LMFDB - Embedded newform 1232.3.m.a.1231.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,3,Mod(1231,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1232.1231");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1232.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$33.5695685692$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{7}, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 9x^{2} + 1 $ x^4 - 9*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1231.3
Root			$0.335437$ of defining polynomial
Character	$\chi$	$=$	1232.1231

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.670873 q^{3} -7.00000 q^{7} -8.54993 q^{9} +O(q^{10})$	$q+0.670873 q^{3} -7.00000 q^{7} -8.54993 q^{9} -11.0000 q^{11} +24.5204 q^{13} -20.4951 q^{17} -4.69611 q^{21} +25.0000 q^{25} -11.7738 q^{27} +51.0534 q^{31} -7.37961 q^{33} +52.6498 q^{37} +16.4501 q^{39} -38.9777 q^{41} +52.6498 q^{43} -92.0437 q^{47} +49.0000 q^{49} -13.7496 q^{51} +52.6498 q^{53} +114.551 q^{59} +59.1039 q^{61} +59.8495 q^{63} +106.501 q^{73} +16.7718 q^{75} +77.0000 q^{77} -157.949 q^{79} +69.0506 q^{81} -171.643 q^{91} +34.2504 q^{93} +94.0492 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{7} + 36 q^{9}+O(q^{10}) $ 4 * q - 28 * q^7 + 36 * q^9	$ 4 q - 28 q^{7} + 36 q^{9} - 44 q^{11} + 100 q^{25} + 136 q^{39} + 196 q^{49} + 296 q^{51} - 252 q^{63} + 308 q^{77} + 908 q^{81} + 488 q^{93} - 396 q^{99}+O(q^{100}) $ 4 * q - 28 * q^7 + 36 * q^9 - 44 * q^11 + 100 * q^25 + 136 * q^39 + 196 * q^49 + 296 * q^51 - 252 * q^63 + 308 * q^77 + 908 * q^81 + 488 * q^93 - 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	0.670873	0.223624	0.111812	−	0.993729i	$-0.464334\pi$
$3$	0.670873	0.223624	0.111812	+	0.993729i	$0.464334\pi$
$4$	0	0
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	−7.00000	−1.00000
$7$	−7.00000	−1.00000
$8$	0	0
$9$	−8.54993	−0.949992
$10$	0	0
$11$	−11.0000	−1.00000
$11$	−11.0000	−1.00000
$12$	0	0
$13$	24.5204	1.88618	0.943091	−	0.332533i	$-0.107903\pi$
$13$	24.5204	1.88618	0.943091	+	0.332533i	$0.107903\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−20.4951	−1.20560	−0.602798	−	0.797894i	$-0.705948\pi$
$17$	−20.4951	−1.20560	−0.602798	+	0.797894i	$0.705948\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	−4.69611	−0.223624
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	25.0000	1.00000
$26$	0	0
$27$	−11.7738	−0.436066
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	51.0534	1.64688	0.823442	−	0.567401i	$-0.192051\pi$
$31$	51.0534	1.64688	0.823442	+	0.567401i	$0.192051\pi$
$32$	0	0
$33$	−7.37961	−0.223624
$34$	0	0
$35$	0	0
$36$	0	0
$37$	52.6498	1.42297	0.711484	−	0.702703i	$-0.248024\pi$
$37$	52.6498	1.42297	0.711484	+	0.702703i	$0.248024\pi$
$38$	0	0
$39$	16.4501	0.421797
$40$	0	0
$41$	−38.9777	−0.950674	−0.475337	−	0.879804i	$-0.657674\pi$
$41$	−38.9777	−0.950674	−0.475337	+	0.879804i	$0.657674\pi$
$42$	0	0
$43$	52.6498	1.22441	0.612207	−	0.790698i	$-0.290282\pi$
$43$	52.6498	1.22441	0.612207	+	0.790698i	$0.290282\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−92.0437	−1.95838	−0.979188	−	0.202956i	$-0.934945\pi$
$47$	−92.0437	−1.95838	−0.979188	+	0.202956i	$0.934945\pi$
$48$	0	0
$49$	49.0000	1.00000
$50$	0	0
$51$	−13.7496	−0.269601
$52$	0	0
$53$	52.6498	0.993392	0.496696	−	0.867925i	$-0.334546\pi$
$53$	52.6498	0.993392	0.496696	+	0.867925i	$0.334546\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	114.551	1.94155	0.970775	−	0.239993i	$-0.0771451\pi$
$59$	114.551	1.94155	0.970775	+	0.239993i	$0.0771451\pi$
$60$	0	0
$61$	59.1039	0.968916	0.484458	−	0.874815i	$-0.339017\pi$
$61$	59.1039	0.968916	0.484458	+	0.874815i	$0.339017\pi$
$62$	0	0
$63$	59.8495	0.949992
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	106.501	1.45892	0.729458	−	0.684025i	$-0.239772\pi$
$73$	106.501	1.45892	0.729458	+	0.684025i	$0.239772\pi$
$74$	0	0
$75$	16.7718	0.223624
$76$	0	0
$77$	77.0000	1.00000
$78$	0	0
$79$	−157.949	−1.99936	−0.999679	−	0.0253165i	$-0.991941\pi$
$79$	−157.949	−1.99936	−0.999679	+	0.0253165i	$0.991941\pi$
$80$	0	0
$81$	69.0506	0.852477
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	−171.643	−1.88618
$92$	0	0
$93$	34.2504	0.368283
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	94.0492	0.949992
$100$	0	0
$101$	−134.678	−1.33344	−0.666721	−	0.745308i	$-0.732303\pi$
$101$	−134.678	−1.33344	−0.666721	+	0.745308i	$0.732303\pi$
$102$	0	0
$103$	0.368933	0.00358187	0.00179094	−	0.999998i	$-0.499430\pi$
$103$	0.368933	0.00358187	0.00179094	+	0.999998i	$0.499430\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−38.0000	−0.355140	−0.177570	−	0.984108i	$-0.556824\pi$
$107$	−38.0000	−0.355140	−0.177570	+	0.984108i	$0.556824\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	35.3213	0.318210
$112$	0	0
$113$	82.0000	0.725664	0.362832	−	0.931855i	$-0.381810\pi$
$113$	82.0000	0.725664	0.362832	+	0.931855i	$0.381810\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−209.647	−1.79186
$118$	0	0
$119$	143.466	1.20560
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	−26.1491	−0.212594
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−142.000	−1.11811	−0.559055	−	0.829130i	$-0.688836\pi$
$127$	−142.000	−1.11811	−0.559055	+	0.829130i	$0.688836\pi$
$128$	0	0
$129$	35.3213	0.273809
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	263.249	1.92153	0.960763	−	0.277372i	$-0.0894635\pi$
$137$	263.249	1.92153	0.960763	+	0.277372i	$0.0894635\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	−61.7496	−0.437941
$142$	0	0
$143$	−269.724	−1.88618
$144$	0	0
$145$	0	0
$146$	0	0
$147$	32.8728	0.223624
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	263.249	1.74337	0.871685	−	0.490066i	$-0.163027\pi$
$151$	263.249	1.74337	0.871685	+	0.490066i	$0.163027\pi$
$152$	0	0
$153$	175.232	1.14531
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	35.3213	0.222147
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	432.249	2.55769
$170$	0	0
$171$	0	0
$172$	0	0
$173$	313.096	1.80980	0.904902	−	0.425621i	$-0.139944\pi$
$173$	313.096	1.80980	0.904902	+	0.425621i	$0.139944\pi$
$174$	0	0
$175$	−175.000	−1.00000
$176$	0	0
$177$	76.8495	0.434178
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	39.6512	0.216673
$184$	0	0
$185$	0	0
$186$	0	0
$187$	225.447	1.20560
$188$	0	0
$189$	82.4165	0.436066
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	−396.720	−1.99357	−0.996784	−	0.0801294i	$-0.974467\pi$
$199$	−396.720	−1.99357	−0.996784	+	0.0801294i	$0.974467\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	26.0000	0.123223	0.0616114	−	0.998100i	$-0.480376\pi$
$211$	26.0000	0.123223	0.0616114	+	0.998100i	$0.480376\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−357.374	−1.64688
$218$	0	0
$219$	71.4486	0.326250
$220$	0	0
$221$	−502.549	−2.27398
$222$	0	0
$223$	445.761	1.99893	0.999464	−	0.0327349i	$-0.0104217\pi$
$223$	445.761	1.99893	0.999464	+	0.0327349i	$0.0104217\pi$
$224$	0	0
$225$	−213.748	−0.949992
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	51.6573	0.223624
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−105.964	−0.447106
$238$	0	0
$239$	226.000	0.945607	0.472803	−	0.881168i	$-0.343242\pi$
$239$	226.000	0.945607	0.472803	+	0.881168i	$0.343242\pi$
$240$	0	0
$241$	−452.168	−1.87621	−0.938107	−	0.346344i	$-0.887423\pi$
$241$	−452.168	−1.87621	−0.938107	+	0.346344i	$0.887423\pi$
$242$	0	0
$243$	152.288	0.626701
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−346.942	−1.38224	−0.691119	−	0.722741i	$-0.742882\pi$
$251$	−346.942	−1.38224	−0.691119	+	0.722741i	$0.742882\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−368.549	−1.42297
$260$	0	0
$261$	0	0
$262$	0	0
$263$	482.000	1.83270	0.916350	−	0.400379i	$-0.131121\pi$
$263$	482.000	1.83270	0.916350	+	0.400379i	$0.131121\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	−115.150	−0.421797
$274$	0	0
$275$	−275.000	−1.00000
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	−436.503	−1.56453
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	272.844	0.950674
$288$	0	0
$289$	131.051	0.453462
$290$	0	0
$291$	0	0
$292$	0	0
$293$	504.496	1.72183	0.860915	−	0.508750i	$-0.169892\pi$
$293$	504.496	1.72183	0.860915	+	0.508750i	$0.169892\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	129.512	0.436066
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−368.549	−1.22441
$302$	0	0
$303$	−90.3516	−0.298190
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0.247507	0.000800994 0
$310$	0	0
$311$	604.959	1.94521	0.972603	−	0.232473i	$-0.0746817\pi$
$311$	604.959	1.94521	0.972603	+	0.232473i	$0.0746817\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−598.000	−1.88644	−0.943218	−	0.332175i	$-0.892217\pi$
$317$	−598.000	−1.88644	−0.943218	+	0.332175i	$0.892217\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−25.4932	−0.0794180
$322$	0	0
$323$	0	0
$324$	0	0
$325$	613.009	1.88618
$326$	0	0
$327$	0	0
$328$	0	0
$329$	644.306	1.95838
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	−450.152	−1.35181
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	55.0116	0.162276
$340$	0	0
$341$	−561.587	−1.64688
$342$	0	0
$343$	−343.000	−1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	52.6498	0.151728	0.0758642	−	0.997118i	$-0.475828\pi$
$347$	52.6498	0.151728	0.0758642	+	0.997118i	$0.475828\pi$
$348$	0	0
$349$	−624.179	−1.78848	−0.894240	−	0.447588i	$-0.852283\pi$
$349$	−624.179	−1.78848	−0.894240	+	0.447588i	$0.852283\pi$
$350$	0	0
$351$	−288.698	−0.822500
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	96.2475	0.269601
$358$	0	0
$359$	263.249	0.733284	0.366642	−	0.930362i	$-0.380507\pi$
$359$	263.249	0.733284	0.366642	+	0.930362i	$0.380507\pi$
$360$	0	0
$361$	361.000	1.00000
$362$	0	0
$363$	81.1757	0.223624
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−442.642	−1.20611	−0.603054	−	0.797700i	$-0.706050\pi$
$367$	−442.642	−1.20611	−0.603054	+	0.797700i	$0.706050\pi$
$368$	0	0
$369$	333.256	0.903133
$370$	0	0
$371$	−368.549	−0.993392
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	−95.2640	−0.250037
$382$	0	0
$383$	−634.611	−1.65695	−0.828474	−	0.560027i	$-0.810791\pi$
$383$	−634.611	−1.65695	−0.828474	+	0.560027i	$0.810791\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−450.152	−1.16318
$388$	0	0
$389$	−454.000	−1.16710	−0.583548	−	0.812079i	$-0.698336\pi$
$389$	−454.000	−1.16710	−0.583548	+	0.812079i	$0.698336\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−494.000	−1.23192	−0.615960	−	0.787777i	$-0.711232\pi$
$401$	−494.000	−1.23192	−0.615960	+	0.787777i	$0.711232\pi$
$402$	0	0
$403$	1251.85	3.10632
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−579.148	−1.42297
$408$	0	0
$409$	−387.194	−0.946685	−0.473342	−	0.880879i	$-0.656953\pi$
$409$	−387.194	−0.946685	−0.473342	+	0.880879i	$0.656953\pi$
$410$	0	0
$411$	176.607	0.429700
$412$	0	0
$413$	−801.860	−1.94155
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	142.560	0.340239	0.170119	−	0.985423i	$-0.445585\pi$
$419$	142.560	0.340239	0.170119	+	0.985423i	$0.445585\pi$
$420$	0	0
$421$	−789.747	−1.87588	−0.937942	−	0.346793i	$-0.887271\pi$
$421$	−789.747	−1.87588	−0.937942	+	0.346793i	$0.887271\pi$
$422$	0	0
$423$	786.967	1.86044
$424$	0	0
$425$	−512.378	−1.20560
$426$	0	0
$427$	−413.727	−0.968916
$428$	0	0
$429$	−180.951	−0.421797
$430$	0	0
$431$	684.447	1.58804	0.794022	−	0.607889i	$-0.207983\pi$
$431$	684.447	1.58804	0.794022	+	0.607889i	$0.207983\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−418.947	−0.949992
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−157.949	−0.351780	−0.175890	−	0.984410i	$-0.556280\pi$
$449$	−157.949	−0.351780	−0.175890	+	0.984410i	$0.556280\pi$
$450$	0	0
$451$	428.754	0.950674
$452$	0	0
$453$	176.607	0.389860
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	241.305	0.525720
$460$	0	0
$461$	264.223	0.573152	0.286576	−	0.958057i	$-0.407483\pi$
$461$	264.223	0.573152	0.286576	+	0.958057i	$0.407483\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−683.820	−1.46428	−0.732141	−	0.681153i	$-0.761479\pi$
$467$	−683.820	−1.46428	−0.732141	+	0.681153i	$0.761479\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−579.148	−1.22441
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−450.152	−0.943715
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	1290.99	2.68398
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	895.046	1.82291	0.911453	−	0.411405i	$-0.134962\pi$
$491$	895.046	1.82291	0.911453	+	0.411405i	$0.134962\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	289.984	0.571961
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	−745.506	−1.45892
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	1012.48	1.95838
$518$	0	0
$519$	210.048	0.404716
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−117.403	−0.223624
$526$	0	0
$527$	−1046.35	−1.98548
$528$	0	0
$529$	529.000	1.00000
$530$	0	0
$531$	−979.406	−1.84446
$532$	0	0
$533$	−955.747	−1.79315
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−539.000	−1.00000
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	698.000	1.27605	0.638026	−	0.770015i	$-0.279751\pi$
$547$	698.000	1.27605	0.638026	+	0.770015i	$0.279751\pi$
$548$	0	0
$549$	−505.334	−0.920462
$550$	0	0
$551$	0	0
$552$	0	0
$553$	1105.65	1.99936
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	1290.99	2.30947
$560$	0	0
$561$	151.246	0.269601
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−483.354	−0.852477
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	442.000	0.774081	0.387040	−	0.922063i	$-0.373497\pi$
$571$	442.000	0.774081	0.387040	+	0.922063i	$0.373497\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−579.148	−0.993392
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1017.24	1.73295	0.866476	−	0.499218i	$-0.166379\pi$
$587$	1017.24	1.73295	0.866476	+	0.499218i	$0.166379\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−1088.96	−1.83636	−0.918179	−	0.396167i	$-0.870340\pi$
$593$	−1088.96	−1.83636	−0.918179	+	0.396167i	$0.870340\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−266.149	−0.445811
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−53.2670	−0.0886306	−0.0443153	−	0.999018i	$-0.514111\pi$
$601$	−53.2670	−0.0886306	−0.0443153	+	0.999018i	$0.514111\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−2256.95	−3.69385
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	1105.65	1.79197	0.895985	−	0.444084i	$-0.146471\pi$
$617$	1105.65	1.79197	0.895985	+	0.444084i	$0.146471\pi$
$618$	0	0
$619$	−1207.91	−1.95138	−0.975691	−	0.219151i	$-0.929671\pi$
$619$	−1207.91	−1.95138	−0.975691	+	0.219151i	$0.929671\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−1079.06	−1.71552
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	17.4427	0.0275556
$634$	0	0
$635$	0	0
$636$	0	0
$637$	1201.50	1.88618
$638$	0	0
$639$	0	0
$640$	0	0
$641$	684.447	1.06778	0.533890	−	0.845554i	$-0.320730\pi$
$641$	684.447	1.06778	0.533890	+	0.845554i	$0.320730\pi$
$642$	0	0
$643$	259.460	0.403515	0.201757	−	0.979436i	$-0.435335\pi$
$643$	259.460	0.403515	0.201757	+	0.979436i	$0.435335\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−90.2320	−0.139462	−0.0697311	−	0.997566i	$-0.522214\pi$
$647$	−90.2320	−0.139462	−0.0697311	+	0.997566i	$0.522214\pi$
$648$	0	0
$649$	−1260.07	−1.94155
$650$	0	0
$651$	−239.752	−0.368283
$652$	0	0
$653$	−998.000	−1.52833	−0.764165	−	0.645020i	$-0.776849\pi$
$653$	−998.000	−1.52833	−0.764165	+	0.645020i	$0.776849\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−910.575	−1.38596
$658$	0	0
$659$	1316.24	1.99734	0.998668	−	0.0515933i	$-0.0164300\pi$
$659$	1316.24	1.99734	0.998668	+	0.0515933i	$0.0164300\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	−337.146	−0.508517
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	299.049	0.447009
$670$	0	0
$671$	−650.142	−0.968916
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−294.345	−0.436066
$676$	0	0
$677$	1231.89	1.81963	0.909814	−	0.415015i	$-0.136224\pi$
$677$	1231.89	1.81963	0.909814	+	0.415015i	$0.136224\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	1290.99	1.87372
$690$	0	0
$691$	1319.54	1.90961	0.954803	−	0.297238i	$-0.0960655\pi$
$691$	1319.54	1.90961	0.954803	+	0.297238i	$0.0960655\pi$
$692$	0	0
$693$	−658.345	−0.949992
$694$	0	0
$695$	0	0
$696$	0	0
$697$	798.852	1.14613
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	942.743	1.33344
$708$	0	0
$709$	1354.00	1.90973	0.954866	−	0.297037i	$-0.0959984\pi$
$709$	1354.00	1.90973	0.954866	+	0.297037i	$0.0959984\pi$
$710$	0	0
$711$	1350.46	1.89938
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	151.617	0.211461
$718$	0	0
$719$	1114.75	1.55042	0.775212	−	0.631701i	$-0.217643\pi$
$719$	1114.75	1.55042	0.775212	+	0.631701i	$0.217643\pi$
$720$	0	0
$721$	−2.58253	−0.00358187
$722$	0	0
$723$	−303.347	−0.419568
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−805.717	−1.10828	−0.554138	−	0.832425i	$-0.686952\pi$
$727$	−805.717	−1.10828	−0.554138	+	0.832425i	$0.686952\pi$
$728$	0	0
$729$	−519.290	−0.712331
$730$	0	0
$731$	−1079.06	−1.47615
$732$	0	0
$733$	−928.286	−1.26642	−0.633210	−	0.773980i	$-0.718263\pi$
$733$	−928.286	−1.26642	−0.633210	+	0.773980i	$0.718263\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	106.000	0.143437	0.0717185	−	0.997425i	$-0.477152\pi$
$739$	106.000	0.143437	0.0717185	+	0.997425i	$0.477152\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−782.000	−1.05249	−0.526245	−	0.850333i	$-0.676401\pi$
$743$	−782.000	−1.05249	−0.526245	+	0.850333i	$0.676401\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	266.000	0.355140
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	−232.754	−0.309102
$754$	0	0
$755$	0	0
$756$	0	0
$757$	1258.00	1.66182	0.830911	−	0.556405i	$-0.187820\pi$
$757$	1258.00	1.66182	0.830911	+	0.556405i	$0.187820\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	1505.27	1.97801	0.989007	−	0.147866i	$-0.0472404\pi$
$761$	1505.27	1.97801	0.989007	+	0.147866i	$0.0472404\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	2808.84	3.66212
$768$	0	0
$769$	1103.99	1.43561	0.717807	−	0.696242i	$-0.245146\pi$
$769$	1103.99	1.43561	0.717807	+	0.696242i	$0.245146\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	1276.33	1.64688
$776$	0	0
$777$	−247.249	−0.318210
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	323.361	0.409837
$790$	0	0
$791$	−574.000	−0.725664
$792$	0	0
$793$	1449.25	1.82755
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	1886.45	2.36101
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−1171.51	−1.45892
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	1467.53	1.79186
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−184.490	−0.223624
$826$	0	0
$827$	−1632.14	−1.97357	−0.986786	−	0.162031i	$-0.948195\pi$
$827$	−1632.14	−1.97357	−0.986786	+	0.162031i	$0.948195\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−1004.26	−1.20560
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−601.091	−0.718150
$838$	0	0
$839$	−951.196	−1.13373	−0.566863	−	0.823812i	$-0.691843\pi$
$839$	−951.196	−1.13373	−0.566863	+	0.823812i	$0.691843\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−847.000	−1.00000
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−1597.85	−1.87321	−0.936606	−	0.350384i	$-0.886051\pi$
$853$	−1597.85	−1.87321	−0.936606	+	0.350384i	$0.886051\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−626.897	−0.731502	−0.365751	−	0.930713i	$-0.619188\pi$
$857$	−626.897	−0.731502	−0.365751	+	0.930713i	$0.619188\pi$
$858$	0	0
$859$	−761.943	−0.887012	−0.443506	−	0.896271i	$-0.646266\pi$
$859$	−761.943	−0.887012	−0.443506	+	0.896271i	$0.646266\pi$
$860$	0	0
$861$	183.044	0.212594
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	87.9184	0.101405
$868$	0	0
$869$	1737.44	1.99936
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	338.453	0.385043
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	994.000	1.11811
$890$	0	0
$891$	−759.557	−0.852477
$892$	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
$901$	−1079.06	−1.19763
$902$	0	0
$903$	−247.249	−0.273809
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	1151.48	1.26676
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−1726.00	−1.87813	−0.939064	−	0.343742i	$-0.888306\pi$
$919$	−1726.00	−1.87813	−0.939064	+	0.343742i	$0.888306\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1316.24	1.42297
$926$	0	0
$927$	−3.15435	−0.00340275
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	405.851	0.434996
$934$	0	0
$935$	0	0
$936$	0	0
$937$	440.428	0.470041	0.235020	−	0.971990i	$-0.424484\pi$
$937$	440.428	0.470041	0.235020	+	0.971990i	$0.424484\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	395.412	0.420205	0.210102	−	0.977679i	$-0.432620\pi$
$941$	395.412	0.420205	0.210102	+	0.977679i	$0.432620\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	2611.44	2.75178
$950$	0	0
$951$	−401.182	−0.421853
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−1842.74	−1.92153
$960$	0	0
$961$	1645.45	1.71222
$962$	0	0
$963$	324.897	0.337380
$964$	0	0
$965$	0	0
$966$	0	0
$967$	263.249	0.272233	0.136116	−	0.990693i	$-0.456538\pi$
$967$	263.249	0.272233	0.136116	+	0.990693i	$0.456538\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	1940.23	1.99818	0.999088	−	0.0426941i	$-0.0135941\pi$
$971$	1940.23	1.99818	0.999088	+	0.0426941i	$0.0135941\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	411.252	0.421797
$976$	0	0
$977$	−1646.00	−1.68475	−0.842375	−	0.538892i	$-0.818843\pi$
$977$	−1646.00	−1.68475	−0.842375	+	0.538892i	$0.818843\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	1927.42	1.96075	0.980374	−	0.197146i	$-0.0631672\pi$
$983$	1927.42	1.96075	0.980374	+	0.197146i	$0.0631672\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	432.248	0.437941
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−733.263	−0.735469	−0.367735	−	0.929931i	$-0.619867\pi$
$997$	−733.263	−0.735469	−0.367735	+	0.929931i	$0.619867\pi$
$998$	0	0
$999$	−619.887	−0.620508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.3.m.a.1231.3	yes	4
4.3	odd	2		1232.3.m.b.1231.2	yes	4
7.6	odd	2	inner	1232.3.m.a.1231.2	✓	4
11.10	odd	2		1232.3.m.b.1231.3	yes	4
28.27	even	2		1232.3.m.b.1231.3	yes	4
44.43	even	2	inner	1232.3.m.a.1231.2	✓	4
77.76	even	2		1232.3.m.b.1231.2	yes	4
308.307	odd	2	CM	1232.3.m.a.1231.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.3.m.a.1231.2	✓	4	7.6	odd	2	inner
1232.3.m.a.1231.2	✓	4	44.43	even	2	inner
1232.3.m.a.1231.3	yes	4	1.1	even	1	trivial
1232.3.m.a.1231.3	yes	4	308.307	odd	2	CM
1232.3.m.b.1231.2	yes	4	4.3	odd	2
1232.3.m.b.1231.2	yes	4	77.76	even	2
1232.3.m.b.1231.3	yes	4	11.10	odd	2
1232.3.m.b.1231.3	yes	4	28.27	even	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1232.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.670873 q^{3} -7.00000 q^{7} -8.54993 q^{9} +O(q^{10})\)	\(q+0.670873 q^{3} -7.00000 q^{7} -8.54993 q^{9} -11.0000 q^{11} +24.5204 q^{13} -20.4951 q^{17} -4.69611 q^{21} +25.0000 q^{25} -11.7738 q^{27} +51.0534 q^{31} -7.37961 q^{33} +52.6498 q^{37} +16.4501 q^{39} -38.9777 q^{41} +52.6498 q^{43} -92.0437 q^{47} +49.0000 q^{49} -13.7496 q^{51} +52.6498 q^{53} +114.551 q^{59} +59.1039 q^{61} +59.8495 q^{63} +106.501 q^{73} +16.7718 q^{75} +77.0000 q^{77} -157.949 q^{79} +69.0506 q^{81} -171.643 q^{91} +34.2504 q^{93} +94.0492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{7} + 36 q^{9}+O(q^{10}) \) 4 * q - 28 * q^7 + 36 * q^9	\( 4 q - 28 q^{7} + 36 q^{9} - 44 q^{11} + 100 q^{25} + 136 q^{39} + 196 q^{49} + 296 q^{51} - 252 q^{63} + 308 q^{77} + 908 q^{81} + 488 q^{93} - 396 q^{99}+O(q^{100}) \) 4 * q - 28 * q^7 + 36 * q^9 - 44 * q^11 + 100 * q^25 + 136 * q^39 + 196 * q^49 + 296 * q^51 - 252 * q^63 + 308 * q^77 + 908 * q^81 + 488 * q^93 - 396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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