# Properties

 Label 546.2.s.a.127.1 Level $546$ Weight $2$ Character 546.127 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.s (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: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 127.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.127 Dual form 546.2.s.a.43.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.732051i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.00000 q^{14} +(-0.633975 + 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86603 - 3.23205i) q^{17} -1.00000i q^{18} +(0.866025 + 0.500000i) q^{19} +(-0.633975 - 0.366025i) q^{20} -1.00000i q^{21} +(-0.866025 + 1.50000i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-3.00000 - 2.00000i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(-3.23205 - 5.59808i) q^{29} +(0.366025 - 0.633975i) q^{30} -2.19615i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +3.73205i q^{34} +(0.366025 - 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -1.00000 q^{38} +(2.00000 - 3.00000i) q^{39} +0.732051 q^{40} +(2.59808 - 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.63397 - 2.83013i) q^{43} -1.73205i q^{44} +(0.633975 + 0.366025i) q^{45} +(3.00000 + 1.73205i) q^{46} -2.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-3.86603 + 2.23205i) q^{50} -3.73205 q^{51} +(3.59808 + 0.232051i) q^{52} +7.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.00000i q^{57} +(5.59808 + 3.23205i) q^{58} +(0.803848 + 0.464102i) q^{59} +0.732051i q^{60} +(-2.59808 + 4.50000i) q^{61} +(1.09808 + 1.90192i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.36603 - 1.16987i) q^{65} +1.73205 q^{66} +(7.73205 - 4.46410i) q^{67} +(-1.86603 - 3.23205i) q^{68} +(-1.73205 + 3.00000i) q^{69} +0.732051i q^{70} +(-1.90192 - 1.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} +5.46410i q^{73} +(-3.36603 + 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(0.866025 - 0.500000i) q^{76} +1.73205 q^{77} +(-0.232051 + 3.59808i) q^{78} +2.07180 q^{79} +(-0.633975 + 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -0.196152i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-2.36603 - 1.36603i) q^{85} +3.26795i q^{86} +(-3.23205 + 5.59808i) q^{87} +(0.866025 + 1.50000i) q^{88} +(-9.06218 + 5.23205i) q^{89} -0.732051 q^{90} +(-0.232051 + 3.59808i) q^{91} -3.46410 q^{92} +(-1.90192 + 1.09808i) q^{93} +(1.23205 + 2.13397i) q^{94} +(0.366025 - 0.633975i) q^{95} -1.00000i q^{96} +(13.5622 + 7.83013i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.73205i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 $$4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 4 q^{25} - 12 q^{26} + 4 q^{27} - 6 q^{29} - 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 4 q^{40} + 2 q^{42} + 10 q^{43} + 6 q^{45} + 12 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{50} - 8 q^{51} + 4 q^{52} + 28 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 24 q^{59} - 6 q^{62} - 4 q^{64} + 6 q^{65} + 24 q^{67} - 4 q^{68} - 18 q^{71} - 10 q^{74} - 2 q^{75} + 6 q^{78} + 36 q^{79} - 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{85} - 6 q^{87} - 12 q^{89} + 4 q^{90} + 6 q^{91} - 18 q^{93} - 2 q^{94} - 2 q^{95} + 30 q^{97}+O(q^{100})$$ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^20 + 4 * q^25 - 12 * q^26 + 4 * q^27 - 6 * q^29 - 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 4 * q^38 + 8 * q^39 - 4 * q^40 + 2 * q^42 + 10 * q^43 + 6 * q^45 + 12 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^50 - 8 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 24 * q^59 - 6 * q^62 - 4 * q^64 + 6 * q^65 + 24 * q^67 - 4 * q^68 - 18 * q^71 - 10 * q^74 - 2 * q^75 + 6 * q^78 + 36 * q^79 - 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^85 - 6 * q^87 - 12 * q^89 + 4 * q^90 + 6 * q^91 - 18 * q^93 - 2 * q^94 - 2 * q^95 + 30 * q^97

## Character values

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

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.732051i 0.327383i −0.986512 0.163692i $$-0.947660\pi$$
0.986512 0.163692i $$-0.0523402\pi$$
$$6$$ 0.866025 + 0.500000i 0.353553 + 0.204124i
$$7$$ 0.866025 + 0.500000i 0.327327 + 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0.366025 + 0.633975i 0.115747 + 0.200480i
$$11$$ 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i $$-0.582576\pi$$
0.708787 + 0.705422i $$0.249243\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 1.59808 + 3.23205i 0.443227 + 0.896410i
$$14$$ −1.00000 −0.267261
$$15$$ −0.633975 + 0.366025i −0.163692 + 0.0945074i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.86603 3.23205i 0.452578 0.783887i −0.545968 0.837806i $$-0.683838\pi$$
0.998545 + 0.0539188i $$0.0171712\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 0.866025 + 0.500000i 0.198680 + 0.114708i 0.596040 0.802955i $$-0.296740\pi$$
−0.397360 + 0.917663i $$0.630073\pi$$
$$20$$ −0.633975 0.366025i −0.141761 0.0818458i
$$21$$ 1.00000i 0.218218i
$$22$$ −0.866025 + 1.50000i −0.184637 + 0.319801i
$$23$$ −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i $$-0.284285\pi$$
−0.988152 + 0.153481i $$0.950952\pi$$
$$24$$ 0.866025 0.500000i 0.176777 0.102062i
$$25$$ 4.46410 0.892820
$$26$$ −3.00000 2.00000i −0.588348 0.392232i
$$27$$ 1.00000 0.192450
$$28$$ 0.866025 0.500000i 0.163663 0.0944911i
$$29$$ −3.23205 5.59808i −0.600177 1.03954i −0.992794 0.119835i $$-0.961764\pi$$
0.392617 0.919702i $$-0.371570\pi$$
$$30$$ 0.366025 0.633975i 0.0668268 0.115747i
$$31$$ 2.19615i 0.394441i −0.980359 0.197220i $$-0.936809\pi$$
0.980359 0.197220i $$-0.0631914\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ −1.50000 0.866025i −0.261116 0.150756i
$$34$$ 3.73205i 0.640041i
$$35$$ 0.366025 0.633975i 0.0618696 0.107161i
$$36$$ 0.500000 + 0.866025i 0.0833333 + 0.144338i
$$37$$ 5.83013 3.36603i 0.958467 0.553371i 0.0627661 0.998028i $$-0.480008\pi$$
0.895701 + 0.444657i $$0.146674\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 2.00000 3.00000i 0.320256 0.480384i
$$40$$ 0.732051 0.115747
$$41$$ 2.59808 1.50000i 0.405751 0.234261i −0.283211 0.959058i $$-0.591400\pi$$
0.688963 + 0.724797i $$0.258066\pi$$
$$42$$ 0.500000 + 0.866025i 0.0771517 + 0.133631i
$$43$$ 1.63397 2.83013i 0.249179 0.431590i −0.714119 0.700024i $$-0.753173\pi$$
0.963298 + 0.268434i $$0.0865060\pi$$
$$44$$ 1.73205i 0.261116i
$$45$$ 0.633975 + 0.366025i 0.0945074 + 0.0545638i
$$46$$ 3.00000 + 1.73205i 0.442326 + 0.255377i
$$47$$ 2.46410i 0.359426i −0.983719 0.179713i $$-0.942483\pi$$
0.983719 0.179713i $$-0.0575169\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ 0.500000 + 0.866025i 0.0714286 + 0.123718i
$$50$$ −3.86603 + 2.23205i −0.546739 + 0.315660i
$$51$$ −3.73205 −0.522592
$$52$$ 3.59808 + 0.232051i 0.498963 + 0.0321797i
$$53$$ 7.00000 0.961524 0.480762 0.876851i $$-0.340360\pi$$
0.480762 + 0.876851i $$0.340360\pi$$
$$54$$ −0.866025 + 0.500000i −0.117851 + 0.0680414i
$$55$$ −0.633975 1.09808i −0.0854851 0.148065i
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 1.00000i 0.132453i
$$58$$ 5.59808 + 3.23205i 0.735063 + 0.424389i
$$59$$ 0.803848 + 0.464102i 0.104652 + 0.0604209i 0.551413 0.834233i $$-0.314089\pi$$
−0.446760 + 0.894654i $$0.647422\pi$$
$$60$$ 0.732051i 0.0945074i
$$61$$ −2.59808 + 4.50000i −0.332650 + 0.576166i −0.983030 0.183442i $$-0.941276\pi$$
0.650381 + 0.759608i $$0.274609\pi$$
$$62$$ 1.09808 + 1.90192i 0.139456 + 0.241545i
$$63$$ −0.866025 + 0.500000i −0.109109 + 0.0629941i
$$64$$ −1.00000 −0.125000
$$65$$ 2.36603 1.16987i 0.293469 0.145105i
$$66$$ 1.73205 0.213201
$$67$$ 7.73205 4.46410i 0.944620 0.545377i 0.0532147 0.998583i $$-0.483053\pi$$
0.891406 + 0.453206i $$0.149720\pi$$
$$68$$ −1.86603 3.23205i −0.226289 0.391944i
$$69$$ −1.73205 + 3.00000i −0.208514 + 0.361158i
$$70$$ 0.732051i 0.0874968i
$$71$$ −1.90192 1.09808i −0.225717 0.130318i 0.382878 0.923799i $$-0.374933\pi$$
−0.608595 + 0.793481i $$0.708266\pi$$
$$72$$ −0.866025 0.500000i −0.102062 0.0589256i
$$73$$ 5.46410i 0.639525i 0.947498 + 0.319762i $$0.103603\pi$$
−0.947498 + 0.319762i $$0.896397\pi$$
$$74$$ −3.36603 + 5.83013i −0.391293 + 0.677738i
$$75$$ −2.23205 3.86603i −0.257735 0.446410i
$$76$$ 0.866025 0.500000i 0.0993399 0.0573539i
$$77$$ 1.73205 0.197386
$$78$$ −0.232051 + 3.59808i −0.0262746 + 0.407402i
$$79$$ 2.07180 0.233095 0.116548 0.993185i $$-0.462817\pi$$
0.116548 + 0.993185i $$0.462817\pi$$
$$80$$ −0.633975 + 0.366025i −0.0708805 + 0.0409229i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −1.50000 + 2.59808i −0.165647 + 0.286910i
$$83$$ 0.196152i 0.0215305i −0.999942 0.0107653i $$-0.996573\pi$$
0.999942 0.0107653i $$-0.00342676\pi$$
$$84$$ −0.866025 0.500000i −0.0944911 0.0545545i
$$85$$ −2.36603 1.36603i −0.256631 0.148166i
$$86$$ 3.26795i 0.352392i
$$87$$ −3.23205 + 5.59808i −0.346512 + 0.600177i
$$88$$ 0.866025 + 1.50000i 0.0923186 + 0.159901i
$$89$$ −9.06218 + 5.23205i −0.960589 + 0.554596i −0.896354 0.443339i $$-0.853794\pi$$
−0.0642347 + 0.997935i $$0.520461\pi$$
$$90$$ −0.732051 −0.0771649
$$91$$ −0.232051 + 3.59808i −0.0243255 + 0.377181i
$$92$$ −3.46410 −0.361158
$$93$$ −1.90192 + 1.09808i −0.197220 + 0.113865i
$$94$$ 1.23205 + 2.13397i 0.127076 + 0.220103i
$$95$$ 0.366025 0.633975i 0.0375534 0.0650444i
$$96$$ 1.00000i 0.102062i
$$97$$ 13.5622 + 7.83013i 1.37703 + 0.795029i 0.991801 0.127792i $$-0.0407889\pi$$
0.385230 + 0.922821i $$0.374122\pi$$
$$98$$ −0.866025 0.500000i −0.0874818 0.0505076i
$$99$$ 1.73205i 0.174078i
$$100$$ 2.23205 3.86603i 0.223205 0.386603i
$$101$$ 1.53590 + 2.66025i 0.152828 + 0.264705i 0.932266 0.361774i $$-0.117829\pi$$
−0.779438 + 0.626479i $$0.784495\pi$$
$$102$$ 3.23205 1.86603i 0.320021 0.184764i
$$103$$ −14.7321 −1.45159 −0.725796 0.687910i $$-0.758528\pi$$
−0.725796 + 0.687910i $$0.758528\pi$$
$$104$$ −3.23205 + 1.59808i −0.316929 + 0.156704i
$$105$$ −0.732051 −0.0714408
$$106$$ −6.06218 + 3.50000i −0.588811 + 0.339950i
$$107$$ −5.42820 9.40192i −0.524764 0.908918i −0.999584 0.0288353i $$-0.990820\pi$$
0.474820 0.880083i $$-0.342513\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 4.73205i 0.453248i −0.973982 0.226624i $$-0.927231\pi$$
0.973982 0.226624i $$-0.0727689\pi$$
$$110$$ 1.09808 + 0.633975i 0.104697 + 0.0604471i
$$111$$ −5.83013 3.36603i −0.553371 0.319489i
$$112$$ 1.00000i 0.0944911i
$$113$$ −7.63397 + 13.2224i −0.718144 + 1.24386i 0.243590 + 0.969878i $$0.421675\pi$$
−0.961734 + 0.273984i $$0.911659\pi$$
$$114$$ 0.500000 + 0.866025i 0.0468293 + 0.0811107i
$$115$$ −2.19615 + 1.26795i −0.204792 + 0.118237i
$$116$$ −6.46410 −0.600177
$$117$$ −3.59808 0.232051i −0.332642 0.0214531i
$$118$$ −0.928203 −0.0854480
$$119$$ 3.23205 1.86603i 0.296282 0.171058i
$$120$$ −0.366025 0.633975i −0.0334134 0.0578737i
$$121$$ −4.00000 + 6.92820i −0.363636 + 0.629837i
$$122$$ 5.19615i 0.470438i
$$123$$ −2.59808 1.50000i −0.234261 0.135250i
$$124$$ −1.90192 1.09808i −0.170798 0.0986102i
$$125$$ 6.92820i 0.619677i
$$126$$ 0.500000 0.866025i 0.0445435 0.0771517i
$$127$$ −7.73205 13.3923i −0.686109 1.18837i −0.973087 0.230438i $$-0.925984\pi$$
0.286978 0.957937i $$-0.407349\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ −3.26795 −0.287727
$$130$$ −1.46410 + 2.19615i −0.128410 + 0.192615i
$$131$$ −13.8564 −1.21064 −0.605320 0.795982i $$-0.706955\pi$$
−0.605320 + 0.795982i $$0.706955\pi$$
$$132$$ −1.50000 + 0.866025i −0.130558 + 0.0753778i
$$133$$ 0.500000 + 0.866025i 0.0433555 + 0.0750939i
$$134$$ −4.46410 + 7.73205i −0.385640 + 0.667947i
$$135$$ 0.732051i 0.0630049i
$$136$$ 3.23205 + 1.86603i 0.277146 + 0.160010i
$$137$$ 12.4641 + 7.19615i 1.06488 + 0.614809i 0.926778 0.375609i $$-0.122567\pi$$
0.138102 + 0.990418i $$0.455900\pi$$
$$138$$ 3.46410i 0.294884i
$$139$$ −5.79423 + 10.0359i −0.491460 + 0.851234i −0.999952 0.00983316i $$-0.996870\pi$$
0.508492 + 0.861067i $$0.330203\pi$$
$$140$$ −0.366025 0.633975i −0.0309348 0.0535806i
$$141$$ −2.13397 + 1.23205i −0.179713 + 0.103757i
$$142$$ 2.19615 0.184297
$$143$$ 5.19615 + 3.46410i 0.434524 + 0.289683i
$$144$$ 1.00000 0.0833333
$$145$$ −4.09808 + 2.36603i −0.340327 + 0.196488i
$$146$$ −2.73205 4.73205i −0.226106 0.391627i
$$147$$ 0.500000 0.866025i 0.0412393 0.0714286i
$$148$$ 6.73205i 0.553371i
$$149$$ 12.0000 + 6.92820i 0.983078 + 0.567581i 0.903198 0.429224i $$-0.141213\pi$$
0.0798802 + 0.996804i $$0.474546\pi$$
$$150$$ 3.86603 + 2.23205i 0.315660 + 0.182246i
$$151$$ 5.19615i 0.422857i −0.977393 0.211428i $$-0.932188\pi$$
0.977393 0.211428i $$-0.0678115\pi$$
$$152$$ −0.500000 + 0.866025i −0.0405554 + 0.0702439i
$$153$$ 1.86603 + 3.23205i 0.150859 + 0.261296i
$$154$$ −1.50000 + 0.866025i −0.120873 + 0.0697863i
$$155$$ −1.60770 −0.129133
$$156$$ −1.59808 3.23205i −0.127948 0.258771i
$$157$$ −0.535898 −0.0427693 −0.0213847 0.999771i $$-0.506807\pi$$
−0.0213847 + 0.999771i $$0.506807\pi$$
$$158$$ −1.79423 + 1.03590i −0.142741 + 0.0824117i
$$159$$ −3.50000 6.06218i −0.277568 0.480762i
$$160$$ 0.366025 0.633975i 0.0289368 0.0501201i
$$161$$ 3.46410i 0.273009i
$$162$$ 0.866025 + 0.500000i 0.0680414 + 0.0392837i
$$163$$ 2.36603 + 1.36603i 0.185321 + 0.106995i 0.589790 0.807556i $$-0.299210\pi$$
−0.404469 + 0.914552i $$0.632544\pi$$
$$164$$ 3.00000i 0.234261i
$$165$$ −0.633975 + 1.09808i −0.0493549 + 0.0854851i
$$166$$ 0.0980762 + 0.169873i 0.00761219 + 0.0131847i
$$167$$ −12.0000 + 6.92820i −0.928588 + 0.536120i −0.886365 0.462988i $$-0.846777\pi$$
−0.0422232 + 0.999108i $$0.513444\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ −7.89230 + 10.3301i −0.607100 + 0.794625i
$$170$$ 2.73205 0.209539
$$171$$ −0.866025 + 0.500000i −0.0662266 + 0.0382360i
$$172$$ −1.63397 2.83013i −0.124589 0.215795i
$$173$$ −4.56218 + 7.90192i −0.346856 + 0.600772i −0.985689 0.168573i $$-0.946084\pi$$
0.638833 + 0.769345i $$0.279417\pi$$
$$174$$ 6.46410i 0.490042i
$$175$$ 3.86603 + 2.23205i 0.292244 + 0.168727i
$$176$$ −1.50000 0.866025i −0.113067 0.0652791i
$$177$$ 0.928203i 0.0697680i
$$178$$ 5.23205 9.06218i 0.392159 0.679239i
$$179$$ 5.73205 + 9.92820i 0.428434 + 0.742069i 0.996734 0.0807523i $$-0.0257323\pi$$
−0.568301 + 0.822821i $$0.692399\pi$$
$$180$$ 0.633975 0.366025i 0.0472537 0.0272819i
$$181$$ 2.66025 0.197735 0.0988676 0.995101i $$-0.468478\pi$$
0.0988676 + 0.995101i $$0.468478\pi$$
$$182$$ −1.59808 3.23205i −0.118457 0.239576i
$$183$$ 5.19615 0.384111
$$184$$ 3.00000 1.73205i 0.221163 0.127688i
$$185$$ −2.46410 4.26795i −0.181164 0.313786i
$$186$$ 1.09808 1.90192i 0.0805149 0.139456i
$$187$$ 6.46410i 0.472702i
$$188$$ −2.13397 1.23205i −0.155636 0.0898565i
$$189$$ 0.866025 + 0.500000i 0.0629941 + 0.0363696i
$$190$$ 0.732051i 0.0531085i
$$191$$ −11.5622 + 20.0263i −0.836610 + 1.44905i 0.0561031 + 0.998425i $$0.482132\pi$$
−0.892713 + 0.450626i $$0.851201\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ −1.03590 + 0.598076i −0.0745656 + 0.0430505i −0.536819 0.843697i $$-0.680374\pi$$
0.462254 + 0.886748i $$0.347041\pi$$
$$194$$ −15.6603 −1.12434
$$195$$ −2.19615 1.46410i −0.157270 0.104846i
$$196$$ 1.00000 0.0714286
$$197$$ 23.0885 13.3301i 1.64498 0.949732i 0.665961 0.745987i $$-0.268022\pi$$
0.979024 0.203745i $$-0.0653114\pi$$
$$198$$ −0.866025 1.50000i −0.0615457 0.106600i
$$199$$ −8.09808 + 14.0263i −0.574057 + 0.994297i 0.422086 + 0.906556i $$0.361298\pi$$
−0.996143 + 0.0877408i $$0.972035\pi$$
$$200$$ 4.46410i 0.315660i
$$201$$ −7.73205 4.46410i −0.545377 0.314873i
$$202$$ −2.66025 1.53590i −0.187175 0.108065i
$$203$$ 6.46410i 0.453691i
$$204$$ −1.86603 + 3.23205i −0.130648 + 0.226289i
$$205$$ −1.09808 1.90192i −0.0766930 0.132836i
$$206$$ 12.7583 7.36603i 0.888915 0.513215i
$$207$$ 3.46410 0.240772
$$208$$ 2.00000 3.00000i 0.138675 0.208013i
$$209$$ 1.73205 0.119808
$$210$$ 0.633975 0.366025i 0.0437484 0.0252582i
$$211$$ −13.0000 22.5167i −0.894957 1.55011i −0.833858 0.551979i $$-0.813873\pi$$
−0.0610990 0.998132i $$-0.519461\pi$$
$$212$$ 3.50000 6.06218i 0.240381 0.416352i
$$213$$ 2.19615i 0.150478i
$$214$$ 9.40192 + 5.42820i 0.642702 + 0.371064i
$$215$$ −2.07180 1.19615i −0.141295 0.0815769i
$$216$$ 1.00000i 0.0680414i
$$217$$ 1.09808 1.90192i 0.0745423 0.129111i
$$218$$ 2.36603 + 4.09808i 0.160247 + 0.277557i
$$219$$ 4.73205 2.73205i 0.319762 0.184615i
$$220$$ −1.26795 −0.0854851
$$221$$ 13.4282 + 0.866025i 0.903279 + 0.0582552i
$$222$$ 6.73205 0.451826
$$223$$ 21.1244 12.1962i 1.41459 0.816715i 0.418775 0.908090i $$-0.362460\pi$$
0.995817 + 0.0913753i $$0.0291263\pi$$
$$224$$ 0.500000 + 0.866025i 0.0334077 + 0.0578638i
$$225$$ −2.23205 + 3.86603i −0.148803 + 0.257735i
$$226$$ 15.2679i 1.01561i
$$227$$ 15.9282 + 9.19615i 1.05719 + 0.610370i 0.924654 0.380808i $$-0.124354\pi$$
0.132538 + 0.991178i $$0.457687\pi$$
$$228$$ −0.866025 0.500000i −0.0573539 0.0331133i
$$229$$ 19.9282i 1.31689i 0.752628 + 0.658446i $$0.228786\pi$$
−0.752628 + 0.658446i $$0.771214\pi$$
$$230$$ 1.26795 2.19615i 0.0836061 0.144810i
$$231$$ −0.866025 1.50000i −0.0569803 0.0986928i
$$232$$ 5.59808 3.23205i 0.367532 0.212195i
$$233$$ 9.12436 0.597756 0.298878 0.954291i $$-0.403388\pi$$
0.298878 + 0.954291i $$0.403388\pi$$
$$234$$ 3.23205 1.59808i 0.211286 0.104470i
$$235$$ −1.80385 −0.117670
$$236$$ 0.803848 0.464102i 0.0523260 0.0302104i
$$237$$ −1.03590 1.79423i −0.0672888 0.116548i
$$238$$ −1.86603 + 3.23205i −0.120956 + 0.209503i
$$239$$ 0.732051i 0.0473524i −0.999720 0.0236762i $$-0.992463\pi$$
0.999720 0.0236762i $$-0.00753708\pi$$
$$240$$ 0.633975 + 0.366025i 0.0409229 + 0.0236268i
$$241$$ −6.92820 4.00000i −0.446285 0.257663i 0.259975 0.965615i $$-0.416286\pi$$
−0.706260 + 0.707953i $$0.749619\pi$$
$$242$$ 8.00000i 0.514259i
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 2.59808 + 4.50000i 0.166325 + 0.288083i
$$245$$ 0.633975 0.366025i 0.0405032 0.0233845i
$$246$$ 3.00000 0.191273
$$247$$ −0.232051 + 3.59808i −0.0147650 + 0.228940i
$$248$$ 2.19615 0.139456
$$249$$ −0.169873 + 0.0980762i −0.0107653 + 0.00621533i
$$250$$ 3.46410 + 6.00000i 0.219089 + 0.379473i
$$251$$ 6.56218 11.3660i 0.414201 0.717417i −0.581143 0.813801i $$-0.697394\pi$$
0.995344 + 0.0963841i $$0.0307277\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ −5.19615 3.00000i −0.326679 0.188608i
$$254$$ 13.3923 + 7.73205i 0.840308 + 0.485152i
$$255$$ 2.73205i 0.171088i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 10.3301 + 17.8923i 0.644376 + 1.11609i 0.984445 + 0.175691i $$0.0562160\pi$$
−0.340070 + 0.940400i $$0.610451\pi$$
$$258$$ 2.83013 1.63397i 0.176196 0.101727i
$$259$$ 6.73205 0.418309
$$260$$ 0.169873 2.63397i 0.0105351 0.163352i
$$261$$ 6.46410 0.400118
$$262$$ 12.0000 6.92820i 0.741362 0.428026i
$$263$$ 7.56218 + 13.0981i 0.466304 + 0.807662i 0.999259 0.0384813i $$-0.0122520\pi$$
−0.532955 + 0.846143i $$0.678919\pi$$
$$264$$ 0.866025 1.50000i 0.0533002 0.0923186i
$$265$$ 5.12436i 0.314787i
$$266$$ −0.866025 0.500000i −0.0530994 0.0306570i
$$267$$ 9.06218 + 5.23205i 0.554596 + 0.320196i
$$268$$ 8.92820i 0.545377i
$$269$$ 4.92820 8.53590i 0.300478 0.520443i −0.675766 0.737116i $$-0.736187\pi$$
0.976244 + 0.216673i $$0.0695205\pi$$
$$270$$ 0.366025 + 0.633975i 0.0222756 + 0.0385825i
$$271$$ −24.2942 + 14.0263i −1.47577 + 0.852036i −0.999626 0.0273321i $$-0.991299\pi$$
−0.476143 + 0.879368i $$0.657965\pi$$
$$272$$ −3.73205 −0.226289
$$273$$ 3.23205 1.59808i 0.195613 0.0967200i
$$274$$ −14.3923 −0.869471
$$275$$ 6.69615 3.86603i 0.403793 0.233130i
$$276$$ 1.73205 + 3.00000i 0.104257 + 0.180579i
$$277$$ 4.66025 8.07180i 0.280008 0.484987i −0.691379 0.722493i $$-0.742996\pi$$
0.971386 + 0.237505i $$0.0763297\pi$$
$$278$$ 11.5885i 0.695029i
$$279$$ 1.90192 + 1.09808i 0.113865 + 0.0657401i
$$280$$ 0.633975 + 0.366025i 0.0378872 + 0.0218742i
$$281$$ 0.339746i 0.0202675i 0.999949 + 0.0101338i $$0.00322574\pi$$
−0.999949 + 0.0101338i $$0.996774\pi$$
$$282$$ 1.23205 2.13397i 0.0733676 0.127076i
$$283$$ −4.92820 8.53590i −0.292951 0.507406i 0.681555 0.731767i $$-0.261304\pi$$
−0.974506 + 0.224360i $$0.927971\pi$$
$$284$$ −1.90192 + 1.09808i −0.112858 + 0.0651588i
$$285$$ −0.732051 −0.0433629
$$286$$ −6.23205 0.401924i −0.368509 0.0237663i
$$287$$ 3.00000 0.177084
$$288$$ −0.866025 + 0.500000i −0.0510310 + 0.0294628i
$$289$$ 1.53590 + 2.66025i 0.0903470 + 0.156486i
$$290$$ 2.36603 4.09808i 0.138938 0.240647i
$$291$$ 15.6603i 0.918020i
$$292$$ 4.73205 + 2.73205i 0.276922 + 0.159881i
$$293$$ −14.7846 8.53590i −0.863726 0.498673i 0.00153218 0.999999i $$-0.499512\pi$$
−0.865258 + 0.501326i $$0.832846\pi$$
$$294$$ 1.00000i 0.0583212i
$$295$$ 0.339746 0.588457i 0.0197808 0.0342613i
$$296$$ 3.36603 + 5.83013i 0.195646 + 0.338869i
$$297$$ 1.50000 0.866025i 0.0870388 0.0502519i
$$298$$ −13.8564 −0.802680
$$299$$ 6.92820 10.3923i 0.400668 0.601003i
$$300$$ −4.46410 −0.257735
$$301$$ 2.83013 1.63397i 0.163126 0.0941807i
$$302$$ 2.59808 + 4.50000i 0.149502 + 0.258946i
$$303$$ 1.53590 2.66025i 0.0882351 0.152828i
$$304$$ 1.00000i 0.0573539i
$$305$$ 3.29423 + 1.90192i 0.188627 + 0.108904i
$$306$$ −3.23205 1.86603i −0.184764 0.106674i
$$307$$ 8.60770i 0.491267i −0.969363 0.245634i $$-0.921004\pi$$
0.969363 0.245634i $$-0.0789960\pi$$
$$308$$ 0.866025 1.50000i 0.0493464 0.0854704i
$$309$$ 7.36603 + 12.7583i 0.419039 + 0.725796i
$$310$$ 1.39230 0.803848i 0.0790776 0.0456555i
$$311$$ −4.26795 −0.242013 −0.121007 0.992652i $$-0.538612\pi$$
−0.121007 + 0.992652i $$0.538612\pi$$
$$312$$ 3.00000 + 2.00000i 0.169842 + 0.113228i
$$313$$ 13.5167 0.764007 0.382003 0.924161i $$-0.375234\pi$$
0.382003 + 0.924161i $$0.375234\pi$$
$$314$$ 0.464102 0.267949i 0.0261908 0.0151212i
$$315$$ 0.366025 + 0.633975i 0.0206232 + 0.0357204i
$$316$$ 1.03590 1.79423i 0.0582738 0.100933i
$$317$$ 11.8564i 0.665922i −0.942941 0.332961i $$-0.891952\pi$$
0.942941 0.332961i $$-0.108048\pi$$
$$318$$ 6.06218 + 3.50000i 0.339950 + 0.196270i
$$319$$ −9.69615 5.59808i −0.542880 0.313432i
$$320$$ 0.732051i 0.0409229i
$$321$$ −5.42820 + 9.40192i −0.302973 + 0.524764i
$$322$$ 1.73205 + 3.00000i 0.0965234 + 0.167183i
$$323$$ 3.23205 1.86603i 0.179836 0.103828i
$$324$$ −1.00000 −0.0555556
$$325$$ 7.13397 + 14.4282i 0.395722 + 0.800333i
$$326$$ −2.73205 −0.151314
$$327$$ −4.09808 + 2.36603i −0.226624 + 0.130842i
$$328$$ 1.50000 + 2.59808i 0.0828236 + 0.143455i
$$329$$ 1.23205 2.13397i 0.0679252 0.117650i
$$330$$ 1.26795i 0.0697983i
$$331$$ 24.1244 + 13.9282i 1.32599 + 0.765563i 0.984678 0.174385i $$-0.0557937\pi$$
0.341317 + 0.939948i $$0.389127\pi$$
$$332$$ −0.169873 0.0980762i −0.00932299 0.00538263i
$$333$$ 6.73205i 0.368914i
$$334$$ 6.92820 12.0000i 0.379094 0.656611i
$$335$$ −3.26795 5.66025i −0.178547 0.309253i
$$336$$ −0.866025 + 0.500000i −0.0472456 + 0.0272772i
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ 1.66987 12.8923i 0.0908291 0.701249i
$$339$$ 15.2679 0.829241
$$340$$ −2.36603 + 1.36603i −0.128316 + 0.0740831i
$$341$$ −1.90192 3.29423i −0.102995 0.178392i
$$342$$ 0.500000 0.866025i 0.0270369 0.0468293i
$$343$$ 1.00000i 0.0539949i
$$344$$ 2.83013 + 1.63397i 0.152590 + 0.0880980i
$$345$$ 2.19615 + 1.26795i 0.118237 + 0.0682641i
$$346$$ 9.12436i 0.490528i
$$347$$ −2.69615 + 4.66987i −0.144737 + 0.250692i −0.929275 0.369389i $$-0.879567\pi$$
0.784538 + 0.620081i $$0.212900\pi$$
$$348$$ 3.23205 + 5.59808i 0.173256 + 0.300088i
$$349$$ −20.5359 + 11.8564i −1.09926 + 0.634659i −0.936027 0.351928i $$-0.885526\pi$$
−0.163235 + 0.986587i $$0.552193\pi$$
$$350$$ −4.46410 −0.238616
$$351$$ 1.59808 + 3.23205i 0.0852990 + 0.172514i
$$352$$ 1.73205 0.0923186
$$353$$ −8.19615 + 4.73205i −0.436237 + 0.251862i −0.702000 0.712177i $$-0.747709\pi$$
0.265763 + 0.964038i $$0.414376\pi$$
$$354$$ 0.464102 + 0.803848i 0.0246667 + 0.0427240i
$$355$$ −0.803848 + 1.39230i −0.0426638 + 0.0738959i
$$356$$ 10.4641i 0.554596i
$$357$$ −3.23205 1.86603i −0.171058 0.0987605i
$$358$$ −9.92820 5.73205i −0.524722 0.302948i
$$359$$ 3.80385i 0.200759i 0.994949 + 0.100380i $$0.0320058\pi$$
−0.994949 + 0.100380i $$0.967994\pi$$
$$360$$ −0.366025 + 0.633975i −0.0192912 + 0.0334134i
$$361$$ −9.00000 15.5885i −0.473684 0.820445i
$$362$$ −2.30385 + 1.33013i −0.121088 + 0.0699099i
$$363$$ 8.00000 0.419891
$$364$$ 3.00000 + 2.00000i 0.157243 + 0.104828i
$$365$$ 4.00000 0.209370
$$366$$ −4.50000 + 2.59808i −0.235219 + 0.135804i
$$367$$ −12.6603 21.9282i −0.660860 1.14464i −0.980390 0.197067i $$-0.936858\pi$$
0.319530 0.947576i $$-0.396475\pi$$
$$368$$ −1.73205 + 3.00000i −0.0902894 + 0.156386i
$$369$$ 3.00000i 0.156174i
$$370$$ 4.26795 + 2.46410i 0.221880 + 0.128103i
$$371$$ 6.06218 + 3.50000i 0.314733 + 0.181711i
$$372$$ 2.19615i 0.113865i
$$373$$ −4.83013 + 8.36603i −0.250094 + 0.433176i −0.963552 0.267523i $$-0.913795\pi$$
0.713457 + 0.700699i $$0.247128\pi$$
$$374$$ 3.23205 + 5.59808i 0.167125 + 0.289470i
$$375$$ −6.00000 + 3.46410i −0.309839 + 0.178885i
$$376$$ 2.46410 0.127076
$$377$$ 12.9282 19.3923i 0.665836 0.998755i
$$378$$ −1.00000 −0.0514344
$$379$$ 24.6340 14.2224i 1.26536 0.730557i 0.291255 0.956645i $$-0.405927\pi$$
0.974107 + 0.226088i $$0.0725937\pi$$
$$380$$ −0.366025 0.633975i −0.0187767 0.0325222i
$$381$$ −7.73205 + 13.3923i −0.396125 + 0.686109i
$$382$$ 23.1244i 1.18314i
$$383$$ −4.79423 2.76795i −0.244974 0.141436i 0.372487 0.928037i $$-0.378505\pi$$
−0.617461 + 0.786602i $$0.711838\pi$$
$$384$$ −0.866025 0.500000i −0.0441942 0.0255155i
$$385$$ 1.26795i 0.0646207i
$$386$$ 0.598076 1.03590i 0.0304413 0.0527258i
$$387$$ 1.63397 + 2.83013i 0.0830596 + 0.143863i
$$388$$ 13.5622 7.83013i 0.688515 0.397514i
$$389$$ −8.39230 −0.425507 −0.212753 0.977106i $$-0.568243\pi$$
−0.212753 + 0.977106i $$0.568243\pi$$
$$390$$ 2.63397 + 0.169873i 0.133376 + 0.00860185i
$$391$$ −12.9282 −0.653807
$$392$$ −0.866025 + 0.500000i −0.0437409 + 0.0252538i
$$393$$ 6.92820 + 12.0000i 0.349482 + 0.605320i
$$394$$ −13.3301 + 23.0885i −0.671562 + 1.16318i
$$395$$ 1.51666i 0.0763115i
$$396$$ 1.50000 + 0.866025i 0.0753778 + 0.0435194i
$$397$$ 6.99038 + 4.03590i 0.350837 + 0.202556i 0.665054 0.746795i $$-0.268409\pi$$
−0.314217 + 0.949351i $$0.601742\pi$$
$$398$$ 16.1962i 0.811840i
$$399$$ 0.500000 0.866025i 0.0250313 0.0433555i
$$400$$ −2.23205 3.86603i −0.111603 0.193301i
$$401$$ −33.5885 + 19.3923i −1.67733 + 0.968405i −0.713973 + 0.700173i $$0.753106\pi$$
−0.963354 + 0.268233i $$0.913560\pi$$
$$402$$ 8.92820 0.445298
$$403$$ 7.09808 3.50962i 0.353580 0.174827i
$$404$$ 3.07180 0.152828
$$405$$ −0.633975 + 0.366025i −0.0315025 + 0.0181879i
$$406$$ 3.23205 + 5.59808i 0.160404 + 0.277828i
$$407$$ 5.83013 10.0981i 0.288989 0.500543i
$$408$$ 3.73205i 0.184764i
$$409$$ −33.5429 19.3660i −1.65859 0.957588i −0.973366 0.229258i $$-0.926370\pi$$
−0.685226 0.728331i $$-0.740297\pi$$
$$410$$ 1.90192 + 1.09808i 0.0939293 + 0.0542301i
$$411$$ 14.3923i 0.709920i
$$412$$ −7.36603 + 12.7583i −0.362898 + 0.628558i
$$413$$ 0.464102 + 0.803848i 0.0228369 + 0.0395548i
$$414$$ −3.00000 + 1.73205i −0.147442 + 0.0851257i
$$415$$ −0.143594 −0.00704873
$$416$$ −0.232051 + 3.59808i −0.0113772 + 0.176410i
$$417$$ 11.5885 0.567489
$$418$$ −1.50000 + 0.866025i −0.0733674 + 0.0423587i
$$419$$ −0.366025 0.633975i −0.0178815 0.0309717i 0.856946 0.515406i $$-0.172359\pi$$
−0.874828 + 0.484434i $$0.839025\pi$$
$$420$$ −0.366025 + 0.633975i −0.0178602 + 0.0309348i
$$421$$ 22.3923i 1.09133i −0.838002 0.545667i $$-0.816276\pi$$
0.838002 0.545667i $$-0.183724\pi$$
$$422$$ 22.5167 + 13.0000i 1.09609 + 0.632830i
$$423$$ 2.13397 + 1.23205i 0.103757 + 0.0599044i
$$424$$ 7.00000i 0.339950i
$$425$$ 8.33013 14.4282i 0.404071 0.699871i
$$426$$ −1.09808 1.90192i −0.0532020 0.0921485i
$$427$$ −4.50000 + 2.59808i −0.217770 + 0.125730i
$$428$$ −10.8564 −0.524764
$$429$$ 0.401924 6.23205i 0.0194051 0.300886i
$$430$$ 2.39230 0.115367
$$431$$ −12.2942 + 7.09808i −0.592192 + 0.341902i −0.765964 0.642884i $$-0.777738\pi$$
0.173772 + 0.984786i $$0.444405\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −13.5359 + 23.4449i −0.650494 + 1.12669i 0.332509 + 0.943100i $$0.392105\pi$$
−0.983003 + 0.183588i $$0.941229\pi$$
$$434$$ 2.19615i 0.105419i
$$435$$ 4.09808 + 2.36603i 0.196488 + 0.113442i
$$436$$ −4.09808 2.36603i −0.196262 0.113312i
$$437$$ 3.46410i 0.165710i
$$438$$ −2.73205 + 4.73205i −0.130542 + 0.226106i
$$439$$ −12.5885 21.8038i −0.600814 1.04064i −0.992698 0.120626i $$-0.961510\pi$$
0.391884 0.920015i $$-0.371824\pi$$
$$440$$ 1.09808 0.633975i 0.0523487 0.0302236i
$$441$$ −1.00000 −0.0476190
$$442$$ −12.0622 + 5.96410i −0.573739 + 0.283683i
$$443$$ −33.6410 −1.59833 −0.799166 0.601110i $$-0.794725\pi$$
−0.799166 + 0.601110i $$0.794725\pi$$
$$444$$ −5.83013 + 3.36603i −0.276686 + 0.159744i
$$445$$ 3.83013 + 6.63397i 0.181565 + 0.314481i
$$446$$ −12.1962 + 21.1244i −0.577505 + 1.00027i
$$447$$ 13.8564i 0.655386i
$$448$$ −0.866025 0.500000i −0.0409159 0.0236228i
$$449$$ 17.8301 + 10.2942i 0.841456 + 0.485815i 0.857759 0.514052i $$-0.171856\pi$$
−0.0163031 + 0.999867i $$0.505190\pi$$
$$450$$ 4.46410i 0.210440i
$$451$$ 2.59808 4.50000i 0.122339 0.211897i
$$452$$ 7.63397 + 13.2224i 0.359072 + 0.621931i
$$453$$ −4.50000 + 2.59808i −0.211428 + 0.122068i
$$454$$ −18.3923 −0.863194
$$455$$ 2.63397 + 0.169873i 0.123483 + 0.00796377i
$$456$$ 1.00000 0.0468293
$$457$$ 10.2679 5.92820i 0.480314 0.277310i −0.240233 0.970715i $$-0.577224\pi$$
0.720548 + 0.693406i $$0.243891\pi$$
$$458$$ −9.96410 17.2583i −0.465592 0.806429i
$$459$$ 1.86603 3.23205i 0.0870986 0.150859i
$$460$$ 2.53590i 0.118237i
$$461$$ −23.3205 13.4641i −1.08614 0.627086i −0.153597 0.988134i $$-0.549086\pi$$
−0.932547 + 0.361048i $$0.882419\pi$$
$$462$$ 1.50000 + 0.866025i 0.0697863 + 0.0402911i
$$463$$ 6.26795i 0.291296i 0.989336 + 0.145648i $$0.0465267\pi$$
−0.989336 + 0.145648i $$0.953473\pi$$
$$464$$ −3.23205 + 5.59808i −0.150044 + 0.259884i
$$465$$ 0.803848 + 1.39230i 0.0372775 + 0.0645666i
$$466$$ −7.90192 + 4.56218i −0.366050 + 0.211339i
$$467$$ 13.8564 0.641198 0.320599 0.947215i $$-0.396116\pi$$
0.320599 + 0.947215i $$0.396116\pi$$
$$468$$ −2.00000 + 3.00000i −0.0924500 + 0.138675i
$$469$$ 8.92820 0.412266
$$470$$ 1.56218 0.901924i 0.0720579 0.0416026i
$$471$$ 0.267949 + 0.464102i 0.0123464 + 0.0213847i
$$472$$ −0.464102 + 0.803848i −0.0213620 + 0.0370001i
$$473$$ 5.66025i 0.260259i
$$474$$ 1.79423 + 1.03590i 0.0824117 + 0.0475804i
$$475$$ 3.86603 + 2.23205i 0.177385 + 0.102414i
$$476$$ 3.73205i 0.171058i
$$477$$ −3.50000 + 6.06218i −0.160254 + 0.277568i
$$478$$ 0.366025 + 0.633975i 0.0167416 + 0.0289973i
$$479$$ −28.1147 + 16.2321i −1.28460 + 0.741661i −0.977685 0.210077i $$-0.932628\pi$$
−0.306910 + 0.951738i $$0.599295\pi$$
$$480$$ −0.732051 −0.0334134
$$481$$ 20.1962 + 13.4641i 0.920865 + 0.613910i
$$482$$ 8.00000 0.364390
$$483$$ −3.00000 + 1.73205i −0.136505 + 0.0788110i
$$484$$ 4.00000 + 6.92820i 0.181818 + 0.314918i
$$485$$ 5.73205 9.92820i 0.260279 0.450816i
$$486$$ 1.00000i 0.0453609i
$$487$$ −14.4282 8.33013i −0.653804 0.377474i 0.136108 0.990694i $$-0.456541\pi$$
−0.789912 + 0.613220i $$0.789874\pi$$
$$488$$ −4.50000 2.59808i −0.203705 0.117609i
$$489$$ 2.73205i 0.123548i
$$490$$ −0.366025 + 0.633975i −0.0165353 + 0.0286401i
$$491$$ 17.7321 + 30.7128i 0.800236 + 1.38605i 0.919460 + 0.393182i $$0.128626\pi$$
−0.119224 + 0.992867i $$0.538041\pi$$
$$492$$ −2.59808 + 1.50000i −0.117130 + 0.0676252i
$$493$$ −24.1244 −1.08651
$$494$$ −1.59808 3.23205i −0.0719008 0.145417i
$$495$$ 1.26795 0.0569901
$$496$$ −1.90192 + 1.09808i −0.0853989 + 0.0493051i
$$497$$ −1.09808 1.90192i −0.0492554 0.0853129i
$$498$$ 0.0980762 0.169873i 0.00439490 0.00761219i
$$499$$ 11.5167i 0.515557i 0.966204 + 0.257778i $$0.0829904\pi$$
−0.966204 + 0.257778i $$0.917010\pi$$
$$500$$ −6.00000 3.46410i −0.268328 0.154919i
$$501$$ 12.0000 + 6.92820i 0.536120 + 0.309529i
$$502$$ 13.1244i 0.585769i
$$503$$ −3.46410 + 6.00000i −0.154457 + 0.267527i −0.932861 0.360236i $$-0.882696\pi$$
0.778404 + 0.627763i $$0.216029\pi$$
$$504$$ −0.500000 0.866025i −0.0222718 0.0385758i
$$505$$ 1.94744 1.12436i 0.0866600 0.0500332i
$$506$$ 6.00000 0.266733
$$507$$ 12.8923 + 1.66987i 0.572567 + 0.0741617i
$$508$$ −15.4641 −0.686109
$$509$$ −19.3468 + 11.1699i −0.857531 + 0.495096i −0.863185 0.504888i $$-0.831534\pi$$
0.00565352 + 0.999984i $$0.498200\pi$$
$$510$$ −1.36603 2.36603i −0.0604886 0.104769i
$$511$$ −2.73205 + 4.73205i −0.120859 + 0.209334i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0.866025 + 0.500000i 0.0382360 + 0.0220755i
$$514$$ −17.8923 10.3301i −0.789196 0.455642i
$$515$$ 10.7846i 0.475227i
$$516$$ −1.63397 + 2.83013i −0.0719317 + 0.124589i
$$517$$ −2.13397 3.69615i −0.0938521 0.162557i
$$518$$ −5.83013 + 3.36603i −0.256161 + 0.147895i
$$519$$ 9.12436 0.400515
$$520$$ 1.16987 + 2.36603i 0.0513023 + 0.103757i
$$521$$ 7.05256 0.308978 0.154489 0.987994i $$-0.450627\pi$$
0.154489 + 0.987994i $$0.450627\pi$$
$$522$$ −5.59808 + 3.23205i −0.245021 + 0.141463i
$$523$$ 6.93782 + 12.0167i 0.303370 + 0.525452i 0.976897 0.213711i $$-0.0685549\pi$$
−0.673527 + 0.739162i $$0.735222\pi$$
$$524$$ −6.92820 + 12.0000i −0.302660 + 0.524222i
$$525$$ 4.46410i 0.194829i
$$526$$ −13.0981 7.56218i −0.571103 0.329727i
$$527$$ −7.09808 4.09808i −0.309197 0.178515i
$$528$$ 1.73205i 0.0753778i
$$529$$ 5.50000 9.52628i 0.239130 0.414186i
$$530$$ 2.56218 + 4.43782i 0.111294 + 0.192767i
$$531$$ −0.803848 + 0.464102i −0.0348840 + 0.0201403i
$$532$$ 1.00000 0.0433555
$$533$$ 9.00000 + 6.00000i 0.389833 + 0.259889i
$$534$$ −10.4641 −0.452826
$$535$$ −6.88269 + 3.97372i −0.297564 + 0.171799i
$$536$$ 4.46410 + 7.73205i 0.192820 + 0.333974i
$$537$$ 5.73205 9.92820i 0.247356 0.428434i
$$538$$ 9.85641i 0.424940i
$$539$$ 1.50000 + 0.866025i 0.0646096 + 0.0373024i
$$540$$ −0.633975 0.366025i −0.0272819 0.0157512i
$$541$$ 24.3397i 1.04645i 0.852195 + 0.523224i $$0.175271\pi$$
−0.852195 + 0.523224i $$0.824729\pi$$
$$542$$ 14.0263 24.2942i 0.602480 1.04353i
$$543$$ −1.33013 2.30385i −0.0570812 0.0988676i
$$544$$ 3.23205 1.86603i 0.138573 0.0800052i
$$545$$ −3.46410 −0.148386
$$546$$ −2.00000 + 3.00000i −0.0855921 + 0.128388i
$$547$$ −1.26795 −0.0542136 −0.0271068 0.999633i $$-0.508629\pi$$
−0.0271068 + 0.999633i $$0.508629\pi$$
$$548$$ 12.4641 7.19615i 0.532440 0.307404i
$$549$$ −2.59808 4.50000i −0.110883 0.192055i
$$550$$ −3.86603 + 6.69615i −0.164848 + 0.285525i
$$551$$ 6.46410i 0.275380i
$$552$$ −3.00000 1.73205i −0.127688 0.0737210i
$$553$$ 1.79423 + 1.03590i 0.0762984 + 0.0440509i
$$554$$ 9.32051i 0.395990i
$$555$$ −2.46410 + 4.26795i −0.104595 + 0.181164i
$$556$$ 5.79423 + 10.0359i 0.245730 + 0.425617i
$$557$$ 11.3038 6.52628i 0.478959 0.276527i −0.241023 0.970519i $$-0.577483\pi$$
0.719983 + 0.693992i $$0.244150\pi$$
$$558$$ −2.19615 −0.0929705
$$559$$ 11.7583 + 0.758330i 0.497324 + 0.0320740i
$$560$$ −0.732051 −0.0309348
$$561$$ −5.59808 + 3.23205i −0.236351 + 0.136457i
$$562$$ −0.169873 0.294229i −0.00716566 0.0124113i
$$563$$ −18.0981 + 31.3468i −0.762743 + 1.32111i 0.178689 + 0.983906i $$0.442815\pi$$
−0.941432 + 0.337204i $$0.890519\pi$$
$$564$$ 2.46410i 0.103757i
$$565$$ 9.67949 + 5.58846i 0.407219 + 0.235108i
$$566$$ 8.53590 + 4.92820i 0.358791 + 0.207148i
$$567$$ 1.00000i 0.0419961i
$$568$$ 1.09808 1.90192i 0.0460743 0.0798029i
$$569$$ −19.2224 33.2942i −0.805846 1.39577i −0.915718 0.401821i $$-0.868377\pi$$
0.109872 0.993946i $$-0.464956\pi$$
$$570$$ 0.633975 0.366025i 0.0265543 0.0153311i
$$571$$ −16.9808 −0.710623 −0.355311 0.934748i $$-0.615625\pi$$
−0.355311 + 0.934748i $$0.615625\pi$$
$$572$$ 5.59808 2.76795i 0.234067 0.115734i
$$573$$ 23.1244 0.966034
$$574$$ −2.59808 + 1.50000i −0.108442 + 0.0626088i
$$575$$ −7.73205 13.3923i −0.322449 0.558498i
$$576$$ 0.500000 0.866025i 0.0208333 0.0360844i
$$577$$ 10.3397i 0.430449i 0.976565 + 0.215225i $$0.0690484\pi$$
−0.976565 + 0.215225i $$0.930952\pi$$
$$578$$ −2.66025 1.53590i −0.110652 0.0638850i
$$579$$ 1.03590 + 0.598076i 0.0430505 + 0.0248552i
$$580$$ 4.73205i 0.196488i
$$581$$ 0.0980762 0.169873i 0.00406889 0.00704752i
$$582$$ 7.83013 + 13.5622i 0.324569 + 0.562170i
$$583$$ 10.5000 6.06218i 0.434866 0.251070i
$$584$$ −5.46410 −0.226106
$$585$$ −0.169873 + 2.63397i −0.00702338 + 0.108901i
$$586$$ 17.0718 0.705229
$$587$$ 10.6865 6.16987i 0.441080 0.254658i −0.262975 0.964803i $$-0.584704\pi$$
0.704056 + 0.710145i $$0.251370\pi$$
$$588$$ −0.500000 0.866025i −0.0206197 0.0357143i
$$589$$ 1.09808 1.90192i 0.0452454 0.0783674i
$$590$$ 0.679492i 0.0279742i
$$591$$ −23.0885 13.3301i −0.949732 0.548328i
$$592$$ −5.83013 3.36603i −0.239617 0.138343i
$$593$$ 0.464102i 0.0190584i −0.999955 0.00952918i $$-0.996967\pi$$
0.999955 0.00952918i $$-0.00303328\pi$$
$$594$$ −0.866025 + 1.50000i −0.0355335 + 0.0615457i
$$595$$ −1.36603 2.36603i −0.0560016 0.0969976i
$$596$$ 12.0000 6.92820i 0.491539 0.283790i
$$597$$ 16.1962 0.662864
$$598$$ −0.803848 + 12.4641i −0.0328718 + 0.509695i
$$599$$ −28.6410 −1.17024 −0.585120 0.810947i $$-0.698953\pi$$
−0.585120 + 0.810947i $$0.698953\pi$$
$$600$$ 3.86603 2.23205i 0.157830 0.0911231i
$$601$$ 11.3660 + 19.6865i 0.463630 + 0.803030i 0.999139 0.0414993i $$-0.0132134\pi$$
−0.535509 + 0.844530i $$0.679880\pi$$
$$602$$ −1.63397 + 2.83013i −0.0665958 + 0.115347i
$$603$$ 8.92820i 0.363585i
$$604$$ −4.50000 2.59808i −0.183102 0.105714i
$$605$$ 5.07180 + 2.92820i 0.206198 + 0.119048i
$$606$$ 3.07180i 0.124783i
$$607$$ 15.7583 27.2942i 0.639611 1.10784i −0.345907 0.938269i $$-0.612429\pi$$
0.985518 0.169570i $$-0.0542378\pi$$
$$608$$ 0.500000 + 0.866025i 0.0202777 + 0.0351220i
$$609$$ −5.59808 + 3.23205i −0.226845 + 0.130969i
$$610$$ −3.80385 −0.154013
$$611$$ 7.96410 3.93782i 0.322193 0.159307i
$$612$$ 3.73205 0.150859
$$613$$ 3.46410 2.00000i 0.139914 0.0807792i −0.428409 0.903585i $$-0.640926\pi$$
0.568323 + 0.822806i $$0.307592\pi$$
$$614$$ 4.30385 + 7.45448i 0.173689 + 0.300838i
$$615$$ −1.09808 + 1.90192i −0.0442787 + 0.0766930i
$$616$$ 1.73205i 0.0697863i
$$617$$ 1.90192 + 1.09808i 0.0765686 + 0.0442069i 0.537795 0.843075i $$-0.319257\pi$$
−0.461227 + 0.887282i $$0.652591\pi$$
$$618$$ −12.7583 7.36603i −0.513215 0.296305i
$$619$$ 22.0718i 0.887140i −0.896240 0.443570i $$-0.853712\pi$$
0.896240 0.443570i $$-0.146288\pi$$
$$620$$ −0.803848 + 1.39230i −0.0322833 + 0.0559163i
$$621$$ −1.73205 3.00000i −0.0695048 0.120386i
$$622$$ 3.69615 2.13397i 0.148202 0.0855646i
$$623$$ −10.4641 −0.419235
$$624$$ −3.59808 0.232051i −0.144038 0.00928947i
$$625$$ 17.2487 0.689948
$$626$$ −11.7058 + 6.75833i −0.467857 + 0.270117i
$$627$$ −0.866025 1.50000i −0.0345857 0.0599042i
$$628$$ −0.267949 + 0.464102i −0.0106923 + 0.0185197i
$$629$$ 25.1244i 1.00177i
$$630$$ −0.633975 0.366025i −0.0252582 0.0145828i
$$631$$ 14.5526 + 8.40192i 0.579328 + 0.334475i 0.760866 0.648909i $$-0.224774\pi$$
−0.181538 + 0.983384i $$0.558108\pi$$
$$632$$ 2.07180i 0.0824117i
$$633$$ −13.0000 + 22.5167i −0.516704 + 0.894957i
$$634$$ 5.92820 + 10.2679i 0.235439 + 0.407792i
$$635$$ −9.80385 + 5.66025i −0.389054 + 0.224620i
$$636$$ −7.00000 −0.277568
$$637$$ −2.00000 + 3.00000i −0.0792429 + 0.118864i
$$638$$ 11.1962 0.443260
$$639$$ 1.90192 1.09808i 0.0752389 0.0434392i
$$640$$ −0.366025 0.633975i −0.0144684 0.0250600i
$$641$$ 15.5885 27.0000i 0.615707 1.06644i −0.374553 0.927206i $$-0.622204\pi$$
0.990260 0.139230i $$-0.0444629\pi$$
$$642$$ 10.8564i 0.428468i
$$643$$ 28.4545 + 16.4282i 1.12214 + 0.647865i 0.941945 0.335767i $$-0.108995\pi$$
0.180190 + 0.983632i $$0.442329\pi$$
$$644$$ −3.00000 1.73205i −0.118217 0.0682524i
$$645$$ 2.39230i 0.0941969i
$$646$$ −1.86603 + 3.23205i −0.0734178 + 0.127163i
$$647$$ 17.9186 + 31.0359i 0.704452 + 1.22015i 0.966889 + 0.255198i $$0.0821406\pi$$
−0.262437 + 0.964949i $$0.584526\pi$$
$$648$$ 0.866025 0.500000i 0.0340207 0.0196419i
$$649$$ 1.60770 0.0631076
$$650$$ −13.3923 8.92820i −0.525289 0.350193i
$$651$$ −2.19615 −0.0860740
$$652$$ 2.36603 1.36603i 0.0926607 0.0534977i
$$653$$ −23.3564 40.4545i −0.914007 1.58311i −0.808349 0.588704i $$-0.799638\pi$$
−0.105658 0.994403i $$-0.533695\pi$$
$$654$$ 2.36603 4.09808i 0.0925189 0.160247i
$$655$$ 10.1436i 0.396343i
$$656$$ −2.59808 1.50000i −0.101438 0.0585652i
$$657$$ −4.73205 2.73205i −0.184615 0.106587i
$$658$$ 2.46410i 0.0960607i
$$659$$ −9.30385 + 16.1147i −0.362426 + 0.627741i −0.988360 0.152136i $$-0.951385\pi$$
0.625933 + 0.779877i $$0.284718\pi$$
$$660$$ 0.633975 + 1.09808i 0.0246774 + 0.0427426i
$$661$$ 10.7321 6.19615i 0.417428 0.241002i −0.276548 0.961000i $$-0.589190\pi$$
0.693976 + 0.719998i $$0.255857\pi$$
$$662$$ −27.8564 −1.08267
$$663$$ −5.96410 12.0622i −0.231627 0.468456i
$$664$$ 0.196152 0.00761219
$$665$$ 0.633975 0.366025i 0.0245845 0.0141939i
$$666$$ −3.36603 5.83013i −0.130431 0.225913i
$$667$$ −11.1962 + 19.3923i −0.433517 + 0.750873i
$$668$$ 13.8564i 0.536120i
$$669$$ −21.1244 12.1962i −0.816715 0.471530i
$$670$$ 5.66025 + 3.26795i 0.218675 + 0.126252i
$$671$$ 9.00000i 0.347441i
$$672$$ 0.500000 0.866025i 0.0192879 0.0334077i
$$673$$ −16.3564 28.3301i −0.630493 1.09205i −0.987451 0.157926i $$-0.949519\pi$$
0.356958 0.934120i $$-0.383814\pi$$
$$674$$ 16.4545 9.50000i 0.633803 0.365926i
$$675$$ 4.46410 0.171823
$$676$$ 5.00000 + 12.0000i 0.192308 + 0.461538i
$$677$$ 36.7321 1.41173 0.705864 0.708348i $$-0.250559\pi$$
0.705864 + 0.708348i $$0.250559\pi$$
$$678$$ −13.2224 + 7.63397i −0.507804 + 0.293181i
$$679$$ 7.83013 + 13.5622i 0.300493 + 0.520469i
$$680$$ 1.36603 2.36603i 0.0523847 0.0907329i
$$681$$ 18.3923i 0.704795i
$$682$$ 3.29423 + 1.90192i 0.126143 + 0.0728284i
$$683$$ 25.6410 + 14.8038i 0.981126 + 0.566453i 0.902610 0.430459i $$-0.141648\pi$$
0.0785163 + 0.996913i $$0.474982\pi$$
$$684$$ 1.00000i 0.0382360i
$$685$$ 5.26795 9.12436i 0.201278 0.348624i
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ 17.2583 9.96410i 0.658446 0.380154i
$$688$$ −3.26795 −0.124589
$$689$$ 11.1865 + 22.6244i 0.426173 + 0.861919i
$$690$$ −2.53590 −0.0965400
$$691$$ 37.8564 21.8564i 1.44013 0.831457i 0.442268 0.896883i $$-0.354174\pi$$
0.997857 + 0.0654260i $$0.0208406\pi$$
$$692$$ 4.56218 + 7.90192i 0.173428 + 0.300386i
$$693$$ −0.866025 + 1.50000i −0.0328976 + 0.0569803i
$$694$$ 5.39230i 0.204689i
$$695$$ 7.34679 + 4.24167i 0.278680 + 0.160896i
$$696$$ −5.59808 3.23205i −0.212195 0.122511i
$$697$$ 11.1962i 0.424085i
$$698$$ 11.8564 20.5359i 0.448772 0.777295i
$$699$$ −4.56218 7.90192i −0.172557 0.298878i
$$700$$ 3.86603 2.23205i 0.146122 0.0843636i
$$701$$ −1.14359 −0.0431929 −0.0215965 0.999767i $$-0.506875\pi$$
−0.0215965 + 0.999767i $$0.506875\pi$$
$$702$$ −3.00000 2.00000i −0.113228 0.0754851i
$$703$$ 6.73205 0.253904
$$704$$ −1.50000 + 0.866025i −0.0565334 + 0.0326396i
$$705$$ 0.901924 + 1.56218i 0.0339684 + 0.0588350i
$$706$$ 4.73205 8.19615i 0.178093 0.308466i
$$707$$ 3.07180i 0.115527i
$$708$$ −0.803848 0.464102i −0.0302104 0.0174420i
$$709$$ −27.7583 16.0263i −1.04249 0.601880i −0.121950 0.992536i $$-0.538915\pi$$
−0.920536 + 0.390657i $$0.872248\pi$$
$$710$$ 1.60770i 0.0603357i
$$711$$ −1.03590 + 1.79423i −0.0388492 + 0.0672888i
$$712$$ −5.23205 9.06218i −0.196079 0.339619i
$$713$$ −6.58846 + 3.80385i −0.246740 + 0.142455i
$$714$$ 3.73205 0.139668
$$715$$ 2.53590 3.80385i 0.0948372 0.142256i
$$716$$ 11.4641 0.428434
$$717$$ −0.633975 + 0.366025i −0.0236762 + 0.0136695i
$$718$$ −1.90192 3.29423i −0.0709792 0.122940i
$$719$$ 13.2583 22.9641i 0.494452 0.856416i −0.505527 0.862811i $$-0.668702\pi$$
0.999980 + 0.00639415i $$0.00203533\pi$$
$$720$$ 0.732051i 0.0272819i
$$721$$ −12.7583 7.36603i −0.475145 0.274325i
$$722$$ 15.5885 + 9.00000i 0.580142 + 0.334945i
$$723$$ 8.00000i 0.297523i
$$724$$ 1.33013 2.30385i 0.0494338 0.0856218i
$$725$$ −14.4282 24.9904i −0.535850 0.928119i
$$726$$ −6.92820 + 4.00000i −0.257130 + 0.148454i
$$727$$ 19.3205 0.716558 0.358279 0.933615i $$-0.383364\pi$$
0.358279 + 0.933615i $$0.383364\pi$$
$$728$$ −3.59808 0.232051i −0.133354 0.00860038i
$$729$$ 1.00000 0.0370370
$$730$$ −3.46410 + 2.00000i −0.128212 + 0.0740233i
$$731$$ −6.09808 10.5622i −0.225545 0.390656i
$$732$$ 2.59808 4.50000i 0.0960277 0.166325i
$$733$$ 48.1769i 1.77945i 0.456492 + 0.889727i $$0.349106\pi$$
−0.456492 + 0.889727i $$0.650894\pi$$
$$734$$ 21.9282 + 12.6603i 0.809385 + 0.467299i
$$735$$ −0.633975 0.366025i −0.0233845 0.0135011i
$$736$$ 3.46410i 0.127688i
$$737$$ 7.73205 13.3923i 0.284814 0.493312i
$$738$$ −1.50000 2.59808i −0.0552158 0.0956365i
$$739$$ 13.1436 7.58846i 0.483495 0.279146i −0.238377 0.971173i $$-0.576615\pi$$
0.721872 + 0.692027i $$0.243282\pi$$
$$740$$ −4.92820 −0.181164
$$741$$ 3.23205 1.59808i 0.118732 0.0587068i
$$742$$ −7.00000 −0.256978
$$743$$ −12.1699 + 7.02628i −0.446469 + 0.257769i −0.706338 0.707875i $$-0.749654\pi$$
0.259869 + 0.965644i $$0.416321\pi$$
$$744$$ −1.09808 1.90192i −0.0402574 0.0697279i
$$745$$ 5.07180 8.78461i 0.185816 0.321843i
$$746$$ 9.66025i 0.353687i
$$747$$ 0.169873 + 0.0980762i 0.00621533 + 0.00358842i
$$748$$ −5.59808 3.23205i −0.204686 0.118175i
$$749$$ 10.8564i 0.396684i
$$750$$ 3.46410 6.00000i 0.126491 0.219089i
$$751$$ −9.57180 16.5788i −0.349280 0.604970i 0.636842 0.770994i $$-0.280240\pi$$
−0.986122 + 0.166024i $$0.946907\pi$$
$$752$$ −2.13397 + 1.23205i −0.0778180 + 0.0449283i
$$753$$ −13.1244 −0.478278
$$754$$ −1.50000 + 23.2583i −0.0546268 + 0.847018i
$$755$$ −3.80385 −0.138436
$$756$$ 0.866025 0.500000i 0.0314970 0.0181848i
$$757$$ 0.294229 + 0.509619i 0.0106939 + 0.0185224i 0.871323 0.490710i $$-0.163263\pi$$
−0.860629 + 0.509233i $$0.829929\pi$$
$$758$$ −14.2224 + 24.6340i −0.516582 + 0.894746i
$$759$$ 6.00000i 0.217786i
$$760$$ 0.633975 + 0.366025i 0.0229967 + 0.0132771i
$$761$$ 13.2679 + 7.66025i 0.480963 + 0.277684i 0.720818 0.693125i $$-0.243767\pi$$
−0.239855 + 0.970809i $$0.577100\pi$$
$$762$$ 15.4641i 0.560205i
$$763$$ 2.36603 4.09808i 0.0856559 0.148360i
$$764$$ 11.5622 + 20.0263i 0.418305 + 0.724525i
$$765$$ 2.36603 1.36603i 0.0855438 0.0493888i
$$766$$ 5.53590 0.200020
$$767$$ −0.215390 + 3.33975i −0.00777729 + 0.120591i
$$768$$ 1.00000 0.0360844
$$769$$ 36.6340 21.1506i 1.32105 0.762711i 0.337158 0.941448i $$-0.390534\pi$$
0.983897 + 0.178737i $$0.0572010\pi$$
$$770$$ 0.633975 + 1.09808i 0.0228469 + 0.0395719i
$$771$$ 10.3301 17.8923i 0.372030 0.644376i
$$772$$ 1.19615i 0.0430505i
$$773$$ −40.8564 23.5885i −1.46950 0.848418i −0.470088 0.882620i $$-0.655778\pi$$