LMFDB - Embedded newform 1792.2.f.k.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:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 448)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1791.1
Root			$-1.38255 + 0.297594i$ of defining polynomial
Character	$\chi$	$=$	1792.1791
Dual form			1792.2.f.k.1791.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.36028 q^{3} -2.16991i q^{5} -2.64575i q^{7} +8.29150 q^{9} +O(q^{10})$	$q-3.36028 q^{3} -2.16991i q^{5} -2.64575i q^{7} +8.29150 q^{9} +4.55066i q^{13} +7.29150i q^{15} -0.979531 q^{19} +8.89047i q^{21} +6.00000i q^{23} +0.291503 q^{25} -17.7809 q^{27} -5.74103 q^{35} -15.2915i q^{39} -17.9918i q^{45} -7.00000 q^{49} +3.29150 q^{57} +14.4207 q^{59} +15.6110i q^{61} -21.9373i q^{63} +9.87451 q^{65} -20.1617i q^{69} +15.8745i q^{71} -0.979531 q^{75} +5.29150i q^{79} +34.8745 q^{81} +1.40122 q^{83} +12.0399 q^{91} +2.12549i q^{95} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 152 q^{81}+O(q^{100}) $ 8 * q + 24 * q^9 - 40 * q^25 - 56 * q^49 - 16 * q^57 - 48 * q^65 + 152 * 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
$3$	−3.36028	−1.94006	−0.970030	−	0.242984i	$-0.921874\pi$
$3$	−3.36028	−1.94006	−0.970030	+	0.242984i	$0.921874\pi$
$4$	0	0
$5$	− 2.16991i	− 0.970412i	−0.874400	−	0.485206i	$-0.838745\pi$
$5$	− 2.16991i	− 0.970412i	0.874400	−	0.485206i	$-0.161255\pi$
$6$	0	0
$7$	− 2.64575i	− 1.00000i
$7$	− 2.64575i	− 1.00000i
$8$	0	0
$9$	8.29150	2.76383
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	4.55066i	1.26213i	0.775732	+	0.631063i	$0.217381\pi$
$13$	4.55066i	1.26213i	−0.775732	+	0.631063i	$0.782619\pi$
$14$	0	0
$15$	7.29150i	1.88266i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−0.979531	−0.224720	−0.112360	−	0.993668i	$-0.535841\pi$
$19$	−0.979531	−0.224720	−0.112360	+	0.993668i	$0.535841\pi$
$20$	0	0
$21$	8.89047i	1.94006i
$22$	0	0
$23$	6.00000i	1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$	6.00000i	1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	0	0
$25$	0.291503	0.0583005
$26$	0	0
$27$	−17.7809	−3.42194
$28$	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
$35$	−5.74103	−0.970412
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	− 15.2915i	− 2.44860i
$40$	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
$45$	− 17.9918i	− 2.68206i
$46$	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
$57$	3.29150	0.435970
$58$	0	0
$59$	14.4207	1.87741	0.938705	−	0.344721i	$-0.112026\pi$
$59$	14.4207	1.87741	0.938705	+	0.344721i	$0.112026\pi$
$60$	0	0
$61$	15.6110i	1.99879i	0.0347968	+	0.999394i	$0.488922\pi$
$61$	15.6110i	1.99879i	−0.0347968	+	0.999394i	$0.511078\pi$
$62$	0	0
$63$	− 21.9373i	− 2.76383i
$64$	0	0
$65$	9.87451	1.22478
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	− 20.1617i	− 2.42718i
$70$	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
$75$	−0.979531	−0.113107
$76$	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
$81$	34.8745	3.87495
$82$	0	0
$83$	1.40122	0.153804	0.0769020	−	0.997039i	$-0.475497\pi$
$83$	1.40122	0.153804	0.0769020	+	0.997039i	$0.475497\pi$
$84$	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
$91$	12.0399	1.26213
$92$	0	0
$93$	0	0
$94$	0	0
$95$	2.12549i	0.218071i
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	− 17.9918i	− 1.79025i	−0.445815	−	0.895125i	$-0.647086\pi$
$101$	− 17.9918i	− 1.79025i	0.445815	−	0.895125i	$-0.352914\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	19.2915	1.88266
$106$	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
$113$	15.8745	1.49335	0.746674	−	0.665190i	$-0.231650\pi$
$113$	15.8745	1.49335	0.746674	+	0.665190i	$0.231650\pi$
$114$	0	0
$115$	13.0194	1.21407
$116$	0	0
$117$	37.7318i	3.48831i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 11.4821i	− 1.02699i
$126$	0	0
$127$	2.00000i	0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$	2.00000i	0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	18.7605	1.63911	0.819555	−	0.573000i	$-0.194221\pi$
$131$	18.7605	1.63911	0.819555	+	0.573000i	$0.194221\pi$
$132$	0	0
$133$	2.59160i	0.224720i
$134$	0	0
$135$	38.5830i	3.32070i
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	19.1822	1.62701	0.813505	−	0.581558i	$-0.197557\pi$
$139$	19.1822	1.62701	0.813505	+	0.581558i	$0.197557\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	23.5220	1.94006
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	− 10.0000i	− 0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$	− 10.0000i	− 0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	− 17.5701i	− 1.40225i	−0.713040	−	0.701123i	$-0.752682\pi$
$157$	− 17.5701i	− 1.40225i	0.713040	−	0.701123i	$-0.247318\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	15.8745	1.25109
$162$	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
$169$	−7.70850	−0.592961
$170$	0	0
$171$	−8.12179	−0.621089
$172$	0	0
$173$	9.31216i	0.707991i	0.935247	+	0.353995i	$0.115177\pi$
$173$	9.31216i	0.707991i	−0.935247	+	0.353995i	$0.884823\pi$
$174$	0	0
$175$	− 0.771243i	− 0.0583005i
$176$	0	0
$177$	−48.4575	−3.64229
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	24.7124i	1.83686i	0.395589	+	0.918428i	$0.370540\pi$
$181$	24.7124i	1.83686i	−0.395589	+	0.918428i	$0.629460\pi$
$182$	0	0
$183$	− 52.4575i	− 3.87777i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	47.0440i	3.42194i
$190$	0	0
$191$	− 15.8745i	− 1.14864i	−0.818631	−	0.574320i	$-0.805267\pi$
$191$	− 15.8745i	− 1.14864i	0.818631	−	0.574320i	$-0.194733\pi$
$192$	0	0
$193$	−26.4575	−1.90445	−0.952227	−	0.305392i	$-0.901213\pi$
$193$	−26.4575	−1.90445	−0.952227	+	0.305392i	$0.901213\pi$
$194$	0	0
$195$	−33.1811	−2.37615
$196$	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
$207$	49.7490i	3.45780i
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	− 53.3428i	− 3.65499i
$214$	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
$225$	2.41699	0.161133
$226$	0	0
$227$	25.9027	1.71922	0.859612	−	0.510947i	$-0.170705\pi$
$227$	25.9027	1.71922	0.859612	+	0.510947i	$0.170705\pi$
$228$	0	0
$229$	− 8.46878i	− 0.559633i	−0.960053	−	0.279817i	$-0.909726\pi$
$229$	− 8.46878i	− 0.559633i	0.960053	−	0.279817i	$-0.0902736\pi$
$230$	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
$237$	− 17.7809i	− 1.15500i
$238$	0	0
$239$	− 30.0000i	− 1.94054i	−0.242028	−	0.970269i	$-0.577812\pi$
$239$	− 30.0000i	− 1.94054i	0.242028	−	0.970269i	$-0.422188\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−63.8454	−4.09568
$244$	0	0
$245$	15.1894i	0.970412i
$246$	0	0
$247$	− 4.45751i	− 0.283625i
$248$	0	0
$249$	−4.70850	−0.298389
$250$	0	0
$251$	21.5629	1.36104	0.680520	−	0.732730i	$-0.261754\pi$
$251$	21.5629	1.36104	0.680520	+	0.732730i	$0.261754\pi$
$252$	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
$269$	− 4.97235i	− 0.303169i	−0.988444	−	0.151585i	$-0.951562\pi$
$269$	− 4.97235i	− 0.303169i	0.988444	−	0.151585i	$-0.0484376\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	−40.4575	−2.44860
$274$	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	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−32.2016	−1.91419	−0.957094	−	0.289779i	$-0.906418\pi$
$283$	−32.2016	−1.91419	−0.957094	+	0.289779i	$0.906418\pi$
$284$	0	0
$285$	− 7.14226i	− 0.423071i
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	31.0112i	1.81170i	0.423603	+	0.905848i	$0.360765\pi$
$293$	31.0112i	1.81170i	−0.423603	+	0.905848i	$0.639235\pi$
$294$	0	0
$295$	− 31.2915i	− 1.82186i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−27.3040	−1.57903
$300$	0	0
$301$	0	0
$302$	0	0
$303$	60.4575i	3.47319i
$304$	0	0
$305$	33.8745	1.93965
$306$	0	0
$307$	13.9990	0.798964	0.399482	−	0.916741i	$-0.369190\pi$
$307$	13.9990	0.798964	0.399482	+	0.916741i	$0.369190\pi$
$308$	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
$315$	−47.6018	−2.68206
$316$	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
$325$	1.32653i	0.0735826i
$326$	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
$337$	−26.4575	−1.44123	−0.720616	−	0.693334i	$-0.756141\pi$
$337$	−26.4575	−1.44123	−0.720616	+	0.693334i	$0.756141\pi$
$338$	0	0
$339$	−53.3428	−2.89719
$340$	0	0
$341$	0	0
$342$	0	0
$343$	18.5203i	1.00000i
$344$	0	0
$345$	−43.7490	−2.35537
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	− 28.6305i	− 1.53255i	−0.642510	−	0.766277i	$-0.722107\pi$
$349$	− 28.6305i	− 1.53255i	0.642510	−	0.766277i	$-0.277893\pi$
$350$	0	0
$351$	− 80.9150i	− 4.31892i
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	34.4462	1.82821
$356$	0	0
$357$	0	0
$358$	0	0
$359$	6.00000i	0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$	6.00000i	0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	0	0
$361$	−18.0405	−0.949501
$362$	0	0
$363$	−36.9631	−1.94006
$364$	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
$375$	38.5830i	1.99242i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	− 6.72057i	− 0.344305i
$382$	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
$393$	−63.0405	−3.17997
$394$	0	0
$395$	11.4821	0.577726
$396$	0	0
$397$	37.7318i	1.89370i	0.321668	+	0.946852i	$0.395756\pi$
$397$	37.7318i	1.89370i	−0.321668	+	0.946852i	$0.604244\pi$
$398$	0	0
$399$	− 8.70850i	− 0.435970i
$400$	0	0
$401$	15.8745	0.792735	0.396368	−	0.918092i	$-0.370271\pi$
$401$	15.8745	0.792735	0.396368	+	0.918092i	$0.370271\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	− 75.6744i	− 3.76029i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	60.4851	2.98351
$412$	0	0
$413$	− 38.1535i	− 1.87741i
$414$	0	0
$415$	− 3.04052i	− 0.149253i
$416$	0	0
$417$	−64.4575	−3.15650
$418$	0	0
$419$	−12.8833	−0.629390	−0.314695	−	0.949193i	$-0.601902\pi$
$419$	−12.8833	−0.629390	−0.314695	+	0.949193i	$0.601902\pi$
$420$	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
$427$	41.3029	1.99879
$428$	0	0
$429$	0	0
$430$	0	0
$431$	18.0000i	0.867029i	0.901146	+	0.433515i	$0.142727\pi$
$431$	18.0000i	0.867029i	−0.901146	+	0.433515i	$0.857273\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	− 5.87719i	− 0.281144i
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−58.0405	−2.76383
$442$	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
$453$	33.6028i	1.57880i
$454$	0	0
$455$	− 26.1255i	− 1.22478i
$456$	0	0
$457$	5.29150	0.247526	0.123763	−	0.992312i	$-0.460504\pi$
$457$	5.29150	0.247526	0.123763	+	0.992312i	$0.460504\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	42.4933i	1.97911i	0.144154	+	0.989555i	$0.453954\pi$
$461$	42.4933i	1.97911i	−0.144154	+	0.989555i	$0.546046\pi$
$462$	0	0
$463$	26.4575i	1.22958i	0.788689	+	0.614792i	$0.210760\pi$
$463$	26.4575i	1.22958i	−0.788689	+	0.614792i	$0.789240\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	11.6182	0.537627	0.268814	−	0.963192i	$-0.413368\pi$
$467$	11.6182	0.537627	0.268814	+	0.963192i	$0.413368\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	59.0405i	2.72044i
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−0.285536	−0.0131013
$476$	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
$483$	−53.3428	−2.42718
$484$	0	0
$485$	0	0
$486$	0	0
$487$	38.0000i	1.72194i	0.508652	+	0.860972i	$0.330144\pi$
$487$	38.0000i	1.72194i	−0.508652	+	0.860972i	$0.669856\pi$
$488$	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
$505$	−39.0405	−1.73728
$506$	0	0
$507$	25.9027	1.15038
$508$	0	0
$509$	25.1340i	1.11405i	0.830497	+	0.557024i	$0.188057\pi$
$509$	25.1340i	1.11405i	−0.830497	+	0.557024i	$0.811943\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	17.4170	0.768979
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	− 31.2915i	− 1.37354i
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	−25.0594	−1.09577	−0.547885	−	0.836554i	$-0.684567\pi$
$523$	−25.0594	−1.09577	−0.547885	+	0.836554i	$0.684567\pi$
$524$	0	0
$525$	2.59160i	0.113107i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−13.0000	−0.565217
$530$	0	0
$531$	119.569	5.18885
$532$	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
$543$	− 83.0405i	− 3.56361i
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	129.439i	5.52432i
$550$	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
$563$	8.54348	0.360065	0.180032	−	0.983661i	$-0.442380\pi$
$563$	8.54348	0.360065	0.180032	+	0.983661i	$0.442380\pi$
$564$	0	0
$565$	− 34.4462i	− 1.44916i
$566$	0	0
$567$	− 92.2693i	− 3.87495i
$568$	0	0
$569$	47.6235	1.99648	0.998241	−	0.0592869i	$-0.0188827\pi$
$569$	47.6235	1.99648	0.998241	+	0.0592869i	$0.0188827\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	53.3428i	2.22843i
$574$	0	0
$575$	1.74902i	0.0729390i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	88.9047	3.69475
$580$	0	0
$581$	− 3.70728i	− 0.153804i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	81.8745	3.38509
$586$	0	0
$587$	31.7799	1.31170	0.655849	−	0.754892i	$-0.272311\pi$
$587$	31.7799	1.31170	0.655849	+	0.754892i	$0.272311\pi$
$588$	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	$-0.574243\pi$
$599$	− 47.6235i	− 1.94584i	0.231133	−	0.972922i	$-0.425757\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 23.8690i	− 0.970412i
$606$	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
$617$	47.6235	1.91725	0.958625	−	0.284670i	$-0.0918842\pi$
$617$	47.6235	1.91725	0.958625	+	0.284670i	$0.0918842\pi$
$618$	0	0
$619$	26.3244	1.05807	0.529034	−	0.848601i	$-0.322554\pi$
$619$	26.3244	1.05807	0.529034	+	0.848601i	$0.322554\pi$
$620$	0	0
$621$	− 106.686i	− 4.28115i
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−23.4575	−0.938301
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	37.0405i	1.47456i	0.675587	+	0.737280i	$0.263890\pi$
$631$	37.0405i	1.47456i	−0.675587	+	0.737280i	$0.736110\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	4.33981	0.172220
$636$	0	0
$637$	− 31.8546i	− 1.26213i
$638$	0	0
$639$	131.624i	5.20695i
$640$	0	0
$641$	15.8745	0.627005	0.313503	−	0.949587i	$-0.398498\pi$
$641$	15.8745	0.627005	0.313503	+	0.949587i	$0.398498\pi$
$642$	0	0
$643$	−15.2640	−0.601955	−0.300978	−	0.953631i	$-0.597313\pi$
$643$	−15.2640	−0.601955	−0.300978	+	0.953631i	$0.597313\pi$
$644$	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
$655$	− 40.7085i	− 1.59061i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	− 30.5895i	− 1.18980i	−0.803801	−	0.594898i	$-0.797193\pi$
$661$	− 30.5895i	− 1.18980i	0.803801	−	0.594898i	$-0.202807\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	5.62352	0.218071
$666$	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	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	0	0
$675$	−5.18319	−0.199501
$676$	0	0
$677$	− 51.1729i	− 1.96674i	−0.181625	−	0.983368i	$-0.558136\pi$
$677$	− 51.1729i	− 1.96674i	0.181625	−	0.983368i	$-0.441864\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−87.0405	−3.33540
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	39.0583i	1.49234i
$686$	0	0
$687$	28.4575i	1.08572i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−52.3633	−1.99199	−0.995997	−	0.0893857i	$-0.971510\pi$
$691$	−52.3633	−1.99199	−0.995997	+	0.0893857i	$0.971510\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	− 41.6235i	− 1.57887i
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−20.1617	−0.762585
$700$	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
$707$	−47.6018	−1.79025
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	43.8745i	1.64542i
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	100.808i	3.76476i
$718$	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
$729$	109.915	4.07093
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 42.9150i	− 1.58510i	−0.609806	−	0.792551i	$-0.708753\pi$
$733$	− 42.9150i	− 1.58510i	0.609806	−	0.792551i	$-0.291247\pi$
$734$	0	0
$735$	− 51.0405i	− 1.88266i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	14.9785i	0.550249i
$742$	0	0
$743$	54.0000i	1.98107i	0.137268	+	0.990534i	$0.456168\pi$
$743$	54.0000i	1.98107i	−0.137268	+	0.990534i	$0.543832\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	11.6182	0.425089
$748$	0	0
$749$	0	0
$750$	0	0
$751$	50.0000i	1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$	50.0000i	1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$	0	0
$753$	−72.4575	−2.64050
$754$	0	0
$755$	−21.6991	−0.789710
$756$	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
$767$	65.6235i	2.36953i
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 16.4544i	− 0.591824i	−0.955215	−	0.295912i	$-0.904376\pi$
$773$	− 16.4544i	− 0.591824i	0.955215	−	0.295912i	$-0.0956236\pi$
$774$	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
$785$	−38.1255	−1.36076
$786$	0	0
$787$	−45.2211	−1.61196	−0.805978	−	0.591945i	$-0.798360\pi$
$787$	−45.2211	−1.61196	−0.805978	+	0.591945i	$0.798360\pi$
$788$	0	0
$789$	− 53.3428i	− 1.89906i
$790$	0	0
$791$	− 42.0000i	− 1.49335i
$792$	0	0
$793$	−71.0405	−2.52272
$794$	0	0
$795$	0	0
$796$	0	0
$797$	− 8.04710i	− 0.285043i	−0.989792	−	0.142521i	$-0.954479\pi$
$797$	− 8.04710i	− 0.285043i	0.989792	−	0.142521i	$-0.0455210\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 34.4462i	− 1.21407i
$806$	0	0
$807$	16.7085i	0.588167i
$808$	0	0
$809$	47.6235	1.67435	0.837177	−	0.546932i	$-0.184204\pi$
$809$	47.6235	1.67435	0.837177	+	0.546932i	$0.184204\pi$
$810$	0	0
$811$	48.4452	1.70114	0.850570	−	0.525861i	$-0.176257\pi$
$811$	48.4452	1.70114	0.850570	+	0.525861i	$0.176257\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	99.8290	3.48831
$820$	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
$829$	1.32653i	0.0460723i	0.999735	+	0.0230361i	$0.00733328\pi$
$829$	1.32653i	0.0460723i	−0.999735	+	0.0230361i	$0.992667\pi$
$830$	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
$843$	−100.808	−3.47203
$844$	0	0
$845$	16.7267i	0.575417i
$846$	0	0
$847$	− 29.1033i	− 1.00000i
$848$	0	0
$849$	108.207	3.71364
$850$	0	0
$851$	0	0
$852$	0	0
$853$	57.8935i	1.98224i	0.132987	+	0.991118i	$0.457543\pi$
$853$	57.8935i	1.98224i	−0.132987	+	0.991118i	$0.542457\pi$
$854$	0	0
$855$	17.6235i	0.602712i
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−54.3224	−1.85346	−0.926728	−	0.375734i	$-0.877391\pi$
$859$	−54.3224	−1.85346	−0.926728	+	0.375734i	$0.877391\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	− 15.8745i	− 0.540375i	−0.962808	−	0.270187i	$-0.912914\pi$
$863$	− 15.8745i	− 0.540375i	0.962808	−	0.270187i	$-0.0870856\pi$
$864$	0	0
$865$	20.2065	0.687043
$866$	0	0
$867$	−57.1248	−1.94006
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−30.3787	−1.02699
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	− 104.207i	− 3.51480i
$880$	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
$885$	105.148i	3.53452i
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	5.29150	0.177471
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	91.7490	3.06341
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	53.6235	1.78251
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	− 149.179i	− 4.94795i
$910$	0	0
$911$	− 30.0000i	− 0.993944i	−0.867766	−	0.496972i	$-0.834445\pi$
$911$	− 30.0000i	− 0.993944i	0.867766	−	0.496972i	$-0.165555\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−113.828	−3.76304
$916$	0	0
$917$	− 49.6356i	− 1.63911i
$918$	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
$921$	−47.0405	−1.55004
$922$	0	0
$923$	−72.2395	−2.37779
$924$	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
$931$	6.85672	0.224720
$932$	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
$941$	58.3152i	1.90102i	0.310693	+	0.950510i	$0.399439\pi$
$941$	58.3152i	1.90102i	−0.310693	+	0.950510i	$0.600561\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	102.081	3.32070
$946$	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
$955$	−34.4462	−1.11465
$956$	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
$965$	57.4103i	1.84810i
$966$	0	0
$967$	− 58.0000i	− 1.86515i	−0.360971	−	0.932577i	$-0.617555\pi$
$967$	− 58.0000i	− 1.86515i	0.360971	−	0.932577i	$-0.382445\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0.136153	0.00436936	0.00218468	−	0.999998i	$-0.499305\pi$
$971$	0.136153	0.00436936	0.00218468	+	0.999998i	$0.499305\pi$
$972$	0	0
$973$	− 50.7512i	− 1.62701i
$974$	0	0
$975$	− 4.45751i	− 0.142755i
$976$	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
$997$	− 41.6499i	− 1.31907i	−0.751675	−	0.659533i	$-0.770754\pi$
$997$	− 41.6499i	− 1.31907i	0.751675	−	0.659533i	$-0.229246\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.f.k.1791.1		8
4.3	odd	2	inner	1792.2.f.k.1791.7		8
7.6	odd	2	inner	1792.2.f.k.1791.8		8
8.3	odd	2	inner	1792.2.f.k.1791.2		8
8.5	even	2	inner	1792.2.f.k.1791.8		8
16.3	odd	4		448.2.e.a.223.7	yes	8
16.5	even	4		448.2.e.a.223.8	yes	8
16.11	odd	4		448.2.e.a.223.2	yes	8
16.13	even	4		448.2.e.a.223.1	✓	8
28.27	even	2	inner	1792.2.f.k.1791.2		8
48.5	odd	4		4032.2.p.h.1567.4		8
48.11	even	4		4032.2.p.h.1567.3		8
48.29	odd	4		4032.2.p.h.1567.6		8
48.35	even	4		4032.2.p.h.1567.5		8
56.13	odd	2	CM	1792.2.f.k.1791.1		8
56.27	even	2	inner	1792.2.f.k.1791.7		8
112.13	odd	4		448.2.e.a.223.8	yes	8
112.27	even	4		448.2.e.a.223.7	yes	8
112.69	odd	4		448.2.e.a.223.1	✓	8
112.83	even	4		448.2.e.a.223.2	yes	8
336.83	odd	4		4032.2.p.h.1567.3		8
336.125	even	4		4032.2.p.h.1567.4		8
336.251	odd	4		4032.2.p.h.1567.5		8
336.293	even	4		4032.2.p.h.1567.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.e.a.223.1	✓	8	16.13	even	4
448.2.e.a.223.1	✓	8	112.69	odd	4
448.2.e.a.223.2	yes	8	16.11	odd	4
448.2.e.a.223.2	yes	8	112.83	even	4
448.2.e.a.223.7	yes	8	16.3	odd	4
448.2.e.a.223.7	yes	8	112.27	even	4
448.2.e.a.223.8	yes	8	16.5	even	4
448.2.e.a.223.8	yes	8	112.13	odd	4
1792.2.f.k.1791.1		8	1.1	even	1	trivial
1792.2.f.k.1791.1		8	56.13	odd	2	CM
1792.2.f.k.1791.2		8	8.3	odd	2	inner
1792.2.f.k.1791.2		8	28.27	even	2	inner
1792.2.f.k.1791.7		8	4.3	odd	2	inner
1792.2.f.k.1791.7		8	56.27	even	2	inner
1792.2.f.k.1791.8		8	7.6	odd	2	inner
1792.2.f.k.1791.8		8	8.5	even	2	inner
4032.2.p.h.1567.3		8	48.11	even	4
4032.2.p.h.1567.3		8	336.83	odd	4
4032.2.p.h.1567.4		8	48.5	odd	4
4032.2.p.h.1567.4		8	336.125	even	4
4032.2.p.h.1567.5		8	48.35	even	4
4032.2.p.h.1567.5		8	336.251	odd	4
4032.2.p.h.1567.6		8	48.29	odd	4
4032.2.p.h.1567.6		8	336.293	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-3.36028 q^{3} -2.16991i q^{5} -2.64575i q^{7} +8.29150 q^{9} +O(q^{10})\)	\(q-3.36028 q^{3} -2.16991i q^{5} -2.64575i q^{7} +8.29150 q^{9} +4.55066i q^{13} +7.29150i q^{15} -0.979531 q^{19} +8.89047i q^{21} +6.00000i q^{23} +0.291503 q^{25} -17.7809 q^{27} -5.74103 q^{35} -15.2915i q^{39} -17.9918i q^{45} -7.00000 q^{49} +3.29150 q^{57} +14.4207 q^{59} +15.6110i q^{61} -21.9373i q^{63} +9.87451 q^{65} -20.1617i q^{69} +15.8745i q^{71} -0.979531 q^{75} +5.29150i q^{79} +34.8745 q^{81} +1.40122 q^{83} +12.0399 q^{91} +2.12549i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 8 * q + 24 * q^9	\( 8 q + 24 q^{9} - 40 q^{25} - 56 q^{49} - 16 q^{57} - 48 q^{65} + 152 q^{81}+O(q^{100}) \) 8 * q + 24 * q^9 - 40 * q^25 - 56 * q^49 - 16 * q^57 - 48 * q^65 + 152 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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