LMFDB - Embedded newform 2601.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.a (trivial)

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:	yes
Analytic conductor:	$20.7690895657$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{4} +0.837496 q^{7} +O(q^{10})$	$q-2.00000 q^{4} +0.837496 q^{7} -4.24897 q^{13} +4.00000 q^{16} +4.80066 q^{19} -5.00000 q^{25} -1.67499 q^{28} +10.9290 q^{31} -11.7665 q^{37} -0.551689 q^{43} -6.29860 q^{49} +8.49794 q^{52} -9.25402 q^{61} -8.00000 q^{64} +13.8503 q^{67} -17.0000 q^{73} -9.60132 q^{76} -17.0000 q^{79} -3.55850 q^{91} +8.41653 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{4}+O(q^{10}) $ 3 * q - 6 * q^4	$ 3 q - 6 q^{4} + 12 q^{16} - 15 q^{25} + 21 q^{49} - 24 q^{64} - 51 q^{73} - 51 q^{79} - 51 q^{91}+O(q^{100}) $ 3 * q - 6 * q^4 + 12 * q^16 - 15 * q^25 + 21 * q^49 - 24 * q^64 - 51 * q^73 - 51 * q^79 - 51 * q^91

Display 100 coefficients 10 coefficients

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
$7$	0.837496	0.316544	0.158272	−	0.987396i	$-0.449408\pi$
$7$	0.837496	0.316544	0.158272	+	0.987396i	$0.449408\pi$
$8$	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
$13$	−4.24897	−1.17845	−0.589226	−	0.807968i	$-0.700567\pi$
$13$	−4.24897	−1.17845	−0.589226	+	0.807968i	$0.700567\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	0	0
$17$	0	0
$18$	0	0
$19$	4.80066	1.10135	0.550673	−	0.834721i	$-0.314371\pi$
$19$	4.80066	1.10135	0.550673	+	0.834721i	$0.314371\pi$
$20$	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
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	−1.67499	−0.316544
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	10.9290	1.96291	0.981455	−	0.191695i	$-0.0613985\pi$
$31$	10.9290	1.96291	0.981455	+	0.191695i	$0.0613985\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−11.7665	−1.93440	−0.967201	−	0.254011i	$-0.918250\pi$
$37$	−11.7665	−1.93440	−0.967201	+	0.254011i	$0.918250\pi$
$38$	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
$43$	−0.551689	−0.0841318	−0.0420659	−	0.999115i	$-0.513394\pi$
$43$	−0.551689	−0.0841318	−0.0420659	+	0.999115i	$0.513394\pi$
$44$	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
$49$	−6.29860	−0.899800
$50$	0	0
$51$	0	0
$52$	8.49794	1.17845
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	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
$61$	−9.25402	−1.18486	−0.592428	−	0.805623i	$-0.701831\pi$
$61$	−9.25402	−1.18486	−0.592428	+	0.805623i	$0.701831\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	13.8503	1.69208	0.846041	−	0.533118i	$-0.178980\pi$
$67$	13.8503	1.69208	0.846041	+	0.533118i	$0.178980\pi$
$68$	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
$73$	−17.0000	−1.98970	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−17.0000	−1.98970	−0.994850	+	0.101361i	$0.967680\pi$
$74$	0	0
$75$	0	0
$76$	−9.60132	−1.10135
$77$	0	0
$78$	0	0
$79$	−17.0000	−1.91265	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−17.0000	−1.91265	−0.956325	+	0.292306i	$0.905577\pi$
$80$	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
$91$	−3.55850	−0.373032
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	8.41653	0.854569	0.427284	−	0.904117i	$-0.359470\pi$
$97$	8.41653	0.854569	0.427284	+	0.904117i	$0.359470\pi$
$98$	0	0
$99$	0	0
$100$	10.0000	1.00000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	17.5476	1.72901	0.864507	−	0.502621i	$-0.167631\pi$
$103$	17.5476	1.72901	0.864507	+	0.502621i	$0.167631\pi$
$104$	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
$109$	−17.0000	−1.62830	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−17.0000	−1.62830	−0.814152	+	0.580651i	$0.802798\pi$
$110$	0	0
$111$	0	0
$112$	3.34998	0.316544
$113$	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
$121$	−11.0000	−1.00000
$122$	0	0
$123$	0	0
$124$	−21.8580	−1.96291
$125$	0	0
$126$	0	0
$127$	−22.3482	−1.98308	−0.991542	−	0.129783i	$-0.958572\pi$
$127$	−22.3482	−1.98308	−0.991542	+	0.129783i	$0.958572\pi$
$128$	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
$133$	4.02053	0.348625
$134$	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
$139$	−14.2790	−1.21113	−0.605564	−	0.795796i	$-0.707053\pi$
$139$	−14.2790	−1.21113	−0.605564	+	0.795796i	$0.707053\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	23.5330	1.93440
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−18.6509	−1.51779	−0.758896	−	0.651211i	$-0.774261\pi$
$151$	−18.6509	−1.51779	−0.758896	+	0.651211i	$0.774261\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	22.8999	1.82761	0.913806	−	0.406150i	$-0.133129\pi$
$157$	22.8999	1.82761	0.913806	+	0.406150i	$0.133129\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−17.0000	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$164$	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
$169$	5.05375	0.388750
$170$	0	0
$171$	0	0
$172$	1.10338	0.0841318
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−4.18748	−0.316544
$176$	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
$181$	−24.3705	−1.81145	−0.905723	−	0.423870i	$-0.860671\pi$
$181$	−24.3705	−1.81145	−0.905723	+	0.423870i	$0.860671\pi$
$182$	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
$193$	−19.3455	−1.39252	−0.696261	−	0.717788i	$-0.745155\pi$
$193$	−19.3455	−1.39252	−0.696261	+	0.717788i	$0.745155\pi$
$194$	0	0
$195$	0	0
$196$	12.5972	0.899800
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−16.9959	−1.17845
$209$	0	0
$210$	0	0
$211$	−6.74153	−0.464106	−0.232053	−	0.972703i	$-0.574544\pi$
$211$	−6.74153	−0.464106	−0.232053	+	0.972703i	$0.574544\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	9.15301	0.621347
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	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
$229$	−7.00000	−0.462573	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000	−0.462573	−0.231287	+	0.972886i	$0.574293\pi$
$230$	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
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	0	0
$243$	0	0
$244$	18.5080	1.18486
$245$	0	0
$246$	0	0
$247$	−20.3979	−1.29788
$248$	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
$256$	16.0000	1.00000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	−9.85441	−0.612323
$260$	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
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−27.7006	−1.69208
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	12.1952	0.740807	0.370403	−	0.928871i	$-0.379219\pi$
$271$	12.1952	0.740807	0.370403	+	0.928871i	$0.379219\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	15.9540	0.958582	0.479291	−	0.877656i	$-0.340894\pi$
$277$	15.9540	0.958582	0.479291	+	0.877656i	$0.340894\pi$
$278$	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
$283$	33.6245	1.99877	0.999386	−	0.0350443i	$-0.0111572\pi$
$283$	33.6245	1.99877	0.999386	+	0.0350443i	$0.0111572\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	0	0
$290$	0	0
$291$	0	0
$292$	34.0000	1.98970
$293$	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
$301$	−0.462038	−0.0266314
$302$	0	0
$303$	0	0
$304$	19.2026	1.10135
$305$	0	0
$306$	0	0
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	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
$313$	31.1121	1.75856	0.879279	−	0.476308i	$-0.158025\pi$
$313$	31.1121	1.75856	0.879279	+	0.476308i	$0.158025\pi$
$314$	0	0
$315$	0	0
$316$	34.0000	1.91265
$317$	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
$325$	21.2449	1.17845
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	35.6468	1.95933	0.979663	−	0.200648i	$-0.0643046\pi$
$331$	35.6468	1.95933	0.979663	+	0.200648i	$0.0643046\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	34.0000	1.85210	0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000	1.85210	0.926049	+	0.377403i	$0.123183\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−11.1375	−0.601370
$344$	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
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	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
$361$	4.04633	0.212965
$362$	0	0
$363$	0	0
$364$	7.11699	0.373032
$365$	0	0
$366$	0	0
$367$	−16.7915	−0.876509	−0.438254	−	0.898851i	$-0.644403\pi$
$367$	−16.7915	−0.876509	−0.438254	+	0.898851i	$0.644403\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−25.0000	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	36.1370	1.85623	0.928117	−	0.372288i	$-0.121427\pi$
$379$	36.1370	1.85623	0.928117	+	0.372288i	$0.121427\pi$
$380$	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
$388$	−16.8331	−0.854569
$389$	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
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	0	0
$399$	0	0
$400$	−20.0000	−1.00000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	−46.4371	−2.31319
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−40.4475	−2.00000	−1.00000		0.000593299i	$-0.999811\pi$
$409$	−40.4475	−2.00000	−1.00000		0.000593299i	$0.999811\pi$
$410$	0	0
$411$	0	0
$412$	−35.0951	−1.72901
$413$	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
$421$	30.2945	1.47646	0.738231	−	0.674548i	$-0.235661\pi$
$421$	30.2945	1.47646	0.738231	+	0.674548i	$0.235661\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−7.75021	−0.375059
$428$	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
$433$	28.2523	1.35772	0.678859	−	0.734269i	$-0.262475\pi$
$433$	28.2523	1.35772	0.678859	+	0.734269i	$0.262475\pi$
$434$	0	0
$435$	0	0
$436$	34.0000	1.62830
$437$	0	0
$438$	0	0
$439$	−36.9745	−1.76470	−0.882349	−	0.470596i	$-0.844039\pi$
$439$	−36.9745	−1.76470	−0.882349	+	0.470596i	$0.844039\pi$
$440$	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
$448$	−6.69997	−0.316544
$449$	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
$457$	−31.0000	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$458$	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
$463$	40.9992	1.90539	0.952697	−	0.303923i	$-0.0982964\pi$
$463$	40.9992	1.90539	0.952697	+	0.303923i	$0.0982964\pi$
$464$	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
$469$	11.5996	0.535618
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−24.0033	−1.10135
$476$	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
$481$	49.9956	2.27960
$482$	0	0
$483$	0	0
$484$	22.0000	1.00000
$485$	0	0
$486$	0	0
$487$	−4.22905	−0.191636	−0.0958182	−	0.995399i	$-0.530547\pi$
$487$	−4.22905	−0.191636	−0.0958182	+	0.995399i	$0.530547\pi$
$488$	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
$496$	43.7161	1.96291
$497$	0	0
$498$	0	0
$499$	−44.5536	−1.99449	−0.997246	−	0.0741708i	$-0.976369\pi$
$499$	−44.5536	−1.99449	−0.997246	+	0.0741708i	$0.976369\pi$
$500$	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
$508$	44.6965	1.98308
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−14.2374	−0.629827
$512$	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
$523$	35.0000	1.53044	0.765222	−	0.643767i	$-0.222629\pi$
$523$	35.0000	1.53044	0.765222	+	0.643767i	$0.222629\pi$
$524$	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
$532$	−8.04107	−0.348625
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	46.2285	1.97659	0.988295	−	0.152555i	$-0.0487501\pi$
$547$	46.2285	1.97659	0.988295	+	0.152555i	$0.0487501\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−14.2374	−0.605437
$554$	0	0
$555$	0	0
$556$	28.5580	1.21113
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	2.34411	0.0991453
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	41.2036	1.72432	0.862158	−	0.506640i	$-0.169113\pi$
$571$	41.2036	1.72432	0.862158	+	0.506640i	$0.169113\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−44.1448	−1.83777	−0.918885	−	0.394524i	$-0.870909\pi$
$577$	−44.1448	−1.83777	−0.918885	+	0.394524i	$0.870909\pi$
$578$	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
$589$	52.4665	2.16184
$590$	0	0
$591$	0	0
$592$	−47.0660	−1.93440
$593$	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
$601$	38.6495	1.57655	0.788273	−	0.615325i	$-0.210975\pi$
$601$	38.6495	1.57655	0.788273	+	0.615325i	$0.210975\pi$
$602$	0	0
$603$	0	0
$604$	37.3019	1.51779
$605$	0	0
$606$	0	0
$607$	3.39155	0.137659	0.0688294	−	0.997628i	$-0.478074\pi$
$607$	3.39155	0.137659	0.0688294	+	0.997628i	$0.478074\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−49.4971	−1.99917	−0.999585	−	0.0288097i	$-0.990828\pi$
$613$	−49.4971	−1.99917	−0.999585	+	0.0288097i	$0.990828\pi$
$614$	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
$619$	−17.0000	−0.683288	−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000	−0.683288	−0.341644	+	0.939829i	$0.610984\pi$
$620$	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
$628$	−45.7998	−1.82761
$629$	0	0
$630$	0	0
$631$	−33.0529	−1.31582	−0.657908	−	0.753098i	$-0.728558\pi$
$631$	−33.0529	−1.31582	−0.657908	+	0.753098i	$0.728558\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	26.7626	1.06037
$638$	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
$643$	−26.9246	−1.06180	−0.530901	−	0.847434i	$-0.678146\pi$
$643$	−26.9246	−1.06180	−0.530901	+	0.847434i	$0.678146\pi$
$644$	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
$652$	34.0000	1.33154
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	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
$661$	6.84287	0.266157	0.133078	−	0.991106i	$-0.457514\pi$
$661$	6.84287	0.266157	0.133078	+	0.991106i	$0.457514\pi$
$662$	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
$673$	−29.3955	−1.13311	−0.566557	−	0.824023i	$-0.691725\pi$
$673$	−29.3955	−1.13311	−0.566557	+	0.824023i	$0.691725\pi$
$674$	0	0
$675$	0	0
$676$	−10.1075	−0.388750
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	7.04881	0.270508
$680$	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
$688$	−2.20676	−0.0841318
$689$	0	0
$690$	0	0
$691$	−39.5286	−1.50374	−0.751869	−	0.659313i	$-0.770847\pi$
$691$	−39.5286	−1.50374	−0.751869	+	0.659313i	$0.770847\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	8.37496	0.316544
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−56.4870	−2.13045
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−14.3206	−0.537820	−0.268910	−	0.963165i	$-0.586663\pi$
$709$	−14.3206	−0.537820	−0.268910	+	0.963165i	$0.586663\pi$
$710$	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
$721$	14.6960	0.547309
$722$	0	0
$723$	0	0
$724$	48.7410	1.81145
$725$	0	0
$726$	0	0
$727$	53.7461	1.99333	0.996666	−	0.0815889i	$-0.0259995\pi$
$727$	53.7461	1.99333	0.996666	+	0.0815889i	$0.0259995\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	24.9421	0.921259	0.460629	−	0.887593i	$-0.347624\pi$
$733$	24.9421	0.921259	0.460629	+	0.887593i	$0.347624\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	48.3937	1.78019	0.890096	−	0.455773i	$-0.150637\pi$
$739$	48.3937	1.78019	0.890096	+	0.455773i	$0.150637\pi$
$740$	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
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	26.0871	0.951931	0.475965	−	0.879464i	$-0.342099\pi$
$751$	26.0871	0.951931	0.475965	+	0.879464i	$0.342099\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−11.2564	−0.409120	−0.204560	−	0.978854i	$-0.565576\pi$
$757$	−11.2564	−0.409120	−0.204560	+	0.978854i	$0.565576\pi$
$758$	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
$763$	−14.2374	−0.515430
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	47.0000	1.69486	0.847432	−	0.530904i	$-0.178148\pi$
$769$	47.0000	1.69486	0.847432	+	0.530904i	$0.178148\pi$
$770$	0	0
$771$	0	0
$772$	38.6911	1.39252
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	−54.6451	−1.96291
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−25.1944	−0.899800
$785$	0	0
$786$	0	0
$787$	53.8076	1.91803	0.959017	−	0.283350i	$-0.0914459\pi$
$787$	53.8076	1.91803	0.959017	+	0.283350i	$0.0914459\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	39.3201	1.39630
$794$	0	0
$795$	0	0
$796$	34.0000	1.20510
$797$	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
$811$	−49.5785	−1.74094	−0.870469	−	0.492223i	$-0.836184\pi$
$811$	−49.5785	−1.74094	−0.870469	+	0.492223i	$0.836184\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−2.64847	−0.0926583
$818$	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
$823$	−57.1576	−1.99239	−0.996194	−	0.0871670i	$-0.972219\pi$
$823$	−57.1576	−1.99239	−0.996194	+	0.0871670i	$0.972219\pi$
$824$	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
$829$	−42.1026	−1.46228	−0.731141	−	0.682226i	$-0.761012\pi$
$829$	−42.1026	−1.46228	−0.731141	+	0.682226i	$0.761012\pi$
$830$	0	0
$831$	0	0
$832$	33.9918	1.17845
$833$	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
$841$	−29.0000	−1.00000
$842$	0	0
$843$	0	0
$844$	13.4831	0.464106
$845$	0	0
$846$	0	0
$847$	−9.21246	−0.316544
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−52.1326	−1.78499	−0.892493	−	0.451061i	$-0.851046\pi$
$853$	−52.1326	−1.78499	−0.892493	+	0.451061i	$0.851046\pi$
$854$	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
$859$	−58.5467	−1.99759	−0.998795	−	0.0490840i	$-0.984370\pi$
$859$	−58.5467	−1.99759	−0.998795	+	0.0490840i	$0.984370\pi$
$860$	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
$868$	−18.3060	−0.621347
$869$	0	0
$870$	0	0
$871$	−58.8495	−1.99404
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	34.0000	1.14810	0.574049	−	0.818821i	$-0.305372\pi$
$877$	34.0000	1.14810	0.574049	+	0.818821i	$0.305372\pi$
$878$	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
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	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
$889$	−18.7166	−0.627733
$890$	0	0
$891$	0	0
$892$	−10.0000	−0.334825
$893$	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
$907$	51.2951	1.70323	0.851613	−	0.524171i	$-0.175625\pi$
$907$	51.2951	1.70323	0.851613	+	0.524171i	$0.175625\pi$
$908$	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
$916$	14.0000	0.462573
$917$	0	0
$918$	0	0
$919$	53.0000	1.74831	0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000	1.74831	0.874154	+	0.485648i	$0.161416\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	58.8326	1.93440
$926$	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
$931$	−30.2374	−0.990992
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	59.0984	1.93066	0.965331	−	0.261029i	$-0.0840619\pi$
$937$	59.0984	1.93066	0.965331	+	0.261029i	$0.0840619\pi$
$938$	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		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	72.2325	2.34477
$950$	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
$961$	88.4434	2.85301
$962$	0	0
$963$	0	0
$964$	34.0000	1.09507
$965$	0	0
$966$	0	0
$967$	20.0000	0.643157	0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000	0.643157	0.321578	+	0.946883i	$0.395787\pi$
$968$	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
$973$	−11.9586	−0.383375
$974$	0	0
$975$	0	0
$976$	−37.0161	−1.18486
$977$	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
$985$	0	0
$986$	0	0
$987$	0	0
$988$	40.7957	1.29788
$989$	0	0
$990$	0	0
$991$	−17.0000	−0.540023	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	−17.0000	−0.540023	−0.270011	+	0.962857i	$0.587027\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−59.6701	−1.88977	−0.944885	−	0.327403i	$-0.893827\pi$
$997$	−59.6701	−1.88977	−0.944885	+	0.327403i	$0.893827\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.u.1.2	✓	3
3.2	odd	2	CM	2601.2.a.u.1.2	✓	3
17.16	even	2		2601.2.a.v.1.2	yes	3
51.50	odd	2		2601.2.a.v.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2601.2.a.u.1.2	✓	3	1.1	even	1	trivial
2601.2.a.u.1.2	✓	3	3.2	odd	2	CM
2601.2.a.v.1.2	yes	3	17.16	even	2
2601.2.a.v.1.2	yes	3	51.50	odd	2

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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{4} +0.837496 q^{7} +O(q^{10})\)	\(q-2.00000 q^{4} +0.837496 q^{7} -4.24897 q^{13} +4.00000 q^{16} +4.80066 q^{19} -5.00000 q^{25} -1.67499 q^{28} +10.9290 q^{31} -11.7665 q^{37} -0.551689 q^{43} -6.29860 q^{49} +8.49794 q^{52} -9.25402 q^{61} -8.00000 q^{64} +13.8503 q^{67} -17.0000 q^{73} -9.60132 q^{76} -17.0000 q^{79} -3.55850 q^{91} +8.41653 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{4}+O(q^{10}) \) 3 * q - 6 * q^4	\( 3 q - 6 q^{4} + 12 q^{16} - 15 q^{25} + 21 q^{49} - 24 q^{64} - 51 q^{73} - 51 q^{79} - 51 q^{91}+O(q^{100}) \) 3 * q - 6 * q^4 + 12 * q^16 - 15 * q^25 + 21 * q^49 - 24 * q^64 - 51 * q^73 - 51 * q^79 - 51 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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