LMFDB - Embedded newform 1792.2.f.l.1791.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(1791,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1792.1791");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.f (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:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2517630976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 11x^{4} + 4x^{2} + 4 $ x^8 - 2x^6 + 11x^4 + 4*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 896)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1791.1
Root			$-0.435132 - 0.629640i$ of defining polynomial
Character	$\chi$	$=$	1792.1791
Dual form			1792.2.f.l.1791.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.97127 q^{3} -4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} +O(q^{10})$	$q-2.97127 q^{3} -4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} +0.737669i q^{13} +12.7748i q^{15} -5.43275 q^{19} -7.86123i q^{21} -7.48331i q^{23} -13.4853 q^{25} -8.40401 q^{27} +11.3753 q^{35} -2.19181i q^{39} -25.0590i q^{45} -7.00000 q^{49} +16.1421 q^{57} -6.45232 q^{59} +11.4230i q^{61} +15.4206i q^{63} +3.17157 q^{65} +22.2349i q^{69} +15.8745i q^{71} +40.0684 q^{75} +5.29150i q^{79} +7.48528 q^{81} +13.8368 q^{83} -1.95169 q^{91} +23.3578i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 24 q^{9}+O(q^{10}) $ 8 * q + 24 * q^9	$ 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} + 16 q^{57} + 48 q^{65} - 8 q^{81}+O(q^{100}) $ 8 * q + 24 * q^9 - 40 * q^25 - 56 * q^49 + 16 * q^57 + 48 * q^65 - 8 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	−2.97127	−1.71546	−0.857731	−	0.514099i	$-0.828126\pi$
$3$	−2.97127	−1.71546	−0.857731	+	0.514099i	$0.828126\pi$
$4$	0	0
$5$	− 4.29945i	− 1.92277i	−0.275202	−	0.961387i	$-0.588745\pi$
$5$	− 4.29945i	− 1.92277i	0.275202	−	0.961387i	$-0.411255\pi$
$6$	0	0
$7$	2.64575i	1.00000i
$7$	2.64575i	1.00000i
$8$	0	0
$9$	5.82843	1.94281
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	0.737669i	0.204593i	0.994754	+	0.102296i	$0.0326190\pi$
$13$	0.737669i	0.204593i	−0.994754	+	0.102296i	$0.967381\pi$
$14$	0	0
$15$	12.7748i	3.29844i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−5.43275	−1.24636	−0.623179	−	0.782080i	$-0.714159\pi$
$19$	−5.43275	−1.24636	−0.623179	+	0.782080i	$0.714159\pi$
$20$	0	0
$21$	− 7.86123i	− 1.71546i
$22$	0	0
$23$	− 7.48331i	− 1.56038i	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	− 7.48331i	− 1.56038i	0.625543	−	0.780189i	$-0.284877\pi$
$24$	0	0
$25$	−13.4853	−2.69706
$26$	0	0
$27$	−8.40401	−1.61735
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	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
$35$	11.3753	1.92277
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	− 2.19181i	− 0.350971i
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	− 25.0590i	− 3.73558i
$46$	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	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	16.1421	2.13808
$58$	0	0
$59$	−6.45232	−0.840021	−0.420010	−	0.907519i	$-0.637974\pi$
$59$	−6.45232	−0.840021	−0.420010	+	0.907519i	$0.637974\pi$
$60$	0	0
$61$	11.4230i	1.46257i	0.682073	+	0.731284i	$0.261078\pi$
$61$	11.4230i	1.46257i	−0.682073	+	0.731284i	$0.738922\pi$
$62$	0	0
$63$	15.4206i	1.94281i
$64$	0	0
$65$	3.17157	0.393385
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	22.2349i	2.67677i
$70$	0	0
$71$	15.8745i	1.88396i	0.335673	+	0.941979i	$0.391036\pi$
$71$	15.8745i	1.88396i	−0.335673	+	0.941979i	$0.608964\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	40.0684	4.62670
$76$	0	0
$77$	0	0
$78$	0	0
$79$	5.29150i	0.595341i	0.954669	+	0.297670i	$0.0962096\pi$
$79$	5.29150i	0.595341i	−0.954669	+	0.297670i	$0.903790\pi$
$80$	0	0
$81$	7.48528	0.831698
$82$	0	0
$83$	13.8368	1.51878	0.759391	−	0.650635i	$-0.225497\pi$
$83$	13.8368	1.51878	0.759391	+	0.650635i	$0.225497\pi$
$84$	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
$91$	−1.95169	−0.204593
$92$	0	0
$93$	0	0
$94$	0	0
$95$	23.3578i	2.39646i
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	6.38589i	0.635420i	0.948188	+	0.317710i	$0.102914\pi$
$101$	6.38589i	0.635420i	−0.948188	+	0.317710i	$0.897086\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	−33.7990	−3.29844
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−14.1421	−1.33038	−0.665190	−	0.746674i	$-0.731650\pi$
$113$	−14.1421	−1.33038	−0.665190	+	0.746674i	$0.731650\pi$
$114$	0	0
$115$	−32.1741	−3.00025
$116$	0	0
$117$	4.29945i	0.397484i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	36.4821i	3.26305i
$126$	0	0
$127$	− 22.4499i	− 1.99211i	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	− 22.4499i	− 1.99211i	0.0887357	−	0.996055i	$-0.471717\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	3.99084	0.348682	0.174341	−	0.984685i	$-0.444221\pi$
$131$	3.99084	0.348682	0.174341	+	0.984685i	$0.444221\pi$
$132$	0	0
$133$	− 14.3737i	− 1.24636i
$134$	0	0
$135$	36.1326i	3.10980i
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−23.2603	−1.97292	−0.986458	−	0.164012i	$-0.947557\pi$
$139$	−23.2603	−1.97292	−0.986458	+	0.164012i	$0.947557\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	20.7989	1.71546
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	22.4499i	1.82695i	0.406894	+	0.913475i	$0.366612\pi$
$151$	22.4499i	1.82695i	−0.406894	+	0.913475i	$0.633388\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	25.0590i	1.99993i	0.00842626	+	0.999964i	$0.497318\pi$
$157$	25.0590i	1.99993i	−0.00842626	+	0.999964i	$0.502682\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	19.7990	1.56038
$162$	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		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	12.4558	0.958142
$170$	0	0
$171$	−31.6644	−2.42143
$172$	0	0
$173$	10.8119i	0.822014i	0.911632	+	0.411007i	$0.134823\pi$
$173$	10.8119i	0.822014i	−0.911632	+	0.411007i	$0.865177\pi$
$174$	0	0
$175$	− 35.6787i	− 2.69706i
$176$	0	0
$177$	19.1716	1.44102
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	9.94768i	0.739405i	0.929150	+	0.369703i	$0.120540\pi$
$181$	9.94768i	0.739405i	−0.929150	+	0.369703i	$0.879460\pi$
$182$	0	0
$183$	− 33.9408i	− 2.50898i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	− 22.2349i	− 1.61735i
$190$	0	0
$191$	15.8745i	1.14864i	0.818631	+	0.574320i	$0.194733\pi$
$191$	15.8745i	1.14864i	−0.818631	+	0.574320i	$0.805267\pi$
$192$	0	0
$193$	8.48528	0.610784	0.305392	−	0.952227i	$-0.401213\pi$
$193$	8.48528	0.610784	0.305392	+	0.952227i	$0.401213\pi$
$194$	0	0
$195$	−9.42359	−0.674837
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	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
$205$	0	0
$206$	0	0
$207$	− 43.6160i	− 3.03152i
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	− 47.1674i	− 3.23186i
$214$	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		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−78.5980	−5.23987
$226$	0	0
$227$	−29.2029	−1.93826	−0.969132	−	0.246544i	$-0.920705\pi$
$227$	−29.2029	−1.93826	−0.969132	+	0.246544i	$0.920705\pi$
$228$	0	0
$229$	26.5344i	1.75344i	0.481000	+	0.876720i	$0.340274\pi$
$229$	26.5344i	1.75344i	−0.481000	+	0.876720i	$0.659726\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	− 15.7225i	− 1.02128i
$238$	0	0
$239$	7.48331i	0.484055i	0.970269	+	0.242028i	$0.0778125\pi$
$239$	7.48331i	0.484055i	−0.970269	+	0.242028i	$0.922188\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	2.97127	0.190607
$244$	0	0
$245$	30.0962i	1.92277i
$246$	0	0
$247$	− 4.00757i	− 0.254995i
$248$	0	0
$249$	−41.1127	−2.60541
$250$	0	0
$251$	31.6644	1.99864	0.999318	−	0.0369181i	$-0.0117541\pi$
$251$	31.6644	1.99864	0.999318	+	0.0369181i	$0.0117541\pi$
$252$	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
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	15.8745i	0.978864i	0.872041	+	0.489432i	$0.162796\pi$
$263$	15.8745i	0.978864i	−0.872041	+	0.489432i	$0.837204\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	− 19.4108i	− 1.18350i	−0.806122	−	0.591749i	$-0.798438\pi$
$269$	− 19.4108i	− 1.18350i	0.806122	−	0.591749i	$-0.201562\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	5.79899	0.350971
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	0	0
$283$	−15.8759	−0.943725	−0.471863	−	0.881672i	$-0.656418\pi$
$283$	−15.8759	−0.943725	−0.471863	+	0.881672i	$0.656418\pi$
$284$	0	0
$285$	− 69.4023i	− 4.11104i
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 32.1826i	− 1.88013i	−0.340998	−	0.940064i	$-0.610765\pi$
$293$	− 32.1826i	− 1.88013i	0.340998	−	0.940064i	$-0.389235\pi$
$294$	0	0
$295$	27.7414i	1.61517i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	5.52021	0.319242
$300$	0	0
$301$	0	0
$302$	0	0
$303$	− 18.9742i	− 1.09004i
$304$	0	0
$305$	49.1127	2.81218
$306$	0	0
$307$	−12.8172	−0.731515	−0.365758	−	0.930710i	$-0.619190\pi$
$307$	−12.8172	−0.731515	−0.365758	+	0.930710i	$0.619190\pi$
$308$	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
$315$	66.3000	3.73558
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	− 9.94768i	− 0.551798i
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−25.4558	−1.38667	−0.693334	−	0.720616i	$-0.743859\pi$
$337$	−25.4558	−1.38667	−0.693334	+	0.720616i	$0.743859\pi$
$338$	0	0
$339$	42.0201	2.28222
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 18.5203i	− 1.00000i
$344$	0	0
$345$	95.5980	5.14682
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	− 37.2197i	− 1.99233i	−0.0875167	−	0.996163i	$-0.527893\pi$
$349$	− 37.2197i	− 1.99233i	0.0875167	−	0.996163i	$-0.472107\pi$
$350$	0	0
$351$	− 6.19938i	− 0.330898i
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	68.2517	3.62242
$356$	0	0
$357$	0	0
$358$	0	0
$359$	− 37.4166i	− 1.97477i	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	− 37.4166i	− 1.97477i	0.158334	−	0.987386i	$-0.449388\pi$
$360$	0	0
$361$	10.5147	0.553406
$362$	0	0
$363$	−32.6839	−1.71546
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	− 108.398i	− 5.59764i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	66.7048i	3.41739i
$382$	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
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−11.8579	−0.598150
$394$	0	0
$395$	22.7506	1.14470
$396$	0	0
$397$	35.7444i	1.79396i	0.442072	+	0.896980i	$0.354244\pi$
$397$	35.7444i	1.79396i	−0.442072	+	0.896980i	$0.645756\pi$
$398$	0	0
$399$	42.7081i	2.13808i
$400$	0	0
$401$	−36.7696	−1.83618	−0.918092	−	0.396368i	$-0.870271\pi$
$401$	−36.7696	−1.83618	−0.918092	+	0.396368i	$0.870271\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	− 32.1826i	− 1.59917i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−53.4828	−2.63811
$412$	0	0
$413$	− 17.0712i	− 0.840021i
$414$	0	0
$415$	− 59.4905i	− 2.92027i
$416$	0	0
$417$	69.1127	3.38446
$418$	0	0
$419$	−36.5873	−1.78741	−0.893704	−	0.448658i	$-0.851902\pi$
$419$	−36.5873	−1.78741	−0.893704	+	0.448658i	$0.851902\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−30.2225	−1.46257
$428$	0	0
$429$	0	0
$430$	0	0
$431$	37.4166i	1.80229i	0.433515	+	0.901146i	$0.357273\pi$
$431$	37.4166i	1.80229i	−0.433515	+	0.901146i	$0.642727\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	40.6549i	1.94479i
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−40.7990	−1.94281
$442$	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
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	− 66.7048i	− 3.13406i
$454$	0	0
$455$	8.39119i	0.393385i
$456$	0	0
$457$	−42.4264	−1.98462	−0.992312	−	0.123763i	$-0.960504\pi$
$457$	−42.4264	−1.98462	−0.992312	+	0.123763i	$0.960504\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	25.6701i	1.19558i	0.801654	+	0.597789i	$0.203954\pi$
$461$	25.6701i	1.19558i	−0.801654	+	0.597789i	$0.796046\pi$
$462$	0	0
$463$	− 26.4575i	− 1.22958i	−0.788689	−	0.614792i	$-0.789240\pi$
$463$	− 26.4575i	− 1.22958i	0.788689	−	0.614792i	$-0.210760\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	21.2212	0.982000	0.491000	−	0.871160i	$-0.336632\pi$
$467$	21.2212	0.982000	0.491000	+	0.871160i	$0.336632\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	− 74.4571i	− 3.43080i
$472$	0	0
$473$	0	0
$474$	0	0
$475$	73.2621	3.36150
$476$	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
$483$	−58.8281	−2.67677
$484$	0	0
$485$	0	0
$486$	0	0
$487$	22.4499i	1.01730i	0.860972	+	0.508652i	$0.169856\pi$
$487$	22.4499i	1.01730i	−0.860972	+	0.508652i	$0.830144\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−42.0000	−1.88396
$498$	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		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	27.4558	1.22177
$506$	0	0
$507$	−37.0096	−1.64366
$508$	0	0
$509$	− 8.72547i	− 0.386750i	−0.981125	−	0.193375i	$-0.938057\pi$
$509$	− 8.72547i	− 0.386750i	0.981125	−	0.193375i	$-0.0619433\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	45.6569	2.01580
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	− 32.1251i	− 1.41013i
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	−9.33612	−0.408240	−0.204120	−	0.978946i	$-0.565433\pi$
$523$	−9.33612	−0.408240	−0.204120	+	0.978946i	$0.565433\pi$
$524$	0	0
$525$	106.011i	4.62670i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−33.0000	−1.43478
$530$	0	0
$531$	−37.6069	−1.63200
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	− 29.5572i	− 1.26842i
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	66.5782i	2.84149i
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−14.0000	−0.595341
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−39.0488	−1.64571	−0.822855	−	0.568251i	$-0.807620\pi$
$563$	−39.0488	−1.64571	−0.822855	+	0.568251i	$0.807620\pi$
$564$	0	0
$565$	60.8034i	2.55802i
$566$	0	0
$567$	19.8042i	0.831698i
$568$	0	0
$569$	2.82843	0.118574	0.0592869	−	0.998241i	$-0.481117\pi$
$569$	2.82843	0.118574	0.0592869	+	0.998241i	$0.481117\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	− 47.1674i	− 1.97045i
$574$	0	0
$575$	100.915i	4.20843i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	−25.2120	−1.04778
$580$	0	0
$581$	36.6086i	1.51878i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	18.4853	0.764272
$586$	0	0
$587$	3.39359	0.140068	0.0700342	−	0.997545i	$-0.477689\pi$
$587$	3.39359	0.140068	0.0700342	+	0.997545i	$0.477689\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	47.6235i	1.94584i	0.231133	+	0.972922i	$0.425757\pi$
$599$	47.6235i	1.94584i	−0.231133	+	0.972922i	$0.574243\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 47.2940i	− 1.92277i
$606$	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
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	14.1421	0.569341	0.284670	−	0.958625i	$-0.408116\pi$
$617$	14.1421	0.569341	0.284670	+	0.958625i	$0.408116\pi$
$618$	0	0
$619$	48.4724	1.94827	0.974135	−	0.225968i	$-0.0725544\pi$
$619$	48.4724	1.94827	0.974135	+	0.225968i	$0.0725544\pi$
$620$	0	0
$621$	62.8899i	2.52368i
$622$	0	0
$623$	0	0
$624$	0	0
$625$	89.4264	3.57706
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	− 37.0405i	− 1.47456i	−0.675587	−	0.737280i	$-0.736110\pi$
$631$	− 37.0405i	− 1.47456i	0.675587	−	0.737280i	$-0.263890\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	−96.5224	−3.83038
$636$	0	0
$637$	− 5.16368i	− 0.204593i
$638$	0	0
$639$	92.5234i	3.66017i
$640$	0	0
$641$	−48.0833	−1.89917	−0.949587	−	0.313503i	$-0.898498\pi$
$641$	−48.0833	−1.89917	−0.949587	+	0.313503i	$0.898498\pi$
$642$	0	0
$643$	44.9913	1.77428	0.887142	−	0.461496i	$-0.152687\pi$
$643$	44.9913	1.77428	0.887142	+	0.461496i	$0.152687\pi$
$644$	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
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	− 17.1584i	− 0.670436i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	50.8557i	1.97806i	0.147717	+	0.989030i	$0.452807\pi$
$661$	50.8557i	1.97806i	−0.147717	+	0.989030i	$0.547193\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−61.7990	−2.39646
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	0	0
$675$	113.330	4.36209
$676$	0	0
$677$	− 42.8679i	− 1.64755i	−0.566918	−	0.823775i	$-0.691864\pi$
$677$	− 42.8679i	− 1.64755i	0.566918	−	0.823775i	$-0.308136\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	86.7696	3.32502
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	− 77.3901i	− 2.95692i
$686$	0	0
$687$	− 78.8407i	− 3.00796i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−33.7035	−1.28214	−0.641071	−	0.767482i	$-0.721510\pi$
$691$	−33.7035	−1.28214	−0.641071	+	0.767482i	$0.721510\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	100.007i	3.79347i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−17.8276	−0.674302
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−16.8955	−0.635420
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	30.8411i	1.15663i
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	− 22.2349i	− 0.830379i
$718$	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
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−31.2843	−1.15868
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 6.99700i	− 0.258440i	−0.991616	−	0.129220i	$-0.958753\pi$
$733$	− 6.99700i	− 0.258440i	0.991616	−	0.129220i	$-0.0412474\pi$
$734$	0	0
$735$	− 89.4237i	− 3.29844i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	11.9076i	0.437435i
$742$	0	0
$743$	− 7.48331i	− 0.274536i	−0.990534	−	0.137268i	$-0.956168\pi$
$743$	− 7.48331i	− 0.274536i	0.990534	−	0.137268i	$-0.0438322\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	80.6465	2.95070
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 22.4499i	− 0.819210i	−0.912263	−	0.409605i	$-0.865667\pi$
$751$	− 22.4499i	− 0.819210i	0.912263	−	0.409605i	$-0.134333\pi$
$752$	0	0
$753$	−94.0833	−3.42858
$754$	0	0
$755$	96.5224	3.51281
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	− 4.75968i	− 0.171862i
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	25.9233i	0.932395i	0.884681	+	0.466198i	$0.154376\pi$
$773$	25.9233i	0.932395i	−0.884681	+	0.466198i	$0.845624\pi$
$774$	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
$785$	107.740	3.84541
$786$	0	0
$787$	8.49148	0.302688	0.151344	−	0.988481i	$-0.451640\pi$
$787$	8.49148	0.302688	0.151344	+	0.988481i	$0.451640\pi$
$788$	0	0
$789$	− 47.1674i	− 1.67920i
$790$	0	0
$791$	− 37.4166i	− 1.33038i
$792$	0	0
$793$	−8.42641	−0.299230
$794$	0	0
$795$	0	0
$796$	0	0
$797$	45.2075i	1.60133i	0.599111	+	0.800666i	$0.295521\pi$
$797$	45.2075i	1.60133i	−0.599111	+	0.800666i	$0.704479\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 85.1248i	− 3.00025i
$806$	0	0
$807$	57.6747i	2.03025i
$808$	0	0
$809$	−31.1127	−1.09386	−0.546932	−	0.837177i	$-0.684204\pi$
$809$	−31.1127	−1.09386	−0.546932	+	0.837177i	$0.684204\pi$
$810$	0	0
$811$	55.4345	1.94657	0.973284	−	0.229604i	$-0.0737430\pi$
$811$	55.4345	1.94657	0.973284	+	0.229604i	$0.0737430\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−11.3753	−0.397484
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	− 26.4575i	− 0.922251i	−0.887335	−	0.461125i	$-0.847446\pi$
$823$	− 26.4575i	− 0.922251i	0.887335	−	0.461125i	$-0.152554\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	41.6457i	1.44642i	0.690630	+	0.723208i	$0.257333\pi$
$829$	41.6457i	1.44642i	−0.690630	+	0.723208i	$0.742667\pi$
$830$	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
$841$	−29.0000	−1.00000
$842$	0	0
$843$	89.1380	3.07008
$844$	0	0
$845$	− 53.5533i	− 1.84229i
$846$	0	0
$847$	29.1033i	1.00000i
$848$	0	0
$849$	47.1716	1.61892
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 46.4297i	− 1.58972i	−0.606790	−	0.794862i	$-0.707543\pi$
$853$	− 46.4297i	− 1.58972i	0.606790	−	0.794862i	$-0.292457\pi$
$854$	0	0
$855$	136.139i	4.65587i
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−22.8380	−0.779223	−0.389612	−	0.920979i	$-0.627391\pi$
$859$	−22.8380	−0.779223	−0.389612	+	0.920979i	$0.627391\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	15.8745i	0.540375i	0.962808	+	0.270187i	$0.0870856\pi$
$863$	15.8745i	0.540375i	−0.962808	+	0.270187i	$0.912914\pi$
$864$	0	0
$865$	46.4853	1.58055
$866$	0	0
$867$	−50.5115	−1.71546
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−96.5224	−3.26305
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	95.6231i	3.22529i
$880$	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
$885$	− 82.4272i	− 2.77076i
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	59.3970	1.99211
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−16.4020	−0.547648
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	42.7696	1.42171
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	37.2197i	1.23450i
$910$	0	0
$911$	− 52.3832i	− 1.73553i	−0.496972	−	0.867766i	$-0.665555\pi$
$911$	− 52.3832i	− 1.73553i	0.496972	−	0.867766i	$-0.334445\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−145.927	−4.82420
$916$	0	0
$917$	10.5588i	0.348682i
$918$	0	0
$919$	58.2065i	1.92006i	0.279904	+	0.960028i	$0.409697\pi$
$919$	58.2065i	1.92006i	−0.279904	+	0.960028i	$0.590303\pi$
$920$	0	0
$921$	38.0833	1.25489
$922$	0	0
$923$	−11.7101	−0.385444
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	38.0292	1.24636
$932$	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
$941$	− 27.7566i	− 0.904839i	−0.891805	−	0.452419i	$-0.850561\pi$
$941$	− 27.7566i	− 0.904839i	0.891805	−	0.452419i	$-0.149439\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	−95.5980	−3.10980
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	0	0
$955$	68.2517	2.20857
$956$	0	0
$957$	0	0
$958$	0	0
$959$	47.6235i	1.53784i
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	− 36.4821i	− 1.17440i
$966$	0	0
$967$	22.4499i	0.721942i	0.932577	+	0.360971i	$0.117555\pi$
$967$	22.4499i	0.721942i	−0.932577	+	0.360971i	$0.882445\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	43.9717	1.41112	0.705560	−	0.708650i	$-0.250695\pi$
$971$	43.9717	1.41112	0.705560	+	0.708650i	$0.250695\pi$
$972$	0	0
$973$	− 61.5411i	− 1.97292i
$974$	0	0
$975$	29.5572i	0.946588i
$976$	0	0
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	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
$989$	0	0
$990$	0	0
$991$	− 37.0405i	− 1.17663i	−0.808632	−	0.588315i	$-0.799791\pi$
$991$	− 37.0405i	− 1.17663i	0.808632	−	0.588315i	$-0.200209\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	− 63.0164i	− 1.99575i	−0.0651544	−	0.997875i	$-0.520754\pi$
$997$	− 63.0164i	− 1.99575i	0.0651544	−	0.997875i	$-0.479246\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.f.l.1791.1		8
4.3	odd	2	inner	1792.2.f.l.1791.7		8
7.6	odd	2	inner	1792.2.f.l.1791.8		8
8.3	odd	2	inner	1792.2.f.l.1791.2		8
8.5	even	2	inner	1792.2.f.l.1791.8		8
16.3	odd	4		896.2.e.g.447.7	yes	8
16.5	even	4		896.2.e.g.447.8	yes	8
16.11	odd	4		896.2.e.g.447.2	yes	8
16.13	even	4		896.2.e.g.447.1	✓	8
28.27	even	2	inner	1792.2.f.l.1791.2		8
56.13	odd	2	CM	1792.2.f.l.1791.1		8
56.27	even	2	inner	1792.2.f.l.1791.7		8
112.13	odd	4		896.2.e.g.447.8	yes	8
112.27	even	4		896.2.e.g.447.7	yes	8
112.69	odd	4		896.2.e.g.447.1	✓	8
112.83	even	4		896.2.e.g.447.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.e.g.447.1	✓	8	16.13	even	4
896.2.e.g.447.1	✓	8	112.69	odd	4
896.2.e.g.447.2	yes	8	16.11	odd	4
896.2.e.g.447.2	yes	8	112.83	even	4
896.2.e.g.447.7	yes	8	16.3	odd	4
896.2.e.g.447.7	yes	8	112.27	even	4
896.2.e.g.447.8	yes	8	16.5	even	4
896.2.e.g.447.8	yes	8	112.13	odd	4
1792.2.f.l.1791.1		8	1.1	even	1	trivial
1792.2.f.l.1791.1		8	56.13	odd	2	CM
1792.2.f.l.1791.2		8	8.3	odd	2	inner
1792.2.f.l.1791.2		8	28.27	even	2	inner
1792.2.f.l.1791.7		8	4.3	odd	2	inner
1792.2.f.l.1791.7		8	56.27	even	2	inner
1792.2.f.l.1791.8		8	7.6	odd	2	inner
1792.2.f.l.1791.8		8	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.97127 q^{3} -4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} +O(q^{10})\)	\(q-2.97127 q^{3} -4.29945i q^{5} +2.64575i q^{7} +5.82843 q^{9} +0.737669i q^{13} +12.7748i q^{15} -5.43275 q^{19} -7.86123i q^{21} -7.48331i q^{23} -13.4853 q^{25} -8.40401 q^{27} +11.3753 q^{35} -2.19181i q^{39} -25.0590i q^{45} -7.00000 q^{49} +16.1421 q^{57} -6.45232 q^{59} +11.4230i q^{61} +15.4206i q^{63} +3.17157 q^{65} +22.2349i q^{69} +15.8745i q^{71} +40.0684 q^{75} +5.29150i q^{79} +7.48528 q^{81} +13.8368 q^{83} -1.95169 q^{91} +23.3578i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 8 * q + 24 * q^9	\( 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} + 16 q^{57} + 48 q^{65} - 8 q^{81}+O(q^{100}) \) 8 * q + 24 * q^9 - 40 * q^25 - 56 * q^49 + 16 * q^57 + 48 * q^65 - 8 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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