# Properties

 Label 1560.1.cs.b.1403.2 Level $1560$ Weight $1$ Character 1560.1403 Analytic conductor $0.779$ Analytic rank $0$ Dimension $4$ Projective image $D_{4}$ CM discriminant -104 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1560.cs (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.778541419707$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ x^4 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{4}$$ Projective field: Galois closure of 4.2.1521000.2

## Embedding invariants

 Embedding label 1403.2 Root $$-0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1560.1403 Dual form 1560.1.cs.b.467.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +1.00000 q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +1.00000 q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000i q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-1.00000 - 1.00000i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-0.707107 - 0.707107i) q^{20} +(-0.707107 + 0.707107i) q^{24} -1.00000i q^{25} +1.00000i q^{26} +1.00000 q^{27} -1.00000 q^{30} -1.41421 q^{31} +(-0.707107 - 0.707107i) q^{32} -1.41421i q^{34} +1.00000i q^{36} +(1.41421 - 1.41421i) q^{37} +(0.707107 + 0.707107i) q^{39} -1.00000i q^{40} +(1.00000 + 1.00000i) q^{43} +(-0.707107 + 0.707107i) q^{45} -1.00000 q^{48} +1.00000i q^{49} +(0.707107 - 0.707107i) q^{50} +(-1.00000 - 1.00000i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(0.707107 + 0.707107i) q^{54} +(-0.707107 - 0.707107i) q^{60} +(-1.00000 - 1.00000i) q^{62} -1.00000i q^{64} -1.00000 q^{65} +(1.00000 - 1.00000i) q^{68} -1.41421i q^{71} +(-0.707107 + 0.707107i) q^{72} +2.00000 q^{74} -1.00000i q^{75} +1.00000i q^{78} +(0.707107 - 0.707107i) q^{80} +1.00000 q^{81} +1.41421 q^{85} +1.41421i q^{86} -1.00000 q^{90} -1.41421 q^{93} +(-0.707107 - 0.707107i) q^{96} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{3} + 4 q^{9}+O(q^{10})$$ 4 * q + 4 * q^3 + 4 * q^9 $$4 q + 4 q^{3} + 4 q^{9} - 4 q^{10} - 4 q^{16} - 4 q^{17} + 4 q^{27} - 4 q^{30} + 4 q^{43} - 4 q^{48} - 4 q^{51} - 4 q^{62} - 4 q^{65} + 4 q^{68} + 8 q^{74} + 4 q^{81} - 4 q^{90}+O(q^{100})$$ 4 * q + 4 * q^3 + 4 * q^9 - 4 * q^10 - 4 * q^16 - 4 * q^17 + 4 * q^27 - 4 * q^30 + 4 * q^43 - 4 * q^48 - 4 * q^51 - 4 * q^62 - 4 * q^65 + 4 * q^68 + 8 * q^74 + 4 * q^81 - 4 * q^90

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$$.

 $$n$$ $$391$$ $$521$$ $$781$$ $$937$$ $$1081$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$3$$ 1.00000 1.00000
$$4$$ 1.00000i 1.00000i
$$5$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$6$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$9$$ 1.00000 1.00000
$$10$$ −1.00000 −1.00000
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.00000i 1.00000i
$$13$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$14$$ 0 0
$$15$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$16$$ −1.00000 −1.00000
$$17$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$18$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −0.707107 0.707107i −0.707107 0.707107i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$24$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$25$$ 1.00000i 1.00000i
$$26$$ 1.00000i 1.00000i
$$27$$ 1.00000 1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ −1.00000 −1.00000
$$31$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$32$$ −0.707107 0.707107i −0.707107 0.707107i
$$33$$ 0 0
$$34$$ 1.41421i 1.41421i
$$35$$ 0 0
$$36$$ 1.00000i 1.00000i
$$37$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$38$$ 0 0
$$39$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$40$$ 1.00000i 1.00000i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$46$$ 0 0
$$47$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$48$$ −1.00000 −1.00000
$$49$$ 1.00000i 1.00000i
$$50$$ 0.707107 0.707107i 0.707107 0.707107i
$$51$$ −1.00000 1.00000i −1.00000 1.00000i
$$52$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$53$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$54$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ −0.707107 0.707107i −0.707107 0.707107i
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ −1.00000 1.00000i −1.00000 1.00000i
$$63$$ 0 0
$$64$$ 1.00000i 1.00000i
$$65$$ −1.00000 −1.00000
$$66$$ 0 0
$$67$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$68$$ 1.00000 1.00000i 1.00000 1.00000i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$72$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$73$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$74$$ 2.00000 2.00000
$$75$$ 1.00000i 1.00000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 1.00000i 1.00000i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0.707107 0.707107i 0.707107 0.707107i
$$81$$ 1.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$84$$ 0 0
$$85$$ 1.41421 1.41421
$$86$$ 1.41421i 1.41421i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ −1.00000 −1.00000
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −1.41421 −1.41421
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.707107 0.707107i −0.707107 0.707107i
$$97$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$98$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 1.41421i 1.41421i
$$103$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$104$$ −1.00000 −1.00000
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$108$$ 1.00000i 1.00000i
$$109$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$110$$ 0 0
$$111$$ 1.41421 1.41421i 1.41421 1.41421i
$$112$$ 0 0
$$113$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 1.00000i 1.00000i
$$121$$ −1.00000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.41421i 1.41421i
$$125$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$126$$ 0 0
$$127$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ 0.707107 0.707107i 0.707107 0.707107i
$$129$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$130$$ −0.707107 0.707107i −0.707107 0.707107i
$$131$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$136$$ 1.41421 1.41421
$$137$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$138$$ 0 0
$$139$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 1.00000 1.00000i 1.00000 1.00000i
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 1.00000i 1.00000i
$$148$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$149$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$150$$ 0.707107 0.707107i 0.707107 0.707107i
$$151$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$152$$ 0 0
$$153$$ −1.00000 1.00000i −1.00000 1.00000i
$$154$$ 0 0
$$155$$ 1.00000 1.00000i 1.00000 1.00000i
$$156$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$157$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.00000 1.00000
$$161$$ 0 0
$$162$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$163$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$168$$ 0 0
$$169$$ 1.00000i 1.00000i
$$170$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$171$$ 0 0
$$172$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$173$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$180$$ −0.707107 0.707107i −0.707107 0.707107i
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.00000i 2.00000i
$$186$$ −1.00000 1.00000i −1.00000 1.00000i
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.00000i 1.00000i
$$193$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$194$$ 0 0
$$195$$ −1.00000 −1.00000
$$196$$ −1.00000 −1.00000
$$197$$ 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 1.00000 1.00000i 1.00000 1.00000i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −0.707107 0.707107i −0.707107 0.707107i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 1.41421i 1.41421i
$$214$$ 1.41421i 1.41421i
$$215$$ −1.41421 −1.41421
$$216$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$217$$ 0 0
$$218$$ 1.00000 1.00000i 1.00000 1.00000i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1.41421i 1.41421i
$$222$$ 2.00000 2.00000
$$223$$ −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 0.707107i $$-0.750000\pi$$
$$224$$ 0 0
$$225$$ 1.00000i 1.00000i
$$226$$ 1.41421 1.41421
$$227$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$228$$ 0 0
$$229$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$234$$ 1.00000i 1.00000i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$240$$ 0.707107 0.707107i 0.707107 0.707107i
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −0.707107 0.707107i −0.707107 0.707107i
$$243$$ 1.00000 1.00000
$$244$$ 0 0
$$245$$ −0.707107 0.707107i −0.707107 0.707107i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 1.00000 1.00000i 1.00000 1.00000i
$$249$$ 0 0
$$250$$ 1.00000i 1.00000i
$$251$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 1.41421 1.41421
$$256$$ 1.00000 1.00000
$$257$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$258$$ 1.41421i 1.41421i
$$259$$ 0 0
$$260$$ 1.00000i 1.00000i
$$261$$ 0 0
$$262$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$263$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ −1.00000 −1.00000
$$271$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$272$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$278$$ 1.41421 1.41421i 1.41421 1.41421i
$$279$$ −1.41421 −1.41421
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$284$$ 1.41421 1.41421
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.707107 0.707107i −0.707107 0.707107i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$294$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$295$$ 0 0
$$296$$ 2.00000i 2.00000i
$$297$$ 0 0
$$298$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$299$$ 0 0
$$300$$ 1.00000 1.00000
$$301$$ 0 0
$$302$$ −1.00000 1.00000i −1.00000 1.00000i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 1.41421i 1.41421i
$$307$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1.41421 1.41421
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ −1.00000 −1.00000
$$313$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$321$$ −1.00000 1.00000i −1.00000 1.00000i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000i 1.00000i
$$325$$ 0.707107 0.707107i 0.707107 0.707107i
$$326$$ 0 0
$$327$$ 1.41421i 1.41421i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 1.41421 1.41421i 1.41421 1.41421i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$338$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$339$$ 1.00000 1.00000i 1.00000 1.00000i
$$340$$ 1.41421i 1.41421i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −1.41421 −1.41421
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$350$$ 0 0
$$351$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$352$$ 0 0
$$353$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$354$$ 0 0
$$355$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −1.41421 1.41421i −1.41421 1.41421i
$$359$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$360$$ 1.00000i 1.00000i
$$361$$ −1.00000 −1.00000
$$362$$ 0 0
$$363$$ −1.00000 −1.00000
$$364$$ 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 0
$$369$$ 0 0
$$370$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$371$$ 0 0
$$372$$ 1.41421i 1.41421i
$$373$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$374$$ 0 0
$$375$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$384$$ 0.707107 0.707107i 0.707107 0.707107i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ −0.707107 0.707107i −0.707107 0.707107i
$$391$$ 0 0
$$392$$ −0.707107 0.707107i −0.707107 0.707107i
$$393$$ 2.00000i 2.00000i
$$394$$ 2.00000i 2.00000i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000i 1.00000i
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ −1.00000 1.00000i −1.00000 1.00000i
$$404$$ 0 0
$$405$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 1.41421 1.41421
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.00000i 1.00000i
$$417$$ 2.00000i 2.00000i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$422$$ −1.41421 1.41421i −1.41421 1.41421i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$426$$ 1.00000 1.00000i 1.00000 1.00000i
$$427$$ 0 0
$$428$$ 1.00000 1.00000i 1.00000 1.00000i
$$429$$ 0 0
$$430$$ −1.00000 1.00000i −1.00000 1.00000i
$$431$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$432$$ −1.00000 −1.00000
$$433$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.41421 1.41421
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 1.00000i 1.00000i
$$442$$ 1.00000 1.00000i 1.00000 1.00000i
$$443$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$444$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$445$$ 0 0
$$446$$ 2.00000i 2.00000i
$$447$$ 1.41421 1.41421
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0.707107 0.707107i 0.707107 0.707107i
$$451$$ 0 0
$$452$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$453$$ −1.41421 −1.41421
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$458$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$459$$ −1.00000 1.00000i −1.00000 1.00000i
$$460$$ 0 0
$$461$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$462$$ 0 0
$$463$$ 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ 0 0
$$465$$ 1.00000 1.00000i 1.00000 1.00000i
$$466$$ −1.41421 −1.41421
$$467$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$468$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −1.00000 1.00000i −1.00000 1.00000i
$$479$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$480$$ 1.00000 1.00000
$$481$$ 2.00000 2.00000
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000i 1.00000i
$$485$$ 0 0
$$486$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$487$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 1.00000i 1.00000i
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.41421 1.41421
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$501$$ 0 0
$$502$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$503$$ 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
$$507$$ 1.00000i 1.00000i
$$508$$ 0 0
$$509$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$510$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$511$$ 0 0
$$512$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$513$$ 0 0
$$514$$ 1.41421i 1.41421i
$$515$$ 0 0
$$516$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0.707107 0.707107i 0.707107 0.707107i
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$524$$ −2.00000 −2.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$528$$ 0 0
$$529$$ 1.00000i 1.00000i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 1.41421 1.41421
$$536$$ 0 0
$$537$$ −2.00000 −2.00000
$$538$$ 0 0
$$539$$ 0 0
$$540$$ −0.707107 0.707107i −0.707107 0.707107i
$$541$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$542$$ −1.00000 1.00000i −1.00000 1.00000i
$$543$$ 0 0
$$544$$ 1.41421i 1.41421i
$$545$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$546$$ 0 0
$$547$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 2.00000i 2.00000i
$$556$$ 2.00000 2.00000
$$557$$ −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 0.707107i $$-0.750000\pi$$
$$558$$ −1.00000 1.00000i −1.00000 1.00000i
$$559$$ 1.41421i 1.41421i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 1.41421i 1.41421i
$$566$$ 1.41421i 1.41421i
$$567$$ 0 0
$$568$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000i 1.00000i
$$577$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$578$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −1.00000 −1.00000
$$586$$ 0 0
$$587$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$588$$ −1.00000 −1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$592$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$593$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1.41421i 1.41421i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 1.41421i 1.41421i
$$605$$ 0.707107 0.707107i 0.707107 0.707107i
$$606$$ 0 0
$$607$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 1.00000 1.00000i 1.00000 1.00000i
$$613$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −0.707107 0.707107i −0.707107 0.707107i
$$625$$ −1.00000 −1.00000
$$626$$ 1.41421i 1.41421i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −2.82843 −2.82843
$$630$$ 0 0
$$631$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$632$$ 0 0
$$633$$ −2.00000 −2.00000
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$638$$ 0 0
$$639$$ 1.41421i 1.41421i
$$640$$ 1.00000i 1.00000i
$$641$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$642$$ 1.41421i 1.41421i
$$643$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$644$$ 0 0
$$645$$ −1.41421 −1.41421
$$646$$ 0 0
$$647$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$648$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$649$$ 0 0
$$650$$ 1.00000 1.00000
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$654$$ 1.00000 1.00000i 1.00000 1.00000i
$$655$$ −1.41421 1.41421i −1.41421 1.41421i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$662$$ 0 0
$$663$$ 1.41421i 1.41421i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 2.00000 2.00000
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −1.41421 1.41421i −1.41421 1.41421i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$674$$ 1.41421 1.41421
$$675$$ 1.00000i 1.00000i
$$676$$ −1.00000 −1.00000
$$677$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$678$$ 1.41421 1.41421
$$679$$ 0 0
$$680$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.41421i 1.41421i
$$688$$ −1.00000 1.00000i −1.00000 1.00000i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 1.41421i 1.41421i
$$695$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$699$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 1.00000i 1.00000i
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$710$$ 1.41421i 1.41421i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2.00000i 2.00000i
$$717$$ −1.41421 −1.41421
$$718$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0.707107 0.707107i 0.707107 0.707107i
$$721$$ 0 0
$$722$$ −0.707107 0.707107i −0.707107 0.707107i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −0.707107 0.707107i −0.707107 0.707107i
$$727$$ 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
$$731$$ 2.00000i 2.00000i
$$732$$ 0 0
$$733$$ 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ 0 0
$$735$$ −0.707107 0.707107i −0.707107 0.707107i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ −2.00000 −2.00000
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i $$0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$744$$ 1.00000 1.00000i 1.00000 1.00000i
$$745$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 1.00000i 1.00000i
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 2.00000i 2.00000i
$$754$$ 0 0
$$755$$ 1.00000 1.00000i 1.00000 1.00000i
$$756$$ 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
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 1.41421 1.41421
$$766$$ 2.00000 2.00000
$$767$$ 0 0
$$768$$ 1.00000 1.00000
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$772$$ 0 0
$$773$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$774$$ 1.41421i 1.41421i
$$775$$ 1.41421i 1.41421i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 1.00000i 1.00000i
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000i 1.00000i
$$785$$ 0 0
$$786$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$787$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$788$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 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
$$800$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0