LMFDB - Embedded newform 5625.2.a.l.1.3

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:	$0$
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			1.3
Root			$1.33826$ 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)

$f(q)$	$=$	$q-2.00000 q^{4} +3.02701 q^{7} +O(q^{10})$	$q-2.00000 q^{4} +3.02701 q^{7} +3.39675 q^{13} +4.00000 q^{16} +7.92737 q^{19} -6.05402 q^{28} +0.572749 q^{31} +9.67928 q^{37} -13.0760 q^{43} +2.16280 q^{49} -6.79350 q^{52} +15.6076 q^{61} -8.00000 q^{64} +13.2078 q^{67} -16.2348 q^{73} -15.8547 q^{76} -6.94467 q^{79} +10.2820 q^{91} -7.15373 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	3.02701	1.14410	0.572051	−	0.820218i	$-0.306148\pi$
$7$	3.02701	1.14410	0.572051	+	0.820218i	$0.306148\pi$
$8$	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
$13$	3.39675	0.942089	0.471044	−	0.882109i	$-0.343877\pi$
$13$	3.39675	0.942089	0.471044	+	0.882109i	$0.343877\pi$
$14$	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
$19$	7.92737	1.81866	0.909332	−	0.416071i	$-0.136593\pi$
$19$	7.92737	1.81866	0.909332	+	0.416071i	$0.136593\pi$
$20$	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
$28$	−6.05402	−1.14410
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0.572749	0.102869	0.0514344	−	0.998676i	$-0.483621\pi$
$31$	0.572749	0.102869	0.0514344	+	0.998676i	$0.483621\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	9.67928	1.59126	0.795632	−	0.605780i	$-0.207139\pi$
$37$	9.67928	1.59126	0.795632	+	0.605780i	$0.207139\pi$
$38$	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
$43$	−13.0760	−1.99408	−0.997038	−	0.0769089i	$-0.975495\pi$
$43$	−13.0760	−1.99408	−0.997038	+	0.0769089i	$0.975495\pi$
$44$	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
$49$	2.16280	0.308971
$50$	0	0
$51$	0	0
$52$	−6.79350	−0.942089
$53$	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
$61$	15.6076	1.99835	0.999174	−	0.0406463i	$-0.0129417\pi$
$61$	15.6076	1.99835	0.999174	+	0.0406463i	$0.0129417\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	13.2078	1.61358	0.806792	−	0.590836i	$-0.201202\pi$
$67$	13.2078	1.61358	0.806792	+	0.590836i	$0.201202\pi$
$68$	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
$73$	−16.2348	−1.90014	−0.950068	−	0.312044i	$-0.898986\pi$
$73$	−16.2348	−1.90014	−0.950068	+	0.312044i	$0.898986\pi$
$74$	0	0
$75$	0	0
$76$	−15.8547	−1.81866
$77$	0	0
$78$	0	0
$79$	−6.94467	−0.781337	−0.390668	−	0.920532i	$-0.627756\pi$
$79$	−6.94467	−0.781337	−0.390668	+	0.920532i	$0.627756\pi$
$80$	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
$91$	10.2820	1.07785
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−7.15373	−0.726351	−0.363176	−	0.931721i	$-0.618307\pi$
$97$	−7.15373	−0.726351	−0.363176	+	0.931721i	$0.618307\pi$
$98$	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
$103$	−2.88578	−0.284345	−0.142172	−	0.989842i	$-0.545409\pi$
$103$	−2.88578	−0.284345	−0.142172	+	0.989842i	$0.545409\pi$
$104$	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
$109$	−14.1077	−1.35127	−0.675637	−	0.737234i	$-0.736131\pi$
$109$	−14.1077	−1.35127	−0.675637	+	0.737234i	$0.736131\pi$
$110$	0	0
$111$	0	0
$112$	12.1080	1.14410
$113$	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
$124$	−1.14550	−0.102869
$125$	0	0
$126$	0	0
$127$	22.2888	1.97781	0.988905	−	0.148550i	$-0.0474607\pi$
$127$	22.2888	1.97781	0.988905	+	0.148550i	$0.0474607\pi$
$128$	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
$133$	23.9962	2.08074
$134$	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
$139$	23.1250	1.96144	0.980719	−	0.195424i	$-0.0626082\pi$
$139$	23.1250	1.96144	0.980719	+	0.195424i	$0.0626082\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−19.3586	−1.59126
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−23.6978	−1.92850	−0.964248	−	0.265001i	$-0.914628\pi$
$151$	−23.6978	−1.92850	−0.964248	+	0.265001i	$0.914628\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	25.0000	1.99522	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	25.0000	1.99522	0.997609	+	0.0691164i	$0.0220180\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	25.0000	1.95815	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	25.0000	1.95815	0.979076	+	0.203497i	$0.0652307\pi$
$164$	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
$169$	−1.46209	−0.112469
$170$	0	0
$171$	0	0
$172$	26.1521	1.99408
$173$	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
$181$	−26.8723	−1.99740	−0.998701	−	0.0509566i	$-0.983773\pi$
$181$	−26.8723	−1.99740	−0.998701	+	0.0509566i	$0.983773\pi$
$182$	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	$-0.143734\pi$
$193$	25.0000	1.79954	0.899770	+	0.436365i	$0.143734\pi$
$194$	0	0
$195$	0	0
$196$	−4.32559	−0.308971
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	6.37192	0.451694	0.225847	−	0.974163i	$-0.427485\pi$
$199$	6.37192	0.451694	0.225847	+	0.974163i	$0.427485\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	13.5870	0.942089
$209$	0	0
$210$	0	0
$211$	20.6920	1.42449	0.712246	−	0.701930i	$-0.247678\pi$
$211$	20.6920	1.42449	0.712246	+	0.701930i	$0.247678\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	1.73372	0.117692
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−29.5488	−1.97873	−0.989367	−	0.145437i	$-0.953541\pi$
$223$	−29.5488	−1.97873	−0.989367	+	0.145437i	$0.953541\pi$
$224$	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
$229$	17.1979	1.13647	0.568234	−	0.822867i	$-0.307627\pi$
$229$	17.1979	1.13647	0.568234	+	0.822867i	$0.307627\pi$
$230$	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
$241$	29.9625	1.93005	0.965026	−	0.262154i	$-0.0844330\pi$
$241$	29.9625	1.93005	0.965026	+	0.262154i	$0.0844330\pi$
$242$	0	0
$243$	0	0
$244$	−31.2152	−1.99835
$245$	0	0
$246$	0	0
$247$	26.9273	1.71334
$248$	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
$259$	29.2993	1.82057
$260$	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
$268$	−26.4155	−1.61358
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	−25.1253	−1.52625	−0.763125	−	0.646250i	$-0.776336\pi$
$271$	−25.1253	−1.52625	−0.763125	+	0.646250i	$0.776336\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	23.3885	1.40528	0.702639	−	0.711546i	$-0.252005\pi$
$277$	23.3885	1.40528	0.702639	+	0.711546i	$0.252005\pi$
$278$	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	$-0.233379\pi$
$283$	25.0000	1.48610	0.743048	+	0.669238i	$0.233379\pi$
$284$	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
$292$	32.4695	1.90014
$293$	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
$301$	−39.5813	−2.28143
$302$	0	0
$303$	0	0
$304$	31.7095	1.81866
$305$	0	0
$306$	0	0
$307$	−9.16832	−0.523263	−0.261632	−	0.965168i	$-0.584261\pi$
$307$	−9.16832	−0.523263	−0.261632	+	0.965168i	$0.584261\pi$
$308$	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
$313$	31.3698	1.77313	0.886563	−	0.462607i	$-0.153086\pi$
$313$	31.3698	1.77313	0.886563	+	0.462607i	$0.153086\pi$
$314$	0	0
$315$	0	0
$316$	13.8893	0.781337
$317$	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
$331$	−6.58424	−0.361902	−0.180951	−	0.983492i	$-0.557918\pi$
$331$	−6.58424	−0.361902	−0.180951	+	0.983492i	$0.557918\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−17.3345	−0.944269	−0.472134	−	0.881527i	$-0.656516\pi$
$337$	−17.3345	−0.944269	−0.472134	+	0.881527i	$0.656516\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−14.6423	−0.790608
$344$	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
$349$	−28.6193	−1.53196	−0.765979	−	0.642866i	$-0.777745\pi$
$349$	−28.6193	−1.53196	−0.765979	+	0.642866i	$0.777745\pi$
$350$	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
$361$	43.8433	2.30754
$362$	0	0
$363$	0	0
$364$	−20.5640	−1.07785
$365$	0	0
$366$	0	0
$367$	−25.6411	−1.33845	−0.669227	−	0.743058i	$-0.733375\pi$
$367$	−25.6411	−1.33845	−0.669227	+	0.743058i	$0.733375\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	25.0000	1.29445	0.647225	−	0.762299i	$-0.275929\pi$
$373$	25.0000	1.29445	0.647225	+	0.762299i	$0.275929\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−38.7326	−1.98956	−0.994780	−	0.102042i	$-0.967462\pi$
$379$	−38.7326	−1.98956	−0.994780	+	0.102042i	$0.967462\pi$
$380$	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
$388$	14.3075	0.726351
$389$	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
$397$	7.30447	0.366601	0.183300	−	0.983057i	$-0.441322\pi$
$397$	7.30447	0.366601	0.183300	+	0.983057i	$0.441322\pi$
$398$	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
$403$	1.94549	0.0969116
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	9.80842	0.484995	0.242498	−	0.970152i	$-0.422033\pi$
$409$	9.80842	0.484995	0.242498	+	0.970152i	$0.422033\pi$
$410$	0	0
$411$	0	0
$412$	5.77157	0.284345
$413$	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
$421$	38.1599	1.85980	0.929899	−	0.367816i	$-0.119894\pi$
$421$	38.1599	1.85980	0.929899	+	0.367816i	$0.119894\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	47.2443	2.28631
$428$	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
$433$	41.5506	1.99679	0.998396	−	0.0566140i	$-0.0180304\pi$
$433$	41.5506	1.99679	0.998396	+	0.0566140i	$0.0180304\pi$
$434$	0	0
$435$	0	0
$436$	28.2154	1.35127
$437$	0	0
$438$	0	0
$439$	4.43331	0.211590	0.105795	−	0.994388i	$-0.466261\pi$
$439$	4.43331	0.211590	0.105795	+	0.994388i	$0.466261\pi$
$440$	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
$448$	−24.2161	−1.14410
$449$	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
$457$	42.6248	1.99391	0.996953	−	0.0780031i	$-0.0248544\pi$
$457$	42.6248	1.99391	0.996953	+	0.0780031i	$0.0248544\pi$
$458$	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
$463$	30.0598	1.39700	0.698498	−	0.715612i	$-0.253852\pi$
$463$	30.0598	1.39700	0.698498	+	0.715612i	$0.253852\pi$
$464$	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
$469$	39.9800	1.84611
$470$	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
$481$	32.8781	1.49911
$482$	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	$-0.308325\pi$
$487$	25.0000	1.13286	0.566429	+	0.824110i	$0.308325\pi$
$488$	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
$496$	2.29100	0.102869
$497$	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
$508$	−44.5776	−1.97781
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−49.1428	−2.17395
$512$	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
$523$	11.0083	0.481361	0.240681	−	0.970604i	$-0.422629\pi$
$523$	11.0083	0.481361	0.240681	+	0.970604i	$0.422629\pi$
$524$	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
$532$	−47.9925	−2.08074
$533$	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
$547$	−10.7012	−0.457551	−0.228775	−	0.973479i	$-0.573472\pi$
$547$	−10.7012	−0.457551	−0.228775	+	0.973479i	$0.573472\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−21.0216	−0.893929
$554$	0	0
$555$	0	0
$556$	−46.2500	−1.96144
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	−44.4160	−1.87860
$560$	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
$571$	−32.9334	−1.37822	−0.689111	−	0.724656i	$-0.741999\pi$
$571$	−32.9334	−1.37822	−0.689111	+	0.724656i	$0.741999\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−42.1139	−1.75322	−0.876612	−	0.481198i	$-0.840202\pi$
$577$	−42.1139	−1.75322	−0.876612	+	0.481198i	$0.840202\pi$
$578$	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
$589$	4.54040	0.187084
$590$	0	0
$591$	0	0
$592$	38.7171	1.59126
$593$	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
$604$	47.3955	1.92850
$605$	0	0
$606$	0	0
$607$	42.6503	1.73112	0.865560	−	0.500805i	$-0.166962\pi$
$607$	42.6503	1.73112	0.865560	+	0.500805i	$0.166962\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−36.5962	−1.47811	−0.739054	−	0.673646i	$-0.764727\pi$
$613$	−36.5962	−1.47811	−0.739054	+	0.673646i	$0.764727\pi$
$614$	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
$619$	−23.3782	−0.939650	−0.469825	−	0.882760i	$-0.655683\pi$
$619$	−23.3782	−0.939650	−0.469825	+	0.882760i	$0.655683\pi$
$620$	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
$631$	11.4214	0.454680	0.227340	−	0.973815i	$-0.426997\pi$
$631$	11.4214	0.454680	0.227340	+	0.973815i	$0.426997\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	7.34648	0.291078
$638$	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
$643$	−14.0353	−0.553500	−0.276750	−	0.960942i	$-0.589257\pi$
$643$	−14.0353	−0.553500	−0.276750	+	0.960942i	$0.589257\pi$
$644$	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
$661$	−10.3812	−0.403781	−0.201890	−	0.979408i	$-0.564708\pi$
$661$	−10.3812	−0.403781	−0.201890	+	0.979408i	$0.564708\pi$
$662$	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	$-0.913947\pi$
$673$	−50.0000	−1.92736	−0.963679	+	0.267063i	$0.913947\pi$
$674$	0	0
$675$	0	0
$676$	2.92418	0.112469
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	−21.6544	−0.831020
$680$	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
$688$	−52.3041	−1.99408
$689$	0	0
$690$	0	0
$691$	−37.0144	−1.40809	−0.704046	−	0.710154i	$-0.748625\pi$
$691$	−37.0144	−1.40809	−0.704046	+	0.710154i	$0.748625\pi$
$692$	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
$703$	76.7313	2.89398
$704$	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
$721$	−8.73530	−0.325320
$722$	0	0
$723$	0	0
$724$	53.7446	1.99740
$725$	0	0
$726$	0	0
$727$	−27.5152	−1.02048	−0.510241	−	0.860031i	$-0.670444\pi$
$727$	−27.5152	−1.02048	−0.510241	+	0.860031i	$0.670444\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	44.4741	1.63601	0.818003	−	0.575214i	$-0.195081\pi$
$739$	44.4741	1.63601	0.818003	+	0.575214i	$0.195081\pi$
$740$	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
$751$	0.403898	0.0147385	0.00736923	−	0.999973i	$-0.497654\pi$
$751$	0.403898	0.0147385	0.00736923	+	0.999973i	$0.497654\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−43.4779	−1.58023	−0.790115	−	0.612959i	$-0.789979\pi$
$757$	−43.4779	−1.58023	−0.790115	+	0.612959i	$0.789979\pi$
$758$	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
$763$	−42.7042	−1.54600
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	54.9129	1.98021	0.990106	−	0.140324i	$-0.0448144\pi$
$769$	54.9129	1.98021	0.990106	+	0.140324i	$0.0448144\pi$
$770$	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
$784$	8.65118	0.308971
$785$	0	0
$786$	0	0
$787$	25.0000	0.891154	0.445577	−	0.895244i	$-0.352999\pi$
$787$	25.0000	0.891154	0.445577	+	0.895244i	$0.352999\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	53.0151	1.88262
$794$	0	0
$795$	0	0
$796$	−12.7438	−0.451694
$797$	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
$817$	−103.659	−3.62656
$818$	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
$823$	52.8151	1.84102	0.920509	−	0.390721i	$-0.127774\pi$
$823$	52.8151	1.84102	0.920509	+	0.390721i	$0.127774\pi$
$824$	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
$829$	−47.1603	−1.63795	−0.818973	−	0.573832i	$-0.805456\pi$
$829$	−47.1603	−1.63795	−0.818973	+	0.573832i	$0.805456\pi$
$830$	0	0
$831$	0	0
$832$	−27.1740	−0.942089
$833$	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
$844$	−41.3839	−1.42449
$845$	0	0
$846$	0	0
$847$	−33.2971	−1.14410
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0.827599	0.0283364	0.0141682	−	0.999900i	$-0.495490\pi$
$853$	0.827599	0.0283364	0.0141682	+	0.999900i	$0.495490\pi$
$854$	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
$859$	−55.4857	−1.89315	−0.946574	−	0.322488i	$-0.895481\pi$
$859$	−55.4857	−1.89315	−0.946574	+	0.322488i	$0.895481\pi$
$860$	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
$868$	−3.46744	−0.117692
$869$	0	0
$870$	0	0
$871$	44.8634	1.52014
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	25.0000	0.844190	0.422095	−	0.906552i	$-0.361295\pi$
$877$	25.0000	0.844190	0.422095	+	0.906552i	$0.361295\pi$
$878$	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
$883$	−4.41868	−0.148700	−0.0743502	−	0.997232i	$-0.523688\pi$
$883$	−4.41868	−0.148700	−0.0743502	+	0.997232i	$0.523688\pi$
$884$	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
$889$	67.4684	2.26282
$890$	0	0
$891$	0	0
$892$	59.0976	1.97873
$893$	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
$907$	55.1899	1.83255	0.916275	−	0.400549i	$-0.131180\pi$
$907$	55.1899	1.83255	0.916275	+	0.400549i	$0.131180\pi$
$908$	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
$916$	−34.3958	−1.13647
$917$	0	0
$918$	0	0
$919$	36.4416	1.20210	0.601049	−	0.799212i	$-0.294750\pi$
$919$	36.4416	1.20210	0.601049	+	0.799212i	$0.294750\pi$
$920$	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
$931$	17.1453	0.561914
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−58.5867	−1.91394	−0.956971	−	0.290182i	$-0.906284\pi$
$937$	−58.5867	−1.91394	−0.956971	+	0.290182i	$0.906284\pi$
$938$	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
$949$	−55.1454	−1.79010
$950$	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
$961$	−30.6720	−0.989418
$962$	0	0
$963$	0	0
$964$	−59.9249	−1.93005
$965$	0	0
$966$	0	0
$967$	−18.4342	−0.592803	−0.296402	−	0.955063i	$-0.595787\pi$
$967$	−18.4342	−0.592803	−0.296402	+	0.955063i	$0.595787\pi$
$968$	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
$973$	69.9997	2.24409
$974$	0	0
$975$	0	0
$976$	62.4304	1.99835
$977$	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
$988$	−53.8546	−1.71334
$989$	0	0
$990$	0	0
$991$	−52.4014	−1.66459	−0.832293	−	0.554335i	$-0.812973\pi$
$991$	−52.4014	−1.66459	−0.832293	+	0.554335i	$0.812973\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−56.2118	−1.78025	−0.890124	−	0.455719i	$-0.849382\pi$
$997$	−56.2118	−1.78025	−0.890124	+	0.455719i	$0.849382\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5625.2.a.l.1.3	yes	4
3.2	odd	2	CM	5625.2.a.l.1.3	yes	4
5.4	even	2		5625.2.a.k.1.2	✓	4
15.14	odd	2		5625.2.a.k.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5625.2.a.k.1.2	✓	4	5.4	even	2
5625.2.a.k.1.2	✓	4	15.14	odd	2
5625.2.a.l.1.3	yes	4	1.1	even	1	trivial
5625.2.a.l.1.3	yes	4	3.2	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5625 = 3^{2} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5625.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{4} +3.02701 q^{7} +O(q^{10})\)	\(q-2.00000 q^{4} +3.02701 q^{7} +3.39675 q^{13} +4.00000 q^{16} +7.92737 q^{19} -6.05402 q^{28} +0.572749 q^{31} +9.67928 q^{37} -13.0760 q^{43} +2.16280 q^{49} -6.79350 q^{52} +15.6076 q^{61} -8.00000 q^{64} +13.2078 q^{67} -16.2348 q^{73} -15.8547 q^{76} -6.94467 q^{79} +10.2820 q^{91} -7.15373 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 5 q^{7}+O(q^{10}) \) 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

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