LMFDB - Embedded newform 5625.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5625,2,Mod(1,5625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5625, 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("5625.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5625 = 3^{2} \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5625.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:	$44.9158511370$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 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			1.1
Root			$-1.95630$ of defining polynomial
Character	$\chi$	$=$	5625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{4} -5.06316 q^{7} +O(q^{10})$	$q-2.00000 q^{4} -5.06316 q^{7} +6.48692 q^{13} +4.00000 q^{16} -8.54541 q^{19} +10.1263 q^{28} +10.7535 q^{31} +3.49894 q^{37} -9.98586 q^{43} +18.6356 q^{49} -12.9738 q^{52} +5.42685 q^{61} -8.00000 q^{64} +5.11758 q^{67} -0.0544214 q^{73} +17.0908 q^{76} +13.4168 q^{79} -32.8443 q^{91} -15.2439 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 5 q^{7}+O(q^{10}) $ 4 * q - 8 * q^4 - 5 * q^7	$ 4 q - 8 q^{4} - 5 q^{7} - 5 q^{13} + 16 q^{16} + q^{19} + 10 q^{28} + 7 q^{31} + 10 q^{37} - 5 q^{43} + 17 q^{49} + 10 q^{52} + 13 q^{61} - 32 q^{64} - 5 q^{67} + 10 q^{73} - 2 q^{76} + 4 q^{79} - 25 q^{91} - 5 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 - 5 * q^7 - 5 * q^13 + 16 * q^16 + q^19 + 10 * q^28 + 7 * q^31 + 10 * q^37 - 5 * q^43 + 17 * q^49 + 10 * q^52 + 13 * q^61 - 32 * q^64 - 5 * q^67 + 10 * q^73 - 2 * q^76 + 4 * q^79 - 25 * q^91 - 5 * q^97

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
$5$	0	0
$6$	0	0
$7$	−5.06316	−1.91369	−0.956847	−	0.290592i	$-0.906148\pi$
$7$	−5.06316	−1.91369	−0.956847	+	0.290592i	$0.906148\pi$
$8$	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
$13$	6.48692	1.79915	0.899574	−	0.436769i	$-0.143877\pi$
$13$	6.48692	1.79915	0.899574	+	0.436769i	$0.143877\pi$
$14$	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
$19$	−8.54541	−1.96045	−0.980226	−	0.197884i	$-0.936593\pi$
$19$	−8.54541	−1.96045	−0.980226	+	0.197884i	$0.936593\pi$
$20$	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
$25$	0	0
$26$	0	0
$27$	0	0
$28$	10.1263	1.91369
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	10.7535	1.93138	0.965692	−	0.259691i	$-0.0836207\pi$
$31$	10.7535	1.93138	0.965692	+	0.259691i	$0.0836207\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	3.49894	0.575223	0.287611	−	0.957747i	$-0.407139\pi$
$37$	3.49894	0.575223	0.287611	+	0.957747i	$0.407139\pi$
$38$	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
$43$	−9.98586	−1.52283	−0.761415	−	0.648265i	$-0.775495\pi$
$43$	−9.98586	−1.52283	−0.761415	+	0.648265i	$0.775495\pi$
$44$	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
$49$	18.6356	2.66223
$50$	0	0
$51$	0	0
$52$	−12.9738	−1.79915
$53$	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
$61$	5.42685	0.694837	0.347419	−	0.937710i	$-0.387058\pi$
$61$	5.42685	0.694837	0.347419	+	0.937710i	$0.387058\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	5.11758	0.625212	0.312606	−	0.949883i	$-0.398798\pi$
$67$	5.11758	0.625212	0.312606	+	0.949883i	$0.398798\pi$
$68$	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
$73$	−0.0544214	−0.00636955	−0.00318477	−	0.999995i	$-0.501014\pi$
$73$	−0.0544214	−0.00636955	−0.00318477	+	0.999995i	$0.501014\pi$
$74$	0	0
$75$	0	0
$76$	17.0908	1.96045
$77$	0	0
$78$	0	0
$79$	13.4168	1.50951	0.754754	−	0.656007i	$-0.227756\pi$
$79$	13.4168	1.50951	0.754754	+	0.656007i	$0.227756\pi$
$80$	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
$91$	−32.8443	−3.44302
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−15.2439	−1.54778	−0.773892	−	0.633318i	$-0.781693\pi$
$97$	−15.2439	−1.54778	−0.773892	+	0.633318i	$0.781693\pi$
$98$	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
$103$	9.47490	0.933589	0.466795	−	0.884366i	$-0.345409\pi$
$103$	9.47490	0.933589	0.466795	+	0.884366i	$0.345409\pi$
$104$	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
$109$	2.36507	0.226532	0.113266	−	0.993565i	$-0.463869\pi$
$109$	2.36507	0.226532	0.113266	+	0.993565i	$0.463869\pi$
$110$	0	0
$111$	0	0
$112$	−20.2526	−1.91369
$113$	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
$124$	−21.5070	−1.93138
$125$	0	0
$126$	0	0
$127$	−10.0719	−0.893736	−0.446868	−	0.894600i	$-0.647461\pi$
$127$	−10.0719	−0.893736	−0.446868	+	0.894600i	$0.647461\pi$
$128$	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
$133$	43.2668	3.75170
$134$	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
$139$	2.76353	0.234400	0.117200	−	0.993108i	$-0.462608\pi$
$139$	2.76353	0.234400	0.117200	+	0.993108i	$0.462608\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−6.99789	−0.575223
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−13.5170	−1.10000	−0.550000	−	0.835165i	$-0.685372\pi$
$151$	−13.5170	−1.10000	−0.550000	+	0.835165i	$0.685372\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−25.0000	−1.99522	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−25.0000	−1.99522	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−25.0000	−1.95815	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−25.0000	−1.95815	−0.979076	+	0.203497i	$0.934769\pi$
$164$	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
$169$	29.0801	2.23693
$170$	0	0
$171$	0	0
$172$	19.9717	1.52283
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	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
$181$	22.5461	1.67584	0.837918	−	0.545797i	$-0.183773\pi$
$181$	22.5461	1.67584	0.837918	+	0.545797i	$0.183773\pi$
$182$	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
$193$	−25.0000	−1.79954	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000	−1.79954	−0.899770	+	0.436365i	$0.856266\pi$
$194$	0	0
$195$	0	0
$196$	−37.2712	−2.66223
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−24.1703	−1.71339	−0.856693	−	0.515826i	$-0.827485\pi$
$199$	−24.1703	−1.71339	−0.856693	+	0.515826i	$0.827485\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	25.9477	1.79915
$209$	0	0
$210$	0	0
$211$	−28.7264	−1.97761	−0.988803	−	0.149225i	$-0.952322\pi$
$211$	−28.7264	−1.97761	−0.988803	+	0.149225i	$0.952322\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−54.4466	−3.69608
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−26.4586	−1.77180	−0.885901	−	0.463874i	$-0.846459\pi$
$223$	−26.4586	−1.77180	−0.885901	+	0.463874i	$0.846459\pi$
$224$	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
$229$	0.725102	0.0479161	0.0239580	−	0.999713i	$-0.492373\pi$
$229$	0.725102	0.0479161	0.0239580	+	0.999713i	$0.492373\pi$
$230$	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
$241$	−19.4559	−1.25326	−0.626632	−	0.779315i	$-0.715567\pi$
$241$	−19.4559	−1.25326	−0.626632	+	0.779315i	$0.715567\pi$
$242$	0	0
$243$	0	0
$244$	−10.8537	−0.694837
$245$	0	0
$246$	0	0
$247$	−55.4334	−3.52714
$248$	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
$259$	−17.7157	−1.10080
$260$	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
$268$	−10.2352	−0.625212
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	7.82031	0.475050	0.237525	−	0.971381i	$-0.423664\pi$
$271$	7.82031	0.475050	0.237525	+	0.971381i	$0.423664\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	15.2983	0.919187	0.459593	−	0.888129i	$-0.347995\pi$
$277$	15.2983	0.919187	0.459593	+	0.888129i	$0.347995\pi$
$278$	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
$283$	−25.0000	−1.48610	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000	−1.48610	−0.743048	+	0.669238i	$0.766621\pi$
$284$	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
$292$	0.108843	0.00636955
$293$	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
$301$	50.5600	2.91423
$302$	0	0
$303$	0	0
$304$	−34.1816	−1.96045
$305$	0	0
$306$	0	0
$307$	12.4629	0.711294	0.355647	−	0.934620i	$-0.384261\pi$
$307$	12.4629	0.711294	0.355647	+	0.934620i	$0.384261\pi$
$308$	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
$313$	−25.2614	−1.42786	−0.713929	−	0.700218i	$-0.753086\pi$
$313$	−25.2614	−1.42786	−0.713929	+	0.700218i	$0.753086\pi$
$314$	0	0
$315$	0	0
$316$	−26.8336	−1.50951
$317$	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
$329$	0	0
$330$	0	0
$331$	26.3613	1.44895	0.724475	−	0.689301i	$-0.242082\pi$
$331$	26.3613	1.44895	0.724475	+	0.689301i	$0.242082\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−25.4246	−1.38497	−0.692484	−	0.721433i	$-0.743484\pi$
$337$	−25.4246	−1.38497	−0.692484	+	0.721433i	$0.743484\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−58.9128	−3.18099
$344$	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
$349$	37.2718	1.99511	0.997557	−	0.0698585i	$-0.0222548\pi$
$349$	37.2718	1.99511	0.997557	+	0.0698585i	$0.0222548\pi$
$350$	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
$361$	54.0240	2.84337
$362$	0	0
$363$	0	0
$364$	65.6886	3.44302
$365$	0	0
$366$	0	0
$367$	−4.00991	−0.209316	−0.104658	−	0.994508i	$-0.533375\pi$
$367$	−4.00991	−0.209316	−0.104658	+	0.994508i	$0.533375\pi$
$368$	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
$379$	−8.19038	−0.420712	−0.210356	−	0.977625i	$-0.567462\pi$
$379$	−8.19038	−0.420712	−0.210356	+	0.977625i	$0.567462\pi$
$380$	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
$388$	30.4878	1.54778
$389$	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
$397$	28.9357	1.45224	0.726119	−	0.687569i	$-0.241322\pi$
$397$	28.9357	1.45224	0.726119	+	0.687569i	$0.241322\pi$
$398$	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
$403$	69.7570	3.47484
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	40.3506	1.99521	0.997605	−	0.0691646i	$-0.0220334\pi$
$409$	40.3506	1.99521	0.997605	+	0.0691646i	$0.0220334\pi$
$410$	0	0
$411$	0	0
$412$	−18.9498	−0.933589
$413$	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
$421$	−2.56310	−0.124918	−0.0624590	−	0.998048i	$-0.519894\pi$
$421$	−2.56310	−0.124918	−0.0624590	+	0.998048i	$0.519894\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−27.4770	−1.32971
$428$	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
$433$	−15.0806	−0.724729	−0.362365	−	0.932036i	$-0.618030\pi$
$433$	−15.0806	−0.724729	−0.362365	+	0.932036i	$0.618030\pi$
$434$	0	0
$435$	0	0
$436$	−4.73014	−0.226532
$437$	0	0
$438$	0	0
$439$	20.9061	0.997793	0.498897	−	0.866662i	$-0.333739\pi$
$439$	20.9061	0.997793	0.498897	+	0.866662i	$0.333739\pi$
$440$	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
$448$	40.5053	1.91369
$449$	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
$457$	36.4445	1.70480	0.852401	−	0.522889i	$-0.175146\pi$
$457$	36.4445	1.70480	0.852401	+	0.522889i	$0.175146\pi$
$458$	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
$463$	42.4205	1.97145	0.985723	−	0.168375i	$-0.0538520\pi$
$463$	42.4205	1.97145	0.985723	+	0.168375i	$0.0538520\pi$
$464$	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
$469$	−25.9111	−1.19646
$470$	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
$481$	22.6974	1.03491
$482$	0	0
$483$	0	0
$484$	22.0000	1.00000
$485$	0	0
$486$	0	0
$487$	−25.0000	−1.13286	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000	−1.13286	−0.566429	+	0.824110i	$0.691675\pi$
$488$	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
$496$	43.0140	1.93138
$497$	0	0
$498$	0	0
$499$	11.0000	0.492428	0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000	0.492428	0.246214	+	0.969216i	$0.420813\pi$
$500$	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
$508$	20.1438	0.893736
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0.275544	0.0121894
$512$	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
$523$	−45.6229	−1.99495	−0.997474	−	0.0710325i	$-0.977371\pi$
$523$	−45.6229	−1.99495	−0.997474	+	0.0710325i	$0.977371\pi$
$524$	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
$532$	−86.5335	−3.75170
$533$	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	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−35.4226	−1.51456	−0.757280	−	0.653090i	$-0.773472\pi$
$547$	−35.4226	−1.51456	−0.757280	+	0.653090i	$0.773472\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−67.9314	−2.88874
$554$	0	0
$555$	0	0
$556$	−5.52707	−0.234400
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	−64.7775	−2.73980
$560$	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
$571$	−43.1142	−1.80427	−0.902136	−	0.431452i	$-0.858001\pi$
$571$	−43.1142	−1.80427	−0.902136	+	0.431452i	$0.858001\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−20.4827	−0.852706	−0.426353	−	0.904557i	$-0.640202\pi$
$577$	−20.4827	−0.852706	−0.426353	+	0.904557i	$0.640202\pi$
$578$	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
$589$	−91.8929	−3.78638
$590$	0	0
$591$	0	0
$592$	13.9958	0.575223
$593$	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
$601$	23.0000	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$602$	0	0
$603$	0	0
$604$	27.0340	1.10000
$605$	0	0
$606$	0	0
$607$	10.2896	0.417641	0.208821	−	0.977954i	$-0.433038\pi$
$607$	10.2896	0.417641	0.208821	+	0.977954i	$0.433038\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−20.4159	−0.824590	−0.412295	−	0.911050i	$-0.635273\pi$
$613$	−20.4159	−0.824590	−0.412295	+	0.911050i	$0.635273\pi$
$614$	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
$619$	−6.90544	−0.277553	−0.138777	−	0.990324i	$-0.544317\pi$
$619$	−6.90544	−0.277553	−0.138777	+	0.990324i	$0.544317\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	50.0000	1.99522
$629$	0	0
$630$	0	0
$631$	−37.9969	−1.51263	−0.756316	−	0.654206i	$-0.773003\pi$
$631$	−37.9969	−1.51263	−0.756316	+	0.654206i	$0.773003\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	120.887	4.78974
$638$	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
$643$	50.6860	1.99886	0.999431	−	0.0337424i	$-0.0107426\pi$
$643$	50.6860	1.99886	0.999431	+	0.0337424i	$0.0107426\pi$
$644$	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
$652$	50.0000	1.95815
$653$	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
$661$	−51.1041	−1.98772	−0.993860	−	0.110645i	$-0.964708\pi$
$661$	−51.1041	−1.98772	−0.993860	+	0.110645i	$0.964708\pi$
$662$	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
$673$	50.0000	1.92736	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000	1.92736	0.963679	+	0.267063i	$0.0860531\pi$
$674$	0	0
$675$	0	0
$676$	−58.1603	−2.23693
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	77.1823	2.96198
$680$	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
$688$	−39.9434	−1.52283
$689$	0	0
$690$	0	0
$691$	24.0701	0.915669	0.457835	−	0.889037i	$-0.348625\pi$
$691$	24.0701	0.915669	0.457835	+	0.889037i	$0.348625\pi$
$692$	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
$703$	−29.8999	−1.12770
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	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
$721$	−47.9729	−1.78660
$722$	0	0
$723$	0	0
$724$	−45.0921	−1.67584
$725$	0	0
$726$	0	0
$727$	−35.6054	−1.32053	−0.660265	−	0.751033i	$-0.729556\pi$
$727$	−35.6054	−1.32053	−0.660265	+	0.751033i	$0.729556\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−54.3626	−1.99976	−0.999881	−	0.0154516i	$-0.995081\pi$
$739$	−54.3626	−1.99976	−0.999881	+	0.0154516i	$0.995081\pi$
$740$	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
$751$	−32.5417	−1.18746	−0.593731	−	0.804664i	$-0.702346\pi$
$751$	−32.5417	−1.18746	−0.593731	+	0.804664i	$0.702346\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	45.5140	1.65423	0.827117	−	0.562029i	$-0.189979\pi$
$757$	45.5140	1.65423	0.827117	+	0.562029i	$0.189979\pi$
$758$	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
$763$	−11.9747	−0.433514
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	24.3707	0.878831	0.439415	−	0.898284i	$-0.355186\pi$
$769$	24.3707	0.878831	0.439415	+	0.898284i	$0.355186\pi$
$770$	0	0
$771$	0	0
$772$	50.0000	1.79954
$773$	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
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	74.5423	2.66223
$785$	0	0
$786$	0	0
$787$	−25.0000	−0.891154	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	−25.0000	−0.891154	−0.445577	+	0.895244i	$0.647001\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	35.2035	1.25011
$794$	0	0
$795$	0	0
$796$	48.3406	1.71339
$797$	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
$811$	−37.0000	−1.29925	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000	−1.29925	−0.649623	+	0.760257i	$0.725073\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	85.3333	2.98543
$818$	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
$823$	55.9053	1.94874	0.974368	−	0.224962i	$-0.0722258\pi$
$823$	55.9053	1.94874	0.974368	+	0.224962i	$0.0722258\pi$
$824$	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
$829$	18.7308	0.650547	0.325273	−	0.945620i	$-0.394544\pi$
$829$	18.7308	0.650547	0.325273	+	0.945620i	$0.394544\pi$
$830$	0	0
$831$	0	0
$832$	−51.8954	−1.79915
$833$	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
$844$	57.4528	1.97761
$845$	0	0
$846$	0	0
$847$	55.6947	1.91369
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−55.8036	−1.91068	−0.955339	−	0.295511i	$-0.904510\pi$
$853$	−55.8036	−1.91068	−0.955339	+	0.295511i	$0.904510\pi$
$854$	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
$859$	−35.1242	−1.19842	−0.599211	−	0.800591i	$-0.704519\pi$
$859$	−35.1242	−1.19842	−0.599211	+	0.800591i	$0.704519\pi$
$860$	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
$868$	108.893	3.69608
$869$	0	0
$870$	0	0
$871$	33.1973	1.12485
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−25.0000	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$878$	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
$883$	−38.4106	−1.29262	−0.646309	−	0.763076i	$-0.723688\pi$
$883$	−38.4106	−1.29262	−0.646309	+	0.763076i	$0.723688\pi$
$884$	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
$889$	50.9956	1.71034
$890$	0	0
$891$	0	0
$892$	52.9173	1.77180
$893$	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
$907$	30.4686	1.01169	0.505846	−	0.862624i	$-0.331180\pi$
$907$	30.4686	1.01169	0.505846	+	0.862624i	$0.331180\pi$
$908$	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
$916$	−1.45020	−0.0479161
$917$	0	0
$918$	0	0
$919$	−34.8236	−1.14872	−0.574362	−	0.818602i	$-0.694750\pi$
$919$	−34.8236	−1.14872	−0.574362	+	0.818602i	$0.694750\pi$
$920$	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
$931$	−159.249	−5.21916
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−36.9555	−1.20728	−0.603641	−	0.797256i	$-0.706284\pi$
$937$	−36.9555	−1.20728	−0.603641	+	0.797256i	$0.706284\pi$
$938$	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
$949$	−0.353027	−0.0114598
$950$	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
$961$	84.6375	2.73024
$962$	0	0
$963$	0	0
$964$	38.9118	1.25326
$965$	0	0
$966$	0	0
$967$	−50.7949	−1.63345	−0.816726	−	0.577025i	$-0.804213\pi$
$967$	−50.7949	−1.63345	−0.816726	+	0.577025i	$0.804213\pi$
$968$	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
$973$	−13.9922	−0.448570
$974$	0	0
$975$	0	0
$976$	21.7074	0.694837
$977$	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
$988$	110.867	3.52714
$989$	0	0
$990$	0	0
$991$	62.9080	1.99834	0.999170	−	0.0407431i	$-0.0129725\pi$
$991$	62.9080	1.99834	0.999170	+	0.0407431i	$0.0129725\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−62.3922	−1.97598	−0.987990	−	0.154517i	$-0.950618\pi$
$997$	−62.3922	−1.97598	−0.987990	+	0.154517i	$0.950618\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5625.2.a.k.1.1	✓	4
3.2	odd	2	CM	5625.2.a.k.1.1	✓	4
5.4	even	2		5625.2.a.l.1.4	yes	4
15.14	odd	2		5625.2.a.l.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5625.2.a.k.1.1	✓	4	1.1	even	1	trivial
5625.2.a.k.1.1	✓	4	3.2	odd	2	CM
5625.2.a.l.1.4	yes	4	5.4	even	2
5625.2.a.l.1.4	yes	4	15.14	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:	\( N \)	\(=\)	\( 5625 = 3^{2} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5625.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{4} -5.06316 q^{7} +O(q^{10})\)	\(q-2.00000 q^{4} -5.06316 q^{7} +6.48692 q^{13} +4.00000 q^{16} -8.54541 q^{19} +10.1263 q^{28} +10.7535 q^{31} +3.49894 q^{37} -9.98586 q^{43} +18.6356 q^{49} -12.9738 q^{52} +5.42685 q^{61} -8.00000 q^{64} +5.11758 q^{67} -0.0544214 q^{73} +17.0908 q^{76} +13.4168 q^{79} -32.8443 q^{91} -15.2439 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 5 q^{7}+O(q^{10}) \) 4 * q - 8 * q^4 - 5 * q^7	\( 4 q - 8 q^{4} - 5 q^{7} - 5 q^{13} + 16 q^{16} + q^{19} + 10 q^{28} + 7 q^{31} + 10 q^{37} - 5 q^{43} + 17 q^{49} + 10 q^{52} + 13 q^{61} - 32 q^{64} - 5 q^{67} + 10 q^{73} - 2 q^{76} + 4 q^{79} - 25 q^{91} - 5 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 - 5 * q^7 - 5 * q^13 + 16 * q^16 + q^19 + 10 * q^28 + 7 * q^31 + 10 * q^37 - 5 * q^43 + 17 * q^49 + 10 * q^52 + 13 * q^61 - 32 * q^64 - 5 * q^67 + 10 * q^73 - 2 * q^76 + 4 * q^79 - 25 * q^91 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more