# Properties

 Label 722.2.c.g.653.1 Level $722$ Weight $2$ Character 722.653 Analytic conductor $5.765$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.76519902594$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 653.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 722.653 Dual form 722.2.c.g.429.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{10} -2.00000 q^{11} -3.00000 q^{12} +(-1.50000 + 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} -6.00000 q^{18} +2.00000 q^{20} +(-4.50000 - 7.79423i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(-2.50000 + 4.33013i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.00000 q^{26} -9.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(-1.50000 + 2.59808i) q^{29} +6.00000 q^{30} +6.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(-0.500000 + 0.866025i) q^{34} +(3.00000 + 5.19615i) q^{35} +(-3.00000 - 5.19615i) q^{36} -6.00000 q^{37} -9.00000 q^{39} +(1.00000 + 1.73205i) q^{40} +(6.00000 + 10.3923i) q^{41} +(4.50000 - 7.79423i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.00000 - 1.73205i) q^{44} +12.0000 q^{45} -5.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{48} +2.00000 q^{49} +1.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-1.50000 - 2.59808i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(2.00000 + 3.46410i) q^{55} +3.00000 q^{56} -3.00000 q^{58} +(1.50000 + 2.59808i) q^{59} +(3.00000 + 5.19615i) q^{60} +(3.00000 + 5.19615i) q^{62} +(9.00000 - 15.5885i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(7.50000 - 12.9904i) q^{67} -1.00000 q^{68} -15.0000 q^{69} +(-3.00000 + 5.19615i) q^{70} +(3.00000 - 5.19615i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-3.00000 - 5.19615i) q^{74} +3.00000 q^{75} +6.00000 q^{77} +(-4.50000 - 7.79423i) q^{78} +(-6.00000 - 10.3923i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} +2.00000 q^{83} +9.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{86} -9.00000 q^{87} +2.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(6.00000 + 10.3923i) q^{90} +(4.50000 - 7.79423i) q^{91} +(-2.50000 - 4.33013i) q^{92} +(9.00000 + 15.5885i) q^{93} +8.00000 q^{94} +3.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(1.00000 + 1.73205i) q^{98} +(6.00000 - 10.3923i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} - 6 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10})$$ 2 * q + q^2 + 3 * q^3 - q^4 - 2 * q^5 - 3 * q^6 - 6 * q^7 - 2 * q^8 - 6 * q^9 $$2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} - 6 q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{10} - 4 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} - q^{16} + q^{17} - 12 q^{18} + 4 q^{20} - 9 q^{21} - 2 q^{22} - 5 q^{23} - 3 q^{24} + q^{25} - 6 q^{26} - 18 q^{27} + 3 q^{28} - 3 q^{29} + 12 q^{30} + 12 q^{31} + q^{32} - 6 q^{33} - q^{34} + 6 q^{35} - 6 q^{36} - 12 q^{37} - 18 q^{39} + 2 q^{40} + 12 q^{41} + 9 q^{42} + 10 q^{43} + 2 q^{44} + 24 q^{45} - 10 q^{46} + 8 q^{47} + 3 q^{48} + 4 q^{49} + 2 q^{50} - 3 q^{51} - 3 q^{52} - 3 q^{53} - 9 q^{54} + 4 q^{55} + 6 q^{56} - 6 q^{58} + 3 q^{59} + 6 q^{60} + 6 q^{62} + 18 q^{63} + 2 q^{64} + 12 q^{65} + 6 q^{66} + 15 q^{67} - 2 q^{68} - 30 q^{69} - 6 q^{70} + 6 q^{72} + 11 q^{73} - 6 q^{74} + 6 q^{75} + 12 q^{77} - 9 q^{78} - 12 q^{79} - 2 q^{80} - 9 q^{81} - 12 q^{82} + 4 q^{83} + 18 q^{84} + 2 q^{85} - 10 q^{86} - 18 q^{87} + 4 q^{88} + 6 q^{89} + 12 q^{90} + 9 q^{91} - 5 q^{92} + 18 q^{93} + 16 q^{94} + 6 q^{96} + 12 q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100})$$ 2 * q + q^2 + 3 * q^3 - q^4 - 2 * q^5 - 3 * q^6 - 6 * q^7 - 2 * q^8 - 6 * q^9 + 2 * q^10 - 4 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 - q^16 + q^17 - 12 * q^18 + 4 * q^20 - 9 * q^21 - 2 * q^22 - 5 * q^23 - 3 * q^24 + q^25 - 6 * q^26 - 18 * q^27 + 3 * q^28 - 3 * q^29 + 12 * q^30 + 12 * q^31 + q^32 - 6 * q^33 - q^34 + 6 * q^35 - 6 * q^36 - 12 * q^37 - 18 * q^39 + 2 * q^40 + 12 * q^41 + 9 * q^42 + 10 * q^43 + 2 * q^44 + 24 * q^45 - 10 * q^46 + 8 * q^47 + 3 * q^48 + 4 * q^49 + 2 * q^50 - 3 * q^51 - 3 * q^52 - 3 * q^53 - 9 * q^54 + 4 * q^55 + 6 * q^56 - 6 * q^58 + 3 * q^59 + 6 * q^60 + 6 * q^62 + 18 * q^63 + 2 * q^64 + 12 * q^65 + 6 * q^66 + 15 * q^67 - 2 * q^68 - 30 * q^69 - 6 * q^70 + 6 * q^72 + 11 * q^73 - 6 * q^74 + 6 * q^75 + 12 * q^77 - 9 * q^78 - 12 * q^79 - 2 * q^80 - 9 * q^81 - 12 * q^82 + 4 * q^83 + 18 * q^84 + 2 * q^85 - 10 * q^86 - 18 * q^87 + 4 * q^88 + 6 * q^89 + 12 * q^90 + 9 * q^91 - 5 * q^92 + 18 * q^93 + 16 * q^94 + 6 * q^96 + 12 * q^97 + 2 * q^98 + 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$$.

 $$n$$ $$363$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i $$0.166667\pi$$
1.00000i $$0.5\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ −1.50000 + 2.59808i −0.612372 + 1.06066i
$$7$$ −3.00000 −1.13389 −0.566947 0.823754i $$-0.691875\pi$$
−0.566947 + 0.823754i $$0.691875\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −3.00000 + 5.19615i −1.00000 + 1.73205i
$$10$$ 1.00000 1.73205i 0.316228 0.547723i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ −3.00000 −0.866025
$$13$$ −1.50000 + 2.59808i −0.416025 + 0.720577i −0.995535 0.0943882i $$-0.969911\pi$$
0.579510 + 0.814965i $$0.303244\pi$$
$$14$$ −1.50000 2.59808i −0.400892 0.694365i
$$15$$ 3.00000 5.19615i 0.774597 1.34164i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0.500000 + 0.866025i 0.121268 + 0.210042i 0.920268 0.391289i $$-0.127971\pi$$
−0.799000 + 0.601331i $$0.794637\pi$$
$$18$$ −6.00000 −1.41421
$$19$$ 0 0
$$20$$ 2.00000 0.447214
$$21$$ −4.50000 7.79423i −0.981981 1.70084i
$$22$$ −1.00000 1.73205i −0.213201 0.369274i
$$23$$ −2.50000 + 4.33013i −0.521286 + 0.902894i 0.478407 + 0.878138i $$0.341214\pi$$
−0.999694 + 0.0247559i $$0.992119\pi$$
$$24$$ −1.50000 2.59808i −0.306186 0.530330i
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ −3.00000 −0.588348
$$27$$ −9.00000 −1.73205
$$28$$ 1.50000 2.59808i 0.283473 0.490990i
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 6.00000 1.09545
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ −0.500000 + 0.866025i −0.0857493 + 0.148522i
$$35$$ 3.00000 + 5.19615i 0.507093 + 0.878310i
$$36$$ −3.00000 5.19615i −0.500000 0.866025i
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 0 0
$$39$$ −9.00000 −1.44115
$$40$$ 1.00000 + 1.73205i 0.158114 + 0.273861i
$$41$$ 6.00000 + 10.3923i 0.937043 + 1.62301i 0.770950 + 0.636895i $$0.219782\pi$$
0.166092 + 0.986110i $$0.446885\pi$$
$$42$$ 4.50000 7.79423i 0.694365 1.20268i
$$43$$ 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i $$0.109358\pi$$
−0.179069 + 0.983836i $$0.557309\pi$$
$$44$$ 1.00000 1.73205i 0.150756 0.261116i
$$45$$ 12.0000 1.78885
$$46$$ −5.00000 −0.737210
$$47$$ 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i $$-0.635032\pi$$
0.995066 0.0992202i $$-0.0316348\pi$$
$$48$$ 1.50000 2.59808i 0.216506 0.375000i
$$49$$ 2.00000 0.285714
$$50$$ 1.00000 0.141421
$$51$$ −1.50000 + 2.59808i −0.210042 + 0.363803i
$$52$$ −1.50000 2.59808i −0.208013 0.360288i
$$53$$ −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i $$-0.899391\pi$$
0.744423 + 0.667708i $$0.232725\pi$$
$$54$$ −4.50000 7.79423i −0.612372 1.06066i
$$55$$ 2.00000 + 3.46410i 0.269680 + 0.467099i
$$56$$ 3.00000 0.400892
$$57$$ 0 0
$$58$$ −3.00000 −0.393919
$$59$$ 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i $$-0.104104\pi$$
−0.751710 + 0.659494i $$0.770771\pi$$
$$60$$ 3.00000 + 5.19615i 0.387298 + 0.670820i
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 3.00000 + 5.19615i 0.381000 + 0.659912i
$$63$$ 9.00000 15.5885i 1.13389 1.96396i
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 0.744208
$$66$$ 3.00000 5.19615i 0.369274 0.639602i
$$67$$ 7.50000 12.9904i 0.916271 1.58703i 0.111241 0.993793i $$-0.464517\pi$$
0.805030 0.593234i $$-0.202149\pi$$
$$68$$ −1.00000 −0.121268
$$69$$ −15.0000 −1.80579
$$70$$ −3.00000 + 5.19615i −0.358569 + 0.621059i
$$71$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 3.00000 5.19615i 0.353553 0.612372i
$$73$$ 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i $$0.0559458\pi$$
−0.340868 + 0.940111i $$0.610721\pi$$
$$74$$ −3.00000 5.19615i −0.348743 0.604040i
$$75$$ 3.00000 0.346410
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ −4.50000 7.79423i −0.509525 0.882523i
$$79$$ −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i $$-0.930788\pi$$
0.301401 0.953498i $$-0.402546\pi$$
$$80$$ −1.00000 + 1.73205i −0.111803 + 0.193649i
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ −6.00000 + 10.3923i −0.662589 + 1.14764i
$$83$$ 2.00000 0.219529 0.109764 0.993958i $$-0.464990\pi$$
0.109764 + 0.993958i $$0.464990\pi$$
$$84$$ 9.00000 0.981981
$$85$$ 1.00000 1.73205i 0.108465 0.187867i
$$86$$ −5.00000 + 8.66025i −0.539164 + 0.933859i
$$87$$ −9.00000 −0.964901
$$88$$ 2.00000 0.213201
$$89$$ 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i $$-0.730322\pi$$
0.980071 + 0.198650i $$0.0636557\pi$$
$$90$$ 6.00000 + 10.3923i 0.632456 + 1.09545i
$$91$$ 4.50000 7.79423i 0.471728 0.817057i
$$92$$ −2.50000 4.33013i −0.260643 0.451447i
$$93$$ 9.00000 + 15.5885i 0.933257 + 1.61645i
$$94$$ 8.00000 0.825137
$$95$$ 0 0
$$96$$ 3.00000 0.306186
$$97$$ 6.00000 + 10.3923i 0.609208 + 1.05518i 0.991371 + 0.131084i $$0.0418458\pi$$
−0.382164 + 0.924095i $$0.624821\pi$$
$$98$$ 1.00000 + 1.73205i 0.101015 + 0.174964i
$$99$$ 6.00000 10.3923i 0.603023 1.04447i
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i $$-0.999089\pi$$
0.502477 + 0.864590i $$0.332422\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ 1.50000 2.59808i 0.147087 0.254762i
$$105$$ −9.00000 + 15.5885i −0.878310 + 1.52128i
$$106$$ −3.00000 −0.291386
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 4.50000 7.79423i 0.433013 0.750000i
$$109$$ 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i $$-0.120775\pi$$
−0.785203 + 0.619238i $$0.787442\pi$$
$$110$$ −2.00000 + 3.46410i −0.190693 + 0.330289i
$$111$$ −9.00000 15.5885i −0.854242 1.47959i
$$112$$ 1.50000 + 2.59808i 0.141737 + 0.245495i
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 10.0000 0.932505
$$116$$ −1.50000 2.59808i −0.139272 0.241225i
$$117$$ −9.00000 15.5885i −0.832050 1.44115i
$$118$$ −1.50000 + 2.59808i −0.138086 + 0.239172i
$$119$$ −1.50000 2.59808i −0.137505 0.238165i
$$120$$ −3.00000 + 5.19615i −0.273861 + 0.474342i
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ −18.0000 + 31.1769i −1.62301 + 2.81113i
$$124$$ −3.00000 + 5.19615i −0.269408 + 0.466628i
$$125$$ −12.0000 −1.07331
$$126$$ 18.0000 1.60357
$$127$$ 6.00000 10.3923i 0.532414 0.922168i −0.466870 0.884326i $$-0.654618\pi$$
0.999284 0.0378419i $$-0.0120483\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −15.0000 + 25.9808i −1.32068 + 2.28748i
$$130$$ 3.00000 + 5.19615i 0.263117 + 0.455733i
$$131$$ −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i $$-0.957196\pi$$
0.379379 0.925241i $$-0.376138\pi$$
$$132$$ 6.00000 0.522233
$$133$$ 0 0
$$134$$ 15.0000 1.29580
$$135$$ 9.00000 + 15.5885i 0.774597 + 1.34164i
$$136$$ −0.500000 0.866025i −0.0428746 0.0742611i
$$137$$ −9.50000 + 16.4545i −0.811640 + 1.40580i 0.100076 + 0.994980i $$0.468091\pi$$
−0.911716 + 0.410822i $$0.865242\pi$$
$$138$$ −7.50000 12.9904i −0.638442 1.10581i
$$139$$ −3.00000 + 5.19615i −0.254457 + 0.440732i −0.964748 0.263176i $$-0.915230\pi$$
0.710291 + 0.703908i $$0.248563\pi$$
$$140$$ −6.00000 −0.507093
$$141$$ 24.0000 2.02116
$$142$$ 0 0
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 6.00000 0.500000
$$145$$ 6.00000 0.498273
$$146$$ −5.50000 + 9.52628i −0.455183 + 0.788400i
$$147$$ 3.00000 + 5.19615i 0.247436 + 0.428571i
$$148$$ 3.00000 5.19615i 0.246598 0.427121i
$$149$$ 4.00000 + 6.92820i 0.327693 + 0.567581i 0.982054 0.188602i $$-0.0603956\pi$$
−0.654361 + 0.756182i $$0.727062\pi$$
$$150$$ 1.50000 + 2.59808i 0.122474 + 0.212132i
$$151$$ 18.0000 1.46482 0.732410 0.680864i $$-0.238396\pi$$
0.732410 + 0.680864i $$0.238396\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 3.00000 + 5.19615i 0.241747 + 0.418718i
$$155$$ −6.00000 10.3923i −0.481932 0.834730i
$$156$$ 4.50000 7.79423i 0.360288 0.624038i
$$157$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$158$$ 6.00000 10.3923i 0.477334 0.826767i
$$159$$ −9.00000 −0.713746
$$160$$ −2.00000 −0.158114
$$161$$ 7.50000 12.9904i 0.591083 1.02379i
$$162$$ 4.50000 7.79423i 0.353553 0.612372i
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ −12.0000 −0.937043
$$165$$ −6.00000 + 10.3923i −0.467099 + 0.809040i
$$166$$ 1.00000 + 1.73205i 0.0776151 + 0.134433i
$$167$$ −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i $$-0.987025\pi$$
0.534875 + 0.844931i $$0.320359\pi$$
$$168$$ 4.50000 + 7.79423i 0.347183 + 0.601338i
$$169$$ 2.00000 + 3.46410i 0.153846 + 0.266469i
$$170$$ 2.00000 0.153393
$$171$$ 0 0
$$172$$ −10.0000 −0.762493
$$173$$ −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i $$-0.926793\pi$$
0.289412 0.957205i $$-0.406540\pi$$
$$174$$ −4.50000 7.79423i −0.341144 0.590879i
$$175$$ −1.50000 + 2.59808i −0.113389 + 0.196396i
$$176$$ 1.00000 + 1.73205i 0.0753778 + 0.130558i
$$177$$ −4.50000 + 7.79423i −0.338241 + 0.585850i
$$178$$ 6.00000 0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ −6.00000 + 10.3923i −0.447214 + 0.774597i
$$181$$ 9.00000 15.5885i 0.668965 1.15868i −0.309229 0.950988i $$-0.600071\pi$$
0.978194 0.207693i $$-0.0665956\pi$$
$$182$$ 9.00000 0.667124
$$183$$ 0 0
$$184$$ 2.50000 4.33013i 0.184302 0.319221i
$$185$$ 6.00000 + 10.3923i 0.441129 + 0.764057i
$$186$$ −9.00000 + 15.5885i −0.659912 + 1.14300i
$$187$$ −1.00000 1.73205i −0.0731272 0.126660i
$$188$$ 4.00000 + 6.92820i 0.291730 + 0.505291i
$$189$$ 27.0000 1.96396
$$190$$ 0 0
$$191$$ −11.0000 −0.795932 −0.397966 0.917400i $$-0.630284\pi$$
−0.397966 + 0.917400i $$0.630284\pi$$
$$192$$ 1.50000 + 2.59808i 0.108253 + 0.187500i
$$193$$ 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i $$-0.0973836\pi$$
−0.737620 + 0.675216i $$0.764050\pi$$
$$194$$ −6.00000 + 10.3923i −0.430775 + 0.746124i
$$195$$ 9.00000 + 15.5885i 0.644503 + 1.11631i
$$196$$ −1.00000 + 1.73205i −0.0714286 + 0.123718i
$$197$$ 4.00000 0.284988 0.142494 0.989796i $$-0.454488\pi$$
0.142494 + 0.989796i $$0.454488\pi$$
$$198$$ 12.0000 0.852803
$$199$$ 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i $$-0.753524\pi$$
0.963001 + 0.269498i $$0.0868577\pi$$
$$200$$ −0.500000 + 0.866025i −0.0353553 + 0.0612372i
$$201$$ 45.0000 3.17406
$$202$$ −10.0000 −0.703598
$$203$$ 4.50000 7.79423i 0.315838 0.547048i
$$204$$ −1.50000 2.59808i −0.105021 0.181902i
$$205$$ 12.0000 20.7846i 0.838116 1.45166i
$$206$$ −3.00000 5.19615i −0.209020 0.362033i
$$207$$ −15.0000 25.9808i −1.04257 1.80579i
$$208$$ 3.00000 0.208013
$$209$$ 0 0
$$210$$ −18.0000 −1.24212
$$211$$ 1.50000 + 2.59808i 0.103264 + 0.178859i 0.913028 0.407898i $$-0.133738\pi$$
−0.809763 + 0.586756i $$0.800405\pi$$
$$212$$ −1.50000 2.59808i −0.103020 0.178437i
$$213$$ 0 0
$$214$$ 1.50000 + 2.59808i 0.102538 + 0.177601i
$$215$$ 10.0000 17.3205i 0.681994 1.18125i
$$216$$ 9.00000 0.612372
$$217$$ −18.0000 −1.22192
$$218$$ −1.50000 + 2.59808i −0.101593 + 0.175964i
$$219$$ −16.5000 + 28.5788i −1.11497 + 1.93118i
$$220$$ −4.00000 −0.269680
$$221$$ −3.00000 −0.201802
$$222$$ 9.00000 15.5885i 0.604040 1.04623i
$$223$$ 9.00000 + 15.5885i 0.602685 + 1.04388i 0.992413 + 0.122950i $$0.0392356\pi$$
−0.389728 + 0.920930i $$0.627431\pi$$
$$224$$ −1.50000 + 2.59808i −0.100223 + 0.173591i
$$225$$ 3.00000 + 5.19615i 0.200000 + 0.346410i
$$226$$ −6.00000 10.3923i −0.399114 0.691286i
$$227$$ −3.00000 −0.199117 −0.0995585 0.995032i $$-0.531743\pi$$
−0.0995585 + 0.995032i $$0.531743\pi$$
$$228$$ 0 0
$$229$$ −12.0000 −0.792982 −0.396491 0.918039i $$-0.629772\pi$$
−0.396491 + 0.918039i $$0.629772\pi$$
$$230$$ 5.00000 + 8.66025i 0.329690 + 0.571040i
$$231$$ 9.00000 + 15.5885i 0.592157 + 1.02565i
$$232$$ 1.50000 2.59808i 0.0984798 0.170572i
$$233$$ −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i $$-0.318310\pi$$
−0.998886 + 0.0471787i $$0.984977\pi$$
$$234$$ 9.00000 15.5885i 0.588348 1.01905i
$$235$$ −16.0000 −1.04372
$$236$$ −3.00000 −0.195283
$$237$$ 18.0000 31.1769i 1.16923 2.02516i
$$238$$ 1.50000 2.59808i 0.0972306 0.168408i
$$239$$ 1.00000 0.0646846 0.0323423 0.999477i $$-0.489703\pi$$
0.0323423 + 0.999477i $$0.489703\pi$$
$$240$$ −6.00000 −0.387298
$$241$$ 12.0000 20.7846i 0.772988 1.33885i −0.162930 0.986638i $$-0.552095\pi$$
0.935918 0.352217i $$-0.114572\pi$$
$$242$$ −3.50000 6.06218i −0.224989 0.389692i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −2.00000 3.46410i −0.127775 0.221313i
$$246$$ −36.0000 −2.29528
$$247$$ 0 0
$$248$$ −6.00000 −0.381000
$$249$$ 3.00000 + 5.19615i 0.190117 + 0.329293i
$$250$$ −6.00000 10.3923i −0.379473 0.657267i
$$251$$ 10.0000 17.3205i 0.631194 1.09326i −0.356113 0.934443i $$-0.615898\pi$$
0.987308 0.158818i $$-0.0507683\pi$$
$$252$$ 9.00000 + 15.5885i 0.566947 + 0.981981i
$$253$$ 5.00000 8.66025i 0.314347 0.544466i
$$254$$ 12.0000 0.752947
$$255$$ 6.00000 0.375735
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i $$0.356405\pi$$
−0.997374 + 0.0724199i $$0.976928\pi$$
$$258$$ −30.0000 −1.86772
$$259$$ 18.0000 1.11847
$$260$$ −3.00000 + 5.19615i −0.186052 + 0.322252i
$$261$$ −9.00000 15.5885i −0.557086 0.964901i
$$262$$ 7.00000 12.1244i 0.432461 0.749045i
$$263$$ 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i $$-0.0873367\pi$$
−0.715944 + 0.698158i $$0.754003\pi$$
$$264$$ 3.00000 + 5.19615i 0.184637 + 0.319801i
$$265$$ 6.00000 0.368577
$$266$$ 0 0
$$267$$ 18.0000 1.10158
$$268$$ 7.50000 + 12.9904i 0.458135 + 0.793514i
$$269$$ −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i $$-0.225219\pi$$
−0.942871 + 0.333157i $$0.891886\pi$$
$$270$$ −9.00000 + 15.5885i −0.547723 + 0.948683i
$$271$$ 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i $$-0.0582339\pi$$
−0.649211 + 0.760609i $$0.724901\pi$$
$$272$$ 0.500000 0.866025i 0.0303170 0.0525105i
$$273$$ 27.0000 1.63411
$$274$$ −19.0000 −1.14783
$$275$$ −1.00000 + 1.73205i −0.0603023 + 0.104447i
$$276$$ 7.50000 12.9904i 0.451447 0.781929i
$$277$$ 30.0000 1.80253 0.901263 0.433273i $$-0.142641\pi$$
0.901263 + 0.433273i $$0.142641\pi$$
$$278$$ −6.00000 −0.359856
$$279$$ −18.0000 + 31.1769i −1.07763 + 1.86651i
$$280$$ −3.00000 5.19615i −0.179284 0.310530i
$$281$$ 6.00000 10.3923i 0.357930 0.619953i −0.629685 0.776851i $$-0.716816\pi$$
0.987615 + 0.156898i $$0.0501493\pi$$
$$282$$ 12.0000 + 20.7846i 0.714590 + 1.23771i
$$283$$ 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i $$-0.0300609\pi$$
−0.579437 + 0.815017i $$0.696728\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 6.00000 0.354787
$$287$$ −18.0000 31.1769i −1.06251 1.84032i
$$288$$ 3.00000 + 5.19615i 0.176777 + 0.306186i
$$289$$ 8.00000 13.8564i 0.470588 0.815083i
$$290$$ 3.00000 + 5.19615i 0.176166 + 0.305129i
$$291$$ −18.0000 + 31.1769i −1.05518 + 1.82762i
$$292$$ −11.0000 −0.643726
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ −3.00000 + 5.19615i −0.174964 + 0.303046i
$$295$$ 3.00000 5.19615i 0.174667 0.302532i
$$296$$ 6.00000 0.348743
$$297$$ 18.0000 1.04447
$$298$$ −4.00000 + 6.92820i −0.231714 + 0.401340i
$$299$$ −7.50000 12.9904i −0.433736 0.751253i
$$300$$ −1.50000 + 2.59808i −0.0866025 + 0.150000i
$$301$$ −15.0000 25.9808i −0.864586 1.49751i
$$302$$ 9.00000 + 15.5885i 0.517892 + 0.897015i
$$303$$ −30.0000 −1.72345
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −3.00000 5.19615i −0.171499 0.297044i
$$307$$ 6.00000 + 10.3923i 0.342438 + 0.593120i 0.984885 0.173210i $$-0.0554140\pi$$
−0.642447 + 0.766330i $$0.722081\pi$$
$$308$$ −3.00000 + 5.19615i −0.170941 + 0.296078i
$$309$$ −9.00000 15.5885i −0.511992 0.886796i
$$310$$ 6.00000 10.3923i 0.340777 0.590243i
$$311$$ −11.0000 −0.623753 −0.311876 0.950123i $$-0.600957\pi$$
−0.311876 + 0.950123i $$0.600957\pi$$
$$312$$ 9.00000 0.509525
$$313$$ −10.5000 + 18.1865i −0.593495 + 1.02796i 0.400262 + 0.916401i $$0.368919\pi$$
−0.993757 + 0.111563i $$0.964414\pi$$
$$314$$ 0 0
$$315$$ −36.0000 −2.02837
$$316$$ 12.0000 0.675053
$$317$$ −16.5000 + 28.5788i −0.926732 + 1.60515i −0.137981 + 0.990435i $$0.544061\pi$$
−0.788751 + 0.614713i $$0.789272\pi$$
$$318$$ −4.50000 7.79423i −0.252347 0.437079i
$$319$$ 3.00000 5.19615i 0.167968 0.290929i
$$320$$ −1.00000 1.73205i −0.0559017 0.0968246i
$$321$$ 4.50000 + 7.79423i 0.251166 + 0.435031i
$$322$$ 15.0000 0.835917
$$323$$ 0 0
$$324$$ 9.00000 0.500000
$$325$$ 1.50000 + 2.59808i 0.0832050 + 0.144115i
$$326$$ −3.00000 5.19615i −0.166155 0.287788i
$$327$$ −4.50000 + 7.79423i −0.248851 + 0.431022i
$$328$$ −6.00000 10.3923i −0.331295 0.573819i
$$329$$ −12.0000 + 20.7846i −0.661581 + 1.14589i
$$330$$ −12.0000 −0.660578
$$331$$ −9.00000 −0.494685 −0.247342 0.968928i $$-0.579557\pi$$
−0.247342 + 0.968928i $$0.579557\pi$$
$$332$$ −1.00000 + 1.73205i −0.0548821 + 0.0950586i
$$333$$ 18.0000 31.1769i 0.986394 1.70848i
$$334$$ −12.0000 −0.656611
$$335$$ −30.0000 −1.63908
$$336$$ −4.50000 + 7.79423i −0.245495 + 0.425210i
$$337$$ 9.00000 + 15.5885i 0.490261 + 0.849157i 0.999937 0.0112091i $$-0.00356804\pi$$
−0.509676 + 0.860366i $$0.670235\pi$$
$$338$$ −2.00000 + 3.46410i −0.108786 + 0.188422i
$$339$$ −18.0000 31.1769i −0.977626 1.69330i
$$340$$ 1.00000 + 1.73205i 0.0542326 + 0.0939336i
$$341$$ −12.0000 −0.649836
$$342$$ 0 0
$$343$$ 15.0000 0.809924
$$344$$ −5.00000 8.66025i −0.269582 0.466930i
$$345$$ 15.0000 + 25.9808i 0.807573 + 1.39876i
$$346$$ 9.00000 15.5885i 0.483843 0.838041i
$$347$$ −8.00000 13.8564i −0.429463 0.743851i 0.567363 0.823468i $$-0.307964\pi$$
−0.996826 + 0.0796169i $$0.974630\pi$$
$$348$$ 4.50000 7.79423i 0.241225 0.417815i
$$349$$ 28.0000 1.49881 0.749403 0.662114i $$-0.230341\pi$$
0.749403 + 0.662114i $$0.230341\pi$$
$$350$$ −3.00000 −0.160357
$$351$$ 13.5000 23.3827i 0.720577 1.24808i
$$352$$ −1.00000 + 1.73205i −0.0533002 + 0.0923186i
$$353$$ −31.0000 −1.64996 −0.824982 0.565159i $$-0.808815\pi$$
−0.824982 + 0.565159i $$0.808815\pi$$
$$354$$ −9.00000 −0.478345
$$355$$ 0 0
$$356$$ 3.00000 + 5.19615i 0.159000 + 0.275396i
$$357$$ 4.50000 7.79423i 0.238165 0.412514i
$$358$$ 6.00000 + 10.3923i 0.317110 + 0.549250i
$$359$$ −9.50000 16.4545i −0.501391 0.868434i −0.999999 0.00160673i $$-0.999489\pi$$
0.498608 0.866828i $$-0.333845\pi$$
$$360$$ −12.0000 −0.632456
$$361$$ 0 0
$$362$$ 18.0000 0.946059
$$363$$ −10.5000 18.1865i −0.551107 0.954545i
$$364$$ 4.50000 + 7.79423i 0.235864 + 0.408529i
$$365$$ 11.0000 19.0526i 0.575766 0.997257i
$$366$$ 0 0
$$367$$ −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i $$-0.900289\pi$$
0.742538 + 0.669804i $$0.233622\pi$$
$$368$$ 5.00000 0.260643
$$369$$ −72.0000 −3.74817
$$370$$ −6.00000 + 10.3923i −0.311925 + 0.540270i
$$371$$ 4.50000 7.79423i 0.233628 0.404656i
$$372$$ −18.0000 −0.933257
$$373$$ 21.0000 1.08734 0.543669 0.839299i $$-0.317035\pi$$
0.543669 + 0.839299i $$0.317035\pi$$
$$374$$ 1.00000 1.73205i 0.0517088 0.0895622i
$$375$$ −18.0000 31.1769i −0.929516 1.60997i
$$376$$ −4.00000 + 6.92820i −0.206284 + 0.357295i
$$377$$ −4.50000 7.79423i −0.231762 0.401423i
$$378$$ 13.5000 + 23.3827i 0.694365 + 1.20268i
$$379$$ −3.00000 −0.154100 −0.0770498 0.997027i $$-0.524550\pi$$
−0.0770498 + 0.997027i $$0.524550\pi$$
$$380$$ 0 0
$$381$$ 36.0000 1.84434
$$382$$ −5.50000 9.52628i −0.281404 0.487407i
$$383$$ 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i $$-0.0145596\pi$$
−0.539076 + 0.842257i $$0.681226\pi$$
$$384$$ −1.50000 + 2.59808i −0.0765466 + 0.132583i
$$385$$ −6.00000 10.3923i −0.305788 0.529641i
$$386$$ −3.00000 + 5.19615i −0.152696 + 0.264477i
$$387$$ −60.0000 −3.04997
$$388$$ −12.0000 −0.609208
$$389$$ −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i $$0.395740\pi$$
−0.980842 + 0.194804i $$0.937593\pi$$
$$390$$ −9.00000 + 15.5885i −0.455733 + 0.789352i
$$391$$ −5.00000 −0.252861
$$392$$ −2.00000 −0.101015
$$393$$ 21.0000 36.3731i 1.05931 1.83478i
$$394$$ 2.00000 + 3.46410i 0.100759 + 0.174519i
$$395$$ −12.0000 + 20.7846i −0.603786 + 1.04579i
$$396$$ 6.00000 + 10.3923i 0.301511 + 0.522233i
$$397$$ −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i $$-0.182649\pi$$
−0.890028 + 0.455905i $$0.849316\pi$$
$$398$$ 7.00000 0.350878
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i $$0.188949\pi$$
0.0699455 + 0.997551i $$0.477717\pi$$
$$402$$ 22.5000 + 38.9711i 1.12220 + 1.94370i
$$403$$ −9.00000 + 15.5885i −0.448322 + 0.776516i
$$404$$ −5.00000 8.66025i −0.248759 0.430864i
$$405$$ −9.00000 + 15.5885i −0.447214 + 0.774597i
$$406$$ 9.00000 0.446663
$$407$$ 12.0000 0.594818
$$408$$ 1.50000 2.59808i 0.0742611 0.128624i
$$409$$ 3.00000 5.19615i 0.148340 0.256933i −0.782274 0.622935i $$-0.785940\pi$$
0.930614 + 0.366002i $$0.119274\pi$$
$$410$$ 24.0000 1.18528
$$411$$ −57.0000 −2.81160
$$412$$ 3.00000 5.19615i 0.147799 0.255996i
$$413$$ −4.50000 7.79423i −0.221431 0.383529i
$$414$$ 15.0000 25.9808i 0.737210 1.27688i
$$415$$ −2.00000 3.46410i −0.0981761 0.170046i
$$416$$ 1.50000 + 2.59808i 0.0735436 + 0.127381i
$$417$$ −18.0000 −0.881464
$$418$$ 0 0
$$419$$ −14.0000 −0.683945 −0.341972 0.939710i $$-0.611095\pi$$
−0.341972 + 0.939710i $$0.611095\pi$$
$$420$$ −9.00000 15.5885i −0.439155 0.760639i
$$421$$ −13.5000 23.3827i −0.657950 1.13960i −0.981146 0.193270i $$-0.938091\pi$$
0.323196 0.946332i $$-0.395243\pi$$
$$422$$ −1.50000 + 2.59808i −0.0730189 + 0.126472i
$$423$$ 24.0000 + 41.5692i 1.16692 + 2.02116i
$$424$$ 1.50000 2.59808i 0.0728464 0.126174i
$$425$$ 1.00000 0.0485071
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1.50000 + 2.59808i −0.0725052 + 0.125583i
$$429$$ 18.0000 0.869048
$$430$$ 20.0000 0.964486
$$431$$ 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i $$-0.637159\pi$$
0.995706 0.0925683i $$-0.0295076\pi$$
$$432$$ 4.50000 + 7.79423i 0.216506 + 0.375000i
$$433$$ 15.0000 25.9808i 0.720854 1.24856i −0.239804 0.970821i $$-0.577083\pi$$
0.960658 0.277734i $$-0.0895835\pi$$
$$434$$ −9.00000 15.5885i −0.432014 0.748270i
$$435$$ 9.00000 + 15.5885i 0.431517 + 0.747409i
$$436$$ −3.00000 −0.143674
$$437$$ 0 0
$$438$$ −33.0000 −1.57680
$$439$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ −2.00000 3.46410i −0.0953463 0.165145i
$$441$$ −6.00000 + 10.3923i −0.285714 + 0.494872i
$$442$$ −1.50000 2.59808i −0.0713477 0.123578i
$$443$$ 11.0000 19.0526i 0.522626 0.905214i −0.477028 0.878888i $$-0.658286\pi$$
0.999653 0.0263261i $$-0.00838082\pi$$
$$444$$ 18.0000 0.854242
$$445$$ −12.0000 −0.568855
$$446$$ −9.00000 + 15.5885i −0.426162 + 0.738135i
$$447$$ −12.0000 + 20.7846i −0.567581 + 0.983078i
$$448$$ −3.00000 −0.141737
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ −3.00000 + 5.19615i −0.141421 + 0.244949i
$$451$$ −12.0000 20.7846i −0.565058 0.978709i
$$452$$ 6.00000 10.3923i 0.282216 0.488813i
$$453$$ 27.0000 + 46.7654i 1.26857 + 2.19723i
$$454$$ −1.50000 2.59808i −0.0703985 0.121934i
$$455$$ −18.0000 −0.843853
$$456$$ 0 0
$$457$$ 1.00000 0.0467780 0.0233890 0.999726i $$-0.492554\pi$$
0.0233890 + 0.999726i $$0.492554\pi$$
$$458$$ −6.00000 10.3923i −0.280362 0.485601i
$$459$$ −4.50000 7.79423i −0.210042 0.363803i
$$460$$ −5.00000 + 8.66025i −0.233126 + 0.403786i
$$461$$ −2.00000 3.46410i −0.0931493 0.161339i 0.815685 0.578496i $$-0.196360\pi$$
−0.908835 + 0.417156i $$0.863027\pi$$
$$462$$ −9.00000 + 15.5885i −0.418718 + 0.725241i
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ 3.00000 0.139272
$$465$$ 18.0000 31.1769i 0.834730 1.44579i
$$466$$ 7.00000 12.1244i 0.324269 0.561650i
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 18.0000 0.832050
$$469$$ −22.5000 + 38.9711i −1.03895 + 1.79952i
$$470$$ −8.00000 13.8564i −0.369012 0.639148i
$$471$$ 0 0
$$472$$ −1.50000 2.59808i −0.0690431 0.119586i
$$473$$ −10.0000 17.3205i −0.459800 0.796398i
$$474$$ 36.0000 1.65353
$$475$$ 0 0
$$476$$ 3.00000 0.137505
$$477$$ −9.00000 15.5885i −0.412082 0.713746i
$$478$$ 0.500000 + 0.866025i 0.0228695 + 0.0396111i
$$479$$ 20.0000 34.6410i 0.913823 1.58279i 0.105208 0.994450i $$-0.466449\pi$$
0.808615 0.588338i $$-0.200218\pi$$
$$480$$ −3.00000 5.19615i −0.136931 0.237171i
$$481$$ 9.00000 15.5885i 0.410365 0.710772i
$$482$$ 24.0000 1.09317
$$483$$ 45.0000 2.04757
$$484$$ 3.50000 6.06218i 0.159091 0.275554i
$$485$$ 12.0000 20.7846i 0.544892 0.943781i
$$486$$ 0 0
$$487$$ 18.0000 0.815658 0.407829 0.913058i $$-0.366286\pi$$
0.407829 + 0.913058i $$0.366286\pi$$
$$488$$ 0 0
$$489$$ −9.00000 15.5885i −0.406994 0.704934i
$$490$$ 2.00000 3.46410i 0.0903508 0.156492i
$$491$$ −4.00000 6.92820i −0.180517 0.312665i 0.761539 0.648119i $$-0.224444\pi$$
−0.942057 + 0.335453i $$0.891111\pi$$
$$492$$ −18.0000 31.1769i −0.811503 1.40556i
$$493$$ −3.00000 −0.135113
$$494$$ 0 0
$$495$$ −24.0000 −1.07872
$$496$$ −3.00000 5.19615i −0.134704 0.233314i
$$497$$ 0 0
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ −9.00000 15.5885i −0.402895 0.697835i 0.591179 0.806541i $$-0.298663\pi$$
−0.994074 + 0.108705i $$0.965329\pi$$
$$500$$ 6.00000 10.3923i 0.268328 0.464758i
$$501$$ −36.0000 −1.60836
$$502$$ 20.0000 0.892644
$$503$$ −0.500000 + 0.866025i −0.0222939 + 0.0386142i −0.876957 0.480569i $$-0.840430\pi$$
0.854663 + 0.519183i $$0.173764\pi$$
$$504$$ −9.00000 + 15.5885i −0.400892 + 0.694365i
$$505$$ 20.0000 0.889988
$$506$$ 10.0000 0.444554
$$507$$ −6.00000 + 10.3923i −0.266469 + 0.461538i
$$508$$ 6.00000 + 10.3923i 0.266207 + 0.461084i
$$509$$ 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i $$-0.702719\pi$$
0.993593 + 0.113020i $$0.0360525\pi$$
$$510$$ 3.00000 + 5.19615i 0.132842 + 0.230089i
$$511$$ −16.5000 28.5788i −0.729917 1.26425i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ 6.00000 + 10.3923i 0.264392 + 0.457940i
$$516$$ −15.0000 25.9808i −0.660338 1.14374i
$$517$$ −8.00000 + 13.8564i −0.351840 + 0.609404i
$$518$$ 9.00000 + 15.5885i 0.395437 + 0.684917i
$$519$$ 27.0000 46.7654i 1.18517 2.05277i
$$520$$ −6.00000 −0.263117
$$521$$ 12.0000 0.525730 0.262865 0.964833i $$-0.415333\pi$$
0.262865 + 0.964833i $$0.415333\pi$$
$$522$$ 9.00000 15.5885i 0.393919 0.682288i
$$523$$ 4.50000 7.79423i 0.196771 0.340818i −0.750708 0.660634i $$-0.770288\pi$$
0.947480 + 0.319816i $$0.103621\pi$$
$$524$$ 14.0000 0.611593
$$525$$ −9.00000 −0.392792
$$526$$ −4.00000 + 6.92820i −0.174408 + 0.302084i
$$527$$ 3.00000 + 5.19615i 0.130682 + 0.226348i
$$528$$ −3.00000 + 5.19615i −0.130558 + 0.226134i
$$529$$ −1.00000 1.73205i −0.0434783 0.0753066i
$$530$$ 3.00000 + 5.19615i 0.130312 + 0.225706i
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ −36.0000 −1.55933
$$534$$ 9.00000 + 15.5885i 0.389468 + 0.674579i
$$535$$ −3.00000 5.19615i −0.129701 0.224649i
$$536$$ −7.50000 + 12.9904i −0.323951 + 0.561099i
$$537$$ 18.0000 + 31.1769i 0.776757 + 1.34538i
$$538$$ 3.00000 5.19615i 0.129339 0.224022i
$$539$$ −4.00000 −0.172292
$$540$$ −18.0000 −0.774597
$$541$$ −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i $$-0.847023\pi$$
0.843728 + 0.536771i $$0.180356\pi$$
$$542$$ −5.50000 + 9.52628i −0.236245 + 0.409189i
$$543$$ 54.0000 2.31736
$$544$$ 1.00000 0.0428746
$$545$$ 3.00000 5.19615i 0.128506 0.222579i
$$546$$ 13.5000 + 23.3827i 0.577747 + 1.00069i
$$547$$ −18.0000 + 31.1769i −0.769624 + 1.33303i 0.168142 + 0.985763i $$0.446223\pi$$
−0.937767 + 0.347266i $$0.887110\pi$$
$$548$$ −9.50000 16.4545i −0.405820 0.702901i
$$549$$ 0 0
$$550$$ −2.00000 −0.0852803
$$551$$ 0 0
$$552$$ 15.0000 0.638442
$$553$$ 18.0000 + 31.1769i 0.765438 + 1.32578i
$$554$$ 15.0000 + 25.9808i 0.637289 + 1.10382i
$$555$$ −18.0000 + 31.1769i −0.764057 + 1.32339i
$$556$$ −3.00000 5.19615i −0.127228 0.220366i
$$557$$ −11.0000 + 19.0526i −0.466085 + 0.807283i −0.999250 0.0387286i $$-0.987669\pi$$
0.533165 + 0.846011i $$0.321003\pi$$
$$558$$ −36.0000 −1.52400
$$559$$ −30.0000 −1.26886
$$560$$ 3.00000 5.19615i 0.126773 0.219578i
$$561$$ 3.00000 5.19615i 0.126660 0.219382i
$$562$$ 12.0000 0.506189
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ −12.0000 + 20.7846i −0.505291 + 0.875190i
$$565$$ 12.0000 + 20.7846i 0.504844 + 0.874415i
$$566$$ −7.00000 + 12.1244i −0.294232 + 0.509625i
$$567$$ 13.5000 + 23.3827i 0.566947 + 0.981981i
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ −32.0000 −1.33916 −0.669579 0.742741i $$-0.733526\pi$$
−0.669579 + 0.742741i $$0.733526\pi$$
$$572$$ 3.00000 + 5.19615i 0.125436 + 0.217262i
$$573$$ −16.5000 28.5788i −0.689297 1.19390i
$$574$$ 18.0000 31.1769i 0.751305 1.30130i
$$575$$ 2.50000 + 4.33013i 0.104257 + 0.180579i
$$576$$ −3.00000 + 5.19615i −0.125000 + 0.216506i
$$577$$ 15.0000 0.624458 0.312229 0.950007i $$-0.398924\pi$$
0.312229 + 0.950007i $$0.398924\pi$$
$$578$$ 16.0000 0.665512
$$579$$ −9.00000 + 15.5885i −0.374027 + 0.647834i
$$580$$ −3.00000 + 5.19615i −0.124568 + 0.215758i
$$581$$ −6.00000 −0.248922
$$582$$ −36.0000 −1.49225
$$583$$ 3.00000 5.19615i 0.124247 0.215203i
$$584$$ −5.50000 9.52628i −0.227592 0.394200i
$$585$$ −18.0000 + 31.1769i −0.744208 + 1.28901i
$$586$$ 4.50000 + 7.79423i 0.185893 + 0.321977i
$$587$$ 14.0000 + 24.2487i 0.577842 + 1.00085i 0.995726 + 0.0923513i $$0.0294383\pi$$
−0.417885 + 0.908500i $$0.637228\pi$$
$$588$$ −6.00000 −0.247436
$$589$$ 0 0
$$590$$ 6.00000 0.247016
$$591$$ 6.00000 + 10.3923i 0.246807 + 0.427482i
$$592$$ 3.00000 + 5.19615i 0.123299 + 0.213561i
$$593$$ 1.00000 1.73205i 0.0410651 0.0711268i −0.844762 0.535142i $$-0.820258\pi$$
0.885827 + 0.464015i $$0.153592\pi$$
$$594$$ 9.00000 + 15.5885i 0.369274 + 0.639602i
$$595$$ −3.00000 + 5.19615i −0.122988 + 0.213021i
$$596$$ −8.00000 −0.327693
$$597$$ 21.0000 0.859473
$$598$$ 7.50000 12.9904i 0.306698 0.531216i
$$599$$ −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i $$0.429701\pi$$
−0.954521 + 0.298143i $$0.903633\pi$$
$$600$$ −3.00000 −0.122474
$$601$$ 6.00000 0.244745 0.122373 0.992484i $$-0.460950\pi$$
0.122373 + 0.992484i $$0.460950\pi$$
$$602$$ 15.0000 25.9808i 0.611354 1.05890i
$$603$$ 45.0000 + 77.9423i 1.83254 + 3.17406i
$$604$$ −9.00000 + 15.5885i −0.366205 + 0.634285i
$$605$$ 7.00000 + 12.1244i 0.284590 + 0.492925i
$$606$$ −15.0000 25.9808i −0.609333 1.05540i
$$607$$ 12.0000 0.487065 0.243532 0.969893i $$-0.421694\pi$$
0.243532 + 0.969893i $$0.421694\pi$$
$$608$$ 0 0
$$609$$ 27.0000 1.09410
$$610$$ 0 0
$$611$$ 12.0000 + 20.7846i 0.485468 + 0.840855i
$$612$$ 3.00000 5.19615i 0.121268 0.210042i
$$613$$ −9.00000 15.5885i −0.363507 0.629612i 0.625029 0.780602i $$-0.285087\pi$$
−0.988535 + 0.150990i $$0.951754\pi$$
$$614$$ −6.00000 + 10.3923i −0.242140 + 0.419399i
$$615$$ 72.0000 2.90332
$$616$$ −6.00000 −0.241747
$$617$$ −5.00000 + 8.66025i −0.201292 + 0.348649i −0.948945 0.315441i $$-0.897847\pi$$
0.747653 + 0.664090i $$0.231181\pi$$
$$618$$ 9.00000 15.5885i 0.362033 0.627060i
$$619$$ −24.0000 −0.964641 −0.482321 0.875995i $$-0.660206\pi$$
−0.482321 + 0.875995i $$0.660206\pi$$
$$620$$ 12.0000 0.481932
$$621$$ 22.5000 38.9711i 0.902894 1.56386i
$$622$$ −5.50000 9.52628i −0.220530 0.381969i
$$623$$ −9.00000 + 15.5885i −0.360577 + 0.624538i
$$624$$ 4.50000 + 7.79423i 0.180144 + 0.312019i
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ −21.0000 −0.839329
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −3.00000 5.19615i −0.119618 0.207184i
$$630$$ −18.0000 31.1769i −0.717137 1.24212i
$$631$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$632$$ 6.00000 + 10.3923i 0.238667 + 0.413384i
$$633$$ −4.50000 + 7.79423i −0.178859 + 0.309793i
$$634$$ −33.0000 −1.31060
$$635$$ −24.0000 −0.952411
$$636$$ 4.50000 7.79423i 0.178437 0.309061i
$$637$$ −3.00000 + 5.19615i −0.118864 + 0.205879i
$$638$$ 6.00000 0.237542
$$639$$ 0 0
$$640$$ 1.00000 1.73205i 0.0395285 0.0684653i
$$641$$ 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i $$-0.0509845\pi$$
−0.631721 + 0.775196i $$0.717651\pi$$
$$642$$ −4.50000 + 7.79423i −0.177601 + 0.307614i
$$643$$ −16.0000 27.7128i −0.630978 1.09289i −0.987352 0.158543i $$-0.949320\pi$$
0.356374 0.934344i $$-0.384013\pi$$
$$644$$ 7.50000 + 12.9904i 0.295541 + 0.511893i
$$645$$ 60.0000 2.36250
$$646$$ 0 0
$$647$$ −23.0000 −0.904223 −0.452112 0.891961i $$-0.649329\pi$$
−0.452112 + 0.891961i $$0.649329\pi$$
$$648$$ 4.50000 + 7.79423i 0.176777 + 0.306186i
$$649$$ −3.00000 5.19615i −0.117760 0.203967i
$$650$$ −1.50000 + 2.59808i −0.0588348 + 0.101905i
$$651$$ −27.0000 46.7654i −1.05821 1.83288i
$$652$$ 3.00000 5.19615i 0.117489 0.203497i
$$653$$ −10.0000 −0.391330 −0.195665 0.980671i $$-0.562687\pi$$
−0.195665 + 0.980671i $$0.562687\pi$$
$$654$$ −9.00000 −0.351928
$$655$$ −14.0000 + 24.2487i −0.547025 + 0.947476i
$$656$$ 6.00000 10.3923i 0.234261 0.405751i
$$657$$ −66.0000 −2.57491
$$658$$ −24.0000 −0.935617
$$659$$ −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i $$-0.927707\pi$$
0.682161 + 0.731202i $$0.261040\pi$$
$$660$$ −6.00000 10.3923i −0.233550 0.404520i
$$661$$ 7.50000 12.9904i 0.291716 0.505267i −0.682499 0.730886i $$-0.739107\pi$$
0.974216 + 0.225619i $$0.0724404\pi$$
$$662$$ −4.50000 7.79423i −0.174897 0.302931i
$$663$$ −4.50000 7.79423i −0.174766 0.302703i
$$664$$ −2.00000 −0.0776151
$$665$$ 0 0
$$666$$ 36.0000 1.39497
$$667$$ −7.50000 12.9904i −0.290401 0.502990i
$$668$$ −6.00000 10.3923i −0.232147 0.402090i
$$669$$ −27.0000 + 46.7654i −1.04388 + 1.80805i
$$670$$ −15.0000 25.9808i −0.579501 1.00372i
$$671$$ 0 0
$$672$$ −9.00000 −0.347183
$$673$$ 48.0000 1.85026 0.925132 0.379646i $$-0.123954\pi$$
0.925132 + 0.379646i $$0.123954\pi$$
$$674$$ −9.00000 + 15.5885i −0.346667 + 0.600445i
$$675$$ −4.50000 + 7.79423i −0.173205 + 0.300000i
$$676$$ −4.00000 −0.153846
$$677$$ −3.00000 −0.115299 −0.0576497 0.998337i $$-0.518361\pi$$
−0.0576497 + 0.998337i $$0.518361\pi$$
$$678$$ 18.0000 31.1769i 0.691286 1.19734i
$$679$$ −18.0000 31.1769i −0.690777 1.19646i
$$680$$ −1.00000 + 1.73205i −0.0383482 + 0.0664211i
$$681$$ −4.50000 7.79423i −0.172440 0.298675i
$$682$$ −6.00000 10.3923i −0.229752 0.397942i
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 38.0000 1.45191
$$686$$ 7.50000 + 12.9904i 0.286351 + 0.495975i
$$687$$ −18.0000 31.1769i −0.686743 1.18947i
$$688$$ 5.00000 8.66025i 0.190623 0.330169i
$$689$$ −4.50000 7.79423i −0.171436 0.296936i
$$690$$ −15.0000 + 25.9808i −0.571040 + 0.989071i
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 18.0000 0.684257
$$693$$ −18.0000 + 31.1769i −0.683763 + 1.18431i
$$694$$ 8.00000 13.8564i 0.303676 0.525982i
$$695$$ 12.0000 0.455186
$$696$$ 9.00000 0.341144
$$697$$ −6.00000 + 10.3923i −0.227266 + 0.393637i
$$698$$ 14.0000 + 24.2487i 0.529908 + 0.917827i
$$699$$ 21.0000 36.3731i 0.794293 1.37576i
$$700$$ −1.50000 2.59808i −0.0566947 0.0981981i
$$701$$ 20.0000 + 34.6410i 0.755390 + 1.30837i 0.945180 + 0.326549i $$0.105886\pi$$
−0.189791 + 0.981825i $$0.560781\pi$$
$$702$$ 27.0000 1.01905
$$703$$ 0 0
$$704$$ −2.00000 −0.0753778
$$705$$ −24.0000 41.5692i −0.903892 1.56559i
$$706$$ −15.5000 26.8468i −0.583350 1.01039i
$$707$$ 15.0000 25.9808i 0.564133 0.977107i
$$708$$ −4.50000 7.79423i −0.169120 0.292925i
$$709$$ 4.00000 6.92820i 0.150223 0.260194i −0.781086 0.624423i $$-0.785334\pi$$
0.931309 + 0.364229i $$0.118667\pi$$
$$710$$ 0 0
$$711$$ 72.0000 2.70021
$$712$$ −3.00000 + 5.19615i −0.112430 + 0.194734i
$$713$$ −15.0000 + 25.9808i −0.561754 + 0.972987i
$$714$$ 9.00000 0.336817
$$715$$ −12.0000 −0.448775
$$716$$ −6.00000 + 10.3923i −0.224231 + 0.388379i
$$717$$ 1.50000 + 2.59808i 0.0560185 + 0.0970269i
$$718$$ 9.50000 16.4545i 0.354537 0.614076i
$$719$$ 21.5000 + 37.2391i 0.801815 + 1.38878i 0.918421 + 0.395606i $$0.129465\pi$$
−0.116606 + 0.993178i $$0.537201\pi$$
$$720$$ −6.00000 10.3923i −0.223607 0.387298i
$$721$$ 18.0000 0.670355
$$722$$ 0 0
$$723$$ 72.0000 2.67771
$$724$$ 9.00000 + 15.5885i 0.334482 + 0.579340i
$$725$$ 1.50000 + 2.59808i 0.0557086 + 0.0964901i
$$726$$ 10.5000 18.1865i 0.389692 0.674966i
$$727$$ 17.5000 + 30.3109i 0.649039 + 1.12417i 0.983353 + 0.181707i $$0.0581622\pi$$
−0.334314 + 0.942462i $$0.608504\pi$$
$$728$$ −4.50000 + 7.79423i −0.166781 + 0.288873i
$$729$$ −27.0000 −1.00000
$$730$$ 22.0000 0.814257
$$731$$ −5.00000 + 8.66025i −0.184932 + 0.320311i
$$732$$ 0 0
$$733$$ −22.0000 −0.812589 −0.406294 0.913742i $$-0.633179\pi$$
−0.406294 + 0.913742i $$0.633179\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 6.00000 10.3923i 0.221313 0.383326i
$$736$$ 2.50000 + 4.33013i 0.0921512 + 0.159611i
$$737$$ −15.0000 + 25.9808i −0.552532 + 0.957014i
$$738$$ −36.0000 62.3538i −1.32518 2.29528i
$$739$$ 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i $$-0.0958281\pi$$
−0.734311 + 0.678813i $$0.762495\pi$$
$$740$$ −12.0000 −0.441129
$$741$$ 0 0
$$742$$ 9.00000 0.330400
$$743$$ 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i $$-0.131563\pi$$
−0.805735 + 0.592277i $$0.798229\pi$$
$$744$$ −9.00000 15.5885i −0.329956 0.571501i
$$745$$ 8.00000 13.8564i 0.293097 0.507659i
$$746$$ 10.5000 + 18.1865i 0.384432 + 0.665856i
$$747$$ −6.00000 + 10.3923i −0.219529 + 0.380235i
$$748$$ 2.00000 0.0731272
$$749$$ −9.00000 −0.328853
$$750$$ 18.0000 31.1769i 0.657267 1.13842i
$$751$$ 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i $$-0.763072\pi$$
0.954485 + 0.298259i $$0.0964058\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ 60.0000 2.18652
$$754$$ 4.50000 7.79423i 0.163880 0.283849i
$$755$$ −18.0000 31.1769i −0.655087 1.13464i
$$756$$ −13.5000 + 23.3827i −0.490990 + 0.850420i
$$757$$ −6.00000 10.3923i −0.218074 0.377715i 0.736145 0.676824i $$-0.236644\pi$$
−0.954219 + 0.299109i $$0.903311\pi$$
$$758$$ −1.50000 2.59808i −0.0544825 0.0943664i
$$759$$ 30.0000 1.08893
$$760$$ 0 0
$$761$$ −13.0000 −0.471250 −0.235625 0.971844i $$-0.575714\pi$$
−0.235625 + 0.971844i $$0.575714\pi$$
$$762$$ 18.0000 + 31.1769i 0.652071 + 1.12942i
$$763$$ −4.50000 7.79423i −0.162911 0.282170i
$$764$$ 5.50000 9.52628i 0.198983 0.344649i
$$765$$ 6.00000 + 10.3923i 0.216930 + 0.375735i
$$766$$ −9.00000 + 15.5885i −0.325183 + 0.563234i
$$767$$ −9.00000 −0.324971
$$768$$ −3.00000 −0.108253
$$769$$ 7.50000 12.9904i 0.270457 0.468445i −0.698522 0.715589i $$-0.746159\pi$$
0.968979 + 0.247143i $$0.0794919\pi$$
$$770$$ 6.00000 10.3923i 0.216225 0.374513i
$$771$$ −54.0000 −1.94476
$$772$$ −6.00000 −0.215945
$$773$$ 7.50000 12.9904i 0.269756 0.467232i −0.699043 0.715080i $$-0.746390\pi$$
0.968799 + 0.247849i $$0.0797235\pi$$
$$774$$ −30.0000 51.9615i −1.07833 1.86772i
$$775$$ 3.00000 5.19615i 0.107763 0.186651i
$$776$$ −6.00000 10.3923i −0.215387 0.373062i
$$777$$ 27.0000 + 46.7654i 0.968620 + 1.67770i
$$778$$ −26.0000 −0.932145