# Properties

 Label 3800.1.bd.f.3051.1 Level $3800$ Weight $1$ Character 3800.3051 Analytic conductor $1.896$ Analytic rank $0$ Dimension $4$ Projective image $D_{3}$ CM discriminant -40 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(1451,3800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 2]))

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

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

chi := DirichletCharacter("3800.1451");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3800.bd (of order $$6$$, degree $$2$$, 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: $$1.89644704801$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 760) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.14440.1 Artin image: $S_3\times C_{12}$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{24} - \cdots)$$

## Embedding invariants

 Embedding label 3051.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3800.3051 Dual form 3800.1.bd.f.1451.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} -1.00000 q^{11} +(-1.73205 + 1.00000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.00000i q^{18} +(0.500000 - 0.866025i) q^{19} +(0.866025 + 0.500000i) q^{22} +(0.866025 - 0.500000i) q^{23} +2.00000 q^{26} +(0.866025 - 0.500000i) q^{28} +(0.866025 - 0.500000i) q^{32} +(-0.500000 + 0.866025i) q^{36} -1.00000i q^{37} +(-0.866025 + 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{41} +(-0.500000 - 0.866025i) q^{44} -1.00000 q^{46} +(1.73205 - 1.00000i) q^{47} +(-1.73205 - 1.00000i) q^{52} +(0.866025 - 0.500000i) q^{53} -1.00000 q^{56} +(1.00000 - 1.73205i) q^{59} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.866025 - 0.500000i) q^{72} +(-0.500000 + 0.866025i) q^{74} +1.00000 q^{76} +1.00000i q^{77} +(-0.500000 + 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{82} +1.00000i q^{88} +(-0.500000 - 0.866025i) q^{89} +(1.00000 + 1.73205i) q^{91} +(0.866025 + 0.500000i) q^{92} -2.00000 q^{94} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{4} + 2 q^{9}+O(q^{10})$$ 4 * q + 2 * q^4 + 2 * q^9 $$4 q + 2 q^{4} + 2 q^{9} - 4 q^{11} - 2 q^{14} - 2 q^{16} + 2 q^{19} + 8 q^{26} - 2 q^{36} + 2 q^{41} - 2 q^{44} - 4 q^{46} - 4 q^{56} + 4 q^{59} - 4 q^{64} - 2 q^{74} + 4 q^{76} - 2 q^{81} - 2 q^{89} + 4 q^{91} - 8 q^{94} - 2 q^{99}+O(q^{100})$$ 4 * q + 2 * q^4 + 2 * q^9 - 4 * q^11 - 2 * q^14 - 2 * q^16 + 2 * q^19 + 8 * q^26 - 2 * q^36 + 2 * q^41 - 2 * q^44 - 4 * q^46 - 4 * q^56 + 4 * q^59 - 4 * q^64 - 2 * q^74 + 4 * q^76 - 2 * q^81 - 2 * q^89 + 4 * q^91 - 8 * q^94 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$951$$ $$1901$$ $$1977$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.866025 0.500000i
$$3$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 0 0
$$13$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$14$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 1.00000i 1.00000i
$$19$$ 0.500000 0.866025i 0.500000 0.866025i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$23$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.00000 2.00000
$$27$$ 0 0
$$28$$ 0.866025 0.500000i 0.866025 0.500000i
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0.866025 0.500000i 0.866025 0.500000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$37$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$38$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$42$$ 0 0
$$43$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$44$$ −0.500000 0.866025i −0.500000 0.866025i
$$45$$ 0 0
$$46$$ −1.00000 −1.00000
$$47$$ 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i $$-0.166667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.73205 1.00000i −1.73205 1.00000i
$$53$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.00000 −1.00000
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$62$$ 0 0
$$63$$ 0.866025 0.500000i 0.866025 0.500000i
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$72$$ 0.866025 0.500000i 0.866025 0.500000i
$$73$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$74$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$75$$ 0 0
$$76$$ 1.00000 1.00000
$$77$$ 1.00000i 1.00000i
$$78$$ 0 0
$$79$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 1.00000i 1.00000i
$$89$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$92$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$93$$ 0 0
$$94$$ −2.00000 −2.00000
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$98$$ 0 0
$$99$$ −0.500000 0.866025i −0.500000 0.866025i
$$100$$ 0 0
$$101$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$102$$ 0 0
$$103$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$105$$ 0 0
$$106$$ −1.00000 −1.00000
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.73205 1.00000i −1.73205 1.00000i
$$118$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −1.00000 −1.00000
$$127$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$132$$ 0 0
$$133$$ −0.866025 0.500000i −0.866025 0.500000i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$138$$ 0 0
$$139$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1.73205 1.00000i 1.73205 1.00000i
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0.866025 0.500000i 0.866025 0.500000i
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ −0.866025 0.500000i −0.866025 0.500000i
$$153$$ 0 0
$$154$$ 0.500000 0.866025i 0.500000 0.866025i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −0.500000 0.866025i −0.500000 0.866025i
$$162$$ 0.866025 0.500000i 0.866025 0.500000i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 1.00000 1.00000
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 1.50000 2.59808i 1.50000 2.59808i
$$170$$ 0 0
$$171$$ 1.00000 1.00000
$$172$$ 0 0
$$173$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.500000 0.866025i 0.500000 0.866025i
$$177$$ 0 0
$$178$$ 1.00000i 1.00000i
$$179$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$182$$ 2.00000i 2.00000i
$$183$$ 0 0
$$184$$ −0.500000 0.866025i −0.500000 0.866025i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$198$$ 1.00000i 1.00000i
$$199$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0.500000 0.866025i 0.500000 0.866025i
$$207$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$208$$ 2.00000i 2.00000i
$$209$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$210$$ 0 0
$$211$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$212$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$224$$ −0.500000 0.866025i −0.500000 0.866025i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$234$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$235$$ 0 0
$$236$$ 2.00000 2.00000
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.00000i 2.00000i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$252$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$253$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$254$$ 1.00000 1.00000
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.500000 0.866025i
$$257$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ 0 0
$$259$$ −1.00000 −1.00000
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$263$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 2.00000i 2.00000i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −2.00000 −2.00000
$$287$$ −0.866025 0.500000i −0.866025 0.500000i
$$288$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$289$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −1.00000 −1.00000
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$308$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ −0.500000 0.866025i −0.500000 0.866025i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 1.00000i 1.00000i
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −0.866025 0.500000i −0.866025 0.500000i
$$329$$ −1.00000 1.73205i −1.00000 1.73205i
$$330$$ 0 0
$$331$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 0 0
$$333$$ 0.866025 0.500000i 0.866025 0.500000i
$$334$$ 1.00000 1.00000
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$338$$ −2.59808 + 1.50000i −2.59808 + 1.50000i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −0.866025 0.500000i −0.866025 0.500000i
$$343$$ 1.00000i 1.00000i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$347$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0.500000 0.866025i 0.500000 0.866025i
$$357$$ 0 0
$$358$$ −0.866025 0.500000i −0.866025 0.500000i
$$359$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$360$$ 0 0
$$361$$ −0.500000 0.866025i −0.500000 0.866025i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i $$-0.166667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$368$$ 1.00000i 1.00000i
$$369$$ 1.00000 1.00000
$$370$$ 0 0
$$371$$ −0.500000 0.866025i −0.500000 0.866025i
$$372$$ 0 0
$$373$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.00000 1.73205i −1.00000 1.73205i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$395$$ 0 0
$$396$$ 0.500000 0.866025i 0.500000 0.866025i
$$397$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.00000i 1.00000i
$$408$$ 0 0
$$409$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$413$$ −1.73205 1.00000i −1.73205 1.00000i
$$414$$ −0.500000 0.866025i −0.500000 0.866025i
$$415$$ 0 0
$$416$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$417$$ 0 0
$$418$$ 0.866025 0.500000i 0.866025 0.500000i
$$419$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$420$$ 0 0
$$421$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$423$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$424$$ −0.500000 0.866025i −0.500000 0.866025i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ 0 0
$$433$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1.00000i 1.00000i
$$438$$ 0 0
$$439$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$447$$ 0 0
$$448$$ 1.00000i 1.00000i
$$449$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$450$$ 0 0
$$451$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$462$$ 0 0
$$463$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 2.00000i 2.00000i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.73205 1.00000i −1.73205 1.00000i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 0 0
$$481$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$482$$ 2.00000i 2.00000i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 1.00000 1.73205i 1.00000 1.73205i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 2.00000i 2.00000i
$$503$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$504$$ −0.500000 0.866025i −0.500000 0.866025i
$$505$$ 0 0
$$506$$ 1.00000 1.00000
$$507$$ 0 0
$$508$$ −0.866025 0.500000i −0.866025 0.500000i
$$509$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −1.73205 + 1.00000i −1.73205 + 1.00000i
$$518$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$522$$ 0 0
$$523$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$524$$ 1.00000 1.00000
$$525$$ 0 0
$$526$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 2.00000 2.00000
$$532$$ 1.00000i 1.00000i
$$533$$ 2.00000i 2.00000i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 1.00000 1.73205i 1.00000 1.73205i
$$555$$ 0 0
$$556$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$557$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 1.00000i 1.00000i
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$568$$ 0 0
$$569$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$572$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$573$$ 0 0
$$574$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 1.00000i 1.00000i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0.500000 0.866025i 0.500000 0.866025i
$$587$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 1.73205 1.00000i 1.73205 1.00000i
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$608$$ 1.00000i 1.00000i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −2.00000 + 3.46410i −2.00000 + 3.46410i
$$612$$ 0 0
$$613$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 1.00000 1.00000
$$617$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$618$$ 0 0
$$619$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.00000i 1.00000i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 1.00000 1.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$644$$ 0.500000 0.866025i 0.500000 0.866025i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$648$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$649$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$657$$ 0 0
$$658$$ 2.00000i 2.00000i
$$659$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$662$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −1.00000 −1.00000
$$667$$ 0 0
$$668$$ −0.866025 0.500000i −0.866025 0.500000i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 3.00000 3.00000
$$677$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$685$$ 0 0
$$686$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$690$$ 0 0
$$691$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 1.00000i 1.00000i
$$693$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$702$$ 0 0
$$703$$ −0.866025 0.500000i −0.866025 0.500000i
$$704$$ 1.00000 1.00000
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$720$$ 0 0
$$721$$ 1.00000 1.00000
$$722$$ 1.00000i 1.00000i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
−0.866025 0.500000i $$-0.833333\pi$$
$$728$$ 1.73205 1.00000i 1.73205 1.00000i
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$734$$ −2.00000 −2.00000
$$735$$ 0 0
$$736$$ 0.500000 0.866025i 0.500000 0.866025i
$$737$$ 0 0
$$738$$ −0.866025 0.500000i −0.866025 0.500000i
$$739$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 1.00000i 1.00000i
$$743$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0.500000 0.866025i 0.500000 0.866025i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$752$$ 2.00000i 2.00000i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$758$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −1.00000 1.73205i −1.00000 1.73205i
$$767$$ 4.00000i 4.00000i
$$768$$ 0 0
$$769$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.500000 0.866025i −0.500000 0.866025i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0.866025 0.500000i 0.866025 0.500000i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$793$$ 0 0
$$794$$ −0.500000 0.866025i −0.500000 0.866025i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.00000i 1.00000i −0.866025