LMFDB - Embedded newform 444.2.bg.b.209.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(5,444)] 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("444.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 18, 23])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.bg (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			209.10
Character	$\chi$	$=$	444.209
Dual form			444.2.bg.b.17.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21110 + 1.23824i) q^{3} +(2.99415 + 0.261955i) q^{5} +(-1.57171 + 1.31882i) q^{7} +(-0.0664970 + 2.99926i) q^{9} +(0.410422 - 0.710872i) q^{11} +(-0.481628 + 0.224587i) q^{13} +(3.30184 + 4.02475i) q^{15} +(4.05183 + 1.88940i) q^{17} +(-4.58845 - 3.21287i) q^{19} +(-3.53651 - 0.348942i) q^{21} +(0.683726 - 2.55170i) q^{23} +(3.97230 + 0.700424i) q^{25} +(-3.79435 + 3.55005i) q^{27} +(-0.751047 - 2.80295i) q^{29} +(-2.52461 - 2.52461i) q^{31} +(1.37729 - 0.352731i) q^{33} +(-5.05141 + 3.53704i) q^{35} +(4.92239 + 3.57352i) q^{37} +(-0.861391 - 0.324377i) q^{39} +(0.623643 + 0.226987i) q^{41} +(6.36347 - 6.36347i) q^{43} +(-0.984773 + 8.96284i) q^{45} +(0.943574 - 0.544773i) q^{47} +(-0.484555 + 2.74805i) q^{49} +(2.56762 + 7.30541i) q^{51} +(-2.73760 + 3.26255i) q^{53} +(1.41508 - 2.02095i) q^{55} +(-1.57873 - 9.57270i) q^{57} +(0.898184 + 10.2663i) q^{59} +(-2.73787 - 5.87138i) q^{61} +(-3.85098 - 4.80167i) q^{63} +(-1.50090 + 0.546284i) q^{65} +(-4.31473 - 5.14209i) q^{67} +(3.98769 - 2.24373i) q^{69} +(-0.471211 + 0.0830872i) q^{71} -10.2572i q^{73} +(3.94354 + 5.76696i) q^{75} +(0.292448 + 1.65856i) q^{77} +(1.33048 - 15.2074i) q^{79} +(-8.99116 - 0.398884i) q^{81} +(-1.15221 - 3.16568i) q^{83} +(11.6369 + 6.71856i) q^{85} +(2.56114 - 4.32461i) q^{87} +(16.7368 - 1.46428i) q^{89} +(0.460790 - 0.988167i) q^{91} +(0.0685405 - 6.18363i) q^{93} +(-12.8969 - 10.8218i) q^{95} +(-5.38204 - 1.44211i) q^{97} +(2.10480 + 1.27823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{9} - 6 q^{15} + 18 q^{21} - 54 q^{27} + 48 q^{31} + 84 q^{37} - 54 q^{39} + 24 q^{43} + 72 q^{45} + 84 q^{49} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 78 q^{69} - 216 q^{75} - 24 q^{79} - 66 q^{81}+ \cdots - 78 q^{99}+O(q^{100}) $ 144 * q - 6 * q^9 - 6 * q^15 + 18 * q^21 - 54 * q^27 + 48 * q^31 + 84 * q^37 - 54 * q^39 + 24 * q^43 + 72 * q^45 + 84 * q^49 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 78 * q^69 - 216 * q^75 - 24 * q^79 - 66 * q^81 - 72 * q^87 - 48 * q^91 - 48 * q^93 - 24 * q^97 - 78 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$

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
$3$	1.21110	+	1.23824i	0.699226	+	0.714901i
$3$	1.21110	+	1.23824i	0.699226	+	0.714901i
$4$		0			0
$5$	2.99415	+	0.261955i	1.33903	+	0.117150i	0.734051	−	0.679094i	$-0.237627\pi$
$5$	2.99415	+	0.261955i	1.33903	+	0.117150i	0.604976	+	0.796244i	$0.293183\pi$
$6$		0			0
$7$	−1.57171	+	1.31882i	−0.594050	+	0.498467i	−0.889527	−	0.456883i	$-0.848966\pi$
$7$	−1.57171	+	1.31882i	−0.594050	+	0.498467i	0.295477	+	0.955350i	$0.404522\pi$
$8$		0			0
$9$	−0.0664970	+	2.99926i	−0.0221657	+	0.999754i
$10$		0			0
$11$	0.410422	−	0.710872i	0.123747	−	0.214336i	−0.797495	−	0.603325i	$-0.793842\pi$
$11$	0.410422	−	0.710872i	0.123747	−	0.214336i	0.921242	+	0.388989i	$0.127176\pi$
$12$		0			0
$13$	−0.481628	+	0.224587i	−0.133580	+	0.0622892i	−0.488259	−	0.872699i	$-0.662368\pi$
$13$	−0.481628	+	0.224587i	−0.133580	+	0.0622892i	0.354679	+	0.934988i	$0.384590\pi$
$14$		0			0
$15$	3.30184	+	4.02475i	0.852532	+	1.03919i
$16$		0			0
$17$	4.05183	+	1.88940i	0.982714	+	0.458247i	0.846475	−	0.532429i	$-0.178721\pi$
$17$	4.05183	+	1.88940i	0.982714	+	0.458247i	0.136239	+	0.990676i	$0.456498\pi$
$18$		0			0
$19$	−4.58845	−	3.21287i	−1.05266	−	0.737082i	−0.0868228	−	0.996224i	$-0.527671\pi$
$19$	−4.58845	−	3.21287i	−1.05266	−	0.737082i	−0.965839	+	0.259142i	$0.916560\pi$
$20$		0			0
$21$	−3.53651	−	0.348942i	−0.771730	−	0.0761455i
$22$		0			0
$23$	0.683726	−	2.55170i	0.142567	−	0.532067i	−0.857285	−	0.514842i	$-0.827850\pi$
$23$	0.683726	−	2.55170i	0.142567	−	0.532067i	0.999852	−	0.0172242i	$-0.00548291\pi$
$24$		0			0
$25$	3.97230	+	0.700424i	0.794461	+	0.140085i
$26$		0			0
$27$	−3.79435	+	3.55005i	−0.730224	+	0.683208i
$28$		0			0
$29$	−0.751047	−	2.80295i	−0.139466	−	0.520494i	−0.999940	−	0.0109989i	$-0.996499\pi$
$29$	−0.751047	−	2.80295i	−0.139466	−	0.520494i	0.860474	−	0.509495i	$-0.170168\pi$
$30$		0			0
$31$	−2.52461	−	2.52461i	−0.453434	−	0.453434i	0.443059	−	0.896492i	$-0.353893\pi$
$31$	−2.52461	−	2.52461i	−0.453434	−	0.453434i	−0.896492	+	0.443059i	$0.853893\pi$
$32$		0			0
$33$	1.37729	−	0.352731i	0.239756	−	0.0614026i
$34$		0			0
$35$	−5.05141	+	3.53704i	−0.853844	+	0.597868i
$36$		0			0
$37$	4.92239	+	3.57352i	0.809237	+	0.587483i
$37$	4.92239	+	3.57352i	0.809237	+	0.587483i
$38$		0			0
$39$	−0.861391	−	0.324377i	−0.137933	−	0.0519419i
$40$		0			0
$41$	0.623643	+	0.226987i	0.0973967	+	0.0354495i	0.390259	−	0.920705i	$-0.372386\pi$
$41$	0.623643	+	0.226987i	0.0973967	+	0.0354495i	−0.292862	+	0.956155i	$0.594608\pi$
$42$		0			0
$43$	6.36347	−	6.36347i	0.970420	−	0.970420i	−0.0291545	−	0.999575i	$-0.509281\pi$
$43$	6.36347	−	6.36347i	0.970420	−	0.970420i	0.999575	+	0.0291545i	$0.00928147\pi$
$44$		0			0
$45$	−0.984773	+	8.96284i	−0.146801	+	1.33610i
$46$		0			0
$47$	0.943574	−	0.544773i	0.137634	−	0.0794632i	−0.429602	−	0.903018i	$-0.641346\pi$
$47$	0.943574	−	0.544773i	0.137634	−	0.0794632i	0.567236	+	0.823555i	$0.308013\pi$
$48$		0			0
$49$	−0.484555	+	2.74805i	−0.0692222	+	0.392578i
$50$		0			0
$51$	2.56762	+	7.30541i	0.359538	+	1.02296i
$52$		0			0
$53$	−2.73760	+	3.26255i	−0.376039	+	0.448146i	−0.920560	−	0.390602i	$-0.872267\pi$
$53$	−2.73760	+	3.26255i	−0.376039	+	0.448146i	0.544521	+	0.838747i	$0.316711\pi$
$54$		0			0
$55$	1.41508	−	2.02095i	0.190810	−	0.272505i
$56$		0			0
$57$	−1.57873	−	9.57270i	−0.209109	−	1.26794i
$58$		0			0
$59$	0.898184	+	10.2663i	0.116934	+	1.33656i	0.797255	+	0.603643i	$0.206285\pi$
$59$	0.898184	+	10.2663i	0.116934	+	1.33656i	−0.680321	+	0.732914i	$0.738160\pi$
$60$		0			0
$61$	−2.73787	−	5.87138i	−0.350548	−	0.751753i	0.649414	−	0.760435i	$-0.275014\pi$
$61$	−2.73787	−	5.87138i	−0.350548	−	0.751753i	−0.999962	+	0.00868202i	$0.997236\pi$
$62$		0			0
$63$	−3.85098	−	4.80167i	−0.485177	−	0.604953i
$64$		0			0
$65$	−1.50090	+	0.546284i	−0.186164	+	0.0677581i
$66$		0			0
$67$	−4.31473	−	5.14209i	−0.527128	−	0.628207i	0.435123	−	0.900371i	$-0.356705\pi$
$67$	−4.31473	−	5.14209i	−0.527128	−	0.628207i	−0.962251	+	0.272164i	$0.912261\pi$
$68$		0			0
$69$	3.98769	−	2.24373i	0.480061	−	0.270114i
$70$		0			0
$71$	−0.471211	+	0.0830872i	−0.0559224	+	0.00986063i	−0.201539	−	0.979480i	$-0.564594\pi$
$71$	−0.471211	+	0.0830872i	−0.0559224	+	0.00986063i	0.145617	+	0.989341i	$0.453483\pi$
$72$		0			0
$73$		−	10.2572i		−	1.20051i	−0.799808	−	0.600256i	$-0.795065\pi$
$73$		−	10.2572i		−	1.20051i	0.799808	−	0.600256i	$-0.204935\pi$
$74$		0			0
$75$	3.94354	+	5.76696i	0.455361	+	0.665911i
$76$		0			0
$77$	0.292448	+	1.65856i	0.0333276	+	0.189010i
$78$		0			0
$79$	1.33048	−	15.2074i	0.149690	−	1.71097i	−0.435597	−	0.900142i	$-0.643463\pi$
$79$	1.33048	−	15.2074i	0.149690	−	1.71097i	0.585288	−	0.810826i	$-0.300982\pi$
$80$		0			0
$81$	−8.99116	−	0.398884i	−0.999017	−	0.0443204i
$82$		0			0
$83$	−1.15221	−	3.16568i	−0.126472	−	0.347479i	0.860256	−	0.509863i	$-0.170304\pi$
$83$	−1.15221	−	3.16568i	−0.126472	−	0.347479i	−0.986728	+	0.162384i	$0.948082\pi$
$84$		0			0
$85$	11.6369	+	6.71856i	1.26220	+	0.728730i
$86$		0			0
$87$	2.56114	−	4.32461i	0.274583	−	0.463647i
$88$		0			0
$89$	16.7368	−	1.46428i	1.77409	−	0.155213i	0.847381	−	0.530986i	$-0.178178\pi$
$89$	16.7368	−	1.46428i	1.77409	−	0.155213i	0.926712	+	0.375773i	$0.122623\pi$
$90$		0			0
$91$	0.460790	−	0.988167i	0.0483039	−	0.103588i
$92$		0			0
$93$	0.0685405	−	6.18363i	0.00710732	−	0.641213i
$94$		0			0
$95$	−12.8969	−	10.8218i	−1.32319	−	1.11029i
$96$		0			0
$97$	−5.38204	−	1.44211i	−0.546463	−	0.146424i	−0.0249833	−	0.999688i	$-0.507953\pi$
$97$	−5.38204	−	1.44211i	−0.546463	−	0.146424i	−0.521480	+	0.853263i	$0.674620\pi$
$98$		0			0
$99$	2.10480	+	1.27823i	0.211540	+	0.128467i
$100$		0			0
$101$	−8.53934	−	14.7906i	−0.849696	−	1.47172i	−0.881480	−	0.472222i	$-0.843452\pi$
$101$	−8.53934	−	14.7906i	−0.849696	−	1.47172i	0.0317839	−	0.999495i	$-0.489881\pi$
$102$		0			0
$103$	−10.4904	+	2.81090i	−1.03365	+	0.276966i	−0.735480	−	0.677546i	$-0.763043\pi$
$103$	−10.4904	+	2.81090i	−1.03365	+	0.276966i	−0.298171	+	0.954512i	$0.596377\pi$
$104$		0			0
$105$	−10.4975	−	1.97119i	−1.02445	−	0.192369i
$106$		0			0
$107$	−5.85728	+	16.0927i	−0.566244	+	1.55574i	0.244076	+	0.969756i	$0.421515\pi$
$107$	−5.85728	+	16.0927i	−0.566244	+	1.55574i	−0.810320	+	0.585988i	$0.800707\pi$
$108$		0			0
$109$	−0.160749	−	0.229573i	−0.0153969	−	0.0219891i	0.811380	−	0.584519i	$-0.198717\pi$
$109$	−0.160749	−	0.229573i	−0.0153969	−	0.0219891i	−0.826777	+	0.562530i	$0.809828\pi$
$110$		0			0
$111$	1.53660	+	10.4230i	0.145848	+	0.989307i
$112$		0			0
$113$	−11.1943	−	15.9871i	−1.05307	−	1.50394i	−0.851420	−	0.524484i	$-0.824258\pi$
$113$	−11.1943	−	15.9871i	−1.05307	−	1.50394i	−0.201651	−	0.979457i	$-0.564631\pi$
$114$		0			0
$115$	2.71561	−	7.46108i	0.253232	−	0.695750i
$116$		0			0
$117$	−0.641569	−	1.45946i	−0.0593131	−	0.134928i
$118$		0			0
$119$	−8.86009	+	2.37405i	−0.812203	+	0.217629i
$120$		0			0
$121$	5.16311	+	8.94276i	0.469373	+	0.812979i
$122$		0			0
$123$	0.474225	+	1.04713i	0.0427594	+	0.0944161i
$124$		0			0
$125$	−2.80568	−	0.751780i	−0.250948	−	0.0672413i
$126$		0			0
$127$	−1.58109	−	1.32669i	−0.140299	−	0.117725i	0.569937	−	0.821688i	$-0.306967\pi$
$127$	−1.58109	−	1.32669i	−0.140299	−	0.117725i	−0.710236	+	0.703963i	$0.751412\pi$
$128$		0			0
$129$	15.5863	+	0.172762i	1.37230	+	0.0152108i
$130$		0			0
$131$	0.887718	−	1.90372i	0.0775603	−	0.166329i	−0.863704	−	0.504000i	$-0.831861\pi$
$131$	0.887718	−	1.90372i	0.0775603	−	0.166329i	0.941264	+	0.337671i	$0.109639\pi$
$132$		0			0
$133$	11.4489	−	1.00165i	0.992745	−	0.0868540i
$134$		0			0
$135$	−12.2908	+	9.63546i	−1.05783	+	0.829288i
$136$		0			0
$137$	14.0715	+	8.12416i	1.20221	+	0.694094i	0.961045	−	0.276392i	$-0.0891386\pi$
$137$	14.0715	+	8.12416i	1.20221	+	0.694094i	0.241160	+	0.970485i	$0.422472\pi$
$138$		0			0
$139$	6.68166	+	18.3577i	0.566731	+	1.55708i	0.809576	+	0.587015i	$0.199697\pi$
$139$	6.68166	+	18.3577i	0.566731	+	1.55708i	−0.242845	+	0.970065i	$0.578081\pi$
$140$		0			0
$141$	1.81732	+	0.508603i	0.153046	+	0.0428321i
$142$		0			0
$143$	−0.0380183	+	0.434552i	−0.00317925	+	0.0363390i
$144$		0			0
$145$	−1.51451	−	8.58919i	−0.125773	−	0.713294i
$146$		0			0
$147$	−3.98960	+	2.72815i	−0.329057	+	0.225014i
$148$		0			0
$149$		−	9.90807i		−	0.811701i	−0.913940	−	0.405850i	$-0.866975\pi$
$149$		−	9.90807i		−	0.811701i	0.913940	−	0.405850i	$-0.133025\pi$
$150$		0			0
$151$	−15.1398	+	2.66955i	−1.23206	+	0.217245i	−0.751510	−	0.659722i	$-0.770674\pi$
$151$	−15.1398	+	2.66955i	−1.23206	+	0.217245i	−0.480550	+	0.876968i	$0.659563\pi$
$152$		0			0
$153$	−5.93625	+	12.0269i	−0.479917	+	0.972315i
$154$		0			0
$155$	−6.89774	−	8.22041i	−0.554040	−	0.660279i
$156$		0			0
$157$	17.3550	−	6.31672i	1.38508	−	0.504129i	0.461368	−	0.887209i	$-0.347359\pi$
$157$	17.3550	−	6.31672i	1.38508	−	0.504129i	0.923715	+	0.383080i	$0.125137\pi$
$158$		0			0
$159$	−7.35533	+	0.561436i	−0.583316	+	0.0445247i
$160$		0			0
$161$	2.29062	+	4.91225i	0.180526	+	0.387139i
$162$		0			0
$163$	−1.60382	−	18.3318i	−0.125621	−	1.43586i	−0.753451	−	0.657505i	$-0.771612\pi$
$163$	−1.60382	−	18.3318i	−0.125621	−	1.43586i	0.627829	−	0.778351i	$-0.283944\pi$
$164$		0			0
$165$	4.21623	−	0.695342i	0.328233	−	0.0541323i
$166$		0			0
$167$	5.13764	−	7.33732i	0.397563	−	0.567779i	−0.569604	−	0.821919i	$-0.692904\pi$
$167$	5.13764	−	7.33732i	0.397563	−	0.567779i	0.967167	+	0.254140i	$0.0817925\pi$
$168$		0			0
$169$	−8.17471	+	9.74224i	−0.628824	+	0.749403i
$170$		0			0
$171$	9.94135	−	13.5483i	0.760234	−	1.03607i
$172$		0			0
$173$	1.89107	−	10.7248i	0.143776	−	0.815392i	−0.824567	−	0.565765i	$-0.808581\pi$
$173$	1.89107	−	10.7248i	0.143776	−	0.815392i	0.968342	−	0.249627i	$-0.0803080\pi$
$174$		0			0
$175$	−7.16704	+	4.13789i	−0.541777	+	0.312795i
$176$		0			0
$177$	−11.6244	+	13.5456i	−0.873743	+	1.01815i
$178$		0			0
$179$	−10.7982	+	10.7982i	−0.807098	+	0.807098i	−0.984194	−	0.177096i	$-0.943330\pi$
$179$	−10.7982	+	10.7982i	−0.807098	+	0.807098i	0.177096	+	0.984194i	$0.443330\pi$
$180$		0			0
$181$	−13.8429	−	5.03841i	−1.02894	−	0.374502i	−0.228260	−	0.973600i	$-0.573304\pi$
$181$	−13.8429	−	5.03841i	−1.02894	−	0.374502i	−0.800675	+	0.599098i	$0.795526\pi$
$182$		0			0
$183$	3.95438	−	10.5009i	0.292316	−	0.776252i
$184$		0			0
$185$	13.8023	+	11.9891i	1.01477	+	0.881457i
$186$		0			0
$187$	3.00609	−	2.10488i	0.219827	−	0.153924i
$188$		0			0
$189$	1.28174	−	10.5837i	0.0932327	−	0.769853i
$190$		0			0
$191$	7.68038	+	7.68038i	0.555733	+	0.555733i	0.928090	−	0.372357i	$-0.121450\pi$
$191$	7.68038	+	7.68038i	0.555733	+	0.555733i	−0.372357	+	0.928090i	$0.621450\pi$
$192$		0			0
$193$	4.60645	+	17.1915i	0.331579	+	1.23747i	0.907530	+	0.419987i	$0.137965\pi$
$193$	4.60645	+	17.1915i	0.331579	+	1.23747i	−0.575951	+	0.817484i	$0.695368\pi$
$194$		0			0
$195$	−2.49417	−	1.19688i	−0.178611	−	0.0857105i
$196$		0			0
$197$	10.2982	+	1.81585i	0.733714	+	0.129374i	0.528007	−	0.849240i	$-0.322939\pi$
$197$	10.2982	+	1.81585i	0.733714	+	0.129374i	0.205707	+	0.978614i	$0.434051\pi$
$198$		0			0
$199$	−6.45287	+	24.0824i	−0.457432	+	1.70716i	0.223408	+	0.974725i	$0.428282\pi$
$199$	−6.45287	+	24.0824i	−0.457432	+	1.70716i	−0.680839	+	0.732433i	$0.738385\pi$
$200$		0			0
$201$	1.14162	−	11.5703i	0.0805237	−	0.816103i
$202$		0			0
$203$	4.87701	+	3.41492i	0.342299	+	0.239680i
$204$		0			0
$205$	1.80782	+	0.843002i	0.126264	+	0.0588778i
$206$		0			0
$207$	7.60776	+	2.22036i	0.528776	+	0.154325i
$208$		0			0
$209$	−4.16714	+	1.94317i	−0.288247	+	0.134412i
$210$		0			0
$211$	−8.30416	+	14.3832i	−0.571682	+	0.990183i	0.424711	+	0.905329i	$0.360376\pi$
$211$	−8.30416	+	14.3832i	−0.571682	+	0.990183i	−0.996393	+	0.0848537i	$0.972958\pi$
$212$		0			0
$213$	−0.673563	−	0.482847i	−0.0461518	−	0.0330842i
$214$		0			0
$215$	20.7202	−	17.3863i	1.41310	−	1.18573i
$216$		0			0
$217$	7.29746	+	0.638445i	0.495384	+	0.0433405i
$218$		0			0
$219$	12.7009	−	12.4224i	0.858247	−	0.839429i
$220$		0			0
$221$	−2.37581			−0.159815
$222$		0			0
$223$	7.48319			0.501112			0.250556	−	0.968102i	$-0.419387\pi$
$223$	7.48319			0.501112			0.250556	+	0.968102i	$0.419387\pi$
$224$		0			0
$225$	−2.36490	+	11.8674i	−0.157660	+	0.791160i
$226$		0			0
$227$	16.9550	+	1.48337i	1.12534	+	0.0984545i	0.634592	−	0.772847i	$-0.281168\pi$
$227$	16.9550	+	1.48337i	1.12534	+	0.0984545i	0.490748	+	0.871302i	$0.336724\pi$
$228$		0			0
$229$	−5.52665	+	4.63741i	−0.365211	+	0.306449i	−0.806864	−	0.590737i	$-0.798837\pi$
$229$	−5.52665	+	4.63741i	−0.365211	+	0.306449i	0.441652	+	0.897186i	$0.354392\pi$
$230$		0			0
$231$	−1.69952	+	2.37079i	−0.111820	+	0.155987i
$232$		0			0
$233$	−12.7340	+	22.0559i	−0.834231	+	1.44493i	0.0604245	+	0.998173i	$0.480755\pi$
$233$	−12.7340	+	22.0559i	−0.834231	+	1.44493i	−0.894655	+	0.446757i	$0.852579\pi$
$234$		0			0
$235$	2.96791	−	1.38396i	0.193605	−	0.0902796i
$236$		0			0
$237$	20.4418	−	16.7702i	1.32784	−	1.08934i
$238$		0			0
$239$	18.5381	+	8.64444i	1.19913	+	0.559162i	0.916487	−	0.400064i	$-0.131012\pi$
$239$	18.5381	+	8.64444i	1.19913	+	0.559162i	0.282640	+	0.959226i	$0.408790\pi$
$240$		0			0
$241$	7.87365	+	5.51319i	0.507186	+	0.355136i	0.798992	−	0.601342i	$-0.205367\pi$
$241$	7.87365	+	5.51319i	0.507186	+	0.355136i	−0.291805	+	0.956478i	$0.594256\pi$
$242$		0			0
$243$	−10.3952	−	11.6163i	−0.666854	−	0.745188i
$244$		0			0
$245$	−2.17070	+	8.10115i	−0.138681	+	0.517564i
$246$		0			0
$247$	2.93149	+	0.516902i	0.186527	+	0.0328897i
$248$		0			0
$249$	2.52445	−	5.26067i	0.159980	−	0.333381i
$250$		0			0
$251$	4.62723	+	17.2690i	0.292068	+	1.09001i	0.943518	+	0.331321i	$0.107494\pi$
$251$	4.62723	+	17.2690i	0.292068	+	1.09001i	−0.651450	+	0.758692i	$0.725839\pi$
$252$		0			0
$253$	−1.53332	−	1.53332i	−0.0963988	−	0.0963988i
$254$		0			0
$255$	5.77416	+	22.5461i	0.361592	+	1.41189i
$256$		0			0
$257$	−20.7051	+	14.4979i	−1.29155	+	0.904351i	−0.998658	−	0.0517951i	$-0.983506\pi$
$257$	−20.7051	+	14.4979i	−1.29155	+	0.904351i	−0.292890	+	0.956146i	$0.594617\pi$
$258$		0			0
$259$	−12.4494	+	0.875222i	−0.773568	+	0.0543837i
$260$		0			0
$261$	8.45671	−	2.06620i	0.523457	−	0.127895i
$262$		0			0
$263$	9.53968	+	3.47216i	0.588242	+	0.214102i	0.618956	−	0.785426i	$-0.287556\pi$
$263$	9.53968	+	3.47216i	0.588242	+	0.214102i	−0.0307142	+	0.999528i	$0.509778\pi$
$264$		0			0
$265$	−9.05145	+	9.05145i	−0.556026	+	0.556026i
$266$		0			0
$267$	22.0829	+	18.9508i	1.35145	+	1.15977i
$268$		0			0
$269$	8.17337	−	4.71890i	0.498339	−	0.287716i	−0.229688	−	0.973264i	$-0.573771\pi$
$269$	8.17337	−	4.71890i	0.498339	−	0.287716i	0.728027	+	0.685548i	$0.240437\pi$
$270$		0			0
$271$	−0.218445	+	1.23887i	−0.0132696	+	0.0752557i	−0.990723	−	0.135894i	$-0.956609\pi$
$271$	−0.218445	+	1.23887i	−0.0132696	+	0.0752557i	0.977454	+	0.211149i	$0.0677206\pi$
$272$		0			0
$273$	1.78165	−	0.626194i	0.107831	−	0.0378990i
$274$		0			0
$275$	2.12823	−	2.53633i	0.128337	−	0.152946i
$276$		0			0
$277$	−6.08707	+	8.69324i	−0.365737	+	0.522326i	−0.959273	−	0.282481i	$-0.908843\pi$
$277$	−6.08707	+	8.69324i	−0.365737	+	0.522326i	0.593536	+	0.804807i	$0.297731\pi$
$278$		0			0
$279$	7.73985	−	7.40409i	0.463373	−	0.443272i
$280$		0			0
$281$	0.292507	+	3.34337i	0.0174495	+	0.199449i	0.999915	+	0.0130066i	$0.00414024\pi$
$281$	0.292507	+	3.34337i	0.0174495	+	0.199449i	−0.982466	+	0.186442i	$0.940304\pi$
$282$		0			0
$283$	−2.57695	−	5.52629i	−0.153184	−	0.328504i	0.814708	−	0.579872i	$-0.196897\pi$
$283$	−2.57695	−	5.52629i	−0.153184	−	0.328504i	−0.967892	+	0.251368i	$0.919120\pi$
$284$		0			0
$285$	−2.21936	−	29.0757i	−0.131464	−	1.72230i
$286$		0			0
$287$	−1.27954	+	0.465715i	−0.0755289	+	0.0274903i
$288$		0			0
$289$	1.92014	+	2.28833i	0.112949	+	0.134608i
$290$		0			0
$291$	−4.73247	−	8.41082i	−0.277423	−	0.493051i
$292$		0			0
$293$	−25.0104	+	4.41001i	−1.46112	+	0.257635i	−0.847007	−	0.531581i	$-0.821598\pi$
$293$	−25.0104	+	4.41001i	−1.46112	+	0.257635i	−0.614115	+	0.789217i	$0.710487\pi$
$294$		0			0
$295$			30.9741i			1.80338i
$296$		0			0
$297$	0.966347	+	4.15432i	0.0560731	+	0.241058i
$298$		0			0
$299$	0.243777	+	1.38253i	0.0140980	+	0.0799537i
$300$		0			0
$301$	−1.60925	+	18.3938i	−0.0927556	+	1.06020i
$302$		0			0
$303$	7.97238	−	28.4866i	0.458001	−	1.63651i
$304$		0			0
$305$	−6.65957	−	18.2970i	−0.381326	−	1.04768i
$306$		0			0
$307$	1.15252	+	0.665407i	0.0657777	+	0.0379768i	0.532528	−	0.846412i	$-0.321242\pi$
$307$	1.15252	+	0.665407i	0.0657777	+	0.0379768i	−0.466750	+	0.884389i	$0.654575\pi$
$308$		0			0
$309$	−16.1855	−	9.58543i	−0.920759	−	0.545296i
$310$		0			0
$311$	15.8577	−	1.38737i	0.899206	−	0.0786703i	0.371829	−	0.928301i	$-0.378731\pi$
$311$	15.8577	−	1.38737i	0.899206	−	0.0786703i	0.527378	+	0.849631i	$0.323175\pi$
$312$		0			0
$313$	0.139202	−	0.298520i	0.00786818	−	0.0168734i	−0.902334	−	0.431037i	$-0.858148\pi$
$313$	0.139202	−	0.298520i	0.00786818	−	0.0168734i	0.910203	+	0.414163i	$0.135926\pi$
$314$		0			0
$315$	−10.2726	−	15.3857i	−0.578795	−	0.866887i
$316$		0			0
$317$	−8.74100	−	7.33457i	−0.490943	−	0.411950i	0.363421	−	0.931625i	$-0.381609\pi$
$317$	−8.74100	−	7.33457i	−0.490943	−	0.411950i	−0.854364	+	0.519675i	$0.826053\pi$
$318$		0			0
$319$	−2.30078	−	0.616493i	−0.128819	−	0.0345170i
$320$		0			0
$321$	−27.0205	+	12.2371i	−1.50814	+	0.683008i
$322$		0			0
$323$	−12.5212	−	21.6874i	−0.696700	−	1.20672i
$324$		0			0
$325$	−2.07048	+	0.554784i	−0.114850	+	0.0307739i
$326$		0			0
$327$	0.0895853	−	0.477080i	0.00495408	−	0.0263826i
$328$		0			0
$329$	−0.764566	+	2.10063i	−0.0421519	+	0.115811i
$330$		0			0
$331$	6.33413	+	9.04608i	0.348155	+	0.497217i	0.954593	−	0.297914i	$-0.0962908\pi$
$331$	6.33413	+	9.04608i	0.348155	+	0.497217i	−0.606437	+	0.795131i	$0.707402\pi$
$332$		0			0
$333$	−11.0452	+	14.5259i	−0.605276	+	0.796016i
$334$		0			0
$335$	−11.5720	−	16.5265i	−0.632244	−	0.902938i
$336$		0			0
$337$	−4.51437	+	12.4031i	−0.245913	+	0.675641i	0.753913	+	0.656975i	$0.228164\pi$
$337$	−4.51437	+	12.4031i	−0.245913	+	0.675641i	−0.999826	+	0.0186663i	$0.994058\pi$
$338$		0			0
$339$	6.23859	−	33.2232i	0.338834	−	1.80444i
$340$		0			0
$341$	−2.83083	+	0.758519i	−0.153298	+	0.0410761i
$342$		0			0
$343$	−10.0436	−	17.3961i	−0.542305	−	0.939300i
$344$		0			0
$345$	12.5275	−	5.67349i	0.674458	−	0.305451i
$346$		0			0
$347$	19.1680	+	5.13604i	1.02899	+	0.275717i	0.733544	−	0.679642i	$-0.237865\pi$
$347$	19.1680	+	5.13604i	1.02899	+	0.275717i	0.295447	+	0.955359i	$0.404532\pi$
$348$		0			0
$349$	−11.9804	−	10.0527i	−0.641295	−	0.538110i	0.263121	−	0.964763i	$-0.415248\pi$
$349$	−11.9804	−	10.0527i	−0.641295	−	0.538110i	−0.904416	+	0.426653i	$0.859693\pi$
$350$		0			0
$351$	1.03017	−	2.56197i	0.0549866	−	0.136748i
$352$		0			0
$353$	−4.65761	+	9.98827i	−0.247899	+	0.531622i	−0.990401	−	0.138222i	$-0.955861\pi$
$353$	−4.65761	+	9.98827i	−0.247899	+	0.531622i	0.742502	+	0.669844i	$0.233639\pi$
$354$		0			0
$355$	−1.43264	+	0.125340i	−0.0760368	+	0.00665236i
$356$		0			0
$357$	−13.6701	−	8.09575i	−0.723497	−	0.428472i
$358$		0			0
$359$	−24.3763	−	14.0737i	−1.28653	−	0.742780i	−0.308498	−	0.951225i	$-0.599826\pi$
$359$	−24.3763	−	14.0737i	−1.28653	−	0.742780i	−0.978034	+	0.208445i	$0.933160\pi$
$360$		0			0
$361$	4.23296	+	11.6300i	0.222787	+	0.612104i
$362$		0			0
$363$	−4.82031	+	17.2237i	−0.253001	+	0.904011i
$364$		0			0
$365$	2.68692	−	30.7116i	0.140640	−	1.60752i
$366$		0			0
$367$	−5.47520	−	31.0514i	−0.285803	−	1.62087i	−0.702403	−	0.711780i	$-0.747889\pi$
$367$	−5.47520	−	31.0514i	−0.285803	−	1.62087i	0.416600	−	0.909090i	$-0.363222\pi$
$368$		0			0
$369$	−0.722265	+	1.85538i	−0.0375996	+	0.0965870i
$370$		0			0
$371$		−	8.73819i		−	0.453664i
$372$		0			0
$373$	−0.957299	+	0.168798i	−0.0495671	+	0.00874001i	−0.198377	−	0.980126i	$-0.563567\pi$
$373$	−0.957299	+	0.168798i	−0.0495671	+	0.00874001i	0.148810	+	0.988866i	$0.452456\pi$
$374$		0			0
$375$	−2.46706	−	4.38460i	−0.127399	−	0.226420i
$376$		0			0
$377$	0.991231	+	1.18130i	0.0510510	+	0.0608402i
$378$		0			0
$379$	19.0871	−	6.94713i	0.980438	−	0.356850i	0.198427	−	0.980116i	$-0.436417\pi$
$379$	19.0871	−	6.94713i	0.980438	−	0.356850i	0.782010	+	0.623265i	$0.214194\pi$
$380$		0			0
$381$	−0.272082	−	3.56452i	−0.0139392	−	0.182616i
$382$		0			0
$383$	13.1335	+	28.1648i	0.671090	+	1.43916i	0.886545	+	0.462643i	$0.153099\pi$
$383$	13.1335	+	28.1648i	0.671090	+	1.43916i	−0.215455	+	0.976514i	$0.569123\pi$
$384$		0			0
$385$	0.441169	+	5.04259i	0.0224841	+	0.256994i
$386$		0			0
$387$	18.6626	+	19.5089i	0.948672	+	0.991692i
$388$		0			0
$389$	−5.17340	+	7.38838i	−0.262302	+	0.374606i	−0.928602	−	0.371078i	$-0.878988\pi$
$389$	−5.17340	+	7.38838i	−0.262302	+	0.374606i	0.666300	+	0.745684i	$0.267877\pi$
$390$		0			0
$391$	7.59154	−	9.04724i	0.383920	−	0.457539i
$392$		0			0
$393$	3.43238	−	1.20637i	0.173141	−	0.0608534i
$394$		0			0
$395$	7.96730	−	45.1848i	0.400878	−	2.27349i
$396$		0			0
$397$	11.8431	−	6.83764i	0.594390	−	0.343171i	−0.172441	−	0.985020i	$-0.555165\pi$
$397$	11.8431	−	6.83764i	0.594390	−	0.343171i	0.766832	+	0.641848i	$0.221832\pi$
$398$		0			0
$399$	15.1060	+	12.9634i	0.756245	+	0.648984i
$400$		0			0
$401$	−17.3330	+	17.3330i	−0.865567	+	0.865567i	−0.991978	−	0.126411i	$-0.959654\pi$
$401$	−17.3330	+	17.3330i	−0.865567	+	0.865567i	0.126411	+	0.991978i	$0.459654\pi$
$402$		0			0
$403$	1.78292	+	0.648930i	0.0888136	+	0.0323255i
$404$		0			0
$405$	−26.8164	−	3.54959i	−1.33252	−	0.176381i
$406$		0			0
$407$	4.56057	−	2.03254i	0.226059	−	0.100749i
$408$		0			0
$409$	−11.8091	+	8.26882i	−0.583923	+	0.408867i	−0.827869	−	0.560922i	$-0.810447\pi$
$409$	−11.8091	+	8.26882i	−0.583923	+	0.408867i	0.243946	+	0.969789i	$0.421558\pi$
$410$		0			0
$411$	6.98218	+	27.2630i	0.344406	+	1.34479i
$412$		0			0
$413$	−14.9511	−	14.9511i	−0.735695	−	0.735695i
$414$		0			0
$415$	−2.62064	−	9.78037i	−0.128642	−	0.480100i
$416$		0			0
$417$	−14.6392	+	30.5065i	−0.716885	+	1.49391i
$418$		0			0
$419$	−20.8797	−	3.68166i	−1.02004	−	0.179861i	−0.361474	−	0.932382i	$-0.617726\pi$
$419$	−20.8797	−	3.68166i	−1.02004	−	0.179861i	−0.658568	+	0.752522i	$0.728837\pi$
$420$		0			0
$421$	1.30622	−	4.87487i	0.0636611	−	0.237586i	−0.926763	−	0.375647i	$-0.877420\pi$
$421$	1.30622	−	4.87487i	0.0636611	−	0.237586i	0.990424	+	0.138061i	$0.0440870\pi$
$422$		0			0
$423$	1.57117	+	2.86625i	0.0763930	+	0.139362i
$424$		0			0
$425$	14.7717	+	10.3433i	0.716534	+	0.501723i
$426$		0			0
$427$	12.0464	+	5.61734i	0.582967	+	0.271842i
$428$		0			0
$429$	−0.584125	+	0.479207i	−0.0282018	+	0.0231364i
$430$		0			0
$431$	1.41928	−	0.661823i	0.0683645	−	0.0318789i	−0.388135	−	0.921602i	$-0.626881\pi$
$431$	1.41928	−	0.661823i	0.0683645	−	0.0318789i	0.456500	+	0.889723i	$0.349103\pi$
$432$		0			0
$433$	15.4921	−	26.8332i	0.744505	−	1.28952i	−0.205921	−	0.978569i	$-0.566019\pi$
$433$	15.4921	−	26.8332i	0.744505	−	1.28952i	0.950426	−	0.310951i	$-0.100648\pi$
$434$		0			0
$435$	8.80131	−	12.2777i	0.421990	−	0.588669i
$436$		0			0
$437$	−11.3355	+	9.51163i	−0.542251	+	0.455003i
$438$		0			0
$439$	−10.9791	−	0.960551i	−0.524006	−	0.0458446i	−0.177916	−	0.984046i	$-0.556935\pi$
$439$	−10.9791	−	0.960551i	−0.524006	−	0.0458446i	−0.346090	+	0.938201i	$0.612491\pi$
$440$		0			0
$441$	−8.20990	−	1.63605i	−0.390948	−	0.0779069i
$442$		0			0
$443$	−10.6373			−0.505392			−0.252696	−	0.967546i	$-0.581317\pi$
$443$	−10.6373			−0.505392			−0.252696	+	0.967546i	$0.581317\pi$
$444$		0			0
$445$	50.4960			2.39374
$446$		0			0
$447$	12.2686	−	11.9996i	0.580285	−	0.567562i
$448$		0			0
$449$	14.1791	+	1.24051i	0.669153	+	0.0585433i	0.416669	−	0.909058i	$-0.363197\pi$
$449$	14.1791	+	1.24051i	0.669153	+	0.0585433i	0.252483	+	0.967601i	$0.418753\pi$
$450$		0			0
$451$	0.417316	−	0.350170i	0.0196506	−	0.0164888i
$452$		0			0
$453$	−21.6413	−	15.5137i	−1.01680	−	0.728896i
$454$		0			0
$455$	1.63853	−	2.83802i	0.0768155	−	0.133048i
$456$		0			0
$457$	−11.9884	+	5.59030i	−0.560795	+	0.261503i	−0.682281	−	0.731090i	$-0.739012\pi$
$457$	−11.9884	+	5.59030i	−0.560795	+	0.261503i	0.121486	+	0.992593i	$0.461234\pi$
$458$		0			0
$459$	−22.0816	+	7.21517i	−1.03068	+	0.336775i
$460$		0			0
$461$	30.7821	+	14.3539i	1.43366	+	0.668529i	0.975431	−	0.220304i	$-0.0707048\pi$
$461$	30.7821	+	14.3539i	1.43366	+	0.668529i	0.458233	+	0.888832i	$0.348483\pi$
$462$		0			0
$463$	7.93697	+	5.55752i	0.368862	+	0.258280i	0.743281	−	0.668980i	$-0.233269\pi$
$463$	7.93697	+	5.55752i	0.368862	+	0.258280i	−0.374418	+	0.927260i	$0.622158\pi$
$464$		0			0
$465$	1.82505	−	18.4968i	0.0846347	−	0.857768i
$466$		0			0
$467$	−2.20083	+	8.21360i	−0.101842	+	0.380080i	−0.997968	−	0.0637204i	$-0.979703\pi$
$467$	−2.20083	+	8.21360i	−0.101842	+	0.380080i	0.896126	+	0.443800i	$0.146370\pi$
$468$		0			0
$469$	13.5630	+	2.39152i	0.626281	+	0.110430i
$470$		0			0
$471$	28.8403	+	13.8396i	1.32889	+	0.637697i
$472$		0			0
$473$	−1.91190	−	7.13533i	−0.0879095	−	0.328083i
$474$		0			0
$475$	−15.9763	−	15.9763i	−0.733045	−	0.733045i
$476$		0			0
$477$	−9.60320	−	8.42774i	−0.439700	−	0.385880i
$478$		0			0
$479$	−17.5604	+	12.2959i	−0.802357	+	0.561816i	−0.901259	−	0.433281i	$-0.857356\pi$
$479$	−17.5604	+	12.2959i	−0.802357	+	0.561816i	0.0989023	+	0.995097i	$0.468467\pi$
$480$		0			0
$481$	−3.17333	−	0.615602i	−0.144691	−	0.0280691i
$482$		0			0
$483$	−3.30840	+	8.78554i	−0.150538	+	0.399756i
$484$		0			0
$485$	−15.7369	−	5.72776i	−0.714575	−	0.260084i
$486$		0			0
$487$	−10.7631	+	10.7631i	−0.487723	+	0.487723i	−0.907587	−	0.419864i	$-0.862078\pi$
$487$	−10.7631	+	10.7631i	−0.487723	+	0.487723i	0.419864	+	0.907587i	$0.362078\pi$
$488$		0			0
$489$	20.7568	−	24.1874i	0.938656	−	1.09379i
$490$		0			0
$491$	4.50686	−	2.60204i	0.203392	−	0.117428i	−0.394845	−	0.918748i	$-0.629202\pi$
$491$	4.50686	−	2.60204i	0.203392	−	0.117428i	0.598237	+	0.801320i	$0.295868\pi$
$492$		0			0
$493$	2.25277	−	12.7761i	0.101460	−	0.575407i
$494$		0			0
$495$	5.96726	+	4.37860i	0.268208	+	0.196803i
$496$		0			0
$497$	0.631029	−	0.752031i	0.0283055	−	0.0337332i
$498$		0			0
$499$	−5.77465	+	8.24705i	−0.258509	+	0.369189i	−0.927336	−	0.374229i	$-0.877908\pi$
$499$	−5.77465	+	8.24705i	−0.258509	+	0.369189i	0.668828	+	0.743417i	$0.266796\pi$
$500$		0			0
$501$	15.3076	−	2.52453i	0.683892	−	0.112788i
$502$		0			0
$503$	−1.91601	−	21.9001i	−0.0854307	−	0.976478i	−0.911062	−	0.412268i	$-0.864737\pi$
$503$	−1.91601	−	21.9001i	−0.0854307	−	0.976478i	0.825632	−	0.564209i	$-0.190819\pi$
$504$		0			0
$505$	−21.6936	−	46.5222i	−0.965354	−	2.07021i
$506$		0			0
$507$	−21.9636	+	1.67649i	−0.975439	+	0.0744557i
$508$		0			0
$509$	22.0861	−	8.03868i	0.978949	−	0.356308i	0.197517	−	0.980299i	$-0.436712\pi$
$509$	22.0861	−	8.03868i	0.978949	−	0.356308i	0.781431	+	0.623991i	$0.214490\pi$
$510$		0			0
$511$	13.5274	+	16.1213i	0.598416	+	0.713165i
$512$		0			0
$513$	28.8160	−	4.09848i	1.27226	−	0.180953i
$514$		0			0
$515$	−32.1463	+	5.66825i	−1.41653	+	0.249773i
$516$		0			0
$517$		−	0.894347i		−	0.0393333i
$518$		0			0
$519$	15.5702	−	10.6472i	0.683456	−	0.467358i
$520$		0			0
$521$	7.15095	+	40.5551i	0.313289	+	1.77675i	0.581658	+	0.813434i	$0.302404\pi$
$521$	7.15095	+	40.5551i	0.313289	+	1.77675i	−0.268369	+	0.963316i	$0.586485\pi$
$522$		0			0
$523$	2.61732	−	29.9161i	0.114447	−	1.30814i	−0.694173	−	0.719808i	$-0.744230\pi$
$523$	2.61732	−	29.9161i	0.114447	−	1.30814i	0.808620	−	0.588331i	$-0.200215\pi$
$524$		0			0
$525$	−13.8037	−	3.86316i	−0.602442	−	0.168602i
$526$		0			0
$527$	−5.45930	−	14.9993i	−0.237811	−	0.653380i
$528$		0			0
$529$	13.8749	+	8.01067i	0.603256	+	0.348290i
$530$		0			0
$531$	−30.8510	+	2.01121i	−1.33882	+	0.0872792i
$532$		0			0
$533$	−0.351343	+	0.0307385i	−0.0152183	+	0.00133143i
$534$		0			0
$535$	−21.7532	+	46.6498i	−0.940471	+	2.01685i
$536$		0			0
$537$	−26.4485	−	0.293161i	−1.14134	−	0.0126508i
$538$		0			0
$539$	1.75464	+	1.47232i	0.0755777	+	0.0634172i
$540$		0			0
$541$	−33.7425	−	9.04127i	−1.45070	−	0.388715i	−0.554435	−	0.832227i	$-0.687066\pi$
$541$	−33.7425	−	9.04127i	−1.45070	−	0.388715i	−0.896268	+	0.443512i	$0.853732\pi$
$542$		0			0
$543$	−10.5263	−	23.2429i	−0.451727	−	0.997448i
$544$		0			0
$545$	−0.421168	−	0.729485i	−0.0180409	−	0.0312477i
$546$		0			0
$547$	27.5734	−	7.38827i	1.17895	−	0.315900i	0.384442	−	0.923149i	$-0.374394\pi$
$547$	27.5734	−	7.38827i	1.17895	−	0.315900i	0.794511	+	0.607249i	$0.207727\pi$
$548$		0			0
$549$	17.7919	−	7.82116i	0.759338	−	0.333799i
$550$		0			0
$551$	−5.55935	+	15.2742i	−0.236836	+	0.650702i
$552$		0			0
$553$	17.9647	+	25.6563i	0.763938	+	1.09102i
$554$		0			0
$555$	1.87046	+	31.6106i	0.0793967	+	1.34179i
$556$		0			0
$557$	−4.17484	−	5.96229i	−0.176894	−	0.252630i	0.720908	−	0.693031i	$-0.243725\pi$
$557$	−4.17484	−	5.96229i	−0.176894	−	0.252630i	−0.897801	+	0.440401i	$0.854836\pi$
$558$		0			0
$559$	−1.63568	+	4.49398i	−0.0691817	+	0.190075i
$560$		0			0
$561$	6.24702	+	1.17305i	0.263749	+	0.0495263i
$562$		0			0
$563$	−4.91180	+	1.31611i	−0.207008	+	0.0554676i	−0.360833	−	0.932631i	$-0.617507\pi$
$563$	−4.91180	+	1.31611i	−0.207008	+	0.0554676i	0.153825	+	0.988098i	$0.450841\pi$
$564$		0			0
$565$	−29.3296	−	50.8003i	−1.23390	−	2.13718i
$566$		0			0
$567$	14.6575	−	11.2308i	0.615559	−	0.471649i
$568$		0			0
$569$	9.84441	+	2.63780i	0.412699	+	0.110582i	0.459194	−	0.888336i	$-0.348138\pi$
$569$	9.84441	+	2.63780i	0.412699	+	0.110582i	−0.0464945	+	0.998919i	$0.514805\pi$
$570$		0			0
$571$	6.38632	+	5.35876i	0.267259	+	0.224257i	0.766562	−	0.642171i	$-0.221966\pi$
$571$	6.38632	+	5.35876i	0.267259	+	0.224257i	−0.499302	+	0.866428i	$0.666410\pi$
$572$		0			0
$573$	−0.208514	+	18.8119i	−0.00871081	+	0.785877i
$574$		0			0
$575$	4.50324	−	9.65724i	0.187798	−	0.402735i
$576$		0			0
$577$	−32.9324	+	2.88121i	−1.37099	+	0.119946i	−0.748737	−	0.662867i	$-0.769340\pi$
$577$	−32.9324	+	2.88121i	−1.37099	+	0.119946i	−0.622257	+	0.782813i	$0.713784\pi$
$578$		0			0
$579$	−15.7084	+	26.5245i	−0.652820	+	1.10232i
$580$		0			0
$581$	5.98592	+	3.45597i	0.248338	+	0.143378i
$582$		0			0
$583$	1.19568	+	3.28511i	0.0495201	+	0.136055i
$584$		0			0
$585$	−1.53864	−	4.53793i	−0.0636150	−	0.187620i
$586$		0			0
$587$	1.11621	−	12.7583i	0.0460709	−	0.526593i	−0.937734	−	0.347353i	$-0.887081\pi$
$587$	1.11621	−	12.7583i	0.0460709	−	0.526593i	0.983805	−	0.179240i	$-0.0573639\pi$
$588$		0			0
$589$	3.47281	+	19.6953i	0.143095	+	0.811530i
$590$		0			0
$591$	10.2236	+	14.9508i	0.420543	+	0.614994i
$592$		0			0
$593$		−	43.3195i		−	1.77892i	−0.457016	−	0.889459i	$-0.651082\pi$
$593$		−	43.3195i		−	1.77892i	0.457016	−	0.889459i	$-0.348918\pi$
$594$		0			0
$595$	−27.1504	+	4.78734i	−1.11306	+	0.196262i
$596$		0			0
$597$	−37.6350	+	21.1759i	−1.54030	+	0.866671i
$598$		0			0
$599$	27.5928	+	32.8839i	1.12741	+	1.34360i	0.931823	+	0.362912i	$0.118217\pi$
$599$	27.5928	+	32.8839i	1.12741	+	1.34360i	0.195589	+	0.980686i	$0.437338\pi$
$600$		0			0
$601$	−17.1544	+	6.24370i	−0.699744	+	0.254686i	−0.667301	−	0.744788i	$-0.732551\pi$
$601$	−17.1544	+	6.24370i	−0.699744	+	0.254686i	−0.0324422	+	0.999474i	$0.510328\pi$
$602$		0			0
$603$	15.7094	−	12.5991i	0.639736	−	0.513074i
$604$		0			0
$605$	13.1165	+	28.1285i	0.533263	+	1.14359i
$606$		0			0
$607$	3.61651	+	41.3369i	0.146790	+	1.67781i	0.610648	+	0.791902i	$0.290909\pi$
$607$	3.61651	+	41.3369i	0.146790	+	1.67781i	−0.463858	+	0.885909i	$0.653535\pi$
$608$		0			0
$609$	1.67802	+	10.1747i	0.0679968	+	0.412301i
$610$		0			0
$611$	−0.332103	+	0.474292i	−0.0134355	+	0.0191878i
$612$		0			0
$613$	15.7411	−	18.7595i	0.635778	−	0.757691i	−0.347919	−	0.937525i	$-0.613112\pi$
$613$	15.7411	−	18.7595i	0.635778	−	0.757691i	0.983697	+	0.179834i	$0.0575560\pi$
$614$		0			0
$615$	1.14560	+	3.25948i	0.0461952	+	0.131435i
$616$		0			0
$617$	1.14415	−	6.48878i	0.0460616	−	0.261229i	−0.953077	−	0.302728i	$-0.902102\pi$
$617$	1.14415	−	6.48878i	0.0460616	−	0.261229i	0.999139	+	0.0414999i	$0.0132136\pi$
$618$		0			0
$619$	19.4010	−	11.2012i	0.779793	−	0.450214i	−0.0565636	−	0.998399i	$-0.518014\pi$
$619$	19.4010	−	11.2012i	0.779793	−	0.450214i	0.836357	+	0.548185i	$0.184681\pi$
$620$		0			0
$621$	6.46438	+	12.1093i	0.259407	+	0.485930i
$622$		0			0
$623$	−24.3742	+	24.3742i	−0.976531	+	0.976531i
$624$		0			0
$625$	−27.1554	−	9.88374i	−1.08621	−	0.395350i
$626$		0			0
$627$	−7.45292	−	2.80657i	−0.297641	−	0.112084i
$628$		0			0
$629$	13.1929	+	23.7797i	0.526036	+	0.948158i
$630$		0			0
$631$	24.9886	−	17.4972i	0.994780	−	0.696552i	0.0416557	−	0.999132i	$-0.486737\pi$
$631$	24.9886	−	17.4972i	0.994780	−	0.696552i	0.953124	+	0.302580i	$0.0978478\pi$
$632$		0			0
$633$	−27.8671	+	7.13688i	−1.10762	+	0.283666i
$634$		0			0
$635$	−4.38649	−	4.38649i	−0.174073	−	0.174073i
$636$		0			0
$637$	−0.383801	−	1.43236i	−0.0152067	−	0.0567523i
$638$		0			0
$639$	−0.217866	−	1.41881i	−0.00861865	−	0.0561273i
$640$		0			0
$641$	4.52602	+	0.798059i	0.178767	+	0.0315214i	0.262315	−	0.964982i	$-0.415514\pi$
$641$	4.52602	+	0.798059i	0.178767	+	0.0315214i	−0.0835480	+	0.996504i	$0.526625\pi$
$642$		0			0
$643$	6.56104	−	24.4861i	0.258742	−	0.965639i	−0.707228	−	0.706986i	$-0.750055\pi$
$643$	6.56104	−	24.4861i	0.258742	−	0.965639i	0.965970	−	0.258653i	$-0.0832788\pi$
$644$		0			0
$645$	46.6225	+	4.60018i	1.83576	+	0.181132i
$646$		0			0
$647$	−6.04811	−	4.23493i	−0.237776	−	0.166492i	0.448615	−	0.893725i	$-0.351917\pi$
$647$	−6.04811	−	4.23493i	−0.237776	−	0.166492i	−0.686391	+	0.727232i	$0.740806\pi$
$648$		0			0
$649$	7.66665	+	3.57502i	0.300943	+	0.140332i
$650$		0			0
$651$	8.04737	+	9.80926i	0.315401	+	0.384455i
$652$		0			0
$653$	−28.7466	+	13.4047i	−1.12494	+	0.524568i	−0.893851	−	0.448364i	$-0.852007\pi$
$653$	−28.7466	+	13.4047i	−1.12494	+	0.524568i	−0.231090	+	0.972932i	$0.574229\pi$
$654$		0			0
$655$	3.15665	−	5.46748i	0.123341	−	0.213632i
$656$		0			0
$657$	30.7640	+	0.682071i	1.20022	+	0.0266101i
$658$		0			0
$659$	24.4178	−	20.4890i	0.951182	−	0.798137i	−0.0283140	−	0.999599i	$-0.509014\pi$
$659$	24.4178	−	20.4890i	0.951182	−	0.798137i	0.979496	+	0.201462i	$0.0645694\pi$
$660$		0			0
$661$	22.1606	+	1.93880i	0.861946	+	0.0754105i	0.509550	−	0.860441i	$-0.329812\pi$
$661$	22.1606	+	1.93880i	0.861946	+	0.0754105i	0.352395	+	0.935851i	$0.385367\pi$
$662$		0			0
$663$	−2.87734	−	2.94184i	−0.111747	−	0.114252i
$664$		0			0
$665$	34.5422			1.33949
$666$		0			0
$667$	−7.66579			−0.296821
$668$		0			0
$669$	9.06286	+	9.26602i	0.350390	+	0.358245i
$670$		0			0
$671$	−5.29748	−	0.463469i	−0.204507	−	0.0178920i
$672$		0			0
$673$	11.9739	−	10.0473i	0.461561	−	0.387295i	−0.382144	−	0.924103i	$-0.624814\pi$
$673$	11.9739	−	10.0473i	0.461561	−	0.387295i	0.843705	+	0.536807i	$0.180370\pi$
$674$		0			0
$675$	−17.5589	+	11.4442i	−0.675841	+	0.440489i
$676$		0			0
$677$	−0.733041	+	1.26966i	−0.0281730	+	0.0487971i	−0.879768	−	0.475403i	$-0.842302\pi$
$677$	−0.733041	+	1.26966i	−0.0281730	+	0.0487971i	0.851595	+	0.524200i	$0.175636\pi$
$678$		0			0
$679$	10.3609	−	4.83136i	0.397615	−	0.185411i
$680$		0			0
$681$	18.6973	+	22.7909i	0.716482	+	0.873348i
$682$		0			0
$683$	21.4712	+	10.0122i	0.821572	+	0.383105i	0.787500	−	0.616314i	$-0.211375\pi$
$683$	21.4712	+	10.0122i	0.821572	+	0.383105i	0.0340715	+	0.999419i	$0.489153\pi$
$684$		0			0
$685$	40.0040	+	28.0111i	1.52847	+	1.07025i
$686$		0			0
$687$	−12.4355	−	1.22700i	−0.474446	−	0.0468129i
$688$		0			0
$689$	0.585782	−	2.18617i	0.0223165	−	0.0832863i
$690$		0			0
$691$	7.36540	+	1.29872i	0.280193	+	0.0494056i	0.311979	−	0.950089i	$-0.399008\pi$
$691$	7.36540	+	1.29872i	0.280193	+	0.0494056i	−0.0317856	+	0.999495i	$0.510119\pi$
$692$		0			0
$693$	−4.99390	+	0.766841i	−0.189702	+	0.0291299i
$694$		0			0
$695$	15.1970	+	56.7161i	0.576456	+	2.15136i
$696$		0			0
$697$	2.09803	+	2.09803i	0.0794685	+	0.0794685i
$698$		0			0
$699$	−42.7326	+	10.9440i	−1.61630	+	0.413941i
$700$		0			0
$701$	25.2999	−	17.7152i	0.955563	−	0.669092i	0.0118748	−	0.999929i	$-0.496220\pi$
$701$	25.2999	−	17.7152i	0.955563	−	0.669092i	0.943688	+	0.330837i	$0.107331\pi$
$702$		0			0
$703$	−11.1049	−	32.2119i	−0.418830	−	1.21489i
$704$		0			0
$705$	5.30810	+	1.99889i	0.199915	+	0.0752826i
$706$		0			0
$707$	32.9275	+	11.9846i	1.23836	+	0.450728i
$708$		0			0
$709$	−9.93812	+	9.93812i	−0.373234	+	0.373234i	−0.868654	−	0.495420i	$-0.835014\pi$
$709$	−9.93812	+	9.93812i	−0.373234	+	0.373234i	0.495420	+	0.868654i	$0.335014\pi$
$710$		0			0
$711$	45.5226	+	5.00169i	1.70723	+	0.187578i
$712$		0			0
$713$	−8.16820	+	4.71591i	−0.305901	+	0.176612i
$714$		0			0
$715$	−0.227666	+	1.29116i	−0.00851421	+	0.0482865i
$716$		0			0
$717$	11.7474	+	33.4239i	0.438716	+	1.24824i
$718$		0			0
$719$	−31.4445	+	37.4740i	−1.17268	+	1.39755i	−0.272429	+	0.962176i	$0.587827\pi$
$719$	−31.4445	+	37.4740i	−1.17268	+	1.39755i	−0.900252	+	0.435370i	$0.856618\pi$
$720$		0			0
$721$	12.7808	−	18.2529i	0.475982	−	0.679773i
$722$		0			0
$723$	2.70906	+	16.4265i	0.100751	+	0.610908i
$724$		0			0
$725$	−1.02014	−	11.6602i	−0.0378869	−	0.433049i
$726$		0			0
$727$	−0.0465379	−	0.0998008i	−0.00172600	−	0.00370141i	0.905443	−	0.424468i	$-0.139539\pi$
$727$	−0.0465379	−	0.0998008i	−0.00172600	−	0.00370141i	−0.907169	+	0.420767i	$0.861761\pi$
$728$		0			0
$729$	1.79424	−	26.9403i	0.0664534	−	0.997790i
$730$		0			0
$731$	37.8069	−	13.7606i	1.39834	−	0.508954i
$732$		0			0
$733$	−1.53203	−	1.82580i	−0.0565867	−	0.0674374i	0.737009	−	0.675883i	$-0.236238\pi$
$733$	−1.53203	−	1.82580i	−0.0565867	−	0.0674374i	−0.793595	+	0.608446i	$0.791793\pi$
$734$		0			0
$735$	−12.6601	+	7.12341i	−0.466976	+	0.262751i
$736$		0			0
$737$	−5.42623	+	0.956791i	−0.199878	+	0.0352438i
$738$		0			0
$739$			20.5046i			0.754275i	0.926157	+	0.377137i	$0.123092\pi$
$739$			20.5046i			0.754275i	−0.926157	+	0.377137i	$0.876908\pi$
$740$		0			0
$741$	2.91027	+	4.25592i	0.106911	+	0.156345i
$742$		0			0
$743$	−4.98791	−	28.2878i	−0.182989	−	1.03778i	−0.928512	−	0.371301i	$-0.878912\pi$
$743$	−4.98791	−	28.2878i	−0.182989	−	1.03778i	0.745524	−	0.666479i	$-0.232199\pi$
$744$		0			0
$745$	2.59546	−	29.6663i	0.0950905	−	1.08689i
$746$		0			0
$747$	9.57134	−	3.24529i	0.350197	−	0.118739i
$748$		0			0
$749$	−12.0175	−	33.0178i	−0.439110	−	1.20644i
$750$		0			0
$751$	−26.5841	−	15.3484i	−0.970069	−	0.560070i	−0.0708118	−	0.997490i	$-0.522559\pi$
$751$	−26.5841	−	15.3484i	−0.970069	−	0.560070i	−0.899257	+	0.437420i	$0.855892\pi$
$752$		0			0
$753$	−15.7793	+	26.6441i	−0.575029	+	0.970965i
$754$		0			0
$755$	−46.0302	+	4.02712i	−1.67521	+	0.146562i
$756$		0			0
$757$	−0.292104	+	0.626420i	−0.0106167	+	0.0227676i	−0.911545	−	0.411201i	$-0.865109\pi$
$757$	−0.292104	+	0.626420i	−0.0106167	+	0.0227676i	0.900928	+	0.433969i	$0.142887\pi$
$758$		0			0
$759$	0.0416279	−	3.75561i	0.00151100	−	0.136320i
$760$		0			0
$761$	23.9478	+	20.0946i	0.868108	+	0.728429i	0.963699	−	0.266992i	$-0.0860297\pi$
$761$	23.9478	+	20.0946i	0.868108	+	0.728429i	−0.0955911	+	0.995421i	$0.530474\pi$
$762$		0			0
$763$	0.555415	+	0.148823i	0.0201074	+	0.00538776i
$764$		0			0
$765$	−20.9245	+	34.4553i	−0.756528	+	1.24573i
$766$		0			0
$767$	−2.73827	−	4.74282i	−0.0988731	−	0.171253i
$768$		0			0
$769$	−42.5558	+	11.4028i	−1.53460	+	0.411195i	−0.924516	−	0.381142i	$-0.875531\pi$
$769$	−42.5558	+	11.4028i	−1.53460	+	0.411195i	−0.610084	+	0.792337i	$0.708864\pi$
$770$		0			0
$771$	−43.0277	−	8.07966i	−1.54960	−	0.290982i
$772$		0			0
$773$	13.2483	−	36.3993i	0.476506	−	1.30919i	−0.435933	−	0.899979i	$-0.643582\pi$
$773$	13.2483	−	36.3993i	0.476506	−	1.30919i	0.912439	−	0.409212i	$-0.134196\pi$
$774$		0			0
$775$	−8.26022	−	11.7968i	−0.296716	−	0.423754i
$776$		0			0
$777$	−16.1612	−	14.3554i	−0.579778	−	0.514998i
$778$		0			0
$779$	−2.13227	−	3.04520i	−0.0763966	−	0.109106i
$780$		0			0
$781$	−0.134331	+	0.369071i	−0.00480674	+	0.0132064i
$782$		0			0
$783$	12.8003	+	7.96911i	0.457447	+	0.284793i
$784$		0			0
$785$	53.6184	−	14.3670i	1.91372	−	0.512780i
$786$		0			0
$787$	−0.833331	−	1.44337i	−0.0297051	−	0.0514507i	0.850791	−	0.525505i	$-0.176123\pi$
$787$	−0.833331	−	1.44337i	−0.0297051	−	0.0514507i	−0.880496	+	0.474054i	$0.842790\pi$
$788$		0			0
$789$	7.25408	+	16.0176i	0.258252	+	0.570240i
$790$		0			0
$791$	38.6783	+	10.3638i	1.37524	+	0.368495i
$792$		0			0
$793$	2.63727	+	2.21293i	0.0936522	+	0.0785835i
$794$		0			0
$795$	−22.1701	−	0.245737i	−0.786291	−	0.00871540i
$796$		0			0
$797$	−14.4621	+	31.0141i	−0.512274	+	1.09857i	0.464749	+	0.885442i	$0.346144\pi$
$797$	−14.4621	+	31.0141i	−0.512274	+	1.09857i	−0.977023	+	0.213133i	$0.931633\pi$
$798$		0			0
$799$	4.85250	−	0.424539i	0.171669	−	0.0150191i
$800$		0			0
$801$	3.27881	+	50.2953i	0.115851	+	1.77710i
$802$		0			0
$803$	−7.29154	−	4.20977i	−0.257313	−	0.148560i
$804$		0			0
$805$	5.57168	+	15.3081i	0.196376	+	0.539538i
$806$		0			0
$807$	15.7419	+	4.40559i	0.554140	+	0.155084i
$808$		0			0
$809$	3.02028	−	34.5220i	0.106187	−	1.21373i	−0.736919	−	0.675981i	$-0.763720\pi$
$809$	3.02028	−	34.5220i	0.106187	−	1.21373i	0.843107	−	0.537747i	$-0.180724\pi$
$810$		0			0
$811$	−5.52768	−	31.3490i	−0.194103	−	1.10081i	−0.913691	−	0.406411i	$-0.866780\pi$
$811$	−5.52768	−	31.3490i	−0.194103	−	1.10081i	0.719588	−	0.694402i	$-0.244331\pi$
$812$		0			0
$813$	−1.79858	+	1.22990i	−0.0630788	+	0.0431343i
$814$		0			0
$815$		−	55.3083i		−	1.93737i
$816$		0			0
$817$	−49.6434	+	8.75348i	−1.73680	+	0.306245i
$818$		0			0
$819$	2.93313	+	1.44774i	0.102492	+	0.0505881i
$820$		0			0
$821$	−17.3014	−	20.6191i	−0.603824	−	0.719610i	0.374375	−	0.927277i	$-0.377857\pi$
$821$	−17.3014	−	20.6191i	−0.603824	−	0.719610i	−0.978199	+	0.207667i	$0.933413\pi$
$822$		0			0
$823$	31.8100	−	11.5779i	1.10883	−	0.403580i	0.278265	−	0.960504i	$-0.410241\pi$
$823$	31.8100	−	11.5779i	1.10883	−	0.403580i	0.830563	+	0.556924i	$0.188019\pi$
$824$		0			0
$825$	5.71809	−	0.436464i	0.199078	−	0.0151957i
$826$		0			0
$827$	−1.41813	−	3.04118i	−0.0493131	−	0.105752i	0.880107	−	0.474774i	$-0.157470\pi$
$827$	−1.41813	−	3.04118i	−0.0493131	−	0.105752i	−0.929421	+	0.369022i	$0.879693\pi$
$828$		0			0
$829$	1.96317	+	22.4392i	0.0681838	+	0.779345i	0.950912	+	0.309461i	$0.100149\pi$
$829$	1.96317	+	22.4392i	0.0681838	+	0.779345i	−0.882728	+	0.469884i	$0.844296\pi$
$830$		0			0
$831$	−18.1364	+	2.99106i	−0.629144	+	0.103759i
$832$		0			0
$833$	−7.15551	+	10.2191i	−0.247924	+	0.354072i
$834$		0			0
$835$	17.3049	−	20.6232i	0.598862	−	0.713696i
$836$		0			0
$837$	18.5418	+	0.616764i	0.640897	+	0.0213185i
$838$		0			0
$839$	−2.80818	+	15.9260i	−0.0969492	+	0.549826i	0.897183	+	0.441658i	$0.145610\pi$
$839$	−2.80818	+	15.9260i	−0.0969492	+	0.549826i	−0.994133	+	0.108168i	$0.965502\pi$
$840$		0			0
$841$	17.8223	−	10.2897i	0.614562	−	0.354818i
$842$		0			0
$843$	−3.78566	+	4.41134i	−0.130385	+	0.151935i
$844$		0			0
$845$	−27.0284	+	27.0284i	−0.929804	+	0.929804i
$846$		0			0
$847$	−19.9088	−	7.24621i	−0.684075	−	0.248983i
$848$		0			0
$849$	3.72196	−	9.88376i	0.127737	−	0.339210i
$850$		0			0
$851$	12.4841	−	10.1172i	0.427950	−	0.346812i
$852$		0			0
$853$	36.9564	−	25.8771i	1.26536	−	0.886016i	0.268354	−	0.963320i	$-0.413520\pi$
$853$	36.9564	−	25.8771i	1.26536	−	0.886016i	0.997008	+	0.0773048i	$0.0246315\pi$
$854$		0			0
$855$	33.3150	−	37.9616i	1.13935	−	1.29826i
$856$		0			0
$857$	−28.5571	−	28.5571i	−0.975493	−	0.975493i	0.0242136	−	0.999707i	$-0.492292\pi$
$857$	−28.5571	−	28.5571i	−0.975493	−	0.975493i	−0.999707	+	0.0242136i	$0.992292\pi$
$858$		0			0
$859$	−1.99195	−	7.43407i	−0.0679645	−	0.253647i	0.923582	−	0.383402i	$-0.125248\pi$
$859$	−1.99195	−	7.43407i	−0.0679645	−	0.253647i	−0.991546	+	0.129755i	$0.958581\pi$
$860$		0			0
$861$	−2.12631	−	1.02036i	−0.0724646	−	0.0347738i
$862$		0			0
$863$	−41.6134	−	7.33757i	−1.41654	−	0.249774i	−0.587616	−	0.809140i	$-0.699934\pi$
$863$	−41.6134	−	7.33757i	−1.41654	−	0.249774i	−0.828921	+	0.559366i	$0.811045\pi$
$864$		0			0
$865$	8.47158	−	31.6164i	0.288042	−	1.07499i
$866$		0			0
$867$	−0.508043	+	5.14898i	−0.0172540	+	0.174869i
$868$		0			0
$869$	−10.2645	−	7.18726i	−0.348198	−	0.243811i
$870$		0			0
$871$	3.23294	+	1.50755i	0.109544	+	0.0510813i
$872$		0			0
$873$	4.68317	−	16.0463i	0.158501	−	0.543084i
$874$		0			0
$875$	5.40118	−	2.51861i	0.182593	−	0.0851446i
$876$		0			0
$877$	−2.30100	+	3.98545i	−0.0776994	+	0.134579i	−0.902257	−	0.431199i	$-0.858091\pi$
$877$	−2.30100	+	3.98545i	−0.0776994	+	0.134579i	0.824558	+	0.565778i	$0.191424\pi$
$878$		0			0
$879$	−35.7506	−	25.6280i	−1.20584	−	0.864412i
$880$		0			0
$881$	−18.2480	+	15.3119i	−0.614791	+	0.515871i	−0.896161	−	0.443728i	$-0.853656\pi$
$881$	−18.2480	+	15.3119i	−0.614791	+	0.515871i	0.281370	+	0.959599i	$0.409211\pi$
$882$		0			0
$883$	43.0509	+	3.76646i	1.44878	+	0.126752i	0.784219	−	0.620485i	$-0.213064\pi$
$883$	43.0509	+	3.76646i	1.44878	+	0.126752i	0.664558	+	0.747236i	$0.268620\pi$
$884$		0			0
$885$	−38.3536	+	37.5126i	−1.28924	+	1.26097i
$886$		0			0
$887$	−3.94986			−0.132623			−0.0663117	−	0.997799i	$-0.521123\pi$
$887$	−3.94986			−0.132623			−0.0663117	+	0.997799i	$0.521123\pi$
$888$		0			0
$889$	4.23468			0.142027
$890$		0			0
$891$	−3.97373	+	6.22785i	−0.133125	+	0.208641i
$892$		0			0
$893$	−6.07982	−	0.531915i	−0.203453	−	0.0177999i
$894$		0			0
$895$	−35.1602	+	29.5029i	−1.17528	+	0.986175i
$896$		0			0
$897$	−1.41667	+	1.97623i	−0.0473012	+	0.0659844i
$898$		0			0
$899$	−5.18025	+	8.97245i	−0.172771	+	0.299248i
$900$		0			0
$901$	−17.2566	+	8.04688i	−0.574900	+	0.268080i
$902$		0			0
$903$	−24.7250	+	20.2840i	−0.822796	+	0.675010i
$904$		0			0
$905$	−40.1280	−	18.7120i	−1.33390	−	0.622007i
$906$		0			0
$907$	3.66185	+	2.56405i	0.121590	+	0.0851380i	0.632789	−	0.774324i	$-0.281910\pi$
$907$	3.66185	+	2.56405i	0.121590	+	0.0851380i	−0.511200	+	0.859462i	$0.670799\pi$
$908$		0			0
$909$	44.9286	−	24.6282i	1.49019	−	0.816866i
$910$		0			0
$911$	−5.41644	+	20.2144i	−0.179455	+	0.669734i	0.816295	+	0.577635i	$0.196024\pi$
$911$	−5.41644	+	20.2144i	−0.179455	+	0.669734i	−0.995750	+	0.0920991i	$0.970642\pi$
$912$		0			0
$913$	−2.72329	−	0.480190i	−0.0901278	−	0.0158920i
$914$		0			0
$915$	14.5908	−	30.4056i	0.482357	−	1.00518i
$916$		0			0
$917$	1.11543	+	4.16283i	0.0368347	+	0.137469i
$918$		0			0
$919$	−16.9048	−	16.9048i	−0.557639	−	0.557639i	0.370996	−	0.928635i	$-0.379016\pi$
$919$	−16.9048	−	16.9048i	−0.557639	−	0.557639i	−0.928635	+	0.370996i	$0.879016\pi$
$920$		0			0
$921$	0.571873	+	2.23297i	0.0188439	+	0.0735789i
$922$		0			0
$923$	0.208288	−	0.145845i	0.00685589	−	0.00480055i
$924$		0			0
$925$	17.0503	+	17.6429i	0.560609	+	0.580094i
$926$		0			0
$927$	−7.73304	−	31.6504i	−0.253986	−	1.03954i
$928$		0			0
$929$	−27.3266	−	9.94606i	−0.896556	−	0.326320i	−0.147684	−	0.989035i	$-0.547182\pi$
$929$	−27.3266	−	9.94606i	−0.896556	−	0.326320i	−0.748872	+	0.662715i	$0.769404\pi$
$930$		0			0
$931$	11.0525	−	11.0525i	0.362230	−	0.362230i
$932$		0			0
$933$	20.9230	+	17.9554i	0.684990	+	0.587835i
$934$		0			0
$935$	9.55207	−	5.51489i	0.312386	−	0.180356i
$936$		0			0
$937$	−2.44992	+	13.8942i	−0.0800353	+	0.453903i	0.918283	+	0.395926i	$0.129576\pi$
$937$	−2.44992	+	13.8942i	−0.0800353	+	0.453903i	−0.998318	+	0.0579772i	$0.981535\pi$
$938$		0			0
$939$	0.538228	−	0.189170i	0.0175644	−	0.00617333i
$940$		0			0
$941$	9.84466	−	11.7324i	0.320927	−	0.382466i	−0.581328	−	0.813669i	$-0.697467\pi$
$941$	9.84466	−	11.7324i	0.320927	−	0.382466i	0.902254	+	0.431204i	$0.141911\pi$
$942$		0			0
$943$	1.00561	−	1.43615i	0.0327470	−	0.0467676i
$944$		0			0
$945$	6.61017	−	31.3535i	0.215029	−	1.01993i
$946$		0			0
$947$	−2.19983	−	25.1441i	−0.0714847	−	0.817074i	−0.944313	−	0.329047i	$-0.893272\pi$
$947$	−2.19983	−	25.1441i	−0.0714847	−	0.817074i	0.872829	−	0.488027i	$-0.162283\pi$
$948$		0			0
$949$	2.30363	+	4.94015i	0.0747790	+	0.160364i
$950$		0			0
$951$	−1.50419	−	19.7064i	−0.0487769	−	0.639022i
$952$		0			0
$953$	−5.79831	+	2.11041i	−0.187826	+	0.0683630i	−0.434221	−	0.900807i	$-0.642976\pi$
$953$	−5.79831	+	2.11041i	−0.187826	+	0.0683630i	0.246395	+	0.969170i	$0.420754\pi$
$954$		0			0
$955$	20.9843	+	25.0082i	0.679037	+	0.809245i
$956$		0			0
$957$	−2.02310	−	3.59556i	−0.0653975	−	0.116228i
$958$		0			0
$959$	−32.8305	+	5.78891i	−1.06015	+	0.186934i
$960$		0			0
$961$		−	18.2527i		−	0.588796i
$962$		0			0
$963$	−47.8769	−	18.6376i	−1.54281	−	0.600589i
$964$		0			0
$965$	9.28903	+	52.6807i	0.299024	+	1.69585i
$966$		0			0
$967$	−1.44229	+	16.4855i	−0.0463809	+	0.530136i	0.937092	+	0.349082i	$0.113507\pi$
$967$	−1.44229	+	16.4855i	−0.0463809	+	0.530136i	−0.983473	+	0.181054i	$0.942049\pi$
$968$		0			0
$969$	11.6899	−	41.7699i	0.375534	−	1.34184i
$970$		0			0
$971$	8.45036	+	23.2172i	0.271185	+	0.745075i	0.998285	+	0.0585431i	$0.0186455\pi$
$971$	8.45036	+	23.2172i	0.271185	+	0.745075i	−0.727100	+	0.686532i	$0.759132\pi$
$972$		0			0
$973$	−34.7121	−	20.0411i	−1.11282	−	0.642487i
$974$		0			0
$975$	−3.19451	−	1.89186i	−0.102306	−	0.0605882i
$976$		0			0
$977$	12.0089	−	1.05064i	0.384197	−	0.0336129i	0.106579	−	0.994304i	$-0.466010\pi$
$977$	12.0089	−	1.05064i	0.384197	−	0.0336129i	0.277619	+	0.960691i	$0.410455\pi$
$978$		0			0
$979$	5.82822	−	12.4987i	0.186271	−	0.399459i
$980$		0			0
$981$	0.699238	−	0.466861i	0.0223250	−	0.0149057i
$982$		0			0
$983$	−24.5583	−	20.6069i	−0.783288	−	0.657257i	0.160786	−	0.986989i	$-0.448597\pi$
$983$	−24.5583	−	20.6069i	−0.783288	−	0.657257i	−0.944074	+	0.329733i	$0.893041\pi$
$984$		0			0
$985$	30.3586	+	8.13457i	0.967307	+	0.259189i
$986$		0			0
$987$	−3.52705	+	1.59734i	−0.112267	+	0.0508439i
$988$		0			0
$989$	−11.8868	−	20.5886i	−0.377979	−	0.654678i
$990$		0			0
$991$	1.65108	−	0.442405i	0.0524482	−	0.0140535i	−0.232500	−	0.972597i	$-0.574690\pi$
$991$	1.65108	−	0.442405i	0.0524482	−	0.0140535i	0.284948	+	0.958543i	$0.408024\pi$
$992$		0			0
$993$	−3.53002	+	18.7989i	−0.112022	+	0.596564i
$994$		0			0
$995$	−25.6294	+	70.4161i	−0.812506	+	2.23234i
$996$		0			0
$997$	0.991003	+	1.41530i	0.0313854	+	0.0448230i	0.834538	−	0.550950i	$-0.185735\pi$
$997$	0.991003	+	1.41530i	0.0313854	+	0.0448230i	−0.803153	+	0.595773i	$0.796846\pi$
$998$		0			0
$999$	−31.3635	+	3.91557i	−0.992297	+	0.123883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.bg.b.209.10	yes	144
3.2	odd	2	inner	444.2.bg.b.209.8	yes	144
37.17	odd	36	inner	444.2.bg.b.17.8	✓	144
111.17	even	36	inner	444.2.bg.b.17.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.bg.b.17.8	✓	144	37.17	odd	36	inner
444.2.bg.b.17.10	yes	144	111.17	even	36	inner
444.2.bg.b.209.8	yes	144	3.2	odd	2	inner
444.2.bg.b.209.10	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.bg (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21110 + 1.23824i) q^{3} +(2.99415 + 0.261955i) q^{5} +(-1.57171 + 1.31882i) q^{7} +(-0.0664970 + 2.99926i) q^{9} +(0.410422 - 0.710872i) q^{11} +(-0.481628 + 0.224587i) q^{13} +(3.30184 + 4.02475i) q^{15} +(4.05183 + 1.88940i) q^{17} +(-4.58845 - 3.21287i) q^{19} +(-3.53651 - 0.348942i) q^{21} +(0.683726 - 2.55170i) q^{23} +(3.97230 + 0.700424i) q^{25} +(-3.79435 + 3.55005i) q^{27} +(-0.751047 - 2.80295i) q^{29} +(-2.52461 - 2.52461i) q^{31} +(1.37729 - 0.352731i) q^{33} +(-5.05141 + 3.53704i) q^{35} +(4.92239 + 3.57352i) q^{37} +(-0.861391 - 0.324377i) q^{39} +(0.623643 + 0.226987i) q^{41} +(6.36347 - 6.36347i) q^{43} +(-0.984773 + 8.96284i) q^{45} +(0.943574 - 0.544773i) q^{47} +(-0.484555 + 2.74805i) q^{49} +(2.56762 + 7.30541i) q^{51} +(-2.73760 + 3.26255i) q^{53} +(1.41508 - 2.02095i) q^{55} +(-1.57873 - 9.57270i) q^{57} +(0.898184 + 10.2663i) q^{59} +(-2.73787 - 5.87138i) q^{61} +(-3.85098 - 4.80167i) q^{63} +(-1.50090 + 0.546284i) q^{65} +(-4.31473 - 5.14209i) q^{67} +(3.98769 - 2.24373i) q^{69} +(-0.471211 + 0.0830872i) q^{71} -10.2572i q^{73} +(3.94354 + 5.76696i) q^{75} +(0.292448 + 1.65856i) q^{77} +(1.33048 - 15.2074i) q^{79} +(-8.99116 - 0.398884i) q^{81} +(-1.15221 - 3.16568i) q^{83} +(11.6369 + 6.71856i) q^{85} +(2.56114 - 4.32461i) q^{87} +(16.7368 - 1.46428i) q^{89} +(0.460790 - 0.988167i) q^{91} +(0.0685405 - 6.18363i) q^{93} +(-12.8969 - 10.8218i) q^{95} +(-5.38204 - 1.44211i) q^{97} +(2.10480 + 1.27823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{9} - 6 q^{15} + 18 q^{21} - 54 q^{27} + 48 q^{31} + 84 q^{37} - 54 q^{39} + 24 q^{43} + 72 q^{45} + 84 q^{49} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 78 q^{69} - 216 q^{75} - 24 q^{79} - 66 q^{81}+ \cdots - 78 q^{99}+O(q^{100}) \) 144 * q - 6 * q^9 - 6 * q^15 + 18 * q^21 - 54 * q^27 + 48 * q^31 + 84 * q^37 - 54 * q^39 + 24 * q^43 + 72 * q^45 + 84 * q^49 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 78 * q^69 - 216 * q^75 - 24 * q^79 - 66 * q^81 - 72 * q^87 - 48 * q^91 - 48 * q^93 - 24 * q^97 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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