Properties

 Label 840.1.cg.a.149.1 Level $840$ Weight $1$ Character 840.149 Analytic conductor $0.419$ Analytic rank $0$ Dimension $4$ Projective image $D_{6}$ CM discriminant -24 Inner twists $8$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$840 = 2^{3} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 840.cg (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$0.419214610612$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{6}$$ Projective field: Galois closure of 6.0.518616000.10

Embedding invariants

 Embedding label 149.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 840.149 Dual form 840.1.cg.a.389.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000 q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000 q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +(-0.866025 - 1.50000i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.00000i q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{18} +(-0.866025 - 0.500000i) q^{20} +(-0.866025 - 0.500000i) q^{21} +1.73205i q^{22} +(-0.500000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.00000i q^{27} +(0.500000 - 0.866025i) q^{28} +1.73205 q^{29} +(0.866025 - 0.500000i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +(0.866025 + 0.500000i) q^{35} +1.00000 q^{36} +(0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{42} +(0.866025 - 1.50000i) q^{44} +1.00000i q^{45} +1.00000i q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.866025 + 0.500000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 0.866025i) q^{55} +(-0.866025 + 0.500000i) q^{56} +(-1.50000 - 0.866025i) q^{58} +(0.866025 + 1.50000i) q^{59} -1.00000 q^{60} +1.00000i q^{62} -1.00000 q^{63} -1.00000 q^{64} +(0.866025 + 1.50000i) q^{66} +(-0.500000 - 0.866025i) q^{70} +(-0.866025 - 0.500000i) q^{72} -1.00000i q^{75} +(-0.866025 + 1.50000i) q^{77} +(0.500000 - 0.866025i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +1.00000i q^{83} -1.00000i q^{84} +(1.50000 - 0.866025i) q^{87} +(-1.50000 + 0.866025i) q^{88} +(0.500000 - 0.866025i) q^{90} +(-0.866025 - 0.500000i) q^{93} +(0.500000 - 0.866025i) q^{96} +1.73205i q^{97} +(0.866025 - 0.500000i) q^{98} -1.73205 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{4} - 4 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10})$$ 4 * q + 2 * q^4 - 4 * q^6 - 2 * q^7 + 2 * q^9 $$4 q + 2 q^{4} - 4 q^{6} - 2 q^{7} + 2 q^{9} + 4 q^{10} - 2 q^{15} - 2 q^{16} - 2 q^{24} + 2 q^{25} + 2 q^{28} - 2 q^{31} - 6 q^{33} + 4 q^{36} + 2 q^{40} + 2 q^{42} - 2 q^{49} - 2 q^{54} + 6 q^{55} - 6 q^{58} - 4 q^{60} - 4 q^{63} - 4 q^{64} - 2 q^{70} + 2 q^{79} - 2 q^{81} + 6 q^{87} - 6 q^{88} + 2 q^{90} + 2 q^{96}+O(q^{100})$$ 4 * q + 2 * q^4 - 4 * q^6 - 2 * q^7 + 2 * q^9 + 4 * q^10 - 2 * q^15 - 2 * q^16 - 2 * q^24 + 2 * q^25 + 2 * q^28 - 2 * q^31 - 6 * q^33 + 4 * q^36 + 2 * q^40 + 2 * q^42 - 2 * q^49 - 2 * q^54 + 6 * q^55 - 6 * q^58 - 4 * q^60 - 4 * q^63 - 4 * q^64 - 2 * q^70 + 2 * q^79 - 2 * q^81 + 6 * q^87 - 6 * q^88 + 2 * q^90 + 2 * q^96

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$281$$ $$337$$ $$421$$ $$631$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$ $$-1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.866025 0.500000i
$$3$$ 0.866025 0.500000i 0.866025 0.500000i
$$4$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$5$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$6$$ −1.00000 −1.00000
$$7$$ −0.500000 0.866025i −0.500000 0.866025i
$$8$$ 1.00000i 1.00000i
$$9$$ 0.500000 0.866025i 0.500000 0.866025i
$$10$$ 1.00000 1.00000
$$11$$ −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$12$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 1.00000i 1.00000i
$$15$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$16$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$19$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$20$$ −0.866025 0.500000i −0.866025 0.500000i
$$21$$ −0.866025 0.500000i −0.866025 0.500000i
$$22$$ 1.73205i 1.73205i
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ −0.500000 0.866025i −0.500000 0.866025i
$$25$$ 0.500000 0.866025i 0.500000 0.866025i
$$26$$ 0 0
$$27$$ 1.00000i 1.00000i
$$28$$ 0.500000 0.866025i 0.500000 0.866025i
$$29$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$30$$ 0.866025 0.500000i 0.866025 0.500000i
$$31$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$32$$ 0.866025 0.500000i 0.866025 0.500000i
$$33$$ −1.50000 0.866025i −1.50000 0.866025i
$$34$$ 0 0
$$35$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$36$$ 1.00000 1.00000
$$37$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$38$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0.866025 1.50000i 0.866025 1.50000i
$$45$$ 1.00000i 1.00000i
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 1.00000i 1.00000i
$$49$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$50$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$54$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$55$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$56$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$57$$ 0 0
$$58$$ −1.50000 0.866025i −1.50000 0.866025i
$$59$$ 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i $$0.166667\pi$$
1.00000i $$0.5\pi$$
$$60$$ −1.00000 −1.00000
$$61$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 1.00000i 1.00000i
$$63$$ −1.00000 −1.00000
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −0.500000 0.866025i −0.500000 0.866025i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −0.866025 0.500000i −0.866025 0.500000i
$$73$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$74$$ 0 0
$$75$$ 1.00000i 1.00000i
$$76$$ 0 0
$$77$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$78$$ 0 0
$$79$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$80$$ 1.00000i 1.00000i
$$81$$ −0.500000 0.866025i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$84$$ 1.00000i 1.00000i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.50000 0.866025i 1.50000 0.866025i
$$88$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$89$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0.500000 0.866025i 0.500000 0.866025i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −0.866025 0.500000i −0.866025 0.500000i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0.500000 0.866025i 0.500000 0.866025i
$$97$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$98$$ 0.866025 0.500000i 0.866025 0.500000i
$$99$$ −1.73205 −1.73205
$$100$$ 1.00000 1.00000
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$104$$ 0 0
$$105$$ 1.00000 1.00000
$$106$$ 1.00000 1.00000
$$107$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0.866025 0.500000i 0.866025 0.500000i
$$109$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ −0.866025 1.50000i −0.866025 1.50000i
$$111$$ 0 0
$$112$$ 1.00000 1.00000
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$117$$ 0 0
$$118$$ 1.73205i 1.73205i
$$119$$ 0 0
$$120$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$121$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0.500000 0.866025i 0.500000 0.866025i
$$125$$ 1.00000i 1.00000i
$$126$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$127$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$128$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.866025 1.50000i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$132$$ 1.73205i 1.73205i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$136$$ 0 0
$$137$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 1.00000i 1.00000i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$145$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$146$$ 0 0
$$147$$ 1.00000i 1.00000i
$$148$$ 0 0
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$151$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 1.50000 0.866025i 1.50000 0.866025i
$$155$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$156$$ 0 0
$$157$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$158$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$159$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$160$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$161$$ 0 0
$$162$$ 1.00000i 1.00000i
$$163$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$164$$ 0 0
$$165$$ 1.73205 1.73205
$$166$$ 0.500000 0.866025i 0.500000 0.866025i
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$169$$ −1.00000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$174$$ −1.73205 −1.73205
$$175$$ −1.00000 −1.00000
$$176$$ 1.73205 1.73205
$$177$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$178$$ 0 0
$$179$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$180$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$181$$ 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
$$189$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$190$$ 0 0
$$191$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$193$$ 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$194$$ 0.866025 1.50000i 0.866025 1.50000i
$$195$$ 0 0
$$196$$ −1.00000 −1.00000
$$197$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$198$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$199$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$200$$ −0.866025 0.500000i −0.866025 0.500000i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −0.866025 1.50000i −0.866025 1.50000i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ −0.866025 0.500000i −0.866025 0.500000i
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ −0.866025 0.500000i −0.866025 0.500000i
$$213$$ 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
$$219$$ 0 0
$$220$$ 1.73205i 1.73205i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$224$$ −0.866025 0.500000i −0.866025 0.500000i
$$225$$ −0.500000 0.866025i −0.500000 0.866025i
$$226$$ 0 0
$$227$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 1.73205i 1.73205i
$$232$$ 1.73205i 1.73205i
$$233$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$237$$ 1.00000i 1.00000i
$$238$$ 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 $$-0.333333\pi$$
−1.00000 $$\pi$$
$$242$$ 1.73205 1.00000i 1.73205 1.00000i
$$243$$ −0.866025 0.500000i −0.866025 0.500000i
$$244$$ 0 0
$$245$$ 1.00000i 1.00000i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$249$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$250$$ 0.500000 0.866025i 0.500000 0.866025i
$$251$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$252$$ −0.500000 0.866025i −0.500000 0.866025i
$$253$$ 0 0
$$254$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.500000 0.866025i
$$257$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.866025 1.50000i 0.866025 1.50000i
$$262$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$265$$ 0.500000 0.866025i 0.500000 0.866025i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$270$$ 1.00000i 1.00000i
$$271$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.73205 −1.73205
$$276$$ 0 0
$$277$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −1.00000
$$280$$ 0.500000 0.866025i 0.500000 0.866025i
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 1.00000i
$$289$$ 0.500000 0.866025i 0.500000 0.866025i
$$290$$ 1.73205 1.73205
$$291$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$292$$ 0 0
$$293$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$294$$ 0.500000 0.866025i 0.500000 0.866025i
$$295$$ −1.50000 0.866025i −1.50000 0.866025i
$$296$$ 0 0
$$297$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0.866025 0.500000i 0.866025 0.500000i
$$301$$ 0 0
$$302$$ 1.00000i 1.00000i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ −1.73205 −1.73205
$$309$$ 0 0
$$310$$ −0.500000 0.866025i −0.500000 0.866025i
$$311$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ 0 0
$$313$$ 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 $$0$$
0.500000 + 0.866025i $$0.333333\pi$$
$$314$$ 0 0
$$315$$ 0.866025 0.500000i 0.866025 0.500000i
$$316$$ 1.00000 1.00000
$$317$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0.866025 0.500000i 0.866025 0.500000i
$$319$$ −1.50000 2.59808i −1.50000 2.59808i
$$320$$ 0.866025 0.500000i 0.866025 0.500000i
$$321$$ 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
$$330$$ −1.50000 0.866025i −1.50000 0.866025i
$$331$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0.866025 0.500000i 0.866025 0.500000i
$$337$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$338$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$342$$ 0 0
$$343$$ 1.00000 1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.00000 1.73205i −1.00000 1.73205i
$$347$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$351$$ 0 0
$$352$$ −1.50000 0.866025i −1.50000 0.866025i
$$353$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ −0.866025 1.50000i −0.866025 1.50000i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$360$$ 1.00000 1.00000
$$361$$ −0.500000 0.866025i −0.500000 0.866025i
$$362$$ 0 0
$$363$$ 2.00000i 2.00000i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i $$0.666667\pi$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$372$$ 1.00000i 1.00000i
$$373$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$374$$ 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
$$381$$ −0.866025 1.50000i −0.866025 1.50000i
$$382$$ 0 0
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 1.00000 1.00000
$$385$$ 1.73205i 1.73205i
$$386$$ −1.73205 −1.73205
$$387$$ 0 0
$$388$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$389$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$393$$ 1.73205i 1.73205i
$$394$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$395$$ 1.00000i 1.00000i
$$396$$ −0.866025 1.50000i −0.866025 1.50000i
$$397$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$398$$ 2.00000i 2.00000i
$$399$$ 0 0
$$400$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$401$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$406$$ 1.73205i 1.73205i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0.866025 1.50000i 0.866025 1.50000i
$$414$$ 0 0
$$415$$ −0.500000 0.866025i −0.500000 0.866025i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 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
$$428$$ 1.00000i 1.00000i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0.866025 0.500000i 0.866025 0.500000i
$$435$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$440$$ 0.866025 1.50000i 0.866025 1.50000i
$$441$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$442$$ 0 0
$$443$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0.866025 1.50000i 0.866025 1.50000i
$$447$$ 0 0
$$448$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 1.00000i 1.00000i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$454$$ −1.00000 −1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0.866025 1.50000i 0.866025 1.50000i
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$465$$ 1.00000 1.00000
$$466$$ 0 0
$$467$$ −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 0.500000i $$-0.833333\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.50000 0.866025i 1.50000 0.866025i
$$473$$ 0 0
$$474$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.00000i 1.00000i
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 1.00000i 1.00000i
$$481$$ 0 0
$$482$$ 1.00000i 1.00000i
$$483$$ 0 0
$$484$$ −2.00000 −2.00000
$$485$$ −0.866025 1.50000i −0.866025 1.50000i
$$486$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$487$$ 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$491$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 1.50000 0.866025i 1.50000 0.866025i
$$496$$ 1.00000 1.00000
$$497$$ 0 0
$$498$$ 1.00000i 1.00000i
$$499$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$501$$ 0 0
$$502$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 1.00000i 1.00000i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$508$$ 1.50000 0.866025i 1.50000 0.866025i
$$509$$ −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i $$0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 2.00000 2.00000
$$520$$ 0 0
$$521$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$522$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$523$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$524$$ 1.73205 1.73205
$$525$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 1.50000 0.866025i 1.50000 0.866025i
$$529$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$530$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$531$$ 1.73205 1.73205
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −1.00000 −1.00000
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 1.73205i 1.73205i
$$539$$ 1.73205 1.73205
$$540$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$541$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −1.00000 −1.00000
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$558$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$559$$ 0 0
$$560$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$564$$ 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 $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$577$$ 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$578$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$579$$ 0.866025 1.50000i 0.866025 1.50000i
$$580$$ −1.50000 0.866025i −1.50000 0.866025i
$$581$$ 0.866025 0.500000i 0.866025 0.500000i
$$582$$ 1.73205i 1.73205i
$$583$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$587$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$588$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$589$$ 0 0
$$590$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$591$$ −1.00000 1.73205i −1.00000 1.73205i
$$592$$ 0 0
$$593$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$594$$ 1.73205 1.73205
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$598$$ 0 0
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ −1.00000 −1.00000
$$601$$ −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
$$605$$ 2.00000i 2.00000i
$$606$$ 0 0
$$607$$ −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ −1.50000 0.866025i −1.50000 0.866025i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 1.00000i 1.00000i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.500000 0.866025i
$$626$$ −0.866025 1.50000i −0.866025 1.50000i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ −1.00000 −1.00000
$$631$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$632$$ −0.866025 0.500000i −0.866025 0.500000i
$$633$$ 0 0
$$634$$ −0.500000 0.866025i −0.500000 0.866025i
$$635$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$636$$ −1.00000 −1.00000
$$637$$ 0 0
$$638$$ 3.00000i 3.00000i
$$639$$ 0 0
$$640$$ −1.00000 −1.00000
$$641$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ −0.866025 0.500000i −0.866025 0.500000i
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$649$$ 1.50000 2.59808i 1.50000 2.59808i
$$650$$ 0 0
$$651$$ 1.00000i 1.00000i
$$652$$ 0 0
$$653$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$654$$ 0 0
$$655$$ 1.73205i 1.73205i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$661$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 1.00000 1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −1.00000 −1.00000
$$673$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$674$$ 0.866025 1.50000i 0.866025 1.50000i
$$675$$ −0.866025 0.500000i −0.866025 0.500000i
$$676$$ −0.500000 0.866025i −0.500000 0.866025i
$$677$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 1.50000 0.866025i 1.50000 0.866025i
$$680$$ 0 0
$$681$$ 0.500000 0.866025i 0.500000 0.866025i
$$682$$ 1.50000 0.866025i 1.50000 0.866025i
$$683$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −0.866025 0.500000i −0.866025 0.500000i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 2.00000i 2.00000i
$$693$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$694$$ 2.00000 2.00000
$$695$$ 0 0
$$696$$ −0.866025 1.50000i −0.866025 1.50000i
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −0.500000 0.866025i −0.500000 0.866025i
$$701$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 1.73205i 1.73205i
$$709$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 0 0
$$711$$ −0.500000 0.866025i −0.500000 0.866025i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$720$$ −0.866025 0.500000i −0.866025 0.500000i
$$721$$ 0 0
$$722$$ 1.00000i 1.00000i
$$723$$ −0.866025 0.500000i −0.866025 0.500000i
$$724$$ 0 0
$$725$$ 0.866025 1.50000i 0.866025 1.50000i
$$726$$ 1.00000 1.73205i 1.00000 1.73205i
$$727$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$734$$ 1.73205 1.73205
$$735$$ −0.500000 0.866025i −0.500000 0.866025i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −0.500000 0.866025i −0.500000 0.866025i
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$748$$ 0 0
$$749$$ 1.00000i 1.00000i
$$750$$ 1.00000i 1.00000i
$$751$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$754$$ 0 0
$$755$$ −0.866025 0.500000i −0.866025 0.500000i
$$756$$ −0.866025 0.500000i −0.866025 0.500000i
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 1.73205i 1.73205i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.866025 0.500000i −0.866025 0.500000i
$$769$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$770$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$771$$ 0 0
$$772$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$773$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −1.00000
$$776$$ 1.73205 1.73205
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 1.73205i 1.73205i
$$784$$ −0.500000 0.866025i −0.500000 0.866025i
$$785$$ 0 0
$$786$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$787$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$788$$ 1.73205 1.00000i 1.73205 1.00000i
$$789$$ 0 0
$$790$$ 0.500000 0.866025i 0.500000 0.866025i
$$791$$ 0 0
$$792$$ 1.73205i 1.73205i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 1.00000i 1.00000i
$$796$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$797$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$