# Properties

 Label 1134.2.f.n.757.1 Level $1134$ Weight $2$ Character 1134.757 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: $$x^{2} - x + 1$$ 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 757.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.757 Dual form 1134.2.f.n.379.1

## $q$-expansion

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

## Character values

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

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

## 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 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i $$-0.761550\pi$$
0.955901 + 0.293691i $$0.0948835\pi$$
$$6$$ 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 0.945979 + 0.324227i $$0.105104\pi$$
−0.192201 + 0.981356i $$0.561563\pi$$
$$12$$ 0 0
$$13$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$14$$ −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 −0.913434 0.406986i $$-0.866580\pi$$
0.809177 + 0.587565i $$0.199913\pi$$
$$24$$ 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 0.989780 0.142605i $$-0.0455477\pi$$
−0.618389 + 0.785872i $$0.712214\pi$$
$$30$$ 0 0
$$31$$ 4.50000 7.79423i 0.808224 1.39988i −0.105869 0.994380i $$-0.533762\pi$$
0.914093 0.405505i $$-0.132904\pi$$
$$32$$ 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 0.264704 + 0.964330i $$0.414726\pi$$
−0.967486 + 0.252924i $$0.918608\pi$$
$$42$$ 0 0
$$43$$ 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i $$0.109358\pi$$
−0.179069 + 0.983836i $$0.557309\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 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 −0.0991242 + 0.995075i $$0.531604\pi$$
−0.812198 + 0.583382i $$0.801729\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$62$$ 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 −0.511237 0.859440i $$-0.670813\pi$$
0.999915 + 0.0130248i $$0.00414604\pi$$
$$68$$ 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 0.646440 0.762964i $$-0.276257\pi$$
−0.983967 + 0.178352i $$0.942924\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ −9.00000 −0.993884
$$83$$ −2.00000 3.46410i −0.219529 0.380235i 0.735135 0.677920i $$-0.237119\pi$$
−0.954664 + 0.297686i $$0.903785\pi$$
$$84$$ 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 −0.911267 0.411816i $$-0.864894\pi$$
0.0989899 0.995088i $$-0.468439\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ −4.00000 −0.400000
$$101$$ −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i $$-0.921395\pi$$
0.273138 0.961975i $$-0.411939\pi$$
$$102$$ 0 0
$$103$$ 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i $$-0.817645\pi$$
0.889607 + 0.456727i $$0.150978\pi$$
$$104$$ 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 −0.909221 0.416314i $$-0.863322\pi$$
0.815149 + 0.579252i $$0.196655\pi$$
$$114$$ 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 0.241264 0.970460i $$-0.422438\pi$$
0.719811 0.694170i $$-0.244228\pi$$
$$132$$ 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 0.973910 + 0.226935i $$0.0728704\pi$$
−0.290424 + 0.956898i $$0.593796\pi$$
$$138$$ 0 0
$$139$$ 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i $$-0.511026\pi$$
0.882823 0.469706i $$-0.155640\pi$$
$$140$$ −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 −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i $$-0.300055\pi$$
−0.994540 + 0.104357i $$0.966722\pi$$
$$152$$ 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 −0.980329 0.197372i $$-0.936759\pi$$
0.661094 + 0.750303i $$0.270093\pi$$
$$158$$ 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 −0.605121 0.796134i $$-0.706875\pi$$
0.992032 + 0.125983i $$0.0402085\pi$$
$$168$$ 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 0.967851 0.251523i $$-0.0809315\pi$$
−0.701751 + 0.712422i $$0.747598\pi$$
$$174$$ 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 0.806641 0.591041i $$-0.201283\pi$$
−0.915177 + 0.403051i $$0.867950\pi$$
$$192$$ 0 0
$$193$$ 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i $$-0.716141\pi$$
0.987945 + 0.154805i $$0.0494748\pi$$
$$194$$ 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 −0.186966 0.982366i $$-0.559865\pi$$
0.944237 0.329266i $$-0.106801\pi$$
$$212$$ 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 0.770097 0.637927i $$-0.220208\pi$$
−0.937509 + 0.347960i $$0.886874\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −2.00000 −0.133038
$$227$$ 3.00000 + 5.19615i 0.199117 + 0.344881i 0.948242 0.317547i $$-0.102859\pi$$
−0.749125 + 0.662428i $$0.769526\pi$$
$$228$$ 0 0
$$229$$ −14.0000 + 24.2487i −0.925146 + 1.60240i −0.133820 + 0.991006i $$0.542724\pi$$
−0.791326 + 0.611394i $$0.790609\pi$$
$$230$$ −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 −0.157893 0.987456i $$-0.550470\pi$$
0.934109 0.356988i $$-0.116196\pi$$
$$240$$ 0 0
$$241$$ −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i $$-0.315567\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ −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 −0.0460033 0.998941i $$-0.514648\pi$$
0.888110 0.459631i $$-0.152018\pi$$
$$258$$ 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 −0.983728 0.179664i $$-0.942499\pi$$
0.336270 0.941766i $$-0.390834\pi$$
$$264$$ 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 0.996484 + 0.0837823i $$0.0267000\pi$$
−0.425684 + 0.904872i $$0.639967\pi$$
$$278$$ 20.0000 1.19952
$$279$$ 0 0
$$280$$ −1.00000 −0.0597614
$$281$$ −5.00000 8.66025i −0.298275 0.516627i 0.677466 0.735554i $$-0.263078\pi$$
−0.975741 + 0.218926i $$0.929745\pi$$
$$282$$ 0 0
$$283$$ 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i $$-0.630708\pi$$
0.993626 0.112728i $$-0.0359589\pi$$
$$284$$ −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 −0.473763 0.880652i $$-0.657105\pi$$
0.999549 0.0300351i $$-0.00956192\pi$$
$$294$$ 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 −0.956864 0.290537i $$-0.906166\pi$$
0.730044 + 0.683400i $$0.239499\pi$$
$$312$$ 0 0
$$313$$ 4.00000 + 6.92820i 0.226093 + 0.391605i 0.956647 0.291250i $$-0.0940712\pi$$
−0.730554 + 0.682855i $$0.760738\pi$$
$$314$$ −8.00000 −0.451466
$$315$$ 0 0
$$316$$ 6.00000 0.337526
$$317$$ −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i $$-0.997978\pi$$
0.494489 0.869184i $$-0.335355\pi$$
$$318$$ 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 0.915742 0.401768i $$-0.131604\pi$$
−0.805812 + 0.592172i $$0.798271\pi$$
$$332$$ 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 0.219159 + 0.975689i $$0.429669\pi$$
−0.954551 + 0.298047i $$0.903665\pi$$
$$338$$ −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 −0.903475 0.428640i $$-0.858993\pi$$
0.822951 + 0.568112i $$0.192326\pi$$
$$348$$ 0 0
$$349$$ 13.0000 + 22.5167i 0.695874 + 1.20529i 0.969885 + 0.243563i $$0.0783162\pi$$
−0.274011 + 0.961727i $$0.588351\pi$$
$$350$$ −4.00000 −0.213809
$$351$$ 0 0
$$352$$ 5.00000 0.266501
$$353$$ −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i $$-0.192107\pi$$
−0.903179 + 0.429263i $$0.858773\pi$$
$$354$$ 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 −0.809093 0.587680i $$-0.800041\pi$$
−0.104399 0.994535i $$-0.533292\pi$$
$$368$$ 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 −0.557584 0.830120i $$-0.688272\pi$$
0.997697 + 0.0678218i $$0.0216049\pi$$
$$374$$ 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 −0.965028 0.262147i $$-0.915569\pi$$
0.709540 + 0.704665i $$0.248903\pi$$
$$384$$ 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 −0.999967 0.00812520i $$-0.997414\pi$$
0.492947 0.870059i $$-0.335920\pi$$
$$390$$ 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 −0.976050 0.217545i $$-0.930195\pi$$
0.676425 + 0.736512i $$0.263528\pi$$
$$402$$ 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 −0.715523 0.698589i $$-0.753812\pi$$
0.962757 + 0.270367i $$0.0871450\pi$$
$$410$$ −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 −0.783394 0.621525i $$-0.786513\pi$$
0.929954 + 0.367677i $$0.119847\pi$$
$$420$$ 0 0
$$421$$ 13.5000 + 23.3827i 0.657950 + 1.13960i 0.981146 + 0.193270i $$0.0619094\pi$$
−0.323196 + 0.946332i $$0.604757\pi$$
$$422$$ 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 −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ −5.00000 −0.238366
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.50000 + 9.52628i 0.261313 + 0.452607i 0.966591 0.256323i $$-0.0825112\pi$$
−0.705278 + 0.708931i $$0.749178\pi$$
$$444$$ 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 0.672994 0.739648i $$-0.265008\pi$$
−0.977051 + 0.213006i $$0.931675\pi$$
$$458$$ −28.0000 −1.30835
$$459$$ 0 0
$$460$$ −1.00000 −0.0466252
$$461$$ 15.5000 + 26.8468i 0.721907 + 1.25038i 0.960235 + 0.279195i $$0.0900675\pi$$
−0.238328 + 0.971185i $$0.576599\pi$$
$$462$$ 0 0
$$463$$ 7.00000 12.1244i 0.325318 0.563467i −0.656259 0.754536i $$-0.727862\pi$$
0.981577 + 0.191069i $$0.0611955\pi$$
$$464$$ 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 0.956431 + 0.291958i $$0.0943068\pi$$
−0.225372 + 0.974273i $$0.572360\pi$$
$$480$$ 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 −0.746438 0.665455i $$-0.768237\pi$$
0.949520 + 0.313707i $$0.101571\pi$$
$$492$$ 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 −0.955968 0.293471i $$-0.905190\pi$$
0.732137 + 0.681157i $$0.238523\pi$$
$$500$$ −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 −0.594675 0.803966i $$-0.702719\pi$$
0.993593 + 0.113020i $$0.0360525\pi$$
$$510$$ 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 0.708772 0.705438i $$-0.249250\pi$$
−0.965313 + 0.261095i $$0.915916\pi$$
$$548$$ −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 −0.905088 0.425223i $$-0.860196\pi$$
0.820798 + 0.571218i $$0.193529\pi$$
$$564$$ 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 0.987786 + 0.155815i $$0.0498003\pi$$
−0.358954 + 0.933355i $$0.616866\pi$$
$$570$$ 0 0
$$571$$ −9.00000 + 15.5885i −0.376638 + 0.652357i −0.990571 0.137002i $$-0.956253\pi$$
0.613933 + 0.789359i $$0.289587\pi$$
$$572$$ 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 0.973552 0.228464i $$-0.0733702\pi$$
−0.684632 + 0.728889i $$0.740037\pi$$
$$588$$ 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 0.446565 + 0.894751i $$0.352647\pi$$
−0.998160 + 0.0606393i $$0.980686\pi$$
$$600$$ 0 0
$$601$$ −4.00000 6.92820i −0.163163 0.282607i 0.772838 0.634603i $$-0.218836\pi$$
−0.936002 + 0.351996i $$0.885503\pi$$
$$602$$ −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 −0.961718 0.274041i $$-0.911640\pi$$
0.718186 + 0.695852i $$0.244973\pi$$
$$608$$ −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 −0.690021 0.723789i $$-0.742399\pi$$
0.971830 + 0.235681i $$0.0757321\pi$$
$$618$$ 0 0
$$619$$ 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i $$-0.0957138\pi$$
−0.734068 + 0.679076i $$0.762380\pi$$
$$620$$ 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 0.562779 0.826608i $$-0.309732\pi$$
−0.997253 + 0.0740768i $$0.976399\pi$$
$$642$$ 0 0
$$643$$ 6.50000 11.2583i 0.256335 0.443985i −0.708922 0.705287i $$-0.750818\pi$$
0.965257 + 0.261301i $$0.0841516\pi$$
$$644$$ 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 0.407628 + 0.913148i $$0.366356\pi$$
−0.994623 + 0.103558i $$0.966977\pi$$
$$654$$ 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 0.982730 0.185043i $$-0.0592425\pi$$
−0.651617 + 0.758548i $$0.725909\pi$$
$$660$$ 0 0
$$661$$ −14.0000 + 24.2487i −0.544537 + 0.943166i 0.454099 + 0.890951i $$0.349961\pi$$
−0.998636 + 0.0522143i $$0.983372\pi$$
$$662$$ −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 −0.999999 0.00128586i $$-0.999591\pi$$
0.498886 0.866668i $$-0.333743\pi$$
$$674$$ −27.0000 −1.04000
$$675$$ 0 0
$$676$$ −13.0000 −0.500000
$$677$$ 13.5000 + 23.3827i 0.518847 + 0.898670i 0.999760 + 0.0219013i $$0.00697196\pi$$
−0.480913 + 0.876768i $$0.659695\pi$$
$$678$$ 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 0.901557 0.432660i $$-0.142425\pi$$
−0.825473 + 0.564441i $$0.809092\pi$$
$$692$$ −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 0.999390 0.0349269i $$-0.0111198\pi$$
−0.529943 + 0.848034i $$0.677787\pi$$
$$710$$ 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 0.993770 + 0.111454i $$0.0355509\pi$$
−0.400362 + 0.916357i $$0.631116\pi$$
$$728$$ 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 −0.650564 0.759452i $$-0.725467\pi$$
0.982986 + 0.183679i $$0.0588007\pi$$
$$734$$ 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 −0.991798 0.127815i $$-0.959204\pi$$
0.606590 + 0.795015i $$0.292537\pi$$
$$744$$ 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 −0.982197 0.187851i $$-0.939848\pi$$
0.653783 + 0.756682i $$0.273181\pi$$
$$752$$ 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 −0.993572 0.113203i $$-0.963889\pi$$
0.594822 + 0.803857i $$0.297222\pi$$
$$762$$ 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 0.239293 + 0.970947i $$0.423084\pi$$
−0.960512 + 0.278240i $$0.910249\pi$$
$$770$$ −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 $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$788$$ −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
$$792$$ 0 0
$$793$$ 0 0