LMFDB - Embedded newform 8281.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, 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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 637)
Fricke sign:	$1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{4} -3.60555 q^{5} -3.00000 q^{9} +O(q^{10})$	$q-2.00000 q^{4} -3.60555 q^{5} -3.00000 q^{9} +4.00000 q^{16} -3.60555 q^{19} +7.21110 q^{20} -1.00000 q^{23} +8.00000 q^{25} -5.00000 q^{29} +10.8167 q^{31} +6.00000 q^{36} -7.21110 q^{41} -9.00000 q^{43} +10.8167 q^{45} +3.60555 q^{47} +11.0000 q^{53} +14.4222 q^{59} -8.00000 q^{64} -10.8167 q^{73} +7.21110 q^{76} +15.0000 q^{79} -14.4222 q^{80} +9.00000 q^{81} +18.0278 q^{83} +3.60555 q^{89} +2.00000 q^{92} +13.0000 q^{95} +18.0278 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{4} - 6 q^{9}+O(q^{10}) $ 2 * q - 4 * q^4 - 6 * q^9	$ 2 q - 4 q^{4} - 6 q^{9} + 8 q^{16} - 2 q^{23} + 16 q^{25} - 10 q^{29} + 12 q^{36} - 18 q^{43} + 22 q^{53} - 16 q^{64} + 30 q^{79} + 18 q^{81} + 4 q^{92} + 26 q^{95}+O(q^{100}) $ 2 * q - 4 * q^4 - 6 * q^9 + 8 * q^16 - 2 * q^23 + 16 * q^25 - 10 * q^29 + 12 * q^36 - 18 * q^43 + 22 * q^53 - 16 * q^64 + 30 * q^79 + 18 * q^81 + 4 * q^92 + 26 * q^95

Display 100 coefficients 10 coefficients

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−2.00000	−1.00000
$5$	−3.60555	−1.61245	−0.806226	−	0.591608i	$-0.798493\pi$
$5$	−3.60555	−1.61245	−0.806226	+	0.591608i	$0.798493\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−3.60555	−0.827170	−0.413585	−	0.910465i	$-0.635724\pi$
$19$	−3.60555	−0.827170	−0.413585	+	0.910465i	$0.635724\pi$
$20$	7.21110	1.61245
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	8.00000	1.60000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	10.8167	1.94273	0.971364	−	0.237595i	$-0.0763593\pi$
$31$	10.8167	1.94273	0.971364	+	0.237595i	$0.0763593\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	6.00000	1.00000
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−7.21110	−1.12619	−0.563093	−	0.826394i	$-0.690389\pi$
$41$	−7.21110	−1.12619	−0.563093	+	0.826394i	$0.690389\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	0	0
$45$	10.8167	1.61245
$46$	0	0
$47$	3.60555	0.525924	0.262962	−	0.964806i	$-0.415301\pi$
$47$	3.60555	0.525924	0.262962	+	0.964806i	$0.415301\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	0	0
$53$	11.0000	1.51097	0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000	1.51097	0.755483	+	0.655168i	$0.227402\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	14.4222	1.87761	0.938806	−	0.344447i	$-0.111934\pi$
$59$	14.4222	1.87761	0.938806	+	0.344447i	$0.111934\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−10.8167	−1.26599	−0.632997	−	0.774154i	$-0.718175\pi$
$73$	−10.8167	−1.26599	−0.632997	+	0.774154i	$0.718175\pi$
$74$	0	0
$75$	0	0
$76$	7.21110	0.827170
$77$	0	0
$78$	0	0
$79$	15.0000	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$80$	−14.4222	−1.61245
$81$	9.00000	1.00000
$82$	0	0
$83$	18.0278	1.97880	0.989402	−	0.145204i	$-0.0463840\pi$
$83$	18.0278	1.97880	0.989402	+	0.145204i	$0.0463840\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	3.60555	0.382188	0.191094	−	0.981572i	$-0.438797\pi$
$89$	3.60555	0.382188	0.191094	+	0.981572i	$0.438797\pi$
$90$	0	0
$91$	0	0
$92$	2.00000	0.208514
$93$	0	0
$94$	0	0
$95$	13.0000	1.33377
$96$	0	0
$97$	18.0278	1.83044	0.915221	−	0.402953i	$-0.132016\pi$
$97$	18.0278	1.83044	0.915221	+	0.402953i	$0.132016\pi$
$98$	0	0
$99$	0	0
$100$	−16.0000	−1.60000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−19.0000	−1.78737	−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000	−1.78737	−0.893685	+	0.448695i	$0.851889\pi$
$114$	0	0
$115$	3.60555	0.336219
$116$	10.0000	0.928477
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	−21.6333	−1.94273
$125$	−10.8167	−0.967471
$126$	0	0
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	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
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−12.0000	−1.00000
$145$	18.0278	1.49712
$146$	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
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−39.0000	−3.13256
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	14.4222	1.12619
$165$	0	0
$166$	0	0
$167$	−18.0278	−1.39503	−0.697515	−	0.716570i	$-0.745711\pi$
$167$	−18.0278	−1.39503	−0.697515	+	0.716570i	$0.745711\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	10.8167	0.827170
$172$	18.0000	1.37249
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−25.0000	−1.86859	−0.934294	−	0.356504i	$-0.883969\pi$
$179$	−25.0000	−1.86859	−0.934294	+	0.356504i	$0.883969\pi$
$180$	−21.6333	−1.61245
$181$	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
$188$	−7.21110	−0.525924
$189$	0	0
$190$	0	0
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	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
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	26.0000	1.81592
$206$	0	0
$207$	3.00000	0.208514
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	−22.0000	−1.51097
$213$	0	0
$214$	0	0
$215$	32.4500	2.21307
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	18.0278	1.20723	0.603614	−	0.797277i	$-0.293727\pi$
$223$	18.0278	1.20723	0.603614	+	0.797277i	$0.293727\pi$
$224$	0	0
$225$	−24.0000	−1.60000
$226$	0	0
$227$	−14.4222	−0.957235	−0.478618	−	0.878023i	$-0.658862\pi$
$227$	−14.4222	−0.957235	−0.478618	+	0.878023i	$0.658862\pi$
$228$	0	0
$229$	−21.6333	−1.42957	−0.714785	−	0.699345i	$-0.753475\pi$
$229$	−21.6333	−1.42957	−0.714785	+	0.699345i	$0.753475\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−29.0000	−1.89985	−0.949927	−	0.312473i	$-0.898843\pi$
$233$	−29.0000	−1.89985	−0.949927	+	0.312473i	$0.898843\pi$
$234$	0	0
$235$	−13.0000	−0.848026
$236$	−28.8444	−1.87761
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−10.8167	−0.696762	−0.348381	−	0.937353i	$-0.613268\pi$
$241$	−10.8167	−0.696762	−0.348381	+	0.937353i	$0.613268\pi$
$242$	0	0
$243$	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		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	15.0000	0.928477
$262$	0	0
$263$	−31.0000	−1.91154	−0.955771	−	0.294112i	$-0.904976\pi$
$263$	−31.0000	−1.91154	−0.955771	+	0.294112i	$0.904976\pi$
$264$	0	0
$265$	−39.6611	−2.43636
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	28.8444	1.75217	0.876087	−	0.482154i	$-0.160145\pi$
$271$	28.8444	1.75217	0.876087	+	0.482154i	$0.160145\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	0	0
$279$	−32.4500	−1.94273
$280$	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	0
$292$	21.6333	1.26599
$293$	−18.0278	−1.05319	−0.526596	−	0.850115i	$-0.676532\pi$
$293$	−18.0278	−1.05319	−0.526596	+	0.850115i	$0.676532\pi$
$294$	0	0
$295$	−52.0000	−3.02756
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−14.4222	−0.827170
$305$	0	0
$306$	0	0
$307$	32.4500	1.85202	0.926009	−	0.377503i	$-0.123217\pi$
$307$	32.4500	1.85202	0.926009	+	0.377503i	$0.123217\pi$
$308$	0	0
$309$	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	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	−30.0000	−1.68763
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	28.8444	1.61245
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−18.0000	−1.00000
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	−36.0555	−1.97880
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−23.0000	−1.25289	−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000	−1.25289	−0.626445	+	0.779466i	$0.715491\pi$
$338$	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
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	32.4500	1.73701	0.868503	−	0.495683i	$-0.165082\pi$
$349$	32.4500	1.73701	0.868503	+	0.495683i	$0.165082\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	36.0555	1.91904	0.959521	−	0.281638i	$-0.0908778\pi$
$353$	36.0555	1.91904	0.959521	+	0.281638i	$0.0908778\pi$
$354$	0	0
$355$	0	0
$356$	−7.21110	−0.382188
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−6.00000	−0.315789
$362$	0	0
$363$	0	0
$364$	0	0
$365$	39.0000	2.04135
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−4.00000	−0.208514
$369$	21.6333	1.12619
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	−26.0000	−1.33377
$381$	0	0
$382$	0	0
$383$	−28.8444	−1.47388	−0.736940	−	0.675958i	$-0.763730\pi$
$383$	−28.8444	−1.47388	−0.736940	+	0.675958i	$0.763730\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	27.0000	1.37249
$388$	−36.0555	−1.83044
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−54.0833	−2.72122
$396$	0	0
$397$	3.60555	0.180957	0.0904787	−	0.995898i	$-0.471160\pi$
$397$	3.60555	0.180957	0.0904787	+	0.995898i	$0.471160\pi$
$398$	0	0
$399$	0	0
$400$	32.0000	1.60000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−32.4500	−1.61245
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−39.6611	−1.96111	−0.980557	−	0.196236i	$-0.937128\pi$
$409$	−39.6611	−1.96111	−0.980557	+	0.196236i	$0.937128\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−65.0000	−3.19072
$416$	0	0
$417$	0	0
$418$	0	0
$419$	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	$0.5\pi$
$422$	0	0
$423$	−10.8167	−0.525924
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−16.0000	−0.773389
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	3.60555	0.172477
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−41.0000	−1.94797	−0.973984	−	0.226615i	$-0.927234\pi$
$443$	−41.0000	−1.94797	−0.973984	+	0.226615i	$0.927234\pi$
$444$	0	0
$445$	−13.0000	−0.616259
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	0	0
$452$	38.0000	1.78737
$453$	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
$460$	−7.21110	−0.336219
$461$	−7.21110	−0.335855	−0.167927	−	0.985799i	$-0.553707\pi$
$461$	−7.21110	−0.335855	−0.167927	+	0.985799i	$0.553707\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	−20.0000	−0.928477
$465$	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
$473$	0	0
$474$	0	0
$475$	−28.8444	−1.32347
$476$	0	0
$477$	−33.0000	−1.51097
$478$	0	0
$479$	39.6611	1.81216	0.906080	−	0.423106i	$-0.139060\pi$
$479$	39.6611	1.81216	0.906080	+	0.423106i	$0.139060\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	22.0000	1.00000
$485$	−65.0000	−2.95150
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	40.0000	1.80517	0.902587	−	0.430507i	$-0.141665\pi$
$491$	40.0000	1.80517	0.902587	+	0.430507i	$0.141665\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	43.2666	1.94273
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	21.6333	0.967471
$501$	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
$507$	0	0
$508$	−24.0000	−1.06483
$509$	−3.60555	−0.159813	−0.0799066	−	0.996802i	$-0.525462\pi$
$509$	−3.60555	−0.159813	−0.0799066	+	0.996802i	$0.525462\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	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
$529$	−22.0000	−0.956522
$530$	0	0
$531$	−43.2666	−1.87761
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−28.8444	−1.24705
$536$	0	0
$537$	0	0
$538$	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
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	37.0000	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	18.0278	0.768008
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	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
$565$	68.5055	2.88205
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−1.00000	−0.0419222	−0.0209611	−	0.999780i	$-0.506673\pi$
$569$	−1.00000	−0.0419222	−0.0209611	+	0.999780i	$0.506673\pi$
$570$	0	0
$571$	3.00000	0.125546	0.0627730	−	0.998028i	$-0.480006\pi$
$571$	3.00000	0.125546	0.0627730	+	0.998028i	$0.480006\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−8.00000	−0.333623
$576$	24.0000	1.00000
$577$	36.0555	1.50101	0.750505	−	0.660864i	$-0.229810\pi$
$577$	36.0555	1.50101	0.750505	+	0.660864i	$0.229810\pi$
$578$	0	0
$579$	0	0
$580$	−36.0555	−1.49712
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	18.0278	0.744085	0.372043	−	0.928216i	$-0.378658\pi$
$587$	18.0278	0.744085	0.372043	+	0.928216i	$0.378658\pi$
$588$	0	0
$589$	−39.0000	−1.60697
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−46.8722	−1.92481	−0.962405	−	0.271620i	$-0.912441\pi$
$593$	−46.8722	−1.92481	−0.962405	+	0.271620i	$0.912441\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	11.0000	0.449448	0.224724	−	0.974422i	$-0.427852\pi$
$599$	11.0000	0.449448	0.224724	+	0.974422i	$0.427852\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	39.6611	1.61245
$606$	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
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	0	0
$619$	14.4222	0.579677	0.289839	−	0.957076i	$-0.406398\pi$
$619$	14.4222	0.579677	0.289839	+	0.957076i	$0.406398\pi$
$620$	78.0000	3.13256
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.00000	−0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	−43.2666	−1.71698
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	17.0000	0.671460	0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000	0.671460	0.335730	+	0.941958i	$0.391017\pi$
$642$	0	0
$643$	43.2666	1.70627	0.853134	−	0.521691i	$-0.174699\pi$
$643$	43.2666	1.70627	0.853134	+	0.521691i	$0.174699\pi$
$644$	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
$653$	−34.0000	−1.33052	−0.665261	−	0.746611i	$-0.731680\pi$
$653$	−34.0000	−1.33052	−0.665261	+	0.746611i	$0.731680\pi$
$654$	0	0
$655$	0	0
$656$	−28.8444	−1.12619
$657$	32.4500	1.26599
$658$	0	0
$659$	−19.0000	−0.740135	−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000	−0.740135	−0.370067	+	0.929005i	$0.620665\pi$
$660$	0	0
$661$	−10.8167	−0.420719	−0.210360	−	0.977624i	$-0.567463\pi$
$661$	−10.8167	−0.420719	−0.210360	+	0.977624i	$0.567463\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	5.00000	0.193601
$668$	36.0555	1.39503
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−51.0000	−1.96591	−0.982953	−	0.183858i	$-0.941141\pi$
$673$	−51.0000	−1.96591	−0.982953	+	0.183858i	$0.941141\pi$
$674$	0	0
$675$	0	0
$676$	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
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	−21.6333	−0.827170
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−36.0000	−1.37249
$689$	0	0
$690$	0	0
$691$	46.8722	1.78310	0.891551	−	0.452921i	$-0.149618\pi$
$691$	46.8722	1.78310	0.891551	+	0.452921i	$0.149618\pi$
$692$	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
$701$	−23.0000	−0.868698	−0.434349	−	0.900745i	$-0.643022\pi$
$701$	−23.0000	−0.868698	−0.434349	+	0.900745i	$0.643022\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	−45.0000	−1.68763
$712$	0	0
$713$	−10.8167	−0.405087
$714$	0	0
$715$	0	0
$716$	50.0000	1.86859
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	43.2666	1.61245
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−40.0000	−1.48556
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−54.0833	−1.99761	−0.998806	−	0.0488615i	$-0.984441\pi$
$733$	−54.0833	−1.99761	−0.998806	+	0.0488615i	$0.984441\pi$
$734$	0	0
$735$	0	0
$736$	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
$747$	−54.0833	−1.97880
$748$	0	0
$749$	0	0
$750$	0	0
$751$	27.0000	0.985244	0.492622	−	0.870243i	$-0.336039\pi$
$751$	27.0000	0.985244	0.492622	+	0.870243i	$0.336039\pi$
$752$	14.4222	0.525924
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−47.0000	−1.70824	−0.854122	−	0.520073i	$-0.825905\pi$
$757$	−47.0000	−1.70824	−0.854122	+	0.520073i	$0.825905\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−46.8722	−1.69911	−0.849557	−	0.527496i	$-0.823131\pi$
$761$	−46.8722	−1.69911	−0.849557	+	0.527496i	$0.823131\pi$
$762$	0	0
$763$	0	0
$764$	40.0000	1.44715
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−32.4500	−1.17018	−0.585088	−	0.810970i	$-0.698940\pi$
$769$	−32.4500	−1.17018	−0.585088	+	0.810970i	$0.698940\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	36.0555	1.29683	0.648413	−	0.761288i	$-0.275433\pi$
$773$	36.0555	1.29683	0.648413	+	0.761288i	$0.275433\pi$
$774$	0	0
$775$	86.5332	3.10837
$776$	0	0
$777$	0	0
$778$	0	0
$779$	26.0000	0.931547
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	39.6611	1.41376	0.706882	−	0.707331i	$-0.250101\pi$
$787$	39.6611	1.41376	0.706882	+	0.707331i	$0.250101\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−10.8167	−0.382188
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−31.0000	−1.08990	−0.544951	−	0.838468i	$-0.683452\pi$
$809$	−31.0000	−1.08990	−0.544951	+	0.838468i	$0.683452\pi$
$810$	0	0
$811$	43.2666	1.51930	0.759648	−	0.650334i	$-0.225371\pi$
$811$	43.2666	1.51930	0.759648	+	0.650334i	$0.225371\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	32.4500	1.13528
$818$	0	0
$819$	0	0
$820$	−52.0000	−1.81592
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	−6.00000	−0.208514
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	65.0000	2.24942
$836$	0	0
$837$	0	0
$838$	0	0
$839$	57.6888	1.99164	0.995820	−	0.0913415i	$-0.0291155\pi$
$839$	57.6888	1.99164	0.995820	+	0.0913415i	$0.0291155\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	0	0
$844$	10.0000	0.344214
$845$	0	0
$846$	0	0
$847$	0	0
$848$	44.0000	1.51097
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−18.0278	−0.617259	−0.308629	−	0.951182i	$-0.599870\pi$
$853$	−18.0278	−0.617259	−0.308629	+	0.951182i	$0.599870\pi$
$854$	0	0
$855$	−39.0000	−1.33377
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	−64.8999	−2.21307
$861$	0	0
$862$	0	0
$863$	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
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−54.0833	−1.83044
$874$	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
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	0	0
$885$	0	0
$886$	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
$892$	−36.0555	−1.20723
$893$	−13.0000	−0.435028
$894$	0	0
$895$	90.1388	3.01301
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−54.0833	−1.80378
$900$	48.0000	1.60000
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−53.0000	−1.75984	−0.879918	−	0.475125i	$-0.842403\pi$
$907$	−53.0000	−1.75984	−0.879918	+	0.475125i	$0.842403\pi$
$908$	28.8444	0.957235
$909$	0	0
$910$	0	0
$911$	37.0000	1.22586	0.612932	−	0.790135i	$-0.289990\pi$
$911$	37.0000	1.22586	0.612932	+	0.790135i	$0.289990\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	43.2666	1.42957
$917$	0	0
$918$	0	0
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	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
$929$	−3.60555	−0.118294	−0.0591472	−	0.998249i	$-0.518838\pi$
$929$	−3.60555	−0.118294	−0.0591472	+	0.998249i	$0.518838\pi$
$930$	0	0
$931$	0	0
$932$	58.0000	1.89985
$933$	0	0
$934$	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
$939$	0	0
$940$	26.0000	0.848026
$941$	61.2944	1.99814	0.999070	−	0.0431245i	$-0.0137312\pi$
$941$	61.2944	1.99814	0.999070	+	0.0431245i	$0.0137312\pi$
$942$	0	0
$943$	7.21110	0.234826
$944$	57.6888	1.87761
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	61.0000	1.97598	0.987992	−	0.154506i	$-0.0493785\pi$
$953$	61.0000	1.97598	0.987992	+	0.154506i	$0.0493785\pi$
$954$	0	0
$955$	72.1110	2.33346
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	86.0000	2.77419
$962$	0	0
$963$	−24.0000	−0.773389
$964$	21.6333	0.696762
$965$	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
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−61.2944	−1.95499	−0.977493	−	0.210966i	$-0.932339\pi$
$983$	−61.2944	−1.95499	−0.977493	+	0.210966i	$0.932339\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	9.00000	0.286183
$990$	0	0
$991$	60.0000	1.90596	0.952981	−	0.303029i	$-0.0979978\pi$
$991$	60.0000	1.90596	0.952981	+	0.303029i	$0.0979978\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.u.1.1		2
7.6	odd	2	inner	8281.2.a.u.1.2		2
13.5	odd	4		637.2.c.b.246.2	yes	2
13.8	odd	4		637.2.c.b.246.1	✓	2
13.12	even	2	inner	8281.2.a.u.1.2		2
91.5	even	12		637.2.r.b.116.1		4
91.18	odd	12		637.2.r.b.324.1		4
91.31	even	12		637.2.r.b.324.2		4
91.34	even	4		637.2.c.b.246.2	yes	2
91.44	odd	12		637.2.r.b.116.2		4
91.47	even	12		637.2.r.b.116.2		4
91.60	odd	12		637.2.r.b.324.2		4
91.73	even	12		637.2.r.b.324.1		4
91.83	even	4		637.2.c.b.246.1	✓	2
91.86	odd	12		637.2.r.b.116.1		4
91.90	odd	2	CM	8281.2.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.b.246.1	✓	2	13.8	odd	4
637.2.c.b.246.1	✓	2	91.83	even	4
637.2.c.b.246.2	yes	2	13.5	odd	4
637.2.c.b.246.2	yes	2	91.34	even	4
637.2.r.b.116.1		4	91.5	even	12
637.2.r.b.116.1		4	91.86	odd	12
637.2.r.b.116.2		4	91.44	odd	12
637.2.r.b.116.2		4	91.47	even	12
637.2.r.b.324.1		4	91.18	odd	12
637.2.r.b.324.1		4	91.73	even	12
637.2.r.b.324.2		4	91.31	even	12
637.2.r.b.324.2		4	91.60	odd	12
8281.2.a.u.1.1		2	1.1	even	1	trivial
8281.2.a.u.1.1		2	91.90	odd	2	CM
8281.2.a.u.1.2		2	7.6	odd	2	inner
8281.2.a.u.1.2		2	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{4} -3.60555 q^{5} -3.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{4} -3.60555 q^{5} -3.00000 q^{9} +4.00000 q^{16} -3.60555 q^{19} +7.21110 q^{20} -1.00000 q^{23} +8.00000 q^{25} -5.00000 q^{29} +10.8167 q^{31} +6.00000 q^{36} -7.21110 q^{41} -9.00000 q^{43} +10.8167 q^{45} +3.60555 q^{47} +11.0000 q^{53} +14.4222 q^{59} -8.00000 q^{64} -10.8167 q^{73} +7.21110 q^{76} +15.0000 q^{79} -14.4222 q^{80} +9.00000 q^{81} +18.0278 q^{83} +3.60555 q^{89} +2.00000 q^{92} +13.0000 q^{95} +18.0278 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{4} - 6 q^{9}+O(q^{10}) \) 2 * q - 4 * q^4 - 6 * q^9	\( 2 q - 4 q^{4} - 6 q^{9} + 8 q^{16} - 2 q^{23} + 16 q^{25} - 10 q^{29} + 12 q^{36} - 18 q^{43} + 22 q^{53} - 16 q^{64} + 30 q^{79} + 18 q^{81} + 4 q^{92} + 26 q^{95}+O(q^{100}) \) 2 * q - 4 * q^4 - 6 * q^9 + 8 * q^16 - 2 * q^23 + 16 * q^25 - 10 * q^29 + 12 * q^36 - 18 * q^43 + 22 * q^53 - 16 * q^64 + 30 * q^79 + 18 * q^81 + 4 * q^92 + 26 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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