LMFDB - Embedded newform 2736.2.f.i.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:	$8$
Coefficient field:	8.0.691798081536.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} - 12x^{5} + 127x^{4} - 144x^{3} - 282x^{2} + 900x + 1350 $ x^8 - 14x^6 - 12x^5 + 127x^4 - 144x^3 - 282x^2 + 900x + 1350
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 684)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1025.3
Root			$1.31342 + 1.93185i$ of defining polynomial
Character	$\chi$	$=$	2736.1025
Dual form			2736.2.f.i.1025.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09409i q^{5} +4.77753 q^{7} +O(q^{10})$	$q-2.09409i q^{5} +4.77753 q^{7} -2.91628i q^{11} +6.02211i q^{17} +4.35890 q^{19} -8.99284i q^{23} +0.614779 q^{25} -10.0046i q^{35} +10.8248 q^{43} +13.6852i q^{47} +15.8248 q^{49} -6.10695 q^{55} -15.1698 q^{61} -16.8248 q^{73} -13.9326i q^{77} -17.4781i q^{83} +12.6108 q^{85} -9.12793i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 40 q^{25} - 4 q^{43} + 36 q^{49} - 28 q^{55} - 44 q^{73} + 52 q^{85}+O(q^{100}) $ 8 * q - 40 * q^25 - 4 * q^43 + 36 * 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
$5$	− 2.09409i	− 0.936506i	−0.883594	−	0.468253i	$-0.844884\pi$
$5$	− 2.09409i	− 0.936506i	0.883594	−	0.468253i	$-0.155116\pi$
$6$	0	0
$7$	4.77753	1.80573	0.902867	−	0.429919i	$-0.141458\pi$
$7$	4.77753	1.80573	0.902867	+	0.429919i	$0.141458\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 2.91628i	− 0.879291i	−0.898171	−	0.439645i	$-0.855104\pi$
$11$	− 2.91628i	− 0.879291i	0.898171	−	0.439645i	$-0.144896\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	6.02211i	1.46058i	0.683140	+	0.730288i	$0.260614\pi$
$17$	6.02211i	1.46058i	−0.683140	+	0.730288i	$0.739386\pi$
$18$	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	$-0.613071\pi$
$23$	− 8.99284i	− 1.87514i	0.347801	−	0.937568i	$-0.386929\pi$
$24$	0	0
$25$	0.614779	0.122956
$26$	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
$35$	− 10.0046i	− 1.69108i
$36$	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
$43$	10.8248	1.65076	0.825380	−	0.564578i	$-0.190961\pi$
$43$	10.8248	1.65076	0.825380	+	0.564578i	$0.190961\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	13.6852i	1.99619i	0.0616809	+	0.998096i	$0.480354\pi$
$47$	13.6852i	1.99619i	−0.0616809	+	0.998096i	$0.519646\pi$
$48$	0	0
$49$	15.8248	2.26068
$50$	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
$55$	−6.10695	−0.823461
$56$	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
$61$	−15.1698	−1.94230	−0.971149	−	0.238474i	$-0.923353\pi$
$61$	−15.1698	−1.94230	−0.971149	+	0.238474i	$0.923353\pi$
$62$	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
$73$	−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
$77$	− 13.9326i	− 1.58777i
$78$	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	$-0.591198\pi$
$83$	− 17.4781i	− 1.91847i	0.282604	−	0.959237i	$-0.408802\pi$
$84$	0	0
$85$	12.6108	1.36784
$86$	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
$95$	− 9.12793i	− 0.936506i
$96$	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	$-0.915755\pi$
$101$	− 5.25776i	− 0.523167i	0.965181	−	0.261583i	$-0.0842446\pi$
$102$	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
$115$	−18.8318	−1.75608
$116$	0	0
$117$	0	0
$118$	0	0
$119$	28.7708i	2.63741i
$120$	0	0
$121$	2.49532	0.226848
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 11.7579i	− 1.05166i
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	1.12065i	0.0979117i	0.998801	+	0.0489558i	$0.0155894\pi$
$131$	1.12065i	0.0979117i	−0.998801	+	0.0489558i	$0.984411\pi$
$132$	0	0
$133$	20.8248	1.80573
$134$	0	0
$135$	0	0
$136$	0	0
$137$	21.0881i	1.80168i	0.434151	+	0.900840i	$0.357048\pi$
$137$	21.0881i	1.80168i	−0.434151	+	0.900840i	$0.642952\pi$
$138$	0	0
$139$	−3.10302	−0.263195	−0.131597	−	0.991303i	$-0.542011\pi$
$139$	−3.10302	−0.263195	−0.131597	+	0.991303i	$0.542011\pi$
$140$	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
$149$	− 23.8989i	− 1.95787i	−0.204167	−	0.978936i	$-0.565449\pi$
$149$	− 23.8989i	− 1.95787i	0.204167	−	0.978936i	$-0.434551\pi$
$150$	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
$161$	− 42.9635i	− 3.38600i
$162$	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
$175$	2.93712	0.222026
$176$	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
$187$	17.5621	1.28427
$188$	0	0
$189$	0	0
$190$	0	0
$191$	− 22.0616i	− 1.59632i	−0.602446	−	0.798160i	$-0.705807\pi$
$191$	− 22.0616i	− 1.59632i	0.602446	−	0.798160i	$-0.294193\pi$
$192$	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	$0.0366790\pi$
$197$	3.22752i	0.229951i	−0.993368	+	0.114976i	$0.963321\pi$
$198$	0	0
$199$	−1.17525	−0.0833111	−0.0416556	−	0.999132i	$-0.513263\pi$
$199$	−1.17525	−0.0833111	−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
$209$	− 12.7118i	− 0.879291i
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	− 22.6680i	− 1.54595i
$216$	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
$229$	−7.28929	−0.481690	−0.240845	−	0.970564i	$-0.577424\pi$
$229$	−7.28929	−0.481690	−0.240845	+	0.970564i	$0.577424\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	29.7314i	1.94777i	0.227040	+	0.973885i	$0.427095\pi$
$233$	29.7314i	1.94777i	−0.227040	+	0.973885i	$0.572905\pi$
$234$	0	0
$235$	28.6581	1.86945
$236$	0	0
$237$	0	0
$238$	0	0
$239$	3.06753i	0.198422i	0.995066	+	0.0992111i	$0.0316319\pi$
$239$	3.06753i	0.198422i	−0.995066	+	0.0992111i	$0.968368\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	− 33.1385i	− 2.11714i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	27.0047i	1.70452i	0.523117	+	0.852261i	$0.324769\pi$
$251$	27.0047i	1.70452i	−0.523117	+	0.852261i	$0.675231\pi$
$252$	0	0
$253$	−26.2256	−1.64879
$254$	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
$263$	− 26.6256i	− 1.64180i	−0.571068	−	0.820902i	$-0.693471\pi$
$263$	− 26.6256i	− 1.64180i	0.571068	−	0.820902i	$-0.306529\pi$
$264$	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
$275$	− 1.79287i	− 0.108114i
$276$	0	0
$277$	26.3994	1.58619	0.793093	−	0.609101i	$-0.208470\pi$
$277$	26.3994	1.58619	0.793093	+	0.609101i	$0.208470\pi$
$278$	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
$283$	−26.8248	−1.59457	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	−26.8248	−1.59457	−0.797283	+	0.603606i	$0.793730\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−19.2658	−1.13328
$290$	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
$301$	51.7155	2.98083
$302$	0	0
$303$	0	0
$304$	0	0
$305$	31.7670i	1.81897i
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	− 32.6792i	− 1.85307i	−0.376209	−	0.926535i	$-0.622773\pi$
$311$	− 32.6792i	− 1.85307i	0.376209	−	0.926535i	$-0.377227\pi$
$312$	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
$323$	26.2498i	1.46058i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	65.3814i	3.60459i
$330$	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
$343$	42.1605	2.27645
$344$	0	0
$345$	0	0
$346$	0	0
$347$	36.8674i	1.97915i	0.144029	+	0.989573i	$0.453994\pi$
$347$	36.8674i	1.97915i	−0.144029	+	0.989573i	$0.546006\pi$
$348$	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
$353$	14.7582i	0.785498i	0.919646	+	0.392749i	$0.128476\pi$
$353$	14.7582i	0.785498i	−0.919646	+	0.392749i	$0.871524\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	24.3029i	1.28266i	0.767267	+	0.641328i	$0.221616\pi$
$359$	24.3029i	1.28266i	−0.767267	+	0.641328i	$0.778384\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	35.2326i	1.84416i
$366$	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
$385$	−29.1761	−1.48695
$386$	0	0
$387$	0	0
$388$	0	0
$389$	35.9431i	1.82239i	0.411979	+	0.911193i	$0.364838\pi$
$389$	35.9431i	1.82239i	−0.411979	+	0.911193i	$0.635162\pi$
$390$	0	0
$391$	54.1558	2.73878
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−30.4743	−1.52946	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	−30.4743	−1.52946	−0.764730	+	0.644351i	$0.777127\pi$
$398$	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
$415$	−36.6008	−1.79666
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 34.4487i	− 1.68293i	−0.540313	−	0.841464i	$-0.681694\pi$
$419$	− 34.4487i	− 1.68293i	0.540313	−	0.841464i	$-0.318306\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	3.70227i	0.179586i
$426$	0	0
$427$	−72.4743	−3.50728
$428$	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
$443$	− 20.1147i	− 0.955678i	−0.878448	−	0.477839i	$-0.841420\pi$
$443$	− 20.1147i	− 0.955678i	0.878448	−	0.477839i	$-0.158580\pi$
$444$	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
$457$	−42.4743	−1.98686	−0.993431	−	0.114433i	$-0.963495\pi$
$457$	−42.4743	−1.98686	−0.993431	+	0.114433i	$0.963495\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 11.4756i	− 0.534470i	−0.963631	−	0.267235i	$-0.913890\pi$
$461$	− 11.4756i	− 0.534470i	0.963631	−	0.267235i	$-0.0861100\pi$
$462$	0	0
$463$	9.17525	0.426410	0.213205	−	0.977007i	$-0.431610\pi$
$463$	9.17525	0.426410	0.213205	+	0.977007i	$0.431610\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 15.3396i	− 0.709832i	−0.934898	−	0.354916i	$-0.884510\pi$
$467$	− 15.3396i	− 0.709832i	0.934898	−	0.354916i	$-0.115490\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	− 31.5680i	− 1.45150i
$474$	0	0
$475$	2.67976	0.122956
$476$	0	0
$477$	0	0
$478$	0	0
$479$	27.9936i	1.27906i	0.768765	+	0.639531i	$0.220871\pi$
$479$	27.9936i	1.27906i	−0.768765	+	0.639531i	$0.779129\pi$
$480$	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	$0.307777\pi$
$491$	36.4789i	1.64627i	−0.567845	+	0.823135i	$0.692223\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−44.6722	−1.99980	−0.999902	−	0.0139987i	$-0.995544\pi$
$499$	−44.6722	−1.99980	−0.999902	+	0.0139987i	$0.995544\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	24.9483i	1.11239i	0.831052	+	0.556195i	$0.187739\pi$
$503$	24.9483i	1.11239i	−0.831052	+	0.556195i	$0.812261\pi$
$504$	0	0
$505$	−11.0102	−0.489949
$506$	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
$511$	−80.3807	−3.55583
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	39.9099	1.75523
$518$	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
$539$	− 46.1494i	− 1.98779i
$540$	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	1.00000			$0$
$547$	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
$557$	44.2703i	1.87579i	0.346913	+	0.937897i	$0.387230\pi$
$557$	44.2703i	1.87579i	−0.346913	+	0.937897i	$0.612770\pi$
$558$	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
$575$	− 5.52861i	− 0.230559i
$576$	0	0
$577$	21.3759	0.889889	0.444945	−	0.895558i	$-0.353223\pi$
$577$	21.3759	0.889889	0.444945	+	0.895558i	$0.353223\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 83.5022i	− 3.46425i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	44.5024i	1.83681i	0.395642	+	0.918405i	$0.370522\pi$
$587$	44.5024i	1.83681i	−0.395642	+	0.918405i	$0.629478\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	48.6993i	1.99984i	0.0126486	+	0.999920i	$0.495974\pi$
$593$	48.6993i	1.99984i	−0.0126486	+	0.999920i	$0.504026\pi$
$594$	0	0
$595$	60.2486	2.46995
$596$	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
$605$	− 5.22544i	− 0.212444i
$606$	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
$613$	18.5188	0.747969	0.373985	−	0.927435i	$-0.377991\pi$
$613$	18.5188	0.747969	0.373985	+	0.927435i	$0.377991\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 0.147209i	− 0.00592641i	−0.999996	−	0.00296321i	$-0.999057\pi$
$617$	− 0.147209i	− 0.00592641i	0.999996	−	0.00296321i	$-0.000943219\pi$
$618$	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
$625$	−21.5482	−0.861926
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−10.9836	−0.437249	−0.218624	−	0.975809i	$-0.570157\pi$
$631$	−10.9836	−0.437249	−0.218624	+	0.975809i	$0.570157\pi$
$632$	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
$643$	−13.1752	−0.519581	−0.259791	−	0.965665i	$-0.583654\pi$
$643$	−13.1752	−0.519581	−0.259791	+	0.965665i	$0.583654\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	50.7140i	1.99377i	0.0788426	+	0.996887i	$0.474878\pi$
$647$	50.7140i	1.99377i	−0.0788426	+	0.996887i	$0.525122\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	31.7058i	1.24074i	0.784308	+	0.620372i	$0.213018\pi$
$653$	31.7058i	1.24074i	−0.784308	+	0.620372i	$0.786982\pi$
$654$	0	0
$655$	2.34675	0.0916949
$656$	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
$665$	− 43.6089i	− 1.69108i
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	44.2394i	1.70784i
$672$	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
$685$	44.1605	1.68729
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−16.4743	−0.626710	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	−16.4743	−0.626710	−0.313355	+	0.949636i	$0.601453\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	6.49801i	0.246483i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	− 47.6842i	− 1.80101i	−0.434850	−	0.900503i	$-0.643198\pi$
$701$	− 47.6842i	− 1.80101i	0.434850	−	0.900503i	$-0.356802\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 25.1191i	− 0.944700i
$708$	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
$719$	8.36973i	0.312138i	0.987746	+	0.156069i	$0.0498823\pi$
$719$	8.36973i	0.312138i	−0.987746	+	0.156069i	$0.950118\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−52.4743	−1.94616	−0.973081	−	0.230463i	$-0.925976\pi$
$727$	−52.4743	−1.94616	−0.973081	+	0.230463i	$0.925976\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	65.1878i	2.41106i
$732$	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
$739$	54.2273	1.99478	0.997392	−	0.0721811i	$-0.0229959\pi$
$739$	54.2273	1.99478	0.997392	+	0.0721811i	$0.0229959\pi$
$740$	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
$745$	−50.0464	−1.83356
$746$	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
$757$	0.591258	0.0214896	0.0107448	−	0.999942i	$-0.496580\pi$
$757$	0.591258	0.0214896	0.0107448	+	0.999942i	$0.496580\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	18.4454i	0.668646i	0.942459	+	0.334323i	$0.108508\pi$
$761$	18.4454i	0.668646i	−0.942459	+	0.334323i	$0.891492\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	55.0645	1.98568	0.992839	−	0.119459i	$-0.0381161\pi$
$769$	55.0645	1.98568	0.992839	+	0.119459i	$0.0381161\pi$
$770$	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
$785$	− 36.5117i	− 1.30316i
$786$	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
$799$	−82.4137	−2.91559
$800$	0	0
$801$	0	0
$802$	0	0
$803$	49.0657i	1.73149i
$804$	0	0
$805$	−89.9696	−3.17101
$806$	0	0
$807$	0	0
$808$	0	0
$809$	53.4408i	1.87888i	0.342718	+	0.939438i	$0.388653\pi$
$809$	53.4408i	1.87888i	−0.342718	+	0.939438i	$0.611347\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	− 18.2559i	− 0.639475i
$816$	0	0
$817$	47.1840	1.65076
$818$	0	0
$819$	0	0
$820$	0	0
$821$	56.8349i	1.98355i	0.127987	+	0.991776i	$0.459148\pi$
$821$	56.8349i	1.98355i	−0.127987	+	0.991776i	$0.540852\pi$
$822$	0	0
$823$	20.5386	0.715931	0.357966	−	0.933735i	$-0.383471\pi$
$823$	20.5386	0.715931	0.357966	+	0.933735i	$0.383471\pi$
$824$	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
$833$	95.2983i	3.30189i
$834$	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
$845$	− 27.2232i	− 0.936506i
$846$	0	0
$847$	11.9215	0.409627
$848$	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
$859$	41.3232	1.40993	0.704965	−	0.709242i	$-0.250963\pi$
$859$	41.3232	1.40993	0.704965	+	0.709242i	$0.250963\pi$
$860$	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
$875$	− 56.1735i	− 1.89901i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	46.2172i	1.55710i	0.627584	+	0.778549i	$0.284044\pi$
$881$	46.2172i	1.55710i	−0.627584	+	0.778549i	$0.715956\pi$
$882$	0	0
$883$	−28.9111	−0.972938	−0.486469	−	0.873698i	$-0.661715\pi$
$883$	−28.9111	−0.972938	−0.486469	+	0.873698i	$0.661715\pi$
$884$	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
$893$	59.6524i	1.99619i
$894$	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
$913$	−50.9711	−1.68690
$914$	0	0
$915$	0	0
$916$	0	0
$917$	5.35394i	0.176803i
$918$	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	$-0.943849\pi$
$929$	− 10.6977i	− 0.350980i	0.984481	−	0.175490i	$-0.0561509\pi$
$930$	0	0
$931$	68.9785	2.26068
$932$	0	0
$933$	0	0
$934$	0	0
$935$	− 36.7767i	− 1.20273i
$936$	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		−	1.00000i	$-0.5\pi$
$941$	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	$-0.791492\pi$
$947$	− 37.4940i	− 1.21839i	0.793019	−	0.609196i	$-0.208508\pi$
$948$	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
$955$	−46.1990	−1.49496
$956$	0	0
$957$	0	0
$958$	0	0
$959$	100.749i	3.25336i
$960$	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
$973$	−14.8248	−0.475260
$974$	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
$985$	6.75873	0.215351
$986$	0	0
$987$	0	0
$988$	0	0
$989$	− 97.3453i	− 3.09540i
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	2.46108i	0.0780214i
$996$	0	0
$997$	−56.7390	−1.79694	−0.898472	−	0.439031i	$-0.855322\pi$
$997$	−56.7390	−1.79694	−0.898472	+	0.439031i	$0.855322\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.f.i.1025.3		8
3.2	odd	2	inner	2736.2.f.i.1025.6		8
4.3	odd	2		684.2.d.a.341.3	✓	8
12.11	even	2		684.2.d.a.341.6	yes	8
19.18	odd	2	CM	2736.2.f.i.1025.3		8
57.56	even	2	inner	2736.2.f.i.1025.6		8
76.75	even	2		684.2.d.a.341.3	✓	8
228.227	odd	2		684.2.d.a.341.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.d.a.341.3	✓	8	4.3	odd	2
684.2.d.a.341.3	✓	8	76.75	even	2
684.2.d.a.341.6	yes	8	12.11	even	2
684.2.d.a.341.6	yes	8	228.227	odd	2
2736.2.f.i.1025.3		8	1.1	even	1	trivial
2736.2.f.i.1025.3		8	19.18	odd	2	CM
2736.2.f.i.1025.6		8	3.2	odd	2	inner
2736.2.f.i.1025.6		8	57.56	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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.09409i q^{5} +4.77753 q^{7} +O(q^{10})\)	\(q-2.09409i q^{5} +4.77753 q^{7} -2.91628i q^{11} +6.02211i q^{17} +4.35890 q^{19} -8.99284i q^{23} +0.614779 q^{25} -10.0046i q^{35} +10.8248 q^{43} +13.6852i q^{47} +15.8248 q^{49} -6.10695 q^{55} -15.1698 q^{61} -16.8248 q^{73} -13.9326i q^{77} -17.4781i q^{83} +12.6108 q^{85} -9.12793i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 40 q^{25} - 4 q^{43} + 36 q^{49} - 28 q^{55} - 44 q^{73} + 52 q^{85}+O(q^{100}) \) 8 * q - 40 * q^25 - 4 * q^43 + 36 * 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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