# Properties

 Label 1407.1.cg.a.1145.1 Level $1407$ Weight $1$ Character 1407.1145 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.cg (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 1145.1 Root $$0.580057 - 0.814576i$$ of defining polynomial Character $$\chi$$ $$=$$ 1407.1145 Dual form 1407.1.cg.a.1262.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.580057 + 0.814576i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.654861 + 0.755750i) q^{7} +(-0.327068 + 0.945001i) q^{9} +O(q^{10})$$ $$q+(0.580057 + 0.814576i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-0.654861 + 0.755750i) q^{7} +(-0.327068 + 0.945001i) q^{9} +(0.841254 + 0.540641i) q^{12} +(-0.0623191 + 1.30824i) q^{13} +(0.723734 - 0.690079i) q^{16} +(-0.379436 - 1.09631i) q^{19} +(-0.995472 - 0.0950560i) q^{21} +(-0.888835 + 0.458227i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(-0.327068 + 0.945001i) q^{28} +(1.70566 + 0.879330i) q^{31} +(0.0475819 + 0.998867i) q^{36} +(0.888835 - 1.53951i) q^{37} +(-1.10181 + 0.708089i) q^{39} +(-0.239446 - 1.66538i) q^{43} +(0.981929 + 0.189251i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(0.428368 + 1.23769i) q^{52} +(0.672932 - 0.945001i) q^{57} +(0.273507 - 1.12741i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.841254 + 0.540641i) q^{67} +(-1.38884 + 0.407799i) q^{73} +(-0.888835 - 0.458227i) q^{75} +(-0.759713 - 0.876756i) q^{76} +(-1.49547 - 0.961081i) q^{79} +(-0.786053 - 0.618159i) q^{81} +(-0.959493 + 0.281733i) q^{84} +(-0.947890 - 0.903811i) q^{91} +(0.273100 + 1.89945i) q^{93} +(0.995472 + 1.72421i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + q^{3} + q^{4} - 2q^{7} + q^{9} + O(q^{10})$$ $$20q + q^{3} + q^{4} - 2q^{7} + q^{9} - 2q^{12} + 2q^{13} + q^{16} - q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} + 2q^{31} + q^{36} - q^{37} - 4q^{39} - 4q^{43} + q^{48} - 2q^{49} - 9q^{52} + 21q^{57} - q^{61} - 10q^{63} - 2q^{64} - 2q^{67} - 9q^{73} + q^{75} + 2q^{76} - 9q^{79} + q^{81} - 2q^{84} + 2q^{91} - 4q^{93} - q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$337$$ $$470$$ $$1207$$ $$\chi(n)$$ $$e\left(\frac{20}{33}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## 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 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$3$$ 0.580057 + 0.814576i 0.580057 + 0.814576i
$$4$$ 0.928368 0.371662i 0.928368 0.371662i
$$5$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$6$$ 0 0
$$7$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$8$$ 0 0
$$9$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$10$$ 0 0
$$11$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$12$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$13$$ −0.0623191 + 1.30824i −0.0623191 + 1.30824i 0.723734 + 0.690079i $$0.242424\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.723734 0.690079i 0.723734 0.690079i
$$17$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$18$$ 0 0
$$19$$ −0.379436 1.09631i −0.379436 1.09631i −0.959493 0.281733i $$-0.909091\pi$$
0.580057 0.814576i $$-0.303030\pi$$
$$20$$ 0 0
$$21$$ −0.995472 0.0950560i −0.995472 0.0950560i
$$22$$ 0 0
$$23$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$24$$ 0 0
$$25$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$26$$ 0 0
$$27$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$28$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0 0
$$31$$ 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i $$0.0606061\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$37$$ 0.888835 1.53951i 0.888835 1.53951i 0.0475819 0.998867i $$-0.484848\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$38$$ 0 0
$$39$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$40$$ 0 0
$$41$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$42$$ 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 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$48$$ 0.981929 + 0.189251i 0.981929 + 0.189251i
$$49$$ −0.142315 0.989821i −0.142315 0.989821i
$$50$$ 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
$$57$$ 0.672932 0.945001i 0.672932 0.945001i
$$58$$ 0 0
$$59$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$60$$ 0 0
$$61$$ 0.273507 1.12741i 0.273507 1.12741i −0.654861 0.755750i $$-0.727273\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$62$$ 0 0
$$63$$ −0.500000 0.866025i −0.500000 0.866025i
$$64$$ 0.415415 0.909632i 0.415415 0.909632i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$72$$ 0 0
$$73$$ −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i $$-0.848485\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ −0.888835 0.458227i −0.888835 0.458227i
$$76$$ −0.759713 0.876756i −0.759713 0.876756i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.49547 0.961081i −1.49547 0.961081i −0.995472 0.0950560i $$-0.969697\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$80$$ 0 0
$$81$$ −0.786053 0.618159i −0.786053 0.618159i
$$82$$ 0 0
$$83$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$84$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$85$$ 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
$$91$$ −0.947890 0.903811i −0.947890 0.903811i
$$92$$ 0 0
$$93$$ 0.273100 + 1.89945i 0.273100 + 1.89945i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0.995472 + 1.72421i 0.995472 + 1.72421i 0.580057 + 0.814576i $$0.303030\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$101$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$102$$ 0 0
$$103$$ −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i $$-0.787879\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$108$$ −0.786053 + 0.618159i −0.786053 + 0.618159i
$$109$$ 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
$$111$$ 1.76962 0.168978i 1.76962 0.168978i
$$112$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$113$$ 0 0 0.235759 0.971812i $$-0.424242\pi$$
−0.235759 + 0.971812i $$0.575758\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.21590 0.486774i −1.21590 0.486774i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.888835 + 0.458227i −0.888835 + 0.458227i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.91030 + 0.182411i 1.91030 + 0.182411i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.0934441 0.0180099i 0.0934441 0.0180099i −0.142315 0.989821i $$-0.545455\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$128$$ 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
$$133$$ 1.07701 + 0.431171i 1.07701 + 0.431171i
$$134$$ 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
$$144$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0.723734 0.690079i 0.723734 0.690079i
$$148$$ 0.252989 1.75958i 0.252989 1.75958i
$$149$$ 0 0 −0.981929 0.189251i $$-0.939394\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$150$$ 0 0
$$151$$ −0.205996 1.43273i −0.205996 1.43273i −0.786053 0.618159i $$-0.787879\pi$$
0.580057 0.814576i $$-0.303030\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.759713 + 1.06687i −0.759713 + 1.06687i
$$157$$ −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i $$0.363636\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1.57211 −1.57211 −0.786053 0.618159i $$-0.787879\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$168$$ 0 0
$$169$$ −0.712131 0.0680003i −0.712131 0.0680003i
$$170$$ 0 0
$$171$$ 1.16011 1.16011
$$172$$ −0.841254 1.45709i −0.841254 1.45709i
$$173$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$174$$ 0 0
$$175$$ 0.235759 0.971812i 0.235759 0.971812i
$$176$$ 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
$$181$$ 0.481929 + 0.676774i 0.481929 + 0.676774i 0.981929 0.189251i $$-0.0606061\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ 1.07701 0.431171i 1.07701 0.431171i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0.415415 0.909632i 0.415415 0.909632i
$$190$$ 0 0
$$191$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$192$$ 0.981929 0.189251i 0.981929 0.189251i
$$193$$ 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i $$0.424242\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.500000 0.866025i
$$197$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$198$$ 0 0
$$199$$ −1.21590 1.40323i −1.21590 1.40323i −0.888835 0.458227i $$-0.848485\pi$$
−0.327068 0.945001i $$-0.606061\pi$$
$$200$$ 0 0
$$201$$ 0.0475819 + 0.998867i 0.0475819 + 0.998867i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i $$-0.727273\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −1.78153 + 0.713215i −1.78153 + 0.713215i
$$218$$ 0 0
$$219$$ −1.13779 0.894765i −1.13779 0.894765i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −0.827068 1.81103i −0.827068 1.81103i −0.500000 0.866025i $$-0.666667\pi$$
−0.327068 0.945001i $$-0.606061\pi$$
$$224$$ 0 0
$$225$$ −0.142315 0.989821i −0.142315 0.989821i
$$226$$ 0 0
$$227$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$228$$ 0.273507 1.12741i 0.273507 1.12741i
$$229$$ 0.0800569 + 1.68060i 0.0800569 + 1.68060i 0.580057 + 0.814576i $$0.303030\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −0.0845850 1.77566i −0.0845850 1.77566i
$$238$$ 0 0
$$239$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ 0 0
$$241$$ 0.0224357 0.0924813i 0.0224357 0.0924813i −0.959493 0.281733i $$-0.909091\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$242$$ 0 0
$$243$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$244$$ −0.165101 1.14831i −0.165101 1.14831i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.45788 0.428072i 1.45788 0.428072i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$252$$ −0.786053 0.618159i −0.786053 0.618159i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$257$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$258$$ 0 0
$$259$$ 0.581419 + 1.67990i 0.581419 + 1.67990i
$$260$$ 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
$$271$$ 0.651174 0.0621796i 0.651174 0.0621796i 0.235759 0.971812i $$-0.424242\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$272$$ 0 0
$$273$$ 0.186393 1.29639i 0.186393 1.29639i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 1.82318 0.351390i 1.82318 0.351390i 0.841254 0.540641i $$-0.181818\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$278$$ 0 0
$$279$$ −1.38884 + 1.32425i −1.38884 + 1.32425i
$$280$$ 0 0
$$281$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$282$$ 0 0
$$283$$ −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i $$-0.181818\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$290$$ 0 0
$$291$$ −0.827068 + 1.81103i −0.827068 + 1.81103i
$$292$$ −1.13779 + 0.894765i −1.13779 + 0.894765i
$$293$$ 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
$$300$$ −0.995472 0.0950560i −0.995472 0.0950560i
$$301$$ 1.41542 + 0.909632i 1.41542 + 0.909632i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.03115 0.531595i −1.03115 0.531595i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0.252989 + 0.130425i 0.252989 + 0.130425i 0.580057 0.814576i $$-0.303030\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$308$$ 0 0
$$309$$ −0.607279 0.243118i −0.607279 0.243118i
$$310$$ 0 0
$$311$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$312$$ 0 0
$$313$$ 1.13915 1.59971i 1.13915 1.59971i 0.415415 0.909632i $$-0.363636\pi$$
0.723734 0.690079i $$-0.242424\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −1.74555 0.336426i −1.74555 0.336426i
$$317$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.959493 0.281733i −0.959493 0.281733i
$$325$$ −0.544078 1.19136i −0.544078 1.19136i
$$326$$ 0 0
$$327$$ 1.70566 + 0.879330i 1.70566 + 0.879330i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i $$0.181818\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$332$$ 0 0
$$333$$ 1.16413 + 1.34347i 1.16413 + 1.34347i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −0.786053 + 0.618159i −0.786053 + 0.618159i
$$337$$ −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i −0.959493 0.281733i $$-0.909091\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 0.0475819 0.998867i $$-0.484848\pi$$
−0.0475819 + 0.998867i $$0.515152\pi$$
$$348$$ 0 0
$$349$$ −0.279486 + 1.94387i −0.279486 + 1.94387i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$350$$ 0 0
$$351$$ −0.308779 1.27280i −0.308779 1.27280i
$$352$$ 0 0
$$353$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$354$$ 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
$$361$$ −0.271868 + 0.213799i −0.271868 + 0.213799i
$$362$$ 0 0
$$363$$ −0.888835 0.458227i −0.888835 0.458227i
$$364$$ −1.21590 0.486774i −1.21590 0.486774i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i $$-0.727273\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0.959493 + 1.66189i 0.959493 + 1.66189i
$$373$$ −1.30972 −1.30972 −0.654861 0.755750i $$-0.727273\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −1.95496 + 0.186677i −1.95496 + 0.186677i −0.995472 0.0950560i $$-0.969697\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$380$$ 0 0
$$381$$ 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
$$382$$ 0 0
$$383$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 1.65210 + 0.318417i 1.65210 + 0.318417i
$$388$$ 1.56499 + 1.23072i 1.56499 + 1.23072i
$$389$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −0.370638 1.52779i −0.370638 1.52779i −0.786053 0.618159i $$-0.787879\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$398$$ 0 0
$$399$$ 0.273507 + 1.12741i 0.273507 + 1.12741i
$$400$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$401$$ 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
$$409$$ −0.473420 + 1.36786i −0.473420 + 1.36786i 0.415415 + 0.909632i $$0.363636\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −0.379436 + 0.532843i −0.379436 + 0.532843i
$$413$$ 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 0.786053 0.618159i $$-0.212121\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$420$$ 0 0
$$421$$ 1.65210 + 0.318417i 1.65210 + 0.318417i 0.928368 0.371662i $$-0.121212\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0.672932 + 0.945001i 0.672932 + 0.945001i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$433$$ 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i 1.00000 $$0$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.25667 1.45027i 1.25667 1.45027i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i $$-0.545455\pi$$
0.928368 0.371662i $$-0.121212\pi$$
$$440$$ 0 0
$$441$$ 0.981929 + 0.189251i 0.981929 + 0.189251i
$$442$$ 0 0
$$443$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$444$$ 1.58006 0.814576i 1.58006 0.814576i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$449$$ 0 0 −0.580057 0.814576i $$-0.696970\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 1.04758 0.998867i 1.04758 0.998867i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −0.550294 0.353653i −0.550294 0.353653i 0.235759 0.971812i $$-0.424242\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$458$$ 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
$$463$$ 1.42131 + 1.35522i 1.42131 + 1.35522i 0.841254 + 0.540641i $$0.181818\pi$$
0.580057 + 0.814576i $$0.303030\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$468$$ −1.30972 −1.30972
$$469$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$470$$ 0 0
$$471$$ −1.28605 + 0.247866i −1.28605 + 0.247866i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0.839614 + 0.800570i 0.839614 + 0.800570i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$480$$ 0 0
$$481$$ 1.95865 + 1.25875i 1.95865 + 1.25875i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i $$-0.909091\pi$$
1.00000 $$0$$
$$488$$ 0 0
$$489$$ −0.911911 1.28060i −0.911911 1.28060i
$$490$$ 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
$$499$$ −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i $$-0.848485\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.327068 0.945001i $$-0.606061\pi$$
0.327068 + 0.945001i $$0.393939\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.357685 0.619529i −0.357685 0.619529i
$$508$$ 0.0800569 0.0514495i 0.0800569 0.0514495i
$$509$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$510$$ 0 0
$$511$$ 0.601300 1.31666i 0.601300 1.31666i
$$512$$ 0 0
$$513$$ 0.672932 + 0.945001i 0.672932 + 0.945001i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0.698939 1.53046i 0.698939 1.53046i
$$517$$ 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
$$523$$ −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i $$0.787879\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$524$$ 0 0
$$525$$ 0.928368 0.371662i 0.928368 0.371662i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.327068 + 0.945001i −0.327068 + 0.945001i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 1.16011 1.16011
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.437742 + 1.80440i 0.437742 + 1.80440i 0.580057 + 0.814576i $$0.303030\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$542$$ 0 0
$$543$$ −0.271738 + 0.785135i −0.271738 + 0.785135i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.13779 + 1.08488i −1.13779 + 1.08488i −0.142315 + 0.989821i $$0.545455\pi$$
−0.995472 + 0.0950560i $$0.969697\pi$$
$$548$$ 0 0
$$549$$ 0.975950 + 0.627205i 0.975950 + 0.627205i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 1.70566 0.500828i 1.70566 0.500828i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.827068 + 0.0789754i −0.827068 + 0.0789754i
$$557$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$558$$ 0 0
$$559$$ 2.19364 0.209467i 2.19364 0.209467i
$$560$$ 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
$$567$$ 0.981929 0.189251i 0.981929 0.189251i
$$568$$ 0 0
$$569$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$570$$ 0 0
$$571$$ −1.15486 + 1.62177i −1.15486 + 1.62177i −0.500000 + 0.866025i $$0.666667\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.723734 + 0.690079i 0.723734 + 0.690079i
$$577$$ −1.13779 + 0.894765i −1.13779 + 0.894765i −0.995472 0.0950560i $$-0.969697\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$578$$ 0 0
$$579$$ −1.54370 + 1.21398i −1.54370 + 1.21398i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 −0.235759 0.971812i $$-0.575758\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$588$$ 0.415415 0.909632i 0.415415 0.909632i
$$589$$ 0.316827 2.20358i 0.316827 2.20358i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.419102 1.72756i −0.419102 1.72756i
$$593$$ 0 0 −0.995472 0.0950560i $$-0.969697\pi$$
0.995472 + 0.0950560i $$0.0303030\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0.437742 1.80440i 0.437742 1.80440i
$$598$$ 0 0
$$599$$ 0 0 0.928368 0.371662i $$-0.121212\pi$$
−0.928368 + 0.371662i $$0.878788\pi$$
$$600$$ 0 0
$$601$$ −0.154218 + 0.445585i −0.154218 + 0.445585i −0.995472 0.0950560i $$-0.969697\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$602$$ 0 0
$$603$$ −0.786053 + 0.618159i −0.786053 + 0.618159i
$$604$$ −0.723734 1.25354i −0.723734 1.25354i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −0.279486 + 1.94387i −0.279486 + 1.94387i 0.0475819 + 0.998867i $$0.484848\pi$$
−0.327068 + 0.945001i $$0.606061\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0.771316 + 1.68895i 0.771316 + 1.68895i 0.723734 + 0.690079i $$0.242424\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$614$$ 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
$$619$$ 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 $$0$$
0.841254 + 0.540641i $$0.181818\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −0.308779 + 1.27280i −0.308779 + 1.27280i
$$625$$ 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
$$631$$ −0.738471 0.380708i −0.738471 0.380708i 0.0475819 0.998867i $$-0.484848\pi$$
−0.786053 + 0.618159i $$0.787879\pi$$
$$632$$ 0 0
$$633$$ 0.471518 0.471518
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.30379 0.124497i 1.30379 0.124497i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ 0 0
$$643$$ 1.50842 0.442913i 1.50842 0.442913i 0.580057 0.814576i $$-0.303030\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −1.61435 1.03748i −1.61435 1.03748i
$$652$$ −1.45949 + 0.584293i −1.45949 + 0.584293i
$$653$$ 0 0 −0.928368 0.371662i $$-0.878788\pi$$
0.928368 + 0.371662i $$0.121212\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0.0688733 1.44583i 0.0688733 1.44583i
$$658$$ 0 0
$$659$$ 0 0 0.723734 0.690079i $$-0.242424\pi$$
−0.723734 + 0.690079i $$0.757576\pi$$
$$660$$ 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
$$669$$ 0.995472 1.72421i 0.995472 1.72421i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.195876 0.428908i 0.195876 0.428908i −0.786053 0.618159i $$-0.787879\pi$$
0.981929 + 0.189251i $$0.0606061\pi$$
$$674$$ 0 0
$$675$$ 0.723734 0.690079i 0.723734 0.690079i
$$676$$ −0.686393 + 0.201543i −0.686393 + 0.201543i
$$677$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$678$$ 0 0
$$679$$ −1.95496 0.376789i −1.95496 0.376789i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$684$$ 1.07701 0.431171i 1.07701 0.431171i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −1.32254 + 1.04006i −1.32254 + 1.04006i
$$688$$ −1.32254 1.04006i −1.32254 1.04006i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i −0.327068 0.945001i $$-0.606061\pi$$
0.235759 + 0.971812i $$0.424242\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −0.142315 0.989821i −0.142315 0.989821i
$$701$$ 0 0 −0.0475819 0.998867i $$-0.515152\pi$$
0.0475819 + 0.998867i $$0.484848\pi$$
$$702$$ 0 0
$$703$$ −2.02503 0.390293i −2.02503 0.390293i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0.0395325 + 0.829889i 0.0395325 + 0.829889i 0.928368 + 0.371662i $$0.121212\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$710$$ 0 0
$$711$$ 1.39734 1.09888i 1.39734 1.09888i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.786053 0.618159i $$-0.787879\pi$$
0.786053 + 0.618159i $$0.212121\pi$$
$$720$$ 0 0
$$721$$ 0.0930932 0.647478i 0.0930932 0.647478i
$$722$$ 0 0
$$723$$ 0.0883470 0.0353688i 0.0883470 0.0353688i
$$724$$ 0.698939 + 0.449181i 0.698939 + 0.449181i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i $$0.484848\pi$$
−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
$$732$$ 0.839614 0.800570i 0.839614 0.800570i
$$733$$ 0.0930932 0.647478i 0.0930932 0.647478i −0.888835 0.458227i $$-0.848485\pi$$
0.981929 0.189251i $$-0.0606061\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i $$-0.181818\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$740$$ 0 0
$$741$$ 1.19435 + 0.939247i 1.19435 + 0.939247i
$$742$$ 0 0
$$743$$ 0 0 −0.723734 0.690079i $$-0.757576\pi$$
0.723734 + 0.690079i $$0.242424\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 1.72373 0.690079i 1.72373 0.690079i 0.723734 0.690079i $$-0.242424\pi$$
1.00000 $$0$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0.0475819 0.998867i 0.0475819 0.998867i
$$757$$ 0.839614 + 1.17907i 0.839614 + 1.17907i 0.981929 + 0.189251i $$0.0606061\pi$$
−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
$$763$$ −0.452418 + 1.86489i −0.452418 + 1.86489i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.841254 0.540641i 0.841254 0.540641i
$$769$$ −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i $$-0.787879\pi$$
−0.888835 + 0.458227i $$0.848485\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0.815816 + 1.78639i 0.815816 + 1.78639i
$$773$$ 0 0 −0.888835 0.458227i $$-0.848485\pi$$
0.888835 + 0.458227i $$0.151515\pi$$
$$774$$ 0 0
$$775$$ −1.91899 −1.91899
$$776$$ 0 0
$$777$$ −1.03115 + 1.44805i −1.03115 + 1.44805i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.786053 0.618159i −0.786053 0.618159i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i $$-0.727273\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1.45788 + 0.428072i 1.45788 + 0.428072i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −1.65033 0.850806i −1.65033 0.850806i
$$797$$ 0 0 0.981929 0.189251i $$-0.0606061\pi$$
−0.981929 + 0.189251i $$0.939394\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0