# Properties

 Label 2888.1.s.a.477.1 Level $2888$ Weight $1$ Character 2888.477 Analytic conductor $1.441$ Analytic rank $0$ Dimension $6$ Projective image $D_{3}$ CM discriminant -152 Inner twists $12$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(333,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

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

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

chi := DirichletCharacter("2888.333");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2888.s (of order $$18$$, degree $$6$$, 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: $$6$$ Coefficient field: $$\Q(\zeta_{18})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{3} + 1$$ x^6 - x^3 + 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 3.1.152.1

## Embedding invariants

 Embedding label 477.1 Root $$0.939693 + 0.342020i$$ of defining polynomial Character $$\chi$$ $$=$$ 2888.477 Dual form 2888.1.s.a.333.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$$ $$q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.500000 + 0.866025i) q^{12} +(-0.766044 + 0.642788i) q^{13} +(0.939693 - 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +(0.173648 - 0.984808i) q^{21} +(0.939693 + 0.342020i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(-0.173648 - 0.984808i) q^{29} +(0.766044 - 0.642788i) q^{32} +(0.939693 + 0.342020i) q^{34} +2.00000 q^{37} +1.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(0.500000 - 0.866025i) q^{46} +(0.347296 + 1.96962i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-0.500000 - 0.866025i) q^{50} +(0.766044 - 0.642788i) q^{51} +(0.939693 - 0.342020i) q^{52} +(0.939693 + 0.342020i) q^{53} +(0.766044 + 0.642788i) q^{54} -1.00000 q^{56} -1.00000 q^{58} +(-0.173648 + 0.984808i) q^{59} +(-0.500000 - 0.866025i) q^{64} +(-0.173648 - 0.984808i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(-0.766044 - 0.642788i) q^{73} +(0.347296 - 1.96962i) q^{74} -1.00000 q^{75} +(0.173648 - 0.984808i) q^{78} +(0.939693 - 0.342020i) q^{81} +(-0.500000 + 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{87} +(-0.939693 - 0.342020i) q^{91} +(-0.766044 - 0.642788i) q^{92} +2.00000 q^{94} -1.00000 q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 3 q^{7} - 3 q^{8}+O(q^{10})$$ 6 * q + 3 * q^7 - 3 * q^8 $$6 q + 3 q^{7} - 3 q^{8} + 3 q^{12} + 3 q^{26} - 3 q^{27} + 12 q^{37} + 6 q^{39} + 3 q^{46} - 3 q^{50} - 6 q^{56} - 6 q^{58} - 3 q^{64} + 3 q^{68} - 3 q^{69} - 6 q^{75} - 3 q^{84} - 3 q^{87} + 12 q^{94} - 6 q^{96}+O(q^{100})$$ 6 * q + 3 * q^7 - 3 * q^8 + 3 * q^12 + 3 * q^26 - 3 * q^27 + 12 * q^37 + 6 * q^39 + 3 * q^46 - 3 * q^50 - 6 * q^56 - 6 * q^58 - 3 * q^64 + 3 * q^68 - 3 * q^69 - 6 * q^75 - 3 * q^84 - 3 * q^87 + 12 * q^94 - 6 * q^96

## Character values

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

 $$n$$ $$1445$$ $$2167$$ $$2529$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.173648 0.984808i 0.173648 0.984808i
$$3$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$4$$ −0.939693 0.342020i −0.939693 0.342020i
$$5$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$6$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$7$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$8$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$13$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$14$$ 0.939693 0.342020i 0.939693 0.342020i
$$15$$ 0 0
$$16$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$17$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 0.173648 0.984808i 0.173648 0.984808i
$$22$$ 0 0
$$23$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$24$$ 0.939693 0.342020i 0.939693 0.342020i
$$25$$ 0.766044 0.642788i 0.766044 0.642788i
$$26$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$27$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$28$$ −0.173648 0.984808i −0.173648 0.984808i
$$29$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ 0.766044 0.642788i 0.766044 0.642788i
$$33$$ 0 0
$$34$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$38$$ 0 0
$$39$$ 1.00000 1.00000
$$40$$ 0 0
$$41$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$42$$ −0.939693 0.342020i −0.939693 0.342020i
$$43$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0.500000 0.866025i 0.500000 0.866025i
$$47$$ 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i $$0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$48$$ −0.173648 0.984808i −0.173648 0.984808i
$$49$$ 0 0
$$50$$ −0.500000 0.866025i −0.500000 0.866025i
$$51$$ 0.766044 0.642788i 0.766044 0.642788i
$$52$$ 0.939693 0.342020i 0.939693 0.342020i
$$53$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$54$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$55$$ 0 0
$$56$$ −1.00000 −1.00000
$$57$$ 0 0
$$58$$ −1.00000 −1.00000
$$59$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.500000 0.866025i −0.500000 0.866025i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$68$$ 0.500000 0.866025i 0.500000 0.866025i
$$69$$ −0.500000 0.866025i −0.500000 0.866025i
$$70$$ 0 0
$$71$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$72$$ 0 0
$$73$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$74$$ 0.347296 1.96962i 0.347296 1.96962i
$$75$$ −1.00000 −1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0.173648 0.984808i 0.173648 0.984808i
$$79$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$80$$ 0 0
$$81$$ 0.939693 0.342020i 0.939693 0.342020i
$$82$$ 0 0
$$83$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$84$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$88$$ 0 0
$$89$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$90$$ 0 0
$$91$$ −0.939693 0.342020i −0.939693 0.342020i
$$92$$ −0.766044 0.642788i −0.766044 0.642788i
$$93$$ 0 0
$$94$$ 2.00000 2.00000
$$95$$ 0 0
$$96$$ −1.00000 −1.00000
$$97$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$101$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$102$$ −0.500000 0.866025i −0.500000 0.866025i
$$103$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$104$$ −0.173648 0.984808i −0.173648 0.984808i
$$105$$ 0 0
$$106$$ 0.500000 0.866025i 0.500000 0.866025i
$$107$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 0.766044 0.642788i 0.766044 0.642788i
$$109$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$110$$ 0 0
$$111$$ −1.53209 1.28558i −1.53209 1.28558i
$$112$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$117$$ 0 0
$$118$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$119$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$120$$ 0 0
$$121$$ −0.500000 0.866025i −0.500000 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$128$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1.00000 −1.00000
$$135$$ 0 0
$$136$$ −0.766044 0.642788i −0.766044 0.642788i
$$137$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$138$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$139$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$140$$ 0 0
$$141$$ 1.00000 1.73205i 1.00000 1.73205i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$147$$ 0 0
$$148$$ −1.87939 0.684040i −1.87939 0.684040i
$$149$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$150$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.939693 0.342020i −0.939693 0.342020i
$$157$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$158$$ 0 0
$$159$$ −0.500000 0.866025i −0.500000 0.866025i
$$160$$ 0 0
$$161$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$162$$ −0.173648 0.984808i −0.173648 0.984808i
$$163$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$168$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0.347296 1.96962i 0.347296 1.96962i 0.173648 0.984808i $$-0.444444\pi$$
0.173648 0.984808i $$-0.444444\pi$$
$$174$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$175$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$176$$ 0 0
$$177$$ 0.766044 0.642788i 0.766044 0.642788i
$$178$$ 0 0
$$179$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ 0 0
$$181$$ 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i $$0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$182$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$183$$ 0 0
$$184$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0.347296 1.96962i 0.347296 1.96962i
$$189$$ −1.00000 −1.00000
$$190$$ 0 0
$$191$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$193$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$198$$ 0 0
$$199$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$200$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$201$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$202$$ 0 0
$$203$$ 0.766044 0.642788i 0.766044 0.642788i
$$204$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.00000 −1.00000
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$212$$ −0.766044 0.642788i −0.766044 0.642788i
$$213$$ 0 0
$$214$$ 0.939693 0.342020i 0.939693 0.342020i
$$215$$ 0 0
$$216$$ −0.500000 0.866025i −0.500000 0.866025i
$$217$$ 0 0
$$218$$ −0.173648 0.984808i −0.173648 0.984808i
$$219$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$220$$ 0 0
$$221$$ −0.500000 0.866025i −0.500000 0.866025i
$$222$$ −1.53209 + 1.28558i −1.53209 + 1.28558i
$$223$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$224$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$233$$ −1.87939 + 0.684040i −1.87939 + 0.684040i −0.939693 + 0.342020i $$0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0.500000 0.866025i 0.500000 0.866025i
$$237$$ 0 0
$$238$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$239$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$240$$ 0 0
$$241$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$242$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$257$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$258$$ 0 0
$$259$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i $$0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$269$$ 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i $$0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$270$$ 0 0
$$271$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$272$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$273$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$274$$ 0.500000 0.866025i 0.500000 0.866025i
$$275$$ 0 0
$$276$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$277$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$282$$ −1.53209 1.28558i −1.53209 1.28558i
$$283$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$293$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$300$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i $$0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$313$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$318$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0.173648 0.984808i 0.173648 0.984808i
$$322$$ 1.00000 1.00000
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$326$$ 0 0
$$327$$ −0.939693 0.342020i −0.939693 0.342020i
$$328$$ 0 0
$$329$$ −1.53209 + 1.28558i −1.53209 + 1.28558i
$$330$$ 0 0
$$331$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0.766044 0.642788i 0.766044 0.642788i
$$337$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.00000 1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.87939 0.684040i −1.87939 0.684040i
$$347$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$348$$ 0.766044 0.642788i 0.766044 0.642788i
$$349$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 0.500000 0.866025i 0.500000 0.866025i
$$351$$ −0.173648 0.984808i −0.173648 0.984808i
$$352$$ 0 0
$$353$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$354$$ −0.500000 0.866025i −0.500000 0.866025i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$358$$ 1.53209 + 1.28558i 1.53209 + 1.28558i
$$359$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 2.00000 2.00000
$$363$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$364$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.53209 1.28558i 1.53209 1.28558i 0.766044 0.642788i $$-0.222222\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$368$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$372$$ 0 0
$$373$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.87939 0.684040i −1.87939 0.684040i
$$377$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$378$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$379$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$383$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$384$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$390$$ 0 0
$$391$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$398$$ −1.00000 −1.00000
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$402$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −0.500000 0.866025i −0.500000 0.866025i
$$407$$ 0 0
$$408$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$409$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$410$$ 0 0
$$411$$ −0.500000 0.866025i −0.500000 0.866025i
$$412$$ 0 0
$$413$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$422$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$423$$ 0 0
$$424$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$425$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.173648 0.984808i −0.173648 0.984808i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$432$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$433$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.00000 −1.00000
$$437$$ 0 0
$$438$$ 1.00000 1.00000
$$439$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$443$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$444$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0.500000 0.866025i 0.500000 0.866025i
$$449$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$455$$ 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
$$459$$ −0.766044 0.642788i −0.766044 0.642788i
$$460$$ 0 0
$$461$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$462$$ 0 0
$$463$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$464$$ 0.500000 0.866025i 0.500000 0.866025i
$$465$$ 0 0
$$466$$ 0.347296 + 1.96962i 0.347296 + 1.96962i
$$467$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0.766044 0.642788i 0.766044 0.642788i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.766044 0.642788i −0.766044 0.642788i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 1.00000 1.00000
$$477$$ 0 0
$$478$$ −0.766044 0.642788i −0.766044 0.642788i
$$479$$ −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 0.342020i $$-0.888889\pi$$
$$480$$ 0 0
$$481$$ −1.53209 + 1.28558i −1.53209 + 1.28558i
$$482$$ 0 0
$$483$$ 0.500000 0.866025i 0.500000 0.866025i
$$484$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$492$$ 0 0
$$493$$ 1.00000 1.00000
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 0.342020i $$-0.888889\pi$$
$$510$$ 0 0
$$511$$ 0.173648 0.984808i 0.173648 0.984808i
$$512$$ 1.00000 1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 1.87939 0.684040i 1.87939 0.684040i
$$519$$ −1.53209 + 1.28558i −1.53209 + 1.28558i
$$520$$ 0 0
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$524$$ 0 0
$$525$$ −0.500000 0.866025i −0.500000 0.866025i
$$526$$ 1.53209 1.28558i 1.53209 1.28558i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$537$$ 1.87939 0.684040i 1.87939 0.684040i
$$538$$ 1.53209 1.28558i 1.53209 1.28558i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$542$$ −0.173648 0.984808i −0.173648 0.984808i
$$543$$ 1.00000 1.73205i 1.00000 1.73205i
$$544$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$545$$ 0 0
$$546$$ 0.939693 0.342020i 0.939693 0.342020i
$$547$$ −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 0.342020i $$-0.888889\pi$$
$$548$$ −0.766044 0.642788i −0.766044 0.642788i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 1.00000 1.00000
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$564$$ −1.53209 + 1.28558i −1.53209 + 1.28558i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$574$$ 0 0
$$575$$ 0.939693 0.342020i 0.939693 0.342020i
$$576$$ 0 0
$$577$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0.939693 0.342020i 0.939693 0.342020i
$$585$$ 0 0
$$586$$ −0.766044 0.642788i −0.766044 0.642788i
$$587$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.53209 + 1.28558i 1.53209 + 1.28558i
$$593$$ −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 0.342020i $$-0.888889\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$598$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$599$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$600$$ 0.500000 0.866025i 0.500000 0.866025i
$$601$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
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
$$609$$ −1.00000 −1.00000
$$610$$ 0 0
$$611$$ −1.53209 1.28558i −1.53209 1.28558i
$$612$$ 0 0
$$613$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$614$$ 1.53209 1.28558i 1.53209 1.28558i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i $$0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$618$$ 0 0
$$619$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$620$$ 0 0
$$621$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$622$$ 0.939693 0.342020i 0.939693 0.342020i
$$623$$ 0 0
$$624$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$625$$ 0.173648 0.984808i 0.173648 0.984808i
$$626$$ −1.00000 −1.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −0.347296 + 1.96962i −0.347296 + 1.96962i
$$630$$ 0 0
$$631$$ −1.87939 0.684040i −1.87939 0.684040i −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 0.342020i $$-0.888889\pi$$
$$632$$ 0 0
$$633$$ 0.766044 0.642788i 0.766044 0.642788i
$$634$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$635$$ 0 0
$$636$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$642$$ −0.939693 0.342020i −0.939693 0.342020i
$$643$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$644$$ 0.173648 0.984808i 0.173648 0.984808i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$649$$ 0 0
$$650$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$654$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$659$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$660$$ 0 0
$$661$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$662$$ −0.766044 0.642788i −0.766044 0.642788i
$$663$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0.173648 0.984808i 0.173648 0.984808i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −0.500000 0.866025i −0.500000 0.866025i
$$673$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$674$$ 0 0
$$675$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$676$$ 0 0
$$677$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$682$$ 0 0
$$683$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.173648 0.984808i 0.173648 0.984808i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$690$$ 0 0
$$691$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$692$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ −0.500000 0.866025i −0.500000 0.866025i
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 1.87939 + 0.684040i 1.87939 + 0.684040i
$$700$$ −0.766044 0.642788i −0.766044 0.642788i
$$701$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$702$$ −1.00000 −1.00000
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −0.766044 0.642788i −0.766044 0.642788i
$$707$$ 0 0
$$708$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$709$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0.500000 0.866025i 0.500000 0.866025i
$$715$$ 0 0
$$716$$ 1.53209 1.28558i 1.53209 1.28558i
$$717$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$718$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$719$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0.347296 1.96962i 0.347296 1.96962i
$$725$$ −0.766044 0.642788i −0.766044 0.642788i
$$726$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$727$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$728$$ 0.766044 0.642788i 0.766044 0.642788i
$$729$$ −0.500000 0.866025i −0.500000 0.866025i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ −1.00000 1.73205i −1.00000 1.73205i
$$735$$ 0 0
$$736$$ 0.939693 0.342020i 0.939693 0.342020i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 1.00000 1.00000
$$743$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0.939693 0.342020i 0.939693 0.342020i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$750$$ 0 0
$$751$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$752$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$753$$ 0 0
$$754$$ 0.766044 0.642788i 0.766044 0.642788i
$$755$$ 0 0
$$756$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$757$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$758$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$759$$ 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
$$763$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$764$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −0.500000 0.866025i −0.500000 0.866025i
$$768$$ 0.500000 0.866025i 0.500000 0.866025i
$$769$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0.347296 1.96962i 0.347296 1.96962i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$783$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$788$$ 0 0
$$789$$ −0.347296 1.96962i −0.347296 1.96962i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0