# Properties

 Label 1134.2.f.n.379.1 Level $1134$ Weight $2$ Character 1134.379 Analytic conductor $9.055$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.f (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ 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 378) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 379.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.379 Dual form 1134.2.f.n.757.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -1.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(4.50000 + 7.79423i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +1.00000 q^{35} +5.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -5.00000 q^{44} -1.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} -12.0000 q^{53} +5.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(-7.00000 - 12.1244i) q^{59} +9.00000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +(0.500000 - 0.866025i) q^{70} +13.0000 q^{71} -2.00000 q^{73} +(2.50000 - 4.33013i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(-3.00000 + 5.19615i) q^{79} -1.00000 q^{80} -9.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(-2.50000 + 4.33013i) q^{88} +9.00000 q^{89} +(-0.500000 + 0.866025i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-8.00000 + 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8}+O(q^{10})$$ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 $$2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 5 q^{11} - q^{14} - q^{16} - 4 q^{17} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} + 4 q^{25} - 2 q^{28} + 4 q^{29} + 9 q^{31} + q^{32} - 2 q^{34} + 2 q^{35} + 10 q^{37} - q^{38} - q^{40} - 9 q^{41} + 10 q^{43} - 10 q^{44} - 2 q^{46} + 6 q^{47} - q^{49} - 4 q^{50} - 24 q^{53} + 10 q^{55} - q^{56} - 4 q^{58} - 14 q^{59} + 18 q^{62} + 2 q^{64} + 8 q^{67} + 2 q^{68} + q^{70} + 26 q^{71} - 4 q^{73} + 5 q^{74} + q^{76} - 5 q^{77} - 6 q^{79} - 2 q^{80} - 18 q^{82} - 4 q^{83} - 2 q^{85} - 10 q^{86} - 5 q^{88} + 18 q^{89} - q^{92} - 6 q^{94} - q^{95} - 16 q^{97} - 2 q^{98}+O(q^{100})$$ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 + 2 * q^10 + 5 * q^11 - q^14 - q^16 - 4 * q^17 - 2 * q^19 + q^20 - 5 * q^22 - q^23 + 4 * q^25 - 2 * q^28 + 4 * q^29 + 9 * q^31 + q^32 - 2 * q^34 + 2 * q^35 + 10 * q^37 - q^38 - q^40 - 9 * q^41 + 10 * q^43 - 10 * q^44 - 2 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 24 * q^53 + 10 * q^55 - q^56 - 4 * q^58 - 14 * q^59 + 18 * q^62 + 2 * q^64 + 8 * q^67 + 2 * q^68 + q^70 + 26 * q^71 - 4 * q^73 + 5 * q^74 + q^76 - 5 * q^77 - 6 * q^79 - 2 * q^80 - 18 * q^82 - 4 * q^83 - 2 * q^85 - 10 * q^86 - 5 * q^88 + 18 * q^89 - q^92 - 6 * q^94 - q^95 - 16 * q^97 - 2 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i $$-0.0948835\pi$$
−0.732294 + 0.680989i $$0.761550\pi$$
$$6$$ 0 0
$$7$$ 0.500000 0.866025i 0.188982 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i $$-0.561563\pi$$
0.945979 0.324227i $$-0.105104\pi$$
$$12$$ 0 0
$$13$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416 −0.114708 0.993399i $$-0.536593\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ 0 0
$$22$$ −2.50000 4.33013i −0.533002 0.923186i
$$23$$ −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i $$-0.199913\pi$$
−0.913434 + 0.406986i $$0.866580\pi$$
$$24$$ 0 0
$$25$$ 2.00000 3.46410i 0.400000 0.692820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i $$-0.712214\pi$$
0.989780 + 0.142605i $$0.0455477\pi$$
$$30$$ 0 0
$$31$$ 4.50000 + 7.79423i 0.808224 + 1.39988i 0.914093 + 0.405505i $$0.132904\pi$$
−0.105869 + 0.994380i $$0.533762\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ −1.00000 + 1.73205i −0.171499 + 0.297044i
$$35$$ 1.00000 0.169031
$$36$$ 0 0
$$37$$ 5.00000 0.821995 0.410997 0.911636i $$-0.365181\pi$$
0.410997 + 0.911636i $$0.365181\pi$$
$$38$$ −0.500000 + 0.866025i −0.0811107 + 0.140488i
$$39$$ 0 0
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i $$-0.918608\pi$$
0.264704 0.964330i $$-0.414726\pi$$
$$42$$ 0 0
$$43$$ 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i $$-0.557309\pi$$
0.941562 0.336840i $$-0.109358\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −12.0000 −1.64833 −0.824163 0.566352i $$-0.808354\pi$$
−0.824163 + 0.566352i $$0.808354\pi$$
$$54$$ 0 0
$$55$$ 5.00000 0.674200
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 0 0
$$58$$ −2.00000 3.46410i −0.262613 0.454859i
$$59$$ −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i $$-0.801729\pi$$
−0.0991242 0.995075i $$-0.531604\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 9.00000 1.14300
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i $$-0.00414604\pi$$
−0.511237 + 0.859440i $$0.670813\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 0 0
$$70$$ 0.500000 0.866025i 0.0597614 0.103510i
$$71$$ 13.0000 1.54282 0.771408 0.636341i $$-0.219553\pi$$
0.771408 + 0.636341i $$0.219553\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 2.50000 4.33013i 0.290619 0.503367i
$$75$$ 0 0
$$76$$ 0.500000 + 0.866025i 0.0573539 + 0.0993399i
$$77$$ −2.50000 4.33013i −0.284901 0.493464i
$$78$$ 0 0
$$79$$ −3.00000 + 5.19615i −0.337526 + 0.584613i −0.983967 0.178352i $$-0.942924\pi$$
0.646440 + 0.762964i $$0.276257\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ −9.00000 −0.993884
$$83$$ −2.00000 + 3.46410i −0.219529 + 0.380235i −0.954664 0.297686i $$-0.903785\pi$$
0.735135 + 0.677920i $$0.237119\pi$$
$$84$$ 0 0
$$85$$ −1.00000 1.73205i −0.108465 0.187867i
$$86$$ −5.00000 8.66025i −0.539164 0.933859i
$$87$$ 0 0
$$88$$ −2.50000 + 4.33013i −0.266501 + 0.461593i
$$89$$ 9.00000 0.953998 0.476999 0.878904i $$-0.341725\pi$$
0.476999 + 0.878904i $$0.341725\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.500000 + 0.866025i −0.0521286 + 0.0902894i
$$93$$ 0 0
$$94$$ −3.00000 5.19615i −0.309426 0.535942i
$$95$$ −0.500000 0.866025i −0.0512989 0.0888523i
$$96$$ 0 0
$$97$$ −8.00000 + 13.8564i −0.812277 + 1.40690i 0.0989899 + 0.995088i $$0.468439\pi$$
−0.911267 + 0.411816i $$0.864894\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ −4.00000 −0.400000
$$101$$ −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i $$0.411939\pi$$
−0.969664 + 0.244443i $$0.921395\pi$$
$$102$$ 0 0
$$103$$ 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i $$-0.150978\pi$$
−0.840341 + 0.542059i $$0.817645\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −6.00000 + 10.3923i −0.582772 + 1.00939i
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 7.00000 0.670478 0.335239 0.942133i $$-0.391183\pi$$
0.335239 + 0.942133i $$0.391183\pi$$
$$110$$ 2.50000 4.33013i 0.238366 0.412861i
$$111$$ 0 0
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ −1.00000 1.73205i −0.0940721 0.162938i 0.815149 0.579252i $$-0.196655\pi$$
−0.909221 + 0.416314i $$0.863322\pi$$
$$114$$ 0 0
$$115$$ 0.500000 0.866025i 0.0466252 0.0807573i
$$116$$ −4.00000 −0.371391
$$117$$ 0 0
$$118$$ −14.0000 −1.28880
$$119$$ −1.00000 + 1.73205i −0.0916698 + 0.158777i
$$120$$ 0 0
$$121$$ −7.00000 12.1244i −0.636364 1.10221i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 4.50000 7.79423i 0.404112 0.699942i
$$125$$ 9.00000 0.804984
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 11.0000 + 19.0526i 0.961074 + 1.66463i 0.719811 + 0.694170i $$0.244228\pi$$
0.241264 + 0.970460i $$0.422438\pi$$
$$132$$ 0 0
$$133$$ −0.500000 + 0.866025i −0.0433555 + 0.0750939i
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i $$-0.593796\pi$$
0.973910 0.226935i $$-0.0728704\pi$$
$$138$$ 0 0
$$139$$ 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i $$0.155640\pi$$
−0.0346338 + 0.999400i $$0.511026\pi$$
$$140$$ −0.500000 0.866025i −0.0422577 0.0731925i
$$141$$ 0 0
$$142$$ 6.50000 11.2583i 0.545468 0.944778i
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −2.50000 4.33013i −0.205499 0.355934i
$$149$$ 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ 0 0
$$151$$ −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i $$-0.966722\pi$$
0.587646 + 0.809118i $$0.300055\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 0 0
$$154$$ −5.00000 −0.402911
$$155$$ −4.50000 + 7.79423i −0.361449 + 0.626048i
$$156$$ 0 0
$$157$$ −4.00000 6.92820i −0.319235 0.552931i 0.661094 0.750303i $$-0.270093\pi$$
−0.980329 + 0.197372i $$0.936759\pi$$
$$158$$ 3.00000 + 5.19615i 0.238667 + 0.413384i
$$159$$ 0 0
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ −4.50000 + 7.79423i −0.351391 + 0.608627i
$$165$$ 0 0
$$166$$ 2.00000 + 3.46410i 0.155230 + 0.268866i
$$167$$ 5.00000 + 8.66025i 0.386912 + 0.670151i 0.992032 0.125983i $$-0.0402085\pi$$
−0.605121 + 0.796134i $$0.706875\pi$$
$$168$$ 0 0
$$169$$ 6.50000 11.2583i 0.500000 0.866025i
$$170$$ −2.00000 −0.153393
$$171$$ 0 0
$$172$$ −10.0000 −0.762493
$$173$$ 3.50000 6.06218i 0.266100 0.460899i −0.701751 0.712422i $$-0.747598\pi$$
0.967851 + 0.251523i $$0.0809315\pi$$
$$174$$ 0 0
$$175$$ −2.00000 3.46410i −0.151186 0.261861i
$$176$$ 2.50000 + 4.33013i 0.188445 + 0.326396i
$$177$$ 0 0
$$178$$ 4.50000 7.79423i 0.337289 0.584202i
$$179$$ −24.0000 −1.79384 −0.896922 0.442189i $$-0.854202\pi$$
−0.896922 + 0.442189i $$0.854202\pi$$
$$180$$ 0 0
$$181$$ 18.0000 1.33793 0.668965 0.743294i $$-0.266738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0.500000 + 0.866025i 0.0368605 + 0.0638442i
$$185$$ 2.50000 + 4.33013i 0.183804 + 0.318357i
$$186$$ 0 0
$$187$$ −5.00000 + 8.66025i −0.365636 + 0.633300i
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ −1.00000 −0.0725476
$$191$$ −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i $$-0.867950\pi$$
0.806641 + 0.591041i $$0.201283\pi$$
$$192$$ 0 0
$$193$$ 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i $$-0.0494748\pi$$
−0.628037 + 0.778183i $$0.716141\pi$$
$$194$$ 8.00000 + 13.8564i 0.574367 + 0.994832i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ 10.0000 0.712470 0.356235 0.934396i $$-0.384060\pi$$
0.356235 + 0.934396i $$0.384060\pi$$
$$198$$ 0 0
$$199$$ −13.0000 −0.921546 −0.460773 0.887518i $$-0.652428\pi$$
−0.460773 + 0.887518i $$0.652428\pi$$
$$200$$ −2.00000 + 3.46410i −0.141421 + 0.244949i
$$201$$ 0 0
$$202$$ 7.00000 + 12.1244i 0.492518 + 0.853067i
$$203$$ −2.00000 3.46410i −0.140372 0.243132i
$$204$$ 0 0
$$205$$ 4.50000 7.79423i 0.314294 0.544373i
$$206$$ 1.00000 0.0696733
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −2.50000 + 4.33013i −0.172929 + 0.299521i
$$210$$ 0 0
$$211$$ 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i $$0.106801\pi$$
−0.186966 + 0.982366i $$0.559865\pi$$
$$212$$ 6.00000 + 10.3923i 0.412082 + 0.713746i
$$213$$ 0 0
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ 9.00000 0.610960
$$218$$ 3.50000 6.06218i 0.237050 0.410582i
$$219$$ 0 0
$$220$$ −2.50000 4.33013i −0.168550 0.291937i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −2.50000 + 4.33013i −0.167412 + 0.289967i −0.937509 0.347960i $$-0.886874\pi$$
0.770097 + 0.637927i $$0.220208\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −2.00000 −0.133038
$$227$$ 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i $$-0.769526\pi$$
0.948242 + 0.317547i $$0.102859\pi$$
$$228$$ 0 0
$$229$$ −14.0000 24.2487i −0.925146 1.60240i −0.791326 0.611394i $$-0.790609\pi$$
−0.133820 0.991006i $$-0.542724\pi$$
$$230$$ −0.500000 0.866025i −0.0329690 0.0571040i
$$231$$ 0 0
$$232$$ −2.00000 + 3.46410i −0.131306 + 0.227429i
$$233$$ −14.0000 −0.917170 −0.458585 0.888650i $$-0.651644\pi$$
−0.458585 + 0.888650i $$0.651644\pi$$
$$234$$ 0 0
$$235$$ 6.00000 0.391397
$$236$$ −7.00000 + 12.1244i −0.455661 + 0.789228i
$$237$$ 0 0
$$238$$ 1.00000 + 1.73205i 0.0648204 + 0.112272i
$$239$$ 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i $$0.116196\pi$$
−0.157893 + 0.987456i $$0.550470\pi$$
$$240$$ 0 0
$$241$$ −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i $$-0.982234\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ −14.0000 −0.899954
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0.500000 0.866025i 0.0319438 0.0553283i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −4.50000 7.79423i −0.285750 0.494934i
$$249$$ 0 0
$$250$$ 4.50000 7.79423i 0.284605 0.492950i
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ −5.00000 −0.314347
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 13.5000 + 23.3827i 0.842107 + 1.45857i 0.888110 + 0.459631i $$0.152018\pi$$
−0.0460033 + 0.998941i $$0.514648\pi$$
$$258$$ 0 0
$$259$$ 2.50000 4.33013i 0.155342 0.269061i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 22.0000 1.35916
$$263$$ −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i $$0.390834\pi$$
−0.983728 + 0.179664i $$0.942499\pi$$
$$264$$ 0 0
$$265$$ −6.00000 10.3923i −0.368577 0.638394i
$$266$$ 0.500000 + 0.866025i 0.0306570 + 0.0530994i
$$267$$ 0 0
$$268$$ 4.00000 6.92820i 0.244339 0.423207i
$$269$$ −13.0000 −0.792624 −0.396312 0.918116i $$-0.629710\pi$$
−0.396312 + 0.918116i $$0.629710\pi$$
$$270$$ 0 0
$$271$$ 24.0000 1.45790 0.728948 0.684569i $$-0.240010\pi$$
0.728948 + 0.684569i $$0.240010\pi$$
$$272$$ 1.00000 1.73205i 0.0606339 0.105021i
$$273$$ 0 0
$$274$$ −8.00000 13.8564i −0.483298 0.837096i
$$275$$ −10.0000 17.3205i −0.603023 1.04447i
$$276$$ 0 0
$$277$$ 9.50000 16.4545i 0.570800 0.988654i −0.425684 0.904872i $$-0.639967\pi$$
0.996484 0.0837823i $$-0.0267000\pi$$
$$278$$ 20.0000 1.19952
$$279$$ 0 0
$$280$$ −1.00000 −0.0597614
$$281$$ −5.00000 + 8.66025i −0.298275 + 0.516627i −0.975741 0.218926i $$-0.929745\pi$$
0.677466 + 0.735554i $$0.263078\pi$$
$$282$$ 0 0
$$283$$ 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i $$0.0359589\pi$$
−0.399188 + 0.916869i $$0.630708\pi$$
$$284$$ −6.50000 11.2583i −0.385704 0.668059i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −9.00000 −0.531253
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 2.00000 3.46410i 0.117444 0.203419i
$$291$$ 0 0
$$292$$ 1.00000 + 1.73205i 0.0585206 + 0.101361i
$$293$$ 9.00000 + 15.5885i 0.525786 + 0.910687i 0.999549 + 0.0300351i $$0.00956192\pi$$
−0.473763 + 0.880652i $$0.657105\pi$$
$$294$$ 0 0
$$295$$ 7.00000 12.1244i 0.407556 0.705907i
$$296$$ −5.00000 −0.290619
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −5.00000 8.66025i −0.288195 0.499169i
$$302$$ 5.00000 + 8.66025i 0.287718 + 0.498342i
$$303$$ 0 0
$$304$$ 0.500000 0.866025i 0.0286770 0.0496700i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −5.00000 −0.285365 −0.142683 0.989769i $$-0.545573\pi$$
−0.142683 + 0.989769i $$0.545573\pi$$
$$308$$ −2.50000 + 4.33013i −0.142451 + 0.246732i
$$309$$ 0 0
$$310$$ 4.50000 + 7.79423i 0.255583 + 0.442682i
$$311$$ −4.00000 6.92820i −0.226819 0.392862i 0.730044 0.683400i $$-0.239499\pi$$
−0.956864 + 0.290537i $$0.906166\pi$$
$$312$$ 0 0
$$313$$ 4.00000 6.92820i 0.226093 0.391605i −0.730554 0.682855i $$-0.760738\pi$$
0.956647 + 0.291250i $$0.0940712\pi$$
$$314$$ −8.00000 −0.451466
$$315$$ 0 0
$$316$$ 6.00000 0.337526
$$317$$ −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i $$0.335355\pi$$
−0.999980 + 0.00635137i $$0.997978\pi$$
$$318$$ 0 0
$$319$$ −10.0000 17.3205i −0.559893 0.969762i
$$320$$ 0.500000 + 0.866025i 0.0279508 + 0.0484123i
$$321$$ 0 0
$$322$$ −0.500000 + 0.866025i −0.0278639 + 0.0482617i
$$323$$ 2.00000 0.111283
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −2.00000 + 3.46410i −0.110770 + 0.191859i
$$327$$ 0 0
$$328$$ 4.50000 + 7.79423i 0.248471 + 0.430364i
$$329$$ −3.00000 5.19615i −0.165395 0.286473i
$$330$$ 0 0
$$331$$ 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i $$-0.798271\pi$$
0.915742 + 0.401768i $$0.131604\pi$$
$$332$$ 4.00000 0.219529
$$333$$ 0 0
$$334$$ 10.0000 0.547176
$$335$$ −4.00000 + 6.92820i −0.218543 + 0.378528i
$$336$$ 0 0
$$337$$ −13.5000 23.3827i −0.735392 1.27374i −0.954551 0.298047i $$-0.903665\pi$$
0.219159 0.975689i $$-0.429669\pi$$
$$338$$ −6.50000 11.2583i −0.353553 0.612372i
$$339$$ 0 0
$$340$$ −1.00000 + 1.73205i −0.0542326 + 0.0939336i
$$341$$ 45.0000 2.43689
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ −5.00000 + 8.66025i −0.269582 + 0.466930i
$$345$$ 0 0
$$346$$ −3.50000 6.06218i −0.188161 0.325905i
$$347$$ −1.50000 2.59808i −0.0805242 0.139472i 0.822951 0.568112i $$-0.192326\pi$$
−0.903475 + 0.428640i $$0.858993\pi$$
$$348$$ 0 0
$$349$$ 13.0000 22.5167i 0.695874 1.20529i −0.274011 0.961727i $$-0.588351\pi$$
0.969885 0.243563i $$-0.0783162\pi$$
$$350$$ −4.00000 −0.213809
$$351$$ 0 0
$$352$$ 5.00000 0.266501
$$353$$ −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i $$-0.858773\pi$$
0.823343 + 0.567545i $$0.192107\pi$$
$$354$$ 0 0
$$355$$ 6.50000 + 11.2583i 0.344984 + 0.597530i
$$356$$ −4.50000 7.79423i −0.238500 0.413093i
$$357$$ 0 0
$$358$$ −12.0000 + 20.7846i −0.634220 + 1.09850i
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 9.00000 15.5885i 0.473029 0.819311i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.00000 1.73205i −0.0523424 0.0906597i
$$366$$ 0 0
$$367$$ −17.5000 + 30.3109i −0.913493 + 1.58222i −0.104399 + 0.994535i $$0.533292\pi$$
−0.809093 + 0.587680i $$0.800041\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ 0 0
$$370$$ 5.00000 0.259938
$$371$$ −6.00000 + 10.3923i −0.311504 + 0.539542i
$$372$$ 0 0
$$373$$ 8.50000 + 14.7224i 0.440113 + 0.762299i 0.997697 0.0678218i $$-0.0216049\pi$$
−0.557584 + 0.830120i $$0.688272\pi$$
$$374$$ 5.00000 + 8.66025i 0.258544 + 0.447811i
$$375$$ 0 0
$$376$$ −3.00000 + 5.19615i −0.154713 + 0.267971i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −14.0000 −0.719132 −0.359566 0.933120i $$-0.617075\pi$$
−0.359566 + 0.933120i $$0.617075\pi$$
$$380$$ −0.500000 + 0.866025i −0.0256495 + 0.0444262i
$$381$$ 0 0
$$382$$ 1.50000 + 2.59808i 0.0767467 + 0.132929i
$$383$$ −5.00000 8.66025i −0.255488 0.442518i 0.709540 0.704665i $$-0.248903\pi$$
−0.965028 + 0.262147i $$0.915569\pi$$
$$384$$ 0 0
$$385$$ 2.50000 4.33013i 0.127412 0.220684i
$$386$$ 10.0000 0.508987
$$387$$ 0 0
$$388$$ 16.0000 0.812277
$$389$$ −10.0000 + 17.3205i −0.507020 + 0.878185i 0.492947 + 0.870059i $$0.335920\pi$$
−0.999967 + 0.00812520i $$0.997414\pi$$
$$390$$ 0 0
$$391$$ 1.00000 + 1.73205i 0.0505722 + 0.0875936i
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ 0 0
$$394$$ 5.00000 8.66025i 0.251896 0.436297i
$$395$$ −6.00000 −0.301893
$$396$$ 0 0
$$397$$ −30.0000 −1.50566 −0.752828 0.658217i $$-0.771311\pi$$
−0.752828 + 0.658217i $$0.771311\pi$$
$$398$$ −6.50000 + 11.2583i −0.325816 + 0.564329i
$$399$$ 0 0
$$400$$ 2.00000 + 3.46410i 0.100000 + 0.173205i
$$401$$ −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i $$-0.263528\pi$$
−0.976050 + 0.217545i $$0.930195\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 14.0000 0.696526
$$405$$ 0 0
$$406$$ −4.00000 −0.198517
$$407$$ 12.5000 21.6506i 0.619602 1.07318i
$$408$$ 0 0
$$409$$ 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i $$-0.0871450\pi$$
−0.715523 + 0.698589i $$0.753812\pi$$
$$410$$ −4.50000 7.79423i −0.222239 0.384930i
$$411$$ 0 0
$$412$$ 0.500000 0.866025i 0.0246332 0.0426660i
$$413$$ −14.0000 −0.688895
$$414$$ 0 0
$$415$$ −4.00000 −0.196352
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 2.50000 + 4.33013i 0.122279 + 0.211793i
$$419$$ 3.00000 + 5.19615i 0.146560 + 0.253849i 0.929954 0.367677i $$-0.119847\pi$$
−0.783394 + 0.621525i $$0.786513\pi$$
$$420$$ 0 0
$$421$$ 13.5000 23.3827i 0.657950 1.13960i −0.323196 0.946332i $$-0.604757\pi$$
0.981146 0.193270i $$-0.0619094\pi$$
$$422$$ 22.0000 1.07094
$$423$$ 0 0
$$424$$ 12.0000 0.582772
$$425$$ −4.00000 + 6.92820i −0.194029 + 0.336067i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 6.00000 + 10.3923i 0.290021 + 0.502331i
$$429$$ 0 0
$$430$$ 5.00000 8.66025i 0.241121 0.417635i
$$431$$ 15.0000 0.722525 0.361262 0.932464i $$-0.382346\pi$$
0.361262 + 0.932464i $$0.382346\pi$$
$$432$$ 0 0
$$433$$ −4.00000 −0.192228 −0.0961139 0.995370i $$-0.530641\pi$$
−0.0961139 + 0.995370i $$0.530641\pi$$
$$434$$ 4.50000 7.79423i 0.216007 0.374135i
$$435$$ 0 0
$$436$$ −3.50000 6.06218i −0.167620 0.290326i
$$437$$ 0.500000 + 0.866025i 0.0239182 + 0.0414276i
$$438$$ 0 0
$$439$$ −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i $$0.360782\pi$$
−0.996284 + 0.0861252i $$0.972552\pi$$
$$440$$ −5.00000 −0.238366
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i $$-0.749178\pi$$
0.966591 + 0.256323i $$0.0825112\pi$$
$$444$$ 0 0
$$445$$ 4.50000 + 7.79423i 0.213320 + 0.369482i
$$446$$ 2.50000 + 4.33013i 0.118378 + 0.205037i
$$447$$ 0 0
$$448$$ 0.500000 0.866025i 0.0236228 0.0409159i
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ 0 0
$$451$$ −45.0000 −2.11897
$$452$$ −1.00000 + 1.73205i −0.0470360 + 0.0814688i
$$453$$ 0 0
$$454$$ −3.00000 5.19615i −0.140797 0.243868i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −6.50000 + 11.2583i −0.304057 + 0.526642i −0.977051 0.213006i $$-0.931675\pi$$
0.672994 + 0.739648i $$0.265008\pi$$
$$458$$ −28.0000 −1.30835
$$459$$ 0 0
$$460$$ −1.00000 −0.0466252
$$461$$ 15.5000 26.8468i 0.721907 1.25038i −0.238328 0.971185i $$-0.576599\pi$$
0.960235 0.279195i $$-0.0900675\pi$$
$$462$$ 0 0
$$463$$ 7.00000 + 12.1244i 0.325318 + 0.563467i 0.981577 0.191069i $$-0.0611955\pi$$
−0.656259 + 0.754536i $$0.727862\pi$$
$$464$$ 2.00000 + 3.46410i 0.0928477 + 0.160817i
$$465$$ 0 0
$$466$$ −7.00000 + 12.1244i −0.324269 + 0.561650i
$$467$$ 26.0000 1.20314 0.601568 0.798821i $$-0.294543\pi$$
0.601568 + 0.798821i $$0.294543\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 3.00000 5.19615i 0.138380 0.239681i
$$471$$ 0 0
$$472$$ 7.00000 + 12.1244i 0.322201 + 0.558069i
$$473$$ −25.0000 43.3013i −1.14950 1.99099i
$$474$$ 0 0
$$475$$ −2.00000 + 3.46410i −0.0917663 + 0.158944i
$$476$$ 2.00000 0.0916698
$$477$$ 0 0
$$478$$ 24.0000 1.09773
$$479$$ 16.0000 27.7128i 0.731059 1.26623i −0.225372 0.974273i $$-0.572360\pi$$
0.956431 0.291958i $$-0.0943068\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 7.00000 + 12.1244i 0.318841 + 0.552249i
$$483$$ 0 0
$$484$$ −7.00000 + 12.1244i −0.318182 + 0.551107i
$$485$$ −16.0000 −0.726523
$$486$$ 0 0
$$487$$ 26.0000 1.17817 0.589086 0.808070i $$-0.299488\pi$$
0.589086 + 0.808070i $$0.299488\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −0.500000 0.866025i −0.0225877 0.0391230i
$$491$$ 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i $$-0.101571\pi$$
−0.746438 + 0.665455i $$0.768237\pi$$
$$492$$ 0 0
$$493$$ −4.00000 + 6.92820i −0.180151 + 0.312031i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −9.00000 −0.404112
$$497$$ 6.50000 11.2583i 0.291565 0.505005i
$$498$$ 0 0
$$499$$ −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i $$-0.238523\pi$$
−0.955968 + 0.293471i $$0.905190\pi$$
$$500$$ −4.50000 7.79423i −0.201246 0.348569i
$$501$$ 0 0
$$502$$ 12.0000 20.7846i 0.535586 0.927663i
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 0 0
$$505$$ −14.0000 −0.622992
$$506$$ −2.50000 + 4.33013i −0.111139 + 0.192498i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i $$-0.0360525\pi$$
−0.594675 + 0.803966i $$0.702719\pi$$
$$510$$ 0 0
$$511$$ −1.00000 + 1.73205i −0.0442374 + 0.0766214i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 27.0000 1.19092
$$515$$ −0.500000 + 0.866025i −0.0220326 + 0.0381616i
$$516$$ 0 0
$$517$$ −15.0000 25.9808i −0.659699 1.14263i
$$518$$ −2.50000 4.33013i −0.109844 0.190255i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ 11.0000 0.480996 0.240498 0.970650i $$-0.422689\pi$$
0.240498 + 0.970650i $$0.422689\pi$$
$$524$$ 11.0000 19.0526i 0.480537 0.832315i
$$525$$ 0 0
$$526$$ 10.5000 + 18.1865i 0.457822 + 0.792971i
$$527$$ −9.00000 15.5885i −0.392046 0.679044i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ −12.0000 −0.521247
$$531$$ 0 0
$$532$$ 1.00000 0.0433555
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −6.00000 10.3923i −0.259403 0.449299i
$$536$$ −4.00000 6.92820i −0.172774 0.299253i
$$537$$ 0 0
$$538$$ −6.50000 + 11.2583i −0.280235 + 0.485381i
$$539$$ −5.00000 −0.215365
$$540$$ 0 0
$$541$$ −3.00000 −0.128980 −0.0644900 0.997918i $$-0.520542\pi$$
−0.0644900 + 0.997918i $$0.520542\pi$$
$$542$$ 12.0000 20.7846i 0.515444 0.892775i
$$543$$ 0 0
$$544$$ −1.00000 1.73205i −0.0428746 0.0742611i
$$545$$ 3.50000 + 6.06218i 0.149924 + 0.259675i
$$546$$ 0 0
$$547$$ −6.00000 + 10.3923i −0.256541 + 0.444343i −0.965313 0.261095i $$-0.915916\pi$$
0.708772 + 0.705438i $$0.249250\pi$$
$$548$$ −16.0000 −0.683486
$$549$$ 0 0
$$550$$ −20.0000 −0.852803
$$551$$ −2.00000 + 3.46410i −0.0852029 + 0.147576i
$$552$$ 0 0
$$553$$ 3.00000 + 5.19615i 0.127573 + 0.220963i
$$554$$ −9.50000 16.4545i −0.403616 0.699084i
$$555$$ 0 0
$$556$$ 10.0000 17.3205i 0.424094 0.734553i
$$557$$ −22.0000 −0.932170 −0.466085 0.884740i $$-0.654336\pi$$
−0.466085 + 0.884740i $$0.654336\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −0.500000 + 0.866025i −0.0211289 + 0.0365963i
$$561$$ 0 0
$$562$$ 5.00000 + 8.66025i 0.210912 + 0.365311i
$$563$$ −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i $$-0.193529\pi$$
−0.905088 + 0.425223i $$0.860196\pi$$
$$564$$ 0 0
$$565$$ 1.00000 1.73205i 0.0420703 0.0728679i
$$566$$ 20.0000 0.840663
$$567$$ 0 0
$$568$$ −13.0000 −0.545468
$$569$$ 15.0000 25.9808i 0.628833 1.08917i −0.358954 0.933355i $$-0.616866\pi$$
0.987786 0.155815i $$-0.0498003\pi$$
$$570$$ 0 0
$$571$$ −9.00000 15.5885i −0.376638 0.652357i 0.613933 0.789359i $$-0.289587\pi$$
−0.990571 + 0.137002i $$0.956253\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −4.50000 + 7.79423i −0.187826 + 0.325325i
$$575$$ −4.00000 −0.166812
$$576$$ 0 0
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ −6.50000 + 11.2583i −0.270364 + 0.468285i
$$579$$ 0 0
$$580$$ −2.00000 3.46410i −0.0830455 0.143839i
$$581$$ 2.00000 + 3.46410i 0.0829740 + 0.143715i
$$582$$ 0 0
$$583$$ −30.0000 + 51.9615i −1.24247 + 2.15203i
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ 18.0000 0.743573
$$587$$ 7.00000 12.1244i 0.288921 0.500426i −0.684632 0.728889i $$-0.740037\pi$$
0.973552 + 0.228464i $$0.0733702\pi$$
$$588$$ 0 0
$$589$$ −4.50000 7.79423i −0.185419 0.321156i
$$590$$ −7.00000 12.1244i −0.288185 0.499152i
$$591$$ 0 0
$$592$$ −2.50000 + 4.33013i −0.102749 + 0.177967i
$$593$$ −9.00000 −0.369586 −0.184793 0.982777i $$-0.559161\pi$$
−0.184793 + 0.982777i $$0.559161\pi$$
$$594$$ 0 0
$$595$$ −2.00000 −0.0819920
$$596$$ 3.00000 5.19615i 0.122885 0.212843i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −13.5000 23.3827i −0.551595 0.955391i −0.998160 0.0606393i $$-0.980686\pi$$
0.446565 0.894751i $$-0.352647\pi$$
$$600$$ 0 0
$$601$$ −4.00000 + 6.92820i −0.163163 + 0.282607i −0.936002 0.351996i $$-0.885503\pi$$
0.772838 + 0.634603i $$0.218836\pi$$
$$602$$ −10.0000 −0.407570
$$603$$ 0 0
$$604$$ 10.0000 0.406894
$$605$$ 7.00000 12.1244i 0.284590 0.492925i
$$606$$ 0 0
$$607$$ −6.00000 10.3923i −0.243532 0.421811i 0.718186 0.695852i $$-0.244973\pi$$
−0.961718 + 0.274041i $$0.911640\pi$$
$$608$$ −0.500000 0.866025i −0.0202777 0.0351220i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −15.0000 −0.605844 −0.302922 0.953015i $$-0.597962\pi$$
−0.302922 + 0.953015i $$0.597962\pi$$
$$614$$ −2.50000 + 4.33013i −0.100892 + 0.174750i
$$615$$ 0 0
$$616$$ 2.50000 + 4.33013i 0.100728 + 0.174466i
$$617$$ 7.00000 + 12.1244i 0.281809 + 0.488108i 0.971830 0.235681i $$-0.0757321\pi$$
−0.690021 + 0.723789i $$0.742399\pi$$
$$618$$ 0 0
$$619$$ 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i $$-0.762380\pi$$
0.955131 + 0.296183i $$0.0957138\pi$$
$$620$$ 9.00000 0.361449
$$621$$ 0 0
$$622$$ −8.00000 −0.320771
$$623$$ 4.50000 7.79423i 0.180289 0.312269i
$$624$$ 0 0
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ −4.00000 6.92820i −0.159872 0.276907i
$$627$$ 0 0
$$628$$ −4.00000 + 6.92820i −0.159617 + 0.276465i
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ 3.00000 5.19615i 0.119334 0.206692i
$$633$$ 0 0
$$634$$ 9.00000 + 15.5885i 0.357436 + 0.619097i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −20.0000 −0.791808
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ −11.0000 + 19.0526i −0.434474 + 0.752531i −0.997253 0.0740768i $$-0.976399\pi$$
0.562779 + 0.826608i $$0.309732\pi$$
$$642$$ 0 0
$$643$$ 6.50000 + 11.2583i 0.256335 + 0.443985i 0.965257 0.261301i $$-0.0841516\pi$$
−0.708922 + 0.705287i $$0.750818\pi$$
$$644$$ 0.500000 + 0.866025i 0.0197028 + 0.0341262i
$$645$$ 0 0
$$646$$ 1.00000 1.73205i 0.0393445 0.0681466i
$$647$$ −42.0000 −1.65119 −0.825595 0.564263i $$-0.809160\pi$$
−0.825595 + 0.564263i $$0.809160\pi$$
$$648$$ 0 0
$$649$$ −70.0000 −2.74774
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 2.00000 + 3.46410i 0.0783260 + 0.135665i
$$653$$ −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i $$-0.966977\pi$$
0.407628 0.913148i $$-0.366356\pi$$
$$654$$ 0 0
$$655$$ −11.0000 + 19.0526i −0.429806 + 0.744445i
$$656$$ 9.00000 0.351391
$$657$$ 0 0
$$658$$ −6.00000 −0.233904
$$659$$ 8.50000 14.7224i 0.331113 0.573505i −0.651617 0.758548i $$-0.725909\pi$$
0.982730 + 0.185043i $$0.0592425\pi$$
$$660$$ 0 0
$$661$$ −14.0000 24.2487i −0.544537 0.943166i −0.998636 0.0522143i $$-0.983372\pi$$
0.454099 0.890951i $$-0.349961\pi$$
$$662$$ −2.00000 3.46410i −0.0777322 0.134636i
$$663$$ 0 0
$$664$$ 2.00000 3.46410i 0.0776151 0.134433i
$$665$$ −1.00000 −0.0387783
$$666$$ 0 0
$$667$$ −4.00000 −0.154881
$$668$$ 5.00000 8.66025i 0.193456 0.335075i
$$669$$ 0 0
$$670$$ 4.00000 + 6.92820i 0.154533 + 0.267660i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −13.0000 + 22.5167i −0.501113 + 0.867953i 0.498886 + 0.866668i $$0.333743\pi$$
−0.999999 + 0.00128586i $$0.999591\pi$$
$$674$$ −27.0000 −1.04000
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i $$-0.659695\pi$$
0.999760 0.0219013i $$-0.00697196\pi$$
$$678$$ 0 0
$$679$$ 8.00000 + 13.8564i 0.307012 + 0.531760i
$$680$$ 1.00000 + 1.73205i 0.0383482 + 0.0664211i
$$681$$ 0 0
$$682$$ 22.5000 38.9711i 0.861570 1.49228i
$$683$$ 9.00000 0.344375 0.172188 0.985064i $$-0.444916\pi$$
0.172188 + 0.985064i $$0.444916\pi$$
$$684$$ 0 0
$$685$$ 16.0000 0.611329
$$686$$ −0.500000 + 0.866025i −0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ 5.00000 + 8.66025i 0.190623 + 0.330169i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 2.00000 3.46410i 0.0760836 0.131781i −0.825473 0.564441i $$-0.809092\pi$$
0.901557 + 0.432660i $$0.142425\pi$$
$$692$$ −7.00000 −0.266100
$$693$$ 0 0
$$694$$ −3.00000 −0.113878
$$695$$ −10.0000 + 17.3205i −0.379322 + 0.657004i
$$696$$ 0 0
$$697$$ 9.00000 + 15.5885i 0.340899 + 0.590455i
$$698$$ −13.0000 22.5167i −0.492057 0.852268i
$$699$$ 0 0
$$700$$ −2.00000 + 3.46410i −0.0755929 + 0.130931i
$$701$$ 20.0000 0.755390 0.377695 0.925930i $$-0.376717\pi$$
0.377695 + 0.925930i $$0.376717\pi$$
$$702$$ 0 0
$$703$$ −5.00000 −0.188579
$$704$$ 2.50000 4.33013i 0.0942223 0.163198i
$$705$$ 0 0
$$706$$ 1.50000 + 2.59808i 0.0564532 + 0.0977799i
$$707$$ 7.00000 + 12.1244i 0.263262 + 0.455983i
$$708$$ 0 0
$$709$$ 12.5000 21.6506i 0.469447 0.813107i −0.529943 0.848034i $$-0.677787\pi$$
0.999390 + 0.0349269i $$0.0111198\pi$$
$$710$$ 13.0000 0.487881
$$711$$ 0 0
$$712$$ −9.00000 −0.337289
$$713$$ 4.50000 7.79423i 0.168526 0.291896i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 + 20.7846i 0.448461 + 0.776757i
$$717$$ 0 0
$$718$$ −2.00000 + 3.46410i −0.0746393 + 0.129279i
$$719$$ 30.0000 1.11881 0.559406 0.828894i $$-0.311029\pi$$
0.559406 + 0.828894i $$0.311029\pi$$
$$720$$ 0 0
$$721$$ 1.00000 0.0372419
$$722$$ −9.00000 + 15.5885i −0.334945 + 0.580142i
$$723$$ 0 0
$$724$$ −9.00000 15.5885i −0.334482 0.579340i
$$725$$ −8.00000 13.8564i −0.297113 0.514614i
$$726$$ 0 0
$$727$$ 16.0000 27.7128i 0.593407 1.02781i −0.400362 0.916357i $$-0.631116\pi$$
0.993770 0.111454i $$-0.0355509\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2.00000 −0.0740233
$$731$$ −10.0000 + 17.3205i −0.369863 + 0.640622i
$$732$$ 0 0
$$733$$ 9.00000 + 15.5885i 0.332423 + 0.575773i 0.982986 0.183679i $$-0.0588007\pi$$
−0.650564 + 0.759452i $$0.725467\pi$$
$$734$$ 17.5000 + 30.3109i 0.645937 + 1.11880i
$$735$$ 0 0
$$736$$ 0.500000 0.866025i 0.0184302 0.0319221i
$$737$$ 40.0000 1.47342
$$738$$ 0 0
$$739$$ 18.0000 0.662141 0.331070 0.943606i $$-0.392590\pi$$
0.331070 + 0.943606i $$0.392590\pi$$
$$740$$ 2.50000 4.33013i 0.0919018 0.159179i
$$741$$ 0 0
$$742$$ 6.00000 + 10.3923i 0.220267 + 0.381514i
$$743$$ −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i $$-0.292537\pi$$
−0.991798 + 0.127815i $$0.959204\pi$$
$$744$$ 0 0
$$745$$ −3.00000 + 5.19615i −0.109911 + 0.190372i
$$746$$ 17.0000 0.622414
$$747$$ 0 0
$$748$$ 10.0000 0.365636
$$749$$ −6.00000 + 10.3923i −0.219235 + 0.379727i
$$750$$ 0 0
$$751$$ −9.00000 15.5885i −0.328415 0.568831i 0.653783 0.756682i $$-0.273181\pi$$
−0.982197 + 0.187851i $$0.939848\pi$$
$$752$$ 3.00000 + 5.19615i 0.109399 + 0.189484i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10.0000 −0.363937
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ −7.00000 + 12.1244i −0.254251 + 0.440376i
$$759$$ 0 0
$$760$$ 0.500000 + 0.866025i 0.0181369 + 0.0314140i
$$761$$ −11.0000 19.0526i −0.398750 0.690655i 0.594822 0.803857i $$-0.297222\pi$$
−0.993572 + 0.113203i $$0.963889\pi$$
$$762$$ 0 0
$$763$$ 3.50000 6.06218i 0.126709 0.219466i
$$764$$ 3.00000 0.108536
$$765$$ 0 0
$$766$$ −10.0000 −0.361315
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −20.0000 34.6410i −0.721218 1.24919i −0.960512 0.278240i $$-0.910249\pi$$
0.239293 0.970947i $$-0.423084\pi$$
$$770$$ −2.50000 4.33013i −0.0900937 0.156047i
$$771$$ 0 0
$$772$$ 5.00000 8.66025i 0.179954 0.311689i
$$773$$ −19.0000 −0.683383 −0.341691 0.939812i $$-0.611000\pi$$
−0.341691 + 0.939812i $$0.611000\pi$$
$$774$$ 0 0
$$775$$ 36.0000 1.29316
$$776$$ 8.00000 13.8564i 0.287183 0.497416i
$$777$$ 0 0
$$778$$ 10.0000 + 17.3205i 0.358517 + 0.620970i
$$779$$ 4.50000 + 7.79423i 0.161229 + 0.279257i
$$780$$ 0 0
$$781$$ 32.5000 56.2917i 1.16294 2.01427i
$$782$$ 2.00000 0.0715199
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 4.00000 6.92820i 0.142766 0.247278i
$$786$$ 0 0
$$787$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$788$$ −5.00000 8.66025i −0.178118 0.308509i
$$789$$ 0 0
$$790$$ −3.00000 + 5.19615i −0.106735 + 0.184871i
$$791$$ −2.00000 −0.0711118