LMFDB - Embedded newform 40.3.e.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(19,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("40.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.e (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	40.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

$q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -18.0000 q^{11} +6.00000 q^{13} -12.0000 q^{14} +16.0000 q^{16} +18.0000 q^{18} -2.00000 q^{19} -20.0000 q^{20} -36.0000 q^{22} +26.0000 q^{23} +25.0000 q^{25} +12.0000 q^{26} -24.0000 q^{28} +32.0000 q^{32} +30.0000 q^{35} +36.0000 q^{36} +54.0000 q^{37} -4.00000 q^{38} -40.0000 q^{40} -78.0000 q^{41} -72.0000 q^{44} -45.0000 q^{45} +52.0000 q^{46} -86.0000 q^{47} -13.0000 q^{49} +50.0000 q^{50} +24.0000 q^{52} -74.0000 q^{53} +90.0000 q^{55} -48.0000 q^{56} +78.0000 q^{59} -54.0000 q^{63} +64.0000 q^{64} -30.0000 q^{65} +60.0000 q^{70} +72.0000 q^{72} +108.000 q^{74} -8.00000 q^{76} +108.000 q^{77} -80.0000 q^{80} +81.0000 q^{81} -156.000 q^{82} -144.000 q^{88} +18.0000 q^{89} -90.0000 q^{90} -36.0000 q^{91} +104.000 q^{92} -172.000 q^{94} +10.0000 q^{95} -26.0000 q^{98} -162.000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	2.00000	1.00000
$2$	2.00000	1.00000
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	4.00000	1.00000
$5$	−5.00000	−1.00000
$5$	−5.00000	−1.00000
$6$	0	0
$7$	−6.00000	−0.857143	−0.428571	−	0.903508i	$-0.640983\pi$
$7$	−6.00000	−0.857143	−0.428571	+	0.903508i	$0.640983\pi$
$8$	8.00000	1.00000
$9$	9.00000	1.00000
$10$	−10.0000	−1.00000
$11$	−18.0000	−1.63636	−0.818182	−	0.574960i	$-0.805018\pi$
$11$	−18.0000	−1.63636	−0.818182	+	0.574960i	$0.805018\pi$
$12$	0	0
$13$	6.00000	0.461538	0.230769	−	0.973009i	$-0.425876\pi$
$13$	6.00000	0.461538	0.230769	+	0.973009i	$0.425876\pi$
$14$	−12.0000	−0.857143
$15$	0	0
$16$	16.0000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	18.0000	1.00000
$19$	−2.00000	−0.105263	−0.0526316	−	0.998614i	$-0.516761\pi$
$19$	−2.00000	−0.105263	−0.0526316	+	0.998614i	$0.516761\pi$
$20$	−20.0000	−1.00000
$21$	0	0
$22$	−36.0000	−1.63636
$23$	26.0000	1.13043	0.565217	−	0.824942i	$-0.308792\pi$
$23$	26.0000	1.13043	0.565217	+	0.824942i	$0.308792\pi$
$24$	0	0
$25$	25.0000	1.00000
$26$	12.0000	0.461538
$27$	0	0
$28$	−24.0000	−0.857143
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	32.0000	1.00000
$33$	0	0
$34$	0	0
$35$	30.0000	0.857143
$36$	36.0000	1.00000
$37$	54.0000	1.45946	0.729730	−	0.683736i	$-0.239646\pi$
$37$	54.0000	1.45946	0.729730	+	0.683736i	$0.239646\pi$
$38$	−4.00000	−0.105263
$39$	0	0
$40$	−40.0000	−1.00000
$41$	−78.0000	−1.90244	−0.951220	−	0.308515i	$-0.900168\pi$
$41$	−78.0000	−1.90244	−0.951220	+	0.308515i	$0.900168\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−72.0000	−1.63636
$45$	−45.0000	−1.00000
$46$	52.0000	1.13043
$47$	−86.0000	−1.82979	−0.914894	−	0.403695i	$-0.867726\pi$
$47$	−86.0000	−1.82979	−0.914894	+	0.403695i	$0.867726\pi$
$48$	0	0
$49$	−13.0000	−0.265306
$50$	50.0000	1.00000
$51$	0	0
$52$	24.0000	0.461538
$53$	−74.0000	−1.39623	−0.698113	−	0.715987i	$-0.745977\pi$
$53$	−74.0000	−1.39623	−0.698113	+	0.715987i	$0.745977\pi$
$54$	0	0
$55$	90.0000	1.63636
$56$	−48.0000	−0.857143
$57$	0	0
$58$	0	0
$59$	78.0000	1.32203	0.661017	−	0.750371i	$-0.270125\pi$
$59$	78.0000	1.32203	0.661017	+	0.750371i	$0.270125\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−54.0000	−0.857143
$64$	64.0000	1.00000
$65$	−30.0000	−0.461538
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	60.0000	0.857143
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	72.0000	1.00000
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	108.000	1.45946
$75$	0	0
$76$	−8.00000	−0.105263
$77$	108.000	1.40260
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−80.0000	−1.00000
$81$	81.0000	1.00000
$82$	−156.000	−1.90244
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	−144.000	−1.63636
$89$	18.0000	0.202247	0.101124	−	0.994874i	$-0.467756\pi$
$89$	18.0000	0.202247	0.101124	+	0.994874i	$0.467756\pi$
$90$	−90.0000	−1.00000
$91$	−36.0000	−0.395604
$92$	104.000	1.13043
$93$	0	0
$94$	−172.000	−1.82979
$95$	10.0000	0.105263
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−26.0000	−0.265306
$99$	−162.000	−1.63636
$100$	100.000	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	186.000	1.80583	0.902913	−	0.429824i	$-0.141424\pi$
$103$	186.000	1.80583	0.902913	+	0.429824i	$0.141424\pi$
$104$	48.0000	0.461538
$105$	0	0
$106$	−148.000	−1.39623
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	180.000	1.63636
$111$	0	0
$112$	−96.0000	−0.857143
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	−130.000	−1.13043
$116$	0	0
$117$	54.0000	0.461538
$118$	156.000	1.32203
$119$	0	0
$120$	0	0
$121$	203.000	1.67769
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−125.000	−1.00000
$126$	−108.000	−0.857143
$127$	−246.000	−1.93701	−0.968504	−	0.248998i	$-0.919899\pi$
$127$	−246.000	−1.93701	−0.968504	+	0.248998i	$0.919899\pi$
$128$	128.000	1.00000
$129$	0	0
$130$	−60.0000	−0.461538
$131$	222.000	1.69466	0.847328	−	0.531070i	$-0.178210\pi$
$131$	222.000	1.69466	0.847328	+	0.531070i	$0.178210\pi$
$132$	0	0
$133$	12.0000	0.0902256
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−82.0000	−0.589928	−0.294964	−	0.955508i	$-0.595308\pi$
$139$	−82.0000	−0.589928	−0.294964	+	0.955508i	$0.595308\pi$
$140$	120.000	0.857143
$141$	0	0
$142$	0	0
$143$	−108.000	−0.755245
$144$	144.000	1.00000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	216.000	1.45946
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	−16.0000	−0.105263
$153$	0	0
$154$	216.000	1.40260
$155$	0	0
$156$	0	0
$157$	−186.000	−1.18471	−0.592357	−	0.805676i	$-0.701802\pi$
$157$	−186.000	−1.18471	−0.592357	+	0.805676i	$0.701802\pi$
$158$	0	0
$159$	0	0
$160$	−160.000	−1.00000
$161$	−156.000	−0.968944
$162$	162.000	1.00000
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	−312.000	−1.90244
$165$	0	0
$166$	0	0
$167$	314.000	1.88024	0.940120	−	0.340844i	$-0.110713\pi$
$167$	314.000	1.88024	0.940120	+	0.340844i	$0.110713\pi$
$168$	0	0
$169$	−133.000	−0.786982
$170$	0	0
$171$	−18.0000	−0.105263
$172$	0	0
$173$	166.000	0.959538	0.479769	−	0.877395i	$-0.340721\pi$
$173$	166.000	0.959538	0.479769	+	0.877395i	$0.340721\pi$
$174$	0	0
$175$	−150.000	−0.857143
$176$	−288.000	−1.63636
$177$	0	0
$178$	36.0000	0.202247
$179$	318.000	1.77654	0.888268	−	0.459325i	$-0.151909\pi$
$179$	318.000	1.77654	0.888268	+	0.459325i	$0.151909\pi$
$180$	−180.000	−1.00000
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	−72.0000	−0.395604
$183$	0	0
$184$	208.000	1.13043
$185$	−270.000	−1.45946
$186$	0	0
$187$	0	0
$188$	−344.000	−1.82979
$189$	0	0
$190$	20.0000	0.105263
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	−52.0000	−0.265306
$197$	−106.000	−0.538071	−0.269036	−	0.963130i	$-0.586705\pi$
$197$	−106.000	−0.538071	−0.269036	+	0.963130i	$0.586705\pi$
$198$	−324.000	−1.63636
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	200.000	1.00000
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	390.000	1.90244
$206$	372.000	1.80583
$207$	234.000	1.13043
$208$	96.0000	0.461538
$209$	36.0000	0.172249
$210$	0	0
$211$	62.0000	0.293839	0.146919	−	0.989148i	$-0.453064\pi$
$211$	62.0000	0.293839	0.146919	+	0.989148i	$0.453064\pi$
$212$	−296.000	−1.39623
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	360.000	1.63636
$221$	0	0
$222$	0	0
$223$	−54.0000	−0.242152	−0.121076	−	0.992643i	$-0.538635\pi$
$223$	−54.0000	−0.242152	−0.121076	+	0.992643i	$0.538635\pi$
$224$	−192.000	−0.857143
$225$	225.000	1.00000
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	−260.000	−1.13043
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	108.000	0.461538
$235$	430.000	1.82979
$236$	312.000	1.32203
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	−158.000	−0.655602	−0.327801	−	0.944747i	$-0.606307\pi$
$241$	−158.000	−0.655602	−0.327801	+	0.944747i	$0.606307\pi$
$242$	406.000	1.67769
$243$	0	0
$244$	0	0
$245$	65.0000	0.265306
$246$	0	0
$247$	−12.0000	−0.0485830
$248$	0	0
$249$	0	0
$250$	−250.000	−1.00000
$251$	−498.000	−1.98406	−0.992032	−	0.125987i	$-0.959790\pi$
$251$	−498.000	−1.98406	−0.992032	+	0.125987i	$0.959790\pi$
$252$	−216.000	−0.857143
$253$	−468.000	−1.84980
$254$	−492.000	−1.93701
$255$	0	0
$256$	256.000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−324.000	−1.25097
$260$	−120.000	−0.461538
$261$	0	0
$262$	444.000	1.69466
$263$	−454.000	−1.72624	−0.863118	−	0.505003i	$-0.831492\pi$
$263$	−454.000	−1.72624	−0.863118	+	0.505003i	$0.831492\pi$
$264$	0	0
$265$	370.000	1.39623
$266$	24.0000	0.0902256
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−450.000	−1.63636
$276$	0	0
$277$	−426.000	−1.53791	−0.768953	−	0.639305i	$-0.779222\pi$
$277$	−426.000	−1.53791	−0.768953	+	0.639305i	$0.779222\pi$
$278$	−164.000	−0.589928
$279$	0	0
$280$	240.000	0.857143
$281$	−78.0000	−0.277580	−0.138790	−	0.990322i	$-0.544321\pi$
$281$	−78.0000	−0.277580	−0.138790	+	0.990322i	$0.544321\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	−216.000	−0.755245
$287$	468.000	1.63066
$288$	288.000	1.00000
$289$	289.000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	566.000	1.93174	0.965870	−	0.259026i	$-0.0834016\pi$
$293$	566.000	1.93174	0.965870	+	0.259026i	$0.0834016\pi$
$294$	0	0
$295$	−390.000	−1.32203
$296$	432.000	1.45946
$297$	0	0
$298$	0	0
$299$	156.000	0.521739
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−32.0000	−0.105263
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	432.000	1.40260
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	−372.000	−1.18471
$315$	270.000	0.857143
$316$	0	0
$317$	−346.000	−1.09148	−0.545741	−	0.837954i	$-0.683752\pi$
$317$	−346.000	−1.09148	−0.545741	+	0.837954i	$0.683752\pi$
$318$	0	0
$319$	0	0
$320$	−320.000	−1.00000
$321$	0	0
$322$	−312.000	−0.968944
$323$	0	0
$324$	324.000	1.00000
$325$	150.000	0.461538
$326$	0	0
$327$	0	0
$328$	−624.000	−1.90244
$329$	516.000	1.56839
$330$	0	0
$331$	−338.000	−1.02115	−0.510574	−	0.859834i	$-0.670567\pi$
$331$	−338.000	−1.02115	−0.510574	+	0.859834i	$0.670567\pi$
$332$	0	0
$333$	486.000	1.45946
$334$	628.000	1.88024
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−266.000	−0.786982
$339$	0	0
$340$	0	0
$341$	0	0
$342$	−36.0000	−0.105263
$343$	372.000	1.08455
$344$	0	0
$345$	0	0
$346$	332.000	0.959538
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−300.000	−0.857143
$351$	0	0
$352$	−576.000	−1.63636
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	72.0000	0.202247
$357$	0	0
$358$	636.000	1.77654
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−360.000	−1.00000
$361$	−357.000	−0.988920
$362$	0	0
$363$	0	0
$364$	−144.000	−0.395604
$365$	0	0
$366$	0	0
$367$	234.000	0.637602	0.318801	−	0.947822i	$-0.396720\pi$
$367$	234.000	0.637602	0.318801	+	0.947822i	$0.396720\pi$
$368$	416.000	1.13043
$369$	−702.000	−1.90244
$370$	−540.000	−1.45946
$371$	444.000	1.19677
$372$	0	0
$373$	−234.000	−0.627346	−0.313673	−	0.949531i	$-0.601560\pi$
$373$	−234.000	−0.627346	−0.313673	+	0.949531i	$0.601560\pi$
$374$	0	0
$375$	0	0
$376$	−688.000	−1.82979
$377$	0	0
$378$	0	0
$379$	398.000	1.05013	0.525066	−	0.851062i	$-0.324041\pi$
$379$	398.000	1.05013	0.525066	+	0.851062i	$0.324041\pi$
$380$	40.0000	0.105263
$381$	0	0
$382$	0	0
$383$	586.000	1.53003	0.765013	−	0.644015i	$-0.222732\pi$
$383$	586.000	1.53003	0.765013	+	0.644015i	$0.222732\pi$
$384$	0	0
$385$	−540.000	−1.40260
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	−104.000	−0.265306
$393$	0	0
$394$	−212.000	−0.538071
$395$	0	0
$396$	−648.000	−1.63636
$397$	774.000	1.94962	0.974811	−	0.223032i	$-0.0715955\pi$
$397$	774.000	1.94962	0.974811	+	0.223032i	$0.0715955\pi$
$398$	0	0
$399$	0	0
$400$	400.000	1.00000
$401$	642.000	1.60100	0.800499	−	0.599334i	$-0.204568\pi$
$401$	642.000	1.60100	0.800499	+	0.599334i	$0.204568\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−405.000	−1.00000
$406$	0	0
$407$	−972.000	−2.38821
$408$	0	0
$409$	−622.000	−1.52078	−0.760391	−	0.649465i	$-0.774993\pi$
$409$	−622.000	−1.52078	−0.760391	+	0.649465i	$0.774993\pi$
$410$	780.000	1.90244
$411$	0	0
$412$	744.000	1.80583
$413$	−468.000	−1.13317
$414$	468.000	1.13043
$415$	0	0
$416$	192.000	0.461538
$417$	0	0
$418$	72.0000	0.172249
$419$	−162.000	−0.386635	−0.193317	−	0.981136i	$-0.561925\pi$
$419$	−162.000	−0.386635	−0.193317	+	0.981136i	$0.561925\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	124.000	0.293839
$423$	−774.000	−1.82979
$424$	−592.000	−1.39623
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−52.0000	−0.118993
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	720.000	1.63636
$441$	−117.000	−0.265306
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	−90.0000	−0.202247
$446$	−108.000	−0.242152
$447$	0	0
$448$	−384.000	−0.857143
$449$	258.000	0.574610	0.287305	−	0.957839i	$-0.407241\pi$
$449$	258.000	0.574610	0.287305	+	0.957839i	$0.407241\pi$
$450$	450.000	1.00000
$451$	1404.00	3.11308
$452$	0	0
$453$	0	0
$454$	0	0
$455$	180.000	0.395604
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	−520.000	−1.13043
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	426.000	0.920086	0.460043	−	0.887897i	$-0.347834\pi$
$463$	426.000	0.920086	0.460043	+	0.887897i	$0.347834\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	216.000	0.461538
$469$	0	0
$470$	860.000	1.82979
$471$	0	0
$472$	624.000	1.32203
$473$	0	0
$474$	0	0
$475$	−50.0000	−0.105263
$476$	0	0
$477$	−666.000	−1.39623
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	324.000	0.673597
$482$	−316.000	−0.655602
$483$	0	0
$484$	812.000	1.67769
$485$	0	0
$486$	0	0
$487$	−6.00000	−0.0123203	−0.00616016	−	0.999981i	$-0.501961\pi$
$487$	−6.00000	−0.0123203	−0.00616016	+	0.999981i	$0.501961\pi$
$488$	0	0
$489$	0	0
$490$	130.000	0.265306
$491$	−978.000	−1.99185	−0.995927	−	0.0901668i	$-0.971260\pi$
$491$	−978.000	−1.99185	−0.995927	+	0.0901668i	$0.971260\pi$
$492$	0	0
$493$	0	0
$494$	−24.0000	−0.0485830
$495$	810.000	1.63636
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−962.000	−1.92786	−0.963928	−	0.266164i	$-0.914244\pi$
$499$	−962.000	−1.92786	−0.963928	+	0.266164i	$0.914244\pi$
$500$	−500.000	−1.00000
$501$	0	0
$502$	−996.000	−1.98406
$503$	−614.000	−1.22068	−0.610338	−	0.792141i	$-0.708966\pi$
$503$	−614.000	−1.22068	−0.610338	+	0.792141i	$0.708966\pi$
$504$	−432.000	−0.857143
$505$	0	0
$506$	−936.000	−1.84980
$507$	0	0
$508$	−984.000	−1.93701
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	512.000	1.00000
$513$	0	0
$514$	0	0
$515$	−930.000	−1.80583
$516$	0	0
$517$	1548.00	2.99420
$518$	−648.000	−1.25097
$519$	0	0
$520$	−240.000	−0.461538
$521$	402.000	0.771593	0.385797	−	0.922584i	$-0.373927\pi$
$521$	402.000	0.771593	0.385797	+	0.922584i	$0.373927\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	888.000	1.69466
$525$	0	0
$526$	−908.000	−1.72624
$527$	0	0
$528$	0	0
$529$	147.000	0.277883
$530$	740.000	1.39623
$531$	702.000	1.32203
$532$	48.0000	0.0902256
$533$	−468.000	−0.878049
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	234.000	0.434137
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	−900.000	−1.63636
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−852.000	−1.53791
$555$	0	0
$556$	−328.000	−0.589928
$557$	934.000	1.67684	0.838420	−	0.545025i	$-0.183480\pi$
$557$	934.000	1.67684	0.838420	+	0.545025i	$0.183480\pi$
$558$	0	0
$559$	0	0
$560$	480.000	0.857143
$561$	0	0
$562$	−156.000	−0.277580
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−486.000	−0.857143
$568$	0	0
$569$	978.000	1.71880	0.859402	−	0.511300i	$-0.170836\pi$
$569$	978.000	1.71880	0.859402	+	0.511300i	$0.170836\pi$
$570$	0	0
$571$	−818.000	−1.43257	−0.716287	−	0.697806i	$-0.754160\pi$
$571$	−818.000	−1.43257	−0.716287	+	0.697806i	$0.754160\pi$
$572$	−432.000	−0.755245
$573$	0	0
$574$	936.000	1.63066
$575$	650.000	1.13043
$576$	576.000	1.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	578.000	1.00000
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1332.00	2.28473
$584$	0	0
$585$	−270.000	−0.461538
$586$	1132.00	1.93174
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	−780.000	−1.32203
$591$	0	0
$592$	864.000	1.45946
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	312.000	0.521739
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	562.000	0.935108	0.467554	−	0.883964i	$-0.345135\pi$
$601$	562.000	0.935108	0.467554	+	0.883964i	$0.345135\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−1015.00	−1.67769
$606$	0	0
$607$	−1206.00	−1.98682	−0.993410	−	0.114613i	$-0.963437\pi$
$607$	−1206.00	−1.98682	−0.993410	+	0.114613i	$0.963437\pi$
$608$	−64.0000	−0.105263
$609$	0	0
$610$	0	0
$611$	−516.000	−0.844517
$612$	0	0
$613$	−1194.00	−1.94780	−0.973899	−	0.226982i	$-0.927114\pi$
$613$	−1194.00	−1.94780	−0.973899	+	0.226982i	$0.927114\pi$
$614$	0	0
$615$	0	0
$616$	864.000	1.40260
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	878.000	1.41842	0.709208	−	0.704999i	$-0.249053\pi$
$619$	878.000	1.41842	0.709208	+	0.704999i	$0.249053\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−108.000	−0.173355
$624$	0	0
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	−744.000	−1.18471
$629$	0	0
$630$	540.000	0.857143
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	−692.000	−1.09148
$635$	1230.00	1.93701
$636$	0	0
$637$	−78.0000	−0.122449
$638$	0	0
$639$	0	0
$640$	−640.000	−1.00000
$641$	−1278.00	−1.99376	−0.996880	−	0.0789336i	$-0.974848\pi$
$641$	−1278.00	−1.99376	−0.996880	+	0.0789336i	$0.974848\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	−624.000	−0.968944
$645$	0	0
$646$	0	0
$647$	−326.000	−0.503864	−0.251932	−	0.967745i	$-0.581066\pi$
$647$	−326.000	−0.503864	−0.251932	+	0.967745i	$0.581066\pi$
$648$	648.000	1.00000
$649$	−1404.00	−2.16333
$650$	300.000	0.461538
$651$	0	0
$652$	0	0
$653$	1286.00	1.96937	0.984686	−	0.174337i	$-0.0557782\pi$
$653$	1286.00	1.96937	0.984686	+	0.174337i	$0.0557782\pi$
$654$	0	0
$655$	−1110.00	−1.69466
$656$	−1248.00	−1.90244
$657$	0	0
$658$	1032.00	1.56839
$659$	−642.000	−0.974203	−0.487102	−	0.873345i	$-0.661946\pi$
$659$	−642.000	−0.974203	−0.487102	+	0.873345i	$0.661946\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−676.000	−1.02115
$663$	0	0
$664$	0	0
$665$	−60.0000	−0.0902256
$666$	972.000	1.45946
$667$	0	0
$668$	1256.00	1.88024
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	−532.000	−0.786982
$677$	−1066.00	−1.57459	−0.787297	−	0.616574i	$-0.788520\pi$
$677$	−1066.00	−1.57459	−0.787297	+	0.616574i	$0.788520\pi$
$678$	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			$\pi$
$684$	−72.0000	−0.105263
$685$	0	0
$686$	744.000	1.08455
$687$	0	0
$688$	0	0
$689$	−444.000	−0.644412
$690$	0	0
$691$	382.000	0.552822	0.276411	−	0.961040i	$-0.410855\pi$
$691$	382.000	0.552822	0.276411	+	0.961040i	$0.410855\pi$
$692$	664.000	0.959538
$693$	972.000	1.40260
$694$	0	0
$695$	410.000	0.589928
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−600.000	−0.857143
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	−108.000	−0.153627
$704$	−1152.00	−1.63636
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	144.000	0.202247
$713$	0	0
$714$	0	0
$715$	540.000	0.755245
$716$	1272.00	1.77654
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−720.000	−1.00000
$721$	−1116.00	−1.54785
$722$	−714.000	−0.988920
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	1434.00	1.97249	0.986245	−	0.165291i	$-0.0528563\pi$
$727$	1434.00	1.97249	0.986245	+	0.165291i	$0.0528563\pi$
$728$	−288.000	−0.395604
$729$	729.000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−954.000	−1.30150	−0.650750	−	0.759292i	$-0.725546\pi$
$733$	−954.000	−1.30150	−0.650750	+	0.759292i	$0.725546\pi$
$734$	468.000	0.637602
$735$	0	0
$736$	832.000	1.13043
$737$	0	0
$738$	−1404.00	−1.90244
$739$	1438.00	1.94587	0.972936	−	0.231073i	$-0.0742236\pi$
$739$	1438.00	1.94587	0.972936	+	0.231073i	$0.0742236\pi$
$740$	−1080.00	−1.45946
$741$	0	0
$742$	888.000	1.19677
$743$	−134.000	−0.180350	−0.0901750	−	0.995926i	$-0.528743\pi$
$743$	−134.000	−0.180350	−0.0901750	+	0.995926i	$0.528743\pi$
$744$	0	0
$745$	0	0
$746$	−468.000	−0.627346
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−1376.00	−1.82979
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	534.000	0.705416	0.352708	−	0.935733i	$-0.385261\pi$
$757$	534.000	0.705416	0.352708	+	0.935733i	$0.385261\pi$
$758$	796.000	1.05013
$759$	0	0
$760$	80.0000	0.105263
$761$	−1038.00	−1.36399	−0.681997	−	0.731355i	$-0.738888\pi$
$761$	−1038.00	−1.36399	−0.681997	+	0.731355i	$0.738888\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	1172.00	1.53003
$767$	468.000	0.610169
$768$	0	0
$769$	1378.00	1.79194	0.895969	−	0.444117i	$-0.146483\pi$
$769$	1378.00	1.79194	0.895969	+	0.444117i	$0.146483\pi$
$770$	−1080.00	−1.40260
$771$	0	0
$772$	0	0
$773$	1046.00	1.35317	0.676585	−	0.736365i	$-0.263459\pi$
$773$	1046.00	1.35317	0.676585	+	0.736365i	$0.263459\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	156.000	0.200257
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−208.000	−0.265306
$785$	930.000	1.18471
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−424.000	−0.538071
$789$	0	0
$790$	0	0
$791$	0	0
$792$	−1296.00	−1.63636
$793$	0	0
$794$	1548.00	1.94962
$795$	0	0
$796$	0	0
$797$	−26.0000	−0.0326223	−0.0163112	−	0.999867i	$-0.505192\pi$
$797$	−26.0000	−0.0326223	−0.0163112	+	0.999867i	$0.505192\pi$
$798$	0	0
$799$	0	0
$800$	800.000	1.00000
$801$	162.000	0.202247
$802$	1284.00	1.60100
$803$	0	0
$804$	0	0
$805$	780.000	0.968944
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−942.000	−1.16440	−0.582200	−	0.813045i	$-0.697808\pi$
$809$	−942.000	−1.16440	−0.582200	+	0.813045i	$0.697808\pi$
$810$	−810.000	−1.00000
$811$	−1618.00	−1.99507	−0.997534	−	0.0701862i	$-0.977641\pi$
$811$	−1618.00	−1.99507	−0.997534	+	0.0701862i	$0.977641\pi$
$812$	0	0
$813$	0	0
$814$	−1944.00	−2.38821
$815$	0	0
$816$	0	0
$817$	0	0
$818$	−1244.00	−1.52078
$819$	−324.000	−0.395604
$820$	1560.00	1.90244
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	666.000	0.809235	0.404617	−	0.914486i	$-0.367405\pi$
$823$	666.000	0.809235	0.404617	+	0.914486i	$0.367405\pi$
$824$	1488.00	1.80583
$825$	0	0
$826$	−936.000	−1.13317
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	936.000	1.13043
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	384.000	0.461538
$833$	0	0
$834$	0	0
$835$	−1570.00	−1.88024
$836$	144.000	0.172249
$837$	0	0
$838$	−324.000	−0.386635
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	248.000	0.293839
$845$	665.000	0.786982
$846$	−1548.00	−1.82979
$847$	−1218.00	−1.43802
$848$	−1184.00	−1.39623
$849$	0	0
$850$	0	0
$851$	1404.00	1.64982
$852$	0	0
$853$	−1674.00	−1.96249	−0.981243	−	0.192777i	$-0.938251\pi$
$853$	−1674.00	−1.96249	−0.981243	+	0.192777i	$0.938251\pi$
$854$	0	0
$855$	90.0000	0.105263
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−1522.00	−1.77183	−0.885914	−	0.463850i	$-0.846468\pi$
$859$	−1522.00	−1.77183	−0.885914	+	0.463850i	$0.846468\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−1654.00	−1.91657	−0.958285	−	0.285814i	$-0.907736\pi$
$863$	−1654.00	−1.91657	−0.958285	+	0.285814i	$0.907736\pi$
$864$	0	0
$865$	−830.000	−0.959538
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	−104.000	−0.118993
$875$	750.000	0.857143
$876$	0	0
$877$	−1626.00	−1.85405	−0.927024	−	0.375002i	$-0.877642\pi$
$877$	−1626.00	−1.85405	−0.927024	+	0.375002i	$0.877642\pi$
$878$	0	0
$879$	0	0
$880$	1440.00	1.63636
$881$	1602.00	1.81839	0.909194	−	0.416373i	$-0.136699\pi$
$881$	1602.00	1.81839	0.909194	+	0.416373i	$0.136699\pi$
$882$	−234.000	−0.265306
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	1754.00	1.97745	0.988726	−	0.149736i	$-0.0478423\pi$
$887$	1754.00	1.97745	0.988726	+	0.149736i	$0.0478423\pi$
$888$	0	0
$889$	1476.00	1.66029
$890$	−180.000	−0.202247
$891$	−1458.00	−1.63636
$892$	−216.000	−0.242152
$893$	172.000	0.192609
$894$	0	0
$895$	−1590.00	−1.77654
$896$	−768.000	−0.857143
$897$	0	0
$898$	516.000	0.574610
$899$	0	0
$900$	900.000	1.00000
$901$	0	0
$902$	2808.00	3.11308
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	360.000	0.395604
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−1332.00	−1.45256
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	−1040.00	−1.13043
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1350.00	1.45946
$926$	852.000	0.920086
$927$	1674.00	1.80583
$928$	0	0
$929$	−702.000	−0.755651	−0.377826	−	0.925877i	$-0.623328\pi$
$929$	−702.000	−0.755651	−0.377826	+	0.925877i	$0.623328\pi$
$930$	0	0
$931$	26.0000	0.0279270
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	432.000	0.461538
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	1720.00	1.82979
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	−2028.00	−2.15058
$944$	1248.00	1.32203
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	−100.000	−0.105263
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	−1332.00	−1.39623
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	648.000	0.673597
$963$	0	0
$964$	−632.000	−0.655602
$965$	0	0
$966$	0	0
$967$	954.000	0.986556	0.493278	−	0.869872i	$-0.335798\pi$
$967$	954.000	0.986556	0.493278	+	0.869872i	$0.335798\pi$
$968$	1624.00	1.67769
$969$	0	0
$970$	0	0
$971$	1902.00	1.95881	0.979403	−	0.201917i	$-0.0647171\pi$
$971$	1902.00	1.95881	0.979403	+	0.201917i	$0.0647171\pi$
$972$	0	0
$973$	492.000	0.505653
$974$	−12.0000	−0.0123203
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	−324.000	−0.330950
$980$	260.000	0.265306
$981$	0	0
$982$	−1956.00	−1.99185
$983$	346.000	0.351984	0.175992	−	0.984392i	$-0.443687\pi$
$983$	346.000	0.351984	0.175992	+	0.984392i	$0.443687\pi$
$984$	0	0
$985$	530.000	0.538071
$986$	0	0
$987$	0	0
$988$	−48.0000	−0.0485830
$989$	0	0
$990$	1620.00	1.63636
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−426.000	−0.427282	−0.213641	−	0.976912i	$-0.568532\pi$
$997$	−426.000	−0.427282	−0.213641	+	0.976912i	$0.568532\pi$
$998$	−1924.00	−1.92786
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.e.b.19.1	yes	1
3.2	odd	2		360.3.p.a.19.1		1
4.3	odd	2		160.3.e.a.79.1		1
5.2	odd	4		200.3.g.c.51.2		2
5.3	odd	4		200.3.g.c.51.1		2
5.4	even	2		40.3.e.a.19.1	✓	1
8.3	odd	2		40.3.e.a.19.1	✓	1
8.5	even	2		160.3.e.b.79.1		1
12.11	even	2		1440.3.p.b.559.1		1
15.14	odd	2		360.3.p.b.19.1		1
16.3	odd	4		1280.3.h.b.1279.2		2
16.5	even	4		1280.3.h.c.1279.1		2
16.11	odd	4		1280.3.h.b.1279.1		2
16.13	even	4		1280.3.h.c.1279.2		2
20.3	even	4		800.3.g.c.751.1		2
20.7	even	4		800.3.g.c.751.2		2
20.19	odd	2		160.3.e.b.79.1		1
24.5	odd	2		1440.3.p.a.559.1		1
24.11	even	2		360.3.p.b.19.1		1
40.3	even	4		200.3.g.c.51.2		2
40.13	odd	4		800.3.g.c.751.2		2
40.19	odd	2	CM	40.3.e.b.19.1	yes	1
40.27	even	4		200.3.g.c.51.1		2
40.29	even	2		160.3.e.a.79.1		1
40.37	odd	4		800.3.g.c.751.1		2
60.59	even	2		1440.3.p.a.559.1		1
80.19	odd	4		1280.3.h.c.1279.1		2
80.29	even	4		1280.3.h.b.1279.1		2
80.59	odd	4		1280.3.h.c.1279.2		2
80.69	even	4		1280.3.h.b.1279.2		2
120.29	odd	2		1440.3.p.b.559.1		1
120.59	even	2		360.3.p.a.19.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.a.19.1	✓	1	5.4	even	2
40.3.e.a.19.1	✓	1	8.3	odd	2
40.3.e.b.19.1	yes	1	1.1	even	1	trivial
40.3.e.b.19.1	yes	1	40.19	odd	2	CM
160.3.e.a.79.1		1	4.3	odd	2
160.3.e.a.79.1		1	40.29	even	2
160.3.e.b.79.1		1	8.5	even	2
160.3.e.b.79.1		1	20.19	odd	2
200.3.g.c.51.1		2	5.3	odd	4
200.3.g.c.51.1		2	40.27	even	4
200.3.g.c.51.2		2	5.2	odd	4
200.3.g.c.51.2		2	40.3	even	4
360.3.p.a.19.1		1	3.2	odd	2
360.3.p.a.19.1		1	120.59	even	2
360.3.p.b.19.1		1	15.14	odd	2
360.3.p.b.19.1		1	24.11	even	2
800.3.g.c.751.1		2	20.3	even	4
800.3.g.c.751.1		2	40.37	odd	4
800.3.g.c.751.2		2	20.7	even	4
800.3.g.c.751.2		2	40.13	odd	4
1280.3.h.b.1279.1		2	16.11	odd	4
1280.3.h.b.1279.1		2	80.29	even	4
1280.3.h.b.1279.2		2	16.3	odd	4
1280.3.h.b.1279.2		2	80.69	even	4
1280.3.h.c.1279.1		2	16.5	even	4
1280.3.h.c.1279.1		2	80.19	odd	4
1280.3.h.c.1279.2		2	16.13	even	4
1280.3.h.c.1279.2		2	80.59	odd	4
1440.3.p.a.559.1		1	24.5	odd	2
1440.3.p.a.559.1		1	60.59	even	2
1440.3.p.b.559.1		1	12.11	even	2
1440.3.p.b.559.1		1	120.29	odd	2

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.e (of order \(2\), degree \(1\), minimal)

\(n\)	\(17\)	\(21\)	\(31\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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