LMFDB - Embedded newform 1008.2.k.a.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(881,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1008.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.k (of order $2$, degree $1$, not 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:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 8x^{2} + 9 $ x^4 + 8*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			881.4
Root			$-2.57794i$ of defining polynomial
Character	$\chi$	$=$	1008.881
Dual form			1008.2.k.a.881.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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	0
$3$	0	0
$4$	0	0
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	2.64575	1.00000
$7$	2.64575	1.00000
$8$	0	0
$9$	0	0
$10$	0	0
$11$	6.57008i	1.98096i	0.137675	+	0.990478i	$0.456037\pi$
$11$	6.57008i	1.98096i	−0.137675	+	0.990478i	$0.543963\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	− 1.91520i	− 0.399346i	−0.979863	−	0.199673i	$-0.936012\pi$
$23$	− 1.91520i	− 0.399346i	0.979863	−	0.199673i	$-0.0639880\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	8.89753i	1.65223i	0.563502	+	0.826115i	$0.309454\pi$
$29$	8.89753i	1.65223i	−0.563502	+	0.826115i	$0.690546\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	10.5830	1.73984	0.869918	−	0.493197i	$-0.164172\pi$
$37$	10.5830	1.73984	0.869918	+	0.493197i	$0.164172\pi$
$38$	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
$43$	5.29150	0.806947	0.403473	−	0.914991i	$-0.367803\pi$
$43$	5.29150	0.806947	0.403473	+	0.914991i	$0.367803\pi$
$44$	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
$49$	7.00000	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0.412247i	0.0566265i	0.999599	+	0.0283132i	$0.00901359\pi$
$53$	0.412247i	0.0566265i	−0.999599	+	0.0283132i	$0.990986\pi$
$54$	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
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	15.0554i	1.78674i	0.449319	+	0.893372i	$0.351667\pi$
$71$	15.0554i	1.78674i	−0.449319	+	0.893372i	$0.648333\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	17.3828i	1.98096i
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	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
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 10.4005i	− 1.00545i	−0.864446	−	0.502726i	$-0.832330\pi$
$107$	− 10.4005i	− 1.00545i	0.864446	−	0.502726i	$-0.167670\pi$
$108$	0	0
$109$	10.5830	1.01367	0.506834	−	0.862044i	$-0.330816\pi$
$109$	10.5830	1.01367	0.506834	+	0.862044i	$0.330816\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	− 13.5524i	− 1.27490i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	− 13.5524i	− 1.27490i	0.770490	−	0.637452i	$-0.220012\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−32.1660	−2.92418
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	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
$137$	− 22.0377i	− 1.88281i	−0.337282	−	0.941404i	$-0.609507\pi$
$137$	− 22.0377i	− 1.88281i	0.337282	−	0.941404i	$-0.390493\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	− 8.07303i	− 0.661369i	−0.943741	−	0.330684i	$-0.892720\pi$
$149$	− 8.07303i	− 0.661369i	0.943741	−	0.330684i	$-0.107280\pi$
$150$	0	0
$151$	5.29150	0.430616	0.215308	−	0.976546i	$-0.430924\pi$
$151$	5.29150	0.430616	0.215308	+	0.976546i	$0.430924\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	− 5.06713i	− 0.399346i
$162$	0	0
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	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
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	−13.2288	−1.00000
$176$	0	0
$177$	0	0
$178$	0	0
$179$	− 15.8799i	− 1.18692i	−0.804865	−	0.593458i	$-0.797762\pi$
$179$	− 15.8799i	− 1.18692i	0.804865	−	0.593458i	$-0.202238\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	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
$191$	− 24.3651i	− 1.76300i	−0.472184	−	0.881500i	$-0.656534\pi$
$191$	− 24.3651i	− 1.76300i	0.472184	−	0.881500i	$-0.343466\pi$
$192$	0	0
$193$	−21.1660	−1.52356	−0.761781	−	0.647834i	$-0.775675\pi$
$193$	−21.1660	−1.52356	−0.761781	+	0.647834i	$0.775675\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	25.8681i	1.84303i	0.388348	+	0.921513i	$0.373046\pi$
$197$	25.8681i	1.84303i	−0.388348	+	0.921513i	$0.626954\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	23.5406i	1.65223i
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−26.4575	−1.82141	−0.910705	−	0.413057i	$-0.864461\pi$
$211$	−26.4575	−1.82141	−0.910705	+	0.413057i	$0.864461\pi$
$212$	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
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	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	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 30.5230i	− 1.99963i	−0.0193169	−	0.999813i	$-0.506149\pi$
$233$	− 30.5230i	− 1.99963i	0.0193169	−	0.999813i	$-0.493851\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 7.39458i	− 0.478316i	−0.970981	−	0.239158i	$-0.923129\pi$
$239$	− 7.39458i	− 0.478316i	0.970981	−	0.239158i	$-0.0768713\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	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
$253$	12.5830	0.791087
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	28.0000	1.73984
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 18.8858i	− 1.16455i	−0.812993	−	0.582273i	$-0.802164\pi$
$263$	− 18.8858i	− 1.16455i	0.812993	−	0.582273i	$-0.197836\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 32.8504i	− 1.98096i
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	3.41815i	0.203910i	0.994789	+	0.101955i	$0.0325097\pi$
$281$	3.41815i	0.203910i	−0.994789	+	0.101955i	$0.967490\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	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
$301$	14.0000	0.806947
$302$	0	0
$303$	0	0
$304$	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	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	− 16.5583i	− 0.930008i	−0.885309	−	0.465004i	$-0.846053\pi$
$317$	− 16.5583i	− 0.930008i	0.885309	−	0.465004i	$-0.153947\pi$
$318$	0	0
$319$	−58.4575	−3.27299
$320$	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
$331$	5.29150	0.290847	0.145424	−	0.989369i	$-0.453545\pi$
$331$	5.29150	0.290847	0.145424	+	0.989369i	$0.453545\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−21.1660	−1.15299	−0.576493	−	0.817102i	$-0.695579\pi$
$337$	−21.1660	−1.15299	−0.576493	+	0.817102i	$0.695579\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	18.5203	1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	29.0200i	1.55788i	0.627100	+	0.778938i	$0.284242\pi$
$347$	29.0200i	1.55788i	−0.627100	+	0.778938i	$0.715758\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	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
$359$	20.5347i	1.08378i	0.840449	+	0.541891i	$0.182292\pi$
$359$	20.5347i	1.08378i	−0.840449	+	0.541891i	$0.817708\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	1.09070i	0.0566265i
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	37.0405	1.90264	0.951322	−	0.308199i	$-0.0997264\pi$
$379$	37.0405	1.90264	0.951322	+	0.308199i	$0.0997264\pi$
$380$	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
$389$	34.3534i	1.74179i	0.491473	+	0.870893i	$0.336458\pi$
$389$	34.3534i	1.74179i	−0.491473	+	0.870893i	$0.663542\pi$
$390$	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
$401$	− 39.0083i	− 1.94798i	−0.226592	−	0.973990i	$-0.572758\pi$
$401$	− 39.0083i	− 1.94798i	0.226592	−	0.973990i	$-0.427242\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	69.5312i	3.44654i
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	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
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	− 41.3357i	− 1.99107i	−0.0943889	−	0.995535i	$-0.530090\pi$
$431$	− 41.3357i	− 1.99107i	0.0943889	−	0.995535i	$-0.469910\pi$
$432$	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
$441$	0	0
$442$	0	0
$443$	12.0495i	0.572487i	0.958157	+	0.286244i	$0.0924067\pi$
$443$	12.0495i	0.572487i	−0.958157	+	0.286244i	$0.907593\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	31.3475i	1.47938i	0.672948	+	0.739689i	$0.265028\pi$
$449$	31.3475i	1.47938i	−0.672948	+	0.739689i	$0.734972\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	42.3320	1.98021	0.990104	−	0.140334i	$-0.0448177\pi$
$457$	42.3320	1.98021	0.990104	+	0.140334i	$0.0448177\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	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
$469$	10.5830	0.488678
$470$	0	0
$471$	0	0
$472$	0	0
$473$	34.7656i	1.59852i
$474$	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
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	37.0405	1.67847	0.839233	−	0.543772i	$-0.183004\pi$
$487$	37.0405	1.67847	0.839233	+	0.543772i	$0.183004\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 27.3710i	− 1.23524i	−0.786478	−	0.617619i	$-0.788097\pi$
$491$	− 27.3710i	− 1.23524i	0.786478	−	0.617619i	$-0.211903\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	39.8328i	1.78674i
$498$	0	0
$499$	−26.4575	−1.18440	−0.592200	−	0.805791i	$-0.701741\pi$
$499$	−26.4575	−1.18440	−0.592200	+	0.805791i	$0.701741\pi$
$500$	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
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	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
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	19.3320	0.840523
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	45.9906i	1.98096i
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−21.1660	−0.900070
$554$	0	0
$555$	0	0
$556$	0	0
$557$	− 25.0436i	− 1.06113i	−0.847644	−	0.530566i	$-0.821980\pi$
$557$	− 25.0436i	− 1.06113i	0.847644	−	0.530566i	$-0.178020\pi$
$558$	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
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	14.3769i	0.602711i	0.953512	+	0.301356i	$0.0974392\pi$
$569$	14.3769i	0.602711i	−0.953512	+	0.301356i	$0.902561\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	9.57598i	0.399346i
$576$	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
$583$	−2.70850	−0.112174
$584$	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
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	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
$599$	3.56418i	0.145629i	0.997346	+	0.0728143i	$0.0231980\pi$
$599$	3.56418i	0.145629i	−0.997346	+	0.0728143i	$0.976802\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	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
$611$	0	0
$612$	0	0
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	48.3180i	1.94521i	0.232462	+	0.972605i	$0.425322\pi$
$617$	48.3180i	1.94521i	−0.232462	+	0.972605i	$0.574678\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	− 47.4935i	− 1.87588i	−0.346795	−	0.937941i	$-0.612730\pi$
$641$	− 47.4935i	− 1.87588i	0.346795	−	0.937941i	$-0.387270\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	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
$653$	42.8387i	1.67641i	0.545358	+	0.838203i	$0.316394\pi$
$653$	42.8387i	1.67641i	−0.545358	+	0.838203i	$0.683606\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 49.8210i	− 1.94075i	−0.241604	−	0.970375i	$-0.577673\pi$
$659$	− 49.8210i	− 1.94075i	0.241604	−	0.970375i	$-0.422327\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	17.0405	0.659812
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	42.3320	1.63178	0.815890	−	0.578208i	$-0.196248\pi$
$673$	42.3320	1.63178	0.815890	+	0.578208i	$0.196248\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	40.5112i	1.55012i	0.631889	+	0.775059i	$0.282280\pi$
$683$	40.5112i	1.55012i	−0.631889	+	0.775059i	$0.717720\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	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
$701$	− 36.0024i	− 1.35979i	−0.733309	−	0.679895i	$-0.762025\pi$
$701$	− 36.0024i	− 1.35979i	0.733309	−	0.679895i	$-0.237975\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−52.9150	−1.98727	−0.993633	−	0.112667i	$-0.964061\pi$
$709$	−52.9150	−1.98727	−0.993633	+	0.112667i	$0.964061\pi$
$710$	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
$725$	− 44.4876i	− 1.65223i
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	26.2803i	0.968049i
$738$	0	0
$739$	52.0000	1.91285	0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000	1.91285	0.956425	+	0.291977i	$0.0943129\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	54.4759i	1.99853i	0.0383863	+	0.999263i	$0.487778\pi$
$743$	54.4759i	1.99853i	−0.0383863	+	0.999263i	$0.512222\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	− 27.5171i	− 1.00545i
$750$	0	0
$751$	−26.4575	−0.965448	−0.482724	−	0.875772i	$-0.660353\pi$
$751$	−26.4575	−0.965448	−0.482724	+	0.875772i	$0.660353\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	10.5830	0.384646	0.192323	−	0.981332i	$-0.438398\pi$
$757$	10.5830	0.384646	0.192323	+	0.981332i	$0.438398\pi$
$758$	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
$763$	28.0000	1.01367
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	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
$781$	−98.9150	−3.53946
$782$	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
$789$	0	0
$790$	0	0
$791$	− 35.8563i	− 1.27490i
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	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
$809$	56.8033i	1.99710i	0.0538482	+	0.998549i	$0.482851\pi$
$809$	56.8033i	1.99710i	−0.0538482	+	0.998549i	$0.517149\pi$
$810$	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
$819$	0	0
$820$	0	0
$821$	− 52.9729i	− 1.84877i	−0.381464	−	0.924384i	$-0.624580\pi$
$821$	− 52.9729i	− 1.84877i	0.381464	−	0.924384i	$-0.375420\pi$
$822$	0	0
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 4.92110i	− 0.171123i	−0.996333	−	0.0855616i	$-0.972732\pi$
$827$	− 4.92110i	− 0.171123i	0.996333	−	0.0855616i	$-0.0272685\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	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
$841$	−50.1660	−1.72986
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−85.1033	−2.92418
$848$	0	0
$849$	0	0
$850$	0	0
$851$	− 20.2685i	− 0.694797i
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	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
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	− 46.8151i	− 1.59360i	−0.604240	−	0.796802i	$-0.706523\pi$
$863$	− 46.8151i	− 1.59360i	0.604240	−	0.796802i	$-0.293477\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	− 52.5607i	− 1.78300i
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	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
$883$	−58.2065	−1.95881	−0.979403	−	0.201916i	$-0.935283\pi$
$883$	−58.2065	−1.95881	−0.979403	+	0.201916i	$0.935283\pi$
$884$	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
$889$	42.3320	1.41977
$890$	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
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	5.29150	0.175701	0.0878507	−	0.996134i	$-0.472000\pi$
$907$	5.29150	0.175701	0.0878507	+	0.996134i	$0.472000\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	− 29.8445i	− 0.988793i	−0.869236	−	0.494397i	$-0.835389\pi$
$911$	− 29.8445i	− 0.988793i	0.869236	−	0.494397i	$-0.164611\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	37.0405	1.22185	0.610927	−	0.791687i	$-0.290797\pi$
$919$	37.0405	1.22185	0.610927	+	0.791687i	$0.290797\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−52.9150	−1.73984
$926$	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
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	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
$947$	− 55.3004i	− 1.79702i	−0.438953	−	0.898510i	$-0.644650\pi$
$947$	− 55.3004i	− 1.79702i	0.438953	−	0.898510i	$-0.355350\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	− 55.9788i	− 1.81333i	−0.421849	−	0.906666i	$-0.638619\pi$
$953$	− 55.9788i	− 1.81333i	0.421849	−	0.906666i	$-0.361381\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	− 58.3063i	− 1.88281i
$960$	0	0
$961$	31.0000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	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
$977$	− 2.59365i	− 0.0829783i	−0.999139	−	0.0414892i	$-0.986790\pi$
$977$	− 2.59365i	− 0.0829783i	0.999139	−	0.0414892i	$-0.0132102\pi$
$978$	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
$988$	0	0
$989$	− 10.1343i	− 0.322251i
$990$	0	0
$991$	−58.2065	−1.84899	−0.924496	−	0.381193i	$-0.875513\pi$
$991$	−58.2065	−1.84899	−0.924496	+	0.381193i	$0.875513\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.k.a.881.4		4
3.2	odd	2	inner	1008.2.k.a.881.3		4
4.3	odd	2		63.2.c.a.62.3	yes	4
7.6	odd	2	CM	1008.2.k.a.881.4		4
8.3	odd	2		4032.2.k.c.3905.2		4
8.5	even	2		4032.2.k.b.3905.3		4
12.11	even	2		63.2.c.a.62.2	✓	4
20.3	even	4		1575.2.g.d.1574.6		8
20.7	even	4		1575.2.g.d.1574.3		8
20.19	odd	2		1575.2.b.a.251.2		4
21.20	even	2	inner	1008.2.k.a.881.3		4
24.5	odd	2		4032.2.k.b.3905.4		4
24.11	even	2		4032.2.k.c.3905.1		4
28.3	even	6		441.2.p.b.215.2		8
28.11	odd	6		441.2.p.b.215.2		8
28.19	even	6		441.2.p.b.80.3		8
28.23	odd	6		441.2.p.b.80.3		8
28.27	even	2		63.2.c.a.62.3	yes	4
36.7	odd	6		567.2.o.f.377.3		8
36.11	even	6		567.2.o.f.377.2		8
36.23	even	6		567.2.o.f.188.3		8
36.31	odd	6		567.2.o.f.188.2		8
56.13	odd	2		4032.2.k.b.3905.3		4
56.27	even	2		4032.2.k.c.3905.2		4
60.23	odd	4		1575.2.g.d.1574.4		8
60.47	odd	4		1575.2.g.d.1574.5		8
60.59	even	2		1575.2.b.a.251.3		4
84.11	even	6		441.2.p.b.215.3		8
84.23	even	6		441.2.p.b.80.2		8
84.47	odd	6		441.2.p.b.80.2		8
84.59	odd	6		441.2.p.b.215.3		8
84.83	odd	2		63.2.c.a.62.2	✓	4
140.27	odd	4		1575.2.g.d.1574.3		8
140.83	odd	4		1575.2.g.d.1574.6		8
140.139	even	2		1575.2.b.a.251.2		4
168.83	odd	2		4032.2.k.c.3905.1		4
168.125	even	2		4032.2.k.b.3905.4		4
252.83	odd	6		567.2.o.f.377.2		8
252.139	even	6		567.2.o.f.188.2		8
252.167	odd	6		567.2.o.f.188.3		8
252.223	even	6		567.2.o.f.377.3		8
420.83	even	4		1575.2.g.d.1574.4		8
420.167	even	4		1575.2.g.d.1574.5		8
420.419	odd	2		1575.2.b.a.251.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.c.a.62.2	✓	4	12.11	even	2
63.2.c.a.62.2	✓	4	84.83	odd	2
63.2.c.a.62.3	yes	4	4.3	odd	2
63.2.c.a.62.3	yes	4	28.27	even	2
441.2.p.b.80.2		8	84.23	even	6
441.2.p.b.80.2		8	84.47	odd	6
441.2.p.b.80.3		8	28.19	even	6
441.2.p.b.80.3		8	28.23	odd	6
441.2.p.b.215.2		8	28.3	even	6
441.2.p.b.215.2		8	28.11	odd	6
441.2.p.b.215.3		8	84.11	even	6
441.2.p.b.215.3		8	84.59	odd	6
567.2.o.f.188.2		8	36.31	odd	6
567.2.o.f.188.2		8	252.139	even	6
567.2.o.f.188.3		8	36.23	even	6
567.2.o.f.188.3		8	252.167	odd	6
567.2.o.f.377.2		8	36.11	even	6
567.2.o.f.377.2		8	252.83	odd	6
567.2.o.f.377.3		8	36.7	odd	6
567.2.o.f.377.3		8	252.223	even	6
1008.2.k.a.881.3		4	3.2	odd	2	inner
1008.2.k.a.881.3		4	21.20	even	2	inner
1008.2.k.a.881.4		4	1.1	even	1	trivial
1008.2.k.a.881.4		4	7.6	odd	2	CM
1575.2.b.a.251.2		4	20.19	odd	2
1575.2.b.a.251.2		4	140.139	even	2
1575.2.b.a.251.3		4	60.59	even	2
1575.2.b.a.251.3		4	420.419	odd	2
1575.2.g.d.1574.3		8	20.7	even	4
1575.2.g.d.1574.3		8	140.27	odd	4
1575.2.g.d.1574.4		8	60.23	odd	4
1575.2.g.d.1574.4		8	420.83	even	4
1575.2.g.d.1574.5		8	60.47	odd	4
1575.2.g.d.1574.5		8	420.167	even	4
1575.2.g.d.1574.6		8	20.3	even	4
1575.2.g.d.1574.6		8	140.83	odd	4
4032.2.k.b.3905.3		4	8.5	even	2
4032.2.k.b.3905.3		4	56.13	odd	2
4032.2.k.b.3905.4		4	24.5	odd	2
4032.2.k.b.3905.4		4	168.125	even	2
4032.2.k.c.3905.1		4	24.11	even	2
4032.2.k.c.3905.1		4	168.83	odd	2
4032.2.k.c.3905.2		4	8.3	odd	2
4032.2.k.c.3905.2		4	56.27	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.k (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.64575 q^{7} +O(q^{10})\)	\(q+2.64575 q^{7} +6.57008i q^{11} -1.91520i q^{23} -5.00000 q^{25} +8.89753i q^{29} +10.5830 q^{37} +5.29150 q^{43} +7.00000 q^{49} +0.412247i q^{53} +4.00000 q^{67} +15.0554i q^{71} +17.3828i q^{77} -8.00000 q^{79} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 20 q^{25} + 28 q^{49} + 16 q^{67} - 32 q^{79}+O(q^{100}) \) 4 * q - 20 * q^25 + 28 * q^49 + 16 * q^67 - 32 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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