LMFDB - Embedded newform 484.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(1,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("484.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$484 = 2^{2} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	484.a (trivial)

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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x - 8$ x^2 - x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	484.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.37228 q^{3} -1.37228 q^{5} +8.37228 q^{9} -4.62772 q^{15} +7.37228 q^{23} -3.11684 q^{25} +18.1168 q^{27} -6.11684 q^{31} -12.1168 q^{37} -11.4891 q^{45} -12.0000 q^{47} -7.00000 q^{49} +6.00000 q^{53} +4.62772 q^{59} +2.11684 q^{67} +24.8614 q^{69} -12.8614 q^{71} -10.5109 q^{75} +35.9783 q^{81} +18.8614 q^{89} -20.6277 q^{93} +0.116844 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{3} + 3 q^{5} + 11 q^{9} - 15 q^{15} + 9 q^{23} + 11 q^{25} + 19 q^{27} + 5 q^{31} - 7 q^{37} - 24 q^{47} - 14 q^{49} + 12 q^{53} + 15 q^{59} - 13 q^{67} + 21 q^{69} + 3 q^{71} - 44 q^{75} + 26 q^{81}+ \cdots - 17 q^{97}+O(q^{100})$ 2 * q + q^3 + 3 * q^5 + 11 * q^9 - 15 * q^15 + 9 * q^23 + 11 * q^25 + 19 * q^27 + 5 * q^31 - 7 * q^37 - 24 * q^47 - 14 * q^49 + 12 * q^53 + 15 * q^59 - 13 * q^67 + 21 * q^69 + 3 * q^71 - 44 * q^75 + 26 * q^81 + 9 * q^89 - 47 * q^93 - 17 * q^97

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0	0
$2$	0	0
$3$	3.37228	1.94699	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	3.37228	1.94699	0.973494	+	0.228714i	$0.0734519\pi$
$4$	0	0
$5$	−1.37228	−0.613703	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	−1.37228	−0.613703	−0.306851	+	0.951757i	$0.599275\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	8.37228	2.79076
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	−4.62772	−1.19487
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	7.37228	1.53723	0.768613	−	0.639713i	$-0.220947\pi$
$23$	7.37228	1.53723	0.768613	+	0.639713i	$0.220947\pi$
$24$	0	0
$25$	−3.11684	−0.623369
$26$	0	0
$27$	18.1168	3.48659
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−6.11684	−1.09862	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	−6.11684	−1.09862	−0.549309	+	0.835619i	$0.685109\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−12.1168	−1.99200	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−12.1168	−1.99200	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	−11.4891	−1.71270
$46$	0	0
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	4.62772	0.602478	0.301239	−	0.953549i	$-0.402600\pi$
$59$	4.62772	0.602478	0.301239	+	0.953549i	$0.402600\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	2.11684	0.258614	0.129307	−	0.991605i	$-0.458725\pi$
$67$	2.11684	0.258614	0.129307	+	0.991605i	$0.458725\pi$
$68$	0	0
$69$	24.8614	2.99296
$70$	0	0
$71$	−12.8614	−1.52637	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	−12.8614	−1.52637	−0.763184	+	0.646181i	$0.776365\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	−10.5109	−1.21369
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	35.9783	3.99758
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	18.8614	1.99931	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	18.8614	1.99931	0.999653	+	0.0263586i	$0.00839118\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−20.6277	−2.13899
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0.116844	0.0118637	0.00593185	−	0.999982i	$-0.498112\pi$
$97$	0.116844	0.0118637	0.00593185	+	0.999982i	$0.498112\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	−40.8614	−3.87839
$112$	0	0
$113$	−13.3723	−1.25796	−0.628979	−	0.777422i	$-0.716527\pi$
$113$	−13.3723	−1.25796	−0.628979	+	0.777422i	$0.716527\pi$
$114$	0	0
$115$	−10.1168	−0.943401
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	0	0
$125$	11.1386	0.996266
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−24.8614	−2.13973
$136$	0	0
$137$	21.6060	1.84592	0.922961	−	0.384893i	$-0.125762\pi$
$137$	21.6060	1.84592	0.922961	+	0.384893i	$0.125762\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−40.4674	−3.40797
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−23.6060	−1.94699
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	8.39403	0.674225
$156$	0	0
$157$	20.1168	1.60550	0.802749	−	0.596316i	$-0.203370\pi$
$157$	20.1168	1.60550	0.802749	+	0.596316i	$0.203370\pi$
$158$	0	0
$159$	20.2337	1.60464
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	15.6060	1.17302
$178$	0	0
$179$	−24.8614	−1.85823	−0.929114	−	0.369792i	$-0.879429\pi$
$179$	−24.8614	−1.85823	−0.929114	+	0.369792i	$0.879429\pi$
$180$	0	0
$181$	3.88316	0.288633	0.144316	−	0.989532i	$-0.453902\pi$
$181$	3.88316	0.288633	0.144316	+	0.989532i	$0.453902\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	16.6277	1.22249
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	27.6060	1.99750	0.998749	−	0.0500060i	$-0.0159241\pi$
$191$	27.6060	1.99750	0.998749	+	0.0500060i	$0.0159241\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	0	0
$201$	7.13859	0.503518
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	61.7228	4.29003
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	−43.3723	−2.97182
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	26.3505	1.76456	0.882281	−	0.470723i	$-0.156007\pi$
$223$	26.3505	1.76456	0.882281	+	0.470723i	$0.156007\pi$
$224$	0	0
$225$	−26.0951	−1.73967
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	28.3505	1.87346	0.936728	−	0.350058i	$-0.113838\pi$
$229$	28.3505	1.87346	0.936728	+	0.350058i	$0.113838\pi$
$230$	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
$235$	16.4674	1.07421
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	66.9783	4.29666
$244$	0	0
$245$	9.60597	0.613703
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−0.861407	−0.0543715	−0.0271858	−	0.999630i	$-0.508655\pi$
$251$	−0.861407	−0.0543715	−0.0271858	+	0.999630i	$0.508655\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	−8.23369	−0.505791
$266$	0	0
$267$	63.6060	3.89262
$268$	0	0
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	−51.2119	−3.06598
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0.394031	0.0230985
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−6.35053	−0.369742
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	−13.4891	−0.767370
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	16.3505	0.924187	0.462093	−	0.886831i	$-0.347098\pi$
$313$	16.3505	0.924187	0.462093	+	0.886831i	$0.347098\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	33.6060	1.88750	0.943750	−	0.330661i	$-0.107272\pi$
$317$	33.6060	1.88750	0.943750	+	0.330661i	$0.107272\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	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
$331$	−26.1168	−1.43551	−0.717756	−	0.696295i	$-0.754831\pi$
$331$	−26.1168	−1.43551	−0.717756	+	0.696295i	$0.754831\pi$
$332$	0	0
$333$	−101.446	−5.55919
$334$	0	0
$335$	−2.90491	−0.158712
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	0	0
$339$	−45.0951	−2.44923
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−34.1168	−1.83679
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−27.0951	−1.44213	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	−27.0951	−1.44213	−0.721063	+	0.692869i	$0.756346\pi$
$354$	0	0
$355$	17.6495	0.936737
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	9.88316	0.515897	0.257948	−	0.966159i	$-0.416954\pi$
$367$	9.88316	0.515897	0.257948	+	0.966159i	$0.416954\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	37.5625	1.93972
$376$	0	0
$377$	0	0
$378$	0	0
$379$	38.3505	1.96993	0.984967	−	0.172741i	$-0.0552624\pi$
$379$	38.3505	1.96993	0.984967	+	0.172741i	$0.0552624\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−16.6277	−0.849637	−0.424818	−	0.905279i	$-0.639662\pi$
$383$	−16.6277	−0.849637	−0.424818	+	0.905279i	$0.639662\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	39.0951	1.98220	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	39.0951	1.98220	0.991100	+	0.133120i	$0.0424994\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−49.3723	−2.45333
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	72.8614	3.59399
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	0	0
$423$	−100.467	−4.88489
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−40.3505	−1.93912	−0.969561	−	0.244848i	$-0.921262\pi$
$433$	−40.3505	−1.93912	−0.969561	+	0.244848i	$0.921262\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−58.6060	−2.79076
$442$	0	0
$443$	21.0951	1.00226	0.501129	−	0.865373i	$-0.332918\pi$
$443$	21.0951	1.00226	0.501129	+	0.865373i	$0.332918\pi$
$444$	0	0
$445$	−25.8832	−1.22698
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−5.13859	−0.242505	−0.121253	−	0.992622i	$-0.538691\pi$
$449$	−5.13859	−0.242505	−0.121253	+	0.992622i	$0.538691\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	−10.3505	−0.481030	−0.240515	−	0.970645i	$-0.577316\pi$
$463$	−10.3505	−0.481030	−0.240515	+	0.970645i	$0.577316\pi$
$464$	0	0
$465$	28.3070	1.31271
$466$	0	0
$467$	−35.8397	−1.65846	−0.829231	−	0.558906i	$-0.811221\pi$
$467$	−35.8397	−1.65846	−0.829231	+	0.558906i	$0.811221\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	67.8397	3.12589
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	50.2337	2.30004
$478$	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
$484$	0	0
$485$	−0.160343	−0.00728079
$486$	0	0
$487$	−30.1168	−1.36472	−0.682362	−	0.731014i	$-0.739047\pi$
$487$	−30.1168	−1.36472	−0.682362	+	0.731014i	$0.739047\pi$
$488$	0	0
$489$	−53.9565	−2.44000
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−43.8397	−1.94699
$508$	0	0
$509$	25.3723	1.12461	0.562303	−	0.826931i	$-0.309915\pi$
$509$	25.3723	1.12461	0.562303	+	0.826931i	$0.309915\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	5.48913	0.241880
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−29.8397	−1.30730	−0.653650	−	0.756797i	$-0.726763\pi$
$521$	−29.8397	−1.30730	−0.653650	+	0.756797i	$0.726763\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	31.3505	1.36307
$530$	0	0
$531$	38.7446	1.68137
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−83.8397	−3.61795
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	13.0951	0.561964
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	56.0733	2.38018
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	18.3505	0.772013
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	93.0951	3.88910
$574$	0	0
$575$	−22.9783	−0.958259
$576$	0	0
$577$	32.1168	1.33704	0.668521	−	0.743693i	$-0.266928\pi$
$577$	32.1168	1.33704	0.668521	+	0.743693i	$0.266928\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−48.0000	−1.98117	−0.990586	−	0.136892i	$-0.956289\pi$
$587$	−48.0000	−1.98117	−0.990586	+	0.136892i	$0.956289\pi$
$588$	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
$597$	−67.4456	−2.76037
$598$	0	0
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	17.7228	0.721729
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	−42.5842	−1.71160	−0.855802	−	0.517303i	$-0.826936\pi$
$619$	−42.5842	−1.71160	−0.855802	+	0.517303i	$0.826936\pi$
$620$	0	0
$621$	133.562	5.35968
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0.298936	0.0119574
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−46.5842	−1.85449	−0.927244	−	0.374457i	$-0.877829\pi$
$631$	−46.5842	−1.85449	−0.927244	+	0.374457i	$0.877829\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−107.679	−4.25973
$640$	0	0
$641$	2.39403	0.0945585	0.0472793	−	0.998882i	$-0.484945\pi$
$641$	2.39403	0.0945585	0.0472793	+	0.998882i	$0.484945\pi$
$642$	0	0
$643$	−46.3505	−1.82789	−0.913943	−	0.405842i	$-0.866978\pi$
$643$	−46.3505	−1.82789	−0.913943	+	0.405842i	$0.866978\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−23.8397	−0.937234	−0.468617	−	0.883402i	$-0.655247\pi$
$647$	−23.8397	−0.937234	−0.468617	+	0.883402i	$0.655247\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−22.6277	−0.885491	−0.442746	−	0.896647i	$-0.645995\pi$
$653$	−22.6277	−0.885491	−0.442746	+	0.896647i	$0.645995\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	36.5842	1.42296	0.711481	−	0.702706i	$-0.248025\pi$
$661$	36.5842	1.42296	0.711481	+	0.702706i	$0.248025\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	88.8614	3.43558
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	−56.4674	−2.17343
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	0	0
$685$	−29.6495	−1.13285
$686$	0	0
$687$	95.6060	3.64760
$688$	0	0
$689$	0	0
$690$	0	0
$691$	34.5842	1.31565	0.657823	−	0.753173i	$-0.271478\pi$
$691$	34.5842	1.31565	0.657823	+	0.753173i	$0.271478\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	55.5326	2.09148
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−52.5842	−1.97484	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−52.5842	−1.97484	−0.987421	+	0.158114i	$0.949459\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−45.0951	−1.68882
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−11.1386	−0.415399	−0.207700	−	0.978193i	$-0.566598\pi$
$719$	−11.1386	−0.415399	−0.207700	+	0.978193i	$0.566598\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	17.8832	0.663250	0.331625	−	0.943411i	$-0.392403\pi$
$727$	17.8832	0.663250	0.331625	+	0.943411i	$0.392403\pi$
$728$	0	0
$729$	117.935	4.36795
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	32.3940	1.19487
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	54.5842	1.99181	0.995903	−	0.0904254i	$-0.0288227\pi$
$751$	54.5842	1.99181	0.995903	+	0.0904254i	$0.0288227\pi$
$752$	0	0
$753$	−2.90491	−0.105861
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−38.0000	−1.38113	−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000	−1.38113	−0.690567	+	0.723269i	$0.742639\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	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		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	60.7011	2.18610
$772$	0	0
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	0	0
$775$	19.0652	0.684844
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−27.6060	−0.985299
$786$	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
$792$	0	0
$793$	0	0
$794$	0	0
$795$	−27.7663	−0.984770
$796$	0	0
$797$	−47.3288	−1.67647	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	−47.3288	−1.67647	−0.838236	+	0.545308i	$0.816413\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	157.913	5.57958
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	101.168	3.56130
$808$	0	0
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	21.9565	0.769103
$816$	0	0
$817$	0	0
$818$	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
$823$	50.3505	1.75511	0.877555	−	0.479477i	$-0.159174\pi$
$823$	50.3505	1.75511	0.877555	+	0.479477i	$0.159174\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	28.5842	0.992771	0.496385	−	0.868102i	$-0.334660\pi$
$829$	28.5842	0.992771	0.496385	+	0.868102i	$0.334660\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−110.818	−3.83043
$838$	0	0
$839$	−9.09509	−0.313998	−0.156999	−	0.987599i	$-0.550182\pi$
$839$	−9.09509	−0.313998	−0.156999	+	0.987599i	$0.550182\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	17.8397	0.613703
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	−89.3288	−3.06215
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	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
$859$	58.5842	1.99887	0.999434	−	0.0336436i	$-0.0107111\pi$
$859$	58.5842	1.99887	0.999434	+	0.0336436i	$0.0107111\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−57.3288	−1.94699
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0.978251	0.0331088
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−42.8614	−1.44404	−0.722019	−	0.691873i	$-0.756786\pi$
$881$	−42.8614	−1.44404	−0.722019	+	0.691873i	$0.756786\pi$
$882$	0	0
$883$	−56.0000	−1.88455	−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000	−1.88455	−0.942275	+	0.334840i	$0.891318\pi$
$884$	0	0
$885$	−21.4158	−0.719884
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	34.1168	1.14040
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−5.32878	−0.177135
$906$	0	0
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−60.0000	−1.98789	−0.993944	−	0.109885i	$-0.964952\pi$
$911$	−60.0000	−1.98789	−0.993944	+	0.109885i	$0.964952\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	37.7663	1.24175
$926$	0	0
$927$	−33.4891	−1.09993
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−40.4674	−1.32484
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	0	0
$939$	55.1386	1.79938
$940$	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
$946$	0	0
$947$	−8.39403	−0.272769	−0.136385	−	0.990656i	$-0.543548\pi$
$947$	−8.39403	−0.272769	−0.136385	+	0.990656i	$0.543548\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	113.329	3.67494
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	−37.8832	−1.22587
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	6.41578	0.206961
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	59.8397	1.92035	0.960173	−	0.279406i	$-0.0901376\pi$
$971$	59.8397	1.92035	0.960173	+	0.279406i	$0.0901376\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−35.3288	−1.13027	−0.565134	−	0.824999i	$-0.691176\pi$
$977$	−35.3288	−1.13027	−0.565134	+	0.824999i	$0.691176\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−57.0951	−1.82105	−0.910525	−	0.413453i	$-0.864323\pi$
$983$	−57.0951	−1.82105	−0.910525	+	0.413453i	$0.864323\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	0	0
$993$	−88.0733	−2.79492
$994$	0	0
$995$	27.4456	0.870085
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	−219.519	−6.94527

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.a.d.1.2	✓	2
3.2	odd	2		4356.2.a.n.1.2		2
4.3	odd	2		1936.2.a.s.1.1		2
8.3	odd	2		7744.2.a.cn.1.2		2
8.5	even	2		7744.2.a.bx.1.1		2
11.2	odd	10		484.2.e.g.81.2		8
11.3	even	5		484.2.e.g.9.1		8
11.4	even	5		484.2.e.g.269.1		8
11.5	even	5		484.2.e.g.245.2		8
11.6	odd	10		484.2.e.g.245.2		8
11.7	odd	10		484.2.e.g.269.1		8
11.8	odd	10		484.2.e.g.9.1		8
11.9	even	5		484.2.e.g.81.2		8
11.10	odd	2	CM	484.2.a.d.1.2	✓	2
33.32	even	2		4356.2.a.n.1.2		2
44.43	even	2		1936.2.a.s.1.1		2
88.21	odd	2		7744.2.a.bx.1.1		2
88.43	even	2		7744.2.a.cn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
484.2.a.d.1.2	✓	2	1.1	even	1	trivial
484.2.a.d.1.2	✓	2	11.10	odd	2	CM
484.2.e.g.9.1		8	11.3	even	5
484.2.e.g.9.1		8	11.8	odd	10
484.2.e.g.81.2		8	11.2	odd	10
484.2.e.g.81.2		8	11.9	even	5
484.2.e.g.245.2		8	11.5	even	5
484.2.e.g.245.2		8	11.6	odd	10
484.2.e.g.269.1		8	11.4	even	5
484.2.e.g.269.1		8	11.7	odd	10
1936.2.a.s.1.1		2	4.3	odd	2
1936.2.a.s.1.1		2	44.43	even	2
4356.2.a.n.1.2		2	3.2	odd	2
4356.2.a.n.1.2		2	33.32	even	2
7744.2.a.bx.1.1		2	8.5	even	2
7744.2.a.bx.1.1		2	88.21	odd	2
7744.2.a.cn.1.2		2	8.3	odd	2
7744.2.a.cn.1.2		2	88.43	even	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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	484.2.a.d.1.2

Level	$484$
Weight	$2$
Character	484.1
Self dual	yes
Analytic conductor	$3.865$
Analytic rank	$0$
Dimension	$2$
CM discriminant	-11
Inner twists	$2$