# Properties

 Label 570.2.i.h.121.1 Level $570$ Weight $2$ Character 570.121 Analytic conductor $4.551$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{19})$$ Defining polynomial: $$x^{4} + 19 x^{2} + 361$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 121.1 Root $$2.17945 + 3.77492i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.121 Dual form 570.2.i.h.391.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(2.00000 - 3.46410i) q^{13} +(-2.17945 - 3.77492i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.67945 - 2.90889i) q^{17} -1.00000 q^{18} +(-2.17945 - 3.77492i) q^{19} -1.00000 q^{20} +(2.17945 + 3.77492i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{26} +1.00000 q^{27} +(2.17945 - 3.77492i) q^{28} +(-4.67945 + 8.10504i) q^{29} +1.00000 q^{30} -10.7178 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(1.67945 - 2.90889i) q^{34} +(-2.17945 - 3.77492i) q^{35} +(-0.500000 - 0.866025i) q^{36} -7.00000 q^{37} +(2.17945 - 3.77492i) q^{38} -4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.17945 + 5.50697i) q^{41} +(-2.17945 + 3.77492i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} -1.00000 q^{45} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +12.0000 q^{49} -1.00000 q^{50} +(-1.67945 + 2.90889i) q^{51} +(2.00000 + 3.46410i) q^{52} +(6.53835 - 11.3248i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +4.35890 q^{56} +(-2.17945 + 3.77492i) q^{57} -9.35890 q^{58} +(-6.35890 - 11.0139i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.67945 + 4.64094i) q^{61} +(-5.35890 - 9.28189i) q^{62} +(2.17945 - 3.77492i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(-1.50000 + 2.59808i) q^{66} +(-5.67945 + 9.83710i) q^{67} +3.35890 q^{68} -3.00000 q^{69} +(2.17945 - 3.77492i) q^{70} +(5.03835 + 8.72668i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.32055 - 4.01931i) q^{73} +(-3.50000 - 6.06218i) q^{74} +1.00000 q^{75} +4.35890 q^{76} +13.0767 q^{77} +(-2.00000 - 3.46410i) q^{78} +(2.35890 + 4.08573i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.17945 + 5.50697i) q^{82} -6.00000 q^{83} -4.35890 q^{84} +(1.67945 - 2.90889i) q^{85} +(-5.00000 + 8.66025i) q^{86} +9.35890 q^{87} +3.00000 q^{88} +(-0.179449 + 0.310816i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-8.71780 + 15.0997i) q^{91} +(1.50000 + 2.59808i) q^{92} +(5.35890 + 9.28189i) q^{93} +6.00000 q^{94} +(2.17945 - 3.77492i) q^{95} -1.00000 q^{96} +(7.03835 + 12.1908i) q^{97} +(6.00000 + 10.3923i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} + 4q^{12} + 8q^{13} + 2q^{15} - 2q^{16} + 2q^{17} - 4q^{18} - 4q^{20} - 6q^{22} + 6q^{23} + 2q^{24} - 2q^{25} + 16q^{26} + 4q^{27} - 10q^{29} + 4q^{30} - 8q^{31} + 2q^{32} + 6q^{33} - 2q^{34} - 2q^{36} - 28q^{37} - 16q^{39} - 2q^{40} + 4q^{41} + 20q^{43} + 6q^{44} - 4q^{45} + 12q^{46} + 12q^{47} - 2q^{48} + 48q^{49} - 4q^{50} + 2q^{51} + 8q^{52} + 2q^{54} - 6q^{55} - 20q^{58} - 8q^{59} + 2q^{60} - 2q^{61} - 4q^{62} + 4q^{64} + 16q^{65} - 6q^{66} - 14q^{67} - 4q^{68} - 12q^{69} - 6q^{71} + 2q^{72} - 18q^{73} - 14q^{74} + 4q^{75} - 8q^{78} - 8q^{79} + 2q^{80} - 2q^{81} - 4q^{82} - 24q^{83} - 2q^{85} - 20q^{86} + 20q^{87} + 12q^{88} + 8q^{89} - 2q^{90} + 6q^{92} + 4q^{93} + 24q^{94} - 4q^{96} + 2q^{97} + 24q^{98} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ −4.35890 −1.64751 −0.823754 0.566947i $$-0.808125\pi$$
−0.823754 + 0.566947i $$0.808125\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i $$-0.646166\pi$$
0.997927 0.0643593i $$-0.0205004\pi$$
$$14$$ −2.17945 3.77492i −0.582482 1.00889i
$$15$$ 0.500000 0.866025i 0.129099 0.223607i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.67945 2.90889i −0.407326 0.705510i 0.587263 0.809396i $$-0.300205\pi$$
−0.994589 + 0.103886i $$0.966872\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −2.17945 3.77492i −0.500000 0.866025i
$$20$$ −1.00000 −0.223607
$$21$$ 2.17945 + 3.77492i 0.475595 + 0.823754i
$$22$$ −1.50000 2.59808i −0.319801 0.553912i
$$23$$ 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i $$-0.732076\pi$$
0.978961 + 0.204046i $$0.0654092\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 4.00000 0.784465
$$27$$ 1.00000 0.192450
$$28$$ 2.17945 3.77492i 0.411877 0.713392i
$$29$$ −4.67945 + 8.10504i −0.868952 + 1.50507i −0.00588307 + 0.999983i $$0.501873\pi$$
−0.863069 + 0.505086i $$0.831461\pi$$
$$30$$ 1.00000 0.182574
$$31$$ −10.7178 −1.92497 −0.962487 0.271329i $$-0.912537\pi$$
−0.962487 + 0.271329i $$0.912537\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 1.50000 + 2.59808i 0.261116 + 0.452267i
$$34$$ 1.67945 2.90889i 0.288023 0.498871i
$$35$$ −2.17945 3.77492i −0.368394 0.638077i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ −7.00000 −1.15079 −0.575396 0.817875i $$-0.695152\pi$$
−0.575396 + 0.817875i $$0.695152\pi$$
$$38$$ 2.17945 3.77492i 0.353553 0.612372i
$$39$$ −4.00000 −0.640513
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ 3.17945 + 5.50697i 0.496547 + 0.860044i 0.999992 0.00398308i $$-0.00126786\pi$$
−0.503445 + 0.864027i $$0.667935\pi$$
$$42$$ −2.17945 + 3.77492i −0.336296 + 0.582482i
$$43$$ 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i $$0.109358\pi$$
−0.179069 + 0.983836i $$0.557309\pi$$
$$44$$ 1.50000 2.59808i 0.226134 0.391675i
$$45$$ −1.00000 −0.149071
$$46$$ 3.00000 0.442326
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ 12.0000 1.71429
$$50$$ −1.00000 −0.141421
$$51$$ −1.67945 + 2.90889i −0.235170 + 0.407326i
$$52$$ 2.00000 + 3.46410i 0.277350 + 0.480384i
$$53$$ 6.53835 11.3248i 0.898111 1.55557i 0.0682050 0.997671i $$-0.478273\pi$$
0.829906 0.557903i $$-0.188394\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ −1.50000 2.59808i −0.202260 0.350325i
$$56$$ 4.35890 0.582482
$$57$$ −2.17945 + 3.77492i −0.288675 + 0.500000i
$$58$$ −9.35890 −1.22888
$$59$$ −6.35890 11.0139i −0.827858 1.43389i −0.899715 0.436477i $$-0.856226\pi$$
0.0718571 0.997415i $$-0.477107\pi$$
$$60$$ 0.500000 + 0.866025i 0.0645497 + 0.111803i
$$61$$ −2.67945 + 4.64094i −0.343068 + 0.594212i −0.985001 0.172549i $$-0.944800\pi$$
0.641933 + 0.766761i $$0.278133\pi$$
$$62$$ −5.35890 9.28189i −0.680581 1.17880i
$$63$$ 2.17945 3.77492i 0.274585 0.475595i
$$64$$ 1.00000 0.125000
$$65$$ 4.00000 0.496139
$$66$$ −1.50000 + 2.59808i −0.184637 + 0.319801i
$$67$$ −5.67945 + 9.83710i −0.693855 + 1.20179i 0.276710 + 0.960953i $$0.410756\pi$$
−0.970565 + 0.240839i $$0.922577\pi$$
$$68$$ 3.35890 0.407326
$$69$$ −3.00000 −0.361158
$$70$$ 2.17945 3.77492i 0.260494 0.451189i
$$71$$ 5.03835 + 8.72668i 0.597942 + 1.03567i 0.993124 + 0.117063i $$0.0373480\pi$$
−0.395183 + 0.918603i $$0.629319\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −2.32055 4.01931i −0.271600 0.470425i 0.697672 0.716418i $$-0.254219\pi$$
−0.969272 + 0.245993i $$0.920886\pi$$
$$74$$ −3.50000 6.06218i −0.406867 0.704714i
$$75$$ 1.00000 0.115470
$$76$$ 4.35890 0.500000
$$77$$ 13.0767 1.49023
$$78$$ −2.00000 3.46410i −0.226455 0.392232i
$$79$$ 2.35890 + 4.08573i 0.265397 + 0.459681i 0.967668 0.252229i $$-0.0811637\pi$$
−0.702271 + 0.711910i $$0.747830\pi$$
$$80$$ 0.500000 0.866025i 0.0559017 0.0968246i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −3.17945 + 5.50697i −0.351111 + 0.608143i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ −4.35890 −0.475595
$$85$$ 1.67945 2.90889i 0.182162 0.315514i
$$86$$ −5.00000 + 8.66025i −0.539164 + 0.933859i
$$87$$ 9.35890 1.00338
$$88$$ 3.00000 0.319801
$$89$$ −0.179449 + 0.310816i −0.0190216 + 0.0329464i −0.875380 0.483436i $$-0.839388\pi$$
0.856358 + 0.516383i $$0.172722\pi$$
$$90$$ −0.500000 0.866025i −0.0527046 0.0912871i
$$91$$ −8.71780 + 15.0997i −0.913874 + 1.58288i
$$92$$ 1.50000 + 2.59808i 0.156386 + 0.270868i
$$93$$ 5.35890 + 9.28189i 0.555692 + 0.962487i
$$94$$ 6.00000 0.618853
$$95$$ 2.17945 3.77492i 0.223607 0.387298i
$$96$$ −1.00000 −0.102062
$$97$$ 7.03835 + 12.1908i 0.714636 + 1.23779i 0.963100 + 0.269145i $$0.0867410\pi$$
−0.248464 + 0.968641i $$0.579926\pi$$
$$98$$ 6.00000 + 10.3923i 0.606092 + 1.04978i
$$99$$ 1.50000 2.59808i 0.150756 0.261116i
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ 6.35890 11.0139i 0.632734 1.09593i −0.354256 0.935148i $$-0.615266\pi$$
0.986990 0.160779i $$-0.0514007\pi$$
$$102$$ −3.35890 −0.332581
$$103$$ −10.3589 −1.02069 −0.510346 0.859969i $$-0.670483\pi$$
−0.510346 + 0.859969i $$0.670483\pi$$
$$104$$ −2.00000 + 3.46410i −0.196116 + 0.339683i
$$105$$ −2.17945 + 3.77492i −0.212692 + 0.368394i
$$106$$ 13.0767 1.27012
$$107$$ 9.35890 0.904759 0.452379 0.891826i $$-0.350575\pi$$
0.452379 + 0.891826i $$0.350575\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ −5.32055 9.21546i −0.509616 0.882681i −0.999938 0.0111398i $$-0.996454\pi$$
0.490322 0.871542i $$-0.336879\pi$$
$$110$$ 1.50000 2.59808i 0.143019 0.247717i
$$111$$ 3.50000 + 6.06218i 0.332205 + 0.575396i
$$112$$ 2.17945 + 3.77492i 0.205939 + 0.356696i
$$113$$ 3.35890 0.315979 0.157989 0.987441i $$-0.449499\pi$$
0.157989 + 0.987441i $$0.449499\pi$$
$$114$$ −4.35890 −0.408248
$$115$$ 3.00000 0.279751
$$116$$ −4.67945 8.10504i −0.434476 0.752534i
$$117$$ 2.00000 + 3.46410i 0.184900 + 0.320256i
$$118$$ 6.35890 11.0139i 0.585384 1.01391i
$$119$$ 7.32055 + 12.6796i 0.671074 + 1.16233i
$$120$$ −0.500000 + 0.866025i −0.0456435 + 0.0790569i
$$121$$ −2.00000 −0.181818
$$122$$ −5.35890 −0.485172
$$123$$ 3.17945 5.50697i 0.286681 0.496547i
$$124$$ 5.35890 9.28189i 0.481243 0.833538i
$$125$$ −1.00000 −0.0894427
$$126$$ 4.35890 0.388322
$$127$$ 5.17945 8.97107i 0.459602 0.796054i −0.539338 0.842089i $$-0.681325\pi$$
0.998940 + 0.0460357i $$0.0146588\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 5.00000 8.66025i 0.440225 0.762493i
$$130$$ 2.00000 + 3.46410i 0.175412 + 0.303822i
$$131$$ 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i $$-0.124830\pi$$
−0.793028 + 0.609185i $$0.791497\pi$$
$$132$$ −3.00000 −0.261116
$$133$$ 9.50000 + 16.4545i 0.823754 + 1.42678i
$$134$$ −11.3589 −0.981259
$$135$$ 0.500000 + 0.866025i 0.0430331 + 0.0745356i
$$136$$ 1.67945 + 2.90889i 0.144012 + 0.249435i
$$137$$ −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i $$0.337990\pi$$
−0.999893 + 0.0146279i $$0.995344\pi$$
$$138$$ −1.50000 2.59808i −0.127688 0.221163i
$$139$$ −0.641101 + 1.11042i −0.0543775 + 0.0941846i −0.891933 0.452168i $$-0.850651\pi$$
0.837555 + 0.546353i $$0.183984\pi$$
$$140$$ 4.35890 0.368394
$$141$$ −6.00000 −0.505291
$$142$$ −5.03835 + 8.72668i −0.422809 + 0.732326i
$$143$$ −6.00000 + 10.3923i −0.501745 + 0.869048i
$$144$$ 1.00000 0.0833333
$$145$$ −9.35890 −0.777214
$$146$$ 2.32055 4.01931i 0.192050 0.332641i
$$147$$ −6.00000 10.3923i −0.494872 0.857143i
$$148$$ 3.50000 6.06218i 0.287698 0.498308i
$$149$$ 5.03835 + 8.72668i 0.412758 + 0.714917i 0.995190 0.0979619i $$-0.0312323\pi$$
−0.582433 + 0.812879i $$0.697899\pi$$
$$150$$ 0.500000 + 0.866025i 0.0408248 + 0.0707107i
$$151$$ −2.07670 −0.168999 −0.0844996 0.996424i $$-0.526929\pi$$
−0.0844996 + 0.996424i $$0.526929\pi$$
$$152$$ 2.17945 + 3.77492i 0.176777 + 0.306186i
$$153$$ 3.35890 0.271551
$$154$$ 6.53835 + 11.3248i 0.526875 + 0.912574i
$$155$$ −5.35890 9.28189i −0.430437 0.745539i
$$156$$ 2.00000 3.46410i 0.160128 0.277350i
$$157$$ −2.50000 4.33013i −0.199522 0.345582i 0.748852 0.662738i $$-0.230606\pi$$
−0.948373 + 0.317156i $$0.897272\pi$$
$$158$$ −2.35890 + 4.08573i −0.187664 + 0.325043i
$$159$$ −13.0767 −1.03705
$$160$$ 1.00000 0.0790569
$$161$$ −6.53835 + 11.3248i −0.515294 + 0.892515i
$$162$$ 0.500000 0.866025i 0.0392837 0.0680414i
$$163$$ −4.71780 −0.369526 −0.184763 0.982783i $$-0.559152\pi$$
−0.184763 + 0.982783i $$0.559152\pi$$
$$164$$ −6.35890 −0.496547
$$165$$ −1.50000 + 2.59808i −0.116775 + 0.202260i
$$166$$ −3.00000 5.19615i −0.232845 0.403300i
$$167$$ 11.2178 19.4298i 0.868059 1.50352i 0.00408215 0.999992i $$-0.498701\pi$$
0.863977 0.503531i $$-0.167966\pi$$
$$168$$ −2.17945 3.77492i −0.168148 0.291241i
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 3.35890 0.257616
$$171$$ 4.35890 0.333333
$$172$$ −10.0000 −0.762493
$$173$$ −9.17945 15.8993i −0.697901 1.20880i −0.969193 0.246302i $$-0.920784\pi$$
0.271292 0.962497i $$-0.412549\pi$$
$$174$$ 4.67945 + 8.10504i 0.354748 + 0.614442i
$$175$$ 2.17945 3.77492i 0.164751 0.285357i
$$176$$ 1.50000 + 2.59808i 0.113067 + 0.195837i
$$177$$ −6.35890 + 11.0139i −0.477964 + 0.827858i
$$178$$ −0.358899 −0.0269006
$$179$$ 15.7178 1.17480 0.587402 0.809296i $$-0.300151\pi$$
0.587402 + 0.809296i $$0.300151\pi$$
$$180$$ 0.500000 0.866025i 0.0372678 0.0645497i
$$181$$ −9.03835 + 15.6549i −0.671815 + 1.16362i 0.305574 + 0.952168i $$0.401152\pi$$
−0.977389 + 0.211450i $$0.932182\pi$$
$$182$$ −17.4356 −1.29241
$$183$$ 5.35890 0.396141
$$184$$ −1.50000 + 2.59808i −0.110581 + 0.191533i
$$185$$ −3.50000 6.06218i −0.257325 0.445700i
$$186$$ −5.35890 + 9.28189i −0.392934 + 0.680581i
$$187$$ 5.03835 + 8.72668i 0.368441 + 0.638158i
$$188$$ 3.00000 + 5.19615i 0.218797 + 0.378968i
$$189$$ −4.35890 −0.317063
$$190$$ 4.35890 0.316228
$$191$$ −19.4356 −1.40631 −0.703155 0.711036i $$-0.748226\pi$$
−0.703155 + 0.711036i $$0.748226\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −12.0383 20.8510i −0.866539 1.50089i −0.865511 0.500891i $$-0.833006\pi$$
−0.00102867 0.999999i $$-0.500327\pi$$
$$194$$ −7.03835 + 12.1908i −0.505324 + 0.875247i
$$195$$ −2.00000 3.46410i −0.143223 0.248069i
$$196$$ −6.00000 + 10.3923i −0.428571 + 0.742307i
$$197$$ −5.64110 −0.401912 −0.200956 0.979600i $$-0.564405\pi$$
−0.200956 + 0.979600i $$0.564405\pi$$
$$198$$ 3.00000 0.213201
$$199$$ −8.32055 + 14.4116i −0.589828 + 1.02161i 0.404426 + 0.914571i $$0.367471\pi$$
−0.994255 + 0.107042i $$0.965862\pi$$
$$200$$ 0.500000 0.866025i 0.0353553 0.0612372i
$$201$$ 11.3589 0.801195
$$202$$ 12.7178 0.894821
$$203$$ 20.3972 35.3291i 1.43161 2.47961i
$$204$$ −1.67945 2.90889i −0.117585 0.203663i
$$205$$ −3.17945 + 5.50697i −0.222062 + 0.384623i
$$206$$ −5.17945 8.97107i −0.360869 0.625044i
$$207$$ 1.50000 + 2.59808i 0.104257 + 0.180579i
$$208$$ −4.00000 −0.277350
$$209$$ 6.53835 + 11.3248i 0.452267 + 0.783349i
$$210$$ −4.35890 −0.300793
$$211$$ −7.53835 13.0568i −0.518961 0.898867i −0.999757 0.0220348i $$-0.992986\pi$$
0.480796 0.876833i $$-0.340348\pi$$
$$212$$ 6.53835 + 11.3248i 0.449056 + 0.777787i
$$213$$ 5.03835 8.72668i 0.345222 0.597942i
$$214$$ 4.67945 + 8.10504i 0.319881 + 0.554049i
$$215$$ −5.00000 + 8.66025i −0.340997 + 0.590624i
$$216$$ −1.00000 −0.0680414
$$217$$ 46.7178 3.17141
$$218$$ 5.32055 9.21546i 0.360353 0.624150i
$$219$$ −2.32055 + 4.01931i −0.156808 + 0.271600i
$$220$$ 3.00000 0.202260
$$221$$ −13.4356 −0.903776
$$222$$ −3.50000 + 6.06218i −0.234905 + 0.406867i
$$223$$ −10.1794 17.6313i −0.681666 1.18068i −0.974472 0.224509i $$-0.927922\pi$$
0.292806 0.956172i $$-0.405411\pi$$
$$224$$ −2.17945 + 3.77492i −0.145621 + 0.252222i
$$225$$ −0.500000 0.866025i −0.0333333 0.0577350i
$$226$$ 1.67945 + 2.90889i 0.111715 + 0.193497i
$$227$$ −3.35890 −0.222938 −0.111469 0.993768i $$-0.535556\pi$$
−0.111469 + 0.993768i $$0.535556\pi$$
$$228$$ −2.17945 3.77492i −0.144338 0.250000i
$$229$$ 8.71780 0.576088 0.288044 0.957617i $$-0.406995\pi$$
0.288044 + 0.957617i $$0.406995\pi$$
$$230$$ 1.50000 + 2.59808i 0.0989071 + 0.171312i
$$231$$ −6.53835 11.3248i −0.430192 0.745114i
$$232$$ 4.67945 8.10504i 0.307221 0.532122i
$$233$$ −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i $$-0.229636\pi$$
−0.947403 + 0.320043i $$0.896303\pi$$
$$234$$ −2.00000 + 3.46410i −0.130744 + 0.226455i
$$235$$ 6.00000 0.391397
$$236$$ 12.7178 0.827858
$$237$$ 2.35890 4.08573i 0.153227 0.265397i
$$238$$ −7.32055 + 12.6796i −0.474521 + 0.821894i
$$239$$ −13.4356 −0.869076 −0.434538 0.900653i $$-0.643088\pi$$
−0.434538 + 0.900653i $$0.643088\pi$$
$$240$$ −1.00000 −0.0645497
$$241$$ 2.00000 3.46410i 0.128831 0.223142i −0.794393 0.607404i $$-0.792211\pi$$
0.923224 + 0.384262i $$0.125544\pi$$
$$242$$ −1.00000 1.73205i −0.0642824 0.111340i
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ −2.67945 4.64094i −0.171534 0.297106i
$$245$$ 6.00000 + 10.3923i 0.383326 + 0.663940i
$$246$$ 6.35890 0.405429
$$247$$ −17.4356 −1.10940
$$248$$ 10.7178 0.680581
$$249$$ 3.00000 + 5.19615i 0.190117 + 0.329293i
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ 2.17945 + 3.77492i 0.137292 + 0.237797i
$$253$$ −4.50000 + 7.79423i −0.282913 + 0.490019i
$$254$$ 10.3589 0.649975
$$255$$ −3.35890 −0.210342
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 3.71780 6.43941i 0.231910 0.401680i −0.726460 0.687208i $$-0.758836\pi$$
0.958370 + 0.285529i $$0.0921692\pi$$
$$258$$ 10.0000 0.622573
$$259$$ 30.5123 1.89594
$$260$$ −2.00000 + 3.46410i −0.124035 + 0.214834i
$$261$$ −4.67945 8.10504i −0.289651 0.501690i
$$262$$ −1.50000 + 2.59808i −0.0926703 + 0.160510i
$$263$$ 4.14110 + 7.17260i 0.255351 + 0.442281i 0.964991 0.262284i $$-0.0844756\pi$$
−0.709640 + 0.704565i $$0.751142\pi$$
$$264$$ −1.50000 2.59808i −0.0923186 0.159901i
$$265$$ 13.0767 0.803295
$$266$$ −9.50000 + 16.4545i −0.582482 + 1.00889i
$$267$$ 0.358899 0.0219643
$$268$$ −5.67945 9.83710i −0.346928 0.600896i
$$269$$ −1.67945 2.90889i −0.102398 0.177358i 0.810274 0.586051i $$-0.199318\pi$$
−0.912672 + 0.408693i $$0.865985\pi$$
$$270$$ −0.500000 + 0.866025i −0.0304290 + 0.0527046i
$$271$$ 2.35890 + 4.08573i 0.143293 + 0.248191i 0.928735 0.370745i $$-0.120898\pi$$
−0.785442 + 0.618935i $$0.787564\pi$$
$$272$$ −1.67945 + 2.90889i −0.101832 + 0.176377i
$$273$$ 17.4356 1.05525
$$274$$ −12.0000 −0.724947
$$275$$ 1.50000 2.59808i 0.0904534 0.156670i
$$276$$ 1.50000 2.59808i 0.0902894 0.156386i
$$277$$ −4.00000 −0.240337 −0.120168 0.992754i $$-0.538343\pi$$
−0.120168 + 0.992754i $$0.538343\pi$$
$$278$$ −1.28220 −0.0769014
$$279$$ 5.35890 9.28189i 0.320829 0.555692i
$$280$$ 2.17945 + 3.77492i 0.130247 + 0.225594i
$$281$$ −0.538348 + 0.932447i −0.0321152 + 0.0556251i −0.881636 0.471930i $$-0.843558\pi$$
0.849521 + 0.527555i $$0.176891\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ −4.35890 7.54983i −0.259110 0.448791i 0.706894 0.707319i $$-0.250096\pi$$
−0.966004 + 0.258528i $$0.916762\pi$$
$$284$$ −10.0767 −0.597942
$$285$$ −4.35890 −0.258199
$$286$$ −12.0000 −0.709575
$$287$$ −13.8589 24.0043i −0.818065 1.41693i
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ 2.85890 4.95176i 0.168171 0.291280i
$$290$$ −4.67945 8.10504i −0.274787 0.475945i
$$291$$ 7.03835 12.1908i 0.412595 0.714636i
$$292$$ 4.64110 0.271600
$$293$$ 5.64110 0.329557 0.164778 0.986331i $$-0.447309\pi$$
0.164778 + 0.986331i $$0.447309\pi$$
$$294$$ 6.00000 10.3923i 0.349927 0.606092i
$$295$$ 6.35890 11.0139i 0.370229 0.641256i
$$296$$ 7.00000 0.406867
$$297$$ −3.00000 −0.174078
$$298$$ −5.03835 + 8.72668i −0.291864 + 0.505523i
$$299$$ −6.00000 10.3923i −0.346989 0.601003i
$$300$$ −0.500000 + 0.866025i −0.0288675 + 0.0500000i
$$301$$ −21.7945 37.7492i −1.25621 2.17583i
$$302$$ −1.03835 1.79847i −0.0597502 0.103490i
$$303$$ −12.7178 −0.730618
$$304$$ −2.17945 + 3.77492i −0.125000 + 0.216506i
$$305$$ −5.35890 −0.306850
$$306$$ 1.67945 + 2.90889i 0.0960077 + 0.166290i
$$307$$ 0.679449 + 1.17684i 0.0387782 + 0.0671659i 0.884763 0.466041i $$-0.154320\pi$$
−0.845985 + 0.533207i $$0.820987\pi$$
$$308$$ −6.53835 + 11.3248i −0.372557 + 0.645288i
$$309$$ 5.17945 + 8.97107i 0.294649 + 0.510346i
$$310$$ 5.35890 9.28189i 0.304365 0.527176i
$$311$$ 1.43560 0.0814052 0.0407026 0.999171i $$-0.487040\pi$$
0.0407026 + 0.999171i $$0.487040\pi$$
$$312$$ 4.00000 0.226455
$$313$$ 8.71780 15.0997i 0.492759 0.853484i −0.507206 0.861825i $$-0.669322\pi$$
0.999965 + 0.00834102i $$0.00265506\pi$$
$$314$$ 2.50000 4.33013i 0.141083 0.244363i
$$315$$ 4.35890 0.245596
$$316$$ −4.71780 −0.265397
$$317$$ −9.53835 + 16.5209i −0.535727 + 0.927906i 0.463401 + 0.886149i $$0.346629\pi$$
−0.999128 + 0.0417576i $$0.986704\pi$$
$$318$$ −6.53835 11.3248i −0.366652 0.635061i
$$319$$ 14.0383 24.3151i 0.785997 1.36139i
$$320$$ 0.500000 + 0.866025i 0.0279508 + 0.0484123i
$$321$$ −4.67945 8.10504i −0.261181 0.452379i
$$322$$ −13.0767 −0.728736
$$323$$ −7.32055 + 12.6796i −0.407326 + 0.705510i
$$324$$ 1.00000 0.0555556
$$325$$ 2.00000 + 3.46410i 0.110940 + 0.192154i
$$326$$ −2.35890 4.08573i −0.130647 0.226288i
$$327$$ −5.32055 + 9.21546i −0.294227 + 0.509616i
$$328$$ −3.17945 5.50697i −0.175556 0.304071i
$$329$$ −13.0767 + 22.6495i −0.720942 + 1.24871i
$$330$$ −3.00000 −0.165145
$$331$$ 14.3589 0.789236 0.394618 0.918845i $$-0.370877\pi$$
0.394618 + 0.918845i $$0.370877\pi$$
$$332$$ 3.00000 5.19615i 0.164646 0.285176i
$$333$$ 3.50000 6.06218i 0.191799 0.332205i
$$334$$ 22.4356 1.22762
$$335$$ −11.3589 −0.620603
$$336$$ 2.17945 3.77492i 0.118899 0.205939i
$$337$$ −11.0767 19.1854i −0.603386 1.04510i −0.992304 0.123823i $$-0.960484\pi$$
0.388918 0.921272i $$-0.372849\pi$$
$$338$$ 1.50000 2.59808i 0.0815892 0.141317i
$$339$$ −1.67945 2.90889i −0.0912152 0.157989i
$$340$$ 1.67945 + 2.90889i 0.0910809 + 0.157757i
$$341$$ 32.1534 1.74120
$$342$$ 2.17945 + 3.77492i 0.117851 + 0.204124i
$$343$$ −21.7945 −1.17679
$$344$$ −5.00000 8.66025i −0.269582 0.466930i
$$345$$ −1.50000 2.59808i −0.0807573 0.139876i
$$346$$ 9.17945 15.8993i 0.493490 0.854750i
$$347$$ 3.71780 + 6.43941i 0.199582 + 0.345686i 0.948393 0.317098i $$-0.102708\pi$$
−0.748811 + 0.662784i $$0.769375\pi$$
$$348$$ −4.67945 + 8.10504i −0.250845 + 0.434476i
$$349$$ 0.0766968 0.00410549 0.00205274 0.999998i $$-0.499347\pi$$
0.00205274 + 0.999998i $$0.499347\pi$$
$$350$$ 4.35890 0.232993
$$351$$ 2.00000 3.46410i 0.106752 0.184900i
$$352$$ −1.50000 + 2.59808i −0.0799503 + 0.138478i
$$353$$ −10.0767 −0.536328 −0.268164 0.963373i $$-0.586417\pi$$
−0.268164 + 0.963373i $$0.586417\pi$$
$$354$$ −12.7178 −0.675943
$$355$$ −5.03835 + 8.72668i −0.267408 + 0.463164i
$$356$$ −0.179449 0.310816i −0.00951080 0.0164732i
$$357$$ 7.32055 12.6796i 0.387445 0.671074i
$$358$$ 7.85890 + 13.6120i 0.415356 + 0.719417i
$$359$$ −7.67945 13.3012i −0.405306 0.702010i 0.589051 0.808096i $$-0.299502\pi$$
−0.994357 + 0.106085i $$0.966168\pi$$
$$360$$ 1.00000 0.0527046
$$361$$ −9.50000 + 16.4545i −0.500000 + 0.866025i
$$362$$ −18.0767 −0.950090
$$363$$ 1.00000 + 1.73205i 0.0524864 + 0.0909091i
$$364$$ −8.71780 15.0997i −0.456937 0.791438i
$$365$$ 2.32055 4.01931i 0.121463 0.210380i
$$366$$ 2.67945 + 4.64094i 0.140057 + 0.242586i
$$367$$ −7.35890 + 12.7460i −0.384131 + 0.665335i −0.991648 0.128972i $$-0.958832\pi$$
0.607517 + 0.794307i $$0.292166\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ −6.35890 −0.331031
$$370$$ 3.50000 6.06218i 0.181956 0.315158i
$$371$$ −28.5000 + 49.3634i −1.47965 + 2.56282i
$$372$$ −10.7178 −0.555692
$$373$$ 11.0000 0.569558 0.284779 0.958593i $$-0.408080\pi$$
0.284779 + 0.958593i $$0.408080\pi$$
$$374$$ −5.03835 + 8.72668i −0.260527 + 0.451246i
$$375$$ 0.500000 + 0.866025i 0.0258199 + 0.0447214i
$$376$$ −3.00000 + 5.19615i −0.154713 + 0.267971i
$$377$$ 18.7178 + 32.4202i 0.964016 + 1.66972i
$$378$$ −2.17945 3.77492i −0.112099 0.194161i
$$379$$ 14.7178 0.756002 0.378001 0.925805i $$-0.376611\pi$$
0.378001 + 0.925805i $$0.376611\pi$$
$$380$$ 2.17945 + 3.77492i 0.111803 + 0.193649i
$$381$$ −10.3589 −0.530702
$$382$$ −9.71780 16.8317i −0.497206 0.861186i
$$383$$ −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i $$-0.215654\pi$$
−0.932436 + 0.361335i $$0.882321\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ 6.53835 + 11.3248i 0.333225 + 0.577163i
$$386$$ 12.0383 20.8510i 0.612736 1.06129i
$$387$$ −10.0000 −0.508329
$$388$$ −14.0767 −0.714636
$$389$$ −2.03835 + 3.53052i −0.103348 + 0.179005i −0.913062 0.407820i $$-0.866289\pi$$
0.809714 + 0.586825i $$0.199622\pi$$
$$390$$ 2.00000 3.46410i 0.101274 0.175412i
$$391$$ −10.0767 −0.509600
$$392$$ −12.0000 −0.606092
$$393$$ 1.50000 2.59808i 0.0756650 0.131056i
$$394$$ −2.82055 4.88534i −0.142097 0.246120i
$$395$$ −2.35890 + 4.08573i −0.118689 + 0.205576i
$$396$$ 1.50000 + 2.59808i 0.0753778 + 0.130558i
$$397$$ −3.21780 5.57339i −0.161497 0.279720i 0.773909 0.633297i $$-0.218299\pi$$
−0.935406 + 0.353576i $$0.884965\pi$$
$$398$$ −16.6411 −0.834143
$$399$$ 9.50000 16.4545i 0.475595 0.823754i
$$400$$ 1.00000 0.0500000
$$401$$ 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i $$-0.0182907\pi$$
−0.548911 + 0.835881i $$0.684957\pi$$
$$402$$ 5.67945 + 9.83710i 0.283265 + 0.490630i
$$403$$ −21.4356 + 37.1275i −1.06778 + 1.84945i
$$404$$ 6.35890 + 11.0139i 0.316367 + 0.547964i
$$405$$ 0.500000 0.866025i 0.0248452 0.0430331i
$$406$$ 40.7945 2.02460
$$407$$ 21.0000 1.04093
$$408$$ 1.67945 2.90889i 0.0831451 0.144012i
$$409$$ −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i $$-0.921004\pi$$
0.697406 + 0.716677i $$0.254338\pi$$
$$410$$ −6.35890 −0.314044
$$411$$ 12.0000 0.591916
$$412$$ 5.17945 8.97107i 0.255173 0.441973i
$$413$$ 27.7178 + 48.0086i 1.36390 + 2.36235i
$$414$$ −1.50000 + 2.59808i −0.0737210 + 0.127688i
$$415$$ −3.00000 5.19615i −0.147264 0.255069i
$$416$$ −2.00000 3.46410i −0.0980581 0.169842i
$$417$$ 1.28220 0.0627897
$$418$$ −6.53835 + 11.3248i −0.319801 + 0.553912i
$$419$$ 15.7178 0.767865 0.383932 0.923361i $$-0.374570\pi$$
0.383932 + 0.923361i $$0.374570\pi$$
$$420$$ −2.17945 3.77492i −0.106346 0.184197i
$$421$$ −18.0383 31.2433i −0.879135 1.52271i −0.852291 0.523067i $$-0.824788\pi$$
−0.0268440 0.999640i $$-0.508546\pi$$
$$422$$ 7.53835 13.0568i 0.366961 0.635595i
$$423$$ 3.00000 + 5.19615i 0.145865 + 0.252646i
$$424$$ −6.53835 + 11.3248i −0.317530 + 0.549979i
$$425$$ 3.35890 0.162931
$$426$$ 10.0767 0.488218
$$427$$ 11.6794 20.2294i 0.565208 0.978969i
$$428$$ −4.67945 + 8.10504i −0.226190 + 0.391772i
$$429$$ 12.0000 0.579365
$$430$$ −10.0000 −0.482243
$$431$$ −5.39725 + 9.34831i −0.259976 + 0.450292i −0.966235 0.257661i $$-0.917048\pi$$
0.706259 + 0.707954i $$0.250381\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −18.3972 + 31.8650i −0.884115 + 1.53133i −0.0373910 + 0.999301i $$0.511905\pi$$
−0.846724 + 0.532032i $$0.821429\pi$$
$$434$$ 23.3589 + 40.4588i 1.12126 + 1.94208i
$$435$$ 4.67945 + 8.10504i 0.224362 + 0.388607i
$$436$$ 10.6411 0.509616
$$437$$ −13.0767 −0.625543
$$438$$ −4.64110 −0.221760
$$439$$ −11.6794 20.2294i −0.557430 0.965497i −0.997710 0.0676362i $$-0.978454\pi$$
0.440280 0.897860i $$-0.354879\pi$$
$$440$$ 1.50000 + 2.59808i 0.0715097 + 0.123858i
$$441$$ −6.00000 + 10.3923i −0.285714 + 0.494872i
$$442$$ −6.71780 11.6356i −0.319533 0.553447i
$$443$$ 1.32055 2.28726i 0.0627412 0.108671i −0.832949 0.553350i $$-0.813349\pi$$
0.895690 + 0.444679i $$0.146682\pi$$
$$444$$ −7.00000 −0.332205
$$445$$ −0.358899 −0.0170134
$$446$$ 10.1794 17.6313i 0.482011 0.834867i
$$447$$ 5.03835 8.72668i 0.238306 0.412758i
$$448$$ −4.35890 −0.205939
$$449$$ 0.358899 0.0169375 0.00846874 0.999964i $$-0.497304\pi$$
0.00846874 + 0.999964i $$0.497304\pi$$
$$450$$ 0.500000 0.866025i 0.0235702 0.0408248i
$$451$$ −9.53835 16.5209i −0.449143 0.777939i
$$452$$ −1.67945 + 2.90889i −0.0789947 + 0.136823i
$$453$$ 1.03835 + 1.79847i 0.0487859 + 0.0844996i
$$454$$ −1.67945 2.90889i −0.0788205 0.136521i
$$455$$ −17.4356 −0.817393
$$456$$ 2.17945 3.77492i 0.102062 0.176777i
$$457$$ −30.6411 −1.43333 −0.716665 0.697417i $$-0.754332\pi$$
−0.716665 + 0.697417i $$0.754332\pi$$
$$458$$ 4.35890 + 7.54983i 0.203678 + 0.352781i
$$459$$ −1.67945 2.90889i −0.0783900 0.135775i
$$460$$ −1.50000 + 2.59808i −0.0699379 + 0.121136i
$$461$$ −9.00000 15.5885i −0.419172 0.726027i 0.576685 0.816967i $$-0.304346\pi$$
−0.995856 + 0.0909401i $$0.971013\pi$$
$$462$$ 6.53835 11.3248i 0.304191 0.526875i
$$463$$ −17.7945 −0.826980 −0.413490 0.910509i $$-0.635690\pi$$
−0.413490 + 0.910509i $$0.635690\pi$$
$$464$$ 9.35890 0.434476
$$465$$ −5.35890 + 9.28189i −0.248513 + 0.430437i
$$466$$ 3.00000 5.19615i 0.138972 0.240707i
$$467$$ 28.7945 1.33245 0.666225 0.745751i $$-0.267909\pi$$
0.666225 + 0.745751i $$0.267909\pi$$
$$468$$ −4.00000 −0.184900
$$469$$ 24.7561 42.8789i 1.14313 1.97996i
$$470$$ 3.00000 + 5.19615i 0.138380 + 0.239681i
$$471$$ −2.50000 + 4.33013i −0.115194 + 0.199522i
$$472$$ 6.35890 + 11.0139i 0.292692 + 0.506957i
$$473$$ −15.0000 25.9808i −0.689701 1.19460i
$$474$$ 4.71780 0.216696
$$475$$ 4.35890 0.200000
$$476$$ −14.6411 −0.671074
$$477$$ 6.53835 + 11.3248i 0.299370 + 0.518525i
$$478$$ −6.71780 11.6356i −0.307265 0.532198i
$$479$$ 11.0383 19.1190i 0.504355 0.873569i −0.495632 0.868532i $$-0.665064\pi$$
0.999987 0.00503606i $$-0.00160303\pi$$
$$480$$ −0.500000 0.866025i −0.0228218 0.0395285i
$$481$$ −14.0000 + 24.2487i −0.638345 + 1.10565i
$$482$$ 4.00000 0.182195
$$483$$ 13.0767 0.595010
$$484$$ 1.00000 1.73205i 0.0454545 0.0787296i
$$485$$ −7.03835 + 12.1908i −0.319595 + 0.553555i
$$486$$ −1.00000 −0.0453609
$$487$$ −9.64110 −0.436880 −0.218440 0.975850i $$-0.570097\pi$$
−0.218440 + 0.975850i $$0.570097\pi$$
$$488$$ 2.67945 4.64094i 0.121293 0.210086i
$$489$$ 2.35890 + 4.08573i 0.106673 + 0.184763i
$$490$$ −6.00000 + 10.3923i −0.271052 + 0.469476i
$$491$$ −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i $$-0.276576\pi$$
−0.984145 + 0.177365i $$0.943243\pi$$
$$492$$ 3.17945 + 5.50697i 0.143341 + 0.248273i
$$493$$ 31.4356 1.41579
$$494$$ −8.71780 15.0997i −0.392232 0.679366i
$$495$$ 3.00000 0.134840
$$496$$ 5.35890 + 9.28189i 0.240622 + 0.416769i
$$497$$ −21.9617 38.0387i −0.985115 1.70627i
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ 7.82055 + 13.5456i 0.350096 + 0.606384i 0.986266 0.165165i $$-0.0528157\pi$$
−0.636170 + 0.771549i $$0.719482\pi$$
$$500$$ 0.500000 0.866025i 0.0223607 0.0387298i
$$501$$ −22.4356 −1.00235
$$502$$ 12.0000 0.535586
$$503$$ −14.9356 + 25.8692i −0.665945 + 1.15345i 0.313083 + 0.949726i $$0.398638\pi$$
−0.979028 + 0.203725i $$0.934695\pi$$
$$504$$ −2.17945 + 3.77492i −0.0970804 + 0.168148i
$$505$$ 12.7178 0.565935
$$506$$ −9.00000 −0.400099
$$507$$ −1.50000 + 2.59808i −0.0666173 + 0.115385i
$$508$$ 5.17945 + 8.97107i 0.229801 + 0.398027i
$$509$$ −12.3589 + 21.4062i −0.547799 + 0.948815i 0.450626 + 0.892713i $$0.351201\pi$$
−0.998425 + 0.0561023i $$0.982133\pi$$
$$510$$ −1.67945 2.90889i −0.0743673 0.128808i
$$511$$ 10.1150 + 17.5198i 0.447463 + 0.775029i
$$512$$ −1.00000 −0.0441942
$$513$$ −2.17945 3.77492i −0.0962250 0.166667i
$$514$$ 7.43560 0.327970
$$515$$ −5.17945 8.97107i −0.228234 0.395313i
$$516$$ 5.00000 + 8.66025i 0.220113 + 0.381246i
$$517$$ −9.00000 + 15.5885i −0.395820 + 0.685580i
$$518$$ 15.2561 + 26.4244i 0.670317 + 1.16102i
$$519$$ −9.17945 + 15.8993i −0.402933 + 0.697901i
$$520$$ −4.00000 −0.175412
$$521$$ 23.2822 1.02001 0.510006 0.860171i $$-0.329643\pi$$
0.510006 + 0.860171i $$0.329643\pi$$
$$522$$ 4.67945 8.10504i 0.204814 0.354748i
$$523$$ 19.3972 33.5970i 0.848182 1.46910i −0.0346461 0.999400i $$-0.511030\pi$$
0.882829 0.469695i $$-0.155636\pi$$
$$524$$ −3.00000 −0.131056
$$525$$ −4.35890 −0.190238
$$526$$ −4.14110 + 7.17260i −0.180561 + 0.312740i
$$527$$ 18.0000 + 31.1769i 0.784092 + 1.35809i
$$528$$ 1.50000 2.59808i 0.0652791 0.113067i
$$529$$ 7.00000 + 12.1244i 0.304348 + 0.527146i
$$530$$ 6.53835 + 11.3248i 0.284008 + 0.491916i
$$531$$ 12.7178 0.551905
$$532$$ −19.0000 −0.823754
$$533$$ 25.4356 1.10174
$$534$$ 0.179449 + 0.310816i 0.00776554 + 0.0134503i
$$535$$ 4.67945 + 8.10504i 0.202310 + 0.350412i
$$536$$ 5.67945 9.83710i 0.245315 0.424898i
$$537$$ −7.85890 13.6120i −0.339137 0.587402i
$$538$$ 1.67945 2.90889i 0.0724062 0.125411i
$$539$$ −36.0000 −1.55063
$$540$$ −1.00000 −0.0430331
$$541$$ 4.64110 8.03862i 0.199537 0.345607i −0.748842 0.662749i $$-0.769390\pi$$
0.948378 + 0.317142i $$0.102723\pi$$
$$542$$ −2.35890 + 4.08573i −0.101323 + 0.175497i
$$543$$ 18.0767 0.775745
$$544$$ −3.35890 −0.144012
$$545$$ 5.32055 9.21546i 0.227907 0.394747i
$$546$$ 8.71780 + 15.0997i 0.373087 + 0.646206i
$$547$$ 3.07670 5.32900i 0.131550 0.227851i −0.792724 0.609580i $$-0.791338\pi$$
0.924274 + 0.381729i $$0.124671\pi$$
$$548$$ −6.00000 10.3923i −0.256307 0.443937i
$$549$$ −2.67945 4.64094i −0.114356 0.198071i
$$550$$ 3.00000 0.127920
$$551$$ 40.7945 1.73790
$$552$$ 3.00000 0.127688
$$553$$ −10.2822 17.8093i −0.437244 0.757328i
$$554$$ −2.00000 3.46410i −0.0849719 0.147176i
$$555$$ −3.50000 + 6.06218i −0.148567 + 0.257325i
$$556$$ −0.641101 1.11042i −0.0271887 0.0470923i
$$557$$ 5.46165 9.45986i 0.231418 0.400827i −0.726808 0.686841i $$-0.758997\pi$$
0.958226 + 0.286014i $$0.0923303\pi$$
$$558$$ 10.7178 0.453721
$$559$$ 40.0000 1.69182
$$560$$ −2.17945 + 3.77492i −0.0920985 + 0.159519i
$$561$$ 5.03835 8.72668i 0.212719 0.368441i
$$562$$ −1.07670 −0.0454177
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 3.00000 5.19615i 0.126323 0.218797i
$$565$$ 1.67945 + 2.90889i 0.0706550 + 0.122378i
$$566$$ 4.35890 7.54983i 0.183218 0.317343i
$$567$$ 2.17945 + 3.77492i 0.0915283 + 0.158532i
$$568$$ −5.03835 8.72668i −0.211404 0.366163i
$$569$$ −37.7945 −1.58443 −0.792214 0.610244i $$-0.791072\pi$$
−0.792214 + 0.610244i $$0.791072\pi$$
$$570$$ −2.17945 3.77492i −0.0912871 0.158114i
$$571$$ 34.1534 1.42928 0.714638 0.699495i $$-0.246592\pi$$
0.714638 + 0.699495i $$0.246592\pi$$
$$572$$ −6.00000 10.3923i −0.250873 0.434524i
$$573$$ 9.71780 + 16.8317i 0.405967 + 0.703155i
$$574$$ 13.8589 24.0043i 0.578459 1.00192i
$$575$$ 1.50000 + 2.59808i 0.0625543 + 0.108347i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 18.7945 0.782425 0.391213 0.920300i $$-0.372056\pi$$
0.391213 + 0.920300i $$0.372056\pi$$
$$578$$ 5.71780 0.237829
$$579$$ −12.0383 + 20.8510i −0.500297 + 0.866539i
$$580$$ 4.67945 8.10504i 0.194304 0.336544i
$$581$$ 26.1534 1.08503
$$582$$ 14.0767 0.583498
$$583$$ −19.6150 + 33.9743i −0.812372 + 1.40707i
$$584$$ 2.32055 + 4.01931i 0.0960251 + 0.166320i
$$585$$ −2.00000 + 3.46410i −0.0826898 + 0.143223i
$$586$$ 2.82055 + 4.88534i 0.116516 + 0.201811i
$$587$$ 21.3589 + 36.9947i 0.881576 + 1.52693i 0.849588 + 0.527446i $$0.176850\pi$$
0.0319878 + 0.999488i $$0.489816\pi$$
$$588$$ 12.0000 0.494872
$$589$$ 23.3589 + 40.4588i 0.962487 + 1.66708i
$$590$$ 12.7178 0.523583
$$591$$ 2.82055 + 4.88534i 0.116022 + 0.200956i
$$592$$ 3.50000 + 6.06218i 0.143849 + 0.249154i
$$593$$ −3.96165 + 6.86178i −0.162686 + 0.281780i −0.935831 0.352449i $$-0.885349\pi$$
0.773145 + 0.634229i $$0.218682\pi$$
$$594$$ −1.50000 2.59808i −0.0615457 0.106600i
$$595$$ −7.32055 + 12.6796i −0.300113 + 0.519812i
$$596$$ −10.0767 −0.412758
$$597$$ 16.6411 0.681075
$$598$$ 6.00000 10.3923i 0.245358 0.424973i
$$599$$ −13.3206 + 23.0719i −0.544263 + 0.942691i 0.454390 + 0.890803i $$0.349857\pi$$
−0.998653 + 0.0518882i $$0.983476\pi$$
$$600$$ −1.00000 −0.0408248
$$601$$ 5.71780 0.233234 0.116617 0.993177i $$-0.462795\pi$$
0.116617 + 0.993177i $$0.462795\pi$$
$$602$$ 21.7945 37.7492i 0.888277 1.53854i
$$603$$ −5.67945 9.83710i −0.231285 0.400597i
$$604$$ 1.03835 1.79847i 0.0422498 0.0731788i
$$605$$ −1.00000 1.73205i −0.0406558 0.0704179i
$$606$$ −6.35890 11.0139i −0.258313 0.447411i
$$607$$ −35.7945 −1.45285 −0.726427 0.687244i $$-0.758820\pi$$
−0.726427 + 0.687244i $$0.758820\pi$$
$$608$$ −4.35890 −0.176777
$$609$$ −40.7945 −1.65308
$$610$$ −2.67945 4.64094i −0.108488 0.187906i
$$611$$ −12.0000 20.7846i −0.485468 0.840855i
$$612$$ −1.67945 + 2.90889i −0.0678877 + 0.117585i
$$613$$ −3.21780 5.57339i −0.129966 0.225107i 0.793697 0.608313i $$-0.208153\pi$$
−0.923663 + 0.383206i $$0.874820\pi$$
$$614$$ −0.679449 + 1.17684i −0.0274203 + 0.0474934i
$$615$$ 6.35890 0.256416
$$616$$ −13.0767 −0.526875
$$617$$ 0.717798 1.24326i 0.0288975 0.0500519i −0.851215 0.524817i $$-0.824134\pi$$
0.880112 + 0.474765i $$0.157467\pi$$
$$618$$ −5.17945 + 8.97107i −0.208348 + 0.360869i
$$619$$ −3.64110 −0.146348 −0.0731741 0.997319i $$-0.523313\pi$$
−0.0731741 + 0.997319i $$0.523313\pi$$
$$620$$ 10.7178 0.430437
$$621$$ 1.50000 2.59808i 0.0601929 0.104257i
$$622$$ 0.717798 + 1.24326i 0.0287811 + 0.0498503i
$$623$$ 0.782202 1.35481i 0.0313383 0.0542795i
$$624$$ 2.00000 + 3.46410i 0.0800641 + 0.138675i
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 17.4356 0.696867
$$627$$ 6.53835 11.3248i 0.261116 0.452267i
$$628$$ 5.00000 0.199522
$$629$$ 11.7561 + 20.3622i 0.468748 + 0.811896i
$$630$$ 2.17945 + 3.77492i 0.0868313 + 0.150396i
$$631$$ −20.6794 + 35.8179i −0.823236 + 1.42589i 0.0800242 + 0.996793i $$0.474500\pi$$
−0.903260 + 0.429093i $$0.858833\pi$$
$$632$$ −2.35890 4.08573i −0.0938320 0.162522i
$$633$$ −7.53835 + 13.0568i −0.299622 + 0.518961i
$$634$$ −19.0767 −0.757632
$$635$$ 10.3589 0.411080
$$636$$ 6.53835 11.3248i 0.259262 0.449056i
$$637$$ 24.0000 41.5692i 0.950915 1.64703i
$$638$$ 28.0767 1.11157
$$639$$ −10.0767 −0.398628
$$640$$ −0.500000 + 0.866025i −0.0197642 + 0.0342327i
$$641$$ 5.64110 + 9.77067i 0.222810 + 0.385918i 0.955660 0.294472i $$-0.0951437\pi$$
−0.732850 + 0.680390i $$0.761810\pi$$
$$642$$ 4.67945 8.10504i 0.184683 0.319881i
$$643$$ 19.7561 + 34.2186i 0.779106 + 1.34945i 0.932457 + 0.361280i $$0.117660\pi$$
−0.153351 + 0.988172i $$0.549007\pi$$
$$644$$ −6.53835 11.3248i −0.257647 0.446258i
$$645$$ 10.0000 0.393750
$$646$$ −14.6411 −0.576046
$$647$$ −17.1534 −0.674369 −0.337185 0.941438i $$-0.609475\pi$$
−0.337185 + 0.941438i $$0.609475\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ 19.0767 + 33.0418i 0.748826 + 1.29700i
$$650$$ −2.00000 + 3.46410i −0.0784465 + 0.135873i
$$651$$ −23.3589 40.4588i −0.915507 1.58571i
$$652$$ 2.35890 4.08573i 0.0923816 0.160010i
$$653$$ −25.0767 −0.981327 −0.490663 0.871349i $$-0.663246\pi$$
−0.490663 + 0.871349i $$0.663246\pi$$
$$654$$ −10.6411 −0.416100
$$655$$ −1.50000 + 2.59808i −0.0586098 + 0.101515i
$$656$$ 3.17945 5.50697i 0.124137 0.215011i
$$657$$ 4.64110 0.181067
$$658$$ −26.1534 −1.01957
$$659$$ 19.8589 34.3966i 0.773593 1.33990i −0.161989 0.986793i $$-0.551791\pi$$
0.935582 0.353110i $$-0.114876\pi$$
$$660$$ −1.50000 2.59808i −0.0583874 0.101130i
$$661$$ 8.71780 15.0997i 0.339083 0.587309i −0.645177 0.764033i $$-0.723217\pi$$
0.984261 + 0.176724i $$0.0565499\pi$$
$$662$$ 7.17945 + 12.4352i 0.279037 + 0.483307i
$$663$$ 6.71780 + 11.6356i 0.260898 + 0.451888i
$$664$$ 6.00000 0.232845
$$665$$ −9.50000 + 16.4545i −0.368394 + 0.638077i
$$666$$ 7.00000 0.271244
$$667$$ 14.0383 + 24.3151i 0.543567 + 0.941486i
$$668$$ 11.2178 + 19.4298i 0.434030 + 0.751761i
$$669$$ −10.1794 + 17.6313i −0.393560 + 0.681666i
$$670$$ −5.67945 9.83710i −0.219416 0.380040i
$$671$$ 8.03835 13.9228i 0.310317 0.537485i
$$672$$ 4.35890 0.168148
$$673$$ −21.2822 −0.820369 −0.410184 0.912003i $$-0.634536\pi$$
−0.410184 + 0.912003i $$0.634536\pi$$
$$674$$ 11.0767 19.1854i 0.426658 0.738994i
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 3.00000 0.115385
$$677$$ 7.07670 0.271980 0.135990 0.990710i $$-0.456579\pi$$
0.135990 + 0.990710i $$0.456579\pi$$
$$678$$ 1.67945 2.90889i 0.0644989 0.111715i
$$679$$ −30.6794 53.1384i −1.17737 2.03926i
$$680$$ −1.67945 + 2.90889i −0.0644039 + 0.111551i
$$681$$ 1.67945 + 2.90889i 0.0643566 + 0.111469i
$$682$$ 16.0767 + 27.8457i 0.615609 + 1.06627i
$$683$$ −22.7945 −0.872207 −0.436104 0.899896i $$-0.643642\pi$$
−0.436104 + 0.899896i $$0.643642\pi$$
$$684$$ −2.17945 + 3.77492i −0.0833333 + 0.144338i
$$685$$ −12.0000 −0.458496
$$686$$ −10.8972 18.8746i −0.416059 0.720635i
$$687$$ −4.35890 7.54983i −0.166302 0.288044i
$$688$$ 5.00000 8.66025i 0.190623 0.330169i
$$689$$ −26.1534 45.2990i −0.996365 1.72575i
$$690$$ 1.50000 2.59808i 0.0571040 0.0989071i
$$691$$ 31.6411 1.20368 0.601842 0.798615i $$-0.294434\pi$$
0.601842 + 0.798615i $$0.294434\pi$$
$$692$$ 18.3589 0.697901
$$693$$ −6.53835 + 11.3248i −0.248371 + 0.430192i
$$694$$ −3.71780 + 6.43941i −0.141126 + 0.244437i
$$695$$ −1.28220 −0.0486367
$$696$$ −9.35890 −0.354748
$$697$$ 10.6794 18.4973i 0.404513 0.700637i
$$698$$ 0.0383484 + 0.0664214i 0.00145151 + 0.00251409i
$$699$$ −3.00000 + 5.19615i −0.113470 + 0.196537i
$$700$$ 2.17945 + 3.77492i 0.0823754 + 0.142678i
$$701$$ −9.00000 15.5885i −0.339925 0.588768i 0.644493 0.764610i $$-0.277068\pi$$
−0.984418 + 0.175842i $$0.943735\pi$$
$$702$$ 4.00000 0.150970
$$703$$ 15.2561 + 26.4244i 0.575396 + 0.996616i
$$704$$ −3.00000 −0.113067
$$705$$ −3.00000 5.19615i −0.112987 0.195698i
$$706$$ −5.03835 8.72668i −0.189621 0.328433i
$$707$$ −27.7178 + 48.0086i −1.04244 + 1.80555i
$$708$$ −6.35890 11.0139i −0.238982 0.413929i
$$709$$ 13.3972 23.2047i 0.503144 0.871471i −0.496849 0.867837i $$-0.665510\pi$$
0.999993 0.00363441i $$-0.00115687\pi$$
$$710$$ −10.0767 −0.378172
$$711$$ −4.71780 −0.176931
$$712$$ 0.179449 0.310816i 0.00672515 0.0116483i
$$713$$ −16.0767 + 27.8457i −0.602077 + 1.04283i
$$714$$ 14.6411 0.547929
$$715$$ −12.0000 −0.448775
$$716$$ −7.85890 + 13.6120i −0.293701 + 0.508705i
$$717$$ 6.71780 + 11.6356i 0.250881 + 0.434538i
$$718$$ 7.67945 13.3012i 0.286595 0.496396i
$$719$$ 8.64110 + 14.9668i 0.322259 + 0.558168i 0.980954 0.194242i $$-0.0622246\pi$$
−0.658695 + 0.752410i $$0.728891\pi$$
$$720$$ 0.500000 + 0.866025i 0.0186339 + 0.0322749i
$$721$$ 45.1534 1.68160
$$722$$ −19.0000 −0.707107
$$723$$ −4.00000 −0.148762
$$724$$ −9.03835 15.6549i −0.335908 0.581809i
$$725$$ −4.67945 8.10504i −0.173790 0.301014i
$$726$$ −1.00000 + 1.73205i −0.0371135 + 0.0642824i
$$727$$ 15.0767 + 26.1136i 0.559164 + 0.968500i 0.997567 + 0.0697214i $$0.0222110\pi$$
−0.438403 + 0.898779i $$0.644456\pi$$
$$728$$ 8.71780 15.0997i 0.323103 0.559631i
$$729$$ 1.00000 0.0370370
$$730$$ 4.64110 0.171775
$$731$$ 16.7945 29.0889i 0.621167 1.07589i
$$732$$ −2.67945 + 4.64094i −0.0990353 + 0.171534i
$$733$$ 9.56440 0.353269 0.176635 0.984276i $$-0.443479\pi$$
0.176635 + 0.984276i $$0.443479\pi$$
$$734$$ −14.7178 −0.543244
$$735$$ 6.00000 10.3923i 0.221313 0.383326i
$$736$$ −1.50000 2.59808i −0.0552907 0.0957664i
$$737$$ 17.0383 29.5113i 0.627616 1.08706i
$$738$$ −3.17945 5.50697i −0.117037 0.202714i
$$739$$ 8.17945 + 14.1672i 0.300886 + 0.521150i 0.976337 0.216255i $$-0.0693843\pi$$
−0.675451 + 0.737405i $$0.736051\pi$$
$$740$$ 7.00000 0.257325
$$741$$ 8.71780 + 15.0997i 0.320256 + 0.554700i
$$742$$ −57.0000 −2.09254
$$743$$ −4.50000 7.79423i −0.165089 0.285943i 0.771598 0.636111i $$-0.219458\pi$$
−0.936687 + 0.350168i $$0.886124\pi$$
$$744$$ −5.35890 9.28189i −0.196467 0.340290i
$$745$$ −5.03835 + 8.72668i −0.184591 + 0.319721i
$$746$$ 5.50000 + 9.52628i 0.201369 + 0.348782i
$$747$$ 3.00000 5.19615i 0.109764 0.190117i
$$748$$ −10.0767 −0.368441
$$749$$ −40.7945 −1.49060
$$750$$ −0.500000 + 0.866025i −0.0182574 + 0.0316228i
$$751$$ −11.4356 + 19.8070i −0.417291 + 0.722769i −0.995666 0.0930021i $$-0.970354\pi$$
0.578375 + 0.815771i $$0.303687\pi$$
$$752$$ −6.00000 −0.218797
$$753$$ −12.0000 −0.437304
$$754$$ −18.7178 + 32.4202i −0.681662 + 1.18067i
$$755$$ −1.03835 1.79847i −0.0377894 0.0654531i
$$756$$ 2.17945 3.77492i 0.0792658 0.137292i
$$757$$ −24.9356 43.1897i −0.906300 1.56976i −0.819163 0.573561i $$-0.805562\pi$$
−0.0871365 0.996196i $$-0.527772\pi$$
$$758$$ 7.35890 + 12.7460i 0.267287 + 0.462955i
$$759$$ 9.00000 0.326679
$$760$$ −2.17945 + 3.77492i −0.0790569 + 0.136931i
$$761$$ −7.07670 −0.256530 −0.128265 0.991740i $$-0.540941\pi$$
−0.128265 + 0.991740i $$0.540941\pi$$
$$762$$ −5.17945 8.97107i −0.187632 0.324988i
$$763$$ 23.1917 + 40.1693i 0.839597 + 1.45423i
$$764$$ 9.71780 16.8317i 0.351578 0.608950i
$$765$$ 1.67945 + 2.90889i 0.0607206 + 0.105171i
$$766$$ 3.00000 5.19615i 0.108394 0.187745i
$$767$$ −50.8712 −1.83685
$$768$$ 1.00000 0.0360844
$$769$$ −1.35890 + 2.35368i −0.0490031 + 0.0848759i −0.889487 0.456961i $$-0.848938\pi$$
0.840483 + 0.541837i $$0.182271\pi$$
$$770$$ −6.53835 + 11.3248i −0.235626 + 0.408116i
$$771$$ −7.43560 −0.267786
$$772$$ 24.0767 0.866539
$$773$$ 0.897247 1.55408i 0.0322717 0.0558963i −0.849438 0.527688i $$-0.823059\pi$$
0.881710 + 0.471791i $$0.156392\pi$$
$$774$$ −5.00000 8.66025i −0.179721 0.311286i
$$775$$ 5.35890 9.28189i 0.192497 0.333415i
$$776$$ −7.03835 12.1908i −0.252662 0.437623i
$$777$$ −15.2561 26.4244i −0.547311 0.947971i
$$778$$ −4.07670