# Properties

 Label 1014.2.e.b.991.1 Level $1014$ Weight $2$ Character 1014.991 Analytic conductor $8.097$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1014 = 2 \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1014.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.09683076496$$ 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: no (minimal twist has level 78) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 991.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1014.991 Dual form 1014.2.e.b.529.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +1.00000 q^{12} +2.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +1.00000 q^{18} +(3.00000 - 5.19615i) q^{19} +(-1.00000 + 1.73205i) q^{20} +2.00000 q^{21} +(2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(5.00000 + 8.66025i) q^{29} +(-1.00000 + 1.73205i) q^{30} +10.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{34} +(-2.00000 + 3.46410i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.00000 + 6.92820i) q^{37} -6.00000 q^{38} +2.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(2.00000 - 3.46410i) q^{43} +(-1.00000 + 1.73205i) q^{45} +(2.00000 - 3.46410i) q^{46} +12.0000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +2.00000 q^{51} -6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} -6.00000 q^{57} +(5.00000 - 8.66025i) q^{58} +(2.00000 - 3.46410i) q^{59} +2.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-5.00000 - 8.66025i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(2.00000 - 3.46410i) q^{69} +4.00000 q^{70} +(-0.500000 + 0.866025i) q^{72} +4.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 + 0.866025i) q^{75} +(3.00000 + 5.19615i) q^{76} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -4.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(-2.00000 + 3.46410i) q^{85} -4.00000 q^{86} +(5.00000 - 8.66025i) q^{87} +(-3.00000 - 5.19615i) q^{89} +2.00000 q^{90} -4.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(6.00000 - 10.3923i) q^{95} +1.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 $$2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + 6 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{23} - q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} + 10 q^{29} - 2 q^{30} + 20 q^{31} - q^{32} + 4 q^{34} - 4 q^{35} - q^{36} + 8 q^{37} - 12 q^{38} + 4 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} - 2 q^{45} + 4 q^{46} + 24 q^{47} - q^{48} + 3 q^{49} + q^{50} + 4 q^{51} - 12 q^{53} - q^{54} - 2 q^{56} - 12 q^{57} + 10 q^{58} + 4 q^{59} + 4 q^{60} - 2 q^{61} - 10 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{67} - 2 q^{68} + 4 q^{69} + 8 q^{70} - q^{72} + 8 q^{73} + 8 q^{74} + q^{75} + 6 q^{76} - 2 q^{80} - q^{81} - 10 q^{82} - 8 q^{83} - 2 q^{84} - 4 q^{85} - 8 q^{86} + 10 q^{87} - 6 q^{89} + 4 q^{90} - 8 q^{92} - 10 q^{93} - 12 q^{94} + 12 q^{95} + 2 q^{96} + 12 q^{97} + 3 q^{98}+O(q^{100})$$ 2 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 - 2 * q^10 + 2 * q^12 + 4 * q^14 - 2 * q^15 - q^16 - 2 * q^17 + 2 * q^18 + 6 * q^19 - 2 * q^20 + 4 * q^21 + 4 * q^23 - q^24 - 2 * q^25 + 2 * q^27 - 2 * q^28 + 10 * q^29 - 2 * q^30 + 20 * q^31 - q^32 + 4 * q^34 - 4 * q^35 - q^36 + 8 * q^37 - 12 * q^38 + 4 * q^40 - 10 * q^41 - 2 * q^42 + 4 * q^43 - 2 * q^45 + 4 * q^46 + 24 * q^47 - q^48 + 3 * q^49 + q^50 + 4 * q^51 - 12 * q^53 - q^54 - 2 * q^56 - 12 * q^57 + 10 * q^58 + 4 * q^59 + 4 * q^60 - 2 * q^61 - 10 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^67 - 2 * q^68 + 4 * q^69 + 8 * q^70 - q^72 + 8 * q^73 + 8 * q^74 + q^75 + 6 * q^76 - 2 * q^80 - q^81 - 10 * q^82 - 8 * q^83 - 2 * q^84 - 4 * q^85 - 8 * q^86 + 10 * q^87 - 6 * q^89 + 4 * q^90 - 8 * q^92 - 10 * q^93 - 12 * q^94 + 12 * q^95 + 2 * q^96 + 12 * q^97 + 3 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$$.

 $$n$$ $$677$$ $$847$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 2.00000 0.894427 0.447214 0.894427i $$-0.352416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ −0.500000 + 0.866025i −0.204124 + 0.353553i
$$7$$ −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i $$-0.956709\pi$$
0.612801 + 0.790237i $$0.290043\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −1.00000 1.73205i −0.316228 0.547723i
$$11$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 0 0
$$14$$ 2.00000 0.534522
$$15$$ −1.00000 1.73205i −0.258199 0.447214i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i $$-0.591714\pi$$
0.972404 0.233301i $$-0.0749529\pi$$
$$20$$ −1.00000 + 1.73205i −0.223607 + 0.387298i
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ −1.00000 1.73205i −0.188982 0.327327i
$$29$$ 5.00000 + 8.66025i 0.928477 + 1.60817i 0.785872 + 0.618389i $$0.212214\pi$$
0.142605 + 0.989780i $$0.454452\pi$$
$$30$$ −1.00000 + 1.73205i −0.182574 + 0.316228i
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ −2.00000 + 3.46410i −0.338062 + 0.585540i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i $$0.0617599\pi$$
−0.323640 + 0.946180i $$0.604907\pi$$
$$38$$ −6.00000 −0.973329
$$39$$ 0 0
$$40$$ 2.00000 0.316228
$$41$$ −5.00000 8.66025i −0.780869 1.35250i −0.931436 0.363905i $$-0.881443\pi$$
0.150567 0.988600i $$-0.451890\pi$$
$$42$$ −1.00000 1.73205i −0.154303 0.267261i
$$43$$ 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i $$-0.734678\pi$$
0.977261 + 0.212041i $$0.0680112\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 1.73205i −0.149071 + 0.258199i
$$46$$ 2.00000 3.46410i 0.294884 0.510754i
$$47$$ 12.0000 1.75038 0.875190 0.483779i $$-0.160736\pi$$
0.875190 + 0.483779i $$0.160736\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ 0.500000 + 0.866025i 0.0707107 + 0.122474i
$$51$$ 2.00000 0.280056
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 0 0
$$56$$ −1.00000 + 1.73205i −0.133631 + 0.231455i
$$57$$ −6.00000 −0.794719
$$58$$ 5.00000 8.66025i 0.656532 1.13715i
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 2.00000 0.258199
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ −5.00000 8.66025i −0.635001 1.09985i
$$63$$ −1.00000 1.73205i −0.125988 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.00000 + 1.73205i 0.122169 + 0.211604i 0.920623 0.390453i $$-0.127682\pi$$
−0.798454 + 0.602056i $$0.794348\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ 2.00000 3.46410i 0.240772 0.417029i
$$70$$ 4.00000 0.478091
$$71$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ −0.500000 + 0.866025i −0.0589256 + 0.102062i
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 4.00000 6.92820i 0.464991 0.805387i
$$75$$ 0.500000 + 0.866025i 0.0577350 + 0.100000i
$$76$$ 3.00000 + 5.19615i 0.344124 + 0.596040i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −1.00000 1.73205i −0.111803 0.193649i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −5.00000 + 8.66025i −0.552158 + 0.956365i
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ −1.00000 + 1.73205i −0.109109 + 0.188982i
$$85$$ −2.00000 + 3.46410i −0.216930 + 0.375735i
$$86$$ −4.00000 −0.431331
$$87$$ 5.00000 8.66025i 0.536056 0.928477i
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ −5.00000 8.66025i −0.518476 0.898027i
$$94$$ −6.00000 10.3923i −0.618853 1.07188i
$$95$$ 6.00000 10.3923i 0.615587 1.06623i
$$96$$ 1.00000 0.102062
$$97$$ 6.00000 10.3923i 0.609208 1.05518i −0.382164 0.924095i $$-0.624821\pi$$
0.991371 0.131084i $$-0.0418458\pi$$
$$98$$ 1.50000 2.59808i 0.151523 0.262445i
$$99$$ 0 0
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i $$-0.134941\pi$$
−0.811976 + 0.583691i $$0.801608\pi$$
$$102$$ −1.00000 1.73205i −0.0990148 0.171499i
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ 4.00000 0.390360
$$106$$ 3.00000 + 5.19615i 0.291386 + 0.504695i
$$107$$ −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i $$-0.293050\pi$$
−0.992003 + 0.126217i $$0.959717\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ 4.00000 6.92820i 0.379663 0.657596i
$$112$$ 2.00000 0.188982
$$113$$ −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i $$0.395477\pi$$
−0.981003 + 0.193993i $$0.937856\pi$$
$$114$$ 3.00000 + 5.19615i 0.280976 + 0.486664i
$$115$$ 4.00000 + 6.92820i 0.373002 + 0.646058i
$$116$$ −10.0000 −0.928477
$$117$$ 0 0
$$118$$ −4.00000 −0.368230
$$119$$ −2.00000 3.46410i −0.183340 0.317554i
$$120$$ −1.00000 1.73205i −0.0912871 0.158114i
$$121$$ 5.50000 9.52628i 0.500000 0.866025i
$$122$$ 2.00000 0.181071
$$123$$ −5.00000 + 8.66025i −0.450835 + 0.780869i
$$124$$ −5.00000 + 8.66025i −0.449013 + 0.777714i
$$125$$ −12.0000 −1.07331
$$126$$ −1.00000 + 1.73205i −0.0890871 + 0.154303i
$$127$$ 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i $$-0.0511671\pi$$
−0.632166 + 0.774833i $$0.717834\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ 6.00000 + 10.3923i 0.520266 + 0.901127i
$$134$$ 1.00000 1.73205i 0.0863868 0.149626i
$$135$$ 2.00000 0.172133
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i $$-0.860562\pi$$
0.820141 + 0.572161i $$0.193895\pi$$
$$138$$ −4.00000 −0.340503
$$139$$ 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i $$-0.511026\pi$$
0.882823 0.469706i $$-0.155640\pi$$
$$140$$ −2.00000 3.46410i −0.169031 0.292770i
$$141$$ −6.00000 10.3923i −0.505291 0.875190i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 10.0000 + 17.3205i 0.830455 + 1.43839i
$$146$$ −2.00000 3.46410i −0.165521 0.286691i
$$147$$ 1.50000 2.59808i 0.123718 0.214286i
$$148$$ −8.00000 −0.657596
$$149$$ −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i $$0.361067\pi$$
−0.996207 + 0.0870170i $$0.972267\pi$$
$$150$$ 0.500000 0.866025i 0.0408248 0.0707107i
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 3.00000 5.19615i 0.243332 0.421464i
$$153$$ −1.00000 1.73205i −0.0808452 0.140028i
$$154$$ 0 0
$$155$$ 20.0000 1.60644
$$156$$ 0 0
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ 0 0
$$159$$ 3.00000 + 5.19615i 0.237915 + 0.412082i
$$160$$ −1.00000 + 1.73205i −0.0790569 + 0.136931i
$$161$$ −8.00000 −0.630488
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ −7.00000 + 12.1244i −0.548282 + 0.949653i 0.450110 + 0.892973i $$0.351385\pi$$
−0.998392 + 0.0566798i $$0.981949\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 0 0
$$166$$ 2.00000 + 3.46410i 0.155230 + 0.268866i
$$167$$ −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i $$-0.320359\pi$$
−0.999169 + 0.0407502i $$0.987025\pi$$
$$168$$ 2.00000 0.154303
$$169$$ 0 0
$$170$$ 4.00000 0.306786
$$171$$ 3.00000 + 5.19615i 0.229416 + 0.397360i
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i $$-0.906580\pi$$
0.729155 + 0.684349i $$0.239913\pi$$
$$174$$ −10.0000 −0.758098
$$175$$ 1.00000 1.73205i 0.0755929 0.130931i
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ −3.00000 + 5.19615i −0.224860 + 0.389468i
$$179$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$180$$ −1.00000 1.73205i −0.0745356 0.129099i
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 2.00000 + 3.46410i 0.147442 + 0.255377i
$$185$$ 8.00000 + 13.8564i 0.588172 + 1.01874i
$$186$$ −5.00000 + 8.66025i −0.366618 + 0.635001i
$$187$$ 0 0
$$188$$ −6.00000 + 10.3923i −0.437595 + 0.757937i
$$189$$ −1.00000 + 1.73205i −0.0727393 + 0.125988i
$$190$$ −12.0000 −0.870572
$$191$$ −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i $$-0.976283\pi$$
0.563081 + 0.826402i $$0.309616\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i $$0.0286631\pi$$
−0.420096 + 0.907480i $$0.638004\pi$$
$$194$$ −12.0000 −0.861550
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ 11.0000 + 19.0526i 0.783718 + 1.35744i 0.929762 + 0.368161i $$0.120012\pi$$
−0.146045 + 0.989278i $$0.546654\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 1.00000 1.73205i 0.0705346 0.122169i
$$202$$ 1.00000 1.73205i 0.0703598 0.121867i
$$203$$ −20.0000 −1.40372
$$204$$ −1.00000 + 1.73205i −0.0700140 + 0.121268i
$$205$$ −10.0000 17.3205i −0.698430 1.20972i
$$206$$ −8.00000 13.8564i −0.557386 0.965422i
$$207$$ −4.00000 −0.278019
$$208$$ 0 0
$$209$$ 0 0
$$210$$ −2.00000 3.46410i −0.138013 0.239046i
$$211$$ −6.00000 10.3923i −0.413057 0.715436i 0.582165 0.813070i $$-0.302206\pi$$
−0.995222 + 0.0976347i $$0.968872\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ −4.00000 + 6.92820i −0.273434 + 0.473602i
$$215$$ 4.00000 6.92820i 0.272798 0.472500i
$$216$$ 1.00000 0.0680414
$$217$$ −10.0000 + 17.3205i −0.678844 + 1.17579i
$$218$$ −2.00000 3.46410i −0.135457 0.234619i
$$219$$ −2.00000 3.46410i −0.135147 0.234082i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −8.00000 −0.536925
$$223$$ 7.00000 + 12.1244i 0.468755 + 0.811907i 0.999362 0.0357107i $$-0.0113695\pi$$
−0.530607 + 0.847618i $$0.678036\pi$$
$$224$$ −1.00000 1.73205i −0.0668153 0.115728i
$$225$$ 0.500000 0.866025i 0.0333333 0.0577350i
$$226$$ 14.0000 0.931266
$$227$$ −4.00000 + 6.92820i −0.265489 + 0.459841i −0.967692 0.252136i $$-0.918867\pi$$
0.702202 + 0.711977i $$0.252200\pi$$
$$228$$ 3.00000 5.19615i 0.198680 0.344124i
$$229$$ −4.00000 −0.264327 −0.132164 0.991228i $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 4.00000 6.92820i 0.263752 0.456832i
$$231$$ 0 0
$$232$$ 5.00000 + 8.66025i 0.328266 + 0.568574i
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ 24.0000 1.56559
$$236$$ 2.00000 + 3.46410i 0.130189 + 0.225494i
$$237$$ 0 0
$$238$$ −2.00000 + 3.46410i −0.129641 + 0.224544i
$$239$$ −16.0000 −1.03495 −0.517477 0.855697i $$-0.673129\pi$$
−0.517477 + 0.855697i $$0.673129\pi$$
$$240$$ −1.00000 + 1.73205i −0.0645497 + 0.111803i
$$241$$ 10.0000 17.3205i 0.644157 1.11571i −0.340339 0.940303i $$-0.610542\pi$$
0.984496 0.175409i $$-0.0561248\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ −1.00000 1.73205i −0.0640184 0.110883i
$$245$$ 3.00000 + 5.19615i 0.191663 + 0.331970i
$$246$$ 10.0000 0.637577
$$247$$ 0 0
$$248$$ 10.0000 0.635001
$$249$$ 2.00000 + 3.46410i 0.126745 + 0.219529i
$$250$$ 6.00000 + 10.3923i 0.379473 + 0.657267i
$$251$$ −14.0000 + 24.2487i −0.883672 + 1.53057i −0.0364441 + 0.999336i $$0.511603\pi$$
−0.847228 + 0.531229i $$0.821730\pi$$
$$252$$ 2.00000 0.125988
$$253$$ 0 0
$$254$$ 4.00000 6.92820i 0.250982 0.434714i
$$255$$ 4.00000 0.250490
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 2.00000 + 3.46410i 0.124515 + 0.215666i
$$259$$ −16.0000 −0.994192
$$260$$ 0 0
$$261$$ −10.0000 −0.618984
$$262$$ 4.00000 + 6.92820i 0.247121 + 0.428026i
$$263$$ −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ 0 0
$$265$$ −12.0000 −0.737154
$$266$$ 6.00000 10.3923i 0.367884 0.637193i
$$267$$ −3.00000 + 5.19615i −0.183597 + 0.317999i
$$268$$ −2.00000 −0.122169
$$269$$ 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i $$-0.734725\pi$$
0.977229 + 0.212187i $$0.0680585\pi$$
$$270$$ −1.00000 1.73205i −0.0608581 0.105409i
$$271$$ −5.00000 8.66025i −0.303728 0.526073i 0.673249 0.739416i $$-0.264898\pi$$
−0.976977 + 0.213343i $$0.931565\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ 2.00000 + 3.46410i 0.120386 + 0.208514i
$$277$$ −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i $$-0.852470\pi$$
0.834419 + 0.551131i $$0.185804\pi$$
$$278$$ −20.0000 −1.19952
$$279$$ −5.00000 + 8.66025i −0.299342 + 0.518476i
$$280$$ −2.00000 + 3.46410i −0.119523 + 0.207020i
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ −6.00000 + 10.3923i −0.357295 + 0.618853i
$$283$$ 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i $$-0.128734\pi$$
−0.800439 + 0.599414i $$0.795400\pi$$
$$284$$ 0 0
$$285$$ −12.0000 −0.710819
$$286$$ 0 0
$$287$$ 20.0000 1.18056
$$288$$ −0.500000 0.866025i −0.0294628 0.0510310i
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 10.0000 17.3205i 0.587220 1.01710i
$$291$$ −12.0000 −0.703452
$$292$$ −2.00000 + 3.46410i −0.117041 + 0.202721i
$$293$$ −7.00000 + 12.1244i −0.408944 + 0.708312i −0.994772 0.102123i $$-0.967436\pi$$
0.585827 + 0.810436i $$0.300770\pi$$
$$294$$ −3.00000 −0.174964
$$295$$ 4.00000 6.92820i 0.232889 0.403376i
$$296$$ 4.00000 + 6.92820i 0.232495 + 0.402694i
$$297$$ 0 0
$$298$$ 14.0000 0.810998
$$299$$ 0 0
$$300$$ −1.00000 −0.0577350
$$301$$ 4.00000 + 6.92820i 0.230556 + 0.399335i
$$302$$ 5.00000 + 8.66025i 0.287718 + 0.498342i
$$303$$ 1.00000 1.73205i 0.0574485 0.0995037i
$$304$$ −6.00000 −0.344124
$$305$$ −2.00000 + 3.46410i −0.114520 + 0.198354i
$$306$$ −1.00000 + 1.73205i −0.0571662 + 0.0990148i
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 0 0
$$309$$ −8.00000 13.8564i −0.455104 0.788263i
$$310$$ −10.0000 17.3205i −0.567962 0.983739i
$$311$$ 28.0000 1.58773 0.793867 0.608091i $$-0.208065\pi$$
0.793867 + 0.608091i $$0.208065\pi$$
$$312$$ 0 0
$$313$$ −26.0000 −1.46961 −0.734803 0.678280i $$-0.762726\pi$$
−0.734803 + 0.678280i $$0.762726\pi$$
$$314$$ 1.00000 + 1.73205i 0.0564333 + 0.0977453i
$$315$$ −2.00000 3.46410i −0.112687 0.195180i
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 3.00000 5.19615i 0.168232 0.291386i
$$319$$ 0 0
$$320$$ 2.00000 0.111803
$$321$$ −4.00000 + 6.92820i −0.223258 + 0.386695i
$$322$$ 4.00000 + 6.92820i 0.222911 + 0.386094i
$$323$$ 6.00000 + 10.3923i 0.333849 + 0.578243i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 14.0000 0.775388
$$327$$ −2.00000 3.46410i −0.110600 0.191565i
$$328$$ −5.00000 8.66025i −0.276079 0.478183i
$$329$$ −12.0000 + 20.7846i −0.661581 + 1.14589i
$$330$$ 0 0
$$331$$ 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i $$-0.744713\pi$$
0.970091 + 0.242742i $$0.0780468\pi$$
$$332$$ 2.00000 3.46410i 0.109764 0.190117i
$$333$$ −8.00000 −0.438397
$$334$$ −6.00000 + 10.3923i −0.328305 + 0.568642i
$$335$$ 2.00000 + 3.46410i 0.109272 + 0.189264i
$$336$$ −1.00000 1.73205i −0.0545545 0.0944911i
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ 14.0000 0.760376
$$340$$ −2.00000 3.46410i −0.108465 0.187867i
$$341$$ 0 0
$$342$$ 3.00000 5.19615i 0.162221 0.280976i
$$343$$ −20.0000 −1.07990
$$344$$ 2.00000 3.46410i 0.107833 0.186772i
$$345$$ 4.00000 6.92820i 0.215353 0.373002i
$$346$$ 6.00000 0.322562
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 5.00000 + 8.66025i 0.268028 + 0.464238i
$$349$$ −8.00000 13.8564i −0.428230 0.741716i 0.568486 0.822693i $$-0.307529\pi$$
−0.996716 + 0.0809766i $$0.974196\pi$$
$$350$$ −2.00000 −0.106904
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −13.0000 22.5167i −0.691920 1.19844i −0.971208 0.238233i $$-0.923432\pi$$
0.279288 0.960207i $$-0.409902\pi$$
$$354$$ 2.00000 + 3.46410i 0.106299 + 0.184115i
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ −2.00000 + 3.46410i −0.105851 + 0.183340i
$$358$$ 0 0
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ −1.00000 + 1.73205i −0.0527046 + 0.0912871i
$$361$$ −8.50000 14.7224i −0.447368 0.774865i
$$362$$ 11.0000 + 19.0526i 0.578147 + 1.00138i
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 8.00000 0.418739
$$366$$ −1.00000 1.73205i −0.0522708 0.0905357i
$$367$$ −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i $$-0.233622\pi$$
−0.951336 + 0.308155i $$0.900289\pi$$
$$368$$ 2.00000 3.46410i 0.104257 0.180579i
$$369$$ 10.0000 0.520579
$$370$$ 8.00000 13.8564i 0.415900 0.720360i
$$371$$ 6.00000 10.3923i 0.311504 0.539542i
$$372$$ 10.0000 0.518476
$$373$$ 3.00000 5.19615i 0.155334 0.269047i −0.777847 0.628454i $$-0.783688\pi$$
0.933181 + 0.359408i $$0.117021\pi$$
$$374$$ 0 0
$$375$$ 6.00000 + 10.3923i 0.309839 + 0.536656i
$$376$$ 12.0000 0.618853
$$377$$ 0 0
$$378$$ 2.00000 0.102869
$$379$$ −17.0000 29.4449i −0.873231 1.51248i −0.858635 0.512588i $$-0.828687\pi$$
−0.0145964 0.999893i $$-0.504646\pi$$
$$380$$ 6.00000 + 10.3923i 0.307794 + 0.533114i
$$381$$ 4.00000 6.92820i 0.204926 0.354943i
$$382$$ 12.0000 0.613973
$$383$$ 2.00000 3.46410i 0.102195 0.177007i −0.810394 0.585886i $$-0.800747\pi$$
0.912589 + 0.408879i $$0.134080\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 0 0
$$386$$ 8.00000 13.8564i 0.407189 0.705273i
$$387$$ 2.00000 + 3.46410i 0.101666 + 0.176090i
$$388$$ 6.00000 + 10.3923i 0.304604 + 0.527589i
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ 1.50000 + 2.59808i 0.0757614 + 0.131223i
$$393$$ 4.00000 + 6.92820i 0.201773 + 0.349482i
$$394$$ 11.0000 19.0526i 0.554172 0.959854i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 4.00000 6.92820i 0.200754 0.347717i −0.748017 0.663679i $$-0.768994\pi$$
0.948772 + 0.315963i $$0.102327\pi$$
$$398$$ 0 0
$$399$$ 6.00000 10.3923i 0.300376 0.520266i
$$400$$ 0.500000 + 0.866025i 0.0250000 + 0.0433013i
$$401$$ −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i $$-0.897170\pi$$
0.199207 0.979957i $$-0.436163\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ 0 0
$$404$$ −2.00000 −0.0995037
$$405$$ −1.00000 1.73205i −0.0496904 0.0860663i
$$406$$ 10.0000 + 17.3205i 0.496292 + 0.859602i
$$407$$ 0 0
$$408$$ 2.00000 0.0990148
$$409$$ −2.00000 + 3.46410i −0.0988936 + 0.171289i −0.911227 0.411905i $$-0.864864\pi$$
0.812333 + 0.583193i $$0.198197\pi$$
$$410$$ −10.0000 + 17.3205i −0.493865 + 0.855399i
$$411$$ 2.00000 0.0986527
$$412$$ −8.00000 + 13.8564i −0.394132 + 0.682656i
$$413$$ 4.00000 + 6.92820i 0.196827 + 0.340915i
$$414$$ 2.00000 + 3.46410i 0.0982946 + 0.170251i
$$415$$ −8.00000 −0.392705
$$416$$ 0 0
$$417$$ −20.0000 −0.979404
$$418$$ 0 0
$$419$$ −20.0000 34.6410i −0.977064 1.69232i −0.672949 0.739689i $$-0.734973\pi$$
−0.304115 0.952635i $$-0.598361\pi$$
$$420$$ −2.00000 + 3.46410i −0.0975900 + 0.169031i
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ −6.00000 + 10.3923i −0.292075 + 0.505889i
$$423$$ −6.00000 + 10.3923i −0.291730 + 0.505291i
$$424$$ −6.00000 −0.291386
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ −2.00000 3.46410i −0.0967868 0.167640i
$$428$$ 8.00000 0.386695
$$429$$ 0 0
$$430$$ −8.00000 −0.385794
$$431$$ 10.0000 + 17.3205i 0.481683 + 0.834300i 0.999779 0.0210230i $$-0.00669232\pi$$
−0.518096 + 0.855323i $$0.673359\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i $$0.381462\pi$$
−0.988591 + 0.150624i $$0.951872\pi$$
$$434$$ 20.0000 0.960031
$$435$$ 10.0000 17.3205i 0.479463 0.830455i
$$436$$ −2.00000 + 3.46410i −0.0957826 + 0.165900i
$$437$$ 24.0000 1.14808
$$438$$ −2.00000 + 3.46410i −0.0955637 + 0.165521i
$$439$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ −16.0000 −0.760183 −0.380091 0.924949i $$-0.624107\pi$$
−0.380091 + 0.924949i $$0.624107\pi$$
$$444$$ 4.00000 + 6.92820i 0.189832 + 0.328798i
$$445$$ −6.00000 10.3923i −0.284427 0.492642i
$$446$$ 7.00000 12.1244i 0.331460 0.574105i
$$447$$ 14.0000 0.662177
$$448$$ −1.00000 + 1.73205i −0.0472456 + 0.0818317i
$$449$$ −3.00000 + 5.19615i −0.141579 + 0.245222i −0.928091 0.372353i $$-0.878551\pi$$
0.786513 + 0.617574i $$0.211885\pi$$
$$450$$ −1.00000 −0.0471405
$$451$$ 0 0
$$452$$ −7.00000 12.1244i −0.329252 0.570282i
$$453$$ 5.00000 + 8.66025i 0.234920 + 0.406894i
$$454$$ 8.00000 0.375459
$$455$$ 0 0
$$456$$ −6.00000 −0.280976
$$457$$ −14.0000 24.2487i −0.654892 1.13431i −0.981921 0.189292i $$-0.939381\pi$$
0.327028 0.945015i $$-0.393953\pi$$
$$458$$ 2.00000 + 3.46410i 0.0934539 + 0.161867i
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ −8.00000 −0.373002
$$461$$ 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i $$-0.587131\pi$$
0.968945 0.247276i $$-0.0795353\pi$$
$$462$$ 0 0
$$463$$ −6.00000 −0.278844 −0.139422 0.990233i $$-0.544524\pi$$
−0.139422 + 0.990233i $$0.544524\pi$$
$$464$$ 5.00000 8.66025i 0.232119 0.402042i
$$465$$ −10.0000 17.3205i −0.463739 0.803219i
$$466$$ −3.00000 5.19615i −0.138972 0.240707i
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ −12.0000 20.7846i −0.553519 0.958723i
$$471$$ 1.00000 + 1.73205i 0.0460776 + 0.0798087i
$$472$$ 2.00000 3.46410i 0.0920575 0.159448i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −3.00000 + 5.19615i −0.137649 + 0.238416i
$$476$$ 4.00000 0.183340
$$477$$ 3.00000 5.19615i 0.137361 0.237915i
$$478$$ 8.00000 + 13.8564i 0.365911 + 0.633777i
$$479$$ 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i $$0.0180558\pi$$
−0.450098 + 0.892979i $$0.648611\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ 0 0
$$482$$ −20.0000 −0.910975
$$483$$ 4.00000 + 6.92820i 0.182006 + 0.315244i
$$484$$ 5.50000 + 9.52628i 0.250000 + 0.433013i
$$485$$ 12.0000 20.7846i 0.544892 0.943781i
$$486$$ 1.00000 0.0453609
$$487$$ −9.00000 + 15.5885i −0.407829 + 0.706380i −0.994646 0.103339i $$-0.967047\pi$$
0.586817 + 0.809719i $$0.300381\pi$$
$$488$$ −1.00000 + 1.73205i −0.0452679 + 0.0784063i
$$489$$ 14.0000 0.633102
$$490$$ 3.00000 5.19615i 0.135526 0.234738i
$$491$$ −14.0000 24.2487i −0.631811 1.09433i −0.987181 0.159603i $$-0.948978\pi$$
0.355370 0.934726i $$-0.384355\pi$$
$$492$$ −5.00000 8.66025i −0.225417 0.390434i
$$493$$ −20.0000 −0.900755
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −5.00000 8.66025i −0.224507 0.388857i
$$497$$ 0 0
$$498$$ 2.00000 3.46410i 0.0896221 0.155230i
$$499$$ 14.0000 0.626726 0.313363 0.949633i $$-0.398544\pi$$
0.313363 + 0.949633i $$0.398544\pi$$
$$500$$ 6.00000 10.3923i 0.268328 0.464758i
$$501$$ −6.00000 + 10.3923i −0.268060 + 0.464294i
$$502$$ 28.0000 1.24970
$$503$$ −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i $$0.346375\pi$$
−0.999161 + 0.0409609i $$0.986958\pi$$
$$504$$ −1.00000 1.73205i −0.0445435 0.0771517i
$$505$$ 2.00000 + 3.46410i 0.0889988 + 0.154150i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −8.00000 −0.354943
$$509$$ 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i $$-0.124214\pi$$
−0.791849 + 0.610718i $$0.790881\pi$$
$$510$$ −2.00000 3.46410i −0.0885615 0.153393i
$$511$$ −4.00000 + 6.92820i −0.176950 + 0.306486i
$$512$$ 1.00000 0.0441942
$$513$$ 3.00000 5.19615i 0.132453 0.229416i
$$514$$ 9.00000 15.5885i 0.396973 0.687577i
$$515$$ 32.0000 1.41009
$$516$$ 2.00000 3.46410i 0.0880451 0.152499i
$$517$$ 0 0
$$518$$ 8.00000 + 13.8564i 0.351500 + 0.608816i
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 5.00000 + 8.66025i 0.218844 + 0.379049i
$$523$$ −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i $$-0.194540\pi$$
−0.906434 + 0.422347i $$0.861206\pi$$
$$524$$ 4.00000 6.92820i 0.174741 0.302660i
$$525$$ −2.00000 −0.0872872
$$526$$ −12.0000 + 20.7846i −0.523225 + 0.906252i
$$527$$ −10.0000 + 17.3205i −0.435607 + 0.754493i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 6.00000 + 10.3923i 0.260623 + 0.451413i
$$531$$ 2.00000 + 3.46410i 0.0867926 + 0.150329i
$$532$$ −12.0000 −0.520266
$$533$$ 0 0
$$534$$ 6.00000 0.259645
$$535$$ −8.00000 13.8564i −0.345870 0.599065i
$$536$$ 1.00000 + 1.73205i 0.0431934 + 0.0748132i
$$537$$ 0 0
$$538$$ −10.0000 −0.431131
$$539$$ 0 0
$$540$$ −1.00000 + 1.73205i −0.0430331 + 0.0745356i
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ −5.00000 + 8.66025i −0.214768 + 0.371990i
$$543$$ 11.0000 + 19.0526i 0.472055 + 0.817624i
$$544$$ −1.00000 1.73205i −0.0428746 0.0742611i
$$545$$ 8.00000 0.342682
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ −1.00000 1.73205i −0.0427179 0.0739895i
$$549$$ −1.00000 1.73205i −0.0426790 0.0739221i
$$550$$ 0 0
$$551$$ 60.0000 2.55609
$$552$$ 2.00000 3.46410i 0.0851257 0.147442i
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 8.00000 13.8564i 0.339581 0.588172i
$$556$$ 10.0000 + 17.3205i 0.424094 + 0.734553i
$$557$$ 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i $$-0.0421286\pi$$
−0.609912 + 0.792469i $$0.708795\pi$$
$$558$$ 10.0000 0.423334
$$559$$ 0 0
$$560$$ 4.00000 0.169031
$$561$$ 0 0
$$562$$ −5.00000 8.66025i −0.210912 0.365311i
$$563$$ −8.00000 + 13.8564i −0.337160 + 0.583978i −0.983897 0.178735i $$-0.942800\pi$$
0.646737 + 0.762713i $$0.276133\pi$$
$$564$$ 12.0000 0.505291
$$565$$ −14.0000 + 24.2487i −0.588984 + 1.02015i
$$566$$ 2.00000 3.46410i 0.0840663 0.145607i
$$567$$ 2.00000 0.0839921
$$568$$ 0 0
$$569$$ 5.00000 + 8.66025i 0.209611 + 0.363057i 0.951592 0.307364i $$-0.0994469\pi$$
−0.741981 + 0.670421i $$0.766114\pi$$
$$570$$ 6.00000 + 10.3923i 0.251312 + 0.435286i
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ 0 0
$$573$$ 12.0000 0.501307
$$574$$ −10.0000 17.3205i −0.417392 0.722944i
$$575$$ −2.00000 3.46410i −0.0834058 0.144463i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 8.00000 0.333044 0.166522 0.986038i $$-0.446746\pi$$
0.166522 + 0.986038i $$0.446746\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ 8.00000 13.8564i 0.332469 0.575853i
$$580$$ −20.0000 −0.830455
$$581$$ 4.00000 6.92820i 0.165948 0.287430i
$$582$$ 6.00000 + 10.3923i 0.248708 + 0.430775i
$$583$$ 0 0
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ 14.0000 0.578335
$$587$$ −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i $$-0.970562\pi$$
0.417885 0.908500i $$-0.362772\pi$$
$$588$$ 1.50000 + 2.59808i 0.0618590 + 0.107143i
$$589$$ 30.0000 51.9615i 1.23613 2.14104i
$$590$$ −8.00000 −0.329355
$$591$$ 11.0000 19.0526i 0.452480 0.783718i
$$592$$ 4.00000 6.92820i 0.164399 0.284747i
$$593$$ −26.0000 −1.06769 −0.533846 0.845582i $$-0.679254\pi$$
−0.533846 + 0.845582i $$0.679254\pi$$
$$594$$ 0 0
$$595$$ −4.00000 6.92820i −0.163984 0.284029i
$$596$$ −7.00000 12.1244i −0.286731 0.496633i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0.500000 + 0.866025i 0.0204124 + 0.0353553i
$$601$$ −11.0000 19.0526i −0.448699 0.777170i 0.549602 0.835426i $$-0.314779\pi$$
−0.998302 + 0.0582563i $$0.981446\pi$$
$$602$$ 4.00000 6.92820i 0.163028 0.282372i
$$603$$ −2.00000 −0.0814463
$$604$$ 5.00000 8.66025i 0.203447 0.352381i
$$605$$ 11.0000 19.0526i 0.447214 0.774597i
$$606$$ −2.00000 −0.0812444
$$607$$ 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i $$-0.608345\pi$$
0.983262 0.182199i $$-0.0583216\pi$$
$$608$$ 3.00000 + 5.19615i 0.121666 + 0.210732i
$$609$$ 10.0000 + 17.3205i 0.405220 + 0.701862i
$$610$$ 4.00000 0.161955
$$611$$ 0 0
$$612$$ 2.00000 0.0808452
$$613$$ −8.00000 13.8564i −0.323117 0.559655i 0.658012 0.753007i $$-0.271397\pi$$
−0.981129 + 0.193352i $$0.938064\pi$$
$$614$$ −1.00000 1.73205i −0.0403567 0.0698999i
$$615$$ −10.0000 + 17.3205i −0.403239 + 0.698430i
$$616$$ 0 0
$$617$$ 11.0000 19.0526i 0.442843 0.767027i −0.555056 0.831813i $$-0.687303\pi$$
0.997899 + 0.0647859i $$0.0206365\pi$$
$$618$$ −8.00000 + 13.8564i −0.321807 + 0.557386i
$$619$$ 26.0000 1.04503 0.522514 0.852631i $$-0.324994\pi$$
0.522514 + 0.852631i $$0.324994\pi$$
$$620$$ −10.0000 + 17.3205i −0.401610 + 0.695608i
$$621$$ 2.00000 + 3.46410i 0.0802572 + 0.139010i
$$622$$ −14.0000 24.2487i −0.561349 0.972285i
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 13.0000 + 22.5167i 0.519584 + 0.899947i
$$627$$ 0 0
$$628$$ 1.00000 1.73205i 0.0399043 0.0691164i
$$629$$ −16.0000 −0.637962
$$630$$ −2.00000 + 3.46410i −0.0796819 + 0.138013i
$$631$$ 5.00000 8.66025i 0.199047 0.344759i −0.749173 0.662375i $$-0.769549\pi$$
0.948220 + 0.317615i $$0.102882\pi$$
$$632$$ 0 0
$$633$$ −6.00000 + 10.3923i −0.238479 + 0.413057i
$$634$$ −9.00000 15.5885i −0.357436 0.619097i
$$635$$ 8.00000 + 13.8564i 0.317470 + 0.549875i
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 1.73205i −0.0395285 0.0684653i
$$641$$ −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i $$-0.949015\pi$$
0.631721 + 0.775196i $$0.282349\pi$$
$$642$$ 8.00000 0.315735
$$643$$ −3.00000 + 5.19615i −0.118308 + 0.204916i −0.919097 0.394030i $$-0.871080\pi$$
0.800789 + 0.598947i $$0.204414\pi$$
$$644$$ 4.00000 6.92820i 0.157622 0.273009i
$$645$$ −8.00000 −0.315000
$$646$$ 6.00000 10.3923i 0.236067 0.408880i
$$647$$ −16.0000 27.7128i −0.629025 1.08950i −0.987748 0.156059i $$-0.950121\pi$$
0.358723 0.933444i $$-0.383212\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 20.0000 0.783862
$$652$$ −7.00000 12.1244i −0.274141 0.474826i
$$653$$ 13.0000 + 22.5167i 0.508729 + 0.881145i 0.999949 + 0.0101092i $$0.00321793\pi$$
−0.491220 + 0.871036i $$0.663449\pi$$
$$654$$ −2.00000 + 3.46410i −0.0782062 + 0.135457i
$$655$$ −16.0000 −0.625172
$$656$$ −5.00000 + 8.66025i −0.195217 + 0.338126i
$$657$$ −2.00000 + 3.46410i −0.0780274 + 0.135147i
$$658$$ 24.0000 0.935617
$$659$$ −10.0000 + 17.3205i −0.389545 + 0.674711i −0.992388 0.123148i $$-0.960701\pi$$
0.602844 + 0.797859i $$0.294034\pi$$
$$660$$ 0 0
$$661$$ −20.0000 34.6410i −0.777910 1.34738i −0.933144 0.359502i $$-0.882947\pi$$
0.155235 0.987878i $$-0.450387\pi$$
$$662$$ −10.0000 −0.388661
$$663$$ 0 0
$$664$$ −4.00000 −0.155230
$$665$$ 12.0000 + 20.7846i 0.465340 + 0.805993i
$$666$$ 4.00000 + 6.92820i 0.154997 + 0.268462i
$$667$$ −20.0000 + 34.6410i −0.774403 + 1.34131i
$$668$$ 12.0000 0.464294
$$669$$ 7.00000 12.1244i 0.270636 0.468755i
$$670$$ 2.00000 3.46410i 0.0772667 0.133830i
$$671$$ 0 0
$$672$$ −1.00000 + 1.73205i −0.0385758 + 0.0668153i
$$673$$ −3.00000 5.19615i −0.115642 0.200297i 0.802395 0.596794i $$-0.203559\pi$$
−0.918036 + 0.396497i $$0.870226\pi$$
$$674$$ −1.00000 1.73205i −0.0385186 0.0667161i
$$675$$ −1.00000 −0.0384900
$$676$$ 0 0
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ −7.00000 12.1244i −0.268833 0.465633i
$$679$$ 12.0000 + 20.7846i 0.460518 + 0.797640i
$$680$$ −2.00000 + 3.46410i −0.0766965 + 0.132842i
$$681$$ 8.00000 0.306561
$$682$$ 0 0
$$683$$ −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i $$-0.985185\pi$$
0.539750 + 0.841825i $$0.318519\pi$$
$$684$$ −6.00000 −0.229416
$$685$$ −2.00000 + 3.46410i −0.0764161 + 0.132357i
$$686$$ 10.0000 + 17.3205i 0.381802 + 0.661300i
$$687$$ 2.00000 + 3.46410i 0.0763048 + 0.132164i
$$688$$ −4.00000 −0.152499
$$689$$ 0 0
$$690$$ −8.00000 −0.304555
$$691$$ 5.00000 + 8.66025i 0.190209 + 0.329452i 0.945319 0.326146i $$-0.105750\pi$$
−0.755110 + 0.655598i $$0.772417\pi$$
$$692$$ −3.00000 5.19615i −0.114043 0.197528i
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 20.0000 34.6410i 0.758643 1.31401i
$$696$$ 5.00000 8.66025i 0.189525 0.328266i
$$697$$ 20.0000 0.757554
$$698$$ −8.00000 + 13.8564i −0.302804 + 0.524473i
$$699$$ −3.00000 5.19615i −0.113470 0.196537i
$$700$$ 1.00000 + 1.73205i 0.0377964 + 0.0654654i
$$701$$ −22.0000 −0.830929 −0.415464 0.909610i $$-0.636381\pi$$
−0.415464 + 0.909610i $$0.636381\pi$$
$$702$$ 0 0
$$703$$ 48.0000 1.81035
$$704$$ 0 0
$$705$$ −12.0000 20.7846i −0.451946 0.782794i
$$706$$ −13.0000 + 22.5167i −0.489261 + 0.847426i
$$707$$ −4.00000 −0.150435
$$708$$ 2.00000 3.46410i 0.0751646 0.130189i
$$709$$ −18.0000 + 31.1769i −0.676004 + 1.17087i 0.300170 + 0.953886i $$0.402957\pi$$
−0.976174 + 0.216988i $$0.930377\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −3.00000 5.19615i −0.112430 0.194734i
$$713$$ 20.0000 + 34.6410i 0.749006 + 1.29732i
$$714$$ 4.00000 0.149696
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 8.00000 + 13.8564i 0.298765 + 0.517477i
$$718$$ 2.00000 + 3.46410i 0.0746393 + 0.129279i
$$719$$ 10.0000 17.3205i 0.372937 0.645946i −0.617079 0.786901i $$-0.711684\pi$$
0.990016 + 0.140955i $$0.0450174\pi$$
$$720$$ 2.00000 0.0745356
$$721$$ −16.0000 + 27.7128i −0.595871 + 1.03208i
$$722$$ −8.50000 + 14.7224i −0.316337 + 0.547912i
$$723$$ −20.0000 −0.743808
$$724$$ 11.0000 19.0526i 0.408812 0.708083i
$$725$$ −5.00000 8.66025i −0.185695 0.321634i
$$726$$ 5.50000 + 9.52628i 0.204124 + 0.353553i
$$727$$ −8.00000 −0.296704 −0.148352 0.988935i $$-0.547397\pi$$
−0.148352 + 0.988935i $$0.547397\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ −4.00000 6.92820i −0.148047 0.256424i
$$731$$ 4.00000 + 6.92820i 0.147945 + 0.256249i
$$732$$ −1.00000 + 1.73205i −0.0369611 + 0.0640184i
$$733$$ −44.0000 −1.62518 −0.812589 0.582838i $$-0.801942\pi$$
−0.812589 + 0.582838i $$0.801942\pi$$
$$734$$ −4.00000 + 6.92820i −0.147643 + 0.255725i
$$735$$ 3.00000 5.19615i 0.110657 0.191663i
$$736$$ −4.00000 −0.147442
$$737$$ 0 0
$$738$$ −5.00000 8.66025i −0.184053 0.318788i
$$739$$ −13.0000 22.5167i −0.478213 0.828289i 0.521475 0.853266i $$-0.325382\pi$$
−0.999688 + 0.0249776i $$0.992049\pi$$
$$740$$ −16.0000 −0.588172
$$741$$ 0 0
$$742$$ −12.0000 −0.440534
$$743$$ −8.00000 13.8564i −0.293492 0.508342i 0.681141 0.732152i $$-0.261484\pi$$
−0.974633 + 0.223810i $$0.928151\pi$$
$$744$$ −5.00000 8.66025i −0.183309 0.317500i
$$745$$ −14.0000 + 24.2487i −0.512920 + 0.888404i
$$746$$ −6.00000 −0.219676
$$747$$ 2.00000 3.46410i 0.0731762 0.126745i
$$748$$ 0 0
$$749$$ 16.0000 0.584627
$$750$$ 6.00000 10.3923i 0.219089 0.379473i
$$751$$ 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i $$0.0317870\pi$$
−0.411170 + 0.911559i $$0.634880\pi$$
$$752$$ −6.00000 10.3923i −0.218797 0.378968i
$$753$$ 28.0000 1.02038
$$754$$ 0 0
$$755$$ −20.0000 −0.727875
$$756$$ −1.00000 1.73205i −0.0363696 0.0629941i
$$757$$ 11.0000 + 19.0526i 0.399802 + 0.692477i 0.993701 0.112062i $$-0.0357456\pi$$
−0.593899 + 0.804539i $$0.702412\pi$$
$$758$$ −17.0000 + 29.4449i −0.617468 + 1.06949i
$$759$$ 0 0
$$760$$ 6.00000 10.3923i 0.217643 0.376969i
$$761$$ 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i $$-0.650337\pi$$
0.998684 0.0512772i $$-0.0163292\pi$$
$$762$$ −8.00000 −0.289809
$$763$$ −4.00000 + 6.92820i −0.144810 + 0.250818i
$$764$$ −6.00000 10.3923i −0.217072 0.375980i
$$765$$ −2.00000 3.46410i −0.0723102 0.125245i
$$766$$ −4.00000 −0.144526
$$767$$ 0 0
$$768$$ 1.00000 0.0360844
$$769$$ −12.0000 20.7846i −0.432731 0.749512i 0.564376 0.825518i $$-0.309117\pi$$
−0.997107 + 0.0760054i $$0.975783\pi$$
$$770$$ 0 0
$$771$$ 9.00000 15.5885i 0.324127 0.561405i
$$772$$ −16.0000 −0.575853
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ 2.00000 3.46410i 0.0718885 0.124515i
$$775$$ −10.0000 −0.359211
$$776$$ 6.00000 10.3923i 0.215387 0.373062i
$$777$$ 8.00000 + 13.8564i 0.286998 + 0.497096i
$$778$$ 15.0000 + 25.9808i 0.537776 + 0.931455i
$$779$$ −60.0000 −2.14972
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 4.00000 + 6.92820i 0.143040 + 0.247752i
$$783$$ 5.00000