LMFDB - Embedded newform 7744.2.a.cf.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7744,2,Mod(1,7744)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7744, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7744.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7744 = 2^{6} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7744.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:	$61.8361513253$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 3872)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	7744.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46410 q^{5} -3.00000 q^{9} -0.464102 q^{13} +5.92820 q^{17} +1.07180 q^{25} -8.46410 q^{29} -11.3923 q^{37} -11.9282 q^{41} -7.39230 q^{45} -7.00000 q^{49} +3.53590 q^{53} +10.0000 q^{61} -1.14359 q^{65} -6.00000 q^{73} +9.00000 q^{81} +14.6077 q^{85} -18.8564 q^{89} -15.9282 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} - 6 q^{9} + 6 q^{13} - 2 q^{17} + 16 q^{25} - 10 q^{29} - 2 q^{37} - 10 q^{41} + 6 q^{45} - 14 q^{49} + 14 q^{53} + 20 q^{61} - 30 q^{65} - 12 q^{73} + 18 q^{81} + 50 q^{85} - 10 q^{89} - 18 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 - 6 * q^9 + 6 * q^13 - 2 * q^17 + 16 * q^25 - 10 * q^29 - 2 * q^37 - 10 * q^41 + 6 * q^45 - 14 * q^49 + 14 * q^53 + 20 * q^61 - 30 * q^65 - 12 * q^73 + 18 * q^81 + 50 * q^85 - 10 * q^89 - 18 * q^97

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	0	0
$5$	2.46410	1.10198	0.550990	−	0.834512i	$-0.314250\pi$
$5$	2.46410	1.10198	0.550990	+	0.834512i	$0.314250\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−0.464102	−0.128719	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	−0.464102	−0.128719	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	5.92820	1.43780	0.718900	−	0.695113i	$-0.244646\pi$
$17$	5.92820	1.43780	0.718900	+	0.695113i	$0.244646\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	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
$25$	1.07180	0.214359
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−8.46410	−1.57174	−0.785872	−	0.618389i	$-0.787786\pi$
$29$	−8.46410	−1.57174	−0.785872	+	0.618389i	$0.787786\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−11.3923	−1.87288	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−11.3923	−1.87288	−0.936442	+	0.350823i	$0.885902\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−11.9282	−1.86287	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−11.9282	−1.86287	−0.931436	+	0.363905i	$0.881443\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	−7.39230	−1.10198
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	3.53590	0.485693	0.242846	−	0.970065i	$-0.421919\pi$
$53$	3.53590	0.485693	0.242846	+	0.970065i	$0.421919\pi$
$54$	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
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.14359	−0.141845
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	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
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	14.6077	1.58443
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−18.8564	−1.99878	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−18.8564	−1.99878	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−15.9282	−1.61726	−0.808632	−	0.588315i	$-0.799792\pi$
$97$	−15.9282	−1.61726	−0.808632	+	0.588315i	$0.799792\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	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
$109$	20.3205	1.94635	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	20.3205	1.94635	0.973176	+	0.230063i	$0.0738931\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	20.8564	1.96201	0.981003	−	0.193993i	$-0.0621440\pi$
$113$	20.8564	1.96201	0.981003	+	0.193993i	$0.0621440\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.39230	0.128719
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−9.67949	−0.865760
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	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
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−20.8564	−1.73203
$146$	0	0
$147$	0	0
$148$	0	0
$149$	24.3205	1.99241	0.996207	−	0.0870170i	$-0.0277334\pi$
$149$	24.3205	1.99241	0.996207	+	0.0870170i	$0.0277334\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	−17.7846	−1.43780
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	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
$169$	−12.7846	−0.983432
$170$	0	0
$171$	0	0
$172$	0	0
$173$	26.0000	1.97674	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	26.0000	1.97674	0.988372	+	0.152057i	$0.0485898\pi$
$174$	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
$181$	−26.3205	−1.95639	−0.978194	−	0.207693i	$-0.933404\pi$
$181$	−26.3205	−1.95639	−0.978194	+	0.207693i	$0.933404\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−28.0718	−2.06388
$186$	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
$193$	−13.7846	−0.992238	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−13.7846	−0.992238	−0.496119	+	0.868255i	$0.665242\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−25.2487	−1.79890	−0.899448	−	0.437028i	$-0.856031\pi$
$197$	−25.2487	−1.79890	−0.899448	+	0.437028i	$0.856031\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−29.3923	−2.05285
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−2.75129	−0.185072
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−3.21539	−0.214359
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	18.4641	1.22014	0.610071	−	0.792347i	$-0.291141\pi$
$229$	18.4641	1.22014	0.610071	+	0.792347i	$0.291141\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0.856406	0.0561051	0.0280525	−	0.999606i	$-0.491069\pi$
$233$	0.856406	0.0561051	0.0280525	+	0.999606i	$0.491069\pi$
$234$	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
$241$	−30.0000	−1.93247	−0.966235	−	0.257663i	$-0.917048\pi$
$241$	−30.0000	−1.93247	−0.966235	+	0.257663i	$0.917048\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−17.2487	−1.10198
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	26.7128	1.66630	0.833150	−	0.553047i	$-0.186535\pi$
$257$	26.7128	1.66630	0.833150	+	0.553047i	$0.186535\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	25.3923	1.57174
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	8.71281	0.535224
$266$	0	0
$267$	0	0
$268$	0	0
$269$	4.32051	0.263426	0.131713	−	0.991288i	$-0.457952\pi$
$269$	4.32051	0.263426	0.131713	+	0.991288i	$0.457952\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	15.2487	0.916206	0.458103	−	0.888899i	$-0.348529\pi$
$277$	15.2487	0.916206	0.458103	+	0.888899i	$0.348529\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	18.1436	1.06727
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−13.5359	−0.790776	−0.395388	−	0.918514i	$-0.629390\pi$
$293$	−13.5359	−0.790776	−0.395388	+	0.918514i	$0.629390\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	24.6410	1.41094
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	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
$313$	−33.7846	−1.90962	−0.954810	−	0.297218i	$-0.903941\pi$
$313$	−33.7846	−1.90962	−0.954810	+	0.297218i	$0.903941\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−0.497423	−0.0275920
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	34.1769	1.87288
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−36.7128	−1.99987	−0.999937	−	0.0112091i	$-0.996432\pi$
$337$	−36.7128	−1.99987	−0.999937	+	0.0112091i	$0.996432\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	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
$349$	26.1769	1.40122	0.700609	−	0.713545i	$-0.252912\pi$
$349$	26.1769	1.40122	0.700609	+	0.713545i	$0.252912\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−3.14359	−0.167317	−0.0836583	−	0.996495i	$-0.526660\pi$
$353$	−3.14359	−0.167317	−0.0836583	+	0.996495i	$0.526660\pi$
$354$	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
$365$	−14.7846	−0.773862
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	35.7846	1.86287
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	3.92820	0.202313
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	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
$388$	0	0
$389$	−34.3205	−1.74012	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−34.3205	−1.74012	−0.870059	+	0.492947i	$0.835920\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	29.3923	1.47516	0.737579	−	0.675261i	$-0.235969\pi$
$397$	29.3923	1.47516	0.737579	+	0.675261i	$0.235969\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−35.6410	−1.77983	−0.889914	−	0.456129i	$-0.849236\pi$
$401$	−35.6410	−1.77983	−0.889914	+	0.456129i	$0.849236\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	22.1769	1.10198
$406$	0	0
$407$	0	0
$408$	0	0
$409$	37.6410	1.86123	0.930614	−	0.366002i	$-0.119274\pi$
$409$	37.6410	1.86123	0.930614	+	0.366002i	$0.119274\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	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
$421$	39.2487	1.91287	0.956433	−	0.291953i	$-0.0943052\pi$
$421$	39.2487	1.91287	0.956433	+	0.291953i	$0.0943052\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	6.35383	0.308206
$426$	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
$433$	3.78461	0.181877	0.0909384	−	0.995857i	$-0.471013\pi$
$433$	3.78461	0.181877	0.0909384	+	0.995857i	$0.471013\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	21.0000	1.00000
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	−46.4641	−2.20261
$446$	0	0
$447$	0	0
$448$	0	0
$449$	41.6410	1.96516	0.982581	−	0.185837i	$-0.0594997\pi$
$449$	41.6410	1.96516	0.982581	+	0.185837i	$0.0594997\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−27.9282	−1.30643	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−27.9282	−1.30643	−0.653213	+	0.757174i	$0.726579\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	1.67949	0.0782217	0.0391109	−	0.999235i	$-0.487547\pi$
$461$	1.67949	0.0782217	0.0391109	+	0.999235i	$0.487547\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−10.6077	−0.485693
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	5.28719	0.241075
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−39.2487	−1.78219
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	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
$493$	−50.1769	−2.25985
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	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
$505$	4.92820	0.219302
$506$	0	0
$507$	0	0
$508$	0	0
$509$	10.0000	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$510$	0	0
$511$	0	0
$512$	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
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	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
$533$	5.53590	0.239786
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	42.0000	1.80572	0.902861	−	0.429934i	$-0.141463\pi$
$541$	42.0000	1.80572	0.902861	+	0.429934i	$0.141463\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	50.0718	2.14484
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	−30.0000	−1.28037
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	51.3923	2.16209
$566$	0	0
$567$	0	0
$568$	0	0
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	40.5692	1.68892	0.844459	−	0.535620i	$-0.179922\pi$
$577$	40.5692	1.68892	0.844459	+	0.535620i	$0.179922\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	3.43078	0.141845
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	9.14359	0.375482	0.187741	−	0.982219i	$-0.439883\pi$
$593$	9.14359	0.375482	0.187741	+	0.982219i	$0.439883\pi$
$594$	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
$601$	−46.5692	−1.89960	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−46.5692	−1.89960	−0.949799	+	0.312861i	$0.898713\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−48.1769	−1.94585	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−48.1769	−1.94585	−0.972924	+	0.231127i	$0.925759\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−8.71281	−0.350765	−0.175382	−	0.984500i	$-0.556116\pi$
$617$	−8.71281	−0.350765	−0.175382	+	0.984500i	$0.556116\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−29.2102	−1.16841
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−67.5359	−2.69283
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	3.24871	0.128719
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−18.0718	−0.713793	−0.356897	−	0.934144i	$-0.616165\pi$
$641$	−18.0718	−0.713793	−0.356897	+	0.934144i	$0.616165\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	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
$652$	0	0
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	18.0000	0.702247
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	−14.6077	−0.568173	−0.284087	−	0.958799i	$-0.591690\pi$
$661$	−14.6077	−0.568173	−0.284087	+	0.958799i	$0.591690\pi$
$662$	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
$673$	−46.0000	−1.77317	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000	−1.77317	−0.886585	+	0.462566i	$0.846929\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	44.0333	1.69234	0.846169	−	0.532915i	$-0.178903\pi$
$677$	44.0333	1.69234	0.846169	+	0.532915i	$0.178903\pi$
$678$	0	0
$679$	0	0
$680$	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
$685$	−54.2102	−2.07127
$686$	0	0
$687$	0	0
$688$	0	0
$689$	−1.64102	−0.0625177
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−70.7128	−2.67844
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−50.0333	−1.88973	−0.944866	−	0.327457i	$-0.893808\pi$
$701$	−50.0333	−1.88973	−0.944866	+	0.327457i	$0.893808\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	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
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−9.07180	−0.336918
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	30.4641	1.12522	0.562609	−	0.826723i	$-0.309798\pi$
$733$	30.4641	1.12522	0.562609	+	0.826723i	$0.309798\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	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
$745$	59.9282	2.19560
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−54.0333	−1.96387	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−54.0333	−1.96387	−0.981937	+	0.189207i	$0.939408\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−15.6410	−0.566986	−0.283493	−	0.958974i	$-0.591493\pi$
$761$	−15.6410	−0.566986	−0.283493	+	0.958974i	$0.591493\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−43.8231	−1.58443
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−4.21539	−0.152011	−0.0760054	−	0.997107i	$-0.524217\pi$
$769$	−4.21539	−0.152011	−0.0760054	+	0.997107i	$0.524217\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	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
$784$	0	0
$785$	−54.2102	−1.93485
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−4.64102	−0.164807
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	56.5692	1.99878
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	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
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	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
$829$	9.67949	0.336183	0.168091	−	0.985771i	$-0.446240\pi$
$829$	9.67949	0.336183	0.168091	+	0.985771i	$0.446240\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−41.4974	−1.43780
$834$	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
$841$	42.6410	1.47038
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−31.5026	−1.08372
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	54.1769	1.85498	0.927491	−	0.373845i	$-0.121961\pi$
$853$	54.1769	1.85498	0.927491	+	0.373845i	$0.121961\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	58.0000	1.98124	0.990621	−	0.136637i	$-0.0436295\pi$
$857$	58.0000	1.98124	0.990621	+	0.136637i	$0.0436295\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	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
$865$	64.0666	2.17833
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	47.7846	1.61726
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−18.6077	−0.628337	−0.314169	−	0.949367i	$-0.601726\pi$
$877$	−18.6077	−0.628337	−0.314169	+	0.949367i	$0.601726\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−52.7128	−1.77594	−0.887970	−	0.459902i	$-0.847885\pi$
$881$	−52.7128	−1.77594	−0.887970	+	0.459902i	$0.847885\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	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
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	20.9615	0.698330
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−64.8564	−2.15590
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	−6.00000	−0.199007
$910$	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
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−12.2102	−0.401470
$926$	0	0
$927$	0	0
$928$	0	0
$929$	57.6410	1.89114	0.945570	−	0.325418i	$-0.105505\pi$
$929$	57.6410	1.89114	0.945570	+	0.325418i	$0.105505\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	60.5692	1.97871	0.989355	−	0.145522i	$-0.0464860\pi$
$937$	60.5692	1.97871	0.989355	+	0.145522i	$0.0464860\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−46.3205	−1.51001	−0.755003	−	0.655722i	$-0.772364\pi$
$941$	−46.3205	−1.51001	−0.755003	+	0.655722i	$0.772364\pi$
$942$	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
$949$	2.78461	0.0903923
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−61.4974	−1.99210	−0.996048	−	0.0888114i	$-0.971693\pi$
$953$	−61.4974	−1.99210	−0.996048	+	0.0888114i	$0.971693\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	−33.9667	−1.09343
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	37.9282	1.21343	0.606715	−	0.794919i	$-0.292487\pi$
$977$	37.9282	1.21343	0.606715	+	0.794919i	$0.292487\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−60.9615	−1.94635
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	−62.2154	−1.98235
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	20.6077	0.652652	0.326326	−	0.945257i	$-0.394189\pi$
$997$	20.6077	0.652652	0.326326	+	0.945257i	$0.394189\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7744.2.a.cf.1.2		2
4.3	odd	2	CM	7744.2.a.cf.1.2		2
8.3	odd	2		3872.2.a.v.1.1	✓	2
8.5	even	2		3872.2.a.v.1.1	✓	2
11.10	odd	2		7744.2.a.ce.1.2		2
44.43	even	2		7744.2.a.ce.1.2		2
88.21	odd	2		3872.2.a.w.1.1	yes	2
88.43	even	2		3872.2.a.w.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3872.2.a.v.1.1	✓	2	8.3	odd	2
3872.2.a.v.1.1	✓	2	8.5	even	2
3872.2.a.w.1.1	yes	2	88.21	odd	2
3872.2.a.w.1.1	yes	2	88.43	even	2
7744.2.a.ce.1.2		2	11.10	odd	2
7744.2.a.ce.1.2		2	44.43	even	2
7744.2.a.cf.1.2		2	1.1	even	1	trivial
7744.2.a.cf.1.2		2	4.3	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:	\( N \)	\(=\)	\( 7744 = 2^{6} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7744.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46410 q^{5} -3.00000 q^{9} -0.464102 q^{13} +5.92820 q^{17} +1.07180 q^{25} -8.46410 q^{29} -11.3923 q^{37} -11.9282 q^{41} -7.39230 q^{45} -7.00000 q^{49} +3.53590 q^{53} +10.0000 q^{61} -1.14359 q^{65} -6.00000 q^{73} +9.00000 q^{81} +14.6077 q^{85} -18.8564 q^{89} -15.9282 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} - 6 q^{9} + 6 q^{13} - 2 q^{17} + 16 q^{25} - 10 q^{29} - 2 q^{37} - 10 q^{41} + 6 q^{45} - 14 q^{49} + 14 q^{53} + 20 q^{61} - 30 q^{65} - 12 q^{73} + 18 q^{81} + 50 q^{85} - 10 q^{89} - 18 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 - 6 * q^9 + 6 * q^13 - 2 * q^17 + 16 * q^25 - 10 * q^29 - 2 * q^37 - 10 * q^41 + 6 * q^45 - 14 * q^49 + 14 * q^53 + 20 * q^61 - 30 * q^65 - 12 * q^73 + 18 * q^81 + 50 * q^85 - 10 * q^89 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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