LMFDB - Embedded newform 5184.2.c.g.5183.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5184,2,Mod(5183,5184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5184, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("5184.5183");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5184 = 2^{6} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5184.c (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:	$41.3944484078$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 1296)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			5183.4
Root			$-1.93185i$ of defining polynomial
Character	$\chi$	$=$	5184.5183
Dual form			5184.2.c.g.5183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.34607i q^{5} +O(q^{10})$	$q+3.34607i q^{5} +7.19615 q^{13} -4.00240i q^{17} -6.19615 q^{25} -10.6945i q^{29} +11.3923 q^{37} -12.7279i q^{41} +7.00000 q^{49} -12.7279i q^{53} +5.39230 q^{61} +24.0788i q^{65} -13.1962 q^{73} +13.3923 q^{85} -18.0430i q^{89} -8.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 8 q^{13} - 4 q^{25} + 4 q^{37} + 28 q^{49} - 20 q^{61} - 32 q^{73} + 12 q^{85} - 32 q^{97}+O(q^{100}) $ 4 * q + 8 * q^13 - 4 * q^25 + 4 * q^37 + 28 * q^49 - 20 * q^61 - 32 * q^73 + 12 * q^85 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	0	0
$3$	0	0
$4$	0	0
$5$	3.34607i	1.49641i	0.663470	+	0.748203i	$0.269083\pi$
$5$	3.34607i	1.49641i	−0.663470	+	0.748203i	$0.730917\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	7.19615	1.99585	0.997927	−	0.0643593i	$-0.0205004\pi$
$13$	7.19615	1.99585	0.997927	+	0.0643593i	$0.0205004\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	− 4.00240i	− 0.970726i	−0.874313	−	0.485363i	$-0.838688\pi$
$17$	− 4.00240i	− 0.970726i	0.874313	−	0.485363i	$-0.161312\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−6.19615	−1.23923
$26$	0	0
$27$	0	0
$28$	0	0
$29$	− 10.6945i	− 1.98593i	−0.118428	−	0.992963i	$-0.537786\pi$
$29$	− 10.6945i	− 1.98593i	0.118428	−	0.992963i	$-0.462214\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	11.3923	1.87288	0.936442	−	0.350823i	$-0.114098\pi$
$37$	11.3923	1.87288	0.936442	+	0.350823i	$0.114098\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	− 12.7279i	− 1.98777i	−0.110432	−	0.993884i	$-0.535223\pi$
$41$	− 12.7279i	− 1.98777i	0.110432	−	0.993884i	$-0.464777\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	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
$49$	7.00000	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	− 12.7279i	− 1.74831i	−0.485643	−	0.874157i	$-0.661414\pi$
$53$	− 12.7279i	− 1.74831i	0.485643	−	0.874157i	$-0.338586\pi$
$54$	0	0
$55$	0	0
$56$	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
$61$	5.39230	0.690414	0.345207	−	0.938527i	$-0.387809\pi$
$61$	5.39230	0.690414	0.345207	+	0.938527i	$0.387809\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	24.0788i	2.98661i
$66$	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
$73$	−13.1962	−1.54449	−0.772246	−	0.635323i	$-0.780867\pi$
$73$	−13.1962	−1.54449	−0.772246	+	0.635323i	$0.780867\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	13.3923	1.45260
$86$	0	0
$87$	0	0
$88$	0	0
$89$	− 18.0430i	− 1.91255i	−0.292462	−	0.956277i	$-0.594474\pi$
$89$	− 18.0430i	− 1.91255i	0.292462	−	0.956277i	$-0.405526\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	12.7279i	1.26648i	0.773957	+	0.633238i	$0.218274\pi$
$101$	12.7279i	1.26648i	−0.773957	+	0.633238i	$0.781726\pi$
$102$	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
$109$	−4.80385	−0.460125	−0.230063	−	0.973176i	$-0.573893\pi$
$109$	−4.80385	−0.460125	−0.230063	+	0.973176i	$0.573893\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	− 9.38186i	− 0.882571i	−0.897367	−	0.441285i	$-0.854523\pi$
$113$	− 9.38186i	− 0.882571i	0.897367	−	0.441285i	$-0.145477\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 4.00240i	− 0.357986i
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	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
$137$	2.03339i	0.173724i	0.996220	+	0.0868620i	$0.0276839\pi$
$137$	2.03339i	0.173724i	−0.996220	+	0.0868620i	$0.972316\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	35.7846	2.97175
$146$	0	0
$147$	0	0
$148$	0	0
$149$	18.6993i	1.53191i	0.642894	+	0.765955i	$0.277733\pi$
$149$	18.6993i	1.53191i	−0.642894	+	0.765955i	$0.722267\pi$
$150$	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
$157$	−0.607695	−0.0484994	−0.0242497	−	0.999706i	$-0.507720\pi$
$157$	−0.607695	−0.0484994	−0.0242497	+	0.999706i	$0.507720\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	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
$169$	38.7846	2.98343
$170$	0	0
$171$	0	0
$172$	0	0
$173$	24.0788i	1.83068i	0.402685	+	0.915338i	$0.368077\pi$
$173$	24.0788i	1.83068i	−0.402685	+	0.915338i	$0.631923\pi$
$174$	0	0
$175$	0	0
$176$	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
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	38.1194i	2.80259i
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	13.7846	0.992238	0.496119	−	0.868255i	$-0.334758\pi$
$193$	13.7846	0.992238	0.496119	+	0.868255i	$0.334758\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 5.31508i	− 0.378684i	−0.981911	−	0.189342i	$-0.939365\pi$
$197$	− 5.31508i	− 0.378684i	0.981911	−	0.189342i	$-0.0606355\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	42.5885	2.97451
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	− 28.8019i	− 1.93743i
$222$	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
$229$	−23.9808	−1.58469	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	−23.9808	−1.58469	−0.792347	+	0.610071i	$0.791141\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 8.72552i	− 0.571628i	−0.958285	−	0.285814i	$-0.907736\pi$
$233$	− 8.72552i	− 0.571628i	0.958285	−	0.285814i	$-0.0922639\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	29.9808	1.93123	0.965615	−	0.259975i	$-0.0837143\pi$
$241$	29.9808	1.93123	0.965615	+	0.259975i	$0.0837143\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	23.4225i	1.49641i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	31.4273i	1.96038i	0.198062	+	0.980189i	$0.436535\pi$
$257$	31.4273i	1.96038i	−0.198062	+	0.980189i	$0.563465\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	42.5885	2.61619
$266$	0	0
$267$	0	0
$268$	0	0
$269$	− 26.0478i	− 1.58816i	−0.607811	−	0.794082i	$-0.707952\pi$
$269$	− 26.0478i	− 1.58816i	0.607811	−	0.794082i	$-0.292048\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	1.37705i	0.0821478i	0.999156	+	0.0410739i	$0.0130779\pi$
$281$	1.37705i	0.0821478i	−0.999156	+	0.0410739i	$0.986922\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	0.980762	0.0576919
$290$	0	0
$291$	0	0
$292$	0	0
$293$	12.6636i	0.739813i	0.929069	+	0.369906i	$0.120610\pi$
$293$	12.6636i	0.739813i	−0.929069	+	0.369906i	$0.879390\pi$
$294$	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
$305$	18.0430i	1.03314i
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	7.78461	0.440012	0.220006	−	0.975499i	$-0.429392\pi$
$313$	7.78461	0.440012	0.220006	+	0.975499i	$0.429392\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	32.7399i	1.83886i	0.393256	+	0.919429i	$0.371349\pi$
$317$	32.7399i	1.83886i	−0.393256	+	0.919429i	$0.628651\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−44.5885	−2.47332
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	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
$337$	−32.0000	−1.74315	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000	−1.74315	−0.871576	+	0.490261i	$0.836901\pi$
$338$	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		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 12.7279i	− 0.677439i	−0.940887	−	0.338719i	$-0.890006\pi$
$353$	− 12.7279i	− 0.677439i	0.940887	−	0.338719i	$-0.109994\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	− 44.1552i	− 2.31119i
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 76.9595i	− 3.96362i
$378$	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
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	38.1838i	1.93599i	0.250962	+	0.967997i	$0.419253\pi$
$389$	38.1838i	1.93599i	−0.250962	+	0.967997i	$0.580747\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	29.3923	1.47516	0.737579	−	0.675261i	$-0.235969\pi$
$397$	29.3923	1.47516	0.737579	+	0.675261i	$0.235969\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	− 38.1194i	− 1.90359i	−0.306732	−	0.951796i	$-0.599236\pi$
$401$	− 38.1194i	− 1.90359i	0.306732	−	0.951796i	$-0.400764\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−25.1962	−1.24587	−0.622935	−	0.782274i	$-0.714060\pi$
$409$	−25.1962	−1.24587	−0.622935	+	0.782274i	$0.714060\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−11.9808	−0.583907	−0.291953	−	0.956433i	$-0.594305\pi$
$421$	−11.9808	−0.583907	−0.291953	+	0.956433i	$0.594305\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	24.7995i	1.20295i
$426$	0	0
$427$	0	0
$428$	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
$433$	37.7846	1.81581	0.907906	−	0.419173i	$-0.137680\pi$
$433$	37.7846	1.81581	0.907906	+	0.419173i	$0.137680\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	60.3731	2.86196
$446$	0	0
$447$	0	0
$448$	0	0
$449$	38.1838i	1.80200i	0.433816	+	0.901002i	$0.357167\pi$
$449$	38.1838i	1.80200i	−0.433816	+	0.901002i	$0.642833\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−32.3731	−1.51435	−0.757174	−	0.653213i	$-0.773421\pi$
$457$	−32.3731	−1.51435	−0.757174	+	0.653213i	$0.773421\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 12.7279i	− 0.592798i	−0.955064	−	0.296399i	$-0.904214\pi$
$461$	− 12.7279i	− 0.592798i	0.955064	−	0.296399i	$-0.0957859\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	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
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	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
$481$	81.9808	3.73800
$482$	0	0
$483$	0	0
$484$	0	0
$485$	− 26.7685i	− 1.21550i
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	−42.8038	−1.92779
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	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
$505$	−42.5885	−1.89516
$506$	0	0
$507$	0	0
$508$	0	0
$509$	38.1838i	1.69247i	0.532813	+	0.846233i	$0.321135\pi$
$509$	38.1838i	1.69247i	−0.532813	+	0.846233i	$0.678865\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	12.7279i	0.557620i	0.960346	+	0.278810i	$0.0899400\pi$
$521$	12.7279i	0.557620i	−0.960346	+	0.278810i	$0.910060\pi$
$522$	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
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	− 91.5921i	− 3.96729i
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	26.3731	1.13387	0.566933	−	0.823764i	$-0.308130\pi$
$541$	26.3731	1.13387	0.566933	+	0.823764i	$0.308130\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	− 16.0740i	− 0.688534i
$546$	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
$557$	29.4582i	1.24819i	0.781350	+	0.624093i	$0.214531\pi$
$557$	29.4582i	1.24819i	−0.781350	+	0.624093i	$0.785469\pi$
$558$	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
$565$	31.3923	1.32068
$566$	0	0
$567$	0	0
$568$	0	0
$569$	− 14.7613i	− 0.618826i	−0.950928	−	0.309413i	$-0.899867\pi$
$569$	− 14.7613i	− 0.618826i	0.950928	−	0.309413i	$-0.100133\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−42.5692	−1.77218	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−42.5692	−1.77218	−0.886090	+	0.463513i	$0.846589\pi$
$578$	0	0
$579$	0	0
$580$	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
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 27.3605i	− 1.12356i	−0.827286	−	0.561780i	$-0.810117\pi$
$593$	− 27.3605i	− 1.12356i	0.827286	−	0.561780i	$-0.189883\pi$
$594$	0	0
$595$	0	0
$596$	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
$601$	−36.5692	−1.49169	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	−36.5692	−1.49169	−0.745845	+	0.666120i	$0.767954\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 36.8067i	− 1.49641i
$606$	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
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	40.7448i	1.64032i	0.572133	+	0.820161i	$0.306116\pi$
$617$	40.7448i	1.64032i	−0.572133	+	0.820161i	$0.693884\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−17.5885	−0.703538
$626$	0	0
$627$	0	0
$628$	0	0
$629$	− 45.5966i	− 1.81806i
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	50.3731	1.99585
$638$	0	0
$639$	0	0
$640$	0	0
$641$	20.6684i	0.816351i	0.912903	+	0.408176i	$0.133835\pi$
$641$	20.6684i	0.816351i	−0.912903	+	0.408176i	$0.866165\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	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
$653$	12.7279i	0.498082i	0.968493	+	0.249041i	$0.0801154\pi$
$653$	12.7279i	0.498082i	−0.968493	+	0.249041i	$0.919885\pi$
$654$	0	0
$655$	0	0
$656$	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
$661$	35.3923	1.37660	0.688301	−	0.725426i	$-0.258357\pi$
$661$	35.3923	1.37660	0.688301	+	0.725426i	$0.258357\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	43.7846	1.68777	0.843886	−	0.536522i	$-0.180262\pi$
$673$	43.7846	1.68777	0.843886	+	0.536522i	$0.180262\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	− 38.1838i	− 1.46752i	−0.679408	−	0.733761i	$-0.737763\pi$
$677$	− 38.1838i	− 1.46752i	0.679408	−	0.733761i	$-0.262237\pi$
$678$	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
$685$	−6.80385	−0.259962
$686$	0	0
$687$	0	0
$688$	0	0
$689$	− 91.5921i	− 3.48938i
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−50.9423	−1.92958
$698$	0	0
$699$	0	0
$700$	0	0
$701$	52.8163i	1.99485i	0.0717494	+	0.997423i	$0.477142\pi$
$701$	52.8163i	1.99485i	−0.0717494	+	0.997423i	$0.522858\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−47.9808	−1.80196	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−47.9808	−1.80196	−0.900978	+	0.433865i	$0.857149\pi$
$710$	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
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	66.2650i	2.46102i
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	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
$745$	−62.5692	−2.29236
$746$	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
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	− 28.8019i	− 1.04407i	−0.852925	−	0.522034i	$-0.825173\pi$
$761$	− 28.8019i	− 1.04407i	0.852925	−	0.522034i	$-0.174827\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−4.21539	−0.152011	−0.0760054	−	0.997107i	$-0.524217\pi$
$769$	−4.21539	−0.152011	−0.0760054	+	0.997107i	$0.524217\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 21.4534i	− 0.771627i	−0.922577	−	0.385813i	$-0.873921\pi$
$773$	− 21.4534i	− 0.771627i	0.922577	−	0.385813i	$-0.126079\pi$
$774$	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
$785$	− 2.03339i	− 0.0725747i
$786$	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
$793$	38.8038	1.37797
$794$	0	0
$795$	0	0
$796$	0	0
$797$	− 34.7090i	− 1.22945i	−0.788740	−	0.614727i	$-0.789266\pi$
$797$	− 34.7090i	− 1.22945i	0.788740	−	0.614727i	$-0.210734\pi$
$798$	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
$809$	51.5037i	1.81077i	0.424589	+	0.905386i	$0.360418\pi$
$809$	51.5037i	1.81077i	−0.424589	+	0.905386i	$0.639582\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	14.1050i	0.492267i	0.969236	+	0.246133i	$0.0791601\pi$
$821$	14.1050i	0.492267i	−0.969236	+	0.246133i	$0.920840\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	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
$829$	20.0000	0.694629	0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000	0.694629	0.347314	+	0.937749i	$0.387094\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	− 28.0168i	− 0.970726i
$834$	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
$841$	−85.3731	−2.94390
$842$	0	0
$843$	0	0
$844$	0	0
$845$	129.776i	4.46442i
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 7.28410i	− 0.248820i	−0.992231	−	0.124410i	$-0.960296\pi$
$857$	− 7.28410i	− 0.248820i	0.992231	−	0.124410i	$-0.0397038\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	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
$865$	−80.5692	−2.73944
$866$	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
$875$	0	0
$876$	0	0
$877$	−18.6077	−0.628337	−0.314169	−	0.949367i	$-0.601726\pi$
$877$	−18.6077	−0.628337	−0.314169	+	0.949367i	$0.601726\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	12.7279i	0.428815i	0.976744	+	0.214407i	$0.0687820\pi$
$881$	12.7279i	0.428815i	−0.976744	+	0.214407i	$0.931218\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	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
$901$	−50.9423	−1.69713
$902$	0	0
$903$	0	0
$904$	0	0
$905$	66.9213i	2.22454i
$906$	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
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−70.5885	−2.32093
$926$	0	0
$927$	0	0
$928$	0	0
$929$	54.7853i	1.79745i	0.438514	+	0.898725i	$0.355505\pi$
$929$	54.7853i	1.79745i	−0.438514	+	0.898725i	$0.644495\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−60.5692	−1.97871	−0.989355	−	0.145522i	$-0.953514\pi$
$937$	−60.5692	−1.97871	−0.989355	+	0.145522i	$0.953514\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 50.8473i	− 1.65758i	−0.559563	−	0.828788i	$-0.689031\pi$
$941$	− 50.8473i	− 1.65758i	0.559563	−	0.828788i	$-0.310969\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	−94.9615	−3.08258
$950$	0	0
$951$	0	0
$952$	0	0
$953$	60.8211i	1.97019i	0.172011	+	0.985095i	$0.444974\pi$
$953$	60.8211i	1.97019i	−0.172011	+	0.985095i	$0.555026\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	31.0000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	46.1242i	1.48479i
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	38.1838i	1.22161i	0.791782	+	0.610803i	$0.209153\pi$
$977$	38.1838i	1.22161i	−0.791782	+	0.610803i	$0.790847\pi$
$978$	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
$985$	17.7846	0.566665
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	41.3923	1.31091	0.655454	−	0.755235i	$-0.272477\pi$
$997$	41.3923	1.31091	0.655454	+	0.755235i	$0.272477\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5184.2.c.g.5183.4		4
3.2	odd	2	inner	5184.2.c.g.5183.1		4
4.3	odd	2	CM	5184.2.c.g.5183.4		4
8.3	odd	2		1296.2.c.e.1295.1	✓	4
8.5	even	2		1296.2.c.e.1295.1	✓	4
12.11	even	2	inner	5184.2.c.g.5183.1		4
24.5	odd	2		1296.2.c.e.1295.4	yes	4
24.11	even	2		1296.2.c.e.1295.4	yes	4
72.5	odd	6		1296.2.s.k.431.4		8
72.11	even	6		1296.2.s.k.863.1		8
72.13	even	6		1296.2.s.k.431.1		8
72.29	odd	6		1296.2.s.k.863.1		8
72.43	odd	6		1296.2.s.k.863.4		8
72.59	even	6		1296.2.s.k.431.4		8
72.61	even	6		1296.2.s.k.863.4		8
72.67	odd	6		1296.2.s.k.431.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1296.2.c.e.1295.1	✓	4	8.3	odd	2
1296.2.c.e.1295.1	✓	4	8.5	even	2
1296.2.c.e.1295.4	yes	4	24.5	odd	2
1296.2.c.e.1295.4	yes	4	24.11	even	2
1296.2.s.k.431.1		8	72.13	even	6
1296.2.s.k.431.1		8	72.67	odd	6
1296.2.s.k.431.4		8	72.5	odd	6
1296.2.s.k.431.4		8	72.59	even	6
1296.2.s.k.863.1		8	72.11	even	6
1296.2.s.k.863.1		8	72.29	odd	6
1296.2.s.k.863.4		8	72.43	odd	6
1296.2.s.k.863.4		8	72.61	even	6
5184.2.c.g.5183.1		4	3.2	odd	2	inner
5184.2.c.g.5183.1		4	12.11	even	2	inner
5184.2.c.g.5183.4		4	1.1	even	1	trivial
5184.2.c.g.5183.4		4	4.3	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:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.34607i q^{5} +O(q^{10})\)	\(q+3.34607i q^{5} +7.19615 q^{13} -4.00240i q^{17} -6.19615 q^{25} -10.6945i q^{29} +11.3923 q^{37} -12.7279i q^{41} +7.00000 q^{49} -12.7279i q^{53} +5.39230 q^{61} +24.0788i q^{65} -13.1962 q^{73} +13.3923 q^{85} -18.0430i q^{89} -8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 8 q^{13} - 4 q^{25} + 4 q^{37} + 28 q^{49} - 20 q^{61} - 32 q^{73} + 12 q^{85} - 32 q^{97}+O(q^{100}) \) 4 * q + 8 * q^13 - 4 * q^25 + 4 * q^37 + 28 * q^49 - 20 * q^61 - 32 * q^73 + 12 * q^85 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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