LMFDB - Embedded newform 2940.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(1,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, 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("2940.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.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:	$23.4760181943$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2940.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{9} -2.00000 q^{11} +1.00000 q^{13} -1.00000 q^{15} -4.00000 q^{17} -1.00000 q^{19} +4.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} -5.00000 q^{31} +2.00000 q^{33} -5.00000 q^{37} -1.00000 q^{39} +2.00000 q^{41} -9.00000 q^{43} +1.00000 q^{45} -2.00000 q^{47} +4.00000 q^{51} +12.0000 q^{53} -2.00000 q^{55} +1.00000 q^{57} -8.00000 q^{59} -14.0000 q^{61} +1.00000 q^{65} +9.00000 q^{67} -4.00000 q^{69} +2.00000 q^{71} +1.00000 q^{73} -1.00000 q^{75} -3.00000 q^{79} +1.00000 q^{81} -18.0000 q^{83} -4.00000 q^{85} -4.00000 q^{89} +5.00000 q^{93} -1.00000 q^{95} +10.0000 q^{97} -2.00000 q^{99} +O(q^{100})$

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
$3$	−1.00000	−0.577350
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0	0
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	0	0
$33$	2.00000	0.348155
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	0	0
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	4.00000	0.560112
$52$	0	0
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	1.00000	0.132453
$58$	0	0
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	9.00000	1.09952	0.549762	−	0.835321i	$-0.314718\pi$
$67$	9.00000	1.09952	0.549762	+	0.835321i	$0.314718\pi$
$68$	0	0
$69$	−4.00000	−0.481543
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0	0
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	0	0
$75$	−1.00000	−0.115470
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−18.0000	−1.97576	−0.987878	−	0.155230i	$-0.950388\pi$
$83$	−18.0000	−1.97576	−0.987878	+	0.155230i	$0.950388\pi$
$84$	0	0
$85$	−4.00000	−0.433861
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	5.00000	0.518476
$94$	0	0
$95$	−1.00000	−0.102598
$96$	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
$99$	−2.00000	−0.201008
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	13.0000	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$110$	0	0
$111$	5.00000	0.474579
$112$	0	0
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	0	0
$117$	1.00000	0.0924500
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	−2.00000	−0.180334
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−9.00000	−0.798621	−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000	−0.798621	−0.399310	+	0.916816i	$0.630750\pi$
$128$	0	0
$129$	9.00000	0.792406
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	0	0
$143$	−2.00000	−0.167248
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	−4.00000	−0.323381
$154$	0	0
$155$	−5.00000	−0.401610
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0	0
$159$	−12.0000	−0.951662
$160$	0	0
$161$	0	0
$162$	0	0
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	0	0
$165$	2.00000	0.155700
$166$	0	0
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	0	0
$173$	−16.0000	−1.21646	−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000	−1.21646	−0.608229	+	0.793762i	$0.708120\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	8.00000	0.601317
$178$	0	0
$179$	−26.0000	−1.94333	−0.971666	−	0.236360i	$-0.924046\pi$
$179$	−26.0000	−1.94333	−0.971666	+	0.236360i	$0.924046\pi$
$180$	0	0
$181$	17.0000	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	0	0
$185$	−5.00000	−0.367607
$186$	0	0
$187$	8.00000	0.585018
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−10.0000	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$192$	0	0
$193$	−17.0000	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	−9.00000	−0.634811
$202$	0	0
$203$	0	0
$204$	0	0
$205$	2.00000	0.139686
$206$	0	0
$207$	4.00000	0.278019
$208$	0	0
$209$	2.00000	0.138343
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	0	0
$213$	−2.00000	−0.137038
$214$	0	0
$215$	−9.00000	−0.613795
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−1.00000	−0.0675737
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	0	0
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−2.00000	−0.131024	−0.0655122	−	0.997852i	$-0.520868\pi$
$233$	−2.00000	−0.131024	−0.0655122	+	0.997852i	$0.520868\pi$
$234$	0	0
$235$	−2.00000	−0.130466
$236$	0	0
$237$	3.00000	0.194871
$238$	0	0
$239$	26.0000	1.68180	0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000	1.68180	0.840900	+	0.541190i	$0.182026\pi$
$240$	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
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	0	0
$249$	18.0000	1.14070
$250$	0	0
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	−8.00000	−0.502956
$254$	0	0
$255$	4.00000	0.250490
$256$	0	0
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	4.00000	0.244796
$268$	0	0
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−2.00000	−0.120605
$276$	0	0
$277$	5.00000	0.300421	0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000	0.300421	0.150210	+	0.988654i	$0.452005\pi$
$278$	0	0
$279$	−5.00000	−0.299342
$280$	0	0
$281$	−20.0000	−1.19310	−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000	−1.19310	−0.596550	+	0.802576i	$0.703462\pi$
$282$	0	0
$283$	−25.0000	−1.48610	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000	−1.48610	−0.743048	+	0.669238i	$0.766621\pi$
$284$	0	0
$285$	1.00000	0.0592349
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−10.0000	−0.586210
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	0	0
$297$	2.00000	0.116052
$298$	0	0
$299$	4.00000	0.231326
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−6.00000	−0.344691
$304$	0	0
$305$	−14.0000	−0.801638
$306$	0	0
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	0	0
$309$	1.00000	0.0568880
$310$	0	0
$311$	26.0000	1.47432	0.737162	−	0.675716i	$-0.236165\pi$
$311$	26.0000	1.47432	0.737162	+	0.675716i	$0.236165\pi$
$312$	0	0
$313$	19.0000	1.07394	0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000	1.07394	0.536972	+	0.843600i	$0.319568\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−4.00000	−0.224662	−0.112331	−	0.993671i	$-0.535832\pi$
$317$	−4.00000	−0.224662	−0.112331	+	0.993671i	$0.535832\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−4.00000	−0.223258
$322$	0	0
$323$	4.00000	0.222566
$324$	0	0
$325$	1.00000	0.0554700
$326$	0	0
$327$	−13.0000	−0.718902
$328$	0	0
$329$	0	0
$330$	0	0
$331$	1.00000	0.0549650	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	1.00000	0.0549650	0.0274825	+	0.999622i	$0.491251\pi$
$332$	0	0
$333$	−5.00000	−0.273998
$334$	0	0
$335$	9.00000	0.491723
$336$	0	0
$337$	−7.00000	−0.381314	−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000	−0.381314	−0.190657	+	0.981657i	$0.561062\pi$
$338$	0	0
$339$	14.0000	0.760376
$340$	0	0
$341$	10.0000	0.541530
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−4.00000	−0.215353
$346$	0	0
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	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
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	0	0
$355$	2.00000	0.106149
$356$	0	0
$357$	0	0
$358$	0	0
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0	0
$363$	7.00000	0.367405
$364$	0	0
$365$	1.00000	0.0523424
$366$	0	0
$367$	1.00000	0.0521996	0.0260998	−	0.999659i	$-0.491691\pi$
$367$	1.00000	0.0521996	0.0260998	+	0.999659i	$0.491691\pi$
$368$	0	0
$369$	2.00000	0.104116
$370$	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	$0.724071\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−11.0000	−0.565032	−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000	−0.565032	−0.282516	+	0.959263i	$0.591169\pi$
$380$	0	0
$381$	9.00000	0.461084
$382$	0	0
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−9.00000	−0.457496
$388$	0	0
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	0	0
$393$	18.0000	0.907980
$394$	0	0
$395$	−3.00000	−0.150946
$396$	0	0
$397$	31.0000	1.55585	0.777923	−	0.628360i	$-0.216273\pi$
$397$	31.0000	1.55585	0.777923	+	0.628360i	$0.216273\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	−5.00000	−0.249068
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	10.0000	0.495682
$408$	0	0
$409$	13.0000	0.642809	0.321404	−	0.946942i	$-0.395845\pi$
$409$	13.0000	0.642809	0.321404	+	0.946942i	$0.395845\pi$
$410$	0	0
$411$	−16.0000	−0.789222
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−18.0000	−0.883585
$416$	0	0
$417$	13.0000	0.636613
$418$	0	0
$419$	−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
$421$	−35.0000	−1.70580	−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000	−1.70580	−0.852898	+	0.522078i	$0.825157\pi$
$422$	0	0
$423$	−2.00000	−0.0972433
$424$	0	0
$425$	−4.00000	−0.194029
$426$	0	0
$427$	0	0
$428$	0	0
$429$	2.00000	0.0965609
$430$	0	0
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	0	0
$433$	27.0000	1.29754	0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000	1.29754	0.648769	+	0.760986i	$0.275284\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−4.00000	−0.191346
$438$	0	0
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	−4.00000	−0.189618
$446$	0	0
$447$	−12.0000	−0.567581
$448$	0	0
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	−4.00000	−0.188353
$452$	0	0
$453$	16.0000	0.751746
$454$	0	0
$455$	0	0
$456$	0	0
$457$	1.00000	0.0467780	0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000	0.0467780	0.0233890	+	0.999726i	$0.492554\pi$
$458$	0	0
$459$	4.00000	0.186704
$460$	0	0
$461$	−16.0000	−0.745194	−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000	−0.745194	−0.372597	+	0.927993i	$0.621533\pi$
$462$	0	0
$463$	41.0000	1.90543	0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000	1.90543	0.952716	+	0.303863i	$0.0982765\pi$
$464$	0	0
$465$	5.00000	0.231869
$466$	0	0
$467$	34.0000	1.57333	0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000	1.57333	0.786666	+	0.617379i	$0.211805\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	22.0000	1.01371
$472$	0	0
$473$	18.0000	0.827641
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	12.0000	0.549442
$478$	0	0
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	−5.00000	−0.227980
$482$	0	0
$483$	0	0
$484$	0	0
$485$	10.0000	0.454077
$486$	0	0
$487$	33.0000	1.49537	0.747686	−	0.664052i	$-0.231165\pi$
$487$	33.0000	1.49537	0.747686	+	0.664052i	$0.231165\pi$
$488$	0	0
$489$	−12.0000	−0.542659
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−5.00000	−0.223831	−0.111915	−	0.993718i	$-0.535699\pi$
$499$	−5.00000	−0.223831	−0.111915	+	0.993718i	$0.535699\pi$
$500$	0	0
$501$	−2.00000	−0.0893534
$502$	0	0
$503$	10.0000	0.445878	0.222939	−	0.974832i	$-0.428435\pi$
$503$	10.0000	0.445878	0.222939	+	0.974832i	$0.428435\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	0	0
$507$	12.0000	0.532939
$508$	0	0
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	1.00000	0.0441511
$514$	0	0
$515$	−1.00000	−0.0440653
$516$	0	0
$517$	4.00000	0.175920
$518$	0	0
$519$	16.0000	0.702322
$520$	0	0
$521$	36.0000	1.57719	0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000	1.57719	0.788594	+	0.614914i	$0.210809\pi$
$522$	0	0
$523$	29.0000	1.26808	0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000	1.26808	0.634041	+	0.773300i	$0.281395\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	20.0000	0.871214
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−8.00000	−0.347170
$532$	0	0
$533$	2.00000	0.0866296
$534$	0	0
$535$	4.00000	0.172935
$536$	0	0
$537$	26.0000	1.12198
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−31.0000	−1.33279	−0.666397	−	0.745597i	$-0.732164\pi$
$541$	−31.0000	−1.33279	−0.666397	+	0.745597i	$0.732164\pi$
$542$	0	0
$543$	−17.0000	−0.729540
$544$	0	0
$545$	13.0000	0.556859
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	0	0
$549$	−14.0000	−0.597505
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	5.00000	0.212238
$556$	0	0
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	−9.00000	−0.380659
$560$	0	0
$561$	−8.00000	−0.337760
$562$	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
$565$	−14.0000	−0.588984
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−5.00000	−0.209243	−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000	−0.209243	−0.104622	+	0.994512i	$0.533363\pi$
$572$	0	0
$573$	10.0000	0.417756
$574$	0	0
$575$	4.00000	0.166812
$576$	0	0
$577$	−13.0000	−0.541197	−0.270599	−	0.962692i	$-0.587222\pi$
$577$	−13.0000	−0.541197	−0.270599	+	0.962692i	$0.587222\pi$
$578$	0	0
$579$	17.0000	0.706496
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−24.0000	−0.993978
$584$	0	0
$585$	1.00000	0.0413449
$586$	0	0
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	0	0
$589$	5.00000	0.206021
$590$	0	0
$591$	−12.0000	−0.493614
$592$	0	0
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	16.0000	0.654836
$598$	0	0
$599$	−28.0000	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$599$	−28.0000	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$600$	0	0
$601$	23.0000	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$602$	0	0
$603$	9.00000	0.366508
$604$	0	0
$605$	−7.00000	−0.284590
$606$	0	0
$607$	9.00000	0.365299	0.182649	−	0.983178i	$-0.441533\pi$
$607$	9.00000	0.365299	0.182649	+	0.983178i	$0.441533\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−2.00000	−0.0809113
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	0	0
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	34.0000	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$618$	0	0
$619$	−11.0000	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−2.00000	−0.0798723
$628$	0	0
$629$	20.0000	0.797452
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	28.0000	1.11290
$634$	0	0
$635$	−9.00000	−0.357154
$636$	0	0
$637$	0	0
$638$	0	0
$639$	2.00000	0.0791188
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	0	0
$643$	7.00000	0.276053	0.138027	−	0.990429i	$-0.455924\pi$
$643$	7.00000	0.276053	0.138027	+	0.990429i	$0.455924\pi$
$644$	0	0
$645$	9.00000	0.354375
$646$	0	0
$647$	−14.0000	−0.550397	−0.275198	−	0.961387i	$-0.588744\pi$
$647$	−14.0000	−0.550397	−0.275198	+	0.961387i	$0.588744\pi$
$648$	0	0
$649$	16.0000	0.628055
$650$	0	0
$651$	0	0
$652$	0	0
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	0	0
$655$	−18.0000	−0.703318
$656$	0	0
$657$	1.00000	0.0390137
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	35.0000	1.36134	0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000	1.36134	0.680671	+	0.732589i	$0.261688\pi$
$662$	0	0
$663$	4.00000	0.155347
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	28.0000	1.08093
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	0	0
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	24.0000	0.922395	0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000	0.922395	0.461197	+	0.887298i	$0.347420\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−18.0000	−0.689761
$682$	0	0
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	0	0
$685$	16.0000	0.611329
$686$	0	0
$687$	−1.00000	−0.0381524
$688$	0	0
$689$	12.0000	0.457164
$690$	0	0
$691$	−11.0000	−0.418460	−0.209230	−	0.977866i	$-0.567096\pi$
$691$	−11.0000	−0.418460	−0.209230	+	0.977866i	$0.567096\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−13.0000	−0.493118
$696$	0	0
$697$	−8.00000	−0.303022
$698$	0	0
$699$	2.00000	0.0756469
$700$	0	0
$701$	36.0000	1.35970	0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000	1.35970	0.679851	+	0.733351i	$0.262045\pi$
$702$	0	0
$703$	5.00000	0.188579
$704$	0	0
$705$	2.00000	0.0753244
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	−3.00000	−0.112509
$712$	0	0
$713$	−20.0000	−0.749006
$714$	0	0
$715$	−2.00000	−0.0747958
$716$	0	0
$717$	−26.0000	−0.970988
$718$	0	0
$719$	42.0000	1.56634	0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000	1.56634	0.783168	+	0.621810i	$0.213603\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	18.0000	0.669427
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−3.00000	−0.111264	−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000	−0.111264	−0.0556319	+	0.998451i	$0.517717\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	36.0000	1.33151
$732$	0	0
$733$	9.00000	0.332423	0.166211	−	0.986090i	$-0.446847\pi$
$733$	9.00000	0.332423	0.166211	+	0.986090i	$0.446847\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−18.0000	−0.663039
$738$	0	0
$739$	15.0000	0.551784	0.275892	−	0.961189i	$-0.411027\pi$
$739$	15.0000	0.551784	0.275892	+	0.961189i	$0.411027\pi$
$740$	0	0
$741$	1.00000	0.0367359
$742$	0	0
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	0	0
$745$	12.0000	0.439646
$746$	0	0
$747$	−18.0000	−0.658586
$748$	0	0
$749$	0	0
$750$	0	0
$751$	31.0000	1.13121	0.565603	−	0.824678i	$-0.308643\pi$
$751$	31.0000	1.13121	0.565603	+	0.824678i	$0.308643\pi$
$752$	0	0
$753$	−4.00000	−0.145768
$754$	0	0
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	0	0
$759$	8.00000	0.290382
$760$	0	0
$761$	20.0000	0.724999	0.362500	−	0.931984i	$-0.381923\pi$
$761$	20.0000	0.724999	0.362500	+	0.931984i	$0.381923\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−4.00000	−0.144620
$766$	0	0
$767$	−8.00000	−0.288863
$768$	0	0
$769$	31.0000	1.11789	0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000	1.11789	0.558944	+	0.829205i	$0.311207\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	0	0
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	0	0
$775$	−5.00000	−0.179605
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	−4.00000	−0.143131
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−22.0000	−0.785214
$786$	0	0
$787$	−16.0000	−0.570338	−0.285169	−	0.958477i	$-0.592050\pi$
$787$	−16.0000	−0.570338	−0.285169	+	0.958477i	$0.592050\pi$
$788$	0	0
$789$	−12.0000	−0.427211
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−14.0000	−0.497155
$794$	0	0
$795$	−12.0000	−0.425596
$796$	0	0
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	0	0
$801$	−4.00000	−0.141333
$802$	0	0
$803$	−2.00000	−0.0705785
$804$	0	0
$805$	0	0
$806$	0	0
$807$	18.0000	0.633630
$808$	0	0
$809$	46.0000	1.61727	0.808637	−	0.588308i	$-0.200206\pi$
$809$	46.0000	1.61727	0.808637	+	0.588308i	$0.200206\pi$
$810$	0	0
$811$	48.0000	1.68551	0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000	1.68551	0.842754	+	0.538299i	$0.180933\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	12.0000	0.420342
$816$	0	0
$817$	9.00000	0.314870
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−50.0000	−1.74501	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000	−1.74501	−0.872506	+	0.488603i	$0.837507\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	2.00000	0.0696311
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	0	0
$829$	5.00000	0.173657	0.0868286	−	0.996223i	$-0.472327\pi$
$829$	5.00000	0.173657	0.0868286	+	0.996223i	$0.472327\pi$
$830$	0	0
$831$	−5.00000	−0.173448
$832$	0	0
$833$	0	0
$834$	0	0
$835$	2.00000	0.0692129
$836$	0	0
$837$	5.00000	0.172825
$838$	0	0
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	20.0000	0.688837
$844$	0	0
$845$	−12.0000	−0.412813
$846$	0	0
$847$	0	0
$848$	0	0
$849$	25.0000	0.857998
$850$	0	0
$851$	−20.0000	−0.685591
$852$	0	0
$853$	−29.0000	−0.992941	−0.496471	−	0.868054i	$-0.665371\pi$
$853$	−29.0000	−0.992941	−0.496471	+	0.868054i	$0.665371\pi$
$854$	0	0
$855$	−1.00000	−0.0341993
$856$	0	0
$857$	44.0000	1.50301	0.751506	−	0.659727i	$-0.229328\pi$
$857$	44.0000	1.50301	0.751506	+	0.659727i	$0.229328\pi$
$858$	0	0
$859$	8.00000	0.272956	0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000	0.272956	0.136478	+	0.990643i	$0.456422\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	30.0000	1.02121	0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000	1.02121	0.510606	+	0.859815i	$0.329421\pi$
$864$	0	0
$865$	−16.0000	−0.544016
$866$	0	0
$867$	1.00000	0.0339618
$868$	0	0
$869$	6.00000	0.203536
$870$	0	0
$871$	9.00000	0.304953
$872$	0	0
$873$	10.0000	0.338449
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	24.0000	0.808581	0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000	0.808581	0.404290	+	0.914631i	$0.367519\pi$
$882$	0	0
$883$	1.00000	0.0336527	0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000	0.0336527	0.0168263	+	0.999858i	$0.494644\pi$
$884$	0	0
$885$	8.00000	0.268917
$886$	0	0
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	0	0
$893$	2.00000	0.0669274
$894$	0	0
$895$	−26.0000	−0.869084
$896$	0	0
$897$	−4.00000	−0.133556
$898$	0	0
$899$	0	0
$900$	0	0
$901$	−48.0000	−1.59911
$902$	0	0
$903$	0	0
$904$	0	0
$905$	17.0000	0.565099
$906$	0	0
$907$	9.00000	0.298840	0.149420	−	0.988774i	$-0.452259\pi$
$907$	9.00000	0.298840	0.149420	+	0.988774i	$0.452259\pi$
$908$	0	0
$909$	6.00000	0.199007
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	36.0000	1.19143
$914$	0	0
$915$	14.0000	0.462826
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−11.0000	−0.362857	−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000	−0.362857	−0.181428	+	0.983404i	$0.558072\pi$
$920$	0	0
$921$	19.0000	0.626071
$922$	0	0
$923$	2.00000	0.0658308
$924$	0	0
$925$	−5.00000	−0.164399
$926$	0	0
$927$	−1.00000	−0.0328443
$928$	0	0
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−26.0000	−0.851202
$934$	0	0
$935$	8.00000	0.261628
$936$	0	0
$937$	−21.0000	−0.686040	−0.343020	−	0.939328i	$-0.611450\pi$
$937$	−21.0000	−0.686040	−0.343020	+	0.939328i	$0.611450\pi$
$938$	0	0
$939$	−19.0000	−0.620042
$940$	0	0
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	1.00000	0.0324614
$950$	0	0
$951$	4.00000	0.129709
$952$	0	0
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	0	0
$955$	−10.0000	−0.323592
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	4.00000	0.128898
$964$	0	0
$965$	−17.0000	−0.547249
$966$	0	0
$967$	37.0000	1.18984	0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000	1.18984	0.594920	+	0.803785i	$0.297184\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−1.00000	−0.0320256
$976$	0	0
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	8.00000	0.255681
$980$	0	0
$981$	13.0000	0.415058
$982$	0	0
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	12.0000	0.382352
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−36.0000	−1.14473
$990$	0	0
$991$	−53.0000	−1.68360	−0.841800	−	0.539789i	$-0.818504\pi$
$991$	−53.0000	−1.68360	−0.841800	+	0.539789i	$0.818504\pi$
$992$	0	0
$993$	−1.00000	−0.0317340
$994$	0	0
$995$	−16.0000	−0.507234
$996$	0	0
$997$	11.0000	0.348373	0.174187	−	0.984713i	$-0.444270\pi$
$997$	11.0000	0.348373	0.174187	+	0.984713i	$0.444270\pi$
$998$	0	0
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.a.d.1.1		1
3.2	odd	2		8820.2.a.j.1.1		1
7.2	even	3		420.2.q.a.361.1	yes	2
7.3	odd	6		2940.2.q.h.961.1		2
7.4	even	3		420.2.q.a.121.1	✓	2
7.5	odd	6		2940.2.q.h.361.1		2
7.6	odd	2		2940.2.a.h.1.1		1
21.2	odd	6		1260.2.s.d.361.1		2
21.11	odd	6		1260.2.s.d.541.1		2
21.20	even	2		8820.2.a.y.1.1		1
28.11	odd	6		1680.2.bg.a.961.1		2
28.23	odd	6		1680.2.bg.a.1201.1		2
35.2	odd	12		2100.2.bc.c.949.1		4
35.4	even	6		2100.2.q.a.1801.1		2
35.9	even	6		2100.2.q.a.1201.1		2
35.18	odd	12		2100.2.bc.c.1549.1		4
35.23	odd	12		2100.2.bc.c.949.2		4
35.32	odd	12		2100.2.bc.c.1549.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.a.121.1	✓	2	7.4	even	3
420.2.q.a.361.1	yes	2	7.2	even	3
1260.2.s.d.361.1		2	21.2	odd	6
1260.2.s.d.541.1		2	21.11	odd	6
1680.2.bg.a.961.1		2	28.11	odd	6
1680.2.bg.a.1201.1		2	28.23	odd	6
2100.2.q.a.1201.1		2	35.9	even	6
2100.2.q.a.1801.1		2	35.4	even	6
2100.2.bc.c.949.1		4	35.2	odd	12
2100.2.bc.c.949.2		4	35.23	odd	12
2100.2.bc.c.1549.1		4	35.18	odd	12
2100.2.bc.c.1549.2		4	35.32	odd	12
2940.2.a.d.1.1		1	1.1	even	1	trivial
2940.2.a.h.1.1		1	7.6	odd	2
2940.2.q.h.361.1		2	7.5	odd	6
2940.2.q.h.961.1		2	7.3	odd	6
8820.2.a.j.1.1		1	3.2	odd	2
8820.2.a.y.1.1		1	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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