LMFDB - Embedded newform 1008.2.df.d.929.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.2
Root			$-0.268067 - 1.71118i$ of defining polynomial
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.d.689.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42826 - 0.979841i) q^{3} -1.68574 q^{5} +(0.0236360 - 2.64565i) q^{7} +(1.07983 + 2.79892i) q^{9} -3.90538i q^{11} +(5.24391 - 3.02757i) q^{13} +(2.40766 + 1.65175i) q^{15} +(0.201244 + 0.348565i) q^{17} +(0.145617 + 0.0840718i) q^{19} +(-2.62607 + 3.75550i) q^{21} +8.88395i q^{23} -2.15829 q^{25} +(1.20023 - 5.05563i) q^{27} +(-6.15380 - 3.55290i) q^{29} +(-5.44527 - 3.14383i) q^{31} +(-3.82665 + 5.57788i) q^{33} +(-0.0398441 + 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} +(-10.4562 - 0.814049i) q^{39} +(-1.64707 - 2.85281i) q^{41} +(-1.80474 + 3.12590i) q^{43} +(-1.82030 - 4.71825i) q^{45} +(-4.38482 - 7.59474i) q^{47} +(-6.99888 - 0.125065i) q^{49} +(0.0541101 - 0.695026i) q^{51} +(-4.94628 + 2.85574i) q^{53} +6.58345i q^{55} +(-0.125601 - 0.262757i) q^{57} +(-2.25163 + 3.89994i) q^{59} +(4.43678 - 2.56157i) q^{61} +(7.43049 - 2.79068i) q^{63} +(-8.83986 + 5.10369i) q^{65} +(-2.95521 + 5.11857i) q^{67} +(8.70486 - 12.6886i) q^{69} +11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(3.08259 + 2.11478i) q^{75} +(-10.3323 - 0.0923076i) q^{77} +(0.603968 + 1.04610i) q^{79} +(-6.66796 + 6.04470i) q^{81} +(0.181350 - 0.314108i) q^{83} +(-0.339244 - 0.587588i) q^{85} +(5.30793 + 11.1042i) q^{87} +(1.38526 - 2.39934i) q^{89} +(-7.88594 - 13.9451i) q^{91} +(4.69679 + 9.82569i) q^{93} +(-0.245471 - 0.141723i) q^{95} +(0.508914 + 0.293821i) q^{97} +(10.9309 - 4.21713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.42826	−	0.979841i	−0.824603	−	0.565711i
$3$	−1.42826	−	0.979841i	−0.824603	−	0.565711i
$4$		0			0
$5$	−1.68574			−0.753885			−0.376942	−	0.926237i	$-0.623025\pi$
$5$	−1.68574			−0.753885			−0.376942	+	0.926237i	$0.623025\pi$
$6$		0			0
$7$	0.0236360	−	2.64565i	0.00893357	−	0.999960i
$7$	0.0236360	−	2.64565i	0.00893357	−	0.999960i
$8$		0			0
$9$	1.07983	+	2.79892i	0.359942	+	0.932975i
$10$		0			0
$11$		−	3.90538i		−	1.17752i	−0.808309	−	0.588758i	$-0.799617\pi$
$11$		−	3.90538i		−	1.17752i	0.808309	−	0.588758i	$-0.200383\pi$
$12$		0			0
$13$	5.24391	−	3.02757i	1.45440	−	0.839698i	0.455673	−	0.890147i	$-0.349399\pi$
$13$	5.24391	−	3.02757i	1.45440	−	0.839698i	0.998727	+	0.0504496i	$0.0160654\pi$
$14$		0			0
$15$	2.40766	+	1.65175i	0.621656	+	0.426481i
$16$		0			0
$17$	0.201244	+	0.348565i	0.0488088	+	0.0845393i	0.889398	−	0.457134i	$-0.151124\pi$
$17$	0.201244	+	0.348565i	0.0488088	+	0.0845393i	−0.840589	+	0.541674i	$0.817791\pi$
$18$		0			0
$19$	0.145617	+	0.0840718i	0.0334067	+	0.0192874i	0.516610	−	0.856221i	$-0.327194\pi$
$19$	0.145617	+	0.0840718i	0.0334067	+	0.0192874i	−0.483204	+	0.875508i	$0.660527\pi$
$20$		0			0
$21$	−2.62607	+	3.75550i	−0.573055	+	0.819517i
$22$		0			0
$23$			8.88395i			1.85243i	0.376993	+	0.926216i	$0.376958\pi$
$23$			8.88395i			1.85243i	−0.376993	+	0.926216i	$0.623042\pi$
$24$		0			0
$25$	−2.15829			−0.431658
$26$		0			0
$27$	1.20023	−	5.05563i	0.230985	−	0.972957i
$28$		0			0
$29$	−6.15380	−	3.55290i	−1.14273	−	0.659757i	−0.195627	−	0.980678i	$-0.562674\pi$
$29$	−6.15380	−	3.55290i	−1.14273	−	0.659757i	−0.947106	+	0.320921i	$0.896007\pi$
$30$		0			0
$31$	−5.44527	−	3.14383i	−0.978000	−	0.564649i	−0.0763342	−	0.997082i	$-0.524322\pi$
$31$	−5.44527	−	3.14383i	−0.978000	−	0.564649i	−0.901666	+	0.432434i	$0.857655\pi$
$32$		0			0
$33$	−3.82665	+	5.57788i	−0.666134	+	0.970984i
$34$		0			0
$35$	−0.0398441	+	4.45986i	−0.00673488	+	0.753855i
$36$		0			0
$37$	3.13257	−	5.42578i	0.514992	−	0.891992i	−0.484857	−	0.874594i	$-0.661128\pi$
$37$	3.13257	−	5.42578i	0.514992	−	0.891992i	0.999849	−	0.0173987i	$-0.00553846\pi$
$38$		0			0
$39$	−10.4562	−	0.814049i	−1.67433	−	0.130352i
$40$		0			0
$41$	−1.64707	−	2.85281i	−0.257229	−	0.445534i	0.708269	−	0.705942i	$-0.249476\pi$
$41$	−1.64707	−	2.85281i	−0.257229	−	0.445534i	−0.965499	+	0.260408i	$0.916143\pi$
$42$		0			0
$43$	−1.80474	+	3.12590i	−0.275220	+	0.476695i	−0.970191	−	0.242343i	$-0.922084\pi$
$43$	−1.80474	+	3.12590i	−0.275220	+	0.476695i	0.694971	+	0.719038i	$0.255417\pi$
$44$		0			0
$45$	−1.82030	−	4.71825i	−0.271355	−	0.703355i
$46$		0			0
$47$	−4.38482	−	7.59474i	−0.639592	−	1.10781i	−0.985522	−	0.169546i	$-0.945770\pi$
$47$	−4.38482	−	7.59474i	−0.639592	−	1.10781i	0.345930	−	0.938260i	$-0.387563\pi$
$48$		0			0
$49$	−6.99888	−	0.125065i	−0.999840	−	0.0178664i
$50$		0			0
$51$	0.0541101	−	0.695026i	0.00757693	−	0.0973231i
$52$		0			0
$53$	−4.94628	+	2.85574i	−0.679424	+	0.392266i	−0.799638	−	0.600482i	$-0.794975\pi$
$53$	−4.94628	+	2.85574i	−0.679424	+	0.392266i	0.120214	+	0.992748i	$0.461642\pi$
$54$		0			0
$55$			6.58345i			0.887712i
$56$		0			0
$57$	−0.125601	−	0.262757i	−0.0166362	−	0.0348030i
$58$		0			0
$59$	−2.25163	+	3.89994i	−0.293138	+	0.507729i	−0.974550	−	0.224171i	$-0.928033\pi$
$59$	−2.25163	+	3.89994i	−0.293138	+	0.507729i	0.681412	+	0.731900i	$0.261366\pi$
$60$		0			0
$61$	4.43678	−	2.56157i	0.568071	−	0.327976i	−0.188308	−	0.982110i	$-0.560300\pi$
$61$	4.43678	−	2.56157i	0.568071	−	0.327976i	0.756379	+	0.654134i	$0.226967\pi$
$62$		0			0
$63$	7.43049	−	2.79068i	0.936153	−	0.351593i
$64$		0			0
$65$	−8.83986	+	5.10369i	−1.09645	+	0.633035i
$66$		0			0
$67$	−2.95521	+	5.11857i	−0.361036	+	0.625332i	−0.988132	−	0.153610i	$-0.950910\pi$
$67$	−2.95521	+	5.11857i	−0.361036	+	0.625332i	0.627096	+	0.778942i	$0.284243\pi$
$68$		0			0
$69$	8.70486	−	12.6886i	1.04794	−	1.52752i
$70$		0			0
$71$			11.4308i			1.35658i	0.734792	+	0.678292i	$0.237280\pi$
$71$			11.4308i			1.35658i	−0.734792	+	0.678292i	$0.762720\pi$
$72$		0			0
$73$	−6.05559	+	3.49620i	−0.708753	+	0.409199i	−0.810599	−	0.585601i	$-0.800858\pi$
$73$	−6.05559	+	3.49620i	−0.708753	+	0.409199i	0.101846	+	0.994800i	$0.467525\pi$
$74$		0			0
$75$	3.08259	+	2.11478i	0.355947	+	0.244194i
$76$		0			0
$77$	−10.3323	−	0.0923076i	−1.17747	−	0.0105194i
$78$		0			0
$79$	0.603968	+	1.04610i	0.0679517	+	0.117696i	0.898000	−	0.439996i	$-0.145020\pi$
$79$	0.603968	+	1.04610i	0.0679517	+	0.117696i	−0.830048	+	0.557692i	$0.811687\pi$
$80$		0			0
$81$	−6.66796	+	6.04470i	−0.740884	+	0.671633i
$82$		0			0
$83$	0.181350	−	0.314108i	0.0199058	−	0.0344779i	−0.855901	−	0.517140i	$-0.826997\pi$
$83$	0.181350	−	0.314108i	0.0199058	−	0.0344779i	0.875807	+	0.482662i	$0.160330\pi$
$84$		0			0
$85$	−0.339244	−	0.587588i	−0.0367962	−	0.0637329i
$86$		0			0
$87$	5.30793	+	11.1042i	0.569069	+	1.19049i
$88$		0			0
$89$	1.38526	−	2.39934i	0.146837	−	0.254329i	−0.783220	−	0.621745i	$-0.786424\pi$
$89$	1.38526	−	2.39934i	0.146837	−	0.254329i	0.930057	+	0.367416i	$0.119757\pi$
$90$		0			0
$91$	−7.88594	−	13.9451i	−0.826671	−	1.46184i
$92$		0			0
$93$	4.69679	+	9.82569i	0.487034	+	1.01888i
$94$		0			0
$95$	−0.245471	−	0.141723i	−0.0251848	−	0.0145405i
$96$		0			0
$97$	0.508914	+	0.293821i	0.0516723	+	0.0298330i	0.525614	−	0.850723i	$-0.323836\pi$
$97$	0.508914	+	0.293821i	0.0516723	+	0.0298330i	−0.473941	+	0.880556i	$0.657169\pi$
$98$		0			0
$99$	10.9309	−	4.21713i	1.09859	−	0.423837i
$100$		0			0
$101$	13.8466			1.37779			0.688893	−	0.724863i	$-0.258097\pi$
$101$	13.8466			1.37779			0.688893	+	0.724863i	$0.258097\pi$
$102$		0			0
$103$		−	12.0793i		−	1.19021i	−0.803647	−	0.595106i	$-0.797110\pi$
$103$		−	12.0793i		−	1.19021i	0.803647	−	0.595106i	$-0.202890\pi$
$104$		0			0
$105$	4.42686	−	6.33078i	0.432018	−	0.617821i
$106$		0			0
$107$	−15.9299	−	9.19711i	−1.54000	−	0.889118i	−0.998838	−	0.0481978i	$-0.984652\pi$
$107$	−15.9299	−	9.19711i	−1.54000	−	0.889118i	−0.541159	−	0.840920i	$-0.682014\pi$
$108$		0			0
$109$	−5.51036	−	9.54422i	−0.527796	−	0.914170i	−0.999475	−	0.0323997i	$-0.989685\pi$
$109$	−5.51036	−	9.54422i	−0.527796	−	0.914170i	0.471679	−	0.881771i	$-0.343648\pi$
$110$		0			0
$111$	−9.79051	+	4.67997i	−0.929274	+	0.444203i
$112$		0			0
$113$	−7.36811	+	4.25398i	−0.693133	+	0.400181i	−0.804785	−	0.593567i	$-0.797719\pi$
$113$	−7.36811	+	4.25398i	−0.693133	+	0.400181i	0.111652	+	0.993747i	$0.464386\pi$
$114$		0			0
$115$		−	14.9760i		−	1.39652i
$116$		0			0
$117$	14.1365	+	11.4081i	1.30692	+	1.05468i
$118$		0			0
$119$	0.926935	−	0.524181i	0.0849720	−	0.0480516i
$120$		0			0
$121$	−4.25200			−0.386545
$122$		0			0
$123$	−0.442862	+	5.68841i	−0.0399315	+	0.512906i
$124$		0			0
$125$	12.0670			1.07930
$126$		0			0
$127$	10.6312			0.943365			0.471682	−	0.881769i	$-0.343647\pi$
$127$	10.6312			0.943365			0.471682	+	0.881769i	$0.343647\pi$
$128$		0			0
$129$	5.64050	−	2.69622i	0.496619	−	0.237389i
$130$		0			0
$131$	−6.33480			−0.553474			−0.276737	−	0.960946i	$-0.589253\pi$
$131$	−6.33480			−0.553474			−0.276737	+	0.960946i	$0.589253\pi$
$132$		0			0
$133$	0.225866	−	0.383263i	0.0195851	−	0.0332331i
$134$		0			0
$135$	−2.02328	+	8.52247i	−0.174136	+	0.733498i
$136$		0			0
$137$			16.6459i			1.42216i	0.703113	+	0.711078i	$0.251793\pi$
$137$			16.6459i			1.42216i	−0.703113	+	0.711078i	$0.748207\pi$
$138$		0			0
$139$	4.24007	−	2.44800i	0.359638	−	0.207637i	−0.309284	−	0.950970i	$-0.600089\pi$
$139$	4.24007	−	2.44800i	0.359638	−	0.207637i	0.668922	+	0.743333i	$0.266756\pi$
$140$		0			0
$141$	−1.17898	+	15.1437i	−0.0992884	+	1.27533i
$142$		0			0
$143$	−11.8238	−	20.4795i	−0.988758	−	1.71258i
$144$		0			0
$145$	10.3737	+	5.98926i	0.861489	+	0.497381i
$146$		0			0
$147$	9.87365	+	7.03641i	0.814365	+	0.580354i
$148$		0			0
$149$			5.28696i			0.433125i	0.976269	+	0.216562i	$0.0694845\pi$
$149$			5.28696i			0.433125i	−0.976269	+	0.216562i	$0.930516\pi$
$150$		0			0
$151$	14.5833			1.18677			0.593385	−	0.804919i	$-0.297791\pi$
$151$	14.5833			1.18677			0.593385	+	0.804919i	$0.297791\pi$
$152$		0			0
$153$	−0.758298	+	0.939655i	−0.0613047	+	0.0759666i
$154$		0			0
$155$	9.17930	+	5.29967i	0.737299	+	0.425680i
$156$		0			0
$157$	−15.4160	−	8.90044i	−1.23033	−	0.710332i	−0.263232	−	0.964732i	$-0.584789\pi$
$157$	−15.4160	−	8.90044i	−1.23033	−	0.710332i	−0.967099	+	0.254400i	$0.918122\pi$
$158$		0			0
$159$	9.86272	+	0.767846i	0.782165	+	0.0608942i
$160$		0			0
$161$	23.5038	+	0.209981i	1.85236	+	0.0165488i
$162$		0			0
$163$	−0.0482228	+	0.0835243i	−0.00377710	+	0.00654213i	−0.867908	−	0.496725i	$-0.834536\pi$
$163$	−0.0482228	+	0.0835243i	−0.00377710	+	0.00654213i	0.864131	+	0.503267i	$0.167869\pi$
$164$		0			0
$165$	6.45073	−	9.40284i	0.502188	−	0.732010i
$166$		0			0
$167$	2.47872	+	4.29327i	0.191809	+	0.332224i	0.945850	−	0.324604i	$-0.105231\pi$
$167$	2.47872	+	4.29327i	0.191809	+	0.332224i	−0.754041	+	0.656828i	$0.771898\pi$
$168$		0			0
$169$	11.8324	−	20.4943i	0.910185	−	1.57649i
$170$		0			0
$171$	−0.0780701	+	0.498353i	−0.00597017	+	0.0381100i
$172$		0			0
$173$	−7.40033	−	12.8177i	−0.562637	−	0.974515i	−0.997265	−	0.0739055i	$-0.976454\pi$
$173$	−7.40033	−	12.8177i	−0.562637	−	0.974515i	0.434629	−	0.900610i	$-0.356880\pi$
$174$		0			0
$175$	−0.0510133	+	5.71007i	−0.00385625	+	0.431641i
$176$		0			0
$177$	7.03723	−	3.36387i	0.528950	−	0.252844i
$178$		0			0
$179$	−0.592751	+	0.342225i	−0.0443043	+	0.0255791i	−0.521989	−	0.852952i	$-0.674810\pi$
$179$	−0.592751	+	0.342225i	−0.0443043	+	0.0255791i	0.477684	+	0.878532i	$0.341476\pi$
$180$		0			0
$181$			7.84745i			0.583297i	0.956526	+	0.291648i	$0.0942037\pi$
$181$			7.84745i			0.583297i	−0.956526	+	0.291648i	$0.905796\pi$
$182$		0			0
$183$	−8.84678	−	0.688752i	−0.653973	−	0.0509140i
$184$		0			0
$185$	−5.28070	+	9.14644i	−0.388245	+	0.672459i
$186$		0			0
$187$	1.36128	−	0.785934i	0.0995464	−	0.0574732i
$188$		0			0
$189$	−13.3470	−	3.29489i	−0.970855	−	0.239668i
$190$		0			0
$191$	16.9694	−	9.79729i	1.22786	−	0.708907i	0.261281	−	0.965263i	$-0.415855\pi$
$191$	16.9694	−	9.79729i	1.22786	−	0.708907i	0.966582	+	0.256356i	$0.0825219\pi$
$192$		0			0
$193$	−9.18116	+	15.9022i	−0.660875	+	1.14467i	0.319512	+	0.947582i	$0.396481\pi$
$193$	−9.18116	+	15.9022i	−0.660875	+	1.14467i	−0.980386	+	0.197086i	$0.936852\pi$
$194$		0			0
$195$	17.6264	+	1.37227i	1.26225	+	0.0982705i
$196$		0			0
$197$		−	5.92313i		−	0.422006i	−0.977485	−	0.211003i	$-0.932327\pi$
$197$		−	5.92313i		−	0.422006i	0.977485	−	0.211003i	$-0.0676730\pi$
$198$		0			0
$199$	13.6268	−	7.86741i	0.965975	−	0.557706i	0.0679681	−	0.997687i	$-0.478348\pi$
$199$	13.6268	−	7.86741i	0.965975	−	0.557706i	0.898007	+	0.439982i	$0.145015\pi$
$200$		0			0
$201$	9.23617	−	4.41499i	0.651469	−	0.311409i
$202$		0			0
$203$	−9.54517	+	16.1968i	−0.669939	+	1.13679i
$204$		0			0
$205$	2.77653	+	4.80909i	0.193921	+	0.335881i
$206$		0			0
$207$	−24.8655	+	9.59312i	−1.72827	+	0.666768i
$208$		0			0
$209$	0.328332	−	0.568688i	0.0227112	−	0.0393370i
$210$		0			0
$211$	−5.06619	−	8.77489i	−0.348771	−	0.604088i	0.637261	−	0.770648i	$-0.280067\pi$
$211$	−5.06619	−	8.77489i	−0.348771	−	0.604088i	−0.986031	+	0.166560i	$0.946734\pi$
$212$		0			0
$213$	11.2003	−	16.3261i	0.767435	−	1.11864i
$214$		0			0
$215$	3.04231	−	5.26944i	0.207484	−	0.359373i
$216$		0			0
$217$	−8.44616	+	14.3320i	−0.573363	+	0.972917i
$218$		0			0
$219$	12.0746	+	0.940052i	0.815928	+	0.0635228i
$220$		0			0
$221$	2.11061	+	1.21856i	0.141975	+	0.0819693i
$222$		0			0
$223$	13.3944	+	7.73325i	0.896955	+	0.517857i	0.876211	−	0.481928i	$-0.160063\pi$
$223$	13.3944	+	7.73325i	0.896955	+	0.517857i	0.0207437	+	0.999785i	$0.493397\pi$
$224$		0			0
$225$	−2.33058	−	6.04089i	−0.155372	−	0.402726i
$226$		0			0
$227$	−28.0719			−1.86320			−0.931600	−	0.363486i	$-0.881586\pi$
$227$	−28.0719			−1.86320			−0.931600	+	0.363486i	$0.881586\pi$
$228$		0			0
$229$		−	17.0264i		−	1.12514i	−0.826751	−	0.562568i	$-0.809814\pi$
$229$		−	17.0264i		−	1.12514i	0.826751	−	0.562568i	$-0.190186\pi$
$230$		0			0
$231$	14.6666	+	10.2558i	0.964995	+	0.674782i
$232$		0			0
$233$	−16.0015	−	9.23847i	−1.04829	−	0.605233i	−0.126122	−	0.992015i	$-0.540253\pi$
$233$	−16.0015	−	9.23847i	−1.04829	−	0.605233i	−0.922171	+	0.386782i	$0.873587\pi$
$234$		0			0
$235$	7.39166	+	12.8027i	0.482179	+	0.835158i
$236$		0			0
$237$	0.162394	−	2.08590i	0.0105486	−	0.135493i
$238$		0			0
$239$	6.06656	−	3.50253i	0.392413	−	0.226560i	−0.290792	−	0.956786i	$-0.593919\pi$
$239$	6.06656	−	3.50253i	0.392413	−	0.226560i	0.683205	+	0.730226i	$0.260585\pi$
$240$		0			0
$241$		−	6.21759i		−	0.400510i	−0.979744	−	0.200255i	$-0.935823\pi$
$241$		−	6.21759i		−	0.400510i	0.979744	−	0.200255i	$-0.0641771\pi$
$242$		0			0
$243$	15.4464	−	2.09984i	0.990886	−	0.134705i
$244$		0			0
$245$	11.7983	+	0.210827i	0.753764	+	0.0134692i
$246$		0			0
$247$	1.01813			0.0647823
$248$		0			0
$249$	−0.566791	+	0.270932i	−0.0359189	+	0.0171696i
$250$		0			0
$251$	9.81844			0.619734			0.309867	−	0.950780i	$-0.399715\pi$
$251$	9.81844			0.619734			0.309867	+	0.950780i	$0.399715\pi$
$252$		0			0
$253$	34.6952			2.18127
$254$		0			0
$255$	−0.0912155	+	1.17163i	−0.00571213	+	0.0733704i
$256$		0			0
$257$	−1.33581			−0.0833254			−0.0416627	−	0.999132i	$-0.513265\pi$
$257$	−1.33581			−0.0833254			−0.0416627	+	0.999132i	$0.513265\pi$
$258$		0			0
$259$	−14.2806	−	8.41593i	−0.887356	−	0.522940i
$260$		0			0
$261$	3.29927	−	21.0605i	0.204219	−	1.30361i
$262$		0			0
$263$		−	20.3502i		−	1.25485i	−0.778678	−	0.627424i	$-0.784109\pi$
$263$		−	20.3502i		−	1.25485i	0.778678	−	0.627424i	$-0.215891\pi$
$264$		0			0
$265$	8.33814	−	4.81402i	0.512208	−	0.295723i
$266$		0			0
$267$	−4.32947	+	2.06954i	−0.264959	+	0.126654i
$268$		0			0
$269$	−13.3614	−	23.1426i	−0.814659	−	1.41103i	−0.909572	−	0.415546i	$-0.863591\pi$
$269$	−13.3614	−	23.1426i	−0.814659	−	1.41103i	0.0949131	−	0.995486i	$-0.469743\pi$
$270$		0			0
$271$	−3.76517	−	2.17382i	−0.228718	−	0.132050i	0.381263	−	0.924467i	$-0.375489\pi$
$271$	−3.76517	−	2.17382i	−0.228718	−	0.132050i	−0.609980	+	0.792417i	$0.708823\pi$
$272$		0			0
$273$	−2.40083	+	27.6441i	−0.145305	+	1.67310i
$274$		0			0
$275$			8.42894i			0.508284i
$276$		0			0
$277$	−4.39803			−0.264252			−0.132126	−	0.991233i	$-0.542180\pi$
$277$	−4.39803			−0.264252			−0.132126	+	0.991233i	$0.542180\pi$
$278$		0			0
$279$	2.91940	−	18.6357i	0.174780	−	1.11569i
$280$		0			0
$281$	4.62273	+	2.66893i	0.275769	+	0.159215i	0.631506	−	0.775371i	$-0.282437\pi$
$281$	4.62273	+	2.66893i	0.275769	+	0.159215i	−0.355738	+	0.934586i	$0.615770\pi$
$282$		0			0
$283$	15.5431	+	8.97381i	0.923941	+	0.533437i	0.884890	−	0.465800i	$-0.154233\pi$
$283$	15.5431	+	8.97381i	0.923941	+	0.533437i	0.0390505	+	0.999237i	$0.487567\pi$
$284$		0			0
$285$	0.211730	+	0.442939i	0.0125418	+	0.0262375i
$286$		0			0
$287$	−7.58645	+	4.29014i	−0.447814	+	0.253239i
$288$		0			0
$289$	8.41900	−	14.5821i	0.495235	−	0.857773i
$290$		0			0
$291$	−0.438960	−	0.918306i	−0.0257323	−	0.0538320i
$292$		0			0
$293$	13.1126	+	22.7117i	0.766048	+	1.32683i	0.939691	+	0.342026i	$0.111113\pi$
$293$	13.1126	+	22.7117i	0.766048	+	1.32683i	−0.173642	+	0.984809i	$0.555554\pi$
$294$		0			0
$295$	3.79566	−	6.57428i	0.220992	−	0.382769i
$296$		0			0
$297$	−19.7442	−	4.68737i	−1.14567	−	0.271989i
$298$		0			0
$299$	26.8968	+	46.5867i	1.55548	+	2.69418i
$300$		0			0
$301$	8.22735	+	4.84858i	0.474217	+	0.279467i
$302$		0			0
$303$	−19.7764	−	13.5674i	−1.13613	−	0.779429i
$304$		0			0
$305$	−7.47924	+	4.31814i	−0.428260	+	0.247256i
$306$		0			0
$307$		−	7.19520i		−	0.410652i	−0.978694	−	0.205326i	$-0.934175\pi$
$307$		−	7.19520i		−	0.410652i	0.978694	−	0.205326i	$-0.0658254\pi$
$308$		0			0
$309$	−11.8358	+	17.2524i	−0.673317	+	0.981454i
$310$		0			0
$311$	−1.08721	+	1.88311i	−0.0616503	+	0.106781i	−0.895203	−	0.445658i	$-0.852970\pi$
$311$	−1.08721	+	1.88311i	−0.0616503	+	0.106781i	0.833553	+	0.552440i	$0.186303\pi$
$312$		0			0
$313$	−10.2870	+	5.93922i	−0.581457	+	0.335704i	−0.761712	−	0.647916i	$-0.775641\pi$
$313$	−10.2870	+	5.93922i	−0.581457	+	0.335704i	0.180255	+	0.983620i	$0.442308\pi$
$314$		0			0
$315$	−12.5258	+	4.70435i	−0.705752	+	0.265060i
$316$		0			0
$317$	7.09969	−	4.09901i	0.398758	−	0.230223i	−0.287190	−	0.957874i	$-0.592721\pi$
$317$	7.09969	−	4.09901i	0.398758	−	0.230223i	0.685948	+	0.727651i	$0.259388\pi$
$318$		0			0
$319$	−13.8754	+	24.0329i	−0.776875	+	1.34559i
$320$		0			0
$321$	13.7402	+	28.7445i	0.766903	+	1.60436i
$322$		0			0
$323$			0.0676757i			0.00376558i
$324$		0			0
$325$	−11.3179	+	6.53438i	−0.627803	+	0.362462i
$326$		0			0
$327$	−1.48162	+	19.0308i	−0.0819336	+	1.05241i
$328$		0			0
$329$	−20.1966	+	11.4212i	−1.11348	+	0.629670i
$330$		0			0
$331$	8.58540	+	14.8704i	0.471897	+	0.817349i	0.999483	−	0.0321526i	$-0.0102363\pi$
$331$	8.58540	+	14.8704i	0.471897	+	0.817349i	−0.527586	+	0.849501i	$0.676903\pi$
$332$		0			0
$333$	18.5690	+	2.90895i	1.01757	+	0.159409i
$334$		0			0
$335$	4.98170	−	8.62856i	0.272179	−	0.471428i
$336$		0			0
$337$	3.95399	+	6.84850i	0.215387	+	0.373062i	0.953392	−	0.301733i	$-0.0975653\pi$
$337$	3.95399	+	6.84850i	0.215387	+	0.373062i	−0.738005	+	0.674795i	$0.764232\pi$
$338$		0			0
$339$	14.6918	+	1.14380i	0.797947	+	0.0621229i
$340$		0			0
$341$	−12.2779	+	21.2659i	−0.664883	+	1.15161i
$342$		0			0
$343$	−0.496303	+	18.5136i	−0.0267979	+	0.999641i
$344$		0			0
$345$	−14.6741	+	21.3896i	−0.790027	+	1.15158i
$346$		0			0
$347$	0.443850	+	0.256257i	0.0238271	+	0.0137566i	0.511866	−	0.859065i	$-0.328954\pi$
$347$	0.443850	+	0.256257i	0.0238271	+	0.0137566i	−0.488039	+	0.872822i	$0.662288\pi$
$348$		0			0
$349$	−5.74612	−	3.31752i	−0.307583	−	0.177583i	0.338262	−	0.941052i	$-0.390161\pi$
$349$	−5.74612	−	3.31752i	−0.307583	−	0.177583i	−0.645844	+	0.763469i	$0.723494\pi$
$350$		0			0
$351$	−9.01239	−	30.1451i	−0.481046	−	1.60903i
$352$		0			0
$353$	18.0687			0.961702			0.480851	−	0.876802i	$-0.340328\pi$
$353$	18.0687			0.961702			0.480851	+	0.876802i	$0.340328\pi$
$354$		0			0
$355$		−	19.2693i		−	1.02271i
$356$		0			0
$357$	−1.83751	−	0.159584i	−0.0972515	−	0.00844607i
$358$		0			0
$359$	1.52677	+	0.881479i	0.0805796	+	0.0465227i	0.539748	−	0.841826i	$-0.318519\pi$
$359$	1.52677	+	0.881479i	0.0805796	+	0.0465227i	−0.459169	+	0.888349i	$0.651853\pi$
$360$		0			0
$361$	−9.48586	−	16.4300i	−0.499256	−	0.864737i
$362$		0			0
$363$	6.07294	+	4.16628i	0.318747	+	0.218673i
$364$		0			0
$365$	10.2081	−	5.89367i	0.534318	−	0.308489i
$366$		0			0
$367$		−	33.4417i		−	1.74564i	−0.488038	−	0.872822i	$-0.662287\pi$
$367$		−	33.4417i		−	1.74564i	0.488038	−	0.872822i	$-0.337713\pi$
$368$		0			0
$369$	6.20625	−	7.69056i	0.323085	−	0.400355i
$370$		0			0
$371$	7.43836	+	13.1536i	0.386180	+	0.682902i
$372$		0			0
$373$	25.5688			1.32390			0.661952	−	0.749546i	$-0.269728\pi$
$373$	25.5688			1.32390			0.661952	+	0.749546i	$0.269728\pi$
$374$		0			0
$375$	−17.2347	−	11.8237i	−0.889999	−	0.610575i
$376$		0			0
$377$	−43.0267			−2.21599
$378$		0			0
$379$	−25.7920			−1.32485			−0.662423	−	0.749130i	$-0.730472\pi$
$379$	−25.7920			−1.32485			−0.662423	+	0.749130i	$0.730472\pi$
$380$		0			0
$381$	−15.1840	−	10.4169i	−0.777902	−	0.533672i
$382$		0			0
$383$	−32.8316			−1.67762			−0.838808	−	0.544427i	$-0.816747\pi$
$383$	−32.8316			−1.67762			−0.838808	+	0.544427i	$0.816747\pi$
$384$		0			0
$385$	17.4175	+	0.155606i	0.887676	+	0.00793044i
$386$		0			0
$387$	−10.6979	−	1.67590i	−0.543807	−	0.0851908i
$388$		0			0
$389$		−	20.1544i		−	1.02187i	−0.859619	−	0.510935i	$-0.829299\pi$
$389$		−	20.1544i		−	1.02187i	0.859619	−	0.510935i	$-0.170701\pi$
$390$		0			0
$391$	−3.09663	+	1.78784i	−0.156603	+	0.0904150i
$392$		0			0
$393$	9.04771	+	6.20709i	0.456396	+	0.313106i
$394$		0			0
$395$	−1.01813	−	1.76346i	−0.0512278	−	0.0887291i
$396$		0			0
$397$	−30.2125	−	17.4432i	−1.51632	−	0.875449i	−0.999816	−	0.0191652i	$-0.993899\pi$
$397$	−30.2125	−	17.4432i	−1.51632	−	0.875449i	−0.516506	−	0.856284i	$-0.672768\pi$
$398$		0			0
$399$	−0.698131	+	0.326085i	−0.0349503	+	0.0163246i
$400$		0			0
$401$		−	9.66245i		−	0.482520i	−0.970461	−	0.241260i	$-0.922439\pi$
$401$		−	9.66245i		−	0.482520i	0.970461	−	0.241260i	$-0.0775606\pi$
$402$		0			0
$403$	−38.0727			−1.89654
$404$		0			0
$405$	11.2404	−	10.1898i	0.558541	−	0.506334i
$406$		0			0
$407$	−21.1897	−	12.2339i	−1.05034	−	0.606412i
$408$		0			0
$409$	32.1202	+	18.5446i	1.58824	+	0.916973i	0.993597	+	0.112986i	$0.0360416\pi$
$409$	32.1202	+	18.5446i	1.58824	+	0.916973i	0.594647	+	0.803987i	$0.297292\pi$
$410$		0			0
$411$	16.3103	−	23.7746i	0.804530	−	1.17271i
$412$		0			0
$413$	10.2646	+	6.04920i	0.505090	+	0.297662i
$414$		0			0
$415$	−0.305709	+	0.529504i	−0.0150067	+	0.0259923i
$416$		0			0
$417$	−8.45455	−	0.658216i	−0.414021	−	0.0322330i
$418$		0			0
$419$	1.84193	+	3.19031i	0.0899841	+	0.155857i	0.907504	−	0.420043i	$-0.137985\pi$
$419$	1.84193	+	3.19031i	0.0899841	+	0.155857i	−0.817520	+	0.575900i	$0.804652\pi$
$420$		0			0
$421$	−8.55139	+	14.8114i	−0.416769	+	0.721866i	−0.995612	−	0.0935732i	$-0.970171\pi$
$421$	−8.55139	+	14.8114i	−0.416769	+	0.721866i	0.578843	+	0.815439i	$0.303504\pi$
$422$		0			0
$423$	16.5223	−	20.4738i	0.803339	−	0.995469i
$424$		0			0
$425$	−0.434342	−	0.752303i	−0.0210687	−	0.0364921i
$426$		0			0
$427$	−6.67215	−	11.7987i	−0.322888	−	0.570978i
$428$		0			0
$429$	−3.17917	+	40.8354i	−0.153492	+	1.97155i
$430$		0			0
$431$	27.3242	−	15.7756i	1.31616	−	0.759885i	0.333051	−	0.942909i	$-0.391922\pi$
$431$	27.3242	−	15.7756i	1.31616	−	0.759885i	0.983108	+	0.183024i	$0.0585887\pi$
$432$		0			0
$433$			10.0692i			0.483893i	0.970290	+	0.241947i	$0.0777859\pi$
$433$			10.0692i			0.483893i	−0.970290	+	0.241947i	$0.922214\pi$
$434$		0			0
$435$	−8.94777	−	18.7188i	−0.429013	−	0.897496i
$436$		0			0
$437$	−0.746890	+	1.29365i	−0.0357286	+	0.0618837i
$438$		0			0
$439$	−24.1966	+	13.9699i	−1.15484	+	0.666748i	−0.950062	−	0.312060i	$-0.898981\pi$
$439$	−24.1966	+	13.9699i	−1.15484	+	0.666748i	−0.204779	+	0.978808i	$0.565648\pi$
$440$		0			0
$441$	−7.20752	−	19.7244i	−0.343215	−	0.939257i
$442$		0			0
$443$	30.1930	−	17.4319i	1.43451	−	0.828215i	0.437050	−	0.899437i	$-0.356023\pi$
$443$	30.1930	−	17.4319i	1.43451	−	0.828215i	0.997460	+	0.0712223i	$0.0226900\pi$
$444$		0			0
$445$	−2.33518	+	4.04466i	−0.110698	+	0.191735i
$446$		0			0
$447$	5.18038	−	7.55113i	0.245023	−	0.357156i
$448$		0			0
$449$		−	23.2411i		−	1.09682i	−0.836211	−	0.548408i	$-0.815234\pi$
$449$		−	23.2411i		−	1.09682i	0.836211	−	0.548408i	$-0.184766\pi$
$450$		0			0
$451$	−11.1413	+	6.43244i	−0.524624	+	0.302892i
$452$		0			0
$453$	−20.8286	−	14.2893i	−0.978614	−	0.671369i
$454$		0			0
$455$	13.2936	+	23.5078i	0.623215	+	1.10206i
$456$		0			0
$457$	3.10938	+	5.38560i	0.145451	+	0.251928i	0.929541	−	0.368719i	$-0.120203\pi$
$457$	3.10938	+	5.38560i	0.145451	+	0.251928i	−0.784090	+	0.620647i	$0.786870\pi$
$458$		0			0
$459$	2.00375	−	0.599056i	0.0935272	−	0.0279616i
$460$		0			0
$461$	2.17165	−	3.76140i	0.101144	−	0.175186i	−0.811012	−	0.585029i	$-0.801083\pi$
$461$	2.17165	−	3.76140i	0.101144	−	0.175186i	0.912156	+	0.409843i	$0.134416\pi$
$462$		0			0
$463$	−3.57451	−	6.19124i	−0.166122	−	0.287731i	0.770931	−	0.636918i	$-0.219791\pi$
$463$	−3.57451	−	6.19124i	−0.166122	−	0.287731i	−0.937053	+	0.349187i	$0.886458\pi$
$464$		0			0
$465$	−7.91755	−	16.5635i	−0.367168	−	0.768115i
$466$		0			0
$467$	0.944451	−	1.63584i	0.0437040	−	0.0756975i	−0.843346	−	0.537371i	$-0.819417\pi$
$467$	0.944451	−	1.63584i	0.0437040	−	0.0756975i	0.887050	+	0.461673i	$0.152751\pi$
$468$		0			0
$469$	13.4721	+	7.93941i	0.622082	+	0.366608i
$470$		0			0
$471$	13.2970	+	27.8173i	0.612693	+	1.28175i
$472$		0			0
$473$	12.2078	+	7.04818i	0.561316	+	0.324076i
$474$		0			0
$475$	−0.314283	−	0.181451i	−0.0144203	−	0.00832555i
$476$		0			0
$477$	−13.3341	−	10.7606i	−0.610527	−	0.492693i
$478$		0			0
$479$	10.4498			0.477465			0.238732	−	0.971085i	$-0.423268\pi$
$479$	10.4498			0.477465			0.238732	+	0.971085i	$0.423268\pi$
$480$		0			0
$481$		−	37.9364i		−	1.72975i
$482$		0			0
$483$	−33.3637	−	23.3299i	−1.51810	−	1.06155i
$484$		0			0
$485$	−0.857895	−	0.495306i	−0.0389550	−	0.0224907i
$486$		0			0
$487$	11.8298	+	20.4898i	0.536060	+	0.928483i	0.999111	+	0.0421513i	$0.0134212\pi$
$487$	11.8298	+	20.4898i	0.536060	+	0.928483i	−0.463052	+	0.886331i	$0.653246\pi$
$488$		0			0
$489$	0.150715	−	0.0720434i	0.00681557	−	0.00325792i
$490$		0			0
$491$	11.6767	−	6.74152i	0.526960	−	0.304241i	−0.212817	−	0.977092i	$-0.568264\pi$
$491$	11.6767	−	6.74152i	0.526960	−	0.304241i	0.739778	+	0.672851i	$0.234931\pi$
$492$		0			0
$493$		−	2.86000i		−	0.128808i
$494$		0			0
$495$	−18.4266	+	7.10897i	−0.828213	+	0.319524i
$496$		0			0
$497$	30.2418	+	0.270178i	1.35653	+	0.0121191i
$498$		0			0
$499$	12.0807			0.540807			0.270403	−	0.962747i	$-0.412843\pi$
$499$	12.0807			0.540807			0.270403	+	0.962747i	$0.412843\pi$
$500$		0			0
$501$	0.666475	−	8.56064i	0.0297759	−	0.382461i
$502$		0			0
$503$	20.5283			0.915310			0.457655	−	0.889130i	$-0.348690\pi$
$503$	20.5283			0.915310			0.457655	+	0.889130i	$0.348690\pi$
$504$		0			0
$505$	−23.3417			−1.03869
$506$		0			0
$507$	−36.9809	+	17.6773i	−1.64238	+	0.785074i
$508$		0			0
$509$	8.18085			0.362610			0.181305	−	0.983427i	$-0.441968\pi$
$509$	8.18085			0.362610			0.181305	+	0.983427i	$0.441968\pi$
$510$		0			0
$511$	9.10656	+	16.1036i	0.402851	+	0.712380i
$512$		0			0
$513$	0.599810	−	0.635279i	0.0264823	−	0.0280482i
$514$		0			0
$515$			20.3626i			0.897283i
$516$		0			0
$517$	−29.6603	+	17.1244i	−1.30446	+	0.753131i
$518$		0			0
$519$	−1.98979	+	25.5582i	−0.0873421	+	1.12188i
$520$		0			0
$521$	−13.8746	−	24.0314i	−0.607856	−	1.05284i	−0.991593	−	0.129395i	$-0.958697\pi$
$521$	−13.8746	−	24.0314i	−0.607856	−	1.05284i	0.383738	−	0.923442i	$-0.374637\pi$
$522$		0			0
$523$	−19.8843	−	11.4802i	−0.869478	−	0.501993i	−0.00230311	−	0.999997i	$-0.500733\pi$
$523$	−19.8843	−	11.4802i	−0.869478	−	0.501993i	−0.867175	+	0.498004i	$0.834066\pi$
$524$		0			0
$525$	5.66782	−	8.10545i	0.247364	−	0.353751i
$526$		0			0
$527$		−	2.53071i		−	0.110239i
$528$		0			0
$529$	−55.9246			−2.43151
$530$		0			0
$531$	−13.3470	−	2.09089i	−0.579211	−	0.0907370i
$532$		0			0
$533$	−17.2742	−	9.97325i	−0.748228	−	0.431990i
$534$		0			0
$535$	26.8536	+	15.5039i	1.16098	+	0.670292i
$536$		0			0
$537$	1.18193	+	0.0920169i	0.0510039	+	0.00397082i
$538$		0			0
$539$	−0.488426	+	27.3333i	−0.0210380	+	1.17733i
$540$		0			0
$541$	−2.60405	+	4.51035i	−0.111957	+	0.193915i	−0.916559	−	0.399899i	$-0.869045\pi$
$541$	−2.60405	+	4.51035i	−0.111957	+	0.193915i	0.804602	+	0.593814i	$0.202379\pi$
$542$		0			0
$543$	7.68925	−	11.2082i	0.329977	−	0.480988i
$544$		0			0
$545$	9.28902	+	16.0890i	0.397898	+	0.689179i
$546$		0			0
$547$	−10.6224	+	18.3985i	−0.454181	+	0.786664i	−0.998641	−	0.0521229i	$-0.983401\pi$
$547$	−10.6224	+	18.3985i	−0.454181	+	0.786664i	0.544460	+	0.838787i	$0.316735\pi$
$548$		0			0
$549$	11.9606	+	9.65215i	0.510466	+	0.411944i
$550$		0			0
$551$	−0.597397	−	1.03472i	−0.0254500	−	0.0440807i
$552$		0			0
$553$	2.78189	−	1.57316i	0.118298	−	0.0668976i
$554$		0			0
$555$	16.5042	−	7.88920i	0.700566	−	0.334878i
$556$		0			0
$557$	−11.0945	+	6.40543i	−0.470090	+	0.271407i	−0.716277	−	0.697816i	$-0.754156\pi$
$557$	−11.0945	+	6.40543i	−0.470090	+	0.271407i	0.246187	+	0.969222i	$0.420822\pi$
$558$		0			0
$559$			21.8559i			0.924406i
$560$		0			0
$561$	−2.71434	−	0.211321i	−0.114600	−	0.00892197i
$562$		0			0
$563$	18.7396	−	32.4580i	0.789781	−	1.36794i	−0.136319	−	0.990665i	$-0.543527\pi$
$563$	18.7396	−	32.4580i	0.789781	−	1.36794i	0.926101	−	0.377277i	$-0.123139\pi$
$564$		0			0
$565$	12.4207	−	7.17109i	0.522542	−	0.301690i
$566$		0			0
$567$	15.8345	+	17.7839i	0.664988	+	0.746854i
$568$		0			0
$569$	5.94906	−	3.43469i	0.249397	−	0.143990i	−0.370091	−	0.928996i	$-0.620673\pi$
$569$	5.94906	−	3.43469i	0.249397	−	0.143990i	0.619488	+	0.785006i	$0.287340\pi$
$570$		0			0
$571$	0.0847909	−	0.146862i	0.00354839	−	0.00614599i	−0.864246	−	0.503070i	$-0.832204\pi$
$571$	0.0847909	−	0.146862i	0.00354839	−	0.00614599i	0.867794	+	0.496924i	$0.165537\pi$
$572$		0			0
$573$	−33.8364	−	2.63428i	−1.41354	−	0.110049i
$574$		0			0
$575$		−	19.1741i		−	0.799617i
$576$		0			0
$577$	−5.41193	+	3.12458i	−0.225302	+	0.130078i	−0.608403	−	0.793628i	$-0.708189\pi$
$577$	−5.41193	+	3.12458i	−0.225302	+	0.130078i	0.383101	+	0.923706i	$0.374856\pi$
$578$		0			0
$579$	28.6947	−	13.7164i	1.19251	−	0.570033i
$580$		0			0
$581$	−0.826733	−	0.487213i	−0.0342987	−	0.0202130i
$582$		0			0
$583$	11.1527	+	19.3171i	0.461900	+	0.800033i
$584$		0			0
$585$	−23.8304	−	19.2310i	−0.985264	−	0.795104i
$586$		0			0
$587$	−10.7881	+	18.6855i	−0.445273	+	0.771235i	−0.998071	−	0.0620801i	$-0.980227\pi$
$587$	−10.7881	+	18.6855i	−0.445273	+	0.771235i	0.552799	+	0.833315i	$0.313560\pi$
$588$		0			0
$589$	−0.528615	−	0.915588i	−0.0217812	−	0.0377261i
$590$		0			0
$591$	−5.80373	+	8.45975i	−0.238733	+	0.347987i
$592$		0			0
$593$	4.13036	−	7.15399i	0.169613	−	0.293779i	−0.768671	−	0.639645i	$-0.779081\pi$
$593$	4.13036	−	7.15399i	0.169613	−	0.293779i	0.938284	+	0.345866i	$0.112415\pi$
$594$		0			0
$595$	−1.56257	+	0.883632i	−0.0640591	+	0.0362254i
$596$		0			0
$597$	−27.1713	−	2.11538i	−1.11205	−	0.0865766i
$598$		0			0
$599$	−30.7618	−	17.7603i	−1.25689	−	0.725667i	−0.284422	−	0.958699i	$-0.591802\pi$
$599$	−30.7618	−	17.7603i	−1.25689	−	0.725667i	−0.972469	+	0.233033i	$0.925135\pi$
$600$		0			0
$601$	35.8981	+	20.7258i	1.46432	+	0.845423i	0.999206	−	0.0398308i	$-0.0126819\pi$
$601$	35.8981	+	20.7258i	1.46432	+	0.845423i	0.465109	+	0.885254i	$0.346015\pi$
$602$		0			0
$603$	−17.5176	−	2.74424i	−0.713371	−	0.111754i
$604$		0			0
$605$	7.16776			0.291411
$606$		0			0
$607$			2.41990i			0.0982206i	0.998793	+	0.0491103i	$0.0156386\pi$
$607$			2.41990i			0.0982206i	−0.998793	+	0.0491103i	$0.984361\pi$
$608$		0			0
$609$	29.5032	−	13.7804i	1.19553	−	0.558411i
$610$		0			0
$611$	−45.9873	−	26.5508i	−1.86045	−	1.07413i
$612$		0			0
$613$	21.3228	+	36.9321i	0.861219	+	1.49168i	0.870753	+	0.491720i	$0.163632\pi$
$613$	21.3228	+	36.9321i	0.861219	+	1.49168i	−0.00953416	+	0.999955i	$0.503035\pi$
$614$		0			0
$615$	0.746549	−	9.58916i	0.0301038	−	0.386672i
$616$		0			0
$617$	13.2535	−	7.65193i	0.533567	−	0.308055i	−0.208901	−	0.977937i	$-0.566989\pi$
$617$	13.2535	−	7.65193i	0.533567	−	0.308055i	0.742468	+	0.669882i	$0.233655\pi$
$618$		0			0
$619$			27.6178i			1.11005i	0.831833	+	0.555026i	$0.187292\pi$
$619$			27.6178i			1.11005i	−0.831833	+	0.555026i	$0.812708\pi$
$620$		0			0
$621$	44.9140	+	10.6628i	1.80234	+	0.427884i
$622$		0			0
$623$	−6.31506	−	3.72162i	−0.253008	−	0.149103i
$624$		0			0
$625$	−9.55034			−0.382014
$626$		0			0
$627$	−1.02617	+	0.490519i	−0.0409811	+	0.0195894i
$628$		0			0
$629$	2.52164			0.100545
$630$		0			0
$631$	−8.28775			−0.329930			−0.164965	−	0.986299i	$-0.552751\pi$
$631$	−8.28775			−0.329930			−0.164965	+	0.986299i	$0.552751\pi$
$632$		0			0
$633$	−1.36219	+	17.4968i	−0.0541421	+	0.695437i
$634$		0			0
$635$	−17.9214			−0.711188
$636$		0			0
$637$	−37.0802	+	20.5338i	−1.46917	+	0.813579i
$638$		0			0
$639$	−31.9939	+	12.3432i	−1.26566	+	0.488291i
$640$		0			0
$641$		−	9.91088i		−	0.391456i	−0.980658	−	0.195728i	$-0.937293\pi$
$641$		−	9.91088i		−	0.391456i	0.980658	−	0.195728i	$-0.0627070\pi$
$642$		0			0
$643$	−6.83668	+	3.94716i	−0.269612	+	0.155661i	−0.628711	−	0.777639i	$-0.716417\pi$
$643$	−6.83668	+	3.94716i	−0.269612	+	0.155661i	0.359099	+	0.933299i	$0.383084\pi$
$644$		0			0
$645$	−9.50841	+	4.54512i	−0.374393	+	0.178964i
$646$		0			0
$647$	−2.15966	−	3.74063i	−0.0849049	−	0.147060i	0.820446	−	0.571724i	$-0.193725\pi$
$647$	−2.15966	−	3.74063i	−0.0849049	−	0.147060i	−0.905351	+	0.424665i	$0.860392\pi$
$648$		0			0
$649$	15.2308	+	8.79348i	0.597859	+	0.345174i
$650$		0			0
$651$	26.1063	−	12.1938i	1.02319	−	0.477912i
$652$		0			0
$653$		−	43.3997i		−	1.69836i	−0.528102	−	0.849181i	$-0.677096\pi$
$653$		−	43.3997i		−	1.69836i	0.528102	−	0.849181i	$-0.322904\pi$
$654$		0			0
$655$	10.6788			0.417256
$656$		0			0
$657$	−16.3246	−	13.1739i	−0.636882	−	0.513961i
$658$		0			0
$659$	9.34894	+	5.39761i	0.364183	+	0.210261i	0.670914	−	0.741535i	$-0.265902\pi$
$659$	9.34894	+	5.39761i	0.364183	+	0.210261i	−0.306731	+	0.951796i	$0.599235\pi$
$660$		0			0
$661$	3.39495	+	1.96008i	0.132048	+	0.0762381i	0.564569	−	0.825386i	$-0.309042\pi$
$661$	3.39495	+	1.96008i	0.132048	+	0.0762381i	−0.432521	+	0.901624i	$0.642376\pi$
$662$		0			0
$663$	−1.82049	−	3.80848i	−0.0707021	−	0.147909i
$664$		0			0
$665$	−0.380751	+	0.646081i	−0.0147649	+	0.0250539i
$666$		0			0
$667$	31.5638	−	54.6701i	1.22216	−	2.11683i
$668$		0			0
$669$	−11.5532	−	24.1694i	−0.446674	−	0.934444i
$670$		0			0
$671$	−10.0039	−	17.3273i	−0.386197	−	0.668913i
$672$		0			0
$673$	−12.3404	+	21.3742i	−0.475687	+	0.823915i	−0.999612	−	0.0278497i	$-0.991134\pi$
$673$	−12.3404	+	21.3742i	−0.475687	+	0.823915i	0.523925	+	0.851765i	$0.324467\pi$
$674$		0			0
$675$	−2.59045	+	10.9115i	−0.0997065	+	0.419985i
$676$		0			0
$677$	7.36327	+	12.7536i	0.282994	+	0.490159i	0.972121	−	0.234481i	$-0.0753392\pi$
$677$	7.36327	+	12.7536i	0.282994	+	0.490159i	−0.689127	+	0.724641i	$0.742006\pi$
$678$		0			0
$679$	0.789376	−	1.33946i	0.0302935	−	0.0514038i
$680$		0			0
$681$	40.0939	+	27.5060i	1.53640	+	1.05403i
$682$		0			0
$683$	1.60128	−	0.924499i	0.0612712	−	0.0353750i	−0.469051	−	0.883171i	$-0.655404\pi$
$683$	1.60128	−	0.924499i	0.0612712	−	0.0353750i	0.530323	+	0.847796i	$0.322071\pi$
$684$		0			0
$685$		−	28.0606i		−	1.07214i
$686$		0			0
$687$	−16.6831	+	24.3180i	−0.636502	+	0.927790i
$688$		0			0
$689$	−17.2919	+	29.9505i	−0.658769	+	1.14102i
$690$		0			0
$691$	33.7613	−	19.4921i	1.28434	−	0.741514i	0.306701	−	0.951806i	$-0.400775\pi$
$691$	33.7613	−	19.4921i	1.28434	−	0.741514i	0.977639	+	0.210292i	$0.0674415\pi$
$692$		0			0
$693$	−10.8987	−	29.0189i	−0.414006	−	1.10234i
$694$		0			0
$695$	−7.14764	+	4.12669i	−0.271126	+	0.156534i
$696$		0			0
$697$	0.662926	−	1.14822i	0.0251101	−	0.0434920i
$698$		0			0
$699$	13.8020	+	28.8738i	0.522040	+	1.09211i
$700$		0			0
$701$			25.4389i			0.960813i	0.877046	+	0.480406i	$0.159511\pi$
$701$			25.4389i			0.960813i	−0.877046	+	0.480406i	$0.840489\pi$
$702$		0			0
$703$	0.912310	−	0.526722i	0.0344084	−	0.0198657i
$704$		0			0
$705$	1.98746	−	25.5282i	0.0748520	−	0.961448i
$706$		0			0
$707$	0.327278	−	36.6331i	0.0123086	−	1.37773i
$708$		0			0
$709$	7.14517	+	12.3758i	0.268342	+	0.464783i	0.968434	−	0.249270i	$-0.0801908\pi$
$709$	7.14517	+	12.3758i	0.268342	+	0.464783i	−0.700092	+	0.714053i	$0.746857\pi$
$710$		0			0
$711$	−2.27578	+	2.82007i	−0.0853486	+	0.105761i
$712$		0			0
$713$	27.9296	−	48.3756i	1.04597	−	1.81168i
$714$		0			0
$715$	19.9319	+	34.5230i	0.745410	+	1.29109i
$716$		0			0
$717$	−12.0965	−	0.941755i	−0.451753	−	0.0351705i
$718$		0			0
$719$	16.7344	−	28.9848i	0.624088	−	1.08095i	−0.364629	−	0.931153i	$-0.618804\pi$
$719$	16.7344	−	28.9848i	0.624088	−	1.08095i	0.988716	−	0.149799i	$-0.0478626\pi$
$720$		0			0
$721$	−31.9577	−	0.285507i	−1.19017	−	0.0106329i
$722$		0			0
$723$	−6.09225	+	8.88030i	−0.226573	+	0.330262i
$724$		0			0
$725$	13.2817	+	7.66819i	0.493269	+	0.284789i
$726$		0			0
$727$	−12.1354	−	7.00636i	−0.450076	−	0.259851i	0.257786	−	0.966202i	$-0.417007\pi$
$727$	−12.1354	−	7.00636i	−0.450076	−	0.259851i	−0.707862	+	0.706350i	$0.750340\pi$
$728$		0			0
$729$	−24.1189	−	12.1359i	−0.893292	−	0.449477i
$730$		0			0
$731$	−1.45277			−0.0537326
$732$		0			0
$733$			27.3077i			1.00863i	0.863519	+	0.504316i	$0.168255\pi$
$733$			27.3077i			1.00863i	−0.863519	+	0.504316i	$0.831745\pi$
$734$		0			0
$735$	−16.6444	−	11.8615i	−0.613937	−	0.437520i
$736$		0			0
$737$	19.9899	+	11.5412i	0.736339	+	0.425126i
$738$		0			0
$739$	−26.3157	−	45.5801i	−0.968039	−	1.67669i	−0.701220	−	0.712945i	$-0.747361\pi$
$739$	−26.3157	−	45.5801i	−0.968039	−	1.67669i	−0.266819	−	0.963747i	$-0.585973\pi$
$740$		0			0
$741$	−1.45416	−	0.997609i	−0.0534197	−	0.0366481i
$742$		0			0
$743$	30.9523	−	17.8703i	1.13553	−	0.655599i	0.190211	−	0.981743i	$-0.439083\pi$
$743$	30.9523	−	17.8703i	1.13553	−	0.655599i	0.945320	+	0.326144i	$0.105750\pi$
$744$		0			0
$745$		−	8.91243i		−	0.326526i
$746$		0			0
$747$	1.07499	+	0.168404i	0.0393319	+	0.00616159i
$748$		0			0
$749$	−24.7088	+	41.9274i	−0.902840	+	1.53199i
$750$		0			0
$751$	33.1282			1.20887			0.604433	−	0.796656i	$-0.293400\pi$
$751$	33.1282			1.20887			0.604433	+	0.796656i	$0.293400\pi$
$752$		0			0
$753$	−14.0232	−	9.62051i	−0.511035	−	0.350591i
$754$		0			0
$755$	−24.5836			−0.894687
$756$		0			0
$757$	−13.6903			−0.497584			−0.248792	−	0.968557i	$-0.580034\pi$
$757$	−13.6903			−0.497584			−0.248792	+	0.968557i	$0.580034\pi$
$758$		0			0
$759$	−49.5536	−	33.9958i	−1.79868	−	1.23397i
$760$		0			0
$761$	−13.0347			−0.472509			−0.236255	−	0.971691i	$-0.575920\pi$
$761$	−13.0347			−0.472509			−0.236255	+	0.971691i	$0.575920\pi$
$762$		0			0
$763$	−25.3809	+	14.3529i	−0.918849	+	0.519609i
$764$		0			0
$765$	1.27829	−	1.58401i	0.0462167	−	0.0572701i
$766$		0			0
$767$			27.2679i			0.984588i
$768$		0			0
$769$	−18.4866	+	10.6732i	−0.666642	+	0.384886i	−0.794803	−	0.606867i	$-0.792426\pi$
$769$	−18.4866	+	10.6732i	−0.666642	+	0.384886i	0.128161	+	0.991753i	$0.459093\pi$
$770$		0			0
$771$	1.90788	+	1.30888i	0.0687104	+	0.0471381i
$772$		0			0
$773$	−5.73940	−	9.94093i	−0.206432	−	0.357550i	0.744156	−	0.668006i	$-0.232852\pi$
$773$	−5.73940	−	9.94093i	−0.206432	−	0.357550i	−0.950588	+	0.310455i	$0.899518\pi$
$774$		0			0
$775$	11.7525	+	6.78529i	0.422161	+	0.243735i
$776$		0			0
$777$	12.1501	+	26.0128i	0.435884	+	0.933206i
$778$		0			0
$779$		−	0.553889i		−	0.0198451i
$780$		0			0
$781$	44.6416			1.59740
$782$		0			0
$783$	−25.3482	+	26.8471i	−0.905870	+	0.959436i
$784$		0			0
$785$	25.9873	+	15.0038i	0.927528	+	0.535509i
$786$		0			0
$787$	−35.6808	−	20.6003i	−1.27188	−	0.734322i	−0.296541	−	0.955020i	$-0.595833\pi$
$787$	−35.6808	−	20.6003i	−1.27188	−	0.734322i	−0.975342	+	0.220698i	$0.929166\pi$
$788$		0			0
$789$	−19.9400	+	29.0653i	−0.709881	+	1.03475i
$790$		0			0
$791$	11.0804	+	19.5939i	0.393972	+	0.696681i
$792$		0			0
$793$	15.5107	−	26.8653i	0.550801	−	0.954016i
$794$		0			0
$795$	−16.6260	−	1.29439i	−0.589662	−	0.0459072i
$796$		0			0
$797$	25.0066	+	43.3127i	0.885779	+	1.53421i	0.844819	+	0.535053i	$0.179708\pi$
$797$	25.0066	+	43.3127i	0.885779	+	1.53421i	0.0409600	+	0.999161i	$0.486958\pi$
$798$		0			0
$799$	1.76484	−	3.05679i	0.0624355	−	0.108141i
$800$		0			0
$801$	8.21141	+	1.28637i	0.290136	+	0.0454516i
$802$		0			0
$803$	13.6540	+	23.6494i	0.481838	+	0.834568i
$804$		0			0
$805$	−39.6212	−	0.353973i	−1.39646	−	0.0124759i
$806$		0			0
$807$	−3.59259	+	46.1456i	−0.126465	+	1.62440i
$808$		0			0
$809$	43.8995	−	25.3454i	1.54343	−	0.891097i	0.544807	−	0.838562i	$-0.316603\pi$
$809$	43.8995	−	25.3454i	1.54343	−	0.891097i	0.998619	−	0.0525356i	$-0.0167303\pi$
$810$		0			0
$811$		−	8.96566i		−	0.314827i	−0.987533	−	0.157413i	$-0.949684\pi$
$811$		−	8.96566i		−	0.314827i	0.987533	−	0.157413i	$-0.0503155\pi$
$812$		0			0
$813$	3.24762	+	6.79403i	0.113899	+	0.238277i
$814$		0			0
$815$	0.0812910	−	0.140800i	0.00284750	−	0.00493201i
$816$		0			0
$817$	−0.525599	+	0.303455i	−0.0183884	+	0.0106165i
$818$		0			0
$819$	30.5158	−	37.1304i	1.06631	−	1.29744i
$820$		0			0
$821$	−28.2190	+	16.2922i	−0.984849	+	0.568603i	−0.903731	−	0.428102i	$-0.859183\pi$
$821$	−28.2190	+	16.2922i	−0.984849	+	0.568603i	−0.0811184	+	0.996704i	$0.525849\pi$
$822$		0			0
$823$	−10.0877	+	17.4724i	−0.351636	+	0.609051i	−0.986536	−	0.163543i	$-0.947708\pi$
$823$	−10.0877	+	17.4724i	−0.351636	+	0.609051i	0.634901	+	0.772594i	$0.281041\pi$
$824$		0			0
$825$	8.25902	−	12.0387i	0.287542	−	0.419133i
$826$		0			0
$827$		−	0.253288i		−	0.00880770i	−0.999990	−	0.00440385i	$-0.998598\pi$
$827$		−	0.253288i		−	0.00880770i	0.999990	−	0.00440385i	$-0.00140179\pi$
$828$		0			0
$829$	−6.10909	+	3.52708i	−0.212177	+	0.122501i	−0.602323	−	0.798253i	$-0.705758\pi$
$829$	−6.10909	+	3.52708i	−0.212177	+	0.122501i	0.390146	+	0.920753i	$0.372425\pi$
$830$		0			0
$831$	6.28151	+	4.30937i	0.217903	+	0.149490i
$832$		0			0
$833$	−1.36489	−	2.46473i	−0.0472906	−	0.0853979i
$834$		0			0
$835$	−4.17848	−	7.23733i	−0.144602	−	0.250458i
$836$		0			0
$837$	−22.4297	+	23.7560i	−0.775282	+	0.821127i
$838$		0			0
$839$	17.0936	−	29.6069i	0.590136	−	1.02215i	−0.404078	−	0.914725i	$-0.632408\pi$
$839$	17.0936	−	29.6069i	0.590136	−	1.02215i	0.994214	−	0.107420i	$-0.0342591\pi$
$840$		0			0
$841$	10.7462	+	18.6130i	0.370558	+	0.641826i
$842$		0			0
$843$	−3.98731	−	8.34145i	−0.137330	−	0.287295i
$844$		0			0
$845$	−19.9463	+	34.5480i	−0.686174	+	1.18849i
$846$		0			0
$847$	−0.100500	+	11.2493i	−0.00345323	+	0.386530i
$848$		0			0
$849$	−13.4066	−	28.0466i	−0.460113	−	0.962558i
$850$		0			0
$851$	48.2024	+	27.8296i	1.65236	+	0.953988i
$852$		0			0
$853$	−21.7586	−	12.5623i	−0.745000	−	0.430126i	0.0788844	−	0.996884i	$-0.474864\pi$
$853$	−21.7586	−	12.5623i	−0.745000	−	0.430126i	−0.823884	+	0.566758i	$0.808198\pi$
$854$		0			0
$855$	0.131606	−	0.840092i	0.00450082	−	0.0287305i
$856$		0			0
$857$	42.1907			1.44121			0.720604	−	0.693347i	$-0.243865\pi$
$857$	42.1907			1.44121			0.720604	+	0.693347i	$0.243865\pi$
$858$		0			0
$859$		−	4.71278i		−	0.160798i	−0.996763	−	0.0803990i	$-0.974381\pi$
$859$		−	4.71278i		−	0.160798i	0.996763	−	0.0803990i	$-0.0256195\pi$
$860$		0			0
$861$	15.0390	+	1.30611i	0.512529	+	0.0445120i
$862$		0			0
$863$	−30.8409	−	17.8060i	−1.04984	−	0.606123i	−0.127232	−	0.991873i	$-0.540609\pi$
$863$	−30.8409	−	17.8060i	−1.04984	−	0.606123i	−0.922603	+	0.385750i	$0.873943\pi$
$864$		0			0
$865$	12.4750	+	21.6074i	0.424163	+	0.734672i
$866$		0			0
$867$	−26.3127	+	12.5777i	−0.893625	+	0.427162i
$868$		0			0
$869$	4.08543	−	2.35873i	0.138589	−	0.0800143i
$870$		0			0
$871$			35.7884i			1.21264i
$872$		0			0
$873$	−0.272846	+	1.74169i	−0.00923444	+	0.0589471i
$874$		0			0
$875$	0.285216	−	31.9250i	0.00964205	−	1.07926i
$876$		0			0
$877$	40.9064			1.38131			0.690655	−	0.723184i	$-0.257322\pi$
$877$	40.9064			1.38131			0.690655	+	0.723184i	$0.257322\pi$
$878$		0			0
$879$	3.52570	−	45.2865i	0.118919	−	1.52747i
$880$		0			0
$881$	37.4443			1.26153			0.630765	−	0.775974i	$-0.282741\pi$
$881$	37.4443			1.26153			0.630765	+	0.775974i	$0.282741\pi$
$882$		0			0
$883$	49.8357			1.67711			0.838553	−	0.544821i	$-0.183402\pi$
$883$	49.8357			1.67711			0.838553	+	0.544821i	$0.183402\pi$
$884$		0			0
$885$	−11.8629	+	5.67060i	−0.398768	+	0.190615i
$886$		0			0
$887$	−28.8965			−0.970248			−0.485124	−	0.874445i	$-0.661226\pi$
$887$	−28.8965			−0.970248			−0.485124	+	0.874445i	$0.661226\pi$
$888$		0			0
$889$	0.251279	−	28.1263i	0.00842761	−	0.943327i
$890$		0			0
$891$	23.6068	+	26.0409i	0.790859	+	0.872403i
$892$		0			0
$893$		−	1.47456i		−	0.0493443i
$894$		0			0
$895$	0.999223	−	0.576902i	0.0334003	−	0.0192837i
$896$		0			0
$897$	7.23198	−	92.8922i	0.241469	−	3.10158i
$898$		0			0
$899$	22.3394	+	38.6930i	0.745062	+	1.29048i
$900$		0			0
$901$	−1.99082	−	1.14940i	−0.0663238	−	0.0382920i
$902$		0			0
$903$	−6.99993	−	14.9865i	−0.232943	−	0.498719i
$904$		0			0
$905$		−	13.2287i		−	0.439738i
$906$		0			0
$907$	14.8700			0.493749			0.246874	−	0.969048i	$-0.420597\pi$
$907$	14.8700			0.493749			0.246874	+	0.969048i	$0.420597\pi$
$908$		0			0
$909$	14.9519	+	38.7555i	0.495923	+	1.28544i
$910$		0			0
$911$	−7.81616	−	4.51266i	−0.258961	−	0.149511i	0.364899	−	0.931047i	$-0.381103\pi$
$911$	−7.81616	−	4.51266i	−0.258961	−	0.149511i	−0.623861	+	0.781536i	$0.714437\pi$
$912$		0			0
$913$	−1.22671	−	0.708243i	−0.0405982	−	0.0234394i
$914$		0			0
$915$	14.9134	+	1.16106i	0.493020	+	0.0383833i
$916$		0			0
$917$	−0.149729	+	16.7596i	−0.00494450	+	0.553452i
$918$		0			0
$919$	−13.2083	+	22.8774i	−0.435702	+	0.754657i	−0.997353	−	0.0727170i	$-0.976833\pi$
$919$	−13.2083	+	22.8774i	−0.435702	+	0.754657i	0.561651	+	0.827374i	$0.310166\pi$
$920$		0			0
$921$	−7.05015	+	10.2766i	−0.232310	+	0.338625i
$922$		0			0
$923$	34.6075	+	59.9420i	1.13912	+	1.97302i
$924$		0			0
$925$	−6.76100	+	11.7104i	−0.222300	+	0.385036i
$926$		0			0
$927$	33.8092	−	13.0436i	1.11044	−	0.428407i
$928$		0			0
$929$	11.1259	+	19.2706i	0.365029	+	0.632249i	0.988781	−	0.149373i	$-0.0477257\pi$
$929$	11.1259	+	19.2706i	0.365029	+	0.632249i	−0.623752	+	0.781623i	$0.714392\pi$
$930$		0			0
$931$	−1.00864	−	0.606620i	−0.0330568	−	0.0198812i
$932$		0			0
$933$	3.39797	−	1.62427i	0.111244	−	0.0531761i
$934$		0			0
$935$	−2.29476	+	1.32488i	−0.0750465	+	0.0433281i
$936$		0			0
$937$		−	14.6822i		−	0.479647i	−0.970817	−	0.239823i	$-0.922910\pi$
$937$		−	14.6822i		−	0.479647i	0.970817	−	0.239823i	$-0.0770896\pi$
$938$		0			0
$939$	20.5120	+	1.59693i	0.669383	+	0.0521137i
$940$		0			0
$941$	23.0396	−	39.9058i	0.751070	−	1.30089i	−0.196235	−	0.980557i	$-0.562871\pi$
$941$	23.0396	−	39.9058i	0.751070	−	1.30089i	0.947305	−	0.320334i	$-0.103795\pi$
$942$		0			0
$943$	25.3442	−	14.6325i	0.825322	−	0.476500i
$944$		0			0
$945$	22.4996	+	5.55432i	0.731913	+	0.180682i
$946$		0			0
$947$	−6.96116	+	4.01903i	−0.226207	+	0.130601i	−0.608821	−	0.793308i	$-0.708357\pi$
$947$	−6.96116	+	4.01903i	−0.226207	+	0.130601i	0.382614	+	0.923908i	$0.375024\pi$
$948$		0			0
$949$	−21.1700	+	36.6675i	−0.687206	+	1.19028i
$950$		0			0
$951$	−14.1565	−	1.10213i	−0.459057	−	0.0357392i
$952$		0			0
$953$		−	54.9348i		−	1.77951i	−0.456437	−	0.889756i	$-0.650875\pi$
$953$		−	54.9348i		−	1.77951i	0.456437	−	0.889756i	$-0.349125\pi$
$954$		0			0
$955$	−28.6060	+	16.5157i	−0.925667	+	0.534434i
$956$		0			0
$957$	43.3661	−	20.7295i	1.40183	−	0.670089i
$958$		0			0
$959$	44.0392	+	0.393443i	1.42210	+	0.0127049i
$960$		0			0
$961$	4.26733	+	7.39124i	0.137656	+	0.238427i
$962$		0			0
$963$	8.54055	−	54.5177i	0.275215	−	1.75681i
$964$		0			0
$965$	15.4770	−	26.8070i	0.498223	−	0.862948i
$966$		0			0
$967$	26.5917	+	46.0582i	0.855132	+	1.48113i	0.876522	+	0.481361i	$0.159857\pi$
$967$	26.5917	+	46.0582i	0.855132	+	1.48113i	−0.0213900	+	0.999771i	$0.506809\pi$
$968$		0			0
$969$	0.0663114	−	0.0966582i	0.00213023	−	0.00310511i
$970$		0			0
$971$	−7.61403	+	13.1879i	−0.244346	+	0.423219i	−0.961947	−	0.273234i	$-0.911907\pi$
$971$	−7.61403	+	13.1879i	−0.244346	+	0.423219i	0.717602	+	0.696454i	$0.245240\pi$
$972$		0			0
$973$	−6.37634	−	11.2756i	−0.204416	−	0.361479i
$974$		0			0
$975$	22.5675	+	1.75695i	0.722737	+	0.0562676i
$976$		0			0
$977$	1.49418	+	0.862667i	0.0478031	+	0.0275992i	0.523711	−	0.851896i	$-0.324547\pi$
$977$	1.49418	+	0.862667i	0.0478031	+	0.0275992i	−0.475908	+	0.879495i	$0.657880\pi$
$978$		0			0
$979$	−9.37033	−	5.40997i	−0.299477	−	0.172903i
$980$		0			0
$981$	20.7633	−	25.7292i	0.662922	−	0.821469i
$982$		0			0
$983$	60.2383			1.92130			0.960651	−	0.277758i	$-0.0895912\pi$
$983$	60.2383			1.92130			0.960651	+	0.277758i	$0.0895912\pi$
$984$		0			0
$985$			9.98485i			0.318144i
$986$		0			0
$987$	40.0369	+	3.47711i	1.27439	+	0.110678i
$988$		0			0
$989$	−27.7703	−	16.0332i	−0.883044	−	0.509826i
$990$		0			0
$991$	2.87312	+	4.97639i	0.0912676	+	0.158080i	0.908045	−	0.418873i	$-0.137575\pi$
$991$	2.87312	+	4.97639i	0.0912676	+	0.158080i	−0.816777	+	0.576953i	$0.804241\pi$
$992$		0			0
$993$	2.30843	−	29.6510i	0.0732558	−	0.940946i
$994$		0			0
$995$	−22.9711	+	13.2624i	−0.728234	+	0.420446i
$996$		0			0
$997$		−	0.0259240i		−	0.000821020i	−1.00000		0.000410510i	$-0.999869\pi$
$997$		−	0.0259240i		−	0.000821020i	1.00000		0.000410510i	$-0.000130669\pi$
$998$		0			0
$999$	−23.6709	−	22.3494i	−0.748915	−	0.707102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.d.929.2		16
3.2	odd	2		3024.2.df.d.1601.6		16
4.3	odd	2		252.2.bm.a.173.7	yes	16
7.3	odd	6		1008.2.ca.d.353.5		16
9.4	even	3		3024.2.ca.d.2609.6		16
9.5	odd	6		1008.2.ca.d.257.5		16
12.11	even	2		756.2.bm.a.89.6		16
21.17	even	6		3024.2.ca.d.2033.6		16
28.3	even	6		252.2.w.a.101.4	yes	16
28.11	odd	6		1764.2.w.b.1109.5		16
28.19	even	6		1764.2.x.a.1469.8		16
28.23	odd	6		1764.2.x.b.1469.1		16
28.27	even	2		1764.2.bm.a.1685.2		16
36.7	odd	6		2268.2.t.a.2105.6		16
36.11	even	6		2268.2.t.b.2105.3		16
36.23	even	6		252.2.w.a.5.4	✓	16
36.31	odd	6		756.2.w.a.341.6		16
63.31	odd	6		3024.2.df.d.17.6		16
63.59	even	6	inner	1008.2.df.d.689.2		16
84.11	even	6		5292.2.w.b.521.3		16
84.23	even	6		5292.2.x.b.4409.3		16
84.47	odd	6		5292.2.x.a.4409.6		16
84.59	odd	6		756.2.w.a.521.6		16
84.83	odd	2		5292.2.bm.a.4625.3		16
252.23	even	6		1764.2.x.a.293.8		16
252.31	even	6		756.2.bm.a.17.6		16
252.59	odd	6		252.2.bm.a.185.7	yes	16
252.67	odd	6		5292.2.bm.a.2285.3		16
252.95	even	6		1764.2.bm.a.1697.2		16
252.103	even	6		5292.2.x.b.881.3		16
252.115	even	6		2268.2.t.b.1781.3		16
252.131	odd	6		1764.2.x.b.293.1		16
252.139	even	6		5292.2.w.b.1097.3		16
252.167	odd	6		1764.2.w.b.509.5		16
252.227	odd	6		2268.2.t.a.1781.6		16
252.247	odd	6		5292.2.x.a.881.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.4	✓	16	36.23	even	6
252.2.w.a.101.4	yes	16	28.3	even	6
252.2.bm.a.173.7	yes	16	4.3	odd	2
252.2.bm.a.185.7	yes	16	252.59	odd	6
756.2.w.a.341.6		16	36.31	odd	6
756.2.w.a.521.6		16	84.59	odd	6
756.2.bm.a.17.6		16	252.31	even	6
756.2.bm.a.89.6		16	12.11	even	2
1008.2.ca.d.257.5		16	9.5	odd	6
1008.2.ca.d.353.5		16	7.3	odd	6
1008.2.df.d.689.2		16	63.59	even	6	inner
1008.2.df.d.929.2		16	1.1	even	1	trivial
1764.2.w.b.509.5		16	252.167	odd	6
1764.2.w.b.1109.5		16	28.11	odd	6
1764.2.x.a.293.8		16	252.23	even	6
1764.2.x.a.1469.8		16	28.19	even	6
1764.2.x.b.293.1		16	252.131	odd	6
1764.2.x.b.1469.1		16	28.23	odd	6
1764.2.bm.a.1685.2		16	28.27	even	2
1764.2.bm.a.1697.2		16	252.95	even	6
2268.2.t.a.1781.6		16	252.227	odd	6
2268.2.t.a.2105.6		16	36.7	odd	6
2268.2.t.b.1781.3		16	252.115	even	6
2268.2.t.b.2105.3		16	36.11	even	6
3024.2.ca.d.2033.6		16	21.17	even	6
3024.2.ca.d.2609.6		16	9.4	even	3
3024.2.df.d.17.6		16	63.31	odd	6
3024.2.df.d.1601.6		16	3.2	odd	2
5292.2.w.b.521.3		16	84.11	even	6
5292.2.w.b.1097.3		16	252.139	even	6
5292.2.x.a.881.6		16	252.247	odd	6
5292.2.x.a.4409.6		16	84.47	odd	6
5292.2.x.b.881.3		16	252.103	even	6
5292.2.x.b.4409.3		16	84.23	even	6
5292.2.bm.a.2285.3		16	252.67	odd	6
5292.2.bm.a.4625.3		16	84.83	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42826 - 0.979841i) q^{3} -1.68574 q^{5} +(0.0236360 - 2.64565i) q^{7} +(1.07983 + 2.79892i) q^{9} -3.90538i q^{11} +(5.24391 - 3.02757i) q^{13} +(2.40766 + 1.65175i) q^{15} +(0.201244 + 0.348565i) q^{17} +(0.145617 + 0.0840718i) q^{19} +(-2.62607 + 3.75550i) q^{21} +8.88395i q^{23} -2.15829 q^{25} +(1.20023 - 5.05563i) q^{27} +(-6.15380 - 3.55290i) q^{29} +(-5.44527 - 3.14383i) q^{31} +(-3.82665 + 5.57788i) q^{33} +(-0.0398441 + 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} +(-10.4562 - 0.814049i) q^{39} +(-1.64707 - 2.85281i) q^{41} +(-1.80474 + 3.12590i) q^{43} +(-1.82030 - 4.71825i) q^{45} +(-4.38482 - 7.59474i) q^{47} +(-6.99888 - 0.125065i) q^{49} +(0.0541101 - 0.695026i) q^{51} +(-4.94628 + 2.85574i) q^{53} +6.58345i q^{55} +(-0.125601 - 0.262757i) q^{57} +(-2.25163 + 3.89994i) q^{59} +(4.43678 - 2.56157i) q^{61} +(7.43049 - 2.79068i) q^{63} +(-8.83986 + 5.10369i) q^{65} +(-2.95521 + 5.11857i) q^{67} +(8.70486 - 12.6886i) q^{69} +11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(3.08259 + 2.11478i) q^{75} +(-10.3323 - 0.0923076i) q^{77} +(0.603968 + 1.04610i) q^{79} +(-6.66796 + 6.04470i) q^{81} +(0.181350 - 0.314108i) q^{83} +(-0.339244 - 0.587588i) q^{85} +(5.30793 + 11.1042i) q^{87} +(1.38526 - 2.39934i) q^{89} +(-7.88594 - 13.9451i) q^{91} +(4.69679 + 9.82569i) q^{93} +(-0.245471 - 0.141723i) q^{95} +(0.508914 + 0.293821i) q^{97} +(10.9309 - 4.21713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

Database

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