# Properties

 Label 1110.2.ba.a.529.3 Level $1110$ Weight $2$ Character 1110.529 Analytic conductor $8.863$ Analytic rank $0$ Dimension $36$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.ba (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$36$$ Relative dimension: $$18$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 529.3 Character $$\chi$$ $$=$$ 1110.529 Dual form 1110.2.ba.a.619.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) q^{5} +1.00000i q^{6} +(-0.916644 - 0.529225i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.491597 + 2.18136i) q^{5} +1.00000i q^{6} +(-0.916644 - 0.529225i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.13491 - 0.664945i) q^{10} -0.825600 q^{11} +(0.866025 - 0.500000i) q^{12} +(1.81865 - 3.14999i) q^{13} +1.05845i q^{14} +(1.51642 - 1.64331i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.742138 - 1.28542i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.75785 + 2.74695i) q^{19} +(-1.64331 - 1.51642i) q^{20} +(0.529225 + 0.916644i) q^{21} +(0.412800 + 0.714991i) q^{22} -2.23982 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.51666 - 2.14470i) q^{25} -3.63729 q^{26} -1.00000i q^{27} +(0.916644 - 0.529225i) q^{28} +2.02537i q^{29} +(-2.18136 - 0.491597i) q^{30} +6.27676i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.714991 + 0.412800i) q^{33} +(-0.742138 + 1.28542i) q^{34} +(1.60505 - 1.73937i) q^{35} -1.00000 q^{36} +(-5.95462 - 1.24197i) q^{37} -5.49389i q^{38} +(-3.14999 + 1.81865i) q^{39} +(-0.491597 + 2.18136i) q^{40} +(-1.42858 + 2.47438i) q^{41} +(0.529225 - 0.916644i) q^{42} -10.6694 q^{43} +(0.412800 - 0.714991i) q^{44} +(-2.13491 + 0.664945i) q^{45} +(1.11991 + 1.93975i) q^{46} +11.7632i q^{47} +1.00000i q^{48} +(-2.93984 - 5.09196i) q^{49} +(0.400968 + 4.98390i) q^{50} +1.48428i q^{51} +(1.81865 + 3.14999i) q^{52} +(-8.00978 + 4.62445i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.405862 - 1.80093i) q^{55} +(-0.916644 - 0.529225i) q^{56} +(-2.74695 - 4.75785i) q^{57} +(1.75402 - 1.01268i) q^{58} +(-6.33426 + 3.65709i) q^{59} +(0.664945 + 2.13491i) q^{60} +(-5.60990 - 3.23888i) q^{61} +(5.43583 - 3.13838i) q^{62} -1.05845i q^{63} +1.00000 q^{64} +(5.97722 + 5.51565i) q^{65} -0.825600i q^{66} +(11.2463 + 6.49307i) q^{67} +1.48428 q^{68} +(1.93975 + 1.11991i) q^{69} +(-2.30886 - 0.520331i) q^{70} +(-0.701131 + 1.21439i) q^{71} +(0.500000 + 0.866025i) q^{72} -8.82512i q^{73} +(1.90173 + 5.77784i) q^{74} +(2.83920 + 4.11570i) q^{75} +(-4.75785 + 2.74695i) q^{76} +(0.756782 + 0.436928i) q^{77} +(3.14999 + 1.81865i) q^{78} +(-3.10453 - 1.79240i) q^{79} +(2.13491 - 0.664945i) q^{80} +(-0.500000 + 0.866025i) q^{81} +2.85716 q^{82} +(-13.4101 + 7.74230i) q^{83} -1.05845 q^{84} +(3.16880 - 0.986962i) q^{85} +(5.33471 + 9.23999i) q^{86} +(1.01268 - 1.75402i) q^{87} -0.825600 q^{88} +(-2.86558 + 1.65444i) q^{89} +(1.64331 + 1.51642i) q^{90} +(-3.33410 + 1.92495i) q^{91} +(1.11991 - 1.93975i) q^{92} +(3.13838 - 5.43583i) q^{93} +(10.1872 - 5.88160i) q^{94} +(-8.33102 + 9.02819i) q^{95} +(0.866025 - 0.500000i) q^{96} +5.18358 q^{97} +(-2.93984 + 5.09196i) q^{98} +(-0.412800 - 0.714991i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$36q - 18q^{2} - 18q^{4} + 2q^{5} + 36q^{8} + 18q^{9} + O(q^{10})$$ $$36q - 18q^{2} - 18q^{4} + 2q^{5} + 36q^{8} + 18q^{9} + 2q^{10} + 4q^{11} - 14q^{13} - 2q^{15} - 18q^{16} + 18q^{18} + 6q^{19} - 4q^{20} - 2q^{22} - 20q^{23} + 4q^{25} + 28q^{26} - 2q^{30} - 18q^{32} - 6q^{33} - 40q^{35} - 36q^{36} + 20q^{37} + 6q^{39} + 2q^{40} + 10q^{41} - 2q^{44} - 2q^{45} + 10q^{46} + 10q^{49} - 2q^{50} - 14q^{52} - 12q^{53} + 56q^{55} + 8q^{57} + 30q^{58} + 18q^{59} + 4q^{60} - 6q^{61} - 12q^{62} + 36q^{64} + 40q^{65} + 36q^{67} + 12q^{69} + 20q^{70} - 24q^{71} + 18q^{72} - 34q^{74} + 8q^{75} - 6q^{76} - 24q^{77} - 6q^{78} + 2q^{80} - 18q^{81} - 20q^{82} + 36q^{83} + 26q^{85} - 10q^{87} + 4q^{88} + 4q^{90} - 36q^{91} + 10q^{92} + 12q^{93} + 12q^{94} - 30q^{95} + 52q^{97} + 10q^{98} + 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$667$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.491597 + 2.18136i −0.219849 + 0.975534i
$$6$$ 1.00000i 0.408248i
$$7$$ −0.916644 0.529225i −0.346459 0.200028i 0.316666 0.948537i $$-0.397437\pi$$
−0.663125 + 0.748509i $$0.730770\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 2.13491 0.664945i 0.675118 0.210274i
$$11$$ −0.825600 −0.248928 −0.124464 0.992224i $$-0.539721\pi$$
−0.124464 + 0.992224i $$0.539721\pi$$
$$12$$ 0.866025 0.500000i 0.250000 0.144338i
$$13$$ 1.81865 3.14999i 0.504402 0.873649i −0.495585 0.868559i $$-0.665046\pi$$
0.999987 0.00509014i $$-0.00162025\pi$$
$$14$$ 1.05845i 0.282883i
$$15$$ 1.51642 1.64331i 0.391537 0.424302i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −0.742138 1.28542i −0.179995 0.311760i 0.761884 0.647714i $$-0.224275\pi$$
−0.941879 + 0.335954i $$0.890941\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ 4.75785 + 2.74695i 1.09153 + 0.630193i 0.933982 0.357319i $$-0.116309\pi$$
0.157543 + 0.987512i $$0.449643\pi$$
$$20$$ −1.64331 1.51642i −0.367456 0.339081i
$$21$$ 0.529225 + 0.916644i 0.115486 + 0.200028i
$$22$$ 0.412800 + 0.714991i 0.0880093 + 0.152437i
$$23$$ −2.23982 −0.467036 −0.233518 0.972353i $$-0.575024\pi$$
−0.233518 + 0.972353i $$0.575024\pi$$
$$24$$ −0.866025 0.500000i −0.176777 0.102062i
$$25$$ −4.51666 2.14470i −0.903333 0.428940i
$$26$$ −3.63729 −0.713332
$$27$$ 1.00000i 0.192450i
$$28$$ 0.916644 0.529225i 0.173229 0.100014i
$$29$$ 2.02537i 0.376101i 0.982159 + 0.188050i $$0.0602168\pi$$
−0.982159 + 0.188050i $$0.939783\pi$$
$$30$$ −2.18136 0.491597i −0.398260 0.0897529i
$$31$$ 6.27676i 1.12734i 0.826000 + 0.563669i $$0.190611\pi$$
−0.826000 + 0.563669i $$0.809389\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0.714991 + 0.412800i 0.124464 + 0.0718593i
$$34$$ −0.742138 + 1.28542i −0.127276 + 0.220448i
$$35$$ 1.60505 1.73937i 0.271303 0.294007i
$$36$$ −1.00000 −0.166667
$$37$$ −5.95462 1.24197i −0.978934 0.204179i
$$38$$ 5.49389i 0.891227i
$$39$$ −3.14999 + 1.81865i −0.504402 + 0.291216i
$$40$$ −0.491597 + 2.18136i −0.0777283 + 0.344903i
$$41$$ −1.42858 + 2.47438i −0.223107 + 0.386433i −0.955750 0.294181i $$-0.904953\pi$$
0.732643 + 0.680613i $$0.238287\pi$$
$$42$$ 0.529225 0.916644i 0.0816612 0.141441i
$$43$$ −10.6694 −1.62707 −0.813536 0.581515i $$-0.802460\pi$$
−0.813536 + 0.581515i $$0.802460\pi$$
$$44$$ 0.412800 0.714991i 0.0622319 0.107789i
$$45$$ −2.13491 + 0.664945i −0.318254 + 0.0991241i
$$46$$ 1.11991 + 1.93975i 0.165122 + 0.286000i
$$47$$ 11.7632i 1.71584i 0.513783 + 0.857920i $$0.328244\pi$$
−0.513783 + 0.857920i $$0.671756\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −2.93984 5.09196i −0.419977 0.727422i
$$50$$ 0.400968 + 4.98390i 0.0567054 + 0.704829i
$$51$$ 1.48428i 0.207840i
$$52$$ 1.81865 + 3.14999i 0.252201 + 0.436825i
$$53$$ −8.00978 + 4.62445i −1.10023 + 0.635217i −0.936281 0.351252i $$-0.885756\pi$$
−0.163947 + 0.986469i $$0.552423\pi$$
$$54$$ −0.866025 + 0.500000i −0.117851 + 0.0680414i
$$55$$ 0.405862 1.80093i 0.0547265 0.242837i
$$56$$ −0.916644 0.529225i −0.122492 0.0707206i
$$57$$ −2.74695 4.75785i −0.363842 0.630193i
$$58$$ 1.75402 1.01268i 0.230314 0.132972i
$$59$$ −6.33426 + 3.65709i −0.824651 + 0.476112i −0.852018 0.523513i $$-0.824621\pi$$
0.0273670 + 0.999625i $$0.491288\pi$$
$$60$$ 0.664945 + 2.13491i 0.0858440 + 0.275616i
$$61$$ −5.60990 3.23888i −0.718274 0.414696i 0.0958432 0.995396i $$-0.469445\pi$$
−0.814117 + 0.580701i $$0.802779\pi$$
$$62$$ 5.43583 3.13838i 0.690351 0.398574i
$$63$$ 1.05845i 0.133352i
$$64$$ 1.00000 0.125000
$$65$$ 5.97722 + 5.51565i 0.741383 + 0.684132i
$$66$$ 0.825600i 0.101624i
$$67$$ 11.2463 + 6.49307i 1.37396 + 0.793255i 0.991424 0.130686i $$-0.0417179\pi$$
0.382535 + 0.923941i $$0.375051\pi$$
$$68$$ 1.48428 0.179995
$$69$$ 1.93975 + 1.11991i 0.233518 + 0.134822i
$$70$$ −2.30886 0.520331i −0.275962 0.0621914i
$$71$$ −0.701131 + 1.21439i −0.0832089 + 0.144122i −0.904627 0.426205i $$-0.859850\pi$$
0.821418 + 0.570327i $$0.193184\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 8.82512i 1.03290i −0.856317 0.516451i $$-0.827253\pi$$
0.856317 0.516451i $$-0.172747\pi$$
$$74$$ 1.90173 + 5.77784i 0.221072 + 0.671660i
$$75$$ 2.83920 + 4.11570i 0.327842 + 0.475240i
$$76$$ −4.75785 + 2.74695i −0.545763 + 0.315096i
$$77$$ 0.756782 + 0.436928i 0.0862433 + 0.0497926i
$$78$$ 3.14999 + 1.81865i 0.356666 + 0.205921i
$$79$$ −3.10453 1.79240i −0.349287 0.201661i 0.315084 0.949064i $$-0.397967\pi$$
−0.664371 + 0.747403i $$0.731300\pi$$
$$80$$ 2.13491 0.664945i 0.238690 0.0743431i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 2.85716 0.315521
$$83$$ −13.4101 + 7.74230i −1.47195 + 0.849828i −0.999503 0.0315331i $$-0.989961\pi$$
−0.472443 + 0.881361i $$0.656628\pi$$
$$84$$ −1.05845 −0.115486
$$85$$ 3.16880 0.986962i 0.343705 0.107051i
$$86$$ 5.33471 + 9.23999i 0.575257 + 0.996374i
$$87$$ 1.01268 1.75402i 0.108571 0.188050i
$$88$$ −0.825600 −0.0880093
$$89$$ −2.86558 + 1.65444i −0.303751 + 0.175371i −0.644127 0.764919i $$-0.722779\pi$$
0.340376 + 0.940289i $$0.389446\pi$$
$$90$$ 1.64331 + 1.51642i 0.173221 + 0.159844i
$$91$$ −3.33410 + 1.92495i −0.349509 + 0.201789i
$$92$$ 1.11991 1.93975i 0.116759 0.202232i
$$93$$ 3.13838 5.43583i 0.325435 0.563669i
$$94$$ 10.1872 5.88160i 1.05073 0.606641i
$$95$$ −8.33102 + 9.02819i −0.854745 + 0.926273i
$$96$$ 0.866025 0.500000i 0.0883883 0.0510310i
$$97$$ 5.18358 0.526313 0.263157 0.964753i $$-0.415236\pi$$
0.263157 + 0.964753i $$0.415236\pi$$
$$98$$ −2.93984 + 5.09196i −0.296969 + 0.514365i
$$99$$ −0.412800 0.714991i −0.0414880 0.0718593i
$$100$$ 4.11570 2.83920i 0.411570 0.283920i
$$101$$ −10.5205 −1.04682 −0.523412 0.852080i $$-0.675341\pi$$
−0.523412 + 0.852080i $$0.675341\pi$$
$$102$$ 1.28542 0.742138i 0.127276 0.0734826i
$$103$$ 16.1758 1.59385 0.796923 0.604081i $$-0.206460\pi$$
0.796923 + 0.604081i $$0.206460\pi$$
$$104$$ 1.81865 3.14999i 0.178333 0.308882i
$$105$$ −2.25970 + 0.703810i −0.220524 + 0.0686849i
$$106$$ 8.00978 + 4.62445i 0.777979 + 0.449166i
$$107$$ 12.2112 + 7.05015i 1.18050 + 0.681563i 0.956131 0.292940i $$-0.0946337\pi$$
0.224372 + 0.974504i $$0.427967\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ −4.54656 + 2.62496i −0.435481 + 0.251425i −0.701679 0.712493i $$-0.747566\pi$$
0.266198 + 0.963918i $$0.414233\pi$$
$$110$$ −1.76258 + 0.548978i −0.168056 + 0.0523430i
$$111$$ 4.53587 + 4.05289i 0.430525 + 0.384683i
$$112$$ 1.05845i 0.100014i
$$113$$ −1.67721 2.90502i −0.157779 0.273281i 0.776288 0.630378i $$-0.217100\pi$$
−0.934067 + 0.357097i $$0.883767\pi$$
$$114$$ −2.74695 + 4.75785i −0.257275 + 0.445613i
$$115$$ 1.10109 4.88587i 0.102677 0.455609i
$$116$$ −1.75402 1.01268i −0.162856 0.0940252i
$$117$$ 3.63729 0.336268
$$118$$ 6.33426 + 3.65709i 0.583116 + 0.336662i
$$119$$ 1.57103i 0.144016i
$$120$$ 1.51642 1.64331i 0.138429 0.150013i
$$121$$ −10.3184 −0.938035
$$122$$ 6.47775i 0.586468i
$$123$$ 2.47438 1.42858i 0.223107 0.128811i
$$124$$ −5.43583 3.13838i −0.488152 0.281835i
$$125$$ 6.89874 8.79815i 0.617042 0.786930i
$$126$$ −0.916644 + 0.529225i −0.0816612 + 0.0471471i
$$127$$ −5.43873 + 3.14005i −0.482609 + 0.278634i −0.721503 0.692411i $$-0.756548\pi$$
0.238894 + 0.971046i $$0.423215\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 9.23999 + 5.33471i 0.813536 + 0.469695i
$$130$$ 1.78808 7.93425i 0.156825 0.695879i
$$131$$ 11.2829 6.51420i 0.985794 0.569148i 0.0817796 0.996650i $$-0.473940\pi$$
0.904014 + 0.427502i $$0.140606\pi$$
$$132$$ −0.714991 + 0.412800i −0.0622319 + 0.0359296i
$$133$$ −2.90750 5.03594i −0.252113 0.436672i
$$134$$ 12.9861i 1.12183i
$$135$$ 2.18136 + 0.491597i 0.187742 + 0.0423099i
$$136$$ −0.742138 1.28542i −0.0636378 0.110224i
$$137$$ 7.15737i 0.611496i 0.952113 + 0.305748i $$0.0989064\pi$$
−0.952113 + 0.305748i $$0.901094\pi$$
$$138$$ 2.23982i 0.190667i
$$139$$ −5.76530 9.98579i −0.489006 0.846983i 0.510914 0.859632i $$-0.329307\pi$$
−0.999920 + 0.0126486i $$0.995974\pi$$
$$140$$ 0.703810 + 2.25970i 0.0594828 + 0.190979i
$$141$$ 5.88160 10.1872i 0.495320 0.857920i
$$142$$ 1.40226 0.117675
$$143$$ −1.50147 + 2.60063i −0.125560 + 0.217476i
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ −4.41805 0.995663i −0.366899 0.0826853i
$$146$$ −7.64277 + 4.41256i −0.632520 + 0.365186i
$$147$$ 5.87968i 0.484948i
$$148$$ 4.05289 4.53587i 0.333145 0.372846i
$$149$$ −3.03860 −0.248932 −0.124466 0.992224i $$-0.539722\pi$$
−0.124466 + 0.992224i $$0.539722\pi$$
$$150$$ 2.14470 4.51666i 0.175114 0.368784i
$$151$$ −4.20011 + 7.27481i −0.341800 + 0.592015i −0.984767 0.173879i $$-0.944370\pi$$
0.642967 + 0.765894i $$0.277703\pi$$
$$152$$ 4.75785 + 2.74695i 0.385913 + 0.222807i
$$153$$ 0.742138 1.28542i 0.0599983 0.103920i
$$154$$ 0.873856i 0.0704173i
$$155$$ −13.6919 3.08563i −1.09976 0.247844i
$$156$$ 3.63729i 0.291216i
$$157$$ 12.7985 7.38920i 1.02143 0.589722i 0.106911 0.994269i $$-0.465904\pi$$
0.914517 + 0.404546i $$0.132571\pi$$
$$158$$ 3.58480i 0.285191i
$$159$$ 9.24890 0.733485
$$160$$ −1.64331 1.51642i −0.129915 0.119883i
$$161$$ 2.05312 + 1.18537i 0.161809 + 0.0934203i
$$162$$ 1.00000 0.0785674
$$163$$ 1.76345 + 3.05439i 0.138124 + 0.239238i 0.926787 0.375588i $$-0.122559\pi$$
−0.788662 + 0.614827i $$0.789226\pi$$
$$164$$ −1.42858 2.47438i −0.111554 0.193216i
$$165$$ −1.25195 + 1.35672i −0.0974644 + 0.105621i
$$166$$ 13.4101 + 7.74230i 1.04082 + 0.600919i
$$167$$ −10.7385 + 18.5996i −0.830969 + 1.43928i 0.0663009 + 0.997800i $$0.478880\pi$$
−0.897270 + 0.441482i $$0.854453\pi$$
$$168$$ 0.529225 + 0.916644i 0.0408306 + 0.0707206i
$$169$$ −0.114948 0.199096i −0.00884218 0.0153151i
$$170$$ −2.43913 2.25078i −0.187073 0.172627i
$$171$$ 5.49389i 0.420128i
$$172$$ 5.33471 9.23999i 0.406768 0.704543i
$$173$$ −2.69931 + 1.55845i −0.205225 + 0.118487i −0.599090 0.800681i $$-0.704471\pi$$
0.393865 + 0.919168i $$0.371138\pi$$
$$174$$ −2.02537 −0.153543
$$175$$ 3.00515 + 4.35626i 0.227168 + 0.329302i
$$176$$ 0.412800 + 0.714991i 0.0311160 + 0.0538944i
$$177$$ 7.31417 0.549767
$$178$$ 2.86558 + 1.65444i 0.214784 + 0.124006i
$$179$$ 10.0254i 0.749333i 0.927160 + 0.374666i $$0.122243\pi$$
−0.927160 + 0.374666i $$0.877757\pi$$
$$180$$ 0.491597 2.18136i 0.0366415 0.162589i
$$181$$ 0.887705 1.53755i 0.0659826 0.114285i −0.831147 0.556053i $$-0.812315\pi$$
0.897129 + 0.441768i $$0.145648\pi$$
$$182$$ 3.33410 + 1.92495i 0.247140 + 0.142686i
$$183$$ 3.23888 + 5.60990i 0.239425 + 0.414696i
$$184$$ −2.23982 −0.165122
$$185$$ 5.63646 12.3786i 0.414401 0.910094i
$$186$$ −6.27676 −0.460234
$$187$$ 0.612709 + 1.06124i 0.0448058 + 0.0776058i
$$188$$ −10.1872 5.88160i −0.742981 0.428960i
$$189$$ −0.529225 + 0.916644i −0.0384954 + 0.0666761i
$$190$$ 11.9842 + 2.70078i 0.869422 + 0.195935i
$$191$$ 19.2656i 1.39401i −0.717066 0.697006i $$-0.754515\pi$$
0.717066 0.697006i $$-0.245485\pi$$
$$192$$ −0.866025 0.500000i −0.0625000 0.0360844i
$$193$$ −18.5203 −1.33312 −0.666561 0.745451i $$-0.732234\pi$$
−0.666561 + 0.745451i $$0.732234\pi$$
$$194$$ −2.59179 4.48912i −0.186080 0.322300i
$$195$$ −2.41860 7.76530i −0.173199 0.556085i
$$196$$ 5.87968 0.419977
$$197$$ −4.21694 + 2.43465i −0.300444 + 0.173462i −0.642642 0.766166i $$-0.722162\pi$$
0.342198 + 0.939628i $$0.388829\pi$$
$$198$$ −0.412800 + 0.714991i −0.0293364 + 0.0508122i
$$199$$ 17.8813i 1.26757i −0.773509 0.633785i $$-0.781500\pi$$
0.773509 0.633785i $$-0.218500\pi$$
$$200$$ −4.51666 2.14470i −0.319376 0.151653i
$$201$$ −6.49307 11.2463i −0.457986 0.793255i
$$202$$ 5.26023 + 9.11098i 0.370108 + 0.641046i
$$203$$ 1.07187 1.85654i 0.0752308 0.130304i
$$204$$ −1.28542 0.742138i −0.0899975 0.0519601i
$$205$$ −4.69522 4.33265i −0.327928 0.302605i
$$206$$ −8.08789 14.0086i −0.563510 0.976028i
$$207$$ −1.11991 1.93975i −0.0778393 0.134822i
$$208$$ −3.63729 −0.252201
$$209$$ −3.92808 2.26788i −0.271711 0.156872i
$$210$$ 1.73937 + 1.60505i 0.120028 + 0.110759i
$$211$$ −0.395745 −0.0272442 −0.0136221 0.999907i $$-0.504336\pi$$
−0.0136221 + 0.999907i $$0.504336\pi$$
$$212$$ 9.24890i 0.635217i
$$213$$ 1.21439 0.701131i 0.0832089 0.0480407i
$$214$$ 14.1003i 0.963876i
$$215$$ 5.24506 23.2739i 0.357710 1.58726i
$$216$$ 1.00000i 0.0680414i
$$217$$ 3.32182 5.75355i 0.225500 0.390577i
$$218$$ 4.54656 + 2.62496i 0.307932 + 0.177785i
$$219$$ −4.41256 + 7.64277i −0.298173 + 0.516451i
$$220$$ 1.35672 + 1.25195i 0.0914701 + 0.0844066i
$$221$$ −5.39875 −0.363159
$$222$$ 1.24197 5.95462i 0.0833557 0.399648i
$$223$$ 25.5883i 1.71352i −0.515713 0.856761i $$-0.672473\pi$$
0.515713 0.856761i $$-0.327527\pi$$
$$224$$ 0.916644 0.529225i 0.0612459 0.0353603i
$$225$$ −0.400968 4.98390i −0.0267312 0.332260i
$$226$$ −1.67721 + 2.90502i −0.111567 + 0.193239i
$$227$$ −11.6633 + 20.2013i −0.774117 + 1.34081i 0.161172 + 0.986926i $$0.448473\pi$$
−0.935289 + 0.353884i $$0.884861\pi$$
$$228$$ 5.49389 0.363842
$$229$$ −11.6531 + 20.1837i −0.770055 + 1.33377i 0.167477 + 0.985876i $$0.446438\pi$$
−0.937532 + 0.347899i $$0.886895\pi$$
$$230$$ −4.78183 + 1.48936i −0.315304 + 0.0982055i
$$231$$ −0.436928 0.756782i −0.0287478 0.0497926i
$$232$$ 2.02537i 0.132972i
$$233$$ 0.508726i 0.0333277i −0.999861 0.0166639i $$-0.994695\pi$$
0.999861 0.0166639i $$-0.00530452\pi$$
$$234$$ −1.81865 3.14999i −0.118889 0.205921i
$$235$$ −25.6598 5.78276i −1.67386 0.377226i
$$236$$ 7.31417i 0.476112i
$$237$$ 1.79240 + 3.10453i 0.116429 + 0.201661i
$$238$$ 1.36055 0.785516i 0.0881916 0.0509174i
$$239$$ 5.12135 2.95681i 0.331273 0.191260i −0.325133 0.945668i $$-0.605409\pi$$
0.656406 + 0.754408i $$0.272076\pi$$
$$240$$ −2.18136 0.491597i −0.140806 0.0317324i
$$241$$ 1.48624 + 0.858078i 0.0957368 + 0.0552737i 0.547104 0.837065i $$-0.315730\pi$$
−0.451367 + 0.892338i $$0.649064\pi$$
$$242$$ 5.15919 + 8.93598i 0.331645 + 0.574427i
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ 5.60990 3.23888i 0.359137 0.207348i
$$245$$ 12.5526 3.90966i 0.801957 0.249779i
$$246$$ −2.47438 1.42858i −0.157761 0.0910831i
$$247$$ 17.3057 9.99145i 1.10113 0.635740i
$$248$$ 6.27676i 0.398574i
$$249$$ 15.4846 0.981297
$$250$$ −11.0688 1.57541i −0.700052 0.0996379i
$$251$$ 16.7132i 1.05493i −0.849576 0.527465i $$-0.823142\pi$$
0.849576 0.527465i $$-0.176858\pi$$
$$252$$ 0.916644 + 0.529225i 0.0577432 + 0.0333380i
$$253$$ 1.84920 0.116258
$$254$$ 5.43873 + 3.14005i 0.341256 + 0.197024i
$$255$$ −3.23774 0.729666i −0.202755 0.0456934i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −1.47817 2.56026i −0.0922055 0.159705i 0.816233 0.577722i $$-0.196058\pi$$
−0.908439 + 0.418018i $$0.862725\pi$$
$$258$$ 10.6694i 0.664249i
$$259$$ 4.80099 + 4.28978i 0.298319 + 0.266554i
$$260$$ −7.76530 + 2.41860i −0.481583 + 0.149995i
$$261$$ −1.75402 + 1.01268i −0.108571 + 0.0626835i
$$262$$ −11.2829 6.51420i −0.697062 0.402449i
$$263$$ −15.9056 9.18313i −0.980784 0.566256i −0.0782774 0.996932i $$-0.524942\pi$$
−0.902507 + 0.430676i $$0.858275\pi$$
$$264$$ 0.714991 + 0.412800i 0.0440046 + 0.0254061i
$$265$$ −6.15001 19.7456i −0.377792 1.21296i
$$266$$ −2.90750 + 5.03594i −0.178271 + 0.308774i
$$267$$ 3.30888 0.202500
$$268$$ −11.2463 + 6.49307i −0.686979 + 0.396628i
$$269$$ 23.1442 1.41113 0.705563 0.708648i $$-0.250694\pi$$
0.705563 + 0.708648i $$0.250694\pi$$
$$270$$ −0.664945 2.13491i −0.0404672 0.129927i
$$271$$ 8.12733 + 14.0769i 0.493700 + 0.855113i 0.999974 0.00725939i $$-0.00231076\pi$$
−0.506274 + 0.862373i $$0.668977\pi$$
$$272$$ −0.742138 + 1.28542i −0.0449987 + 0.0779401i
$$273$$ 3.84989 0.233006
$$274$$ 6.19847 3.57869i 0.374463 0.216196i
$$275$$ 3.72896 + 1.77066i 0.224865 + 0.106775i
$$276$$ −1.93975 + 1.11991i −0.116759 + 0.0674108i
$$277$$ −2.33406 + 4.04271i −0.140240 + 0.242903i −0.927587 0.373607i $$-0.878121\pi$$
0.787347 + 0.616510i $$0.211454\pi$$
$$278$$ −5.76530 + 9.98579i −0.345779 + 0.598908i
$$279$$ −5.43583 + 3.13838i −0.325435 + 0.187890i
$$280$$ 1.60505 1.73937i 0.0959201 0.103947i
$$281$$ 12.2372 7.06515i 0.730010 0.421471i −0.0884158 0.996084i $$-0.528180\pi$$
0.818426 + 0.574612i $$0.194847\pi$$
$$282$$ −11.7632 −0.700489
$$283$$ −5.01437 + 8.68515i −0.298073 + 0.516278i −0.975695 0.219132i $$-0.929677\pi$$
0.677622 + 0.735411i $$0.263011\pi$$
$$284$$ −0.701131 1.21439i −0.0416045 0.0720611i
$$285$$ 11.7290 3.65313i 0.694765 0.216393i
$$286$$ 3.00295 0.177568
$$287$$ 2.61900 1.51208i 0.154595 0.0892554i
$$288$$ −1.00000 −0.0589256
$$289$$ 7.39846 12.8145i 0.435204 0.753795i
$$290$$ 1.34676 + 4.32398i 0.0790842 + 0.253913i
$$291$$ −4.48912 2.59179i −0.263157 0.151934i
$$292$$ 7.64277 + 4.41256i 0.447260 + 0.258225i
$$293$$ −0.821707 0.474413i −0.0480046 0.0277155i 0.475806 0.879550i $$-0.342157\pi$$
−0.523810 + 0.851835i $$0.675490\pi$$
$$294$$ 5.09196 2.93984i 0.296969 0.171455i
$$295$$ −4.86352 15.6151i −0.283165 0.909147i
$$296$$ −5.95462 1.24197i −0.346105 0.0721881i
$$297$$ 0.825600i 0.0479062i
$$298$$ 1.51930 + 2.63151i 0.0880107 + 0.152439i
$$299$$ −4.07345 + 7.05542i −0.235574 + 0.408026i
$$300$$ −4.98390 + 0.400968i −0.287745 + 0.0231499i
$$301$$ 9.78007 + 5.64652i 0.563714 + 0.325460i
$$302$$ 8.40022 0.483379
$$303$$ 9.11098 + 5.26023i 0.523412 + 0.302192i
$$304$$ 5.49389i 0.315096i
$$305$$ 9.82296 10.6450i 0.562461 0.609530i
$$306$$ −1.48428 −0.0848504
$$307$$ 12.8973i 0.736088i 0.929808 + 0.368044i $$0.119972\pi$$
−0.929808 + 0.368044i $$0.880028\pi$$
$$308$$ −0.756782 + 0.436928i −0.0431216 + 0.0248963i
$$309$$ −14.0086 8.08789i −0.796923 0.460104i
$$310$$ 4.17370 + 13.4003i 0.237050 + 0.761087i
$$311$$ −22.1356 + 12.7800i −1.25520 + 0.724688i −0.972137 0.234414i $$-0.924683\pi$$
−0.283060 + 0.959102i $$0.591349\pi$$
$$312$$ −3.14999 + 1.81865i −0.178333 + 0.102961i
$$313$$ 2.35334 + 4.07611i 0.133019 + 0.230395i 0.924839 0.380359i $$-0.124200\pi$$
−0.791820 + 0.610754i $$0.790866\pi$$
$$314$$ −12.7985 7.38920i −0.722259 0.416997i
$$315$$ 2.30886 + 0.520331i 0.130090 + 0.0293173i
$$316$$ 3.10453 1.79240i 0.174643 0.100830i
$$317$$ 21.7227 12.5416i 1.22007 0.704407i 0.255137 0.966905i $$-0.417880\pi$$
0.964933 + 0.262498i $$0.0845462\pi$$
$$318$$ −4.62445 8.00978i −0.259326 0.449166i
$$319$$ 1.67214i 0.0936219i
$$320$$ −0.491597 + 2.18136i −0.0274811 + 0.121942i
$$321$$ −7.05015 12.2112i −0.393501 0.681563i
$$322$$ 2.37074i 0.132116i
$$323$$ 8.15446i 0.453726i
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ −14.9700 + 10.3270i −0.830386 + 0.572838i
$$326$$ 1.76345 3.05439i 0.0976686 0.169167i
$$327$$ 5.24991 0.290321
$$328$$ −1.42858 + 2.47438i −0.0788803 + 0.136625i
$$329$$ 6.22538 10.7827i 0.343216 0.594468i
$$330$$ 1.80093 + 0.405862i 0.0991380 + 0.0223420i
$$331$$ 7.92971 4.57822i 0.435856 0.251642i −0.265982 0.963978i $$-0.585696\pi$$
0.701838 + 0.712336i $$0.252363\pi$$
$$332$$ 15.4846i 0.849828i
$$333$$ −1.90173 5.77784i −0.104214 0.316624i
$$334$$ 21.4770 1.17517
$$335$$ −19.6924 + 21.3403i −1.07591 + 1.16595i
$$336$$ 0.529225 0.916644i 0.0288716 0.0500070i
$$337$$ 8.94213 + 5.16274i 0.487109 + 0.281232i 0.723374 0.690456i $$-0.242590\pi$$
−0.236266 + 0.971689i $$0.575924\pi$$
$$338$$ −0.114948 + 0.199096i −0.00625236 + 0.0108294i
$$339$$ 3.35443i 0.182188i
$$340$$ −0.729666 + 3.23774i −0.0395717 + 0.175591i
$$341$$ 5.18209i 0.280626i
$$342$$ 4.75785 2.74695i 0.257275 0.148538i
$$343$$ 13.6325i 0.736086i
$$344$$ −10.6694 −0.575257
$$345$$ −3.39651 + 3.68074i −0.182862 + 0.198164i
$$346$$ 2.69931 + 1.55845i 0.145116 + 0.0837827i
$$347$$ 25.3284 1.35970 0.679850 0.733351i $$-0.262045\pi$$
0.679850 + 0.733351i $$0.262045\pi$$
$$348$$ 1.01268 + 1.75402i 0.0542855 + 0.0940252i
$$349$$ 11.2916 + 19.5576i 0.604426 + 1.04690i 0.992142 + 0.125117i $$0.0399308\pi$$
−0.387716 + 0.921779i $$0.626736\pi$$
$$350$$ 2.27006 4.78066i 0.121340 0.255537i
$$351$$ −3.14999 1.81865i −0.168134 0.0970722i
$$352$$ 0.412800 0.714991i 0.0220023 0.0381091i
$$353$$ −11.5240 19.9601i −0.613360 1.06237i −0.990670 0.136283i $$-0.956484\pi$$
0.377310 0.926087i $$-0.376849\pi$$
$$354$$ −3.65709 6.33426i −0.194372 0.336662i
$$355$$ −2.30436 2.12641i −0.122303 0.112858i
$$356$$ 3.30888i 0.175371i
$$357$$ 0.785516 1.36055i 0.0415739 0.0720081i
$$358$$ 8.68224 5.01269i 0.458871 0.264929i
$$359$$ −15.2488 −0.804799 −0.402400 0.915464i $$-0.631824\pi$$
−0.402400 + 0.915464i $$0.631824\pi$$
$$360$$ −2.13491 + 0.664945i −0.112520 + 0.0350457i
$$361$$ 5.59142 + 9.68463i 0.294285 + 0.509717i
$$362$$ −1.77541 −0.0933135
$$363$$ 8.93598 + 5.15919i 0.469017 + 0.270787i
$$364$$ 3.84989i 0.201789i
$$365$$ 19.2508 + 4.33840i 1.00763 + 0.227082i
$$366$$ 3.23888 5.60990i 0.169299 0.293234i
$$367$$ 5.59808 + 3.23205i 0.292217 + 0.168712i 0.638941 0.769255i $$-0.279373\pi$$
−0.346724 + 0.937967i $$0.612706\pi$$
$$368$$ 1.11991 + 1.93975i 0.0583795 + 0.101116i
$$369$$ −2.85716 −0.148738
$$370$$ −13.5384 + 1.30799i −0.703830 + 0.0679993i
$$371$$ 9.78949 0.508245
$$372$$ 3.13838 + 5.43583i 0.162717 + 0.281835i
$$373$$ 22.1461 + 12.7860i 1.14668 + 0.662036i 0.948076 0.318044i $$-0.103026\pi$$
0.198604 + 0.980080i $$0.436359\pi$$
$$374$$ 0.612709 1.06124i 0.0316824 0.0548756i
$$375$$ −10.3736 + 4.17005i −0.535688 + 0.215340i
$$376$$ 11.7632i 0.606641i
$$377$$ 6.37988 + 3.68342i 0.328580 + 0.189706i
$$378$$ 1.05845 0.0544408
$$379$$ 0.395361 + 0.684786i 0.0203084 + 0.0351751i 0.876001 0.482309i $$-0.160202\pi$$
−0.855693 + 0.517484i $$0.826869\pi$$
$$380$$ −3.65313 11.7290i −0.187402 0.601684i
$$381$$ 6.28010 0.321739
$$382$$ −16.6845 + 9.63281i −0.853654 + 0.492857i
$$383$$ −7.08892 + 12.2784i −0.362227 + 0.627396i −0.988327 0.152347i $$-0.951317\pi$$
0.626100 + 0.779743i $$0.284650\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ −1.32513 + 1.43602i −0.0675348 + 0.0731864i
$$386$$ 9.26016 + 16.0391i 0.471330 + 0.816367i
$$387$$ −5.33471 9.23999i −0.271179 0.469695i
$$388$$ −2.59179 + 4.48912i −0.131578 + 0.227900i
$$389$$ 14.9727 + 8.64452i 0.759149 + 0.438295i 0.828990 0.559264i $$-0.188916\pi$$
−0.0698414 + 0.997558i $$0.522249\pi$$
$$390$$ −5.51565 + 5.97722i −0.279296 + 0.302668i
$$391$$ 1.66226 + 2.87912i 0.0840641 + 0.145603i
$$392$$ −2.93984 5.09196i −0.148484 0.257183i
$$393$$ −13.0284 −0.657196
$$394$$ 4.21694 + 2.43465i 0.212446 + 0.122656i
$$395$$ 5.43605 5.89095i 0.273517 0.296406i
$$396$$ 0.825600 0.0414880
$$397$$ 5.32580i 0.267294i 0.991029 + 0.133647i $$0.0426689\pi$$
−0.991029 + 0.133647i $$0.957331\pi$$
$$398$$ −15.4856 + 8.94064i −0.776225 + 0.448154i
$$399$$ 5.81501i 0.291115i
$$400$$ 0.400968 + 4.98390i 0.0200484 + 0.249195i
$$401$$ 29.8380i 1.49004i −0.667043 0.745019i $$-0.732440\pi$$
0.667043 0.745019i $$-0.267560\pi$$
$$402$$ −6.49307 + 11.2463i −0.323845 + 0.560916i
$$403$$ 19.7717 + 11.4152i 0.984899 + 0.568632i
$$404$$ 5.26023 9.11098i 0.261706 0.453288i
$$405$$ −1.64331 1.51642i −0.0816570 0.0753513i
$$406$$ −2.14375 −0.106392
$$407$$ 4.91613 + 1.02537i 0.243684 + 0.0508258i
$$408$$ 1.48428i 0.0734826i
$$409$$ −6.17878 + 3.56732i −0.305521 + 0.176393i −0.644921 0.764250i $$-0.723110\pi$$
0.339399 + 0.940642i $$0.389776\pi$$
$$410$$ −1.40457 + 6.23251i −0.0693669 + 0.307801i
$$411$$ 3.57869 6.19847i 0.176524 0.305748i
$$412$$ −8.08789 + 14.0086i −0.398462 + 0.690156i
$$413$$ 7.74169 0.380943
$$414$$ −1.11991 + 1.93975i −0.0550407 + 0.0953333i
$$415$$ −10.2964 33.0583i −0.505431 1.62277i
$$416$$ 1.81865 + 3.14999i 0.0891665 + 0.154441i
$$417$$ 11.5306i 0.564655i
$$418$$ 4.53576i 0.221851i
$$419$$ 3.74432 + 6.48535i 0.182922 + 0.316830i 0.942874 0.333149i $$-0.108111\pi$$
−0.759952 + 0.649979i $$0.774778\pi$$
$$420$$ 0.520331 2.30886i 0.0253895 0.112661i
$$421$$ 11.6772i 0.569114i 0.958659 + 0.284557i $$0.0918465\pi$$
−0.958659 + 0.284557i $$0.908153\pi$$
$$422$$ 0.197873 + 0.342726i 0.00963229 + 0.0166836i
$$423$$ −10.1872 + 5.88160i −0.495320 + 0.285973i
$$424$$ −8.00978 + 4.62445i −0.388989 + 0.224583i
$$425$$ 0.595147 + 7.39748i 0.0288689 + 0.358831i
$$426$$ −1.21439 0.701131i −0.0588376 0.0339699i
$$427$$ 3.42819 + 5.93779i 0.165902 + 0.287350i
$$428$$ −12.2112 + 7.05015i −0.590251 + 0.340782i
$$429$$ 2.60063 1.50147i 0.125560 0.0724919i
$$430$$ −22.7783 + 7.09458i −1.09847 + 0.342131i
$$431$$ −12.6642 7.31168i −0.610013 0.352191i 0.162957 0.986633i $$-0.447897\pi$$
−0.772971 + 0.634442i $$0.781230\pi$$
$$432$$ −0.866025 + 0.500000i −0.0416667 + 0.0240563i
$$433$$ 39.9241i 1.91863i −0.282341 0.959314i $$-0.591111\pi$$
0.282341 0.959314i $$-0.408889\pi$$
$$434$$ −6.64363 −0.318905
$$435$$ 3.32831 + 3.07130i 0.159580 + 0.147257i
$$436$$ 5.24991i 0.251425i
$$437$$ −10.6568 6.15268i −0.509782 0.294323i
$$438$$ 8.82512 0.421680
$$439$$ 1.05841 + 0.611072i 0.0505151 + 0.0291649i 0.525045 0.851075i $$-0.324049\pi$$
−0.474530 + 0.880239i $$0.657382\pi$$
$$440$$ 0.405862 1.80093i 0.0193487 0.0858560i
$$441$$ 2.93984 5.09196i 0.139992 0.242474i
$$442$$ 2.69937 + 4.67545i 0.128396 + 0.222389i
$$443$$ 7.35235i 0.349321i −0.984629 0.174660i $$-0.944117\pi$$
0.984629 0.174660i $$-0.0558828\pi$$
$$444$$ −5.77784 + 1.90173i −0.274204 + 0.0902522i
$$445$$ −2.20022 7.06418i −0.104301 0.334874i
$$446$$ −22.1602 + 12.7942i −1.04931 + 0.605822i
$$447$$ 2.63151 + 1.51930i 0.124466 + 0.0718605i
$$448$$ −0.916644 0.529225i −0.0433074 0.0250035i
$$449$$ 10.2005 + 5.88927i 0.481392 + 0.277932i 0.720997 0.692939i $$-0.243684\pi$$
−0.239604 + 0.970871i $$0.577018\pi$$
$$450$$ −4.11570 + 2.83920i −0.194016 + 0.133841i
$$451$$ 1.17944 2.04285i 0.0555375 0.0961939i
$$452$$ 3.35443 0.157779
$$453$$ 7.27481 4.20011i 0.341800 0.197338i
$$454$$ 23.3265 1.09477
$$455$$ −2.55996 8.21918i −0.120013 0.385321i
$$456$$ −2.74695 4.75785i −0.128638 0.222807i
$$457$$ 7.85584 13.6067i 0.367481 0.636496i −0.621690 0.783263i $$-0.713554\pi$$
0.989171 + 0.146768i $$0.0468870\pi$$
$$458$$ 23.3061 1.08902
$$459$$ −1.28542 + 0.742138i −0.0599983 + 0.0346401i
$$460$$ 3.68074 + 3.39651i 0.171615 + 0.158363i
$$461$$ −21.3746 + 12.3407i −0.995517 + 0.574762i −0.906919 0.421306i $$-0.861572\pi$$
−0.0885978 + 0.996067i $$0.528239\pi$$
$$462$$ −0.436928 + 0.756782i −0.0203277 + 0.0352087i
$$463$$ −18.6610 + 32.3218i −0.867249 + 1.50212i −0.00245324 + 0.999997i $$0.500781\pi$$
−0.864796 + 0.502123i $$0.832552\pi$$
$$464$$ 1.75402 1.01268i 0.0814282 0.0470126i
$$465$$ 10.3147 + 9.51817i 0.478332 + 0.441395i
$$466$$ −0.440570 + 0.254363i −0.0204090 + 0.0117831i
$$467$$ 9.17134 0.424399 0.212200 0.977226i $$-0.431937\pi$$
0.212200 + 0.977226i $$0.431937\pi$$
$$468$$ −1.81865 + 3.14999i −0.0840670 + 0.145608i
$$469$$ −6.87259 11.9037i −0.317347 0.549661i
$$470$$ 7.82188 + 25.1134i 0.360797 + 1.15840i
$$471$$ −14.7784 −0.680953
$$472$$ −6.33426 + 3.65709i −0.291558 + 0.168331i
$$473$$ 8.80868 0.405023
$$474$$ 1.79240 3.10453i 0.0823276 0.142596i
$$475$$ −15.5982 22.6112i −0.715696 1.03747i
$$476$$ −1.36055 0.785516i −0.0623609 0.0360041i
$$477$$ −8.00978 4.62445i −0.366743 0.211739i
$$478$$ −5.12135 2.95681i −0.234245 0.135242i
$$479$$ −3.81113 + 2.20036i −0.174135 + 0.100537i −0.584534 0.811369i $$-0.698723\pi$$
0.410399 + 0.911906i $$0.365389\pi$$
$$480$$ 0.664945 + 2.13491i 0.0303504 + 0.0974449i
$$481$$ −14.7415 + 16.4983i −0.672157 + 0.752257i
$$482$$ 1.71616i 0.0781688i
$$483$$ −1.18537 2.05312i −0.0539362 0.0934203i
$$484$$ 5.15919 8.93598i 0.234509 0.406181i
$$485$$ −2.54823 + 11.3073i −0.115709 + 0.513437i
$$486$$ −0.866025 0.500000i −0.0392837 0.0226805i
$$487$$ 21.3719 0.968451 0.484226 0.874943i $$-0.339101\pi$$
0.484226 + 0.874943i $$0.339101\pi$$
$$488$$ −5.60990 3.23888i −0.253948 0.146617i
$$489$$ 3.52691i 0.159492i
$$490$$ −9.66217 8.91604i −0.436492 0.402786i
$$491$$ 17.2381 0.777944 0.388972 0.921250i $$-0.372830\pi$$
0.388972 + 0.921250i $$0.372830\pi$$
$$492$$ 2.85716i 0.128811i
$$493$$ 2.60345 1.50310i 0.117253 0.0676963i
$$494$$ −17.3057 9.99145i −0.778620 0.449536i
$$495$$ 1.76258 0.548978i 0.0792222 0.0246747i
$$496$$ 5.43583 3.13838i 0.244076 0.140917i
$$497$$ 1.28538 0.742112i 0.0576570 0.0332883i
$$498$$ −7.74230 13.4101i −0.346941 0.600919i
$$499$$ 27.1360 + 15.6670i 1.21478 + 0.701351i 0.963796 0.266642i $$-0.0859140\pi$$
0.250979 + 0.967992i $$0.419247\pi$$
$$500$$ 4.17005 + 10.3736i 0.186490 + 0.463920i
$$501$$ 18.5996 10.7385i 0.830969 0.479760i
$$502$$ −14.4741 + 8.35662i −0.646011 + 0.372974i
$$503$$ −7.38550 12.7921i −0.329303 0.570370i 0.653070 0.757297i $$-0.273481\pi$$
−0.982374 + 0.186927i $$0.940147\pi$$
$$504$$ 1.05845i 0.0471471i
$$505$$ 5.17182 22.9489i 0.230143 1.02121i
$$506$$ −0.924600 1.60145i −0.0411035 0.0711933i
$$507$$ 0.229897i 0.0102101i
$$508$$ 6.28010i 0.278634i
$$509$$ 10.6815 + 18.5009i 0.473449 + 0.820039i 0.999538 0.0303912i $$-0.00967531\pi$$
−0.526089 + 0.850430i $$0.676342\pi$$
$$510$$ 0.986962 + 3.16880i 0.0437034 + 0.140317i
$$511$$ −4.67047 + 8.08949i −0.206609 + 0.357858i
$$512$$ 1.00000 0.0441942
$$513$$ 2.74695 4.75785i 0.121281 0.210064i
$$514$$ −1.47817 + 2.56026i −0.0651991 + 0.112928i
$$515$$ −7.95196 + 35.2852i −0.350405 + 1.55485i
$$516$$ −9.23999 + 5.33471i −0.406768 + 0.234848i
$$517$$ 9.71171i 0.427120i
$$518$$ 1.31456 6.30267i 0.0577586 0.276923i
$$519$$ 3.11690 0.136817
$$520$$ 5.97722 + 5.51565i 0.262118 + 0.241877i
$$521$$ 16.6844 28.8982i 0.730957 1.26606i −0.225517 0.974239i $$-0.572407\pi$$
0.956474 0.291816i $$-0.0942595\pi$$
$$522$$ 1.75402 + 1.01268i 0.0767713 + 0.0443239i
$$523$$ −6.52639 + 11.3040i −0.285379 + 0.494291i −0.972701 0.232062i $$-0.925453\pi$$
0.687322 + 0.726353i $$0.258786\pi$$
$$524$$ 13.0284i 0.569148i
$$525$$ −0.424404 5.27520i −0.0185225 0.230229i
$$526$$ 18.3663i 0.800807i
$$527$$ 8.06828 4.65822i 0.351460 0.202915i
$$528$$ 0.825600i 0.0359296i
$$529$$ −17.9832 −0.781878
$$530$$ −14.0252 + 15.1989i −0.609215 + 0.660196i
$$531$$ −6.33426 3.65709i −0.274884 0.158704i
$$532$$ 5.81501 0.252113
$$533$$ 5.19617 + 9.00003i 0.225071 + 0.389835i
$$534$$ −1.65444 2.86558i −0.0715947 0.124006i
$$535$$ −21.3819 + 23.1712i −0.924420 + 1.00178i
$$536$$ 11.2463 + 6.49307i 0.485768 + 0.280458i
$$537$$ 5.01269 8.68224i 0.216314 0.374666i
$$538$$ −11.5721 20.0434i −0.498908 0.864134i
$$539$$ 2.42713 + 4.20392i 0.104544 + 0.181076i
$$540$$ −1.51642 + 1.64331i −0.0652561 + 0.0707170i
$$541$$ 21.6228i 0.929635i 0.885406 + 0.464818i $$0.153880\pi$$
−0.885406 + 0.464818i $$0.846120\pi$$
$$542$$ 8.12733 14.0769i 0.349099 0.604657i
$$543$$ −1.53755 + 0.887705i −0.0659826 + 0.0380951i
$$544$$ 1.48428 0.0636378
$$545$$ −3.49090 11.2081i −0.149534 0.480102i
$$546$$ −1.92495 3.33410i −0.0823801 0.142686i
$$547$$ −19.0025 −0.812488 −0.406244 0.913765i $$-0.633162\pi$$
−0.406244 + 0.913765i $$0.633162\pi$$
$$548$$ −6.19847 3.57869i −0.264785 0.152874i
$$549$$ 6.47775i 0.276464i
$$550$$ −0.331039 4.11471i −0.0141156 0.175452i
$$551$$ −5.56357 + 9.63638i −0.237016 + 0.410524i
$$552$$ 1.93975 + 1.11991i 0.0825610 + 0.0476666i
$$553$$ 1.89716 + 3.28599i 0.0806757 + 0.139734i
$$554$$ 4.66812 0.198329
$$555$$ −11.0706 + 7.90197i −0.469922 + 0.335420i
$$556$$ 11.5306 0.489006
$$557$$ 18.9136 + 32.7593i 0.801395 + 1.38806i 0.918698 + 0.394960i $$0.129242\pi$$
−0.117304 + 0.993096i $$0.537425\pi$$
$$558$$ 5.43583 + 3.13838i 0.230117 + 0.132858i
$$559$$ −19.4039 + 33.6086i −0.820698 + 1.42149i
$$560$$ −2.30886 0.520331i −0.0975671 0.0219880i
$$561$$ 1.22542i 0.0517372i
$$562$$ −12.2372 7.06515i −0.516195 0.298025i
$$563$$ 2.80373 0.118163 0.0590815 0.998253i $$-0.481183\pi$$
0.0590815 + 0.998253i $$0.481183\pi$$
$$564$$ 5.88160 + 10.1872i 0.247660 + 0.428960i
$$565$$ 7.16141 2.23051i 0.301283 0.0938383i
$$566$$ 10.0287 0.421539
$$567$$ 0.916644 0.529225i 0.0384954 0.0222254i
$$568$$ −0.701131 + 1.21439i −0.0294188 + 0.0509549i
$$569$$ 39.6236i 1.66111i 0.556937 + 0.830555i $$0.311976\pi$$
−0.556937 + 0.830555i $$0.688024\pi$$
$$570$$ −9.02819 8.33102i −0.378149 0.348948i
$$571$$ −3.77916 6.54570i −0.158153 0.273929i 0.776050 0.630672i $$-0.217221\pi$$
−0.934203 + 0.356743i $$0.883887\pi$$
$$572$$ −1.50147 2.60063i −0.0627798 0.108738i
$$573$$ −9.63281 + 16.6845i −0.402416 + 0.697006i
$$574$$ −2.61900 1.51208i −0.109315 0.0631131i
$$575$$ 10.1165 + 4.80375i 0.421889 + 0.200330i
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ −14.7782 25.5966i −0.615224 1.06560i −0.990345 0.138624i $$-0.955732\pi$$
0.375121 0.926976i $$-0.377601\pi$$
$$578$$ −14.7969 −0.615471
$$579$$ 16.0391 + 9.26016i 0.666561 + 0.384839i
$$580$$ 3.07130 3.32831i 0.127529 0.138201i
$$581$$ 16.3897 0.679958
$$582$$ 5.18358i 0.214867i
$$583$$ 6.61288 3.81795i 0.273877 0.158123i
$$584$$ 8.82512i 0.365186i
$$585$$ −1.78808 + 7.93425i −0.0739281 + 0.328041i
$$586$$ 0.948825i 0.0391956i
$$587$$ 16.1870 28.0366i 0.668108 1.15720i −0.310325 0.950631i $$-0.600438\pi$$
0.978433 0.206566i $$-0.0662288\pi$$
$$588$$ −5.09196 2.93984i −0.209989 0.121237i
$$589$$ −17.2419 + 29.8639i −0.710441 + 1.23052i
$$590$$ −11.0913 + 12.0195i −0.456623 + 0.494835i
$$591$$ 4.86930 0.200296
$$592$$ 1.90173 + 5.77784i 0.0781607 + 0.237468i
$$593$$ 8.03864i 0.330107i −0.986285 0.165054i $$-0.947220\pi$$
0.986285 0.165054i $$-0.0527797\pi$$
$$594$$ 0.714991 0.412800i 0.0293364 0.0169374i
$$595$$ −3.42699 0.772315i −0.140493 0.0316618i
$$596$$ 1.51930 2.63151i 0.0622330 0.107791i
$$597$$ −8.94064 + 15.4856i −0.365916 + 0.633785i
$$598$$ 8.14690 0.333151
$$599$$ −1.25133 + 2.16737i −0.0511279 + 0.0885562i −0.890457 0.455068i $$-0.849615\pi$$
0.839329 + 0.543624i $$0.182948\pi$$
$$600$$ 2.83920 + 4.11570i 0.115910 + 0.168023i
$$601$$ 8.38293 + 14.5197i 0.341947 + 0.592269i 0.984794 0.173725i $$-0.0555804\pi$$
−0.642847 + 0.765994i $$0.722247\pi$$
$$602$$ 11.2930i 0.460270i
$$603$$ 12.9861i 0.528837i
$$604$$ −4.20011 7.27481i −0.170900 0.296008i
$$605$$ 5.07249 22.5081i 0.206226 0.915085i
$$606$$ 10.5205i 0.427364i
$$607$$ −5.24017 9.07623i −0.212692 0.368393i 0.739864 0.672756i $$-0.234890\pi$$
−0.952556 + 0.304363i $$0.901556\pi$$
$$608$$ −4.75785 + 2.74695i −0.192956 + 0.111403i
$$609$$ −1.85654 + 1.07187i −0.0752308 + 0.0434345i
$$610$$ −14.1303 3.18444i −0.572120 0.128934i
$$611$$ 37.0540 + 21.3931i 1.49904 + 0.865473i
$$612$$ 0.742138 + 1.28542i 0.0299992 + 0.0519601i
$$613$$ 5.61834 3.24375i 0.226923 0.131014i −0.382229 0.924068i $$-0.624843\pi$$
0.609152 + 0.793054i $$0.291510\pi$$
$$614$$ 11.1694 6.44866i 0.450760 0.260247i
$$615$$ 1.89986 + 6.09979i 0.0766096 + 0.245967i
$$616$$ 0.756782 + 0.436928i 0.0304916 + 0.0176043i
$$617$$ −20.5224 + 11.8486i −0.826200 + 0.477007i −0.852550 0.522646i $$-0.824945\pi$$
0.0263501 + 0.999653i $$0.491612\pi$$
$$618$$ 16.1758i 0.650685i
$$619$$ −31.0146 −1.24658 −0.623291 0.781990i $$-0.714205\pi$$
−0.623291 + 0.781990i $$0.714205\pi$$
$$620$$ 9.51817 10.3147i 0.382259 0.414248i
$$621$$ 2.23982i 0.0898811i
$$622$$ 22.1356 + 12.7800i 0.887558 + 0.512432i
$$623$$ 3.50229 0.140316
$$624$$ 3.14999 + 1.81865i 0.126100 + 0.0728041i
$$625$$ 15.8005 + 19.3738i 0.632021 + 0.774951i
$$626$$ 2.35334 4.07611i 0.0940585 0.162914i
$$627$$ 2.26788 + 3.92808i 0.0905703 + 0.156872i
$$628$$ 14.7784i 0.589722i
$$629$$ 2.82270 + 8.57591i 0.112548 + 0.341944i
$$630$$ −0.703810 2.25970i −0.0280405 0.0900285i
$$631$$ 9.21344 5.31938i 0.366781 0.211761i −0.305270 0.952266i $$-0.598747\pi$$
0.672051 + 0.740504i $$0.265413\pi$$
$$632$$ −3.10453 1.79240i −0.123491 0.0712978i
$$633$$ 0.342726 + 0.197873i 0.0136221 + 0.00786473i
$$634$$ −21.7227 12.5416i −0.862719 0.498091i
$$635$$ −4.17592 13.4075i −0.165716 0.532059i
$$636$$ −4.62445 + 8.00978i −0.183371 + 0.317609i
$$637$$ −21.3861 −0.847349
$$638$$ −1.44812 + 0.836071i −0.0573315 + 0.0331004i
$$639$$ −1.40226 −0.0554726
$$640$$ 2.13491 0.664945i 0.0843898 0.0262842i
$$641$$ 4.38870 + 7.60145i 0.173343 + 0.300239i 0.939587 0.342311i $$-0.111210\pi$$
−0.766243 + 0.642550i $$0.777876\pi$$
$$642$$ −7.05015 + 12.2112i −0.278247 + 0.481938i
$$643$$ 26.7207 1.05376 0.526882 0.849939i $$-0.323361\pi$$
0.526882 + 0.849939i $$0.323361\pi$$
$$644$$ −2.05312 + 1.18537i −0.0809044 + 0.0467102i
$$645$$ −16.1793 + 17.5332i −0.637059 + 0.690370i
$$646$$ −7.06197 + 4.07723i −0.277849 + 0.160416i
$$647$$ −9.72305 + 16.8408i −0.382252 + 0.662081i −0.991384 0.130989i $$-0.958185\pi$$
0.609131 + 0.793069i $$0.291518\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ 5.22957 3.01929i 0.205278 0.118518i
$$650$$ 16.4284 + 7.80090i 0.644376 + 0.305977i
$$651$$ −5.75355 + 3.32182i −0.225500 + 0.130192i
$$652$$ −3.52691 −0.138124
$$653$$ 12.7773 22.1309i 0.500014 0.866049i −0.499986 0.866033i $$-0.666662\pi$$
1.00000 1.60106e-5i $$-5.09633e-6\pi$$
$$654$$ −2.62496 4.54656i −0.102644 0.177785i
$$655$$ 8.66317 + 27.8145i 0.338498 + 1.08680i
$$656$$ 2.85716 0.111554
$$657$$ 7.64277 4.41256i 0.298173 0.172150i
$$658$$ −12.4508 −0.485381
$$659$$ 1.11439 1.93019i 0.0434106 0.0751893i −0.843504 0.537123i $$-0.819511\pi$$
0.886914 + 0.461934i $$0.152844\pi$$
$$660$$ −0.548978 1.76258i −0.0213690 0.0686085i
$$661$$ 10.9781 + 6.33818i 0.426997 + 0.246527i 0.698066 0.716033i $$-0.254044\pi$$
−0.271070 + 0.962560i $$0.587377\pi$$
$$662$$ −7.92971 4.57822i −0.308197 0.177938i
$$663$$ 4.67545 + 2.69937i 0.181580 + 0.104835i
$$664$$ −13.4101 + 7.74230i −0.520411 + 0.300460i
$$665$$ 12.4145 3.86666i 0.481415 0.149943i
$$666$$ −4.05289 + 4.53587i −0.157046 + 0.175761i
$$667$$ 4.53646i 0.175653i
$$668$$ −10.7385 18.5996i −0.415485 0.719641i
$$669$$ −12.7942 + 22.1602i −0.494651 + 0.856761i
$$670$$ 28.3275 + 6.38395i 1.09439 + 0.246634i
$$671$$ 4.63153 + 2.67402i 0.178798 + 0.103229i
$$672$$ −1.05845 −0.0408306
$$673$$ −34.8308 20.1096i −1.34263 0.775168i −0.355438 0.934700i $$-0.615668\pi$$
−0.987193 + 0.159532i $$0.949002\pi$$
$$674$$ 10.3255i 0.397723i
$$675$$ −2.14470 + 4.51666i −0.0825495 + 0.173847i
$$676$$ 0.229897 0.00884218
$$677$$ 29.7892i 1.14489i −0.819942 0.572446i $$-0.805995\pi$$
0.819942 0.572446i $$-0.194005\pi$$
$$678$$ 2.90502 1.67721i 0.111567 0.0644130i
$$679$$ −4.75150 2.74328i −0.182346 0.105277i
$$680$$ 3.16880 0.986962i 0.121518 0.0378483i
$$681$$ 20.2013 11.6633i 0.774117 0.446937i
$$682$$ −4.48782 + 2.59105i −0.171848 + 0.0992163i
$$683$$ −10.7369 18.5968i −0.410835 0.711587i 0.584146 0.811649i $$-0.301429\pi$$
−0.994981 + 0.100061i $$0.968096\pi$$
$$684$$ −4.75785 2.74695i −0.181921 0.105032i
$$685$$ −15.6128 3.51854i −0.596535 0.134437i
$$686$$ 11.8061 6.81625i 0.450759 0.260246i
$$687$$ 20.1837 11.6531i 0.770055 0.444592i
$$688$$ 5.33471 + 9.23999i 0.203384 + 0.352271i
$$689$$ 33.6410i 1.28162i
$$690$$ 4.88587 + 1.10109i 0.186002 + 0.0419178i
$$691$$ 7.87430 + 13.6387i 0.299553 + 0.518840i 0.976034 0.217620i $$-0.0698293\pi$$
−0.676481 + 0.736460i $$0.736496\pi$$
$$692$$ 3.11690i 0.118487i
$$693$$ 0.873856i 0.0331950i
$$694$$ −12.6642 21.9350i −0.480727 0.832643i
$$695$$ 24.6168 7.66721i 0.933768 0.290834i
$$696$$ 1.01268 1.75402i 0.0383856 0.0664859i
$$697$$ 4.24082 0.160633
$$698$$ 11.2916 19.5576i 0.427394 0.740268i
$$699$$ −0.254363 + 0.440570i −0.00962089 + 0.0166639i
$$700$$ −5.27520 + 0.424404i −0.199384 + 0.0160410i
$$701$$ −32.3179 + 18.6588i −1.22063 + 0.704732i −0.965053 0.262056i $$-0.915600\pi$$
−0.255579 + 0.966788i $$0.582266\pi$$
$$702$$ 3.63729i 0.137281i
$$703$$ −24.9196 22.2661i −0.939859 0.839783i
$$704$$ −0.825600 −0.0311160
$$705$$ 19.3307 + 17.8379i 0.728035 + 0.671815i
$$706$$ −11.5240 + 19.9601i −0.433711 + 0.751209i
$$707$$ 9.64351 + 5.56768i 0.362682 + 0.209394i
$$708$$ −3.65709 + 6.33426i −0.137442 + 0.238056i
$$709$$ 27.0809i 1.01705i −0.861048 0.508523i $$-0.830192\pi$$
0.861048 0.508523i $$-0.169808\pi$$
$$710$$ −0.689348 + 3.05884i −0.0258708 + 0.114796i
$$711$$ 3.58480i 0.134440i
$$712$$ −2.86558 + 1.65444i −0.107392 + 0.0620028i
$$713$$ 14.0588i 0.526508i
$$714$$ −1.57103 −0.0587944
$$715$$ −4.93479 4.55372i −0.184551 0.170299i
$$716$$ −8.68224 5.01269i −0.324471 0.187333i
$$717$$ −5.91363 −0.220849
$$718$$ 7.62438 + 13.2058i 0.284539 + 0.492837i
$$719$$ −0.353769 0.612746i −0.0131934 0.0228516i 0.859353 0.511382i $$-0.170866\pi$$
−0.872547 + 0.488531i $$0.837533\pi$$
$$720$$ 1.64331 + 1.51642i 0.0612427 + 0.0565135i
$$721$$ −14.8274 8.56062i −0.552202 0.318814i
$$722$$ 5.59142 9.68463i 0.208091 0.360425i
$$723$$ −0.858078 1.48624i −0.0319123 0.0552737i
$$724$$ 0.887705 + 1.53755i 0.0329913 + 0.0571426i
$$725$$ 4.34380 9.14790i 0.161325 0.339744i
$$726$$ 10.3184i 0.382951i
$$727$$ −25.3278 + 43.8690i −0.939356 + 1.62701i −0.172680 + 0.984978i $$0.555243\pi$$
−0.766676 + 0.642034i $$0.778091\pi$$
$$728$$ −3.33410 + 1.92495i −0.123570 + 0.0713432i
$$729$$ −1.00000 −0.0370370
$$730$$ −5.86821 18.8408i −0.217192 0.697331i
$$731$$ 7.91819 + 13.7147i 0.292865 + 0.507257i
$$732$$ −6.47775 −0.239425
$$733$$ 29.3112 + 16.9228i 1.08263 + 0.625058i 0.931605 0.363471i $$-0.118408\pi$$
0.151027 + 0.988530i $$0.451742\pi$$
$$734$$ 6.46411i 0.238595i
$$735$$ −12.8257 2.89043i −0.473083 0.106615i
$$736$$ 1.11991 1.93975i 0.0412805 0.0715000i
$$737$$ −9.28497 5.36068i −0.342016 0.197463i
$$738$$ 1.42858 + 2.47438i 0.0525868 + 0.0910831i
$$739$$ −13.7161 −0.504555 −0.252277 0.967655i $$-0.581180\pi$$
−0.252277 + 0.967655i $$0.581180\pi$$
$$740$$ 7.90197 + 11.0706i 0.290482 + 0.406964i
$$741$$ −19.9829 −0.734090
$$742$$ −4.89475 8.47795i −0.179692 0.311235i
$$743$$ 13.8765 + 8.01159i 0.509079 + 0.293917i 0.732455 0.680816i $$-0.238375\pi$$
−0.223376 + 0.974732i $$0.571708\pi$$
$$744$$ 3.13838 5.43583i 0.115059 0.199287i
$$745$$ 1.49377 6.62829i 0.0547274 0.242842i
$$746$$ 25.5721i 0.936260i
$$747$$ −13.4101 7.74230i −0.490649 0.283276i
$$748$$ −1.22542 −0.0448058
$$749$$ −7.46223 12.9250i −0.272664 0.472268i
$$750$$ 8.79815 + 6.89874i 0.321263 + 0.251906i
$$751$$ 33.4440 1.22039 0.610195 0.792251i $$-0.291091\pi$$
0.610195 + 0.792251i $$0.291091\pi$$
$$752$$ 10.1872 5.88160i 0.371490 0.214480i
$$753$$ −8.35662 + 14.4741i −0.304532 + 0.527465i
$$754$$ 7.36685i 0.268285i
$$755$$ −13.8042 12.7382i −0.502387 0.463592i
$$756$$ −0.529225 0.916644i −0.0192477 0.0333380i
$$757$$ 25.2767 + 43.7805i 0.918697 + 1.59123i 0.801396 + 0.598134i $$0.204091\pi$$
0.117301 + 0.993096i $$0.462576\pi$$
$$758$$ 0.395361 0.684786i 0.0143602 0.0248726i
$$759$$ −1.60145 0.924600i −0.0581291 0.0335608i
$$760$$ −8.33102 + 9.02819i −0.302198 + 0.327487i
$$761$$ −19.6784 34.0840i −0.713341 1.23554i −0.963596 0.267362i $$-0.913848\pi$$
0.250255 0.968180i $$-0.419485\pi$$
$$762$$ −3.14005 5.43873i −0.113752 0.197024i
$$763$$ 5.55677 0.201169
$$764$$ 16.6845 + 9.63281i 0.603625 + 0.348503i
$$765$$ 2.43913 + 2.25078i 0.0881871 + 0.0813771i
$$766$$ 14.1778 0.512267
$$767$$ 26.6038i 0.960607i
$$768$$ 0.866025 0.500000i 0.0312500 0.0180422i
$$769$$ 4.77703i 0.172264i 0.996284 + 0.0861320i $$0.0274507\pi$$
−0.996284 + 0.0861320i $$0.972549\pi$$
$$770$$ 1.90619 + 0.429585i 0.0686945 + 0.0154812i
$$771$$ 2.95633i 0.106470i
$$772$$ 9.26016 16.0391i 0.333280 0.577259i
$$773$$ 11.8192 + 6.82383i 0.425108 + 0.245436i 0.697260 0.716818i $$-0.254402\pi$$
−0.272153 + 0.962254i $$0.587736\pi$$
$$774$$ −5.33471 + 9.23999i −0.191752 + 0.332125i
$$775$$ 13.4618 28.3500i 0.483561 1.01836i
$$776$$ 5.18358 0.186080
$$777$$