# Properties

 Label 570.2.i.f.391.2 Level $570$ Weight $2$ Character 570.391 Analytic conductor $4.551$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 391.2 Root $$-1.22474 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.391 Dual form 570.2.i.f.121.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(2.44949 + 4.24264i) q^{13} +(-1.72474 + 2.98735i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.22474 - 5.58542i) q^{17} +1.00000 q^{18} +(3.17423 + 2.98735i) q^{19} +1.00000 q^{20} +(1.72474 - 2.98735i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-1.94949 - 3.37662i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.89898 q^{26} -1.00000 q^{27} +(-1.72474 - 2.98735i) q^{28} +(2.67423 + 4.63191i) q^{29} -1.00000 q^{30} +8.89898 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(3.22474 + 5.58542i) q^{34} +(-1.72474 + 2.98735i) q^{35} +(-0.500000 + 0.866025i) q^{36} -0.101021 q^{37} +(-4.17423 + 1.25529i) q^{38} +4.89898 q^{39} +(-0.500000 + 0.866025i) q^{40} +(5.17423 - 8.96204i) q^{41} +(1.72474 + 2.98735i) q^{42} +(-3.89898 + 6.75323i) q^{43} +(1.50000 + 2.59808i) q^{44} +1.00000 q^{45} +3.89898 q^{46} +(5.44949 + 9.43879i) q^{47} +(0.500000 + 0.866025i) q^{48} +4.89898 q^{49} +1.00000 q^{50} +(-3.22474 - 5.58542i) q^{51} +(2.44949 - 4.24264i) q^{52} +(1.27526 + 2.20881i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} +3.44949 q^{56} +(4.17423 - 1.25529i) q^{57} -5.34847 q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-3.77526 - 6.53893i) q^{61} +(-4.44949 + 7.70674i) q^{62} +(-1.72474 - 2.98735i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-1.50000 - 2.59808i) q^{66} +(-3.67423 - 6.36396i) q^{67} -6.44949 q^{68} -3.89898 q^{69} +(-1.72474 - 2.98735i) q^{70} +(-5.67423 + 9.82806i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.77526 + 4.80688i) q^{73} +(0.0505103 - 0.0874863i) q^{74} -1.00000 q^{75} +(1.00000 - 4.24264i) q^{76} -10.3485 q^{77} +(-2.44949 + 4.24264i) q^{78} +(1.44949 - 2.51059i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.17423 + 8.96204i) q^{82} -7.79796 q^{83} -3.44949 q^{84} +(3.22474 + 5.58542i) q^{85} +(-3.89898 - 6.75323i) q^{86} +5.34847 q^{87} -3.00000 q^{88} +(0.275255 + 0.476756i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(8.44949 + 14.6349i) q^{91} +(-1.94949 + 3.37662i) q^{92} +(4.44949 - 7.70674i) q^{93} -10.8990 q^{94} +(-4.17423 + 1.25529i) q^{95} -1.00000 q^{96} +(6.77526 - 11.7351i) q^{97} +(-2.44949 + 4.24264i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} + O(q^{10})$$ $$4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} - 4q^{12} - 2q^{14} + 2q^{15} - 2q^{16} + 8q^{17} + 4q^{18} - 2q^{19} + 4q^{20} + 2q^{21} + 6q^{22} + 2q^{23} + 2q^{24} - 2q^{25} - 4q^{27} - 2q^{28} - 4q^{29} - 4q^{30} + 16q^{31} - 2q^{32} - 6q^{33} + 8q^{34} - 2q^{35} - 2q^{36} - 20q^{37} - 2q^{38} - 2q^{40} + 6q^{41} + 2q^{42} + 4q^{43} + 6q^{44} + 4q^{45} - 4q^{46} + 12q^{47} + 2q^{48} + 4q^{50} - 8q^{51} + 10q^{53} + 2q^{54} + 6q^{55} + 4q^{56} + 2q^{57} + 8q^{58} + 12q^{59} + 2q^{60} - 20q^{61} - 8q^{62} - 2q^{63} + 4q^{64} - 6q^{66} - 16q^{68} + 4q^{69} - 2q^{70} - 8q^{71} - 2q^{72} - 16q^{73} + 10q^{74} - 4q^{75} + 4q^{76} - 12q^{77} - 4q^{79} - 2q^{80} - 2q^{81} + 6q^{82} + 8q^{83} - 4q^{84} + 8q^{85} + 4q^{86} - 8q^{87} - 12q^{88} + 6q^{89} - 2q^{90} + 24q^{91} + 2q^{92} + 8q^{93} - 24q^{94} - 2q^{95} - 4q^{96} + 32q^{97} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0.500000 + 0.866025i 0.204124 + 0.353553i
$$7$$ 3.44949 1.30378 0.651892 0.758312i $$-0.273975\pi$$
0.651892 + 0.758312i $$0.273975\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 2.44949 + 4.24264i 0.679366 + 1.17670i 0.975172 + 0.221449i $$0.0710785\pi$$
−0.295806 + 0.955248i $$0.595588\pi$$
$$14$$ −1.72474 + 2.98735i −0.460957 + 0.798402i
$$15$$ 0.500000 + 0.866025i 0.129099 + 0.223607i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 3.22474 5.58542i 0.782116 1.35466i −0.148592 0.988899i $$-0.547474\pi$$
0.930707 0.365765i $$-0.119193\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 3.17423 + 2.98735i 0.728219 + 0.685344i
$$20$$ 1.00000 0.223607
$$21$$ 1.72474 2.98735i 0.376370 0.651892i
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ −1.94949 3.37662i −0.406497 0.704073i 0.587998 0.808863i $$-0.299916\pi$$
−0.994494 + 0.104790i $$0.966583\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −4.89898 −0.960769
$$27$$ −1.00000 −0.192450
$$28$$ −1.72474 2.98735i −0.325946 0.564555i
$$29$$ 2.67423 + 4.63191i 0.496593 + 0.860124i 0.999992 0.00392972i $$-0.00125087\pi$$
−0.503399 + 0.864054i $$0.667918\pi$$
$$30$$ −1.00000 −0.182574
$$31$$ 8.89898 1.59830 0.799152 0.601129i $$-0.205282\pi$$
0.799152 + 0.601129i $$0.205282\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ 3.22474 + 5.58542i 0.553039 + 0.957892i
$$35$$ −1.72474 + 2.98735i −0.291535 + 0.504954i
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ −0.101021 −0.0166077 −0.00830384 0.999966i $$-0.502643\pi$$
−0.00830384 + 0.999966i $$0.502643\pi$$
$$38$$ −4.17423 + 1.25529i −0.677150 + 0.203636i
$$39$$ 4.89898 0.784465
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ 5.17423 8.96204i 0.808080 1.39964i −0.106113 0.994354i $$-0.533840\pi$$
0.914192 0.405281i $$-0.132826\pi$$
$$42$$ 1.72474 + 2.98735i 0.266134 + 0.460957i
$$43$$ −3.89898 + 6.75323i −0.594589 + 1.02986i 0.399016 + 0.916944i $$0.369352\pi$$
−0.993605 + 0.112914i $$0.963982\pi$$
$$44$$ 1.50000 + 2.59808i 0.226134 + 0.391675i
$$45$$ 1.00000 0.149071
$$46$$ 3.89898 0.574873
$$47$$ 5.44949 + 9.43879i 0.794890 + 1.37679i 0.922909 + 0.385018i $$0.125805\pi$$
−0.128019 + 0.991772i $$0.540862\pi$$
$$48$$ 0.500000 + 0.866025i 0.0721688 + 0.125000i
$$49$$ 4.89898 0.699854
$$50$$ 1.00000 0.141421
$$51$$ −3.22474 5.58542i −0.451555 0.782116i
$$52$$ 2.44949 4.24264i 0.339683 0.588348i
$$53$$ 1.27526 + 2.20881i 0.175170 + 0.303403i 0.940220 0.340568i $$-0.110619\pi$$
−0.765050 + 0.643971i $$0.777286\pi$$
$$54$$ 0.500000 0.866025i 0.0680414 0.117851i
$$55$$ 1.50000 2.59808i 0.202260 0.350325i
$$56$$ 3.44949 0.460957
$$57$$ 4.17423 1.25529i 0.552891 0.166268i
$$58$$ −5.34847 −0.702288
$$59$$ 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i $$-0.705612\pi$$
0.992524 + 0.122047i $$0.0389457\pi$$
$$60$$ 0.500000 0.866025i 0.0645497 0.111803i
$$61$$ −3.77526 6.53893i −0.483372 0.837225i 0.516446 0.856320i $$-0.327255\pi$$
−0.999818 + 0.0190952i $$0.993921\pi$$
$$62$$ −4.44949 + 7.70674i −0.565086 + 0.978757i
$$63$$ −1.72474 2.98735i −0.217297 0.376370i
$$64$$ 1.00000 0.125000
$$65$$ −4.89898 −0.607644
$$66$$ −1.50000 2.59808i −0.184637 0.319801i
$$67$$ −3.67423 6.36396i −0.448879 0.777482i 0.549434 0.835537i $$-0.314843\pi$$
−0.998313 + 0.0580554i $$0.981510\pi$$
$$68$$ −6.44949 −0.782116
$$69$$ −3.89898 −0.469382
$$70$$ −1.72474 2.98735i −0.206146 0.357056i
$$71$$ −5.67423 + 9.82806i −0.673408 + 1.16638i 0.303524 + 0.952824i $$0.401837\pi$$
−0.976932 + 0.213553i $$0.931497\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ −2.77526 + 4.80688i −0.324819 + 0.562603i −0.981476 0.191587i $$-0.938637\pi$$
0.656657 + 0.754190i $$0.271970\pi$$
$$74$$ 0.0505103 0.0874863i 0.00587170 0.0101701i
$$75$$ −1.00000 −0.115470
$$76$$ 1.00000 4.24264i 0.114708 0.486664i
$$77$$ −10.3485 −1.17932
$$78$$ −2.44949 + 4.24264i −0.277350 + 0.480384i
$$79$$ 1.44949 2.51059i 0.163080 0.282463i −0.772892 0.634538i $$-0.781190\pi$$
0.935972 + 0.352075i $$0.114524\pi$$
$$80$$ −0.500000 0.866025i −0.0559017 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 5.17423 + 8.96204i 0.571399 + 0.989691i
$$83$$ −7.79796 −0.855937 −0.427969 0.903794i $$-0.640771\pi$$
−0.427969 + 0.903794i $$0.640771\pi$$
$$84$$ −3.44949 −0.376370
$$85$$ 3.22474 + 5.58542i 0.349773 + 0.605824i
$$86$$ −3.89898 6.75323i −0.420438 0.728220i
$$87$$ 5.34847 0.573416
$$88$$ −3.00000 −0.319801
$$89$$ 0.275255 + 0.476756i 0.0291770 + 0.0505360i 0.880245 0.474519i $$-0.157378\pi$$
−0.851068 + 0.525055i $$0.824045\pi$$
$$90$$ −0.500000 + 0.866025i −0.0527046 + 0.0912871i
$$91$$ 8.44949 + 14.6349i 0.885747 + 1.53416i
$$92$$ −1.94949 + 3.37662i −0.203248 + 0.352036i
$$93$$ 4.44949 7.70674i 0.461391 0.799152i
$$94$$ −10.8990 −1.12414
$$95$$ −4.17423 + 1.25529i −0.428267 + 0.128791i
$$96$$ −1.00000 −0.102062
$$97$$ 6.77526 11.7351i 0.687923 1.19152i −0.284586 0.958651i $$-0.591856\pi$$
0.972509 0.232867i $$-0.0748106\pi$$
$$98$$ −2.44949 + 4.24264i −0.247436 + 0.428571i
$$99$$ 1.50000 + 2.59808i 0.150756 + 0.261116i
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ 5.44949 + 9.43879i 0.542244 + 0.939195i 0.998775 + 0.0494871i $$0.0157587\pi$$
−0.456530 + 0.889708i $$0.650908\pi$$
$$102$$ 6.44949 0.638595
$$103$$ −13.2474 −1.30531 −0.652655 0.757655i $$-0.726345\pi$$
−0.652655 + 0.757655i $$0.726345\pi$$
$$104$$ 2.44949 + 4.24264i 0.240192 + 0.416025i
$$105$$ 1.72474 + 2.98735i 0.168318 + 0.291535i
$$106$$ −2.55051 −0.247727
$$107$$ −17.3485 −1.67714 −0.838570 0.544794i $$-0.816608\pi$$
−0.838570 + 0.544794i $$0.816608\pi$$
$$108$$ 0.500000 + 0.866025i 0.0481125 + 0.0833333i
$$109$$ 6.67423 11.5601i 0.639276 1.10726i −0.346316 0.938118i $$-0.612568\pi$$
0.985592 0.169140i $$-0.0540991\pi$$
$$110$$ 1.50000 + 2.59808i 0.143019 + 0.247717i
$$111$$ −0.0505103 + 0.0874863i −0.00479422 + 0.00830384i
$$112$$ −1.72474 + 2.98735i −0.162973 + 0.282278i
$$113$$ −14.4495 −1.35929 −0.679647 0.733539i $$-0.737867\pi$$
−0.679647 + 0.733539i $$0.737867\pi$$
$$114$$ −1.00000 + 4.24264i −0.0936586 + 0.397360i
$$115$$ 3.89898 0.363582
$$116$$ 2.67423 4.63191i 0.248296 0.430062i
$$117$$ 2.44949 4.24264i 0.226455 0.392232i
$$118$$ 3.00000 + 5.19615i 0.276172 + 0.478345i
$$119$$ 11.1237 19.2669i 1.01971 1.76619i
$$120$$ 0.500000 + 0.866025i 0.0456435 + 0.0790569i
$$121$$ −2.00000 −0.181818
$$122$$ 7.55051 0.683591
$$123$$ −5.17423 8.96204i −0.466545 0.808080i
$$124$$ −4.44949 7.70674i −0.399576 0.692086i
$$125$$ 1.00000 0.0894427
$$126$$ 3.44949 0.307305
$$127$$ −7.17423 12.4261i −0.636610 1.10264i −0.986172 0.165728i $$-0.947003\pi$$
0.349561 0.936914i $$-0.386331\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 3.89898 + 6.75323i 0.343286 + 0.594589i
$$130$$ 2.44949 4.24264i 0.214834 0.372104i
$$131$$ 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i $$-0.791497\pi$$
0.924084 + 0.382190i $$0.124830\pi$$
$$132$$ 3.00000 0.261116
$$133$$ 10.9495 + 10.3048i 0.949441 + 0.893541i
$$134$$ 7.34847 0.634811
$$135$$ 0.500000 0.866025i 0.0430331 0.0745356i
$$136$$ 3.22474 5.58542i 0.276520 0.478946i
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ 1.94949 3.37662i 0.165952 0.287437i
$$139$$ −7.34847 12.7279i −0.623289 1.07957i −0.988869 0.148788i $$-0.952463\pi$$
0.365580 0.930780i $$-0.380871\pi$$
$$140$$ 3.44949 0.291535
$$141$$ 10.8990 0.917860
$$142$$ −5.67423 9.82806i −0.476171 0.824753i
$$143$$ −7.34847 12.7279i −0.614510 1.06436i
$$144$$ 1.00000 0.0833333
$$145$$ −5.34847 −0.444166
$$146$$ −2.77526 4.80688i −0.229682 0.397820i
$$147$$ 2.44949 4.24264i 0.202031 0.349927i
$$148$$ 0.0505103 + 0.0874863i 0.00415192 + 0.00719133i
$$149$$ −9.22474 + 15.9777i −0.755721 + 1.30895i 0.189295 + 0.981920i $$0.439380\pi$$
−0.945015 + 0.327026i $$0.893954\pi$$
$$150$$ 0.500000 0.866025i 0.0408248 0.0707107i
$$151$$ −19.3485 −1.57456 −0.787278 0.616598i $$-0.788510\pi$$
−0.787278 + 0.616598i $$0.788510\pi$$
$$152$$ 3.17423 + 2.98735i 0.257464 + 0.242306i
$$153$$ −6.44949 −0.521410
$$154$$ 5.17423 8.96204i 0.416952 0.722182i
$$155$$ −4.44949 + 7.70674i −0.357392 + 0.619020i
$$156$$ −2.44949 4.24264i −0.196116 0.339683i
$$157$$ −0.601021 + 1.04100i −0.0479667 + 0.0830807i −0.889012 0.457884i $$-0.848607\pi$$
0.841045 + 0.540965i $$0.181941\pi$$
$$158$$ 1.44949 + 2.51059i 0.115315 + 0.199732i
$$159$$ 2.55051 0.202269
$$160$$ 1.00000 0.0790569
$$161$$ −6.72474 11.6476i −0.529984 0.917959i
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −12.6969 −0.994501 −0.497250 0.867607i $$-0.665657\pi$$
−0.497250 + 0.867607i $$0.665657\pi$$
$$164$$ −10.3485 −0.808080
$$165$$ −1.50000 2.59808i −0.116775 0.202260i
$$166$$ 3.89898 6.75323i 0.302619 0.524152i
$$167$$ −9.84847 17.0580i −0.762097 1.31999i −0.941768 0.336265i $$-0.890836\pi$$
0.179670 0.983727i $$-0.442497\pi$$
$$168$$ 1.72474 2.98735i 0.133067 0.230479i
$$169$$ −5.50000 + 9.52628i −0.423077 + 0.732791i
$$170$$ −6.44949 −0.494653
$$171$$ 1.00000 4.24264i 0.0764719 0.324443i
$$172$$ 7.79796 0.594589
$$173$$ 4.72474 8.18350i 0.359216 0.622180i −0.628614 0.777717i $$-0.716378\pi$$
0.987830 + 0.155537i $$0.0497109\pi$$
$$174$$ −2.67423 + 4.63191i −0.202733 + 0.351144i
$$175$$ −1.72474 2.98735i −0.130378 0.225822i
$$176$$ 1.50000 2.59808i 0.113067 0.195837i
$$177$$ −3.00000 5.19615i −0.225494 0.390567i
$$178$$ −0.550510 −0.0412625
$$179$$ −1.20204 −0.0898448 −0.0449224 0.998990i $$-0.514304\pi$$
−0.0449224 + 0.998990i $$0.514304\pi$$
$$180$$ −0.500000 0.866025i −0.0372678 0.0645497i
$$181$$ 8.57321 + 14.8492i 0.637242 + 1.10374i 0.986035 + 0.166536i $$0.0532582\pi$$
−0.348793 + 0.937200i $$0.613409\pi$$
$$182$$ −16.8990 −1.25264
$$183$$ −7.55051 −0.558150
$$184$$ −1.94949 3.37662i −0.143718 0.248927i
$$185$$ 0.0505103 0.0874863i 0.00371359 0.00643212i
$$186$$ 4.44949 + 7.70674i 0.326252 + 0.565086i
$$187$$ −9.67423 + 16.7563i −0.707450 + 1.22534i
$$188$$ 5.44949 9.43879i 0.397445 0.688395i
$$189$$ −3.44949 −0.250913
$$190$$ 1.00000 4.24264i 0.0725476 0.307794i
$$191$$ 15.7980 1.14310 0.571550 0.820567i $$-0.306342\pi$$
0.571550 + 0.820567i $$0.306342\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ 3.32577 5.76039i 0.239394 0.414642i −0.721147 0.692782i $$-0.756385\pi$$
0.960541 + 0.278140i $$0.0897180\pi$$
$$194$$ 6.77526 + 11.7351i 0.486435 + 0.842530i
$$195$$ −2.44949 + 4.24264i −0.175412 + 0.303822i
$$196$$ −2.44949 4.24264i −0.174964 0.303046i
$$197$$ 11.4495 0.815742 0.407871 0.913039i $$-0.366271\pi$$
0.407871 + 0.913039i $$0.366271\pi$$
$$198$$ −3.00000 −0.213201
$$199$$ −0.775255 1.34278i −0.0549564 0.0951872i 0.837238 0.546838i $$-0.184169\pi$$
−0.892195 + 0.451651i $$0.850835\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ −7.34847 −0.518321
$$202$$ −10.8990 −0.766850
$$203$$ 9.22474 + 15.9777i 0.647450 + 1.12142i
$$204$$ −3.22474 + 5.58542i −0.225777 + 0.391058i
$$205$$ 5.17423 + 8.96204i 0.361384 + 0.625936i
$$206$$ 6.62372 11.4726i 0.461497 0.799336i
$$207$$ −1.94949 + 3.37662i −0.135499 + 0.234691i
$$208$$ −4.89898 −0.339683
$$209$$ −9.52270 8.96204i −0.658699 0.619917i
$$210$$ −3.44949 −0.238037
$$211$$ 5.82577 10.0905i 0.401062 0.694660i −0.592792 0.805355i $$-0.701974\pi$$
0.993854 + 0.110695i $$0.0353078\pi$$
$$212$$ 1.27526 2.20881i 0.0875849 0.151701i
$$213$$ 5.67423 + 9.82806i 0.388792 + 0.673408i
$$214$$ 8.67423 15.0242i 0.592958 1.02703i
$$215$$ −3.89898 6.75323i −0.265908 0.460567i
$$216$$ −1.00000 −0.0680414
$$217$$ 30.6969 2.08384
$$218$$ 6.67423 + 11.5601i 0.452036 + 0.782950i
$$219$$ 2.77526 + 4.80688i 0.187534 + 0.324819i
$$220$$ −3.00000 −0.202260
$$221$$ 31.5959 2.12537
$$222$$ −0.0505103 0.0874863i −0.00339003 0.00587170i
$$223$$ −0.724745 + 1.25529i −0.0485325 + 0.0840608i −0.889271 0.457380i $$-0.848788\pi$$
0.840739 + 0.541441i $$0.182121\pi$$
$$224$$ −1.72474 2.98735i −0.115239 0.199600i
$$225$$ −0.500000 + 0.866025i −0.0333333 + 0.0577350i
$$226$$ 7.22474 12.5136i 0.480583 0.832394i
$$227$$ 3.34847 0.222246 0.111123 0.993807i $$-0.464555\pi$$
0.111123 + 0.993807i $$0.464555\pi$$
$$228$$ −3.17423 2.98735i −0.210219 0.197842i
$$229$$ −20.6969 −1.36769 −0.683846 0.729626i $$-0.739694\pi$$
−0.683846 + 0.729626i $$0.739694\pi$$
$$230$$ −1.94949 + 3.37662i −0.128546 + 0.222647i
$$231$$ −5.17423 + 8.96204i −0.340440 + 0.589659i
$$232$$ 2.67423 + 4.63191i 0.175572 + 0.304100i
$$233$$ 4.10102 7.10318i 0.268667 0.465345i −0.699851 0.714289i $$-0.746750\pi$$
0.968518 + 0.248944i $$0.0800836\pi$$
$$234$$ 2.44949 + 4.24264i 0.160128 + 0.277350i
$$235$$ −10.8990 −0.710971
$$236$$ −6.00000 −0.390567
$$237$$ −1.44949 2.51059i −0.0941545 0.163080i
$$238$$ 11.1237 + 19.2669i 0.721044 + 1.24888i
$$239$$ −10.2020 −0.659915 −0.329958 0.943996i $$-0.607034\pi$$
−0.329958 + 0.943996i $$0.607034\pi$$
$$240$$ −1.00000 −0.0645497
$$241$$ 11.3485 + 19.6561i 0.731019 + 1.26616i 0.956448 + 0.291903i $$0.0942883\pi$$
−0.225429 + 0.974260i $$0.572378\pi$$
$$242$$ 1.00000 1.73205i 0.0642824 0.111340i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ −3.77526 + 6.53893i −0.241686 + 0.418612i
$$245$$ −2.44949 + 4.24264i −0.156492 + 0.271052i
$$246$$ 10.3485 0.659794
$$247$$ −4.89898 + 20.7846i −0.311715 + 1.32249i
$$248$$ 8.89898 0.565086
$$249$$ −3.89898 + 6.75323i −0.247088 + 0.427969i
$$250$$ −0.500000 + 0.866025i −0.0316228 + 0.0547723i
$$251$$ 10.8990 + 18.8776i 0.687937 + 1.19154i 0.972504 + 0.232886i $$0.0748170\pi$$
−0.284566 + 0.958656i $$0.591850\pi$$
$$252$$ −1.72474 + 2.98735i −0.108649 + 0.188185i
$$253$$ 5.84847 + 10.1298i 0.367690 + 0.636858i
$$254$$ 14.3485 0.900303
$$255$$ 6.44949 0.403883
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 1.89898 + 3.28913i 0.118455 + 0.205170i 0.919156 0.393895i $$-0.128873\pi$$
−0.800701 + 0.599065i $$0.795539\pi$$
$$258$$ −7.79796 −0.485480
$$259$$ −0.348469 −0.0216528
$$260$$ 2.44949 + 4.24264i 0.151911 + 0.263117i
$$261$$ 2.67423 4.63191i 0.165531 0.286708i
$$262$$ 1.50000 + 2.59808i 0.0926703 + 0.160510i
$$263$$ −9.94949 + 17.2330i −0.613512 + 1.06263i 0.377132 + 0.926160i $$0.376910\pi$$
−0.990644 + 0.136474i $$0.956423\pi$$
$$264$$ −1.50000 + 2.59808i −0.0923186 + 0.159901i
$$265$$ −2.55051 −0.156677
$$266$$ −14.3990 + 4.33013i −0.882858 + 0.265497i
$$267$$ 0.550510 0.0336907
$$268$$ −3.67423 + 6.36396i −0.224440 + 0.388741i
$$269$$ −0.123724 + 0.214297i −0.00754361 + 0.0130659i −0.869773 0.493453i $$-0.835735\pi$$
0.862229 + 0.506519i $$0.169068\pi$$
$$270$$ 0.500000 + 0.866025i 0.0304290 + 0.0527046i
$$271$$ 2.55051 4.41761i 0.154932 0.268351i −0.778102 0.628138i $$-0.783817\pi$$
0.933034 + 0.359787i $$0.117151\pi$$
$$272$$ 3.22474 + 5.58542i 0.195529 + 0.338666i
$$273$$ 16.8990 1.02277
$$274$$ −12.0000 −0.724947
$$275$$ 1.50000 + 2.59808i 0.0904534 + 0.156670i
$$276$$ 1.94949 + 3.37662i 0.117345 + 0.203248i
$$277$$ −3.10102 −0.186322 −0.0931611 0.995651i $$-0.529697\pi$$
−0.0931611 + 0.995651i $$0.529697\pi$$
$$278$$ 14.6969 0.881464
$$279$$ −4.44949 7.70674i −0.266384 0.461391i
$$280$$ −1.72474 + 2.98735i −0.103073 + 0.178528i
$$281$$ 0.174235 + 0.301783i 0.0103940 + 0.0180029i 0.871176 0.490972i $$-0.163358\pi$$
−0.860782 + 0.508974i $$0.830025\pi$$
$$282$$ −5.44949 + 9.43879i −0.324512 + 0.562072i
$$283$$ −8.34847 + 14.4600i −0.496265 + 0.859556i −0.999991 0.00430747i $$-0.998629\pi$$
0.503726 + 0.863864i $$0.331962\pi$$
$$284$$ 11.3485 0.673408
$$285$$ −1.00000 + 4.24264i −0.0592349 + 0.251312i
$$286$$ 14.6969 0.869048
$$287$$ 17.8485 30.9145i 1.05356 1.82482i
$$288$$ −0.500000 + 0.866025i −0.0294628 + 0.0510310i
$$289$$ −12.2980 21.3007i −0.723409 1.25298i
$$290$$ 2.67423 4.63191i 0.157036 0.271995i
$$291$$ −6.77526 11.7351i −0.397172 0.687923i
$$292$$ 5.55051 0.324819
$$293$$ −6.55051 −0.382685 −0.191342 0.981523i $$-0.561284\pi$$
−0.191342 + 0.981523i $$0.561284\pi$$
$$294$$ 2.44949 + 4.24264i 0.142857 + 0.247436i
$$295$$ 3.00000 + 5.19615i 0.174667 + 0.302532i
$$296$$ −0.101021 −0.00587170
$$297$$ 3.00000 0.174078
$$298$$ −9.22474 15.9777i −0.534375 0.925565i
$$299$$ 9.55051 16.5420i 0.552320 0.956647i
$$300$$ 0.500000 + 0.866025i 0.0288675 + 0.0500000i
$$301$$ −13.4495 + 23.2952i −0.775216 + 1.34271i
$$302$$ 9.67423 16.7563i 0.556690 0.964215i
$$303$$ 10.8990 0.626130
$$304$$ −4.17423 + 1.25529i −0.239409 + 0.0719961i
$$305$$ 7.55051 0.432341
$$306$$ 3.22474 5.58542i 0.184346 0.319297i
$$307$$ −7.12372 + 12.3387i −0.406572 + 0.704204i −0.994503 0.104707i $$-0.966609\pi$$
0.587931 + 0.808911i $$0.299943\pi$$
$$308$$ 5.17423 + 8.96204i 0.294829 + 0.510659i
$$309$$ −6.62372 + 11.4726i −0.376811 + 0.652655i
$$310$$ −4.44949 7.70674i −0.252714 0.437714i
$$311$$ 9.79796 0.555591 0.277796 0.960640i $$-0.410396\pi$$
0.277796 + 0.960640i $$0.410396\pi$$
$$312$$ 4.89898 0.277350
$$313$$ 3.79796 + 6.57826i 0.214673 + 0.371825i 0.953171 0.302430i $$-0.0977980\pi$$
−0.738498 + 0.674256i $$0.764465\pi$$
$$314$$ −0.601021 1.04100i −0.0339175 0.0587469i
$$315$$ 3.44949 0.194357
$$316$$ −2.89898 −0.163080
$$317$$ −2.27526 3.94086i −0.127791 0.221341i 0.795029 0.606571i $$-0.207455\pi$$
−0.922820 + 0.385230i $$0.874122\pi$$
$$318$$ −1.27526 + 2.20881i −0.0715128 + 0.123864i
$$319$$ −8.02270 13.8957i −0.449185 0.778012i
$$320$$ −0.500000 + 0.866025i −0.0279508 + 0.0484123i
$$321$$ −8.67423 + 15.0242i −0.484149 + 0.838570i
$$322$$ 13.4495 0.749511
$$323$$ 26.9217 8.09601i 1.49796 0.450474i
$$324$$ 1.00000 0.0555556
$$325$$ 2.44949 4.24264i 0.135873 0.235339i
$$326$$ 6.34847 10.9959i 0.351609 0.609005i
$$327$$ −6.67423 11.5601i −0.369086 0.639276i
$$328$$ 5.17423 8.96204i 0.285699 0.494846i
$$329$$ 18.7980 + 32.5590i 1.03637 + 1.79504i
$$330$$ 3.00000 0.165145
$$331$$ 3.65153 0.200706 0.100353 0.994952i $$-0.468003\pi$$
0.100353 + 0.994952i $$0.468003\pi$$
$$332$$ 3.89898 + 6.75323i 0.213984 + 0.370632i
$$333$$ 0.0505103 + 0.0874863i 0.00276795 + 0.00479422i
$$334$$ 19.6969 1.07777
$$335$$ 7.34847 0.401490
$$336$$ 1.72474 + 2.98735i 0.0940925 + 0.162973i
$$337$$ −11.2474 + 19.4812i −0.612688 + 1.06121i 0.378098 + 0.925766i $$0.376578\pi$$
−0.990785 + 0.135440i $$0.956755\pi$$
$$338$$ −5.50000 9.52628i −0.299161 0.518161i
$$339$$ −7.22474 + 12.5136i −0.392394 + 0.679647i
$$340$$ 3.22474 5.58542i 0.174886 0.302912i
$$341$$ −26.6969 −1.44572
$$342$$ 3.17423 + 2.98735i 0.171643 + 0.161537i
$$343$$ −7.24745 −0.391325
$$344$$ −3.89898 + 6.75323i −0.210219 + 0.364110i
$$345$$ 1.94949 3.37662i 0.104957 0.181791i
$$346$$ 4.72474 + 8.18350i 0.254004 + 0.439948i
$$347$$ 3.89898 6.75323i 0.209308 0.362532i −0.742189 0.670191i $$-0.766212\pi$$
0.951497 + 0.307659i $$0.0995455\pi$$
$$348$$ −2.67423 4.63191i −0.143354 0.248296i
$$349$$ 24.0454 1.28712 0.643561 0.765395i $$-0.277456\pi$$
0.643561 + 0.765395i $$0.277456\pi$$
$$350$$ 3.44949 0.184383
$$351$$ −2.44949 4.24264i −0.130744 0.226455i
$$352$$ 1.50000 + 2.59808i 0.0799503 + 0.138478i
$$353$$ −20.6515 −1.09917 −0.549585 0.835438i $$-0.685214\pi$$
−0.549585 + 0.835438i $$0.685214\pi$$
$$354$$ 6.00000 0.318896
$$355$$ −5.67423 9.82806i −0.301157 0.521619i
$$356$$ 0.275255 0.476756i 0.0145885 0.0252680i
$$357$$ −11.1237 19.2669i −0.588730 1.01971i
$$358$$ 0.601021 1.04100i 0.0317649 0.0550185i
$$359$$ −10.7753 + 18.6633i −0.568696 + 0.985011i 0.427999 + 0.903779i $$0.359219\pi$$
−0.996695 + 0.0812316i $$0.974115\pi$$
$$360$$ 1.00000 0.0527046
$$361$$ 1.15153 + 18.9651i 0.0606069 + 0.998162i
$$362$$ −17.1464 −0.901196
$$363$$ −1.00000 + 1.73205i −0.0524864 + 0.0909091i
$$364$$ 8.44949 14.6349i 0.442874 0.767080i
$$365$$ −2.77526 4.80688i −0.145263 0.251604i
$$366$$ 3.77526 6.53893i 0.197336 0.341796i
$$367$$ −5.55051 9.61377i −0.289734 0.501834i 0.684012 0.729471i $$-0.260234\pi$$
−0.973746 + 0.227636i $$0.926900\pi$$
$$368$$ 3.89898 0.203248
$$369$$ −10.3485 −0.538720
$$370$$ 0.0505103 + 0.0874863i 0.00262590 + 0.00454820i
$$371$$ 4.39898 + 7.61926i 0.228384 + 0.395572i
$$372$$ −8.89898 −0.461391
$$373$$ 5.89898 0.305438 0.152719 0.988270i $$-0.451197\pi$$
0.152719 + 0.988270i $$0.451197\pi$$
$$374$$ −9.67423 16.7563i −0.500243 0.866446i
$$375$$ 0.500000 0.866025i 0.0258199 0.0447214i
$$376$$ 5.44949 + 9.43879i 0.281036 + 0.486769i
$$377$$ −13.1010 + 22.6916i −0.674737 + 1.16868i
$$378$$ 1.72474 2.98735i 0.0887113 0.153652i
$$379$$ 22.6969 1.16586 0.582932 0.812521i $$-0.301906\pi$$
0.582932 + 0.812521i $$0.301906\pi$$
$$380$$ 3.17423 + 2.98735i 0.162835 + 0.153248i
$$381$$ −14.3485 −0.735094
$$382$$ −7.89898 + 13.6814i −0.404147 + 0.700003i
$$383$$ 9.24745 16.0171i 0.472523 0.818433i −0.526983 0.849876i $$-0.676677\pi$$
0.999506 + 0.0314428i $$0.0100102\pi$$
$$384$$ 0.500000 + 0.866025i 0.0255155 + 0.0441942i
$$385$$ 5.17423 8.96204i 0.263703 0.456748i
$$386$$ 3.32577 + 5.76039i 0.169277 + 0.293196i
$$387$$ 7.79796 0.396393
$$388$$ −13.5505 −0.687923
$$389$$ −5.57321 9.65309i −0.282573 0.489431i 0.689445 0.724338i $$-0.257855\pi$$
−0.972018 + 0.234907i $$0.924521\pi$$
$$390$$ −2.44949 4.24264i −0.124035 0.214834i
$$391$$ −25.1464 −1.27171
$$392$$ 4.89898 0.247436
$$393$$ −1.50000 2.59808i −0.0756650 0.131056i
$$394$$ −5.72474 + 9.91555i −0.288408 + 0.499538i
$$395$$ 1.44949 + 2.51059i 0.0729317 + 0.126321i
$$396$$ 1.50000 2.59808i 0.0753778 0.130558i
$$397$$ 18.7474 32.4715i 0.940907 1.62970i 0.177162 0.984182i $$-0.443308\pi$$
0.763745 0.645518i $$-0.223358\pi$$
$$398$$ 1.55051 0.0777201
$$399$$ 14.3990 4.33013i 0.720851 0.216777i
$$400$$ 1.00000 0.0500000
$$401$$ −7.89898 + 13.6814i −0.394456 + 0.683218i −0.993032 0.117848i $$-0.962400\pi$$
0.598575 + 0.801066i $$0.295734\pi$$
$$402$$ 3.67423 6.36396i 0.183254 0.317406i
$$403$$ 21.7980 + 37.7552i 1.08583 + 1.88072i
$$404$$ 5.44949 9.43879i 0.271122 0.469598i
$$405$$ −0.500000 0.866025i −0.0248452 0.0430331i
$$406$$ −18.4495 −0.915633
$$407$$ 0.303062 0.0150222
$$408$$ −3.22474 5.58542i −0.159649 0.276520i
$$409$$ −19.7474 34.2036i −0.976448 1.69126i −0.675070 0.737754i $$-0.735886\pi$$
−0.301379 0.953505i $$-0.597447\pi$$
$$410$$ −10.3485 −0.511074
$$411$$ 12.0000 0.591916
$$412$$ 6.62372 + 11.4726i 0.326327 + 0.565216i
$$413$$ 10.3485 17.9241i 0.509215 0.881986i
$$414$$ −1.94949 3.37662i −0.0958122 0.165952i
$$415$$ 3.89898 6.75323i 0.191393 0.331503i
$$416$$ 2.44949 4.24264i 0.120096 0.208013i
$$417$$ −14.6969 −0.719712
$$418$$ 12.5227 3.76588i 0.612505 0.184195i
$$419$$ 12.1010 0.591174 0.295587 0.955316i $$-0.404485\pi$$
0.295587 + 0.955316i $$0.404485\pi$$
$$420$$ 1.72474 2.98735i 0.0841589 0.145768i
$$421$$ 16.6742 28.8806i 0.812652 1.40756i −0.0983489 0.995152i $$-0.531356\pi$$
0.911001 0.412403i $$-0.135311\pi$$
$$422$$ 5.82577 + 10.0905i 0.283594 + 0.491199i
$$423$$ 5.44949 9.43879i 0.264963 0.458930i
$$424$$ 1.27526 + 2.20881i 0.0619319 + 0.107269i
$$425$$ −6.44949 −0.312846
$$426$$ −11.3485 −0.549835
$$427$$ −13.0227 22.5560i −0.630213 1.09156i
$$428$$ 8.67423 + 15.0242i 0.419285 + 0.726223i
$$429$$ −14.6969 −0.709575
$$430$$ 7.79796 0.376051
$$431$$ −12.6742 21.9524i −0.610496 1.05741i −0.991157 0.132696i $$-0.957637\pi$$
0.380660 0.924715i $$-0.375697\pi$$
$$432$$ 0.500000 0.866025i 0.0240563 0.0416667i
$$433$$ 5.67423 + 9.82806i 0.272686 + 0.472307i 0.969549 0.244898i $$-0.0787546\pi$$
−0.696862 + 0.717205i $$0.745421\pi$$
$$434$$ −15.3485 + 26.5843i −0.736750 + 1.27609i
$$435$$ −2.67423 + 4.63191i −0.128220 + 0.222083i
$$436$$ −13.3485 −0.639276
$$437$$ 3.89898 16.5420i 0.186513 0.791310i
$$438$$ −5.55051 −0.265214
$$439$$ 5.67423 9.82806i 0.270816 0.469068i −0.698255 0.715849i $$-0.746040\pi$$
0.969071 + 0.246782i $$0.0793730\pi$$
$$440$$ 1.50000 2.59808i 0.0715097 0.123858i
$$441$$ −2.44949 4.24264i −0.116642 0.202031i
$$442$$ −15.7980 + 27.3629i −0.751432 + 1.30152i
$$443$$ −13.1237 22.7310i −0.623527 1.07998i −0.988824 0.149089i $$-0.952366\pi$$
0.365297 0.930891i $$-0.380968\pi$$
$$444$$ 0.101021 0.00479422
$$445$$ −0.550510 −0.0260967
$$446$$ −0.724745 1.25529i −0.0343177 0.0594399i
$$447$$ 9.22474 + 15.9777i 0.436315 + 0.755721i
$$448$$ 3.44949 0.162973
$$449$$ 33.2474 1.56904 0.784522 0.620101i $$-0.212908\pi$$
0.784522 + 0.620101i $$0.212908\pi$$
$$450$$ −0.500000 0.866025i −0.0235702 0.0408248i
$$451$$ −15.5227 + 26.8861i −0.730936 + 1.26602i
$$452$$ 7.22474 + 12.5136i 0.339823 + 0.588591i
$$453$$ −9.67423 + 16.7563i −0.454535 + 0.787278i
$$454$$ −1.67423 + 2.89986i −0.0785757 + 0.136097i
$$455$$ −16.8990 −0.792236
$$456$$ 4.17423 1.25529i 0.195476 0.0587846i
$$457$$ 32.0454 1.49902 0.749510 0.661992i $$-0.230289\pi$$
0.749510 + 0.661992i $$0.230289\pi$$
$$458$$ 10.3485 17.9241i 0.483552 0.837537i
$$459$$ −3.22474 + 5.58542i −0.150518 + 0.260705i
$$460$$ −1.94949 3.37662i −0.0908954 0.157435i
$$461$$ 4.10102 7.10318i 0.191004 0.330828i −0.754580 0.656209i $$-0.772159\pi$$
0.945583 + 0.325381i $$0.105492\pi$$
$$462$$ −5.17423 8.96204i −0.240727 0.416952i
$$463$$ −30.3485 −1.41041 −0.705206 0.709002i $$-0.749146\pi$$
−0.705206 + 0.709002i $$0.749146\pi$$
$$464$$ −5.34847 −0.248296
$$465$$ 4.44949 + 7.70674i 0.206340 + 0.357392i
$$466$$ 4.10102 + 7.10318i 0.189976 + 0.329048i
$$467$$ −15.7526 −0.728941 −0.364471 0.931215i $$-0.618750\pi$$
−0.364471 + 0.931215i $$0.618750\pi$$
$$468$$ −4.89898 −0.226455
$$469$$ −12.6742 21.9524i −0.585242 1.01367i
$$470$$ 5.44949 9.43879i 0.251366 0.435379i
$$471$$ 0.601021 + 1.04100i 0.0276936 + 0.0479667i
$$472$$ 3.00000 5.19615i 0.138086 0.239172i
$$473$$ 11.6969 20.2597i 0.537826 0.931542i
$$474$$ 2.89898 0.133155
$$475$$ 1.00000 4.24264i 0.0458831 0.194666i
$$476$$ −22.2474 −1.01971
$$477$$ 1.27526 2.20881i 0.0583899 0.101134i
$$478$$ 5.10102 8.83523i 0.233315 0.404114i
$$479$$ 17.0227 + 29.4842i 0.777787 + 1.34717i 0.933215 + 0.359320i $$0.116991\pi$$
−0.155427 + 0.987847i $$0.549675\pi$$
$$480$$ 0.500000 0.866025i 0.0228218 0.0395285i
$$481$$ −0.247449 0.428594i −0.0112827 0.0195422i
$$482$$ −22.6969 −1.03382
$$483$$ −13.4495 −0.611973
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ 6.77526 + 11.7351i 0.307648 + 0.532863i
$$486$$ −1.00000 −0.0453609
$$487$$ 6.14643 0.278521 0.139261 0.990256i $$-0.455527\pi$$
0.139261 + 0.990256i $$0.455527\pi$$
$$488$$ −3.77526 6.53893i −0.170898 0.296004i
$$489$$ −6.34847 + 10.9959i −0.287088 + 0.497250i
$$490$$ −2.44949 4.24264i −0.110657 0.191663i
$$491$$ 17.3990 30.1359i 0.785205 1.36001i −0.143672 0.989625i $$-0.545891\pi$$
0.928877 0.370389i $$-0.120776\pi$$
$$492$$ −5.17423 + 8.96204i −0.233273 + 0.404040i
$$493$$ 34.4949 1.55357
$$494$$ −15.5505 14.6349i −0.699651 0.658457i
$$495$$ −3.00000 −0.134840
$$496$$ −4.44949 + 7.70674i −0.199788 + 0.346043i
$$497$$ −19.5732 + 33.9018i −0.877979 + 1.52070i
$$498$$ −3.89898 6.75323i −0.174717 0.302619i
$$499$$ −7.72474 + 13.3797i −0.345807 + 0.598955i −0.985500 0.169675i $$-0.945728\pi$$
0.639693 + 0.768631i $$0.279062\pi$$
$$500$$ −0.500000 0.866025i −0.0223607 0.0387298i
$$501$$ −19.6969 −0.879994
$$502$$ −21.7980 −0.972891
$$503$$ −15.8485 27.4504i −0.706648 1.22395i −0.966093 0.258193i $$-0.916873\pi$$
0.259445 0.965758i $$-0.416460\pi$$
$$504$$ −1.72474 2.98735i −0.0768262 0.133067i
$$505$$ −10.8990 −0.484998
$$506$$ −11.6969 −0.519992
$$507$$ 5.50000 + 9.52628i 0.244264 + 0.423077i
$$508$$ −7.17423 + 12.4261i −0.318305 + 0.551321i
$$509$$ −3.44949 5.97469i −0.152896 0.264824i 0.779395 0.626533i $$-0.215527\pi$$
−0.932291 + 0.361709i $$0.882193\pi$$
$$510$$ −3.22474 + 5.58542i −0.142794 + 0.247327i
$$511$$ −9.57321 + 16.5813i −0.423494 + 0.733513i
$$512$$ 1.00000 0.0441942
$$513$$ −3.17423 2.98735i −0.140146 0.131895i
$$514$$ −3.79796 −0.167521
$$515$$ 6.62372 11.4726i 0.291876 0.505544i
$$516$$ 3.89898 6.75323i 0.171643 0.297294i
$$517$$ −16.3485 28.3164i −0.719005 1.24535i
$$518$$ 0.174235 0.301783i 0.00765543 0.0132596i
$$519$$ −4.72474 8.18350i −0.207393 0.359216i
$$520$$ −4.89898 −0.214834
$$521$$ 10.8990 0.477493 0.238746 0.971082i $$-0.423264\pi$$
0.238746 + 0.971082i $$0.423264\pi$$
$$522$$ 2.67423 + 4.63191i 0.117048 + 0.202733i
$$523$$ 15.5732 + 26.9736i 0.680969 + 1.17947i 0.974685 + 0.223580i $$0.0717745\pi$$
−0.293716 + 0.955893i $$0.594892\pi$$
$$524$$ −3.00000 −0.131056
$$525$$ −3.44949 −0.150548
$$526$$ −9.94949 17.2330i −0.433818 0.751395i
$$527$$ 28.6969 49.7046i 1.25006 2.16516i
$$528$$ −1.50000 2.59808i −0.0652791 0.113067i
$$529$$ 3.89898 6.75323i 0.169521 0.293619i
$$530$$ 1.27526 2.20881i 0.0553935 0.0959444i
$$531$$ −6.00000 −0.260378
$$532$$ 3.44949 14.6349i 0.149554 0.634505i
$$533$$ 50.6969 2.19593
$$534$$ −0.275255 + 0.476756i −0.0119115 + 0.0206312i
$$535$$ 8.67423 15.0242i 0.375020 0.649553i
$$536$$ −3.67423 6.36396i −0.158703 0.274881i
$$537$$ −0.601021 + 1.04100i −0.0259359 + 0.0449224i
$$538$$ −0.123724 0.214297i −0.00533414 0.00923899i
$$539$$ −14.6969 −0.633042
$$540$$ −1.00000 −0.0430331
$$541$$ −14.4495 25.0273i −0.621232 1.07601i −0.989257 0.146189i $$-0.953299\pi$$
0.368025 0.929816i $$-0.380034\pi$$
$$542$$ 2.55051 + 4.41761i 0.109554 + 0.189753i
$$543$$ 17.1464 0.735824
$$544$$ −6.44949 −0.276520
$$545$$ 6.67423 + 11.5601i 0.285893 + 0.495181i
$$546$$ −8.44949 + 14.6349i −0.361605 + 0.626318i
$$547$$ 16.3485 + 28.3164i 0.699010 + 1.21072i 0.968810 + 0.247805i $$0.0797091\pi$$
−0.269800 + 0.962916i $$0.586958\pi$$
$$548$$ 6.00000 10.3923i 0.256307 0.443937i
$$549$$ −3.77526 + 6.53893i −0.161124 + 0.279075i
$$550$$ −3.00000 −0.127920
$$551$$ −5.34847 + 22.6916i −0.227852 + 0.966696i
$$552$$ −3.89898 −0.165952
$$553$$ 5.00000 8.66025i 0.212622 0.368271i
$$554$$ 1.55051 2.68556i 0.0658749 0.114099i
$$555$$ −0.0505103 0.0874863i −0.00214404 0.00371359i
$$556$$ −7.34847 + 12.7279i −0.311645 + 0.539784i
$$557$$ 1.82577 + 3.16232i 0.0773602 + 0.133992i 0.902110 0.431506i $$-0.142018\pi$$
−0.824750 + 0.565497i $$0.808684\pi$$
$$558$$ 8.89898 0.376724
$$559$$ −38.2020 −1.61577
$$560$$ −1.72474 2.98735i −0.0728838 0.126238i
$$561$$ 9.67423 + 16.7563i 0.408447 + 0.707450i
$$562$$ −0.348469 −0.0146993
$$563$$ −29.3939 −1.23880 −0.619402 0.785074i $$-0.712625\pi$$
−0.619402 + 0.785074i $$0.712625\pi$$
$$564$$ −5.44949 9.43879i −0.229465 0.397445i
$$565$$ 7.22474 12.5136i 0.303947 0.526452i
$$566$$ −8.34847 14.4600i −0.350912 0.607798i
$$567$$ −1.72474 + 2.98735i −0.0724325 + 0.125457i
$$568$$ −5.67423 + 9.82806i −0.238086 + 0.412376i
$$569$$ −2.55051 −0.106923 −0.0534615 0.998570i $$-0.517025\pi$$
−0.0534615 + 0.998570i $$0.517025\pi$$
$$570$$ −3.17423 2.98735i −0.132954 0.125126i
$$571$$ −27.7980 −1.16331 −0.581654 0.813436i $$-0.697594\pi$$
−0.581654 + 0.813436i $$0.697594\pi$$
$$572$$ −7.34847 + 12.7279i −0.307255 + 0.532181i
$$573$$ 7.89898 13.6814i 0.329985 0.571550i
$$574$$ 17.8485 + 30.9145i 0.744981 + 1.29034i
$$575$$ −1.94949 + 3.37662i −0.0812993 + 0.140815i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −23.1464 −0.963598 −0.481799 0.876282i $$-0.660017\pi$$
−0.481799 + 0.876282i $$0.660017\pi$$
$$578$$ 24.5959 1.02306
$$579$$ −3.32577 5.76039i −0.138214 0.239394i
$$580$$ 2.67423 + 4.63191i 0.111042 + 0.192330i
$$581$$ −26.8990 −1.11596
$$582$$ 13.5505 0.561687
$$583$$ −3.82577 6.62642i −0.158447 0.274438i
$$584$$ −2.77526 + 4.80688i −0.114841 + 0.198910i
$$585$$ 2.44949 + 4.24264i 0.101274 + 0.175412i
$$586$$ 3.27526 5.67291i 0.135300 0.234346i
$$587$$ −8.24745 + 14.2850i −0.340409 + 0.589605i −0.984509 0.175336i $$-0.943899\pi$$
0.644100 + 0.764941i $$0.277232\pi$$
$$588$$ −4.89898 −0.202031
$$589$$ 28.2474 + 26.5843i 1.16392 + 1.09539i
$$590$$ −6.00000 −0.247016
$$591$$ 5.72474 9.91555i 0.235485 0.407871i
$$592$$ 0.0505103 0.0874863i 0.00207596 0.00359567i
$$593$$ 0.426786 + 0.739215i 0.0175260 + 0.0303559i 0.874655 0.484745i $$-0.161088\pi$$
−0.857129 + 0.515101i $$0.827754\pi$$
$$594$$ −1.50000 + 2.59808i −0.0615457 + 0.106600i
$$595$$ 11.1237 + 19.2669i 0.456028 + 0.789864i
$$596$$ 18.4495 0.755721
$$597$$ −1.55051 −0.0634582
$$598$$ 9.55051 + 16.5420i 0.390549 + 0.676451i
$$599$$ −5.32577 9.22450i −0.217605 0.376903i 0.736470 0.676470i $$-0.236491\pi$$
−0.954075 + 0.299567i $$0.903158\pi$$
$$600$$ −1.00000 −0.0408248
$$601$$ 19.0000 0.775026 0.387513 0.921864i $$-0.373334\pi$$
0.387513 + 0.921864i $$0.373334\pi$$
$$602$$ −13.4495 23.2952i −0.548160 0.949441i
$$603$$ −3.67423 + 6.36396i −0.149626 + 0.259161i
$$604$$ 9.67423 + 16.7563i 0.393639 + 0.681803i
$$605$$ 1.00000 1.73205i 0.0406558 0.0704179i
$$606$$ −5.44949 + 9.43879i −0.221370 + 0.383425i
$$607$$ 24.5505 0.996474 0.498237 0.867041i $$-0.333981\pi$$
0.498237 + 0.867041i $$0.333981\pi$$
$$608$$ 1.00000 4.24264i 0.0405554 0.172062i
$$609$$ 18.4495 0.747611
$$610$$ −3.77526 + 6.53893i −0.152856 + 0.264754i
$$611$$ −26.6969 + 46.2405i −1.08004 + 1.87069i
$$612$$ 3.22474 + 5.58542i 0.130353 + 0.225777i
$$613$$ 18.7474 32.4715i 0.757202 1.31151i −0.187070 0.982347i $$-0.559899\pi$$
0.944272 0.329166i $$-0.106768\pi$$
$$614$$ −7.12372 12.3387i −0.287490 0.497947i
$$615$$ 10.3485 0.417291
$$616$$ −10.3485 −0.416952
$$617$$ 11.7980 + 20.4347i 0.474968 + 0.822669i 0.999589 0.0286672i $$-0.00912632\pi$$
−0.524621 + 0.851336i $$0.675793\pi$$
$$618$$ −6.62372 11.4726i −0.266445 0.461497i
$$619$$ −21.0454 −0.845886 −0.422943 0.906156i $$-0.639003\pi$$
−0.422943 + 0.906156i $$0.639003\pi$$
$$620$$ 8.89898 0.357392
$$621$$ 1.94949 + 3.37662i 0.0782303 + 0.135499i
$$622$$ −4.89898 + 8.48528i −0.196431 + 0.340229i
$$623$$ 0.949490 + 1.64456i 0.0380405 + 0.0658881i
$$624$$ −2.44949 + 4.24264i −0.0980581 + 0.169842i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −7.59592 −0.303594
$$627$$ −12.5227 + 3.76588i −0.500109 + 0.150395i
$$628$$ 1.20204 0.0479667
$$629$$ −0.325765 + 0.564242i −0.0129891 + 0.0224978i
$$630$$ −1.72474 + 2.98735i −0.0687155 + 0.119019i
$$631$$ 0.876276 + 1.51775i 0.0348840 + 0.0604208i 0.882940 0.469485i $$-0.155560\pi$$
−0.848056 + 0.529906i $$0.822227\pi$$
$$632$$ 1.44949 2.51059i 0.0576576 0.0998659i
$$633$$ −5.82577 10.0905i −0.231553 0.401062i
$$634$$ 4.55051 0.180724
$$635$$ 14.3485 0.569402
$$636$$ −1.27526 2.20881i −0.0505672 0.0875849i
$$637$$ 12.0000 + 20.7846i 0.475457 + 0.823516i
$$638$$ 16.0454 0.635244
$$639$$ 11.3485 0.448939
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ 20.3485 35.2446i 0.803716 1.39208i −0.113438 0.993545i $$-0.536186\pi$$
0.917154 0.398532i $$-0.130480\pi$$
$$642$$ −8.67423 15.0242i −0.342345 0.592958i
$$643$$ 2.12372 3.67840i 0.0837515 0.145062i −0.821107 0.570774i $$-0.806643\pi$$
0.904859 + 0.425712i $$0.139976\pi$$
$$644$$ −6.72474 + 11.6476i −0.264992 + 0.458980i
$$645$$ −7.79796 −0.307044
$$646$$ −6.44949 + 27.3629i −0.253752 + 1.07658i
$$647$$ 9.89898 0.389169 0.194585 0.980886i $$-0.437664\pi$$
0.194585 + 0.980886i $$0.437664\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ −9.00000 + 15.5885i −0.353281 + 0.611900i
$$650$$ 2.44949 + 4.24264i 0.0960769 + 0.166410i
$$651$$ 15.3485 26.5843i 0.601554 1.04192i
$$652$$ 6.34847 + 10.9959i 0.248625 + 0.430632i
$$653$$ −25.6515 −1.00382 −0.501911 0.864919i $$-0.667370\pi$$
−0.501911 + 0.864919i $$0.667370\pi$$
$$654$$ 13.3485 0.521966
$$655$$ 1.50000 + 2.59808i 0.0586098 + 0.101515i
$$656$$ 5.17423 + 8.96204i 0.202020 + 0.349909i
$$657$$ 5.55051 0.216546
$$658$$ −37.5959 −1.46564
$$659$$ 8.29796 + 14.3725i 0.323243 + 0.559873i 0.981155 0.193222i $$-0.0618937\pi$$
−0.657913 + 0.753094i $$0.728560\pi$$
$$660$$ −1.50000 + 2.59808i −0.0583874 + 0.101130i
$$661$$ −2.89898 5.02118i −0.112757 0.195301i 0.804124 0.594462i $$-0.202635\pi$$
−0.916881 + 0.399161i $$0.869302\pi$$
$$662$$ −1.82577 + 3.16232i −0.0709604 + 0.122907i
$$663$$ 15.7980 27.3629i 0.613542 1.06269i
$$664$$ −7.79796 −0.302619
$$665$$ −14.3990 + 4.33013i −0.558368 + 0.167915i
$$666$$ −0.101021 −0.00391447
$$667$$ 10.4268 18.0597i 0.403727 0.699275i
$$668$$ −9.84847 + 17.0580i −0.381049 + 0.659996i
$$669$$ 0.724745 + 1.25529i 0.0280203 + 0.0485325i
$$670$$ −3.67423 + 6.36396i −0.141948 + 0.245861i
$$671$$ 11.3258 + 19.6168i 0.437226 + 0.757298i
$$672$$ −3.44949 −0.133067
$$673$$ 8.49490 0.327454 0.163727 0.986506i $$-0.447648\pi$$
0.163727 + 0.986506i $$0.447648\pi$$
$$674$$ −11.2474 19.4812i −0.433236 0.750386i
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ 11.0000 0.423077
$$677$$ −23.9444 −0.920258 −0.460129 0.887852i $$-0.652197\pi$$
−0.460129 + 0.887852i $$0.652197\pi$$
$$678$$ −7.22474 12.5136i −0.277465 0.480583i
$$679$$ 23.3712 40.4801i 0.896903 1.55348i
$$680$$ 3.22474 + 5.58542i 0.123663 + 0.214191i
$$681$$ 1.67423 2.89986i 0.0641568 0.111123i
$$682$$ 13.3485 23.1202i 0.511139 0.885319i
$$683$$ −42.2474 −1.61655 −0.808277 0.588803i $$-0.799600\pi$$
−0.808277 + 0.588803i $$0.799600\pi$$
$$684$$ −4.17423 + 1.25529i −0.159606 + 0.0479974i
$$685$$ −12.0000 −0.458496
$$686$$ 3.62372 6.27647i 0.138354 0.239637i
$$687$$ −10.3485 + 17.9241i −0.394819 + 0.683846i
$$688$$ −3.89898 6.75323i −0.148647 0.257465i
$$689$$ −6.24745 + 10.8209i −0.238009 + 0.412243i
$$690$$ 1.94949 + 3.37662i 0.0742158 + 0.128546i
$$691$$ −26.5505 −1.01003 −0.505015 0.863111i $$-0.668513\pi$$
−0.505015 + 0.863111i $$0.668513\pi$$
$$692$$ −9.44949 −0.359216
$$693$$ 5.17423 + 8.96204i 0.196553 + 0.340440i
$$694$$ 3.89898 + 6.75323i 0.148003 + 0.256349i
$$695$$ 14.6969 0.557487
$$696$$ 5.34847 0.202733
$$697$$ −33.3712 57.8006i −1.26402 2.18935i
$$698$$ −12.0227 + 20.8239i −0.455066 + 0.788198i
$$699$$ −4.10102 7.10318i −0.155115 0.268667i
$$700$$ −1.72474 + 2.98735i −0.0651892 + 0.112911i
$$701$$ −11.8990 + 20.6096i −0.449418 + 0.778415i −0.998348 0.0574531i $$-0.981702\pi$$
0.548930 + 0.835868i $$0.315035\pi$$
$$702$$ 4.89898 0.184900
$$703$$ −0.320663 0.301783i −0.0120940 0.0113820i
$$704$$ −3.00000 −0.113067
$$705$$ −5.44949 + 9.43879i −0.205240 + 0.355486i
$$706$$ 10.3258 17.8848i 0.388615 0.673101i
$$707$$ 18.7980 + 32.5590i 0.706970 + 1.22451i
$$708$$ −3.00000 + 5.19615i −0.112747 + 0.195283i
$$709$$ 4.47219 + 7.74607i 0.167957 + 0.290910i 0.937701 0.347442i $$-0.112950\pi$$
−0.769745 + 0.638352i $$0.779616\pi$$
$$710$$ 11.3485 0.425900
$$711$$ −2.89898 −0.108720
$$712$$ 0.275255 + 0.476756i 0.0103156 + 0.0178672i
$$713$$ −17.3485 30.0484i −0.649705 1.12532i
$$714$$ 22.2474 0.832590
$$715$$ 14.6969 0.549634
$$716$$ 0.601021 + 1.04100i 0.0224612 + 0.0389039i
$$717$$ −5.10102 + 8.83523i −0.190501 + 0.329958i
$$718$$ −10.7753 18.6633i −0.402129 0.696508i
$$719$$ 2.65153 4.59259i 0.0988854 0.171275i −0.812338 0.583187i $$-0.801806\pi$$
0.911224 + 0.411912i $$0.135139\pi$$
$$720$$ −0.500000 + 0.866025i −0.0186339 + 0.0322749i
$$721$$ −45.6969 −1.70184
$$722$$ −17.0000 8.48528i −0.632674 0.315789i
$$723$$ 22.6969 0.844108
$$724$$ 8.57321 14.8492i 0.318621 0.551868i
$$725$$ 2.67423 4.63191i 0.0993186 0.172025i
$$726$$ −1.00000 1.73205i −0.0371135 0.0642824i
$$727$$ −13.8990 + 24.0737i −0.515485 + 0.892846i 0.484354 + 0.874872i $$0.339055\pi$$
−0.999838 + 0.0179734i $$0.994279\pi$$
$$728$$ 8.44949 + 14.6349i 0.313159 + 0.542407i
$$729$$ 1.00000 0.0370370
$$730$$ 5.55051 0.205434
$$731$$ 25.1464 + 43.5549i 0.930074 + 1.61094i
$$732$$ 3.77526 + 6.53893i 0.139537 + 0.241686i
$$733$$ 36.5959 1.35170 0.675851 0.737039i $$-0.263776\pi$$
0.675851 + 0.737039i $$0.263776\pi$$
$$734$$ 11.1010 0.409746
$$735$$ 2.44949 + 4.24264i 0.0903508 + 0.156492i
$$736$$ −1.94949 + 3.37662i −0.0718591 + 0.124464i
$$737$$ 11.0227 + 19.0919i 0.406027 + 0.703259i
$$738$$ 5.17423 8.96204i 0.190466 0.329897i
$$739$$ 7.97219 13.8082i 0.293262 0.507944i −0.681317 0.731988i $$-0.738593\pi$$
0.974579 + 0.224044i $$0.0719259\pi$$
$$740$$ −0.101021 −0.00371359
$$741$$ 15.5505 + 14.6349i 0.571262 + 0.537628i
$$742$$ −8.79796 −0.322983
$$743$$ −4.84847 + 8.39780i −0.177873 + 0.308085i −0.941152 0.337984i $$-0.890255\pi$$
0.763279 + 0.646069i $$0.223588\pi$$
$$744$$ 4.44949 7.70674i 0.163126 0.282543i
$$745$$ −9.22474 15.9777i −0.337969 0.585379i
$$746$$ −2.94949 + 5.10867i −0.107988 + 0.187042i
$$747$$ 3.89898 + 6.75323i 0.142656 + 0.247088i
$$748$$ 19.3485 0.707450
$$749$$ −59.8434 −2.18663
$$750$$ 0.500000 + 0.866025i 0.0182574 + 0.0316228i
$$751$$ −26.4949 45.8905i −0.966813 1.67457i −0.704664 0.709541i $$-0.748902\pi$$
−0.262148 0.965028i $$-0.584431\pi$$
$$752$$ −10.8990 −0.397445
$$753$$ 21.7980 0.794362
$$754$$ −13.1010 22.6916i −0.477111 0.826381i
$$755$$ 9.67423 16.7563i 0.352081 0.609823i
$$756$$ 1.72474 + 2.98735i 0.0627284 + 0.108649i
$$757$$ −27.1969 + 47.1065i −0.988490 + 1.71211i −0.363224 + 0.931702i $$0.618324\pi$$
−0.625265 + 0.780412i $$0.715009\pi$$
$$758$$ −11.3485 + 19.6561i −0.412195 + 0.713943i
$$759$$ 11.6969 0.424572
$$760$$ −4.17423 + 1.25529i −0.151415 + 0.0455343i
$$761$$ 16.5505 0.599956 0.299978 0.953946i $$-0.403021\pi$$
0.299978 + 0.953946i $$0.403021\pi$$
$$762$$ 7.17423 12.4261i 0.259895 0.450152i
$$763$$ 23.0227 39.8765i 0.833478 1.44363i
$$764$$ −7.89898 13.6814i −0.285775 0.494977i
$$765$$ 3.22474 5.58542i 0.116591 0.201941i
$$766$$ 9.24745 + 16.0171i 0.334124 + 0.578720i
$$767$$ 29.3939 1.06135
$$768$$ −1.00000 −0.0360844
$$769$$ 7.10102 + 12.2993i 0.256069 + 0.443525i 0.965185 0.261567i $$-0.0842391\pi$$
−0.709116 + 0.705092i $$0.750906\pi$$
$$770$$ 5.17423 + 8.96204i 0.186466 + 0.322969i
$$771$$ 3.79796 0.136780
$$772$$ −6.65153 −0.239394
$$773$$ 0.477296 + 0.826701i 0.0171671 + 0.0297344i 0.874481 0.485059i $$-0.161202\pi$$
−0.857314 + 0.514794i $$0.827869\pi$$
$$774$$ −3.89898 + 6.75323i −0.140146 + 0.242740i
$$775$$ −4.44949 7.70674i −0.159830 0.276834i
$$776$$ 6.77526 11.7351i 0.243217 0.421265i
$$777$$ −0.174235 + 0.301783i −0.00625063 + 0.0108264i
$$778$$ 11.1464