# Properties

 Label 760.1.bz.a.139.1 Level $760$ Weight $1$ Character 760.139 Analytic conductor $0.379$ Analytic rank $0$ Dimension $6$ Projective image $D_{9}$ CM discriminant -40 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,1,Mod(99,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 9, 2]))

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

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

chi := DirichletCharacter("760.99");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$760 = 2^{3} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 760.bz (of order $$18$$, degree $$6$$, 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: $$0.379289409601$$ 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: yes Projective image: $$D_{9}$$ Projective field: Galois closure of 9.1.43477921384960000.1

## Embedding invariants

 Embedding label 139.1 Root $$0.939693 - 0.342020i$$ of defining polynomial Character $$\chi$$ $$=$$ 760.139 Dual form 760.1.bz.a.339.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.173648 + 0.300767i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$$ $$q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.173648 + 0.300767i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(-0.766044 - 1.32683i) q^{11} +(0.939693 - 0.342020i) q^{13} +(0.0603074 + 0.342020i) q^{14} +(-0.939693 - 0.342020i) q^{16} +1.00000 q^{18} +(0.766044 - 0.642788i) q^{19} +1.00000 q^{20} +(-1.43969 - 0.524005i) q^{22} +(-0.326352 + 1.85083i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(0.500000 - 0.866025i) q^{26} +(0.266044 + 0.223238i) q^{28} +(-0.939693 + 0.342020i) q^{32} +(-0.326352 - 0.118782i) q^{35} +(0.766044 - 0.642788i) q^{36} -1.87939 q^{37} +(0.173648 - 0.984808i) q^{38} +(0.766044 - 0.642788i) q^{40} +(-1.43969 - 0.524005i) q^{41} +(-1.43969 + 0.524005i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.939693 + 1.62760i) q^{46} +(-0.766044 - 0.642788i) q^{47} +(0.439693 + 0.761570i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.173648 - 0.984808i) q^{52} +(0.0603074 - 0.342020i) q^{53} +(1.17365 - 0.984808i) q^{55} +0.347296 q^{56} +(-0.766044 + 0.642788i) q^{59} +(-0.326352 + 0.118782i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.500000 + 0.866025i) q^{65} +(-0.326352 + 0.118782i) q^{70} +(0.173648 - 0.984808i) q^{72} +(-1.43969 + 1.20805i) q^{74} +(-0.500000 - 0.866025i) q^{76} +0.532089 q^{77} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-1.43969 + 0.524005i) q^{82} +(-0.766044 + 1.32683i) q^{88} +(1.76604 - 0.642788i) q^{89} +(0.173648 + 0.984808i) q^{90} +(-0.0603074 + 0.342020i) q^{91} +(1.76604 + 0.642788i) q^{92} -1.00000 q^{94} +(0.766044 + 0.642788i) q^{95} +(0.826352 + 0.300767i) q^{98} +(0.266044 - 1.50881i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 3 q^{8}+O(q^{10})$$ 6 * q - 3 * q^8 $$6 q - 3 q^{8} + 6 q^{14} + 6 q^{18} + 6 q^{20} - 3 q^{22} - 3 q^{23} + 3 q^{26} - 3 q^{28} - 3 q^{35} - 3 q^{41} - 3 q^{44} - 3 q^{45} - 3 q^{49} - 3 q^{50} + 6 q^{53} + 6 q^{55} - 3 q^{63} - 3 q^{64} + 3 q^{65} - 3 q^{70} - 3 q^{74} - 3 q^{76} - 6 q^{77} - 3 q^{82} + 6 q^{89} - 6 q^{91} + 6 q^{92} - 6 q^{94} + 6 q^{98} - 3 q^{99}+O(q^{100})$$ 6 * q - 3 * q^8 + 6 * q^14 + 6 * q^18 + 6 * q^20 - 3 * q^22 - 3 * q^23 + 3 * q^26 - 3 * q^28 - 3 * q^35 - 3 * q^41 - 3 * q^44 - 3 * q^45 - 3 * q^49 - 3 * q^50 + 6 * q^53 + 6 * q^55 - 3 * q^63 - 3 * q^64 + 3 * q^65 - 3 * q^70 - 3 * q^74 - 3 * q^76 - 6 * q^77 - 3 * q^82 + 6 * q^89 - 6 * q^91 + 6 * q^92 - 6 * q^94 + 6 * q^98 - 3 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$381$$ $$401$$ $$457$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.766044 0.642788i 0.766044 0.642788i
$$3$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$4$$ 0.173648 0.984808i 0.173648 0.984808i
$$5$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$6$$ 0 0
$$7$$ −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$8$$ −0.500000 0.866025i −0.500000 0.866025i
$$9$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$10$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$11$$ −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 0.984808i $$-0.444444\pi$$
$$12$$ 0 0
$$13$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$14$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i
$$15$$ 0 0
$$16$$ −0.939693 0.342020i −0.939693 0.342020i
$$17$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$18$$ 1.00000 1.00000
$$19$$ 0.766044 0.642788i 0.766044 0.642788i
$$20$$ 1.00000 1.00000
$$21$$ 0 0
$$22$$ −1.43969 0.524005i −1.43969 0.524005i
$$23$$ −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i $$0.444444\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0 0
$$25$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$26$$ 0.500000 0.866025i 0.500000 0.866025i
$$27$$ 0 0
$$28$$ 0.266044 + 0.223238i 0.266044 + 0.223238i
$$29$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −0.326352 0.118782i −0.326352 0.118782i
$$36$$ 0.766044 0.642788i 0.766044 0.642788i
$$37$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$38$$ 0.173648 0.984808i 0.173648 0.984808i
$$39$$ 0 0
$$40$$ 0.766044 0.642788i 0.766044 0.642788i
$$41$$ −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i $$-0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$44$$ −1.43969 + 0.524005i −1.43969 + 0.524005i
$$45$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$46$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$47$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$48$$ 0 0
$$49$$ 0.439693 + 0.761570i 0.439693 + 0.761570i
$$50$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$51$$ 0 0
$$52$$ −0.173648 0.984808i −0.173648 0.984808i
$$53$$ 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i $$-0.888889\pi$$
1.00000 $$0$$
$$54$$ 0 0
$$55$$ 1.17365 0.984808i 1.17365 0.984808i
$$56$$ 0.347296 0.347296
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$62$$ 0 0
$$63$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$64$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$65$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$66$$ 0 0
$$67$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$71$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$72$$ 0.173648 0.984808i 0.173648 0.984808i
$$73$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$74$$ −1.43969 + 1.20805i −1.43969 + 1.20805i
$$75$$ 0 0
$$76$$ −0.500000 0.866025i −0.500000 0.866025i
$$77$$ 0.532089 0.532089
$$78$$ 0 0
$$79$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$80$$ 0.173648 0.984808i 0.173648 0.984808i
$$81$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$82$$ −1.43969 + 0.524005i −1.43969 + 0.524005i
$$83$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.766044 + 1.32683i −0.766044 + 1.32683i
$$89$$ 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i $$-0.222222\pi$$
1.00000 $$0$$
$$90$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$91$$ −0.0603074 + 0.342020i −0.0603074 + 0.342020i
$$92$$ 1.76604 + 0.642788i 1.76604 + 0.642788i
$$93$$ 0 0
$$94$$ −1.00000 −1.00000
$$95$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$96$$ 0 0
$$97$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$98$$ 0.826352 + 0.300767i 0.826352 + 0.300767i
$$99$$ 0.266044 1.50881i 0.266044 1.50881i
$$100$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$101$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$102$$ 0 0
$$103$$ −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i $$-0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$104$$ −0.766044 0.642788i −0.766044 0.642788i
$$105$$ 0 0
$$106$$ −0.173648 0.300767i −0.173648 0.300767i
$$107$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 0 0
$$109$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$110$$ 0.266044 1.50881i 0.266044 1.50881i
$$111$$ 0 0
$$112$$ 0.266044 0.223238i 0.266044 0.223238i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ −1.87939 −1.87939
$$116$$ 0 0
$$117$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$118$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.673648 + 1.16679i −0.673648 + 1.16679i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −0.500000 0.866025i −0.500000 0.866025i
$$126$$ −0.173648 + 0.300767i −0.173648 + 0.300767i
$$127$$ 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i $$-0.222222\pi$$
1.00000 $$0$$
$$128$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$129$$ 0 0
$$130$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$131$$ −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i $$0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$132$$ 0 0
$$133$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$138$$ 0 0
$$139$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$140$$ −0.173648 + 0.300767i −0.173648 + 0.300767i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1.17365 0.984808i −1.17365 0.984808i
$$144$$ −0.500000 0.866025i −0.500000 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −0.326352 + 1.85083i −0.326352 + 1.85083i
$$149$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ −0.939693 0.342020i −0.939693 0.342020i
$$153$$ 0 0
$$154$$ 0.407604 0.342020i 0.407604 0.342020i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.326352 1.85083i −0.326352 1.85083i −0.500000 0.866025i $$-0.666667\pi$$
0.173648 0.984808i $$-0.444444\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −0.500000 0.866025i −0.500000 0.866025i
$$161$$ −0.500000 0.419550i −0.500000 0.419550i
$$162$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$163$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$164$$ −0.766044 + 1.32683i −0.766044 + 1.32683i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i $$-0.666667\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 1.00000 1.00000
$$172$$ 0 0
$$173$$ 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i $$-0.444444\pi$$
1.00000 $$0$$
$$174$$ 0 0
$$175$$ 0.0603074 0.342020i 0.0603074 0.342020i
$$176$$ 0.266044 + 1.50881i 0.266044 + 1.50881i
$$177$$ 0 0
$$178$$ 0.939693 1.62760i 0.939693 1.62760i
$$179$$ 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i $$0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$180$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$181$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$182$$ 0.173648 + 0.300767i 0.173648 + 0.300767i
$$183$$ 0 0
$$184$$ 1.76604 0.642788i 1.76604 0.642788i
$$185$$ −0.326352 1.85083i −0.326352 1.85083i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$189$$ 0 0
$$190$$ 1.00000 1.00000
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.826352 0.300767i 0.826352 0.300767i
$$197$$ −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i $$0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$198$$ −0.766044 1.32683i −0.766044 1.32683i
$$199$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$200$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0.266044 1.50881i 0.266044 1.50881i
$$206$$ −0.326352 0.118782i −0.326352 0.118782i
$$207$$ −1.43969 + 1.20805i −1.43969 + 1.20805i
$$208$$ −1.00000 −1.00000
$$209$$ −1.43969 0.524005i −1.43969 0.524005i
$$210$$ 0 0
$$211$$ 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i $$-0.444444\pi$$
1.00000 $$0$$
$$212$$ −0.326352 0.118782i −0.326352 0.118782i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −0.766044 1.32683i −0.766044 1.32683i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i $$0.222222\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$224$$ 0.0603074 0.342020i 0.0603074 0.342020i
$$225$$ −0.939693 0.342020i −0.939693 0.342020i
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ −1.43969 + 1.20805i −1.43969 + 1.20805i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$234$$ 0.939693 0.342020i 0.939693 0.342020i
$$235$$ 0.500000 0.866025i 0.500000 0.866025i
$$236$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$240$$ 0 0
$$241$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$242$$ 0.233956 + 1.32683i 0.233956 + 1.32683i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.673648 + 0.565258i −0.673648 + 0.565258i
$$246$$ 0 0
$$247$$ 0.500000 0.866025i 0.500000 0.866025i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −0.939693 0.342020i −0.939693 0.342020i
$$251$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$252$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i
$$253$$ 2.70574 0.984808i 2.70574 0.984808i
$$254$$ 0.939693 1.62760i 0.939693 1.62760i
$$255$$ 0 0
$$256$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$257$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$258$$ 0 0
$$259$$ 0.326352 0.565258i 0.326352 0.565258i
$$260$$ 0.939693 0.342020i 0.939693 0.342020i
$$261$$ 0 0
$$262$$ −0.326352 + 1.85083i −0.326352 + 1.85083i
$$263$$ −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i $$-0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$264$$ 0 0
$$265$$ 0.347296 0.347296
$$266$$ 0.266044 + 0.223238i 0.266044 + 0.223238i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$276$$ 0 0
$$277$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$278$$ 0.500000 0.866025i 0.500000 0.866025i
$$279$$ 0 0
$$280$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i
$$281$$ 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i $$-0.888889\pi$$
1.00000 $$0$$
$$282$$ 0 0
$$283$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −1.53209 −1.53209
$$287$$ 0.407604 0.342020i 0.407604 0.342020i
$$288$$ −0.939693 0.342020i −0.939693 0.342020i
$$289$$ 0.173648 0.984808i 0.173648 0.984808i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i $$-0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$294$$ 0 0
$$295$$ −0.766044 0.642788i −0.766044 0.642788i
$$296$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0.326352 + 1.85083i 0.326352 + 1.85083i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$308$$ 0.0923963 0.524005i 0.0923963 0.524005i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$314$$ −1.43969 1.20805i −1.43969 1.20805i
$$315$$ −0.173648 0.300767i −0.173648 0.300767i
$$316$$ 0 0
$$317$$ −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i $$-0.888889\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.939693 0.342020i −0.939693 0.342020i
$$321$$ 0 0
$$322$$ −0.652704 −0.652704
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0.266044 + 1.50881i 0.266044 + 1.50881i
$$329$$ 0.326352 0.118782i 0.326352 0.118782i
$$330$$ 0 0
$$331$$ −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i $$-0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$332$$ 0 0
$$333$$ −1.43969 1.20805i −1.43969 1.20805i
$$334$$ −0.766044 1.32683i −0.766044 1.32683i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.766044 0.642788i 0.766044 0.642788i
$$343$$ −0.652704 −0.652704
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0.266044 1.50881i 0.266044 1.50881i
$$347$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$350$$ −0.173648 0.300767i −0.173648 0.300767i
$$351$$ 0 0
$$352$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$353$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.326352 1.85083i −0.326352 1.85083i
$$357$$ 0 0
$$358$$ 1.76604 + 0.642788i 1.76604 + 0.642788i
$$359$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$360$$ 1.00000 1.00000
$$361$$ 0.173648 0.984808i 0.173648 0.984808i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0.326352 + 0.118782i 0.326352 + 0.118782i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$368$$ 0.939693 1.62760i 0.939693 1.62760i
$$369$$ −0.766044 1.32683i −0.766044 1.32683i
$$370$$ −1.43969 1.20805i −1.43969 1.20805i
$$371$$ 0.0923963 + 0.0775297i 0.0923963 + 0.0775297i
$$372$$ 0 0
$$373$$ −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$380$$ 0.766044 0.642788i 0.766044 0.642788i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$384$$ 0 0
$$385$$ 0.0923963 + 0.524005i 0.0923963 + 0.524005i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.439693 0.761570i 0.439693 0.761570i
$$393$$ 0 0
$$394$$ 0.266044 + 1.50881i 0.266044 + 1.50881i
$$395$$ 0 0
$$396$$ −1.43969 0.524005i −1.43969 0.524005i
$$397$$ 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i $$-0.444444\pi$$
1.00000 $$0$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 1.53209 1.28558i 1.53209 1.28558i 0.766044 0.642788i $$-0.222222\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$406$$ 0 0
$$407$$ 1.43969 + 2.49362i 1.43969 + 2.49362i
$$408$$ 0 0
$$409$$ 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i $$-0.222222\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ −0.766044 1.32683i −0.766044 1.32683i
$$411$$ 0 0
$$412$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$413$$ −0.0603074 0.342020i −0.0603074 0.342020i
$$414$$ −0.326352 + 1.85083i −0.326352 + 1.85083i
$$415$$ 0 0
$$416$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$417$$ 0 0
$$418$$ −1.43969 + 0.524005i −1.43969 + 0.524005i
$$419$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$422$$ 0.266044 1.50881i 0.266044 1.50881i
$$423$$ −0.173648 0.984808i −0.173648 0.984808i
$$424$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$432$$ 0 0
$$433$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$438$$ 0 0
$$439$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$440$$ −1.43969 0.524005i −1.43969 0.524005i
$$441$$ −0.152704 + 0.866025i −0.152704 + 0.866025i
$$442$$ 0 0
$$443$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$444$$ 0 0
$$445$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$446$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$447$$ 0 0
$$448$$ −0.173648 0.300767i −0.173648 0.300767i
$$449$$ −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i $$0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$450$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$451$$ 0.407604 + 2.31164i 0.407604 + 2.31164i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −0.347296 −0.347296
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −0.326352 + 1.85083i −0.326352 + 1.85083i
$$461$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$462$$ 0 0
$$463$$ −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i $$0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 0.500000 0.866025i 0.500000 0.866025i
$$469$$ 0 0
$$470$$ −0.173648 0.984808i −0.173648 0.984808i
$$471$$ 0 0
$$472$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$476$$ 0 0
$$477$$ 0.266044 0.223238i 0.266044 0.223238i
$$478$$ 0 0
$$479$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$480$$ 0 0
$$481$$ −1.76604 + 0.642788i −1.76604 + 0.642788i
$$482$$ 0.500000 0.866025i 0.500000 0.866025i
$$483$$ 0 0
$$484$$ 1.03209 + 0.866025i 1.03209 + 0.866025i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −0.152704 + 0.866025i −0.152704 + 0.866025i
$$491$$ 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 $$0$$
0.766044 + 0.642788i $$0.222222\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −0.173648 0.984808i −0.173648 0.984808i
$$495$$ 1.53209 1.53209
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 $$0$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$500$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$501$$ 0 0
$$502$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$503$$ 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 $$0$$
0.173648 + 0.984808i $$0.444444\pi$$
$$504$$ 0.266044 + 0.223238i 0.266044 + 0.223238i
$$505$$ 0 0
$$506$$ 1.43969 2.49362i 1.43969 2.49362i
$$507$$ 0 0
$$508$$ −0.326352 1.85083i −0.326352 1.85083i
$$509$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.266044 0.223238i 0.266044 0.223238i
$$516$$ 0 0
$$517$$ −0.266044 + 1.50881i −0.266044 + 1.50881i
$$518$$ −0.113341 0.642788i −0.113341 0.642788i
$$519$$ 0 0
$$520$$ 0.500000 0.866025i 0.500000 0.866025i
$$521$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$522$$ 0 0
$$523$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$524$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$525$$ 0 0
$$526$$ −1.43969 + 0.524005i −1.43969 + 0.524005i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −2.37939 0.866025i −2.37939 0.866025i
$$530$$ 0.266044 0.223238i 0.266044 0.223238i
$$531$$ −1.00000 −1.00000
$$532$$ 0.347296 0.347296
$$533$$ −1.53209 −1.53209
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0.673648 1.16679i 0.673648 1.16679i
$$540$$ 0 0
$$541$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 1.53209 1.53209
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$555$$ 0 0
$$556$$ −0.173648 0.984808i −0.173648 0.984808i
$$557$$ −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i $$-0.666667\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0.266044 + 0.223238i 0.266044 + 0.223238i
$$561$$ 0 0
$$562$$ −0.173648 0.300767i −0.173648 0.300767i
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −0.326352 0.118782i −0.326352 0.118782i
$$568$$ 0 0
$$569$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ −1.17365 + 0.984808i −1.17365 + 0.984808i
$$573$$ 0 0
$$574$$ 0.0923963 0.524005i 0.0923963 0.524005i
$$575$$ −0.326352 1.85083i −0.326352 1.85083i
$$576$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$577$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ −0.500000 0.866025i −0.500000 0.866025i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −0.500000 + 0.181985i −0.500000 + 0.181985i
$$584$$ 0 0
$$585$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$586$$ −0.326352 0.118782i −0.326352 0.118782i
$$587$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −1.00000 −1.00000
$$591$$ 0 0
$$592$$ 1.76604 + 0.642788i 1.76604 + 0.642788i
$$593$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 1.43969 + 1.20805i 1.43969 + 1.20805i
$$599$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$600$$ 0 0
$$601$$ −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i $$0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.26604 0.460802i −1.26604 0.460802i
$$606$$ 0 0
$$607$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$608$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −0.939693 0.342020i −0.939693 0.342020i
$$612$$ 0 0
$$613$$ 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i $$0.222222\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −0.266044 0.460802i −0.266044 0.460802i
$$617$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$618$$ 0 0
$$619$$ −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i $$-0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −0.113341 + 0.642788i −0.113341 + 0.642788i
$$624$$ 0 0
$$625$$ 0.766044 0.642788i 0.766044 0.642788i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −1.87939 −1.87939
$$629$$ 0 0
$$630$$ −0.326352 0.118782i −0.326352 0.118782i
$$631$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −0.766044 + 1.32683i −0.766044 + 1.32683i
$$635$$ 0.939693 + 1.62760i 0.939693 + 1.62760i
$$636$$ 0 0
$$637$$ 0.673648 + 0.565258i 0.673648 + 0.565258i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$641$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$644$$ −0.500000 + 0.419550i −0.500000 + 0.419550i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$648$$ 0.766044 0.642788i 0.766044 0.642788i
$$649$$ 1.43969 + 0.524005i 1.43969 + 0.524005i
$$650$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$654$$ 0 0
$$655$$ −1.43969 1.20805i −1.43969 1.20805i
$$656$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$657$$ 0 0
$$658$$ 0.173648 0.300767i 0.173648 0.300767i
$$659$$ −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i $$-0.888889\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$662$$ −0.326352 0.118782i −0.326352 0.118782i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −0.326352 + 0.118782i −0.326352 + 0.118782i
$$666$$ −1.87939 −1.87939
$$667$$ 0 0
$$668$$ −1.43969 0.524005i −1.43969 0.524005i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0.173648 0.984808i 0.173648 0.984808i
$$685$$ 0 0
$$686$$ −0.500000 + 0.419550i −0.500000 + 0.419550i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −0.0603074 0.342020i −0.0603074 0.342020i
$$690$$ 0 0
$$691$$ 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$692$$ −0.766044 1.32683i −0.766044 1.32683i
$$693$$ 0.407604 + 0.342020i 0.407604 + 0.342020i
$$694$$ 0 0
$$695$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −0.326352 0.118782i −0.326352 0.118782i
$$701$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$702$$ 0 0
$$703$$ −1.43969 + 1.20805i −1.43969 + 1.20805i
$$704$$ 1.53209 1.53209
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −1.43969 1.20805i −1.43969 1.20805i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0.766044 1.32683i 0.766044 1.32683i
$$716$$ 1.76604 0.642788i 1.76604 0.642788i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$720$$ 0.766044 0.642788i 0.766044 0.642788i
$$721$$ 0.120615 0.120615
$$722$$ −0.500000 0.866025i −0.500000 0.866025i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i $$0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$728$$ 0.326352 0.118782i 0.326352 0.118782i
$$729$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i $$-0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$734$$ 0.500000 0.866025i 0.500000 0.866025i
$$735$$ 0 0
$$736$$ −0.326352 1.85083i −0.326352 1.85083i
$$737$$ 0 0
$$738$$ −1.43969 0.524005i −1.43969 0.524005i
$$739$$ −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i $$0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$740$$ −1.87939 −1.87939
$$741$$ 0 0
$$742$$ 0.120615 0.120615
$$743$$ 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i $$-0.666667\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0.0603074 + 0.342020i 0.0603074 + 0.342020i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$752$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i $$-0.666667\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$758$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$759$$ 0 0
$$760$$ 0.173648 0.984808i 0.173648 0.984808i
$$761$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0.939693 0.342020i 0.939693 0.342020i
$$767$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$768$$ 0 0
$$769$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$770$$ 0.407604 + 0.342020i 0.407604 + 0.342020i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i $$-0.222222\pi$$
1.00000 $$0$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.43969 + 0.524005i −1.43969 + 0.524005i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.152704 0.866025i −0.152704 0.866025i
$$785$$ 1.76604 0.642788i 1.76604 0.642788i
$$786$$ 0 0
$$787$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$788$$ 1.17365 + 0.984808i 1.17365 + 0.984808i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0