# Properties

 Label 273.1.s.b.107.2 Level $273$ Weight $1$ Character 273.107 Analytic conductor $0.136$ Analytic rank $0$ Dimension $4$ Projective image $A_{4}$ CM/RM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,1,Mod(74,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.74");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 273.s (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$0.136244748449$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$A_{4}$$ Projective field: Galois closure of 4.0.74529.1

## Embedding invariants

 Embedding label 107.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 273.107 Dual form 273.1.s.b.74.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{13} +(0.866025 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{15} -1.00000 q^{16} -1.00000i q^{17} +(-0.866025 + 0.500000i) q^{18} -1.00000i q^{21} -1.00000i q^{23} +(-0.500000 + 0.866025i) q^{24} -1.00000i q^{26} +1.00000i q^{27} +(-0.866025 + 0.500000i) q^{29} +(0.866025 - 0.500000i) q^{30} +(0.500000 + 0.866025i) q^{31} +1.00000 q^{34} +1.00000i q^{35} +1.00000 q^{37} +(-0.866025 - 0.500000i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.866025 - 0.500000i) q^{41} +1.00000 q^{42} +(-0.500000 + 0.866025i) q^{43} -1.00000i q^{45} +1.00000 q^{46} +(-0.866025 - 0.500000i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{51} +(0.866025 - 0.500000i) q^{53} -1.00000 q^{54} +(0.866025 - 0.500000i) q^{56} +(-0.500000 - 0.866025i) q^{58} +1.00000i q^{59} +(-0.866025 + 0.500000i) q^{62} +(0.500000 - 0.866025i) q^{63} -1.00000 q^{64} +(0.866025 + 0.500000i) q^{65} +(0.500000 - 0.866025i) q^{69} -1.00000 q^{70} +(0.866025 + 0.500000i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-0.500000 - 0.866025i) q^{73} +1.00000i q^{74} +(0.500000 - 0.866025i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(-0.500000 + 0.866025i) q^{85} +(-0.866025 - 0.500000i) q^{86} -1.00000 q^{87} +1.00000i q^{89} +1.00000 q^{90} +(0.500000 + 0.866025i) q^{91} +1.00000i q^{93} +(0.500000 - 0.866025i) q^{94} +(0.500000 - 0.866025i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^6 - 2 * q^7 + 2 * q^9 $$4 q - 2 q^{6} - 2 q^{7} + 2 q^{9} + 2 q^{10} - 4 q^{13} - 2 q^{15} - 4 q^{16} - 2 q^{24} + 2 q^{31} + 4 q^{34} + 4 q^{37} + 2 q^{40} + 4 q^{42} - 2 q^{43} + 4 q^{46} - 2 q^{49} + 2 q^{51} - 4 q^{54} - 2 q^{58} + 2 q^{63} - 4 q^{64} + 2 q^{69} - 4 q^{70} - 2 q^{73} + 2 q^{78} - 2 q^{79} - 2 q^{81} + 2 q^{82} - 2 q^{85} - 4 q^{87} + 4 q^{90} + 2 q^{91} + 2 q^{94} + 2 q^{97}+O(q^{100})$$ 4 * q - 2 * q^6 - 2 * q^7 + 2 * q^9 + 2 * q^10 - 4 * q^13 - 2 * q^15 - 4 * q^16 - 2 * q^24 + 2 * q^31 + 4 * q^34 + 4 * q^37 + 2 * q^40 + 4 * q^42 - 2 * q^43 + 4 * q^46 - 2 * q^49 + 2 * q^51 - 4 * q^54 - 2 * q^58 + 2 * q^63 - 4 * q^64 + 2 * q^69 - 4 * q^70 - 2 * q^73 + 2 * q^78 - 2 * q^79 - 2 * q^81 + 2 * q^82 - 2 * q^85 - 4 * q^87 + 4 * q^90 + 2 * q^91 + 2 * q^94 + 2 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$$.

 $$n$$ $$92$$ $$106$$ $$157$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

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