LMFDB - Embedded newform 588.4.f.a.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(293,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("588.293");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.f (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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			293.2
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	588.293
Dual form			588.4.f.a.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.19615i q^{3} -27.0000 q^{9} +91.7987i q^{13} -126.440i q^{19} -125.000 q^{25} -140.296i q^{27} +188.794i q^{31} -323.000 q^{37} -477.000 q^{39} -71.0000 q^{43} +657.000 q^{57} -935.307i q^{61} -127.000 q^{67} -1217.63i q^{73} -649.519i q^{75} -1387.00 q^{79} +729.000 q^{81} -981.000 q^{93} -1371.78i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 54 q^{9} - 250 q^{25} - 646 q^{37} - 954 q^{39} - 142 q^{43} + 1314 q^{57} - 254 q^{67} - 2774 q^{79} + 1458 q^{81} - 1962 q^{93}+O(q^{100}) $ 2 * q - 54 * q^9 - 250 * q^25 - 646 * q^37 - 954 * q^39 - 142 * q^43 + 1314 * q^57 - 254 * q^67 - 2774 * q^79 + 1458 * q^81 - 1962 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	5.19615i	1.00000i
$3$	5.19615i	1.00000i
$4$	0	0
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−27.0000	−1.00000
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	91.7987i	1.95849i	0.202679	+	0.979245i	$0.435035\pi$
$13$	91.7987i	1.95849i	−0.202679	+	0.979245i	$0.564965\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	− 126.440i	− 1.52670i	−0.645986	−	0.763349i	$-0.723554\pi$
$19$	− 126.440i	− 1.52670i	0.645986	−	0.763349i	$-0.276446\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	−125.000	−1.00000
$26$	0	0
$27$	− 140.296i	− 1.00000i
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	188.794i	1.09382i	0.837192	+	0.546908i	$0.184195\pi$
$31$	188.794i	1.09382i	−0.837192	+	0.546908i	$0.815805\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−323.000	−1.43516	−0.717579	−	0.696477i	$-0.754750\pi$
$37$	−323.000	−1.43516	−0.717579	+	0.696477i	$0.754750\pi$
$38$	0	0
$39$	−477.000	−1.95849
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−71.0000	−0.251800	−0.125900	−	0.992043i	$-0.540182\pi$
$43$	−71.0000	−0.251800	−0.125900	+	0.992043i	$0.540182\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	657.000	1.52670
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	− 935.307i	− 1.96318i	−0.191006	−	0.981589i	$-0.561175\pi$
$61$	− 935.307i	− 1.96318i	0.191006	−	0.981589i	$-0.438825\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−127.000	−0.231575	−0.115787	−	0.993274i	$-0.536939\pi$
$67$	−127.000	−0.231575	−0.115787	+	0.993274i	$0.536939\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	− 1217.63i	− 1.95223i	−0.217248	−	0.976117i	$-0.569708\pi$
$73$	− 1217.63i	− 1.95223i	0.217248	−	0.976117i	$-0.430292\pi$
$74$	0	0
$75$	− 649.519i	− 1.00000i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−1387.00	−1.97531	−0.987656	−	0.156637i	$-0.949935\pi$
$79$	−1387.00	−1.97531	−0.987656	+	0.156637i	$0.949935\pi$
$80$	0	0
$81$	729.000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−981.000	−1.09382
$94$	0	0
$95$	0	0
$96$	0	0
$97$	− 1371.78i	− 1.43591i	−0.696088	−	0.717957i	$-0.745078\pi$
$97$	− 1371.78i	− 1.43591i	0.696088	−	0.717957i	$-0.254922\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	1061.75i	1.01570i	0.861446	+	0.507850i	$0.169560\pi$
$103$	1061.75i	1.01570i	−0.861446	+	0.507850i	$0.830440\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	−2213.00	−1.94465	−0.972325	−	0.233630i	$-0.924939\pi$
$109$	−2213.00	−1.94465	−0.972325	+	0.233630i	$0.924939\pi$
$110$	0	0
$111$	− 1678.36i	− 1.43516i
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	− 2478.56i	− 1.95849i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1331.00	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	2267.00	1.58397	0.791983	−	0.610543i	$-0.209049\pi$
$127$	2267.00	1.58397	0.791983	+	0.610543i	$0.209049\pi$
$128$	0	0
$129$	− 368.927i	− 0.251800i
$130$	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	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	3244.13i	1.97959i	0.142484	+	0.989797i	$0.454491\pi$
$139$	3244.13i	1.97959i	−0.142484	+	0.989797i	$0.545509\pi$
$140$	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
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	−1748.00	−0.942054	−0.471027	−	0.882119i	$-0.656117\pi$
$151$	−1748.00	−0.942054	−0.471027	+	0.882119i	$0.656117\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	810.600i	0.412057i	0.978546	+	0.206028i	$0.0660539\pi$
$157$	810.600i	0.412057i	−0.978546	+	0.206028i	$0.933946\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−3400.00	−1.63379	−0.816897	−	0.576783i	$-0.804308\pi$
$163$	−3400.00	−1.63379	−0.816897	+	0.576783i	$0.804308\pi$
$164$	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
$169$	−6230.00	−2.83569
$170$	0	0
$171$	3413.87i	1.52670i
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	1279.99i	0.525639i	0.964845	+	0.262819i	$0.0846523\pi$
$181$	1279.99i	0.525639i	−0.964845	+	0.262819i	$0.915348\pi$
$182$	0	0
$183$	4860.00	1.96318
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	3961.00	1.47730	0.738650	−	0.674089i	$-0.235464\pi$
$193$	3961.00	1.47730	0.738650	+	0.674089i	$0.235464\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	− 2026.50i	− 0.721883i	−0.932588	−	0.360942i	$-0.882455\pi$
$199$	− 2026.50i	− 0.721883i	0.932588	−	0.360942i	$-0.117545\pi$
$200$	0	0
$201$	− 659.911i	− 0.231575i
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−6032.00	−1.96806	−0.984028	−	0.178011i	$-0.943034\pi$
$211$	−6032.00	−1.96806	−0.984028	+	0.178011i	$0.943034\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	6327.00	1.95223
$220$	0	0
$221$	0	0
$222$	0	0
$223$	5830.08i	1.75072i	0.483469	+	0.875362i	$0.339377\pi$
$223$	5830.08i	1.75072i	−0.483469	+	0.875362i	$0.660623\pi$
$224$	0	0
$225$	3375.00	1.00000
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	6517.71i	1.88080i	0.340076	+	0.940398i	$0.389547\pi$
$229$	6517.71i	1.88080i	−0.340076	+	0.940398i	$0.610453\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	− 7207.06i	− 1.97531i
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	1247.08i	0.333325i	0.986014	+	0.166662i	$0.0532990\pi$
$241$	1247.08i	0.333325i	−0.986014	+	0.166662i	$0.946701\pi$
$242$	0	0
$243$	3788.00i	1.00000i
$244$	0	0
$245$	0	0
$246$	0	0
$247$	11607.0	2.99002
$248$	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
$256$	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
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	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
$271$	8885.42i	1.99170i	0.0910064	+	0.995850i	$0.470992\pi$
$271$	8885.42i	1.99170i	−0.0910064	+	0.995850i	$0.529008\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	9197.00	1.99492	0.997462	−	0.0711951i	$-0.0226813\pi$
$277$	9197.00	1.99492	0.997462	+	0.0711951i	$0.0226813\pi$
$278$	0	0
$279$	− 5097.43i	− 1.09382i
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	− 999.393i	− 0.209921i	−0.994476	−	0.104961i	$-0.966528\pi$
$283$	− 999.393i	− 0.209921i	0.994476	−	0.104961i	$-0.0334717\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−4913.00	−1.00000
$290$	0	0
$291$	7128.00	1.43591
$292$	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
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	10009.5i	1.86083i	0.366513	+	0.930413i	$0.380552\pi$
$307$	10009.5i	1.86083i	−0.366513	+	0.930413i	$0.619448\pi$
$308$	0	0
$309$	−5517.00	−1.01570
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	6299.47i	1.13759i	0.822478	+	0.568797i	$0.192591\pi$
$313$	6299.47i	1.13759i	−0.822478	+	0.568797i	$0.807409\pi$
$314$	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
$323$	0	0
$324$	0	0
$325$	− 11474.8i	− 1.95849i
$326$	0	0
$327$	− 11499.1i	− 1.94465i
$328$	0	0
$329$	0	0
$330$	0	0
$331$	10891.0	1.80853	0.904265	−	0.426971i	$-0.140420\pi$
$331$	10891.0	1.80853	0.904265	+	0.426971i	$0.140420\pi$
$332$	0	0
$333$	8721.00	1.43516
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−12293.0	−1.98707	−0.993535	−	0.113529i	$-0.963785\pi$
$337$	−12293.0	−1.98707	−0.993535	+	0.113529i	$0.963785\pi$
$338$	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
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	− 5300.08i	− 0.812913i	−0.913670	−	0.406456i	$-0.866764\pi$
$349$	− 5300.08i	− 0.812913i	0.913670	−	0.406456i	$-0.133236\pi$
$350$	0	0
$351$	12879.0	1.95849
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	−9128.00	−1.33081
$362$	0	0
$363$	6916.08i	1.00000i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	10446.0i	1.48577i	0.669420	+	0.742884i	$0.266543\pi$
$367$	10446.0i	1.48577i	−0.669420	+	0.742884i	$0.733457\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−12601.0	−1.74921	−0.874605	−	0.484837i	$-0.838879\pi$
$373$	−12601.0	−1.74921	−0.874605	+	0.484837i	$0.838879\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	6103.00	0.827151	0.413575	−	0.910470i	$-0.364280\pi$
$379$	6103.00	0.827151	0.413575	+	0.910470i	$0.364280\pi$
$380$	0	0
$381$	11779.7i	1.58397i
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1917.00	0.251800
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	6857.19i	0.866883i	0.901182	+	0.433441i	$0.142701\pi$
$397$	6857.19i	0.866883i	−0.901182	+	0.433441i	$0.857299\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	−17331.0	−2.14223
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	− 29.4449i	− 0.00355979i	−0.999998	−	0.00177990i	$-0.999433\pi$
$409$	− 29.4449i	− 0.00355979i	0.999998	−	0.00177990i	$-0.000566559\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−16857.0	−1.97959
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−6679.00	−0.773194	−0.386597	−	0.922249i	$-0.626350\pi$
$421$	−6679.00	−0.773194	−0.386597	+	0.922249i	$0.626350\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	− 6673.59i	− 0.740675i	−0.928897	−	0.370338i	$-0.879242\pi$
$433$	− 6673.59i	− 0.740675i	0.928897	−	0.370338i	$-0.120758\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	− 10756.0i	− 1.16938i	−0.811257	−	0.584690i	$-0.801216\pi$
$439$	− 10756.0i	− 1.16938i	0.811257	−	0.584690i	$-0.198784\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	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
$453$	− 9082.87i	− 0.942054i
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−6497.00	−0.665026	−0.332513	−	0.943099i	$-0.607897\pi$
$457$	−6497.00	−0.665026	−0.332513	+	0.943099i	$0.607897\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	11969.0	1.20140	0.600698	−	0.799476i	$-0.294889\pi$
$463$	11969.0	1.20140	0.600698	+	0.799476i	$0.294889\pi$
$464$	0	0
$465$	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
$471$	−4212.00	−0.412057
$472$	0	0
$473$	0	0
$474$	0	0
$475$	15805.0i	1.52670i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	− 29651.0i	− 2.81074i
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	6103.00	0.567871	0.283936	−	0.958843i	$-0.408360\pi$
$487$	6103.00	0.567871	0.283936	+	0.958843i	$0.408360\pi$
$488$	0	0
$489$	− 17666.9i	− 1.63379i
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−21743.0	−1.95060	−0.975301	−	0.220880i	$-0.929107\pi$
$499$	−21743.0	−1.95060	−0.975301	+	0.220880i	$0.929107\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	− 32372.0i	− 2.83569i
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−17739.0	−1.52670
$514$	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
$523$	91.7987i	0.00767510i	0.999993	+	0.00383755i	$0.00122153\pi$
$523$	91.7987i	0.00767510i	−0.999993	+	0.00383755i	$0.998778\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	12167.0	1.00000
$530$	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
$539$	0	0
$540$	0	0
$541$	1889.00	0.150119	0.0750596	−	0.997179i	$-0.476085\pi$
$541$	1889.00	0.150119	0.0750596	+	0.997179i	$0.476085\pi$
$542$	0	0
$543$	−6651.00	−0.525639
$544$	0	0
$545$	0	0
$546$	0	0
$547$	1640.00	0.128193	0.0640963	−	0.997944i	$-0.479584\pi$
$547$	1640.00	0.128193	0.0640963	+	0.997944i	$0.479584\pi$
$548$	0	0
$549$	25253.3i	1.96318i
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	− 6517.71i	− 0.493148i
$560$	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
$571$	−23941.0	−1.75464	−0.877320	−	0.479905i	$-0.840671\pi$
$571$	−23941.0	−1.75464	−0.877320	+	0.479905i	$0.840671\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	− 25999.8i	− 1.87589i	−0.346789	−	0.937943i	$-0.612728\pi$
$577$	− 25999.8i	− 1.87589i	0.346789	−	0.937943i	$-0.387272\pi$
$578$	0	0
$579$	20582.0i	1.47730i
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	23871.0	1.66993
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	10530.0	0.721883
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	− 23817.4i	− 1.61653i	−0.588820	−	0.808264i	$-0.700407\pi$
$601$	− 23817.4i	− 1.61653i	0.588820	−	0.808264i	$-0.299593\pi$
$602$	0	0
$603$	3429.00	0.231575
$604$	0	0
$605$	0	0
$606$	0	0
$607$	− 29273.4i	− 1.95745i	−0.205184	−	0.978723i	$-0.565779\pi$
$607$	− 29273.4i	− 1.95745i	0.205184	−	0.978723i	$-0.434221\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	17390.0	1.14580	0.572900	−	0.819625i	$-0.305818\pi$
$613$	17390.0	1.14580	0.572900	+	0.819625i	$0.305818\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	15368.5i	0.997919i	0.866625	+	0.498959i	$0.166284\pi$
$619$	15368.5i	0.997919i	−0.866625	+	0.498959i	$0.833716\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	15625.0	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	1892.00	0.119365	0.0596825	−	0.998217i	$-0.480991\pi$
$631$	1892.00	0.119365	0.0596825	+	0.998217i	$0.480991\pi$
$632$	0	0
$633$	− 31343.2i	− 1.96806i
$634$	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
$643$	− 26315.0i	− 1.61394i	−0.590592	−	0.806971i	$-0.701106\pi$
$643$	− 26315.0i	− 1.61394i	0.590592	−	0.806971i	$-0.298894\pi$
$644$	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
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	32876.1i	1.95223i
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	− 4175.97i	− 0.245729i	−0.992423	−	0.122864i	$-0.960792\pi$
$661$	− 4175.97i	− 0.245729i	0.992423	−	0.122864i	$-0.0392080\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	−30294.0	−1.75072
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−9899.00	−0.566981	−0.283491	−	0.958975i	$-0.591492\pi$
$673$	−9899.00	−0.566981	−0.283491	+	0.958975i	$0.591492\pi$
$674$	0	0
$675$	17537.0i	1.00000i
$676$	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	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−33867.0	−1.88080
$688$	0	0
$689$	0	0
$690$	0	0
$691$	30208.7i	1.66309i	0.555460	+	0.831543i	$0.312542\pi$
$691$	30208.7i	1.66309i	−0.555460	+	0.831543i	$0.687458\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	40840.0i	2.19105i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−36146.0	−1.91466	−0.957328	−	0.289003i	$-0.906676\pi$
$709$	−36146.0	−1.91466	−0.957328	+	0.289003i	$0.906676\pi$
$710$	0	0
$711$	37449.0	1.97531
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−6480.00	−0.333325
$724$	0	0
$725$	0	0
$726$	0	0
$727$	− 9510.69i	− 0.485188i	−0.970128	−	0.242594i	$-0.922002\pi$
$727$	− 9510.69i	− 0.485188i	0.970128	−	0.242594i	$-0.0779984\pi$
$728$	0	0
$729$	−19683.0	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	5329.52i	0.268554i	0.990944	+	0.134277i	$0.0428712\pi$
$733$	5329.52i	0.268554i	−0.990944	+	0.134277i	$0.957129\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	6047.00	0.301005	0.150502	−	0.988610i	$-0.451911\pi$
$739$	6047.00	0.301005	0.150502	+	0.988610i	$0.451911\pi$
$740$	0	0
$741$	60311.7i	2.99002i
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	17569.0	0.853664	0.426832	−	0.904331i	$-0.359630\pi$
$751$	17569.0	0.853664	0.426832	+	0.904331i	$0.359630\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	41470.0	1.99109	0.995543	−	0.0943039i	$-0.0300625\pi$
$757$	41470.0	1.99109	0.995543	+	0.0943039i	$0.0300625\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	25189.2i	1.18120i	0.806963	+	0.590602i	$0.201110\pi$
$769$	25189.2i	1.18120i	−0.806963	+	0.590602i	$0.798890\pi$
$770$	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
$775$	− 23599.2i	− 1.09382i
$776$	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
$785$	0	0
$786$	0	0
$787$	− 8137.17i	− 0.368563i	−0.982874	−	0.184281i	$-0.941004\pi$
$787$	− 8137.17i	− 0.368563i	0.982874	−	0.184281i	$-0.0589958\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	85860.0	3.84487
$794$	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
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	24162.1i	1.04617i	0.852280	+	0.523087i	$0.175220\pi$
$811$	24162.1i	1.04617i	−0.852280	+	0.523087i	$0.824780\pi$
$812$	0	0
$813$	−46170.0	−1.99170
$814$	0	0
$815$	0	0
$816$	0	0
$817$	8977.22i	0.384422i
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	−12220.0	−0.517573	−0.258786	−	0.965935i	$-0.583323\pi$
$823$	−12220.0	−0.517573	−0.258786	+	0.965935i	$0.583323\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	37071.1i	1.55311i	0.630047	+	0.776557i	$0.283036\pi$
$829$	37071.1i	1.55311i	−0.630047	+	0.776557i	$0.716964\pi$
$830$	0	0
$831$	47789.0i	1.99492i
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	26487.0	1.09382
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	24389.0	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	5193.00	0.209921
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 49133.1i	− 1.97220i	−0.166159	−	0.986099i	$-0.553137\pi$
$853$	− 49133.1i	− 1.97220i	0.166159	−	0.986099i	$-0.446863\pi$
$854$	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
$859$	39438.8i	1.56651i	0.621699	+	0.783256i	$0.286443\pi$
$859$	39438.8i	1.56651i	−0.621699	+	0.783256i	$0.713557\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 25528.7i	− 1.00000i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	− 11658.4i	− 0.453537i
$872$	0	0
$873$	37038.2i	1.43591i
$874$	0	0
$875$	0	0
$876$	0	0
$877$	50150.0	1.93095	0.965476	−	0.260491i	$-0.0838846\pi$
$877$	50150.0	1.93095	0.965476	+	0.260491i	$0.0838846\pi$
$878$	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
$883$	−52109.0	−1.98597	−0.992983	−	0.118260i	$-0.962269\pi$
$883$	−52109.0	−1.98597	−0.992983	+	0.118260i	$0.962269\pi$
$884$	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
$893$	0	0
$894$	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
$907$	49447.0	1.81021	0.905105	−	0.425188i	$-0.139792\pi$
$907$	49447.0	1.81021	0.905105	+	0.425188i	$0.139792\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−46817.0	−1.68047	−0.840234	−	0.542224i	$-0.817583\pi$
$919$	−46817.0	−1.68047	−0.840234	+	0.542224i	$0.817583\pi$
$920$	0	0
$921$	−52011.0	−1.86083
$922$	0	0
$923$	0	0
$924$	0	0
$925$	40375.0	1.43516
$926$	0	0
$927$	− 28667.2i	− 1.01570i
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	− 40840.0i	− 1.42389i	−0.702235	−	0.711945i	$-0.747814\pi$
$937$	− 40840.0i	− 1.42389i	0.702235	−	0.711945i	$-0.252186\pi$
$938$	0	0
$939$	−32733.0	−1.13759
$940$	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
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	111777.	3.82343
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−5852.00	−0.196435
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−3907.00	−0.129928	−0.0649641	−	0.997888i	$-0.520693\pi$
$967$	−3907.00	−0.129928	−0.0649641	+	0.997888i	$0.520693\pi$
$968$	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
$975$	59625.0	1.95849
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	59751.0	1.94465
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	14041.0	0.450078	0.225039	−	0.974350i	$-0.427749\pi$
$991$	14041.0	0.450078	0.225039	+	0.974350i	$0.427749\pi$
$992$	0	0
$993$	56591.3i	1.80853i
$994$	0	0
$995$	0	0
$996$	0	0
$997$	2928.90i	0.0930382i	0.998917	+	0.0465191i	$0.0148128\pi$
$997$	2928.90i	0.0930382i	−0.998917	+	0.0465191i	$0.985187\pi$
$998$	0	0
$999$	45315.6i	1.43516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.f.a.293.2		2
3.2	odd	2	CM	588.4.f.a.293.2		2
7.2	even	3		84.4.k.a.17.1	yes	2
7.3	odd	6		84.4.k.a.5.1	✓	2
7.4	even	3		588.4.k.b.509.1		2
7.5	odd	6		588.4.k.b.521.1		2
7.6	odd	2	inner	588.4.f.a.293.1		2
21.2	odd	6		84.4.k.a.17.1	yes	2
21.5	even	6		588.4.k.b.521.1		2
21.11	odd	6		588.4.k.b.509.1		2
21.17	even	6		84.4.k.a.5.1	✓	2
21.20	even	2	inner	588.4.f.a.293.1		2
28.3	even	6		336.4.bc.b.257.1		2
28.23	odd	6		336.4.bc.b.17.1		2
84.23	even	6		336.4.bc.b.17.1		2
84.59	odd	6		336.4.bc.b.257.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.a.5.1	✓	2	7.3	odd	6
84.4.k.a.5.1	✓	2	21.17	even	6
84.4.k.a.17.1	yes	2	7.2	even	3
84.4.k.a.17.1	yes	2	21.2	odd	6
336.4.bc.b.17.1		2	28.23	odd	6
336.4.bc.b.17.1		2	84.23	even	6
336.4.bc.b.257.1		2	28.3	even	6
336.4.bc.b.257.1		2	84.59	odd	6
588.4.f.a.293.1		2	7.6	odd	2	inner
588.4.f.a.293.1		2	21.20	even	2	inner
588.4.f.a.293.2		2	1.1	even	1	trivial
588.4.f.a.293.2		2	3.2	odd	2	CM
588.4.k.b.509.1		2	7.4	even	3
588.4.k.b.509.1		2	21.11	odd	6
588.4.k.b.521.1		2	7.5	odd	6
588.4.k.b.521.1		2	21.5	even	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.19615i q^{3} -27.0000 q^{9} +91.7987i q^{13} -126.440i q^{19} -125.000 q^{25} -140.296i q^{27} +188.794i q^{31} -323.000 q^{37} -477.000 q^{39} -71.0000 q^{43} +657.000 q^{57} -935.307i q^{61} -127.000 q^{67} -1217.63i q^{73} -649.519i q^{75} -1387.00 q^{79} +729.000 q^{81} -981.000 q^{93} -1371.78i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 54 q^{9} - 250 q^{25} - 646 q^{37} - 954 q^{39} - 142 q^{43} + 1314 q^{57} - 254 q^{67} - 2774 q^{79} + 1458 q^{81} - 1962 q^{93}+O(q^{100}) \) 2 * q - 54 * q^9 - 250 * q^25 - 646 * q^37 - 954 * q^39 - 142 * q^43 + 1314 * q^57 - 254 * q^67 - 2774 * q^79 + 1458 * q^81 - 1962 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more