LMFDB - Embedded newform 728.1.di.a.555.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,1,Mod(555,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2, 4]))

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

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

chi := DirichletCharacter("728.555");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	728.di (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:	$0.363319329197$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.529984.4

Embedding invariants

Embedding label			555.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	728.555
Dual form			728.1.di.a.627.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000 q^{8} -1.00000i q^{10} +1.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000i q^{13} +1.00000i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{19} +(0.866025 - 0.500000i) q^{20} +(0.866025 + 0.500000i) q^{21} +(0.500000 + 0.866025i) q^{22} +(1.73205 - 1.00000i) q^{23} -1.00000 q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-0.866025 - 0.500000i) q^{29} -1.00000i q^{30} +(-0.866025 + 0.500000i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{33} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{38} +1.00000i q^{39} +(0.866025 + 0.500000i) q^{40} +(0.500000 - 0.866025i) q^{41} +1.00000i q^{42} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.73205 + 1.00000i) q^{46} +(-0.866025 - 0.500000i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.866025 - 0.500000i) q^{52} +(0.866025 - 0.500000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.866025 - 0.500000i) q^{55} +(-0.866025 - 0.500000i) q^{56} -1.00000 q^{57} -1.00000i q^{58} +(0.866025 - 0.500000i) q^{60} -1.00000i q^{61} +(-0.866025 - 0.500000i) q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} -1.00000 q^{67} +(1.73205 - 1.00000i) q^{69} +(0.500000 - 0.866025i) q^{70} +(-0.866025 + 0.500000i) q^{71} +(0.500000 + 0.866025i) q^{73} +(0.500000 - 0.866025i) q^{76} +(0.866025 + 0.500000i) q^{77} +(-0.866025 + 0.500000i) q^{78} +(0.866025 + 0.500000i) q^{79} +1.00000i q^{80} -1.00000 q^{81} +1.00000 q^{82} +(-0.866025 + 0.500000i) q^{84} +(0.500000 - 0.866025i) q^{86} +(-0.866025 - 0.500000i) q^{87} -1.00000 q^{88} +(-0.500000 + 0.866025i) q^{91} +2.00000i q^{92} +(-0.866025 + 0.500000i) q^{93} -1.00000i q^{94} +(0.866025 + 0.500000i) q^{95} +(0.500000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} + 4 q^{11} - 2 q^{12} - 2 q^{16} - 4 q^{19} + 2 q^{22} - 4 q^{24} - 4 q^{27} + 2 q^{32} + 4 q^{33} - 2 q^{35} - 2 q^{38} + 2 q^{41} - 2 q^{43} - 2 q^{44}+ \cdots - 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 + 4 * q^11 - 2 * q^12 - 2 * q^16 - 4 * q^19 + 2 * q^22 - 4 * q^24 - 4 * q^27 + 2 * q^32 + 4 * q^33 - 2 * q^35 - 2 * q^38 + 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 + 2 * q^49 - 2 * q^54 - 4 * q^57 + 4 * q^64 + 2 * q^65 + 2 * q^66 - 4 * q^67 + 2 * q^70 + 2 * q^73 + 2 * q^76 - 4 * q^81 + 4 * q^82 + 2 * q^86 - 4 * q^88 - 2 * q^91 + 2 * q^96 + 2 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.500000	+	0.866025i
$2$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$4$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$5$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$6$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i
$8$	−1.00000			−1.00000
$9$		0			0
$10$		−	1.00000i		−	1.00000i
$11$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$11$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$13$			1.00000i			1.00000i
$13$			1.00000i			1.00000i
$14$			1.00000i			1.00000i
$15$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$20$	0.866025	−	0.500000i	0.866025	−	0.500000i
$21$	0.866025	+	0.500000i	0.866025	+	0.500000i
$22$	0.500000	+	0.866025i	0.500000	+	0.866025i
$23$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$23$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$24$	−1.00000			−1.00000
$25$		0			0
$26$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$27$	−1.00000			−1.00000
$28$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$29$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$29$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$30$		−	1.00000i		−	1.00000i
$31$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$31$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$32$	0.500000	−	0.866025i	0.500000	−	0.866025i
$33$	1.00000			1.00000
$34$		0			0
$35$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$36$		0			0
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$			1.00000i			1.00000i
$40$	0.866025	+	0.500000i	0.866025	+	0.500000i
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$42$			1.00000i			1.00000i
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$44$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$45$		0			0
$46$	1.73205	+	1.00000i	1.73205	+	1.00000i
$47$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$47$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$		0			0
$51$		0			0
$52$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$53$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$53$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$56$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$57$	−1.00000			−1.00000
$58$		−	1.00000i		−	1.00000i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	0.866025	−	0.500000i	0.866025	−	0.500000i
$61$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$61$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$62$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$63$		0			0
$64$	1.00000			1.00000
$65$	0.500000	−	0.866025i	0.500000	−	0.866025i
$66$	0.500000	+	0.866025i	0.500000	+	0.866025i
$67$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	1.73205	−	1.00000i	1.73205	−	1.00000i
$70$	0.500000	−	0.866025i	0.500000	−	0.866025i
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$		0			0
$76$	0.500000	−	0.866025i	0.500000	−	0.866025i
$77$	0.866025	+	0.500000i	0.866025	+	0.500000i
$78$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$79$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$79$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$80$			1.00000i			1.00000i
$81$	−1.00000			−1.00000
$82$	1.00000			1.00000
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$85$		0			0
$86$	0.500000	−	0.866025i	0.500000	−	0.866025i
$87$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$88$	−1.00000			−1.00000
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$92$			2.00000i			2.00000i
$93$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$94$		−	1.00000i		−	1.00000i
$95$	0.866025	+	0.500000i	0.866025	+	0.500000i
$96$	0.500000	−	0.866025i	0.500000	−	0.866025i
$97$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$97$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$98$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$99$		0			0
$100$		0			0
$101$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$101$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$104$		−	1.00000i		−	1.00000i
$105$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$106$	0.866025	+	0.500000i	0.866025	+	0.500000i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	0.500000	−	0.866025i	0.500000	−	0.866025i
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$110$		−	1.00000i		−	1.00000i
$111$		0			0
$112$		−	1.00000i		−	1.00000i
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$114$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$115$	−2.00000			−2.00000
$116$	0.866025	−	0.500000i	0.866025	−	0.500000i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.866025	+	0.500000i	0.866025	+	0.500000i
$121$		0			0
$122$	0.866025	−	0.500000i	0.866025	−	0.500000i
$123$	0.500000	−	0.866025i	0.500000	−	0.866025i
$124$		−	1.00000i		−	1.00000i
$125$			1.00000i			1.00000i
$126$		0			0
$127$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$127$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$130$	1.00000			1.00000
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$132$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$133$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$134$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$135$	0.866025	+	0.500000i	0.866025	+	0.500000i
$136$		0			0
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$	1.73205	+	1.00000i	1.73205	+	1.00000i
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$140$	1.00000			1.00000
$141$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$142$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$143$			1.00000i			1.00000i
$144$		0			0
$145$	0.500000	+	0.866025i	0.500000	+	0.866025i
$146$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$147$	0.500000	+	0.866025i	0.500000	+	0.866025i
$148$		0			0
$149$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$149$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$152$	1.00000			1.00000
$153$		0			0
$154$			1.00000i			1.00000i
$155$	1.00000			1.00000
$156$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$157$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$157$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$158$			1.00000i			1.00000i
$159$	0.866025	−	0.500000i	0.866025	−	0.500000i
$160$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$161$	2.00000			2.00000
$162$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$163$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$163$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$164$	0.500000	+	0.866025i	0.500000	+	0.866025i
$165$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$166$		0			0
$167$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$167$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$168$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$169$	−1.00000			−1.00000
$170$		0			0
$171$		0			0
$172$	1.00000			1.00000
$173$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$173$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$174$		−	1.00000i		−	1.00000i
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$177$		0			0
$178$		0			0
$179$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$179$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−1.00000			−1.00000
$183$		−	1.00000i		−	1.00000i
$184$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$185$		0			0
$186$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$187$		0			0
$188$	0.866025	−	0.500000i	0.866025	−	0.500000i
$189$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$190$			1.00000i			1.00000i
$191$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$191$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$192$	1.00000			1.00000
$193$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$193$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$194$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$195$	0.500000	−	0.866025i	0.500000	−	0.866025i
$196$	−1.00000			−1.00000
$197$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$197$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$		0			0
$201$	−1.00000			−1.00000
$202$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$203$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$204$		0			0
$205$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$206$		−	1.00000i		−	1.00000i
$207$		0			0
$208$	0.866025	−	0.500000i	0.866025	−	0.500000i
$209$	−1.00000			−1.00000
$210$	0.500000	−	0.866025i	0.500000	−	0.866025i
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$212$			1.00000i			1.00000i
$213$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$214$		0			0
$215$			1.00000i			1.00000i
$216$	1.00000			1.00000
$217$	−1.00000			−1.00000
$218$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$219$	0.500000	+	0.866025i	0.500000	+	0.866025i
$220$	0.866025	−	0.500000i	0.866025	−	0.500000i
$221$		0			0
$222$		0			0
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$224$	0.866025	−	0.500000i	0.866025	−	0.500000i
$225$		0			0
$226$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$230$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$231$	0.866025	+	0.500000i	0.866025	+	0.500000i
$232$	0.866025	+	0.500000i	0.866025	+	0.500000i
$233$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$233$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$234$		0			0
$235$	0.500000	+	0.866025i	0.500000	+	0.866025i
$236$		0			0
$237$	0.866025	+	0.500000i	0.866025	+	0.500000i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$			1.00000i			1.00000i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$		0			0
$243$		0			0
$244$	0.866025	+	0.500000i	0.866025	+	0.500000i
$245$		−	1.00000i		−	1.00000i
$246$	1.00000			1.00000
$247$		−	1.00000i		−	1.00000i
$248$	0.866025	−	0.500000i	0.866025	−	0.500000i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$251$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$251$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$252$		0			0
$253$	1.73205	−	1.00000i	1.73205	−	1.00000i
$254$			1.00000i			1.00000i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$258$	0.500000	−	0.866025i	0.500000	−	0.866025i
$259$		0			0
$260$	0.500000	+	0.866025i	0.500000	+	0.866025i
$261$		0			0
$262$	1.00000			1.00000
$263$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$263$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	−1.00000			−1.00000
$265$	−1.00000			−1.00000
$266$		−	1.00000i		−	1.00000i
$267$		0			0
$268$	0.500000	−	0.866025i	0.500000	−	0.866025i
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$			1.00000i			1.00000i
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		0			0
$273$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$274$		0			0
$275$		0			0
$276$			2.00000i			2.00000i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$279$		0			0
$280$	0.500000	+	0.866025i	0.500000	+	0.866025i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		−	1.00000i		−	1.00000i
$283$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$283$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$284$		−	1.00000i		−	1.00000i
$285$	0.866025	+	0.500000i	0.866025	+	0.500000i
$286$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$287$	0.866025	−	0.500000i	0.866025	−	0.500000i
$288$		0			0
$289$	0.500000	+	0.866025i	0.500000	+	0.866025i
$290$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$291$	0.500000	+	0.866025i	0.500000	+	0.866025i
$292$	−1.00000			−1.00000
$293$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$293$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$294$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$295$		0			0
$296$		0			0
$297$	−1.00000			−1.00000
$298$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$299$	1.00000	+	1.73205i	1.00000	+	1.73205i
$300$		0			0
$301$		−	1.00000i		−	1.00000i
$302$	0.866025	+	0.500000i	0.866025	+	0.500000i
$303$			1.00000i			1.00000i
$304$	0.500000	+	0.866025i	0.500000	+	0.866025i
$305$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$309$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$310$	0.500000	+	0.866025i	0.500000	+	0.866025i
$311$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$311$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$312$		−	1.00000i		−	1.00000i
$313$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$313$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$314$	0.866025	+	0.500000i	0.866025	+	0.500000i
$315$		0			0
$316$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$318$	0.866025	+	0.500000i	0.866025	+	0.500000i
$319$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$320$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$321$		0			0
$322$	1.00000	+	1.73205i	1.00000	+	1.73205i
$323$		0			0
$324$	0.500000	−	0.866025i	0.500000	−	0.866025i
$325$		0			0
$326$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$327$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$328$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$329$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$330$		−	1.00000i		−	1.00000i
$331$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$331$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$		0			0
$334$		−	1.00000i		−	1.00000i
$335$	0.866025	+	0.500000i	0.866025	+	0.500000i
$336$		−	1.00000i		−	1.00000i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$339$	0.500000	+	0.866025i	0.500000	+	0.866025i
$340$		0			0
$341$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$342$		0			0
$343$			1.00000i			1.00000i
$344$	0.500000	+	0.866025i	0.500000	+	0.866025i
$345$	−2.00000			−2.00000
$346$	0.866025	−	0.500000i	0.866025	−	0.500000i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	0.866025	−	0.500000i	0.866025	−	0.500000i
$349$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$349$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$350$		0			0
$351$		−	1.00000i		−	1.00000i
$352$	0.500000	−	0.866025i	0.500000	−	0.866025i
$353$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$353$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	1.00000			1.00000
$356$		0			0
$357$		0			0
$358$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$		0			0
$364$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$365$		−	1.00000i		−	1.00000i
$366$	0.866025	−	0.500000i	0.866025	−	0.500000i
$367$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$368$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$369$		0			0
$370$		0			0
$371$	1.00000			1.00000
$372$		−	1.00000i		−	1.00000i
$373$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$373$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$374$		0			0
$375$			1.00000i			1.00000i
$376$	0.866025	+	0.500000i	0.866025	+	0.500000i
$377$	0.500000	−	0.866025i	0.500000	−	0.866025i
$378$		−	1.00000i		−	1.00000i
$379$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$379$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$380$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$381$	0.866025	+	0.500000i	0.866025	+	0.500000i
$382$	0.866025	−	0.500000i	0.866025	−	0.500000i
$383$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$383$			1.00000i			1.00000i	−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
$386$	0.500000	+	0.866025i	0.500000	+	0.866025i
$387$		0			0
$388$	−1.00000			−1.00000
$389$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$389$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$390$	1.00000			1.00000
$391$		0			0
$392$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$393$	0.500000	−	0.866025i	0.500000	−	0.866025i
$394$			1.00000i			1.00000i
$395$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$396$		0			0
$397$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$397$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$398$		0			0
$399$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$400$		0			0
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$403$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$404$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$405$	0.866025	+	0.500000i	0.866025	+	0.500000i
$406$	0.500000	−	0.866025i	0.500000	−	0.866025i
$407$		0			0
$408$		0			0
$409$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$409$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$410$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$411$		0			0
$412$	0.866025	−	0.500000i	0.866025	−	0.500000i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.866025	+	0.500000i	0.866025	+	0.500000i
$417$	0.500000	+	0.866025i	0.500000	+	0.866025i
$418$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$420$	1.00000			1.00000
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−1.00000			−1.00000
$423$		0			0
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$		0			0
$426$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$427$	0.500000	−	0.866025i	0.500000	−	0.866025i
$428$		0			0
$429$			1.00000i			1.00000i
$430$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$431$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$431$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$432$	0.500000	+	0.866025i	0.500000	+	0.866025i
$433$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$433$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$434$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$435$	0.500000	+	0.866025i	0.500000	+	0.866025i
$436$		−	1.00000i		−	1.00000i
$437$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$438$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$	0.866025	+	0.500000i	0.866025	+	0.500000i
$441$		0			0
$442$		0			0
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		−	1.00000i		−	1.00000i
$447$			1.00000i			1.00000i
$448$	0.866025	+	0.500000i	0.866025	+	0.500000i
$449$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$449$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$450$		0			0
$451$	0.500000	−	0.866025i	0.500000	−	0.866025i
$452$	−1.00000			−1.00000
$453$	0.866025	−	0.500000i	0.866025	−	0.500000i
$454$		0			0
$455$	0.866025	−	0.500000i	0.866025	−	0.500000i
$456$	1.00000			1.00000
$457$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$457$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$458$			1.00000i			1.00000i
$459$		0			0
$460$	1.00000	−	1.73205i	1.00000	−	1.73205i
$461$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$461$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$462$			1.00000i			1.00000i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$			1.00000i			1.00000i
$465$	1.00000			1.00000
$466$	−1.00000			−1.00000
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$468$		0			0
$469$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$470$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$471$	0.866025	−	0.500000i	0.866025	−	0.500000i
$472$		0			0
$473$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$474$			1.00000i			1.00000i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$480$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$481$		0			0
$482$		0			0
$483$	2.00000			2.00000
$484$		0			0
$485$		−	1.00000i		−	1.00000i
$486$		0			0
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$			1.00000i			1.00000i
$489$	−1.00000			−1.00000
$490$	0.866025	−	0.500000i	0.866025	−	0.500000i
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$492$	0.500000	+	0.866025i	0.500000	+	0.866025i
$493$		0			0
$494$	0.866025	−	0.500000i	0.866025	−	0.500000i
$495$		0			0
$496$	0.866025	+	0.500000i	0.866025	+	0.500000i
$497$	−1.00000			−1.00000
$498$		0			0
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$501$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$502$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$		0			0
$505$	0.500000	−	0.866025i	0.500000	−	0.866025i
$506$	1.73205	+	1.00000i	1.73205	+	1.00000i
$507$	−1.00000			−1.00000
$508$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$			1.00000i			1.00000i
$512$	−1.00000			−1.00000
$513$	1.00000			1.00000
$514$	1.00000	−	1.73205i	1.00000	−	1.73205i
$515$	0.500000	+	0.866025i	0.500000	+	0.866025i
$516$	1.00000			1.00000
$517$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$518$		0			0
$519$		−	1.00000i		−	1.00000i
$520$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$524$	0.500000	+	0.866025i	0.500000	+	0.866025i
$525$		0			0
$526$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$527$		0			0
$528$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$529$	1.50000	−	2.59808i	1.50000	−	2.59808i
$530$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$531$		0			0
$532$	0.866025	−	0.500000i	0.866025	−	0.500000i
$533$	0.866025	+	0.500000i	0.866025	+	0.500000i
$534$		0			0
$535$		0			0
$536$	1.00000			1.00000
$537$	−1.00000			−1.00000
$538$		0			0
$539$	0.500000	+	0.866025i	0.500000	+	0.866025i
$540$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$541$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$541$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.00000			1.00000
$546$	−1.00000			−1.00000
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.866025	+	0.500000i	0.866025	+	0.500000i
$552$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$553$	0.500000	+	0.866025i	0.500000	+	0.866025i
$554$		0			0
$555$		0			0
$556$	−1.00000			−1.00000
$557$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$558$		0			0
$559$	0.866025	−	0.500000i	0.866025	−	0.500000i
$560$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	0.866025	−	0.500000i	0.866025	−	0.500000i
$565$		−	1.00000i		−	1.00000i
$566$	0.500000	+	0.866025i	0.500000	+	0.866025i
$567$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$568$	0.866025	−	0.500000i	0.866025	−	0.500000i
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$			1.00000i			1.00000i
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$572$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$573$		−	1.00000i		−	1.00000i
$574$	0.866025	+	0.500000i	0.866025	+	0.500000i
$575$		0			0
$576$		0			0
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$579$	1.00000			1.00000
$580$	−1.00000			−1.00000
$581$		0			0
$582$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$583$	0.866025	−	0.500000i	0.866025	−	0.500000i
$584$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$585$		0			0
$586$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$588$	−1.00000			−1.00000
$589$	0.866025	−	0.500000i	0.866025	−	0.500000i
$590$		0			0
$591$	0.866025	+	0.500000i	0.866025	+	0.500000i
$592$		0			0
$593$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$593$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$594$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$595$		0			0
$596$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$597$		0			0
$598$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$599$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$599$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$602$	0.866025	−	0.500000i	0.866025	−	0.500000i
$603$		0			0
$604$			1.00000i			1.00000i
$605$		0			0
$606$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$607$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$607$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$608$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$609$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$610$	−1.00000			−1.00000
$611$	0.500000	−	0.866025i	0.500000	−	0.866025i
$612$		0			0
$613$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$613$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$614$		0			0
$615$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$616$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$618$		−	1.00000i		−	1.00000i
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$620$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$621$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$622$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$623$		0			0
$624$	0.866025	−	0.500000i	0.866025	−	0.500000i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$	−1.00000			−1.00000
$627$	−1.00000			−1.00000
$628$			1.00000i			1.00000i
$629$		0			0
$630$		0			0
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$632$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$633$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$634$		−	1.00000i		−	1.00000i
$635$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$636$			1.00000i			1.00000i
$637$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$638$		−	1.00000i		−	1.00000i
$639$		0			0
$640$		−	1.00000i		−	1.00000i
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$644$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$645$			1.00000i			1.00000i
$646$		0			0
$647$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$647$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$648$	1.00000			1.00000
$649$		0			0
$650$		0			0
$651$	−1.00000			−1.00000
$652$	0.500000	−	0.866025i	0.500000	−	0.866025i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$655$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$656$	−1.00000			−1.00000
$657$		0			0
$658$	0.500000	−	0.866025i	0.500000	−	0.866025i
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$660$	0.866025	−	0.500000i	0.866025	−	0.500000i
$661$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$661$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$662$	0.500000	+	0.866025i	0.500000	+	0.866025i
$663$		0			0
$664$		0			0
$665$	0.500000	+	0.866025i	0.500000	+	0.866025i
$666$		0			0
$667$	−2.00000			−2.00000
$668$	0.866025	−	0.500000i	0.866025	−	0.500000i
$669$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$670$			1.00000i			1.00000i
$671$		−	1.00000i		−	1.00000i
$672$	0.866025	−	0.500000i	0.866025	−	0.500000i
$673$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$673$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$674$		0			0
$675$		0			0
$676$	0.500000	−	0.866025i	0.500000	−	0.866025i
$677$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$677$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$678$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$679$			1.00000i			1.00000i
$680$		0			0
$681$		0			0
$682$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$		0			0
$685$		0			0
$686$	−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
$689$	0.500000	+	0.866025i	0.500000	+	0.866025i
$690$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	0.866025	+	0.500000i	0.866025	+	0.500000i
$693$		0			0
$694$		0			0
$695$		−	1.00000i		−	1.00000i
$696$	0.866025	+	0.500000i	0.866025	+	0.500000i
$697$		0			0
$698$			1.00000i			1.00000i
$699$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$700$		0			0
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$702$	0.866025	−	0.500000i	0.866025	−	0.500000i
$703$		0			0
$704$	1.00000			1.00000
$705$	0.500000	+	0.866025i	0.500000	+	0.866025i
$706$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$707$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$708$		0			0
$709$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$709$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$710$	0.500000	+	0.866025i	0.500000	+	0.866025i
$711$		0			0
$712$		0			0
$713$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$714$		0			0
$715$	0.500000	−	0.866025i	0.500000	−	0.866025i
$716$	0.500000	−	0.866025i	0.500000	−	0.866025i
$717$		0			0
$718$		−	1.00000i		−	1.00000i
$719$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$719$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	0.500000	−	0.866025i	0.500000	−	0.866025i
$729$	1.00000			1.00000
$730$	0.866025	−	0.500000i	0.866025	−	0.500000i
$731$		0			0
$732$	0.866025	+	0.500000i	0.866025	+	0.500000i
$733$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$733$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$734$	0.866025	−	0.500000i	0.866025	−	0.500000i
$735$		−	1.00000i		−	1.00000i
$736$		−	2.00000i		−	2.00000i
$737$	−1.00000			−1.00000
$738$		0			0
$739$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$739$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		−	1.00000i		−	1.00000i
$742$	0.500000	+	0.866025i	0.500000	+	0.866025i
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$744$	0.866025	−	0.500000i	0.866025	−	0.500000i
$745$	0.500000	−	0.866025i	0.500000	−	0.866025i
$746$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$751$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$751$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$752$			1.00000i			1.00000i
$753$	0.500000	+	0.866025i	0.500000	+	0.866025i
$754$	1.00000			1.00000
$755$	−1.00000			−1.00000
$756$	0.866025	−	0.500000i	0.866025	−	0.500000i
$757$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$757$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$758$	−1.00000			−1.00000
$759$	1.73205	−	1.00000i	1.73205	−	1.00000i
$760$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$761$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$761$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$762$			1.00000i			1.00000i
$763$	−1.00000			−1.00000
$764$	0.866025	+	0.500000i	0.866025	+	0.500000i
$765$		0			0
$766$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$767$		0			0
$768$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$770$	0.500000	−	0.866025i	0.500000	−	0.866025i
$771$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$772$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$		0			0
$775$		0			0
$776$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$777$		0			0
$778$	0.866025	+	0.500000i	0.866025	+	0.500000i
$779$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$780$	0.500000	+	0.866025i	0.500000	+	0.866025i
$781$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$782$		0			0
$783$	0.866025	+	0.500000i	0.866025	+	0.500000i
$784$	0.500000	−	0.866025i	0.500000	−	0.866025i
$785$	−1.00000			−1.00000
$786$	1.00000			1.00000
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$789$			1.00000i			1.00000i
$790$	0.500000	−	0.866025i	0.500000	−	0.866025i
$791$			1.00000i			1.00000i
$792$		0			0
$793$	1.00000			1.00000
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$	−1.00000			−1.00000
$796$		0			0
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$798$		−	1.00000i		−	1.00000i
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.500000	+	0.866025i	0.500000	+	0.866025i
$804$	0.500000	−	0.866025i	0.500000	−	0.866025i
$805$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$806$	0.500000	−	0.866025i	0.500000	−	0.866025i
$807$		0			0
$808$		−	1.00000i		−	1.00000i
$809$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$809$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$810$			1.00000i			1.00000i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	1.00000			1.00000
$813$		0			0
$814$		0			0
$815$	0.866025	+	0.500000i	0.866025	+	0.500000i
$816$		0			0
$817$	0.500000	+	0.866025i	0.500000	+	0.866025i
$818$	2.00000			2.00000
$819$		0			0
$820$		−	1.00000i		−	1.00000i
$821$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$821$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$822$		0			0
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$	0.866025	+	0.500000i	0.866025	+	0.500000i
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$829$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$830$		0			0
$831$		0			0
$832$			1.00000i			1.00000i
$833$		0			0
$834$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$835$	0.500000	+	0.866025i	0.500000	+	0.866025i
$836$	0.500000	−	0.866025i	0.500000	−	0.866025i
$837$	0.866025	−	0.500000i	0.866025	−	0.500000i
$838$	1.00000			1.00000
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$840$	0.500000	+	0.866025i	0.500000	+	0.866025i
$841$		0			0
$842$		0			0
$843$		0			0
$844$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$845$	0.866025	+	0.500000i	0.866025	+	0.500000i
$846$		0			0
$847$		0			0
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$	1.00000			1.00000
$850$		0			0
$851$		0			0
$852$		−	1.00000i		−	1.00000i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	1.00000			1.00000
$855$		0			0
$856$		0			0
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$858$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$860$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$861$	0.866025	−	0.500000i	0.866025	−	0.500000i
$862$	0.866025	−	0.500000i	0.866025	−	0.500000i
$863$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$864$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$865$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$866$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$867$	0.500000	+	0.866025i	0.500000	+	0.866025i
$868$	0.500000	−	0.866025i	0.500000	−	0.866025i
$869$	0.866025	+	0.500000i	0.866025	+	0.500000i
$870$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$871$		−	1.00000i		−	1.00000i
$872$	0.866025	−	0.500000i	0.866025	−	0.500000i
$873$		0			0
$874$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$875$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$876$	−1.00000			−1.00000
$877$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$877$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$878$		0			0
$879$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$880$			1.00000i			1.00000i
$881$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$881$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$	1.00000			1.00000
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$		0			0
$891$	−1.00000			−1.00000
$892$	0.866025	−	0.500000i	0.866025	−	0.500000i
$893$	0.866025	+	0.500000i	0.866025	+	0.500000i
$894$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$895$	0.866025	+	0.500000i	0.866025	+	0.500000i
$896$			1.00000i			1.00000i
$897$	1.00000	+	1.73205i	1.00000	+	1.73205i
$898$	0.500000	−	0.866025i	0.500000	−	0.866025i
$899$	1.00000			1.00000
$900$		0			0
$901$		0			0
$902$	1.00000			1.00000
$903$		−	1.00000i		−	1.00000i
$904$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$905$		0			0
$906$	0.866025	+	0.500000i	0.866025	+	0.500000i
$907$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$907$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$		0			0
$910$	0.866025	+	0.500000i	0.866025	+	0.500000i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	0.500000	+	0.866025i	0.500000	+	0.866025i
$913$		0			0
$914$		0			0
$915$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$916$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$917$	0.866025	−	0.500000i	0.866025	−	0.500000i
$918$		0			0
$919$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$919$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$920$	2.00000			2.00000
$921$		0			0
$922$	0.866025	+	0.500000i	0.866025	+	0.500000i
$923$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$924$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$929$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$929$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$930$	0.500000	+	0.866025i	0.500000	+	0.866025i
$931$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$932$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$933$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$934$	−1.00000			−1.00000
$935$		0			0
$936$		0			0
$937$	−2.00000			−2.00000			−1.00000			$\pi$
$937$	−2.00000			−2.00000			−1.00000			$\pi$
$938$		−	1.00000i		−	1.00000i
$939$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$940$	−1.00000			−1.00000
$941$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$941$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$942$	0.866025	+	0.500000i	0.866025	+	0.500000i
$943$		−	2.00000i		−	2.00000i
$944$		0			0
$945$	0.500000	+	0.866025i	0.500000	+	0.866025i
$946$	0.500000	−	0.866025i	0.500000	−	0.866025i
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$949$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$950$		0			0
$951$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$952$		0			0
$953$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$953$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$954$		0			0
$955$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$956$		0			0
$957$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$958$	0.866025	−	0.500000i	0.866025	−	0.500000i
$959$		0			0
$960$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$961$		0			0
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$966$	1.00000	+	1.73205i	1.00000	+	1.73205i
$967$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$967$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$968$		0			0
$969$		0			0
$970$	0.866025	−	0.500000i	0.866025	−	0.500000i
$971$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$			1.00000i			1.00000i
$974$		0			0
$975$		0			0
$976$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$977$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$978$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$979$		0			0
$980$	0.866025	+	0.500000i	0.866025	+	0.500000i
$981$		0			0
$982$	1.00000			1.00000
$983$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$983$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$984$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$985$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$986$		0			0
$987$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$988$	0.866025	+	0.500000i	0.866025	+	0.500000i
$989$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$990$		0			0
$991$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$991$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$992$			1.00000i			1.00000i
$993$	1.00000			1.00000
$994$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$995$		0			0
$996$		0			0
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$	1.00000			1.00000
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.1.di.a.555.1	yes	4
4.3	odd	2		2912.1.dy.a.1647.1		4
7.4	even	3		728.1.bx.a.347.2	yes	4
8.3	odd	2	inner	728.1.di.a.555.2	yes	4
8.5	even	2		2912.1.dy.a.1647.2		4
13.3	even	3		728.1.bx.a.107.1	✓	4
28.11	odd	6		2912.1.cn.a.2895.2		4
52.3	odd	6		2912.1.cn.a.1199.1		4
56.11	odd	6		728.1.bx.a.347.1	yes	4
56.53	even	6		2912.1.cn.a.2895.1		4
91.81	even	3	inner	728.1.di.a.627.2	yes	4
104.3	odd	6		728.1.bx.a.107.2	yes	4
104.29	even	6		2912.1.cn.a.1199.2		4
364.263	odd	6		2912.1.dy.a.2447.2		4
728.445	even	6		2912.1.dy.a.2447.1		4
728.627	odd	6	inner	728.1.di.a.627.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.1.bx.a.107.1	✓	4	13.3	even	3
728.1.bx.a.107.2	yes	4	104.3	odd	6
728.1.bx.a.347.1	yes	4	56.11	odd	6
728.1.bx.a.347.2	yes	4	7.4	even	3
728.1.di.a.555.1	yes	4	1.1	even	1	trivial
728.1.di.a.555.2	yes	4	8.3	odd	2	inner
728.1.di.a.627.1	yes	4	728.627	odd	6	inner
728.1.di.a.627.2	yes	4	91.81	even	3	inner
2912.1.cn.a.1199.1		4	52.3	odd	6
2912.1.cn.a.1199.2		4	104.29	even	6
2912.1.cn.a.2895.1		4	56.53	even	6
2912.1.cn.a.2895.2		4	28.11	odd	6
2912.1.dy.a.1647.1		4	4.3	odd	2
2912.1.dy.a.1647.2		4	8.5	even	2
2912.1.dy.a.2447.1		4	728.445	even	6
2912.1.dy.a.2447.2		4	364.263	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	728.di (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000 q^{8} -1.00000i q^{10} +1.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000i q^{13} +1.00000i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{19} +(0.866025 - 0.500000i) q^{20} +(0.866025 + 0.500000i) q^{21} +(0.500000 + 0.866025i) q^{22} +(1.73205 - 1.00000i) q^{23} -1.00000 q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-0.866025 - 0.500000i) q^{29} -1.00000i q^{30} +(-0.866025 + 0.500000i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{33} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{38} +1.00000i q^{39} +(0.866025 + 0.500000i) q^{40} +(0.500000 - 0.866025i) q^{41} +1.00000i q^{42} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.73205 + 1.00000i) q^{46} +(-0.866025 - 0.500000i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.866025 - 0.500000i) q^{52} +(0.866025 - 0.500000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.866025 - 0.500000i) q^{55} +(-0.866025 - 0.500000i) q^{56} -1.00000 q^{57} -1.00000i q^{58} +(0.866025 - 0.500000i) q^{60} -1.00000i q^{61} +(-0.866025 - 0.500000i) q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} -1.00000 q^{67} +(1.73205 - 1.00000i) q^{69} +(0.500000 - 0.866025i) q^{70} +(-0.866025 + 0.500000i) q^{71} +(0.500000 + 0.866025i) q^{73} +(0.500000 - 0.866025i) q^{76} +(0.866025 + 0.500000i) q^{77} +(-0.866025 + 0.500000i) q^{78} +(0.866025 + 0.500000i) q^{79} +1.00000i q^{80} -1.00000 q^{81} +1.00000 q^{82} +(-0.866025 + 0.500000i) q^{84} +(0.500000 - 0.866025i) q^{86} +(-0.866025 - 0.500000i) q^{87} -1.00000 q^{88} +(-0.500000 + 0.866025i) q^{91} +2.00000i q^{92} +(-0.866025 + 0.500000i) q^{93} -1.00000i q^{94} +(0.866025 + 0.500000i) q^{95} +(0.500000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{8} + 4 q^{11} - 2 q^{12} - 2 q^{16} - 4 q^{19} + 2 q^{22} - 4 q^{24} - 4 q^{27} + 2 q^{32} + 4 q^{33} - 2 q^{35} - 2 q^{38} + 2 q^{41} - 2 q^{43} - 2 q^{44}+ \cdots - 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^8 + 4 * q^11 - 2 * q^12 - 2 * q^16 - 4 * q^19 + 2 * q^22 - 4 * q^24 - 4 * q^27 + 2 * q^32 + 4 * q^33 - 2 * q^35 - 2 * q^38 + 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 + 2 * q^49 - 2 * q^54 - 4 * q^57 + 4 * q^64 + 2 * q^65 + 2 * q^66 - 4 * q^67 + 2 * q^70 + 2 * q^73 + 2 * q^76 - 4 * q^81 + 4 * q^82 + 2 * q^86 - 4 * q^88 - 2 * q^91 + 2 * q^96 + 2 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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