LMFDB - Embedded newform 2960.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2960,2,Mod(1,2960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2960, 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("2960.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2960 = 2^{4} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2960.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:	$23.6357189983$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1480)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2960.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +3.00000 q^{11} -1.00000 q^{15} -8.00000 q^{17} -1.00000 q^{21} +4.00000 q^{23} +1.00000 q^{25} +5.00000 q^{27} -8.00000 q^{29} -6.00000 q^{31} -3.00000 q^{33} +1.00000 q^{35} +1.00000 q^{37} +3.00000 q^{41} -2.00000 q^{43} -2.00000 q^{45} -3.00000 q^{47} -6.00000 q^{49} +8.00000 q^{51} -1.00000 q^{53} +3.00000 q^{55} +4.00000 q^{59} -6.00000 q^{61} -2.00000 q^{63} -4.00000 q^{67} -4.00000 q^{69} +1.00000 q^{71} +9.00000 q^{73} -1.00000 q^{75} +3.00000 q^{77} -10.0000 q^{79} +1.00000 q^{81} -5.00000 q^{83} -8.00000 q^{85} +8.00000 q^{87} +6.00000 q^{89} +6.00000 q^{93} -10.0000 q^{97} -6.00000 q^{99} +O(q^{100})$

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	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	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
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0	0
$17$	−8.00000	−1.94029	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−8.00000	−1.94029	−0.970143	+	0.242536i	$0.922021\pi$
$18$	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
$23$	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
$27$	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
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	0	0
$33$	−3.00000	−0.522233
$34$	0	0
$35$	1.00000	0.169031
$36$	0	0
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0	0
$39$	0	0
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	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
$51$	8.00000	1.12022
$52$	0	0
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	3.00000	0.404520
$56$	0	0
$57$	0	0
$58$	0	0
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	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
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	−4.00000	−0.481543
$70$	0	0
$71$	1.00000	0.118678	0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000	0.118678	0.0593391	+	0.998238i	$0.481101\pi$
$72$	0	0
$73$	9.00000	1.05337	0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000	1.05337	0.526685	+	0.850060i	$0.323435\pi$
$74$	0	0
$75$	−1.00000	−0.115470
$76$	0	0
$77$	3.00000	0.341882
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−5.00000	−0.548821	−0.274411	−	0.961613i	$-0.588483\pi$
$83$	−5.00000	−0.548821	−0.274411	+	0.961613i	$0.588483\pi$
$84$	0	0
$85$	−8.00000	−0.867722
$86$	0	0
$87$	8.00000	0.857690
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	6.00000	0.622171
$94$	0	0
$95$	0	0
$96$	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
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	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
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	0	0
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−8.00000	−0.733359
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	−3.00000	−0.270501
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	0	0
$129$	2.00000	0.176090
$130$	0	0
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	5.00000	0.430331
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	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
$149$	−1.00000	−0.0819232	−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000	−0.0819232	−0.0409616	+	0.999161i	$0.513042\pi$
$150$	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
$153$	16.0000	1.29352
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−15.0000	−1.19713	−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000	−1.19713	−0.598565	+	0.801074i	$0.704262\pi$
$158$	0	0
$159$	1.00000	0.0793052
$160$	0	0
$161$	4.00000	0.315244
$162$	0	0
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	0	0
$165$	−3.00000	−0.233550
$166$	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
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	0	0
$177$	−4.00000	−0.300658
$178$	0	0
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	−19.0000	−1.41226	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000	−1.41226	−0.706129	+	0.708083i	$0.749560\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	0	0
$185$	1.00000	0.0735215
$186$	0	0
$187$	−24.0000	−1.75505
$188$	0	0
$189$	5.00000	0.363696
$190$	0	0
$191$	4.00000	0.289430	0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000	0.289430	0.144715	+	0.989473i	$0.453773\pi$
$192$	0	0
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−15.0000	−1.06871	−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000	−1.06871	−0.534353	+	0.845262i	$0.679445\pi$
$198$	0	0
$199$	22.0000	1.55954	0.779769	−	0.626067i	$-0.215336\pi$
$199$	22.0000	1.55954	0.779769	+	0.626067i	$0.215336\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	−8.00000	−0.561490
$204$	0	0
$205$	3.00000	0.209529
$206$	0	0
$207$	−8.00000	−0.556038
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−21.0000	−1.44570	−0.722850	−	0.691005i	$-0.757168\pi$
$211$	−21.0000	−1.44570	−0.722850	+	0.691005i	$0.757168\pi$
$212$	0	0
$213$	−1.00000	−0.0685189
$214$	0	0
$215$	−2.00000	−0.136399
$216$	0	0
$217$	−6.00000	−0.407307
$218$	0	0
$219$	−9.00000	−0.608164
$220$	0	0
$221$	0	0
$222$	0	0
$223$	13.0000	0.870544	0.435272	−	0.900299i	$-0.356652\pi$
$223$	13.0000	0.870544	0.435272	+	0.900299i	$0.356652\pi$
$224$	0	0
$225$	−2.00000	−0.133333
$226$	0	0
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	15.0000	0.991228	0.495614	−	0.868543i	$-0.334943\pi$
$229$	15.0000	0.991228	0.495614	+	0.868543i	$0.334943\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	−3.00000	−0.195698
$236$	0	0
$237$	10.0000	0.649570
$238$	0	0
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	0	0
$241$	24.0000	1.54598	0.772988	−	0.634421i	$-0.218761\pi$
$241$	24.0000	1.54598	0.772988	+	0.634421i	$0.218761\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	0	0
$245$	−6.00000	−0.383326
$246$	0	0
$247$	0	0
$248$	0	0
$249$	5.00000	0.316862
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	0	0
$255$	8.00000	0.500979
$256$	0	0
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	1.00000	0.0621370
$260$	0	0
$261$	16.0000	0.990375
$262$	0	0
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	−1.00000	−0.0614295
$266$	0	0
$267$	−6.00000	−0.367194
$268$	0	0
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−19.0000	−1.15417	−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000	−1.15417	−0.577084	+	0.816685i	$0.695809\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	3.00000	0.180907
$276$	0	0
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	0	0
$279$	12.0000	0.718421
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	3.00000	0.177084
$288$	0	0
$289$	47.0000	2.76471
$290$	0	0
$291$	10.0000	0.586210
$292$	0	0
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	0	0
$297$	15.0000	0.870388
$298$	0	0
$299$	0	0
$300$	0	0
$301$	−2.00000	−0.115278
$302$	0	0
$303$	5.00000	0.287242
$304$	0	0
$305$	−6.00000	−0.343559
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	0	0
$309$	−10.0000	−0.568880
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	0	0
$315$	−2.00000	−0.112687
$316$	0	0
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	−24.0000	−1.34374
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	2.00000	0.110600
$328$	0	0
$329$	−3.00000	−0.165395
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	0	0
$333$	−2.00000	−0.109599
$334$	0	0
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−15.0000	−0.817102	−0.408551	−	0.912735i	$-0.633966\pi$
$337$	−15.0000	−0.817102	−0.408551	+	0.912735i	$0.633966\pi$
$338$	0	0
$339$	−6.00000	−0.325875
$340$	0	0
$341$	−18.0000	−0.974755
$342$	0	0
$343$	−13.0000	−0.701934
$344$	0	0
$345$	−4.00000	−0.215353
$346$	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
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	1.00000	0.0530745
$356$	0	0
$357$	8.00000	0.423405
$358$	0	0
$359$	−15.0000	−0.791670	−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000	−0.791670	−0.395835	+	0.918322i	$0.629545\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	2.00000	0.104973
$364$	0	0
$365$	9.00000	0.471082
$366$	0	0
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−1.00000	−0.0519174
$372$	0	0
$373$	−1.00000	−0.0517780	−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000	−0.0517780	−0.0258890	+	0.999665i	$0.508242\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−29.0000	−1.48963	−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000	−1.48963	−0.744815	+	0.667271i	$0.767462\pi$
$380$	0	0
$381$	−7.00000	−0.358621
$382$	0	0
$383$	−34.0000	−1.73732	−0.868659	−	0.495410i	$-0.835018\pi$
$383$	−34.0000	−1.73732	−0.868659	+	0.495410i	$0.835018\pi$
$384$	0	0
$385$	3.00000	0.152894
$386$	0	0
$387$	4.00000	0.203331
$388$	0	0
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	−32.0000	−1.61831
$392$	0	0
$393$	2.00000	0.100887
$394$	0	0
$395$	−10.0000	−0.503155
$396$	0	0
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	3.00000	0.148704
$408$	0	0
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	18.0000	0.887875
$412$	0	0
$413$	4.00000	0.196827
$414$	0	0
$415$	−5.00000	−0.245440
$416$	0	0
$417$	12.0000	0.587643
$418$	0	0
$419$	−29.0000	−1.41674	−0.708371	−	0.705840i	$-0.750570\pi$
$419$	−29.0000	−1.41674	−0.708371	+	0.705840i	$0.750570\pi$
$420$	0	0
$421$	−4.00000	−0.194948	−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000	−0.194948	−0.0974740	+	0.995238i	$0.531076\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	−8.00000	−0.388057
$426$	0	0
$427$	−6.00000	−0.290360
$428$	0	0
$429$	0	0
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	0	0
$433$	7.00000	0.336399	0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000	0.336399	0.168199	+	0.985753i	$0.446205\pi$
$434$	0	0
$435$	8.00000	0.383571
$436$	0	0
$437$	0	0
$438$	0	0
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	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
$445$	6.00000	0.284427
$446$	0	0
$447$	1.00000	0.0472984
$448$	0	0
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	0	0
$453$	16.0000	0.751746
$454$	0	0
$455$	0	0
$456$	0	0
$457$	42.0000	1.96468	0.982339	−	0.187112i	$-0.0599128\pi$
$457$	42.0000	1.96468	0.982339	+	0.187112i	$0.0599128\pi$
$458$	0	0
$459$	−40.0000	−1.86704
$460$	0	0
$461$	26.0000	1.21094	0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000	1.21094	0.605470	+	0.795868i	$0.292985\pi$
$462$	0	0
$463$	30.0000	1.39422	0.697109	−	0.716965i	$-0.254469\pi$
$463$	30.0000	1.39422	0.697109	+	0.716965i	$0.254469\pi$
$464$	0	0
$465$	6.00000	0.278243
$466$	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
$469$	−4.00000	−0.184703
$470$	0	0
$471$	15.0000	0.691164
$472$	0	0
$473$	−6.00000	−0.275880
$474$	0	0
$475$	0	0
$476$	0	0
$477$	2.00000	0.0915737
$478$	0	0
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	−4.00000	−0.182006
$484$	0	0
$485$	−10.0000	−0.454077
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	0	0
$489$	−8.00000	−0.361773
$490$	0	0
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	0	0
$493$	64.0000	2.88242
$494$	0	0
$495$	−6.00000	−0.269680
$496$	0	0
$497$	1.00000	0.0448561
$498$	0	0
$499$	−26.0000	−1.16392	−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000	−1.16392	−0.581960	+	0.813217i	$0.697714\pi$
$500$	0	0
$501$	−2.00000	−0.0893534
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−5.00000	−0.222497
$506$	0	0
$507$	13.0000	0.577350
$508$	0	0
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	9.00000	0.398137
$512$	0	0
$513$	0	0
$514$	0	0
$515$	10.0000	0.440653
$516$	0	0
$517$	−9.00000	−0.395820
$518$	0	0
$519$	9.00000	0.395056
$520$	0	0
$521$	−17.0000	−0.744784	−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000	−0.744784	−0.372392	+	0.928076i	$0.621462\pi$
$522$	0	0
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	0	0
$525$	−1.00000	−0.0436436
$526$	0	0
$527$	48.0000	2.09091
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−8.00000	−0.347170
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	20.0000	0.863064
$538$	0	0
$539$	−18.0000	−0.775315
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	0	0
$543$	19.0000	0.815368
$544$	0	0
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	0	0
$549$	12.0000	0.512148
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−10.0000	−0.425243
$554$	0	0
$555$	−1.00000	−0.0424476
$556$	0	0
$557$	32.0000	1.35588	0.677942	−	0.735116i	$-0.262872\pi$
$557$	32.0000	1.35588	0.677942	+	0.735116i	$0.262872\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	24.0000	1.01328
$562$	0	0
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	0	0
$567$	1.00000	0.0419961
$568$	0	0
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	−41.0000	−1.71580	−0.857898	−	0.513820i	$-0.828230\pi$
$571$	−41.0000	−1.71580	−0.857898	+	0.513820i	$0.828230\pi$
$572$	0	0
$573$	−4.00000	−0.167102
$574$	0	0
$575$	4.00000	0.166812
$576$	0	0
$577$	−36.0000	−1.49870	−0.749350	−	0.662174i	$-0.769634\pi$
$577$	−36.0000	−1.49870	−0.749350	+	0.662174i	$0.769634\pi$
$578$	0	0
$579$	−8.00000	−0.332469
$580$	0	0
$581$	−5.00000	−0.207435
$582$	0	0
$583$	−3.00000	−0.124247
$584$	0	0
$585$	0	0
$586$	0	0
$587$	14.0000	0.577842	0.288921	−	0.957353i	$-0.406704\pi$
$587$	14.0000	0.577842	0.288921	+	0.957353i	$0.406704\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	15.0000	0.617018
$592$	0	0
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	0	0
$595$	−8.00000	−0.327968
$596$	0	0
$597$	−22.0000	−0.900400
$598$	0	0
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	0	0
$605$	−2.00000	−0.0813116
$606$	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
$609$	8.00000	0.324176
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−19.0000	−0.767403	−0.383701	−	0.923457i	$-0.625351\pi$
$613$	−19.0000	−0.767403	−0.383701	+	0.923457i	$0.625351\pi$
$614$	0	0
$615$	−3.00000	−0.120972
$616$	0	0
$617$	−33.0000	−1.32853	−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000	−1.32853	−0.664265	+	0.747497i	$0.731255\pi$
$618$	0	0
$619$	−29.0000	−1.16561	−0.582804	−	0.812613i	$-0.698045\pi$
$619$	−29.0000	−1.16561	−0.582804	+	0.812613i	$0.698045\pi$
$620$	0	0
$621$	20.0000	0.802572
$622$	0	0
$623$	6.00000	0.240385
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−8.00000	−0.318981
$630$	0	0
$631$	34.0000	1.35352	0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000	1.35352	0.676759	+	0.736204i	$0.263384\pi$
$632$	0	0
$633$	21.0000	0.834675
$634$	0	0
$635$	7.00000	0.277787
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−2.00000	−0.0791188
$640$	0	0
$641$	31.0000	1.22443	0.612213	−	0.790693i	$-0.290279\pi$
$641$	31.0000	1.22443	0.612213	+	0.790693i	$0.290279\pi$
$642$	0	0
$643$	8.00000	0.315489	0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000	0.315489	0.157745	+	0.987480i	$0.449578\pi$
$644$	0	0
$645$	2.00000	0.0787499
$646$	0	0
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	0	0
$651$	6.00000	0.235159
$652$	0	0
$653$	34.0000	1.33052	0.665261	−	0.746611i	$-0.268320\pi$
$653$	34.0000	1.33052	0.665261	+	0.746611i	$0.268320\pi$
$654$	0	0
$655$	−2.00000	−0.0781465
$656$	0	0
$657$	−18.0000	−0.702247
$658$	0	0
$659$	37.0000	1.44132	0.720658	−	0.693291i	$-0.243840\pi$
$659$	37.0000	1.44132	0.720658	+	0.693291i	$0.243840\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−32.0000	−1.23904
$668$	0	0
$669$	−13.0000	−0.502609
$670$	0	0
$671$	−18.0000	−0.694882
$672$	0	0
$673$	13.0000	0.501113	0.250557	−	0.968102i	$-0.419386\pi$
$673$	13.0000	0.501113	0.250557	+	0.968102i	$0.419386\pi$
$674$	0	0
$675$	5.00000	0.192450
$676$	0	0
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	0	0
$679$	−10.0000	−0.383765
$680$	0	0
$681$	−12.0000	−0.459841
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	−18.0000	−0.687745
$686$	0	0
$687$	−15.0000	−0.572286
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	0	0
$693$	−6.00000	−0.227921
$694$	0	0
$695$	−12.0000	−0.455186
$696$	0	0
$697$	−24.0000	−0.909065
$698$	0	0
$699$	6.00000	0.226941
$700$	0	0
$701$	−4.00000	−0.151078	−0.0755390	−	0.997143i	$-0.524068\pi$
$701$	−4.00000	−0.151078	−0.0755390	+	0.997143i	$0.524068\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	3.00000	0.112987
$706$	0	0
$707$	−5.00000	−0.188044
$708$	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
$711$	20.0000	0.750059
$712$	0	0
$713$	−24.0000	−0.898807
$714$	0	0
$715$	0	0
$716$	0	0
$717$	14.0000	0.522840
$718$	0	0
$719$	43.0000	1.60363	0.801815	−	0.597573i	$-0.203868\pi$
$719$	43.0000	1.60363	0.801815	+	0.597573i	$0.203868\pi$
$720$	0	0
$721$	10.0000	0.372419
$722$	0	0
$723$	−24.0000	−0.892570
$724$	0	0
$725$	−8.00000	−0.297113
$726$	0	0
$727$	34.0000	1.26099	0.630495	−	0.776193i	$-0.282852\pi$
$727$	34.0000	1.26099	0.630495	+	0.776193i	$0.282852\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	16.0000	0.591781
$732$	0	0
$733$	−47.0000	−1.73598	−0.867992	−	0.496578i	$-0.834590\pi$
$733$	−47.0000	−1.73598	−0.867992	+	0.496578i	$0.834590\pi$
$734$	0	0
$735$	6.00000	0.221313
$736$	0	0
$737$	−12.0000	−0.442026
$738$	0	0
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	47.0000	1.72426	0.862131	−	0.506685i	$-0.169129\pi$
$743$	47.0000	1.72426	0.862131	+	0.506685i	$0.169129\pi$
$744$	0	0
$745$	−1.00000	−0.0366372
$746$	0	0
$747$	10.0000	0.365881
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−7.00000	−0.255434	−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000	−0.255434	−0.127717	+	0.991811i	$0.540765\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	0	0
$759$	−12.0000	−0.435572
$760$	0	0
$761$	−31.0000	−1.12375	−0.561875	−	0.827222i	$-0.689920\pi$
$761$	−31.0000	−1.12375	−0.561875	+	0.827222i	$0.689920\pi$
$762$	0	0
$763$	−2.00000	−0.0724049
$764$	0	0
$765$	16.0000	0.578481
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−44.0000	−1.58668	−0.793340	−	0.608778i	$-0.791660\pi$
$769$	−44.0000	−1.58668	−0.793340	+	0.608778i	$0.791660\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	0	0
$773$	9.00000	0.323708	0.161854	−	0.986815i	$-0.448253\pi$
$773$	9.00000	0.323708	0.161854	+	0.986815i	$0.448253\pi$
$774$	0	0
$775$	−6.00000	−0.215526
$776$	0	0
$777$	−1.00000	−0.0358748
$778$	0	0
$779$	0	0
$780$	0	0
$781$	3.00000	0.107348
$782$	0	0
$783$	−40.0000	−1.42948
$784$	0	0
$785$	−15.0000	−0.535373
$786$	0	0
$787$	−7.00000	−0.249523	−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000	−0.249523	−0.124762	+	0.992187i	$0.539817\pi$
$788$	0	0
$789$	−9.00000	−0.320408
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	0	0
$794$	0	0
$795$	1.00000	0.0354663
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	0	0
$801$	−12.0000	−0.423999
$802$	0	0
$803$	27.0000	0.952809
$804$	0	0
$805$	4.00000	0.140981
$806$	0	0
$807$	14.0000	0.492823
$808$	0	0
$809$	4.00000	0.140633	0.0703163	−	0.997525i	$-0.477599\pi$
$809$	4.00000	0.140633	0.0703163	+	0.997525i	$0.477599\pi$
$810$	0	0
$811$	55.0000	1.93131	0.965656	−	0.259825i	$-0.0836650\pi$
$811$	55.0000	1.93131	0.965656	+	0.259825i	$0.0836650\pi$
$812$	0	0
$813$	19.0000	0.666359
$814$	0	0
$815$	8.00000	0.280228
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	5.00000	0.174501	0.0872506	−	0.996186i	$-0.472192\pi$
$821$	5.00000	0.174501	0.0872506	+	0.996186i	$0.472192\pi$
$822$	0	0
$823$	48.0000	1.67317	0.836587	−	0.547833i	$-0.184547\pi$
$823$	48.0000	1.67317	0.836587	+	0.547833i	$0.184547\pi$
$824$	0	0
$825$	−3.00000	−0.104447
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−56.0000	−1.94496	−0.972480	−	0.232986i	$-0.925151\pi$
$829$	−56.0000	−1.94496	−0.972480	+	0.232986i	$0.925151\pi$
$830$	0	0
$831$	14.0000	0.485655
$832$	0	0
$833$	48.0000	1.66310
$834$	0	0
$835$	2.00000	0.0692129
$836$	0	0
$837$	−30.0000	−1.03695
$838$	0	0
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	0	0
$843$	6.00000	0.206651
$844$	0	0
$845$	−13.0000	−0.447214
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	0	0
$849$	16.0000	0.549119
$850$	0	0
$851$	4.00000	0.137118
$852$	0	0
$853$	−32.0000	−1.09566	−0.547830	−	0.836590i	$-0.684546\pi$
$853$	−32.0000	−1.09566	−0.547830	+	0.836590i	$0.684546\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	−3.00000	−0.102240
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	−9.00000	−0.306009
$866$	0	0
$867$	−47.0000	−1.59620
$868$	0	0
$869$	−30.0000	−1.01768
$870$	0	0
$871$	0	0
$872$	0	0
$873$	20.0000	0.676897
$874$	0	0
$875$	1.00000	0.0338062
$876$	0	0
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	0	0
$879$	−22.0000	−0.742042
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	0	0
$883$	48.0000	1.61533	0.807664	−	0.589643i	$-0.200731\pi$
$883$	48.0000	1.61533	0.807664	+	0.589643i	$0.200731\pi$
$884$	0	0
$885$	−4.00000	−0.134459
$886$	0	0
$887$	−33.0000	−1.10803	−0.554016	−	0.832506i	$-0.686905\pi$
$887$	−33.0000	−1.10803	−0.554016	+	0.832506i	$0.686905\pi$
$888$	0	0
$889$	7.00000	0.234772
$890$	0	0
$891$	3.00000	0.100504
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−20.0000	−0.668526
$896$	0	0
$897$	0	0
$898$	0	0
$899$	48.0000	1.60089
$900$	0	0
$901$	8.00000	0.266519
$902$	0	0
$903$	2.00000	0.0665558
$904$	0	0
$905$	−19.0000	−0.631581
$906$	0	0
$907$	−54.0000	−1.79304	−0.896520	−	0.443003i	$-0.853913\pi$
$907$	−54.0000	−1.79304	−0.896520	+	0.443003i	$0.853913\pi$
$908$	0	0
$909$	10.0000	0.331679
$910$	0	0
$911$	34.0000	1.12647	0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000	1.12647	0.563235	+	0.826297i	$0.309557\pi$
$912$	0	0
$913$	−15.0000	−0.496428
$914$	0	0
$915$	6.00000	0.198354
$916$	0	0
$917$	−2.00000	−0.0660458
$918$	0	0
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	0	0
$921$	11.0000	0.362462
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1.00000	0.0328798
$926$	0	0
$927$	−20.0000	−0.656886
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−24.0000	−0.785725
$934$	0	0
$935$	−24.0000	−0.784884
$936$	0	0
$937$	59.0000	1.92745	0.963723	−	0.266904i	$-0.0860008\pi$
$937$	59.0000	1.92745	0.963723	+	0.266904i	$0.0860008\pi$
$938$	0	0
$939$	10.0000	0.326338
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	0	0
$945$	5.00000	0.162650
$946$	0	0
$947$	−16.0000	−0.519930	−0.259965	−	0.965618i	$-0.583711\pi$
$947$	−16.0000	−0.519930	−0.259965	+	0.965618i	$0.583711\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	2.00000	0.0648544
$952$	0	0
$953$	3.00000	0.0971795	0.0485898	−	0.998819i	$-0.484527\pi$
$953$	3.00000	0.0971795	0.0485898	+	0.998819i	$0.484527\pi$
$954$	0	0
$955$	4.00000	0.129437
$956$	0	0
$957$	24.0000	0.775810
$958$	0	0
$959$	−18.0000	−0.581250
$960$	0	0
$961$	5.00000	0.161290
$962$	0	0
$963$	0	0
$964$	0	0
$965$	8.00000	0.257529
$966$	0	0
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	−12.0000	−0.384702
$974$	0	0
$975$	0	0
$976$	0	0
$977$	28.0000	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$978$	0	0
$979$	18.0000	0.575282
$980$	0	0
$981$	4.00000	0.127710
$982$	0	0
$983$	−5.00000	−0.159475	−0.0797376	−	0.996816i	$-0.525408\pi$
$983$	−5.00000	−0.159475	−0.0797376	+	0.996816i	$0.525408\pi$
$984$	0	0
$985$	−15.0000	−0.477940
$986$	0	0
$987$	3.00000	0.0954911
$988$	0	0
$989$	−8.00000	−0.254385
$990$	0	0
$991$	−6.00000	−0.190596	−0.0952981	−	0.995449i	$-0.530380\pi$
$991$	−6.00000	−0.190596	−0.0952981	+	0.995449i	$0.530380\pi$
$992$	0	0
$993$	8.00000	0.253872
$994$	0	0
$995$	22.0000	0.697447
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	0	0
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2960.2.a.f.1.1		1
4.3	odd	2		1480.2.a.c.1.1	✓	1
20.19	odd	2		7400.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1480.2.a.c.1.1	✓	1	4.3	odd	2
2960.2.a.f.1.1		1	1.1	even	1	trivial
7400.2.a.c.1.1		1	20.19	odd	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:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2960.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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