# Properties

 Label 99.1.h.a.76.1 Level $99$ Weight $1$ Character 99.76 Analytic conductor $0.049$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -11 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 99.h (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.0494074362507$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.891.1 Artin image: $C_3\times S_3$ Artin field: Galois closure of 6.0.107811.1

## Embedding invariants

 Embedding label 76.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 99.76 Dual form 99.1.h.a.43.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{20} +(-1.00000 + 1.73205i) q^{23} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{31} +1.00000 q^{33} +1.00000 q^{36} -1.00000 q^{37} +1.00000 q^{44} -1.00000 q^{45} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} -1.00000 q^{53} -1.00000 q^{55} +(0.500000 - 0.866025i) q^{59} -1.00000 q^{60} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{67} +(-1.00000 - 1.73205i) q^{69} -1.00000 q^{71} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +2.00000 q^{89} +(-1.00000 - 1.73205i) q^{92} +(0.500000 + 0.866025i) q^{93} +(0.500000 + 0.866025i) q^{97} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} - q^{4} + q^{5} - q^{9}+O(q^{10})$$ 2 * q - q^3 - q^4 + q^5 - q^9 $$2 q - q^{3} - q^{4} + q^{5} - q^{9} - q^{11} - q^{12} + q^{15} - q^{16} + q^{20} - 2 q^{23} + 2 q^{27} + q^{31} + 2 q^{33} + 2 q^{36} - 2 q^{37} + 2 q^{44} - 2 q^{45} + q^{47} + 2 q^{48} - q^{49} - 2 q^{53} - 2 q^{55} + q^{59} - 2 q^{60} + 2 q^{64} + q^{67} - 2 q^{69} - 2 q^{71} - 2 q^{80} - q^{81} + 4 q^{89} - 2 q^{92} + q^{93} + q^{97} - q^{99}+O(q^{100})$$ 2 * q - q^3 - q^4 + q^5 - q^9 - q^11 - q^12 + q^15 - q^16 + q^20 - 2 * q^23 + 2 * q^27 + q^31 + 2 * q^33 + 2 * q^36 - 2 * q^37 + 2 * q^44 - 2 * q^45 + q^47 + 2 * q^48 - q^49 - 2 * q^53 - 2 * q^55 + q^59 - 2 * q^60 + 2 * q^64 + q^67 - 2 * q^69 - 2 * q^71 - 2 * q^80 - q^81 + 4 * q^89 - 2 * q^92 + q^93 + q^97 - q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$3$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$4$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$5$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$6$$ 0 0
$$7$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.500000 0.866025i
$$10$$ 0 0
$$11$$ −0.500000 0.866025i −0.500000 0.866025i
$$12$$ −0.500000 0.866025i −0.500000 0.866025i
$$13$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0 0
$$15$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$16$$ −0.500000 0.866025i −0.500000 0.866025i
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 1.00000
$$28$$ 0 0
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$32$$ 0 0
$$33$$ 1.00000 1.00000
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$44$$ 1.00000 1.00000
$$45$$ −1.00000 −1.00000
$$46$$ 0 0
$$47$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$48$$ 1.00000 1.00000
$$49$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −1.00000
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$60$$ −1.00000 −1.00000
$$61$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$68$$ 0 0
$$69$$ −1.00000 1.73205i −1.00000 1.73205i
$$70$$ 0 0
$$71$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ −1.00000 −1.00000
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −1.00000 1.73205i −1.00000 1.73205i
$$93$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$98$$ 0 0
$$99$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$100$$ 0 0
$$101$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$102$$ 0 0
$$103$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0.500000 0.866025i 0.500000 0.866025i
$$112$$ 0 0
$$113$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$114$$ 0 0
$$115$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$125$$ 1.00000 1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.500000 0.866025i 0.500000 0.866025i
$$136$$ 0 0
$$137$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$140$$ 0 0
$$141$$ −1.00000 −1.00000
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.500000 0.866025i −0.500000 0.866025i
$$148$$ 0.500000 0.866025i 0.500000 0.866025i
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −0.500000 0.866025i −0.500000 0.866025i
$$156$$ 0 0
$$157$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$158$$ 0 0
$$159$$ 0.500000 0.866025i 0.500000 0.866025i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0.500000 0.866025i 0.500000 0.866025i
$$166$$ 0 0
$$167$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ −0.500000 0.866025i −0.500000 0.866025i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$177$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$178$$ 0 0
$$179$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ 0.500000 0.866025i 0.500000 0.866025i
$$181$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −1.00000 −1.00000
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$193$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.500000 0.866025i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ 0 0
$$201$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.00000 2.00000
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0.500000 0.866025i 0.500000 0.866025i
$$213$$ 0.500000 0.866025i 0.500000 0.866025i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0.500000 0.866025i 0.500000 0.866025i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0 0
$$229$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 1.00000 1.00000
$$236$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ 0.500000 0.866025i 0.500000 0.866025i
$$241$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.500000 0.866025i
$$244$$ 0 0
$$245$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$252$$ 0 0
$$253$$ 2.00000 2.00000
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$264$$ 0 0
$$265$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$266$$ 0 0
$$267$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$268$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$269$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 2.00000 2.00000
$$277$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −1.00000
$$280$$ 0 0
$$281$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$284$$ 0.500000 0.866025i 0.500000 0.866025i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ −1.00000 −1.00000
$$292$$ 0 0
$$293$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ −0.500000 0.866025i −0.500000 0.866025i
$$296$$ 0 0
$$297$$ −0.500000 0.866025i −0.500000 0.866025i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$310$$ 0 0
$$311$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$312$$ 0 0
$$313$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.500000 0.866025i 0.500000 0.866025i
$$321$$ 0 0
$$322$$ 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
$$330$$ 0 0
$$331$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 0 0
$$333$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$334$$ 0 0
$$335$$ −0.500000 0.866025i −0.500000 0.866025i
$$336$$ 0 0
$$337$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$338$$ 0 0
$$339$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$340$$ 0 0
$$341$$ −1.00000 −1.00000
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −2.00000 −2.00000
$$346$$ 0 0
$$347$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$354$$ 0 0
$$355$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$356$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ −0.500000 0.866025i −0.500000 0.866025i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$368$$ 2.00000 2.00000
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −1.00000 −1.00000
$$373$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 0 0
$$375$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −1.00000 −1.00000
$$389$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −0.500000 0.866025i −0.500000 0.866025i
$$397$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$406$$ 0 0
$$407$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$408$$ 0 0
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ −1.00000 −1.00000
$$412$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ 0 0
$$423$$ 0.500000 0.866025i 0.500000 0.866025i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −0.500000 0.866025i −0.500000 0.866025i
$$433$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$445$$ 1.00000 1.73205i 1.00000 1.73205i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −2.00000 −2.00000
$$461$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 0 0
$$463$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$464$$ 0 0
$$465$$ 1.00000 1.00000
$$466$$ 0 0
$$467$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.500000 0.866025i −0.500000 0.866025i
$$485$$ 1.00000 1.00000
$$486$$ 0 0
$$487$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$488$$ 0 0
$$489$$ 0.500000 0.866025i 0.500000 0.866025i
$$490$$ 0 0
$$491$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$492$$ 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
$$498$$ 0 0
$$499$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$500$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.00000 1.00000
$$508$$ 0 0
$$509$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −0.500000 0.866025i −0.500000 0.866025i
$$516$$ 0 0
$$517$$ 0.500000 0.866025i 0.500000 0.866025i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −0.500000 0.866025i −0.500000 0.866025i
$$529$$ −1.50000 2.59808i −1.50000 2.59808i
$$530$$ 0 0
$$531$$ −1.00000 −1.00000
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0.500000 0.866025i 0.500000 0.866025i
$$538$$ 0 0
$$539$$ 1.00000 1.00000
$$540$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0.500000 0.866025i 0.500000 0.866025i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$548$$ −1.00000 −1.00000
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −0.500000 0.866025i −0.500000 0.866025i
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0.500000 0.866025i 0.500000 0.866025i
$$565$$ −0.500000 0.866025i −0.500000 0.866025i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 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
$$573$$ −1.00000 −1.00000
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 1.00000 1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0.500000 0.866025i 0.500000 0.866025i
$$598$$ 0 0
$$599$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$602$$ 0 0
$$603$$ −1.00000 −1.00000
$$604$$ 0 0
$$605$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$606$$ 0 0
$$607$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$618$$ 0 0
$$619$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$620$$ 1.00000 1.00000
$$621$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.500000 0.866025i 0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$640$$ 0 0
$$641$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$642$$ 0 0
$$643$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$648$$ 0 0
$$649$$ −1.00000 −1.00000
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0.500000 0.866025i 0.500000 0.866025i
$$653$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$661$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 2.00000 2.00000
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$684$$ 0 0
$$685$$ 1.00000 1.00000
$$686$$ 0 0
$$687$$ −1.00000 1.73205i −1.00000 1.73205i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.500000 0.866025i −0.500000 0.866025i
$$705$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ −1.00000 −1.00000
$$709$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.500000 0.866025i 0.500000 0.866025i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$720$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0.500000 0.866025i 0.500000 0.866025i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ 0 0
$$735$$ −1.00000 −1.00000
$$736$$ 0 0
$$737$$ −1.00000 −1.00000
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ −0.500000 0.866025i −0.500000 0.866025i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$752$$ 0.500000 0.866025i 0.500000 0.866025i
$$753$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$758$$ 0 0
$$759$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$760$$ 0 0
$$761$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1.00000 −1.00000
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.500000 0.866025i −0.500000 0.866025i
$$769$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ −1.00000 1.73205i −1.00000 1.73205i
$$772$$ 0 0
$$773$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ −0.500000 0.866025i −0.500000 0.866025i
$$786$$ 0 0
$$787$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −0.500000 0.866025i −0.500000 0.866025i
$$796$$ 0.500000 0.866025i 0.500000 0.866025i
$$797$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −1.00000 1.73205i −1.00000 1.73205i
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −1.00000 −1.00000
$$805$$ 0 0