LMFDB - Embedded newform 3952.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3952,2,Mod(1,3952)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3952, 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("3952.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3952 = 2^{4} \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3952.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:	$31.5568788788$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3952.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} -1.00000 q^{13} +1.00000 q^{15} -3.00000 q^{17} +1.00000 q^{19} +1.00000 q^{21} -6.00000 q^{23} -4.00000 q^{25} -5.00000 q^{27} -8.00000 q^{29} +8.00000 q^{31} +1.00000 q^{35} -5.00000 q^{37} -1.00000 q^{39} -2.00000 q^{41} +1.00000 q^{43} -2.00000 q^{45} -3.00000 q^{47} -6.00000 q^{49} -3.00000 q^{51} -2.00000 q^{53} +1.00000 q^{57} +10.0000 q^{59} -14.0000 q^{61} -2.00000 q^{63} -1.00000 q^{65} +4.00000 q^{67} -6.00000 q^{69} -3.00000 q^{71} +16.0000 q^{73} -4.00000 q^{75} -4.00000 q^{79} +1.00000 q^{81} -16.0000 q^{83} -3.00000 q^{85} -8.00000 q^{87} +8.00000 q^{89} -1.00000 q^{91} +8.00000 q^{93} +1.00000 q^{95} -10.0000 q^{97} +O(q^{100})$

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
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	1.00000	0.258199
$16$	0	0
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	1.00000	0.218218
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	1.00000	0.169031
$36$	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	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	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
$49$	−6.00000	−0.857143
$50$	0	0
$51$	−3.00000	−0.420084
$52$	0	0
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.00000	0.132453
$58$	0	0
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	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
$63$	−2.00000	−0.251976
$64$	0	0
$65$	−1.00000	−0.124035
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	0	0
$73$	16.0000	1.87266	0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000	1.87266	0.936329	+	0.351123i	$0.114200\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	0	0
$77$	0	0
$78$	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
$85$	−3.00000	−0.325396
$86$	0	0
$87$	−8.00000	−0.857690
$88$	0	0
$89$	8.00000	0.847998	0.423999	−	0.905663i	$-0.360626\pi$
$89$	8.00000	0.847998	0.423999	+	0.905663i	$0.360626\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	1.00000	0.102598
$96$	0	0
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	0	0
$99$	0	0
$100$	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
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	0	0
$105$	1.00000	0.0975900
$106$	0	0
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	0	0
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	−5.00000	−0.474579
$112$	0	0
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	−2.00000	−0.180334
$124$	0	0
$125$	−9.00000	−0.804984
$126$	0	0
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	0	0
$129$	1.00000	0.0880451
$130$	0	0
$131$	−19.0000	−1.66004	−0.830019	−	0.557735i	$-0.811670\pi$
$131$	−19.0000	−1.66004	−0.830019	+	0.557735i	$0.811670\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	0	0
$135$	−5.00000	−0.430331
$136$	0	0
$137$	4.00000	0.341743	0.170872	−	0.985293i	$-0.445342\pi$
$137$	4.00000	0.341743	0.170872	+	0.985293i	$0.445342\pi$
$138$	0	0
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−8.00000	−0.664364
$146$	0	0
$147$	−6.00000	−0.494872
$148$	0	0
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	5.00000	0.406894	0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000	0.406894	0.203447	+	0.979086i	$0.434786\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	8.00000	0.642575
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	−2.00000	−0.158610
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−2.00000	−0.152944
$172$	0	0
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	0	0
$177$	10.0000	0.751646
$178$	0	0
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	0	0
$183$	−14.0000	−1.03491
$184$	0	0
$185$	−5.00000	−0.367607
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−14.0000	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	7.00000	0.498729	0.249365	−	0.968410i	$-0.419778\pi$
$197$	7.00000	0.498729	0.249365	+	0.968410i	$0.419778\pi$
$198$	0	0
$199$	26.0000	1.84309	0.921546	−	0.388270i	$-0.126927\pi$
$199$	26.0000	1.84309	0.921546	+	0.388270i	$0.126927\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	−8.00000	−0.561490
$204$	0	0
$205$	−2.00000	−0.139686
$206$	0	0
$207$	12.0000	0.834058
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	0	0
$213$	−3.00000	−0.205557
$214$	0	0
$215$	1.00000	0.0681994
$216$	0	0
$217$	8.00000	0.543075
$218$	0	0
$219$	16.0000	1.08118
$220$	0	0
$221$	3.00000	0.201802
$222$	0	0
$223$	−7.00000	−0.468755	−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000	−0.468755	−0.234377	+	0.972146i	$0.575305\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	0	0
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	0	0
$229$	11.0000	0.726900	0.363450	−	0.931614i	$-0.381599\pi$
$229$	11.0000	0.726900	0.363450	+	0.931614i	$0.381599\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−3.00000	−0.196537	−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000	−0.196537	−0.0982683	+	0.995160i	$0.531330\pi$
$234$	0	0
$235$	−3.00000	−0.195698
$236$	0	0
$237$	−4.00000	−0.259828
$238$	0	0
$239$	1.00000	0.0646846	0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000	0.0646846	0.0323423	+	0.999477i	$0.489703\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	−6.00000	−0.383326
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	0	0
$249$	−16.0000	−1.01396
$250$	0	0
$251$	28.0000	1.76734	0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000	1.76734	0.883672	+	0.468106i	$0.155064\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	−3.00000	−0.187867
$256$	0	0
$257$	−17.0000	−1.06043	−0.530215	−	0.847863i	$-0.677889\pi$
$257$	−17.0000	−1.06043	−0.530215	+	0.847863i	$0.677889\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	16.0000	0.990375
$262$	0	0
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	−2.00000	−0.122859
$266$	0	0
$267$	8.00000	0.489592
$268$	0	0
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	0	0
$273$	−1.00000	−0.0605228
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−30.0000	−1.80253	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−30.0000	−1.80253	−0.901263	+	0.433273i	$0.857359\pi$
$278$	0	0
$279$	−16.0000	−0.957895
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	−32.0000	−1.90220	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−32.0000	−1.90220	−0.951101	+	0.308879i	$0.900046\pi$
$284$	0	0
$285$	1.00000	0.0592349
$286$	0	0
$287$	−2.00000	−0.118056
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−10.0000	−0.586210
$292$	0	0
$293$	11.0000	0.642627	0.321313	−	0.946973i	$-0.395876\pi$
$293$	11.0000	0.642627	0.321313	+	0.946973i	$0.395876\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	0	0
$297$	0	0
$298$	0	0
$299$	6.00000	0.346989
$300$	0	0
$301$	1.00000	0.0576390
$302$	0	0
$303$	6.00000	0.344691
$304$	0	0
$305$	−14.0000	−0.801638
$306$	0	0
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	0	0
$309$	10.0000	0.568880
$310$	0	0
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	0	0
$313$	−9.00000	−0.508710	−0.254355	−	0.967111i	$-0.581863\pi$
$313$	−9.00000	−0.508710	−0.254355	+	0.967111i	$0.581863\pi$
$314$	0	0
$315$	−2.00000	−0.112687
$316$	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
$319$	0	0
$320$	0	0
$321$	−8.00000	−0.446516
$322$	0	0
$323$	−3.00000	−0.166924
$324$	0	0
$325$	4.00000	0.221880
$326$	0	0
$327$	19.0000	1.05070
$328$	0	0
$329$	−3.00000	−0.165395
$330$	0	0
$331$	−32.0000	−1.75888	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−32.0000	−1.75888	−0.879440	+	0.476011i	$0.842082\pi$
$332$	0	0
$333$	10.0000	0.547997
$334$	0	0
$335$	4.00000	0.218543
$336$	0	0
$337$	−23.0000	−1.25289	−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000	−1.25289	−0.626445	+	0.779466i	$0.715491\pi$
$338$	0	0
$339$	−10.0000	−0.543125
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−13.0000	−0.701934
$344$	0	0
$345$	−6.00000	−0.323029
$346$	0	0
$347$	17.0000	0.912608	0.456304	−	0.889824i	$-0.349173\pi$
$347$	17.0000	0.912608	0.456304	+	0.889824i	$0.349173\pi$
$348$	0	0
$349$	−11.0000	−0.588817	−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000	−0.588817	−0.294408	+	0.955680i	$0.595123\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	0	0
$353$	−8.00000	−0.425797	−0.212899	−	0.977074i	$-0.568290\pi$
$353$	−8.00000	−0.425797	−0.212899	+	0.977074i	$0.568290\pi$
$354$	0	0
$355$	−3.00000	−0.159223
$356$	0	0
$357$	−3.00000	−0.158777
$358$	0	0
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	−11.0000	−0.577350
$364$	0	0
$365$	16.0000	0.837478
$366$	0	0
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	0	0
$369$	4.00000	0.208232
$370$	0	0
$371$	−2.00000	−0.103835
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	0	0
$377$	8.00000	0.412021
$378$	0	0
$379$	10.0000	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	0	0
$383$	1.00000	0.0510976	0.0255488	−	0.999674i	$-0.491867\pi$
$383$	1.00000	0.0510976	0.0255488	+	0.999674i	$0.491867\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−2.00000	−0.101666
$388$	0	0
$389$	−36.0000	−1.82527	−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000	−1.82527	−0.912636	+	0.408773i	$0.865957\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	0	0
$393$	−19.0000	−0.958423
$394$	0	0
$395$	−4.00000	−0.201262
$396$	0	0
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	0	0
$399$	1.00000	0.0500626
$400$	0	0
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−8.00000	−0.395575	−0.197787	−	0.980245i	$-0.563376\pi$
$409$	−8.00000	−0.395575	−0.197787	+	0.980245i	$0.563376\pi$
$410$	0	0
$411$	4.00000	0.197305
$412$	0	0
$413$	10.0000	0.492068
$414$	0	0
$415$	−16.0000	−0.785409
$416$	0	0
$417$	13.0000	0.636613
$418$	0	0
$419$	−17.0000	−0.830504	−0.415252	−	0.909706i	$-0.636307\pi$
$419$	−17.0000	−0.830504	−0.415252	+	0.909706i	$0.636307\pi$
$420$	0	0
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	12.0000	0.582086
$426$	0	0
$427$	−14.0000	−0.677507
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−5.00000	−0.240842	−0.120421	−	0.992723i	$-0.538424\pi$
$431$	−5.00000	−0.240842	−0.120421	+	0.992723i	$0.538424\pi$
$432$	0	0
$433$	29.0000	1.39365	0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000	1.39365	0.696826	+	0.717241i	$0.254595\pi$
$434$	0	0
$435$	−8.00000	−0.383571
$436$	0	0
$437$	−6.00000	−0.287019
$438$	0	0
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	0	0
$443$	−17.0000	−0.807694	−0.403847	−	0.914826i	$-0.632327\pi$
$443$	−17.0000	−0.807694	−0.403847	+	0.914826i	$0.632327\pi$
$444$	0	0
$445$	8.00000	0.379236
$446$	0	0
$447$	10.0000	0.472984
$448$	0	0
$449$	26.0000	1.22702	0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000	1.22702	0.613508	+	0.789689i	$0.289758\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	5.00000	0.234920
$454$	0	0
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	0	0
$459$	15.0000	0.700140
$460$	0	0
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	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
$465$	8.00000	0.370991
$466$	0	0
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	0	0
$469$	4.00000	0.184703
$470$	0	0
$471$	10.0000	0.460776
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	4.00000	0.183147
$478$	0	0
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	5.00000	0.227980
$482$	0	0
$483$	−6.00000	−0.273009
$484$	0	0
$485$	−10.0000	−0.454077
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	0	0
$489$	−18.0000	−0.813988
$490$	0	0
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	0	0
$493$	24.0000	1.08091
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−3.00000	−0.134568
$498$	0	0
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	0	0
$507$	1.00000	0.0444116
$508$	0	0
$509$	−14.0000	−0.620539	−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000	−0.620539	−0.310270	+	0.950649i	$0.600419\pi$
$510$	0	0
$511$	16.0000	0.707798
$512$	0	0
$513$	−5.00000	−0.220755
$514$	0	0
$515$	10.0000	0.440653
$516$	0	0
$517$	0	0
$518$	0	0
$519$	2.00000	0.0877903
$520$	0	0
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	0	0
$525$	−4.00000	−0.174574
$526$	0	0
$527$	−24.0000	−1.04546
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	−20.0000	−0.867926
$532$	0	0
$533$	2.00000	0.0866296
$534$	0	0
$535$	−8.00000	−0.345870
$536$	0	0
$537$	−1.00000	−0.0431532
$538$	0	0
$539$	0	0
$540$	0	0
$541$	35.0000	1.50477	0.752384	−	0.658725i	$-0.228904\pi$
$541$	35.0000	1.50477	0.752384	+	0.658725i	$0.228904\pi$
$542$	0	0
$543$	−16.0000	−0.686626
$544$	0	0
$545$	19.0000	0.813871
$546$	0	0
$547$	1.00000	0.0427569	0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000	0.0427569	0.0213785	+	0.999771i	$0.493195\pi$
$548$	0	0
$549$	28.0000	1.19501
$550$	0	0
$551$	−8.00000	−0.340811
$552$	0	0
$553$	−4.00000	−0.170097
$554$	0	0
$555$	−5.00000	−0.212238
$556$	0	0
$557$	−21.0000	−0.889799	−0.444899	−	0.895581i	$-0.646761\pi$
$557$	−21.0000	−0.889799	−0.444899	+	0.895581i	$0.646761\pi$
$558$	0	0
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	0	0
$562$	0	0
$563$	19.0000	0.800755	0.400377	−	0.916350i	$-0.368879\pi$
$563$	19.0000	0.800755	0.400377	+	0.916350i	$0.368879\pi$
$564$	0	0
$565$	−10.0000	−0.420703
$566$	0	0
$567$	1.00000	0.0419961
$568$	0	0
$569$	−23.0000	−0.964210	−0.482105	−	0.876113i	$-0.660128\pi$
$569$	−23.0000	−0.964210	−0.482105	+	0.876113i	$0.660128\pi$
$570$	0	0
$571$	7.00000	0.292941	0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000	0.292941	0.146470	+	0.989215i	$0.453209\pi$
$572$	0	0
$573$	−14.0000	−0.584858
$574$	0	0
$575$	24.0000	1.00087
$576$	0	0
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	0	0
$579$	−16.0000	−0.664937
$580$	0	0
$581$	−16.0000	−0.663792
$582$	0	0
$583$	0	0
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	0	0
$591$	7.00000	0.287942
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	0	0
$597$	26.0000	1.06411
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−25.0000	−1.01977	−0.509886	−	0.860242i	$-0.670312\pi$
$601$	−25.0000	−1.01977	−0.509886	+	0.860242i	$0.670312\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	0	0
$605$	−11.0000	−0.447214
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	−8.00000	−0.324176
$610$	0	0
$611$	3.00000	0.121367
$612$	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
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	36.0000	1.44696	0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000	1.44696	0.723481	+	0.690344i	$0.242541\pi$
$620$	0	0
$621$	30.0000	1.20386
$622$	0	0
$623$	8.00000	0.320513
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	15.0000	0.598089
$630$	0	0
$631$	7.00000	0.278666	0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000	0.278666	0.139333	+	0.990246i	$0.455504\pi$
$632$	0	0
$633$	−1.00000	−0.0397464
$634$	0	0
$635$	2.00000	0.0793676
$636$	0	0
$637$	6.00000	0.237729
$638$	0	0
$639$	6.00000	0.237356
$640$	0	0
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	0	0
$645$	1.00000	0.0393750
$646$	0	0
$647$	34.0000	1.33668	0.668339	−	0.743857i	$-0.267006\pi$
$647$	34.0000	1.33668	0.668339	+	0.743857i	$0.267006\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	8.00000	0.313545
$652$	0	0
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	0	0
$655$	−19.0000	−0.742391
$656$	0	0
$657$	−32.0000	−1.24844
$658$	0	0
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	0	0
$663$	3.00000	0.116510
$664$	0	0
$665$	1.00000	0.0387783
$666$	0	0
$667$	48.0000	1.85857
$668$	0	0
$669$	−7.00000	−0.270636
$670$	0	0
$671$	0	0
$672$	0	0
$673$	7.00000	0.269830	0.134915	−	0.990857i	$-0.456924\pi$
$673$	7.00000	0.269830	0.134915	+	0.990857i	$0.456924\pi$
$674$	0	0
$675$	20.0000	0.769800
$676$	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
$681$	14.0000	0.536481
$682$	0	0
$683$	−14.0000	−0.535695	−0.267848	−	0.963461i	$-0.586312\pi$
$683$	−14.0000	−0.535695	−0.267848	+	0.963461i	$0.586312\pi$
$684$	0	0
$685$	4.00000	0.152832
$686$	0	0
$687$	11.0000	0.419676
$688$	0	0
$689$	2.00000	0.0761939
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	13.0000	0.493118
$696$	0	0
$697$	6.00000	0.227266
$698$	0	0
$699$	−3.00000	−0.113470
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	−5.00000	−0.188579
$704$	0	0
$705$	−3.00000	−0.112987
$706$	0	0
$707$	6.00000	0.225653
$708$	0	0
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	0	0
$713$	−48.0000	−1.79761
$714$	0	0
$715$	0	0
$716$	0	0
$717$	1.00000	0.0373457
$718$	0	0
$719$	−34.0000	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$720$	0	0
$721$	10.0000	0.372419
$722$	0	0
$723$	18.0000	0.669427
$724$	0	0
$725$	32.0000	1.18845
$726$	0	0
$727$	48.0000	1.78022	0.890111	−	0.455744i	$-0.150627\pi$
$727$	48.0000	1.78022	0.890111	+	0.455744i	$0.150627\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−3.00000	−0.110959
$732$	0	0
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	0	0
$735$	−6.00000	−0.221313
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	0	0
$741$	−1.00000	−0.0367359
$742$	0	0
$743$	−25.0000	−0.917161	−0.458581	−	0.888653i	$-0.651642\pi$
$743$	−25.0000	−0.917161	−0.458581	+	0.888653i	$0.651642\pi$
$744$	0	0
$745$	10.0000	0.366372
$746$	0	0
$747$	32.0000	1.17082
$748$	0	0
$749$	−8.00000	−0.292314
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	0	0
$753$	28.0000	1.02038
$754$	0	0
$755$	5.00000	0.181969
$756$	0	0
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	19.0000	0.687846
$764$	0	0
$765$	6.00000	0.216930
$766$	0	0
$767$	−10.0000	−0.361079
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	−17.0000	−0.612240
$772$	0	0
$773$	11.0000	0.395643	0.197821	−	0.980238i	$-0.436613\pi$
$773$	11.0000	0.395643	0.197821	+	0.980238i	$0.436613\pi$
$774$	0	0
$775$	−32.0000	−1.14947
$776$	0	0
$777$	−5.00000	−0.179374
$778$	0	0
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	0	0
$782$	0	0
$783$	40.0000	1.42948
$784$	0	0
$785$	10.0000	0.356915
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	0	0
$789$	−6.00000	−0.213606
$790$	0	0
$791$	−10.0000	−0.355559
$792$	0	0
$793$	14.0000	0.497155
$794$	0	0
$795$	−2.00000	−0.0709327
$796$	0	0
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	0	0
$799$	9.00000	0.318397
$800$	0	0
$801$	−16.0000	−0.565332
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−6.00000	−0.211472
$806$	0	0
$807$	18.0000	0.633630
$808$	0	0
$809$	−45.0000	−1.58212	−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000	−1.58212	−0.791058	+	0.611741i	$0.790469\pi$
$810$	0	0
$811$	22.0000	0.772524	0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000	0.772524	0.386262	+	0.922389i	$0.373766\pi$
$812$	0	0
$813$	5.00000	0.175358
$814$	0	0
$815$	−18.0000	−0.630512
$816$	0	0
$817$	1.00000	0.0349856
$818$	0	0
$819$	2.00000	0.0698857
$820$	0	0
$821$	25.0000	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$822$	0	0
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	42.0000	1.46048	0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000	1.46048	0.730242	+	0.683189i	$0.239408\pi$
$828$	0	0
$829$	32.0000	1.11141	0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000	1.11141	0.555703	+	0.831381i	$0.312449\pi$
$830$	0	0
$831$	−30.0000	−1.04069
$832$	0	0
$833$	18.0000	0.623663
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−40.0000	−1.38260
$838$	0	0
$839$	32.0000	1.10476	0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000	1.10476	0.552381	+	0.833592i	$0.313719\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	0	0
$843$	−22.0000	−0.757720
$844$	0	0
$845$	1.00000	0.0344010
$846$	0	0
$847$	−11.0000	−0.377964
$848$	0	0
$849$	−32.0000	−1.09824
$850$	0	0
$851$	30.0000	1.02839
$852$	0	0
$853$	−5.00000	−0.171197	−0.0855984	−	0.996330i	$-0.527280\pi$
$853$	−5.00000	−0.171197	−0.0855984	+	0.996330i	$0.527280\pi$
$854$	0	0
$855$	−2.00000	−0.0683986
$856$	0	0
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	12.0000	0.409435	0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000	0.409435	0.204717	+	0.978821i	$0.434372\pi$
$860$	0	0
$861$	−2.00000	−0.0681598
$862$	0	0
$863$	−29.0000	−0.987171	−0.493586	−	0.869697i	$-0.664314\pi$
$863$	−29.0000	−0.987171	−0.493586	+	0.869697i	$0.664314\pi$
$864$	0	0
$865$	2.00000	0.0680020
$866$	0	0
$867$	−8.00000	−0.271694
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−4.00000	−0.135535
$872$	0	0
$873$	20.0000	0.676897
$874$	0	0
$875$	−9.00000	−0.304256
$876$	0	0
$877$	13.0000	0.438979	0.219489	−	0.975615i	$-0.429561\pi$
$877$	13.0000	0.438979	0.219489	+	0.975615i	$0.429561\pi$
$878$	0	0
$879$	11.0000	0.371021
$880$	0	0
$881$	−31.0000	−1.04442	−0.522208	−	0.852818i	$-0.674892\pi$
$881$	−31.0000	−1.04442	−0.522208	+	0.852818i	$0.674892\pi$
$882$	0	0
$883$	−25.0000	−0.841317	−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000	−0.841317	−0.420658	+	0.907219i	$0.638201\pi$
$884$	0	0
$885$	10.0000	0.336146
$886$	0	0
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	0	0
$889$	2.00000	0.0670778
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−3.00000	−0.100391
$894$	0	0
$895$	−1.00000	−0.0334263
$896$	0	0
$897$	6.00000	0.200334
$898$	0	0
$899$	−64.0000	−2.13452
$900$	0	0
$901$	6.00000	0.199889
$902$	0	0
$903$	1.00000	0.0332779
$904$	0	0
$905$	−16.0000	−0.531858
$906$	0	0
$907$	35.0000	1.16216	0.581078	−	0.813848i	$-0.302631\pi$
$907$	35.0000	1.16216	0.581078	+	0.813848i	$0.302631\pi$
$908$	0	0
$909$	−12.0000	−0.398015
$910$	0	0
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−14.0000	−0.462826
$916$	0	0
$917$	−19.0000	−0.627435
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	0	0
$923$	3.00000	0.0987462
$924$	0	0
$925$	20.0000	0.657596
$926$	0	0
$927$	−20.0000	−0.656886
$928$	0	0
$929$	−60.0000	−1.96854	−0.984268	−	0.176682i	$-0.943464\pi$
$929$	−60.0000	−1.96854	−0.984268	+	0.176682i	$0.943464\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	0	0
$933$	14.0000	0.458339
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	−9.00000	−0.293704
$940$	0	0
$941$	37.0000	1.20617	0.603083	−	0.797679i	$-0.293939\pi$
$941$	37.0000	1.20617	0.603083	+	0.797679i	$0.293939\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	0	0
$945$	−5.00000	−0.162650
$946$	0	0
$947$	58.0000	1.88475	0.942373	−	0.334563i	$-0.108589\pi$
$947$	58.0000	1.88475	0.942373	+	0.334563i	$0.108589\pi$
$948$	0	0
$949$	−16.0000	−0.519382
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	−3.00000	−0.0971795	−0.0485898	−	0.998819i	$-0.515473\pi$
$953$	−3.00000	−0.0971795	−0.0485898	+	0.998819i	$0.515473\pi$
$954$	0	0
$955$	−14.0000	−0.453029
$956$	0	0
$957$	0	0
$958$	0	0
$959$	4.00000	0.129167
$960$	0	0
$961$	33.0000	1.06452
$962$	0	0
$963$	16.0000	0.515593
$964$	0	0
$965$	−16.0000	−0.515058
$966$	0	0
$967$	−33.0000	−1.06121	−0.530604	−	0.847620i	$-0.678035\pi$
$967$	−33.0000	−1.06121	−0.530604	+	0.847620i	$0.678035\pi$
$968$	0	0
$969$	−3.00000	−0.0963739
$970$	0	0
$971$	−39.0000	−1.25157	−0.625785	−	0.779996i	$-0.715221\pi$
$971$	−39.0000	−1.25157	−0.625785	+	0.779996i	$0.715221\pi$
$972$	0	0
$973$	13.0000	0.416761
$974$	0	0
$975$	4.00000	0.128103
$976$	0	0
$977$	−46.0000	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$977$	−46.0000	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−38.0000	−1.21325
$982$	0	0
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	0	0
$985$	7.00000	0.223039
$986$	0	0
$987$	−3.00000	−0.0954911
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−62.0000	−1.96949	−0.984747	−	0.173990i	$-0.944334\pi$
$991$	−62.0000	−1.96949	−0.984747	+	0.173990i	$0.944334\pi$
$992$	0	0
$993$	−32.0000	−1.01549
$994$	0	0
$995$	26.0000	0.824255
$996$	0	0
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	0	0
$999$	25.0000	0.790965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3952.2.a.i.1.1		1
4.3	odd	2		494.2.a.a.1.1	✓	1
12.11	even	2		4446.2.a.n.1.1		1
52.51	odd	2		6422.2.a.e.1.1		1
76.75	even	2		9386.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.a.a.1.1	✓	1	4.3	odd	2
3952.2.a.i.1.1		1	1.1	even	1	trivial
4446.2.a.n.1.1		1	12.11	even	2
6422.2.a.e.1.1		1	52.51	odd	2
9386.2.a.l.1.1		1	76.75	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:	\( N \)	\(=\)	\( 3952 = 2^{4} \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3952.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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