# Properties

 Label 3267.1.bf.a.2290.1 Level $3267$ Weight $1$ Character 3267.2290 Analytic conductor $1.630$ Analytic rank $0$ Dimension $24$ Projective image $D_{9}$ CM discriminant -11 Inner twists $16$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3267 = 3^{3} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3267.bf (of order $$90$$, degree $$24$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.63044539627$$ Analytic rank: $$0$$ Dimension: $$24$$ Coefficient field: $$\Q(\zeta_{45})$$ Defining polynomial: $$x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1$$ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 297) Projective image: $$D_{9}$$ Projective field: Galois closure of 9.1.459450093735369.1

## Embedding invariants

 Embedding label 2290.1 Root $$0.961262 + 0.275637i$$ of defining polynomial Character $$\chi$$ $$=$$ 3267.2290 Dual form 3267.1.bf.a.2635.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.997564 - 0.0697565i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.213817 - 0.273673i) q^{5} +(0.990268 + 0.139173i) q^{9} +O(q^{10})$$ $$q+(-0.997564 - 0.0697565i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.213817 - 0.273673i) q^{5} +(0.990268 + 0.139173i) q^{9} +(0.766044 - 0.642788i) q^{12} +(0.194206 + 0.287922i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(0.343916 + 0.0483343i) q^{20} +(-0.173648 + 0.984808i) q^{23} +(0.212743 - 0.853264i) q^{25} +(-0.978148 - 0.207912i) q^{27} +(-1.35275 - 0.719272i) q^{31} +(-0.809017 + 0.587785i) q^{36} +(0.317271 - 0.141258i) q^{37} +(-0.173648 - 0.300767i) q^{45} +(1.35192 + 1.30553i) q^{47} +(-0.104528 + 0.994522i) q^{48} +(-0.615661 - 0.788011i) q^{49} +(0.473442 - 1.45710i) q^{53} +(1.47274 + 0.422301i) q^{59} +(-0.339707 - 0.0722070i) q^{60} +(0.669131 + 0.743145i) q^{64} +(1.17365 + 0.984808i) q^{67} +(0.241922 - 0.970296i) q^{69} +(1.83832 + 0.390746i) q^{71} +(-0.271745 + 0.836345i) q^{75} +(-0.280969 + 0.204136i) q^{80} +(0.961262 + 0.275637i) q^{81} +(0.500000 + 0.866025i) q^{89} +(-0.559193 - 0.829038i) q^{92} +(1.29929 + 0.811883i) q^{93} +(1.15707 - 1.48098i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q + 3 q^{5}+O(q^{10})$$ 24 * q + 3 * q^5 $$24 q + 3 q^{5} + 3 q^{15} - 6 q^{20} + 3 q^{25} + 3 q^{27} + 3 q^{31} - 6 q^{36} + 3 q^{47} + 3 q^{48} + 3 q^{59} + 3 q^{64} + 24 q^{67} - 6 q^{75} + 12 q^{89} - 6 q^{93} - 6 q^{97}+O(q^{100})$$ 24 * q + 3 * q^5 + 3 * q^15 - 6 * q^20 + 3 * q^25 + 3 * q^27 + 3 * q^31 - 6 * q^36 + 3 * q^47 + 3 * q^48 + 3 * q^59 + 3 * q^64 + 24 * q^67 - 6 * q^75 + 12 * q^89 - 6 * q^93 - 6 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times$$.

 $$n$$ $$244$$ $$3026$$ $$\chi(n)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{9}\right)$$

## 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 −0.374607 0.927184i $$-0.622222\pi$$
0.374607 + 0.927184i $$0.377778\pi$$
$$3$$ −0.997564 0.0697565i −0.997564 0.0697565i
$$4$$ −0.719340 + 0.694658i −0.719340 + 0.694658i
$$5$$ −0.213817 0.273673i −0.213817 0.273673i 0.669131 0.743145i $$-0.266667\pi$$
−0.882948 + 0.469472i $$0.844444\pi$$
$$6$$ 0 0
$$7$$ 0 0 0.438371 0.898794i $$-0.355556\pi$$
−0.438371 + 0.898794i $$0.644444\pi$$
$$8$$ 0 0
$$9$$ 0.990268 + 0.139173i 0.990268 + 0.139173i
$$10$$ 0 0
$$11$$ 0 0
$$12$$ 0.766044 0.642788i 0.766044 0.642788i
$$13$$ 0 0 0.848048 0.529919i $$-0.177778\pi$$
−0.848048 + 0.529919i $$0.822222\pi$$
$$14$$ 0 0
$$15$$ 0.194206 + 0.287922i 0.194206 + 0.287922i
$$16$$ 0.0348995 0.999391i 0.0348995 0.999391i
$$17$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$18$$ 0 0
$$19$$ 0 0 −0.913545 0.406737i $$-0.866667\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$20$$ 0.343916 + 0.0483343i 0.343916 + 0.0483343i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$24$$ 0 0
$$25$$ 0.212743 0.853264i 0.212743 0.853264i
$$26$$ 0 0
$$27$$ −0.978148 0.207912i −0.978148 0.207912i
$$28$$ 0 0
$$29$$ 0 0 0.997564 0.0697565i $$-0.0222222\pi$$
−0.997564 + 0.0697565i $$0.977778\pi$$
$$30$$ 0 0
$$31$$ −1.35275 0.719272i −1.35275 0.719272i −0.374607 0.927184i $$-0.622222\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$37$$ 0.317271 0.141258i 0.317271 0.141258i −0.241922 0.970296i $$-0.577778\pi$$
0.559193 + 0.829038i $$0.311111\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 −0.997564 0.0697565i $$-0.977778\pi$$
0.997564 + 0.0697565i $$0.0222222\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$44$$ 0 0
$$45$$ −0.173648 0.300767i −0.173648 0.300767i
$$46$$ 0 0
$$47$$ 1.35192 + 1.30553i 1.35192 + 1.30553i 0.913545 + 0.406737i $$0.133333\pi$$
0.438371 + 0.898794i $$0.355556\pi$$
$$48$$ −0.104528 + 0.994522i −0.104528 + 0.994522i
$$49$$ −0.615661 0.788011i −0.615661 0.788011i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0.473442 1.45710i 0.473442 1.45710i −0.374607 0.927184i $$-0.622222\pi$$
0.848048 0.529919i $$-0.177778\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.47274 + 0.422301i 1.47274 + 0.422301i 0.913545 0.406737i $$-0.133333\pi$$
0.559193 + 0.829038i $$0.311111\pi$$
$$60$$ −0.339707 0.0722070i −0.339707 0.0722070i
$$61$$ 0 0 0.882948 0.469472i $$-0.155556\pi$$
−0.882948 + 0.469472i $$0.844444\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0.669131 + 0.743145i 0.669131 + 0.743145i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 $$0$$
0.173648 + 0.984808i $$0.444444\pi$$
$$68$$ 0 0
$$69$$ 0.241922 0.970296i 0.241922 0.970296i
$$70$$ 0 0
$$71$$ 1.83832 + 0.390746i 1.83832 + 0.390746i 0.990268 0.139173i $$-0.0444444\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$72$$ 0 0
$$73$$ 0 0 0.104528 0.994522i $$-0.466667\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$74$$ 0 0
$$75$$ −0.271745 + 0.836345i −0.271745 + 0.836345i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.374607 0.927184i $$-0.622222\pi$$
0.374607 + 0.927184i $$0.377778\pi$$
$$80$$ −0.280969 + 0.204136i −0.280969 + 0.204136i
$$81$$ 0.961262 + 0.275637i 0.961262 + 0.275637i
$$82$$ 0 0
$$83$$ 0 0 −0.848048 0.529919i $$-0.822222\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.559193 0.829038i −0.559193 0.829038i
$$93$$ 1.29929 + 0.811883i 1.29929 + 0.811883i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.15707 1.48098i 1.15707 1.48098i 0.309017 0.951057i $$-0.400000\pi$$
0.848048 0.529919i $$-0.177778\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0.439693 + 0.761570i 0.439693 + 0.761570i
$$101$$ 0 0 −0.990268 0.139173i $$-0.955556\pi$$
0.990268 + 0.139173i $$0.0444444\pi$$
$$102$$ 0 0
$$103$$ 0.333843 + 0.0957278i 0.333843 + 0.0957278i 0.438371 0.898794i $$-0.355556\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$108$$ 0.848048 0.529919i 0.848048 0.529919i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$112$$ 0 0
$$113$$ −1.05094 + 1.55808i −1.05094 + 1.55808i −0.241922 + 0.970296i $$0.577778\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$114$$ 0 0
$$115$$ 0.306644 0.163046i 0.306644 0.163046i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.47274 0.422301i 1.47274 0.422301i
$$125$$ −0.596274 + 0.265478i −0.596274 + 0.265478i
$$126$$ 0 0
$$127$$ 0 0 0.669131 0.743145i $$-0.266667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.152245 + 0.312148i 0.152245 + 0.312148i
$$136$$ 0 0
$$137$$ 1.29929 + 0.811883i 1.29929 + 0.811883i 0.990268 0.139173i $$-0.0444444\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.719340 0.694658i $$-0.244444\pi$$
−0.719340 + 0.694658i $$0.755556\pi$$
$$140$$ 0 0
$$141$$ −1.25755 1.39666i −1.25755 1.39666i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.173648 0.984808i 0.173648 0.984808i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0.559193 + 0.829038i 0.559193 + 0.829038i
$$148$$ −0.130100 + 0.322008i −0.130100 + 0.322008i
$$149$$ 0 0 0.374607 0.927184i $$-0.377778\pi$$
−0.374607 + 0.927184i $$0.622222\pi$$
$$150$$ 0 0
$$151$$ 0 0 0.961262 0.275637i $$-0.0888889\pi$$
−0.961262 + 0.275637i $$0.911111\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0.0923963 + 0.524005i 0.0923963 + 0.524005i
$$156$$ 0 0
$$157$$ 0.856733 1.27016i 0.856733 1.27016i −0.104528 0.994522i $$-0.533333\pi$$
0.961262 0.275637i $$-0.0888889\pi$$
$$158$$ 0 0
$$159$$ −0.573931 + 1.42053i −0.573931 + 1.42053i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −0.580762 + 1.78740i −0.580762 + 1.78740i 0.0348995 + 0.999391i $$0.488889\pi$$
−0.615661 + 0.788011i $$0.711111\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.0348995 0.999391i $$-0.511111\pi$$
0.0348995 + 0.999391i $$0.488889\pi$$
$$168$$ 0 0
$$169$$ 0.438371 0.898794i 0.438371 0.898794i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.961262 0.275637i $$-0.0888889\pi$$
−0.961262 + 0.275637i $$0.911111\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1.43969 0.524005i −1.43969 0.524005i
$$178$$ 0 0
$$179$$ −0.160147 1.52370i −0.160147 1.52370i −0.719340 0.694658i $$-0.755556\pi$$
0.559193 0.829038i $$-0.311111\pi$$
$$180$$ 0.333843 + 0.0957278i 0.333843 + 0.0957278i
$$181$$ 0.232387 0.258091i 0.232387 0.258091i −0.615661 0.788011i $$-0.711111\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.106497 0.0566252i −0.106497 0.0566252i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −1.87939 −1.87939
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1.87481 0.131099i 1.87481 0.131099i 0.913545 0.406737i $$-0.133333\pi$$
0.961262 + 0.275637i $$0.0888889\pi$$
$$192$$ −0.615661 0.788011i −0.615661 0.788011i
$$193$$ 0 0 0.990268 0.139173i $$-0.0444444\pi$$
−0.990268 + 0.139173i $$0.955556\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.990268 + 0.139173i 0.990268 + 0.139173i
$$197$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$198$$ 0 0
$$199$$ 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$200$$ 0 0
$$201$$ −1.10209 1.06428i −1.10209 1.06428i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 −0.0348995 0.999391i $$-0.511111\pi$$
0.0348995 + 0.999391i $$0.488889\pi$$
$$212$$ 0.671624 + 1.37703i 0.671624 + 1.37703i
$$213$$ −1.80658 0.518029i −1.80658 0.518029i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0.719340 + 0.694658i 0.719340 + 0.694658i 0.961262 0.275637i $$-0.0888889\pi$$
−0.241922 + 0.970296i $$0.577778\pi$$
$$224$$ 0 0
$$225$$ 0.329424 0.815352i 0.329424 0.815352i
$$226$$ 0 0
$$227$$ 0 0 −0.559193 0.829038i $$-0.688889\pi$$
0.559193 + 0.829038i $$0.311111\pi$$
$$228$$ 0 0
$$229$$ −0.848048 + 0.529919i −0.848048 + 0.529919i −0.882948 0.469472i $$-0.844444\pi$$
0.0348995 + 0.999391i $$0.488889\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.669131 0.743145i $$-0.733333\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$234$$ 0 0
$$235$$ 0.0682261 0.649128i 0.0682261 0.649128i
$$236$$ −1.35275 + 0.719272i −1.35275 + 0.719272i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.438371 0.898794i $$-0.644444\pi$$
0.438371 + 0.898794i $$0.355556\pi$$
$$240$$ 0.294524 0.184039i 0.294524 0.184039i
$$241$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$242$$ 0 0
$$243$$ −0.939693 0.342020i −0.939693 0.342020i
$$244$$ 0 0
$$245$$ −0.0840186 + 0.336980i −0.0840186 + 0.336980i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.95630 + 0.415823i −1.95630 + 0.415823i −0.978148 + 0.207912i $$0.933333\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.997564 0.0697565i −0.997564 0.0697565i
$$257$$ 0.241922 + 0.970296i 0.241922 + 0.970296i 0.961262 + 0.275637i $$0.0888889\pi$$
−0.719340 + 0.694658i $$0.755556\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$264$$ 0 0
$$265$$ −0.500000 + 0.181985i −0.500000 + 0.181985i
$$266$$ 0 0
$$267$$ −0.438371 0.898794i −0.438371 0.898794i
$$268$$ −1.52836 + 0.106873i −1.52836 + 0.106873i
$$269$$ −0.580762 1.78740i −0.580762 1.78740i −0.615661 0.788011i $$-0.711111\pi$$
0.0348995 0.999391i $$-0.488889\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$277$$ 0 0 −0.990268 0.139173i $$-0.955556\pi$$
0.990268 + 0.139173i $$0.0444444\pi$$
$$278$$ 0 0
$$279$$ −1.23949 0.900539i −1.23949 0.900539i
$$280$$ 0 0
$$281$$ 0 0 0.0348995 0.999391i $$-0.488889\pi$$
−0.0348995 + 0.999391i $$0.511111\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.997564 0.0697565i $$-0.977778\pi$$
0.997564 + 0.0697565i $$0.0222222\pi$$
$$284$$ −1.59381 + 0.995922i −1.59381 + 0.995922i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$290$$ 0 0
$$291$$ −1.25755 + 1.39666i −1.25755 + 1.39666i
$$292$$ 0 0
$$293$$ 0 0 0.719340 0.694658i $$-0.244444\pi$$
−0.719340 + 0.694658i $$0.755556\pi$$
$$294$$ 0 0
$$295$$ −0.199324 0.493344i −0.199324 0.493344i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.385497 0.790386i −0.385497 0.790386i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$308$$ 0 0
$$309$$ −0.326352 0.118782i −0.326352 0.118782i
$$310$$ 0 0
$$311$$ −1.52836 0.106873i −1.52836 0.106873i −0.719340 0.694658i $$-0.755556\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$312$$ 0 0
$$313$$ −0.0348995 + 0.999391i −0.0348995 + 0.999391i 0.848048 + 0.529919i $$0.177778\pi$$
−0.882948 + 0.469472i $$0.844444\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.98054 + 0.278346i 1.98054 + 0.278346i 0.990268 + 0.139173i $$0.0444444\pi$$
0.990268 + 0.139173i $$0.0444444\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.0603074 0.342020i 0.0603074 0.342020i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.882948 + 0.469472i −0.882948 + 0.469472i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.326352 1.85083i −0.326352 1.85083i −0.500000 0.866025i $$-0.666667\pi$$
0.173648 0.984808i $$-0.444444\pi$$
$$332$$ 0 0
$$333$$ 0.333843 0.0957278i 0.333843 0.0957278i
$$334$$ 0 0
$$335$$ 0.0185696 0.531765i 0.0185696 0.531765i
$$336$$ 0 0
$$337$$ 0 0 −0.241922 0.970296i $$-0.577778\pi$$
0.241922 + 0.970296i $$0.422222\pi$$
$$338$$ 0 0
$$339$$ 1.15707 1.48098i 1.15707 1.48098i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −0.317271 + 0.141258i −0.317271 + 0.141258i
$$346$$ 0 0
$$347$$ 0 0 0.990268 0.139173i $$-0.0444444\pi$$
−0.990268 + 0.139173i $$0.955556\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.241922 0.970296i $$-0.422222\pi$$
−0.241922 + 0.970296i $$0.577778\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$354$$ 0 0
$$355$$ −0.286126 0.586646i −0.286126 0.586646i
$$356$$ −0.961262 0.275637i −0.961262 0.275637i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.104528 0.994522i $$-0.466667\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$360$$ 0 0
$$361$$ 0.669131 + 0.743145i 0.669131 + 0.743145i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.05094 1.55808i −1.05094 1.55808i −0.809017 0.587785i $$-0.800000\pi$$
−0.241922 0.970296i $$-0.577778\pi$$
$$368$$ 0.978148 + 0.207912i 0.978148 + 0.207912i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −1.49861 + 0.318539i −1.49861 + 0.318539i
$$373$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$374$$ 0 0
$$375$$ 0.613341 0.223238i 0.613341 0.223238i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i $$-0.933333\pi$$
0.669131 0.743145i $$-0.266667\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.0534691 + 1.53116i 0.0534691 + 1.53116i 0.669131 + 0.743145i $$0.266667\pi$$
−0.615661 + 0.788011i $$0.711111\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0.196449 + 1.86909i 0.196449 + 1.86909i
$$389$$ −1.05094 1.55808i −1.05094 1.55808i −0.809017 0.587785i $$-0.800000\pi$$
−0.241922 0.970296i $$-0.577778\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 0.984808i $$-0.444444\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.845319 0.242391i −0.845319 0.242391i
$$401$$ 0.343916 0.0483343i 0.343916 0.0483343i 0.0348995 0.999391i $$-0.488889\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −0.130100 0.322008i −0.130100 0.322008i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 −0.882948 0.469472i $$-0.844444\pi$$
0.882948 + 0.469472i $$0.155556\pi$$
$$410$$ 0 0
$$411$$ −1.23949 0.900539i −1.23949 0.900539i
$$412$$ −0.306644 + 0.163046i −0.306644 + 0.163046i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i $$-0.222222\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$420$$ 0 0
$$421$$ 0.333843 0.0957278i 0.333843 0.0957278i −0.104528 0.994522i $$-0.533333\pi$$
0.438371 + 0.898794i $$0.355556\pi$$
$$422$$ 0 0
$$423$$ 1.15707 + 1.48098i 1.15707 + 1.48098i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$432$$ −0.241922 + 0.970296i −0.241922 + 0.970296i
$$433$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$440$$ 0 0
$$441$$ −0.500000 0.866025i −0.500000 0.866025i
$$442$$ 0 0
$$443$$ 0.333843 0.0957278i 0.333843 0.0957278i −0.104528 0.994522i $$-0.533333\pi$$
0.438371 + 0.898794i $$0.355556\pi$$
$$444$$ 0.152245 0.312148i 0.152245 0.312148i
$$445$$ 0.130100 0.322008i 0.130100 0.322008i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.232387 + 0.258091i 0.232387 + 0.258091i 0.848048 0.529919i $$-0.177778\pi$$
−0.615661 + 0.788011i $$0.711111\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −0.326352 1.85083i −0.326352 1.85083i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.848048 0.529919i $$-0.822222\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −0.107320 + 0.330298i −0.107320 + 0.330298i
$$461$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$462$$ 0 0
$$463$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$464$$ 0 0
$$465$$ −0.0556184 0.529174i −0.0556184 0.529174i
$$466$$ 0 0
$$467$$ −1.25755 + 1.39666i −1.25755 + 1.39666i −0.374607 + 0.927184i $$0.622222\pi$$
−0.882948 + 0.469472i $$0.844444\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −0.943248 + 1.20730i −0.943248 + 1.20730i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.671624 1.37703i 0.671624 1.37703i
$$478$$ 0 0
$$479$$ 0 0 0.882948 0.469472i $$-0.155556\pi$$
−0.882948 + 0.469472i $$0.844444\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −0.652704 −0.652704
$$486$$ 0 0
$$487$$ −0.280969 + 0.204136i −0.280969 + 0.204136i −0.719340 0.694658i $$-0.755556\pi$$
0.438371 + 0.898794i $$0.355556\pi$$
$$488$$ 0 0
$$489$$ 0.704030 1.74254i 0.704030 1.74254i
$$490$$ 0 0
$$491$$ 0 0 −0.961262 0.275637i $$-0.911111\pi$$
0.961262 + 0.275637i $$0.0888889\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −0.766044 + 1.32683i −0.766044 + 1.32683i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −0.0840186 0.336980i −0.0840186 0.336980i 0.913545 0.406737i $$-0.133333\pi$$
−0.997564 + 0.0697565i $$0.977778\pi$$
$$500$$ 0.244507 0.605176i 0.244507 0.605176i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.104528 0.994522i $$-0.533333\pi$$
0.104528 + 0.994522i $$0.466667\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$508$$ 0 0
$$509$$ −0.438371 0.898794i −0.438371 0.898794i −0.997564 0.0697565i $$-0.977778\pi$$
0.559193 0.829038i $$-0.311111\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −0.0451831 0.111832i −0.0451831 0.111832i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −0.0363024 + 0.345394i −0.0363024 + 0.345394i 0.961262 + 0.275637i $$0.0888889\pi$$
−0.997564 + 0.0697565i $$0.977778\pi$$
$$522$$ 0 0
$$523$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 1.39963 + 0.623157i 1.39963 + 0.623157i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0.0534691 + 1.53116i 0.0534691 + 1.53116i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ −0.326352 0.118782i −0.326352 0.118782i
$$541$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$542$$ 0 0
$$543$$ −0.249824 + 0.241252i −0.249824 + 0.241252i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 −0.719340 0.694658i $$-0.755556\pi$$
0.719340 + 0.694658i $$0.244444\pi$$
$$548$$ −1.49861 + 0.318539i −1.49861 + 0.318539i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0.102287 + 0.0639161i 0.102287 + 0.0639161i
$$556$$ 0 0
$$557$$ 0 0 0.913545 0.406737i $$-0.133333\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.882948 0.469472i $$-0.844444\pi$$
0.882948 + 0.469472i $$0.155556\pi$$
$$564$$ 1.87481 + 0.131099i 1.87481 + 0.131099i
$$565$$ 0.651114 0.0455303i 0.651114 0.0455303i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 0.241922 0.970296i $$-0.422222\pi$$
−0.241922 + 0.970296i $$0.577778\pi$$
$$570$$ 0 0
$$571$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$572$$ 0 0
$$573$$ −1.87939 −1.87939
$$574$$ 0 0
$$575$$ 0.803358 + 0.357678i 0.803358 + 0.357678i
$$576$$ 0.559193 + 0.829038i 0.559193 + 0.829038i
$$577$$ −0.339707 0.0722070i −0.339707 0.0722070i 0.0348995 0.999391i $$-0.488889\pi$$
−0.374607 + 0.927184i $$0.622222\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.152245 0.312148i 0.152245 0.312148i −0.809017 0.587785i $$-0.800000\pi$$
0.961262 + 0.275637i $$0.0888889\pi$$
$$588$$ −0.978148 0.207912i −0.978148 0.207912i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.130100 0.322008i −0.130100 0.322008i
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −1.05094 + 1.55808i −1.05094 + 1.55808i
$$598$$ 0 0
$$599$$ 0.615661 + 0.788011i 0.615661 + 0.788011i 0.990268 0.139173i $$-0.0444444\pi$$
−0.374607 + 0.927184i $$0.622222\pi$$
$$600$$ 0 0
$$601$$ 0 0 0.438371 0.898794i $$-0.355556\pi$$
−0.438371 + 0.898794i $$0.644444\pi$$
$$602$$ 0 0
$$603$$ 1.02517 + 1.13856i 1.02517 + 1.13856i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 0.848048 0.529919i $$-0.177778\pi$$
−0.848048 + 0.529919i $$0.822222\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.913545 0.406737i $$-0.866667\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i $$-0.666667\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$618$$ 0 0
$$619$$ −0.0840186 + 0.336980i −0.0840186 + 0.336980i −0.997564 0.0697565i $$-0.977778\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$620$$ −0.430469 0.312754i −0.430469 0.312754i
$$621$$ 0.374607 0.927184i 0.374607 0.927184i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.576303 0.306426i −0.576303 0.306426i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.266044 + 1.50881i 0.266044 + 1.50881i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1.39963 0.623157i 1.39963 0.623157i 0.438371 0.898794i $$-0.355556\pi$$
0.961262 + 0.275637i $$0.0888889\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ −0.573931 1.42053i −0.573931 1.42053i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 1.76604 + 0.642788i 1.76604 + 0.642788i
$$640$$ 0 0
$$641$$ 0.719340 + 0.694658i 0.719340 + 0.694658i 0.961262 0.275637i $$-0.0888889\pi$$
−0.241922 + 0.970296i $$0.577778\pi$$
$$642$$ 0 0
$$643$$ 0.615661 + 0.788011i 0.615661 + 0.788011i 0.990268 0.139173i $$-0.0444444\pi$$
−0.374607 + 0.927184i $$0.622222\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i $$-0.400000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.823868 1.68918i −0.823868 1.68918i
$$653$$ 0.333843 + 0.0957278i 0.333843 + 0.0957278i 0.438371 0.898794i $$-0.355556\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$660$$ 0 0
$$661$$ −1.43969 1.20805i −1.43969 1.20805i −0.939693 0.342020i $$-0.888889\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −0.669131 0.743145i −0.669131 0.743145i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 −0.374607 0.927184i $$-0.622222\pi$$
0.374607 + 0.927184i $$0.377778\pi$$
$$674$$ 0 0
$$675$$ −0.385497 + 0.790386i −0.385497 + 0.790386i
$$676$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$677$$ 0 0 −0.848048 0.529919i $$-0.822222\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i $$0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$684$$ 0 0
$$685$$ −0.0556184 0.529174i −0.0556184 0.529174i
$$686$$ 0 0
$$687$$ 0.882948 0.469472i 0.882948 0.469472i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.213817 + 0.273673i −0.213817 + 0.273673i −0.882948 0.469472i $$-0.844444\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$692$$ 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 0
$$701$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −0.113341 + 0.642788i −0.113341 + 0.642788i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 1.39963 0.623157i 1.39963 0.623157i
$$709$$ −0.306644 + 0.163046i −0.306644 + 0.163046i −0.615661 0.788011i $$-0.711111\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0.943248 1.20730i 0.943248 1.20730i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.71690 + 0.764415i −1.71690 + 0.764415i −0.719340 + 0.694658i $$0.755556\pi$$
−0.997564 + 0.0697565i $$0.977778\pi$$
$$720$$ −0.306644 + 0.163046i −0.306644 + 0.163046i
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0.0121205 + 0.347085i 0.0121205 + 0.347085i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i $$0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$728$$ 0 0
$$729$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.719340 0.694658i $$-0.244444\pi$$
−0.719340 + 0.694658i $$0.755556\pi$$
$$734$$ 0 0
$$735$$ 0.107320 0.330298i 0.107320 0.330298i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 −0.669131 0.743145i $$-0.733333\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$740$$ 0.115942 0.0332459i 0.115942 0.0332459i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.374607 0.927184i $$-0.377778\pi$$
−0.374607 + 0.927184i $$0.622222\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.05094 + 1.55808i −1.05094 + 1.55808i −0.241922 + 0.970296i $$0.577778\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$752$$ 1.35192 1.30553i 1.35192 1.30553i
$$753$$ 1.98054 0.278346i 1.98054 0.278346i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0.473442 1.45710i 0.473442 1.45710i −0.374607 0.927184i $$-0.622222\pi$$
0.848048 0.529919i $$-0.177778\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.0348995 0.999391i $$-0.511111\pi$$
0.0348995 + 0.999391i $$0.488889\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1.25755 + 1.39666i −1.25755 + 1.39666i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.990268 + 0.139173i 0.990268 + 0.139173i
$$769$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$770$$ 0 0
$$771$$ −0.173648 0.984808i −0.173648 0.984808i
$$772$$ 0 0
$$773$$ −0.209057 1.98904i −0.209057 1.98904i −0.104528 0.994522i $$-0.533333\pi$$
−0.104528 0.994522i $$-0.533333\pi$$
$$774$$ 0 0
$$775$$ −0.901517 + 1.00124i −0.901517 + 1.00124i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$785$$ −0.530793 + 0.0371166i −0.530793 + 0.0371166i
$$786$$ 0 0
$$787$$ 0 0 0.990268 0.139173i $$-0.0444444\pi$$
−0.990268 + 0.139173i $$0.955556\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0.511477 0.146664i 0.511477 0.146664i
$$796$$ 0.454664 + 1.82356i 0.454664 + 1.82356i
$$797$$ −0.130100 + 0.322008i −0.130100 + 0.322008i −0.978148 0.207912i $$-0.933333\pi$$
0.848048 + 0.529919i $$0.177778\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0.374607 + 0.927184i 0.374607 + 0.927184i
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 1.53209 1.53209