# Properties

 Label 28.2.f.a.19.2 Level $28$ Weight $2$ Character 28.19 Analytic conductor $0.224$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 28.f (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.223581125660$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 19.2 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 28.19 Dual form 28.2.f.a.3.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 - 2.36603i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(3.00000 + 1.73205i) q^{12} +3.46410i q^{13} +(-2.09808 + 3.09808i) q^{14} +3.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.50000 + 0.866025i) q^{17} +(2.59808 - 4.50000i) q^{19} +3.46410 q^{20} +(1.50000 - 4.33013i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-4.73205 + 1.26795i) q^{26} -5.19615 q^{27} +(-5.00000 - 1.73205i) q^{28} +4.00000 q^{29} +(-4.09808 + 1.09808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(5.46410 + 1.46410i) q^{32} +(1.50000 + 0.866025i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(7.09808 + 1.90192i) q^{38} +(5.19615 - 3.00000i) q^{39} +(1.26795 + 4.73205i) q^{40} -3.46410i q^{41} +(6.46410 + 0.464102i) q^{42} +2.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(0.366025 - 1.36603i) q^{46} +(-4.33013 + 7.50000i) q^{47} -6.92820 q^{48} +(-1.00000 + 6.92820i) q^{49} +(2.00000 - 2.00000i) q^{50} +(2.59808 + 1.50000i) q^{51} +(-3.46410 - 6.00000i) q^{52} +(0.500000 + 0.866025i) q^{53} +(-1.90192 - 7.09808i) q^{54} +1.73205 q^{55} +(0.535898 - 7.46410i) q^{56} -9.00000 q^{57} +(1.46410 + 5.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 + 1.73205i) q^{62} +8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(-0.633975 + 2.36603i) q^{66} +(-2.59808 + 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} +1.73205i q^{69} +(5.83013 - 2.83013i) q^{70} -14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-4.09808 - 1.09808i) q^{74} +(-1.73205 + 3.00000i) q^{75} +10.3923i q^{76} +(-2.50000 - 0.866025i) q^{77} +(6.00000 + 6.00000i) q^{78} +(-7.79423 - 4.50000i) q^{79} +(-6.00000 + 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.73205 - 1.26795i) q^{82} +13.8564 q^{83} +(1.73205 + 9.00000i) q^{84} +3.00000 q^{85} +(-2.73205 + 0.732051i) q^{86} +(-3.46410 - 6.00000i) q^{87} +(2.73205 + 0.732051i) q^{88} +(13.5000 + 7.79423i) q^{89} +(-6.92820 + 6.00000i) q^{91} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-11.8301 - 3.16987i) q^{94} +(-7.79423 + 4.50000i) q^{95} +(-2.53590 - 9.46410i) q^{96} -17.3205i q^{97} +(-9.83013 + 1.16987i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + O(q^{10})$$ $$4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + 6 q^{10} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 6 q^{17} + 6 q^{21} - 4 q^{22} - 12 q^{24} - 4 q^{25} - 12 q^{26} - 20 q^{28} + 16 q^{29} - 6 q^{30} + 8 q^{32} + 6 q^{33} - 6 q^{37} + 18 q^{38} + 12 q^{40} + 12 q^{42} + 4 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{50} + 2 q^{53} - 18 q^{54} + 16 q^{56} - 36 q^{57} - 8 q^{58} - 12 q^{60} - 18 q^{61} + 12 q^{65} - 6 q^{66} + 6 q^{70} + 30 q^{73} - 6 q^{74} - 10 q^{77} + 24 q^{78} - 24 q^{80} + 18 q^{81} + 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} + 54 q^{89} + 8 q^{92} + 6 q^{93} - 30 q^{94} - 24 q^{96} - 22 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$17$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ −0.866025 1.50000i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i $$-0.459925\pi$$
−0.796387 + 0.604787i $$0.793258\pi$$
$$6$$ 1.73205 1.73205i 0.707107 0.707107i
$$7$$ 1.73205 + 2.00000i 0.654654 + 0.755929i
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 0 0
$$10$$ 0.633975 2.36603i 0.200480 0.748203i
$$11$$ −0.866025 + 0.500000i −0.261116 + 0.150756i −0.624844 0.780750i $$-0.714837\pi$$
0.363727 + 0.931505i $$0.381504\pi$$
$$12$$ 3.00000 + 1.73205i 0.866025 + 0.500000i
$$13$$ 3.46410i 0.960769i 0.877058 + 0.480384i $$0.159503\pi$$
−0.877058 + 0.480384i $$0.840497\pi$$
$$14$$ −2.09808 + 3.09808i −0.560734 + 0.827996i
$$15$$ 3.00000i 0.774597i
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ −1.50000 + 0.866025i −0.363803 + 0.210042i −0.670748 0.741685i $$-0.734027\pi$$
0.306944 + 0.951727i $$0.400693\pi$$
$$18$$ 0 0
$$19$$ 2.59808 4.50000i 0.596040 1.03237i −0.397360 0.917663i $$-0.630073\pi$$
0.993399 0.114708i $$-0.0365932\pi$$
$$20$$ 3.46410 0.774597
$$21$$ 1.50000 4.33013i 0.327327 0.944911i
$$22$$ −1.00000 1.00000i −0.213201 0.213201i
$$23$$ −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i $$-0.366580\pi$$
−0.587565 + 0.809177i $$0.699913\pi$$
$$24$$ −1.26795 + 4.73205i −0.258819 + 0.965926i
$$25$$ −1.00000 1.73205i −0.200000 0.346410i
$$26$$ −4.73205 + 1.26795i −0.928032 + 0.248665i
$$27$$ −5.19615 −1.00000
$$28$$ −5.00000 1.73205i −0.944911 0.327327i
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ −4.09808 + 1.09808i −0.748203 + 0.200480i
$$31$$ 0.866025 + 1.50000i 0.155543 + 0.269408i 0.933257 0.359211i $$-0.116954\pi$$
−0.777714 + 0.628619i $$0.783621\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ 1.50000 + 0.866025i 0.261116 + 0.150756i
$$34$$ −1.73205 1.73205i −0.297044 0.297044i
$$35$$ −0.866025 4.50000i −0.146385 0.760639i
$$36$$ 0 0
$$37$$ −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i $$-0.912646\pi$$
0.715981 + 0.698119i $$0.245980\pi$$
$$38$$ 7.09808 + 1.90192i 1.15146 + 0.308533i
$$39$$ 5.19615 3.00000i 0.832050 0.480384i
$$40$$ 1.26795 + 4.73205i 0.200480 + 0.748203i
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 6.46410 + 0.464102i 0.997433 + 0.0716124i
$$43$$ 2.00000i 0.304997i 0.988304 + 0.152499i $$0.0487319\pi$$
−0.988304 + 0.152499i $$0.951268\pi$$
$$44$$ 1.00000 1.73205i 0.150756 0.261116i
$$45$$ 0 0
$$46$$ 0.366025 1.36603i 0.0539675 0.201409i
$$47$$ −4.33013 + 7.50000i −0.631614 + 1.09399i 0.355608 + 0.934635i $$0.384274\pi$$
−0.987222 + 0.159352i $$0.949059\pi$$
$$48$$ −6.92820 −1.00000
$$49$$ −1.00000 + 6.92820i −0.142857 + 0.989743i
$$50$$ 2.00000 2.00000i 0.282843 0.282843i
$$51$$ 2.59808 + 1.50000i 0.363803 + 0.210042i
$$52$$ −3.46410 6.00000i −0.480384 0.832050i
$$53$$ 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i $$-0.144788\pi$$
−0.829640 + 0.558298i $$0.811454\pi$$
$$54$$ −1.90192 7.09808i −0.258819 0.965926i
$$55$$ 1.73205 0.233550
$$56$$ 0.535898 7.46410i 0.0716124 0.997433i
$$57$$ −9.00000 −1.19208
$$58$$ 1.46410 + 5.46410i 0.192246 + 0.717472i
$$59$$ 2.59808 + 4.50000i 0.338241 + 0.585850i 0.984102 0.177605i $$-0.0568349\pi$$
−0.645861 + 0.763455i $$0.723502\pi$$
$$60$$ −3.00000 5.19615i −0.387298 0.670820i
$$61$$ −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i $$-0.441276\pi$$
−0.759608 + 0.650381i $$0.774609\pi$$
$$62$$ −1.73205 + 1.73205i −0.219971 + 0.219971i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 3.00000 5.19615i 0.372104 0.644503i
$$66$$ −0.633975 + 2.36603i −0.0780369 + 0.291238i
$$67$$ −2.59808 + 1.50000i −0.317406 + 0.183254i −0.650236 0.759733i $$-0.725330\pi$$
0.332830 + 0.942987i $$0.391996\pi$$
$$68$$ 1.73205 3.00000i 0.210042 0.363803i
$$69$$ 1.73205i 0.208514i
$$70$$ 5.83013 2.83013i 0.696833 0.338265i
$$71$$ 14.0000i 1.66149i −0.556650 0.830747i $$-0.687914\pi$$
0.556650 0.830747i $$-0.312086\pi$$
$$72$$ 0 0
$$73$$ 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i $$-0.497494\pi$$
0.869935 + 0.493166i $$0.164160\pi$$
$$74$$ −4.09808 1.09808i −0.476392 0.127649i
$$75$$ −1.73205 + 3.00000i −0.200000 + 0.346410i
$$76$$ 10.3923i 1.19208i
$$77$$ −2.50000 0.866025i −0.284901 0.0986928i
$$78$$ 6.00000 + 6.00000i 0.679366 + 0.679366i
$$79$$ −7.79423 4.50000i −0.876919 0.506290i −0.00727784 0.999974i $$-0.502317\pi$$
−0.869641 + 0.493684i $$0.835650\pi$$
$$80$$ −6.00000 + 3.46410i −0.670820 + 0.387298i
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ 4.73205 1.26795i 0.522568 0.140022i
$$83$$ 13.8564 1.52094 0.760469 0.649374i $$-0.224969\pi$$
0.760469 + 0.649374i $$0.224969\pi$$
$$84$$ 1.73205 + 9.00000i 0.188982 + 0.981981i
$$85$$ 3.00000 0.325396
$$86$$ −2.73205 + 0.732051i −0.294605 + 0.0789391i
$$87$$ −3.46410 6.00000i −0.371391 0.643268i
$$88$$ 2.73205 + 0.732051i 0.291238 + 0.0780369i
$$89$$ 13.5000 + 7.79423i 1.43100 + 0.826187i 0.997197 0.0748225i $$-0.0238390\pi$$
0.433800 + 0.901009i $$0.357172\pi$$
$$90$$ 0 0
$$91$$ −6.92820 + 6.00000i −0.726273 + 0.628971i
$$92$$ 2.00000 0.208514
$$93$$ 1.50000 2.59808i 0.155543 0.269408i
$$94$$ −11.8301 3.16987i −1.22018 0.326947i
$$95$$ −7.79423 + 4.50000i −0.799671 + 0.461690i
$$96$$ −2.53590 9.46410i −0.258819 0.965926i
$$97$$ 17.3205i 1.75863i −0.476240 0.879316i $$-0.658000\pi$$
0.476240 0.879316i $$-0.342000\pi$$
$$98$$ −9.83013 + 1.16987i −0.992993 + 0.118175i
$$99$$ 0 0
$$100$$ 3.46410 + 2.00000i 0.346410 + 0.200000i
$$101$$ −7.50000 + 4.33013i −0.746278 + 0.430864i −0.824347 0.566084i $$-0.808458\pi$$
0.0780696 + 0.996948i $$0.475124\pi$$
$$102$$ −1.09808 + 4.09808i −0.108726 + 0.405770i
$$103$$ 4.33013 7.50000i 0.426660 0.738997i −0.569914 0.821705i $$-0.693023\pi$$
0.996574 + 0.0827075i $$0.0263567\pi$$
$$104$$ 6.92820 6.92820i 0.679366 0.679366i
$$105$$ −6.00000 + 5.19615i −0.585540 + 0.507093i
$$106$$ −1.00000 + 1.00000i −0.0971286 + 0.0971286i
$$107$$ 11.2583 + 6.50000i 1.08838 + 0.628379i 0.933146 0.359498i $$-0.117052\pi$$
0.155238 + 0.987877i $$0.450386\pi$$
$$108$$ 9.00000 5.19615i 0.866025 0.500000i
$$109$$ −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i $$-0.308513\pi$$
−0.996962 + 0.0778949i $$0.975180\pi$$
$$110$$ 0.633975 + 2.36603i 0.0604471 + 0.225592i
$$111$$ 5.19615 0.493197
$$112$$ 10.3923 2.00000i 0.981981 0.188982i
$$113$$ −16.0000 −1.50515 −0.752577 0.658505i $$-0.771189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ −3.29423 12.2942i −0.308533 1.15146i
$$115$$ 0.866025 + 1.50000i 0.0807573 + 0.139876i
$$116$$ −6.92820 + 4.00000i −0.643268 + 0.371391i
$$117$$ 0 0
$$118$$ −5.19615 + 5.19615i −0.478345 + 0.478345i
$$119$$ −4.33013 1.50000i −0.396942 0.137505i
$$120$$ 6.00000 6.00000i 0.547723 0.547723i
$$121$$ −5.00000 + 8.66025i −0.454545 + 0.787296i
$$122$$ 1.90192 7.09808i 0.172192 0.642630i
$$123$$ −5.19615 + 3.00000i −0.468521 + 0.270501i
$$124$$ −3.00000 1.73205i −0.269408 0.155543i
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 6.00000i 0.532414i 0.963916 + 0.266207i $$0.0857705\pi$$
−0.963916 + 0.266207i $$0.914230\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ 3.00000 1.73205i 0.264135 0.152499i
$$130$$ 8.19615 + 2.19615i 0.718850 + 0.192615i
$$131$$ −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i $$-0.906223\pi$$
0.729921 + 0.683531i $$0.239557\pi$$
$$132$$ −3.46410 −0.301511
$$133$$ 13.5000 2.59808i 1.17060 0.225282i
$$134$$ −3.00000 3.00000i −0.259161 0.259161i
$$135$$ 7.79423 + 4.50000i 0.670820 + 0.387298i
$$136$$ 4.73205 + 1.26795i 0.405770 + 0.108726i
$$137$$ −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i $$-0.180268\pi$$
−0.886594 + 0.462549i $$0.846935\pi$$
$$138$$ −2.36603 + 0.633975i −0.201409 + 0.0539675i
$$139$$ −6.92820 −0.587643 −0.293821 0.955860i $$-0.594927\pi$$
−0.293821 + 0.955860i $$0.594927\pi$$
$$140$$ 6.00000 + 6.92820i 0.507093 + 0.585540i
$$141$$ 15.0000 1.26323
$$142$$ 19.1244 5.12436i 1.60488 0.430026i
$$143$$ −1.73205 3.00000i −0.144841 0.250873i
$$144$$ 0 0
$$145$$ −6.00000 3.46410i −0.498273 0.287678i
$$146$$ 8.66025 + 8.66025i 0.716728 + 0.716728i
$$147$$ 11.2583 4.50000i 0.928571 0.371154i
$$148$$ 6.00000i 0.493197i
$$149$$ −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i $$-0.846375\pi$$
0.844818 + 0.535054i $$0.179709\pi$$
$$150$$ −4.73205 1.26795i −0.386370 0.103528i
$$151$$ 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i $$-0.574731\pi$$
0.725956 + 0.687741i $$0.241398\pi$$
$$152$$ −14.1962 + 3.80385i −1.15146 + 0.308533i
$$153$$ 0 0
$$154$$ 0.267949 3.73205i 0.0215920 0.300737i
$$155$$ 3.00000i 0.240966i
$$156$$ −6.00000 + 10.3923i −0.480384 + 0.832050i
$$157$$ 1.50000 0.866025i 0.119713 0.0691164i −0.438948 0.898513i $$-0.644649\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 3.29423 12.2942i 0.262075 0.978076i
$$159$$ 0.866025 1.50000i 0.0686803 0.118958i
$$160$$ −6.92820 6.92820i −0.547723 0.547723i
$$161$$ −0.500000 2.59808i −0.0394055 0.204757i
$$162$$ −9.00000 + 9.00000i −0.707107 + 0.707107i
$$163$$ −18.1865 10.5000i −1.42448 0.822423i −0.427802 0.903873i $$-0.640712\pi$$
−0.996678 + 0.0814491i $$0.974045\pi$$
$$164$$ 3.46410 + 6.00000i 0.270501 + 0.468521i
$$165$$ −1.50000 2.59808i −0.116775 0.202260i
$$166$$ 5.07180 + 18.9282i 0.393648 + 1.46911i
$$167$$ −17.3205 −1.34030 −0.670151 0.742225i $$-0.733770\pi$$
−0.670151 + 0.742225i $$0.733770\pi$$
$$168$$ −11.6603 + 5.66025i −0.899608 + 0.436698i
$$169$$ 1.00000 0.0769231
$$170$$ 1.09808 + 4.09808i 0.0842186 + 0.314308i
$$171$$ 0 0
$$172$$ −2.00000 3.46410i −0.152499 0.264135i
$$173$$ −10.5000 6.06218i −0.798300 0.460899i 0.0445762 0.999006i $$-0.485806\pi$$
−0.842876 + 0.538107i $$0.819140\pi$$
$$174$$ 6.92820 6.92820i 0.525226 0.525226i
$$175$$ 1.73205 5.00000i 0.130931 0.377964i
$$176$$ 4.00000i 0.301511i
$$177$$ 4.50000 7.79423i 0.338241 0.585850i
$$178$$ −5.70577 + 21.2942i −0.427666 + 1.59607i
$$179$$ 16.4545 9.50000i 1.22987 0.710063i 0.262864 0.964833i $$-0.415333\pi$$
0.967002 + 0.254770i $$0.0819996\pi$$
$$180$$ 0 0
$$181$$ 6.92820i 0.514969i 0.966282 + 0.257485i $$0.0828937\pi$$
−0.966282 + 0.257485i $$0.917106\pi$$
$$182$$ −10.7321 7.26795i −0.795513 0.538736i
$$183$$ 9.00000i 0.665299i
$$184$$ 0.732051 + 2.73205i 0.0539675 + 0.201409i
$$185$$ 4.50000 2.59808i 0.330847 0.191014i
$$186$$ 4.09808 + 1.09808i 0.300486 + 0.0805149i
$$187$$ 0.866025 1.50000i 0.0633300 0.109691i
$$188$$ 17.3205i 1.26323i
$$189$$ −9.00000 10.3923i −0.654654 0.755929i
$$190$$ −9.00000 9.00000i −0.652929 0.652929i
$$191$$ 0.866025 + 0.500000i 0.0626634 + 0.0361787i 0.531004 0.847369i $$-0.321815\pi$$
−0.468341 + 0.883548i $$0.655148\pi$$
$$192$$ 12.0000 6.92820i 0.866025 0.500000i
$$193$$ 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i $$0.0148568\pi$$
−0.459049 + 0.888411i $$0.651810\pi$$
$$194$$ 23.6603 6.33975i 1.69871 0.455167i
$$195$$ −10.3923 −0.744208
$$196$$ −5.19615 13.0000i −0.371154 0.928571i
$$197$$ 16.0000 1.13995 0.569976 0.821661i $$-0.306952\pi$$
0.569976 + 0.821661i $$0.306952\pi$$
$$198$$ 0 0
$$199$$ 11.2583 + 19.5000i 0.798082 + 1.38232i 0.920864 + 0.389885i $$0.127485\pi$$
−0.122782 + 0.992434i $$0.539182\pi$$
$$200$$ −1.46410 + 5.46410i −0.103528 + 0.386370i
$$201$$ 4.50000 + 2.59808i 0.317406 + 0.183254i
$$202$$ −8.66025 8.66025i −0.609333 0.609333i
$$203$$ 6.92820 + 8.00000i 0.486265 + 0.561490i
$$204$$ −6.00000 −0.420084
$$205$$ −3.00000 + 5.19615i −0.209529 + 0.362915i
$$206$$ 11.8301 + 3.16987i 0.824244 + 0.220856i
$$207$$ 0 0
$$208$$ 12.0000 + 6.92820i 0.832050 + 0.480384i
$$209$$ 5.19615i 0.359425i
$$210$$ −9.29423 6.29423i −0.641363 0.434343i
$$211$$ 10.0000i 0.688428i 0.938891 + 0.344214i $$0.111855\pi$$
−0.938891 + 0.344214i $$0.888145\pi$$
$$212$$ −1.73205 1.00000i −0.118958 0.0686803i
$$213$$ −21.0000 + 12.1244i −1.43890 + 0.830747i
$$214$$ −4.75833 + 17.7583i −0.325273 + 1.21393i
$$215$$ 1.73205 3.00000i 0.118125 0.204598i
$$216$$ 10.3923 + 10.3923i 0.707107 + 0.707107i
$$217$$ −1.50000 + 4.33013i −0.101827 + 0.293948i
$$218$$ 9.00000 9.00000i 0.609557 0.609557i
$$219$$ −12.9904 7.50000i −0.877809 0.506803i
$$220$$ −3.00000 + 1.73205i −0.202260 + 0.116775i
$$221$$ −3.00000 5.19615i −0.201802 0.349531i
$$222$$ 1.90192 + 7.09808i 0.127649 + 0.476392i
$$223$$ 6.92820 0.463947 0.231973 0.972722i $$-0.425482\pi$$
0.231973 + 0.972722i $$0.425482\pi$$
$$224$$ 6.53590 + 13.4641i 0.436698 + 0.899608i
$$225$$ 0 0
$$226$$ −5.85641 21.8564i −0.389562 1.45387i
$$227$$ −9.52628 16.5000i −0.632281 1.09514i −0.987084 0.160202i $$-0.948785\pi$$
0.354803 0.934941i $$-0.384548\pi$$
$$228$$ 15.5885 9.00000i 1.03237 0.596040i
$$229$$ −13.5000 7.79423i −0.892105 0.515057i −0.0174746 0.999847i $$-0.505563\pi$$
−0.874630 + 0.484790i $$0.838896\pi$$
$$230$$ −1.73205 + 1.73205i −0.114208 + 0.114208i
$$231$$ 0.866025 + 4.50000i 0.0569803 + 0.296078i
$$232$$ −8.00000 8.00000i −0.525226 0.525226i
$$233$$ 3.50000 6.06218i 0.229293 0.397146i −0.728306 0.685252i $$-0.759692\pi$$
0.957599 + 0.288106i $$0.0930254\pi$$
$$234$$ 0 0
$$235$$ 12.9904 7.50000i 0.847399 0.489246i
$$236$$ −9.00000 5.19615i −0.585850 0.338241i
$$237$$ 15.5885i 1.01258i
$$238$$ 0.464102 6.46410i 0.0300832 0.419005i
$$239$$ 20.0000i 1.29369i 0.762620 + 0.646846i $$0.223912\pi$$
−0.762620 + 0.646846i $$0.776088\pi$$
$$240$$ 10.3923 + 6.00000i 0.670820 + 0.387298i
$$241$$ −4.50000 + 2.59808i −0.289870 + 0.167357i −0.637883 0.770133i $$-0.720190\pi$$
0.348013 + 0.937490i $$0.386857\pi$$
$$242$$ −13.6603 3.66025i −0.878114 0.235290i
$$243$$ 0 0
$$244$$ 10.3923 0.665299
$$245$$ 7.50000 9.52628i 0.479157 0.608612i
$$246$$ −6.00000 6.00000i −0.382546 0.382546i
$$247$$ 15.5885 + 9.00000i 0.991870 + 0.572656i
$$248$$ 1.26795 4.73205i 0.0805149 0.300486i
$$249$$ −12.0000 20.7846i −0.760469 1.31717i
$$250$$ −16.5622 + 4.43782i −1.04748 + 0.280673i
$$251$$ −3.46410 −0.218652 −0.109326 0.994006i $$-0.534869\pi$$
−0.109326 + 0.994006i $$0.534869\pi$$
$$252$$ 0 0
$$253$$ 1.00000 0.0628695
$$254$$ −8.19615 + 2.19615i −0.514272 + 0.137799i
$$255$$ −2.59808 4.50000i −0.162698 0.281801i
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 4.50000 + 2.59808i 0.280702 + 0.162064i 0.633741 0.773545i $$-0.281518\pi$$
−0.353039 + 0.935609i $$0.614852\pi$$
$$258$$ 3.46410 + 3.46410i 0.215666 + 0.215666i
$$259$$ −7.79423 + 1.50000i −0.484310 + 0.0932055i
$$260$$ 12.0000i 0.744208i
$$261$$ 0 0
$$262$$ −7.09808 1.90192i −0.438521 0.117501i
$$263$$ −19.9186 + 11.5000i −1.22823 + 0.709120i −0.966660 0.256063i $$-0.917574\pi$$
−0.261573 + 0.965184i $$0.584241\pi$$
$$264$$ −1.26795 4.73205i −0.0780369 0.291238i
$$265$$ 1.73205i 0.106399i
$$266$$ 8.49038 + 17.4904i 0.520579 + 1.07240i
$$267$$ 27.0000i 1.65237i
$$268$$ 3.00000 5.19615i 0.183254 0.317406i
$$269$$ 19.5000 11.2583i 1.18894 0.686433i 0.230871 0.972984i $$-0.425842\pi$$
0.958065 + 0.286552i $$0.0925091\pi$$
$$270$$ −3.29423 + 12.2942i −0.200480 + 0.748203i
$$271$$ 7.79423 13.5000i 0.473466 0.820067i −0.526073 0.850439i $$-0.676336\pi$$
0.999539 + 0.0303728i $$0.00966946\pi$$
$$272$$ 6.92820i 0.420084i
$$273$$ 15.0000 + 5.19615i 0.907841 + 0.314485i
$$274$$ 1.00000 1.00000i 0.0604122 0.0604122i
$$275$$ 1.73205 + 1.00000i 0.104447 + 0.0603023i
$$276$$ −1.73205 3.00000i −0.104257 0.180579i
$$277$$ 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i $$-0.0389525\pi$$
−0.601975 + 0.798515i $$0.705619\pi$$
$$278$$ −2.53590 9.46410i −0.152093 0.567619i
$$279$$ 0 0
$$280$$ −7.26795 + 10.7321i −0.434343 + 0.641363i
$$281$$ −4.00000 −0.238620 −0.119310 0.992857i $$-0.538068\pi$$
−0.119310 + 0.992857i $$0.538068\pi$$
$$282$$ 5.49038 + 20.4904i 0.326947 + 1.22018i
$$283$$ −6.06218 10.5000i −0.360359 0.624160i 0.627661 0.778487i $$-0.284012\pi$$
−0.988020 + 0.154327i $$0.950679\pi$$
$$284$$ 14.0000 + 24.2487i 0.830747 + 1.43890i
$$285$$ 13.5000 + 7.79423i 0.799671 + 0.461690i
$$286$$ 3.46410 3.46410i 0.204837 0.204837i
$$287$$ 6.92820 6.00000i 0.408959 0.354169i
$$288$$ 0 0
$$289$$ −7.00000 + 12.1244i −0.411765 + 0.713197i
$$290$$ 2.53590 9.46410i 0.148913 0.555751i
$$291$$ −25.9808 + 15.0000i −1.52302 + 0.879316i
$$292$$ −8.66025 + 15.0000i −0.506803 + 0.877809i
$$293$$ 20.7846i 1.21425i −0.794606 0.607125i $$-0.792323\pi$$
0.794606 0.607125i $$-0.207677\pi$$
$$294$$ 10.2679 + 13.7321i 0.598839 + 0.800869i
$$295$$ 9.00000i 0.524000i
$$296$$ 8.19615 2.19615i 0.476392 0.127649i
$$297$$ 4.50000 2.59808i 0.261116 0.150756i
$$298$$ −1.36603 0.366025i −0.0791317 0.0212033i
$$299$$ 1.73205 3.00000i 0.100167 0.173494i
$$300$$ 6.92820i 0.400000i
$$301$$ −4.00000 + 3.46410i −0.230556 + 0.199667i
$$302$$ 7.00000 + 7.00000i 0.402805 + 0.402805i
$$303$$ 12.9904 + 7.50000i 0.746278 + 0.430864i
$$304$$ −10.3923 18.0000i −0.596040 1.03237i
$$305$$ 4.50000 + 7.79423i 0.257669 + 0.446296i
$$306$$ 0 0
$$307$$ 20.7846 1.18624 0.593120 0.805114i $$-0.297896\pi$$
0.593120 + 0.805114i $$0.297896\pi$$
$$308$$ 5.19615 1.00000i 0.296078 0.0569803i
$$309$$ −15.0000 −0.853320
$$310$$ 4.09808 1.09808i 0.232755 0.0623665i
$$311$$ −4.33013 7.50000i −0.245539 0.425286i 0.716744 0.697336i $$-0.245632\pi$$
−0.962283 + 0.272050i $$0.912298\pi$$
$$312$$ −16.3923 4.39230i −0.928032 0.248665i
$$313$$ 1.50000 + 0.866025i 0.0847850 + 0.0489506i 0.541793 0.840512i $$-0.317746\pi$$
−0.457008 + 0.889463i $$0.651079\pi$$
$$314$$ 1.73205 + 1.73205i 0.0977453 + 0.0977453i
$$315$$ 0 0
$$316$$ 18.0000 1.01258
$$317$$ −5.50000 + 9.52628i −0.308911 + 0.535049i −0.978124 0.208021i $$-0.933298\pi$$
0.669214 + 0.743070i $$0.266631\pi$$
$$318$$ 2.36603 + 0.633975i 0.132680 + 0.0355515i
$$319$$ −3.46410 + 2.00000i −0.193952 + 0.111979i
$$320$$ 6.92820 12.0000i 0.387298 0.670820i
$$321$$ 22.5167i 1.25676i
$$322$$ 3.36603 1.63397i 0.187581 0.0910578i
$$323$$ 9.00000i 0.500773i
$$324$$ −15.5885 9.00000i −0.866025 0.500000i
$$325$$ 6.00000 3.46410i 0.332820 0.192154i
$$326$$ 7.68653 28.6865i 0.425718 1.58880i
$$327$$ −7.79423 + 13.5000i −0.431022 + 0.746552i
$$328$$ −6.92820 + 6.92820i −0.382546 + 0.382546i
$$329$$ −22.5000 + 4.33013i −1.24047 + 0.238728i
$$330$$ 3.00000 3.00000i 0.165145 0.165145i
$$331$$ 6.06218 + 3.50000i 0.333207 + 0.192377i 0.657264 0.753660i $$-0.271714\pi$$
−0.324057 + 0.946038i $$0.605047\pi$$
$$332$$ −24.0000 + 13.8564i −1.31717 + 0.760469i
$$333$$ 0 0
$$334$$ −6.33975 23.6603i −0.346895 1.29463i
$$335$$ 5.19615 0.283896
$$336$$ −12.0000 13.8564i −0.654654 0.755929i
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0.366025 + 1.36603i 0.0199092 + 0.0743020i
$$339$$ 13.8564 + 24.0000i 0.752577 + 1.30350i
$$340$$ −5.19615 + 3.00000i −0.281801 + 0.162698i
$$341$$ −1.50000 0.866025i −0.0812296 0.0468979i
$$342$$ 0 0
$$343$$ −15.5885 + 10.0000i −0.841698 + 0.539949i
$$344$$ 4.00000 4.00000i 0.215666 0.215666i
$$345$$ 1.50000 2.59808i 0.0807573 0.139876i
$$346$$ 4.43782 16.5622i 0.238579 0.890388i
$$347$$ 11.2583 6.50000i 0.604379 0.348938i −0.166383 0.986061i $$-0.553209\pi$$
0.770762 + 0.637123i $$0.219876\pi$$
$$348$$ 12.0000 + 6.92820i 0.643268 + 0.371391i
$$349$$ 10.3923i 0.556287i 0.960539 + 0.278144i $$0.0897191\pi$$
−0.960539 + 0.278144i $$0.910281\pi$$
$$350$$ 7.46410 + 0.535898i 0.398973 + 0.0286450i
$$351$$ 18.0000i 0.960769i
$$352$$ −5.46410 + 1.46410i −0.291238 + 0.0780369i
$$353$$ −25.5000 + 14.7224i −1.35723 + 0.783596i −0.989249 0.146238i $$-0.953283\pi$$
−0.367979 + 0.929834i $$0.619950\pi$$
$$354$$ 12.2942 + 3.29423i 0.653431 + 0.175086i
$$355$$ −12.1244 + 21.0000i −0.643494 + 1.11456i
$$356$$ −31.1769 −1.65237
$$357$$ 1.50000 + 7.79423i 0.0793884 + 0.412514i
$$358$$ 19.0000 + 19.0000i 1.00418 + 1.00418i
$$359$$ −19.9186 11.5000i −1.05126 0.606947i −0.128260 0.991741i $$-0.540939\pi$$
−0.923003 + 0.384794i $$0.874273\pi$$
$$360$$ 0 0
$$361$$ −4.00000 6.92820i −0.210526 0.364642i
$$362$$ −9.46410 + 2.53590i −0.497422 + 0.133284i
$$363$$ 17.3205 0.909091
$$364$$ 6.00000 17.3205i 0.314485 0.907841i
$$365$$ −15.0000 −0.785136
$$366$$ −12.2942 + 3.29423i −0.642630 + 0.172192i
$$367$$ −0.866025 1.50000i −0.0452062 0.0782994i 0.842537 0.538639i $$-0.181061\pi$$
−0.887743 + 0.460339i $$0.847728\pi$$
$$368$$ −3.46410 + 2.00000i −0.180579 + 0.104257i
$$369$$ 0 0
$$370$$ 5.19615 + 5.19615i 0.270135 + 0.270135i
$$371$$ −0.866025 + 2.50000i −0.0449618 + 0.129794i
$$372$$ 6.00000i 0.311086i
$$373$$ 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i $$-0.563010\pi$$
0.947444 0.319921i $$-0.103656\pi$$
$$374$$ 2.36603 + 0.633975i 0.122344 + 0.0327820i
$$375$$ 18.1865 10.5000i 0.939149 0.542218i
$$376$$ 23.6603 6.33975i 1.22018 0.326947i
$$377$$ 13.8564i 0.713641i
$$378$$ 10.9019 16.0981i 0.560734 0.827996i
$$379$$ 8.00000i 0.410932i −0.978664 0.205466i $$-0.934129\pi$$
0.978664 0.205466i $$-0.0658711\pi$$
$$380$$ 9.00000 15.5885i 0.461690 0.799671i
$$381$$ 9.00000 5.19615i 0.461084 0.266207i
$$382$$ −0.366025 + 1.36603i −0.0187275 + 0.0698919i
$$383$$ 2.59808 4.50000i 0.132755 0.229939i −0.791982 0.610544i $$-0.790951\pi$$
0.924738 + 0.380605i $$0.124284\pi$$
$$384$$ 13.8564 + 13.8564i 0.707107 + 0.707107i
$$385$$ 3.00000 + 3.46410i 0.152894 + 0.176547i
$$386$$ −15.0000 + 15.0000i −0.763480 + 0.763480i
$$387$$ 0 0
$$388$$ 17.3205 + 30.0000i 0.879316 + 1.52302i
$$389$$ 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i $$-0.00669738\pi$$
−0.518110 + 0.855314i $$0.673364\pi$$
$$390$$ −3.80385 14.1962i −0.192615 0.718850i
$$391$$ 1.73205 0.0875936
$$392$$ 15.8564 11.8564i 0.800869 0.598839i
$$393$$ 9.00000 0.453990
$$394$$ 5.85641 + 21.8564i 0.295041 + 1.10111i
$$395$$ 7.79423 + 13.5000i 0.392170 + 0.679259i
$$396$$ 0 0
$$397$$ 16.5000 + 9.52628i 0.828111 + 0.478110i 0.853206 0.521575i $$-0.174655\pi$$
−0.0250943 + 0.999685i $$0.507989\pi$$
$$398$$ −22.5167 + 22.5167i −1.12866 + 1.12866i
$$399$$ −15.5885 18.0000i −0.780399 0.901127i
$$400$$ −8.00000 −0.400000
$$401$$ 11.5000 19.9186i 0.574283 0.994687i −0.421837 0.906672i $$-0.638614\pi$$
0.996119 0.0880147i $$-0.0280523\pi$$
$$402$$ −1.90192 + 7.09808i −0.0948593 + 0.354020i
$$403$$ −5.19615 + 3.00000i −0.258839 + 0.149441i
$$404$$ 8.66025 15.0000i 0.430864 0.746278i
$$405$$ 15.5885i 0.774597i
$$406$$ −8.39230 + 12.3923i −0.416503 + 0.615020i
$$407$$ 3.00000i 0.148704i
$$408$$ −2.19615 8.19615i −0.108726 0.405770i
$$409$$ 22.5000 12.9904i 1.11255 0.642333i 0.173064 0.984911i $$-0.444633\pi$$
0.939490 + 0.342578i $$0.111300\pi$$
$$410$$ −8.19615 2.19615i −0.404779 0.108460i
$$411$$ −0.866025 + 1.50000i −0.0427179 + 0.0739895i
$$412$$ 17.3205i 0.853320i
$$413$$ −4.50000 + 12.9904i −0.221431 + 0.639215i
$$414$$ 0 0
$$415$$ −20.7846 12.0000i −1.02028 0.589057i
$$416$$ −5.07180 + 18.9282i −0.248665 + 0.928032i
$$417$$ 6.00000 + 10.3923i 0.293821 + 0.508913i
$$418$$ −7.09808 + 1.90192i −0.347178 + 0.0930261i
$$419$$ −20.7846 −1.01539 −0.507697 0.861536i $$-0.669503\pi$$
−0.507697 + 0.861536i $$0.669503\pi$$
$$420$$ 5.19615 15.0000i 0.253546 0.731925i
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −13.6603 + 3.66025i −0.664971 + 0.178178i
$$423$$ 0 0
$$424$$ 0.732051 2.73205i 0.0355515 0.132680i
$$425$$ 3.00000 + 1.73205i 0.145521 + 0.0840168i
$$426$$ −24.2487 24.2487i −1.17485 1.17485i
$$427$$ −2.59808 13.5000i −0.125730 0.653311i
$$428$$ −26.0000 −1.25676
$$429$$ −3.00000 + 5.19615i −0.144841 + 0.250873i
$$430$$ 4.73205 + 1.26795i 0.228200 + 0.0611459i
$$431$$ 19.9186 11.5000i 0.959444 0.553936i 0.0634424 0.997985i $$-0.479792\pi$$
0.896002 + 0.444050i $$0.146459\pi$$
$$432$$ −10.3923 + 18.0000i −0.500000 + 0.866025i
$$433$$ 10.3923i 0.499422i −0.968320 0.249711i $$-0.919664\pi$$
0.968320 0.249711i $$-0.0803357\pi$$
$$434$$ −6.46410 0.464102i −0.310287 0.0222776i
$$435$$ 12.0000i 0.575356i
$$436$$ 15.5885 + 9.00000i 0.746552 + 0.431022i
$$437$$ −4.50000 + 2.59808i −0.215264 + 0.124283i
$$438$$ 5.49038 20.4904i 0.262341 0.979068i
$$439$$ −11.2583 + 19.5000i −0.537331 + 0.930684i 0.461716 + 0.887028i $$0.347234\pi$$
−0.999047 + 0.0436563i $$0.986099\pi$$
$$440$$ −3.46410 3.46410i −0.165145 0.165145i
$$441$$ 0 0
$$442$$ 6.00000 6.00000i 0.285391 0.285391i
$$443$$ 14.7224 + 8.50000i 0.699484 + 0.403847i 0.807155 0.590339i $$-0.201006\pi$$
−0.107671 + 0.994187i $$0.534339\pi$$
$$444$$ −9.00000 + 5.19615i −0.427121 + 0.246598i
$$445$$ −13.5000 23.3827i −0.639961 1.10845i
$$446$$ 2.53590 + 9.46410i 0.120078 + 0.448138i
$$447$$ 1.73205 0.0819232
$$448$$ −16.0000 + 13.8564i −0.755929 + 0.654654i
$$449$$ 8.00000 0.377543 0.188772 0.982021i $$-0.439549\pi$$
0.188772 + 0.982021i $$0.439549\pi$$
$$450$$ 0 0
$$451$$ 1.73205 + 3.00000i 0.0815591 + 0.141264i
$$452$$ 27.7128 16.0000i 1.30350 0.752577i
$$453$$ −10.5000 6.06218i −0.493333 0.284826i
$$454$$ 19.0526 19.0526i 0.894181 0.894181i
$$455$$ 15.5885 3.00000i 0.730798 0.140642i
$$456$$ 18.0000 + 18.0000i 0.842927 + 0.842927i
$$457$$ −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i $$-0.947436\pi$$
0.635561 + 0.772051i $$0.280769\pi$$
$$458$$ 5.70577 21.2942i 0.266613 0.995014i
$$459$$ 7.79423 4.50000i 0.363803 0.210042i
$$460$$ −3.00000 1.73205i −0.139876 0.0807573i
$$461$$ 17.3205i 0.806696i −0.915047 0.403348i $$-0.867846\pi$$
0.915047 0.403348i $$-0.132154\pi$$
$$462$$ −5.83013 + 2.83013i −0.271242 + 0.131669i
$$463$$ 30.0000i 1.39422i −0.716965 0.697109i $$-0.754469\pi$$
0.716965 0.697109i $$-0.245531\pi$$
$$464$$ 8.00000 13.8564i 0.371391 0.643268i
$$465$$ −4.50000 + 2.59808i −0.208683 + 0.120483i
$$466$$ 9.56218 + 2.56218i 0.442959 + 0.118691i
$$467$$ 4.33013 7.50000i 0.200374 0.347059i −0.748275 0.663389i $$-0.769117\pi$$
0.948649 + 0.316330i $$0.102451\pi$$
$$468$$ 0 0
$$469$$ −7.50000 2.59808i −0.346318 0.119968i
$$470$$ 15.0000 + 15.0000i 0.691898 + 0.691898i
$$471$$ −2.59808 1.50000i −0.119713 0.0691164i
$$472$$ 3.80385 14.1962i 0.175086 0.653431i
$$473$$ −1.00000 1.73205i −0.0459800 0.0796398i
$$474$$ −21.2942 + 5.70577i −0.978076 + 0.262075i
$$475$$ −10.3923 −0.476832
$$476$$ 9.00000 1.73205i 0.412514 0.0793884i
$$477$$ 0 0
$$478$$ −27.3205 + 7.32051i −1.24961 + 0.334832i
$$479$$ 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i $$-0.0773304\pi$$
−0.693647 + 0.720315i $$0.743997\pi$$
$$480$$ −4.39230 + 16.3923i −0.200480 + 0.748203i
$$481$$ −9.00000 5.19615i −0.410365 0.236924i
$$482$$ −5.19615 5.19615i −0.236678 0.236678i
$$483$$ −3.46410 + 3.00000i −0.157622 + 0.136505i
$$484$$ 20.0000i 0.909091i
$$485$$ −15.0000 + 25.9808i −0.681115 + 1.17973i
$$486$$ 0 0
$$487$$ −26.8468 + 15.5000i −1.21654 + 0.702372i −0.964177 0.265260i $$-0.914542\pi$$
−0.252367 + 0.967632i $$0.581209\pi$$
$$488$$ 3.80385 + 14.1962i 0.172192 + 0.642630i
$$489$$ 36.3731i 1.64485i
$$490$$ 15.7583 + 6.75833i 0.711889 + 0.305310i
$$491$$ 32.0000i 1.44414i 0.691820 + 0.722070i $$0.256809\pi$$
−0.691820 + 0.722070i $$0.743191\pi$$
$$492$$ 6.00000 10.3923i 0.270501 0.468521i
$$493$$ −6.00000 + 3.46410i −0.270226 + 0.156015i
$$494$$ −6.58846 + 24.5885i −0.296429 + 1.10629i
$$495$$ 0 0
$$496$$ 6.92820 0.311086
$$497$$ 28.0000 24.2487i 1.25597 1.08770i
$$498$$ 24.0000 24.0000i 1.07547 1.07547i
$$499$$ 30.3109 + 17.5000i 1.35690 + 0.783408i 0.989205 0.146538i $$-0.0468131\pi$$
0.367697 + 0.929946i $$0.380146\pi$$
$$500$$ −12.1244 21.0000i −0.542218 0.939149i
$$501$$ 15.0000 + 25.9808i 0.670151 + 1.16073i
$$502$$ −1.26795 4.73205i −0.0565913 0.211202i
$$503$$ −6.92820 −0.308913 −0.154457 0.988000i $$-0.549363\pi$$
−0.154457 + 0.988000i $$0.549363\pi$$
$$504$$ 0 0
$$505$$ 15.0000 0.667491
$$506$$ 0.366025 + 1.36603i 0.0162718 + 0.0607272i
$$507$$ −0.866025 1.50000i −0.0384615 0.0666173i
$$508$$ −6.00000 10.3923i −0.266207 0.461084i
$$509$$ 10.5000 + 6.06218i 0.465404 + 0.268701i 0.714314 0.699825i $$-0.246739\pi$$
−0.248910 + 0.968527i $$0.580072\pi$$
$$510$$ 5.19615 5.19615i 0.230089 0.230089i
$$511$$ 21.6506 + 7.50000i 0.957768 + 0.331780i
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ −13.5000 + 23.3827i −0.596040 + 1.03237i
$$514$$ −1.90192 + 7.09808i −0.0838903 + 0.313083i
$$515$$ −12.9904 + 7.50000i −0.572425 + 0.330489i
$$516$$ −3.46410 + 6.00000i −0.152499 + 0.264135i
$$517$$ 8.66025i 0.380878i
$$518$$ −4.90192 10.0981i −0.215378 0.443684i
$$519$$ 21.0000i 0.921798i
$$520$$ −16.3923 + 4.39230i −0.718850 + 0.192615i
$$521$$ 1.50000 0.866025i 0.0657162 0.0379413i −0.466782 0.884372i $$-0.654587\pi$$
0.532498 + 0.846431i $$0.321253\pi$$
$$522$$ 0 0
$$523$$ 12.9904 22.5000i 0.568030 0.983856i −0.428731 0.903432i $$-0.641039\pi$$
0.996761 0.0804241i $$-0.0256275\pi$$
$$524$$ 10.3923i 0.453990i
$$525$$ −9.00000 + 1.73205i −0.392792 + 0.0755929i
$$526$$ −23.0000 23.0000i −1.00285 1.00285i
$$527$$ −2.59808 1.50000i −0.113174 0.0653410i
$$528$$ 6.00000 3.46410i 0.261116 0.150756i
$$529$$ −11.0000 19.0526i −0.478261 0.828372i
$$530$$ 2.36603 0.633975i 0.102774 0.0275381i
$$531$$ 0 0
$$532$$ −20.7846 + 18.0000i −0.901127 + 0.780399i
$$533$$ 12.0000 0.519778
$$534$$ 36.8827 9.88269i 1.59607 0.427666i
$$535$$ −11.2583 19.5000i −0.486740 0.843059i
$$536$$ 8.19615 + 2.19615i 0.354020 + 0.0948593i
$$537$$ −28.5000 16.4545i −1.22987 0.710063i
$$538$$ 22.5167 + 22.5167i 0.970762 + 0.970762i
$$539$$ −2.59808 6.50000i −0.111907 0.279975i
$$540$$ −18.0000 −0.774597
$$541$$ 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i $$-0.699407\pi$$
0.994715 + 0.102677i $$0.0327407\pi$$
$$542$$ 21.2942 + 5.70577i 0.914665 + 0.245084i
$$543$$ 10.3923 6.00000i 0.445976 0.257485i
$$544$$ −9.46410 + 2.53590i −0.405770 + 0.108726i
$$545$$ 15.5885i 0.667736i
$$546$$ −1.60770 + 22.3923i −0.0688030 + 0.958302i
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 1.73205 + 1.00000i 0.0739895 + 0.0427179i
$$549$$ 0 0
$$550$$ −0.732051 + 2.73205i −0.0312148 + 0.116495i
$$551$$ 10.3923 18.0000i 0.442727 0.766826i
$$552$$ 3.46410 3.46410i 0.147442 0.147442i
$$553$$ −4.50000 23.3827i −0.191359 0.994333i
$$554$$ −13.0000 + 13.0000i −0.552317 + 0.552317i
$$555$$ −7.79423 4.50000i −0.330847 0.191014i
$$556$$ 12.0000 6.92820i 0.508913 0.293821i
$$557$$ −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i $$-0.879909\pi$$
0.145802 0.989314i $$-0.453424\pi$$
$$558$$ 0 0
$$559$$ −6.92820 −0.293032
$$560$$ −17.3205 6.00000i −0.731925 0.253546i
$$561$$ −3.00000 −0.126660
$$562$$ −1.46410 5.46410i −0.0617594 0.230489i
$$563$$ −11.2583 19.5000i −0.474482 0.821827i 0.525091 0.851046i $$-0.324031\pi$$
−0.999573 + 0.0292191i $$0.990698\pi$$
$$564$$ −25.9808 + 15.0000i −1.09399 + 0.631614i
$$565$$ 24.0000 + 13.8564i 1.00969 + 0.582943i
$$566$$ 12.1244 12.1244i 0.509625 0.509625i
$$567$$ −7.79423 + 22.5000i −0.327327 + 0.944911i
$$568$$ −28.0000 + 28.0000i −1.17485 + 1.17485i
$$569$$ 6.50000 11.2583i 0.272494 0.471974i −0.697006 0.717066i $$-0.745485\pi$$
0.969500 + 0.245092i $$0.0788181\pi$$
$$570$$ −5.70577 + 21.2942i −0.238988 + 0.891917i
$$571$$ −18.1865 + 10.5000i −0.761083 + 0.439411i −0.829684 0.558233i $$-0.811480\pi$$
0.0686016 + 0.997644i $$0.478146\pi$$
$$572$$ 6.00000 + 3.46410i 0.250873 + 0.144841i
$$573$$ 1.73205i 0.0723575i
$$574$$ 10.7321 + 7.26795i 0.447947 + 0.303358i
$$575$$ 2.00000i 0.0834058i
$$576$$ 0 0
$$577$$ −28.5000 + 16.4545i −1.18647 + 0.685009i −0.957503 0.288425i $$-0.906868\pi$$
−0.228968 + 0.973434i $$0.573535\pi$$
$$578$$ −19.1244 5.12436i −0.795468 0.213145i
$$579$$ 12.9904 22.5000i 0.539862 0.935068i
$$580$$ 13.8564 0.575356
$$581$$ 24.0000 + 27.7128i 0.995688 + 1.14972i
$$582$$ −30.0000 30.0000i −1.24354 1.24354i
$$583$$ −0.866025 0.500000i −0.0358671 0.0207079i
$$584$$ −23.6603 6.33975i −0.979068 0.262341i
$$585$$ 0 0
$$586$$ 28.3923 7.60770i 1.17288 0.314271i
$$587$$ 6.92820 0.285958 0.142979 0.989726i $$-0.454332\pi$$
0.142979 + 0.989726i $$0.454332\pi$$
$$588$$ −15.0000 + 19.0526i −0.618590 + 0.785714i
$$589$$ 9.00000 0.370839
$$590$$ 12.2942 3.29423i 0.506145 0.135621i
$$591$$ −13.8564 24.0000i −0.569976 0.987228i
$$592$$ 6.00000 + 10.3923i 0.246598 + 0.427121i
$$593$$ −13.5000 7.79423i −0.554379 0.320071i 0.196508 0.980502i $$-0.437040\pi$$
−0.750886 + 0.660432i $$0.770373\pi$$
$$594$$ 5.19615 + 5.19615i 0.213201 + 0.213201i
$$595$$ 5.19615 + 6.00000i 0.213021 + 0.245976i
$$596$$ 2.00000i 0.0819232i
$$597$$ 19.5000 33.7750i 0.798082 1.38232i
$$598$$ 4.73205 + 1.26795i 0.193508 + 0.0518503i
$$599$$ 14.7224 8.50000i 0.601542 0.347301i −0.168106 0.985769i $$-0.553765\pi$$
0.769648 + 0.638468i $$0.220432\pi$$
$$600$$ 9.46410 2.53590i 0.386370 0.103528i
$$601$$ 38.1051i 1.55434i 0.629291 + 0.777170i $$0.283346\pi$$
−0.629291 + 0.777170i $$0.716654\pi$$
$$602$$ −6.19615 4.19615i −0.252536 0.171022i
$$603$$ 0 0
$$604$$ −7.00000 + 12.1244i −0.284826 + 0.493333i
$$605$$ 15.0000 8.66025i 0.609837 0.352089i
$$606$$ −5.49038 + 20.4904i −0.223031 + 0.832365i
$$607$$ −7.79423 + 13.5000i −0.316358 + 0.547948i −0.979725 0.200346i $$-0.935793\pi$$
0.663367 + 0.748294i $$0.269127\pi$$
$$608$$ 20.7846 20.7846i 0.842927 0.842927i
$$609$$ 6.00000 17.3205i 0.243132 0.701862i
$$610$$ −9.00000 + 9.00000i −0.364399 + 0.364399i
$$611$$ −25.9808 15.0000i −1.05107 0.606835i
$$612$$ 0 0
$$613$$ 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i $$0.0486583\pi$$
−0.362300 + 0.932062i $$0.618008\pi$$
$$614$$ 7.60770 + 28.3923i 0.307022 + 1.14582i
$$615$$ 10.3923 0.419058
$$616$$ 3.26795 + 6.73205i 0.131669 + 0.271242i
$$617$$ 20.0000 0.805170 0.402585 0.915383i $$-0.368112\pi$$
0.402585 + 0.915383i $$0.368112\pi$$
$$618$$ −5.49038 20.4904i −0.220856 0.824244i
$$619$$ −7.79423 13.5000i −0.313276 0.542611i 0.665793 0.746136i $$-0.268093\pi$$
−0.979070 + 0.203526i $$0.934760\pi$$
$$620$$ 3.00000 + 5.19615i 0.120483 + 0.208683i
$$621$$ 4.50000 + 2.59808i 0.180579 + 0.104257i
$$622$$ 8.66025 8.66025i 0.347245 0.347245i
$$623$$ 7.79423 + 40.5000i 0.312269 + 1.62260i
$$624$$ 24.0000i 0.960769i
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ −0.633975 + 2.36603i −0.0253387 + 0.0945654i
$$627$$ 7.79423 4.50000i 0.311272 0.179713i
$$628$$ −1.73205 + 3.00000i −0.0691164 + 0.119713i
$$629$$ 5.19615i 0.207184i
$$630$$ 0 0
$$631$$ 30.0000i 1.19428i 0.802137 + 0.597141i $$0.203697\pi$$
−0.802137 + 0.597141i $$0.796303\pi$$
$$632$$ 6.58846 + 24.5885i 0.262075 + 0.978076i
$$633$$ 15.0000 8.66025i 0.596196 0.344214i
$$634$$ −15.0263 4.02628i −0.596770 0.159904i
$$635$$ 5.19615 9.00000i 0.206203 0.357154i
$$636$$ 3.46410i 0.137361i
$$637$$ −24.0000 3.46410i −0.950915 0.137253i
$$638$$ −4.00000 4.00000i −0.158362 0.158362i
$$639$$ 0 0
$$640$$ 18.9282 + 5.07180i 0.748203 + 0.200480i
$$641$$ 6.50000 + 11.2583i 0.256735 + 0.444677i 0.965365 0.260902i $$-0.0840201\pi$$
−0.708631 + 0.705580i $$0.750687\pi$$
$$642$$ 30.7583 8.24167i 1.21393 0.325273i
$$643$$ −13.8564 −0.546443 −0.273222 0.961951i $$-0.588089\pi$$
−0.273222 + 0.961951i $$0.588089\pi$$
$$644$$ 3.46410 + 4.00000i 0.136505 + 0.157622i
$$645$$ −6.00000 −0.236250
$$646$$ −12.2942 + 3.29423i −0.483710 + 0.129610i
$$647$$ 16.4545 + 28.5000i 0.646892 + 1.12045i 0.983861 + 0.178935i $$0.0572651\pi$$
−0.336968 + 0.941516i $$0.609402\pi$$
$$648$$ 6.58846 24.5885i 0.258819 0.965926i
$$649$$ −4.50000 2.59808i −0.176640 0.101983i
$$650$$ 6.92820 + 6.92820i 0.271746 + 0.271746i
$$651$$ 7.79423 1.50000i 0.305480 0.0587896i
$$652$$ 42.0000 1.64485
$$653$$ −15.5000 + 26.8468i −0.606562 + 1.05060i 0.385241 + 0.922816i $$0.374118\pi$$
−0.991803 + 0.127780i $$0.959215\pi$$
$$654$$ −21.2942 5.70577i −0.832670 0.223113i
$$655$$ 7.79423 4.50000i 0.304546 0.175830i
$$656$$ −12.0000 6.92820i −0.468521 0.270501i
$$657$$ 0 0
$$658$$ −14.1506 29.1506i −0.551649 1.13641i
$$659$$ 38.0000i 1.48027i −0.672458 0.740135i $$-0.734762\pi$$
0.672458 0.740135i $$-0.265238\pi$$
$$660$$ 5.19615 + 3.00000i 0.202260 + 0.116775i
$$661$$ −34.5000 + 19.9186i −1.34189 + 0.774743i −0.987085 0.160196i $$-0.948788\pi$$
−0.354809 + 0.934939i $$0.615454\pi$$
$$662$$ −2.56218 + 9.56218i −0.0995819 + 0.371645i
$$663$$ −5.19615 + 9.00000i −0.201802 + 0.349531i
$$664$$ −27.7128 27.7128i −1.07547 1.07547i
$$665$$ −22.5000 7.79423i −0.872513 0.302247i
$$666$$ 0 0
$$667$$ −3.46410 2.00000i −0.134131 0.0774403i
$$668$$ 30.0000 17.3205i 1.16073 0.670151i
$$669$$ −6.00000 10.3923i −0.231973 0.401790i
$$670$$ 1.90192 + 7.09808i 0.0734777 + 0.274223i
$$671$$ 5.19615 0.200595
$$672$$ 14.5359 21.4641i 0.560734 0.827996i
$$673$$ 24.0000 0.925132 0.462566 0.886585i $$-0.346929\pi$$
0.462566 + 0.886585i $$0.346929\pi$$
$$674$$ 0 0
$$675$$ 5.19615 + 9.00000i 0.200000 + 0.346410i
$$676$$ −1.73205 + 1.00000i −0.0666173 + 0.0384615i
$$677$$ −37.5000 21.6506i −1.44124 0.832102i −0.443309 0.896369i $$-0.646196\pi$$
−0.997933 + 0.0642672i $$0.979529\pi$$
$$678$$ −27.7128 + 27.7128i −1.06430 + 1.06430i
$$679$$ 34.6410 30.0000i 1.32940 1.15129i
$$680$$ −6.00000 6.00000i −0.230089 0.230089i
$$681$$ −16.5000 + 28.5788i −0.632281 + 1.09514i
$$682$$ 0.633975 2.36603i 0.0242761 0.0905998i
$$683$$ −21.6506 + 12.5000i −0.828439 + 0.478299i −0.853318 0.521391i $$-0.825413\pi$$
0.0248792 + 0.999690i $$0.492080\pi$$
$$684$$ 0 0
$$685$$ 1.73205i 0.0661783i
$$686$$ −19.3660 17.6340i −0.739398 0.673268i
$$687$$ 27.0000i 1.03011i
$$688$$ 6.92820 + 4.00000i 0.264135 + 0.152499i
$$689$$ −3.00000 + 1.73205i −0.114291 + 0.0659859i
$$690$$ 4.09808 + 1.09808i 0.156011 + 0.0418030i
$$691$$ −6.06218 + 10.5000i −0.230616 + 0.399439i −0.957990 0.286803i $$-0.907407\pi$$
0.727373 + 0.686242i $$0.240741\pi$$
$$692$$ 24.2487 0.921798
$$693$$ 0 0
$$694$$ 13.0000 + 13.0000i 0.493473 + 0.493473i
$$695$$ 10.3923 + 6.00000i 0.394203 + 0.227593i
$$696$$ −5.07180 + 18.9282i −0.192246 + 0.717472i
$$697$$ 3.00000 + 5.19615i 0.113633 + 0.196818i
$$698$$ −14.1962 + 3.80385i −0.537332 + 0.143978i
$$699$$ −12.1244 −0.458585
$$700$$ 2.00000 + 10.3923i 0.0755929 + 0.392792i
$$701$$ −26.0000 −0.982006 −0.491003 0.871158i $$-0.663370\pi$$
−0.491003 + 0.871158i $$0.663370\pi$$
$$702$$ 24.5885 6.58846i 0.928032 0.248665i
$$703$$ 7.79423 + 13.5000i 0.293965 + 0.509162i
$$704$$ −4.00000 6.92820i −0.150756 0.261116i
$$705$$ −22.5000 12.9904i −0.847399 0.489246i
$$706$$ −29.4449 29.4449i −1.10817 1.10817i
$$707$$ −21.6506 7.50000i −0.814256 0.282067i
$$708$$ 18.0000i 0.676481i
$$709$$ 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i $$-0.779279\pi$$
0.938069 + 0.346449i $$0.112613\pi$$
$$710$$ −33.1244 8.87564i −1.24313 0.333097i
$$711$$ 0 0
$$712$$ −11.4115 42.5885i −0.427666 1.59607i
$$713$$ 1.73205i 0.0648658i
$$714$$ −10.0981 + 4.90192i −0.377911 + 0.183450i
$$715$$ 6.00000i 0.224387i
$$716$$ −19.0000 + 32.9090i −0.710063 + 1.22987i
$$717$$ 30.0000 17.3205i 1.12037 0.646846i
$$718$$ 8.41858 31.4186i 0.314179 1.17253i
$$719$$ −12.9904 + 22.5000i −0.484459 + 0.839108i −0.999841 0.0178527i $$-0.994317\pi$$
0.515381 + 0.856961i $$0.327650\pi$$
$$720$$ 0 0
$$721$$ 22.5000 4.33013i 0.837944 0.161262i
$$722$$ 8.00000 8.00000i 0.297729 0.297729i
$$723$$ 7.79423 + 4.50000i 0.289870 + 0.167357i
$$724$$ −6.92820 12.0000i −0.257485 0.445976i
$$725$$ −4.00000 6.92820i −0.148556 0.257307i
$$726$$ 6.33975 + 23.6603i 0.235290 + 0.878114i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 25.8564 + 1.85641i 0.958302 + 0.0688030i
$$729$$ 27.0000 1.00000
$$730$$ −5.49038 20.4904i −0.203208 0.758383i
$$731$$ −1.73205 3.00000i −0.0640622 0.110959i
$$732$$ −9.00000 15.5885i −0.332650 0.576166i
$$733$$ 37.5000 + 21.6506i 1.38509 + 0.799684i 0.992757 0.120137i $$-0.0383334\pi$$
0.392337 + 0.919822i $$0.371667\pi$$
$$734$$ 1.73205 1.73205i 0.0639312 0.0639312i
$$735$$ −20.7846 3.00000i −0.766652 0.110657i
$$736$$ −4.00000 4.00000i −0.147442 0.147442i
$$737$$ 1.50000 2.59808i 0.0552532 0.0957014i
$$738$$ 0 0
$$739$$ 44.1673 25.5000i 1.62472 0.938033i 0.639087 0.769135i $$-0.279313\pi$$
0.985634 0.168898i $$-0.0540208\pi$$
$$740$$ −5.19615 + 9.00000i −0.191014 + 0.330847i
$$741$$ 31.1769i 1.14531i
$$742$$ −3.73205 0.267949i −0.137008 0.00983672i
$$743$$ 34.0000i 1.24734i −0.781688 0.623670i $$-0.785641\pi$$
0.781688 0.623670i $$-0.214359\pi$$
$$744$$ −8.19615 + 2.19615i −0.300486 + 0.0805149i
$$745$$ 1.50000 0.866025i 0.0549557 0.0317287i
$$746$$ 39.6147 + 10.6147i 1.45040 + 0.388633i
$$747$$ 0 0
$$748$$ 3.46410i 0.126660i
$$749$$ 6.50000 + 33.7750i 0.237505 + 1.23411i
$$750$$ 21.0000 + 21.0000i 0.766812 + 0.766812i
$$751$$ 21.6506 + 12.5000i 0.790043 + 0.456131i 0.839978 0.542621i $$-0.182568\pi$$
−0.0499348 + 0.998752i $$0.515901\pi$$
$$752$$ 17.3205 + 30.0000i 0.631614 + 1.09399i
$$753$$ 3.00000 + 5.19615i 0.109326 + 0.189358i
$$754$$ −18.9282 + 5.07180i −0.689325 + 0.184704i
$$755$$ −12.1244 −0.441250
$$756$$ 25.9808 + 9.00000i 0.944911 + 0.327327i
$$757$$ −48.0000 −1.74459 −0.872295 0.488980i $$-0.837369\pi$$
−0.872295 + 0.488980i $$0.837369\pi$$
$$758$$ 10.9282 2.92820i 0.396930 0.106357i
$$759$$ −0.866025 1.50000i −0.0314347 0.0544466i
$$760$$ 24.5885 + 6.58846i 0.891917 + 0.238988i
$$761$$ 16.5000 + 9.52628i 0.598125 + 0.345327i 0.768303 0.640086i $$-0.221101\pi$$
−0.170179 + 0.985413i $$0.554435\pi$$
$$762$$ 10.3923 + 10.3923i 0.376473 + 0.376473i
$$763$$ 7.79423 22.5000i 0.282170 0.814555i
$$764$$ −2.00000 −0.0723575
$$765$$ 0 0
$$766$$ 7.09808 + 1.90192i 0.256464 + 0.0687193i
$$767$$ −15.5885 + 9.00000i −0.562867 + 0.324971i
$$768$$ −13.8564 + 24.0000i −0.500000 + 0.866025i
$$769$$ 3.46410i 0.124919i −0.998048 0.0624593i $$-0.980106\pi$$
0.998048 0.0624593i $$-0.0198944\pi$$
$$770$$ −3.63397 + 5.36603i −0.130959 + 0.193378i
$$771$$ 9.00000i 0.324127i
$$772$$ −25.9808 15.0000i −0.935068 0.539862i
$$773$$ 22.5000 12.9904i 0.809269 0.467232i −0.0374331 0.999299i $$-0.511918\pi$$
0.846702 + 0.532068i $$0.178585\pi$$
$$774$$ 0 0
$$775$$ 1.73205 3.00000i 0.0622171 0.107763i