LMFDB - Embedded newform 3528.1.ce.a.3019.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3528,1,Mod(2419,3528)]

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, 4, 4]))

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

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

chi := DirichletCharacter("3528.2419");

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.ce (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 72)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.648.1
Artin image:	$C_3\times S_3$
Artin field:	Galois closure of 6.0.99574272.2

Embedding invariants

Embedding label			3019.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3528.3019
Dual form			3528.1.ce.a.2419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +1.00000 q^{32} +(0.500000 + 0.866025i) q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{41} +(0.500000 + 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{50} -1.00000 q^{51} +1.00000 q^{54} +(0.500000 + 0.866025i) q^{57} -1.00000 q^{59} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} -1.00000 q^{67} +(0.500000 + 0.866025i) q^{68} +(-0.500000 - 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-0.500000 + 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(0.500000 + 0.866025i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(-0.500000 + 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{6} + 2 q^{8} - q^{9} + q^{11} - q^{12} + 2 q^{16} + q^{17} - q^{18} + q^{19} + q^{22} - q^{24} - q^{25} + 2 q^{27} + 2 q^{32} + q^{33} + q^{34} - q^{36} + q^{38} + q^{41} + q^{43} + q^{44} - q^{48} - q^{50} - 2 q^{51} + 2 q^{54} + q^{57} - 2 q^{59} + 2 q^{64} + q^{66} - 2 q^{67} + q^{68} - q^{72} + q^{73} - q^{75} + q^{76} - q^{81} + q^{82} - 2 q^{83} + q^{86} + q^{88} - 2 q^{89} - q^{96} + q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^6 + 2 * q^8 - q^9 + q^11 - q^12 + 2 * q^16 + q^17 - q^18 + q^19 + q^22 - q^24 - q^25 + 2 * q^27 + 2 * q^32 + q^33 + q^34 - q^36 + q^38 + q^41 + q^43 + q^44 - q^48 - q^50 - 2 * q^51 + 2 * q^54 + q^57 - 2 * q^59 + 2 * q^64 + q^66 - 2 * q^67 + q^68 - q^72 + q^73 - q^75 + q^76 - q^81 + q^82 - 2 * q^83 + q^86 + 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 $\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times$.

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

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 $

$2$	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			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	−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			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$12$	−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
$16$	1.00000			1.00000
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$20$		0			0
$21$		0			0
$22$	0.500000	−	0.866025i	0.500000	−	0.866025i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		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		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.00000			1.00000
$33$	0.500000	+	0.866025i	0.500000	+	0.866025i
$34$	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	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	0.500000	−	0.866025i	0.500000	−	0.866025i
$39$		0			0
$40$		0			0
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$42$		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		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$49$		0			0
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$	−1.00000			−1.00000
$52$		0			0
$53$		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
$57$	0.500000	+	0.866025i	0.500000	+	0.866025i
$58$		0			0
$59$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$59$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			1.00000
$65$		0			0
$66$	0.500000	+	0.866025i	0.500000	+	0.866025i
$67$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$68$	0.500000	+	0.866025i	0.500000	+	0.866025i
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$76$	0.500000	−	0.866025i	0.500000	−	0.866025i
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$	0.500000	−	0.866025i	0.500000	−	0.866025i
$83$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$		0			0
$88$	0.500000	−	0.866025i	0.500000	−	0.866025i
$89$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$89$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$90$		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	1.00000			$0$
$97$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$98$		0			0
$99$	−1.00000			−1.00000
$100$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$	−1.00000			−1.00000
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$108$	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
$113$	−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	$0.666667\pi$
$114$	0.500000	+	0.866025i	0.500000	+	0.866025i
$115$		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			$\pi$
$128$	1.00000			1.00000
$129$	−1.00000			−1.00000
$130$		0			0
$131$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$132$	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
$137$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$138$		0			0
$139$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$139$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$140$		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		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	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		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		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	$0.666667\pi$
$164$	0.500000	−	0.866025i	0.500000	−	0.866025i
$165$		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
$169$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$170$		0			0
$171$	−1.00000			−1.00000
$172$	0.500000	+	0.866025i	0.500000	+	0.866025i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	−	0.866025i	0.500000	−	0.866025i
$177$	0.500000	−	0.866025i	0.500000	−	0.866025i
$178$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$179$	−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
$187$	1.00000			1.00000
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−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	$0.666667\pi$
$194$	0.500000	+	0.866025i	0.500000	+	0.866025i
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−1.00000			−1.00000
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$201$	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
$214$	0.500000	−	0.866025i	0.500000	−	0.866025i
$215$		0			0
$216$	1.00000			1.00000
$217$		0			0
$218$		0			0
$219$	−1.00000			−1.00000
$220$		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
$227$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$227$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$228$	0.500000	+	0.866025i	0.500000	+	0.866025i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		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			$0$
$234$		0			0
$235$		0			0
$236$	−1.00000			−1.00000
$237$		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
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$	0.500000	+	0.866025i	0.500000	+	0.866025i
$247$		0			0
$248$		0			0
$249$	2.00000			2.00000
$250$		0			0
$251$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.00000			1.00000
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$258$	−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		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	0.500000	+	0.866025i	0.500000	+	0.866025i
$265$		0			0
$266$		0			0
$267$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$268$	−1.00000			−1.00000
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$		0			0
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$	0.500000	+	0.866025i	0.500000	+	0.866025i
$273$		0			0
$274$	0.500000	−	0.866025i	0.500000	−	0.866025i
$275$	0.500000	+	0.866025i	0.500000	+	0.866025i
$276$		0			0
$277$		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
$281$	−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
$283$	2.00000			2.00000			1.00000			$0$
$283$	2.00000			2.00000			1.00000			$0$
$284$		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
$291$	−1.00000			−1.00000
$292$	0.500000	+	0.866025i	0.500000	+	0.866025i
$293$		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
$297$	0.500000	−	0.866025i	0.500000	−	0.866025i
$298$		0			0
$299$		0			0
$300$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.500000	−	0.866025i	0.500000	−	0.866025i
$305$		0			0
$306$	0.500000	−	0.866025i	0.500000	−	0.866025i
$307$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$313$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		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
$326$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$327$		0			0
$328$	0.500000	−	0.866025i	0.500000	−	0.866025i
$329$		0			0
$330$		0			0
$331$	2.00000			2.00000			1.00000			$0$
$331$	2.00000			2.00000			1.00000			$0$
$332$	−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			$0$
$338$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$339$	−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
$347$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$347$	−1.00000			−1.00000			−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
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$354$	0.500000	−	0.866025i	0.500000	−	0.866025i
$355$		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	$-0.333333\pi$
$359$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$		0			0
$369$	−1.00000			−1.00000
$370$		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	$0.333333\pi$
$374$	1.00000			1.00000
$375$		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		−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
$387$	0.500000	−	0.866025i	0.500000	−	0.866025i
$388$	0.500000	+	0.866025i	0.500000	+	0.866025i
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	2.00000			2.00000
$394$		0			0
$395$		0			0
$396$	−1.00000			−1.00000
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	0.500000	−	0.866025i	0.500000	−	0.866025i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.00000			−1.00000
$409$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$409$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$	0.500000	+	0.866025i	0.500000	+	0.866025i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.500000	+	0.866025i	0.500000	+	0.866025i
$418$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$419$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$419$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$420$		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
$425$	−1.00000			−1.00000
$426$		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	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	1.00000			1.00000
$433$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$433$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.00000			−1.00000
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$443$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$444$		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	$0.666667\pi$
$450$	1.00000			1.00000
$451$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$452$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$453$		0			0
$454$	0.500000	−	0.866025i	0.500000	−	0.866025i
$455$		0			0
$456$	0.500000	+	0.866025i	0.500000	+	0.866025i
$457$	−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			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
$466$	0.500000	−	0.866025i	0.500000	−	0.866025i
$467$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$467$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.00000			−1.00000
$473$	1.00000			1.00000
$474$		0			0
$475$	0.500000	+	0.866025i	0.500000	+	0.866025i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$		0			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	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		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			$0$
$492$	0.500000	+	0.866025i	0.500000	+	0.866025i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.00000			2.00000
$499$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$499$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$	−1.00000			−1.00000
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.00000			1.00000
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		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
$514$	0.500000	+	0.866025i	0.500000	+	0.866025i
$515$		0			0
$516$	−1.00000			−1.00000
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$523$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$524$	−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
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$	0.500000	+	0.866025i	0.500000	+	0.866025i
$532$		0			0
$533$		0			0
$534$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$535$		0			0
$536$	−1.00000			−1.00000
$537$	2.00000			2.00000
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$		0			0
$544$	0.500000	+	0.866025i	0.500000	+	0.866025i
$545$		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
$556$	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
$561$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$562$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$563$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$563$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$	2.00000			2.00000
$567$		0			0
$568$		0			0
$569$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			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	1.00000			$0$
$587$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$588$		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	$0.666667\pi$
$593$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$594$	0.500000	−	0.866025i	0.500000	−	0.866025i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$601$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$601$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	0.500000	+	0.866025i	0.500000	+	0.866025i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−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			0
$611$		0			0
$612$	0.500000	−	0.866025i	0.500000	−	0.866025i
$613$		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
$617$	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
$619$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$619$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$	−1.00000			−1.00000
$627$	1.00000			1.00000
$628$		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
$641$	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			$0$
$642$	0.500000	+	0.866025i	0.500000	+	0.866025i
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$644$		0			0
$645$		0			0
$646$	1.00000			1.00000
$647$		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
$649$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$650$		0			0
$651$		0			0
$652$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		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		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	2.00000			2.00000
$663$		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
$675$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$679$		0			0
$680$		0			0
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$		0			0
$683$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$683$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$684$	−1.00000			−1.00000
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.500000	+	0.866025i	0.500000	+	0.866025i
$689$		0			0
$690$		0			0
$691$	2.00000			2.00000			1.00000			$0$
$691$	2.00000			2.00000			1.00000			$0$
$692$		0			0
$693$		0			0
$694$	−1.00000			−1.00000
$695$		0			0
$696$		0			0
$697$	1.00000			1.00000
$698$		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
$704$	0.500000	−	0.866025i	0.500000	−	0.866025i
$705$		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		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$		0			0
$712$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$717$		0			0
$718$		0			0
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	0.500000	+	0.866025i	0.500000	+	0.866025i
$724$		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
$731$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$732$		0			0
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$738$	−1.00000			−1.00000
$739$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$739$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$740$		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		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$	0.500000	−	0.866025i	0.500000	−	0.866025i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	−1.00000			−1.00000
$759$		0			0
$760$		0			0
$761$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$762$		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	$0.666667\pi$
$769$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$	−1.00000			−1.00000
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	0.500000	−	0.866025i	0.500000	−	0.866025i
$775$		0			0
$776$	0.500000	+	0.866025i	0.500000	+	0.866025i
$777$		0			0
$778$		0			0
$779$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	2.00000			2.00000
$787$	2.00000			2.00000			1.00000			$0$
$787$	2.00000			2.00000			1.00000			$0$
$788$		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
$801$	2.00000			2.00000
$802$	0.500000	+	0.866025i	0.500000	+	0.866025i
$803$	1.00000			1.00000
$804$	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	1.00000			$0$
$809$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$811$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.00000			−1.00000
$817$	1.00000			1.00000
$818$	−1.00000			−1.00000
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.500000	+	0.866025i	0.500000	+	0.866025i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		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	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		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
$843$	2.00000			2.00000
$844$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$850$	−1.00000			−1.00000
$851$		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
$857$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$857$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	1.00000			1.00000
$865$		0			0
$866$	−1.00000			−1.00000
$867$		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		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.00000			2.00000			1.00000			$0$
$881$	2.00000			2.00000			1.00000			$0$
$882$		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
$886$	−1.00000			−1.00000
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.500000	+	0.866025i	0.500000	+	0.866025i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.00000			−1.00000
$899$		0			0
$900$	1.00000			1.00000
$901$		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
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$908$	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	$0.333333\pi$
$912$	0.500000	+	0.866025i	0.500000	+	0.866025i
$913$	−2.00000			−2.00000
$914$	−1.00000			−1.00000
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.500000	+	0.866025i	0.500000	+	0.866025i
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	0.500000	−	0.866025i	0.500000	−	0.866025i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.00000			2.00000			1.00000			$0$
$929$	2.00000			2.00000			1.00000			$0$
$930$		0			0
$931$		0			0
$932$	0.500000	−	0.866025i	0.500000	−	0.866025i
$933$		0			0
$934$	0.500000	−	0.866025i	0.500000	−	0.866025i
$935$		0			0
$936$		0			0
$937$	2.00000			2.00000			1.00000			$0$
$937$	2.00000			2.00000			1.00000			$0$
$938$		0			0
$939$	0.500000	−	0.866025i	0.500000	−	0.866025i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$	−1.00000			−1.00000
$945$		0			0
$946$	1.00000			1.00000
$947$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$947$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$	0.500000	+	0.866025i	0.500000	+	0.866025i
$951$		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
$961$	1.00000			1.00000
$962$		0			0
$963$	−1.00000			−1.00000
$964$	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
$969$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$970$		0			0
$971$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$971$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$978$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$979$	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		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	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	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$994$		0			0
$995$		0			0
$996$	2.00000			2.00000
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$	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.ce.a.3019.1		2
7.2	even	3		72.1.p.a.67.1	yes	2
7.3	odd	6		3528.1.ba.a.67.1		2
7.4	even	3		3528.1.ba.b.67.1		2
7.5	odd	6		3528.1.cg.a.3235.1		2
7.6	odd	2		3528.1.ce.b.3019.1		2
8.3	odd	2	CM	3528.1.ce.a.3019.1		2
9.7	even	3		3528.1.ba.b.1843.1		2
21.2	odd	6		216.1.p.a.91.1		2
28.23	odd	6		288.1.t.a.175.1		2
35.2	odd	12		1800.1.ba.b.499.2		4
35.9	even	6		1800.1.bk.d.1651.1		2
35.23	odd	12		1800.1.ba.b.499.1		4
56.3	even	6		3528.1.ba.a.67.1		2
56.11	odd	6		3528.1.ba.b.67.1		2
56.19	even	6		3528.1.cg.a.3235.1		2
56.27	even	2		3528.1.ce.b.3019.1		2
56.37	even	6		288.1.t.a.175.1		2
56.51	odd	6		72.1.p.a.67.1	yes	2
63.2	odd	6		216.1.p.a.19.1		2
63.16	even	3		72.1.p.a.43.1	✓	2
63.23	odd	6		648.1.b.a.163.1		1
63.25	even	3	inner	3528.1.ce.a.2419.1		2
63.34	odd	6		3528.1.ba.a.1843.1		2
63.52	odd	6		3528.1.ce.b.2419.1		2
63.58	even	3		648.1.b.b.163.1		1
63.61	odd	6		3528.1.cg.a.2059.1		2
72.43	odd	6		3528.1.ba.b.1843.1		2
84.23	even	6		864.1.t.a.847.1		2
112.37	even	12		2304.1.o.c.2047.1		4
112.51	odd	12		2304.1.o.c.2047.1		4
112.93	even	12		2304.1.o.c.2047.2		4
112.107	odd	12		2304.1.o.c.2047.2		4
168.107	even	6		216.1.p.a.91.1		2
168.149	odd	6		864.1.t.a.847.1		2
252.23	even	6		2592.1.b.a.1135.1		1
252.79	odd	6		288.1.t.a.79.1		2
252.191	even	6		864.1.t.a.559.1		2
252.247	odd	6		2592.1.b.b.1135.1		1
280.107	even	12		1800.1.ba.b.499.2		4
280.163	even	12		1800.1.ba.b.499.1		4
280.219	odd	6		1800.1.bk.d.1651.1		2
315.79	even	6		1800.1.bk.d.1051.1		2
315.142	odd	12		1800.1.ba.b.1699.1		4
315.268	odd	12		1800.1.ba.b.1699.2		4
504.115	even	6		3528.1.ce.b.2419.1		2
504.149	odd	6		2592.1.b.a.1135.1		1
504.187	even	6		3528.1.cg.a.2059.1		2
504.205	even	6		288.1.t.a.79.1		2
504.275	even	6		648.1.b.a.163.1		1
504.317	odd	6		864.1.t.a.559.1		2
504.331	odd	6		72.1.p.a.43.1	✓	2
504.373	even	6		2592.1.b.b.1135.1		1
504.403	odd	6	inner	3528.1.ce.a.2419.1		2
504.443	even	6		216.1.p.a.19.1		2
504.475	even	6		3528.1.ba.a.1843.1		2
504.499	odd	6		648.1.b.b.163.1		1
1008.205	even	12		2304.1.o.c.511.1		4
1008.331	odd	12		2304.1.o.c.511.1		4
1008.709	even	12		2304.1.o.c.511.2		4
1008.835	odd	12		2304.1.o.c.511.2		4
2520.1339	odd	6		1800.1.bk.d.1051.1		2
2520.1843	even	12		1800.1.ba.b.1699.2		4
2520.2347	even	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	63.16	even	3
72.1.p.a.43.1	✓	2	504.331	odd	6
72.1.p.a.67.1	yes	2	7.2	even	3
72.1.p.a.67.1	yes	2	56.51	odd	6
216.1.p.a.19.1		2	63.2	odd	6
216.1.p.a.19.1		2	504.443	even	6
216.1.p.a.91.1		2	21.2	odd	6
216.1.p.a.91.1		2	168.107	even	6
288.1.t.a.79.1		2	252.79	odd	6
288.1.t.a.79.1		2	504.205	even	6
288.1.t.a.175.1		2	28.23	odd	6
288.1.t.a.175.1		2	56.37	even	6
648.1.b.a.163.1		1	63.23	odd	6
648.1.b.a.163.1		1	504.275	even	6
648.1.b.b.163.1		1	63.58	even	3
648.1.b.b.163.1		1	504.499	odd	6
864.1.t.a.559.1		2	252.191	even	6
864.1.t.a.559.1		2	504.317	odd	6
864.1.t.a.847.1		2	84.23	even	6
864.1.t.a.847.1		2	168.149	odd	6
1800.1.ba.b.499.1		4	35.23	odd	12
1800.1.ba.b.499.1		4	280.163	even	12
1800.1.ba.b.499.2		4	35.2	odd	12
1800.1.ba.b.499.2		4	280.107	even	12
1800.1.ba.b.1699.1		4	315.142	odd	12
1800.1.ba.b.1699.1		4	2520.2347	even	12
1800.1.ba.b.1699.2		4	315.268	odd	12
1800.1.ba.b.1699.2		4	2520.1843	even	12
1800.1.bk.d.1051.1		2	315.79	even	6
1800.1.bk.d.1051.1		2	2520.1339	odd	6
1800.1.bk.d.1651.1		2	35.9	even	6
1800.1.bk.d.1651.1		2	280.219	odd	6
2304.1.o.c.511.1		4	1008.205	even	12
2304.1.o.c.511.1		4	1008.331	odd	12
2304.1.o.c.511.2		4	1008.709	even	12
2304.1.o.c.511.2		4	1008.835	odd	12
2304.1.o.c.2047.1		4	112.37	even	12
2304.1.o.c.2047.1		4	112.51	odd	12
2304.1.o.c.2047.2		4	112.93	even	12
2304.1.o.c.2047.2		4	112.107	odd	12
2592.1.b.a.1135.1		1	252.23	even	6
2592.1.b.a.1135.1		1	504.149	odd	6
2592.1.b.b.1135.1		1	252.247	odd	6
2592.1.b.b.1135.1		1	504.373	even	6
3528.1.ba.a.67.1		2	7.3	odd	6
3528.1.ba.a.67.1		2	56.3	even	6
3528.1.ba.a.1843.1		2	63.34	odd	6
3528.1.ba.a.1843.1		2	504.475	even	6
3528.1.ba.b.67.1		2	7.4	even	3
3528.1.ba.b.67.1		2	56.11	odd	6
3528.1.ba.b.1843.1		2	9.7	even	3
3528.1.ba.b.1843.1		2	72.43	odd	6
3528.1.ce.a.2419.1		2	63.25	even	3	inner
3528.1.ce.a.2419.1		2	504.403	odd	6	inner
3528.1.ce.a.3019.1		2	1.1	even	1	trivial
3528.1.ce.a.3019.1		2	8.3	odd	2	CM
3528.1.ce.b.2419.1		2	63.52	odd	6
3528.1.ce.b.2419.1		2	504.115	even	6
3528.1.ce.b.3019.1		2	7.6	odd	2
3528.1.ce.b.3019.1		2	56.27	even	2
3528.1.cg.a.2059.1		2	63.61	odd	6
3528.1.cg.a.2059.1		2	504.187	even	6
3528.1.cg.a.3235.1		2	7.5	odd	6
3528.1.cg.a.3235.1		2	56.19	even	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.ce (of order \(6\), degree \(2\), not minimal)

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

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