LMFDB - Embedded newform 675.4.b.h.649.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,4,Mod(649,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.649"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	675.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,16,0,0,0,0,0,0,0,0,0,0,0,128,0,0,326] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$39.8262892539$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			649.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	675.649
Dual form			675.4.b.h.649.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{4} +37.0000i q^{7} -70.0000i q^{13} +64.0000 q^{16} +163.000 q^{19} +296.000i q^{28} -19.0000 q^{31} +433.000i q^{37} +449.000i q^{43} -1026.00 q^{49} -560.000i q^{52} +719.000 q^{61} +512.000 q^{64} +880.000i q^{67} -271.000i q^{73} +1304.00 q^{76} -503.000 q^{79} +2590.00 q^{91} +523.000i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{4} + 128 q^{16} + 326 q^{19} - 38 q^{31} - 2052 q^{49} + 1438 q^{61} + 1024 q^{64} + 2608 q^{76} - 1006 q^{79} + 5180 q^{91}+O(q^{100}) $ 2 * q + 16 * q^4 + 128 * q^16 + 326 * q^19 - 38 * q^31 - 2052 * q^49 + 1438 * q^61 + 1024 * q^64 + 2608 * q^76 - 1006 * q^79 + 5180 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$1$	$-1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	0	0
$3$	0	0
$4$	8.00000	1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	37.0000i	1.99781i	0.0467610	+	0.998906i	$0.485110\pi$
$7$	37.0000i	1.99781i	−0.0467610	+	0.998906i	$0.514890\pi$
$8$	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
$13$	− 70.0000i	− 1.49342i	−0.665148	−	0.746712i	$-0.731631\pi$
$13$	− 70.0000i	− 1.49342i	0.665148	−	0.746712i	$-0.268369\pi$
$14$	0	0
$15$	0	0
$16$	64.0000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	163.000	1.96815	0.984073	−	0.177766i	$-0.0568871\pi$
$19$	163.000	1.96815	0.984073	+	0.177766i	$0.0568871\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	296.000i	1.99781i
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−19.0000	−0.110081	−0.0550403	−	0.998484i	$-0.517529\pi$
$31$	−19.0000	−0.110081	−0.0550403	+	0.998484i	$0.517529\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	433.000i	1.92391i	0.273204	+	0.961956i	$0.411917\pi$
$37$	433.000i	1.92391i	−0.273204	+	0.961956i	$0.588083\pi$
$38$	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
$43$	449.000i	1.59237i	0.605054	+	0.796184i	$0.293151\pi$
$43$	449.000i	1.59237i	−0.605054	+	0.796184i	$0.706849\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	−1026.00	−2.99125
$50$	0	0
$51$	0	0
$52$	− 560.000i	− 1.49342i
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	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
$61$	719.000	1.50916	0.754578	−	0.656210i	$-0.227842\pi$
$61$	719.000	1.50916	0.754578	+	0.656210i	$0.227842\pi$
$62$	0	0
$63$	0	0
$64$	512.000	1.00000
$65$	0	0
$66$	0	0
$67$	880.000i	1.60461i	0.596912	+	0.802307i	$0.296394\pi$
$67$	880.000i	1.60461i	−0.596912	+	0.802307i	$0.703606\pi$
$68$	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
$73$	− 271.000i	− 0.434495i	−0.976117	−	0.217248i	$-0.930292\pi$
$73$	− 271.000i	− 0.434495i	0.976117	−	0.217248i	$-0.0697079\pi$
$74$	0	0
$75$	0	0
$76$	1304.00	1.96815
$77$	0	0
$78$	0	0
$79$	−503.000	−0.716353	−0.358177	−	0.933654i	$-0.616601\pi$
$79$	−503.000	−0.716353	−0.358177	+	0.933654i	$0.616601\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	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
$91$	2590.00	2.98358
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	523.000i	0.547450i	0.961808	+	0.273725i	$0.0882557\pi$
$97$	523.000i	0.547450i	−0.961808	+	0.273725i	$0.911744\pi$
$98$	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
$103$	− 19.0000i	− 0.0181760i	−0.999959	−	0.00908799i	$-0.997107\pi$
$103$	− 19.0000i	− 0.0181760i	0.999959	−	0.00908799i	$-0.00289284\pi$
$104$	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
$111$	0	0
$112$	2368.00i	1.99781i
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−1331.00	−1.00000
$122$	0	0
$123$	0	0
$124$	−152.000	−0.110081
$125$	0	0
$126$	0	0
$127$	− 380.000i	− 0.265508i	−0.991149	−	0.132754i	$-0.957618\pi$
$127$	− 380.000i	− 0.265508i	0.991149	−	0.132754i	$-0.0423821\pi$
$128$	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
$133$	6031.00i	3.93199i
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	3043.00	1.85686	0.928431	−	0.371504i	$-0.121158\pi$
$139$	3043.00	1.85686	0.928431	+	0.371504i	$0.121158\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	3464.00i	1.92391i
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	1961.00	1.05685	0.528424	−	0.848981i	$-0.322783\pi$
$151$	1961.00	1.05685	0.528424	+	0.848981i	$0.322783\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	− 1223.00i	− 0.621694i	−0.950460	−	0.310847i	$-0.899387\pi$
$157$	− 1223.00i	− 0.621694i	0.950460	−	0.310847i	$-0.100613\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	− 3400.00i	− 1.63379i	−0.576783	−	0.816897i	$-0.695692\pi$
$163$	− 3400.00i	− 1.63379i	0.576783	−	0.816897i	$-0.304308\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−2703.00	−1.23031
$170$	0	0
$171$	0	0
$172$	3592.00i	1.59237i
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	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
$181$	3458.00	1.42006	0.710031	−	0.704171i	$-0.248681\pi$
$181$	3458.00	1.42006	0.710031	+	0.704171i	$0.248681\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	− 3961.00i	− 1.47730i	−0.674089	−	0.738650i	$-0.735464\pi$
$193$	− 3961.00i	− 1.47730i	0.674089	−	0.738650i	$-0.264536\pi$
$194$	0	0
$195$	0	0
$196$	−8208.00	−2.99125
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	5236.00	1.86518	0.932588	−	0.360942i	$-0.117545\pi$
$199$	5236.00	1.86518	0.932588	+	0.360942i	$0.117545\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	− 4480.00i	− 1.49342i
$209$	0	0
$210$	0	0
$211$	6032.00	1.96806	0.984028	−	0.178011i	$-0.0569664\pi$
$211$	6032.00	1.96806	0.984028	+	0.178011i	$0.0569664\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	− 703.000i	− 0.219921i
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 3439.00i	− 1.03270i	−0.856377	−	0.516351i	$-0.827290\pi$
$223$	− 3439.00i	− 1.03270i	0.856377	−	0.516351i	$-0.172710\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−2357.00	−0.680153	−0.340076	−	0.940398i	$-0.610453\pi$
$229$	−2357.00	−0.680153	−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
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−7378.00	−1.97203	−0.986014	−	0.166662i	$-0.946701\pi$
$241$	−7378.00	−1.97203	−0.986014	+	0.166662i	$0.946701\pi$
$242$	0	0
$243$	0	0
$244$	5752.00	1.50916
$245$	0	0
$246$	0	0
$247$	− 11410.0i	− 2.93927i
$248$	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
$256$	4096.00	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−16021.0	−3.84362
$260$	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
$268$	7040.00i	1.60461i
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	−8101.00	−1.81587	−0.907935	−	0.419111i	$-0.862342\pi$
$271$	−8101.00	−1.81587	−0.907935	+	0.419111i	$0.862342\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	− 9197.00i	− 1.99492i	−0.0711951	−	0.997462i	$-0.522681\pi$
$277$	− 9197.00i	− 1.99492i	0.0711951	−	0.997462i	$-0.477319\pi$
$278$	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
$283$	− 9469.00i	− 1.98895i	−0.104961	−	0.994476i	$-0.533472\pi$
$283$	− 9469.00i	− 1.98895i	0.104961	−	0.994476i	$-0.466528\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	4913.00	1.00000
$290$	0	0
$291$	0	0
$292$	− 2168.00i	− 0.434495i
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−16613.0	−3.18125
$302$	0	0
$303$	0	0
$304$	10432.0	1.96815
$305$	0	0
$306$	0	0
$307$	6697.00i	1.24501i	0.782616	+	0.622505i	$0.213885\pi$
$307$	6697.00i	1.24501i	−0.782616	+	0.622505i	$0.786115\pi$
$308$	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
$313$	10010.0i	1.80766i	0.427888	+	0.903832i	$0.359258\pi$
$313$	10010.0i	1.80766i	−0.427888	+	0.903832i	$0.640742\pi$
$314$	0	0
$315$	0	0
$316$	−4024.00	−0.716353
$317$	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
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−10891.0	−1.80853	−0.904265	−	0.426971i	$-0.859580\pi$
$331$	−10891.0	−1.80853	−0.904265	+	0.426971i	$0.859580\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	4930.00i	0.796897i	0.917191	+	0.398448i	$0.130451\pi$
$337$	4930.00i	0.796897i	−0.917191	+	0.398448i	$0.869549\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 25271.0i	− 3.97815i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−1367.00	−0.209667	−0.104834	−	0.994490i	$-0.533431\pi$
$349$	−1367.00	−0.209667	−0.104834	+	0.994490i	$0.533431\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	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
$361$	19710.0	2.87360
$362$	0	0
$363$	0	0
$364$	20720.0	2.98358
$365$	0	0
$366$	0	0
$367$	− 4340.00i	− 0.617292i	−0.951177	−	0.308646i	$-0.900124\pi$
$367$	− 4340.00i	− 0.617292i	0.951177	−	0.308646i	$-0.0998758\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	251.000i	0.0348426i	0.999848	+	0.0174213i	$0.00554565\pi$
$373$	251.000i	0.0348426i	−0.999848	+	0.0174213i	$0.994454\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	8584.00	1.16340	0.581702	−	0.813402i	$-0.302387\pi$
$379$	8584.00	1.16340	0.581702	+	0.813402i	$0.302387\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	4184.00i	0.547450i
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	− 13067.0i	− 1.65192i	−0.563726	−	0.825962i	$-0.690632\pi$
$397$	− 13067.0i	− 1.65192i	0.563726	−	0.825962i	$-0.309368\pi$
$398$	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
$403$	1330.00i	0.164397i
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−8246.00	−0.996916	−0.498458	−	0.866914i	$-0.666100\pi$
$409$	−8246.00	−0.996916	−0.498458	+	0.866914i	$0.666100\pi$
$410$	0	0
$411$	0	0
$412$	− 152.000i	− 0.0181760i
$413$	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
$421$	−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
$427$	26603.0i	3.01501i
$428$	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
$433$	− 14149.0i	− 1.57034i	−0.619280	−	0.785170i	$-0.712575\pi$
$433$	− 14149.0i	− 1.57034i	0.619280	−	0.785170i	$-0.287425\pi$
$434$	0	0
$435$	0	0
$436$	−17704.0	−1.94465
$437$	0	0
$438$	0	0
$439$	−1853.00	−0.201455	−0.100728	−	0.994914i	$-0.532117\pi$
$439$	−1853.00	−0.201455	−0.100728	+	0.994914i	$0.532117\pi$
$440$	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
$448$	18944.0i	1.99781i
$449$	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
$457$	− 12710.0i	− 1.30098i	−0.759514	−	0.650491i	$-0.774563\pi$
$457$	− 12710.0i	− 1.30098i	0.759514	−	0.650491i	$-0.225437\pi$
$458$	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
$463$	11969.0i	1.20140i	0.799476	+	0.600698i	$0.205111\pi$
$463$	11969.0i	1.20140i	−0.799476	+	0.600698i	$0.794889\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	−32560.0	−3.20572
$470$	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
$481$	30310.0	2.87322
$482$	0	0
$483$	0	0
$484$	−10648.0	−1.00000
$485$	0	0
$486$	0	0
$487$	− 20900.0i	− 1.94470i	−0.233526	−	0.972351i	$-0.575026\pi$
$487$	− 20900.0i	− 1.94470i	0.233526	−	0.972351i	$-0.424974\pi$
$488$	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
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−1216.00	−0.110081
$497$	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	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	− 3040.00i	− 0.265508i
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	10027.0	0.868040
$512$	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
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	23921.0i	1.99999i	0.00383755	+	0.999993i	$0.498778\pi$
$523$	23921.0i	1.99999i	−0.00383755	+	0.999993i	$0.501222\pi$
$524$	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
$532$	48248.0i	3.93199i
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	20789.0	1.65211	0.826053	−	0.563593i	$-0.190581\pi$
$541$	20789.0	1.65211	0.826053	+	0.563593i	$0.190581\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 21293.0i	− 1.66439i	−0.554481	−	0.832196i	$-0.687083\pi$
$547$	− 21293.0i	− 1.66439i	0.554481	−	0.832196i	$-0.312917\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	− 18611.0i	− 1.43114i
$554$	0	0
$555$	0	0
$556$	24344.0	1.85686
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	31430.0	2.37808
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	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
$571$	629.000	0.0460995	0.0230498	−	0.999734i	$-0.492662\pi$
$571$	629.000	0.0460995	0.0230498	+	0.999734i	$0.492662\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	9613.00i	0.693578i	0.937943	+	0.346789i	$0.112728\pi$
$577$	9613.00i	0.693578i	−0.937943	+	0.346789i	$0.887272\pi$
$578$	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	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	−3097.00	−0.216655
$590$	0	0
$591$	0	0
$592$	27712.0i	1.92391i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	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
$601$	17351.0	1.17764	0.588820	−	0.808264i	$-0.299593\pi$
$601$	17351.0	1.17764	0.588820	+	0.808264i	$0.299593\pi$
$602$	0	0
$603$	0	0
$604$	15688.0	1.05685
$605$	0	0
$606$	0	0
$607$	− 6137.00i	− 0.410368i	−0.978723	−	0.205184i	$-0.934221\pi$
$607$	− 6137.00i	− 0.410368i	0.978723	−	0.205184i	$-0.0657792\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	12851.0i	0.846732i	0.905959	+	0.423366i	$0.139152\pi$
$613$	12851.0i	0.846732i	−0.905959	+	0.423366i	$0.860848\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	−26693.0	−1.73325	−0.866625	−	0.498959i	$-0.833716\pi$
$619$	−26693.0	−1.73325	−0.866625	+	0.498959i	$0.833716\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	− 9784.00i	− 0.621694i
$629$	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
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	71820.0i	4.46721i
$638$	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
$643$	13160.0i	0.807122i	0.914953	+	0.403561i	$0.132228\pi$
$643$	13160.0i	0.807122i	−0.914953	+	0.403561i	$0.867772\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	− 27200.0i	− 1.63379i
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	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
$661$	33731.0	1.98485	0.992423	−	0.122864i	$-0.0392080\pi$
$661$	33731.0	1.98485	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
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	9899.00i	0.566981i	0.958975	+	0.283491i	$0.0914925\pi$
$673$	9899.00i	0.566981i	−0.958975	+	0.283491i	$0.908508\pi$
$674$	0	0
$675$	0	0
$676$	−21624.0	−1.23031
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	−19351.0	−1.09370
$680$	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
$687$	0	0
$688$	28736.0i	1.59237i
$689$	0	0
$690$	0	0
$691$	−16072.0	−0.884816	−0.442408	−	0.896814i	$-0.645876\pi$
$691$	−16072.0	−0.884816	−0.442408	+	0.896814i	$0.645876\pi$
$692$	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		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	70579.0i	3.78654i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	27523.0	1.45790	0.728948	−	0.684569i	$-0.240010\pi$
$709$	27523.0	1.45790	0.728948	+	0.684569i	$0.240010\pi$
$710$	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
$721$	703.000	0.0363122
$722$	0	0
$723$	0	0
$724$	27664.0	1.42006
$725$	0	0
$726$	0	0
$727$	− 38033.0i	− 1.94026i	−0.242594	−	0.970128i	$-0.577998\pi$
$727$	− 38033.0i	− 1.94026i	0.242594	−	0.970128i	$-0.422002\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	15050.0i	0.758369i	0.925321	+	0.379184i	$0.123795\pi$
$733$	15050.0i	0.758369i	−0.925321	+	0.379184i	$0.876205\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−31376.0	−1.56182	−0.780910	−	0.624644i	$-0.785244\pi$
$739$	−31376.0	−1.56182	−0.780910	+	0.624644i	$0.785244\pi$
$740$	0	0
$741$	0	0
$742$	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	$-0.640370\pi$
$751$	−17569.0	−0.853664	−0.426832	+	0.904331i	$0.640370\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	− 17333.0i	− 0.832204i	−0.909318	−	0.416102i	$-0.863396\pi$
$757$	− 17333.0i	− 0.832204i	0.909318	−	0.416102i	$-0.136604\pi$
$758$	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
$763$	− 81881.0i	− 3.88505i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	4606.00	0.215990	0.107995	−	0.994151i	$-0.465557\pi$
$769$	4606.00	0.215990	0.107995	+	0.994151i	$0.465557\pi$
$770$	0	0
$771$	0	0
$772$	− 31688.0i	− 1.47730i
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−65664.0	−2.99125
$785$	0	0
$786$	0	0
$787$	28747.0i	1.30206i	0.759053	+	0.651029i	$0.225662\pi$
$787$	28747.0i	1.30206i	−0.759053	+	0.651029i	$0.774338\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	− 50330.0i	− 2.25381i
$794$	0	0
$795$	0	0
$796$	41888.0	1.86518
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	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		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	−40609.0	−1.75829	−0.879146	−	0.476552i	$-0.841886\pi$
$811$	−40609.0	−1.75829	−0.879146	+	0.476552i	$0.841886\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	73187.0i	3.13401i
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	− 12220.0i	− 0.517573i	−0.965935	−	0.258786i	$-0.916677\pi$
$823$	− 12220.0i	− 0.517573i	0.965935	−	0.258786i	$-0.0833226\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−30077.0	−1.26009	−0.630047	−	0.776557i	$-0.716964\pi$
$829$	−30077.0	−1.26009	−0.630047	+	0.776557i	$0.716964\pi$
$830$	0	0
$831$	0	0
$832$	− 35840.0i	− 1.49342i
$833$	0	0
$834$	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
$841$	−24389.0	−1.00000
$842$	0	0
$843$	0	0
$844$	48256.0	1.96806
$845$	0	0
$846$	0	0
$847$	− 49247.0i	− 1.99781i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 46690.0i	− 1.87413i	−0.349151	−	0.937066i	$-0.613530\pi$
$853$	− 46690.0i	− 1.87413i	0.349151	−	0.937066i	$-0.386470\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	49807.0	1.97834	0.989169	−	0.146779i	$-0.0468906\pi$
$859$	49807.0	1.97834	0.989169	+	0.146779i	$0.0468906\pi$
$860$	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
$867$	0	0
$868$	− 5624.00i	− 0.219921i
$869$	0	0
$870$	0	0
$871$	61600.0	2.39637
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	13357.0i	0.514292i	0.966373	+	0.257146i	$0.0827821\pi$
$877$	13357.0i	0.514292i	−0.966373	+	0.257146i	$0.917218\pi$
$878$	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
$883$	− 31429.0i	− 1.19781i	−0.800818	−	0.598907i	$-0.795602\pi$
$883$	− 31429.0i	− 1.19781i	0.800818	−	0.598907i	$-0.204398\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	14060.0	0.530436
$890$	0	0
$891$	0	0
$892$	− 27512.0i	− 1.03270i
$893$	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
$907$	− 4607.00i	− 0.168658i	−0.996438	−	0.0843291i	$-0.973125\pi$
$907$	− 4607.00i	− 0.168658i	0.996438	−	0.0843291i	$-0.0268747\pi$
$908$	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
$916$	−18856.0	−0.680153
$917$	0	0
$918$	0	0
$919$	49573.0	1.77939	0.889697	−	0.456552i	$-0.150916\pi$
$919$	49573.0	1.77939	0.889697	+	0.456552i	$0.150916\pi$
$920$	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
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	−167238.	−5.88722
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	− 40283.0i	− 1.40447i	−0.711945	−	0.702235i	$-0.752186\pi$
$937$	− 40283.0i	− 1.40447i	0.711945	−	0.702235i	$-0.247814\pi$
$938$	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
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	−18970.0	−0.648885
$950$	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
$961$	−29430.0	−0.987882
$962$	0	0
$963$	0	0
$964$	−59024.0	−1.97203
$965$	0	0
$966$	0	0
$967$	− 53927.0i	− 1.79336i	−0.442683	−	0.896678i	$-0.645973\pi$
$967$	− 53927.0i	− 1.79336i	0.442683	−	0.896678i	$-0.354027\pi$
$968$	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
$973$	112591.i	3.70966i
$974$	0	0
$975$	0	0
$976$	46016.0	1.50916
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	− 91280.0i	− 2.93927i
$989$	0	0
$990$	0	0
$991$	−14041.0	−0.450078	−0.225039	−	0.974350i	$-0.572251\pi$
$991$	−14041.0	−0.450078	−0.225039	+	0.974350i	$0.572251\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	− 28910.0i	− 0.918344i	−0.888347	−	0.459172i	$-0.848146\pi$
$997$	− 28910.0i	− 0.918344i	0.888347	−	0.459172i	$-0.151854\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.4.b.h.649.2		2
3.2	odd	2	CM	675.4.b.h.649.2		2
5.2	odd	4		675.4.a.d.1.1	✓	1
5.3	odd	4		675.4.a.g.1.1	yes	1
5.4	even	2	inner	675.4.b.h.649.1		2
15.2	even	4		675.4.a.d.1.1	✓	1
15.8	even	4		675.4.a.g.1.1	yes	1
15.14	odd	2	inner	675.4.b.h.649.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.4.a.d.1.1	✓	1	5.2	odd	4
675.4.a.d.1.1	✓	1	15.2	even	4
675.4.a.g.1.1	yes	1	5.3	odd	4
675.4.a.g.1.1	yes	1	15.8	even	4
675.4.b.h.649.1		2	5.4	even	2	inner
675.4.b.h.649.1		2	15.14	odd	2	inner
675.4.b.h.649.2		2	1.1	even	1	trivial
675.4.b.h.649.2		2	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	675.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+8.00000 q^{4} +37.0000i q^{7} -70.0000i q^{13} +64.0000 q^{16} +163.000 q^{19} +296.000i q^{28} -19.0000 q^{31} +433.000i q^{37} +449.000i q^{43} -1026.00 q^{49} -560.000i q^{52} +719.000 q^{61} +512.000 q^{64} +880.000i q^{67} -271.000i q^{73} +1304.00 q^{76} -503.000 q^{79} +2590.00 q^{91} +523.000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{4} + 128 q^{16} + 326 q^{19} - 38 q^{31} - 2052 q^{49} + 1438 q^{61} + 1024 q^{64} + 2608 q^{76} - 1006 q^{79} + 5180 q^{91}+O(q^{100}) \) 2 * q + 16 * q^4 + 128 * q^16 + 326 * q^19 - 38 * q^31 - 2052 * q^49 + 1438 * q^61 + 1024 * q^64 + 2608 * q^76 - 1006 * q^79 + 5180 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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