LMFDB - Embedded newform 5850.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5850,2,Mod(1,5850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5850, 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("5850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5850.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:	$46.7124851824$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{7} +1.00000 q^{8} -2.00000 q^{11} -1.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +2.00000 q^{19} -2.00000 q^{22} -6.00000 q^{23} -1.00000 q^{26} -4.00000 q^{28} +2.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +4.00000 q^{34} +6.00000 q^{37} +2.00000 q^{38} +6.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -6.00000 q^{46} +8.00000 q^{47} +9.00000 q^{49} -1.00000 q^{52} +10.0000 q^{53} -4.00000 q^{56} +2.00000 q^{58} +14.0000 q^{59} +10.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +4.00000 q^{68} -8.00000 q^{71} -10.0000 q^{73} +6.00000 q^{74} +2.00000 q^{76} +8.00000 q^{77} -8.00000 q^{79} +6.00000 q^{82} +12.0000 q^{83} -8.00000 q^{86} -2.00000 q^{88} +18.0000 q^{89} +4.00000 q^{91} -6.00000 q^{92} +8.00000 q^{94} -6.00000 q^{97} +9.00000 q^{98} +O(q^{100})$

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
$5$	0	0
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	−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
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−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
$25$	0	0
$26$	−1.00000	−0.196116
$27$	0	0
$28$	−4.00000	−0.755929
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	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
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	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
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	−1.00000	−0.138675
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	0	0
$56$	−4.00000	−0.534522
$57$	0	0
$58$	2.00000	0.262613
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	6.00000	0.697486
$75$	0	0
$76$	2.00000	0.229416
$77$	8.00000	0.911685
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	0	0
$82$	6.00000	0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	0	0
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−2.00000	−0.213201
$89$	18.0000	1.90800	0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000	1.90800	0.953998	+	0.299813i	$0.0969242\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	−6.00000	−0.625543
$93$	0	0
$94$	8.00000	0.825137
$95$	0	0
$96$	0	0
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	0	0
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	10.0000	0.971286
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	0	0
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	0	0
$112$	−4.00000	−0.377964
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	0	0
$116$	2.00000	0.185695
$117$	0	0
$118$	14.0000	1.28880
$119$	−16.0000	−1.46672
$120$	0	0
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	0	0
$124$	−4.00000	−0.359211
$125$	0	0
$126$	0	0
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−8.00000	−0.693688
$134$	−4.00000	−0.345547
$135$	0	0
$136$	4.00000	0.342997
$137$	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
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	0	0
$142$	−8.00000	−0.671345
$143$	2.00000	0.167248
$144$	0	0
$145$	0	0
$146$	−10.0000	−0.827606
$147$	0	0
$148$	6.00000	0.493197
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	8.00000	0.644658
$155$	0	0
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	0	0
$161$	24.0000	1.89146
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	−8.00000	−0.609994
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	18.0000	1.34916
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	4.00000	0.296500
$183$	0	0
$184$	−6.00000	−0.442326
$185$	0	0
$186$	0	0
$187$	−8.00000	−0.585018
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	9.00000	0.642857
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	0	0
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	0	0
$202$	14.0000	0.985037
$203$	−8.00000	−0.561490
$204$	0	0
$205$	0	0
$206$	−6.00000	−0.418040
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	−8.00000	−0.546869
$215$	0	0
$216$	0	0
$217$	16.0000	1.08615
$218$	12.0000	0.812743
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	−12.0000	−0.798228
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	0	0
$232$	2.00000	0.131306
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	0	0
$235$	0	0
$236$	14.0000	0.911322
$237$	0	0
$238$	−16.0000	−1.03713
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−30.0000	−1.93247	−0.966235	−	0.257663i	$-0.917048\pi$
$241$	−30.0000	−1.93247	−0.966235	+	0.257663i	$0.917048\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	−2.00000	−0.127257
$248$	−4.00000	−0.254000
$249$	0	0
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	18.0000	1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	0	0
$259$	−24.0000	−1.49129
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−10.0000	−0.616626	−0.308313	−	0.951285i	$-0.599764\pi$
$263$	−10.0000	−0.616626	−0.308313	+	0.951285i	$0.599764\pi$
$264$	0	0
$265$	0	0
$266$	−8.00000	−0.490511
$267$	0	0
$268$	−4.00000	−0.244339
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	2.00000	0.120824
$275$	0	0
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	16.0000	0.959616
$279$	0	0
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	2.00000	0.118262
$287$	−24.0000	−1.41668
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−10.0000	−0.585206
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	0	0
$296$	6.00000	0.348743
$297$	0	0
$298$	0	0
$299$	6.00000	0.346989
$300$	0	0
$301$	32.0000	1.84445
$302$	8.00000	0.460348
$303$	0	0
$304$	2.00000	0.114708
$305$	0	0
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	8.00000	0.455842
$309$	0	0
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	0	0
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	−4.00000	−0.223957
$320$	0	0
$321$	0	0
$322$	24.0000	1.33747
$323$	8.00000	0.445132
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	6.00000	0.331295
$329$	−32.0000	−1.76422
$330$	0	0
$331$	18.0000	0.989369	0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000	0.989369	0.494685	+	0.869072i	$0.335284\pi$
$332$	12.0000	0.658586
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	1.00000	0.0543928
$339$	0	0
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	−8.00000	−0.431959
$344$	−8.00000	−0.431331
$345$	0	0
$346$	10.0000	0.537603
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	0	0
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	0	0
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	0	0
$355$	0	0
$356$	18.0000	0.953998
$357$	0	0
$358$	0	0
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	6.00000	0.315353
$363$	0	0
$364$	4.00000	0.209657
$365$	0	0
$366$	0	0
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	0	0
$371$	−40.0000	−2.07670
$372$	0	0
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	8.00000	0.412568
$377$	−2.00000	−0.103005
$378$	0	0
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	0	0
$386$	−6.00000	−0.305392
$387$	0	0
$388$	−6.00000	−0.304604
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	9.00000	0.454569
$393$	0	0
$394$	26.0000	1.30986
$395$	0	0
$396$	0	0
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	24.0000	1.20301
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	14.0000	0.696526
$405$	0	0
$406$	−8.00000	−0.397033
$407$	−12.0000	−0.594818
$408$	0	0
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	0	0
$411$	0	0
$412$	−6.00000	−0.295599
$413$	−56.0000	−2.75558
$414$	0	0
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	0	0
$418$	−4.00000	−0.195646
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	−28.0000	−1.36302
$423$	0	0
$424$	10.0000	0.485643
$425$	0	0
$426$	0	0
$427$	−40.0000	−1.93574
$428$	−8.00000	−0.386695
$429$	0	0
$430$	0	0
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	12.0000	0.574696
$437$	−12.0000	−0.574038
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	0	0
$442$	−4.00000	−0.190261
$443$	8.00000	0.380091	0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000	0.380091	0.190046	+	0.981775i	$0.439136\pi$
$444$	0	0
$445$	0	0
$446$	16.0000	0.757622
$447$	0	0
$448$	−4.00000	−0.188982
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−12.0000	−0.565058
$452$	−12.0000	−0.564433
$453$	0	0
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	−16.0000	−0.747631
$459$	0	0
$460$	0	0
$461$	4.00000	0.186299	0.0931493	−	0.995652i	$-0.470307\pi$
$461$	4.00000	0.186299	0.0931493	+	0.995652i	$0.470307\pi$
$462$	0	0
$463$	36.0000	1.67306	0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000	1.67306	0.836531	+	0.547920i	$0.184580\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−4.00000	−0.185296
$467$	−16.0000	−0.740392	−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000	−0.740392	−0.370196	+	0.928954i	$0.620709\pi$
$468$	0	0
$469$	16.0000	0.738811
$470$	0	0
$471$	0	0
$472$	14.0000	0.644402
$473$	16.0000	0.735681
$474$	0	0
$475$	0	0
$476$	−16.0000	−0.733359
$477$	0	0
$478$	12.0000	0.548867
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−30.0000	−1.36646
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	0	0
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	0	0
$493$	8.00000	0.360302
$494$	−2.00000	−0.0899843
$495$	0	0
$496$	−4.00000	−0.179605
$497$	32.0000	1.43540
$498$	0	0
$499$	30.0000	1.34298	0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000	1.34298	0.671492	+	0.741012i	$0.265654\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	18.0000	0.802580	0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000	0.802580	0.401290	+	0.915951i	$0.368562\pi$
$504$	0	0
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	18.0000	0.798621
$509$	16.0000	0.709188	0.354594	−	0.935020i	$-0.384619\pi$
$509$	16.0000	0.709188	0.354594	+	0.935020i	$0.384619\pi$
$510$	0	0
$511$	40.0000	1.76950
$512$	1.00000	0.0441942
$513$	0	0
$514$	−12.0000	−0.529297
$515$	0	0
$516$	0	0
$517$	−16.0000	−0.703679
$518$	−24.0000	−1.05450
$519$	0	0
$520$	0	0
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	0	0
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	0	0
$525$	0	0
$526$	−10.0000	−0.436021
$527$	−16.0000	−0.696971
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−8.00000	−0.346844
$533$	−6.00000	−0.259889
$534$	0	0
$535$	0	0
$536$	−4.00000	−0.172774
$537$	0	0
$538$	14.0000	0.603583
$539$	−18.0000	−0.775315
$540$	0	0
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	4.00000	0.171499
$545$	0	0
$546$	0	0
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	0	0
$551$	4.00000	0.170406
$552$	0	0
$553$	32.0000	1.36078
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	16.0000	0.678551
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	−16.0000	−0.674320	−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000	−0.674320	−0.337160	+	0.941447i	$0.609466\pi$
$564$	0	0
$565$	0	0
$566$	4.00000	0.168133
$567$	0	0
$568$	−8.00000	−0.335673
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	0	0
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	−24.0000	−1.00174
$575$	0	0
$576$	0	0
$577$	−26.0000	−1.08239	−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000	−1.08239	−0.541197	+	0.840896i	$0.682029\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	−48.0000	−1.99138
$582$	0	0
$583$	−20.0000	−0.828315
$584$	−10.0000	−0.413803
$585$	0	0
$586$	−14.0000	−0.578335
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	0	0
$591$	0	0
$592$	6.00000	0.246598
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	6.00000	0.245358
$599$	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
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	32.0000	1.30422
$603$	0	0
$604$	8.00000	0.325515
$605$	0	0
$606$	0	0
$607$	−18.0000	−0.730597	−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000	−0.730597	−0.365299	+	0.930890i	$0.619033\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	0	0
$611$	−8.00000	−0.323645
$612$	0	0
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	8.00000	0.322329
$617$	−34.0000	−1.36879	−0.684394	−	0.729112i	$-0.739933\pi$
$617$	−34.0000	−1.36879	−0.684394	+	0.729112i	$0.739933\pi$
$618$	0	0
$619$	42.0000	1.68812	0.844061	−	0.536247i	$-0.180158\pi$
$619$	42.0000	1.68812	0.844061	+	0.536247i	$0.180158\pi$
$620$	0	0
$621$	0	0
$622$	−8.00000	−0.320771
$623$	−72.0000	−2.88462
$624$	0	0
$625$	0	0
$626$	−8.00000	−0.319744
$627$	0	0
$628$	10.0000	0.399043
$629$	24.0000	0.956943
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	−30.0000	−1.19145
$635$	0	0
$636$	0	0
$637$	−9.00000	−0.356593
$638$	−4.00000	−0.158362
$639$	0	0
$640$	0	0
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	24.0000	0.945732
$645$	0	0
$646$	8.00000	0.314756
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	0	0
$649$	−28.0000	−1.09910
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	−32.0000	−1.24749
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	24.0000	0.933492	0.466746	−	0.884391i	$-0.345426\pi$
$661$	24.0000	0.933492	0.466746	+	0.884391i	$0.345426\pi$
$662$	18.0000	0.699590
$663$	0	0
$664$	12.0000	0.465690
$665$	0	0
$666$	0	0
$667$	−12.0000	−0.464642
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−20.0000	−0.772091
$672$	0	0
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	32.0000	1.23259
$675$	0	0
$676$	1.00000	0.0384615
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	0	0
$679$	24.0000	0.921035
$680$	0	0
$681$	0	0
$682$	8.00000	0.306336
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	0	0
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−8.00000	−0.304997
$689$	−10.0000	−0.380970
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	10.0000	0.380143
$693$	0	0
$694$	−24.0000	−0.911028
$695$	0	0
$696$	0	0
$697$	24.0000	0.909065
$698$	−28.0000	−1.05982
$699$	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
$703$	12.0000	0.452589
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−26.0000	−0.978523
$707$	−56.0000	−2.10610
$708$	0	0
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	0	0
$711$	0	0
$712$	18.0000	0.674579
$713$	24.0000	0.898807
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−20.0000	−0.746393
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	24.0000	0.893807
$722$	−15.0000	−0.558242
$723$	0	0
$724$	6.00000	0.222988
$725$	0	0
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	4.00000	0.148250
$729$	0	0
$730$	0	0
$731$	−32.0000	−1.18356
$732$	0	0
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−22.0000	−0.812035
$735$	0	0
$736$	−6.00000	−0.221163
$737$	8.00000	0.294684
$738$	0	0
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	0	0
$741$	0	0
$742$	−40.0000	−1.46845
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	0	0
$745$	0	0
$746$	2.00000	0.0732252
$747$	0	0
$748$	−8.00000	−0.292509
$749$	32.0000	1.16925
$750$	0	0
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	−2.00000	−0.0728357
$755$	0	0
$756$	0	0
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	26.0000	0.944363
$759$	0	0
$760$	0	0
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	0	0
$763$	−48.0000	−1.73772
$764$	0	0
$765$	0	0
$766$	−12.0000	−0.433578
$767$	−14.0000	−0.505511
$768$	0	0
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	0	0
$772$	−6.00000	−0.215945
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	0	0
$775$	0	0
$776$	−6.00000	−0.215387
$777$	0	0
$778$	26.0000	0.932145
$779$	12.0000	0.429945
$780$	0	0
$781$	16.0000	0.572525
$782$	−24.0000	−0.858238
$783$	0	0
$784$	9.00000	0.321429
$785$	0	0
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	26.0000	0.926212
$789$	0	0
$790$	0	0
$791$	48.0000	1.70668
$792$	0	0
$793$	−10.0000	−0.355110
$794$	−6.00000	−0.212932
$795$	0	0
$796$	24.0000	0.850657
$797$	34.0000	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$798$	0	0
$799$	32.0000	1.13208
$800$	0	0
$801$	0	0
$802$	18.0000	0.635602
$803$	20.0000	0.705785
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	14.0000	0.492518
$809$	−14.0000	−0.492214	−0.246107	−	0.969243i	$-0.579151\pi$
$809$	−14.0000	−0.492214	−0.246107	+	0.969243i	$0.579151\pi$
$810$	0	0
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−8.00000	−0.280745
$813$	0	0
$814$	−12.0000	−0.420600
$815$	0	0
$816$	0	0
$817$	−16.0000	−0.559769
$818$	−2.00000	−0.0699284
$819$	0	0
$820$	0	0
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	0	0
$823$	−26.0000	−0.906303	−0.453152	−	0.891434i	$-0.649700\pi$
$823$	−26.0000	−0.906303	−0.453152	+	0.891434i	$0.649700\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	−56.0000	−1.94849
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	42.0000	1.45872	0.729360	−	0.684130i	$-0.239818\pi$
$829$	42.0000	1.45872	0.729360	+	0.684130i	$0.239818\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	36.0000	1.24733
$834$	0	0
$835$	0	0
$836$	−4.00000	−0.138343
$837$	0	0
$838$	−16.0000	−0.552711
$839$	−16.0000	−0.552381	−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000	−0.552381	−0.276191	+	0.961103i	$0.589072\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	28.0000	0.964944
$843$	0	0
$844$	−28.0000	−0.963800
$845$	0	0
$846$	0	0
$847$	28.0000	0.962091
$848$	10.0000	0.343401
$849$	0	0
$850$	0	0
$851$	−36.0000	−1.23406
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	−40.0000	−1.36877
$855$	0	0
$856$	−8.00000	−0.273434
$857$	−40.0000	−1.36637	−0.683187	−	0.730243i	$-0.739407\pi$
$857$	−40.0000	−1.36637	−0.683187	+	0.730243i	$0.739407\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	0	0
$862$	8.00000	0.272481
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	16.0000	0.543075
$869$	16.0000	0.542763
$870$	0	0
$871$	4.00000	0.135535
$872$	12.0000	0.406371
$873$	0	0
$874$	−12.0000	−0.405906
$875$	0	0
$876$	0	0
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	0	0
$881$	46.0000	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$882$	0	0
$883$	−48.0000	−1.61533	−0.807664	−	0.589643i	$-0.799269\pi$
$883$	−48.0000	−1.61533	−0.807664	+	0.589643i	$0.799269\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	8.00000	0.268765
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	0	0
$889$	−72.0000	−2.41480
$890$	0	0
$891$	0	0
$892$	16.0000	0.535720
$893$	16.0000	0.535420
$894$	0	0
$895$	0	0
$896$	−4.00000	−0.133631
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−8.00000	−0.266815
$900$	0	0
$901$	40.0000	1.33259
$902$	−12.0000	−0.399556
$903$	0	0
$904$	−12.0000	−0.399114
$905$	0	0
$906$	0	0
$907$	32.0000	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	26.0000	0.860004
$915$	0	0
$916$	−16.0000	−0.528655
$917$	0	0
$918$	0	0
$919$	−24.0000	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$920$	0	0
$921$	0	0
$922$	4.00000	0.131733
$923$	8.00000	0.263323
$924$	0	0
$925$	0	0
$926$	36.0000	1.18303
$927$	0	0
$928$	2.00000	0.0656532
$929$	−46.0000	−1.50921	−0.754606	−	0.656179i	$-0.772172\pi$
$929$	−46.0000	−1.50921	−0.754606	+	0.656179i	$0.772172\pi$
$930$	0	0
$931$	18.0000	0.589926
$932$	−4.00000	−0.131024
$933$	0	0
$934$	−16.0000	−0.523536
$935$	0	0
$936$	0	0
$937$	−16.0000	−0.522697	−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000	−0.522697	−0.261349	+	0.965244i	$0.584167\pi$
$938$	16.0000	0.522419
$939$	0	0
$940$	0	0
$941$	−40.0000	−1.30396	−0.651981	−	0.758235i	$-0.726062\pi$
$941$	−40.0000	−1.30396	−0.651981	+	0.758235i	$0.726062\pi$
$942$	0	0
$943$	−36.0000	−1.17232
$944$	14.0000	0.455661
$945$	0	0
$946$	16.0000	0.520205
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	10.0000	0.324614
$950$	0	0
$951$	0	0
$952$	−16.0000	−0.518563
$953$	−48.0000	−1.55487	−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000	−1.55487	−0.777436	+	0.628962i	$0.783480\pi$
$954$	0	0
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	12.0000	0.387702
$959$	−8.00000	−0.258333
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−6.00000	−0.193448
$963$	0	0
$964$	−30.0000	−0.966235
$965$	0	0
$966$	0	0
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	−64.0000	−2.05175
$974$	40.0000	1.28168
$975$	0	0
$976$	10.0000	0.320092
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	0	0
$979$	−36.0000	−1.15056
$980$	0	0
$981$	0	0
$982$	−8.00000	−0.255290
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	0	0
$986$	8.00000	0.254772
$987$	0	0
$988$	−2.00000	−0.0636285
$989$	48.0000	1.52631
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	32.0000	1.01498
$995$	0	0
$996$	0	0
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	30.0000	0.949633
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5850.2.a.bd.1.1		1
3.2	odd	2		1950.2.a.g.1.1		1
5.2	odd	4		1170.2.e.b.469.2		2
5.3	odd	4		1170.2.e.b.469.1		2
5.4	even	2		5850.2.a.x.1.1		1
15.2	even	4		390.2.e.b.79.1	✓	2
15.8	even	4		390.2.e.b.79.2	yes	2
15.14	odd	2		1950.2.a.u.1.1		1
60.23	odd	4		3120.2.l.h.1249.1		2
60.47	odd	4		3120.2.l.h.1249.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.e.b.79.1	✓	2	15.2	even	4
390.2.e.b.79.2	yes	2	15.8	even	4
1170.2.e.b.469.1		2	5.3	odd	4
1170.2.e.b.469.2		2	5.2	odd	4
1950.2.a.g.1.1		1	3.2	odd	2
1950.2.a.u.1.1		1	15.14	odd	2
3120.2.l.h.1249.1		2	60.23	odd	4
3120.2.l.h.1249.2		2	60.47	odd	4
5850.2.a.x.1.1		1	5.4	even	2
5850.2.a.bd.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:	\( N \)	\(=\)	\( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5850.a (trivial)

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