# Properties

 Label 536.1.ba.a.323.1 Level $536$ Weight $1$ Character 536.323 Analytic conductor $0.267$ Analytic rank $0$ Dimension $20$ Projective image $D_{33}$ CM discriminant -8 Inner twists $4$

# Related objects

## 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 323.1 Root $$-0.786053 + 0.618159i$$ of defining polynomial Character $$\chi$$ $$=$$ 536.323 Dual form 536.1.ba.a.307.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.928368 + 0.371662i) q^{2} +(-0.759713 + 0.876756i) q^{3} +(0.723734 + 0.690079i) q^{4} +(-1.03115 + 0.531595i) q^{6} +(0.415415 + 0.909632i) q^{8} +(-0.0492216 - 0.342344i) q^{9} +O(q^{10})$$ $$q+(0.928368 + 0.371662i) q^{2} +(-0.759713 + 0.876756i) q^{3} +(0.723734 + 0.690079i) q^{4} +(-1.03115 + 0.531595i) q^{6} +(0.415415 + 0.909632i) q^{8} +(-0.0492216 - 0.342344i) q^{9} +(-0.738471 - 0.380708i) q^{11} +(-1.15486 + 0.110276i) q^{12} +(0.0475819 + 0.998867i) q^{16} +(0.341254 - 0.325385i) q^{17} +(0.0815405 - 0.336115i) q^{18} +(-0.0748038 - 0.0588264i) q^{19} +(-0.544078 - 0.627899i) q^{22} +(-1.11312 - 0.326842i) q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.638404 - 0.410277i) q^{27} +(-0.327068 + 0.945001i) q^{32} +(0.894814 - 0.358230i) q^{33} +(0.437742 - 0.175245i) q^{34} +(0.200621 - 0.281733i) q^{36} +(-0.0475819 - 0.0824143i) q^{38} +(-0.0671040 - 0.276606i) q^{41} +(1.70566 + 0.500828i) q^{43} +(-0.271738 - 0.785135i) q^{44} +(-0.911911 - 0.717135i) q^{48} +(0.235759 - 0.971812i) q^{49} +(0.723734 - 0.690079i) q^{50} +(0.0260280 + 0.546395i) q^{51} +(-0.440189 - 0.618159i) q^{54} +(0.108406 - 0.0208935i) q^{57} +(-0.827068 - 1.81103i) q^{59} +(-0.654861 + 0.755750i) q^{64} +0.963857 q^{66} +(0.841254 - 0.540641i) q^{67} +0.471518 q^{68} +(0.290959 - 0.186988i) q^{72} +(-1.28656 + 0.663268i) q^{73} +(0.481929 + 1.05528i) q^{75} +(-0.0135432 - 0.0941952i) q^{76} +(1.17657 - 0.345472i) q^{81} +(0.0405070 - 0.281733i) q^{82} +(0.0800569 + 1.68060i) q^{83} +(1.39734 + 1.09888i) q^{86} +(0.0395325 - 0.829889i) q^{88} +(-1.21590 - 1.40323i) q^{89} +(-0.580057 - 1.00469i) q^{96} +(-0.723734 + 1.25354i) q^{97} +(0.580057 - 0.814576i) q^{98} +(-0.0939844 + 0.271550i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10})$$ $$20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$135$$ $$269$$ $$337$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{4}{33}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$3$$ −0.759713 + 0.876756i −0.759713 + 0.876756i −0.995472 0.0950560i $$-0.969697\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$4$$ 0.723734 + 0.690079i 0.723734 + 0.690079i
$$5$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$6$$ −1.03115 + 0.531595i −1.03115 + 0.531595i
$$7$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$8$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$9$$ −0.0492216 0.342344i −0.0492216 0.342344i
$$10$$ 0 0
$$11$$ −0.738471 0.380708i −0.738471 0.380708i 0.0475819 0.998867i $$-0.484848\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$12$$ −1.15486 + 0.110276i −1.15486 + 0.110276i
$$13$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$17$$ 0.341254 0.325385i 0.341254 0.325385i −0.500000 0.866025i $$-0.666667\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$18$$ 0.0815405 0.336115i 0.0815405 0.336115i
$$19$$ −0.0748038 0.0588264i −0.0748038 0.0588264i 0.580057 0.814576i $$-0.303030\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.544078 0.627899i −0.544078 0.627899i
$$23$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$24$$ −1.11312 0.326842i −1.11312 0.326842i
$$25$$ 0.415415 0.909632i 0.415415 0.909632i
$$26$$ 0 0
$$27$$ −0.638404 0.410277i −0.638404 0.410277i
$$28$$ 0 0
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$32$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$33$$ 0.894814 0.358230i 0.894814 0.358230i
$$34$$ 0.437742 0.175245i 0.437742 0.175245i
$$35$$ 0 0
$$36$$ 0.200621 0.281733i 0.200621 0.281733i
$$37$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ −0.0475819 0.0824143i −0.0475819 0.0824143i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i $$-0.121212\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$42$$ 0 0
$$43$$ 1.70566 + 0.500828i 1.70566 + 0.500828i 0.981929 0.189251i $$-0.0606061\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$44$$ −0.271738 0.785135i −0.271738 0.785135i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$48$$ −0.911911 0.717135i −0.911911 0.717135i
$$49$$ 0.235759 0.971812i 0.235759 0.971812i
$$50$$ 0.723734 0.690079i 0.723734 0.690079i
$$51$$ 0.0260280 + 0.546395i 0.0260280 + 0.546395i
$$52$$ 0 0
$$53$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$54$$ −0.440189 0.618159i −0.440189 0.618159i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.108406 0.0208935i 0.108406 0.0208935i
$$58$$ 0 0
$$59$$ −0.827068 1.81103i −0.827068 1.81103i −0.500000 0.866025i $$-0.666667\pi$$
−0.327068 0.945001i $$-0.606061\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.888835 0.458227i $$-0.151515\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$65$$ 0 0
$$66$$ 0.963857 0.963857
$$67$$ 0.841254 0.540641i 0.841254 0.540641i
$$68$$ 0.471518 0.471518
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$72$$ 0.290959 0.186988i 0.290959 0.186988i
$$73$$ −1.28656 + 0.663268i −1.28656 + 0.663268i −0.959493 0.281733i $$-0.909091\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$74$$ 0 0
$$75$$ 0.481929 + 1.05528i 0.481929 + 1.05528i
$$76$$ −0.0135432 0.0941952i −0.0135432 0.0941952i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.995472 0.0950560i $$-0.0303030\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$80$$ 0 0
$$81$$ 1.17657 0.345472i 1.17657 0.345472i
$$82$$ 0.0405070 0.281733i 0.0405070 0.281733i
$$83$$ 0.0800569 + 1.68060i 0.0800569 + 1.68060i 0.580057 + 0.814576i $$0.303030\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.39734 + 1.09888i 1.39734 + 1.09888i
$$87$$ 0 0
$$88$$ 0.0395325 0.829889i 0.0395325 0.829889i
$$89$$ −1.21590 1.40323i −1.21590 1.40323i −0.888835 0.458227i $$-0.848485\pi$$
−0.327068 0.945001i $$-0.606061\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.580057 1.00469i −0.580057 1.00469i
$$97$$ −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i $$0.424242\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$98$$ 0.580057 0.814576i 0.580057 0.814576i
$$99$$ −0.0939844 + 0.271550i −0.0939844 + 0.271550i
$$100$$ 0.928368 0.371662i 0.928368 0.371662i
$$101$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$102$$ −0.178911 + 0.516929i −0.178911 + 0.516929i
$$103$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i $$-0.545455\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$108$$ −0.178911 0.737481i −0.178911 0.737481i
$$109$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.0947329 + 1.98869i −0.0947329 + 1.98869i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$114$$ 0.108406 + 0.0208935i 0.108406 + 0.0208935i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −0.0947329 1.98869i −0.0947329 1.98869i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.179656 0.252292i −0.179656 0.252292i
$$122$$ 0 0
$$123$$ 0.293496 + 0.151308i 0.293496 + 0.151308i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$128$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$129$$ −1.73492 + 1.11496i −1.73492 + 1.11496i
$$130$$ 0 0
$$131$$ 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i $$-0.727273\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$132$$ 0.894814 + 0.358230i 0.894814 + 0.358230i
$$133$$ 0 0
$$134$$ 0.981929 0.189251i 0.981929 0.189251i
$$135$$ 0 0
$$136$$ 0.437742 + 0.175245i 0.437742 + 0.175245i
$$137$$ −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i $$0.666667\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$138$$ 0 0
$$139$$ −0.841254 + 0.540641i −0.841254 + 0.540641i −0.888835 0.458227i $$-0.848485\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.339614 0.0654552i 0.339614 0.0654552i
$$145$$ 0 0
$$146$$ −1.44091 + 0.137591i −1.44091 + 0.137591i
$$147$$ 0.672932 + 0.945001i 0.672932 + 0.945001i
$$148$$ 0 0
$$149$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$150$$ 0.0552004 + 1.15880i 0.0552004 + 1.15880i
$$151$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$152$$ 0.0224357 0.0924813i 0.0224357 0.0924813i
$$153$$ −0.128190 0.100810i −0.128190 0.100810i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.22069 + 0.116562i 1.22069 + 0.116562i
$$163$$ 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i $$0.121212\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$164$$ 0.142315 0.246497i 0.142315 0.246497i
$$165$$ 0 0
$$166$$ −0.550294 + 1.58997i −0.550294 + 1.58997i
$$167$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$168$$ 0 0
$$169$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$170$$ 0 0
$$171$$ −0.0164569 + 0.0285041i −0.0164569 + 0.0285041i
$$172$$ 0.888835 + 1.53951i 0.888835 + 1.53951i
$$173$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.345139 0.755750i 0.345139 0.755750i
$$177$$ 2.21616 + 0.650724i 2.21616 + 0.650724i
$$178$$ −0.607279 1.75462i −0.607279 1.75462i
$$179$$ −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i $$-0.909091\pi$$
−0.142315 0.989821i $$-0.545455\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.375883 + 0.110369i −0.375883 + 0.110369i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$192$$ −0.165101 1.14831i −0.165101 1.14831i
$$193$$ −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i $$-0.727273\pi$$
−0.142315 0.989821i $$-0.545455\pi$$
$$194$$ −1.13779 + 0.894765i −1.13779 + 0.894765i
$$195$$ 0 0
$$196$$ 0.841254 0.540641i 0.841254 0.540641i
$$197$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$198$$ −0.188177 + 0.217168i −0.188177 + 0.217168i
$$199$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$200$$ 1.00000 1.00000
$$201$$ −0.165101 + 1.14831i −0.165101 + 1.14831i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.358218 + 0.413406i −0.358218 + 0.413406i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0.0328448 + 0.0719200i 0.0328448 + 0.0719200i
$$210$$ 0 0
$$211$$ 1.82318 0.351390i 1.82318 0.351390i 0.841254 0.540641i $$-0.181818\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −0.759713 1.06687i −0.759713 1.06687i
$$215$$ 0 0
$$216$$ 0.107999 0.751148i 0.107999 0.751148i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.395893 1.63189i 0.395893 1.63189i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$224$$ 0 0
$$225$$ −0.331854 0.0974412i −0.331854 0.0974412i
$$226$$ −0.827068 + 1.81103i −0.827068 + 1.81103i
$$227$$ −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i $$-0.787879\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$228$$ 0.0928751 + 0.0596872i 0.0928751 + 0.0596872i
$$229$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.327068 0.945001i 0.327068 0.945001i −0.654861 0.755750i $$-0.727273\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0.651174 1.88144i 0.651174 1.88144i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$240$$ 0 0
$$241$$ 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 $$0$$
0.415415 + 0.909632i $$0.363636\pi$$
$$242$$ −0.0730196 0.300991i −0.0730196 0.300991i
$$243$$ −0.275714 + 0.603730i −0.275714 + 0.603730i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.216237 + 0.249551i 0.216237 + 0.249551i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.53430 1.20658i −1.53430 1.20658i
$$250$$ 0 0
$$251$$ −1.13779 + 1.08488i −1.13779 + 1.08488i −0.142315 + 0.989821i $$0.545455\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.995472 + 0.0950560i −0.995472 + 0.0950560i
$$257$$ 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i $$0.0606061\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$258$$ −2.02503 + 0.390293i −2.02503 + 0.390293i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0.252989 0.130425i 0.252989 0.130425i
$$263$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$264$$ 0.697576 + 0.665138i 0.697576 + 0.665138i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 2.15402 2.15402
$$268$$ 0.981929 + 0.189251i 0.981929 + 0.189251i
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$272$$ 0.341254 + 0.325385i 0.341254 + 0.325385i
$$273$$ 0 0
$$274$$ −1.74555 + 0.899892i −1.74555 + 0.899892i
$$275$$ −0.653077 + 0.513585i −0.653077 + 0.513585i
$$276$$ 0 0
$$277$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$278$$ −0.981929 + 0.189251i −0.981929 + 0.189251i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.273507 + 0.384087i 0.273507 + 0.384087i 0.928368 0.371662i $$-0.121212\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$282$$ 0 0
$$283$$ 0.142315 0.989821i 0.142315 0.989821i −0.786053 0.618159i $$-0.787879\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.339614 + 0.0654552i 0.339614 + 0.0654552i
$$289$$ −0.0370031 + 0.776790i −0.0370031 + 0.776790i
$$290$$ 0 0
$$291$$ −0.549222 1.58687i −0.549222 1.58687i
$$292$$ −1.38884 0.407799i −1.38884 0.407799i
$$293$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$294$$ 0.273507 + 1.12741i 0.273507 + 1.12741i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.315247 + 0.546024i 0.315247 + 0.546024i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.379436 + 1.09631i −0.379436 + 1.09631i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.0552004 0.0775182i 0.0552004 0.0775182i
$$305$$ 0 0
$$306$$ −0.0815405 0.141232i −0.0815405 0.141232i
$$307$$ 1.76962 + 0.168978i 1.76962 + 0.168978i 0.928368 0.371662i $$-0.121212\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$312$$ 0 0
$$313$$ −0.0623191 0.0719200i −0.0623191 0.0719200i 0.723734 0.690079i $$-0.242424\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.45788 0.428072i 1.45788 0.428072i
$$322$$ 0 0
$$323$$ −0.0446683 + 0.00426530i −0.0446683 + 0.00426530i
$$324$$ 1.08993 + 0.561897i 1.08993 + 0.561897i
$$325$$ 0 0
$$326$$ 0.223734 + 1.55610i 0.223734 + 1.55610i
$$327$$ 0 0
$$328$$ 0.223734 0.175946i 0.223734 0.175946i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i 0.723734 0.690079i $$-0.242424\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$332$$ −1.10181 + 1.27155i −1.10181 + 1.27155i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.78153 0.713215i −1.78153 0.713215i −0.995472 0.0950560i $$-0.969697\pi$$
−0.786053 0.618159i $$-0.787879\pi$$
$$338$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$339$$ −1.67162 1.59389i −1.67162 1.59389i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −0.0258720 + 0.0203459i −0.0258720 + 0.0203459i
$$343$$ 0 0
$$344$$ 0.252989 + 1.75958i 0.252989 + 1.75958i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.995472 0.0950560i 0.995472 0.0950560i 0.415415 0.909632i $$-0.363636\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.601300 0.573338i 0.601300 0.573338i
$$353$$ −0.308779 + 1.27280i −0.308779 + 1.27280i 0.580057 + 0.814576i $$0.303030\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$354$$ 1.81556 + 1.42778i 1.81556 + 1.42778i
$$355$$ 0 0
$$356$$ 0.0883470 1.85463i 0.0883470 1.85463i
$$357$$ 0 0
$$358$$ −0.550294 1.58997i −0.550294 1.58997i
$$359$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$360$$ 0 0
$$361$$ −0.233624 0.963011i −0.233624 0.963011i
$$362$$ 0 0
$$363$$ 0.357685 + 0.0341548i 0.357685 + 0.0341548i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.327068 0.945001i $$-0.393939\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$368$$ 0 0
$$369$$ −0.0913915 + 0.0365876i −0.0913915 + 0.0365876i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$374$$ −0.389977 0.0372383i −0.389977 0.0372383i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0.0930932 + 0.268975i 0.0930932 + 0.268975i 0.981929 0.189251i $$-0.0606061\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$384$$ 0.273507 1.12741i 0.273507 1.12741i
$$385$$ 0 0
$$386$$ −0.0913090 1.91681i −0.0913090 1.91681i
$$387$$ 0.0874998 0.608574i 0.0874998 0.608574i
$$388$$ −1.38884 + 0.407799i −1.38884 + 0.407799i
$$389$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.981929 0.189251i 0.981929 0.189251i
$$393$$ 0.0469928 + 0.326842i 0.0469928 + 0.326842i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −0.255411 + 0.131673i −0.255411 + 0.131673i
$$397$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$401$$ −1.91899 −1.91899 −0.959493 0.281733i $$-0.909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$402$$ −0.580057 + 1.00469i −0.580057 + 1.00469i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −0.486206 + 0.250657i −0.486206 + 0.250657i
$$409$$ 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i $$-0.484848\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$410$$ 0 0
$$411$$ −0.324236 2.25511i −0.324236 2.25511i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.165101 1.14831i 0.165101 1.14831i
$$418$$ 0.00376206 + 0.0789754i 0.00376206 + 0.0789754i
$$419$$ 1.04758 0.998867i 1.04758 0.998867i 0.0475819 0.998867i $$-0.484848\pi$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$422$$ 1.82318 + 0.351390i 1.82318 + 0.351390i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −0.154218 0.445585i −0.154218 0.445585i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.308779 1.27280i −0.308779 1.27280i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ 0.379436 0.657203i 0.379436 0.657203i
$$433$$ 1.13915 1.59971i 1.13915 1.59971i 0.415415 0.909632i $$-0.363636\pi$$
0.723734 0.690079i $$-0.242424\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0.974048 1.36786i 0.974048 1.36786i
$$439$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ −0.344298 0.0328765i −0.344298 0.0328765i
$$442$$ 0 0
$$443$$ 0.111165 + 0.458227i 0.111165 + 0.458227i 1.00000 $$0$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i $$-0.303030\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$450$$ −0.271868 0.213799i −0.271868 0.213799i
$$451$$ −0.0557520 + 0.229813i −0.0557520 + 0.229813i
$$452$$ −1.44091 + 1.37391i −1.44091 + 1.37391i
$$453$$ 0 0
$$454$$ 0.223734 1.55610i 0.223734 1.55610i
$$455$$ 0 0
$$456$$ 0.0640388 + 0.0899299i 0.0640388 + 0.0899299i
$$457$$ −1.84833 + 0.176494i −1.84833 + 0.176494i −0.959493 0.281733i $$-0.909091\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$458$$ 0 0
$$459$$ −0.351355 + 0.0677182i −0.351355 + 0.0677182i
$$460$$ 0 0
$$461$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.888835 0.458227i $$-0.151515\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0.654861 0.755750i 0.654861 0.755750i
$$467$$ 0.771316 + 0.308788i 0.771316 + 0.308788i 0.723734 0.690079i $$-0.242424\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.30379 1.50465i 1.30379 1.50465i
$$473$$ −1.06891 1.01921i −1.06891 1.01921i
$$474$$ 0 0
$$475$$ −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.975950 + 1.37053i 0.975950 + 1.37053i
$$483$$ 0 0
$$484$$ 0.0440780 0.306569i 0.0440780 0.306569i
$$485$$ 0 0
$$486$$ −0.480348 + 0.458011i −0.480348 + 0.458011i
$$487$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$488$$ 0 0
$$489$$ −1.79086 0.345161i −1.79086 0.345161i
$$490$$ 0 0
$$491$$ 0.654861 + 0.755750i 0.654861 + 0.755750i 0.981929 0.189251i $$-0.0606061\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$492$$ 0.107999 + 0.312042i 0.107999 + 0.312042i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −0.975950 1.69039i −0.975950 1.69039i
$$499$$ 0.327068 0.566498i 0.327068 0.566498i −0.654861 0.755750i $$-0.727273\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −1.45949 + 0.584293i −1.45949 + 0.584293i
$$503$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.580057 1.00469i −0.580057 1.00469i
$$508$$ 0 0
$$509$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.959493 0.281733i −0.959493 0.281733i
$$513$$ 0.0236199 + 0.0682453i 0.0236199 + 0.0682453i
$$514$$ 1.25667 + 1.45027i 1.25667 + 1.45027i
$$515$$ 0 0
$$516$$ −2.02503 0.390293i −2.02503 0.390293i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0.0930932 0.647478i 0.0930932 0.647478i −0.888835 0.458227i $$-0.848485\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$522$$ 0 0
$$523$$ 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i $$0.242424\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$524$$ 0.283341 0.0270558i 0.283341 0.0270558i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.400401 + 0.876756i 0.400401 + 0.876756i
$$529$$ −0.786053 + 0.618159i −0.786053 + 0.618159i
$$530$$ 0 0
$$531$$ −0.579284 + 0.372283i −0.579284 + 0.372283i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 1.99973 + 0.800570i 1.99973 + 0.800570i
$$535$$ 0 0
$$536$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$537$$ 1.95190 1.95190
$$538$$ 0 0
$$539$$ −0.544078 + 0.627899i −0.544078 + 0.627899i
$$540$$ 0 0
$$541$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0.195876 + 0.428908i 0.195876 + 0.428908i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.49547 0.770969i −1.49547 0.770969i −0.500000 0.866025i $$-0.666667\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$548$$ −1.95496 + 0.186677i −1.95496 + 0.186677i
$$549$$ 0 0
$$550$$ −0.797176 + 0.234072i −0.797176 + 0.234072i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.981929 0.189251i −0.981929 0.189251i
$$557$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0.188796 0.413406i 0.188796 0.413406i
$$562$$ 0.111165 + 0.458227i 0.111165 + 0.458227i
$$563$$ −0.550294 0.353653i −0.550294 0.353653i 0.235759 0.971812i $$-0.424242\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.500000 0.866025i 0.500000 0.866025i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.34378 0.537970i 1.34378 0.537970i 0.415415 0.909632i $$-0.363636\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$570$$ 0 0
$$571$$ −0.154218 + 0.445585i −0.154218 + 0.445585i −0.995472 0.0950560i $$-0.969697\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.290959 + 0.186988i 0.290959 + 0.186988i
$$577$$ 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i $$0.303030\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$578$$ −0.323056 + 0.707394i −0.323056 + 0.707394i
$$579$$ 2.13606 + 0.627205i 2.13606 + 0.627205i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0.0799009 1.67733i 0.0799009 1.67733i
$$583$$ 0 0
$$584$$ −1.13779 0.894765i −1.13779 0.894765i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.0688733 + 1.44583i 0.0688733 + 1.44583i 0.723734 + 0.690079i $$0.242424\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$588$$ −0.165101 + 1.14831i −0.165101 + 1.14831i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i $$-0.303030\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$594$$ 0.0897286 + 0.624076i 0.0897286 + 0.624076i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$600$$ −0.759713 + 0.876756i −0.759713 + 0.876756i
$$601$$ −1.45949 0.584293i −1.45949 0.584293i −0.500000 0.866025i $$-0.666667\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$602$$ 0 0
$$603$$ −0.226493 0.261387i −0.226493 0.261387i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$608$$ 0.0800569 0.0514495i 0.0800569 0.0514495i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.0232089 0.161421i −0.0232089 0.161421i
$$613$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$614$$ 1.58006 + 0.814576i 1.58006 + 0.814576i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$618$$ 0 0
$$619$$ 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i $$0.424242\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.654861 0.755750i −0.654861 0.755750i
$$626$$ −0.0311250 0.0899299i −0.0311250 0.0899299i
$$627$$ −0.0880089 0.0258417i −0.0880089 0.0258417i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$632$$ 0 0
$$633$$ −1.07701 + 1.86544i −1.07701 + 1.86544i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i $$0.121212\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$642$$ 1.51255 + 0.144431i 1.51255 + 0.144431i
$$643$$ −1.67489 1.07639i −1.67489 1.07639i −0.888835 0.458227i $$-0.848485\pi$$
−0.786053 0.618159i $$-0.787879\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −0.0430538 0.0126417i −0.0430538 0.0126417i
$$647$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$648$$ 0.803018 + 0.926732i 0.803018 + 0.926732i
$$649$$ −0.0787070 + 1.65226i −0.0787070 + 1.65226i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.370638 + 1.52779i −0.370638 + 1.52779i
$$653$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.273100 0.0801894i 0.273100 0.0801894i
$$657$$ 0.290392 + 0.407799i 0.290392 + 0.407799i
$$658$$ 0 0
$$659$$ 0.888835 + 0.458227i 0.888835 + 0.458227i 0.841254 0.540641i $$-0.181818\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$662$$ 0.0395325 + 0.0865641i 0.0395325 + 0.0865641i
$$663$$ 0 0
$$664$$ −1.49547 + 0.770969i −1.49547 + 0.770969i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.428368 0.494363i 0.428368 0.494363i −0.500000 0.866025i $$-0.666667\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$674$$ −1.38884 1.32425i −1.38884 1.32425i
$$675$$ −0.638404 + 0.410277i −0.638404 + 0.410277i
$$676$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$677$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$678$$ −0.959493 2.10100i −0.959493 2.10100i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.62108 + 0.835724i 1.62108 + 0.835724i
$$682$$ 0 0
$$683$$ 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i $$0.242424\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$684$$ −0.0315805 + 0.00927288i −0.0315805 + 0.00927288i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −0.419102 + 1.72756i −0.419102 + 1.72756i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.0623191 + 1.30824i −0.0623191 + 1.30824i 0.723734 + 0.690079i $$0.242424\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0.959493 + 0.281733i 0.959493 + 0.281733i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −0.112903 0.0725583i −0.112903 0.0725583i
$$698$$ 0 0
$$699$$ 0.580057 + 1.00469i 0.580057 + 1.00469i
$$700$$ 0 0
$$701$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.771316 0.308788i 0.771316 0.308788i
$$705$$ 0 0
$$706$$ −0.759713 + 1.06687i −0.759713 + 1.06687i
$$707$$ 0 0
$$708$$ 1.15486 + 2.00028i 1.15486 + 2.00028i
$$709$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0.771316 1.68895i 0.771316 1.68895i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.0800569 1.68060i 0.0800569 1.68060i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.141026 0.980857i 0.141026 0.980857i
$$723$$ −1.87283 + 0.549914i −1.87283 + 0.549914i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.319369 + 0.164646i 0.319369 + 0.164646i
$$727$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$728$$ 0 0
$$729$$ 0.189539 + 0.415033i 0.189539 + 0.415033i
$$730$$ 0 0
$$731$$ 0.745025 0.384087i 0.745025 0.384087i
$$732$$ 0 0
$$733$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.827068 + 0.0789754i −0.827068 + 0.0789754i
$$738$$ −0.0984432 −0.0984432
$$739$$ −1.84833 0.739959i −1.84833 0.739959i −0.959493 0.281733i $$-0.909091\pi$$
−0.888835 0.458227i $$-0.848485\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.888835 0.458227i $$-0.151515\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.571403 0.110129i 0.571403 0.110129i
$$748$$ −0.348202 0.179511i −0.348202 0.179511i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$752$$ 0 0
$$753$$ −0.0867810 1.82176i −0.0867810 1.82176i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$758$$ −0.0135432 + 0.284307i −0.0135432 + 0.284307i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i $$-0.181818\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.672932 0.945001i 0.672932 0.945001i
$$769$$ 0.514186 1.48564i 0.514186 1.48564i −0.327068 0.945001i $$-0.606061\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$770$$ 0 0
$$771$$ −2.06677 + 0.827411i −2.06677 + 0.827411i
$$772$$ 0.627639 1.81344i 0.627639 1.81344i
$$773$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$774$$ 0.307416 0.532461i 0.307416 0.532461i
$$775$$ 0 0
$$776$$ −1.44091 0.137591i −1.44091 0.137591i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.0112521 + 0.0246387i −0.0112521 + 0.0246387i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.981929 + 0.189251i 0.981929 + 0.189251i
$$785$$ 0 0
$$786$$ −0.0778483 + 0.320895i −0.0778483 + 0.320895i
$$787$$ −0.947890 + 0.903811i −0.947890 + 0.903811i −0.995472 0.0950560i $$-0.969697\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −0.286053 + 0.0273148i −0.286053 + 0.0273148i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.