# Properties

 Label 546.2.l.i.295.2 Level $546$ Weight $2$ Character 546.295 Analytic conductor $4.360$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.l (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{17})$$ Defining polynomial: $$x^{4} - x^{3} + 5 x^{2} + 4 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 295.2 Root $$-0.780776 - 1.35234i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.295 Dual form 546.2.l.i.211.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280776 + 0.486319i) q^{10} +(0.780776 - 1.35234i) q^{11} +1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(2.34233 + 4.05703i) q^{19} +(-0.280776 - 0.486319i) q^{20} -1.00000 q^{21} +(0.780776 + 1.35234i) q^{22} +(0.438447 - 0.759413i) q^{23} +(-0.500000 + 0.866025i) q^{24} -4.68466 q^{25} +(-2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.280776 - 0.486319i) q^{30} -3.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -5.00000 q^{34} +(0.280776 + 0.486319i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.40388 + 9.35980i) q^{37} -4.68466 q^{38} +(-2.84233 - 2.21837i) q^{39} +0.561553 q^{40} +(2.06155 - 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(5.56155 + 9.63289i) q^{43} -1.56155 q^{44} +(-0.280776 - 0.486319i) q^{45} +(0.438447 + 0.759413i) q^{46} +4.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.34233 - 4.05703i) q^{50} -5.00000 q^{51} +(3.34233 - 1.35234i) q^{52} -12.1231 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.438447 - 0.759413i) q^{55} +(0.500000 + 0.866025i) q^{56} -4.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.43845 - 4.22351i) q^{59} +0.561553 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.56155 - 2.70469i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-0.280776 + 2.00514i) q^{65} -1.56155 q^{66} +(3.56155 - 6.16879i) q^{67} +(2.50000 - 4.33013i) q^{68} +(0.438447 + 0.759413i) q^{69} -0.561553 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(-5.40388 - 9.35980i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.34233 - 4.05703i) q^{76} +1.56155 q^{77} +(3.34233 - 1.35234i) q^{78} +5.56155 q^{79} +(-0.280776 + 0.486319i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.06155 + 3.57071i) q^{82} +6.24621 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.40388 + 2.43160i) q^{85} -11.1231 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.780776 - 1.35234i) q^{88} +(-1.34233 + 2.32498i) q^{89} +0.561553 q^{90} +(-3.34233 + 1.35234i) q^{91} -0.876894 q^{92} +(1.56155 - 2.70469i) q^{93} +(-2.34233 + 4.05703i) q^{94} +(1.31534 + 2.27824i) q^{95} +1.00000 q^{96} +(2.12311 + 3.67733i) q^{97} +(-0.500000 - 0.866025i) q^{98} -1.56155 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10})$$ $$4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + 3q^{10} - q^{11} + 4q^{12} - 2q^{13} - 4q^{14} + 3q^{15} - 2q^{16} + 10q^{17} + 4q^{18} - 3q^{19} + 3q^{20} - 4q^{21} - q^{22} + 10q^{23} - 2q^{24} + 6q^{25} + q^{26} + 4q^{27} + 2q^{28} + 2q^{29} + 3q^{30} + 4q^{31} - 2q^{32} - q^{33} - 20q^{34} - 3q^{35} - 2q^{36} - q^{37} + 6q^{38} + q^{39} - 6q^{40} + 2q^{42} + 14q^{43} + 2q^{44} + 3q^{45} + 10q^{46} - 6q^{47} - 2q^{48} - 2q^{49} - 3q^{50} - 20q^{51} + q^{52} - 32q^{53} - 2q^{54} + 10q^{55} + 2q^{56} + 6q^{57} + 2q^{58} - 18q^{59} - 6q^{60} + 2q^{61} - 2q^{62} + 2q^{63} + 4q^{64} + 3q^{65} + 2q^{66} + 6q^{67} + 10q^{68} + 10q^{69} + 6q^{70} + 8q^{71} - 2q^{72} - 18q^{73} - q^{74} - 3q^{75} - 3q^{76} - 2q^{77} + q^{78} + 14q^{79} + 3q^{80} - 2q^{81} - 8q^{83} + 2q^{84} - 15q^{85} - 28q^{86} + 2q^{87} - q^{88} + 7q^{89} - 6q^{90} - q^{91} - 20q^{92} - 2q^{93} + 3q^{94} + 30q^{95} + 4q^{96} - 8q^{97} - 2q^{98} + 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0.561553 0.251134 0.125567 0.992085i $$-0.459925\pi$$
0.125567 + 0.992085i $$0.459925\pi$$
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.280776 + 0.486319i −0.0887893 + 0.153788i
$$11$$ 0.780776 1.35234i 0.235413 0.407747i −0.723980 0.689821i $$-0.757689\pi$$
0.959393 + 0.282074i $$0.0910224\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −0.500000 + 3.57071i −0.138675 + 0.990338i
$$14$$ −1.00000 −0.267261
$$15$$ −0.280776 + 0.486319i −0.0724962 + 0.125567i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i $$0.0406959\pi$$
−0.385499 + 0.922708i $$0.625971\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 2.34233 + 4.05703i 0.537367 + 0.930747i 0.999045 + 0.0436994i $$0.0139144\pi$$
−0.461678 + 0.887048i $$0.652752\pi$$
$$20$$ −0.280776 0.486319i −0.0627835 0.108744i
$$21$$ −1.00000 −0.218218
$$22$$ 0.780776 + 1.35234i 0.166462 + 0.288321i
$$23$$ 0.438447 0.759413i 0.0914226 0.158349i −0.816687 0.577080i $$-0.804192\pi$$
0.908110 + 0.418732i $$0.137525\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ −4.68466 −0.936932
$$26$$ −2.84233 2.21837i −0.557427 0.435058i
$$27$$ 1.00000 0.192450
$$28$$ 0.500000 0.866025i 0.0944911 0.163663i
$$29$$ 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i $$-0.803736\pi$$
0.908708 + 0.417432i $$0.137070\pi$$
$$30$$ −0.280776 0.486319i −0.0512625 0.0887893i
$$31$$ −3.12311 −0.560926 −0.280463 0.959865i $$-0.590488\pi$$
−0.280463 + 0.959865i $$0.590488\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0.780776 + 1.35234i 0.135916 + 0.235413i
$$34$$ −5.00000 −0.857493
$$35$$ 0.280776 + 0.486319i 0.0474599 + 0.0822029i
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ −5.40388 + 9.35980i −0.888393 + 1.53874i −0.0466177 + 0.998913i $$0.514844\pi$$
−0.841775 + 0.539829i $$0.818489\pi$$
$$38$$ −4.68466 −0.759952
$$39$$ −2.84233 2.21837i −0.455137 0.355223i
$$40$$ 0.561553 0.0887893
$$41$$ 2.06155 3.57071i 0.321960 0.557652i −0.658932 0.752202i $$-0.728992\pi$$
0.980892 + 0.194551i $$0.0623249\pi$$
$$42$$ 0.500000 0.866025i 0.0771517 0.133631i
$$43$$ 5.56155 + 9.63289i 0.848129 + 1.46900i 0.882876 + 0.469606i $$0.155604\pi$$
−0.0347472 + 0.999396i $$0.511063\pi$$
$$44$$ −1.56155 −0.235413
$$45$$ −0.280776 0.486319i −0.0418557 0.0724962i
$$46$$ 0.438447 + 0.759413i 0.0646455 + 0.111969i
$$47$$ 4.68466 0.683328 0.341664 0.939822i $$-0.389010\pi$$
0.341664 + 0.939822i $$0.389010\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ −0.500000 + 0.866025i −0.0714286 + 0.123718i
$$50$$ 2.34233 4.05703i 0.331255 0.573751i
$$51$$ −5.00000 −0.700140
$$52$$ 3.34233 1.35234i 0.463498 0.187536i
$$53$$ −12.1231 −1.66524 −0.832618 0.553847i $$-0.813159\pi$$
−0.832618 + 0.553847i $$0.813159\pi$$
$$54$$ −0.500000 + 0.866025i −0.0680414 + 0.117851i
$$55$$ 0.438447 0.759413i 0.0591202 0.102399i
$$56$$ 0.500000 + 0.866025i 0.0668153 + 0.115728i
$$57$$ −4.68466 −0.620498
$$58$$ 0.500000 + 0.866025i 0.0656532 + 0.113715i
$$59$$ −2.43845 4.22351i −0.317459 0.549855i 0.662498 0.749063i $$-0.269496\pi$$
−0.979957 + 0.199209i $$0.936163\pi$$
$$60$$ 0.561553 0.0724962
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 1.56155 2.70469i 0.198317 0.343496i
$$63$$ 0.500000 0.866025i 0.0629941 0.109109i
$$64$$ 1.00000 0.125000
$$65$$ −0.280776 + 2.00514i −0.0348260 + 0.248708i
$$66$$ −1.56155 −0.192214
$$67$$ 3.56155 6.16879i 0.435113 0.753638i −0.562192 0.827007i $$-0.690042\pi$$
0.997305 + 0.0733691i $$0.0233751\pi$$
$$68$$ 2.50000 4.33013i 0.303170 0.525105i
$$69$$ 0.438447 + 0.759413i 0.0527828 + 0.0914226i
$$70$$ −0.561553 −0.0671184
$$71$$ 2.00000 + 3.46410i 0.237356 + 0.411113i 0.959955 0.280155i $$-0.0903858\pi$$
−0.722599 + 0.691268i $$0.757052\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ −6.56155 −0.767972 −0.383986 0.923339i $$-0.625449\pi$$
−0.383986 + 0.923339i $$0.625449\pi$$
$$74$$ −5.40388 9.35980i −0.628189 1.08805i
$$75$$ 2.34233 4.05703i 0.270469 0.468466i
$$76$$ 2.34233 4.05703i 0.268684 0.465374i
$$77$$ 1.56155 0.177955
$$78$$ 3.34233 1.35234i 0.378444 0.153123i
$$79$$ 5.56155 0.625724 0.312862 0.949799i $$-0.398712\pi$$
0.312862 + 0.949799i $$0.398712\pi$$
$$80$$ −0.280776 + 0.486319i −0.0313918 + 0.0543721i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 2.06155 + 3.57071i 0.227660 + 0.394319i
$$83$$ 6.24621 0.685611 0.342805 0.939406i $$-0.388623\pi$$
0.342805 + 0.939406i $$0.388623\pi$$
$$84$$ 0.500000 + 0.866025i 0.0545545 + 0.0944911i
$$85$$ 1.40388 + 2.43160i 0.152272 + 0.263744i
$$86$$ −11.1231 −1.19944
$$87$$ 0.500000 + 0.866025i 0.0536056 + 0.0928477i
$$88$$ 0.780776 1.35234i 0.0832310 0.144160i
$$89$$ −1.34233 + 2.32498i −0.142287 + 0.246448i −0.928357 0.371689i $$-0.878779\pi$$
0.786071 + 0.618137i $$0.212112\pi$$
$$90$$ 0.561553 0.0591929
$$91$$ −3.34233 + 1.35234i −0.350371 + 0.141764i
$$92$$ −0.876894 −0.0914226
$$93$$ 1.56155 2.70469i 0.161925 0.280463i
$$94$$ −2.34233 + 4.05703i −0.241593 + 0.418451i
$$95$$ 1.31534 + 2.27824i 0.134951 + 0.233742i
$$96$$ 1.00000 0.102062
$$97$$ 2.12311 + 3.67733i 0.215569 + 0.373376i 0.953448 0.301556i $$-0.0975061\pi$$
−0.737880 + 0.674932i $$0.764173\pi$$
$$98$$ −0.500000 0.866025i −0.0505076 0.0874818i
$$99$$ −1.56155 −0.156942
$$100$$ 2.34233 + 4.05703i 0.234233 + 0.405703i
$$101$$ 7.71922 13.3701i 0.768091 1.33037i −0.170505 0.985357i $$-0.554540\pi$$
0.938597 0.345017i $$-0.112127\pi$$
$$102$$ 2.50000 4.33013i 0.247537 0.428746i
$$103$$ 13.3693 1.31732 0.658659 0.752442i $$-0.271124\pi$$
0.658659 + 0.752442i $$0.271124\pi$$
$$104$$ −0.500000 + 3.57071i −0.0490290 + 0.350137i
$$105$$ −0.561553 −0.0548019
$$106$$ 6.06155 10.4989i 0.588750 1.01975i
$$107$$ 6.78078 11.7446i 0.655522 1.13540i −0.326240 0.945287i $$-0.605782\pi$$
0.981763 0.190111i $$-0.0608848\pi$$
$$108$$ −0.500000 0.866025i −0.0481125 0.0833333i
$$109$$ 9.12311 0.873835 0.436918 0.899502i $$-0.356070\pi$$
0.436918 + 0.899502i $$0.356070\pi$$
$$110$$ 0.438447 + 0.759413i 0.0418043 + 0.0724072i
$$111$$ −5.40388 9.35980i −0.512914 0.888393i
$$112$$ −1.00000 −0.0944911
$$113$$ 5.96543 + 10.3324i 0.561181 + 0.971994i 0.997394 + 0.0721503i $$0.0229861\pi$$
−0.436213 + 0.899844i $$0.643681\pi$$
$$114$$ 2.34233 4.05703i 0.219379 0.379976i
$$115$$ 0.246211 0.426450i 0.0229593 0.0397667i
$$116$$ −1.00000 −0.0928477
$$117$$ 3.34233 1.35234i 0.308998 0.125024i
$$118$$ 4.87689 0.448955
$$119$$ −2.50000 + 4.33013i −0.229175 + 0.396942i
$$120$$ −0.280776 + 0.486319i −0.0256313 + 0.0443946i
$$121$$ 4.28078 + 7.41452i 0.389161 + 0.674047i
$$122$$ −1.00000 −0.0905357
$$123$$ 2.06155 + 3.57071i 0.185884 + 0.321960i
$$124$$ 1.56155 + 2.70469i 0.140232 + 0.242888i
$$125$$ −5.43845 −0.486430
$$126$$ 0.500000 + 0.866025i 0.0445435 + 0.0771517i
$$127$$ 7.12311 12.3376i 0.632073 1.09478i −0.355054 0.934846i $$-0.615537\pi$$
0.987127 0.159937i $$-0.0511292\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ −11.1231 −0.979335
$$130$$ −1.59612 1.24573i −0.139989 0.109258i
$$131$$ 16.4924 1.44095 0.720475 0.693481i $$-0.243924\pi$$
0.720475 + 0.693481i $$0.243924\pi$$
$$132$$ 0.780776 1.35234i 0.0679579 0.117706i
$$133$$ −2.34233 + 4.05703i −0.203106 + 0.351789i
$$134$$ 3.56155 + 6.16879i 0.307671 + 0.532902i
$$135$$ 0.561553 0.0483308
$$136$$ 2.50000 + 4.33013i 0.214373 + 0.371305i
$$137$$ −7.40388 12.8239i −0.632556 1.09562i −0.987027 0.160553i $$-0.948672\pi$$
0.354471 0.935067i $$-0.384661\pi$$
$$138$$ −0.876894 −0.0746462
$$139$$ −2.34233 4.05703i −0.198674 0.344113i 0.749425 0.662089i $$-0.230330\pi$$
−0.948099 + 0.317976i $$0.896997\pi$$
$$140$$ 0.280776 0.486319i 0.0237299 0.0411015i
$$141$$ −2.34233 + 4.05703i −0.197260 + 0.341664i
$$142$$ −4.00000 −0.335673
$$143$$ 4.43845 + 3.46410i 0.371162 + 0.289683i
$$144$$ 1.00000 0.0833333
$$145$$ 0.280776 0.486319i 0.0233172 0.0403866i
$$146$$ 3.28078 5.68247i 0.271519 0.470285i
$$147$$ −0.500000 0.866025i −0.0412393 0.0714286i
$$148$$ 10.8078 0.888393
$$149$$ −1.40388 2.43160i −0.115010 0.199204i 0.802773 0.596284i $$-0.203357\pi$$
−0.917784 + 0.397080i $$0.870024\pi$$
$$150$$ 2.34233 + 4.05703i 0.191250 + 0.331255i
$$151$$ −21.5616 −1.75465 −0.877327 0.479893i $$-0.840676\pi$$
−0.877327 + 0.479893i $$0.840676\pi$$
$$152$$ 2.34233 + 4.05703i 0.189988 + 0.329069i
$$153$$ 2.50000 4.33013i 0.202113 0.350070i
$$154$$ −0.780776 + 1.35234i −0.0629168 + 0.108975i
$$155$$ −1.75379 −0.140868
$$156$$ −0.500000 + 3.57071i −0.0400320 + 0.285886i
$$157$$ 14.8078 1.18179 0.590894 0.806749i $$-0.298775\pi$$
0.590894 + 0.806749i $$0.298775\pi$$
$$158$$ −2.78078 + 4.81645i −0.221227 + 0.383176i
$$159$$ 6.06155 10.4989i 0.480712 0.832618i
$$160$$ −0.280776 0.486319i −0.0221973 0.0384469i
$$161$$ 0.876894 0.0691090
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −3.56155 6.16879i −0.278962 0.483177i 0.692165 0.721739i $$-0.256657\pi$$
−0.971127 + 0.238563i $$0.923324\pi$$
$$164$$ −4.12311 −0.321960
$$165$$ 0.438447 + 0.759413i 0.0341331 + 0.0591202i
$$166$$ −3.12311 + 5.40938i −0.242400 + 0.419849i
$$167$$ 6.24621 10.8188i 0.483346 0.837180i −0.516471 0.856305i $$-0.672755\pi$$
0.999817 + 0.0191244i $$0.00608786\pi$$
$$168$$ −1.00000 −0.0771517
$$169$$ −12.5000 3.57071i −0.961538 0.274670i
$$170$$ −2.80776 −0.215346
$$171$$ 2.34233 4.05703i 0.179122 0.310249i
$$172$$ 5.56155 9.63289i 0.424064 0.734501i
$$173$$ 6.56155 + 11.3649i 0.498866 + 0.864061i 0.999999 0.00130937i $$-0.000416786\pi$$
−0.501134 + 0.865370i $$0.667083\pi$$
$$174$$ −1.00000 −0.0758098
$$175$$ −2.34233 4.05703i −0.177063 0.306683i
$$176$$ 0.780776 + 1.35234i 0.0588532 + 0.101937i
$$177$$ 4.87689 0.366570
$$178$$ −1.34233 2.32498i −0.100612 0.174265i
$$179$$ −8.24621 + 14.2829i −0.616351 + 1.06755i 0.373795 + 0.927511i $$0.378056\pi$$
−0.990146 + 0.140040i $$0.955277\pi$$
$$180$$ −0.280776 + 0.486319i −0.0209278 + 0.0362481i
$$181$$ −3.24621 −0.241289 −0.120644 0.992696i $$-0.538496\pi$$
−0.120644 + 0.992696i $$0.538496\pi$$
$$182$$ 0.500000 3.57071i 0.0370625 0.264679i
$$183$$ −1.00000 −0.0739221
$$184$$ 0.438447 0.759413i 0.0323228 0.0559847i
$$185$$ −3.03457 + 5.25602i −0.223106 + 0.386430i
$$186$$ 1.56155 + 2.70469i 0.114499 + 0.198317i
$$187$$ 7.80776 0.570960
$$188$$ −2.34233 4.05703i −0.170832 0.295890i
$$189$$ 0.500000 + 0.866025i 0.0363696 + 0.0629941i
$$190$$ −2.63068 −0.190850
$$191$$ −11.1231 19.2658i −0.804840 1.39402i −0.916399 0.400265i $$-0.868918\pi$$
0.111560 0.993758i $$-0.464415\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −2.18466 + 3.78394i −0.157255 + 0.272374i −0.933878 0.357592i $$-0.883598\pi$$
0.776623 + 0.629966i $$0.216931\pi$$
$$194$$ −4.24621 −0.304860
$$195$$ −1.59612 1.24573i −0.114300 0.0892087i
$$196$$ 1.00000 0.0714286
$$197$$ −1.78078 + 3.08440i −0.126875 + 0.219754i −0.922464 0.386082i $$-0.873828\pi$$
0.795589 + 0.605836i $$0.207161\pi$$
$$198$$ 0.780776 1.35234i 0.0554874 0.0961069i
$$199$$ −11.8078 20.4516i −0.837030 1.44978i −0.892367 0.451311i $$-0.850956\pi$$
0.0553365 0.998468i $$-0.482377\pi$$
$$200$$ −4.68466 −0.331255
$$201$$ 3.56155 + 6.16879i 0.251213 + 0.435113i
$$202$$ 7.71922 + 13.3701i 0.543123 + 0.940716i
$$203$$ 1.00000 0.0701862
$$204$$ 2.50000 + 4.33013i 0.175035 + 0.303170i
$$205$$ 1.15767 2.00514i 0.0808552 0.140045i
$$206$$ −6.68466 + 11.5782i −0.465742 + 0.806689i
$$207$$ −0.876894 −0.0609484
$$208$$ −2.84233 2.21837i −0.197080 0.153816i
$$209$$ 7.31534 0.506013
$$210$$ 0.280776 0.486319i 0.0193754 0.0335592i
$$211$$ 5.56155 9.63289i 0.382873 0.663156i −0.608599 0.793478i $$-0.708268\pi$$
0.991472 + 0.130323i $$0.0416013\pi$$
$$212$$ 6.06155 + 10.4989i 0.416309 + 0.721069i
$$213$$ −4.00000 −0.274075
$$214$$ 6.78078 + 11.7446i 0.463524 + 0.802848i
$$215$$ 3.12311 + 5.40938i 0.212994 + 0.368916i
$$216$$ 1.00000 0.0680414
$$217$$ −1.56155 2.70469i −0.106005 0.183606i
$$218$$ −4.56155 + 7.90084i −0.308947 + 0.535112i
$$219$$ 3.28078 5.68247i 0.221694 0.383986i
$$220$$ −0.876894 −0.0591202
$$221$$ −16.7116 + 6.76172i −1.12415 + 0.454843i
$$222$$ 10.8078 0.725370
$$223$$ −8.24621 + 14.2829i −0.552207 + 0.956451i 0.445908 + 0.895079i $$0.352881\pi$$
−0.998115 + 0.0613719i $$0.980452\pi$$
$$224$$ 0.500000 0.866025i 0.0334077 0.0578638i
$$225$$ 2.34233 + 4.05703i 0.156155 + 0.270469i
$$226$$ −11.9309 −0.793630
$$227$$ −2.43845 4.22351i −0.161845 0.280324i 0.773685 0.633570i $$-0.218411\pi$$
−0.935531 + 0.353246i $$0.885078\pi$$
$$228$$ 2.34233 + 4.05703i 0.155125 + 0.268684i
$$229$$ 2.19224 0.144867 0.0724335 0.997373i $$-0.476923\pi$$
0.0724335 + 0.997373i $$0.476923\pi$$
$$230$$ 0.246211 + 0.426450i 0.0162347 + 0.0281193i
$$231$$ −0.780776 + 1.35234i −0.0513713 + 0.0889777i
$$232$$ 0.500000 0.866025i 0.0328266 0.0568574i
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ −0.500000 + 3.57071i −0.0326860 + 0.233425i
$$235$$ 2.63068 0.171607
$$236$$ −2.43845 + 4.22351i −0.158729 + 0.274927i
$$237$$ −2.78078 + 4.81645i −0.180631 + 0.312862i
$$238$$ −2.50000 4.33013i −0.162051 0.280680i
$$239$$ 4.00000 0.258738 0.129369 0.991596i $$-0.458705\pi$$
0.129369 + 0.991596i $$0.458705\pi$$
$$240$$ −0.280776 0.486319i −0.0181240 0.0313918i
$$241$$ −11.8423 20.5115i −0.762831 1.32126i −0.941385 0.337333i $$-0.890475\pi$$
0.178554 0.983930i $$-0.442858\pi$$
$$242$$ −8.56155 −0.550357
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0.500000 0.866025i 0.0320092 0.0554416i
$$245$$ −0.280776 + 0.486319i −0.0179381 + 0.0310698i
$$246$$ −4.12311 −0.262880
$$247$$ −15.6577 + 6.33527i −0.996274 + 0.403104i
$$248$$ −3.12311 −0.198317
$$249$$ −3.12311 + 5.40938i −0.197919 + 0.342805i
$$250$$ 2.71922 4.70983i 0.171979 0.297876i
$$251$$ 12.2462 + 21.2111i 0.772974 + 1.33883i 0.935926 + 0.352196i $$0.114565\pi$$
−0.162952 + 0.986634i $$0.552102\pi$$
$$252$$ −1.00000 −0.0629941
$$253$$ −0.684658 1.18586i −0.0430441 0.0745546i
$$254$$ 7.12311 + 12.3376i 0.446943 + 0.774129i
$$255$$ −2.80776 −0.175829
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 15.6231 27.0600i 0.974543 1.68796i 0.293106 0.956080i $$-0.405311\pi$$
0.681436 0.731877i $$-0.261356\pi$$
$$258$$ 5.56155 9.63289i 0.346247 0.599718i
$$259$$ −10.8078 −0.671562
$$260$$ 1.87689 0.759413i 0.116400 0.0470968i
$$261$$ −1.00000 −0.0618984
$$262$$ −8.24621 + 14.2829i −0.509453 + 0.882398i
$$263$$ −6.24621 + 10.8188i −0.385158 + 0.667113i −0.991791 0.127869i $$-0.959186\pi$$
0.606633 + 0.794982i $$0.292520\pi$$
$$264$$ 0.780776 + 1.35234i 0.0480535 + 0.0832310i
$$265$$ −6.80776 −0.418198
$$266$$ −2.34233 4.05703i −0.143617 0.248753i
$$267$$ −1.34233 2.32498i −0.0821492 0.142287i
$$268$$ −7.12311 −0.435113
$$269$$ 6.56155 + 11.3649i 0.400065 + 0.692933i 0.993733 0.111777i $$-0.0356542\pi$$
−0.593668 + 0.804710i $$0.702321\pi$$
$$270$$ −0.280776 + 0.486319i −0.0170875 + 0.0295964i
$$271$$ −2.43845 + 4.22351i −0.148125 + 0.256560i −0.930535 0.366204i $$-0.880657\pi$$
0.782409 + 0.622764i $$0.213990\pi$$
$$272$$ −5.00000 −0.303170
$$273$$ 0.500000 3.57071i 0.0302614 0.216109i
$$274$$ 14.8078 0.894570
$$275$$ −3.65767 + 6.33527i −0.220566 + 0.382031i
$$276$$ 0.438447 0.759413i 0.0263914 0.0457113i
$$277$$ −0.280776 0.486319i −0.0168702 0.0292201i 0.857467 0.514539i $$-0.172037\pi$$
−0.874337 + 0.485319i $$0.838704\pi$$
$$278$$ 4.68466 0.280967
$$279$$ 1.56155 + 2.70469i 0.0934877 + 0.161925i
$$280$$ 0.280776 + 0.486319i 0.0167796 + 0.0290631i
$$281$$ −12.8078 −0.764047 −0.382024 0.924153i $$-0.624773\pi$$
−0.382024 + 0.924153i $$0.624773\pi$$
$$282$$ −2.34233 4.05703i −0.139484 0.241593i
$$283$$ 12.2462 21.2111i 0.727962 1.26087i −0.229782 0.973242i $$-0.573801\pi$$
0.957743 0.287624i $$-0.0928655\pi$$
$$284$$ 2.00000 3.46410i 0.118678 0.205557i
$$285$$ −2.63068 −0.155828
$$286$$ −5.21922 + 2.11176i −0.308619 + 0.124871i
$$287$$ 4.12311 0.243379
$$288$$ −0.500000 + 0.866025i −0.0294628 + 0.0510310i
$$289$$ −4.00000 + 6.92820i −0.235294 + 0.407541i
$$290$$ 0.280776 + 0.486319i 0.0164878 + 0.0285576i
$$291$$ −4.24621 −0.248917
$$292$$ 3.28078 + 5.68247i 0.191993 + 0.332541i
$$293$$ −3.84233 6.65511i −0.224471 0.388796i 0.731689 0.681638i $$-0.238732\pi$$
−0.956161 + 0.292843i $$0.905399\pi$$
$$294$$ 1.00000 0.0583212
$$295$$ −1.36932 2.37173i −0.0797247 0.138087i
$$296$$ −5.40388 + 9.35980i −0.314094 + 0.544027i
$$297$$ 0.780776 1.35234i 0.0453052 0.0784710i
$$298$$ 2.80776 0.162649
$$299$$ 2.49242 + 1.94528i 0.144141 + 0.112498i
$$300$$ −4.68466 −0.270469
$$301$$ −5.56155 + 9.63289i −0.320563 + 0.555231i
$$302$$ 10.7808 18.6729i 0.620364 1.07450i
$$303$$ 7.71922 + 13.3701i 0.443458 + 0.768091i
$$304$$ −4.68466 −0.268684
$$305$$ 0.280776 + 0.486319i 0.0160772 + 0.0278465i
$$306$$ 2.50000 + 4.33013i 0.142915 + 0.247537i
$$307$$ −5.06913 −0.289311 −0.144655 0.989482i $$-0.546207\pi$$
−0.144655 + 0.989482i $$0.546207\pi$$
$$308$$ −0.780776 1.35234i −0.0444889 0.0770570i
$$309$$ −6.68466 + 11.5782i −0.380277 + 0.658659i
$$310$$ 0.876894 1.51883i 0.0498043 0.0862635i
$$311$$ 18.4384 1.04555 0.522774 0.852471i $$-0.324897\pi$$
0.522774 + 0.852471i $$0.324897\pi$$
$$312$$ −2.84233 2.21837i −0.160915 0.125590i
$$313$$ −13.6155 −0.769595 −0.384798 0.923001i $$-0.625729\pi$$
−0.384798 + 0.923001i $$0.625729\pi$$
$$314$$ −7.40388 + 12.8239i −0.417825 + 0.723695i
$$315$$ 0.280776 0.486319i 0.0158200 0.0274010i
$$316$$ −2.78078 4.81645i −0.156431 0.270946i
$$317$$ −7.43845 −0.417785 −0.208892 0.977939i $$-0.566986\pi$$
−0.208892 + 0.977939i $$0.566986\pi$$
$$318$$ 6.06155 + 10.4989i 0.339915 + 0.588750i
$$319$$ −0.780776 1.35234i −0.0437151 0.0757168i
$$320$$ 0.561553 0.0313918
$$321$$ 6.78078 + 11.7446i 0.378466 + 0.655522i
$$322$$ −0.438447 + 0.759413i −0.0244337 + 0.0423204i
$$323$$ −11.7116 + 20.2852i −0.651653 + 1.12870i
$$324$$ 1.00000 0.0555556
$$325$$ 2.34233 16.7276i 0.129929 0.927879i
$$326$$ 7.12311 0.394512
$$327$$ −4.56155 + 7.90084i −0.252254 + 0.436918i
$$328$$ 2.06155 3.57071i 0.113830 0.197160i
$$329$$ 2.34233 + 4.05703i 0.129137 + 0.223671i
$$330$$ −0.876894 −0.0482714
$$331$$ 5.31534 + 9.20644i 0.292158 + 0.506032i 0.974320 0.225169i $$-0.0722935\pi$$
−0.682162 + 0.731201i $$0.738960\pi$$
$$332$$ −3.12311 5.40938i −0.171403 0.296878i
$$333$$ 10.8078 0.592262
$$334$$ 6.24621 + 10.8188i 0.341777 + 0.591976i
$$335$$ 2.00000 3.46410i 0.109272 0.189264i
$$336$$ 0.500000 0.866025i 0.0272772 0.0472456i
$$337$$ 3.49242 0.190244 0.0951222 0.995466i $$-0.469676\pi$$
0.0951222 + 0.995466i $$0.469676\pi$$
$$338$$ 9.34233 9.03996i 0.508156 0.491709i
$$339$$ −11.9309 −0.647996
$$340$$ 1.40388 2.43160i 0.0761362 0.131872i
$$341$$ −2.43845 + 4.22351i −0.132049 + 0.228716i
$$342$$ 2.34233 + 4.05703i 0.126659 + 0.219379i
$$343$$ −1.00000 −0.0539949
$$344$$ 5.56155 + 9.63289i 0.299859 + 0.519371i
$$345$$ 0.246211 + 0.426450i 0.0132556 + 0.0229593i
$$346$$ −13.1231 −0.705503
$$347$$ 6.34233 + 10.9852i 0.340474 + 0.589718i 0.984521 0.175268i $$-0.0560791\pi$$
−0.644047 + 0.764986i $$0.722746\pi$$
$$348$$ 0.500000 0.866025i 0.0268028 0.0464238i
$$349$$ −13.2462 + 22.9431i −0.709053 + 1.22812i 0.256155 + 0.966636i $$0.417544\pi$$
−0.965209 + 0.261481i $$0.915789\pi$$
$$350$$ 4.68466 0.250406
$$351$$ −0.500000 + 3.57071i −0.0266880 + 0.190591i
$$352$$ −1.56155 −0.0832310
$$353$$ −5.40388 + 9.35980i −0.287620 + 0.498172i −0.973241 0.229786i $$-0.926197\pi$$
0.685621 + 0.727958i $$0.259531\pi$$
$$354$$ −2.43845 + 4.22351i −0.129602 + 0.224477i
$$355$$ 1.12311 + 1.94528i 0.0596083 + 0.103245i
$$356$$ 2.68466 0.142287
$$357$$ −2.50000 4.33013i −0.132314 0.229175i
$$358$$ −8.24621 14.2829i −0.435826 0.754872i
$$359$$ −29.3693 −1.55005 −0.775027 0.631929i $$-0.782264\pi$$
−0.775027 + 0.631929i $$0.782264\pi$$
$$360$$ −0.280776 0.486319i −0.0147982 0.0256313i
$$361$$ −1.47301 + 2.55133i −0.0775270 + 0.134281i
$$362$$ 1.62311 2.81130i 0.0853085 0.147759i
$$363$$ −8.56155 −0.449365
$$364$$ 2.84233 + 2.21837i 0.148979 + 0.116274i
$$365$$ −3.68466 −0.192864
$$366$$ 0.500000 0.866025i 0.0261354 0.0452679i
$$367$$ 6.68466 11.5782i 0.348936 0.604375i −0.637124 0.770761i $$-0.719876\pi$$
0.986061 + 0.166385i $$0.0532096\pi$$
$$368$$ 0.438447 + 0.759413i 0.0228556 + 0.0395871i
$$369$$ −4.12311 −0.214640
$$370$$ −3.03457 5.25602i −0.157760 0.273248i
$$371$$ −6.06155 10.4989i −0.314700 0.545077i
$$372$$ −3.12311 −0.161925
$$373$$ −8.71922 15.1021i −0.451464 0.781959i 0.547013 0.837124i $$-0.315765\pi$$
−0.998477 + 0.0551651i $$0.982431\pi$$
$$374$$ −3.90388 + 6.76172i −0.201865 + 0.349640i
$$375$$ 2.71922 4.70983i 0.140420 0.243215i
$$376$$ 4.68466 0.241593
$$377$$ 2.84233 + 2.21837i 0.146387 + 0.114252i
$$378$$ −1.00000 −0.0514344
$$379$$ 16.2462 28.1393i 0.834512 1.44542i −0.0599155 0.998203i $$-0.519083\pi$$
0.894427 0.447213i $$-0.147584\pi$$
$$380$$ 1.31534 2.27824i 0.0674756 0.116871i
$$381$$ 7.12311 + 12.3376i 0.364928 + 0.632073i
$$382$$ 22.2462 1.13822
$$383$$ −10.3423 17.9134i −0.528468 0.915334i −0.999449 0.0331905i $$-0.989433\pi$$
0.470981 0.882144i $$-0.343900\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 0.876894 0.0446907
$$386$$ −2.18466 3.78394i −0.111196 0.192597i
$$387$$ 5.56155 9.63289i 0.282710 0.489667i
$$388$$ 2.12311 3.67733i 0.107784 0.186688i
$$389$$ 6.31534 0.320201 0.160100 0.987101i $$-0.448818\pi$$
0.160100 + 0.987101i $$0.448818\pi$$
$$390$$ 1.87689 0.759413i 0.0950402 0.0384544i
$$391$$ 4.38447 0.221732
$$392$$ −0.500000 + 0.866025i −0.0252538 + 0.0437409i
$$393$$ −8.24621 + 14.2829i −0.415966 + 0.720475i
$$394$$ −1.78078 3.08440i −0.0897142 0.155390i
$$395$$ 3.12311 0.157140
$$396$$ 0.780776 + 1.35234i 0.0392355 + 0.0679579i
$$397$$ 5.34233 + 9.25319i 0.268124 + 0.464404i 0.968377 0.249490i $$-0.0802630\pi$$
−0.700254 + 0.713894i $$0.746930\pi$$
$$398$$ 23.6155 1.18374
$$399$$ −2.34233 4.05703i −0.117263 0.203106i
$$400$$ 2.34233 4.05703i 0.117116 0.202852i
$$401$$ 15.0885 26.1341i 0.753486 1.30508i −0.192638 0.981270i $$-0.561704\pi$$
0.946124 0.323806i $$-0.104962\pi$$
$$402$$ −7.12311 −0.355268
$$403$$ 1.56155 11.1517i 0.0777865 0.555507i
$$404$$ −15.4384 −0.768091
$$405$$ −0.280776 + 0.486319i −0.0139519 + 0.0241654i
$$406$$ −0.500000 + 0.866025i −0.0248146 + 0.0429801i
$$407$$ 8.43845 + 14.6158i 0.418278 + 0.724479i
$$408$$ −5.00000 −0.247537
$$409$$ 17.2808 + 29.9312i 0.854479 + 1.48000i 0.877127 + 0.480258i $$0.159457\pi$$
−0.0226477 + 0.999744i $$0.507210\pi$$
$$410$$ 1.15767 + 2.00514i 0.0571733 + 0.0990270i
$$411$$ 14.8078 0.730413
$$412$$ −6.68466 11.5782i −0.329329 0.570415i
$$413$$ 2.43845 4.22351i 0.119988 0.207826i
$$414$$ 0.438447 0.759413i 0.0215485 0.0373231i
$$415$$ 3.50758 0.172180
$$416$$ 3.34233 1.35234i 0.163871 0.0663041i
$$417$$ 4.68466 0.229409
$$418$$ −3.65767 + 6.33527i −0.178903 + 0.309868i
$$419$$ 13.3693 23.1563i 0.653134 1.13126i −0.329224 0.944252i $$-0.606787\pi$$
0.982358 0.187009i $$-0.0598795\pi$$
$$420$$ 0.280776 + 0.486319i 0.0137005 + 0.0237299i
$$421$$ 12.5616 0.612213 0.306106 0.951997i $$-0.400974\pi$$
0.306106 + 0.951997i $$0.400974\pi$$
$$422$$ 5.56155 + 9.63289i 0.270732 + 0.468922i
$$423$$ −2.34233 4.05703i −0.113888 0.197260i
$$424$$ −12.1231 −0.588750
$$425$$ −11.7116 20.2852i −0.568098 0.983975i
$$426$$ 2.00000 3.46410i 0.0969003 0.167836i
$$427$$ −0.500000 + 0.866025i −0.0241967 + 0.0419099i
$$428$$ −13.5616 −0.655522
$$429$$ −5.21922 + 2.11176i −0.251986 + 0.101957i
$$430$$ −6.24621 −0.301219
$$431$$ −15.3693 + 26.6204i −0.740314 + 1.28226i 0.212038 + 0.977261i $$0.431990\pi$$
−0.952352 + 0.305000i $$0.901344\pi$$
$$432$$ −0.500000 + 0.866025i −0.0240563 + 0.0416667i
$$433$$ 8.84233 + 15.3154i 0.424935 + 0.736009i 0.996414 0.0846072i $$-0.0269635\pi$$
−0.571479 + 0.820617i $$0.693630\pi$$
$$434$$ 3.12311 0.149914
$$435$$ 0.280776 + 0.486319i 0.0134622 + 0.0233172i
$$436$$ −4.56155 7.90084i −0.218459 0.378382i
$$437$$ 4.10795 0.196510
$$438$$ 3.28078 + 5.68247i 0.156762 + 0.271519i
$$439$$ −2.24621 + 3.89055i −0.107206 + 0.185686i −0.914637 0.404275i $$-0.867524\pi$$
0.807431 + 0.589961i $$0.200857\pi$$
$$440$$ 0.438447 0.759413i 0.0209021 0.0362036i
$$441$$ 1.00000 0.0476190
$$442$$ 2.50000 17.8536i 0.118913 0.849208i
$$443$$ 27.4233 1.30292 0.651460 0.758683i $$-0.274157\pi$$
0.651460 + 0.758683i $$0.274157\pi$$
$$444$$ −5.40388 + 9.35980i −0.256457 + 0.444196i
$$445$$ −0.753789 + 1.30560i −0.0357330 + 0.0618914i
$$446$$ −8.24621 14.2829i −0.390469 0.676313i
$$447$$ 2.80776 0.132803
$$448$$ 0.500000 + 0.866025i 0.0236228 + 0.0409159i
$$449$$ −9.00000 15.5885i −0.424736 0.735665i 0.571660 0.820491i $$-0.306300\pi$$
−0.996396 + 0.0848262i $$0.972967\pi$$
$$450$$ −4.68466 −0.220837
$$451$$ −3.21922 5.57586i −0.151587 0.262557i
$$452$$ 5.96543 10.3324i 0.280590 0.485997i
$$453$$ 10.7808 18.6729i 0.506525 0.877327i
$$454$$ 4.87689 0.228884
$$455$$ −1.87689 + 0.759413i −0.0879902 + 0.0356018i
$$456$$ −4.68466 −0.219379
$$457$$ 12.8423 22.2436i 0.600739 1.04051i −0.391971 0.919978i $$-0.628206\pi$$
0.992709 0.120532i $$-0.0384602\pi$$
$$458$$ −1.09612 + 1.89853i −0.0512182 + 0.0887126i
$$459$$ 2.50000 + 4.33013i 0.116690 + 0.202113i
$$460$$ −0.492423 −0.0229593
$$461$$ 3.52699 + 6.10892i 0.164268 + 0.284521i 0.936395 0.350947i $$-0.114140\pi$$
−0.772127 + 0.635468i $$0.780807\pi$$
$$462$$ −0.780776 1.35234i −0.0363250 0.0629168i
$$463$$ 0.684658 0.0318188 0.0159094 0.999873i $$-0.494936\pi$$
0.0159094 + 0.999873i $$0.494936\pi$$
$$464$$ 0.500000 + 0.866025i 0.0232119 + 0.0402042i
$$465$$ 0.876894 1.51883i 0.0406650 0.0704339i
$$466$$ 3.00000 5.19615i 0.138972 0.240707i
$$467$$ 28.0000 1.29569 0.647843 0.761774i $$-0.275671\pi$$
0.647843 + 0.761774i $$0.275671\pi$$
$$468$$ −2.84233 2.21837i −0.131387 0.102544i
$$469$$ 7.12311 0.328914
$$470$$ −1.31534 + 2.27824i −0.0606722 + 0.105087i
$$471$$ −7.40388 + 12.8239i −0.341153 + 0.590894i
$$472$$ −2.43845 4.22351i −0.112239 0.194403i
$$473$$ 17.3693 0.798642
$$474$$ −2.78078 4.81645i −0.127725 0.221227i
$$475$$ −10.9730 19.0058i −0.503476 0.872047i
$$476$$ 5.00000 0.229175
$$477$$ 6.06155 + 10.4989i 0.277539 + 0.480712i
$$478$$ −2.00000 + 3.46410i −0.0914779 + 0.158444i
$$479$$ −0.780776 + 1.35234i −0.0356746 + 0.0617902i −0.883311 0.468787i $$-0.844691\pi$$
0.847637 + 0.530577i $$0.178025\pi$$
$$480$$ 0.561553 0.0256313
$$481$$ −30.7192 23.9756i −1.40068 1.09319i
$$482$$ 23.6847 1.07881
$$483$$ −0.438447 + 0.759413i −0.0199500 + 0.0345545i
$$484$$ 4.28078 7.41452i 0.194581 0.337024i
$$485$$ 1.19224 + 2.06501i 0.0541366 + 0.0937674i
$$486$$ 1.00000 0.0453609
$$487$$ −5.65767 9.79937i −0.256374 0.444052i 0.708894 0.705315i $$-0.249194\pi$$
−0.965268 + 0.261263i $$0.915861\pi$$
$$488$$ 0.500000 + 0.866025i 0.0226339 + 0.0392031i
$$489$$ 7.12311 0.322118
$$490$$ −0.280776 0.486319i −0.0126842 0.0219697i
$$491$$ 9.12311 15.8017i 0.411720 0.713120i −0.583358 0.812215i $$-0.698262\pi$$
0.995078 + 0.0990952i $$0.0315948\pi$$
$$492$$ 2.06155 3.57071i 0.0929420 0.160980i
$$493$$ 5.00000 0.225189
$$494$$ 2.34233 16.7276i 0.105386 0.752609i
$$495$$ −0.876894 −0.0394135
$$496$$ 1.56155 2.70469i 0.0701158 0.121444i
$$497$$ −2.00000 + 3.46410i −0.0897123 + 0.155386i
$$498$$ −3.12311 5.40938i −0.139950 0.242400i
$$499$$ −2.63068 −0.117766 −0.0588828 0.998265i $$-0.518754\pi$$
−0.0588828 + 0.998265i $$0.518754\pi$$
$$500$$ 2.71922 + 4.70983i 0.121607 + 0.210630i
$$501$$ 6.24621 + 10.8188i 0.279060 + 0.483346i
$$502$$ −24.4924 −1.09315
$$503$$ 6.24621 + 10.8188i 0.278505 + 0.482384i 0.971013 0.239025i $$-0.0768279\pi$$
−0.692509 + 0.721410i $$0.743495\pi$$
$$504$$ 0.500000 0.866025i 0.0222718 0.0385758i
$$505$$ 4.33475 7.50801i 0.192894 0.334102i
$$506$$ 1.36932 0.0608736
$$507$$ 9.34233 9.03996i 0.414907 0.401479i
$$508$$ −14.2462 −0.632073
$$509$$ −19.8423 + 34.3679i −0.879496 + 1.52333i −0.0276006 + 0.999619i $$0.508787\pi$$
−0.851895 + 0.523712i $$0.824547\pi$$
$$510$$ 1.40388 2.43160i 0.0621649 0.107673i
$$511$$ −3.28078 5.68247i −0.145133 0.251378i
$$512$$ 1.00000 0.0441942
$$513$$ 2.34233 + 4.05703i 0.103416 + 0.179122i
$$514$$ 15.6231 + 27.0600i 0.689106 + 1.19357i
$$515$$ 7.50758 0.330823
$$516$$ 5.56155 + 9.63289i 0.244834 + 0.424064i
$$517$$ 3.65767 6.33527i 0.160864 0.278625i
$$518$$ 5.40388 9.35980i 0.237433 0.411246i
$$519$$ −13.1231 −0.576040
$$520$$ −0.280776 + 2.00514i −0.0123129 + 0.0879314i
$$521$$ −17.0000 −0.744784 −0.372392 0.928076i $$-0.621462\pi$$
−0.372392 + 0.928076i $$0.621462\pi$$
$$522$$ 0.500000 0.866025i 0.0218844 0.0379049i
$$523$$ −17.9039 + 31.0104i −0.782882 + 1.35599i 0.147374 + 0.989081i $$0.452918\pi$$
−0.930256 + 0.366911i $$0.880415\pi$$
$$524$$ −8.24621 14.2829i −0.360237 0.623949i
$$525$$ 4.68466 0.204455
$$526$$ −6.24621 10.8188i −0.272348 0.471720i
$$527$$ −7.80776 13.5234i −0.340112 0.589090i
$$528$$ −1.56155 −0.0679579
$$529$$ 11.1155 + 19.2527i 0.483284 + 0.837072i
$$530$$ 3.40388 5.89570i 0.147855 0.256093i
$$531$$ −2.43845 + 4.22351i −0.105820 + 0.183285i
$$532$$ 4.68466 0.203106
$$533$$ 11.7192 + 9.14657i 0.507616 + 0.396182i
$$534$$ 2.68466 0.116177
$$535$$ 3.80776 6.59524i 0.164624 0.285137i
$$536$$ 3.56155 6.16879i 0.153836 0.266451i
$$537$$ −8.24621 14.2829i −0.355850 0.616351i
$$538$$ −13.1231 −0.565777
$$539$$ 0.780776 + 1.35234i 0.0336304 + 0.0582496i
$$540$$ −0.280776 0.486319i −0.0120827 0.0209278i
$$541$$ −2.56155 −0.110130 −0.0550649 0.998483i $$-0.517537\pi$$
−0.0550649 + 0.998483i $$0.517537\pi$$
$$542$$ −2.43845 4.22351i −0.104740 0.181415i
$$543$$ 1.62311 2.81130i 0.0696541 0.120644i
$$544$$ 2.50000 4.33013i 0.107187 0.185653i
$$545$$ 5.12311 0.219450
$$546$$ 2.84233 + 2.21837i 0.121640 + 0.0949375i
$$547$$ 26.7386 1.14326 0.571631 0.820511i $$-0.306311\pi$$
0.571631 + 0.820511i $$0.306311\pi$$
$$548$$ −7.40388 + 12.8239i −0.316278 + 0.547810i
$$549$$ 0.500000 0.866025i 0.0213395 0.0369611i
$$550$$ −3.65767 6.33527i −0.155964 0.270137i
$$551$$ 4.68466 0.199573
$$552$$ 0.438447 + 0.759413i 0.0186616 + 0.0323228i
$$553$$ 2.78078 + 4.81645i 0.118251 + 0.204816i
$$554$$ 0.561553 0.0238581
$$555$$ −3.03457 5.25602i −0.128810 0.223106i
$$556$$ −2.34233 + 4.05703i −0.0993369 + 0.172057i
$$557$$ 13.8693 24.0224i 0.587662 1.01786i −0.406876 0.913483i $$-0.633382\pi$$
0.994538 0.104377i $$-0.0332848\pi$$
$$558$$ −3.12311 −0.132212
$$559$$ −37.1771 + 15.0423i −1.57242 + 0.636220i
$$560$$ −0.561553 −0.0237299
$$561$$ −3.90388 + 6.76172i −0.164822 + 0.285480i
$$562$$ 6.40388 11.0918i 0.270131 0.467881i
$$563$$ 12.6847 + 21.9705i 0.534595 + 0.925945i 0.999183 + 0.0404182i $$0.0128690\pi$$
−0.464588 + 0.885527i $$0.653798\pi$$
$$564$$ 4.68466 0.197260
$$565$$ 3.34991 + 5.80221i 0.140932 + 0.244101i
$$566$$ 12.2462 + 21.2111i 0.514747 + 0.891567i
$$567$$ −1.00000 −0.0419961
$$568$$ 2.00000 + 3.46410i 0.0839181 + 0.145350i
$$569$$ 14.8078 25.6478i 0.620774 1.07521i −0.368568 0.929601i $$-0.620152\pi$$
0.989342 0.145611i $$-0.0465148\pi$$
$$570$$ 1.31534 2.27824i 0.0550936 0.0954249i
$$571$$ 30.2462 1.26576 0.632882 0.774248i $$-0.281872\pi$$
0.632882 + 0.774248i $$0.281872\pi$$
$$572$$ 0.780776 5.57586i 0.0326459 0.233138i
$$573$$ 22.2462 0.929349
$$574$$ −2.06155 + 3.57071i −0.0860476 + 0.149039i
$$575$$ −2.05398 + 3.55759i −0.0856567 + 0.148362i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ 43.6847 1.81862 0.909308 0.416124i $$-0.136612\pi$$
0.909308 + 0.416124i $$0.136612\pi$$
$$578$$ −4.00000 6.92820i −0.166378 0.288175i
$$579$$ −2.18466 3.78394i −0.0907913 0.157255i
$$580$$ −0.561553 −0.0233172
$$581$$ 3.12311 + 5.40938i 0.129568 + 0.224419i
$$582$$ 2.12311 3.67733i 0.0880056 0.152430i
$$583$$ −9.46543 + 16.3946i −0.392018 + 0.678996i
$$584$$ −6.56155 −0.271519
$$585$$ 1.87689 0.759413i 0.0776000 0.0313979i
$$586$$ 7.68466 0.317450
$$587$$ −3.31534 + 5.74234i −0.136839 + 0.237012i −0.926298 0.376791i $$-0.877028\pi$$
0.789460 + 0.613803i $$0.210361\pi$$
$$588$$ −0.500000 + 0.866025i −0.0206197 + 0.0357143i
$$589$$ −7.31534 12.6705i −0.301423 0.522081i
$$590$$ 2.73863 0.112748
$$591$$ −1.78078 3.08440i −0.0732514 0.126875i
$$592$$ −5.40388 9.35980i −0.222098 0.384685i
$$593$$ −8.61553 −0.353797 −0.176899 0.984229i $$-0.556606\pi$$
−0.176899 + 0.984229i $$0.556606\pi$$
$$594$$ 0.780776 + 1.35234i 0.0320356 + 0.0554874i
$$595$$ −1.40388 + 2.43160i −0.0575536 + 0.0996857i
$$596$$ −1.40388 + 2.43160i −0.0575052 + 0.0996020i
$$597$$ 23.6155 0.966519
$$598$$ −2.93087 + 1.18586i −0.119852 + 0.0484936i
$$599$$ −31.1231 −1.27166 −0.635828 0.771831i $$-0.719341\pi$$
−0.635828 + 0.771831i $$0.719341\pi$$
$$600$$ 2.34233 4.05703i 0.0956252 0.165628i
$$601$$ −4.03457 + 6.98807i −0.164573 + 0.285049i −0.936504 0.350658i $$-0.885958\pi$$
0.771930 + 0.635707i $$0.219291\pi$$
$$602$$ −5.56155 9.63289i −0.226672 0.392607i
$$603$$ −7.12311 −0.290075
$$604$$ 10.7808 + 18.6729i 0.438664 + 0.759788i
$$605$$ 2.40388 + 4.16365i 0.0977317 + 0.169276i
$$606$$ −15.4384 −0.627144
$$607$$ −6.43845 11.1517i −0.261329 0.452634i 0.705267 0.708942i $$-0.250827\pi$$
−0.966595 + 0.256308i $$0.917494\pi$$
$$608$$ 2.34233 4.05703i 0.0949940 0.164534i
$$609$$ −0.500000 + 0.866025i −0.0202610 + 0.0350931i
$$610$$ −0.561553 −0.0227366
$$611$$ −2.34233 + 16.7276i −0.0947605 + 0.676725i
$$612$$ −5.00000 −0.202113
$$613$$ 8.65009 14.9824i 0.349374 0.605133i −0.636764 0.771058i $$-0.719728\pi$$
0.986138 + 0.165925i $$0.0530609\pi$$
$$614$$ 2.53457 4.39000i 0.102287 0.177166i
$$615$$ 1.15767 + 2.00514i 0.0466818 + 0.0808552i
$$616$$ 1.56155 0.0629168
$$617$$ −17.2116 29.8114i −0.692915 1.20016i −0.970879 0.239572i $$-0.922993\pi$$
0.277964 0.960592i $$-0.410340\pi$$
$$618$$ −6.68466 11.5782i −0.268896 0.465742i
$$619$$ 16.6847 0.670613 0.335307 0.942109i $$-0.391160\pi$$
0.335307 + 0.942109i $$0.391160\pi$$
$$620$$ 0.876894 + 1.51883i 0.0352169 + 0.0609975i
$$621$$ 0.438447 0.759413i 0.0175943 0.0304742i
$$622$$ −9.21922 + 15.9682i −0.369657 + 0.640265i
$$623$$ −2.68466 −0.107559
$$624$$ 3.34233 1.35234i 0.133800 0.0541371i
$$625$$ 20.3693 0.814773
$$626$$ 6.80776 11.7914i 0.272093 0.471279i
$$627$$ −3.65767 + 6.33527i −0.146073 + 0.253006i
$$628$$ −7.40388 12.8239i −0.295447 0.511729i
$$629$$ −54.0388 −2.15467
$$630$$ 0.280776 + 0.486319i 0.0111864 + 0.0193754i
$$631$$ −21.9039 37.9386i −0.871980 1.51031i −0.859946 0.510386i $$-0.829503\pi$$
−0.0120342 0.999928i $$-0.503831\pi$$
$$632$$ 5.56155 0.221227
$$633$$ 5.56155 + 9.63289i 0.221052 + 0.382873i
$$634$$ 3.71922 6.44188i 0.147709 0.255840i
$$635$$ 4.00000 6.92820i 0.158735 0.274937i
$$636$$ −12.1231 −0.480712
$$637$$ −2.84233 2.21837i −0.112617 0.0878950i
$$638$$ 1.56155 0.0618225
$$639$$ 2.00000 3.46410i 0.0791188 0.137038i
$$640$$ −0.280776 + 0.486319i −0.0110987 + 0.0192234i
$$641$$ −4.03457 6.98807i −0.159356 0.276012i 0.775281 0.631617i $$-0.217608\pi$$
−0.934637 + 0.355604i $$0.884275\pi$$
$$642$$ −13.5616 −0.535232
$$643$$ 11.2192 + 19.4323i 0.442443 + 0.766334i 0.997870 0.0652314i $$-0.0207786\pi$$
−0.555427 + 0.831565i $$0.687445\pi$$
$$644$$ −0.438447 0.759413i −0.0172772 0.0299251i
$$645$$ −6.24621 −0.245944
$$646$$ −11.7116 20.2852i −0.460789 0.798109i
$$647$$ 0.0961180 0.166481i 0.00377879 0.00654505i −0.864130 0.503269i $$-0.832131\pi$$
0.867909 + 0.496724i $$0.165464\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ −7.61553 −0.298936
$$650$$ 13.3153 + 10.3923i 0.522271 + 0.407620i
$$651$$ 3.12311 0.122404
$$652$$ −3.56155 + 6.16879i −0.139481 + 0.241588i
$$653$$ −0.903882 + 1.56557i −0.0353716 + 0.0612655i −0.883169 0.469054i $$-0.844595\pi$$
0.847798 + 0.530320i $$0.177928\pi$$
$$654$$ −4.56155 7.90084i −0.178371 0.308947i
$$655$$ 9.26137 0.361872
$$656$$ 2.06155 + 3.57071i 0.0804901 + 0.139413i
$$657$$ 3.28078 + 5.68247i 0.127995 + 0.221694i
$$658$$ −4.68466 −0.182627
$$659$$ 20.3423 + 35.2339i 0.792425 + 1.37252i 0.924462 + 0.381275i $$0.124515\pi$$
−0.132037 + 0.991245i $$0.542152\pi$$
$$660$$ 0.438447 0.759413i 0.0170665 0.0295601i
$$661$$ −5.40388 + 9.35980i −0.210187 + 0.364054i −0.951773 0.306804i $$-0.900741\pi$$
0.741586 + 0.670858i $$0.234074\pi$$
$$662$$ −10.6307 −0.413173
$$663$$ 2.50000 17.8536i 0.0970920 0.693375i
$$664$$ 6.24621 0.242400
$$665$$ −1.31534 + 2.27824i −0.0510068 + 0.0883463i
$$666$$ −5.40388 + 9.35980i −0.209396 + 0.362685i
$$667$$ −0.438447 0.759413i −0.0169767 0.0294046i
$$668$$ −12.4924 −0.483346
$$669$$ −8.24621 14.2829i −0.318817 0.552207i
$$670$$ 2.00000 + 3.46410i 0.0772667 + 0.133830i
$$671$$ 1.56155 0.0602831
$$672$$ 0.500000 + 0.866025i 0.0192879 + 0.0334077i
$$673$$ −12.6231 + 21.8639i −0.486585 + 0.842790i −0.999881 0.0154217i $$-0.995091\pi$$
0.513296 + 0.858212i $$0.328424\pi$$
$$674$$ −1.74621 + 3.02453i −0.0672615 + 0.116500i
$$675$$ −4.68466 −0.180313
$$676$$ 3.15767 + 12.6107i 0.121449 + 0.485026i
$$677$$ −49.6155 −1.90688 −0.953440 0.301583i $$-0.902485\pi$$
−0.953440 + 0.301583i $$0.902485\pi$$
$$678$$ 5.96543 10.3324i 0.229101 0.396815i
$$679$$ −2.12311 + 3.67733i −0.0814773 + 0.141123i
$$680$$ 1.40388 + 2.43160i 0.0538364 + 0.0932474i
$$681$$ 4.87689 0.186883
$$682$$ −2.43845 4.22351i −0.0933730 0.161727i
$$683$$ −2.00000 3.46410i −0.0765279 0.132550i 0.825222 0.564809i $$-0.191050\pi$$
−0.901750 + 0.432259i $$0.857717\pi$$
$$684$$ −4.68466 −0.179122
$$685$$ −4.15767 7.20130i −0.158856 0.275147i
$$686$$ 0.500000 0.866025i 0.0190901 0.0330650i
$$687$$ −1.09612 + 1.89853i −0.0418195 + 0.0724335i
$$688$$ −11.1231 −0.424064
$$689$$ 6.06155 43.2881i 0.230927 1.64915i
$$690$$ −0.492423 −0.0187462
$$691$$ −2.24621 + 3.89055i −0.0854499 + 0.148004i −0.905583 0.424169i $$-0.860566\pi$$
0.820133 + 0.572173i $$0.193899\pi$$
$$692$$ 6.56155 11.3649i 0.249433 0.432030i
$$693$$ −0.780776 1.35234i −0.0296592 0.0513713i
$$694$$ −12.6847 −0.481503
$$695$$ −1.31534 2.27824i −0.0498937 0.0864185i
$$696$$ 0.500000 + 0.866025i 0.0189525 + 0.0328266i
$$697$$ 20.6155 0.780869
$$698$$ −13.2462 22.9431i −0.501376 0.868410i
$$699$$ 3.00000 5.19615i 0.113470 0.196537i
$$700$$ −2.34233 + 4.05703i −0.0885317 + 0.153341i
$$701$$ −28.0540 −1.05958 −0.529792 0.848128i $$-0.677730\pi$$
−0.529792 + 0.848128i $$0.677730\pi$$
$$702$$ −2.84233 2.21837i −0.107277 0.0837270i
$$703$$ −50.6307 −1.90957
$$704$$ 0.780776 1.35234i 0.0294266 0.0509684i
$$705$$ −1.31534 + 2.27824i −0.0495386 + 0.0858034i
$$706$$ −5.40388 9.35980i −0.203378 0.352261i
$$707$$ 15.4384 0.580623
$$708$$ −2.43845 4.22351i −0.0916425 0.158729i
$$709$$ 16.6501 + 28.8388i 0.625307 + 1.08306i 0.988481 + 0.151343i $$0.0483597\pi$$
−0.363174 + 0.931721i $$0.618307\pi$$
$$710$$ −2.24621 −0.0842988
$$711$$ −2.78078 4.81645i −0.104287 0.180631i
$$712$$ −1.34233 + 2.32498i −0.0503059 + 0.0871324i
$$713$$ −1.36932 + 2.37173i −0.0512813 + 0.0888219i
$$714$$ 5.00000 0.187120
$$715$$ 2.49242 + 1.94528i 0.0932113 + 0.0727492i
$$716$$ 16.4924 0.616351
$$717$$ −2.00000 + 3.46410i −0.0746914 + 0.129369i
$$718$$ 14.6847 25.4346i 0.548027 0.949210i
$$719$$ 3.46543 + 6.00231i 0.129239 + 0.223848i 0.923382 0.383883i $$-0.125413\pi$$
−0.794143 + 0.607731i $$0.792080\pi$$
$$720$$ 0.561553 0.0209278
$$721$$ 6.68466 + 11.5782i 0.248950 + 0.431194i
$$722$$ −1.47301 2.55133i −0.0548198 0.0949508i
$$723$$ 23.6847 0.880842
$$724$$ 1.62311 + 2.81130i 0.0603222 + 0.104481i
$$725$$ −2.34233 + 4.05703i −0.0869919 + 0.150674i
$$726$$ 4.28078 7.41452i 0.158875 0.275179i
$$727$$ 33.7538 1.25186 0.625929 0.779880i $$-0.284720\pi$$
0.625929 + 0.779880i $$0.284720\pi$$
$$728$$ −3.34233 + 1.35234i −0.123875 + 0.0501212i
$$729$$ 1.00000 0.0370370
$$730$$ 1.84233 3.19101i 0.0681877 0.118104i
$$731$$ −27.8078 + 48.1645i −1.02851 + 1.78143i
$$732$$ 0.500000 + 0.866025i 0.0184805 + 0.0320092i
$$733$$ −8.61553 −0.318222 −0.159111 0.987261i $$-0.550863\pi$$
−0.159111 + 0.987261i $$0.550863\pi$$
$$734$$ 6.68466 + 11.5782i 0.246735 + 0.427358i
$$735$$ −0.280776 0.486319i −0.0103566 0.0179381i
$$736$$ −0.876894 −0.0323228
$$737$$ −5.56155 9.63289i −0.204862 0.354832i
$$738$$ 2.06155 3.57071i 0.0758868 0.131440i
$$739$$ −11.3153 + 19.5987i −0.416242 + 0.720952i −0.995558 0.0941513i $$-0.969986\pi$$
0.579316 + 0.815103i $$0.303320\pi$$
$$740$$ 6.06913 0.223106
$$741$$ 2.34233 16.7276i 0.0860476 0.614503i
$$742$$ 12.1231 0.445053
$$743$$ −16.6847 + 28.8987i −0.612101 + 1.06019i 0.378785 + 0.925485i $$0.376342\pi$$
−0.990886 + 0.134705i $$0.956991\pi$$
$$744$$ 1.56155 2.70469i 0.0572493 0.0991587i
$$745$$ −0.788354 1.36547i −0.0288831 0.0500269i
$$746$$ 17.4384 0.638467
$$747$$ −3.12311 5.40938i −0.114268 0.197919i
$$748$$ −3.90388 6.76172i −0.142740 0.247233i
$$749$$ 13.5616 0.495528
$$750$$ 2.71922 + 4.70983i 0.0992920 + 0.171979i
$$751$$ −9.90388 + 17.1540i −0.361398 + 0.625959i −0.988191 0.153226i $$-0.951034\pi$$
0.626793 + 0.779186i $$0.284367\pi$$
$$752$$ −2.34233 + 4.05703i −0.0854160 + 0.147945i
$$753$$ −24.4924 −0.892553
$$754$$ −3.34233 + 1.35234i −0.121720 + 0.0492495i
$$755$$ −12.1080 −0.440653
$$756$$ 0.500000 0.866025i 0.0181848 0.0314970i
$$757$$ −0.561553 + 0.972638i −0.0204100 + 0.0353511i −0.876050 0.482220i $$-0.839830\pi$$
0.855640 + 0.517571i $$0.173164\pi$$
$$758$$ 16.2462 + 28.1393i 0.590089 + 1.02206i
$$759$$ 1.36932 0.0497031
$$760$$ 1.31534 + 2.27824i 0.0477125 + 0.0826404i
$$761$$ 4.75379 + 8.23380i 0.172325 + 0.298475i 0.939232 0.343283i $$-0.111539\pi$$
−0.766907 + 0.641758i $$0.778205\pi$$
$$762$$ −14.2462 −0.516086
$$763$$ 4.56155 + 7.90084i 0.165139 + 0.286030i
$$764$$ −11.1231 + 19.2658i −0.402420 + 0.697012i
$$765$$ 1.40388 2.43160i 0.0507575 0.0879145i
$$766$$ 20.6847 0.747367
$$767$$ 16.3002 6.59524i 0.588566 0.238140i
$$768$$ 1.00000 0.0360844
$$769$$ −21.4924 + 37.2260i −0.775037 + 1.34240i 0.159737 + 0.987160i $$0.448935\pi$$
−0.934774 + 0.355243i $$0.884398\pi$$
$$770$$ −0.438447 + 0.759413i −0.0158005 + 0.0273673i
$$771$$ 15.6231 + 27.0600i 0.562652 + 0.974543i
$$772$$ 4.36932 0.157255
$$773$$ 3.24621 + 5.62260i 0.116758 + 0.202231i 0.918481 0.395465i $$-0.129416\pi$$
−0.801723 + 0.597696i $$0.796083\pi$$
$$774$$ 5.56155 + 9.63289i 0.199906 + 0.346247i
$$775$$ 14.6307 0.525550
$$776$$ 2.12311 + 3.67733i 0.0762151