LMFDB - Embedded newform 9680.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9680,2,Mod(1,9680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9680, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("9680.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9680 = 2^{4} \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9680.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$77.2951891566$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9680.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} +1.00000 q^{5} +3.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} +1.00000 q^{5} +3.00000 q^{7} -2.00000 q^{9} +6.00000 q^{13} +1.00000 q^{15} +7.00000 q^{17} +5.00000 q^{19} +3.00000 q^{21} +6.00000 q^{23} +1.00000 q^{25} -5.00000 q^{27} -5.00000 q^{29} +3.00000 q^{31} +3.00000 q^{35} +3.00000 q^{37} +6.00000 q^{39} -2.00000 q^{41} +4.00000 q^{43} -2.00000 q^{45} +2.00000 q^{47} +2.00000 q^{49} +7.00000 q^{51} -1.00000 q^{53} +5.00000 q^{57} +10.0000 q^{59} -7.00000 q^{61} -6.00000 q^{63} +6.00000 q^{65} -8.00000 q^{67} +6.00000 q^{69} -7.00000 q^{71} -14.0000 q^{73} +1.00000 q^{75} +10.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} +7.00000 q^{85} -5.00000 q^{87} -15.0000 q^{89} +18.0000 q^{91} +3.00000 q^{93} +5.00000 q^{95} -12.0000 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0	0
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	0	0
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	3.00000	0.507093
$36$	0	0
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	0	0
$39$	6.00000	0.960769
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	0	0
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	7.00000	0.980196
$52$	0	0
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	5.00000	0.662266
$58$	0	0
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	0	0
$63$	−6.00000	−0.755929
$64$	0	0
$65$	6.00000	0.744208
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	0	0
$71$	−7.00000	−0.830747	−0.415374	−	0.909651i	$-0.636349\pi$
$71$	−7.00000	−0.830747	−0.415374	+	0.909651i	$0.636349\pi$
$72$	0	0
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	0	0
$75$	1.00000	0.115470
$76$	0	0
$77$	0	0
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	7.00000	0.759257
$86$	0	0
$87$	−5.00000	−0.536056
$88$	0	0
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	18.0000	1.88691
$92$	0	0
$93$	3.00000	0.311086
$94$	0	0
$95$	5.00000	0.512989
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	3.00000	0.292770
$106$	0	0
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	0	0
$113$	−16.0000	−1.50515	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000	−1.50515	−0.752577	+	0.658505i	$0.771189\pi$
$114$	0	0
$115$	6.00000	0.559503
$116$	0	0
$117$	−12.0000	−1.10940
$118$	0	0
$119$	21.0000	1.92507
$120$	0	0
$121$	0	0
$122$	0	0
$123$	−2.00000	−0.180334
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	0	0
$129$	4.00000	0.352180
$130$	0	0
$131$	17.0000	1.48530	0.742648	−	0.669681i	$-0.233569\pi$
$131$	17.0000	1.48530	0.742648	+	0.669681i	$0.233569\pi$
$132$	0	0
$133$	15.0000	1.30066
$134$	0	0
$135$	−5.00000	−0.430331
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−5.00000	−0.415227
$146$	0	0
$147$	2.00000	0.164957
$148$	0	0
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	0	0
$153$	−14.0000	−1.13183
$154$	0	0
$155$	3.00000	0.240966
$156$	0	0
$157$	3.00000	0.239426	0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000	0.239426	0.119713	+	0.992809i	$0.461803\pi$
$158$	0	0
$159$	−1.00000	−0.0793052
$160$	0	0
$161$	18.0000	1.41860
$162$	0	0
$163$	−19.0000	−1.48819	−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000	−1.48819	−0.744097	+	0.668071i	$0.767120\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	−10.0000	−0.764719
$172$	0	0
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	3.00000	0.226779
$176$	0	0
$177$	10.0000	0.751646
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	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
$183$	−7.00000	−0.517455
$184$	0	0
$185$	3.00000	0.220564
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−15.0000	−1.09109
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	0	0
$195$	6.00000	0.429669
$196$	0	0
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	25.0000	1.77220	0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000	1.77220	0.886102	+	0.463491i	$0.153403\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	0	0
$203$	−15.0000	−1.05279
$204$	0	0
$205$	−2.00000	−0.139686
$206$	0	0
$207$	−12.0000	−0.834058
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	0	0
$213$	−7.00000	−0.479632
$214$	0	0
$215$	4.00000	0.272798
$216$	0	0
$217$	9.00000	0.610960
$218$	0	0
$219$	−14.0000	−0.946032
$220$	0	0
$221$	42.0000	2.82523
$222$	0	0
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	0	0
$225$	−2.00000	−0.133333
$226$	0	0
$227$	−2.00000	−0.132745	−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000	−0.132745	−0.0663723	+	0.997795i	$0.521143\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−9.00000	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$234$	0	0
$235$	2.00000	0.130466
$236$	0	0
$237$	10.0000	0.649570
$238$	0	0
$239$	10.0000	0.646846	0.323423	−	0.946254i	$-0.395166\pi$
$239$	10.0000	0.646846	0.323423	+	0.946254i	$0.395166\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	2.00000	0.127775
$246$	0	0
$247$	30.0000	1.90885
$248$	0	0
$249$	−6.00000	−0.380235
$250$	0	0
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	7.00000	0.438357
$256$	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
$259$	9.00000	0.559233
$260$	0	0
$261$	10.0000	0.618984
$262$	0	0
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	−1.00000	−0.0614295
$266$	0	0
$267$	−15.0000	−0.917985
$268$	0	0
$269$	−20.0000	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	0	0
$273$	18.0000	1.08941
$274$	0	0
$275$	0	0
$276$	0	0
$277$	12.0000	0.721010	0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000	0.721010	0.360505	+	0.932757i	$0.382604\pi$
$278$	0	0
$279$	−6.00000	−0.359211
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	0	0
$285$	5.00000	0.296174
$286$	0	0
$287$	−6.00000	−0.354169
$288$	0	0
$289$	32.0000	1.88235
$290$	0	0
$291$	−12.0000	−0.703452
$292$	0	0
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	0	0
$297$	0	0
$298$	0	0
$299$	36.0000	2.08193
$300$	0	0
$301$	12.0000	0.691669
$302$	0	0
$303$	−2.00000	−0.114897
$304$	0	0
$305$	−7.00000	−0.400819
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	0	0
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	0	0
$315$	−6.00000	−0.338062
$316$	0	0
$317$	−7.00000	−0.393159	−0.196580	−	0.980488i	$-0.562983\pi$
$317$	−7.00000	−0.393159	−0.196580	+	0.980488i	$0.562983\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	8.00000	0.446516
$322$	0	0
$323$	35.0000	1.94745
$324$	0	0
$325$	6.00000	0.332820
$326$	0	0
$327$	10.0000	0.553001
$328$	0	0
$329$	6.00000	0.330791
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	0	0
$333$	−6.00000	−0.328798
$334$	0	0
$335$	−8.00000	−0.437087
$336$	0	0
$337$	17.0000	0.926049	0.463025	−	0.886345i	$-0.346764\pi$
$337$	17.0000	0.926049	0.463025	+	0.886345i	$0.346764\pi$
$338$	0	0
$339$	−16.0000	−0.869001
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−15.0000	−0.809924
$344$	0	0
$345$	6.00000	0.323029
$346$	0	0
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	0	0
$351$	−30.0000	−1.60128
$352$	0	0
$353$	34.0000	1.80964	0.904819	−	0.425797i	$-0.140006\pi$
$353$	34.0000	1.80964	0.904819	+	0.425797i	$0.140006\pi$
$354$	0	0
$355$	−7.00000	−0.371521
$356$	0	0
$357$	21.0000	1.11144
$358$	0	0
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	0	0
$369$	4.00000	0.208232
$370$	0	0
$371$	−3.00000	−0.155752
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	−30.0000	−1.54508
$378$	0	0
$379$	30.0000	1.54100	0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000	1.54100	0.770498	+	0.637442i	$0.220007\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	0	0
$383$	−34.0000	−1.73732	−0.868659	−	0.495410i	$-0.835018\pi$
$383$	−34.0000	−1.73732	−0.868659	+	0.495410i	$0.835018\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.00000	−0.406663
$388$	0	0
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	42.0000	2.12403
$392$	0	0
$393$	17.0000	0.857537
$394$	0	0
$395$	10.0000	0.503155
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	0	0
$399$	15.0000	0.750939
$400$	0	0
$401$	−13.0000	−0.649189	−0.324595	−	0.945853i	$-0.605228\pi$
$401$	−13.0000	−0.649189	−0.324595	+	0.945853i	$0.605228\pi$
$402$	0	0
$403$	18.0000	0.896644
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	0	0
$413$	30.0000	1.47620
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−20.0000	−0.979404
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	32.0000	1.55958	0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000	1.55958	0.779792	+	0.626038i	$0.215325\pi$
$422$	0	0
$423$	−4.00000	−0.194487
$424$	0	0
$425$	7.00000	0.339550
$426$	0	0
$427$	−21.0000	−1.01626
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	0	0
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	−5.00000	−0.239732
$436$	0	0
$437$	30.0000	1.43509
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	0	0
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	−15.0000	−0.711068
$446$	0	0
$447$	−15.0000	−0.709476
$448$	0	0
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	2.00000	0.0939682
$454$	0	0
$455$	18.0000	0.843853
$456$	0	0
$457$	−3.00000	−0.140334	−0.0701670	−	0.997535i	$-0.522353\pi$
$457$	−3.00000	−0.140334	−0.0701670	+	0.997535i	$0.522353\pi$
$458$	0	0
$459$	−35.0000	−1.63366
$460$	0	0
$461$	−27.0000	−1.25752	−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000	−1.25752	−0.628758	+	0.777601i	$0.716436\pi$
$462$	0	0
$463$	−34.0000	−1.58011	−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000	−1.58011	−0.790057	+	0.613033i	$0.789949\pi$
$464$	0	0
$465$	3.00000	0.139122
$466$	0	0
$467$	−23.0000	−1.06431	−0.532157	−	0.846646i	$-0.678618\pi$
$467$	−23.0000	−1.06431	−0.532157	+	0.846646i	$0.678618\pi$
$468$	0	0
$469$	−24.0000	−1.10822
$470$	0	0
$471$	3.00000	0.138233
$472$	0	0
$473$	0	0
$474$	0	0
$475$	5.00000	0.229416
$476$	0	0
$477$	2.00000	0.0915737
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	18.0000	0.820729
$482$	0	0
$483$	18.0000	0.819028
$484$	0	0
$485$	−12.0000	−0.544892
$486$	0	0
$487$	12.0000	0.543772	0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000	0.543772	0.271886	+	0.962329i	$0.412353\pi$
$488$	0	0
$489$	−19.0000	−0.859210
$490$	0	0
$491$	−3.00000	−0.135388	−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000	−0.135388	−0.0676941	+	0.997706i	$0.521564\pi$
$492$	0	0
$493$	−35.0000	−1.57632
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−21.0000	−0.941979
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	3.00000	0.134030
$502$	0	0
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	−2.00000	−0.0889988
$506$	0	0
$507$	23.0000	1.02147
$508$	0	0
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	0	0
$511$	−42.0000	−1.85797
$512$	0	0
$513$	−25.0000	−1.10378
$514$	0	0
$515$	−4.00000	−0.176261
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−14.0000	−0.614532
$520$	0	0
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	0	0
$525$	3.00000	0.130931
$526$	0	0
$527$	21.0000	0.914774
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	−20.0000	−0.867926
$532$	0	0
$533$	−12.0000	−0.519778
$534$	0	0
$535$	8.00000	0.345870
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	0	0
$543$	2.00000	0.0858282
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	0	0
$549$	14.0000	0.597505
$550$	0	0
$551$	−25.0000	−1.06504
$552$	0	0
$553$	30.0000	1.27573
$554$	0	0
$555$	3.00000	0.127343
$556$	0	0
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	0	0
$559$	24.0000	1.01509
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	0	0
$565$	−16.0000	−0.673125
$566$	0	0
$567$	3.00000	0.125988
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	27.0000	1.12991	0.564957	−	0.825120i	$-0.308893\pi$
$571$	27.0000	1.12991	0.564957	+	0.825120i	$0.308893\pi$
$572$	0	0
$573$	−12.0000	−0.501307
$574$	0	0
$575$	6.00000	0.250217
$576$	0	0
$577$	38.0000	1.58196	0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000	1.58196	0.790980	+	0.611842i	$0.209571\pi$
$578$	0	0
$579$	11.0000	0.457144
$580$	0	0
$581$	−18.0000	−0.746766
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−12.0000	−0.496139
$586$	0	0
$587$	27.0000	1.11441	0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000	1.11441	0.557205	+	0.830375i	$0.311874\pi$
$588$	0	0
$589$	15.0000	0.618064
$590$	0	0
$591$	12.0000	0.493614
$592$	0	0
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	21.0000	0.860916
$596$	0	0
$597$	25.0000	1.02318
$598$	0	0
$599$	−45.0000	−1.83865	−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000	−1.83865	−0.919325	+	0.393499i	$0.871265\pi$
$600$	0	0
$601$	−42.0000	−1.71322	−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000	−1.71322	−0.856608	+	0.515968i	$0.827432\pi$
$602$	0	0
$603$	16.0000	0.651570
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−47.0000	−1.90767	−0.953836	−	0.300329i	$-0.902903\pi$
$607$	−47.0000	−1.90767	−0.953836	+	0.300329i	$0.902903\pi$
$608$	0	0
$609$	−15.0000	−0.607831
$610$	0	0
$611$	12.0000	0.485468
$612$	0	0
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	0	0
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	8.00000	0.322068	0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000	0.322068	0.161034	+	0.986949i	$0.448517\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	0	0
$623$	−45.0000	−1.80289
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	21.0000	0.837325
$630$	0	0
$631$	33.0000	1.31371	0.656855	−	0.754017i	$-0.271887\pi$
$631$	33.0000	1.31371	0.656855	+	0.754017i	$0.271887\pi$
$632$	0	0
$633$	−23.0000	−0.914168
$634$	0	0
$635$	8.00000	0.317470
$636$	0	0
$637$	12.0000	0.475457
$638$	0	0
$639$	14.0000	0.553831
$640$	0	0
$641$	−33.0000	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$642$	0	0
$643$	−19.0000	−0.749287	−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000	−0.749287	−0.374643	+	0.927169i	$0.622235\pi$
$644$	0	0
$645$	4.00000	0.157500
$646$	0	0
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	9.00000	0.352738
$652$	0	0
$653$	−31.0000	−1.21312	−0.606562	−	0.795036i	$-0.707452\pi$
$653$	−31.0000	−1.21312	−0.606562	+	0.795036i	$0.707452\pi$
$654$	0	0
$655$	17.0000	0.664245
$656$	0	0
$657$	28.0000	1.09238
$658$	0	0
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	0	0
$663$	42.0000	1.63114
$664$	0	0
$665$	15.0000	0.581675
$666$	0	0
$667$	−30.0000	−1.16160
$668$	0	0
$669$	6.00000	0.231973
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−29.0000	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$674$	0	0
$675$	−5.00000	−0.192450
$676$	0	0
$677$	−28.0000	−1.07613	−0.538064	−	0.842904i	$-0.680844\pi$
$677$	−28.0000	−1.07613	−0.538064	+	0.842904i	$0.680844\pi$
$678$	0	0
$679$	−36.0000	−1.38155
$680$	0	0
$681$	−2.00000	−0.0766402
$682$	0	0
$683$	31.0000	1.18618	0.593091	−	0.805135i	$-0.297907\pi$
$683$	31.0000	1.18618	0.593091	+	0.805135i	$0.297907\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	0	0
$687$	10.0000	0.381524
$688$	0	0
$689$	−6.00000	−0.228582
$690$	0	0
$691$	38.0000	1.44559	0.722794	−	0.691063i	$-0.242858\pi$
$691$	38.0000	1.44559	0.722794	+	0.691063i	$0.242858\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−20.0000	−0.758643
$696$	0	0
$697$	−14.0000	−0.530288
$698$	0	0
$699$	−9.00000	−0.340411
$700$	0	0
$701$	−7.00000	−0.264386	−0.132193	−	0.991224i	$-0.542202\pi$
$701$	−7.00000	−0.264386	−0.132193	+	0.991224i	$0.542202\pi$
$702$	0	0
$703$	15.0000	0.565736
$704$	0	0
$705$	2.00000	0.0753244
$706$	0	0
$707$	−6.00000	−0.225653
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	−20.0000	−0.750059
$712$	0	0
$713$	18.0000	0.674105
$714$	0	0
$715$	0	0
$716$	0	0
$717$	10.0000	0.373457
$718$	0	0
$719$	−25.0000	−0.932343	−0.466171	−	0.884694i	$-0.654367\pi$
$719$	−25.0000	−0.932343	−0.466171	+	0.884694i	$0.654367\pi$
$720$	0	0
$721$	−12.0000	−0.446903
$722$	0	0
$723$	18.0000	0.669427
$724$	0	0
$725$	−5.00000	−0.185695
$726$	0	0
$727$	22.0000	0.815935	0.407967	−	0.912996i	$-0.366238\pi$
$727$	22.0000	0.815935	0.407967	+	0.912996i	$0.366238\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	28.0000	1.03562
$732$	0	0
$733$	−24.0000	−0.886460	−0.443230	−	0.896408i	$-0.646168\pi$
$733$	−24.0000	−0.886460	−0.443230	+	0.896408i	$0.646168\pi$
$734$	0	0
$735$	2.00000	0.0737711
$736$	0	0
$737$	0	0
$738$	0	0
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	0	0
$741$	30.0000	1.10208
$742$	0	0
$743$	−21.0000	−0.770415	−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000	−0.770415	−0.385208	+	0.922830i	$0.625870\pi$
$744$	0	0
$745$	−15.0000	−0.549557
$746$	0	0
$747$	12.0000	0.439057
$748$	0	0
$749$	24.0000	0.876941
$750$	0	0
$751$	−17.0000	−0.620339	−0.310169	−	0.950681i	$-0.600386\pi$
$751$	−17.0000	−0.620339	−0.310169	+	0.950681i	$0.600386\pi$
$752$	0	0
$753$	−2.00000	−0.0728841
$754$	0	0
$755$	2.00000	0.0727875
$756$	0	0
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	0	0
$763$	30.0000	1.08607
$764$	0	0
$765$	−14.0000	−0.506171
$766$	0	0
$767$	60.0000	2.16647
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	0	0
$773$	19.0000	0.683383	0.341691	−	0.939812i	$-0.389000\pi$
$773$	19.0000	0.683383	0.341691	+	0.939812i	$0.389000\pi$
$774$	0	0
$775$	3.00000	0.107763
$776$	0	0
$777$	9.00000	0.322873
$778$	0	0
$779$	−10.0000	−0.358287
$780$	0	0
$781$	0	0
$782$	0	0
$783$	25.0000	0.893427
$784$	0	0
$785$	3.00000	0.107075
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	0	0
$789$	9.00000	0.320408
$790$	0	0
$791$	−48.0000	−1.70668
$792$	0	0
$793$	−42.0000	−1.49146
$794$	0	0
$795$	−1.00000	−0.0354663
$796$	0	0
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	14.0000	0.495284
$800$	0	0
$801$	30.0000	1.06000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	18.0000	0.634417
$806$	0	0
$807$	−20.0000	−0.704033
$808$	0	0
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	7.00000	0.245803	0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000	0.245803	0.122902	+	0.992419i	$0.460780\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	0	0
$815$	−19.0000	−0.665541
$816$	0	0
$817$	20.0000	0.699711
$818$	0	0
$819$	−36.0000	−1.25794
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	8.00000	0.278187	0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000	0.278187	0.139094	+	0.990279i	$0.455581\pi$
$828$	0	0
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	12.0000	0.416275
$832$	0	0
$833$	14.0000	0.485071
$834$	0	0
$835$	3.00000	0.103819
$836$	0	0
$837$	−15.0000	−0.518476
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	18.0000	0.619953
$844$	0	0
$845$	23.0000	0.791224
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−6.00000	−0.205919
$850$	0	0
$851$	18.0000	0.617032
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	0	0
$855$	−10.0000	−0.341993
$856$	0	0
$857$	7.00000	0.239115	0.119558	−	0.992827i	$-0.461852\pi$
$857$	7.00000	0.239115	0.119558	+	0.992827i	$0.461852\pi$
$858$	0	0
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	0	0
$861$	−6.00000	−0.204479
$862$	0	0
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	0	0
$865$	−14.0000	−0.476014
$866$	0	0
$867$	32.0000	1.08678
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−48.0000	−1.62642
$872$	0	0
$873$	24.0000	0.812277
$874$	0	0
$875$	3.00000	0.101419
$876$	0	0
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	0	0
$879$	6.00000	0.202375
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	0	0
$883$	−9.00000	−0.302874	−0.151437	−	0.988467i	$-0.548390\pi$
$883$	−9.00000	−0.302874	−0.151437	+	0.988467i	$0.548390\pi$
$884$	0	0
$885$	10.0000	0.336146
$886$	0	0
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	24.0000	0.804934
$890$	0	0
$891$	0	0
$892$	0	0
$893$	10.0000	0.334637
$894$	0	0
$895$	0	0
$896$	0	0
$897$	36.0000	1.20201
$898$	0	0
$899$	−15.0000	−0.500278
$900$	0	0
$901$	−7.00000	−0.233204
$902$	0	0
$903$	12.0000	0.399335
$904$	0	0
$905$	2.00000	0.0664822
$906$	0	0
$907$	57.0000	1.89265	0.946327	−	0.323211i	$-0.104762\pi$
$907$	57.0000	1.89265	0.946327	+	0.323211i	$0.104762\pi$
$908$	0	0
$909$	4.00000	0.132672
$910$	0	0
$911$	−27.0000	−0.894550	−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000	−0.894550	−0.447275	+	0.894397i	$0.647605\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−7.00000	−0.231413
$916$	0	0
$917$	51.0000	1.68417
$918$	0	0
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	−2.00000	−0.0659022
$922$	0	0
$923$	−42.0000	−1.38245
$924$	0	0
$925$	3.00000	0.0986394
$926$	0	0
$927$	8.00000	0.262754
$928$	0	0
$929$	35.0000	1.14831	0.574156	−	0.818746i	$-0.305330\pi$
$929$	35.0000	1.14831	0.574156	+	0.818746i	$0.305330\pi$
$930$	0	0
$931$	10.0000	0.327737
$932$	0	0
$933$	3.00000	0.0982156
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	−6.00000	−0.195803
$940$	0	0
$941$	−17.0000	−0.554184	−0.277092	−	0.960843i	$-0.589371\pi$
$941$	−17.0000	−0.554184	−0.277092	+	0.960843i	$0.589371\pi$
$942$	0	0
$943$	−12.0000	−0.390774
$944$	0	0
$945$	−15.0000	−0.487950
$946$	0	0
$947$	27.0000	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$948$	0	0
$949$	−84.0000	−2.72676
$950$	0	0
$951$	−7.00000	−0.226991
$952$	0	0
$953$	−39.0000	−1.26333	−0.631667	−	0.775240i	$-0.717629\pi$
$953$	−39.0000	−1.26333	−0.631667	+	0.775240i	$0.717629\pi$
$954$	0	0
$955$	−12.0000	−0.388311
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−36.0000	−1.16250
$960$	0	0
$961$	−22.0000	−0.709677
$962$	0	0
$963$	−16.0000	−0.515593
$964$	0	0
$965$	11.0000	0.354103
$966$	0	0
$967$	−27.0000	−0.868261	−0.434131	−	0.900850i	$-0.642944\pi$
$967$	−27.0000	−0.868261	−0.434131	+	0.900850i	$0.642944\pi$
$968$	0	0
$969$	35.0000	1.12436
$970$	0	0
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	0	0
$973$	−60.0000	−1.92351
$974$	0	0
$975$	6.00000	0.192154
$976$	0	0
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−20.0000	−0.638551
$982$	0	0
$983$	−54.0000	−1.72233	−0.861166	−	0.508323i	$-0.830265\pi$
$983$	−54.0000	−1.72233	−0.861166	+	0.508323i	$0.830265\pi$
$984$	0	0
$985$	12.0000	0.382352
$986$	0	0
$987$	6.00000	0.190982
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	0	0
$995$	25.0000	0.792553
$996$	0	0
$997$	32.0000	1.01345	0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000	1.01345	0.506725	+	0.862108i	$0.330856\pi$
$998$	0	0
$999$	−15.0000	−0.474579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9680.2.a.x.1.1		1
4.3	odd	2		1210.2.a.b.1.1		1
11.10	odd	2		880.2.a.i.1.1		1
20.19	odd	2		6050.2.a.bj.1.1		1
33.32	even	2		7920.2.a.d.1.1		1
44.43	even	2		110.2.a.b.1.1	✓	1
55.32	even	4		4400.2.b.i.4049.1		2
55.43	even	4		4400.2.b.i.4049.2		2
55.54	odd	2		4400.2.a.l.1.1		1
88.21	odd	2		3520.2.a.h.1.1		1
88.43	even	2		3520.2.a.y.1.1		1
132.131	odd	2		990.2.a.d.1.1		1
220.43	odd	4		550.2.b.a.199.1		2
220.87	odd	4		550.2.b.a.199.2		2
220.219	even	2		550.2.a.f.1.1		1
308.307	odd	2		5390.2.a.bf.1.1		1
660.263	even	4		4950.2.c.m.199.2		2
660.527	even	4		4950.2.c.m.199.1		2
660.659	odd	2		4950.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.a.b.1.1	✓	1	44.43	even	2
550.2.a.f.1.1		1	220.219	even	2
550.2.b.a.199.1		2	220.43	odd	4
550.2.b.a.199.2		2	220.87	odd	4
880.2.a.i.1.1		1	11.10	odd	2
990.2.a.d.1.1		1	132.131	odd	2
1210.2.a.b.1.1		1	4.3	odd	2
3520.2.a.h.1.1		1	88.21	odd	2
3520.2.a.y.1.1		1	88.43	even	2
4400.2.a.l.1.1		1	55.54	odd	2
4400.2.b.i.4049.1		2	55.32	even	4
4400.2.b.i.4049.2		2	55.43	even	4
4950.2.a.bc.1.1		1	660.659	odd	2
4950.2.c.m.199.1		2	660.527	even	4
4950.2.c.m.199.2		2	660.263	even	4
5390.2.a.bf.1.1		1	308.307	odd	2
6050.2.a.bj.1.1		1	20.19	odd	2
7920.2.a.d.1.1		1	33.32	even	2
9680.2.a.x.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9680.a (trivial)

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