Properties

 Label 168.1.s.b.53.1 Level $168$ Weight $1$ Character 168.53 Analytic conductor $0.084$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -24 Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 168.s (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$0.0838429221223$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ 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 3.1.1176.1 Artin image: $C_6\times S_3$ Artin field: Galois closure of 12.0.458838245376.1

Embedding invariants

 Embedding label 53.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 168.53 Dual form 168.1.s.b.149.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -1.00000 q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} -1.00000 q^{22} +(-0.500000 + 0.866025i) q^{24} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +1.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.00000 q^{35} +1.00000 q^{36} +(0.500000 + 0.866025i) q^{40} +(-0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} -1.00000 q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{53} +(-0.500000 - 0.866025i) q^{54} +1.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(0.500000 + 0.866025i) q^{58} +(-0.500000 + 0.866025i) q^{59} +(0.500000 - 0.866025i) q^{60} +1.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(0.500000 + 0.866025i) q^{70} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-0.500000 - 0.866025i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +1.00000 q^{83} -1.00000 q^{84} +(0.500000 - 0.866025i) q^{87} +(0.500000 - 0.866025i) q^{88} -1.00000 q^{90} +(-0.500000 - 0.866025i) q^{93} +(-0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(0.500000 - 0.866025i) q^{98} +1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 $$2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + q^{10} - q^{11} + q^{12} - 2 q^{14} - 2 q^{15} - q^{16} + q^{18} + 2 q^{20} + q^{21} - 2 q^{22} - q^{24} - 2 q^{27} - q^{28} + 2 q^{29} - q^{30} + q^{31} + q^{32} + q^{33} + 2 q^{35} + 2 q^{36} + q^{40} - q^{42} - q^{44} - q^{45} - 2 q^{48} - q^{49} - q^{53} - q^{54} + 2 q^{55} + q^{56} + q^{58} - q^{59} + q^{60} + 2 q^{62} + 2 q^{63} + 2 q^{64} - q^{66} + q^{70} + q^{72} - 2 q^{73} - q^{77} + q^{79} - q^{80} - q^{81} + 2 q^{83} - 2 q^{84} + q^{87} + q^{88} - 2 q^{90} - q^{93} - q^{96} - 2 q^{97} + q^{98} + 2 q^{99}+O(q^{100})$$ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 - q^7 - 2 * q^8 - q^9 + q^10 - q^11 + q^12 - 2 * q^14 - 2 * q^15 - q^16 + q^18 + 2 * q^20 + q^21 - 2 * q^22 - q^24 - 2 * q^27 - q^28 + 2 * q^29 - q^30 + q^31 + q^32 + q^33 + 2 * q^35 + 2 * q^36 + q^40 - q^42 - q^44 - q^45 - 2 * q^48 - q^49 - q^53 - q^54 + 2 * q^55 + q^56 + q^58 - q^59 + q^60 + 2 * q^62 + 2 * q^63 + 2 * q^64 - q^66 + q^70 + q^72 - 2 * q^73 - q^77 + q^79 - q^80 - q^81 + 2 * q^83 - 2 * q^84 + q^87 + q^88 - 2 * q^90 - q^93 - q^96 - 2 * q^97 + q^98 + 2 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$-1$$ $$1$$

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 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$6$$ 1.00000 1.00000
$$7$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$8$$ −1.00000 −1.00000
$$9$$ −0.500000 0.866025i −0.500000 0.866025i
$$10$$ 0.500000 0.866025i 0.500000 0.866025i
$$11$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$12$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ −1.00000 −1.00000
$$15$$ −1.00000 −1.00000
$$16$$ −0.500000 0.866025i −0.500000 0.866025i
$$17$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0.500000 0.866025i 0.500000 0.866025i
$$19$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$20$$ 1.00000 1.00000
$$21$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$22$$ −1.00000 −1.00000
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.00000 −1.00000
$$28$$ −0.500000 0.866025i −0.500000 0.866025i
$$29$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ −0.500000 0.866025i −0.500000 0.866025i
$$31$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$32$$ 0.500000 0.866025i 0.500000 0.866025i
$$33$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$34$$ 0 0
$$35$$ 1.00000 1.00000
$$36$$ 1.00000 1.00000
$$37$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −0.500000 0.866025i −0.500000 0.866025i
$$45$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$46$$ 0 0
$$47$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$48$$ −1.00000 −1.00000
$$49$$ −0.500000 0.866025i −0.500000 0.866025i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$54$$ −0.500000 0.866025i −0.500000 0.866025i
$$55$$ 1.00000 1.00000
$$56$$ 0.500000 0.866025i 0.500000 0.866025i
$$57$$ 0 0
$$58$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$59$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$60$$ 0.500000 0.866025i 0.500000 0.866025i
$$61$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$62$$ 1.00000 1.00000
$$63$$ 1.00000 1.00000
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 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
$$73$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.500000 0.866025i −0.500000 0.866025i
$$78$$ 0 0
$$79$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$80$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$84$$ −1.00000 −1.00000
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0.500000 0.866025i 0.500000 0.866025i
$$88$$ 0.500000 0.866025i 0.500000 0.866025i
$$89$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$90$$ −1.00000 −1.00000
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −0.500000 0.866025i −0.500000 0.866025i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.500000 0.866025i −0.500000 0.866025i
$$97$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$98$$ 0.500000 0.866025i 0.500000 0.866025i
$$99$$ 1.00000 1.00000
$$100$$ 0 0
$$101$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$102$$ 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
$$106$$ −1.00000 −1.00000
$$107$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$108$$ 0.500000 0.866025i 0.500000 0.866025i
$$109$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$111$$ 0 0
$$112$$ 1.00000 1.00000
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$117$$ 0 0
$$118$$ −1.00000 −1.00000
$$119$$ 0 0
$$120$$ 1.00000 1.00000
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$125$$ −1.00000 −1.00000
$$126$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$127$$ −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
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$132$$ −1.00000 −1.00000
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$136$$ 0 0
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$145$$ −0.500000 0.866025i −0.500000 0.866025i
$$146$$ −2.00000 −2.00000
$$147$$ −1.00000 −1.00000
$$148$$ 0 0
$$149$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0 0
$$151$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0.500000 0.866025i 0.500000 0.866025i
$$155$$ −1.00000 −1.00000
$$156$$ 0 0
$$157$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$159$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$160$$ −1.00000 −1.00000
$$161$$ 0 0
$$162$$ −1.00000 −1.00000
$$163$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$164$$ 0 0
$$165$$ 0.500000 0.866025i 0.500000 0.866025i
$$166$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ −0.500000 0.866025i −0.500000 0.866025i
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 1.00000 1.00000
$$175$$ 0 0
$$176$$ 1.00000 1.00000
$$177$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$178$$ 0 0
$$179$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$180$$ −0.500000 0.866025i −0.500000 0.866025i
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0.500000 0.866025i 0.500000 0.866025i
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 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
$$193$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$194$$ −0.500000 0.866025i −0.500000 0.866025i
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$198$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$199$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 2.00000 2.00000
$$203$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.00000 1.73205i 1.00000 1.73205i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 1.00000 1.00000
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ −0.500000 0.866025i −0.500000 0.866025i
$$213$$ 0 0
$$214$$ 0.500000 0.866025i 0.500000 0.866025i
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$218$$ 0 0
$$219$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$220$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$224$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$230$$ 0 0
$$231$$ −1.00000 −1.00000
$$232$$ −1.00000 −1.00000
$$233$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −0.500000 0.866025i −0.500000 0.866025i
$$237$$ 1.00000 1.00000
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$241$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$244$$ 0 0
$$245$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$249$$ 0.500000 0.866025i 0.500000 0.866025i
$$250$$ −0.500000 0.866025i −0.500000 0.866025i
$$251$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$252$$ −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 $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −0.500000 0.866025i −0.500000 0.866025i
$$262$$ 0.500000 0.866025i 0.500000 0.866025i
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ −0.500000 0.866025i −0.500000 0.866025i
$$265$$ 1.00000 1.00000
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$270$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$271$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −1.00000
$$280$$ −1.00000 −1.00000
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −1.00000
$$289$$ −0.500000 0.866025i −0.500000 0.866025i
$$290$$ 0.500000 0.866025i 0.500000 0.866025i
$$291$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$292$$ −1.00000 1.73205i −1.00000 1.73205i
$$293$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$294$$ −0.500000 0.866025i −0.500000 0.866025i
$$295$$ 1.00000 1.00000
$$296$$ 0 0
$$297$$ 0.500000 0.866025i 0.500000 0.866025i
$$298$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 1.00000 1.00000
$$303$$ −1.00000 1.73205i −1.00000 1.73205i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 1.00000 1.00000
$$309$$ −2.00000 −2.00000
$$310$$ −0.500000 0.866025i −0.500000 0.866025i
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$314$$ 0 0
$$315$$ −0.500000 0.866025i −0.500000 0.866025i
$$316$$ −1.00000 −1.00000
$$317$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$318$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$319$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$320$$ −0.500000 0.866025i −0.500000 0.866025i
$$321$$ −1.00000 −1.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.500000 0.866025i −0.500000 0.866025i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 1.00000 1.00000
$$331$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0.500000 0.866025i 0.500000 0.866025i
$$337$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$338$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$342$$ 0 0
$$343$$ 1.00000 1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$347$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$348$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 2.00000 2.00000
$$359$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ 0.500000 0.866025i 0.500000 0.866025i
$$361$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.00000 2.00000
$$366$$ 0 0
$$367$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −0.500000 0.866025i −0.500000 0.866025i
$$372$$ 1.00000 1.00000
$$373$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$374$$ 0 0
$$375$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 1.00000 1.00000
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$382$$ 0 0
$$383$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 1.00000 1.00000
$$385$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$386$$ 1.00000 1.00000
$$387$$ 0 0
$$388$$ 0.500000 0.866025i 0.500000 0.866025i
$$389$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$393$$ −1.00000 −1.00000
$$394$$ −1.00000 1.73205i −1.00000 1.73205i
$$395$$ 0.500000 0.866025i 0.500000 0.866025i
$$396$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$397$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$398$$ −2.00000 −2.00000
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$405$$ 1.00000 1.00000
$$406$$ −1.00000 −1.00000
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 2.00000 2.00000
$$413$$ −0.500000 0.866025i −0.500000 0.866025i
$$414$$ 0 0
$$415$$ −0.500000 0.866025i −0.500000 0.866025i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$420$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0.500000 0.866025i 0.500000 0.866025i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1.00000 1.00000
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$433$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$434$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$435$$ −1.00000 −1.00000
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$439$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ −1.00000 −1.00000
$$441$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$442$$ 0 0
$$443$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −0.500000 0.866025i −0.500000 0.866025i
$$447$$ 2.00000 2.00000
$$448$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −0.500000 0.866025i −0.500000 0.866025i
$$454$$ −1.00000 −1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$462$$ −0.500000 0.866025i −0.500000 0.866025i
$$463$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$464$$ −0.500000 0.866025i −0.500000 0.866025i
$$465$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$466$$ 0 0
$$467$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0.500000 0.866025i 0.500000 0.866025i
$$473$$ 0 0
$$474$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.00000 1.00000
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$481$$ 0 0
$$482$$ 1.00000 1.00000
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$486$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$487$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −1.00000 −1.00000
$$491$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −0.500000 0.866025i −0.500000 0.866025i
$$496$$ −1.00000 −1.00000
$$497$$ 0 0
$$498$$ 1.00000 1.00000
$$499$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$500$$ 0.500000 0.866025i 0.500000 0.866025i
$$501$$ 0 0
$$502$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ −1.00000 −1.00000
$$505$$ −2.00000 −2.00000
$$506$$ 0 0
$$507$$ 0.500000 0.866025i 0.500000 0.866025i
$$508$$ 0.500000 0.866025i 0.500000 0.866025i
$$509$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ −1.00000 1.73205i −1.00000 1.73205i
$$512$$ −1.00000 −1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 2.00000 2.00000
$$520$$ 0 0
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0.500000 0.866025i 0.500000 0.866025i
$$523$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$524$$ 1.00000 1.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.500000 0.866025i 0.500000 0.866025i
$$529$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$530$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$531$$ 1.00000 1.00000
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$536$$ 0 0
$$537$$ −1.00000 1.73205i −1.00000 1.73205i
$$538$$ −1.00000 −1.00000
$$539$$ 1.00000 1.00000
$$540$$ −1.00000 −1.00000
$$541$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −1.00000 −1.00000
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$558$$ −0.500000 0.866025i −0.500000 0.866025i
$$559$$ 0 0
$$560$$ −0.500000 0.866025i −0.500000 0.866025i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −0.500000 0.866025i −0.500000 0.866025i
$$568$$ 0 0
$$569$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 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 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$578$$ 0.500000 0.866025i 0.500000 0.866025i
$$579$$ −0.500000 0.866025i −0.500000 0.866025i
$$580$$ 1.00000 1.00000
$$581$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$582$$ −1.00000 −1.00000
$$583$$ −0.500000 0.866025i −0.500000 0.866025i
$$584$$ 1.00000 1.73205i 1.00000 1.73205i
$$585$$ 0 0
$$586$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$587$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$588$$ 0.500000 0.866025i 0.500000 0.866025i
$$589$$ 0 0
$$590$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$591$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$592$$ 0 0
$$593$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ 1.00000 1.00000
$$595$$ 0 0
$$596$$ −2.00000 −2.00000
$$597$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$605$$ 0 0
$$606$$ 1.00000 1.73205i 1.00000 1.73205i
$$607$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$608$$ 0 0
$$609$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ −1.00000 1.73205i −1.00000 1.73205i
$$619$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$620$$ 0.500000 0.866025i 0.500000 0.866025i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$626$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0.500000 0.866025i 0.500000 0.866025i
$$631$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$632$$ −0.500000 0.866025i −0.500000 0.866025i
$$633$$ 0 0
$$634$$ 0.500000 0.866025i 0.500000 0.866025i
$$635$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$636$$ −1.00000 −1.00000
$$637$$ 0 0
$$638$$ −1.00000 −1.00000
$$639$$ 0 0
$$640$$ 0.500000 0.866025i 0.500000 0.866025i
$$641$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ −0.500000 0.866025i −0.500000 0.866025i
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ 0.500000 0.866025i 0.500000 0.866025i
$$649$$ −0.500000 0.866025i −0.500000 0.866025i
$$650$$ 0 0
$$651$$ 1.00000 1.00000
$$652$$ 0 0
$$653$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$656$$ 0 0
$$657$$ 2.00000 2.00000
$$658$$ 0 0
$$659$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$660$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$661$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −1.00000 −1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 1.00000
$$673$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$674$$ −0.500000 0.866025i −0.500000 0.866025i
$$675$$ 0 0
$$676$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$677$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0.500000 0.866025i 0.500000 0.866025i
$$680$$ 0 0
$$681$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$682$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$683$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$692$$ −2.00000 −2.00000
$$693$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$694$$ 2.00000 2.00000
$$695$$ 0 0
$$696$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$708$$ −1.00000 −1.00000
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ 0.500000 0.866025i 0.500000 0.866025i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 1.00000 1.00000
$$721$$ 2.00000 2.00000
$$722$$ −1.00000 −1.00000
$$723$$ −0.500000 0.866025i −0.500000 0.866025i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$734$$ 1.00000 1.00000
$$735$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0.500000 0.866025i 0.500000 0.866025i
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$745$$ 1.00000 1.73205i 1.00000 1.73205i
$$746$$ 0 0
$$747$$ −0.500000 0.866025i −0.500000 0.866025i
$$748$$ 0 0
$$749$$ 1.00000 1.00000
$$750$$ −1.00000 −1.00000
$$751$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0 0
$$753$$ 0.500000 0.866025i 0.500000 0.866025i
$$754$$ 0 0
$$755$$ −1.00000 −1.00000
$$756$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$762$$ −1.00000 −1.00000
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$769$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ −1.00000 −1.00000
$$771$$ 0 0
$$772$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$773$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1.00000 1.00000
$$777$$ 0 0
$$778$$ 2.00000 2.00000
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −1.00000 −1.00000
$$784$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$785$$ 0 0
$$786$$ −0.500000 0.866025i −0.500000 0.866025i
$$787$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 1.00000 1.73205i 1.00000 1.73205i
$$789$$ 0 0
$$790$$ 1.00000 1.00000
$$791$$ 0 0
$$792$$ −1.00000 −1.00000
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0.500000 0.866025i 0.500000 0.866025i
$$796$$ −1.00000 1.73205i −1.00000 1.73205i
$$797$$ 1.00000 1.00000 0.500000 0.866025i