LMFDB - Embedded newform 1152.2.d.g.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(577,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1152.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.d (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:	$9.19876631285$
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} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			577.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1152.577
Dual form			1152.2.d.g.577.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.46410i q^{5} +4.89898 q^{7} +O(q^{10})$	$q-3.46410i q^{5} +4.89898 q^{7} -5.65685i q^{11} -7.00000 q^{25} +10.3923i q^{29} -4.89898 q^{31} -16.9706i q^{35} +17.0000 q^{49} +3.46410i q^{53} -19.5959 q^{55} -11.3137i q^{59} -14.0000 q^{73} -27.7128i q^{77} +14.6969 q^{79} -5.65685i q^{83} +2.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 28 q^{25} + 68 q^{49} - 56 q^{73} + 8 q^{97}+O(q^{100}) $ 4 * q - 28 * q^25 + 68 * q^49 - 56 * q^73 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$1$	$-1$

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
$5$	− 3.46410i	− 1.54919i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$	− 3.46410i	− 1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$	0	0
$7$	4.89898	1.85164	0.925820	−	0.377964i	$-0.123376\pi$
$7$	4.89898	1.85164	0.925820	+	0.377964i	$0.123376\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	− 5.65685i	− 1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$	− 5.65685i	− 1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	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
$25$	−7.00000	−1.40000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	10.3923i	1.92980i	0.262613	+	0.964901i	$0.415416\pi$
$29$	10.3923i	1.92980i	−0.262613	+	0.964901i	$0.584584\pi$
$30$	0	0
$31$	−4.89898	−0.879883	−0.439941	−	0.898027i	$-0.645001\pi$
$31$	−4.89898	−0.879883	−0.439941	+	0.898027i	$0.645001\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 16.9706i	− 2.86855i
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	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
$49$	17.0000	2.42857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	3.46410i	0.475831i	0.971286	+	0.237915i	$0.0764641\pi$
$53$	3.46410i	0.475831i	−0.971286	+	0.237915i	$0.923536\pi$
$54$	0	0
$55$	−19.5959	−2.64231
$56$	0	0
$57$	0	0
$58$	0	0
$59$	− 11.3137i	− 1.47292i	−0.676481	−	0.736460i	$-0.736496\pi$
$59$	− 11.3137i	− 1.47292i	0.676481	−	0.736460i	$-0.263504\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	− 27.7128i	− 3.15817i
$78$	0	0
$79$	14.6969	1.65353	0.826767	−	0.562544i	$-0.190177\pi$
$79$	14.6969	1.65353	0.826767	+	0.562544i	$0.190177\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	− 5.65685i	− 0.620920i	−0.950586	−	0.310460i	$-0.899517\pi$
$83$	− 5.65685i	− 0.620920i	0.950586	−	0.310460i	$-0.100483\pi$
$84$	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
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	3.46410i	0.344691i	0.985037	+	0.172345i	$0.0551346\pi$
$101$	3.46410i	0.344691i	−0.985037	+	0.172345i	$0.944865\pi$
$102$	0	0
$103$	14.6969	1.44813	0.724066	−	0.689730i	$-0.242271\pi$
$103$	14.6969	1.44813	0.724066	+	0.689730i	$0.242271\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 11.3137i	− 1.09374i	−0.837218	−	0.546869i	$-0.815820\pi$
$107$	− 11.3137i	− 1.09374i	0.837218	−	0.546869i	$-0.184180\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−21.0000	−1.90909
$122$	0	0
$123$	0	0
$124$	0	0
$125$	6.92820i	0.619677i
$126$	0	0
$127$	4.89898	0.434714	0.217357	−	0.976092i	$-0.430256\pi$
$127$	4.89898	0.434714	0.217357	+	0.976092i	$0.430256\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	22.6274i	1.97697i	0.151330	+	0.988483i	$0.451644\pi$
$131$	22.6274i	1.97697i	−0.151330	+	0.988483i	$0.548356\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	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
$145$	36.0000	2.98964
$146$	0	0
$147$	0	0
$148$	0	0
$149$	24.2487i	1.98653i	0.115857	+	0.993266i	$0.463039\pi$
$149$	24.2487i	1.98653i	−0.115857	+	0.993266i	$0.536961\pi$
$150$	0	0
$151$	24.4949	1.99337	0.996683	−	0.0813788i	$-0.0259324\pi$
$151$	24.4949	1.99337	0.996683	+	0.0813788i	$0.0259324\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	16.9706i	1.36311i
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	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
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	17.3205i	1.31685i	0.752645	+	0.658427i	$0.228778\pi$
$173$	17.3205i	1.31685i	−0.752645	+	0.658427i	$0.771222\pi$
$174$	0	0
$175$	−34.2929	−2.59230
$176$	0	0
$177$	0	0
$178$	0	0
$179$	− 11.3137i	− 0.845626i	−0.906217	−	0.422813i	$-0.861043\pi$
$179$	− 11.3137i	− 0.845626i	0.906217	−	0.422813i	$-0.138957\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	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
$193$	−26.0000	−1.87152	−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000	−1.87152	−0.935760	+	0.352636i	$0.885285\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 24.2487i	− 1.72765i	−0.503793	−	0.863825i	$-0.668062\pi$
$197$	− 24.2487i	− 1.72765i	0.503793	−	0.863825i	$-0.331938\pi$
$198$	0	0
$199$	−24.4949	−1.73640	−0.868199	−	0.496217i	$-0.834722\pi$
$199$	−24.4949	−1.73640	−0.868199	+	0.496217i	$0.834722\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	50.9117i	3.57330i
$204$	0	0
$205$	0	0
$206$	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
$217$	−24.0000	−1.62923
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−14.6969	−0.984180	−0.492090	−	0.870544i	$-0.663767\pi$
$223$	−14.6969	−0.984180	−0.492090	+	0.870544i	$0.663767\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	28.2843i	1.87729i	0.344881	+	0.938647i	$0.387919\pi$
$227$	28.2843i	1.87729i	−0.344881	+	0.938647i	$0.612081\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	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
$236$	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
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	− 58.8897i	− 3.76233i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	− 5.65685i	− 0.357057i	−0.983935	−	0.178529i	$-0.942866\pi$
$251$	− 5.65685i	− 0.357057i	0.983935	−	0.178529i	$-0.0571337\pi$
$252$	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		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	0	0
$268$	0	0
$269$	10.3923i	0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$269$	10.3923i	0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$270$	0	0
$271$	24.4949	1.48796	0.743980	−	0.668202i	$-0.232936\pi$
$271$	24.4949	1.48796	0.743980	+	0.668202i	$0.232936\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	39.5980i	2.38785i
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	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
$283$	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
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	31.1769i	1.82137i	0.413096	+	0.910687i	$0.364447\pi$
$293$	31.1769i	1.82137i	−0.413096	+	0.910687i	$0.635553\pi$
$294$	0	0
$295$	−39.1918	−2.28184
$296$	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
$307$	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
$313$	34.0000	1.92179	0.960897	−	0.276907i	$-0.0893093\pi$
$313$	34.0000	1.92179	0.960897	+	0.276907i	$0.0893093\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	− 17.3205i	− 0.972817i	−0.873732	−	0.486408i	$-0.838307\pi$
$317$	− 17.3205i	− 0.972817i	0.873732	−	0.486408i	$-0.161693\pi$
$318$	0	0
$319$	58.7878	3.29148
$320$	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
$331$	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
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	27.7128i	1.50073i
$342$	0	0
$343$	48.9898	2.64520
$344$	0	0
$345$	0	0
$346$	0	0
$347$	28.2843i	1.51838i	0.650870	+	0.759190i	$0.274404\pi$
$347$	28.2843i	1.51838i	−0.650870	+	0.759190i	$0.725596\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	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		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	48.4974i	2.53847i
$366$	0	0
$367$	−4.89898	−0.255725	−0.127862	−	0.991792i	$-0.540812\pi$
$367$	−4.89898	−0.255725	−0.127862	+	0.991792i	$0.540812\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	16.9706i	0.881068i
$372$	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
$385$	−96.0000	−4.89261
$386$	0	0
$387$	0	0
$388$	0	0
$389$	24.2487i	1.22946i	0.788738	+	0.614729i	$0.210735\pi$
$389$	24.2487i	1.22946i	−0.788738	+	0.614729i	$0.789265\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	− 50.9117i	− 2.56165i
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	− 55.4256i	− 2.72732i
$414$	0	0
$415$	−19.5959	−0.961926
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 39.5980i	− 1.93449i	−0.253849	−	0.967244i	$-0.581697\pi$
$419$	− 39.5980i	− 1.93449i	0.253849	−	0.967244i	$-0.418303\pi$
$420$	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
$427$	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
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−24.4949	−1.16908	−0.584539	−	0.811366i	$-0.698725\pi$
$439$	−24.4949	−1.16908	−0.584539	+	0.811366i	$0.698725\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	28.2843i	1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$	28.2843i	1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 38.1051i	− 1.77473i	−0.461065	−	0.887366i	$-0.652533\pi$
$461$	− 38.1051i	− 1.77473i	0.461065	−	0.887366i	$-0.347467\pi$
$462$	0	0
$463$	−34.2929	−1.59372	−0.796862	−	0.604161i	$-0.793508\pi$
$463$	−34.2929	−1.59372	−0.796862	+	0.604161i	$0.793508\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 39.5980i	− 1.83238i	−0.400749	−	0.916188i	$-0.631250\pi$
$467$	− 39.5980i	− 1.83238i	0.400749	−	0.916188i	$-0.368750\pi$
$468$	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
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	− 6.92820i	− 0.314594i
$486$	0	0
$487$	44.0908	1.99795	0.998973	−	0.0453143i	$-0.0144289\pi$
$487$	44.0908	1.99795	0.998973	+	0.0453143i	$0.0144289\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	22.6274i	1.02116i	0.859830	+	0.510581i	$0.170569\pi$
$491$	22.6274i	1.02116i	−0.859830	+	0.510581i	$0.829431\pi$
$492$	0	0
$493$	0	0
$494$	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
$505$	12.0000	0.533993
$506$	0	0
$507$	0	0
$508$	0	0
$509$	− 45.0333i	− 1.99607i	−0.0626839	−	0.998033i	$-0.519966\pi$
$509$	− 45.0333i	− 1.99607i	0.0626839	−	0.998033i	$-0.480034\pi$
$510$	0	0
$511$	−68.5857	−3.03405
$512$	0	0
$513$	0	0
$514$	0	0
$515$	− 50.9117i	− 2.24344i
$516$	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
$523$	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
$533$	0	0
$534$	0	0
$535$	−39.1918	−1.69441
$536$	0	0
$537$	0	0
$538$	0	0
$539$	− 96.1665i	− 4.14219i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	72.0000	3.06175
$554$	0	0
$555$	0	0
$556$	0	0
$557$	45.0333i	1.90812i	0.299611	+	0.954062i	$0.403143\pi$
$557$	45.0333i	1.90812i	−0.299611	+	0.954062i	$0.596857\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	28.2843i	1.19204i	0.802970	+	0.596020i	$0.203252\pi$
$563$	28.2843i	1.19204i	−0.802970	+	0.596020i	$0.796748\pi$
$564$	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
$571$	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
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 27.7128i	− 1.14972i
$582$	0	0
$583$	19.5959	0.811580
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 45.2548i	− 1.86787i	−0.357447	−	0.933933i	$-0.616353\pi$
$587$	− 45.2548i	− 1.86787i	0.357447	−	0.933933i	$-0.383647\pi$
$588$	0	0
$589$	0	0
$590$	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
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	72.7461i	2.95755i
$606$	0	0
$607$	44.0908	1.78959	0.894795	−	0.446476i	$-0.147321\pi$
$607$	44.0908	1.78959	0.894795	+	0.446476i	$0.147321\pi$
$608$	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
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	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
$625$	−11.0000	−0.440000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	4.89898	0.195025	0.0975126	−	0.995234i	$-0.468911\pi$
$631$	4.89898	0.195025	0.0975126	+	0.995234i	$0.468911\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	− 16.9706i	− 0.673456i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	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
$649$	−64.0000	−2.51222
$650$	0	0
$651$	0	0
$652$	0	0
$653$	17.3205i	0.677804i	0.940822	+	0.338902i	$0.110055\pi$
$653$	17.3205i	0.677804i	−0.940822	+	0.338902i	$0.889945\pi$
$654$	0	0
$655$	78.3837	3.06270
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 45.2548i	− 1.76288i	−0.472298	−	0.881439i	$-0.656575\pi$
$659$	− 45.2548i	− 1.76288i	0.472298	−	0.881439i	$-0.343425\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	51.9615i	1.99704i	0.0543526	+	0.998522i	$0.482690\pi$
$677$	51.9615i	1.99704i	−0.0543526	+	0.998522i	$0.517310\pi$
$678$	0	0
$679$	9.79796	0.376011
$680$	0	0
$681$	0	0
$682$	0	0
$683$	− 5.65685i	− 0.216454i	−0.994126	−	0.108227i	$-0.965483\pi$
$683$	− 5.65685i	− 0.216454i	0.994126	−	0.108227i	$-0.0345173\pi$
$684$	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			$\pi$
$692$	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
$701$	38.1051i	1.43921i	0.694383	+	0.719605i	$0.255677\pi$
$701$	38.1051i	1.43921i	−0.694383	+	0.719605i	$0.744323\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	16.9706i	0.638244i
$708$	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
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	72.0000	2.68142
$722$	0	0
$723$	0	0
$724$	0	0
$725$	− 72.7461i	− 2.70172i
$726$	0	0
$727$	−53.8888	−1.99862	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$	−53.8888	−1.99862	−0.999312	+	0.0370879i	$0.988192\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	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
$745$	84.0000	3.07752
$746$	0	0
$747$	0	0
$748$	0	0
$749$	− 55.4256i	− 2.02521i
$750$	0	0
$751$	53.8888	1.96643	0.983215	−	0.182453i	$-0.0584036\pi$
$751$	53.8888	1.96643	0.983215	+	0.182453i	$0.0584036\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	− 84.8528i	− 3.08811i
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	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
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 51.9615i	− 1.86893i	−0.356060	−	0.934463i	$-0.615880\pi$
$773$	− 51.9615i	− 1.86893i	0.356060	−	0.934463i	$-0.384120\pi$
$774$	0	0
$775$	34.2929	1.23184
$776$	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
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	17.3205i	0.613524i	0.951786	+	0.306762i	$0.0992455\pi$
$797$	17.3205i	0.613524i	−0.951786	+	0.306762i	$0.900754\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	79.1960i	2.79476i
$804$	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
$821$	31.1769i	1.08808i	0.839059	+	0.544041i	$0.183106\pi$
$821$	31.1769i	1.08808i	−0.839059	+	0.544041i	$0.816894\pi$
$822$	0	0
$823$	−34.2929	−1.19537	−0.597687	−	0.801730i	$-0.703913\pi$
$823$	−34.2929	−1.19537	−0.597687	+	0.801730i	$0.703913\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	56.5685i	1.96708i	0.180688	+	0.983540i	$0.442168\pi$
$827$	56.5685i	1.96708i	−0.180688	+	0.983540i	$0.557832\pi$
$828$	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
$836$	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
$841$	−79.0000	−2.72414
$842$	0	0
$843$	0	0
$844$	0	0
$845$	− 45.0333i	− 1.54919i
$846$	0	0
$847$	−102.879	−3.53495
$848$	0	0
$849$	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
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	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
$865$	60.0000	2.04006
$866$	0	0
$867$	0	0
$868$	0	0
$869$	− 83.1384i	− 2.82028i
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	33.9411i	1.14742i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	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
$889$	24.0000	0.804934
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−39.1918	−1.31004
$896$	0	0
$897$	0	0
$898$	0	0
$899$	− 50.9117i	− 1.69800i
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	−32.0000	−1.05905
$914$	0	0
$915$	0	0
$916$	0	0
$917$	110.851i	3.66063i
$918$	0	0
$919$	−34.2929	−1.13122	−0.565608	−	0.824674i	$-0.691359\pi$
$919$	−34.2929	−1.13122	−0.565608	+	0.824674i	$0.691359\pi$
$920$	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
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−58.0000	−1.89478	−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000	−1.89478	−0.947389	+	0.320085i	$0.896288\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 38.1051i	− 1.24219i	−0.783735	−	0.621096i	$-0.786688\pi$
$941$	− 38.1051i	− 1.24219i	0.783735	−	0.621096i	$-0.213312\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	56.5685i	1.83823i	0.393989	+	0.919115i	$0.371095\pi$
$947$	56.5685i	1.83823i	−0.393989	+	0.919115i	$0.628905\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−7.00000	−0.225806
$962$	0	0
$963$	0	0
$964$	0	0
$965$	90.0666i	2.89935i
$966$	0	0
$967$	−4.89898	−0.157541	−0.0787703	−	0.996893i	$-0.525099\pi$
$967$	−4.89898	−0.157541	−0.0787703	+	0.996893i	$0.525099\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	62.2254i	1.99691i	0.0555842	+	0.998454i	$0.482298\pi$
$971$	62.2254i	1.99691i	−0.0555842	+	0.998454i	$0.517702\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	−84.0000	−2.67646
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−24.4949	−0.778106	−0.389053	−	0.921215i	$-0.627198\pi$
$991$	−24.4949	−0.778106	−0.389053	+	0.921215i	$0.627198\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	84.8528i	2.69002i
$996$	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	1152.2.d.g.577.2	yes	4
3.2	odd	2	inner	1152.2.d.g.577.4	yes	4
4.3	odd	2	inner	1152.2.d.g.577.1	✓	4
8.3	odd	2	inner	1152.2.d.g.577.3	yes	4
8.5	even	2	inner	1152.2.d.g.577.4	yes	4
12.11	even	2	inner	1152.2.d.g.577.3	yes	4
16.3	odd	4		2304.2.a.z.1.2		4
16.5	even	4		2304.2.a.z.1.3		4
16.11	odd	4		2304.2.a.z.1.4		4
16.13	even	4		2304.2.a.z.1.1		4
24.5	odd	2	CM	1152.2.d.g.577.2	yes	4
24.11	even	2	inner	1152.2.d.g.577.1	✓	4
48.5	odd	4		2304.2.a.z.1.1		4
48.11	even	4		2304.2.a.z.1.2		4
48.29	odd	4		2304.2.a.z.1.3		4
48.35	even	4		2304.2.a.z.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.d.g.577.1	✓	4	4.3	odd	2	inner
1152.2.d.g.577.1	✓	4	24.11	even	2	inner
1152.2.d.g.577.2	yes	4	1.1	even	1	trivial
1152.2.d.g.577.2	yes	4	24.5	odd	2	CM
1152.2.d.g.577.3	yes	4	8.3	odd	2	inner
1152.2.d.g.577.3	yes	4	12.11	even	2	inner
1152.2.d.g.577.4	yes	4	3.2	odd	2	inner
1152.2.d.g.577.4	yes	4	8.5	even	2	inner
2304.2.a.z.1.1		4	16.13	even	4
2304.2.a.z.1.1		4	48.5	odd	4
2304.2.a.z.1.2		4	16.3	odd	4
2304.2.a.z.1.2		4	48.11	even	4
2304.2.a.z.1.3		4	16.5	even	4
2304.2.a.z.1.3		4	48.29	odd	4
2304.2.a.z.1.4		4	16.11	odd	4
2304.2.a.z.1.4		4	48.35	even	4

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.46410i q^{5} +4.89898 q^{7} +O(q^{10})\)	\(q-3.46410i q^{5} +4.89898 q^{7} -5.65685i q^{11} -7.00000 q^{25} +10.3923i q^{29} -4.89898 q^{31} -16.9706i q^{35} +17.0000 q^{49} +3.46410i q^{53} -19.5959 q^{55} -11.3137i q^{59} -14.0000 q^{73} -27.7128i q^{77} +14.6969 q^{79} -5.65685i q^{83} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 28 q^{25} + 68 q^{49} - 56 q^{73} + 8 q^{97}+O(q^{100}) \) 4 * q - 28 * q^25 + 68 * q^49 - 56 * q^73 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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