344982i
$$589$$ 8.55495i 0.352501i
$$590$$ −24.3859 15.2786i −1.00395 0.629011i
$$591$$ −9.66152 −0.397422
$$592$$ −2.30359 3.00034i −0.0946771 0.123313i
$$593$$ 7.76120i 0.318714i 0.987221 + 0.159357i $$0.0509421\pi$$
−0.987221 + 0.159357i $$0.949058\pi$$
$$594$$ 1.35793 + 0.316523i 0.0557164 + 0.0129871i
$$595$$ −38.8106 13.3239i −1.59108 0.546228i
$$596$$ −9.28415 + 18.8331i −0.380293 + 0.771434i
$$597$$ 23.0668 0.944062
$$598$$ −24.0947 5.61631i −0.985307 0.229668i
$$599$$ 5.64903 0.230813 0.115407 0.993318i $$-0.463183\pi$$
0.115407 + 0.993318i $$0.463183\pi$$
$$600$$ 13.7939 3.11916i 0.563132 0.127339i
$$601$$ −37.7299 −1.53903 −0.769516 0.638627i $$-0.779503\pi$$
−0.769516 + 0.638627i $$0.779503\pi$$
$$602$$ −47.2702 11.0183i −1.92659 0.449074i
$$603$$ −8.45963 −0.344503
$$604$$ −8.45963 4.17034i −0.344217 0.169689i
$$605$$ −21.2081 7.28090i −0.862233 0.296010i
$$606$$ −6.00000 1.39856i −0.243733 0.0568124i
$$607$$ 0.113292i 0.00459837i −0.999997 0.00229919i $$-0.999268\pi$$
0.999997 0.00229919i $$-0.000731854\pi$$
$$608$$ −6.08627 13.4200i −0.246831 0.544254i
$$609$$ 30.8106 1.24851
$$610$$ −29.5264 18.4994i −1.19549 0.749018i
$$611$$ 12.8831i 0.521194i
$$612$$ 4.00000 8.11409i 0.161690 0.327993i
$$613$$ −0.703366 −0.0284087 −0.0142044 0.999899i $$-0.504522\pi$$
−0.0142044 + 0.999899i $$0.504522\pi$$
$$614$$ −0.364887 + 1.56542i −0.0147256 + 0.0631750i
$$615$$ 1.20189 + 0.412617i 0.0484649 + 0.0166383i
$$616$$ 7.17548 8.74714i 0.289108 0.352432i
$$617$$ 24.4809i 0.985564i 0.870153 + 0.492782i $$0.164020\pi$$
−0.870153 + 0.492782i $$0.835980\pi$$
$$618$$ −20.7632 4.83975i −0.835219 0.194683i
$$619$$ 39.4966i 1.58750i −0.608243 0.793751i $$-0.708126\pi$$
0.608243 0.793751i $$-0.291874\pi$$
$$620$$ −10.3510 10.4197i −0.415705 0.418465i
$$621$$ 3.53729i 0.141947i
$$622$$ 1.64903 7.07459i 0.0661202 0.283665i
$$623$$ 50.1084i 2.00755i
$$624$$ −12.0474 15.6912i −0.482281 0.628152i
$$625$$ 6.13659 + 24.2351i 0.245464 + 0.969406i
$$626$$ −31.7827 7.40831i −1.27029 0.296095i
$$627$$ 2.56829 0.102568
$$628$$ 16.0474 + 7.91086i 0.640360 + 0.315678i
$$629$$ 4.27748i 0.170554i
$$630$$ 10.8719 + 6.81163i 0.433146 + 0.271382i
$$631$$ 17.3400 0.690294 0.345147 0.938549i $$-0.387829\pi$$
0.345147 + 0.938549i $$0.387829\pi$$
$$632$$ −5.89134 + 7.18172i −0.234345 + 0.285674i
$$633$$ 6.44154i 0.256028i
$$634$$ 0.533409 2.28840i 0.0211844 0.0908840i
$$635$$ −0.837003 + 2.43806i −0.0332155 + 0.0967516i
$$636$$ 0.412259 + 0.203231i 0.0163471 + 0.00805863i
$$637$$ −46.7842 −1.85366
$$638$$ −2.40378 + 10.3126i −0.0951666 + 0.408278i
$$639$$ 1.43171 0.0566374
$$640$$ 23.6503 + 8.98122i 0.934861 + 0.355014i
$$641$$ 38.7019 1.52863 0.764317 0.644840i $$-0.223076\pi$$
0.764317 + 0.644840i $$0.223076\pi$$
$$642$$ −1.28415 + 5.50917i −0.0506812 + 0.217430i
$$643$$ −1.13659 −0.0448227 −0.0224113 0.999749i $$-0.507134\pi$$
−0.0224113 + 0.999749i $$0.507134\pi$$
$$644$$ 25.7438 + 12.6909i 1.01445 + 0.500091i
$$645$$ 17.8913 + 6.14222i 0.704471 + 0.241850i
$$646$$ 3.78267 16.2282i 0.148827 0.638490i
$$647$$ 6.54868i 0.257455i 0.991680 + 0.128728i $$0.0410893\pi$$
−0.991680 + 0.128728i $$0.958911\pi$$
$$648$$ −1.79387 + 2.18678i −0.0704699 + 0.0859050i
$$649$$ 8.97208 0.352185
$$650$$ 27.1840 22.0003i 1.06624 0.862923i
$$651$$ 13.3239i 0.522206i
$$652$$ 28.3121 + 13.9570i 1.10879 + 0.546598i
$$653$$ 8.74226 0.342111 0.171056 0.985261i $$-0.445282\pi$$
0.171056 + 0.985261i $$0.445282\pi$$
$$654$$ −5.74378 1.33883i −0.224599 0.0523525i
$$655$$ −2.82452 + 8.22739i −0.110363 + 0.321471i
$$656$$ 1.38433 + 1.80304i 0.0540492 + 0.0703969i
$$657$$ 11.9507i 0.466242i
$$658$$ 3.39281 14.5556i 0.132266 0.567438i
$$659$$ 35.5336i 1.38419i 0.721804 + 0.692097i $$0.243313\pi$$
−0.721804 + 0.692097i $$0.756687\pi$$
$$660$$ −3.12811 + 3.10748i −0.121762 + 0.120958i
$$661$$ 23.3028i 0.906373i −0.891416 0.453186i $$-0.850287\pi$$
0.891416 0.453186i $$-0.149713\pi$$
$$662$$ 35.6825 + 8.31732i 1.38684 + 0.323262i
$$663$$ 22.3704i 0.868795i
$$664$$ −17.7438 + 21.6302i −0.688592 + 0.839415i
$$665$$ 22.3510 + 7.67324i 0.866733 + 0.297555i
$$666$$ −0.303594 + 1.30246i −0.0117640 + 0.0504694i
$$667$$ −26.8634 −1.04016
$$668$$ 4.87189 9.88274i 0.188499 0.382375i
$$669$$ 17.9796i 0.695133i
$$670$$ 14.2034 22.6697i 0.548726 0.875808i
$$671$$ 10.8634 0.419377
$$672$$ 9.47908 + 20.9011i 0.365663 + 0.806277i
$$673$$ 14.3634i 0.553670i 0.960917 + 0.276835i $$0.0892856\pi$$
−0.960917 + 0.276835i $$0.910714\pi$$
$$674$$ 11.0279 + 2.57053i 0.424780 + 0.0990130i
$$675$$ −3.94567 3.07111i −0.151869 0.118207i
$$676$$ −20.5571 10.1340i −0.790658 0.389770i
$$677$$ 24.3076 0.934217 0.467109 0.884200i $$-0.345296\pi$$
0.467109 + 0.884200i $$0.345296\pi$$
$$678$$ −1.77018 0.412617i −0.0679835 0.0158465i
$$679$$ −13.1366 −0.504136
$$680$$ 15.0279 + 24.3423i 0.576295 + 0.933484i
$$681$$ −7.02792 −0.269311
$$682$$ 4.45963 + 1.03951i 0.170768 + 0.0398048i
$$683$$ 38.5933 1.47673 0.738365 0.674401i $$-0.235598\pi$$
0.738365 + 0.674401i $$0.235598\pi$$
$$684$$ −2.30359 + 4.67289i −0.0880801 + 0.178673i
$$685$$ −12.7159 + 37.0393i −0.485848 + 1.41520i
$$686$$ 13.7438 + 3.20357i 0.524740 + 0.122313i
$$687$$ 4.17034i 0.159108i
$$688$$ 20.6072 + 26.8401i 0.785642 + 1.02327i
$$689$$ 1.13659 0.0433006
$$690$$ −9.47908 5.93899i −0.360862 0.226093i
$$691$$ 13.4090i 0.510102i 0.966928 + 0.255051i $$0.0820923\pi$$
−0.966928 + 0.255051i $$0.917908\pi$$
$$692$$ −18.5459 9.14256i −0.705009 0.347548i
$$693$$ −4.00000 −0.151947
$$694$$ −7.39281 + 31.7162i −0.280627 + 1.20393i
$$695$$ 12.2423 35.6599i 0.464377 1.35266i
$$696$$ −16.6072 13.6233i −0.629494 0.516389i
$$697$$ 2.57053i 0.0973657i
$$698$$ −29.5264 6.88240i −1.11759 0.260503i
$$699$$ 23.9894i 0.907362i
$$700$$ −36.5070 + 17.6975i −1.37983 + 0.668903i
$$701$$ 15.6013i 0.589253i −0.955613 0.294626i $$-0.904805\pi$$
0.955613 0.294626i $$-0.0951952\pi$$
$$702$$ −1.58774 + 6.81163i −0.0599254 + 0.257089i
$$703$$ 2.46339i 0.0929086i
$$704$$ −7.73530 + 1.54206i −0.291535 + 0.0581187i
$$705$$ −1.89134 + 5.50917i −0.0712318 + 0.207487i
$$706$$ 6.22982 + 1.45212i 0.234462 + 0.0546514i
$$707$$ 17.6740 0.664699
$$708$$ −8.04737 + 16.3243i −0.302439 + 0.613504i
$$709$$ 15.7873i 0.592906i −0.955047 0.296453i $$-0.904196\pi$$
0.955047 0.296453i $$-0.0958038\pi$$
$$710$$ −2.40378 + 3.83662i −0.0902123 + 0.143986i
$$711$$ 3.28415 0.123165
$$712$$ −22.1560 + 27.0089i −0.830333 + 1.01220i
$$713$$ 11.6170i 0.435060i
$$714$$ −5.89134 + 25.2747i −0.220478 + 0.945880i
$$715$$ −3.54037 + 10.3126i −0.132402 + 0.385668i
$$716$$ −14.3036 + 29.0152i −0.534550 + 1.08435i
$$717$$ −8.91926 −0.333096
$$718$$ −3.32304 + 14.2563i −0.124015 + 0.532041i
$$719$$ −22.5683 −0.841655 −0.420828 0.907141i $$-0.638260\pi$$
−0.420828 + 0.907141i $$0.638260\pi$$
$$720$$ −2.84820 8.47866i −0.106146 0.315981i
$$721$$ 61.1616 2.27778
$$722$$ 3.92126 16.8228i 0.145934 0.626079i
$$723$$ 16.3510 0.608099
$$724$$ 7.17548 14.5556i 0.266675 0.540956i
$$725$$ 23.3230 29.9647i 0.866196 1.11286i
$$726$$ −3.21933 + 13.8114i −0.119481 + 0.512589i
$$727$$ 2.79096i 0.103511i 0.998660 + 0.0517554i $$0.0164816\pi$$
−0.998660 + 0.0517554i $$0.983518\pi$$
$$728$$ 43.8774 + 35.9937i 1.62621 + 1.33401i
$$729$$ 1.00000 0.0370370
$$730$$ 32.0250 + 20.0648i 1.18530 + 0.742632i
$$731$$ 38.2649i 1.41528i
$$732$$ −9.74378 + 19.7655i −0.360140 + 0.730553i
$$733$$ 16.4860 0.608926 0.304463 0.952524i $$-0.401523\pi$$
0.304463 + 0.952524i $$0.401523\pi$$
$$734$$ −0.668481 0.155818i −0.0246741 0.00575135i
$$735$$ −20.0062 6.86828i −0.737941 0.253340i
$$736$$ −8.26470 18.2234i −0.304641 0.671724i
$$737$$ 8.34068i 0.307233i
$$738$$ 0.182443 0.782708i 0.00671584 0.0288119i
$$739$$ 14.8894i 0.547714i −0.961770 0.273857i $$-0.911701\pi$$
0.961770 0.273857i $$-0.0882995\pi$$
$$740$$ −2.98055 3.00034i −0.109567 0.110295i
$$741$$ 12.8831i 0.473272i
$$742$$ −1.28415 0.299325i −0.0471425 0.0109886i
$$743$$ 41.4301i 1.51992i −0.649968 0.759961i $$-0.725218\pi$$
0.649968 0.759961i $$-0.274782\pi$$
$$744$$ −5.89134 + 7.18172i −0.215987 + 0.263295i
$$745$$ −7.62263 + 22.2035i −0.279271 + 0.813475i
$$746$$ −9.65751 + 41.4321i −0.353587 + 1.51694i
$$747$$ 9.89134 0.361905
$$748$$ −8.00000 3.94376i −0.292509 0.144198i
$$749$$ 16.2282i 0.592965i
$$750$$ 14.8544 5.41714i 0.542408 0.197806i
$$751$$ 30.5544 1.11494 0.557472 0.830195i $$-0.311771\pi$$
0.557472 + 0.830195i $$0.311771\pi$$
$$752$$ −8.26470 + 6.34545i −0.301383 + 0.231395i
$$753$$ 4.22391i 0.153928i
$$754$$ −51.7299 12.0578i −1.88389 0.439121i
$$755$$ −9.97359 3.42400i −0.362976 0.124612i
$$756$$ 3.58774 7.27782i 0.130485 0.264692i
$$757$$ −0.433223 −0.0157457 −0.00787287 0.999969i $$-0.502506\pi$$
−0.00787287 + 0.999969i $$0.502506\pi$$
$$758$$ −46.3983 10.8151i −1.68526 0.392823i
$$759$$ 3.48755 0.126590
$$760$$ −8.65456 14.0187i −0.313934 0.508511i
$$761$$ −14.9193 −0.540823 −0.270411 0.962745i $$-0.587160\pi$$
−0.270411 + 0.962745i $$0.587160\pi$$
$$762$$ 1.58774 + 0.370091i 0.0575178 + 0.0134070i
$$763$$ 16.9193 0.612518
$$764$$ 44.7019 + 22.0367i 1.61726 + 0.797259i
$$765$$ 3.28415 9.56622i 0.118739 0.345867i
$$766$$ 7.12811 + 1.66151i 0.257549 + 0.0600328i
$$767$$ 45.0057i 1.62506i
$$768$$ 4.13235 15.4572i 0.149113 0.557762i
$$769$$ 31.3789 1.13155 0.565776 0.824559i $$-0.308577\pi$$
0.565776 + 0.824559i $$0.308577\pi$$
$$770$$ 6.71585 10.7190i 0.242023 0.386287i
$$771$$ 24.6952i 0.889375i
$$772$$ −0.919260 + 1.86474i −0.0330849 + 0.0671135i
$$773$$ −13.4192 −0.482656 −0.241328 0.970444i $$-0.577583\pi$$
−0.241328 + 0.970444i $$0.577583\pi$$
$$774$$ 2.71585 11.6514i 0.0976193 0.418800i
$$775$$ −12.9582 10.0860i −0.465471 0.362299