# Properties

 Label 1407.1.cz.a.557.1 Level $1407$ Weight $1$ Character 1407.557 Analytic conductor $0.702$ Analytic rank $0$ Dimension $20$ Projective image $D_{33}$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1407 = 3 \cdot 7 \cdot 67$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1407.cz (of order $$66$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.702184472775$$ 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: $$\Z[a_1, a_2, a_3]$$ 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 557.1 Root $$0.235759 - 0.971812i$$ of defining polynomial Character $$\chi$$ $$=$$ 1407.557 Dual form 1407.1.cz.a.485.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.580057 + 0.814576i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0475819 + 0.998867i) q^{7} +(-0.327068 + 0.945001i) q^{9} +O(q^{10})$$ $$q+(0.580057 + 0.814576i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.0475819 + 0.998867i) q^{7} +(-0.327068 + 0.945001i) q^{9} +(-0.888835 + 0.458227i) q^{12} +(1.16413 - 0.600149i) q^{13} +(-0.959493 - 0.281733i) q^{16} +(1.30379 - 1.50465i) q^{19} +(-0.786053 + 0.618159i) q^{21} +(-0.888835 + 0.458227i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(-0.995472 - 0.0950560i) q^{28} +(-1.61435 + 1.03748i) q^{31} +(-0.888835 - 0.458227i) q^{36} +0.0951638 q^{37} +(1.16413 + 0.600149i) q^{39} +(-0.239446 - 1.66538i) q^{43} +(-0.327068 - 0.945001i) q^{48} +(-0.995472 + 0.0950560i) q^{49} +(0.428368 + 1.23769i) q^{52} +(1.98193 + 0.189251i) q^{57} +(1.91030 - 0.560914i) q^{61} +(-0.959493 - 0.281733i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.0475819 - 0.998867i) q^{67} +(0.341254 + 0.325385i) q^{73} +(-0.888835 - 0.458227i) q^{75} +(1.30379 + 1.50465i) q^{76} +(-0.0845850 + 0.0436066i) q^{79} +(-0.786053 - 0.618159i) q^{81} +(-0.500000 - 0.866025i) q^{84} +(0.654861 + 1.13425i) q^{91} +(-1.78153 - 0.713215i) q^{93} +(-0.580057 + 1.00469i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10})$$ $$20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1407\mathbb{Z}\right)^\times$$.

 $$n$$ $$337$$ $$470$$ $$1207$$ $$\chi(n)$$ $$e\left(\frac{31}{33}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$3$$ 0.580057 + 0.814576i 0.580057 + 0.814576i
$$4$$ −0.142315 + 0.989821i −0.142315 + 0.989821i
$$5$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$6$$ 0 0
$$7$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$8$$ 0 0
$$9$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$10$$ 0 0
$$11$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$12$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$13$$ 1.16413 0.600149i 1.16413 0.600149i 0.235759 0.971812i $$-0.424242\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.959493 0.281733i −0.959493 0.281733i
$$17$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$18$$ 0 0
$$19$$ 1.30379 1.50465i 1.30379 1.50465i 0.580057 0.814576i $$-0.303030\pi$$
0.723734 0.690079i $$-0.242424\pi$$
$$20$$ 0 0
$$21$$ −0.786053 + 0.618159i −0.786053 + 0.618159i
$$22$$ 0 0
$$23$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$24$$ 0 0
$$25$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$26$$ 0 0
$$27$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$28$$ −0.995472 0.0950560i −0.995472 0.0950560i
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i $$0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.888835 0.458227i −0.888835 0.458227i
$$37$$ 0.0951638 0.0951638 0.0475819 0.998867i $$-0.484848\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$38$$ 0 0
$$39$$ 1.16413 + 0.600149i 1.16413 + 0.600149i
$$40$$ 0 0
$$41$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$42$$ 0 0
$$43$$ −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i $$-0.727273\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$48$$ −0.327068 0.945001i −0.327068 0.945001i
$$49$$ −0.995472 + 0.0950560i −0.995472 + 0.0950560i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.428368 + 1.23769i 0.428368 + 1.23769i
$$53$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.98193 + 0.189251i 1.98193 + 0.189251i
$$58$$ 0 0
$$59$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$60$$ 0 0
$$61$$ 1.91030 0.560914i 1.91030 0.560914i 0.928368 0.371662i $$-0.121212\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$62$$ 0 0
$$63$$ −0.959493 0.281733i −0.959493 0.281733i
$$64$$ 0.415415 0.909632i 0.415415 0.909632i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$72$$ 0 0
$$73$$ 0.341254 + 0.325385i 0.341254 + 0.325385i 0.841254 0.540641i $$-0.181818\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ −0.888835 0.458227i −0.888835 0.458227i
$$76$$ 1.30379 + 1.50465i 1.30379 + 1.50465i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i −0.500000 0.866025i $$-0.666667\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$80$$ 0 0
$$81$$ −0.786053 0.618159i −0.786053 0.618159i
$$82$$ 0 0
$$83$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$84$$ −0.500000 0.866025i −0.500000 0.866025i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$90$$ 0 0
$$91$$ 0.654861 + 1.13425i 0.654861 + 1.13425i
$$92$$ 0 0
$$93$$ −1.78153 0.713215i −1.78153 0.713215i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i $$0.363636\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.327068 0.945001i −0.327068 0.945001i
$$101$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$102$$ 0 0
$$103$$ 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i $$0.424242\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$108$$ −0.142315 0.989821i −0.142315 0.989821i
$$109$$ 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i $$-0.242424\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$110$$ 0 0
$$111$$ 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
$$112$$ 0.235759 0.971812i 0.235759 0.971812i
$$113$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.186393 + 1.29639i 0.186393 + 1.29639i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −0.797176 1.74557i −0.797176 1.74557i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.581419 1.67990i 0.581419 1.67990i −0.142315 0.989821i $$-0.545455\pi$$
0.723734 0.690079i $$-0.242424\pi$$
$$128$$ 0 0
$$129$$ 1.21769 1.16106i 1.21769 1.16106i
$$130$$ 0 0
$$131$$ 0 0 0.995472 0.0950560i $$-0.0303030\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$132$$ 0 0
$$133$$ 1.56499 + 1.23072i 1.56499 + 1.23072i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$138$$ 0 0
$$139$$ −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i $$-0.545455\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.580057 0.814576i 0.580057 0.814576i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.654861 0.755750i −0.654861 0.755750i
$$148$$ −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
$$149$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$150$$ 0 0
$$151$$ −0.370638 + 0.291473i −0.370638 + 0.291473i −0.786053 0.618159i $$-0.787879\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.759713 + 1.06687i −0.759713 + 1.06687i
$$157$$ 1.30379 0.124497i 1.30379 0.124497i 0.580057 0.814576i $$-0.303030\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −0.928368 + 1.60798i −0.928368 + 1.60798i −0.142315 + 0.989821i $$0.545455\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$168$$ 0 0
$$169$$ 0.414955 0.582723i 0.414955 0.582723i
$$170$$ 0 0
$$171$$ 0.995472 + 1.72421i 0.995472 + 1.72421i
$$172$$ 1.68251 1.68251
$$173$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$174$$ 0 0
$$175$$ −0.500000 0.866025i −0.500000 0.866025i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$180$$ 0 0
$$181$$ −0.827068 + 0.0789754i −0.827068 + 0.0789754i −0.500000 0.866025i $$-0.666667\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$182$$ 0 0
$$183$$ 1.56499 + 1.23072i 1.56499 + 1.23072i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −0.327068 0.945001i −0.327068 0.945001i
$$190$$ 0 0
$$191$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$192$$ 0.981929 0.189251i 0.981929 0.189251i
$$193$$ −0.0311250 0.653395i −0.0311250 0.653395i −0.959493 0.281733i $$-0.909091\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$197$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$198$$ 0 0
$$199$$ 0.514186 1.48564i 0.514186 1.48564i −0.327068 0.945001i $$-0.606061\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$200$$ 0 0
$$201$$ 0.841254 0.540641i 0.841254 0.540641i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.28605 + 0.247866i −1.28605 + 0.247866i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.44091 0.137591i −1.44091 0.137591i −0.654861 0.755750i $$-0.727273\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −1.11312 1.56316i −1.11312 1.56316i
$$218$$ 0 0
$$219$$ −0.0671040 + 0.466718i −0.0671040 + 0.466718i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0.481929 + 1.05528i 0.481929 + 1.05528i 0.981929 + 0.189251i $$0.0606061\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$224$$ 0 0
$$225$$ −0.142315 0.989821i −0.142315 0.989821i
$$226$$ 0 0
$$227$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$228$$ −0.469383 + 1.93482i −0.469383 + 1.93482i
$$229$$ 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i $$-0.363636\pi$$
1.00000 $$0$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −0.0845850 0.0436066i −0.0845850 0.0436066i
$$238$$ 0 0
$$239$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$240$$ 0 0
$$241$$ −0.419102 + 1.72756i −0.419102 + 1.72756i 0.235759 + 0.971812i $$0.424242\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$242$$ 0 0
$$243$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$244$$ 0.283341 + 1.97068i 0.283341 + 1.97068i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0.614761 2.53408i 0.614761 2.53408i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$252$$ 0.415415 0.909632i 0.415415 0.909632i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$257$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$258$$ 0 0
$$259$$ 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0.981929 + 0.189251i 0.981929 + 0.189251i
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ −1.95496 + 0.186677i −1.95496 + 0.186677i −0.995472 0.0950560i $$-0.969697\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$272$$ 0 0
$$273$$ −0.544078 + 1.19136i −0.544078 + 1.19136i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.54370 + 0.297523i −1.54370 + 0.297523i −0.888835 0.458227i $$-0.848485\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$278$$ 0 0
$$279$$ −0.452418 1.86489i −0.452418 1.86489i
$$280$$ 0 0
$$281$$ 0 0 0.888835 0.458227i $$-0.151515\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$282$$ 0 0
$$283$$ −0.473420 1.36786i −0.473420 1.36786i −0.888835 0.458227i $$-0.848485\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0.235759 0.971812i 0.235759 0.971812i
$$290$$ 0 0
$$291$$ −1.15486 + 0.110276i −1.15486 + 0.110276i
$$292$$ −0.370638 + 0.291473i −0.370638 + 0.291473i
$$293$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0.580057 0.814576i 0.580057 0.814576i
$$301$$ 1.65210 0.318417i 1.65210 0.318417i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.67489 + 1.07639i −1.67489 + 1.07639i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −0.0135432 0.284307i −0.0135432 0.284307i −0.995472 0.0950560i $$-0.969697\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$308$$ 0 0
$$309$$ −1.54370 + 1.21398i −1.54370 + 1.21398i
$$310$$ 0 0
$$311$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$312$$ 0 0
$$313$$ −0.379436 + 0.532843i −0.379436 + 0.532843i −0.959493 0.281733i $$-0.909091\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −0.0311250 0.0899299i −0.0311250 0.0899299i
$$317$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.723734 0.690079i 0.723734 0.690079i
$$325$$ −0.759713 + 1.06687i −0.759713 + 1.06687i
$$326$$ 0 0
$$327$$ 1.70566 + 0.879330i 1.70566 + 0.879330i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.653077 0.513585i −0.653077 0.513585i 0.235759 0.971812i $$-0.424242\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$332$$ 0 0
$$333$$ −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0.928368 0.371662i 0.928368 0.371662i
$$337$$ −1.74555 + 0.336426i −1.74555 + 0.336426i −0.959493 0.281733i $$-0.909091\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −0.142315 0.989821i −0.142315 0.989821i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$348$$ 0 0
$$349$$ 0.0930932 0.647478i 0.0930932 0.647478i −0.888835 0.458227i $$-0.848485\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$350$$ 0 0
$$351$$ −0.947890 + 0.903811i −0.947890 + 0.903811i
$$352$$ 0 0
$$353$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$360$$ 0 0
$$361$$ −0.421801 2.93369i −0.421801 2.93369i
$$362$$ 0 0
$$363$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$364$$ −1.21590 + 0.486774i −1.21590 + 0.486774i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.601300 + 1.31666i 0.601300 + 1.31666i 0.928368 + 0.371662i $$0.121212\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0.959493 1.66189i 0.959493 1.66189i
$$373$$ 0.654861 1.13425i 0.654861 1.13425i −0.327068 0.945001i $$-0.606061\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i $$-0.303030\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$380$$ 0 0
$$381$$ 1.70566 0.500828i 1.70566 0.500828i
$$382$$ 0 0
$$383$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 1.65210 + 0.318417i 1.65210 + 0.318417i
$$388$$ −0.911911 0.717135i −0.911911 0.717135i
$$389$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i $$0.303030\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$398$$ 0 0
$$399$$ −0.0947329 + 1.98869i −0.0947329 + 1.98869i
$$400$$ 0.981929 0.189251i 0.981929 0.189251i
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ −1.25667 + 2.17661i −1.25667 + 2.17661i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −0.308779 0.356349i −0.308779 0.356349i 0.580057 0.814576i $$-0.303030\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −1.95496 0.186677i −1.95496 0.186677i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −0.271738 0.785135i −0.271738 0.785135i
$$418$$ 0 0
$$419$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$420$$ 0 0
$$421$$ −0.550294 1.58997i −0.550294 1.58997i −0.786053 0.618159i $$-0.787879\pi$$
0.235759 0.971812i $$-0.424242\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0.651174 + 1.88144i 0.651174 + 1.88144i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 1.00000 1.00000
$$433$$ 1.58006 + 0.814576i 1.58006 + 0.814576i 1.00000 $$0$$
0.580057 + 0.814576i $$0.303030\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0.627639 + 1.81344i 0.627639 + 1.81344i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 1.85674 1.85674 0.928368 0.371662i $$-0.121212\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$440$$ 0 0
$$441$$ 0.235759 0.971812i 0.235759 0.971812i
$$442$$ 0 0
$$443$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$444$$ −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$449$$ 0 0 0.995472 0.0950560i $$-0.0303030\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −0.452418 0.132842i −0.452418 0.132842i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i $$0.787879\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$462$$ 0 0
$$463$$ −0.154218 + 0.635697i −0.154218 + 0.635697i 0.841254 + 0.540641i $$0.181818\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$468$$ −1.30972 −1.30972
$$469$$ 1.00000 1.00000
$$470$$ 0 0
$$471$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −0.469383 + 1.93482i −0.469383 + 1.93482i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.580057 0.814576i $$-0.303030\pi$$
−0.580057 + 0.814576i $$0.696970\pi$$
$$480$$ 0 0
$$481$$ 0.110783 0.0571125i 0.110783 0.0571125i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −0.264241 + 0.105786i −0.264241 + 0.105786i −0.500000 0.866025i $$-0.666667\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$488$$ 0 0
$$489$$ −1.84833 + 0.176494i −1.84833 + 0.176494i
$$490$$ 0 0
$$491$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.84125 0.540641i 1.84125 0.540641i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.77767 −1.77767 −0.888835 0.458227i $$-0.848485\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.715370 0.715370
$$508$$ 1.58006 + 0.814576i 1.58006 + 0.814576i
$$509$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$510$$ 0 0
$$511$$ −0.308779 + 0.356349i −0.308779 + 0.356349i
$$512$$ 0 0
$$513$$ −0.827068 + 1.81103i −0.827068 + 1.81103i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0.975950 + 1.37053i 0.975950 + 1.37053i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$522$$ 0 0
$$523$$ −0.550294 0.353653i −0.550294 0.353653i 0.235759 0.971812i $$-0.424242\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$524$$ 0 0
$$525$$ 0.415415 0.909632i 0.415415 0.909632i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.654861 0.755750i −0.654861 0.755750i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −1.44091 + 1.37391i −1.44091 + 1.37391i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i $$-0.787879\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$542$$ 0 0
$$543$$ −0.544078 0.627899i −0.544078 0.627899i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i $$0.303030\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$548$$ 0 0
$$549$$ −0.0947329 + 1.98869i −0.0947329 + 1.98869i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −0.0475819 0.0824143i −0.0475819 0.0824143i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.345139 0.755750i 0.345139 0.755750i
$$557$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$558$$ 0 0
$$559$$ −1.27822 1.79501i −1.27822 1.79501i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0.580057 0.814576i 0.580057 0.814576i
$$568$$ 0 0
$$569$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$570$$ 0 0
$$571$$ 0.481929 + 1.05528i 0.481929 + 1.05528i 0.981929 + 0.189251i $$0.0606061\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.723734 + 0.690079i 0.723734 + 0.690079i
$$577$$ −0.0671040 0.466718i −0.0671040 0.466718i −0.995472 0.0950560i $$-0.969697\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$578$$ 0 0
$$579$$ 0.514186 0.404360i 0.514186 0.404360i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$588$$ 0.841254 0.540641i 0.841254 0.540641i
$$589$$ −0.543727 + 3.78171i −0.543727 + 3.78171i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.0913090 0.0268107i −0.0913090 0.0268107i
$$593$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.50842 0.442913i 1.50842 0.442913i
$$598$$ 0 0
$$599$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$600$$ 0 0
$$601$$ 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i $$-0.303030\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$602$$ 0 0
$$603$$ 0.928368 + 0.371662i 0.928368 + 0.371662i
$$604$$ −0.235759 0.408346i −0.235759 0.408346i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0.514186 + 0.404360i 0.514186 + 0.404360i 0.841254 0.540641i $$-0.181818\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$618$$ 0 0
$$619$$ −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i $$-0.666667\pi$$
0.0475819 0.998867i $$-0.484848\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −0.947890 0.903811i −0.947890 0.903811i
$$625$$ 0.580057 0.814576i 0.580057 0.814576i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −0.0623191 + 1.30824i −0.0623191 + 1.30824i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0.0395325 + 0.829889i 0.0395325 + 0.829889i 0.928368 + 0.371662i $$0.121212\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$632$$ 0 0
$$633$$ −0.723734 1.25354i −0.723734 1.25354i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −1.78153 + 0.523103i −1.78153 + 0.523103i −0.995472 0.0950560i $$-0.969697\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.995472 0.0950560i $$-0.0303030\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0.627639 1.81344i 0.627639 1.81344i
$$652$$ −1.45949 1.14776i −1.45949 1.14776i
$$653$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −0.419102 + 0.216062i −0.419102 + 0.216062i
$$658$$ 0 0
$$659$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$660$$ 0 0
$$661$$ −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i $$-0.606061\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −0.580057 + 1.00469i −0.580057 + 1.00469i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.601300 1.31666i 0.601300 1.31666i −0.327068 0.945001i $$-0.606061\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$674$$ 0 0
$$675$$ 0.723734 0.690079i 0.723734 0.690079i
$$676$$ 0.517738 + 0.493662i 0.517738 + 0.493662i
$$677$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$678$$ 0 0
$$679$$ −1.03115 0.531595i −1.03115 0.531595i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$684$$ −1.84833 + 0.739959i −1.84833 + 0.739959i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.56199 + 0.625325i 1.56199 + 0.625325i
$$688$$ −0.239446 + 1.66538i −0.239446 + 1.66538i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.419102 + 1.72756i −0.419102 + 1.72756i 0.235759 + 0.971812i $$0.424242\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0.928368 0.371662i 0.928368 0.371662i
$$701$$ 0 0 −0.888835 0.458227i $$-0.848485\pi$$
0.888835 + 0.458227i $$0.151515\pi$$
$$702$$ 0 0
$$703$$ 0.124074 0.143189i 0.124074 0.143189i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i $$-0.545455\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$710$$ 0 0
$$711$$ −0.0135432 0.0941952i −0.0135432 0.0941952i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$720$$ 0 0
$$721$$ −1.95496 + 0.186677i −1.95496 + 0.186677i
$$722$$ 0 0
$$723$$ −1.65033 + 0.660694i −1.65033 + 0.660694i
$$724$$ 0.0395325 0.829889i 0.0395325 0.829889i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.84833 0.176494i −1.84833 0.176494i −0.888835 0.458227i $$-0.848485\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$728$$ 0 0
$$729$$ 0.841254 0.540641i 0.841254 0.540641i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −1.44091 + 1.37391i −1.44091 + 1.37391i
$$733$$ −1.54370 1.21398i −1.54370 1.21398i −0.888835 0.458227i $$-0.848485\pi$$
−0.654861 0.755750i $$-0.727273\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i $$-0.848485\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$740$$ 0 0
$$741$$ 2.42080 0.969140i 2.42080 0.969140i
$$742$$ 0 0
$$743$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.45949 + 0.584293i −1.45949 + 0.584293i −0.959493 0.281733i $$-0.909091\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0.981929 0.189251i 0.981929 0.189251i
$$757$$ −0.469383 + 0.0448206i −0.469383 + 0.0448206i −0.327068 0.945001i $$-0.606061\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$762$$ 0 0
$$763$$ 0.959493 + 1.66189i 0.959493 + 1.66189i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$769$$ 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i $$-0.484848\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0.651174 + 0.0621796i 0.651174 + 0.0621796i
$$773$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$774$$ 0 0
$$775$$ 0.959493 1.66189i 0.959493 1.66189i
$$776$$ 0 0
$$777$$ −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 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 0
$$787$$ −1.32254 + 1.04006i −1.32254 + 1.04006i −0.327068 + 0.945001i $$0.606061\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1.88720 1.79944i 1.88720 1.79944i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.39734 + 0.720381i 1.39734 + 0.720381i
$$797$$ 0 0 0.327068 0.945001i $$-0.393939\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0