LMFDB - Embedded newform 9280.2.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9280,2,Mod(1,9280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9280.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9280 = 2^{6} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9280.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,-2,0,-1,0,4,0,1,0,2,0,-2,0,2,0,6,0,-6,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	yes
Analytic conductor:	$74.1011730757$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4640)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9280.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -1.00000 q^{5} +4.00000 q^{7} +1.00000 q^{9} +2.00000 q^{11} -2.00000 q^{13} +2.00000 q^{15} +6.00000 q^{17} -6.00000 q^{19} -8.00000 q^{21} +4.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} +1.00000 q^{29} +2.00000 q^{31} -4.00000 q^{33} -4.00000 q^{35} +2.00000 q^{37} +4.00000 q^{39} -6.00000 q^{41} +6.00000 q^{43} -1.00000 q^{45} -6.00000 q^{47} +9.00000 q^{49} -12.0000 q^{51} -2.00000 q^{53} -2.00000 q^{55} +12.0000 q^{57} +12.0000 q^{59} +6.00000 q^{61} +4.00000 q^{63} +2.00000 q^{65} +8.00000 q^{67} -8.00000 q^{69} +6.00000 q^{73} -2.00000 q^{75} +8.00000 q^{77} -14.0000 q^{79} -11.0000 q^{81} -12.0000 q^{83} -6.00000 q^{85} -2.00000 q^{87} +2.00000 q^{89} -8.00000 q^{91} -4.00000 q^{93} +6.00000 q^{95} +14.0000 q^{97} +2.00000 q^{99} +O(q^{100})$

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
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	0	0
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	−8.00000	−1.74574
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	0	0
$33$	−4.00000	−0.696311
$34$	0	0
$35$	−4.00000	−0.676123
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	−12.0000	−1.68034
$52$	0	0
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	12.0000	1.58944
$58$	0	0
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	0	0
$63$	4.00000	0.503953
$64$	0	0
$65$	2.00000	0.248069
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0	0
$69$	−8.00000	−0.963087
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	0	0
$75$	−2.00000	−0.230940
$76$	0	0
$77$	8.00000	0.911685
$78$	0	0
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	0	0
$87$	−2.00000	−0.214423
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	0	0
$93$	−4.00000	−0.414781
$94$	0	0
$95$	6.00000	0.615587
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	0	0
$99$	2.00000	0.201008
$100$	0	0
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	0	0
$105$	8.00000	0.780720
$106$	0	0
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	0	0
$117$	−2.00000	−0.184900
$118$	0	0
$119$	24.0000	2.20008
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	12.0000	1.08200
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	14.0000	1.24230	0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000	1.24230	0.621150	+	0.783692i	$0.286666\pi$
$128$	0	0
$129$	−12.0000	−1.05654
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	−24.0000	−2.08106
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	0	0
$143$	−4.00000	−0.334497
$144$	0	0
$145$	−1.00000	−0.0830455
$146$	0	0
$147$	−18.0000	−1.48461
$148$	0	0
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	−2.00000	−0.160644
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0	0
$159$	4.00000	0.317221
$160$	0	0
$161$	16.0000	1.26098
$162$	0	0
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	0	0
$165$	4.00000	0.311400
$166$	0	0
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−6.00000	−0.458831
$172$	0	0
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	4.00000	0.302372
$176$	0	0
$177$	−24.0000	−1.80395
$178$	0	0
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	−12.0000	−0.887066
$184$	0	0
$185$	−2.00000	−0.147043
$186$	0	0
$187$	12.0000	0.877527
$188$	0	0
$189$	16.0000	1.16383
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	0	0
$195$	−4.00000	−0.286446
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	0	0
$201$	−16.0000	−1.12855
$202$	0	0
$203$	4.00000	0.280745
$204$	0	0
$205$	6.00000	0.419058
$206$	0	0
$207$	4.00000	0.278019
$208$	0	0
$209$	−12.0000	−0.830057
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−6.00000	−0.409197
$216$	0	0
$217$	8.00000	0.543075
$218$	0	0
$219$	−12.0000	−0.810885
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	30.0000	1.98246	0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000	1.98246	0.991228	+	0.132164i	$0.0421925\pi$
$230$	0	0
$231$	−16.0000	−1.05272
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	6.00000	0.391397
$236$	0	0
$237$	28.0000	1.81880
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	0	0
$245$	−9.00000	−0.574989
$246$	0	0
$247$	12.0000	0.763542
$248$	0	0
$249$	24.0000	1.52094
$250$	0	0
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	0	0
$255$	12.0000	0.751469
$256$	0	0
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	0	0
$261$	1.00000	0.0618984
$262$	0	0
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	0	0
$267$	−4.00000	−0.244796
$268$	0	0
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−10.0000	−0.607457	−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000	−0.607457	−0.303728	+	0.952759i	$0.598232\pi$
$272$	0	0
$273$	16.0000	0.968364
$274$	0	0
$275$	2.00000	0.120605
$276$	0	0
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	0	0
$279$	2.00000	0.119737
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	0	0
$285$	−12.0000	−0.710819
$286$	0	0
$287$	−24.0000	−1.41668
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−28.0000	−1.64139
$292$	0	0
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	0	0
$297$	8.00000	0.464207
$298$	0	0
$299$	−8.00000	−0.462652
$300$	0	0
$301$	24.0000	1.38334
$302$	0	0
$303$	−28.0000	−1.60856
$304$	0	0
$305$	−6.00000	−0.343559
$306$	0	0
$307$	−18.0000	−1.02731	−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000	−1.02731	−0.513657	+	0.857996i	$0.671710\pi$
$308$	0	0
$309$	−24.0000	−1.36531
$310$	0	0
$311$	10.0000	0.567048	0.283524	−	0.958965i	$-0.408496\pi$
$311$	10.0000	0.567048	0.283524	+	0.958965i	$0.408496\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	0	0
$315$	−4.00000	−0.225374
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	2.00000	0.111979
$320$	0	0
$321$	24.0000	1.33955
$322$	0	0
$323$	−36.0000	−2.00309
$324$	0	0
$325$	−2.00000	−0.110940
$326$	0	0
$327$	−4.00000	−0.221201
$328$	0	0
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−26.0000	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	0	0
$335$	−8.00000	−0.437087
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0	0
$339$	4.00000	0.217250
$340$	0	0
$341$	4.00000	0.216612
$342$	0	0
$343$	8.00000	0.431959
$344$	0	0
$345$	8.00000	0.430706
$346$	0	0
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−8.00000	−0.427008
$352$	0	0
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−48.0000	−2.54043
$358$	0	0
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	0	0
$363$	14.0000	0.734809
$364$	0	0
$365$	−6.00000	−0.314054
$366$	0	0
$367$	30.0000	1.56599	0.782994	−	0.622030i	$-0.213692\pi$
$367$	30.0000	1.56599	0.782994	+	0.622030i	$0.213692\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−8.00000	−0.415339
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	0	0
$377$	−2.00000	−0.103005
$378$	0	0
$379$	18.0000	0.924598	0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000	0.924598	0.462299	+	0.886724i	$0.347025\pi$
$380$	0	0
$381$	−28.0000	−1.43448
$382$	0	0
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	−8.00000	−0.407718
$386$	0	0
$387$	6.00000	0.304997
$388$	0	0
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	0	0
$393$	36.0000	1.81596
$394$	0	0
$395$	14.0000	0.704416
$396$	0	0
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	0	0
$399$	48.0000	2.40301
$400$	0	0
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	4.00000	0.198273
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	0	0
$413$	48.0000	2.36193
$414$	0	0
$415$	12.0000	0.589057
$416$	0	0
$417$	24.0000	1.17529
$418$	0	0
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	0	0
$423$	−6.00000	−0.291730
$424$	0	0
$425$	6.00000	0.291043
$426$	0	0
$427$	24.0000	1.16144
$428$	0	0
$429$	8.00000	0.386244
$430$	0	0
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	0	0
$433$	−10.0000	−0.480569	−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000	−0.480569	−0.240285	+	0.970702i	$0.577241\pi$
$434$	0	0
$435$	2.00000	0.0958927
$436$	0	0
$437$	−24.0000	−1.14808
$438$	0	0
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	0	0
$443$	2.00000	0.0950229	0.0475114	−	0.998871i	$-0.484871\pi$
$443$	2.00000	0.0950229	0.0475114	+	0.998871i	$0.484871\pi$
$444$	0	0
$445$	−2.00000	−0.0948091
$446$	0	0
$447$	−44.0000	−2.08113
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−12.0000	−0.565058
$452$	0	0
$453$	16.0000	0.751746
$454$	0	0
$455$	8.00000	0.375046
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	0	0
$459$	24.0000	1.12022
$460$	0	0
$461$	22.0000	1.02464	0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000	1.02464	0.512321	+	0.858794i	$0.328786\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	4.00000	0.185496
$466$	0	0
$467$	22.0000	1.01804	0.509019	−	0.860755i	$-0.330008\pi$
$467$	22.0000	1.01804	0.509019	+	0.860755i	$0.330008\pi$
$468$	0	0
$469$	32.0000	1.47762
$470$	0	0
$471$	44.0000	2.02741
$472$	0	0
$473$	12.0000	0.551761
$474$	0	0
$475$	−6.00000	−0.275299
$476$	0	0
$477$	−2.00000	−0.0915737
$478$	0	0
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	0	0
$483$	−32.0000	−1.45605
$484$	0	0
$485$	−14.0000	−0.635707
$486$	0	0
$487$	36.0000	1.63132	0.815658	−	0.578535i	$-0.196375\pi$
$487$	36.0000	1.63132	0.815658	+	0.578535i	$0.196375\pi$
$488$	0	0
$489$	28.0000	1.26620
$490$	0	0
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	0	0
$493$	6.00000	0.270226
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	0	0
$497$	0	0
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	0	0
$501$	32.0000	1.42965
$502$	0	0
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	0	0
$505$	−14.0000	−0.622992
$506$	0	0
$507$	18.0000	0.799408
$508$	0	0
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	24.0000	1.06170
$512$	0	0
$513$	−24.0000	−1.05963
$514$	0	0
$515$	−12.0000	−0.528783
$516$	0	0
$517$	−12.0000	−0.527759
$518$	0	0
$519$	−28.0000	−1.22906
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	0	0
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	0	0
$525$	−8.00000	−0.349149
$526$	0	0
$527$	12.0000	0.522728
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	12.0000	0.518805
$536$	0	0
$537$	−32.0000	−1.38090
$538$	0	0
$539$	18.0000	0.775315
$540$	0	0
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	0	0
$543$	−4.00000	−0.171656
$544$	0	0
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	0	0
$549$	6.00000	0.256074
$550$	0	0
$551$	−6.00000	−0.255609
$552$	0	0
$553$	−56.0000	−2.38136
$554$	0	0
$555$	4.00000	0.169791
$556$	0	0
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	0	0
$561$	−24.0000	−1.01328
$562$	0	0
$563$	10.0000	0.421450	0.210725	−	0.977545i	$-0.432418\pi$
$563$	10.0000	0.421450	0.210725	+	0.977545i	$0.432418\pi$
$564$	0	0
$565$	2.00000	0.0841406
$566$	0	0
$567$	−44.0000	−1.84783
$568$	0	0
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	0	0
$575$	4.00000	0.166812
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	0	0
$579$	−28.0000	−1.16364
$580$	0	0
$581$	−48.0000	−1.99138
$582$	0	0
$583$	−4.00000	−0.165663
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	0	0
$591$	12.0000	0.493614
$592$	0	0
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	0	0
$595$	−24.0000	−0.983904
$596$	0	0
$597$	8.00000	0.327418
$598$	0	0
$599$	−22.0000	−0.898896	−0.449448	−	0.893307i	$-0.648379\pi$
$599$	−22.0000	−0.898896	−0.449448	+	0.893307i	$0.648379\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	0	0
$605$	7.00000	0.284590
$606$	0	0
$607$	10.0000	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$608$	0	0
$609$	−8.00000	−0.324176
$610$	0	0
$611$	12.0000	0.485468
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	0	0
$615$	−12.0000	−0.483887
$616$	0	0
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	0	0
$619$	−2.00000	−0.0803868	−0.0401934	−	0.999192i	$-0.512797\pi$
$619$	−2.00000	−0.0803868	−0.0401934	+	0.999192i	$0.512797\pi$
$620$	0	0
$621$	16.0000	0.642058
$622$	0	0
$623$	8.00000	0.320513
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	24.0000	0.958468
$628$	0	0
$629$	12.0000	0.478471
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	0	0
$633$	20.0000	0.794929
$634$	0	0
$635$	−14.0000	−0.555573
$636$	0	0
$637$	−18.0000	−0.713186
$638$	0	0
$639$	0	0
$640$	0	0
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	0	0
$643$	8.00000	0.315489	0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000	0.315489	0.157745	+	0.987480i	$0.449578\pi$
$644$	0	0
$645$	12.0000	0.472500
$646$	0	0
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	0	0
$651$	−16.0000	−0.627089
$652$	0	0
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	0	0
$655$	18.0000	0.703318
$656$	0	0
$657$	6.00000	0.234082
$658$	0	0
$659$	50.0000	1.94772	0.973862	−	0.227142i	$-0.0729380\pi$
$659$	50.0000	1.94772	0.973862	+	0.227142i	$0.0729380\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	24.0000	0.930680
$666$	0	0
$667$	4.00000	0.154881
$668$	0	0
$669$	8.00000	0.309298
$670$	0	0
$671$	12.0000	0.463255
$672$	0	0
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	0	0
$675$	4.00000	0.153960
$676$	0	0
$677$	−38.0000	−1.46046	−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000	−1.46046	−0.730229	+	0.683202i	$0.760587\pi$
$678$	0	0
$679$	56.0000	2.14908
$680$	0	0
$681$	24.0000	0.919682
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	0	0
$685$	−6.00000	−0.229248
$686$	0	0
$687$	−60.0000	−2.28914
$688$	0	0
$689$	4.00000	0.152388
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	0	0
$693$	8.00000	0.303895
$694$	0	0
$695$	12.0000	0.455186
$696$	0	0
$697$	−36.0000	−1.36360
$698$	0	0
$699$	12.0000	0.453882
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	−12.0000	−0.452589
$704$	0	0
$705$	−12.0000	−0.451946
$706$	0	0
$707$	56.0000	2.10610
$708$	0	0
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	0	0
$711$	−14.0000	−0.525041
$712$	0	0
$713$	8.00000	0.299602
$714$	0	0
$715$	4.00000	0.149592
$716$	0	0
$717$	−40.0000	−1.49383
$718$	0	0
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	0	0
$721$	48.0000	1.78761
$722$	0	0
$723$	−4.00000	−0.148762
$724$	0	0
$725$	1.00000	0.0371391
$726$	0	0
$727$	−2.00000	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	36.0000	1.33151
$732$	0	0
$733$	42.0000	1.55131	0.775653	−	0.631160i	$-0.217421\pi$
$733$	42.0000	1.55131	0.775653	+	0.631160i	$0.217421\pi$
$734$	0	0
$735$	18.0000	0.663940
$736$	0	0
$737$	16.0000	0.589368
$738$	0	0
$739$	34.0000	1.25071	0.625355	−	0.780340i	$-0.284954\pi$
$739$	34.0000	1.25071	0.625355	+	0.780340i	$0.284954\pi$
$740$	0	0
$741$	−24.0000	−0.881662
$742$	0	0
$743$	2.00000	0.0733729	0.0366864	−	0.999327i	$-0.488320\pi$
$743$	2.00000	0.0733729	0.0366864	+	0.999327i	$0.488320\pi$
$744$	0	0
$745$	−22.0000	−0.806018
$746$	0	0
$747$	−12.0000	−0.439057
$748$	0	0
$749$	−48.0000	−1.75388
$750$	0	0
$751$	22.0000	0.802791	0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000	0.802791	0.401396	+	0.915905i	$0.368525\pi$
$752$	0	0
$753$	28.0000	1.02038
$754$	0	0
$755$	8.00000	0.291150
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	0	0
$759$	−16.0000	−0.580763
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	8.00000	0.289619
$764$	0	0
$765$	−6.00000	−0.216930
$766$	0	0
$767$	−24.0000	−0.866590
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	4.00000	0.144056
$772$	0	0
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	0	0
$775$	2.00000	0.0718421
$776$	0	0
$777$	−16.0000	−0.573997
$778$	0	0
$779$	36.0000	1.28983
$780$	0	0
$781$	0	0
$782$	0	0
$783$	4.00000	0.142948
$784$	0	0
$785$	22.0000	0.785214
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	0	0
$789$	−12.0000	−0.427211
$790$	0	0
$791$	−8.00000	−0.284447
$792$	0	0
$793$	−12.0000	−0.426132
$794$	0	0
$795$	−4.00000	−0.141865
$796$	0	0
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	0	0
$801$	2.00000	0.0706665
$802$	0	0
$803$	12.0000	0.423471
$804$	0	0
$805$	−16.0000	−0.563926
$806$	0	0
$807$	−12.0000	−0.422420
$808$	0	0
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−8.00000	−0.280918	−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000	−0.280918	−0.140459	+	0.990086i	$0.544858\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	0	0
$815$	14.0000	0.490399
$816$	0	0
$817$	−36.0000	−1.25948
$818$	0	0
$819$	−8.00000	−0.279543
$820$	0	0
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	0	0
$823$	6.00000	0.209147	0.104573	−	0.994517i	$-0.466652\pi$
$823$	6.00000	0.209147	0.104573	+	0.994517i	$0.466652\pi$
$824$	0	0
$825$	−4.00000	−0.139262
$826$	0	0
$827$	−14.0000	−0.486828	−0.243414	−	0.969923i	$-0.578267\pi$
$827$	−14.0000	−0.486828	−0.243414	+	0.969923i	$0.578267\pi$
$828$	0	0
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	0	0
$831$	−60.0000	−2.08138
$832$	0	0
$833$	54.0000	1.87099
$834$	0	0
$835$	16.0000	0.553703
$836$	0	0
$837$	8.00000	0.276520
$838$	0	0
$839$	22.0000	0.759524	0.379762	−	0.925084i	$-0.376006\pi$
$839$	22.0000	0.759524	0.379762	+	0.925084i	$0.376006\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	44.0000	1.51544
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	−28.0000	−0.962091
$848$	0	0
$849$	32.0000	1.09824
$850$	0	0
$851$	8.00000	0.274236
$852$	0	0
$853$	−38.0000	−1.30110	−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000	−1.30110	−0.650548	+	0.759465i	$0.725461\pi$
$854$	0	0
$855$	6.00000	0.205196
$856$	0	0
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	0	0
$859$	54.0000	1.84246	0.921228	−	0.389023i	$-0.127187\pi$
$859$	54.0000	1.84246	0.921228	+	0.389023i	$0.127187\pi$
$860$	0	0
$861$	48.0000	1.63584
$862$	0	0
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	0	0
$865$	−14.0000	−0.476014
$866$	0	0
$867$	−38.0000	−1.29055
$868$	0	0
$869$	−28.0000	−0.949835
$870$	0	0
$871$	−16.0000	−0.542139
$872$	0	0
$873$	14.0000	0.473828
$874$	0	0
$875$	−4.00000	−0.135225
$876$	0	0
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	0	0
$879$	−36.0000	−1.21425
$880$	0	0
$881$	58.0000	1.95407	0.977035	−	0.213080i	$-0.0683494\pi$
$881$	58.0000	1.95407	0.977035	+	0.213080i	$0.0683494\pi$
$882$	0	0
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	0	0
$885$	24.0000	0.806751
$886$	0	0
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	0	0
$889$	56.0000	1.87818
$890$	0	0
$891$	−22.0000	−0.737028
$892$	0	0
$893$	36.0000	1.20469
$894$	0	0
$895$	−16.0000	−0.534821
$896$	0	0
$897$	16.0000	0.534224
$898$	0	0
$899$	2.00000	0.0667037
$900$	0	0
$901$	−12.0000	−0.399778
$902$	0	0
$903$	−48.0000	−1.59734
$904$	0	0
$905$	−2.00000	−0.0664822
$906$	0	0
$907$	−30.0000	−0.996134	−0.498067	−	0.867139i	$-0.665957\pi$
$907$	−30.0000	−0.996134	−0.498067	+	0.867139i	$0.665957\pi$
$908$	0	0
$909$	14.0000	0.464351
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	0	0
$915$	12.0000	0.396708
$916$	0	0
$917$	−72.0000	−2.37765
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	36.0000	1.18624
$922$	0	0
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	0	0
$927$	12.0000	0.394132
$928$	0	0
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	−54.0000	−1.76978
$932$	0	0
$933$	−20.0000	−0.654771
$934$	0	0
$935$	−12.0000	−0.392442
$936$	0	0
$937$	6.00000	0.196011	0.0980057	−	0.995186i	$-0.468754\pi$
$937$	6.00000	0.196011	0.0980057	+	0.995186i	$0.468754\pi$
$938$	0	0
$939$	−44.0000	−1.43589
$940$	0	0
$941$	−46.0000	−1.49956	−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000	−1.49956	−0.749779	+	0.661689i	$0.769840\pi$
$942$	0	0
$943$	−24.0000	−0.781548
$944$	0	0
$945$	−16.0000	−0.520480
$946$	0	0
$947$	54.0000	1.75476	0.877382	−	0.479792i	$-0.159288\pi$
$947$	54.0000	1.75476	0.877382	+	0.479792i	$0.159288\pi$
$948$	0	0
$949$	−12.0000	−0.389536
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	6.00000	0.194155
$956$	0	0
$957$	−4.00000	−0.129302
$958$	0	0
$959$	24.0000	0.775000
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	−12.0000	−0.386695
$964$	0	0
$965$	−14.0000	−0.450676
$966$	0	0
$967$	−14.0000	−0.450210	−0.225105	−	0.974335i	$-0.572272\pi$
$967$	−14.0000	−0.450210	−0.225105	+	0.974335i	$0.572272\pi$
$968$	0	0
$969$	72.0000	2.31297
$970$	0	0
$971$	−22.0000	−0.706014	−0.353007	−	0.935621i	$-0.614841\pi$
$971$	−22.0000	−0.706014	−0.353007	+	0.935621i	$0.614841\pi$
$972$	0	0
$973$	−48.0000	−1.53881
$974$	0	0
$975$	4.00000	0.128103
$976$	0	0
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	4.00000	0.127841
$980$	0	0
$981$	2.00000	0.0638551
$982$	0	0
$983$	42.0000	1.33959	0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000	1.33959	0.669796	+	0.742545i	$0.266382\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	0	0
$987$	48.0000	1.52786
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	0	0
$993$	52.0000	1.65017
$994$	0	0
$995$	4.00000	0.126809
$996$	0	0
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9280.2.a.a.1.1		1
4.3	odd	2		9280.2.a.r.1.1		1
8.3	odd	2		4640.2.a.b.1.1	✓	1
8.5	even	2		4640.2.a.f.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4640.2.a.b.1.1	✓	1	8.3	odd	2
4640.2.a.f.1.1	yes	1	8.5	even	2
9280.2.a.a.1.1		1	1.1	even	1	trivial
9280.2.a.r.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9280.a (trivial)

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L-functions

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