LMFDB - Embedded newform 1792.2.f.l.1791.4

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			1791.4
Root			$-1.52009 + 1.05050i$ of defining polynomial
Character	$\chi$	$=$	1792.1791
Dual form			1792.2.f.l.1791.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78089 q^{3} +1.23074i q^{5} +2.64575i q^{7} +0.171573 q^{9} +O(q^{10})$	$q-1.78089 q^{3} +1.23074i q^{5} +2.64575i q^{7} +0.171573 q^{9} -7.17327i q^{13} -2.19181i q^{15} +6.81801 q^{19} -4.71179i q^{21} +7.48331i q^{23} +3.48528 q^{25} +5.03712 q^{27} -3.25623 q^{35} +12.7748i q^{39} +0.211161i q^{45} -7.00000 q^{49} -12.1421 q^{57} -13.9416 q^{59} +10.6543i q^{61} +0.453939i q^{63} +8.82843 q^{65} -13.3270i q^{69} +15.8745i q^{71} -6.20691 q^{75} +5.29150i q^{79} -9.48528 q^{81} -11.8551 q^{83} +18.9787 q^{91} +8.39119i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.78089	−1.02820	−0.514099	−	0.857731i	$-0.671874\pi$
$3$	−1.78089	−1.02820	−0.514099	+	0.857731i	$0.671874\pi$
$4$	0	0
$5$	1.23074i	0.550403i	0.961387	+	0.275202i	$0.0887446\pi$
$5$	1.23074i	0.550403i	−0.961387	+	0.275202i	$0.911255\pi$
$6$	0	0
$7$	2.64575i	1.00000i
$7$	2.64575i	1.00000i
$8$	0	0
$9$	0.171573	0.0571910
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	− 7.17327i	− 1.98951i	−0.102296	−	0.994754i	$-0.532619\pi$
$13$	− 7.17327i	− 1.98951i	0.102296	−	0.994754i	$-0.467381\pi$
$14$	0	0
$15$	− 2.19181i	− 0.565923i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	6.81801	1.56416	0.782080	−	0.623179i	$-0.214159\pi$
$19$	6.81801	1.56416	0.782080	+	0.623179i	$0.214159\pi$
$20$	0	0
$21$	− 4.71179i	− 1.02820i
$22$	0	0
$23$	7.48331i	1.56038i	0.625543	+	0.780189i	$0.284877\pi$
$23$	7.48331i	1.56038i	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	3.48528	0.697056
$26$	0	0
$27$	5.03712	0.969394
$28$	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
$35$	−3.25623	−0.550403
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	12.7748i	2.04561i
$40$	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
$45$	0.211161i	0.0314781i
$46$	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
$57$	−12.1421	−1.60827
$58$	0	0
$59$	−13.9416	−1.81504	−0.907519	−	0.420010i	$-0.862026\pi$
$59$	−13.9416	−1.81504	−0.907519	+	0.420010i	$0.862026\pi$
$60$	0	0
$61$	10.6543i	1.36415i	0.731284	+	0.682073i	$0.238922\pi$
$61$	10.6543i	1.36415i	−0.731284	+	0.682073i	$0.761078\pi$
$62$	0	0
$63$	0.453939i	0.0571910i
$64$	0	0
$65$	8.82843	1.09503
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	− 13.3270i	− 1.60438i
$70$	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
$75$	−6.20691	−0.716712
$76$	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
$81$	−9.48528	−1.05392
$82$	0	0
$83$	−11.8551	−1.30127	−0.650635	−	0.759391i	$-0.725497\pi$
$83$	−11.8551	−1.30127	−0.650635	+	0.759391i	$0.725497\pi$
$84$	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
$91$	18.9787	1.98951
$92$	0	0
$93$	0	0
$94$	0	0
$95$	8.39119i	0.860918i
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	19.0583i	1.89638i	0.317710	+	0.948188i	$0.397086\pi$
$101$	19.0583i	1.89638i	−0.317710	+	0.948188i	$0.602914\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	5.79899	0.565923
$106$	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	$-0.268350\pi$
$113$	14.1421	1.33038	0.665190	+	0.746674i	$0.268350\pi$
$114$	0	0
$115$	−9.21001	−0.858838
$116$	0	0
$117$	− 1.23074i	− 0.113782i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	10.4432i	0.934065i
$126$	0	0
$127$	22.4499i	1.99211i	0.0887357	+	0.996055i	$0.471717\pi$
$127$	22.4499i	1.99211i	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	22.5405	1.96937	0.984685	−	0.174341i	$-0.0557795\pi$
$131$	22.5405	1.96937	0.984685	+	0.174341i	$0.0557795\pi$
$132$	0	0
$133$	18.0388i	1.56416i
$134$	0	0
$135$	6.19938i	0.533558i
$136$	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
$139$	−3.86733	−0.328023	−0.164012	−	0.986458i	$-0.552443\pi$
$139$	−3.86733	−0.328023	−0.164012	+	0.986458i	$0.552443\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	12.4662	1.02820
$148$	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	$-0.633388\pi$
$151$	− 22.4499i	− 1.82695i	0.406894	−	0.913475i	$-0.366612\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	− 0.211161i	− 0.0168525i	−0.999964	−	0.00842626i	$-0.997318\pi$
$157$	− 0.211161i	− 0.0168525i	0.999964	−	0.00842626i	$-0.00268219\pi$
$158$	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
$169$	−38.4558	−2.95814
$170$	0	0
$171$	1.16979	0.0894558
$172$	0	0
$173$	− 23.9813i	− 1.82326i	−0.411007	−	0.911632i	$-0.634823\pi$
$173$	− 23.9813i	− 1.82326i	0.411007	−	0.911632i	$-0.365177\pi$
$174$	0	0
$175$	9.22119i	0.697056i
$176$	0	0
$177$	24.8284	1.86622
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	25.0009i	1.85830i	0.369703	+	0.929150i	$0.379460\pi$
$181$	25.0009i	1.85830i	−0.369703	+	0.929150i	$0.620540\pi$
$182$	0	0
$183$	− 18.9742i	− 1.40261i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	13.3270i	0.969394i
$190$	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	$-0.598787\pi$
$193$	−8.48528	−0.610784	−0.305392	+	0.952227i	$0.598787\pi$
$194$	0	0
$195$	−15.7225	−1.12591
$196$	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
$207$	1.28393i	0.0892396i
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	− 28.2708i	− 1.93708i
$214$	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
$225$	0.597980	0.0398653
$226$	0	0
$227$	−7.42912	−0.493088	−0.246544	−	0.969132i	$-0.579295\pi$
$227$	−7.42912	−0.493088	−0.246544	+	0.969132i	$0.579295\pi$
$228$	0	0
$229$	− 14.5577i	− 0.962000i	−0.876720	−	0.481000i	$-0.840274\pi$
$229$	− 14.5577i	− 0.962000i	0.876720	−	0.481000i	$-0.159726\pi$
$230$	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
$237$	− 9.42359i	− 0.612128i
$238$	0	0
$239$	− 7.48331i	− 0.484055i	−0.970269	−	0.242028i	$-0.922188\pi$
$239$	− 7.48331i	− 0.484055i	0.970269	−	0.242028i	$-0.0778125\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	1.78089	0.114244
$244$	0	0
$245$	− 8.61517i	− 0.550403i
$246$	0	0
$247$	− 48.9075i	− 3.11191i
$248$	0	0
$249$	21.1127	1.33796
$250$	0	0
$251$	−1.16979	−0.0738362	−0.0369181	−	0.999318i	$-0.511754\pi$
$251$	−1.16979	−0.0738362	−0.0369181	+	0.999318i	$0.511754\pi$
$252$	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
$269$	26.4428i	1.61224i	0.591749	+	0.806122i	$0.298438\pi$
$269$	26.4428i	1.61224i	−0.591749	+	0.806122i	$0.701562\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	−33.7990	−2.04561
$274$	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
$283$	−29.6640	−1.76334	−0.881672	−	0.471863i	$-0.843582\pi$
$283$	−29.6640	−1.76334	−0.881672	+	0.471863i	$0.843582\pi$
$284$	0	0
$285$	− 14.9438i	− 0.885194i
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 11.6739i	− 0.681997i	−0.940064	−	0.340998i	$-0.889235\pi$
$293$	− 11.6739i	− 0.681997i	0.940064	−	0.340998i	$-0.110765\pi$
$294$	0	0
$295$	− 17.1584i	− 0.999003i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	53.6799	3.10439
$300$	0	0
$301$	0	0
$302$	0	0
$303$	− 33.9408i	− 1.94985i
$304$	0	0
$305$	−13.1127	−0.750831
$306$	0	0
$307$	32.6147	1.86142	0.930710	−	0.365758i	$-0.119190\pi$
$307$	32.6147	1.86142	0.930710	+	0.365758i	$0.119190\pi$
$308$	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
$315$	−0.558681	−0.0314781
$316$	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
$325$	− 25.0009i	− 1.38680i
$326$	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	$-0.256141\pi$
$337$	25.4558	1.38667	0.693334	+	0.720616i	$0.256141\pi$
$338$	0	0
$339$	−25.1856	−1.36789
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 18.5203i	− 1.00000i
$344$	0	0
$345$	16.4020	0.883055
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	− 3.26989i	− 0.175033i	−0.996163	−	0.0875167i	$-0.972107\pi$
$349$	− 3.26989i	− 0.175033i	0.996163	−	0.0875167i	$-0.0278931\pi$
$350$	0	0
$351$	− 36.1326i	− 1.92862i
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	−19.5374	−1.03694
$356$	0	0
$357$	0	0
$358$	0	0
$359$	37.4166i	1.97477i	0.158334	+	0.987386i	$0.449388\pi$
$359$	37.4166i	1.97477i	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	27.4853	1.44659
$362$	0	0
$363$	−19.5898	−1.02820
$364$	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
$375$	− 18.5981i	− 0.960404i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	− 39.9809i	− 2.04828i
$382$	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
$393$	−40.1421	−2.02490
$394$	0	0
$395$	−6.51246	−0.327677
$396$	0	0
$397$	17.6164i	0.884144i	0.896980	+	0.442072i	$0.145756\pi$
$397$	17.6164i	0.884144i	−0.896980	+	0.442072i	$0.854244\pi$
$398$	0	0
$399$	− 32.1251i	− 1.60827i
$400$	0	0
$401$	36.7696	1.83618	0.918092	−	0.396368i	$-0.129729\pi$
$401$	36.7696	1.83618	0.918092	+	0.396368i	$0.129729\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	− 11.6739i	− 0.580081i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−32.0560	−1.58121
$412$	0	0
$413$	− 36.8859i	− 1.81504i
$414$	0	0
$415$	− 14.5906i	− 0.716223i
$416$	0	0
$417$	6.88730	0.337273
$418$	0	0
$419$	18.3676	0.897316	0.448658	−	0.893704i	$-0.351902\pi$
$419$	18.3676	0.897316	0.448658	+	0.893704i	$0.351902\pi$
$420$	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
$427$	−28.1887	−1.36415
$428$	0	0
$429$	0	0
$430$	0	0
$431$	− 37.4166i	− 1.80229i	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	− 37.4166i	− 1.80229i	0.433515	−	0.901146i	$-0.357273\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	51.0213i	2.44068i
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−1.20101	−0.0571910
$442$	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
$453$	39.9809i	1.87847i
$454$	0	0
$455$	23.3578i	1.09503i
$456$	0	0
$457$	42.4264	1.98462	0.992312	−	0.123763i	$-0.0394963\pi$
$457$	42.4264	1.98462	0.992312	+	0.123763i	$0.0394963\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	34.4245i	1.60331i	0.597789	+	0.801654i	$0.296046\pi$
$461$	34.4245i	1.60331i	−0.597789	+	0.801654i	$0.703954\pi$
$462$	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
$467$	−37.6518	−1.74232	−0.871160	−	0.491000i	$-0.836632\pi$
$467$	−37.6518	−1.74232	−0.871160	+	0.491000i	$0.836632\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0.376056i	0.0173277i
$472$	0	0
$473$	0	0
$474$	0	0
$475$	23.7627	1.09031
$476$	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
$483$	35.2598	1.60438
$484$	0	0
$485$	0	0
$486$	0	0
$487$	− 22.4499i	− 1.01730i	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	− 22.4499i	− 1.01730i	0.860972	−	0.508652i	$-0.169856\pi$
$488$	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
$505$	−23.4558	−1.04377
$506$	0	0
$507$	68.4857	3.04156
$508$	0	0
$509$	44.2704i	1.96225i	0.193375	+	0.981125i	$0.438057\pi$
$509$	44.2704i	1.96225i	−0.193375	+	0.981125i	$0.561943\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	34.3431	1.51629
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	42.7081i	1.87468i
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	44.7754	1.95789	0.978946	−	0.204120i	$-0.0654333\pi$
$523$	44.7754	1.95789	0.978946	+	0.204120i	$0.0654333\pi$
$524$	0	0
$525$	− 16.4219i	− 0.716712i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−33.0000	−1.43478
$530$	0	0
$531$	−2.39200	−0.103804
$532$	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
$543$	− 44.5238i	− 1.91070i
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	1.82799i	0.0780169i
$550$	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
$563$	26.9665	1.13650	0.568251	−	0.822855i	$-0.307620\pi$
$563$	26.9665	1.13650	0.568251	+	0.822855i	$0.307620\pi$
$564$	0	0
$565$	17.4053i	0.732246i
$566$	0	0
$567$	− 25.0957i	− 1.05392i
$568$	0	0
$569$	−2.82843	−0.118574	−0.0592869	−	0.998241i	$-0.518883\pi$
$569$	−2.82843	−0.118574	−0.0592869	+	0.998241i	$0.518883\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	− 28.2708i	− 1.18103i
$574$	0	0
$575$	26.0815i	1.08767i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	15.1114	0.628007
$580$	0	0
$581$	− 31.3657i	− 1.30127i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	1.51472	0.0626259
$586$	0	0
$587$	−48.3372	−1.99509	−0.997545	−	0.0700342i	$-0.977689\pi$
$587$	−48.3372	−1.99509	−0.997545	+	0.0700342i	$0.977689\pi$
$588$	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
$605$	13.5381i	0.550403i
$606$	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	$-0.591884\pi$
$617$	−14.1421	−0.569341	−0.284670	+	0.958625i	$0.591884\pi$
$618$	0	0
$619$	−11.2440	−0.451936	−0.225968	−	0.974135i	$-0.572554\pi$
$619$	−11.2440	−0.451936	−0.225968	+	0.974135i	$0.572554\pi$
$620$	0	0
$621$	37.6944i	1.51262i
$622$	0	0
$623$	0	0
$624$	0	0
$625$	4.57359	0.182944
$626$	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
$635$	−27.6300	−1.09646
$636$	0	0
$637$	50.2129i	1.98951i
$638$	0	0
$639$	2.72363i	0.107745i
$640$	0	0
$641$	48.0833	1.89917	0.949587	−	0.313503i	$-0.101502\pi$
$641$	48.0833	1.89917	0.949587	+	0.313503i	$0.101502\pi$
$642$	0	0
$643$	−23.4047	−0.922992	−0.461496	−	0.887142i	$-0.652687\pi$
$643$	−23.4047	−0.922992	−0.461496	+	0.887142i	$0.652687\pi$
$644$	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
$655$	27.7414i	1.08395i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	− 7.59560i	− 0.295434i	−0.989030	−	0.147717i	$-0.952807\pi$
$661$	− 7.59560i	− 0.295434i	0.989030	−	0.147717i	$-0.0471926\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−22.2010	−0.860918
$666$	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
$675$	17.5558	0.675722
$676$	0	0
$677$	− 29.5015i	− 1.13384i	−0.823775	−	0.566918i	$-0.808136\pi$
$677$	− 29.5015i	− 1.13384i	0.823775	−	0.566918i	$-0.191864\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	13.2304	0.506992
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	22.1533i	0.846434i
$686$	0	0
$687$	25.9257i	0.989127i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−40.3494	−1.53496	−0.767482	−	0.641071i	$-0.778490\pi$
$691$	−40.3494	−1.53496	−0.767482	+	0.641071i	$0.778490\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	− 4.75968i	− 0.180545i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−10.6853	−0.404157
$700$	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
$707$	−50.4236	−1.89638
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	0.907878i	0.0340481i
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	13.3270i	0.497705i
$718$	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
$729$	25.2843	0.936454
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 53.6940i	− 1.98323i	−0.129220	−	0.991616i	$-0.541247\pi$
$733$	− 53.6940i	− 1.98323i	0.129220	−	0.991616i	$-0.458753\pi$
$734$	0	0
$735$	15.3427i	0.565923i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	87.0989i	3.19966i
$742$	0	0
$743$	7.48331i	0.274536i	0.990534	+	0.137268i	$0.0438322\pi$
$743$	7.48331i	0.274536i	−0.990534	+	0.137268i	$0.956168\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−2.03402	−0.0744209
$748$	0	0
$749$	0	0
$750$	0	0
$751$	22.4499i	0.819210i	0.912263	+	0.409605i	$0.134333\pi$
$751$	22.4499i	0.819210i	−0.912263	+	0.409605i	$0.865667\pi$
$752$	0	0
$753$	2.08326	0.0759183
$754$	0	0
$755$	27.6300	1.00556
$756$	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
$767$	100.007i	3.61103i
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 49.1933i	− 1.76936i	−0.466198	−	0.884681i	$-0.654376\pi$
$773$	− 49.1933i	− 1.76936i	0.466198	−	0.884681i	$-0.345624\pi$
$774$	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
$785$	0.259885	0.00927568
$786$	0	0
$787$	55.4608	1.97696	0.988481	−	0.151344i	$-0.0483602\pi$
$787$	55.4608	1.97696	0.988481	+	0.151344i	$0.0483602\pi$
$788$	0	0
$789$	− 28.2708i	− 1.00647i
$790$	0	0
$791$	37.4166i	1.33038i
$792$	0	0
$793$	76.4264	2.71398
$794$	0	0
$795$	0	0
$796$	0	0
$797$	− 33.8272i	− 1.19822i	−0.800666	−	0.599111i	$-0.795521\pi$
$797$	− 33.8272i	− 1.19822i	0.800666	−	0.599111i	$-0.204479\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 24.3674i	− 0.858838i
$806$	0	0
$807$	− 47.0917i	− 1.65771i
$808$	0	0
$809$	31.1127	1.09386	0.546932	−	0.837177i	$-0.315796\pi$
$809$	31.1127	1.09386	0.546932	+	0.837177i	$0.315796\pi$
$810$	0	0
$811$	13.0773	0.459208	0.229604	−	0.973284i	$-0.426257\pi$
$811$	13.0773	0.459208	0.229604	+	0.973284i	$0.426257\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	3.25623	0.113782
$820$	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
$829$	− 39.7697i	− 1.38126i	−0.723208	−	0.690630i	$-0.757333\pi$
$829$	− 39.7697i	− 1.38126i	0.723208	−	0.690630i	$-0.242667\pi$
$830$	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
$843$	53.4267	1.84011
$844$	0	0
$845$	− 47.3291i	− 1.62817i
$846$	0	0
$847$	29.1033i	1.00000i
$848$	0	0
$849$	52.8284	1.81307
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 35.4440i	− 1.21358i	−0.794862	−	0.606790i	$-0.792457\pi$
$853$	− 35.4440i	− 1.21358i	0.794862	−	0.606790i	$-0.207543\pi$
$854$	0	0
$855$	1.43970i	0.0492367i
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−53.9854	−1.84196	−0.920979	−	0.389612i	$-0.872609\pi$
$859$	−53.9854	−1.84196	−0.920979	+	0.389612i	$0.872609\pi$
$860$	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
$865$	29.5147	1.00353
$866$	0	0
$867$	−30.2751	−1.02820
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−27.6300	−0.934065
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	20.7900i	0.701228i
$880$	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
$885$	30.5573i	1.02717i
$886$	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
$897$	−95.5980	−3.19192
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−30.7696	−1.02281
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	3.26989i	0.108456i
$910$	0	0
$911$	52.3832i	1.73553i	0.496972	+	0.867766i	$0.334445\pi$
$911$	52.3832i	1.73553i	−0.496972	+	0.867766i	$0.665555\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	23.3523	0.772003
$916$	0	0
$917$	59.6365i	1.96937i
$918$	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
$921$	−58.0833	−1.91391
$922$	0	0
$923$	113.872	3.74815
$924$	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
$931$	−47.7261	−1.56416
$932$	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
$941$	− 54.7135i	− 1.78361i	−0.452419	−	0.891805i	$-0.649439\pi$
$941$	− 54.7135i	− 1.78361i	0.452419	−	0.891805i	$-0.350561\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	−16.4020	−0.533558
$946$	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
$955$	−19.5374	−0.632215
$956$	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
$965$	− 10.4432i	− 0.336177i
$966$	0	0
$967$	− 22.4499i	− 0.721942i	−0.932577	−	0.360971i	$-0.882445\pi$
$967$	− 22.4499i	− 0.721942i	0.932577	−	0.360971i	$-0.117555\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−44.1643	−1.41730	−0.708650	−	0.705560i	$-0.750695\pi$
$971$	−44.1643	−1.41730	−0.708650	+	0.705560i	$0.750695\pi$
$972$	0	0
$973$	− 10.2320i	− 0.328023i
$974$	0	0
$975$	44.5238i	1.42590i
$976$	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
$997$	4.11454i	0.130309i	0.997875	+	0.0651544i	$0.0207540\pi$
$997$	4.11454i	0.130309i	−0.997875	+	0.0651544i	$0.979246\pi$
$998$	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.1791.4		8
4.3	odd	2	inner	1792.2.f.l.1791.6		8
7.6	odd	2	inner	1792.2.f.l.1791.5		8
8.3	odd	2	inner	1792.2.f.l.1791.3		8
8.5	even	2	inner	1792.2.f.l.1791.5		8
16.3	odd	4		896.2.e.g.447.6	yes	8
16.5	even	4		896.2.e.g.447.5	yes	8
16.11	odd	4		896.2.e.g.447.3	✓	8
16.13	even	4		896.2.e.g.447.4	yes	8
28.27	even	2	inner	1792.2.f.l.1791.3		8
56.13	odd	2	CM	1792.2.f.l.1791.4		8
56.27	even	2	inner	1792.2.f.l.1791.6		8
112.13	odd	4		896.2.e.g.447.5	yes	8
112.27	even	4		896.2.e.g.447.6	yes	8
112.69	odd	4		896.2.e.g.447.4	yes	8
112.83	even	4		896.2.e.g.447.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.e.g.447.3	✓	8	16.11	odd	4
896.2.e.g.447.3	✓	8	112.83	even	4
896.2.e.g.447.4	yes	8	16.13	even	4
896.2.e.g.447.4	yes	8	112.69	odd	4
896.2.e.g.447.5	yes	8	16.5	even	4
896.2.e.g.447.5	yes	8	112.13	odd	4
896.2.e.g.447.6	yes	8	16.3	odd	4
896.2.e.g.447.6	yes	8	112.27	even	4
1792.2.f.l.1791.3		8	8.3	odd	2	inner
1792.2.f.l.1791.3		8	28.27	even	2	inner
1792.2.f.l.1791.4		8	1.1	even	1	trivial
1792.2.f.l.1791.4		8	56.13	odd	2	CM
1792.2.f.l.1791.5		8	7.6	odd	2	inner
1792.2.f.l.1791.5		8	8.5	even	2	inner
1792.2.f.l.1791.6		8	4.3	odd	2	inner
1792.2.f.l.1791.6		8	56.27	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)

\(f(q)\)	\(=\)	\(q-1.78089 q^{3} +1.23074i q^{5} +2.64575i q^{7} +0.171573 q^{9} +O(q^{10})\)	\(q-1.78089 q^{3} +1.23074i q^{5} +2.64575i q^{7} +0.171573 q^{9} -7.17327i q^{13} -2.19181i q^{15} +6.81801 q^{19} -4.71179i q^{21} +7.48331i q^{23} +3.48528 q^{25} +5.03712 q^{27} -3.25623 q^{35} +12.7748i q^{39} +0.211161i q^{45} -7.00000 q^{49} -12.1421 q^{57} -13.9416 q^{59} +10.6543i q^{61} +0.453939i q^{63} +8.82843 q^{65} -13.3270i q^{69} +15.8745i q^{71} -6.20691 q^{75} +5.29150i q^{79} -9.48528 q^{81} -11.8551 q^{83} +18.9787 q^{91} +8.39119i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more