LMFDB - Embedded newform 8550.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8550,2,Mod(1,8550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8550, 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("8550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8550.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:	$68.2720937282$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{19} +3.00000 q^{23} +1.00000 q^{26} +1.00000 q^{28} +3.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +10.0000 q^{37} +1.00000 q^{38} -6.00000 q^{41} -2.00000 q^{43} +3.00000 q^{46} -6.00000 q^{49} +1.00000 q^{52} +3.00000 q^{53} +1.00000 q^{56} +3.00000 q^{58} -3.00000 q^{59} +8.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +7.00000 q^{67} -3.00000 q^{68} -12.0000 q^{71} +13.0000 q^{73} +10.0000 q^{74} +1.00000 q^{76} +14.0000 q^{79} -6.00000 q^{82} +6.00000 q^{83} -2.00000 q^{86} -6.00000 q^{89} +1.00000 q^{91} +3.00000 q^{92} +10.0000 q^{97} -6.00000 q^{98} +O(q^{100})$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	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
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	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
$17$	−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
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	0	0
$22$	0	0
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	0	0
$45$	0	0
$46$	3.00000	0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	−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
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	1.00000	0.114708
$77$	0	0
$78$	0	0
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	0	0
$86$	−2.00000	−0.215666
$87$	0	0
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	3.00000	0.312772
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	0	0
$101$	−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
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	3.00000	0.291386
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−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
$116$	3.00000	0.278543
$117$	0	0
$118$	−3.00000	−0.276172
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−11.0000	−1.00000
$122$	8.00000	0.724286
$123$	0	0
$124$	2.00000	0.179605
$125$	0	0
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	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
$133$	1.00000	0.0867110
$134$	7.00000	0.604708
$135$	0	0
$136$	−3.00000	−0.257248
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	0	0
$144$	0	0
$145$	0	0
$146$	13.0000	1.07589
$147$	0	0
$148$	10.0000	0.821995
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	0	0
$155$	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	$0.369342\pi$
$158$	14.0000	1.11378
$159$	0	0
$160$	0	0
$161$	3.00000	0.236433
$162$	0	0
$163$	22.0000	1.72317	0.861586	−	0.507611i	$-0.169471\pi$
$163$	22.0000	1.72317	0.861586	+	0.507611i	$0.169471\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	6.00000	0.465690
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−2.00000	−0.152499
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	1.00000	0.0741249
$183$	0	0
$184$	3.00000	0.221163
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	27.0000	1.95365	0.976826	−	0.214036i	$-0.0686611\pi$
$191$	27.0000	1.95365	0.976826	+	0.214036i	$0.0686611\pi$
$192$	0	0
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	−6.00000	−0.428571
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−19.0000	−1.34687	−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000	−1.34687	−0.673437	+	0.739244i	$0.735183\pi$
$200$	0	0
$201$	0	0
$202$	−12.0000	−0.844317
$203$	3.00000	0.210559
$204$	0	0
$205$	0	0
$206$	−8.00000	−0.557386
$207$	0	0
$208$	1.00000	0.0693375
$209$	0	0
$210$	0	0
$211$	−25.0000	−1.72107	−0.860535	−	0.509390i	$-0.829871\pi$
$211$	−25.0000	−1.72107	−0.860535	+	0.509390i	$0.829871\pi$
$212$	3.00000	0.206041
$213$	0	0
$214$	15.0000	1.02538
$215$	0	0
$216$	0	0
$217$	2.00000	0.135769
$218$	11.0000	0.745014
$219$	0	0
$220$	0	0
$221$	−3.00000	−0.201802
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−12.0000	−0.798228
$227$	−15.0000	−0.995585	−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000	−0.995585	−0.497792	+	0.867296i	$0.665856\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	−3.00000	−0.195283
$237$	0	0
$238$	−3.00000	−0.194461
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	−11.0000	−0.707107
$243$	0	0
$244$	8.00000	0.512148
$245$	0	0
$246$	0	0
$247$	1.00000	0.0636285
$248$	2.00000	0.127000
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	1.00000	0.0613139
$267$	0	0
$268$	7.00000	0.427593
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	−7.00000	−0.425220	−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000	−0.425220	−0.212610	+	0.977137i	$0.568196\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	9.00000	0.543710
$275$	0	0
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	8.00000	0.479808
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	0	0
$287$	−6.00000	−0.354169
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	13.0000	0.760767
$293$	21.0000	1.22683	0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000	1.22683	0.613417	+	0.789760i	$0.289795\pi$
$294$	0	0
$295$	0	0
$296$	10.0000	0.581238
$297$	0	0
$298$	12.0000	0.695141
$299$	3.00000	0.173494
$300$	0	0
$301$	−2.00000	−0.115278
$302$	−10.0000	−0.575435
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	14.0000	0.787562
$317$	9.00000	0.505490	0.252745	−	0.967533i	$-0.418667\pi$
$317$	9.00000	0.505490	0.252745	+	0.967533i	$0.418667\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	3.00000	0.167183
$323$	−3.00000	−0.166924
$324$	0	0
$325$	0	0
$326$	22.0000	1.21847
$327$	0	0
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	5.00000	0.274825	0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000	0.274825	0.137412	+	0.990514i	$0.456121\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	18.0000	0.984916
$335$	0	0
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−13.0000	−0.701934
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−33.0000	−1.75641	−0.878206	−	0.478282i	$-0.841260\pi$
$353$	−33.0000	−1.75641	−0.878206	+	0.478282i	$0.841260\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	0	0
$359$	33.0000	1.74167	0.870837	−	0.491572i	$-0.163578\pi$
$359$	33.0000	1.74167	0.870837	+	0.491572i	$0.163578\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	1.00000	0.0524142
$365$	0	0
$366$	0	0
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	3.00000	0.156386
$369$	0	0
$370$	0	0
$371$	3.00000	0.155752
$372$	0	0
$373$	31.0000	1.60512	0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000	1.60512	0.802560	+	0.596572i	$0.203471\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	3.00000	0.154508
$378$	0	0
$379$	35.0000	1.79783	0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000	1.79783	0.898915	+	0.438124i	$0.144357\pi$
$380$	0	0
$381$	0	0
$382$	27.0000	1.38144
$383$	−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
$386$	22.0000	1.11977
$387$	0	0
$388$	10.0000	0.507673
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	−6.00000	−0.303046
$393$	0	0
$394$	6.00000	0.302276
$395$	0	0
$396$	0	0
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	−19.0000	−0.952384
$399$	0	0
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	2.00000	0.0996271
$404$	−12.0000	−0.597022
$405$	0	0
$406$	3.00000	0.148888
$407$	0	0
$408$	0	0
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	0	0
$411$	0	0
$412$	−8.00000	−0.394132
$413$	−3.00000	−0.147620
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	0	0
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	−25.0000	−1.21698
$423$	0	0
$424$	3.00000	0.145693
$425$	0	0
$426$	0	0
$427$	8.00000	0.387147
$428$	15.0000	0.725052
$429$	0	0
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	11.0000	0.526804
$437$	3.00000	0.143509
$438$	0	0
$439$	38.0000	1.81364	0.906821	−	0.421517i	$-0.138502\pi$
$439$	38.0000	1.81364	0.906821	+	0.421517i	$0.138502\pi$
$440$	0	0
$441$	0	0
$442$	−3.00000	−0.142695
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	0	0
$446$	−14.0000	−0.662919
$447$	0	0
$448$	1.00000	0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	0	0
$452$	−12.0000	−0.564433
$453$	0	0
$454$	−15.0000	−0.703985
$455$	0	0
$456$	0	0
$457$	−35.0000	−1.63723	−0.818615	−	0.574342i	$-0.805258\pi$
$457$	−35.0000	−1.63723	−0.818615	+	0.574342i	$0.805258\pi$
$458$	26.0000	1.21490
$459$	0	0
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−6.00000	−0.277945
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	7.00000	0.323230
$470$	0	0
$471$	0	0
$472$	−3.00000	−0.138086
$473$	0	0
$474$	0	0
$475$	0	0
$476$	−3.00000	−0.137505
$477$	0	0
$478$	15.0000	0.686084
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	−4.00000	−0.182195
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	0	0
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	8.00000	0.362143
$489$	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
$493$	−9.00000	−0.405340
$494$	1.00000	0.0449921
$495$	0	0
$496$	2.00000	0.0898027
$497$	−12.0000	−0.538274
$498$	0	0
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	39.0000	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−2.00000	−0.0887357
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	13.0000	0.575086
$512$	1.00000	0.0441942
$513$	0	0
$514$	18.0000	0.793946
$515$	0	0
$516$	0	0
$517$	0	0
$518$	10.0000	0.439375
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−6.00000	−0.261364
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	0	0
$532$	1.00000	0.0433555
$533$	−6.00000	−0.259889
$534$	0	0
$535$	0	0
$536$	7.00000	0.302354
$537$	0	0
$538$	−18.0000	−0.776035
$539$	0	0
$540$	0	0
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	−7.00000	−0.300676
$543$	0	0
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	9.00000	0.384461
$549$	0	0
$550$	0	0
$551$	3.00000	0.127804
$552$	0	0
$553$	14.0000	0.595341
$554$	−8.00000	−0.339887
$555$	0	0
$556$	8.00000	0.339276
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	−2.00000	−0.0845910
$560$	0	0
$561$	0	0
$562$	−18.0000	−0.759284
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	0	0
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	0	0
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	6.00000	0.248922
$582$	0	0
$583$	0	0
$584$	13.0000	0.537944
$585$	0	0
$586$	21.0000	0.867502
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	0	0
$589$	2.00000	0.0824086
$590$	0	0
$591$	0	0
$592$	10.0000	0.410997
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	0	0
$596$	12.0000	0.491539
$597$	0	0
$598$	3.00000	0.122679
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	−2.00000	−0.0815139
$603$	0	0
$604$	−10.0000	−0.406894
$605$	0	0
$606$	0	0
$607$	10.0000	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	0	0
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	0	0
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	0	0
$622$	3.00000	0.120289
$623$	−6.00000	−0.240385
$624$	0	0
$625$	0	0
$626$	1.00000	0.0399680
$627$	0	0
$628$	10.0000	0.399043
$629$	−30.0000	−1.19618
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	14.0000	0.556890
$633$	0	0
$634$	9.00000	0.357436
$635$	0	0
$636$	0	0
$637$	−6.00000	−0.237729
$638$	0	0
$639$	0	0
$640$	0	0
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−50.0000	−1.97181	−0.985904	−	0.167313i	$-0.946491\pi$
$643$	−50.0000	−1.97181	−0.985904	+	0.167313i	$0.946491\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−3.00000	−0.118033
$647$	−33.0000	−1.29736	−0.648682	−	0.761060i	$-0.724679\pi$
$647$	−33.0000	−1.29736	−0.648682	+	0.761060i	$0.724679\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	22.0000	0.861586
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	0	0
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	−49.0000	−1.90588	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−49.0000	−1.90588	−0.952940	+	0.303160i	$0.901958\pi$
$662$	5.00000	0.194331
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	9.00000	0.348481
$668$	18.0000	0.696441
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−20.0000	−0.770943	−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000	−0.770943	−0.385472	+	0.922720i	$0.625961\pi$
$674$	−2.00000	−0.0770371
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−15.0000	−0.576497	−0.288248	−	0.957556i	$-0.593073\pi$
$677$	−15.0000	−0.576497	−0.288248	+	0.957556i	$0.593073\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−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
$685$	0	0
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−2.00000	−0.0762493
$689$	3.00000	0.114291
$690$	0	0
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−30.0000	−1.13878
$695$	0	0
$696$	0	0
$697$	18.0000	0.681799
$698$	14.0000	0.529908
$699$	0	0
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	0	0
$703$	10.0000	0.377157
$704$	0	0
$705$	0	0
$706$	−33.0000	−1.24197
$707$	−12.0000	−0.451306
$708$	0	0
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	0	0
$711$	0	0
$712$	−6.00000	−0.224860
$713$	6.00000	0.224702
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	33.0000	1.23155
$719$	−33.0000	−1.23069	−0.615346	−	0.788257i	$-0.710984\pi$
$719$	−33.0000	−1.23069	−0.615346	+	0.788257i	$0.710984\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	1.00000	0.0372161
$723$	0	0
$724$	2.00000	0.0743294
$725$	0	0
$726$	0	0
$727$	13.0000	0.482143	0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000	0.482143	0.241072	+	0.970507i	$0.422501\pi$
$728$	1.00000	0.0370625
$729$	0	0
$730$	0	0
$731$	6.00000	0.221918
$732$	0	0
$733$	4.00000	0.147743	0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000	0.147743	0.0738717	+	0.997268i	$0.476464\pi$
$734$	16.0000	0.590571
$735$	0	0
$736$	3.00000	0.110581
$737$	0	0
$738$	0	0
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	0	0
$741$	0	0
$742$	3.00000	0.110133
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	0	0
$745$	0	0
$746$	31.0000	1.13499
$747$	0	0
$748$	0	0
$749$	15.0000	0.548088
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	0	0
$753$	0	0
$754$	3.00000	0.109254
$755$	0	0
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	35.0000	1.27126
$759$	0	0
$760$	0	0
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	0	0
$763$	11.0000	0.398227
$764$	27.0000	0.976826
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−3.00000	−0.108324
$768$	0	0
$769$	−55.0000	−1.98335	−0.991675	−	0.128763i	$-0.958899\pi$
$769$	−55.0000	−1.98335	−0.991675	+	0.128763i	$0.958899\pi$
$770$	0	0
$771$	0	0
$772$	22.0000	0.791797
$773$	21.0000	0.755318	0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000	0.755318	0.377659	+	0.925945i	$0.376729\pi$
$774$	0	0
$775$	0	0
$776$	10.0000	0.358979
$777$	0	0
$778$	24.0000	0.860442
$779$	−6.00000	−0.214972
$780$	0	0
$781$	0	0
$782$	−9.00000	−0.321839
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	0	0
$791$	−12.0000	−0.426671
$792$	0	0
$793$	8.00000	0.284088
$794$	−8.00000	−0.283909
$795$	0	0
$796$	−19.0000	−0.673437
$797$	−33.0000	−1.16892	−0.584460	−	0.811423i	$-0.698694\pi$
$797$	−33.0000	−1.16892	−0.584460	+	0.811423i	$0.698694\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	−6.00000	−0.211867
$803$	0	0
$804$	0	0
$805$	0	0
$806$	2.00000	0.0704470
$807$	0	0
$808$	−12.0000	−0.422159
$809$	−33.0000	−1.16022	−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000	−1.16022	−0.580109	+	0.814539i	$0.696990\pi$
$810$	0	0
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	3.00000	0.105279
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−2.00000	−0.0699711
$818$	−22.0000	−0.769212
$819$	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
$823$	31.0000	1.08059	0.540296	−	0.841475i	$-0.318312\pi$
$823$	31.0000	1.08059	0.540296	+	0.841475i	$0.318312\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	−3.00000	−0.104383
$827$	33.0000	1.14752	0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000	1.14752	0.573761	+	0.819023i	$0.305484\pi$
$828$	0	0
$829$	−13.0000	−0.451509	−0.225754	−	0.974184i	$-0.572485\pi$
$829$	−13.0000	−0.451509	−0.225754	+	0.974184i	$0.572485\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	0.0346688
$833$	18.0000	0.623663
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	30.0000	1.03633
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	17.0000	0.585859
$843$	0	0
$844$	−25.0000	−0.860535
$845$	0	0
$846$	0	0
$847$	−11.0000	−0.377964
$848$	3.00000	0.103020
$849$	0	0
$850$	0	0
$851$	30.0000	1.02839
$852$	0	0
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	15.0000	0.512689
$857$	48.0000	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$857$	48.0000	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$858$	0	0
$859$	−16.0000	−0.545913	−0.272956	−	0.962026i	$-0.588002\pi$
$859$	−16.0000	−0.545913	−0.272956	+	0.962026i	$0.588002\pi$
$860$	0	0
$861$	0	0
$862$	−24.0000	−0.817443
$863$	−12.0000	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$864$	0	0
$865$	0	0
$866$	4.00000	0.135926
$867$	0	0
$868$	2.00000	0.0678844
$869$	0	0
$870$	0	0
$871$	7.00000	0.237186
$872$	11.0000	0.372507
$873$	0	0
$874$	3.00000	0.101477
$875$	0	0
$876$	0	0
$877$	31.0000	1.04680	0.523398	−	0.852088i	$-0.324664\pi$
$877$	31.0000	1.04680	0.523398	+	0.852088i	$0.324664\pi$
$878$	38.0000	1.28244
$879$	0	0
$880$	0	0
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	0	0
$883$	−38.0000	−1.27880	−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000	−1.27880	−0.639401	+	0.768874i	$0.720818\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	−24.0000	−0.806296
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	0	0
$889$	−2.00000	−0.0670778
$890$	0	0
$891$	0	0
$892$	−14.0000	−0.468755
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	30.0000	1.00111
$899$	6.00000	0.200111
$900$	0	0
$901$	−9.00000	−0.299833
$902$	0	0
$903$	0	0
$904$	−12.0000	−0.399114
$905$	0	0
$906$	0	0
$907$	−35.0000	−1.16216	−0.581078	−	0.813848i	$-0.697369\pi$
$907$	−35.0000	−1.16216	−0.581078	+	0.813848i	$0.697369\pi$
$908$	−15.0000	−0.497792
$909$	0	0
$910$	0	0
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	0	0
$913$	0	0
$914$	−35.0000	−1.15770
$915$	0	0
$916$	26.0000	0.859064
$917$	0	0
$918$	0	0
$919$	−1.00000	−0.0329870	−0.0164935	−	0.999864i	$-0.505250\pi$
$919$	−1.00000	−0.0329870	−0.0164935	+	0.999864i	$0.505250\pi$
$920$	0	0
$921$	0	0
$922$	−6.00000	−0.197599
$923$	−12.0000	−0.394985
$924$	0	0
$925$	0	0
$926$	16.0000	0.525793
$927$	0	0
$928$	3.00000	0.0984798
$929$	−21.0000	−0.688988	−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000	−0.688988	−0.344494	+	0.938789i	$0.611949\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−6.00000	−0.196537
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	−47.0000	−1.53542	−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000	−1.53542	−0.767712	+	0.640796i	$0.778605\pi$
$938$	7.00000	0.228558
$939$	0	0
$940$	0	0
$941$	−45.0000	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$942$	0	0
$943$	−18.0000	−0.586161
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	0	0
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	0	0
$949$	13.0000	0.421998
$950$	0	0
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	0	0
$955$	0	0
$956$	15.0000	0.485135
$957$	0	0
$958$	24.0000	0.775405
$959$	9.00000	0.290625
$960$	0	0
$961$	−27.0000	−0.870968
$962$	10.0000	0.322413
$963$	0	0
$964$	−4.00000	−0.128831
$965$	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	$0.750165\pi$
$968$	−11.0000	−0.353553
$969$	0	0
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	8.00000	0.256468
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	8.00000	0.256074
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	−30.0000	−0.957338
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	0	0
$985$	0	0
$986$	−9.00000	−0.286618
$987$	0	0
$988$	1.00000	0.0318142
$989$	−6.00000	−0.190789
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	−12.0000	−0.380617
$995$	0	0
$996$	0	0
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8550.2.a.bd.1.1		1
3.2	odd	2		950.2.a.a.1.1		1
5.4	even	2		1710.2.a.d.1.1		1
12.11	even	2		7600.2.a.m.1.1		1
15.2	even	4		950.2.b.e.799.1		2
15.8	even	4		950.2.b.e.799.2		2
15.14	odd	2		190.2.a.c.1.1	✓	1
60.59	even	2		1520.2.a.d.1.1		1
105.104	even	2		9310.2.a.o.1.1		1
120.29	odd	2		6080.2.a.h.1.1		1
120.59	even	2		6080.2.a.p.1.1		1
285.284	even	2		3610.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.c.1.1	✓	1	15.14	odd	2
950.2.a.a.1.1		1	3.2	odd	2
950.2.b.e.799.1		2	15.2	even	4
950.2.b.e.799.2		2	15.8	even	4
1520.2.a.d.1.1		1	60.59	even	2
1710.2.a.d.1.1		1	5.4	even	2
3610.2.a.b.1.1		1	285.284	even	2
6080.2.a.h.1.1		1	120.29	odd	2
6080.2.a.p.1.1		1	120.59	even	2
7600.2.a.m.1.1		1	12.11	even	2
8550.2.a.bd.1.1		1	1.1	even	1	trivial
9310.2.a.o.1.1		1	105.104	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8550.a (trivial)

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L-functions

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