# Properties

 Label 171.1.o.a.94.1 Level $171$ Weight $1$ Character 171.94 Analytic conductor $0.085$ 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] = [171,1,Mod(94,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("171.94");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 171.o (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: $$0.0853401171602$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$A_{4}$$ Projective field: Galois closure of 4.0.29241.1 Artin image: $\SL(2,3):C_2$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{16} - \cdots)$$

## Embedding invariants

 Embedding label 94.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 171.94 Dual form 171.1.o.a.151.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} -1.00000i q^{10} +(0.500000 + 0.866025i) q^{11} +(0.866025 + 0.500000i) q^{13} +(0.866025 + 0.500000i) q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.866025 - 0.500000i) q^{18} +1.00000i q^{19} +(0.866025 - 0.500000i) q^{21} +(-0.866025 - 0.500000i) q^{22} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{24} -1.00000 q^{26} -1.00000i q^{27} +(0.866025 - 0.500000i) q^{29} +1.00000 q^{30} +(-0.866025 - 0.500000i) q^{31} +(-0.866025 + 0.500000i) q^{33} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.866025 + 0.500000i) q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{45} +1.00000i q^{46} +(-0.500000 - 0.866025i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.500000 + 0.866025i) q^{54} -1.00000 q^{55} +(-0.866025 + 0.500000i) q^{56} -1.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.500000 + 0.866025i) q^{61} +1.00000 q^{62} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} +(-0.866025 + 0.500000i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-0.866025 - 0.500000i) q^{67} +(0.866025 + 0.500000i) q^{69} +(-0.866025 + 0.500000i) q^{70} +1.00000i q^{72} +(0.500000 - 0.866025i) q^{77} -1.00000i q^{78} +(0.866025 - 0.500000i) q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} +(0.500000 + 0.866025i) q^{83} +(0.866025 + 0.500000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(0.866025 - 0.500000i) q^{88} +1.00000i q^{90} -1.00000i q^{91} +(0.500000 - 0.866025i) q^{93} +(0.866025 + 0.500000i) q^{94} +(-0.866025 - 0.500000i) q^{95} +(-0.866025 + 0.500000i) q^{97} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10})$$ 4 * q - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^9 $$4 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9} + 2 q^{11} + 2 q^{16} + 2 q^{23} + 4 q^{24} - 4 q^{26} + 4 q^{30} + 4 q^{35} - 2 q^{38} - 2 q^{39} - 2 q^{42} - 2 q^{43} + 2 q^{45} - 2 q^{47} + 2 q^{54} - 4 q^{55} - 4 q^{57} - 2 q^{58} + 2 q^{61} + 4 q^{62} + 2 q^{63} - 4 q^{64} + 2 q^{66} + 2 q^{77} - 4 q^{80} + 4 q^{81} - 4 q^{82} + 2 q^{83} + 2 q^{87} + 2 q^{93} - 2 q^{99}+O(q^{100})$$ 4 * q - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^9 + 2 * q^11 + 2 * q^16 + 2 * q^23 + 4 * q^24 - 4 * q^26 + 4 * q^30 + 4 * q^35 - 2 * q^38 - 2 * q^39 - 2 * q^42 - 2 * q^43 + 2 * q^45 - 2 * q^47 + 2 * q^54 - 4 * q^55 - 4 * q^57 - 2 * q^58 + 2 * q^61 + 4 * q^62 + 2 * q^63 - 4 * q^64 + 2 * q^66 + 2 * q^77 - 4 * q^80 + 4 * q^81 - 4 * q^82 + 2 * q^83 + 2 * q^87 + 2 * q^93 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$$.

 $$n$$ $$20$$ $$154$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

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