LMFDB - Embedded newform 8.3.d.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8,3,Mod(3,8)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	yes
Analytic conductor:	$0.217984211488$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	8.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +4.00000 q^{6} -8.00000 q^{8} -5.00000 q^{9} +14.0000 q^{11} -8.00000 q^{12} +16.0000 q^{16} +2.00000 q^{17} +10.0000 q^{18} -34.0000 q^{19} -28.0000 q^{22} +16.0000 q^{24} +25.0000 q^{25} +28.0000 q^{27} -32.0000 q^{32} -28.0000 q^{33} -4.00000 q^{34} -20.0000 q^{36} +68.0000 q^{38} -46.0000 q^{41} +14.0000 q^{43} +56.0000 q^{44} -32.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -4.00000 q^{51} -56.0000 q^{54} +68.0000 q^{57} -82.0000 q^{59} +64.0000 q^{64} +56.0000 q^{66} +62.0000 q^{67} +8.00000 q^{68} +40.0000 q^{72} -142.000 q^{73} -50.0000 q^{75} -136.000 q^{76} -11.0000 q^{81} +92.0000 q^{82} +158.000 q^{83} -28.0000 q^{86} -112.000 q^{88} +146.000 q^{89} +64.0000 q^{96} -94.0000 q^{97} -98.0000 q^{98} -70.0000 q^{99} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.00000	−1.00000
$2$	−2.00000	−1.00000
$3$	−2.00000	−0.666667	−0.333333	−	0.942809i	$-0.608173\pi$
$3$	−2.00000	−0.666667	−0.333333	+	0.942809i	$0.608173\pi$
$4$	4.00000	1.00000
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	4.00000	0.666667
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−8.00000	−1.00000
$9$	−5.00000	−0.555556
$10$	0	0
$11$	14.0000	1.27273	0.636364	−	0.771389i	$-0.280438\pi$
$11$	14.0000	1.27273	0.636364	+	0.771389i	$0.280438\pi$
$12$	−8.00000	−0.666667
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	1.00000
$17$	2.00000	0.117647	0.0588235	−	0.998268i	$-0.481265\pi$
$17$	2.00000	0.117647	0.0588235	+	0.998268i	$0.481265\pi$
$18$	10.0000	0.555556
$19$	−34.0000	−1.78947	−0.894737	−	0.446594i	$-0.852637\pi$
$19$	−34.0000	−1.78947	−0.894737	+	0.446594i	$0.852637\pi$
$20$	0	0
$21$	0	0
$22$	−28.0000	−1.27273
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	16.0000	0.666667
$25$	25.0000	1.00000
$26$	0	0
$27$	28.0000	1.03704
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−32.0000	−1.00000
$33$	−28.0000	−0.848485
$34$	−4.00000	−0.117647
$35$	0	0
$36$	−20.0000	−0.555556
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	68.0000	1.78947
$39$	0	0
$40$	0	0
$41$	−46.0000	−1.12195	−0.560976	−	0.827832i	$-0.689574\pi$
$41$	−46.0000	−1.12195	−0.560976	+	0.827832i	$0.689574\pi$
$42$	0	0
$43$	14.0000	0.325581	0.162791	−	0.986661i	$-0.447950\pi$
$43$	14.0000	0.325581	0.162791	+	0.986661i	$0.447950\pi$
$44$	56.0000	1.27273
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−32.0000	−0.666667
$49$	49.0000	1.00000
$50$	−50.0000	−1.00000
$51$	−4.00000	−0.0784314
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−56.0000	−1.03704
$55$	0	0
$56$	0	0
$57$	68.0000	1.19298
$58$	0	0
$59$	−82.0000	−1.38983	−0.694915	−	0.719092i	$-0.744558\pi$
$59$	−82.0000	−1.38983	−0.694915	+	0.719092i	$0.744558\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	64.0000	1.00000
$65$	0	0
$66$	56.0000	0.848485
$67$	62.0000	0.925373	0.462687	−	0.886522i	$-0.346886\pi$
$67$	62.0000	0.925373	0.462687	+	0.886522i	$0.346886\pi$
$68$	8.00000	0.117647
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	40.0000	0.555556
$73$	−142.000	−1.94521	−0.972603	−	0.232473i	$-0.925318\pi$
$73$	−142.000	−1.94521	−0.972603	+	0.232473i	$0.925318\pi$
$74$	0	0
$75$	−50.0000	−0.666667
$76$	−136.000	−1.78947
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−11.0000	−0.135802
$82$	92.0000	1.12195
$83$	158.000	1.90361	0.951807	−	0.306697i	$-0.0992238\pi$
$83$	158.000	1.90361	0.951807	+	0.306697i	$0.0992238\pi$
$84$	0	0
$85$	0	0
$86$	−28.0000	−0.325581
$87$	0	0
$88$	−112.000	−1.27273
$89$	146.000	1.64045	0.820225	−	0.572041i	$-0.193848\pi$
$89$	146.000	1.64045	0.820225	+	0.572041i	$0.193848\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	64.0000	0.666667
$97$	−94.0000	−0.969072	−0.484536	−	0.874771i	$-0.661012\pi$
$97$	−94.0000	−0.969072	−0.484536	+	0.874771i	$0.661012\pi$
$98$	−98.0000	−1.00000
$99$	−70.0000	−0.707071
$100$	100.000	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	8.00000	0.0784314
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−178.000	−1.66355	−0.831776	−	0.555112i	$-0.812675\pi$
$107$	−178.000	−1.66355	−0.831776	+	0.555112i	$0.812675\pi$
$108$	112.000	1.03704
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	98.0000	0.867257	0.433628	−	0.901092i	$-0.357233\pi$
$113$	98.0000	0.867257	0.433628	+	0.901092i	$0.357233\pi$
$114$	−136.000	−1.19298
$115$	0	0
$116$	0	0
$117$	0	0
$118$	164.000	1.38983
$119$	0	0
$120$	0	0
$121$	75.0000	0.619835
$122$	0	0
$123$	92.0000	0.747967
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−128.000	−1.00000
$129$	−28.0000	−0.217054
$130$	0	0
$131$	62.0000	0.473282	0.236641	−	0.971597i	$-0.423953\pi$
$131$	62.0000	0.473282	0.236641	+	0.971597i	$0.423953\pi$
$132$	−112.000	−0.848485
$133$	0	0
$134$	−124.000	−0.925373
$135$	0	0
$136$	−16.0000	−0.117647
$137$	−238.000	−1.73723	−0.868613	−	0.495491i	$-0.834988\pi$
$137$	−238.000	−1.73723	−0.868613	+	0.495491i	$0.834988\pi$
$138$	0	0
$139$	206.000	1.48201	0.741007	−	0.671497i	$-0.234348\pi$
$139$	206.000	1.48201	0.741007	+	0.671497i	$0.234348\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−80.0000	−0.555556
$145$	0	0
$146$	284.000	1.94521
$147$	−98.0000	−0.666667
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	100.000	0.666667
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	272.000	1.78947
$153$	−10.0000	−0.0653595
$154$	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
$161$	0	0
$162$	22.0000	0.135802
$163$	−322.000	−1.97546	−0.987730	−	0.156171i	$-0.950085\pi$
$163$	−322.000	−1.97546	−0.987730	+	0.156171i	$0.950085\pi$
$164$	−184.000	−1.12195
$165$	0	0
$166$	−316.000	−1.90361
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	169.000	1.00000
$170$	0	0
$171$	170.000	0.994152
$172$	56.0000	0.325581
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	224.000	1.27273
$177$	164.000	0.926554
$178$	−292.000	−1.64045
$179$	−34.0000	−0.189944	−0.0949721	−	0.995480i	$-0.530276\pi$
$179$	−34.0000	−0.189944	−0.0949721	+	0.995480i	$0.530276\pi$
$180$	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
$187$	28.0000	0.149733
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−128.000	−0.666667
$193$	98.0000	0.507772	0.253886	−	0.967234i	$-0.418291\pi$
$193$	98.0000	0.507772	0.253886	+	0.967234i	$0.418291\pi$
$194$	188.000	0.969072
$195$	0	0
$196$	196.000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	140.000	0.707071
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−200.000	−1.00000
$201$	−124.000	−0.616915
$202$	0	0
$203$	0	0
$204$	−16.0000	−0.0784314
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−476.000	−2.27751
$210$	0	0
$211$	−226.000	−1.07109	−0.535545	−	0.844507i	$-0.679894\pi$
$211$	−226.000	−1.07109	−0.535545	+	0.844507i	$0.679894\pi$
$212$	0	0
$213$	0	0
$214$	356.000	1.66355
$215$	0	0
$216$	−224.000	−1.03704
$217$	0	0
$218$	0	0
$219$	284.000	1.29680
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	−125.000	−0.555556
$226$	−196.000	−0.867257
$227$	446.000	1.96476	0.982379	−	0.186900i	$-0.0598442\pi$
$227$	446.000	1.96476	0.982379	+	0.186900i	$0.0598442\pi$
$228$	272.000	1.19298
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	434.000	1.86266	0.931330	−	0.364175i	$-0.118649\pi$
$233$	434.000	1.86266	0.931330	+	0.364175i	$0.118649\pi$
$234$	0	0
$235$	0	0
$236$	−328.000	−1.38983
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	194.000	0.804979	0.402490	−	0.915425i	$-0.368145\pi$
$241$	194.000	0.804979	0.402490	+	0.915425i	$0.368145\pi$
$242$	−150.000	−0.619835
$243$	−230.000	−0.946502
$244$	0	0
$245$	0	0
$246$	−184.000	−0.747967
$247$	0	0
$248$	0	0
$249$	−316.000	−1.26908
$250$	0	0
$251$	−466.000	−1.85657	−0.928287	−	0.371865i	$-0.878718\pi$
$251$	−466.000	−1.85657	−0.928287	+	0.371865i	$0.878718\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	256.000	1.00000
$257$	386.000	1.50195	0.750973	−	0.660333i	$-0.229585\pi$
$257$	386.000	1.50195	0.750973	+	0.660333i	$0.229585\pi$
$258$	56.0000	0.217054
$259$	0	0
$260$	0	0
$261$	0	0
$262$	−124.000	−0.473282
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	224.000	0.848485
$265$	0	0
$266$	0	0
$267$	−292.000	−1.09363
$268$	248.000	0.925373
$269$	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			$\pi$
$272$	32.0000	0.117647
$273$	0	0
$274$	476.000	1.73723
$275$	350.000	1.27273
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	−412.000	−1.48201
$279$	0	0
$280$	0	0
$281$	−238.000	−0.846975	−0.423488	−	0.905902i	$-0.639194\pi$
$281$	−238.000	−0.846975	−0.423488	+	0.905902i	$0.639194\pi$
$282$	0	0
$283$	−82.0000	−0.289753	−0.144876	−	0.989450i	$-0.546278\pi$
$283$	−82.0000	−0.289753	−0.144876	+	0.989450i	$0.546278\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	160.000	0.555556
$289$	−285.000	−0.986159
$290$	0	0
$291$	188.000	0.646048
$292$	−568.000	−1.94521
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	196.000	0.666667
$295$	0	0
$296$	0	0
$297$	392.000	1.31987
$298$	0	0
$299$	0	0
$300$	−200.000	−0.666667
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−544.000	−1.78947
$305$	0	0
$306$	20.0000	0.0653595
$307$	542.000	1.76547	0.882736	−	0.469869i	$-0.155699\pi$
$307$	542.000	1.76547	0.882736	+	0.469869i	$0.155699\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	−526.000	−1.68051	−0.840256	−	0.542191i	$-0.817595\pi$
$313$	−526.000	−1.68051	−0.840256	+	0.542191i	$0.817595\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	356.000	1.10903
$322$	0	0
$323$	−68.0000	−0.210526
$324$	−44.0000	−0.135802
$325$	0	0
$326$	644.000	1.97546
$327$	0	0
$328$	368.000	1.12195
$329$	0	0
$330$	0	0
$331$	14.0000	0.0422961	0.0211480	−	0.999776i	$-0.493268\pi$
$331$	14.0000	0.0422961	0.0211480	+	0.999776i	$0.493268\pi$
$332$	632.000	1.90361
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−478.000	−1.41840	−0.709199	−	0.705009i	$-0.750943\pi$
$337$	−478.000	−1.41840	−0.709199	+	0.705009i	$0.750943\pi$
$338$	−338.000	−1.00000
$339$	−196.000	−0.578171
$340$	0	0
$341$	0	0
$342$	−340.000	−0.994152
$343$	0	0
$344$	−112.000	−0.325581
$345$	0	0
$346$	0	0
$347$	−658.000	−1.89625	−0.948127	−	0.317892i	$-0.897025\pi$
$347$	−658.000	−1.89625	−0.948127	+	0.317892i	$0.897025\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	−448.000	−1.27273
$353$	194.000	0.549575	0.274788	−	0.961505i	$-0.411392\pi$
$353$	194.000	0.549575	0.274788	+	0.961505i	$0.411392\pi$
$354$	−328.000	−0.926554
$355$	0	0
$356$	584.000	1.64045
$357$	0	0
$358$	68.0000	0.189944
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	795.000	2.20222
$362$	0	0
$363$	−150.000	−0.413223
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	230.000	0.623306
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	−56.0000	−0.149733
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	686.000	1.81003	0.905013	−	0.425383i	$-0.139861\pi$
$379$	686.000	1.81003	0.905013	+	0.425383i	$0.139861\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	256.000	0.666667
$385$	0	0
$386$	−196.000	−0.507772
$387$	−70.0000	−0.180879
$388$	−376.000	−0.969072
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	−392.000	−1.00000
$393$	−124.000	−0.315522
$394$	0	0
$395$	0	0
$396$	−280.000	−0.707071
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	400.000	1.00000
$401$	−766.000	−1.91022	−0.955112	−	0.296244i	$-0.904266\pi$
$401$	−766.000	−1.91022	−0.955112	+	0.296244i	$0.904266\pi$
$402$	248.000	0.616915
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	32.0000	0.0784314
$409$	−334.000	−0.816626	−0.408313	−	0.912842i	$-0.633883\pi$
$409$	−334.000	−0.816626	−0.408313	+	0.912842i	$0.633883\pi$
$410$	0	0
$411$	476.000	1.15815
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−412.000	−0.988010
$418$	952.000	2.27751
$419$	−514.000	−1.22673	−0.613365	−	0.789799i	$-0.710185\pi$
$419$	−514.000	−1.22673	−0.613365	+	0.789799i	$0.710185\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	452.000	1.07109
$423$	0	0
$424$	0	0
$425$	50.0000	0.117647
$426$	0	0
$427$	0	0
$428$	−712.000	−1.66355
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	448.000	1.03704
$433$	578.000	1.33487	0.667436	−	0.744667i	$-0.267392\pi$
$433$	578.000	1.33487	0.667436	+	0.744667i	$0.267392\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	−568.000	−1.29680
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−245.000	−0.555556
$442$	0	0
$443$	878.000	1.98194	0.990971	−	0.134079i	$-0.0428076\pi$
$443$	878.000	1.98194	0.990971	+	0.134079i	$0.0428076\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	866.000	1.92873	0.964365	−	0.264574i	$-0.0852315\pi$
$449$	866.000	1.92873	0.964365	+	0.264574i	$0.0852315\pi$
$450$	250.000	0.555556
$451$	−644.000	−1.42794
$452$	392.000	0.867257
$453$	0	0
$454$	−892.000	−1.96476
$455$	0	0
$456$	−544.000	−1.19298
$457$	−238.000	−0.520788	−0.260394	−	0.965502i	$-0.583852\pi$
$457$	−238.000	−0.520788	−0.260394	+	0.965502i	$0.583852\pi$
$458$	0	0
$459$	56.0000	0.122004
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	−868.000	−1.86266
$467$	−34.0000	−0.0728051	−0.0364026	−	0.999337i	$-0.511590\pi$
$467$	−34.0000	−0.0728051	−0.0364026	+	0.999337i	$0.511590\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	656.000	1.38983
$473$	196.000	0.414376
$474$	0	0
$475$	−850.000	−1.78947
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	−388.000	−0.804979
$483$	0	0
$484$	300.000	0.619835
$485$	0	0
$486$	460.000	0.946502
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	644.000	1.31697
$490$	0	0
$491$	782.000	1.59267	0.796334	−	0.604857i	$-0.206770\pi$
$491$	782.000	1.59267	0.796334	+	0.604857i	$0.206770\pi$
$492$	368.000	0.747967
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	632.000	1.26908
$499$	−802.000	−1.60721	−0.803607	−	0.595160i	$-0.797089\pi$
$499$	−802.000	−1.60721	−0.803607	+	0.595160i	$0.797089\pi$
$500$	0	0
$501$	0	0
$502$	932.000	1.85657
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−338.000	−0.666667
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	−512.000	−1.00000
$513$	−952.000	−1.85575
$514$	−772.000	−1.50195
$515$	0	0
$516$	−112.000	−0.217054
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−1006.00	−1.93090	−0.965451	−	0.260584i	$-0.916085\pi$
$521$	−1006.00	−1.93090	−0.965451	+	0.260584i	$0.916085\pi$
$522$	0	0
$523$	398.000	0.760994	0.380497	−	0.924782i	$-0.375753\pi$
$523$	398.000	0.760994	0.380497	+	0.924782i	$0.375753\pi$
$524$	248.000	0.473282
$525$	0	0
$526$	0	0
$527$	0	0
$528$	−448.000	−0.848485
$529$	529.000	1.00000
$530$	0	0
$531$	410.000	0.772128
$532$	0	0
$533$	0	0
$534$	584.000	1.09363
$535$	0	0
$536$	−496.000	−0.925373
$537$	68.0000	0.126629
$538$	0	0
$539$	686.000	1.27273
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	−64.0000	−0.117647
$545$	0	0
$546$	0	0
$547$	1022.00	1.86837	0.934186	−	0.356785i	$-0.116127\pi$
$547$	1022.00	1.86837	0.934186	+	0.356785i	$0.116127\pi$
$548$	−952.000	−1.73723
$549$	0	0
$550$	−700.000	−1.27273
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	824.000	1.48201
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−56.0000	−0.0998217
$562$	476.000	0.846975
$563$	−226.000	−0.401421	−0.200710	−	0.979651i	$-0.564325\pi$
$563$	−226.000	−0.401421	−0.200710	+	0.979651i	$0.564325\pi$
$564$	0	0
$565$	0	0
$566$	164.000	0.289753
$567$	0	0
$568$	0	0
$569$	626.000	1.10018	0.550088	−	0.835107i	$-0.314594\pi$
$569$	626.000	1.10018	0.550088	+	0.835107i	$0.314594\pi$
$570$	0	0
$571$	−658.000	−1.15236	−0.576182	−	0.817321i	$-0.695458\pi$
$571$	−658.000	−1.15236	−0.576182	+	0.817321i	$0.695458\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−320.000	−0.555556
$577$	2.00000	0.00346620	0.00173310	−	0.999998i	$-0.499448\pi$
$577$	2.00000	0.00346620	0.00173310	+	0.999998i	$0.499448\pi$
$578$	570.000	0.986159
$579$	−196.000	−0.338515
$580$	0	0
$581$	0	0
$582$	−376.000	−0.646048
$583$	0	0
$584$	1136.00	1.94521
$585$	0	0
$586$	0	0
$587$	−1138.00	−1.93867	−0.969336	−	0.245741i	$-0.920969\pi$
$587$	−1138.00	−1.93867	−0.969336	+	0.245741i	$0.920969\pi$
$588$	−392.000	−0.666667
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−862.000	−1.45363	−0.726813	−	0.686836i	$-0.758999\pi$
$593$	−862.000	−1.45363	−0.726813	+	0.686836i	$0.758999\pi$
$594$	−784.000	−1.31987
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	400.000	0.666667
$601$	914.000	1.52080	0.760399	−	0.649456i	$-0.225003\pi$
$601$	914.000	1.52080	0.760399	+	0.649456i	$0.225003\pi$
$602$	0	0
$603$	−310.000	−0.514096
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	1088.00	1.78947
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−40.0000	−0.0653595
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	−1084.00	−1.76547
$615$	0	0
$616$	0	0
$617$	−334.000	−0.541329	−0.270665	−	0.962674i	$-0.587243\pi$
$617$	−334.000	−0.541329	−0.270665	+	0.962674i	$0.587243\pi$
$618$	0	0
$619$	−562.000	−0.907916	−0.453958	−	0.891023i	$-0.649988\pi$
$619$	−562.000	−0.907916	−0.453958	+	0.891023i	$0.649988\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	625.000	1.00000
$626$	1052.00	1.68051
$627$	952.000	1.51834
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	452.000	0.714060
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	482.000	0.751950	0.375975	−	0.926630i	$-0.377308\pi$
$641$	482.000	0.751950	0.375975	+	0.926630i	$0.377308\pi$
$642$	−712.000	−1.10903
$643$	1214.00	1.88802	0.944012	−	0.329910i	$-0.107018\pi$
$643$	1214.00	1.88802	0.944012	+	0.329910i	$0.107018\pi$
$644$	0	0
$645$	0	0
$646$	136.000	0.210526
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	88.0000	0.135802
$649$	−1148.00	−1.76888
$650$	0	0
$651$	0	0
$652$	−1288.00	−1.97546
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	−736.000	−1.12195
$657$	710.000	1.08067
$658$	0	0
$659$	−994.000	−1.50835	−0.754173	−	0.656676i	$-0.771962\pi$
$659$	−994.000	−1.50835	−0.754173	+	0.656676i	$0.771962\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−28.0000	−0.0422961
$663$	0	0
$664$	−1264.00	−1.90361
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−1246.00	−1.85141	−0.925706	−	0.378244i	$-0.876528\pi$
$673$	−1246.00	−1.85141	−0.925706	+	0.378244i	$0.876528\pi$
$674$	956.000	1.41840
$675$	700.000	1.03704
$676$	676.000	1.00000
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	392.000	0.578171
$679$	0	0
$680$	0	0
$681$	−892.000	−1.30984
$682$	0	0
$683$	398.000	0.582723	0.291362	−	0.956613i	$-0.405892\pi$
$683$	398.000	0.582723	0.291362	+	0.956613i	$0.405892\pi$
$684$	680.000	0.994152
$685$	0	0
$686$	0	0
$687$	0	0
$688$	224.000	0.325581
$689$	0	0
$690$	0	0
$691$	734.000	1.06223	0.531114	−	0.847300i	$-0.321773\pi$
$691$	734.000	1.06223	0.531114	+	0.847300i	$0.321773\pi$
$692$	0	0
$693$	0	0
$694$	1316.00	1.89625
$695$	0	0
$696$	0	0
$697$	−92.0000	−0.131994
$698$	0	0
$699$	−868.000	−1.24177
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	896.000	1.27273
$705$	0	0
$706$	−388.000	−0.549575
$707$	0	0
$708$	656.000	0.926554
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	−1168.00	−1.64045
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−136.000	−0.189944
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−1590.00	−2.20222
$723$	−388.000	−0.536653
$724$	0	0
$725$	0	0
$726$	300.000	0.413223
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	559.000	0.766804
$730$	0	0
$731$	28.0000	0.0383037
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	868.000	1.17775
$738$	−460.000	−0.623306
$739$	−322.000	−0.435724	−0.217862	−	0.975980i	$-0.569908\pi$
$739$	−322.000	−0.435724	−0.217862	+	0.975980i	$0.569908\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−790.000	−1.05756
$748$	112.000	0.149733
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	932.000	1.23772
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−1372.00	−1.81003
$759$	0	0
$760$	0	0
$761$	1394.00	1.83180	0.915900	−	0.401406i	$-0.131478\pi$
$761$	1394.00	1.83180	0.915900	+	0.401406i	$0.131478\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−512.000	−0.666667
$769$	−1054.00	−1.37061	−0.685306	−	0.728256i	$-0.740331\pi$
$769$	−1054.00	−1.37061	−0.685306	+	0.728256i	$0.740331\pi$
$770$	0	0
$771$	−772.000	−1.00130
$772$	392.000	0.507772
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	140.000	0.180879
$775$	0	0
$776$	752.000	0.969072
$777$	0	0
$778$	0	0
$779$	1564.00	2.00770
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	784.000	1.00000
$785$	0	0
$786$	248.000	0.315522
$787$	926.000	1.17662	0.588310	−	0.808635i	$-0.299793\pi$
$787$	926.000	1.17662	0.588310	+	0.808635i	$0.299793\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	560.000	0.707071
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−800.000	−1.00000
$801$	−730.000	−0.911361
$802$	1532.00	1.91022
$803$	−1988.00	−2.47572
$804$	−496.000	−0.616915
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1582.00	−1.95550	−0.977750	−	0.209772i	$-0.932728\pi$
$809$	−1582.00	−1.95550	−0.977750	+	0.209772i	$0.932728\pi$
$810$	0	0
$811$	−178.000	−0.219482	−0.109741	−	0.993960i	$-0.535002\pi$
$811$	−178.000	−0.219482	−0.109741	+	0.993960i	$0.535002\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−64.0000	−0.0784314
$817$	−476.000	−0.582619
$818$	668.000	0.816626
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	−952.000	−1.15815
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−700.000	−0.848485
$826$	0	0
$827$	1262.00	1.52600	0.762999	−	0.646400i	$-0.223726\pi$
$827$	1262.00	1.52600	0.762999	+	0.646400i	$0.223726\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	98.0000	0.117647
$834$	824.000	0.988010
$835$	0	0
$836$	−1904.00	−2.27751
$837$	0	0
$838$	1028.00	1.22673
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	476.000	0.564650
$844$	−904.000	−1.07109
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	164.000	0.193168
$850$	−100.000	−0.117647
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	1424.00	1.66355
$857$	1202.00	1.40257	0.701284	−	0.712882i	$-0.252611\pi$
$857$	1202.00	1.40257	0.701284	+	0.712882i	$0.252611\pi$
$858$	0	0
$859$	1646.00	1.91618	0.958091	−	0.286465i	$-0.0924801\pi$
$859$	1646.00	1.91618	0.958091	+	0.286465i	$0.0924801\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	−896.000	−1.03704
$865$	0	0
$866$	−1156.00	−1.33487
$867$	570.000	0.657439
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	470.000	0.538373
$874$	0	0
$875$	0	0
$876$	1136.00	1.29680
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−1438.00	−1.63224	−0.816118	−	0.577885i	$-0.803878\pi$
$881$	−1438.00	−1.63224	−0.816118	+	0.577885i	$0.803878\pi$
$882$	490.000	0.555556
$883$	−1762.00	−1.99547	−0.997735	−	0.0672672i	$-0.978572\pi$
$883$	−1762.00	−1.99547	−0.997735	+	0.0672672i	$0.978572\pi$
$884$	0	0
$885$	0	0
$886$	−1756.00	−1.98194
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−154.000	−0.172840
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−1732.00	−1.92873
$899$	0	0
$900$	−500.000	−0.555556
$901$	0	0
$902$	1288.00	1.42794
$903$	0	0
$904$	−784.000	−0.867257
$905$	0	0
$906$	0	0
$907$	−1714.00	−1.88975	−0.944873	−	0.327436i	$-0.893815\pi$
$907$	−1714.00	−1.88975	−0.944873	+	0.327436i	$0.893815\pi$
$908$	1784.00	1.96476
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	1088.00	1.19298
$913$	2212.00	2.42278
$914$	476.000	0.520788
$915$	0	0
$916$	0	0
$917$	0	0
$918$	−112.000	−0.122004
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	−1084.00	−1.17698
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	1058.00	1.13886	0.569429	−	0.822040i	$-0.307164\pi$
$929$	1058.00	1.13886	0.569429	+	0.822040i	$0.307164\pi$
$930$	0	0
$931$	−1666.00	−1.78947
$932$	1736.00	1.86266
$933$	0	0
$934$	68.0000	0.0728051
$935$	0	0
$936$	0	0
$937$	−718.000	−0.766275	−0.383138	−	0.923691i	$-0.625157\pi$
$937$	−718.000	−0.766275	−0.383138	+	0.923691i	$0.625157\pi$
$938$	0	0
$939$	1052.00	1.12034
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−1312.00	−1.38983
$945$	0	0
$946$	−392.000	−0.414376
$947$	−994.000	−1.04963	−0.524815	−	0.851216i	$-0.675866\pi$
$947$	−994.000	−1.04963	−0.524815	+	0.851216i	$0.675866\pi$
$948$	0	0
$949$	0	0
$950$	1700.00	1.78947
$951$	0	0
$952$	0	0
$953$	−142.000	−0.149003	−0.0745016	−	0.997221i	$-0.523737\pi$
$953$	−142.000	−0.149003	−0.0745016	+	0.997221i	$0.523737\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	0	0
$963$	890.000	0.924195
$964$	776.000	0.804979
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−600.000	−0.619835
$969$	136.000	0.140351
$970$	0	0
$971$	974.000	1.00309	0.501545	−	0.865132i	$-0.332765\pi$
$971$	974.000	1.00309	0.501545	+	0.865132i	$0.332765\pi$
$972$	−920.000	−0.946502
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−1918.00	−1.96315	−0.981576	−	0.191071i	$-0.938804\pi$
$977$	−1918.00	−1.96315	−0.981576	+	0.191071i	$0.938804\pi$
$978$	−1288.00	−1.31697
$979$	2044.00	2.08784
$980$	0	0
$981$	0	0
$982$	−1564.00	−1.59267
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	−736.000	−0.747967
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	−28.0000	−0.0281974
$994$	0	0
$995$	0	0
$996$	−1264.00	−1.26908
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1604.00	1.60721
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.3.d.a.3.1	✓	1
3.2	odd	2		72.3.b.a.19.1		1
4.3	odd	2		32.3.d.a.15.1		1
5.2	odd	4		200.3.e.a.99.1		2
5.3	odd	4		200.3.e.a.99.2		2
5.4	even	2		200.3.g.a.51.1		1
7.2	even	3		392.3.k.d.67.1		2
7.3	odd	6		392.3.k.b.275.1		2
7.4	even	3		392.3.k.d.275.1		2
7.5	odd	6		392.3.k.b.67.1		2
7.6	odd	2		392.3.g.a.99.1		1
8.3	odd	2	CM	8.3.d.a.3.1	✓	1
8.5	even	2		32.3.d.a.15.1		1
12.11	even	2		288.3.b.a.271.1		1
16.3	odd	4		256.3.c.e.255.2		2
16.5	even	4		256.3.c.e.255.2		2
16.11	odd	4		256.3.c.e.255.1		2
16.13	even	4		256.3.c.e.255.1		2
20.3	even	4		800.3.e.a.399.2		2
20.7	even	4		800.3.e.a.399.1		2
20.19	odd	2		800.3.g.a.751.1		1
24.5	odd	2		288.3.b.a.271.1		1
24.11	even	2		72.3.b.a.19.1		1
28.27	even	2		1568.3.g.a.687.1		1
40.3	even	4		200.3.e.a.99.2		2
40.13	odd	4		800.3.e.a.399.2		2
40.19	odd	2		200.3.g.a.51.1		1
40.27	even	4		200.3.e.a.99.1		2
40.29	even	2		800.3.g.a.751.1		1
40.37	odd	4		800.3.e.a.399.1		2
48.5	odd	4		2304.3.g.j.1279.1		2
48.11	even	4		2304.3.g.j.1279.2		2
48.29	odd	4		2304.3.g.j.1279.2		2
48.35	even	4		2304.3.g.j.1279.1		2
56.3	even	6		392.3.k.b.275.1		2
56.11	odd	6		392.3.k.d.275.1		2
56.13	odd	2		1568.3.g.a.687.1		1
56.19	even	6		392.3.k.b.67.1		2
56.27	even	2		392.3.g.a.99.1		1
56.51	odd	6		392.3.k.d.67.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.3.d.a.3.1	✓	1	1.1	even	1	trivial
8.3.d.a.3.1	✓	1	8.3	odd	2	CM
32.3.d.a.15.1		1	4.3	odd	2
32.3.d.a.15.1		1	8.5	even	2
72.3.b.a.19.1		1	3.2	odd	2
72.3.b.a.19.1		1	24.11	even	2
200.3.e.a.99.1		2	5.2	odd	4
200.3.e.a.99.1		2	40.27	even	4
200.3.e.a.99.2		2	5.3	odd	4
200.3.e.a.99.2		2	40.3	even	4
200.3.g.a.51.1		1	5.4	even	2
200.3.g.a.51.1		1	40.19	odd	2
256.3.c.e.255.1		2	16.11	odd	4
256.3.c.e.255.1		2	16.13	even	4
256.3.c.e.255.2		2	16.3	odd	4
256.3.c.e.255.2		2	16.5	even	4
288.3.b.a.271.1		1	12.11	even	2
288.3.b.a.271.1		1	24.5	odd	2
392.3.g.a.99.1		1	7.6	odd	2
392.3.g.a.99.1		1	56.27	even	2
392.3.k.b.67.1		2	7.5	odd	6
392.3.k.b.67.1		2	56.19	even	6
392.3.k.b.275.1		2	7.3	odd	6
392.3.k.b.275.1		2	56.3	even	6
392.3.k.d.67.1		2	7.2	even	3
392.3.k.d.67.1		2	56.51	odd	6
392.3.k.d.275.1		2	7.4	even	3
392.3.k.d.275.1		2	56.11	odd	6
800.3.e.a.399.1		2	20.7	even	4
800.3.e.a.399.1		2	40.37	odd	4
800.3.e.a.399.2		2	20.3	even	4
800.3.e.a.399.2		2	40.13	odd	4
800.3.g.a.751.1		1	20.19	odd	2
800.3.g.a.751.1		1	40.29	even	2
1568.3.g.a.687.1		1	28.27	even	2
1568.3.g.a.687.1		1	56.13	odd	2
2304.3.g.j.1279.1		2	48.5	odd	4
2304.3.g.j.1279.1		2	48.35	even	4
2304.3.g.j.1279.2		2	48.11	even	4
2304.3.g.j.1279.2		2	48.29	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(5\)	\(7\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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