# Properties

 Label 210.2.n.a.109.2 Level $210$ Weight $2$ Character 210.109 Analytic conductor $1.677$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## 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 109.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 210.109 Dual form 210.2.n.a.79.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -1.00000 q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -1.00000 q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.23205 - 0.133975i) 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} +(1.96410 + 4.59808i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} +(1.86603 + 1.23205i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} -2.00000 q^{34} +(0.767949 + 5.86603i) q^{35} +1.00000 q^{36} +(4.33013 - 2.50000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-1.23205 + 1.86603i) q^{40} -9.00000 q^{41} +(1.73205 + 2.00000i) q^{42} +10.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(0.133975 - 2.23205i) 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} +(2.23205 + 0.133975i) q^{60} +(1.00000 + 1.73205i) q^{61} -6.00000i q^{62} +(0.866025 - 2.50000i) q^{63} -1.00000 q^{64} +(1.23205 - 1.86603i) q^{65} +(-2.50000 + 4.33013i) q^{66} +(5.19615 + 3.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} -3.00000 q^{69} +(3.59808 + 4.69615i) q^{70} -2.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(0.598076 - 4.96410i) q^{75} +7.00000 q^{76} +(-12.9904 + 2.50000i) q^{77} -1.00000i q^{78} +(-7.00000 - 12.1244i) q^{79} +(-0.133975 + 2.23205i) 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} +(0.937822 - 15.6244i) 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
$$5$$ −1.86603 1.23205i −0.834512 0.550990i
$$6$$ −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
$$10$$ −2.23205 0.133975i −0.705836 0.0423665i
$$11$$ 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 $$0.0442844\pi$$
−0.990338 + 0.138675i $$0.955716\pi$$
$$14$$ −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 0.275029 0.961436i $$-0.411312\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 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 −0.204046 0.978961i $$-0.565409\pi$$
0.745782 + 0.666190i $$0.232076\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 1.96410 + 4.59808i 0.392820 + 0.919615i
$$26$$ 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 $$0.5\pi$$
$$30$$ 1.86603 + 1.23205i 0.340688 + 0.224941i
$$31$$ 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
$$35$$ 0.767949 + 5.86603i 0.129807 + 0.991539i
$$36$$ 1.00000 0.166667
$$37$$ 4.33013 2.50000i 0.711868 0.410997i −0.0998840 0.994999i $$-0.531847\pi$$
0.811752 + 0.584002i $$0.198514\pi$$
$$38$$ 6.06218 + 3.50000i 0.983415 + 0.567775i
$$39$$ 0.500000 0.866025i 0.0800641 0.138675i
$$40$$ −1.23205 + 1.86603i −0.194804 + 0.295045i
$$41$$ −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 $$0.276025\pi$$
−0.646997 + 0.762493i $$0.723975\pi$$
$$44$$ −2.50000 4.33013i −0.376889 0.652791i
$$45$$ 0.133975 2.23205i 0.0199718 0.332734i
$$46$$ 1.50000 2.59808i 0.221163 0.383065i
$$47$$ 11.2583 6.50000i 1.64220 0.948122i 0.662145 0.749375i $$-0.269646\pi$$
0.980051 0.198747i $$-0.0636872\pi$$
$$48$$ 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 0.558298 0.829640i $$-0.311454\pi$$
−0.439340 + 0.898321i $$0.644788\pi$$
$$54$$ −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 $$0.0828195\pi$$
$$60$$ 2.23205 + 0.133975i 0.288157 + 0.0172960i
$$61$$ 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
$$65$$ 1.23205 1.86603i 0.152817 0.231452i
$$66$$ −2.50000 + 4.33013i −0.307729 + 0.533002i
$$67$$ 5.19615 + 3.00000i 0.634811 + 0.366508i 0.782613 0.622509i $$-0.213886\pi$$
−0.147802 + 0.989017i $$0.547220\pi$$
$$68$$ −1.73205 + 1.00000i −0.210042 + 0.121268i
$$69$$ −3.00000 −0.361158
$$70$$ 3.59808 + 4.69615i 0.430052 + 0.561298i
$$71$$ −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 0.283387 0.959006i $$-0.408542\pi$$
−0.688830 + 0.724923i $$0.741875\pi$$
$$74$$ 2.50000 4.33013i 0.290619 0.503367i
$$75$$ 0.598076 4.96410i 0.0690599 0.573205i
$$76$$ 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 $$-0.455323\pi$$
$$80$$ −0.133975 + 2.23205i −0.0149788 + 0.249551i
$$81$$ −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 $$-0.815077\pi$$
0.835940 0.548821i $$-0.184923\pi$$
$$84$$ 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
$$95$$ 0.937822 15.6244i 0.0962185 1.60303i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 8.00000i 0.812277i −0.913812 0.406138i $$-0.866875\pi$$
0.913812 0.406138i $$-0.133125\pi$$
$$98$$ 2.59808 + 6.50000i 0.262445 + 0.656599i
$$99$$ 5.00000 0.502519
$$100$$ 4.96410 + 0.598076i 0.496410 + 0.0598076i
$$101$$ −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
$$105$$ 2.26795 5.46410i 0.221329 0.533242i
$$106$$ 1.00000 0.0971286
$$107$$ −10.3923 + 6.00000i −1.00466 + 0.580042i −0.909624 0.415432i $$-0.863630\pi$$
−0.0950377 + 0.995474i $$0.530297\pi$$
$$108$$ −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 $$0.835851\pi$$
$$110$$ −6.16025 + 9.33013i −0.587357 + 0.889593i
$$111$$ −5.00000 −0.474579
$$112$$ −0.866025 + 2.50000i −0.0818317 + 0.236228i
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ −3.50000 6.06218i −0.327805 0.567775i
$$115$$ −6.69615 0.401924i −0.624419 0.0374796i
$$116$$ 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 $$-0.869250\pi$$
0.916816 0.399310i $$-0.130750\pi$$
$$128$$ −0.866025 + 0.500000i −0.0765466 + 0.0441942i
$$129$$ 5.00000 8.66025i 0.440225 0.762493i
$$130$$ 0.133975 2.23205i 0.0117503 0.195764i
$$131$$ 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
$$135$$ −1.23205 + 1.86603i −0.106038 + 0.160602i
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −3.46410 2.00000i −0.295958 0.170872i 0.344668 0.938725i $$-0.387992\pi$$
−0.640626 + 0.767853i $$0.721325\pi$$
$$138$$ −2.59808 + 1.50000i −0.221163 + 0.127688i
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 5.46410 + 2.26795i 0.461801 + 0.191677i
$$141$$ −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 $$0.912374\pi$$
$$150$$ −1.96410 4.59808i −0.160368 0.375431i
$$151$$ 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 0.876717 0.481006i $$-0.159728\pi$$
0.0217953 + 0.999762i $$0.493062\pi$$
$$158$$ −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 −0.848339 0.529454i $$-0.822397\pi$$
0.0343508 + 0.999410i $$0.489064\pi$$
$$164$$ −4.50000 + 7.79423i −0.351391 + 0.608627i
$$165$$ 11.1603 + 0.669873i 0.868825 + 0.0521495i
$$166$$ −5.00000 8.66025i −0.388075 0.672166i
$$167$$ 19.0000i 1.47026i 0.677924 + 0.735132i $$0.262880\pi$$
−0.677924 + 0.735132i $$0.737120\pi$$
$$168$$ 2.59808 0.500000i 0.200446 0.0385758i
$$169$$ 12.0000 0.923077
$$170$$ 3.73205 + 2.46410i 0.286235 + 0.188988i
$$171$$ −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 −0.251523 0.967851i $$-0.580932\pi$$
0.712422 + 0.701751i $$0.247598\pi$$
$$174$$ 0 0
$$175$$ 5.79423 11.8923i 0.438003 0.898974i
$$176$$ −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 $$0.301518\pi$$
$$180$$ −1.86603 1.23205i −0.139085 0.0918316i
$$181$$ −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
$$185$$ −11.1603 0.669873i −0.820518 0.0492500i
$$186$$ −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 0.941932 0.335805i $$-0.109008\pi$$
0.180150 + 0.983639i $$0.442342\pi$$
$$194$$ −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 $$0.411776\pi$$
−0.273629 + 0.961835i $$0.588224\pi$$
$$198$$ 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 $$0.331945\pi$$
$$200$$ 4.59808 1.96410i 0.325133 0.138883i
$$201$$ −3.00000 5.19615i −0.211604 0.366508i
$$202$$ 8.00000i 0.562878i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 16.7942 + 11.0885i 1.17296 + 0.774451i
$$206$$ 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
$$210$$ −0.767949 5.86603i −0.0529935 0.404794i
$$211$$ 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
$$215$$ 12.3205 18.6603i 0.840252 1.27262i
$$216$$ −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
$$220$$ −0.669873 + 11.1603i −0.0451628 + 0.752424i
$$221$$ 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 $$0.179960\pi$$
−0.844396 + 0.535720i $$0.820040\pi$$
$$224$$ 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 0.845120 0.534577i $$-0.179529\pi$$
−0.0403978 + 0.999184i $$0.512863\pi$$
$$228$$ −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
$$235$$ −29.0167 1.74167i −1.89284 0.113614i
$$236$$ −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 $$0.723912\pi$$
$$240$$ 1.23205 1.86603i 0.0795285 0.120451i
$$241$$ 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
$$245$$ 10.4019 11.6962i 0.664555 0.747240i
$$246$$ 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
$$250$$ −3.76795 10.5263i −0.238306 0.665740i
$$251$$ −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
$$255$$ 0.267949 4.46410i 0.0167796 0.279553i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 8.66025 5.00000i 0.540212 0.311891i −0.204953 0.978772i $$-0.565704\pi$$
0.745165 + 0.666880i $$0.232371\pi$$
$$258$$ 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 −0.304487 0.952517i $$-0.598485\pi$$
−0.977147 + 0.212565i $$0.931818\pi$$
$$264$$ 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 $$0.0263084\pi$$
$$270$$ −0.133975 + 2.23205i −0.00815343 + 0.135838i
$$271$$ −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
$$275$$ 24.8205 + 2.99038i 1.49673 + 0.180327i
$$276$$ −1.50000 + 2.59808i −0.0902894 + 0.156386i
$$277$$ 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i $$-0.314196\pi$$
−0.447062 + 0.894503i $$0.647530\pi$$
$$278$$ 6.92820 4.00000i 0.415526 0.239904i
$$279$$ 6.00000 0.359211
$$280$$ 5.86603 0.767949i 0.350562 0.0458937i
$$281$$ −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 −0.351895 0.936039i $$-0.614463\pi$$
−0.986581 + 0.163270i $$0.947796\pi$$
$$284$$ −1.00000 + 1.73205i −0.0593391 + 0.102778i
$$285$$ −8.62436 + 13.0622i −0.510863 + 0.773737i
$$286$$ 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 $$0.00929925\pi$$
−0.999573 + 0.0292103i $$0.990701\pi$$
$$294$$ 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
$$305$$ 0.267949 4.46410i 0.0153427 0.255614i
$$306$$ −1.00000 1.73205i −0.0571662 0.0990148i
$$307$$ 2.00000i 0.114146i −0.998370 0.0570730i $$-0.981823\pi$$
0.998370 0.0570730i $$-0.0181768\pi$$
$$308$$ −4.33013 + 12.5000i −0.246732 + 0.712254i
$$309$$ 0 0
$$310$$ −7.39230 + 11.1962i −0.419855 + 0.635899i
$$311$$ 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 −0.724370 0.689412i $$-0.757869\pi$$
0.234863 + 0.972028i $$0.424536\pi$$
$$314$$ 13.0000 0.733632
$$315$$ −4.69615 + 3.59808i −0.264598 + 0.202729i
$$316$$ −14.0000 −0.787562
$$317$$ −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i $$-0.684554\pi$$
0.450570 + 0.892741i $$0.351221\pi$$
$$318$$ −0.866025 0.500000i −0.0485643 0.0280386i
$$319$$ 0 0
$$320$$ 1.86603 + 1.23205i 0.104314 + 0.0688737i
$$321$$ 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
$$325$$ −4.59808 + 1.96410i −0.255055 + 0.108949i
$$326$$ −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 $$0.124528\pi$$
−0.924445 + 0.381314i $$0.875472\pi$$
$$338$$ 10.3923 6.00000i 0.565267 0.326357i
$$339$$ 3.00000 5.19615i 0.162938 0.282216i
$$340$$ 4.46410 + 0.267949i 0.242100 + 0.0145316i
$$341$$ −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
$$345$$ 5.59808 + 3.69615i 0.301390 + 0.198994i
$$346$$ 3.50000 6.06218i 0.188161 0.325905i
$$347$$ −13.8564 8.00000i −0.743851 0.429463i 0.0796169 0.996826i $$-0.474630\pi$$
−0.823468 + 0.567363i $$0.807964\pi$$
$$348$$ 0 0
$$349$$ 24.0000 1.28469 0.642345 0.766415i $$-0.277962\pi$$
0.642345 + 0.766415i $$0.277962\pi$$
$$350$$ −0.928203 13.1962i −0.0496145 0.705364i
$$351$$ 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
$$355$$ 3.73205 + 2.46410i 0.198077 + 0.130781i
$$356$$ 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 $$-0.431317\pi$$
$$360$$ −2.23205 0.133975i −0.117639 0.00706108i
$$361$$ −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 $$-0.916954\pi$$
−0.706469 0.707744i $$-0.749713\pi$$
$$368$$ −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 −0.359408 0.933181i $$-0.617021\pi$$
0.628454 + 0.777847i $$0.283688\pi$$
$$374$$ −5.00000 + 8.66025i −0.258544 + 0.447811i
$$375$$ −7.23205 + 8.52628i −0.373461 + 0.440295i
$$376$$ −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 $$0.491824\pi$$
$$380$$ −13.0622 8.62436i −0.670076 0.442420i
$$381$$ −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 −0.685736 0.727851i $$-0.740519\pi$$
0.287469 + 0.957790i $$0.407186\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 27.3205 + 11.3397i 1.39238 + 0.577927i
$$386$$ 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 $$0.118061\pi$$
$$390$$ −1.23205 + 1.86603i −0.0623873 + 0.0944899i
$$391$$ −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
$$395$$ −1.87564 + 31.2487i −0.0943739 + 1.57229i
$$396$$ 2.50000 4.33013i 0.125630 0.217597i
$$397$$ 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i $$-0.650684\pi$$
0.542834 + 0.839840i $$0.317351\pi$$
$$398$$ 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 $$0.0871450\pi$$
$$410$$ 20.0885 + 1.20577i 0.992098 + 0.0595488i
$$411$$ 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
$$415$$ −12.3205 + 18.6603i −0.604790 + 0.915996i
$$416$$ 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 $$0.523347\pi$$
$$420$$ −3.59808 4.69615i −0.175568 0.229149i
$$421$$ −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
$$425$$ 1.19615 9.92820i 0.0580219 0.481589i
$$426$$ 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
$$430$$ 1.33975 22.3205i 0.0646083 1.07639i
$$431$$ −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 $$0.0306413\pi$$
−0.995370 + 0.0961139i $$0.969359\pi$$
$$434$$ −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 −0.618333 0.785916i $$-0.712192\pi$$
0.371457 + 0.928450i $$0.378858\pi$$
$$444$$ −2.50000 + 4.33013i −0.118645 + 0.205499i
$$445$$ 1.33975 22.3205i 0.0635100 1.05809i
$$446$$ 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 $$0.568118\pi$$
$$450$$ −0.598076 + 4.96410i −0.0281936 + 0.234010i
$$451$$ −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
$$455$$ −5.86603 + 0.767949i −0.275004 + 0.0360020i
$$456$$ −7.00000 −0.327805
$$457$$ 32.9090 19.0000i 1.53942 0.888783i 0.540544 0.841316i $$-0.318219\pi$$
0.998873 0.0474665i $$-0.0151147\pi$$
$$458$$ −3.46410 2.00000i −0.161867 0.0934539i
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ −3.69615 + 5.59808i −0.172334 + 0.261012i
$$461$$ −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 $$-0.886673\pi$$
0.937288 0.348555i $$-0.113327\pi$$
$$464$$ 0 0
$$465$$ 13.3923 + 0.803848i 0.621053 + 0.0372775i
$$466$$ 0 0
$$467$$ −1.73205 + 1.00000i −0.0801498 + 0.0462745i −0.539539 0.841960i $$-0.681402\pi$$
0.459390 + 0.888235i $$0.348068\pi$$
$$468$$ 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 $$0.108162\pi$$
$$480$$ 0.133975 2.23205i 0.00611508 0.101879i
$$481$$ 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
$$485$$ −9.85641 + 14.9282i −0.447556 + 0.677855i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ 20.7846 + 12.0000i 0.941841 + 0.543772i 0.890537 0.454911i $$-0.150329\pi$$
0.0513038 + 0.998683i $$0.483662\pi$$
$$488$$ 1.73205 1.00000i 0.0784063 0.0452679i
$$489$$ 12.0000 0.542659
$$490$$ 3.16025 15.3301i 0.142766 0.692545i
$$491$$ 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
$$495$$ −9.33013 6.16025i −0.419358 0.276883i
$$496$$ −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 $$-0.382272\pi$$
$$500$$ −8.52628 7.23205i −0.381307 0.323427i
$$501$$ 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 $$0.179709\pi$$
−0.844818 + 0.535054i $$0.820291\pi$$
$$504$$ −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
$$520$$ −1.86603 1.23205i −0.0818306 0.0540290i
$$521$$ 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 −0.255273 0.966869i $$-0.582165\pi$$
0.709697 + 0.704507i $$0.248832\pi$$
$$524$$ 17.0000 0.742648
$$525$$ −10.9641 + 7.40192i −0.478513 + 0.323046i
$$526$$ −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
$$530$$ −1.86603 1.23205i −0.0810550 0.0535169i
$$531$$ 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
$$535$$ 26.7846 + 1.60770i 1.15800 + 0.0695067i
$$536$$ 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 $$0.0967526\pi$$
−0.954160 + 0.299298i $$0.903247\pi$$
$$548$$ −3.46410 + 2.00000i −0.147979 + 0.0854358i
$$549$$ −1.00000 + 1.73205i −0.0426790 + 0.0739221i
$$550$$ 22.9904 9.82051i 0.980313 0.418748i
$$551$$ 0 0
$$552$$ 3.00000i 0.127688i
$$553$$ −12.1244 + 35.0000i −0.515580 + 1.48835i
$$554$$ 2.00000 0.0849719
$$555$$ 9.33013 + 6.16025i 0.396042 + 0.261488i
$$556$$ 4.00000 6.92820i 0.169638 0.293821i
$$557$$ −33.7750 19.5000i −1.43109 0.826242i −0.433888 0.900967i $$-0.642859\pi$$
−0.997204 + 0.0747252i $$0.976192\pi$$
$$558$$ 5.19615 3.00000i 0.219971 0.127000i
$$559$$ −10.0000 −0.422955
$$560$$ 4.69615 3.59808i 0.198449 0.152046i
$$561$$ 10.0000 0.422200
$$562$$ −9.52628 + 5.50000i −0.401842 + 0.232003i
$$563$$ −25.9808 15.0000i −1.09496 0.632175i −0.160066 0.987106i $$-0.551171\pi$$
−0.934892 + 0.354932i $$0.884504\pi$$
$$564$$ −6.50000 + 11.2583i −0.273699 + 0.474061i
$$565$$ 7.39230 11.1962i 0.310997 0.471026i
$$566$$ −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 $$0.853363\pi$$
$$570$$ −0.937822 + 15.6244i −0.0392810 + 0.654432i
$$571$$ 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 0.865775 0.500433i $$-0.166826\pi$$
−0.000500448 1.00000i $$0.500159\pi$$
$$578$$ −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
$$585$$ 2.23205 + 0.133975i 0.0922839 + 0.00553917i
$$586$$ 0.500000 + 0.866025i 0.0206548 + 0.0357752i
$$587$$ 2.00000i 0.0825488i −0.999148 0.0412744i $$-0.986858\pi$$
0.999148 0.0412744i $$-0.0131418\pi$$
$$588$$ −2.59808 6.50000i −0.107143 0.268055i
$$589$$ 42.0000 1.73058
$$590$$ −4.92820 + 7.46410i −0.202891 + 0.307292i
$$591$$ 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 −0.962575 0.271016i $$-0.912640\pi$$
−0.246581 + 0.969122i $$0.579307\pi$$
$$594$$ −5.00000 −0.205152
$$595$$ 4.53590 10.9282i 0.185954 0.448013i
$$596$$ −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 $$0.972825\pi$$
$$600$$ −4.96410 0.598076i −0.202659 0.0244164i
$$601$$ −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
$$605$$ −1.87564 + 31.2487i −0.0762558 + 1.27044i
$$606$$ 4.00000 6.92820i 0.162489 0.281439i
$$607$$ −11.2583 + 6.50000i −0.456962 + 0.263827i −0.710766 0.703429i $$-0.751651\pi$$
0.253804 + 0.967256i $$0.418318\pi$$
$$608$$ 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 0.129433 0.991588i $$-0.458684\pi$$
−0.794024 + 0.607887i $$0.792017\pi$$
$$614$$ −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 $$-0.793622\pi$$
0.797077 0.603877i $$-0.206378\pi$$
$$618$$ 0 0
$$619$$ 7.50000 12.9904i 0.301450 0.522127i −0.675014 0.737805i $$-0.735863\pi$$
0.976465 + 0.215677i $$0.0691959\pi$$
$$620$$ −0.803848 + 13.3923i −0.0322833 + 0.537848i
$$621$$ −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
$$625$$ −17.2846 + 18.0622i −0.691384 + 0.722487i
$$626$$ −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
$$630$$ −2.26795 + 5.46410i −0.0903573 + 0.217695i
$$631$$ 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
$$635$$ −11.0885 + 16.7942i −0.440032 + 0.666459i
$$636$$ −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
$$640$$ 2.23205 + 0.133975i 0.0882296 + 0.00529581i
$$641$$ 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 $$0.269604\pi$$
−0.662246 + 0.749287i $$0.730396\pi$$
$$644$$ −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 0.482880 0.875687i $$-0.339591\pi$$
−0.516927 + 0.856030i $$0.672924\pi$$
$$648$$ 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 −0.412876 0.910787i $$-0.635476\pi$$
0.582327 + 0.812955i $$0.302142\pi$$
$$654$$ 9.00000 15.5885i 0.351928 0.609557i
$$655$$ 2.27757 37.9449i 0.0889920 1.48263i
$$656$$ 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 $$0.252657\pi$$
$$660$$ 6.16025 9.33013i 0.239788 0.363175i
$$661$$ −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
$$665$$ −32.8731 + 25.1865i −1.27476 + 0.976692i
$$666$$ 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
$$670$$ −11.1962 7.39230i −0.432545 0.285590i
$$671$$ 10.0000 0.386046
$$672$$ 0.866025 2.50000i 0.0334077 0.0964396i
$$673$$ 36.0000i 1.38770i 0.720121 + 0.693849i $$0.244086\pi$$
−0.720121 + 0.693849i $$0.755914\pi$$
$$674$$ 7.00000 + 12.1244i 0.269630 + 0.467013i
$$675$$ 4.59808 1.96410i 0.176980 0.0755983i
$$676$$ 6.00000 10.3923i 0.230769 0.399704i
$$677$$ −28.5788 + 16.5000i −1.09837 + 0.634147i −0.935793 0.352549i $$-0.885315\pi$$
−0.162581 + 0.986695i $$0.551982\pi$$
$$678$$ 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 0.564809 0.825222i $$-0.308950\pi$$
−0.432259 + 0.901750i $$0.642283\pi$$
$$684$$ 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
$$690$$ 6.69615 + 0.401924i 0.254918 + 0.0153010i
$$691$$ 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
$$695$$ −14.9282 9.85641i −0.566259 0.373875i
$$696$$ 0 0
$$697$$ 15.5885 + 9.00000i 0.590455 + 0.340899i
$$698$$ 20.7846 12.0000i 0.786709 0.454207i
$$699$$ 0 0
$$700$$ −7.40192 10.9641i −0.279766 0.414404i
$$701$$ 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
$$705$$ 24.2583 + 16.0167i 0.913622 + 0.603222i
$$706$$ 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 $$0.736198\pi$$
$$710$$ 4.46410 + 0.267949i 0.167535 + 0.0100560i
$$711$$ 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 $$-0.559070\pi$$
0.184510 0.982831i $$-0.440930\pi$$
$$728$$ −1.73205 2.00000i −0.0641941 0.0741249i
$$729$$ −1.00000 −0.0370370
$$730$$ 7.46410 + 4.92820i 0.276259 + 0.182401i
$$731$$ 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 −0.796734 0.604331i $$-0.793441\pi$$
0.124999 + 0.992157i $$0.460107\pi$$
$$734$$ −37.0000 −1.36569
$$735$$ −14.8564 + 4.92820i −0.547987 + 0.181780i
$$736$$ −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 $$-0.165674\pi$$
$$740$$ −6.16025 + 9.33013i −0.226455 + 0.342982i
$$741$$ 7.00000 0.257151
$$742$$ −1.73205 2.00000i −0.0635856 0.0734223i
$$743$$ 31.0000i 1.13728i −0.822587 0.568640i $$-0.807470\pi$$
0.822587 0.568640i $$-0.192530\pi$$
$$744$$ 3.00000 + 5.19615i 0.109985 + 0.190500i
$$745$$ −0.803848 + 13.3923i −0.0294507 + 0.490656i
$$746$$ 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 $$0.156646\pi$$
−0.881334 + 0.472493i $$0.843354\pi$$
$$758$$ 0.866025 0.500000i 0.0314555 0.0181608i
$$759$$ −7.50000 + 12.9904i −0.272233 + 0.471521i
$$760$$ −15.6244 0.937822i −0.566755 0.0340184i
$$761$$ 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
$$765$$ −2.46410 + 3.73205i −0.0890898 + 0.134933i
$$766$$ −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 $$0.871449\pi$$
$$770$$ 29.3301 3.83975i 1.05698 0.138375i
$$771$$ −10.0000 −0.360141
$$772$$ 15.5885 9.00000i 0.561041 0.323917i
$$773$$ 32.0429 + 18.5000i 1.15250 + 0.665399i 0.949496 0.313778i $$-0.101595\pi$$
0.203008 + 0.979177i $$0.434928\pi$$
$$774$$ −5.00000 + 8.66025i −0.179721 + 0.311286i
$$775$$ 29.7846 + 3.58846i 1.06989 + 0.128901i