LMFDB - Embedded newform 2576.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2576,2,Mod(1,2576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2576, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2576.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2576 = 2^{4} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2576.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:	$20.5694635607$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 644)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2576.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +2.00000 q^{11} -3.00000 q^{13} -1.00000 q^{21} +1.00000 q^{23} -5.00000 q^{25} -5.00000 q^{27} +1.00000 q^{29} +5.00000 q^{31} +2.00000 q^{33} -8.00000 q^{37} -3.00000 q^{39} -7.00000 q^{41} +4.00000 q^{43} -3.00000 q^{47} +1.00000 q^{49} -12.0000 q^{53} -4.00000 q^{59} -6.00000 q^{61} +2.00000 q^{63} +12.0000 q^{67} +1.00000 q^{69} -13.0000 q^{71} +3.00000 q^{73} -5.00000 q^{75} -2.00000 q^{77} -4.00000 q^{79} +1.00000 q^{81} -16.0000 q^{83} +1.00000 q^{87} +4.00000 q^{89} +3.00000 q^{91} +5.00000 q^{93} +10.0000 q^{97} -4.00000 q^{99} +O(q^{100})$

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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0	0
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	0	0
$33$	2.00000	0.348155
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	0	0
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	0	0
$65$	0	0
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	0	0
$69$	1.00000	0.120386
$70$	0	0
$71$	−13.0000	−1.54282	−0.771408	−	0.636341i	$-0.780447\pi$
$71$	−13.0000	−1.54282	−0.771408	+	0.636341i	$0.780447\pi$
$72$	0	0
$73$	3.00000	0.351123	0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000	0.351123	0.175562	+	0.984468i	$0.443826\pi$
$74$	0	0
$75$	−5.00000	−0.577350
$76$	0	0
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1.00000	0.107211
$88$	0	0
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	3.00000	0.314485
$92$	0	0
$93$	5.00000	0.518476
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	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
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	0	0
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	6.00000	0.554700
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	−7.00000	−0.631169
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	0	0
$129$	4.00000	0.352180
$130$	0	0
$131$	−3.00000	−0.262111	−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000	−0.262111	−0.131056	+	0.991375i	$0.541837\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	0	0
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	0	0
$143$	−6.00000	−0.501745
$144$	0	0
$145$	0	0
$146$	0	0
$147$	1.00000	0.0824786
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	11.0000	0.895167	0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000	0.895167	0.447584	+	0.894242i	$0.352285\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	0	0
$159$	−12.0000	−0.951662
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	9.00000	0.704934	0.352467	−	0.935824i	$-0.385343\pi$
$163$	9.00000	0.704934	0.352467	+	0.935824i	$0.385343\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	0	0
$173$	26.0000	1.97674	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	26.0000	1.97674	0.988372	+	0.152057i	$0.0485898\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	0	0
$177$	−4.00000	−0.300658
$178$	0	0
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	0	0
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	5.00000	0.363696
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−19.0000	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	9.00000	0.641223	0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000	0.641223	0.320612	+	0.947211i	$0.396112\pi$
$198$	0	0
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	0	0
$201$	12.0000	0.846415
$202$	0	0
$203$	−1.00000	−0.0701862
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−2.00000	−0.139010
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	0	0
$213$	−13.0000	−0.890745
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−5.00000	−0.339422
$218$	0	0
$219$	3.00000	0.202721
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−20.0000	−1.33930	−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000	−1.33930	−0.669650	+	0.742677i	$0.733556\pi$
$224$	0	0
$225$	10.0000	0.666667
$226$	0	0
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	0	0
$233$	−1.00000	−0.0655122	−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000	−0.0655122	−0.0327561	+	0.999463i	$0.510428\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−4.00000	−0.259828
$238$	0	0
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−16.0000	−1.01396
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	0	0
$255$	0	0
$256$	0	0
$257$	5.00000	0.311891	0.155946	−	0.987766i	$-0.450158\pi$
$257$	5.00000	0.311891	0.155946	+	0.987766i	$0.450158\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	0	0
$261$	−2.00000	−0.123797
$262$	0	0
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	4.00000	0.244796
$268$	0	0
$269$	−5.00000	−0.304855	−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000	−0.304855	−0.152428	+	0.988315i	$0.548709\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	3.00000	0.181568
$274$	0	0
$275$	−10.0000	−0.603023
$276$	0	0
$277$	−3.00000	−0.180253	−0.0901263	−	0.995930i	$-0.528727\pi$
$277$	−3.00000	−0.180253	−0.0901263	+	0.995930i	$0.528727\pi$
$278$	0	0
$279$	−10.0000	−0.598684
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	10.0000	0.594438	0.297219	−	0.954809i	$-0.403941\pi$
$283$	10.0000	0.594438	0.297219	+	0.954809i	$0.403941\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	7.00000	0.413197
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	10.0000	0.586210
$292$	0	0
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−10.0000	−0.580259
$298$	0	0
$299$	−3.00000	−0.173494
$300$	0	0
$301$	−4.00000	−0.230556
$302$	0	0
$303$	−10.0000	−0.574485
$304$	0	0
$305$	0	0
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	0	0
$309$	−14.0000	−0.796432
$310$	0	0
$311$	13.0000	0.737162	0.368581	−	0.929596i	$-0.379844\pi$
$311$	13.0000	0.737162	0.368581	+	0.929596i	$0.379844\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	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
$319$	2.00000	0.111979
$320$	0	0
$321$	8.00000	0.446516
$322$	0	0
$323$	0	0
$324$	0	0
$325$	15.0000	0.832050
$326$	0	0
$327$	−4.00000	−0.221201
$328$	0	0
$329$	3.00000	0.165395
$330$	0	0
$331$	29.0000	1.59398	0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000	1.59398	0.796992	+	0.603990i	$0.206423\pi$
$332$	0	0
$333$	16.0000	0.876795
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0	0
$339$	4.00000	0.217250
$340$	0	0
$341$	10.0000	0.541530
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−25.0000	−1.33822	−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000	−1.33822	−0.669110	+	0.743164i	$0.733324\pi$
$350$	0	0
$351$	15.0000	0.800641
$352$	0	0
$353$	7.00000	0.372572	0.186286	−	0.982496i	$-0.440355\pi$
$353$	7.00000	0.372572	0.186286	+	0.982496i	$0.440355\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	−7.00000	−0.367405
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−24.0000	−1.25279	−0.626395	−	0.779506i	$-0.715470\pi$
$367$	−24.0000	−1.25279	−0.626395	+	0.779506i	$0.715470\pi$
$368$	0	0
$369$	14.0000	0.728811
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.00000	−0.154508
$378$	0	0
$379$	14.0000	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$380$	0	0
$381$	−7.00000	−0.358621
$382$	0	0
$383$	−14.0000	−0.715367	−0.357683	−	0.933843i	$-0.616433\pi$
$383$	−14.0000	−0.715367	−0.357683	+	0.933843i	$0.616433\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.00000	−0.406663
$388$	0	0
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−3.00000	−0.151330
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−27.0000	−1.35509	−0.677546	−	0.735481i	$-0.736956\pi$
$397$	−27.0000	−1.35509	−0.677546	+	0.735481i	$0.736956\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	−15.0000	−0.747203
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−16.0000	−0.793091
$408$	0	0
$409$	−21.0000	−1.03838	−0.519192	−	0.854658i	$-0.673767\pi$
$409$	−21.0000	−1.03838	−0.519192	+	0.854658i	$0.673767\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	0	0
$413$	4.00000	0.196827
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−1.00000	−0.0489702
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	−28.0000	−1.36464	−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000	−1.36464	−0.682318	+	0.731055i	$0.739028\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	0	0
$426$	0	0
$427$	6.00000	0.290360
$428$	0	0
$429$	−6.00000	−0.289683
$430$	0	0
$431$	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
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	7.00000	0.334092	0.167046	−	0.985949i	$-0.446577\pi$
$439$	7.00000	0.334092	0.167046	+	0.985949i	$0.446577\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	23.0000	1.09276	0.546381	−	0.837536i	$-0.316005\pi$
$443$	23.0000	1.09276	0.546381	+	0.837536i	$0.316005\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	−14.0000	−0.659234
$452$	0	0
$453$	11.0000	0.516825
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	15.0000	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	42.0000	1.94353	0.971764	−	0.235954i	$-0.0758216\pi$
$467$	42.0000	1.94353	0.971764	+	0.235954i	$0.0758216\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	0	0
$471$	12.0000	0.552931
$472$	0	0
$473$	8.00000	0.367840
$474$	0	0
$475$	0	0
$476$	0	0
$477$	24.0000	1.09888
$478$	0	0
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	24.0000	1.09431
$482$	0	0
$483$	−1.00000	−0.0455016
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−31.0000	−1.40474	−0.702372	−	0.711810i	$-0.747876\pi$
$487$	−31.0000	−1.40474	−0.702372	+	0.711810i	$0.747876\pi$
$488$	0	0
$489$	9.00000	0.406994
$490$	0	0
$491$	17.0000	0.767199	0.383600	−	0.923499i	$-0.374684\pi$
$491$	17.0000	0.767199	0.383600	+	0.923499i	$0.374684\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	13.0000	0.583130
$498$	0	0
$499$	19.0000	0.850557	0.425278	−	0.905063i	$-0.360176\pi$
$499$	19.0000	0.850557	0.425278	+	0.905063i	$0.360176\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−4.00000	−0.177646
$508$	0	0
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−3.00000	−0.132712
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−6.00000	−0.263880
$518$	0	0
$519$	26.0000	1.14127
$520$	0	0
$521$	−32.0000	−1.40195	−0.700973	−	0.713188i	$-0.747251\pi$
$521$	−32.0000	−1.40195	−0.700973	+	0.713188i	$0.747251\pi$
$522$	0	0
$523$	10.0000	0.437269	0.218635	−	0.975807i	$-0.429840\pi$
$523$	10.0000	0.437269	0.218635	+	0.975807i	$0.429840\pi$
$524$	0	0
$525$	5.00000	0.218218
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	8.00000	0.347170
$532$	0	0
$533$	21.0000	0.909611
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−3.00000	−0.129460
$538$	0	0
$539$	2.00000	0.0861461
$540$	0	0
$541$	45.0000	1.93470	0.967351	−	0.253442i	$-0.0815627\pi$
$541$	45.0000	1.93470	0.967351	+	0.253442i	$0.0815627\pi$
$542$	0	0
$543$	−18.0000	−0.772454
$544$	0	0
$545$	0	0
$546$	0	0
$547$	17.0000	0.726868	0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000	0.726868	0.363434	+	0.931620i	$0.381604\pi$
$548$	0	0
$549$	12.0000	0.512148
$550$	0	0
$551$	0	0
$552$	0	0
$553$	4.00000	0.170097
$554$	0	0
$555$	0	0
$556$	0	0
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	−4.00000	−0.167689	−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000	−0.167689	−0.0838444	+	0.996479i	$0.526720\pi$
$570$	0	0
$571$	−10.0000	−0.418487	−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000	−0.418487	−0.209243	+	0.977864i	$0.567100\pi$
$572$	0	0
$573$	8.00000	0.334205
$574$	0	0
$575$	−5.00000	−0.208514
$576$	0	0
$577$	19.0000	0.790980	0.395490	−	0.918470i	$-0.370575\pi$
$577$	19.0000	0.790980	0.395490	+	0.918470i	$0.370575\pi$
$578$	0	0
$579$	−19.0000	−0.789613
$580$	0	0
$581$	16.0000	0.663792
$582$	0	0
$583$	−24.0000	−0.993978
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−7.00000	−0.288921	−0.144460	−	0.989511i	$-0.546145\pi$
$587$	−7.00000	−0.288921	−0.144460	+	0.989511i	$0.546145\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	9.00000	0.370211
$592$	0	0
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	2.00000	0.0818546
$598$	0	0
$599$	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
$601$	−45.0000	−1.83559	−0.917794	−	0.397057i	$-0.870032\pi$
$601$	−45.0000	−1.83559	−0.917794	+	0.397057i	$0.870032\pi$
$602$	0	0
$603$	−24.0000	−0.977356
$604$	0	0
$605$	0	0
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	0	0
$609$	−1.00000	−0.0405220
$610$	0	0
$611$	9.00000	0.364101
$612$	0	0
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	0	0
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	0	0
$623$	−4.00000	−0.160257
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	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	$0.603171\pi$
$632$	0	0
$633$	−12.0000	−0.476957
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−3.00000	−0.118864
$638$	0	0
$639$	26.0000	1.02854
$640$	0	0
$641$	4.00000	0.157991	0.0789953	−	0.996875i	$-0.474829\pi$
$641$	4.00000	0.157991	0.0789953	+	0.996875i	$0.474829\pi$
$642$	0	0
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	21.0000	0.825595	0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000	0.825595	0.412798	+	0.910823i	$0.364552\pi$
$648$	0	0
$649$	−8.00000	−0.314027
$650$	0	0
$651$	−5.00000	−0.195965
$652$	0	0
$653$	−5.00000	−0.195665	−0.0978326	−	0.995203i	$-0.531191\pi$
$653$	−5.00000	−0.195665	−0.0978326	+	0.995203i	$0.531191\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−6.00000	−0.234082
$658$	0	0
$659$	14.0000	0.545363	0.272681	−	0.962104i	$-0.412090\pi$
$659$	14.0000	0.545363	0.272681	+	0.962104i	$0.412090\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.00000	0.0387202
$668$	0	0
$669$	−20.0000	−0.773245
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	43.0000	1.65753	0.828764	−	0.559598i	$-0.189045\pi$
$673$	43.0000	1.65753	0.828764	+	0.559598i	$0.189045\pi$
$674$	0	0
$675$	25.0000	0.962250
$676$	0	0
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−10.0000	−0.383765
$680$	0	0
$681$	20.0000	0.766402
$682$	0	0
$683$	−23.0000	−0.880071	−0.440035	−	0.897980i	$-0.645034\pi$
$683$	−23.0000	−0.880071	−0.440035	+	0.897980i	$0.645034\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	10.0000	0.381524
$688$	0	0
$689$	36.0000	1.37149
$690$	0	0
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	0	0
$693$	4.00000	0.151947
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−1.00000	−0.0378235
$700$	0	0
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	10.0000	0.376089
$708$	0	0
$709$	16.0000	0.600893	0.300446	−	0.953799i	$-0.402864\pi$
$709$	16.0000	0.600893	0.300446	+	0.953799i	$0.402864\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	0	0
$713$	5.00000	0.187251
$714$	0	0
$715$	0	0
$716$	0	0
$717$	15.0000	0.560185
$718$	0	0
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	14.0000	0.521387
$722$	0	0
$723$	−18.0000	−0.669427
$724$	0	0
$725$	−5.00000	−0.185695
$726$	0	0
$727$	−20.0000	−0.741759	−0.370879	−	0.928681i	$-0.620944\pi$
$727$	−20.0000	−0.741759	−0.370879	+	0.928681i	$0.620944\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−24.0000	−0.886460	−0.443230	−	0.896408i	$-0.646168\pi$
$733$	−24.0000	−0.886460	−0.443230	+	0.896408i	$0.646168\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	24.0000	0.884051
$738$	0	0
$739$	9.00000	0.331070	0.165535	−	0.986204i	$-0.447065\pi$
$739$	9.00000	0.331070	0.165535	+	0.986204i	$0.447065\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	32.0000	1.17082
$748$	0	0
$749$	−8.00000	−0.292314
$750$	0	0
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	0	0
$753$	2.00000	0.0728841
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	0	0
$759$	2.00000	0.0725954
$760$	0	0
$761$	−37.0000	−1.34125	−0.670624	−	0.741797i	$-0.733974\pi$
$761$	−37.0000	−1.34125	−0.670624	+	0.741797i	$0.733974\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	0	0
$765$	0	0
$766$	0	0
$767$	12.0000	0.433295
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	5.00000	0.180071
$772$	0	0
$773$	26.0000	0.935155	0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000	0.935155	0.467578	+	0.883952i	$0.345127\pi$
$774$	0	0
$775$	−25.0000	−0.898027
$776$	0	0
$777$	8.00000	0.286998
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−26.0000	−0.930353
$782$	0	0
$783$	−5.00000	−0.178685
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−8.00000	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$788$	0	0
$789$	−18.0000	−0.640817
$790$	0	0
$791$	−4.00000	−0.142224
$792$	0	0
$793$	18.0000	0.639199
$794$	0	0
$795$	0	0
$796$	0	0
$797$	32.0000	1.13350	0.566749	−	0.823890i	$-0.308201\pi$
$797$	32.0000	1.13350	0.566749	+	0.823890i	$0.308201\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−8.00000	−0.282666
$802$	0	0
$803$	6.00000	0.211735
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−5.00000	−0.176008
$808$	0	0
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	0	0
$811$	37.0000	1.29925	0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000	1.29925	0.649623	+	0.760257i	$0.274927\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−6.00000	−0.209657
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	11.0000	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$824$	0	0
$825$	−10.0000	−0.348155
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	0	0
$831$	−3.00000	−0.104069
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−25.0000	−0.864126
$838$	0	0
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	0	0
$843$	22.0000	0.757720
$844$	0	0
$845$	0	0
$846$	0	0
$847$	7.00000	0.240523
$848$	0	0
$849$	10.0000	0.343199
$850$	0	0
$851$	−8.00000	−0.274236
$852$	0	0
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−51.0000	−1.74213	−0.871063	−	0.491171i	$-0.836569\pi$
$857$	−51.0000	−1.74213	−0.871063	+	0.491171i	$0.836569\pi$
$858$	0	0
$859$	29.0000	0.989467	0.494734	−	0.869045i	$-0.335266\pi$
$859$	29.0000	0.989467	0.494734	+	0.869045i	$0.335266\pi$
$860$	0	0
$861$	7.00000	0.238559
$862$	0	0
$863$	57.0000	1.94030	0.970151	−	0.242500i	$-0.0779676\pi$
$863$	57.0000	1.94030	0.970151	+	0.242500i	$0.0779676\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−17.0000	−0.577350
$868$	0	0
$869$	−8.00000	−0.271381
$870$	0	0
$871$	−36.0000	−1.21981
$872$	0	0
$873$	−20.0000	−0.676897
$874$	0	0
$875$	0	0
$876$	0	0
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	0	0
$879$	−22.0000	−0.742042
$880$	0	0
$881$	−58.0000	−1.95407	−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000	−1.95407	−0.977035	+	0.213080i	$0.931651\pi$
$882$	0	0
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	25.0000	0.839418	0.419709	−	0.907659i	$-0.362132\pi$
$887$	25.0000	0.839418	0.419709	+	0.907659i	$0.362132\pi$
$888$	0	0
$889$	7.00000	0.234772
$890$	0	0
$891$	2.00000	0.0670025
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−3.00000	−0.100167
$898$	0	0
$899$	5.00000	0.166759
$900$	0	0
$901$	0	0
$902$	0	0
$903$	−4.00000	−0.133112
$904$	0	0
$905$	0	0
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	0	0
$909$	20.0000	0.663358
$910$	0	0
$911$	10.0000	0.331315	0.165657	−	0.986183i	$-0.447025\pi$
$911$	10.0000	0.331315	0.165657	+	0.986183i	$0.447025\pi$
$912$	0	0
$913$	−32.0000	−1.05905
$914$	0	0
$915$	0	0
$916$	0	0
$917$	3.00000	0.0990687
$918$	0	0
$919$	−18.0000	−0.593765	−0.296883	−	0.954914i	$-0.595947\pi$
$919$	−18.0000	−0.593765	−0.296883	+	0.954914i	$0.595947\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	0	0
$923$	39.0000	1.28370
$924$	0	0
$925$	40.0000	1.31519
$926$	0	0
$927$	28.0000	0.919641
$928$	0	0
$929$	−15.0000	−0.492134	−0.246067	−	0.969253i	$-0.579138\pi$
$929$	−15.0000	−0.492134	−0.246067	+	0.969253i	$0.579138\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	13.0000	0.425601
$934$	0	0
$935$	0	0
$936$	0	0
$937$	4.00000	0.130674	0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000	0.130674	0.0653372	+	0.997863i	$0.479188\pi$
$938$	0	0
$939$	14.0000	0.456873
$940$	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
$943$	−7.00000	−0.227951
$944$	0	0
$945$	0	0
$946$	0	0
$947$	27.0000	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$948$	0	0
$949$	−9.00000	−0.292152
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	−10.0000	−0.323932	−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000	−0.323932	−0.161966	+	0.986796i	$0.551783\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	2.00000	0.0646508
$958$	0	0
$959$	−10.0000	−0.322917
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	−16.0000	−0.515593
$964$	0	0
$965$	0	0
$966$	0	0
$967$	41.0000	1.31847	0.659236	−	0.751936i	$-0.270880\pi$
$967$	41.0000	1.31847	0.659236	+	0.751936i	$0.270880\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	52.0000	1.66876	0.834380	−	0.551190i	$-0.185826\pi$
$971$	52.0000	1.66876	0.834380	+	0.551190i	$0.185826\pi$
$972$	0	0
$973$	1.00000	0.0320585
$974$	0	0
$975$	15.0000	0.480384
$976$	0	0
$977$	−16.0000	−0.511885	−0.255943	−	0.966692i	$-0.582386\pi$
$977$	−16.0000	−0.511885	−0.255943	+	0.966692i	$0.582386\pi$
$978$	0	0
$979$	8.00000	0.255681
$980$	0	0
$981$	8.00000	0.255420
$982$	0	0
$983$	−56.0000	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$983$	−56.0000	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	3.00000	0.0954911
$988$	0	0
$989$	4.00000	0.127193
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	0	0
$993$	29.0000	0.920287
$994$	0	0
$995$	0	0
$996$	0	0
$997$	34.0000	1.07679	0.538395	−	0.842692i	$-0.319031\pi$
$997$	34.0000	1.07679	0.538395	+	0.842692i	$0.319031\pi$
$998$	0	0
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2576.2.a.l.1.1		1
4.3	odd	2		644.2.a.a.1.1	✓	1
12.11	even	2		5796.2.a.e.1.1		1
28.27	even	2		4508.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.a.a.1.1	✓	1	4.3	odd	2
2576.2.a.l.1.1		1	1.1	even	1	trivial
4508.2.a.c.1.1		1	28.27	even	2
5796.2.a.e.1.1		1	12.11	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:	\( N \)	\(=\)	\( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2576.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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