LMFDB - Embedded newform 841.2.d.q.571.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,4,6,-6,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			571.1
Character	$\chi$	$=$	841.571
Dual form			841.2.d.q.190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36873 + 0.659148i) q^{2} +(-1.94206 - 2.43527i) q^{3} +(0.191979 - 0.240734i) q^{4} +(-1.68890 + 0.813330i) q^{5} +(4.26336 + 2.05313i) q^{6} +(-0.214022 - 0.268375i) q^{7} +(0.572010 - 2.50614i) q^{8} +(-1.49136 + 6.53408i) q^{9} +(1.77555 - 2.22647i) q^{10} +(0.288000 + 1.26181i) q^{11} -0.959085 q^{12} +(-0.319472 - 1.39970i) q^{13} +(0.469838 + 0.226262i) q^{14} +(5.26061 + 2.53338i) q^{15} +(1.00602 + 4.40766i) q^{16} +1.26174 q^{17} +(-2.26565 - 9.92644i) q^{18} +(-2.62376 + 3.29009i) q^{19} +(-0.128436 + 0.562717i) q^{20} +(-0.237921 + 1.04240i) q^{21} +(-1.22591 - 1.53725i) q^{22} +(7.21405 + 3.47410i) q^{23} +(-7.21399 + 3.47408i) q^{24} +(-0.926581 + 1.16190i) q^{25} +(1.35988 + 1.70523i) q^{26} +(10.3894 - 5.00329i) q^{27} -0.105695 q^{28} -8.87025 q^{30} +(3.92624 - 1.89078i) q^{31} +(-1.07680 - 1.35026i) q^{32} +(2.51353 - 3.15186i) q^{33} +(-1.72698 + 0.831672i) q^{34} +(0.579739 + 0.279188i) q^{35} +(1.28666 + 1.61343i) q^{36} +(0.686548 - 3.00796i) q^{37} +(1.42257 - 6.23270i) q^{38} +(-2.78820 + 3.49629i) q^{39} +(1.07225 + 4.69785i) q^{40} -3.71066 q^{41} +(-0.361445 - 1.58360i) q^{42} +(-8.30336 - 3.99869i) q^{43} +(0.359050 + 0.172909i) q^{44} +(-2.79561 - 12.2484i) q^{45} -12.1641 q^{46} +(1.61329 + 7.06830i) q^{47} +(8.78007 - 11.0099i) q^{48} +(1.53143 - 6.70962i) q^{49} +(0.502382 - 2.20108i) q^{50} +(-2.45037 - 3.07267i) q^{51} +(-0.398286 - 0.191805i) q^{52} +(4.68568 - 2.25651i) q^{53} +(-10.9225 + 13.6964i) q^{54} +(-1.51267 - 1.89683i) q^{55} +(-0.795009 + 0.382856i) q^{56} +13.1077 q^{57} -5.46060 q^{59} +(1.61980 - 0.780053i) q^{60} +(-7.23734 - 9.07534i) q^{61} +(-4.12768 + 5.17595i) q^{62} +(2.07277 - 0.998193i) q^{63} +(-5.78270 - 2.78480i) q^{64} +(1.67797 + 2.10411i) q^{65} +(-1.36281 + 5.97085i) q^{66} +(1.42769 - 6.25513i) q^{67} +(0.242227 - 0.303743i) q^{68} +(-5.54975 - 24.3150i) q^{69} -0.977535 q^{70} +(-1.44040 - 6.31082i) q^{71} +(15.5222 + 7.47512i) q^{72} +(-13.6060 - 6.55229i) q^{73} +(1.04299 + 4.56964i) q^{74} +4.62900 q^{75} +(0.288329 + 1.26325i) q^{76} +(0.277000 - 0.347347i) q^{77} +(1.51173 - 6.62333i) q^{78} +(-1.01524 + 4.44807i) q^{79} +(-5.28395 - 6.62586i) q^{80} +(-14.2461 - 6.86055i) q^{81} +(5.07890 - 2.44587i) q^{82} +(6.92802 - 8.68746i) q^{83} +(0.205265 + 0.257395i) q^{84} +(-2.13095 + 1.02621i) q^{85} +14.0008 q^{86} +3.32701 q^{88} +(0.623900 - 0.300455i) q^{89} +(11.8999 + 14.9220i) q^{90} +(-0.307270 + 0.385304i) q^{91} +(2.22128 - 1.06971i) q^{92} +(-12.2295 - 5.88944i) q^{93} +(-6.86723 - 8.61123i) q^{94} +(1.75533 - 7.69060i) q^{95} +(-1.19704 + 5.24459i) q^{96} +(5.92370 - 7.42809i) q^{97} +(2.32651 + 10.1931i) q^{98} -8.67427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) $ 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−1.36873	+	0.659148i	−0.967841	+	0.466088i	−0.849907	−	0.526933i	$-0.823342\pi$
$2$	−1.36873	+	0.659148i	−0.967841	+	0.466088i	−0.117935	+	0.993021i	$0.537627\pi$
$3$	−1.94206	−	2.43527i	−1.12125	−	1.40600i	−0.902751	−	0.430164i	$-0.858456\pi$
$3$	−1.94206	−	2.43527i	−1.12125	−	1.40600i	−0.218498	−	0.975838i	$-0.570116\pi$
$4$	0.191979	−	0.240734i	0.0959894	−	0.120367i
$5$	−1.68890	+	0.813330i	−0.755298	+	0.363732i	−0.771578	−	0.636135i	$-0.780532\pi$
$5$	−1.68890	+	0.813330i	−0.755298	+	0.363732i	0.0162798	+	0.999867i	$0.494818\pi$
$6$	4.26336	+	2.05313i	1.74051	+	0.838186i
$7$	−0.214022	−	0.268375i	−0.0808928	−	0.101436i	0.739738	−	0.672895i	$-0.234949\pi$
$7$	−0.214022	−	0.268375i	−0.0808928	−	0.101436i	−0.820631	+	0.571458i	$0.806378\pi$
$8$	0.572010	−	2.50614i	0.202236	−	0.886054i
$9$	−1.49136	+	6.53408i	−0.497120	+	2.17803i
$10$	1.77555	−	2.22647i	0.561477	−	0.704070i
$11$	0.288000	+	1.26181i	0.0868352	+	0.380450i	0.999607	−	0.0280192i	$-0.00891994\pi$
$11$	0.288000	+	1.26181i	0.0868352	+	0.380450i	−0.912772	+	0.408469i	$0.866063\pi$
$12$	−0.959085			−0.276864
$13$	−0.319472	−	1.39970i	−0.0886055	−	0.388206i	0.911107	−	0.412169i	$-0.135229\pi$
$13$	−0.319472	−	1.39970i	−0.0886055	−	0.388206i	−0.999713	+	0.0239631i	$0.992372\pi$
$14$	0.469838	+	0.226262i	0.125570	+	0.0604711i
$15$	5.26061	+	2.53338i	1.35828	+	0.654115i
$16$	1.00602	+	4.40766i	0.251505	+	1.10192i
$17$	1.26174			0.306016			0.153008	−	0.988225i	$-0.451104\pi$
$17$	1.26174			0.306016			0.153008	+	0.988225i	$0.451104\pi$
$18$	−2.26565	−	9.92644i	−0.534018	−	2.33968i
$19$	−2.62376	+	3.29009i	−0.601931	+	0.754798i	−0.985678	−	0.168641i	$-0.946062\pi$
$19$	−2.62376	+	3.29009i	−0.601931	+	0.754798i	0.383747	+	0.923438i	$0.374634\pi$
$20$	−0.128436	+	0.562717i	−0.0287193	+	0.125827i
$21$	−0.237921	+	1.04240i	−0.0519187	+	0.227471i
$22$	−1.22591	−	1.53725i	−0.261366	−	0.327742i
$23$	7.21405	+	3.47410i	1.50423	+	0.724400i	0.991002	−	0.133850i	$-0.0427341\pi$
$23$	7.21405	+	3.47410i	1.50423	+	0.724400i	0.513231	+	0.858250i	$0.328448\pi$
$24$	−7.21399	+	3.47408i	−1.47255	+	0.709143i
$25$	−0.926581	+	1.16190i	−0.185316	+	0.232379i
$26$	1.35988	+	1.70523i	0.266694	+	0.334424i
$27$	10.3894	−	5.00329i	1.99945	−	0.962884i
$28$	−0.105695			−0.0199744
$29$		0			0
$29$		0			0
$30$	−8.87025			−1.61948
$31$	3.92624	−	1.89078i	0.705174	−	0.339594i	−0.0466924	−	0.998909i	$-0.514868\pi$
$31$	3.92624	−	1.89078i	0.705174	−	0.339594i	0.751866	+	0.659315i	$0.229154\pi$
$32$	−1.07680	−	1.35026i	−0.190353	−	0.238695i
$33$	2.51353	−	3.15186i	0.437549	−	0.548669i
$34$	−1.72698	+	0.831672i	−0.296175	+	0.142630i
$35$	0.579739	+	0.279188i	0.0979938	+	0.0471913i
$36$	1.28666	+	1.61343i	0.214444	+	0.268904i
$37$	0.686548	−	3.00796i	0.112868	−	0.494506i	−0.886620	−	0.462499i	$-0.846953\pi$
$37$	0.686548	−	3.00796i	0.112868	−	0.494506i	0.999488	−	0.0320072i	$-0.0101900\pi$
$38$	1.42257	−	6.23270i	0.230772	−	1.01108i
$39$	−2.78820	+	3.49629i	−0.446469	+	0.559855i
$40$	1.07225	+	4.69785i	0.169538	+	0.742795i
$41$	−3.71066			−0.579507			−0.289754	−	0.957101i	$-0.593573\pi$
$41$	−3.71066			−0.579507			−0.289754	+	0.957101i	$0.593573\pi$
$42$	−0.361445	−	1.58360i	−0.0557722	−	0.244354i
$43$	−8.30336	−	3.99869i	−1.26625	−	0.609794i	−0.324430	−	0.945910i	$-0.605172\pi$
$43$	−8.30336	−	3.99869i	−1.26625	−	0.609794i	−0.941821	+	0.336115i	$0.890887\pi$
$44$	0.359050	+	0.172909i	0.0541288	+	0.0260671i
$45$	−2.79561	−	12.2484i	−0.416744	−	1.82588i
$46$	−12.1641			−1.79349
$47$	1.61329	+	7.06830i	0.235323	+	1.03102i	0.945149	+	0.326640i	$0.105917\pi$
$47$	1.61329	+	7.06830i	0.235323	+	1.03102i	−0.709826	+	0.704377i	$0.751226\pi$
$48$	8.78007	−	11.0099i	1.26729	−	1.58914i
$49$	1.53143	−	6.70962i	0.218775	−	0.958517i
$50$	0.502382	−	2.20108i	0.0710476	−	0.311280i
$51$	−2.45037	−	3.07267i	−0.343120	−	0.430259i
$52$	−0.398286	−	0.191805i	−0.0552324	−	0.0265985i
$53$	4.68568	−	2.25651i	0.643628	−	0.309955i	−0.0834478	−	0.996512i	$-0.526593\pi$
$53$	4.68568	−	2.25651i	0.643628	−	0.309955i	0.727076	+	0.686557i	$0.240879\pi$
$54$	−10.9225	+	13.6964i	−1.48636	+	1.86384i
$55$	−1.51267	−	1.89683i	−0.203968	−	0.255768i
$56$	−0.795009	+	0.382856i	−0.106238	+	0.0511613i
$57$	13.1077			1.73616
$58$		0			0
$59$	−5.46060			−0.710910			−0.355455	−	0.934693i	$-0.615674\pi$
$59$	−5.46060			−0.710910			−0.355455	+	0.934693i	$0.615674\pi$
$60$	1.61980	−	0.780053i	0.209115	−	0.100704i
$61$	−7.23734	−	9.07534i	−0.926647	−	1.16198i	−0.986498	−	0.163771i	$-0.947634\pi$
$61$	−7.23734	−	9.07534i	−0.926647	−	1.16198i	0.0598519	−	0.998207i	$-0.480937\pi$
$62$	−4.12768	+	5.17595i	−0.524216	+	0.657346i
$63$	2.07277	−	0.998193i	0.261144	−	0.125760i
$64$	−5.78270	−	2.78480i	−0.722838	−	0.348100i
$65$	1.67797	+	2.10411i	0.208127	+	0.260983i
$66$	−1.36281	+	5.97085i	−0.167750	+	0.734961i
$67$	1.42769	−	6.25513i	0.174420	−	0.764185i	−0.809723	−	0.586812i	$-0.800383\pi$
$67$	1.42769	−	6.25513i	0.174420	−	0.764185i	0.984144	−	0.177373i	$-0.0567600\pi$
$68$	0.242227	−	0.303743i	0.0293743	−	0.0368342i
$69$	−5.54975	−	24.3150i	−0.668111	−	2.92719i
$70$	−0.977535			−0.116838
$71$	−1.44040	−	6.31082i	−0.170944	−	0.748957i	−0.985611	−	0.169028i	$-0.945937\pi$
$71$	−1.44040	−	6.31082i	−0.170944	−	0.748957i	0.814667	−	0.579929i	$-0.196920\pi$
$72$	15.5222	+	7.47512i	1.82931	+	0.880951i
$73$	−13.6060	−	6.55229i	−1.59246	−	0.766888i	−0.593189	−	0.805064i	$-0.702131\pi$
$73$	−13.6060	−	6.55229i	−1.59246	−	0.766888i	−0.999271	+	0.0381755i	$0.987845\pi$
$74$	1.04299	+	4.56964i	0.121245	+	0.531210i
$75$	4.62900			0.534511
$76$	0.288329	+	1.26325i	0.0330737	+	0.144905i
$77$	0.277000	−	0.347347i	0.0315671	−	0.0395839i
$78$	1.51173	−	6.62333i	0.171170	−	0.749945i
$79$	−1.01524	+	4.44807i	−0.114224	+	0.500447i	0.885158	+	0.465290i	$0.154050\pi$
$79$	−1.01524	+	4.44807i	−0.114224	+	0.500447i	−0.999382	+	0.0351565i	$0.988807\pi$
$80$	−5.28395	−	6.62586i	−0.590763	−	0.740794i
$81$	−14.2461	−	6.86055i	−1.58290	−	0.762284i
$82$	5.07890	−	2.44587i	0.560871	−	0.270101i
$83$	6.92802	−	8.68746i	0.760449	−	0.953572i	−0.239401	−	0.970921i	$-0.576951\pi$
$83$	6.92802	−	8.68746i	0.760449	−	0.953572i	0.999850	+	0.0173484i	$0.00552246\pi$
$84$	0.205265	+	0.257395i	0.0223963	+	0.0280841i
$85$	−2.13095	+	1.02621i	−0.231133	+	0.111308i
$86$	14.0008			1.50975
$87$		0			0
$88$	3.32701			0.354660
$89$	0.623900	−	0.300455i	0.0661333	−	0.0318481i	−0.400525	−	0.916286i	$-0.631172\pi$
$89$	0.623900	−	0.300455i	0.0661333	−	0.0318481i	0.466658	+	0.884438i	$0.345458\pi$
$90$	11.8999	+	14.9220i	1.25436	+	1.57292i
$91$	−0.307270	+	0.385304i	−0.0322106	+	0.0403909i
$92$	2.22128	−	1.06971i	0.231584	−	0.111525i
$93$	−12.2295	−	5.88944i	−1.26814	−	0.610706i
$94$	−6.86723	−	8.61123i	−0.708300	−	0.888180i
$95$	1.75533	−	7.69060i	0.180093	−	0.789039i
$96$	−1.19704	+	5.24459i	−0.122173	+	0.535274i
$97$	5.92370	−	7.42809i	0.601461	−	0.754208i	−0.384144	−	0.923273i	$-0.625503\pi$
$97$	5.92370	−	7.42809i	0.601461	−	0.754208i	0.985605	+	0.169065i	$0.0540748\pi$
$98$	2.32651	+	10.1931i	0.235013	+	1.02966i
$99$	−8.67427			−0.871797
$100$	0.101824	+	0.446119i	0.0101824	+	0.0446119i
$101$	5.63739	+	2.71483i	0.560942	+	0.270135i	0.692796	−	0.721134i	$-0.256379\pi$
$101$	5.63739	+	2.71483i	0.560942	+	0.270135i	−0.131854	+	0.991269i	$0.542093\pi$
$102$	5.37925	+	2.59051i	0.532625	+	0.256499i
$103$	−0.702027	−	3.07578i	−0.0691728	−	0.303066i	0.928493	−	0.371350i	$-0.121105\pi$
$103$	−0.702027	−	3.07578i	−0.0691728	−	0.303066i	−0.997666	+	0.0682837i	$0.978248\pi$
$104$	−3.69058			−0.361891
$105$	−0.445992	−	1.95402i	−0.0435243	−	0.190693i
$106$	−4.92608	+	6.17711i	−0.478464	+	0.599974i
$107$	−3.62758	+	15.8935i	−0.350691	+	1.53648i	0.424898	+	0.905241i	$0.360310\pi$
$107$	−3.62758	+	15.8935i	−0.350691	+	1.53648i	−0.775590	+	0.631237i	$0.782547\pi$
$108$	0.790092	−	3.46162i	0.0760266	−	0.333094i
$109$	3.62435	+	4.54480i	0.347150	+	0.435313i	0.924499	−	0.381185i	$-0.124484\pi$
$109$	3.62435	+	4.54480i	0.347150	+	0.435313i	−0.577348	+	0.816498i	$0.695913\pi$
$110$	3.32073	+	1.59918i	0.316619	+	0.152476i
$111$	−8.65851	+	4.16972i	−0.821829	+	0.395772i
$112$	0.967596	−	1.21333i	0.0914293	−	0.114649i
$113$	4.46275	+	5.59611i	0.419820	+	0.526438i	0.946100	−	0.323873i	$-0.104985\pi$
$113$	4.46275	+	5.59611i	0.419820	+	0.526438i	−0.526280	+	0.850311i	$0.676414\pi$
$114$	−17.9410	+	8.63993i	−1.68033	+	0.809203i
$115$	−15.0094			−1.39963
$116$		0			0
$117$	9.62217			0.889570
$118$	7.47412	−	3.59934i	0.688048	−	0.331347i
$119$	−0.270040	−	0.338619i	−0.0247545	−	0.0310412i
$120$	9.35812	−	11.7347i	0.854276	−	1.07123i
$121$	8.40144	−	4.04592i	0.763767	−	0.367811i
$122$	15.8880	+	7.65125i	1.43843	+	0.692712i
$123$	7.20631	+	9.03643i	0.649771	+	0.814788i
$124$	0.298581	−	1.30817i	0.0268134	−	0.117477i
$125$	2.70551	−	11.8536i	0.241988	−	1.06022i
$126$	−2.17911	+	2.73252i	−0.194131	+	0.243432i
$127$	3.61489	+	15.8379i	0.320770	+	1.40538i	0.836187	+	0.548444i	$0.184780\pi$
$127$	3.61489	+	15.8379i	0.320770	+	1.40538i	−0.515417	+	0.856939i	$0.672363\pi$
$128$	13.2047			1.16714
$129$	6.38775	+	27.9866i	0.562410	+	2.46408i
$130$	−3.68361	−	1.77394i	−0.323074	−	0.155584i
$131$	1.81892	+	0.875947i	0.158920	+	0.0765319i	0.511653	−	0.859192i	$-0.329033\pi$
$131$	1.81892	+	0.875947i	0.158920	+	0.0765319i	−0.352733	+	0.935724i	$0.614748\pi$
$132$	−0.276216	−	1.21018i	−0.0240415	−	0.105333i
$133$	1.44452			0.125256
$134$	2.16892	+	9.50267i	0.187366	+	0.820905i
$135$	−13.4774	+	16.9001i	−1.15995	+	1.45453i
$136$	0.721727	−	3.16209i	0.0618876	−	0.271147i
$137$	3.01424	−	13.2063i	0.257524	−	1.12829i	−0.666365	−	0.745626i	$-0.732151\pi$
$137$	3.01424	−	13.2063i	0.257524	−	1.12829i	0.923889	−	0.382661i	$-0.124992\pi$
$138$	23.6233	+	29.6227i	2.01095	+	2.52165i
$139$	3.56716	+	1.71785i	0.302563	+	0.145706i	0.579005	−	0.815324i	$-0.303441\pi$
$139$	3.56716	+	1.71785i	0.302563	+	0.145706i	−0.276442	+	0.961030i	$0.589155\pi$
$140$	0.178508	−	0.0859647i	0.0150866	−	0.00726534i
$141$	14.0801	−	17.6559i	1.18576	−	1.48689i
$142$	6.13130	+	7.68840i	0.514527	+	0.645196i
$143$	1.67414	−	0.806225i	0.139999	−	0.0674199i
$144$	−30.3003			−2.52503
$145$		0			0
$146$	22.9419			1.89869
$147$	−19.3138	+	9.30105i	−1.59298	+	0.767137i
$148$	−0.592316	−	0.742741i	−0.0486881	−	0.0610529i
$149$	5.15946	−	6.46975i	0.422679	−	0.530023i	−0.524207	−	0.851591i	$-0.675638\pi$
$149$	5.15946	−	6.46975i	0.422679	−	0.530023i	0.946887	+	0.321568i	$0.104210\pi$
$150$	−6.33587	+	3.05119i	−0.517322	+	0.249129i
$151$	3.03762	+	1.46284i	0.247198	+	0.119044i	0.553381	−	0.832929i	$-0.313338\pi$
$151$	3.03762	+	1.46284i	0.247198	+	0.119044i	−0.306183	+	0.951973i	$0.599052\pi$
$152$	6.74460	+	8.45746i	0.547059	+	0.685991i
$153$	−1.88171	+	8.24429i	−0.152127	+	0.666511i
$154$	−0.150186	+	0.658010i	−0.0121024	+	0.0530240i
$155$	−5.09319	+	6.38666i	−0.409095	+	0.512989i
$156$	0.306401	+	1.34243i	0.0245317	+	0.107480i
$157$	−5.15580			−0.411478			−0.205739	−	0.978607i	$-0.565960\pi$
$157$	−5.15580			−0.411478			−0.205739	+	0.978607i	$0.565960\pi$
$158$	−1.54234	−	6.75742i	−0.122702	−	0.537592i
$159$	−14.5951	−	7.02861i	−1.15746	−	0.557405i
$160$	2.91682	+	1.40466i	0.230595	+	0.111048i
$161$	−0.611603	−	2.67961i	−0.0482010	−	0.211183i
$162$	24.0212			1.88729
$163$	−3.84308	−	16.8376i	−0.301013	−	1.31882i	−0.868601	−	0.495512i	$-0.834981\pi$
$163$	−3.84308	−	16.8376i	−0.301013	−	1.31882i	0.567588	−	0.823313i	$-0.307877\pi$
$164$	−0.712367	+	0.893280i	−0.0556265	+	0.0697535i
$165$	−1.68158	+	7.36750i	−0.130911	+	0.573559i
$166$	−3.75630	+	16.4574i	−0.291545	+	1.27734i
$167$	−7.15623	−	8.97363i	−0.553766	−	0.694400i	0.423626	−	0.905837i	$-0.360757\pi$
$167$	−7.15623	−	8.97363i	−0.553766	−	0.694400i	−0.977392	+	0.211437i	$0.932186\pi$
$168$	2.47631	+	1.19253i	0.191051	+	0.0920055i
$169$	9.85551	−	4.74616i	0.758116	−	0.365089i
$170$	2.24027	−	2.80922i	0.171821	−	0.215457i
$171$	−17.5847	−	22.0505i	−1.34474	−	1.68625i
$172$	−2.55669	+	1.23124i	−0.194946	+	0.0938809i
$173$	0.0869329			0.00660938			0.00330469	−	0.999995i	$-0.498948\pi$
$173$	0.0869329			0.00660938			0.00330469	+	0.999995i	$0.498948\pi$
$174$		0			0
$175$	0.510133			0.0385624
$176$	−5.27189	+	2.53881i	−0.397384	+	0.191370i
$177$	10.6048	+	13.2980i	0.797107	+	0.999540i
$178$	−0.655910	+	0.822485i	−0.0491625	+	0.0616479i
$179$	−14.3779	+	6.92404i	−1.07466	+	0.517527i	−0.885604	−	0.464440i	$-0.846256\pi$
$179$	−14.3779	+	6.92404i	−1.07466	+	0.517527i	−0.189051	+	0.981967i	$0.560541\pi$
$180$	−3.48529	−	1.67843i	−0.259778	−	0.125103i
$181$	−15.4225	−	19.3392i	−1.14635	−	1.43747i	−0.880870	−	0.473358i	$-0.843042\pi$
$181$	−15.4225	−	19.3392i	−1.14635	−	1.43747i	−0.265478	−	0.964117i	$-0.585530\pi$
$182$	0.166598	−	0.729916i	0.0123491	−	0.0541050i
$183$	−8.04551	+	35.2497i	−0.594741	+	2.60573i
$184$	12.8331	−	16.0922i	0.946068	−	1.18633i
$185$	1.28696	+	5.63853i	0.0946190	+	0.414553i
$186$	20.6210			1.51201
$187$	0.363380	+	1.59207i	0.0265730	+	0.116424i
$188$	2.01130	+	0.968590i	0.146689	+	0.0706417i
$189$	−3.56633	−	1.71745i	−0.259412	−	0.124926i
$190$	2.66666	+	11.6834i	0.193460	+	0.847603i
$191$	19.9308			1.44214			0.721071	−	0.692861i	$-0.243650\pi$
$191$	19.9308			1.44214			0.721071	+	0.692861i	$0.243650\pi$
$192$	4.44862	+	19.4907i	0.321051	+	1.40662i
$193$	6.43206	−	8.06554i	0.462990	−	0.580571i	−0.494449	−	0.869206i	$-0.664630\pi$
$193$	6.43206	−	8.06554i	0.462990	−	0.580571i	0.957439	+	0.288636i	$0.0932017\pi$
$194$	−3.21177	+	14.0717i	−0.230592	+	1.01029i
$195$	1.86534	−	8.17261i	0.133580	−	0.585252i
$196$	−1.32123	−	1.65677i	−0.0943736	−	0.118341i
$197$	−4.84127	−	2.33143i	−0.344926	−	0.166108i	0.253397	−	0.967362i	$-0.418452\pi$
$197$	−4.84127	−	2.33143i	−0.344926	−	0.166108i	−0.598324	+	0.801255i	$0.704166\pi$
$198$	11.8728	−	5.71763i	0.843761	−	0.406334i
$199$	−0.397021	+	0.497848i	−0.0281441	+	0.0352915i	−0.795704	−	0.605685i	$-0.792899\pi$
$199$	−0.397021	+	0.497848i	−0.0281441	+	0.0352915i	0.767560	+	0.640977i	$0.221471\pi$
$200$	2.38186	+	2.98676i	0.168423	+	0.211196i
$201$	−18.0056	+	8.67102i	−1.27001	+	0.611606i
$202$	−9.50557			−0.668809
$203$		0			0
$204$	−1.21011			−0.0847249
$205$	6.26692	−	3.01799i	0.437700	−	0.210785i
$206$	2.98829	+	3.74719i	0.208204	+	0.261079i
$207$	−33.4588	+	41.9560i	−2.32555	+	2.91614i
$208$	5.84799	−	2.81625i	0.405485	−	0.195271i
$209$	−4.90710	−	2.36314i	−0.339431	−	0.163462i
$210$	1.89843	+	2.38056i	0.131004	+	0.164274i
$211$	−3.63540	+	15.9277i	−0.250271	+	1.09651i	0.681029	+	0.732256i	$0.261533\pi$
$211$	−3.63540	+	15.9277i	−0.250271	+	1.09651i	−0.931300	+	0.364253i	$0.881324\pi$
$212$	0.356335	−	1.56120i	0.0244732	−	0.107224i
$213$	−12.5712	+	15.7638i	−0.861363	+	1.08011i
$214$	−5.51095	−	24.1450i	−0.376721	−	1.65052i
$215$	17.2758			1.17820
$216$	−6.59609	−	28.8993i	−0.448807	−	1.96635i
$217$	−1.34774	−	0.649038i	−0.0914906	−	0.0440596i
$218$	−7.95647	−	3.83164i	−0.538880	−	0.259511i
$219$	10.4670	+	45.8591i	0.707297	+	3.09887i
$220$	−0.747031			−0.0503648
$221$	−0.403089	−	1.76605i	−0.0271147	−	0.118797i
$222$	9.10274	−	11.4145i	0.610936	−	0.766089i
$223$	3.71922	−	16.2949i	0.249057	−	1.09119i	−0.683438	−	0.730008i	$-0.739516\pi$
$223$	3.71922	−	16.2949i	0.249057	−	1.09119i	0.932495	−	0.361182i	$-0.117627\pi$
$224$	−0.131919	+	0.577973i	−0.00881418	+	0.0386174i
$225$	−6.21005	−	7.78715i	−0.414003	−	0.519144i
$226$	−9.79698	−	4.71798i	−0.651686	−	0.313835i
$227$	9.93950	−	4.78661i	0.659708	−	0.317699i	−0.0739059	−	0.997265i	$-0.523546\pi$
$227$	9.93950	−	4.78661i	0.659708	−	0.317699i	0.733614	+	0.679567i	$0.237832\pi$
$228$	2.51641	−	3.15547i	0.166653	−	0.208976i
$229$	9.11867	+	11.4344i	0.602579	+	0.755610i	0.985777	−	0.168056i	$-0.0537490\pi$
$229$	9.11867	+	11.4344i	0.602579	+	0.755610i	−0.383199	+	0.923666i	$0.625178\pi$
$230$	20.5439	−	9.89340i	1.35462	−	0.652351i
$231$	−1.38383			−0.0910495
$232$		0			0
$233$	−9.55115			−0.625717			−0.312858	−	0.949800i	$-0.601286\pi$
$233$	−9.55115			−0.625717			−0.312858	+	0.949800i	$0.601286\pi$
$234$	−13.1702	+	6.34243i	−0.860963	+	0.414618i
$235$	−8.47355	−	10.6255i	−0.552753	−	0.693131i
$236$	−1.04832	+	1.31455i	−0.0682398	+	0.0855701i
$237$	12.8039	−	6.16603i	0.831702	−	0.400527i
$238$	0.592813	+	0.285484i	0.0384263	+	0.0185052i
$239$	−9.07818	−	11.3837i	−0.587218	−	0.736349i	0.396107	−	0.918204i	$-0.370361\pi$
$239$	−9.07818	−	11.3837i	−0.587218	−	0.736349i	−0.983325	+	0.181856i	$0.941790\pi$
$240$	−5.87399	+	25.7356i	−0.379164	+	1.66123i
$241$	1.57091	−	6.88260i	0.101191	−	0.443347i	−0.898796	−	0.438366i	$-0.855557\pi$
$241$	1.57091	−	6.88260i	0.101191	−	0.443347i	0.999988	−	0.00498109i	$-0.00158554\pi$
$242$	−8.83248	+	11.0756i	−0.567773	+	0.711965i
$243$	3.26153	+	14.2897i	0.209227	+	0.916685i
$244$	−3.57416			−0.228812
$245$	2.87071	+	12.5774i	0.183403	+	0.803541i
$246$	−15.8199	−	7.61845i	−1.00864	−	0.485735i
$247$	5.44334	+	2.62137i	0.346351	+	0.166794i
$248$	−2.49271	−	10.9213i	−0.158287	−	0.693501i
$249$	−34.6109			−2.19338
$250$	4.11016	+	18.0078i	0.259949	+	1.13891i
$251$	8.35582	−	10.4779i	0.527415	−	0.661357i	−0.444750	−	0.895655i	$-0.646708\pi$
$251$	8.35582	−	10.4779i	0.527415	−	0.661357i	0.972165	+	0.234298i	$0.0752790\pi$
$252$	0.157629	−	0.690617i	0.00992969	−	0.0435048i
$253$	−2.30601	+	10.1033i	−0.144978	+	0.635189i
$254$	−15.3873	−	19.2951i	−0.965487	−	1.21068i
$255$	6.63751	+	3.19646i	0.415657	+	0.200170i
$256$	−6.50831	+	3.13424i	−0.406769	+	0.195890i
$257$	−6.72970	+	8.43877i	−0.419787	+	0.526396i	−0.946091	−	0.323900i	$-0.895006\pi$
$257$	−6.72970	+	8.43877i	−0.419787	+	0.526396i	0.526304	+	0.850296i	$0.323577\pi$
$258$	−27.1904	−	34.0957i	−1.69280	−	2.12271i
$259$	−0.954199	+	0.459518i	−0.0592911	+	0.0285531i
$260$	0.828665			0.0513916
$261$		0			0
$262$	−3.06700			−0.189480
$263$	0.713958	−	0.343824i	0.0440246	−	0.0212011i	−0.411742	−	0.911300i	$-0.635079\pi$
$263$	0.713958	−	0.343824i	0.0440246	−	0.0212011i	0.455767	+	0.890099i	$0.349365\pi$
$264$	−6.46125	−	8.10215i	−0.397663	−	0.498653i
$265$	−6.07835	+	7.62201i	−0.373390	+	0.468216i
$266$	−1.97716	+	0.952152i	−0.121228	+	0.0583802i
$267$	−1.94334	−	0.935862i	−0.118930	−	0.0572738i
$268$	−1.23173	−	1.54455i	−0.0752401	−	0.0943481i
$269$	4.23061	−	18.5355i	0.257945	−	1.13013i	−0.665500	−	0.746398i	$-0.731782\pi$
$269$	4.23061	−	18.5355i	0.257945	−	1.13013i	0.923445	−	0.383732i	$-0.125361\pi$
$270$	7.30729	−	32.0153i	0.444708	−	1.94839i
$271$	−14.2687	+	17.8924i	−0.866764	+	1.08689i	0.128693	+	0.991684i	$0.458922\pi$
$271$	−14.2687	+	17.8924i	−0.866764	+	1.08689i	−0.995458	+	0.0952038i	$0.969650\pi$
$272$	1.26933	+	5.56131i	0.0769646	+	0.337204i
$273$	1.53505			0.0929057
$274$	4.57918	+	20.0627i	0.276638	+	1.21203i
$275$	−1.73295	−	0.834543i	−0.104501	−	0.0503248i
$276$	−6.91888	−	3.33196i	−0.416468	−	0.200560i
$277$	−7.27672	−	31.8814i	−0.437216	−	1.91557i	−0.400637	−	0.916237i	$-0.631211\pi$
$277$	−7.27672	−	31.8814i	−0.437216	−	1.91557i	−0.0365790	−	0.999331i	$-0.511646\pi$
$278$	−6.01481			−0.360745
$279$	6.49905	+	28.4742i	0.389088	+	1.70471i
$280$	1.03130	−	1.29321i	0.0616320	−	0.0772840i
$281$	−2.92139	+	12.7994i	−0.174275	+	0.763551i	0.809931	+	0.586525i	$0.199505\pi$
$281$	−2.92139	+	12.7994i	−0.174275	+	0.763551i	−0.984206	+	0.177025i	$0.943353\pi$
$282$	−7.63407	+	33.4470i	−0.454602	+	1.99174i
$283$	5.39440	+	6.76437i	0.320664	+	0.402100i	0.915871	−	0.401472i	$-0.131501\pi$
$283$	5.39440	+	6.76437i	0.320664	+	0.402100i	−0.595207	+	0.803572i	$0.702930\pi$
$284$	−1.79576	−	0.864790i	−0.106558	−	0.0513159i
$285$	−22.1376	+	10.6609i	−1.31132	+	0.631498i
$286$	−1.76004	+	2.20702i	−0.104073	+	0.130504i
$287$	0.794162	+	0.995848i	0.0468779	+	0.0587831i
$288$	10.4286	−	5.02216i	0.614513	−	0.295934i
$289$	−15.4080			−0.906354
$290$		0			0
$291$	−29.5936			−1.73481
$292$	−4.18942	+	2.01752i	−0.245167	+	0.118066i
$293$	15.5400	+	19.4865i	0.907857	+	1.13842i	0.989897	+	0.141787i	$0.0452849\pi$
$293$	15.5400	+	19.4865i	0.907857	+	1.13842i	−0.0820404	+	0.996629i	$0.526144\pi$
$294$	20.3047	−	25.4613i	1.18420	−	1.48493i
$295$	9.22240	−	4.44127i	0.536949	−	0.258581i
$296$	−7.14567	−	3.44117i	−0.415333	−	0.200014i
$297$	9.30536	+	11.6686i	0.539952	+	0.677078i
$298$	−2.79740	+	12.2562i	−0.162049	+	0.709984i
$299$	2.55801	−	11.2074i	0.147933	−	0.648138i
$300$	0.888670	−	1.11436i	0.0513074	−	0.0643374i
$301$	0.703954	+	3.08422i	0.0405752	+	0.177772i
$302$	−5.12192			−0.294734
$303$	−4.33683	−	19.0009i	−0.249144	−	1.09157i
$304$	−17.1411	−	8.25473i	−0.983111	−	0.473442i
$305$	19.6044	+	9.44097i	1.12254	+	0.540588i
$306$	−2.85865	−	12.5246i	−0.163418	−	0.715982i
$307$	1.25116			0.0714076			0.0357038	−	0.999362i	$-0.488633\pi$
$307$	1.25116			0.0714076			0.0357038	+	0.999362i	$0.488633\pi$
$308$	−0.0304401	−	0.133367i	−0.00173448	−	0.00759927i
$309$	−6.12697	+	7.68298i	−0.348551	+	0.437069i
$310$	2.76148	−	12.0988i	0.156841	−	0.687166i
$311$	6.59743	−	28.9052i	0.374106	−	1.63906i	−0.341011	−	0.940059i	$-0.610769\pi$
$311$	6.59743	−	28.9052i	0.374106	−	1.63906i	0.715117	−	0.699005i	$-0.246373\pi$
$312$	7.16732	+	8.98754i	0.405770	+	0.508819i
$313$	−16.3444	−	7.87102i	−0.923837	−	0.444897i	−0.0893977	−	0.995996i	$-0.528494\pi$
$313$	−16.3444	−	7.87102i	−0.923837	−	0.444897i	−0.834440	+	0.551099i	$0.814209\pi$
$314$	7.05693	−	3.39844i	0.398245	−	0.191785i
$315$	−2.68883	+	3.37169i	−0.151499	+	0.189973i
$316$	0.875896	+	1.09834i	0.0492730	+	0.0617864i
$317$	19.4920	−	9.38687i	1.09478	−	0.527219i	0.202768	−	0.979227i	$-0.435006\pi$
$317$	19.4920	−	9.38687i	1.09478	−	0.527219i	0.892014	+	0.452007i	$0.149292\pi$
$318$	24.6097			1.38004
$319$		0			0
$320$	12.0314			0.672573
$321$	45.7498	−	22.0319i	2.55350	−	1.22970i
$322$	2.60338	+	3.26453i	0.145081	+	0.181925i
$323$	−3.31049	+	4.15123i	−0.184201	+	0.230980i
$324$	−4.38652	+	2.11243i	−0.243695	+	0.117357i
$325$	1.92232	+	0.925739i	0.106631	+	0.0513508i
$326$	16.3586	+	20.5131i	0.906021	+	1.13611i
$327$	4.02908	−	17.6525i	0.222808	−	0.976187i
$328$	−2.12253	+	9.29942i	−0.117197	+	0.513475i
$329$	1.55168	−	1.94574i	0.0855467	−	0.107272i
$330$	−2.55463	−	11.1926i	−0.140628	−	0.616131i
$331$	−5.52251			−0.303545			−0.151772	−	0.988415i	$-0.548498\pi$
$331$	−5.52251			−0.303545			−0.151772	+	0.988415i	$0.548498\pi$
$332$	−0.761333	−	3.33562i	−0.0417836	−	0.183066i
$333$	18.6304	+	8.97191i	1.02094	+	0.491658i
$334$	15.7099	+	7.56550i	0.859609	+	0.413966i
$335$	2.67626	+	11.7254i	0.146220	+	0.640630i
$336$	−4.83390			−0.263711
$337$	−5.30559	−	23.2453i	−0.289014	−	1.26625i	−0.885881	−	0.463912i	$-0.846445\pi$
$337$	−5.30559	−	23.2453i	−0.289014	−	1.26625i	0.596867	−	0.802340i	$-0.296412\pi$
$338$	−10.3611	+	12.9925i	−0.563572	+	0.706697i
$339$	4.96109	−	21.7360i	0.269449	−	1.18053i
$340$	−0.162053	+	0.710001i	−0.00878856	+	0.0385052i
$341$	3.51656	+	4.40963i	0.190432	+	0.238795i
$342$	38.6034	+	18.5904i	2.08743	+	1.00525i
$343$	−4.29335	+	2.06757i	−0.231819	+	0.111638i
$344$	−14.7709	+	18.5221i	−0.796393	+	0.998645i
$345$	29.1491	+	36.5518i	1.56933	+	1.96788i
$346$	−0.118988	+	0.0573016i	−0.00639683	+	0.00308055i
$347$	9.05255			0.485966			0.242983	−	0.970030i	$-0.421874\pi$
$347$	9.05255			0.485966			0.242983	+	0.970030i	$0.421874\pi$
$348$		0			0
$349$	0.312863			0.0167472			0.00837358	−	0.999965i	$-0.497335\pi$
$349$	0.312863			0.0167472			0.00837358	+	0.999965i	$0.497335\pi$
$350$	−0.698236	+	0.336253i	−0.0373223	+	0.0179735i
$351$	−10.3222	−	12.9437i	−0.550960	−	0.690882i
$352$	1.39366	−	1.74759i	0.0742822	−	0.0931470i
$353$	22.5990	−	10.8831i	1.20282	−	0.579250i	0.278345	−	0.960481i	$-0.410214\pi$
$353$	22.5990	−	10.8831i	1.20282	−	0.579250i	0.924480	+	0.381231i	$0.124500\pi$
$354$	−23.2805	−	11.2113i	−1.23735	−	0.595875i
$355$	7.56548	+	9.48681i	0.401534	+	0.503507i
$356$	0.0474461	−	0.207875i	0.00251464	−	0.0110173i
$357$	−0.300194	+	1.31524i	−0.0158880	+	0.0696097i
$358$	15.1156	−	18.9543i	0.798883	−	1.00177i
$359$	−2.09660	−	9.18582i	−0.110654	−	0.484809i	−0.999639	−	0.0268715i	$-0.991446\pi$
$359$	−2.09660	−	9.18582i	−0.110654	−	0.484809i	0.888984	−	0.457937i	$-0.151412\pi$
$360$	−32.2952			−1.70211
$361$	0.287327	+	1.25886i	0.0151225	+	0.0662559i
$362$	33.8568	+	16.3046i	1.77947	+	0.856949i
$363$	−26.1690	−	12.6023i	−1.37352	−	0.661450i
$364$	0.0337665	+	0.147941i	0.00176984	+	0.00775419i
$365$	28.3083			1.48172
$366$	−12.2226	−	53.5507i	−0.638885	−	2.79914i
$367$	7.16724	−	8.98743i	0.374127	−	0.469140i	−0.558750	−	0.829336i	$-0.688719\pi$
$367$	7.16724	−	8.98743i	0.374127	−	0.469140i	0.932877	+	0.360196i	$0.117290\pi$
$368$	−8.05519	+	35.2921i	−0.419906	+	1.83973i
$369$	5.53392	−	24.2457i	0.288085	−	1.26218i
$370$	−5.47813	−	6.86936i	−0.284794	−	0.357121i
$371$	−1.60843	−	0.774579i	−0.0835055	−	0.0402141i
$372$	−3.76560	+	1.81342i	−0.195237	+	0.0940213i
$373$	5.01983	−	6.29467i	0.259917	−	0.325926i	−0.634701	−	0.772758i	$-0.718877\pi$
$373$	5.01983	−	6.29467i	0.259917	−	0.325926i	0.894618	+	0.446832i	$0.147448\pi$
$374$	−1.54678	−	1.93960i	−0.0799822	−	0.100294i
$375$	−34.1210	+	16.4318i	−1.76200	+	0.848534i
$376$	18.6370			0.961129
$377$		0			0
$378$	6.01342			0.309297
$379$	−4.22985	+	2.03699i	−0.217273	+	0.104633i	−0.539355	−	0.842079i	$-0.681332\pi$
$379$	−4.22985	+	2.03699i	−0.217273	+	0.104633i	0.322082	+	0.946712i	$0.395617\pi$
$380$	−1.51440	−	1.89900i	−0.0776871	−	0.0974166i
$381$	31.5491	−	39.5613i	1.61631	−	2.02679i
$382$	−27.2800	+	13.1373i	−1.39577	+	0.672165i
$383$	20.7717	+	10.0031i	1.06138	+	0.511135i	0.881320	−	0.472520i	$-0.156656\pi$
$383$	20.7717	+	10.0031i	1.06138	+	0.511135i	0.180062	+	0.983655i	$0.442370\pi$
$384$	−25.6443	−	32.1569i	−1.30865	−	1.64100i
$385$	−0.185317	+	0.811926i	−0.00944462	+	0.0413796i
$386$	−3.48739	+	15.2793i	−0.177504	+	0.777694i
$387$	38.5110	−	48.2913i	1.95763	−	2.45479i
$388$	−0.650967	−	2.85207i	−0.0330478	−	0.144792i
$389$	−8.70383			−0.441302			−0.220651	−	0.975353i	$-0.570818\pi$
$389$	−8.70383			−0.441302			−0.220651	+	0.975353i	$0.570818\pi$
$390$	2.83379	+	12.4157i	0.143495	+	0.628692i
$391$	9.10223	+	4.38340i	0.460320	+	0.221678i
$392$	−15.9393	−	7.67594i	−0.805054	−	0.387694i
$393$	−1.39929	−	6.13070i	−0.0705850	−	0.309253i
$394$	8.16317			0.411255
$395$	−1.90311	−	8.33806i	−0.0957558	−	0.419533i
$396$	−1.66528	+	2.08819i	−0.0836833	+	0.104936i
$397$	3.58476	−	15.7058i	0.179914	−	0.788254i	−0.801754	−	0.597654i	$-0.796100\pi$
$397$	3.58476	−	15.7058i	0.179914	−	0.788254i	0.981668	−	0.190600i	$-0.0610433\pi$
$398$	0.215260	−	0.943117i	0.0107900	−	0.0472742i
$399$	−2.80534	−	3.51779i	−0.140443	−	0.176110i
$400$	−6.05340	−	2.91516i	−0.302670	−	0.145758i
$401$	15.2184	−	7.32879i	0.759970	−	0.365982i	−0.0134224	−	0.999910i	$-0.504273\pi$
$401$	15.2184	−	7.32879i	0.759970	−	0.365982i	0.773392	+	0.633928i	$0.218558\pi$
$402$	18.9293	−	23.7366i	0.944110	−	1.18388i
$403$	−3.90084	−	4.89150i	−0.194315	−	0.243663i
$404$	1.73581	−	0.835922i	0.0863598	−	0.0415887i
$405$	29.6401			1.47283
$406$		0			0
$407$	3.99320			0.197936
$408$	−9.10217	+	4.38337i	−0.450624	+	0.217009i
$409$	5.69741	+	7.14433i	0.281719	+	0.353264i	0.902477	−	0.430738i	$-0.141747\pi$
$409$	5.69741	+	7.14433i	0.281719	+	0.353264i	−0.620758	+	0.784002i	$0.713175\pi$
$410$	−6.58844	+	8.26165i	−0.325380	+	0.408014i
$411$	−38.0146	+	18.3069i	−1.87512	+	0.903010i
$412$	−0.875220	−	0.421484i	−0.0431190	−	0.0207650i
$413$	1.16869	+	1.46549i	0.0575075	+	0.0721121i
$414$	18.1410	−	79.4809i	0.891581	−	3.90627i
$415$	−4.63494	+	20.3070i	−0.227520	+	0.996831i
$416$	−1.54595	+	1.93856i	−0.0757966	+	0.0950460i
$417$	−2.74421	−	12.0232i	−0.134384	−	0.588776i
$418$	8.27418			0.404703
$419$	−4.15038	−	18.1840i	−0.202759	−	0.888347i	−0.969247	−	0.246088i	$-0.920855\pi$
$419$	−4.15038	−	18.1840i	−0.202759	−	0.888347i	0.766488	−	0.642259i	$-0.222002\pi$
$420$	−0.556019	−	0.267765i	−0.0271310	−	0.0130656i
$421$	−11.7549	−	5.66085i	−0.572898	−	0.275893i	0.124922	−	0.992167i	$-0.460132\pi$
$421$	−11.7549	−	5.66085i	−0.572898	−	0.275893i	−0.697820	+	0.716274i	$0.745846\pi$
$422$	−5.52283	−	24.1971i	−0.268847	−	1.17790i
$423$	−48.5908			−2.36257
$424$	−2.97486	−	13.0337i	−0.144472	−	0.632973i
$425$	−1.16910	+	1.46601i	−0.0567098	+	0.0711118i
$426$	6.81596	−	29.8627i	0.330234	−	1.44685i
$427$	−0.886645	+	3.88465i	−0.0429078	+	0.187991i
$428$	3.12967	+	3.92449i	0.151279	+	0.189697i
$429$	−5.21466	−	2.51125i	−0.251766	−	0.121244i
$430$	−23.6460	+	11.3873i	−1.14031	+	0.549144i
$431$	−10.5194	+	13.1909i	−0.506700	+	0.635382i	−0.967726	−	0.252005i	$-0.918910\pi$
$431$	−10.5194	+	13.1909i	−0.506700	+	0.635382i	0.461026	+	0.887387i	$0.347482\pi$
$432$	32.5048	+	40.7597i	1.56389	+	1.96105i
$433$	−3.24083	+	1.56070i	−0.155745	+	0.0750026i	−0.510132	−	0.860096i	$-0.670404\pi$
$433$	−3.24083	+	1.56070i	−0.155745	+	0.0750026i	0.354388	+	0.935099i	$0.384689\pi$
$434$	2.27251			0.109084
$435$		0			0
$436$	1.78989			0.0857200
$437$	−30.3580	+	14.6196i	−1.45222	+	0.699352i
$438$	−44.5545	−	55.8696i	−2.12890	−	2.66955i
$439$	10.8255	−	13.5747i	0.516673	−	0.647887i	−0.453226	−	0.891396i	$-0.649727\pi$
$439$	10.8255	−	13.5747i	0.516673	−	0.647887i	0.969899	+	0.243508i	$0.0782983\pi$
$440$	−5.61898	+	2.70596i	−0.267874	+	0.129001i
$441$	41.5572	+	20.0129i	1.97892	+	0.952996i
$442$	1.71581	+	2.15156i	0.0816128	+	0.102339i
$443$	2.83361	−	12.4149i	0.134629	−	0.589848i	−0.861935	−	0.507019i	$-0.830747\pi$
$443$	2.83361	−	12.4149i	0.134629	−	0.589848i	0.996564	−	0.0828287i	$-0.0263954\pi$
$444$	−0.658458	+	2.88489i	−0.0312490	+	0.136911i
$445$	−0.809335	+	1.01487i	−0.0383662	+	0.0481096i
$446$	5.65016	+	24.7550i	0.267543	+	1.17218i
$447$	−25.7755			−1.21914
$448$	0.490254	+	2.14794i	0.0231623	+	0.101481i
$449$	20.8677	+	10.0493i	0.984806	+	0.474258i	0.855755	−	0.517381i	$-0.173093\pi$
$449$	20.8677	+	10.0493i	0.984806	+	0.474258i	0.129050	+	0.991638i	$0.458807\pi$
$450$	13.6328	+	6.56521i	0.642656	+	0.309487i
$451$	−1.06867	−	4.68214i	−0.0503216	−	0.220473i
$452$	2.20393			0.103664
$453$	−2.33683	−	10.2383i	−0.109794	−	0.481039i
$454$	−10.4495	+	13.1032i	−0.490417	+	0.614964i
$455$	0.205568	−	0.900651i	0.00963717	−	0.0422232i
$456$	7.49775	−	32.8498i	0.351114	−	1.53833i
$457$	19.4647	+	24.4079i	0.910518	+	1.14175i	0.989450	+	0.144874i	$0.0462776\pi$
$457$	19.4647	+	24.4079i	0.910518	+	1.14175i	−0.0789321	+	0.996880i	$0.525151\pi$
$458$	−20.0180	−	9.64017i	−0.935381	−	0.450456i
$459$	13.1088	−	6.31284i	0.611864	−	0.294658i
$460$	−2.88148	+	3.61326i	−0.134350	+	0.168469i
$461$	−8.78073	−	11.0107i	−0.408959	−	0.512819i	0.534110	−	0.845415i	$-0.320647\pi$
$461$	−8.78073	−	11.0107i	−0.408959	−	0.512819i	−0.943069	+	0.332596i	$0.892075\pi$
$462$	1.89410	−	0.912150i	0.0881215	−	0.0424371i
$463$	20.1157			0.934856			0.467428	−	0.884031i	$-0.345181\pi$
$463$	20.1157			0.934856			0.467428	+	0.884031i	$0.345181\pi$
$464$		0			0
$465$	25.4445			1.17996
$466$	13.0730	−	6.29562i	0.605594	−	0.291639i
$467$	−11.4029	−	14.2988i	−0.527666	−	0.661672i	0.444551	−	0.895753i	$-0.353363\pi$
$467$	−11.4029	−	14.2988i	−0.527666	−	0.661672i	−0.972217	+	0.234082i	$0.924792\pi$
$468$	1.84725	−	2.31638i	0.0853893	−	0.107075i
$469$	−1.98428	+	0.955578i	−0.0916255	+	0.0441245i
$470$	18.6018	+	8.95816i	0.858038	+	0.413209i
$471$	10.0129	+	12.5558i	0.461369	+	0.578538i
$472$	−3.12352	+	13.6850i	−0.143772	+	0.629905i
$473$	2.65422	−	11.6289i	0.122041	−	0.534697i
$474$	−13.4608	+	16.8793i	−0.618275	+	0.775293i
$475$	−1.39161	−	6.09706i	−0.0638516	−	0.279752i
$476$	−0.133359			−0.00611250
$477$	7.75614	+	33.9819i	0.355129	+	1.55592i
$478$	19.9291	+	9.59737i	0.911537	+	0.438973i
$479$	14.5727	+	7.01785i	0.665845	+	0.320654i	0.736098	−	0.676875i	$-0.236666\pi$
$479$	14.5727	+	7.01785i	0.665845	+	0.320654i	−0.0702531	+	0.997529i	$0.522381\pi$
$480$	−2.24390	−	9.83116i	−0.102419	−	0.448729i
$481$	−4.42957			−0.201971
$482$	2.38649	+	10.4559i	0.108702	+	0.476254i
$483$	−5.33778	+	6.69337i	−0.242878	+	0.304559i
$484$	0.638909	−	2.79924i	0.0290413	−	0.127238i
$485$	−3.96304	+	17.3632i	−0.179952	+	0.788423i
$486$	−13.8832	−	17.4090i	−0.629755	−	0.789688i
$487$	25.7826	+	12.4162i	1.16832	+	0.562634i	0.914488	−	0.404614i	$-0.132594\pi$
$487$	25.7826	+	12.4162i	1.16832	+	0.562634i	0.253834	+	0.967248i	$0.418308\pi$
$488$	−26.8839	+	12.9466i	−1.21698	+	0.586065i
$489$	−33.5406	+	42.0586i	−1.51676	+	1.90195i
$490$	−12.2196	−	15.3229i	−0.552026	−	0.692219i
$491$	0.766413	−	0.369085i	0.0345877	−	0.0166566i	−0.416510	−	0.909131i	$-0.636747\pi$
$491$	0.766413	−	0.369085i	0.0345877	−	0.0166566i	0.451098	+	0.892475i	$0.351033\pi$
$492$	3.55883			0.160445
$493$		0			0
$494$	−9.17836			−0.412954
$495$	14.6500	−	7.05504i	0.658466	−	0.317101i
$496$	12.2838	+	15.4034i	0.551558	+	0.691632i
$497$	−1.38539	+	1.73722i	−0.0621432	+	0.0779252i
$498$	47.3731	−	22.8137i	2.12284	−	1.02231i
$499$	−12.7520	−	6.14103i	−0.570857	−	0.274910i	0.126107	−	0.992017i	$-0.459752\pi$
$499$	−12.7520	−	6.14103i	−0.570857	−	0.274910i	−0.696963	+	0.717107i	$0.745466\pi$
$500$	−2.33417	−	2.92695i	−0.104387	−	0.130897i
$501$	−7.95535	+	34.8546i	−0.355419	+	1.55719i
$502$	−4.53044	+	19.8491i	−0.202203	+	0.885910i
$503$	1.71164	−	2.14633i	0.0763184	−	0.0957002i	−0.742207	−	0.670171i	$-0.766221\pi$
$503$	1.71164	−	2.14633i	0.0763184	−	0.0957002i	0.818525	+	0.574471i	$0.194792\pi$
$504$	−1.31597	−	5.76562i	−0.0586178	−	0.256821i
$505$	−11.7290			−0.521935
$506$	−3.50325	−	15.3487i	−0.155738	−	0.682334i
$507$	−30.6981	−	14.7834i	−1.36335	−	0.656556i
$508$	4.50669	+	2.17031i	0.199952	+	0.0962919i
$509$	−0.154470	−	0.676777i	−0.00684675	−	0.0299976i	0.971389	−	0.237493i	$-0.0763258\pi$
$509$	−0.154470	−	0.676777i	−0.00684675	−	0.0299976i	−0.978236	+	0.207496i	$0.933469\pi$
$510$	−11.1919			−0.495587
$511$	1.15351	+	5.05384i	0.0510281	+	0.223569i
$512$	−9.62376	+	12.0678i	−0.425314	+	0.533327i
$513$	−10.7981	+	47.3096i	−0.476748	+	2.08877i
$514$	3.64877	−	15.9863i	0.160940	−	0.705126i
$515$	3.68728	+	4.62370i	0.162481	+	0.203745i
$516$	7.96363	+	3.83508i	0.350579	+	0.168830i
$517$	−8.45422	+	4.07134i	−0.371816	+	0.179057i
$518$	1.00316	−	1.25792i	0.0440761	−	0.0552697i
$519$	−0.168829	−	0.211705i	−0.00741076	−	0.00929280i
$520$	6.23301	−	3.00166i	0.273335	−	0.131631i
$521$	−9.95886			−0.436306			−0.218153	−	0.975915i	$-0.570003\pi$
$521$	−9.95886			−0.436306			−0.218153	+	0.975915i	$0.570003\pi$
$522$		0			0
$523$	−11.1552			−0.487783			−0.243891	−	0.969803i	$-0.578424\pi$
$523$	−11.1552			−0.487783			−0.243891	+	0.969803i	$0.578424\pi$
$524$	0.560065	−	0.269713i	0.0244666	−	0.0117825i
$525$	−0.990708	−	1.24231i	−0.0432380	−	0.0542188i
$526$	−0.750589	+	0.941208i	−0.0327272	+	0.0410386i
$527$	4.95389	−	2.38567i	0.215795	−	0.103921i
$528$	16.4210	+	7.90794i	0.714633	+	0.344149i
$529$	25.6328	+	32.1425i	1.11447	+	1.39750i
$530$	3.29562	−	14.4390i	0.143152	−	0.627192i
$531$	8.14373	−	35.6800i	0.353408	−	1.54838i
$532$	0.277317	−	0.347745i	0.0120232	−	0.0150766i
$533$	1.18545	+	5.19379i	0.0513475	+	0.224968i
$534$	3.27679			0.141800
$535$	−6.80002	−	29.7928i	−0.293990	−	1.28806i
$536$	−14.8596	−	7.15599i	−0.641836	−	0.309092i
$537$	44.7846	+	21.5671i	1.93260	+	0.930691i
$538$	6.42706	+	28.1588i	0.277090	+	1.21401i
$539$	8.90731			0.383665
$540$	1.48105	+	6.48892i	0.0637344	+	0.279239i
$541$	8.99034	−	11.2735i	0.386525	−	0.484687i	−0.550061	−	0.835124i	$-0.685396\pi$
$541$	8.99034	−	11.2735i	0.386525	−	0.484687i	0.936586	+	0.350437i	$0.113967\pi$
$542$	7.73636	−	33.8952i	0.332305	−	1.45592i
$543$	−17.1447	+	75.1159i	−0.735750	+	3.22353i
$544$	−1.35864	−	1.70368i	−0.0582512	−	0.0730447i
$545$	−9.81758	−	4.72790i	−0.420539	−	0.202521i
$546$	−2.10108	+	1.01183i	−0.0899180	+	0.0433022i
$547$	9.69249	−	12.1540i	0.414421	−	0.519668i	−0.530181	−	0.847884i	$-0.677876\pi$
$547$	9.69249	−	12.1540i	0.414421	−	0.519668i	0.944602	+	0.328217i	$0.106448\pi$
$548$	−2.60052	−	3.26095i	−0.111089	−	0.139301i
$549$	70.0924	−	33.7547i	2.99147	−	1.44062i
$550$	2.92203			0.124596
$551$		0			0
$552$	−64.1114			−2.72876
$553$	1.41104	−	0.679519i	0.0600034	−	0.0288961i
$554$	30.9745	+	38.8407i	1.31598	+	1.65018i
$555$	11.2320	−	14.0844i	0.476771	−	0.597852i
$556$	1.09836	−	0.528945i	0.0465810	−	0.0224322i
$557$	−32.9800	−	15.8823i	−1.39741	−	0.672955i	−0.424773	−	0.905300i	$-0.639646\pi$
$557$	−32.9800	−	15.8823i	−1.39741	−	0.672955i	−0.972634	+	0.232345i	$0.925360\pi$
$558$	−27.6642	−	34.6898i	−1.17112	−	1.46854i
$559$	−2.94426	+	12.8997i	−0.124529	+	0.545597i
$560$	−0.647335	+	2.83616i	−0.0273549	+	0.119850i
$561$	3.17141	−	3.97683i	0.133897	−	0.167902i
$562$	−4.43812	−	19.4447i	−0.187211	−	0.820224i
$563$	−21.5620			−0.908728			−0.454364	−	0.890816i	$-0.650133\pi$
$563$	−21.5620			−0.908728			−0.454364	+	0.890816i	$0.650133\pi$
$564$	−1.54729	−	6.77910i	−0.0651525	−	0.285452i
$565$	−12.0886	−	5.82157i	−0.508572	−	0.244915i
$566$	−11.8422	−	5.70291i	−0.497766	−	0.239711i
$567$	1.20777	+	5.29161i	0.0507218	+	0.222227i
$568$	−16.6397			−0.698188
$569$	−0.199063	−	0.872151i	−0.00834514	−	0.0365625i	0.970584	−	0.240763i	$-0.0773977\pi$
$569$	−0.199063	−	0.872151i	−0.00834514	−	0.0365625i	−0.978929	+	0.204201i	$0.934541\pi$
$570$	23.2734	−	29.1839i	0.974815	−	1.22238i
$571$	−4.59752	+	20.1430i	−0.192400	+	0.842960i	0.782913	+	0.622132i	$0.213733\pi$
$571$	−4.59752	+	20.1430i	−0.192400	+	0.842960i	−0.975313	+	0.220828i	$0.929124\pi$
$572$	0.127314	−	0.557801i	0.00532328	−	0.0233228i
$573$	−38.7068	−	48.5368i	−1.61700	−	2.02765i
$574$	−1.74341	−	0.839581i	−0.0727685	−	0.0350434i
$575$	−10.7209	+	5.16293i	−0.447094	+	0.215309i
$576$	26.8202	−	33.6315i	1.11751	−	1.40131i
$577$	−14.2675	−	17.8909i	−0.593964	−	0.744807i	0.390460	−	0.920620i	$-0.372316\pi$
$577$	−14.2675	−	17.8909i	−0.593964	−	0.744807i	−0.984424	+	0.175813i	$0.943745\pi$
$578$	21.0895	−	10.1562i	0.877207	−	0.422441i
$579$	−32.1332			−1.33541
$580$		0			0
$581$	−3.81425			−0.158242
$582$	40.5057	−	19.5065i	1.67902	−	0.808572i
$583$	4.19675	+	5.26256i	0.173812	+	0.217953i
$584$	−24.2037	+	30.3505i	−1.00156	+	1.25591i
$585$	−16.2509	+	7.82600i	−0.671890	+	0.323565i
$586$	−34.1147	−	16.4288i	−1.40926	−	0.678666i
$587$	5.96520	+	7.48013i	0.246210	+	0.308738i	0.889545	−	0.456847i	$-0.151021\pi$
$587$	5.96520	+	7.48013i	0.246210	+	0.308738i	−0.643335	+	0.765585i	$0.722450\pi$
$588$	−1.46877	+	6.43510i	−0.0605710	+	0.265379i
$589$	−4.08068	+	17.8786i	−0.168141	+	0.736676i
$590$	−9.69556	+	12.1578i	−0.399160	+	0.500531i
$591$	3.72438	+	16.3176i	0.153200	+	0.671215i
$592$	13.9488			0.573291
$593$	−8.02406	−	35.1557i	−0.329509	−	1.44367i	−0.820069	−	0.572265i	$-0.806065\pi$
$593$	−8.02406	−	35.1557i	−0.329509	−	1.44367i	0.490560	−	0.871407i	$-0.336792\pi$
$594$	−20.4279	−	9.83754i	−0.838166	−	0.403639i
$595$	0.731478	+	0.352261i	0.0299877	+	0.0144413i
$596$	−0.566982	−	2.48411i	−0.0232245	−	0.101753i
$597$	1.98343			0.0811764
$598$	3.88607	+	17.0260i	0.158913	+	0.696245i
$599$	−11.9549	+	14.9909i	−0.488462	+	0.612512i	−0.963583	−	0.267408i	$-0.913833\pi$
$599$	−11.9549	+	14.9909i	−0.488462	+	0.612512i	0.475121	+	0.879920i	$0.342404\pi$
$600$	2.64783	−	11.6009i	0.108097	−	0.473606i
$601$	−2.09521	+	9.17971i	−0.0854653	+	0.374448i	−0.999515	−	0.0311552i	$-0.990081\pi$
$601$	−2.09521	+	9.17971i	−0.0854653	+	0.374448i	0.914049	+	0.405603i	$0.132939\pi$
$602$	−2.99649	−	3.75747i	−0.122128	−	0.153143i
$603$	38.7423	+	18.6573i	1.57771	+	0.759784i
$604$	0.935314	−	0.450424i	0.0380574	−	0.0183275i
$605$	−10.8985	+	13.6663i	−0.443087	+	0.555614i
$606$	18.4604	+	23.1486i	0.749901	+	0.940347i
$607$	−26.4951	+	12.7594i	−1.07540	+	0.517886i	−0.885844	−	0.463983i	$-0.846420\pi$
$607$	−26.4951	+	12.7594i	−1.07540	+	0.517886i	−0.189558	+	0.981869i	$0.560706\pi$
$608$	7.26775			0.294746
$609$		0			0
$610$	−33.0562			−1.33841
$611$	9.37808	−	4.51624i	0.379396	−	0.182708i
$612$	1.62343	+	2.03572i	0.0656233	+	0.0822891i
$613$	−8.97729	+	11.2572i	−0.362589	+	0.454673i	−0.929345	−	0.369214i	$-0.879627\pi$
$613$	−8.97729	+	11.2572i	−0.362589	+	0.454673i	0.566755	+	0.823886i	$0.308199\pi$
$614$	−1.71251	+	0.824701i	−0.0691113	+	0.0332822i
$615$	−19.5203	−	9.40049i	−0.787135	−	0.379064i
$616$	−0.712054	−	0.892887i	−0.0286895	−	0.0359754i
$617$	−9.36724	+	41.0405i	−0.377111	+	1.65223i	0.329149	+	0.944278i	$0.393238\pi$
$617$	−9.36724	+	41.0405i	−0.377111	+	1.65223i	−0.706260	+	0.707952i	$0.749619\pi$
$618$	3.32198	−	14.5545i	0.133630	−	0.585469i
$619$	−19.0794	+	23.9248i	−0.766866	+	0.961619i	−0.999941	−	0.0108396i	$-0.996550\pi$
$619$	−19.0794	+	23.9248i	−0.766866	+	0.961619i	0.233076	+	0.972459i	$0.425121\pi$
$620$	0.559701	+	2.45221i	0.0224781	+	0.0984831i
$621$	92.3319			3.70515
$622$	10.0227	+	43.9122i	0.401873	+	1.76072i
$623$	−0.214163	−	0.103135i	−0.00858026	−	0.00413204i
$624$	−18.2155	−	8.77210i	−0.729202	−	0.351165i
$625$	3.41811	+	14.9757i	0.136724	+	0.599029i
$626$	27.5592			1.10149
$627$	3.77502	+	16.5394i	0.150760	+	0.660522i
$628$	−0.989805	+	1.24118i	−0.0394975	+	0.0495283i
$629$	0.866243	−	3.79526i	0.0345394	−	0.151327i
$630$	1.45786	−	6.38729i	0.0580824	−	0.254476i
$631$	2.81289	+	3.52725i	0.111979	+	0.140418i	0.834662	−	0.550762i	$-0.185663\pi$
$631$	2.81289	+	3.52725i	0.111979	+	0.140418i	−0.722683	+	0.691180i	$0.757091\pi$
$632$	10.5668	+	5.08868i	0.420323	+	0.202417i
$633$	45.8484	−	22.0794i	1.82231	−	0.877578i
$634$	−20.4921	+	25.6963i	−0.813845	+	1.02053i
$635$	−18.9866	−	23.8084i	−0.753460	−	0.944809i
$636$	−4.49397	+	2.16418i	−0.178197	+	0.0858154i
$637$	−9.88068			−0.391487
$638$		0			0
$639$	43.3835			1.71623
$640$	−22.3014	+	10.7398i	−0.881539	+	0.424527i
$641$	−24.3974	−	30.5933i	−0.963638	−	1.20836i	−0.978029	−	0.208468i	$-0.933152\pi$
$641$	−24.3974	−	30.5933i	−0.963638	−	1.20836i	0.0143908	−	0.999896i	$-0.495419\pi$
$642$	−48.0970	+	60.3117i	−1.89824	+	2.38031i
$643$	17.4221	−	8.39003i	0.687060	−	0.330870i	−0.0575766	−	0.998341i	$-0.518337\pi$
$643$	17.4221	−	8.39003i	0.687060	−	0.330870i	0.744636	+	0.667471i	$0.232623\pi$
$644$	−0.762487	−	0.367194i	−0.0300462	−	0.0144695i
$645$	−33.5506	−	42.0711i	−1.32105	−	1.65655i
$646$	1.79491	−	7.86403i	0.0706199	−	0.309406i
$647$	6.63138	−	29.0540i	0.260707	−	1.14223i	−0.659781	−	0.751458i	$-0.729351\pi$
$647$	6.63138	−	29.0540i	0.260707	−	1.14223i	0.920487	−	0.390772i	$-0.127792\pi$
$648$	−25.3424	+	31.7784i	−0.995544	+	1.24837i
$649$	−1.57265	−	6.89024i	−0.0617320	−	0.270466i
$650$	−3.24134			−0.127136
$651$	1.03681	+	4.54258i	0.0406359	+	0.178038i
$652$	−4.79118	−	2.30731i	−0.187637	−	0.0903612i
$653$	−5.63471	−	2.71353i	−0.220503	−	0.106189i	0.320371	−	0.947292i	$-0.396192\pi$
$653$	−5.63471	−	2.71353i	−0.220503	−	0.106189i	−0.540875	+	0.841103i	$0.681907\pi$
$654$	6.12089	+	26.8174i	0.239346	+	1.04864i
$655$	−3.78441			−0.147869
$656$	−3.73299	−	16.3553i	−0.145749	−	0.638568i
$657$	63.1046	−	79.1307i	2.46195	−	3.08718i
$658$	−0.841302	+	3.68599i	−0.0327974	+	0.143695i
$659$	8.77215	−	38.4333i	0.341715	−	1.49715i	−0.453739	−	0.891135i	$-0.649910\pi$
$659$	8.77215	−	38.4333i	0.341715	−	1.49715i	0.795453	−	0.606015i	$-0.207233\pi$
$660$	1.45078	+	1.81922i	0.0564715	+	0.0708130i
$661$	8.82922	+	4.25193i	0.343417	+	0.165381i	0.597640	−	0.801765i	$-0.296105\pi$
$661$	8.82922	+	4.25193i	0.343417	+	0.165381i	−0.254223	+	0.967146i	$0.581820\pi$
$662$	7.55885	−	3.64015i	0.293783	−	0.141479i
$663$	−3.51798	+	4.41140i	−0.136627	+	0.171325i
$664$	−17.8091	−	22.3319i	−0.691127	−	0.866646i
$665$	−2.43965	+	1.17487i	−0.0946054	+	0.0455595i
$666$	−31.4139			−1.21726
$667$		0			0
$668$	−3.53410			−0.136738
$669$	−46.9055	+	22.5885i	−1.81347	+	0.873321i
$670$	−11.3919	−	14.2850i	−0.440107	−	0.551877i
$671$	9.36700	−	11.7458i	0.361609	−	0.453443i
$672$	1.66371	−	0.801201i	0.0641791	−	0.0309070i
$673$	41.7409	+	20.1014i	1.60899	+	0.774851i	0.999834	−	0.0181962i	$-0.00579235\pi$
$673$	41.7409	+	20.1014i	1.60899	+	0.774851i	0.609160	+	0.793047i	$0.291507\pi$
$674$	22.5840	+	28.3195i	0.869904	+	1.09083i
$675$	−3.81336	+	16.7074i	−0.146776	+	0.643068i
$676$	0.749487	−	3.28372i	0.0288264	−	0.126297i
$677$	12.3154	−	15.4430i	0.473319	−	0.593523i	−0.486661	−	0.873591i	$-0.661785\pi$
$677$	12.3154	−	15.4430i	0.473319	−	0.593523i	0.959980	+	0.280068i	$0.0903569\pi$
$678$	7.53679	+	33.0208i	0.289449	+	1.26816i
$679$	−3.26132			−0.125158
$680$	1.35290	+	5.92745i	0.0518814	+	0.227307i
$681$	−30.9598	−	14.9094i	−1.18638	−	0.571331i
$682$	−7.71983	−	3.71768i	−0.295608	−	0.142357i
$683$	−0.654206	−	2.86626i	−0.0250325	−	0.109675i	0.960868	−	0.277006i	$-0.0893422\pi$
$683$	−0.654206	−	2.86626i	−0.0250325	−	0.109675i	−0.985901	+	0.167331i	$0.946485\pi$
$684$	−8.68420			−0.332049
$685$	5.65030	+	24.7556i	0.215887	+	0.945862i
$686$	4.51362	−	5.65991i	0.172331	−	0.216096i
$687$	10.1369	−	44.4128i	0.386748	−	1.69445i
$688$	9.27151	−	40.6212i	0.353473	−	1.54867i
$689$	−4.65537	−	5.83764i	−0.177355	−	0.222397i
$690$	−63.9904	−	30.8162i	−2.43607	−	1.17315i
$691$	−21.1143	+	10.1681i	−0.803227	+	0.386814i	−0.790006	−	0.613099i	$-0.789923\pi$
$691$	−21.1143	+	10.1681i	−0.803227	+	0.386814i	−0.0132210	+	0.999913i	$0.504209\pi$
$692$	0.0166893	−	0.0209277i	0.000634431	−	0.000795551i
$693$	1.85649	+	2.32796i	0.0705220	+	0.0884319i
$694$	−12.3905	+	5.96697i	−0.470338	+	0.226503i
$695$	−7.42175			−0.281523
$696$		0			0
$697$	−4.68187			−0.177339
$698$	−0.428226	+	0.206223i	−0.0162086	+	0.00780565i
$699$	18.5489	+	23.2596i	0.701584	+	0.879758i
$700$	0.0979347	−	0.122806i	0.00370158	−	0.00464164i
$701$	−36.1947	+	17.4305i	−1.36706	+	0.658340i	−0.966198	−	0.257801i	$-0.917002\pi$
$701$	−36.1947	+	17.4305i	−1.36706	+	0.658340i	−0.400858	+	0.916140i	$0.631288\pi$
$702$	22.6602	+	10.9126i	0.855253	+	0.411868i
$703$	8.09512	+	10.1510i	0.305313	+	0.382851i
$704$	1.84847	−	8.09869i	0.0696670	−	0.305231i
$705$	−9.41976	+	41.2707i	−0.354769	+	1.55434i
$706$	−23.7585	+	29.7922i	−0.894162	+	1.12124i
$707$	−0.477935	−	2.09397i	−0.0179746	−	0.0787518i
$708$	5.23718			0.196825
$709$	−7.71404	−	33.7974i	−0.289707	−	1.26929i	−0.884929	−	0.465727i	$-0.845793\pi$
$709$	−7.71404	−	33.7974i	−0.289707	−	1.26929i	0.595222	−	0.803561i	$-0.297064\pi$
$710$	−16.6083	−	7.99815i	−0.623300	−	0.300165i
$711$	−27.5499	−	13.2673i	−1.03320	−	0.497564i
$712$	−0.396104	−	1.73544i	−0.0148446	−	0.0650385i
$713$	34.8929			1.30675
$714$	−0.456049	−	1.99808i	−0.0170672	−	0.0747764i
$715$	−2.17173	+	2.72326i	−0.0812180	+	0.101844i
$716$	−1.09340	+	4.79052i	−0.0408625	+	0.179030i
$717$	−10.0919	+	44.2155i	−0.376889	+	1.65126i
$718$	8.92451	+	11.1910i	0.333060	+	0.417644i
$719$	−18.2296	−	8.77889i	−0.679848	−	0.327397i	0.0618942	−	0.998083i	$-0.480286\pi$
$719$	−18.2296	−	8.77889i	−0.679848	−	0.327397i	−0.741742	+	0.670685i	$0.766000\pi$
$720$	51.1741	−	24.6442i	1.90715	−	0.918434i
$721$	−0.675215	+	0.846692i	−0.0251463	+	0.0315325i
$722$	−1.22305	−	1.53366i	−0.0455172	−	0.0570768i
$723$	−19.8118	+	9.54084i	−0.736807	+	0.354828i
$724$	−7.61641			−0.283062
$725$		0			0
$726$	44.1252			1.63764
$727$	−31.4246	+	15.1333i	−1.16547	+	0.561262i	−0.913646	−	0.406510i	$-0.866745\pi$
$727$	−31.4246	+	15.1333i	−1.16547	+	0.561262i	−0.251826	+	0.967772i	$0.581031\pi$
$728$	0.789865	+	0.990460i	0.0292744	+	0.0367089i
$729$	−1.11065	+	1.39271i	−0.0411351	+	0.0515818i
$730$	−38.7465	+	18.6593i	−1.43407	+	0.690613i
$731$	−10.4767	−	5.04529i	−0.387493	−	0.186607i
$732$	6.94123	+	8.70402i	0.256555	+	0.321710i
$733$	10.8632	−	47.5950i	0.401243	−	1.75796i	−0.221133	−	0.975244i	$-0.570976\pi$
$733$	10.8632	−	47.5950i	0.401243	−	1.75796i	0.622376	−	0.782718i	$-0.286167\pi$
$734$	−3.88600	+	17.0257i	−0.143435	+	0.628429i
$735$	25.0542	−	31.4170i	0.924140	−	1.15883i
$736$	−3.07713	−	13.4818i	−0.113424	−	0.496945i
$737$	8.30395			0.305880
$738$	8.40703	+	36.8336i	0.309467	+	1.35586i
$739$	27.4335	+	13.2113i	1.00916	+	0.485985i	0.864037	−	0.503428i	$-0.167928\pi$
$739$	27.4335	+	13.2113i	1.00916	+	0.485985i	0.145122	+	0.989414i	$0.453643\pi$
$740$	1.60445	+	0.772664i	0.0589809	+	0.0284037i
$741$	−4.18755	−	18.3468i	−0.153833	−	0.673988i
$742$	2.71208			0.0995634
$743$	7.75238	+	33.9654i	0.284407	+	1.24607i	0.892078	+	0.451881i	$0.149247\pi$
$743$	7.75238	+	33.9654i	0.284407	+	1.24607i	−0.607671	+	0.794189i	$0.707896\pi$
$744$	−21.7552	+	27.2801i	−0.797584	+	1.00014i
$745$	−3.45175	+	15.1231i	−0.126462	+	0.554067i
$746$	−2.72170	+	11.9245i	−0.0996485	+	0.436589i
$747$	46.4323	+	58.2243i	1.69887	+	2.13032i
$748$	0.453027	+	0.218166i	0.0165643	+	0.00797695i
$749$	5.04179	−	2.42800i	0.184223	−	0.0887172i
$750$	35.8716	−	44.9815i	1.30984	−	1.64249i
$751$	−15.0147	−	18.8279i	−0.547895	−	0.687039i	0.428373	−	0.903602i	$-0.359087\pi$
$751$	−15.0147	−	18.8279i	−0.547895	−	0.687039i	−0.976269	+	0.216563i	$0.930515\pi$
$752$	−29.5317	+	14.2217i	−1.07691	+	0.518612i
$753$	−41.7439			−1.52123
$754$		0			0
$755$	−6.32000			−0.230008
$756$	−1.09811	+	0.528822i	−0.0399379	+	0.0192331i
$757$	6.27609	+	7.86997i	0.228109	+	0.286039i	0.882693	−	0.469950i	$-0.155728\pi$
$757$	6.27609	+	7.86997i	0.228109	+	0.286039i	−0.654585	+	0.755989i	$0.727156\pi$
$758$	4.44687	−	5.57619i	0.161517	−	0.202537i
$759$	29.0826	−	14.0054i	1.05563	−	0.508365i
$760$	−18.2697	−	8.79820i	−0.662710	−	0.319144i
$761$	−30.2600	−	37.9449i	−1.09692	−	1.37550i	−0.920296	−	0.391223i	$-0.872052\pi$
$761$	−30.2600	−	37.9449i	−1.09692	−	1.37550i	−0.176629	−	0.984278i	$-0.556519\pi$
$762$	−17.1056	+	74.9444i	−0.619670	+	2.71495i
$763$	0.444019	−	1.94537i	0.0160746	−	0.0704273i
$764$	3.82629	−	4.79802i	0.138430	−	0.173586i
$765$	−3.52732	−	15.4542i	−0.127531	−	0.558748i
$766$	−35.0244			−1.26548
$767$	1.74451	+	7.64319i	0.0629905	+	0.275980i
$768$	20.2722	+	9.76259i	0.731511	+	0.352277i
$769$	−6.76731	−	3.25896i	−0.244035	−	0.117521i	0.307869	−	0.951429i	$-0.400384\pi$
$769$	−6.76731	−	3.25896i	−0.244035	−	0.117521i	−0.551904	+	0.833908i	$0.686099\pi$
$770$	−0.281530	−	1.23346i	−0.0101456	−	0.0444509i
$771$	33.6201			1.21080
$772$	−0.706831	−	3.09683i	−0.0254394	−	0.111457i
$773$	−24.9493	+	31.2854i	−0.897363	+	1.12526i	0.0941903	+	0.995554i	$0.469974\pi$
$773$	−24.9493	+	31.2854i	−0.897363	+	1.12526i	−0.991553	+	0.129703i	$0.958598\pi$
$774$	−20.8803	+	91.4824i	−0.750526	+	3.28827i
$775$	−1.44109	+	6.31384i	−0.0517656	+	0.226800i
$776$	−15.2274	−	19.0946i	−0.546632	−	0.685455i
$777$	2.97216	+	1.43132i	0.106626	+	0.0513482i
$778$	11.9132	−	5.73711i	0.427110	−	0.205685i
$779$	9.73586	−	12.2084i	0.348823	−	0.437410i
$780$	−1.60932	−	2.01802i	−0.0576228	−	0.0722567i
$781$	7.54822	−	3.63503i	0.270096	−	0.130072i
$782$	−15.3479			−0.548838
$783$		0			0
$784$	31.1144			1.11123
$785$	8.70762	−	4.19337i	0.310788	−	0.149668i
$786$	5.95630	+	7.46896i	0.212454	+	0.266409i
$787$	22.0970	−	27.7087i	0.787671	−	0.987709i	−0.212274	−	0.977210i	$-0.568087\pi$
$787$	22.0970	−	27.7087i	0.787671	−	0.987709i	0.999945	−	0.0104983i	$-0.00334176\pi$
$788$	−1.49068	+	0.717872i	−0.0531031	+	0.0255731i
$789$	−2.22385	−	1.07095i	−0.0791713	−	0.0381269i
$790$	8.10086	+	10.1582i	0.288216	+	0.361411i
$791$	0.546730	−	2.39538i	0.0194395	−	0.0851700i
$792$	−4.96177	+	21.7389i	−0.176309	+	0.772459i
$793$	−10.3906	+	13.0294i	−0.368981	+	0.462687i
$794$	5.44589	+	23.8600i	0.193268	+	0.846760i
$795$	30.3661			1.07698
$796$	0.0436293	+	0.191153i	0.00154640	+	0.00677523i
$797$	−0.989731	−	0.476629i	−0.0350581	−	0.0168831i	0.416273	−	0.909240i	$-0.363336\pi$
$797$	−0.989731	−	0.476629i	−0.0350581	−	0.0168831i	−0.451331	+	0.892357i	$0.649050\pi$
$798$	6.15851	+	2.96578i	0.218009	+	0.104988i
$799$	2.03555	+	8.91834i	0.0720127	+	0.315508i
$800$	2.56661			0.0907433
$801$	1.03273	+	4.52470i	0.0364898	+	0.159872i
$802$	−15.9992	+	20.0623i	−0.564950	+	0.708425i
$803$	4.34923	−	19.0552i	0.153481	−	0.672444i
$804$	−1.36928	+	5.99920i	−0.0482907	+	0.211575i
$805$	3.21234	+	4.02814i	0.113220	+	0.141973i
$806$	8.56344	+	4.12393i	0.301634	+	0.145259i
$807$	−53.3550	+	25.6944i	−1.87818	+	0.904486i
$808$	10.0284	−	12.5752i	0.352797	−	0.442394i
$809$	20.8619	+	26.1600i	0.733467	+	0.919738i	0.999016	−	0.0443591i	$-0.0141246\pi$
$809$	20.8619	+	26.1600i	0.733467	+	0.919738i	−0.265549	+	0.964097i	$0.585553\pi$
$810$	−40.5694	+	19.5372i	−1.42546	+	0.686467i
$811$	45.3840			1.59365			0.796823	−	0.604212i	$-0.206512\pi$
$811$	45.3840			1.59365			0.796823	+	0.604212i	$0.206512\pi$
$812$		0			0
$813$	71.2836			2.50002
$814$	−5.46563	+	2.63211i	−0.191570	+	0.0922554i
$815$	20.1851	+	25.3113i	0.707053	+	0.886617i
$816$	11.0781	−	13.8916i	0.387813	−	0.486302i
$817$	34.9420	−	16.8272i	1.22247	−	0.588709i
$818$	−12.5074	−	6.02325i	−0.437311	−	0.210598i
$819$	−2.05936	−	2.58235i	−0.0719598	−	0.0902347i
$820$	0.476584	−	2.08805i	0.0166430	−	0.0729178i
$821$	−0.919994	+	4.03076i	−0.0321080	+	0.140674i	−0.988441	−	0.151604i	$-0.951556\pi$
$821$	−0.919994	+	4.03076i	−0.0321080	+	0.140674i	0.956333	+	0.292278i	$0.0944133\pi$
$822$	39.9649	−	50.1144i	1.39394	−	1.74794i
$823$	−5.31742	−	23.2971i	−0.185354	−	0.812087i	−0.979025	−	0.203740i	$-0.934690\pi$
$823$	−5.31742	−	23.2971i	−0.185354	−	0.812087i	0.793671	−	0.608347i	$-0.208167\pi$
$824$	−8.10991			−0.282522
$825$	1.33315	+	5.84091i	0.0464143	+	0.203355i
$826$	−2.56560	−	1.23553i	−0.0892687	−	0.0429895i
$827$	41.4049	+	19.9396i	1.43979	+	0.693367i	0.980789	−	0.195069i	$-0.0624931\pi$
$827$	41.4049	+	19.9396i	1.43979	+	0.693367i	0.459001	+	0.888436i	$0.348207\pi$
$828$	3.67685	+	16.1093i	0.127779	+	0.559838i
$829$	7.40477			0.257178			0.128589	−	0.991698i	$-0.458955\pi$
$829$	7.40477			0.257178			0.128589	+	0.991698i	$0.458955\pi$
$830$	−7.04131	−	30.8500i	−0.244407	−	1.07082i
$831$	−63.5078	+	79.6363i	−2.20306	+	2.76255i
$832$	−2.05047	+	8.98370i	−0.0710873	+	0.311454i
$833$	1.93226	−	8.46578i	0.0669488	−	0.293322i
$834$	11.6811	+	14.6477i	0.404484	+	0.507207i
$835$	19.3847	+	9.33516i	0.670834	+	0.323057i
$836$	−1.51095	+	0.727634i	−0.0522572	+	0.0251657i
$837$	31.3314	−	39.2883i	1.08297	−	1.35800i
$838$	17.6667	+	22.1534i	0.610287	+	0.765275i
$839$	−2.70393	+	1.30214i	−0.0933500	+	0.0449550i	−0.479976	−	0.877282i	$-0.659355\pi$
$839$	−2.70393	+	1.30214i	−0.0933500	+	0.0449550i	0.386626	+	0.922237i	$0.373640\pi$
$840$	−5.15215			−0.177766
$841$		0			0
$842$	19.8206			0.683064
$843$	36.8435	−	17.7429i	1.26896	−	0.611098i
$844$	3.13642	+	3.93295i	0.107960	+	0.135378i
$845$	−12.7847	+	16.0316i	−0.439808	+	0.551502i
$846$	66.5079	−	32.0285i	2.28659	−	1.10116i
$847$	−2.88392	−	1.38882i	−0.0990926	−	0.0477205i
$848$	14.6598	+	18.3828i	0.503420	+	0.631268i
$849$	5.99678	−	26.2736i	0.205809	−	0.901708i
$850$	0.633874	−	2.77719i	0.0217417	−	0.0952567i
$851$	15.4028	−	19.3145i	0.528000	−	0.662091i
$852$	1.38147	+	6.05262i	0.0473284	+	0.207359i
$853$	51.1705			1.75204			0.876022	−	0.482272i	$-0.160188\pi$
$853$	51.1705			1.75204			0.876022	+	0.482272i	$0.160188\pi$
$854$	−1.34697	−	5.90148i	−0.0460925	−	0.201944i
$855$	47.6331	+	22.9389i	1.62902	+	0.784494i
$856$	37.7562	+	18.1824i	1.29048	+	0.621463i
$857$	5.43222	+	23.8001i	0.185561	+	0.812996i	0.978920	+	0.204242i	$0.0654731\pi$
$857$	5.43222	+	23.8001i	0.185561	+	0.812996i	−0.793359	+	0.608754i	$0.791670\pi$
$858$	8.79276			0.300180
$859$	−0.254119	−	1.11337i	−0.00867044	−	0.0379877i	0.970408	−	0.241473i	$-0.0776304\pi$
$859$	−0.254119	−	1.11337i	−0.00867044	−	0.0379877i	−0.979078	+	0.203485i	$0.934773\pi$
$860$	3.31658	−	4.15886i	0.113095	−	0.141816i
$861$	0.882844	−	3.86799i	0.0300872	−	0.131821i
$862$	5.70349	−	24.9886i	0.194262	−	0.851116i
$863$	26.0757	+	32.6978i	0.887626	+	1.11305i	0.992941	+	0.118608i	$0.0378433\pi$
$863$	26.0757	+	32.6978i	0.887626	+	1.11305i	−0.105315	+	0.994439i	$0.533585\pi$
$864$	−17.9431	−	8.64096i	−0.610438	−	0.293971i
$865$	−0.146821	+	0.0707051i	−0.00499205	+	0.00240405i
$866$	3.40711	−	4.27238i	0.115778	−	0.145181i
$867$	29.9233	+	37.5226i	1.01625	+	1.27433i
$868$	−0.414983	+	0.199845i	−0.0140854	+	0.00678319i
$869$	−5.90501			−0.200314
$870$		0			0
$871$	−9.21139			−0.312116
$872$	13.4631	−	6.48347i	0.455917	−	0.219558i
$873$	39.7013	+	49.7839i	1.34369	+	1.68493i
$874$	31.9155	−	40.0208i	1.07956	−	1.35372i
$875$	−3.76026	+	1.81084i	−0.127120	+	0.0612177i
$876$	13.0493	+	6.28421i	0.440895	+	0.212324i
$877$	−14.4718	−	18.1470i	−0.488677	−	0.612781i	0.474957	−	0.880009i	$-0.342464\pi$
$877$	−14.4718	−	18.1470i	−0.488677	−	0.612781i	−0.963633	+	0.267228i	$0.913892\pi$
$878$	−5.86947	+	25.7158i	−0.198085	+	0.867867i
$879$	17.2753	−	75.6881i	0.582682	−	2.55290i
$880$	6.83880	−	8.57558i	0.230536	−	0.289083i
$881$	6.08501	+	26.6602i	0.205009	+	0.898203i	0.967832	+	0.251596i	$0.0809555\pi$
$881$	6.08501	+	26.6602i	0.205009	+	0.898203i	−0.762823	+	0.646607i	$0.776187\pi$
$882$	−70.0723			−2.35946
$883$	0.776276	+	3.40109i	0.0261238	+	0.114456i	0.986309	−	0.164909i	$-0.0527332\pi$
$883$	0.776276	+	3.40109i	0.0261238	+	0.114456i	−0.960185	+	0.279365i	$0.909876\pi$
$884$	−0.502533	−	0.242007i	−0.0169020	−	0.00813958i
$885$	−28.7261	−	13.8338i	−0.965618	−	0.465017i
$886$	4.30477	+	18.8604i	0.144621	+	0.633628i
$887$	−33.9445			−1.13975			−0.569873	−	0.821733i	$-0.693007\pi$
$887$	−33.9445			−1.13975			−0.569873	+	0.821733i	$0.693007\pi$
$888$	5.49714	+	24.0846i	0.184472	+	0.808225i
$889$	3.47683	−	4.35980i	0.116609	−	0.146223i
$890$	0.438813	−	1.92256i	0.0147090	−	0.0644445i
$891$	4.55384	−	19.9517i	0.152559	−	0.668407i
$892$	−3.20874	−	4.02363i	−0.107436	−	0.134721i
$893$	−27.4882	−	13.2376i	−0.919858	−	0.442980i
$894$	35.2799	−	16.9899i	1.17994	−	0.568227i
$895$	18.6513	−	23.3880i	0.623444	−	0.781774i
$896$	−2.82610	−	3.54381i	−0.0944132	−	0.118390i
$897$	−32.2607	+	15.5359i	−1.07715	+	0.518729i
$898$	−35.1863			−1.17418
$899$		0			0
$900$	−3.06683			−0.102228
$901$	5.91210	−	2.84712i	0.196961	−	0.0948512i
$902$	4.54895	+	5.70420i	0.151463	+	0.189929i
$903$	6.14378	−	7.70406i	0.204452	−	0.256375i
$904$	16.5774	−	7.98324i	0.551355	−	0.265519i
$905$	41.7763	+	20.1184i	1.38869	+	0.668758i
$906$	9.94708	+	12.4732i	0.330470	+	0.414396i
$907$	6.23857	−	27.3330i	0.207148	−	0.907577i	−0.759305	−	0.650735i	$-0.774461\pi$
$907$	6.23857	−	27.3330i	0.207148	−	0.907577i	0.966453	−	0.256842i	$-0.0826819\pi$
$908$	0.755874	−	3.31170i	0.0250846	−	0.109903i
$909$	−26.1463	+	32.7864i	−0.867217	+	1.08746i
$910$	0.312295	+	1.36825i	0.0103525	+	0.0453571i
$911$	−23.6980			−0.785151			−0.392576	−	0.919720i	$-0.628416\pi$
$911$	−23.6980			−0.785151			−0.392576	+	0.919720i	$0.628416\pi$
$912$	13.1866	+	57.7744i	0.436653	+	1.91310i
$913$	12.9572	+	6.23985i	0.428820	+	0.206509i
$914$	−42.7304	−	20.5779i	−1.41339	−	0.680655i
$915$	−15.0816	−	66.0768i	−0.498582	−	2.18443i
$916$	4.50325			0.148792
$917$	−0.154207	−	0.675626i	−0.00509237	−	0.0223111i
$918$	−13.7813	+	17.2812i	−0.454851	+	0.570365i
$919$	−10.1217	+	44.3460i	−0.333883	+	1.46284i	0.477659	+	0.878545i	$0.341486\pi$
$919$	−10.1217	+	44.3460i	−0.333883	+	1.46284i	−0.811542	+	0.584294i	$0.801372\pi$
$920$	−8.58552	+	37.6156i	−0.283056	+	1.24015i
$921$	−2.42983	−	3.04691i	−0.0800657	−	0.100399i
$922$	19.2762	+	9.28291i	0.634827	+	0.305716i
$923$	−8.37307	+	4.03226i	−0.275603	+	0.132723i
$924$	−0.265667	+	0.333135i	−0.00873979	+	0.0109594i
$925$	2.85880	+	3.58482i	0.0939967	+	0.117868i
$926$	−27.5331	+	13.2592i	−0.904793	+	0.435725i
$927$	21.1444			0.694472
$928$		0			0
$929$	−1.45656			−0.0477883			−0.0238942	−	0.999714i	$-0.507606\pi$
$929$	−1.45656			−0.0477883			−0.0238942	+	0.999714i	$0.507606\pi$
$930$	−34.8268	+	16.7717i	−1.14201	+	0.549965i
$931$	18.0571	+	22.6429i	0.591799	+	0.742092i
$932$	−1.83362	+	2.29928i	−0.0600622	+	0.0753156i
$933$	−83.2044	+	40.0691i	−2.72399	+	1.31181i
$934$	25.0327	+	12.0551i	0.819094	+	0.394455i
$935$	−1.90859	−	2.39330i	−0.0624176	−	0.0782692i
$936$	5.50398	−	24.1145i	0.179903	−	0.788208i
$937$	−2.22625	+	9.75382i	−0.0727283	+	0.318644i	−0.998186	−	0.0602078i	$-0.980824\pi$
$937$	−2.22625	+	9.75382i	−0.0727283	+	0.318644i	0.925458	+	0.378851i	$0.123681\pi$
$938$	2.08608	−	2.61587i	0.0681130	−	0.0854110i
$939$	12.5737	+	55.0888i	0.410326	+	1.79776i
$940$	−4.18466			−0.136489
$941$	11.0745	+	48.5207i	0.361019	+	1.58173i	0.750613	+	0.660742i	$0.229758\pi$
$941$	11.0745	+	48.5207i	0.361019	+	1.58173i	−0.389594	+	0.920987i	$0.627385\pi$
$942$	−21.9811	−	10.5855i	−0.716182	−	0.344895i
$943$	−26.7688	−	12.8912i	−0.871713	−	0.419795i
$944$	−5.49347	−	24.0685i	−0.178797	−	0.783363i
$945$	7.42003			0.241373
$946$	4.03223	+	17.6664i	0.131099	+	0.574383i
$947$	13.7332	−	17.2209i	0.446271	−	0.559606i	−0.506913	−	0.861997i	$-0.669214\pi$
$947$	13.7332	−	17.2209i	0.446271	−	0.559606i	0.953184	+	0.302391i	$0.0977850\pi$
$948$	0.973704	−	4.26608i	0.0316244	−	0.138556i
$949$	−4.82450	+	21.1375i	−0.156610	+	0.686153i
$950$	5.92362	+	7.42798i	0.192187	+	0.240995i
$951$	−60.7142	−	29.2384i	−1.96879	−	0.948121i
$952$	−1.00309	+	0.483064i	−0.0325104	+	0.0156562i
$953$	−17.1227	+	21.4712i	−0.554660	+	0.695522i	−0.977561	−	0.210654i	$-0.932441\pi$
$953$	−17.1227	+	21.4712i	−0.554660	+	0.695522i	0.422900	+	0.906176i	$0.361012\pi$
$954$	−33.0152	−	41.3997i	−1.06891	−	1.34037i
$955$	−33.6611	+	16.2103i	−1.08925	+	0.524554i
$956$	−4.48325			−0.144999
$957$		0			0
$958$	−24.5720			−0.793885
$959$	−4.18935	+	2.01748i	−0.135281	+	0.0651479i
$960$	−23.3656	−	29.2995i	−0.754122	−	0.945639i
$961$	−7.48785	+	9.38946i	−0.241543	+	0.302886i
$962$	6.06291	−	2.91974i	0.195476	−	0.0941362i
$963$	−98.4390	−	47.4057i	−3.17215	−	1.52763i
$964$	−1.35529	−	1.69948i	−0.0436511	−	0.0547367i
$965$	−4.30313	+	18.8533i	−0.138523	+	0.606908i
$966$	2.89409	−	12.6798i	0.0931158	−	0.407967i
$967$	−16.5361	+	20.7357i	−0.531766	+	0.666814i	−0.973061	−	0.230548i	$-0.925948\pi$
$967$	−16.5361	+	20.7357i	−0.531766	+	0.666814i	0.441294	+	0.897362i	$0.354519\pi$
$968$	−5.33393	−	23.3695i	−0.171439	−	0.751124i
$969$	16.5385			0.531293
$970$	−6.02057	−	26.3779i	−0.193309	−	0.846942i
$971$	44.9272	+	21.6358i	1.44178	+	0.694326i	0.981147	−	0.193263i	$-0.0619071\pi$
$971$	44.9272	+	21.6358i	1.44178	+	0.694326i	0.460636	+	0.887589i	$0.347621\pi$
$972$	4.06616	+	1.95816i	0.130422	+	0.0628080i
$973$	−0.302422	−	1.32500i	−0.00969519	−	0.0424774i
$974$	−43.4737			−1.39299
$975$	−1.47883	−	6.47919i	−0.0473606	−	0.207500i
$976$	32.7201	−	41.0297i	1.04734	−	1.31333i
$977$	11.2500	−	49.2895i	0.359920	−	1.57691i	−0.393470	−	0.919337i	$-0.628726\pi$
$977$	11.2500	−	49.2895i	0.359920	−	1.57691i	0.753390	−	0.657574i	$-0.228417\pi$
$978$	18.1854	−	79.6752i	0.581503	−	2.54773i
$979$	0.558800	+	0.700713i	0.0178593	+	0.0223949i
$980$	3.57893	+	1.72352i	0.114325	+	0.0550558i
$981$	−35.1013	+	16.9039i	−1.12070	+	0.539699i
$982$	−0.805734	+	1.01036i	−0.0257120	+	0.0322418i
$983$	−3.53431	−	4.43189i	−0.112727	−	0.141355i	0.722267	−	0.691615i	$-0.243100\pi$
$983$	−3.53431	−	4.43189i	−0.112727	−	0.141355i	−0.834994	+	0.550259i	$0.814529\pi$
$984$	26.7686	−	12.8911i	0.853353	−	0.410953i
$985$	10.0726			0.320941
$986$		0			0
$987$	−7.75184			−0.246744
$988$	1.67606	−	0.807148i	0.0533226	−	0.0256788i
$989$	−46.0090	−	57.6934i	−1.46300	−	1.83454i
$990$	−15.4016	+	19.3130i	−0.489494	+	0.613806i
$991$	−15.0189	+	7.23272i	−0.477091	+	0.229755i	−0.656945	−	0.753938i	$-0.728152\pi$
$991$	−15.0189	+	7.23272i	−0.477091	+	0.229755i	0.179854	+	0.983693i	$0.442437\pi$
$992$	−6.78083	−	3.26548i	−0.215292	−	0.103679i
$993$	10.7250	+	13.4488i	0.340349	+	0.426784i
$994$	0.751144	−	3.29098i	0.0238248	−	0.104383i
$995$	0.265612	−	1.16372i	0.00842048	−	0.0368925i
$996$	−6.64456	+	8.33201i	−0.210541	+	0.264010i
$997$	−4.20341	−	18.4164i	−0.133123	−	0.583252i	−0.996851	−	0.0792935i	$-0.974734\pi$
$997$	−4.20341	−	18.4164i	−0.133123	−	0.583252i	0.863728	−	0.503959i	$-0.168124\pi$
$998$	21.5019			0.680631
$999$	−7.91687	−	34.6861i	−0.250479	−	1.09742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.q.571.1		48
29.2	odd	28		841.2.e.m.196.4		96
29.3	odd	28		841.2.e.m.267.4		96
29.4	even	14		841.2.a.j.1.1	yes	8
29.5	even	14		841.2.d.p.645.8		48
29.6	even	14		841.2.d.p.778.1		48
29.7	even	7	inner	841.2.d.q.574.8		48
29.8	odd	28		841.2.e.m.236.4		96
29.9	even	14		841.2.d.p.605.8		48
29.10	odd	28		841.2.b.f.840.13		16
29.11	odd	28		841.2.e.m.651.4		96
29.12	odd	4		841.2.e.m.270.4		96
29.13	even	14		841.2.d.p.190.8		48
29.14	odd	28		841.2.e.m.63.13		96
29.15	odd	28		841.2.e.m.63.4		96
29.16	even	7	inner	841.2.d.q.190.1		48
29.17	odd	4		841.2.e.m.270.13		96
29.18	odd	28		841.2.e.m.651.13		96
29.19	odd	28		841.2.b.f.840.4		16
29.20	even	7	inner	841.2.d.q.605.1		48
29.21	odd	28		841.2.e.m.236.13		96
29.22	even	14		841.2.d.p.574.1		48
29.23	even	7	inner	841.2.d.q.778.8		48
29.24	even	7	inner	841.2.d.q.645.1		48
29.25	even	7		841.2.a.i.1.8	✓	8
29.26	odd	28		841.2.e.m.267.13		96
29.27	odd	28		841.2.e.m.196.13		96
29.28	even	2		841.2.d.p.571.8		48
87.62	odd	14		7569.2.a.bd.1.8		8
87.83	odd	14		7569.2.a.bi.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.8	✓	8	29.25	even	7
841.2.a.j.1.1	yes	8	29.4	even	14
841.2.b.f.840.4		16	29.19	odd	28
841.2.b.f.840.13		16	29.10	odd	28
841.2.d.p.190.8		48	29.13	even	14
841.2.d.p.571.8		48	29.28	even	2
841.2.d.p.574.1		48	29.22	even	14
841.2.d.p.605.8		48	29.9	even	14
841.2.d.p.645.8		48	29.5	even	14
841.2.d.p.778.1		48	29.6	even	14
841.2.d.q.190.1		48	29.16	even	7	inner
841.2.d.q.571.1		48	1.1	even	1	trivial
841.2.d.q.574.8		48	29.7	even	7	inner
841.2.d.q.605.1		48	29.20	even	7	inner
841.2.d.q.645.1		48	29.24	even	7	inner
841.2.d.q.778.8		48	29.23	even	7	inner
841.2.e.m.63.4		96	29.15	odd	28
841.2.e.m.63.13		96	29.14	odd	28
841.2.e.m.196.4		96	29.2	odd	28
841.2.e.m.196.13		96	29.27	odd	28
841.2.e.m.236.4		96	29.8	odd	28
841.2.e.m.236.13		96	29.21	odd	28
841.2.e.m.267.4		96	29.3	odd	28
841.2.e.m.267.13		96	29.26	odd	28
841.2.e.m.270.4		96	29.12	odd	4
841.2.e.m.270.13		96	29.17	odd	4
841.2.e.m.651.4		96	29.11	odd	28
841.2.e.m.651.13		96	29.18	odd	28
7569.2.a.bd.1.8		8	87.62	odd	14
7569.2.a.bi.1.1		8	87.83	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36873 + 0.659148i) q^{2} +(-1.94206 - 2.43527i) q^{3} +(0.191979 - 0.240734i) q^{4} +(-1.68890 + 0.813330i) q^{5} +(4.26336 + 2.05313i) q^{6} +(-0.214022 - 0.268375i) q^{7} +(0.572010 - 2.50614i) q^{8} +(-1.49136 + 6.53408i) q^{9} +(1.77555 - 2.22647i) q^{10} +(0.288000 + 1.26181i) q^{11} -0.959085 q^{12} +(-0.319472 - 1.39970i) q^{13} +(0.469838 + 0.226262i) q^{14} +(5.26061 + 2.53338i) q^{15} +(1.00602 + 4.40766i) q^{16} +1.26174 q^{17} +(-2.26565 - 9.92644i) q^{18} +(-2.62376 + 3.29009i) q^{19} +(-0.128436 + 0.562717i) q^{20} +(-0.237921 + 1.04240i) q^{21} +(-1.22591 - 1.53725i) q^{22} +(7.21405 + 3.47410i) q^{23} +(-7.21399 + 3.47408i) q^{24} +(-0.926581 + 1.16190i) q^{25} +(1.35988 + 1.70523i) q^{26} +(10.3894 - 5.00329i) q^{27} -0.105695 q^{28} -8.87025 q^{30} +(3.92624 - 1.89078i) q^{31} +(-1.07680 - 1.35026i) q^{32} +(2.51353 - 3.15186i) q^{33} +(-1.72698 + 0.831672i) q^{34} +(0.579739 + 0.279188i) q^{35} +(1.28666 + 1.61343i) q^{36} +(0.686548 - 3.00796i) q^{37} +(1.42257 - 6.23270i) q^{38} +(-2.78820 + 3.49629i) q^{39} +(1.07225 + 4.69785i) q^{40} -3.71066 q^{41} +(-0.361445 - 1.58360i) q^{42} +(-8.30336 - 3.99869i) q^{43} +(0.359050 + 0.172909i) q^{44} +(-2.79561 - 12.2484i) q^{45} -12.1641 q^{46} +(1.61329 + 7.06830i) q^{47} +(8.78007 - 11.0099i) q^{48} +(1.53143 - 6.70962i) q^{49} +(0.502382 - 2.20108i) q^{50} +(-2.45037 - 3.07267i) q^{51} +(-0.398286 - 0.191805i) q^{52} +(4.68568 - 2.25651i) q^{53} +(-10.9225 + 13.6964i) q^{54} +(-1.51267 - 1.89683i) q^{55} +(-0.795009 + 0.382856i) q^{56} +13.1077 q^{57} -5.46060 q^{59} +(1.61980 - 0.780053i) q^{60} +(-7.23734 - 9.07534i) q^{61} +(-4.12768 + 5.17595i) q^{62} +(2.07277 - 0.998193i) q^{63} +(-5.78270 - 2.78480i) q^{64} +(1.67797 + 2.10411i) q^{65} +(-1.36281 + 5.97085i) q^{66} +(1.42769 - 6.25513i) q^{67} +(0.242227 - 0.303743i) q^{68} +(-5.54975 - 24.3150i) q^{69} -0.977535 q^{70} +(-1.44040 - 6.31082i) q^{71} +(15.5222 + 7.47512i) q^{72} +(-13.6060 - 6.55229i) q^{73} +(1.04299 + 4.56964i) q^{74} +4.62900 q^{75} +(0.288329 + 1.26325i) q^{76} +(0.277000 - 0.347347i) q^{77} +(1.51173 - 6.62333i) q^{78} +(-1.01524 + 4.44807i) q^{79} +(-5.28395 - 6.62586i) q^{80} +(-14.2461 - 6.86055i) q^{81} +(5.07890 - 2.44587i) q^{82} +(6.92802 - 8.68746i) q^{83} +(0.205265 + 0.257395i) q^{84} +(-2.13095 + 1.02621i) q^{85} +14.0008 q^{86} +3.32701 q^{88} +(0.623900 - 0.300455i) q^{89} +(11.8999 + 14.9220i) q^{90} +(-0.307270 + 0.385304i) q^{91} +(2.22128 - 1.06971i) q^{92} +(-12.2295 - 5.88944i) q^{93} +(-6.86723 - 8.61123i) q^{94} +(1.75533 - 7.69060i) q^{95} +(-1.19704 + 5.24459i) q^{96} +(5.92370 - 7.42809i) q^{97} +(2.32651 + 10.1931i) q^{98} -8.67427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) \) 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

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