LMFDB - Embedded newform 7605.2.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7605,2,Mod(1,7605)] 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("7605.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-2,0,2,1,0,5,0,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$60.7262307372$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} +5.00000 q^{7} -2.00000 q^{10} -2.00000 q^{11} -10.0000 q^{14} -4.00000 q^{16} -2.00000 q^{17} +2.00000 q^{20} +4.00000 q^{22} -6.00000 q^{23} +1.00000 q^{25} +10.0000 q^{28} +4.00000 q^{29} -7.00000 q^{31} +8.00000 q^{32} +4.00000 q^{34} +5.00000 q^{35} -2.00000 q^{37} -6.00000 q^{41} +1.00000 q^{43} -4.00000 q^{44} +12.0000 q^{46} +8.00000 q^{47} +18.0000 q^{49} -2.00000 q^{50} +4.00000 q^{53} -2.00000 q^{55} -8.00000 q^{58} -12.0000 q^{59} -13.0000 q^{61} +14.0000 q^{62} -8.00000 q^{64} -7.00000 q^{67} -4.00000 q^{68} -10.0000 q^{70} -12.0000 q^{71} +15.0000 q^{73} +4.00000 q^{74} -10.0000 q^{77} +3.00000 q^{79} -4.00000 q^{80} +12.0000 q^{82} -8.00000 q^{83} -2.00000 q^{85} -2.00000 q^{86} -14.0000 q^{89} -12.0000 q^{92} -16.0000 q^{94} -5.00000 q^{97} -36.0000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	0	0
$9$	0	0
$10$	−2.00000	−0.632456
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−10.0000	−2.67261
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−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
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	4.00000	0.852803
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	10.0000	1.88982
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	4.00000	0.685994
$35$	5.00000	0.845154
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	0	0
$40$	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
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	12.0000	1.76930
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	−2.00000	−0.282843
$51$	0	0
$52$	0	0
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	0	0
$58$	−8.00000	−1.05045
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−13.0000	−1.66448	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000	−1.66448	−0.832240	+	0.554416i	$0.812942\pi$
$62$	14.0000	1.77800
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	−10.0000	−1.19523
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	15.0000	1.75562	0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000	1.75562	0.877809	+	0.479012i	$0.159005\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	0	0
$77$	−10.0000	−1.13961
$78$	0	0
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	12.0000	1.32518
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−2.00000	−0.215666
$87$	0	0
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	0	0
$92$	−12.0000	−1.25109
$93$	0	0
$94$	−16.0000	−1.65027
$95$	0	0
$96$	0	0
$97$	−5.00000	−0.507673	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000	−0.507673	−0.253837	+	0.967247i	$0.581693\pi$
$98$	−36.0000	−3.63655
$99$	0	0
$100$	2.00000	0.200000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	0	0
$105$	0	0
$106$	−8.00000	−0.777029
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	4.00000	0.381385
$111$	0	0
$112$	−20.0000	−1.88982
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	8.00000	0.742781
$117$	0	0
$118$	24.0000	2.20938
$119$	−10.0000	−0.916698
$120$	0	0
$121$	−7.00000	−0.636364
$122$	26.0000	2.35393
$123$	0	0
$124$	−14.0000	−1.25724
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	0	0
$134$	14.0000	1.20942
$135$	0	0
$136$	0	0
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	−3.00000	−0.254457	−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000	−0.254457	−0.127228	+	0.991873i	$0.540608\pi$
$140$	10.0000	0.845154
$141$	0	0
$142$	24.0000	2.01404
$143$	0	0
$144$	0	0
$145$	4.00000	0.332182
$146$	−30.0000	−2.48282
$147$	0	0
$148$	−4.00000	−0.328798
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	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
$153$	0	0
$154$	20.0000	1.61165
$155$	−7.00000	−0.562254
$156$	0	0
$157$	−15.0000	−1.19713	−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000	−1.19713	−0.598565	+	0.801074i	$0.704262\pi$
$158$	−6.00000	−0.477334
$159$	0	0
$160$	8.00000	0.632456
$161$	−30.0000	−2.36433
$162$	0	0
$163$	−15.0000	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$163$	−15.0000	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	16.0000	1.24184
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	0	0
$170$	4.00000	0.306786
$171$	0	0
$172$	2.00000	0.152499
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	8.00000	0.603023
$177$	0	0
$178$	28.0000	2.09869
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	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
$183$	0	0
$184$	0	0
$185$	−2.00000	−0.147043
$186$	0	0
$187$	4.00000	0.292509
$188$	16.0000	1.16692
$189$	0	0
$190$	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	$-0.629567\pi$
$193$	−11.0000	−0.791797	−0.395899	+	0.918294i	$0.629567\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	36.0000	2.57143
$197$	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
$199$	17.0000	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$199$	17.0000	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$200$	0	0
$201$	0	0
$202$	−36.0000	−2.53295
$203$	20.0000	1.40372
$204$	0	0
$205$	−6.00000	−0.419058
$206$	14.0000	0.975426
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	15.0000	1.03264	0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000	1.03264	0.516321	+	0.856395i	$0.327301\pi$
$212$	8.00000	0.549442
$213$	0	0
$214$	8.00000	0.546869
$215$	1.00000	0.0681994
$216$	0	0
$217$	−35.0000	−2.37595
$218$	22.0000	1.49003
$219$	0	0
$220$	−4.00000	−0.269680
$221$	0	0
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	40.0000	2.67261
$225$	0	0
$226$	−4.00000	−0.266076
$227$	−10.0000	−0.663723	−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000	−0.663723	−0.331862	+	0.943328i	$0.607677\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	12.0000	0.791257
$231$	0	0
$232$	0	0
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	0	0
$235$	8.00000	0.521862
$236$	−24.0000	−1.56227
$237$	0	0
$238$	20.0000	1.29641
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	−26.0000	−1.66448
$245$	18.0000	1.14998
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	−2.00000	−0.126491
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	22.0000	1.38040
$255$	0	0
$256$	16.0000	1.00000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	0	0
$261$	0	0
$262$	−8.00000	−0.494242
$263$	10.0000	0.616626	0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000	0.616626	0.308313	+	0.951285i	$0.400236\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	0	0
$267$	0	0
$268$	−14.0000	−0.855186
$269$	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
$271$	29.0000	1.76162	0.880812	−	0.473466i	$-0.156997\pi$
$271$	29.0000	1.76162	0.880812	+	0.473466i	$0.156997\pi$
$272$	8.00000	0.485071
$273$	0	0
$274$	−4.00000	−0.241649
$275$	−2.00000	−0.120605
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	6.00000	0.359856
$279$	0	0
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	0	0
$283$	5.00000	0.297219	0.148610	−	0.988896i	$-0.452520\pi$
$283$	5.00000	0.297219	0.148610	+	0.988896i	$0.452520\pi$
$284$	−24.0000	−1.42414
$285$	0	0
$286$	0	0
$287$	−30.0000	−1.77084
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−8.00000	−0.469776
$291$	0	0
$292$	30.0000	1.75562
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	0	0
$297$	0	0
$298$	−24.0000	−1.39028
$299$	0	0
$300$	0	0
$301$	5.00000	0.288195
$302$	16.0000	0.920697
$303$	0	0
$304$	0	0
$305$	−13.0000	−0.744378
$306$	0	0
$307$	−31.0000	−1.76926	−0.884632	−	0.466290i	$-0.845590\pi$
$307$	−31.0000	−1.76926	−0.884632	+	0.466290i	$0.845590\pi$
$308$	−20.0000	−1.13961
$309$	0	0
$310$	14.0000	0.795147
$311$	22.0000	1.24751	0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000	1.24751	0.623753	+	0.781622i	$0.285607\pi$
$312$	0	0
$313$	−31.0000	−1.75222	−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000	−1.75222	−0.876112	+	0.482108i	$0.839871\pi$
$314$	30.0000	1.69300
$315$	0	0
$316$	6.00000	0.337526
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	−8.00000	−0.447914
$320$	−8.00000	−0.447214
$321$	0	0
$322$	60.0000	3.34367
$323$	0	0
$324$	0	0
$325$	0	0
$326$	30.0000	1.66155
$327$	0	0
$328$	0	0
$329$	40.0000	2.20527
$330$	0	0
$331$	9.00000	0.494685	0.247342	−	0.968928i	$-0.420443\pi$
$331$	9.00000	0.494685	0.247342	+	0.968928i	$0.420443\pi$
$332$	−16.0000	−0.878114
$333$	0	0
$334$	24.0000	1.31322
$335$	−7.00000	−0.382451
$336$	0	0
$337$	−1.00000	−0.0544735	−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000	−0.0544735	−0.0272367	+	0.999629i	$0.508671\pi$
$338$	0	0
$339$	0	0
$340$	−4.00000	−0.216930
$341$	14.0000	0.758143
$342$	0	0
$343$	55.0000	2.96972
$344$	0	0
$345$	0	0
$346$	0	0
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	0	0
$349$	3.00000	0.160586	0.0802932	−	0.996771i	$-0.474414\pi$
$349$	3.00000	0.160586	0.0802932	+	0.996771i	$0.474414\pi$
$350$	−10.0000	−0.534522
$351$	0	0
$352$	−16.0000	−0.852803
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−12.0000	−0.636894
$356$	−28.0000	−1.48400
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−2.00000	−0.105556	−0.0527780	−	0.998606i	$-0.516808\pi$
$359$	−2.00000	−0.105556	−0.0527780	+	0.998606i	$0.516808\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	44.0000	2.31259
$363$	0	0
$364$	0	0
$365$	15.0000	0.785136
$366$	0	0
$367$	7.00000	0.365397	0.182699	−	0.983169i	$-0.441517\pi$
$367$	7.00000	0.365397	0.182699	+	0.983169i	$0.441517\pi$
$368$	24.0000	1.25109
$369$	0	0
$370$	4.00000	0.207950
$371$	20.0000	1.03835
$372$	0	0
$373$	13.0000	0.673114	0.336557	−	0.941663i	$-0.390737\pi$
$373$	13.0000	0.673114	0.336557	+	0.941663i	$0.390737\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	0	0
$381$	0	0
$382$	24.0000	1.22795
$383$	18.0000	0.919757	0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000	0.919757	0.459879	+	0.887982i	$0.347893\pi$
$384$	0	0
$385$	−10.0000	−0.509647
$386$	22.0000	1.11977
$387$	0	0
$388$	−10.0000	−0.507673
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	0	0
$393$	0	0
$394$	−24.0000	−1.20910
$395$	3.00000	0.150946
$396$	0	0
$397$	−15.0000	−0.752828	−0.376414	−	0.926451i	$-0.622843\pi$
$397$	−15.0000	−0.752828	−0.376414	+	0.926451i	$0.622843\pi$
$398$	−34.0000	−1.70427
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	0	0
$403$	0	0
$404$	36.0000	1.79107
$405$	0	0
$406$	−40.0000	−1.98517
$407$	4.00000	0.198273
$408$	0	0
$409$	−15.0000	−0.741702	−0.370851	−	0.928692i	$-0.620934\pi$
$409$	−15.0000	−0.741702	−0.370851	+	0.928692i	$0.620934\pi$
$410$	12.0000	0.592638
$411$	0	0
$412$	−14.0000	−0.689730
$413$	−60.0000	−2.95241
$414$	0	0
$415$	−8.00000	−0.392705
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−38.0000	−1.85642	−0.928211	−	0.372055i	$-0.878653\pi$
$419$	−38.0000	−1.85642	−0.928211	+	0.372055i	$0.878653\pi$
$420$	0	0
$421$	−23.0000	−1.12095	−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000	−1.12095	−0.560476	+	0.828171i	$0.689382\pi$
$422$	−30.0000	−1.46038
$423$	0	0
$424$	0	0
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	−65.0000	−3.14557
$428$	−8.00000	−0.386695
$429$	0	0
$430$	−2.00000	−0.0964486
$431$	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
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	70.0000	3.36011
$435$	0	0
$436$	−22.0000	−1.05361
$437$	0	0
$438$	0	0
$439$	15.0000	0.715911	0.357955	−	0.933739i	$-0.383474\pi$
$439$	15.0000	0.715911	0.357955	+	0.933739i	$0.383474\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	0	0
$445$	−14.0000	−0.663664
$446$	16.0000	0.757622
$447$	0	0
$448$	−40.0000	−1.88982
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	0	0
$451$	12.0000	0.565058
$452$	4.00000	0.188144
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	0	0
$457$	35.0000	1.63723	0.818615	−	0.574342i	$-0.194742\pi$
$457$	35.0000	1.63723	0.818615	+	0.574342i	$0.194742\pi$
$458$	−28.0000	−1.30835
$459$	0	0
$460$	−12.0000	−0.559503
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	0	0
$463$	3.00000	0.139422	0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000	0.139422	0.0697109	+	0.997567i	$0.477792\pi$
$464$	−16.0000	−0.742781
$465$	0	0
$466$	−28.0000	−1.29707
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	0	0
$469$	−35.0000	−1.61615
$470$	−16.0000	−0.738025
$471$	0	0
$472$	0	0
$473$	−2.00000	−0.0919601
$474$	0	0
$475$	0	0
$476$	−20.0000	−0.916698
$477$	0	0
$478$	24.0000	1.09773
$479$	−42.0000	−1.91903	−0.959514	−	0.281659i	$-0.909115\pi$
$479$	−42.0000	−1.91903	−0.959514	+	0.281659i	$0.909115\pi$
$480$	0	0
$481$	0	0
$482$	−20.0000	−0.910975
$483$	0	0
$484$	−14.0000	−0.636364
$485$	−5.00000	−0.227038
$486$	0	0
$487$	−28.0000	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$488$	0	0
$489$	0	0
$490$	−36.0000	−1.62631
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	0	0
$493$	−8.00000	−0.360302
$494$	0	0
$495$	0	0
$496$	28.0000	1.25724
$497$	−60.0000	−2.69137
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	2.00000	0.0894427
$501$	0	0
$502$	0	0
$503$	6.00000	0.267527	0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000	0.267527	0.133763	+	0.991013i	$0.457294\pi$
$504$	0	0
$505$	18.0000	0.800989
$506$	−24.0000	−1.06693
$507$	0	0
$508$	−22.0000	−0.976092
$509$	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
$511$	75.0000	3.31780
$512$	−32.0000	−1.41421
$513$	0	0
$514$	−44.0000	−1.94076
$515$	−7.00000	−0.308457
$516$	0	0
$517$	−16.0000	−0.703679
$518$	20.0000	0.878750
$519$	0	0
$520$	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
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	−20.0000	−0.872041
$527$	14.0000	0.609850
$528$	0	0
$529$	13.0000	0.565217
$530$	−8.00000	−0.347498
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−4.00000	−0.172935
$536$	0	0
$537$	0	0
$538$	−12.0000	−0.517357
$539$	−36.0000	−1.55063
$540$	0	0
$541$	29.0000	1.24681	0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000	1.24681	0.623404	+	0.781900i	$0.285749\pi$
$542$	−58.0000	−2.49131
$543$	0	0
$544$	−16.0000	−0.685994
$545$	−11.0000	−0.471188
$546$	0	0
$547$	−9.00000	−0.384812	−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000	−0.384812	−0.192406	+	0.981315i	$0.561629\pi$
$548$	4.00000	0.170872
$549$	0	0
$550$	4.00000	0.170561
$551$	0	0
$552$	0	0
$553$	15.0000	0.637865
$554$	−20.0000	−0.849719
$555$	0	0
$556$	−6.00000	−0.254457
$557$	20.0000	0.847427	0.423714	−	0.905796i	$-0.360726\pi$
$557$	20.0000	0.847427	0.423714	+	0.905796i	$0.360726\pi$
$558$	0	0
$559$	0	0
$560$	−20.0000	−0.845154
$561$	0	0
$562$	−24.0000	−1.01238
$563$	−26.0000	−1.09577	−0.547885	−	0.836554i	$-0.684567\pi$
$563$	−26.0000	−1.09577	−0.547885	+	0.836554i	$0.684567\pi$
$564$	0	0
$565$	2.00000	0.0841406
$566$	−10.0000	−0.420331
$567$	0	0
$568$	0	0
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	0	0
$573$	0	0
$574$	60.0000	2.50435
$575$	−6.00000	−0.250217
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	26.0000	1.08146
$579$	0	0
$580$	8.00000	0.332182
$581$	−40.0000	−1.65948
$582$	0	0
$583$	−8.00000	−0.331326
$584$	0	0
$585$	0	0
$586$	32.0000	1.32191
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	0	0
$589$	0	0
$590$	24.0000	0.988064
$591$	0	0
$592$	8.00000	0.328798
$593$	10.0000	0.410651	0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000	0.410651	0.205325	+	0.978694i	$0.434175\pi$
$594$	0	0
$595$	−10.0000	−0.409960
$596$	24.0000	0.983078
$597$	0	0
$598$	0	0
$599$	16.0000	0.653742	0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000	0.653742	0.326871	+	0.945069i	$0.394006\pi$
$600$	0	0
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	−10.0000	−0.407570
$603$	0	0
$604$	−16.0000	−0.651031
$605$	−7.00000	−0.284590
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	0	0
$609$	0	0
$610$	26.0000	1.05271
$611$	0	0
$612$	0	0
$613$	−15.0000	−0.605844	−0.302922	−	0.953015i	$-0.597962\pi$
$613$	−15.0000	−0.605844	−0.302922	+	0.953015i	$0.597962\pi$
$614$	62.0000	2.50212
$615$	0	0
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	37.0000	1.48716	0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000	1.48716	0.743578	+	0.668649i	$0.233127\pi$
$620$	−14.0000	−0.562254
$621$	0	0
$622$	−44.0000	−1.76424
$623$	−70.0000	−2.80449
$624$	0	0
$625$	1.00000	0.0400000
$626$	62.0000	2.47802
$627$	0	0
$628$	−30.0000	−1.19713
$629$	4.00000	0.159490
$630$	0	0
$631$	7.00000	0.278666	0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000	0.278666	0.139333	+	0.990246i	$0.455504\pi$
$632$	0	0
$633$	0	0
$634$	24.0000	0.953162
$635$	−11.0000	−0.436522
$636$	0	0
$637$	0	0
$638$	16.0000	0.633446
$639$	0	0
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	0	0
$643$	−19.0000	−0.749287	−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000	−0.749287	−0.374643	+	0.927169i	$0.622235\pi$
$644$	−60.0000	−2.36433
$645$	0	0
$646$	0	0
$647$	−38.0000	−1.49393	−0.746967	−	0.664861i	$-0.768491\pi$
$647$	−38.0000	−1.49393	−0.746967	+	0.664861i	$0.768491\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	0	0
$651$	0	0
$652$	−30.0000	−1.17489
$653$	−42.0000	−1.64359	−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000	−1.64359	−0.821794	+	0.569785i	$0.807026\pi$
$654$	0	0
$655$	4.00000	0.156293
$656$	24.0000	0.937043
$657$	0	0
$658$	−80.0000	−3.11872
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	35.0000	1.36134	0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000	1.36134	0.680671	+	0.732589i	$0.261688\pi$
$662$	−18.0000	−0.699590
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−24.0000	−0.929284
$668$	−24.0000	−0.928588
$669$	0	0
$670$	14.0000	0.540867
$671$	26.0000	1.00372
$672$	0	0
$673$	33.0000	1.27206	0.636028	−	0.771666i	$-0.280576\pi$
$673$	33.0000	1.27206	0.636028	+	0.771666i	$0.280576\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	0	0
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	0	0
$679$	−25.0000	−0.959412
$680$	0	0
$681$	0	0
$682$	−28.0000	−1.07218
$683$	20.0000	0.765279	0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000	0.765279	0.382639	+	0.923898i	$0.375015\pi$
$684$	0	0
$685$	2.00000	0.0764161
$686$	−110.000	−4.19982
$687$	0	0
$688$	−4.00000	−0.152499
$689$	0	0
$690$	0	0
$691$	37.0000	1.40755	0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000	1.40755	0.703773	+	0.710425i	$0.251497\pi$
$692$	0	0
$693$	0	0
$694$	−32.0000	−1.21470
$695$	−3.00000	−0.113796
$696$	0	0
$697$	12.0000	0.454532
$698$	−6.00000	−0.227103
$699$	0	0
$700$	10.0000	0.377964
$701$	−40.0000	−1.51078	−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000	−1.51078	−0.755390	+	0.655276i	$0.772552\pi$
$702$	0	0
$703$	0	0
$704$	16.0000	0.603023
$705$	0	0
$706$	12.0000	0.451626
$707$	90.0000	3.38480
$708$	0	0
$709$	−23.0000	−0.863783	−0.431892	−	0.901926i	$-0.642154\pi$
$709$	−23.0000	−0.863783	−0.431892	+	0.901926i	$0.642154\pi$
$710$	24.0000	0.900704
$711$	0	0
$712$	0	0
$713$	42.0000	1.57291
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	0	0
$718$	4.00000	0.149279
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	0	0
$721$	−35.0000	−1.30347
$722$	38.0000	1.41421
$723$	0	0
$724$	−44.0000	−1.63525
$725$	4.00000	0.148556
$726$	0	0
$727$	9.00000	0.333792	0.166896	−	0.985975i	$-0.446626\pi$
$727$	9.00000	0.333792	0.166896	+	0.985975i	$0.446626\pi$
$728$	0	0
$729$	0	0
$730$	−30.0000	−1.11035
$731$	−2.00000	−0.0739727
$732$	0	0
$733$	7.00000	0.258551	0.129275	−	0.991609i	$-0.458735\pi$
$733$	7.00000	0.258551	0.129275	+	0.991609i	$0.458735\pi$
$734$	−14.0000	−0.516749
$735$	0	0
$736$	−48.0000	−1.76930
$737$	14.0000	0.515697
$738$	0	0
$739$	−36.0000	−1.32428	−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000	−1.32428	−0.662141	+	0.749380i	$0.730352\pi$
$740$	−4.00000	−0.147043
$741$	0	0
$742$	−40.0000	−1.46845
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	12.0000	0.439646
$746$	−26.0000	−0.951928
$747$	0	0
$748$	8.00000	0.292509
$749$	−20.0000	−0.730784
$750$	0	0
$751$	−28.0000	−1.02173	−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000	−1.02173	−0.510867	+	0.859660i	$0.670676\pi$
$752$	−32.0000	−1.16692
$753$	0	0
$754$	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	$0.488428\pi$
$758$	10.0000	0.363216
$759$	0	0
$760$	0	0
$761$	36.0000	1.30500	0.652499	−	0.757789i	$-0.273720\pi$
$761$	36.0000	1.30500	0.652499	+	0.757789i	$0.273720\pi$
$762$	0	0
$763$	−55.0000	−1.99113
$764$	−24.0000	−0.868290
$765$	0	0
$766$	−36.0000	−1.30073
$767$	0	0
$768$	0	0
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	20.0000	0.720750
$771$	0	0
$772$	−22.0000	−0.791797
$773$	−46.0000	−1.65451	−0.827253	−	0.561830i	$-0.810097\pi$
$773$	−46.0000	−1.65451	−0.827253	+	0.561830i	$0.810097\pi$
$774$	0	0
$775$	−7.00000	−0.251447
$776$	0	0
$777$	0	0
$778$	16.0000	0.573628
$779$	0	0
$780$	0	0
$781$	24.0000	0.858788
$782$	−24.0000	−0.858238
$783$	0	0
$784$	−72.0000	−2.57143
$785$	−15.0000	−0.535373
$786$	0	0
$787$	17.0000	0.605985	0.302992	−	0.952993i	$-0.402014\pi$
$787$	17.0000	0.605985	0.302992	+	0.952993i	$0.402014\pi$
$788$	24.0000	0.854965
$789$	0	0
$790$	−6.00000	−0.213470
$791$	10.0000	0.355559
$792$	0	0
$793$	0	0
$794$	30.0000	1.06466
$795$	0	0
$796$	34.0000	1.20510
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	8.00000	0.282843
$801$	0	0
$802$	32.0000	1.12996
$803$	−30.0000	−1.05868
$804$	0	0
$805$	−30.0000	−1.05736
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−4.00000	−0.140633	−0.0703163	−	0.997525i	$-0.522401\pi$
$809$	−4.00000	−0.140633	−0.0703163	+	0.997525i	$0.522401\pi$
$810$	0	0
$811$	45.0000	1.58016	0.790082	−	0.613001i	$-0.210038\pi$
$811$	45.0000	1.58016	0.790082	+	0.613001i	$0.210038\pi$
$812$	40.0000	1.40372
$813$	0	0
$814$	−8.00000	−0.280400
$815$	−15.0000	−0.525427
$816$	0	0
$817$	0	0
$818$	30.0000	1.04893
$819$	0	0
$820$	−12.0000	−0.419058
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	20.0000	0.697156	0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000	0.697156	0.348578	+	0.937280i	$0.386665\pi$
$824$	0	0
$825$	0	0
$826$	120.000	4.17533
$827$	−46.0000	−1.59958	−0.799788	−	0.600282i	$-0.795055\pi$
$827$	−46.0000	−1.59958	−0.799788	+	0.600282i	$0.795055\pi$
$828$	0	0
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	16.0000	0.555368
$831$	0	0
$832$	0	0
$833$	−36.0000	−1.24733
$834$	0	0
$835$	−12.0000	−0.415277
$836$	0	0
$837$	0	0
$838$	76.0000	2.62538
$839$	34.0000	1.17381	0.586905	−	0.809656i	$-0.300346\pi$
$839$	34.0000	1.17381	0.586905	+	0.809656i	$0.300346\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	46.0000	1.58526
$843$	0	0
$844$	30.0000	1.03264
$845$	0	0
$846$	0	0
$847$	−35.0000	−1.20261
$848$	−16.0000	−0.549442
$849$	0	0
$850$	4.00000	0.137199
$851$	12.0000	0.411355
$852$	0	0
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	130.000	4.44851
$855$	0	0
$856$	0	0
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	0	0
$859$	43.0000	1.46714	0.733571	−	0.679613i	$-0.237852\pi$
$859$	43.0000	1.46714	0.733571	+	0.679613i	$0.237852\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	−56.0000	−1.90737
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	−70.0000	−2.37595
$869$	−6.00000	−0.203536
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	5.00000	0.169031
$876$	0	0
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	−30.0000	−1.01245
$879$	0	0
$880$	8.00000	0.269680
$881$	−20.0000	−0.673817	−0.336909	−	0.941537i	$-0.609381\pi$
$881$	−20.0000	−0.673817	−0.336909	+	0.941537i	$0.609381\pi$
$882$	0	0
$883$	−25.0000	−0.841317	−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000	−0.841317	−0.420658	+	0.907219i	$0.638201\pi$
$884$	0	0
$885$	0	0
$886$	52.0000	1.74697
$887$	44.0000	1.47738	0.738688	−	0.674048i	$-0.235446\pi$
$887$	44.0000	1.47738	0.738688	+	0.674048i	$0.235446\pi$
$888$	0	0
$889$	−55.0000	−1.84464
$890$	28.0000	0.938562
$891$	0	0
$892$	−16.0000	−0.535720
$893$	0	0
$894$	0	0
$895$	6.00000	0.200558
$896$	0	0
$897$	0	0
$898$	36.0000	1.20134
$899$	−28.0000	−0.933852
$900$	0	0
$901$	−8.00000	−0.266519
$902$	−24.0000	−0.799113
$903$	0	0
$904$	0	0
$905$	−22.0000	−0.731305
$906$	0	0
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	−20.0000	−0.663723
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	16.0000	0.529523
$914$	−70.0000	−2.31539
$915$	0	0
$916$	28.0000	0.925146
$917$	20.0000	0.660458
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	0	0
$921$	0	0
$922$	−4.00000	−0.131733
$923$	0	0
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	−6.00000	−0.197172
$927$	0	0
$928$	32.0000	1.05045
$929$	−52.0000	−1.70606	−0.853032	−	0.521858i	$-0.825239\pi$
$929$	−52.0000	−1.70606	−0.853032	+	0.521858i	$0.825239\pi$
$930$	0	0
$931$	0	0
$932$	28.0000	0.917170
$933$	0	0
$934$	−8.00000	−0.261768
$935$	4.00000	0.130814
$936$	0	0
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	70.0000	2.28558
$939$	0	0
$940$	16.0000	0.521862
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	36.0000	1.17232
$944$	48.0000	1.56227
$945$	0	0
$946$	4.00000	0.130051
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	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
$955$	−12.0000	−0.388311
$956$	−24.0000	−0.776215
$957$	0	0
$958$	84.0000	2.71392
$959$	10.0000	0.322917
$960$	0	0
$961$	18.0000	0.580645
$962$	0	0
$963$	0	0
$964$	20.0000	0.644157
$965$	−11.0000	−0.354103
$966$	0	0
$967$	−56.0000	−1.80084	−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000	−1.80084	−0.900419	+	0.435023i	$0.856740\pi$
$968$	0	0
$969$	0	0
$970$	10.0000	0.321081
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	−15.0000	−0.480878
$974$	56.0000	1.79436
$975$	0	0
$976$	52.0000	1.66448
$977$	−60.0000	−1.91957	−0.959785	−	0.280736i	$-0.909421\pi$
$977$	−60.0000	−1.91957	−0.959785	+	0.280736i	$0.909421\pi$
$978$	0	0
$979$	28.0000	0.894884
$980$	36.0000	1.14998
$981$	0	0
$982$	−48.0000	−1.53174
$983$	−38.0000	−1.21201	−0.606006	−	0.795460i	$-0.707229\pi$
$983$	−38.0000	−1.21201	−0.606006	+	0.795460i	$0.707229\pi$
$984$	0	0
$985$	12.0000	0.382352
$986$	16.0000	0.509544
$987$	0	0
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	−56.0000	−1.77800
$993$	0	0
$994$	120.000	3.80617
$995$	17.0000	0.538936
$996$	0	0
$997$	29.0000	0.918439	0.459220	−	0.888323i	$-0.348129\pi$
$997$	29.0000	0.918439	0.459220	+	0.888323i	$0.348129\pi$
$998$	−8.00000	−0.253236
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.a.1.1		1
3.2	odd	2		2535.2.a.m.1.1		1
13.3	even	3		585.2.j.b.451.1		2
13.9	even	3		585.2.j.b.406.1		2
13.12	even	2		7605.2.a.s.1.1		1
39.29	odd	6		195.2.i.a.61.1	yes	2
39.35	odd	6		195.2.i.a.16.1	✓	2
39.38	odd	2		2535.2.a.c.1.1		1
195.29	odd	6		975.2.i.i.451.1		2
195.68	even	12		975.2.bb.f.724.2		4
195.74	odd	6		975.2.i.i.601.1		2
195.107	even	12		975.2.bb.f.724.1		4
195.113	even	12		975.2.bb.f.874.1		4
195.152	even	12		975.2.bb.f.874.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.a.16.1	✓	2	39.35	odd	6
195.2.i.a.61.1	yes	2	39.29	odd	6
585.2.j.b.406.1		2	13.9	even	3
585.2.j.b.451.1		2	13.3	even	3
975.2.i.i.451.1		2	195.29	odd	6
975.2.i.i.601.1		2	195.74	odd	6
975.2.bb.f.724.1		4	195.107	even	12
975.2.bb.f.724.2		4	195.68	even	12
975.2.bb.f.874.1		4	195.113	even	12
975.2.bb.f.874.2		4	195.152	even	12
2535.2.a.c.1.1		1	39.38	odd	2
2535.2.a.m.1.1		1	3.2	odd	2
7605.2.a.a.1.1		1	1.1	even	1	trivial
7605.2.a.s.1.1		1	13.12	even	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:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

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