LMFDB - Embedded newform 1280.2.f.g.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(129,1280)]

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, 1, 1]))

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

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

chi := DirichletCharacter("1280.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			129.2
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1280.129
Dual form			1280.2.f.g.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.23607 q^{3} +2.23607i q^{5} -0.763932i q^{7} +7.47214 q^{9} +O(q^{10})$	$q-3.23607 q^{3} +2.23607i q^{5} -0.763932i q^{7} +7.47214 q^{9} -7.23607i q^{15} +2.47214i q^{21} -5.70820i q^{23} -5.00000 q^{25} -14.4721 q^{27} -6.00000i q^{29} +1.70820 q^{35} +4.47214 q^{41} +11.2361 q^{43} +16.7082i q^{45} +13.7082i q^{47} +6.41641 q^{49} +13.4164i q^{61} -5.70820i q^{63} -8.18034 q^{67} +18.4721i q^{69} +16.1803 q^{75} +24.4164 q^{81} +17.7082 q^{83} +19.4164i q^{87} +6.00000 q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 12 * q^9	$ 4 q - 4 q^{3} + 12 q^{9} - 20 q^{25} - 40 q^{27} - 20 q^{35} + 36 q^{43} - 28 q^{49} + 12 q^{67} + 20 q^{75} + 44 q^{81} + 44 q^{83} + 24 q^{89}+O(q^{100}) $ 4 * q - 4 * q^3 + 12 * q^9 - 20 * q^25 - 40 * q^27 - 20 * q^35 + 36 * q^43 - 28 * q^49 + 12 * q^67 + 20 * q^75 + 44 * q^81 + 44 * q^83 + 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
$3$	−3.23607	−1.86834	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−3.23607	−1.86834	−0.934172	+	0.356822i	$0.883860\pi$
$4$	0	0
$5$	2.23607i	1.00000i
$5$	2.23607i	1.00000i
$6$	0	0
$7$	− 0.763932i	− 0.288739i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	− 0.763932i	− 0.288739i	0.989524	−	0.144370i	$-0.0461154\pi$
$8$	0	0
$9$	7.47214	2.49071
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	− 7.23607i	− 1.86834i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	2.47214i	0.539464i
$22$	0	0
$23$	− 5.70820i	− 1.19024i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	− 5.70820i	− 1.19024i	0.803636	−	0.595121i	$-0.202896\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	−14.4721	−2.78516
$28$	0	0
$29$	− 6.00000i	− 1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$	− 6.00000i	− 1.11417i	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
$35$	1.70820	0.288739
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	4.47214	0.698430	0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214	0.698430	0.349215	+	0.937043i	$0.386448\pi$
$42$	0	0
$43$	11.2361	1.71348	0.856742	−	0.515745i	$-0.172485\pi$
$43$	11.2361	1.71348	0.856742	+	0.515745i	$0.172485\pi$
$44$	0	0
$45$	16.7082i	2.49071i
$46$	0	0
$47$	13.7082i	1.99955i	0.0212814	+	0.999774i	$0.493225\pi$
$47$	13.7082i	1.99955i	−0.0212814	+	0.999774i	$0.506775\pi$
$48$	0	0
$49$	6.41641	0.916630
$50$	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
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	13.4164i	1.71780i	0.512148	+	0.858898i	$0.328850\pi$
$61$	13.4164i	1.71780i	−0.512148	+	0.858898i	$0.671150\pi$
$62$	0	0
$63$	− 5.70820i	− 0.719166i
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−8.18034	−0.999388	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	−8.18034	−0.999388	−0.499694	+	0.866202i	$0.666554\pi$
$68$	0	0
$69$	18.4721i	2.22378i
$70$	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
$75$	16.1803	1.86834
$76$	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
$81$	24.4164	2.71293
$82$	0	0
$83$	17.7082	1.94373	0.971864	−	0.235543i	$-0.0756868\pi$
$83$	17.7082	1.94373	0.971864	+	0.235543i	$0.0756868\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	19.4164i	2.08166i
$88$	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
$101$	− 18.0000i	− 1.79107i	−0.444994	−	0.895533i	$-0.646794\pi$
$101$	− 18.0000i	− 1.79107i	0.444994	−	0.895533i	$-0.353206\pi$
$102$	0	0
$103$	20.1803i	1.98843i	0.107418	+	0.994214i	$0.465742\pi$
$103$	20.1803i	1.98843i	−0.107418	+	0.994214i	$0.534258\pi$
$104$	0	0
$105$	−5.52786	−0.539464
$106$	0	0
$107$	6.29180	0.608251	0.304125	−	0.952632i	$-0.401636\pi$
$107$	6.29180	0.608251	0.304125	+	0.952632i	$0.401636\pi$
$108$	0	0
$109$	13.4164i	1.28506i	0.766261	+	0.642529i	$0.222115\pi$
$109$	13.4164i	1.28506i	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	12.7639	1.19024
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	0	0
$123$	−14.4721	−1.30491
$124$	0	0
$125$	− 11.1803i	− 1.00000i
$126$	0	0
$127$	18.6525i	1.65514i	0.561363	+	0.827570i	$0.310277\pi$
$127$	18.6525i	1.65514i	−0.561363	+	0.827570i	$0.689723\pi$
$128$	0	0
$129$	−36.3607	−3.20138
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	− 32.3607i	− 2.78516i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	− 44.3607i	− 3.73584i
$142$	0	0
$143$	0	0
$144$	0	0
$145$	13.4164	1.11417
$146$	0	0
$147$	−20.7639	−1.71258
$148$	0	0
$149$	4.47214i	0.366372i	0.983078	+	0.183186i	$0.0586410\pi$
$149$	4.47214i	0.366372i	−0.983078	+	0.183186i	$0.941359\pi$
$150$	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		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−4.36068	−0.343670
$162$	0	0
$163$	6.65248	0.521062	0.260531	−	0.965465i	$-0.416102\pi$
$163$	6.65248	0.521062	0.260531	+	0.965465i	$0.416102\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	10.2918i	0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$167$	10.2918i	0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	3.81966i	0.288739i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	− 2.00000i	− 0.148659i	−0.997234	−	0.0743294i	$-0.976318\pi$
$181$	− 2.00000i	− 0.148659i	0.997234	−	0.0743294i	$-0.0236816\pi$
$182$	0	0
$183$	− 43.4164i	− 3.20943i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	11.0557i	0.804186i
$190$	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		−	1.00000i	$-0.5\pi$
$197$	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
$201$	26.4721	1.86720
$202$	0	0
$203$	−4.58359	−0.321705
$204$	0	0
$205$	10.0000i	0.698430i
$206$	0	0
$207$	− 42.6525i	− 2.96455i
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	25.1246i	1.71348i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 23.2361i	− 1.55600i	−0.628263	−	0.778001i	$-0.716234\pi$
$223$	− 23.2361i	− 1.55600i	0.628263	−	0.778001i	$-0.283766\pi$
$224$	0	0
$225$	−37.3607	−2.49071
$226$	0	0
$227$	−13.1246	−0.871111	−0.435556	−	0.900162i	$-0.643448\pi$
$227$	−13.1246	−0.871111	−0.435556	+	0.900162i	$0.643448\pi$
$228$	0	0
$229$	14.0000i	0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$	14.0000i	0.925146i	−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
$235$	−30.6525	−1.99955
$236$	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
$241$	13.4164	0.864227	0.432113	−	0.901819i	$-0.357768\pi$
$241$	13.4164	0.864227	0.432113	+	0.901819i	$0.357768\pi$
$242$	0	0
$243$	−35.5967	−2.28353
$244$	0	0
$245$	14.3475i	0.916630i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−57.3050	−3.63155
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	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
$261$	− 44.8328i	− 2.77508i
$262$	0	0
$263$	9.12461i	0.562648i	0.959613	+	0.281324i	$0.0907735\pi$
$263$	9.12461i	0.562648i	−0.959613	+	0.281324i	$0.909226\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−19.4164	−1.18826
$268$	0	0
$269$	− 22.3607i	− 1.36335i	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	− 22.3607i	− 1.36335i	0.731653	−	0.681677i	$-0.238749\pi$
$270$	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		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−31.3050	−1.86750	−0.933748	−	0.357930i	$-0.883483\pi$
$281$	−31.3050	−1.86750	−0.933748	+	0.357930i	$0.883483\pi$
$282$	0	0
$283$	32.1803	1.91292	0.956461	−	0.291859i	$-0.0942738\pi$
$283$	32.1803	1.91292	0.956461	+	0.291859i	$0.0942738\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	− 3.41641i	− 0.201664i
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	− 8.58359i	− 0.494750i
$302$	0	0
$303$	58.2492i	3.34633i
$304$	0	0
$305$	−30.0000	−1.71780
$306$	0	0
$307$	27.5967	1.57503	0.787515	−	0.616296i	$-0.211367\pi$
$307$	27.5967	1.57503	0.787515	+	0.616296i	$0.211367\pi$
$308$	0	0
$309$	− 65.3050i	− 3.71507i
$310$	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
$315$	12.7639	0.719166
$316$	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
$321$	−20.3607	−1.13642
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	− 43.4164i	− 2.40093i
$328$	0	0
$329$	10.4721	0.577348
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	− 18.2918i	− 0.999388i
$336$	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
$343$	− 10.2492i	− 0.553406i
$344$	0	0
$345$	−41.3050	−2.22378
$346$	0	0
$347$	37.1246	1.99295	0.996477	−	0.0838690i	$-0.0267277\pi$
$347$	37.1246	1.99295	0.996477	+	0.0838690i	$0.0267277\pi$
$348$	0	0
$349$	26.0000i	1.39175i	0.718164	+	0.695874i	$0.244983\pi$
$349$	26.0000i	1.39175i	−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
$363$	−35.5967	−1.86834
$364$	0	0
$365$	0	0
$366$	0	0
$367$	24.7639i	1.29267i	0.763055	+	0.646333i	$0.223698\pi$
$367$	24.7639i	1.29267i	−0.763055	+	0.646333i	$0.776302\pi$
$368$	0	0
$369$	33.4164	1.73959
$370$	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
$375$	36.1803i	1.86834i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	− 60.3607i	− 3.09237i
$382$	0	0
$383$	− 1.12461i	− 0.0574650i	−0.999587	−	0.0287325i	$-0.990853\pi$
$383$	− 1.12461i	− 0.0574650i	0.999587	−	0.0287325i	$-0.00914709\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	83.9574	4.26780
$388$	0	0
$389$	− 31.3050i	− 1.58722i	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	− 31.3050i	− 1.58722i	0.608424	−	0.793612i	$-0.291802\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	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
$405$	54.5967i	2.71293i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	40.2492	1.99020	0.995098	−	0.0988936i	$-0.0315304\pi$
$409$	40.2492	1.99020	0.995098	+	0.0988936i	$0.0315304\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	39.5967i	1.94373i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	40.2492i	1.96163i	0.194948	+	0.980814i	$0.437546\pi$
$421$	40.2492i	1.96163i	−0.194948	+	0.980814i	$0.562454\pi$
$422$	0	0
$423$	102.430i	4.98030i
$424$	0	0
$425$	0	0
$426$	0	0
$427$	10.2492	0.495995
$428$	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
$435$	−43.4164	−2.08166
$436$	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
$441$	47.9443	2.28306
$442$	0	0
$443$	22.2918	1.05912	0.529558	−	0.848274i	$-0.322358\pi$
$443$	22.2918	1.05912	0.529558	+	0.848274i	$0.322358\pi$
$444$	0	0
$445$	13.4164i	0.635999i
$446$	0	0
$447$	− 14.4721i	− 0.684509i
$448$	0	0
$449$	−22.3607	−1.05527	−0.527633	−	0.849473i	$-0.676920\pi$
$449$	−22.3607	−1.05527	−0.527633	+	0.849473i	$0.676920\pi$
$450$	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
$461$	42.0000i	1.95614i	0.208288	+	0.978068i	$0.433211\pi$
$461$	42.0000i	1.95614i	−0.208288	+	0.978068i	$0.566789\pi$
$462$	0	0
$463$	− 38.0689i	− 1.76921i	−0.466340	−	0.884606i	$-0.654428\pi$
$463$	− 38.0689i	− 1.76921i	0.466340	−	0.884606i	$-0.345572\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	2.87539	0.133057	0.0665285	−	0.997785i	$-0.478808\pi$
$467$	2.87539	0.133057	0.0665285	+	0.997785i	$0.478808\pi$
$468$	0	0
$469$	6.24922i	0.288562i
$470$	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
$483$	14.1115	0.642093
$484$	0	0
$485$	0	0
$486$	0	0
$487$	− 42.6525i	− 1.93277i	−0.257103	−	0.966384i	$-0.582768\pi$
$487$	− 42.6525i	− 1.93277i	0.257103	−	0.966384i	$-0.417232\pi$
$488$	0	0
$489$	−21.5279	−0.973524
$490$	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
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	− 33.3050i	− 1.48796i
$502$	0	0
$503$	− 37.7082i	− 1.68133i	−0.541559	−	0.840663i	$-0.682166\pi$
$503$	− 37.7082i	− 1.68133i	0.541559	−	0.840663i	$-0.317834\pi$
$504$	0	0
$505$	40.2492	1.79107
$506$	0	0
$507$	42.0689	1.86834
$508$	0	0
$509$	− 6.00000i	− 0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$	− 6.00000i	− 0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−45.1246	−1.98843
$516$	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
$523$	−3.59675	−0.157275	−0.0786374	−	0.996903i	$-0.525057\pi$
$523$	−3.59675	−0.157275	−0.0786374	+	0.996903i	$0.525057\pi$
$524$	0	0
$525$	− 12.3607i	− 0.539464i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−9.58359	−0.416678
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	14.0689i	0.608251i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	− 38.0000i	− 1.63375i	−0.576816	−	0.816874i	$-0.695705\pi$
$541$	− 38.0000i	− 1.63375i	0.576816	−	0.816874i	$-0.304295\pi$
$542$	0	0
$543$	6.47214i	0.277746i
$544$	0	0
$545$	−30.0000	−1.28506
$546$	0	0
$547$	−35.2361	−1.50659	−0.753293	−	0.657685i	$-0.771536\pi$
$547$	−35.2361	−1.50659	−0.753293	+	0.657685i	$0.771536\pi$
$548$	0	0
$549$	100.249i	4.27853i
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	32.5410	1.37144	0.685720	−	0.727865i	$-0.259487\pi$
$563$	32.5410	1.37144	0.685720	+	0.727865i	$0.259487\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	− 18.6525i	− 0.783330i
$568$	0	0
$569$	−31.3050	−1.31237	−0.656186	−	0.754599i	$-0.727831\pi$
$569$	−31.3050	−1.31237	−0.656186	+	0.754599i	$0.727831\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	28.5410i	1.19024i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 13.5279i	− 0.561230i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−40.5410	−1.67331	−0.836653	−	0.547733i	$-0.815491\pi$
$587$	−40.5410	−1.67331	−0.836653	+	0.547733i	$0.815491\pi$
$588$	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
$601$	40.2492	1.64180	0.820900	−	0.571072i	$-0.193472\pi$
$601$	40.2492	1.64180	0.820900	+	0.571072i	$0.193472\pi$
$602$	0	0
$603$	−61.1246	−2.48919
$604$	0	0
$605$	24.5967i	1.00000i
$606$	0	0
$607$	− 44.1803i	− 1.79322i	−0.442816	−	0.896612i	$-0.646021\pi$
$607$	− 44.1803i	− 1.79322i	0.442816	−	0.896612i	$-0.353979\pi$
$608$	0	0
$609$	14.8328	0.601056
$610$	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
$615$	− 32.3607i	− 1.30491i
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	82.6099i	3.31502i
$622$	0	0
$623$	− 4.58359i	− 0.183638i
$624$	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
$635$	−41.7082	−1.65514
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	49.1935	1.94303	0.971513	−	0.236986i	$-0.0761595\pi$
$641$	49.1935	1.94303	0.971513	+	0.236986i	$0.0761595\pi$
$642$	0	0
$643$	−50.0689	−1.97452	−0.987262	−	0.159103i	$-0.949140\pi$
$643$	−50.0689	−1.97452	−0.987262	+	0.159103i	$0.949140\pi$
$644$	0	0
$645$	− 81.3050i	− 3.20138i
$646$	0	0
$647$	− 20.5410i	− 0.807551i	−0.914858	−	0.403775i	$-0.867698\pi$
$647$	− 20.5410i	− 0.807551i	0.914858	−	0.403775i	$-0.132302\pi$
$648$	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
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	40.2492i	1.56551i	0.622328	+	0.782757i	$0.286187\pi$
$661$	40.2492i	1.56551i	−0.622328	+	0.782757i	$0.713813\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−34.2492	−1.32614
$668$	0	0
$669$	75.1935i	2.90715i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	72.3607	2.78516
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	42.4721	1.62754
$682$	0	0
$683$	−10.8754	−0.416135	−0.208068	−	0.978114i	$-0.566717\pi$
$683$	−10.8754	−0.416135	−0.208068	+	0.978114i	$0.566717\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	− 45.3050i	− 1.72849i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	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
$701$	− 22.3607i	− 0.844551i	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	− 22.3607i	− 0.844551i	0.906467	−	0.422276i	$-0.138769\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	99.1935	3.73584
$706$	0	0
$707$	−13.7508	−0.517151
$708$	0	0
$709$	46.0000i	1.72757i	0.503864	+	0.863783i	$0.331911\pi$
$709$	46.0000i	1.72757i	−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
$721$	15.4164	0.574137
$722$	0	0
$723$	−43.4164	−1.61467
$724$	0	0
$725$	30.0000i	1.11417i
$726$	0	0
$727$	35.0132i	1.29857i	0.760547	+	0.649283i	$0.224931\pi$
$727$	35.0132i	1.29857i	−0.760547	+	0.649283i	$0.775069\pi$
$728$	0	0
$729$	41.9443	1.55349
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	− 46.4296i	− 1.71258i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	− 52.5410i	− 1.92754i	−0.266729	−	0.963772i	$-0.585943\pi$
$743$	− 52.5410i	− 1.92754i	0.266729	−	0.963772i	$-0.414057\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	0	0
$747$	132.318	4.84127
$748$	0	0
$749$	− 4.80650i	− 0.175626i
$750$	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		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	10.2492	0.371047
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	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
$783$	86.8328i	3.10315i
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−2.06888	−0.0737477	−0.0368739	−	0.999320i	$-0.511740\pi$
$787$	−2.06888	−0.0737477	−0.0368739	+	0.999320i	$0.511740\pi$
$788$	0	0
$789$	− 29.5279i	− 1.05122i
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	44.8328	1.58409
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 9.75078i	− 0.343670i
$806$	0	0
$807$	72.3607i	2.54722i
$808$	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	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	14.8754i	0.521062i
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	− 31.3050i	− 1.09255i	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	− 31.3050i	− 1.09255i	0.837606	−	0.546275i	$-0.183955\pi$
$822$	0	0
$823$	− 27.8197i	− 0.969732i	−0.874588	−	0.484866i	$-0.838868\pi$
$823$	− 27.8197i	− 0.969732i	0.874588	−	0.484866i	$-0.161132\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−56.5410	−1.96612	−0.983062	−	0.183274i	$-0.941331\pi$
$827$	−56.5410	−1.96612	−0.983062	+	0.183274i	$0.941331\pi$
$828$	0	0
$829$	13.4164i	0.465971i	0.972480	+	0.232986i	$0.0748495\pi$
$829$	13.4164i	0.465971i	−0.972480	+	0.232986i	$0.925151\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−23.0132	−0.796403
$836$	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
$841$	−7.00000	−0.241379
$842$	0	0
$843$	101.305	3.48913
$844$	0	0
$845$	− 29.0689i	− 1.00000i
$846$	0	0
$847$	− 8.40325i	− 0.288739i
$848$	0	0
$849$	−104.138	−3.57400
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	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	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	11.0557i	0.376778i
$862$	0	0
$863$	− 34.2918i	− 1.16731i	−0.812003	−	0.583653i	$-0.801623\pi$
$863$	− 34.2918i	− 1.16731i	0.812003	−	0.583653i	$-0.198377\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−55.0132	−1.86834
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−8.54102	−0.288739
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−58.1378	−1.95871	−0.979356	−	0.202145i	$-0.935209\pi$
$881$	−58.1378	−1.95871	−0.979356	+	0.202145i	$0.935209\pi$
$882$	0	0
$883$	54.6525	1.83920	0.919601	−	0.392853i	$-0.128512\pi$
$883$	54.6525	1.83920	0.919601	+	0.392853i	$0.128512\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	57.1246i	1.91806i	0.283310	+	0.959028i	$0.408567\pi$
$887$	57.1246i	1.91806i	−0.283310	+	0.959028i	$0.591433\pi$
$888$	0	0
$889$	14.2492	0.477904
$890$	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
$903$	27.7771i	0.924364i
$904$	0	0
$905$	4.47214	0.148659
$906$	0	0
$907$	−45.4853	−1.51031	−0.755157	−	0.655544i	$-0.772439\pi$
$907$	−45.4853	−1.51031	−0.755157	+	0.655544i	$0.772439\pi$
$908$	0	0
$909$	− 134.498i	− 4.46103i
$910$	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
$915$	97.0820	3.20943
$916$	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
$921$	−89.3050	−2.94270
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	150.790i	4.95260i
$928$	0	0
$929$	49.1935	1.61399	0.806993	−	0.590561i	$-0.201093\pi$
$929$	49.1935	1.61399	0.806993	+	0.590561i	$0.201093\pi$
$930$	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
$941$	42.0000i	1.36916i	0.728937	+	0.684580i	$0.240015\pi$
$941$	42.0000i	1.36916i	−0.728937	+	0.684580i	$0.759985\pi$
$942$	0	0
$943$	− 25.5279i	− 0.831302i
$944$	0	0
$945$	−24.7214	−0.804186
$946$	0	0
$947$	49.7082	1.61530	0.807650	−	0.589662i	$-0.200739\pi$
$947$	49.7082	1.61530	0.807650	+	0.589662i	$0.200739\pi$
$948$	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
$963$	47.0132	1.51498
$964$	0	0
$965$	0	0
$966$	0	0
$967$	62.0689i	1.99600i	0.0632081	+	0.998000i	$0.479867\pi$
$967$	62.0689i	1.99600i	−0.0632081	+	0.998000i	$0.520133\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	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
$981$	100.249i	3.20071i
$982$	0	0
$983$	− 4.54102i	− 0.144836i	−0.997374	−	0.0724180i	$-0.976928\pi$
$983$	− 4.54102i	− 0.144836i	0.997374	−	0.0724180i	$-0.0230716\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−33.8885	−1.07868
$988$	0	0
$989$	− 64.1378i	− 2.03946i
$990$	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		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.f.g.129.2		4
4.3	odd	2		1280.2.f.h.129.4		4
5.4	even	2		1280.2.f.h.129.4		4
8.3	odd	2	inner	1280.2.f.g.129.1		4
8.5	even	2		1280.2.f.h.129.3		4
16.3	odd	4		160.2.c.b.129.4	yes	4
16.5	even	4		320.2.c.d.129.4		4
16.11	odd	4		320.2.c.d.129.1		4
16.13	even	4		160.2.c.b.129.1	✓	4
20.19	odd	2	CM	1280.2.f.g.129.2		4
40.19	odd	2		1280.2.f.h.129.3		4
40.29	even	2	inner	1280.2.f.g.129.1		4
48.5	odd	4		2880.2.f.w.1729.4		4
48.11	even	4		2880.2.f.w.1729.3		4
48.29	odd	4		1440.2.f.i.289.2		4
48.35	even	4		1440.2.f.i.289.1		4
80.3	even	4		800.2.a.j.1.1		2
80.13	odd	4		800.2.a.n.1.2		2
80.19	odd	4		160.2.c.b.129.1	✓	4
80.27	even	4		1600.2.a.z.1.1		2
80.29	even	4		160.2.c.b.129.4	yes	4
80.37	odd	4		1600.2.a.bd.1.2		2
80.43	even	4		1600.2.a.bd.1.2		2
80.53	odd	4		1600.2.a.z.1.1		2
80.59	odd	4		320.2.c.d.129.4		4
80.67	even	4		800.2.a.n.1.2		2
80.69	even	4		320.2.c.d.129.1		4
80.77	odd	4		800.2.a.j.1.1		2
240.29	odd	4		1440.2.f.i.289.1		4
240.59	even	4		2880.2.f.w.1729.4		4
240.77	even	4		7200.2.a.cb.1.2		2
240.83	odd	4		7200.2.a.cb.1.2		2
240.149	odd	4		2880.2.f.w.1729.3		4
240.173	even	4		7200.2.a.cr.1.1		2
240.179	even	4		1440.2.f.i.289.2		4
240.227	odd	4		7200.2.a.cr.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.c.b.129.1	✓	4	16.13	even	4
160.2.c.b.129.1	✓	4	80.19	odd	4
160.2.c.b.129.4	yes	4	16.3	odd	4
160.2.c.b.129.4	yes	4	80.29	even	4
320.2.c.d.129.1		4	16.11	odd	4
320.2.c.d.129.1		4	80.69	even	4
320.2.c.d.129.4		4	16.5	even	4
320.2.c.d.129.4		4	80.59	odd	4
800.2.a.j.1.1		2	80.3	even	4
800.2.a.j.1.1		2	80.77	odd	4
800.2.a.n.1.2		2	80.13	odd	4
800.2.a.n.1.2		2	80.67	even	4
1280.2.f.g.129.1		4	8.3	odd	2	inner
1280.2.f.g.129.1		4	40.29	even	2	inner
1280.2.f.g.129.2		4	1.1	even	1	trivial
1280.2.f.g.129.2		4	20.19	odd	2	CM
1280.2.f.h.129.3		4	8.5	even	2
1280.2.f.h.129.3		4	40.19	odd	2
1280.2.f.h.129.4		4	4.3	odd	2
1280.2.f.h.129.4		4	5.4	even	2
1440.2.f.i.289.1		4	48.35	even	4
1440.2.f.i.289.1		4	240.29	odd	4
1440.2.f.i.289.2		4	48.29	odd	4
1440.2.f.i.289.2		4	240.179	even	4
1600.2.a.z.1.1		2	80.27	even	4
1600.2.a.z.1.1		2	80.53	odd	4
1600.2.a.bd.1.2		2	80.37	odd	4
1600.2.a.bd.1.2		2	80.43	even	4
2880.2.f.w.1729.3		4	48.11	even	4
2880.2.f.w.1729.3		4	240.149	odd	4
2880.2.f.w.1729.4		4	48.5	odd	4
2880.2.f.w.1729.4		4	240.59	even	4
7200.2.a.cb.1.2		2	240.77	even	4
7200.2.a.cb.1.2		2	240.83	odd	4
7200.2.a.cr.1.1		2	240.173	even	4
7200.2.a.cr.1.1		2	240.227	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-3.23607 q^{3} +2.23607i q^{5} -0.763932i q^{7} +7.47214 q^{9} +O(q^{10})\)	\(q-3.23607 q^{3} +2.23607i q^{5} -0.763932i q^{7} +7.47214 q^{9} -7.23607i q^{15} +2.47214i q^{21} -5.70820i q^{23} -5.00000 q^{25} -14.4721 q^{27} -6.00000i q^{29} +1.70820 q^{35} +4.47214 q^{41} +11.2361 q^{43} +16.7082i q^{45} +13.7082i q^{47} +6.41641 q^{49} +13.4164i q^{61} -5.70820i q^{63} -8.18034 q^{67} +18.4721i q^{69} +16.1803 q^{75} +24.4164 q^{81} +17.7082 q^{83} +19.4164i q^{87} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 12 * q^9	\( 4 q - 4 q^{3} + 12 q^{9} - 20 q^{25} - 40 q^{27} - 20 q^{35} + 36 q^{43} - 28 q^{49} + 12 q^{67} + 20 q^{75} + 44 q^{81} + 44 q^{83} + 24 q^{89}+O(q^{100}) \) 4 * q - 4 * q^3 + 12 * q^9 - 20 * q^25 - 40 * q^27 - 20 * q^35 + 36 * q^43 - 28 * q^49 + 12 * q^67 + 20 * q^75 + 44 * q^81 + 44 * q^83 + 24 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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