LMFDB - Embedded newform 1280.3.e.b.639.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(639,1280)]

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, 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("1280.639");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1280.e (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			639.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.b.639.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{3} +5.00000i q^{5} -4.00000 q^{7} -7.00000 q^{9} +20.0000 q^{15} +16.0000i q^{21} +44.0000 q^{23} -25.0000 q^{25} -8.00000i q^{27} -22.0000i q^{29} -20.0000i q^{35} -62.0000 q^{41} -76.0000i q^{43} -35.0000i q^{45} +4.00000 q^{47} -33.0000 q^{49} -58.0000i q^{61} +28.0000 q^{63} -116.000i q^{67} -176.000i q^{69} +100.000i q^{75} -95.0000 q^{81} +76.0000i q^{83} -88.0000 q^{87} +142.000 q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{7} - 14 q^{9} + 40 q^{15} + 88 q^{23} - 50 q^{25} - 124 q^{41} + 8 q^{47} - 66 q^{49} + 56 q^{63} - 190 q^{81} - 176 q^{87} + 284 q^{89}+O(q^{100}) $ 2 * q - 8 * q^7 - 14 * q^9 + 40 * q^15 + 88 * q^23 - 50 * q^25 - 124 * q^41 + 8 * q^47 - 66 * q^49 + 56 * q^63 - 190 * q^81 - 176 * q^87 + 284 * q^89

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
$3$	− 4.00000i	− 1.33333i	−0.745356	−	0.666667i	$-0.767720\pi$
$3$	− 4.00000i	− 1.33333i	0.745356	−	0.666667i	$-0.232280\pi$
$4$	0	0
$5$	5.00000i	1.00000i
$5$	5.00000i	1.00000i
$6$	0	0
$7$	−4.00000	−0.571429	−0.285714	−	0.958315i	$-0.592231\pi$
$7$	−4.00000	−0.571429	−0.285714	+	0.958315i	$0.592231\pi$
$8$	0	0
$9$	−7.00000	−0.777778
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	20.0000	1.33333
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	16.0000i	0.761905i
$22$	0	0
$23$	44.0000	1.91304	0.956522	−	0.291661i	$-0.0942079\pi$
$23$	44.0000	1.91304	0.956522	+	0.291661i	$0.0942079\pi$
$24$	0	0
$25$	−25.0000	−1.00000
$26$	0	0
$27$	− 8.00000i	− 0.296296i
$28$	0	0
$29$	− 22.0000i	− 0.758621i	−0.925270	−	0.379310i	$-0.876161\pi$
$29$	− 22.0000i	− 0.758621i	0.925270	−	0.379310i	$-0.123839\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 20.0000i	− 0.571429i
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−62.0000	−1.51220	−0.756098	−	0.654459i	$-0.772896\pi$
$41$	−62.0000	−1.51220	−0.756098	+	0.654459i	$0.772896\pi$
$42$	0	0
$43$	− 76.0000i	− 1.76744i	−0.468014	−	0.883721i	$-0.655030\pi$
$43$	− 76.0000i	− 1.76744i	0.468014	−	0.883721i	$-0.344970\pi$
$44$	0	0
$45$	− 35.0000i	− 0.777778i
$46$	0	0
$47$	4.00000	0.0851064	0.0425532	−	0.999094i	$-0.486451\pi$
$47$	4.00000	0.0851064	0.0425532	+	0.999094i	$0.486451\pi$
$48$	0	0
$49$	−33.0000	−0.673469
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	− 58.0000i	− 0.950820i	−0.879764	−	0.475410i	$-0.842300\pi$
$61$	− 58.0000i	− 0.950820i	0.879764	−	0.475410i	$-0.157700\pi$
$62$	0	0
$63$	28.0000	0.444444
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 116.000i	− 1.73134i	−0.500612	−	0.865672i	$-0.666892\pi$
$67$	− 116.000i	− 1.73134i	0.500612	−	0.865672i	$-0.333108\pi$
$68$	0	0
$69$	− 176.000i	− 2.55072i
$70$	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
$75$	100.000i	1.33333i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−95.0000	−1.17284
$82$	0	0
$83$	76.0000i	0.915663i	0.889039	+	0.457831i	$0.151374\pi$
$83$	76.0000i	0.915663i	−0.889039	+	0.457831i	$0.848626\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−88.0000	−1.01149
$88$	0	0
$89$	142.000	1.59551	0.797753	−	0.602985i	$-0.206022\pi$
$89$	142.000	1.59551	0.797753	+	0.602985i	$0.206022\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	− 122.000i	− 1.20792i	−0.797014	−	0.603960i	$-0.793589\pi$
$101$	− 122.000i	− 1.20792i	0.797014	−	0.603960i	$-0.206411\pi$
$102$	0	0
$103$	44.0000	0.427184	0.213592	−	0.976923i	$-0.431484\pi$
$103$	44.0000	0.427184	0.213592	+	0.976923i	$0.431484\pi$
$104$	0	0
$105$	−80.0000	−0.761905
$106$	0	0
$107$	− 124.000i	− 1.15888i	−0.815015	−	0.579439i	$-0.803272\pi$
$107$	− 124.000i	− 1.15888i	0.815015	−	0.579439i	$-0.196728\pi$
$108$	0	0
$109$	38.0000i	0.348624i	0.984690	+	0.174312i	$0.0557701\pi$
$109$	38.0000i	0.348624i	−0.984690	+	0.174312i	$0.944230\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	220.000i	1.91304i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−121.000	−1.00000
$122$	0	0
$123$	248.000i	2.01626i
$124$	0	0
$125$	− 125.000i	− 1.00000i
$126$	0	0
$127$	−236.000	−1.85827	−0.929134	−	0.369744i	$-0.879446\pi$
$127$	−236.000	−1.85827	−0.929134	+	0.369744i	$0.879446\pi$
$128$	0	0
$129$	−304.000	−2.35659
$130$	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
$135$	40.0000	0.296296
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	− 16.0000i	− 0.113475i
$142$	0	0
$143$	0	0
$144$	0	0
$145$	110.000	0.758621
$146$	0	0
$147$	132.000i	0.897959i
$148$	0	0
$149$	− 278.000i	− 1.86577i	−0.360172	−	0.932886i	$-0.617282\pi$
$149$	− 278.000i	− 1.86577i	0.360172	−	0.932886i	$-0.382718\pi$
$150$	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
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−176.000	−1.09317
$162$	0	0
$163$	− 164.000i	− 1.00613i	−0.864247	−	0.503067i	$-0.832205\pi$
$163$	− 164.000i	− 1.00613i	0.864247	−	0.503067i	$-0.167795\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−244.000	−1.46108	−0.730539	−	0.682871i	$-0.760731\pi$
$167$	−244.000	−1.46108	−0.730539	+	0.682871i	$0.760731\pi$
$168$	0	0
$169$	−169.000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	100.000	0.571429
$176$	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
$181$	358.000i	1.97790i	0.148248	+	0.988950i	$0.452637\pi$
$181$	358.000i	1.97790i	−0.148248	+	0.988950i	$0.547363\pi$
$182$	0	0
$183$	−232.000	−1.26776
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	32.0000i	0.169312i
$190$	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
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	−464.000	−2.30846
$202$	0	0
$203$	88.0000i	0.433498i
$204$	0	0
$205$	− 310.000i	− 1.51220i
$206$	0	0
$207$	−308.000	−1.48792
$208$	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
$215$	380.000	1.76744
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	436.000	1.95516	0.977578	−	0.210571i	$-0.0675325\pi$
$223$	436.000	1.95516	0.977578	+	0.210571i	$0.0675325\pi$
$224$	0	0
$225$	175.000	0.777778
$226$	0	0
$227$	− 356.000i	− 1.56828i	−0.620583	−	0.784141i	$-0.713104\pi$
$227$	− 356.000i	− 1.56828i	0.620583	−	0.784141i	$-0.286896\pi$
$228$	0	0
$229$	262.000i	1.14410i	0.820217	+	0.572052i	$0.193853\pi$
$229$	262.000i	1.14410i	−0.820217	+	0.572052i	$0.806147\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	20.0000i	0.0851064i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	302.000	1.25311	0.626556	−	0.779376i	$-0.284464\pi$
$241$	302.000	1.25311	0.626556	+	0.779376i	$0.284464\pi$
$242$	0	0
$243$	308.000i	1.26749i
$244$	0	0
$245$	− 165.000i	− 0.673469i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	304.000	1.22088
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	154.000i	0.590038i
$262$	0	0
$263$	284.000	1.07985	0.539924	−	0.841714i	$-0.318453\pi$
$263$	284.000	1.07985	0.539924	+	0.841714i	$0.318453\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	− 568.000i	− 2.12734i
$268$	0	0
$269$	38.0000i	0.141264i	0.997502	+	0.0706320i	$0.0225016\pi$
$269$	38.0000i	0.141264i	−0.997502	+	0.0706320i	$0.977498\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	418.000	1.48754	0.743772	−	0.668433i	$-0.233035\pi$
$281$	418.000	1.48754	0.743772	+	0.668433i	$0.233035\pi$
$282$	0	0
$283$	− 316.000i	− 1.11661i	−0.829637	−	0.558304i	$-0.811452\pi$
$283$	− 316.000i	− 1.11661i	0.829637	−	0.558304i	$-0.188548\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	248.000	0.864111
$288$	0	0
$289$	289.000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	304.000i	1.00997i
$302$	0	0
$303$	−488.000	−1.61056
$304$	0	0
$305$	290.000	0.950820
$306$	0	0
$307$	− 596.000i	− 1.94137i	−0.240359	−	0.970684i	$-0.577265\pi$
$307$	− 596.000i	− 1.94137i	0.240359	−	0.970684i	$-0.422735\pi$
$308$	0	0
$309$	− 176.000i	− 0.569579i
$310$	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
$315$	140.000i	0.444444i
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−496.000	−1.54517
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	152.000	0.464832
$328$	0	0
$329$	−16.0000	−0.0486322
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	580.000	1.73134
$336$	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
$343$	328.000	0.956268
$344$	0	0
$345$	880.000	2.55072
$346$	0	0
$347$	116.000i	0.334294i	0.985932	+	0.167147i	$0.0534554\pi$
$347$	116.000i	0.334294i	−0.985932	+	0.167147i	$0.946545\pi$
$348$	0	0
$349$	− 22.0000i	− 0.0630372i	−0.999503	−	0.0315186i	$-0.989966\pi$
$349$	− 22.0000i	− 0.0630372i	0.999503	−	0.0315186i	$-0.0100344\pi$
$350$	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
$361$	−361.000	−1.00000
$362$	0	0
$363$	484.000i	1.33333i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	724.000	1.97275	0.986376	−	0.164506i	$-0.0526031\pi$
$367$	724.000	1.97275	0.986376	+	0.164506i	$0.0526031\pi$
$368$	0	0
$369$	434.000	1.17615
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	−500.000	−1.33333
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	944.000i	2.47769i
$382$	0	0
$383$	−44.0000	−0.114883	−0.0574413	−	0.998349i	$-0.518294\pi$
$383$	−44.0000	−0.114883	−0.0574413	+	0.998349i	$0.518294\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	532.000i	1.37468i
$388$	0	0
$389$	202.000i	0.519280i	0.965705	+	0.259640i	$0.0836039\pi$
$389$	202.000i	0.519280i	−0.965705	+	0.259640i	$0.916396\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−478.000	−1.19202	−0.596010	−	0.802977i	$-0.703248\pi$
$401$	−478.000	−1.19202	−0.596010	+	0.802977i	$0.703248\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	− 475.000i	− 1.17284i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	802.000	1.96088	0.980440	−	0.196818i	$-0.0630607\pi$
$409$	802.000	1.96088	0.980440	+	0.196818i	$0.0630607\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−380.000	−0.915663
$416$	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
$421$	778.000i	1.84798i	0.382415	+	0.923990i	$0.375092\pi$
$421$	778.000i	1.84798i	−0.382415	+	0.923990i	$0.624908\pi$
$422$	0	0
$423$	−28.0000	−0.0661939
$424$	0	0
$425$	0	0
$426$	0	0
$427$	232.000i	0.543326i
$428$	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
$435$	− 440.000i	− 1.01149i
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	231.000	0.523810
$442$	0	0
$443$	− 796.000i	− 1.79684i	−0.439138	−	0.898420i	$-0.644716\pi$
$443$	− 796.000i	− 1.79684i	0.439138	−	0.898420i	$-0.355284\pi$
$444$	0	0
$445$	710.000i	1.59551i
$446$	0	0
$447$	−1112.00	−2.48770
$448$	0	0
$449$	398.000	0.886414	0.443207	−	0.896419i	$-0.353841\pi$
$449$	398.000	0.886414	0.443207	+	0.896419i	$0.353841\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	842.000i	1.82646i	0.407440	+	0.913232i	$0.366422\pi$
$461$	842.000i	1.82646i	−0.407440	+	0.913232i	$0.633578\pi$
$462$	0	0
$463$	−764.000	−1.65011	−0.825054	−	0.565054i	$-0.808855\pi$
$463$	−764.000	−1.65011	−0.825054	+	0.565054i	$0.808855\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	124.000i	0.265525i	0.991148	+	0.132762i	$0.0423847\pi$
$467$	124.000i	0.265525i	−0.991148	+	0.132762i	$0.957615\pi$
$468$	0	0
$469$	464.000i	0.989339i
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	704.000i	1.45756i
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−484.000	−0.993840	−0.496920	−	0.867796i	$-0.665536\pi$
$487$	−484.000	−0.993840	−0.496920	+	0.867796i	$0.665536\pi$
$488$	0	0
$489$	−656.000	−1.34151
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	976.000i	1.94810i
$502$	0	0
$503$	−916.000	−1.82107	−0.910537	−	0.413428i	$-0.864331\pi$
$503$	−916.000	−1.82107	−0.910537	+	0.413428i	$0.864331\pi$
$504$	0	0
$505$	610.000	1.20792
$506$	0	0
$507$	676.000i	1.33333i
$508$	0	0
$509$	− 982.000i	− 1.92927i	−0.263584	−	0.964637i	$-0.584905\pi$
$509$	− 982.000i	− 1.92927i	0.263584	−	0.964637i	$-0.415095\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	220.000i	0.427184i
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−722.000	−1.38580	−0.692898	−	0.721035i	$-0.743667\pi$
$521$	−722.000	−1.38580	−0.692898	+	0.721035i	$0.743667\pi$
$522$	0	0
$523$	164.000i	0.313576i	0.987632	+	0.156788i	$0.0501139\pi$
$523$	164.000i	0.313576i	−0.987632	+	0.156788i	$0.949886\pi$
$524$	0	0
$525$	− 400.000i	− 0.761905i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1407.00	2.65974
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	620.000	1.15888
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	362.000i	0.669131i	0.942372	+	0.334566i	$0.108590\pi$
$541$	362.000i	0.669131i	−0.942372	+	0.334566i	$0.891410\pi$
$542$	0	0
$543$	1432.00	2.63720
$544$	0	0
$545$	−190.000	−0.348624
$546$	0	0
$547$	1084.00i	1.98172i	0.134900	+	0.990859i	$0.456929\pi$
$547$	1084.00i	1.98172i	−0.134900	+	0.990859i	$0.543071\pi$
$548$	0	0
$549$	406.000i	0.739526i
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 1124.00i	− 1.99645i	−0.0595755	−	0.998224i	$-0.518975\pi$
$563$	− 1124.00i	− 1.99645i	0.0595755	−	0.998224i	$-0.481025\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	380.000	0.670194
$568$	0	0
$569$	−158.000	−0.277680	−0.138840	−	0.990315i	$-0.544337\pi$
$569$	−158.000	−0.277680	−0.138840	+	0.990315i	$0.544337\pi$
$570$	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
$575$	−1100.00	−1.91304
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 304.000i	− 0.523236i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1076.00i	1.83305i	0.399978	+	0.916525i	$0.369018\pi$
$587$	1076.00i	1.83305i	−0.399978	+	0.916525i	$0.630982\pi$
$588$	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
$601$	418.000	0.695507	0.347754	−	0.937586i	$-0.386945\pi$
$601$	418.000	0.695507	0.347754	+	0.937586i	$0.386945\pi$
$602$	0	0
$603$	812.000i	1.34660i
$604$	0	0
$605$	− 605.000i	− 1.00000i
$606$	0	0
$607$	964.000	1.58814	0.794069	−	0.607827i	$-0.207959\pi$
$607$	964.000	1.58814	0.794069	+	0.607827i	$0.207959\pi$
$608$	0	0
$609$	352.000	0.577997
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	−1240.00	−2.01626
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	− 352.000i	− 0.566828i
$622$	0	0
$623$	−568.000	−0.911717
$624$	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
$635$	− 1180.00i	− 1.85827i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−1138.00	−1.77535	−0.887676	−	0.460470i	$-0.847681\pi$
$641$	−1138.00	−1.77535	−0.887676	+	0.460470i	$0.847681\pi$
$642$	0	0
$643$	− 404.000i	− 0.628305i	−0.949373	−	0.314152i	$-0.898280\pi$
$643$	− 404.000i	− 0.628305i	0.949373	−	0.314152i	$-0.101720\pi$
$644$	0	0
$645$	− 1520.00i	− 2.35659i
$646$	0	0
$647$	956.000	1.47759	0.738794	−	0.673931i	$-0.235395\pi$
$647$	956.000	1.47759	0.738794	+	0.673931i	$0.235395\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	298.000i	0.450832i	0.974263	+	0.225416i	$0.0723741\pi$
$661$	298.000i	0.450832i	−0.974263	+	0.225416i	$0.927626\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	− 968.000i	− 1.45127i
$668$	0	0
$669$	− 1744.00i	− 2.60688i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	200.000i	0.296296i
$676$	0	0
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−1424.00	−2.09104
$682$	0	0
$683$	− 556.000i	− 0.814056i	−0.913416	−	0.407028i	$-0.866565\pi$
$683$	− 556.000i	− 0.814056i	0.913416	−	0.407028i	$-0.133435\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1048.00	1.52547
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	902.000i	1.28673i	0.765558	+	0.643367i	$0.222463\pi$
$701$	902.000i	1.28673i	−0.765558	+	0.643367i	$0.777537\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	80.0000	0.113475
$706$	0	0
$707$	488.000i	0.690240i
$708$	0	0
$709$	− 698.000i	− 0.984485i	−0.870458	−	0.492243i	$-0.836177\pi$
$709$	− 698.000i	− 0.984485i	0.870458	−	0.492243i	$-0.163823\pi$
$710$	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	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	−176.000	−0.244105
$722$	0	0
$723$	− 1208.00i	− 1.67082i
$724$	0	0
$725$	550.000i	0.758621i
$726$	0	0
$727$	1436.00	1.97524	0.987620	−	0.156863i	$-0.0501381\pi$
$727$	1436.00	1.97524	0.987620	+	0.156863i	$0.0501381\pi$
$728$	0	0
$729$	377.000	0.517147
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	−660.000	−0.897959
$736$	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
$743$	764.000	1.02826	0.514132	−	0.857711i	$-0.328114\pi$
$743$	764.000	1.02826	0.514132	+	0.857711i	$0.328114\pi$
$744$	0	0
$745$	1390.00	1.86577
$746$	0	0
$747$	− 532.000i	− 0.712182i
$748$	0	0
$749$	496.000i	0.662216i
$750$	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
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−242.000	−0.318003	−0.159001	−	0.987278i	$-0.550827\pi$
$761$	−242.000	−0.318003	−0.159001	+	0.987278i	$0.550827\pi$
$762$	0	0
$763$	− 152.000i	− 0.199214i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−1342.00	−1.74512	−0.872562	−	0.488504i	$-0.837543\pi$
$769$	−1342.00	−1.74512	−0.872562	+	0.488504i	$0.837543\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−176.000	−0.224777
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 116.000i	− 0.147395i	−0.997281	−	0.0736976i	$-0.976520\pi$
$787$	− 116.000i	− 0.147395i	0.997281	−	0.0736976i	$-0.0234800\pi$
$788$	0	0
$789$	− 1136.00i	− 1.43980i
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−994.000	−1.24095
$802$	0	0
$803$	0	0
$804$	0	0
$805$	− 880.000i	− 1.09317i
$806$	0	0
$807$	152.000	0.188352
$808$	0	0
$809$	−1298.00	−1.60445	−0.802225	−	0.597022i	$-0.796351\pi$
$809$	−1298.00	−1.60445	−0.802225	+	0.597022i	$0.796351\pi$
$810$	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
$815$	820.000	1.00613
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	− 662.000i	− 0.806334i	−0.915126	−	0.403167i	$-0.867909\pi$
$821$	− 662.000i	− 0.806334i	0.915126	−	0.403167i	$-0.132091\pi$
$822$	0	0
$823$	−1396.00	−1.69623	−0.848117	−	0.529810i	$-0.822263\pi$
$823$	−1396.00	−1.69623	−0.848117	+	0.529810i	$0.822263\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	596.000i	0.720677i	0.932822	+	0.360339i	$0.117339\pi$
$827$	596.000i	0.720677i	−0.932822	+	0.360339i	$0.882661\pi$
$828$	0	0
$829$	1478.00i	1.78287i	0.453148	+	0.891435i	$0.350301\pi$
$829$	1478.00i	1.78287i	−0.453148	+	0.891435i	$0.649699\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	− 1220.00i	− 1.46108i
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	357.000	0.424495
$842$	0	0
$843$	− 1672.00i	− 1.98339i
$844$	0	0
$845$	− 845.000i	− 1.00000i
$846$	0	0
$847$	484.000	0.571429
$848$	0	0
$849$	−1264.00	−1.48881
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	− 992.000i	− 1.15215i
$862$	0	0
$863$	1636.00	1.89571	0.947856	−	0.318698i	$-0.103246\pi$
$863$	1636.00	1.89571	0.947856	+	0.318698i	$0.103246\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 1156.00i	− 1.33333i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	500.000i	0.571429i
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−1618.00	−1.83655	−0.918275	−	0.395944i	$-0.870417\pi$
$881$	−1618.00	−1.83655	−0.918275	+	0.395944i	$0.870417\pi$
$882$	0	0
$883$	1276.00i	1.44507i	0.691332	+	0.722537i	$0.257024\pi$
$883$	1276.00i	1.44507i	−0.691332	+	0.722537i	$0.742976\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−964.000	−1.08681	−0.543405	−	0.839471i	$-0.682865\pi$
$887$	−964.000	−1.08681	−0.543405	+	0.839471i	$0.682865\pi$
$888$	0	0
$889$	944.000	1.06187
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	1216.00	1.34662
$904$	0	0
$905$	−1790.00	−1.97790
$906$	0	0
$907$	1796.00i	1.98015i	0.140525	+	0.990077i	$0.455121\pi$
$907$	1796.00i	1.98015i	−0.140525	+	0.990077i	$0.544879\pi$
$908$	0	0
$909$	854.000i	0.939494i
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	− 1160.00i	− 1.26776i
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	−2384.00	−2.58849
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−308.000	−0.332255
$928$	0	0
$929$	−562.000	−0.604952	−0.302476	−	0.953157i	$-0.597813\pi$
$929$	−562.000	−0.604952	−0.302476	+	0.953157i	$0.597813\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 118.000i	− 0.125399i	−0.998032	−	0.0626993i	$-0.980029\pi$
$941$	− 118.000i	− 0.125399i	0.998032	−	0.0626993i	$-0.0199709\pi$
$942$	0	0
$943$	−2728.00	−2.89290
$944$	0	0
$945$	−160.000	−0.169312
$946$	0	0
$947$	1804.00i	1.90496i	0.304596	+	0.952482i	$0.401478\pi$
$947$	1804.00i	1.90496i	−0.304596	+	0.952482i	$0.598522\pi$
$948$	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
$963$	868.000i	0.901350i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−244.000	−0.252327	−0.126163	−	0.992009i	$-0.540266\pi$
$967$	−244.000	−0.252327	−0.126163	+	0.992009i	$0.540266\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	− 266.000i	− 0.271152i
$982$	0	0
$983$	284.000	0.288911	0.144456	−	0.989511i	$-0.453857\pi$
$983$	284.000	0.288911	0.144456	+	0.989511i	$0.453857\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	64.0000i	0.0648430i
$988$	0	0
$989$	− 3344.00i	− 3.38119i
$990$	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
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.b.639.1		2
4.3	odd	2		1280.3.e.c.639.2		2
5.4	even	2		1280.3.e.c.639.2		2
8.3	odd	2		1280.3.e.c.639.1		2
8.5	even	2	inner	1280.3.e.b.639.2		2
16.3	odd	4		320.3.h.a.319.1		1
16.5	even	4		20.3.d.b.19.1	yes	1
16.11	odd	4		20.3.d.a.19.1	✓	1
16.13	even	4		320.3.h.b.319.1		1
20.19	odd	2	CM	1280.3.e.b.639.1		2
40.19	odd	2	inner	1280.3.e.b.639.2		2
40.29	even	2		1280.3.e.c.639.1		2
48.5	odd	4		180.3.f.a.19.1		1
48.11	even	4		180.3.f.b.19.1		1
80.3	even	4		1600.3.b.f.1151.1		2
80.13	odd	4		1600.3.b.f.1151.2		2
80.19	odd	4		320.3.h.b.319.1		1
80.27	even	4		100.3.b.c.51.1		2
80.29	even	4		320.3.h.a.319.1		1
80.37	odd	4		100.3.b.c.51.2		2
80.43	even	4		100.3.b.c.51.2		2
80.53	odd	4		100.3.b.c.51.1		2
80.59	odd	4		20.3.d.b.19.1	yes	1
80.67	even	4		1600.3.b.f.1151.2		2
80.69	even	4		20.3.d.a.19.1	✓	1
80.77	odd	4		1600.3.b.f.1151.1		2
240.53	even	4		900.3.c.h.451.2		2
240.59	even	4		180.3.f.a.19.1		1
240.107	odd	4		900.3.c.h.451.2		2
240.149	odd	4		180.3.f.b.19.1		1
240.197	even	4		900.3.c.h.451.1		2
240.203	odd	4		900.3.c.h.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.d.a.19.1	✓	1	16.11	odd	4
20.3.d.a.19.1	✓	1	80.69	even	4
20.3.d.b.19.1	yes	1	16.5	even	4
20.3.d.b.19.1	yes	1	80.59	odd	4
100.3.b.c.51.1		2	80.27	even	4
100.3.b.c.51.1		2	80.53	odd	4
100.3.b.c.51.2		2	80.37	odd	4
100.3.b.c.51.2		2	80.43	even	4
180.3.f.a.19.1		1	48.5	odd	4
180.3.f.a.19.1		1	240.59	even	4
180.3.f.b.19.1		1	48.11	even	4
180.3.f.b.19.1		1	240.149	odd	4
320.3.h.a.319.1		1	16.3	odd	4
320.3.h.a.319.1		1	80.29	even	4
320.3.h.b.319.1		1	16.13	even	4
320.3.h.b.319.1		1	80.19	odd	4
900.3.c.h.451.1		2	240.197	even	4
900.3.c.h.451.1		2	240.203	odd	4
900.3.c.h.451.2		2	240.53	even	4
900.3.c.h.451.2		2	240.107	odd	4
1280.3.e.b.639.1		2	1.1	even	1	trivial
1280.3.e.b.639.1		2	20.19	odd	2	CM
1280.3.e.b.639.2		2	8.5	even	2	inner
1280.3.e.b.639.2		2	40.19	odd	2	inner
1280.3.e.c.639.1		2	8.3	odd	2
1280.3.e.c.639.1		2	40.29	even	2
1280.3.e.c.639.2		2	4.3	odd	2
1280.3.e.c.639.2		2	5.4	even	2
1600.3.b.f.1151.1		2	80.3	even	4
1600.3.b.f.1151.1		2	80.77	odd	4
1600.3.b.f.1151.2		2	80.13	odd	4
1600.3.b.f.1151.2		2	80.67	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000i q^{3} +5.00000i q^{5} -4.00000 q^{7} -7.00000 q^{9} +20.0000 q^{15} +16.0000i q^{21} +44.0000 q^{23} -25.0000 q^{25} -8.00000i q^{27} -22.0000i q^{29} -20.0000i q^{35} -62.0000 q^{41} -76.0000i q^{43} -35.0000i q^{45} +4.00000 q^{47} -33.0000 q^{49} -58.0000i q^{61} +28.0000 q^{63} -116.000i q^{67} -176.000i q^{69} +100.000i q^{75} -95.0000 q^{81} +76.0000i q^{83} -88.0000 q^{87} +142.000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{7} - 14 q^{9} + 40 q^{15} + 88 q^{23} - 50 q^{25} - 124 q^{41} + 8 q^{47} - 66 q^{49} + 56 q^{63} - 190 q^{81} - 176 q^{87} + 284 q^{89}+O(q^{100}) \) 2 * q - 8 * q^7 - 14 * q^9 + 40 * q^15 + 88 * q^23 - 50 * q^25 - 124 * q^41 + 8 * q^47 - 66 * q^49 + 56 * q^63 - 190 * q^81 - 176 * q^87 + 284 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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