# Properties

 Label 1089.1.h.a.967.2 Level $1089$ Weight $1$ Character 1089.967 Analytic conductor $0.543$ Analytic rank $0$ Dimension $4$ Projective image $S_{4}$ CM/RM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1089 = 3^{2} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1089.h (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.543481798757$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2 x^{2} + 4$$ 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 967.2 Root $$1.22474 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1089.967 Dual form 1089.1.h.a.241.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.41421i q^{6} +(-1.22474 + 0.707107i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.41421i q^{6} +(-1.22474 + 0.707107i) q^{7} +(-0.500000 - 0.866025i) q^{9} -1.41421i q^{10} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.22474 - 0.707107i) q^{18} +(-0.500000 - 0.866025i) q^{20} +1.41421i q^{21} -1.00000 q^{27} +1.41421i q^{28} +(1.22474 - 0.707107i) q^{29} +(-1.22474 - 0.707107i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(1.22474 + 0.707107i) q^{32} +1.41421i q^{35} -1.00000 q^{36} -1.00000 q^{37} +(1.00000 + 1.73205i) q^{42} -1.00000 q^{45} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(0.500000 - 0.866025i) q^{49} +1.00000 q^{53} +(-1.22474 + 0.707107i) q^{54} +(1.00000 - 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} -1.00000 q^{60} +(-1.22474 + 0.707107i) q^{61} +1.41421i q^{62} +(1.22474 + 0.707107i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{67} +(1.00000 + 1.73205i) q^{70} -1.00000 q^{71} -1.41421i q^{73} +(-1.22474 + 0.707107i) q^{74} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.22474 + 0.707107i) q^{83} +(1.22474 + 0.707107i) q^{84} -1.41421i q^{87} +(-1.22474 + 0.707107i) q^{90} +(0.500000 + 0.866025i) q^{93} +(1.22474 + 0.707107i) q^{94} +(1.22474 - 0.707107i) q^{96} +(-0.500000 - 0.866025i) q^{97} -1.41421i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{3} + 2q^{4} + 2q^{5} - 2q^{9} + O(q^{10})$$ $$4q + 2q^{3} + 2q^{4} + 2q^{5} - 2q^{9} - 2q^{12} - 4q^{14} - 2q^{15} + 2q^{16} - 2q^{20} - 4q^{27} - 2q^{31} - 4q^{36} - 4q^{37} + 4q^{42} - 4q^{45} + 2q^{47} + 4q^{48} + 2q^{49} + 4q^{53} + 4q^{58} - 2q^{59} - 4q^{60} + 4q^{64} + 2q^{67} + 4q^{70} - 4q^{71} + 4q^{80} - 2q^{81} + 2q^{93} - 2q^{97} + O(q^{100})$$

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$3$$ 0.500000 0.866025i 0.500000 0.866025i
$$4$$ 0.500000 0.866025i 0.500000 0.866025i
$$5$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$6$$ 1.41421i 1.41421i
$$7$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.500000 0.866025i
$$10$$ 1.41421i 1.41421i
$$11$$ 0 0
$$12$$ −0.500000 0.866025i −0.500000 0.866025i
$$13$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$15$$ −0.500000 0.866025i −0.500000 0.866025i
$$16$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ −1.22474 0.707107i −1.22474 0.707107i
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ −0.500000 0.866025i −0.500000 0.866025i
$$21$$ 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
$$27$$ −1.00000 −1.00000
$$28$$ 1.41421i 1.41421i
$$29$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$30$$ −1.22474 0.707107i −1.22474 0.707107i
$$31$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$32$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.41421i 1.41421i
$$36$$ −1.00000 −1.00000
$$37$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$42$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$43$$ 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
$$47$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$48$$ 1.00000 1.00000
$$49$$ 0.500000 0.866025i 0.500000 0.866025i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$54$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.00000 1.73205i 1.00000 1.73205i
$$59$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$60$$ −1.00000 −1.00000
$$61$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$62$$ 1.41421i 1.41421i
$$63$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$64$$ 1.00000 1.00000
$$65$$ 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
$$70$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$71$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$72$$ 0 0
$$73$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$74$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ 1.00000 1.00000
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$84$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.41421i 1.41421i
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$94$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$95$$ 0 0
$$96$$ 1.22474 0.707107i 1.22474 0.707107i
$$97$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$98$$ 1.41421i 1.41421i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$102$$ 0 0
$$103$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$104$$ 0 0
$$105$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$106$$ 1.22474 0.707107i 1.22474 0.707107i
$$107$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$108$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$112$$ −1.22474 0.707107i −1.22474 0.707107i
$$113$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.41421i 1.41421i
$$117$$ 0 0
$$118$$ 1.41421i 1.41421i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$123$$ 0 0
$$124$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$125$$ 1.00000 1.00000
$$126$$ 2.00000 2.00000
$$127$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$128$$ 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
$$134$$ 1.41421i 1.41421i
$$135$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$136$$ 0 0
$$137$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$140$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$141$$ 1.00000 1.00000
$$142$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.500000 0.866025i
$$145$$ 1.41421i 1.41421i
$$146$$ −1.00000 1.73205i −1.00000 1.73205i
$$147$$ −0.500000 0.866025i −0.500000 0.866025i
$$148$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$156$$ 0 0
$$157$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0.500000 0.866025i 0.500000 0.866025i
$$160$$ 1.22474 0.707107i 1.22474 0.707107i
$$161$$ 0 0
$$162$$ 1.41421i 1.41421i
$$163$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$167$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ −0.500000 0.866025i −0.500000 0.866025i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ −1.00000 1.73205i −1.00000 1.73205i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$178$$ 0 0
$$179$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$181$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ 1.41421i 1.41421i
$$184$$ 0 0
$$185$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$186$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$187$$ 0 0
$$188$$ 1.00000 1.00000
$$189$$ 1.22474 0.707107i 1.22474 0.707107i
$$190$$ 0 0
$$191$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ 0.500000 0.866025i 0.500000 0.866025i
$$193$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$194$$ −1.22474 0.707107i −1.22474 0.707107i
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.500000 0.866025i
$$197$$ 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
$$201$$ −0.500000 0.866025i −0.500000 0.866025i
$$202$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$203$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.41421i 1.41421i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 2.00000 2.00000
$$211$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$212$$ 0.500000 0.866025i 0.500000 0.866025i
$$213$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$214$$ −1.00000 1.73205i −1.00000 1.73205i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1.41421i 1.41421i
$$218$$ 0 0
$$219$$ −1.22474 0.707107i −1.22474 0.707107i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 1.41421i 1.41421i
$$223$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$224$$ −2.00000 −2.00000
$$225$$ 0 0
$$226$$ 1.41421i 1.41421i
$$227$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$234$$ 0 0
$$235$$ 1.00000 1.00000
$$236$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$240$$ 0.500000 0.866025i 0.500000 0.866025i
$$241$$ 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
$$244$$ 1.41421i 1.41421i
$$245$$ −0.500000 0.866025i −0.500000 0.866025i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 1.41421i 1.41421i
$$250$$ 1.22474 0.707107i 1.22474 0.707107i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 1.22474 0.707107i 1.22474 0.707107i
$$253$$ 0 0
$$254$$ −1.00000 1.73205i −1.00000 1.73205i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$258$$ 0 0
$$259$$ 1.22474 0.707107i 1.22474 0.707107i
$$260$$ 0 0
$$261$$ −1.22474 0.707107i −1.22474 0.707107i
$$262$$ 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
$$268$$ −0.500000 0.866025i −0.500000 0.866025i
$$269$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 1.41421i 1.41421i
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$278$$ 2.00000 2.00000
$$279$$ 1.00000 1.00000
$$280$$ 0 0
$$281$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$282$$ 1.22474 0.707107i 1.22474 0.707107i
$$283$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$284$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.41421i 1.41421i
$$289$$ 1.00000 1.00000
$$290$$ −1.00000 1.73205i −1.00000 1.73205i
$$291$$ −1.00000 −1.00000
$$292$$ −1.22474 0.707107i −1.22474 0.707107i
$$293$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$294$$ −1.22474 0.707107i −1.22474 0.707107i
$$295$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.41421i 1.41421i
$$304$$ 0 0
$$305$$ 1.41421i 1.41421i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ −0.500000 0.866025i −0.500000 0.866025i
$$310$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$311$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ 1.41421i 1.41421i
$$315$$ 1.22474 0.707107i 1.22474 0.707107i
$$316$$ 0 0
$$317$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$318$$ 1.41421i 1.41421i
$$319$$ 0 0
$$320$$ 0.500000 0.866025i 0.500000 0.866025i
$$321$$ −1.22474 0.707107i −1.22474 0.707107i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$327$$ 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 $$\pi$$
$$332$$ 1.41421i 1.41421i
$$333$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$334$$ 0 0
$$335$$ −0.500000 0.866025i −0.500000 0.866025i
$$336$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$337$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$338$$ −1.22474 0.707107i −1.22474 0.707107i
$$339$$ −0.500000 0.866025i −0.500000 0.866025i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$348$$ −1.22474 0.707107i −1.22474 0.707107i
$$349$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$355$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$359$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.22474 0.707107i −1.22474 0.707107i
$$366$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$367$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 1.41421i 1.41421i
$$371$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$372$$ 1.00000 1.00000
$$373$$ 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
$$378$$ 1.00000 1.73205i 1.00000 1.73205i
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ −1.22474 0.707107i −1.22474 0.707107i
$$382$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$383$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −1.00000 −1.00000
$$389$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$402$$ −1.22474 0.707107i −1.22474 0.707107i
$$403$$ 0 0
$$404$$ 1.41421i 1.41421i
$$405$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$406$$ 2.82843i 2.82843i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ 1.00000 1.00000
$$412$$ −0.500000 0.866025i −0.500000 0.866025i
$$413$$ 1.41421i 1.41421i
$$414$$ 0 0
$$415$$ 1.41421i 1.41421i
$$416$$ 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 $$0$$
$$420$$ 1.22474 0.707107i 1.22474 0.707107i
$$421$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$422$$ 2.00000 2.00000
$$423$$ 0.500000 0.866025i 0.500000 0.866025i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 1.41421i 1.41421i
$$427$$ 1.00000 1.73205i 1.00000 1.73205i
$$428$$ −1.22474 0.707107i −1.22474 0.707107i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$432$$ −0.500000 0.866025i −0.500000 0.866025i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ −1.00000 1.73205i −1.00000 1.73205i
$$435$$ −1.22474 0.707107i −1.22474 0.707107i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −2.00000 −2.00000
$$439$$ 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
$$443$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$444$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$449$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$450$$ 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
$$457$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$458$$ 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 $$0.166667\pi$$
$$464$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$465$$ 1.00000 1.00000
$$466$$ −1.00000 1.73205i −1.00000 1.73205i
$$467$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 0 0
$$469$$ 1.41421i 1.41421i
$$470$$ 1.22474 0.707107i 1.22474 0.707107i
$$471$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −0.500000 0.866025i −0.500000 0.866025i
$$478$$ 2.00000 2.00000
$$479$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$480$$ 1.41421i 1.41421i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.00000 −1.00000
$$486$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$487$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$488$$ 0 0
$$489$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$490$$ −1.22474 0.707107i −1.22474 0.707107i
$$491$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −1.00000 −1.00000
$$497$$ 1.22474 0.707107i 1.22474 0.707107i
$$498$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$499$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$500$$ 0.500000 0.866025i 0.500000 0.866025i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$504$$ 0 0
$$505$$ 1.41421i 1.41421i
$$506$$ 0 0
$$507$$ −1.00000 −1.00000
$$508$$ −1.22474 0.707107i −1.22474 0.707107i
$$509$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$510$$ 0 0
$$511$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$512$$ 1.41421i 1.41421i
$$513$$ 0 0
$$514$$ 2.82843i 2.82843i
$$515$$ −0.500000 0.866025i −0.500000 0.866025i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 1.00000 1.73205i 1.00000 1.73205i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ −2.00000 −2.00000
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$530$$ 1.41421i 1.41421i
$$531$$ 1.00000 1.00000
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −1.22474 0.707107i −1.22474 0.707107i
$$536$$ 0 0
$$537$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$538$$ 1.22474 0.707107i 1.22474 0.707107i
$$539$$ 0 0
$$540$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$541$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$542$$ 0 0
$$543$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$548$$ 1.00000 1.00000
$$549$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$556$$ 1.22474 0.707107i 1.22474 0.707107i
$$557$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$558$$ 1.22474 0.707107i 1.22474 0.707107i
$$559$$ 0 0
$$560$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0.500000 0.866025i 0.500000 0.866025i
$$565$$ −0.500000 0.866025i −0.500000 0.866025i
$$566$$ −2.00000 −2.00000
$$567$$ 1.41421i 1.41421i
$$568$$ 0 0
$$569$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$570$$ 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
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$578$$ 1.22474 0.707107i 1.22474 0.707107i
$$579$$ 0 0
$$580$$ −1.22474 0.707107i −1.22474 0.707107i
$$581$$ 1.00000 1.73205i 1.00000 1.73205i
$$582$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −2.00000 −2.00000
$$587$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$588$$ −1.00000 −1.00000
$$589$$ 0 0
$$590$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$591$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$592$$ −0.500000 0.866025i −0.500000 0.866025i
$$593$$ 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
$$597$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$598$$ 0 0
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$602$$ 0 0
$$603$$ −1.00000 −1.00000
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$607$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$608$$ 0 0
$$609$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$610$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 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 $$0$$
$$618$$ −1.22474 0.707107i −1.22474 0.707107i
$$619$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$620$$ 1.00000 1.00000
$$621$$ 0 0
$$622$$ 1.41421i 1.41421i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.500000 0.866025i 0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$629$$ 0 0
$$630$$ 1.00000 1.73205i 1.00000 1.73205i
$$631$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$632$$ 0 0
$$633$$ 1.22474 0.707107i 1.22474 0.707107i
$$634$$ 0 0
$$635$$ −1.22474 0.707107i −1.22474 0.707107i
$$636$$ −0.500000 0.866025i −0.500000 0.866025i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$640$$ 0 0
$$641$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ −2.00000 −2.00000
$$643$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −1.22474 0.707107i −1.22474 0.707107i
$$652$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$653$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$658$$ −2.00000 −2.00000
$$659$$ 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 $$\pi$$
$$662$$ −1.22474 0.707107i −1.22474 0.707107i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$667$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$674$$ −2.00000 −2.00000
$$675$$ 0 0
$$676$$ −1.00000 −1.00000
$$677$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$678$$ −1.22474 0.707107i −1.22474 0.707107i
$$679$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$680$$ 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
$$685$$ 1.00000 1.00000
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 2.00000 2.00000
$$695$$ 1.22474 0.707107i 1.22474 0.707107i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −1.22474 0.707107i −1.22474 0.707107i
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0.500000 0.866025i 0.500000 0.866025i
$$706$$ 0 0
$$707$$ 1.00000 1.73205i 1.00000 1.73205i
$$708$$ 1.00000 1.00000
$$709$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$710$$ 1.41421i 1.41421i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$717$$ 1.22474 0.707107i 1.22474 0.707107i
$$718$$ −1.00000 1.73205i −1.00000 1.73205i
$$719$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$720$$ −0.500000 0.866025i −0.500000 0.866025i
$$721$$ 1.41421i 1.41421i
$$722$$ 1.22474 0.707107i 1.22474 0.707107i
$$723$$ 0 0
$$724$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$725$$ 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
$$729$$ 1.00000 1.00000
$$730$$ −2.00000 −2.00000
$$731$$ 0 0
$$732$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$733$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$734$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$735$$ −1.00000 −1.00000
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$741$$ 0 0
$$742$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$743$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$744$$ 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
$$750$$ 1.41421i 1.41421i
$$751$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$752$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 1.41421i 1.41421i
$$757$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$762$$ −2.00000 −2.00000
$$763$$ 0 0
$$764$$ 1.00000 1.00000
$$765$$ 0 0
$$766$$ 1.41421i 1.41421i
$$767$$ 0 0
$$768$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$769$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 1.41421i 1.41421i
$$778$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$784$$ 1.00000 1.00000
$$785$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$786$$ 0 0
$$787$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 1.41421i 1.41421i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$795$$ −0.500000 0.866025i −0.500000 0.866025i
$$796$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$797$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$798$$ 0 0