LMFDB - Embedded newform 3528.1.bp.b.3253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3528,1,Mod(1501,3528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3528, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 1]))

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

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

chi := DirichletCharacter("3528.1501");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3528.bp (of order $6$, degree $2$, not 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:	$1.76070136457$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.4536.1

Embedding invariants

Embedding label			3253.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3528.3253
Dual form			3528.1.bp.b.1501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +1.00000 q^{32} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 + 0.866025i) q^{38} +2.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +1.00000 q^{45} +(0.500000 + 0.866025i) q^{46} +(0.500000 + 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{52} -1.00000 q^{54} -1.00000 q^{57} -2.00000 q^{59} +(0.500000 - 0.866025i) q^{60} +1.00000 q^{61} +1.00000 q^{64} -2.00000 q^{65} +(-0.500000 + 0.866025i) q^{69} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.500000 + 0.866025i) q^{76} +2.00000 q^{78} -1.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{83} +1.00000 q^{90} +(0.500000 + 0.866025i) q^{92} +1.00000 q^{95} +(0.500000 + 0.866025i) q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{12} + 2 q^{13} + q^{15} + 2 q^{16} - q^{18} - q^{19} - q^{20} + q^{23} + q^{24} + 2 q^{26} - 2 q^{27} + q^{30} + 2 q^{32} - q^{36} - q^{38} + 4 q^{39} - q^{40} + 2 q^{45} + q^{46} + q^{48} + 2 q^{52} - 2 q^{54} - 2 q^{57} - 4 q^{59} + q^{60} + 2 q^{61} + 2 q^{64} - 4 q^{65} - q^{69} - 2 q^{71} - q^{72} - q^{76} + 4 q^{78} - 2 q^{79} - q^{80} - q^{81} + 2 q^{83} + 2 q^{90} + q^{92} + 2 q^{95} + q^{96}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - q^9 - q^10 + q^12 + 2 * q^13 + q^15 + 2 * q^16 - q^18 - q^19 - q^20 + q^23 + q^24 + 2 * q^26 - 2 * q^27 + q^30 + 2 * q^32 - q^36 - q^38 + 4 * q^39 - q^40 + 2 * q^45 + q^46 + q^48 + 2 * q^52 - 2 * q^54 - 2 * q^57 - 4 * q^59 + q^60 + 2 * q^61 + 2 * q^64 - 4 * q^65 - q^69 - 2 * q^71 - q^72 - q^76 + 4 * q^78 - 2 * q^79 - q^80 - q^81 + 2 * q^83 + 2 * q^90 + q^92 + 2 * q^95 + q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$1765$	$2647$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (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 $

$2$	1.00000			1.00000
$2$	1.00000			1.00000
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$4$	1.00000			1.00000
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$6$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$		0			0
$7$		0			0
$8$	1.00000			1.00000
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$13$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$14$		0			0
$15$	0.500000	−	0.866025i	0.500000	−	0.866025i
$16$	1.00000			1.00000
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$19$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$19$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$20$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$21$		0			0
$22$		0			0
$23$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$23$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$24$	0.500000	+	0.866025i	0.500000	+	0.866025i
$25$		0			0
$26$	1.00000	−	1.73205i	1.00000	−	1.73205i
$27$	−1.00000			−1.00000
$28$		0			0
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	0.500000	−	0.866025i	0.500000	−	0.866025i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.00000			1.00000
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$39$	2.00000			2.00000
$40$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$41$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$41$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$		0			0
$45$	1.00000			1.00000
$46$	0.500000	+	0.866025i	0.500000	+	0.866025i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$		0			0
$50$		0			0
$51$		0			0
$52$	1.00000	−	1.73205i	1.00000	−	1.73205i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−1.00000			−1.00000
$55$		0			0
$56$		0			0
$57$	−1.00000			−1.00000
$58$		0			0
$59$	−2.00000			−2.00000			−1.00000			$\pi$
$59$	−2.00000			−2.00000			−1.00000			$\pi$
$60$	0.500000	−	0.866025i	0.500000	−	0.866025i
$61$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$61$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			1.00000
$65$	−2.00000			−2.00000
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$70$		0			0
$71$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$72$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$		0			0
$76$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$77$		0			0
$78$	2.00000			2.00000
$79$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$79$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$80$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$		0			0
$83$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$83$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	1.00000			1.00000
$91$		0			0
$92$	0.500000	+	0.866025i	0.500000	+	0.866025i
$93$		0			0
$94$		0			0
$95$	1.00000			1.00000
$96$	0.500000	+	0.866025i	0.500000	+	0.866025i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$101$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	1.00000	−	1.73205i	1.00000	−	1.73205i
$105$		0			0
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−1.00000			−1.00000
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$114$	−1.00000			−1.00000
$115$	0.500000	−	0.866025i	0.500000	−	0.866025i
$116$		0			0
$117$	1.00000	+	1.73205i	1.00000	+	1.73205i
$118$	−2.00000			−2.00000
$119$		0			0
$120$	0.500000	−	0.866025i	0.500000	−	0.866025i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	1.00000			1.00000
$123$		0			0
$124$		0			0
$125$	−1.00000			−1.00000
$126$		0			0
$127$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$127$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$128$	1.00000			1.00000
$129$		0			0
$130$	−2.00000			−2.00000
$131$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$131$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.500000	+	0.866025i	0.500000	+	0.866025i
$136$		0			0
$137$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$137$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$139$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$139$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$	−1.00000			−1.00000
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$152$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	2.00000			2.00000
$157$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$157$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$158$	−1.00000			−1.00000
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$161$		0			0
$162$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$	1.00000	+	1.73205i	1.00000	+	1.73205i
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$172$		0			0
$173$	−2.00000			−2.00000			−1.00000			$\pi$
$173$	−2.00000			−2.00000			−1.00000			$\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	1.00000			1.00000
$181$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$181$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$182$		0			0
$183$	0.500000	+	0.866025i	0.500000	+	0.866025i
$184$	0.500000	+	0.866025i	0.500000	+	0.866025i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.00000			1.00000
$191$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.500000	+	0.866025i	0.500000	+	0.866025i
$193$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$193$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$		0			0
$201$		0			0
$202$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.00000			−1.00000
$208$	1.00000	−	1.73205i	1.00000	−	1.73205i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$214$		0			0
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$		0			0
$225$		0			0
$226$	0.500000	−	0.866025i	0.500000	−	0.866025i
$227$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$227$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$228$	−1.00000			−1.00000
$229$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$229$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$230$	0.500000	−	0.866025i	0.500000	−	0.866025i
$231$		0			0
$232$		0			0
$233$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$233$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$234$	1.00000	+	1.73205i	1.00000	+	1.73205i
$235$		0			0
$236$	−2.00000			−2.00000
$237$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$238$		0			0
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$240$	0.500000	−	0.866025i	0.500000	−	0.866025i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$	1.00000			1.00000
$245$		0			0
$246$		0			0
$247$	1.00000	+	1.73205i	1.00000	+	1.73205i
$248$		0			0
$249$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$250$	−1.00000			−1.00000
$251$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$251$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$252$		0			0
$253$		0			0
$254$	−1.00000			−1.00000
$255$		0			0
$256$	1.00000			1.00000
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−2.00000
$261$		0			0
$262$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−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			$\pi$
$270$	0.500000	+	0.866025i	0.500000	+	0.866025i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$		0			0
$274$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$275$		0			0
$276$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$277$		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			0
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$283$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$284$	−1.00000			−1.00000
$285$	0.500000	+	0.866025i	0.500000	+	0.866025i
$286$		0			0
$287$		0			0
$288$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$293$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$294$		0			0
$295$	1.00000	+	1.73205i	1.00000	+	1.73205i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.00000			2.00000
$300$		0			0
$301$		0			0
$302$	0.500000	−	0.866025i	0.500000	−	0.866025i
$303$	−1.00000			−1.00000
$304$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$305$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$306$		0			0
$307$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$307$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	2.00000			2.00000
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	1.00000			1.00000
$315$		0			0
$316$	−1.00000			−1.00000
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	1.00000	+	1.73205i	1.00000	+	1.73205i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$337$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$339$	1.00000			1.00000
$340$		0			0
$341$		0			0
$342$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$343$		0			0
$344$		0			0
$345$	1.00000			1.00000
$346$	−2.00000			−2.00000
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$		0			0
$349$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$349$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$350$		0			0
$351$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$355$	0.500000	+	0.866025i	0.500000	+	0.866025i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$360$	1.00000			1.00000
$361$		0			0
$362$	1.00000			1.00000
$363$	0.500000	−	0.866025i	0.500000	−	0.866025i
$364$		0			0
$365$		0			0
$366$	0.500000	+	0.866025i	0.500000	+	0.866025i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	1.00000			1.00000
$381$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$382$	−1.00000			−1.00000
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	0.500000	+	0.866025i	0.500000	+	0.866025i
$385$		0			0
$386$	−1.00000			−1.00000
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$391$		0			0
$392$		0			0
$393$	0.500000	−	0.866025i	0.500000	−	0.866025i
$394$		0			0
$395$	0.500000	+	0.866025i	0.500000	+	0.866025i
$396$		0			0
$397$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$397$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$405$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$	−2.00000			−2.00000
$412$		0			0
$413$		0			0
$414$	−1.00000			−1.00000
$415$	1.00000	−	1.73205i	1.00000	−	1.73205i
$416$	1.00000	−	1.73205i	1.00000	−	1.73205i
$417$	−1.00000			−1.00000
$418$		0			0
$419$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$419$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$431$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$432$	−1.00000			−1.00000
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.00000			−1.00000
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$		0			0
$451$		0			0
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$	1.00000			1.00000
$454$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$455$		0			0
$456$	−1.00000			−1.00000
$457$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$457$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$458$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$459$		0			0
$460$	0.500000	−	0.866025i	0.500000	−	0.866025i
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$464$		0			0
$465$		0			0
$466$	0.500000	−	0.866025i	0.500000	−	0.866025i
$467$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$467$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$468$	1.00000	+	1.73205i	1.00000	+	1.73205i
$469$		0			0
$470$		0			0
$471$	0.500000	+	0.866025i	0.500000	+	0.866025i
$472$	−2.00000			−2.00000
$473$		0			0
$474$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.500000	−	0.866025i	0.500000	−	0.866025i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	0.500000	−	0.866025i	0.500000	−	0.866025i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	0.500000	−	0.866025i	0.500000	−	0.866025i
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$488$	1.00000			1.00000
$489$		0			0
$490$		0			0
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$	1.00000	+	1.73205i	1.00000	+	1.73205i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−1.00000			−1.00000
$501$		0			0
$502$	1.00000			1.00000
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$	1.00000			1.00000
$506$		0			0
$507$	1.50000	−	2.59808i	1.50000	−	2.59808i
$508$	−1.00000			−1.00000
$509$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$509$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$	0.500000	−	0.866025i	0.500000	−	0.866025i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$520$	−2.00000			−2.00000
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$524$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$525$		0			0
$526$	0.500000	−	0.866025i	0.500000	−	0.866025i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$	1.00000	−	1.73205i	1.00000	−	1.73205i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$539$		0			0
$540$	0.500000	+	0.866025i	0.500000	+	0.866025i
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	0.500000	+	0.866025i	0.500000	+	0.866025i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$549$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$550$		0			0
$551$		0			0
$552$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.500000	+	0.866025i	0.500000	+	0.866025i
$563$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$563$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$	−1.00000			−1.00000
$566$	1.00000			1.00000
$567$		0			0
$568$	−1.00000			−1.00000
$569$	2.00000			2.00000			1.00000			$0$
$569$	2.00000			2.00000			1.00000			$0$
$570$	0.500000	+	0.866025i	0.500000	+	0.866025i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−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		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$579$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.00000	−	1.73205i	1.00000	−	1.73205i
$586$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	1.00000	+	1.73205i	1.00000	+	1.73205i
$591$		0			0
$592$		0			0
$593$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$593$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	2.00000			2.00000
$599$	2.00000			2.00000			1.00000			$0$
$599$	2.00000			2.00000			1.00000			$0$
$600$		0			0
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	0.500000	−	0.866025i	0.500000	−	0.866025i
$605$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$606$	−1.00000			−1.00000
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$609$		0			0
$610$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	1.00000			1.00000
$615$		0			0
$616$		0			0
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		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			0
$621$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$622$		0			0
$623$		0			0
$624$	2.00000			2.00000
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$	1.00000			1.00000
$629$		0			0
$630$		0			0
$631$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$632$	−1.00000			−1.00000
$633$		0			0
$634$		0			0
$635$	0.500000	+	0.866025i	0.500000	+	0.866025i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.500000	−	0.866025i	0.500000	−	0.866025i
$640$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$642$		0			0
$643$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	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			0
$664$	1.00000	+	1.73205i	1.00000	+	1.73205i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$674$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$675$		0			0
$676$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$677$	−2.00000			−2.00000			−1.00000			$\pi$
$677$	−2.00000			−2.00000			−1.00000			$\pi$
$678$	1.00000			1.00000
$679$		0			0
$680$		0			0
$681$	−1.00000			−1.00000
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$685$	2.00000			2.00000
$686$		0			0
$687$	0.500000	−	0.866025i	0.500000	−	0.866025i
$688$		0			0
$689$		0			0
$690$	1.00000			1.00000
$691$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$691$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$692$	−2.00000			−2.00000
$693$		0			0
$694$		0			0
$695$	1.00000			1.00000
$696$		0			0
$697$		0			0
$698$	1.00000	+	1.73205i	1.00000	+	1.73205i
$699$	1.00000			1.00000
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$	0.500000	+	0.866025i	0.500000	+	0.866025i
$711$	0.500000	−	0.866025i	0.500000	−	0.866025i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.00000			1.00000
$718$	0.500000	−	0.866025i	0.500000	−	0.866025i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	1.00000			1.00000
$721$		0			0
$722$		0			0
$723$		0			0
$724$	1.00000			1.00000
$725$		0			0
$726$	0.500000	−	0.866025i	0.500000	−	0.866025i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	0.500000	+	0.866025i	0.500000	+	0.866025i
$733$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$733$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$	0.500000	+	0.866025i	0.500000	+	0.866025i
$737$		0			0
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$742$		0			0
$743$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$743$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.00000			−2.00000
$748$		0			0
$749$		0			0
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	0.500000	+	0.866025i	0.500000	+	0.866025i
$754$		0			0
$755$	−1.00000			−1.00000
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	1.00000			1.00000
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$763$		0			0
$764$	−1.00000			−1.00000
$765$		0			0
$766$		0			0
$767$	−2.00000	+	3.46410i	−2.00000	+	3.46410i
$768$	0.500000	+	0.866025i	0.500000	+	0.866025i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000			−1.00000
$773$	−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
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$786$	0.500000	−	0.866025i	0.500000	−	0.866025i
$787$	−2.00000			−2.00000			−1.00000			$\pi$
$787$	−2.00000			−2.00000			−1.00000			$\pi$
$788$		0			0
$789$	1.00000			1.00000
$790$	0.500000	+	0.866025i	0.500000	+	0.866025i
$791$		0			0
$792$		0			0
$793$	1.00000	−	1.73205i	1.00000	−	1.73205i
$794$	1.00000	−	1.73205i	1.00000	−	1.73205i
$795$		0			0
$796$		0			0
$797$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$797$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	0.500000	+	0.866025i	0.500000	+	0.866025i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.500000	−	0.866025i	0.500000	−	0.866025i
$808$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$809$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$810$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−2.00000			−2.00000
$823$	2.00000			2.00000			1.00000			$0$
$823$	2.00000			2.00000			1.00000			$0$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−1.00000			−1.00000
$829$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$829$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$830$	1.00000	−	1.73205i	1.00000	−	1.73205i
$831$		0			0
$832$	1.00000	−	1.73205i	1.00000	−	1.73205i
$833$		0			0
$834$	−1.00000			−1.00000
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$844$		0			0
$845$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.500000	+	0.866025i	0.500000	+	0.866025i
$850$		0			0
$851$		0			0
$852$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$854$		0			0
$855$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$859$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$863$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$863$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$864$	−1.00000			−1.00000
$865$	1.00000	+	1.73205i	1.00000	+	1.73205i
$866$		0			0
$867$	−1.00000			−1.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−1.00000			−1.00000
$875$		0			0
$876$		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
$879$	−1.00000			−1.00000
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.00000	+	1.73205i	1.00000	+	1.73205i
$898$	−1.00000			−1.00000
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.500000	−	0.866025i	0.500000	−	0.866025i
$905$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$906$	1.00000			1.00000
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$909$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$910$		0			0
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$912$	−1.00000			−1.00000
$913$		0			0
$914$	−1.00000			−1.00000
$915$	0.500000	−	0.866025i	0.500000	−	0.866025i
$916$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$917$		0			0
$918$		0			0
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$920$	0.500000	−	0.866025i	0.500000	−	0.866025i
$921$	0.500000	+	0.866025i	0.500000	+	0.866025i
$922$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$923$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$924$		0			0
$925$		0			0
$926$	0.500000	−	0.866025i	0.500000	−	0.866025i
$927$		0			0
$928$		0			0
$929$		0			0		1.00000			$0$
$929$		0			0		−1.00000			$\pi$
$930$		0			0
$931$		0			0
$932$	0.500000	−	0.866025i	0.500000	−	0.866025i
$933$		0			0
$934$	1.00000	−	1.73205i	1.00000	−	1.73205i
$935$		0			0
$936$	1.00000	+	1.73205i	1.00000	+	1.73205i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$941$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$942$	0.500000	+	0.866025i	0.500000	+	0.866025i
$943$		0			0
$944$	−2.00000			−2.00000
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.00000			2.00000			1.00000			$0$
$953$	2.00000			2.00000			1.00000			$0$
$954$		0			0
$955$	0.500000	+	0.866025i	0.500000	+	0.866025i
$956$	0.500000	−	0.866025i	0.500000	−	0.866025i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.500000	−	0.866025i	0.500000	−	0.866025i
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.500000	+	0.866025i	0.500000	+	0.866025i
$966$		0			0
$967$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$967$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$971$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$972$	0.500000	−	0.866025i	0.500000	−	0.866025i
$973$		0			0
$974$	0.500000	+	0.866025i	0.500000	+	0.866025i
$975$		0			0
$976$	1.00000			1.00000
$977$	2.00000			2.00000			1.00000			$0$
$977$	2.00000			2.00000			1.00000			$0$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.00000	+	1.73205i	1.00000	+	1.73205i
$989$		0			0
$990$		0			0
$991$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3528.1.bp.b.3253.1		2
7.2	even	3		504.1.bn.a.13.1	✓	2
7.3	odd	6		3528.1.cw.a.2677.1		2
7.4	even	3		3528.1.cw.b.2677.1		2
7.5	odd	6		504.1.bn.b.13.1	yes	2
7.6	odd	2		3528.1.bp.a.3253.1		2
8.5	even	2		3528.1.bp.a.3253.1		2
9.7	even	3		3528.1.cw.b.2077.1		2
21.2	odd	6		1512.1.bn.b.685.1		2
21.5	even	6		1512.1.bn.a.685.1		2
28.19	even	6		2016.1.bv.a.1777.1		2
28.23	odd	6		2016.1.bv.b.1777.1		2
56.5	odd	6		504.1.bn.a.13.1	✓	2
56.13	odd	2	CM	3528.1.bp.b.3253.1		2
56.19	even	6		2016.1.bv.b.1777.1		2
56.37	even	6		504.1.bn.b.13.1	yes	2
56.45	odd	6		3528.1.cw.b.2677.1		2
56.51	odd	6		2016.1.bv.a.1777.1		2
56.53	even	6		3528.1.cw.a.2677.1		2
63.2	odd	6		1512.1.bn.b.181.1		2
63.16	even	3		504.1.bn.a.349.1	yes	2
63.25	even	3	inner	3528.1.bp.b.1501.1		2
63.34	odd	6		3528.1.cw.a.2077.1		2
63.47	even	6		1512.1.bn.a.181.1		2
63.52	odd	6		3528.1.bp.a.1501.1		2
63.61	odd	6		504.1.bn.b.349.1	yes	2
72.61	even	6		3528.1.cw.a.2077.1		2
168.5	even	6		1512.1.bn.b.685.1		2
168.149	odd	6		1512.1.bn.a.685.1		2
252.79	odd	6		2016.1.bv.b.1105.1		2
252.187	even	6		2016.1.bv.a.1105.1		2
504.61	odd	6		504.1.bn.a.349.1	yes	2
504.173	even	6		1512.1.bn.b.181.1		2
504.187	even	6		2016.1.bv.b.1105.1		2
504.205	even	6		504.1.bn.b.349.1	yes	2
504.277	even	6		3528.1.bp.a.1501.1		2
504.317	odd	6		1512.1.bn.a.181.1		2
504.331	odd	6		2016.1.bv.a.1105.1		2
504.349	odd	6		3528.1.cw.b.2077.1		2
504.493	odd	6	inner	3528.1.bp.b.1501.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.1.bn.a.13.1	✓	2	7.2	even	3
504.1.bn.a.13.1	✓	2	56.5	odd	6
504.1.bn.a.349.1	yes	2	63.16	even	3
504.1.bn.a.349.1	yes	2	504.61	odd	6
504.1.bn.b.13.1	yes	2	7.5	odd	6
504.1.bn.b.13.1	yes	2	56.37	even	6
504.1.bn.b.349.1	yes	2	63.61	odd	6
504.1.bn.b.349.1	yes	2	504.205	even	6
1512.1.bn.a.181.1		2	63.47	even	6
1512.1.bn.a.181.1		2	504.317	odd	6
1512.1.bn.a.685.1		2	21.5	even	6
1512.1.bn.a.685.1		2	168.149	odd	6
1512.1.bn.b.181.1		2	63.2	odd	6
1512.1.bn.b.181.1		2	504.173	even	6
1512.1.bn.b.685.1		2	21.2	odd	6
1512.1.bn.b.685.1		2	168.5	even	6
2016.1.bv.a.1105.1		2	252.187	even	6
2016.1.bv.a.1105.1		2	504.331	odd	6
2016.1.bv.a.1777.1		2	28.19	even	6
2016.1.bv.a.1777.1		2	56.51	odd	6
2016.1.bv.b.1105.1		2	252.79	odd	6
2016.1.bv.b.1105.1		2	504.187	even	6
2016.1.bv.b.1777.1		2	28.23	odd	6
2016.1.bv.b.1777.1		2	56.19	even	6
3528.1.bp.a.1501.1		2	63.52	odd	6
3528.1.bp.a.1501.1		2	504.277	even	6
3528.1.bp.a.3253.1		2	7.6	odd	2
3528.1.bp.a.3253.1		2	8.5	even	2
3528.1.bp.b.1501.1		2	63.25	even	3	inner
3528.1.bp.b.1501.1		2	504.493	odd	6	inner
3528.1.bp.b.3253.1		2	1.1	even	1	trivial
3528.1.bp.b.3253.1		2	56.13	odd	2	CM
3528.1.cw.a.2077.1		2	63.34	odd	6
3528.1.cw.a.2077.1		2	72.61	even	6
3528.1.cw.a.2677.1		2	7.3	odd	6
3528.1.cw.a.2677.1		2	56.53	even	6
3528.1.cw.b.2077.1		2	9.7	even	3
3528.1.cw.b.2077.1		2	504.349	odd	6
3528.1.cw.b.2677.1		2	7.4	even	3
3528.1.cw.b.2677.1		2	56.45	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:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3528.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +1.00000 q^{32} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 + 0.866025i) q^{38} +2.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +1.00000 q^{45} +(0.500000 + 0.866025i) q^{46} +(0.500000 + 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{52} -1.00000 q^{54} -1.00000 q^{57} -2.00000 q^{59} +(0.500000 - 0.866025i) q^{60} +1.00000 q^{61} +1.00000 q^{64} -2.00000 q^{65} +(-0.500000 + 0.866025i) q^{69} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.500000 + 0.866025i) q^{76} +2.00000 q^{78} -1.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{83} +1.00000 q^{90} +(0.500000 + 0.866025i) q^{92} +1.00000 q^{95} +(0.500000 + 0.866025i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{12} + 2 q^{13} + q^{15} + 2 q^{16} - q^{18} - q^{19} - q^{20} + q^{23} + q^{24} + 2 q^{26} - 2 q^{27} + q^{30} + 2 q^{32} - q^{36} - q^{38} + 4 q^{39} - q^{40} + 2 q^{45} + q^{46} + q^{48} + 2 q^{52} - 2 q^{54} - 2 q^{57} - 4 q^{59} + q^{60} + 2 q^{61} + 2 q^{64} - 4 q^{65} - q^{69} - 2 q^{71} - q^{72} - q^{76} + 4 q^{78} - 2 q^{79} - q^{80} - q^{81} + 2 q^{83} + 2 q^{90} + q^{92} + 2 q^{95} + q^{96}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - q^9 - q^10 + q^12 + 2 * q^13 + q^15 + 2 * q^16 - q^18 - q^19 - q^20 + q^23 + q^24 + 2 * q^26 - 2 * q^27 + q^30 + 2 * q^32 - q^36 - q^38 + 4 * q^39 - q^40 + 2 * q^45 + q^46 + q^48 + 2 * q^52 - 2 * q^54 - 2 * q^57 - 4 * q^59 + q^60 + 2 * q^61 + 2 * q^64 - 4 * q^65 - q^69 - 2 * q^71 - q^72 - q^76 + 4 * q^78 - 2 * q^79 - q^80 - q^81 + 2 * q^83 + 2 * q^90 + q^92 + 2 * q^95 + q^96

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