LMFDB - Embedded newform 2736.2.f.e.1025.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(1025,2736)]

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([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("2736.1025");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.f (of order $2$, degree $1$, not 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:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 20x^{2} + 81 $ x^4 + 20*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1025.3
Root			$2.37510i$ of defining polynomial
Character	$\chi$	$=$	2736.1025
Dual form			2736.2.f.e.1025.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37510i q^{5} -4.35890 q^{7} +O(q^{10})$	$q+2.37510i q^{5} -4.35890 q^{7} -6.61774i q^{11} -1.86754i q^{17} +4.35890 q^{19} +8.99284i q^{23} -0.641101 q^{25} -10.3528i q^{35} +1.00000 q^{43} +6.11018i q^{47} +12.0000 q^{49} +15.7178 q^{55} +4.35890 q^{61} +11.0000 q^{73} +28.8461i q^{77} +17.4781i q^{83} +4.43560 q^{85} +10.3528i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 20 q^{25} + 4 q^{43} + 48 q^{49} + 28 q^{55} + 44 q^{73} - 52 q^{85}+O(q^{100}) $ 4 * q - 20 * q^25 + 4 * q^43 + 48 * q^49 + 28 * q^55 + 44 * q^73 - 52 * 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
$5$	2.37510i	1.06218i	0.847316	+	0.531089i	$0.178217\pi$
$5$	2.37510i	1.06218i	−0.847316	+	0.531089i	$0.821783\pi$
$6$	0	0
$7$	−4.35890	−1.64751	−0.823754	−	0.566947i	$-0.808125\pi$
$7$	−4.35890	−1.64751	−0.823754	+	0.566947i	$0.808125\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 6.61774i	− 1.99532i	−0.0683416	−	0.997662i	$-0.521771\pi$
$11$	− 6.61774i	− 1.99532i	0.0683416	−	0.997662i	$-0.478229\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	− 1.86754i	− 0.452945i	−0.974018	−	0.226473i	$-0.927281\pi$
$17$	− 1.86754i	− 0.452945i	0.974018	−	0.226473i	$-0.0727194\pi$
$18$	0	0
$19$	4.35890	1.00000
$19$	4.35890	1.00000
$20$	0	0
$21$	0	0
$22$	0	0
$23$	8.99284i	1.87514i	0.347801	+	0.937568i	$0.386929\pi$
$23$	8.99284i	1.87514i	−0.347801	+	0.937568i	$0.613071\pi$
$24$	0	0
$25$	−0.641101	−0.128220
$26$	0	0
$27$	0	0
$28$	0	0
$29$	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			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 10.3528i	− 1.74995i
$36$	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		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	6.11018i	0.891262i	0.895217	+	0.445631i	$0.147021\pi$
$47$	6.11018i	0.891262i	−0.895217	+	0.445631i	$0.852979\pi$
$48$	0	0
$49$	12.0000	1.71429
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	15.7178	2.11939
$56$	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
$61$	4.35890	0.558100	0.279050	−	0.960277i	$-0.409981\pi$
$61$	4.35890	0.558100	0.279050	+	0.960277i	$0.409981\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	28.8461i	3.28731i
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	17.4781i	1.91847i	0.282604	+	0.959237i	$0.408802\pi$
$83$	17.4781i	1.91847i	−0.282604	+	0.959237i	$0.591198\pi$
$84$	0	0
$85$	4.43560	0.481108
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	10.3528i	1.06218i
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	5.25776i	0.523167i	0.965181	+	0.261583i	$0.0842446\pi$
$101$	5.25776i	0.523167i	−0.965181	+	0.261583i	$0.915755\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	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		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	−21.3589	−1.99173
$116$	0	0
$117$	0	0
$118$	0	0
$119$	8.14042i	0.746231i
$120$	0	0
$121$	−32.7945	−2.98132
$122$	0	0
$123$	0	0
$124$	0	0
$125$	10.3528i	0.925985i
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	20.3608i	1.77893i	0.457003	+	0.889465i	$0.348923\pi$
$131$	20.3608i	1.77893i	−0.457003	+	0.889465i	$0.651077\pi$
$132$	0	0
$133$	−19.0000	−1.64751
$134$	0	0
$135$	0	0
$136$	0	0
$137$	19.3457i	1.65281i	0.563075	+	0.826406i	$0.309618\pi$
$137$	19.3457i	1.65281i	−0.563075	+	0.826406i	$0.690382\pi$
$138$	0	0
$139$	21.7945	1.84858	0.924292	−	0.381685i	$-0.124656\pi$
$139$	21.7945	1.84858	0.924292	+	0.381685i	$0.124656\pi$
$140$	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
$149$	− 7.63286i	− 0.625308i	−0.949867	−	0.312654i	$-0.898782\pi$
$149$	− 7.63286i	− 0.625308i	0.949867	−	0.312654i	$-0.101218\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	17.4356	1.39151	0.695756	−	0.718278i	$-0.255069\pi$
$157$	17.4356	1.39151	0.695756	+	0.718278i	$0.255069\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	− 39.1989i	− 3.08930i
$162$	0	0
$163$	8.71780	0.682831	0.341415	−	0.939913i	$-0.389094\pi$
$163$	8.71780	0.682831	0.341415	+	0.939913i	$0.389094\pi$
$164$	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
$175$	2.79449	0.211244
$176$	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
$187$	−12.3589	−0.903772
$188$	0	0
$189$	0	0
$190$	0	0
$191$	3.39022i	0.245308i	0.992450	+	0.122654i	$0.0391405\pi$
$191$	3.39022i	0.245308i	−0.992450	+	0.122654i	$0.960860\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 3.22752i	− 0.229951i	−0.993368	−	0.114976i	$-0.963321\pi$
$197$	− 3.22752i	− 0.229951i	0.993368	−	0.114976i	$-0.0366790\pi$
$198$	0	0
$199$	25.0000	1.77220	0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000	1.77220	0.886102	+	0.463491i	$0.153403\pi$
$200$	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
$209$	− 28.8461i	− 1.99532i
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	2.37510i	0.161980i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	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
$229$	−21.7945	−1.44022	−0.720110	−	0.693860i	$-0.755909\pi$
$229$	−21.7945	−1.44022	−0.720110	+	0.693860i	$0.755909\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	20.8683i	1.36713i	0.729889	+	0.683565i	$0.239572\pi$
$233$	20.8683i	1.36713i	−0.729889	+	0.683565i	$0.760428\pi$
$234$	0	0
$235$	−14.5123	−0.946678
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 25.1110i	− 1.62429i	−0.583453	−	0.812147i	$-0.698299\pi$
$239$	− 25.1110i	− 1.62429i	0.583453	−	0.812147i	$-0.301701\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	28.5012i	1.82088i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 0.852421i	− 0.0538043i	−0.999638	−	0.0269022i	$-0.991436\pi$
$251$	− 0.852421i	− 0.0538043i	0.999638	−	0.0269022i	$-0.00856426\pi$
$252$	0	0
$253$	59.5123	3.74151
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 29.3536i	− 1.81002i	−0.425388	−	0.905011i	$-0.639862\pi$
$263$	− 29.3536i	− 1.81002i	0.425388	−	0.905011i	$-0.360138\pi$
$264$	0	0
$265$	0	0
$266$	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
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	4.24264i	0.255841i
$276$	0	0
$277$	4.35890	0.261901	0.130950	−	0.991389i	$-0.458197\pi$
$277$	4.35890	0.261901	0.130950	+	0.991389i	$0.458197\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	31.0000	1.84276	0.921379	−	0.388664i	$-0.127063\pi$
$283$	31.0000	1.84276	0.921379	+	0.388664i	$0.127063\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	13.5123	0.794841
$290$	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
$301$	−4.35890	−0.251243
$302$	0	0
$303$	0	0
$304$	0	0
$305$	10.3528i	0.592801i
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	− 27.8309i	− 1.57815i	−0.614298	−	0.789074i	$-0.710561\pi$
$311$	− 27.8309i	− 1.57815i	0.614298	−	0.789074i	$-0.289439\pi$
$312$	0	0
$313$	−34.8712	−1.97104	−0.985518	−	0.169570i	$-0.945762\pi$
$313$	−34.8712	−1.97104	−0.985518	+	0.169570i	$0.945762\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	− 8.14042i	− 0.452945i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	− 26.6337i	− 1.46836i
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	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
$343$	−21.7945	−1.17679
$344$	0	0
$345$	0	0
$346$	0	0
$347$	23.0807i	1.23904i	0.784981	+	0.619520i	$0.212673\pi$
$347$	23.0807i	1.23904i	−0.784981	+	0.619520i	$0.787327\pi$
$348$	0	0
$349$	35.0000	1.87351	0.936754	−	0.349990i	$-0.113815\pi$
$349$	35.0000	1.87351	0.936754	+	0.349990i	$0.113815\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 14.7582i	− 0.785498i	−0.919646	−	0.392749i	$-0.871524\pi$
$353$	− 14.7582i	− 0.785498i	0.919646	−	0.392749i	$-0.128476\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	37.3313i	1.97027i	0.171773	+	0.985137i	$0.445050\pi$
$359$	37.3313i	1.97027i	−0.171773	+	0.985137i	$0.554950\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	26.1261i	1.36750i
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	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	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	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
$385$	−68.5123	−3.49171
$386$	0	0
$387$	0	0
$388$	0	0
$389$	3.89778i	0.197625i	0.995106	+	0.0988126i	$0.0315044\pi$
$389$	3.89778i	0.197625i	−0.995106	+	0.0988126i	$0.968496\pi$
$390$	0	0
$391$	16.7945	0.849334
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	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
$415$	−41.5123	−2.03776
$416$	0	0
$417$	0	0
$418$	0	0
$419$	34.4487i	1.68293i	0.540313	+	0.841464i	$0.318306\pi$
$419$	34.4487i	1.68293i	−0.540313	+	0.841464i	$0.681694\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	1.19728i	0.0580767i
$426$	0	0
$427$	−19.0000	−0.919474
$428$	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
$437$	39.1989i	1.87514i
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	− 42.0815i	− 1.99935i	−0.0254032	−	0.999677i	$-0.508087\pi$
$443$	− 42.0815i	− 1.99935i	0.0254032	−	0.999677i	$-0.491913\pi$
$444$	0	0
$445$	0	0
$446$	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
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	17.0000	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 41.5740i	− 1.93629i	−0.250383	−	0.968147i	$-0.580557\pi$
$461$	− 41.5740i	− 1.93629i	0.250383	−	0.968147i	$-0.419443\pi$
$462$	0	0
$463$	−41.0000	−1.90543	−0.952716	−	0.303863i	$-0.901724\pi$
$463$	−41.0000	−1.90543	−0.952716	+	0.303863i	$0.901724\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	27.3234i	1.26438i	0.774815	+	0.632188i	$0.217843\pi$
$467$	27.3234i	1.26438i	−0.774815	+	0.632188i	$0.782157\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	− 6.61774i	− 0.304284i
$474$	0	0
$475$	−2.79449	−0.128220
$476$	0	0
$477$	0	0
$478$	0	0
$479$	− 27.9936i	− 1.27906i	−0.768765	−	0.639531i	$-0.779129\pi$
$479$	− 27.9936i	− 1.27906i	0.768765	−	0.639531i	$-0.220871\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 36.4789i	− 1.64627i	−0.567845	−	0.823135i	$-0.692223\pi$
$491$	− 36.4789i	− 1.64627i	0.567845	−	0.823135i	$-0.307777\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	21.7945	0.975656	0.487828	−	0.872940i	$-0.337789\pi$
$499$	21.7945	0.975656	0.487828	+	0.872940i	$0.337789\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	− 24.9483i	− 1.11239i	−0.831052	−	0.556195i	$-0.812261\pi$
$503$	− 24.9483i	− 1.11239i	0.831052	−	0.556195i	$-0.187739\pi$
$504$	0	0
$505$	−12.4877	−0.555696
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−47.9479	−2.12109
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	40.4356	1.77836
$518$	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	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−57.8712	−2.51614
$530$	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
$539$	− 79.4129i	− 3.42056i
$540$	0	0
$541$	−25.0000	−1.07483	−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000	−1.07483	−0.537417	+	0.843317i	$0.680600\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	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
$557$	36.3162i	1.53877i	0.638787	+	0.769384i	$0.279437\pi$
$557$	36.3162i	1.53877i	−0.638787	+	0.769384i	$0.720563\pi$
$558$	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		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	− 5.76532i	− 0.240430i
$576$	0	0
$577$	−47.9479	−1.99610	−0.998048	−	0.0624458i	$-0.980110\pi$
$577$	−47.9479	−1.99610	−0.998048	+	0.0624458i	$0.980110\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 76.1854i	− 3.16070i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	38.8540i	1.60368i	0.597541	+	0.801839i	$0.296145\pi$
$587$	38.8540i	1.60368i	−0.597541	+	0.801839i	$0.703855\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 48.6993i	− 1.99984i	−0.0126486	−	0.999920i	$-0.504026\pi$
$593$	− 48.6993i	− 1.99984i	0.0126486	−	0.999920i	$-0.495974\pi$
$594$	0	0
$595$	−19.3343	−0.792630
$596$	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
$605$	− 77.8902i	− 3.16669i
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	30.5123	1.23238	0.616190	−	0.787598i	$-0.288675\pi$
$613$	30.5123	1.23238	0.616190	+	0.787598i	$0.288675\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 43.0967i	− 1.73501i	−0.497432	−	0.867503i	$-0.665723\pi$
$617$	− 43.0967i	− 1.73501i	0.497432	−	0.867503i	$-0.334277\pi$
$618$	0	0
$619$	−43.5890	−1.75199	−0.875995	−	0.482321i	$-0.839794\pi$
$619$	−43.5890	−1.75199	−0.875995	+	0.482321i	$0.839794\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−27.7945	−1.11178
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	47.9479	1.90878	0.954388	−	0.298570i	$-0.0965097\pi$
$631$	47.9479	1.90878	0.954388	+	0.298570i	$0.0965097\pi$
$632$	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		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	49.0000	1.93237	0.966186	−	0.257847i	$-0.0830131\pi$
$643$	49.0000	1.93237	0.966186	+	0.257847i	$0.0830131\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	21.8835i	0.860328i	0.902751	+	0.430164i	$0.141544\pi$
$647$	21.8835i	0.860328i	−0.902751	+	0.430164i	$0.858456\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	50.5668i	1.97883i	0.145104	+	0.989416i	$0.453648\pi$
$653$	50.5668i	1.97883i	−0.145104	+	0.989416i	$0.546352\pi$
$654$	0	0
$655$	−48.3589	−1.88954
$656$	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
$665$	− 45.1269i	− 1.74995i
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	− 28.8461i	− 1.11359i
$672$	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		−	1.00000i	$-0.5\pi$
$677$	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	$0.5\pi$
$684$	0	0
$685$	−45.9479	−1.75558
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−35.0000	−1.33146	−0.665731	−	0.746191i	$-0.731880\pi$
$691$	−35.0000	−1.33146	−0.665731	+	0.746191i	$0.731880\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	51.7641i	1.96352i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	47.6842i	1.80101i	0.434850	+	0.900503i	$0.356802\pi$
$701$	47.6842i	1.80101i	−0.434850	+	0.900503i	$0.643198\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 22.9180i	− 0.861922i
$708$	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
$719$	50.0593i	1.86690i	0.358713	+	0.933448i	$0.383216\pi$
$719$	50.0593i	1.86690i	−0.358713	+	0.933448i	$0.616784\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	37.0000	1.37225	0.686127	−	0.727482i	$-0.259309\pi$
$727$	37.0000	1.37225	0.686127	+	0.727482i	$0.259309\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	− 1.86754i	− 0.0690735i
$732$	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
$739$	−30.5123	−1.12241	−0.561206	−	0.827676i	$-0.689663\pi$
$739$	−30.5123	−1.12241	−0.561206	+	0.827676i	$0.689663\pi$
$740$	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
$745$	18.1288	0.664188
$746$	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
$755$	0	0
$756$	0	0
$757$	−47.9479	−1.74270	−0.871348	−	0.490666i	$-0.836754\pi$
$757$	−47.9479	−1.74270	−0.871348	+	0.490666i	$0.836754\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	− 35.8087i	− 1.29806i	−0.760761	−	0.649032i	$-0.775174\pi$
$761$	− 35.8087i	− 1.29806i	0.760761	−	0.649032i	$-0.224826\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−21.7945	−0.785930	−0.392965	−	0.919554i	$-0.628551\pi$
$769$	−21.7945	−0.785930	−0.392965	+	0.919554i	$0.628551\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	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
$785$	41.4113i	1.47803i
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	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
$799$	11.4110	0.403693
$800$	0	0
$801$	0	0
$802$	0	0
$803$	− 72.7951i	− 2.56889i
$804$	0	0
$805$	93.1013	3.28139
$806$	0	0
$807$	0	0
$808$	0	0
$809$	43.6042i	1.53304i	0.642219	+	0.766521i	$0.278014\pi$
$809$	43.6042i	1.53304i	−0.642219	+	0.766521i	$0.721986\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	20.7056i	0.725287i
$816$	0	0
$817$	4.35890	0.152499
$818$	0	0
$819$	0	0
$820$	0	0
$821$	22.0656i	0.770096i	0.922897	+	0.385048i	$0.125815\pi$
$821$	22.0656i	0.770096i	−0.922897	+	0.385048i	$0.874185\pi$
$822$	0	0
$823$	−56.6657	−1.97524	−0.987621	−	0.156860i	$-0.949863\pi$
$823$	−56.6657	−1.97524	−0.987621	+	0.156860i	$0.949863\pi$
$824$	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
$833$	− 22.4105i	− 0.776477i
$834$	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
$845$	30.8763i	1.06218i
$846$	0	0
$847$	142.948	4.91175
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	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
$859$	−56.6657	−1.93341	−0.966704	−	0.255897i	$-0.917629\pi$
$859$	−56.6657	−1.93341	−0.966704	+	0.255897i	$0.917629\pi$
$860$	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
$875$	− 45.1269i	− 1.52557i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 9.15554i	− 0.308458i	−0.988035	−	0.154229i	$-0.950711\pi$
$881$	− 9.15554i	− 0.308458i	0.988035	−	0.154229i	$-0.0492893\pi$
$882$	0	0
$883$	−30.5123	−1.02682	−0.513410	−	0.858143i	$-0.671618\pi$
$883$	−30.5123	−1.02682	−0.513410	+	0.858143i	$0.671618\pi$
$884$	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
$893$	26.6337i	0.891262i
$894$	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	1.00000			$0$
$907$	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
$913$	115.666	3.82798
$914$	0	0
$915$	0	0
$916$	0	0
$917$	− 88.7506i	− 2.93080i
$918$	0	0
$919$	8.71780	0.287574	0.143787	−	0.989609i	$-0.454072\pi$
$919$	8.71780	0.287574	0.143787	+	0.989609i	$0.454072\pi$
$920$	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
$929$	10.6977i	0.350980i	0.984481	+	0.175490i	$0.0561509\pi$
$929$	10.6977i	0.350980i	−0.984481	+	0.175490i	$0.943849\pi$
$930$	0	0
$931$	52.3068	1.71429
$932$	0	0
$933$	0	0
$934$	0	0
$935$	− 29.3536i	− 0.959966i
$936$	0	0
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	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
$946$	0	0
$947$	37.4940i	1.21839i	0.793019	+	0.609196i	$0.208508\pi$
$947$	37.4940i	1.21839i	−0.793019	+	0.609196i	$0.791492\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	−8.05211	−0.260560
$956$	0	0
$957$	0	0
$958$	0	0
$959$	− 84.3258i	− 2.72302i
$960$	0	0
$961$	31.0000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	61.0246	1.96242	0.981209	−	0.192947i	$-0.0618045\pi$
$967$	61.0246	1.96242	0.981209	+	0.192947i	$0.0618045\pi$
$968$	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
$973$	−95.0000	−3.04556
$974$	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
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	7.66569	0.244249
$986$	0	0
$987$	0	0
$988$	0	0
$989$	8.99284i	0.285956i
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	59.3775i	1.88239i
$996$	0	0
$997$	4.35890	0.138048	0.0690239	−	0.997615i	$-0.478012\pi$
$997$	4.35890	0.138048	0.0690239	+	0.997615i	$0.478012\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.f.e.1025.3		4
3.2	odd	2	inner	2736.2.f.e.1025.2		4
4.3	odd	2		171.2.d.a.170.3	yes	4
12.11	even	2		171.2.d.a.170.2	✓	4
19.18	odd	2	CM	2736.2.f.e.1025.3		4
57.56	even	2	inner	2736.2.f.e.1025.2		4
76.75	even	2		171.2.d.a.170.3	yes	4
228.227	odd	2		171.2.d.a.170.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.d.a.170.2	✓	4	12.11	even	2
171.2.d.a.170.2	✓	4	228.227	odd	2
171.2.d.a.170.3	yes	4	4.3	odd	2
171.2.d.a.170.3	yes	4	76.75	even	2
2736.2.f.e.1025.2		4	3.2	odd	2	inner
2736.2.f.e.1025.2		4	57.56	even	2	inner
2736.2.f.e.1025.3		4	1.1	even	1	trivial
2736.2.f.e.1025.3		4	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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.37510i q^{5} -4.35890 q^{7} +O(q^{10})\)	\(q+2.37510i q^{5} -4.35890 q^{7} -6.61774i q^{11} -1.86754i q^{17} +4.35890 q^{19} +8.99284i q^{23} -0.641101 q^{25} -10.3528i q^{35} +1.00000 q^{43} +6.11018i q^{47} +12.0000 q^{49} +15.7178 q^{55} +4.35890 q^{61} +11.0000 q^{73} +28.8461i q^{77} +17.4781i q^{83} +4.43560 q^{85} +10.3528i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 20 q^{25} + 4 q^{43} + 48 q^{49} + 28 q^{55} + 44 q^{73} - 52 q^{85}+O(q^{100}) \) 4 * q - 20 * q^25 + 4 * q^43 + 48 * q^49 + 28 * q^55 + 44 * q^73 - 52 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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