# Properties

 Label 2001.1.i.c.1931.2 Level 2001 Weight 1 Character 2001.1931 Analytic conductor 0.999 Analytic rank 0 Dimension 4 Projective image $$D_{12}$$ CM discriminant -23 Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ = $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2001.i (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.998629090279$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{12})$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image $$D_{12}$$ Projective field Galois closure of $$\mathbb{Q}[x]/(x^{12} - \cdots)$$

## Embedding invariants

 Embedding label 1931.2 Root $$-0.866025 - 0.500000i$$ Character $$\chi$$ = 2001.1931 Dual form 2001.1.i.c.1172.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 0.366025i) q^{2} +(-0.866025 + 0.500000i) q^{3} -0.732051i q^{4} +(-0.500000 - 0.133975i) q^{6} +(0.633975 - 0.633975i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.366025 + 0.366025i) q^{2} +(-0.866025 + 0.500000i) q^{3} -0.732051i q^{4} +(-0.500000 - 0.133975i) q^{6} +(0.633975 - 0.633975i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{12} +1.00000i q^{13} -0.267949 q^{16} +(0.500000 - 0.133975i) q^{18} -1.00000i q^{23} +(-0.232051 + 0.866025i) q^{24} +1.00000 q^{25} +(-0.366025 + 0.366025i) q^{26} +1.00000i q^{27} +(-0.866025 - 0.500000i) q^{29} +(1.36603 - 1.36603i) q^{31} +(-0.732051 - 0.732051i) q^{32} +(-0.633975 - 0.366025i) q^{36} +(-0.500000 - 0.866025i) q^{39} +(1.36603 - 1.36603i) q^{41} +(0.366025 - 0.366025i) q^{46} +(0.366025 - 0.366025i) q^{47} +(0.232051 - 0.133975i) q^{48} +1.00000 q^{49} +(0.366025 + 0.366025i) q^{50} +0.732051 q^{52} +(-0.366025 + 0.366025i) q^{54} +(-0.133975 - 0.500000i) q^{58} +2.00000i q^{59} +1.00000 q^{62} -0.267949i q^{64} +(0.500000 + 0.866025i) q^{69} -1.73205 q^{71} +(-0.232051 - 0.866025i) q^{72} +(1.36603 + 1.36603i) q^{73} +(-0.866025 + 0.500000i) q^{75} +(0.133975 - 0.500000i) q^{78} +(-0.500000 - 0.866025i) q^{81} +1.00000 q^{82} +1.00000 q^{87} -0.732051 q^{92} +(-0.500000 + 1.86603i) q^{93} +0.267949 q^{94} +(1.00000 + 0.267949i) q^{96} +(0.366025 + 0.366025i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10})$$ $$4q - 2q^{2} - 2q^{6} + 6q^{8} + 2q^{9} - 2q^{12} - 8q^{16} + 2q^{18} + 6q^{24} + 4q^{25} + 2q^{26} + 2q^{31} + 4q^{32} - 6q^{36} - 2q^{39} + 2q^{41} - 2q^{46} - 2q^{47} - 6q^{48} + 4q^{49} - 2q^{50} - 4q^{52} + 2q^{54} - 4q^{58} + 4q^{62} + 2q^{69} + 6q^{72} + 2q^{73} + 4q^{78} - 2q^{81} + 4q^{82} + 4q^{87} + 4q^{92} - 2q^{93} + 8q^{94} + 4q^{96} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$$.

 $$n$$ $$553$$ $$668$$ $$1132$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 0.366025i 0.366025 + 0.366025i 0.866025 0.500000i $$-0.166667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$3$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$4$$ 0.732051i 0.732051i
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ −0.500000 0.133975i −0.500000 0.133975i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0.633975 0.633975i 0.633975 0.633975i
$$9$$ 0.500000 0.866025i 0.500000 0.866025i
$$10$$ 0 0
$$11$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$12$$ 0.366025 + 0.633975i 0.366025 + 0.633975i
$$13$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.267949 −0.267949
$$17$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$18$$ 0.500000 0.133975i 0.500000 0.133975i
$$19$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.00000i 1.00000i
$$24$$ −0.232051 + 0.866025i −0.232051 + 0.866025i
$$25$$ 1.00000 1.00000
$$26$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$27$$ 1.00000i 1.00000i
$$28$$ 0 0
$$29$$ −0.866025 0.500000i −0.866025 0.500000i
$$30$$ 0 0
$$31$$ 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i $$-0.333333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$32$$ −0.732051 0.732051i −0.732051 0.732051i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.633975 0.366025i −0.633975 0.366025i
$$37$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$38$$ 0 0
$$39$$ −0.500000 0.866025i −0.500000 0.866025i
$$40$$ 0 0
$$41$$ 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i $$-0.333333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0.366025 0.366025i 0.366025 0.366025i
$$47$$ 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i $$-0.666667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0.232051 0.133975i 0.232051 0.133975i
$$49$$ 1.00000 1.00000
$$50$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$51$$ 0 0
$$52$$ 0.732051 0.732051
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −0.133975 0.500000i −0.133975 0.500000i
$$59$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$62$$ 1.00000 1.00000
$$63$$ 0 0
$$64$$ 0.267949i 0.267949i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$70$$ 0 0
$$71$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ −0.232051 0.866025i −0.232051 0.866025i
$$73$$ 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i $$0.166667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$74$$ 0 0
$$75$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0.133975 0.500000i 0.133975 0.500000i
$$79$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.500000 0.866025i
$$82$$ 1.00000 1.00000
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.00000 1.00000
$$88$$ 0 0
$$89$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.732051 −0.732051
$$93$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$94$$ 0.267949 0.267949
$$95$$ 0 0
$$96$$ 1.00000 + 0.267949i 1.00000 + 0.267949i
$$97$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$98$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$99$$ 0 0
$$100$$ 0.732051i 0.732051i
$$101$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0.633975 + 0.633975i 0.633975 + 0.633975i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0.732051 0.732051
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −0.366025 + 0.633975i −0.366025 + 0.633975i
$$117$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$118$$ −0.732051 + 0.732051i −0.732051 + 0.732051i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000i 1.00000i
$$122$$ 0 0
$$123$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$124$$ −1.00000 1.00000i −1.00000 1.00000i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$128$$ −0.633975 + 0.633975i −0.633975 + 0.633975i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i $$-0.333333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$138$$ −0.133975 + 0.500000i −0.133975 + 0.500000i
$$139$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$140$$ 0 0
$$141$$ −0.133975 + 0.500000i −0.133975 + 0.500000i
$$142$$ −0.633975 0.633975i −0.633975 0.633975i
$$143$$ 0 0
$$144$$ −0.133975 + 0.232051i −0.133975 + 0.232051i
$$145$$ 0 0
$$146$$ 1.00000i 1.00000i
$$147$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ −0.500000 0.133975i −0.500000 0.133975i
$$151$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.633975 + 0.366025i −0.633975 + 0.366025i
$$157$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0.133975 0.500000i 0.133975 0.500000i
$$163$$ 0.366025 + 0.366025i 0.366025 + 0.366025i 0.866025 0.500000i $$-0.166667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ −1.00000 1.00000i −1.00000 1.00000i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$174$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1.00000 1.73205i −1.00000 1.73205i
$$178$$ 0 0
$$179$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −0.633975 0.633975i −0.633975 0.633975i
$$185$$ 0 0
$$186$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$187$$ 0 0
$$188$$ −0.267949 0.267949i −0.267949 0.267949i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$192$$ 0.133975 + 0.232051i 0.133975 + 0.232051i
$$193$$ −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.732051i 0.732051i
$$197$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0.633975 0.633975i 0.633975 0.633975i
$$201$$ 0 0
$$202$$ 0.732051i 0.732051i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −0.866025 0.500000i −0.866025 0.500000i
$$208$$ 0.267949i 0.267949i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 1.50000 0.866025i 1.50000 0.866025i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0.633975 + 0.633975i 0.633975 + 0.633975i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.86603 0.500000i −1.86603 0.500000i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0.500000 0.866025i 0.500000 0.866025i
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −0.866025 + 0.232051i −0.866025 + 0.232051i
$$233$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$234$$ 0.133975 + 0.500000i 0.133975 + 0.500000i
$$235$$ 0 0
$$236$$ 1.46410 1.46410
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$243$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$247$$ 0 0
$$248$$ 1.73205i 1.73205i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −0.267949 −0.267949
$$255$$ 0 0
$$256$$ −0.732051 −0.732051
$$257$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$262$$ 1.00000 1.00000
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i $$-0.666667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$270$$ 0 0
$$271$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0.633975 0.366025i 0.633975 0.366025i
$$277$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$278$$ −0.633975 0.633975i −0.633975 0.633975i
$$279$$ −0.500000 1.86603i −0.500000 1.86603i
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ −0.232051 + 0.133975i −0.232051 + 0.133975i
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 1.26795i 1.26795i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 + 0.267949i −1.00000 + 0.267949i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.00000 1.00000i 1.00000 1.00000i
$$293$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$294$$ −0.500000 0.133975i −0.500000 0.133975i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.00000 1.00000
$$300$$ 0.366025 + 0.633975i 0.366025 + 0.633975i
$$301$$ 0 0
$$302$$ 0.366025 0.366025i 0.366025 0.366025i
$$303$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i $$0.166667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ −0.866025 0.232051i −0.866025 0.232051i
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.633975 + 0.366025i −0.633975 + 0.366025i
$$325$$ 1.00000i 1.00000i
$$326$$ 0.267949i 0.267949i
$$327$$ 0 0
$$328$$ 1.73205i 1.73205i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.36603 1.36603i −1.36603 1.36603i −0.866025 0.500000i $$-0.833333\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −0.732051 0.732051i −0.732051 0.732051i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0.732051 + 0.732051i 0.732051 + 0.732051i
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0.732051i 0.732051i
$$349$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −1.00000
$$352$$ 0 0
$$353$$ −1.73205 −1.73205 −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ 0.267949 1.00000i 0.267949 1.00000i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −0.366025 0.366025i −0.366025 0.366025i
$$359$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$360$$ 0 0
$$361$$ 1.00000i 1.00000i
$$362$$ 0 0
$$363$$ −0.500000 0.866025i −0.500000 0.866025i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$368$$ 0.267949i 0.267949i
$$369$$ −0.500000 1.86603i −0.500000 1.86603i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0.464102i 0.464102i
$$377$$ 0.500000 0.866025i 0.500000 0.866025i
$$378$$ 0 0
$$379$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$380$$ 0 0
$$381$$ 0.133975 0.500000i 0.133975 0.500000i
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0.232051 0.866025i 0.232051 0.866025i
$$385$$ 0 0
$$386$$ −0.267949 −0.267949
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.633975 0.633975i 0.633975 0.633975i
$$393$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$394$$ −0.633975 + 0.633975i −0.633975 + 0.633975i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.267949 −0.267949
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 1.36603 + 1.36603i 1.36603 + 1.36603i
$$404$$ −0.732051 + 0.732051i −0.732051 + 0.732051i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −1.36603 + 1.36603i −1.36603 + 1.36603i −0.500000 + 0.866025i $$0.666667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −0.133975 0.500000i −0.133975 0.500000i
$$415$$ 0 0
$$416$$ 0.732051 0.732051i 0.732051 0.732051i
$$417$$ 1.50000 0.866025i 1.50000 0.866025i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$422$$ 0.732051i 0.732051i
$$423$$ −0.133975 0.500000i −0.133975 0.500000i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0.866025 + 0.232051i 0.866025 + 0.232051i
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0.267949i 0.267949i
$$433$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −0.500000 0.866025i −0.500000 0.866025i
$$439$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ 0.500000 0.866025i 0.500000 0.866025i
$$442$$ 0 0
$$443$$ −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −0.732051 0.732051i −0.732051 0.732051i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$450$$ 0.500000 0.133975i 0.500000 0.133975i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −1.36603 + 1.36603i −1.36603 + 1.36603i −0.500000 + 0.866025i $$0.666667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$462$$ 0 0
$$463$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$464$$ 0.232051 + 0.133975i 0.232051 + 0.133975i
$$465$$ 0 0
$$466$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$467$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$468$$ 0.366025 0.633975i 0.366025 0.633975i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.26795 + 1.26795i 1.26795 + 1.26795i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −0.633975 + 0.633975i −0.633975 + 0.633975i
$$479$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0.732051 0.732051
$$485$$ 0 0
$$486$$ 0.133975 + 0.500000i 0.133975 + 0.500000i
$$487$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$488$$ 0 0
$$489$$ −0.500000 0.133975i −0.500000 0.133975i
$$490$$ 0 0
$$491$$ 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i $$-0.666667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$492$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$500$$ 0 0
$$501$$ 1.73205 1.00000i 1.73205 1.00000i
$$502$$ 0 0
$$503$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0.267949 + 0.267949i 0.267949 + 0.267949i
$$509$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$513$$ 0 0
$$514$$ −0.633975 + 0.633975i −0.633975 + 0.633975i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ −0.500000 0.133975i −0.500000 0.133975i
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −1.00000 1.00000i −1.00000 1.00000i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$532$$ 0 0
$$533$$ 1.36603 + 1.36603i 1.36603 + 1.36603i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0.866025 0.500000i 0.866025 0.500000i
$$538$$ 0.267949 0.267949
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i $$-0.333333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$542$$ 0.732051i 0.732051i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0.866025 + 0.232051i 0.866025 + 0.232051i
$$553$$ 0 0
$$554$$ −0.366025 0.366025i −0.366025 0.366025i
$$555$$ 0 0
$$556$$ 1.26795i 1.26795i
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0.500000 0.866025i 0.500000 0.866025i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$564$$ 0.366025 + 0.0980762i 0.366025 + 0.0980762i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −1.09808 + 1.09808i −1.09808 + 1.09808i
$$569$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.00000i 1.00000i
$$576$$ −0.232051 0.133975i −0.232051 0.133975i
$$577$$ 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i $$0.166667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$578$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$579$$ 0.133975 0.500000i 0.133975 0.500000i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 1.73205 1.73205
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 0.366025 + 0.633975i 0.366025 + 0.633975i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −0.866025 1.50000i −0.866025 1.50000i
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$599$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$600$$ −0.232051 + 0.866025i −0.232051 + 0.866025i
$$601$$ −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −0.732051 −0.732051
$$605$$ 0 0
$$606$$ 0.366025 + 0.633975i 0.366025 + 0.633975i
$$607$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ −0.732051 −0.732051
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$620$$ 0 0
$$621$$ 1.00000 1.00000
$$622$$ 1.00000i 1.00000i
$$623$$ 0 0
$$624$$ 0.133975 + 0.232051i 0.133975 + 0.232051i
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$634$$ 0.732051 0.732051
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.00000i 1.00000i
$$638$$ 0 0
$$639$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$640$$ 0 0
$$641$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ −0.866025 0.232051i −0.866025 0.232051i
$$649$$ 0 0
$$650$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$651$$ 0 0
$$652$$ 0.267949 0.267949i 0.267949 0.267949i
$$653$$ −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$657$$ 1.86603 0.500000i 1.86603 0.500000i
$$658$$ 0 0
$$659$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 1.00000i 1.00000i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$668$$ 1.46410i 1.46410i
$$669$$ 1.73205 1.00000i 1.73205 1.00000i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$674$$ 0 0
$$675$$ 1.00000i 1.00000i
$$676$$ 0 0
$$677$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 1.46410i 1.46410i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0.633975 0.633975i 0.633975 0.633975i
$$697$$ 0 0
$$698$$ −0.366025 0.366025i −0.366025 0.366025i
$$699$$ −0.500000 0.866025i −0.500000 0.866025i
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ −0.366025 0.366025i −0.366025 0.366025i
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −0.633975 0.633975i −0.633975 0.633975i
$$707$$ 0 0
$$708$$ −1.26795 + 0.732051i −1.26795 + 0.732051i
$$709$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1.36603 1.36603i −1.36603 1.36603i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.732051i 0.732051i
$$717$$ −0.866025 1.50000i −0.866025 1.50000i
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.366025 0.366025i 0.366025 0.366025i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −0.866025 0.500000i −0.866025 0.500000i
$$726$$ 0.133975 0.500000i 0.133975 0.500000i
$$727$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −0.732051 + 0.732051i −0.732051 + 0.732051i
$$737$$ 0 0
$$738$$ 0.500000 0.866025i 0.500000 0.866025i
$$739$$ 1.36603 1.36603i 1.36603 1.36603i 0.500000 0.866025i $$-0.333333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$744$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$752$$ −0.0980762 + 0.0980762i −0.0980762 + 0.0980762i
$$753$$ 0 0
$$754$$ 0.500000 0.133975i 0.500000 0.133975i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$762$$ 0.232051 0.133975i 0.232051 0.133975i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −2.00000 −2.00000
$$768$$ 0.633975 0.366025i 0.633975 0.366025i
$$769$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$770$$ 0 0
$$771$$ −0.866025 1.50000i −0.866025 1.50000i
$$772$$ 0.267949 + 0.267949i 0.267949 + 0.267949i
$$773$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$774$$ 0 0
$$775$$ 1.36603 1.36603i 1.36603 1.36603i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0.500000 0.866025i 0.500000 0.866025i
$$784$$ −0.267949 −0.267949
$$785$$ 0 0
$$786$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 1.26795 1.26795
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0.633975 + 0.633975i 0.633975 + 0.633975i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −0.732051 0.732051i −0.732051 0.732051i
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 1.00000i 1.00000i
$$807$$ −0.133975 + 0.500000i −0.133975 + 0.500000i
$$808$$ −1.26795 −1.26795
$$809$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$