LMFDB - Embedded newform 585.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +O(q^{10})$

$q-2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +2.00000 q^{10} +1.00000 q^{11} -1.00000 q^{13} -6.00000 q^{14} -4.00000 q^{16} +1.00000 q^{17} -2.00000 q^{19} -2.00000 q^{20} -2.00000 q^{22} +3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +6.00000 q^{28} +2.00000 q^{29} -6.00000 q^{31} +8.00000 q^{32} -2.00000 q^{34} -3.00000 q^{35} +11.0000 q^{37} +4.00000 q^{38} +5.00000 q^{41} +4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} +10.0000 q^{47} +2.00000 q^{49} -2.00000 q^{50} -2.00000 q^{52} -11.0000 q^{53} -1.00000 q^{55} -4.00000 q^{58} -8.00000 q^{59} +13.0000 q^{61} +12.0000 q^{62} -8.00000 q^{64} +1.00000 q^{65} +12.0000 q^{67} +2.00000 q^{68} +6.00000 q^{70} +5.00000 q^{71} +10.0000 q^{73} -22.0000 q^{74} -4.00000 q^{76} +3.00000 q^{77} -3.00000 q^{79} +4.00000 q^{80} -10.0000 q^{82} +12.0000 q^{83} -1.00000 q^{85} -8.00000 q^{86} +15.0000 q^{89} -3.00000 q^{91} +6.00000 q^{92} -20.0000 q^{94} +2.00000 q^{95} +17.0000 q^{97} -4.00000 q^{98} +O(q^{100})$

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	0	0
$9$	0	0
$10$	2.00000	0.632456
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−6.00000	−1.60357
$15$	0	0
$16$	−4.00000	−1.00000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	−2.00000	−0.426401
$23$	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
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	6.00000	1.13389
$29$	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
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−3.00000	−0.507093
$36$	0	0
$37$	11.0000	1.80839	0.904194	−	0.427121i	$-0.140472\pi$
$37$	11.0000	1.80839	0.904194	+	0.427121i	$0.140472\pi$
$38$	4.00000	0.648886
$39$	0	0
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	−2.00000	−0.282843
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−11.0000	−1.51097	−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000	−1.51097	−0.755483	+	0.655168i	$0.772598\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	−4.00000	−0.525226
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	12.0000	1.52400
$63$	0	0
$64$	−8.00000	−1.00000
$65$	1.00000	0.124035
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	6.00000	0.717137
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−22.0000	−2.55745
$75$	0	0
$76$	−4.00000	−0.458831
$77$	3.00000	0.341882
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	−10.0000	−1.10432
$83$	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
$85$	−1.00000	−0.108465
$86$	−8.00000	−0.862662
$87$	0	0
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	6.00000	0.625543
$93$	0	0
$94$	−20.0000	−2.06284
$95$	2.00000	0.205196
$96$	0	0
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	−4.00000	−0.404061
$99$	0	0
$100$	2.00000	0.200000
$101$	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
$105$	0	0
$106$	22.0000	2.13683
$107$	−9.00000	−0.870063	−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000	−0.870063	−0.435031	+	0.900415i	$0.643263\pi$
$108$	0	0
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	−12.0000	−1.13389
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	−3.00000	−0.279751
$116$	4.00000	0.371391
$117$	0	0
$118$	16.0000	1.47292
$119$	3.00000	0.275010
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−26.0000	−2.35393
$123$	0	0
$124$	−12.0000	−1.07763
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	10.0000	0.887357	0.443678	−	0.896186i	$-0.353673\pi$
$127$	10.0000	0.887357	0.443678	+	0.896186i	$0.353673\pi$
$128$	0	0
$129$	0	0
$130$	−2.00000	−0.175412
$131$	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
$133$	−6.00000	−0.520266
$134$	−24.0000	−2.07328
$135$	0	0
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	−6.00000	−0.507093
$141$	0	0
$142$	−10.0000	−0.839181
$143$	−1.00000	−0.0836242
$144$	0	0
$145$	−2.00000	−0.166091
$146$	−20.0000	−1.65521
$147$	0	0
$148$	22.0000	1.80839
$149$	−13.0000	−1.06500	−0.532501	−	0.846430i	$-0.678748\pi$
$149$	−13.0000	−1.06500	−0.532501	+	0.846430i	$0.678748\pi$
$150$	0	0
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	0	0
$153$	0	0
$154$	−6.00000	−0.483494
$155$	6.00000	0.481932
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	−8.00000	−0.632456
$161$	9.00000	0.709299
$162$	0	0
$163$	−13.0000	−1.01824	−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000	−1.01824	−0.509119	+	0.860696i	$0.670029\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−24.0000	−1.86276
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.00000	0.153393
$171$	0	0
$172$	8.00000	0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	3.00000	0.226779
$176$	−4.00000	−0.301511
$177$	0	0
$178$	−30.0000	−2.24860
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0	0
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	6.00000	0.444750
$183$	0	0
$184$	0	0
$185$	−11.0000	−0.808736
$186$	0	0
$187$	1.00000	0.0731272
$188$	20.0000	1.45865
$189$	0	0
$190$	−4.00000	−0.290191
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	−34.0000	−2.44106
$195$	0	0
$196$	4.00000	0.285714
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	6.00000	0.421117
$204$	0	0
$205$	−5.00000	−0.349215
$206$	32.0000	2.22955
$207$	0	0
$208$	4.00000	0.277350
$209$	−2.00000	−0.138343
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−22.0000	−1.51097
$213$	0	0
$214$	18.0000	1.23045
$215$	−4.00000	−0.272798
$216$	0	0
$217$	−18.0000	−1.22192
$218$	32.0000	2.16731
$219$	0	0
$220$	−2.00000	−0.134840
$221$	−1.00000	−0.0672673
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	24.0000	1.60357
$225$	0	0
$226$	28.0000	1.86253
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	0	0
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	0	0
$233$	27.0000	1.76883	0.884414	−	0.466702i	$-0.154558\pi$
$233$	27.0000	1.76883	0.884414	+	0.466702i	$0.154558\pi$
$234$	0	0
$235$	−10.0000	−0.652328
$236$	−16.0000	−1.04151
$237$	0	0
$238$	−6.00000	−0.388922
$239$	13.0000	0.840900	0.420450	−	0.907316i	$-0.361872\pi$
$239$	13.0000	0.840900	0.420450	+	0.907316i	$0.361872\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	20.0000	1.28565
$243$	0	0
$244$	26.0000	1.66448
$245$	−2.00000	−0.127775
$246$	0	0
$247$	2.00000	0.127257
$248$	0	0
$249$	0	0
$250$	2.00000	0.126491
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	3.00000	0.188608
$254$	−20.0000	−1.25491
$255$	0	0
$256$	16.0000	1.00000
$257$	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
$259$	33.0000	2.05052
$260$	2.00000	0.124035
$261$	0	0
$262$	−12.0000	−0.741362
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	11.0000	0.675725
$266$	12.0000	0.735767
$267$	0	0
$268$	24.0000	1.46603
$269$	4.00000	0.243884	0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000	0.243884	0.121942	+	0.992537i	$0.461088\pi$
$270$	0	0
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	36.0000	2.17484
$275$	1.00000	0.0603023
$276$	0	0
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	2.00000	0.119952
$279$	0	0
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	10.0000	0.593391
$285$	0	0
$286$	2.00000	0.118262
$287$	15.0000	0.885422
$288$	0	0
$289$	−16.0000	−0.941176
$290$	4.00000	0.234888
$291$	0	0
$292$	20.0000	1.17041
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	8.00000	0.465778
$296$	0	0
$297$	0	0
$298$	26.0000	1.50614
$299$	−3.00000	−0.173494
$300$	0	0
$301$	12.0000	0.691669
$302$	−32.0000	−1.84139
$303$	0	0
$304$	8.00000	0.458831
$305$	−13.0000	−0.744378
$306$	0	0
$307$	−5.00000	−0.285365	−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000	−0.285365	−0.142683	+	0.989769i	$0.545573\pi$
$308$	6.00000	0.341882
$309$	0	0
$310$	−12.0000	−0.681554
$311$	−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
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	20.0000	1.12867
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−28.0000	−1.57264	−0.786318	−	0.617822i	$-0.788015\pi$
$317$	−28.0000	−1.57264	−0.786318	+	0.617822i	$0.788015\pi$
$318$	0	0
$319$	2.00000	0.111979
$320$	8.00000	0.447214
$321$	0	0
$322$	−18.0000	−1.00310
$323$	−2.00000	−0.111283
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	26.0000	1.44001
$327$	0	0
$328$	0	0
$329$	30.0000	1.65395
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	24.0000	1.31717
$333$	0	0
$334$	−24.0000	−1.31322
$335$	−12.0000	−0.655630
$336$	0	0
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	−2.00000	−0.108786
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−6.00000	−0.324918
$342$	0	0
$343$	−15.0000	−0.809924
$344$	0	0
$345$	0	0
$346$	−12.0000	−0.645124
$347$	19.0000	1.01997	0.509987	−	0.860182i	$-0.329650\pi$
$347$	19.0000	1.01997	0.509987	+	0.860182i	$0.329650\pi$
$348$	0	0
$349$	−8.00000	−0.428230	−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000	−0.428230	−0.214115	+	0.976808i	$0.568687\pi$
$350$	−6.00000	−0.320713
$351$	0	0
$352$	8.00000	0.426401
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−5.00000	−0.265372
$356$	30.0000	1.59000
$357$	0	0
$358$	4.00000	0.211407
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	14.0000	0.735824
$363$	0	0
$364$	−6.00000	−0.314485
$365$	−10.0000	−0.523424
$366$	0	0
$367$	36.0000	1.87918	0.939592	−	0.342296i	$-0.111204\pi$
$367$	36.0000	1.87918	0.939592	+	0.342296i	$0.111204\pi$
$368$	−12.0000	−0.625543
$369$	0	0
$370$	22.0000	1.14373
$371$	−33.0000	−1.71327
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	0	0
$377$	−2.00000	−0.103005
$378$	0	0
$379$	−14.0000	−0.719132	−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000	−0.719132	−0.359566	+	0.933120i	$0.617075\pi$
$380$	4.00000	0.205196
$381$	0	0
$382$	−16.0000	−0.818631
$383$	30.0000	1.53293	0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000	1.53293	0.766464	+	0.642287i	$0.222014\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	26.0000	1.32337
$387$	0	0
$388$	34.0000	1.72609
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	3.00000	0.151717
$392$	0	0
$393$	0	0
$394$	0	0
$395$	3.00000	0.150946
$396$	0	0
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	6.00000	0.298881
$404$	0	0
$405$	0	0
$406$	−12.0000	−0.595550
$407$	11.0000	0.545250
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	10.0000	0.493865
$411$	0	0
$412$	−32.0000	−1.57653
$413$	−24.0000	−1.18096
$414$	0	0
$415$	−12.0000	−0.589057
$416$	−8.00000	−0.392232
$417$	0	0
$418$	4.00000	0.195646
$419$	26.0000	1.27018	0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000	1.27018	0.635092	+	0.772437i	$0.280962\pi$
$420$	0	0
$421$	4.00000	0.194948	0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000	0.194948	0.0974740	+	0.995238i	$0.468924\pi$
$422$	8.00000	0.389434
$423$	0	0
$424$	0	0
$425$	1.00000	0.0485071
$426$	0	0
$427$	39.0000	1.88734
$428$	−18.0000	−0.870063
$429$	0	0
$430$	8.00000	0.385794
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	0	0
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	36.0000	1.72806
$435$	0	0
$436$	−32.0000	−1.53252
$437$	−6.00000	−0.287019
$438$	0	0
$439$	−17.0000	−0.811366	−0.405683	−	0.914014i	$-0.632966\pi$
$439$	−17.0000	−0.811366	−0.405683	+	0.914014i	$0.632966\pi$
$440$	0	0
$441$	0	0
$442$	2.00000	0.0951303
$443$	−9.00000	−0.427603	−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000	−0.427603	−0.213801	+	0.976877i	$0.568585\pi$
$444$	0	0
$445$	−15.0000	−0.711068
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−24.0000	−1.13389
$449$	13.0000	0.613508	0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000	0.613508	0.306754	+	0.951789i	$0.400757\pi$
$450$	0	0
$451$	5.00000	0.235441
$452$	−28.0000	−1.31701
$453$	0	0
$454$	44.0000	2.06502
$455$	3.00000	0.140642
$456$	0	0
$457$	−11.0000	−0.514558	−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000	−0.514558	−0.257279	+	0.966337i	$0.582826\pi$
$458$	−36.0000	−1.68217
$459$	0	0
$460$	−6.00000	−0.279751
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	0	0
$463$	27.0000	1.25480	0.627398	−	0.778699i	$-0.284120\pi$
$463$	27.0000	1.25480	0.627398	+	0.778699i	$0.284120\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−54.0000	−2.50150
$467$	23.0000	1.06431	0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000	1.06431	0.532157	+	0.846646i	$0.321382\pi$
$468$	0	0
$469$	36.0000	1.66233
$470$	20.0000	0.922531
$471$	0	0
$472$	0	0
$473$	4.00000	0.183920
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	6.00000	0.275010
$477$	0	0
$478$	−26.0000	−1.18921
$479$	−9.00000	−0.411220	−0.205610	−	0.978634i	$-0.565918\pi$
$479$	−9.00000	−0.411220	−0.205610	+	0.978634i	$0.565918\pi$
$480$	0	0
$481$	−11.0000	−0.501557
$482$	4.00000	0.182195
$483$	0	0
$484$	−20.0000	−0.909091
$485$	−17.0000	−0.771930
$486$	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
$489$	0	0
$490$	4.00000	0.180702
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	0	0
$493$	2.00000	0.0900755
$494$	−4.00000	−0.179969
$495$	0	0
$496$	24.0000	1.07763
$497$	15.0000	0.672842
$498$	0	0
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	−2.00000	−0.0894427
$501$	0	0
$502$	0	0
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	0	0
$505$	0	0
$506$	−6.00000	−0.266733
$507$	0	0
$508$	20.0000	0.887357
$509$	7.00000	0.310270	0.155135	−	0.987893i	$-0.450419\pi$
$509$	7.00000	0.310270	0.155135	+	0.987893i	$0.450419\pi$
$510$	0	0
$511$	30.0000	1.32712
$512$	−32.0000	−1.41421
$513$	0	0
$514$	−36.0000	−1.58789
$515$	16.0000	0.705044
$516$	0	0
$517$	10.0000	0.439799
$518$	−66.0000	−2.89987
$519$	0	0
$520$	0	0
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	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
$525$	0	0
$526$	−16.0000	−0.697633
$527$	−6.00000	−0.261364
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−22.0000	−0.955619
$531$	0	0
$532$	−12.0000	−0.520266
$533$	−5.00000	−0.216574
$534$	0	0
$535$	9.00000	0.389104
$536$	0	0
$537$	0	0
$538$	−8.00000	−0.344904
$539$	2.00000	0.0861461
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−44.0000	−1.88996
$543$	0	0
$544$	8.00000	0.342997
$545$	16.0000	0.685365
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−36.0000	−1.53784
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	−4.00000	−0.170406
$552$	0	0
$553$	−9.00000	−0.382719
$554$	36.0000	1.52949
$555$	0	0
$556$	−2.00000	−0.0848189
$557$	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
$559$	−4.00000	−0.169182
$560$	12.0000	0.507093
$561$	0	0
$562$	60.0000	2.53095
$563$	−21.0000	−0.885044	−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000	−0.885044	−0.442522	+	0.896758i	$0.645916\pi$
$564$	0	0
$565$	14.0000	0.588984
$566$	24.0000	1.00880
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	−31.0000	−1.29731	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−31.0000	−1.29731	−0.648655	+	0.761083i	$0.724668\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	−30.0000	−1.25218
$575$	3.00000	0.125109
$576$	0	0
$577$	−19.0000	−0.790980	−0.395490	−	0.918470i	$-0.629425\pi$
$577$	−19.0000	−0.790980	−0.395490	+	0.918470i	$0.629425\pi$
$578$	32.0000	1.33102
$579$	0	0
$580$	−4.00000	−0.166091
$581$	36.0000	1.49353
$582$	0	0
$583$	−11.0000	−0.455573
$584$	0	0
$585$	0	0
$586$	48.0000	1.98286
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	12.0000	0.494451
$590$	−16.0000	−0.658710
$591$	0	0
$592$	−44.0000	−1.80839
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	−26.0000	−1.06500
$597$	0	0
$598$	6.00000	0.245358
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	0	0
$601$	−37.0000	−1.50926	−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000	−1.50926	−0.754631	+	0.656150i	$0.772184\pi$
$602$	−24.0000	−0.978167
$603$	0	0
$604$	32.0000	1.30206
$605$	10.0000	0.406558
$606$	0	0
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−16.0000	−0.648886
$609$	0	0
$610$	26.0000	1.05271
$611$	−10.0000	−0.404557
$612$	0	0
$613$	13.0000	0.525065	0.262533	−	0.964923i	$-0.415442\pi$
$613$	13.0000	0.525065	0.262533	+	0.964923i	$0.415442\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	0	0
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	0	0
$619$	−34.0000	−1.36658	−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000	−1.36658	−0.683288	+	0.730149i	$0.739451\pi$
$620$	12.0000	0.481932
$621$	0	0
$622$	48.0000	1.92462
$623$	45.0000	1.80289
$624$	0	0
$625$	1.00000	0.0400000
$626$	20.0000	0.799361
$627$	0	0
$628$	−20.0000	−0.798087
$629$	11.0000	0.438599
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	0	0
$633$	0	0
$634$	56.0000	2.22404
$635$	−10.0000	−0.396838
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	−4.00000	−0.158362
$639$	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
$643$	15.0000	0.591542	0.295771	−	0.955259i	$-0.404423\pi$
$643$	15.0000	0.591542	0.295771	+	0.955259i	$0.404423\pi$
$644$	18.0000	0.709299
$645$	0	0
$646$	4.00000	0.157378
$647$	−47.0000	−1.84776	−0.923880	−	0.382682i	$-0.875001\pi$
$647$	−47.0000	−1.84776	−0.923880	+	0.382682i	$0.875001\pi$
$648$	0	0
$649$	−8.00000	−0.314027
$650$	2.00000	0.0784465
$651$	0	0
$652$	−26.0000	−1.01824
$653$	−22.0000	−0.860927	−0.430463	−	0.902608i	$-0.641650\pi$
$653$	−22.0000	−0.860927	−0.430463	+	0.902608i	$0.641650\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	−20.0000	−0.780869
$657$	0	0
$658$	−60.0000	−2.33904
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	6.00000	0.232670
$666$	0	0
$667$	6.00000	0.232321
$668$	24.0000	0.928588
$669$	0	0
$670$	24.0000	0.927201
$671$	13.0000	0.501859
$672$	0	0
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	2.00000	0.0769231
$677$	−3.00000	−0.115299	−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000	−0.115299	−0.0576497	+	0.998337i	$0.518361\pi$
$678$	0	0
$679$	51.0000	1.95720
$680$	0	0
$681$	0	0
$682$	12.0000	0.459504
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	0	0
$685$	18.0000	0.687745
$686$	30.0000	1.14541
$687$	0	0
$688$	−16.0000	−0.609994
$689$	11.0000	0.419067
$690$	0	0
$691$	22.0000	0.836919	0.418460	−	0.908235i	$-0.362570\pi$
$691$	22.0000	0.836919	0.418460	+	0.908235i	$0.362570\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	−38.0000	−1.44246
$695$	1.00000	0.0379322
$696$	0	0
$697$	5.00000	0.189389
$698$	16.0000	0.605609
$699$	0	0
$700$	6.00000	0.226779
$701$	20.0000	0.755390	0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000	0.755390	0.377695	+	0.925930i	$0.376717\pi$
$702$	0	0
$703$	−22.0000	−0.829746
$704$	−8.00000	−0.301511
$705$	0	0
$706$	12.0000	0.451626
$707$	0	0
$708$	0	0
$709$	4.00000	0.150223	0.0751116	−	0.997175i	$-0.476069\pi$
$709$	4.00000	0.150223	0.0751116	+	0.997175i	$0.476069\pi$
$710$	10.0000	0.375293
$711$	0	0
$712$	0	0
$713$	−18.0000	−0.674105
$714$	0	0
$715$	1.00000	0.0373979
$716$	−4.00000	−0.149487
$717$	0	0
$718$	48.0000	1.79134
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	−48.0000	−1.78761
$722$	30.0000	1.11648
$723$	0	0
$724$	−14.0000	−0.520306
$725$	2.00000	0.0742781
$726$	0	0
$727$	38.0000	1.40934	0.704671	−	0.709534i	$-0.251095\pi$
$727$	38.0000	1.40934	0.704671	+	0.709534i	$0.251095\pi$
$728$	0	0
$729$	0	0
$730$	20.0000	0.740233
$731$	4.00000	0.147945
$732$	0	0
$733$	−49.0000	−1.80986	−0.904928	−	0.425564i	$-0.860076\pi$
$733$	−49.0000	−1.80986	−0.904928	+	0.425564i	$0.860076\pi$
$734$	−72.0000	−2.65757
$735$	0	0
$736$	24.0000	0.884652
$737$	12.0000	0.442026
$738$	0	0
$739$	10.0000	0.367856	0.183928	−	0.982940i	$-0.441119\pi$
$739$	10.0000	0.367856	0.183928	+	0.982940i	$0.441119\pi$
$740$	−22.0000	−0.808736
$741$	0	0
$742$	66.0000	2.42294
$743$	34.0000	1.24734	0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000	1.24734	0.623670	+	0.781688i	$0.285641\pi$
$744$	0	0
$745$	13.0000	0.476283
$746$	−8.00000	−0.292901
$747$	0	0
$748$	2.00000	0.0731272
$749$	−27.0000	−0.986559
$750$	0	0
$751$	−5.00000	−0.182453	−0.0912263	−	0.995830i	$-0.529079\pi$
$751$	−5.00000	−0.182453	−0.0912263	+	0.995830i	$0.529079\pi$
$752$	−40.0000	−1.45865
$753$	0	0
$754$	4.00000	0.145671
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	−48.0000	−1.73772
$764$	16.0000	0.578860
$765$	0	0
$766$	−60.0000	−2.16789
$767$	8.00000	0.288863
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	6.00000	0.216225
$771$	0	0
$772$	−26.0000	−0.935760
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	0	0
$775$	−6.00000	−0.215526
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−10.0000	−0.358287
$780$	0	0
$781$	5.00000	0.178914
$782$	−6.00000	−0.214560
$783$	0	0
$784$	−8.00000	−0.285714
$785$	10.0000	0.356915
$786$	0	0
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	0	0
$789$	0	0
$790$	−6.00000	−0.213470
$791$	−42.0000	−1.49335
$792$	0	0
$793$	−13.0000	−0.461644
$794$	58.0000	2.05834
$795$	0	0
$796$	8.00000	0.283552
$797$	47.0000	1.66483	0.832413	−	0.554156i	$-0.186959\pi$
$797$	47.0000	1.66483	0.832413	+	0.554156i	$0.186959\pi$
$798$	0	0
$799$	10.0000	0.353775
$800$	8.00000	0.282843
$801$	0	0
$802$	60.0000	2.11867
$803$	10.0000	0.352892
$804$	0	0
$805$	−9.00000	−0.317208
$806$	−12.0000	−0.422682
$807$	0	0
$808$	0	0
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	0	0
$811$	36.0000	1.26413	0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000	1.26413	0.632065	+	0.774915i	$0.282207\pi$
$812$	12.0000	0.421117
$813$	0	0
$814$	−22.0000	−0.771100
$815$	13.0000	0.455370
$816$	0	0
$817$	−8.00000	−0.279885
$818$	−4.00000	−0.139857
$819$	0	0
$820$	−10.0000	−0.349215
$821$	−27.0000	−0.942306	−0.471153	−	0.882051i	$-0.656162\pi$
$821$	−27.0000	−0.942306	−0.471153	+	0.882051i	$0.656162\pi$
$822$	0	0
$823$	20.0000	0.697156	0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000	0.697156	0.348578	+	0.937280i	$0.386665\pi$
$824$	0	0
$825$	0	0
$826$	48.0000	1.67013
$827$	−26.0000	−0.904109	−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000	−0.904109	−0.452054	+	0.891990i	$0.649309\pi$
$828$	0	0
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	24.0000	0.833052
$831$	0	0
$832$	8.00000	0.277350
$833$	2.00000	0.0692959
$834$	0	0
$835$	−12.0000	−0.415277
$836$	−4.00000	−0.138343
$837$	0	0
$838$	−52.0000	−1.79631
$839$	5.00000	0.172619	0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000	0.172619	0.0863096	+	0.996268i	$0.472493\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−8.00000	−0.275698
$843$	0	0
$844$	−8.00000	−0.275371
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	−30.0000	−1.03081
$848$	44.0000	1.51097
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	33.0000	1.13123
$852$	0	0
$853$	45.0000	1.54077	0.770385	−	0.637579i	$-0.220064\pi$
$853$	45.0000	1.54077	0.770385	+	0.637579i	$0.220064\pi$
$854$	−78.0000	−2.66911
$855$	0	0
$856$	0	0
$857$	−29.0000	−0.990621	−0.495311	−	0.868716i	$-0.664946\pi$
$857$	−29.0000	−0.990621	−0.495311	+	0.868716i	$0.664946\pi$
$858$	0	0
$859$	−29.0000	−0.989467	−0.494734	−	0.869045i	$-0.664734\pi$
$859$	−29.0000	−0.989467	−0.494734	+	0.869045i	$0.664734\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−48.0000	−1.63489
$863$	−34.0000	−1.15737	−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000	−1.15737	−0.578687	+	0.815550i	$0.696435\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	−8.00000	−0.271851
$867$	0	0
$868$	−36.0000	−1.22192
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−12.0000	−0.406604
$872$	0	0
$873$	0	0
$874$	12.0000	0.405906
$875$	−3.00000	−0.101419
$876$	0	0
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	34.0000	1.14744
$879$	0	0
$880$	4.00000	0.134840
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	18.0000	0.604722
$887$	21.0000	0.705111	0.352555	−	0.935791i	$-0.385313\pi$
$887$	21.0000	0.705111	0.352555	+	0.935791i	$0.385313\pi$
$888$	0	0
$889$	30.0000	1.00617
$890$	30.0000	1.00560
$891$	0	0
$892$	16.0000	0.535720
$893$	−20.0000	−0.669274
$894$	0	0
$895$	2.00000	0.0668526
$896$	0	0
$897$	0	0
$898$	−26.0000	−0.867631
$899$	−12.0000	−0.400222
$900$	0	0
$901$	−11.0000	−0.366463
$902$	−10.0000	−0.332964
$903$	0	0
$904$	0	0
$905$	7.00000	0.232688
$906$	0	0
$907$	6.00000	0.199227	0.0996134	−	0.995026i	$-0.468239\pi$
$907$	6.00000	0.199227	0.0996134	+	0.995026i	$0.468239\pi$
$908$	−44.0000	−1.46019
$909$	0	0
$910$	−6.00000	−0.198898
$911$	−44.0000	−1.45779	−0.728893	−	0.684628i	$-0.759965\pi$
$911$	−44.0000	−1.45779	−0.728893	+	0.684628i	$0.759965\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	22.0000	0.727695
$915$	0	0
$916$	36.0000	1.18947
$917$	18.0000	0.594412
$918$	0	0
$919$	37.0000	1.22052	0.610259	−	0.792202i	$-0.291065\pi$
$919$	37.0000	1.22052	0.610259	+	0.792202i	$0.291065\pi$
$920$	0	0
$921$	0	0
$922$	30.0000	0.987997
$923$	−5.00000	−0.164577
$924$	0	0
$925$	11.0000	0.361678
$926$	−54.0000	−1.77455
$927$	0	0
$928$	16.0000	0.525226
$929$	−1.00000	−0.0328089	−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000	−0.0328089	−0.0164045	+	0.999865i	$0.505222\pi$
$930$	0	0
$931$	−4.00000	−0.131095
$932$	54.0000	1.76883
$933$	0	0
$934$	−46.0000	−1.50517
$935$	−1.00000	−0.0327035
$936$	0	0
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	−72.0000	−2.35088
$939$	0	0
$940$	−20.0000	−0.652328
$941$	−37.0000	−1.20617	−0.603083	−	0.797679i	$-0.706061\pi$
$941$	−37.0000	−1.20617	−0.603083	+	0.797679i	$0.706061\pi$
$942$	0	0
$943$	15.0000	0.488467
$944$	32.0000	1.04151
$945$	0	0
$946$	−8.00000	−0.260102
$947$	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
$949$	−10.0000	−0.324614
$950$	4.00000	0.129777
$951$	0	0
$952$	0	0
$953$	1.00000	0.0323932	0.0161966	−	0.999869i	$-0.494844\pi$
$953$	1.00000	0.0323932	0.0161966	+	0.999869i	$0.494844\pi$
$954$	0	0
$955$	−8.00000	−0.258874
$956$	26.0000	0.840900
$957$	0	0
$958$	18.0000	0.581554
$959$	−54.0000	−1.74375
$960$	0	0
$961$	5.00000	0.161290
$962$	22.0000	0.709308
$963$	0	0
$964$	−4.00000	−0.128831
$965$	13.0000	0.418485
$966$	0	0
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	0	0
$969$	0	0
$970$	34.0000	1.09167
$971$	−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
$973$	−3.00000	−0.0961756
$974$	14.0000	0.448589
$975$	0	0
$976$	−52.0000	−1.66448
$977$	−32.0000	−1.02377	−0.511885	−	0.859054i	$-0.671053\pi$
$977$	−32.0000	−1.02377	−0.511885	+	0.859054i	$0.671053\pi$
$978$	0	0
$979$	15.0000	0.479402
$980$	−4.00000	−0.127775
$981$	0	0
$982$	56.0000	1.78703
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	0	0
$986$	−4.00000	−0.127386
$987$	0	0
$988$	4.00000	0.127257
$989$	12.0000	0.381578
$990$	0	0
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	−48.0000	−1.52400
$993$	0	0
$994$	−30.0000	−0.951542
$995$	−4.00000	−0.126809
$996$	0	0
$997$	−36.0000	−1.14013	−0.570066	−	0.821599i	$-0.693082\pi$
$997$	−36.0000	−1.14013	−0.570066	+	0.821599i	$0.693082\pi$
$998$	28.0000	0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.a.b.1.1		1
3.2	odd	2		195.2.a.b.1.1	✓	1
4.3	odd	2		9360.2.a.d.1.1		1
5.2	odd	4		2925.2.c.c.2224.1		2
5.3	odd	4		2925.2.c.c.2224.2		2
5.4	even	2		2925.2.a.q.1.1		1
12.11	even	2		3120.2.a.u.1.1		1
13.12	even	2		7605.2.a.u.1.1		1
15.2	even	4		975.2.c.a.274.2		2
15.8	even	4		975.2.c.a.274.1		2
15.14	odd	2		975.2.a.c.1.1		1
21.20	even	2		9555.2.a.v.1.1		1
39.38	odd	2		2535.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.b.1.1	✓	1	3.2	odd	2
585.2.a.b.1.1		1	1.1	even	1	trivial
975.2.a.c.1.1		1	15.14	odd	2
975.2.c.a.274.1		2	15.8	even	4
975.2.c.a.274.2		2	15.2	even	4
2535.2.a.a.1.1		1	39.38	odd	2
2925.2.a.q.1.1		1	5.4	even	2
2925.2.c.c.2224.1		2	5.2	odd	4
2925.2.c.c.2224.2		2	5.3	odd	4
3120.2.a.u.1.1		1	12.11	even	2
7605.2.a.u.1.1		1	13.12	even	2
9360.2.a.d.1.1		1	4.3	odd	2
9555.2.a.v.1.1		1	21.20	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

Introduction

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Representations

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