# Properties

 Label 1089.1.s.b.94.2 Level $1089$ Weight $1$ Character 1089.94 Analytic conductor $0.543$ Analytic rank $0$ Dimension $16$ Projective image $S_{4}$ CM/RM no Inner twists $16$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1089 = 3^{2} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1089.s (of order $$30$$, degree $$8$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.543481798757$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$2$$ over $$\Q(\zeta_{30})$$ Coefficient field: 16.0.26873856000000000000.1 Defining polynomial: $$x^{16} + 2 x^{14} - 8 x^{10} - 16 x^{8} - 32 x^{6} + 128 x^{2} + 256$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$S_{4}$$ Projective field: Galois closure of 4.2.107811.1

## Embedding invariants

 Embedding label 94.2 Root $$1.05097 + 0.946294i$$ of defining polynomial Character $$\chi$$ $$=$$ 1089.94 Dual form 1089.1.s.b.475.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.05097 + 0.946294i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.104528 + 0.994522i) q^{4} +(-0.669131 - 0.743145i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(0.575212 - 1.29195i) q^{7} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$$ $$q+(1.05097 + 0.946294i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.104528 + 0.994522i) q^{4} +(-0.669131 - 0.743145i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(0.575212 - 1.29195i) q^{7} +(0.669131 - 0.743145i) q^{9} -1.41421i q^{10} +(-0.500000 - 0.866025i) q^{12} +(1.82709 - 0.813473i) q^{14} +(0.913545 + 0.406737i) q^{15} +(0.978148 - 0.207912i) q^{16} +(1.40647 - 0.147826i) q^{18} +(0.669131 - 0.743145i) q^{20} +1.41421i q^{21} +(-0.309017 + 0.951057i) q^{27} +(1.34500 + 0.437016i) q^{28} +(-0.575212 + 1.29195i) q^{29} +(0.575212 + 1.29195i) q^{30} +(-0.978148 - 0.207912i) q^{31} +(1.22474 + 0.707107i) q^{32} +(-1.34500 + 0.437016i) q^{35} +(0.809017 + 0.587785i) q^{36} +(0.809017 - 0.587785i) q^{37} +(-1.33826 + 1.48629i) q^{42} -1.00000 q^{45} +(0.104528 - 0.994522i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-0.669131 - 0.743145i) q^{49} +(0.309017 + 0.951057i) q^{53} +(-1.22474 + 0.707107i) q^{54} +(-1.82709 + 0.813473i) q^{58} +(-0.104528 - 0.994522i) q^{59} +(-0.309017 + 0.951057i) q^{60} +(0.294032 + 1.38331i) q^{61} +(-0.831254 - 1.14412i) q^{62} +(-0.575212 - 1.29195i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.500000 - 0.866025i) q^{67} +(-1.82709 - 0.813473i) q^{70} +(-0.309017 + 0.951057i) q^{71} +(0.831254 + 1.14412i) q^{73} +(1.40647 + 0.147826i) q^{74} +(-0.809017 - 0.587785i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(0.294032 + 1.38331i) q^{83} +(-1.40647 + 0.147826i) q^{84} -1.41421i q^{87} +(-1.05097 - 0.946294i) q^{90} +(0.978148 - 0.207912i) q^{93} +(1.05097 - 0.946294i) q^{94} +(-1.40647 - 0.147826i) q^{96} +(0.669131 - 0.743145i) q^{97} -1.41421i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{9} + O(q^{10})$$ $$16q - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{9} - 8q^{12} + 4q^{14} + 2q^{15} - 2q^{16} + 2q^{20} + 4q^{27} + 2q^{31} + 4q^{36} + 4q^{37} - 4q^{42} - 16q^{45} - 2q^{47} - 4q^{48} - 2q^{49} - 4q^{53} - 4q^{58} + 2q^{59} + 4q^{60} - 4q^{64} + 8q^{67} - 4q^{70} + 4q^{71} - 4q^{80} + 2q^{81} - 2q^{93} + 2q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$$.

 $$n$$ $$244$$ $$848$$ $$\chi(n)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.05097 + 0.946294i 1.05097 + 0.946294i 0.998630 0.0523360i $$-0.0166667\pi$$
0.0523360 + 0.998630i $$0.483333\pi$$
$$3$$ −0.913545 + 0.406737i −0.913545 + 0.406737i
$$4$$ 0.104528 + 0.994522i 0.104528 + 0.994522i
$$5$$ −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i $$-0.400000\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$6$$ −1.34500 0.437016i −1.34500 0.437016i
$$7$$ 0.575212 1.29195i 0.575212 1.29195i −0.358368 0.933580i $$-0.616667\pi$$
0.933580 0.358368i $$-0.116667\pi$$
$$8$$ 0 0
$$9$$ 0.669131 0.743145i 0.669131 0.743145i
$$10$$ 1.41421i 1.41421i
$$11$$ 0 0
$$12$$ −0.500000 0.866025i −0.500000 0.866025i
$$13$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$14$$ 1.82709 0.813473i 1.82709 0.813473i
$$15$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$16$$ 0.978148 0.207912i 0.978148 0.207912i
$$17$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$18$$ 1.40647 0.147826i 1.40647 0.147826i
$$19$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$20$$ 0.669131 0.743145i 0.669131 0.743145i
$$21$$ 1.41421i 1.41421i
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$28$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$29$$ −0.575212 + 1.29195i −0.575212 + 1.29195i 0.358368 + 0.933580i $$0.383333\pi$$
−0.933580 + 0.358368i $$0.883333\pi$$
$$30$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$31$$ −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i $$-0.600000\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$32$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.34500 + 0.437016i −1.34500 + 0.437016i
$$36$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$37$$ 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i $$-0.533333\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 0.913545 0.406737i $$-0.133333\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$42$$ −1.33826 + 1.48629i −1.33826 + 1.48629i
$$43$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −1.00000
$$46$$ 0 0
$$47$$ 0.104528 0.994522i 0.104528 0.994522i −0.809017 0.587785i $$-0.800000\pi$$
0.913545 0.406737i $$-0.133333\pi$$
$$48$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$49$$ −0.669131 0.743145i −0.669131 0.743145i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i $$0.0666667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$54$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.82709 + 0.813473i −1.82709 + 0.813473i
$$59$$ −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i $$-0.866667\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$60$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$61$$ 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i $$0.183333\pi$$
−0.544639 + 0.838671i $$0.683333\pi$$
$$62$$ −0.831254 1.14412i −0.831254 1.14412i
$$63$$ −0.575212 1.29195i −0.575212 1.29195i
$$64$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −1.82709 0.813473i −1.82709 0.813473i
$$71$$ −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i $$0.266667\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$72$$ 0 0
$$73$$ 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i $$0.0500000\pi$$
−0.156434 + 0.987688i $$0.550000\pi$$
$$74$$ 1.40647 + 0.147826i 1.40647 + 0.147826i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.669131 0.743145i $$-0.266667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$80$$ −0.809017 0.587785i −0.809017 0.587785i
$$81$$ −0.104528 0.994522i −0.104528 0.994522i
$$82$$ 0 0
$$83$$ 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i $$0.183333\pi$$
−0.544639 + 0.838671i $$0.683333\pi$$
$$84$$ −1.40647 + 0.147826i −1.40647 + 0.147826i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.41421i 1.41421i
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ −1.05097 0.946294i −1.05097 0.946294i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0.978148 0.207912i 0.978148 0.207912i
$$94$$ 1.05097 0.946294i 1.05097 0.946294i
$$95$$ 0 0
$$96$$ −1.40647 0.147826i −1.40647 0.147826i
$$97$$ 0.669131 0.743145i 0.669131 0.743145i −0.309017 0.951057i $$-0.600000\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$98$$ 1.41421i 1.41421i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1.05097 0.946294i −1.05097 0.946294i −0.0523360 0.998630i $$-0.516667\pi$$
−0.998630 + 0.0523360i $$0.983333\pi$$
$$102$$ 0 0
$$103$$ 0.104528 + 0.994522i 0.104528 + 0.994522i 0.913545 + 0.406737i $$0.133333\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$104$$ 0 0
$$105$$ 1.05097 0.946294i 1.05097 0.946294i
$$106$$ −0.575212 + 1.29195i −0.575212 + 1.29195i
$$107$$ −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i $$0.450000\pi$$
−0.987688 + 0.156434i $$0.950000\pi$$
$$108$$ −0.978148 0.207912i −0.978148 0.207912i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$112$$ 0.294032 1.38331i 0.294032 1.38331i
$$113$$ −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i $$-0.800000\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −1.34500 0.437016i −1.34500 0.437016i
$$117$$ 0 0
$$118$$ 0.831254 1.14412i 0.831254 1.14412i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$123$$ 0 0
$$124$$ 0.104528 0.994522i 0.104528 0.994522i
$$125$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$126$$ 0.618034 1.90211i 0.618034 1.90211i
$$127$$ −1.34500 0.437016i −1.34500 0.437016i −0.453990 0.891007i $$-0.650000\pi$$
−0.891007 + 0.453990i $$0.850000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 1.34500 0.437016i 1.34500 0.437016i
$$135$$ 0.913545 0.406737i 0.913545 0.406737i
$$136$$ 0 0
$$137$$ 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i $$-0.400000\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$138$$ 0 0
$$139$$ −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i $$-0.783333\pi$$
−0.629320 + 0.777146i $$0.716667\pi$$
$$140$$ −0.575212 1.29195i −0.575212 1.29195i
$$141$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$142$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.500000 0.866025i
$$145$$ 1.34500 0.437016i 1.34500 0.437016i
$$146$$ −0.209057 + 1.98904i −0.209057 + 1.98904i
$$147$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$148$$ 0.669131 + 0.743145i 0.669131 + 0.743145i
$$149$$ 0 0 −0.669131 0.743145i $$-0.733333\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$150$$ 0 0
$$151$$ 0 0 0.104528 0.994522i $$-0.466667\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$156$$ 0 0
$$157$$ 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i $$-0.466667\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$158$$ 0 0
$$159$$ −0.669131 0.743145i −0.669131 0.743145i
$$160$$ −0.294032 1.38331i −0.294032 1.38331i
$$161$$ 0 0
$$162$$ 0.831254 1.14412i 0.831254 1.14412i
$$163$$ −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i $$-0.933333\pi$$
0.669131 0.743145i $$-0.266667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$167$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$168$$ 0 0
$$169$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.104528 0.994522i $$-0.466667\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$174$$ 1.33826 1.48629i 1.33826 1.48629i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$178$$ 0 0
$$179$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$180$$ −0.104528 0.994522i −0.104528 0.994522i
$$181$$ −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i $$0.266667\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$182$$ 0 0
$$183$$ −0.831254 1.14412i −0.831254 1.14412i
$$184$$ 0 0
$$185$$ −0.978148 0.207912i −0.978148 0.207912i
$$186$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$187$$ 0 0
$$188$$ 1.00000 1.00000
$$189$$ 1.05097 + 0.946294i 1.05097 + 0.946294i
$$190$$ 0 0
$$191$$ −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i $$-0.533333\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$192$$ −0.669131 0.743145i −0.669131 0.743145i
$$193$$ 0 0 −0.669131 0.743145i $$-0.733333\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$194$$ 1.40647 0.147826i 1.40647 0.147826i
$$195$$ 0 0
$$196$$ 0.669131 0.743145i 0.669131 0.743145i
$$197$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$198$$ 0 0
$$199$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ 0 0
$$201$$ −0.104528 + 0.994522i −0.104528 + 0.994522i
$$202$$ −0.209057 1.98904i −0.209057 1.98904i
$$203$$ 1.33826 + 1.48629i 1.33826 + 1.48629i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −0.831254 + 1.14412i −0.831254 + 1.14412i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 2.00000 2.00000
$$211$$ −0.294032 + 1.38331i −0.294032 + 1.38331i 0.544639 + 0.838671i $$0.316667\pi$$
−0.838671 + 0.544639i $$0.816667\pi$$
$$212$$ −0.913545 + 0.406737i −0.913545 + 0.406737i
$$213$$ −0.104528 0.994522i −0.104528 0.994522i
$$214$$ −1.95630 + 0.415823i −1.95630 + 0.415823i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −0.831254 + 1.14412i −0.831254 + 1.14412i
$$218$$ 0 0
$$219$$ −1.22474 0.707107i −1.22474 0.707107i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −1.34500 + 0.437016i −1.34500 + 0.437016i
$$223$$ 0 0 −0.994522 0.104528i $$-0.966667\pi$$
0.994522 + 0.104528i $$0.0333333\pi$$
$$224$$ 1.61803 1.17557i 1.61803 1.17557i
$$225$$ 0 0
$$226$$ −1.34500 0.437016i −1.34500 0.437016i
$$227$$ 0 0 −0.913545 0.406737i $$-0.866667\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.207912 0.978148i $$-0.433333\pi$$
−0.207912 + 0.978148i $$0.566667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.34500 0.437016i 1.34500 0.437016i 0.453990 0.891007i $$-0.350000\pi$$
0.891007 + 0.453990i $$0.150000\pi$$
$$234$$ 0 0
$$235$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$236$$ 0.978148 0.207912i 0.978148 0.207912i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −0.575212 1.29195i −0.575212 1.29195i −0.933580 0.358368i $$-0.883333\pi$$
0.358368 0.933580i $$-0.383333\pi$$
$$240$$ 0.978148 + 0.207912i 0.978148 + 0.207912i
$$241$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$244$$ −1.34500 + 0.437016i −1.34500 + 0.437016i
$$245$$ −0.104528 + 0.994522i −0.104528 + 0.994522i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −0.831254 1.14412i −0.831254 1.14412i
$$250$$ −1.40647 0.147826i −1.40647 0.147826i
$$251$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$252$$ 1.22474 0.707107i 1.22474 0.707107i
$$253$$ 0 0
$$254$$ −1.00000 1.73205i −1.00000 1.73205i
$$255$$ 0 0
$$256$$ 0.913545 0.406737i 0.913545 0.406737i
$$257$$ 0.209057 + 1.98904i 0.209057 + 1.98904i 0.104528 + 0.994522i $$0.466667\pi$$
0.104528 + 0.994522i $$0.466667\pi$$
$$258$$ 0 0
$$259$$ −0.294032 1.38331i −0.294032 1.38331i
$$260$$ 0 0
$$261$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$262$$ 0 0
$$263$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$264$$ 0 0
$$265$$ 0.500000 0.866025i 0.500000 0.866025i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$269$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$270$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$271$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 0.669131 0.743145i $$-0.266667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$278$$ −1.61803 1.17557i −1.61803 1.17557i
$$279$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$280$$ 0 0
$$281$$ 0 0 0.978148 0.207912i $$-0.0666667\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$282$$ −0.575212 + 1.29195i −0.575212 + 1.29195i
$$283$$ 0.575212 + 1.29195i 0.575212 + 1.29195i 0.933580 + 0.358368i $$0.116667\pi$$
−0.358368 + 0.933580i $$0.616667\pi$$
$$284$$ −0.978148 0.207912i −0.978148 0.207912i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.34500 0.437016i 1.34500 0.437016i
$$289$$ −0.809017 0.587785i −0.809017 0.587785i
$$290$$ 1.82709 + 0.813473i 1.82709 + 0.813473i
$$291$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$292$$ −1.05097 + 0.946294i −1.05097 + 0.946294i
$$293$$ 1.40647 0.147826i 1.40647 0.147826i 0.629320 0.777146i $$-0.283333\pi$$
0.777146 + 0.629320i $$0.216667\pi$$
$$294$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$295$$ −0.669131 + 0.743145i −0.669131 + 0.743145i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$304$$ 0 0
$$305$$ 0.831254 1.14412i 0.831254 1.14412i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ −0.500000 0.866025i −0.500000 0.866025i
$$310$$ −0.294032 + 1.38331i −0.294032 + 1.38331i
$$311$$ 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i $$-0.466667\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.207912 0.978148i $$-0.566667\pi$$
0.207912 + 0.978148i $$0.433333\pi$$
$$314$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$315$$ −0.575212 + 1.29195i −0.575212 + 1.29195i
$$316$$ 0 0
$$317$$ 0 0 −0.743145 0.669131i $$-0.766667\pi$$
0.743145 + 0.669131i $$0.233333\pi$$
$$318$$ 1.41421i 1.41421i
$$319$$ 0 0
$$320$$ 0.500000 0.866025i 0.500000 0.866025i
$$321$$ 0.294032 1.38331i 0.294032 1.38331i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.978148 0.207912i 0.978148 0.207912i
$$325$$ 0 0
$$326$$ 0.575212 1.29195i 0.575212 1.29195i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.22474 0.707107i −1.22474 0.707107i
$$330$$ 0 0
$$331$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$332$$ −1.34500 + 0.437016i −1.34500 + 0.437016i
$$333$$ 0.104528 0.994522i 0.104528 0.994522i
$$334$$ 0 0
$$335$$ −0.978148 + 0.207912i −0.978148 + 0.207912i
$$336$$ 0.294032 + 1.38331i 0.294032 + 1.38331i
$$337$$ 1.40647 0.147826i 1.40647 0.147826i 0.629320 0.777146i $$-0.283333\pi$$
0.777146 + 0.629320i $$0.216667\pi$$
$$338$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$339$$ 0.669131 0.743145i 0.669131 0.743145i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i $$-0.483333\pi$$
0.998630 + 0.0523360i $$0.0166667\pi$$
$$348$$ 1.40647 0.147826i 1.40647 0.147826i
$$349$$ 0 0 0.104528 0.994522i $$-0.466667\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ −0.294032 + 1.38331i −0.294032 + 1.38331i
$$355$$ 0.913545 0.406737i 0.913545 0.406737i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0.294032 + 1.38331i 0.294032 + 1.38331i
$$359$$ 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i $$0.0500000\pi$$
−0.156434 + 0.987688i $$0.550000\pi$$
$$360$$ 0 0
$$361$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$362$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0.294032 1.38331i 0.294032 1.38331i
$$366$$ 0.209057 1.98904i 0.209057 1.98904i
$$367$$ −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i $$-0.533333\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −0.831254 1.14412i −0.831254 1.14412i
$$371$$ 1.40647 + 0.147826i 1.40647 + 0.147826i
$$372$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$373$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 0 0
$$375$$ 0.500000 0.866025i 0.500000 0.866025i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0.209057 + 1.98904i 0.209057 + 1.98904i
$$379$$ 0 0 −0.951057 0.309017i $$-0.900000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$380$$ 0 0
$$381$$ 1.40647 0.147826i 1.40647 0.147826i
$$382$$ −0.575212 1.29195i −0.575212 1.29195i
$$383$$ −0.978148 0.207912i −0.978148 0.207912i −0.309017 0.951057i $$-0.600000\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$389$$ −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i $$-0.533333\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −1.33826 + 1.48629i −1.33826 + 1.48629i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ −1.05097 0.946294i −1.05097 0.946294i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i $$-0.400000\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$402$$ −1.05097 + 0.946294i −1.05097 + 0.946294i
$$403$$ 0 0
$$404$$ 0.831254 1.14412i 0.831254 1.14412i
$$405$$ −0.669131 + 0.743145i −0.669131 + 0.743145i
$$406$$ 2.82843i 2.82843i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$410$$ 0 0
$$411$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$412$$ −0.978148 + 0.207912i −0.978148 + 0.207912i
$$413$$ −1.34500 0.437016i −1.34500 0.437016i
$$414$$ 0 0
$$415$$ 0.831254 1.14412i 0.831254 1.14412i
$$416$$ 0 0
$$417$$ 1.22474 0.707107i 1.22474 0.707107i
$$418$$ 0 0
$$419$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$420$$ 1.05097 + 0.946294i 1.05097 + 0.946294i
$$421$$ −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i $$0.200000\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$422$$ −1.61803 + 1.17557i −1.61803 + 1.17557i
$$423$$ −0.669131 0.743145i −0.669131 0.743145i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0.831254 1.14412i 0.831254 1.14412i
$$427$$ 1.95630 + 0.415823i 1.95630 + 0.415823i
$$428$$ −1.22474 0.707107i −1.22474 0.707107i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.34500 + 0.437016i −1.34500 + 0.437016i −0.891007 0.453990i $$-0.850000\pi$$
−0.453990 + 0.891007i $$0.650000\pi$$
$$432$$ −0.104528 + 0.994522i −0.104528 + 0.994522i
$$433$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$434$$ −1.95630 + 0.415823i −1.95630 + 0.415823i
$$435$$ −1.05097 + 0.946294i −1.05097 + 0.946294i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −0.618034 1.90211i −0.618034 1.90211i
$$439$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$440$$ 0 0
$$441$$ −1.00000 −1.00000
$$442$$ 0 0
$$443$$ −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i $$0.200000\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$444$$ −0.913545 0.406737i −0.913545 0.406737i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 1.40647 + 0.147826i 1.40647 + 0.147826i
$$449$$ 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i $$0.0666667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −0.500000 0.866025i −0.500000 0.866025i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.294032 + 1.38331i 0.294032 + 1.38331i 0.838671 + 0.544639i $$0.183333\pi$$
−0.544639 + 0.838671i $$0.683333\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$464$$ −0.294032 + 1.38331i −0.294032 + 1.38331i
$$465$$ −0.809017 0.587785i −0.809017 0.587785i
$$466$$ 1.82709 + 0.813473i 1.82709 + 0.813473i
$$467$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$468$$ 0 0
$$469$$ −0.831254 1.14412i −0.831254 1.14412i
$$470$$ −1.40647 0.147826i −1.40647 0.147826i
$$471$$ −0.669131 + 0.743145i −0.669131 + 0.743145i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$478$$ 0.618034 1.90211i 0.618034 1.90211i
$$479$$ −0.294032 1.38331i −0.294032 1.38331i −0.838671 0.544639i $$-0.816667\pi$$
0.544639 0.838671i $$-0.316667\pi$$
$$480$$ 0.831254 + 1.14412i 0.831254 + 1.14412i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.00000 −1.00000
$$486$$ −0.294032 + 1.38331i −0.294032 + 1.38331i
$$487$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$488$$ 0 0
$$489$$ 0.669131 + 0.743145i 0.669131 + 0.743145i
$$490$$ −1.05097 + 0.946294i −1.05097 + 0.946294i
$$491$$ −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i $$-0.783333\pi$$
−0.629320 + 0.777146i $$0.716667\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −1.00000 −1.00000
$$497$$ 1.05097 + 0.946294i 1.05097 + 0.946294i
$$498$$ 0.209057 1.98904i 0.209057 1.98904i
$$499$$ −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i $$-0.866667\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$500$$ −0.669131 0.743145i −0.669131 0.743145i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −0.831254 + 1.14412i −0.831254 + 1.14412i 0.156434 + 0.987688i $$0.450000\pi$$
−0.987688 + 0.156434i $$0.950000\pi$$
$$504$$ 0 0
$$505$$ 1.41421i 1.41421i
$$506$$ 0 0
$$507$$ −1.00000 −1.00000
$$508$$ 0.294032 1.38331i 0.294032 1.38331i
$$509$$ 0 0 −0.406737 0.913545i $$-0.633333\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$510$$ 0 0
$$511$$ 1.95630 0.415823i 1.95630 0.415823i
$$512$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$513$$ 0 0
$$514$$ −1.66251 + 2.28825i −1.66251 + 2.28825i
$$515$$ 0.669131 0.743145i 0.669131 0.743145i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 1.00000 1.73205i 1.00000 1.73205i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i $$-0.533333\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$522$$ −0.618034 + 1.90211i −0.618034 + 1.90211i
$$523$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$530$$ 1.34500 0.437016i 1.34500 0.437016i
$$531$$ −0.809017 0.587785i −0.809017 0.587785i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 1.40647 0.147826i 1.40647 0.147826i
$$536$$ 0 0
$$537$$ −0.978148 0.207912i −0.978148 0.207912i
$$538$$ 1.22474 0.707107i 1.22474 0.707107i
$$539$$ 0 0
$$540$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$541$$ −1.34500 + 0.437016i −1.34500 + 0.437016i −0.891007 0.453990i $$-0.850000\pi$$
−0.453990 + 0.891007i $$0.650000\pi$$
$$542$$ 0 0
$$543$$ −0.104528 0.994522i −0.104528 0.994522i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.40647 + 0.147826i 1.40647 + 0.147826i 0.777146 0.629320i $$-0.216667\pi$$
0.629320 + 0.777146i $$0.283333\pi$$
$$548$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$549$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0.978148 0.207912i 0.978148 0.207912i
$$556$$ −0.294032 1.38331i −0.294032 1.38331i
$$557$$ −0.831254 1.14412i −0.831254 1.14412i −0.987688 0.156434i $$-0.950000\pi$$
0.156434 0.987688i $$-0.450000\pi$$
$$558$$ −1.40647 0.147826i −1.40647 0.147826i
$$559$$ 0 0
$$560$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$564$$ −0.913545 + 0.406737i −0.913545 + 0.406737i
$$565$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$566$$ −0.618034 + 1.90211i −0.618034 + 1.90211i
$$567$$ −1.34500 0.437016i −1.34500 0.437016i
$$568$$ 0 0
$$569$$ −1.40647 0.147826i −1.40647 0.147826i −0.629320 0.777146i $$-0.716667\pi$$
−0.777146 + 0.629320i $$0.783333\pi$$
$$570$$ 0 0
$$571$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$572$$ 0 0
$$573$$ 1.00000 1.00000
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.913545 + 0.406737i 0.913545 + 0.406737i
$$577$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$578$$ −0.294032 1.38331i −0.294032 1.38331i
$$579$$ 0 0
$$580$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$581$$ 1.95630 + 0.415823i 1.95630 + 0.415823i
$$582$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$587$$ 0.913545 + 0.406737i 0.913545 + 0.406737i 0.809017 0.587785i $$-0.200000\pi$$
0.104528 + 0.994522i $$0.466667\pi$$
$$588$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$589$$ 0 0
$$590$$ −1.40647 + 0.147826i −1.40647 + 0.147826i
$$591$$ −0.575212 1.29195i −0.575212 1.29195i
$$592$$ 0.669131 0.743145i 0.669131 0.743145i
$$593$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0.913545 0.406737i 0.913545 0.406737i
$$598$$ 0 0
$$599$$ 0 0 0.743145 0.669131i $$-0.233333\pi$$
−0.743145 + 0.669131i $$0.766667\pi$$
$$600$$ 0 0
$$601$$ 0 0 −0.913545 0.406737i $$-0.866667\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$602$$ 0 0
$$603$$ −0.309017 0.951057i −0.309017 0.951057i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$607$$ 0 0 −0.978148 0.207912i $$-0.933333\pi$$
0.978148 + 0.207912i $$0.0666667\pi$$
$$608$$ 0 0
$$609$$ −1.82709 0.813473i −1.82709 0.813473i
$$610$$ 1.95630 0.415823i 1.95630 0.415823i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$618$$ 0.294032 1.38331i 0.294032 1.38331i
$$619$$ −0.104528 + 0.994522i −0.104528 + 0.994522i 0.809017 + 0.587785i $$0.200000\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$620$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$621$$ 0 0
$$622$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.978148 + 0.207912i 0.978148 + 0.207912i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$629$$ 0 0
$$630$$ −1.82709 + 0.813473i −1.82709 + 0.813473i
$$631$$ −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i $$-0.866667\pi$$
0.104528 + 0.994522i $$0.466667\pi$$
$$632$$ 0 0
$$633$$ −0.294032 1.38331i −0.294032 1.38331i
$$634$$ 0 0
$$635$$ 0.575212 + 1.29195i 0.575212 + 1.29195i
$$636$$ 0.669131 0.743145i 0.669131 0.743145i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$640$$ 0 0
$$641$$ 0.209057 1.98904i 0.209057 1.98904i 0.104528 0.994522i $$-0.466667\pi$$
0.104528 0.994522i $$-0.466667\pi$$
$$642$$ 1.61803 1.17557i 1.61803 1.17557i
$$643$$ 0 0 0.743145 0.669131i $$-0.233333\pi$$
−0.743145 + 0.669131i $$0.766667\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 0.951057i $$-0.600000\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0.294032 1.38331i 0.294032 1.38331i
$$652$$ 0.913545 0.406737i 0.913545 0.406737i
$$653$$ −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i $$-0.866667\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 1.40647 + 0.147826i 1.40647 + 0.147826i
$$658$$ −0.618034 1.90211i −0.618034 1.90211i
$$659$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$662$$ 0.294032 1.38331i 0.294032 1.38331i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 1.05097 0.946294i 1.05097 0.946294i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −1.22474 0.707107i −1.22474 0.707107i
$$671$$ 0 0
$$672$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$673$$ 0 0 0.669131 0.743145i $$-0.266667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$674$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$675$$ 0 0
$$676$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$677$$ −0.294032 1.38331i −0.294032 1.38331i −0.838671 0.544639i $$-0.816667\pi$$
0.544639 0.838671i $$-0.316667\pi$$
$$678$$ 1.40647 0.147826i 1.40647 0.147826i
$$679$$ −0.575212 1.29195i −0.575212 1.29195i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$684$$ 0 0
$$685$$ −0.809017 0.587785i −0.809017 0.587785i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i $$-0.933333\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 2.00000 2.00000
$$695$$ 1.05097 + 0.946294i 1.05097 + 0.946294i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −1.05097 + 0.946294i −1.05097 + 0.946294i
$$700$$ 0 0
$$701$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0.500000 0.866025i 0.500000 0.866025i
$$706$$ 0 0
$$707$$ −1.82709 + 0.813473i −1.82709 + 0.813473i
$$708$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$709$$ −0.978148 + 0.207912i −0.978148 + 0.207912i −0.669131 0.743145i $$-0.733333\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$710$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$717$$ 1.05097 + 0.946294i 1.05097 + 0.946294i
$$718$$ −0.209057 + 1.98904i −0.209057 + 1.98904i
$$719$$ 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i $$-0.533333\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$720$$ −0.978148 + 0.207912i −0.978148 + 0.207912i
$$721$$ 1.34500 + 0.437016i 1.34500 + 0.437016i
$$722$$ −0.575212 + 1.29195i −0.575212 + 1.29195i
$$723$$ 0 0
$$724$$ −0.978148 0.207912i −0.978148 0.207912i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$728$$ 0 0
$$729$$ −0.809017 0.587785i −0.809017 0.587785i
$$730$$ 1.61803 1.17557i 1.61803 1.17557i
$$731$$ 0 0
$$732$$ 1.05097 0.946294i 1.05097 0.946294i
$$733$$ −1.40647 + 0.147826i −1.40647 + 0.147826i −0.777146 0.629320i $$-0.783333\pi$$
−0.629320 + 0.777146i $$0.716667\pi$$
$$734$$ −0.575212 1.29195i −0.575212 1.29195i
$$735$$ −0.309017 0.951057i −0.309017 0.951057i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$740$$ 0.104528 0.994522i 0.104528 0.994522i
$$741$$ 0 0
$$742$$ 1.33826 + 1.48629i 1.33826 + 1.48629i
$$743$$ 1.05097 0.946294i 1.05097 0.946294i 0.0523360 0.998630i $$-0.483333\pi$$
0.998630 + 0.0523360i $$0.0166667\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$748$$ 0 0
$$749$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$750$$ 1.34500 0.437016i 1.34500 0.437016i
$$751$$ −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i $$-0.800000\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$752$$ −0.104528 0.994522i −0.104528 0.994522i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −0.831254 + 1.14412i −0.831254 + 1.14412i
$$757$$ −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i $$-0.933333\pi$$
0.669131 0.743145i $$-0.266667\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.294032 + 1.38331i −0.294032 + 1.38331i 0.544639 + 0.838671i $$0.316667\pi$$
−0.838671 + 0.544639i $$0.816667\pi$$
$$762$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$763$$ 0 0
$$764$$ 0.309017 0.951057i 0.309017 0.951057i
$$765$$ 0 0
$$766$$ −0.831254 1.14412i −0.831254 1.14412i
$$767$$ 0 0
$$768$$ −0.669131 + 0.743145i −0.669131 + 0.743145i
$$769$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$770$$ 0 0
$$771$$ −1.00000 1.73205i −1.00000 1.73205i
$$772$$ 0 0
$$773$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0.831254 + 1.14412i 0.831254 + 1.14412i
$$778$$ −0.575212 1.29195i −0.575212 1.29195i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −1.05097 0.946294i −1.05097 0.946294i
$$784$$ −0.809017 0.587785i −0.809017 0.587785i
$$785$$ −0.913545 0.406737i −0.913545 0.406737i
$$786$$ 0 0
$$787$$ 0 0 −0.669131 0.743145i $$-0.733333\pi$$
0.669131 + 0.743145i $$0.266667\pi$$
$$788$$ −1.40647 + 0.147826i −1.40647 + 0.147826i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 1.41421i 1.41421i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −1.05097 0.946294i −1.05097 0.946294i
$$795$$ −0.104528 + 0.994522i −0.104528