# Properties

 Label 3332.1.w.a.2059.1 Level $3332$ Weight $1$ Character 3332.2059 Analytic conductor $1.663$ Analytic rank $0$ Dimension $4$ Projective image $D_{8}$ CM discriminant -4 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(491,3332)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3332.491");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.w (of order $$8$$, degree $$4$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$1.66288462209$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 1$$ x^4 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{8}$$ Projective field: Galois closure of 8.2.3089659810545728.1

## Embedding invariants

 Embedding label 2059.1 Root $$0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.2059 Dual form 3332.1.w.a.1471.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.292893 - 0.707107i) q^{5} +(0.707107 - 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$$ $$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.292893 - 0.707107i) q^{5} +(0.707107 - 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-0.292893 + 0.707107i) q^{10} -2.00000i q^{13} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} -1.00000 q^{18} +(0.707107 - 0.292893i) q^{20} +(0.292893 - 0.292893i) q^{25} +(-1.41421 + 1.41421i) q^{26} +(0.707107 + 1.70711i) q^{29} +(0.707107 + 0.707107i) q^{32} -1.00000 q^{34} +(0.707107 + 0.707107i) q^{36} +(-1.70711 + 0.707107i) q^{37} +(-0.707107 - 0.292893i) q^{40} +(-0.707107 + 1.70711i) q^{41} +(-0.707107 - 0.292893i) q^{45} -0.414214 q^{50} +2.00000 q^{52} +(-1.00000 - 1.00000i) q^{53} +(0.707107 - 1.70711i) q^{58} +(0.707107 - 1.70711i) q^{61} -1.00000i q^{64} +(-1.41421 + 0.585786i) q^{65} +(0.707107 + 0.707107i) q^{68} -1.00000i q^{72} +(-0.292893 - 0.707107i) q^{73} +(1.70711 + 0.707107i) q^{74} +(0.292893 + 0.707107i) q^{80} -1.00000i q^{81} +(1.70711 - 0.707107i) q^{82} +(-0.707107 - 0.292893i) q^{85} +(0.292893 + 0.707107i) q^{90} +(-0.292893 - 0.707107i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{5}+O(q^{10})$$ 4 * q - 4 * q^5 $$4 q - 4 q^{5} - 4 q^{10} - 4 q^{16} - 4 q^{18} + 4 q^{25} - 4 q^{34} - 4 q^{37} + 4 q^{50} + 8 q^{52} - 4 q^{53} - 4 q^{73} + 4 q^{74} + 4 q^{80} + 4 q^{82} + 4 q^{90} - 4 q^{97}+O(q^{100})$$ 4 * q - 4 * q^5 - 4 * q^10 - 4 * q^16 - 4 * q^18 + 4 * q^25 - 4 * q^34 - 4 * q^37 + 4 * q^50 + 8 * q^52 - 4 * q^53 - 4 * q^73 + 4 * q^74 + 4 * q^80 + 4 * q^82 + 4 * q^90 - 4 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 0.707107i −0.707107 0.707107i
$$3$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$4$$ 1.00000i 1.00000i
$$5$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0.707107 0.707107i 0.707107 0.707107i
$$9$$ 0.707107 0.707107i 0.707107 0.707107i
$$10$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$11$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$12$$ 0 0
$$13$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −1.00000
$$17$$ 0.707107 0.707107i 0.707107 0.707107i
$$18$$ −1.00000 −1.00000
$$19$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$20$$ 0.707107 0.292893i 0.707107 0.292893i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$24$$ 0 0
$$25$$ 0.292893 0.292893i 0.292893 0.292893i
$$26$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i $$0.250000\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$32$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$33$$ 0 0
$$34$$ −1.00000 −1.00000
$$35$$ 0 0
$$36$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$37$$ −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i $$0.750000\pi$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −0.707107 0.292893i −0.707107 0.292893i
$$41$$ −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i $$0.5\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$44$$ 0 0
$$45$$ −0.707107 0.292893i −0.707107 0.292893i
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −0.414214 −0.414214
$$51$$ 0 0
$$52$$ 2.00000 2.00000
$$53$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0.707107 1.70711i 0.707107 1.70711i
$$59$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$60$$ 0 0
$$61$$ 0.707107 1.70711i 0.707107 1.70711i 1.00000i $$-0.5\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000i 1.00000i
$$65$$ −1.41421 + 0.585786i −1.41421 + 0.585786i
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$72$$ 1.00000i 1.00000i
$$73$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$74$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$80$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$81$$ 1.00000i 1.00000i
$$82$$ 1.70711 0.707107i 1.70711 0.707107i
$$83$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$84$$ 0 0
$$85$$ −0.707107 0.292893i −0.707107 0.292893i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0.292893 + 0.292893i 0.292893 + 0.292893i
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ −1.41421 1.41421i −1.41421 1.41421i
$$105$$ 0 0
$$106$$ 1.41421i 1.41421i
$$107$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$108$$ 0 0
$$109$$ 0.292893 0.707107i 0.292893 0.707107i −0.707107 0.707107i $$-0.750000\pi$$
1.00000 $$0$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.707107 + 0.292893i 0.707107 + 0.292893i 0.707107 0.707107i $$-0.250000\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$117$$ −1.41421 1.41421i −1.41421 1.41421i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$122$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 0.414214i −1.00000 0.414214i
$$126$$ 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
$$129$$ 0 0
$$130$$ 1.41421 + 0.585786i 1.41421 + 0.585786i
$$131$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.00000i 1.00000i
$$137$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$145$$ 1.00000 1.00000i 1.00000 1.00000i
$$146$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$147$$ 0 0
$$148$$ −0.707107 1.70711i −0.707107 1.70711i
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$152$$ 0 0
$$153$$ 1.00000i 1.00000i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0.292893 0.707107i 0.292893 0.707107i
$$161$$ 0 0
$$162$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$163$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$164$$ −1.70711 0.707107i −1.70711 0.707107i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$168$$ 0 0
$$169$$ −3.00000 −3.00000
$$170$$ 0.292893 + 0.707107i 0.292893 + 0.707107i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i $$0.750000\pi$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$180$$ 0.292893 0.707107i 0.292893 0.707107i
$$181$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$194$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −0.292893 + 0.707107i −0.292893 + 0.707107i 0.707107 + 0.707107i $$0.250000\pi$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$200$$ 0.414214i 0.414214i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1.41421 1.41421
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 2.00000i 2.00000i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$212$$ 1.00000 1.00000i 1.00000 1.00000i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.41421 1.41421i −1.41421 1.41421i
$$222$$ 0 0
$$223$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 0.414214i 0.414214i
$$226$$ −0.292893 0.707107i −0.292893 0.707107i
$$227$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$228$$ 0 0
$$229$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$233$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$234$$ 2.00000i 2.00000i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$0.5\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ 0 0
$$244$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0.414214 + 1.00000i 0.414214 + 1.00000i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −0.585786 1.41421i −0.585786 1.41421i
$$261$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$262$$ 0 0
$$263$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ 0 0
$$265$$ −0.414214 + 1.00000i −0.414214 + 1.00000i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$273$$ 0 0
$$274$$ −1.00000 1.00000i −1.00000 1.00000i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$282$$ 0 0
$$283$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000 1.00000
$$289$$ 1.00000i 1.00000i
$$290$$ −1.41421 −1.41421
$$291$$ 0 0
$$292$$ 0.707107 0.292893i 0.707107 0.292893i
$$293$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1.41421 −1.41421
$$306$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$312$$ 0 0
$$313$$ 0.707107 1.70711i 0.707107 1.70711i 1.00000i $$-0.5\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$314$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ −0.585786 0.585786i −0.585786 0.585786i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$332$$ 0 0
$$333$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$0.5\pi$$
$$338$$ 2.12132 + 2.12132i 2.12132 + 2.12132i
$$339$$ 0 0
$$340$$ 0.292893 0.707107i 0.292893 0.707107i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$347$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.41421i 1.41421i 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
$$359$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$360$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$361$$ 1.00000i 1.00000i
$$362$$ −0.707107 1.70711i −0.707107 1.70711i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −0.414214 + 0.414214i −0.414214 + 0.414214i
$$366$$ 0 0
$$367$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$368$$ 0 0
$$369$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$370$$ 1.41421i 1.41421i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3.41421 1.41421i 3.41421 1.41421i
$$378$$ 0 0
$$379$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −0.707107 1.70711i −0.707107 1.70711i
$$387$$ 0 0
$$388$$ 0.707107 0.292893i 0.707107 0.292893i
$$389$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0.707107 0.292893i 0.707107 0.292893i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.292893 + 0.292893i −0.292893 + 0.292893i
$$401$$ −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i $$0.5\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$410$$ −1.00000 1.00000i −1.00000 1.00000i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.41421 1.41421i 1.41421 1.41421i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$420$$ 0 0
$$421$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ −1.41421 −1.41421
$$425$$ 0.414214i 0.414214i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$432$$ 0 0
$$433$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 2.00000i 2.00000i
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.707107 1.70711i 0.707107 1.70711i 1.00000i $$-0.5\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$450$$ −0.292893 + 0.292893i −0.292893 + 0.292893i
$$451$$ 0 0
$$452$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$458$$ 1.41421 1.41421
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ −0.707107 1.70711i −0.707107 1.70711i
$$465$$ 0 0
$$466$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$467$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$468$$ 1.41421 1.41421i 1.41421 1.41421i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −1.41421 −1.41421
$$478$$ 0 0
$$479$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$480$$ 0 0
$$481$$ 1.41421 + 3.41421i 1.41421 + 3.41421i
$$482$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$483$$ 0 0
$$484$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$485$$ −0.414214 + 0.414214i −0.414214 + 0.414214i
$$486$$ 0 0
$$487$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$488$$ −0.707107 1.70711i −0.707107 1.70711i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$492$$ 0 0
$$493$$ 1.70711 + 0.707107i 1.70711 + 0.707107i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$500$$ 0.414214 1.00000i 0.414214 1.00000i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.707107 0.707107i −0.707107 0.707107i
$$513$$ 0 0
$$514$$ 1.41421i 1.41421i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −0.585786 + 1.41421i −0.585786 + 1.41421i
$$521$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$522$$ −0.707107 1.70711i −0.707107 1.70711i
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$530$$ 1.00000 0.414214i 1.00000 0.414214i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3.41421 + 1.41421i 3.41421 + 1.41421i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.707107 0.292893i 0.707107 0.292893i 1.00000i $$-0.5\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 1.00000 1.00000
$$545$$ −0.585786 −0.585786
$$546$$ 0 0
$$547$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$548$$ 1.41421i 1.41421i
$$549$$ −0.707107 1.70711i −0.707107 1.70711i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1.41421i 1.41421i −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
$$562$$ −1.41421 −1.41421
$$563$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$564$$ 0 0
$$565$$ 0.585786i 0.585786i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$570$$ 0 0
$$571$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.707107 0.707107i −0.707107 0.707107i
$$577$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$578$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$579$$ 0 0
$$580$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −0.707107 0.292893i −0.707107 0.292893i
$$585$$ −0.585786 + 1.41421i −0.585786 + 1.41421i
$$586$$ 1.00000 1.00000i 1.00000 1.00000i
$$587$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.70711 0.707107i 1.70711 0.707107i
$$593$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0.292893 0.707107i 0.292893 0.707107i
$$606$$ 0 0
$$607$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$611$$ 0 0
$$612$$ 1.00000 1.00000
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 $$0$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$618$$ 0 0
$$619$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.414214i 0.414214i
$$626$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$627$$ 0 0
$$628$$ 1.41421 1.41421
$$629$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$630$$ 0 0
$$631$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −0.707107 1.70711i −0.707107 1.70711i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$641$$ −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i $$-0.250000\pi$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ −0.707107 0.707107i −0.707107 0.707107i
$$649$$ 0 0
$$650$$ 0.828427i 0.828427i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0.707107 1.70711i 0.707107 1.70711i 1.00000i $$-0.5\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.707107 1.70711i 0.707107 1.70711i
$$657$$ −0.707107 0.292893i −0.707107 0.292893i
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 1.70711 0.707107i 1.70711 0.707107i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.292893 0.707107i 0.292893 0.707107i −0.707107 0.707107i $$-0.750000\pi$$
1.00000 $$0$$
$$674$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$675$$ 0 0
$$676$$ 3.00000i 3.00000i
$$677$$ 0.707107 0.292893i 0.707107 0.292893i 1.00000i $$-0.5\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$684$$ 0 0
$$685$$ −0.414214 1.00000i −0.414214 1.00000i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$690$$ 0 0
$$691$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$692$$ −0.707107 1.70711i −0.707107 1.70711i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0.707107 + 1.70711i 0.707107 + 1.70711i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 1.00000 1.00000i 1.00000 1.00000i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i $$0.250000\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$720$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$721$$ 0 0
$$722$$ 0.707107 0.707107i 0.707107 0.707107i
$$723$$ 0 0
$$724$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$725$$ 0.707107 + 0.292893i 0.707107 + 0.292893i
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −0.707107 0.707107i −0.707107 0.707107i
$$730$$ 0.585786 0.585786
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 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 0
$$738$$ 0.707107 1.70711i 0.707107 1.70711i
$$739$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$740$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −3.41421 1.41421i −3.41421 1.41421i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i $$-0.250000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −0.707107 + 0.292893i −0.707107 + 0.292893i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −0.707107 + 1.70711i −0.707107 + 1.70711i
$$773$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −0.707107 0.292893i −0.707107 0.292893i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1.00000 + 0.414214i −1.00000 + 0.414214i
$$786$$ 0 0
$$787$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$788$$ −0.707107 0.292893i −0.707107 0.292893i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −3.41421 1.41421i −3.41421 1.41421i
$$794$$ −0.707107 1.70711i −0.707107 1.70711i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0.414214 0.414214