LMFDB - Embedded newform 588.2.n.f.275.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] 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("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Character	$\chi$	$=$	588.275
Dual form			588.2.n.f.263.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41332 + 0.0503882i) q^{2} +(1.22461 - 1.22488i) q^{3} +(1.99492 - 0.142429i) q^{4} +(3.08528 + 1.78129i) q^{5} +(-1.66903 + 1.79285i) q^{6} +(-2.81228 + 0.301817i) q^{8} +(-0.000681912 - 3.00000i) q^{9} +(-4.45023 - 2.36206i) q^{10} +(0.167782 + 0.290607i) q^{11} +(2.26853 - 2.61797i) q^{12} +3.34596 q^{13} +(5.96012 - 1.59774i) q^{15} +(3.95943 - 0.568269i) q^{16} +(-0.290607 + 0.167782i) q^{17} +(0.152128 + 4.23991i) q^{18} +(-1.60172 - 0.924754i) q^{19} +(6.40860 + 3.11410i) q^{20} +(-0.251772 - 0.402265i) q^{22} +(2.22976 - 3.86207i) q^{23} +(-3.07424 + 3.81432i) q^{24} +(3.84596 + 6.66140i) q^{25} +(-4.72890 + 0.168597i) q^{26} +(-3.67549 - 3.67298i) q^{27} +5.91788i q^{29} +(-8.34302 + 2.55842i) q^{30} +(-4.49941 + 2.59774i) q^{31} +(-5.56729 + 1.00265i) q^{32} +(0.561426 + 0.150365i) q^{33} +(0.402265 - 0.251772i) q^{34} +(-0.428647 - 5.98467i) q^{36} +(-1.59774 + 2.76736i) q^{37} +(2.31033 + 1.22626i) q^{38} +(4.09749 - 4.09842i) q^{39} +(-9.21428 - 4.07828i) q^{40} -1.45835i q^{41} +7.49646i q^{43} +(0.376103 + 0.555841i) q^{44} +(5.34176 - 9.25705i) q^{45} +(-2.95676 + 5.57067i) q^{46} +(4.45953 - 7.72413i) q^{47} +(4.15267 - 5.54575i) q^{48} +(-5.77122 - 9.22087i) q^{50} +(-0.150365 + 0.561426i) q^{51} +(6.67494 - 0.476562i) q^{52} +(4.15267 - 2.39755i) q^{53} +(5.37970 + 5.00588i) q^{54} +1.19547i q^{55} +(-3.09419 + 0.829463i) q^{57} +(-0.298191 - 8.36383i) q^{58} +(-7.01223 - 12.1455i) q^{59} +(11.6624 - 4.03625i) q^{60} +(0.176525 - 0.305751i) q^{61} +(6.22819 - 3.89814i) q^{62} +(7.81781 - 1.69759i) q^{64} +(10.3232 + 5.96012i) q^{65} +(-0.801049 - 0.184224i) q^{66} +(-2.76736 + 1.59774i) q^{67} +(-0.555841 + 0.376103i) q^{68} +(-2.00000 - 7.46071i) q^{69} +10.3774 q^{71} +(0.907370 + 8.43663i) q^{72} +(2.34596 + 4.06333i) q^{73} +(2.11866 - 3.99166i) q^{74} +(12.8692 + 3.44673i) q^{75} +(-3.32702 - 1.61668i) q^{76} +(-5.58453 + 5.99882i) q^{78} +(3.46410 + 2.00000i) q^{79} +(13.2282 + 5.29961i) q^{80} +(-9.00000 + 0.00409147i) q^{81} +(0.0734835 + 2.06111i) q^{82} -6.89932 q^{83} -1.19547 q^{85} +(-0.377733 - 10.5949i) q^{86} +(7.24871 + 7.24707i) q^{87} +(-0.559559 - 0.766627i) q^{88} +(-3.35402 - 1.93644i) q^{89} +(-7.08314 + 13.3523i) q^{90} +(3.89814 - 8.02210i) q^{92} +(-2.32808 + 8.69246i) q^{93} +(-5.91352 + 11.1413i) q^{94} +(-3.29450 - 5.70624i) q^{95} +(-5.58960 + 8.04713i) q^{96} -2.00000 q^{97} +(0.871706 - 0.503544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.41332	+	0.0503882i	−0.999365	+	0.0356298i
$2$	−1.41332	+	0.0503882i	−0.999365	+	0.0356298i
$3$	1.22461	−	1.22488i	0.707026	−	0.707187i
$3$	1.22461	−	1.22488i	0.707026	−	0.707187i
$4$	1.99492	−	0.142429i	0.997461	−	0.0712144i
$5$	3.08528	+	1.78129i	1.37978	+	0.796616i	0.992132	−	0.125193i	$-0.0399549\pi$
$5$	3.08528	+	1.78129i	1.37978	+	0.796616i	0.387646	+	0.921808i	$0.373288\pi$
$6$	−1.66903	+	1.79285i	−0.681381	+	0.731929i
$7$		0			0
$7$		0			0
$8$	−2.81228	+	0.301817i	−0.994290	+	0.106709i
$9$	−0.000681912	−	3.00000i	−0.000227304	−	1.00000i
$10$	−4.45023	−	2.36206i	−1.40729	−	0.746948i
$11$	0.167782	+	0.290607i	0.0505881	+	0.0876212i	0.890211	−	0.455549i	$-0.150557\pi$
$11$	0.167782	+	0.290607i	0.0505881	+	0.0876212i	−0.839622	+	0.543170i	$0.817224\pi$
$12$	2.26853	−	2.61797i	0.654869	−	0.755742i
$13$	3.34596			0.928003			0.464002	−	0.885834i	$-0.346413\pi$
$13$	3.34596			0.928003			0.464002	+	0.885834i	$0.346413\pi$
$14$		0			0
$15$	5.96012	−	1.59774i	1.53890	−	0.412533i
$16$	3.95943	−	0.568269i	0.989857	−	0.142067i
$17$	−0.290607	+	0.167782i	−0.0704825	+	0.0406931i	−0.534827	−	0.844962i	$-0.679623\pi$
$17$	−0.290607	+	0.167782i	−0.0704825	+	0.0406931i	0.464345	+	0.885655i	$0.346290\pi$
$18$	0.152128	+	4.23991i	0.0358570	+	0.999357i
$19$	−1.60172	−	0.924754i	−0.367460	−	0.212153i	0.304888	−	0.952388i	$-0.401381\pi$
$19$	−1.60172	−	0.924754i	−0.367460	−	0.212153i	−0.672348	+	0.740235i	$0.734714\pi$
$20$	6.40860	+	3.11410i	1.43301	+	0.696333i
$21$		0			0
$22$	−0.251772	−	0.402265i	−0.0536779	−	0.0857631i
$23$	2.22976	−	3.86207i	0.464938	−	0.805296i	−0.534261	−	0.845320i	$-0.679410\pi$
$23$	2.22976	−	3.86207i	0.464938	−	0.805296i	0.999199	+	0.0400235i	$0.0127433\pi$
$24$	−3.07424	+	3.81432i	−0.627527	+	0.778595i
$25$	3.84596	+	6.66140i	0.769193	+	1.33228i
$26$	−4.72890	+	0.168597i	−0.927414	+	0.0330646i
$27$	−3.67549	−	3.67298i	−0.707348	−	0.706866i
$28$		0			0
$29$			5.91788i			1.09892i	0.835519	+	0.549461i	$0.185167\pi$
$29$			5.91788i			1.09892i	−0.835519	+	0.549461i	$0.814833\pi$
$30$	−8.34302	+	2.55842i	−1.52322	+	0.467102i
$31$	−4.49941	+	2.59774i	−0.808118	+	0.466567i	−0.846302	−	0.532704i	$-0.821176\pi$
$31$	−4.49941	+	2.59774i	−0.808118	+	0.466567i	0.0381840	+	0.999271i	$0.487843\pi$
$32$	−5.56729	+	1.00265i	−0.984167	+	0.177245i
$33$	0.561426	+	0.150365i	0.0977318	+	0.0261752i
$34$	0.402265	−	0.251772i	0.0689878	−	0.0431785i
$35$		0			0
$36$	−0.428647	−	5.98467i	−0.0714411	−	0.997445i
$37$	−1.59774	+	2.76736i	−0.262666	+	0.454951i	−0.966950	−	0.254968i	$-0.917935\pi$
$37$	−1.59774	+	2.76736i	−0.262666	+	0.454951i	0.704283	+	0.709919i	$0.251268\pi$
$38$	2.31033	+	1.22626i	0.374785	+	0.198926i
$39$	4.09749	−	4.09842i	0.656123	−	0.656272i
$40$	−9.21428	−	4.07828i	−1.45691	−	0.644833i
$41$		−	1.45835i		−	0.227756i	−0.993495	−	0.113878i	$-0.963673\pi$
$41$		−	1.45835i		−	0.227756i	0.993495	−	0.113878i	$-0.0363272\pi$
$42$		0			0
$43$			7.49646i			1.14320i	0.820533	+	0.571599i	$0.193677\pi$
$43$			7.49646i			1.14320i	−0.820533	+	0.571599i	$0.806323\pi$
$44$	0.376103	+	0.555841i	0.0566996	+	0.0837962i
$45$	5.34176	−	9.25705i	0.796302	−	1.37996i
$46$	−2.95676	+	5.57067i	−0.435950	+	0.821351i
$47$	4.45953	−	7.72413i	0.650489	−	1.12668i	−0.332515	−	0.943098i	$-0.607897\pi$
$47$	4.45953	−	7.72413i	0.650489	−	1.12668i	0.983004	−	0.183582i	$-0.0587694\pi$
$48$	4.15267	−	5.54575i	0.599387	−	0.800459i
$49$		0			0
$50$	−5.77122	−	9.22087i	−0.816173	−	1.30403i
$51$	−0.150365	+	0.561426i	−0.0210554	+	0.0786154i
$52$	6.67494	−	0.476562i	0.925647	−	0.0660872i
$53$	4.15267	−	2.39755i	0.570413	−	0.329328i	−0.186901	−	0.982379i	$-0.559844\pi$
$53$	4.15267	−	2.39755i	0.570413	−	0.329328i	0.757314	+	0.653050i	$0.226511\pi$
$54$	5.37970	+	5.00588i	0.732084	+	0.681214i
$55$			1.19547i			0.161197i
$56$		0			0
$57$	−3.09419	+	0.829463i	−0.409836	+	0.109865i
$58$	−0.298191	−	8.36383i	−0.0391544	−	1.09822i
$59$	−7.01223	−	12.1455i	−0.912915	−	1.58121i	−0.809926	−	0.586532i	$-0.800493\pi$
$59$	−7.01223	−	12.1455i	−0.912915	−	1.58121i	−0.102989	−	0.994682i	$-0.532841\pi$
$60$	11.6624	−	4.03625i	1.50561	−	0.521078i
$61$	0.176525	−	0.305751i	0.0226018	−	0.0391474i	−0.854503	−	0.519446i	$-0.826138\pi$
$61$	0.176525	−	0.305751i	0.0226018	−	0.0391474i	0.877105	+	0.480299i	$0.159472\pi$
$62$	6.22819	−	3.89814i	0.790981	−	0.495064i
$63$		0			0
$64$	7.81781	−	1.69759i	0.977227	−	0.212199i
$65$	10.3232	+	5.96012i	1.28044	+	0.739262i
$66$	−0.801049	−	0.184224i	−0.0986023	−	0.0226765i
$67$	−2.76736	+	1.59774i	−0.338087	+	0.195194i	−0.659426	−	0.751770i	$-0.729200\pi$
$67$	−2.76736	+	1.59774i	−0.338087	+	0.195194i	0.321339	+	0.946964i	$0.395867\pi$
$68$	−0.555841	+	0.376103i	−0.0674056	+	0.0456091i
$69$	−2.00000	−	7.46071i	−0.240772	−	0.898164i
$70$		0			0
$71$	10.3774			1.23157			0.615786	−	0.787914i	$-0.288839\pi$
$71$	10.3774			1.23157			0.615786	+	0.787914i	$0.288839\pi$
$72$	0.907370	+	8.43663i	0.106935	+	0.994266i
$73$	2.34596	+	4.06333i	0.274574	+	0.475577i	0.970028	−	0.242995i	$-0.0781298\pi$
$73$	2.34596	+	4.06333i	0.274574	+	0.475577i	−0.695453	+	0.718571i	$0.744796\pi$
$74$	2.11866	−	3.99166i	0.246289	−	0.464021i
$75$	12.8692	+	3.44673i	1.48601	+	0.397995i
$76$	−3.32702	−	1.61668i	−0.381635	−	0.185446i
$77$		0			0
$78$	−5.58453	+	5.99882i	−0.632323	+	0.679233i
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	0.682048	−	0.731307i	$-0.261089\pi$
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	−0.292306	+	0.956325i	$0.594423\pi$
$80$	13.2282	+	5.29961i	1.47896	+	0.592514i
$81$	−9.00000	+	0.00409147i	−1.00000	+	0.000454608i
$82$	0.0734835	+	2.06111i	0.00811489	+	0.227611i
$83$	−6.89932			−0.757299			−0.378649	−	0.925540i	$-0.623611\pi$
$83$	−6.89932			−0.757299			−0.378649	+	0.925540i	$0.623611\pi$
$84$		0			0
$85$	−1.19547			−0.129667
$86$	−0.377733	−	10.5949i	−0.0407320	−	1.14247i
$87$	7.24871	+	7.24707i	0.777144	+	0.776967i
$88$	−0.559559	−	0.766627i	−0.0596492	−	0.0817228i
$89$	−3.35402	−	1.93644i	−0.355525	−	0.205263i	0.311591	−	0.950216i	$-0.399138\pi$
$89$	−3.35402	−	1.93644i	−0.355525	−	0.205263i	−0.667116	+	0.744954i	$0.732472\pi$
$90$	−7.08314	+	13.3523i	−0.746629	+	1.40746i
$91$		0			0
$92$	3.89814	−	8.02210i	0.406409	−	0.836362i
$93$	−2.32808	+	8.69246i	−0.241410	+	0.901366i
$94$	−5.91352	+	11.1413i	−0.609933	+	1.14914i
$95$	−3.29450	−	5.70624i	−0.338009	−	0.585448i
$96$	−5.58960	+	8.04713i	−0.570486	+	0.821307i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	0.871706	−	0.503544i	0.0876097	−	0.0506081i
$100$	8.62117	+	12.7412i	0.862117	+	1.27412i
$101$	−11.3906	+	6.57638i	−1.13341	+	0.654374i	−0.944790	−	0.327676i	$-0.893735\pi$
$101$	−11.3906	+	6.57638i	−1.13341	+	0.654374i	−0.188619	+	0.982050i	$0.560401\pi$
$102$	0.184224	−	0.801049i	0.0182409	−	0.0793157i
$103$	−6.83069	−	3.94370i	−0.673048	−	0.388584i	0.124183	−	0.992259i	$-0.460369\pi$
$103$	−6.83069	−	3.94370i	−0.673048	−	0.388584i	−0.797230	+	0.603675i	$0.793702\pi$
$104$	−9.40978	+	1.00987i	−0.922705	+	0.0990259i
$105$		0			0
$106$	−5.74823	+	3.59774i	−0.558317	+	0.349443i
$107$	−4.06592	+	7.04238i	−0.393067	+	0.680812i	−0.992852	−	0.119349i	$-0.961919\pi$
$107$	−4.06592	+	7.04238i	−0.393067	+	0.680812i	0.599785	+	0.800161i	$0.295253\pi$
$108$	−7.85545	−	6.80382i	−0.755891	−	0.654698i
$109$	−9.54143	−	16.5262i	−0.913904	−	1.58293i	−0.808499	−	0.588498i	$-0.799719\pi$
$109$	−9.54143	−	16.5262i	−0.913904	−	1.58293i	−0.105405	−	0.994429i	$-0.533614\pi$
$110$	−0.0602376	−	1.68958i	−0.00574343	−	0.161095i
$111$	1.43310	+	5.34596i	0.136024	+	0.507416i
$112$		0			0
$113$			12.5914i			1.18450i	0.805756	+	0.592248i	$0.201759\pi$
$113$			12.5914i			1.18450i	−0.805756	+	0.592248i	$0.798241\pi$
$114$	4.33127	−	1.32820i	0.405661	−	0.124398i
$115$	13.7589	−	7.94370i	1.28302	−	0.740754i
$116$	0.842876	+	11.8057i	0.0782591	+	1.09613i
$117$	−0.00228165	−	10.0379i	−0.000210939	−	0.928003i
$118$	10.5225	+	16.8122i	0.968674	+	1.54768i
$119$		0			0
$120$	−16.2793	+	6.29214i	−1.48609	+	0.574391i
$121$	5.44370	−	9.42876i	0.494882	−	0.857160i
$122$	−0.234080	+	0.441017i	−0.0211926	+	0.0399278i
$123$	−1.78631	−	1.78590i	−0.161066	−	0.161029i
$124$	−8.60598	+	5.82312i	−0.772840	+	0.522932i
$125$			9.59019i			0.857772i
$126$		0			0
$127$		−	10.1884i		−	0.904073i	−0.891999	−	0.452036i	$-0.850698\pi$
$127$		−	10.1884i		−	0.904073i	0.891999	−	0.452036i	$-0.149302\pi$
$128$	−10.9635	+	2.79315i	−0.969045	+	0.246882i
$129$	9.18229	+	9.18020i	0.808456	+	0.808272i
$130$	−14.8903	−	7.90336i	−1.30597	−	0.693171i
$131$	−5.24357	+	9.08213i	−0.458133	+	0.793509i	−0.998862	−	0.0476872i	$-0.984815\pi$
$131$	−5.24357	+	9.08213i	−0.458133	+	0.793509i	0.540729	+	0.841197i	$0.318148\pi$
$132$	1.14142	+	0.220004i	0.0993477	+	0.0191489i
$133$		0			0
$134$	3.83064	−	2.39755i	0.330917	−	0.207116i
$135$	−4.79727	−	17.8793i	−0.412883	−	1.53880i
$136$	0.766627	−	0.559559i	0.0657378	−	0.0479818i
$137$	7.72413	−	4.45953i	0.659917	−	0.381003i	−0.132328	−	0.991206i	$-0.542245\pi$
$137$	7.72413	−	4.45953i	0.659917	−	0.381003i	0.792245	+	0.610203i	$0.208912\pi$
$138$	3.20256	+	10.4436i	0.272620	+	0.889015i
$139$		−	2.03789i		−	0.172852i	−0.996258	−	0.0864258i	$-0.972455\pi$
$139$		−	2.03789i		−	0.172852i	0.996258	−	0.0864258i	$-0.0275445\pi$
$140$		0			0
$141$	−4.00000	−	14.9214i	−0.336861	−	1.25661i
$142$	−14.6665	+	0.522899i	−1.23079	+	0.0438807i
$143$	0.561392	+	0.972359i	0.0469460	+	0.0813128i
$144$	−1.70751	−	11.8779i	−0.142292	−	0.989825i
$145$	−10.5414	+	18.2583i	−0.875418	+	1.51627i
$146$	−3.52033	−	5.62456i	−0.291345	−	0.465492i
$147$		0			0
$148$	−2.79321	+	5.74823i	−0.229600	+	0.472501i
$149$	−13.3866	−	7.72878i	−1.09668	−	0.633166i	−0.161330	−	0.986900i	$-0.551578\pi$
$149$	−13.3866	−	7.72878i	−1.09668	−	0.633166i	−0.935346	+	0.353734i	$0.884912\pi$
$150$	−18.3620	−	4.22287i	−1.49925	−	0.344796i
$151$	−13.1597	+	7.59774i	−1.07092	+	0.618295i	−0.928432	−	0.371502i	$-0.878843\pi$
$151$	−13.1597	+	7.59774i	−1.07092	+	0.618295i	−0.142486	+	0.989797i	$0.545510\pi$
$152$	4.78359	+	2.11724i	0.388000	+	0.171731i
$153$	0.503544	+	0.871706i	0.0407091	+	0.0704732i
$154$		0			0
$155$	−18.5092			−1.48670
$156$	7.59043	−	8.75962i	0.607721	−	0.701331i
$157$	0.477511	+	0.827074i	0.0381095	+	0.0660077i	0.884451	−	0.466633i	$-0.154533\pi$
$157$	0.477511	+	0.827074i	0.0381095	+	0.0660077i	−0.846342	+	0.532641i	$0.821200\pi$
$158$	−4.99665	−	2.65208i	−0.397512	−	0.210988i
$159$	2.14867	−	8.02259i	0.170401	−	0.636233i
$160$	−18.9626	−	6.82347i	−1.49913	−	0.539443i
$161$		0			0
$162$	12.7196	−	0.459276i	0.999349	−	0.0360841i
$163$	8.56274	+	4.94370i	0.670685	+	0.387220i	0.796336	−	0.604854i	$-0.206769\pi$
$163$	8.56274	+	4.94370i	0.670685	+	0.387220i	−0.125651	+	0.992075i	$0.540102\pi$
$164$	−0.207711	−	2.90929i	−0.0162195	−	0.227177i
$165$	1.46431	+	1.46398i	0.113997	+	0.113971i
$166$	9.75091	−	0.347644i	0.756818	−	0.0269824i
$167$	−1.12278			−0.0868836			−0.0434418	−	0.999056i	$-0.513832\pi$
$167$	−1.12278			−0.0868836			−0.0434418	+	0.999056i	$0.513832\pi$
$168$		0			0
$169$	−1.80453			−0.138810
$170$	1.68958	−	0.0602376i	0.129585	−	0.00462001i
$171$	−2.77317	+	4.80579i	−0.212069	+	0.367508i
$172$	1.06771	+	14.9548i	0.0814122	+	1.14030i
$173$	13.4817	+	7.78365i	1.02499	+	0.591780i	0.915546	−	0.402213i	$-0.131759\pi$
$173$	13.4817	+	7.78365i	1.02499	+	0.591780i	0.109447	+	0.993993i	$0.465092\pi$
$174$	−10.6099	−	9.87714i	−0.804333	−	0.748784i
$175$		0			0
$176$	0.829463	+	1.05529i	0.0625231	+	0.0795456i
$177$	−23.4641	−	6.28433i	−1.76367	−	0.472359i
$178$	4.83786	+	2.56780i	0.362613	+	0.192465i
$179$	10.8555	+	18.8023i	0.811378	+	1.40535i	0.911900	+	0.410413i	$0.134616\pi$
$179$	10.8555	+	18.8023i	0.811378	+	1.40535i	−0.100521	+	0.994935i	$0.532051\pi$
$180$	9.33792	−	19.2279i	0.696007	−	1.43316i
$181$	−16.4288			−1.22115			−0.610573	−	0.791960i	$-0.709061\pi$
$181$	−16.4288			−1.22115			−0.610573	+	0.791960i	$0.709061\pi$
$182$		0			0
$183$	−0.158336	−	0.590648i	−0.0117045	−	0.0436619i
$184$	−5.10508	+	11.5342i	−0.376351	+	0.850311i
$185$	−9.85892	+	5.69205i	−0.724842	+	0.418488i
$186$	2.85231	−	12.4025i	0.209142	−	0.909395i
$187$	−0.0975171	−	0.0563015i	−0.00713116	−	0.00411717i
$188$	7.79627	−	16.0442i	0.568602	−	1.17014i
$189$		0			0
$190$	4.94370	+	7.89872i	0.358654	+	0.573033i
$191$	−6.06041	+	10.4969i	−0.438516	+	0.759532i	−0.997575	−	0.0695960i	$-0.977829\pi$
$191$	−6.06041	+	10.4969i	−0.438516	+	0.759532i	0.559059	+	0.829128i	$0.311162\pi$
$192$	7.49439	−	11.6548i	0.540861	−	0.841112i
$193$	3.84951	+	6.66754i	0.277094	+	0.479940i	0.970661	−	0.240451i	$-0.0772955\pi$
$193$	3.84951	+	6.66754i	0.277094	+	0.479940i	−0.693568	+	0.720392i	$0.743962\pi$
$194$	2.82663	−	0.100776i	0.202940	−	0.00723532i
$195$	19.9423	−	5.34596i	1.42810	−	0.382832i
$196$		0			0
$197$		−	7.04066i		−	0.501626i	−0.968036	−	0.250813i	$-0.919302\pi$
$197$		−	7.04066i		−	0.501626i	0.968036	−	0.250813i	$-0.0806980\pi$
$198$	−1.20662	+	0.755590i	−0.0857509	+	0.0536974i
$199$	−18.5190	+	10.6919i	−1.31277	+	0.757931i	−0.982555	−	0.185974i	$-0.940456\pi$
$199$	−18.5190	+	10.6919i	−1.31277	+	0.757931i	−0.330220	+	0.943904i	$0.607123\pi$
$200$	−12.8264	−	17.5729i	−0.906967	−	1.24259i
$201$	−1.43188	+	5.34629i	−0.100997	+	0.377098i
$202$	15.7672	−	9.86845i	1.10937	−	0.694342i
$203$		0			0
$204$	−0.220004	+	1.14142i	−0.0154033	+	0.0799152i
$205$	2.59774	−	4.49941i	0.181434	−	0.314252i
$206$	9.85263	+	5.22950i	0.686465	+	0.364357i
$207$	−11.5877	−	6.68666i	−0.805402	−	0.464755i
$208$	13.2481	−	1.90141i	0.918591	−	0.131839i
$209$		−	0.620628i		−	0.0429297i
$210$		0			0
$211$			22.9703i			1.58134i	0.612244	+	0.790669i	$0.290267\pi$
$211$			22.9703i			1.58134i	−0.612244	+	0.790669i	$0.709733\pi$
$212$	7.94278	−	5.37438i	0.545512	−	0.369114i
$213$	12.7082	−	12.7111i	0.870754	−	0.870951i
$214$	5.39157	−	10.1580i	0.368560	−	0.694385i
$215$	−13.3533	+	23.1287i	−0.910690	+	1.57736i
$216$	11.4451	+	9.22012i	0.778738	+	0.627350i
$217$		0			0
$218$	14.3178	+	22.8760i	0.969723	+	1.54936i
$219$	7.84999	+	2.10244i	0.530453	+	0.142070i
$220$	0.170269	+	2.38487i	0.0114796	+	0.160788i
$221$	−0.972359	+	0.561392i	−0.0654080	+	0.0377633i
$222$	−2.29479	−	7.48332i	−0.154016	−	0.502248i
$223$			9.68484i			0.648545i	0.945964	+	0.324272i	$0.105119\pi$
$223$			9.68484i			0.648545i	−0.945964	+	0.324272i	$0.894881\pi$
$224$		0			0
$225$	19.9816	−	11.5424i	1.33211	−	0.769495i
$226$	−0.634456	−	17.7956i	−0.0422034	−	1.18374i
$227$	6.70192	+	11.6081i	0.444822	+	0.770454i	0.998040	−	0.0625824i	$-0.0199336\pi$
$227$	6.70192	+	11.6081i	0.444822	+	0.770454i	−0.553218	+	0.833037i	$0.686600\pi$
$228$	−6.05453	+	2.09542i	−0.400971	+	0.138772i
$229$	8.36491	−	14.4884i	0.552769	−	0.957423i	−0.445305	−	0.895379i	$-0.646905\pi$
$229$	8.36491	−	14.4884i	0.552769	−	0.957423i	0.998073	−	0.0620444i	$-0.0197620\pi$
$230$	−19.0454	+	11.9202i	−1.25582	+	0.785997i
$231$		0			0
$232$	−1.78612	−	16.6427i	−0.117264	−	1.09265i
$233$	18.1205	+	10.4619i	1.18712	+	0.685381i	0.957650	−	0.287936i	$-0.0929689\pi$
$233$	18.1205	+	10.4619i	1.18712	+	0.685381i	0.229465	+	0.973317i	$0.426302\pi$
$234$	0.509016	+	14.1866i	0.0332754	+	0.927406i
$235$	27.5178	−	15.8874i	1.79506	−	1.03638i
$236$	−15.7187	−	23.2307i	−1.02320	−	1.51219i
$237$	6.69193	−	1.79391i	0.434687	−	0.116527i
$238$		0			0
$239$	−21.1244			−1.36642			−0.683211	−	0.730221i	$-0.739417\pi$
$239$	−21.1244			−1.36642			−0.683211	+	0.730221i	$0.739417\pi$
$240$	22.6907	−	9.71307i	1.46468	−	0.626976i
$241$	−13.1884	−	22.8429i	−0.849538	−	1.47144i	−0.881621	−	0.471958i	$-0.843547\pi$
$241$	−13.1884	−	22.8429i	−0.849538	−	1.47144i	0.0320824	−	0.999485i	$-0.489786\pi$
$242$	−7.21857	+	13.6001i	−0.464027	+	0.874249i
$243$	−11.0164	+	11.0290i	−0.706705	+	0.707508i
$244$	0.308607	−	0.635092i	0.0197565	−	0.0406576i
$245$		0			0
$246$	2.61460	+	2.43403i	0.166701	+	0.155188i
$247$	−5.35930	−	3.09419i	−0.341004	−	0.196879i
$248$	11.8695	−	8.66355i	0.753717	−	0.550136i
$249$	−8.44894	+	8.45086i	−0.535430	+	0.535552i
$250$	−0.483232	−	13.5540i	−0.0305623	−	0.857228i
$251$	5.60756			0.353946			0.176973	−	0.984216i	$-0.443369\pi$
$251$	5.60756			0.353946			0.176973	+	0.984216i	$0.443369\pi$
$252$		0			0
$253$	1.49646			0.0940814
$254$	0.513374	+	14.3994i	0.0322120	+	0.903499i
$255$	−1.46398	+	1.46431i	−0.0916780	+	0.0916988i
$256$	15.3541	−	4.50004i	0.959634	−	0.281252i
$257$	−15.7389	−	9.08684i	−0.981764	−	0.566821i	−0.0789615	−	0.996878i	$-0.525160\pi$
$257$	−15.7389	−	9.08684i	−0.981764	−	0.566821i	−0.902802	+	0.430056i	$0.858494\pi$
$258$	−13.4400	−	12.5118i	−0.836741	−	0.778953i
$259$		0			0
$260$	21.4429	+	10.4196i	1.32983	+	0.646199i
$261$	17.7536	−	0.00403547i	1.09892	−	0.000249789i
$262$	6.95319	−	13.1001i	0.429569	−	0.809329i
$263$	8.86101	+	15.3477i	0.546393	+	0.946381i	0.998518	+	0.0544262i	$0.0173330\pi$
$263$	8.86101	+	15.3477i	0.546393	+	0.946381i	−0.452124	+	0.891955i	$0.649334\pi$
$264$	−1.62427	−	0.253421i	−0.0999669	−	0.0155970i
$265$	17.0829			1.04939
$266$		0			0
$267$	−6.47927	+	1.73690i	−0.396525	+	0.106297i
$268$	−5.29310	+	3.58151i	−0.323328	+	0.218775i
$269$	−10.8094	+	6.24082i	−0.659061	+	0.380509i	−0.791919	−	0.610626i	$-0.790918\pi$
$269$	−10.8094	+	6.24082i	−0.659061	+	0.380509i	0.132858	+	0.991135i	$0.457585\pi$
$270$	7.68096	+	25.0273i	0.467448	+	1.52311i
$271$	−1.55663	−	0.898721i	−0.0945586	−	0.0545934i	0.451975	−	0.892031i	$-0.350720\pi$
$271$	−1.55663	−	0.898721i	−0.0945586	−	0.0545934i	−0.546534	+	0.837437i	$0.684053\pi$
$272$	−1.05529	+	0.829463i	−0.0639864	+	0.0502936i
$273$		0			0
$274$	−10.6919	+	6.69193i	−0.645923	+	0.404274i
$275$	−1.29057	+	2.23533i	−0.0778241	+	0.134795i
$276$	−5.05246	−	14.5987i	−0.304123	−	0.878737i
$277$	11.6356	+	20.1535i	0.699117	+	1.21091i	0.968773	+	0.247949i	$0.0797567\pi$
$277$	11.6356	+	20.1535i	0.699117	+	1.21091i	−0.269656	+	0.962957i	$0.586910\pi$
$278$	0.102686	+	2.88018i	0.00615867	+	0.172742i
$279$	7.79627	+	13.4965i	0.466751	+	0.808012i
$280$		0			0
$281$		−	23.1693i		−	1.38217i	−0.722775	−	0.691084i	$-0.757134\pi$
$281$		−	23.1693i		−	1.38217i	0.722775	−	0.691084i	$-0.242866\pi$
$282$	6.40513	+	20.8871i	0.381420	+	1.24381i
$283$	−1.60172	+	0.924754i	−0.0952124	+	0.0549709i	−0.546850	−	0.837230i	$-0.684173\pi$
$283$	−1.60172	+	0.924754i	−0.0952124	+	0.0549709i	0.451638	+	0.892201i	$0.350840\pi$
$284$	20.7021	−	1.47804i	1.22844	−	0.0877056i
$285$	−11.0240	−	2.95252i	−0.653003	−	0.174892i
$286$	−0.842420	−	1.34596i	−0.0498133	−	0.0795885i
$287$		0			0
$288$	3.01175	+	16.7012i	0.177469	+	0.984126i
$289$	−8.44370	+	14.6249i	−0.496688	+	0.860289i
$290$	13.9784	−	26.3359i	0.820838	−	1.54650i
$291$	−2.44921	+	2.44977i	−0.143575	+	0.143608i
$292$	5.25875	+	7.77189i	0.307745	+	0.454815i
$293$			1.54919i			0.0905047i	0.998976	+	0.0452523i	$0.0144092\pi$
$293$			1.54919i			0.0905047i	−0.998976	+	0.0452523i	$0.985591\pi$
$294$		0			0
$295$		−	49.9632i		−	2.90897i
$296$	3.65804	−	8.26481i	0.212619	−	0.480382i
$297$	0.450713	−	1.68438i	0.0261530	−	0.0977377i
$298$	19.3090	+	10.2487i	1.11854	+	0.593690i
$299$	7.46071	−	12.9223i	0.431464	−	0.747318i
$300$	26.1640	+	5.04302i	1.51058	+	0.291159i
$301$		0			0
$302$	18.2159	−	11.4011i	1.04821	−	0.656059i
$303$	−5.89372	+	22.0057i	−0.338585	+	1.26419i
$304$	−6.86740	−	2.75129i	−0.393873	−	0.157797i
$305$	1.08926	−	0.628885i	0.0623709	−	0.0360098i
$306$	−0.755590	−	1.20662i	−0.0431942	−	0.0689780i
$307$		−	12.5414i		−	0.715777i	−0.933764	−	0.357889i	$-0.883497\pi$
$307$		−	12.5414i		−	0.715777i	0.933764	−	0.357889i	$-0.116503\pi$
$308$		0			0
$309$	−13.1955	+	3.53732i	−0.750664	+	0.201231i
$310$	26.1594	−	0.932647i	1.48575	−	0.0529708i
$311$	−6.02761	−	10.4401i	−0.341795	−	0.592005i	0.642972	−	0.765890i	$-0.277701\pi$
$311$	−6.02761	−	10.4401i	−0.341795	−	0.592005i	−0.984766	+	0.173885i	$0.944368\pi$
$312$	−10.2863	+	12.7626i	−0.582347	+	0.722539i
$313$	11.0379	−	19.1182i	0.623898	−	1.08062i	−0.364854	−	0.931065i	$-0.618881\pi$
$313$	11.0379	−	19.1182i	0.623898	−	1.08062i	0.988753	−	0.149559i	$-0.0477854\pi$
$314$	−0.716549	−	1.14486i	−0.0404372	−	0.0646079i
$315$		0			0
$316$	7.19547	+	3.49646i	0.404777	+	0.196691i
$317$	−2.99025	−	1.72642i	−0.167949	−	0.0969653i	0.413669	−	0.910427i	$-0.364247\pi$
$317$	−2.99025	−	1.72642i	−0.167949	−	0.0969653i	−0.581618	+	0.813462i	$0.697580\pi$
$318$	−2.63250	+	11.4467i	−0.147624	+	0.641900i
$319$	−1.71977	+	0.992912i	−0.0962889	+	0.0555924i
$320$	27.1440	+	8.68823i	1.51740	+	0.485687i
$321$	3.64695	+	13.6044i	0.203553	+	0.759324i
$322$		0			0
$323$	0.620628			0.0345326
$324$	−17.9537	+	1.29002i	−0.997429	+	0.0716679i
$325$	12.8685	+	22.2888i	0.713813	+	1.23636i
$326$	−12.3510	−	6.55555i	−0.684056	−	0.363078i
$327$	−31.9272	−	8.55099i	−1.76558	−	0.472871i
$328$	0.440155	+	4.10128i	0.0243035	+	0.226455i
$329$		0			0
$330$	−2.14330	−	1.99528i	−0.117985	−	0.109837i
$331$	−23.2913	−	13.4472i	−1.28021	−	0.739127i	−0.303320	−	0.952889i	$-0.598095\pi$
$331$	−23.2913	−	13.4472i	−1.28021	−	0.739127i	−0.976886	+	0.213761i	$0.931428\pi$
$332$	−13.7636	+	0.982662i	−0.755376	+	0.0539306i
$333$	8.30316	+	4.79132i	0.455011	+	0.262563i
$334$	1.58685	−	0.0565750i	0.0868285	−	0.00309565i
$335$	−11.3841			−0.621980
$336$		0			0
$337$	10.5793			0.576292			0.288146	−	0.957586i	$-0.406961\pi$
$337$	10.5793			0.576292			0.288146	+	0.957586i	$0.406961\pi$
$338$	2.55037	−	0.0909270i	0.138722	−	0.00494578i
$339$	15.4230	+	15.4195i	0.837660	+	0.837470i
$340$	−2.38487	+	0.170269i	−0.129338	+	0.00923416i
$341$	−1.50984	−	0.871706i	−0.0817623	−	0.0472055i
$342$	3.67721	−	6.93183i	0.198841	−	0.374831i
$343$		0			0
$344$	−2.26256	−	21.0821i	−0.121989	−	1.13667i
$345$	7.11910	−	26.5809i	0.383280	−	1.43107i
$346$	−19.4461	−	10.3214i	−1.04543	−	0.554884i
$347$	−12.6242	−	21.8657i	−0.677701	−	1.17381i	−0.975672	−	0.219237i	$-0.929643\pi$
$347$	−12.6242	−	21.8657i	−0.677701	−	1.17381i	0.297971	−	0.954575i	$-0.403690\pi$
$348$	15.4928	+	13.4249i	0.830502	+	0.719650i
$349$	21.4359			1.14744			0.573719	−	0.819052i	$-0.305500\pi$
$349$	21.4359			1.14744			0.573719	+	0.819052i	$0.305500\pi$
$350$		0			0
$351$	−12.2980	−	12.2897i	−0.656421	−	0.655974i
$352$	−1.22547	−	1.44966i	−0.0653176	−	0.0772674i
$353$	7.43352	−	4.29175i	0.395647	−	0.228427i	−0.288957	−	0.957342i	$-0.593309\pi$
$353$	7.43352	−	4.29175i	0.395647	−	0.228427i	0.684604	+	0.728915i	$0.259975\pi$
$354$	33.4788	+	7.69943i	1.77938	+	0.409220i
$355$	32.0172	+	18.4851i	1.69930	+	0.981089i
$356$	−6.96681	−	3.38534i	−0.369240	−	0.179423i
$357$		0			0
$358$	−16.2897	−	26.0266i	−0.860935	−	1.37555i
$359$	3.35255	−	5.80678i	0.176941	−	0.306470i	−0.763890	−	0.645346i	$-0.776713\pi$
$359$	3.35255	−	5.80678i	0.176941	−	0.306470i	0.940831	+	0.338876i	$0.110047\pi$
$360$	−12.2286	+	27.6456i	−0.644502	+	1.45705i
$361$	−7.78966	−	13.4921i	−0.409982	−	0.710110i
$362$	23.2191	−	0.827819i	1.22037	−	0.0435092i
$363$	−4.88276	−	18.2144i	−0.256278	−	0.956009i
$364$		0			0
$365$			16.7153i			0.874920i
$366$	0.253540	+	0.826793i	0.0132527	+	0.0432172i
$367$	21.2011	−	12.2404i	1.10669	−	0.638946i	0.168718	−	0.985664i	$-0.446037\pi$
$367$	21.2011	−	12.2404i	1.10669	−	0.638946i	0.937969	+	0.346718i	$0.112704\pi$
$368$	6.63390	−	16.5587i	0.345816	−	0.863181i
$369$	−4.37504		0.000994465i	−0.227756		5.17698e-5i
$370$	13.6469	−	8.54143i	0.709471	−	0.444048i
$371$		0			0
$372$	−3.40628	+	17.6724i	−0.176607	+	0.916269i
$373$	−2.19547	+	3.80267i	−0.113677	+	0.196895i	−0.917250	−	0.398312i	$-0.869596\pi$
$373$	−2.19547	+	3.80267i	−0.113677	+	0.196895i	0.803573	+	0.595206i	$0.202930\pi$
$374$	0.140659	+	0.0746581i	0.00727332	+	0.00386048i
$375$	11.7469	+	11.7442i	0.606605	+	0.606468i
$376$	−10.2102	+	23.0684i	−0.526549	+	1.18966i
$377$			19.8010i			1.01980i
$378$		0			0
$379$			16.8803i			0.867083i	0.901134	+	0.433542i	$0.142736\pi$
$379$			16.8803i			0.867083i	−0.901134	+	0.433542i	$0.857264\pi$
$380$	−7.38501	−	10.9143i	−0.378843	−	0.559891i
$381$	−12.4796	−	12.4768i	−0.639349	−	0.639203i
$382$	8.03635	−	15.1409i	0.411175	−	0.774674i
$383$	11.9202	−	20.6465i	0.609096	−	1.05498i	−0.382294	−	0.924041i	$-0.624866\pi$
$383$	11.9202	−	20.6465i	0.609096	−	1.05498i	0.991390	−	0.130944i	$-0.0418008\pi$
$384$	−10.0047	+	16.8495i	−0.510549	+	0.859849i
$385$		0			0
$386$	−5.77653	−	9.22937i	−0.294018	−	0.469763i
$387$	22.4894	−	0.00511193i	1.14320	−	0.000259854i
$388$	−3.98984	+	0.284858i	−0.202554	+	0.0144615i
$389$	−17.4661	+	10.0841i	−0.885569	+	0.511283i	−0.872490	−	0.488631i	$-0.837496\pi$
$389$	−17.4661	+	10.0841i	−0.885569	+	0.511283i	−0.0130783	+	0.999914i	$0.504163\pi$
$390$	−27.9154	+	8.56039i	−1.41355	+	0.433472i
$391$			1.49646i			0.0756790i
$392$		0			0
$393$	4.70325	+	17.5448i	0.237248	+	0.885018i
$394$	0.354766	+	9.95068i	0.0178729	+	0.501308i
$395$	7.12515	+	12.3411i	0.358505	+	0.620949i
$396$	1.66727	−	1.12869i	0.0837833	−	0.0567186i
$397$	9.16944	−	15.8819i	0.460201	−	0.797091i	−0.538770	−	0.842453i	$-0.681111\pi$
$397$	9.16944	−	15.8819i	0.460201	−	0.797091i	0.998971	+	0.0453617i	$0.0144440\pi$
$398$	25.6344	−	16.0442i	1.28494	−	0.804223i
$399$		0			0
$400$	19.0133	+	24.1898i	0.950664	+	1.20949i
$401$	−7.44989	−	4.30119i	−0.372030	−	0.214791i	0.302315	−	0.953208i	$-0.402240\pi$
$401$	−7.44989	−	4.30119i	−0.372030	−	0.214791i	−0.674345	+	0.738417i	$0.735574\pi$
$402$	1.75431	−	7.62814i	0.0874971	−	0.380457i
$403$	−15.0549	+	8.69193i	−0.749936	+	0.432976i
$404$	−21.7867	+	14.7417i	−1.08393	+	0.733428i
$405$	−27.7748	−	16.0190i	−1.38014	−	0.795988i
$406$		0			0
$407$	−1.07228			−0.0531511
$408$	0.253421	−	1.62427i	0.0125462	−	0.0804133i
$409$	−2.15758	−	3.73704i	−0.106685	−	0.184785i	0.807740	−	0.589539i	$-0.200690\pi$
$409$	−2.15758	−	3.73704i	−0.106685	−	0.184785i	−0.914426	+	0.404754i	$0.867357\pi$
$410$	−3.44470	+	6.48998i	−0.170122	+	0.320517i
$411$	3.99661	−	14.9223i	0.197138	−	0.736064i
$412$	−14.1884	−	6.89448i	−0.699011	−	0.339667i
$413$		0			0
$414$	16.7140	+	8.86648i	0.821450	+	0.435764i
$415$	−21.2863	−	12.2897i	−1.04490	−	0.603276i
$416$	−18.6279	+	3.35484i	−0.913310	+	0.164484i
$417$	−2.49618	−	2.49561i	−0.122238	−	0.122211i
$418$	0.0312723	+	0.877143i	0.00152958	+	0.0429024i
$419$	37.4133			1.82776			0.913879	−	0.405986i	$-0.133072\pi$
$419$	37.4133			1.82776			0.913879	+	0.405986i	$0.133072\pi$
$420$		0			0
$421$	11.9016			0.580047			0.290024	−	0.957020i	$-0.406337\pi$
$421$	11.9016			0.580047			0.290024	+	0.957020i	$0.406337\pi$
$422$	−1.15743	−	32.4642i	−0.0563428	−	1.58033i
$423$	−23.1754	−	13.3733i	−1.12683	−	0.650233i
$424$	−10.9548	+	7.99591i	−0.532014	+	0.388316i
$425$	−2.23533	−	1.29057i	−0.108429	−	0.0626016i
$426$	−17.3202	+	18.6052i	−0.839169	+	0.901423i
$427$		0			0
$428$	−7.10815	+	14.6281i	−0.343586	+	0.707076i
$429$	1.87851	+	0.503117i	0.0906954	+	0.0242907i
$430$	17.7071	−	33.3609i	0.853911	−	1.60881i
$431$	−1.69362	−	2.93344i	−0.0815789	−	0.141299i	0.822349	−	0.568983i	$-0.192663\pi$
$431$	−1.69362	−	2.93344i	−0.0815789	−	0.141299i	−0.903928	+	0.427684i	$0.859330\pi$
$432$	−16.6401	−	12.4542i	−0.800596	−	0.599205i
$433$	−26.7819			−1.28706			−0.643528	−	0.765423i	$-0.722530\pi$
$433$	−26.7819			−1.28706			−0.643528	+	0.765423i	$0.722530\pi$
$434$		0			0
$435$	9.45520	+	35.2713i	0.453342	+	1.69113i
$436$	−21.3882	−	31.6096i	−1.02431	−	1.51383i
$437$	−7.14292	+	4.12397i	−0.341692	+	0.197276i
$438$	−11.2004	−	2.57587i	−0.535178	−	0.123080i
$439$	−3.26907	−	1.88740i	−0.156024	−	0.0900805i	0.419955	−	0.907545i	$-0.362046\pi$
$439$	−3.26907	−	1.88740i	−0.156024	−	0.0900805i	−0.575979	+	0.817464i	$0.695379\pi$
$440$	−0.360814	−	3.36199i	−0.0172011	−	0.160277i
$441$		0			0
$442$	1.34596	−	0.842420i	0.0640209	−	0.0400698i
$443$	3.39479	−	5.87995i	0.161291	−	0.279365i	−0.774041	−	0.633136i	$-0.781767\pi$
$443$	3.39479	−	5.87995i	0.161291	−	0.279365i	0.935332	+	0.353771i	$0.115101\pi$
$444$	3.62034	+	10.4607i	0.171814	+	0.496441i
$445$	−6.89872	−	11.9489i	−0.327031	−	0.566434i
$446$	−0.488001	−	13.6877i	−0.0231075	−	0.648133i
$447$	−25.8602	+	6.93237i	−1.22315	+	0.327890i
$448$		0			0
$449$			12.9080i			0.609168i	0.952485	+	0.304584i	$0.0985174\pi$
$449$			12.9080i			0.609168i	−0.952485	+	0.304584i	$0.901483\pi$
$450$	−27.6587	+	17.3199i	−1.30384	+	0.816470i
$451$	0.423806	−	0.244684i	0.0199562	−	0.0115217i
$452$	1.79337	+	25.1188i	0.0843532	+	1.18149i
$453$	−6.80905	+	25.4233i	−0.319917	+	1.19449i
$454$	−10.0568	−	16.0682i	−0.471991	−	0.754116i
$455$		0			0
$456$	8.45138	−	3.26656i	0.395772	−	0.152971i
$457$	−13.5906	+	23.5397i	−0.635744	+	1.10114i	0.350613	+	0.936520i	$0.385973\pi$
$457$	−13.5906	+	23.5397i	−0.635744	+	1.10114i	−0.986357	+	0.164620i	$0.947360\pi$
$458$	−11.0922	+	20.8982i	−0.518305	+	0.976511i
$459$	1.68438	+	0.450713i	0.0786202	+	0.0210375i
$460$	26.3165	−	17.8067i	1.22701	−	0.830243i
$461$			7.31937i			0.340897i	0.985367	+	0.170448i	$0.0545216\pi$
$461$			7.31937i			0.340897i	−0.985367	+	0.170448i	$0.945478\pi$
$462$		0			0
$463$		−	3.77479i		−	0.175430i	−0.996146	−	0.0877148i	$-0.972044\pi$
$463$		−	3.77479i		−	0.175430i	0.996146	−	0.0877148i	$-0.0279564\pi$
$464$	3.36294	+	23.4314i	0.156121	+	1.08778i
$465$	−22.6665	+	22.6717i	−1.05113	+	1.05137i
$466$	−26.1372	−	13.8729i	−1.21078	−	0.642649i
$467$	−14.7240	+	25.5028i	−0.681346	+	1.18013i	0.293224	+	0.956044i	$0.405272\pi$
$467$	−14.7240	+	25.5028i	−0.681346	+	1.18013i	−0.974570	+	0.224083i	$0.928061\pi$
$468$	−1.43424	−	20.0245i	−0.0662976	−	0.925632i
$469$		0			0
$470$	−38.0908	+	23.8405i	−1.75700	+	1.09968i
$471$	1.59783	+	0.427943i	0.0736242	+	0.0197186i
$472$	23.3861	+	32.0402i	1.07643	+	1.47477i
$473$	−2.17852	+	1.25777i	−0.100168	+	0.0578323i
$474$	−9.36741	+	2.87256i	−0.430260	+	0.131941i
$475$		−	14.2263i		−	0.652746i
$476$		0			0
$477$	−7.19547	−	12.4564i	−0.329458	−	0.570338i
$478$	29.8554	−	1.06442i	1.36555	−	0.0486854i
$479$	−16.8314	−	29.1529i	−0.769047	−	1.33203i	−0.938080	−	0.346419i	$-0.887398\pi$
$479$	−16.8314	−	29.1529i	−0.769047	−	1.33203i	0.169033	−	0.985610i	$-0.445936\pi$
$480$	−31.5797	+	14.8710i	−1.44141	+	0.678764i
$481$	−5.34596	+	9.25948i	−0.243755	+	0.422196i
$482$	19.7904	+	31.6198i	0.901426	+	1.44024i
$483$		0			0
$484$	9.51683	−	19.5850i	0.432583	−	0.890227i
$485$	−6.17056	−	3.56257i	−0.280191	−	0.161768i
$486$	15.0140	−	16.1425i	0.681048	−	0.732239i
$487$	18.3435	−	10.5906i	0.831225	−	0.479908i	−0.0230468	−	0.999734i	$-0.507337\pi$
$487$	18.3435	−	10.5906i	0.831225	−	0.479908i	0.854272	+	0.519826i	$0.174003\pi$
$488$	−0.404158	+	0.913135i	−0.0182954	+	0.0413357i
$489$	16.5414	−	4.43428i	0.748029	−	0.200525i
$490$		0			0
$491$	12.1208			0.547005			0.273502	−	0.961871i	$-0.411818\pi$
$491$	12.1208			0.547005			0.273502	+	0.961871i	$0.411818\pi$
$492$	−3.81791	−	3.30831i	−0.172125	−	0.149150i
$493$	−0.992912	−	1.71977i	−0.0447185	−	0.0774548i
$494$	7.73029	+	4.10302i	0.347802	+	0.184604i
$495$	3.58641		0.000815206i	0.161197		3.66408e-5i
$496$	−16.3389	+	12.8424i	−0.733637	+	0.576642i
$497$		0			0
$498$	11.5152	−	12.3695i	0.516008	−	0.554289i
$499$	31.6786	+	18.2897i	1.41813	+	0.818758i	0.996135	−	0.0878403i	$-0.0279965\pi$
$499$	31.6786	+	18.2897i	1.41813	+	0.818758i	0.421995	+	0.906598i	$0.361330\pi$
$500$	1.36592	+	19.1317i	0.0610857	+	0.855594i
$501$	−1.37497	+	1.37528i	−0.0614290	+	0.0614430i
$502$	−7.92526	+	0.282555i	−0.353721	+	0.0126110i
$503$	−0.890599			−0.0397098			−0.0198549	−	0.999803i	$-0.506320\pi$
$503$	−0.890599			−0.0397098			−0.0198549	+	0.999803i	$0.506320\pi$
$504$		0			0
$505$	−46.8577			−2.08514
$506$	−2.11496	+	0.0754037i	−0.0940217	+	0.00335210i
$507$	−2.20984	+	2.21034i	−0.0981423	+	0.0981646i
$508$	−1.45112	−	20.3250i	−0.0643830	−	0.901777i
$509$	1.34164	+	0.774595i	0.0594671	+	0.0343333i	0.529439	−	0.848348i	$-0.322403\pi$
$509$	1.34164	+	0.774595i	0.0594671	+	0.0343333i	−0.469972	+	0.882681i	$0.655736\pi$
$510$	1.99528	−	2.14330i	0.0883525	−	0.0949071i
$511$		0			0
$512$	−21.4735	+	7.13364i	−0.949004	+	0.315265i
$513$	2.49050	+	9.28201i	0.109958	+	0.409811i
$514$	22.7019	+	12.0495i	1.00134	+	0.531482i
$515$	−14.0497	−	24.3348i	−0.619104	−	1.07232i
$516$	19.6255	+	17.0060i	0.863963	+	0.748646i
$517$	2.99291			0.131628
$518$		0			0
$519$	26.0438	−	6.98159i	1.14320	−	0.306458i
$520$	−30.8307	−	13.6458i	−1.35201	−	0.598407i
$521$	30.7960	−	17.7801i	1.34920	−	0.778959i	0.361061	−	0.932542i	$-0.382415\pi$
$521$	30.7960	−	17.7801i	1.34920	−	0.778959i	0.988136	+	0.153583i	$0.0490814\pi$
$522$	−25.0913	+	0.900277i	−1.09822	+	0.0394040i
$523$	12.1572	+	7.01894i	0.531596	+	0.306917i	0.741666	−	0.670769i	$-0.234036\pi$
$523$	12.1572	+	7.01894i	0.531596	+	0.306917i	−0.210070	+	0.977686i	$0.567369\pi$
$524$	−9.16696	+	18.8650i	−0.400460	+	0.824120i
$525$		0			0
$526$	−13.2967	−	21.2447i	−0.579766	−	0.926312i
$527$	0.871706	−	1.50984i	0.0379721	−	0.0657696i
$528$	2.30837	+	0.276320i	0.100459	+	0.0120253i
$529$	1.55630	+	2.69559i	0.0676653	+	0.117200i
$530$	−24.1435	+	0.860775i	−1.04873	+	0.0373897i
$531$	−36.4318	+	21.0450i	−1.58101	+	0.913274i
$532$		0			0
$533$		−	4.87958i		−	0.211358i
$534$	9.06973	−	2.78127i	0.392486	−	0.120357i
$535$	−25.0890	+	14.4851i	−1.08469	+	0.626247i
$536$	7.30036	−	5.32851i	0.315327	−	0.230157i
$537$	36.3243	+	9.72865i	1.56751	+	0.419822i
$538$	14.9626	−	9.36491i	0.645085	−	0.403750i
$539$		0			0
$540$	−12.1167	−	34.9845i	−0.521420	−	1.50549i
$541$	16.1392	−	27.9539i	0.693877	−	1.20183i	−0.276681	−	0.960962i	$-0.589234\pi$
$541$	16.1392	−	27.9539i	0.693877	−	1.20183i	0.970558	−	0.240868i	$-0.0774322\pi$
$542$	2.24530	+	1.19174i	0.0964437	+	0.0511896i
$543$	−20.1188	+	20.1234i	−0.863382	+	0.863578i
$544$	1.44966	−	1.22547i	0.0621539	−	0.0525415i
$545$		−	67.9841i		−	2.91212i
$546$		0			0
$547$			19.8732i			0.849718i	0.905260	+	0.424859i	$0.139676\pi$
$547$			19.8732i			0.849718i	−0.905260	+	0.424859i	$0.860324\pi$
$548$	14.7739	−	9.99655i	0.631109	−	0.427032i
$549$	−0.917373	−	0.529368i	−0.0391525	−	0.0225929i
$550$	1.71134	−	3.22425i	0.0729719	−	0.137482i
$551$	5.47258	−	9.47878i	0.233140	−	0.403810i
$552$	7.87633	+	20.3780i	0.335239	+	0.867343i
$553$		0			0
$554$	−17.4603	−	27.8969i	−0.741817	−	1.18523i
$555$	−5.10119	+	19.0465i	−0.216533	+	0.808481i
$556$	−0.290254	−	4.06543i	−0.0123095	−	0.172413i
$557$	25.5814	−	14.7694i	1.08392	−	0.625801i	0.151969	−	0.988385i	$-0.451439\pi$
$557$	25.5814	−	14.7694i	1.08392	−	0.625801i	0.931951	+	0.362584i	$0.118105\pi$
$558$	−11.6987	−	18.6819i	−0.495244	−	0.790868i
$559$			25.0829i			1.06089i
$560$		0			0
$561$	−0.188383	+	0.0505000i	−0.00795353	+	0.00213211i
$562$	1.16746	+	32.7456i	0.0492464	+	1.38129i
$563$	10.3742	+	17.9687i	0.437222	+	0.757290i	0.997474	−	0.0710320i	$-0.0226292\pi$
$563$	10.3742	+	17.9687i	0.437222	+	0.757290i	−0.560253	+	0.828322i	$0.689296\pi$
$564$	−10.1049	−	29.1974i	−0.425494	−	1.22943i
$565$	−22.4288	+	38.8479i	−0.943588	+	1.63434i
$566$	2.21714	−	1.38768i	0.0931933	−	0.0583284i
$567$		0			0
$568$	−29.1841	+	3.13208i	−1.22454	+	0.131419i
$569$	−4.10894	−	2.37230i	−0.172256	−	0.0994518i	0.411393	−	0.911458i	$-0.365042\pi$
$569$	−4.10894	−	2.37230i	−0.172256	−	0.0994518i	−0.583649	+	0.812006i	$0.698376\pi$
$570$	15.7291	+	3.61736i	0.658819	+	0.151515i
$571$	15.8172	−	9.13208i	0.661930	−	0.382166i	−0.131082	−	0.991372i	$-0.541845\pi$
$571$	15.8172	−	9.13208i	0.661930	−	0.382166i	0.793012	+	0.609206i	$0.208512\pi$
$572$	1.25843	+	1.85982i	0.0526174	+	0.0777631i
$573$	5.43592	+	20.2779i	0.227089	+	0.847122i
$574$		0			0
$575$	34.3024			1.43051
$576$	−5.09810	−	23.4523i	−0.212421	−	0.977178i
$577$	3.18838	+	5.52244i	0.132734	+	0.229902i	0.924730	−	0.380625i	$-0.124291\pi$
$577$	3.18838	+	5.52244i	0.132734	+	0.229902i	−0.791995	+	0.610527i	$0.790958\pi$
$578$	11.1967	−	21.0951i	0.465721	−	0.877440i
$579$	12.8811	+	3.44991i	0.535320	+	0.143373i
$580$	−18.4288	+	37.9253i	−0.765216	+	1.57476i
$581$		0			0
$582$	3.33807	−	3.58571i	0.138367	−	0.148632i
$583$	1.39349	+	0.804530i	0.0577123	+	0.0333202i
$584$	−7.82388	−	10.7192i	−0.323755	−	0.443562i
$585$	17.8733	−	30.9738i	0.738971	−	1.28061i
$586$	−0.0780609	−	2.18950i	−0.00322467	−	0.0904472i
$587$	−16.8907			−0.697152			−0.348576	−	0.937280i	$-0.613335\pi$
$587$	−16.8907			−0.697152			−0.348576	+	0.937280i	$0.613335\pi$
$588$		0			0
$589$	9.60906			0.395934
$590$	2.51755	+	70.6137i	0.103646	+	2.90712i
$591$	−8.62399	−	8.62203i	−0.354744	−	0.354663i
$592$	−4.75351	+	11.8651i	−0.195368	+	0.487653i
$593$	35.2229	+	20.3360i	1.44643	+	0.835097i	0.998267	−	0.0588537i	$-0.0187445\pi$
$593$	35.2229	+	20.3360i	1.44643	+	0.835097i	0.448165	+	0.893951i	$0.352078\pi$
$594$	−0.552127	+	2.40327i	−0.0226540	+	0.0986075i
$595$		0			0
$596$	−27.8061	−	13.5117i	−1.13898	−	0.553460i
$597$	−9.58205	+	35.7770i	−0.392167	+	1.46425i
$598$	−9.89320	+	18.6393i	−0.404563	+	0.762216i
$599$	3.64587	+	6.31483i	0.148966	+	0.258017i	0.930846	−	0.365413i	$-0.119072\pi$
$599$	3.64587	+	6.31483i	0.148966	+	0.258017i	−0.781879	+	0.623430i	$0.785739\pi$
$600$	−37.2321	−	5.80901i	−1.52000	−	0.237152i
$601$	−30.6778			−1.25137			−0.625686	−	0.780075i	$-0.715181\pi$
$601$	−30.6778			−1.25137			−0.625686	+	0.780075i	$0.715181\pi$
$602$		0			0
$603$	4.79509	+	8.30099i	0.195271	+	0.338042i
$604$	−25.1704	+	17.0312i	−1.02417	+	0.692990i
$605$	33.5907	−	19.3936i	1.36565	−	0.788461i
$606$	7.22086	−	31.3979i	0.293327	−	1.27545i
$607$	−11.5251	−	6.65404i	−0.467791	−	0.270079i	0.247524	−	0.968882i	$-0.420383\pi$
$607$	−11.5251	−	6.65404i	−0.467791	−	0.270079i	−0.715314	+	0.698803i	$0.753716\pi$
$608$	9.84444	+	3.54240i	0.399245	+	0.143663i
$609$		0			0
$610$	−1.50778	+	0.943698i	−0.0610482	+	0.0382092i
$611$	14.9214	−	25.8447i	0.603656	−	1.04556i
$612$	1.12869	+	1.66727i	0.0456245	+	0.0673952i
$613$	−9.84242	−	17.0476i	−0.397532	−	0.688545i	0.595889	−	0.803067i	$-0.296800\pi$
$613$	−9.84242	−	17.0476i	−0.397532	−	0.688545i	−0.993421	+	0.114522i	$0.963466\pi$
$614$	0.631940	+	17.7250i	0.0255030	+	0.715323i
$615$	−2.33005	−	8.69193i	−0.0939568	−	0.350492i
$616$		0			0
$617$		−	10.7470i		−	0.432656i	−0.976321	−	0.216328i	$-0.930592\pi$
$617$		−	10.7470i		−	0.432656i	0.976321	−	0.216328i	$-0.0694081\pi$
$618$	18.4711	−	5.66425i	0.743018	−	0.227850i
$619$	39.6093	−	22.8685i	1.59203	−	0.919161i	0.599075	−	0.800693i	$-0.295535\pi$
$619$	39.6093	−	22.8685i	1.59203	−	0.919161i	0.992958	−	0.118468i	$-0.0377983\pi$
$620$	−36.9245	+	2.63625i	−1.48292	+	0.105874i
$621$	−22.3808	+	6.00509i	−0.898109	+	0.240976i
$622$	9.04498	+	14.4515i	0.362671	+	0.579452i
$623$		0			0
$624$	13.8947	−	18.5559i	0.556233	−	0.742829i
$625$	2.14695	−	3.71862i	0.0858780	−	0.148745i
$626$	−14.6367	+	27.5762i	−0.585000	+	1.10217i
$627$	−0.760197	−	0.760024i	−0.0303593	−	0.0303524i
$628$	1.07040	+	1.58194i	0.0427135	+	0.0631261i
$629$		−	1.07228i		−	0.0427548i
$630$		0			0
$631$			2.61615i			0.104147i	0.998643	+	0.0520736i	$0.0165830\pi$
$631$			2.61615i			0.104147i	−0.998643	+	0.0520736i	$0.983417\pi$
$632$	−10.3457	−	4.57903i	−0.411528	−	0.182144i
$633$	28.1359	+	28.1295i	1.11830	+	1.11805i
$634$	4.31315	+	2.28930i	0.171297	+	0.0909198i
$635$	18.1484	−	31.4340i	0.720198	−	1.24742i
$636$	3.14378	−	16.3105i	0.124659	−	0.646752i
$637$		0			0
$638$	2.38055	−	1.48995i	0.0942470	−	0.0589879i
$639$	−0.00707648	−	31.1322i	−0.000279941	−	1.23157i
$640$	−38.8009	−	10.9115i	−1.53374	−	0.431314i
$641$	19.5572	−	11.2914i	0.772463	−	0.445982i	−0.0612896	−	0.998120i	$-0.519521\pi$
$641$	19.5572	−	11.2914i	0.772463	−	0.445982i	0.833752	+	0.552138i	$0.186188\pi$
$642$	−5.83979	−	19.0436i	−0.230478	−	0.751590i
$643$			9.32332i			0.367676i	0.982957	+	0.183838i	$0.0588521\pi$
$643$			9.32332i			0.367676i	−0.982957	+	0.183838i	$0.941148\pi$
$644$		0			0
$645$	11.9774	+	44.6798i	0.471608	+	1.75926i
$646$	−0.877143	+	0.0312723i	−0.0345107	+	0.00123039i
$647$	7.77102	+	13.4598i	0.305510	+	0.529160i	0.977375	−	0.211515i	$-0.0678396\pi$
$647$	7.77102	+	13.4598i	0.305510	+	0.529160i	−0.671864	+	0.740674i	$0.734506\pi$
$648$	25.3093	−	2.72786i	0.994242	−	0.107161i
$649$	2.35305	−	4.07560i	0.0923653	−	0.159981i
$650$	−19.3103	−	30.8527i	−0.757411	−	1.21014i
$651$		0			0
$652$	17.7861	+	8.64271i	0.696558	+	0.338475i
$653$	8.14471	+	4.70235i	0.318727	+	0.184017i	0.650825	−	0.759228i	$-0.274423\pi$
$653$	8.14471	+	4.70235i	0.318727	+	0.184017i	−0.332098	+	0.943245i	$0.607756\pi$
$654$	45.5541	+	10.4765i	1.78131	+	0.409663i
$655$	−32.3558	+	18.6806i	−1.26424	+	0.729912i
$656$	−0.828734	−	5.77422i	−0.0323566	−	0.225446i
$657$	12.1884	−	7.04066i	0.475514	−	0.274682i
$658$		0			0
$659$	31.2507			1.21735			0.608677	−	0.793418i	$-0.291701\pi$
$659$	31.2507			1.21735			0.608677	+	0.793418i	$0.291701\pi$
$660$	3.12970	+	2.71197i	0.121824	+	0.105563i
$661$	11.9740	+	20.7395i	0.465733	+	0.806674i	0.999234	−	0.0391256i	$-0.0124573\pi$
$661$	11.9740	+	20.7395i	0.465733	+	0.806674i	−0.533501	+	0.845799i	$0.679124\pi$
$662$	33.5955	+	17.8316i	1.30573	+	0.693044i
$663$	−0.503117	+	1.87851i	−0.0195394	+	0.0729553i
$664$	19.4028	−	2.08233i	0.752975	−	0.0808102i
$665$		0			0
$666$	−11.9764	−	6.35326i	−0.464077	−	0.246184i
$667$	22.8552	+	13.1955i	0.884958	+	0.510931i
$668$	−2.23987	+	0.159917i	−0.0866630	+	0.00618737i
$669$	11.8628	+	11.8601i	0.458643	+	0.458538i
$670$	16.0893	−	0.573624i	0.621585	−	0.0221610i
$671$	0.118471			0.00457353
$672$		0			0
$673$	−23.8732			−0.920245			−0.460123	−	0.887855i	$-0.652195\pi$
$673$	−23.8732			−0.920245			−0.460123	+	0.887855i	$0.652195\pi$
$674$	−14.9519	+	0.533073i	−0.575927	+	0.0205332i
$675$	10.3314	−	38.6101i	0.397657	−	1.48610i
$676$	−3.59990	+	0.257017i	−0.138458	+	0.00988527i
$677$	−23.3406	−	13.4757i	−0.897052	−	0.517913i	−0.0208093	−	0.999783i	$-0.506624\pi$
$677$	−23.3406	−	13.4757i	−0.897052	−	0.517913i	−0.876243	+	0.481870i	$0.839958\pi$
$678$	−22.5745	−	21.0154i	−0.866967	−	0.807093i
$679$		0			0
$680$	3.36199	−	0.360814i	0.128927	−	0.0138366i
$681$	22.4257	+	6.00623i	0.859356	+	0.230159i
$682$	2.17780	+	1.15592i	0.0833924	+	0.0442624i
$683$	11.7777	+	20.3996i	0.450661	+	0.780568i	0.998427	−	0.0560632i	$-0.0178548\pi$
$683$	11.7777	+	20.3996i	0.450661	+	0.780568i	−0.547766	+	0.836632i	$0.684522\pi$
$684$	−4.84777	+	9.98216i	−0.185359	+	0.381677i
$685$	31.7748			1.21405
$686$		0			0
$687$	−7.50295	−	27.9887i	−0.286255	−	1.06783i
$688$	4.26000	+	29.6817i	0.162411	+	1.13160i
$689$	13.8947	−	8.02210i	0.529345	−	0.305618i
$690$	−8.72218	+	37.9260i	−0.332048	+	1.44382i
$691$	3.67967	+	2.12446i	0.139981	+	0.0808183i	0.568355	−	0.822783i	$-0.307580\pi$
$691$	3.67967	+	2.12446i	0.139981	+	0.0808183i	−0.428374	+	0.903602i	$0.640913\pi$
$692$	28.0035	+	13.6076i	1.06453	+	0.517283i
$693$		0			0
$694$	18.9437	+	30.2670i	0.719093	+	1.14892i
$695$	3.63007	−	6.28746i	0.137696	−	0.238497i
$696$	−22.5727	−	18.1930i	−0.855615	−	0.689603i
$697$	0.244684	+	0.423806i	0.00926808	+	0.0160528i
$698$	−30.2957	+	1.08012i	−1.14671	+	0.0408830i
$699$	35.0051	−	9.38385i	1.32401	−	0.354930i
$700$		0			0
$701$		−	8.60239i		−	0.324908i	−0.986716	−	0.162454i	$-0.948059\pi$
$701$		−	8.60239i		−	0.324908i	0.986716	−	0.162454i	$-0.0519409\pi$
$702$	18.0003	+	16.7495i	0.679377	+	0.632169i
$703$	5.11825	−	2.95502i	0.193038	−	0.111451i
$704$	1.80502	+	1.98708i	0.0680292	+	0.0748911i
$705$	14.2382	−	53.1619i	0.536242	−	2.00219i
$706$	−10.2897	+	6.44015i	−0.387257	+	0.242378i
$707$		0			0
$708$	−47.7041	−	9.19478i	−1.79283	−	0.345561i
$709$	7.35305	−	12.7359i	0.276150	−	0.478305i	−0.694275	−	0.719710i	$-0.744275\pi$
$709$	7.35305	−	12.7359i	0.276150	−	0.478305i	0.970425	+	0.241405i	$0.0776081\pi$
$710$	−46.1818	−	24.5120i	−1.73317	−	0.919920i
$711$	5.99764	−	10.3937i	0.224929	−	0.389793i
$712$	10.0169	+	4.43352i	0.375399	+	0.166153i
$713$			23.1693i			0.867699i
$714$		0			0
$715$			4.00000i			0.149592i
$716$	24.3339	+	35.9629i	0.909399	+	1.34400i
$717$	−25.8690	+	25.8749i	−0.966096	+	0.966316i
$718$	−4.44562	+	8.37575i	−0.165909	+	0.312580i
$719$	5.46622	−	9.46777i	0.203856	−	0.353088i	−0.745912	−	0.666045i	$-0.767986\pi$
$719$	5.46622	−	9.46777i	0.203856	−	0.353088i	0.949768	+	0.312956i	$0.101319\pi$
$720$	15.8898	−	39.6882i	0.592178	−	1.47909i
$721$		0			0
$722$	11.6891	+	18.6761i	0.435023	+	0.695052i
$723$	−44.1305	−	11.8194i	−1.64123	−	0.439567i
$724$	−32.7742	+	2.33994i	−1.21804	+	0.0869631i
$725$	−39.4214	+	22.7599i	−1.46407	+	0.845283i
$726$	7.81867	+	25.4967i	0.290178	+	0.946271i
$727$		−	38.8803i		−	1.44199i	−0.692940	−	0.720995i	$-0.743685\pi$
$727$		−	38.8803i		−	1.44199i	0.692940	−	0.720995i	$-0.256315\pi$
$728$		0			0
$729$	0.0184116	+	27.0000i	0.000681912	+	1.00000i
$730$	−0.842255	−	23.6240i	−0.0311733	−	0.874365i
$731$	−1.25777	−	2.17852i	−0.0465203	−	0.0805755i
$732$	−0.399992	−	1.15574i	−0.0147841	−	0.0427175i
$733$	−5.56038	+	9.63086i	−0.205377	+	0.355724i	−0.950253	−	0.311480i	$-0.899175\pi$
$733$	−5.56038	+	9.63086i	−0.205377	+	0.355724i	0.744876	+	0.667203i	$0.232509\pi$
$734$	−29.3470	+	18.3679i	−1.08322	+	0.677972i
$735$		0			0
$736$	−8.54143	+	23.7369i	−0.314841	+	0.874954i
$737$	−0.928625	−	0.536142i	−0.0342063	−	0.0197490i
$738$	6.18327	−	0.221856i	0.227609	−	0.00816663i
$739$	−27.6030	+	15.9366i	−1.01539	+	0.586238i	−0.912766	−	0.408482i	$-0.866058\pi$
$739$	−27.6030	+	15.9366i	−1.01539	+	0.586238i	−0.102627	+	0.994720i	$0.532725\pi$
$740$	−18.8571	+	12.7594i	−0.693199	+	0.469044i
$741$	−10.3531	+	2.77535i	−0.380329	+	0.101955i
$742$		0			0
$743$	24.5432			0.900403			0.450202	−	0.892927i	$-0.351352\pi$
$743$	24.5432			0.900403			0.450202	+	0.892927i	$0.351352\pi$
$744$	3.92367	−	25.1483i	0.143849	−	0.921980i
$745$	−27.5343	−	47.6909i	−1.00878	−	1.74726i
$746$	2.91128	−	5.48499i	0.106590	−	0.200820i
$747$	0.00470473	+	20.6980i	0.000172137	+	0.757298i
$748$	−0.202558	−	0.0984279i	−0.00740625	−	0.00359888i
$749$		0			0
$750$	−17.1938	−	16.0064i	−0.627829	−	0.584469i
$751$	−0.370454	−	0.213882i	−0.0135181	−	0.00780467i	0.493226	−	0.869901i	$-0.335818\pi$
$751$	−0.370454	−	0.213882i	−0.0135181	−	0.00780467i	−0.506744	+	0.862097i	$0.669151\pi$
$752$	13.2678	−	33.1173i	0.483827	−	1.20767i
$753$	6.86705	−	6.86861i	0.250249	−	0.250306i
$754$	−0.997736	−	27.9851i	−0.0363354	−	1.01916i
$755$	−54.1350			−1.97017
$756$		0			0
$757$	51.4596			1.87033			0.935166	−	0.354210i	$-0.115250\pi$
$757$	51.4596			1.87033			0.935166	+	0.354210i	$0.115250\pi$
$758$	−0.850568	−	23.8572i	−0.0308940	−	0.866533i
$759$	1.83257	−	1.83299i	0.0665180	−	0.0665332i
$760$	10.9873	+	15.0532i	0.398551	+	0.546037i
$761$	−7.82467	−	4.51758i	−0.283644	−	0.163762i	0.351428	−	0.936215i	$-0.385696\pi$
$761$	−7.82467	−	4.51758i	−0.283644	−	0.163762i	−0.635072	+	0.772453i	$0.719030\pi$
$762$	18.2663	+	17.0048i	0.661717	+	0.616018i
$763$		0			0
$764$	−10.5950	+	21.8037i	−0.383313	+	0.788832i
$765$	0.000815206		3.58641i	2.94738e−5		0.129667i
$766$	−15.8067	+	29.7806i	−0.571120	+	1.07602i
$767$	−23.4627	−	40.6385i	−0.847188	−	1.46737i
$768$	13.2907	−	24.3178i	0.479588	−	0.877494i
$769$	−21.1728			−0.763511			−0.381756	−	0.924263i	$-0.624680\pi$
$769$	−21.1728			−0.763511			−0.381756	+	0.924263i	$0.624680\pi$
$770$		0			0
$771$	−30.4042	+	8.15049i	−1.09498	+	0.293533i
$772$	8.62912	+	12.7529i	0.310569	+	0.458989i
$773$	3.56389	−	2.05761i	0.128184	−	0.0740073i	−0.434537	−	0.900654i	$-0.643088\pi$
$773$	3.56389	−	2.05761i	0.128184	−	0.0740073i	0.562721	+	0.826647i	$0.309755\pi$
$774$	−31.7843	+	1.14042i	−1.14246	+	0.0409917i
$775$	−34.6091	−	19.9816i	−1.24320	−	0.717760i
$776$	5.62456	−	0.603635i	0.201910	−	0.0216692i
$777$		0			0
$778$	24.1771	−	15.1321i	0.866790	−	0.542511i
$779$	−1.34861	+	2.33586i	−0.0483190	+	0.0836910i
$780$	39.0220	−	13.5051i	1.39721	−	0.483562i
$781$	1.74114	+	3.01574i	0.0623029	+	0.107912i
$782$	−0.0754037	−	2.11496i	−0.00269643	−	0.0756310i
$783$	21.7363	−	21.7511i	0.776790	−	0.777320i
$784$		0			0
$785$			3.40234i			0.121435i
$786$	−7.53123	−	24.5593i	−0.268630	−	0.876003i
$787$	−25.9479	+	14.9811i	−0.924944	+	0.534017i	−0.885209	−	0.465193i	$-0.845985\pi$
$787$	−25.9479	+	14.9811i	−0.924944	+	0.534017i	−0.0397353	+	0.999210i	$0.512651\pi$
$788$	−1.00279	−	14.0456i	−0.0357230	−	0.500353i
$789$	29.6504	+	7.94120i	1.05558	+	0.282714i
$790$	−10.6919	−	17.0829i	−0.380402	−	0.607781i
$791$		0			0
$792$	−2.29950	+	1.67920i	−0.0817092	+	0.0596678i
$793$	0.590648	−	1.02303i	0.0209745	−	0.0363289i
$794$	−12.1590	+	22.9082i	−0.431508	+	0.812982i
$795$	20.9198	−	20.9245i	0.741948	−	0.742117i
$796$	−35.4210	+	23.9672i	−1.25547	+	0.849495i
$797$		−	49.0485i		−	1.73739i	−0.495351	−	0.868693i	$-0.664961\pi$
$797$		−	49.0485i		−	1.73739i	0.495351	−	0.868693i	$-0.335039\pi$
$798$		0			0
$799$			2.99291i			0.105882i
$800$	−28.0907	−	33.2298i	−0.993154	−	1.17485i
$801$	−5.80704	+	10.0634i	−0.205182	+	0.355572i
$802$	10.7458	+	5.70356i	0.379446	+	0.201400i
$803$	−0.787220	+	1.36351i	−0.0277804	+	0.0481171i
$804$	−2.09503	+	10.8694i	−0.0738860	+	0.383333i
$805$		0			0
$806$	20.8393	−	13.0430i	0.734033	−	0.459421i
$807$	−5.59299	+	20.8828i	−0.196883	+	0.735110i
$808$	30.0487	−	21.9325i	1.05711	−	0.771582i
$809$	−45.6029	+	26.3289i	−1.60331	+	0.925674i	−0.612495	+	0.790474i	$0.709834\pi$
$809$	−45.6029	+	26.3289i	−1.60331	+	0.925674i	−0.990818	+	0.135199i	$0.956832\pi$
$810$	40.0617	+	21.2403i	1.40763	+	0.746309i
$811$		−	37.5117i		−	1.31721i	−0.752487	−	0.658607i	$-0.771146\pi$
$811$		−	37.5117i		−	1.31721i	0.752487	−	0.658607i	$-0.228854\pi$
$812$		0			0
$813$	−3.00709	+	0.806113i	−0.105463	+	0.0282716i
$814$	1.51548	−	0.0540304i	0.0531174	−	0.00189377i
$815$	17.6123	+	30.5054i	0.616932	+	1.06856i
$816$	−0.276320	+	2.30837i	−0.00967312	+	0.0808093i
$817$	6.93237	−	12.0072i	0.242533	−	0.420080i
$818$	3.23764	+	5.17290i	0.113202	+	0.180866i
$819$		0			0
$820$	4.54143	−	9.34596i	0.158594	−	0.326375i
$821$	1.82782	+	1.05529i	0.0637913	+	0.0368299i	0.531556	−	0.847023i	$-0.321607\pi$
$821$	1.82782	+	1.05529i	0.0637913	+	0.0368299i	−0.467765	+	0.883853i	$0.654941\pi$
$822$	−4.89656	+	21.2913i	−0.170787	+	0.742621i
$823$	45.5154	−	26.2783i	1.58657	−	0.916005i	0.592701	−	0.805423i	$-0.298062\pi$
$823$	45.5154	−	26.2783i	1.58657	−	0.916005i	0.993867	−	0.110582i	$-0.0352716\pi$
$824$	20.4001	+	9.02916i	0.710670	+	0.314546i
$825$	1.15758	+	4.31819i	0.0403018	+	0.150340i
$826$		0			0
$827$	−10.3774			−0.360858			−0.180429	−	0.983588i	$-0.557749\pi$
$827$	−10.3774			−0.360858			−0.180429	+	0.983588i	$0.557749\pi$
$828$	−24.0690	−	11.6889i	−0.836454	−	0.406219i
$829$	−0.717959	−	1.24354i	−0.0249358	−	0.0431900i	0.853288	−	0.521440i	$-0.174605\pi$
$829$	−0.717959	−	1.24354i	−0.0249358	−	0.0431900i	−0.878224	+	0.478250i	$0.841271\pi$
$830$	30.7035	+	16.2966i	1.06574	+	0.565663i
$831$	38.9347	+	10.4278i	1.35063	+	0.361736i
$832$	26.1581	−	5.68007i	0.906869	−	0.196921i
$833$		0			0
$834$	3.65364	+	3.40131i	0.126515	+	0.117778i
$835$	−3.46410	−	2.00000i	−0.119880	−	0.0692129i
$836$	−0.0883952	−	1.23810i	−0.00305721	−	0.0428207i
$837$	26.0790	+	6.97831i	0.901421	+	0.241206i
$838$	−52.8768	+	1.88519i	−1.82660	+	0.0651227i
$839$	1.39275			0.0480832			0.0240416	−	0.999711i	$-0.492347\pi$
$839$	1.39275			0.0480832			0.0240416	+	0.999711i	$0.492347\pi$
$840$		0			0
$841$	−6.02126			−0.207630
$842$	−16.8207	+	0.599699i	−0.579679	+	0.0206670i
$843$	−28.3798	−	28.3733i	−0.977451	−	0.977229i
$844$	3.27163	+	45.8239i	0.112614	+	1.57732i
$845$	−5.56748	−	3.21438i	−0.191527	−	0.110578i
$846$	33.4281	+	17.7330i	1.14928	+	0.609671i
$847$		0			0
$848$	15.0798	−	11.8527i	0.517841	−	0.407025i
$849$	−0.828760	+	3.09438i	−0.0284430	+	0.106199i
$850$	3.22425	+	1.71134i	0.110591	+	0.0586986i
$851$	7.12515	+	12.3411i	0.244247	+	0.423048i
$852$	23.5415	−	27.1677i	0.806518	−	0.930750i
$853$	18.6399			0.638217			0.319108	−	0.947718i	$-0.396617\pi$
$853$	18.6399			0.638217			0.319108	+	0.947718i	$0.396617\pi$
$854$		0			0
$855$	−17.1165	+	9.88740i	−0.585372	+	0.338142i
$856$	9.30898	−	21.0323i	0.318174	−	0.718869i
$857$	−26.7275	+	15.4311i	−0.912994	+	0.527117i	−0.881393	−	0.472383i	$-0.843394\pi$
$857$	−26.7275	+	15.4311i	−0.912994	+	0.527117i	−0.0316005	+	0.999501i	$0.510060\pi$
$858$	−2.68028	−	0.616408i	−0.0915033	−	0.0210438i
$859$	−15.5238	−	8.96264i	−0.529664	−	0.305801i	0.211216	−	0.977439i	$-0.432258\pi$
$859$	−15.5238	−	8.96264i	−0.529664	−	0.305801i	−0.740879	+	0.671638i	$0.765591\pi$
$860$	−23.3447	+	48.0418i	−0.796047	+	1.63821i
$861$		0			0
$862$	2.54143	+	4.06054i	0.0865616	+	0.138302i
$863$	2.52309	−	4.37011i	0.0858868	−	0.148760i	−0.819882	−	0.572533i	$-0.805961\pi$
$863$	2.52309	−	4.37011i	0.0858868	−	0.148760i	0.905769	+	0.423772i	$0.139294\pi$
$864$	24.1452	+	16.7633i	0.821437	+	0.570299i
$865$	27.7298	+	48.0295i	0.942842	+	1.63305i
$866$	37.8513	−	1.34949i	1.28624	−	0.0458576i
$867$	7.57362	+	28.2523i	0.257214	+	0.959499i
$868$		0			0
$869$			1.34226i			0.0455329i
$870$	−15.1404	−	49.3730i	−0.513309	−	1.67390i
$871$	−9.25948	+	5.34596i	−0.313746	+	0.181141i
$872$	31.8211	+	43.5966i	1.07760	+	1.47637i
$873$	0.00136382	+	6.00000i	4.61585e−5	+	0.203069i
$874$	9.88740	−	6.18838i	0.334446	−	0.209325i
$875$		0			0
$876$	15.9596	+	3.07614i	0.539223	+	0.103933i
$877$	0.345963	−	0.599226i	0.0116824	−	0.0202344i	−0.860125	−	0.510083i	$-0.829615\pi$
$877$	0.345963	−	0.599226i	0.0116824	−	0.0202344i	0.871807	+	0.489849i	$0.162948\pi$
$878$	4.71533	+	2.50277i	0.159135	+	0.0844642i
$879$	1.89758	+	1.89715i	0.0640037	+	0.0639892i
$880$	0.679349	+	4.73338i	0.0229008	+	0.159562i
$881$			38.2574i			1.28892i	0.764637	+	0.644462i	$0.222918\pi$
$881$			38.2574i			1.28892i	−0.764637	+	0.644462i	$0.777082\pi$
$882$		0			0
$883$		−	3.42068i		−	0.115115i	−0.998342	−	0.0575575i	$-0.981669\pi$
$883$		−	3.42068i		−	0.115115i	0.998342	−	0.0575575i	$-0.0183312\pi$
$884$	−1.85982	+	1.25843i	−0.0625526	+	0.0423254i
$885$	−61.1991	−	61.1852i	−2.05719	−	2.05672i
$886$	−4.50163	+	8.48128i	−0.151235	+	0.284934i
$887$	8.57714	−	14.8560i	0.287992	−	0.498817i	−0.685338	−	0.728225i	$-0.740346\pi$
$887$	8.57714	−	14.8560i	0.287992	−	0.498817i	0.973330	+	0.229408i	$0.0736790\pi$
$888$	−5.64377	−	14.6018i	−0.189393	−	0.490004i
$889$		0			0
$890$	10.3522	+	16.5400i	0.347005	+	0.554422i
$891$	−1.51123	−	2.61477i	−0.0506280	−	0.0875982i
$892$	1.37940	+	19.3205i	0.0461857	+	0.646898i
$893$	−14.2858	+	8.24793i	−0.478057	+	0.276006i
$894$	36.1993	−	11.1007i	1.21069	−	0.371262i
$895$			77.3470i			2.58543i
$896$		0			0
$897$	−6.69193	−	24.9633i	−0.223437	−	0.833499i
$898$	−0.650413	−	18.2431i	−0.0217045	−	0.608781i
$899$	−15.3731	−	26.6269i	−0.512721	−	0.888058i
$900$	38.2177	−	25.8722i	1.27392	−	0.862407i
$901$	−0.804530	+	1.39349i	−0.0268028	+	0.0464238i
$902$	−0.586642	+	0.367171i	−0.0195330	+	0.0122255i
$903$		0			0
$904$	−3.80029	−	35.4104i	−0.126396	−	1.17773i
$905$	−50.6875	−	29.2645i	−1.68491	−	0.972783i
$906$	8.34231	−	36.2742i	0.277155	−	1.20513i
$907$	26.6652	−	15.3952i	0.885404	−	0.511188i	0.0129679	−	0.999916i	$-0.495872\pi$
$907$	26.6652	−	15.3952i	0.885404	−	0.511188i	0.872437	+	0.488727i	$0.162539\pi$
$908$	15.0231	+	22.2026i	0.498560	+	0.736820i
$909$	19.7369	+	34.1674i	0.654632	+	1.13326i
$910$		0			0
$911$	14.8898			0.493321			0.246661	−	0.969102i	$-0.420667\pi$
$911$	14.8898			0.493321			0.246661	+	0.969102i	$0.420667\pi$
$912$	−11.7799	+	5.04253i	−0.390070	+	0.166975i
$913$	−1.15758	−	2.00499i	−0.0383103	−	0.0663554i
$914$	18.0218	−	33.9538i	0.596107	−	1.12309i
$915$	0.563603	−	2.10435i	0.0186322	−	0.0695678i
$916$	14.6238	−	30.0947i	0.483183	−	0.994358i
$917$		0			0
$918$	−2.40327	−	0.552127i	−0.0793198	−	0.0182229i
$919$	−2.59194	−	1.49646i	−0.0855002	−	0.0493635i	0.456640	−	0.889651i	$-0.349053\pi$
$919$	−2.59194	−	1.49646i	−0.0855002	−	0.0493635i	−0.542141	+	0.840288i	$0.682386\pi$
$920$	−36.2963	+	26.4926i	−1.19665	+	0.873434i
$921$	−15.3618	−	15.3583i	−0.506189	−	0.506074i
$922$	−0.368810	−	10.3446i	−0.0121461	−	0.340680i
$923$	34.7224			1.14290
$924$		0			0
$925$	−24.5793			−0.808163
$926$	0.190205	+	5.33498i	0.00625052	+	0.175318i
$927$	−11.8264	+	20.4947i	−0.388431	+	0.673136i
$928$	−5.93357	−	32.9465i	−0.194779	−	1.08152i
$929$	9.95946	+	5.75009i	0.326759	+	0.188654i	0.654401	−	0.756147i	$-0.272921\pi$
$929$	9.95946	+	5.75009i	0.326759	+	0.188654i	−0.327642	+	0.944802i	$0.606254\pi$
$930$	30.8926	−	33.1844i	1.01301	−	1.08816i
$931$		0			0
$932$	37.6391	+	18.2898i	1.23291	+	0.599101i
$933$	−20.1694	−	5.40192i	−0.660316	−	0.176851i
$934$	19.5247	−	36.7854i	0.638866	−	1.20365i
$935$	−0.200578	−	0.347412i	−0.00655961	−	0.0113616i
$936$	3.03603	+	28.2286i	0.0992356	+	0.922682i
$937$	49.6254			1.62119			0.810595	−	0.585607i	$-0.199144\pi$
$937$	49.6254			1.62119			0.810595	+	0.585607i	$0.199144\pi$
$938$		0			0
$939$	−9.90050	−	36.9324i	−0.323091	−	1.20524i
$940$	52.6330	−	35.6134i	1.71670	−	1.16158i
$941$	28.7399	−	16.5930i	0.936893	−	0.540915i	0.0479080	−	0.998852i	$-0.484745\pi$
$941$	28.7399	−	16.5930i	0.936893	−	0.540915i	0.888985	+	0.457936i	$0.151411\pi$
$942$	−2.27980	−	0.524307i	−0.0742801	−	0.0170828i
$943$	−5.63223	−	3.25177i	−0.183411	−	0.105892i
$944$	−34.6664	−	44.1046i	−1.12829	−	1.43548i
$945$		0			0
$946$	3.01556	−	1.88740i	0.0980443	−	0.0613646i
$947$	−25.0150	+	43.3272i	−0.812877	+	1.40794i	0.0979659	+	0.995190i	$0.468766\pi$
$947$	−25.0150	+	43.3272i	−0.812877	+	1.40794i	−0.910843	+	0.412754i	$0.864567\pi$
$948$	13.0944	−	4.53184i	0.425285	−	0.147187i
$949$	7.84951	+	13.5957i	0.254806	+	0.441337i
$950$	0.716836	+	20.1062i	0.0232572	+	0.652332i
$951$	−5.77653	+	1.54852i	−0.187317	+	0.0502142i
$952$		0			0
$953$		−	45.2664i		−	1.46632i	−0.680055	−	0.733162i	$-0.738044\pi$
$953$		−	45.2664i		−	1.46632i	0.680055	−	0.733162i	$-0.261956\pi$
$954$	10.7971	+	17.2422i	0.349570	+	0.558238i
$955$	−37.3961	+	21.5906i	−1.21011	+	0.698657i
$956$	−42.1415	+	3.00872i	−1.36295	+	0.0973089i
$957$	−0.889843	+	3.32245i	−0.0287645	+	0.107400i
$958$	25.2571	+	40.3541i	0.816019	+	1.30378i
$959$		0			0
$960$	43.8828	−	22.6086i	1.41631	−	0.729690i
$961$	−2.00354	+	3.47024i	−0.0646304	+	0.111943i
$962$	7.08897	−	13.3559i	0.228557	−	0.430613i
$963$	21.1299	+	12.1930i	0.680902	+	0.392912i
$964$	−29.5633	−	43.6915i	−0.952169	−	1.40721i
$965$			27.4283i			0.882948i
$966$		0			0
$967$			3.60059i			0.115787i	0.998323	+	0.0578935i	$0.0184384\pi$
$967$			3.60059i			0.115787i	−0.998323	+	0.0578935i	$0.981562\pi$
$968$	−12.4634	+	28.1593i	−0.400590	+	0.905074i
$969$	0.760024	−	0.760197i	0.0244155	−	0.0244210i
$970$	8.90046	+	4.72412i	0.285776	+	0.151682i
$971$	−16.3513	+	28.3213i	−0.524739	+	0.908875i	0.474846	+	0.880069i	$0.342504\pi$
$971$	−16.3513	+	28.3213i	−0.524739	+	0.908875i	−0.999585	+	0.0288062i	$0.990829\pi$
$972$	−20.4061	+	23.5710i	−0.654526	+	0.756040i
$973$		0			0
$974$	−25.3916	+	15.8922i	−0.813598	+	0.509220i
$975$	43.0600	+	11.5326i	1.37902	+	0.369340i
$976$	0.525191	−	1.31091i	0.0168110	−	0.0419613i
$977$	−15.2472	+	8.80296i	−0.487801	+	0.281632i	−0.723662	−	0.690155i	$-0.757542\pi$
$977$	−15.2472	+	8.80296i	−0.487801	+	0.281632i	0.235861	+	0.971787i	$0.424209\pi$
$978$	−23.1548	+	7.10053i	−0.740410	+	0.227050i
$979$		−	1.29960i		−	0.0415354i
$980$		0			0
$981$	−49.5722	+	28.6356i	−1.58272	+	0.914263i
$982$	−17.1305	+	0.610746i	−0.546657	+	0.0194897i
$983$	22.8085	+	39.5055i	0.727479	+	1.26003i	0.957945	+	0.286951i	$0.0926416\pi$
$983$	22.8085	+	39.5055i	0.727479	+	1.26003i	−0.230466	+	0.973080i	$0.574025\pi$
$984$	5.56261	+	4.48331i	0.177329	+	0.142923i
$985$	12.5414	−	21.7224i	0.399603	−	0.692133i
$986$	1.48995	+	2.38055i	0.0474498	+	0.0758123i
$987$		0			0
$988$	−11.1321	−	5.40935i	−0.354159	−	0.172094i
$989$	28.9518	+	16.7153i	0.920614	+	0.531517i
$990$	−5.06869	+	0.181865i	−0.161094	+	0.00578005i
$991$	−42.8989	+	24.7677i	−1.36273	+	0.786772i	−0.989986	−	0.141163i	$-0.954916\pi$
$991$	−42.8989	+	24.7677i	−1.36273	+	0.786772i	−0.372743	+	0.927935i	$0.621583\pi$
$992$	22.4449	−	18.9737i	0.712626	−	0.602415i
$993$	−44.9940	+	12.0616i	−1.42784	+	0.382763i
$994$		0			0
$995$	−76.1815			−2.41512
$996$	−15.6513	+	18.0622i	−0.495932	+	0.572322i
$997$	27.7629	+	48.0868i	0.879261	+	1.52292i	0.852153	+	0.523292i	$0.175296\pi$
$997$	27.7629	+	48.0868i	0.879261	+	1.52292i	0.0271077	+	0.999633i	$0.491370\pi$
$998$	−45.6935	−	24.2528i	−1.44640	−	0.767710i
$999$	16.0369	−	4.30294i	0.507385	−	0.136139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.f.275.1		24
3.2	odd	2	inner	588.2.n.f.275.12		24
4.3	odd	2	inner	588.2.n.f.275.5		24
7.2	even	3		84.2.e.a.71.10	yes	12
7.3	odd	6		588.2.n.g.263.8		24
7.4	even	3	inner	588.2.n.f.263.8		24
7.5	odd	6		588.2.e.c.491.10		12
7.6	odd	2		588.2.n.g.275.1		24
12.11	even	2	inner	588.2.n.f.275.8		24
21.2	odd	6		84.2.e.a.71.3	✓	12
21.5	even	6		588.2.e.c.491.3		12
21.11	odd	6	inner	588.2.n.f.263.5		24
21.17	even	6		588.2.n.g.263.5		24
21.20	even	2		588.2.n.g.275.12		24
28.3	even	6		588.2.n.g.263.12		24
28.11	odd	6	inner	588.2.n.f.263.12		24
28.19	even	6		588.2.e.c.491.4		12
28.23	odd	6		84.2.e.a.71.4	yes	12
28.27	even	2		588.2.n.g.275.5		24
56.37	even	6		1344.2.h.h.575.5		12
56.51	odd	6		1344.2.h.h.575.8		12
84.11	even	6	inner	588.2.n.f.263.1		24
84.23	even	6		84.2.e.a.71.9	yes	12
84.47	odd	6		588.2.e.c.491.9		12
84.59	odd	6		588.2.n.g.263.1		24
84.83	odd	2		588.2.n.g.275.8		24
168.107	even	6		1344.2.h.h.575.6		12
168.149	odd	6		1344.2.h.h.575.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.3	✓	12	21.2	odd	6
84.2.e.a.71.4	yes	12	28.23	odd	6
84.2.e.a.71.9	yes	12	84.23	even	6
84.2.e.a.71.10	yes	12	7.2	even	3
588.2.e.c.491.3		12	21.5	even	6
588.2.e.c.491.4		12	28.19	even	6
588.2.e.c.491.9		12	84.47	odd	6
588.2.e.c.491.10		12	7.5	odd	6
588.2.n.f.263.1		24	84.11	even	6	inner
588.2.n.f.263.5		24	21.11	odd	6	inner
588.2.n.f.263.8		24	7.4	even	3	inner
588.2.n.f.263.12		24	28.11	odd	6	inner
588.2.n.f.275.1		24	1.1	even	1	trivial
588.2.n.f.275.5		24	4.3	odd	2	inner
588.2.n.f.275.8		24	12.11	even	2	inner
588.2.n.f.275.12		24	3.2	odd	2	inner
588.2.n.g.263.1		24	84.59	odd	6
588.2.n.g.263.5		24	21.17	even	6
588.2.n.g.263.8		24	7.3	odd	6
588.2.n.g.263.12		24	28.3	even	6
588.2.n.g.275.1		24	7.6	odd	2
588.2.n.g.275.5		24	28.27	even	2
588.2.n.g.275.8		24	84.83	odd	2
588.2.n.g.275.12		24	21.20	even	2
1344.2.h.h.575.5		12	56.37	even	6
1344.2.h.h.575.6		12	168.107	even	6
1344.2.h.h.575.7		12	168.149	odd	6
1344.2.h.h.575.8		12	56.51	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41332 + 0.0503882i) q^{2} +(1.22461 - 1.22488i) q^{3} +(1.99492 - 0.142429i) q^{4} +(3.08528 + 1.78129i) q^{5} +(-1.66903 + 1.79285i) q^{6} +(-2.81228 + 0.301817i) q^{8} +(-0.000681912 - 3.00000i) q^{9} +(-4.45023 - 2.36206i) q^{10} +(0.167782 + 0.290607i) q^{11} +(2.26853 - 2.61797i) q^{12} +3.34596 q^{13} +(5.96012 - 1.59774i) q^{15} +(3.95943 - 0.568269i) q^{16} +(-0.290607 + 0.167782i) q^{17} +(0.152128 + 4.23991i) q^{18} +(-1.60172 - 0.924754i) q^{19} +(6.40860 + 3.11410i) q^{20} +(-0.251772 - 0.402265i) q^{22} +(2.22976 - 3.86207i) q^{23} +(-3.07424 + 3.81432i) q^{24} +(3.84596 + 6.66140i) q^{25} +(-4.72890 + 0.168597i) q^{26} +(-3.67549 - 3.67298i) q^{27} +5.91788i q^{29} +(-8.34302 + 2.55842i) q^{30} +(-4.49941 + 2.59774i) q^{31} +(-5.56729 + 1.00265i) q^{32} +(0.561426 + 0.150365i) q^{33} +(0.402265 - 0.251772i) q^{34} +(-0.428647 - 5.98467i) q^{36} +(-1.59774 + 2.76736i) q^{37} +(2.31033 + 1.22626i) q^{38} +(4.09749 - 4.09842i) q^{39} +(-9.21428 - 4.07828i) q^{40} -1.45835i q^{41} +7.49646i q^{43} +(0.376103 + 0.555841i) q^{44} +(5.34176 - 9.25705i) q^{45} +(-2.95676 + 5.57067i) q^{46} +(4.45953 - 7.72413i) q^{47} +(4.15267 - 5.54575i) q^{48} +(-5.77122 - 9.22087i) q^{50} +(-0.150365 + 0.561426i) q^{51} +(6.67494 - 0.476562i) q^{52} +(4.15267 - 2.39755i) q^{53} +(5.37970 + 5.00588i) q^{54} +1.19547i q^{55} +(-3.09419 + 0.829463i) q^{57} +(-0.298191 - 8.36383i) q^{58} +(-7.01223 - 12.1455i) q^{59} +(11.6624 - 4.03625i) q^{60} +(0.176525 - 0.305751i) q^{61} +(6.22819 - 3.89814i) q^{62} +(7.81781 - 1.69759i) q^{64} +(10.3232 + 5.96012i) q^{65} +(-0.801049 - 0.184224i) q^{66} +(-2.76736 + 1.59774i) q^{67} +(-0.555841 + 0.376103i) q^{68} +(-2.00000 - 7.46071i) q^{69} +10.3774 q^{71} +(0.907370 + 8.43663i) q^{72} +(2.34596 + 4.06333i) q^{73} +(2.11866 - 3.99166i) q^{74} +(12.8692 + 3.44673i) q^{75} +(-3.32702 - 1.61668i) q^{76} +(-5.58453 + 5.99882i) q^{78} +(3.46410 + 2.00000i) q^{79} +(13.2282 + 5.29961i) q^{80} +(-9.00000 + 0.00409147i) q^{81} +(0.0734835 + 2.06111i) q^{82} -6.89932 q^{83} -1.19547 q^{85} +(-0.377733 - 10.5949i) q^{86} +(7.24871 + 7.24707i) q^{87} +(-0.559559 - 0.766627i) q^{88} +(-3.35402 - 1.93644i) q^{89} +(-7.08314 + 13.3523i) q^{90} +(3.89814 - 8.02210i) q^{92} +(-2.32808 + 8.69246i) q^{93} +(-5.91352 + 11.1413i) q^{94} +(-3.29450 - 5.70624i) q^{95} +(-5.58960 + 8.04713i) q^{96} -2.00000 q^{97} +(0.871706 - 0.503544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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