Properties

 Label 546.2.q.g.251.1 Level $546$ Weight $2$ Character 546.251 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.q (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2x^{2} - 3x + 9$$ x^4 - x^3 - 2*x^2 - 3*x + 9 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 251.1 Root $$-1.18614 + 1.26217i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.251 Dual form 546.2.q.g.335.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.52434i q^{5} +(-1.68614 - 0.396143i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.52434i q^{5} +(-1.68614 - 0.396143i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +(-2.18614 - 1.26217i) q^{10} +(-0.686141 + 1.18843i) q^{11} +(-1.18614 + 1.26217i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(-4.18614 + 1.26217i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.686141 - 1.18843i) q^{17} +(0.186141 + 2.99422i) q^{18} +(1.68614 + 2.92048i) q^{19} +(-2.18614 + 1.26217i) q^{20} +(-4.55842 + 0.469882i) q^{21} +(0.686141 + 1.18843i) q^{22} +(0.813859 + 0.469882i) q^{23} +(0.500000 + 1.65831i) q^{24} -1.37228 q^{25} +(1.00000 - 3.46410i) q^{26} +(4.00000 + 3.31662i) q^{27} +(-2.50000 + 0.866025i) q^{28} +(-0.686141 - 0.396143i) q^{29} +(-1.00000 + 4.25639i) q^{30} -4.74456 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.31386 + 0.543620i) q^{33} -1.37228 q^{34} +(-6.55842 - 1.26217i) q^{35} +(2.68614 + 1.33591i) q^{36} +(7.11684 + 4.10891i) q^{37} +3.37228 q^{38} +(-3.18614 - 5.37108i) q^{39} +2.52434i q^{40} +(-5.31386 - 3.06796i) q^{41} +(-1.87228 + 4.18265i) q^{42} +(2.00000 + 3.46410i) q^{43} +1.37228 q^{44} +(4.18614 + 6.31084i) q^{45} +(0.813859 - 0.469882i) q^{46} -4.25639i q^{47} +(1.68614 + 0.396143i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-0.686141 + 1.18843i) q^{50} +(-1.62772 + 1.73205i) q^{51} +(-2.50000 - 2.59808i) q^{52} -14.3537i q^{53} +(4.87228 - 1.80579i) q^{54} +(3.00000 + 1.73205i) q^{55} +(-0.500000 + 2.59808i) q^{56} +(4.00000 - 4.25639i) q^{57} +(-0.686141 + 0.396143i) q^{58} +(-8.18614 + 4.72627i) q^{59} +(3.18614 + 2.99422i) q^{60} +(4.50000 - 2.59808i) q^{61} +(-2.37228 + 4.10891i) q^{62} +(3.05842 + 7.32435i) q^{63} +1.00000 q^{64} +(-2.18614 - 8.83518i) q^{65} +(1.62772 - 1.73205i) q^{66} +(-7.11684 - 4.10891i) q^{67} +(-0.686141 + 1.18843i) q^{68} +(0.372281 - 1.58457i) q^{69} +(-4.37228 + 5.04868i) q^{70} +(0.558422 + 0.967215i) q^{71} +(2.50000 - 1.65831i) q^{72} +0.744563 q^{73} +(7.11684 - 4.10891i) q^{74} +(0.686141 + 2.27567i) q^{75} +(1.68614 - 2.92048i) q^{76} +(2.74456 + 2.37686i) q^{77} +(-6.24456 + 0.0737384i) q^{78} +15.3723 q^{79} +(2.18614 + 1.26217i) q^{80} +(3.50000 - 8.29156i) q^{81} +(-5.31386 + 3.06796i) q^{82} +5.04868i q^{83} +(2.68614 + 3.71277i) q^{84} +(-3.00000 + 1.73205i) q^{85} +4.00000 q^{86} +(-0.313859 + 1.33591i) q^{87} +(0.686141 - 1.18843i) q^{88} +(10.8030 + 6.23711i) q^{89} +(7.55842 - 0.469882i) q^{90} +(-0.500000 - 9.52628i) q^{91} -0.939764i q^{92} +(2.37228 + 7.86797i) q^{93} +(-3.68614 - 2.12819i) q^{94} +(7.37228 - 4.25639i) q^{95} +(1.18614 - 1.26217i) q^{96} +(5.37228 + 9.30506i) q^{97} +(-5.50000 + 4.33013i) q^{98} +(-0.255437 - 4.10891i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10})$$ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 $$4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} + 14 q^{13} - 8 q^{14} - 11 q^{15} - 2 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} - 3 q^{20} - q^{21} - 3 q^{22} + 9 q^{23} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 16 q^{27} - 10 q^{28} + 3 q^{29} - 4 q^{30} + 4 q^{31} + 2 q^{32} + 15 q^{33} + 6 q^{34} - 9 q^{35} + 5 q^{36} - 6 q^{37} + 2 q^{38} - 7 q^{39} - 27 q^{41} + 4 q^{42} + 8 q^{43} - 6 q^{44} + 11 q^{45} + 9 q^{46} + q^{48} - 26 q^{49} + 3 q^{50} - 18 q^{51} - 10 q^{52} + 8 q^{54} + 12 q^{55} - 2 q^{56} + 16 q^{57} + 3 q^{58} - 27 q^{59} + 7 q^{60} + 18 q^{61} + 2 q^{62} - 5 q^{63} + 4 q^{64} - 3 q^{65} + 18 q^{66} + 6 q^{67} + 3 q^{68} - 10 q^{69} - 6 q^{70} - 15 q^{71} + 10 q^{72} - 20 q^{73} - 6 q^{74} - 3 q^{75} + q^{76} - 12 q^{77} - 2 q^{78} + 50 q^{79} + 3 q^{80} + 14 q^{81} - 27 q^{82} + 5 q^{84} - 12 q^{85} + 16 q^{86} - 7 q^{87} - 3 q^{88} + 3 q^{89} + 13 q^{90} - 2 q^{91} - 2 q^{93} - 9 q^{94} + 18 q^{95} - q^{96} + 10 q^{97} - 22 q^{98} - 24 q^{99}+O(q^{100})$$ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 3 * q^10 + 3 * q^11 + q^12 + 14 * q^13 - 8 * q^14 - 11 * q^15 - 2 * q^16 + 3 * q^17 - 5 * q^18 + q^19 - 3 * q^20 - q^21 - 3 * q^22 + 9 * q^23 + 2 * q^24 + 6 * q^25 + 4 * q^26 + 16 * q^27 - 10 * q^28 + 3 * q^29 - 4 * q^30 + 4 * q^31 + 2 * q^32 + 15 * q^33 + 6 * q^34 - 9 * q^35 + 5 * q^36 - 6 * q^37 + 2 * q^38 - 7 * q^39 - 27 * q^41 + 4 * q^42 + 8 * q^43 - 6 * q^44 + 11 * q^45 + 9 * q^46 + q^48 - 26 * q^49 + 3 * q^50 - 18 * q^51 - 10 * q^52 + 8 * q^54 + 12 * q^55 - 2 * q^56 + 16 * q^57 + 3 * q^58 - 27 * q^59 + 7 * q^60 + 18 * q^61 + 2 * q^62 - 5 * q^63 + 4 * q^64 - 3 * q^65 + 18 * q^66 + 6 * q^67 + 3 * q^68 - 10 * q^69 - 6 * q^70 - 15 * q^71 + 10 * q^72 - 20 * q^73 - 6 * q^74 - 3 * q^75 + q^76 - 12 * q^77 - 2 * q^78 + 50 * q^79 + 3 * q^80 + 14 * q^81 - 27 * q^82 + 5 * q^84 - 12 * q^85 + 16 * q^86 - 7 * q^87 - 3 * q^88 + 3 * q^89 + 13 * q^90 - 2 * q^91 - 2 * q^93 - 9 * q^94 + 18 * q^95 - q^96 + 10 * q^97 - 22 * q^98 - 24 * q^99

Character values

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

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −0.500000 1.65831i −0.288675 0.957427i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 2.52434i 1.12892i −0.825461 0.564459i $$-0.809085\pi$$
0.825461 0.564459i $$-0.190915\pi$$
$$6$$ −1.68614 0.396143i −0.688364 0.161725i
$$7$$ 0.500000 2.59808i 0.188982 0.981981i
$$8$$ −1.00000 −0.353553
$$9$$ −2.50000 + 1.65831i −0.833333 + 0.552771i
$$10$$ −2.18614 1.26217i −0.691318 0.399133i
$$11$$ −0.686141 + 1.18843i −0.206879 + 0.358325i −0.950730 0.310021i $$-0.899664\pi$$
0.743851 + 0.668346i $$0.232997\pi$$
$$12$$ −1.18614 + 1.26217i −0.342409 + 0.364357i
$$13$$ 3.50000 0.866025i 0.970725 0.240192i
$$14$$ −2.00000 1.73205i −0.534522 0.462910i
$$15$$ −4.18614 + 1.26217i −1.08086 + 0.325891i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −0.686141 1.18843i −0.166414 0.288237i 0.770743 0.637146i $$-0.219885\pi$$
−0.937156 + 0.348910i $$0.886552\pi$$
$$18$$ 0.186141 + 2.99422i 0.0438738 + 0.705744i
$$19$$ 1.68614 + 2.92048i 0.386827 + 0.670004i 0.992021 0.126074i $$-0.0402377\pi$$
−0.605194 + 0.796078i $$0.706904\pi$$
$$20$$ −2.18614 + 1.26217i −0.488836 + 0.282230i
$$21$$ −4.55842 + 0.469882i −0.994729 + 0.102537i
$$22$$ 0.686141 + 1.18843i 0.146286 + 0.253374i
$$23$$ 0.813859 + 0.469882i 0.169701 + 0.0979772i 0.582445 0.812870i $$-0.302096\pi$$
−0.412744 + 0.910847i $$0.635429\pi$$
$$24$$ 0.500000 + 1.65831i 0.102062 + 0.338502i
$$25$$ −1.37228 −0.274456
$$26$$ 1.00000 3.46410i 0.196116 0.679366i
$$27$$ 4.00000 + 3.31662i 0.769800 + 0.638285i
$$28$$ −2.50000 + 0.866025i −0.472456 + 0.163663i
$$29$$ −0.686141 0.396143i −0.127413 0.0735620i 0.434939 0.900460i $$-0.356770\pi$$
−0.562352 + 0.826898i $$0.690103\pi$$
$$30$$ −1.00000 + 4.25639i −0.182574 + 0.777107i
$$31$$ −4.74456 −0.852149 −0.426074 0.904688i $$-0.640104\pi$$
−0.426074 + 0.904688i $$0.640104\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 2.31386 + 0.543620i 0.402791 + 0.0946322i
$$34$$ −1.37228 −0.235344
$$35$$ −6.55842 1.26217i −1.10858 0.213345i
$$36$$ 2.68614 + 1.33591i 0.447690 + 0.222651i
$$37$$ 7.11684 + 4.10891i 1.17000 + 0.675501i 0.953681 0.300821i $$-0.0972608\pi$$
0.216321 + 0.976322i $$0.430594\pi$$
$$38$$ 3.37228 0.547056
$$39$$ −3.18614 5.37108i −0.510191 0.860061i
$$40$$ 2.52434i 0.399133i
$$41$$ −5.31386 3.06796i −0.829885 0.479135i 0.0239280 0.999714i $$-0.492383\pi$$
−0.853813 + 0.520579i $$0.825716\pi$$
$$42$$ −1.87228 + 4.18265i −0.288899 + 0.645397i
$$43$$ 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i $$-0.0680112\pi$$
−0.672264 + 0.740312i $$0.734678\pi$$
$$44$$ 1.37228 0.206879
$$45$$ 4.18614 + 6.31084i 0.624033 + 0.940765i
$$46$$ 0.813859 0.469882i 0.119997 0.0692803i
$$47$$ 4.25639i 0.620858i −0.950597 0.310429i $$-0.899527\pi$$
0.950597 0.310429i $$-0.100473\pi$$
$$48$$ 1.68614 + 0.396143i 0.243373 + 0.0571784i
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ −0.686141 + 1.18843i −0.0970349 + 0.168069i
$$51$$ −1.62772 + 1.73205i −0.227926 + 0.242536i
$$52$$ −2.50000 2.59808i −0.346688 0.360288i
$$53$$ 14.3537i 1.97164i −0.167813 0.985819i $$-0.553670\pi$$
0.167813 0.985819i $$-0.446330\pi$$
$$54$$ 4.87228 1.80579i 0.663034 0.245737i
$$55$$ 3.00000 + 1.73205i 0.404520 + 0.233550i
$$56$$ −0.500000 + 2.59808i −0.0668153 + 0.347183i
$$57$$ 4.00000 4.25639i 0.529813 0.563772i
$$58$$ −0.686141 + 0.396143i −0.0900947 + 0.0520162i
$$59$$ −8.18614 + 4.72627i −1.06574 + 0.615308i −0.927016 0.375022i $$-0.877635\pi$$
−0.138729 + 0.990330i $$0.544302\pi$$
$$60$$ 3.18614 + 2.99422i 0.411329 + 0.386552i
$$61$$ 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i $$-0.558724\pi$$
0.759608 + 0.650381i $$0.225391\pi$$
$$62$$ −2.37228 + 4.10891i −0.301280 + 0.521832i
$$63$$ 3.05842 + 7.32435i 0.385325 + 0.922781i
$$64$$ 1.00000 0.125000
$$65$$ −2.18614 8.83518i −0.271157 1.09587i
$$66$$ 1.62772 1.73205i 0.200358 0.213201i
$$67$$ −7.11684 4.10891i −0.869461 0.501983i −0.00229183 0.999997i $$-0.500730\pi$$
−0.867169 + 0.498014i $$0.834063\pi$$
$$68$$ −0.686141 + 1.18843i −0.0832068 + 0.144118i
$$69$$ 0.372281 1.58457i 0.0448174 0.190760i
$$70$$ −4.37228 + 5.04868i −0.522588 + 0.603432i
$$71$$ 0.558422 + 0.967215i 0.0662725 + 0.114787i 0.897258 0.441507i $$-0.145556\pi$$
−0.830985 + 0.556294i $$0.812223\pi$$
$$72$$ 2.50000 1.65831i 0.294628 0.195434i
$$73$$ 0.744563 0.0871445 0.0435722 0.999050i $$-0.486126\pi$$
0.0435722 + 0.999050i $$0.486126\pi$$
$$74$$ 7.11684 4.10891i 0.827316 0.477651i
$$75$$ 0.686141 + 2.27567i 0.0792287 + 0.262772i
$$76$$ 1.68614 2.92048i 0.193414 0.335002i
$$77$$ 2.74456 + 2.37686i 0.312772 + 0.270868i
$$78$$ −6.24456 + 0.0737384i −0.707057 + 0.00834923i
$$79$$ 15.3723 1.72952 0.864758 0.502188i $$-0.167472\pi$$
0.864758 + 0.502188i $$0.167472\pi$$
$$80$$ 2.18614 + 1.26217i 0.244418 + 0.141115i
$$81$$ 3.50000 8.29156i 0.388889 0.921285i
$$82$$ −5.31386 + 3.06796i −0.586818 + 0.338799i
$$83$$ 5.04868i 0.554164i 0.960846 + 0.277082i $$0.0893674\pi$$
−0.960846 + 0.277082i $$0.910633\pi$$
$$84$$ 2.68614 + 3.71277i 0.293082 + 0.405096i
$$85$$ −3.00000 + 1.73205i −0.325396 + 0.187867i
$$86$$ 4.00000 0.431331
$$87$$ −0.313859 + 1.33591i −0.0336493 + 0.143224i
$$88$$ 0.686141 1.18843i 0.0731428 0.126687i
$$89$$ 10.8030 + 6.23711i 1.14511 + 0.661132i 0.947692 0.319187i $$-0.103410\pi$$
0.197422 + 0.980319i $$0.436743\pi$$
$$90$$ 7.55842 0.469882i 0.796728 0.0495299i
$$91$$ −0.500000 9.52628i −0.0524142 0.998625i
$$92$$ 0.939764i 0.0979772i
$$93$$ 2.37228 + 7.86797i 0.245994 + 0.815870i
$$94$$ −3.68614 2.12819i −0.380196 0.219506i
$$95$$ 7.37228 4.25639i 0.756380 0.436696i
$$96$$ 1.18614 1.26217i 0.121060 0.128820i
$$97$$ 5.37228 + 9.30506i 0.545473 + 0.944786i 0.998577 + 0.0533287i $$0.0169831\pi$$
−0.453104 + 0.891457i $$0.649684\pi$$
$$98$$ −5.50000 + 4.33013i −0.555584 + 0.437409i
$$99$$ −0.255437 4.10891i −0.0256724 0.412961i
$$100$$ 0.686141 + 1.18843i 0.0686141 + 0.118843i
$$101$$ −1.62772 + 2.81929i −0.161964 + 0.280530i −0.935573 0.353133i $$-0.885116\pi$$
0.773609 + 0.633663i $$0.218450\pi$$
$$102$$ 0.686141 + 2.27567i 0.0679380 + 0.225325i
$$103$$ 11.6819i 1.15105i −0.817783 0.575527i $$-0.804797\pi$$
0.817783 0.575527i $$-0.195203\pi$$
$$104$$ −3.50000 + 0.866025i −0.343203 + 0.0849208i
$$105$$ 1.18614 + 11.5070i 0.115755 + 1.12297i
$$106$$ −12.4307 7.17687i −1.20738 0.697079i
$$107$$ −3.68614 2.12819i −0.356353 0.205740i 0.311127 0.950368i $$-0.399294\pi$$
−0.667480 + 0.744628i $$0.732627\pi$$
$$108$$ 0.872281 5.12241i 0.0839353 0.492905i
$$109$$ 19.8997i 1.90605i −0.302891 0.953025i $$-0.597952\pi$$
0.302891 0.953025i $$-0.402048\pi$$
$$110$$ 3.00000 1.73205i 0.286039 0.165145i
$$111$$ 3.25544 13.8564i 0.308992 1.31519i
$$112$$ 2.00000 + 1.73205i 0.188982 + 0.163663i
$$113$$ 14.7446 8.51278i 1.38705 0.800815i 0.394070 0.919081i $$-0.371067\pi$$
0.992982 + 0.118266i $$0.0377335\pi$$
$$114$$ −1.68614 5.59230i −0.157922 0.523767i
$$115$$ 1.18614 2.05446i 0.110608 0.191579i
$$116$$ 0.792287i 0.0735620i
$$117$$ −7.31386 + 7.96916i −0.676167 + 0.736749i
$$118$$ 9.45254i 0.870177i
$$119$$ −3.43070 + 1.18843i −0.314492 + 0.108943i
$$120$$ 4.18614 1.26217i 0.382141 0.115220i
$$121$$ 4.55842 + 7.89542i 0.414402 + 0.717765i
$$122$$ 5.19615i 0.470438i
$$123$$ −2.43070 + 10.3460i −0.219169 + 0.932869i
$$124$$ 2.37228 + 4.10891i 0.213037 + 0.368991i
$$125$$ 9.15759i 0.819080i
$$126$$ 7.87228 + 1.01350i 0.701319 + 0.0902900i
$$127$$ −7.55842 + 13.0916i −0.670701 + 1.16169i 0.307004 + 0.951708i $$0.400673\pi$$
−0.977706 + 0.209981i $$0.932660\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 4.74456 5.04868i 0.417735 0.444511i
$$130$$ −8.74456 2.52434i −0.766949 0.221399i
$$131$$ −18.6060 −1.62561 −0.812806 0.582535i $$-0.802061\pi$$
−0.812806 + 0.582535i $$0.802061\pi$$
$$132$$ −0.686141 2.27567i −0.0597209 0.198072i
$$133$$ 8.43070 2.92048i 0.731035 0.253238i
$$134$$ −7.11684 + 4.10891i −0.614802 + 0.354956i
$$135$$ 8.37228 10.0974i 0.720571 0.869042i
$$136$$ 0.686141 + 1.18843i 0.0588361 + 0.101907i
$$137$$ 0.813859 + 1.40965i 0.0695327 + 0.120434i 0.898696 0.438573i $$-0.144516\pi$$
−0.829163 + 0.559007i $$0.811183\pi$$
$$138$$ −1.18614 1.11469i −0.100971 0.0948889i
$$139$$ 18.1753 10.4935i 1.54161 0.890047i 0.542868 0.839818i $$-0.317338\pi$$
0.998738 0.0502287i $$-0.0159950\pi$$
$$140$$ 2.18614 + 6.31084i 0.184763 + 0.533364i
$$141$$ −7.05842 + 2.12819i −0.594426 + 0.179226i
$$142$$ 1.11684 0.0937235
$$143$$ −1.37228 + 4.75372i −0.114756 + 0.397526i
$$144$$ −0.186141 2.99422i −0.0155117 0.249518i
$$145$$ −1.00000 + 1.73205i −0.0830455 + 0.143839i
$$146$$ 0.372281 0.644810i 0.0308102 0.0533649i
$$147$$ −1.05842 + 12.0781i −0.0872972 + 0.996182i
$$148$$ 8.21782i 0.675501i
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 2.31386 + 0.543620i 0.188926 + 0.0443864i
$$151$$ 3.02167i 0.245900i −0.992413 0.122950i $$-0.960765\pi$$
0.992413 0.122950i $$-0.0392355\pi$$
$$152$$ −1.68614 2.92048i −0.136764 0.236882i
$$153$$ 3.68614 + 1.83324i 0.298007 + 0.148209i
$$154$$ 3.43070 1.18843i 0.276454 0.0957665i
$$155$$ 11.9769i 0.962006i
$$156$$ −3.05842 + 5.44482i −0.244870 + 0.435934i
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 7.68614 13.3128i 0.611477 1.05911i
$$159$$ −23.8030 + 7.17687i −1.88770 + 0.569163i
$$160$$ 2.18614 1.26217i 0.172830 0.0997832i
$$161$$ 1.62772 1.87953i 0.128282 0.148128i
$$162$$ −5.43070 7.17687i −0.426676 0.563868i
$$163$$ −9.00000 + 5.19615i −0.704934 + 0.406994i −0.809183 0.587557i $$-0.800090\pi$$
0.104248 + 0.994551i $$0.466756\pi$$
$$164$$ 6.13592i 0.479135i
$$165$$ 1.37228 5.84096i 0.106832 0.454718i
$$166$$ 4.37228 + 2.52434i 0.339355 + 0.195927i
$$167$$ 5.74456 + 3.31662i 0.444528 + 0.256648i 0.705516 0.708694i $$-0.250715\pi$$
−0.260989 + 0.965342i $$0.584049\pi$$
$$168$$ 4.55842 0.469882i 0.351690 0.0362522i
$$169$$ 11.5000 6.06218i 0.884615 0.466321i
$$170$$ 3.46410i 0.265684i
$$171$$ −9.05842 4.50506i −0.692715 0.344510i
$$172$$ 2.00000 3.46410i 0.152499 0.264135i
$$173$$ 9.55842 + 16.5557i 0.726713 + 1.25870i 0.958265 + 0.285882i $$0.0922865\pi$$
−0.231552 + 0.972823i $$0.574380\pi$$
$$174$$ 1.00000 + 0.939764i 0.0758098 + 0.0712433i
$$175$$ −0.686141 + 3.56529i −0.0518674 + 0.269511i
$$176$$ −0.686141 1.18843i −0.0517198 0.0895813i
$$177$$ 11.9307 + 11.2120i 0.896767 + 0.842749i
$$178$$ 10.8030 6.23711i 0.809718 0.467491i
$$179$$ 1.37228 + 0.792287i 0.102569 + 0.0592183i 0.550407 0.834896i $$-0.314473\pi$$
−0.447838 + 0.894115i $$0.647806\pi$$
$$180$$ 3.37228 6.78073i 0.251355 0.505406i
$$181$$ 12.1244i 0.901196i 0.892727 + 0.450598i $$0.148789\pi$$
−0.892727 + 0.450598i $$0.851211\pi$$
$$182$$ −8.50000 4.33013i −0.630062 0.320970i
$$183$$ −6.55842 6.16337i −0.484813 0.455609i
$$184$$ −0.813859 0.469882i −0.0599985 0.0346402i
$$185$$ 10.3723 17.9653i 0.762585 1.32084i
$$186$$ 8.00000 + 1.87953i 0.586588 + 0.137814i
$$187$$ 1.88316 0.137710
$$188$$ −3.68614 + 2.12819i −0.268839 + 0.155215i
$$189$$ 10.6168 8.73399i 0.772262 0.635304i
$$190$$ 8.51278i 0.617582i
$$191$$ −16.3723 + 9.45254i −1.18466 + 0.683962i −0.957087 0.289800i $$-0.906411\pi$$
−0.227569 + 0.973762i $$0.573078\pi$$
$$192$$ −0.500000 1.65831i −0.0360844 0.119678i
$$193$$ −5.61684 3.24289i −0.404309 0.233428i 0.284032 0.958815i $$-0.408328\pi$$
−0.688342 + 0.725387i $$0.741661\pi$$
$$194$$ 10.7446 0.771415
$$195$$ −13.5584 + 8.04290i −0.970939 + 0.575964i
$$196$$ 1.00000 + 6.92820i 0.0714286 + 0.494872i
$$197$$ 7.80298 13.5152i 0.555940 0.962916i −0.441890 0.897069i $$-0.645692\pi$$
0.997830 0.0658465i $$-0.0209748\pi$$
$$198$$ −3.68614 1.83324i −0.261963 0.130283i
$$199$$ −3.00000 + 1.73205i −0.212664 + 0.122782i −0.602549 0.798082i $$-0.705848\pi$$
0.389885 + 0.920864i $$0.372515\pi$$
$$200$$ 1.37228 0.0970349
$$201$$ −3.25544 + 13.8564i −0.229621 + 0.977356i
$$202$$ 1.62772 + 2.81929i 0.114526 + 0.198365i
$$203$$ −1.37228 + 1.58457i −0.0963153 + 0.111215i
$$204$$ 2.31386 + 0.543620i 0.162003 + 0.0380610i
$$205$$ −7.74456 + 13.4140i −0.540904 + 0.936873i
$$206$$ −10.1168 5.84096i −0.704874 0.406959i
$$207$$ −2.81386 + 0.174928i −0.195577 + 0.0121584i
$$208$$ −1.00000 + 3.46410i −0.0693375 + 0.240192i
$$209$$ −4.62772 −0.320106
$$210$$ 10.5584 + 4.72627i 0.728600 + 0.326144i
$$211$$ −11.3723 + 19.6974i −0.782900 + 1.35602i 0.147345 + 0.989085i $$0.452927\pi$$
−0.930246 + 0.366938i $$0.880406\pi$$
$$212$$ −12.4307 + 7.17687i −0.853744 + 0.492909i
$$213$$ 1.32473 1.40965i 0.0907693 0.0965873i
$$214$$ −3.68614 + 2.12819i −0.251979 + 0.145480i
$$215$$ 8.74456 5.04868i 0.596374 0.344317i
$$216$$ −4.00000 3.31662i −0.272166 0.225668i
$$217$$ −2.37228 + 12.3267i −0.161041 + 0.836793i
$$218$$ −17.2337 9.94987i −1.16721 0.673891i
$$219$$ −0.372281 1.23472i −0.0251564 0.0834345i
$$220$$ 3.46410i 0.233550i
$$221$$ −3.43070 3.56529i −0.230774 0.239827i
$$222$$ −10.3723 9.74749i −0.696142 0.654209i
$$223$$ −3.11684 + 5.39853i −0.208719 + 0.361512i −0.951311 0.308232i $$-0.900263\pi$$
0.742592 + 0.669744i $$0.233596\pi$$
$$224$$ 2.50000 0.866025i 0.167038 0.0578638i
$$225$$ 3.43070 2.27567i 0.228714 0.151711i
$$226$$ 17.0256i 1.13252i
$$227$$ −3.30298 + 1.90698i −0.219227 + 0.126571i −0.605592 0.795775i $$-0.707064\pi$$
0.386365 + 0.922346i $$0.373730\pi$$
$$228$$ −5.68614 1.33591i −0.376574 0.0884726i
$$229$$ −12.1168 −0.800704 −0.400352 0.916362i $$-0.631112\pi$$
−0.400352 + 0.916362i $$0.631112\pi$$
$$230$$ −1.18614 2.05446i −0.0782118 0.135467i
$$231$$ 2.56930 5.73977i 0.169047 0.377649i
$$232$$ 0.686141 + 0.396143i 0.0450473 + 0.0260081i
$$233$$ 28.0627i 1.83845i 0.393737 + 0.919223i $$0.371182\pi$$
−0.393737 + 0.919223i $$0.628818\pi$$
$$234$$ 3.24456 + 10.3186i 0.212104 + 0.674546i
$$235$$ −10.7446 −0.700898
$$236$$ 8.18614 + 4.72627i 0.532872 + 0.307654i
$$237$$ −7.68614 25.4920i −0.499268 1.65589i
$$238$$ −0.686141 + 3.56529i −0.0444759 + 0.231104i
$$239$$ 24.6060 1.59163 0.795814 0.605541i $$-0.207043\pi$$
0.795814 + 0.605541i $$0.207043\pi$$
$$240$$ 1.00000 4.25639i 0.0645497 0.274749i
$$241$$ −0.627719 1.08724i −0.0404349 0.0700353i 0.845100 0.534609i $$-0.179541\pi$$
−0.885535 + 0.464573i $$0.846208\pi$$
$$242$$ 9.11684 0.586053
$$243$$ −15.5000 1.65831i −0.994325 0.106381i
$$244$$ −4.50000 2.59808i −0.288083 0.166325i
$$245$$ −6.55842 + 16.4082i −0.419002 + 1.04828i
$$246$$ 7.74456 + 7.27806i 0.493775 + 0.464032i
$$247$$ 8.43070 + 8.76144i 0.536433 + 0.557477i
$$248$$ 4.74456 0.301280
$$249$$ 8.37228 2.52434i 0.530572 0.159973i
$$250$$ −7.93070 4.57879i −0.501582 0.289588i
$$251$$ −0.558422 0.967215i −0.0352473 0.0610501i 0.847864 0.530214i $$-0.177889\pi$$
−0.883111 + 0.469164i $$0.844555\pi$$
$$252$$ 4.81386 6.31084i 0.303245 0.397546i
$$253$$ −1.11684 + 0.644810i −0.0702154 + 0.0405389i
$$254$$ 7.55842 + 13.0916i 0.474258 + 0.821438i
$$255$$ 4.37228 + 4.10891i 0.273803 + 0.257310i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 11.0584 19.1537i 0.689805 1.19478i −0.282095 0.959386i $$-0.591029\pi$$
0.971901 0.235392i $$-0.0756373\pi$$
$$258$$ −2.00000 6.63325i −0.124515 0.412968i
$$259$$ 14.2337 16.4356i 0.884438 1.02126i
$$260$$ −6.55842 + 6.31084i −0.406736 + 0.391382i
$$261$$ 2.37228 0.147477i 0.146841 0.00912859i
$$262$$ −9.30298 + 16.1132i −0.574740 + 0.995479i
$$263$$ 12.0475 + 6.95565i 0.742884 + 0.428904i 0.823117 0.567872i $$-0.192233\pi$$
−0.0802332 + 0.996776i $$0.525567\pi$$
$$264$$ −2.31386 0.543620i −0.142408 0.0334575i
$$265$$ −36.2337 −2.22582
$$266$$ 1.68614 8.76144i 0.103384 0.537199i
$$267$$ 4.94158 21.0333i 0.302420 1.28722i
$$268$$ 8.21782i 0.501983i
$$269$$ 13.9307 + 24.1287i 0.849370 + 1.47115i 0.881771 + 0.471677i $$0.156351\pi$$
−0.0324014 + 0.999475i $$0.510316\pi$$
$$270$$ −4.55842 12.2993i −0.277417 0.748511i
$$271$$ −2.00000 + 3.46410i −0.121491 + 0.210429i −0.920356 0.391082i $$-0.872101\pi$$
0.798865 + 0.601511i $$0.205434\pi$$
$$272$$ 1.37228 0.0832068
$$273$$ −15.5475 + 5.59230i −0.940980 + 0.338461i
$$274$$ 1.62772 0.0983341
$$275$$ 0.941578 1.63086i 0.0567793 0.0983446i
$$276$$ −1.55842 + 0.469882i −0.0938060 + 0.0282836i
$$277$$ 4.74456 + 8.21782i 0.285073 + 0.493761i 0.972627 0.232372i $$-0.0746488\pi$$
−0.687554 + 0.726133i $$0.741315\pi$$
$$278$$ 20.9870i 1.25872i
$$279$$ 11.8614 7.86797i 0.710124 0.471043i
$$280$$ 6.55842 + 1.26217i 0.391941 + 0.0754290i
$$281$$ −3.25544 −0.194203 −0.0971016 0.995274i $$-0.530957\pi$$
−0.0971016 + 0.995274i $$0.530957\pi$$
$$282$$ −1.68614 + 7.17687i −0.100408 + 0.427376i
$$283$$ 6.55842 + 3.78651i 0.389858 + 0.225084i 0.682098 0.731260i $$-0.261068\pi$$
−0.292241 + 0.956345i $$0.594401\pi$$
$$284$$ 0.558422 0.967215i 0.0331362 0.0573937i
$$285$$ −10.7446 10.0974i −0.636453 0.598115i
$$286$$ 3.43070 + 3.56529i 0.202862 + 0.210820i
$$287$$ −10.6277 + 12.2718i −0.627334 + 0.724383i
$$288$$ −2.68614 1.33591i −0.158282 0.0787191i
$$289$$ 7.55842 13.0916i 0.444613 0.770092i
$$290$$ 1.00000 + 1.73205i 0.0587220 + 0.101710i
$$291$$ 12.7446 13.5615i 0.747099 0.794986i
$$292$$ −0.372281 0.644810i −0.0217861 0.0377347i
$$293$$ −14.7446 + 8.51278i −0.861387 + 0.497322i −0.864476 0.502673i $$-0.832350\pi$$
0.00308982 + 0.999995i $$0.499016\pi$$
$$294$$ 9.93070 + 6.95565i 0.579170 + 0.405662i
$$295$$ 11.9307 + 20.6646i 0.694632 + 1.20314i
$$296$$ −7.11684 4.10891i −0.413658 0.238826i
$$297$$ −6.68614 + 2.47805i −0.387969 + 0.143791i
$$298$$ −6.00000 −0.347571
$$299$$ 3.25544 + 0.939764i 0.188267 + 0.0543479i
$$300$$ 1.62772 1.73205i 0.0939764 0.100000i
$$301$$ 10.0000 3.46410i 0.576390 0.199667i
$$302$$ −2.61684 1.51084i −0.150582 0.0869388i
$$303$$ 5.48913 + 1.28962i 0.315342 + 0.0740868i
$$304$$ −3.37228 −0.193414
$$305$$ −6.55842 11.3595i −0.375534 0.650444i
$$306$$ 3.43070 2.27567i 0.196120 0.130091i
$$307$$ −13.2337 −0.755286 −0.377643 0.925951i $$-0.623265\pi$$
−0.377643 + 0.925951i $$0.623265\pi$$
$$308$$ 0.686141 3.56529i 0.0390965 0.203151i
$$309$$ −19.3723 + 5.84096i −1.10205 + 0.332281i
$$310$$ 10.3723 + 5.98844i 0.589106 + 0.340121i
$$311$$ −4.62772 −0.262414 −0.131207 0.991355i $$-0.541885\pi$$
−0.131207 + 0.991355i $$0.541885\pi$$
$$312$$ 3.18614 + 5.37108i 0.180380 + 0.304078i
$$313$$ 13.8564i 0.783210i −0.920133 0.391605i $$-0.871920\pi$$
0.920133 0.391605i $$-0.128080\pi$$
$$314$$ 0 0
$$315$$ 18.4891 7.72049i 1.04174 0.435000i
$$316$$ −7.68614 13.3128i −0.432379 0.748903i
$$317$$ −26.7446 −1.50212 −0.751062 0.660232i $$-0.770458\pi$$
−0.751062 + 0.660232i $$0.770458\pi$$
$$318$$ −5.68614 + 24.2024i −0.318863 + 1.35720i
$$319$$ 0.941578 0.543620i 0.0527182 0.0304369i
$$320$$ 2.52434i 0.141115i
$$321$$ −1.68614 + 7.17687i −0.0941112 + 0.400574i
$$322$$ −0.813859 2.34941i −0.0453546 0.130927i
$$323$$ 2.31386 4.00772i 0.128747 0.222996i
$$324$$ −8.93070 + 1.11469i −0.496150 + 0.0619273i
$$325$$ −4.80298 + 1.18843i −0.266422 + 0.0659223i
$$326$$ 10.3923i 0.575577i
$$327$$ −33.0000 + 9.94987i −1.82490 + 0.550229i
$$328$$ 5.31386 + 3.06796i 0.293409 + 0.169400i
$$329$$ −11.0584 2.12819i −0.609671 0.117331i
$$330$$ −4.37228 4.10891i −0.240686 0.226188i
$$331$$ −19.1168 + 11.0371i −1.05076 + 0.606655i −0.922861 0.385133i $$-0.874156\pi$$
−0.127896 + 0.991788i $$0.540822\pi$$
$$332$$ 4.37228 2.52434i 0.239960 0.138541i
$$333$$ −24.6060 + 1.52967i −1.34840 + 0.0838255i
$$334$$ 5.74456 3.31662i 0.314328 0.181478i
$$335$$ −10.3723 + 17.9653i −0.566698 + 0.981550i
$$336$$ 1.87228 4.18265i 0.102141 0.228182i
$$337$$ 29.6060 1.61274 0.806370 0.591411i $$-0.201429\pi$$
0.806370 + 0.591411i $$0.201429\pi$$
$$338$$ 0.500000 12.9904i 0.0271964 0.706584i
$$339$$ −21.4891 20.1947i −1.16713 1.09683i
$$340$$ 3.00000 + 1.73205i 0.162698 + 0.0939336i
$$341$$ 3.25544 5.63858i 0.176292 0.305346i
$$342$$ −8.43070 + 5.59230i −0.455880 + 0.302397i
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ −2.00000 3.46410i −0.107833 0.186772i
$$345$$ −4.00000 0.939764i −0.215353 0.0505952i
$$346$$ 19.1168 1.02773
$$347$$ −13.5475 + 7.82168i −0.727270 + 0.419890i −0.817423 0.576038i $$-0.804598\pi$$
0.0901523 + 0.995928i $$0.471265\pi$$
$$348$$ 1.31386 0.396143i 0.0704303 0.0212355i
$$349$$ −1.44158 + 2.49689i −0.0771659 + 0.133655i −0.902026 0.431682i $$-0.857920\pi$$
0.824860 + 0.565337i $$0.191254\pi$$
$$350$$ 2.74456 + 2.37686i 0.146703 + 0.127049i
$$351$$ 16.8723 + 8.14409i 0.900576 + 0.434699i
$$352$$ −1.37228 −0.0731428
$$353$$ 19.6277 + 11.3321i 1.04468 + 0.603145i 0.921155 0.389197i $$-0.127247\pi$$
0.123523 + 0.992342i $$0.460581\pi$$
$$354$$ 15.6753 4.72627i 0.833131 0.251198i
$$355$$ 2.44158 1.40965i 0.129586 0.0748162i
$$356$$ 12.4742i 0.661132i
$$357$$ 3.68614 + 5.09496i 0.195091 + 0.269654i
$$358$$ 1.37228 0.792287i 0.0725273 0.0418737i
$$359$$ 22.3723 1.18076 0.590382 0.807124i $$-0.298977\pi$$
0.590382 + 0.807124i $$0.298977\pi$$
$$360$$ −4.18614 6.31084i −0.220629 0.332611i
$$361$$ 3.81386 6.60580i 0.200729 0.347674i
$$362$$ 10.5000 + 6.06218i 0.551868 + 0.318621i
$$363$$ 10.8139 11.5070i 0.567580 0.603961i
$$364$$ −8.00000 + 5.19615i −0.419314 + 0.272352i
$$365$$ 1.87953i 0.0983790i
$$366$$ −8.61684 + 2.59808i −0.450410 + 0.135804i
$$367$$ −8.23369 4.75372i −0.429795 0.248142i 0.269464 0.963010i $$-0.413153\pi$$
−0.699259 + 0.714868i $$0.746487\pi$$
$$368$$ −0.813859 + 0.469882i −0.0424254 + 0.0244943i
$$369$$ 18.3723 1.14214i 0.956423 0.0594576i
$$370$$ −10.3723 17.9653i −0.539229 0.933972i
$$371$$ −37.2921 7.17687i −1.93611 0.372605i
$$372$$ 5.62772 5.98844i 0.291784 0.310486i
$$373$$ −4.00000 6.92820i −0.207112 0.358729i 0.743691 0.668523i $$-0.233073\pi$$
−0.950804 + 0.309794i $$0.899740\pi$$
$$374$$ 0.941578 1.63086i 0.0486878 0.0843298i
$$375$$ −15.1861 + 4.57879i −0.784209 + 0.236448i
$$376$$ 4.25639i 0.219506i
$$377$$ −2.74456 0.792287i −0.141352 0.0408049i
$$378$$ −2.25544 13.5615i −0.116007 0.697526i
$$379$$ −22.1168 12.7692i −1.13607 0.655908i −0.190613 0.981665i $$-0.561047\pi$$
−0.945453 + 0.325757i $$0.894381\pi$$
$$380$$ −7.37228 4.25639i −0.378190 0.218348i
$$381$$ 25.4891 + 5.98844i 1.30585 + 0.306797i
$$382$$ 18.9051i 0.967268i
$$383$$ 27.4307 15.8371i 1.40164 0.809239i 0.407082 0.913392i $$-0.366546\pi$$
0.994561 + 0.104152i $$0.0332130\pi$$
$$384$$ −1.68614 0.396143i −0.0860455 0.0202156i
$$385$$ 6.00000 6.92820i 0.305788 0.353094i
$$386$$ −5.61684 + 3.24289i −0.285890 + 0.165059i
$$387$$ −10.7446 5.34363i −0.546177 0.271632i
$$388$$ 5.37228 9.30506i 0.272736 0.472393i
$$389$$ 22.6641i 1.14912i 0.818463 + 0.574559i $$0.194826\pi$$
−0.818463 + 0.574559i $$0.805174\pi$$
$$390$$ 0.186141 + 15.7634i 0.00942560 + 0.798210i
$$391$$ 1.28962i 0.0652189i
$$392$$ 6.50000 + 2.59808i 0.328300 + 0.131223i
$$393$$ 9.30298 + 30.8545i 0.469273 + 1.55640i
$$394$$ −7.80298 13.5152i −0.393109 0.680884i
$$395$$ 38.8048i 1.95248i
$$396$$ −3.43070 + 2.27567i −0.172399 + 0.114357i
$$397$$ 6.87228 + 11.9031i 0.344910 + 0.597401i 0.985337 0.170617i $$-0.0545761\pi$$
−0.640427 + 0.768019i $$0.721243\pi$$
$$398$$ 3.46410i 0.173640i
$$399$$ −9.05842 12.5205i −0.453488 0.626809i
$$400$$ 0.686141 1.18843i 0.0343070 0.0594215i
$$401$$ −5.74456 + 9.94987i −0.286870 + 0.496873i −0.973061 0.230548i $$-0.925948\pi$$
0.686191 + 0.727421i $$0.259281\pi$$
$$402$$ 10.3723 + 9.74749i 0.517322 + 0.486161i
$$403$$ −16.6060 + 4.10891i −0.827202 + 0.204679i
$$404$$ 3.25544 0.161964
$$405$$ −20.9307 8.83518i −1.04006 0.439024i
$$406$$ 0.686141 + 1.98072i 0.0340526 + 0.0983014i
$$407$$ −9.76631 + 5.63858i −0.484098 + 0.279494i
$$408$$ 1.62772 1.73205i 0.0805841 0.0857493i
$$409$$ 0.744563 + 1.28962i 0.0368163 + 0.0637676i 0.883846 0.467777i $$-0.154945\pi$$
−0.847030 + 0.531545i $$0.821612\pi$$
$$410$$ 7.74456 + 13.4140i 0.382477 + 0.662469i
$$411$$ 1.93070 2.05446i 0.0952346 0.101339i
$$412$$ −10.1168 + 5.84096i −0.498421 + 0.287764i
$$413$$ 8.18614 + 23.6314i 0.402814 + 1.16282i
$$414$$ −1.25544 + 2.52434i −0.0617014 + 0.124064i
$$415$$ 12.7446 0.625606
$$416$$ 2.50000 + 2.59808i 0.122573 + 0.127381i
$$417$$ −26.4891 24.8935i −1.29718 1.21904i
$$418$$ −2.31386 + 4.00772i −0.113175 + 0.196024i
$$419$$ 8.74456 15.1460i 0.427200 0.739932i −0.569423 0.822045i $$-0.692833\pi$$
0.996623 + 0.0821127i $$0.0261667\pi$$
$$420$$ 9.37228 6.78073i 0.457321 0.330866i
$$421$$ 12.9715i 0.632194i −0.948727 0.316097i $$-0.897627\pi$$
0.948727 0.316097i $$-0.102373\pi$$
$$422$$ 11.3723 + 19.6974i 0.553594 + 0.958853i
$$423$$ 7.05842 + 10.6410i 0.343192 + 0.517382i
$$424$$ 14.3537i 0.697079i
$$425$$ 0.941578 + 1.63086i 0.0456732 + 0.0791084i
$$426$$ −0.558422 1.85208i −0.0270556 0.0897334i
$$427$$ −4.50000 12.9904i −0.217770 0.628649i
$$428$$ 4.25639i 0.205740i
$$429$$ 8.56930 0.101190i 0.413730 0.00488549i
$$430$$ 10.0974i 0.486938i
$$431$$ 9.81386 16.9981i 0.472717 0.818770i −0.526795 0.849992i $$-0.676607\pi$$
0.999512 + 0.0312223i $$0.00993997\pi$$
$$432$$ −4.87228 + 1.80579i −0.234418 + 0.0868811i
$$433$$ 30.3505 17.5229i 1.45855 0.842096i 0.459613 0.888119i $$-0.347988\pi$$
0.998940 + 0.0460230i $$0.0146548\pi$$
$$434$$ 9.48913 + 8.21782i 0.455493 + 0.394468i
$$435$$ 3.37228 + 0.792287i 0.161689 + 0.0379873i
$$436$$ −17.2337 + 9.94987i −0.825344 + 0.476513i
$$437$$ 3.16915i 0.151601i
$$438$$ −1.25544 0.294954i −0.0599871 0.0140934i
$$439$$ 30.3505 + 17.5229i 1.44855 + 0.836322i 0.998395 0.0566279i $$-0.0180349\pi$$
0.450157 + 0.892950i $$0.351368\pi$$
$$440$$ −3.00000 1.73205i −0.143019 0.0825723i
$$441$$ 20.5584 4.28384i 0.978972 0.203992i
$$442$$ −4.80298 + 1.18843i −0.228455 + 0.0565279i
$$443$$ 11.1846i 0.531396i 0.964056 + 0.265698i $$0.0856024\pi$$
−0.964056 + 0.265698i $$0.914398\pi$$
$$444$$ −13.6277 + 4.10891i −0.646743 + 0.195000i
$$445$$ 15.7446 27.2704i 0.746364 1.29274i
$$446$$ 3.11684 + 5.39853i 0.147587 + 0.255628i
$$447$$ −7.11684 + 7.57301i −0.336615 + 0.358191i
$$448$$ 0.500000 2.59808i 0.0236228 0.122748i
$$449$$ −0.302985 0.524785i −0.0142987 0.0247661i 0.858788 0.512332i $$-0.171218\pi$$
−0.873086 + 0.487566i $$0.837885\pi$$
$$450$$ −0.255437 4.10891i −0.0120414 0.193696i
$$451$$ 7.29211 4.21010i 0.343372 0.198246i
$$452$$ −14.7446 8.51278i −0.693526 0.400407i
$$453$$ −5.01087 + 1.51084i −0.235431 + 0.0709852i
$$454$$ 3.81396i 0.178998i
$$455$$ −24.0475 + 1.26217i −1.12737 + 0.0591714i
$$456$$ −4.00000 + 4.25639i −0.187317 + 0.199324i
$$457$$ −16.6753 9.62747i −0.780036 0.450354i 0.0564070 0.998408i $$-0.482036\pi$$
−0.836443 + 0.548054i $$0.815369\pi$$
$$458$$ −6.05842 + 10.4935i −0.283091 + 0.490329i
$$459$$ 1.19702 7.02939i 0.0558719 0.328104i
$$460$$ −2.37228 −0.110608
$$461$$ −13.0693 + 7.54556i −0.608698 + 0.351432i −0.772456 0.635069i $$-0.780972\pi$$
0.163758 + 0.986501i $$0.447638\pi$$
$$462$$ −3.68614 5.09496i −0.171495 0.237039i
$$463$$ 30.7345i 1.42835i −0.699966 0.714176i $$-0.746801\pi$$
0.699966 0.714176i $$-0.253199\pi$$
$$464$$ 0.686141 0.396143i 0.0318533 0.0183905i
$$465$$ 19.8614 5.98844i 0.921051 0.277707i
$$466$$ 24.3030 + 14.0313i 1.12581 + 0.649989i
$$467$$ 19.6277 0.908263 0.454131 0.890935i $$-0.349950\pi$$
0.454131 + 0.890935i $$0.349950\pi$$
$$468$$ 10.5584 + 2.34941i 0.488063 + 0.108601i
$$469$$ −14.2337 + 16.4356i −0.657251 + 0.758928i
$$470$$ −5.37228 + 9.30506i −0.247805 + 0.429211i
$$471$$ 0 0
$$472$$ 8.18614 4.72627i 0.376798 0.217544i
$$473$$ −5.48913 −0.252390
$$474$$ −25.9198 6.08963i −1.19054 0.279706i
$$475$$ −2.31386 4.00772i −0.106167 0.183887i
$$476$$ 2.74456 + 2.37686i 0.125797 + 0.108943i
$$477$$ 23.8030 + 35.8843i 1.08986 + 1.64303i
$$478$$ 12.3030 21.3094i 0.562725 0.974669i
$$479$$ 22.8030 + 13.1653i 1.04189 + 0.601538i 0.920369 0.391050i $$-0.127888\pi$$
0.121526 + 0.992588i $$0.461221\pi$$
$$480$$ −3.18614 2.99422i −0.145427 0.136667i
$$481$$ 28.4674 + 8.21782i 1.29800 + 0.374701i
$$482$$ −1.25544 −0.0571836
$$483$$ −3.93070 1.75950i −0.178853 0.0800601i
$$484$$ 4.55842 7.89542i 0.207201 0.358883i
$$485$$ 23.4891 13.5615i 1.06659 0.615794i
$$486$$ −9.18614 + 12.5942i −0.416692 + 0.571286i
$$487$$ −9.38316 + 5.41737i −0.425191 + 0.245484i −0.697296 0.716783i $$-0.745614\pi$$
0.272105 + 0.962268i $$0.412280\pi$$
$$488$$ −4.50000 + 2.59808i −0.203705 + 0.117609i
$$489$$ 13.1168 + 12.3267i 0.593164 + 0.557434i
$$490$$ 10.9307 + 13.8839i 0.493799 + 0.627209i
$$491$$ 33.6060 + 19.4024i 1.51662 + 0.875619i 0.999810 + 0.0195166i $$0.00621272\pi$$
0.516807 + 0.856102i $$0.327121\pi$$
$$492$$ 10.1753 3.06796i 0.458736 0.138314i
$$493$$ 1.08724i 0.0489669i
$$494$$ 11.8030 2.92048i 0.531041 0.131399i
$$495$$ −10.3723 + 0.644810i −0.466199 + 0.0289821i
$$496$$ 2.37228 4.10891i 0.106519 0.184496i
$$497$$ 2.79211 0.967215i 0.125243 0.0433855i
$$498$$ 2.00000 8.51278i 0.0896221 0.381467i
$$499$$ 23.3639i 1.04591i −0.852360 0.522955i $$-0.824830\pi$$
0.852360 0.522955i $$-0.175170\pi$$
$$500$$ −7.93070 + 4.57879i −0.354672 + 0.204770i
$$501$$ 2.62772 11.1846i 0.117398 0.499691i
$$502$$ −1.11684 −0.0498472
$$503$$ 11.4891 + 19.8997i 0.512275 + 0.887286i 0.999899 + 0.0142322i $$0.00453039\pi$$
−0.487624 + 0.873054i $$0.662136\pi$$
$$504$$ −3.05842 7.32435i −0.136233 0.326252i
$$505$$ 7.11684 + 4.10891i 0.316695 + 0.182844i
$$506$$ 1.28962i 0.0573306i
$$507$$ −15.8030 16.0395i −0.701835 0.712339i
$$508$$ 15.1168 0.670701
$$509$$ 23.1861 + 13.3865i 1.02771 + 0.593347i 0.916327 0.400431i $$-0.131139\pi$$
0.111381 + 0.993778i $$0.464473\pi$$
$$510$$ 5.74456 1.73205i 0.254374 0.0766965i
$$511$$ 0.372281 1.93443i 0.0164688 0.0855742i
$$512$$ −1.00000 −0.0441942
$$513$$ −2.94158 + 17.2742i −0.129874 + 0.762675i
$$514$$ −11.0584 19.1537i −0.487766 0.844836i
$$515$$ −29.4891 −1.29945
$$516$$ −6.74456 1.58457i −0.296913 0.0697570i
$$517$$ 5.05842 + 2.92048i 0.222469 + 0.128443i
$$518$$ −7.11684 20.5446i −0.312696 0.902676i
$$519$$ 22.6753 24.1287i 0.995334 1.05913i
$$520$$ 2.18614 + 8.83518i 0.0958686 + 0.387448i
$$521$$ 16.1168 0.706092 0.353046 0.935606i $$-0.385146\pi$$
0.353046 + 0.935606i $$0.385146\pi$$
$$522$$ 1.05842 2.12819i 0.0463259 0.0931485i
$$523$$ −7.50000 4.33013i −0.327952 0.189343i 0.326979 0.945031i $$-0.393969\pi$$
−0.654932 + 0.755688i $$0.727303\pi$$
$$524$$ 9.30298 + 16.1132i 0.406403 + 0.703910i
$$525$$ 6.25544 0.644810i 0.273010 0.0281418i
$$526$$ 12.0475 6.95565i 0.525298 0.303281i
$$527$$ 3.25544 + 5.63858i 0.141809 + 0.245621i
$$528$$ −1.62772 + 1.73205i −0.0708374 + 0.0753778i
$$529$$ −11.0584 19.1537i −0.480801 0.832772i
$$530$$ −18.1168 + 31.3793i −0.786945 + 1.36303i
$$531$$ 12.6277 25.3909i 0.547996 1.10187i
$$532$$ −6.74456 5.84096i −0.292414 0.253238i
$$533$$ −21.2554 6.13592i −0.920675 0.265776i
$$534$$ −15.7446 14.7962i −0.681334 0.640293i
$$535$$ −5.37228 + 9.30506i −0.232264 + 0.402293i
$$536$$ 7.11684 + 4.10891i 0.307401 + 0.177478i
$$537$$ 0.627719 2.67181i 0.0270881 0.115297i
$$538$$ 27.8614 1.20119
$$539$$ 7.54755 5.94215i 0.325096 0.255947i
$$540$$ −12.9307 2.20193i −0.556449 0.0947561i
$$541$$ 18.6101i 0.800112i −0.916491 0.400056i $$-0.868991\pi$$
0.916491 0.400056i $$-0.131009\pi$$
$$542$$ 2.00000 + 3.46410i 0.0859074 + 0.148796i
$$543$$ 20.1060 6.06218i 0.862830 0.260153i
$$544$$ 0.686141 1.18843i 0.0294180 0.0509535i
$$545$$ −50.2337 −2.15177
$$546$$ −2.93070 + 16.2607i −0.125423 + 0.695895i
$$547$$ 31.4891 1.34638 0.673189 0.739471i $$-0.264924\pi$$
0.673189 + 0.739471i $$0.264924\pi$$
$$548$$ 0.813859 1.40965i 0.0347663 0.0602171i
$$549$$ −6.94158 + 13.9576i −0.296259 + 0.595696i
$$550$$ −0.941578 1.63086i −0.0401490 0.0695401i
$$551$$ 2.67181i 0.113823i
$$552$$ −0.372281 + 1.58457i −0.0158453 + 0.0674439i
$$553$$ 7.68614 39.9384i 0.326848 1.69835i
$$554$$ 9.48913 0.403154
$$555$$ −34.9783 8.21782i −1.48474 0.348827i
$$556$$ −18.1753 10.4935i −0.770803 0.445023i
$$557$$ −7.80298 + 13.5152i −0.330623 + 0.572656i −0.982634 0.185553i $$-0.940592\pi$$
0.652011 + 0.758209i $$0.273926\pi$$
$$558$$ −0.883156 14.2063i −0.0373870 0.601399i
$$559$$ 10.0000 + 10.3923i 0.422955 + 0.439548i
$$560$$ 4.37228 5.04868i 0.184763 0.213345i
$$561$$ −0.941578 3.12286i −0.0397535 0.131847i
$$562$$ −1.62772 + 2.81929i −0.0686612 + 0.118925i
$$563$$ −18.0000 31.1769i −0.758610 1.31395i −0.943560 0.331202i $$-0.892546\pi$$
0.184950 0.982748i $$-0.440788\pi$$
$$564$$ 5.37228 + 5.04868i 0.226214 + 0.212588i
$$565$$ −21.4891 37.2203i −0.904054 1.56587i
$$566$$ 6.55842 3.78651i 0.275671 0.159159i
$$567$$ −19.7921 13.2390i −0.831190 0.555988i
$$568$$ −0.558422 0.967215i −0.0234309 0.0405835i
$$569$$ 19.1644 + 11.0646i 0.803413 + 0.463851i 0.844663 0.535298i $$-0.179801\pi$$
−0.0412501 + 0.999149i $$0.513134\pi$$
$$570$$ −14.1168 + 4.25639i −0.591290 + 0.178281i
$$571$$ 13.4891 0.564502 0.282251 0.959341i $$-0.408919\pi$$
0.282251 + 0.959341i $$0.408919\pi$$
$$572$$ 4.80298 1.18843i 0.200823 0.0496908i
$$573$$ 23.8614 + 22.4241i 0.996825 + 0.936780i
$$574$$ 5.31386 + 15.3398i 0.221796 + 0.640270i
$$575$$ −1.11684 0.644810i −0.0465756 0.0268904i
$$576$$ −2.50000 + 1.65831i −0.104167 + 0.0690963i
$$577$$ −40.2337 −1.67495 −0.837475 0.546475i $$-0.815969\pi$$
−0.837475 + 0.546475i $$0.815969\pi$$
$$578$$ −7.55842 13.0916i −0.314389 0.544538i
$$579$$ −2.56930 + 10.9359i −0.106776 + 0.454482i
$$580$$ 2.00000 0.0830455
$$581$$ 13.1168 + 2.52434i 0.544178 + 0.104727i
$$582$$ −5.37228 17.8178i −0.222688 0.738573i
$$583$$ 17.0584 + 9.84868i 0.706488 + 0.407891i
$$584$$ −0.744563 −0.0308102
$$585$$ 20.1168 + 18.4627i 0.831729 + 0.763337i
$$586$$ 17.0256i 0.703319i
$$587$$ 5.95245 + 3.43665i 0.245684 + 0.141846i 0.617786 0.786346i $$-0.288030\pi$$
−0.372102 + 0.928192i $$0.621363\pi$$
$$588$$ 10.9891 5.12241i 0.453184 0.211245i
$$589$$ −8.00000 13.8564i −0.329634 0.570943i
$$590$$ 23.8614 0.982359
$$591$$ −26.3139 6.18220i −1.08241 0.254302i
$$592$$ −7.11684 + 4.10891i −0.292500 + 0.168875i
$$593$$ 26.3306i 1.08127i −0.841258 0.540634i $$-0.818184\pi$$
0.841258 0.540634i $$-0.181816\pi$$
$$594$$ −1.19702 + 7.02939i −0.0491141 + 0.288419i
$$595$$ 3.00000 + 8.66025i 0.122988 + 0.355036i
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 4.37228 + 4.10891i 0.178946 + 0.168167i
$$598$$ 2.44158 2.34941i 0.0998435 0.0960745i
$$599$$ 13.9113i 0.568401i −0.958765 0.284200i $$-0.908272\pi$$
0.958765 0.284200i $$-0.0917281\pi$$
$$600$$ −0.686141 2.27567i −0.0280116 0.0929039i
$$601$$ 19.8832 + 11.4795i 0.811051 + 0.468260i 0.847321 0.531082i $$-0.178214\pi$$
−0.0362698 + 0.999342i $$0.511548\pi$$
$$602$$ 2.00000 10.3923i 0.0815139 0.423559i
$$603$$ 24.6060 1.52967i 1.00203 0.0622930i
$$604$$ −2.61684 + 1.51084i −0.106478 + 0.0614750i
$$605$$ 19.9307 11.5070i 0.810298 0.467826i
$$606$$ 3.86141 4.10891i 0.156859 0.166913i
$$607$$ −21.3505 + 12.3267i −0.866591 + 0.500327i −0.866214 0.499673i $$-0.833453\pi$$
−0.000377344 1.00000i $$0.500120\pi$$
$$608$$ −1.68614 + 2.92048i −0.0683820 + 0.118441i
$$609$$ 3.31386 + 1.48338i 0.134284 + 0.0601098i
$$610$$ −13.1168 −0.531085
$$611$$ −3.68614 14.8974i −0.149125 0.602683i
$$612$$ −0.255437 4.10891i −0.0103254 0.166093i
$$613$$ 26.2337 + 15.1460i 1.05957 + 0.611742i 0.925313 0.379204i $$-0.123802\pi$$
0.134256 + 0.990947i $$0.457136\pi$$
$$614$$ −6.61684 + 11.4607i −0.267034 + 0.462517i
$$615$$ 26.1168 + 6.13592i 1.05313 + 0.247424i
$$616$$ −2.74456 2.37686i −0.110582 0.0957665i
$$617$$ −3.30298 5.72094i −0.132973 0.230316i 0.791848 0.610718i $$-0.209119\pi$$
−0.924821 + 0.380402i $$0.875786\pi$$
$$618$$ −4.62772 + 19.6974i −0.186154 + 0.792344i
$$619$$ 35.4674 1.42555 0.712777 0.701391i $$-0.247437\pi$$
0.712777 + 0.701391i $$0.247437\pi$$
$$620$$ 10.3723 5.98844i 0.416561 0.240502i
$$621$$ 1.69702 + 4.57879i 0.0680989 + 0.183741i
$$622$$ −2.31386 + 4.00772i −0.0927773 + 0.160695i
$$623$$ 21.6060 24.9484i 0.865625 0.999538i
$$624$$ 6.24456 0.0737384i 0.249983 0.00295190i
$$625$$ −29.9783 −1.19913
$$626$$ −12.0000 6.92820i −0.479616 0.276907i
$$627$$ 2.31386 + 7.67420i 0.0924066 + 0.306478i
$$628$$ 0 0
$$629$$ 11.2772i 0.449650i
$$630$$ 2.55842 19.8723i 0.101930 0.791731i
$$631$$ −28.5000 + 16.4545i −1.13457 + 0.655043i −0.945080 0.326841i $$-0.894016\pi$$
−0.189488 + 0.981883i $$0.560683\pi$$
$$632$$ −15.3723 −0.611477
$$633$$ 38.3505 + 9.01011i 1.52430 + 0.358120i
$$634$$ −13.3723 + 23.1615i −0.531081 + 0.919860i
$$635$$ 33.0475 + 19.0800i 1.31145 + 0.757167i
$$636$$ 18.1168 + 17.0256i 0.718380 + 0.675107i
$$637$$ −25.0000 3.46410i −0.990536 0.137253i
$$638$$ 1.08724i 0.0430443i
$$639$$ −3.00000 1.49200i −0.118678 0.0590226i
$$640$$ −2.18614 1.26217i −0.0864148 0.0498916i
$$641$$ −25.1644 + 14.5287i −0.993934 + 0.573848i −0.906448 0.422318i $$-0.861217\pi$$
−0.0874859 + 0.996166i $$0.527883\pi$$
$$642$$ 5.37228 + 5.04868i 0.212027 + 0.199255i
$$643$$ 15.6168 + 27.0492i 0.615868 + 1.06672i 0.990232 + 0.139433i $$0.0445280\pi$$
−0.374363 + 0.927282i $$0.622139\pi$$
$$644$$ −2.44158 0.469882i −0.0962117 0.0185159i
$$645$$ −12.7446 11.9769i −0.501817 0.471589i
$$646$$ −2.31386 4.00772i −0.0910376 0.157682i
$$647$$ −5.56930 + 9.64630i −0.218952 + 0.379235i −0.954488 0.298250i $$-0.903597\pi$$
0.735536 + 0.677486i $$0.236930\pi$$
$$648$$ −3.50000 + 8.29156i −0.137493 + 0.325723i
$$649$$ 12.9715i 0.509178i
$$650$$ −1.37228 + 4.75372i −0.0538253 + 0.186456i
$$651$$ 21.6277 2.22938i 0.847657 0.0873765i
$$652$$ 9.00000 + 5.19615i 0.352467 + 0.203497i
$$653$$ 22.5475 + 13.0178i 0.882354 + 0.509427i 0.871434 0.490513i $$-0.163191\pi$$
0.0109200 + 0.999940i $$0.496524\pi$$
$$654$$ −7.88316 + 33.5538i −0.308256 + 1.31206i
$$655$$ 46.9678i 1.83518i
$$656$$ 5.31386 3.06796i 0.207471 0.119784i
$$657$$ −1.86141 + 1.23472i −0.0726204 + 0.0481709i
$$658$$ −7.37228 + 8.51278i −0.287401 + 0.331863i
$$659$$ −11.6644 + 6.73444i −0.454380 + 0.262337i −0.709678 0.704526i $$-0.751160\pi$$
0.255298 + 0.966862i $$0.417826\pi$$
$$660$$ −5.74456 + 1.73205i −0.223607 + 0.0674200i
$$661$$ −24.9307 + 43.1812i −0.969692 + 1.67956i −0.273249 + 0.961943i $$0.588098\pi$$
−0.696443 + 0.717613i $$0.745235\pi$$
$$662$$ 22.0742i 0.857939i
$$663$$ −4.19702 + 7.47182i −0.162999 + 0.290182i
$$664$$ 5.04868i 0.195927i
$$665$$ −7.37228 21.2819i −0.285885 0.825278i
$$666$$ −10.9783 + 22.0742i −0.425399 + 0.855359i
$$667$$ −0.372281 0.644810i −0.0144148 0.0249671i
$$668$$ 6.63325i 0.256648i
$$669$$ 10.5109 + 2.46943i 0.406374 + 0.0954739i
$$670$$ 10.3723 + 17.9653i 0.400716 + 0.694061i
$$671$$ 7.13058i 0.275273i
$$672$$ −2.68614 3.71277i −0.103620 0.143223i
$$673$$ 1.31386 2.27567i 0.0506456 0.0877207i −0.839591 0.543219i $$-0.817205\pi$$
0.890237 + 0.455498i $$0.150539\pi$$
$$674$$ 14.8030 25.6395i 0.570190 0.987597i
$$675$$ −5.48913 4.55134i −0.211277 0.175181i
$$676$$ −11.0000 6.92820i −0.423077 0.266469i
$$677$$ 4.37228 0.168040 0.0840202 0.996464i $$-0.473224\pi$$
0.0840202 + 0.996464i $$0.473224\pi$$
$$678$$ −28.2337 + 8.51278i −1.08431 + 0.326931i
$$679$$ 26.8614 9.30506i 1.03085 0.357096i
$$680$$ 3.00000 1.73205i 0.115045 0.0664211i
$$681$$ 4.81386 + 4.52389i 0.184467 + 0.173356i
$$682$$ −3.25544 5.63858i −0.124657 0.215912i
$$683$$ 21.8614 + 37.8651i 0.836503 + 1.44887i 0.892800 + 0.450452i $$0.148737\pi$$
−0.0562969 + 0.998414i $$0.517929\pi$$
$$684$$ 0.627719 + 10.0974i 0.0240014 + 0.386082i
$$685$$ 3.55842 2.05446i 0.135960 0.0784967i
$$686$$ 8.50000 + 16.4545i 0.324532 + 0.628235i
$$687$$ 6.05842 + 20.0935i 0.231143 + 0.766615i
$$688$$ −4.00000 −0.152499
$$689$$ −12.4307 50.2381i −0.473572 1.91392i
$$690$$ −2.81386 + 2.99422i −0.107122 + 0.113988i
$$691$$ 19.5584 33.8762i 0.744037 1.28871i −0.206606 0.978424i $$-0.566242\pi$$
0.950643 0.310286i $$-0.100425\pi$$
$$692$$ 9.55842 16.5557i 0.363357 0.629352i
$$693$$ −10.8030 1.39081i −0.410371 0.0528325i
$$694$$ 15.6434i 0.593814i
$$695$$ −26.4891 45.8805i −1.00479 1.74035i
$$696$$ 0.313859 1.33591i 0.0118968 0.0506374i
$$697$$ 8.42020i 0.318938i
$$698$$ 1.44158 + 2.49689i 0.0545645 + 0.0945085i
$$699$$ 46.5367 14.0313i 1.76018 0.530714i
$$700$$ 3.43070 1.18843i 0.129668 0.0449185i
$$701$$ 22.1668i 0.837229i −0.908164 0.418614i $$-0.862516\pi$$
0.908164 0.418614i $$-0.137484\pi$$
$$702$$ 15.4891 10.5398i 0.584599 0.397798i
$$703$$ 27.7128i 1.04521i
$$704$$ −0.686141 + 1.18843i −0.0258599 + 0.0447907i
$$705$$ 5.37228 + 17.8178i 0.202332 + 0.671059i
$$706$$ 19.6277 11.3321i 0.738699 0.426488i
$$707$$ 6.51087 + 5.63858i 0.244867 + 0.212061i
$$708$$ 3.74456 15.9383i 0.140729 0.598999i
$$709$$ −40.1168 + 23.1615i −1.50662 + 0.869847i −0.506649 + 0.862152i $$0.669116\pi$$
−0.999970 + 0.00769505i $$0.997551\pi$$
$$710$$ 2.81929i 0.105806i
$$711$$ −38.4307 + 25.4920i −1.44126 + 0.956026i
$$712$$ −10.8030 6.23711i −0.404859 0.233745i
$$713$$ −3.86141 2.22938i −0.144611 0.0834911i
$$714$$ 6.25544 0.644810i 0.234104 0.0241314i
$$715$$ 12.0000 + 3.46410i 0.448775 + 0.129550i
$$716$$ 1.58457i 0.0592183i
$$717$$ −12.3030 40.8044i −0.459463 1.52387i
$$718$$ 11.1861 19.3750i 0.417463 0.723067i
$$719$$ −3.94158 6.82701i −0.146996 0.254605i 0.783120 0.621871i $$-0.213627\pi$$
−0.930116 + 0.367266i $$0.880294\pi$$
$$720$$ −7.55842 + 0.469882i −0.281686 + 0.0175115i
$$721$$ −30.3505 5.84096i −1.13031 0.217529i
$$722$$ −3.81386 6.60580i −0.141937 0.245842i
$$723$$ −1.48913 + 1.58457i −0.0553812 + 0.0589309i
$$724$$ 10.5000 6.06218i 0.390229 0.225299i
$$725$$ 0.941578 + 0.543620i 0.0349693 + 0.0201896i
$$726$$ −4.55842 15.1186i −0.169179 0.561103i
$$727$$ 31.5817i 1.17130i 0.810564 + 0.585650i $$0.199161\pi$$
−0.810564 + 0.585650i $$0.800839\pi$$
$$728$$ 0.500000 + 9.52628i 0.0185312 + 0.353067i
$$729$$ 5.00000 + 26.5330i 0.185185 + 0.982704i
$$730$$ −1.62772 0.939764i −0.0602446 0.0347822i
$$731$$ 2.74456 4.75372i 0.101511 0.175823i
$$732$$ −2.05842 + 8.76144i −0.0760815 + 0.323832i
$$733$$ −32.2554 −1.19138 −0.595691 0.803214i $$-0.703122\pi$$
−0.595691 + 0.803214i $$0.703122\pi$$
$$734$$ −8.23369 + 4.75372i −0.303911 + 0.175463i
$$735$$ 30.4891 + 2.67181i 1.12461 + 0.0985514i
$$736$$ 0.939764i 0.0346402i
$$737$$ 9.76631 5.63858i 0.359747 0.207700i
$$738$$ 8.19702 16.4819i 0.301736 0.606708i
$$739$$ −16.8832 9.74749i −0.621057 0.358567i 0.156223 0.987722i $$-0.450068\pi$$
−0.777280 + 0.629154i $$0.783401\pi$$
$$740$$ −20.7446 −0.762585
$$741$$ 10.3139 18.3615i 0.378889 0.674525i
$$742$$ −24.8614 + 28.7075i −0.912691 + 1.05388i
$$743$$ 7.37228 12.7692i 0.270463 0.468455i −0.698518 0.715593i $$-0.746157\pi$$
0.968980 + 0.247138i $$0.0794900\pi$$
$$744$$ −2.37228 7.86797i −0.0869721 0.288454i
$$745$$ −13.1168 + 7.57301i −0.480564 + 0.277454i
$$746$$ −8.00000 −0.292901
$$747$$ −8.37228 12.6217i −0.306326 0.461803i
$$748$$ −0.941578 1.63086i −0.0344275 0.0596302i
$$749$$ −7.37228 + 8.51278i −0.269377 + 0.311050i
$$750$$ −3.62772 + 15.4410i −0.132466 + 0.563825i
$$751$$ 0.500000 0.866025i 0.0182453 0.0316017i −0.856759 0.515718i $$-0.827525\pi$$
0.875004 + 0.484116i $$0.160859\pi$$
$$752$$ 3.68614 + 2.12819i 0.134420 + 0.0776073i
$$753$$ −1.32473 + 1.40965i −0.0482760 + 0.0513703i
$$754$$ −2.05842 + 1.98072i −0.0749633 + 0.0721335i
$$755$$ −7.62772 −0.277601
$$756$$ −12.8723 4.82746i −0.468160 0.175573i
$$757$$ −19.8614 + 34.4010i −0.721875 + 1.25032i 0.238372 + 0.971174i $$0.423386\pi$$
−0.960247 + 0.279150i $$0.909947\pi$$
$$758$$ −22.1168 + 12.7692i −0.803320 + 0.463797i
$$759$$ 1.62772 + 1.52967i 0.0590824 + 0.0555235i
$$760$$ −7.37228 + 4.25639i −0.267421 + 0.154395i
$$761$$ −14.7446 + 8.51278i −0.534490 + 0.308588i −0.742843 0.669466i $$-0.766523\pi$$
0.208353 + 0.978054i $$0.433190\pi$$
$$762$$ 17.9307 19.0800i 0.649561 0.691196i
$$763$$ −51.7011 9.94987i −1.87170 0.360210i
$$764$$ 16.3723 + 9.45254i 0.592328 + 0.341981i
$$765$$ 4.62772 9.30506i 0.167316 0.336425i
$$766$$ 31.6742i 1.14444i
$$767$$ −24.5584 + 23.6314i −0.886753 + 0.853279i
$$768$$ −1.18614 + 1.26217i −0.0428012 + 0.0455446i
$$769$$ 5.11684 8.86263i 0.184518 0.319595i −0.758896 0.651212i $$-0.774261\pi$$
0.943414 + 0.331617i $$0.107594\pi$$