# Properties

 Label 1900.1.j.a.1443.4 Level $1900$ Weight $1$ Character 1900.1443 Analytic conductor $0.948$ Analytic rank $0$ Dimension $8$ Projective image $D_{8}$ CM discriminant -95 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1900.j (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.948223524003$$ 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 8.0.4170272000.1

## Embedding invariants

 Embedding label 1443.4 Root $$0.382683 - 0.923880i$$ of defining polynomial Character $$\chi$$ $$=$$ 1900.1443 Dual form 1900.1.j.a.607.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.923880 + 0.382683i) q^{2} +(-1.30656 - 1.30656i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.707107 - 1.70711i) q^{6} +(0.382683 + 0.923880i) q^{8} +2.41421i q^{9} +O(q^{10})$$ $$q+(0.923880 + 0.382683i) q^{2} +(-1.30656 - 1.30656i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.707107 - 1.70711i) q^{6} +(0.382683 + 0.923880i) q^{8} +2.41421i q^{9} +1.41421i q^{11} -1.84776i q^{12} +(-1.30656 + 1.30656i) q^{13} +1.00000i q^{16} +(-0.923880 + 2.23044i) q^{18} -1.00000 q^{19} +(-0.541196 + 1.30656i) q^{22} +(0.707107 - 1.70711i) q^{24} +(-1.70711 + 0.707107i) q^{26} +(1.84776 - 1.84776i) q^{27} +(-0.382683 + 0.923880i) q^{32} +(1.84776 - 1.84776i) q^{33} +(-1.70711 + 1.70711i) q^{36} +(0.541196 + 0.541196i) q^{37} +(-0.923880 - 0.382683i) q^{38} +3.41421 q^{39} +(-1.00000 + 1.00000i) q^{44} +(1.30656 - 1.30656i) q^{48} -1.00000i q^{49} -1.84776 q^{52} +(0.541196 - 0.541196i) q^{53} +(2.41421 - 1.00000i) q^{54} +(1.30656 + 1.30656i) q^{57} +1.41421 q^{61} +(-0.707107 + 0.707107i) q^{64} +(2.41421 - 1.00000i) q^{66} +(-0.541196 + 0.541196i) q^{67} +(-2.23044 + 0.923880i) q^{72} +(0.292893 + 0.707107i) q^{74} +(-0.707107 - 0.707107i) q^{76} +(3.15432 + 1.30656i) q^{78} -2.41421 q^{81} +(-1.30656 + 0.541196i) q^{88} +(1.70711 - 0.707107i) q^{96} +(0.541196 + 0.541196i) q^{97} +(0.382683 - 0.923880i) q^{98} -3.41421 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q+O(q^{10})$$ 8 * q $$8 q - 8 q^{19} - 8 q^{26} - 8 q^{36} + 16 q^{39} - 8 q^{44} + 8 q^{54} + 8 q^{66} + 8 q^{74} - 8 q^{81} + 8 q^{96} - 16 q^{99}+O(q^{100})$$ 8 * q - 8 * q^19 - 8 * q^26 - 8 * q^36 + 16 * q^39 - 8 * q^44 + 8 * q^54 + 8 * q^66 + 8 * q^74 - 8 * q^81 + 8 * q^96 - 16 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$951$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$3$$ −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
−0.382683 0.923880i $$-0.625000\pi$$
$$4$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$5$$ 0 0
$$6$$ −0.707107 1.70711i −0.707107 1.70711i
$$7$$ 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
$$9$$ 2.41421i 2.41421i
$$10$$ 0 0
$$11$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$12$$ 1.84776i 1.84776i
$$13$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000i 1.00000i
$$17$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$18$$ −0.923880 + 2.23044i −0.923880 + 2.23044i
$$19$$ −1.00000 −1.00000
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$23$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ 0.707107 1.70711i 0.707107 1.70711i
$$25$$ 0 0
$$26$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$27$$ 1.84776 1.84776i 1.84776 1.84776i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$33$$ 1.84776 1.84776i 1.84776 1.84776i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −1.70711 + 1.70711i −1.70711 + 1.70711i
$$37$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$38$$ −0.923880 0.382683i −0.923880 0.382683i
$$39$$ 3.41421 3.41421
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$44$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$48$$ 1.30656 1.30656i 1.30656 1.30656i
$$49$$ 1.00000i 1.00000i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.84776 −1.84776
$$53$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$54$$ 2.41421 1.00000i 2.41421 1.00000i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$65$$ 0 0
$$66$$ 2.41421 1.00000i 2.41421 1.00000i
$$67$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −2.23044 + 0.923880i −2.23044 + 0.923880i
$$73$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$74$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$75$$ 0 0
$$76$$ −0.707107 0.707107i −0.707107 0.707107i
$$77$$ 0 0
$$78$$ 3.15432 + 1.30656i 3.15432 + 1.30656i
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ −2.41421 −2.41421
$$82$$ 0 0
$$83$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.70711 0.707107i 1.70711 0.707107i
$$97$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$98$$ 0.382683 0.923880i 0.382683 0.923880i
$$99$$ −3.41421 −3.41421
$$100$$ 0 0
$$101$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$102$$ 0 0
$$103$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$104$$ −1.70711 0.707107i −1.70711 0.707107i
$$105$$ 0 0
$$106$$ 0.707107 0.292893i 0.707107 0.292893i
$$107$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$108$$ 2.61313 2.61313
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ 1.41421i 1.41421i
$$112$$ 0 0
$$113$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$114$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −3.15432 3.15432i −3.15432 3.15432i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 −1.00000
$$122$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$128$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 2.61313 2.61313
$$133$$ 0 0
$$134$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$138$$ 0 0
$$139$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1.84776 1.84776i −1.84776 1.84776i
$$144$$ −2.41421 −2.41421
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$148$$ 0.765367i 0.765367i
$$149$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ −0.382683 0.923880i −0.382683 0.923880i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.41421 + 2.41421i 2.41421 + 2.41421i
$$157$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$158$$ 0 0
$$159$$ −1.41421 −1.41421
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −2.23044 0.923880i −2.23044 0.923880i
$$163$$ 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
$$167$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$168$$ 0 0
$$169$$ 2.41421i 2.41421i
$$170$$ 0 0
$$171$$ 2.41421i 2.41421i
$$172$$ 0 0
$$173$$ −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i $$0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.41421 −1.41421
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ −1.84776 1.84776i −1.84776 1.84776i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.84776 1.84776
$$193$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$194$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$195$$ 0 0
$$196$$ 0.707107 0.707107i 0.707107 0.707107i
$$197$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$198$$ −3.15432 1.30656i −3.15432 1.30656i
$$199$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$200$$ 0 0
$$201$$ 1.41421 1.41421
$$202$$ −1.30656 0.541196i −1.30656 0.541196i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$207$$ 0 0
$$208$$ −1.30656 1.30656i −1.30656 1.30656i
$$209$$ 1.41421i 1.41421i
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0.765367 0.765367
$$213$$ 0 0
$$214$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$215$$ 0 0
$$216$$ 2.41421 + 1.00000i 2.41421 + 1.00000i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0.541196 1.30656i 0.541196 1.30656i
$$223$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.70711 0.707107i 1.70711 0.707107i
$$227$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$228$$ 1.84776i 1.84776i
$$229$$ 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
$$233$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$234$$ −1.70711 4.12132i −1.70711 4.12132i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −0.923880 0.382683i −0.923880 0.382683i
$$243$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$244$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.30656 1.30656i 1.30656 1.30656i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 1.70711 0.707107i 1.70711 0.707107i
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 2.41421 + 1.00000i 2.41421 + 1.00000i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −0.765367 −0.765367
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$278$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −1.00000 2.41421i −1.00000 2.41421i
$$287$$ 0 0
$$288$$ −2.23044 0.923880i −2.23044 0.923880i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 1.41421i 1.41421i
$$292$$ 0 0
$$293$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$294$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$295$$ 0 0
$$296$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$297$$ 2.61313 + 2.61313i 2.61313 + 2.61313i
$$298$$ 0.541196 1.30656i 0.541196 1.30656i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.84776 + 1.84776i 1.84776 + 1.84776i
$$304$$ 1.00000i 1.00000i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$308$$ 0 0
$$309$$ 1.41421i 1.41421i
$$310$$ 0 0
$$311$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$312$$ 1.30656 + 3.15432i 1.30656 + 3.15432i
$$313$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$318$$ −1.30656 0.541196i −1.30656 0.541196i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.41421 1.41421
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.70711 1.70711i −1.70711 1.70711i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ −1.30656 + 1.30656i −1.30656 + 1.30656i
$$334$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
−0.382683 0.923880i $$-0.625000\pi$$
$$338$$ 0.923880 2.23044i 0.923880 2.23044i
$$339$$ −3.41421 −3.41421
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.923880 2.23044i 0.923880 2.23044i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$347$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 4.82843i 4.82843i
$$352$$ −1.30656 0.541196i −1.30656 0.541196i
$$353$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −1.00000 2.41421i −1.00000 2.41421i
$$367$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ −3.41421 −3.41421
$$382$$ −0.765367 + 1.84776i −0.765367 + 1.84776i
$$383$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$384$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$385$$ 0 0
$$386$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$387$$ 0 0
$$388$$ 0.765367i 0.765367i
$$389$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.923880 0.382683i 0.923880 0.382683i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −2.41421 2.41421i −2.41421 2.41421i
$$397$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$398$$ 1.84776 + 0.765367i 1.84776 + 0.765367i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$403$$ 0 0
$$404$$ −1.00000 1.00000i −1.00000 1.00000i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −0.765367 + 0.765367i −0.765367 + 0.765367i
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0.765367i 0.765367i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.707107 1.70711i −0.707107 1.70711i
$$417$$ −1.84776 1.84776i −1.84776 1.84776i
$$418$$ 0.541196 1.30656i 0.541196 1.30656i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.765367 −0.765367
$$429$$ 4.82843i 4.82843i
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.84776 + 1.84776i 1.84776 + 1.84776i
$$433$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 2.41421 2.41421
$$442$$ 0 0
$$443$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$444$$ 1.00000 1.00000i 1.00000 1.00000i
$$445$$ 0 0
$$446$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$447$$ −1.84776 + 1.84776i −1.84776 + 1.84776i
$$448$$ 0 0
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 1.84776 1.84776
$$453$$ 0 0
$$454$$ 0.707107 0.292893i 0.707107 0.292893i
$$455$$ 0 0
$$456$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$457$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$458$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$462$$ 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 $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$468$$ 4.46088i 4.46088i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$478$$ 0 0
$$479$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$480$$ 0 0
$$481$$ −1.41421 −1.41421
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.707107 0.707107i −0.707107 0.707107i
$$485$$ 0 0
$$486$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$487$$ −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$488$$ 0.541196 + 1.30656i 0.541196 + 1.30656i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 1.70711 0.707107i 1.70711 0.707107i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$500$$ 0 0
$$501$$ 3.41421 3.41421
$$502$$ 0.765367 1.84776i 0.765367 1.84776i
$$503$$ 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
$$507$$ −3.15432 + 3.15432i −3.15432 + 3.15432i
$$508$$ 1.84776 1.84776
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.923880 0.382683i −0.923880 0.382683i
$$513$$ −1.84776 + 1.84776i −1.84776 + 1.84776i
$$514$$ −0.292893 0.707107i −0.292893 0.707107i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 3.41421 3.41421
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 1.84776 + 1.84776i 1.84776 + 1.84776i
$$529$$ 1.00000i 1.00000i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −0.707107 0.292893i −0.707107 0.292893i
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 1.41421 1.41421
$$540$$ 0 0
$$541$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$542$$ 0.541196 1.30656i 0.541196 1.30656i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$548$$ 0 0
$$549$$ 3.41421i 3.41421i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$557$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$572$$ 2.61313i 2.61313i
$$573$$ 2.61313 2.61313i 2.61313 2.61313i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.70711 1.70711i −1.70711 1.70711i
$$577$$ 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
$$579$$ 1.41421 1.41421
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0.541196 1.30656i 0.541196 1.30656i
$$583$$ 0.765367 + 0.765367i 0.765367 + 0.765367i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$587$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$588$$ −1.84776 −1.84776
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.541196 + 0.541196i −0.541196 + 0.541196i
$$593$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$594$$ 1.41421 + 3.41421i 1.41421 + 3.41421i
$$595$$ 0 0
$$596$$ 1.00000 1.00000i 1.00000 1.00000i
$$597$$ −2.61313 2.61313i −2.61313 2.61313i
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ −1.30656 1.30656i −1.30656 1.30656i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 1.00000 + 2.41421i 1.00000 + 2.41421i
$$607$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$608$$ 0.382683 0.923880i 0.382683 0.923880i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$614$$ 0.707107 0.292893i 0.707107 0.292893i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$618$$ 0.541196 1.30656i 0.541196 1.30656i
$$619$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −0.541196 + 1.30656i −0.541196 + 1.30656i
$$623$$ 0 0
$$624$$ 3.41421i 3.41421i
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −1.84776 + 1.84776i −1.84776 + 1.84776i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$635$$ 0 0
$$636$$ −1.00000 1.00000i −1.00000 1.00000i
$$637$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 1.30656 + 0.541196i 1.30656 + 0.541196i
$$643$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$648$$ −0.923880 2.23044i −0.923880 2.23044i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$667$$ 0 0
$$668$$ −1.84776 −1.84776
$$669$$ 3.41421i 3.41421i
$$670$$ 0 0
$$671$$ 2.00000i 2.00000i
$$672$$ 0 0
$$673$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$674$$ −0.707107 1.70711i −0.707107 1.70711i
$$675$$ 0 0
$$676$$ 1.70711 1.70711i 1.70711 1.70711i
$$677$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$678$$ −3.15432 1.30656i −3.15432 1.30656i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −1.41421 −1.41421
$$682$$ 0 0
$$683$$ −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
−0.382683 0.923880i $$-0.625000\pi$$
$$684$$ 1.70711 1.70711i 1.70711 1.70711i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.84776 1.84776i 1.84776 1.84776i
$$688$$ 0 0
$$689$$ 1.41421i 1.41421i
$$690$$ 0 0
$$691$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$692$$ −1.84776 −1.84776
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$702$$ −1.84776 + 4.46088i −1.84776 + 4.46088i
$$703$$ −0.541196 0.541196i −0.541196 0.541196i
$$704$$ −1.00000 1.00000i −1.00000 1.00000i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ −1.30656 0.541196i −1.30656 0.541196i
$$719$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$727$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 1.00000i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 2.61313i 2.61313i
$$733$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.765367 0.765367i −0.765367 0.765367i
$$738$$ 0 0
$$739$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ −3.41421 −3.41421
$$742$$ 0 0
$$743$$ 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i $$0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ −2.61313 + 2.61313i −2.61313 + 2.61313i
$$754$$ 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
$$761$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$762$$ −3.15432 1.30656i −3.15432 1.30656i
$$763$$ 0 0
$$764$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$765$$ 0 0
$$766$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$767$$ 0 0
$$768$$ 1.30656 + 1.30656i 1.30656 + 1.30656i
$$769$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$770$$ 0 0
$$771$$ 1.41421i 1.41421i
$$772$$ −0.765367 −0.765367
$$773$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$777$$ 0 0
$$778$$ 0.765367 1.84776i 0.765367 1.84776i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1.30656 1.30656i 1.30656 1.30656i 0.382683 0.923880i $$-0.375000\pi$$
0.923880 0.382683i $$-0.125000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −1.30656 3.15432i −1.30656 3.15432i
$$793$$ −1.84776 + 1.84776i −1.84776 + 1.84776i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$797$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 1.00000 + 1.00000i 1.00000 + 1.00000i