LMFDB - Embedded newform 1200.4.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,4,Mod(1,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1200.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1200.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:	$70.8022920069$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 60)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1200.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} +22.0000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} +22.0000 q^{7} +9.00000 q^{9} +14.0000 q^{11} +30.0000 q^{13} -62.0000 q^{17} +120.000 q^{19} -66.0000 q^{21} +188.000 q^{23} -27.0000 q^{27} +96.0000 q^{29} -184.000 q^{31} -42.0000 q^{33} -406.000 q^{37} -90.0000 q^{39} +130.000 q^{41} +148.000 q^{43} +448.000 q^{47} +141.000 q^{49} +186.000 q^{51} +414.000 q^{53} -360.000 q^{57} -266.000 q^{59} -838.000 q^{61} +198.000 q^{63} +248.000 q^{67} -564.000 q^{69} -1020.00 q^{71} -484.000 q^{73} +308.000 q^{77} +48.0000 q^{79} +81.0000 q^{81} +548.000 q^{83} -288.000 q^{87} -650.000 q^{89} +660.000 q^{91} +552.000 q^{93} +1816.00 q^{97} +126.000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	22.0000	1.18789	0.593944	−	0.804506i	$-0.297570\pi$
$7$	22.0000	1.18789	0.593944	+	0.804506i	$0.297570\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	14.0000	0.383742	0.191871	−	0.981420i	$-0.438545\pi$
$11$	14.0000	0.383742	0.191871	+	0.981420i	$0.438545\pi$
$12$	0	0
$13$	30.0000	0.640039	0.320019	−	0.947411i	$-0.396311\pi$
$13$	30.0000	0.640039	0.320019	+	0.947411i	$0.396311\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−62.0000	−0.884542	−0.442271	−	0.896882i	$-0.645827\pi$
$17$	−62.0000	−0.884542	−0.442271	+	0.896882i	$0.645827\pi$
$18$	0	0
$19$	120.000	1.44894	0.724471	−	0.689306i	$-0.242084\pi$
$19$	120.000	1.44894	0.724471	+	0.689306i	$0.242084\pi$
$20$	0	0
$21$	−66.0000	−0.685828
$22$	0	0
$23$	188.000	1.70438	0.852189	−	0.523234i	$-0.175274\pi$
$23$	188.000	1.70438	0.852189	+	0.523234i	$0.175274\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	96.0000	0.614716	0.307358	−	0.951594i	$-0.400555\pi$
$29$	96.0000	0.614716	0.307358	+	0.951594i	$0.400555\pi$
$30$	0	0
$31$	−184.000	−1.06604	−0.533022	−	0.846101i	$-0.678944\pi$
$31$	−184.000	−1.06604	−0.533022	+	0.846101i	$0.678944\pi$
$32$	0	0
$33$	−42.0000	−0.221553
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−406.000	−1.80395	−0.901973	−	0.431793i	$-0.857881\pi$
$37$	−406.000	−1.80395	−0.901973	+	0.431793i	$0.857881\pi$
$38$	0	0
$39$	−90.0000	−0.369527
$40$	0	0
$41$	130.000	0.495185	0.247593	−	0.968864i	$-0.420361\pi$
$41$	130.000	0.495185	0.247593	+	0.968864i	$0.420361\pi$
$42$	0	0
$43$	148.000	0.524879	0.262439	−	0.964948i	$-0.415473\pi$
$43$	148.000	0.524879	0.262439	+	0.964948i	$0.415473\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	448.000	1.39037	0.695186	−	0.718830i	$-0.255322\pi$
$47$	448.000	1.39037	0.695186	+	0.718830i	$0.255322\pi$
$48$	0	0
$49$	141.000	0.411079
$50$	0	0
$51$	186.000	0.510690
$52$	0	0
$53$	414.000	1.07297	0.536484	−	0.843911i	$-0.319752\pi$
$53$	414.000	1.07297	0.536484	+	0.843911i	$0.319752\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−360.000	−0.836547
$58$	0	0
$59$	−266.000	−0.586953	−0.293477	−	0.955966i	$-0.594812\pi$
$59$	−266.000	−0.586953	−0.293477	+	0.955966i	$0.594812\pi$
$60$	0	0
$61$	−838.000	−1.75893	−0.879466	−	0.475961i	$-0.842100\pi$
$61$	−838.000	−1.75893	−0.879466	+	0.475961i	$0.842100\pi$
$62$	0	0
$63$	198.000	0.395963
$64$	0	0
$65$	0	0
$66$	0	0
$67$	248.000	0.452209	0.226105	−	0.974103i	$-0.427401\pi$
$67$	248.000	0.452209	0.226105	+	0.974103i	$0.427401\pi$
$68$	0	0
$69$	−564.000	−0.984023
$70$	0	0
$71$	−1020.00	−1.70495	−0.852477	−	0.522765i	$-0.824901\pi$
$71$	−1020.00	−1.70495	−0.852477	+	0.522765i	$0.824901\pi$
$72$	0	0
$73$	−484.000	−0.775999	−0.387999	−	0.921660i	$-0.626834\pi$
$73$	−484.000	−0.775999	−0.387999	+	0.921660i	$0.626834\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	308.000	0.455842
$78$	0	0
$79$	48.0000	0.0683598	0.0341799	−	0.999416i	$-0.489118\pi$
$79$	48.0000	0.0683598	0.0341799	+	0.999416i	$0.489118\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	548.000	0.724709	0.362354	−	0.932040i	$-0.381973\pi$
$83$	548.000	0.724709	0.362354	+	0.932040i	$0.381973\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−288.000	−0.354906
$88$	0	0
$89$	−650.000	−0.774156	−0.387078	−	0.922047i	$-0.626516\pi$
$89$	−650.000	−0.774156	−0.387078	+	0.922047i	$0.626516\pi$
$90$	0	0
$91$	660.000	0.760294
$92$	0	0
$93$	552.000	0.615481
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1816.00	1.90090	0.950448	−	0.310884i	$-0.100625\pi$
$97$	1816.00	1.90090	0.950448	+	0.310884i	$0.100625\pi$
$98$	0	0
$99$	126.000	0.127914
$100$	0	0
$101$	1688.00	1.66299	0.831496	−	0.555530i	$-0.187485\pi$
$101$	1688.00	1.66299	0.831496	+	0.555530i	$0.187485\pi$
$102$	0	0
$103$	−298.000	−0.285076	−0.142538	−	0.989789i	$-0.545526\pi$
$103$	−298.000	−0.285076	−0.142538	+	0.989789i	$0.545526\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	276.000	0.249364	0.124682	−	0.992197i	$-0.460209\pi$
$107$	276.000	0.249364	0.124682	+	0.992197i	$0.460209\pi$
$108$	0	0
$109$	322.000	0.282954	0.141477	−	0.989942i	$-0.454815\pi$
$109$	322.000	0.282954	0.141477	+	0.989942i	$0.454815\pi$
$110$	0	0
$111$	1218.00	1.04151
$112$	0	0
$113$	486.000	0.404593	0.202297	−	0.979324i	$-0.435159\pi$
$113$	486.000	0.404593	0.202297	+	0.979324i	$0.435159\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	270.000	0.213346
$118$	0	0
$119$	−1364.00	−1.05074
$120$	0	0
$121$	−1135.00	−0.852742
$122$	0	0
$123$	−390.000	−0.285895
$124$	0	0
$125$	0	0
$126$	0	0
$127$	502.000	0.350750	0.175375	−	0.984502i	$-0.443886\pi$
$127$	502.000	0.350750	0.175375	+	0.984502i	$0.443886\pi$
$128$	0	0
$129$	−444.000	−0.303039
$130$	0	0
$131$	18.0000	0.0120051	0.00600255	−	0.999982i	$-0.498089\pi$
$131$	18.0000	0.0120051	0.00600255	+	0.999982i	$0.498089\pi$
$132$	0	0
$133$	2640.00	1.72118
$134$	0	0
$135$	0	0
$136$	0	0
$137$	2334.00	1.45553	0.727763	−	0.685829i	$-0.240560\pi$
$137$	2334.00	1.45553	0.727763	+	0.685829i	$0.240560\pi$
$138$	0	0
$139$	1676.00	1.02271	0.511354	−	0.859370i	$-0.329144\pi$
$139$	1676.00	1.02271	0.511354	+	0.859370i	$0.329144\pi$
$140$	0	0
$141$	−1344.00	−0.802732
$142$	0	0
$143$	420.000	0.245610
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−423.000	−0.237336
$148$	0	0
$149$	3452.00	1.89798	0.948989	−	0.315308i	$-0.102108\pi$
$149$	3452.00	1.89798	0.948989	+	0.315308i	$0.102108\pi$
$150$	0	0
$151$	−1720.00	−0.926964	−0.463482	−	0.886106i	$-0.653400\pi$
$151$	−1720.00	−0.926964	−0.463482	+	0.886106i	$0.653400\pi$
$152$	0	0
$153$	−558.000	−0.294847
$154$	0	0
$155$	0	0
$156$	0	0
$157$	1246.00	0.633386	0.316693	−	0.948528i	$-0.397427\pi$
$157$	1246.00	0.633386	0.316693	+	0.948528i	$0.397427\pi$
$158$	0	0
$159$	−1242.00	−0.619478
$160$	0	0
$161$	4136.00	2.02461
$162$	0	0
$163$	1760.00	0.845729	0.422865	−	0.906193i	$-0.361025\pi$
$163$	1760.00	0.845729	0.422865	+	0.906193i	$0.361025\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−2724.00	−1.26221	−0.631106	−	0.775696i	$-0.717399\pi$
$167$	−2724.00	−1.26221	−0.631106	+	0.775696i	$0.717399\pi$
$168$	0	0
$169$	−1297.00	−0.590350
$170$	0	0
$171$	1080.00	0.482980
$172$	0	0
$173$	2378.00	1.04506	0.522532	−	0.852620i	$-0.324988\pi$
$173$	2378.00	1.04506	0.522532	+	0.852620i	$0.324988\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	798.000	0.338878
$178$	0	0
$179$	3094.00	1.29194	0.645968	−	0.763365i	$-0.276454\pi$
$179$	3094.00	1.29194	0.645968	+	0.763365i	$0.276454\pi$
$180$	0	0
$181$	−310.000	−0.127305	−0.0636523	−	0.997972i	$-0.520275\pi$
$181$	−310.000	−0.127305	−0.0636523	+	0.997972i	$0.520275\pi$
$182$	0	0
$183$	2514.00	1.01552
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−868.000	−0.339436
$188$	0	0
$189$	−594.000	−0.228609
$190$	0	0
$191$	516.000	0.195479	0.0977394	−	0.995212i	$-0.468839\pi$
$191$	516.000	0.195479	0.0977394	+	0.995212i	$0.468839\pi$
$192$	0	0
$193$	188.000	0.0701168	0.0350584	−	0.999385i	$-0.488838\pi$
$193$	188.000	0.0701168	0.0350584	+	0.999385i	$0.488838\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−2578.00	−0.932360	−0.466180	−	0.884690i	$-0.654370\pi$
$197$	−2578.00	−0.932360	−0.466180	+	0.884690i	$0.654370\pi$
$198$	0	0
$199$	528.000	0.188085	0.0940425	−	0.995568i	$-0.470021\pi$
$199$	528.000	0.188085	0.0940425	+	0.995568i	$0.470021\pi$
$200$	0	0
$201$	−744.000	−0.261083
$202$	0	0
$203$	2112.00	0.730213
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1692.00	0.568126
$208$	0	0
$209$	1680.00	0.556019
$210$	0	0
$211$	3660.00	1.19415	0.597073	−	0.802187i	$-0.296330\pi$
$211$	3660.00	1.19415	0.597073	+	0.802187i	$0.296330\pi$
$212$	0	0
$213$	3060.00	0.984356
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−4048.00	−1.26634
$218$	0	0
$219$	1452.00	0.448023
$220$	0	0
$221$	−1860.00	−0.566141
$222$	0	0
$223$	2350.00	0.705684	0.352842	−	0.935683i	$-0.385215\pi$
$223$	2350.00	0.705684	0.352842	+	0.935683i	$0.385215\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	3260.00	0.953189	0.476594	−	0.879123i	$-0.341871\pi$
$227$	3260.00	0.953189	0.476594	+	0.879123i	$0.341871\pi$
$228$	0	0
$229$	−466.000	−0.134472	−0.0672361	−	0.997737i	$-0.521418\pi$
$229$	−466.000	−0.134472	−0.0672361	+	0.997737i	$0.521418\pi$
$230$	0	0
$231$	−924.000	−0.263181
$232$	0	0
$233$	3170.00	0.891303	0.445652	−	0.895207i	$-0.352972\pi$
$233$	3170.00	0.891303	0.445652	+	0.895207i	$0.352972\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−144.000	−0.0394675
$238$	0	0
$239$	−292.000	−0.0790289	−0.0395145	−	0.999219i	$-0.512581\pi$
$239$	−292.000	−0.0790289	−0.0395145	+	0.999219i	$0.512581\pi$
$240$	0	0
$241$	−842.000	−0.225054	−0.112527	−	0.993649i	$-0.535894\pi$
$241$	−842.000	−0.225054	−0.112527	+	0.993649i	$0.535894\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	3600.00	0.927379
$248$	0	0
$249$	−1644.00	−0.418411
$250$	0	0
$251$	−5838.00	−1.46809	−0.734046	−	0.679099i	$-0.762371\pi$
$251$	−5838.00	−1.46809	−0.734046	+	0.679099i	$0.762371\pi$
$252$	0	0
$253$	2632.00	0.654041
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−4626.00	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−4626.00	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−8932.00	−2.14289
$260$	0	0
$261$	864.000	0.204905
$262$	0	0
$263$	5468.00	1.28202	0.641010	−	0.767532i	$-0.278516\pi$
$263$	5468.00	1.28202	0.641010	+	0.767532i	$0.278516\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	1950.00	0.446959
$268$	0	0
$269$	−2976.00	−0.674535	−0.337268	−	0.941409i	$-0.609503\pi$
$269$	−2976.00	−0.674535	−0.337268	+	0.941409i	$0.609503\pi$
$270$	0	0
$271$	56.0000	0.0125526	0.00627631	−	0.999980i	$-0.498002\pi$
$271$	56.0000	0.0125526	0.00627631	+	0.999980i	$0.498002\pi$
$272$	0	0
$273$	−1980.00	−0.438956
$274$	0	0
$275$	0	0
$276$	0	0
$277$	4106.00	0.890634	0.445317	−	0.895373i	$-0.353091\pi$
$277$	4106.00	0.890634	0.445317	+	0.895373i	$0.353091\pi$
$278$	0	0
$279$	−1656.00	−0.355348
$280$	0	0
$281$	−2274.00	−0.482760	−0.241380	−	0.970431i	$-0.577600\pi$
$281$	−2274.00	−0.482760	−0.241380	+	0.970431i	$0.577600\pi$
$282$	0	0
$283$	5504.00	1.15611	0.578054	−	0.815998i	$-0.303812\pi$
$283$	5504.00	1.15611	0.578054	+	0.815998i	$0.303812\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	2860.00	0.588225
$288$	0	0
$289$	−1069.00	−0.217586
$290$	0	0
$291$	−5448.00	−1.09748
$292$	0	0
$293$	−8034.00	−1.60188	−0.800941	−	0.598744i	$-0.795667\pi$
$293$	−8034.00	−1.60188	−0.800941	+	0.598744i	$0.795667\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−378.000	−0.0738511
$298$	0	0
$299$	5640.00	1.09087
$300$	0	0
$301$	3256.00	0.623497
$302$	0	0
$303$	−5064.00	−0.960129
$304$	0	0
$305$	0	0
$306$	0	0
$307$	996.000	0.185162	0.0925810	−	0.995705i	$-0.470488\pi$
$307$	996.000	0.185162	0.0925810	+	0.995705i	$0.470488\pi$
$308$	0	0
$309$	894.000	0.164589
$310$	0	0
$311$	8676.00	1.58190	0.790950	−	0.611881i	$-0.209587\pi$
$311$	8676.00	1.58190	0.790950	+	0.611881i	$0.209587\pi$
$312$	0	0
$313$	−1732.00	−0.312775	−0.156387	−	0.987696i	$-0.549985\pi$
$313$	−1732.00	−0.312775	−0.156387	+	0.987696i	$0.549985\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	2938.00	0.520551	0.260275	−	0.965534i	$-0.416187\pi$
$317$	2938.00	0.520551	0.260275	+	0.965534i	$0.416187\pi$
$318$	0	0
$319$	1344.00	0.235892
$320$	0	0
$321$	−828.000	−0.143970
$322$	0	0
$323$	−7440.00	−1.28165
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−966.000	−0.163364
$328$	0	0
$329$	9856.00	1.65161
$330$	0	0
$331$	128.000	0.0212553	0.0106277	−	0.999944i	$-0.496617\pi$
$331$	128.000	0.0212553	0.0106277	+	0.999944i	$0.496617\pi$
$332$	0	0
$333$	−3654.00	−0.601315
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−5596.00	−0.904551	−0.452275	−	0.891878i	$-0.649388\pi$
$337$	−5596.00	−0.904551	−0.452275	+	0.891878i	$0.649388\pi$
$338$	0	0
$339$	−1458.00	−0.233592
$340$	0	0
$341$	−2576.00	−0.409086
$342$	0	0
$343$	−4444.00	−0.699573
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−924.000	−0.142948	−0.0714739	−	0.997442i	$-0.522770\pi$
$347$	−924.000	−0.142948	−0.0714739	+	0.997442i	$0.522770\pi$
$348$	0	0
$349$	−6206.00	−0.951861	−0.475931	−	0.879483i	$-0.657889\pi$
$349$	−6206.00	−0.951861	−0.475931	+	0.879483i	$0.657889\pi$
$350$	0	0
$351$	−810.000	−0.123176
$352$	0	0
$353$	3506.00	0.528628	0.264314	−	0.964437i	$-0.414855\pi$
$353$	3506.00	0.528628	0.264314	+	0.964437i	$0.414855\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	4092.00	0.606643
$358$	0	0
$359$	7104.00	1.04439	0.522193	−	0.852827i	$-0.325114\pi$
$359$	7104.00	1.04439	0.522193	+	0.852827i	$0.325114\pi$
$360$	0	0
$361$	7541.00	1.09943
$362$	0	0
$363$	3405.00	0.492331
$364$	0	0
$365$	0	0
$366$	0	0
$367$	2902.00	0.412761	0.206380	−	0.978472i	$-0.433832\pi$
$367$	2902.00	0.412761	0.206380	+	0.978472i	$0.433832\pi$
$368$	0	0
$369$	1170.00	0.165062
$370$	0	0
$371$	9108.00	1.27457
$372$	0	0
$373$	4542.00	0.630498	0.315249	−	0.949009i	$-0.397912\pi$
$373$	4542.00	0.630498	0.315249	+	0.949009i	$0.397912\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	2880.00	0.393442
$378$	0	0
$379$	−5852.00	−0.793132	−0.396566	−	0.918006i	$-0.629798\pi$
$379$	−5852.00	−0.793132	−0.396566	+	0.918006i	$0.629798\pi$
$380$	0	0
$381$	−1506.00	−0.202506
$382$	0	0
$383$	−8936.00	−1.19219	−0.596094	−	0.802914i	$-0.703282\pi$
$383$	−8936.00	−1.19219	−0.596094	+	0.802914i	$0.703282\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1332.00	0.174960
$388$	0	0
$389$	1924.00	0.250773	0.125386	−	0.992108i	$-0.459983\pi$
$389$	1924.00	0.250773	0.125386	+	0.992108i	$0.459983\pi$
$390$	0	0
$391$	−11656.0	−1.50759
$392$	0	0
$393$	−54.0000	−0.00693114
$394$	0	0
$395$	0	0
$396$	0	0
$397$	9194.00	1.16230	0.581151	−	0.813796i	$-0.302603\pi$
$397$	9194.00	1.16230	0.581151	+	0.813796i	$0.302603\pi$
$398$	0	0
$399$	−7920.00	−0.993724
$400$	0	0
$401$	−10714.0	−1.33424	−0.667122	−	0.744949i	$-0.732474\pi$
$401$	−10714.0	−1.33424	−0.667122	+	0.744949i	$0.732474\pi$
$402$	0	0
$403$	−5520.00	−0.682310
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−5684.00	−0.692249
$408$	0	0
$409$	−12346.0	−1.49259	−0.746296	−	0.665614i	$-0.768170\pi$
$409$	−12346.0	−1.49259	−0.746296	+	0.665614i	$0.768170\pi$
$410$	0	0
$411$	−7002.00	−0.840348
$412$	0	0
$413$	−5852.00	−0.697235
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−5028.00	−0.590461
$418$	0	0
$419$	13562.0	1.58126	0.790629	−	0.612296i	$-0.209754\pi$
$419$	13562.0	1.58126	0.790629	+	0.612296i	$0.209754\pi$
$420$	0	0
$421$	5230.00	0.605450	0.302725	−	0.953078i	$-0.402104\pi$
$421$	5230.00	0.605450	0.302725	+	0.953078i	$0.402104\pi$
$422$	0	0
$423$	4032.00	0.463458
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−18436.0	−2.08942
$428$	0	0
$429$	−1260.00	−0.141803
$430$	0	0
$431$	11552.0	1.29104	0.645522	−	0.763741i	$-0.276640\pi$
$431$	11552.0	1.29104	0.645522	+	0.763741i	$0.276640\pi$
$432$	0	0
$433$	−7972.00	−0.884780	−0.442390	−	0.896823i	$-0.645869\pi$
$433$	−7972.00	−0.884780	−0.442390	+	0.896823i	$0.645869\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	22560.0	2.46954
$438$	0	0
$439$	−7152.00	−0.777554	−0.388777	−	0.921332i	$-0.627102\pi$
$439$	−7152.00	−0.777554	−0.388777	+	0.921332i	$0.627102\pi$
$440$	0	0
$441$	1269.00	0.137026
$442$	0	0
$443$	2652.00	0.284425	0.142213	−	0.989836i	$-0.454578\pi$
$443$	2652.00	0.284425	0.142213	+	0.989836i	$0.454578\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−10356.0	−1.09580
$448$	0	0
$449$	4542.00	0.477395	0.238697	−	0.971094i	$-0.423280\pi$
$449$	4542.00	0.477395	0.238697	+	0.971094i	$0.423280\pi$
$450$	0	0
$451$	1820.00	0.190023
$452$	0	0
$453$	5160.00	0.535183
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−16000.0	−1.63774	−0.818871	−	0.573977i	$-0.805400\pi$
$457$	−16000.0	−1.63774	−0.818871	+	0.573977i	$0.805400\pi$
$458$	0	0
$459$	1674.00	0.170230
$460$	0	0
$461$	2076.00	0.209737	0.104869	−	0.994486i	$-0.466558\pi$
$461$	2076.00	0.209737	0.104869	+	0.994486i	$0.466558\pi$
$462$	0	0
$463$	−5406.00	−0.542631	−0.271315	−	0.962490i	$-0.587459\pi$
$463$	−5406.00	−0.542631	−0.271315	+	0.962490i	$0.587459\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−444.000	−0.0439954	−0.0219977	−	0.999758i	$-0.507003\pi$
$467$	−444.000	−0.0439954	−0.0219977	+	0.999758i	$0.507003\pi$
$468$	0	0
$469$	5456.00	0.537174
$470$	0	0
$471$	−3738.00	−0.365686
$472$	0	0
$473$	2072.00	0.201418
$474$	0	0
$475$	0	0
$476$	0	0
$477$	3726.00	0.357656
$478$	0	0
$479$	1724.00	0.164450	0.0822250	−	0.996614i	$-0.473797\pi$
$479$	1724.00	0.164450	0.0822250	+	0.996614i	$0.473797\pi$
$480$	0	0
$481$	−12180.0	−1.15460
$482$	0	0
$483$	−12408.0	−1.16891
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−17046.0	−1.58609	−0.793047	−	0.609160i	$-0.791507\pi$
$487$	−17046.0	−1.58609	−0.793047	+	0.609160i	$0.791507\pi$
$488$	0	0
$489$	−5280.00	−0.488282
$490$	0	0
$491$	−8814.00	−0.810123	−0.405061	−	0.914290i	$-0.632750\pi$
$491$	−8814.00	−0.810123	−0.405061	+	0.914290i	$0.632750\pi$
$492$	0	0
$493$	−5952.00	−0.543742
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−22440.0	−2.02529
$498$	0	0
$499$	−5256.00	−0.471525	−0.235762	−	0.971811i	$-0.575759\pi$
$499$	−5256.00	−0.471525	−0.235762	+	0.971811i	$0.575759\pi$
$500$	0	0
$501$	8172.00	0.728739
$502$	0	0
$503$	5232.00	0.463784	0.231892	−	0.972742i	$-0.425508\pi$
$503$	5232.00	0.463784	0.231892	+	0.972742i	$0.425508\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	3891.00	0.340839
$508$	0	0
$509$	4128.00	0.359470	0.179735	−	0.983715i	$-0.442476\pi$
$509$	4128.00	0.359470	0.179735	+	0.983715i	$0.442476\pi$
$510$	0	0
$511$	−10648.0	−0.921800
$512$	0	0
$513$	−3240.00	−0.278849
$514$	0	0
$515$	0	0
$516$	0	0
$517$	6272.00	0.533544
$518$	0	0
$519$	−7134.00	−0.603368
$520$	0	0
$521$	−538.000	−0.0452403	−0.0226202	−	0.999744i	$-0.507201\pi$
$521$	−538.000	−0.0452403	−0.0226202	+	0.999744i	$0.507201\pi$
$522$	0	0
$523$	−10336.0	−0.864172	−0.432086	−	0.901833i	$-0.642222\pi$
$523$	−10336.0	−0.864172	−0.432086	+	0.901833i	$0.642222\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	11408.0	0.942961
$528$	0	0
$529$	23177.0	1.90491
$530$	0	0
$531$	−2394.00	−0.195651
$532$	0	0
$533$	3900.00	0.316938
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−9282.00	−0.745899
$538$	0	0
$539$	1974.00	0.157748
$540$	0	0
$541$	−8942.00	−0.710622	−0.355311	−	0.934748i	$-0.615625\pi$
$541$	−8942.00	−0.710622	−0.355311	+	0.934748i	$0.615625\pi$
$542$	0	0
$543$	930.000	0.0734993
$544$	0	0
$545$	0	0
$546$	0	0
$547$	11404.0	0.891407	0.445704	−	0.895181i	$-0.352954\pi$
$547$	11404.0	0.891407	0.445704	+	0.895181i	$0.352954\pi$
$548$	0	0
$549$	−7542.00	−0.586311
$550$	0	0
$551$	11520.0	0.890687
$552$	0	0
$553$	1056.00	0.0812038
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−3114.00	−0.236884	−0.118442	−	0.992961i	$-0.537790\pi$
$557$	−3114.00	−0.236884	−0.118442	+	0.992961i	$0.537790\pi$
$558$	0	0
$559$	4440.00	0.335943
$560$	0	0
$561$	2604.00	0.195973
$562$	0	0
$563$	−3620.00	−0.270985	−0.135493	−	0.990778i	$-0.543262\pi$
$563$	−3620.00	−0.270985	−0.135493	+	0.990778i	$0.543262\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1782.00	0.131988
$568$	0	0
$569$	−6506.00	−0.479342	−0.239671	−	0.970854i	$-0.577040\pi$
$569$	−6506.00	−0.479342	−0.239671	+	0.970854i	$0.577040\pi$
$570$	0	0
$571$	17600.0	1.28991	0.644954	−	0.764222i	$-0.276877\pi$
$571$	17600.0	1.28991	0.644954	+	0.764222i	$0.276877\pi$
$572$	0	0
$573$	−1548.00	−0.112860
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−4864.00	−0.350938	−0.175469	−	0.984485i	$-0.556144\pi$
$577$	−4864.00	−0.350938	−0.175469	+	0.984485i	$0.556144\pi$
$578$	0	0
$579$	−564.000	−0.0404819
$580$	0	0
$581$	12056.0	0.860873
$582$	0	0
$583$	5796.00	0.411742
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−18348.0	−1.29012	−0.645062	−	0.764130i	$-0.723169\pi$
$587$	−18348.0	−1.29012	−0.645062	+	0.764130i	$0.723169\pi$
$588$	0	0
$589$	−22080.0	−1.54464
$590$	0	0
$591$	7734.00	0.538298
$592$	0	0
$593$	−16218.0	−1.12309	−0.561546	−	0.827446i	$-0.689793\pi$
$593$	−16218.0	−1.12309	−0.561546	+	0.827446i	$0.689793\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−1584.00	−0.108591
$598$	0	0
$599$	24576.0	1.67637	0.838187	−	0.545383i	$-0.183616\pi$
$599$	24576.0	1.67637	0.838187	+	0.545383i	$0.183616\pi$
$600$	0	0
$601$	6578.00	0.446460	0.223230	−	0.974766i	$-0.428340\pi$
$601$	6578.00	0.446460	0.223230	+	0.974766i	$0.428340\pi$
$602$	0	0
$603$	2232.00	0.150736
$604$	0	0
$605$	0	0
$606$	0	0
$607$	25346.0	1.69483	0.847415	−	0.530930i	$-0.178157\pi$
$607$	25346.0	1.69483	0.847415	+	0.530930i	$0.178157\pi$
$608$	0	0
$609$	−6336.00	−0.421589
$610$	0	0
$611$	13440.0	0.889892
$612$	0	0
$613$	−27214.0	−1.79309	−0.896544	−	0.442954i	$-0.853930\pi$
$613$	−27214.0	−1.79309	−0.896544	+	0.442954i	$0.853930\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−22478.0	−1.46666	−0.733331	−	0.679872i	$-0.762035\pi$
$617$	−22478.0	−1.46666	−0.733331	+	0.679872i	$0.762035\pi$
$618$	0	0
$619$	−3356.00	−0.217914	−0.108957	−	0.994046i	$-0.534751\pi$
$619$	−3356.00	−0.217914	−0.108957	+	0.994046i	$0.534751\pi$
$620$	0	0
$621$	−5076.00	−0.328008
$622$	0	0
$623$	−14300.0	−0.919611
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−5040.00	−0.321018
$628$	0	0
$629$	25172.0	1.59567
$630$	0	0
$631$	−19952.0	−1.25876	−0.629379	−	0.777098i	$-0.716691\pi$
$631$	−19952.0	−1.25876	−0.629379	+	0.777098i	$0.716691\pi$
$632$	0	0
$633$	−10980.0	−0.689440
$634$	0	0
$635$	0	0
$636$	0	0
$637$	4230.00	0.263106
$638$	0	0
$639$	−9180.00	−0.568318
$640$	0	0
$641$	26434.0	1.62883	0.814415	−	0.580283i	$-0.197058\pi$
$641$	26434.0	1.62883	0.814415	+	0.580283i	$0.197058\pi$
$642$	0	0
$643$	10632.0	0.652076	0.326038	−	0.945357i	$-0.394286\pi$
$643$	10632.0	0.652076	0.326038	+	0.945357i	$0.394286\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−9384.00	−0.570206	−0.285103	−	0.958497i	$-0.592028\pi$
$647$	−9384.00	−0.570206	−0.285103	+	0.958497i	$0.592028\pi$
$648$	0	0
$649$	−3724.00	−0.225239
$650$	0	0
$651$	12144.0	0.731123
$652$	0	0
$653$	3922.00	0.235038	0.117519	−	0.993071i	$-0.462506\pi$
$653$	3922.00	0.235038	0.117519	+	0.993071i	$0.462506\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−4356.00	−0.258666
$658$	0	0
$659$	−12542.0	−0.741376	−0.370688	−	0.928757i	$-0.620878\pi$
$659$	−12542.0	−0.741376	−0.370688	+	0.928757i	$0.620878\pi$
$660$	0	0
$661$	−8662.00	−0.509702	−0.254851	−	0.966980i	$-0.582026\pi$
$661$	−8662.00	−0.509702	−0.254851	+	0.966980i	$0.582026\pi$
$662$	0	0
$663$	5580.00	0.326862
$664$	0	0
$665$	0	0
$666$	0	0
$667$	18048.0	1.04771
$668$	0	0
$669$	−7050.00	−0.407427
$670$	0	0
$671$	−11732.0	−0.674976
$672$	0	0
$673$	−5820.00	−0.333350	−0.166675	−	0.986012i	$-0.553303\pi$
$673$	−5820.00	−0.333350	−0.166675	+	0.986012i	$0.553303\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	778.000	0.0441669	0.0220834	−	0.999756i	$-0.492970\pi$
$677$	778.000	0.0441669	0.0220834	+	0.999756i	$0.492970\pi$
$678$	0	0
$679$	39952.0	2.25805
$680$	0	0
$681$	−9780.00	−0.550324
$682$	0	0
$683$	−5548.00	−0.310817	−0.155409	−	0.987850i	$-0.549669\pi$
$683$	−5548.00	−0.310817	−0.155409	+	0.987850i	$0.549669\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1398.00	0.0776376
$688$	0	0
$689$	12420.0	0.686741
$690$	0	0
$691$	−5488.00	−0.302132	−0.151066	−	0.988524i	$-0.548271\pi$
$691$	−5488.00	−0.302132	−0.151066	+	0.988524i	$0.548271\pi$
$692$	0	0
$693$	2772.00	0.151947
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−8060.00	−0.438012
$698$	0	0
$699$	−9510.00	−0.514594
$700$	0	0
$701$	1216.00	0.0655174	0.0327587	−	0.999463i	$-0.489571\pi$
$701$	1216.00	0.0655174	0.0327587	+	0.999463i	$0.489571\pi$
$702$	0	0
$703$	−48720.0	−2.61381
$704$	0	0
$705$	0	0
$706$	0	0
$707$	37136.0	1.97545
$708$	0	0
$709$	20406.0	1.08091	0.540454	−	0.841374i	$-0.318253\pi$
$709$	20406.0	1.08091	0.540454	+	0.841374i	$0.318253\pi$
$710$	0	0
$711$	432.000	0.0227866
$712$	0	0
$713$	−34592.0	−1.81694
$714$	0	0
$715$	0	0
$716$	0	0
$717$	876.000	0.0456274
$718$	0	0
$719$	−19672.0	−1.02036	−0.510182	−	0.860066i	$-0.670422\pi$
$719$	−19672.0	−1.02036	−0.510182	+	0.860066i	$0.670422\pi$
$720$	0	0
$721$	−6556.00	−0.338638
$722$	0	0
$723$	2526.00	0.129935
$724$	0	0
$725$	0	0
$726$	0	0
$727$	1194.00	0.0609120	0.0304560	−	0.999536i	$-0.490304\pi$
$727$	1194.00	0.0609120	0.0304560	+	0.999536i	$0.490304\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	−9176.00	−0.464277
$732$	0	0
$733$	21802.0	1.09860	0.549301	−	0.835625i	$-0.314894\pi$
$733$	21802.0	1.09860	0.549301	+	0.835625i	$0.314894\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	3472.00	0.173532
$738$	0	0
$739$	−15280.0	−0.760601	−0.380300	−	0.924863i	$-0.624179\pi$
$739$	−15280.0	−0.760601	−0.380300	+	0.924863i	$0.624179\pi$
$740$	0	0
$741$	−10800.0	−0.535422
$742$	0	0
$743$	6672.00	0.329437	0.164719	−	0.986341i	$-0.447328\pi$
$743$	6672.00	0.329437	0.164719	+	0.986341i	$0.447328\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	4932.00	0.241570
$748$	0	0
$749$	6072.00	0.296216
$750$	0	0
$751$	11008.0	0.534870	0.267435	−	0.963576i	$-0.413824\pi$
$751$	11008.0	0.534870	0.267435	+	0.963576i	$0.413824\pi$
$752$	0	0
$753$	17514.0	0.847604
$754$	0	0
$755$	0	0
$756$	0	0
$757$	3242.00	0.155657	0.0778286	−	0.996967i	$-0.475201\pi$
$757$	3242.00	0.155657	0.0778286	+	0.996967i	$0.475201\pi$
$758$	0	0
$759$	−7896.00	−0.377611
$760$	0	0
$761$	17982.0	0.856566	0.428283	−	0.903645i	$-0.359119\pi$
$761$	17982.0	0.856566	0.428283	+	0.903645i	$0.359119\pi$
$762$	0	0
$763$	7084.00	0.336118
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−7980.00	−0.375673
$768$	0	0
$769$	−30462.0	−1.42846	−0.714231	−	0.699910i	$-0.753224\pi$
$769$	−30462.0	−1.42846	−0.714231	+	0.699910i	$0.753224\pi$
$770$	0	0
$771$	13878.0	0.648254
$772$	0	0
$773$	17394.0	0.809339	0.404669	−	0.914463i	$-0.367387\pi$
$773$	17394.0	0.809339	0.404669	+	0.914463i	$0.367387\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	26796.0	1.23720
$778$	0	0
$779$	15600.0	0.717494
$780$	0	0
$781$	−14280.0	−0.654262
$782$	0	0
$783$	−2592.00	−0.118302
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−20336.0	−0.921093	−0.460546	−	0.887636i	$-0.652347\pi$
$787$	−20336.0	−0.921093	−0.460546	+	0.887636i	$0.652347\pi$
$788$	0	0
$789$	−16404.0	−0.740175
$790$	0	0
$791$	10692.0	0.480612
$792$	0	0
$793$	−25140.0	−1.12579
$794$	0	0
$795$	0	0
$796$	0	0
$797$	19546.0	0.868701	0.434351	−	0.900744i	$-0.356978\pi$
$797$	19546.0	0.868701	0.434351	+	0.900744i	$0.356978\pi$
$798$	0	0
$799$	−27776.0	−1.22984
$800$	0	0
$801$	−5850.00	−0.258052
$802$	0	0
$803$	−6776.00	−0.297783
$804$	0	0
$805$	0	0
$806$	0	0
$807$	8928.00	0.389443
$808$	0	0
$809$	3954.00	0.171836	0.0859179	−	0.996302i	$-0.472618\pi$
$809$	3954.00	0.171836	0.0859179	+	0.996302i	$0.472618\pi$
$810$	0	0
$811$	3860.00	0.167131	0.0835653	−	0.996502i	$-0.473369\pi$
$811$	3860.00	0.167131	0.0835653	+	0.996502i	$0.473369\pi$
$812$	0	0
$813$	−168.000	−0.00724725
$814$	0	0
$815$	0	0
$816$	0	0
$817$	17760.0	0.760519
$818$	0	0
$819$	5940.00	0.253431
$820$	0	0
$821$	37016.0	1.57353	0.786764	−	0.617253i	$-0.211755\pi$
$821$	37016.0	1.57353	0.786764	+	0.617253i	$0.211755\pi$
$822$	0	0
$823$	25794.0	1.09249	0.546247	−	0.837624i	$-0.316056\pi$
$823$	25794.0	1.09249	0.546247	+	0.837624i	$0.316056\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−44116.0	−1.85497	−0.927487	−	0.373855i	$-0.878036\pi$
$827$	−44116.0	−1.85497	−0.927487	+	0.373855i	$0.878036\pi$
$828$	0	0
$829$	−11622.0	−0.486910	−0.243455	−	0.969912i	$-0.578281\pi$
$829$	−11622.0	−0.486910	−0.243455	+	0.969912i	$0.578281\pi$
$830$	0	0
$831$	−12318.0	−0.514208
$832$	0	0
$833$	−8742.00	−0.363616
$834$	0	0
$835$	0	0
$836$	0	0
$837$	4968.00	0.205160
$838$	0	0
$839$	2584.00	0.106328	0.0531642	−	0.998586i	$-0.483069\pi$
$839$	2584.00	0.106328	0.0531642	+	0.998586i	$0.483069\pi$
$840$	0	0
$841$	−15173.0	−0.622125
$842$	0	0
$843$	6822.00	0.278721
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−24970.0	−1.01296
$848$	0	0
$849$	−16512.0	−0.667480
$850$	0	0
$851$	−76328.0	−3.07461
$852$	0	0
$853$	39754.0	1.59572	0.797861	−	0.602841i	$-0.205965\pi$
$853$	39754.0	1.59572	0.797861	+	0.602841i	$0.205965\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−18534.0	−0.738751	−0.369375	−	0.929280i	$-0.620428\pi$
$857$	−18534.0	−0.738751	−0.369375	+	0.929280i	$0.620428\pi$
$858$	0	0
$859$	11140.0	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$859$	11140.0	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$860$	0	0
$861$	−8580.00	−0.339612
$862$	0	0
$863$	28356.0	1.11848	0.559241	−	0.829005i	$-0.311093\pi$
$863$	28356.0	1.11848	0.559241	+	0.829005i	$0.311093\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	3207.00	0.125623
$868$	0	0
$869$	672.000	0.0262325
$870$	0	0
$871$	7440.00	0.289431
$872$	0	0
$873$	16344.0	0.633632
$874$	0	0
$875$	0	0
$876$	0	0
$877$	34942.0	1.34539	0.672695	−	0.739920i	$-0.265137\pi$
$877$	34942.0	1.34539	0.672695	+	0.739920i	$0.265137\pi$
$878$	0	0
$879$	24102.0	0.924847
$880$	0	0
$881$	−13890.0	−0.531176	−0.265588	−	0.964087i	$-0.585566\pi$
$881$	−13890.0	−0.531176	−0.265588	+	0.964087i	$0.585566\pi$
$882$	0	0
$883$	11496.0	0.438133	0.219066	−	0.975710i	$-0.429699\pi$
$883$	11496.0	0.438133	0.219066	+	0.975710i	$0.429699\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−29988.0	−1.13517	−0.567587	−	0.823314i	$-0.692123\pi$
$887$	−29988.0	−1.13517	−0.567587	+	0.823314i	$0.692123\pi$
$888$	0	0
$889$	11044.0	0.416652
$890$	0	0
$891$	1134.00	0.0426380
$892$	0	0
$893$	53760.0	2.01457
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−16920.0	−0.629813
$898$	0	0
$899$	−17664.0	−0.655314
$900$	0	0
$901$	−25668.0	−0.949084
$902$	0	0
$903$	−9768.00	−0.359976
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−16764.0	−0.613715	−0.306857	−	0.951755i	$-0.599277\pi$
$907$	−16764.0	−0.613715	−0.306857	+	0.951755i	$0.599277\pi$
$908$	0	0
$909$	15192.0	0.554331
$910$	0	0
$911$	19152.0	0.696525	0.348262	−	0.937397i	$-0.386772\pi$
$911$	19152.0	0.696525	0.348262	+	0.937397i	$0.386772\pi$
$912$	0	0
$913$	7672.00	0.278101
$914$	0	0
$915$	0	0
$916$	0	0
$917$	396.000	0.0142607
$918$	0	0
$919$	−35712.0	−1.28186	−0.640930	−	0.767599i	$-0.721451\pi$
$919$	−35712.0	−1.28186	−0.640930	+	0.767599i	$0.721451\pi$
$920$	0	0
$921$	−2988.00	−0.106903
$922$	0	0
$923$	−30600.0	−1.09124
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−2682.00	−0.0950253
$928$	0	0
$929$	−16098.0	−0.568523	−0.284262	−	0.958747i	$-0.591748\pi$
$929$	−16098.0	−0.568523	−0.284262	+	0.958747i	$0.591748\pi$
$930$	0	0
$931$	16920.0	0.595629
$932$	0	0
$933$	−26028.0	−0.913310
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−24776.0	−0.863817	−0.431909	−	0.901917i	$-0.642160\pi$
$937$	−24776.0	−0.863817	−0.431909	+	0.901917i	$0.642160\pi$
$938$	0	0
$939$	5196.00	0.180580
$940$	0	0
$941$	−39500.0	−1.36840	−0.684199	−	0.729295i	$-0.739848\pi$
$941$	−39500.0	−1.36840	−0.684199	+	0.729295i	$0.739848\pi$
$942$	0	0
$943$	24440.0	0.843983
$944$	0	0
$945$	0	0
$946$	0	0
$947$	22836.0	0.783601	0.391801	−	0.920050i	$-0.371852\pi$
$947$	22836.0	0.783601	0.391801	+	0.920050i	$0.371852\pi$
$948$	0	0
$949$	−14520.0	−0.496669
$950$	0	0
$951$	−8814.00	−0.300540
$952$	0	0
$953$	28478.0	0.967988	0.483994	−	0.875071i	$-0.339186\pi$
$953$	28478.0	0.967988	0.483994	+	0.875071i	$0.339186\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−4032.00	−0.136192
$958$	0	0
$959$	51348.0	1.72900
$960$	0	0
$961$	4065.00	0.136451
$962$	0	0
$963$	2484.00	0.0831213
$964$	0	0
$965$	0	0
$966$	0	0
$967$	24830.0	0.825728	0.412864	−	0.910793i	$-0.364528\pi$
$967$	24830.0	0.825728	0.412864	+	0.910793i	$0.364528\pi$
$968$	0	0
$969$	22320.0	0.739960
$970$	0	0
$971$	−37038.0	−1.22411	−0.612053	−	0.790817i	$-0.709656\pi$
$971$	−37038.0	−1.22411	−0.612053	+	0.790817i	$0.709656\pi$
$972$	0	0
$973$	36872.0	1.21486
$974$	0	0
$975$	0	0
$976$	0	0
$977$	26346.0	0.862726	0.431363	−	0.902178i	$-0.358033\pi$
$977$	26346.0	0.862726	0.431363	+	0.902178i	$0.358033\pi$
$978$	0	0
$979$	−9100.00	−0.297076
$980$	0	0
$981$	2898.00	0.0943181
$982$	0	0
$983$	11464.0	0.371968	0.185984	−	0.982553i	$-0.440453\pi$
$983$	11464.0	0.371968	0.185984	+	0.982553i	$0.440453\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−29568.0	−0.953556
$988$	0	0
$989$	27824.0	0.894592
$990$	0	0
$991$	28952.0	0.928043	0.464021	−	0.885824i	$-0.346406\pi$
$991$	28952.0	0.928043	0.464021	+	0.885824i	$0.346406\pi$
$992$	0	0
$993$	−384.000	−0.0122718
$994$	0	0
$995$	0	0
$996$	0	0
$997$	8022.00	0.254824	0.127412	−	0.991850i	$-0.459333\pi$
$997$	8022.00	0.254824	0.127412	+	0.991850i	$0.459333\pi$
$998$	0	0
$999$	10962.0	0.347170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.4.a.q.1.1		1
4.3	odd	2		300.4.a.f.1.1		1
5.2	odd	4		240.4.f.a.49.2		2
5.3	odd	4		240.4.f.a.49.1		2
5.4	even	2		1200.4.a.w.1.1		1
12.11	even	2		900.4.a.d.1.1		1
15.2	even	4		720.4.f.h.289.2		2
15.8	even	4		720.4.f.h.289.1		2
20.3	even	4		60.4.d.a.49.2	yes	2
20.7	even	4		60.4.d.a.49.1	✓	2
20.19	odd	2		300.4.a.d.1.1		1
40.3	even	4		960.4.f.j.769.1		2
40.13	odd	4		960.4.f.i.769.2		2
40.27	even	4		960.4.f.j.769.2		2
40.37	odd	4		960.4.f.i.769.1		2
60.23	odd	4		180.4.d.b.109.1		2
60.47	odd	4		180.4.d.b.109.2		2
60.59	even	2		900.4.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.d.a.49.1	✓	2	20.7	even	4
60.4.d.a.49.2	yes	2	20.3	even	4
180.4.d.b.109.1		2	60.23	odd	4
180.4.d.b.109.2		2	60.47	odd	4
240.4.f.a.49.1		2	5.3	odd	4
240.4.f.a.49.2		2	5.2	odd	4
300.4.a.d.1.1		1	20.19	odd	2
300.4.a.f.1.1		1	4.3	odd	2
720.4.f.h.289.1		2	15.8	even	4
720.4.f.h.289.2		2	15.2	even	4
900.4.a.d.1.1		1	12.11	even	2
900.4.a.o.1.1		1	60.59	even	2
960.4.f.i.769.1		2	40.37	odd	4
960.4.f.i.769.2		2	40.13	odd	4
960.4.f.j.769.1		2	40.3	even	4
960.4.f.j.769.2		2	40.27	even	4
1200.4.a.q.1.1		1	1.1	even	1	trivial
1200.4.a.w.1.1		1	5.4	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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1200.a (trivial)

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