LMFDB - Embedded newform 1280.2.c.j.769.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(769,1280)]

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([0, 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("1280.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.c (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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 6x^{2} + 4 $ x^4 + 6*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			769.4
Root			$2.28825i$ of defining polynomial
Character	$\chi$	$=$	1280.769
Dual form			1280.2.c.j.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{3} +2.23607 q^{5} -3.16228i q^{7} +1.00000 q^{9} +O(q^{10})$	$q+1.41421i q^{3} +2.23607 q^{5} -3.16228i q^{7} +1.00000 q^{9} +3.16228i q^{15} +4.47214 q^{21} -9.48683i q^{23} +5.00000 q^{25} +5.65685i q^{27} +8.94427 q^{29} -7.07107i q^{35} -12.0000 q^{41} -12.7279i q^{43} +2.23607 q^{45} +9.48683i q^{47} -3.00000 q^{49} +13.4164 q^{61} -3.16228i q^{63} +4.24264i q^{67} +13.4164 q^{69} +7.07107i q^{75} -5.00000 q^{81} +15.5563i q^{83} +12.6491i q^{87} +6.00000 q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^9	$ 4 q + 4 q^{9} + 20 q^{25} - 48 q^{41} - 12 q^{49} - 20 q^{81} + 24 q^{89}+O(q^{100}) $ 4 * q + 4 * q^9 + 20 * q^25 - 48 * q^41 - 12 * q^49 - 20 * q^81 + 24 * 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
$3$	1.41421i	0.816497i	0.912871	+	0.408248i	$0.133860\pi$
$3$	1.41421i	0.816497i	−0.912871	+	0.408248i	$0.866140\pi$
$4$	0	0
$5$	2.23607	1.00000
$5$	2.23607	1.00000
$6$	0	0
$7$	− 3.16228i	− 1.19523i	−0.801784	−	0.597614i	$-0.796115\pi$
$7$	− 3.16228i	− 1.19523i	0.801784	−	0.597614i	$-0.203885\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	3.16228i	0.816497i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	4.47214	0.975900
$22$	0	0
$23$	− 9.48683i	− 1.97814i	−0.147442	−	0.989071i	$-0.547104\pi$
$23$	− 9.48683i	− 1.97814i	0.147442	−	0.989071i	$-0.452896\pi$
$24$	0	0
$25$	5.00000	1.00000
$26$	0	0
$27$	5.65685i	1.08866i
$28$	0	0
$29$	8.94427	1.66091	0.830455	−	0.557086i	$-0.188081\pi$
$29$	8.94427	1.66091	0.830455	+	0.557086i	$0.188081\pi$
$30$	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
$35$	− 7.07107i	− 1.19523i
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	− 12.7279i	− 1.94099i	−0.241121	−	0.970495i	$-0.577515\pi$
$43$	− 12.7279i	− 1.94099i	0.241121	−	0.970495i	$-0.422485\pi$
$44$	0	0
$45$	2.23607	0.333333
$46$	0	0
$47$	9.48683i	1.38380i	0.721995	+	0.691898i	$0.243225\pi$
$47$	9.48683i	1.38380i	−0.721995	+	0.691898i	$0.756775\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	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
$61$	13.4164	1.71780	0.858898	−	0.512148i	$-0.171150\pi$
$61$	13.4164	1.71780	0.858898	+	0.512148i	$0.171150\pi$
$62$	0	0
$63$	− 3.16228i	− 0.398410i
$64$	0	0
$65$	0	0
$66$	0	0
$67$	4.24264i	0.518321i	0.965834	+	0.259161i	$0.0834459\pi$
$67$	4.24264i	0.518321i	−0.965834	+	0.259161i	$0.916554\pi$
$68$	0	0
$69$	13.4164	1.61515
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	7.07107i	0.816497i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	−5.00000	−0.555556
$82$	0	0
$83$	15.5563i	1.70753i	0.520658	+	0.853766i	$0.325687\pi$
$83$	15.5563i	1.70753i	−0.520658	+	0.853766i	$0.674313\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	12.6491i	1.35613i
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	8.94427	0.889988	0.444994	−	0.895533i	$-0.353206\pi$
$101$	8.94427	0.889988	0.444994	+	0.895533i	$0.353206\pi$
$102$	0	0
$103$	15.8114i	1.55794i	0.627060	+	0.778971i	$0.284258\pi$
$103$	15.8114i	1.55794i	−0.627060	+	0.778971i	$0.715742\pi$
$104$	0	0
$105$	10.0000	0.975900
$106$	0	0
$107$	18.3848i	1.77732i	0.458563	+	0.888662i	$0.348364\pi$
$107$	18.3848i	1.77732i	−0.458563	+	0.888662i	$0.651636\pi$
$108$	0	0
$109$	−13.4164	−1.28506	−0.642529	−	0.766261i	$-0.722115\pi$
$109$	−13.4164	−1.28506	−0.642529	+	0.766261i	$0.722115\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	− 21.2132i	− 1.97814i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	− 16.9706i	− 1.53018i
$124$	0	0
$125$	11.1803	1.00000
$126$	0	0
$127$	− 22.1359i	− 1.96425i	−0.188237	−	0.982124i	$-0.560277\pi$
$127$	− 22.1359i	− 1.96425i	0.188237	−	0.982124i	$-0.439723\pi$
$128$	0	0
$129$	18.0000	1.58481
$130$	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
$135$	12.6491i	1.08866i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−13.4164	−1.12987
$142$	0	0
$143$	0	0
$144$	0	0
$145$	20.0000	1.66091
$146$	0	0
$147$	− 4.24264i	− 0.349927i
$148$	0	0
$149$	−4.47214	−0.366372	−0.183186	−	0.983078i	$-0.558641\pi$
$149$	−4.47214	−0.366372	−0.183186	+	0.983078i	$0.558641\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−30.0000	−2.36433
$162$	0	0
$163$	12.7279i	0.996928i	0.866910	+	0.498464i	$0.166102\pi$
$163$	12.7279i	0.996928i	−0.866910	+	0.498464i	$0.833898\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	− 9.48683i	− 0.734113i	−0.930199	−	0.367057i	$-0.880366\pi$
$167$	− 9.48683i	− 0.734113i	0.930199	−	0.367057i	$-0.119634\pi$
$168$	0	0
$169$	13.0000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	− 15.8114i	− 1.19523i
$176$	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
$181$	−26.8328	−1.99447	−0.997234	−	0.0743294i	$-0.976318\pi$
$181$	−26.8328	−1.99447	−0.997234	+	0.0743294i	$0.976318\pi$
$182$	0	0
$183$	18.9737i	1.40257i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	17.8885	1.30120
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−6.00000	−0.423207
$202$	0	0
$203$	− 28.2843i	− 1.98517i
$204$	0	0
$205$	−26.8328	−1.87409
$206$	0	0
$207$	− 9.48683i	− 0.659380i
$208$	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
$215$	− 28.4605i	− 1.94099i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	3.16228i	0.211762i	0.994379	+	0.105881i	$0.0337662\pi$
$223$	3.16228i	0.211762i	−0.994379	+	0.105881i	$0.966234\pi$
$224$	0	0
$225$	5.00000	0.333333
$226$	0	0
$227$	− 9.89949i	− 0.657053i	−0.944495	−	0.328526i	$-0.893448\pi$
$227$	− 9.89949i	− 0.657053i	0.944495	−	0.328526i	$-0.106552\pi$
$228$	0	0
$229$	−26.8328	−1.77316	−0.886581	−	0.462573i	$-0.846926\pi$
$229$	−26.8328	−1.77316	−0.886581	+	0.462573i	$0.846926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	21.2132i	1.38380i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	0	0
$243$	9.89949i	0.635053i
$244$	0	0
$245$	−6.70820	−0.428571
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−22.0000	−1.39419
$250$	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
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	8.94427	0.553637
$262$	0	0
$263$	− 28.4605i	− 1.75495i	−0.479623	−	0.877475i	$-0.659226\pi$
$263$	− 28.4605i	− 1.75495i	0.479623	−	0.877475i	$-0.340774\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	8.48528i	0.519291i
$268$	0	0
$269$	−22.3607	−1.36335	−0.681677	−	0.731653i	$-0.738749\pi$
$269$	−22.3607	−1.36335	−0.681677	+	0.731653i	$0.738749\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	29.6985i	1.76539i	0.469945	+	0.882696i	$0.344274\pi$
$283$	29.6985i	1.76539i	−0.469945	+	0.882696i	$0.655726\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	37.9473i	2.23996i
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−40.2492	−2.31993
$302$	0	0
$303$	12.6491i	0.726672i
$304$	0	0
$305$	30.0000	1.71780
$306$	0	0
$307$	4.24264i	0.242140i	0.992644	+	0.121070i	$0.0386326\pi$
$307$	4.24264i	0.242140i	−0.992644	+	0.121070i	$0.961367\pi$
$308$	0	0
$309$	−22.3607	−1.27205
$310$	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
$315$	− 7.07107i	− 0.398410i
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−26.0000	−1.45118
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	− 18.9737i	− 1.04925i
$328$	0	0
$329$	30.0000	1.65395
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	9.48683i	0.518321i
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 12.6491i	− 0.682988i
$344$	0	0
$345$	30.0000	1.61515
$346$	0	0
$347$	− 24.0416i	− 1.29062i	−0.763920	−	0.645311i	$-0.776728\pi$
$347$	− 24.0416i	− 1.29062i	0.763920	−	0.645311i	$-0.223272\pi$
$348$	0	0
$349$	−26.8328	−1.43633	−0.718164	−	0.695874i	$-0.755017\pi$
$349$	−26.8328	−1.43633	−0.718164	+	0.695874i	$0.755017\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	− 15.5563i	− 0.816497i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	3.16228i	0.165070i	0.996588	+	0.0825348i	$0.0263016\pi$
$367$	3.16228i	0.165070i	−0.996588	+	0.0825348i	$0.973698\pi$
$368$	0	0
$369$	−12.0000	−0.624695
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	15.8114i	0.816497i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	31.3050	1.60380
$382$	0	0
$383$	28.4605i	1.45426i	0.686498	+	0.727132i	$0.259147\pi$
$383$	28.4605i	1.45426i	−0.686498	+	0.727132i	$0.740853\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	− 12.7279i	− 0.646997i
$388$	0	0
$389$	31.3050	1.58722	0.793612	−	0.608424i	$-0.208198\pi$
$389$	31.3050	1.58722	0.793612	+	0.608424i	$0.208198\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−11.1803	−0.555556
$406$	0	0
$407$	0	0
$408$	0	0
$409$	4.00000	0.197787	0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000	0.197787	0.0988936	+	0.995098i	$0.468470\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	34.7851i	1.70753i
$416$	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
$421$	−40.2492	−1.96163	−0.980814	−	0.194948i	$-0.937546\pi$
$421$	−40.2492	−1.96163	−0.980814	+	0.194948i	$0.937546\pi$
$422$	0	0
$423$	9.48683i	0.461266i
$424$	0	0
$425$	0	0
$426$	0	0
$427$	− 42.4264i	− 2.05316i
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	28.2843i	1.35613i
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	41.0122i	1.94855i	0.225367	+	0.974274i	$0.427642\pi$
$443$	41.0122i	1.94855i	−0.225367	+	0.974274i	$0.572358\pi$
$444$	0	0
$445$	13.4164	0.635999
$446$	0	0
$447$	− 6.32456i	− 0.299141i
$448$	0	0
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	8.94427	0.416576	0.208288	−	0.978068i	$-0.433211\pi$
$461$	8.94427	0.416576	0.208288	+	0.978068i	$0.433211\pi$
$462$	0	0
$463$	− 41.1096i	− 1.91053i	−0.295758	−	0.955263i	$-0.595572\pi$
$463$	− 41.1096i	− 1.91053i	0.295758	−	0.955263i	$-0.404428\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 32.5269i	− 1.50517i	−0.658497	−	0.752583i	$-0.728808\pi$
$467$	− 32.5269i	− 1.50517i	0.658497	−	0.752583i	$-0.271192\pi$
$468$	0	0
$469$	13.4164	0.619512
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	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
$483$	− 42.4264i	− 1.93047i
$484$	0	0
$485$	0	0
$486$	0	0
$487$	22.1359i	1.00308i	0.865136	+	0.501538i	$0.167232\pi$
$487$	22.1359i	1.00308i	−0.865136	+	0.501538i	$0.832768\pi$
$488$	0	0
$489$	−18.0000	−0.813988
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	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
$501$	13.4164	0.599401
$502$	0	0
$503$	− 9.48683i	− 0.422997i	−0.977378	−	0.211498i	$-0.932166\pi$
$503$	− 9.48683i	− 0.422997i	0.977378	−	0.211498i	$-0.0678343\pi$
$504$	0	0
$505$	20.0000	0.889988
$506$	0	0
$507$	18.3848i	0.816497i
$508$	0	0
$509$	44.7214	1.98224	0.991120	−	0.132973i	$-0.0424523\pi$
$509$	44.7214	1.98224	0.991120	+	0.132973i	$0.0424523\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	35.3553i	1.55794i
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	29.6985i	1.29862i	0.760522	+	0.649312i	$0.224943\pi$
$523$	29.6985i	1.29862i	−0.760522	+	0.649312i	$0.775057\pi$
$524$	0	0
$525$	22.3607	0.975900
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−67.0000	−2.91304
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	41.1096i	1.77732i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−26.8328	−1.15363	−0.576816	−	0.816874i	$-0.695705\pi$
$541$	−26.8328	−1.15363	−0.576816	+	0.816874i	$0.695705\pi$
$542$	0	0
$543$	− 37.9473i	− 1.62848i
$544$	0	0
$545$	−30.0000	−1.28506
$546$	0	0
$547$	46.6690i	1.99542i	0.0676046	+	0.997712i	$0.478464\pi$
$547$	46.6690i	1.99542i	−0.0676046	+	0.997712i	$0.521536\pi$
$548$	0	0
$549$	13.4164	0.572598
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	1.41421i	0.0596020i	0.999556	+	0.0298010i	$0.00948736\pi$
$563$	1.41421i	0.0596020i	−0.999556	+	0.0298010i	$0.990513\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	15.8114i	0.664016i
$568$	0	0
$569$	36.0000	1.50920	0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000	1.50920	0.754599	+	0.656186i	$0.227831\pi$
$570$	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
$575$	− 47.4342i	− 1.97814i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	49.1935	2.04089
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	9.89949i	0.408596i	0.978909	+	0.204298i	$0.0654911\pi$
$587$	9.89949i	0.408596i	−0.978909	+	0.204298i	$0.934509\pi$
$588$	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
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	0	0
$603$	4.24264i	0.172774i
$604$	0	0
$605$	−24.5967	−1.00000
$606$	0	0
$607$	− 15.8114i	− 0.641764i	−0.947119	−	0.320882i	$-0.896021\pi$
$607$	− 15.8114i	− 0.641764i	0.947119	−	0.320882i	$-0.103979\pi$
$608$	0	0
$609$	40.0000	1.62088
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	− 37.9473i	− 1.53018i
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	53.6656	2.15353
$622$	0	0
$623$	− 18.9737i	− 0.760164i
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	− 49.4975i	− 1.96425i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	− 29.6985i	− 1.17119i	−0.810602	−	0.585597i	$-0.800860\pi$
$643$	− 29.6985i	− 1.17119i	0.810602	−	0.585597i	$-0.199140\pi$
$644$	0	0
$645$	40.2492	1.58481
$646$	0	0
$647$	47.4342i	1.86483i	0.361390	+	0.932415i	$0.382302\pi$
$647$	47.4342i	1.86483i	−0.361390	+	0.932415i	$0.617698\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	40.2492	1.56551	0.782757	−	0.622328i	$-0.213813\pi$
$661$	40.2492	1.56551	0.782757	+	0.622328i	$0.213813\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	− 84.8528i	− 3.28551i
$668$	0	0
$669$	−4.47214	−0.172903
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	28.2843i	1.08866i
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	14.0000	0.536481
$682$	0	0
$683$	43.8406i	1.67751i	0.544505	+	0.838757i	$0.316717\pi$
$683$	43.8406i	1.67751i	−0.544505	+	0.838757i	$0.683283\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	− 37.9473i	− 1.44778i
$688$	0	0
$689$	0	0
$690$	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
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	22.3607	0.844551	0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607	0.844551	0.422276	+	0.906467i	$0.361231\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−30.0000	−1.12987
$706$	0	0
$707$	− 28.2843i	− 1.06374i
$708$	0	0
$709$	−26.8328	−1.00773	−0.503864	−	0.863783i	$-0.668089\pi$
$709$	−26.8328	−1.00773	−0.503864	+	0.863783i	$0.668089\pi$
$710$	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		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	50.0000	1.86210
$722$	0	0
$723$	− 39.5980i	− 1.47266i
$724$	0	0
$725$	44.7214	1.66091
$726$	0	0
$727$	− 53.7587i	− 1.99380i	−0.0786754	−	0.996900i	$-0.525069\pi$
$727$	− 53.7587i	− 1.99380i	0.0786754	−	0.996900i	$-0.474931\pi$
$728$	0	0
$729$	−29.0000	−1.07407
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	− 9.48683i	− 0.349927i
$736$	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
$743$	47.4342i	1.74019i	0.492883	+	0.870095i	$0.335943\pi$
$743$	47.4342i	1.74019i	−0.492883	+	0.870095i	$0.664057\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	0	0
$747$	15.5563i	0.569177i
$748$	0	0
$749$	58.1378	2.12431
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	42.4264i	1.53594i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	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
$783$	50.5964i	1.80817i
$784$	0	0
$785$	0	0
$786$	0	0
$787$	38.1838i	1.36110i	0.732700	+	0.680552i	$0.238260\pi$
$787$	38.1838i	1.36110i	−0.732700	+	0.680552i	$0.761740\pi$
$788$	0	0
$789$	40.2492	1.43291
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	6.00000	0.212000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−67.0820	−2.36433
$806$	0	0
$807$	− 31.6228i	− 1.11317i
$808$	0	0
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	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
$815$	28.4605i	0.996928i
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−31.3050	−1.09255	−0.546275	−	0.837606i	$-0.683955\pi$
$821$	−31.3050	−1.09255	−0.546275	+	0.837606i	$0.683955\pi$
$822$	0	0
$823$	15.8114i	0.551150i	0.961280	+	0.275575i	$0.0888683\pi$
$823$	15.8114i	0.551150i	−0.961280	+	0.275575i	$0.911132\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	32.5269i	1.13107i	0.824724	+	0.565536i	$0.191331\pi$
$827$	32.5269i	1.13107i	−0.824724	+	0.565536i	$0.808669\pi$
$828$	0	0
$829$	13.4164	0.465971	0.232986	−	0.972480i	$-0.425151\pi$
$829$	13.4164	0.465971	0.232986	+	0.972480i	$0.425151\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	− 21.2132i	− 0.734113i
$836$	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
$841$	51.0000	1.75862
$842$	0	0
$843$	− 16.9706i	− 0.584497i
$844$	0	0
$845$	29.0689	1.00000
$846$	0	0
$847$	34.7851i	1.19523i
$848$	0	0
$849$	−42.0000	−1.44144
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	−53.6656	−1.82892
$862$	0	0
$863$	9.48683i	0.322936i	0.986878	+	0.161468i	$0.0516228\pi$
$863$	9.48683i	0.322936i	−0.986878	+	0.161468i	$0.948377\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	24.0416i	0.816497i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	− 35.3553i	− 1.19523i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	0	0
$883$	− 55.1543i	− 1.85609i	−0.372467	−	0.928045i	$-0.621488\pi$
$883$	− 55.1543i	− 1.85609i	0.372467	−	0.928045i	$-0.378512\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	− 28.4605i	− 0.955610i	−0.878466	−	0.477805i	$-0.841433\pi$
$887$	− 28.4605i	− 0.955610i	0.878466	−	0.477805i	$-0.158567\pi$
$888$	0	0
$889$	−70.0000	−2.34772
$890$	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
$901$	0	0
$902$	0	0
$903$	− 56.9210i	− 1.89421i
$904$	0	0
$905$	−60.0000	−1.99447
$906$	0	0
$907$	− 4.24264i	− 0.140875i	−0.997516	−	0.0704373i	$-0.977561\pi$
$907$	− 4.24264i	− 0.140875i	0.997516	−	0.0704373i	$-0.0224395\pi$
$908$	0	0
$909$	8.94427	0.296663
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	42.4264i	1.40257i
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−6.00000	−0.197707
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	15.8114i	0.519314i
$928$	0	0
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	0	0
$931$	0	0
$932$	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
$941$	44.7214	1.45787	0.728937	−	0.684580i	$-0.240015\pi$
$941$	44.7214	1.45787	0.728937	+	0.684580i	$0.240015\pi$
$942$	0	0
$943$	113.842i	3.70721i
$944$	0	0
$945$	40.0000	1.30120
$946$	0	0
$947$	60.8112i	1.97610i	0.154140	+	0.988049i	$0.450739\pi$
$947$	60.8112i	1.97610i	−0.154140	+	0.988049i	$0.549261\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	18.3848i	0.592441i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	41.1096i	1.32200i	0.750388	+	0.660998i	$0.229867\pi$
$967$	41.1096i	1.32200i	−0.750388	+	0.660998i	$0.770133\pi$
$968$	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
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−13.4164	−0.428353
$982$	0	0
$983$	47.4342i	1.51291i	0.654043	+	0.756457i	$0.273072\pi$
$983$	47.4342i	1.51291i	−0.654043	+	0.756457i	$0.726928\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	42.4264i	1.35045i
$988$	0	0
$989$	−120.748	−3.83955
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.c.j.769.4		4
4.3	odd	2	inner	1280.2.c.j.769.2		4
5.2	odd	4		6400.2.a.cn.1.4		4
5.3	odd	4		6400.2.a.cn.1.1		4
5.4	even	2	inner	1280.2.c.j.769.2		4
8.3	odd	2	inner	1280.2.c.j.769.3		4
8.5	even	2	inner	1280.2.c.j.769.1		4
16.3	odd	4		640.2.f.e.449.3	yes	4
16.5	even	4		640.2.f.e.449.4	yes	4
16.11	odd	4		640.2.f.e.449.2	yes	4
16.13	even	4		640.2.f.e.449.1	✓	4
20.3	even	4		6400.2.a.cn.1.4		4
20.7	even	4		6400.2.a.cn.1.1		4
20.19	odd	2	CM	1280.2.c.j.769.4		4
40.3	even	4		6400.2.a.cn.1.2		4
40.13	odd	4		6400.2.a.cn.1.3		4
40.19	odd	2	inner	1280.2.c.j.769.1		4
40.27	even	4		6400.2.a.cn.1.3		4
40.29	even	2	inner	1280.2.c.j.769.3		4
40.37	odd	4		6400.2.a.cn.1.2		4
80.3	even	4		3200.2.d.u.1601.3		4
80.13	odd	4		3200.2.d.u.1601.2		4
80.19	odd	4		640.2.f.e.449.1	✓	4
80.27	even	4		3200.2.d.u.1601.4		4
80.29	even	4		640.2.f.e.449.3	yes	4
80.37	odd	4		3200.2.d.u.1601.1		4
80.43	even	4		3200.2.d.u.1601.1		4
80.53	odd	4		3200.2.d.u.1601.4		4
80.59	odd	4		640.2.f.e.449.4	yes	4
80.67	even	4		3200.2.d.u.1601.2		4
80.69	even	4		640.2.f.e.449.2	yes	4
80.77	odd	4		3200.2.d.u.1601.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.f.e.449.1	✓	4	16.13	even	4
640.2.f.e.449.1	✓	4	80.19	odd	4
640.2.f.e.449.2	yes	4	16.11	odd	4
640.2.f.e.449.2	yes	4	80.69	even	4
640.2.f.e.449.3	yes	4	16.3	odd	4
640.2.f.e.449.3	yes	4	80.29	even	4
640.2.f.e.449.4	yes	4	16.5	even	4
640.2.f.e.449.4	yes	4	80.59	odd	4
1280.2.c.j.769.1		4	8.5	even	2	inner
1280.2.c.j.769.1		4	40.19	odd	2	inner
1280.2.c.j.769.2		4	4.3	odd	2	inner
1280.2.c.j.769.2		4	5.4	even	2	inner
1280.2.c.j.769.3		4	8.3	odd	2	inner
1280.2.c.j.769.3		4	40.29	even	2	inner
1280.2.c.j.769.4		4	1.1	even	1	trivial
1280.2.c.j.769.4		4	20.19	odd	2	CM
3200.2.d.u.1601.1		4	80.37	odd	4
3200.2.d.u.1601.1		4	80.43	even	4
3200.2.d.u.1601.2		4	80.13	odd	4
3200.2.d.u.1601.2		4	80.67	even	4
3200.2.d.u.1601.3		4	80.3	even	4
3200.2.d.u.1601.3		4	80.77	odd	4
3200.2.d.u.1601.4		4	80.27	even	4
3200.2.d.u.1601.4		4	80.53	odd	4
6400.2.a.cn.1.1		4	5.3	odd	4
6400.2.a.cn.1.1		4	20.7	even	4
6400.2.a.cn.1.2		4	40.3	even	4
6400.2.a.cn.1.2		4	40.37	odd	4
6400.2.a.cn.1.3		4	40.13	odd	4
6400.2.a.cn.1.3		4	40.27	even	4
6400.2.a.cn.1.4		4	5.2	odd	4
6400.2.a.cn.1.4		4	20.3	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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{3} +2.23607 q^{5} -3.16228i q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{3} +2.23607 q^{5} -3.16228i q^{7} +1.00000 q^{9} +3.16228i q^{15} +4.47214 q^{21} -9.48683i q^{23} +5.00000 q^{25} +5.65685i q^{27} +8.94427 q^{29} -7.07107i q^{35} -12.0000 q^{41} -12.7279i q^{43} +2.23607 q^{45} +9.48683i q^{47} -3.00000 q^{49} +13.4164 q^{61} -3.16228i q^{63} +4.24264i q^{67} +13.4164 q^{69} +7.07107i q^{75} -5.00000 q^{81} +15.5563i q^{83} +12.6491i q^{87} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^9	\( 4 q + 4 q^{9} + 20 q^{25} - 48 q^{41} - 12 q^{49} - 20 q^{81} + 24 q^{89}+O(q^{100}) \) 4 * q + 4 * q^9 + 20 * q^25 - 48 * q^41 - 12 * q^49 - 20 * q^81 + 24 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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