Properties

 Label 2888.1.k.a.2819.1 Level $2888$ Weight $1$ Character 2888.2819 Analytic conductor $1.441$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -8 Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(2595,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2888.2595");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2888.k (of order $$6$$, degree $$2$$, not 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: $$1.44129975648$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 152) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.2888.1 Artin image: $C_6\times S_3$ Artin field: Galois closure of 12.0.4452139149819904.6

Embedding invariants

 Embedding label 2819.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2888.2819 Dual form 2888.1.k.a.2595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} -1.00000 q^{11} +1.00000 q^{12} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{22} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-0.500000 - 0.866025i) q^{41} +(-1.00000 - 1.73205i) q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{59} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(-0.500000 + 0.866025i) q^{67} +2.00000 q^{68} +(0.500000 + 0.866025i) q^{73} +1.00000 q^{75} +(0.500000 + 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{82} -1.00000 q^{83} +(1.00000 - 1.73205i) q^{86} +1.00000 q^{88} +(1.00000 - 1.73205i) q^{89} -1.00000 q^{96} +(-0.500000 - 0.866025i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{8}+O(q^{10})$$ 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^8 $$2 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{8} - 2 q^{11} + 2 q^{12} - q^{16} - 2 q^{17} - q^{22} + q^{24} - q^{25} - 2 q^{27} + q^{32} + q^{33} + 2 q^{34} - q^{41} - 2 q^{43} + q^{44} - q^{48} + 2 q^{49} - 2 q^{50} - 2 q^{51} - q^{54} - q^{59} + 2 q^{64} - q^{66} - q^{67} + 4 q^{68} + q^{73} + 2 q^{75} + q^{81} + q^{82} - 2 q^{83} + 2 q^{86} + 2 q^{88} + 2 q^{89} - 2 q^{96} - q^{97} + q^{98}+O(q^{100})$$ 2 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^8 - 2 * q^11 + 2 * q^12 - q^16 - 2 * q^17 - q^22 + q^24 - q^25 - 2 * q^27 + q^32 + q^33 + 2 * q^34 - q^41 - 2 * q^43 + q^44 - q^48 + 2 * q^49 - 2 * q^50 - 2 * q^51 - q^54 - q^59 + 2 * q^64 - q^66 - q^67 + 4 * q^68 + q^73 + 2 * q^75 + q^81 + q^82 - 2 * q^83 + 2 * q^86 + 2 * q^88 + 2 * q^89 - 2 * q^96 - q^97 + q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$$.

 $$n$$ $$1445$$ $$2167$$ $$2529$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$3$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$4$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$5$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$6$$ 0.500000 0.866025i 0.500000 0.866025i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 1.00000 1.00000
$$13$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.500000 0.866025i
$$17$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.500000 0.866025i −0.500000 0.866025i
$$23$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$25$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ −1.00000 −1.00000
$$28$$ 0 0
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0.500000 0.866025i 0.500000 0.866025i
$$33$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$34$$ 1.00000 1.73205i 1.00000 1.73205i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$44$$ 0.500000 0.866025i 0.500000 0.866025i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$48$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$49$$ 1.00000 1.00000
$$50$$ −1.00000 −1.00000
$$51$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$52$$ 0 0
$$53$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ −0.500000 0.866025i −0.500000 0.866025i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$67$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$68$$ 2.00000 2.00000
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$72$$ 0 0
$$73$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ 1.00000 1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ 0 0
$$81$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$82$$ 0.500000 0.866025i 0.500000 0.866025i
$$83$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.00000 1.73205i 1.00000 1.73205i
$$87$$ 0 0
$$88$$ 1.00000 1.00000
$$89$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −1.00000
$$97$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$98$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$99$$ 0 0
$$100$$ −0.500000 0.866025i −0.500000 0.866025i
$$101$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$102$$ −2.00000 −2.00000
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$108$$ 0.500000 0.866025i 0.500000 0.866025i
$$109$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0.500000 0.866025i 0.500000 0.866025i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$128$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$129$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$130$$ 0 0
$$131$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ −1.00000 −1.00000
$$133$$ 0 0
$$134$$ −1.00000 −1.00000
$$135$$ 0 0
$$136$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$137$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$138$$ 0 0
$$139$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$147$$ −0.500000 0.866025i −0.500000 0.866025i
$$148$$ 0 0
$$149$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$163$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 1.00000 1.00000
$$165$$ 0 0
$$166$$ −0.500000 0.866025i −0.500000 0.866025i
$$167$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ −0.500000 0.866025i −0.500000 0.866025i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 2.00000
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$177$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$178$$ 2.00000 2.00000
$$179$$ 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 $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ −0.500000 0.866025i −0.500000 0.866025i
$$193$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ 0.500000 0.866025i 0.500000 0.866025i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ 0.500000 0.866025i 0.500000 0.866025i
$$201$$ 1.00000 1.00000
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −1.00000 1.73205i −1.00000 1.73205i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −1.00000 1.73205i −1.00000 1.73205i
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.500000 0.866025i 0.500000 0.866025i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$227$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 1.00000 1.00000
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −1.00000 −1.00000
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$250$$ 0 0
$$251$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$258$$ −2.00000 −2.00000
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$263$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$264$$ −0.500000 0.866025i −0.500000 0.866025i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −2.00000 −2.00000
$$268$$ −0.500000 0.866025i −0.500000 0.866025i
$$269$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$272$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$273$$ 0 0
$$274$$ 1.00000 1.00000
$$275$$ 0.500000 0.866025i 0.500000 0.866025i
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 1.00000 1.00000
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.50000 + 2.59808i −1.50000 + 2.59808i
$$290$$ 0 0
$$291$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$292$$ −1.00000 −1.00000
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0.500000 0.866025i 0.500000 0.866025i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1.00000 1.00000
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ 0 0
$$326$$ −0.500000 0.866025i −0.500000 0.866025i
$$327$$ 0 0
$$328$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ 0.500000 0.866025i 0.500000 0.866025i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$338$$ 0.500000 0.866025i 0.500000 0.866025i
$$339$$ −0.500000 0.866025i −0.500000 0.866025i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$353$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ −1.00000 −1.00000
$$355$$ 0 0
$$356$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$357$$ 0 0
$$358$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$359$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 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
$$383$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 0.500000 0.866025i 0.500000 0.866025i
$$385$$ 0 0
$$386$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$387$$ 0 0
$$388$$ 1.00000 1.00000
$$389$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 −1.00000
$$393$$ 0.500000 0.866025i 0.500000 0.866025i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$402$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 1.00000 1.73205i 1.00000 1.73205i
$$409$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ −1.00000 −1.00000
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.00000 −1.00000
$$418$$ 0 0
$$419$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$422$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.00000 2.00000
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1.00000 1.73205i 1.00000 1.73205i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$433$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 1.00000 1.00000
$$439$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 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
$$452$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$453$$ 0 0
$$454$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$458$$ 0 0
$$459$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$460$$ 0 0
$$461$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$467$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$473$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −1.00000 −1.00000
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$490$$ 0 0
$$491$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$492$$ −0.500000 0.866025i −0.500000 0.866025i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$499$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1.00000 1.00000
$$503$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$508$$ 0 0
$$509$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −1.00000
$$513$$ 0 0
$$514$$ −1.00000 −1.00000
$$515$$ 0 0
$$516$$ −1.00000 1.73205i −1.00000 1.73205i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$522$$ 0 0
$$523$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$524$$ −1.00000 −1.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.500000 0.866025i 0.500000 0.866025i
$$529$$ −0.500000 0.866025i −0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.00000 1.73205i −1.00000 1.73205i
$$535$$ 0 0
$$536$$ 0.500000 0.866025i 0.500000 0.866025i
$$537$$ −0.500000 0.866025i −0.500000 0.866025i
$$538$$ 0 0
$$539$$ −1.00000 −1.00000
$$540$$ 0 0
$$541$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −2.00000 −2.00000
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$548$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$549$$ 0 0
$$550$$ 1.00000 1.00000
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$557$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 1.00000 1.73205i 1.00000 1.73205i
$$562$$ −1.00000 −1.00000
$$563$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ −3.00000 −3.00000
$$579$$ 1.00000 1.73205i 1.00000 1.73205i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −1.00000 −1.00000
$$583$$ 0 0
$$584$$ −0.500000 0.866025i −0.500000 0.866025i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$588$$ 1.00000 1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$594$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ −1.00000 −1.00000
$$601$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$614$$ 0.500000 0.866025i 0.500000 0.866025i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$618$$ 0 0
$$619$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.500000 0.866025i
$$626$$ 1.00000 1.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$632$$ 0 0
$$633$$ 1.00000 1.73205i 1.00000 1.73205i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$642$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$643$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ −0.500000 0.866025i −0.500000 0.866025i
$$649$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0.500000 0.866025i 0.500000 0.866025i
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$663$$ 0 0
$$664$$ 1.00000 1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$674$$ 0.500000 0.866025i 0.500000 0.866025i
$$675$$ 0.500000 0.866025i 0.500000 0.866025i
$$676$$ 1.00000 1.00000
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0.500000 0.866025i 0.500000 0.866025i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.500000 0.866025i −0.500000 0.866025i
$$682$$ 0 0
$$683$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$698$$ 0 0
$$699$$ 0.500000 0.866025i 0.500000 0.866025i
$$700$$ 0 0
$$701$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −1.00000 −1.00000
$$705$$ 0 0
$$706$$ −0.500000 0.866025i −0.500000 0.866025i
$$707$$ 0 0
$$708$$ −0.500000 0.866025i −0.500000 0.866025i
$$709$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$713$$ 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 $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 1.00000 1.00000
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ −2.00000 + 3.46410i −2.00000 + 3.46410i
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0.500000 0.866025i 0.500000 0.866025i
$$738$$ 0 0
$$739$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −2.00000 −2.00000
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0 0
$$753$$ −1.00000 −1.00000
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$758$$ −1.00000 1.73205i −1.00000 1.73205i
$$759$$ 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
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 1.00000 1.00000
$$769$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ 1.00000 1.00000
$$772$$ −2.00000 −2.00000
$$773$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.500000 0.866025i −0.500000 0.866025i
$$785$$ 0 0
$$786$$ 1.00000 1.00000
$$787$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0