LMFDB - Embedded newform 1280.3.e.d.639.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(639,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1280.639");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1280.e (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:	$34.8774738381$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			639.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.d.639.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 3.00000i) q^{5} +9.00000 q^{9} +O(q^{10})$	$q+(4.00000 - 3.00000i) q^{5} +9.00000 q^{9} +24.0000 q^{13} +16.0000i q^{17} +(7.00000 - 24.0000i) q^{25} +42.0000i q^{29} -24.0000 q^{37} +18.0000 q^{41} +(36.0000 - 27.0000i) q^{45} -49.0000 q^{49} +56.0000 q^{53} +22.0000i q^{61} +(96.0000 - 72.0000i) q^{65} -96.0000i q^{73} +81.0000 q^{81} +(48.0000 + 64.0000i) q^{85} +78.0000 q^{89} -144.000i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{5} + 18 q^{9}+O(q^{10}) $ 2 * q + 8 * q^5 + 18 * q^9	$ 2 q + 8 q^{5} + 18 q^{9} + 48 q^{13} + 14 q^{25} - 48 q^{37} + 36 q^{41} + 72 q^{45} - 98 q^{49} + 112 q^{53} + 192 q^{65} + 162 q^{81} + 96 q^{85} + 156 q^{89}+O(q^{100}) $ 2 * q + 8 * q^5 + 18 * q^9 + 48 * q^13 + 14 * q^25 - 48 * q^37 + 36 * q^41 + 72 * q^45 - 98 * q^49 + 112 * q^53 + 192 * q^65 + 162 * q^81 + 96 * q^85 + 156 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$		0			0
$5$	4.00000	−	3.00000i	0.800000	−	0.600000i
$5$	4.00000	−	3.00000i	0.800000	−	0.600000i
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	9.00000			1.00000
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	24.0000			1.84615			0.923077	−	0.384615i	$-0.125666\pi$
$13$	24.0000			1.84615			0.923077	+	0.384615i	$0.125666\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			16.0000i			0.941176i	0.882353	+	0.470588i	$0.155958\pi$
$17$			16.0000i			0.941176i	−0.882353	+	0.470588i	$0.844042\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	7.00000	−	24.0000i	0.280000	−	0.960000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			42.0000i			1.44828i	0.689655	+	0.724138i	$0.257762\pi$
$29$			42.0000i			1.44828i	−0.689655	+	0.724138i	$0.742238\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−24.0000			−0.648649			−0.324324	−	0.945946i	$-0.605137\pi$
$37$	−24.0000			−0.648649			−0.324324	+	0.945946i	$0.605137\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	18.0000			0.439024			0.219512	−	0.975610i	$-0.429553\pi$
$41$	18.0000			0.439024			0.219512	+	0.975610i	$0.429553\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	36.0000	−	27.0000i	0.800000	−	0.600000i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	−49.0000			−1.00000
$50$		0			0
$51$		0			0
$52$		0			0
$53$	56.0000			1.05660			0.528302	−	0.849057i	$-0.322829\pi$
$53$	56.0000			1.05660			0.528302	+	0.849057i	$0.322829\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$			22.0000i			0.360656i	0.983607	+	0.180328i	$0.0577159\pi$
$61$			22.0000i			0.360656i	−0.983607	+	0.180328i	$0.942284\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	96.0000	−	72.0000i	1.47692	−	1.10769i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		−	96.0000i		−	1.31507i	−0.753425	−	0.657534i	$-0.771599\pi$
$73$		−	96.0000i		−	1.31507i	0.753425	−	0.657534i	$-0.228401\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	81.0000			1.00000
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	48.0000	+	64.0000i	0.564706	+	0.752941i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	78.0000			0.876404			0.438202	−	0.898876i	$-0.355615\pi$
$89$	78.0000			0.876404			0.438202	+	0.898876i	$0.355615\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	144.000i		−	1.48454i	−0.670103	−	0.742268i	$-0.733750\pi$
$97$		−	144.000i		−	1.48454i	0.670103	−	0.742268i	$-0.266250\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			198.000i			1.96040i	0.198020	+	0.980198i	$0.436549\pi$
$101$			198.000i			1.96040i	−0.198020	+	0.980198i	$0.563451\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$			182.000i			1.66972i	0.550459	+	0.834862i	$0.314453\pi$
$109$			182.000i			1.66972i	−0.550459	+	0.834862i	$0.685547\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	224.000i		−	1.98230i	−0.132743	−	0.991150i	$-0.542379\pi$
$113$		−	224.000i		−	1.98230i	0.132743	−	0.991150i	$-0.457621\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	216.000			1.84615
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−121.000			−1.00000
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−44.0000	−	117.000i	−0.352000	−	0.936000i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	176.000i		−	1.28467i	−0.766423	−	0.642336i	$-0.777965\pi$
$137$		−	176.000i		−	1.28467i	0.766423	−	0.642336i	$-0.222035\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	126.000	+	168.000i	0.868966	+	1.15862i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	102.000i		−	0.684564i	−0.939597	−	0.342282i	$-0.888800\pi$
$149$		−	102.000i		−	0.684564i	0.939597	−	0.342282i	$-0.111200\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$			144.000i			0.941176i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	264.000			1.68153			0.840764	−	0.541401i	$-0.182106\pi$
$157$	264.000			1.68153			0.840764	+	0.541401i	$0.182106\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		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
$169$	407.000			2.40828
$170$		0			0
$171$		0			0
$172$		0			0
$173$	104.000			0.601156			0.300578	−	0.953757i	$-0.402820\pi$
$173$	104.000			0.601156			0.300578	+	0.953757i	$0.402820\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$			38.0000i			0.209945i	0.994475	+	0.104972i	$0.0334754\pi$
$181$			38.0000i			0.209945i	−0.994475	+	0.104972i	$0.966525\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−96.0000	+	72.0000i	−0.518919	+	0.389189i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$			336.000i			1.74093i	0.492228	+	0.870466i	$0.336183\pi$
$193$			336.000i			1.74093i	−0.492228	+	0.870466i	$0.663817\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	56.0000			0.284264			0.142132	−	0.989848i	$-0.454604\pi$
$197$	56.0000			0.284264			0.142132	+	0.989848i	$0.454604\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	72.0000	−	54.0000i	0.351220	−	0.263415i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$			384.000i			1.73756i
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	63.0000	−	216.000i	0.280000	−	0.960000i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		−	442.000i		−	1.93013i	−0.262009	−	0.965066i	$-0.584385\pi$
$229$		−	442.000i		−	1.93013i	0.262009	−	0.965066i	$-0.415615\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	416.000i		−	1.78541i	−0.450644	−	0.892704i	$-0.648806\pi$
$233$		−	416.000i		−	1.78541i	0.450644	−	0.892704i	$-0.351194\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−418.000			−1.73444			−0.867220	−	0.497925i	$-0.834095\pi$
$241$	−418.000			−1.73444			−0.867220	+	0.497925i	$0.834095\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−196.000	+	147.000i	−0.800000	+	0.600000i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	64.0000i		−	0.249027i	−0.992218	−	0.124514i	$-0.960263\pi$
$257$		−	64.0000i		−	0.249027i	0.992218	−	0.124514i	$-0.0397370\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$			378.000i			1.44828i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	224.000	−	168.000i	0.845283	−	0.633962i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	138.000i		−	0.513011i	−0.966543	−	0.256506i	$-0.917429\pi$
$269$		−	138.000i		−	0.513011i	0.966543	−	0.256506i	$-0.0825712\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−504.000			−1.81949			−0.909747	−	0.415162i	$-0.863725\pi$
$277$	−504.000			−1.81949			−0.909747	+	0.415162i	$0.863725\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−462.000			−1.64413			−0.822064	−	0.569395i	$-0.807178\pi$
$281$	−462.000			−1.64413			−0.822064	+	0.569395i	$0.807178\pi$
$282$		0			0
$283$		0			0		1.00000			$0$
$283$		0			0		−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	33.0000			0.114187
$290$		0			0
$291$		0			0
$292$		0			0
$293$	136.000			0.464164			0.232082	−	0.972696i	$-0.425446\pi$
$293$	136.000			0.464164			0.232082	+	0.972696i	$0.425446\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	66.0000	+	88.0000i	0.216393	+	0.288525i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$			624.000i			1.99361i	0.0798722	+	0.996805i	$0.474549\pi$
$313$			624.000i			1.99361i	−0.0798722	+	0.996805i	$0.525451\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−616.000			−1.94322			−0.971609	−	0.236593i	$-0.923969\pi$
$317$	−616.000			−1.94322			−0.971609	+	0.236593i	$0.923969\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	168.000	−	576.000i	0.516923	−	1.77231i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$	−216.000			−0.648649
$334$		0			0
$335$		0			0
$336$		0			0
$337$			576.000i			1.70920i	0.519288	+	0.854599i	$0.326197\pi$
$337$			576.000i			1.70920i	−0.519288	+	0.854599i	$0.673803\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$		0			0
$349$		−	598.000i		−	1.71347i	−0.515759	−	0.856734i	$-0.672490\pi$
$349$		−	598.000i		−	1.71347i	0.515759	−	0.856734i	$-0.327510\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	544.000i		−	1.54108i	−0.637394	−	0.770538i	$-0.719988\pi$
$353$		−	544.000i		−	1.54108i	0.637394	−	0.770538i	$-0.280012\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−361.000			−1.00000
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−288.000	−	384.000i	−0.789041	−	1.05205i
$366$		0			0
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$		0			0
$369$	162.000			0.439024
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−504.000			−1.35121			−0.675603	−	0.737265i	$-0.736117\pi$
$373$	−504.000			−1.35121			−0.675603	+	0.737265i	$0.736117\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1008.00i			2.67374i
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$			378.000i			0.971722i	0.874036	+	0.485861i	$0.161494\pi$
$389$			378.000i			0.971722i	−0.874036	+	0.485861i	$0.838506\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−456.000			−1.14861			−0.574307	−	0.818640i	$-0.694729\pi$
$397$	−456.000			−1.14861			−0.574307	+	0.818640i	$0.694729\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−798.000			−1.99002			−0.995012	−	0.0997506i	$-0.968195\pi$
$401$	−798.000			−1.99002			−0.995012	+	0.0997506i	$0.968195\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	324.000	−	243.000i	0.800000	−	0.600000i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−782.000			−1.91198			−0.955990	−	0.293399i	$-0.905214\pi$
$409$	−782.000			−1.91198			−0.955990	+	0.293399i	$0.905214\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$			58.0000i			0.137767i	0.997625	+	0.0688836i	$0.0219437\pi$
$421$			58.0000i			0.137767i	−0.997625	+	0.0688836i	$0.978056\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	384.000	+	112.000i	0.903529	+	0.263529i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		0			0
$433$			816.000i			1.88453i	0.334873	+	0.942263i	$0.391307\pi$
$433$			816.000i			1.88453i	−0.334873	+	0.942263i	$0.608693\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−441.000			−1.00000
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	312.000	−	234.000i	0.701124	−	0.525843i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	702.000			1.56347			0.781737	−	0.623608i	$-0.214334\pi$
$449$	702.000			1.56347			0.781737	+	0.623608i	$0.214334\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	336.000i		−	0.735230i	−0.929978	−	0.367615i	$-0.880174\pi$
$457$		−	336.000i		−	0.735230i	0.929978	−	0.367615i	$-0.119826\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			522.000i			1.13232i	0.824295	+	0.566161i	$0.191572\pi$
$461$			522.000i			1.13232i	−0.824295	+	0.566161i	$0.808428\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	504.000			1.05660
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$	−576.000			−1.19751
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−432.000	−	576.000i	−0.890722	−	1.18763i
$486$		0			0
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$	−672.000			−1.36308
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$		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
$505$	594.000	+	792.000i	1.17624	+	1.56832i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	918.000i		−	1.80354i	−0.432220	−	0.901768i	$-0.642270\pi$
$509$		−	918.000i		−	1.80354i	0.432220	−	0.901768i	$-0.357730\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	558.000			1.07102			0.535509	−	0.844530i	$-0.320120\pi$
$521$	558.000			1.07102			0.535509	+	0.844530i	$0.320120\pi$
$522$		0			0
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−529.000			−1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$	432.000			0.810507
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$			682.000i			1.26063i	0.776340	+	0.630314i	$0.217074\pi$
$541$			682.000i			1.26063i	−0.776340	+	0.630314i	$0.782926\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	546.000	+	728.000i	1.00183	+	1.33578i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$			198.000i			0.360656i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1064.00			1.91023			0.955117	−	0.296230i	$-0.0957294\pi$
$557$	1064.00			1.91023			0.955117	+	0.296230i	$0.0957294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$	−672.000	−	896.000i	−1.18938	−	1.58584i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−462.000			−0.811951			−0.405975	−	0.913884i	$-0.633068\pi$
$569$	−462.000			−0.811951			−0.405975	+	0.913884i	$0.633068\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$			96.0000i			0.166378i	0.996534	+	0.0831889i	$0.0265105\pi$
$577$			96.0000i			0.166378i	−0.996534	+	0.0831889i	$0.973490\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	864.000	−	648.000i	1.47692	−	1.10769i
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			736.000i			1.24115i	0.784148	+	0.620573i	$0.213100\pi$
$593$			736.000i			1.24115i	−0.784148	+	0.620573i	$0.786900\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	−1102.00			−1.83361			−0.916805	−	0.399334i	$-0.869241\pi$
$601$	−1102.00			−1.83361			−0.916805	+	0.399334i	$0.869241\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−484.000	+	363.000i	−0.800000	+	0.600000i
$606$		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
$613$	−1224.00			−1.99674			−0.998369	−	0.0570962i	$-0.981816\pi$
$613$	−1224.00			−1.99674			−0.998369	+	0.0570962i	$0.981816\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1216.00i		−	1.97083i	−0.170178	−	0.985413i	$-0.554434\pi$
$617$		−	1216.00i		−	1.97083i	0.170178	−	0.985413i	$-0.445566\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−527.000	−	336.000i	−0.843200	−	0.537600i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	384.000i		−	0.610493i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1176.00			−1.84615
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1218.00			−1.90016			−0.950078	−	0.312012i	$-0.898997\pi$
$641$	−1218.00			−1.90016			−0.950078	+	0.312012i	$0.898997\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1144.00			1.75191			0.875957	−	0.482389i	$-0.160231\pi$
$653$	1144.00			1.75191			0.875957	+	0.482389i	$0.160231\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	864.000i		−	1.31507i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$			1178.00i			1.78215i	0.453858	+	0.891074i	$0.350047\pi$
$661$			1178.00i			1.78215i	−0.453858	+	0.891074i	$0.649953\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	1104.00i		−	1.64042i	−0.572065	−	0.820208i	$-0.693858\pi$
$673$		−	1104.00i		−	1.64042i	0.572065	−	0.820208i	$-0.306142\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−104.000			−0.153619			−0.0768095	−	0.997046i	$-0.524473\pi$
$677$	−104.000			−0.153619			−0.0768095	+	0.997046i	$0.524473\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	−528.000	−	704.000i	−0.770803	−	1.02774i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1344.00			1.95065
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$			288.000i			0.413199i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1302.00i			1.85735i	0.370899	+	0.928673i	$0.379050\pi$
$701$			1302.00i			1.85735i	−0.370899	+	0.928673i	$0.620950\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$			518.000i			0.730606i	0.930889	+	0.365303i	$0.119035\pi$
$709$			518.000i			0.730606i	−0.930889	+	0.365303i	$0.880965\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1008.00	+	294.000i	1.39034	+	0.405517i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	729.000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−216.000			−0.294679			−0.147340	−	0.989086i	$-0.547071\pi$
$733$	−216.000			−0.294679			−0.147340	+	0.989086i	$0.547071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	−306.000	−	408.000i	−0.410738	−	0.547651i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	936.000			1.23646			0.618230	−	0.785997i	$-0.287850\pi$
$757$	936.000			1.23646			0.618230	+	0.785997i	$0.287850\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	78.0000			0.102497			0.0512484	−	0.998686i	$-0.483680\pi$
$761$	78.0000			0.102497			0.0512484	+	0.998686i	$0.483680\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	432.000	+	576.000i	0.564706	+	0.752941i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	962.000			1.25098			0.625488	−	0.780234i	$-0.284900\pi$
$769$	962.000			1.25098			0.625488	+	0.780234i	$0.284900\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1496.00			1.93532			0.967658	−	0.252264i	$-0.0811751\pi$
$773$	1496.00			1.93532			0.967658	+	0.252264i	$0.0811751\pi$
$774$		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
$785$	1056.00	−	792.000i	1.34522	−	1.00892i
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$			528.000i			0.665826i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1144.00			1.43538			0.717691	−	0.696361i	$-0.245199\pi$
$797$	1144.00			1.43538			0.717691	+	0.696361i	$0.245199\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	702.000			0.876404
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1518.00			1.87639			0.938195	−	0.346106i	$-0.112496\pi$
$809$	1518.00			1.87639			0.938195	+	0.346106i	$0.112496\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$			858.000i			1.04507i	0.852619	+	0.522533i	$0.175013\pi$
$821$			858.000i			1.04507i	−0.852619	+	0.522533i	$0.824987\pi$
$822$		0			0
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		−	1258.00i		−	1.51749i	−0.651387	−	0.758745i	$-0.725813\pi$
$829$		−	1258.00i		−	1.51749i	0.651387	−	0.758745i	$-0.274187\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	784.000i		−	0.941176i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$		0			0
$841$	−923.000			−1.09750
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1628.00	−	1221.00i	1.92663	−	1.44497i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1656.00			1.94138			0.970692	−	0.240328i	$-0.0772551\pi$
$853$	1656.00			1.94138			0.970692	+	0.240328i	$0.0772551\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			464.000i			0.541424i	0.962660	+	0.270712i	$0.0872590\pi$
$857$			464.000i			0.541424i	−0.962660	+	0.270712i	$0.912741\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	416.000	−	312.000i	0.480925	−	0.360694i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		−	1296.00i		−	1.48454i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−696.000			−0.793615			−0.396807	−	0.917902i	$-0.629882\pi$
$877$	−696.000			−0.793615			−0.396807	+	0.917902i	$0.629882\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−738.000			−0.837684			−0.418842	−	0.908059i	$-0.637564\pi$
$881$	−738.000			−0.837684			−0.418842	+	0.908059i	$0.637564\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$			896.000i			0.994451i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	114.000	+	152.000i	0.125967	+	0.167956i
$906$		0			0
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$		0			0
$909$			1782.00i			1.96040i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−168.000	+	576.000i	−0.181622	+	0.622703i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−258.000			−0.277718			−0.138859	−	0.990312i	$-0.544343\pi$
$929$	−258.000			−0.277718			−0.138859	+	0.990312i	$0.544343\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1824.00i			1.94664i	0.229456	+	0.973319i	$0.426305\pi$
$937$			1824.00i			1.94664i	−0.229456	+	0.973319i	$0.573695\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			1482.00i			1.57492i	0.616366	+	0.787460i	$0.288604\pi$
$941$			1482.00i			1.57492i	−0.616366	+	0.787460i	$0.711396\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$		−	2304.00i		−	2.42782i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1456.00i		−	1.52781i	−0.645331	−	0.763903i	$-0.723280\pi$
$953$		−	1456.00i		−	1.52781i	0.645331	−	0.763903i	$-0.276720\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	961.000			1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1008.00	+	1344.00i	1.04456	+	1.39275i
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$			496.000i			0.507677i	0.967247	+	0.253838i	$0.0816931\pi$
$977$			496.000i			0.507677i	−0.967247	+	0.253838i	$0.918307\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$			1638.00i			1.66972i
$982$		0			0
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$	224.000	−	168.000i	0.227411	−	0.170558i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−744.000			−0.746239			−0.373119	−	0.927783i	$-0.621712\pi$
$997$	−744.000			−0.746239			−0.373119	+	0.927783i	$0.621712\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.d.639.1		2
4.3	odd	2	CM	1280.3.e.d.639.1		2
5.4	even	2		1280.3.e.a.639.1		2
8.3	odd	2		1280.3.e.a.639.2		2
8.5	even	2		1280.3.e.a.639.2		2
16.3	odd	4		320.3.h.d.319.1		2
16.5	even	4		20.3.d.c.19.1	✓	2
16.11	odd	4		20.3.d.c.19.1	✓	2
16.13	even	4		320.3.h.d.319.1		2
20.19	odd	2		1280.3.e.a.639.1		2
40.19	odd	2	inner	1280.3.e.d.639.2		2
40.29	even	2	inner	1280.3.e.d.639.2		2
48.5	odd	4		180.3.f.c.19.2		2
48.11	even	4		180.3.f.c.19.2		2
80.3	even	4		1600.3.b.a.1151.1		1
80.13	odd	4		1600.3.b.a.1151.1		1
80.19	odd	4		320.3.h.d.319.2		2
80.27	even	4		100.3.b.b.51.1		1
80.29	even	4		320.3.h.d.319.2		2
80.37	odd	4		100.3.b.b.51.1		1
80.43	even	4		100.3.b.a.51.1		1
80.53	odd	4		100.3.b.a.51.1		1
80.59	odd	4		20.3.d.c.19.2	yes	2
80.67	even	4		1600.3.b.c.1151.1		1
80.69	even	4		20.3.d.c.19.2	yes	2
80.77	odd	4		1600.3.b.c.1151.1		1
240.53	even	4		900.3.c.d.451.1		1
240.59	even	4		180.3.f.c.19.1		2
240.107	odd	4		900.3.c.a.451.1		1
240.149	odd	4		180.3.f.c.19.1		2
240.197	even	4		900.3.c.a.451.1		1
240.203	odd	4		900.3.c.d.451.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.d.c.19.1	✓	2	16.5	even	4
20.3.d.c.19.1	✓	2	16.11	odd	4
20.3.d.c.19.2	yes	2	80.59	odd	4
20.3.d.c.19.2	yes	2	80.69	even	4
100.3.b.a.51.1		1	80.43	even	4
100.3.b.a.51.1		1	80.53	odd	4
100.3.b.b.51.1		1	80.27	even	4
100.3.b.b.51.1		1	80.37	odd	4
180.3.f.c.19.1		2	240.59	even	4
180.3.f.c.19.1		2	240.149	odd	4
180.3.f.c.19.2		2	48.5	odd	4
180.3.f.c.19.2		2	48.11	even	4
320.3.h.d.319.1		2	16.3	odd	4
320.3.h.d.319.1		2	16.13	even	4
320.3.h.d.319.2		2	80.19	odd	4
320.3.h.d.319.2		2	80.29	even	4
900.3.c.a.451.1		1	240.107	odd	4
900.3.c.a.451.1		1	240.197	even	4
900.3.c.d.451.1		1	240.53	even	4
900.3.c.d.451.1		1	240.203	odd	4
1280.3.e.a.639.1		2	5.4	even	2
1280.3.e.a.639.1		2	20.19	odd	2
1280.3.e.a.639.2		2	8.3	odd	2
1280.3.e.a.639.2		2	8.5	even	2
1280.3.e.d.639.1		2	1.1	even	1	trivial
1280.3.e.d.639.1		2	4.3	odd	2	CM
1280.3.e.d.639.2		2	40.19	odd	2	inner
1280.3.e.d.639.2		2	40.29	even	2	inner
1600.3.b.a.1151.1		1	80.3	even	4
1600.3.b.a.1151.1		1	80.13	odd	4
1600.3.b.c.1151.1		1	80.67	even	4
1600.3.b.c.1151.1		1	80.77	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 3.00000i) q^{5} +9.00000 q^{9} +O(q^{10})\)	\(q+(4.00000 - 3.00000i) q^{5} +9.00000 q^{9} +24.0000 q^{13} +16.0000i q^{17} +(7.00000 - 24.0000i) q^{25} +42.0000i q^{29} -24.0000 q^{37} +18.0000 q^{41} +(36.0000 - 27.0000i) q^{45} -49.0000 q^{49} +56.0000 q^{53} +22.0000i q^{61} +(96.0000 - 72.0000i) q^{65} -96.0000i q^{73} +81.0000 q^{81} +(48.0000 + 64.0000i) q^{85} +78.0000 q^{89} -144.000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{5} + 18 q^{9}+O(q^{10}) \) 2 * q + 8 * q^5 + 18 * q^9	\( 2 q + 8 q^{5} + 18 q^{9} + 48 q^{13} + 14 q^{25} - 48 q^{37} + 36 q^{41} + 72 q^{45} - 98 q^{49} + 112 q^{53} + 192 q^{65} + 162 q^{81} + 96 q^{85} + 156 q^{89}+O(q^{100}) \) 2 * q + 8 * q^5 + 18 * q^9 + 48 * q^13 + 14 * q^25 - 48 * q^37 + 36 * q^41 + 72 * q^45 - 98 * q^49 + 112 * q^53 + 192 * q^65 + 162 * q^81 + 96 * q^85 + 156 * q^89

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