Properties

 Label 124.1.i.a.67.2 Level $124$ Weight $1$ Character 124.67 Analytic conductor $0.062$ Analytic rank $0$ Dimension $4$ Projective image $A_{4}$ CM/RM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$124 = 2^{2} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 124.i (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$0.0618840615665$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$A_{4}$$ Projective field: Galois closure of 4.0.15376.1 Artin image: $\SL(2,3):C_2$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{16} - \cdots)$$

Embedding invariants

 Embedding label 67.2 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 124.67 Dual form 124.1.i.a.87.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{14} -1.00000i q^{15} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.866025 + 0.500000i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(0.866025 + 0.500000i) q^{28} +1.00000 q^{30} -1.00000i q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} +1.00000i q^{35} +(-0.500000 + 0.866025i) q^{37} +(-0.500000 + 0.866025i) q^{38} +1.00000i q^{39} +(-0.866025 + 0.500000i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{42} +(0.866025 + 0.500000i) q^{43} +(0.866025 - 0.500000i) q^{44} +(0.866025 + 0.500000i) q^{48} +(-0.866025 + 0.500000i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +1.00000 q^{54} +(0.866025 + 0.500000i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 + 0.866025i) q^{57} +(-0.866025 - 0.500000i) q^{59} +1.00000i q^{60} +1.00000 q^{62} -1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} -1.00000i q^{66} +(-0.866025 + 0.500000i) q^{67} +(0.500000 - 0.866025i) q^{68} -1.00000 q^{70} +(0.866025 - 0.500000i) q^{71} +(-0.500000 - 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{74} +(-0.866025 - 0.500000i) q^{76} +1.00000 q^{77} -1.00000 q^{78} +(-0.866025 - 0.500000i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +(0.866025 - 0.500000i) q^{83} +(0.500000 + 0.866025i) q^{84} +1.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{88} -1.00000i q^{91} +(0.500000 - 0.866025i) q^{93} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} - 2 q^{5} - 2 q^{6}+O(q^{10})$$ 4 * q - 4 * q^4 - 2 * q^5 - 2 * q^6 $$4 q - 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{13} + 2 q^{14} + 4 q^{16} - 2 q^{17} + 2 q^{20} - 2 q^{21} - 2 q^{22} + 2 q^{24} + 4 q^{30} - 4 q^{33} - 2 q^{37} - 2 q^{38} - 2 q^{41} - 2 q^{52} + 2 q^{53} + 4 q^{54} - 2 q^{56} + 2 q^{57} + 4 q^{62} - 4 q^{64} + 2 q^{65} + 2 q^{68} - 4 q^{70} - 2 q^{73} + 4 q^{77} - 4 q^{78} - 2 q^{80} + 2 q^{81} + 2 q^{84} + 4 q^{85} - 2 q^{86} + 2 q^{88} + 2 q^{93} - 2 q^{96}+O(q^{100})$$ 4 * q - 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^13 + 2 * q^14 + 4 * q^16 - 2 * q^17 + 2 * q^20 - 2 * q^21 - 2 * q^22 + 2 * q^24 + 4 * q^30 - 4 * q^33 - 2 * q^37 - 2 * q^38 - 2 * q^41 - 2 * q^52 + 2 * q^53 + 4 * q^54 - 2 * q^56 + 2 * q^57 + 4 * q^62 - 4 * q^64 + 2 * q^65 + 2 * q^68 - 4 * q^70 - 2 * q^73 + 4 * q^77 - 4 * q^78 - 2 * q^80 + 2 * q^81 + 2 * q^84 + 4 * q^85 - 2 * q^86 + 2 * q^88 + 2 * q^93 - 2 * q^96

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$$.

 $$n$$ $$63$$ $$65$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 1.00000i
$$3$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$4$$ −1.00000 −1.00000
$$5$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$6$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$7$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ 0 0
$$10$$ 0.866025 0.500000i 0.866025 0.500000i
$$11$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$12$$ −0.866025 0.500000i −0.866025 0.500000i
$$13$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0.500000 0.866025i 0.500000 0.866025i
$$15$$ 1.00000i 1.00000i
$$16$$ 1.00000 1.00000
$$17$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$21$$ −0.500000 0.866025i −0.500000 0.866025i
$$22$$ −0.500000 0.866025i −0.500000 0.866025i
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0.500000 0.866025i 0.500000 0.866025i
$$25$$ 0 0
$$26$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$27$$ 1.00000i 1.00000i
$$28$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 1.00000 1.00000
$$31$$ 1.00000i 1.00000i
$$32$$ 1.00000i 1.00000i
$$33$$ −1.00000 −1.00000
$$34$$ −0.866025 0.500000i −0.866025 0.500000i
$$35$$ 1.00000i 1.00000i
$$36$$ 0 0
$$37$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$38$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$39$$ 1.00000i 1.00000i
$$40$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$41$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$42$$ 0.866025 0.500000i 0.866025 0.500000i
$$43$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0.866025 0.500000i 0.866025 0.500000i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$52$$ −0.500000 0.866025i −0.500000 0.866025i
$$53$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 1.00000 1.00000
$$55$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$56$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$57$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$58$$ 0 0
$$59$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 1.00000i 1.00000i
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 1.00000 1.00000
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0.500000 0.866025i 0.500000 0.866025i
$$66$$ 1.00000i 1.00000i
$$67$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0.500000 0.866025i 0.500000 0.866025i
$$69$$ 0 0
$$70$$ −1.00000 −1.00000
$$71$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ 0 0
$$73$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$74$$ −0.866025 0.500000i −0.866025 0.500000i
$$75$$ 0 0
$$76$$ −0.866025 0.500000i −0.866025 0.500000i
$$77$$ 1.00000 1.00000
$$78$$ −1.00000 −1.00000
$$79$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ −0.500000 0.866025i −0.500000 0.866025i
$$81$$ 0.500000 0.866025i 0.500000 0.866025i
$$82$$ 0.866025 0.500000i 0.866025 0.500000i
$$83$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$84$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$85$$ 1.00000 1.00000
$$86$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$87$$ 0 0
$$88$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 1.00000i 1.00000i
$$92$$ 0 0
$$93$$ 0.500000 0.866025i 0.500000 0.866025i
$$94$$ 0 0
$$95$$ 1.00000i 1.00000i
$$96$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ −0.500000 0.866025i −0.500000 0.866025i
$$103$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0.866025 0.500000i 0.866025 0.500000i
$$105$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$106$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$107$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$108$$ 1.00000i 1.00000i
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$111$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$112$$ −0.866025 0.500000i −0.866025 0.500000i
$$113$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$114$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0.500000 0.866025i 0.500000 0.866025i
$$119$$ 0.866025 0.500000i 0.866025 0.500000i
$$120$$ −1.00000 −1.00000
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 1.00000i 1.00000i
$$124$$ 1.00000i 1.00000i
$$125$$ −1.00000 −1.00000
$$126$$ 0 0
$$127$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$128$$ 1.00000i 1.00000i
$$129$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$130$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$131$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$132$$ 1.00000 1.00000
$$133$$ −0.500000 0.866025i −0.500000 0.866025i
$$134$$ −0.500000 0.866025i −0.500000 0.866025i
$$135$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$136$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$137$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 1.00000i 1.00000i
$$141$$ 0 0
$$142$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$143$$ −0.866025 0.500000i −0.866025 0.500000i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0.866025 0.500000i 0.866025 0.500000i
$$147$$ 0 0
$$148$$ 0.500000 0.866025i 0.500000 0.866025i
$$149$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0.500000 0.866025i 0.500000 0.866025i
$$153$$ 0 0
$$154$$ 1.00000i 1.00000i
$$155$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$156$$ 1.00000i 1.00000i
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0.500000 0.866025i 0.500000 0.866025i
$$159$$ 1.00000i 1.00000i
$$160$$ 0.866025 0.500000i 0.866025 0.500000i
$$161$$ 0 0
$$162$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$165$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$166$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$167$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$168$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$169$$ 0 0
$$170$$ 1.00000i 1.00000i
$$171$$ 0 0
$$172$$ −0.866025 0.500000i −0.866025 0.500000i
$$173$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$177$$ −0.500000 0.866025i −0.500000 0.866025i
$$178$$ 0 0
$$179$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$180$$ 0 0
$$181$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$182$$ 1.00000 1.00000
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.00000 1.00000
$$186$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$187$$ 1.00000i 1.00000i
$$188$$ 0 0
$$189$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$190$$ 1.00000 1.00000
$$191$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$192$$ −0.866025 0.500000i −0.866025 0.500000i
$$193$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0.866025 0.500000i 0.866025 0.500000i
$$196$$ 0 0
$$197$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$198$$ 0 0
$$199$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ 0 0
$$201$$ −1.00000 −1.00000
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0.866025 0.500000i 0.866025 0.500000i
$$205$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$206$$ −0.500000 0.866025i −0.500000 0.866025i
$$207$$ 0 0
$$208$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$209$$ −1.00000 −1.00000
$$210$$ −0.866025 0.500000i −0.866025 0.500000i
$$211$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$212$$ −0.500000 0.866025i −0.500000 0.866025i
$$213$$ 1.00000 1.00000
$$214$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$215$$ 1.00000i 1.00000i
$$216$$ −1.00000 −1.00000
$$217$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$218$$ 0 0
$$219$$ 1.00000i 1.00000i
$$220$$ −0.866025 0.500000i −0.866025 0.500000i
$$221$$ −1.00000 −1.00000
$$222$$ −0.500000 0.866025i −0.500000 0.866025i
$$223$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$224$$ 0.500000 0.866025i 0.500000 0.866025i
$$225$$ 0 0
$$226$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$227$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$228$$ −0.500000 0.866025i −0.500000 0.866025i
$$229$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$230$$ 0 0
$$231$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$237$$ −0.500000 0.866025i −0.500000 0.866025i
$$238$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$239$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$240$$ 1.00000i 1.00000i
$$241$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 1.00000 1.00000
$$247$$ 1.00000i 1.00000i
$$248$$ −1.00000 −1.00000
$$249$$ 1.00000 1.00000
$$250$$ 1.00000i 1.00000i
$$251$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$255$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$256$$ 1.00000 1.00000
$$257$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$259$$ 0.866025 0.500000i 0.866025 0.500000i
$$260$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$261$$ 0 0
$$262$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 1.00000i 1.00000i
$$265$$ 0.500000 0.866025i 0.500000 0.866025i
$$266$$ 0.866025 0.500000i 0.866025 0.500000i
$$267$$ 0 0
$$268$$ 0.866025 0.500000i 0.866025 0.500000i
$$269$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ −0.500000 0.866025i −0.500000 0.866025i
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$273$$ 0.500000 0.866025i 0.500000 0.866025i
$$274$$ 0.866025 0.500000i 0.866025 0.500000i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 1.00000 1.00000
$$281$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$285$$ 0.500000 0.866025i 0.500000 0.866025i
$$286$$ 0.500000 0.866025i 0.500000 0.866025i
$$287$$ 1.00000i 1.00000i
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$293$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$294$$ 0 0
$$295$$ 1.00000i 1.00000i
$$296$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$297$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$298$$ −0.866025 0.500000i −0.866025 0.500000i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −0.500000 0.866025i −0.500000 0.866025i
$$302$$ −2.00000 −2.00000
$$303$$ 0 0
$$304$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$308$$ −1.00000 −1.00000
$$309$$ −1.00000 −1.00000
$$310$$ −0.500000 0.866025i −0.500000 0.866025i
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 1.00000 1.00000
$$313$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$317$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$318$$ −1.00000 −1.00000
$$319$$ 0 0
$$320$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$321$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$322$$ 0 0
$$323$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$324$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$329$$ 0 0
$$330$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$331$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$332$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$333$$ 0 0
$$334$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$335$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$336$$ −0.500000 0.866025i −0.500000 0.866025i
$$337$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 1.00000i 1.00000i
$$340$$ −1.00000 −1.00000
$$341$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$342$$ 0 0
$$343$$ 1.00000i 1.00000i
$$344$$ 0.500000 0.866025i 0.500000 0.866025i
$$345$$ 0 0
$$346$$ 0.866025 0.500000i 0.866025 0.500000i
$$347$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0.866025 0.500000i 0.866025 0.500000i
$$352$$ −0.500000 0.866025i −0.500000 0.866025i
$$353$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$354$$ 0.866025 0.500000i 0.866025 0.500000i
$$355$$ −0.866025 0.500000i −0.866025 0.500000i
$$356$$ 0 0
$$357$$ 1.00000 1.00000
$$358$$ 0.500000 0.866025i 0.500000 0.866025i
$$359$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0.866025 0.500000i 0.866025 0.500000i
$$363$$ 0 0
$$364$$ 1.00000i 1.00000i
$$365$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$366$$ 0 0
$$367$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 1.00000i 1.00000i
$$371$$ 1.00000i 1.00000i
$$372$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$373$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$374$$ 1.00000 1.00000
$$375$$ −0.866025 0.500000i −0.866025 0.500000i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ −0.866025 0.500000i −0.866025 0.500000i
$$379$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$380$$ 1.00000i 1.00000i
$$381$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$382$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$383$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0.500000 0.866025i 0.500000 0.866025i
$$385$$ −0.500000 0.866025i −0.500000 0.866025i
$$386$$ −0.866025 0.500000i −0.866025 0.500000i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$390$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$394$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$395$$ 1.00000i 1.00000i
$$396$$ 0 0
$$397$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$398$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$399$$ 1.00000i 1.00000i
$$400$$ 0 0
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 1.00000i 1.00000i
$$403$$ 0.866025 0.500000i 0.866025 0.500000i
$$404$$ 0 0
$$405$$ −1.00000 −1.00000
$$406$$ 0 0
$$407$$ 1.00000i 1.00000i
$$408$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$409$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$410$$ −0.866025 0.500000i −0.866025 0.500000i
$$411$$ 1.00000i 1.00000i
$$412$$ 0.866025 0.500000i 0.866025 0.500000i
$$413$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$414$$ 0 0
$$415$$ −0.866025 0.500000i −0.866025 0.500000i
$$416$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$417$$ 0 0
$$418$$ 1.00000i 1.00000i
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0.500000 0.866025i 0.500000 0.866025i
$$421$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ 0.500000 0.866025i 0.500000 0.866025i
$$423$$ 0 0
$$424$$ 0.866025 0.500000i 0.866025 0.500000i
$$425$$ 0 0
$$426$$ 1.00000i 1.00000i
$$427$$ 0 0
$$428$$ −0.866025 0.500000i −0.866025 0.500000i
$$429$$ −0.500000 0.866025i −0.500000 0.866025i
$$430$$ 1.00000 1.00000
$$431$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.00000i 1.00000i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ −0.866025 0.500000i −0.866025 0.500000i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 1.00000 1.00000
$$439$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0.500000 0.866025i 0.500000 0.866025i
$$441$$ 0 0
$$442$$ 1.00000i 1.00000i
$$443$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0.866025 0.500000i 0.866025 0.500000i
$$445$$ 0 0
$$446$$ 0.500000 0.866025i 0.500000 0.866025i
$$447$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$448$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$449$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$452$$ −0.500000 0.866025i −0.500000 0.866025i
$$453$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$454$$ −0.500000 0.866025i −0.500000 0.866025i
$$455$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$456$$ 0.866025 0.500000i 0.866025 0.500000i
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$459$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ −1.00000 −1.00000
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 1.00000 1.00000
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$473$$ −1.00000 −1.00000
$$474$$ 0.866025 0.500000i 0.866025 0.500000i
$$475$$ 0 0
$$476$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$477$$ 0 0
$$478$$ −0.500000 0.866025i −0.500000 0.866025i
$$479$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$480$$ 1.00000 1.00000
$$481$$ −1.00000 −1.00000
$$482$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$492$$ 1.00000i 1.00000i
$$493$$ 0 0
$$494$$ −1.00000 −1.00000
$$495$$ 0 0
$$496$$ 1.00000i 1.00000i
$$497$$ −1.00000 −1.00000
$$498$$ 1.00000i 1.00000i
$$499$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$500$$ 1.00000 1.00000
$$501$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$502$$ 0.500000 0.866025i 0.500000 0.866025i
$$503$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −0.866025 0.500000i −0.866025 0.500000i
$$509$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$511$$ 1.00000i 1.00000i
$$512$$ 1.00000i 1.00000i
$$513$$ 0.500000 0.866025i 0.500000 0.866025i
$$514$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$515$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$516$$ −0.500000 0.866025i −0.500000 0.866025i
$$517$$ 0 0
$$518$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$519$$ 1.00000i 1.00000i
$$520$$ −0.866025 0.500000i −0.866025 0.500000i
$$521$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −0.866025 0.500000i −0.866025 0.500000i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$528$$ −1.00000 −1.00000
$$529$$ 1.00000 1.00000
$$530$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$531$$ 0 0
$$532$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$533$$ 0.500000 0.866025i 0.500000 0.866025i
$$534$$ 0 0
$$535$$ 1.00000i 1.00000i
$$536$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$537$$ −0.500000 0.866025i −0.500000 0.866025i
$$538$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$539$$ 0 0
$$540$$ 0.866025 0.500000i 0.866025 0.500000i
$$541$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 1.00000i 1.00000i
$$544$$ −0.866025 0.500000i −0.866025 0.500000i
$$545$$ 0 0
$$546$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$547$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$548$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$554$$ 0 0
$$555$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 1.00000i 1.00000i
$$560$$ 1.00000i 1.00000i
$$561$$ 0.500000 0.866025i 0.500000 0.866025i
$$562$$ 2.00000i 2.00000i
$$563$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$564$$ 0 0
$$565$$ 0.500000 0.866025i 0.500000 0.866025i
$$566$$ 0 0
$$567$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$568$$ −0.500000 0.866025i −0.500000 0.866025i
$$569$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$570$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$571$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$572$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$573$$ 1.00000 1.00000
$$574$$ −1.00000 −1.00000
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$578$$ 0 0
$$579$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$580$$ 0 0
$$581$$ −1.00000 −1.00000
$$582$$ 0 0
$$583$$ −0.866025 0.500000i −0.866025 0.500000i
$$584$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$585$$ 0 0
$$586$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$587$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0.500000 0.866025i 0.500000 0.866025i
$$590$$ −1.00000 −1.00000
$$591$$ 1.00000i 1.00000i
$$592$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$593$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$594$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$595$$ −0.866025 0.500000i −0.866025 0.500000i
$$596$$ 0.500000 0.866025i 0.500000 0.866025i
$$597$$ 1.00000 1.00000
$$598$$ 0 0
$$599$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$602$$ 0.866025 0.500000i 0.866025 0.500000i
$$603$$ 0 0
$$604$$ 2.00000i 2.00000i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$608$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$614$$ 0.500000 0.866025i 0.500000 0.866025i
$$615$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$616$$ 1.00000i 1.00000i
$$617$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$618$$ 1.00000i 1.00000i
$$619$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0.866025 0.500000i 0.866025 0.500000i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 1.00000i 1.00000i
$$625$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$626$$ −0.866025 0.500000i −0.866025 0.500000i
$$627$$ −0.866025 0.500000i −0.866025 0.500000i
$$628$$ 0 0
$$629$$ −0.500000 0.866025i −0.500000 0.866025i
$$630$$ 0 0
$$631$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$632$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$633$$ −0.500000 0.866025i −0.500000 0.866025i
$$634$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$635$$ 1.00000i 1.00000i
$$636$$ 1.00000i 1.00000i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$641$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0.500000 0.866025i 0.500000 0.866025i
$$646$$ −0.500000 0.866025i −0.500000 0.866025i
$$647$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$648$$ −0.866025 0.500000i −0.866025 0.500000i
$$649$$ 1.00000 1.00000
$$650$$ 0 0
$$651$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 1.00000i 1.00000i
$$656$$ −0.500000 0.866025i −0.500000 0.866025i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ −0.500000 0.866025i −0.500000 0.866025i
$$661$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$663$$ −0.866025 0.500000i −0.866025 0.500000i
$$664$$ −0.500000 0.866025i −0.500000 0.866025i
$$665$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −0.866025 0.500000i −0.866025 0.500000i
$$669$$ −0.500000 0.866025i −0.500000 0.866025i
$$670$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$671$$ 0 0
$$672$$ 0.866025 0.500000i 0.866025 0.500000i
$$673$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$674$$ 2.00000i 2.00000i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$678$$ −1.00000 −1.00000
$$679$$ 0 0
$$680$$ 1.00000i 1.00000i
$$681$$ −1.00000 −1.00000
$$682$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$686$$ −1.00000 −1.00000
$$687$$ 0.866025 0.500000i 0.866025 0.500000i
$$688$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$689$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$690$$ 0 0
$$691$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$693$$ 0 0
$$694$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.00000 1.00000
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$702$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$703$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$704$$ 0.866025 0.500000i 0.866025 0.500000i
$$705$$ 0 0
$$706$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$707$$ 0 0
$$708$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$709$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$710$$ 0.500000 0.866025i 0.500000 0.866025i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 1.00000i 1.00000i
$$715$$ 1.00000i 1.00000i
$$716$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$717$$ −1.00000 −1.00000
$$718$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$719$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 1.00000 1.00000
$$722$$ 0 0
$$723$$ 0.866025 0.500000i 0.866025 0.500000i
$$724$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$728$$ −1.00000 −1.00000
$$729$$ −1.00000 −1.00000
$$730$$ −0.866025 0.500000i −0.866025 0.500000i
$$731$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$732$$ 0 0
$$733$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$734$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0.500000 0.866025i 0.500000 0.866025i
$$738$$ 0 0
$$739$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$740$$ −1.00000 −1.00000
$$741$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$742$$ 1.00000 1.00000
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ −0.866025 0.500000i −0.866025 0.500000i
$$745$$ 1.00000 1.00000
$$746$$ 2.00000i 2.00000i
$$747$$ 0 0
$$748$$ 1.00000i 1.00000i
$$749$$ −0.500000 0.866025i −0.500000 0.866025i
$$750$$ 0.500000 0.866025i 0.500000 0.866025i
$$751$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ −0.500000 0.866025i −0.500000 0.866025i
$$754$$ 0 0
$$755$$ 1.73205 1.00000i 1.73205 1.00000i
$$756$$ 0.500000 0.866025i 0.500000 0.866025i
$$757$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$758$$ 0.500000 0.866025i 0.500000 0.866025i
$$759$$ 0 0
$$760$$ −1.00000 −1.00000
$$761$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$762$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$763$$ 0 0
$$764$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$765$$ 0 0
$$766$$ −0.500000 0.866025i −0.500000 0.866025i
$$767$$ 1.00000i 1.00000i
$$768$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$769$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$770$$ 0.866025 0.500000i 0.866025 0.500000i
$$771$$ 1.00000i 1.00000i
$$772$$ 0.500000 0.866025i 0.500000 0.866025i
$$773$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 1.00000 1.00000
$$778$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$779$$ 1.00000i 1.00000i
$$780$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$781$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$787$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$788$$ −0.500000 0.866025i −0.500000 0.866025i
$$789$$ 0 0