# Properties

 Label 536.1.ba.a.211.1 Level $536$ Weight $1$ Character 536.211 Analytic conductor $0.267$ Analytic rank $0$ Dimension $20$ Projective image $D_{33}$ CM discriminant -8 Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$536 = 2^{3} \cdot 67$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 536.ba (of order $$66$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.267498846771$$ Analytic rank: $$0$$ Dimension: $$20$$ Coefficient field: $$\Q(\zeta_{33})$$ Defining polynomial: $$x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{33}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{33} - \cdots)$$

## Embedding invariants

 Embedding label 211.1 Root $$0.235759 - 0.971812i$$ of defining polynomial Character $$\chi$$ $$=$$ 536.211 Dual form 536.1.ba.a.315.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.723734 + 0.690079i) q^{2} +(0.0930932 + 0.647478i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.379436 + 0.532843i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(0.548932 - 0.161181i) q^{9} +O(q^{10})$$ $$q+(0.723734 + 0.690079i) q^{2} +(0.0930932 + 0.647478i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.379436 + 0.532843i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(0.548932 - 0.161181i) q^{9} +(-0.759713 - 1.06687i) q^{11} +(-0.642315 + 0.123796i) q^{12} +(-0.995472 + 0.0950560i) q^{16} +(-0.0845850 + 1.77566i) q^{17} +(0.508508 + 0.262154i) q^{18} +(-0.469383 - 1.93482i) q^{19} +(0.186393 - 1.29639i) q^{22} +(-0.550294 - 0.353653i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.427201 + 0.935439i) q^{27} +(-0.786053 - 0.618159i) q^{32} +(0.620049 - 0.591215i) q^{33} +(-1.28656 + 1.22673i) q^{34} +(0.187118 + 0.540641i) q^{36} +(0.995472 - 1.72421i) q^{38} +(1.70566 - 0.879330i) q^{41} +(0.975950 + 0.627205i) q^{43} +(1.02951 - 0.809616i) q^{44} +(-0.154218 - 0.635697i) q^{48} +(-0.888835 - 0.458227i) q^{49} +(0.0475819 - 0.998867i) q^{50} +(-1.15757 + 0.110535i) q^{51} +(-0.336347 + 0.971812i) q^{54} +(1.20906 - 0.484034i) q^{57} +(-1.28605 + 1.48418i) q^{59} +(-0.142315 - 0.989821i) q^{64} +0.856736 q^{66} +(0.415415 - 0.909632i) q^{67} -1.77767 q^{68} +(-0.237662 + 0.520406i) q^{72} +(0.0552004 - 0.0775182i) q^{73} +(0.428368 - 0.494363i) q^{75} +(1.91030 - 0.560914i) q^{76} +(-0.0846203 + 0.0543822i) q^{81} +(1.84125 + 0.540641i) q^{82} +(-0.827068 + 0.0789754i) q^{83} +(0.273507 + 1.12741i) q^{86} +(1.30379 + 0.124497i) q^{88} +(-0.205996 + 1.43273i) q^{89} +(0.327068 - 0.566498i) q^{96} +(-0.0475819 - 0.0824143i) q^{97} +(-0.327068 - 0.945001i) q^{98} +(-0.588989 - 0.463186i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10})$$ $$20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$$.

 $$n$$ $$135$$ $$269$$ $$337$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{8}{33}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.723734 + 0.690079i 0.723734 + 0.690079i
$$3$$ 0.0930932 + 0.647478i 0.0930932 + 0.647478i 0.981929 + 0.189251i $$0.0606061\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$4$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$5$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$6$$ −0.379436 + 0.532843i −0.379436 + 0.532843i
$$7$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$8$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$9$$ 0.548932 0.161181i 0.548932 0.161181i
$$10$$ 0 0
$$11$$ −0.759713 1.06687i −0.759713 1.06687i −0.995472 0.0950560i $$-0.969697\pi$$
0.235759 0.971812i $$-0.424242\pi$$
$$12$$ −0.642315 + 0.123796i −0.642315 + 0.123796i
$$13$$ 0 0 0.327068 0.945001i $$-0.393939\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.995472 + 0.0950560i −0.995472 + 0.0950560i
$$17$$ −0.0845850 + 1.77566i −0.0845850 + 1.77566i 0.415415 + 0.909632i $$0.363636\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0.508508 + 0.262154i 0.508508 + 0.262154i
$$19$$ −0.469383 1.93482i −0.469383 1.93482i −0.327068 0.945001i $$-0.606061\pi$$
−0.142315 0.989821i $$-0.545455\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0.186393 1.29639i 0.186393 1.29639i
$$23$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$24$$ −0.550294 0.353653i −0.550294 0.353653i
$$25$$ −0.654861 0.755750i −0.654861 0.755750i
$$26$$ 0 0
$$27$$ 0.427201 + 0.935439i 0.427201 + 0.935439i
$$28$$ 0 0
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$32$$ −0.786053 0.618159i −0.786053 0.618159i
$$33$$ 0.620049 0.591215i 0.620049 0.591215i
$$34$$ −1.28656 + 1.22673i −1.28656 + 1.22673i
$$35$$ 0 0
$$36$$ 0.187118 + 0.540641i 0.187118 + 0.540641i
$$37$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$38$$ 0.995472 1.72421i 0.995472 1.72421i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i $$-0.242424\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$42$$ 0 0
$$43$$ 0.975950 + 0.627205i 0.975950 + 0.627205i 0.928368 0.371662i $$-0.121212\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$44$$ 1.02951 0.809616i 1.02951 0.809616i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$48$$ −0.154218 0.635697i −0.154218 0.635697i
$$49$$ −0.888835 0.458227i −0.888835 0.458227i
$$50$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$51$$ −1.15757 + 0.110535i −1.15757 + 0.110535i
$$52$$ 0 0
$$53$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$54$$ −0.336347 + 0.971812i −0.336347 + 0.971812i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.20906 0.484034i 1.20906 0.484034i
$$58$$ 0 0
$$59$$ −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i $$0.666667\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.142315 0.989821i −0.142315 0.989821i
$$65$$ 0 0
$$66$$ 0.856736 0.856736
$$67$$ 0.415415 0.909632i 0.415415 0.909632i
$$68$$ −1.77767 −1.77767
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$72$$ −0.237662 + 0.520406i −0.237662 + 0.520406i
$$73$$ 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i $$-0.787879\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$74$$ 0 0
$$75$$ 0.428368 0.494363i 0.428368 0.494363i
$$76$$ 1.91030 0.560914i 1.91030 0.560914i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$80$$ 0 0
$$81$$ −0.0846203 + 0.0543822i −0.0846203 + 0.0543822i
$$82$$ 1.84125 + 0.540641i 1.84125 + 0.540641i
$$83$$ −0.827068 + 0.0789754i −0.827068 + 0.0789754i −0.500000 0.866025i $$-0.666667\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.273507 + 1.12741i 0.273507 + 1.12741i
$$87$$ 0 0
$$88$$ 1.30379 + 0.124497i 1.30379 + 0.124497i
$$89$$ −0.205996 + 1.43273i −0.205996 + 1.43273i 0.580057 + 0.814576i $$0.303030\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0.327068 0.566498i 0.327068 0.566498i
$$97$$ −0.0475819 0.0824143i −0.0475819 0.0824143i 0.841254 0.540641i $$-0.181818\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$98$$ −0.327068 0.945001i −0.327068 0.945001i
$$99$$ −0.588989 0.463186i −0.588989 0.463186i
$$100$$ 0.723734 0.690079i 0.723734 0.690079i
$$101$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$102$$ −0.914053 0.718819i −0.914053 0.718819i
$$103$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i $$-0.181818\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$108$$ −0.914053 + 0.471227i −0.914053 + 0.471227i
$$109$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.95496 0.186677i −1.95496 0.186677i −0.959493 0.281733i $$-0.909091\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$114$$ 1.20906 + 0.484034i 1.20906 + 0.484034i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −1.95496 + 0.186677i −1.95496 + 0.186677i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.233975 + 0.676026i −0.233975 + 0.676026i
$$122$$ 0 0
$$123$$ 0.728132 + 1.02252i 0.728132 + 1.02252i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$128$$ 0.580057 0.814576i 0.580057 0.814576i
$$129$$ −0.315247 + 0.690294i −0.315247 + 0.690294i
$$130$$ 0 0
$$131$$ 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i $$0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$132$$ 0.620049 + 0.591215i 0.620049 + 0.591215i
$$133$$ 0 0
$$134$$ 0.928368 0.371662i 0.928368 0.371662i
$$135$$ 0 0
$$136$$ −1.28656 1.22673i −1.28656 1.22673i
$$137$$ −0.264241 1.83784i −0.264241 1.83784i −0.500000 0.866025i $$-0.666667\pi$$
0.235759 0.971812i $$-0.424242\pi$$
$$138$$ 0 0
$$139$$ −0.415415 + 0.909632i −0.415415 + 0.909632i 0.580057 + 0.814576i $$0.303030\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.531125 + 0.212630i −0.531125 + 0.212630i
$$145$$ 0 0
$$146$$ 0.0934441 0.0180099i 0.0934441 0.0180099i
$$147$$ 0.213947 0.618159i 0.213947 0.618159i
$$148$$ 0 0
$$149$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$150$$ 0.651174 0.0621796i 0.651174 0.0621796i
$$151$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$152$$ 1.76962 + 0.912303i 1.76962 + 0.912303i
$$153$$ 0.239771 + 0.988348i 0.239771 + 0.988348i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −0.0987706 0.0190365i −0.0987706 0.0190365i
$$163$$ −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i $$-0.909091\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$164$$ 0.959493 + 1.66189i 0.959493 + 1.66189i
$$165$$ 0 0
$$166$$ −0.653077 0.513585i −0.653077 0.513585i
$$167$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$168$$ 0 0
$$169$$ −0.786053 0.618159i −0.786053 0.618159i
$$170$$ 0 0
$$171$$ −0.569516 0.986430i −0.569516 0.986430i
$$172$$ −0.580057 + 1.00469i −0.580057 + 1.00469i
$$173$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$177$$ −1.08070 0.694523i −1.08070 0.694523i
$$178$$ −1.13779 + 0.894765i −1.13779 + 0.894765i
$$179$$ −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i $$0.181818\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1.95865 1.25875i 1.95865 1.25875i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$192$$ 0.627639 0.184291i 0.627639 0.184291i
$$193$$ −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i $$0.545455\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$194$$ 0.0224357 0.0924813i 0.0224357 0.0924813i
$$195$$ 0 0
$$196$$ 0.415415 0.909632i 0.415415 0.909632i
$$197$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$198$$ −0.106636 0.741673i −0.106636 0.741673i
$$199$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$200$$ 1.00000 1.00000
$$201$$ 0.627639 + 0.184291i 0.627639 + 0.184291i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.165489 1.15100i −0.165489 1.15100i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1.70760 + 1.97068i −1.70760 + 1.97068i
$$210$$ 0 0
$$211$$ 1.34378 0.537970i 1.34378 0.537970i 0.415415 0.909632i $$-0.363636\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0.0930932 0.268975i 0.0930932 0.268975i
$$215$$ 0 0
$$216$$ −0.986715 0.289726i −0.986715 0.289726i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.0553301 + 0.0285246i 0.0553301 + 0.0285246i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$224$$ 0 0
$$225$$ −0.481286 0.309304i −0.481286 0.309304i
$$226$$ −1.28605 1.48418i −1.28605 1.48418i
$$227$$ −0.419102 + 0.216062i −0.419102 + 0.216062i −0.654861 0.755750i $$-0.727273\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$228$$ 0.541015 + 1.18466i 0.541015 + 1.18466i
$$229$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i $$-0.121212\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.54370 1.21398i −1.54370 1.21398i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ 0 0
$$241$$ 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 $$0$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$242$$ −0.635847 + 0.327802i −0.635847 + 0.327802i
$$243$$ 0.630351 + 0.727464i 0.630351 + 0.727464i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −0.178645 + 1.24250i −0.178645 + 1.24250i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −0.128129 0.528156i −0.128129 0.528156i
$$250$$ 0 0
$$251$$ 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i $$-0.909091\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.981929 0.189251i 0.981929 0.189251i
$$257$$ 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i $$0.121212\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$258$$ −0.704513 + 0.282044i −0.704513 + 0.282044i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1.11312 + 1.56316i −1.11312 + 1.56316i
$$263$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$264$$ 0.0407651 + 0.855765i 0.0407651 + 0.855765i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.946841 −0.946841
$$268$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$272$$ −0.0845850 1.77566i −0.0845850 1.77566i
$$273$$ 0 0
$$274$$ 1.07701 1.51245i 1.07701 1.51245i
$$275$$ −0.308779 + 1.27280i −0.308779 + 1.27280i
$$276$$ 0 0
$$277$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$278$$ −0.928368 + 0.371662i −0.928368 + 0.371662i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.581419 1.67990i 0.581419 1.67990i −0.142315 0.989821i $$-0.545455\pi$$
0.723734 0.690079i $$-0.242424\pi$$
$$282$$ 0 0
$$283$$ 0.959493 + 0.281733i 0.959493 + 0.281733i 0.723734 0.690079i $$-0.242424\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.531125 0.212630i −0.531125 0.212630i
$$289$$ −2.15033 0.205332i −2.15033 0.205332i
$$290$$ 0 0
$$291$$ 0.0489319 0.0384804i 0.0489319 0.0384804i
$$292$$ 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
$$293$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$294$$ 0.581419 0.299742i 0.581419 0.299742i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.673440 1.16643i 0.673440 1.16643i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0.514186 + 0.404360i 0.514186 + 0.404360i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.651174 + 1.88144i 0.651174 + 1.88144i
$$305$$ 0 0
$$306$$ −0.508508 + 0.880762i −0.508508 + 0.880762i
$$307$$ 1.13915 + 0.219553i 1.13915 + 0.219553i 0.723734 0.690079i $$-0.242424\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$312$$ 0 0
$$313$$ 0.283341 1.97068i 0.283341 1.97068i 0.0475819 0.998867i $$-0.484848\pi$$
0.235759 0.971812i $$-0.424242\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.888835 0.458227i $$-0.848485\pi$$
0.888835 + 0.458227i $$0.151515\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0.156630 0.100660i 0.156630 0.100660i
$$322$$ 0 0
$$323$$ 3.47528 0.669806i 3.47528 0.669806i
$$324$$ −0.0583469 0.0819368i −0.0583469 0.0819368i
$$325$$ 0 0
$$326$$ −0.452418 + 0.132842i −0.452418 + 0.132842i
$$327$$ 0 0
$$328$$ −0.452418 + 1.86489i −0.452418 + 1.86489i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.0947329 1.98869i −0.0947329 1.98869i −0.142315 0.989821i $$-0.545455\pi$$
0.0475819 0.998867i $$-0.484848\pi$$
$$332$$ −0.118239 0.822373i −0.118239 0.822373i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.21769 + 1.16106i 1.21769 + 1.16106i 0.981929 + 0.189251i $$0.0606061\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$338$$ −0.142315 0.989821i −0.142315 0.989821i
$$339$$ −0.0611251 1.28317i −0.0611251 1.28317i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.268537 1.10692i 0.268537 1.10692i
$$343$$ 0 0
$$344$$ −1.11312 + 0.326842i −1.11312 + 0.326842i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −0.981929 + 0.189251i −0.981929 + 0.189251i −0.654861 0.755750i $$-0.727273\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.0623191 + 1.30824i −0.0623191 + 1.30824i
$$353$$ 0.252989 + 0.130425i 0.252989 + 0.130425i 0.580057 0.814576i $$-0.303030\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$354$$ −0.302863 1.24842i −0.302863 1.24842i
$$355$$ 0 0
$$356$$ −1.44091 0.137591i −1.44091 0.137591i
$$357$$ 0 0
$$358$$ −0.653077 + 0.513585i −0.653077 + 0.513585i
$$359$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$360$$ 0 0
$$361$$ −2.63438 + 1.35812i −2.63438 + 1.35812i
$$362$$ 0 0
$$363$$ −0.459493 0.0885600i −0.459493 0.0885600i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$368$$ 0 0
$$369$$ 0.794561 0.757613i 0.794561 0.757613i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 2.28618 + 0.440625i 2.28618 + 0.440625i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.50842 1.18624i 1.50842 1.18624i 0.580057 0.814576i $$-0.303030\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$384$$ 0.581419 + 0.299742i 0.581419 + 0.299742i
$$385$$ 0 0
$$386$$ −1.67489 + 0.159932i −1.67489 + 0.159932i
$$387$$ 0.636823 + 0.186988i 0.636823 + 0.186988i
$$388$$ 0.0800569 0.0514495i 0.0800569 0.0514495i
$$389$$ 0 0 0.327068 0.945001i $$-0.393939\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.928368 0.371662i 0.928368 0.371662i
$$393$$ −1.20443 + 0.353653i −1.20443 + 0.353653i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.434637 0.610362i 0.434637 0.610362i
$$397$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.723734 + 0.690079i 0.723734 + 0.690079i
$$401$$ 1.68251 1.68251 0.841254 0.540641i $$-0.181818\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$402$$ 0.327068 + 0.566498i 0.327068 + 0.566498i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.674512 0.947220i 0.674512 0.947220i
$$409$$ −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i $$-0.969697\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$410$$ 0 0
$$411$$ 1.16536 0.342180i 1.16536 0.342180i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −0.627639 0.184291i −0.627639 0.184291i
$$418$$ −2.59577 + 0.247866i −2.59577 + 0.247866i
$$419$$ 0.00452808 0.0950560i 0.00452808 0.0950560i −0.995472 0.0950560i $$-0.969697\pi$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$422$$ 1.34378 + 0.537970i 1.34378 + 0.537970i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.39734 1.09888i 1.39734 1.09888i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0.252989 0.130425i 0.252989 0.130425i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ −0.514186 0.890596i −0.514186 0.890596i
$$433$$ −0.607279 1.75462i −0.607279 1.75462i −0.654861 0.755750i $$-0.727273\pi$$
0.0475819 0.998867i $$-0.484848\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0.0203600 + 0.0588264i 0.0203600 + 0.0588264i
$$439$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$440$$ 0 0
$$441$$ −0.561767 0.108272i −0.561767 0.108272i
$$442$$ 0 0
$$443$$ 1.58006 0.814576i 1.58006 0.814576i 0.580057 0.814576i $$-0.303030\pi$$
1.00000 $$0$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.21590 0.486774i −1.21590 0.486774i −0.327068 0.945001i $$-0.606061\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$450$$ −0.134879 0.555979i −0.134879 0.555979i
$$451$$ −2.23394 1.15168i −2.23394 1.15168i
$$452$$ 0.0934441 1.96163i 0.0934441 1.96163i
$$453$$ 0 0
$$454$$ −0.452418 0.132842i −0.452418 0.132842i
$$455$$ 0 0
$$456$$ −0.425956 + 1.23072i −0.425956 + 1.23072i
$$457$$ 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i $$-0.303030\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$458$$ 0 0
$$459$$ −1.69715 + 0.679438i −1.69715 + 0.679438i
$$460$$ 0 0
$$461$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0.142315 + 0.989821i 0.142315 + 0.989821i
$$467$$ −0.947890 0.903811i −0.947890 0.903811i 0.0475819 0.998867i $$-0.484848\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.279486 1.94387i −0.279486 1.94387i
$$473$$ −0.0722972 1.51770i −0.0722972 1.51770i
$$474$$ 0 0
$$475$$ −1.15486 + 1.62177i −1.15486 + 1.62177i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −0.271738 + 0.785135i −0.271738 + 0.785135i
$$483$$ 0 0
$$484$$ −0.686393 0.201543i −0.686393 0.201543i
$$485$$ 0 0
$$486$$ −0.0458011 + 0.961482i −0.0458011 + 0.961482i
$$487$$ 0 0 −0.888835 0.458227i $$-0.848485\pi$$
0.888835 + 0.458227i $$0.151515\pi$$
$$488$$ 0 0
$$489$$ −0.286343 0.114634i −0.286343 0.114634i
$$490$$ 0 0
$$491$$ 0.142315 0.989821i 0.142315 0.989821i −0.786053 0.618159i $$-0.787879\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$492$$ −0.986715 + 0.775961i −0.986715 + 0.775961i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0.271738 0.470664i 0.271738 0.470664i
$$499$$ 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i $$0.121212\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0.341254 0.325385i 0.341254 0.325385i
$$503$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.327068 0.566498i 0.327068 0.566498i
$$508$$ 0 0
$$509$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$513$$ 1.60939 1.26564i 1.60939 1.26564i
$$514$$ −0.239446 + 1.66538i −0.239446 + 1.66538i
$$515$$ 0 0
$$516$$ −0.704513 0.282044i −0.704513 0.282044i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.50842 + 0.442913i 1.50842 + 0.442913i 0.928368 0.371662i $$-0.121212\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$522$$ 0 0
$$523$$ −0.607279 + 1.75462i −0.607279 + 1.75462i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$524$$ −1.88431 + 0.363170i −1.88431 + 0.363170i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −0.561043 + 0.647478i −0.561043 + 0.647478i
$$529$$ 0.235759 0.971812i 0.235759 0.971812i
$$530$$ 0 0
$$531$$ −0.466733 + 1.02200i −0.466733 + 1.02200i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −0.685261 0.653395i −0.685261 0.653395i
$$535$$ 0 0
$$536$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$537$$ −0.543476 −0.543476
$$538$$ 0 0
$$539$$ 0.186393 + 1.29639i 0.186393 + 1.29639i
$$540$$ 0 0
$$541$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 1.16413 1.34347i 1.16413 1.34347i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.481929 + 0.676774i 0.481929 + 0.676774i 0.981929 0.189251i $$-0.0606061\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$548$$ 1.82318 0.351390i 1.82318 0.351390i
$$549$$ 0 0
$$550$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.928368 0.371662i −0.928368 0.371662i
$$557$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0.997349 + 1.15100i 0.997349 + 1.15100i
$$562$$ 1.58006 0.814576i 1.58006 0.814576i
$$563$$ −0.653077 1.43004i −0.653077 1.43004i −0.888835 0.458227i $$-0.848485\pi$$
0.235759 0.971812i $$-0.424242\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0.0688733 0.0656706i 0.0688733 0.0656706i −0.654861 0.755750i $$-0.727273\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$570$$ 0 0
$$571$$ 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i $$0.0606061\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.237662 0.520406i −0.237662 0.520406i
$$577$$ −1.28656 + 0.663268i −1.28656 + 0.663268i −0.959493 0.281733i $$-0.909091\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$578$$ −1.41457 1.63251i −1.41457 1.63251i
$$579$$ −0.925874 0.595023i −0.925874 0.595023i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0.0619682 + 0.00591725i 0.0619682 + 0.00591725i
$$583$$ 0 0
$$584$$ 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −0.0947329 + 0.00904590i −0.0947329 + 0.00904590i −0.142315 0.989821i $$-0.545455\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$588$$ 0.627639 + 0.184291i 0.627639 + 0.184291i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.0883470 0.0353688i 0.0883470 0.0353688i −0.327068 0.945001i $$-0.606061\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$594$$ 1.29232 0.379460i 1.29232 0.379460i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$600$$ 0.0930932 + 0.647478i 0.0930932 + 0.647478i
$$601$$ 0.341254 + 0.325385i 0.341254 + 0.325385i 0.841254 0.540641i $$-0.181818\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0.0814192 0.566283i 0.0814192 0.566283i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$608$$ −0.827068 + 1.81103i −0.827068 + 1.81103i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.975820 + 0.286527i −0.975820 + 0.286527i
$$613$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$614$$ 0.672932 + 0.945001i 0.672932 + 0.945001i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i $$0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$618$$ 0 0
$$619$$ −1.84833 + 0.176494i −1.84833 + 0.176494i −0.959493 0.281733i $$-0.909091\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.142315 + 0.989821i −0.142315 + 0.989821i
$$626$$ 1.56499 1.23072i 1.56499 1.23072i
$$627$$ −1.43494 0.922178i −1.43494 0.922178i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$632$$ 0 0
$$633$$ 0.473420 + 0.819988i 0.473420 + 0.819988i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i $$-0.909091\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$642$$ 0.182822 + 0.0352360i 0.182822 + 0.0352360i
$$643$$ 0.815816 + 1.78639i 0.815816 + 1.78639i 0.580057 + 0.814576i $$0.303030\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 2.97740 + 1.91346i 2.97740 + 1.91346i
$$647$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$648$$ 0.0143152 0.0995645i 0.0143152 0.0995645i
$$649$$ 2.56046 + 0.244494i 2.56046 + 0.244494i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.419102 0.216062i −0.419102 0.216062i
$$653$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.61435 + 1.03748i −1.61435 + 1.03748i
$$657$$ 0.0178068 0.0514495i 0.0178068 0.0514495i
$$658$$ 0 0
$$659$$ −0.580057 0.814576i −0.580057 0.814576i 0.415415 0.909632i $$-0.363636\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$662$$ 1.30379 1.50465i 1.30379 1.50465i
$$663$$ 0 0
$$664$$ 0.481929 0.676774i 0.481929 0.676774i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.223734 + 1.55610i 0.223734 + 1.55610i 0.723734 + 0.690079i $$0.242424\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$674$$ 0.0800569 + 1.68060i 0.0800569 + 1.68060i
$$675$$ 0.427201 0.935439i 0.427201 0.935439i
$$676$$ 0.580057 0.814576i 0.580057 0.814576i
$$677$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$678$$ 0.841254 0.970858i 0.841254 0.970858i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.178911 0.251245i −0.178911 0.251245i
$$682$$ 0 0
$$683$$ −0.607279 + 1.75462i −0.607279 + 1.75462i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$684$$ 0.958214 0.615807i 0.958214 0.615807i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.03115 0.531595i −1.03115 0.531595i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0.283341 + 0.0270558i 0.283341 + 0.0270558i 0.235759 0.971812i $$-0.424242\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −0.841254 0.540641i −0.841254 0.540641i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.41712 + 3.10305i 1.41712 + 3.10305i
$$698$$ 0 0
$$699$$ −0.327068 + 0.566498i −0.327068 + 0.566498i
$$700$$ 0 0
$$701$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.947890 + 0.903811i −0.947890 + 0.903811i
$$705$$ 0 0
$$706$$ 0.0930932 + 0.268975i 0.0930932 + 0.268975i
$$707$$ 0 0
$$708$$ 0.642315 1.11252i 0.642315 1.11252i
$$709$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −0.947890 1.09392i −0.947890 1.09392i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −0.827068 0.0789754i −0.827068 0.0789754i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.888835 0.458227i $$-0.848485\pi$$
0.888835 + 0.458227i $$0.151515\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −2.84380 0.835015i −2.84380 0.835015i
$$723$$ −0.457201 + 0.293825i −0.457201 + 0.293825i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −0.271437 0.381180i −0.271437 0.381180i
$$727$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$728$$ 0 0
$$729$$ −0.478207 + 0.551880i −0.478207 + 0.551880i
$$730$$ 0 0
$$731$$ −1.19625 + 1.67990i −1.19625 + 1.67990i
$$732$$ 0 0
$$733$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.28605 + 0.247866i −1.28605 + 0.247866i
$$738$$ 1.09786 1.09786
$$739$$ 1.42131 + 1.35522i 1.42131 + 1.35522i 0.841254 + 0.540641i $$0.181818\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −0.441275 + 0.176660i −0.441275 + 0.176660i
$$748$$ 1.35052 + 1.89654i 1.35052 + 1.89654i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$752$$ 0 0
$$753$$ 0.307040 0.0293188i 0.307040 0.0293188i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$758$$ 1.91030 + 0.182411i 1.91030 + 0.182411i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i $$-0.363636\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.213947 + 0.618159i 0.213947 + 0.618159i
$$769$$ −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i $$-0.363636\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$770$$ 0 0
$$771$$ −0.796533 + 0.759493i −0.796533 + 0.759493i
$$772$$ −1.32254 1.04006i −1.32254 1.04006i
$$773$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$774$$ 0.331854 + 0.574788i 0.331854 + 0.574788i
$$775$$ 0 0
$$776$$ 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −2.50196 2.88741i −2.50196 2.88741i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$785$$ 0 0
$$786$$ −1.11574 0.575202i −1.11574 0.575202i
$$787$$ −0.0135432 + 0.284307i −0.0135432 + 0.284307i 0.981929 + 0.189251i $$0.0606061\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0.735759 0.141806i 0.735759 0.141806i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 +