LMFDB - Embedded newform 2736.2.k.p.2431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(2431,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2736.2431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.k (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:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2702336256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 $ x^8 + 9x^6 + 56x^4 + 225*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			2431.6
Root			$1.52274 - 1.63746i$ of defining polynomial
Character	$\chi$	$=$	2736.2431
Dual form			2736.2.k.p.2431.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.31342 q^{5} +4.77753i q^{7} +O(q^{10})$	$q+1.31342 q^{5} +4.77753i q^{7} -6.27492i q^{11} -8.24163 q^{17} +4.35890i q^{19} +4.00000i q^{23} -3.27492 q^{25} +6.27492i q^{35} +7.40437i q^{43} +10.2749i q^{47} -15.8248 q^{49} -8.24163i q^{55} +3.72508 q^{61} -16.8248 q^{73} +29.9786 q^{77} -16.0000i q^{83} -10.8248 q^{85} +5.72508i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{25} - 36 q^{49} + 60 q^{61} - 44 q^{73} + 4 q^{85}+O(q^{100}) $ 8 * q + 4 * q^25 - 36 * q^49 + 60 * q^61 - 44 * q^73 + 4 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	1.31342	0.587381	0.293691	−	0.955901i	$-0.405116\pi$
$5$	1.31342	0.587381	0.293691	+	0.955901i	$0.405116\pi$
$6$	0	0
$7$	4.77753i	1.80573i	0.429919	+	0.902867i	$0.358542\pi$
$7$	4.77753i	1.80573i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 6.27492i	− 1.89196i	−0.324227	−	0.945979i	$-0.605104\pi$
$11$	− 6.27492i	− 1.89196i	0.324227	−	0.945979i	$-0.394896\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−8.24163	−1.99889	−0.999444	−	0.0333386i	$-0.989386\pi$
$17$	−8.24163	−1.99889	−0.999444	+	0.0333386i	$0.989386\pi$
$18$	0	0
$19$	4.35890i	1.00000i
$19$	4.35890i	1.00000i
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.00000i	0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$	4.00000i	0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	0	0
$25$	−3.27492	−0.654983
$26$	0	0
$27$	0	0
$28$	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	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	6.27492i	1.06065i
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	7.40437i	1.12916i	0.825380	+	0.564578i	$0.190961\pi$
$43$	7.40437i	1.12916i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	10.2749i	1.49875i	0.662145	+	0.749375i	$0.269646\pi$
$47$	10.2749i	1.49875i	−0.662145	+	0.749375i	$0.730354\pi$
$48$	0	0
$49$	−15.8248	−2.26068
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	− 8.24163i	− 1.11130i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	3.72508	0.476948	0.238474	−	0.971149i	$-0.423353\pi$
$61$	3.72508	0.476948	0.238474	+	0.971149i	$0.423353\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	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
$73$	−16.8248	−1.96919	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−16.8248	−1.96919	−0.984594	+	0.174855i	$0.944054\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	29.9786	3.41638
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 16.0000i	− 1.75623i	−0.478451	−	0.878114i	$-0.658802\pi$
$83$	− 16.0000i	− 1.75623i	0.478451	−	0.878114i	$-0.341198\pi$
$84$	0	0
$85$	−10.8248	−1.17411
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	5.72508i	0.587381i
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−17.4356	−1.73491	−0.867453	−	0.497519i	$-0.834245\pi$
$101$	−17.4356	−1.73491	−0.867453	+	0.497519i	$0.834245\pi$
$102$	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
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	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
$115$	5.25370i	0.489910i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	− 39.3746i	− 3.60946i
$120$	0	0
$121$	−28.3746	−2.57951
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−10.8685	−0.972106
$126$	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
$131$	15.3746i	1.34328i	0.740876	+	0.671642i	$0.234411\pi$
$131$	15.3746i	1.34328i	−0.740876	+	0.671642i	$0.765589\pi$
$132$	0	0
$133$	−20.8248	−1.80573
$134$	0	0
$135$	0	0
$136$	0	0
$137$	22.0980	1.88796	0.943981	−	0.329999i	$-0.107048\pi$
$137$	22.0980	1.88796	0.943981	+	0.329999i	$0.107048\pi$
$138$	0	0
$139$	3.10302i	0.263195i	0.991303	+	0.131597i	$0.0420106\pi$
$139$	3.10302i	0.263195i	−0.991303	+	0.131597i	$0.957989\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−20.4235	−1.67316	−0.836580	−	0.547844i	$-0.815449\pi$
$149$	−20.4235	−1.67316	−0.836580	+	0.547844i	$0.815449\pi$
$150$	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
$155$	0	0
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−19.1101	−1.50609
$162$	0	0
$163$	8.71780i	0.682831i	0.939913	+	0.341415i	$0.110906\pi$
$163$	8.71780i	0.682831i	−0.939913	+	0.341415i	$0.889094\pi$
$164$	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	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	− 15.6460i	− 1.18273i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	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
$187$	51.7155i	3.78181i
$188$	0	0
$189$	0	0
$190$	0	0
$191$	27.3746i	1.98076i	0.138390	+	0.990378i	$0.455807\pi$
$191$	27.3746i	1.98076i	−0.138390	+	0.990378i	$0.544193\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	17.4356	1.24223	0.621117	−	0.783718i	$-0.286679\pi$
$197$	17.4356	1.24223	0.621117	+	0.783718i	$0.286679\pi$
$198$	0	0
$199$	28.1890i	1.99826i	0.0416556	+	0.999132i	$0.486737\pi$
$199$	28.1890i	1.99826i	−0.0416556	+	0.999132i	$0.513263\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	27.3517	1.89196
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	9.72508i	0.663245i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−29.3746	−1.94113	−0.970564	−	0.240845i	$-0.922576\pi$
$229$	−29.3746	−1.94113	−0.970564	+	0.240845i	$0.922576\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	16.1222	1.05620	0.528099	−	0.849183i	$-0.322905\pi$
$233$	16.1222	1.05620	0.528099	+	0.849183i	$0.322905\pi$
$234$	0	0
$235$	13.4953i	0.880338i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 23.9244i	− 1.54754i	−0.633465	−	0.773771i	$-0.718368\pi$
$239$	− 23.9244i	− 1.54754i	0.633465	−	0.773771i	$-0.281632\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−20.7846	−1.32788
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 7.37459i	− 0.465480i	−0.972539	−	0.232740i	$-0.925231\pi$
$251$	− 7.37459i	− 0.465480i	0.972539	−	0.232740i	$-0.0747691\pi$
$252$	0	0
$253$	25.0997	1.57800
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	31.9244i	1.96854i	0.176659	+	0.984272i	$0.443471\pi$
$263$	31.9244i	1.96854i	−0.176659	+	0.984272i	$0.556529\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	− 26.1534i	− 1.58871i	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	− 26.1534i	− 1.58871i	0.607457	−	0.794353i	$-0.292190\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	20.5498i	1.23920i
$276$	0	0
$277$	−20.2749	−1.21820	−0.609101	−	0.793093i	$-0.708470\pi$
$277$	−20.2749	−1.21820	−0.609101	+	0.793093i	$0.708470\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	− 20.3084i	− 1.20721i	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	− 20.3084i	− 1.20721i	0.797283	−	0.603606i	$-0.206270\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	50.9244	2.99555
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−35.3746	−2.03896
$302$	0	0
$303$	0	0
$304$	0	0
$305$	4.89261	0.280150
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	− 13.7251i	− 0.778278i	−0.921179	−	0.389139i	$-0.872773\pi$
$311$	− 13.7251i	− 0.778278i	0.921179	−	0.389139i	$-0.127227\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	− 35.9244i	− 1.99889i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−49.0887	−2.70635
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	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
$343$	− 42.1605i	− 2.27645i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	22.2749i	1.19578i	0.801578	+	0.597890i	$0.203994\pi$
$347$	22.2749i	1.19578i	−0.801578	+	0.597890i	$0.796006\pi$
$348$	0	0
$349$	−28.8248	−1.54295	−0.771477	−	0.636257i	$-0.780482\pi$
$349$	−28.8248	−1.54295	−0.771477	+	0.636257i	$0.780482\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−34.8712	−1.85601	−0.928003	−	0.372572i	$-0.878476\pi$
$353$	−34.8712	−1.85601	−0.928003	+	0.372572i	$0.878476\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	3.37459i	0.178104i	0.996027	+	0.0890519i	$0.0283837\pi$
$359$	3.37459i	0.178104i	−0.996027	+	0.0890519i	$0.971616\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−22.0980	−1.15666
$366$	0	0
$367$	− 26.1534i	− 1.36520i	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	− 26.1534i	− 1.36520i	0.730794	−	0.682598i	$-0.239150\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	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		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	39.3746	2.00671
$386$	0	0
$387$	0	0
$388$	0	0
$389$	36.9068	1.87125	0.935624	−	0.352998i	$-0.114838\pi$
$389$	36.9068	1.87125	0.935624	+	0.352998i	$0.114838\pi$
$390$	0	0
$391$	− 32.9665i	− 1.66719i
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	30.4743	1.52946	0.764730	−	0.644351i	$-0.222873\pi$
$397$	30.4743	1.52946	0.764730	+	0.644351i	$0.222873\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	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
$415$	− 21.0148i	− 1.03158i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 40.0000i	− 1.95413i	−0.212946	−	0.977064i	$-0.568306\pi$
$419$	− 40.0000i	− 1.95413i	0.212946	−	0.977064i	$-0.431694\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	26.9906	1.30924
$426$	0	0
$427$	17.7967i	0.861242i
$428$	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
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−17.4356	−0.834058
$438$	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
$443$	− 11.9244i	− 0.566546i	−0.959039	−	0.283273i	$-0.908580\pi$
$443$	− 11.9244i	− 0.566546i	0.959039	−	0.283273i	$-0.0914203\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	42.4743	1.98686	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	42.4743	1.98686	0.993431	+	0.114433i	$0.0365053\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	21.1457	0.984853	0.492427	−	0.870354i	$-0.336110\pi$
$461$	21.1457	0.984853	0.492427	+	0.870354i	$0.336110\pi$
$462$	0	0
$463$	42.0454i	1.95401i	0.213205	+	0.977007i	$0.431610\pi$
$463$	42.0454i	1.95401i	−0.213205	+	0.977007i	$0.568390\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	17.7251i	0.820219i	0.912036	+	0.410110i	$0.134510\pi$
$467$	17.7251i	0.820219i	−0.912036	+	0.410110i	$0.865490\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	46.4618	2.13632
$474$	0	0
$475$	− 14.2750i	− 0.654983i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	− 4.00000i	− 0.182765i	−0.995816	−	0.0913823i	$-0.970871\pi$
$479$	− 4.00000i	− 0.182765i	0.995816	−	0.0913823i	$-0.0291285\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	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
$491$	− 8.00000i	− 0.361035i	−0.983572	−	0.180517i	$-0.942223\pi$
$491$	− 8.00000i	− 0.361035i	0.983572	−	0.180517i	$-0.0577772\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	44.6722i	1.99980i	0.0139987	+	0.999902i	$0.495544\pi$
$499$	44.6722i	1.99980i	−0.0139987	+	0.999902i	$0.504456\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	− 44.0000i	− 1.96186i	−0.194354	−	0.980932i	$-0.562261\pi$
$503$	− 44.0000i	− 1.96186i	0.194354	−	0.980932i	$-0.437739\pi$
$504$	0	0
$505$	−22.9003	−1.01905
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	− 80.3807i	− 3.55583i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	64.4743	2.83557
$518$	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		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	7.00000	0.304348
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	99.2990i	4.27711i
$540$	0	0
$541$	46.4743	1.99808	0.999042	−	0.0437584i	$-0.0139332\pi$
$541$	46.4743	1.99808	0.999042	+	0.0437584i	$0.0139332\pi$
$542$	0	0
$543$	0	0
$544$	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
$555$	0	0
$556$	0	0
$557$	42.8826	1.81700	0.908498	−	0.417889i	$-0.137230\pi$
$557$	42.8826	1.81700	0.908498	+	0.417889i	$0.137230\pi$
$558$	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
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	26.1534i	1.09449i	0.836974	+	0.547243i	$0.184323\pi$
$571$	26.1534i	1.09449i	−0.836974	+	0.547243i	$0.815677\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	− 13.0997i	− 0.546294i
$576$	0	0
$577$	43.0241	1.79112	0.895558	−	0.444945i	$-0.146777\pi$
$577$	43.0241	1.79112	0.895558	+	0.444945i	$0.146777\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	76.4404	3.17128
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	45.0241i	1.85834i	0.369649	+	0.929172i	$0.379478\pi$
$587$	45.0241i	1.85834i	−0.369649	+	0.929172i	$0.620522\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−34.8712	−1.43199	−0.715994	−	0.698106i	$-0.754026\pi$
$593$	−34.8712	−1.43199	−0.715994	+	0.698106i	$0.754026\pi$
$594$	0	0
$595$	− 51.7155i	− 2.12013i
$596$	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			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−37.2679	−1.51515
$606$	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
$613$	45.9244	1.85487	0.927435	−	0.373985i	$-0.122009\pi$
$613$	45.9244	1.85487	0.927435	+	0.373985i	$0.122009\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−35.2323	−1.41840	−0.709199	−	0.705008i	$-0.750943\pi$
$617$	−35.2323	−1.41840	−0.709199	+	0.705008i	$0.750943\pi$
$618$	0	0
$619$	43.5890i	1.75199i	0.482321	+	0.875995i	$0.339794\pi$
$619$	43.5890i	1.75199i	−0.482321	+	0.875995i	$0.660206\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	2.09967	0.0839868
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	− 10.9836i	− 0.437249i	−0.975809	−	0.218624i	$-0.929843\pi$
$631$	− 10.9836i	− 0.437249i	0.975809	−	0.218624i	$-0.0701569\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	48.9736i	1.93133i	0.259791	+	0.965665i	$0.416346\pi$
$643$	48.9736i	1.93133i	−0.259791	+	0.965665i	$0.583654\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	33.0241i	1.29831i	0.760656	+	0.649155i	$0.224878\pi$
$647$	33.0241i	1.29831i	−0.760656	+	0.649155i	$0.775122\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−50.7632	−1.98652	−0.993259	−	0.115920i	$-0.963018\pi$
$653$	−50.7632	−1.98652	−0.993259	+	0.115920i	$0.963018\pi$
$654$	0	0
$655$	20.1934i	0.789020i
$656$	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
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−27.3517	−1.06065
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	− 23.3746i	− 0.902366i
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	29.0241	1.10895
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	− 49.9259i	− 1.89927i	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	− 49.9259i	− 1.89927i	0.313355	−	0.949636i	$-0.398547\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	4.07558i	0.154596i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	17.4356	0.658533	0.329267	−	0.944237i	$-0.393198\pi$
$701$	17.4356	0.658533	0.329267	+	0.944237i	$0.393198\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 83.2990i	− 3.13278i
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	− 43.3746i	− 1.61760i	−0.588084	−	0.808800i	$-0.700118\pi$
$719$	− 43.3746i	− 1.61760i	0.588084	−	0.808800i	$-0.299882\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	12.4279i	0.460925i	0.973081	+	0.230463i	$0.0740239\pi$
$727$	12.4279i	0.460925i	−0.973081	+	0.230463i	$0.925976\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	− 61.0241i	− 2.25706i
$732$	0	0
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	− 54.2273i	− 1.99478i	−0.0721811	−	0.997392i	$-0.522996\pi$
$739$	− 54.2273i	− 1.99478i	0.0721811	−	0.997392i	$-0.477004\pi$
$740$	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
$745$	−26.8248	−0.982783
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	55.0241	1.99988	0.999942	−	0.0107448i	$-0.00342025\pi$
$757$	55.0241	1.99988	0.999942	+	0.0107448i	$0.00342025\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−49.8108	−1.80564	−0.902821	−	0.430017i	$-0.858508\pi$
$761$	−49.8108	−1.80564	−0.902821	+	0.430017i	$0.858508\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	6.62541	0.238919	0.119459	−	0.992839i	$-0.461884\pi$
$769$	6.62541	0.238919	0.119459	+	0.992839i	$0.461884\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	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
$785$	23.6416	0.843806
$786$	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
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	− 84.6820i	− 2.99584i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	105.574i	3.72562i
$804$	0	0
$805$	−25.0997	−0.884647
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−24.0027	−0.843891	−0.421945	−	0.906621i	$-0.638653\pi$
$809$	−24.0027	−0.843891	−0.421945	+	0.906621i	$0.638653\pi$
$810$	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
$815$	11.4502i	0.401082i
$816$	0	0
$817$	−32.2749	−1.12916
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−35.0021	−1.22158	−0.610791	−	0.791792i	$-0.709148\pi$
$821$	−35.0021	−1.22158	−0.610791	+	0.791792i	$0.709148\pi$
$822$	0	0
$823$	20.5386i	0.715931i	0.933735	+	0.357966i	$0.116529\pi$
$823$	20.5386i	0.715931i	−0.933735	+	0.357966i	$0.883471\pi$
$824$	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
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	130.422	4.51884
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	29.0000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	17.0745	0.587381
$846$	0	0
$847$	− 135.560i	− 4.65791i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	41.3232i	1.40993i	0.709242	+	0.704965i	$0.249037\pi$
$859$	41.3232i	1.40993i	−0.709242	+	0.704965i	$0.750963\pi$
$860$	0	0
$861$	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
$873$	0	0
$874$	0	0
$875$	− 51.9244i	− 1.75537i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	6.33694	0.213497	0.106749	−	0.994286i	$-0.465956\pi$
$881$	6.33694	0.213497	0.106749	+	0.994286i	$0.465956\pi$
$882$	0	0
$883$	28.9111i	0.972938i	0.873698	+	0.486469i	$0.161715\pi$
$883$	28.9111i	0.972938i	−0.873698	+	0.486469i	$0.838285\pi$
$884$	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
$892$	0	0
$893$	−44.7873	−1.49875
$894$	0	0
$895$	0	0
$896$	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
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	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
$913$	−100.399	−3.32271
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−73.4525	−2.42561
$918$	0	0
$919$	− 8.71780i	− 0.287574i	−0.989609	−	0.143787i	$-0.954072\pi$
$919$	− 8.71780i	− 0.287574i	0.989609	−	0.143787i	$-0.0459280\pi$
$920$	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
$929$	34.8712	1.14409	0.572043	−	0.820223i	$-0.306151\pi$
$929$	34.8712	1.14409	0.572043	+	0.820223i	$0.306151\pi$
$930$	0	0
$931$	− 68.9785i	− 2.26068i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	67.9244i	2.22137i
$936$	0	0
$937$	10.4743	0.342179	0.171089	−	0.985255i	$-0.445271\pi$
$937$	10.4743	0.342179	0.171089	+	0.985255i	$0.445271\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	− 8.00000i	− 0.259965i	−0.991516	−	0.129983i	$-0.958508\pi$
$947$	− 8.00000i	− 0.259965i	0.991516	−	0.129983i	$-0.0414921\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	35.9544i	1.16346i
$956$	0	0
$957$	0	0
$958$	0	0
$959$	105.574i	3.40916i
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	61.0246i	1.96242i	0.192947	+	0.981209i	$0.438195\pi$
$967$	61.0246i	1.96242i	−0.192947	+	0.981209i	$0.561805\pi$
$968$	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
$973$	−14.8248	−0.475260
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	22.9003	0.729665
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−29.6175	−0.941782
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	37.0241i	1.17374i
$996$	0	0
$997$	27.7251	0.878062	0.439031	−	0.898472i	$-0.355322\pi$
$997$	27.7251	0.878062	0.439031	+	0.898472i	$0.355322\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.k.p.2431.6	yes	8
3.2	odd	2	inner	2736.2.k.p.2431.4	yes	8
4.3	odd	2	inner	2736.2.k.p.2431.5	yes	8
12.11	even	2	inner	2736.2.k.p.2431.3	✓	8
19.18	odd	2	CM	2736.2.k.p.2431.6	yes	8
57.56	even	2	inner	2736.2.k.p.2431.4	yes	8
76.75	even	2	inner	2736.2.k.p.2431.5	yes	8
228.227	odd	2	inner	2736.2.k.p.2431.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2736.2.k.p.2431.3	✓	8	12.11	even	2	inner
2736.2.k.p.2431.3	✓	8	228.227	odd	2	inner
2736.2.k.p.2431.4	yes	8	3.2	odd	2	inner
2736.2.k.p.2431.4	yes	8	57.56	even	2	inner
2736.2.k.p.2431.5	yes	8	4.3	odd	2	inner
2736.2.k.p.2431.5	yes	8	76.75	even	2	inner
2736.2.k.p.2431.6	yes	8	1.1	even	1	trivial
2736.2.k.p.2431.6	yes	8	19.18	odd	2	CM

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.31342 q^{5} +4.77753i q^{7} +O(q^{10})\)	\(q+1.31342 q^{5} +4.77753i q^{7} -6.27492i q^{11} -8.24163 q^{17} +4.35890i q^{19} +4.00000i q^{23} -3.27492 q^{25} +6.27492i q^{35} +7.40437i q^{43} +10.2749i q^{47} -15.8248 q^{49} -8.24163i q^{55} +3.72508 q^{61} -16.8248 q^{73} +29.9786 q^{77} -16.0000i q^{83} -10.8248 q^{85} +5.72508i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{25} - 36 q^{49} + 60 q^{61} - 44 q^{73} + 4 q^{85}+O(q^{100}) \) 8 * q + 4 * q^25 - 36 * q^49 + 60 * q^61 - 44 * q^73 + 4 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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