LMFDB - Embedded newform 9702.2.a.cf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.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:	$77.4708600410$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} +1.00000 q^{8} +3.00000 q^{10} +1.00000 q^{11} +2.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} +2.00000 q^{19} +3.00000 q^{20} +1.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} +2.00000 q^{26} +6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +2.00000 q^{37} +2.00000 q^{38} +3.00000 q^{40} +3.00000 q^{41} +2.00000 q^{43} +1.00000 q^{44} -3.00000 q^{46} +9.00000 q^{47} +4.00000 q^{50} +2.00000 q^{52} -6.00000 q^{53} +3.00000 q^{55} +6.00000 q^{58} +12.0000 q^{59} +5.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +5.00000 q^{67} -3.00000 q^{68} -12.0000 q^{71} -16.0000 q^{73} +2.00000 q^{74} +2.00000 q^{76} +17.0000 q^{79} +3.00000 q^{80} +3.00000 q^{82} -9.00000 q^{83} -9.00000 q^{85} +2.00000 q^{86} +1.00000 q^{88} +6.00000 q^{89} -3.00000 q^{92} +9.00000 q^{94} +6.00000 q^{95} +17.0000 q^{97} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0	0
$10$	3.00000	0.948683
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	1.00000	0.213201
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	3.00000	0.474342
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−3.00000	−0.442326
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	0	0
$50$	4.00000	0.565685
$51$	0	0
$52$	2.00000	0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	3.00000	0.404520
$56$	0	0
$57$	0	0
$58$	6.00000	0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	0	0
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	−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
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	2.00000	0.229416
$77$	0	0
$78$	0	0
$79$	17.0000	1.91265	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	17.0000	1.91265	0.956325	+	0.292306i	$0.0944227\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	3.00000	0.331295
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	2.00000	0.215666
$87$	0	0
$88$	1.00000	0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	0	0
$94$	9.00000	0.928279
$95$	6.00000	0.615587
$96$	0	0
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	0	0
$99$	0	0
$100$	4.00000	0.400000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	0	0
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	3.00000	0.286039
$111$	0	0
$112$	0	0
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	−9.00000	−0.839254
$116$	6.00000	0.557086
$117$	0	0
$118$	12.0000	1.10469
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	5.00000	0.452679
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−3.00000	−0.268328
$126$	0	0
$127$	11.0000	0.976092	0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000	0.976092	0.488046	+	0.872818i	$0.337710\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	6.00000	0.526235
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	5.00000	0.431934
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	2.00000	0.167248
$144$	0	0
$145$	18.0000	1.49482
$146$	−16.0000	−1.32417
$147$	0	0
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−1.00000	−0.0813788	−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000	−0.0813788	−0.0406894	+	0.999172i	$0.512955\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	0	0
$155$	−12.0000	−0.963863
$156$	0	0
$157$	20.0000	1.59617	0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000	1.59617	0.798087	+	0.602542i	$0.205846\pi$
$158$	17.0000	1.35245
$159$	0	0
$160$	3.00000	0.237171
$161$	0	0
$162$	0	0
$163$	−1.00000	−0.0783260	−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000	−0.0783260	−0.0391630	+	0.999233i	$0.512469\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	−9.00000	−0.698535
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−9.00000	−0.690268
$171$	0	0
$172$	2.00000	0.152499
$173$	−12.0000	−0.912343	−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000	−0.912343	−0.456172	+	0.889892i	$0.650780\pi$
$174$	0	0
$175$	0	0
$176$	1.00000	0.0753778
$177$	0	0
$178$	6.00000	0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	0	0
$184$	−3.00000	−0.221163
$185$	6.00000	0.441129
$186$	0	0
$187$	−3.00000	−0.219382
$188$	9.00000	0.656392
$189$	0	0
$190$	6.00000	0.435286
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	17.0000	1.22053
$195$	0	0
$196$	0	0
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	−12.0000	−0.844317
$203$	0	0
$204$	0	0
$205$	9.00000	0.628587
$206$	14.0000	0.975426
$207$	0	0
$208$	2.00000	0.138675
$209$	2.00000	0.138343
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−3.00000	−0.205076
$215$	6.00000	0.409197
$216$	0	0
$217$	0	0
$218$	11.0000	0.745014
$219$	0	0
$220$	3.00000	0.202260
$221$	−6.00000	−0.403604
$222$	0	0
$223$	20.0000	1.33930	0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000	1.33930	0.669650	+	0.742677i	$0.266444\pi$
$224$	0	0
$225$	0	0
$226$	6.00000	0.399114
$227$	21.0000	1.39382	0.696909	−	0.717159i	$-0.254558\pi$
$227$	21.0000	1.39382	0.696909	+	0.717159i	$0.254558\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−9.00000	−0.593442
$231$	0	0
$232$	6.00000	0.393919
$233$	−27.0000	−1.76883	−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000	−1.76883	−0.884414	+	0.466702i	$0.845442\pi$
$234$	0	0
$235$	27.0000	1.76129
$236$	12.0000	0.781133
$237$	0	0
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	5.00000	0.320092
$245$	0	0
$246$	0	0
$247$	4.00000	0.254514
$248$	−4.00000	−0.254000
$249$	0	0
$250$	−3.00000	−0.189737
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	−3.00000	−0.188608
$254$	11.0000	0.690201
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	0	0
$260$	6.00000	0.372104
$261$	0	0
$262$	12.0000	0.741362
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	−18.0000	−1.10573
$266$	0	0
$267$	0	0
$268$	5.00000	0.305424
$269$	−9.00000	−0.548740	−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000	−0.548740	−0.274370	+	0.961624i	$0.588469\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	−18.0000	−1.08742
$275$	4.00000	0.241209
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	14.0000	0.839664
$279$	0	0
$280$	0	0
$281$	−3.00000	−0.178965	−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000	−0.178965	−0.0894825	+	0.995988i	$0.528521\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	18.0000	1.05700
$291$	0	0
$292$	−16.0000	−0.936329
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	36.0000	2.09600
$296$	2.00000	0.116248
$297$	0	0
$298$	−6.00000	−0.347571
$299$	−6.00000	−0.346989
$300$	0	0
$301$	0	0
$302$	−1.00000	−0.0575435
$303$	0	0
$304$	2.00000	0.114708
$305$	15.0000	0.858898
$306$	0	0
$307$	−22.0000	−1.25561	−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000	−1.25561	−0.627803	+	0.778372i	$0.716046\pi$
$308$	0	0
$309$	0	0
$310$	−12.0000	−0.681554
$311$	−21.0000	−1.19080	−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000	−1.19080	−0.595400	+	0.803429i	$0.703007\pi$
$312$	0	0
$313$	2.00000	0.113047	0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000	0.113047	0.0565233	+	0.998401i	$0.481998\pi$
$314$	20.0000	1.12867
$315$	0	0
$316$	17.0000	0.956325
$317$	33.0000	1.85346	0.926732	−	0.375722i	$-0.122605\pi$
$317$	33.0000	1.85346	0.926732	+	0.375722i	$0.122605\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	−6.00000	−0.333849
$324$	0	0
$325$	8.00000	0.443760
$326$	−1.00000	−0.0553849
$327$	0	0
$328$	3.00000	0.165647
$329$	0	0
$330$	0	0
$331$	11.0000	0.604615	0.302307	−	0.953211i	$-0.402243\pi$
$331$	11.0000	0.604615	0.302307	+	0.953211i	$0.402243\pi$
$332$	−9.00000	−0.493939
$333$	0	0
$334$	12.0000	0.656611
$335$	15.0000	0.819538
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	−9.00000	−0.488094
$341$	−4.00000	−0.216612
$342$	0	0
$343$	0	0
$344$	2.00000	0.107833
$345$	0	0
$346$	−12.0000	−0.645124
$347$	33.0000	1.77153	0.885766	−	0.464131i	$-0.153633\pi$
$347$	33.0000	1.77153	0.885766	+	0.464131i	$0.153633\pi$
$348$	0	0
$349$	11.0000	0.588817	0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000	0.588817	0.294408	+	0.955680i	$0.404877\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	12.0000	0.638696	0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000	0.638696	0.319348	+	0.947638i	$0.396536\pi$
$354$	0	0
$355$	−36.0000	−1.91068
$356$	6.00000	0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	−48.0000	−2.51243
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	6.00000	0.311925
$371$	0	0
$372$	0	0
$373$	−1.00000	−0.0517780	−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000	−0.0517780	−0.0258890	+	0.999665i	$0.508242\pi$
$374$	−3.00000	−0.155126
$375$	0	0
$376$	9.00000	0.464140
$377$	12.0000	0.618031
$378$	0	0
$379$	29.0000	1.48963	0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000	1.48963	0.744815	+	0.667271i	$0.232538\pi$
$380$	6.00000	0.307794
$381$	0	0
$382$	−24.0000	−1.22795
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	0	0
$386$	2.00000	0.101797
$387$	0	0
$388$	17.0000	0.863044
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	9.00000	0.455150
$392$	0	0
$393$	0	0
$394$	−12.0000	−0.604551
$395$	51.0000	2.56609
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	4.00000	0.200000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	−12.0000	−0.597022
$405$	0	0
$406$	0	0
$407$	2.00000	0.0991363
$408$	0	0
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	9.00000	0.444478
$411$	0	0
$412$	14.0000	0.689730
$413$	0	0
$414$	0	0
$415$	−27.0000	−1.32538
$416$	2.00000	0.0980581
$417$	0	0
$418$	2.00000	0.0978232
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	−22.0000	−1.07094
$423$	0	0
$424$	−6.00000	−0.291386
$425$	−12.0000	−0.582086
$426$	0	0
$427$	0	0
$428$	−3.00000	−0.145010
$429$	0	0
$430$	6.00000	0.289346
$431$	6.00000	0.289010	0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	0	0
$433$	35.0000	1.68199	0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000	1.68199	0.840996	+	0.541041i	$0.181970\pi$
$434$	0	0
$435$	0	0
$436$	11.0000	0.526804
$437$	−6.00000	−0.287019
$438$	0	0
$439$	−19.0000	−0.906821	−0.453410	−	0.891302i	$-0.649793\pi$
$439$	−19.0000	−0.906821	−0.453410	+	0.891302i	$0.649793\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	−6.00000	−0.285391
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	0	0
$445$	18.0000	0.853282
$446$	20.0000	0.947027
$447$	0	0
$448$	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
$451$	3.00000	0.141264
$452$	6.00000	0.282216
$453$	0	0
$454$	21.0000	0.985579
$455$	0	0
$456$	0	0
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	−9.00000	−0.419627
$461$	−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
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−27.0000	−1.25075
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	27.0000	1.24542
$471$	0	0
$472$	12.0000	0.552345
$473$	2.00000	0.0919601
$474$	0	0
$475$	8.00000	0.367065
$476$	0	0
$477$	0	0
$478$	−6.00000	−0.274434
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	−10.0000	−0.455488
$483$	0	0
$484$	1.00000	0.0454545
$485$	51.0000	2.31579
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	5.00000	0.226339
$489$	0	0
$490$	0	0
$491$	3.00000	0.135388	0.0676941	−	0.997706i	$-0.478436\pi$
$491$	3.00000	0.135388	0.0676941	+	0.997706i	$0.478436\pi$
$492$	0	0
$493$	−18.0000	−0.810679
$494$	4.00000	0.179969
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	24.0000	1.07117
$503$	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
$505$	−36.0000	−1.60198
$506$	−3.00000	−0.133366
$507$	0	0
$508$	11.0000	0.488046
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	42.0000	1.85074
$516$	0	0
$517$	9.00000	0.395820
$518$	0	0
$519$	0	0
$520$	6.00000	0.263117
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	12.0000	0.523225
$527$	12.0000	0.522728
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−18.0000	−0.781870
$531$	0	0
$532$	0	0
$533$	6.00000	0.259889
$534$	0	0
$535$	−9.00000	−0.389104
$536$	5.00000	0.215967
$537$	0	0
$538$	−9.00000	−0.388018
$539$	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	$0.335379\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	−3.00000	−0.128624
$545$	33.0000	1.41356
$546$	0	0
$547$	−46.0000	−1.96682	−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−46.0000	−1.96682	−0.983409	+	0.181402i	$0.941936\pi$
$548$	−18.0000	−0.768922
$549$	0	0
$550$	4.00000	0.170561
$551$	12.0000	0.511217
$552$	0	0
$553$	0	0
$554$	−10.0000	−0.424859
$555$	0	0
$556$	14.0000	0.593732
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	0	0
$562$	−3.00000	−0.126547
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	18.0000	0.757266
$566$	14.0000	0.588464
$567$	0	0
$568$	−12.0000	−0.503509
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	38.0000	1.59025	0.795125	−	0.606445i	$-0.207405\pi$
$571$	38.0000	1.59025	0.795125	+	0.606445i	$0.207405\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	−12.0000	−0.500435
$576$	0	0
$577$	17.0000	0.707719	0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000	0.707719	0.353860	+	0.935299i	$0.384869\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	18.0000	0.747409
$581$	0	0
$582$	0	0
$583$	−6.00000	−0.248495
$584$	−16.0000	−0.662085
$585$	0	0
$586$	24.0000	0.991431
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	36.0000	1.48210
$591$	0	0
$592$	2.00000	0.0821995
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	−6.00000	−0.245358
$599$	−27.0000	−1.10319	−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000	−1.10319	−0.551595	+	0.834112i	$0.685981\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	0	0
$603$	0	0
$604$	−1.00000	−0.0406894
$605$	3.00000	0.121967
$606$	0	0
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	15.0000	0.607332
$611$	18.0000	0.728202
$612$	0	0
$613$	−31.0000	−1.25208	−0.626039	−	0.779792i	$-0.715325\pi$
$613$	−31.0000	−1.25208	−0.626039	+	0.779792i	$0.715325\pi$
$614$	−22.0000	−0.887848
$615$	0	0
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	0	0
$619$	11.0000	0.442127	0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000	0.442127	0.221064	+	0.975259i	$0.429047\pi$
$620$	−12.0000	−0.481932
$621$	0	0
$622$	−21.0000	−0.842023
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	2.00000	0.0799361
$627$	0	0
$628$	20.0000	0.798087
$629$	−6.00000	−0.239236
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	17.0000	0.676224
$633$	0	0
$634$	33.0000	1.31060
$635$	33.0000	1.30957
$636$	0	0
$637$	0	0
$638$	6.00000	0.237542
$639$	0	0
$640$	3.00000	0.118585
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	0	0
$645$	0	0
$646$	−6.00000	−0.236067
$647$	−39.0000	−1.53325	−0.766624	−	0.642096i	$-0.778065\pi$
$647$	−39.0000	−1.53325	−0.766624	+	0.642096i	$0.778065\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	8.00000	0.313786
$651$	0	0
$652$	−1.00000	−0.0391630
$653$	21.0000	0.821794	0.410897	−	0.911682i	$-0.365216\pi$
$653$	21.0000	0.821794	0.410897	+	0.911682i	$0.365216\pi$
$654$	0	0
$655$	36.0000	1.40664
$656$	3.00000	0.117130
$657$	0	0
$658$	0	0
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	0	0
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	11.0000	0.427527
$663$	0	0
$664$	−9.00000	−0.349268
$665$	0	0
$666$	0	0
$667$	−18.0000	−0.696963
$668$	12.0000	0.464294
$669$	0	0
$670$	15.0000	0.579501
$671$	5.00000	0.193023
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−22.0000	−0.847408
$675$	0	0
$676$	−9.00000	−0.346154
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	0	0
$680$	−9.00000	−0.345134
$681$	0	0
$682$	−4.00000	−0.153168
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	0	0
$685$	−54.0000	−2.06323
$686$	0	0
$687$	0	0
$688$	2.00000	0.0762493
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−19.0000	−0.722794	−0.361397	−	0.932412i	$-0.617700\pi$
$691$	−19.0000	−0.722794	−0.361397	+	0.932412i	$0.617700\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	33.0000	1.25266
$695$	42.0000	1.59315
$696$	0	0
$697$	−9.00000	−0.340899
$698$	11.0000	0.416356
$699$	0	0
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	1.00000	0.0376889
$705$	0	0
$706$	12.0000	0.451626
$707$	0	0
$708$	0	0
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	−36.0000	−1.35106
$711$	0	0
$712$	6.00000	0.224860
$713$	12.0000	0.449404
$714$	0	0
$715$	6.00000	0.224387
$716$	−12.0000	−0.448461
$717$	0	0
$718$	−30.0000	−1.11959
$719$	21.0000	0.783168	0.391584	−	0.920142i	$-0.371927\pi$
$719$	21.0000	0.783168	0.391584	+	0.920142i	$0.371927\pi$
$720$	0	0
$721$	0	0
$722$	−15.0000	−0.558242
$723$	0	0
$724$	−10.0000	−0.371647
$725$	24.0000	0.891338
$726$	0	0
$727$	14.0000	0.519231	0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000	0.519231	0.259616	+	0.965712i	$0.416404\pi$
$728$	0	0
$729$	0	0
$730$	−48.0000	−1.77656
$731$	−6.00000	−0.221918
$732$	0	0
$733$	−49.0000	−1.80986	−0.904928	−	0.425564i	$-0.860076\pi$
$733$	−49.0000	−1.80986	−0.904928	+	0.425564i	$0.860076\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	−3.00000	−0.110581
$737$	5.00000	0.184177
$738$	0	0
$739$	38.0000	1.39785	0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000	1.39785	0.698926	+	0.715194i	$0.253662\pi$
$740$	6.00000	0.220564
$741$	0	0
$742$	0	0
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	−18.0000	−0.659469
$746$	−1.00000	−0.0366126
$747$	0	0
$748$	−3.00000	−0.109691
$749$	0	0
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	12.0000	0.437014
$755$	−3.00000	−0.109181
$756$	0	0
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	29.0000	1.05333
$759$	0	0
$760$	6.00000	0.217643
$761$	−15.0000	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$762$	0	0
$763$	0	0
$764$	−24.0000	−0.868290
$765$	0	0
$766$	−24.0000	−0.867155
$767$	24.0000	0.866590
$768$	0	0
$769$	−46.0000	−1.65880	−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000	−1.65880	−0.829401	+	0.558653i	$0.811318\pi$
$770$	0	0
$771$	0	0
$772$	2.00000	0.0719816
$773$	27.0000	0.971123	0.485561	−	0.874203i	$-0.338615\pi$
$773$	27.0000	0.971123	0.485561	+	0.874203i	$0.338615\pi$
$774$	0	0
$775$	−16.0000	−0.574737
$776$	17.0000	0.610264
$777$	0	0
$778$	−21.0000	−0.752886
$779$	6.00000	0.214972
$780$	0	0
$781$	−12.0000	−0.429394
$782$	9.00000	0.321839
$783$	0	0
$784$	0	0
$785$	60.0000	2.14149
$786$	0	0
$787$	−22.0000	−0.784215	−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000	−0.784215	−0.392108	+	0.919919i	$0.628254\pi$
$788$	−12.0000	−0.427482
$789$	0	0
$790$	51.0000	1.81450
$791$	0	0
$792$	0	0
$793$	10.0000	0.355110
$794$	2.00000	0.0709773
$795$	0	0
$796$	2.00000	0.0708881
$797$	27.0000	0.956389	0.478195	−	0.878254i	$-0.341291\pi$
$797$	27.0000	0.956389	0.478195	+	0.878254i	$0.341291\pi$
$798$	0	0
$799$	−27.0000	−0.955191
$800$	4.00000	0.141421
$801$	0	0
$802$	−30.0000	−1.05934
$803$	−16.0000	−0.564628
$804$	0	0
$805$	0	0
$806$	−8.00000	−0.281788
$807$	0	0
$808$	−12.0000	−0.422159
$809$	9.00000	0.316423	0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000	0.316423	0.158212	+	0.987405i	$0.449427\pi$
$810$	0	0
$811$	26.0000	0.912983	0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000	0.912983	0.456492	+	0.889728i	$0.349106\pi$
$812$	0	0
$813$	0	0
$814$	2.00000	0.0701000
$815$	−3.00000	−0.105085
$816$	0	0
$817$	4.00000	0.139942
$818$	14.0000	0.489499
$819$	0	0
$820$	9.00000	0.314294
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	0	0
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	0	0
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	−27.0000	−0.937184
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	36.0000	1.24583
$836$	2.00000	0.0691714
$837$	0	0
$838$	24.0000	0.829066
$839$	−33.0000	−1.13929	−0.569643	−	0.821892i	$-0.692919\pi$
$839$	−33.0000	−1.13929	−0.569643	+	0.821892i	$0.692919\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	20.0000	0.689246
$843$	0	0
$844$	−22.0000	−0.757271
$845$	−27.0000	−0.928828
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	0	0
$850$	−12.0000	−0.411597
$851$	−6.00000	−0.205677
$852$	0	0
$853$	17.0000	0.582069	0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000	0.582069	0.291034	+	0.956713i	$0.406001\pi$
$854$	0	0
$855$	0	0
$856$	−3.00000	−0.102538
$857$	21.0000	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$858$	0	0
$859$	35.0000	1.19418	0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000	1.19418	0.597092	+	0.802173i	$0.296323\pi$
$860$	6.00000	0.204598
$861$	0	0
$862$	6.00000	0.204361
$863$	−39.0000	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$864$	0	0
$865$	−36.0000	−1.22404
$866$	35.0000	1.18935
$867$	0	0
$868$	0	0
$869$	17.0000	0.576686
$870$	0	0
$871$	10.0000	0.338837
$872$	11.0000	0.372507
$873$	0	0
$874$	−6.00000	−0.202953
$875$	0	0
$876$	0	0
$877$	−37.0000	−1.24940	−0.624701	−	0.780864i	$-0.714779\pi$
$877$	−37.0000	−1.24940	−0.624701	+	0.780864i	$0.714779\pi$
$878$	−19.0000	−0.641219
$879$	0	0
$880$	3.00000	0.101130
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	−13.0000	−0.437485	−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000	−0.437485	−0.218742	+	0.975783i	$0.570195\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	−18.0000	−0.604722
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	0	0
$889$	0	0
$890$	18.0000	0.603361
$891$	0	0
$892$	20.0000	0.669650
$893$	18.0000	0.602347
$894$	0	0
$895$	−36.0000	−1.20335
$896$	0	0
$897$	0	0
$898$	−30.0000	−1.00111
$899$	−24.0000	−0.800445
$900$	0	0
$901$	18.0000	0.599667
$902$	3.00000	0.0998891
$903$	0	0
$904$	6.00000	0.199557
$905$	−30.0000	−0.997234
$906$	0	0
$907$	47.0000	1.56061	0.780305	−	0.625400i	$-0.215064\pi$
$907$	47.0000	1.56061	0.780305	+	0.625400i	$0.215064\pi$
$908$	21.0000	0.696909
$909$	0	0
$910$	0	0
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	0	0
$913$	−9.00000	−0.297857
$914$	38.0000	1.25693
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	−7.00000	−0.230909	−0.115454	−	0.993313i	$-0.536832\pi$
$919$	−7.00000	−0.230909	−0.115454	+	0.993313i	$0.536832\pi$
$920$	−9.00000	−0.296721
$921$	0	0
$922$	−6.00000	−0.197599
$923$	−24.0000	−0.789970
$924$	0	0
$925$	8.00000	0.263038
$926$	−16.0000	−0.525793
$927$	0	0
$928$	6.00000	0.196960
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	0	0
$931$	0	0
$932$	−27.0000	−0.884414
$933$	0	0
$934$	0	0
$935$	−9.00000	−0.294331
$936$	0	0
$937$	−34.0000	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$938$	0	0
$939$	0	0
$940$	27.0000	0.880643
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	0	0
$943$	−9.00000	−0.293080
$944$	12.0000	0.390567
$945$	0	0
$946$	2.00000	0.0650256
$947$	−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
$949$	−32.0000	−1.03876
$950$	8.00000	0.259554
$951$	0	0
$952$	0	0
$953$	−27.0000	−0.874616	−0.437308	−	0.899312i	$-0.644068\pi$
$953$	−27.0000	−0.874616	−0.437308	+	0.899312i	$0.644068\pi$
$954$	0	0
$955$	−72.0000	−2.32987
$956$	−6.00000	−0.194054
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	4.00000	0.128965
$963$	0	0
$964$	−10.0000	−0.322078
$965$	6.00000	0.193147
$966$	0	0
$967$	−43.0000	−1.38279	−0.691393	−	0.722478i	$-0.743003\pi$
$967$	−43.0000	−1.38279	−0.691393	+	0.722478i	$0.743003\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	51.0000	1.63751
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	0	0
$973$	0	0
$974$	8.00000	0.256337
$975$	0	0
$976$	5.00000	0.160046
$977$	36.0000	1.15174	0.575871	−	0.817541i	$-0.304663\pi$
$977$	36.0000	1.15174	0.575871	+	0.817541i	$0.304663\pi$
$978$	0	0
$979$	6.00000	0.191761
$980$	0	0
$981$	0	0
$982$	3.00000	0.0957338
$983$	45.0000	1.43528	0.717639	−	0.696416i	$-0.245223\pi$
$983$	45.0000	1.43528	0.717639	+	0.696416i	$0.245223\pi$
$984$	0	0
$985$	−36.0000	−1.14706
$986$	−18.0000	−0.573237
$987$	0	0
$988$	4.00000	0.127257
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−22.0000	−0.698853	−0.349427	−	0.936964i	$-0.613624\pi$
$991$	−22.0000	−0.698853	−0.349427	+	0.936964i	$0.613624\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	6.00000	0.190213
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−28.0000	−0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.cf.1.1		1
3.2	odd	2		3234.2.a.h.1.1		1
7.2	even	3		1386.2.k.c.991.1		2
7.4	even	3		1386.2.k.c.793.1		2
7.6	odd	2		9702.2.a.bd.1.1		1
21.2	odd	6		462.2.i.c.67.1	✓	2
21.11	odd	6		462.2.i.c.331.1	yes	2
21.20	even	2		3234.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.c.67.1	✓	2	21.2	odd	6
462.2.i.c.331.1	yes	2	21.11	odd	6
1386.2.k.c.793.1		2	7.4	even	3
1386.2.k.c.991.1		2	7.2	even	3
3234.2.a.g.1.1		1	21.20	even	2
3234.2.a.h.1.1		1	3.2	odd	2
9702.2.a.bd.1.1		1	7.6	odd	2
9702.2.a.cf.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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

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