LMFDB - Embedded newform 320.6.c.c.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(129,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("320.129");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.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:	$51.3228223402$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			129.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	320.129
Dual form			320.6.c.c.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-41.0000 + 38.0000i) q^{5} +243.000 q^{9} +O(q^{10})$	$q+(-41.0000 + 38.0000i) q^{5} +243.000 q^{9} -244.000i q^{13} -808.000i q^{17} +(237.000 - 3116.00i) q^{25} -2950.00 q^{29} +11292.0i q^{37} +20950.0 q^{41} +(-9963.00 + 9234.00i) q^{45} +16807.0 q^{49} +40244.0i q^{53} +18950.0 q^{61} +(9272.00 + 10004.0i) q^{65} -20144.0i q^{73} +59049.0 q^{81} +(30704.0 + 33128.0i) q^{85} +51050.0 q^{89} +160808. i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 82 q^{5} + 486 q^{9}+O(q^{10}) $ 2 * q - 82 * q^5 + 486 * q^9	$ 2 q - 82 q^{5} + 486 q^{9} + 474 q^{25} - 5900 q^{29} + 41900 q^{41} - 19926 q^{45} + 33614 q^{49} + 37900 q^{61} + 18544 q^{65} + 118098 q^{81} + 61408 q^{85} + 102100 q^{89}+O(q^{100}) $ 2 * q - 82 * q^5 + 486 * q^9 + 474 * q^25 - 5900 * q^29 + 41900 * q^41 - 19926 * q^45 + 33614 * q^49 + 37900 * q^61 + 18544 * q^65 + 118098 * q^81 + 61408 * q^85 + 102100 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$-1$	$1$

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
$5$	−41.0000	+	38.0000i	−0.733430	+	0.679765i
$5$	−41.0000	+	38.0000i	−0.733430	+	0.679765i
$6$		0			0
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		0			0
$9$	243.000			1.00000
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$		−	244.000i		−	0.400434i	−0.979752	−	0.200217i	$-0.935835\pi$
$13$		−	244.000i		−	0.400434i	0.979752	−	0.200217i	$-0.0641648\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	808.000i		−	0.678093i	−0.940770	−	0.339046i	$-0.889896\pi$
$17$		−	808.000i		−	0.678093i	0.940770	−	0.339046i	$-0.110104\pi$
$18$		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		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	237.000	−	3116.00i	0.0758400	−	0.997120i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2950.00			−0.651369			−0.325684	−	0.945479i	$-0.605595\pi$
$29$	−2950.00			−0.651369			−0.325684	+	0.945479i	$0.605595\pi$
$30$		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
$35$		0			0
$36$		0			0
$37$			11292.0i			1.35602i	0.735052	+	0.678011i	$0.237158\pi$
$37$			11292.0i			1.35602i	−0.735052	+	0.678011i	$0.762842\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	20950.0			1.94637			0.973183	−	0.230033i	$-0.0738836\pi$
$41$	20950.0			1.94637			0.973183	+	0.230033i	$0.0738836\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	−9963.00	+	9234.00i	−0.733430	+	0.679765i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	16807.0			1.00000
$50$		0			0
$51$		0			0
$52$		0			0
$53$			40244.0i			1.96794i	0.178339	+	0.983969i	$0.442928\pi$
$53$			40244.0i			1.96794i	−0.178339	+	0.983969i	$0.557072\pi$
$54$		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
$61$	18950.0			0.652056			0.326028	−	0.945360i	$-0.394290\pi$
$61$	18950.0			0.652056			0.326028	+	0.945360i	$0.394290\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9272.00	+	10004.0i	0.272201	+	0.293691i
$66$		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			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$		−	20144.0i		−	0.442424i	−0.975226	−	0.221212i	$-0.928999\pi$
$73$		−	20144.0i		−	0.442424i	0.975226	−	0.221212i	$-0.0710013\pi$
$74$		0			0
$75$		0			0
$76$		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
$81$	59049.0			1.00000
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	30704.0	+	33128.0i	0.460943	+	0.497334i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	51050.0			0.683157			0.341579	−	0.939853i	$-0.389038\pi$
$89$	51050.0			0.683157			0.341579	+	0.939853i	$0.389038\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$			160808.i			1.73531i	0.497162	+	0.867657i	$0.334375\pi$
$97$			160808.i			1.73531i	−0.497162	+	0.867657i	$0.665625\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	98002.0			0.955942			0.477971	−	0.878376i	$-0.341372\pi$
$101$	98002.0			0.955942			0.477971	+	0.878376i	$0.341372\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	246486.			1.98713			0.993564	−	0.113269i	$-0.0361321\pi$
$109$	246486.			1.98713			0.993564	+	0.113269i	$0.0361321\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			244144.i			1.79866i	0.437267	+	0.899332i	$0.355947\pi$
$113$			244144.i			1.79866i	−0.437267	+	0.899332i	$0.644053\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	59292.0i		−	0.400434i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−161051.			−1.00000
$122$		0			0
$123$		0			0
$124$		0			0
$125$	108691.	+	136762.i	0.622184	+	0.782871i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		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
$137$			432808.i			1.97013i	0.172196	+	0.985063i	$0.444914\pi$
$137$			432808.i			1.97013i	−0.172196	+	0.985063i	$0.555086\pi$
$138$		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
$145$	120950.	−	112100.i	0.477734	−	0.442778i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	47614.0			0.175699			0.0878494	−	0.996134i	$-0.472001\pi$
$149$	47614.0			0.175699			0.0878494	+	0.996134i	$0.472001\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$		−	196344.i		−	0.678093i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	371292.i		−	1.20217i	−0.799185	−	0.601086i	$-0.794735\pi$
$157$		−	371292.i		−	1.20217i	0.799185	−	0.601086i	$-0.205265\pi$
$158$		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		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	311757.			0.839652
$170$		0			0
$171$		0			0
$172$		0			0
$173$			544244.i			1.38254i	0.722596	+	0.691271i	$0.242949\pi$
$173$			544244.i			1.38254i	−0.722596	+	0.691271i	$0.757051\pi$
$174$		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
$181$	−439902.			−0.998067			−0.499033	−	0.866583i	$-0.666311\pi$
$181$	−439902.			−0.998067			−0.499033	+	0.866583i	$0.666311\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−429096.	−	462972.i	−0.921775	−	0.994547i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$		−	907656.i		−	1.75399i	−0.480496	−	0.876997i	$-0.659543\pi$
$193$		−	907656.i		−	1.75399i	0.480496	−	0.876997i	$-0.340457\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.02091e6i		−	1.87422i	−0.349031	−	0.937111i	$-0.613489\pi$
$197$		−	1.02091e6i		−	1.87422i	0.349031	−	0.937111i	$-0.386511\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−858950.	+	796100.i	−1.42752	+	1.32307i
$206$		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
$221$	−197152.			−0.271532
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	57591.0	−	757188.i	0.0758400	−	0.997120i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$	−1.25115e6			−1.57660			−0.788298	−	0.615293i	$-0.789038\pi$
$229$	−1.25115e6			−1.57660			−0.788298	+	0.615293i	$0.789038\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	619856.i		−	0.747999i	−0.927429	−	0.373999i	$-0.877986\pi$
$233$		−	619856.i		−	0.747999i	0.927429	−	0.373999i	$-0.122014\pi$
$234$		0			0
$235$		0			0
$236$		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
$241$	477150.			0.529191			0.264595	−	0.964360i	$-0.414762\pi$
$241$	477150.			0.529191			0.264595	+	0.964360i	$0.414762\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−689087.	+	638666.i	−0.733430	+	0.679765i
$246$		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
$257$			2.01539e6i			1.90339i	0.307052	+	0.951693i	$0.400657\pi$
$257$			2.01539e6i			1.90339i	−0.307052	+	0.951693i	$0.599343\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−716850.			−0.651369
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	−1.52927e6	−	1.65000e6i	−1.33773	−	1.44335i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.35141e6			1.98129			0.990646	−	0.136458i	$-0.0435720\pi$
$269$	2.35141e6			1.98129			0.990646	+	0.136458i	$0.0435720\pi$
$270$		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
$277$		−	2.45109e6i		−	1.91938i	−0.281067	−	0.959688i	$-0.590688\pi$
$277$		−	2.45109e6i		−	1.91938i	0.281067	−	0.959688i	$-0.409312\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.64305e6			−1.99682			−0.998412	−	0.0563421i	$-0.982056\pi$
$281$	−2.64305e6			−1.99682			−0.998412	+	0.0563421i	$0.982056\pi$
$282$		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
$289$	766993.			0.540190
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	1.62424e6i		−	1.10531i	−0.833412	−	0.552653i	$-0.813616\pi$
$293$		−	1.62424e6i		−	1.10531i	0.833412	−	0.552653i	$-0.186384\pi$
$294$		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
$305$	−776950.	+	720100.i	−0.478237	+	0.443244i
$306$		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			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		−	1.91566e6i		−	1.10524i	−0.833433	−	0.552620i	$-0.813628\pi$
$313$		−	1.91566e6i		−	1.10524i	0.833433	−	0.552620i	$-0.186372\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.51509e6i		−	1.96467i	−0.187144	−	0.982333i	$-0.559923\pi$
$317$		−	3.51509e6i		−	1.96467i	0.187144	−	0.982333i	$-0.440077\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−760304.	−	57828.0i	−0.399281	−	0.0303689i
$326$		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
$333$			2.74396e6i			1.35602i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			3.48861e6i			1.67331i	0.547727	+	0.836657i	$0.315493\pi$
$337$			3.48861e6i			1.67331i	−0.547727	+	0.836657i	$0.684507\pi$
$338$		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
$349$	4.44505e6			1.95350			0.976749	−	0.214385i	$-0.0687747\pi$
$349$	4.44505e6			1.95350			0.976749	+	0.214385i	$0.0687747\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			3.78786e6i			1.61792i	0.587865	+	0.808959i	$0.299969\pi$
$353$			3.78786e6i			1.61792i	−0.587865	+	0.808959i	$0.700031\pi$
$354$		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
$361$	−2.47610e6			−1.00000
$362$		0			0
$363$		0			0
$364$		0			0
$365$	765472.	+	825904.i	0.300744	+	0.324487i
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$	5.09085e6			1.94637
$370$		0			0
$371$		0			0
$372$		0			0
$373$			1.50404e6i			0.559743i	0.960038	+	0.279871i	$0.0902918\pi$
$373$			1.50404e6i			0.559743i	−0.960038	+	0.279871i	$0.909708\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			719800.i			0.260831i
$378$		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		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.28629e6			1.77124			0.885618	−	0.464414i	$-0.153735\pi$
$389$	5.28629e6			1.77124			0.885618	+	0.464414i	$0.153735\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$			6.27529e6i			1.99829i	0.0413901	+	0.999143i	$0.486821\pi$
$397$			6.27529e6i			1.99829i	−0.0413901	+	0.999143i	$0.513179\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.59200e6			0.494405			0.247202	−	0.968964i	$-0.420489\pi$
$401$	1.59200e6			0.494405			0.247202	+	0.968964i	$0.420489\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.42101e6	+	2.24386e6i	−0.733430	+	0.679765i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	4.58449e6			1.35513			0.677567	−	0.735461i	$-0.263034\pi$
$409$	4.58449e6			1.35513			0.677567	+	0.735461i	$0.263034\pi$
$410$		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
$421$	−5.94885e6			−1.63579			−0.817895	−	0.575367i	$-0.804859\pi$
$421$	−5.94885e6			−1.63579			−0.817895	+	0.575367i	$0.804859\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.51773e6	−	191496.i	−0.676140	−	0.0514265i
$426$		0			0
$427$		0			0
$428$		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
$433$		−	532344.i		−	0.136450i	−0.997670	−	0.0682249i	$-0.978266\pi$
$433$		−	532344.i		−	0.136450i	0.997670	−	0.0682249i	$-0.0217335\pi$
$434$		0			0
$435$		0			0
$436$		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
$441$	4.08410e6			1.00000
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	−2.09305e6	+	1.93990e6i	−0.501048	+	0.464386i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.48961e6			1.98734			0.993670	−	0.112340i	$-0.0358346\pi$
$449$	8.48961e6			1.98734			0.993670	+	0.112340i	$0.0358346\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	7.21681e6i		−	1.61642i	−0.588893	−	0.808211i	$-0.700436\pi$
$457$		−	7.21681e6i		−	1.61642i	0.588893	−	0.808211i	$-0.299564\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.86580e6			1.50466			0.752331	−	0.658785i	$-0.228929\pi$
$461$	6.86580e6			1.50466			0.752331	+	0.658785i	$0.228929\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		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
$477$			9.77929e6i			1.96794i
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$	2.75525e6			0.542998
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.11070e6	−	6.59313e6i	−1.17961	−	1.27273i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		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
$493$			2.38360e6i			0.441688i
$494$		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		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$	−4.01808e6	+	3.72408e6i	−0.701117	+	0.649816i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.05090e7			1.79791			0.898957	−	0.438037i	$-0.144326\pi$
$509$	1.05090e7			1.79791			0.898957	+	0.438037i	$0.144326\pi$
$510$		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
$521$	−7.27410e6			−1.17405			−0.587023	−	0.809570i	$-0.699700\pi$
$521$	−7.27410e6			−1.17405			−0.587023	+	0.809570i	$0.699700\pi$
$522$		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
$529$	6.43634e6			1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	5.11180e6i		−	0.779392i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.25380e6			−1.21244			−0.606221	−	0.795297i	$-0.707315\pi$
$541$	−8.25380e6			−1.21244			−0.606221	+	0.795297i	$0.707315\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.01059e7	+	9.36647e6i	−1.45742	+	1.35078i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$	4.60485e6			0.652056
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$			491092.i			0.0670695i	0.999438	+	0.0335347i	$0.0106764\pi$
$557$			491092.i			0.0670695i	−0.999438	+	0.0335347i	$0.989324\pi$
$558$		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
$565$	−9.27747e6	−	1.00099e7i	−1.22267	−	1.31919i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.96659e6			−0.513613			−0.256807	−	0.966463i	$-0.582670\pi$
$569$	−3.96659e6			−0.513613			−0.256807	+	0.966463i	$0.582670\pi$
$570$		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
$577$		−	1.56490e7i		−	1.95680i	−0.206712	−	0.978402i	$-0.566276\pi$
$577$		−	1.56490e7i		−	1.95680i	0.206712	−	0.978402i	$-0.433724\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.25310e6	+	2.43097e6i	0.272201	+	0.293691i
$586$		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
$593$			1.70359e7i			1.98942i	0.102706	+	0.994712i	$0.467250\pi$
$593$			1.70359e7i			1.98942i	−0.102706	+	0.994712i	$0.532750\pi$
$594$		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
$601$	−1.51550e7			−1.71148			−0.855739	−	0.517408i	$-0.826897\pi$
$601$	−1.51550e7			−1.71148			−0.855739	+	0.517408i	$0.826897\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.60309e6	−	6.11994e6i	0.733430	−	0.679765i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		−	1.48960e7i		−	1.60110i	−0.599263	−	0.800552i	$-0.704540\pi$
$613$		−	1.48960e7i		−	1.60110i	0.599263	−	0.800552i	$-0.295460\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	6.62461e6i		−	0.700563i	−0.936644	−	0.350282i	$-0.886086\pi$
$617$		−	6.62461e6i		−	0.700563i	0.936644	−	0.350282i	$-0.113914\pi$
$618$		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
$625$	−9.65329e6	−	1.47698e6i	−0.988497	−	0.151243i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.12394e6			0.919508
$630$		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
$635$		0			0
$636$		0			0
$637$		−	4.10091e6i		−	0.400434i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.45952e7			−1.40303			−0.701514	−	0.712655i	$-0.747492\pi$
$641$	−1.45952e7			−1.40303			−0.701514	+	0.712655i	$0.747492\pi$
$642$		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		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	1.93996e7i		−	1.78036i	−0.455605	−	0.890182i	$-0.650577\pi$
$653$		−	1.93996e7i		−	1.78036i	0.455605	−	0.890182i	$-0.349423\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	4.89499e6i		−	0.442424i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−8.60525e6			−0.766055			−0.383027	−	0.923737i	$-0.625119\pi$
$661$	−8.60525e6			−0.766055			−0.383027	+	0.923737i	$0.625119\pi$
$662$		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
$673$		−	1.57963e7i		−	1.34437i	−0.740383	−	0.672185i	$-0.765356\pi$
$673$		−	1.57963e7i		−	1.34437i	0.740383	−	0.672185i	$-0.234644\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			2.34115e7i			1.96317i	0.191032	+	0.981584i	$0.438817\pi$
$677$			2.34115e7i			1.96317i	−0.191032	+	0.981584i	$0.561183\pi$
$678$		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
$685$	−1.64467e7	−	1.77451e7i	−1.33922	−	1.44495i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.81954e6			0.788030
$690$		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
$697$		−	1.69276e7i		−	1.31982i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.11650e7			−1.62676			−0.813381	−	0.581731i	$-0.802376\pi$
$701$	−2.11650e7			−1.62676			−0.813381	+	0.581731i	$0.802376\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.98715e6			−0.297884			−0.148942	−	0.988846i	$-0.547587\pi$
$709$	−3.98715e6			−0.297884			−0.148942	+	0.988846i	$0.547587\pi$
$710$		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
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−699150.	+	9.19220e6i	−0.0493998	+	0.649493i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	1.43489e7			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$			1.05122e7i			0.722662i	0.932438	+	0.361331i	$0.117678\pi$
$733$			1.05122e7i			0.722662i	−0.932438	+	0.361331i	$0.882322\pi$
$734$		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		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$	−1.95217e6	+	1.80933e6i	−0.128863	+	0.119434i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		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
$757$			3.00451e6i			0.190561i	0.995450	+	0.0952804i	$0.0303748\pi$
$757$			3.00451e6i			0.190561i	−0.995450	+	0.0952804i	$0.969625\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.95198e7			1.22184			0.610919	−	0.791693i	$-0.290800\pi$
$761$	1.95198e7			1.22184			0.610919	+	0.791693i	$0.290800\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	7.46107e6	+	8.05010e6i	0.460943	+	0.497334i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−2.02848e7			−1.23695			−0.618477	−	0.785803i	$-0.712250\pi$
$769$	−2.02848e7			−1.23695			−0.618477	+	0.785803i	$0.712250\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			3.28636e7i			1.97818i	0.147312	+	0.989090i	$0.452938\pi$
$773$			3.28636e7i			1.97818i	−0.147312	+	0.989090i	$0.547062\pi$
$774$		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
$785$	1.41091e7	+	1.52230e7i	0.817194	+	0.881709i
$786$		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
$793$		−	4.62380e6i		−	0.261106i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.49645e7i			0.834481i	0.908796	+	0.417241i	$0.137003\pi$
$797$			1.49645e7i			0.834481i	−0.908796	+	0.417241i	$0.862997\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	1.24052e7			0.683157
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.87790e7			1.54598			0.772992	−	0.634415i	$-0.218759\pi$
$809$	2.87790e7			1.54598			0.772992	+	0.634415i	$0.218759\pi$
$810$		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
$821$	3.21148e7			1.66283			0.831413	−	0.555655i	$-0.187533\pi$
$821$	3.21148e7			1.66283			0.831413	+	0.555655i	$0.187533\pi$
$822$		0			0
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$	−7.96819e6			−0.402692			−0.201346	−	0.979520i	$-0.564532\pi$
$829$	−7.96819e6			−0.402692			−0.201346	+	0.979520i	$0.564532\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	1.35801e7i		−	0.678093i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−1.18086e7			−0.575719
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.27820e7	+	1.18468e7i	−0.615826	+	0.570766i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	7.55204e6i		−	0.355379i	−0.984087	−	0.177690i	$-0.943138\pi$
$853$		−	7.55204e6i		−	0.355379i	0.984087	−	0.177690i	$-0.0568623\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			2.72168e7i			1.26586i	0.774210	+	0.632929i	$0.218148\pi$
$857$			2.72168e7i			1.26586i	−0.774210	+	0.632929i	$0.781852\pi$
$858$		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		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$	−2.06813e7	−	2.23140e7i	−0.939803	−	1.01400i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$			3.90763e7i			1.73531i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	3.88193e7i		−	1.70431i	−0.523289	−	0.852155i	$-0.675295\pi$
$877$		−	3.88193e7i		−	1.70431i	0.523289	−	0.852155i	$-0.324705\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4.40848e7			1.91359			0.956794	−	0.290765i	$-0.0939099\pi$
$881$	4.40848e7			1.91359			0.956794	+	0.290765i	$0.0939099\pi$
$882$		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		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		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
$901$	3.25172e7			1.33444
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.80360e7	−	1.67163e7i	0.732012	−	0.678450i
$906$		0			0
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$		0			0
$909$	2.38145e7			0.955942
$910$		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
$915$		0			0
$916$		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
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	3.51859e7	+	2.67620e6i	1.35212	+	0.102841i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.76633e7			−1.81194			−0.905972	−	0.423337i	$-0.860859\pi$
$929$	−4.76633e7			−1.81194			−0.905972	+	0.423337i	$0.860859\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$			5.26070e7i			1.95747i	0.205135	+	0.978734i	$0.434237\pi$
$937$			5.26070e7i			1.95747i	−0.205135	+	0.978734i	$0.565763\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.85570e6			−0.178763			−0.0893816	−	0.995997i	$-0.528489\pi$
$941$	−4.85570e6			−0.178763			−0.0893816	+	0.995997i	$0.528489\pi$
$942$		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
$949$	−4.91514e6			−0.177162
$950$		0			0
$951$		0			0
$952$		0			0
$953$			3.17799e7i			1.13350i	0.823890	+	0.566749i	$0.191799\pi$
$953$			3.17799e7i			1.13350i	−0.823890	+	0.566749i	$0.808201\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.86292e7			−1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.44909e7	+	3.72139e7i	1.19230	+	1.28643i
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		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
$977$			3.57128e7i			1.19698i	0.801130	+	0.598491i	$0.204233\pi$
$977$			3.57128e7i			1.19698i	−0.801130	+	0.598491i	$0.795767\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.98961e7			1.98713
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$	3.87945e7	+	4.18572e7i	1.27403	+	1.37461i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		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
$997$		−	5.12753e7i		−	1.63369i	−0.576856	−	0.816846i	$-0.695720\pi$
$997$		−	5.12753e7i		−	1.63369i	0.576856	−	0.816846i	$-0.304280\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.c.c.129.2		2
4.3	odd	2	CM	320.6.c.c.129.2		2
5.4	even	2	inner	320.6.c.c.129.1		2
8.3	odd	2		160.6.c.a.129.1	✓	2
8.5	even	2		160.6.c.a.129.1	✓	2
20.19	odd	2	inner	320.6.c.c.129.1		2
40.3	even	4		800.6.a.b.1.1		1
40.13	odd	4		800.6.a.b.1.1		1
40.19	odd	2		160.6.c.a.129.2	yes	2
40.27	even	4		800.6.a.c.1.1		1
40.29	even	2		160.6.c.a.129.2	yes	2
40.37	odd	4		800.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.c.a.129.1	✓	2	8.3	odd	2
160.6.c.a.129.1	✓	2	8.5	even	2
160.6.c.a.129.2	yes	2	40.19	odd	2
160.6.c.a.129.2	yes	2	40.29	even	2
320.6.c.c.129.1		2	5.4	even	2	inner
320.6.c.c.129.1		2	20.19	odd	2	inner
320.6.c.c.129.2		2	1.1	even	1	trivial
320.6.c.c.129.2		2	4.3	odd	2	CM
800.6.a.b.1.1		1	40.3	even	4
800.6.a.b.1.1		1	40.13	odd	4
800.6.a.c.1.1		1	40.27	even	4
800.6.a.c.1.1		1	40.37	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-41.0000 + 38.0000i) q^{5} +243.000 q^{9} +O(q^{10})\)	\(q+(-41.0000 + 38.0000i) q^{5} +243.000 q^{9} -244.000i q^{13} -808.000i q^{17} +(237.000 - 3116.00i) q^{25} -2950.00 q^{29} +11292.0i q^{37} +20950.0 q^{41} +(-9963.00 + 9234.00i) q^{45} +16807.0 q^{49} +40244.0i q^{53} +18950.0 q^{61} +(9272.00 + 10004.0i) q^{65} -20144.0i q^{73} +59049.0 q^{81} +(30704.0 + 33128.0i) q^{85} +51050.0 q^{89} +160808. i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 82 q^{5} + 486 q^{9}+O(q^{10}) \) 2 * q - 82 * q^5 + 486 * q^9	\( 2 q - 82 q^{5} + 486 q^{9} + 474 q^{25} - 5900 q^{29} + 41900 q^{41} - 19926 q^{45} + 33614 q^{49} + 37900 q^{61} + 18544 q^{65} + 118098 q^{81} + 61408 q^{85} + 102100 q^{89}+O(q^{100}) \) 2 * q - 82 * q^5 + 486 * q^9 + 474 * q^25 - 5900 * q^29 + 41900 * q^41 - 19926 * q^45 + 33614 * q^49 + 37900 * q^61 + 18544 * q^65 + 118098 * q^81 + 61408 * q^85 + 102100 * q^89

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