# Properties

 Label 1560.1.cs.d.467.4 Level $1560$ Weight $1$ Character 1560.467 Analytic conductor $0.779$ Analytic rank $0$ Dimension $8$ Projective image $D_{8}$ CM discriminant -39 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: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{16})$$ Defining polynomial: $$x^{8} + 1$$ x^8 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{8}$$ Projective field: Galois closure of 8.2.49353408000000.10

## Embedding invariants

 Embedding label 467.4 Root $$0.382683 + 0.923880i$$ of defining polynomial Character $$\chi$$ $$=$$ 1560.467 Dual form 1560.1.cs.d.1403.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.923880 - 0.382683i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.382683 + 0.923880i) q^{5} +(0.382683 - 0.923880i) q^{6} +(0.382683 - 0.923880i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(0.923880 - 0.382683i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.382683 + 0.923880i) q^{5} +(0.382683 - 0.923880i) q^{6} +(0.382683 - 0.923880i) q^{8} -1.00000i q^{9} +(0.707107 + 0.707107i) q^{10} -1.84776 q^{11} -1.00000i q^{12} +(0.707107 + 0.707107i) q^{13} +(0.923880 + 0.382683i) q^{15} -1.00000i q^{16} +(-0.382683 - 0.923880i) q^{18} +(0.923880 + 0.382683i) q^{20} +(-1.70711 + 0.707107i) q^{22} +(-0.382683 - 0.923880i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.923880 + 0.382683i) q^{26} +(-0.707107 - 0.707107i) q^{27} +1.00000 q^{30} +(-0.382683 - 0.923880i) q^{32} +(-1.30656 + 1.30656i) q^{33} +(-0.707107 - 0.707107i) q^{36} +1.00000 q^{39} +1.00000 q^{40} +0.765367 q^{41} +(-1.00000 + 1.00000i) q^{43} +(-1.30656 + 1.30656i) q^{44} +(0.923880 - 0.382683i) q^{45} +(-0.541196 + 0.541196i) q^{47} +(-0.707107 - 0.707107i) q^{48} -1.00000i q^{49} +(-0.382683 + 0.923880i) q^{50} +1.00000 q^{52} +(-0.923880 - 0.382683i) q^{54} +(-0.707107 - 1.70711i) q^{55} +0.765367i q^{59} +(0.923880 - 0.382683i) q^{60} +1.41421i q^{61} +(-0.707107 - 0.707107i) q^{64} +(-0.382683 + 0.923880i) q^{65} +(-0.707107 + 1.70711i) q^{66} +1.84776i q^{71} +(-0.923880 - 0.382683i) q^{72} +1.00000i q^{75} +(0.923880 - 0.382683i) q^{78} -1.41421 q^{79} +(0.923880 - 0.382683i) q^{80} -1.00000 q^{81} +(0.707107 - 0.292893i) q^{82} +(1.30656 - 1.30656i) q^{83} +(-0.541196 + 1.30656i) q^{86} +(-0.707107 + 1.70711i) q^{88} -1.84776i q^{89} +(0.707107 - 0.707107i) q^{90} +(-0.292893 + 0.707107i) q^{94} +(-0.923880 - 0.382683i) q^{96} +(-0.382683 - 0.923880i) q^{98} +1.84776i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q+O(q^{10})$$ 8 * q $$8 q - 8 q^{22} + 8 q^{30} + 8 q^{39} + 8 q^{40} - 8 q^{43} + 8 q^{52} - 8 q^{81} - 8 q^{94}+O(q^{100})$$ 8 * q - 8 * q^22 + 8 * q^30 + 8 * q^39 + 8 * q^40 - 8 * q^43 + 8 * q^52 - 8 * q^81 - 8 * q^94

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.923880 0.382683i 0.923880 0.382683i
$$3$$ 0.707107 0.707107i 0.707107 0.707107i
$$4$$ 0.707107 0.707107i 0.707107 0.707107i
$$5$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$6$$ 0.382683 0.923880i 0.382683 0.923880i
$$7$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$8$$ 0.382683 0.923880i 0.382683 0.923880i
$$9$$ 1.00000i 1.00000i
$$10$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$11$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$12$$ 1.00000i 1.00000i
$$13$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$14$$ 0 0
$$15$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$16$$ 1.00000i 1.00000i
$$17$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$18$$ −0.382683 0.923880i −0.382683 0.923880i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$21$$ 0 0
$$22$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$23$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ −0.382683 0.923880i −0.382683 0.923880i
$$25$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$26$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$27$$ −0.707107 0.707107i −0.707107 0.707107i
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 1.00000 1.00000
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −0.382683 0.923880i −0.382683 0.923880i
$$33$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.707107 0.707107i −0.707107 0.707107i
$$37$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$38$$ 0 0
$$39$$ 1.00000 1.00000
$$40$$ 1.00000 1.00000
$$41$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$42$$ 0 0
$$43$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$44$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$45$$ 0.923880 0.382683i 0.923880 0.382683i
$$46$$ 0 0
$$47$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$48$$ −0.707107 0.707107i −0.707107 0.707107i
$$49$$ 1.00000i 1.00000i
$$50$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$51$$ 0 0
$$52$$ 1.00000 1.00000
$$53$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$54$$ −0.923880 0.382683i −0.923880 0.382683i
$$55$$ −0.707107 1.70711i −0.707107 1.70711i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$60$$ 0.923880 0.382683i 0.923880 0.382683i
$$61$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.707107 0.707107i −0.707107 0.707107i
$$65$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$66$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$67$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.84776i 1.84776i 0.382683 + 0.923880i $$0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$72$$ −0.923880 0.382683i −0.923880 0.382683i
$$73$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$74$$ 0 0
$$75$$ 1.00000i 1.00000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0.923880 0.382683i 0.923880 0.382683i
$$79$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$80$$ 0.923880 0.382683i 0.923880 0.382683i
$$81$$ −1.00000 −1.00000
$$82$$ 0.707107 0.292893i 0.707107 0.292893i
$$83$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$87$$ 0 0
$$88$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$89$$ 1.84776i 1.84776i −0.382683 0.923880i $$-0.625000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$90$$ 0.707107 0.707107i 0.707107 0.707107i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$95$$ 0 0
$$96$$ −0.923880 0.382683i −0.923880 0.382683i
$$97$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$98$$ −0.382683 0.923880i −0.382683 0.923880i
$$99$$ 1.84776i 1.84776i
$$100$$ 1.00000i 1.00000i
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$104$$ 0.923880 0.382683i 0.923880 0.382683i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$108$$ −1.00000 −1.00000
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ −1.30656 1.30656i −1.30656 1.30656i
$$111$$ 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 0
$$117$$ 0.707107 0.707107i 0.707107 0.707107i
$$118$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$119$$ 0 0
$$120$$ 0.707107 0.707107i 0.707107 0.707107i
$$121$$ 2.41421 2.41421
$$122$$ 0.541196 + 1.30656i 0.541196 + 1.30656i
$$123$$ 0.541196 0.541196i 0.541196 0.541196i
$$124$$ 0 0
$$125$$ −0.923880 0.382683i −0.923880 0.382683i
$$126$$ 0 0
$$127$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$128$$ −0.923880 0.382683i −0.923880 0.382683i
$$129$$ 1.41421i 1.41421i
$$130$$ 1.00000i 1.00000i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 1.84776i 1.84776i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.382683 0.923880i 0.382683 0.923880i
$$136$$ 0 0
$$137$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0.765367i 0.765367i
$$142$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$143$$ −1.30656 1.30656i −1.30656 1.30656i
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.707107 0.707107i −0.707107 0.707107i
$$148$$ 0 0
$$149$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$150$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0.707107 0.707107i 0.707107 0.707107i
$$157$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$158$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$159$$ 0 0
$$160$$ 0.707107 0.707107i 0.707107 0.707107i
$$161$$ 0 0
$$162$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$163$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$164$$ 0.541196 0.541196i 0.541196 0.541196i
$$165$$ −1.70711 0.707107i −1.70711 0.707107i
$$166$$ 0.707107 1.70711i 0.707107 1.70711i
$$167$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$168$$ 0 0
$$169$$ 1.00000i 1.00000i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 1.41421i 1.41421i
$$173$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.84776i 1.84776i
$$177$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$178$$ −0.707107 1.70711i −0.707107 1.70711i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0.382683 0.923880i 0.382683 0.923880i
$$181$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0.765367i 0.765367i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ −1.00000 −1.00000
$$193$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$194$$ 0 0
$$195$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$196$$ −0.707107 0.707107i −0.707107 0.707107i
$$197$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$198$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$199$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$200$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$206$$ −1.30656 0.541196i −1.30656 0.541196i
$$207$$ 0 0
$$208$$ 0.707107 0.707107i 0.707107 0.707107i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$212$$ 0 0
$$213$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$214$$ 0 0
$$215$$ −1.30656 0.541196i −1.30656 0.541196i
$$216$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −1.70711 0.707107i −1.70711 0.707107i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$226$$ 0 0
$$227$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$234$$ 0.382683 0.923880i 0.382683 0.923880i
$$235$$ −0.707107 0.292893i −0.707107 0.292893i
$$236$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$237$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$238$$ 0 0
$$239$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$240$$ 0.382683 0.923880i 0.382683 0.923880i
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 2.23044 0.923880i 2.23044 0.923880i
$$243$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$244$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$245$$ 0.923880 0.382683i 0.923880 0.382683i
$$246$$ 0.292893 0.707107i 0.292893 0.707107i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 1.84776i 1.84776i
$$250$$ −1.00000 −1.00000
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0.765367 1.84776i 0.765367 1.84776i
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$258$$ 0.541196 + 1.30656i 0.541196 + 1.30656i
$$259$$ 0 0
$$260$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.30656 1.30656i −1.30656 1.30656i
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 1.00000i 1.00000i
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −0.707107 0.292893i −0.707107 0.292893i
$$275$$ 1.30656 1.30656i 1.30656 1.30656i
$$276$$ 0 0
$$277$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$282$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$283$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$284$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$285$$ 0 0
$$286$$ −1.70711 0.707107i −1.70711 0.707107i
$$287$$ 0 0
$$288$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
−0.382683 0.923880i $$-0.625000\pi$$
$$294$$ −0.923880 0.382683i −0.923880 0.382683i
$$295$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$296$$ 0 0
$$297$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$298$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$299$$ 0 0
$$300$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$306$$ 0 0
$$307$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 0 0
$$309$$ −1.41421 −1.41421
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0.382683 0.923880i 0.382683 0.923880i
$$313$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$314$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$315$$ 0 0
$$316$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$317$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.382683 0.923880i 0.382683 0.923880i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$325$$ −1.00000 −1.00000
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0.292893 0.707107i 0.292893 0.707107i
$$329$$ 0 0
$$330$$ −1.84776 −1.84776
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 1.84776i 1.84776i
$$333$$ 0 0
$$334$$ 0.707107 1.70711i 0.707107 1.70711i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 0.707107i $$-0.750000\pi$$
$$338$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0.541196 + 1.30656i 0.541196 + 1.30656i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 1.00000i 1.00000i
$$352$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$353$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$354$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$355$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$356$$ −1.30656 1.30656i −1.30656 1.30656i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$360$$ 1.00000i 1.00000i
$$361$$ −1.00000 −1.00000
$$362$$ 0.765367 + 1.84776i 0.765367 + 1.84776i
$$363$$ 1.70711 1.70711i 1.70711 1.70711i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$367$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$368$$ 0 0
$$369$$ 0.765367i 0.765367i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$374$$ 0 0
$$375$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$376$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 2.00000i 2.00000i
$$382$$ 0 0
$$383$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$384$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$385$$ 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
$$392$$ −0.923880 0.382683i −0.923880 0.382683i
$$393$$ 0 0
$$394$$ 0.292893 0.707107i 0.292893 0.707107i
$$395$$ −0.541196 1.30656i −0.541196 1.30656i
$$396$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$397$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$398$$ 1.30656 0.541196i 1.30656 0.541196i
$$399$$ 0 0
$$400$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$401$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −0.382683 0.923880i −0.382683 0.923880i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$411$$ −0.765367 −0.765367
$$412$$ −1.41421 −1.41421
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$416$$ 0.382683 0.923880i 0.382683 0.923880i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 1.30656 0.541196i 1.30656 0.541196i
$$423$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −1.84776 −1.84776
$$430$$ −1.41421 −1.41421
$$431$$ 0.765367i 0.765367i 0.923880 + 0.382683i $$0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$432$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$433$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$440$$ −1.84776 −1.84776
$$441$$ −1.00000 −1.00000
$$442$$ 0 0
$$443$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$444$$ 0 0
$$445$$ 1.70711 0.707107i 1.70711 0.707107i
$$446$$ 0 0
$$447$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$448$$ 0 0
$$449$$ 0.765367i 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$450$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$451$$ −1.41421 −1.41421
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0.765367i 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$468$$ 1.00000i 1.00000i
$$469$$ 0 0
$$470$$ −0.765367 −0.765367
$$471$$ 1.41421i 1.41421i
$$472$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$473$$ 1.84776 1.84776i 1.84776 1.84776i
$$474$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 1.70711 0.707107i 1.70711 0.707107i
$$479$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$480$$ 1.00000i 1.00000i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.70711 1.70711i 1.70711 1.70711i
$$485$$ 0 0
$$486$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$487$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$488$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$489$$ 0 0
$$490$$ 0.707107 0.707107i 0.707107 0.707107i
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0.765367i 0.765367i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −0.707107 1.70711i −0.707107 1.70711i
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$501$$ 1.84776i 1.84776i
$$502$$ 0 0
$$503$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$508$$ 2.00000i 2.00000i
$$509$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.541196 1.30656i 0.541196 1.30656i
$$516$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$517$$ 1.00000 1.00000i 1.00000 1.00000i
$$518$$ 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 $$0$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$529$$ 1.00000i 1.00000i
$$530$$ 0 0
$$531$$ 0.765367 0.765367
$$532$$ 0 0
$$533$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$534$$ −1.70711 0.707107i −1.70711 0.707107i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.84776i 1.84776i
$$540$$ −0.382683 0.923880i −0.382683 0.923880i
$$541$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$542$$ 0 0
$$543$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$548$$ −0.765367 −0.765367
$$549$$ 1.41421 1.41421
$$550$$ 0.707107 1.70711i 0.707107 1.70711i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0.541196 1.30656i 0.541196 1.30656i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$558$$ 0 0
$$559$$ −1.41421 −1.41421
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 1.70711 0.707107i 1.70711 0.707107i
$$563$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$564$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$572$$ −1.84776 −1.84776
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$577$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$578$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$586$$ −1.70711 0.707107i −1.70711 0.707107i
$$587$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$588$$ −1.00000 −1.00000
$$589$$ 0 0
$$590$$ −0.541196 + 0.541196i −0.541196 + 0.541196i
$$591$$ 0.765367i 0.765367i
$$592$$ 0 0
$$593$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$594$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$595$$ 0 0
$$596$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$597$$ 1.00000 1.00000i 1.00000 1.00000i
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$601$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0.923880 + 2.23044i 0.923880 + 2.23044i
$$606$$ 0 0
$$607$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$611$$ −0.765367 −0.765367
$$612$$ 0 0
$$613$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$614$$ 0 0
$$615$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$616$$ 0 0
$$617$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$618$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 1.00000i 1.00000i
$$625$$ 1.00000i 1.00000i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.41421i 1.41421i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$633$$ 1.00000 1.00000i 1.00000 1.00000i
$$634$$ 0.292893 0.707107i 0.292893 0.707107i
$$635$$ 1.84776 + 0.765367i 1.84776 + 0.765367i
$$636$$ 0 0
$$637$$ 0.707107 0.707107i 0.707107 0.707107i
$$638$$ 0 0
$$639$$ 1.84776 1.84776
$$640$$ 1.00000i 1.00000i
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$644$$ 0 0
$$645$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$646$$ 0 0
$$647$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$648$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$649$$ 1.41421i 1.41421i
$$650$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.765367i 0.765367i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −0.707107 1.70711i −0.707107 1.70711i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.84776i 1.84776i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 2.61313i 2.61313i
$$672$$ 0 0
$$673$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$674$$ −1.84776 0.765367i −1.84776 0.765367i
$$675$$ 1.00000 1.00000
$$676$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$677$$ 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
$$681$$ 0.765367 0.765367
$$682$$ 0 0
$$683$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$684$$ 0 0
$$685$$ 0.292893 0.707107i 0.292893 0.707107i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 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
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ −0.382683 0.923880i −0.382683 0.923880i
$$703$$ 0 0
$$704$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$705$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$706$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$707$$ 0 0
$$708$$ 0.765367 0.765367
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$711$$ 1.41421i 1.41421i
$$712$$ −1.70711 0.707107i −1.70711 0.707107i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0.707107 1.70711i 0.707107 1.70711i
$$716$$ 0 0
$$717$$ 1.30656 1.30656i 1.30656 1.30656i
$$718$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ −0.382683 0.923880i −0.382683 0.923880i
$$721$$ 0 0
$$722$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$723$$ 0 0
$$724$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$725$$ 0 0
$$726$$ 0.923880 2.23044i 0.923880 2.23044i
$$727$$ −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i $$0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 1.00000i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 1.41421 1.41421
$$733$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ 0.541196 1.30656i 0.541196 1.30656i
$$735$$ 0.382683 0.923880i 0.382683 0.923880i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −0.292893 0.707107i −0.292893 0.707107i
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$744$$ 0 0
$$745$$ −0.707107 1.70711i −0.707107 1.70711i
$$746$$ 0 0
$$747$$ −1.30656 1.30656i −1.30656 1.30656i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$751$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0.541196 + 0.541196i 0.541196 + 0.541196i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$762$$ −0.765367 1.84776i −0.765367 1.84776i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −0.707107 0.292893i −0.707107 0.292893i
$$767$$ −0.541196 + 0.541196i −0.541196 + 0.541196i
$$768$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$774$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$781$$ 3.41421i 3.41421i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ −1.30656 0.541196i −1.30656 0.541196i
$$786$$ 0 0
$$787$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$788$$ 0.765367i 0.765367i
$$789$$ 0 0
$$790$$ −1.00000 1.00000i −1.00000 1.00000i
$$791$$ 0 0
$$792$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$793$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.00000 1.00000i 1.00000 1.00000i
$$797$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$798$$ 0 0
$$799$$ 0 0