LMFDB - Embedded newform 2790.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(1,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, 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("2790.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.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:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2790.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{8} -1.00000 q^{10} +4.00000 q^{11} +6.00000 q^{13} +1.00000 q^{16} +4.00000 q^{17} +8.00000 q^{19} +1.00000 q^{20} -4.00000 q^{22} -2.00000 q^{23} +1.00000 q^{25} -6.00000 q^{26} -2.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} -4.00000 q^{34} -2.00000 q^{37} -8.00000 q^{38} -1.00000 q^{40} -4.00000 q^{43} +4.00000 q^{44} +2.00000 q^{46} -7.00000 q^{49} -1.00000 q^{50} +6.00000 q^{52} -14.0000 q^{53} +4.00000 q^{55} +2.00000 q^{58} -8.00000 q^{59} +12.0000 q^{61} +1.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +10.0000 q^{67} +4.00000 q^{68} -6.00000 q^{71} +6.00000 q^{73} +2.00000 q^{74} +8.00000 q^{76} +8.00000 q^{79} +1.00000 q^{80} -12.0000 q^{83} +4.00000 q^{85} +4.00000 q^{86} -4.00000 q^{88} +6.00000 q^{89} -2.00000 q^{92} +8.00000 q^{95} -14.0000 q^{97} +7.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	0	0
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−8.00000	−1.29777
$39$	0	0
$40$	−1.00000	−0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	2.00000	0.294884
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	0	0
$52$	6.00000	0.832050
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	0	0
$57$	0	0
$58$	2.00000	0.262613
$59$	−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
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	1.00000	0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	8.00000	0.917663
$77$	0	0
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	4.00000	0.431331
$87$	0	0
$88$	−4.00000	−0.426401
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	−2.00000	−0.208514
$93$	0	0
$94$	0	0
$95$	8.00000	0.820783
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	14.0000	1.35980
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	0	0
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	−2.00000	−0.186501
$116$	−2.00000	−0.185695
$117$	0	0
$118$	8.00000	0.736460
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	−12.0000	−1.08643
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−6.00000	−0.526235
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	0	0
$134$	−10.0000	−0.863868
$135$	0	0
$136$	−4.00000	−0.342997
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	0	0
$141$	0	0
$142$	6.00000	0.503509
$143$	24.0000	2.00698
$144$	0	0
$145$	−2.00000	−0.166091
$146$	−6.00000	−0.496564
$147$	0	0
$148$	−2.00000	−0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	−8.00000	−0.648886
$153$	0	0
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	0	0
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	0	0
$165$	0	0
$166$	12.0000	0.931381
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−4.00000	−0.306786
$171$	0	0
$172$	−4.00000	−0.304997
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	2.00000	0.147442
$185$	−2.00000	−0.147043
$186$	0	0
$187$	16.0000	1.17004
$188$	0	0
$189$	0	0
$190$	−8.00000	−0.580381
$191$	14.0000	1.01300	0.506502	−	0.862239i	$-0.330938\pi$
$191$	14.0000	1.01300	0.506502	+	0.862239i	$0.330938\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	−7.00000	−0.500000
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−10.0000	−0.703598
$203$	0	0
$204$	0	0
$205$	0	0
$206$	4.00000	0.278693
$207$	0	0
$208$	6.00000	0.416025
$209$	32.0000	2.21349
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	−14.0000	−0.961524
$213$	0	0
$214$	4.00000	0.273434
$215$	−4.00000	−0.272798
$216$	0	0
$217$	0	0
$218$	−18.0000	−1.21911
$219$	0	0
$220$	4.00000	0.269680
$221$	24.0000	1.61441
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	0	0
$226$	−10.0000	−0.665190
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	−8.00000	−0.528655	−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000	−0.528655	−0.264327	+	0.964433i	$0.585150\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	2.00000	0.131306
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−5.00000	−0.321412
$243$	0	0
$244$	12.0000	0.768221
$245$	−7.00000	−0.447214
$246$	0	0
$247$	48.0000	3.05417
$248$	1.00000	0.0635001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	0	0
$259$	0	0
$260$	6.00000	0.372104
$261$	0	0
$262$	−4.00000	−0.247121
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	−14.0000	−0.860013
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	0	0
$275$	4.00000	0.241209
$276$	0	0
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	22.0000	1.31947
$279$	0	0
$280$	0	0
$281$	32.0000	1.90896	0.954480	−	0.298275i	$-0.0964112\pi$
$281$	32.0000	1.90896	0.954480	+	0.298275i	$0.0964112\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−24.0000	−1.41915
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	2.00000	0.117444
$291$	0	0
$292$	6.00000	0.351123
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	2.00000	0.116248
$297$	0	0
$298$	10.0000	0.579284
$299$	−12.0000	−0.693978
$300$	0	0
$301$	0	0
$302$	−4.00000	−0.230174
$303$	0	0
$304$	8.00000	0.458831
$305$	12.0000	0.687118
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	0	0
$309$	0	0
$310$	1.00000	0.0567962
$311$	−14.0000	−0.793867	−0.396934	−	0.917847i	$-0.629926\pi$
$311$	−14.0000	−0.793867	−0.396934	+	0.917847i	$0.629926\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	8.00000	0.450035
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	0	0
$319$	−8.00000	−0.447914
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	32.0000	1.78053
$324$	0	0
$325$	6.00000	0.332820
$326$	18.0000	0.996928
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−30.0000	−1.64895	−0.824475	−	0.565899i	$-0.808529\pi$
$331$	−30.0000	−1.64895	−0.824475	+	0.565899i	$0.808529\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	18.0000	0.984916
$335$	10.0000	0.546358
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−23.0000	−1.25104
$339$	0	0
$340$	4.00000	0.216930
$341$	−4.00000	−0.216612
$342$	0	0
$343$	0	0
$344$	4.00000	0.215666
$345$	0	0
$346$	−14.0000	−0.752645
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	0	0
$352$	−4.00000	−0.213201
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	0	0
$355$	−6.00000	−0.318447
$356$	6.00000	0.317999
$357$	0	0
$358$	20.0000	1.05703
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	0	0
$363$	0	0
$364$	0	0
$365$	6.00000	0.314054
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−2.00000	−0.104257
$369$	0	0
$370$	2.00000	0.103975
$371$	0	0
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−16.0000	−0.827340
$375$	0	0
$376$	0	0
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	8.00000	0.410391
$381$	0	0
$382$	−14.0000	−0.716302
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	0	0
$385$	0	0
$386$	10.0000	0.508987
$387$	0	0
$388$	−14.0000	−0.710742
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	7.00000	0.353553
$393$	0	0
$394$	−10.0000	−0.503793
$395$	8.00000	0.402524
$396$	0	0
$397$	4.00000	0.200754	0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000	0.200754	0.100377	+	0.994949i	$0.467995\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	1.00000	0.0500000
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	0	0
$403$	−6.00000	−0.298881
$404$	10.0000	0.497519
$405$	0	0
$406$	0	0
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	0	0
$411$	0	0
$412$	−4.00000	−0.197066
$413$	0	0
$414$	0	0
$415$	−12.0000	−0.589057
$416$	−6.00000	−0.294174
$417$	0	0
$418$	−32.0000	−1.56517
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−8.00000	−0.389434
$423$	0	0
$424$	14.0000	0.679900
$425$	4.00000	0.194029
$426$	0	0
$427$	0	0
$428$	−4.00000	−0.193347
$429$	0	0
$430$	4.00000	0.192897
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242982\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	0	0
$436$	18.0000	0.862044
$437$	−16.0000	−0.765384
$438$	0	0
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	−24.0000	−1.14156
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	0	0
$445$	6.00000	0.284427
$446$	8.00000	0.378811
$447$	0	0
$448$	0	0
$449$	42.0000	1.98210	0.991051	−	0.133482i	$-0.0426157\pi$
$449$	42.0000	1.98210	0.991051	+	0.133482i	$0.0426157\pi$
$450$	0	0
$451$	0	0
$452$	10.0000	0.470360
$453$	0	0
$454$	−4.00000	−0.187729
$455$	0	0
$456$	0	0
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	8.00000	0.373815
$459$	0	0
$460$	−2.00000	−0.0932505
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	10.0000	0.463241
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	8.00000	0.368230
$473$	−16.0000	−0.735681
$474$	0	0
$475$	8.00000	0.367065
$476$	0	0
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−42.0000	−1.91903	−0.959514	−	0.281659i	$-0.909115\pi$
$479$	−42.0000	−1.91903	−0.959514	+	0.281659i	$0.909115\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	−10.0000	−0.455488
$483$	0	0
$484$	5.00000	0.227273
$485$	−14.0000	−0.635707
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−12.0000	−0.543214
$489$	0	0
$490$	7.00000	0.316228
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	0	0
$493$	−8.00000	−0.360302
$494$	−48.0000	−2.15962
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	0	0
$498$	0	0
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−4.00000	−0.178529
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	8.00000	0.355643
$507$	0	0
$508$	16.0000	0.709885
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	22.0000	0.970378
$515$	−4.00000	−0.176261
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−6.00000	−0.263117
$521$	−4.00000	−0.175243	−0.0876216	−	0.996154i	$-0.527927\pi$
$521$	−4.00000	−0.175243	−0.0876216	+	0.996154i	$0.527927\pi$
$522$	0	0
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	6.00000	0.261612
$527$	−4.00000	−0.174243
$528$	0	0
$529$	−19.0000	−0.826087
$530$	14.0000	0.608121
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−4.00000	−0.172935
$536$	−10.0000	−0.431934
$537$	0	0
$538$	−18.0000	−0.776035
$539$	−28.0000	−1.20605
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−4.00000	−0.171815
$543$	0	0
$544$	−4.00000	−0.171499
$545$	18.0000	0.771035
$546$	0	0
$547$	−38.0000	−1.62476	−0.812381	−	0.583127i	$-0.801829\pi$
$547$	−38.0000	−1.62476	−0.812381	+	0.583127i	$0.801829\pi$
$548$	0	0
$549$	0	0
$550$	−4.00000	−0.170561
$551$	−16.0000	−0.681623
$552$	0	0
$553$	0	0
$554$	−18.0000	−0.764747
$555$	0	0
$556$	−22.0000	−0.933008
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	0	0
$559$	−24.0000	−1.01509
$560$	0	0
$561$	0	0
$562$	−32.0000	−1.34984
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	10.0000	0.420703
$566$	−6.00000	−0.252199
$567$	0	0
$568$	6.00000	0.251754
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	24.0000	1.00349
$573$	0	0
$574$	0	0
$575$	−2.00000	−0.0834058
$576$	0	0
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	−2.00000	−0.0830455
$581$	0	0
$582$	0	0
$583$	−56.0000	−2.31928
$584$	−6.00000	−0.248282
$585$	0	0
$586$	6.00000	0.247858
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	8.00000	0.329355
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	22.0000	0.903432	0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000	0.903432	0.451716	+	0.892162i	$0.350812\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	12.0000	0.490716
$599$	−2.00000	−0.0817178	−0.0408589	−	0.999165i	$-0.513009\pi$
$599$	−2.00000	−0.0817178	−0.0408589	+	0.999165i	$0.513009\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	0	0
$604$	4.00000	0.162758
$605$	5.00000	0.203279
$606$	0	0
$607$	36.0000	1.46119	0.730597	−	0.682808i	$-0.239242\pi$
$607$	36.0000	1.46119	0.730597	+	0.682808i	$0.239242\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	−12.0000	−0.485866
$611$	0	0
$612$	0	0
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−2.00000	−0.0807134
$615$	0	0
$616$	0	0
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	0	0
$619$	−34.0000	−1.36658	−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000	−1.36658	−0.683288	+	0.730149i	$0.739451\pi$
$620$	−1.00000	−0.0401610
$621$	0	0
$622$	14.0000	0.561349
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	22.0000	0.879297
$627$	0	0
$628$	−12.0000	−0.478852
$629$	−8.00000	−0.318981
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	−22.0000	−0.873732
$635$	16.0000	0.634941
$636$	0	0
$637$	−42.0000	−1.66410
$638$	8.00000	0.316723
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	0	0
$645$	0	0
$646$	−32.0000	−1.25902
$647$	−30.0000	−1.17942	−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000	−1.17942	−0.589711	+	0.807614i	$0.700758\pi$
$648$	0	0
$649$	−32.0000	−1.25611
$650$	−6.00000	−0.235339
$651$	0	0
$652$	−18.0000	−0.704934
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	4.00000	0.156293
$656$	0	0
$657$	0	0
$658$	0	0
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	30.0000	1.16598
$663$	0	0
$664$	12.0000	0.465690
$665$	0	0
$666$	0	0
$667$	4.00000	0.154881
$668$	−18.0000	−0.696441
$669$	0	0
$670$	−10.0000	−0.386334
$671$	48.0000	1.85302
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	23.0000	0.884615
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	0	0
$680$	−4.00000	−0.153393
$681$	0	0
$682$	4.00000	0.153168
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−84.0000	−3.20015
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	20.0000	0.759190
$695$	−22.0000	−0.834508
$696$	0	0
$697$	0	0
$698$	26.0000	0.984115
$699$	0	0
$700$	0	0
$701$	50.0000	1.88847	0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000	1.88847	0.944237	+	0.329267i	$0.106802\pi$
$702$	0	0
$703$	−16.0000	−0.603451
$704$	4.00000	0.150756
$705$	0	0
$706$	24.0000	0.903252
$707$	0	0
$708$	0	0
$709$	−4.00000	−0.150223	−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000	−0.150223	−0.0751116	+	0.997175i	$0.523931\pi$
$710$	6.00000	0.225176
$711$	0	0
$712$	−6.00000	−0.224860
$713$	2.00000	0.0749006
$714$	0	0
$715$	24.0000	0.897549
$716$	−20.0000	−0.747435
$717$	0	0
$718$	−14.0000	−0.522475
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	0	0
$722$	−45.0000	−1.67473
$723$	0	0
$724$	0	0
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	0	0
$729$	0	0
$730$	−6.00000	−0.222070
$731$	−16.0000	−0.591781
$732$	0	0
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	2.00000	0.0737210
$737$	40.0000	1.47342
$738$	0	0
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	0	0
$743$	54.0000	1.98107	0.990534	−	0.137268i	$-0.0438322\pi$
$743$	54.0000	1.98107	0.990534	+	0.137268i	$0.0438322\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	−4.00000	−0.146450
$747$	0	0
$748$	16.0000	0.585018
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	12.0000	0.437014
$755$	4.00000	0.145575
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	−8.00000	−0.290191
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	0	0
$763$	0	0
$764$	14.0000	0.506502
$765$	0	0
$766$	10.0000	0.361315
$767$	−48.0000	−1.73318
$768$	0	0
$769$	−50.0000	−1.80305	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000	−1.80305	−0.901523	+	0.432731i	$0.857550\pi$
$770$	0	0
$771$	0	0
$772$	−10.0000	−0.359908
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	14.0000	0.502571
$777$	0	0
$778$	−6.00000	−0.215110
$779$	0	0
$780$	0	0
$781$	−24.0000	−0.858788
$782$	8.00000	0.286079
$783$	0	0
$784$	−7.00000	−0.250000
$785$	−12.0000	−0.428298
$786$	0	0
$787$	16.0000	0.570338	0.285169	−	0.958477i	$-0.407950\pi$
$787$	16.0000	0.570338	0.285169	+	0.958477i	$0.407950\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	−8.00000	−0.284627
$791$	0	0
$792$	0	0
$793$	72.0000	2.55679
$794$	−4.00000	−0.141955
$795$	0	0
$796$	4.00000	0.141776
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−34.0000	−1.20058
$803$	24.0000	0.846942
$804$	0	0
$805$	0	0
$806$	6.00000	0.211341
$807$	0	0
$808$	−10.0000	−0.351799
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	−36.0000	−1.26413	−0.632065	−	0.774915i	$-0.717793\pi$
$811$	−36.0000	−1.26413	−0.632065	+	0.774915i	$0.717793\pi$
$812$	0	0
$813$	0	0
$814$	8.00000	0.280400
$815$	−18.0000	−0.630512
$816$	0	0
$817$	−32.0000	−1.11954
$818$	6.00000	0.209785
$819$	0	0
$820$	0	0
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	0	0
$823$	−56.0000	−1.95204	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−56.0000	−1.95204	−0.976019	+	0.217687i	$0.930149\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	8.00000	0.278187	0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000	0.278187	0.139094	+	0.990279i	$0.455581\pi$
$828$	0	0
$829$	32.0000	1.11141	0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000	1.11141	0.555703	+	0.831381i	$0.312449\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	6.00000	0.208013
$833$	−28.0000	−0.970143
$834$	0	0
$835$	−18.0000	−0.622916
$836$	32.0000	1.10674
$837$	0	0
$838$	0	0
$839$	−34.0000	−1.17381	−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000	−1.17381	−0.586905	+	0.809656i	$0.699654\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	22.0000	0.758170
$843$	0	0
$844$	8.00000	0.275371
$845$	23.0000	0.791224
$846$	0	0
$847$	0	0
$848$	−14.0000	−0.480762
$849$	0	0
$850$	−4.00000	−0.137199
$851$	4.00000	0.137118
$852$	0	0
$853$	−20.0000	−0.684787	−0.342393	−	0.939557i	$-0.611238\pi$
$853$	−20.0000	−0.684787	−0.342393	+	0.939557i	$0.611238\pi$
$854$	0	0
$855$	0	0
$856$	4.00000	0.136717
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	−4.00000	−0.136399
$861$	0	0
$862$	−30.0000	−1.02180
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	0	0
$865$	14.0000	0.476014
$866$	−14.0000	−0.475739
$867$	0	0
$868$	0	0
$869$	32.0000	1.08553
$870$	0	0
$871$	60.0000	2.03302
$872$	−18.0000	−0.609557
$873$	0	0
$874$	16.0000	0.541208
$875$	0	0
$876$	0	0
$877$	16.0000	0.540282	0.270141	−	0.962821i	$-0.412930\pi$
$877$	16.0000	0.540282	0.270141	+	0.962821i	$0.412930\pi$
$878$	−16.0000	−0.539974
$879$	0	0
$880$	4.00000	0.134840
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	0	0
$883$	28.0000	0.942275	0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000	0.942275	0.471138	+	0.882060i	$0.343844\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−4.00000	−0.134383
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	0	0
$890$	−6.00000	−0.201120
$891$	0	0
$892$	−8.00000	−0.267860
$893$	0	0
$894$	0	0
$895$	−20.0000	−0.668526
$896$	0	0
$897$	0	0
$898$	−42.0000	−1.40156
$899$	2.00000	0.0667037
$900$	0	0
$901$	−56.0000	−1.86563
$902$	0	0
$903$	0	0
$904$	−10.0000	−0.332595
$905$	0	0
$906$	0	0
$907$	−14.0000	−0.464862	−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000	−0.464862	−0.232431	+	0.972613i	$0.574668\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	0	0
$913$	−48.0000	−1.58857
$914$	34.0000	1.12462
$915$	0	0
$916$	−8.00000	−0.264327
$917$	0	0
$918$	0	0
$919$	−8.00000	−0.263896	−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000	−0.263896	−0.131948	+	0.991257i	$0.542123\pi$
$920$	2.00000	0.0659380
$921$	0	0
$922$	−14.0000	−0.461065
$923$	−36.0000	−1.18495
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	0	0
$927$	0	0
$928$	2.00000	0.0656532
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−56.0000	−1.83533
$932$	−10.0000	−0.327561
$933$	0	0
$934$	−28.0000	−0.916188
$935$	16.0000	0.523256
$936$	0	0
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	0	0
$944$	−8.00000	−0.260378
$945$	0	0
$946$	16.0000	0.520205
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	0	0
$949$	36.0000	1.16861
$950$	−8.00000	−0.259554
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	14.0000	0.453029
$956$	24.0000	0.776215
$957$	0	0
$958$	42.0000	1.35696
$959$	0	0
$960$	0	0
$961$	1.00000	0.0322581
$962$	12.0000	0.386896
$963$	0	0
$964$	10.0000	0.322078
$965$	−10.0000	−0.321911
$966$	0	0
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	14.0000	0.449513
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	0	0
$973$	0	0
$974$	16.0000	0.512673
$975$	0	0
$976$	12.0000	0.384111
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	−7.00000	−0.223607
$981$	0	0
$982$	20.0000	0.638226
$983$	−50.0000	−1.59475	−0.797376	−	0.603483i	$-0.793779\pi$
$983$	−50.0000	−1.59475	−0.797376	+	0.603483i	$0.793779\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	8.00000	0.254772
$987$	0	0
$988$	48.0000	1.52708
$989$	8.00000	0.254385
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	1.00000	0.0317500
$993$	0	0
$994$	0	0
$995$	4.00000	0.126809
$996$	0	0
$997$	44.0000	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$997$	44.0000	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$998$	14.0000	0.443162
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.a.i.1.1	✓	1
3.2	odd	2		2790.2.a.s.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.a.i.1.1	✓	1	1.1	even	1	trivial
2790.2.a.s.1.1	yes	1	3.2	odd	2

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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:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.a (trivial)

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