# Properties

 Label 210.2.n.a.109.1 Level $210$ Weight $2$ Character 210.109 Analytic conductor $1.677$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 210.n (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.67685844245$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 109.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 210.109 Dual form 210.2.n.a.79.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} -1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} -1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.23205 + 1.86603i) q^{10} +(2.50000 - 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} -1.00000i q^{13} +(-2.50000 - 0.866025i) q^{14} +(1.00000 - 2.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.50000 + 6.06218i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(0.500000 + 2.59808i) q^{21} +5.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000i q^{27} +(2.59808 - 0.500000i) q^{28} +(0.133975 + 2.23205i) q^{30} +(3.00000 - 5.19615i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 - 2.50000i) q^{33} -2.00000 q^{34} +(4.23205 - 4.13397i) q^{35} +1.00000 q^{36} +(-4.33013 + 2.50000i) q^{37} +(-6.06218 - 3.50000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(2.23205 - 0.133975i) q^{40} -9.00000 q^{41} +(-1.73205 - 2.00000i) q^{42} -10.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(1.86603 - 1.23205i) q^{45} +(1.50000 - 2.59808i) q^{46} +(-11.2583 + 6.50000i) q^{47} -1.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-10.0000 - 5.00000i) q^{55} +(-2.00000 + 1.73205i) q^{56} +7.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(-1.23205 - 1.86603i) q^{60} +(1.00000 + 1.73205i) q^{61} +6.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(-2.23205 + 0.133975i) q^{65} +(-2.50000 + 4.33013i) q^{66} +(-5.19615 - 3.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -3.00000 q^{69} +(-1.59808 + 5.69615i) q^{70} -2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(3.46410 + 2.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-4.59808 - 1.96410i) q^{75} +7.00000 q^{76} +(12.9904 - 2.50000i) q^{77} +1.00000i q^{78} +(-7.00000 - 12.1244i) q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.79423 - 4.50000i) q^{82} +10.0000i q^{83} +(2.50000 + 0.866025i) q^{84} +(2.00000 - 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(5.00000 + 8.66025i) q^{89} +(-1.00000 + 2.00000i) q^{90} +(2.00000 - 1.73205i) q^{91} +3.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(6.50000 - 11.2583i) q^{94} +(13.0622 - 8.62436i) q^{95} +(0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(-2.59808 - 6.50000i) q^{98} +5.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} - 2q^{10} + 10q^{11} - 10q^{14} + 4q^{15} - 2q^{16} + 14q^{19} - 8q^{20} + 2q^{21} - 2q^{24} - 6q^{25} + 2q^{26} + 4q^{30} + 12q^{31} - 8q^{34} + 10q^{35} + 4q^{36} + 2q^{39} + 2q^{40} - 36q^{41} - 10q^{44} + 4q^{45} + 6q^{46} - 4q^{49} + 16q^{50} + 4q^{51} - 2q^{54} - 40q^{55} - 8q^{56} + 8q^{59} + 2q^{60} + 4q^{61} - 4q^{64} - 2q^{65} - 10q^{66} - 12q^{69} + 4q^{70} - 8q^{71} + 10q^{74} - 8q^{75} + 28q^{76} - 28q^{79} - 4q^{80} - 2q^{81} + 10q^{84} + 8q^{85} + 20q^{86} + 20q^{89} - 4q^{90} + 8q^{91} + 26q^{94} + 28q^{95} + 2q^{96} + 20q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$71$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0.866025 + 0.500000i 0.500000 + 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −0.133975 2.23205i −0.0599153 0.998203i
$$6$$ −1.00000 −0.408248
$$7$$ 1.73205 + 2.00000i 0.654654 + 0.755929i
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 1.23205 + 1.86603i 0.389609 + 0.590089i
$$11$$ 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i $$-0.561563\pi$$
0.945979 0.324227i $$-0.105104\pi$$
$$12$$ 0.866025 0.500000i 0.250000 0.144338i
$$13$$ 1.00000i 0.277350i −0.990338 0.138675i $$-0.955716\pi$$
0.990338 0.138675i $$-0.0442844\pi$$
$$14$$ −2.50000 0.866025i −0.668153 0.231455i
$$15$$ 1.00000 2.00000i 0.258199 0.516398i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i $$-0.255354\pi$$
−0.275029 + 0.961436i $$0.588688\pi$$
$$18$$ −0.866025 0.500000i −0.204124 0.117851i
$$19$$ 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i $$0.130073\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ −2.00000 1.00000i −0.447214 0.223607i
$$21$$ 0.500000 + 2.59808i 0.109109 + 0.566947i
$$22$$ 5.00000i 1.06600i
$$23$$ −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i $$-0.767924\pi$$
0.204046 + 0.978961i $$0.434591\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ −4.96410 + 0.598076i −0.992820 + 0.119615i
$$26$$ 0.500000 + 0.866025i 0.0980581 + 0.169842i
$$27$$ 1.00000i 0.192450i
$$28$$ 2.59808 0.500000i 0.490990 0.0944911i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0.133975 + 2.23205i 0.0244603 + 0.407515i
$$31$$ 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i $$-0.652205\pi$$
0.998968 0.0454165i $$-0.0144615\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 4.33013 2.50000i 0.753778 0.435194i
$$34$$ −2.00000 −0.342997
$$35$$ 4.23205 4.13397i 0.715347 0.698769i
$$36$$ 1.00000 0.166667
$$37$$ −4.33013 + 2.50000i −0.711868 + 0.410997i −0.811752 0.584002i $$-0.801486\pi$$
0.0998840 + 0.994999i $$0.468153\pi$$
$$38$$ −6.06218 3.50000i −0.983415 0.567775i
$$39$$ 0.500000 0.866025i 0.0800641 0.138675i
$$40$$ 2.23205 0.133975i 0.352918 0.0211832i
$$41$$ −9.00000 −1.40556 −0.702782 0.711405i $$-0.748059\pi$$
−0.702782 + 0.711405i $$0.748059\pi$$
$$42$$ −1.73205 2.00000i −0.267261 0.308607i
$$43$$ 10.0000i 1.52499i −0.646997 0.762493i $$-0.723975\pi$$
0.646997 0.762493i $$-0.276025\pi$$
$$44$$ −2.50000 4.33013i −0.376889 0.652791i
$$45$$ 1.86603 1.23205i 0.278171 0.183663i
$$46$$ 1.50000 2.59808i 0.221163 0.383065i
$$47$$ −11.2583 + 6.50000i −1.64220 + 0.948122i −0.662145 + 0.749375i $$0.730354\pi$$
−0.980051 + 0.198747i $$0.936313\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −1.00000 + 6.92820i −0.142857 + 0.989743i
$$50$$ 4.00000 3.00000i 0.565685 0.424264i
$$51$$ 1.00000 + 1.73205i 0.140028 + 0.242536i
$$52$$ −0.866025 0.500000i −0.120096 0.0693375i
$$53$$ −0.866025 0.500000i −0.118958 0.0686803i 0.439340 0.898321i $$-0.355212\pi$$
−0.558298 + 0.829640i $$0.688546\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ −10.0000 5.00000i −1.34840 0.674200i
$$56$$ −2.00000 + 1.73205i −0.267261 + 0.231455i
$$57$$ 7.00000i 0.927173i
$$58$$ 0 0
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ −1.23205 1.86603i −0.159057 0.240903i
$$61$$ 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i $$-0.125799\pi$$
−0.794879 + 0.606768i $$0.792466\pi$$
$$62$$ 6.00000i 0.762001i
$$63$$ −0.866025 + 2.50000i −0.109109 + 0.314970i
$$64$$ −1.00000 −0.125000
$$65$$ −2.23205 + 0.133975i −0.276852 + 0.0166175i
$$66$$ −2.50000 + 4.33013i −0.307729 + 0.533002i
$$67$$ −5.19615 3.00000i −0.634811 0.366508i 0.147802 0.989017i $$-0.452780\pi$$
−0.782613 + 0.622509i $$0.786114\pi$$
$$68$$ 1.73205 1.00000i 0.210042 0.121268i
$$69$$ −3.00000 −0.361158
$$70$$ −1.59808 + 5.69615i −0.191007 + 0.680820i
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ −0.866025 + 0.500000i −0.102062 + 0.0589256i
$$73$$ 3.46410 + 2.00000i 0.405442 + 0.234082i 0.688830 0.724923i $$-0.258125\pi$$
−0.283387 + 0.959006i $$0.591458\pi$$
$$74$$ 2.50000 4.33013i 0.290619 0.503367i
$$75$$ −4.59808 1.96410i −0.530940 0.226795i
$$76$$ 7.00000 0.802955
$$77$$ 12.9904 2.50000i 1.48039 0.284901i
$$78$$ 1.00000i 0.113228i
$$79$$ −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i $$-0.878010\pi$$
0.139895 0.990166i $$-0.455323\pi$$
$$80$$ −1.86603 + 1.23205i −0.208628 + 0.137747i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 7.79423 4.50000i 0.860729 0.496942i
$$83$$ 10.0000i 1.09764i 0.835940 + 0.548821i $$0.184923\pi$$
−0.835940 + 0.548821i $$0.815077\pi$$
$$84$$ 2.50000 + 0.866025i 0.272772 + 0.0944911i
$$85$$ 2.00000 4.00000i 0.216930 0.433861i
$$86$$ 5.00000 + 8.66025i 0.539164 + 0.933859i
$$87$$ 0 0
$$88$$ 4.33013 + 2.50000i 0.461593 + 0.266501i
$$89$$ 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i $$0.0111410\pi$$
−0.469389 + 0.882992i $$0.655526\pi$$
$$90$$ −1.00000 + 2.00000i −0.105409 + 0.210819i
$$91$$ 2.00000 1.73205i 0.209657 0.181568i
$$92$$ 3.00000i 0.312772i
$$93$$ 5.19615 3.00000i 0.538816 0.311086i
$$94$$ 6.50000 11.2583i 0.670424 1.16121i
$$95$$ 13.0622 8.62436i 1.34015 0.884840i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 8.00000i 0.812277i 0.913812 + 0.406138i $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ −2.59808 6.50000i −0.262445 0.656599i
$$99$$ 5.00000 0.502519
$$100$$ −1.96410 + 4.59808i −0.196410 + 0.459808i
$$101$$ −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i $$-0.963634\pi$$
0.595466 + 0.803380i $$0.296967\pi$$
$$102$$ −1.73205 1.00000i −0.171499 0.0990148i
$$103$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 5.73205 1.46410i 0.559391 0.142882i
$$106$$ 1.00000 0.0971286
$$107$$ 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i $$-0.469703\pi$$
0.909624 + 0.415432i $$0.136370\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ −9.00000 + 15.5885i −0.862044 + 1.49310i 0.00790932 + 0.999969i $$0.497482\pi$$
−0.869953 + 0.493135i $$0.835851\pi$$
$$110$$ 11.1603 0.669873i 1.06409 0.0638699i
$$111$$ −5.00000 −0.474579
$$112$$ 0.866025 2.50000i 0.0818317 0.236228i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ −3.50000 6.06218i −0.327805 0.567775i
$$115$$ 3.69615 + 5.59808i 0.344668 + 0.522023i
$$116$$ 0 0
$$117$$ 0.866025 0.500000i 0.0800641 0.0462250i
$$118$$ 4.00000i 0.368230i
$$119$$ 1.00000 + 5.19615i 0.0916698 + 0.476331i
$$120$$ 2.00000 + 1.00000i 0.182574 + 0.0912871i
$$121$$ −7.00000 12.1244i −0.636364 1.10221i
$$122$$ −1.73205 1.00000i −0.156813 0.0905357i
$$123$$ −7.79423 4.50000i −0.702782 0.405751i
$$124$$ −3.00000 5.19615i −0.269408 0.466628i
$$125$$ 2.00000 + 11.0000i 0.178885 + 0.983870i
$$126$$ −0.500000 2.59808i −0.0445435 0.231455i
$$127$$ 9.00000i 0.798621i 0.916816 + 0.399310i $$0.130750\pi$$
−0.916816 + 0.399310i $$0.869250\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 5.00000 8.66025i 0.440225 0.762493i
$$130$$ 1.86603 1.23205i 0.163661 0.108058i
$$131$$ 8.50000 + 14.7224i 0.742648 + 1.28630i 0.951285 + 0.308312i $$0.0997640\pi$$
−0.208637 + 0.977993i $$0.566903\pi$$
$$132$$ 5.00000i 0.435194i
$$133$$ −6.06218 + 17.5000i −0.525657 + 1.51744i
$$134$$ 6.00000 0.518321
$$135$$ 2.23205 0.133975i 0.192104 0.0115307i
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ 3.46410 + 2.00000i 0.295958 + 0.170872i 0.640626 0.767853i $$-0.278675\pi$$
−0.344668 + 0.938725i $$0.612008\pi$$
$$138$$ 2.59808 1.50000i 0.221163 0.127688i
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ −1.46410 5.73205i −0.123739 0.484447i
$$141$$ −13.0000 −1.09480
$$142$$ 1.73205 1.00000i 0.145350 0.0839181i
$$143$$ −4.33013 2.50000i −0.362103 0.209061i
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ −4.33013 + 5.50000i −0.357143 + 0.453632i
$$148$$ 5.00000i 0.410997i
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 4.96410 0.598076i 0.405317 0.0488327i
$$151$$ 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i $$-0.480389\pi$$
0.833597 0.552372i $$-0.186277\pi$$
$$152$$ −6.06218 + 3.50000i −0.491708 + 0.283887i
$$153$$ 2.00000i 0.161690i
$$154$$ −10.0000 + 8.66025i −0.805823 + 0.697863i
$$155$$ −12.0000 6.00000i −0.963863 0.481932i
$$156$$ −0.500000 0.866025i −0.0400320 0.0693375i
$$157$$ −11.2583 6.50000i −0.898513 0.518756i −0.0217953 0.999762i $$-0.506938\pi$$
−0.876717 + 0.481006i $$0.840272\pi$$
$$158$$ 12.1244 + 7.00000i 0.964562 + 0.556890i
$$159$$ −0.500000 0.866025i −0.0396526 0.0686803i
$$160$$ 1.00000 2.00000i 0.0790569 0.158114i
$$161$$ −7.50000 2.59808i −0.591083 0.204757i
$$162$$ 1.00000i 0.0785674i
$$163$$ 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i $$-0.510936\pi$$
0.848339 + 0.529454i $$0.177603\pi$$
$$164$$ −4.50000 + 7.79423i −0.351391 + 0.608627i
$$165$$ −6.16025 9.33013i −0.479575 0.726349i
$$166$$ −5.00000 8.66025i −0.388075 0.672166i
$$167$$ 19.0000i 1.47026i −0.677924 0.735132i $$-0.737120\pi$$
0.677924 0.735132i $$-0.262880\pi$$
$$168$$ −2.59808 + 0.500000i −0.200446 + 0.0385758i
$$169$$ 12.0000 0.923077
$$170$$ 0.267949 + 4.46410i 0.0205508 + 0.342381i
$$171$$ −3.50000 + 6.06218i −0.267652 + 0.463586i
$$172$$ −8.66025 5.00000i −0.660338 0.381246i
$$173$$ −6.06218 + 3.50000i −0.460899 + 0.266100i −0.712422 0.701751i $$-0.752402\pi$$
0.251523 + 0.967851i $$0.419068\pi$$
$$174$$ 0 0
$$175$$ −9.79423 8.89230i −0.740374 0.672195i
$$176$$ −5.00000 −0.376889
$$177$$ 3.46410 2.00000i 0.260378 0.150329i
$$178$$ −8.66025 5.00000i −0.649113 0.374766i
$$179$$ −5.50000 + 9.52628i −0.411089 + 0.712028i −0.995009 0.0997838i $$-0.968185\pi$$
0.583920 + 0.811811i $$0.301518\pi$$
$$180$$ −0.133975 2.23205i −0.00998588 0.166367i
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ −0.866025 + 2.50000i −0.0641941 + 0.185312i
$$183$$ 2.00000i 0.147844i
$$184$$ −1.50000 2.59808i −0.110581 0.191533i
$$185$$ 6.16025 + 9.33013i 0.452911 + 0.685965i
$$186$$ −3.00000 + 5.19615i −0.219971 + 0.381000i
$$187$$ 8.66025 5.00000i 0.633300 0.365636i
$$188$$ 13.0000i 0.948122i
$$189$$ −2.00000 + 1.73205i −0.145479 + 0.125988i
$$190$$ −7.00000 + 14.0000i −0.507833 + 1.01567i
$$191$$ 8.00000 + 13.8564i 0.578860 + 1.00261i 0.995610 + 0.0935936i $$0.0298354\pi$$
−0.416751 + 0.909021i $$0.636831\pi$$
$$192$$ −0.866025 0.500000i −0.0625000 0.0360844i
$$193$$ −15.5885 9.00000i −1.12208 0.647834i −0.180150 0.983639i $$-0.557658\pi$$
−0.941932 + 0.335805i $$0.890992\pi$$
$$194$$ −4.00000 6.92820i −0.287183 0.497416i
$$195$$ −2.00000 1.00000i −0.143223 0.0716115i
$$196$$ 5.50000 + 4.33013i 0.392857 + 0.309295i
$$197$$ 27.0000i 1.92367i −0.273629 0.961835i $$-0.588224\pi$$
0.273629 0.961835i $$-0.411776\pi$$
$$198$$ −4.33013 + 2.50000i −0.307729 + 0.177667i
$$199$$ −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i $$-0.998611\pi$$
0.503774 + 0.863836i $$0.331945\pi$$
$$200$$ −0.598076 4.96410i −0.0422904 0.351015i
$$201$$ −3.00000 5.19615i −0.211604 0.366508i
$$202$$ 8.00000i 0.562878i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 1.20577 + 20.0885i 0.0842147 + 1.40304i
$$206$$ 0 0
$$207$$ −2.59808 1.50000i −0.180579 0.104257i
$$208$$ −0.866025 + 0.500000i −0.0600481 + 0.0346688i
$$209$$ 35.0000 2.42100
$$210$$ −4.23205 + 4.13397i −0.292039 + 0.285271i
$$211$$ 19.0000 1.30801 0.654007 0.756489i $$-0.273087\pi$$
0.654007 + 0.756489i $$0.273087\pi$$
$$212$$ −0.866025 + 0.500000i −0.0594789 + 0.0343401i
$$213$$ −1.73205 1.00000i −0.118678 0.0685189i
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ −22.3205 + 1.33975i −1.52225 + 0.0913699i
$$216$$ −1.00000 −0.0680414
$$217$$ 15.5885 3.00000i 1.05821 0.203653i
$$218$$ 18.0000i 1.21911i
$$219$$ 2.00000 + 3.46410i 0.135147 + 0.234082i
$$220$$ −9.33013 + 6.16025i −0.629037 + 0.415324i
$$221$$ 1.00000 1.73205i 0.0672673 0.116510i
$$222$$ 4.33013 2.50000i 0.290619 0.167789i
$$223$$ 16.0000i 1.07144i −0.844396 0.535720i $$-0.820040\pi$$
0.844396 0.535720i $$-0.179960\pi$$
$$224$$ 0.500000 + 2.59808i 0.0334077 + 0.173591i
$$225$$ −3.00000 4.00000i −0.200000 0.266667i
$$226$$ 3.00000 + 5.19615i 0.199557 + 0.345643i
$$227$$ −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i $$-0.487137\pi$$
−0.845120 + 0.534577i $$0.820471\pi$$
$$228$$ 6.06218 + 3.50000i 0.401478 + 0.231793i
$$229$$ −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i $$-0.208859\pi$$
−0.924510 + 0.381157i $$0.875526\pi$$
$$230$$ −6.00000 3.00000i −0.395628 0.197814i
$$231$$ 12.5000 + 4.33013i 0.822440 + 0.284901i
$$232$$ 0 0
$$233$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ −0.500000 + 0.866025i −0.0326860 + 0.0566139i
$$235$$ 16.0167 + 24.2583i 1.04481 + 1.58244i
$$236$$ −2.00000 3.46410i −0.130189 0.225494i
$$237$$ 14.0000i 0.909398i
$$238$$ −3.46410 4.00000i −0.224544 0.259281i
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ −2.23205 + 0.133975i −0.144078 + 0.00864802i
$$241$$ 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ 12.1244 + 7.00000i 0.779383 + 0.449977i
$$243$$ −0.866025 + 0.500000i −0.0555556 + 0.0320750i
$$244$$ 2.00000 0.128037
$$245$$ 15.5981 + 1.30385i 0.996525 + 0.0832998i
$$246$$ 9.00000 0.573819
$$247$$ 6.06218 3.50000i 0.385727 0.222700i
$$248$$ 5.19615 + 3.00000i 0.329956 + 0.190500i
$$249$$ −5.00000 + 8.66025i −0.316862 + 0.548821i
$$250$$ −7.23205 8.52628i −0.457395 0.539249i
$$251$$ −3.00000 −0.189358 −0.0946792 0.995508i $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 1.73205 + 2.00000i 0.109109 + 0.125988i
$$253$$ 15.0000i 0.943042i
$$254$$ −4.50000 7.79423i −0.282355 0.489053i
$$255$$ 3.73205 2.46410i 0.233710 0.154308i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −8.66025 + 5.00000i −0.540212 + 0.311891i −0.745165 0.666880i $$-0.767629\pi$$
0.204953 + 0.978772i $$0.434296\pi$$
$$258$$ 10.0000i 0.622573i
$$259$$ −12.5000 4.33013i −0.776712 0.269061i
$$260$$ −1.00000 + 2.00000i −0.0620174 + 0.124035i
$$261$$ 0 0
$$262$$ −14.7224 8.50000i −0.909555 0.525132i
$$263$$ 20.7846 + 12.0000i 1.28163 + 0.739952i 0.977147 0.212565i $$-0.0681817\pi$$
0.304487 + 0.952517i $$0.401515\pi$$
$$264$$ 2.50000 + 4.33013i 0.153864 + 0.266501i
$$265$$ −1.00000 + 2.00000i −0.0614295 + 0.122859i
$$266$$ −3.50000 18.1865i −0.214599 1.11509i
$$267$$ 10.0000i 0.611990i
$$268$$ −5.19615 + 3.00000i −0.317406 + 0.183254i
$$269$$ 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i $$-0.692975\pi$$
0.996586 + 0.0825561i $$0.0263084\pi$$
$$270$$ −1.86603 + 1.23205i −0.113563 + 0.0749802i
$$271$$ −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i $$-0.244792\pi$$
−0.961563 + 0.274586i $$0.911459\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 2.59808 0.500000i 0.157243 0.0302614i
$$274$$ −4.00000 −0.241649
$$275$$ −9.82051 + 22.9904i −0.592199 + 1.38637i
$$276$$ −1.50000 + 2.59808i −0.0902894 + 0.156386i
$$277$$ −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i $$-0.352470\pi$$
−0.551131 + 0.834419i $$0.685804\pi$$
$$278$$ −6.92820 + 4.00000i −0.415526 + 0.239904i
$$279$$ 6.00000 0.359211
$$280$$ 4.13397 + 4.23205i 0.247052 + 0.252913i
$$281$$ −11.0000 −0.656205 −0.328102 0.944642i $$-0.606409\pi$$
−0.328102 + 0.944642i $$0.606409\pi$$
$$282$$ 11.2583 6.50000i 0.670424 0.387069i
$$283$$ 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i $$-0.0522041\pi$$
0.351895 + 0.936039i $$0.385537\pi$$
$$284$$ −1.00000 + 1.73205i −0.0593391 + 0.102778i
$$285$$ 15.6244 0.937822i 0.925507 0.0555518i
$$286$$ 5.00000 0.295656
$$287$$ −15.5885 18.0000i −0.920158 1.06251i
$$288$$ 1.00000i 0.0589256i
$$289$$ −6.50000 11.2583i −0.382353 0.662255i
$$290$$ 0 0
$$291$$ −4.00000 + 6.92820i −0.234484 + 0.406138i
$$292$$ 3.46410 2.00000i 0.202721 0.117041i
$$293$$ 1.00000i 0.0584206i −0.999573 0.0292103i $$-0.990701\pi$$
0.999573 0.0292103i $$-0.00929925\pi$$
$$294$$ 1.00000 6.92820i 0.0583212 0.404061i
$$295$$ −8.00000 4.00000i −0.465778 0.232889i
$$296$$ −2.50000 4.33013i −0.145310 0.251684i
$$297$$ 4.33013 + 2.50000i 0.251259 + 0.145065i
$$298$$ 5.19615 + 3.00000i 0.301005 + 0.173785i
$$299$$ 1.50000 + 2.59808i 0.0867472 + 0.150251i
$$300$$ −4.00000 + 3.00000i −0.230940 + 0.173205i
$$301$$ 20.0000 17.3205i 1.15278 0.998337i
$$302$$ 22.0000i 1.26596i
$$303$$ −6.92820 + 4.00000i −0.398015 + 0.229794i
$$304$$ 3.50000 6.06218i 0.200739 0.347690i
$$305$$ 3.73205 2.46410i 0.213697 0.141094i
$$306$$ −1.00000 1.73205i −0.0571662 0.0990148i
$$307$$ 2.00000i 0.114146i 0.998370 + 0.0570730i $$0.0181768\pi$$
−0.998370 + 0.0570730i $$0.981823\pi$$
$$308$$ 4.33013 12.5000i 0.246732 0.712254i
$$309$$ 0 0
$$310$$ 13.3923 0.803848i 0.760632 0.0456555i
$$311$$ 13.0000 22.5167i 0.737162 1.27680i −0.216606 0.976259i $$-0.569499\pi$$
0.953768 0.300544i $$-0.0971681\pi$$
$$312$$ 0.866025 + 0.500000i 0.0490290 + 0.0283069i
$$313$$ 8.66025 5.00000i 0.489506 0.282617i −0.234863 0.972028i $$-0.575464\pi$$
0.724370 + 0.689412i $$0.242131\pi$$
$$314$$ 13.0000 0.733632
$$315$$ 5.69615 + 1.59808i 0.320942 + 0.0900414i
$$316$$ −14.0000 −0.787562
$$317$$ 1.73205 1.00000i 0.0972817 0.0561656i −0.450570 0.892741i $$-0.648779\pi$$
0.547852 + 0.836576i $$0.315446\pi$$
$$318$$ 0.866025 + 0.500000i 0.0485643 + 0.0280386i
$$319$$ 0 0
$$320$$ 0.133975 + 2.23205i 0.00748941 + 0.124775i
$$321$$ 12.0000 0.669775
$$322$$ 7.79423 1.50000i 0.434355 0.0835917i
$$323$$ 14.0000i 0.778981i
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ 0.598076 + 4.96410i 0.0331753 + 0.275359i
$$326$$ −6.00000 + 10.3923i −0.332309 + 0.575577i
$$327$$ −15.5885 + 9.00000i −0.862044 + 0.497701i
$$328$$ 9.00000i 0.496942i
$$329$$ −32.5000 11.2583i −1.79178 0.620692i
$$330$$ 10.0000 + 5.00000i 0.550482 + 0.275241i
$$331$$ 7.50000 + 12.9904i 0.412237 + 0.714016i 0.995134 0.0985303i $$-0.0314141\pi$$
−0.582897 + 0.812546i $$0.698081\pi$$
$$332$$ 8.66025 + 5.00000i 0.475293 + 0.274411i
$$333$$ −4.33013 2.50000i −0.237289 0.136999i
$$334$$ 9.50000 + 16.4545i 0.519817 + 0.900349i
$$335$$ −6.00000 + 12.0000i −0.327815 + 0.655630i
$$336$$ 2.00000 1.73205i 0.109109 0.0944911i
$$337$$ 14.0000i 0.762629i −0.924445 0.381314i $$-0.875472\pi$$
0.924445 0.381314i $$-0.124528\pi$$
$$338$$ −10.3923 + 6.00000i −0.565267 + 0.326357i
$$339$$ 3.00000 5.19615i 0.162938 0.282216i
$$340$$ −2.46410 3.73205i −0.133635 0.202399i
$$341$$ −15.0000 25.9808i −0.812296 1.40694i
$$342$$ 7.00000i 0.378517i
$$343$$ −15.5885 + 10.0000i −0.841698 + 0.539949i
$$344$$ 10.0000 0.539164
$$345$$ 0.401924 + 6.69615i 0.0216388 + 0.360509i
$$346$$ 3.50000 6.06218i 0.188161 0.325905i
$$347$$ 13.8564 + 8.00000i 0.743851 + 0.429463i 0.823468 0.567363i $$-0.192036\pi$$
−0.0796169 + 0.996826i $$0.525370\pi$$
$$348$$ 0 0
$$349$$ 24.0000 1.28469 0.642345 0.766415i $$-0.277962\pi$$
0.642345 + 0.766415i $$0.277962\pi$$
$$350$$ 12.9282 + 2.80385i 0.691042 + 0.149872i
$$351$$ 1.00000 0.0533761
$$352$$ 4.33013 2.50000i 0.230797 0.133250i
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ −2.00000 + 3.46410i −0.106299 + 0.184115i
$$355$$ 0.267949 + 4.46410i 0.0142213 + 0.236930i
$$356$$ 10.0000 0.529999
$$357$$ −1.73205 + 5.00000i −0.0916698 + 0.264628i
$$358$$ 11.0000i 0.581368i
$$359$$ −14.0000 24.2487i −0.738892 1.27980i −0.952995 0.302987i $$-0.902016\pi$$
0.214103 0.976811i $$-0.431317\pi$$
$$360$$ 1.23205 + 1.86603i 0.0649348 + 0.0983482i
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ 1.73205 1.00000i 0.0910346 0.0525588i
$$363$$ 14.0000i 0.734809i
$$364$$ −0.500000 2.59808i −0.0262071 0.136176i
$$365$$ 4.00000 8.00000i 0.209370 0.418739i
$$366$$ −1.00000 1.73205i −0.0522708 0.0905357i
$$367$$ 32.0429 + 18.5000i 1.67263 + 0.965692i 0.966159 + 0.257948i $$0.0830464\pi$$
0.706469 + 0.707744i $$0.250287\pi$$
$$368$$ 2.59808 + 1.50000i 0.135434 + 0.0781929i
$$369$$ −4.50000 7.79423i −0.234261 0.405751i
$$370$$ −10.0000 5.00000i −0.519875 0.259938i
$$371$$ −0.500000 2.59808i −0.0259587 0.134885i
$$372$$ 6.00000i 0.311086i
$$373$$ −5.19615 + 3.00000i −0.269047 + 0.155334i −0.628454 0.777847i $$-0.716312\pi$$
0.359408 + 0.933181i $$0.382979\pi$$
$$374$$ −5.00000 + 8.66025i −0.258544 + 0.447811i
$$375$$ −3.76795 + 10.5263i −0.194576 + 0.543575i
$$376$$ −6.50000 11.2583i −0.335212 0.580604i
$$377$$ 0 0
$$378$$ 0.866025 2.50000i 0.0445435 0.128586i
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ −0.937822 15.6244i −0.0481093 0.801513i
$$381$$ −4.50000 + 7.79423i −0.230542 + 0.399310i
$$382$$ −13.8564 8.00000i −0.708955 0.409316i
$$383$$ 7.79423 4.50000i 0.398266 0.229939i −0.287469 0.957790i $$-0.592814\pi$$
0.685736 + 0.727851i $$0.259481\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ −7.32051 28.6603i −0.373088 1.46066i
$$386$$ 18.0000 0.916176
$$387$$ 8.66025 5.00000i 0.440225 0.254164i
$$388$$ 6.92820 + 4.00000i 0.351726 + 0.203069i
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 2.23205 0.133975i 0.113024 0.00678407i
$$391$$ −6.00000 −0.303433
$$392$$ −6.92820 1.00000i −0.349927 0.0505076i
$$393$$ 17.0000i 0.857537i
$$394$$ 13.5000 + 23.3827i 0.680120 + 1.17800i
$$395$$ −26.1244 + 17.2487i −1.31446 + 0.867877i
$$396$$ 2.50000 4.33013i 0.125630 0.217597i
$$397$$ −1.73205 + 1.00000i −0.0869291 + 0.0501886i −0.542834 0.839840i $$-0.682649\pi$$
0.455905 + 0.890028i $$0.349316\pi$$
$$398$$ 14.0000i 0.701757i
$$399$$ −14.0000 + 12.1244i −0.700877 + 0.606977i
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i $$0.0688266\pi$$
−0.302556 + 0.953131i $$0.597840\pi$$
$$402$$ 5.19615 + 3.00000i 0.259161 + 0.149626i
$$403$$ −5.19615 3.00000i −0.258839 0.149441i
$$404$$ 4.00000 + 6.92820i 0.199007 + 0.344691i
$$405$$ 2.00000 + 1.00000i 0.0993808 + 0.0496904i
$$406$$ 0 0
$$407$$ 25.0000i 1.23920i
$$408$$ −1.73205 + 1.00000i −0.0857493 + 0.0495074i
$$409$$ 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i $$-0.753812\pi$$
0.962757 + 0.270367i $$0.0871450\pi$$
$$410$$ −11.0885 16.7942i −0.547620 0.829408i
$$411$$ 2.00000 + 3.46410i 0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ 10.3923 2.00000i 0.511372 0.0984136i
$$414$$ 3.00000 0.147442
$$415$$ 22.3205 1.33975i 1.09567 0.0657655i
$$416$$ 0.500000 0.866025i 0.0245145 0.0424604i
$$417$$ 6.92820 + 4.00000i 0.339276 + 0.195881i
$$418$$ −30.3109 + 17.5000i −1.48255 + 0.855953i
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ 1.59808 5.69615i 0.0779781 0.277944i
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −16.4545 + 9.50000i −0.800992 + 0.462453i
$$423$$ −11.2583 6.50000i −0.547399 0.316041i
$$424$$ 0.500000 0.866025i 0.0242821 0.0420579i
$$425$$ −9.19615 3.92820i −0.446079 0.190546i
$$426$$ 2.00000 0.0969003
$$427$$ −1.73205 + 5.00000i −0.0838198 + 0.241967i
$$428$$ 12.0000i 0.580042i
$$429$$ −2.50000 4.33013i −0.120701 0.209061i
$$430$$ 18.6603 12.3205i 0.899877 0.594148i
$$431$$ −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i $$-0.976060\pi$$
0.563658 + 0.826008i $$0.309393\pi$$
$$432$$ 0.866025 0.500000i 0.0416667 0.0240563i
$$433$$ 4.00000i 0.192228i −0.995370 0.0961139i $$-0.969359\pi$$
0.995370 0.0961139i $$-0.0306413\pi$$
$$434$$ −12.0000 + 10.3923i −0.576018 + 0.498847i
$$435$$ 0 0
$$436$$ 9.00000 + 15.5885i 0.431022 + 0.746552i
$$437$$ −18.1865 10.5000i −0.869980 0.502283i
$$438$$ −3.46410 2.00000i −0.165521 0.0955637i
$$439$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 5.00000 10.0000i 0.238366 0.476731i
$$441$$ −6.50000 + 2.59808i −0.309524 + 0.123718i
$$442$$ 2.00000i 0.0951303i
$$443$$ 5.19615 3.00000i 0.246877 0.142534i −0.371457 0.928450i $$-0.621142\pi$$
0.618333 + 0.785916i $$0.287808\pi$$
$$444$$ −2.50000 + 4.33013i −0.118645 + 0.205499i
$$445$$ 18.6603 12.3205i 0.884581 0.584048i
$$446$$ 8.00000 + 13.8564i 0.378811 + 0.656120i
$$447$$ 6.00000i 0.283790i
$$448$$ −1.73205 2.00000i −0.0818317 0.0944911i
$$449$$ −9.00000 −0.424736 −0.212368 0.977190i $$-0.568118\pi$$
−0.212368 + 0.977190i $$0.568118\pi$$
$$450$$ 4.59808 + 1.96410i 0.216755 + 0.0925886i
$$451$$ −22.5000 + 38.9711i −1.05948 + 1.83508i
$$452$$ −5.19615 3.00000i −0.244406 0.141108i
$$453$$ 19.0526 11.0000i 0.895167 0.516825i
$$454$$ 14.0000 0.657053
$$455$$ −4.13397 4.23205i −0.193804 0.198402i
$$456$$ −7.00000 −0.327805
$$457$$ −32.9090 + 19.0000i −1.53942 + 0.888783i −0.540544 + 0.841316i $$0.681781\pi$$
−0.998873 + 0.0474665i $$0.984885\pi$$
$$458$$ 3.46410 + 2.00000i 0.161867 + 0.0934539i
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ 6.69615 0.401924i 0.312210 0.0187398i
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ −12.9904 + 2.50000i −0.604367 + 0.116311i
$$463$$ 15.0000i 0.697109i 0.937288 + 0.348555i $$0.113327\pi$$
−0.937288 + 0.348555i $$0.886673\pi$$
$$464$$ 0 0
$$465$$ −7.39230 11.1962i −0.342810 0.519209i
$$466$$ 0 0
$$467$$ 1.73205 1.00000i 0.0801498 0.0462745i −0.459390 0.888235i $$-0.651932\pi$$
0.539539 + 0.841960i $$0.318598\pi$$
$$468$$ 1.00000i 0.0462250i
$$469$$ −3.00000 15.5885i −0.138527 0.719808i
$$470$$ −26.0000 13.0000i −1.19929 0.599645i
$$471$$ −6.50000 11.2583i −0.299504 0.518756i
$$472$$ 3.46410 + 2.00000i 0.159448 + 0.0920575i
$$473$$ −43.3013 25.0000i −1.99099 1.14950i
$$474$$ 7.00000 + 12.1244i 0.321521 + 0.556890i
$$475$$ −21.0000 28.0000i −0.963546 1.28473i
$$476$$ 5.00000 + 1.73205i 0.229175 + 0.0793884i
$$477$$ 1.00000i 0.0457869i
$$478$$ 17.3205 10.0000i 0.792222 0.457389i
$$479$$ 4.00000 6.92820i 0.182765 0.316558i −0.760056 0.649857i $$-0.774829\pi$$
0.942821 + 0.333300i $$0.108162\pi$$
$$480$$ 1.86603 1.23205i 0.0851720 0.0562352i
$$481$$ 2.50000 + 4.33013i 0.113990 + 0.197437i
$$482$$ 1.00000i 0.0455488i
$$483$$ −5.19615 6.00000i −0.236433 0.273009i
$$484$$ −14.0000 −0.636364
$$485$$ 17.8564 1.07180i 0.810818 0.0486678i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −20.7846 12.0000i −0.941841 0.543772i −0.0513038 0.998683i $$-0.516338\pi$$
−0.890537 + 0.454911i $$0.849671\pi$$
$$488$$ −1.73205 + 1.00000i −0.0784063 + 0.0452679i
$$489$$ 12.0000 0.542659
$$490$$ −14.1603 + 6.66987i −0.639695 + 0.301314i
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ −7.79423 + 4.50000i −0.351391 + 0.202876i
$$493$$ 0 0
$$494$$ −3.50000 + 6.06218i −0.157472 + 0.272750i
$$495$$ −0.669873 11.1603i −0.0301086 0.501616i
$$496$$ −6.00000 −0.269408
$$497$$ −3.46410 4.00000i −0.155386 0.179425i
$$498$$ 10.0000i 0.448111i
$$499$$ −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i $$-0.951061\pi$$
0.361478 0.932381i $$-0.382272\pi$$
$$500$$ 10.5263 + 3.76795i 0.470750 + 0.168508i
$$501$$ 9.50000 16.4545i 0.424429 0.735132i
$$502$$ 2.59808 1.50000i 0.115958 0.0669483i
$$503$$ 24.0000i 1.07011i −0.844818 0.535054i $$-0.820291\pi$$
0.844818 0.535054i $$-0.179709\pi$$
$$504$$ −2.50000 0.866025i −0.111359 0.0385758i
$$505$$ 16.0000 + 8.00000i 0.711991 + 0.355995i
$$506$$ −7.50000 12.9904i −0.333416 0.577493i
$$507$$ 10.3923 + 6.00000i 0.461538 + 0.266469i
$$508$$ 7.79423 + 4.50000i 0.345813 + 0.199655i
$$509$$ 7.00000 + 12.1244i 0.310270 + 0.537403i 0.978421 0.206623i $$-0.0662474\pi$$
−0.668151 + 0.744026i $$0.732914\pi$$
$$510$$ −2.00000 + 4.00000i −0.0885615 + 0.177123i
$$511$$ 2.00000 + 10.3923i 0.0884748 + 0.459728i
$$512$$ 1.00000i 0.0441942i
$$513$$ −6.06218 + 3.50000i −0.267652 + 0.154529i
$$514$$ 5.00000 8.66025i 0.220541 0.381987i
$$515$$ 0 0
$$516$$ −5.00000 8.66025i −0.220113 0.381246i
$$517$$ 65.0000i 2.85870i
$$518$$ 12.9904 2.50000i 0.570765 0.109844i
$$519$$ −7.00000 −0.307266
$$520$$ −0.133975 2.23205i −0.00587517 0.0978819i
$$521$$ 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i $$-0.726763\pi$$
0.982231 + 0.187678i $$0.0600963\pi$$
$$522$$ 0 0
$$523$$ −10.3923 + 6.00000i −0.454424 + 0.262362i −0.709697 0.704507i $$-0.751168\pi$$
0.255273 + 0.966869i $$0.417835\pi$$
$$524$$ 17.0000 0.742648
$$525$$ −4.03590 12.5981i −0.176141 0.549825i
$$526$$ −24.0000 −1.04645
$$527$$ 10.3923 6.00000i 0.452696 0.261364i
$$528$$ −4.33013 2.50000i −0.188445 0.108799i
$$529$$ −7.00000 + 12.1244i −0.304348 + 0.527146i
$$530$$ −0.133975 2.23205i −0.00581948 0.0969541i
$$531$$ 4.00000 0.173585
$$532$$ 12.1244 + 14.0000i 0.525657 + 0.606977i
$$533$$ 9.00000i 0.389833i
$$534$$ −5.00000 8.66025i −0.216371 0.374766i
$$535$$ −14.7846 22.3923i −0.639194 0.968104i
$$536$$ 3.00000 5.19615i 0.129580 0.224440i
$$537$$ −9.52628 + 5.50000i −0.411089 + 0.237343i
$$538$$ 14.0000i 0.603583i
$$539$$ 27.5000 + 21.6506i 1.18451 + 0.932559i
$$540$$ 1.00000 2.00000i 0.0430331 0.0860663i
$$541$$ −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i $$-0.194071\pi$$
−0.905811 + 0.423681i $$0.860738\pi$$
$$542$$ 6.92820 + 4.00000i 0.297592 + 0.171815i
$$543$$ −1.73205 1.00000i −0.0743294 0.0429141i
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ 36.0000 + 18.0000i 1.54207 + 0.771035i
$$546$$ −2.00000 + 1.73205i −0.0855921 + 0.0741249i
$$547$$ 14.0000i 0.598597i −0.954160 0.299298i $$-0.903247\pi$$
0.954160 0.299298i $$-0.0967526\pi$$
$$548$$ 3.46410 2.00000i 0.147979 0.0854358i
$$549$$ −1.00000 + 1.73205i −0.0426790 + 0.0739221i
$$550$$ −2.99038 24.8205i −0.127510 1.05835i
$$551$$ 0 0
$$552$$ 3.00000i 0.127688i
$$553$$ 12.1244 35.0000i 0.515580 1.48835i
$$554$$ 2.00000 0.0849719
$$555$$ 0.669873 + 11.1603i 0.0284345 + 0.473726i
$$556$$ 4.00000 6.92820i 0.169638 0.293821i
$$557$$ 33.7750 + 19.5000i 1.43109 + 0.826242i 0.997204 0.0747252i $$-0.0238080\pi$$
0.433888 + 0.900967i $$0.357141\pi$$
$$558$$ −5.19615 + 3.00000i −0.219971 + 0.127000i
$$559$$ −10.0000 −0.422955
$$560$$ −5.69615 1.59808i −0.240706 0.0675310i
$$561$$ 10.0000 0.422200
$$562$$ 9.52628 5.50000i 0.401842 0.232003i
$$563$$ 25.9808 + 15.0000i 1.09496 + 0.632175i 0.934892 0.354932i $$-0.115496\pi$$
0.160066 + 0.987106i $$0.448829\pi$$
$$564$$ −6.50000 + 11.2583i −0.273699 + 0.474061i
$$565$$ −13.3923 + 0.803848i −0.563418 + 0.0338181i
$$566$$ −26.0000 −1.09286
$$567$$ −2.59808 + 0.500000i −0.109109 + 0.0209980i
$$568$$ 2.00000i 0.0839181i
$$569$$ −1.50000 2.59808i −0.0628833 0.108917i 0.832870 0.553469i $$-0.186696\pi$$
−0.895753 + 0.444552i $$0.853363\pi$$
$$570$$ −13.0622 + 8.62436i −0.547114 + 0.361235i
$$571$$ 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i $$-0.779798\pi$$
0.937503 + 0.347977i $$0.113131\pi$$
$$572$$ −4.33013 + 2.50000i −0.181052 + 0.104530i
$$573$$ 16.0000i 0.668410i
$$574$$ 22.5000 + 7.79423i 0.939132 + 0.325325i
$$575$$ 12.0000 9.00000i 0.500435 0.375326i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −20.7846 12.0000i −0.865275 0.499567i 0.000500448 1.00000i $$-0.499841\pi$$
−0.865775 + 0.500433i $$0.833174\pi$$
$$578$$ 11.2583 + 6.50000i 0.468285 + 0.270364i
$$579$$ −9.00000 15.5885i −0.374027 0.647834i
$$580$$ 0 0
$$581$$ −20.0000 + 17.3205i −0.829740 + 0.718576i
$$582$$ 8.00000i 0.331611i
$$583$$ −4.33013 + 2.50000i −0.179336 + 0.103539i
$$584$$ −2.00000 + 3.46410i −0.0827606 + 0.143346i
$$585$$ −1.23205 1.86603i −0.0509390 0.0771507i
$$586$$ 0.500000 + 0.866025i 0.0206548 + 0.0357752i
$$587$$ 2.00000i 0.0825488i 0.999148 + 0.0412744i $$0.0131418\pi$$
−0.999148 + 0.0412744i $$0.986858\pi$$
$$588$$ 2.59808 + 6.50000i 0.107143 + 0.268055i
$$589$$ 42.0000 1.73058
$$590$$ 8.92820 0.535898i 0.367568 0.0220626i
$$591$$ 13.5000 23.3827i 0.555316 0.961835i
$$592$$ 4.33013 + 2.50000i 0.177967 + 0.102749i
$$593$$ 29.4449 17.0000i 1.20916 0.698106i 0.246581 0.969122i $$-0.420693\pi$$
0.962575 + 0.271016i $$0.0873596\pi$$
$$594$$ −5.00000 −0.205152
$$595$$ 11.4641 2.92820i 0.469982 0.120045i
$$596$$ −6.00000 −0.245770
$$597$$ −12.1244 + 7.00000i −0.496217 + 0.286491i
$$598$$ −2.59808 1.50000i −0.106243 0.0613396i
$$599$$ −14.0000 + 24.2487i −0.572024 + 0.990775i 0.424333 + 0.905506i $$0.360508\pi$$
−0.996358 + 0.0852695i $$0.972825\pi$$
$$600$$ 1.96410 4.59808i 0.0801841 0.187716i
$$601$$ −30.0000 −1.22373 −0.611863 0.790964i $$-0.709580\pi$$
−0.611863 + 0.790964i $$0.709580\pi$$
$$602$$ −8.66025 + 25.0000i −0.352966 + 1.01892i
$$603$$ 6.00000i 0.244339i
$$604$$ −11.0000 19.0526i −0.447584 0.775238i
$$605$$ −26.1244 + 17.2487i −1.06211 + 0.701260i
$$606$$ 4.00000 6.92820i 0.162489 0.281439i
$$607$$ 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i $$-0.581682\pi$$
0.710766 + 0.703429i $$0.248349\pi$$
$$608$$ 7.00000i 0.283887i
$$609$$ 0 0
$$610$$ −2.00000 + 4.00000i −0.0809776 + 0.161955i
$$611$$ 6.50000 + 11.2583i 0.262962 + 0.455463i
$$612$$ 1.73205 + 1.00000i 0.0700140 + 0.0404226i
$$613$$ 16.4545 + 9.50000i 0.664590 + 0.383701i 0.794024 0.607887i $$-0.207983\pi$$
−0.129433 + 0.991588i $$0.541316\pi$$
$$614$$ −1.00000 1.73205i −0.0403567 0.0698999i
$$615$$ −9.00000 + 18.0000i −0.362915 + 0.725830i
$$616$$ 2.50000 + 12.9904i 0.100728 + 0.523397i
$$617$$ 30.0000i 1.20775i 0.797077 + 0.603877i $$0.206378\pi$$
−0.797077 + 0.603877i $$0.793622\pi$$
$$618$$ 0 0
$$619$$ 7.50000 12.9904i 0.301450 0.522127i −0.675014 0.737805i $$-0.735863\pi$$
0.976465 + 0.215677i $$0.0691959\pi$$
$$620$$ −11.1962 + 7.39230i −0.449648 + 0.296882i
$$621$$ −1.50000 2.59808i −0.0601929 0.104257i
$$622$$ 26.0000i 1.04251i
$$623$$ −8.66025 + 25.0000i −0.346966 + 1.00160i
$$624$$ −1.00000 −0.0400320
$$625$$ 24.2846 5.93782i 0.971384 0.237513i
$$626$$ −5.00000 + 8.66025i −0.199840 + 0.346133i
$$627$$ 30.3109 + 17.5000i 1.21050 + 0.698883i
$$628$$ −11.2583 + 6.50000i −0.449256 + 0.259378i
$$629$$ −10.0000 −0.398726
$$630$$ −5.73205 + 1.46410i −0.228370 + 0.0583312i
$$631$$ 18.0000 0.716569 0.358284 0.933613i $$-0.383362\pi$$
0.358284 + 0.933613i $$0.383362\pi$$
$$632$$ 12.1244 7.00000i 0.482281 0.278445i
$$633$$ 16.4545 + 9.50000i 0.654007 + 0.377591i
$$634$$ −1.00000 + 1.73205i −0.0397151 + 0.0687885i
$$635$$ 20.0885 1.20577i 0.797186 0.0478496i
$$636$$ −1.00000 −0.0396526
$$637$$ 6.92820 + 1.00000i 0.274505 + 0.0396214i
$$638$$ 0 0
$$639$$ −1.00000 1.73205i −0.0395594 0.0685189i
$$640$$ −1.23205 1.86603i −0.0487011 0.0737611i
$$641$$ 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i $$-0.607385\pi$$
0.982708 0.185164i $$-0.0592817\pi$$
$$642$$ −10.3923 + 6.00000i −0.410152 + 0.236801i
$$643$$ 38.0000i 1.49857i −0.662246 0.749287i $$-0.730396\pi$$
0.662246 0.749287i $$-0.269604\pi$$
$$644$$ −6.00000 + 5.19615i −0.236433 + 0.204757i
$$645$$ −20.0000 10.0000i −0.787499 0.393750i
$$646$$ −7.00000 12.1244i −0.275411 0.477026i
$$647$$ 0.866025 + 0.500000i 0.0340470 + 0.0196570i 0.516927 0.856030i $$-0.327076\pi$$
−0.482880 + 0.875687i $$0.660409\pi$$
$$648$$ −0.866025 0.500000i −0.0340207 0.0196419i
$$649$$ −10.0000 17.3205i −0.392534 0.679889i
$$650$$ −3.00000 4.00000i −0.117670 0.156893i
$$651$$ 15.0000 + 5.19615i 0.587896 + 0.203653i
$$652$$ 12.0000i 0.469956i
$$653$$ −4.33013 + 2.50000i −0.169451 + 0.0978326i −0.582327 0.812955i $$-0.697858\pi$$
0.412876 + 0.910787i $$0.364524\pi$$
$$654$$ 9.00000 15.5885i 0.351928 0.609557i
$$655$$ 31.7224 20.9449i 1.23950 0.818384i
$$656$$ 4.50000 + 7.79423i 0.175695 + 0.304314i
$$657$$ 4.00000i 0.156055i
$$658$$ 33.7750 6.50000i 1.31669 0.253396i
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ −11.1603 + 0.669873i −0.434412 + 0.0260748i
$$661$$ −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i $$0.450387\pi$$
−0.933144 + 0.359502i $$0.882947\pi$$
$$662$$ −12.9904 7.50000i −0.504885 0.291496i
$$663$$ 1.73205 1.00000i 0.0672673 0.0388368i
$$664$$ −10.0000 −0.388075
$$665$$ 39.8731 + 11.1865i 1.54621 + 0.433795i
$$666$$ 5.00000 0.193746
$$667$$ 0 0
$$668$$ −16.4545 9.50000i −0.636643 0.367566i
$$669$$ 8.00000 13.8564i 0.309298 0.535720i
$$670$$ −0.803848 13.3923i −0.0310553 0.517390i
$$671$$ 10.0000 0.386046
$$672$$ −0.866025 + 2.50000i −0.0334077 + 0.0964396i
$$673$$ 36.0000i 1.38770i −0.720121 0.693849i $$-0.755914\pi$$
0.720121 0.693849i $$-0.244086\pi$$
$$674$$ 7.00000 + 12.1244i 0.269630 + 0.467013i
$$675$$ −0.598076 4.96410i −0.0230200 0.191068i
$$676$$ 6.00000 10.3923i 0.230769 0.399704i
$$677$$ 28.5788 16.5000i 1.09837 0.634147i 0.162581 0.986695i $$-0.448018\pi$$
0.935793 + 0.352549i $$0.114685\pi$$
$$678$$ 6.00000i 0.230429i
$$679$$ −16.0000 + 13.8564i −0.614024 + 0.531760i
$$680$$ 4.00000 + 2.00000i 0.153393 + 0.0766965i
$$681$$ −7.00000 12.1244i −0.268241 0.464606i
$$682$$ 25.9808 + 15.0000i 0.994855 + 0.574380i
$$683$$ −3.46410 2.00000i −0.132550 0.0765279i 0.432259 0.901750i $$-0.357717\pi$$
−0.564809 + 0.825222i $$0.691050\pi$$
$$684$$ 3.50000 + 6.06218i 0.133826 + 0.231793i
$$685$$ 4.00000 8.00000i 0.152832 0.305664i
$$686$$ 8.50000 16.4545i 0.324532 0.628235i
$$687$$ 4.00000i 0.152610i
$$688$$ −8.66025 + 5.00000i −0.330169 + 0.190623i
$$689$$ −0.500000 + 0.866025i −0.0190485 + 0.0329929i
$$690$$ −3.69615 5.59808i −0.140710 0.213115i
$$691$$ 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i $$-0.0424468\pi$$
−0.610704 + 0.791859i $$0.709113\pi$$
$$692$$ 7.00000i 0.266100i
$$693$$ 8.66025 + 10.0000i 0.328976 + 0.379869i
$$694$$ −16.0000 −0.607352
$$695$$ −1.07180 17.8564i −0.0406556 0.677332i
$$696$$ 0 0
$$697$$ −15.5885 9.00000i −0.590455 0.340899i
$$698$$ −20.7846 + 12.0000i −0.786709 + 0.454207i
$$699$$ 0 0
$$700$$ −12.5981 + 4.03590i −0.476163 + 0.152543i
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ −0.866025 + 0.500000i −0.0326860 + 0.0188713i
$$703$$ −30.3109 17.5000i −1.14320 0.660025i
$$704$$ −2.50000 + 4.33013i −0.0942223 + 0.163198i
$$705$$ 1.74167 + 29.0167i 0.0655951 + 1.09283i
$$706$$ 0 0
$$707$$ −20.7846 + 4.00000i −0.781686 + 0.150435i
$$708$$ 4.00000i 0.150329i
$$709$$ 8.00000 + 13.8564i 0.300446 + 0.520388i 0.976237 0.216705i $$-0.0695310\pi$$
−0.675791 + 0.737093i $$0.736198\pi$$
$$710$$ −2.46410 3.73205i −0.0924761 0.140061i
$$711$$ 7.00000 12.1244i 0.262521 0.454699i
$$712$$ −8.66025 + 5.00000i −0.324557 + 0.187383i
$$713$$ 18.0000i 0.674105i
$$714$$ −1.00000 5.19615i −0.0374241 0.194461i
$$715$$ −5.00000 + 10.0000i −0.186989 + 0.373979i
$$716$$ 5.50000 + 9.52628i 0.205545 + 0.356014i
$$717$$ −17.3205 10.0000i −0.646846 0.373457i
$$718$$ 24.2487 + 14.0000i 0.904954 + 0.522475i
$$719$$ −1.00000 1.73205i −0.0372937 0.0645946i 0.846776 0.531949i $$-0.178540\pi$$
−0.884070 + 0.467355i $$0.845207\pi$$
$$720$$ −2.00000 1.00000i −0.0745356 0.0372678i
$$721$$ 0 0
$$722$$ 30.0000i 1.11648i
$$723$$ 0.866025 0.500000i 0.0322078 0.0185952i
$$724$$ −1.00000 + 1.73205i −0.0371647 + 0.0643712i
$$725$$ 0 0
$$726$$ 7.00000 + 12.1244i 0.259794 + 0.449977i
$$727$$ 53.0000i 1.96566i 0.184510 + 0.982831i $$0.440930\pi$$
−0.184510 + 0.982831i $$0.559070\pi$$
$$728$$ 1.73205 + 2.00000i 0.0641941 + 0.0741249i
$$729$$ −1.00000 −0.0370370
$$730$$ 0.535898 + 8.92820i 0.0198345 + 0.330448i
$$731$$ 10.0000 17.3205i 0.369863 0.640622i
$$732$$ 1.73205 + 1.00000i 0.0640184 + 0.0369611i
$$733$$ 18.1865 10.5000i 0.671735 0.387826i −0.124999 0.992157i $$-0.539893\pi$$
0.796734 + 0.604331i $$0.206559\pi$$
$$734$$ −37.0000 −1.36569
$$735$$ 12.8564 + 8.92820i 0.474216 + 0.329322i
$$736$$ −3.00000 −0.110581
$$737$$ −25.9808 + 15.0000i −0.957014 + 0.552532i
$$738$$ 7.79423 + 4.50000i 0.286910 + 0.165647i
$$739$$ 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i $$-0.500993\pi$$
0.867581 0.497296i $$-0.165674\pi$$
$$740$$ 11.1603 0.669873i 0.410259 0.0246250i
$$741$$ 7.00000 0.257151
$$742$$ 1.73205 + 2.00000i 0.0635856 + 0.0734223i
$$743$$ 31.0000i 1.13728i 0.822587 + 0.568640i $$0.192530\pi$$
−0.822587 + 0.568640i $$0.807470\pi$$
$$744$$ 3.00000 + 5.19615i 0.109985 + 0.190500i
$$745$$ −11.1962 + 7.39230i −0.410195 + 0.270833i
$$746$$ 3.00000 5.19615i 0.109838 0.190245i
$$747$$ −8.66025 + 5.00000i −0.316862 + 0.182940i
$$748$$ 10.0000i 0.365636i
$$749$$ 30.0000 + 10.3923i 1.09618 + 0.379727i
$$750$$ −2.00000 11.0000i −0.0730297 0.401663i
$$751$$ −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i $$-0.189918\pi$$
−0.900207 + 0.435463i $$0.856585\pi$$
$$752$$ 11.2583 + 6.50000i 0.410549 + 0.237031i
$$753$$ −2.59808 1.50000i −0.0946792 0.0546630i
$$754$$ 0 0
$$755$$ −44.0000 22.0000i −1.60132 0.800662i
$$756$$ 0.500000 + 2.59808i 0.0181848 + 0.0944911i
$$757$$ 26.0000i 0.944986i −0.881334 0.472493i $$-0.843354\pi$$
0.881334 0.472493i $$-0.156646\pi$$
$$758$$ −0.866025 + 0.500000i −0.0314555 + 0.0181608i
$$759$$ −7.50000 + 12.9904i −0.272233 + 0.471521i
$$760$$ 8.62436 + 13.0622i 0.312838 + 0.473815i
$$761$$ 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i $$-0.149350\pi$$
−0.837557 + 0.546350i $$0.816017\pi$$
$$762$$ 9.00000i 0.326036i
$$763$$ −46.7654 + 9.00000i −1.69302 + 0.325822i
$$764$$ 16.0000 0.578860
$$765$$ 4.46410 0.267949i 0.161400 0.00968772i
$$766$$ −4.50000 + 7.79423i −0.162592 + 0.281617i
$$767$$ −3.46410 2.00000i −0.125081 0.0722158i
$$768$$ −0.866025 + 0.500000i −0.0312500 + 0.0180422i
$$769$$ −51.0000 −1.83911 −0.919554 0.392965i $$-0.871449\pi$$
−0.919554 + 0.392965i $$0.871449\pi$$
$$770$$ 20.6699 + 21.1603i 0.744891 + 0.762563i
$$771$$ −10.0000 −0.360141
$$772$$ −15.5885 + 9.00000i −0.561041 + 0.323917i
$$773$$ −32.0429 18.5000i −1.15250 0.665399i −0.203008 0.979177i $$-0.565072\pi$$
−0.949496 + 0.313778i $$0.898405\pi$$
$$774$$ −5.00000 + 8.66025i −0.179721 + 0.311286i
$$775$$ −11.7846 + 27.5885i −0.423316 +