LMFDB - Embedded newform 7280.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7280,2,Mod(1,7280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7280.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:	$58.1310926715$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3640)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-2.00000 q^{3} -1.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} -6.00000 q^{11} -1.00000 q^{13} +2.00000 q^{15} -2.00000 q^{17} -2.00000 q^{19} +2.00000 q^{21} +2.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} +10.0000 q^{29} +6.00000 q^{31} +12.0000 q^{33} +1.00000 q^{35} +6.00000 q^{37} +2.00000 q^{39} -2.00000 q^{41} -10.0000 q^{43} -1.00000 q^{45} +1.00000 q^{49} +4.00000 q^{51} +14.0000 q^{53} +6.00000 q^{55} +4.00000 q^{57} +2.00000 q^{59} +2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{65} -8.00000 q^{67} -4.00000 q^{69} +10.0000 q^{71} +2.00000 q^{73} -2.00000 q^{75} +6.00000 q^{77} -4.00000 q^{79} -11.0000 q^{81} +4.00000 q^{83} +2.00000 q^{85} -20.0000 q^{87} -2.00000 q^{89} +1.00000 q^{91} -12.0000 q^{93} +2.00000 q^{95} +14.0000 q^{97} -6.00000 q^{99} +O(q^{100})$

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
$3$	−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
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	2.00000	0.516398
$16$	0	0
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	0	0
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	0	0
$33$	12.0000	2.08893
$34$	0	0
$35$	1.00000	0.169031
$36$	0	0
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	0	0
$39$	2.00000	0.320256
$40$	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
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	0	0
$53$	14.0000	1.92305	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000	1.92305	0.961524	+	0.274721i	$0.0885855\pi$
$54$	0	0
$55$	6.00000	0.809040
$56$	0	0
$57$	4.00000	0.529813
$58$	0	0
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	0	0
$65$	1.00000	0.124035
$66$	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
$69$	−4.00000	−0.481543
$70$	0	0
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	0	0
$75$	−2.00000	−0.230940
$76$	0	0
$77$	6.00000	0.683763
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	0	0
$87$	−20.0000	−2.14423
$88$	0	0
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	0	0
$93$	−12.0000	−1.24434
$94$	0	0
$95$	2.00000	0.205196
$96$	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
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	0	0
$105$	−2.00000	−0.195180
$106$	0	0
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−12.0000	−1.13899
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	−2.00000	−0.186501
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	2.00000	0.183340
$120$	0	0
$121$	25.0000	2.27273
$122$	0	0
$123$	4.00000	0.360668
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	22.0000	1.95218	0.976092	−	0.217357i	$-0.0697436\pi$
$127$	22.0000	1.95218	0.976092	+	0.217357i	$0.0697436\pi$
$128$	0	0
$129$	20.0000	1.76090
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	2.00000	0.173422
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	6.00000	0.501745
$144$	0	0
$145$	−10.0000	−0.830455
$146$	0	0
$147$	−2.00000	−0.164957
$148$	0	0
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−6.00000	−0.481932
$156$	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
$159$	−28.0000	−2.22054
$160$	0	0
$161$	−2.00000	−0.157622
$162$	0	0
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	0	0
$165$	−12.0000	−0.934199
$166$	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
$169$	1.00000	0.0769231
$170$	0	0
$171$	−2.00000	−0.152944
$172$	0	0
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−4.00000	−0.300658
$178$	0	0
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	0	0
$185$	−6.00000	−0.441129
$186$	0	0
$187$	12.0000	0.877527
$188$	0	0
$189$	−4.00000	−0.290957
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	0	0
$195$	−2.00000	−0.143223
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	16.0000	1.12855
$202$	0	0
$203$	−10.0000	−0.701862
$204$	0	0
$205$	2.00000	0.139686
$206$	0	0
$207$	2.00000	0.139010
$208$	0	0
$209$	12.0000	0.830057
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	0	0
$213$	−20.0000	−1.37038
$214$	0	0
$215$	10.0000	0.681994
$216$	0	0
$217$	−6.00000	−0.407307
$218$	0	0
$219$	−4.00000	−0.270295
$220$	0	0
$221$	2.00000	0.134535
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	−12.0000	−0.789542
$232$	0	0
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	8.00000	0.519656
$238$	0	0
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	2.00000	0.127257
$248$	0	0
$249$	−8.00000	−0.506979
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	0	0
$255$	−4.00000	−0.250490
$256$	0	0
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−6.00000	−0.372822
$260$	0	0
$261$	10.0000	0.618984
$262$	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
$265$	−14.0000	−0.860013
$266$	0	0
$267$	4.00000	0.244796
$268$	0	0
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	18.0000	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$271$	18.0000	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$272$	0	0
$273$	−2.00000	−0.121046
$274$	0	0
$275$	−6.00000	−0.361814
$276$	0	0
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	0	0
$279$	6.00000	0.359211
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	0	0
$285$	−4.00000	−0.236940
$286$	0	0
$287$	2.00000	0.118056
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−28.0000	−1.64139
$292$	0	0
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	0	0
$295$	−2.00000	−0.116445
$296$	0	0
$297$	−24.0000	−1.39262
$298$	0	0
$299$	−2.00000	−0.115663
$300$	0	0
$301$	10.0000	0.576390
$302$	0	0
$303$	36.0000	2.06815
$304$	0	0
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	−28.0000	−1.59286
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	0	0
$315$	1.00000	0.0563436
$316$	0	0
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	0	0
$319$	−60.0000	−3.35936
$320$	0	0
$321$	36.0000	2.00932
$322$	0	0
$323$	4.00000	0.222566
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	0	0
$327$	20.0000	1.10600
$328$	0	0
$329$	0	0
$330$	0	0
$331$	6.00000	0.329790	0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000	0.329790	0.164895	+	0.986311i	$0.447272\pi$
$332$	0	0
$333$	6.00000	0.328798
$334$	0	0
$335$	8.00000	0.437087
$336$	0	0
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	0	0
$339$	12.0000	0.651751
$340$	0	0
$341$	−36.0000	−1.94951
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	4.00000	0.215353
$346$	0	0
$347$	22.0000	1.18102	0.590511	−	0.807030i	$-0.298926\pi$
$347$	22.0000	1.18102	0.590511	+	0.807030i	$0.298926\pi$
$348$	0	0
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	0	0
$353$	2.00000	0.106449	0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000	0.106449	0.0532246	+	0.998583i	$0.483050\pi$
$354$	0	0
$355$	−10.0000	−0.530745
$356$	0	0
$357$	−4.00000	−0.211702
$358$	0	0
$359$	34.0000	1.79445	0.897226	−	0.441572i	$-0.145579\pi$
$359$	34.0000	1.79445	0.897226	+	0.441572i	$0.145579\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	0	0
$363$	−50.0000	−2.62432
$364$	0	0
$365$	−2.00000	−0.104685
$366$	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
$369$	−2.00000	−0.104116
$370$	0	0
$371$	−14.0000	−0.726844
$372$	0	0
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	0	0
$377$	−10.0000	−0.515026
$378$	0	0
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	0	0
$381$	−44.0000	−2.25419
$382$	0	0
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	0	0
$385$	−6.00000	−0.305788
$386$	0	0
$387$	−10.0000	−0.508329
$388$	0	0
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	−4.00000	−0.202289
$392$	0	0
$393$	24.0000	1.21064
$394$	0	0
$395$	4.00000	0.201262
$396$	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
$399$	−4.00000	−0.200250
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	−6.00000	−0.298881
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	−36.0000	−1.78445
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	20.0000	0.986527
$412$	0	0
$413$	−2.00000	−0.0984136
$414$	0	0
$415$	−4.00000	−0.196352
$416$	0	0
$417$	32.0000	1.56705
$418$	0	0
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	−2.00000	−0.0967868
$428$	0	0
$429$	−12.0000	−0.579365
$430$	0	0
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	0	0
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	20.0000	0.958927
$436$	0	0
$437$	−4.00000	−0.191346
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	10.0000	0.475114	0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000	0.475114	0.237557	+	0.971374i	$0.423653\pi$
$444$	0	0
$445$	2.00000	0.0948091
$446$	0	0
$447$	−28.0000	−1.32435
$448$	0	0
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	0	0
$451$	12.0000	0.565058
$452$	0	0
$453$	4.00000	0.187936
$454$	0	0
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	0	0
$459$	−8.00000	−0.373408
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	36.0000	1.67306	0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000	1.67306	0.836531	+	0.547920i	$0.184580\pi$
$464$	0	0
$465$	12.0000	0.556487
$466$	0	0
$467$	14.0000	0.647843	0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000	0.647843	0.323921	+	0.946084i	$0.394999\pi$
$468$	0	0
$469$	8.00000	0.369406
$470$	0	0
$471$	44.0000	2.02741
$472$	0	0
$473$	60.0000	2.75880
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	0	0
$477$	14.0000	0.641016
$478$	0	0
$479$	−34.0000	−1.55350	−0.776750	−	0.629809i	$-0.783133\pi$
$479$	−34.0000	−1.55350	−0.776750	+	0.629809i	$0.783133\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	0	0
$483$	4.00000	0.182006
$484$	0	0
$485$	−14.0000	−0.635707
$486$	0	0
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	0	0
$489$	48.0000	2.17064
$490$	0	0
$491$	8.00000	0.361035	0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000	0.361035	0.180517	+	0.983572i	$0.442223\pi$
$492$	0	0
$493$	−20.0000	−0.900755
$494$	0	0
$495$	6.00000	0.269680
$496$	0	0
$497$	−10.0000	−0.448561
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	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
$505$	18.0000	0.800989
$506$	0	0
$507$	−2.00000	−0.0888231
$508$	0	0
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	0	0
$513$	−8.00000	−0.353209
$514$	0	0
$515$	−14.0000	−0.616914
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−36.0000	−1.58022
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	0	0
$523$	6.00000	0.262362	0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000	0.262362	0.131181	+	0.991358i	$0.458123\pi$
$524$	0	0
$525$	2.00000	0.0872872
$526$	0	0
$527$	−12.0000	−0.522728
$528$	0	0
$529$	−19.0000	−0.826087
$530$	0	0
$531$	2.00000	0.0867926
$532$	0	0
$533$	2.00000	0.0866296
$534$	0	0
$535$	18.0000	0.778208
$536$	0	0
$537$	−8.00000	−0.345225
$538$	0	0
$539$	−6.00000	−0.258438
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	0	0
$543$	44.0000	1.88822
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	0	0
$549$	2.00000	0.0853579
$550$	0	0
$551$	−20.0000	−0.852029
$552$	0	0
$553$	4.00000	0.170097
$554$	0	0
$555$	12.0000	0.509372
$556$	0	0
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	0	0
$559$	10.0000	0.422955
$560$	0	0
$561$	−24.0000	−1.01328
$562$	0	0
$563$	−22.0000	−0.927189	−0.463595	−	0.886047i	$-0.653441\pi$
$563$	−22.0000	−0.927189	−0.463595	+	0.886047i	$0.653441\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	0	0
$567$	11.0000	0.461957
$568$	0	0
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	0	0
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	0	0
$573$	−16.0000	−0.668410
$574$	0	0
$575$	2.00000	0.0834058
$576$	0	0
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	0	0
$579$	−44.0000	−1.82858
$580$	0	0
$581$	−4.00000	−0.165948
$582$	0	0
$583$	−84.0000	−3.47892
$584$	0	0
$585$	1.00000	0.0413449
$586$	0	0
$587$	−24.0000	−0.990586	−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000	−0.990586	−0.495293	+	0.868726i	$0.664939\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	0	0
$591$	−36.0000	−1.48084
$592$	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
$595$	−2.00000	−0.0819920
$596$	0	0
$597$	32.0000	1.30967
$598$	0	0
$599$	4.00000	0.163436	0.0817178	−	0.996656i	$-0.473959\pi$
$599$	4.00000	0.163436	0.0817178	+	0.996656i	$0.473959\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	0	0
$605$	−25.0000	−1.01639
$606$	0	0
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	0	0
$609$	20.0000	0.810441
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	0	0
$615$	−4.00000	−0.161296
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	34.0000	1.36658	0.683288	−	0.730149i	$-0.260549\pi$
$619$	34.0000	1.36658	0.683288	+	0.730149i	$0.260549\pi$
$620$	0	0
$621$	8.00000	0.321029
$622$	0	0
$623$	2.00000	0.0801283
$624$	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
$631$	38.0000	1.51276	0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000	1.51276	0.756378	+	0.654135i	$0.226967\pi$
$632$	0	0
$633$	−24.0000	−0.953914
$634$	0	0
$635$	−22.0000	−0.873043
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	0	0
$639$	10.0000	0.395594
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	−20.0000	−0.787499
$646$	0	0
$647$	50.0000	1.96570	0.982851	−	0.184399i	$-0.0590339\pi$
$647$	50.0000	1.96570	0.982851	+	0.184399i	$0.0590339\pi$
$648$	0	0
$649$	−12.0000	−0.471041
$650$	0	0
$651$	12.0000	0.470317
$652$	0	0
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	0	0
$655$	12.0000	0.468879
$656$	0	0
$657$	2.00000	0.0780274
$658$	0	0
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	0	0
$663$	−4.00000	−0.155347
$664$	0	0
$665$	−2.00000	−0.0775567
$666$	0	0
$667$	20.0000	0.774403
$668$	0	0
$669$	−16.0000	−0.618596
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	0	0
$675$	4.00000	0.153960
$676$	0	0
$677$	−46.0000	−1.76792	−0.883962	−	0.467559i	$-0.845134\pi$
$677$	−46.0000	−1.76792	−0.883962	+	0.467559i	$0.845134\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	0	0
$681$	−48.0000	−1.83936
$682$	0	0
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	0	0
$685$	10.0000	0.382080
$686$	0	0
$687$	−52.0000	−1.98392
$688$	0	0
$689$	−14.0000	−0.533358
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	0	0
$693$	6.00000	0.227921
$694$	0	0
$695$	16.0000	0.606915
$696$	0	0
$697$	4.00000	0.151511
$698$	0	0
$699$	−36.0000	−1.36165
$700$	0	0
$701$	−2.00000	−0.0755390	−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000	−0.0755390	−0.0377695	+	0.999286i	$0.512025\pi$
$702$	0	0
$703$	−12.0000	−0.452589
$704$	0	0
$705$	0	0
$706$	0	0
$707$	18.0000	0.676960
$708$	0	0
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	0	0
$713$	12.0000	0.449404
$714$	0	0
$715$	−6.00000	−0.224387
$716$	0	0
$717$	−12.0000	−0.448148
$718$	0	0
$719$	−32.0000	−1.19340	−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000	−1.19340	−0.596699	+	0.802465i	$0.703521\pi$
$720$	0	0
$721$	−14.0000	−0.521387
$722$	0	0
$723$	20.0000	0.743808
$724$	0	0
$725$	10.0000	0.371391
$726$	0	0
$727$	42.0000	1.55769	0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000	1.55769	0.778847	+	0.627214i	$0.215805\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	20.0000	0.739727
$732$	0	0
$733$	−30.0000	−1.10808	−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000	−1.10808	−0.554038	+	0.832492i	$0.686914\pi$
$734$	0	0
$735$	2.00000	0.0737711
$736$	0	0
$737$	48.0000	1.76810
$738$	0	0
$739$	−26.0000	−0.956425	−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000	−0.956425	−0.478213	+	0.878244i	$0.658715\pi$
$740$	0	0
$741$	−4.00000	−0.146944
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	−14.0000	−0.512920
$746$	0	0
$747$	4.00000	0.146352
$748$	0	0
$749$	18.0000	0.657706
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	2.00000	0.0727875
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	0	0
$759$	24.0000	0.871145
$760$	0	0
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	0	0
$765$	2.00000	0.0723102
$766$	0	0
$767$	−2.00000	−0.0722158
$768$	0	0
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	0	0
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	6.00000	0.215526
$776$	0	0
$777$	12.0000	0.430498
$778$	0	0
$779$	4.00000	0.143315
$780$	0	0
$781$	−60.0000	−2.14697
$782$	0	0
$783$	40.0000	1.42948
$784$	0	0
$785$	22.0000	0.785214
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	0	0
$789$	−12.0000	−0.427211
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	0	0
$795$	28.0000	0.993058
$796$	0	0
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−2.00000	−0.0706665
$802$	0	0
$803$	−12.0000	−0.423471
$804$	0	0
$805$	2.00000	0.0704907
$806$	0	0
$807$	20.0000	0.704033
$808$	0	0
$809$	−34.0000	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$810$	0	0
$811$	−14.0000	−0.491606	−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000	−0.491606	−0.245803	+	0.969320i	$0.579052\pi$
$812$	0	0
$813$	−36.0000	−1.26258
$814$	0	0
$815$	24.0000	0.840683
$816$	0	0
$817$	20.0000	0.699711
$818$	0	0
$819$	1.00000	0.0349428
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	−38.0000	−1.32460	−0.662298	−	0.749240i	$-0.730419\pi$
$823$	−38.0000	−1.32460	−0.662298	+	0.749240i	$0.730419\pi$
$824$	0	0
$825$	12.0000	0.417786
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	52.0000	1.80386
$832$	0	0
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	16.0000	0.553703
$836$	0	0
$837$	24.0000	0.829561
$838$	0	0
$839$	−18.0000	−0.621429	−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000	−0.621429	−0.310715	+	0.950503i	$0.600568\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	0	0
$843$	−20.0000	−0.688837
$844$	0	0
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	−25.0000	−0.859010
$848$	0	0
$849$	28.0000	0.960958
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	0	0
$855$	2.00000	0.0683986
$856$	0	0
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	0	0
$859$	−24.0000	−0.818869	−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000	−0.818869	−0.409435	+	0.912339i	$0.634274\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	0	0
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	0	0
$867$	26.0000	0.883006
$868$	0	0
$869$	24.0000	0.814144
$870$	0	0
$871$	8.00000	0.271070
$872$	0	0
$873$	14.0000	0.473828
$874$	0	0
$875$	1.00000	0.0338062
$876$	0	0
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	0	0
$879$	−28.0000	−0.944417
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	−18.0000	−0.605748	−0.302874	−	0.953031i	$-0.597946\pi$
$883$	−18.0000	−0.605748	−0.302874	+	0.953031i	$0.597946\pi$
$884$	0	0
$885$	4.00000	0.134459
$886$	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
$889$	−22.0000	−0.737856
$890$	0	0
$891$	66.0000	2.21108
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−4.00000	−0.133705
$896$	0	0
$897$	4.00000	0.133556
$898$	0	0
$899$	60.0000	2.00111
$900$	0	0
$901$	−28.0000	−0.932815
$902$	0	0
$903$	−20.0000	−0.665558
$904$	0	0
$905$	22.0000	0.731305
$906$	0	0
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	0	0
$909$	−18.0000	−0.597022
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	0	0
$915$	4.00000	0.132236
$916$	0	0
$917$	12.0000	0.396275
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	24.0000	0.790827
$922$	0	0
$923$	−10.0000	−0.329154
$924$	0	0
$925$	6.00000	0.197279
$926$	0	0
$927$	14.0000	0.459820
$928$	0	0
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	0	0
$933$	24.0000	0.785725
$934$	0	0
$935$	−12.0000	−0.392442
$936$	0	0
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	52.0000	1.69696
$940$	0	0
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	−4.00000	−0.130258
$944$	0	0
$945$	4.00000	0.130120
$946$	0	0
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	−2.00000	−0.0649227
$950$	0	0
$951$	−28.0000	−0.907962
$952$	0	0
$953$	−38.0000	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$954$	0	0
$955$	−8.00000	−0.258874
$956$	0	0
$957$	120.000	3.87905
$958$	0	0
$959$	10.0000	0.322917
$960$	0	0
$961$	5.00000	0.161290
$962$	0	0
$963$	−18.0000	−0.580042
$964$	0	0
$965$	−22.0000	−0.708205
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	16.0000	0.512936
$974$	0	0
$975$	2.00000	0.0640513
$976$	0	0
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	0	0
$979$	12.0000	0.383522
$980$	0	0
$981$	−10.0000	−0.319275
$982$	0	0
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−20.0000	−0.635963
$990$	0	0
$991$	24.0000	0.762385	0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000	0.762385	0.381193	+	0.924496i	$0.375513\pi$
$992$	0	0
$993$	−12.0000	−0.380808
$994$	0	0
$995$	16.0000	0.507234
$996$	0	0
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	0	0
$999$	24.0000	0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7280.2.a.a.1.1		1
4.3	odd	2		3640.2.a.h.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.2.a.h.1.1	✓	1	4.3	odd	2
7280.2.a.a.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:	\( N \)	\(=\)	\( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7280.a (trivial)

Introduction

L-functions

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