# Properties

 Label 930.2.i.f.211.1 Level $930$ Weight $2$ Character 930.211 Analytic conductor $7.426$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 211.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 930.211 Dual form 930.2.i.f.811.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.500000 - 0.866025i) q^{21} +(-2.50000 + 4.33013i) q^{22} -4.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +3.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} +5.00000 q^{33} +(1.00000 + 1.73205i) q^{34} -1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +(1.00000 + 1.73205i) q^{38} +4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{45} -4.00000 q^{46} +2.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.00000 - 1.73205i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +1.00000 q^{54} +(-2.50000 - 4.33013i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.00000 - 1.73205i) q^{57} +3.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +1.00000 q^{60} +(3.50000 - 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +5.00000 q^{66} +(2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(2.00000 + 3.46410i) q^{69} -1.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.00000 + 1.73205i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(0.500000 - 0.866025i) q^{84} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +18.0000 q^{89} +(-0.500000 - 0.866025i) q^{90} -4.00000 q^{91} -4.00000 q^{92} +(-5.50000 - 0.866025i) q^{93} +2.00000 q^{94} -2.00000 q^{95} +(-0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(3.00000 - 5.19615i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9 $$2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} - q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - q^{20} + q^{21} - 5 q^{22} - 8 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} + 10 q^{33} + 2 q^{34} - 2 q^{35} - q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} - q^{40} - 4 q^{41} + q^{42} + 4 q^{43} - 5 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} - q^{48} + 6 q^{49} - q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} - 5 q^{55} + q^{56} + 2 q^{57} + 6 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{65} + 10 q^{66} + 4 q^{67} + 2 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - q^{72} - 2 q^{73} + 4 q^{74} - q^{75} + 2 q^{76} - 10 q^{77} + 8 q^{78} - q^{80} - q^{81} - 4 q^{82} - 9 q^{83} + q^{84} - 4 q^{85} + 4 q^{86} - 3 q^{87} - 5 q^{88} + 36 q^{89} - q^{90} - 8 q^{91} - 8 q^{92} - 11 q^{93} + 4 q^{94} - 4 q^{95} - q^{96} - 2 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + q^7 + 2 * q^8 - q^9 - q^10 - 5 * q^11 - q^12 - 4 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 - q^18 + 2 * q^19 - q^20 + q^21 - 5 * q^22 - 8 * q^23 - q^24 - q^25 - 4 * q^26 + 2 * q^27 + q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 + 2 * q^32 + 10 * q^33 + 2 * q^34 - 2 * q^35 - q^36 + 4 * q^37 + 2 * q^38 + 8 * q^39 - q^40 - 4 * q^41 + q^42 + 4 * q^43 - 5 * q^44 - q^45 - 8 * q^46 + 4 * q^47 - q^48 + 6 * q^49 - q^50 + 2 * q^51 - 4 * q^52 - 3 * q^53 + 2 * q^54 - 5 * q^55 + q^56 + 2 * q^57 + 6 * q^58 - 3 * q^59 + 2 * q^60 + 7 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^65 + 10 * q^66 + 4 * q^67 + 2 * q^68 + 4 * q^69 - 2 * q^70 - 8 * q^71 - q^72 - 2 * q^73 + 4 * q^74 - q^75 + 2 * q^76 - 10 * q^77 + 8 * q^78 - q^80 - q^81 - 4 * q^82 - 9 * q^83 + q^84 - 4 * q^85 + 4 * q^86 - 3 * q^87 - 5 * q^88 + 36 * q^89 - q^90 - 8 * q^91 - 8 * q^92 - 11 * q^93 + 4 * q^94 - 4 * q^95 - q^96 - 2 * q^97 + 6 * q^98 - 5 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$$.

 $$n$$ $$187$$ $$311$$ $$871$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ 1.00000 0.500000
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i $$-0.106148\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i $$0.438437\pi$$
−0.945979 + 0.324227i $$0.894896\pi$$
$$12$$ −0.500000 0.866025i −0.144338 0.250000i
$$13$$ −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i $$0.353834\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ 0.500000 + 0.866025i 0.133631 + 0.231455i
$$15$$ 1.00000 0.258199
$$16$$ 1.00000 0.250000
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ −0.500000 + 0.866025i −0.117851 + 0.204124i
$$19$$ 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i $$-0.0929851\pi$$
−0.728219 + 0.685344i $$0.759652\pi$$
$$20$$ −0.500000 + 0.866025i −0.111803 + 0.193649i
$$21$$ 0.500000 0.866025i 0.109109 0.188982i
$$22$$ −2.50000 + 4.33013i −0.533002 + 0.923186i
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −2.00000 + 3.46410i −0.392232 + 0.679366i
$$27$$ 1.00000 0.192450
$$28$$ 0.500000 + 0.866025i 0.0944911 + 0.163663i
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 1.00000 0.182574
$$31$$ 3.50000 4.33013i 0.628619 0.777714i
$$32$$ 1.00000 0.176777
$$33$$ 5.00000 0.870388
$$34$$ 1.00000 + 1.73205i 0.171499 + 0.297044i
$$35$$ −1.00000 −0.169031
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i $$-0.0600231\pi$$
−0.653476 + 0.756948i $$0.726690\pi$$
$$38$$ 1.00000 + 1.73205i 0.162221 + 0.280976i
$$39$$ 4.00000 0.640513
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ −2.00000 + 3.46410i −0.312348 + 0.541002i −0.978870 0.204483i $$-0.934449\pi$$
0.666523 + 0.745485i $$0.267782\pi$$
$$42$$ 0.500000 0.866025i 0.0771517 0.133631i
$$43$$ 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i $$-0.0680112\pi$$
−0.672264 + 0.740312i $$0.734678\pi$$
$$44$$ −2.50000 + 4.33013i −0.376889 + 0.652791i
$$45$$ −0.500000 0.866025i −0.0745356 0.129099i
$$46$$ −4.00000 −0.589768
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ 3.00000 5.19615i 0.428571 0.742307i
$$50$$ −0.500000 0.866025i −0.0707107 0.122474i
$$51$$ 1.00000 1.73205i 0.140028 0.242536i
$$52$$ −2.00000 + 3.46410i −0.277350 + 0.480384i
$$53$$ −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i $$-0.899391\pi$$
0.744423 + 0.667708i $$0.232725\pi$$
$$54$$ 1.00000 0.136083
$$55$$ −2.50000 4.33013i −0.337100 0.583874i
$$56$$ 0.500000 + 0.866025i 0.0668153 + 0.115728i
$$57$$ 1.00000 1.73205i 0.132453 0.229416i
$$58$$ 3.00000 0.393919
$$59$$ −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i $$-0.229229\pi$$
−0.946993 + 0.321253i $$0.895896\pi$$
$$60$$ 1.00000 0.129099
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 3.50000 4.33013i 0.444500 0.549927i
$$63$$ −1.00000 −0.125988
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 3.46410i −0.248069 0.429669i
$$66$$ 5.00000 0.615457
$$67$$ 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i $$-0.754762\pi$$
0.961946 + 0.273241i $$0.0880957\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 2.00000 + 3.46410i 0.240772 + 0.417029i
$$70$$ −1.00000 −0.119523
$$71$$ −4.00000 + 6.92820i −0.474713 + 0.822226i −0.999581 0.0289572i $$-0.990781\pi$$
0.524868 + 0.851184i $$0.324115\pi$$
$$72$$ −0.500000 + 0.866025i −0.0589256 + 0.102062i
$$73$$ −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i $$-0.870674\pi$$
0.801553 + 0.597924i $$0.204008\pi$$
$$74$$ 2.00000 + 3.46410i 0.232495 + 0.402694i
$$75$$ −0.500000 + 0.866025i −0.0577350 + 0.100000i
$$76$$ 1.00000 + 1.73205i 0.114708 + 0.198680i
$$77$$ −5.00000 −0.569803
$$78$$ 4.00000 0.452911
$$79$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −2.00000 + 3.46410i −0.220863 + 0.382546i
$$83$$ −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i $$-0.997777\pi$$
0.506036 + 0.862512i $$0.331110\pi$$
$$84$$ 0.500000 0.866025i 0.0545545 0.0944911i
$$85$$ −2.00000 −0.216930
$$86$$ 2.00000 + 3.46410i 0.215666 + 0.373544i
$$87$$ −1.50000 2.59808i −0.160817 0.278543i
$$88$$ −2.50000 + 4.33013i −0.266501 + 0.461593i
$$89$$ 18.0000 1.90800 0.953998 0.299813i $$-0.0969242\pi$$
0.953998 + 0.299813i $$0.0969242\pi$$
$$90$$ −0.500000 0.866025i −0.0527046 0.0912871i
$$91$$ −4.00000 −0.419314
$$92$$ −4.00000 −0.417029
$$93$$ −5.50000 0.866025i −0.570323 0.0898027i
$$94$$ 2.00000 0.206284
$$95$$ −2.00000 −0.205196
$$96$$ −0.500000 0.866025i −0.0510310 0.0883883i
$$97$$ −1.00000 −0.101535 −0.0507673 0.998711i $$-0.516167\pi$$
−0.0507673 + 0.998711i $$0.516167\pi$$
$$98$$ 3.00000 5.19615i 0.303046 0.524891i
$$99$$ −2.50000 4.33013i −0.251259 0.435194i
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ −5.00000 −0.497519 −0.248759 0.968565i $$-0.580023\pi$$
−0.248759 + 0.968565i $$0.580023\pi$$
$$102$$ 1.00000 1.73205i 0.0990148 0.171499i
$$103$$ 2.50000 4.33013i 0.246332 0.426660i −0.716173 0.697923i $$-0.754108\pi$$
0.962505 + 0.271263i $$0.0874412\pi$$
$$104$$ −2.00000 + 3.46410i −0.196116 + 0.339683i
$$105$$ 0.500000 + 0.866025i 0.0487950 + 0.0845154i
$$106$$ −1.50000 + 2.59808i −0.145693 + 0.252347i
$$107$$ −8.50000 14.7224i −0.821726 1.42327i −0.904396 0.426694i $$-0.859678\pi$$
0.0826699 0.996577i $$-0.473655\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ −2.50000 4.33013i −0.238366 0.412861i
$$111$$ 2.00000 3.46410i 0.189832 0.328798i
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ 2.00000 3.46410i 0.188144 0.325875i −0.756487 0.654008i $$-0.773086\pi$$
0.944632 + 0.328133i $$0.106419\pi$$
$$114$$ 1.00000 1.73205i 0.0936586 0.162221i
$$115$$ 2.00000 3.46410i 0.186501 0.323029i
$$116$$ 3.00000 0.278543
$$117$$ −2.00000 3.46410i −0.184900 0.320256i
$$118$$ −1.50000 2.59808i −0.138086 0.239172i
$$119$$ −1.00000 + 1.73205i −0.0916698 + 0.158777i
$$120$$ 1.00000 0.0912871
$$121$$ −7.00000 12.1244i −0.636364 1.10221i
$$122$$ 0 0
$$123$$ 4.00000 0.360668
$$124$$ 3.50000 4.33013i 0.314309 0.388857i
$$125$$ 1.00000 0.0894427
$$126$$ −1.00000 −0.0890871
$$127$$ −8.50000 14.7224i −0.754253 1.30640i −0.945745 0.324910i $$-0.894666\pi$$
0.191492 0.981494i $$-0.438667\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 2.00000 3.46410i 0.176090 0.304997i
$$130$$ −2.00000 3.46410i −0.175412 0.303822i
$$131$$ −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i $$-0.222575\pi$$
−0.940072 + 0.340977i $$0.889242\pi$$
$$132$$ 5.00000 0.435194
$$133$$ −1.00000 + 1.73205i −0.0867110 + 0.150188i
$$134$$ 2.00000 3.46410i 0.172774 0.299253i
$$135$$ −0.500000 + 0.866025i −0.0430331 + 0.0745356i
$$136$$ 1.00000 + 1.73205i 0.0857493 + 0.148522i
$$137$$ −7.00000 + 12.1244i −0.598050 + 1.03585i 0.395058 + 0.918656i $$0.370724\pi$$
−0.993109 + 0.117198i $$0.962609\pi$$
$$138$$ 2.00000 + 3.46410i 0.170251 + 0.294884i
$$139$$ 10.0000 0.848189 0.424094 0.905618i $$-0.360592\pi$$
0.424094 + 0.905618i $$0.360592\pi$$
$$140$$ −1.00000 −0.0845154
$$141$$ −1.00000 1.73205i −0.0842152 0.145865i
$$142$$ −4.00000 + 6.92820i −0.335673 + 0.581402i
$$143$$ −10.0000 17.3205i −0.836242 1.44841i
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ −1.50000 + 2.59808i −0.124568 + 0.215758i
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ −6.00000 −0.494872
$$148$$ 2.00000 + 3.46410i 0.164399 + 0.284747i
$$149$$ 5.50000 + 9.52628i 0.450578 + 0.780423i 0.998422 0.0561570i $$-0.0178847\pi$$
−0.547844 + 0.836580i $$0.684551\pi$$
$$150$$ −0.500000 + 0.866025i −0.0408248 + 0.0707107i
$$151$$ −5.00000 −0.406894 −0.203447 0.979086i $$-0.565214\pi$$
−0.203447 + 0.979086i $$0.565214\pi$$
$$152$$ 1.00000 + 1.73205i 0.0811107 + 0.140488i
$$153$$ −2.00000 −0.161690
$$154$$ −5.00000 −0.402911
$$155$$ 2.00000 + 5.19615i 0.160644 + 0.417365i
$$156$$ 4.00000 0.320256
$$157$$ 8.00000 0.638470 0.319235 0.947676i $$-0.396574\pi$$
0.319235 + 0.947676i $$0.396574\pi$$
$$158$$ 0 0
$$159$$ 3.00000 0.237915
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ −2.00000 3.46410i −0.157622 0.273009i
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −8.00000 −0.626608 −0.313304 0.949653i $$-0.601436\pi$$
−0.313304 + 0.949653i $$0.601436\pi$$
$$164$$ −2.00000 + 3.46410i −0.156174 + 0.270501i
$$165$$ −2.50000 + 4.33013i −0.194625 + 0.337100i
$$166$$ −4.50000 + 7.79423i −0.349268 + 0.604949i
$$167$$ −8.00000 13.8564i −0.619059 1.07224i −0.989658 0.143448i $$-0.954181\pi$$
0.370599 0.928793i $$-0.379152\pi$$
$$168$$ 0.500000 0.866025i 0.0385758 0.0668153i
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ −2.00000 −0.153393
$$171$$ −2.00000 −0.152944
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i $$-0.796953\pi$$
0.917397 + 0.397974i $$0.130287\pi$$
$$174$$ −1.50000 2.59808i −0.113715 0.196960i
$$175$$ 0.500000 0.866025i 0.0377964 0.0654654i
$$176$$ −2.50000 + 4.33013i −0.188445 + 0.326396i
$$177$$ −1.50000 + 2.59808i −0.112747 + 0.195283i
$$178$$ 18.0000 1.34916
$$179$$ 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i $$-0.0574756\pi$$
−0.647397 + 0.762153i $$0.724142\pi$$
$$180$$ −0.500000 0.866025i −0.0372678 0.0645497i
$$181$$ 11.0000 19.0526i 0.817624 1.41617i −0.0898051 0.995959i $$-0.528624\pi$$
0.907429 0.420206i $$-0.138042\pi$$
$$182$$ −4.00000 −0.296500
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ −4.00000 −0.294086
$$186$$ −5.50000 0.866025i −0.403280 0.0635001i
$$187$$ −10.0000 −0.731272
$$188$$ 2.00000 0.145865
$$189$$ 0.500000 + 0.866025i 0.0363696 + 0.0629941i
$$190$$ −2.00000 −0.145095
$$191$$ 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i $$-0.739868\pi$$
0.973674 + 0.227946i $$0.0732010\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −0.500000 0.866025i −0.0359908 0.0623379i 0.847469 0.530845i $$-0.178125\pi$$
−0.883460 + 0.468507i $$0.844792\pi$$
$$194$$ −1.00000 −0.0717958
$$195$$ −2.00000 + 3.46410i −0.143223 + 0.248069i
$$196$$ 3.00000 5.19615i 0.214286 0.371154i
$$197$$ −13.0000 + 22.5167i −0.926212 + 1.60425i −0.136611 + 0.990625i $$0.543621\pi$$
−0.789601 + 0.613621i $$0.789712\pi$$
$$198$$ −2.50000 4.33013i −0.177667 0.307729i
$$199$$ 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i $$-0.776623\pi$$
0.940927 + 0.338608i $$0.109956\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ −4.00000 −0.282138
$$202$$ −5.00000 −0.351799
$$203$$ 1.50000 + 2.59808i 0.105279 + 0.182349i
$$204$$ 1.00000 1.73205i 0.0700140 0.121268i
$$205$$ −2.00000 3.46410i −0.139686 0.241943i
$$206$$ 2.50000 4.33013i 0.174183 0.301694i
$$207$$ 2.00000 3.46410i 0.139010 0.240772i
$$208$$ −2.00000 + 3.46410i −0.138675 + 0.240192i
$$209$$ −10.0000 −0.691714
$$210$$ 0.500000 + 0.866025i 0.0345033 + 0.0597614i
$$211$$ −11.0000 19.0526i −0.757271 1.31163i −0.944237 0.329266i $$-0.893199\pi$$
0.186966 0.982366i $$-0.440135\pi$$
$$212$$ −1.50000 + 2.59808i −0.103020 + 0.178437i
$$213$$ 8.00000 0.548151
$$214$$ −8.50000 14.7224i −0.581048 1.00640i
$$215$$ −4.00000 −0.272798
$$216$$ 1.00000 0.0680414
$$217$$ 5.50000 + 0.866025i 0.373364 + 0.0587896i
$$218$$ 14.0000 0.948200
$$219$$ 2.00000 0.135147
$$220$$ −2.50000 4.33013i −0.168550 0.291937i
$$221$$ −8.00000 −0.538138
$$222$$ 2.00000 3.46410i 0.134231 0.232495i
$$223$$ −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i $$-0.198694\pi$$
−0.911869 + 0.410481i $$0.865361\pi$$
$$224$$ 0.500000 + 0.866025i 0.0334077 + 0.0578638i
$$225$$ 1.00000 0.0666667
$$226$$ 2.00000 3.46410i 0.133038 0.230429i
$$227$$ −2.50000 + 4.33013i −0.165931 + 0.287401i −0.936985 0.349368i $$-0.886396\pi$$
0.771055 + 0.636769i $$0.219730\pi$$
$$228$$ 1.00000 1.73205i 0.0662266 0.114708i
$$229$$ 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i $$0.209391\pi$$
0.133820 + 0.991006i $$0.457276\pi$$
$$230$$ 2.00000 3.46410i 0.131876 0.228416i
$$231$$ 2.50000 + 4.33013i 0.164488 + 0.284901i
$$232$$ 3.00000 0.196960
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ −2.00000 3.46410i −0.130744 0.226455i
$$235$$ −1.00000 + 1.73205i −0.0652328 + 0.112987i
$$236$$ −1.50000 2.59808i −0.0976417 0.169120i
$$237$$ 0 0
$$238$$ −1.00000 + 1.73205i −0.0648204 + 0.112272i
$$239$$ 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i $$-0.550470\pi$$
0.934109 0.356988i $$-0.116196\pi$$
$$240$$ 1.00000 0.0645497
$$241$$ −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i $$-0.239053\pi$$
−0.956456 + 0.291877i $$0.905720\pi$$
$$242$$ −7.00000 12.1244i −0.449977 0.779383i
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 3.00000 + 5.19615i 0.191663 + 0.331970i
$$246$$ 4.00000 0.255031
$$247$$ −8.00000 −0.509028
$$248$$ 3.50000 4.33013i 0.222250 0.274963i
$$249$$ 9.00000 0.570352
$$250$$ 1.00000 0.0632456
$$251$$ 14.0000 + 24.2487i 0.883672 + 1.53057i 0.847228 + 0.531229i $$0.178270\pi$$
0.0364441 + 0.999336i $$0.488397\pi$$
$$252$$ −1.00000 −0.0629941
$$253$$ 10.0000 17.3205i 0.628695 1.08893i
$$254$$ −8.50000 14.7224i −0.533337 0.923768i
$$255$$ 1.00000 + 1.73205i 0.0626224 + 0.108465i
$$256$$ 1.00000 0.0625000
$$257$$ −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i $$-0.955440\pi$$
0.615948 + 0.787787i $$0.288773\pi$$
$$258$$ 2.00000 3.46410i 0.124515 0.215666i
$$259$$ −2.00000 + 3.46410i −0.124274 + 0.215249i
$$260$$ −2.00000 3.46410i −0.124035 0.214834i
$$261$$ −1.50000 + 2.59808i −0.0928477 + 0.160817i
$$262$$ −2.00000 3.46410i −0.123560 0.214013i
$$263$$ −14.0000 −0.863277 −0.431638 0.902047i $$-0.642064\pi$$
−0.431638 + 0.902047i $$0.642064\pi$$
$$264$$ 5.00000 0.307729
$$265$$ −1.50000 2.59808i −0.0921443 0.159599i
$$266$$ −1.00000 + 1.73205i −0.0613139 + 0.106199i
$$267$$ −9.00000 15.5885i −0.550791 0.953998i
$$268$$ 2.00000 3.46410i 0.122169 0.211604i
$$269$$ −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i $$-0.931941\pi$$
0.672374 + 0.740212i $$0.265275\pi$$
$$270$$ −0.500000 + 0.866025i −0.0304290 + 0.0527046i
$$271$$ 15.0000 0.911185 0.455593 0.890188i $$-0.349427\pi$$
0.455593 + 0.890188i $$0.349427\pi$$
$$272$$ 1.00000 + 1.73205i 0.0606339 + 0.105021i
$$273$$ 2.00000 + 3.46410i 0.121046 + 0.209657i
$$274$$ −7.00000 + 12.1244i −0.422885 + 0.732459i
$$275$$ 5.00000 0.301511
$$276$$ 2.00000 + 3.46410i 0.120386 + 0.208514i
$$277$$ 18.0000 1.08152 0.540758 0.841178i $$-0.318138\pi$$
0.540758 + 0.841178i $$0.318138\pi$$
$$278$$ 10.0000 0.599760
$$279$$ 2.00000 + 5.19615i 0.119737 + 0.311086i
$$280$$ −1.00000 −0.0597614
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ −1.00000 1.73205i −0.0595491 0.103142i
$$283$$ 12.0000 0.713326 0.356663 0.934233i $$-0.383914\pi$$
0.356663 + 0.934233i $$0.383914\pi$$
$$284$$ −4.00000 + 6.92820i −0.237356 + 0.411113i
$$285$$ 1.00000 + 1.73205i 0.0592349 + 0.102598i
$$286$$ −10.0000 17.3205i −0.591312 1.02418i
$$287$$ −4.00000 −0.236113
$$288$$ −0.500000 + 0.866025i −0.0294628 + 0.0510310i
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ −1.50000 + 2.59808i −0.0880830 + 0.152564i
$$291$$ 0.500000 + 0.866025i 0.0293105 + 0.0507673i
$$292$$ −1.00000 + 1.73205i −0.0585206 + 0.101361i
$$293$$ −9.50000 16.4545i −0.554996 0.961281i −0.997904 0.0647140i $$-0.979386\pi$$
0.442908 0.896567i $$-0.353947\pi$$
$$294$$ −6.00000 −0.349927
$$295$$ 3.00000 0.174667
$$296$$ 2.00000 + 3.46410i 0.116248 + 0.201347i
$$297$$ −2.50000 + 4.33013i −0.145065 + 0.251259i
$$298$$ 5.50000 + 9.52628i 0.318606 + 0.551843i
$$299$$ 8.00000 13.8564i 0.462652 0.801337i
$$300$$ −0.500000 + 0.866025i −0.0288675 + 0.0500000i
$$301$$ −2.00000 + 3.46410i −0.115278 + 0.199667i
$$302$$ −5.00000 −0.287718
$$303$$ 2.50000 + 4.33013i 0.143621 + 0.248759i
$$304$$ 1.00000 + 1.73205i 0.0573539 + 0.0993399i
$$305$$ 0 0
$$306$$ −2.00000 −0.114332
$$307$$ −1.00000 1.73205i −0.0570730 0.0988534i 0.836077 0.548612i $$-0.184843\pi$$
−0.893150 + 0.449758i $$0.851510\pi$$
$$308$$ −5.00000 −0.284901
$$309$$ −5.00000 −0.284440
$$310$$ 2.00000 + 5.19615i 0.113592 + 0.295122i
$$311$$ 20.0000 1.13410 0.567048 0.823685i $$-0.308085\pi$$
0.567048 + 0.823685i $$0.308085\pi$$
$$312$$ 4.00000 0.226455
$$313$$ 17.5000 + 30.3109i 0.989158 + 1.71327i 0.621757 + 0.783210i $$0.286419\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ 8.00000 0.451466
$$315$$ 0.500000 0.866025i 0.0281718 0.0487950i
$$316$$ 0 0
$$317$$ 0.500000 + 0.866025i 0.0280828 + 0.0486408i 0.879725 0.475482i $$-0.157726\pi$$
−0.851642 + 0.524123i $$0.824393\pi$$
$$318$$ 3.00000 0.168232
$$319$$ −7.50000 + 12.9904i −0.419919 + 0.727322i
$$320$$ −0.500000 + 0.866025i −0.0279508 + 0.0484123i
$$321$$ −8.50000 + 14.7224i −0.474424 + 0.821726i
$$322$$ −2.00000 3.46410i −0.111456 0.193047i
$$323$$ −2.00000 + 3.46410i −0.111283 + 0.192748i
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 4.00000 0.221880
$$326$$ −8.00000 −0.443079
$$327$$ −7.00000 12.1244i −0.387101 0.670478i
$$328$$ −2.00000 + 3.46410i −0.110432 + 0.191273i
$$329$$ 1.00000 + 1.73205i 0.0551318 + 0.0954911i
$$330$$ −2.50000 + 4.33013i −0.137620 + 0.238366i
$$331$$ −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i $$-0.868396\pi$$
0.805812 + 0.592172i $$0.201729\pi$$
$$332$$ −4.50000 + 7.79423i −0.246970 + 0.427764i
$$333$$ −4.00000 −0.219199
$$334$$ −8.00000 13.8564i −0.437741 0.758189i
$$335$$ 2.00000 + 3.46410i 0.109272 + 0.189264i
$$336$$ 0.500000 0.866025i 0.0272772 0.0472456i
$$337$$ −3.00000 −0.163420 −0.0817102 0.996656i $$-0.526038\pi$$
−0.0817102 + 0.996656i $$0.526038\pi$$
$$338$$ −1.50000 2.59808i −0.0815892 0.141317i
$$339$$ −4.00000 −0.217250
$$340$$ −2.00000 −0.108465
$$341$$ 10.0000 + 25.9808i 0.541530 + 1.40694i
$$342$$ −2.00000 −0.108148
$$343$$ 13.0000 0.701934
$$344$$ 2.00000 + 3.46410i 0.107833 + 0.186772i
$$345$$ −4.00000 −0.215353
$$346$$ 1.50000 2.59808i 0.0806405 0.139673i
$$347$$ 0.500000 + 0.866025i 0.0268414 + 0.0464907i 0.879134 0.476575i $$-0.158122\pi$$
−0.852293 + 0.523065i $$0.824788\pi$$
$$348$$ −1.50000 2.59808i −0.0804084 0.139272i
$$349$$ 34.0000 1.81998 0.909989 0.414632i $$-0.136090\pi$$
0.909989 + 0.414632i $$0.136090\pi$$
$$350$$ 0.500000 0.866025i 0.0267261 0.0462910i
$$351$$ −2.00000 + 3.46410i −0.106752 + 0.184900i
$$352$$ −2.50000 + 4.33013i −0.133250 + 0.230797i
$$353$$ 7.00000 + 12.1244i 0.372572 + 0.645314i 0.989960 0.141344i $$-0.0451425\pi$$
−0.617388 + 0.786659i $$0.711809\pi$$
$$354$$ −1.50000 + 2.59808i −0.0797241 + 0.138086i
$$355$$ −4.00000 6.92820i −0.212298 0.367711i
$$356$$ 18.0000 0.953998
$$357$$ 2.00000 0.105851
$$358$$ 4.50000 + 7.79423i 0.237832 + 0.411938i
$$359$$ −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i $$0.343642\pi$$
−0.999476 + 0.0323801i $$0.989691\pi$$
$$360$$ −0.500000 0.866025i −0.0263523 0.0456435i
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ 11.0000 19.0526i 0.578147 1.00138i
$$363$$ −7.00000 + 12.1244i −0.367405 + 0.636364i
$$364$$ −4.00000 −0.209657
$$365$$ −1.00000 1.73205i −0.0523424 0.0906597i
$$366$$ 0 0
$$367$$ 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i $$-0.617863\pi$$
0.988269 0.152721i $$-0.0488036\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ −2.00000 3.46410i −0.104116 0.180334i
$$370$$ −4.00000 −0.207950
$$371$$ −3.00000 −0.155752
$$372$$ −5.50000 0.866025i −0.285162 0.0449013i
$$373$$ 2.00000 0.103556 0.0517780 0.998659i $$-0.483511\pi$$
0.0517780 + 0.998659i $$0.483511\pi$$
$$374$$ −10.0000 −0.517088
$$375$$ −0.500000 0.866025i −0.0258199 0.0447214i
$$376$$ 2.00000 0.103142
$$377$$ −6.00000 + 10.3923i −0.309016 + 0.535231i
$$378$$ 0.500000 + 0.866025i 0.0257172 + 0.0445435i
$$379$$ −1.00000 1.73205i −0.0513665 0.0889695i 0.839199 0.543825i $$-0.183024\pi$$
−0.890565 + 0.454855i $$0.849691\pi$$
$$380$$ −2.00000 −0.102598
$$381$$ −8.50000 + 14.7224i −0.435468 + 0.754253i
$$382$$ 4.00000 6.92820i 0.204658 0.354478i
$$383$$ 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i $$-0.579593\pi$$
0.962818 0.270151i $$-0.0870736\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 2.50000 4.33013i 0.127412 0.220684i
$$386$$ −0.500000 0.866025i −0.0254493 0.0440795i
$$387$$ −4.00000 −0.203331
$$388$$ −1.00000 −0.0507673
$$389$$ 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i $$-0.0158346\pi$$
−0.542445 + 0.840091i $$0.682501\pi$$
$$390$$ −2.00000 + 3.46410i −0.101274 + 0.175412i
$$391$$ −4.00000 6.92820i −0.202289 0.350374i
$$392$$ 3.00000 5.19615i 0.151523 0.262445i
$$393$$ −2.00000 + 3.46410i −0.100887 + 0.174741i
$$394$$ −13.0000 + 22.5167i −0.654931 + 1.13437i
$$395$$ 0 0
$$396$$ −2.50000 4.33013i −0.125630 0.217597i
$$397$$ −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i $$-0.182649\pi$$
−0.890028 + 0.455905i $$0.849316\pi$$
$$398$$ 2.50000 4.33013i 0.125314 0.217050i
$$399$$ 2.00000 0.100125
$$400$$ −0.500000 0.866025i −0.0250000 0.0433013i
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ −4.00000 −0.199502
$$403$$ 8.00000 + 20.7846i 0.398508 + 1.03536i
$$404$$ −5.00000 −0.248759
$$405$$ 1.00000 0.0496904
$$406$$ 1.50000 + 2.59808i 0.0744438 + 0.128940i
$$407$$ −20.0000 −0.991363
$$408$$ 1.00000 1.73205i 0.0495074 0.0857493i
$$409$$ 8.50000 + 14.7224i 0.420298 + 0.727977i 0.995968 0.0897044i $$-0.0285922\pi$$
−0.575670 + 0.817682i $$0.695259\pi$$
$$410$$ −2.00000 3.46410i −0.0987730 0.171080i
$$411$$ 14.0000 0.690569
$$412$$ 2.50000 4.33013i 0.123166 0.213330i
$$413$$ 1.50000 2.59808i 0.0738102 0.127843i
$$414$$ 2.00000 3.46410i 0.0982946 0.170251i
$$415$$ −4.50000 7.79423i −0.220896 0.382604i
$$416$$ −2.00000 + 3.46410i −0.0980581 + 0.169842i
$$417$$ −5.00000 8.66025i −0.244851 0.424094i
$$418$$ −10.0000 −0.489116
$$419$$ 9.00000 0.439679 0.219839 0.975536i $$-0.429447\pi$$
0.219839 + 0.975536i $$0.429447\pi$$
$$420$$ 0.500000 + 0.866025i 0.0243975 + 0.0422577i
$$421$$ −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i $$-0.995377\pi$$
0.512524 + 0.858673i $$0.328710\pi$$
$$422$$ −11.0000 19.0526i −0.535472 0.927464i
$$423$$ −1.00000 + 1.73205i −0.0486217 + 0.0842152i
$$424$$ −1.50000 + 2.59808i −0.0728464 + 0.126174i
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 8.00000 0.387601
$$427$$ 0 0
$$428$$ −8.50000 14.7224i −0.410863 0.711636i
$$429$$ −10.0000 + 17.3205i −0.482805 + 0.836242i
$$430$$ −4.00000 −0.192897
$$431$$ 11.0000 + 19.0526i 0.529851 + 0.917729i 0.999394 + 0.0348195i $$0.0110856\pi$$
−0.469542 + 0.882910i $$0.655581\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −22.0000 −1.05725 −0.528626 0.848855i $$-0.677293\pi$$
−0.528626 + 0.848855i $$0.677293\pi$$
$$434$$ 5.50000 + 0.866025i 0.264008 + 0.0415705i
$$435$$ 3.00000 0.143839
$$436$$ 14.0000 0.670478
$$437$$ −4.00000 6.92820i −0.191346 0.331421i
$$438$$ 2.00000 0.0955637
$$439$$ 4.50000 7.79423i 0.214773 0.371998i −0.738429 0.674331i $$-0.764432\pi$$
0.953202 + 0.302333i $$0.0977654\pi$$
$$440$$ −2.50000 4.33013i −0.119183 0.206431i
$$441$$ 3.00000 + 5.19615i 0.142857 + 0.247436i
$$442$$ −8.00000 −0.380521
$$443$$ −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i $$-0.863626\pi$$
0.814595 + 0.580030i $$0.196959\pi$$
$$444$$ 2.00000 3.46410i 0.0949158 0.164399i
$$445$$ −9.00000 + 15.5885i −0.426641 + 0.738964i
$$446$$ −1.50000 2.59808i −0.0710271 0.123022i
$$447$$ 5.50000 9.52628i 0.260141 0.450578i
$$448$$ 0.500000 + 0.866025i 0.0236228 + 0.0409159i
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ −10.0000 17.3205i −0.470882 0.815591i
$$452$$ 2.00000 3.46410i 0.0940721 0.162938i
$$453$$ 2.50000 + 4.33013i 0.117460 + 0.203447i
$$454$$ −2.50000 + 4.33013i −0.117331 + 0.203223i
$$455$$ 2.00000 3.46410i 0.0937614 0.162400i
$$456$$ 1.00000 1.73205i 0.0468293 0.0811107i
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ 14.0000 + 24.2487i 0.654177 + 1.13307i
$$459$$ 1.00000 + 1.73205i 0.0466760 + 0.0808452i
$$460$$ 2.00000 3.46410i 0.0932505 0.161515i
$$461$$ 21.0000 0.978068 0.489034 0.872265i $$-0.337349\pi$$
0.489034 + 0.872265i $$0.337349\pi$$
$$462$$ 2.50000 + 4.33013i 0.116311 + 0.201456i
$$463$$ 5.00000 0.232370 0.116185 0.993228i $$-0.462933\pi$$
0.116185 + 0.993228i $$0.462933\pi$$
$$464$$ 3.00000 0.139272
$$465$$ 3.50000 4.33013i 0.162309 0.200805i
$$466$$ 4.00000 0.185296
$$467$$ 33.0000 1.52706 0.763529 0.645774i $$-0.223465\pi$$
0.763529 + 0.645774i $$0.223465\pi$$
$$468$$ −2.00000 3.46410i −0.0924500 0.160128i
$$469$$ 4.00000 0.184703
$$470$$ −1.00000 + 1.73205i −0.0461266 + 0.0798935i
$$471$$ −4.00000 6.92820i −0.184310 0.319235i
$$472$$ −1.50000 2.59808i −0.0690431 0.119586i
$$473$$ −20.0000 −0.919601
$$474$$ 0 0
$$475$$ 1.00000 1.73205i 0.0458831 0.0794719i
$$476$$ −1.00000 + 1.73205i −0.0458349 + 0.0793884i
$$477$$ −1.50000 2.59808i −0.0686803 0.118958i
$$478$$ 12.0000 20.7846i 0.548867 0.950666i
$$479$$ −7.00000 12.1244i −0.319838 0.553976i 0.660616 0.750724i $$-0.270295\pi$$
−0.980454 + 0.196748i $$0.936962\pi$$
$$480$$ 1.00000 0.0456435
$$481$$ −16.0000 −0.729537
$$482$$ −3.50000 6.06218i −0.159421 0.276125i
$$483$$ −2.00000 + 3.46410i −0.0910032 + 0.157622i
$$484$$ −7.00000 12.1244i −0.318182 0.551107i
$$485$$ 0.500000 0.866025i 0.0227038 0.0393242i
$$486$$ −0.500000 + 0.866025i −0.0226805 + 0.0392837i
$$487$$ −21.5000 + 37.2391i −0.974258 + 1.68746i −0.291896 + 0.956450i $$0.594286\pi$$
−0.682362 + 0.731014i $$0.739047\pi$$
$$488$$ 0 0
$$489$$ 4.00000 + 6.92820i 0.180886 + 0.313304i
$$490$$ 3.00000 + 5.19615i 0.135526 + 0.234738i
$$491$$ 7.50000 12.9904i 0.338470 0.586248i −0.645675 0.763612i $$-0.723424\pi$$
0.984145 + 0.177365i $$0.0567572\pi$$
$$492$$ 4.00000 0.180334
$$493$$ 3.00000 + 5.19615i 0.135113 + 0.234023i
$$494$$ −8.00000 −0.359937
$$495$$ 5.00000 0.224733
$$496$$ 3.50000 4.33013i 0.157155 0.194428i
$$497$$ −8.00000 −0.358849
$$498$$ 9.00000 0.403300
$$499$$ 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i $$0.0874801\pi$$
−0.246214 + 0.969216i $$0.579187\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ −8.00000 + 13.8564i −0.357414 + 0.619059i
$$502$$ 14.0000 + 24.2487i 0.624851 + 1.08227i
$$503$$ −18.0000 31.1769i −0.802580 1.39011i −0.917912 0.396783i $$-0.870127\pi$$
0.115332 0.993327i $$-0.463207\pi$$
$$504$$ −1.00000 −0.0445435
$$505$$ 2.50000 4.33013i 0.111249 0.192688i
$$506$$ 10.0000 17.3205i 0.444554 0.769991i
$$507$$ −1.50000 + 2.59808i −0.0666173 + 0.115385i
$$508$$ −8.50000 14.7224i −0.377127 0.653202i
$$509$$ 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i $$-0.769415\pi$$
0.948353 + 0.317217i $$0.102748\pi$$
$$510$$ 1.00000 + 1.73205i 0.0442807 + 0.0766965i
$$511$$ −2.00000 −0.0884748
$$512$$ 1.00000 0.0441942
$$513$$ 1.00000 + 1.73205i 0.0441511 + 0.0764719i
$$514$$ −6.00000 + 10.3923i −0.264649 + 0.458385i
$$515$$ 2.50000 + 4.33013i 0.110163 + 0.190808i
$$516$$ 2.00000 3.46410i 0.0880451 0.152499i
$$517$$ −5.00000 + 8.66025i −0.219900 + 0.380878i
$$518$$ −2.00000 + 3.46410i −0.0878750 + 0.152204i
$$519$$ −3.00000 −0.131685
$$520$$ −2.00000 3.46410i −0.0877058 0.151911i
$$521$$ 14.0000 + 24.2487i 0.613351 + 1.06236i 0.990671 + 0.136272i $$0.0435123\pi$$
−0.377320 + 0.926083i $$0.623154\pi$$
$$522$$ −1.50000 + 2.59808i −0.0656532 + 0.113715i
$$523$$ −24.0000 −1.04945 −0.524723 0.851273i $$-0.675831\pi$$
−0.524723 + 0.851273i $$0.675831\pi$$
$$524$$ −2.00000 3.46410i −0.0873704 0.151330i
$$525$$ −1.00000 −0.0436436
$$526$$ −14.0000 −0.610429
$$527$$ 11.0000 + 1.73205i 0.479168 + 0.0754493i
$$528$$ 5.00000 0.217597
$$529$$ −7.00000 −0.304348
$$530$$ −1.50000 2.59808i −0.0651558 0.112853i
$$531$$ 3.00000 0.130189
$$532$$ −1.00000 + 1.73205i −0.0433555 + 0.0750939i
$$533$$ −8.00000 13.8564i −0.346518 0.600188i
$$534$$ −9.00000 15.5885i −0.389468 0.674579i
$$535$$ 17.0000 0.734974
$$536$$ 2.00000 3.46410i 0.0863868 0.149626i
$$537$$ 4.50000 7.79423i 0.194189 0.336346i
$$538$$ −5.00000 + 8.66025i −0.215565 + 0.373370i
$$539$$ 15.0000 + 25.9808i 0.646096 + 1.11907i
$$540$$ −0.500000 + 0.866025i −0.0215166 + 0.0372678i
$$541$$ −16.0000 27.7128i −0.687894 1.19147i −0.972518 0.232828i $$-0.925202\pi$$
0.284624 0.958639i $$-0.408131\pi$$
$$542$$ 15.0000 0.644305
$$543$$ −22.0000 −0.944110
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ −7.00000 + 12.1244i −0.299847 + 0.519350i
$$546$$ 2.00000 + 3.46410i 0.0855921 + 0.148250i
$$547$$ −21.0000 + 36.3731i −0.897895 + 1.55520i −0.0677151 + 0.997705i $$0.521571\pi$$
−0.830180 + 0.557495i $$0.811762\pi$$
$$548$$ −7.00000 + 12.1244i −0.299025 + 0.517927i
$$549$$ 0 0
$$550$$ 5.00000 0.213201
$$551$$ 3.00000 + 5.19615i 0.127804 + 0.221364i
$$552$$ 2.00000 + 3.46410i 0.0851257 + 0.147442i
$$553$$ 0 0
$$554$$ 18.0000 0.764747
$$555$$ 2.00000 + 3.46410i 0.0848953 + 0.147043i
$$556$$ 10.0000 0.424094
$$557$$ 13.0000 0.550828 0.275414 0.961326i $$-0.411185\pi$$
0.275414 + 0.961326i $$0.411185\pi$$
$$558$$ 2.00000 + 5.19615i 0.0846668 + 0.219971i
$$559$$ −16.0000 −0.676728
$$560$$ −1.00000 −0.0422577
$$561$$ 5.00000 + 8.66025i 0.211100 + 0.365636i
$$562$$ −10.0000 −0.421825
$$563$$ 8.50000 14.7224i 0.358232 0.620477i −0.629433 0.777055i $$-0.716713\pi$$
0.987666 + 0.156578i $$0.0500463\pi$$
$$564$$ −1.00000 1.73205i −0.0421076 0.0729325i
$$565$$ 2.00000 + 3.46410i 0.0841406 + 0.145736i
$$566$$ 12.0000 0.504398
$$567$$ 0.500000 0.866025i 0.0209980 0.0363696i
$$568$$ −4.00000 + 6.92820i −0.167836 + 0.290701i
$$569$$ 12.0000 20.7846i 0.503066 0.871336i −0.496928 0.867792i $$-0.665539\pi$$
0.999994 0.00354413i $$-0.00112814\pi$$
$$570$$ 1.00000 + 1.73205i 0.0418854 + 0.0725476i
$$571$$ 15.0000 25.9808i 0.627730 1.08726i −0.360276 0.932846i $$-0.617317\pi$$
0.988006 0.154415i $$-0.0493493\pi$$
$$572$$ −10.0000 17.3205i −0.418121 0.724207i
$$573$$ −8.00000 −0.334205
$$574$$ −4.00000 −0.166957
$$575$$ 2.00000 + 3.46410i 0.0834058 + 0.144463i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 9.00000 + 15.5885i 0.374675 + 0.648956i 0.990278 0.139100i $$-0.0444210\pi$$
−0.615603 + 0.788056i $$0.711088\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ −0.500000 + 0.866025i −0.0207793 + 0.0359908i
$$580$$ −1.50000 + 2.59808i −0.0622841 + 0.107879i
$$581$$ −9.00000 −0.373383
$$582$$ 0.500000 + 0.866025i 0.0207257 + 0.0358979i
$$583$$ −7.50000 12.9904i −0.310618 0.538007i
$$584$$ −1.00000 + 1.73205i −0.0413803 + 0.0716728i
$$585$$ 4.00000 0.165380
$$586$$ −9.50000 16.4545i −0.392441 0.679728i
$$587$$ 27.0000 1.11441 0.557205 0.830375i $$-0.311874\pi$$
0.557205 + 0.830375i $$0.311874\pi$$
$$588$$ −6.00000 −0.247436
$$589$$ 11.0000 + 1.73205i 0.453247 + 0.0713679i
$$590$$ 3.00000 0.123508
$$591$$ 26.0000 1.06950
$$592$$ 2.00000 + 3.46410i 0.0821995 + 0.142374i
$$593$$ 22.0000 0.903432 0.451716 0.892162i $$-0.350812\pi$$
0.451716 + 0.892162i $$0.350812\pi$$
$$594$$ −2.50000 + 4.33013i −0.102576 + 0.177667i
$$595$$ −1.00000 1.73205i −0.0409960 0.0710072i
$$596$$ 5.50000 + 9.52628i 0.225289 + 0.390212i
$$597$$ −5.00000 −0.204636
$$598$$ 8.00000 13.8564i 0.327144 0.566631i
$$599$$ 18.0000 31.1769i 0.735460 1.27385i −0.219061 0.975711i $$-0.570299\pi$$
0.954521 0.298143i $$-0.0963673\pi$$
$$600$$ −0.500000 + 0.866025i −0.0204124 + 0.0353553i
$$601$$ 21.0000 + 36.3731i 0.856608 + 1.48369i 0.875145 + 0.483860i $$0.160766\pi$$
−0.0185374 + 0.999828i $$0.505901\pi$$
$$602$$ −2.00000 + 3.46410i −0.0815139 + 0.141186i
$$603$$ 2.00000 + 3.46410i 0.0814463 + 0.141069i
$$604$$ −5.00000 −0.203447
$$605$$ 14.0000 0.569181
$$606$$ 2.50000 + 4.33013i 0.101556 + 0.175899i
$$607$$ −24.0000 + 41.5692i −0.974130 + 1.68724i −0.291353 + 0.956616i $$0.594105\pi$$
−0.682777 + 0.730627i $$0.739228\pi$$
$$608$$ 1.00000 + 1.73205i 0.0405554 + 0.0702439i
$$609$$ 1.50000 2.59808i 0.0607831 0.105279i
$$610$$ 0 0
$$611$$ −4.00000 + 6.92820i −0.161823 + 0.280285i
$$612$$ −2.00000 −0.0808452
$$613$$ −12.0000 20.7846i −0.484675 0.839482i 0.515170 0.857088i $$-0.327729\pi$$
−0.999845 + 0.0176058i $$0.994396\pi$$
$$614$$ −1.00000 1.73205i −0.0403567 0.0698999i
$$615$$ −2.00000 + 3.46410i −0.0806478 + 0.139686i
$$616$$ −5.00000 −0.201456
$$617$$ −6.00000 10.3923i −0.241551 0.418378i 0.719605 0.694383i $$-0.244323\pi$$
−0.961156 + 0.276005i $$0.910989\pi$$
$$618$$ −5.00000 −0.201129
$$619$$ −34.0000 −1.36658 −0.683288 0.730149i $$-0.739451\pi$$
−0.683288 + 0.730149i $$0.739451\pi$$
$$620$$ 2.00000 + 5.19615i 0.0803219 + 0.208683i
$$621$$ −4.00000 −0.160514
$$622$$ 20.0000 0.801927
$$623$$ 9.00000 + 15.5885i 0.360577 + 0.624538i
$$624$$ 4.00000 0.160128
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 17.5000 + 30.3109i 0.699441 + 1.21147i
$$627$$ 5.00000 + 8.66025i 0.199681 + 0.345857i
$$628$$ 8.00000 0.319235
$$629$$ −4.00000 + 6.92820i −0.159490 + 0.276246i
$$630$$ 0.500000 0.866025i 0.0199205 0.0345033i
$$631$$ −5.50000 + 9.52628i −0.218952 + 0.379235i −0.954488 0.298250i $$-0.903597\pi$$
0.735536 + 0.677485i $$0.236930\pi$$
$$632$$ 0 0
$$633$$ −11.0000 + 19.0526i −0.437211 + 0.757271i
$$634$$ 0.500000 + 0.866025i 0.0198575 + 0.0343943i
$$635$$ 17.0000 0.674624
$$636$$ 3.00000 0.118958
$$637$$ 12.0000 + 20.7846i 0.475457 + 0.823516i
$$638$$ −7.50000 + 12.9904i −0.296928 + 0.514294i
$$639$$ −4.00000 6.92820i −0.158238 0.274075i
$$640$$ −0.500000 + 0.866025i −0.0197642 + 0.0342327i
$$641$$ −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i $$-0.909493\pi$$
0.722862 + 0.690992i $$0.242826\pi$$
$$642$$ −8.50000 + 14.7224i −0.335468 + 0.581048i
$$643$$ −16.0000 −0.630978 −0.315489 0.948929i $$-0.602169\pi$$
−0.315489 + 0.948929i $$0.602169\pi$$
$$644$$ −2.00000 3.46410i −0.0788110 0.136505i
$$645$$ 2.00000 + 3.46410i 0.0787499 + 0.136399i
$$646$$ −2.00000 + 3.46410i −0.0786889 + 0.136293i
$$647$$ 18.0000 0.707653 0.353827 0.935311i $$-0.384880\pi$$
0.353827 + 0.935311i $$0.384880\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 15.0000 0.588802
$$650$$ 4.00000 0.156893
$$651$$ −2.00000 5.19615i −0.0783862 0.203653i
$$652$$ −8.00000 −0.313304
$$653$$ 21.0000 0.821794 0.410897 0.911682i $$-0.365216\pi$$
0.410897 + 0.911682i $$0.365216\pi$$
$$654$$ −7.00000 12.1244i −0.273722 0.474100i
$$655$$ 4.00000 0.156293
$$656$$ −2.00000 + 3.46410i −0.0780869 + 0.135250i
$$657$$ −1.00000 1.73205i −0.0390137 0.0675737i
$$658$$ 1.00000 + 1.73205i 0.0389841 + 0.0675224i
$$659$$ 15.0000 0.584317 0.292159 0.956370i $$-0.405627\pi$$
0.292159 + 0.956370i $$0.405627\pi$$
$$660$$ −2.50000 + 4.33013i −0.0973124 + 0.168550i
$$661$$ 18.0000 31.1769i 0.700119 1.21264i −0.268306 0.963334i $$-0.586464\pi$$
0.968424 0.249308i $$-0.0802030\pi$$
$$662$$ −2.00000 + 3.46410i −0.0777322 + 0.134636i
$$663$$ 4.00000 + 6.92820i 0.155347 + 0.269069i
$$664$$ −4.50000 + 7.79423i −0.174634 + 0.302475i
$$665$$ −1.00000 1.73205i −0.0387783 0.0671660i
$$666$$ −4.00000 −0.154997
$$667$$ −12.0000 −0.464642
$$668$$ −8.00000 13.8564i −0.309529 0.536120i
$$669$$ −1.50000 + 2.59808i −0.0579934 + 0.100447i
$$670$$ 2.00000 + 3.46410i 0.0772667 + 0.133830i
$$671$$ 0 0
$$672$$ 0.500000 0.866025i 0.0192879 0.0334077i
$$673$$ −16.5000 + 28.5788i −0.636028 + 1.10163i 0.350268 + 0.936650i $$0.386091\pi$$
−0.986296 + 0.164984i $$0.947243\pi$$
$$674$$ −3.00000 −0.115556
$$675$$ −0.500000 0.866025i −0.0192450 0.0333333i
$$676$$ −1.50000 2.59808i −0.0576923 0.0999260i
$$677$$ 23.5000 40.7032i 0.903178 1.56435i 0.0798344 0.996808i $$-0.474561\pi$$
0.823344 0.567543i $$-0.192106\pi$$
$$678$$ −4.00000 −0.153619
$$679$$ −0.500000 0.866025i −0.0191882 0.0332350i
$$680$$ −2.00000 −0.0766965
$$681$$ 5.00000 0.191600
$$682$$ 10.0000 + 25.9808i 0.382920 + 0.994855i
$$683$$ −9.00000 −0.344375 −0.172188 0.985064i $$-0.555084\pi$$
−0.172188 + 0.985064i $$0.555084\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ −7.00000 12.1244i −0.267456 0.463248i
$$686$$ 13.0000 0.496342
$$687$$ 14.0000 24.2487i 0.534133 0.925146i
$$688$$ 2.00000 + 3.46410i 0.0762493 + 0.132068i
$$689$$ −6.00000 10.3923i −0.228582 0.395915i
$$690$$ −4.00000 −0.152277
$$691$$ −5.00000 + 8.66025i −0.190209 + 0.329452i −0.945319 0.326146i $$-0.894250\pi$$
0.755110 + 0.655598i $$0.227583\pi$$
$$692$$ 1.50000 2.59808i 0.0570214 0.0987640i
$$693$$ 2.50000 4.33013i 0.0949671 0.164488i
$$694$$ 0.500000 + 0.866025i 0.0189797 + 0.0328739i
$$695$$ −5.00000 + 8.66025i −0.189661 + 0.328502i
$$696$$ −1.50000 2.59808i −0.0568574 0.0984798i
$$697$$ −8.00000 −0.303022
$$698$$ 34.0000 1.28692
$$699$$ −2.00000 3.46410i −0.0756469 0.131024i
$$700$$ 0.500000 0.866025i 0.0188982 0.0327327i
$$701$$ 4.50000 + 7.79423i 0.169963 + 0.294384i 0.938406 0.345533i $$-0.112302\pi$$
−0.768444 + 0.639917i $$0.778969\pi$$
$$702$$ −2.00000 + 3.46410i −0.0754851 + 0.130744i
$$703$$ −4.00000 + 6.92820i −0.150863 + 0.261302i
$$704$$ −2.50000 + 4.33013i −0.0942223 + 0.163198i
$$705$$ 2.00000 0.0753244
$$706$$ 7.00000 + 12.1244i 0.263448 + 0.456306i
$$707$$ −2.50000 4.33013i −0.0940222 0.162851i
$$708$$ −1.50000 + 2.59808i −0.0563735 + 0.0976417i
$$709$$ 12.0000 0.450669 0.225335 0.974281i $$-0.427652\pi$$
0.225335 + 0.974281i $$0.427652\pi$$
$$710$$ −4.00000 6.92820i −0.150117 0.260011i
$$711$$ 0 0
$$712$$ 18.0000 0.674579
$$713$$ −14.0000 + 17.3205i −0.524304 + 0.648658i
$$714$$ 2.00000 0.0748481
$$715$$ 20.0000 0.747958
$$716$$ 4.50000 + 7.79423i 0.168173 + 0.291284i
$$717$$ −24.0000 −0.896296
$$718$$ −10.0000 + 17.3205i −0.373197 + 0.646396i
$$719$$ −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i $$-0.880269\pi$$
0.146920 0.989148i $$-0.453064\pi$$
$$720$$ −0.500000 0.866025i −0.0186339 0.0322749i
$$721$$ 5.00000 0.186210
$$722$$ 7.50000 12.9904i 0.279121 0.483452i
$$723$$ −3.50000 + 6.06218i −0.130166 + 0.225455i
$$724$$ 11.0000 19.0526i 0.408812 0.708083i
$$725$$ −1.50000 2.59808i −0.0557086 0.0964901i
$$726$$ −7.00000 + 12.1244i −0.259794 + 0.449977i
$$727$$ 13.5000 + 23.3827i 0.500687 + 0.867216i 1.00000 0.000793791i $$0.000252672\pi$$
−0.499312 + 0.866422i $$0.666414\pi$$
$$728$$ −4.00000 −0.148250
$$729$$ 1.00000 0.0370370
$$730$$ −1.00000 1.73205i −0.0370117 0.0641061i
$$731$$ −4.00000 + 6.92820i −0.147945 + 0.256249i
$$732$$ 0 0
$$733$$ 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i $$-0.700154\pi$$
0.994471 + 0.105010i $$0.0334875\pi$$
$$734$$ 12.0000 20.7846i 0.442928 0.767174i
$$735$$ 3.00000 5.19615i 0.110657 0.191663i
$$736$$ −4.00000 −0.147442
$$737$$ 10.0000 + 17.3205i 0.368355 + 0.638009i
$$738$$ −2.00000 3.46410i −0.0736210 0.127515i
$$739$$ −21.0000 + 36.3731i −0.772497 + 1.33800i 0.163693 + 0.986511i $$0.447659\pi$$
−0.936190 + 0.351494i $$0.885674\pi$$
$$740$$ −4.00000 −0.147043
$$741$$ 4.00000 + 6.92820i 0.146944 + 0.254514i
$$742$$ −3.00000 −0.110133
$$743$$ −46.0000 −1.68758 −0.843788 0.536676i $$-0.819680\pi$$
−0.843788 + 0.536676i $$0.819680\pi$$
$$744$$ −5.50000 0.866025i −0.201640 0.0317500i
$$745$$ −11.0000 −0.403009
$$746$$ 2.00000 0.0732252
$$747$$ −4.50000 7.79423i −0.164646 0.285176i
$$748$$ −10.0000 −0.365636
$$749$$ 8.50000 14.7224i 0.310583 0.537946i
$$750$$ −0.500000 0.866025i −0.0182574 0.0316228i
$$751$$ −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i $$-0.254907\pi$$
−0.969801 + 0.243898i $$0.921574\pi$$
$$752$$ 2.00000 0.0729325
$$753$$ 14.0000 24.2487i 0.510188 0.883672i
$$754$$ −6.00000 + 10.3923i −0.218507 + 0.378465i
$$755$$ 2.50000 4.33013i 0.0909843 0.157589i
$$756$$ 0.500000 + 0.866025i 0.0181848 + 0.0314970i
$$757$$ 10.0000 17.3205i 0.363456 0.629525i −0.625071 0.780568i $$-0.714930\pi$$
0.988527 + 0.151043i $$0.0482633\pi$$
$$758$$ −1.00000 1.73205i −0.0363216 0.0629109i
$$759$$ −20.0000 −0.725954
$$760$$ −2.00000 −0.0725476
$$761$$ −25.0000 43.3013i −0.906249 1.56967i −0.819231 0.573463i $$-0.805600\pi$$
−0.0870179 0.996207i $$-0.527734\pi$$
$$762$$ −8.50000 + 14.7224i −0.307923 + 0.533337i
$$763$$ 7.00000 + 12.1244i 0.253417 + 0.438931i
$$764$$ 4.00000 6.92820i 0.144715 0.250654i
$$765$$ 1.00000 1.73205i 0.0361551 0.0626224i
$$766$$ 14.0000 24.2487i 0.505841 0.876142i
$$767$$ 12.0000 0.433295
$$768$$ −0.500000 0.866025i −0.0180422 0.0312500i
$$769$$ 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i $$-0.0305530\pi$$
−0.580696 + 0.814120i $$0.697220\pi$$
$$770$$ 2.50000 4.33013i 0.0900937 0.156047i
$$771$$ 12.0000 0.432169
$$772$$ −0.500000 0.866025i −0.0179954 0.0311689i
$$773$$ 18.0000 0.647415 0.323708 0.946157i $$-0.395071\pi$$
0.323708 + 0.946157i $$0.395071\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ −5.50000 0.866025i −0.197566 0.0311086i
$$776$$ −1.00000 −0.0358979