LMFDB - Embedded newform 5733.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5733,2,Mod(1,5733)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5733, 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("5733.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5733 = 3^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5733.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:	$45.7782354788$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5733.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +4.00000 q^{5} -3.00000 q^{8} +4.00000 q^{10} +5.00000 q^{11} +1.00000 q^{13} -1.00000 q^{16} +3.00000 q^{17} +5.00000 q^{19} -4.00000 q^{20} +5.00000 q^{22} -6.00000 q^{23} +11.0000 q^{25} +1.00000 q^{26} -7.00000 q^{29} +5.00000 q^{32} +3.00000 q^{34} +5.00000 q^{38} -12.0000 q^{40} +8.00000 q^{41} +2.00000 q^{43} -5.00000 q^{44} -6.00000 q^{46} +9.00000 q^{47} +11.0000 q^{50} -1.00000 q^{52} -9.00000 q^{53} +20.0000 q^{55} -7.00000 q^{58} -9.00000 q^{59} -1.00000 q^{61} +7.00000 q^{64} +4.00000 q^{65} +7.00000 q^{67} -3.00000 q^{68} +3.00000 q^{71} +6.00000 q^{73} -5.00000 q^{76} -10.0000 q^{79} -4.00000 q^{80} +8.00000 q^{82} +12.0000 q^{85} +2.00000 q^{86} -15.0000 q^{88} -8.00000 q^{89} +6.00000 q^{92} +9.00000 q^{94} +20.0000 q^{95} -18.0000 q^{97} +O(q^{100})$

Coefficient data

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

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

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

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−3.00000	−1.06066
$9$	0	0
$10$	4.00000	1.26491
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−1.00000	−0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−4.00000	−0.894427
$21$	0	0
$22$	5.00000	1.06600
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	1.00000	0.196116
$27$	0	0
$28$	0	0
$29$	−7.00000	−1.29987	−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000	−1.29987	−0.649934	+	0.759991i	$0.725203\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	3.00000	0.514496
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	5.00000	0.811107
$39$	0	0
$40$	−12.0000	−1.89737
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	−6.00000	−0.884652
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	0	0
$50$	11.0000	1.55563
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	20.0000	2.69680
$56$	0	0
$57$	0	0
$58$	−7.00000	−0.919145
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	0	0
$63$	0	0
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	0	0
$75$	0	0
$76$	−5.00000	−0.573539
$77$	0	0
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	8.00000	0.883452
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	2.00000	0.215666
$87$	0	0
$88$	−15.0000	−1.59901
$89$	−8.00000	−0.847998	−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000	−0.847998	−0.423999	+	0.905663i	$0.639374\pi$
$90$	0	0
$91$	0	0
$92$	6.00000	0.625543
$93$	0	0
$94$	9.00000	0.928279
$95$	20.0000	2.05196
$96$	0	0
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	0	0
$99$	0	0
$100$	−11.0000	−1.10000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−9.00000	−0.874157
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	20.0000	1.90693
$111$	0	0
$112$	0	0
$113$	11.0000	1.03479	0.517396	−	0.855746i	$-0.326901\pi$
$113$	11.0000	1.03479	0.517396	+	0.855746i	$0.326901\pi$
$114$	0	0
$115$	−24.0000	−2.23801
$116$	7.00000	0.649934
$117$	0	0
$118$	−9.00000	−0.828517
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−1.00000	−0.0905357
$123$	0	0
$124$	0	0
$125$	24.0000	2.14663
$126$	0	0
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	4.00000	0.350823
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	0	0
$133$	0	0
$134$	7.00000	0.604708
$135$	0	0
$136$	−9.00000	−0.771744
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	0	0
$142$	3.00000	0.251754
$143$	5.00000	0.418121
$144$	0	0
$145$	−28.0000	−2.32527
$146$	6.00000	0.496564
$147$	0	0
$148$	0	0
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−1.00000	−0.0813788	−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000	−0.0813788	−0.0406894	+	0.999172i	$0.512955\pi$
$152$	−15.0000	−1.21666
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	−10.0000	−0.795557
$159$	0	0
$160$	20.0000	1.58114
$161$	0	0
$162$	0	0
$163$	1.00000	0.0783260	0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000	0.0783260	0.0391630	+	0.999233i	$0.487531\pi$
$164$	−8.00000	−0.624695
$165$	0	0
$166$	0	0
$167$	7.00000	0.541676	0.270838	−	0.962625i	$-0.412699\pi$
$167$	7.00000	0.541676	0.270838	+	0.962625i	$0.412699\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	12.0000	0.920358
$171$	0	0
$172$	−2.00000	−0.152499
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	0	0
$175$	0	0
$176$	−5.00000	−0.376889
$177$	0	0
$178$	−8.00000	−0.599625
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	−1.00000	−0.0743294	−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000	−0.0743294	−0.0371647	+	0.999309i	$0.511833\pi$
$182$	0	0
$183$	0	0
$184$	18.0000	1.32698
$185$	0	0
$186$	0	0
$187$	15.0000	1.09691
$188$	−9.00000	−0.656392
$189$	0	0
$190$	20.0000	1.45095
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	0	0
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	0	0
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	−6.00000	−0.425329	−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000	−0.425329	−0.212664	+	0.977125i	$0.568214\pi$
$200$	−33.0000	−2.33345
$201$	0	0
$202$	2.00000	0.140720
$203$	0	0
$204$	0	0
$205$	32.0000	2.23498
$206$	−14.0000	−0.975426
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	25.0000	1.72929
$210$	0	0
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	9.00000	0.618123
$213$	0	0
$214$	8.00000	0.546869
$215$	8.00000	0.545595
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	−20.0000	−1.34840
$221$	3.00000	0.201802
$222$	0	0
$223$	−7.00000	−0.468755	−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000	−0.468755	−0.234377	+	0.972146i	$0.575305\pi$
$224$	0	0
$225$	0	0
$226$	11.0000	0.731709
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	−24.0000	−1.58251
$231$	0	0
$232$	21.0000	1.37872
$233$	−9.00000	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$234$	0	0
$235$	36.0000	2.34838
$236$	9.00000	0.585850
$237$	0	0
$238$	0	0
$239$	21.0000	1.35838	0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000	1.35838	0.679189	+	0.733964i	$0.262332\pi$
$240$	0	0
$241$	16.0000	1.03065	0.515325	−	0.856995i	$-0.327671\pi$
$241$	16.0000	1.03065	0.515325	+	0.856995i	$0.327671\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	1.00000	0.0640184
$245$	0	0
$246$	0	0
$247$	5.00000	0.318142
$248$	0	0
$249$	0	0
$250$	24.0000	1.51789
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	0	0
$253$	−30.0000	−1.88608
$254$	18.0000	1.12942
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−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
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−2.00000	−0.123560
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	−36.0000	−2.21146
$266$	0	0
$267$	0	0
$268$	−7.00000	−0.427593
$269$	−9.00000	−0.548740	−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000	−0.548740	−0.274370	+	0.961624i	$0.588469\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	0	0
$275$	55.0000	3.31662
$276$	0	0
$277$	31.0000	1.86261	0.931305	−	0.364241i	$-0.118672\pi$
$277$	31.0000	1.86261	0.931305	+	0.364241i	$0.118672\pi$
$278$	12.0000	0.719712
$279$	0	0
$280$	0	0
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−3.00000	−0.178017
$285$	0	0
$286$	5.00000	0.295656
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	−28.0000	−1.64422
$291$	0	0
$292$	−6.00000	−0.351123
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	0	0
$295$	−36.0000	−2.09600
$296$	0	0
$297$	0	0
$298$	18.0000	1.04271
$299$	−6.00000	−0.346989
$300$	0	0
$301$	0	0
$302$	−1.00000	−0.0575435
$303$	0	0
$304$	−5.00000	−0.286770
$305$	−4.00000	−0.229039
$306$	0	0
$307$	17.0000	0.970241	0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000	0.970241	0.485121	+	0.874447i	$0.338776\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	10.0000	0.562544
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	−35.0000	−1.95962
$320$	28.0000	1.56525
$321$	0	0
$322$	0	0
$323$	15.0000	0.834622
$324$	0	0
$325$	11.0000	0.610170
$326$	1.00000	0.0553849
$327$	0	0
$328$	−24.0000	−1.32518
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	0	0
$333$	0	0
$334$	7.00000	0.383023
$335$	28.0000	1.52980
$336$	0	0
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	1.00000	0.0543928
$339$	0	0
$340$	−12.0000	−0.650791
$341$	0	0
$342$	0	0
$343$	0	0
$344$	−6.00000	−0.323498
$345$	0	0
$346$	11.0000	0.591364
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	0	0
$352$	25.0000	1.33250
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	0	0
$355$	12.0000	0.636894
$356$	8.00000	0.423999
$357$	0	0
$358$	10.0000	0.528516
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−1.00000	−0.0525588
$363$	0	0
$364$	0	0
$365$	24.0000	1.25622
$366$	0	0
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−25.0000	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$374$	15.0000	0.775632
$375$	0	0
$376$	−27.0000	−1.39242
$377$	−7.00000	−0.360518
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−20.0000	−1.02598
$381$	0	0
$382$	−4.00000	−0.204658
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−4.00000	−0.203595
$387$	0	0
$388$	18.0000	0.913812
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	−18.0000	−0.910299
$392$	0	0
$393$	0	0
$394$	−10.0000	−0.503793
$395$	−40.0000	−2.01262
$396$	0	0
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	−6.00000	−0.300753
$399$	0	0
$400$	−11.0000	−0.550000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	0	0
$404$	−2.00000	−0.0995037
$405$	0	0
$406$	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	$0.790517\pi$
$410$	32.0000	1.58037
$411$	0	0
$412$	14.0000	0.689730
$413$	0	0
$414$	0	0
$415$	0	0
$416$	5.00000	0.245145
$417$	0	0
$418$	25.0000	1.22279
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−14.0000	−0.681509
$423$	0	0
$424$	27.0000	1.31124
$425$	33.0000	1.60074
$426$	0	0
$427$	0	0
$428$	−8.00000	−0.386695
$429$	0	0
$430$	8.00000	0.385794
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−37.0000	−1.77811	−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−37.0000	−1.77811	−0.889053	+	0.457804i	$0.848636\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−30.0000	−1.43509
$438$	0	0
$439$	18.0000	0.859093	0.429547	−	0.903045i	$-0.358673\pi$
$439$	18.0000	0.859093	0.429547	+	0.903045i	$0.358673\pi$
$440$	−60.0000	−2.86039
$441$	0	0
$442$	3.00000	0.142695
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	−32.0000	−1.51695
$446$	−7.00000	−0.331460
$447$	0	0
$448$	0	0
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	40.0000	1.88353
$452$	−11.0000	−0.517396
$453$	0	0
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	−38.0000	−1.77757	−0.888783	−	0.458329i	$-0.848448\pi$
$457$	−38.0000	−1.77757	−0.888783	+	0.458329i	$0.848448\pi$
$458$	−2.00000	−0.0934539
$459$	0	0
$460$	24.0000	1.11901
$461$	8.00000	0.372597	0.186299	−	0.982493i	$-0.440351\pi$
$461$	8.00000	0.372597	0.186299	+	0.982493i	$0.440351\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	7.00000	0.324967
$465$	0	0
$466$	−9.00000	−0.416917
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	0	0
$469$	0	0
$470$	36.0000	1.66056
$471$	0	0
$472$	27.0000	1.24278
$473$	10.0000	0.459800
$474$	0	0
$475$	55.0000	2.52357
$476$	0	0
$477$	0	0
$478$	21.0000	0.960518
$479$	−7.00000	−0.319838	−0.159919	−	0.987130i	$-0.551123\pi$
$479$	−7.00000	−0.319838	−0.159919	+	0.987130i	$0.551123\pi$
$480$	0	0
$481$	0	0
$482$	16.0000	0.728780
$483$	0	0
$484$	−14.0000	−0.636364
$485$	−72.0000	−3.26935
$486$	0	0
$487$	−29.0000	−1.31412	−0.657058	−	0.753840i	$-0.728199\pi$
$487$	−29.0000	−1.31412	−0.657058	+	0.753840i	$0.728199\pi$
$488$	3.00000	0.135804
$489$	0	0
$490$	0	0
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	0	0
$493$	−21.0000	−0.945792
$494$	5.00000	0.224961
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	−24.0000	−1.07331
$501$	0	0
$502$	−14.0000	−0.624851
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	8.00000	0.355995
$506$	−30.0000	−1.33366
$507$	0	0
$508$	−18.0000	−0.798621
$509$	−40.0000	−1.77297	−0.886484	−	0.462758i	$-0.846860\pi$
$509$	−40.0000	−1.77297	−0.886484	+	0.462758i	$0.846860\pi$
$510$	0	0
$511$	0	0
$512$	−11.0000	−0.486136
$513$	0	0
$514$	−22.0000	−0.970378
$515$	−56.0000	−2.46765
$516$	0	0
$517$	45.0000	1.97910
$518$	0	0
$519$	0	0
$520$	−12.0000	−0.526235
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	0	0
$523$	38.0000	1.66162	0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000	1.66162	0.830812	+	0.556553i	$0.187876\pi$
$524$	2.00000	0.0873704
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	−36.0000	−1.56374
$531$	0	0
$532$	0	0
$533$	8.00000	0.346518
$534$	0	0
$535$	32.0000	1.38348
$536$	−21.0000	−0.907062
$537$	0	0
$538$	−9.00000	−0.388018
$539$	0	0
$540$	0	0
$541$	−4.00000	−0.171973	−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000	−0.171973	−0.0859867	+	0.996296i	$0.527404\pi$
$542$	5.00000	0.214768
$543$	0	0
$544$	15.0000	0.643120
$545$	0	0
$546$	0	0
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	0	0
$549$	0	0
$550$	55.0000	2.34521
$551$	−35.0000	−1.49105
$552$	0	0
$553$	0	0
$554$	31.0000	1.31706
$555$	0	0
$556$	−12.0000	−0.508913
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	0	0
$559$	2.00000	0.0845910
$560$	0	0
$561$	0	0
$562$	16.0000	0.674919
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	0	0
$565$	44.0000	1.85109
$566$	14.0000	0.588464
$567$	0	0
$568$	−9.00000	−0.377632
$569$	11.0000	0.461144	0.230572	−	0.973055i	$-0.425940\pi$
$569$	11.0000	0.461144	0.230572	+	0.973055i	$0.425940\pi$
$570$	0	0
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	−5.00000	−0.209061
$573$	0	0
$574$	0	0
$575$	−66.0000	−2.75239
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	28.0000	1.16264
$581$	0	0
$582$	0	0
$583$	−45.0000	−1.86371
$584$	−18.0000	−0.744845
$585$	0	0
$586$	−10.0000	−0.413096
$587$	−29.0000	−1.19696	−0.598479	−	0.801138i	$-0.704228\pi$
$587$	−29.0000	−1.19696	−0.598479	+	0.801138i	$0.704228\pi$
$588$	0	0
$589$	0	0
$590$	−36.0000	−1.48210
$591$	0	0
$592$	0	0
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	−6.00000	−0.245358
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−9.00000	−0.367118	−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000	−0.367118	−0.183559	+	0.983009i	$0.558762\pi$
$602$	0	0
$603$	0	0
$604$	1.00000	0.0406894
$605$	56.0000	2.27672
$606$	0	0
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	25.0000	1.01388
$609$	0	0
$610$	−4.00000	−0.161955
$611$	9.00000	0.364101
$612$	0	0
$613$	−8.00000	−0.323117	−0.161558	−	0.986863i	$-0.551652\pi$
$613$	−8.00000	−0.323117	−0.161558	+	0.986863i	$0.551652\pi$
$614$	17.0000	0.686064
$615$	0	0
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	41.0000	1.64000
$626$	−2.00000	−0.0799361
$627$	0	0
$628$	7.00000	0.279330
$629$	0	0
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	30.0000	1.19334
$633$	0	0
$634$	6.00000	0.238290
$635$	72.0000	2.85723
$636$	0	0
$637$	0	0
$638$	−35.0000	−1.38566
$639$	0	0
$640$	−12.0000	−0.474342
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	37.0000	1.45914	0.729569	−	0.683907i	$-0.239721\pi$
$643$	37.0000	1.45914	0.729569	+	0.683907i	$0.239721\pi$
$644$	0	0
$645$	0	0
$646$	15.0000	0.590167
$647$	−22.0000	−0.864909	−0.432455	−	0.901656i	$-0.642352\pi$
$647$	−22.0000	−0.864909	−0.432455	+	0.901656i	$0.642352\pi$
$648$	0	0
$649$	−45.0000	−1.76640
$650$	11.0000	0.431455
$651$	0	0
$652$	−1.00000	−0.0391630
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	−8.00000	−0.312586
$656$	−8.00000	−0.312348
$657$	0	0
$658$	0	0
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	42.0000	1.62625
$668$	−7.00000	−0.270838
$669$	0	0
$670$	28.0000	1.08173
$671$	−5.00000	−0.193023
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	7.00000	0.269630
$675$	0	0
$676$	−1.00000	−0.0384615
$677$	−39.0000	−1.49889	−0.749446	−	0.662066i	$-0.769680\pi$
$677$	−39.0000	−1.49889	−0.749446	+	0.662066i	$0.769680\pi$
$678$	0	0
$679$	0	0
$680$	−36.0000	−1.38054
$681$	0	0
$682$	0	0
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−2.00000	−0.0762493
$689$	−9.00000	−0.342873
$690$	0	0
$691$	−17.0000	−0.646710	−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000	−0.646710	−0.323355	+	0.946278i	$0.604811\pi$
$692$	−11.0000	−0.418157
$693$	0	0
$694$	28.0000	1.06287
$695$	48.0000	1.82074
$696$	0	0
$697$	24.0000	0.909065
$698$	2.00000	0.0757011
$699$	0	0
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	0	0
$703$	0	0
$704$	35.0000	1.31911
$705$	0	0
$706$	−14.0000	−0.526897
$707$	0	0
$708$	0	0
$709$	−42.0000	−1.57734	−0.788672	−	0.614815i	$-0.789231\pi$
$709$	−42.0000	−1.57734	−0.788672	+	0.614815i	$0.789231\pi$
$710$	12.0000	0.450352
$711$	0	0
$712$	24.0000	0.899438
$713$	0	0
$714$	0	0
$715$	20.0000	0.747958
$716$	−10.0000	−0.373718
$717$	0	0
$718$	−32.0000	−1.19423
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	0	0
$722$	6.00000	0.223297
$723$	0	0
$724$	1.00000	0.0371647
$725$	−77.0000	−2.85971
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	0	0
$730$	24.0000	0.888280
$731$	6.00000	0.221918
$732$	0	0
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	−18.0000	−0.664392
$735$	0	0
$736$	−30.0000	−1.10581
$737$	35.0000	1.28924
$738$	0	0
$739$	−36.0000	−1.32428	−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000	−1.32428	−0.662141	+	0.749380i	$0.730352\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	9.00000	0.330178	0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000	0.330178	0.165089	+	0.986279i	$0.447209\pi$
$744$	0	0
$745$	72.0000	2.63788
$746$	−25.0000	−0.915315
$747$	0	0
$748$	−15.0000	−0.548454
$749$	0	0
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−9.00000	−0.328196
$753$	0	0
$754$	−7.00000	−0.254925
$755$	−4.00000	−0.145575
$756$	0	0
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	−60.0000	−2.17643
$761$	48.0000	1.74000	0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000	1.74000	0.869999	+	0.493053i	$0.164119\pi$
$762$	0	0
$763$	0	0
$764$	4.00000	0.144715
$765$	0	0
$766$	24.0000	0.867155
$767$	−9.00000	−0.324971
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	0	0
$772$	4.00000	0.143963
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	0	0
$775$	0	0
$776$	54.0000	1.93849
$777$	0	0
$778$	−9.00000	−0.322666
$779$	40.0000	1.43315
$780$	0	0
$781$	15.0000	0.536742
$782$	−18.0000	−0.643679
$783$	0	0
$784$	0	0
$785$	−28.0000	−0.999363
$786$	0	0
$787$	11.0000	0.392108	0.196054	−	0.980593i	$-0.437187\pi$
$787$	11.0000	0.392108	0.196054	+	0.980593i	$0.437187\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	−40.0000	−1.42314
$791$	0	0
$792$	0	0
$793$	−1.00000	−0.0355110
$794$	6.00000	0.212932
$795$	0	0
$796$	6.00000	0.212664
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	0	0
$799$	27.0000	0.955191
$800$	55.0000	1.94454
$801$	0	0
$802$	−6.00000	−0.211867
$803$	30.0000	1.05868
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−6.00000	−0.211079
$809$	3.00000	0.105474	0.0527372	−	0.998608i	$-0.483205\pi$
$809$	3.00000	0.105474	0.0527372	+	0.998608i	$0.483205\pi$
$810$	0	0
$811$	−44.0000	−1.54505	−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000	−1.54505	−0.772524	+	0.634985i	$0.781006\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	4.00000	0.140114
$816$	0	0
$817$	10.0000	0.349856
$818$	−32.0000	−1.11885
$819$	0	0
$820$	−32.0000	−1.11749
$821$	−32.0000	−1.11681	−0.558404	−	0.829569i	$-0.688586\pi$
$821$	−32.0000	−1.11681	−0.558404	+	0.829569i	$0.688586\pi$
$822$	0	0
$823$	36.0000	1.25488	0.627441	−	0.778664i	$-0.284103\pi$
$823$	36.0000	1.25488	0.627441	+	0.778664i	$0.284103\pi$
$824$	42.0000	1.46314
$825$	0	0
$826$	0	0
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	0	0
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	0	0
$831$	0	0
$832$	7.00000	0.242681
$833$	0	0
$834$	0	0
$835$	28.0000	0.968980
$836$	−25.0000	−0.864643
$837$	0	0
$838$	−6.00000	−0.207267
$839$	25.0000	0.863096	0.431548	−	0.902090i	$-0.357968\pi$
$839$	25.0000	0.863096	0.431548	+	0.902090i	$0.357968\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	−22.0000	−0.758170
$843$	0	0
$844$	14.0000	0.481900
$845$	4.00000	0.137604
$846$	0	0
$847$	0	0
$848$	9.00000	0.309061
$849$	0	0
$850$	33.0000	1.13189
$851$	0	0
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	0	0
$856$	−24.0000	−0.820303
$857$	1.00000	0.0341593	0.0170797	−	0.999854i	$-0.494563\pi$
$857$	1.00000	0.0341593	0.0170797	+	0.999854i	$0.494563\pi$
$858$	0	0
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	0	0
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	0	0
$865$	44.0000	1.49604
$866$	−37.0000	−1.25731
$867$	0	0
$868$	0	0
$869$	−50.0000	−1.69613
$870$	0	0
$871$	7.00000	0.237186
$872$	0	0
$873$	0	0
$874$	−30.0000	−1.01477
$875$	0	0
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	18.0000	0.607471
$879$	0	0
$880$	−20.0000	−0.674200
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	32.0000	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	24.0000	0.806296
$887$	−46.0000	−1.54453	−0.772264	−	0.635301i	$-0.780876\pi$
$887$	−46.0000	−1.54453	−0.772264	+	0.635301i	$0.780876\pi$
$888$	0	0
$889$	0	0
$890$	−32.0000	−1.07264
$891$	0	0
$892$	7.00000	0.234377
$893$	45.0000	1.50587
$894$	0	0
$895$	40.0000	1.33705
$896$	0	0
$897$	0	0
$898$	36.0000	1.20134
$899$	0	0
$900$	0	0
$901$	−27.0000	−0.899500
$902$	40.0000	1.33185
$903$	0	0
$904$	−33.0000	−1.09756
$905$	−4.00000	−0.132964
$906$	0	0
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	0	0
$911$	−42.0000	−1.39152	−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000	−1.39152	−0.695761	+	0.718273i	$0.744933\pi$
$912$	0	0
$913$	0	0
$914$	−38.0000	−1.25693
$915$	0	0
$916$	2.00000	0.0660819
$917$	0	0
$918$	0	0
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	72.0000	2.37377
$921$	0	0
$922$	8.00000	0.263466
$923$	3.00000	0.0987462
$924$	0	0
$925$	0	0
$926$	40.0000	1.31448
$927$	0	0
$928$	−35.0000	−1.14893
$929$	26.0000	0.853032	0.426516	−	0.904480i	$-0.359741\pi$
$929$	26.0000	0.853032	0.426516	+	0.904480i	$0.359741\pi$
$930$	0	0
$931$	0	0
$932$	9.00000	0.294805
$933$	0	0
$934$	−18.0000	−0.588978
$935$	60.0000	1.96221
$936$	0	0
$937$	33.0000	1.07806	0.539032	−	0.842286i	$-0.318790\pi$
$937$	33.0000	1.07806	0.539032	+	0.842286i	$0.318790\pi$
$938$	0	0
$939$	0	0
$940$	−36.0000	−1.17419
$941$	−16.0000	−0.521585	−0.260793	−	0.965395i	$-0.583984\pi$
$941$	−16.0000	−0.521585	−0.260793	+	0.965395i	$0.583984\pi$
$942$	0	0
$943$	−48.0000	−1.56310
$944$	9.00000	0.292925
$945$	0	0
$946$	10.0000	0.325128
$947$	−11.0000	−0.357452	−0.178726	−	0.983899i	$-0.557198\pi$
$947$	−11.0000	−0.357452	−0.178726	+	0.983899i	$0.557198\pi$
$948$	0	0
$949$	6.00000	0.194768
$950$	55.0000	1.78444
$951$	0	0
$952$	0	0
$953$	43.0000	1.39291	0.696453	−	0.717602i	$-0.254760\pi$
$953$	43.0000	1.39291	0.696453	+	0.717602i	$0.254760\pi$
$954$	0	0
$955$	−16.0000	−0.517748
$956$	−21.0000	−0.679189
$957$	0	0
$958$	−7.00000	−0.226160
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	−16.0000	−0.515325
$965$	−16.0000	−0.515058
$966$	0	0
$967$	−47.0000	−1.51142	−0.755709	−	0.654907i	$-0.772708\pi$
$967$	−47.0000	−1.51142	−0.755709	+	0.654907i	$0.772708\pi$
$968$	−42.0000	−1.34993
$969$	0	0
$970$	−72.0000	−2.31178
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	−29.0000	−0.929220
$975$	0	0
$976$	1.00000	0.0320092
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	0	0
$979$	−40.0000	−1.27841
$980$	0	0
$981$	0	0
$982$	−2.00000	−0.0638226
$983$	15.0000	0.478426	0.239213	−	0.970967i	$-0.423111\pi$
$983$	15.0000	0.478426	0.239213	+	0.970967i	$0.423111\pi$
$984$	0	0
$985$	−40.0000	−1.27451
$986$	−21.0000	−0.668776
$987$	0	0
$988$	−5.00000	−0.159071
$989$	−12.0000	−0.381578
$990$	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
$993$	0	0
$994$	0	0
$995$	−24.0000	−0.760851
$996$	0	0
$997$	−49.0000	−1.55185	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−49.0000	−1.55185	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−32.0000	−1.01294
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.k.1.1		1
3.2	odd	2		1911.2.a.b.1.1		1
7.3	odd	6		819.2.j.a.352.1		2
7.5	odd	6		819.2.j.a.235.1		2
7.6	odd	2		5733.2.a.i.1.1		1
21.5	even	6		273.2.i.a.235.1	yes	2
21.17	even	6		273.2.i.a.79.1	✓	2
21.20	even	2		1911.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.a.79.1	✓	2	21.17	even	6
273.2.i.a.235.1	yes	2	21.5	even	6
819.2.j.a.235.1		2	7.5	odd	6
819.2.j.a.352.1		2	7.3	odd	6
1911.2.a.b.1.1		1	3.2	odd	2
1911.2.a.c.1.1		1	21.20	even	2
5733.2.a.i.1.1		1	7.6	odd	2
5733.2.a.k.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)

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