LMFDB - Embedded newform 1280.3.h.c.1279.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(1279,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1280.1279");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.8774738381$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1279.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.1279
Dual form			1280.3.h.c.1279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.00000i q^{5} +6.00000 q^{7} -9.00000 q^{9} +O(q^{10})$	$q+5.00000i q^{5} +6.00000 q^{7} -9.00000 q^{9} +18.0000i q^{11} +6.00000i q^{13} -2.00000i q^{19} -26.0000 q^{23} -25.0000 q^{25} +30.0000i q^{35} -54.0000i q^{37} +78.0000 q^{41} -45.0000i q^{45} -86.0000 q^{47} -13.0000 q^{49} +74.0000i q^{53} -90.0000 q^{55} -78.0000i q^{59} -54.0000 q^{63} -30.0000 q^{65} +108.000i q^{77} +81.0000 q^{81} -18.0000 q^{89} +36.0000i q^{91} +10.0000 q^{95} -162.000i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 12 q^{7} - 18 q^{9}+O(q^{10}) $ 2 * q + 12 * q^7 - 18 * q^9	$ 2 q + 12 q^{7} - 18 q^{9} - 52 q^{23} - 50 q^{25} + 156 q^{41} - 172 q^{47} - 26 q^{49} - 180 q^{55} - 108 q^{63} - 60 q^{65} + 162 q^{81} - 36 q^{89} + 20 q^{95}+O(q^{100}) $ 2 * q + 12 * q^7 - 18 * q^9 - 52 * q^23 - 50 * q^25 + 156 * q^41 - 172 * q^47 - 26 * q^49 - 180 * q^55 - 108 * q^63 - 60 * q^65 + 162 * q^81 - 36 * q^89 + 20 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	0	0
$5$	5.00000i	1.00000i
$5$	5.00000i	1.00000i
$6$	0	0
$7$	6.00000	0.857143	0.428571	−	0.903508i	$-0.359017\pi$
$7$	6.00000	0.857143	0.428571	+	0.903508i	$0.359017\pi$
$8$	0	0
$9$	−9.00000	−1.00000
$10$	0	0
$11$	18.0000i	1.63636i	0.574960	+	0.818182i	$0.305018\pi$
$11$	18.0000i	1.63636i	−0.574960	+	0.818182i	$0.694982\pi$
$12$	0	0
$13$	6.00000i	0.461538i	0.973009	+	0.230769i	$0.0741242\pi$
$13$	6.00000i	0.461538i	−0.973009	+	0.230769i	$0.925876\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	− 2.00000i	− 0.105263i	−0.998614	−	0.0526316i	$-0.983239\pi$
$19$	− 2.00000i	− 0.105263i	0.998614	−	0.0526316i	$-0.0167609\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−26.0000	−1.13043	−0.565217	−	0.824942i	$-0.691208\pi$
$23$	−26.0000	−1.13043	−0.565217	+	0.824942i	$0.691208\pi$
$24$	0	0
$25$	−25.0000	−1.00000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	30.0000i	0.857143i
$36$	0	0
$37$	− 54.0000i	− 1.45946i	−0.683736	−	0.729730i	$-0.739646\pi$
$37$	− 54.0000i	− 1.45946i	0.683736	−	0.729730i	$-0.260354\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	78.0000	1.90244	0.951220	−	0.308515i	$-0.0998320\pi$
$41$	78.0000	1.90244	0.951220	+	0.308515i	$0.0998320\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	− 45.0000i	− 1.00000i
$46$	0	0
$47$	−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
$50$	0	0
$51$	0	0
$52$	0	0
$53$	74.0000i	1.39623i	0.715987	+	0.698113i	$0.245977\pi$
$53$	74.0000i	1.39623i	−0.715987	+	0.698113i	$0.754023\pi$
$54$	0	0
$55$	−90.0000	−1.63636
$56$	0	0
$57$	0	0
$58$	0	0
$59$	− 78.0000i	− 1.32203i	−0.750371	−	0.661017i	$-0.770125\pi$
$59$	− 78.0000i	− 1.32203i	0.750371	−	0.661017i	$-0.229875\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	−54.0000	−0.857143
$64$	0	0
$65$	−30.0000	−0.461538
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	108.000i	1.40260i
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	81.0000	1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−18.0000	−0.202247	−0.101124	−	0.994874i	$-0.532244\pi$
$89$	−18.0000	−0.202247	−0.101124	+	0.994874i	$0.532244\pi$
$90$	0	0
$91$	36.0000i	0.395604i
$92$	0	0
$93$	0	0
$94$	0	0
$95$	10.0000	0.105263
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	− 162.000i	− 1.63636i
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−186.000	−1.80583	−0.902913	−	0.429824i	$-0.858576\pi$
$103$	−186.000	−1.80583	−0.902913	+	0.429824i	$0.858576\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	− 130.000i	− 1.13043i
$116$	0	0
$117$	− 54.0000i	− 0.461538i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−203.000	−1.67769
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 125.000i	− 1.00000i
$126$	0	0
$127$	−246.000	−1.93701	−0.968504	−	0.248998i	$-0.919899\pi$
$127$	−246.000	−1.93701	−0.968504	+	0.248998i	$0.919899\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	222.000i	1.69466i	0.531070	+	0.847328i	$0.321790\pi$
$131$	222.000i	1.69466i	−0.531070	+	0.847328i	$0.678210\pi$
$132$	0	0
$133$	− 12.0000i	− 0.0902256i
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	82.0000i	0.589928i	0.955508	+	0.294964i	$0.0953077\pi$
$139$	82.0000i	0.589928i	−0.955508	+	0.294964i	$0.904692\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−108.000	−0.755245
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	− 186.000i	− 1.18471i	−0.805676	−	0.592357i	$-0.798198\pi$
$157$	− 186.000i	− 1.18471i	0.805676	−	0.592357i	$-0.201802\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−156.000	−0.968944
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−314.000	−1.88024	−0.940120	−	0.340844i	$-0.889287\pi$
$167$	−314.000	−1.88024	−0.940120	+	0.340844i	$0.889287\pi$
$168$	0	0
$169$	133.000	0.786982
$170$	0	0
$171$	18.0000i	0.105263i
$172$	0	0
$173$	166.000i	0.959538i	0.877395	+	0.479769i	$0.159279\pi$
$173$	166.000i	0.959538i	−0.877395	+	0.479769i	$0.840721\pi$
$174$	0	0
$175$	−150.000	−0.857143
$176$	0	0
$177$	0	0
$178$	0	0
$179$	318.000i	1.77654i	0.459325	+	0.888268i	$0.348091\pi$
$179$	318.000i	1.77654i	−0.459325	+	0.888268i	$0.651909\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	270.000	1.45946
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	106.000i	0.538071i	0.963130	+	0.269036i	$0.0867049\pi$
$197$	106.000i	0.538071i	−0.963130	+	0.269036i	$0.913295\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	390.000i	1.90244i
$206$	0	0
$207$	234.000	1.13043
$208$	0	0
$209$	36.0000	0.172249
$210$	0	0
$211$	62.0000i	0.293839i	0.989148	+	0.146919i	$0.0469358\pi$
$211$	62.0000i	0.293839i	−0.989148	+	0.146919i	$0.953064\pi$
$212$	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
$221$	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	$0.538635\pi$
$224$	0	0
$225$	225.000	1.00000
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	− 430.000i	− 1.82979i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	−158.000	−0.655602	−0.327801	−	0.944747i	$-0.606307\pi$
$241$	−158.000	−0.655602	−0.327801	+	0.944747i	$0.606307\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	− 65.0000i	− 0.265306i
$246$	0	0
$247$	12.0000	0.0485830
$248$	0	0
$249$	0	0
$250$	0	0
$251$	498.000i	1.98406i	0.125987	+	0.992032i	$0.459790\pi$
$251$	498.000i	1.98406i	−0.125987	+	0.992032i	$0.540210\pi$
$252$	0	0
$253$	− 468.000i	− 1.84980i
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	− 324.000i	− 1.25097i
$260$	0	0
$261$	0	0
$262$	0	0
$263$	454.000	1.72624	0.863118	−	0.505003i	$-0.168508\pi$
$263$	454.000	1.72624	0.863118	+	0.505003i	$0.168508\pi$
$264$	0	0
$265$	−370.000	−1.39623
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	− 450.000i	− 1.63636i
$276$	0	0
$277$	426.000i	1.53791i	0.639305	+	0.768953i	$0.279222\pi$
$277$	426.000i	1.53791i	−0.639305	+	0.768953i	$0.720778\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	78.0000	0.277580	0.138790	−	0.990322i	$-0.455679\pi$
$281$	78.0000	0.277580	0.138790	+	0.990322i	$0.455679\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	468.000	1.63066
$288$	0	0
$289$	289.000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 566.000i	− 1.93174i	−0.259026	−	0.965870i	$-0.583402\pi$
$293$	− 566.000i	− 1.93174i	0.259026	−	0.965870i	$-0.416598\pi$
$294$	0	0
$295$	390.000	1.32203
$296$	0	0
$297$	0	0
$298$	0	0
$299$	− 156.000i	− 0.521739i
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	− 270.000i	− 0.857143i
$316$	0	0
$317$	− 346.000i	− 1.09148i	−0.837954	−	0.545741i	$-0.816248\pi$
$317$	− 346.000i	− 1.09148i	0.837954	−	0.545741i	$-0.183752\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	− 150.000i	− 0.461538i
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−516.000	−1.56839
$330$	0	0
$331$	338.000i	1.02115i	0.859834	+	0.510574i	$0.170567\pi$
$331$	338.000i	1.02115i	−0.859834	+	0.510574i	$0.829433\pi$
$332$	0	0
$333$	486.000i	1.45946i
$334$	0	0
$335$	0	0
$336$	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
$343$	−372.000	−1.08455
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	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	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	357.000	0.988920
$362$	0	0
$363$	0	0
$364$	0	0
$365$	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	$0.396720\pi$
$368$	0	0
$369$	−702.000	−1.90244
$370$	0	0
$371$	444.000i	1.19677i
$372$	0	0
$373$	234.000i	0.627346i	0.949531	+	0.313673i	$0.101560\pi$
$373$	234.000i	0.627346i	−0.949531	+	0.313673i	$0.898440\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	− 398.000i	− 1.05013i	−0.851062	−	0.525066i	$-0.824041\pi$
$379$	− 398.000i	− 1.05013i	0.851062	−	0.525066i	$-0.175959\pi$
$380$	0	0
$381$	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		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	774.000i	1.94962i	0.223032	+	0.974811i	$0.428404\pi$
$397$	774.000i	1.94962i	−0.223032	+	0.974811i	$0.571596\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	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
$405$	405.000i	1.00000i
$406$	0	0
$407$	972.000	2.38821
$408$	0	0
$409$	622.000	1.52078	0.760391	−	0.649465i	$-0.225007\pi$
$409$	622.000	1.52078	0.760391	+	0.649465i	$0.225007\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	− 468.000i	− 1.13317i
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 162.000i	− 0.386635i	−0.981136	−	0.193317i	$-0.938075\pi$
$419$	− 162.000i	− 0.386635i	0.981136	−	0.193317i	$-0.0619247\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	774.000	1.82979
$424$	0	0
$425$	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
$437$	52.0000i	0.118993i
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	117.000	0.265306
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	− 90.0000i	− 0.202247i
$446$	0	0
$447$	0	0
$448$	0	0
$449$	258.000	0.574610	0.287305	−	0.957839i	$-0.407241\pi$
$449$	258.000	0.574610	0.287305	+	0.957839i	$0.407241\pi$
$450$	0	0
$451$	1404.00i	3.11308i
$452$	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
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	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		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	50.0000i	0.105263i
$476$	0	0
$477$	− 666.000i	− 1.39623i
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	324.000	0.673597
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	6.00000	0.0123203	0.00616016	−	0.999981i	$-0.498039\pi$
$487$	6.00000	0.0123203	0.00616016	+	0.999981i	$0.498039\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	978.000i	1.99185i	0.0901668	+	0.995927i	$0.471260\pi$
$491$	978.000i	1.99185i	−0.0901668	+	0.995927i	$0.528740\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	810.000	1.63636
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 962.000i	− 1.92786i	−0.266164	−	0.963928i	$-0.585756\pi$
$499$	− 962.000i	− 1.92786i	0.266164	−	0.963928i	$-0.414244\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	614.000	1.22068	0.610338	−	0.792141i	$-0.291034\pi$
$503$	614.000	1.22068	0.610338	+	0.792141i	$0.291034\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	− 930.000i	− 1.80583i
$516$	0	0
$517$	− 1548.00i	− 2.99420i
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−402.000	−0.771593	−0.385797	−	0.922584i	$-0.626073\pi$
$521$	−402.000	−0.771593	−0.385797	+	0.922584i	$0.626073\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	147.000	0.277883
$530$	0	0
$531$	702.000i	1.32203i
$532$	0	0
$533$	468.000i	0.878049i
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	− 234.000i	− 0.434137i
$540$	0	0
$541$	0	0		−	1.00000i	$-0.5\pi$
$541$	0	0			1.00000i	$0.5\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	934.000i	1.67684i	0.545025	+	0.838420i	$0.316520\pi$
$557$	934.000i	1.67684i	−0.545025	+	0.838420i	$0.683480\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	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	$-0.829164\pi$
$569$	−978.000	−1.71880	−0.859402	+	0.511300i	$0.829164\pi$
$570$	0	0
$571$	818.000i	1.43257i	0.697806	+	0.716287i	$0.254160\pi$
$571$	818.000i	1.43257i	−0.697806	+	0.716287i	$0.745840\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	650.000	1.13043
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−1332.00	−2.28473
$584$	0	0
$585$	270.000	0.461538
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	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	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−562.000	−0.935108	−0.467554	−	0.883964i	$-0.654865\pi$
$601$	−562.000	−0.935108	−0.467554	+	0.883964i	$0.654865\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 1015.00i	− 1.67769i
$606$	0	0
$607$	−1206.00	−1.98682	−0.993410	−	0.114613i	$-0.963437\pi$
$607$	−1206.00	−1.98682	−0.993410	+	0.114613i	$0.963437\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	− 516.000i	− 0.844517i
$612$	0	0
$613$	1194.00i	1.94780i	0.226982	+	0.973899i	$0.427114\pi$
$613$	1194.00i	1.94780i	−0.226982	+	0.973899i	$0.572886\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	− 878.000i	− 1.41842i	−0.704999	−	0.709208i	$-0.749053\pi$
$619$	− 878.000i	− 1.41842i	0.704999	−	0.709208i	$-0.250947\pi$
$620$	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
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	− 1230.00i	− 1.93701i
$636$	0	0
$637$	− 78.0000i	− 0.122449i
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−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		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	326.000	0.503864	0.251932	−	0.967745i	$-0.418934\pi$
$647$	326.000	0.503864	0.251932	+	0.967745i	$0.418934\pi$
$648$	0	0
$649$	1404.00	2.16333
$650$	0	0
$651$	0	0
$652$	0	0
$653$	1286.00i	1.96937i	0.174337	+	0.984686i	$0.444222\pi$
$653$	1286.00i	1.96937i	−0.174337	+	0.984686i	$0.555778\pi$
$654$	0	0
$655$	−1110.00	−1.69466
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 642.000i	− 0.974203i	−0.873345	−	0.487102i	$-0.838054\pi$
$659$	− 642.000i	− 0.974203i	0.873345	−	0.487102i	$-0.161946\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	60.0000	0.0902256
$666$	0	0
$667$	0	0
$668$	0	0
$669$	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
$676$	0	0
$677$	1066.00i	1.57459i	0.616574	+	0.787297i	$0.288520\pi$
$677$	1066.00i	1.57459i	−0.616574	+	0.787297i	$0.711480\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	−444.000	−0.644412
$690$	0	0
$691$	382.000i	0.552822i	0.961040	+	0.276411i	$0.0891451\pi$
$691$	382.000i	0.552822i	−0.961040	+	0.276411i	$0.910855\pi$
$692$	0	0
$693$	− 972.000i	− 1.40260i
$694$	0	0
$695$	−410.000	−0.589928
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−108.000	−0.153627
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	− 540.000i	− 0.755245i
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	−1116.00	−1.54785
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−1434.00	−1.97249	−0.986245	−	0.165291i	$-0.947144\pi$
$727$	−1434.00	−1.97249	−0.986245	+	0.165291i	$0.947144\pi$
$728$	0	0
$729$	−729.000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 954.000i	− 1.30150i	−0.759292	−	0.650750i	$-0.774454\pi$
$733$	− 954.000i	− 1.30150i	0.759292	−	0.650750i	$-0.225546\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	1438.00i	1.94587i	0.231073	+	0.972936i	$0.425776\pi$
$739$	1438.00i	1.94587i	−0.231073	+	0.972936i	$0.574224\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	134.000	0.180350	0.0901750	−	0.995926i	$-0.471257\pi$
$743$	134.000	0.180350	0.0901750	+	0.995926i	$0.471257\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	− 534.000i	− 0.705416i	−0.935733	−	0.352708i	$-0.885261\pi$
$757$	− 534.000i	− 0.705416i	0.935733	−	0.352708i	$-0.114739\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	1038.00	1.36399	0.681997	−	0.731355i	$-0.261112\pi$
$761$	1038.00	1.36399	0.681997	+	0.731355i	$0.261112\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	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	$0.146483\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	− 1046.00i	− 1.35317i	−0.736365	−	0.676585i	$-0.763459\pi$
$773$	− 1046.00i	− 1.35317i	0.736365	−	0.676585i	$-0.236541\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	− 156.000i	− 0.200257i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	930.000	1.18471
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	− 26.0000i	− 0.0326223i	−0.999867	−	0.0163112i	$-0.994808\pi$
$797$	− 26.0000i	− 0.0326223i	0.999867	−	0.0163112i	$-0.00519224\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	162.000	0.202247
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 780.000i	− 0.968944i
$806$	0	0
$807$	0	0
$808$	0	0
$809$	942.000	1.16440	0.582200	−	0.813045i	$-0.302192\pi$
$809$	942.000	1.16440	0.582200	+	0.813045i	$0.302192\pi$
$810$	0	0
$811$	1618.00i	1.99507i	0.0701862	+	0.997534i	$0.477641\pi$
$811$	1618.00i	1.99507i	−0.0701862	+	0.997534i	$0.522359\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	− 324.000i	− 0.395604i
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	−666.000	−0.809235	−0.404617	−	0.914486i	$-0.632595\pi$
$823$	−666.000	−0.809235	−0.404617	+	0.914486i	$0.632595\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	− 1570.00i	− 1.88024i
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−841.000	−1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	665.000i	0.786982i
$846$	0	0
$847$	−1218.00	−1.43802
$848$	0	0
$849$	0	0
$850$	0	0
$851$	1404.00i	1.64982i
$852$	0	0
$853$	1674.00i	1.96249i	0.192777	+	0.981243i	$0.438251\pi$
$853$	1674.00i	1.96249i	−0.192777	+	0.981243i	$0.561749\pi$
$854$	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
$859$	1522.00i	1.77183i	0.463850	+	0.885914i	$0.346468\pi$
$859$	1522.00i	1.77183i	−0.463850	+	0.885914i	$0.653532\pi$
$860$	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
$874$	0	0
$875$	− 750.000i	− 0.857143i
$876$	0	0
$877$	− 1626.00i	− 1.85405i	−0.375002	−	0.927024i	$-0.622358\pi$
$877$	− 1626.00i	− 1.85405i	0.375002	−	0.927024i	$-0.377642\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1602.00	1.81839	0.909194	−	0.416373i	$-0.136699\pi$
$881$	1602.00	1.81839	0.909194	+	0.416373i	$0.136699\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−1754.00	−1.97745	−0.988726	−	0.149736i	$-0.952158\pi$
$887$	−1754.00	−1.97745	−0.988726	+	0.149736i	$0.952158\pi$
$888$	0	0
$889$	−1476.00	−1.66029
$890$	0	0
$891$	1458.00i	1.63636i
$892$	0	0
$893$	172.000i	0.192609i
$894$	0	0
$895$	−1590.00	−1.77654
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	1332.00i	1.45256i
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1350.00i	1.45946i
$926$	0	0
$927$	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
$931$	26.0000i	0.0279270i
$932$	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
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−2028.00	−2.15058
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	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
$961$	961.000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−954.000	−0.986556	−0.493278	−	0.869872i	$-0.664202\pi$
$967$	−954.000	−0.986556	−0.493278	+	0.869872i	$0.664202\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	− 1902.00i	− 1.95881i	−0.201917	−	0.979403i	$-0.564717\pi$
$971$	− 1902.00i	− 1.95881i	0.201917	−	0.979403i	$-0.435283\pi$
$972$	0	0
$973$	492.000i	0.505653i
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	− 324.000i	− 0.330950i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−346.000	−0.351984	−0.175992	−	0.984392i	$-0.556313\pi$
$983$	−346.000	−0.351984	−0.175992	+	0.984392i	$0.556313\pi$
$984$	0	0
$985$	−530.000	−0.538071
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	426.000i	0.427282i	0.976912	+	0.213641i	$0.0685323\pi$
$997$	426.000i	0.427282i	−0.976912	+	0.213641i	$0.931468\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.h.c.1279.2		2
4.3	odd	2		1280.3.h.b.1279.2		2
5.4	even	2		1280.3.h.b.1279.1		2
8.3	odd	2		1280.3.h.b.1279.1		2
8.5	even	2	inner	1280.3.h.c.1279.1		2
16.3	odd	4		40.3.e.a.19.1	✓	1
16.5	even	4		40.3.e.b.19.1	yes	1
16.11	odd	4		160.3.e.a.79.1		1
16.13	even	4		160.3.e.b.79.1		1
20.19	odd	2	inner	1280.3.h.c.1279.1		2
40.19	odd	2	CM	1280.3.h.c.1279.2		2
40.29	even	2		1280.3.h.b.1279.2		2
48.5	odd	4		360.3.p.a.19.1		1
48.11	even	4		1440.3.p.b.559.1		1
48.29	odd	4		1440.3.p.a.559.1		1
48.35	even	4		360.3.p.b.19.1		1
80.3	even	4		200.3.g.c.51.2		2
80.13	odd	4		800.3.g.c.751.2		2
80.19	odd	4		40.3.e.b.19.1	yes	1
80.27	even	4		800.3.g.c.751.2		2
80.29	even	4		160.3.e.a.79.1		1
80.37	odd	4		200.3.g.c.51.2		2
80.43	even	4		800.3.g.c.751.1		2
80.53	odd	4		200.3.g.c.51.1		2
80.59	odd	4		160.3.e.b.79.1		1
80.67	even	4		200.3.g.c.51.1		2
80.69	even	4		40.3.e.a.19.1	✓	1
80.77	odd	4		800.3.g.c.751.1		2
240.29	odd	4		1440.3.p.b.559.1		1
240.59	even	4		1440.3.p.a.559.1		1
240.149	odd	4		360.3.p.b.19.1		1
240.179	even	4		360.3.p.a.19.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.a.19.1	✓	1	16.3	odd	4
40.3.e.a.19.1	✓	1	80.69	even	4
40.3.e.b.19.1	yes	1	16.5	even	4
40.3.e.b.19.1	yes	1	80.19	odd	4
160.3.e.a.79.1		1	16.11	odd	4
160.3.e.a.79.1		1	80.29	even	4
160.3.e.b.79.1		1	16.13	even	4
160.3.e.b.79.1		1	80.59	odd	4
200.3.g.c.51.1		2	80.53	odd	4
200.3.g.c.51.1		2	80.67	even	4
200.3.g.c.51.2		2	80.3	even	4
200.3.g.c.51.2		2	80.37	odd	4
360.3.p.a.19.1		1	48.5	odd	4
360.3.p.a.19.1		1	240.179	even	4
360.3.p.b.19.1		1	48.35	even	4
360.3.p.b.19.1		1	240.149	odd	4
800.3.g.c.751.1		2	80.43	even	4
800.3.g.c.751.1		2	80.77	odd	4
800.3.g.c.751.2		2	80.13	odd	4
800.3.g.c.751.2		2	80.27	even	4
1280.3.h.b.1279.1		2	5.4	even	2
1280.3.h.b.1279.1		2	8.3	odd	2
1280.3.h.b.1279.2		2	4.3	odd	2
1280.3.h.b.1279.2		2	40.29	even	2
1280.3.h.c.1279.1		2	8.5	even	2	inner
1280.3.h.c.1279.1		2	20.19	odd	2	inner
1280.3.h.c.1279.2		2	1.1	even	1	trivial
1280.3.h.c.1279.2		2	40.19	odd	2	CM
1440.3.p.a.559.1		1	48.29	odd	4
1440.3.p.a.559.1		1	240.59	even	4
1440.3.p.b.559.1		1	48.11	even	4
1440.3.p.b.559.1		1	240.29	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.00000i q^{5} +6.00000 q^{7} -9.00000 q^{9} +O(q^{10})\)	\(q+5.00000i q^{5} +6.00000 q^{7} -9.00000 q^{9} +18.0000i q^{11} +6.00000i q^{13} -2.00000i q^{19} -26.0000 q^{23} -25.0000 q^{25} +30.0000i q^{35} -54.0000i q^{37} +78.0000 q^{41} -45.0000i q^{45} -86.0000 q^{47} -13.0000 q^{49} +74.0000i q^{53} -90.0000 q^{55} -78.0000i q^{59} -54.0000 q^{63} -30.0000 q^{65} +108.000i q^{77} +81.0000 q^{81} -18.0000 q^{89} +36.0000i q^{91} +10.0000 q^{95} -162.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 12 q^{7} - 18 q^{9}+O(q^{10}) \) 2 * q + 12 * q^7 - 18 * q^9	\( 2 q + 12 q^{7} - 18 q^{9} - 52 q^{23} - 50 q^{25} + 156 q^{41} - 172 q^{47} - 26 q^{49} - 180 q^{55} - 108 q^{63} - 60 q^{65} + 162 q^{81} - 36 q^{89} + 20 q^{95}+O(q^{100}) \) 2 * q + 12 * q^7 - 18 * q^9 - 52 * q^23 - 50 * q^25 + 156 * q^41 - 172 * q^47 - 26 * q^49 - 180 * q^55 - 108 * q^63 - 60 * q^65 + 162 * q^81 - 36 * q^89 + 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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