# Properties

 Label 210.2.i.d.121.1 Level $210$ Weight $2$ Character 210.121 Analytic conductor $1.677$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$210 = 2 \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 210.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.67685844245$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ 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 121.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 210.121 Dual form 210.2.i.d.151.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} -1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} +1.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(-0.500000 - 2.59808i) q^{35} +1.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} -11.0000 q^{41} +(2.00000 - 1.73205i) q^{42} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.50000 + 6.06218i) q^{46} +(2.50000 - 4.33013i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +3.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +2.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} -7.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} -6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(5.50000 + 9.52628i) q^{74} +(0.500000 - 0.866025i) q^{75} -3.00000 q^{76} +(2.50000 + 0.866025i) q^{77} +1.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.50000 + 9.52628i) q^{82} +8.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} +1.00000 q^{90} +(2.00000 - 1.73205i) q^{91} +7.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-2.50000 - 4.33013i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(-0.500000 + 0.866025i) q^{96} -16.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} + O(q^{10})$$ $$2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} - q^{14} + 2q^{15} - q^{16} + q^{18} + 3q^{19} - 2q^{20} + 5q^{21} + 2q^{22} - 7q^{23} - q^{24} - q^{25} + q^{26} - 2q^{27} - 5q^{28} - 16q^{29} + q^{30} + 2q^{31} + q^{32} - q^{33} - q^{35} + 2q^{36} - 11q^{37} - 3q^{38} + q^{39} - q^{40} - 22q^{41} + 4q^{42} + 16q^{43} + q^{44} + q^{45} + 7q^{46} + 5q^{47} - 2q^{48} + 2q^{49} - 2q^{50} - q^{52} + 11q^{53} - q^{54} + 2q^{55} - 4q^{56} + 6q^{57} - 8q^{58} - 4q^{59} - q^{60} + 4q^{62} + q^{63} + 2q^{64} + q^{65} + q^{66} - 14q^{69} - 5q^{70} - 12q^{71} + q^{72} + 6q^{73} + 11q^{74} + q^{75} - 6q^{76} + 5q^{77} + 2q^{78} + 8q^{79} + q^{80} - q^{81} - 11q^{82} + 16q^{83} - q^{84} + 8q^{86} - 8q^{87} - q^{88} + 10q^{89} + 2q^{90} + 4q^{91} + 14q^{92} - 2q^{93} - 5q^{94} - 3q^{95} - q^{96} - 32q^{97} - 11q^{98} - 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$71$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 1.00000 0.408248
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i $$-0.118496\pi$$
−0.780750 + 0.624844i $$0.785163\pi$$
$$12$$ 0.500000 0.866025i 0.144338 0.250000i
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ −0.500000 2.59808i −0.133631 0.694365i
$$15$$ 1.00000 0.258199
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0.500000 + 0.866025i 0.117851 + 0.204124i
$$19$$ 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i $$-0.721509\pi$$
0.985194 + 0.171442i $$0.0548427\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 2.50000 + 0.866025i 0.545545 + 0.188982i
$$22$$ 1.00000 0.213201
$$23$$ −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i $$0.427054\pi$$
−0.956967 + 0.290196i $$0.906280\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0.500000 0.866025i 0.0980581 0.169842i
$$27$$ −1.00000 −0.192450
$$28$$ −2.50000 0.866025i −0.472456 0.163663i
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 0.500000 0.866025i 0.0912871 0.158114i
$$31$$ 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i $$-0.109185\pi$$
−0.762140 + 0.647412i $$0.775851\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −0.500000 + 0.866025i −0.0870388 + 0.150756i
$$34$$ 0 0
$$35$$ −0.500000 2.59808i −0.0845154 0.439155i
$$36$$ 1.00000 0.166667
$$37$$ −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i $$0.526194\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −1.50000 2.59808i −0.243332 0.421464i
$$39$$ 0.500000 + 0.866025i 0.0800641 + 0.138675i
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ −11.0000 −1.71791 −0.858956 0.512050i $$-0.828886\pi$$
−0.858956 + 0.512050i $$0.828886\pi$$
$$42$$ 2.00000 1.73205i 0.308607 0.267261i
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0.500000 0.866025i 0.0753778 0.130558i
$$45$$ 0.500000 + 0.866025i 0.0745356 + 0.129099i
$$46$$ 3.50000 + 6.06218i 0.516047 + 0.893819i
$$47$$ 2.50000 4.33013i 0.364662 0.631614i −0.624059 0.781377i $$-0.714518\pi$$
0.988722 + 0.149763i $$0.0478510\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ −0.500000 0.866025i −0.0693375 0.120096i
$$53$$ 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i $$0.105931\pi$$
−0.189651 + 0.981852i $$0.560736\pi$$
$$54$$ −0.500000 + 0.866025i −0.0680414 + 0.117851i
$$55$$ 1.00000 0.134840
$$56$$ −2.00000 + 1.73205i −0.267261 + 0.231455i
$$57$$ 3.00000 0.397360
$$58$$ −4.00000 + 6.92820i −0.525226 + 0.909718i
$$59$$ −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i $$-0.250514\pi$$
−0.966342 + 0.257260i $$0.917180\pi$$
$$60$$ −0.500000 0.866025i −0.0645497 0.111803i
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0.500000 + 2.59808i 0.0629941 + 0.327327i
$$64$$ 1.00000 0.125000
$$65$$ 0.500000 0.866025i 0.0620174 0.107417i
$$66$$ 0.500000 + 0.866025i 0.0615457 + 0.106600i
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0 0
$$69$$ −7.00000 −0.842701
$$70$$ −2.50000 0.866025i −0.298807 0.103510i
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i $$-0.0524664\pi$$
−0.635323 + 0.772246i $$0.719133\pi$$
$$74$$ 5.50000 + 9.52628i 0.639362 + 1.10741i
$$75$$ 0.500000 0.866025i 0.0577350 0.100000i
$$76$$ −3.00000 −0.344124
$$77$$ 2.50000 + 0.866025i 0.284901 + 0.0986928i
$$78$$ 1.00000 0.113228
$$79$$ 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i $$-0.684745\pi$$
0.998388 + 0.0567635i $$0.0180781\pi$$
$$80$$ 0.500000 + 0.866025i 0.0559017 + 0.0968246i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −5.50000 + 9.52628i −0.607373 + 1.05200i
$$83$$ 8.00000 0.878114 0.439057 0.898459i $$-0.355313\pi$$
0.439057 + 0.898459i $$0.355313\pi$$
$$84$$ −0.500000 2.59808i −0.0545545 0.283473i
$$85$$ 0 0
$$86$$ 4.00000 6.92820i 0.431331 0.747087i
$$87$$ −4.00000 6.92820i −0.428845 0.742781i
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i $$-0.655526\pi$$
0.999388 0.0349934i $$-0.0111410\pi$$
$$90$$ 1.00000 0.105409
$$91$$ 2.00000 1.73205i 0.209657 0.181568i
$$92$$ 7.00000 0.729800
$$93$$ −1.00000 + 1.73205i −0.103695 + 0.179605i
$$94$$ −2.50000 4.33013i −0.257855 0.446619i
$$95$$ −1.50000 2.59808i −0.153897 0.266557i
$$96$$ −0.500000 + 0.866025i −0.0510310 + 0.0883883i
$$97$$ −16.0000 −1.62455 −0.812277 0.583272i $$-0.801772\pi$$
−0.812277 + 0.583272i $$0.801772\pi$$
$$98$$ −5.50000 4.33013i −0.555584 0.437409i
$$99$$ −1.00000 −0.100504
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 0 0
$$103$$ 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i $$-0.544314\pi$$
0.927030 0.374987i $$-0.122353\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 2.00000 1.73205i 0.195180 0.169031i
$$106$$ 11.0000 1.06841
$$107$$ 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i $$-0.672747\pi$$
0.999818 + 0.0190994i $$0.00607989\pi$$
$$108$$ 0.500000 + 0.866025i 0.0481125 + 0.0833333i
$$109$$ −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i $$-0.259440\pi$$
−0.973176 + 0.230063i $$0.926107\pi$$
$$110$$ 0.500000 0.866025i 0.0476731 0.0825723i
$$111$$ −11.0000 −1.04407
$$112$$ 0.500000 + 2.59808i 0.0472456 + 0.245495i
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 1.50000 2.59808i 0.140488 0.243332i
$$115$$ 3.50000 + 6.06218i 0.326377 + 0.565301i
$$116$$ 4.00000 + 6.92820i 0.371391 + 0.643268i
$$117$$ −0.500000 + 0.866025i −0.0462250 + 0.0800641i
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ −1.00000 −0.0912871
$$121$$ 5.00000 8.66025i 0.454545 0.787296i
$$122$$ 0 0
$$123$$ −5.50000 9.52628i −0.495918 0.858956i
$$124$$ 1.00000 1.73205i 0.0898027 0.155543i
$$125$$ −1.00000 −0.0894427
$$126$$ 2.50000 + 0.866025i 0.222718 + 0.0771517i
$$127$$ −17.0000 −1.50851 −0.754253 0.656584i $$-0.772001\pi$$
−0.754253 + 0.656584i $$0.772001\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 4.00000 + 6.92820i 0.352180 + 0.609994i
$$130$$ −0.500000 0.866025i −0.0438529 0.0759555i
$$131$$ 2.50000 4.33013i 0.218426 0.378325i −0.735901 0.677089i $$-0.763241\pi$$
0.954327 + 0.298764i $$0.0965744\pi$$
$$132$$ 1.00000 0.0870388
$$133$$ −1.50000 7.79423i −0.130066 0.675845i
$$134$$ 0 0
$$135$$ −0.500000 + 0.866025i −0.0430331 + 0.0745356i
$$136$$ 0 0
$$137$$ 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i $$0.112540\pi$$
−0.169226 + 0.985577i $$0.554127\pi$$
$$138$$ −3.50000 + 6.06218i −0.297940 + 0.516047i
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ −2.00000 + 1.73205i −0.169031 + 0.146385i
$$141$$ 5.00000 0.421076
$$142$$ −3.00000 + 5.19615i −0.251754 + 0.436051i
$$143$$ 0.500000 + 0.866025i 0.0418121 + 0.0724207i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ −4.00000 + 6.92820i −0.332182 + 0.575356i
$$146$$ 6.00000 0.496564
$$147$$ 6.50000 2.59808i 0.536111 0.214286i
$$148$$ 11.0000 0.904194
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ −0.500000 0.866025i −0.0408248 0.0707107i
$$151$$ −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i $$-0.245171\pi$$
−0.961888 + 0.273442i $$0.911838\pi$$
$$152$$ −1.50000 + 2.59808i −0.121666 + 0.210732i
$$153$$ 0 0
$$154$$ 2.00000 1.73205i 0.161165 0.139573i
$$155$$ 2.00000 0.160644
$$156$$ 0.500000 0.866025i 0.0400320 0.0693375i
$$157$$ 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i $$-0.0765542\pi$$
−0.691888 + 0.722005i $$0.743221\pi$$
$$158$$ −4.00000 6.92820i −0.318223 0.551178i
$$159$$ −5.50000 + 9.52628i −0.436178 + 0.755483i
$$160$$ 1.00000 0.0790569
$$161$$ 3.50000 + 18.1865i 0.275839 + 1.43330i
$$162$$ −1.00000 −0.0785674
$$163$$ −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i $$0.382224\pi$$
−0.988227 + 0.152992i $$0.951109\pi$$
$$164$$ 5.50000 + 9.52628i 0.429478 + 0.743877i
$$165$$ 0.500000 + 0.866025i 0.0389249 + 0.0674200i
$$166$$ 4.00000 6.92820i 0.310460 0.537733i
$$167$$ −3.00000 −0.232147 −0.116073 0.993241i $$-0.537031\pi$$
−0.116073 + 0.993241i $$0.537031\pi$$
$$168$$ −2.50000 0.866025i −0.192879 0.0668153i
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 1.50000 + 2.59808i 0.114708 + 0.198680i
$$172$$ −4.00000 6.92820i −0.304997 0.528271i
$$173$$ 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i $$-0.640193\pi$$
0.996544 0.0830722i $$-0.0264732\pi$$
$$174$$ −8.00000 −0.606478
$$175$$ −2.50000 0.866025i −0.188982 0.0654654i
$$176$$ −1.00000 −0.0753778
$$177$$ 2.00000 3.46410i 0.150329 0.260378i
$$178$$ −5.00000 8.66025i −0.374766 0.649113i
$$179$$ 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i $$0.0846670\pi$$
−0.254770 + 0.967002i $$0.582000\pi$$
$$180$$ 0.500000 0.866025i 0.0372678 0.0645497i
$$181$$ −24.0000 −1.78391 −0.891953 0.452128i $$-0.850665\pi$$
−0.891953 + 0.452128i $$0.850665\pi$$
$$182$$ −0.500000 2.59808i −0.0370625 0.192582i
$$183$$ 0 0
$$184$$ 3.50000 6.06218i 0.258023 0.446910i
$$185$$ 5.50000 + 9.52628i 0.404368 + 0.700386i
$$186$$ 1.00000 + 1.73205i 0.0733236 + 0.127000i
$$187$$ 0 0
$$188$$ −5.00000 −0.364662
$$189$$ −2.00000 + 1.73205i −0.145479 + 0.125988i
$$190$$ −3.00000 −0.217643
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i $$-0.875812\pi$$
0.133056 0.991109i $$-0.457521\pi$$
$$194$$ −8.00000 + 13.8564i −0.574367 + 0.994832i
$$195$$ 1.00000 0.0716115
$$196$$ −6.50000 + 2.59808i −0.464286 + 0.185577i
$$197$$ −1.00000 −0.0712470 −0.0356235 0.999365i $$-0.511342\pi$$
−0.0356235 + 0.999365i $$0.511342\pi$$
$$198$$ −0.500000 + 0.866025i −0.0355335 + 0.0615457i
$$199$$ 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i $$0.157129\pi$$
−0.0299585 + 0.999551i $$0.509538\pi$$
$$200$$ 0.500000 + 0.866025i 0.0353553 + 0.0612372i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −16.0000 + 13.8564i −1.12298 + 0.972529i
$$204$$ 0 0
$$205$$ −5.50000 + 9.52628i −0.384137 + 0.665344i
$$206$$ −8.00000 13.8564i −0.557386 0.965422i
$$207$$ −3.50000 6.06218i −0.243267 0.421350i
$$208$$ −0.500000 + 0.866025i −0.0346688 + 0.0600481i
$$209$$ 3.00000 0.207514
$$210$$ −0.500000 2.59808i −0.0345033 0.179284i
$$211$$ 5.00000 0.344214 0.172107 0.985078i $$-0.444942\pi$$
0.172107 + 0.985078i $$0.444942\pi$$
$$212$$ 5.50000 9.52628i 0.377742 0.654268i
$$213$$ −3.00000 5.19615i −0.205557 0.356034i
$$214$$ −5.00000 8.66025i −0.341793 0.592003i
$$215$$ 4.00000 6.92820i 0.272798 0.472500i
$$216$$ 1.00000 0.0680414
$$217$$ 5.00000 + 1.73205i 0.339422 + 0.117579i
$$218$$ −6.00000 −0.406371
$$219$$ −3.00000 + 5.19615i −0.202721 + 0.351123i
$$220$$ −0.500000 0.866025i −0.0337100 0.0583874i
$$221$$ 0 0
$$222$$ −5.50000 + 9.52628i −0.369136 + 0.639362i
$$223$$ 12.0000 0.803579 0.401790 0.915732i $$-0.368388\pi$$
0.401790 + 0.915732i $$0.368388\pi$$
$$224$$ 2.50000 + 0.866025i 0.167038 + 0.0578638i
$$225$$ 1.00000 0.0666667
$$226$$ 3.00000 5.19615i 0.199557 0.345643i
$$227$$ −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i $$-0.252200\pi$$
−0.967692 + 0.252136i $$0.918867\pi$$
$$228$$ −1.50000 2.59808i −0.0993399 0.172062i
$$229$$ −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i $$-0.986407\pi$$
0.536515 + 0.843891i $$0.319740\pi$$
$$230$$ 7.00000 0.461566
$$231$$ 0.500000 + 2.59808i 0.0328976 + 0.170941i
$$232$$ 8.00000 0.525226
$$233$$ −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i $$0.367385\pi$$
−0.994283 + 0.106773i $$0.965948\pi$$
$$234$$ 0.500000 + 0.866025i 0.0326860 + 0.0566139i
$$235$$ −2.50000 4.33013i −0.163082 0.282466i
$$236$$ −2.00000 + 3.46410i −0.130189 + 0.225494i
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ −18.0000 −1.16432 −0.582162 0.813073i $$-0.697793\pi$$
−0.582162 + 0.813073i $$0.697793\pi$$
$$240$$ −0.500000 + 0.866025i −0.0322749 + 0.0559017i
$$241$$ −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i $$-0.239053\pi$$
−0.956456 + 0.291877i $$0.905720\pi$$
$$242$$ −5.00000 8.66025i −0.321412 0.556702i
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ −5.50000 4.33013i −0.351382 0.276642i
$$246$$ −11.0000 −0.701334
$$247$$ 1.50000 2.59808i 0.0954427 0.165312i
$$248$$ −1.00000 1.73205i −0.0635001 0.109985i
$$249$$ 4.00000 + 6.92820i 0.253490 + 0.439057i
$$250$$ −0.500000 + 0.866025i −0.0316228 + 0.0547723i
$$251$$ 13.0000 0.820553 0.410276 0.911961i $$-0.365432\pi$$
0.410276 + 0.911961i $$0.365432\pi$$
$$252$$ 2.00000 1.73205i 0.125988 0.109109i
$$253$$ −7.00000 −0.440086
$$254$$ −8.50000 + 14.7224i −0.533337 + 0.923768i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 10.0000 17.3205i 0.623783 1.08042i −0.364992 0.931011i $$-0.618928\pi$$
0.988775 0.149413i $$-0.0477384\pi$$
$$258$$ 8.00000 0.498058
$$259$$ 5.50000 + 28.5788i 0.341753 + 1.77580i
$$260$$ −1.00000 −0.0620174
$$261$$ 4.00000 6.92820i 0.247594 0.428845i
$$262$$ −2.50000 4.33013i −0.154451 0.267516i
$$263$$ −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ 0.500000 0.866025i 0.0307729 0.0533002i
$$265$$ 11.0000 0.675725
$$266$$ −7.50000 2.59808i −0.459855 0.159298i
$$267$$ 10.0000 0.611990
$$268$$ 0 0
$$269$$ −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i $$-0.957952\pi$$
0.381577 0.924337i $$-0.375381\pi$$
$$270$$ 0.500000 + 0.866025i 0.0304290 + 0.0527046i
$$271$$ −16.0000 + 27.7128i −0.971931 + 1.68343i −0.282218 + 0.959350i $$0.591070\pi$$
−0.689713 + 0.724083i $$0.742263\pi$$
$$272$$ 0 0
$$273$$ 2.50000 + 0.866025i 0.151307 + 0.0524142i
$$274$$ 18.0000 1.08742
$$275$$ 0.500000 0.866025i 0.0301511 0.0522233i
$$276$$ 3.50000 + 6.06218i 0.210675 + 0.364900i
$$277$$ 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i $$0.0631696\pi$$
−0.319447 + 0.947604i $$0.603497\pi$$
$$278$$ 10.0000 17.3205i 0.599760 1.03882i
$$279$$ −2.00000 −0.119737
$$280$$ 0.500000 + 2.59808i 0.0298807 + 0.155265i
$$281$$ −1.00000 −0.0596550 −0.0298275 0.999555i $$-0.509496\pi$$
−0.0298275 + 0.999555i $$0.509496\pi$$
$$282$$ 2.50000 4.33013i 0.148873 0.257855i
$$283$$ 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i $$-0.0300609\pi$$
−0.579437 + 0.815017i $$0.696728\pi$$
$$284$$ 3.00000 + 5.19615i 0.178017 + 0.308335i
$$285$$ 1.50000 2.59808i 0.0888523 0.153897i
$$286$$ 1.00000 0.0591312
$$287$$ −22.0000 + 19.0526i −1.29862 + 1.12464i
$$288$$ −1.00000 −0.0589256
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 4.00000 + 6.92820i 0.234888 + 0.406838i
$$291$$ −8.00000 13.8564i −0.468968 0.812277i
$$292$$ 3.00000 5.19615i 0.175562 0.304082i
$$293$$ 27.0000 1.57736 0.788678 0.614806i $$-0.210766\pi$$
0.788678 + 0.614806i $$0.210766\pi$$
$$294$$ 1.00000 6.92820i 0.0583212 0.404061i
$$295$$ −4.00000 −0.232889
$$296$$ 5.50000 9.52628i 0.319681 0.553704i
$$297$$ −0.500000 0.866025i −0.0290129 0.0502519i
$$298$$ 0 0
$$299$$ −3.50000 + 6.06218i −0.202410 + 0.350585i
$$300$$ −1.00000 −0.0577350
$$301$$ 16.0000 13.8564i 0.922225 0.798670i
$$302$$ −6.00000 −0.345261
$$303$$ 0 0
$$304$$ 1.50000 + 2.59808i 0.0860309 + 0.149010i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ −0.500000 2.59808i −0.0284901 0.148039i
$$309$$ 16.0000 0.910208
$$310$$ 1.00000 1.73205i 0.0567962 0.0983739i
$$311$$ −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i $$-0.277171\pi$$
−0.984475 + 0.175525i $$0.943838\pi$$
$$312$$ −0.500000 0.866025i −0.0283069 0.0490290i
$$313$$ 6.00000 10.3923i 0.339140 0.587408i −0.645131 0.764072i $$-0.723197\pi$$
0.984271 + 0.176664i $$0.0565306\pi$$
$$314$$ 7.00000 0.395033
$$315$$ 2.50000 + 0.866025i 0.140859 + 0.0487950i
$$316$$ −8.00000 −0.450035
$$317$$ 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i $$-0.664645\pi$$
0.999980 0.00635137i $$-0.00202172\pi$$
$$318$$ 5.50000 + 9.52628i 0.308425 + 0.534207i
$$319$$ −4.00000 6.92820i −0.223957 0.387905i
$$320$$ 0.500000 0.866025i 0.0279508 0.0484123i
$$321$$ 10.0000 0.558146
$$322$$ 17.5000 + 6.06218i 0.975237 + 0.337832i
$$323$$ 0 0
$$324$$ −0.500000 + 0.866025i −0.0277778 + 0.0481125i
$$325$$ −0.500000 0.866025i −0.0277350 0.0480384i
$$326$$ 8.00000 + 13.8564i 0.443079 + 0.767435i
$$327$$ 3.00000 5.19615i 0.165900 0.287348i
$$328$$ 11.0000 0.607373
$$329$$ −2.50000 12.9904i −0.137829 0.716183i
$$330$$ 1.00000 0.0550482
$$331$$ 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i $$-0.717040\pi$$
0.987504 + 0.157593i $$0.0503735\pi$$
$$332$$ −4.00000 6.92820i −0.219529 0.380235i
$$333$$ −5.50000 9.52628i −0.301398 0.522037i
$$334$$ −1.50000 + 2.59808i −0.0820763 + 0.142160i
$$335$$ 0 0
$$336$$ −2.00000 + 1.73205i −0.109109 + 0.0944911i
$$337$$ −12.0000 −0.653682 −0.326841 0.945079i $$-0.605984\pi$$
−0.326841 + 0.945079i $$0.605984\pi$$
$$338$$ −6.00000 + 10.3923i −0.326357 + 0.565267i
$$339$$ 3.00000 + 5.19615i 0.162938 + 0.282216i
$$340$$ 0 0
$$341$$ −1.00000 + 1.73205i −0.0541530 + 0.0937958i
$$342$$ 3.00000 0.162221
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ −8.00000 −0.431331
$$345$$ −3.50000 + 6.06218i −0.188434 + 0.326377i
$$346$$ −7.50000 12.9904i −0.403202 0.698367i
$$347$$ −7.00000 12.1244i −0.375780 0.650870i 0.614664 0.788789i $$-0.289292\pi$$
−0.990443 + 0.137920i $$0.955958\pi$$
$$348$$ −4.00000 + 6.92820i −0.214423 + 0.371391i
$$349$$ 12.0000 0.642345 0.321173 0.947021i $$-0.395923\pi$$
0.321173 + 0.947021i $$0.395923\pi$$
$$350$$ −2.00000 + 1.73205i −0.106904 + 0.0925820i
$$351$$ −1.00000 −0.0533761
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i $$-0.946141\pi$$
0.347024 0.937856i $$-0.387192\pi$$
$$354$$ −2.00000 3.46410i −0.106299 0.184115i
$$355$$ −3.00000 + 5.19615i −0.159223 + 0.275783i
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ 19.0000 1.00418
$$359$$ −2.00000 + 3.46410i −0.105556 + 0.182828i −0.913965 0.405793i $$-0.866996\pi$$
0.808409 + 0.588621i $$0.200329\pi$$
$$360$$ −0.500000 0.866025i −0.0263523 0.0456435i
$$361$$ 5.00000 + 8.66025i 0.263158 + 0.455803i
$$362$$ −12.0000 + 20.7846i −0.630706 + 1.09241i
$$363$$ 10.0000 0.524864
$$364$$ −2.50000 0.866025i −0.131036 0.0453921i
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i $$-0.940389\pi$$
0.330021 0.943974i $$-0.392944\pi$$
$$368$$ −3.50000 6.06218i −0.182450 0.316013i
$$369$$ 5.50000 9.52628i 0.286319 0.495918i
$$370$$ 11.0000 0.571863
$$371$$ 27.5000 + 9.52628i 1.42773 + 0.494580i
$$372$$ 2.00000 0.103695
$$373$$ −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i $$-0.882979\pi$$
0.777847 + 0.628454i $$0.216312\pi$$
$$374$$ 0 0
$$375$$ −0.500000 0.866025i −0.0258199 0.0447214i
$$376$$ −2.50000 + 4.33013i −0.128928 + 0.223309i
$$377$$ −8.00000 −0.412021
$$378$$ 0.500000 + 2.59808i 0.0257172 + 0.133631i
$$379$$ −19.0000 −0.975964 −0.487982 0.872854i $$-0.662267\pi$$
−0.487982 + 0.872854i $$0.662267\pi$$
$$380$$ −1.50000 + 2.59808i −0.0769484 + 0.133278i
$$381$$ −8.50000 14.7224i −0.435468 0.754253i
$$382$$ −3.00000 5.19615i −0.153493 0.265858i
$$383$$ −17.5000 + 30.3109i −0.894208 + 1.54881i −0.0594268 + 0.998233i $$0.518927\pi$$
−0.834781 + 0.550581i $$0.814406\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 2.00000 1.73205i 0.101929 0.0882735i
$$386$$ −22.0000 −1.11977
$$387$$ −4.00000 + 6.92820i −0.203331 + 0.352180i
$$388$$ 8.00000 + 13.8564i 0.406138 + 0.703452i
$$389$$ −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i $$-0.248252\pi$$
−0.964490 + 0.264120i $$0.914918\pi$$
$$390$$ 0.500000 0.866025i 0.0253185 0.0438529i
$$391$$ 0 0
$$392$$ −1.00000 + 6.92820i −0.0505076 + 0.349927i
$$393$$ 5.00000 0.252217
$$394$$ −0.500000 + 0.866025i −0.0251896 + 0.0436297i
$$395$$ −4.00000 6.92820i −0.201262 0.348596i
$$396$$ 0.500000 + 0.866025i 0.0251259 + 0.0435194i
$$397$$ −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i $$-0.947600\pi$$
0.635161 + 0.772380i $$0.280934\pi$$
$$398$$ 24.0000 1.20301
$$399$$ 6.00000 5.19615i 0.300376 0.260133i
$$400$$ 1.00000 0.0500000
$$401$$ 2.50000 4.33013i 0.124844 0.216236i −0.796828 0.604206i $$-0.793490\pi$$
0.921672 + 0.387970i $$0.126824\pi$$
$$402$$ 0 0
$$403$$ 1.00000 + 1.73205i 0.0498135 + 0.0862796i
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 4.00000 + 20.7846i 0.198517 + 1.03152i
$$407$$ −11.0000 −0.545250
$$408$$ 0 0
$$409$$ −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i $$-0.182412\pi$$
−0.889689 + 0.456566i $$0.849079\pi$$
$$410$$ 5.50000 + 9.52628i 0.271626 + 0.470469i
$$411$$ −9.00000 + 15.5885i −0.443937 + 0.768922i
$$412$$ −16.0000 −0.788263
$$413$$ −10.0000 3.46410i −0.492068 0.170457i
$$414$$ −7.00000 −0.344031
$$415$$ 4.00000 6.92820i 0.196352 0.340092i
$$416$$ 0.500000 + 0.866025i 0.0245145 + 0.0424604i
$$417$$ 10.0000 + 17.3205i 0.489702 + 0.848189i
$$418$$ 1.50000 2.59808i 0.0733674 0.127076i
$$419$$ −5.00000 −0.244266 −0.122133 0.992514i $$-0.538973\pi$$
−0.122133 + 0.992514i $$0.538973\pi$$
$$420$$ −2.50000 0.866025i −0.121988 0.0422577i
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 2.50000 4.33013i 0.121698 0.210787i
$$423$$ 2.50000 + 4.33013i 0.121554 + 0.210538i
$$424$$ −5.50000 9.52628i −0.267104 0.462637i
$$425$$ 0 0
$$426$$ −6.00000 −0.290701
$$427$$ 0 0
$$428$$ −10.0000 −0.483368
$$429$$ −0.500000 + 0.866025i −0.0241402 + 0.0418121i
$$430$$ −4.00000 6.92820i −0.192897 0.334108i
$$431$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$432$$ 0.500000 0.866025i 0.0240563 0.0416667i
$$433$$ −32.0000 −1.53782 −0.768911 0.639356i $$-0.779201\pi$$
−0.768911 + 0.639356i $$0.779201\pi$$
$$434$$ 4.00000 3.46410i 0.192006 0.166282i
$$435$$ −8.00000 −0.383571
$$436$$ −3.00000 + 5.19615i −0.143674 + 0.248851i
$$437$$ 10.5000 + 18.1865i 0.502283 + 0.869980i
$$438$$ 3.00000 + 5.19615i 0.143346 + 0.248282i
$$439$$ −16.0000 + 27.7128i −0.763638 + 1.32266i 0.177325 + 0.984152i $$0.443256\pi$$
−0.940963 + 0.338508i $$0.890078\pi$$
$$440$$ −1.00000 −0.0476731
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 0 0
$$443$$ −8.00000 + 13.8564i −0.380091 + 0.658338i −0.991075 0.133306i $$-0.957441\pi$$
0.610984 + 0.791643i $$0.290774\pi$$
$$444$$ 5.50000 + 9.52628i 0.261018 + 0.452097i
$$445$$ −5.00000 8.66025i −0.237023 0.410535i
$$446$$ 6.00000 10.3923i 0.284108 0.492090i
$$447$$ 0 0
$$448$$ 2.00000 1.73205i 0.0944911 0.0818317i
$$449$$ 11.0000 0.519122 0.259561 0.965727i $$-0.416422\pi$$
0.259561 + 0.965727i $$0.416422\pi$$
$$450$$ 0.500000 0.866025i 0.0235702 0.0408248i
$$451$$ −5.50000 9.52628i −0.258985 0.448575i
$$452$$ −3.00000 5.19615i −0.141108 0.244406i
$$453$$ 3.00000 5.19615i 0.140952 0.244137i
$$454$$ −8.00000 −0.375459
$$455$$ −0.500000 2.59808i −0.0234404 0.121800i
$$456$$ −3.00000 −0.140488
$$457$$ 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i $$-0.695012\pi$$
0.996038 + 0.0889312i $$0.0283451\pi$$
$$458$$ 7.00000 + 12.1244i 0.327089 + 0.566534i
$$459$$ 0 0
$$460$$ 3.50000 6.06218i 0.163188 0.282650i
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 2.50000 + 0.866025i 0.116311 + 0.0402911i
$$463$$ −13.0000 −0.604161 −0.302081 0.953282i $$-0.597681\pi$$
−0.302081 + 0.953282i $$0.597681\pi$$
$$464$$ 4.00000 6.92820i 0.185695 0.321634i
$$465$$ 1.00000 + 1.73205i 0.0463739 + 0.0803219i
$$466$$ 9.00000 + 15.5885i 0.416917 + 0.722121i
$$467$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 0 0
$$470$$ −5.00000 −0.230633
$$471$$ −3.50000 + 6.06218i −0.161271 + 0.279330i
$$472$$ 2.00000 + 3.46410i 0.0920575 + 0.159448i
$$473$$ 4.00000 + 6.92820i 0.183920 + 0.318559i
$$474$$ 4.00000 6.92820i 0.183726 0.318223i
$$475$$ −3.00000 −0.137649
$$476$$ 0 0
$$477$$ −11.0000 −0.503655
$$478$$ −9.00000 + 15.5885i −0.411650 + 0.712999i
$$479$$ −11.0000 19.0526i −0.502603 0.870534i −0.999995 0.00300810i $$-0.999042\pi$$
0.497393 0.867526i $$-0.334291\pi$$
$$480$$ 0.500000 + 0.866025i 0.0228218 + 0.0395285i
$$481$$ −5.50000 + 9.52628i −0.250778 + 0.434361i
$$482$$ −7.00000 −0.318841
$$483$$ −14.0000 + 12.1244i −0.637022 + 0.551677i
$$484$$ −10.0000 −0.454545
$$485$$ −8.00000 + 13.8564i −0.363261 + 0.629187i
$$486$$ −0.500000 0.866025i −0.0226805 0.0392837i
$$487$$ 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i $$-0.0485850\pi$$
−0.625859 + 0.779936i $$0.715252\pi$$
$$488$$ 0 0
$$489$$ −16.0000 −0.723545
$$490$$ −6.50000 + 2.59808i −0.293640 + 0.117369i
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ −5.50000 + 9.52628i −0.247959 + 0.429478i
$$493$$ 0 0
$$494$$ −1.50000 2.59808i −0.0674882 0.116893i
$$495$$ −0.500000 + 0.866025i −0.0224733 + 0.0389249i
$$496$$ −2.00000 −0.0898027
$$497$$ −12.0000 + 10.3923i −0.538274 + 0.466159i
$$498$$ 8.00000 0.358489
$$499$$ 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i $$-0.579187\pi$$
0.962472 0.271380i $$-0.0874801\pi$$
$$500$$ 0.500000 + 0.866025i 0.0223607 + 0.0387298i
$$501$$ −1.50000 2.59808i −0.0670151 0.116073i
$$502$$ 6.50000 11.2583i 0.290109 0.502484i
$$503$$ 36.0000 1.60516 0.802580 0.596544i $$-0.203460\pi$$
0.802580 + 0.596544i $$0.203460\pi$$
$$504$$ −0.500000 2.59808i −0.0222718 0.115728i
$$505$$ 0 0
$$506$$ −3.50000 + 6.06218i −0.155594 + 0.269497i
$$507$$ −6.00000 10.3923i −0.266469 0.461538i
$$508$$ 8.50000 + 14.7224i 0.377127 + 0.653202i
$$509$$ 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i $$-0.561692\pi$$
0.946111 0.323843i $$-0.104975\pi$$
$$510$$ 0 0
$$511$$ 15.0000 + 5.19615i 0.663561 + 0.229864i
$$512$$ −1.00000 −0.0441942
$$513$$ −1.50000 + 2.59808i −0.0662266 + 0.114708i
$$514$$ −10.0000 17.3205i −0.441081 0.763975i
$$515$$ −8.00000 13.8564i −0.352522 0.610586i
$$516$$ 4.00000 6.92820i 0.176090 0.304997i
$$517$$ 5.00000 0.219900
$$518$$ 27.5000 + 9.52628i 1.20828 + 0.418561i
$$519$$ 15.0000 0.658427
$$520$$ −0.500000 + 0.866025i −0.0219265 + 0.0379777i
$$521$$ 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i $$0.0905145\pi$$
−0.236963 + 0.971519i $$0.576152\pi$$
$$522$$ −4.00000 6.92820i −0.175075 0.303239i
$$523$$ −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i $$-0.847256\pi$$
0.843334 + 0.537390i $$0.180590\pi$$
$$524$$ −5.00000 −0.218426
$$525$$ −0.500000 2.59808i −0.0218218 0.113389i
$$526$$ −24.0000 −1.04645
$$527$$ 0 0
$$528$$ −0.500000 0.866025i −0.0217597 0.0376889i
$$529$$ −13.0000 22.5167i −0.565217 0.978985i
$$530$$ 5.50000 9.52628i 0.238905 0.413795i
$$531$$ 4.00000 0.173585
$$532$$ −6.00000 + 5.19615i −0.260133 + 0.225282i
$$533$$ −11.0000 −0.476463
$$534$$ 5.00000 8.66025i 0.216371 0.374766i
$$535$$ −5.00000 8.66025i −0.216169 0.374415i
$$536$$ 0 0
$$537$$ −9.50000 + 16.4545i −0.409955 + 0.710063i
$$538$$ −20.0000 −0.862261
$$539$$ 6.50000 2.59808i 0.279975 0.111907i
$$540$$ 1.00000 0.0430331
$$541$$ 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i $$-0.764369\pi$$
0.953262 + 0.302144i $$0.0977023\pi$$
$$542$$ 16.0000 + 27.7128i 0.687259 + 1.19037i
$$543$$ −12.0000 20.7846i −0.514969 0.891953i
$$544$$ 0 0
$$545$$ −6.00000 −0.257012
$$546$$ 2.00000 1.73205i 0.0855921 0.0741249i
$$547$$ 16.0000 0.684111 0.342055 0.939680i $$-0.388877\pi$$
0.342055 + 0.939680i $$0.388877\pi$$
$$548$$ 9.00000 15.5885i 0.384461 0.665906i
$$549$$ 0 0
$$550$$ −0.500000 0.866025i −0.0213201 0.0369274i
$$551$$ −12.0000 + 20.7846i −0.511217 + 0.885454i
$$552$$ 7.00000 0.297940
$$553$$ −4.00000 20.7846i −0.170097 0.883852i
$$554$$ 22.0000 0.934690
$$555$$ −5.50000 + 9.52628i −0.233462 + 0.404368i
$$556$$ −10.0000 17.3205i −0.424094 0.734553i
$$557$$ 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i $$0.0797613\pi$$
−0.269642 + 0.962961i $$0.586905\pi$$
$$558$$ −1.00000 + 1.73205i −0.0423334 + 0.0733236i
$$559$$ 8.00000 0.338364
$$560$$ 2.50000 + 0.866025i 0.105644 + 0.0365963i
$$561$$ 0 0
$$562$$ −0.500000 + 0.866025i −0.0210912 + 0.0365311i
$$563$$ 19.0000 + 32.9090i 0.800755 + 1.38695i 0.919120 + 0.393977i $$0.128901\pi$$
−0.118366 + 0.992970i $$0.537765\pi$$
$$564$$ −2.50000 4.33013i −0.105269 0.182331i
$$565$$ 3.00000 5.19615i 0.126211 0.218604i
$$566$$ 14.0000 0.588464
$$567$$ −2.50000 0.866025i −0.104990 0.0363696i
$$568$$ 6.00000 0.251754
$$569$$ 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i $$-0.772922\pi$$
0.944800 + 0.327647i $$0.106256\pi$$
$$570$$ −1.50000 2.59808i −0.0628281 0.108821i
$$571$$ 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i $$0.0668588\pi$$
−0.308443 + 0.951243i $$0.599808\pi$$
$$572$$ 0.500000 0.866025i 0.0209061 0.0362103i
$$573$$ 6.00000 0.250654
$$574$$ 5.50000 + 28.5788i 0.229566 + 1.19286i
$$575$$ 7.00000 0.291920
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i $$-0.0725410\pi$$
−0.682730 + 0.730670i $$0.739208\pi$$
$$578$$ −8.50000 14.7224i −0.353553 0.612372i
$$579$$ 11.0000 19.0526i 0.457144 0.791797i
$$580$$ 8.00000 0.332182
$$581$$ 16.0000 13.8564i 0.663792 0.574861i
$$582$$ −16.0000 −0.663221
$$583$$ −5.50000 + 9.52628i −0.227787 + 0.394538i
$$584$$ −3.00000 5.19615i −0.124141 0.215018i
$$585$$ 0.500000 + 0.866025i 0.0206725 + 0.0358057i
$$586$$ 13.5000 23.3827i 0.557680 0.965930i
$$587$$ −18.0000 −0.742940 −0.371470 0.928445i $$-0.621146\pi$$
−0.371470 + 0.928445i $$0.621146\pi$$
$$588$$ −5.50000 4.33013i −0.226816 0.178571i
$$589$$ 6.00000 0.247226
$$590$$ −2.00000 + 3.46410i −0.0823387 + 0.142615i
$$591$$ −0.500000 0.866025i −0.0205673 0.0356235i
$$592$$ −5.50000 9.52628i −0.226049 0.391528i
$$593$$ −8.00000 + 13.8564i −0.328521 + 0.569014i −0.982219 0.187741i $$-0.939883\pi$$
0.653698 + 0.756756i $$0.273217\pi$$
$$594$$ −1.00000 −0.0410305
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −12.0000 + 20.7846i −0.491127 + 0.850657i
$$598$$ 3.50000 + 6.06218i 0.143126 + 0.247901i
$$599$$ −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i $$-0.179676\pi$$
−0.885732 + 0.464198i $$0.846343\pi$$
$$600$$ −0.500000 + 0.866025i −0.0204124 + 0.0353553i
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ −4.00000 20.7846i −0.163028 0.847117i
$$603$$ 0 0
$$604$$ −3.00000 + 5.19615i −0.122068 + 0.211428i
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ 0 0
$$607$$ 18.5000 32.0429i 0.750892 1.30058i −0.196499 0.980504i $$-0.562957\pi$$
0.947391 0.320079i $$-0.103709\pi$$
$$608$$ 3.00000 0.121666
$$609$$ −20.0000 6.92820i −0.810441 0.280745i
$$610$$ 0 0
$$611$$ 2.50000 4.33013i 0.101139 0.175178i
$$612$$ 0 0
$$613$$ 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i $$0.143847\pi$$
−0.0716275 + 0.997431i $$0.522819\pi$$
$$614$$ 10.0000 17.3205i 0.403567 0.698999i
$$615$$ −11.0000 −0.443563
$$616$$ −2.50000 0.866025i −0.100728 0.0348932i
$$617$$ 28.0000 1.12724 0.563619 0.826035i $$-0.309409\pi$$
0.563619 + 0.826035i $$0.309409\pi$$
$$618$$ 8.00000 13.8564i 0.321807 0.557386i
$$619$$ −14.5000 25.1147i −0.582804 1.00945i −0.995145 0.0984169i $$-0.968622\pi$$
0.412341 0.911030i $$-0.364711\pi$$
$$620$$ −1.00000 1.73205i −0.0401610 0.0695608i
$$621$$ 3.50000 6.06218i 0.140450 0.243267i
$$622$$ −12.0000 −0.481156
$$623$$ −5.00000 25.9808i −0.200321 1.04090i
$$624$$ −1.00000 −0.0400320
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −6.00000 10.3923i −0.239808 0.415360i
$$627$$ 1.50000 + 2.59808i 0.0599042 + 0.103757i
$$628$$ 3.50000 6.06218i 0.139665 0.241907i
$$629$$ 0 0
$$630$$ 2.00000 1.73205i 0.0796819 0.0690066i
$$631$$ −26.0000 −1.03504 −0.517522 0.855670i $$-0.673145\pi$$
−0.517522 + 0.855670i $$0.673145\pi$$
$$632$$ −4.00000 + 6.92820i −0.159111 + 0.275589i
$$633$$ 2.50000 + 4.33013i 0.0993661 + 0.172107i
$$634$$ −9.00000 15.5885i −0.357436 0.619097i
$$635$$ −8.50000 + 14.7224i −0.337312 + 0.584242i
$$636$$ 11.0000 0.436178
$$637$$ 1.00000 6.92820i 0.0396214 0.274505i
$$638$$ −8.00000 −0.316723
$$639$$ 3.00000 5.19615i 0.118678 0.205557i
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i $$-0.147797\pi$$
−0.834881 + 0.550431i $$0.814464\pi$$
$$642$$ 5.00000 8.66025i 0.197334 0.341793i
$$643$$ −10.0000 −0.394362 −0.197181 0.980367i $$-0.563179\pi$$
−0.197181 + 0.980367i $$0.563179\pi$$
$$644$$ 14.0000 12.1244i 0.551677 0.477767i
$$645$$ 8.00000 0.315000
$$646$$ 0 0
$$647$$ 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i $$-0.0582109\pi$$
−0.649155 + 0.760656i $$0.724878\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ 2.00000 3.46410i 0.0785069 0.135978i
$$650$$ −1.00000 −0.0392232
$$651$$ 1.00000 + 5.19615i 0.0391931 + 0.203653i
$$652$$ 16.0000 0.626608
$$653$$ −3.50000 + 6.06218i −0.136966 + 0.237231i −0.926347 0.376672i $$-0.877068\pi$$
0.789381 + 0.613904i $$0.210402\pi$$
$$654$$ −3.00000 5.19615i −0.117309 0.203186i
$$655$$ −2.50000 4.33013i −0.0976831 0.169192i
$$656$$ 5.50000 9.52628i 0.214739 0.371939i
$$657$$ −6.00000 −0.234082
$$658$$ −12.5000 4.33013i −0.487301 0.168806i
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0.500000 0.866025i 0.0194625 0.0337100i
$$661$$ 12.0000 + 20.7846i 0.466746 + 0.808428i 0.999278 0.0379819i $$-0.0120929\pi$$
−0.532533 + 0.846410i $$0.678760\pi$$
$$662$$ −6.50000 11.2583i −0.252630 0.437567i
$$663$$ 0 0
$$664$$ −8.00000 −0.310460
$$665$$ −7.50000 2.59808i −0.290838 0.100749i
$$666$$ −11.0000 −0.426241
$$667$$ 28.0000 48.4974i 1.08416 1.87783i
$$668$$ 1.50000 + 2.59808i 0.0580367 + 0.100523i
$$669$$ 6.00000 + 10.3923i 0.231973 + 0.401790i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0.500000 + 2.59808i 0.0192879 + 0.100223i
$$673$$ 28.0000 1.07932 0.539660 0.841883i $$-0.318553\pi$$
0.539660 + 0.841883i $$0.318553\pi$$
$$674$$ −6.00000 + 10.3923i −0.231111 + 0.400297i
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ 6.50000 11.2583i 0.249815 0.432693i −0.713659 0.700493i $$-0.752963\pi$$
0.963474 + 0.267800i $$0.0862968\pi$$
$$678$$ 6.00000 0.230429
$$679$$ −32.0000 + 27.7128i −1.22805 + 1.06352i
$$680$$ 0 0
$$681$$ 4.00000 6.92820i 0.153280 0.265489i
$$682$$ 1.00000 + 1.73205i 0.0382920 + 0.0663237i
$$683$$ −2.00000 3.46410i −0.0765279 0.132550i 0.825222 0.564809i $$-0.191050\pi$$
−0.901750 + 0.432259i $$0.857717\pi$$
$$684$$ 1.50000 2.59808i 0.0573539 0.0993399i
$$685$$ 18.0000 0.687745
$$686$$ −18.5000 + 0.866025i −0.706333 + 0.0330650i
$$687$$ −14.0000 −0.534133
$$688$$ −4.00000 + 6.92820i −0.152499 + 0.264135i
$$689$$ 5.50000 + 9.52628i 0.209533 + 0.362922i
$$690$$ 3.50000 + 6.06218i 0.133243 + 0.230783i
$$691$$ 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i $$-0.760033\pi$$
0.957290 + 0.289130i $$0.0933661\pi$$
$$692$$ −15.0000 −0.570214
$$693$$ −2.00000 + 1.73205i −0.0759737 + 0.0657952i
$$694$$ −14.0000 −0.531433
$$695$$ 10.0000 17.3205i 0.379322 0.657004i
$$696$$ 4.00000 + 6.92820i 0.151620 + 0.262613i
$$697$$ 0 0
$$698$$ 6.00000 10.3923i 0.227103 0.393355i
$$699$$ −18.0000 −0.680823
$$700$$ 0.500000 + 2.59808i 0.0188982 + 0.0981981i
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ −0.500000 + 0.866025i −0.0188713 + 0.0326860i
$$703$$ 16.5000 + 28.5788i 0.622309 + 1.07787i
$$704$$ 0.500000 + 0.866025i 0.0188445 + 0.0326396i
$$705$$ 2.50000 4.33013i 0.0941554 0.163082i
$$706$$ −24.0000 −0.903252
$$707$$ 0 0
$$708$$ −4.00000 −0.150329
$$709$$ −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i $$0.476184\pi$$
−0.900978 + 0.433865i $$0.857149\pi$$
$$710$$ 3.00000 + 5.19615i 0.112588 + 0.195008i
$$711$$ 4.00000 + 6.92820i 0.150012 + 0.259828i
$$712$$ −5.00000 + 8.66025i −0.187383 + 0.324557i
$$713$$ −14.0000 −0.524304
$$714$$ 0 0
$$715$$ 1.00000 0.0373979
$$716$$ 9.50000 16.4545i 0.355032 0.614933i
$$717$$ −9.00000 15.5885i −0.336111 0.582162i
$$718$$ 2.00000 + 3.46410i 0.0746393 + 0.129279i
$$719$$ −1.00000 + 1.73205i −0.0372937 + 0.0645946i −0.884070 0.467355i $$-0.845207\pi$$
0.846776 + 0.531949i $$0.178540\pi$$
$$720$$ −1.00000 −0.0372678
$$721$$ −8.00000 41.5692i −0.297936 1.54812i
$$722$$ 10.0000 0.372161
$$723$$ 3.50000 6.06218i 0.130166 0.225455i
$$724$$ 12.0000 + 20.7846i 0.445976 + 0.772454i
$$725$$ 4.00000 + 6.92820i 0.148556 + 0.257307i
$$726$$ 5.00000 8.66025i 0.185567 0.321412i
$$727$$ 11.0000 0.407967 0.203984 0.978974i $$-0.434611\pi$$
0.203984 + 0.978974i $$0.434611\pi$$
$$728$$ −2.00000 + 1.73205i −0.0741249 + 0.0641941i
$$729$$ 1.00000 0.0370370
$$730$$ 3.00000 5.19615i 0.111035 0.192318i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i $$-0.898450\pi$$
0.746394 + 0.665505i $$0.231784\pi$$
$$734$$ −25.0000 −0.922767
$$735$$ 1.00000 6.92820i 0.0368856 0.255551i
$$736$$ −7.00000 −0.258023
$$737$$ 0 0
$$738$$ −5.50000 9.52628i −0.202458 0.350667i
$$739$$ 9.50000 + 16.4545i 0.349463 + 0.605288i 0.986154 0.165831i $$-0.0530307\pi$$
−0.636691 + 0.771119i $$0.719697\pi$$
$$740$$ 5.50000 9.52628i 0.202184 0.350193i
$$741$$ 3.00000 0.110208
$$742$$ 22.0000 19.0526i 0.807645 0.699441i
$$743$$ 49.0000 1.79764 0.898818 0.438322i $$-0.144427\pi$$
0.898818 + 0.438322i $$0.144427\pi$$
$$744$$ 1.00000 1.73205i 0.0366618 0.0635001i
$$745$$ 0 0
$$746$$ 3.00000 + 5.19615i 0.109838 + 0.190245i
$$747$$ −4.00000 + 6.92820i −0.146352 + 0.253490i
$$748$$ 0 0
$$749$$ −5.00000 25.9808i −0.182696 0.949316i
$$750$$ −1.00000 −0.0365148
$$751$$ −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i $$-0.990660\pi$$
0.525193 + 0.850983i $$0.323993\pi$$
$$752$$ 2.50000 + 4.33013i 0.0911656 + 0.157903i
$$753$$ 6.50000 + 11.2583i 0.236873 + 0.410276i
$$754$$ −4.00000 + 6.92820i −0.145671 + 0.252310i
$$755$$ −6.00000 −0.218362
$$756$$ 2.50000 + 0.866025i 0.0909241 + 0.0314970i
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ −9.50000 + 16.4545i −0.345056 + 0.597654i
$$759$$ −3.50000 6.06218i −0.127042 0.220043i
$$760$$ 1.50000 + 2.59808i 0.0544107 + 0.0942421i
$$761$$ −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i $$-0.996108\pi$$
0.510551 + 0.859848i $$0.329442\pi$$
$$762$$ −17.0000 −0.615845
$$763$$ −15.0000 5.19615i −0.543036 0.188113i
$$764$$ −6.00000 −0.217072
$$765$$ 0 0
$$766$$ 17.5000 + 30.3109i 0.632301 + 1.09518i
$$767$$ −2.00000 3.46410i −0.0722158 0.125081i
$$768$$ 0.500000 0.866025i 0.0180422 0.0312500i
$$769$$ −5.00000 −0.180305 −0.0901523 0.995928i $$-0.528735\pi$$
−0.0901523 + 0.995928i $$0.528735\pi$$
$$770$$ −0.500000 2.59808i −0.0180187 0.0936282i
$$771$$ 20.0000 0.720282
$$772$$ −11.0000 + 19.0526i −0.395899 + 0.685717i
$$773$$ −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i $$-0.964427\pi$$
0.400298 0.916385i $$-0.368907\pi$$
$$774$$ 4.00000 + 6.92820i 0.143777 + 0.249029i
$$775$$ 1.00000 1.73205i 0.0359211 0.0622171i
$$776$$ 16.0000 0.574367
$$777$$ −22.0000 + 19.0526i −0.789246 + 0.683507i
$$778$$ −10.0000 −0.358517
$$779$$ −16.5000 + 28.5788i −0.591174 + 1.02394i
$$780$$ −0.500000 0.866025i −0.0179029 0.0310087i
$$781$$ −3.00000