LMFDB - Embedded newform 1449.2.h.b.1126.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1449,2,Mod(1126,1449)] 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("1449.1126"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1449, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1449 = 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1449.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5703232529$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{7}, \sqrt{-23})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - x^{2} + 2x + 162 $ x^4 - 2x^3 - x^2 + 2x + 162
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1126.1
Root			$-2.14575 + 2.39792i$ of defining polynomial
Character	$\chi$	$=$	1449.1126
Dual form			1449.2.h.b.1126.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1449\mathbb{Z}\right)^\times$.

$n$	$442$	$829$	$1289$
$\chi(n)$	$-1$	$-1$	$1$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	0	0
$3$	0	0
$4$	−2.00000	−1.00000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−2.64575	−1.00000
$7$	−2.64575	−1.00000
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 4.79583i	− 1.44600i	−0.690849	−	0.722999i	$-0.742763\pi$
$11$	− 4.79583i	− 1.44600i	0.690849	−	0.722999i	$-0.257237\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	2.64575	0.606977	0.303488	−	0.952835i	$-0.401849\pi$
$19$	2.64575	0.606977	0.303488	+	0.952835i	$0.401849\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.79583i	1.00000i
$23$	4.79583i	1.00000i
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	5.29150	1.00000
$29$	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
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	12.6886i	1.98162i	0.135250	+	0.990811i	$0.456816\pi$
$41$	12.6886i	1.98162i	−0.135250	+	0.990811i	$0.543184\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	9.59166i	1.44600i
$45$	0	0
$46$	0	0
$47$	12.6886i	1.85082i	0.378968	+	0.925410i	$0.376279\pi$
$47$	12.6886i	1.85082i	−0.378968	+	0.925410i	$0.623721\pi$
$48$	0	0
$49$	7.00000	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	− 4.79583i	− 0.658758i	−0.944198	−	0.329379i	$-0.893161\pi$
$53$	− 4.79583i	− 0.658758i	0.944198	−	0.329379i	$-0.106839\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	12.6886i	1.65191i	0.563735	+	0.825956i	$0.309364\pi$
$59$	12.6886i	1.65191i	−0.563735	+	0.825956i	$0.690636\pi$
$60$	0	0
$61$	−13.2288	−1.69377	−0.846884	−	0.531777i	$-0.821524\pi$
$61$	−13.2288	−1.69377	−0.846884	+	0.531777i	$0.821524\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	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
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	−5.29150	−0.606977
$77$	12.6886i	1.44600i
$78$	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
$85$	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
$92$	− 9.59166i	− 1.00000i
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.5830	1.07454	0.537271	−	0.843410i	$-0.319455\pi$
$97$	10.5830	1.07454	0.537271	+	0.843410i	$0.319455\pi$
$98$	0	0
$99$	0	0
$100$	10.0000	1.00000
$101$	12.6886i	1.26256i	0.775555	+	0.631280i	$0.217470\pi$
$101$	12.6886i	1.26256i	−0.775555	+	0.631280i	$0.782530\pi$
$102$	0	0
$103$	18.5203	1.82486	0.912428	−	0.409238i	$-0.134205\pi$
$103$	18.5203	1.82486	0.912428	+	0.409238i	$0.134205\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	9.59166i	0.927261i	0.886029	+	0.463631i	$0.153453\pi$
$107$	9.59166i	0.927261i	−0.886029	+	0.463631i	$0.846547\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	−10.5830	−1.00000
$113$	− 19.1833i	− 1.80462i	−0.431092	−	0.902308i	$-0.641872\pi$
$113$	− 19.1833i	− 1.80462i	0.431092	−	0.902308i	$-0.358128\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−12.0000	−1.09091
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	5.00000	0.443678	0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000	0.443678	0.221839	+	0.975083i	$0.428794\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	12.6886i	1.10861i	0.832315	+	0.554303i	$0.187015\pi$
$131$	12.6886i	1.10861i	−0.832315	+	0.554303i	$0.812985\pi$
$132$	0	0
$133$	−7.00000	−0.606977
$134$	0	0
$135$	0	0
$136$	0	0
$137$	− 4.79583i	− 0.409736i	−0.978790	−	0.204868i	$-0.934324\pi$
$137$	− 4.79583i	− 0.409736i	0.978790	−	0.204868i	$-0.0656764\pi$
$138$	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
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	23.9792i	1.96445i	0.187710	+	0.982225i	$0.439894\pi$
$149$	23.9792i	1.96445i	−0.187710	+	0.982225i	$0.560106\pi$
$150$	0	0
$151$	11.0000	0.895167	0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000	0.895167	0.447584	+	0.894242i	$0.352285\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	2.64575	0.211154	0.105577	−	0.994411i	$-0.466331\pi$
$157$	2.64575	0.211154	0.105577	+	0.994411i	$0.466331\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	− 12.6886i	− 1.00000i
$162$	0	0
$163$	−13.0000	−1.01824	−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000	−1.01824	−0.509119	+	0.860696i	$0.670029\pi$
$164$	− 25.3772i	− 1.98162i
$165$	0	0
$166$	0	0
$167$	12.6886i	0.981872i	0.871196	+	0.490936i	$0.163345\pi$
$167$	12.6886i	0.981872i	−0.871196	+	0.490936i	$0.836655\pi$
$168$	0	0
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	− 25.3772i	− 1.92939i	−0.263371	−	0.964695i	$-0.584834\pi$
$173$	− 25.3772i	− 1.92939i	0.263371	−	0.964695i	$-0.415166\pi$
$174$	0	0
$175$	13.2288	1.00000
$176$	− 19.1833i	− 1.44600i
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−21.1660	−1.57326	−0.786629	−	0.617426i	$-0.788175\pi$
$181$	−21.1660	−1.57326	−0.786629	+	0.617426i	$0.788175\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	− 25.3772i	− 1.85082i
$189$	0	0
$190$	0	0
$191$	23.9792i	1.73507i	0.497375	+	0.867535i	$0.334297\pi$
$191$	23.9792i	1.73507i	−0.497375	+	0.867535i	$0.665703\pi$
$192$	0	0
$193$	17.0000	1.22369	0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000	1.22369	0.611843	+	0.790979i	$0.290428\pi$
$194$	0	0
$195$	0	0
$196$	−14.0000	−1.00000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−13.2288	−0.937762	−0.468881	−	0.883261i	$-0.655343\pi$
$199$	−13.2288	−0.937762	−0.468881	+	0.883261i	$0.655343\pi$
$200$	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
$209$	− 12.6886i	− 0.877687i
$210$	0	0
$211$	−19.0000	−1.30801	−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000	−1.30801	−0.654007	+	0.756489i	$0.726913\pi$
$212$	9.59166i	0.658758i
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	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
$229$	−29.1033	−1.92320	−0.961599	−	0.274459i	$-0.911501\pi$
$229$	−29.1033	−1.92320	−0.961599	+	0.274459i	$0.911501\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	− 25.3772i	− 1.65191i
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	18.5203	1.19299	0.596497	−	0.802615i	$-0.296559\pi$
$241$	18.5203	1.19299	0.596497	+	0.802615i	$0.296559\pi$
$242$	0	0
$243$	0	0
$244$	26.4575	1.69377
$245$	0	0
$246$	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
$253$	23.0000	1.44600
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	12.6886i	0.791492i	0.918360	+	0.395746i	$0.129514\pi$
$257$	12.6886i	0.791492i	−0.918360	+	0.395746i	$0.870486\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 4.79583i	− 0.295724i	−0.989008	−	0.147862i	$-0.952761\pi$
$263$	− 4.79583i	− 0.295724i	0.989008	−	0.147862i	$-0.0472391\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	− 25.3772i	− 1.54727i	−0.633630	−	0.773636i	$-0.718436\pi$
$269$	− 25.3772i	− 1.54727i	0.633630	−	0.773636i	$-0.281564\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	23.9792i	1.44600i
$276$	0	0
$277$	−25.0000	−1.50210	−0.751052	−	0.660243i	$-0.770453\pi$
$277$	−25.0000	−1.50210	−0.751052	+	0.660243i	$0.770453\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	− 19.1833i	− 1.14438i	−0.820121	−	0.572191i	$-0.806094\pi$
$281$	− 19.1833i	− 1.14438i	0.820121	−	0.572191i	$-0.193906\pi$
$282$	0	0
$283$	−5.29150	−0.314547	−0.157274	−	0.987555i	$-0.550270\pi$
$283$	−5.29150	−0.314547	−0.157274	+	0.987555i	$0.550270\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	− 33.5708i	− 1.98162i
$288$	0	0
$289$	−17.0000	−1.00000
$290$	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
$301$	0	0
$302$	0	0
$303$	0	0
$304$	10.5830	0.606977
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	− 25.3772i	− 1.44600i
$309$	0	0
$310$	0	0
$311$	12.6886i	0.719503i	0.933048	+	0.359752i	$0.117139\pi$
$311$	12.6886i	0.719503i	−0.933048	+	0.359752i	$0.882861\pi$
$312$	0	0
$313$	34.3948	1.94411	0.972054	−	0.234759i	$-0.0754301\pi$
$313$	34.3948	1.94411	0.972054	+	0.234759i	$0.0754301\pi$
$314$	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
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	− 33.5708i	− 1.85082i
$330$	0	0
$331$	29.0000	1.59398	0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000	1.59398	0.796992	+	0.603990i	$0.206423\pi$
$332$	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
$343$	−18.5203	−1.00000
$344$	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
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 25.3772i	− 1.35069i	−0.737502	−	0.675345i	$-0.763995\pi$
$353$	− 25.3772i	− 1.35069i	0.737502	−	0.675345i	$-0.236005\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	9.59166i	0.506229i	0.967436	+	0.253114i	$0.0814549\pi$
$359$	9.59166i	0.506229i	−0.967436	+	0.253114i	$0.918545\pi$
$360$	0	0
$361$	−12.0000	−0.631579
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−29.1033	−1.51918	−0.759589	−	0.650403i	$-0.774600\pi$
$367$	−29.1033	−1.51918	−0.759589	+	0.650403i	$0.774600\pi$
$368$	19.1833i	1.00000i
$369$	0	0
$370$	0	0
$371$	12.6886i	0.658758i
$372$	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
$385$	0	0
$386$	0	0
$387$	0	0
$388$	−21.1660	−1.07454
$389$	38.3667i	1.94527i	0.232346	+	0.972633i	$0.425360\pi$
$389$	38.3667i	1.94527i	−0.232346	+	0.972633i	$0.574640\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	−20.0000	−1.00000
$401$	23.9792i	1.19746i	0.800950	+	0.598731i	$0.204328\pi$
$401$	23.9792i	1.19746i	−0.800950	+	0.598731i	$0.795672\pi$
$402$	0	0
$403$	0	0
$404$	− 25.3772i	− 1.26256i
$405$	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
$412$	−37.0405	−1.82486
$413$	− 33.5708i	− 1.65191i
$414$	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
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	35.0000	1.69377
$428$	− 19.1833i	− 0.927261i
$429$	0	0
$430$	0	0
$431$	− 4.79583i	− 0.231007i	−0.993307	−	0.115504i	$-0.963152\pi$
$431$	− 4.79583i	− 0.231007i	0.993307	−	0.115504i	$-0.0368482\pi$
$432$	0	0
$433$	2.64575	0.127147	0.0635733	−	0.997977i	$-0.479750\pi$
$433$	2.64575	0.127147	0.0635733	+	0.997977i	$0.479750\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	12.6886i	0.606977i
$438$	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
$445$	0	0
$446$	0	0
$447$	0	0
$448$	21.1660	1.00000
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	60.8523	2.86542
$452$	38.3667i	1.80462i
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 25.3772i	− 1.18193i	−0.806696	−	0.590966i	$-0.798747\pi$
$461$	− 25.3772i	− 1.18193i	0.806696	−	0.590966i	$-0.201253\pi$
$462$	0	0
$463$	−37.0000	−1.71954	−0.859768	−	0.510685i	$-0.829392\pi$
$463$	−37.0000	−1.71954	−0.859768	+	0.510685i	$0.829392\pi$
$464$	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
$475$	−13.2288	−0.606977
$476$	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
$481$	0	0
$482$	0	0
$483$	0	0
$484$	24.0000	1.09091
$485$	0	0
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	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
$496$	0	0
$497$	0	0
$498$	0	0
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	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
$507$	0	0
$508$	−10.0000	−0.443678
$509$	12.6886i	0.562411i	0.959648	+	0.281206i	$0.0907343\pi$
$509$	12.6886i	0.562411i	−0.959648	+	0.281206i	$0.909266\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	60.8523	2.67628
$518$	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
$523$	−44.9778	−1.96674	−0.983370	−	0.181612i	$-0.941869\pi$
$523$	−44.9778	−1.96674	−0.983370	+	0.181612i	$0.941869\pi$
$524$	− 25.3772i	− 1.10861i
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	14.0000	0.606977
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	− 33.5708i	− 1.44600i
$540$	0	0
$541$	41.0000	1.76273	0.881364	−	0.472438i	$-0.156626\pi$
$541$	41.0000	1.76273	0.881364	+	0.472438i	$0.156626\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	9.59166i	0.409736i
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	38.3667i	1.62565i	0.582510	+	0.812824i	$0.302071\pi$
$557$	38.3667i	1.62565i	−0.582510	+	0.812824i	$0.697929\pi$
$558$	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
$569$	23.9792i	1.00526i	0.864502	+	0.502629i	$0.167634\pi$
$569$	23.9792i	1.00526i	−0.864502	+	0.502629i	$0.832366\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	− 23.9792i	− 1.00000i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−23.0000	−0.952563
$584$	0	0
$585$	0	0
$586$	0	0
$587$	12.6886i	0.523714i	0.965107	+	0.261857i	$0.0843348\pi$
$587$	12.6886i	0.523714i	−0.965107	+	0.261857i	$0.915665\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 25.3772i	− 1.04211i	−0.853522	−	0.521057i	$-0.825538\pi$
$593$	− 25.3772i	− 1.04211i	0.853522	−	0.521057i	$-0.174462\pi$
$594$	0	0
$595$	0	0
$596$	− 47.9583i	− 1.96445i
$597$	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
$604$	−22.0000	−0.895167
$605$	0	0
$606$	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
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 19.1833i	− 0.772292i	−0.922438	−	0.386146i	$-0.873806\pi$
$617$	− 19.1833i	− 0.772292i	0.922438	−	0.386146i	$-0.126194\pi$
$618$	0	0
$619$	−37.0405	−1.48878	−0.744392	−	0.667743i	$-0.767261\pi$
$619$	−37.0405	−1.48878	−0.744392	+	0.667743i	$0.767261\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	−5.29150	−0.211154
$629$	0	0
$630$	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
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	− 4.79583i	− 0.189424i	−0.995505	−	0.0947120i	$-0.969807\pi$
$641$	− 4.79583i	− 0.189424i	0.995505	−	0.0947120i	$-0.0301930\pi$
$642$	0	0
$643$	−29.1033	−1.14772	−0.573860	−	0.818953i	$-0.694555\pi$
$643$	−29.1033	−1.14772	−0.573860	+	0.818953i	$0.694555\pi$
$644$	25.3772i	1.00000i
$645$	0	0
$646$	0	0
$647$	50.7543i	1.99536i	0.0680939	+	0.997679i	$0.478308\pi$
$647$	50.7543i	1.99536i	−0.0680939	+	0.997679i	$0.521692\pi$
$648$	0	0
$649$	60.8523	2.38866
$650$	0	0
$651$	0	0
$652$	26.0000	1.01824
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	50.7543i	1.98162i
$657$	0	0
$658$	0	0
$659$	− 47.9583i	− 1.86819i	−0.357024	−	0.934095i	$-0.616208\pi$
$659$	− 47.9583i	− 1.86819i	0.357024	−	0.934095i	$-0.383792\pi$
$660$	0	0
$661$	−44.9778	−1.74943	−0.874716	−	0.484635i	$-0.838952\pi$
$661$	−44.9778	−1.74943	−0.874716	+	0.484635i	$0.838952\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	− 25.3772i	− 0.981872i
$669$	0	0
$670$	0	0
$671$	63.4429i	2.44919i
$672$	0	0
$673$	47.0000	1.81172	0.905858	−	0.423581i	$-0.139227\pi$
$673$	47.0000	1.81172	0.905858	+	0.423581i	$0.139227\pi$
$674$	0	0
$675$	0	0
$676$	−26.0000	−1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	−28.0000	−1.07454
$680$	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
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	50.7543i	1.92939i
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−26.4575	−1.00000
$701$	52.7541i	1.99250i	0.0865407	+	0.996248i	$0.472419\pi$
$701$	52.7541i	1.99250i	−0.0865407	+	0.996248i	$0.527581\pi$
$702$	0	0
$703$	0	0
$704$	38.3667i	1.44600i
$705$	0	0
$706$	0	0
$707$	− 33.5708i	− 1.26256i
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	50.7543i	1.89282i	0.322973	+	0.946408i	$0.395318\pi$
$719$	50.7543i	1.89282i	−0.322973	+	0.946408i	$0.604682\pi$
$720$	0	0
$721$	−49.0000	−1.82486
$722$	0	0
$723$	0	0
$724$	42.3320	1.57326
$725$	0	0
$726$	0	0
$727$	34.3948	1.27563	0.637816	−	0.770189i	$-0.279838\pi$
$727$	34.3948	1.27563	0.637816	+	0.770189i	$0.279838\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−21.1660	−0.781784	−0.390892	−	0.920436i	$-0.627833\pi$
$733$	−21.1660	−0.781784	−0.390892	+	0.920436i	$0.627833\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	32.0000	1.17714	0.588570	−	0.808447i	$-0.299691\pi$
$739$	32.0000	1.17714	0.588570	+	0.808447i	$0.299691\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	52.7541i	1.93536i	0.252178	+	0.967681i	$0.418853\pi$
$743$	52.7541i	1.93536i	−0.252178	+	0.967681i	$0.581147\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	− 25.3772i	− 0.927261i
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	50.7543i	1.85082i
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	12.6886i	0.459961i	0.973195	+	0.229980i	$0.0738662\pi$
$761$	12.6886i	0.459961i	−0.973195	+	0.229980i	$0.926134\pi$
$762$	0	0
$763$	0	0
$764$	− 47.9583i	− 1.73507i
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−52.9150	−1.90816	−0.954082	−	0.299545i	$-0.903165\pi$
$769$	−52.9150	−1.90816	−0.954082	+	0.299545i	$0.903165\pi$
$770$	0	0
$771$	0	0
$772$	−34.0000	−1.22369
$773$	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
$779$	33.5708i	1.20280i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	28.0000	1.00000
$785$	0	0
$786$	0	0
$787$	50.2693	1.79191	0.895953	−	0.444149i	$-0.146494\pi$
$787$	50.2693	1.79191	0.895953	+	0.444149i	$0.146494\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	50.7543i	1.80462i
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	26.4575	0.937762
$797$	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		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	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
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	53.0000	1.84746	0.923732	−	0.383040i	$-0.125123\pi$
$823$	53.0000	1.84746	0.923732	+	0.383040i	$0.125123\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	52.7541i	1.83444i	0.398379	+	0.917221i	$0.369573\pi$
$827$	52.7541i	1.83444i	−0.398379	+	0.917221i	$0.630427\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	25.3772i	0.877687i
$837$	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
$844$	38.0000	1.30801
$845$	0	0
$846$	0	0
$847$	31.7490	1.09091
$848$	− 19.1833i	− 0.658758i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	12.6886i	0.433434i	0.976235	+	0.216717i	$0.0695348\pi$
$857$	12.6886i	0.433434i	−0.976235	+	0.216717i	$0.930465\pi$
$858$	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
$865$	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
$875$	0	0
$876$	0	0
$877$	−55.0000	−1.85722	−0.928609	−	0.371060i	$-0.878995\pi$
$877$	−55.0000	−1.85722	−0.928609	+	0.371060i	$0.878995\pi$
$878$	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
$883$	−40.0000	−1.34611	−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000	−1.34611	−0.673054	+	0.739594i	$0.735018\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	50.7543i	1.70416i	0.523409	+	0.852081i	$0.324660\pi$
$887$	50.7543i	1.70416i	−0.523409	+	0.852081i	$0.675340\pi$
$888$	0	0
$889$	−13.2288	−0.443678
$890$	0	0
$891$	0	0
$892$	0	0
$893$	33.5708i	1.12340i
$894$	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
$911$	− 47.9583i	− 1.58893i	−0.607310	−	0.794465i	$-0.707751\pi$
$911$	− 47.9583i	− 1.58893i	0.607310	−	0.794465i	$-0.292249\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	58.2065	1.92320
$917$	− 33.5708i	− 1.10861i
$918$	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
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	− 25.3772i	− 0.832597i	−0.909228	−	0.416299i	$-0.863327\pi$
$929$	− 25.3772i	− 0.832597i	0.909228	−	0.416299i	$-0.136673\pi$
$930$	0	0
$931$	18.5203	0.606977
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−44.9778	−1.46936	−0.734680	−	0.678414i	$-0.762668\pi$
$937$	−44.9778	−1.46936	−0.734680	+	0.678414i	$0.762668\pi$
$938$	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
$943$	−60.8523	−1.98162
$944$	50.7543i	1.65191i
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	52.7541i	1.70887i	0.519555	+	0.854437i	$0.326098\pi$
$953$	52.7541i	1.70887i	−0.519555	+	0.854437i	$0.673902\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	12.6886i	0.409736i
$960$	0	0
$961$	31.0000	1.00000
$962$	0	0
$963$	0	0
$964$	−37.0405	−1.19299
$965$	0	0
$966$	0	0
$967$	44.0000	1.41494	0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000	1.41494	0.707472	+	0.706741i	$0.249835\pi$
$968$	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
$976$	−52.9150	−1.69377
$977$	− 62.3458i	− 1.99462i	−0.0733048	−	0.997310i	$-0.523355\pi$
$977$	− 62.3458i	− 1.99462i	0.0733048	−	0.997310i	$-0.476645\pi$
$978$	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
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	59.0000	1.87420	0.937098	−	0.349065i	$-0.113501\pi$
$991$	59.0000	1.87420	0.937098	+	0.349065i	$0.113501\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1449.2.h.b.1126.1	✓	4
3.2	odd	2	inner	1449.2.h.b.1126.2	yes	4
7.6	odd	2	inner	1449.2.h.b.1126.3	yes	4
21.20	even	2	inner	1449.2.h.b.1126.4	yes	4
23.22	odd	2	inner	1449.2.h.b.1126.4	yes	4
69.68	even	2	inner	1449.2.h.b.1126.3	yes	4
161.160	even	2	inner	1449.2.h.b.1126.2	yes	4
483.482	odd	2	CM	1449.2.h.b.1126.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1449.2.h.b.1126.1	✓	4	1.1	even	1	trivial
1449.2.h.b.1126.1	✓	4	483.482	odd	2	CM
1449.2.h.b.1126.2	yes	4	3.2	odd	2	inner
1449.2.h.b.1126.2	yes	4	161.160	even	2	inner
1449.2.h.b.1126.3	yes	4	7.6	odd	2	inner
1449.2.h.b.1126.3	yes	4	69.68	even	2	inner
1449.2.h.b.1126.4	yes	4	21.20	even	2	inner
1449.2.h.b.1126.4	yes	4	23.22	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1449.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{4} -2.64575 q^{7} -4.79583i q^{11} +4.00000 q^{16} +2.64575 q^{19} +4.79583i q^{23} -5.00000 q^{25} +5.29150 q^{28} +12.6886i q^{41} +9.59166i q^{44} +12.6886i q^{47} +7.00000 q^{49} -4.79583i q^{53} +12.6886i q^{59} -13.2288 q^{61} -8.00000 q^{64} -5.29150 q^{76} +12.6886i q^{77} -9.59166i q^{92} +10.5830 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 16 q^{16} - 20 q^{25} + 28 q^{49} - 32 q^{64}+O(q^{100}) \) 4 * q - 8 * q^4 + 16 * q^16 - 20 * q^25 + 28 * q^49 - 32 * q^64

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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