LMFDB - Embedded newform 1280.3.e.e.639.4

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:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			639.4
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.e.639.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.47214i q^{3} +5.00000i q^{5} -13.4164 q^{7} -11.0000 q^{9} +O(q^{10})$	$q+4.47214i q^{3} +5.00000i q^{5} -13.4164 q^{7} -11.0000 q^{9} -22.3607 q^{15} -60.0000i q^{21} -13.4164 q^{23} -25.0000 q^{25} -8.94427i q^{27} +22.0000i q^{29} -67.0820i q^{35} +62.0000 q^{41} -40.2492i q^{43} -55.0000i q^{45} -93.9149 q^{47} +131.000 q^{49} -58.0000i q^{61} +147.580 q^{63} -67.0820i q^{67} -60.0000i q^{69} -111.803i q^{75} -59.0000 q^{81} +147.580i q^{83} -98.3870 q^{87} +142.000 q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 44 q^{9}+O(q^{10}) $ 4 * q - 44 * q^9	$ 4 q - 44 q^{9} - 100 q^{25} + 248 q^{41} + 524 q^{49} - 236 q^{81} + 568 q^{89}+O(q^{100}) $ 4 * q - 44 * q^9 - 100 * q^25 + 248 * q^41 + 524 * q^49 - 236 * q^81 + 568 * q^89

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	4.47214i	1.49071i	0.666667	+	0.745356i	$0.267720\pi$
$3$	4.47214i	1.49071i	−0.666667	+	0.745356i	$0.732280\pi$
$4$	0	0
$5$	5.00000i	1.00000i
$5$	5.00000i	1.00000i
$6$	0	0
$7$	−13.4164	−1.91663	−0.958315	−	0.285714i	$-0.907769\pi$
$7$	−13.4164	−1.91663	−0.958315	+	0.285714i	$0.907769\pi$
$8$	0	0
$9$	−11.0000	−1.22222
$10$	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
$15$	−22.3607	−1.49071
$16$	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
$21$	− 60.0000i	− 2.85714i
$22$	0	0
$23$	−13.4164	−0.583322	−0.291661	−	0.956522i	$-0.594208\pi$
$23$	−13.4164	−0.583322	−0.291661	+	0.956522i	$0.594208\pi$
$24$	0	0
$25$	−25.0000	−1.00000
$26$	0	0
$27$	− 8.94427i	− 0.331269i
$28$	0	0
$29$	22.0000i	0.758621i	0.925270	+	0.379310i	$0.123839\pi$
$29$	22.0000i	0.758621i	−0.925270	+	0.379310i	$0.876161\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 67.0820i	− 1.91663i
$36$	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	$-0.227104\pi$
$41$	62.0000	1.51220	0.756098	+	0.654459i	$0.227104\pi$
$42$	0	0
$43$	− 40.2492i	− 0.936028i	−0.883721	−	0.468014i	$-0.844970\pi$
$43$	− 40.2492i	− 0.936028i	0.883721	−	0.468014i	$-0.155030\pi$
$44$	0	0
$45$	− 55.0000i	− 1.22222i
$46$	0	0
$47$	−93.9149	−1.99819	−0.999094	−	0.0425532i	$-0.986451\pi$
$47$	−93.9149	−1.99819	−0.999094	+	0.0425532i	$0.986451\pi$
$48$	0	0
$49$	131.000	2.67347
$50$	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
$63$	147.580	2.34255
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 67.0820i	− 1.00122i	−0.865672	−	0.500612i	$-0.833108\pi$
$67$	− 67.0820i	− 1.00122i	0.865672	−	0.500612i	$-0.166892\pi$
$68$	0	0
$69$	− 60.0000i	− 0.869565i
$70$	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
$75$	− 111.803i	− 1.49071i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−59.0000	−0.728395
$82$	0	0
$83$	147.580i	1.77808i	0.457831	+	0.889039i	$0.348626\pi$
$83$	147.580i	1.77808i	−0.457831	+	0.889039i	$0.651374\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−98.3870	−1.13088
$88$	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	$0.206411\pi$
$101$	122.000i	1.20792i	−0.797014	+	0.603960i	$0.793589\pi$
$102$	0	0
$103$	201.246	1.95385	0.976923	−	0.213592i	$-0.0685164\pi$
$103$	201.246	1.95385	0.976923	+	0.213592i	$0.0685164\pi$
$104$	0	0
$105$	300.000	2.85714
$106$	0	0
$107$	174.413i	1.63003i	0.579439	+	0.815015i	$0.303272\pi$
$107$	174.413i	1.63003i	−0.579439	+	0.815015i	$0.696728\pi$
$108$	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
$115$	− 67.0820i	− 0.583322i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−121.000	−1.00000
$122$	0	0
$123$	277.272i	2.25425i
$124$	0	0
$125$	− 125.000i	− 1.00000i
$126$	0	0
$127$	−93.9149	−0.739487	−0.369744	−	0.929134i	$-0.620554\pi$
$127$	−93.9149	−0.739487	−0.369744	+	0.929134i	$0.620554\pi$
$128$	0	0
$129$	180.000	1.39535
$130$	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
$135$	44.7214	0.331269
$136$	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
$141$	− 420.000i	− 2.97872i
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−110.000	−0.758621
$146$	0	0
$147$	585.850i	3.98537i
$148$	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
$161$	180.000	1.11801
$162$	0	0
$163$	− 281.745i	− 1.72849i	−0.503067	−	0.864247i	$-0.667795\pi$
$163$	− 281.745i	− 1.72849i	0.503067	−	0.864247i	$-0.332205\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−228.079	−1.36574	−0.682871	−	0.730539i	$-0.739269\pi$
$167$	−228.079	−1.36574	−0.682871	+	0.730539i	$0.739269\pi$
$168$	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
$175$	335.410	1.91663
$176$	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	$-0.547363\pi$
$181$	− 358.000i	− 1.97790i	0.148248	−	0.988950i	$-0.452637\pi$
$182$	0	0
$183$	259.384	1.41740
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	120.000i	0.634921i
$190$	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
$201$	300.000	1.49254
$202$	0	0
$203$	− 295.161i	− 1.45399i
$204$	0	0
$205$	310.000i	1.51220i
$206$	0	0
$207$	147.580	0.712949
$208$	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
$215$	201.246	0.936028
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−93.9149	−0.421143	−0.210571	−	0.977578i	$-0.567532\pi$
$223$	−93.9149	−0.421143	−0.210571	+	0.977578i	$0.567532\pi$
$224$	0	0
$225$	275.000	1.22222
$226$	0	0
$227$	− 281.745i	− 1.24117i	−0.784141	−	0.620583i	$-0.786896\pi$
$227$	− 281.745i	− 1.24117i	0.784141	−	0.620583i	$-0.213104\pi$
$228$	0	0
$229$	− 262.000i	− 1.14410i	−0.820217	−	0.572052i	$-0.806147\pi$
$229$	− 262.000i	− 1.14410i	0.820217	−	0.572052i	$-0.193853\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	− 469.574i	− 1.99819i
$236$	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	$-0.715536\pi$
$241$	−302.000	−1.25311	−0.626556	+	0.779376i	$0.715536\pi$
$242$	0	0
$243$	− 344.354i	− 1.41710i
$244$	0	0
$245$	655.000i	2.67347i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−660.000	−2.65060
$250$	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
$261$	− 242.000i	− 0.927203i
$262$	0	0
$263$	−442.741	−1.68343	−0.841714	−	0.539924i	$-0.818453\pi$
$263$	−442.741	−1.68343	−0.841714	+	0.539924i	$0.818453\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	635.043i	2.37844i
$268$	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	$-0.766965\pi$
$281$	−418.000	−1.48754	−0.743772	+	0.668433i	$0.766965\pi$
$282$	0	0
$283$	− 469.574i	− 1.65927i	−0.558304	−	0.829637i	$-0.688548\pi$
$283$	− 469.574i	− 1.65927i	0.558304	−	0.829637i	$-0.311452\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−831.817	−2.89832
$288$	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
$301$	540.000i	1.79402i
$302$	0	0
$303$	−545.601	−1.80066
$304$	0	0
$305$	290.000	0.950820
$306$	0	0
$307$	147.580i	0.480718i	0.970684	+	0.240359i	$0.0772652\pi$
$307$	147.580i	0.480718i	−0.970684	+	0.240359i	$0.922735\pi$
$308$	0	0
$309$	900.000i	2.91262i
$310$	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
$315$	737.902i	2.34255i
$316$	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
$321$	−780.000	−2.42991
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−169.941	−0.519698
$328$	0	0
$329$	1260.00	3.82979
$330$	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
$335$	335.410	1.00122
$336$	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
$343$	−1100.15	−3.20742
$344$	0	0
$345$	300.000	0.869565
$346$	0	0
$347$	− 684.237i	− 1.97186i	−0.167147	−	0.985932i	$-0.553455\pi$
$347$	− 684.237i	− 1.97186i	0.167147	−	0.985932i	$-0.446545\pi$
$348$	0	0
$349$	22.0000i	0.0630372i	0.999503	+	0.0315186i	$0.0100344\pi$
$349$	22.0000i	0.0630372i	−0.999503	+	0.0315186i	$0.989966\pi$
$350$	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
$363$	− 541.128i	− 1.49071i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	120.748	0.329013	0.164506	−	0.986376i	$-0.447397\pi$
$367$	120.748	0.329013	0.164506	+	0.986376i	$0.447397\pi$
$368$	0	0
$369$	−682.000	−1.84824
$370$	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
$375$	559.017	1.49071
$376$	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
$381$	− 420.000i	− 1.10236i
$382$	0	0
$383$	764.735	1.99670	0.998349	−	0.0574413i	$-0.0182942\pi$
$383$	764.735	1.99670	0.998349	+	0.0574413i	$0.0182942\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	442.741i	1.14403i
$388$	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
$405$	− 295.000i	− 0.728395i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−802.000	−1.96088	−0.980440	−	0.196818i	$-0.936939\pi$
$409$	−802.000	−1.96088	−0.980440	+	0.196818i	$0.936939\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−737.902	−1.77808
$416$	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
$423$	1033.06	2.44223
$424$	0	0
$425$	0	0
$426$	0	0
$427$	778.152i	1.82237i
$428$	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
$435$	− 491.935i	− 1.13088i
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−1441.00	−3.26757
$442$	0	0
$443$	389.076i	0.878275i	0.898420	+	0.439138i	$0.144716\pi$
$443$	389.076i	0.878275i	−0.898420	+	0.439138i	$0.855284\pi$
$444$	0	0
$445$	710.000i	1.59551i
$446$	0	0
$447$	1243.25	2.78133
$448$	0	0
$449$	−398.000	−0.886414	−0.443207	−	0.896419i	$-0.646159\pi$
$449$	−398.000	−0.886414	−0.443207	+	0.896419i	$0.646159\pi$
$450$	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	$-0.633578\pi$
$461$	− 842.000i	− 1.82646i	0.407440	−	0.913232i	$-0.366422\pi$
$462$	0	0
$463$	−523.240	−1.13011	−0.565054	−	0.825054i	$-0.691145\pi$
$463$	−523.240	−1.13011	−0.565054	+	0.825054i	$0.691145\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 925.732i	− 1.98230i	−0.132762	−	0.991148i	$-0.542385\pi$
$467$	− 925.732i	− 1.98230i	0.132762	−	0.991148i	$-0.457615\pi$
$468$	0	0
$469$	900.000i	1.91898i
$470$	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
$483$	804.984i	1.66663i
$484$	0	0
$485$	0	0
$486$	0	0
$487$	845.234	1.73559	0.867796	−	0.496920i	$-0.165536\pi$
$487$	845.234	1.73559	0.867796	+	0.496920i	$0.165536\pi$
$488$	0	0
$489$	1260.00	2.57669
$490$	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
$501$	− 1020.00i	− 2.03593i
$502$	0	0
$503$	415.909	0.826856	0.413428	−	0.910537i	$-0.364331\pi$
$503$	415.909	0.826856	0.413428	+	0.910537i	$0.364331\pi$
$504$	0	0
$505$	−610.000	−1.20792
$506$	0	0
$507$	− 755.791i	− 1.49071i
$508$	0	0
$509$	982.000i	1.92927i	0.263584	+	0.964637i	$0.415095\pi$
$509$	982.000i	1.92927i	−0.263584	+	0.964637i	$0.584905\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	1006.23i	1.95385i
$516$	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
$523$	1033.06i	1.97526i	0.156788	+	0.987632i	$0.449886\pi$
$523$	1033.06i	1.97526i	−0.156788	+	0.987632i	$0.550114\pi$
$524$	0	0
$525$	1500.00i	2.85714i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−349.000	−0.659735
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−872.067	−1.63003
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	− 362.000i	− 0.669131i	−0.942372	−	0.334566i	$-0.891410\pi$
$541$	− 362.000i	− 0.669131i	0.942372	−	0.334566i	$-0.108590\pi$
$542$	0	0
$543$	1601.02	2.94848
$544$	0	0
$545$	−190.000	−0.348624
$546$	0	0
$547$	147.580i	0.269800i	0.990859	+	0.134900i	$0.0430713\pi$
$547$	147.580i	0.269800i	−0.990859	+	0.134900i	$0.956929\pi$
$548$	0	0
$549$	638.000i	1.16211i
$550$	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
$563$	− 67.0820i	− 0.119151i	−0.998224	−	0.0595755i	$-0.981025\pi$
$563$	− 67.0820i	− 0.119151i	0.998224	−	0.0595755i	$-0.0189747\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	791.568	1.39606
$568$	0	0
$569$	158.000	0.277680	0.138840	−	0.990315i	$-0.455663\pi$
$569$	158.000	0.277680	0.138840	+	0.990315i	$0.455663\pi$
$570$	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
$575$	335.410	0.583322
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 1980.00i	− 3.40792i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 469.574i	− 0.799956i	−0.916525	−	0.399978i	$-0.869018\pi$
$587$	− 469.574i	− 0.799956i	0.916525	−	0.399978i	$-0.130982\pi$
$588$	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	$-0.613055\pi$
$601$	−418.000	−0.695507	−0.347754	+	0.937586i	$0.613055\pi$
$602$	0	0
$603$	737.902i	1.22372i
$604$	0	0
$605$	− 605.000i	− 1.00000i
$606$	0	0
$607$	−737.902	−1.21565	−0.607827	−	0.794069i	$-0.707959\pi$
$607$	−737.902	−1.21565	−0.607827	+	0.794069i	$0.707959\pi$
$608$	0	0
$609$	1320.00	2.16749
$610$	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
$615$	−1386.36	−2.25425
$616$	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
$621$	120.000i	0.193237i
$622$	0	0
$623$	−1905.13	−3.05799
$624$	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
$635$	− 469.574i	− 0.739487i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	1138.00	1.77535	0.887676	−	0.460470i	$-0.152319\pi$
$641$	1138.00	1.77535	0.887676	+	0.460470i	$0.152319\pi$
$642$	0	0
$643$	1220.89i	1.89875i	0.314152	+	0.949373i	$0.398280\pi$
$643$	1220.89i	1.89875i	−0.314152	+	0.949373i	$0.601720\pi$
$644$	0	0
$645$	900.000i	1.39535i
$646$	0	0
$647$	−872.067	−1.34786	−0.673931	−	0.738794i	$-0.735395\pi$
$647$	−872.067	−1.34786	−0.673931	+	0.738794i	$0.735395\pi$
$648$	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
$667$	− 295.161i	− 0.442520i
$668$	0	0
$669$	− 420.000i	− 0.627803i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	223.607i	0.331269i
$676$	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
$681$	1260.00	1.85022
$682$	0	0
$683$	1247.73i	1.82683i	0.407028	+	0.913416i	$0.366565\pi$
$683$	1247.73i	1.82683i	−0.407028	+	0.913416i	$0.633435\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1171.70	1.70553
$688$	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
$705$	2100.00	2.97872
$706$	0	0
$707$	− 1636.80i	− 2.31514i
$708$	0	0
$709$	698.000i	0.984485i	0.870458	+	0.492243i	$0.163823\pi$
$709$	698.000i	0.984485i	−0.870458	+	0.492243i	$0.836177\pi$
$710$	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
$721$	−2700.00	−3.74480
$722$	0	0
$723$	− 1350.59i	− 1.86803i
$724$	0	0
$725$	− 550.000i	− 0.758621i
$726$	0	0
$727$	−228.079	−0.313726	−0.156863	−	0.987620i	$-0.550138\pi$
$727$	−228.079	−0.313726	−0.156863	+	0.987620i	$0.550138\pi$
$728$	0	0
$729$	1009.00	1.38409
$730$	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
$735$	−2929.25	−3.98537
$736$	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
$743$	1274.56	1.71542	0.857711	−	0.514132i	$-0.171886\pi$
$743$	1274.56	1.71542	0.857711	+	0.514132i	$0.171886\pi$
$744$	0	0
$745$	1390.00	1.86577
$746$	0	0
$747$	− 1623.39i	− 2.17321i
$748$	0	0
$749$	− 2340.00i	− 3.12417i
$750$	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
$763$	− 509.823i	− 0.668183i
$764$	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
$783$	196.774	0.251308
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 1569.72i	− 1.99456i	−0.0736976	−	0.997281i	$-0.523480\pi$
$787$	− 1569.72i	− 1.99456i	0.0736976	−	0.997281i	$-0.476520\pi$
$788$	0	0
$789$	− 1980.00i	− 2.50951i
$790$	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
$801$	−1562.00	−1.95006
$802$	0	0
$803$	0	0
$804$	0	0
$805$	900.000i	1.11801i
$806$	0	0
$807$	−169.941	−0.210584
$808$	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
$815$	1408.72	1.72849
$816$	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
$823$	−872.067	−1.05962	−0.529810	−	0.848117i	$-0.677737\pi$
$823$	−872.067	−1.05962	−0.529810	+	0.848117i	$0.677737\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 1542.89i	− 1.86564i	−0.360339	−	0.932822i	$-0.617339\pi$
$827$	− 1542.89i	− 1.86564i	0.360339	−	0.932822i	$-0.382661\pi$
$828$	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
$835$	− 1140.39i	− 1.36574i
$836$	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
$843$	− 1869.35i	− 2.21750i
$844$	0	0
$845$	− 845.000i	− 1.00000i
$846$	0	0
$847$	1623.39	1.91663
$848$	0	0
$849$	2100.00	2.47350
$850$	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
$861$	− 3720.00i	− 4.32056i
$862$	0	0
$863$	550.073	0.637396	0.318698	−	0.947856i	$-0.396754\pi$
$863$	550.073	0.637396	0.318698	+	0.947856i	$0.396754\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	1292.45i	1.49071i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	1677.05i	1.91663i
$876$	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	$-0.129583\pi$
$881$	1618.00	1.83655	0.918275	+	0.395944i	$0.129583\pi$
$882$	0	0
$883$	1220.89i	1.38266i	0.722537	+	0.691332i	$0.242976\pi$
$883$	1220.89i	1.38266i	−0.722537	+	0.691332i	$0.757024\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	1489.22	1.67894	0.839471	−	0.543405i	$-0.182865\pi$
$887$	1489.22	1.67894	0.839471	+	0.543405i	$0.182865\pi$
$888$	0	0
$889$	1260.00	1.41732
$890$	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
$903$	−2414.95	−2.67437
$904$	0	0
$905$	1790.00	1.97790
$906$	0	0
$907$	− 254.912i	− 0.281049i	−0.990077	−	0.140525i	$-0.955121\pi$
$907$	− 254.912i	− 0.281049i	0.990077	−	0.140525i	$-0.0448789\pi$
$908$	0	0
$909$	− 1342.00i	− 1.47635i
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	1296.92i	1.41740i
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	−660.000	−0.716612
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−2213.71	−2.38803
$928$	0	0
$929$	562.000	0.604952	0.302476	−	0.953157i	$-0.402187\pi$
$929$	562.000	0.604952	0.302476	+	0.953157i	$0.402187\pi$
$930$	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	$0.0199709\pi$
$941$	118.000i	0.125399i	−0.998032	+	0.0626993i	$0.980029\pi$
$942$	0	0
$943$	−831.817	−0.882097
$944$	0	0
$945$	−600.000	−0.634921
$946$	0	0
$947$	576.906i	0.609193i	0.952482	+	0.304596i	$0.0985216\pi$
$947$	576.906i	0.609193i	−0.952482	+	0.304596i	$0.901478\pi$
$948$	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
$963$	− 1918.55i	− 1.99226i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	1918.55	1.98402	0.992009	−	0.126163i	$-0.0402664\pi$
$967$	1918.55	1.98402	0.992009	+	0.126163i	$0.0402664\pi$
$968$	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
$981$	− 418.000i	− 0.426096i
$982$	0	0
$983$	−1945.38	−1.97902	−0.989511	−	0.144456i	$-0.953857\pi$
$983$	−1945.38	−1.97902	−0.989511	+	0.144456i	$0.953857\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	5634.89i	5.70911i
$988$	0	0
$989$	540.000i	0.546006i
$990$	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.e.639.4		4
4.3	odd	2	inner	1280.3.e.e.639.2		4
5.4	even	2	inner	1280.3.e.e.639.2		4
8.3	odd	2	inner	1280.3.e.e.639.3		4
8.5	even	2	inner	1280.3.e.e.639.1		4
16.3	odd	4		80.3.h.a.79.2	yes	2
16.5	even	4		320.3.h.c.319.2		2
16.11	odd	4		320.3.h.c.319.1		2
16.13	even	4		80.3.h.a.79.1	✓	2
20.19	odd	2	CM	1280.3.e.e.639.4		4
40.19	odd	2	inner	1280.3.e.e.639.1		4
40.29	even	2	inner	1280.3.e.e.639.3		4
48.29	odd	4		720.3.j.a.559.2		2
48.35	even	4		720.3.j.a.559.1		2
80.3	even	4		400.3.b.b.351.2		2
80.13	odd	4		400.3.b.b.351.1		2
80.19	odd	4		80.3.h.a.79.1	✓	2
80.27	even	4		1600.3.b.d.1151.2		2
80.29	even	4		80.3.h.a.79.2	yes	2
80.37	odd	4		1600.3.b.d.1151.1		2
80.43	even	4		1600.3.b.d.1151.1		2
80.53	odd	4		1600.3.b.d.1151.2		2
80.59	odd	4		320.3.h.c.319.2		2
80.67	even	4		400.3.b.b.351.1		2
80.69	even	4		320.3.h.c.319.1		2
80.77	odd	4		400.3.b.b.351.2		2
240.29	odd	4		720.3.j.a.559.1		2
240.77	even	4		3600.3.e.o.3151.2		2
240.83	odd	4		3600.3.e.o.3151.2		2
240.173	even	4		3600.3.e.o.3151.1		2
240.179	even	4		720.3.j.a.559.2		2
240.227	odd	4		3600.3.e.o.3151.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.h.a.79.1	✓	2	16.13	even	4
80.3.h.a.79.1	✓	2	80.19	odd	4
80.3.h.a.79.2	yes	2	16.3	odd	4
80.3.h.a.79.2	yes	2	80.29	even	4
320.3.h.c.319.1		2	16.11	odd	4
320.3.h.c.319.1		2	80.69	even	4
320.3.h.c.319.2		2	16.5	even	4
320.3.h.c.319.2		2	80.59	odd	4
400.3.b.b.351.1		2	80.13	odd	4
400.3.b.b.351.1		2	80.67	even	4
400.3.b.b.351.2		2	80.3	even	4
400.3.b.b.351.2		2	80.77	odd	4
720.3.j.a.559.1		2	48.35	even	4
720.3.j.a.559.1		2	240.29	odd	4
720.3.j.a.559.2		2	48.29	odd	4
720.3.j.a.559.2		2	240.179	even	4
1280.3.e.e.639.1		4	8.5	even	2	inner
1280.3.e.e.639.1		4	40.19	odd	2	inner
1280.3.e.e.639.2		4	4.3	odd	2	inner
1280.3.e.e.639.2		4	5.4	even	2	inner
1280.3.e.e.639.3		4	8.3	odd	2	inner
1280.3.e.e.639.3		4	40.29	even	2	inner
1280.3.e.e.639.4		4	1.1	even	1	trivial
1280.3.e.e.639.4		4	20.19	odd	2	CM
1600.3.b.d.1151.1		2	80.37	odd	4
1600.3.b.d.1151.1		2	80.43	even	4
1600.3.b.d.1151.2		2	80.27	even	4
1600.3.b.d.1151.2		2	80.53	odd	4
3600.3.e.o.3151.1		2	240.173	even	4
3600.3.e.o.3151.1		2	240.227	odd	4
3600.3.e.o.3151.2		2	240.77	even	4
3600.3.e.o.3151.2		2	240.83	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.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.47214i q^{3} +5.00000i q^{5} -13.4164 q^{7} -11.0000 q^{9} +O(q^{10})\)	\(q+4.47214i q^{3} +5.00000i q^{5} -13.4164 q^{7} -11.0000 q^{9} -22.3607 q^{15} -60.0000i q^{21} -13.4164 q^{23} -25.0000 q^{25} -8.94427i q^{27} +22.0000i q^{29} -67.0820i q^{35} +62.0000 q^{41} -40.2492i q^{43} -55.0000i q^{45} -93.9149 q^{47} +131.000 q^{49} -58.0000i q^{61} +147.580 q^{63} -67.0820i q^{67} -60.0000i q^{69} -111.803i q^{75} -59.0000 q^{81} +147.580i q^{83} -98.3870 q^{87} +142.000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 44 q^{9}+O(q^{10}) \) 4 * q - 44 * q^9	\( 4 q - 44 q^{9} - 100 q^{25} + 248 q^{41} + 524 q^{49} - 236 q^{81} + 568 q^{89}+O(q^{100}) \) 4 * q - 44 * q^9 - 100 * q^25 + 248 * q^41 + 524 * q^49 - 236 * q^81 + 568 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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