# Properties

 Label 1800.1.ba.c.499.1 Level 1800 Weight 1 Character 1800.499 Analytic conductor 0.898 Analytic rank 0 Dimension 4 Projective image $$D_{3}$$ CM disc. -8 Inner twists 8

# Related objects

## Newspace parameters

 Level: $$N$$ = $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 1800.ba (of order $$6$$ and degree $$2$$)

## Newform invariants

 Self dual: No Analytic conductor: $$0.898317022739$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Projective image $$D_{3}$$ Projective field Galois closure of 3.1.16200.1

## Embedding invariants

 Embedding label 499.1 Root $$0.866025 + 0.500000i$$ Character $$\chi$$ = 1800.499 Dual form 1800.1.ba.c.1699.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-0.500000 - 0.866025i) q^{16} +1.00000i q^{17} +(-0.866025 - 0.500000i) q^{18} -2.00000 q^{19} +(-0.866025 - 0.500000i) q^{22} +(0.500000 - 0.866025i) q^{24} -1.00000i q^{27} +(0.866025 + 0.500000i) q^{32} -1.00000i q^{33} +(-0.500000 - 0.866025i) q^{34} +1.00000 q^{36} +(1.73205 - 1.00000i) q^{38} +(-1.00000 + 1.73205i) q^{41} +(-0.866025 + 0.500000i) q^{43} +1.00000 q^{44} +1.00000i q^{48} +(0.500000 - 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{51} +(0.500000 + 0.866025i) q^{54} +(1.73205 + 1.00000i) q^{57} +(-0.500000 + 0.866025i) q^{59} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(1.73205 + 1.00000i) q^{67} +(0.866025 + 0.500000i) q^{68} +(-0.866025 + 0.500000i) q^{72} +2.00000i q^{73} +(-1.00000 + 1.73205i) q^{76} +(-0.500000 + 0.866025i) q^{81} -2.00000i q^{82} +(-0.866025 + 0.500000i) q^{83} +(0.500000 - 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{88} +1.00000 q^{89} +(-0.500000 - 0.866025i) q^{96} +(0.866025 - 0.500000i) q^{97} +1.00000i q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} + 4q^{6} + 2q^{9} + 2q^{11} - 2q^{16} - 8q^{19} + 2q^{24} - 2q^{34} + 4q^{36} - 4q^{41} + 4q^{44} + 2q^{49} + 2q^{51} + 2q^{54} - 2q^{59} - 4q^{64} + 2q^{66} - 4q^{76} - 2q^{81} + 2q^{86} + 4q^{89} - 2q^{96} - 2q^{99} + O(q^{100})$$

## Character Values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$901$$ $$1001$$ $$1351$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

## 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 0
$$6$$ 1.00000 1.00000
$$7$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$13$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.500000 0.866025i
$$17$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ −0.866025 0.500000i −0.866025 0.500000i
$$19$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.866025 0.500000i −0.866025 0.500000i
$$23$$ 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 0
$$26$$ 0 0
$$27$$ 1.00000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$33$$ 1.00000i 1.00000i
$$34$$ −0.500000 0.866025i −0.500000 0.866025i
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 1.73205 1.00000i 1.73205 1.00000i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$42$$ 0 0
$$43$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$44$$ 1.00000 1.00000
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 1.00000i 1.00000i
$$49$$ 0.500000 0.866025i 0.500000 0.866025i
$$50$$ 0 0
$$51$$ 0.500000 0.866025i 0.500000 0.866025i
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$58$$ 0 0
$$59$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$60$$ 0 0
$$61$$ 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
$$66$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$67$$ 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$68$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$73$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ 2.00000i 2.00000i
$$83$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.500000 0.866025i 0.500000 0.866025i
$$87$$ 0 0
$$88$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$89$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.500000 0.866025i −0.500000 0.866025i
$$97$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$98$$ 1.00000i 1.00000i
$$99$$ −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 $$0.333333\pi$$
$$102$$ 1.00000i 1.00000i
$$103$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$108$$ −0.866025 0.500000i −0.866025 0.500000i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$114$$ −2.00000 −2.00000
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 1.00000i 1.00000i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 1.73205 1.00000i 1.73205 1.00000i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.866025 0.500000i 0.866025 0.500000i
$$129$$ 1.00000 1.00000
$$130$$ 0 0
$$131$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ −0.866025 0.500000i −0.866025 0.500000i
$$133$$ 0 0
$$134$$ −2.00000 −2.00000
$$135$$ 0 0
$$136$$ −1.00000 −1.00000
$$137$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$138$$ 0 0
$$139$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.500000 0.866025i
$$145$$ 0 0
$$146$$ −1.00000 1.73205i −1.00000 1.73205i
$$147$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$148$$ 0 0
$$149$$ 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 $$0.333333\pi$$
$$152$$ 2.00000i 2.00000i
$$153$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000i 1.00000i
$$163$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$164$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$165$$ 0 0
$$166$$ 0.500000 0.866025i 0.500000 0.866025i
$$167$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$168$$ 0 0
$$169$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$170$$ 0 0
$$171$$ −1.00000 1.73205i −1.00000 1.73205i
$$172$$ 1.00000i 1.00000i
$$173$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.500000 0.866025i 0.500000 0.866025i
$$177$$ 0.866025 0.500000i 0.866025 0.500000i
$$178$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$179$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$193$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$194$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.500000 0.866025i
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 1.00000i 1.00000i
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ −1.00000 1.73205i −1.00000 1.73205i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.500000 0.866025i −0.500000 0.866025i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1.00000 1.73205i −1.00000 1.73205i
$$210$$ 0 0
$$211$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 1.00000 1.73205i 1.00000 1.73205i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1.00000 −1.00000
$$227$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 1.73205 1.00000i 1.73205 1.00000i
$$229$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 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 0
$$241$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$242$$ 0 0
$$243$$ 0.866025 0.500000i 0.866025 0.500000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 1.00000 1.00000
$$250$$ 0 0
$$251$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 2.00000i 2.00000i
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 1.00000 1.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.866025 0.500000i −0.866025 0.500000i
$$268$$ 1.73205 1.00000i 1.73205 1.00000i
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0.866025 0.500000i 0.866025 0.500000i
$$273$$ 0 0
$$274$$ 1.00000 1.73205i 1.00000 1.73205i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$278$$ 1.00000i 1.00000i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$282$$ 0 0
$$283$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 1.00000i
$$289$$ 0 0
$$290$$ 0 0
$$291$$ −1.00000 −1.00000
$$292$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$293$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$294$$ 0.500000 0.866025i 0.500000 0.866025i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.866025 0.500000i 0.866025 0.500000i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$305$$ 0 0
$$306$$ 0.500000 0.866025i 0.500000 0.866025i
$$307$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$322$$ 0 0
$$323$$ 2.00000i 2.00000i
$$324$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$327$$ 0 0
$$328$$ −1.73205 1.00000i −1.73205 1.00000i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 1.00000i 1.00000i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$338$$ −0.866025 0.500000i −0.866025 0.500000i
$$339$$ −0.500000 0.866025i −0.500000 0.866025i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$343$$ 0 0
$$344$$ −0.500000 0.866025i −0.500000 0.866025i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 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
$$352$$ 1.00000i 1.00000i
$$353$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$354$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$355$$ 0 0
$$356$$ 0.500000 0.866025i 0.500000 0.866025i
$$357$$ 0 0
$$358$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 3.00000 3.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −2.00000
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$374$$ 0.500000 0.866025i 0.500000 0.866025i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ −1.00000 −1.00000
$$385$$ 0 0
$$386$$ −1.00000 −1.00000
$$387$$ −0.866025 0.500000i −0.866025 0.500000i
$$388$$ 1.00000i 1.00000i
$$389$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$393$$ 1.73205 1.00000i 1.73205 1.00000i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 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 $$0$$
$$402$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$409$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$410$$ 0 0
$$411$$ 2.00000 2.00000
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.866025 0.500000i 0.866025 0.500000i
$$418$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$419$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$422$$ 1.00000i 1.00000i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1.73205 1.00000i −1.73205 1.00000i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$433$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 2.00000i 2.00000i
$$439$$ 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
$$443$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ −2.00000 −2.00000
$$452$$ 0.866025 0.500000i 0.866025 0.500000i
$$453$$ 0 0
$$454$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$455$$ 0 0
$$456$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$457$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$458$$ 0 0
$$459$$ 1.00000 1.00000
$$460$$ 0 0
$$461$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$467$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.866025 0.500000i −0.866025 0.500000i
$$473$$ −0.866025 0.500000i −0.866025 0.500000i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$490$$ 0 0
$$491$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$492$$ 2.00000i 2.00000i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$499$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.00000i 1.00000i
$$508$$ 0 0
$$509$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 1.00000i
$$513$$ 2.00000i 2.00000i
$$514$$ 1.00000 1.00000
$$515$$ 0 0
$$516$$ 0.500000 0.866025i 0.500000 0.866025i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$524$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$529$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ −1.00000 −1.00000
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 1.00000 1.00000
$$535$$ 0 0
$$536$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$537$$ −0.866025 0.500000i −0.866025 0.500000i
$$538$$ 0 0
$$539$$ 1.00000 1.00000
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$548$$ 2.00000i 2.00000i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 1.00000 1.00000
$$562$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$563$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −1.00000 −1.00000
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$-1.00000\pi$$
$$570$$ 0 0
$$571$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$578$$ 0 0
$$579$$ −0.500000 0.866025i −0.500000 0.866025i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0.866025 0.500000i 0.866025 0.500000i
$$583$$ 0 0
$$584$$ −2.00000 −2.00000
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$588$$ 1.00000i 1.00000i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$594$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 2.00000i 2.00000i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$608$$ −1.73205 1.00000i −1.73205 1.00000i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 1.00000i 1.00000i
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ −0.500000 0.866025i −0.500000 0.866025i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$618$$ 0 0
$$619$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$-1.00000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0.500000 0.866025i 0.500000 0.866025i
$$627$$ 2.00000i 2.00000i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 2.00000i 2.00000i
$$643$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$647$$ 0 0 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 0
$$652$$ −0.866025 0.500000i −0.866025 0.500000i
$$653$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 2.00000 2.00000
$$657$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$658$$ 0 0
$$659$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$-1.00000\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ −0.866025 0.500000i −0.866025 0.500000i
$$663$$ 0 0
$$664$$ −0.500000 0.866025i −0.500000 0.866025i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i $$-0.166667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$674$$ 1.00000 1.00000
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$678$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −1.00000 −1.00000
$$682$$ 0 0
$$683$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ −2.00000 −2.00000
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$689$$ 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
$$694$$ 1.00000 1.00000
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.73205 1.00000i −1.73205 1.00000i
$$698$$ 0 0
$$699$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$700$$ 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 0
$$706$$ 0.500000 0.866025i 0.500000 0.866025i
$$707$$ 0 0
$$708$$ 1.00000i 1.00000i
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 1.00000i 1.00000i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.500000 0.866025i 0.500000 0.866025i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −2.59808 + 1.50000i −2.59808 + 1.50000i
$$723$$ 2.00000i 2.00000i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ −0.500000 0.866025i −0.500000 0.866025i
$$732$$ 0 0
$$733$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.00000i 2.00000i
$$738$$ 1.73205 1.00000i 1.73205 1.00000i
$$739$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −0.866025 0.500000i −0.866025 0.500000i
$$748$$ 1.00000i 1.00000i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0 0
$$753$$ −1.73205 1.00000i −1.73205 1.00000i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.866025 0.500000i 0.866025 0.500000i
$$769$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$770$$ 0 0
$$771$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$772$$ 0.866025 0.500000i 0.866025 0.500000i
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 1.00000 1.00000
$$775$$ 0 0
$$776$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 2.00000 3.46410i 2.00000 3.46410i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 0 0
$$786$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$787$$ 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −0.866025 0.500000i −0.866025 0.500000i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$802$$ 1.00000i 1.00000i
$$803$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$804$$ −2.00000 −2.00000
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$810$$ 0 0
$$811$$ −1.00000