LMFDB - Embedded newform 1062.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1062,2,Mod(1,1062)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1062, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1062.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1062 = 2 \cdot 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1062.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:	$8.48011269466$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 354)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1062.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +5.00000 q^{11} +1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +5.00000 q^{22} +6.00000 q^{23} -5.00000 q^{25} +1.00000 q^{26} -1.00000 q^{28} +10.0000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -1.00000 q^{34} +9.00000 q^{37} +5.00000 q^{41} +3.00000 q^{43} +5.00000 q^{44} +6.00000 q^{46} -6.00000 q^{49} -5.00000 q^{50} +1.00000 q^{52} -4.00000 q^{53} -1.00000 q^{56} +10.0000 q^{58} +1.00000 q^{59} +6.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} -1.00000 q^{68} -1.00000 q^{71} +9.00000 q^{74} -5.00000 q^{77} -3.00000 q^{79} +5.00000 q^{82} -7.00000 q^{83} +3.00000 q^{86} +5.00000 q^{88} -16.0000 q^{89} -1.00000 q^{91} +6.00000 q^{92} -12.0000 q^{97} -6.00000 q^{98} +O(q^{100})$

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
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	5.00000	1.06600
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	1.00000	0.196116
$27$	0	0
$28$	−1.00000	−0.188982
$29$	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
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−1.00000	−0.171499
$35$	0	0
$36$	0	0
$37$	9.00000	1.47959	0.739795	−	0.672832i	$-0.234922\pi$
$37$	9.00000	1.47959	0.739795	+	0.672832i	$0.234922\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	3.00000	0.457496	0.228748	−	0.973486i	$-0.426537\pi$
$43$	3.00000	0.457496	0.228748	+	0.973486i	$0.426537\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	6.00000	0.884652
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−5.00000	−0.707107
$51$	0	0
$52$	1.00000	0.138675
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	10.0000	1.31306
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	9.00000	1.04623
$75$	0	0
$76$	0	0
$77$	−5.00000	−0.569803
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	0	0
$81$	0	0
$82$	5.00000	0.552158
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	0	0
$85$	0	0
$86$	3.00000	0.323498
$87$	0	0
$88$	5.00000	0.533002
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	6.00000	0.625543
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−5.00000	−0.500000
$101$	−17.0000	−1.69156	−0.845782	−	0.533529i	$-0.820865\pi$
$101$	−17.0000	−1.69156	−0.845782	+	0.533529i	$0.820865\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−4.00000	−0.388514
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	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
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−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
$115$	0	0
$116$	10.0000	0.928477
$117$	0	0
$118$	1.00000	0.0920575
$119$	1.00000	0.0916698
$120$	0	0
$121$	14.0000	1.27273
$122$	6.00000	0.543214
$123$	0	0
$124$	−8.00000	−0.718421
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	20.0000	1.74741	0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000	1.74741	0.873704	+	0.486458i	$0.161711\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	5.00000	0.427179	0.213589	−	0.976924i	$-0.431485\pi$
$137$	5.00000	0.427179	0.213589	+	0.976924i	$0.431485\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	0	0
$142$	−1.00000	−0.0839181
$143$	5.00000	0.418121
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	9.00000	0.739795
$149$	−21.0000	−1.72039	−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000	−1.72039	−0.860194	+	0.509968i	$0.829657\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	0	0
$153$	0	0
$154$	−5.00000	−0.402911
$155$	0	0
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	−3.00000	−0.238667
$159$	0	0
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	−7.00000	−0.543305
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	3.00000	0.228748
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	5.00000	0.376889
$177$	0	0
$178$	−16.0000	−1.19925
$179$	−5.00000	−0.373718	−0.186859	−	0.982387i	$-0.559831\pi$
$179$	−5.00000	−0.373718	−0.186859	+	0.982387i	$0.559831\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	6.00000	0.442326
$185$	0	0
$186$	0	0
$187$	−5.00000	−0.365636
$188$	0	0
$189$	0	0
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	0	0
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	−6.00000	−0.428571
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−5.00000	−0.353553
$201$	0	0
$202$	−17.0000	−1.19612
$203$	−10.0000	−0.701862
$204$	0	0
$205$	0	0
$206$	4.00000	0.278693
$207$	0	0
$208$	1.00000	0.0693375
$209$	0	0
$210$	0	0
$211$	−3.00000	−0.206529	−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000	−0.206529	−0.103264	+	0.994654i	$0.532929\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	6.00000	0.410152
$215$	0	0
$216$	0	0
$217$	8.00000	0.543075
$218$	−10.0000	−0.677285
$219$	0	0
$220$	0	0
$221$	−1.00000	−0.0672673
$222$	0	0
$223$	−9.00000	−0.602685	−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000	−0.602685	−0.301342	+	0.953516i	$0.597435\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−7.00000	−0.464606	−0.232303	−	0.972643i	$-0.574626\pi$
$227$	−7.00000	−0.464606	−0.232303	+	0.972643i	$0.574626\pi$
$228$	0	0
$229$	−25.0000	−1.65205	−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000	−1.65205	−0.826023	+	0.563636i	$0.809402\pi$
$230$	0	0
$231$	0	0
$232$	10.0000	0.656532
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	0	0
$235$	0	0
$236$	1.00000	0.0650945
$237$	0	0
$238$	1.00000	0.0648204
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	15.0000	0.966235	0.483117	−	0.875556i	$-0.339504\pi$
$241$	15.0000	0.966235	0.483117	+	0.875556i	$0.339504\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	6.00000	0.384111
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−8.00000	−0.508001
$249$	0	0
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	30.0000	1.88608
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	21.0000	1.30994	0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000	1.30994	0.654972	+	0.755653i	$0.272680\pi$
$258$	0	0
$259$	−9.00000	−0.559233
$260$	0	0
$261$	0	0
$262$	20.0000	1.23560
$263$	−3.00000	−0.184988	−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000	−0.184988	−0.0924940	+	0.995713i	$0.529484\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	4.00000	0.244339
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	−15.0000	−0.911185	−0.455593	−	0.890188i	$-0.650573\pi$
$271$	−15.0000	−0.911185	−0.455593	+	0.890188i	$0.650573\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	5.00000	0.302061
$275$	−25.0000	−1.50756
$276$	0	0
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	0	0
$283$	31.0000	1.84276	0.921379	−	0.388664i	$-0.127063\pi$
$283$	31.0000	1.84276	0.921379	+	0.388664i	$0.127063\pi$
$284$	−1.00000	−0.0593391
$285$	0	0
$286$	5.00000	0.295656
$287$	−5.00000	−0.295141
$288$	0	0
$289$	−16.0000	−0.941176
$290$	0	0
$291$	0	0
$292$	0	0
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	9.00000	0.523114
$297$	0	0
$298$	−21.0000	−1.21650
$299$	6.00000	0.346989
$300$	0	0
$301$	−3.00000	−0.172917
$302$	−10.0000	−0.575435
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	−5.00000	−0.284901
$309$	0	0
$310$	0	0
$311$	−7.00000	−0.396934	−0.198467	−	0.980108i	$-0.563596\pi$
$311$	−7.00000	−0.396934	−0.198467	+	0.980108i	$0.563596\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	−3.00000	−0.168763
$317$	−32.0000	−1.79730	−0.898650	−	0.438667i	$-0.855451\pi$
$317$	−32.0000	−1.79730	−0.898650	+	0.438667i	$0.855451\pi$
$318$	0	0
$319$	50.0000	2.79946
$320$	0	0
$321$	0	0
$322$	−6.00000	−0.334367
$323$	0	0
$324$	0	0
$325$	−5.00000	−0.277350
$326$	14.0000	0.775388
$327$	0	0
$328$	5.00000	0.276079
$329$	0	0
$330$	0	0
$331$	34.0000	1.86881	0.934405	−	0.356214i	$-0.115932\pi$
$331$	34.0000	1.86881	0.934405	+	0.356214i	$0.115932\pi$
$332$	−7.00000	−0.384175
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	−40.0000	−2.16612
$342$	0	0
$343$	13.0000	0.701934
$344$	3.00000	0.161749
$345$	0	0
$346$	9.00000	0.483843
$347$	36.0000	1.93258	0.966291	−	0.257454i	$-0.0828835\pi$
$347$	36.0000	1.93258	0.966291	+	0.257454i	$0.0828835\pi$
$348$	0	0
$349$	−7.00000	−0.374701	−0.187351	−	0.982293i	$-0.559990\pi$
$349$	−7.00000	−0.374701	−0.187351	+	0.982293i	$0.559990\pi$
$350$	5.00000	0.267261
$351$	0	0
$352$	5.00000	0.266501
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	0	0
$355$	0	0
$356$	−16.0000	−0.847998
$357$	0	0
$358$	−5.00000	−0.264258
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−22.0000	−1.15629
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	0	0
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	4.00000	0.207670
$372$	0	0
$373$	24.0000	1.24267	0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000	1.24267	0.621336	+	0.783544i	$0.286590\pi$
$374$	−5.00000	−0.258544
$375$	0	0
$376$	0	0
$377$	10.0000	0.515026
$378$	0	0
$379$	14.0000	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$380$	0	0
$381$	0	0
$382$	12.0000	0.613973
$383$	21.0000	1.07305	0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000	1.07305	0.536525	+	0.843884i	$0.319737\pi$
$384$	0	0
$385$	0	0
$386$	13.0000	0.661683
$387$	0	0
$388$	−12.0000	−0.609208
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	−6.00000	−0.303433
$392$	−6.00000	−0.303046
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−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
$403$	−8.00000	−0.398508
$404$	−17.0000	−0.845782
$405$	0	0
$406$	−10.0000	−0.496292
$407$	45.0000	2.23057
$408$	0	0
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	0	0
$411$	0	0
$412$	4.00000	0.197066
$413$	−1.00000	−0.0492068
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	0	0
$419$	35.0000	1.70986	0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000	1.70986	0.854931	+	0.518742i	$0.173599\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−3.00000	−0.146038
$423$	0	0
$424$	−4.00000	−0.194257
$425$	5.00000	0.242536
$426$	0	0
$427$	−6.00000	−0.290360
$428$	6.00000	0.290021
$429$	0	0
$430$	0	0
$431$	−26.0000	−1.25238	−0.626188	−	0.779672i	$-0.715386\pi$
$431$	−26.0000	−1.25238	−0.626188	+	0.779672i	$0.715386\pi$
$432$	0	0
$433$	−31.0000	−1.48976	−0.744882	−	0.667196i	$-0.767494\pi$
$433$	−31.0000	−1.48976	−0.744882	+	0.667196i	$0.767494\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−10.0000	−0.478913
$437$	0	0
$438$	0	0
$439$	−11.0000	−0.525001	−0.262501	−	0.964932i	$-0.584547\pi$
$439$	−11.0000	−0.525001	−0.262501	+	0.964932i	$0.584547\pi$
$440$	0	0
$441$	0	0
$442$	−1.00000	−0.0475651
$443$	−17.0000	−0.807694	−0.403847	−	0.914826i	$-0.632327\pi$
$443$	−17.0000	−0.807694	−0.403847	+	0.914826i	$0.632327\pi$
$444$	0	0
$445$	0	0
$446$	−9.00000	−0.426162
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	31.0000	1.46298	0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000	1.46298	0.731490	+	0.681852i	$0.238825\pi$
$450$	0	0
$451$	25.0000	1.17720
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−7.00000	−0.328526
$455$	0	0
$456$	0	0
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	−25.0000	−1.16817
$459$	0	0
$460$	0	0
$461$	20.0000	0.931493	0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000	0.931493	0.465746	+	0.884918i	$0.345786\pi$
$462$	0	0
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	10.0000	0.464238
$465$	0	0
$466$	−20.0000	−0.926482
$467$	−13.0000	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	1.00000	0.0460287
$473$	15.0000	0.689701
$474$	0	0
$475$	0	0
$476$	1.00000	0.0458349
$477$	0	0
$478$	−8.00000	−0.365911
$479$	28.0000	1.27935	0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000	1.27935	0.639676	+	0.768644i	$0.279068\pi$
$480$	0	0
$481$	9.00000	0.410365
$482$	15.0000	0.683231
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	6.00000	0.271607
$489$	0	0
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	0	0
$493$	−10.0000	−0.450377
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	1.00000	0.0448561
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	0	0
$501$	0	0
$502$	−4.00000	−0.178529
$503$	26.0000	1.15928	0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000	1.15928	0.579641	+	0.814872i	$0.303193\pi$
$504$	0	0
$505$	0	0
$506$	30.0000	1.33366
$507$	0	0
$508$	−8.00000	−0.354943
$509$	10.0000	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	21.0000	0.926270
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−9.00000	−0.395437
$519$	0	0
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	20.0000	0.873704
$525$	0	0
$526$	−3.00000	−0.130806
$527$	8.00000	0.348485
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	0	0
$533$	5.00000	0.216574
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	−3.00000	−0.129339
$539$	−30.0000	−1.29219
$540$	0	0
$541$	−11.0000	−0.472927	−0.236463	−	0.971640i	$-0.575988\pi$
$541$	−11.0000	−0.472927	−0.236463	+	0.971640i	$0.575988\pi$
$542$	−15.0000	−0.644305
$543$	0	0
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	0	0
$547$	−30.0000	−1.28271	−0.641354	−	0.767245i	$-0.721627\pi$
$547$	−30.0000	−1.28271	−0.641354	+	0.767245i	$0.721627\pi$
$548$	5.00000	0.213589
$549$	0	0
$550$	−25.0000	−1.06600
$551$	0	0
$552$	0	0
$553$	3.00000	0.127573
$554$	−26.0000	−1.10463
$555$	0	0
$556$	4.00000	0.169638
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	3.00000	0.126886
$560$	0	0
$561$	0	0
$562$	7.00000	0.295277
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	0	0
$566$	31.0000	1.30303
$567$	0	0
$568$	−1.00000	−0.0419591
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	5.00000	0.209061
$573$	0	0
$574$	−5.00000	−0.208696
$575$	−30.0000	−1.25109
$576$	0	0
$577$	−23.0000	−0.957503	−0.478751	−	0.877951i	$-0.658910\pi$
$577$	−23.0000	−0.957503	−0.478751	+	0.877951i	$0.658910\pi$
$578$	−16.0000	−0.665512
$579$	0	0
$580$	0	0
$581$	7.00000	0.290409
$582$	0	0
$583$	−20.0000	−0.828315
$584$	0	0
$585$	0	0
$586$	12.0000	0.495715
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	9.00000	0.369898
$593$	2.00000	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$594$	0	0
$595$	0	0
$596$	−21.0000	−0.860194
$597$	0	0
$598$	6.00000	0.245358
$599$	33.0000	1.34834	0.674172	−	0.738575i	$-0.264501\pi$
$599$	33.0000	1.34834	0.674172	+	0.738575i	$0.264501\pi$
$600$	0	0
$601$	−48.0000	−1.95796	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−48.0000	−1.95796	−0.978980	+	0.203954i	$0.934621\pi$
$602$	−3.00000	−0.122271
$603$	0	0
$604$	−10.0000	−0.406894
$605$	0	0
$606$	0	0
$607$	37.0000	1.50178	0.750892	−	0.660425i	$-0.229624\pi$
$607$	37.0000	1.50178	0.750892	+	0.660425i	$0.229624\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	37.0000	1.49442	0.747208	−	0.664590i	$-0.231394\pi$
$613$	37.0000	1.49442	0.747208	+	0.664590i	$0.231394\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	0	0
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	0	0
$621$	0	0
$622$	−7.00000	−0.280674
$623$	16.0000	0.641026
$624$	0	0
$625$	25.0000	1.00000
$626$	14.0000	0.559553
$627$	0	0
$628$	−6.00000	−0.239426
$629$	−9.00000	−0.358854
$630$	0	0
$631$	−27.0000	−1.07485	−0.537427	−	0.843311i	$-0.680603\pi$
$631$	−27.0000	−1.07485	−0.537427	+	0.843311i	$0.680603\pi$
$632$	−3.00000	−0.119334
$633$	0	0
$634$	−32.0000	−1.27088
$635$	0	0
$636$	0	0
$637$	−6.00000	−0.237729
$638$	50.0000	1.97952
$639$	0	0
$640$	0	0
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	0	0
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	0	0
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	0	0
$649$	5.00000	0.196267
$650$	−5.00000	−0.196116
$651$	0	0
$652$	14.0000	0.548282
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	0	0
$655$	0	0
$656$	5.00000	0.195217
$657$	0	0
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	34.0000	1.32145
$663$	0	0
$664$	−7.00000	−0.271653
$665$	0	0
$666$	0	0
$667$	60.0000	2.32321
$668$	0	0
$669$	0	0
$670$	0	0
$671$	30.0000	1.15814
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	0	0
$679$	12.0000	0.460518
$680$	0	0
$681$	0	0
$682$	−40.0000	−1.53168
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	0	0
$685$	0	0
$686$	13.0000	0.496342
$687$	0	0
$688$	3.00000	0.114374
$689$	−4.00000	−0.152388
$690$	0	0
$691$	25.0000	0.951045	0.475522	−	0.879704i	$-0.342259\pi$
$691$	25.0000	0.951045	0.475522	+	0.879704i	$0.342259\pi$
$692$	9.00000	0.342129
$693$	0	0
$694$	36.0000	1.36654
$695$	0	0
$696$	0	0
$697$	−5.00000	−0.189389
$698$	−7.00000	−0.264954
$699$	0	0
$700$	5.00000	0.188982
$701$	47.0000	1.77517	0.887583	−	0.460648i	$-0.152383\pi$
$701$	47.0000	1.77517	0.887583	+	0.460648i	$0.152383\pi$
$702$	0	0
$703$	0	0
$704$	5.00000	0.188445
$705$	0	0
$706$	24.0000	0.903252
$707$	17.0000	0.639351
$708$	0	0
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	0	0
$712$	−16.0000	−0.599625
$713$	−48.0000	−1.79761
$714$	0	0
$715$	0	0
$716$	−5.00000	−0.186859
$717$	0	0
$718$	−11.0000	−0.410516
$719$	4.00000	0.149175	0.0745874	−	0.997214i	$-0.476236\pi$
$719$	4.00000	0.149175	0.0745874	+	0.997214i	$0.476236\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	−19.0000	−0.707107
$723$	0	0
$724$	−22.0000	−0.817624
$725$	−50.0000	−1.85695
$726$	0	0
$727$	11.0000	0.407967	0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000	0.407967	0.203984	+	0.978974i	$0.434611\pi$
$728$	−1.00000	−0.0370625
$729$	0	0
$730$	0	0
$731$	−3.00000	−0.110959
$732$	0	0
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−32.0000	−1.18114
$735$	0	0
$736$	6.00000	0.221163
$737$	20.0000	0.736709
$738$	0	0
$739$	37.0000	1.36107	0.680534	−	0.732717i	$-0.261748\pi$
$739$	37.0000	1.36107	0.680534	+	0.732717i	$0.261748\pi$
$740$	0	0
$741$	0	0
$742$	4.00000	0.146845
$743$	−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
$745$	0	0
$746$	24.0000	0.878702
$747$	0	0
$748$	−5.00000	−0.182818
$749$	−6.00000	−0.219235
$750$	0	0
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	0	0
$753$	0	0
$754$	10.0000	0.364179
$755$	0	0
$756$	0	0
$757$	−40.0000	−1.45382	−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000	−1.45382	−0.726912	+	0.686730i	$0.759045\pi$
$758$	14.0000	0.508503
$759$	0	0
$760$	0	0
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	12.0000	0.434145
$765$	0	0
$766$	21.0000	0.758761
$767$	1.00000	0.0361079
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	0	0
$772$	13.0000	0.467880
$773$	2.00000	0.0719350	0.0359675	−	0.999353i	$-0.488549\pi$
$773$	2.00000	0.0719350	0.0359675	+	0.999353i	$0.488549\pi$
$774$	0	0
$775$	40.0000	1.43684
$776$	−12.0000	−0.430775
$777$	0	0
$778$	22.0000	0.788738
$779$	0	0
$780$	0	0
$781$	−5.00000	−0.178914
$782$	−6.00000	−0.214560
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	−46.0000	−1.63972	−0.819861	−	0.572562i	$-0.805950\pi$
$787$	−46.0000	−1.63972	−0.819861	+	0.572562i	$0.805950\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	6.00000	0.213066
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−21.0000	−0.743858	−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000	−0.743858	−0.371929	+	0.928261i	$0.621304\pi$
$798$	0	0
$799$	0	0
$800$	−5.00000	−0.176777
$801$	0	0
$802$	−16.0000	−0.564980
$803$	0	0
$804$	0	0
$805$	0	0
$806$	−8.00000	−0.281788
$807$	0	0
$808$	−17.0000	−0.598058
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	0	0
$811$	−21.0000	−0.737410	−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000	−0.737410	−0.368705	+	0.929547i	$0.620199\pi$
$812$	−10.0000	−0.350931
$813$	0	0
$814$	45.0000	1.57725
$815$	0	0
$816$	0	0
$817$	0	0
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	21.0000	0.732905	0.366453	−	0.930437i	$-0.380572\pi$
$821$	21.0000	0.732905	0.366453	+	0.930437i	$0.380572\pi$
$822$	0	0
$823$	28.0000	0.976019	0.488009	−	0.872838i	$-0.337723\pi$
$823$	28.0000	0.976019	0.488009	+	0.872838i	$0.337723\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	−1.00000	−0.0347945
$827$	−26.0000	−0.904109	−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000	−0.904109	−0.452054	+	0.891990i	$0.649309\pi$
$828$	0	0
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	0.0346688
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	35.0000	1.20905
$839$	−54.0000	−1.86429	−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000	−1.86429	−0.932144	+	0.362089i	$0.882064\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	1.00000	0.0344623
$843$	0	0
$844$	−3.00000	−0.103264
$845$	0	0
$846$	0	0
$847$	−14.0000	−0.481046
$848$	−4.00000	−0.137361
$849$	0	0
$850$	5.00000	0.171499
$851$	54.0000	1.85110
$852$	0	0
$853$	44.0000	1.50653	0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000	1.50653	0.753266	+	0.657716i	$0.228477\pi$
$854$	−6.00000	−0.205316
$855$	0	0
$856$	6.00000	0.205076
$857$	−2.00000	−0.0683187	−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000	−0.0683187	−0.0341593	+	0.999416i	$0.510875\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	−26.0000	−0.885564
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	0	0
$866$	−31.0000	−1.05342
$867$	0	0
$868$	8.00000	0.271538
$869$	−15.0000	−0.508840
$870$	0	0
$871$	4.00000	0.135535
$872$	−10.0000	−0.338643
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−44.0000	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$877$	−44.0000	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$878$	−11.0000	−0.371232
$879$	0	0
$880$	0	0
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	0	0
$883$	−40.0000	−1.34611	−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000	−1.34611	−0.673054	+	0.739594i	$0.735018\pi$
$884$	−1.00000	−0.0336336
$885$	0	0
$886$	−17.0000	−0.571126
$887$	42.0000	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	−9.00000	−0.301342
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	31.0000	1.03448
$899$	−80.0000	−2.66815
$900$	0	0
$901$	4.00000	0.133259
$902$	25.0000	0.832409
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	−7.00000	−0.232303
$909$	0	0
$910$	0	0
$911$	−1.00000	−0.0331315	−0.0165657	−	0.999863i	$-0.505273\pi$
$911$	−1.00000	−0.0331315	−0.0165657	+	0.999863i	$0.505273\pi$
$912$	0	0
$913$	−35.0000	−1.15833
$914$	−4.00000	−0.132308
$915$	0	0
$916$	−25.0000	−0.826023
$917$	−20.0000	−0.660458
$918$	0	0
$919$	−34.0000	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$920$	0	0
$921$	0	0
$922$	20.0000	0.658665
$923$	−1.00000	−0.0329154
$924$	0	0
$925$	−45.0000	−1.47959
$926$	20.0000	0.657241
$927$	0	0
$928$	10.0000	0.328266
$929$	32.0000	1.04989	0.524943	−	0.851137i	$-0.324087\pi$
$929$	32.0000	1.04989	0.524943	+	0.851137i	$0.324087\pi$
$930$	0	0
$931$	0	0
$932$	−20.0000	−0.655122
$933$	0	0
$934$	−13.0000	−0.425373
$935$	0	0
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−4.00000	−0.130605
$939$	0	0
$940$	0	0
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	0	0
$943$	30.0000	0.976934
$944$	1.00000	0.0325472
$945$	0	0
$946$	15.0000	0.487692
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	1.00000	0.0324102
$953$	−21.0000	−0.680257	−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000	−0.680257	−0.340128	+	0.940379i	$0.610471\pi$
$954$	0	0
$955$	0	0
$956$	−8.00000	−0.258738
$957$	0	0
$958$	28.0000	0.904639
$959$	−5.00000	−0.161458
$960$	0	0
$961$	33.0000	1.06452
$962$	9.00000	0.290172
$963$	0	0
$964$	15.0000	0.483117
$965$	0	0
$966$	0	0
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	−7.00000	−0.224294
$975$	0	0
$976$	6.00000	0.192055
$977$	48.0000	1.53566	0.767828	−	0.640656i	$-0.221338\pi$
$977$	48.0000	1.53566	0.767828	+	0.640656i	$0.221338\pi$
$978$	0	0
$979$	−80.0000	−2.55681
$980$	0	0
$981$	0	0
$982$	−30.0000	−0.957338
$983$	14.0000	0.446531	0.223265	−	0.974758i	$-0.428328\pi$
$983$	14.0000	0.446531	0.223265	+	0.974758i	$0.428328\pi$
$984$	0	0
$985$	0	0
$986$	−10.0000	−0.318465
$987$	0	0
$988$	0	0
$989$	18.0000	0.572367
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	1.00000	0.0317181
$995$	0	0
$996$	0	0
$997$	−20.0000	−0.633406	−0.316703	−	0.948525i	$-0.602576\pi$
$997$	−20.0000	−0.633406	−0.316703	+	0.948525i	$0.602576\pi$
$998$	24.0000	0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1062.2.a.k.1.1		1
3.2	odd	2		354.2.a.a.1.1	✓	1
4.3	odd	2		8496.2.a.j.1.1		1
12.11	even	2		2832.2.a.e.1.1		1
15.14	odd	2		8850.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.a.a.1.1	✓	1	3.2	odd	2
1062.2.a.k.1.1		1	1.1	even	1	trivial
2832.2.a.e.1.1		1	12.11	even	2
8496.2.a.j.1.1		1	4.3	odd	2
8850.2.a.be.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1062 = 2 \cdot 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1062.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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