LMFDB - Embedded newform 2299.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,2,Mod(1,2299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2299, 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("2299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.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:	$18.3576074247$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} -3.00000 q^{5} +4.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} -3.00000 q^{5} +4.00000 q^{7} -2.00000 q^{9} -2.00000 q^{12} -2.00000 q^{13} -3.00000 q^{15} +4.00000 q^{16} -1.00000 q^{19} +6.00000 q^{20} +4.00000 q^{21} +3.00000 q^{23} +4.00000 q^{25} -5.00000 q^{27} -8.00000 q^{28} +6.00000 q^{29} -7.00000 q^{31} -12.0000 q^{35} +4.00000 q^{36} -7.00000 q^{37} -2.00000 q^{39} +10.0000 q^{43} +6.00000 q^{45} +4.00000 q^{48} +9.00000 q^{49} +4.00000 q^{52} +6.00000 q^{53} -1.00000 q^{57} +3.00000 q^{59} +6.00000 q^{60} +10.0000 q^{61} -8.00000 q^{63} -8.00000 q^{64} +6.00000 q^{65} +11.0000 q^{67} +3.00000 q^{69} +15.0000 q^{71} -8.00000 q^{73} +4.00000 q^{75} +2.00000 q^{76} +16.0000 q^{79} -12.0000 q^{80} +1.00000 q^{81} -8.00000 q^{84} +6.00000 q^{87} +9.00000 q^{89} -8.00000 q^{91} -6.00000 q^{92} -7.00000 q^{93} +3.00000 q^{95} -1.00000 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	−2.00000	−1.00000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	0	0
$11$	0	0
$12$	−2.00000	−0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−3.00000	−0.774597
$16$	4.00000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	6.00000	1.34164
$21$	4.00000	0.872872
$22$	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
$25$	4.00000	0.800000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	−8.00000	−1.51186
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−12.0000	−2.02837
$36$	4.00000	0.666667
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	0	0
$45$	6.00000	0.894427
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	4.00000	0.577350
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	4.00000	0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−1.00000	−0.132453
$58$	0	0
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	6.00000	0.774597
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	−8.00000	−1.00791
$64$	−8.00000	−1.00000
$65$	6.00000	0.744208
$66$	0	0
$67$	11.0000	1.34386	0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000	1.34386	0.671932	+	0.740613i	$0.265465\pi$
$68$	0	0
$69$	3.00000	0.361158
$70$	0	0
$71$	15.0000	1.78017	0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000	1.78017	0.890086	+	0.455792i	$0.150644\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	0	0
$75$	4.00000	0.461880
$76$	2.00000	0.229416
$77$	0	0
$78$	0	0
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	−12.0000	−1.34164
$81$	1.00000	0.111111
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−8.00000	−0.872872
$85$	0	0
$86$	0	0
$87$	6.00000	0.643268
$88$	0	0
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	−6.00000	−0.625543
$93$	−7.00000	−0.725866
$94$	0	0
$95$	3.00000	0.307794
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	0	0
$99$	0	0
$100$	−8.00000	−0.800000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	0	0
$105$	−12.0000	−1.17108
$106$	0	0
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	10.0000	0.962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	16.0000	1.51186
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	−9.00000	−0.839254
$116$	−12.0000	−1.11417
$117$	4.00000	0.369800
$118$	0	0
$119$	0	0
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	14.0000	1.25724
$125$	3.00000	0.268328
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	10.0000	0.880451
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	0	0
$135$	15.0000	1.29099
$136$	0	0
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	0	0
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	24.0000	2.02837
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−8.00000	−0.666667
$145$	−18.0000	−1.49482
$146$	0	0
$147$	9.00000	0.742307
$148$	14.0000	1.15079
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	21.0000	1.68676
$156$	4.00000	0.320256
$157$	17.0000	1.35675	0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000	1.35675	0.678374	+	0.734717i	$0.262685\pi$
$158$	0	0
$159$	6.00000	0.475831
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	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
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	−20.0000	−1.52499
$173$	−24.0000	−1.82469	−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000	−1.82469	−0.912343	+	0.409426i	$0.865729\pi$
$174$	0	0
$175$	16.0000	1.20949
$176$	0	0
$177$	3.00000	0.225494
$178$	0	0
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	−12.0000	−0.894427
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	0	0
$185$	21.0000	1.54395
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−20.0000	−1.45479
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−8.00000	−0.577350
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	0	0
$195$	6.00000	0.429669
$196$	−18.0000	−1.28571
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	11.0000	0.775880
$202$	0	0
$203$	24.0000	1.68447
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−6.00000	−0.417029
$208$	−8.00000	−0.554700
$209$	0	0
$210$	0	0
$211$	22.0000	1.51454	0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000	1.51454	0.757271	+	0.653101i	$0.226532\pi$
$212$	−12.0000	−0.824163
$213$	15.0000	1.02778
$214$	0	0
$215$	−30.0000	−2.04598
$216$	0	0
$217$	−28.0000	−1.90076
$218$	0	0
$219$	−8.00000	−0.540590
$220$	0	0
$221$	0	0
$222$	0	0
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	0	0
$225$	−8.00000	−0.533333
$226$	0	0
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	2.00000	0.132453
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	0	0
$236$	−6.00000	−0.390567
$237$	16.0000	1.03931
$238$	0	0
$239$	18.0000	1.16432	0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000	1.16432	0.582162	+	0.813073i	$0.302207\pi$
$240$	−12.0000	−0.774597
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	−20.0000	−1.28037
$245$	−27.0000	−1.72497
$246$	0	0
$247$	2.00000	0.127257
$248$	0	0
$249$	0	0
$250$	0	0
$251$	21.0000	1.32551	0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000	1.32551	0.662754	+	0.748837i	$0.269387\pi$
$252$	16.0000	1.00791
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	−28.0000	−1.73984
$260$	−12.0000	−0.744208
$261$	−12.0000	−0.742781
$262$	0	0
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	0	0
$265$	−18.0000	−1.10573
$266$	0	0
$267$	9.00000	0.550791
$268$	−22.0000	−1.34386
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	0	0
$273$	−8.00000	−0.484182
$274$	0	0
$275$	0	0
$276$	−6.00000	−0.361158
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	0	0
$279$	14.0000	0.838158
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−30.0000	−1.78017
$285$	3.00000	0.177705
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	−1.00000	−0.0586210
$292$	16.0000	0.936329
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	−9.00000	−0.524000
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−6.00000	−0.346989
$300$	−8.00000	−0.461880
$301$	40.0000	2.30556
$302$	0	0
$303$	0	0
$304$	−4.00000	−0.229416
$305$	−30.0000	−1.71780
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	0	0
$315$	24.0000	1.35225
$316$	−32.0000	−1.80014
$317$	15.0000	0.842484	0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000	0.842484	0.421242	+	0.906948i	$0.361594\pi$
$318$	0	0
$319$	0	0
$320$	24.0000	1.34164
$321$	18.0000	1.00466
$322$	0	0
$323$	0	0
$324$	−2.00000	−0.111111
$325$	−8.00000	−0.443760
$326$	0	0
$327$	−2.00000	−0.110600
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−7.00000	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$332$	0	0
$333$	14.0000	0.767195
$334$	0	0
$335$	−33.0000	−1.80298
$336$	16.0000	0.872872
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	0	0
$339$	−9.00000	−0.488813
$340$	0	0
$341$	0	0
$342$	0	0
$343$	8.00000	0.431959
$344$	0	0
$345$	−9.00000	−0.484544
$346$	0	0
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	−12.0000	−0.643268
$349$	28.0000	1.49881	0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000	1.49881	0.749403	+	0.662114i	$0.230341\pi$
$350$	0	0
$351$	10.0000	0.533761
$352$	0	0
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	0	0
$355$	−45.0000	−2.38835
$356$	−18.0000	−0.953998
$357$	0	0
$358$	0	0
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	0	0
$364$	16.0000	0.838628
$365$	24.0000	1.25622
$366$	0	0
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	12.0000	0.625543
$369$	0	0
$370$	0	0
$371$	24.0000	1.24602
$372$	14.0000	0.725866
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	3.00000	0.154919
$376$	0	0
$377$	−12.0000	−0.618031
$378$	0	0
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	−6.00000	−0.307794
$381$	−2.00000	−0.102463
$382$	0	0
$383$	33.0000	1.68622	0.843111	−	0.537740i	$-0.180722\pi$
$383$	33.0000	1.68622	0.843111	+	0.537740i	$0.180722\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−20.0000	−1.01666
$388$	2.00000	0.101535
$389$	−3.00000	−0.152106	−0.0760530	−	0.997104i	$-0.524232\pi$
$389$	−3.00000	−0.152106	−0.0760530	+	0.997104i	$0.524232\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	6.00000	0.302660
$394$	0	0
$395$	−48.0000	−2.41514
$396$	0	0
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	0	0
$399$	−4.00000	−0.200250
$400$	16.0000	0.800000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	14.0000	0.697390
$404$	0	0
$405$	−3.00000	−0.149071
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	0	0
$411$	21.0000	1.03585
$412$	32.0000	1.57653
$413$	12.0000	0.590481
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−8.00000	−0.391762
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	24.0000	1.17108
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	40.0000	1.93574
$428$	−36.0000	−1.74013
$429$	0	0
$430$	0	0
$431$	6.00000	0.289010	0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	−20.0000	−0.962250
$433$	−13.0000	−0.624740	−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000	−0.624740	−0.312370	+	0.949960i	$0.601123\pi$
$434$	0	0
$435$	−18.0000	−0.863034
$436$	4.00000	0.191565
$437$	−3.00000	−0.143509
$438$	0	0
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	0	0
$441$	−18.0000	−0.857143
$442$	0	0
$443$	−27.0000	−1.28281	−0.641404	−	0.767203i	$-0.721648\pi$
$443$	−27.0000	−1.28281	−0.641404	+	0.767203i	$0.721648\pi$
$444$	14.0000	0.664411
$445$	−27.0000	−1.27992
$446$	0	0
$447$	6.00000	0.283790
$448$	−32.0000	−1.51186
$449$	−27.0000	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$450$	0	0
$451$	0	0
$452$	18.0000	0.846649
$453$	10.0000	0.469841
$454$	0	0
$455$	24.0000	1.12514
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	0	0
$459$	0	0
$460$	18.0000	0.839254
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	29.0000	1.34774	0.673872	−	0.738848i	$-0.264630\pi$
$463$	29.0000	1.34774	0.673872	+	0.738848i	$0.264630\pi$
$464$	24.0000	1.11417
$465$	21.0000	0.973852
$466$	0	0
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−8.00000	−0.369800
$469$	44.0000	2.03173
$470$	0	0
$471$	17.0000	0.783319
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	−12.0000	−0.549442
$478$	0	0
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	14.0000	0.638345
$482$	0	0
$483$	12.0000	0.546019
$484$	0	0
$485$	3.00000	0.136223
$486$	0	0
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	0	0
$489$	−4.00000	−0.180886
$490$	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
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−28.0000	−1.25724
$497$	60.0000	2.69137
$498$	0	0
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	−6.00000	−0.268328
$501$	18.0000	0.804181
$502$	0	0
$503$	−18.0000	−0.802580	−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000	−0.802580	−0.401290	+	0.915951i	$0.631438\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	4.00000	0.177471
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	−32.0000	−1.41560
$512$	0	0
$513$	5.00000	0.220755
$514$	0	0
$515$	48.0000	2.11513
$516$	−20.0000	−0.880451
$517$	0	0
$518$	0	0
$519$	−24.0000	−1.05348
$520$	0	0
$521$	39.0000	1.70862	0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000	1.70862	0.854311	+	0.519763i	$0.173980\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−12.0000	−0.524222
$525$	16.0000	0.698297
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	−6.00000	−0.260378
$532$	8.00000	0.346844
$533$	0	0
$534$	0	0
$535$	−54.0000	−2.33462
$536$	0	0
$537$	15.0000	0.647298
$538$	0	0
$539$	0	0
$540$	−30.0000	−1.29099
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	0	0
$543$	−7.00000	−0.300399
$544$	0	0
$545$	6.00000	0.257012
$546$	0	0
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	−42.0000	−1.79415
$549$	−20.0000	−0.853579
$550$	0	0
$551$	−6.00000	−0.255609
$552$	0	0
$553$	64.0000	2.72156
$554$	0	0
$555$	21.0000	0.891400
$556$	16.0000	0.678551
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	0	0
$559$	−20.0000	−0.845910
$560$	−48.0000	−2.02837
$561$	0	0
$562$	0	0
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	0	0
$565$	27.0000	1.13590
$566$	0	0
$567$	4.00000	0.167984
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	46.0000	1.92504	0.962520	−	0.271211i	$-0.0874240\pi$
$571$	46.0000	1.92504	0.962520	+	0.271211i	$0.0874240\pi$
$572$	0	0
$573$	−15.0000	−0.626634
$574$	0	0
$575$	12.0000	0.500435
$576$	16.0000	0.666667
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	0	0
$579$	4.00000	0.166234
$580$	36.0000	1.49482
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−12.0000	−0.496139
$586$	0	0
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	−18.0000	−0.742307
$589$	7.00000	0.288430
$590$	0	0
$591$	−12.0000	−0.493614
$592$	−28.0000	−1.15079
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−20.0000	−0.815817	−0.407909	−	0.913023i	$-0.633742\pi$
$601$	−20.0000	−0.815817	−0.407909	+	0.913023i	$0.633742\pi$
$602$	0	0
$603$	−22.0000	−0.895909
$604$	−20.0000	−0.813788
$605$	0	0
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	0	0
$609$	24.0000	0.972529
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	0	0
$619$	−13.0000	−0.522514	−0.261257	−	0.965269i	$-0.584137\pi$
$619$	−13.0000	−0.522514	−0.261257	+	0.965269i	$0.584137\pi$
$620$	−42.0000	−1.68676
$621$	−15.0000	−0.601929
$622$	0	0
$623$	36.0000	1.44231
$624$	−8.00000	−0.320256
$625$	−29.0000	−1.16000
$626$	0	0
$627$	0	0
$628$	−34.0000	−1.35675
$629$	0	0
$630$	0	0
$631$	−1.00000	−0.0398094	−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	−1.00000	−0.0398094	−0.0199047	+	0.999802i	$0.506336\pi$
$632$	0	0
$633$	22.0000	0.874421
$634$	0	0
$635$	6.00000	0.238103
$636$	−12.0000	−0.475831
$637$	−18.0000	−0.713186
$638$	0	0
$639$	−30.0000	−1.18678
$640$	0	0
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	0	0
$643$	−7.00000	−0.276053	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000	−0.276053	−0.138027	+	0.990429i	$0.544076\pi$
$644$	−24.0000	−0.945732
$645$	−30.0000	−1.18125
$646$	0	0
$647$	21.0000	0.825595	0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000	0.825595	0.412798	+	0.910823i	$0.364552\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−28.0000	−1.09741
$652$	8.00000	0.313304
$653$	27.0000	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	0	0
$655$	−18.0000	−0.703318
$656$	0	0
$657$	16.0000	0.624219
$658$	0	0
$659$	18.0000	0.701180	0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000	0.701180	0.350590	+	0.936529i	$0.385981\pi$
$660$	0	0
$661$	−13.0000	−0.505641	−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000	−0.505641	−0.252821	+	0.967513i	$0.581358\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	12.0000	0.465340
$666$	0	0
$667$	18.0000	0.696963
$668$	−36.0000	−1.39288
$669$	5.00000	0.193311
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	0	0
$675$	−20.0000	−0.769800
$676$	18.0000	0.692308
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	0	0
$681$	12.0000	0.459841
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−4.00000	−0.152944
$685$	−63.0000	−2.40711
$686$	0	0
$687$	−13.0000	−0.495981
$688$	40.0000	1.52499
$689$	−12.0000	−0.457164
$690$	0	0
$691$	17.0000	0.646710	0.323355	−	0.946278i	$-0.395189\pi$
$691$	17.0000	0.646710	0.323355	+	0.946278i	$0.395189\pi$
$692$	48.0000	1.82469
$693$	0	0
$694$	0	0
$695$	24.0000	0.910372
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−18.0000	−0.680823
$700$	−32.0000	−1.20949
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	7.00000	0.264010
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	−6.00000	−0.225494
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	0	0
$711$	−32.0000	−1.20009
$712$	0	0
$713$	−21.0000	−0.786456
$714$	0	0
$715$	0	0
$716$	−30.0000	−1.12115
$717$	18.0000	0.672222
$718$	0	0
$719$	−9.00000	−0.335643	−0.167822	−	0.985817i	$-0.553673\pi$
$719$	−9.00000	−0.335643	−0.167822	+	0.985817i	$0.553673\pi$
$720$	24.0000	0.894427
$721$	−64.0000	−2.38348
$722$	0	0
$723$	−20.0000	−0.743808
$724$	14.0000	0.520306
$725$	24.0000	0.891338
$726$	0	0
$727$	35.0000	1.29808	0.649039	−	0.760755i	$-0.275171\pi$
$727$	35.0000	1.29808	0.649039	+	0.760755i	$0.275171\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	−20.0000	−0.739221
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	0	0
$735$	−27.0000	−0.995910
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−44.0000	−1.61857	−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000	−1.61857	−0.809283	+	0.587419i	$0.800144\pi$
$740$	−42.0000	−1.54395
$741$	2.00000	0.0734718
$742$	0	0
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	−18.0000	−0.659469
$746$	0	0
$747$	0	0
$748$	0	0
$749$	72.0000	2.63082
$750$	0	0
$751$	−1.00000	−0.0364905	−0.0182453	−	0.999834i	$-0.505808\pi$
$751$	−1.00000	−0.0364905	−0.0182453	+	0.999834i	$0.505808\pi$
$752$	0	0
$753$	21.0000	0.765283
$754$	0	0
$755$	−30.0000	−1.09181
$756$	40.0000	1.45479
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	−8.00000	−0.289619
$764$	30.0000	1.08536
$765$	0	0
$766$	0	0
$767$	−6.00000	−0.216647
$768$	16.0000	0.577350
$769$	28.0000	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	−8.00000	−0.287926
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−28.0000	−1.00579
$776$	0	0
$777$	−28.0000	−1.00449
$778$	0	0
$779$	0	0
$780$	−12.0000	−0.429669
$781$	0	0
$782$	0	0
$783$	−30.0000	−1.07211
$784$	36.0000	1.28571
$785$	−51.0000	−1.82027
$786$	0	0
$787$	−20.0000	−0.712923	−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000	−0.712923	−0.356462	+	0.934310i	$0.616017\pi$
$788$	24.0000	0.854965
$789$	30.0000	1.06803
$790$	0	0
$791$	−36.0000	−1.28001
$792$	0	0
$793$	−20.0000	−0.710221
$794$	0	0
$795$	−18.0000	−0.638394
$796$	32.0000	1.13421
$797$	51.0000	1.80651	0.903256	−	0.429101i	$-0.141170\pi$
$797$	51.0000	1.80651	0.903256	+	0.429101i	$0.141170\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−18.0000	−0.635999
$802$	0	0
$803$	0	0
$804$	−22.0000	−0.775880
$805$	−36.0000	−1.26883
$806$	0	0
$807$	−30.0000	−1.05605
$808$	0	0
$809$	24.0000	0.843795	0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000	0.843795	0.421898	+	0.906644i	$0.361364\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	−48.0000	−1.68447
$813$	16.0000	0.561144
$814$	0	0
$815$	12.0000	0.420342
$816$	0	0
$817$	−10.0000	−0.349856
$818$	0	0
$819$	16.0000	0.559085
$820$	0	0
$821$	−36.0000	−1.25641	−0.628204	−	0.778048i	$-0.716210\pi$
$821$	−36.0000	−1.25641	−0.628204	+	0.778048i	$0.716210\pi$
$822$	0	0
$823$	−13.0000	−0.453152	−0.226576	−	0.973994i	$-0.572753\pi$
$823$	−13.0000	−0.453152	−0.226576	+	0.973994i	$0.572753\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	42.0000	1.46048	0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000	1.46048	0.730242	+	0.683189i	$0.239408\pi$
$828$	12.0000	0.417029
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	0	0
$831$	−26.0000	−0.901930
$832$	16.0000	0.554700
$833$	0	0
$834$	0	0
$835$	−54.0000	−1.86875
$836$	0	0
$837$	35.0000	1.20978
$838$	0	0
$839$	33.0000	1.13929	0.569643	−	0.821892i	$-0.307081\pi$
$839$	33.0000	1.13929	0.569643	+	0.821892i	$0.307081\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	30.0000	1.03325
$844$	−44.0000	−1.51454
$845$	27.0000	0.928828
$846$	0	0
$847$	0	0
$848$	24.0000	0.824163
$849$	−14.0000	−0.480479
$850$	0	0
$851$	−21.0000	−0.719871
$852$	−30.0000	−1.02778
$853$	22.0000	0.753266	0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000	0.753266	0.376633	+	0.926363i	$0.377082\pi$
$854$	0	0
$855$	−6.00000	−0.205196
$856$	0	0
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	5.00000	0.170598	0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000	0.170598	0.0852989	+	0.996355i	$0.472815\pi$
$860$	60.0000	2.04598
$861$	0	0
$862$	0	0
$863$	−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
$865$	72.0000	2.44807
$866$	0	0
$867$	−17.0000	−0.577350
$868$	56.0000	1.90076
$869$	0	0
$870$	0	0
$871$	−22.0000	−0.745442
$872$	0	0
$873$	2.00000	0.0676897
$874$	0	0
$875$	12.0000	0.405674
$876$	16.0000	0.540590
$877$	4.00000	0.135070	0.0675352	−	0.997717i	$-0.478487\pi$
$877$	4.00000	0.135070	0.0675352	+	0.997717i	$0.478487\pi$
$878$	0	0
$879$	−18.0000	−0.607125
$880$	0	0
$881$	9.00000	0.303218	0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000	0.303218	0.151609	+	0.988441i	$0.451555\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	0	0
$885$	−9.00000	−0.302532
$886$	0	0
$887$	−54.0000	−1.81314	−0.906571	−	0.422053i	$-0.861310\pi$
$887$	−54.0000	−1.81314	−0.906571	+	0.422053i	$0.861310\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	0	0
$892$	−10.0000	−0.334825
$893$	0	0
$894$	0	0
$895$	−45.0000	−1.50418
$896$	0	0
$897$	−6.00000	−0.200334
$898$	0	0
$899$	−42.0000	−1.40078
$900$	16.0000	0.533333
$901$	0	0
$902$	0	0
$903$	40.0000	1.33112
$904$	0	0
$905$	21.0000	0.698064
$906$	0	0
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	−24.0000	−0.796468
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	0	0
$915$	−30.0000	−0.991769
$916$	26.0000	0.859064
$917$	24.0000	0.792550
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	−2.00000	−0.0659022
$922$	0	0
$923$	−30.0000	−0.987462
$924$	0	0
$925$	−28.0000	−0.920634
$926$	0	0
$927$	32.0000	1.05102
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	−9.00000	−0.294963
$932$	36.0000	1.17922
$933$	−24.0000	−0.785725
$934$	0	0
$935$	0	0
$936$	0	0
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	0	0
$939$	−1.00000	−0.0326338
$940$	0	0
$941$	24.0000	0.782378	0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000	0.782378	0.391189	+	0.920310i	$0.372064\pi$
$942$	0	0
$943$	0	0
$944$	12.0000	0.390567
$945$	60.0000	1.95180
$946$	0	0
$947$	−3.00000	−0.0974869	−0.0487435	−	0.998811i	$-0.515522\pi$
$947$	−3.00000	−0.0974869	−0.0487435	+	0.998811i	$0.515522\pi$
$948$	−32.0000	−1.03931
$949$	16.0000	0.519382
$950$	0	0
$951$	15.0000	0.486408
$952$	0	0
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	0	0
$955$	45.0000	1.45617
$956$	−36.0000	−1.16432
$957$	0	0
$958$	0	0
$959$	84.0000	2.71250
$960$	24.0000	0.774597
$961$	18.0000	0.580645
$962$	0	0
$963$	−36.0000	−1.16008
$964$	40.0000	1.28831
$965$	−12.0000	−0.386294
$966$	0	0
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−15.0000	−0.481373	−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000	−0.481373	−0.240686	+	0.970603i	$0.577373\pi$
$972$	−32.0000	−1.02640
$973$	−32.0000	−1.02587
$974$	0	0
$975$	−8.00000	−0.256205
$976$	40.0000	1.28037
$977$	−9.00000	−0.287936	−0.143968	−	0.989582i	$-0.545986\pi$
$977$	−9.00000	−0.287936	−0.143968	+	0.989582i	$0.545986\pi$
$978$	0	0
$979$	0	0
$980$	54.0000	1.72497
$981$	4.00000	0.127710
$982$	0	0
$983$	−15.0000	−0.478426	−0.239213	−	0.970967i	$-0.576889\pi$
$983$	−15.0000	−0.478426	−0.239213	+	0.970967i	$0.576889\pi$
$984$	0	0
$985$	36.0000	1.14706
$986$	0	0
$987$	0	0
$988$	−4.00000	−0.127257
$989$	30.0000	0.953945
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	0	0
$993$	−7.00000	−0.222138
$994$	0	0
$995$	48.0000	1.52170
$996$	0	0
$997$	40.0000	1.26681	0.633406	−	0.773819i	$-0.281656\pi$
$997$	40.0000	1.26681	0.633406	+	0.773819i	$0.281656\pi$
$998$	0	0
$999$	35.0000	1.10735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.c.1.1		1
11.10	odd	2		209.2.a.a.1.1	✓	1
33.32	even	2		1881.2.a.c.1.1		1
44.43	even	2		3344.2.a.d.1.1		1
55.54	odd	2		5225.2.a.b.1.1		1
209.208	even	2		3971.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.a.1.1	✓	1	11.10	odd	2
1881.2.a.c.1.1		1	33.32	even	2
2299.2.a.c.1.1		1	1.1	even	1	trivial
3344.2.a.d.1.1		1	44.43	even	2
3971.2.a.a.1.1		1	209.208	even	2
5225.2.a.b.1.1		1	55.54	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:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

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