LMFDB - Embedded newform 396.1.d.a.395.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [396,1,Mod(395,396)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("396.395"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(396, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$N$	$=$	$396 = 2^{2} \cdot 3^{2} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	396.d (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.197629745003$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 1$ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2$
Twist minimal:	yes
Projective image:	$D_{4}$
Projective field:	Galois closure of 4.0.4752.1

Embedding invariants

Embedding label			395.3
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	396.395
Dual form			396.1.d.a.395.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} -1.41421i q^{5} +1.41421 q^{7} -1.00000i q^{8} +1.41421 q^{10} +1.00000i q^{11} +1.41421i q^{14} +1.00000 q^{16} -1.41421 q^{19} +1.41421i q^{20} -1.00000 q^{22} -1.00000 q^{25} -1.41421 q^{28} +1.00000i q^{32} -2.00000i q^{35} -1.41421i q^{38} -1.41421 q^{40} -1.41421 q^{43} -1.00000i q^{44} +1.00000 q^{49} -1.00000i q^{50} +1.41421i q^{53} +1.41421 q^{55} -1.41421i q^{56} -1.00000 q^{64} +2.00000 q^{70} +1.41421 q^{76} +1.41421i q^{77} -1.41421 q^{79} -1.41421i q^{80} -1.41421i q^{86} +1.00000 q^{88} -1.41421i q^{89} +2.00000i q^{95} -2.00000 q^{97} +1.00000i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{4} + 4 q^{16} - 4 q^{22} - 4 q^{25} + 4 q^{49} - 4 q^{64} + 8 q^{70} + 4 q^{88} - 8 q^{97}+O(q^{100})$ 4 * q - 4 * q^4 + 4 * q^16 - 4 * q^22 - 4 * q^25 + 4 * q^49 - 4 * q^64 + 8 * q^70 + 4 * q^88 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$ .

$n$	$145$	$199$	$353$
$\chi(n)$	$-1$	$-1$	$-1$

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

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	1.00000i	1.00000i
$2$	1.00000i	1.00000i
$3$	0	0
$3$	0	0
$4$	−1.00000	−1.00000
$5$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$5$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$6$	0	0
$7$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$7$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$8$	− 1.00000i	− 1.00000i
$9$	0	0
$10$	1.41421	1.41421
$11$	1.00000i	1.00000i
$11$	1.00000i	1.00000i
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	1.41421i	1.41421i
$15$	0	0
$16$	1.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$19$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$20$	1.41421i	1.41421i
$21$	0	0
$22$	−1.00000	−1.00000
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−1.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	−1.41421	−1.41421
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	1.00000i	1.00000i
$33$	0	0
$34$	0	0
$35$	− 2.00000i	− 2.00000i
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	− 1.41421i	− 1.41421i
$39$	0	0
$40$	−1.41421	−1.41421
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$43$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$44$	− 1.00000i	− 1.00000i
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	1.00000	1.00000
$50$	− 1.00000i	− 1.00000i
$51$	0	0
$52$	0	0
$53$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$53$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$54$	0	0
$55$	1.41421	1.41421
$56$	− 1.41421i	− 1.41421i
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	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	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	2.00000	2.00000
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	1.41421	1.41421
$77$	1.41421i	1.41421i
$78$	0	0
$79$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$79$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$80$	− 1.41421i	− 1.41421i
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	− 1.41421i	− 1.41421i
$87$	0	0
$88$	1.00000	1.00000
$89$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$89$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	2.00000i	2.00000i
$96$	0	0
$97$	−2.00000	−2.00000	−1.00000			$\pi$
$97$	−2.00000	−2.00000	−1.00000			$\pi$
$98$	1.00000i	1.00000i
$99$	0	0
$100$	1.00000	1.00000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	−1.41421	−1.41421
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	1.41421i	1.41421i
$111$	0	0
$112$	1.41421	1.41421
$113$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$113$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−1.00000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$127$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$128$	− 1.00000i	− 1.00000i
$129$	0	0
$130$	0	0
$131$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$131$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$132$	0	0
$133$	−2.00000	−2.00000
$134$	0	0
$135$	0	0
$136$	0	0
$137$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$137$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$138$	0	0
$139$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$139$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$140$	2.00000i	2.00000i
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$151$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$152$	1.41421i	1.41421i
$153$	0	0
$154$	−1.41421	−1.41421
$155$	0	0
$156$	0	0
$157$	2.00000	2.00000	1.00000			$0$
$157$	2.00000	2.00000	1.00000			$0$
$158$	− 1.41421i	− 1.41421i
$159$	0	0
$160$	1.41421	1.41421
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$167$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	1.41421	1.41421
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−1.41421	−1.41421
$176$	1.00000i	1.00000i
$177$	0	0
$178$	1.41421	1.41421
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	−2.00000	−2.00000
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	− 2.00000i	− 2.00000i
$195$	0	0
$196$	−1.00000	−1.00000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	1.00000i	1.00000i
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	− 1.41421i	− 1.41421i
$210$	0	0
$211$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$211$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$212$	− 1.41421i	− 1.41421i
$213$	0	0
$214$	0	0
$215$	2.00000i	2.00000i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	−1.41421	−1.41421
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	1.41421i	1.41421i
$225$	0	0
$226$	−1.41421	−1.41421
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	2.00000	2.00000	1.00000			$0$
$229$	2.00000	2.00000	1.00000			$0$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$239$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	− 1.00000i	− 1.00000i
$243$	0	0
$244$	0	0
$245$	− 1.41421i	− 1.41421i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	1.41421i	1.41421i
$255$	0	0
$256$	1.00000	1.00000
$257$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$257$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	2.00000	2.00000
$263$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$263$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$264$	0	0
$265$	2.00000	2.00000
$266$	− 2.00000i	− 2.00000i
$267$	0	0
$268$	0	0
$269$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$269$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$270$	0	0
$271$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$271$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$272$	0	0
$273$	0	0
$274$	−1.41421	−1.41421
$275$	− 1.00000i	− 1.00000i
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	1.41421i	1.41421i
$279$	0	0
$280$	−2.00000	−2.00000
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$283$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−1.00000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−2.00000	−2.00000
$302$	1.41421i	1.41421i
$303$	0	0
$304$	−1.41421	−1.41421
$305$	0	0
$306$	0	0
$307$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$307$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$308$	− 1.41421i	− 1.41421i
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	2.00000i	2.00000i
$315$	0	0
$316$	1.41421	1.41421
$317$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$317$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$318$	0	0
$319$	0	0
$320$	1.41421i	1.41421i
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	−2.00000	−2.00000
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	1.00000i	1.00000i
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	1.41421i	1.41421i
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	− 1.41421i	− 1.41421i
$351$	0	0
$352$	−1.00000	−1.00000
$353$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$353$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$354$	0	0
$355$	0	0
$356$	1.41421i	1.41421i
$357$	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
$363$	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	0
$370$	0	0
$371$	2.00000i	2.00000i
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	− 2.00000i	− 2.00000i
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	2.00000	2.00000
$386$	0	0
$387$	0	0
$388$	2.00000	2.00000
$389$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$389$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$390$	0	0
$391$	0	0
$392$	− 1.00000i	− 1.00000i
$393$	0	0
$394$	0	0
$395$	2.00000i	2.00000i
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	−1.00000	−1.00000
$401$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$401$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	1.41421	1.41421
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	− 1.41421i	− 1.41421i
$423$	0	0
$424$	1.41421	1.41421
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	−2.00000	−2.00000
$431$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$431$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$439$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$440$	− 1.41421i	− 1.41421i
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	−2.00000	−2.00000
$446$	0	0
$447$	0	0
$448$	−1.41421	−1.41421
$449$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$449$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$450$	0	0
$451$	0	0
$452$	− 1.41421i	− 1.41421i
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	2.00000i	2.00000i
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	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		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	− 1.41421i	− 1.41421i
$474$	0	0
$475$	1.41421	1.41421
$476$	0	0
$477$	0	0
$478$	2.00000	2.00000
$479$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$479$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	1.00000	1.00000
$485$	2.82843i	2.82843i
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	1.41421	1.41421
$491$	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
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$503$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−1.41421	−1.41421
$509$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$509$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$510$	0	0
$511$	0	0
$512$	1.00000i	1.00000i
$513$	0	0
$514$	1.41421	1.41421
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$521$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$522$	0	0
$523$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$523$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$524$	2.00000i	2.00000i
$525$	0	0
$526$	2.00000	2.00000
$527$	0	0
$528$	0	0
$529$	−1.00000	−1.00000
$530$	2.00000i	2.00000i
$531$	0	0
$532$	2.00000	2.00000
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	1.41421	1.41421
$539$	1.00000i	1.00000i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	− 1.41421i	− 1.41421i
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$547$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$548$	− 1.41421i	− 1.41421i
$549$	0	0
$550$	1.00000	1.00000
$551$	0	0
$552$	0	0
$553$	−2.00000	−2.00000
$554$	0	0
$555$	0	0
$556$	−1.41421	−1.41421
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	− 2.00000i	− 2.00000i
$561$	0	0
$562$	0	0
$563$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$563$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$564$	0	0
$565$	2.00000	2.00000
$566$	1.41421i	1.41421i
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$571$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−2.00000	−2.00000	−1.00000			$\pi$
$577$	−2.00000	−2.00000	−1.00000			$\pi$
$578$	− 1.00000i	− 1.00000i
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−1.41421	−1.41421
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	− 2.00000i	− 2.00000i
$603$	0	0
$604$	−1.41421	−1.41421
$605$	1.41421i	1.41421i
$606$	0	0
$607$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$607$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$608$	− 1.41421i	− 1.41421i
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	− 1.41421i	− 1.41421i
$615$	0	0
$616$	1.41421	1.41421
$617$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$617$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	− 2.00000i	− 2.00000i
$624$	0	0
$625$	−1.00000	−1.00000
$626$	0	0
$627$	0	0
$628$	−2.00000	−2.00000
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	1.41421i	1.41421i
$633$	0	0
$634$	1.41421	1.41421
$635$	− 2.00000i	− 2.00000i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	−1.41421	−1.41421
$641$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$641$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$653$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$654$	0	0
$655$	−2.82843	−2.82843
$656$	0	0
$657$	0	0
$658$	0	0
$659$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$659$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$660$	0	0
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	2.82843i	2.82843i
$666$	0	0
$667$	0	0
$668$	− 2.00000i	− 2.00000i
$669$	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
$675$	0	0
$676$	−1.00000	−1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	−2.82843	−2.82843
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	2.00000	2.00000
$686$	0	0
$687$	0	0
$688$	−1.41421	−1.41421
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	− 2.00000i	− 2.00000i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	1.41421	1.41421
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	− 1.00000i	− 1.00000i
$705$	0	0
$706$	−1.41421	−1.41421
$707$	0	0
$708$	0	0
$709$	2.00000	2.00000	1.00000			$0$
$709$	2.00000	2.00000	1.00000			$0$
$710$	0	0
$711$	0	0
$712$	−1.41421	−1.41421
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	1.00000i	1.00000i
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	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	0
$738$	0	0
$739$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$739$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$740$	0	0
$741$	0	0
$742$	−2.00000	−2.00000
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	− 2.00000i	− 2.00000i
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	2.00000	2.00000
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	2.00000i	2.00000i
$771$	0	0
$772$	0	0
$773$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$773$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$774$	0	0
$775$	0	0
$776$	2.00000i	2.00000i
$777$	0	0
$778$	−1.41421	−1.41421
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	1.00000
$785$	− 2.82843i	− 2.82843i
$786$	0	0
$787$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$787$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$788$	0	0
$789$	0	0
$790$	−2.00000	−2.00000
$791$	2.00000i	2.00000i
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$797$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$798$	0	0
$799$	0	0
$800$	− 1.00000i	− 1.00000i
$801$	0	0
$802$	−1.41421	−1.41421
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$811$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	2.00000	2.00000
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	2.82843	2.82843
$836$	1.41421i	1.41421i
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−1.00000	−1.00000
$842$	0	0
$843$	0	0
$844$	1.41421	1.41421
$845$	− 1.41421i	− 1.41421i
$846$	0	0
$847$	−1.41421	−1.41421
$848$	1.41421i	1.41421i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	− 2.00000i	− 2.00000i
$861$	0	0
$862$	2.00000	2.00000
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	− 1.41421i	− 1.41421i
$870$	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			$\pi$
$878$	1.41421i	1.41421i
$879$	0	0
$880$	1.41421	1.41421
$881$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$881$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	2.00000	2.00000
$890$	− 2.00000i	− 2.00000i
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	− 1.41421i	− 1.41421i
$897$	0	0
$898$	1.41421	1.41421
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	1.41421	1.41421
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−2.00000	−2.00000
$917$	− 2.82843i	− 2.82843i
$918$	0	0
$919$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$919$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	− 1.41421i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$929$	− 1.41421i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$930$	0	0
$931$	−1.41421	−1.41421
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	1.41421	1.41421
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	1.41421i	1.41421i
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	2.00000i	2.00000i
$957$	0	0
$958$	2.00000	2.00000
$959$	2.00000i	2.00000i
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$967$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$968$	1.00000i	1.00000i
$969$	0	0
$970$	−2.82843	−2.82843
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	2.00000	2.00000
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.41421i	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$977$	1.41421i	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$978$	0	0
$979$	1.41421	1.41421
$980$	1.41421i	1.41421i
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	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			$\pi$
$998$	0	0
$999$	0	0

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.1.d.a.395.3	yes	4
3.2	odd	2	inner	396.1.d.a.395.2	yes	4
4.3	odd	2	inner	396.1.d.a.395.1	✓	4
9.2	odd	6		3564.1.o.e.1187.1		8
9.4	even	3		3564.1.o.e.2375.1		8
9.5	odd	6		3564.1.o.e.2375.4		8
9.7	even	3		3564.1.o.e.1187.4		8
11.10	odd	2	inner	396.1.d.a.395.1	✓	4
12.11	even	2	inner	396.1.d.a.395.4	yes	4
33.32	even	2	inner	396.1.d.a.395.4	yes	4
36.7	odd	6		3564.1.o.e.1187.2		8
36.11	even	6		3564.1.o.e.1187.3		8
36.23	even	6		3564.1.o.e.2375.2		8
36.31	odd	6		3564.1.o.e.2375.3		8
44.43	even	2	RM	396.1.d.a.395.3	yes	4
99.32	even	6		3564.1.o.e.2375.2		8
99.43	odd	6		3564.1.o.e.1187.2		8
99.65	even	6		3564.1.o.e.1187.3		8
99.76	odd	6		3564.1.o.e.2375.3		8
132.131	odd	2	inner	396.1.d.a.395.2	yes	4
396.43	even	6		3564.1.o.e.1187.4		8
396.131	odd	6		3564.1.o.e.2375.4		8
396.175	even	6		3564.1.o.e.2375.1		8
396.263	odd	6		3564.1.o.e.1187.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.1.d.a.395.1	✓	4	4.3	odd	2	inner
396.1.d.a.395.1	✓	4	11.10	odd	2	inner
396.1.d.a.395.2	yes	4	3.2	odd	2	inner
396.1.d.a.395.2	yes	4	132.131	odd	2	inner
396.1.d.a.395.3	yes	4	1.1	even	1	trivial
396.1.d.a.395.3	yes	4	44.43	even	2	RM
396.1.d.a.395.4	yes	4	12.11	even	2	inner
396.1.d.a.395.4	yes	4	33.32	even	2	inner
3564.1.o.e.1187.1		8	9.2	odd	6
3564.1.o.e.1187.1		8	396.263	odd	6
3564.1.o.e.1187.2		8	36.7	odd	6
3564.1.o.e.1187.2		8	99.43	odd	6
3564.1.o.e.1187.3		8	36.11	even	6
3564.1.o.e.1187.3		8	99.65	even	6
3564.1.o.e.1187.4		8	9.7	even	3
3564.1.o.e.1187.4		8	396.43	even	6
3564.1.o.e.2375.1		8	9.4	even	3
3564.1.o.e.2375.1		8	396.175	even	6
3564.1.o.e.2375.2		8	36.23	even	6
3564.1.o.e.2375.2		8	99.32	even	6
3564.1.o.e.2375.3		8	36.31	odd	6
3564.1.o.e.2375.3		8	99.76	odd	6
3564.1.o.e.2375.4		8	9.5	odd	6
3564.1.o.e.2375.4		8	396.131	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	396.1.d.a.395.3

Level	$396$
Weight	$1$
Character	396.395
Analytic conductor	$0.198$
Analytic rank	$0$
Dimension	$4$
Projective image	$D_{4}$
RM discriminant	44
Inner twists	$8$