LMFDB - Embedded newform 3332.1.g.g.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(883,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3332.883");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3332 = 2^{2} \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3332.g (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$1.66288462209$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 476)
Projective image:	$D_{6}$
Projective field:	Galois closure of 6.2.188737808.1

Embedding invariants

Embedding label			883.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	3332.883

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	$q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} +1.73205 q^{11} -1.73205 q^{12} +1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} -1.73205 q^{22} +1.73205 q^{24} +1.00000 q^{25} -1.00000 q^{26} -1.73205 q^{27} -1.00000 q^{32} -3.00000 q^{33} -1.00000 q^{34} +2.00000 q^{36} -1.73205 q^{39} +1.73205 q^{44} -1.73205 q^{48} -1.00000 q^{50} -1.73205 q^{51} +1.00000 q^{52} -1.00000 q^{53} +1.73205 q^{54} +1.00000 q^{64} +3.00000 q^{66} +1.00000 q^{68} -1.73205 q^{71} -2.00000 q^{72} -1.73205 q^{75} +1.73205 q^{78} +1.73205 q^{79} +1.00000 q^{81} -1.73205 q^{88} +1.00000 q^{89} +1.73205 q^{96} +3.46410 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} + 2 q^{13} + 2 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{25} - 2 q^{26} - 2 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} - 2 q^{50} + 2 q^{52} - 2 q^{53} + 2 q^{64} + 6 q^{66} + 2 q^{68} - 4 q^{72} + 2 q^{81} + 2 q^{89}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 + 2 * q^13 + 2 * q^16 + 2 * q^17 - 4 * q^18 + 2 * q^25 - 2 * q^26 - 2 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 - 2 * q^50 + 2 * q^52 - 2 * q^53 + 2 * q^64 + 6 * q^66 + 2 * q^68 - 4 * q^72 + 2 * q^81 + 2 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$.

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	1.00000
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	1.73205	1.73205
$7$	0	0
$7$	0	0
$8$	−1.00000	−1.00000
$9$	2.00000	2.00000
$10$	0	0
$11$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$11$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.73205	−1.73205
$13$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$13$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	1.00000	1.00000
$17$	1.00000	1.00000
$18$	−2.00000	−2.00000
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	−1.73205	−1.73205
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.73205	1.73205
$25$	1.00000	1.00000
$26$	−1.00000	−1.00000
$27$	−1.73205	−1.73205
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−1.00000
$33$	−3.00000	−3.00000
$34$	−1.00000	−1.00000
$35$	0	0
$36$	2.00000	2.00000
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−1.73205	−1.73205
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	1.73205	1.73205
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−1.73205	−1.73205
$49$	0	0
$50$	−1.00000	−1.00000
$51$	−1.73205	−1.73205
$52$	1.00000	1.00000
$53$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$54$	1.73205	1.73205
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	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
$66$	3.00000	3.00000
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	1.00000	1.00000
$69$	0	0
$70$	0	0
$71$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$72$	−2.00000	−2.00000
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	−1.73205	−1.73205
$76$	0	0
$77$	0	0
$78$	1.73205	1.73205
$79$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$79$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$80$	0	0
$81$	1.00000	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	−1.73205	−1.73205
$89$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$89$	1.00000	1.00000	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
$96$	1.73205	1.73205
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	3.46410	3.46410
$100$	1.00000	1.00000
$101$	−2.00000	−2.00000	−1.00000			$\pi$
$101$	−2.00000	−2.00000	−1.00000			$\pi$
$102$	1.73205	1.73205
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−1.00000	−1.00000
$105$	0	0
$106$	1.00000	1.00000
$107$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$107$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$108$	−1.73205	−1.73205
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	2.00000	2.00000
$118$	0	0
$119$	0	0
$120$	0	0
$121$	2.00000	2.00000
$122$	0	0
$123$	0	0
$124$	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
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−3.00000	−3.00000
$133$	0	0
$134$	0	0
$135$	0	0
$136$	−1.00000	−1.00000
$137$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$137$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$138$	0	0
$139$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$139$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$140$	0	0
$141$	0	0
$142$	1.73205	1.73205
$143$	1.73205	1.73205
$144$	2.00000	2.00000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$150$	1.73205	1.73205
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	2.00000	2.00000
$154$	0	0
$155$	0	0
$156$	−1.73205	−1.73205
$157$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$157$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$158$	−1.73205	−1.73205
$159$	1.73205	1.73205
$160$	0	0
$161$	0	0
$162$	−1.00000	−1.00000
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$167$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	1.73205	1.73205
$177$	0	0
$178$	−1.00000	−1.00000
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	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
$187$	1.73205	1.73205
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−1.73205	−1.73205
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−3.46410	−3.46410
$199$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$199$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$200$	−1.00000	−1.00000
$201$	0	0
$202$	2.00000	2.00000
$203$	0	0
$204$	−1.73205	−1.73205
$205$	0	0
$206$	0	0
$207$	0	0
$208$	1.00000	1.00000
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−1.00000	−1.00000
$213$	3.00000	3.00000
$214$	1.73205	1.73205
$215$	0	0
$216$	1.73205	1.73205
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	1.00000	1.00000
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	2.00000	2.00000
$226$	0	0
$227$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$227$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$228$	0	0
$229$	−2.00000	−2.00000	−1.00000			$\pi$
$229$	−2.00000	−2.00000	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−2.00000	−2.00000
$235$	0	0
$236$	0	0
$237$	−3.00000	−3.00000
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−2.00000	−2.00000
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	3.00000	3.00000
$265$	0	0
$266$	0	0
$267$	−1.73205	−1.73205
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.00000	1.00000
$273$	0	0
$274$	−1.00000	−1.00000
$275$	1.73205	1.73205
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	−1.73205	−1.73205
$279$	0	0
$280$	0	0
$281$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$282$	0	0
$283$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$284$	−1.73205	−1.73205
$285$	0	0
$286$	−1.73205	−1.73205
$287$	0	0
$288$	−2.00000	−2.00000
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−3.00000	−3.00000
$298$	1.00000	1.00000
$299$	0	0
$300$	−1.73205	−1.73205
$301$	0	0
$302$	0	0
$303$	3.46410	3.46410
$304$	0	0
$305$	0	0
$306$	−2.00000	−2.00000
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$311$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$312$	1.73205	1.73205
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	1.00000	1.00000
$315$	0	0
$316$	1.73205	1.73205
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	−1.73205	−1.73205
$319$	0	0
$320$	0	0
$321$	3.00000	3.00000
$322$	0	0
$323$	0	0
$324$	1.00000	1.00000
$325$	1.00000	1.00000
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	−1.73205	−1.73205
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	2.00000	2.00000	1.00000			$0$
$349$	2.00000	2.00000	1.00000			$0$
$350$	0	0
$351$	−1.73205	−1.73205
$352$	−1.73205	−1.73205
$353$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$354$	0	0
$355$	0	0
$356$	1.00000	1.00000
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	−3.46410	−3.46410
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$367$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$373$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$374$	−1.73205	−1.73205
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$379$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	1.73205	1.73205
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$389$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	3.46410	3.46410
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	−1.73205	−1.73205
$399$	0	0
$400$	1.00000	1.00000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	−2.00000	−2.00000
$405$	0	0
$406$	0	0
$407$	0	0
$408$	1.73205	1.73205
$409$	−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
$411$	−1.73205	−1.73205
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−1.00000	−1.00000
$417$	−3.00000	−3.00000
$418$	0	0
$419$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$419$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$420$	0	0
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$421$	−2.00000	−2.00000	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	1.00000	1.00000
$425$	1.00000	1.00000
$426$	−3.00000	−3.00000
$427$	0	0
$428$	−1.73205	−1.73205
$429$	−3.00000	−3.00000
$430$	0	0
$431$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$431$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$432$	−1.73205	−1.73205
$433$	−2.00000	−2.00000	−1.00000			$\pi$
$433$	−2.00000	−2.00000	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$439$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$440$	0	0
$441$	0	0
$442$	−1.00000	−1.00000
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	1.73205	1.73205
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−2.00000	−2.00000
$451$	0	0
$452$	0	0
$453$	0	0
$454$	−1.73205	−1.73205
$455$	0	0
$456$	0	0
$457$	−2.00000	−2.00000	−1.00000			$\pi$
$457$	−2.00000	−2.00000	−1.00000			$\pi$
$458$	2.00000	2.00000
$459$	−1.73205	−1.73205
$460$	0	0
$461$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	2.00000	2.00000
$469$	0	0
$470$	0	0
$471$	1.73205	1.73205
$472$	0	0
$473$	0	0
$474$	3.00000	3.00000
$475$	0	0
$476$	0	0
$477$	−2.00000	−2.00000
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	2.00000	2.00000
$485$	0	0
$486$	0	0
$487$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$487$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$499$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$500$	0	0
$501$	−3.00000	−3.00000
$502$	0	0
$503$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	2.00000	2.00000	1.00000			$0$
$509$	2.00000	2.00000	1.00000			$0$
$510$	0	0
$511$	0	0
$512$	−1.00000	−1.00000
$513$	0	0
$514$	−1.00000	−1.00000
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	−3.00000	−3.00000
$529$	−1.00000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	1.73205	1.73205
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	−1.00000	−1.00000
$545$	0	0
$546$	0	0
$547$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$547$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$548$	1.00000	1.00000
$549$	0	0
$550$	−1.73205	−1.73205
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	1.73205	1.73205
$557$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$557$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−3.00000	−3.00000
$562$	1.00000	1.00000
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	1.73205	1.73205
$567$	0	0
$568$	1.73205	1.73205
$569$	−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
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	1.73205	1.73205
$573$	0	0
$574$	0	0
$575$	0	0
$576$	2.00000	2.00000
$577$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$577$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$578$	−1.00000	−1.00000
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−1.73205	−1.73205
$584$	0	0
$585$	0	0
$586$	1.00000	1.00000
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$593$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$594$	3.00000	3.00000
$595$	0	0
$596$	−1.00000	−1.00000
$597$	−3.00000	−3.00000
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	1.73205	1.73205
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	−3.46410	−3.46410
$607$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$607$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	2.00000	2.00000
$613$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$619$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$620$	0	0
$621$	0	0
$622$	1.73205	1.73205
$623$	0	0
$624$	−1.73205	−1.73205
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	−1.00000	−1.00000
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	−1.73205	−1.73205
$633$	0	0
$634$	0	0
$635$	0	0
$636$	1.73205	1.73205
$637$	0	0
$638$	0	0
$639$	−3.46410	−3.46410
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	−3.00000	−3.00000
$643$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$643$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−1.00000	−1.00000
$649$	0	0
$650$	−1.00000	−1.00000
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	2.00000	2.00000	1.00000			$0$
$661$	2.00000	2.00000	1.00000			$0$
$662$	0	0
$663$	−1.73205	−1.73205
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	1.73205	1.73205
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−1.73205	−1.73205
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−3.00000	−3.00000
$682$	0	0
$683$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$683$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	3.46410	3.46410
$688$	0	0
$689$	−1.00000	−1.00000
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−2.00000	−2.00000
$699$	0	0
$700$	0	0
$701$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$702$	1.73205	1.73205
$703$	0	0
$704$	1.73205	1.73205
$705$	0	0
$706$	1.00000	1.00000
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	3.46410	3.46410
$712$	−1.00000	−1.00000
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$719$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$720$	0	0
$721$	0	0
$722$	−1.00000	−1.00000
$723$	0	0
$724$	0	0
$725$	0	0
$726$	3.46410	3.46410
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	−1.00000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$733$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$734$	−1.73205	−1.73205
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$743$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$744$	0	0
$745$	0	0
$746$	−1.00000	−1.00000
$747$	0	0
$748$	1.73205	1.73205
$749$	0	0
$750$	0	0
$751$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$751$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$757$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$758$	1.73205	1.73205
$759$	0	0
$760$	0	0
$761$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$761$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−1.73205	−1.73205
$769$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$770$	0	0
$771$	−1.73205	−1.73205
$772$	0	0
$773$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$773$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−1.00000	−1.00000
$779$	0	0
$780$	0	0
$781$	−3.00000	−3.00000
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	−3.46410	−3.46410
$793$	0	0
$794$	0	0
$795$	0	0
$796$	1.73205	1.73205
$797$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−1.00000
$801$	2.00000	2.00000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	2.00000	2.00000
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$811$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−1.73205	−1.73205
$817$	0	0
$818$	1.00000	1.00000
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	1.73205	1.73205
$823$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$824$	0	0
$825$	−3.00000	−3.00000
$826$	0	0
$827$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$827$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$828$	0	0
$829$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	1.00000
$833$	0	0
$834$	3.00000	3.00000
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−1.73205	−1.73205
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	2.00000	2.00000
$843$	1.73205	1.73205
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−1.00000	−1.00000
$849$	3.00000	3.00000
$850$	−1.00000	−1.00000
$851$	0	0
$852$	3.00000	3.00000
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	1.73205	1.73205
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	3.00000	3.00000
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	1.73205	1.73205
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	1.73205	1.73205
$865$	0	0
$866$	2.00000	2.00000
$867$	−1.73205	−1.73205
$868$	0	0
$869$	3.00000	3.00000
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	1.73205	1.73205
$879$	1.73205	1.73205
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	1.00000	1.00000
$885$	0	0
$886$	0	0
$887$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$887$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1.73205	1.73205
$892$	0	0
$893$	0	0
$894$	−1.73205	−1.73205
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	2.00000	2.00000
$901$	−1.00000	−1.00000
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	1.73205	1.73205
$909$	−4.00000	−4.00000
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	2.00000	2.00000
$915$	0	0
$916$	−2.00000	−2.00000
$917$	0	0
$918$	1.73205	1.73205
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	1.00000	1.00000
$923$	−1.73205	−1.73205
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	3.00000	3.00000
$934$	0	0
$935$	0	0
$936$	−2.00000	−2.00000
$937$	2.00000	2.00000	1.00000			$0$
$937$	2.00000	2.00000	1.00000			$0$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	−1.73205	−1.73205
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$947$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$948$	−3.00000	−3.00000
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$953$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$954$	2.00000	2.00000
$955$	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
$963$	−3.46410	−3.46410
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−2.00000	−2.00000
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	−1.73205	−1.73205
$975$	−1.73205	−1.73205
$976$	0	0
$977$	2.00000	2.00000	1.00000			$0$
$977$	2.00000	2.00000	1.00000			$0$
$978$	0	0
$979$	1.73205	1.73205
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$991$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.73205	1.73205
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.g.g.883.1		2
4.3	odd	2	inner	3332.1.g.g.883.2		2
7.2	even	3		476.1.o.c.67.2	yes	4
7.3	odd	6		3332.1.o.f.2039.1		4
7.4	even	3		476.1.o.c.135.2	yes	4
7.5	odd	6		3332.1.o.f.67.1		4
7.6	odd	2		3332.1.g.f.883.2		2
17.16	even	2	inner	3332.1.g.g.883.2		2
28.3	even	6		3332.1.o.f.2039.2		4
28.11	odd	6		476.1.o.c.135.1	yes	4
28.19	even	6		3332.1.o.f.67.2		4
28.23	odd	6		476.1.o.c.67.1	✓	4
28.27	even	2		3332.1.g.f.883.1		2
68.67	odd	2	CM	3332.1.g.g.883.1		2
119.16	even	6		476.1.o.c.67.1	✓	4
119.33	odd	6		3332.1.o.f.67.2		4
119.67	even	6		476.1.o.c.135.1	yes	4
119.101	odd	6		3332.1.o.f.2039.2		4
119.118	odd	2		3332.1.g.f.883.1		2
476.67	odd	6		476.1.o.c.135.2	yes	4
476.135	odd	6		476.1.o.c.67.2	yes	4
476.271	even	6		3332.1.o.f.67.1		4
476.339	even	6		3332.1.o.f.2039.1		4
476.475	even	2		3332.1.g.f.883.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.1.o.c.67.1	✓	4	28.23	odd	6
476.1.o.c.67.1	✓	4	119.16	even	6
476.1.o.c.67.2	yes	4	7.2	even	3
476.1.o.c.67.2	yes	4	476.135	odd	6
476.1.o.c.135.1	yes	4	28.11	odd	6
476.1.o.c.135.1	yes	4	119.67	even	6
476.1.o.c.135.2	yes	4	7.4	even	3
476.1.o.c.135.2	yes	4	476.67	odd	6
3332.1.g.f.883.1		2	28.27	even	2
3332.1.g.f.883.1		2	119.118	odd	2
3332.1.g.f.883.2		2	7.6	odd	2
3332.1.g.f.883.2		2	476.475	even	2
3332.1.g.g.883.1		2	1.1	even	1	trivial
3332.1.g.g.883.1		2	68.67	odd	2	CM
3332.1.g.g.883.2		2	4.3	odd	2	inner
3332.1.g.g.883.2		2	17.16	even	2	inner
3332.1.o.f.67.1		4	7.5	odd	6
3332.1.o.f.67.1		4	476.271	even	6
3332.1.o.f.67.2		4	28.19	even	6
3332.1.o.f.67.2		4	119.33	odd	6
3332.1.o.f.2039.1		4	7.3	odd	6
3332.1.o.f.2039.1		4	476.339	even	6
3332.1.o.f.2039.2		4	28.3	even	6
3332.1.o.f.2039.2		4	119.101	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:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +1.73205 q^{6} -1.00000 q^{8} +2.00000 q^{9} +1.73205 q^{11} -1.73205 q^{12} +1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} -1.73205 q^{22} +1.73205 q^{24} +1.00000 q^{25} -1.00000 q^{26} -1.73205 q^{27} -1.00000 q^{32} -3.00000 q^{33} -1.00000 q^{34} +2.00000 q^{36} -1.73205 q^{39} +1.73205 q^{44} -1.73205 q^{48} -1.00000 q^{50} -1.73205 q^{51} +1.00000 q^{52} -1.00000 q^{53} +1.73205 q^{54} +1.00000 q^{64} +3.00000 q^{66} +1.00000 q^{68} -1.73205 q^{71} -2.00000 q^{72} -1.73205 q^{75} +1.73205 q^{78} +1.73205 q^{79} +1.00000 q^{81} -1.73205 q^{88} +1.00000 q^{89} +1.73205 q^{96} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} + 2 q^{13} + 2 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{25} - 2 q^{26} - 2 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} - 2 q^{50} + 2 q^{52} - 2 q^{53} + 2 q^{64} + 6 q^{66} + 2 q^{68} - 4 q^{72} + 2 q^{81} + 2 q^{89}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 + 2 * q^13 + 2 * q^16 + 2 * q^17 - 4 * q^18 + 2 * q^25 - 2 * q^26 - 2 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 - 2 * q^50 + 2 * q^52 - 2 * q^53 + 2 * q^64 + 6 * q^66 + 2 * q^68 - 4 * q^72 + 2 * q^81 + 2 * q^89

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