# Properties

 Label 180.1.p.a.139.1 Level $180$ Weight $1$ Character 180.139 Analytic conductor $0.090$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -20 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$180 = 2^{2} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 180.p (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.0898317022739$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.1620.1 Artin image: $C_3\times S_3$ Artin field: Galois closure of 6.0.648000.1

## Embedding invariants

 Embedding label 139.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 180.139 Dual form 180.1.p.a.79.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{20} -1.00000 q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -1.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} -1.00000 q^{35} +1.00000 q^{36} +(-0.500000 + 0.866025i) q^{40} +(0.500000 - 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +1.00000 q^{45} -1.00000 q^{46} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{50} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +1.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{67} +(0.500000 + 0.866025i) q^{69} +(0.500000 + 0.866025i) q^{70} +(-0.500000 - 0.866025i) q^{72} +1.00000 q^{75} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -1.00000 q^{82} +(0.500000 + 0.866025i) q^{83} +(0.500000 - 0.866025i) q^{84} +(-1.00000 + 1.73205i) q^{86} -1.00000 q^{87} -1.00000 q^{89} +(-0.500000 - 0.866025i) q^{90} +(0.500000 + 0.866025i) q^{92} +(0.500000 - 0.866025i) q^{94} +(-0.500000 - 0.866025i) q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + O(q^{10})$$ $$2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + 2 q^{10} - q^{12} + q^{14} - q^{15} - q^{16} - q^{18} - q^{20} - 2 q^{21} + q^{23} - q^{24} - q^{25} + 2 q^{27} - 2 q^{28} + q^{29} - q^{30} - q^{32} - 2 q^{35} + 2 q^{36} - q^{40} + q^{41} + q^{42} - 2 q^{43} + 2 q^{45} - 2 q^{46} + q^{47} + 2 q^{48} - q^{50} - q^{54} + q^{56} + q^{58} + 2 q^{60} + q^{61} + q^{63} + 2 q^{64} + q^{67} + q^{69} + q^{70} - q^{72} + 2 q^{75} + 2 q^{80} - q^{81} - 2 q^{82} + q^{83} + q^{84} - 2 q^{86} - 2 q^{87} - 2 q^{89} - q^{90} + q^{92} + q^{94} - q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$$.

 $$n$$ $$37$$ $$91$$ $$101$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.500000 0.866025i
$$3$$ −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
$$6$$ 1.00000 1.00000
$$7$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$8$$ 1.00000 1.00000
$$9$$ −0.500000 0.866025i −0.500000 0.866025i
$$10$$ 1.00000 1.00000
$$11$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$12$$ −0.500000 0.866025i −0.500000 0.866025i
$$13$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0.500000 0.866025i 0.500000 0.866025i
$$15$$ −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 $$\pi$$
$$18$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ −0.500000 0.866025i −0.500000 0.866025i
$$21$$ −1.00000 −1.00000
$$22$$ 0 0
$$23$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$24$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$25$$ −0.500000 0.866025i −0.500000 0.866025i
$$26$$ 0 0
$$27$$ 1.00000 1.00000
$$28$$ −1.00000 −1.00000
$$29$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$31$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.00000 −1.00000
$$36$$ 1.00000 1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$41$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$42$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$43$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$44$$ 0 0
$$45$$ 1.00000 1.00000
$$46$$ −1.00000 −1.00000
$$47$$ 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 0
$$50$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ −0.500000 0.866025i −0.500000 0.866025i
$$55$$ 0 0
$$56$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$57$$ 0 0
$$58$$ 0.500000 0.866025i 0.500000 0.866025i
$$59$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$60$$ 1.00000 1.00000
$$61$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 0 0
$$63$$ 0.500000 0.866025i 0.500000 0.866025i
$$64$$ 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
$$69$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$70$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −0.500000 0.866025i −0.500000 0.866025i
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 1.00000 1.00000
$$76$$ 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
$$82$$ −1.00000 −1.00000
$$83$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0.500000 0.866025i 0.500000 0.866025i
$$85$$ 0 0
$$86$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$87$$ −1.00000 −1.00000
$$88$$ 0 0
$$89$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ −0.500000 0.866025i −0.500000 0.866025i
$$91$$ 0 0
$$92$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$93$$ 0 0
$$94$$ 0.500000 0.866025i 0.500000 0.866025i
$$95$$ 0 0
$$96$$ −0.500000 0.866025i −0.500000 0.866025i
$$97$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$102$$ 0 0
$$103$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$104$$ 0 0
$$105$$ 0.500000 0.866025i 0.500000 0.866025i
$$106$$ 0 0
$$107$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$109$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.500000 0.866025i 0.500000 0.866025i
$$113$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$114$$ 0 0
$$115$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$116$$ −1.00000 −1.00000
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ −0.500000 0.866025i −0.500000 0.866025i
$$121$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$122$$ 0.500000 0.866025i 0.500000 0.866025i
$$123$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$124$$ 0 0
$$125$$ 1.00000 1.00000
$$126$$ −1.00000 −1.00000
$$127$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$128$$ −0.500000 0.866025i −0.500000 0.866025i
$$129$$ 2.00000 2.00000
$$130$$ 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
$$134$$ −1.00000 −1.00000
$$135$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$136$$ 0 0
$$137$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0.500000 0.866025i 0.500000 0.866025i
$$139$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$140$$ 0.500000 0.866025i 0.500000 0.866025i
$$141$$ −1.00000 −1.00000
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$145$$ −1.00000 −1.00000
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$150$$ −0.500000 0.866025i −0.500000 0.866025i
$$151$$ 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 0
$$156$$ 0 0
$$157$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −0.500000 0.866025i −0.500000 0.866025i
$$161$$ 1.00000 1.00000
$$162$$ 1.00000 1.00000
$$163$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$164$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$165$$ 0 0
$$166$$ 0.500000 0.866025i 0.500000 0.866025i
$$167$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$168$$ −1.00000 −1.00000
$$169$$ −0.500000 0.866025i −0.500000 0.866025i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 2.00000
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$175$$ 0.500000 0.866025i 0.500000 0.866025i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ −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
$$183$$ −1.00000 −1.00000
$$184$$ 0.500000 0.866025i 0.500000 0.866025i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −1.00000 −1.00000
$$189$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$193$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ −0.500000 0.866025i −0.500000 0.866025i
$$201$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$202$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$203$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$204$$ 0 0
$$205$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$206$$ 2.00000 2.00000
$$207$$ −1.00000 −1.00000
$$208$$ 0 0
$$209$$ 0 0
$$210$$ −1.00000 −1.00000
$$211$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$215$$ 2.00000 2.00000
$$216$$ 1.00000 1.00000
$$217$$ 0 0
$$218$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$224$$ −1.00000 −1.00000
$$225$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$226$$ 0 0
$$227$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$228$$ 0 0
$$229$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$230$$ 0.500000 0.866025i 0.500000 0.866025i
$$231$$ 0 0
$$232$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ −1.00000 −1.00000
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$241$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ 1.00000 1.00000
$$243$$ −0.500000 0.866025i −0.500000 0.866025i
$$244$$ −1.00000 −1.00000
$$245$$ 0 0
$$246$$ 0.500000 0.866025i 0.500000 0.866025i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.00000 −1.00000
$$250$$ −0.500000 0.866025i −0.500000 0.866025i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$253$$ 0 0
$$254$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ −1.00000 1.73205i −1.00000 1.73205i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.500000 0.866025i 0.500000 0.866025i
$$262$$ 0 0
$$263$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.500000 0.866025i 0.500000 0.866025i
$$268$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$269$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 1.00000 1.00000
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −1.00000 −1.00000
$$277$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ −1.00000 −1.00000
$$281$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$282$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$283$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1.00000 1.00000
$$288$$ 1.00000 1.00000
$$289$$ 1.00000 1.00000
$$290$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −1.00000 −1.00000
$$299$$ 0 0
$$300$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$301$$ 1.00000 1.73205i 1.00000 1.73205i
$$302$$ 0 0
$$303$$ 2.00000 2.00000
$$304$$ 0 0
$$305$$ −1.00000 −1.00000
$$306$$ 0 0
$$307$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$308$$ 0 0
$$309$$ −1.00000 1.73205i −1.00000 1.73205i
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$314$$ 0 0
$$315$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$316$$ 0 0
$$317$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$321$$ 0.500000 0.866025i 0.500000 0.866025i
$$322$$ −0.500000 0.866025i −0.500000 0.866025i
$$323$$ 0 0
$$324$$ −0.500000 0.866025i −0.500000 0.866025i
$$325$$ 0 0
$$326$$ −1.00000 1.73205i −1.00000 1.73205i
$$327$$ 0.500000 0.866025i 0.500000 0.866025i
$$328$$ 0.500000 0.866025i 0.500000 0.866025i
$$329$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$330$$ 0 0
$$331$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ −1.00000 −1.00000
$$333$$ 0 0
$$334$$ −1.00000 −1.00000
$$335$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$336$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$337$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$338$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.00000 1.00000
$$344$$ −1.00000 1.73205i −1.00000 1.73205i
$$345$$ −1.00000 −1.00000
$$346$$ 0 0
$$347$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0.500000 0.866025i 0.500000 0.866025i
$$349$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$350$$ −1.00000 −1.00000
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0.500000 0.866025i 0.500000 0.866025i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 1.00000 1.00000
$$361$$ 1.00000 1.00000
$$362$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$363$$ −0.500000 0.866025i −0.500000 0.866025i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$367$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$368$$ −1.00000 −1.00000
$$369$$ −1.00000 −1.00000
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 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
$$376$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$377$$ 0 0
$$378$$ 0.500000 0.866025i 0.500000 0.866025i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0.500000 0.866025i 0.500000 0.866025i
$$382$$ 0 0
$$383$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$384$$ 1.00000 1.00000
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$388$$ 0 0
$$389$$ 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
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$401$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0.500000 0.866025i 0.500000 0.866025i
$$403$$ 0 0
$$404$$ 2.00000 2.00000
$$405$$ −0.500000 0.866025i −0.500000 0.866025i
$$406$$ 1.00000 1.00000
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0.500000 0.866025i 0.500000 0.866025i
$$411$$ 0 0
$$412$$ −1.00000 1.73205i −1.00000 1.73205i
$$413$$ 0 0
$$414$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$415$$ −1.00000 −1.00000
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$420$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$421$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$422$$ 0 0
$$423$$ 0.500000 0.866025i 0.500000 0.866025i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$428$$ 0.500000 0.866025i 0.500000 0.866025i
$$429$$ 0 0
$$430$$ −1.00000 1.73205i −1.00000 1.73205i
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −0.500000 0.866025i −0.500000 0.866025i
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0.500000 0.866025i 0.500000 0.866025i
$$436$$ 0.500000 0.866025i 0.500000 0.866025i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0 0
$$445$$ 0.500000 0.866025i 0.500000 0.866025i
$$446$$ 0.500000 0.866025i 0.500000 0.866025i
$$447$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$448$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$449$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$450$$ 1.00000 1.00000
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$458$$ −1.00000 −1.00000
$$459$$ 0 0
$$460$$ −1.00000 −1.00000
$$461$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$462$$ 0 0
$$463$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$464$$ 0.500000 0.866025i 0.500000 0.866025i
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$468$$ 0 0
$$469$$ 1.00000 1.00000
$$470$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 1.00000 1.00000
$$481$$ 0 0
$$482$$ 0.500000 0.866025i 0.500000 0.866025i
$$483$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$484$$ −0.500000 0.866025i −0.500000 0.866025i
$$485$$ 0 0
$$486$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$487$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$488$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$489$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$490$$ 0 0
$$491$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$492$$ −1.00000 −1.00000
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$499$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$501$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$502$$ 0 0
$$503$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$504$$ 0.500000 0.866025i 0.500000 0.866025i
$$505$$ 2.00000 2.00000
$$506$$ 0 0
$$507$$ 1.00000 1.00000
$$508$$ 0.500000 0.866025i 0.500000 0.866025i
$$509$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.00000 1.73205i −1.00000 1.73205i
$$516$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ −1.00000 −1.00000
$$523$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$524$$ 0 0
$$525$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$526$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.00000 −1.00000
$$535$$ 0.500000 0.866025i 0.500000 0.866025i
$$536$$ 0.500000 0.866025i 0.500000 0.866025i
$$537$$ 0 0
$$538$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$539$$ 0 0
$$540$$ −0.500000 0.866025i −0.500000 0.866025i
$$541$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ 0 0
$$543$$ 0.500000 0.866025i 0.500000 0.866025i
$$544$$ 0 0
$$545$$ 0.500000 0.866025i 0.500000 0.866025i
$$546$$ 0 0
$$547$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$548$$ 0 0
$$549$$ 0.500000 0.866025i 0.500000 0.866025i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$561$$ 0 0
$$562$$ 0.500000 0.866025i 0.500000 0.866025i
$$563$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$564$$ 0.500000 0.866025i 0.500000 0.866025i
$$565$$ 0 0
$$566$$ −1.00000 −1.00000
$$567$$ −1.00000 −1.00000
$$568$$ 0 0
$$569$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$570$$ 0 0
$$571$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −0.500000 0.866025i −0.500000 0.866025i
$$575$$ −1.00000 −1.00000
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −0.500000 0.866025i −0.500000 0.866025i
$$579$$ 0 0
$$580$$ 0.500000 0.866025i 0.500000 0.866025i
$$581$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 1.00000 1.00000
$$601$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$602$$ −2.00000 −2.00000
$$603$$ −1.00000 −1.00000
$$604$$ 0 0
$$605$$ −0.500000 0.866025i −0.500000 0.866025i
$$606$$ −1.00000 1.73205i −1.00000 1.73205i
$$607$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$608$$ 0 0
$$609$$ −0.500000 0.866025i −0.500000 0.866025i
$$610$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$615$$ −1.00000 −1.00000
$$616$$ 0 0
$$617$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$618$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$619$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 0 0
$$621$$ 0.500000 0.866025i 0.500000 0.866025i
$$622$$ 0 0
$$623$$ −0.500000 0.866025i −0.500000 0.866025i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0.500000 0.866025i 0.500000 0.866025i
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.500000 0.866025i 0.500000 0.866025i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.00000 1.00000
$$641$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ −1.00000 −1.00000
$$643$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$644$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$645$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$646$$ 0 0
$$647$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$653$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$654$$ −1.00000 −1.00000
$$655$$ 0 0
$$656$$ −1.00000 −1.00000
$$657$$ 0 0
$$658$$ 1.00000 1.00000
$$659$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000 1.00000
$$668$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$669$$ −1.00000 −1.00000
$$670$$ 0.500000 0.866025i 0.500000 0.866025i
$$671$$ 0 0
$$672$$ 0.500000 0.866025i 0.500000 0.866025i
$$673$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$674$$ 0 0
$$675$$ −0.500000 0.866025i −0.500000 0.866025i
$$676$$ 1.00000 1.00000
$$677$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 2.00000 2.00000
$$682$$ 0 0
$$683$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −0.500000 0.866025i −0.500000 0.866025i
$$687$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$688$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$689$$ 0 0
$$690$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$691$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 2.00000 2.00000
$$695$$ 0 0
$$696$$ −1.00000 −1.00000
$$697$$ 0 0
$$698$$ 0.500000 0.866025i 0.500000 0.866025i
$$699$$ 0 0
$$700$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$701$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$702$$ 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
$$708$$ 0 0
$$709$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −1.00000 −1.00000
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ −0.500000 0.866025i −0.500000 0.866025i
$$721$$ −2.00000 −2.00000
$$722$$ −0.500000 0.866025i −0.500000 0.866025i
$$723$$ −1.00000 −1.00000
$$724$$ 0.500000 0.866025i 0.500000 0.866025i
$$725$$ 0.500000 0.866025i 0.500000 0.866025i
$$726$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$727$$ 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
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0.500000 0.866025i 0.500000 0.866025i
$$733$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$735$$ 0 0
$$736$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$737$$ 0 0
$$738$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$744$$ 0 0
$$745$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$746$$ 0 0
$$747$$ 0.500000 0.866025i 0.500000 0.866025i
$$748$$ 0 0
$$749$$ −0.500000 0.866025i −0.500000 0.866025i
$$750$$ 1.00000 1.00000
$$751$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0.500000 0.866025i 0.500000 0.866025i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −1.00000 −1.00000
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$762$$ −1.00000 −1.00000
$$763$$ −0.500000 0.866025i −0.500000 0.866025i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 2.00000 2.00000
$$767$$ 0 0
$$768$$ −0.500000 0.866025i −0.500000 0.866025i
$$769$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 2.00000 2.00000
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0.500000 0.866025i 0.500000 0.866025i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 0 0
$$789$$ 2.00000 2.00000
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$798$$ 0 0
$$799$$