LMFDB - Embedded newform 1287.1.bg.a.1264.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1287,1,Mod(1231,1287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1287, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1287.1231");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1287 = 3^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1287.bg (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:	$0.642296671259$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.1656369.1

Embedding invariants

Embedding label			1264.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1287.1264
Dual form			1287.1.bg.a.1231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000i q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.866025 - 0.500000i) q^{11} -1.00000 q^{12} +(0.866025 - 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{19} -1.00000 q^{20} +(0.866025 + 0.500000i) q^{21} +1.00000 q^{23} -1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(1.73205 + 1.00000i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.866025 + 0.500000i) q^{33} +(0.866025 + 0.500000i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{37} -1.00000i q^{39} -1.00000i q^{41} -1.00000i q^{43} +1.00000i q^{44} -1.00000 q^{45} +(-0.500000 - 0.866025i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.866025 + 0.500000i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-0.866025 + 0.500000i) q^{55} +(-0.866025 + 0.500000i) q^{57} +(-0.500000 + 0.866025i) q^{60} +1.00000i q^{61} +(0.866025 - 0.500000i) q^{63} +1.00000 q^{64} -1.00000i q^{65} -1.00000 q^{67} +1.00000i q^{68} +(0.500000 - 0.866025i) q^{69} +(0.500000 - 0.866025i) q^{71} +1.00000i q^{76} +(0.500000 - 0.866025i) q^{77} +(0.866025 - 0.500000i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{83} -1.00000i q^{84} +(-0.866025 + 0.500000i) q^{85} +(1.73205 - 1.00000i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(0.500000 + 0.866025i) q^{91} +(-0.500000 - 0.866025i) q^{92} +(0.500000 + 0.866025i) q^{93} +(-0.866025 + 0.500000i) q^{95} +1.00000 q^{97} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9} - 4 q^{12} - 2 q^{15} - 2 q^{16} - 4 q^{20} + 4 q^{23} - 4 q^{27} - 2 q^{31} - 2 q^{36} + 2 q^{37} - 4 q^{45} - 2 q^{47} + 2 q^{48} - 2 q^{60} + 4 q^{64} - 4 q^{67} + 2 q^{69} + 2 q^{71} + 2 q^{77} + 2 q^{80} - 2 q^{81} - 2 q^{89} + 2 q^{91} - 2 q^{92} + 2 q^{93} + 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9 - 4 * q^12 - 2 * q^15 - 2 * q^16 - 4 * q^20 + 4 * q^23 - 4 * q^27 - 2 * q^31 - 2 * q^36 + 2 * q^37 - 4 * q^45 - 2 * q^47 + 2 * q^48 - 2 * q^60 + 4 * q^64 - 4 * q^67 + 2 * q^69 + 2 * q^71 + 2 * q^77 + 2 * q^80 - 2 * q^81 - 2 * q^89 + 2 * q^91 - 2 * q^92 + 2 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times$.

$n$	$496$	$937$	$1145$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (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			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	0.500000	−	0.866025i	0.500000	−	0.866025i
$3$	0.500000	−	0.866025i	0.500000	−	0.866025i
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$6$		0			0
$7$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$7$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$10$		0			0
$11$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$11$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$12$	−1.00000			−1.00000
$13$	0.866025	−	0.500000i	0.866025	−	0.500000i
$13$	0.866025	−	0.500000i	0.866025	−	0.500000i
$14$		0			0
$15$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$17$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$19$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$20$	−1.00000			−1.00000
$21$	0.866025	+	0.500000i	0.866025	+	0.500000i
$22$		0			0
$23$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$23$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.00000			−1.00000
$28$	0.866025	−	0.500000i	0.866025	−	0.500000i
$29$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$29$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$31$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$32$		0			0
$33$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$34$		0			0
$35$	0.866025	+	0.500000i	0.866025	+	0.500000i
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$37$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		−	1.00000i		−	1.00000i
$40$		0			0
$41$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$41$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$42$		0			0
$43$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$43$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$44$			1.00000i			1.00000i
$45$	−1.00000			−1.00000
$46$		0			0
$47$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$47$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$		0			0
$50$		0			0
$51$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$52$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$56$		0			0
$57$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$61$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$61$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$	0.866025	−	0.500000i	0.866025	−	0.500000i
$64$	1.00000			1.00000
$65$		−	1.00000i		−	1.00000i
$66$		0			0
$67$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$68$			1.00000i			1.00000i
$69$	0.500000	−	0.866025i	0.500000	−	0.866025i
$70$		0			0
$71$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$		0			0
$76$			1.00000i			1.00000i
$77$	0.500000	−	0.866025i	0.500000	−	0.866025i
$78$		0			0
$79$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$79$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$80$	0.500000	+	0.866025i	0.500000	+	0.866025i
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$		0			0
$83$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$83$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$84$		−	1.00000i		−	1.00000i
$85$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$86$		0			0
$87$	1.73205	−	1.00000i	1.73205	−	1.00000i
$88$		0			0
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$90$		0			0
$91$	0.500000	+	0.866025i	0.500000	+	0.866025i
$92$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$93$	0.500000	+	0.866025i	0.500000	+	0.866025i
$94$		0			0
$95$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$96$		0			0
$97$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$97$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$98$		0			0
$99$			1.00000i			1.00000i
$100$		0			0
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$104$		0			0
$105$	0.866025	−	0.500000i	0.866025	−	0.500000i
$106$		0			0
$107$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$107$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$108$	0.500000	+	0.866025i	0.500000	+	0.866025i
$109$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$109$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$110$		0			0
$111$	1.00000			1.00000
$112$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$	0.500000	−	0.866025i	0.500000	−	0.866025i
$116$		−	2.00000i		−	2.00000i
$117$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$118$		0			0
$119$	0.500000	−	0.866025i	0.500000	−	0.866025i
$120$		0			0
$121$	0.500000	+	0.866025i	0.500000	+	0.866025i
$122$		0			0
$123$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$124$	1.00000			1.00000
$125$	1.00000			1.00000
$126$		0			0
$127$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$127$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$128$		0			0
$129$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$130$		0			0
$131$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$131$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$132$	0.866025	+	0.500000i	0.866025	+	0.500000i
$133$	0.500000	−	0.866025i	0.500000	−	0.866025i
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$136$		0			0
$137$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$137$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		−	1.00000i		−	1.00000i
$141$	−1.00000			−1.00000
$142$		0			0
$143$	−1.00000			−1.00000
$144$	1.00000			1.00000
$145$	1.73205	−	1.00000i	1.73205	−	1.00000i
$146$		0			0
$147$		0			0
$148$	0.500000	−	0.866025i	0.500000	−	0.866025i
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		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	$0.166667\pi$
$152$		0			0
$153$			1.00000i			1.00000i
$154$		0			0
$155$	0.500000	+	0.866025i	0.500000	+	0.866025i
$156$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$157$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$157$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.00000i			1.00000i
$162$		0			0
$163$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$163$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$164$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$165$			1.00000i			1.00000i
$166$		0			0
$167$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$167$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	0.500000	−	0.866025i	0.500000	−	0.866025i
$170$		0			0
$171$			1.00000i			1.00000i
$172$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$173$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$173$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$174$		0			0
$175$		0			0
$176$	0.866025	−	0.500000i	0.866025	−	0.500000i
$177$		0			0
$178$		0			0
$179$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$179$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$180$	0.500000	+	0.866025i	0.500000	+	0.866025i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	0.866025	+	0.500000i	0.866025	+	0.500000i
$184$		0			0
$185$	1.00000			1.00000
$186$		0			0
$187$	0.500000	+	0.866025i	0.500000	+	0.866025i
$188$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$189$		−	1.00000i		−	1.00000i
$190$		0			0
$191$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$191$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$193$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$194$		0			0
$195$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$196$		0			0
$197$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$197$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$198$		0			0
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$200$		0			0
$201$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$202$		0			0
$203$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$204$	0.866025	+	0.500000i	0.866025	+	0.500000i
$205$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$206$		0			0
$207$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$208$			1.00000i			1.00000i
$209$	0.500000	+	0.866025i	0.500000	+	0.866025i
$210$		0			0
$211$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$211$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$212$		0			0
$213$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$214$		0			0
$215$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$216$		0			0
$217$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$218$		0			0
$219$		0			0
$220$	0.866025	+	0.500000i	0.866025	+	0.500000i
$221$	−1.00000			−1.00000
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$227$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$228$	0.866025	+	0.500000i	0.866025	+	0.500000i
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$230$		0			0
$231$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$	−1.00000			−1.00000
$236$		0			0
$237$		−	1.00000i		−	1.00000i
$238$		0			0
$239$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$239$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$240$	1.00000			1.00000
$241$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$241$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.500000	+	0.866025i
$244$	0.866025	−	0.500000i	0.866025	−	0.500000i
$245$		0			0
$246$		0			0
$247$	−1.00000			−1.00000
$248$		0			0
$249$			1.00000i			1.00000i
$250$		0			0
$251$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$251$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$252$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$253$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$254$		0			0
$255$			1.00000i			1.00000i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$260$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$261$		−	2.00000i		−	2.00000i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.00000			−1.00000
$268$	0.500000	+	0.866025i	0.500000	+	0.866025i
$269$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$269$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$270$		0			0
$271$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$271$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$272$	0.866025	−	0.500000i	0.866025	−	0.500000i
$273$	1.00000			1.00000
$274$		0			0
$275$		0			0
$276$	−1.00000			−1.00000
$277$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$278$		0			0
$279$	1.00000			1.00000
$280$		0			0
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$282$		0			0
$283$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$283$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$284$	−1.00000			−1.00000
$285$			1.00000i			1.00000i
$286$		0			0
$287$	1.00000			1.00000
$288$		0			0
$289$		0			0
$290$		0			0
$291$	0.500000	−	0.866025i	0.500000	−	0.866025i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.866025	+	0.500000i	0.866025	+	0.500000i
$298$		0			0
$299$	0.866025	−	0.500000i	0.866025	−	0.500000i
$300$		0			0
$301$	1.00000			1.00000
$302$		0			0
$303$		0			0
$304$	0.866025	−	0.500000i	0.866025	−	0.500000i
$305$	0.866025	+	0.500000i	0.866025	+	0.500000i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−1.00000			−1.00000
$309$	0.500000	+	0.866025i	0.500000	+	0.866025i
$310$		0			0
$311$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$311$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$312$		0			0
$313$	−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			0
$315$		−	1.00000i		−	1.00000i
$316$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$317$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$317$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$		−	1.00000i		−	1.00000i
$322$		0			0
$323$	0.500000	+	0.866025i	0.500000	+	0.866025i
$324$	1.00000			1.00000
$325$		0			0
$326$		0			0
$327$	1.73205	+	1.00000i	1.73205	+	1.00000i
$328$		0			0
$329$	0.866025	−	0.500000i	0.866025	−	0.500000i
$330$		0			0
$331$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$331$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$332$	0.866025	+	0.500000i	0.866025	+	0.500000i
$333$	0.500000	−	0.866025i	0.500000	−	0.866025i
$334$		0			0
$335$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$336$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$337$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$337$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$338$		0			0
$339$		0			0
$340$	0.866025	+	0.500000i	0.866025	+	0.500000i
$341$	0.866025	−	0.500000i	0.866025	−	0.500000i
$342$		0			0
$343$			1.00000i			1.00000i
$344$		0			0
$345$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$352$		0			0
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$356$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$357$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	1.00000			1.00000
$364$	0.500000	−	0.866025i	0.500000	−	0.866025i
$365$		0			0
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$369$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$370$		0			0
$371$		0			0
$372$	0.500000	−	0.866025i	0.500000	−	0.866025i
$373$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$373$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.500000	−	0.866025i
$376$		0			0
$377$	2.00000			2.00000
$378$		0			0
$379$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$379$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$380$	0.866025	+	0.500000i	0.866025	+	0.500000i
$381$		−	1.00000i		−	1.00000i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$386$		0			0
$387$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$388$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$389$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$389$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$390$		0			0
$391$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$392$		0			0
$393$	0.866025	−	0.500000i	0.866025	−	0.500000i
$394$		0			0
$395$		−	1.00000i		−	1.00000i
$396$	0.866025	−	0.500000i	0.866025	−	0.500000i
$397$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$397$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$398$		0			0
$399$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$400$		0			0
$401$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$401$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$			1.00000i			1.00000i
$404$		0			0
$405$	0.500000	+	0.866025i	0.500000	+	0.866025i
$406$		0			0
$407$		−	1.00000i		−	1.00000i
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$	0.500000	−	0.866025i	0.500000	−	0.866025i
$412$	1.00000			1.00000
$413$		0			0
$414$		0			0
$415$			1.00000i			1.00000i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$421$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$421$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$422$		0			0
$423$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.00000			−1.00000
$428$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$429$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$430$		0			0
$431$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$431$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$433$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$434$		0			0
$435$		−	2.00000i		−	2.00000i
$436$	1.73205	−	1.00000i	1.73205	−	1.00000i
$437$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$438$		0			0
$439$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$439$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$444$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$445$	−1.00000			−1.00000
$446$		0			0
$447$		0			0
$448$			1.00000i			1.00000i
$449$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$450$		0			0
$451$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$452$		0			0
$453$		−	1.00000i		−	1.00000i
$454$		0			0
$455$	1.00000			1.00000
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$	0.866025	+	0.500000i	0.866025	+	0.500000i
$460$	−1.00000			−1.00000
$461$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$461$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$464$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$465$	1.00000			1.00000
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$			1.00000i			1.00000i
$469$		−	1.00000i		−	1.00000i
$470$		0			0
$471$	0.500000	+	0.866025i	0.500000	+	0.866025i
$472$		0			0
$473$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$474$		0			0
$475$		0			0
$476$	−1.00000			−1.00000
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	0.866025	+	0.500000i	0.866025	+	0.500000i
$482$		0			0
$483$	0.866025	+	0.500000i	0.866025	+	0.500000i
$484$	0.500000	−	0.866025i	0.500000	−	0.866025i
$485$	0.500000	−	0.866025i	0.500000	−	0.866025i
$486$		0			0
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$488$		0			0
$489$	0.500000	+	0.866025i	0.500000	+	0.866025i
$490$		0			0
$491$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$491$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$492$			1.00000i			1.00000i
$493$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$494$		0			0
$495$	0.866025	+	0.500000i	0.866025	+	0.500000i
$496$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$497$	0.866025	+	0.500000i	0.866025	+	0.500000i
$498$		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			$0$
$500$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$501$	0.866025	+	0.500000i	0.866025	+	0.500000i
$502$		0			0
$503$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$503$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$508$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$509$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$509$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.866025	+	0.500000i	0.866025	+	0.500000i
$514$		0			0
$515$	0.500000	+	0.866025i	0.500000	+	0.866025i
$516$			1.00000i			1.00000i
$517$			1.00000i			1.00000i
$518$		0			0
$519$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$520$		0			0
$521$	−2.00000			−2.00000			−1.00000			$\pi$
$521$	−2.00000			−2.00000			−1.00000			$\pi$
$522$		0			0
$523$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$523$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$524$		−	1.00000i		−	1.00000i
$525$		0			0
$526$		0			0
$527$	0.866025	−	0.500000i	0.866025	−	0.500000i
$528$		−	1.00000i		−	1.00000i
$529$		0			0
$530$		0			0
$531$		0			0
$532$	−1.00000			−1.00000
$533$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$534$		0			0
$535$		−	1.00000i		−	1.00000i
$536$		0			0
$537$	−1.00000			−1.00000
$538$		0			0
$539$		0			0
$540$	1.00000			1.00000
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.73205	+	1.00000i	1.73205	+	1.00000i
$546$		0			0
$547$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$547$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$548$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$549$	0.866025	−	0.500000i	0.866025	−	0.500000i
$550$		0			0
$551$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$552$		0			0
$553$	0.500000	+	0.866025i	0.500000	+	0.866025i
$554$		0			0
$555$	0.500000	−	0.866025i	0.500000	−	0.866025i
$556$		0			0
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$558$		0			0
$559$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$560$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$561$	1.00000			1.00000
$562$		0			0
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$	0.500000	+	0.866025i	0.500000	+	0.866025i
$565$		0			0
$566$		0			0
$567$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$568$		0			0
$569$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$569$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$570$		0			0
$571$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$571$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$572$	0.500000	+	0.866025i	0.500000	+	0.866025i
$573$	0.500000	−	0.866025i	0.500000	−	0.866025i
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$		0			0			−	1.00000i	$-0.5\pi$
$577$		0			0				1.00000i	$0.5\pi$
$578$		0			0
$579$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$580$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$581$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$586$		0			0
$587$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$587$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$588$		0			0
$589$	0.866025	−	0.500000i	0.866025	−	0.500000i
$590$		0			0
$591$			1.00000i			1.00000i
$592$	−1.00000			−1.00000
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$596$		0			0
$597$	0.500000	+	0.866025i	0.500000	+	0.866025i
$598$		0			0
$599$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$599$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$600$		0			0
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	0.500000	+	0.866025i	0.500000	+	0.866025i
$604$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$605$	1.00000			1.00000
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$	1.00000	+	1.73205i	1.00000	+	1.73205i
$610$		0			0
$611$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$612$	0.866025	−	0.500000i	0.866025	−	0.500000i
$613$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$613$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$614$		0			0
$615$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$616$		0			0
$617$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$617$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$618$		0			0
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$620$	0.500000	−	0.866025i	0.500000	−	0.866025i
$621$	−1.00000			−1.00000
$622$		0			0
$623$	0.866025	−	0.500000i	0.866025	−	0.500000i
$624$	0.866025	+	0.500000i	0.866025	+	0.500000i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$	1.00000			1.00000
$628$	1.00000			1.00000
$629$		−	1.00000i		−	1.00000i
$630$		0			0
$631$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$632$		0			0
$633$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$634$		0			0
$635$		−	1.00000i		−	1.00000i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.00000			−1.00000
$640$		0			0
$641$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$641$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$643$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$644$	0.866025	−	0.500000i	0.866025	−	0.500000i
$645$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$646$		0			0
$647$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$647$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$652$	1.00000			1.00000
$653$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$653$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	0.866025	−	0.500000i	0.866025	−	0.500000i
$656$	0.866025	+	0.500000i	0.866025	+	0.500000i
$657$		0			0
$658$		0			0
$659$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$659$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$660$	0.866025	−	0.500000i	0.866025	−	0.500000i
$661$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$661$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$664$		0			0
$665$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$666$		0			0
$667$	1.73205	+	1.00000i	1.73205	+	1.00000i
$668$	0.866025	−	0.500000i	0.866025	−	0.500000i
$669$		0			0
$670$		0			0
$671$	0.500000	−	0.866025i	0.500000	−	0.866025i
$672$		0			0
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$		0			0
$676$	−1.00000			−1.00000
$677$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$677$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$678$		0			0
$679$			1.00000i			1.00000i
$680$		0			0
$681$	0.866025	+	0.500000i	0.866025	+	0.500000i
$682$		0			0
$683$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$683$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$684$	0.866025	−	0.500000i	0.866025	−	0.500000i
$685$	0.500000	−	0.866025i	0.500000	−	0.866025i
$686$		0			0
$687$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$688$	0.866025	+	0.500000i	0.866025	+	0.500000i
$689$		0			0
$690$		0			0
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$693$	−1.00000			−1.00000
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		−	1.00000i		−	1.00000i
$704$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$705$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$709$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$712$		0			0
$713$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$714$		0			0
$715$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$716$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$717$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$718$		0			0
$719$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$720$	0.500000	−	0.866025i	0.500000	−	0.866025i
$721$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$722$		0			0
$723$	0.866025	+	0.500000i	0.866025	+	0.500000i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$727$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$732$		−	1.00000i		−	1.00000i
$733$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$733$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.866025	+	0.500000i	0.866025	+	0.500000i
$738$		0			0
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$740$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$741$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$742$		0			0
$743$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.866025	+	0.500000i	0.866025	+	0.500000i
$748$	0.500000	−	0.866025i	0.500000	−	0.866025i
$749$	0.500000	+	0.866025i	0.500000	+	0.866025i
$750$		0			0
$751$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$751$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$752$	1.00000			1.00000
$753$	0.500000	+	0.866025i	0.500000	+	0.866025i
$754$		0			0
$755$		−	1.00000i		−	1.00000i
$756$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$757$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$757$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$760$		0			0
$761$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$761$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	−2.00000			−2.00000
$764$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$765$	0.866025	+	0.500000i	0.866025	+	0.500000i
$766$		0			0
$767$		0			0
$768$	−1.00000			−1.00000
$769$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$769$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$770$		0			0
$771$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$772$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$773$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$773$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			1.00000i			1.00000i
$778$		0			0
$779$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$780$			1.00000i			1.00000i
$781$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$782$		0			0
$783$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$784$		0			0
$785$	0.500000	+	0.866025i	0.500000	+	0.866025i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	0.866025	+	0.500000i	0.866025	+	0.500000i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.500000	+	0.866025i	0.500000	+	0.866025i
$794$		0			0
$795$		0			0
$796$	1.00000			1.00000
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$			1.00000i			1.00000i
$800$		0			0
$801$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$802$		0			0
$803$		0			0
$804$	1.00000			1.00000
$805$	0.866025	+	0.500000i	0.866025	+	0.500000i
$806$		0			0
$807$	0.500000	+	0.866025i	0.500000	+	0.866025i
$808$		0			0
$809$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$809$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	2.00000			2.00000
$813$		−	1.00000i		−	1.00000i
$814$		0			0
$815$	0.500000	+	0.866025i	0.500000	+	0.866025i
$816$		−	1.00000i		−	1.00000i
$817$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$818$		0			0
$819$	0.500000	−	0.866025i	0.500000	−	0.866025i
$820$			1.00000i			1.00000i
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$829$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$829$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$832$	0.866025	−	0.500000i	0.866025	−	0.500000i
$833$		0			0
$834$		0			0
$835$	0.866025	+	0.500000i	0.866025	+	0.500000i
$836$	0.500000	−	0.866025i	0.500000	−	0.866025i
$837$	0.500000	−	0.866025i	0.500000	−	0.866025i
$838$		0			0
$839$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$839$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	1.50000	+	2.59808i	1.50000	+	2.59808i
$842$		0			0
$843$			1.00000i			1.00000i
$844$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$845$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$846$		0			0
$847$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$848$		0			0
$849$	0.866025	+	0.500000i	0.866025	+	0.500000i
$850$		0			0
$851$	0.500000	+	0.866025i	0.500000	+	0.866025i
$852$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$854$		0			0
$855$	0.866025	+	0.500000i	0.866025	+	0.500000i
$856$		0			0
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	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			$0$
$860$			1.00000i			1.00000i
$861$	0.500000	−	0.866025i	0.500000	−	0.866025i
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$866$		0			0
$867$		0			0
$868$			1.00000i			1.00000i
$869$	−1.00000			−1.00000
$870$		0			0
$871$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$872$		0			0
$873$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$874$		0			0
$875$			1.00000i			1.00000i
$876$		0			0
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$		−	1.00000i		−	1.00000i
$881$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$881$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	0.500000	+	0.866025i	0.500000	+	0.866025i
$885$		0			0
$886$		0			0
$887$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$888$		0			0
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$		0			0
$891$	0.866025	−	0.500000i	0.866025	−	0.500000i
$892$		0			0
$893$			1.00000i			1.00000i
$894$		0			0
$895$	−1.00000			−1.00000
$896$		0			0
$897$		−	1.00000i		−	1.00000i
$898$		0			0
$899$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.500000	−	0.866025i	0.500000	−	0.866025i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	0.866025	−	0.500000i	0.866025	−	0.500000i
$909$		0			0
$910$		0			0
$911$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$911$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$912$		−	1.00000i		−	1.00000i
$913$	1.00000			1.00000
$914$		0			0
$915$	0.866025	−	0.500000i	0.866025	−	0.500000i
$916$	−1.00000			−1.00000
$917$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$918$		0			0
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.00000i		−	1.00000i
$924$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$925$		0			0
$926$		0			0
$927$	1.00000			1.00000
$928$		0			0
$929$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$929$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.500000	+	0.866025i	0.500000	+	0.866025i
$934$		0			0
$935$	1.00000			1.00000
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	−1.00000			−1.00000
$940$	0.500000	+	0.866025i	0.500000	+	0.866025i
$941$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$941$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$942$		0			0
$943$		−	1.00000i		−	1.00000i
$944$		0			0
$945$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$946$		0			0
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$949$		0			0
$950$		0			0
$951$	1.00000			1.00000
$952$		0			0
$953$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$953$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$954$		0			0
$955$	0.500000	−	0.866025i	0.500000	−	0.866025i
$956$			1.00000i			1.00000i
$957$	−2.00000			−2.00000
$958$		0			0
$959$			1.00000i			1.00000i
$960$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$961$		0			0
$962$		0			0
$963$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$964$	0.866025	−	0.500000i	0.866025	−	0.500000i
$965$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$966$		0			0
$967$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$967$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$968$		0			0
$969$	1.00000			1.00000
$970$		0			0
$971$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$972$	0.500000	−	0.866025i	0.500000	−	0.866025i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$977$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$977$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$			1.00000i			1.00000i
$980$		0			0
$981$	1.73205	−	1.00000i	1.73205	−	1.00000i
$982$		0			0
$983$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$983$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$984$		0			0
$985$			1.00000i			1.00000i
$986$		0			0
$987$		−	1.00000i		−	1.00000i
$988$	0.500000	+	0.866025i	0.500000	+	0.866025i
$989$		−	1.00000i		−	1.00000i
$990$		0			0
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$994$		0			0
$995$	0.500000	+	0.866025i	0.500000	+	0.866025i
$996$	0.866025	−	0.500000i	0.866025	−	0.500000i
$997$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$998$		0			0
$999$	−0.500000	−	0.866025i	−0.500000	−	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1287.1.bg.a.1264.2	yes	4
3.2	odd	2		3861.1.bg.a.2980.2		4
9.2	odd	6		3861.1.s.a.1693.2		4
9.7	even	3		1287.1.s.a.835.2	yes	4
11.10	odd	2	inner	1287.1.bg.a.1264.1	yes	4
13.9	even	3		1287.1.s.a.373.1	✓	4
33.32	even	2		3861.1.bg.a.2980.1		4
39.35	odd	6		3861.1.s.a.2089.1		4
99.43	odd	6		1287.1.s.a.835.1	yes	4
99.65	even	6		3861.1.s.a.1693.1		4
117.61	even	3	inner	1287.1.bg.a.1231.2	yes	4
117.74	odd	6		3861.1.bg.a.802.2		4
143.87	odd	6		1287.1.s.a.373.2	yes	4
429.230	even	6		3861.1.s.a.2089.2		4
1287.659	even	6		3861.1.bg.a.802.1		4
1287.1231	odd	6	inner	1287.1.bg.a.1231.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1287.1.s.a.373.1	✓	4	13.9	even	3
1287.1.s.a.373.2	yes	4	143.87	odd	6
1287.1.s.a.835.1	yes	4	99.43	odd	6
1287.1.s.a.835.2	yes	4	9.7	even	3
1287.1.bg.a.1231.1	yes	4	1287.1231	odd	6	inner
1287.1.bg.a.1231.2	yes	4	117.61	even	3	inner
1287.1.bg.a.1264.1	yes	4	11.10	odd	2	inner
1287.1.bg.a.1264.2	yes	4	1.1	even	1	trivial
3861.1.s.a.1693.1		4	99.65	even	6
3861.1.s.a.1693.2		4	9.2	odd	6
3861.1.s.a.2089.1		4	39.35	odd	6
3861.1.s.a.2089.2		4	429.230	even	6
3861.1.bg.a.802.1		4	1287.659	even	6
3861.1.bg.a.802.2		4	117.74	odd	6
3861.1.bg.a.2980.1		4	33.32	even	2
3861.1.bg.a.2980.2		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1287.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000i q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.866025 - 0.500000i) q^{11} -1.00000 q^{12} +(0.866025 - 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{19} -1.00000 q^{20} +(0.866025 + 0.500000i) q^{21} +1.00000 q^{23} -1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(1.73205 + 1.00000i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.866025 + 0.500000i) q^{33} +(0.866025 + 0.500000i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{37} -1.00000i q^{39} -1.00000i q^{41} -1.00000i q^{43} +1.00000i q^{44} -1.00000 q^{45} +(-0.500000 - 0.866025i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.866025 + 0.500000i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-0.866025 + 0.500000i) q^{55} +(-0.866025 + 0.500000i) q^{57} +(-0.500000 + 0.866025i) q^{60} +1.00000i q^{61} +(0.866025 - 0.500000i) q^{63} +1.00000 q^{64} -1.00000i q^{65} -1.00000 q^{67} +1.00000i q^{68} +(0.500000 - 0.866025i) q^{69} +(0.500000 - 0.866025i) q^{71} +1.00000i q^{76} +(0.500000 - 0.866025i) q^{77} +(0.866025 - 0.500000i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{83} -1.00000i q^{84} +(-0.866025 + 0.500000i) q^{85} +(1.73205 - 1.00000i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(0.500000 + 0.866025i) q^{91} +(-0.500000 - 0.866025i) q^{92} +(0.500000 + 0.866025i) q^{93} +(-0.866025 + 0.500000i) q^{95} +1.00000 q^{97} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9} - 4 q^{12} - 2 q^{15} - 2 q^{16} - 4 q^{20} + 4 q^{23} - 4 q^{27} - 2 q^{31} - 2 q^{36} + 2 q^{37} - 4 q^{45} - 2 q^{47} + 2 q^{48} - 2 q^{60} + 4 q^{64} - 4 q^{67} + 2 q^{69} + 2 q^{71} + 2 q^{77} + 2 q^{80} - 2 q^{81} - 2 q^{89} + 2 q^{91} - 2 q^{92} + 2 q^{93} + 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9 - 4 * q^12 - 2 * q^15 - 2 * q^16 - 4 * q^20 + 4 * q^23 - 4 * q^27 - 2 * q^31 - 2 * q^36 + 2 * q^37 - 4 * q^45 - 2 * q^47 + 2 * q^48 - 2 * q^60 + 4 * q^64 - 4 * q^67 + 2 * q^69 + 2 * q^71 + 2 * q^77 + 2 * q^80 - 2 * q^81 - 2 * q^89 + 2 * q^91 - 2 * q^92 + 2 * q^93 + 4 * q^97

Introduction

L-functions

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