LMFDB - Embedded newform 252.2.w.a.101.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(5,252)] 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("252.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$-0.268067 + 1.71118i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.134439 + 1.72683i) q^{3} +(-0.842869 + 1.45989i) q^{5} +(-2.27938 + 1.34329i) q^{7} +(-2.96385 - 0.464306i) q^{9} +(3.38216 - 1.95269i) q^{11} +(-5.24391 + 3.02757i) q^{13} +(-2.40766 - 1.65175i) q^{15} +(-0.201244 + 0.348565i) q^{17} +(-0.145617 + 0.0840718i) q^{19} +(-2.01319 - 4.11668i) q^{21} +(7.69373 + 4.44198i) q^{23} +(1.07914 + 1.86913i) q^{25} +(1.20023 - 5.05563i) q^{27} +(-6.15380 - 3.55290i) q^{29} +6.28766i q^{31} +(2.91726 + 6.10292i) q^{33} +(-0.0398441 - 4.45986i) q^{35} +(3.13257 + 5.42578i) q^{37} +(-4.52310 - 9.46234i) q^{39} +(1.64707 + 2.85281i) q^{41} +(1.80474 - 3.12590i) q^{43} +(3.17597 - 3.93555i) q^{45} +8.76965 q^{47} +(3.39113 - 6.12374i) q^{49} +(-0.574855 - 0.394374i) q^{51} +(4.94628 + 2.85574i) q^{53} +6.58345i q^{55} +(-0.125601 - 0.262757i) q^{57} +4.50326 q^{59} -5.12315i q^{61} +(7.37944 - 2.92299i) q^{63} -10.2074i q^{65} -5.91041 q^{67} +(-8.70486 + 12.6886i) q^{69} -11.4308i q^{71} +(-6.05559 - 3.49620i) q^{73} +(-3.37275 + 1.61221i) q^{75} +(-5.08619 + 8.99415i) q^{77} +1.20794 q^{79} +(8.56884 + 2.75227i) q^{81} +(0.181350 - 0.314108i) q^{83} +(-0.339244 - 0.587588i) q^{85} +(6.96255 - 10.1489i) q^{87} +(-1.38526 - 2.39934i) q^{89} +(7.88594 - 13.9451i) q^{91} +(-10.8577 - 0.845308i) q^{93} -0.283446i q^{95} +(-0.508914 - 0.293821i) q^{97} +(-10.9309 + 4.21713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47}+ \cdots - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−0.134439	+	1.72683i	−0.0776185	+	0.996983i
$3$	−0.134439	+	1.72683i	−0.0776185	+	0.996983i
$4$		0			0
$5$	−0.842869	+	1.45989i	−0.376942	+	0.652883i	−0.990616	−	0.136677i	$-0.956358\pi$
$5$	−0.842869	+	1.45989i	−0.376942	+	0.652883i	0.613673	+	0.789560i	$0.289691\pi$
$6$		0			0
$7$	−2.27938	+	1.34329i	−0.861524	+	0.507717i
$7$	−2.27938	+	1.34329i	−0.861524	+	0.507717i
$8$		0			0
$9$	−2.96385	−	0.464306i	−0.987951	−	0.154769i
$10$		0			0
$11$	3.38216	−	1.95269i	1.01976	−	0.588758i	0.105725	−	0.994395i	$-0.466284\pi$
$11$	3.38216	−	1.95269i	1.01976	−	0.588758i	0.914034	+	0.405637i	$0.132950\pi$
$12$		0			0
$13$	−5.24391	+	3.02757i	−1.45440	+	0.839698i	−0.998727	−	0.0504496i	$-0.983935\pi$
$13$	−5.24391	+	3.02757i	−1.45440	+	0.839698i	−0.455673	+	0.890147i	$0.650601\pi$
$14$		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	$-0.848876\pi$
$17$	−0.201244	+	0.348565i	−0.0488088	+	0.0845393i	0.840589	+	0.541674i	$0.182209\pi$
$18$		0			0
$19$	−0.145617	+	0.0840718i	−0.0334067	+	0.0192874i	−0.516610	−	0.856221i	$-0.672806\pi$
$19$	−0.145617	+	0.0840718i	−0.0334067	+	0.0192874i	0.483204	+	0.875508i	$0.339473\pi$
$20$		0			0
$21$	−2.01319	−	4.11668i	−0.439315	−	0.898333i
$22$		0			0
$23$	7.69373	+	4.44198i	1.60425	+	0.926216i	0.990623	+	0.136623i	$0.0436248\pi$
$23$	7.69373	+	4.44198i	1.60425	+	0.926216i	0.613630	+	0.789593i	$0.289709\pi$
$24$		0			0
$25$	1.07914	+	1.86913i	0.215829	+	0.373827i
$26$		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
$31$			6.28766i			1.12930i	0.825331	+	0.564649i	$0.190988\pi$
$31$			6.28766i			1.12930i	−0.825331	+	0.564649i	$0.809012\pi$
$32$		0			0
$33$	2.91726	+	6.10292i	0.507830	+	1.06238i
$34$		0			0
$35$	−0.0398441	−	4.45986i	−0.00673488	−	0.753855i
$36$		0			0
$37$	3.13257	+	5.42578i	0.514992	+	0.891992i	0.999849	+	0.0173987i	$0.00553846\pi$
$37$	3.13257	+	5.42578i	0.514992	+	0.891992i	−0.484857	+	0.874594i	$0.661128\pi$
$38$		0			0
$39$	−4.52310	−	9.46234i	−0.724276	−	1.51519i
$40$		0			0
$41$	1.64707	+	2.85281i	0.257229	+	0.445534i	0.965499	−	0.260408i	$-0.0838571\pi$
$41$	1.64707	+	2.85281i	0.257229	+	0.445534i	−0.708269	+	0.705942i	$0.750524\pi$
$42$		0			0
$43$	1.80474	−	3.12590i	0.275220	−	0.476695i	−0.694971	−	0.719038i	$-0.744583\pi$
$43$	1.80474	−	3.12590i	0.275220	−	0.476695i	0.970191	+	0.242343i	$0.0779161\pi$
$44$		0			0
$45$	3.17597	−	3.93555i	0.473446	−	0.586678i
$46$		0			0
$47$	8.76965			1.27918			0.639592	−	0.768714i	$-0.279103\pi$
$47$	8.76965			1.27918			0.639592	+	0.768714i	$0.279103\pi$
$48$		0			0
$49$	3.39113	−	6.12374i	0.484447	−	0.874820i
$50$		0			0
$51$	−0.574855	−	0.394374i	−0.0804958	−	0.0552234i
$52$		0			0
$53$	4.94628	+	2.85574i	0.679424	+	0.392266i	0.799638	−	0.600482i	$-0.205025\pi$
$53$	4.94628	+	2.85574i	0.679424	+	0.392266i	−0.120214	+	0.992748i	$0.538358\pi$
$54$		0			0
$55$			6.58345i			0.887712i
$56$		0			0
$57$	−0.125601	−	0.262757i	−0.0166362	−	0.0348030i
$58$		0			0
$59$	4.50326			0.586275			0.293138	−	0.956070i	$-0.405301\pi$
$59$	4.50326			0.586275			0.293138	+	0.956070i	$0.405301\pi$
$60$		0			0
$61$		−	5.12315i		−	0.655952i	−0.944686	−	0.327976i	$-0.893634\pi$
$61$		−	5.12315i		−	0.655952i	0.944686	−	0.327976i	$-0.106366\pi$
$62$		0			0
$63$	7.37944	−	2.92299i	0.929722	−	0.368262i
$64$		0			0
$65$		−	10.2074i		−	1.26607i
$66$		0			0
$67$	−5.91041			−0.722072			−0.361036	−	0.932552i	$-0.617577\pi$
$67$	−5.91041			−0.722072			−0.361036	+	0.932552i	$0.617577\pi$
$68$		0			0
$69$	−8.70486	+	12.6886i	−1.04794	+	1.52752i
$70$		0			0
$71$		−	11.4308i		−	1.35658i	−0.734792	−	0.678292i	$-0.762720\pi$
$71$		−	11.4308i		−	1.35658i	0.734792	−	0.678292i	$-0.237280\pi$
$72$		0			0
$73$	−6.05559	−	3.49620i	−0.708753	−	0.409199i	0.101846	−	0.994800i	$-0.467525\pi$
$73$	−6.05559	−	3.49620i	−0.708753	−	0.409199i	−0.810599	+	0.585601i	$0.800858\pi$
$74$		0			0
$75$	−3.37275	+	1.61221i	−0.389451	+	0.186162i
$76$		0			0
$77$	−5.08619	+	8.99415i	−0.579625	+	1.02498i
$78$		0			0
$79$	1.20794			0.135903			0.0679517	−	0.997689i	$-0.478354\pi$
$79$	1.20794			0.135903			0.0679517	+	0.997689i	$0.478354\pi$
$80$		0			0
$81$	8.56884	+	2.75227i	0.952093	+	0.305808i
$82$		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
$87$	6.96255	−	10.1489i	0.746464	−	1.08808i
$88$		0			0
$89$	−1.38526	−	2.39934i	−0.146837	−	0.254329i	0.783220	−	0.621745i	$-0.213576\pi$
$89$	−1.38526	−	2.39934i	−0.146837	−	0.254329i	−0.930057	+	0.367416i	$0.880243\pi$
$90$		0			0
$91$	7.88594	−	13.9451i	0.826671	−	1.46184i
$92$		0			0
$93$	−10.8577	−	0.845308i	−1.12589	−	0.0876544i
$94$		0			0
$95$		−	0.283446i		−	0.0290809i
$96$		0			0
$97$	−0.508914	−	0.293821i	−0.0516723	−	0.0298330i	0.473941	−	0.880556i	$-0.342831\pi$
$97$	−0.508914	−	0.293821i	−0.0516723	−	0.0298330i	−0.525614	+	0.850723i	$0.676164\pi$
$98$		0			0
$99$	−10.9309	+	4.21713i	−1.09859	+	0.423837i
$100$		0			0
$101$	6.92329	+	11.9915i	0.688893	+	1.19320i	0.972196	+	0.234167i	$0.0752364\pi$
$101$	6.92329	+	11.9915i	0.688893	+	1.19320i	−0.283303	+	0.959030i	$0.591430\pi$
$102$		0			0
$103$	10.4610	+	6.03967i	1.03075	+	0.595106i	0.917201	−	0.398425i	$-0.130443\pi$
$103$	10.4610	+	6.03967i	1.03075	+	0.595106i	0.113554	+	0.993532i	$0.463777\pi$
$104$		0			0
$105$	7.70676	+	0.530777i	0.752103	+	0.0517985i
$106$		0			0
$107$	−15.9299	+	9.19711i	−1.54000	+	0.889118i	−0.541159	+	0.840920i	$0.682014\pi$
$107$	−15.9299	+	9.19711i	−1.54000	+	0.889118i	−0.998838	+	0.0481978i	$0.984652\pi$
$108$		0			0
$109$	−5.51036	+	9.54422i	−0.527796	+	0.914170i	0.471679	+	0.881771i	$0.343648\pi$
$109$	−5.51036	+	9.54422i	−0.527796	+	0.914170i	−0.999475	+	0.0323997i	$0.989685\pi$
$110$		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
$115$	−12.9696	+	7.48801i	−1.20942	+	0.698260i
$116$		0			0
$117$	16.9479	−	6.53850i	1.56683	−	0.604485i
$118$		0			0
$119$	−0.00951320	−	1.06484i	−0.000872074	−	0.0976137i
$120$		0			0
$121$	2.12600	−	3.68234i	0.193273	−	0.334758i
$122$		0			0
$123$	−5.14774	+	2.46067i	−0.464156	+	0.221871i
$124$		0			0
$125$	−12.0670			−1.07930
$126$		0			0
$127$	−10.6312			−0.943365			−0.471682	−	0.881769i	$-0.656353\pi$
$127$	−10.6312			−0.943365			−0.471682	+	0.881769i	$0.656353\pi$
$128$		0			0
$129$	5.15525	+	3.53671i	0.453894	+	0.311390i
$130$		0			0
$131$	3.16740	−	5.48610i	0.276737	−	0.479322i	−0.693835	−	0.720134i	$-0.744080\pi$
$131$	3.16740	−	5.48610i	0.276737	−	0.479322i	0.970572	+	0.240812i	$0.0774136\pi$
$132$		0			0
$133$	0.218982	−	0.387237i	0.0189882	−	0.0335777i
$134$		0			0
$135$	6.36904	+	6.01345i	0.548160	+	0.517555i
$136$		0			0
$137$	14.4158	−	8.32296i	1.23162	−	0.711078i	0.264255	−	0.964453i	$-0.414874\pi$
$137$	14.4158	−	8.32296i	1.23162	−	0.711078i	0.967368	+	0.253375i	$0.0815406\pi$
$138$		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
$147$	10.1187	+	6.67916i	0.834579	+	0.550888i
$148$		0			0
$149$	−4.57864	−	2.64348i	−0.375097	−	0.216562i	0.300586	−	0.953755i	$-0.402818\pi$
$149$	−4.57864	−	2.64348i	−0.375097	−	0.216562i	−0.675683	+	0.737192i	$0.736151\pi$
$150$		0			0
$151$	7.29163	+	12.6295i	0.593385	+	1.02777i	0.993773	+	0.111427i	$0.0355421\pi$
$151$	7.29163	+	12.6295i	0.593385	+	1.02777i	−0.400388	+	0.916346i	$0.631125\pi$
$152$		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
$157$		−	17.8009i		−	1.42066i	−0.703867	−	0.710332i	$-0.748545\pi$
$157$		−	17.8009i		−	1.42066i	0.703867	−	0.710332i	$-0.251455\pi$
$158$		0			0
$159$	−5.59634	+	8.15744i	−0.443818	+	0.646927i
$160$		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	$-0.165464\pi$
$163$	0.0482228	+	0.0835243i	0.00377710	+	0.00654213i	−0.864131	+	0.503267i	$0.832131\pi$
$164$		0			0
$165$	−11.3685	−	0.885074i	−0.885034	−	0.0689029i
$166$		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
$171$	0.470621	−	0.181566i	0.0359893	−	0.0138847i
$172$		0			0
$173$	−14.8007			−1.12527			−0.562637	−	0.826704i	$-0.690213\pi$
$173$	−14.8007			−1.12527			−0.562637	+	0.826704i	$0.690213\pi$
$174$		0			0
$175$	−4.97057	−	2.81086i	−0.375740	−	0.212481i
$176$		0			0
$177$	−0.605415	+	7.77635i	−0.0455058	+	0.584506i
$178$		0			0
$179$	−0.592751	−	0.342225i	−0.0443043	−	0.0255791i	0.477684	−	0.878532i	$-0.341476\pi$
$179$	−0.592751	−	0.342225i	−0.0443043	−	0.0255791i	−0.521989	+	0.852952i	$0.674810\pi$
$180$		0			0
$181$		−	7.84745i		−	0.583297i	−0.956526	−	0.291648i	$-0.905796\pi$
$181$		−	7.84745i		−	0.583297i	0.956526	−	0.291648i	$-0.0942037\pi$
$182$		0			0
$183$	8.84678	+	0.688752i	0.653973	+	0.0509140i
$184$		0			0
$185$	−10.5614			−0.776489
$186$		0			0
$187$			1.57187i			0.114946i
$188$		0			0
$189$	4.05541	+	13.1360i	0.294987	+	0.955501i
$190$		0			0
$191$		−	19.5946i		−	1.41781i	−0.705302	−	0.708907i	$-0.749189\pi$
$191$		−	19.5946i		−	1.41781i	0.705302	−	0.708907i	$-0.250811\pi$
$192$		0			0
$193$	18.3623			1.32175			0.660875	−	0.750496i	$-0.270186\pi$
$193$	18.3623			1.32175			0.660875	+	0.750496i	$0.270186\pi$
$194$		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	$-0.521652\pi$
$199$	−13.6268	−	7.86741i	−0.965975	−	0.557706i	−0.898007	+	0.439982i	$0.854985\pi$
$200$		0			0
$201$	0.794591	−	10.2062i	0.0560461	−	0.719893i
$202$		0			0
$203$	18.7994	−	0.167953i	1.31946	−	0.0117880i
$204$		0			0
$205$	−5.55306			−0.387842
$206$		0			0
$207$	−20.7406	−	16.7376i	−1.44157	−	1.16334i
$208$		0			0
$209$	−0.328332	+	0.568688i	−0.0227112	+	0.0393370i
$210$		0			0
$211$	5.06619	+	8.77489i	0.348771	+	0.604088i	0.986031	−	0.166560i	$-0.0532659\pi$
$211$	5.06619	+	8.77489i	0.348771	+	0.604088i	−0.637261	+	0.770648i	$0.719933\pi$
$212$		0			0
$213$	19.7390	+	1.53675i	1.35249	+	0.105296i
$214$		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
$219$	6.85143	−	9.98692i	0.462977	−	0.674853i
$220$		0			0
$221$		−	2.43712i		−	0.163939i
$222$		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
$227$	14.0360	+	24.3110i	0.931600	+	1.61358i	0.780588	+	0.625046i	$0.214920\pi$
$227$	14.0360	+	24.3110i	0.931600	+	1.61358i	0.151011	+	0.988532i	$0.451747\pi$
$228$		0			0
$229$	−14.7453	−	8.51319i	−0.974396	−	0.562568i	−0.0738222	−	0.997271i	$-0.523520\pi$
$229$	−14.7453	−	8.51319i	−0.974396	−	0.562568i	−0.900573	+	0.434704i	$0.856853\pi$
$230$		0			0
$231$	−14.8475	−	9.99212i	−0.976897	−	0.657433i
$232$		0			0
$233$	16.0015	−	9.23847i	1.04829	−	0.605233i	0.126122	−	0.992015i	$-0.459747\pi$
$233$	16.0015	−	9.23847i	1.04829	−	0.605233i	0.922171	+	0.386782i	$0.126413\pi$
$234$		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	−0.683205	−	0.730226i	$-0.739415\pi$
$239$	−6.06656	+	3.50253i	−0.392413	+	0.226560i	0.290792	+	0.956786i	$0.406081\pi$
$240$		0			0
$241$	5.38459	−	3.10879i	0.346852	−	0.200255i	−0.316446	−	0.948611i	$-0.602490\pi$
$241$	5.38459	−	3.10879i	0.346852	−	0.200255i	0.663298	+	0.748355i	$0.269156\pi$
$242$		0			0
$243$	−5.90468	+	14.4269i	−0.378785	+	0.925485i
$244$		0			0
$245$	6.08172	+	10.1122i	0.388547	+	0.646044i
$246$		0			0
$247$	0.509067	−	0.881730i	0.0323912	−	0.0561031i
$248$		0			0
$249$	0.518029	+	0.355389i	0.0328288	+	0.0225219i
$250$		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
$255$	1.06027	−	0.506821i	0.0663967	−	0.0317383i
$256$		0			0
$257$	−0.667904	+	1.15684i	−0.0416627	+	0.0721619i	−0.886105	−	0.463485i	$-0.846599\pi$
$257$	−0.667904	+	1.15684i	−0.0416627	+	0.0721619i	0.844442	+	0.535647i	$0.179932\pi$
$258$		0			0
$259$	−14.4287	−	8.15944i	−0.896558	−	0.507003i
$260$		0			0
$261$	16.5893	+	13.3875i	1.02685	+	0.828667i
$262$		0			0
$263$	17.6238	−	10.1751i	1.08673	−	0.627424i	0.154026	−	0.988067i	$-0.450776\pi$
$263$	17.6238	−	10.1751i	1.08673	−	0.627424i	0.932704	+	0.360643i	$0.117443\pi$
$264$		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	−0.0949131	−	0.995486i	$-0.530257\pi$
$269$	13.3614	−	23.1426i	0.814659	−	1.41103i	0.909572	−	0.415546i	$-0.136409\pi$
$270$		0			0
$271$	3.76517	−	2.17382i	0.228718	−	0.132050i	−0.381263	−	0.924467i	$-0.624511\pi$
$271$	3.76517	−	2.17382i	0.228718	−	0.132050i	0.609980	+	0.792417i	$0.291177\pi$
$272$		0			0
$273$	23.0206	+	15.4924i	1.39327	+	0.937643i
$274$		0			0
$275$	7.29968	+	4.21447i	0.440187	+	0.254142i
$276$		0			0
$277$	2.19901	+	3.80880i	0.132126	+	0.228849i	0.924496	−	0.381192i	$-0.124486\pi$
$277$	2.19901	+	3.80880i	0.132126	+	0.228849i	−0.792370	+	0.610041i	$0.791153\pi$
$278$		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
$283$		−	17.9476i		−	1.06687i	−0.845840	−	0.533437i	$-0.820900\pi$
$283$		−	17.9476i		−	1.06687i	0.845840	−	0.533437i	$-0.179100\pi$
$284$		0			0
$285$	0.489462	+	0.0381063i	0.0289932	+	0.00225722i
$286$		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
$291$	0.575796	−	0.839304i	0.0337538	−	0.0492009i
$292$		0			0
$293$	−13.1126	−	22.7117i	−0.766048	−	1.32683i	−0.939691	−	0.342026i	$-0.888887\pi$
$293$	−13.1126	−	22.7117i	−0.766048	−	1.32683i	0.173642	−	0.984809i	$-0.444446\pi$
$294$		0			0
$295$	−3.79566	+	6.57428i	−0.220992	+	0.382769i
$296$		0			0
$297$	−5.81271	−	19.4426i	−0.337287	−	1.12818i
$298$		0			0
$299$	−53.7936			−3.11097
$300$		0			0
$301$	0.0853135	+	9.54939i	0.00491739	+	0.550417i
$302$		0			0
$303$	−21.6380	+	10.3432i	−1.24307	+	0.594201i
$304$		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
$311$	2.17443			0.123301			0.0616503	−	0.998098i	$-0.480364\pi$
$311$	2.17443			0.123301			0.0616503	+	0.998098i	$0.480364\pi$
$312$		0			0
$313$			11.8784i			0.671409i	0.941967	+	0.335704i	$0.108974\pi$
$313$			11.8784i			0.671409i	−0.941967	+	0.335704i	$0.891026\pi$
$314$		0			0
$315$	−1.95265	+	13.2369i	−0.110019	+	0.745814i
$316$		0			0
$317$			8.19801i			0.460446i	0.973138	+	0.230223i	$0.0739456\pi$
$317$			8.19801i			0.460446i	−0.973138	+	0.230223i	$0.926054\pi$
$318$		0			0
$319$	−27.7509			−1.55375
$320$		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
$327$	−15.7404	−	10.7985i	−0.870446	−	0.597161i
$328$		0			0
$329$	−19.9893	+	11.7802i	−1.10205	+	0.649463i
$330$		0			0
$331$	17.1708			0.943793			0.471897	−	0.881654i	$-0.343570\pi$
$331$	17.1708			0.943793			0.471897	+	0.881654i	$0.343570\pi$
$332$		0			0
$333$	−6.76526	−	17.5357i	−0.370734	−	0.960949i
$334$		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
$339$	−6.35532	−	13.2953i	−0.345173	−	0.722103i
$340$		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
$345$	−11.1869	−	23.4029i	−0.602280	−	1.25997i
$346$		0			0
$347$			0.512514i			0.0275132i	0.999905	+	0.0137566i	$0.00437900\pi$
$347$			0.512514i			0.0275132i	−0.999905	+	0.0137566i	$0.995621\pi$
$348$		0			0
$349$	5.74612	+	3.31752i	0.307583	+	0.177583i	0.645844	−	0.763469i	$-0.276506\pi$
$349$	5.74612	+	3.31752i	0.307583	+	0.177583i	−0.338262	+	0.941052i	$0.609839\pi$
$350$		0			0
$351$	9.01239	+	30.1451i	0.481046	+	1.60903i
$352$		0			0
$353$	9.03437	+	15.6480i	0.480851	+	0.832858i	0.999759	−	0.0219721i	$-0.00699449\pi$
$353$	9.03437	+	15.6480i	0.480851	+	0.832858i	−0.518908	+	0.854830i	$0.673661\pi$
$354$		0			0
$355$	16.6877	+	9.63465i	0.885691	+	0.511354i
$356$		0			0
$357$	1.84007	+	0.126729i	0.0973869	+	0.00670719i
$358$		0			0
$359$	1.52677	−	0.881479i	0.0805796	−	0.0465227i	−0.459169	−	0.888349i	$-0.651853\pi$
$359$	1.52677	−	0.881479i	0.0805796	−	0.0465227i	0.539748	+	0.841826i	$0.318519\pi$
$360$		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
$367$	−28.9614	+	16.7209i	−1.51177	+	0.872822i	−0.511867	+	0.859065i	$0.671046\pi$
$367$	−28.9614	+	16.7209i	−1.51177	+	0.872822i	−0.999905	+	0.0137576i	$0.995621\pi$
$368$		0			0
$369$	−3.55710	−	9.22005i	−0.185175	−	0.479977i
$370$		0			0
$371$	−15.1105	+	0.134996i	−0.784500	+	0.00700867i
$372$		0			0
$373$	−12.7844	+	22.1433i	−0.661952	+	1.14653i	0.318150	+	0.948040i	$0.396938\pi$
$373$	−12.7844	+	22.1433i	−0.661952	+	1.14653i	−0.980102	+	0.198494i	$0.936395\pi$
$374$		0			0
$375$	1.62228	−	20.8376i	0.0837741	−	1.07605i
$376$		0			0
$377$	43.0267			2.21599
$378$		0			0
$379$	25.7920			1.32485			0.662423	−	0.749130i	$-0.269528\pi$
$379$	25.7920			1.32485			0.662423	+	0.749130i	$0.269528\pi$
$380$		0			0
$381$	1.42925	−	18.3582i	0.0732226	−	0.940519i
$382$		0			0
$383$	16.4158	−	28.4330i	0.838808	−	1.45286i	−0.0520838	−	0.998643i	$-0.516586\pi$
$383$	16.4158	−	28.4330i	0.838808	−	1.45286i	0.890892	−	0.454215i	$-0.150080\pi$
$384$		0			0
$385$	−8.84349	−	15.0062i	−0.450706	−	0.764785i
$386$		0			0
$387$	−6.80034	+	8.42674i	−0.345681	+	0.428355i
$388$		0			0
$389$	−17.4542	+	10.0772i	−0.884965	+	0.510935i	−0.872292	−	0.488985i	$-0.837367\pi$
$389$	−17.4542	+	10.0772i	−0.884965	+	0.510935i	−0.0126730	+	0.999920i	$0.504034\pi$
$390$		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	−0.516506	+	0.856284i	$0.672768\pi$
$397$	−30.2125	+	17.4432i	−1.51632	+	0.875449i	−0.999816	+	0.0191652i	$0.993899\pi$
$398$		0			0
$399$	0.639251	+	0.430204i	0.0320026	+	0.0215372i
$400$		0			0
$401$	8.36793	+	4.83122i	0.417874	+	0.241260i	0.694167	−	0.719814i	$-0.255773\pi$
$401$	8.36793	+	4.83122i	0.417874	+	0.241260i	−0.276293	+	0.961073i	$0.589106\pi$
$402$		0			0
$403$	−19.0364	−	32.9719i	−0.948268	−	1.64245i
$404$		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
$409$			37.0893i			1.83395i	0.398949	+	0.916973i	$0.369375\pi$
$409$			37.0893i			1.83395i	−0.398949	+	0.916973i	$0.630625\pi$
$410$		0			0
$411$	12.4342	+	26.0125i	0.613336	+	1.28310i
$412$		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
$417$	3.65725	+	7.65097i	0.179096	+	0.374669i
$418$		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
$423$	−25.9919	−	4.07180i	−1.26377	−	0.197978i
$424$		0			0
$425$	−0.868685			−0.0421374
$426$		0			0
$427$	6.88188	+	11.6776i	0.333038	+	0.565118i
$428$		0			0
$429$	−33.7749	−	23.1709i	−1.63067	−	1.11870i
$430$		0			0
$431$	27.3242	+	15.7756i	1.31616	+	0.759885i	0.983108	−	0.183024i	$-0.0585887\pi$
$431$	27.3242	+	15.7756i	1.31616	+	0.759885i	0.333051	+	0.942909i	$0.391922\pi$
$432$		0			0
$433$		−	10.0692i		−	0.483893i	−0.970290	−	0.241947i	$-0.922214\pi$
$433$		−	10.0692i		−	0.483893i	0.970290	−	0.241947i	$-0.0777859\pi$
$434$		0			0
$435$	8.94777	+	18.7188i	0.429013	+	0.897496i
$436$		0			0
$437$	−1.49378			−0.0714572
$438$		0			0
$439$		−	27.9398i		−	1.33350i	−0.745283	−	0.666748i	$-0.767686\pi$
$439$		−	27.9398i		−	1.33350i	0.745283	−	0.666748i	$-0.232314\pi$
$440$		0			0
$441$	−12.8941	+	16.5753i	−0.614005	+	0.789302i
$442$		0			0
$443$		−	34.8638i		−	1.65643i	−0.560411	−	0.828215i	$-0.689357\pi$
$443$		−	34.8638i		−	1.65643i	0.560411	−	0.828215i	$-0.310643\pi$
$444$		0			0
$445$	4.67037			0.221397
$446$		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
$453$	−22.7892	+	10.8935i	−1.07073	+	0.511820i
$454$		0			0
$455$	13.7115	+	23.2665i	0.642805	+	1.09075i
$456$		0			0
$457$	−6.21876			−0.290901			−0.145451	−	0.989366i	$-0.546463\pi$
$457$	−6.21876			−0.290901			−0.145451	+	0.989366i	$0.546463\pi$
$458$		0			0
$459$	1.52068	+	1.43577i	0.0709790	+	0.0670162i
$460$		0			0
$461$	−2.17165	+	3.76140i	−0.101144	+	0.175186i	−0.912156	−	0.409843i	$-0.865584\pi$
$461$	−2.17165	+	3.76140i	−0.101144	+	0.175186i	0.811012	+	0.585029i	$0.198917\pi$
$462$		0			0
$463$	3.57451	+	6.19124i	0.166122	+	0.287731i	0.937053	−	0.349187i	$-0.113542\pi$
$463$	3.57451	+	6.19124i	0.166122	+	0.287731i	−0.770931	+	0.636918i	$0.780209\pi$
$464$		0			0
$465$	10.3857	−	15.1386i	0.481624	−	0.702034i
$466$		0			0
$467$	0.944451	+	1.63584i	0.0437040	+	0.0756975i	0.887050	−	0.461673i	$-0.152751\pi$
$467$	0.944451	+	1.63584i	0.0437040	+	0.0756975i	−0.843346	+	0.537371i	$0.819417\pi$
$468$		0			0
$469$	13.4721	−	7.93941i	0.622082	−	0.366608i
$470$		0			0
$471$	30.7390	+	2.39314i	1.41638	+	0.110270i
$472$		0			0
$473$		−	14.0964i		−	0.648152i
$474$		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
$479$	−5.22491	−	9.04981i	−0.238732	−	0.413497i	0.721618	−	0.692291i	$-0.243399\pi$
$479$	−5.22491	−	9.04981i	−0.238732	−	0.413497i	−0.960351	+	0.278794i	$0.910065\pi$
$480$		0			0
$481$	−32.8539	−	18.9682i	−1.49801	−	0.864875i
$482$		0			0
$483$	2.79723	−	40.6152i	0.127278	−	1.84805i
$484$		0			0
$485$	0.857895	−	0.495306i	0.0389550	−	0.0224907i
$486$		0			0
$487$	−11.8298	+	20.4898i	−0.536060	+	0.928483i	0.463052	+	0.886331i	$0.346754\pi$
$487$	−11.8298	+	20.4898i	−0.536060	+	0.928483i	−0.999111	+	0.0421513i	$0.986579\pi$
$488$		0			0
$489$	−0.150715	+	0.0720434i	−0.00681557	+	0.00325792i
$490$		0			0
$491$	−11.6767	+	6.74152i	−0.526960	+	0.304241i	−0.739778	−	0.672851i	$-0.765069\pi$
$491$	−11.6767	+	6.74152i	−0.526960	+	0.304241i	0.212817	+	0.977092i	$0.431736\pi$
$492$		0			0
$493$	2.47683	−	1.43000i	0.111551	−	0.0644039i
$494$		0			0
$495$	3.05674	−	19.5124i	0.137390	−	0.877016i
$496$		0			0
$497$	15.3549	+	26.0551i	0.688761	+	1.16873i
$498$		0			0
$499$	6.04035	−	10.4622i	0.270403	−	0.468352i	−0.698562	−	0.715550i	$-0.746176\pi$
$499$	6.04035	−	10.4622i	0.270403	−	0.468352i	0.968965	+	0.247197i	$0.0795096\pi$
$500$		0			0
$501$	−7.74697	+	3.70314i	−0.346109	+	0.165444i
$502$		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
$507$	33.7994	+	23.1877i	1.50108	+	1.02980i
$508$		0			0
$509$	4.09043	−	7.08483i	0.181305	−	0.314029i	−0.761020	−	0.648728i	$-0.775301\pi$
$509$	4.09043	−	7.08483i	0.181305	−	0.314029i	0.942325	+	0.334699i	$0.108635\pi$
$510$		0			0
$511$	18.4994	−	0.165272i	0.818365	−	0.00731121i
$512$		0			0
$513$	0.250262	+	0.837090i	0.0110493	+	0.0369584i
$514$		0			0
$515$	−17.6345	+	10.1813i	−0.777070	+	0.448642i
$516$		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	−0.383738	−	0.923442i	$-0.625363\pi$
$521$	13.8746	−	24.0314i	0.607856	−	1.05284i	0.991593	−	0.129395i	$-0.0413034\pi$
$522$		0			0
$523$	19.8843	−	11.4802i	0.869478	−	0.501993i	0.00230311	−	0.999997i	$-0.499267\pi$
$523$	19.8843	−	11.4802i	0.869478	−	0.501993i	0.867175	+	0.498004i	$0.165934\pi$
$524$		0			0
$525$	5.52210	−	8.20542i	0.241004	−	0.358114i
$526$		0			0
$527$	−2.19166	−	1.26535i	−0.0954700	−	0.0551196i
$528$		0			0
$529$	27.9623	+	48.4322i	1.21575	+	2.10575i
$530$		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
$535$		−	31.0078i		−	1.34058i
$536$		0			0
$537$	0.670652	−	0.977569i	0.0289408	−	0.0421852i
$538$		0			0
$539$	−0.488426	−	27.3333i	−0.0210380	−	1.17733i
$540$		0			0
$541$	−2.60405	−	4.51035i	−0.111957	−	0.193915i	0.804602	−	0.593814i	$-0.202379\pi$
$541$	−2.60405	−	4.51035i	−0.111957	−	0.193915i	−0.916559	+	0.399899i	$0.869045\pi$
$542$		0			0
$543$	13.5512	+	1.05501i	0.581537	+	0.0452746i
$544$		0			0
$545$	−9.28902	−	16.0890i	−0.397898	−	0.689179i
$546$		0			0
$547$	10.6224	−	18.3985i	0.454181	−	0.786664i	−0.544460	−	0.838787i	$-0.683265\pi$
$547$	10.6224	−	18.3985i	0.454181	−	0.786664i	0.998641	+	0.0521229i	$0.0165988\pi$
$548$		0			0
$549$	−2.37871	+	15.1843i	−0.101521	+	0.648048i
$550$		0			0
$551$	1.19479			0.0509000
$552$		0			0
$553$	−2.75334	+	1.62261i	−0.117084	+	0.0690005i
$554$		0			0
$555$	1.41987	−	18.2377i	0.0602700	−	0.774147i
$556$		0			0
$557$	11.0945	+	6.40543i	0.470090	+	0.271407i	0.716277	−	0.697816i	$-0.245844\pi$
$557$	11.0945	+	6.40543i	0.470090	+	0.271407i	−0.246187	+	0.969222i	$0.579178\pi$
$558$		0			0
$559$			21.8559i			0.924406i
$560$		0			0
$561$	−2.71434	−	0.211321i	−0.114600	−	0.00892197i
$562$		0			0
$563$	−37.4793			−1.57956			−0.789781	−	0.613388i	$-0.789806\pi$
$563$	−37.4793			−1.57956			−0.789781	+	0.613388i	$0.789806\pi$
$564$		0			0
$565$		−	14.3422i		−	0.603380i
$566$		0			0
$567$	−23.2287	+	5.23699i	−0.975515	+	0.219933i
$568$		0			0
$569$			6.86938i			0.287979i	0.989579	+	0.143990i	$0.0459932\pi$
$569$			6.86938i			0.287979i	−0.989579	+	0.143990i	$0.954007\pi$
$570$		0			0
$571$	0.169582			0.00709678			0.00354839	−	0.999994i	$-0.498871\pi$
$571$	0.169582			0.00709678			0.00354839	+	0.999994i	$0.498871\pi$
$572$		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	0.383101	−	0.923706i	$-0.374856\pi$
$577$	−5.41193	−	3.12458i	−0.225302	−	0.130078i	−0.608403	+	0.793628i	$0.708189\pi$
$578$		0			0
$579$	−2.46862	+	31.7085i	−0.102592	+	1.31776i
$580$		0			0
$581$	0.00857280	+	0.959578i	0.000355660	+	0.0398100i
$582$		0			0
$583$	22.3055			0.923799
$584$		0			0
$585$	−4.73935	+	30.2532i	−0.195948	+	1.25082i
$586$		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
$591$	10.2282	+	0.796302i	0.420733	+	0.0327555i
$592$		0			0
$593$	−4.13036	−	7.15399i	−0.169613	−	0.293779i	0.768671	−	0.639645i	$-0.220919\pi$
$593$	−4.13036	−	7.15399i	−0.169613	−	0.293779i	−0.938284	+	0.345866i	$0.887585\pi$
$594$		0			0
$595$	1.56257	+	0.883632i	0.0640591	+	0.0362254i
$596$		0			0
$597$	15.4176	−	22.4733i	0.631001	−	0.919772i
$598$		0			0
$599$		−	35.5206i		−	1.45133i	−0.688047	−	0.725667i	$-0.741532\pi$
$599$		−	35.5206i		−	1.45133i	0.688047	−	0.725667i	$-0.258468\pi$
$600$		0			0
$601$	−35.8981	−	20.7258i	−1.46432	−	0.845423i	−0.465109	−	0.885254i	$-0.653985\pi$
$601$	−35.8981	−	20.7258i	−1.46432	−	0.845423i	−0.999206	+	0.0398308i	$0.987318\pi$
$602$		0			0
$603$	17.5176	+	2.74424i	0.713371	+	0.111754i
$604$		0			0
$605$	3.58388	+	6.20746i	0.145705	+	0.252369i
$606$		0			0
$607$	−2.09569	−	1.20995i	−0.0850616	−	0.0491103i	0.456866	−	0.889536i	$-0.348972\pi$
$607$	−2.09569	−	1.20995i	−0.0850616	−	0.0491103i	−0.541927	+	0.840425i	$0.682305\pi$
$608$		0			0
$609$	−2.23736	+	32.4859i	−0.0906622	+	1.31640i
$610$		0			0
$611$	−45.9873	+	26.5508i	−1.86045	+	1.07413i
$612$		0			0
$613$	21.3228	−	36.9321i	0.861219	−	1.49168i	−0.00953416	−	0.999955i	$-0.503035\pi$
$613$	21.3228	−	36.9321i	0.861219	−	1.49168i	0.870753	−	0.491720i	$-0.163632\pi$
$614$		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
$619$	23.9177	−	13.8089i	0.961334	−	0.555026i	0.0647505	−	0.997901i	$-0.479375\pi$
$619$	23.9177	−	13.8089i	0.961334	−	0.555026i	0.896583	+	0.442875i	$0.146042\pi$
$620$		0			0
$621$	31.6913	−	33.5653i	1.27173	−	1.34693i
$622$		0			0
$623$	6.38054	+	3.60819i	0.255631	+	0.144559i
$624$		0			0
$625$	4.77517	−	8.27084i	0.191007	−	0.330834i
$626$		0			0
$627$	−0.937885	−	0.643427i	−0.0374555	−	0.0256960i
$628$		0			0
$629$	−2.52164			−0.100545
$630$		0			0
$631$	8.28775			0.329930			0.164965	−	0.986299i	$-0.447249\pi$
$631$	8.28775			0.329930			0.164965	+	0.986299i	$0.447249\pi$
$632$		0			0
$633$	−15.8338	+	7.56873i	−0.629337	+	0.300830i
$634$		0			0
$635$	8.96069	−	15.5204i	0.355594	−	0.615907i
$636$		0			0
$637$	0.757287	+	42.3793i	0.0300048	+	1.67913i
$638$		0			0
$639$	−5.30738	+	33.8792i	−0.209957	+	1.34024i
$640$		0			0
$641$	−8.58307	+	4.95544i	−0.339011	+	0.195728i	−0.659835	−	0.751411i	$-0.729374\pi$
$641$	−8.58307	+	4.95544i	−0.339011	+	0.195728i	0.320824	+	0.947139i	$0.396040\pi$
$642$		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	−0.905351	−	0.424665i	$-0.860392\pi$
$647$	−2.15966	+	3.74063i	−0.0849049	+	0.147060i	0.820446	+	0.571724i	$0.193725\pi$
$648$		0			0
$649$	15.2308	−	8.79348i	0.597859	−	0.345174i
$650$		0			0
$651$	25.8843	−	12.6583i	1.01448	−	0.496117i
$652$		0			0
$653$	37.5853	+	21.6999i	1.47082	+	0.849181i	0.999463	−	0.0327591i	$-0.0104294\pi$
$653$	37.5853	+	21.6999i	1.47082	+	0.849181i	0.471361	+	0.881940i	$0.343763\pi$
$654$		0			0
$655$	5.33940	+	9.24812i	0.208628	+	0.361354i
$656$		0			0
$657$	16.3246	+	13.1739i	0.636882	+	0.513961i
$658$		0			0
$659$	−9.34894	−	5.39761i	−0.364183	−	0.210261i	0.306731	−	0.951796i	$-0.400765\pi$
$659$	−9.34894	−	5.39761i	−0.364183	−	0.210261i	−0.670914	+	0.741535i	$0.734098\pi$
$660$		0			0
$661$			3.92015i			0.152476i	0.997090	+	0.0762381i	$0.0242909\pi$
$661$			3.92015i			0.152476i	−0.997090	+	0.0762381i	$0.975709\pi$
$662$		0			0
$663$	4.20848	+	0.327645i	0.163444	+	0.0127247i
$664$		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
$669$	−15.1547	+	22.0901i	−0.585915	+	0.854053i
$670$		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
$675$	10.7449	−	3.21236i	0.413571	−	0.123644i
$676$		0			0
$677$	14.7265			0.565987			0.282994	−	0.959122i	$-0.408672\pi$
$677$	14.7265			0.565987			0.282994	+	0.959122i	$0.408672\pi$
$678$		0			0
$679$	1.55469	−	0.0138895i	0.0596637	−	0.000533031i
$680$		0			0
$681$	−43.8678	+	20.9693i	−1.68102	+	0.803545i
$682$		0			0
$683$	1.60128	+	0.924499i	0.0612712	+	0.0353750i	0.530323	−	0.847796i	$-0.322071\pi$
$683$	1.60128	+	0.924499i	0.0612712	+	0.0353750i	−0.469051	+	0.883171i	$0.655404\pi$
$684$		0			0
$685$			28.0606i			1.07214i
$686$		0			0
$687$	16.6831	−	24.3180i	0.636502	−	0.927790i
$688$		0			0
$689$	−34.5838			−1.31754
$690$		0			0
$691$			38.9842i			1.48303i	0.670938	+	0.741514i	$0.265892\pi$
$691$			38.9842i			1.48303i	−0.670938	+	0.741514i	$0.734108\pi$
$692$		0			0
$693$	19.2507	−	24.2958i	0.731275	−	0.922920i
$694$		0			0
$695$			8.25339i			0.313069i
$696$		0			0
$697$	−1.32585			−0.0502202
$698$		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
$705$	−21.1144	−	14.4853i	−0.795213	−	0.545548i
$706$		0			0
$707$	−31.8889	−	18.0331i	−1.19930	−	0.678206i
$708$		0			0
$709$	−14.2903			−0.536685			−0.268342	−	0.963324i	$-0.586476\pi$
$709$	−14.2903			−0.536685			−0.268342	+	0.963324i	$0.586476\pi$
$710$		0			0
$711$	−3.58014	−	0.560852i	−0.134266	−	0.0210336i
$712$		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
$717$	−5.23267	−	10.9468i	−0.195418	−	0.408814i
$718$		0			0
$719$	16.7344	+	28.9848i	0.624088	+	1.08095i	0.988716	+	0.149799i	$0.0478626\pi$
$719$	16.7344	+	28.9848i	0.624088	+	1.08095i	−0.364629	+	0.931153i	$0.618804\pi$
$720$		0			0
$721$	−31.9577	+	0.285507i	−1.19017	+	0.0106329i
$722$		0			0
$723$	4.64445	+	9.71619i	0.172729	+	0.361349i
$724$		0			0
$725$		−	15.3364i		−	0.569579i
$726$		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
$731$	0.726384	+	1.25813i	0.0268663	+	0.0465338i
$732$		0			0
$733$	23.6491	+	13.6538i	0.873501	+	0.504316i	0.868510	−	0.495672i	$-0.165078\pi$
$733$	23.6491	+	13.6538i	0.873501	+	0.504316i	0.00499085	+	0.999988i	$0.498411\pi$
$734$		0			0
$735$	−18.2796	+	9.14259i	−0.674254	+	0.337230i
$736$		0			0
$737$	−19.9899	+	11.5412i	−0.736339	+	0.425126i
$738$		0			0
$739$	26.3157	−	45.5801i	0.968039	−	1.67669i	0.266819	−	0.963747i	$-0.414027\pi$
$739$	26.3157	−	45.5801i	0.968039	−	1.67669i	0.701220	−	0.712945i	$-0.252639\pi$
$740$		0			0
$741$	1.45416	+	0.997609i	0.0534197	+	0.0366481i
$742$		0			0
$743$	−30.9523	+	17.8703i	−1.13553	+	0.655599i	−0.945320	−	0.326144i	$-0.894250\pi$
$743$	−30.9523	+	17.8703i	−1.13553	+	0.655599i	−0.190211	+	0.981743i	$0.560917\pi$
$744$		0			0
$745$	7.71839	−	4.45621i	0.282780	−	0.163263i
$746$		0			0
$747$	−0.683338	+	0.846768i	−0.0250020	+	0.0309816i
$748$		0			0
$749$	23.9558	−	42.3621i	0.875325	−	1.54788i
$750$		0			0
$751$	16.5641	−	28.6899i	0.604433	−	1.04691i	−0.387708	−	0.921782i	$-0.626733\pi$
$751$	16.5641	−	28.6899i	0.604433	−	1.04691i	0.992141	−	0.125126i	$-0.0399336\pi$
$752$		0			0
$753$	−1.31998	+	16.9547i	−0.0481029	+	0.617865i
$754$		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
$759$	−4.66440	+	59.9126i	−0.169307	+	2.17469i
$760$		0			0
$761$	−6.51737	+	11.2884i	−0.236255	+	0.409205i	−0.959637	−	0.281243i	$-0.909253\pi$
$761$	−6.51737	+	11.2884i	−0.236255	+	0.409205i	0.723382	+	0.690448i	$0.242587\pi$
$762$		0			0
$763$	−0.260486	−	29.1569i	−0.00943021	−	1.05555i
$764$		0			0
$765$	0.732649	+	1.89904i	0.0264890	+	0.0686599i
$766$		0			0
$767$	−23.6147	+	13.6340i	−0.852678	+	0.492294i
$768$		0			0
$769$	18.4866	−	10.6732i	0.666642	−	0.384886i	−0.128161	−	0.991753i	$-0.540907\pi$
$769$	18.4866	−	10.6732i	0.666642	−	0.384886i	0.794803	+	0.606867i	$0.207574\pi$
$770$		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	$-0.767148\pi$
$773$	5.73940	−	9.94093i	0.206432	−	0.357550i	0.950588	+	0.310455i	$0.100482\pi$
$774$		0			0
$775$	−11.7525	+	6.78529i	−0.422161	+	0.243735i
$776$		0			0
$777$	16.0297	−	23.8189i	0.575063	−	0.854500i
$778$		0			0
$779$	−0.479682	−	0.276944i	−0.0171864	−	0.00992256i
$780$		0			0
$781$	−22.3208	−	38.6607i	−0.798701	−	1.38339i
$782$		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
$787$			41.2006i			1.46864i	0.678802	+	0.734322i	$0.262500\pi$
$787$			41.2006i			1.46864i	−0.678802	+	0.734322i	$0.737500\pi$
$788$		0			0
$789$	15.2013	+	31.8012i	0.541181	+	1.13215i
$790$		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
$795$	−7.19201	−	15.0457i	−0.255074	−	0.533616i
$796$		0			0
$797$	−25.0066	−	43.3127i	−0.885779	−	1.53421i	−0.844819	−	0.535053i	$-0.820292\pi$
$797$	−25.0066	−	43.3127i	−0.885779	−	1.53421i	−0.0409600	−	0.999161i	$-0.513042\pi$
$798$		0			0
$799$	−1.76484	+	3.05679i	−0.0624355	+	0.108141i
$800$		0			0
$801$	2.99168	+	7.75447i	0.105706	+	0.273991i
$802$		0			0
$803$	−27.3079			−0.963677
$804$		0			0
$805$	19.5041	−	34.4900i	0.687428	−	1.21561i
$806$		0			0
$807$	38.1670	+	26.1841i	1.34354	+	0.921724i
$808$		0			0
$809$	−43.8995	−	25.3454i	−1.54343	−	0.891097i	−0.998619	−	0.0525356i	$-0.983270\pi$
$809$	−43.8995	−	25.3454i	−1.54343	−	0.891097i	−0.544807	−	0.838562i	$-0.683397\pi$
$810$		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
$815$	−0.162582			−0.00569500
$816$		0			0
$817$			0.606910i			0.0212331i
$818$		0			0
$819$	−29.8476	+	37.6697i	−1.04296	+	1.31629i
$820$		0			0
$821$		−	32.5845i		−	1.13721i	−0.822612	−	0.568603i	$-0.807484\pi$
$821$		−	32.5845i		−	1.13721i	0.822612	−	0.568603i	$-0.192516\pi$
$822$		0			0
$823$	−20.1754			−0.703271			−0.351636	−	0.936137i	$-0.614374\pi$
$823$	−20.1754			−0.703271			−0.351636	+	0.936137i	$0.614374\pi$
$824$		0			0
$825$	−8.25902	+	12.0387i	−0.287542	+	0.419133i
$826$		0			0
$827$			0.253288i			0.00880770i	0.999990	+	0.00440385i	$0.00140179\pi$
$827$			0.253288i			0.00880770i	−0.999990	+	0.00440385i	$0.998598\pi$
$828$		0			0
$829$	−6.10909	−	3.52708i	−0.212177	−	0.122501i	0.390146	−	0.920753i	$-0.372425\pi$
$829$	−6.10909	−	3.52708i	−0.212177	−	0.122501i	−0.602323	+	0.798253i	$0.705758\pi$
$830$		0			0
$831$	−6.87277	+	3.28526i	−0.238414	+	0.113964i
$832$		0			0
$833$	1.45208	+	2.41439i	0.0503114	+	0.0836538i
$834$		0			0
$835$	−8.35695			−0.289204
$836$		0			0
$837$	31.7881	+	7.54666i	1.09876	+	0.260851i
$838$		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
$843$	−5.23026	+	7.62383i	−0.180140	+	0.262579i
$844$		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
$849$	30.9924	+	2.41286i	1.06366	+	0.0828092i
$850$		0			0
$851$			55.6593i			1.90798i
$852$		0			0
$853$	21.7586	+	12.5623i	0.745000	+	0.430126i	0.823884	−	0.566758i	$-0.191802\pi$
$853$	21.7586	+	12.5623i	0.745000	+	0.430126i	−0.0788844	+	0.996884i	$0.525136\pi$
$854$		0			0
$855$	−0.131606	+	0.840092i	−0.00450082	+	0.0287305i
$856$		0			0
$857$	21.0954	+	36.5383i	0.720604	+	1.24812i	0.960758	+	0.277388i	$0.0894688\pi$
$857$	21.0954	+	36.5383i	0.720604	+	1.24812i	−0.240154	+	0.970735i	$0.577198\pi$
$858$		0			0
$859$	4.08139	+	2.35639i	0.139255	+	0.0803990i	0.568009	−	0.823022i	$-0.307714\pi$
$859$	4.08139	+	2.35639i	0.139255	+	0.0803990i	−0.428754	+	0.903421i	$0.641047\pi$
$860$		0			0
$861$	8.42823	−	12.5237i	0.287233	−	0.426807i
$862$		0			0
$863$	−30.8409	+	17.8060i	−1.04984	+	0.606123i	−0.922603	−	0.385750i	$-0.873943\pi$
$863$	−30.8409	+	17.8060i	−1.04984	+	0.606123i	−0.127232	+	0.991873i	$0.540609\pi$
$864$		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
$871$	30.9937	−	17.8942i	1.05018	−	0.606322i
$872$		0			0
$873$	1.37192	+	1.10713i	0.0464325	+	0.0374708i
$874$		0			0
$875$	27.5053	−	16.2095i	0.929847	−	0.547981i
$876$		0			0
$877$	−20.4532	+	35.4260i	−0.690655	+	1.19625i	0.280969	+	0.959717i	$0.409344\pi$
$877$	−20.4532	+	35.4260i	−0.690655	+	1.19625i	−0.971624	+	0.236532i	$0.923989\pi$
$878$		0			0
$879$	40.9821	−	19.5899i	1.38229	−	0.660750i
$880$		0			0
$881$	−37.4443			−1.26153			−0.630765	−	0.775974i	$-0.717259\pi$
$881$	−37.4443			−1.26153			−0.630765	+	0.775974i	$0.717259\pi$
$882$		0			0
$883$	−49.8357			−1.67711			−0.838553	−	0.544821i	$-0.816598\pi$
$883$	−49.8357			−1.67711			−0.838553	+	0.544821i	$0.816598\pi$
$884$		0			0
$885$	−10.8423	−	7.43828i	−0.364461	−	0.250035i
$886$		0			0
$887$	14.4482	−	25.0251i	0.485124	−	0.840260i	−0.514730	−	0.857352i	$-0.672108\pi$
$887$	14.4482	−	25.0251i	0.485124	−	0.840260i	0.999854	+	0.0170929i	$0.00544110\pi$
$888$		0			0
$889$	24.2325	−	14.2808i	0.812731	−	0.478962i
$890$		0			0
$891$	34.3555	−	7.42368i	1.15095	−	0.248703i
$892$		0			0
$893$	−1.27701	+	0.737280i	−0.0427334	+	0.0246721i
$894$		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
$903$	−16.5016	−	1.13649i	−0.549139	−	0.0378200i
$904$		0			0
$905$	11.4564	+	6.61437i	0.380825	+	0.219869i
$906$		0			0
$907$	7.43498	+	12.8778i	0.246874	+	0.427599i	0.962657	−	0.270724i	$-0.0872632\pi$
$907$	7.43498	+	12.8778i	0.246874	+	0.427599i	−0.715783	+	0.698323i	$0.753930\pi$
$908$		0			0
$909$	−14.9519	−	38.7555i	−0.495923	−	1.28544i
$910$		0			0
$911$	7.81616	+	4.51266i	0.258961	+	0.149511i	0.623861	−	0.781536i	$-0.285563\pi$
$911$	7.81616	+	4.51266i	0.258961	+	0.149511i	−0.364899	+	0.931047i	$0.618897\pi$
$912$		0			0
$913$		−	1.41649i		−	0.0468788i
$914$		0			0
$915$	−8.46218	+	12.3348i	−0.279751	+	0.407776i
$916$		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	$-0.0231670\pi$
$919$	13.2083	+	22.8774i	0.435702	+	0.754657i	−0.561651	+	0.827374i	$0.689834\pi$
$920$		0			0
$921$	12.4249	+	0.967317i	0.409413	+	0.0318742i
$922$		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
$927$	−28.2007	−	22.7578i	−0.926231	−	0.747464i
$928$		0			0
$929$	22.2518			0.730058			0.365029	−	0.930996i	$-0.381059\pi$
$929$	22.2518			0.730058			0.365029	+	0.930996i	$0.381059\pi$
$930$		0			0
$931$	0.0210289	+	1.17682i	0.000689194	+	0.0385686i
$932$		0			0
$933$	−0.292329	+	3.75486i	−0.00957041	+	0.122929i
$934$		0			0
$935$	−2.29476	−	1.32488i	−0.0750465	−	0.0433281i
$936$		0			0
$937$			14.6822i			0.479647i	0.970817	+	0.239823i	$0.0770896\pi$
$937$			14.6822i			0.479647i	−0.970817	+	0.239823i	$0.922910\pi$
$938$		0			0
$939$	−20.5120	−	1.59693i	−0.669383	−	0.0521137i
$940$		0			0
$941$	46.0792			1.50214			0.751070	−	0.660223i	$-0.229538\pi$
$941$	46.0792			1.50214			0.751070	+	0.660223i	$0.229538\pi$
$942$		0			0
$943$			29.2650i			0.952999i
$944$		0			0
$945$	−22.5953	−	5.15144i	−0.735024	−	0.167576i
$946$		0			0
$947$			8.03805i			0.261202i	0.991435	+	0.130601i	$0.0416906\pi$
$947$			8.03805i			0.261202i	−0.991435	+	0.130601i	$0.958309\pi$
$948$		0			0
$949$	42.3400			1.37441
$950$		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
$957$	3.73080	−	47.9209i	0.120600	−	1.54906i
$958$		0			0
$959$	−21.6789	+	38.3358i	−0.700047	+	1.23793i
$960$		0			0
$961$	−8.53466			−0.275312
$962$		0			0
$963$	51.4840	−	19.8625i	1.65905	−	0.640061i
$964$		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	$-0.840143\pi$
$967$	−26.5917	−	46.0582i	−0.855132	−	1.48113i	0.0213900	−	0.999771i	$-0.493191\pi$
$968$		0			0
$969$	0.116864	+	0.00909827i	0.00375422	+	0.000292279i
$970$		0			0
$971$	−7.61403	−	13.1879i	−0.244346	−	0.423219i	0.717602	−	0.696454i	$-0.245240\pi$
$971$	−7.61403	−	13.1879i	−0.244346	−	0.423219i	−0.961947	+	0.273234i	$0.911907\pi$
$972$		0			0
$973$	−6.37634	+	11.2756i	−0.204416	+	0.361479i
$974$		0			0
$975$	12.8053	−	18.6655i	0.410098	−	0.597775i
$976$		0			0
$977$		−	1.72533i		−	0.0551983i	−0.999619	−	0.0275992i	$-0.991214\pi$
$977$		−	1.72533i		−	0.0551983i	0.999619	−	0.0275992i	$-0.00878620\pi$
$978$		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
$983$	−30.1191	−	52.1679i	−0.960651	−	1.66390i	−0.720871	−	0.693070i	$-0.756258\pi$
$983$	−30.1191	−	52.1679i	−0.960651	−	1.66390i	−0.239780	−	0.970827i	$-0.577075\pi$
$984$		0			0
$985$	8.64713	+	4.99242i	0.275521	+	0.159072i
$986$		0			0
$987$	−17.6550	−	36.1018i	−0.561965	−	1.14913i
$988$		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	$-0.862425\pi$
$991$	−2.87312	+	4.97639i	−0.0912676	+	0.158080i	0.816777	+	0.576953i	$0.195759\pi$
$992$		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
$997$	0.0224508	−	0.0129620i	0.000711024	−	0.000410510i	−0.499644	−	0.866231i	$-0.666536\pi$
$997$	0.0224508	−	0.0129620i	0.000711024	−	0.000410510i	0.500355	+	0.865820i	$0.333203\pi$
$998$		0			0
$999$	31.1906	−	9.32495i	0.986826	−	0.295028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.w.a.101.4	yes	16
3.2	odd	2		756.2.w.a.521.6		16
4.3	odd	2		1008.2.ca.d.353.5		16
7.2	even	3		1764.2.bm.a.1685.2		16
7.3	odd	6		1764.2.x.b.1469.1		16
7.4	even	3		1764.2.x.a.1469.8		16
7.5	odd	6		252.2.bm.a.173.7	yes	16
7.6	odd	2		1764.2.w.b.1109.5		16
9.2	odd	6		2268.2.t.a.1781.6		16
9.4	even	3		756.2.bm.a.17.6		16
9.5	odd	6		252.2.bm.a.185.7	yes	16
9.7	even	3		2268.2.t.b.1781.3		16
12.11	even	2		3024.2.ca.d.2033.6		16
21.2	odd	6		5292.2.bm.a.4625.3		16
21.5	even	6		756.2.bm.a.89.6		16
21.11	odd	6		5292.2.x.a.4409.6		16
21.17	even	6		5292.2.x.b.4409.3		16
21.20	even	2		5292.2.w.b.521.3		16
28.19	even	6		1008.2.df.d.929.2		16
36.23	even	6		1008.2.df.d.689.2		16
36.31	odd	6		3024.2.df.d.17.6		16
63.4	even	3		5292.2.x.b.881.3		16
63.5	even	6	inner	252.2.w.a.5.4	✓	16
63.13	odd	6		5292.2.bm.a.2285.3		16
63.23	odd	6		1764.2.w.b.509.5		16
63.31	odd	6		5292.2.x.a.881.6		16
63.32	odd	6		1764.2.x.b.293.1		16
63.40	odd	6		756.2.w.a.341.6		16
63.41	even	6		1764.2.bm.a.1697.2		16
63.47	even	6		2268.2.t.b.2105.3		16
63.58	even	3		5292.2.w.b.1097.3		16
63.59	even	6		1764.2.x.a.293.8		16
63.61	odd	6		2268.2.t.a.2105.6		16
84.47	odd	6		3024.2.df.d.1601.6		16
252.103	even	6		3024.2.ca.d.2609.6		16
252.131	odd	6		1008.2.ca.d.257.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.4	✓	16	63.5	even	6	inner
252.2.w.a.101.4	yes	16	1.1	even	1	trivial
252.2.bm.a.173.7	yes	16	7.5	odd	6
252.2.bm.a.185.7	yes	16	9.5	odd	6
756.2.w.a.341.6		16	63.40	odd	6
756.2.w.a.521.6		16	3.2	odd	2
756.2.bm.a.17.6		16	9.4	even	3
756.2.bm.a.89.6		16	21.5	even	6
1008.2.ca.d.257.5		16	252.131	odd	6
1008.2.ca.d.353.5		16	4.3	odd	2
1008.2.df.d.689.2		16	36.23	even	6
1008.2.df.d.929.2		16	28.19	even	6
1764.2.w.b.509.5		16	63.23	odd	6
1764.2.w.b.1109.5		16	7.6	odd	2
1764.2.x.a.293.8		16	63.59	even	6
1764.2.x.a.1469.8		16	7.4	even	3
1764.2.x.b.293.1		16	63.32	odd	6
1764.2.x.b.1469.1		16	7.3	odd	6
1764.2.bm.a.1685.2		16	7.2	even	3
1764.2.bm.a.1697.2		16	63.41	even	6
2268.2.t.a.1781.6		16	9.2	odd	6
2268.2.t.a.2105.6		16	63.61	odd	6
2268.2.t.b.1781.3		16	9.7	even	3
2268.2.t.b.2105.3		16	63.47	even	6
3024.2.ca.d.2033.6		16	12.11	even	2
3024.2.ca.d.2609.6		16	252.103	even	6
3024.2.df.d.17.6		16	36.31	odd	6
3024.2.df.d.1601.6		16	84.47	odd	6
5292.2.w.b.521.3		16	21.20	even	2
5292.2.w.b.1097.3		16	63.58	even	3
5292.2.x.a.881.6		16	63.31	odd	6
5292.2.x.a.4409.6		16	21.11	odd	6
5292.2.x.b.881.3		16	63.4	even	3
5292.2.x.b.4409.3		16	21.17	even	6
5292.2.bm.a.2285.3		16	63.13	odd	6
5292.2.bm.a.4625.3		16	21.2	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.134439 + 1.72683i) q^{3} +(-0.842869 + 1.45989i) q^{5} +(-2.27938 + 1.34329i) q^{7} +(-2.96385 - 0.464306i) q^{9} +(3.38216 - 1.95269i) q^{11} +(-5.24391 + 3.02757i) q^{13} +(-2.40766 - 1.65175i) q^{15} +(-0.201244 + 0.348565i) q^{17} +(-0.145617 + 0.0840718i) q^{19} +(-2.01319 - 4.11668i) q^{21} +(7.69373 + 4.44198i) q^{23} +(1.07914 + 1.86913i) q^{25} +(1.20023 - 5.05563i) q^{27} +(-6.15380 - 3.55290i) q^{29} +6.28766i q^{31} +(2.91726 + 6.10292i) q^{33} +(-0.0398441 - 4.45986i) q^{35} +(3.13257 + 5.42578i) q^{37} +(-4.52310 - 9.46234i) q^{39} +(1.64707 + 2.85281i) q^{41} +(1.80474 - 3.12590i) q^{43} +(3.17597 - 3.93555i) q^{45} +8.76965 q^{47} +(3.39113 - 6.12374i) q^{49} +(-0.574855 - 0.394374i) q^{51} +(4.94628 + 2.85574i) q^{53} +6.58345i q^{55} +(-0.125601 - 0.262757i) q^{57} +4.50326 q^{59} -5.12315i q^{61} +(7.37944 - 2.92299i) q^{63} -10.2074i q^{65} -5.91041 q^{67} +(-8.70486 + 12.6886i) q^{69} -11.4308i q^{71} +(-6.05559 - 3.49620i) q^{73} +(-3.37275 + 1.61221i) q^{75} +(-5.08619 + 8.99415i) q^{77} +1.20794 q^{79} +(8.56884 + 2.75227i) q^{81} +(0.181350 - 0.314108i) q^{83} +(-0.339244 - 0.587588i) q^{85} +(6.96255 - 10.1489i) q^{87} +(-1.38526 - 2.39934i) q^{89} +(7.88594 - 13.9451i) q^{91} +(-10.8577 - 0.845308i) q^{93} -0.283446i q^{95} +(-0.508914 - 0.293821i) q^{97} +(-10.9309 + 4.21713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47}+ \cdots - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more