LMFDB - Embedded newform 3528.1.ba.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3528,1,Mod(67,3528)]

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([3, 3, 2, 4]))

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

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

chi := DirichletCharacter("3528.67");

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.ba (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 72)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.648.1
Artin image:	$C_3^2\times D_6$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{36} - \cdots)$

Embedding invariants

Embedding label			67.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3528.67
Dual form			3528.1.ba.a.1843.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{22} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{32} +1.00000 q^{33} +(-0.500000 - 0.866025i) q^{34} +(-0.500000 - 0.866025i) q^{36} +1.00000 q^{38} +(-0.500000 + 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{57} +(-0.500000 - 0.866025i) q^{59} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(0.500000 + 0.866025i) q^{67} +1.00000 q^{68} +1.00000 q^{72} +(-0.500000 + 0.866025i) q^{73} -1.00000 q^{75} +(-0.500000 + 0.866025i) q^{76} +1.00000 q^{81} +(-0.500000 - 0.866025i) q^{82} +(1.00000 + 1.73205i) q^{83} -1.00000 q^{86} -1.00000 q^{88} +(1.00000 + 1.73205i) q^{89} +(0.500000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{11} + q^{12} - q^{16} - q^{17} - q^{18} - q^{19} + q^{22} - 2 q^{24} + 2 q^{25} - 2 q^{27} - q^{32} + 2 q^{33} - q^{34} - q^{36} + 2 q^{38} - q^{41} + q^{43} + q^{44} + q^{48} - q^{50} + q^{51} + q^{54} + q^{57} - q^{59} + 2 q^{64} - q^{66} + q^{67} + 2 q^{68} + 2 q^{72} - q^{73} - 2 q^{75} - q^{76} + 2 q^{81} - q^{82} + 2 q^{83} - 2 q^{86} - 2 q^{88} + 2 q^{89} + q^{96} - q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 + 2 * q^8 + 2 * q^9 - 2 * q^11 + q^12 - q^16 - q^17 - q^18 - q^19 + q^22 - 2 * q^24 + 2 * q^25 - 2 * q^27 - q^32 + 2 * q^33 - q^34 - q^36 + 2 * q^38 - q^41 + q^43 + q^44 + q^48 - q^50 + q^51 + q^54 + q^57 - q^59 + 2 * q^64 - q^66 + q^67 + 2 * q^68 + 2 * q^72 - q^73 - 2 * q^75 - q^76 + 2 * q^81 - q^82 + 2 * q^83 - 2 * q^86 - 2 * q^88 + 2 * q^89 + q^96 - q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$	$1765$	$2647$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$3$	−1.00000			−1.00000
$3$	−1.00000			−1.00000
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$		0			0		1.00000			$0$
$5$		0			0		−1.00000			$\pi$
$6$	0.500000	−	0.866025i	0.500000	−	0.866025i
$7$		0			0
$7$		0			0
$8$	1.00000			1.00000
$9$	1.00000			1.00000
$10$		0			0
$11$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$11$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$18$	−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			0
$21$		0			0
$22$	0.500000	−	0.866025i	0.500000	−	0.866025i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.00000			−1.00000
$25$	1.00000			1.00000
$26$		0			0
$27$	−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			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$33$	1.00000			1.00000
$34$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$41$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$43$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$44$	0.500000	+	0.866025i	0.500000	+	0.866025i
$45$		0			0
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.500000	−	0.866025i	0.500000	−	0.866025i
$49$		0			0
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$	0.500000	−	0.866025i	0.500000	−	0.866025i
$52$		0			0
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$		0			0
$56$		0			0
$57$	0.500000	+	0.866025i	0.500000	+	0.866025i
$58$		0			0
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			1.00000
$65$		0			0
$66$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$68$	1.00000			1.00000
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	1.00000			1.00000
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$74$		0			0
$75$	−1.00000			−1.00000
$76$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$77$		0			0
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	1.00000			1.00000
$82$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$83$	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
$86$	−1.00000			−1.00000
$87$		0			0
$88$	−1.00000			−1.00000
$89$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$89$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.500000	+	0.866025i	0.500000	+	0.866025i
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$98$		0			0
$99$	−1.00000			−1.00000
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	0.500000	+	0.866025i	0.500000	+	0.866025i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$107$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.500000	+	0.866025i	0.500000	+	0.866025i
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$113$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$114$	−1.00000			−1.00000
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.00000			1.00000
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$	0.500000	−	0.866025i	0.500000	−	0.866025i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$130$		0			0
$131$	−2.00000			−2.00000			−1.00000			$\pi$
$131$	−2.00000			−2.00000			−1.00000			$\pi$
$132$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$133$		0			0
$134$	−1.00000			−1.00000
$135$		0			0
$136$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$137$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$137$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	−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
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$147$		0			0
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	0.500000	−	0.866025i	0.500000	−	0.866025i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$153$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$163$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$163$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$164$	1.00000			1.00000
$165$		0			0
$166$	−2.00000			−2.00000
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$172$	0.500000	−	0.866025i	0.500000	−	0.866025i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	−	0.866025i	0.500000	−	0.866025i
$177$	0.500000	+	0.866025i	0.500000	+	0.866025i
$178$	−2.00000			−2.00000
$179$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$179$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.500000	−	0.866025i	0.500000	−	0.866025i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−1.00000			−1.00000
$193$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$193$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$194$	1.00000			1.00000
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.500000	−	0.866025i	0.500000	−	0.866025i
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	1.00000			1.00000
$201$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$202$		0			0
$203$		0			0
$204$	−1.00000			−1.00000
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.500000	+	0.866025i	0.500000	+	0.866025i
$210$		0			0
$211$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$211$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$		0			0
$214$	−1.00000			−1.00000
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$		0			0
$219$	0.500000	−	0.866025i	0.500000	−	0.866025i
$220$		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
$225$	1.00000			1.00000
$226$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$227$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$227$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$233$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$		0			0
$236$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$		0			0
$241$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$241$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$242$		0			0
$243$	−1.00000			−1.00000
$244$		0			0
$245$		0			0
$246$	0.500000	+	0.866025i	0.500000	+	0.866025i
$247$		0			0
$248$		0			0
$249$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$250$		0			0
$251$	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
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$258$	1.00000			1.00000
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.00000	−	1.73205i	1.00000	−	1.73205i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	1.00000			1.00000
$265$		0			0
$266$		0			0
$267$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$268$	0.500000	−	0.866025i	0.500000	−	0.866025i
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$273$		0			0
$274$	0.500000	−	0.866025i	0.500000	−	0.866025i
$275$	−1.00000			−1.00000
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$279$		0			0
$280$		0			0
$281$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$282$		0			0
$283$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$283$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$289$		0			0
$290$		0			0
$291$	0.500000	+	0.866025i	0.500000	+	0.866025i
$292$	1.00000			1.00000
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.00000			1.00000
$298$		0			0
$299$		0			0
$300$	0.500000	+	0.866025i	0.500000	+	0.866025i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.00000			1.00000
$305$		0			0
$306$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$307$	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		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		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
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$322$		0			0
$323$	1.00000			1.00000
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$		0			0
$326$	2.00000			2.00000
$327$		0			0
$328$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$329$		0			0
$330$		0			0
$331$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$331$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$332$	1.00000	−	1.73205i	1.00000	−	1.73205i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$338$	1.00000			1.00000
$339$	1.00000	−	1.73205i	1.00000	−	1.73205i
$340$		0			0
$341$		0			0
$342$	1.00000			1.00000
$343$		0			0
$344$	0.500000	+	0.866025i	0.500000	+	0.866025i
$345$		0			0
$346$		0			0
$347$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$347$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	+	0.866025i	0.500000	+	0.866025i
$353$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$353$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$354$	−1.00000			−1.00000
$355$		0			0
$356$	1.00000	−	1.73205i	1.00000	−	1.73205i
$357$		0			0
$358$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	0.500000	+	0.866025i	0.500000	+	0.866025i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$379$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$	0.500000	−	0.866025i	0.500000	−	0.866025i
$385$		0			0
$386$	−1.00000			−1.00000
$387$	0.500000	+	0.866025i	0.500000	+	0.866025i
$388$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	2.00000			2.00000
$394$		0			0
$395$		0			0
$396$	0.500000	+	0.866025i	0.500000	+	0.866025i
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$402$	1.00000			1.00000
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.500000	−	0.866025i	0.500000	−	0.866025i
$409$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$409$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$410$		0			0
$411$	1.00000			1.00000
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.500000	−	0.866025i	0.500000	−	0.866025i
$418$	−1.00000			−1.00000
$419$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$419$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$420$		0			0
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$423$		0			0
$424$		0			0
$425$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$426$		0			0
$427$		0			0
$428$	0.500000	−	0.866025i	0.500000	−	0.866025i
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$433$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.500000	+	0.866025i	0.500000	+	0.866025i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		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	$0.666667\pi$
$450$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$451$	0.500000	−	0.866025i	0.500000	−	0.866025i
$452$	2.00000			2.00000
$453$		0			0
$454$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$455$		0			0
$456$	0.500000	+	0.866025i	0.500000	+	0.866025i
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$458$		0			0
$459$	0.500000	−	0.866025i	0.500000	−	0.866025i
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$	−1.00000			−1.00000
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$473$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$474$		0			0
$475$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$483$		0			0
$484$		0			0
$485$		0			0
$486$	0.500000	−	0.866025i	0.500000	−	0.866025i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$	1.00000	+	1.73205i	1.00000	+	1.73205i
$490$		0			0
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$492$	−1.00000			−1.00000
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.00000			2.00000
$499$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.500000	+	0.866025i	0.500000	+	0.866025i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$	0.500000	+	0.866025i	0.500000	+	0.866025i
$514$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$515$		0			0
$516$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$522$		0			0
$523$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$523$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$524$	1.00000	+	1.73205i	1.00000	+	1.73205i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$529$	1.00000			1.00000
$530$		0			0
$531$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$532$		0			0
$533$		0			0
$534$	2.00000			2.00000
$535$		0			0
$536$	0.500000	+	0.866025i	0.500000	+	0.866025i
$537$	1.00000	−	1.73205i	1.00000	−	1.73205i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$		0			0
$543$		0			0
$544$	1.00000			1.00000
$545$		0			0
$546$		0			0
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$548$	0.500000	+	0.866025i	0.500000	+	0.866025i
$549$		0			0
$550$	0.500000	−	0.866025i	0.500000	−	0.866025i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.00000			1.00000
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$562$	2.00000			2.00000
$563$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$563$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	−2.00000			−2.00000
$567$		0			0
$568$		0			0
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$570$		0			0
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.00000			1.00000
$577$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$577$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$578$		0			0
$579$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$580$		0			0
$581$		0			0
$582$	−1.00000			−1.00000
$583$		0			0
$584$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$585$		0			0
$586$		0			0
$587$	−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
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$593$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$594$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	−1.00000			−1.00000
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$602$		0			0
$603$	0.500000	+	0.866025i	0.500000	+	0.866025i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.00000			1.00000
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$615$		0			0
$616$		0			0
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$618$		0			0
$619$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$619$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.00000			1.00000
$626$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$627$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	1.00000	−	1.73205i	1.00000	−	1.73205i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$642$	1.00000			1.00000
$643$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$643$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$647$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$647$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$648$	1.00000			1.00000
$649$	0.500000	+	0.866025i	0.500000	+	0.866025i
$650$		0			0
$651$		0			0
$652$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$657$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$658$		0			0
$659$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$659$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$663$		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
$673$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$674$	0.500000	+	0.866025i	0.500000	+	0.866025i
$675$	−1.00000			−1.00000
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	1.00000	+	1.73205i	1.00000	+	1.73205i
$679$		0			0
$680$		0			0
$681$	−1.00000			−1.00000
$682$		0			0
$683$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$684$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.00000			−1.00000
$689$		0			0
$690$		0			0
$691$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$691$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$692$		0			0
$693$		0			0
$694$	−1.00000			−1.00000
$695$		0			0
$696$		0			0
$697$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$698$		0			0
$699$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	−1.00000			−1.00000
$705$		0			0
$706$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$707$		0			0
$708$	0.500000	−	0.866025i	0.500000	−	0.866025i
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	1.00000	+	1.73205i	1.00000	+	1.73205i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.00000			2.00000
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.00000			−1.00000
$724$		0			0
$725$		0			0
$726$		0			0
$727$		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
$731$	−1.00000			−1.00000
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$738$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$743$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.00000	+	1.73205i	1.00000	+	1.73205i
$748$	−1.00000			−1.00000
$749$		0			0
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	−1.00000			−1.00000
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	0.500000	−	0.866025i	0.500000	−	0.866025i
$759$		0			0
$760$		0			0
$761$	−2.00000			−2.00000			−1.00000			$\pi$
$761$	−2.00000			−2.00000			−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.500000	+	0.866025i	0.500000	+	0.866025i
$769$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$	0.500000	−	0.866025i	0.500000	−	0.866025i
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	−1.00000			−1.00000
$775$		0			0
$776$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$777$		0			0
$778$		0			0
$779$	1.00000			1.00000
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$787$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$787$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.00000			−1.00000
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$797$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$801$	1.00000	+	1.73205i	1.00000	+	1.73205i
$802$	0.500000	−	0.866025i	0.500000	−	0.866025i
$803$	0.500000	−	0.866025i	0.500000	−	0.866025i
$804$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$810$		0			0
$811$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$811$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.500000	+	0.866025i	0.500000	+	0.866025i
$817$	0.500000	−	0.866025i	0.500000	−	0.866025i
$818$	1.00000			1.00000
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	1.00000			1.00000
$826$		0			0
$827$	2.00000			2.00000			1.00000			$0$
$827$	2.00000			2.00000			1.00000			$0$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$	0.500000	+	0.866025i	0.500000	+	0.866025i
$835$		0			0
$836$	0.500000	−	0.866025i	0.500000	−	0.866025i
$837$		0			0
$838$	1.00000	+	1.73205i	1.00000	+	1.73205i
$839$		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
$843$	1.00000	+	1.73205i	1.00000	+	1.73205i
$844$	2.00000			2.00000
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$850$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$		0			0
$855$		0			0
$856$	0.500000	+	0.866025i	0.500000	+	0.866025i
$857$	−2.00000			−2.00000			−1.00000			$\pi$
$857$	−2.00000			−2.00000			−1.00000			$\pi$
$858$		0			0
$859$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$859$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.500000	+	0.866025i	0.500000	+	0.866025i
$865$		0			0
$866$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$874$		0			0
$875$		0			0
$876$	−1.00000			−1.00000
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.00000			−2.00000			−1.00000			$\pi$
$881$	−2.00000			−2.00000			−1.00000			$\pi$
$882$		0			0
$883$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$	0.500000	+	0.866025i	0.500000	+	0.866025i
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.00000			−1.00000
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.500000	−	0.866025i	0.500000	−	0.866025i
$899$		0			0
$900$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$901$		0			0
$902$	0.500000	+	0.866025i	0.500000	+	0.866025i
$903$		0			0
$904$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$905$		0			0
$906$		0			0
$907$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$907$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$908$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$909$		0			0
$910$		0			0
$911$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$911$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$912$	−1.00000			−1.00000
$913$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$914$	0.500000	+	0.866025i	0.500000	+	0.866025i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.500000	+	0.866025i	0.500000	+	0.866025i
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	−1.00000			−1.00000
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$930$		0			0
$931$		0			0
$932$	0.500000	−	0.866025i	0.500000	−	0.866025i
$933$		0			0
$934$	1.00000			1.00000
$935$		0			0
$936$		0			0
$937$	−2.00000			−2.00000			−1.00000			$\pi$
$937$	−2.00000			−2.00000			−1.00000			$\pi$
$938$		0			0
$939$	0.500000	−	0.866025i	0.500000	−	0.866025i
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$		0			0
$943$		0			0
$944$	1.00000			1.00000
$945$		0			0
$946$	1.00000			1.00000
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$	1.00000			1.00000
$951$		0			0
$952$		0			0
$953$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$	0.500000	+	0.866025i	0.500000	+	0.866025i
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$		0			0
$966$		0			0
$967$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$967$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$	−1.00000			−1.00000
$970$		0			0
$971$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$971$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$972$	0.500000	+	0.866025i	0.500000	+	0.866025i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$977$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$978$	−2.00000			−2.00000
$979$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$980$		0			0
$981$		0			0
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	0.500000	−	0.866025i	0.500000	−	0.866025i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$	1.00000	−	1.73205i	1.00000	−	1.73205i
$994$		0			0
$995$		0			0
$996$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$	0.500000	−	0.866025i	0.500000	−	0.866025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3528.1.ba.a.67.1		2
7.2	even	3		3528.1.ce.b.3019.1		2
7.3	odd	6		72.1.p.a.67.1	yes	2
7.4	even	3		3528.1.cg.a.3235.1		2
7.5	odd	6		3528.1.ce.a.3019.1		2
7.6	odd	2		3528.1.ba.b.67.1		2
8.3	odd	2	CM	3528.1.ba.a.67.1		2
9.7	even	3		3528.1.ce.b.2419.1		2
21.17	even	6		216.1.p.a.91.1		2
28.3	even	6		288.1.t.a.175.1		2
35.3	even	12		1800.1.ba.b.499.1		4
35.17	even	12		1800.1.ba.b.499.2		4
35.24	odd	6		1800.1.bk.d.1651.1		2
56.3	even	6		72.1.p.a.67.1	yes	2
56.11	odd	6		3528.1.cg.a.3235.1		2
56.19	even	6		3528.1.ce.a.3019.1		2
56.27	even	2		3528.1.ba.b.67.1		2
56.45	odd	6		288.1.t.a.175.1		2
56.51	odd	6		3528.1.ce.b.3019.1		2
63.16	even	3	inner	3528.1.ba.a.1843.1		2
63.25	even	3		3528.1.cg.a.2059.1		2
63.31	odd	6		648.1.b.b.163.1		1
63.34	odd	6		3528.1.ce.a.2419.1		2
63.38	even	6		216.1.p.a.19.1		2
63.52	odd	6		72.1.p.a.43.1	✓	2
63.59	even	6		648.1.b.a.163.1		1
63.61	odd	6		3528.1.ba.b.1843.1		2
72.43	odd	6		3528.1.ce.b.2419.1		2
84.59	odd	6		864.1.t.a.847.1		2
112.3	even	12		2304.1.o.c.2047.1		4
112.45	odd	12		2304.1.o.c.2047.2		4
112.59	even	12		2304.1.o.c.2047.2		4
112.101	odd	12		2304.1.o.c.2047.1		4
168.59	odd	6		216.1.p.a.91.1		2
168.101	even	6		864.1.t.a.847.1		2
252.31	even	6		2592.1.b.b.1135.1		1
252.59	odd	6		2592.1.b.a.1135.1		1
252.115	even	6		288.1.t.a.79.1		2
252.227	odd	6		864.1.t.a.559.1		2
280.3	odd	12		1800.1.ba.b.499.1		4
280.59	even	6		1800.1.bk.d.1651.1		2
280.227	odd	12		1800.1.ba.b.499.2		4
315.52	even	12		1800.1.ba.b.1699.1		4
315.178	even	12		1800.1.ba.b.1699.2		4
315.304	odd	6		1800.1.bk.d.1051.1		2
504.59	odd	6		648.1.b.a.163.1		1
504.101	even	6		864.1.t.a.559.1		2
504.115	even	6		72.1.p.a.43.1	✓	2
504.157	odd	6		2592.1.b.b.1135.1		1
504.187	even	6		3528.1.ba.b.1843.1		2
504.227	odd	6		216.1.p.a.19.1		2
504.283	even	6		648.1.b.b.163.1		1
504.331	odd	6	inner	3528.1.ba.a.1843.1		2
504.403	odd	6		3528.1.cg.a.2059.1		2
504.437	even	6		2592.1.b.a.1135.1		1
504.475	even	6		3528.1.ce.a.2419.1		2
504.493	odd	6		288.1.t.a.79.1		2
1008.115	even	12		2304.1.o.c.511.2		4
1008.493	odd	12		2304.1.o.c.511.1		4
1008.619	even	12		2304.1.o.c.511.1		4
1008.997	odd	12		2304.1.o.c.511.2		4
2520.619	even	6		1800.1.bk.d.1051.1		2
2520.1123	odd	12		1800.1.ba.b.1699.2		4
2520.1627	odd	12		1800.1.ba.b.1699.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.1.p.a.43.1	✓	2	63.52	odd	6
72.1.p.a.43.1	✓	2	504.115	even	6
72.1.p.a.67.1	yes	2	7.3	odd	6
72.1.p.a.67.1	yes	2	56.3	even	6
216.1.p.a.19.1		2	63.38	even	6
216.1.p.a.19.1		2	504.227	odd	6
216.1.p.a.91.1		2	21.17	even	6
216.1.p.a.91.1		2	168.59	odd	6
288.1.t.a.79.1		2	252.115	even	6
288.1.t.a.79.1		2	504.493	odd	6
288.1.t.a.175.1		2	28.3	even	6
288.1.t.a.175.1		2	56.45	odd	6
648.1.b.a.163.1		1	63.59	even	6
648.1.b.a.163.1		1	504.59	odd	6
648.1.b.b.163.1		1	63.31	odd	6
648.1.b.b.163.1		1	504.283	even	6
864.1.t.a.559.1		2	252.227	odd	6
864.1.t.a.559.1		2	504.101	even	6
864.1.t.a.847.1		2	84.59	odd	6
864.1.t.a.847.1		2	168.101	even	6
1800.1.ba.b.499.1		4	35.3	even	12
1800.1.ba.b.499.1		4	280.3	odd	12
1800.1.ba.b.499.2		4	35.17	even	12
1800.1.ba.b.499.2		4	280.227	odd	12
1800.1.ba.b.1699.1		4	315.52	even	12
1800.1.ba.b.1699.1		4	2520.1627	odd	12
1800.1.ba.b.1699.2		4	315.178	even	12
1800.1.ba.b.1699.2		4	2520.1123	odd	12
1800.1.bk.d.1051.1		2	315.304	odd	6
1800.1.bk.d.1051.1		2	2520.619	even	6
1800.1.bk.d.1651.1		2	35.24	odd	6
1800.1.bk.d.1651.1		2	280.59	even	6
2304.1.o.c.511.1		4	1008.493	odd	12
2304.1.o.c.511.1		4	1008.619	even	12
2304.1.o.c.511.2		4	1008.115	even	12
2304.1.o.c.511.2		4	1008.997	odd	12
2304.1.o.c.2047.1		4	112.3	even	12
2304.1.o.c.2047.1		4	112.101	odd	12
2304.1.o.c.2047.2		4	112.45	odd	12
2304.1.o.c.2047.2		4	112.59	even	12
2592.1.b.a.1135.1		1	252.59	odd	6
2592.1.b.a.1135.1		1	504.437	even	6
2592.1.b.b.1135.1		1	252.31	even	6
2592.1.b.b.1135.1		1	504.157	odd	6
3528.1.ba.a.67.1		2	1.1	even	1	trivial
3528.1.ba.a.67.1		2	8.3	odd	2	CM
3528.1.ba.a.1843.1		2	63.16	even	3	inner
3528.1.ba.a.1843.1		2	504.331	odd	6	inner
3528.1.ba.b.67.1		2	7.6	odd	2
3528.1.ba.b.67.1		2	56.27	even	2
3528.1.ba.b.1843.1		2	63.61	odd	6
3528.1.ba.b.1843.1		2	504.187	even	6
3528.1.ce.a.2419.1		2	63.34	odd	6
3528.1.ce.a.2419.1		2	504.475	even	6
3528.1.ce.a.3019.1		2	7.5	odd	6
3528.1.ce.a.3019.1		2	56.19	even	6
3528.1.ce.b.2419.1		2	9.7	even	3
3528.1.ce.b.2419.1		2	72.43	odd	6
3528.1.ce.b.3019.1		2	7.2	even	3
3528.1.ce.b.3019.1		2	56.51	odd	6
3528.1.cg.a.2059.1		2	63.25	even	3
3528.1.cg.a.2059.1		2	504.403	odd	6
3528.1.cg.a.3235.1		2	7.4	even	3
3528.1.cg.a.3235.1		2	56.11	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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{22} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{32} +1.00000 q^{33} +(-0.500000 - 0.866025i) q^{34} +(-0.500000 - 0.866025i) q^{36} +1.00000 q^{38} +(-0.500000 + 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{57} +(-0.500000 - 0.866025i) q^{59} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(0.500000 + 0.866025i) q^{67} +1.00000 q^{68} +1.00000 q^{72} +(-0.500000 + 0.866025i) q^{73} -1.00000 q^{75} +(-0.500000 + 0.866025i) q^{76} +1.00000 q^{81} +(-0.500000 - 0.866025i) q^{82} +(1.00000 + 1.73205i) q^{83} -1.00000 q^{86} -1.00000 q^{88} +(1.00000 + 1.73205i) q^{89} +(0.500000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{11} + q^{12} - q^{16} - q^{17} - q^{18} - q^{19} + q^{22} - 2 q^{24} + 2 q^{25} - 2 q^{27} - q^{32} + 2 q^{33} - q^{34} - q^{36} + 2 q^{38} - q^{41} + q^{43} + q^{44} + q^{48} - q^{50} + q^{51} + q^{54} + q^{57} - q^{59} + 2 q^{64} - q^{66} + q^{67} + 2 q^{68} + 2 q^{72} - q^{73} - 2 q^{75} - q^{76} + 2 q^{81} - q^{82} + 2 q^{83} - 2 q^{86} - 2 q^{88} + 2 q^{89} + q^{96} - q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 + 2 * q^8 + 2 * q^9 - 2 * q^11 + q^12 - q^16 - q^17 - q^18 - q^19 + q^22 - 2 * q^24 + 2 * q^25 - 2 * q^27 - q^32 + 2 * q^33 - q^34 - q^36 + 2 * q^38 - q^41 + q^43 + q^44 + q^48 - q^50 + q^51 + q^54 + q^57 - q^59 + 2 * q^64 - q^66 + q^67 + 2 * q^68 + 2 * q^72 - q^73 - 2 * q^75 - q^76 + 2 * q^81 - q^82 + 2 * q^83 - 2 * q^86 - 2 * q^88 + 2 * q^89 + q^96 - q^97 - 2 * q^99

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