LMFDB - Embedded newform 867.2.i.h.503.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,8,-16,0,8,16,0,-8,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			503.3
Character	$\chi$	$=$	867.503
Dual form			867.2.i.h.131.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.774648 + 0.320870i) q^{2} +(-0.00133765 - 1.73205i) q^{3} +(-0.917091 - 0.917091i) q^{4} +(0.159652 + 0.802626i) q^{5} +(0.554726 - 1.34216i) q^{6} +(-0.191449 - 0.0380817i) q^{7} +(-1.05790 - 2.55399i) q^{8} +(-3.00000 + 0.00463376i) q^{9} +(-0.133864 + 0.672980i) q^{10} +(-3.67179 + 2.45341i) q^{11} +(-1.58722 + 1.58968i) q^{12} +(-3.75023 + 3.75023i) q^{13} +(-0.136087 - 0.0909302i) q^{14} +(1.38998 - 0.277599i) q^{15} +0.276039i q^{16} +(-2.32543 - 0.959018i) q^{18} +(0.210831 - 0.508991i) q^{19} +(0.589666 - 0.882497i) q^{20} +(-0.0657033 + 0.331651i) q^{21} +(-3.63157 + 0.722364i) q^{22} +(-2.29752 - 3.43849i) q^{23} +(-4.42222 + 1.83574i) q^{24} +(4.00068 - 1.65713i) q^{25} +(-4.10844 + 1.70177i) q^{26} +(0.0120389 + 5.19614i) q^{27} +(0.140652 + 0.210501i) q^{28} +(-0.606965 + 0.120733i) q^{29} +(1.16581 + 0.230959i) q^{30} +(-0.369997 + 0.553739i) q^{31} +(-2.20436 + 5.32181i) q^{32} +(4.25434 + 6.35644i) q^{33} -0.159742i q^{35} +(2.75552 + 2.74702i) q^{36} +(-1.63319 - 1.09126i) q^{37} +(0.326640 - 0.326640i) q^{38} +(6.50060 + 6.49057i) q^{39} +(1.88100 - 1.25684i) q^{40} +(-1.55975 + 7.84141i) q^{41} +(-0.157314 + 0.235831i) q^{42} +(-2.95422 - 7.13212i) q^{43} +(5.61737 + 1.11736i) q^{44} +(-0.482675 - 2.40714i) q^{45} +(-0.676466 - 3.40082i) q^{46} +(7.05884 + 7.05884i) q^{47} +(0.478114 - 0.000369245i) q^{48} +(-6.43195 - 2.66420i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(-10.7049 - 4.43410i) q^{53} +(-1.65796 + 4.02904i) q^{54} +(-2.55538 - 2.55538i) q^{55} +(0.105274 + 0.529246i) q^{56} +(-0.881880 - 0.364489i) q^{57} +(-0.508924 - 0.101231i) q^{58} +(-0.0995233 - 0.240270i) q^{59} +(-1.52932 - 1.02015i) q^{60} +(2.05830 - 10.3478i) q^{61} +(-0.464295 + 0.310232i) q^{62} +(0.574524 + 0.113358i) q^{63} +(-3.02483 + 3.02483i) q^{64} +(-3.60876 - 2.41130i) q^{65} +(1.25603 + 6.28910i) q^{66} -5.40994i q^{67} +(-5.95256 + 3.98403i) q^{69} +(0.0512564 - 0.123744i) q^{70} +(-3.61943 + 5.41686i) q^{71} +(3.18552 + 7.65705i) q^{72} +(-11.3822 + 2.26406i) q^{73} +(-0.914994 - 1.36939i) q^{74} +(-2.87559 - 6.92716i) q^{75} +(-0.660143 + 0.273440i) q^{76} +(0.796392 - 0.329876i) q^{77} +(2.95305 + 7.11375i) q^{78} +(-6.00531 - 8.98758i) q^{79} +(-0.221556 + 0.0440703i) q^{80} +(8.99996 - 0.0278025i) q^{81} +(-3.72433 + 5.57385i) q^{82} +(1.05744 - 2.55289i) q^{83} +(0.364410 - 0.243898i) q^{84} -6.47280i q^{86} +(0.209927 + 1.05113i) q^{87} +(10.1503 + 6.78225i) q^{88} +(-3.69661 + 3.69661i) q^{89} +(0.398473 - 2.01956i) q^{90} +(0.860794 - 0.575164i) q^{91} +(-1.04637 + 5.26045i) q^{92} +(0.959599 + 0.640112i) q^{93} +(3.20315 + 7.73308i) q^{94} +(0.442189 + 0.0879569i) q^{95} +(9.22058 + 3.81095i) q^{96} +(-0.481692 - 2.42163i) q^{97} +(-4.12764 - 4.12764i) q^{98} +(11.0040 - 7.37724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.774648	+	0.320870i	0.547759	+	0.226889i	0.639361	−	0.768907i	$-0.279199\pi$
$2$	0.774648	+	0.320870i	0.547759	+	0.226889i	−0.0916024	+	0.995796i	$0.529199\pi$
$3$	−0.00133765	−	1.73205i	−0.000772294	−	1.00000i
$3$	−0.00133765	−	1.73205i	−0.000772294	−	1.00000i
$4$	−0.917091	−	0.917091i	−0.458546	−	0.458546i
$5$	0.159652	+	0.802626i	0.0713987	+	0.358945i	0.999924	−	0.0123235i	$-0.00392281\pi$
$5$	0.159652	+	0.802626i	0.0713987	+	0.358945i	−0.928525	+	0.371269i	$0.878923\pi$
$6$	0.554726	−	1.34216i	0.226466	−	0.547934i
$7$	−0.191449	−	0.0380817i	−0.0723611	−	0.0143935i	0.158777	−	0.987314i	$-0.449245\pi$
$7$	−0.191449	−	0.0380817i	−0.0723611	−	0.0143935i	−0.231138	+	0.972921i	$0.574245\pi$
$8$	−1.05790	−	2.55399i	−0.374023	−	0.902970i
$9$	−3.00000	+	0.00463376i	−0.999999	+	0.00154459i
$10$	−0.133864	+	0.672980i	−0.0423316	+	0.212815i
$11$	−3.67179	+	2.45341i	−1.10709	+	0.739731i	−0.968100	−	0.250563i	$-0.919384\pi$
$11$	−3.67179	+	2.45341i	−1.10709	+	0.739731i	−0.138986	+	0.990294i	$0.544384\pi$
$12$	−1.58722	+	1.58968i	−0.458191	+	0.458900i
$13$	−3.75023	+	3.75023i	−1.04013	+	1.04013i	−0.0409655	+	0.999161i	$0.513043\pi$
$13$	−3.75023	+	3.75023i	−1.04013	+	1.04013i	−0.999161	+	0.0409655i	$0.986957\pi$
$14$	−0.136087	−	0.0909302i	−0.0363707	−	0.0243021i
$15$	1.38998	−	0.277599i	0.358890	−	0.0716759i
$16$			0.276039i			0.0690098i
$17$		0			0
$17$		0			0
$18$	−2.32543	−	0.959018i	−0.548109	−	0.226043i
$19$	0.210831	−	0.508991i	0.0483680	−	0.116771i	−0.897849	−	0.440304i	$-0.854871\pi$
$19$	0.210831	−	0.508991i	0.0483680	−	0.116771i	0.946217	+	0.323533i	$0.104871\pi$
$20$	0.589666	−	0.882497i	0.131853	−	0.197332i
$21$	−0.0657033	+	0.331651i	−0.0143376	+	0.0723722i
$22$	−3.63157	+	0.722364i	−0.774253	+	0.154009i
$23$	−2.29752	−	3.43849i	−0.479067	−	0.716974i	0.510686	−	0.859768i	$-0.329392\pi$
$23$	−2.29752	−	3.43849i	−0.479067	−	0.716974i	−0.989753	+	0.142793i	$0.954392\pi$
$24$	−4.42222	+	1.83574i	−0.902681	+	0.374720i
$25$	4.00068	−	1.65713i	0.800136	−	0.331427i
$26$	−4.10844	+	1.70177i	−0.805732	+	0.333745i
$27$	0.0120389	+	5.19614i	0.00231688	+	0.999997i
$28$	0.140652	+	0.210501i	0.0265808	+	0.0397810i
$29$	−0.606965	+	0.120733i	−0.112711	+	0.0224195i	−0.251123	−	0.967955i	$-0.580800\pi$
$29$	−0.606965	+	0.120733i	−0.112711	+	0.0224195i	0.138413	+	0.990375i	$0.455800\pi$
$30$	1.16581	+	0.230959i	0.212848	+	0.0421672i
$31$	−0.369997	+	0.553739i	−0.0664533	+	0.0994545i	−0.863208	−	0.504849i	$-0.831548\pi$
$31$	−0.369997	+	0.553739i	−0.0664533	+	0.0994545i	0.796755	+	0.604303i	$0.206548\pi$
$32$	−2.20436	+	5.32181i	−0.389680	+	0.940771i
$33$	4.25434	+	6.35644i	0.740586	+	1.10651i
$34$		0			0
$35$		−	0.159742i		−	0.0270014i
$36$	2.75552	+	2.74702i	0.459253	+	0.457837i
$37$	−1.63319	−	1.09126i	−0.268495	−	0.179402i	0.414034	−	0.910262i	$-0.364120\pi$
$37$	−1.63319	−	1.09126i	−0.268495	−	0.179402i	−0.682528	+	0.730859i	$0.739120\pi$
$38$	0.326640	−	0.326640i	0.0529880	−	0.0529880i
$39$	6.50060	+	6.49057i	1.04093	+	1.03932i
$40$	1.88100	−	1.25684i	0.297412	−	0.198725i
$41$	−1.55975	+	7.84141i	−0.243592	+	1.22462i	0.644373	+	0.764712i	$0.277119\pi$
$41$	−1.55975	+	7.84141i	−0.243592	+	1.22462i	−0.887965	+	0.459911i	$0.847881\pi$
$42$	−0.157314	+	0.235831i	−0.0242740	+	0.0363895i
$43$	−2.95422	−	7.13212i	−0.450514	−	1.08764i	−0.972127	−	0.234455i	$-0.924669\pi$
$43$	−2.95422	−	7.13212i	−0.450514	−	1.08764i	0.521613	−	0.853182i	$-0.325331\pi$
$44$	5.61737	+	1.11736i	0.846850	+	0.168449i
$45$	−0.482675	−	2.40714i	−0.0719530	−	0.358835i
$46$	−0.676466	−	3.40082i	−0.0997395	−	0.501424i
$47$	7.05884	+	7.05884i	1.02964	+	1.02964i	0.999547	+	0.0300900i	$0.00957939\pi$
$47$	7.05884	+	7.05884i	1.02964	+	1.02964i	0.0300900	+	0.999547i	$0.490421\pi$
$48$	0.478114		0.000369245i	0.0690098		5.32959e-5i
$49$	−6.43195	−	2.66420i	−0.918851	−	0.380600i
$50$	3.63084			0.513479
$51$		0			0
$52$	6.87860			0.953891
$53$	−10.7049	−	4.43410i	−1.47043	−	0.609071i	−0.503471	−	0.864012i	$-0.667944\pi$
$53$	−10.7049	−	4.43410i	−1.47043	−	0.609071i	−0.966957	+	0.254941i	$0.917944\pi$
$54$	−1.65796	+	4.02904i	−0.225619	+	0.548283i
$55$	−2.55538	−	2.55538i	−0.344568	−	0.344568i
$56$	0.105274	+	0.529246i	0.0140678	+	0.0707234i
$57$	−0.881880	−	0.364489i	−0.116808	−	0.0482778i
$58$	−0.508924	−	0.101231i	−0.0668249	−	0.0132923i
$59$	−0.0995233	−	0.240270i	−0.0129568	−	0.0312805i	0.917269	−	0.398269i	$-0.130389\pi$
$59$	−0.0995233	−	0.240270i	−0.0129568	−	0.0312805i	−0.930226	+	0.366988i	$0.880389\pi$
$60$	−1.52932	−	1.02015i	−0.197434	−	0.131701i
$61$	2.05830	−	10.3478i	0.263539	−	1.32490i	−0.591488	−	0.806314i	$-0.701459\pi$
$61$	2.05830	−	10.3478i	0.263539	−	1.32490i	0.855026	−	0.518584i	$-0.173541\pi$
$62$	−0.464295	+	0.310232i	−0.0589655	+	0.0393995i
$63$	0.574524	+	0.113358i	0.0723832	+	0.0142817i
$64$	−3.02483	+	3.02483i	−0.378104	+	0.378104i
$65$	−3.60876	−	2.41130i	−0.447612	−	0.299085i
$66$	1.25603	+	6.28910i	0.154606	+	0.774134i
$67$		−	5.40994i		−	0.660929i	−0.943818	−	0.330465i	$-0.892795\pi$
$67$		−	5.40994i		−	0.660929i	0.943818	−	0.330465i	$-0.107205\pi$
$68$		0			0
$69$	−5.95256	+	3.98403i	−0.716604	+	0.479621i
$70$	0.0512564	−	0.123744i	0.00612632	−	0.0147902i
$71$	−3.61943	+	5.41686i	−0.429548	+	0.642864i	−0.981601	−	0.190945i	$-0.938845\pi$
$71$	−3.61943	+	5.41686i	−0.429548	+	0.642864i	0.552053	+	0.833809i	$0.313845\pi$
$72$	3.18552	+	7.65705i	0.375417	+	0.902392i
$73$	−11.3822	+	2.26406i	−1.33218	+	0.264988i	−0.809290	−	0.587409i	$-0.800148\pi$
$73$	−11.3822	+	2.26406i	−1.33218	+	0.264988i	−0.522895	+	0.852397i	$0.675148\pi$
$74$	−0.914994	−	1.36939i	−0.106366	−	0.159188i
$75$	−2.87559	−	6.92716i	−0.332045	−	0.799879i
$76$	−0.660143	+	0.273440i	−0.0757236	+	0.0313657i
$77$	0.796392	−	0.329876i	0.0907573	−	0.0375929i
$78$	2.95305	+	7.11375i	0.334367	+	0.805474i
$79$	−6.00531	−	8.98758i	−0.675650	−	1.01118i	−0.997916	−	0.0645322i	$-0.979444\pi$
$79$	−6.00531	−	8.98758i	−0.675650	−	1.01118i	0.322266	−	0.946649i	$-0.395556\pi$
$80$	−0.221556	+	0.0440703i	−0.0247708	+	0.00492721i
$81$	8.99996	−	0.0278025i	0.999995	−	0.00308917i
$82$	−3.72433	+	5.57385i	−0.411283	+	0.615529i
$83$	1.05744	−	2.55289i	0.116069	−	0.280216i	−0.855159	−	0.518365i	$-0.826541\pi$
$83$	1.05744	−	2.55289i	0.116069	−	0.280216i	0.971229	+	0.238149i	$0.0765408\pi$
$84$	0.364410	−	0.243898i	0.0397604	−	0.0266115i
$85$		0			0
$86$		−	6.47280i		−	0.697980i
$87$	0.209927	+	1.05113i	0.0225066	+	0.112693i
$88$	10.1503	+	6.78225i	1.08203	+	0.722990i
$89$	−3.69661	+	3.69661i	−0.391839	+	0.391839i	−0.875343	−	0.483503i	$-0.839364\pi$
$89$	−3.69661	+	3.69661i	−0.391839	+	0.391839i	0.483503	+	0.875343i	$0.339364\pi$
$90$	0.398473	−	2.01956i	0.0420028	−	0.212880i
$91$	0.860794	−	0.575164i	0.0902357	−	0.0602936i
$92$	−1.04637	+	5.26045i	−0.109091	+	0.548440i
$93$	0.959599	+	0.640112i	0.0995057	+	0.0663765i
$94$	3.20315	+	7.73308i	0.330379	+	0.797606i
$95$	0.442189	+	0.0879569i	0.0453677	+	0.00902419i
$96$	9.22058	+	3.81095i	0.941072	+	0.388953i
$97$	−0.481692	−	2.42163i	−0.0489084	−	0.245879i	0.948595	−	0.316491i	$-0.102505\pi$
$97$	−0.481692	−	2.42163i	−0.0489084	−	0.245879i	−0.997504	+	0.0706120i	$0.977505\pi$
$98$	−4.12764	−	4.12764i	−0.416954	−	0.416954i
$99$	11.0040	−	7.37724i	1.10594	−	0.741441i
$100$	−5.18873	−	2.14924i	−0.518873	−	0.214924i
$101$	−6.79257			−0.675886			−0.337943	−	0.941167i	$-0.609731\pi$
$101$	−6.79257			−0.675886			−0.337943	+	0.941167i	$0.609731\pi$
$102$		0			0
$103$	2.47763			0.244128			0.122064	−	0.992522i	$-0.461049\pi$
$103$	2.47763			0.244128			0.122064	+	0.992522i	$0.461049\pi$
$104$	13.5454	+	5.61068i	1.32823	+	0.550172i
$105$	−0.276681		0.000213679i	−0.0270013		2.08530e-5i
$106$	−6.86974	−	6.86974i	−0.667248	−	0.667248i
$107$	−0.802606	−	4.03497i	−0.0775909	−	0.390076i	−0.999993	−	0.00384387i	$-0.998776\pi$
$107$	−0.802606	−	4.03497i	−0.0775909	−	0.390076i	0.922402	−	0.386232i	$-0.126224\pi$
$108$	4.75429	−	4.77637i	0.457482	−	0.459607i
$109$	12.4053	+	2.46757i	1.18821	+	0.236350i	0.749332	−	0.662195i	$-0.230375\pi$
$109$	12.4053	+	2.46757i	1.18821	+	0.236350i	0.438881	+	0.898545i	$0.355375\pi$
$110$	−1.15958	−	2.79947i	−0.110561	−	0.266919i
$111$	−1.88794	+	2.83023i	−0.179195	+	0.268633i
$112$	0.0105120	−	0.0528476i	0.000993294	−	0.00499363i
$113$	−1.02794	+	0.686845i	−0.0967001	+	0.0646130i	−0.602980	−	0.797756i	$-0.706020\pi$
$113$	−1.02794	+	0.686845i	−0.0967001	+	0.0646130i	0.506280	+	0.862369i	$0.331020\pi$
$114$	−0.566193	−	0.565320i	−0.0530289	−	0.0529470i
$115$	2.39302	−	2.39302i	0.223150	−	0.223150i
$116$	0.667365	+	0.445919i	0.0619633	+	0.0414026i
$117$	11.2333	−	11.2680i	1.03852	−	1.04173i
$118$		−	0.218059i		−	0.0200740i
$119$		0			0
$120$	−2.17943	−	3.25631i	−0.198954	−	0.297259i
$121$	3.25330	−	7.85415i	0.295754	−	0.714014i
$122$	4.91475	−	7.35545i	0.444961	−	0.665931i
$123$	13.5838	+	2.69108i	1.22481	+	0.242647i
$124$	0.847150	−	0.168509i	0.0760763	−	0.0151325i
$125$	4.24203	+	6.34865i	0.379419	+	0.567841i
$126$	0.408681	+	0.272160i	0.0364082	+	0.0242459i
$127$	−8.17992	+	3.38823i	−0.725850	+	0.300657i	−0.714845	−	0.699282i	$-0.753503\pi$
$127$	−8.17992	+	3.38823i	−0.725850	+	0.300657i	−0.0110047	+	0.999939i	$0.503503\pi$
$128$	7.32985	−	3.03612i	0.647873	−	0.268358i
$129$	−12.3492	+	5.12640i	−1.08729	+	0.451354i
$130$	−2.02181	−	3.02585i	−0.177324	−	0.265385i
$131$	9.64343	−	1.91820i	0.842551	−	0.167594i	0.245098	−	0.969498i	$-0.421180\pi$
$131$	9.64343	−	1.91820i	0.842551	−	0.167594i	0.597452	+	0.801904i	$0.296180\pi$
$132$	1.92782	−	9.73106i	0.167795	−	0.846980i
$133$	−0.0597467	+	0.0894173i	−0.00518070	+	0.00775346i
$134$	1.73589	−	4.19080i	0.149958	−	0.362030i
$135$	−4.16863	+	0.839238i	−0.358779	+	0.0722301i
$136$		0			0
$137$			12.6644i			1.08200i	0.841024	+	0.540998i	$0.181953\pi$
$137$			12.6644i			1.08200i	−0.841024	+	0.540998i	$0.818047\pi$
$138$	−5.88949	+	1.17622i	−0.501347	+	0.100127i
$139$	−9.89935	−	6.61453i	−0.839652	−	0.561038i	0.0597233	−	0.998215i	$-0.480978\pi$
$139$	−9.89935	−	6.61453i	−0.839652	−	0.561038i	−0.899375	+	0.437177i	$0.855978\pi$
$140$	−0.146498	+	0.146498i	−0.0123814	+	0.0123814i
$141$	12.2168	−	12.2357i	1.02884	−	1.03043i
$142$	−4.54189	+	3.03480i	−0.381147	+	0.254675i
$143$	4.56920	−	22.9709i	0.382095	−	1.92092i
$144$	−0.00127910	−	0.828117i	−0.000106592	−	0.0690097i
$145$	−0.193807	−	0.467891i	−0.0160948	−	0.0388562i
$146$	−9.54366	−	1.89835i	−0.789839	−	0.157109i
$147$	−4.60593	+	11.1440i	−0.379891	+	0.919144i
$148$	0.496997	+	2.49857i	0.0408529	+	0.205381i
$149$	−8.98104	−	8.98104i	−0.735756	−	0.735756i	0.235998	−	0.971754i	$-0.424164\pi$
$149$	−8.98104	−	8.98104i	−0.735756	−	0.735756i	−0.971754	+	0.235998i	$0.924164\pi$
$150$	−0.00485680	−	6.28880i	−0.000396556	−	0.513478i
$151$	0.732249	+	0.303307i	0.0595895	+	0.0246828i	0.412279	−	0.911058i	$-0.364733\pi$
$151$	0.732249	+	0.303307i	0.0595895	+	0.0246828i	−0.352690	+	0.935740i	$0.614733\pi$
$152$	−1.52299			−0.123531
$153$		0			0
$154$	0.722771			0.0582426
$155$	−0.503516	−	0.208563i	−0.0404434	−	0.0167522i
$156$	−0.00920118	−	11.9141i	−0.000736684	−	0.953890i
$157$	−1.66767	−	1.66767i	−0.133095	−	0.133095i	0.637421	−	0.770516i	$-0.280001\pi$
$157$	−1.66767	−	1.66767i	−0.133095	−	0.133095i	−0.770516	+	0.637421i	$0.780001\pi$
$158$	−1.76816	−	8.88913i	−0.140667	−	0.707181i
$159$	−7.66577	+	18.5473i	−0.607935	+	1.47090i
$160$	−4.62335	−	0.919642i	−0.365508	−	0.0727041i
$161$	0.308916	+	0.745790i	0.0243460	+	0.0587765i
$162$	6.98072	+	2.86628i	0.548457	+	0.225196i
$163$	3.14715	−	15.8218i	0.246504	−	1.23926i	−0.637012	−	0.770854i	$-0.719830\pi$
$163$	3.14715	−	15.8218i	0.246504	−	1.23926i	0.883515	−	0.468403i	$-0.155170\pi$
$164$	8.62172	−	5.76085i	0.673243	−	0.449847i
$165$	−4.42263	+	4.42947i	−0.344301	+	0.344834i
$166$	1.63829	−	1.63829i	0.127156	−	0.127156i
$167$	7.62247	+	5.09317i	0.589844	+	0.394121i	0.814369	−	0.580347i	$-0.197083\pi$
$167$	7.62247	+	5.09317i	0.589844	+	0.394121i	−0.224525	+	0.974468i	$0.572083\pi$
$168$	0.916539	−	0.183047i	0.0707125	−	0.0141224i
$169$		−	15.1284i		−	1.16372i
$170$		0			0
$171$	−0.630134	+	1.52795i	−0.0481875	+	0.116845i
$172$	−3.83151	+	9.25009i	−0.292150	+	0.705313i
$173$	0.647630	−	0.969247i	0.0492384	−	0.0736905i	−0.806034	−	0.591870i	$-0.798390\pi$
$173$	0.647630	−	0.969247i	0.0492384	−	0.0736905i	0.855272	+	0.518179i	$0.173390\pi$
$174$	−0.174657	+	0.881617i	−0.0132407	+	0.0668352i
$175$	−0.829034	+	0.164905i	−0.0626691	+	0.0124657i
$176$	−0.677238	−	1.01356i	−0.0510487	−	0.0763998i
$177$	−0.416027	+	0.172701i	−0.0312705	+	0.0129810i
$178$	−4.04970	+	1.67744i	−0.303538	+	0.125729i
$179$	9.50468	−	3.93697i	0.710413	−	0.294263i	0.00193768	−	0.999998i	$-0.499383\pi$
$179$	9.50468	−	3.93697i	0.710413	−	0.294263i	0.708476	+	0.705735i	$0.249383\pi$
$180$	−1.76491	+	2.65022i	−0.131548	+	0.197536i
$181$	7.15635	+	10.7102i	0.531928	+	0.796086i	0.995966	−	0.0897290i	$-0.0286001\pi$
$181$	7.15635	+	10.7102i	0.531928	+	0.796086i	−0.464039	+	0.885815i	$0.653600\pi$
$182$	0.851365	−	0.169347i	0.0631074	−	0.0125528i
$183$	−17.9256	−	3.55124i	−1.32510	−	0.262515i
$184$	−6.35131	+	9.50541i	−0.468225	+	0.700748i
$185$	0.615133	−	1.48506i	0.0452255	−	0.109184i
$186$	0.537959	+	0.803768i	0.0394450	+	0.0589351i
$187$		0			0
$188$		−	12.9472i		−	0.944271i
$189$	0.195573	−	0.995256i	0.0142258	−	0.0723942i
$190$	0.314318	+	0.210021i	0.0228031	+	0.0152365i
$191$	11.7655	−	11.7655i	0.851319	−	0.851319i	−0.138977	−	0.990296i	$-0.544381\pi$
$191$	11.7655	−	11.7655i	0.851319	−	0.851319i	0.990296	+	0.138977i	$0.0443814\pi$
$192$	5.24321	+	5.23512i	0.378396	+	0.377812i
$193$	2.47380	−	1.65294i	0.178068	−	0.118981i	−0.463342	−	0.886180i	$-0.653350\pi$
$193$	2.47380	−	1.65294i	0.178068	−	0.118981i	0.641410	+	0.767198i	$0.278350\pi$
$194$	0.403886	−	2.03047i	0.0289973	−	0.145779i
$195$	−4.17166	+	6.25379i	−0.298739	+	0.447843i
$196$	3.45537	+	8.34201i	0.246812	+	0.595858i
$197$	−13.3085	−	2.64722i	−0.948190	−	0.188607i	−0.303311	−	0.952892i	$-0.598092\pi$
$197$	−13.3085	−	2.64722i	−0.948190	−	0.188607i	−0.644879	+	0.764285i	$0.723092\pi$
$198$	10.8914	−	2.18392i	0.774015	−	0.155204i
$199$	0.839234	+	4.21912i	0.0594917	+	0.299085i	0.999064	−	0.0432667i	$-0.0137765\pi$
$199$	0.839234	+	4.21912i	0.0594917	+	0.299085i	−0.939572	+	0.342352i	$0.888777\pi$
$200$	−8.46460	−	8.46460i	−0.598538	−	0.598538i
$201$	−9.37029	+	0.00723662i	−0.660929	+	0.000510432i
$202$	−5.26185	−	2.17953i	−0.370223	−	0.153351i
$203$	0.120801			0.00847855
$204$		0			0
$205$	−6.54274			−0.456965
$206$	1.91929	+	0.794996i	0.133723	+	0.0553900i
$207$	6.90850	+	10.3048i	0.480174	+	0.716234i
$208$	−1.03521	−	1.03521i	−0.0717789	−	0.0717789i
$209$	0.474638	+	2.38616i	0.0328314	+	0.165054i
$210$	−0.214399	−	0.0886132i	−0.0147950	−	0.00611489i
$211$	15.2290	+	3.02923i	1.04840	+	0.208541i	0.689090	−	0.724676i	$-0.258011\pi$
$211$	15.2290	+	3.02923i	1.04840	+	0.208541i	0.359314	+	0.933217i	$0.383011\pi$
$212$	5.75087	+	13.8838i	0.394971	+	0.953545i
$213$	9.38712	+	6.26179i	0.643195	+	0.429051i
$214$	0.672964	−	3.38322i	0.0460029	−	0.231272i
$215$	5.25278	−	3.50979i	0.358236	−	0.239366i
$216$	13.2581	−	5.52772i	0.902101	−	0.376114i
$217$	0.0919229	−	0.0919229i	0.00624014	−	0.00624014i
$218$	8.81798	+	5.89198i	0.597229	+	0.399056i
$219$	3.93669	+	19.7115i	0.266017	+	1.33198i
$220$			4.68704i			0.316000i
$221$		0			0
$222$	−2.37062	+	1.58665i	−0.159106	+	0.106489i
$223$	6.37645	−	15.3941i	0.426999	−	1.03087i	−0.553235	−	0.833025i	$-0.686607\pi$
$223$	6.37645	−	15.3941i	0.426999	−	1.03087i	0.980234	−	0.197841i	$-0.0633931\pi$
$224$	0.624687	−	0.934911i	0.0417387	−	0.0624664i
$225$	−11.9943	+	4.98994i	−0.799623	+	0.332662i
$226$	−1.01668	+	0.202230i	−0.0676283	+	0.0134521i
$227$	10.6940	+	16.0046i	0.709783	+	1.06227i	0.994610	+	0.103687i	$0.0330640\pi$
$227$	10.6940	+	16.0046i	0.709783	+	1.06227i	−0.284827	+	0.958579i	$0.591936\pi$
$228$	0.474495	+	1.14303i	0.0314242	+	0.0756993i
$229$	10.1448	−	4.20213i	0.670391	−	0.277685i	−0.0214129	−	0.999771i	$-0.506816\pi$
$229$	10.1448	−	4.20213i	0.670391	−	0.277685i	0.691803	+	0.722086i	$0.256816\pi$
$230$	2.62159	−	1.08590i	0.172863	−	0.0716020i
$231$	−0.572428	−	1.37895i	−0.0376630	−	0.0907283i
$232$	0.950455	+	1.42246i	0.0624004	+	0.0933889i
$233$	−23.0354	+	4.58203i	−1.50910	+	0.300179i	−0.879183	−	0.476484i	$-0.841911\pi$
$233$	−23.0354	+	4.58203i	−1.50910	+	0.300179i	−0.629917	+	0.776662i	$0.716911\pi$
$234$	12.3174	−	5.12435i	0.805215	−	0.334989i
$235$	−4.53865	+	6.79257i	−0.296069	+	0.443098i
$236$	−0.129078	+	0.311622i	−0.00840226	+	0.0202849i
$237$	−15.5589	+	10.4135i	−1.01066	+	0.676431i
$238$		0			0
$239$			13.7217i			0.887582i	0.896130	+	0.443791i	$0.146367\pi$
$239$			13.7217i			0.887582i	−0.896130	+	0.443791i	$0.853633\pi$
$240$	0.0766283	+	0.383688i	0.00494634	+	0.0247669i
$241$	−3.55549	−	2.37570i	−0.229029	−	0.153032i	0.435761	−	0.900062i	$-0.356479\pi$
$241$	−3.55549	−	2.37570i	−0.229029	−	0.153032i	−0.664790	+	0.747030i	$0.731479\pi$
$242$	5.04032	−	5.04032i	0.324004	−	0.324004i
$243$	−0.0601942	−	15.5883i	−0.00386146	−	0.999993i
$244$	−11.3775	+	7.60221i	−0.728371	+	0.486682i
$245$	1.11148	−	5.58780i	0.0710100	−	0.356992i
$246$	9.65918	+	6.44327i	0.615847	+	0.410808i
$247$	1.11817	+	2.69950i	0.0711474	+	0.171765i
$248$	1.80566	+	0.359168i	0.114659	+	0.0228072i
$249$	−4.42314	−	1.82813i	−0.280305	−	0.115853i
$250$	1.24899	+	6.27911i	0.0789932	+	0.397126i
$251$	6.57161	+	6.57161i	0.414796	+	0.414796i	0.883406	−	0.468609i	$-0.155245\pi$
$251$	6.57161	+	6.57161i	0.414796	+	0.414796i	−0.468609	+	0.883406i	$0.655245\pi$
$252$	−0.422932	−	0.630851i	−0.0266422	−	0.0397398i
$253$	16.8721	+	6.98863i	1.06074	+	0.439372i
$254$	−7.42374			−0.465807
$255$		0			0
$256$	15.2078			0.950486
$257$	−14.5315	−	6.01912i	−0.906447	−	0.375463i	−0.119752	−	0.992804i	$-0.538210\pi$
$257$	−14.5315	−	6.01912i	−0.906447	−	0.375463i	−0.786696	+	0.617341i	$0.788210\pi$
$258$	−11.2112	+	0.00865836i	−0.697980	+	0.000539046i
$259$	0.271116	+	0.271116i	0.0168463	+	0.0168463i
$260$	1.09818	+	5.52095i	0.0681065	+	0.342395i
$261$	1.82033	−	0.365010i	0.112676	−	0.0225936i
$262$	8.08576	+	1.60836i	0.499540	+	0.0993647i
$263$	5.90932	+	14.2664i	0.364384	+	0.879701i	0.994648	+	0.103320i	$0.0329466\pi$
$263$	5.90932	+	14.2664i	0.364384	+	0.879701i	−0.630264	+	0.776381i	$0.717053\pi$
$264$	11.7336	−	17.5900i	0.722154	−	1.08259i
$265$	1.84987	−	9.29993i	0.113637	−	0.571290i
$266$	−0.0749740	+	0.0500960i	−0.00459695	+	0.00307158i
$267$	6.40765	+	6.39776i	0.392142	+	0.391537i
$268$	−4.96141	+	4.96141i	−0.303066	+	0.303066i
$269$	−20.2365	−	13.5216i	−1.23384	−	0.824426i	−0.244444	−	0.969663i	$-0.578605\pi$
$269$	−20.2365	−	13.5216i	−1.23384	−	0.824426i	−0.989397	+	0.145237i	$0.953605\pi$
$270$	−3.49851	−	0.687475i	−0.212913	−	0.0418384i
$271$			5.62528i			0.341711i	0.985296	+	0.170856i	$0.0546532\pi$
$271$			5.62528i			0.341711i	−0.985296	+	0.170856i	$0.945347\pi$
$272$		0			0
$273$	−0.997365	−	1.49017i	−0.0603633	−	0.0901891i
$274$	−4.06363	+	9.81047i	−0.245493	+	0.592672i
$275$	−10.6240	+	15.9000i	−0.640652	+	0.958804i
$276$	9.11276	+	1.80533i	0.548524	+	0.108668i
$277$	8.69401	−	1.72935i	0.522373	−	0.103906i	0.0731408	−	0.997322i	$-0.476698\pi$
$277$	8.69401	−	1.72935i	0.522373	−	0.103906i	0.449232	+	0.893415i	$0.351698\pi$
$278$	−5.54611	−	8.30034i	−0.332633	−	0.497821i
$279$	1.10742	−	1.66293i	0.0662996	−	0.0995570i
$280$	−0.407979	+	0.168991i	−0.0243814	+	0.0100991i
$281$	−6.66883	+	2.76232i	−0.397829	+	0.164786i	−0.572623	−	0.819819i	$-0.694074\pi$
$281$	−6.66883	+	2.76232i	−0.397829	+	0.164786i	0.174794	+	0.984605i	$0.444074\pi$
$282$	13.3898	−	5.55836i	0.797351	−	0.330995i
$283$	−2.74547	−	4.10889i	−0.163201	−	0.244248i	0.740851	−	0.671669i	$-0.234422\pi$
$283$	−2.74547	−	4.10889i	−0.163201	−	0.244248i	−0.904053	+	0.427421i	$0.859422\pi$
$284$	8.28711	−	1.64841i	0.491750	−	0.0978151i
$285$	0.151754	−	0.766012i	0.00898915	−	0.0453746i
$286$	10.9102	−	16.3282i	0.645133	−	0.965509i
$287$	0.597228	−	1.44184i	0.0352532	−	0.0851088i
$288$	6.58842	−	15.9756i	0.388227	−	0.941372i
$289$		0			0
$290$		−	0.424637i		−	0.0249356i
$291$	−4.19374	+	0.837554i	−0.245841	+	0.0490983i
$292$	12.5149	+	8.36216i	0.732377	+	0.489359i
$293$	−13.5083	+	13.5083i	−0.789165	+	0.789165i	−0.981357	−	0.192192i	$-0.938440\pi$
$293$	−13.5083	+	13.5083i	−0.789165	+	0.789165i	0.192192	+	0.981357i	$0.438440\pi$
$294$	−7.14376	+	7.15480i	−0.416632	+	0.417276i
$295$	0.176958	−	0.118240i	0.0103029	−	0.00688418i
$296$	−1.05932	+	5.32559i	−0.0615720	+	0.309543i
$297$	−12.7925	−	19.0496i	−0.742294	−	1.10537i
$298$	−4.07540	−	9.83889i	−0.236082	−	0.569952i
$299$	21.5114	+	4.27887i	1.24403	+	0.247454i
$300$	−3.71566	+	8.99002i	−0.214523	+	0.519039i
$301$	0.293981	+	1.47794i	0.0169448	+	0.0851872i
$302$	0.469913	+	0.469913i	0.0270404	+	0.0270404i
$303$	0.00908610	+	11.7651i	0.000521983	+	0.675886i
$304$	0.140502	+	0.0581977i	0.00805832	+	0.00333786i
$305$	8.63402			0.494382
$306$		0			0
$307$	−4.98811			−0.284687			−0.142343	−	0.989817i	$-0.545464\pi$
$307$	−4.98811			−0.284687			−0.142343	+	0.989817i	$0.545464\pi$
$308$	−1.03289	−	0.427838i	−0.0588544	−	0.0243783i
$309$	−0.00331421	−	4.29138i	−0.000188539	−	0.244128i
$310$	−0.323126	−	0.323126i	−0.0183523	−	0.0183523i
$311$	2.04185	+	10.2651i	0.115783	+	0.582080i	0.994500	+	0.104737i	$0.0334000\pi$
$311$	2.04185	+	10.2651i	0.115783	+	0.582080i	−0.878717	+	0.477343i	$0.841600\pi$
$312$	9.69986	−	23.4688i	0.549146	−	1.32866i
$313$	−23.5532	−	4.68503i	−1.33131	−	0.264814i	−0.522375	−	0.852716i	$-0.674954\pi$
$313$	−23.5532	−	4.68503i	−1.33131	−	0.264814i	−0.808932	+	0.587902i	$0.799954\pi$
$314$	−0.756754	−	1.82697i	−0.0427061	−	0.103102i
$315$	0.000740207		0.479226i	4.17060e−5		0.0270013i
$316$	−2.73501	+	13.7498i	−0.153857	+	0.773489i
$317$	8.17832	−	5.46458i	0.459340	−	0.306921i	−0.304285	−	0.952581i	$-0.598418\pi$
$317$	8.17832	−	5.46458i	0.459340	−	0.306921i	0.763625	+	0.645660i	$0.223418\pi$
$318$	−11.8895	+	11.9079i	−0.666733	+	0.667763i
$319$	1.93244	−	1.93244i	0.108196	−	0.108196i
$320$	−2.91073	−	1.94489i	−0.162715	−	0.108723i
$321$	−6.98771	+	1.39555i	−0.390016	+	0.0778921i
$322$			0.676847i			0.0377192i
$323$		0			0
$324$	−8.27928	−	8.22829i	−0.459960	−	0.457127i
$325$	−8.78882	+	21.2181i	−0.487516	+	1.17697i
$326$	7.51466	−	11.2465i	0.416198	−	0.622885i
$327$	4.25736	−	21.4899i	0.235432	−	1.18839i
$328$	21.6769	−	4.31180i	1.19691	−	0.238080i
$329$	−1.08260	−	1.62022i	−0.0596856	−	0.0893258i
$330$	−4.84727	+	2.01219i	−0.266833	+	0.110767i
$331$	−3.87936	+	1.60689i	−0.213229	+	0.0883224i	−0.486741	−	0.873546i	$-0.661815\pi$
$331$	−3.87936	+	1.60689i	−0.213229	+	0.0883224i	0.273512	+	0.961869i	$0.411815\pi$
$332$	−3.31100	+	1.37146i	−0.181715	+	0.0752687i
$333$	4.90462	+	3.26622i	0.268772	+	0.178988i
$334$	4.27048	+	6.39123i	0.233671	+	0.349713i
$335$	4.34216	−	0.863709i	0.237238	−	0.0471895i
$336$	−0.0915487	−	0.0181367i	−0.00499439	−	0.000989437i
$337$	3.21434	−	4.81060i	0.175096	−	0.262050i	−0.733533	−	0.679654i	$-0.762130\pi$
$337$	3.21434	−	4.81060i	0.175096	−	0.262050i	0.908629	+	0.417604i	$0.137130\pi$
$338$	4.85425	−	11.7192i	0.264036	−	0.637440i
$339$	1.19103	+	1.77952i	0.0646876	+	0.0966502i
$340$		0			0
$341$		−	2.94097i		−	0.159262i
$342$	−0.978404	+	0.981432i	−0.0529061	+	0.0530697i
$343$	2.26606	+	1.51413i	0.122356	+	0.0817554i
$344$	−15.0901	+	15.0901i	−0.813602	+	0.813602i
$345$	−4.14802	−	4.14162i	−0.223322	−	0.222977i
$346$	0.812687	−	0.543020i	0.0436903	−	0.0291930i
$347$	−0.00369437	+	0.0185728i	−0.000198324	+	0.000997042i	−0.980884	−	0.194592i	$-0.937662\pi$
$347$	−0.00369437	+	0.0185728i	−0.000198324	+	0.000997042i	0.980686	+	0.195589i	$0.0626618\pi$
$348$	0.771462	−	1.15651i	0.0413547	−	0.0619953i
$349$	2.37825	+	5.74159i	0.127305	+	0.307340i	0.974662	−	0.223682i	$-0.0718078\pi$
$349$	2.37825	+	5.74159i	0.127305	+	0.307340i	−0.847358	+	0.531023i	$0.821808\pi$
$350$	−0.695123	−	0.138268i	−0.0371559	−	0.00739076i
$351$	−19.5319	−	19.4416i	−1.04253	−	1.03771i
$352$	−4.96262	−	24.9488i	−0.264508	−	1.32977i
$353$	8.61113	+	8.61113i	0.458324	+	0.458324i	0.898105	−	0.439781i	$-0.144944\pi$
$353$	8.61113	+	8.61113i	0.458324	+	0.458324i	−0.439781	+	0.898105i	$0.644944\pi$
$354$	−0.377689		0.000291687i	−0.0200740		1.55030e-5i
$355$	−4.92557	−	2.04024i	−0.261422	−	0.108285i
$356$	6.78025			0.359352
$357$		0			0
$358$	8.62604			0.455900
$359$	29.4053	+	12.1801i	1.55195	+	0.642840i	0.983668	−	0.179992i	$-0.0576073\pi$
$359$	29.4053	+	12.1801i	1.55195	+	0.642840i	0.568284	+	0.822832i	$0.307607\pi$
$360$	−5.63717	+	3.77924i	−0.297105	+	0.199184i
$361$	13.2204	+	13.2204i	0.695811	+	0.695811i
$362$	2.10706	+	10.5929i	0.110745	+	0.556752i
$363$	−13.6081	−	5.62437i	−0.714242	−	0.295203i
$364$	−1.31690	−	0.261949i	−0.0690246	−	0.0137298i
$365$	−3.63439	−	8.77418i	−0.190232	−	0.459262i
$366$	−12.7466	−	8.50276i	−0.666274	−	0.444446i
$367$	−6.56004	+	32.9795i	−0.342431	+	1.72152i	0.298928	+	0.954276i	$0.403371\pi$
$367$	−6.56004	+	32.9795i	−0.342431	+	1.72152i	−0.641359	+	0.767241i	$0.721629\pi$
$368$	0.949158	−	0.634207i	0.0494783	−	0.0330603i
$369$	4.64292	−	23.5314i	0.241701	−	1.22500i
$370$	0.953024	−	0.953024i	0.0495453	−	0.0495453i
$371$	1.88058	+	1.25657i	0.0976351	+	0.0652377i
$372$	−0.292999	−	1.46708i	−0.0151913	−	0.0760646i
$373$		−	15.2764i		−	0.790981i	−0.918470	−	0.395490i	$-0.870575\pi$
$373$		−	15.2764i		−	0.790981i	0.918470	−	0.395490i	$-0.129425\pi$
$374$		0			0
$375$	10.9905	−	7.35591i	0.567547	−	0.379857i
$376$	10.5607	−	25.4957i	0.544624	−	1.31484i
$377$	1.82348	−	2.72903i	0.0939140	−	0.140552i
$378$	0.470848	−	0.708220i	0.0242178	−	0.0364269i
$379$	−37.2855	+	7.41655i	−1.91523	+	0.380963i	−0.999770	−	0.0214486i	$-0.993172\pi$
$379$	−37.2855	+	7.41655i	−1.91523	+	0.380963i	−0.915459	+	0.402411i	$0.868172\pi$
$380$	−0.324864	−	0.486193i	−0.0166651	−	0.0249412i
$381$	5.87953	+	14.1635i	0.301217	+	0.725618i
$382$	12.8893	−	5.33891i	0.659472	−	0.273162i
$383$	−31.8268	+	13.1831i	−1.62627	+	0.673624i	−0.994807	−	0.101781i	$-0.967546\pi$
$383$	−31.8268	+	13.1831i	−1.62627	+	0.673624i	−0.631465	+	0.775404i	$0.717546\pi$
$384$	−5.26852	−	12.6916i	−0.268858	−	0.647666i
$385$	0.391913	+	0.586540i	0.0199738	+	0.0298928i
$386$	2.44670	−	0.486680i	0.124534	−	0.0247714i
$387$	8.89570	+	21.3826i	0.452194	+	1.08694i
$388$	−1.77910	+	2.66261i	−0.0903201	+	0.135174i
$389$	−0.288821	+	0.697275i	−0.0146438	+	0.0353532i	−0.931032	−	0.364937i	$-0.881091\pi$
$389$	−0.288821	+	0.697275i	−0.0146438	+	0.0353532i	0.916389	+	0.400290i	$0.131091\pi$
$390$	−5.23822	+	3.50592i	−0.265248	+	0.177529i
$391$		0			0
$392$			19.2456i			0.972048i
$393$	−3.33532	−	16.7003i	−0.168244	−	0.842421i
$394$	−9.45998	−	6.32096i	−0.476587	−	0.318445i
$395$	6.25490	−	6.25490i	0.314718	−	0.314718i
$396$	−16.8573	−	3.32606i	−0.847110	−	0.167141i
$397$	16.7515	−	11.1930i	0.840734	−	0.561761i	−0.0589706	−	0.998260i	$-0.518782\pi$
$397$	16.7515	−	11.1930i	0.840734	−	0.561761i	0.899705	+	0.436499i	$0.143782\pi$
$398$	−0.703675	+	3.53761i	−0.0352720	+	0.177325i
$399$	0.154955	+	0.103365i	0.00775746	+	0.00517471i
$400$	0.457434	+	1.10434i	0.0228717	+	0.0552172i
$401$	−15.4656	−	3.07630i	−0.772315	−	0.153623i	−0.206825	−	0.978378i	$-0.566313\pi$
$401$	−15.4656	−	3.07630i	−0.772315	−	0.153623i	−0.565490	+	0.824755i	$0.691313\pi$
$402$	−7.26100	−	3.00104i	−0.362146	−	0.149678i
$403$	−0.689076	−	3.46422i	−0.0343253	−	0.172565i
$404$	6.22941	+	6.22941i	0.309925	+	0.309925i
$405$	1.45918	+	7.21916i	0.0725072	+	0.358723i
$406$	0.0935781	+	0.0387613i	0.00464420	+	0.00192369i
$407$	8.67405			0.429957
$408$		0			0
$409$	−28.3555			−1.40209			−0.701045	−	0.713117i	$-0.747283\pi$
$409$	−28.3555			−1.40209			−0.701045	+	0.713117i	$0.747283\pi$
$410$	−5.06832	−	2.09937i	−0.250306	−	0.103680i
$411$	21.9354	−	0.0169406i	1.08199	−	0.000835618i
$412$	−2.27221	−	2.27221i	−0.111944	−	0.111944i
$413$	0.00990378	+	0.0497897i	0.000487333	+	0.00244999i
$414$	2.04515	+	10.1993i	0.100514	+	0.501270i
$415$	2.21784	+	0.441155i	0.108869	+	0.0216555i
$416$	−11.6911	−	28.2248i	−0.573204	−	1.38384i
$417$	−11.4435	+	17.1550i	−0.560389	+	0.840085i
$418$	−0.397971	+	2.00073i	−0.0194654	+	0.0978591i
$419$	−29.2939	+	19.5736i	−1.43110	+	0.956231i	−0.432595	+	0.901588i	$0.642402\pi$
$419$	−29.2939	+	19.5736i	−1.43110	+	0.956231i	−0.998506	+	0.0546430i	$0.982598\pi$
$420$	0.253938	+	0.253546i	0.0123909	+	0.0123718i
$421$	−0.00892902	+	0.00892902i	−0.000435174	+	0.000435174i	−0.707324	−	0.706889i	$-0.750098\pi$
$421$	−0.00892902	+	0.00892902i	−0.000435174	+	0.000435174i	0.706889	+	0.707324i	$0.250098\pi$
$422$	10.8251	+	7.23309i	0.526957	+	0.352102i
$423$	−21.2092	−	21.1438i	−1.03123	−	1.02805i
$424$			32.0309i			1.55556i
$425$		0			0
$426$	5.26250	+	7.86273i	0.254969	+	0.380951i
$427$	−0.788122	+	1.90269i	−0.0381399	+	0.0920779i
$428$	−2.96438	+	4.43650i	−0.143289	+	0.214447i
$429$	−39.7929	−	7.88335i	−1.92122	−	0.380612i
$430$	5.19524	−	1.03340i	0.250537	−	0.0498349i
$431$	−6.58741	−	9.85875i	−0.317304	−	0.474879i	0.638194	−	0.769875i	$-0.279682\pi$
$431$	−6.58741	−	9.85875i	−0.317304	−	0.474879i	−0.955499	+	0.294996i	$0.904682\pi$
$432$	−1.43434	+	0.00332320i	−0.0690096	+	0.000159887i
$433$	−0.501414	+	0.207692i	−0.0240964	+	0.00998106i	−0.394699	−	0.918810i	$-0.629151\pi$
$433$	−0.501414	+	0.207692i	−0.0240964	+	0.00998106i	0.370603	+	0.928791i	$0.379151\pi$
$434$	0.100703	−	0.0417126i	0.00483391	−	0.00200227i
$435$	−0.810151	+	0.336309i	−0.0388438	+	0.0161248i
$436$	−9.11381	−	13.6398i	−0.436472	−	0.653227i
$437$	−2.23455	+	0.444480i	−0.106893	+	0.0212623i
$438$	−3.27528	+	16.5326i	−0.156499	+	0.789960i
$439$	16.9177	−	25.3191i	0.807436	−	1.20841i	−0.167487	−	0.985874i	$-0.553565\pi$
$439$	16.9177	−	25.3191i	0.807436	−	1.20841i	0.974924	−	0.222540i	$-0.0714347\pi$
$440$	−3.82308	+	9.22974i	−0.182258	+	0.440010i
$441$	19.3082	+	7.96279i	0.919437	+	0.379181i
$442$		0			0
$443$		−	40.2451i		−	1.91210i	−0.293203	−	0.956050i	$-0.594721\pi$
$443$		−	40.2451i		−	1.91210i	0.293203	−	0.956050i	$-0.405279\pi$
$444$	4.32699	−	0.864166i	0.205350	−	0.0410115i
$445$	−3.55716	−	2.37682i	−0.168626	−	0.112672i
$446$	9.87902	−	9.87902i	0.467785	−	0.467785i
$447$	−15.5436	+	15.5676i	−0.735187	+	0.736324i
$448$	0.694294	−	0.463912i	0.0328023	−	0.0219178i
$449$	−7.10838	+	35.7362i	−0.335465	+	1.68650i	0.333139	+	0.942878i	$0.391892\pi$
$449$	−7.10838	+	35.7362i	−0.335465	+	1.68650i	−0.668604	+	0.743619i	$0.733108\pi$
$450$	−10.8925	+	0.0168245i	−0.513478	+	0.000793112i
$451$	−13.5111	−	32.6187i	−0.636214	−	1.53596i
$452$	1.57261	+	0.312812i	0.0739694	+	0.0147134i
$453$	0.524364	−	1.26870i	0.0246368	−	0.0596086i
$454$	3.14865	+	15.8293i	0.147774	+	0.742908i
$455$	0.599070	+	0.599070i	0.0280848	+	0.0280848i
$456$	0.00203724	+	2.63790i	9.54023e−5	+	0.123531i
$457$	−19.6921	−	8.15675i	−0.921160	−	0.381557i	−0.128842	−	0.991665i	$-0.541126\pi$
$457$	−19.6921	−	8.15675i	−0.921160	−	0.381557i	−0.792318	+	0.610108i	$0.791126\pi$
$458$	9.20703			0.430216
$459$		0			0
$460$	−4.38923			−0.204649
$461$	5.67952	+	2.35253i	0.264521	+	0.109568i	0.511002	−	0.859579i	$-0.329274\pi$
$461$	5.67952	+	2.35253i	0.264521	+	0.109568i	−0.246481	+	0.969148i	$0.579274\pi$
$462$	−0.000966816	−	1.25188i	−4.49804e−5	−	0.0582425i
$463$	25.6637	+	25.6637i	1.19270	+	1.19270i	0.976307	+	0.216388i	$0.0694277\pi$
$463$	25.6637	+	25.6637i	1.19270	+	1.19270i	0.216388	+	0.976307i	$0.430572\pi$
$464$	−0.0333270	−	0.167546i	−0.00154717	−	0.00777813i
$465$	−0.360569	+	0.872394i	−0.0167210	+	0.0404563i
$466$	−19.3146	−	3.84191i	−0.894730	−	0.177973i
$467$	−2.94293	−	7.10485i	−0.136182	−	0.328773i	0.841046	−	0.540964i	$-0.181940\pi$
$467$	−2.94293	−	7.10485i	−0.136182	−	0.328773i	−0.977228	+	0.212190i	$0.931940\pi$
$468$	−20.6358	+	0.0318738i	−0.953889	+	0.00147337i
$469$	−0.206020	+	1.03573i	−0.00951310	+	0.0478256i
$470$	−5.69538	+	3.80553i	−0.262708	+	0.175536i
$471$	−2.88626	+	2.89073i	−0.132992	+	0.133198i
$472$	−0.508362	+	0.508362i	−0.0233993	+	0.0233993i
$473$	28.3453	+	18.9397i	1.30332	+	0.870849i
$474$	−15.3941	+	3.07443i	−0.707072	+	0.141213i
$475$		−	2.38569i		−	0.109463i
$476$		0			0
$477$	32.1351	+	13.2527i	1.47137	+	0.606799i
$478$	−4.40287	+	10.6295i	−0.201383	+	0.486181i
$479$	1.27558	−	1.90904i	0.0582826	−	0.0872260i	−0.801184	−	0.598418i	$-0.795796\pi$
$479$	1.27558	−	1.90904i	0.0582826	−	0.0872260i	0.859466	+	0.511192i	$0.170796\pi$
$480$	−1.58668	+	8.00911i	−0.0724218	+	0.365564i
$481$	10.2173	−	2.03235i	0.465870	−	0.0926672i
$482$	−1.99196	−	2.98118i	−0.0907313	−	0.135789i
$483$	1.29133	−	0.536056i	0.0587577	−	0.0243914i
$484$	−10.1865	+	4.21940i	−0.463025	+	0.191791i
$485$	1.86676	−	0.773237i	0.0847652	−	0.0351109i
$486$	4.95520	−	12.0948i	0.224772	−	0.548631i
$487$	15.5987	+	23.3450i	0.706842	+	1.05786i	0.994960	+	0.100269i	$0.0319705\pi$
$487$	15.5987	+	23.3450i	0.706842	+	1.05786i	−0.288118	+	0.957595i	$0.593030\pi$
$488$	−28.6056	+	5.69000i	−1.29491	+	0.257574i
$489$	−27.4083	−	5.42985i	−1.23945	−	0.245546i
$490$	2.65396	−	3.97194i	0.119894	−	0.179434i
$491$	−5.17526	+	12.4942i	−0.233556	+	0.563854i	−0.996591	−	0.0825033i	$-0.973709\pi$
$491$	−5.17526	+	12.4942i	−0.233556	+	0.563854i	0.763035	+	0.646357i	$0.223709\pi$
$492$	−9.98962	−	14.9256i	−0.450367	−	0.672896i
$493$		0			0
$494$			2.44995i			0.110228i
$495$	7.67798	+	7.65430i	0.345099	+	0.344035i
$496$	−0.152854	−	0.102134i	−0.00686333	−	0.00458593i
$497$	0.899222	−	0.899222i	0.0403356	−	0.0403356i
$498$	−2.83979	−	2.83541i	−0.127254	−	0.127058i
$499$	12.6659	−	8.46309i	0.567004	−	0.378860i	−0.238776	−	0.971075i	$-0.576746\pi$
$499$	12.6659	−	8.46309i	0.567004	−	0.378860i	0.805780	+	0.592215i	$0.201746\pi$
$500$	1.93196	−	9.71263i	0.0863999	−	0.434362i
$501$	8.81143	−	13.2093i	0.393666	−	0.590148i
$502$	2.98205	+	7.19931i	0.133096	+	0.321321i
$503$	23.9263	+	4.75924i	1.06682	+	0.212204i	0.697126	−	0.716949i	$-0.254462\pi$
$503$	23.9263	+	4.75924i	1.06682	+	0.212204i	0.369696	+	0.929153i	$0.379462\pi$
$504$	−0.318273	−	1.58725i	−0.0141770	−	0.0707016i
$505$	−1.08445	−	5.45190i	−0.0482574	−	0.242606i
$506$	10.8275	+	10.8275i	0.481339	+	0.481339i
$507$	−26.2032	+	0.0202366i	−1.16372	+	0.000898737i
$508$	10.6090	+	4.39441i	0.470700	+	0.194971i
$509$	18.8631			0.836090			0.418045	−	0.908426i	$-0.362715\pi$
$509$	18.8631			0.836090			0.418045	+	0.908426i	$0.362715\pi$
$510$		0			0
$511$	2.26533			0.100212
$512$	−2.87903	−	1.19253i	−0.127236	−	0.0527030i
$513$	2.64733	+	1.08938i	0.116882	+	0.0480973i
$514$	−9.32541	−	9.32541i	−0.411326	−	0.411326i
$515$	0.395559	+	1.98861i	0.0174304	+	0.0876286i
$516$	16.0268	+	6.62400i	0.705538	+	0.291605i
$517$	−43.2368	−	8.60033i	−1.90155	−	0.378242i
$518$	0.123027	+	0.297013i	0.00540548	+	0.0130500i
$519$	−1.67965	−	1.12043i	−0.0737285	−	0.0491815i
$520$	−2.34073	+	11.7676i	−0.102648	+	0.516045i
$521$	27.4188	−	18.3207i	1.20124	−	0.802643i	0.216433	−	0.976298i	$-0.430558\pi$
$521$	27.4188	−	18.3207i	1.20124	−	0.802643i	0.984807	+	0.173655i	$0.0555578\pi$
$522$	1.52724	+	0.301335i	0.0668454	+	0.0131891i
$523$	9.24397	−	9.24397i	0.404211	−	0.404211i	−0.475503	−	0.879714i	$-0.657734\pi$
$523$	9.24397	−	9.24397i	0.404211	−	0.404211i	0.879714	+	0.475503i	$0.157734\pi$
$524$	−10.6031	−	7.08475i	−0.463197	−	0.309499i
$525$	0.286733	+	1.43571i	0.0125141	+	0.0626594i
$526$			12.9475i			0.564539i
$527$		0			0
$528$	−1.75463	+	1.17437i	−0.0763604	+	0.0511077i
$529$	2.25714	−	5.44921i	0.0981363	−	0.236922i
$530$	4.41706	−	6.61060i	0.191865	−	0.287146i
$531$	0.299683	+	0.720349i	0.0130051	+	0.0312605i
$532$	0.136797	−	0.0272106i	0.00593090	−	0.00117973i
$533$	−23.5576	−	35.2565i	−1.02039	−	1.52713i
$534$	2.91083	+	7.01203i	0.125964	+	0.303440i
$535$	3.11044	−	1.28839i	0.134476	−	0.0557018i
$536$	−13.8169	+	5.72315i	−0.596800	+	0.247202i
$537$	−6.83174	−	16.4573i	−0.294811	−	0.710186i
$538$	−11.3375	−	16.9678i	−0.488794	−	0.731532i
$539$	30.1532	−	5.99784i	1.29879	−	0.258345i
$540$	4.59268	+	3.05336i	0.197637	+	0.131396i
$541$	−9.26903	+	13.8721i	−0.398507	+	0.596408i	−0.975408	−	0.220406i	$-0.929262\pi$
$541$	−9.26903	+	13.8721i	−0.398507	+	0.596408i	0.576901	+	0.816814i	$0.304262\pi$
$542$	−1.80498	+	4.35761i	−0.0775306	+	0.187176i
$543$	18.5411	−	12.4095i	0.795675	−	0.532542i
$544$		0			0
$545$			10.3508i			0.443379i
$546$	−0.294456	−	1.47438i	−0.0126016	−	0.0630977i
$547$	−9.01564	−	6.02406i	−0.385481	−	0.257570i	0.347697	−	0.937607i	$-0.386964\pi$
$547$	−9.01564	−	6.02406i	−0.385481	−	0.257570i	−0.733178	+	0.680037i	$0.761964\pi$
$548$	11.6144	−	11.6144i	0.496144	−	0.496144i
$549$	−6.12695	+	31.0529i	−0.261492	+	1.32530i
$550$	−13.3317	+	8.90795i	−0.568465	+	0.379836i
$551$	−0.0665151	+	0.334394i	−0.00283364	+	0.0142457i
$552$	16.4723	+	10.9881i	0.701109	+	0.467683i
$553$	0.807451	+	1.94936i	0.0343363	+	0.0828952i
$554$	7.28969	+	1.45001i	0.309709	+	0.0616050i
$555$	−2.57303	−	1.06346i	−0.109219	−	0.0451412i
$556$	3.01248	+	15.1447i	0.127757	+	0.642280i
$557$	8.63556	+	8.63556i	0.365900	+	0.365900i	0.865980	−	0.500079i	$-0.166696\pi$
$557$	8.63556	+	8.63556i	0.365900	+	0.365900i	−0.500079	+	0.865980i	$0.666696\pi$
$558$	1.39145	−	0.932847i	0.0589046	−	0.0394905i
$559$	37.8261	+	15.6681i	1.59987	+	0.662689i
$560$	0.0440951			0.00186336
$561$		0			0
$562$	−6.05234			−0.255302
$563$	−21.7414	−	9.00559i	−0.916292	−	0.379541i	−0.125830	−	0.992052i	$-0.540159\pi$
$563$	−21.7414	−	9.00559i	−0.916292	−	0.379541i	−0.790462	+	0.612511i	$0.790159\pi$
$564$	−22.4252	+	0.0173188i	−0.944271	+	0.000729255i
$565$	−0.715392	−	0.715392i	−0.0300968	−	0.0300968i
$566$	−0.808357	−	4.06388i	−0.0339778	−	0.170818i
$567$	−1.72410	−	0.337411i	−0.0724052	−	0.0141699i
$568$	17.6636	+	3.51350i	0.741147	+	0.147423i
$569$	−0.717701	−	1.73268i	−0.0300876	−	0.0726379i	0.908122	−	0.418707i	$-0.137516\pi$
$569$	−0.717701	−	1.73268i	−0.0300876	−	0.0726379i	−0.938209	+	0.346069i	$0.887516\pi$
$570$	0.363346	−	0.544696i	0.0152189	−	0.0228148i
$571$	−7.81421	+	39.2847i	−0.327014	+	1.64401i	0.371512	+	0.928428i	$0.378839\pi$
$571$	−7.81421	+	39.2847i	−0.327014	+	1.64401i	−0.698526	+	0.715584i	$0.746161\pi$
$572$	−25.2568	+	16.8760i	−1.05604	+	0.705623i
$573$	−20.3941	−	20.3626i	−0.851976	−	0.850661i
$574$	0.925283	−	0.925283i	0.0386205	−	0.0386205i
$575$	−14.8897	−	9.94898i	−0.620943	−	0.414901i
$576$	9.06047	−	9.08851i	0.377520	−	0.378688i
$577$			31.8433i			1.32565i	0.748773	+	0.662826i	$0.230643\pi$
$577$			31.8433i			1.32565i	−0.748773	+	0.662826i	$0.769357\pi$
$578$		0			0
$579$	−2.86629	−	4.28254i	−0.119119	−	0.177976i
$580$	−0.251360	+	0.606837i	−0.0104372	+	0.0251975i
$581$	−0.299665	+	0.448480i	−0.0124322	+	0.0186061i
$582$	−3.51742	−	0.696834i	−0.145802	−	0.0288847i
$583$	50.1847	−	9.98236i	2.07844	−	0.413427i
$584$	17.8235	+	26.6748i	0.737544	+	1.10381i
$585$	10.8375	+	7.21717i	0.448073	+	0.298393i
$586$	−14.7986	+	6.12978i	−0.611325	+	0.253219i
$587$	11.6364	−	4.81996i	0.480286	−	0.198941i	−0.129387	−	0.991594i	$-0.541301\pi$
$587$	11.6364	−	4.81996i	0.480286	−	0.198941i	0.609673	+	0.792653i	$0.291301\pi$
$588$	14.4442	−	5.99604i	0.595667	−	0.247272i
$589$	0.203842	+	0.305070i	0.00839914	+	0.0125702i
$590$	0.175020	−	0.0348136i	0.00720546	−	0.00143325i
$591$	−4.56732	+	23.0545i	−0.187874	+	0.948336i
$592$	0.301231	−	0.450825i	0.0123805	−	0.0185288i
$593$	−7.05301	+	17.0275i	−0.289632	+	0.699234i	−0.999989	−	0.00460731i	$-0.998533\pi$
$593$	−7.05301	+	17.0275i	−0.289632	+	0.699234i	0.710357	+	0.703841i	$0.248533\pi$
$594$	−3.79722	−	18.8614i	−0.155802	−	0.773895i
$595$		0			0
$596$			16.4729i			0.674755i
$597$	7.30660	−	1.45924i	0.299039	−	0.0597227i
$598$	15.2908	+	10.2170i	0.625286	+	0.417803i
$599$	−12.3968	+	12.3968i	−0.506519	+	0.506519i	−0.913456	−	0.406937i	$-0.866597\pi$
$599$	−12.3968	+	12.3968i	−0.506519	+	0.506519i	0.406937	+	0.913456i	$0.366597\pi$
$600$	−14.6498	+	14.6724i	−0.598075	+	0.599000i
$601$	11.2873	−	7.54195i	0.460419	−	0.307642i	−0.303642	−	0.952786i	$-0.598203\pi$
$601$	11.2873	−	7.54195i	0.460419	−	0.307642i	0.764061	+	0.645144i	$0.223203\pi$
$602$	−0.246495	+	1.23921i	−0.0100464	+	0.0505066i
$603$	0.0250684	+	16.2298i	0.00102086	+	0.660929i
$604$	−0.393378	−	0.949699i	−0.0160063	−	0.0386427i
$605$	6.82334	+	1.35725i	0.277408	+	0.0551800i
$606$	−3.76802	+	9.11671i	−0.153065	+	0.370341i
$607$	0.807003	+	4.05708i	0.0327552	+	0.164672i	0.993701	−	0.112066i	$-0.0357468\pi$
$607$	0.807003	+	4.05708i	0.0327552	+	0.164672i	−0.960946	+	0.276737i	$0.910747\pi$
$608$	2.24400	+	2.24400i	0.0910064	+	0.0910064i
$609$	−0.000161589	−	0.209233i	−6.54793e−6	−	0.00847855i
$610$	6.68833	+	2.77040i	0.270802	+	0.112170i
$611$	−52.9445			−2.14190
$612$		0			0
$613$	−27.1330			−1.09589			−0.547947	−	0.836513i	$-0.684590\pi$
$613$	−27.1330			−1.09589			−0.547947	+	0.836513i	$0.684590\pi$
$614$	−3.86403	−	1.60053i	−0.155940	−	0.0645923i
$615$	0.00875191	+	11.3323i	0.000352911	+	0.456964i
$616$	−1.68500	−	1.68500i	−0.0678906	−	0.0678906i
$617$	−2.48894	−	12.5128i	−0.100201	−	0.503745i	−0.997993	−	0.0633250i	$-0.979830\pi$
$617$	−2.48894	−	12.5128i	−0.100201	−	0.503745i	0.897792	−	0.440420i	$-0.145170\pi$
$618$	1.37441	−	3.32537i	0.0552867	−	0.133766i
$619$	3.81263	+	0.758379i	0.153243	+	0.0304818i	0.271115	−	0.962547i	$-0.412608\pi$
$619$	3.81263	+	0.758379i	0.153243	+	0.0304818i	−0.117873	+	0.993029i	$0.537608\pi$
$620$	0.270499	+	0.653042i	0.0108635	+	0.0262268i
$621$	17.8392	−	11.9797i	0.715863	−	0.480727i
$622$	−1.71204	+	8.60700i	−0.0686465	+	0.345109i
$623$	0.848486	−	0.566940i	0.0339939	−	0.0227140i
$624$	−1.79165	+	1.79442i	−0.0717235	+	0.0718343i
$625$	10.8916	−	10.8916i	0.435663	−	0.435663i
$626$	−16.7422	−	11.1868i	−0.669152	−	0.447113i
$627$	4.13232	−	0.825288i	0.165029	−	0.0329588i
$628$			3.05882i			0.122060i
$629$		0			0
$630$	−0.153196	+	0.371469i	−0.00610346	+	0.0147997i
$631$	−13.4198	+	32.3983i	−0.534234	+	1.28976i	0.394461	+	0.918913i	$0.370931\pi$
$631$	−13.4198	+	32.3983i	−0.534234	+	1.28976i	−0.928696	+	0.370843i	$0.879069\pi$
$632$	−16.6012	+	24.8454i	−0.660359	+	0.988296i
$633$	5.22640	−	26.3814i	0.207731	−	1.04857i
$634$	8.08874	−	1.60895i	0.321245	−	0.0638996i
$635$	−4.02543	−	6.02448i	−0.159744	−	0.239074i
$636$	24.0398	−	9.97937i	0.953240	−	0.395708i
$637$	34.1127	−	14.1299i	1.35159	−	0.559848i
$638$	2.11702	−	0.876899i	0.0838137	−	0.0347168i
$639$	10.8332	−	16.2673i	0.428554	−	0.643526i
$640$	3.60710	+	5.39841i	0.142583	+	0.213391i
$641$	−2.19355	+	0.436325i	−0.0866402	+	0.0172338i	−0.238220	−	0.971211i	$-0.576564\pi$
$641$	−2.19355	+	0.436325i	−0.0866402	+	0.0172338i	0.151580	+	0.988445i	$0.451564\pi$
$642$	−5.86080	−	1.16108i	−0.231307	−	0.0458242i
$643$	−2.03342	+	3.04323i	−0.0801904	+	0.120013i	−0.869397	−	0.494115i	$-0.835492\pi$
$643$	−2.03342	+	3.04323i	−0.0801904	+	0.120013i	0.789206	+	0.614128i	$0.210492\pi$
$644$	0.400653	−	0.967262i	0.0157879	−	0.0381155i
$645$	−6.08617	−	9.09338i	−0.239643	−	0.358051i
$646$		0			0
$647$		−	28.3391i		−	1.11413i	−0.830470	−	0.557063i	$-0.811928\pi$
$647$		−	28.3391i		−	1.11413i	0.830470	−	0.557063i	$-0.188072\pi$
$648$	−9.59202	−	22.9564i	−0.376810	−	0.901811i
$649$	0.954911	+	0.638051i	0.0374835	+	0.0250457i
$650$	−13.6165	+	13.6165i	−0.534082	+	0.534082i
$651$	−0.159338	−	0.159092i	−0.00624495	−	0.00623532i
$652$	−17.3962	+	11.6238i	−0.681289	+	0.455223i
$653$	−1.98888	+	9.99878i	−0.0778309	+	0.391282i	0.922159	+	0.386811i	$0.126423\pi$
$653$	−1.98888	+	9.99878i	−0.0778309	+	0.391282i	−0.999990	+	0.00447157i	$0.998577\pi$
$654$	10.1934	−	15.2811i	0.398594	−	0.597537i
$655$	3.07919	+	7.43383i	0.120314	+	0.290464i
$656$	−2.16454	−	0.430553i	−0.0845109	−	0.0168103i
$657$	34.1360	−	6.84491i	1.33177	−	0.267045i
$658$	−0.318752	−	1.60248i	−0.0124263	−	0.0624710i
$659$	−27.6176	−	27.6176i	−1.07583	−	1.07583i	−0.996879	−	0.0789501i	$-0.974843\pi$
$659$	−27.6176	−	27.6176i	−1.07583	−	1.07583i	−0.0789501	−	0.996879i	$-0.525157\pi$
$660$	8.11819	−	0.00626963i	0.316000	−	0.000244045i
$661$	1.89254	+	0.783917i	0.0736114	+	0.0304909i	0.419185	−	0.907901i	$-0.362316\pi$
$661$	1.89254	+	0.783917i	0.0736114	+	0.0304909i	−0.345574	+	0.938392i	$0.612316\pi$
$662$	−3.52074			−0.136838
$663$		0			0
$664$	−7.63870			−0.296439
$665$	−0.0813074	−	0.0336786i	−0.00315296	−	0.00130600i
$666$	2.75132	+	4.10391i	0.106612	+	0.159023i
$667$	1.80965	+	1.80965i	0.0700701	+	0.0700701i
$668$	−2.31960	−	11.6614i	−0.0897479	−	0.451193i
$669$	−26.6719	−	11.0237i	−1.03120	−	0.426203i
$670$	3.64078	+	0.724197i	0.140656	+	0.0279782i
$671$	17.8297	+	43.0448i	0.688309	+	1.66172i
$672$	−1.62015	−	1.08074i	−0.0624986	−	0.0416904i
$673$	3.31745	−	16.6779i	0.127878	−	0.642887i	−0.862675	−	0.505759i	$-0.831213\pi$
$673$	3.31745	−	16.6779i	0.127878	−	0.642887i	0.990553	−	0.137129i	$-0.0437874\pi$
$674$	4.03356	−	2.69514i	0.155367	−	0.103813i
$675$	8.65887	+	20.7681i	0.333280	+	0.799366i
$676$	−13.8741	+	13.8741i	−0.533621	+	0.533621i
$677$	−18.2198	−	12.1741i	−0.700245	−	0.467889i	0.153791	−	0.988103i	$-0.450852\pi$
$677$	−18.2198	−	12.1741i	−0.700245	−	0.467889i	−0.854035	+	0.520215i	$0.825852\pi$
$678$	0.351632	+	1.76066i	0.0135043	+	0.0676179i
$679$			0.481963i			0.0184960i
$680$		0			0
$681$	27.7066	−	18.5439i	1.06172	−	0.710603i
$682$	0.943667	−	2.27821i	0.0361349	−	0.0872373i
$683$	20.1716	−	30.1890i	0.771847	−	1.15515i	−0.212198	−	0.977227i	$-0.568062\pi$
$683$	20.1716	−	30.1890i	0.771847	−	1.15515i	0.984044	−	0.177923i	$-0.0569379\pi$
$684$	1.97916	−	0.823378i	0.0756750	−	0.0314827i
$685$	−10.1648	+	2.02190i	−0.388377	+	0.0772530i
$686$	1.26956	+	1.90003i	0.0484720	+	0.0725434i
$687$	−7.29188	−	17.5658i	−0.278202	−	0.670176i
$688$	1.96874	−	0.815481i	0.0750577	−	0.0310899i
$689$	56.7746	−	23.5168i	2.16294	−	0.895919i
$690$	−1.88434	−	4.53928i	−0.0717355	−	0.172807i
$691$	−1.59686	−	2.38987i	−0.0607475	−	0.0909151i	0.799852	−	0.600197i	$-0.204911\pi$
$691$	−1.59686	−	2.38987i	−0.0607475	−	0.0909151i	−0.860600	+	0.509282i	$0.829911\pi$
$692$	−1.48282	+	0.294952i	−0.0563685	+	0.0112124i
$693$	−2.38765	+	0.993319i	−0.0906991	+	0.0377331i
$694$	−0.00882130	+	0.0132020i	−0.000334852	+	0.000501141i
$695$	3.72855	−	9.00150i	0.141432	−	0.341447i
$696$	2.46250	−	1.64814i	0.0933406	−	0.0624725i
$697$		0			0
$698$			5.21082i			0.197232i
$699$	7.96712	+	39.8924i	0.301344	+	1.50887i
$700$	0.911533	+	0.609067i	0.0344527	+	0.0230206i
$701$	−3.87452	+	3.87452i	−0.146339	+	0.146339i	−0.776480	−	0.630142i	$-0.782997\pi$
$701$	−3.87452	+	3.87452i	−0.146339	+	0.146339i	0.630142	+	0.776480i	$0.282997\pi$
$702$	−8.89210	−	21.3275i	−0.335611	−	0.804956i
$703$	−0.899770	+	0.601207i	−0.0339355	+	0.0226750i
$704$	3.68539	−	18.5277i	0.138898	−	0.698290i
$705$	11.7711	+	7.85208i	0.443327	+	0.295726i
$706$	3.90754	+	9.43364i	0.147062	+	0.355040i
$707$	1.30043	+	0.258672i	0.0489079	+	0.00972838i
$708$	0.539917	+	0.223153i	0.0202913	+	0.00838659i
$709$	7.32963	+	36.8486i	0.275270	+	1.38388i	0.832733	+	0.553675i	$0.186775\pi$
$709$	7.32963	+	36.8486i	0.275270	+	1.38388i	−0.557463	+	0.830202i	$0.688225\pi$
$710$	−3.16093	−	3.16093i	−0.118628	−	0.118628i
$711$	18.0575	+	26.9349i	0.677211	+	1.01014i
$712$	13.3517	+	5.53046i	0.500376	+	0.207263i
$713$	2.75410			0.103142
$714$		0			0
$715$	19.1665			0.716788
$716$	−12.3272	−	5.10610i	−0.460690	−	0.190824i
$717$	23.7667	−	0.0183548i	0.887582	−	0.000685474i
$718$	18.8705	+	18.8705i	0.704242	+	0.704242i
$719$	4.79617	+	24.1120i	0.178867	+	0.899225i	0.961092	+	0.276229i	$0.0890848\pi$
$719$	4.79617	+	24.1120i	0.178867	+	0.899225i	−0.782225	+	0.622996i	$0.785915\pi$
$720$	0.664464	−	0.133237i	0.0247631	−	0.00496546i
$721$	−0.474341	−	0.0943522i	−0.0176654	−	0.00351386i
$722$	5.99913	+	14.4832i	0.223265	+	0.539009i
$723$	−4.11008	+	6.16146i	−0.152855	+	0.229147i
$724$	3.25924	−	16.3853i	0.121129	−	0.608955i
$725$	−2.22820	+	1.48884i	−0.0827533	+	0.0552940i
$726$	−8.73683	−	8.72334i	−0.324254	−	0.323754i
$727$	26.6720	−	26.6720i	0.989211	−	0.989211i	−0.0107310	−	0.999942i	$-0.503416\pi$
$727$	26.6720	−	26.6720i	0.989211	−	0.989211i	0.999942	+	0.0107310i	$0.00341584\pi$
$728$	−2.37959	−	1.58999i	−0.0881935	−	0.0589290i
$729$	−26.9997	+	0.125111i	−0.999989	+	0.00463375i
$730$		−	7.96307i		−	0.294726i
$731$		0			0
$732$	13.1826	+	19.6963i	0.487244	+	0.727995i
$733$	7.27415	−	17.5613i	0.268677	−	0.648643i	−0.730745	−	0.682651i	$-0.760827\pi$
$733$	7.27415	−	17.5613i	0.268677	−	0.648643i	0.999422	+	0.0340076i	$0.0108270\pi$
$734$	−15.6638	+	23.4426i	−0.578163	+	0.865282i
$735$	−9.67984	−	1.91767i	−0.357046	−	0.0707343i
$736$	23.3635	−	4.64730i	0.861192	−	0.171302i
$737$	13.2728	+	19.8642i	0.488910	+	0.731706i
$738$	11.1471	−	16.7388i	0.410332	−	0.616164i
$739$	−33.5289	+	13.8881i	−1.23338	+	0.510884i	−0.901640	−	0.432487i	$-0.857636\pi$
$739$	−33.5289	+	13.8881i	−1.23338	+	0.510884i	−0.331742	+	0.943370i	$0.607636\pi$
$740$	−1.92607	+	0.797805i	−0.0708038	+	0.0293279i
$741$	4.67417	−	1.94034i	0.171710	−	0.0712800i
$742$	1.05360	+	1.57682i	0.0386788	+	0.0578868i
$743$	0.174867	−	0.0347832i	0.00641525	−	0.00127607i	−0.191882	−	0.981418i	$-0.561459\pi$
$743$	0.174867	−	0.0347832i	0.00641525	−	0.00127607i	0.198297	+	0.980142i	$0.436459\pi$
$744$	0.619682	−	3.12797i	0.0227186	−	0.114677i
$745$	5.77458	−	8.64227i	0.211564	−	0.316628i
$746$	4.90173	−	11.8338i	0.179465	−	0.433267i
$747$	−3.16049	+	7.66355i	−0.115636	+	0.280395i
$748$		0			0
$749$			0.803058i			0.0293431i
$750$	10.8741	−	2.17172i	0.397065	−	0.0792999i
$751$	−31.5832	−	21.1032i	−1.15249	−	0.770067i	−0.175734	−	0.984438i	$-0.556230\pi$
$751$	−31.5832	−	21.1032i	−1.15249	−	0.770067i	−0.976752	+	0.214371i	$0.931230\pi$
$752$	−1.94852	+	1.94852i	−0.0710551	+	0.0710551i
$753$	11.3736	−	11.3911i	0.414476	−	0.415116i
$754$	2.28822	−	1.52894i	0.0833320	−	0.0556807i
$755$	−0.126537	+	0.636146i	−0.00460516	+	0.0231517i
$756$	−1.09210	+	0.733383i	−0.0397193	+	0.0266729i
$757$	−7.33808	−	17.7157i	−0.266707	−	0.643888i	0.732617	−	0.680641i	$-0.238299\pi$
$757$	−7.33808	−	17.7157i	−0.266707	−	0.643888i	−0.999324	+	0.0367531i	$0.988299\pi$
$758$	−31.2629	−	6.21858i	−1.13552	−	0.225869i
$759$	12.0821	−	29.2326i	0.438552	−	1.06108i
$760$	−0.243149	−	1.22239i	−0.00881996	−	0.0443409i
$761$	−21.9157	−	21.9157i	−0.794443	−	0.794443i	0.187770	−	0.982213i	$-0.439874\pi$
$761$	−21.9157	−	21.9157i	−0.794443	−	0.794443i	−0.982213	+	0.187770i	$0.939874\pi$
$762$	0.00993038	+	12.8583i	0.000359740	+	0.465807i
$763$	−2.28102	−	0.944829i	−0.0825785	−	0.0342051i
$764$	−21.5800			−0.780737
$765$		0			0
$766$	−28.8846			−1.04364
$767$	1.27430	+	0.527834i	0.0460124	+	0.0190590i
$768$	−0.0203427	−	26.3406i	−0.000734055	−	0.950486i
$769$	−13.1164	−	13.1164i	−0.472990	−	0.472990i	0.429891	−	0.902881i	$-0.358552\pi$
$769$	−13.1164	−	13.1164i	−0.472990	−	0.472990i	−0.902881	+	0.429891i	$0.858552\pi$
$770$	0.115392	+	0.580115i	0.00415844	+	0.0209059i
$771$	−10.4060	+	25.1773i	−0.374763	+	0.906737i
$772$	−3.78460	−	0.752804i	−0.136211	−	0.0270940i
$773$	−15.6889	−	37.8763i	−0.564289	−	1.36232i	−0.906306	−	0.422621i	$-0.861110\pi$
$773$	−15.6889	−	37.8763i	−0.564289	−	1.36232i	0.342017	−	0.939694i	$-0.388890\pi$
$774$	0.0299934	+	19.4184i	0.00107809	+	0.697979i
$775$	−0.562617	+	2.82847i	−0.0202098	+	0.101601i
$776$	−5.67523	+	3.79206i	−0.203729	+	0.136127i
$777$	0.469224	−	0.469950i	0.0168333	−	0.0168593i
$778$	−0.447469	+	0.447469i	−0.0160425	+	0.0160425i
$779$	3.66236	+	2.44711i	0.131218	+	0.0876769i
$780$	9.56109	−	1.90950i	0.342342	−	0.0683709i
$781$		−	28.7696i		−	1.02946i
$782$		0			0
$783$	−0.634651	−	3.15242i	−0.0226806	−	0.112658i
$784$	0.735425	−	1.77547i	0.0262652	−	0.0634097i
$785$	1.07227	−	1.60477i	0.0382710	−	0.0572766i
$786$	2.77494	−	14.0071i	0.0989788	−	0.499616i
$787$	14.7477	−	2.93350i	0.525700	−	0.104568i	0.0748960	−	0.997191i	$-0.476138\pi$
$787$	14.7477	−	2.93350i	0.525700	−	0.104568i	0.450804	+	0.892623i	$0.351138\pi$
$788$	9.77735	+	14.6328i	0.348304	+	0.521273i
$789$	24.7021	−	10.2543i	0.879419	−	0.365063i
$790$	6.85236	−	2.83834i	0.243796	−	0.100984i
$791$	0.222954	−	0.0923506i	0.00792734	−	0.00328361i
$792$	−30.4824	−	20.2997i	−1.08315	−	0.721318i
$793$	31.0875	+	46.5257i	1.10395	+	1.65217i
$794$	16.5680	−	3.29558i	0.587977	−	0.116956i
$795$	−16.1104	−	3.19163i	−0.571378	−	0.113195i
$796$	3.09966	−	4.63897i	0.109865	−	0.164424i
$797$	6.21185	−	14.9967i	0.220035	−	0.531211i	−0.774859	−	0.632134i	$-0.782179\pi$
$797$	6.21185	−	14.9967i	0.220035	−	0.531211i	0.994894	+	0.100922i	$0.0321794\pi$
$798$	0.0868691	+	0.129792i	0.00307513	+	0.00459458i
$799$		0			0
$800$			24.9438i			0.881895i
$801$	11.0727	−	11.1069i	0.391234	−	0.392444i
$802$	−10.9933	−	7.34549i	−0.388187	−	0.259378i
$803$	36.2384	−	36.2384i	1.27882	−	1.27882i
$804$	8.60005	+	8.58677i	0.303300	+	0.302832i
$805$	−0.549272	+	0.367012i	−0.0193593	+	0.0129355i
$806$	0.577772	−	2.90465i	0.0203511	−	0.102312i
$807$	−23.3930	+	35.0687i	−0.823473	+	1.23448i
$808$	7.18583	+	17.3481i	0.252797	+	0.610305i
$809$	−37.0970	−	7.37905i	−1.30426	−	0.259434i	−0.506412	−	0.862292i	$-0.669028\pi$
$809$	−37.0970	−	7.37905i	−1.30426	−	0.259434i	−0.797848	+	0.602858i	$0.794028\pi$
$810$	−1.18606	+	6.06052i	−0.0416739	+	0.212945i
$811$	−6.74744	−	33.9217i	−0.236935	−	1.19115i	−0.897717	−	0.440573i	$-0.854775\pi$
$811$	−6.74744	−	33.9217i	−0.236935	−	1.19115i	0.660782	−	0.750578i	$-0.270225\pi$
$812$	−0.110785	−	0.110785i	−0.00388780	−	0.00388780i
$813$	9.74327	−	0.00752467i	0.341711	−	0.000263902i
$814$	6.71933	+	2.78324i	0.235513	+	0.0975525i
$815$	13.2014			0.462426
$816$		0			0
$817$	−4.25303			−0.148795
$818$	−21.9656	−	9.09843i	−0.768007	−	0.318119i
$819$	−2.57971	+	1.72948i	−0.0901425	+	0.0604329i
$820$	6.00029	+	6.00029i	0.209539	+	0.209539i
$821$	−9.82356	−	49.3864i	−0.342845	−	1.72360i	−0.639657	−	0.768660i	$-0.720924\pi$
$821$	−9.82356	−	49.3864i	−0.342845	−	1.72360i	0.296813	−	0.954936i	$-0.404076\pi$
$822$	16.9977	+	7.02529i	0.592862	+	0.245035i
$823$	23.4287	+	4.66026i	0.816674	+	0.162447i	0.585715	−	0.810517i	$-0.300814\pi$
$823$	23.4287	+	4.66026i	0.816674	+	0.162447i	0.230959	+	0.972963i	$0.425814\pi$
$824$	−2.62107	−	6.32783i	−0.0913094	−	0.220440i
$825$	27.5537	+	18.3801i	0.959298	+	0.639912i
$826$	−0.00830405	+	0.0417473i	−0.000288935	+	0.00145257i
$827$	−5.58417	+	3.73122i	−0.194181	+	0.129747i	−0.648860	−	0.760908i	$-0.724754\pi$
$827$	−5.58417	+	3.73122i	−0.194181	+	0.129747i	0.454679	+	0.890655i	$0.349754\pi$
$828$	3.11472	−	15.7862i	0.108244	−	0.548607i
$829$	17.6880	−	17.6880i	0.614331	−	0.614331i	−0.329741	−	0.944072i	$-0.606961\pi$
$829$	17.6880	−	17.6880i	0.614331	−	0.614331i	0.944072	+	0.329741i	$0.106961\pi$
$830$	1.57649	+	1.05338i	0.0547208	+	0.0365632i
$831$	−3.00694	−	15.0562i	−0.104310	−	0.522292i
$832$		−	22.6876i		−	0.786552i
$833$		0			0
$834$	−14.3692	+	9.61724i	−0.497564	+	0.333018i
$835$	−2.87097	+	6.93113i	−0.0993539	+	0.239862i
$836$	1.75304	−	2.62362i	0.0606303	−	0.0907397i
$837$	−2.88176	−	1.91589i	−0.0996082	−	0.0662227i
$838$	−28.9730	+	5.76309i	−1.00086	+	0.199083i
$839$	24.4659	+	36.6159i	0.844658	+	1.26412i	0.962553	+	0.271094i	$0.0873854\pi$
$839$	24.4659	+	36.6159i	0.844658	+	1.26412i	−0.117895	+	0.993026i	$0.537615\pi$
$840$	0.293246	+	0.706415i	0.0101179	+	0.0243736i
$841$	−26.4387	+	10.9513i	−0.911679	+	0.377630i
$842$	−0.00978190	+	0.00405180i	−0.000337107	+	0.000139634i
$843$	4.79339	+	11.5470i	0.165093	+	0.397701i
$844$	−11.1883	−	16.7444i	−0.385116	−	0.576367i
$845$	12.1425	−	2.41529i	0.417713	−	0.0830884i
$846$	−9.64526	−	23.1844i	−0.331611	−	0.797095i
$847$	−0.921941	+	1.37978i	−0.0316783	+	0.0474099i
$848$	1.22399	−	2.95497i	0.0420319	−	0.101474i
$849$	−7.11313	+	4.76079i	−0.244122	+	0.163390i
$850$		0			0
$851$			8.12291i			0.278450i
$852$	−2.86621	−	14.3515i	−0.0981948	−	0.491674i
$853$	26.9089	+	17.9800i	0.921344	+	0.615623i	0.923177	−	0.384376i	$-0.125583\pi$
$853$	26.9089	+	17.9800i	0.921344	+	0.615623i	−0.00183231	+	0.999998i	$0.500583\pi$
$854$	−1.22103	+	1.22103i	−0.0417829	+	0.0417829i
$855$	−1.32697	−	0.261821i	−0.0453816	−	0.00895411i
$856$	−9.45620	+	6.31843i	−0.323206	+	0.215959i
$857$	4.83803	−	24.3224i	0.165264	−	0.830838i	−0.805831	−	0.592145i	$-0.798281\pi$
$857$	4.83803	−	24.3224i	0.165264	−	0.830838i	0.971095	−	0.238693i	$-0.0767189\pi$
$858$	−28.2959	−	18.8751i	−0.966007	−	0.644387i
$859$	16.0644	+	38.7830i	0.548112	+	1.32326i	0.918881	+	0.394534i	$0.129094\pi$
$859$	16.0644	+	38.7830i	0.548112	+	1.32326i	−0.370770	+	0.928725i	$0.620906\pi$
$860$	−8.03608	−	1.59848i	−0.274028	−	0.0545076i
$861$	−2.49813	−	1.03250i	−0.0851360	−	0.0351875i
$862$	−1.93955	−	9.75076i	−0.0660613	−	0.332112i
$863$	−0.148288	−	0.148288i	−0.00504779	−	0.00504779i	0.704578	−	0.709626i	$-0.251136\pi$
$863$	−0.148288	−	0.148288i	−0.00504779	−	0.00504779i	−0.709626	+	0.704578i	$0.751136\pi$
$864$	−27.6794	−	11.3901i	−0.941671	−	0.387499i
$865$	0.881339	+	0.365062i	0.0299664	+	0.0124125i
$866$	−0.455061			−0.0154636
$867$		0			0
$868$	−0.168603			−0.00572278
$869$	44.1005	+	18.2670i	1.49601	+	0.619666i
$870$	−0.735493		0.000568017i	−0.0249355		1.92576e-5i
$871$	20.2885	+	20.2885i	0.687450	+	0.687450i
$872$	−6.82138	−	34.2934i	−0.231001	−	1.16132i
$873$	1.45630	+	7.26265i	0.0492881	+	0.245803i
$874$	−1.87361	−	0.372684i	−0.0633758	−	0.0126062i
$875$	−0.570368	−	1.37699i	−0.0192820	−	0.0465507i
$876$	14.4669	−	21.6876i	0.488793	−	0.732755i
$877$	−1.44266	+	7.25275i	−0.0487152	+	0.244908i	−0.997468	−	0.0711099i	$-0.977346\pi$
$877$	−1.44266	+	7.25275i	−0.0487152	+	0.244908i	0.948753	+	0.316018i	$0.102346\pi$
$878$	21.2294	−	14.1850i	0.716456	−	0.478721i
$879$	23.4152	+	23.3790i	0.789774	+	0.788555i
$880$	0.705386	−	0.705386i	0.0237786	−	0.0237786i
$881$	41.3971	+	27.6606i	1.39470	+	0.931911i	0.999914	+	0.0131394i	$0.00418253\pi$
$881$	41.3971	+	27.6606i	1.39470	+	0.931911i	0.394790	+	0.918772i	$0.370817\pi$
$882$	12.4020	+	12.3638i	0.417598	+	0.416310i
$883$			28.6327i			0.963566i	0.876291	+	0.481783i	$0.160011\pi$
$883$			28.6327i			0.963566i	−0.876291	+	0.481783i	$0.839989\pi$
$884$		0			0
$885$	−0.205034	−	0.306342i	−0.00689214	−	0.0102976i
$886$	12.9134	−	31.1758i	0.433835	−	1.04737i
$887$	23.7610	−	35.5608i	0.797816	−	1.19402i	−0.179818	−	0.983700i	$-0.557551\pi$
$887$	23.7610	−	35.5608i	0.797816	−	1.19402i	0.977634	−	0.210315i	$-0.0674491\pi$
$888$	9.22560	+	1.82768i	0.309591	+	0.0613329i
$889$	1.69507	−	0.337170i	0.0568508	−	0.0113083i
$890$	−1.99290	−	2.98259i	−0.0668022	−	0.0999765i
$891$	−32.9777	+	22.1827i	−1.10480	+	0.743148i
$892$	−19.9656	+	8.27003i	−0.668498	+	0.276901i
$893$	5.08111	−	2.10466i	0.170033	−	0.0704299i
$894$	−17.0360	+	7.07196i	−0.569769	+	0.236522i
$895$	4.67736	+	7.00016i	0.156347	+	0.233990i
$896$	−1.51892	+	0.302131i	−0.0507434	+	0.0100935i
$897$	7.38245	−	37.2645i	0.246493	−	1.24422i
$898$	−16.9732	+	25.4021i	−0.566402	+	0.847680i
$899$	0.157720	−	0.380771i	0.00526027	−	0.0126994i
$900$	15.5761	+	6.42368i	0.519204	+	0.214123i
$901$		0			0
$902$		−	29.6033i		−	0.985683i
$903$	2.55948	−	0.511167i	0.0851740	−	0.0170106i
$904$	2.84164	+	1.89872i	0.0945116	+	0.0631506i
$905$	−7.45379	+	7.45379i	−0.247772	+	0.247772i
$906$	0.813284	−	0.814541i	0.0270196	−	0.0270613i
$907$	−6.76450	+	4.51990i	−0.224612	+	0.150081i	−0.662785	−	0.748810i	$-0.730626\pi$
$907$	−6.76450	+	4.51990i	−0.224612	+	0.150081i	0.438173	+	0.898891i	$0.355626\pi$
$908$	4.87038	−	24.4851i	0.161629	−	0.812565i
$909$	20.3777	−	0.0314752i	0.675885	−	0.00104396i
$910$	0.271845	+	0.656291i	0.00901157	+	0.0217558i
$911$	−2.90793	−	0.578423i	−0.0963440	−	0.0191640i	0.146683	−	0.989184i	$-0.453140\pi$
$911$	−2.90793	−	0.578423i	−0.0963440	−	0.0191640i	−0.243027	+	0.970020i	$0.578140\pi$
$912$	0.100613	−	0.243434i	0.00333164	−	0.00806089i
$913$	2.38058	+	11.9680i	0.0787858	+	0.396083i
$914$	−12.6372	−	12.6372i	−0.418002	−	0.418002i
$915$	−0.0115493	−	14.9546i	−0.000381809	−	0.494382i
$916$	−13.1575	−	5.45001i	−0.434736	−	0.180073i
$917$	−1.91928			−0.0633802
$918$		0			0
$919$	36.7672			1.21284			0.606418	−	0.795146i	$-0.292606\pi$
$919$	36.7672			1.21284			0.606418	+	0.795146i	$0.292606\pi$
$920$	−8.64329	−	3.58017i	−0.284961	−	0.118035i
$921$	0.00667236	+	8.63966i	0.000219862	+	0.284687i
$922$	3.64477	+	3.64477i	0.120034	+	0.120034i
$923$	−6.74078	−	33.8882i	−0.221875	−	1.11544i
$924$	−0.739655	+	1.78959i	−0.0243328	+	0.0588733i
$925$	−8.34224	−	1.65937i	−0.274291	−	0.0545599i
$926$	11.6457	+	28.1151i	0.382700	+	0.923919i
$927$	−7.43288	+	0.0114807i	−0.244128	+	0.000377077i
$928$	0.695455	−	3.49629i	0.0228294	−	0.114771i
$929$	23.4065	−	15.6397i	0.767941	−	0.513122i	−0.108812	−	0.994062i	$-0.534705\pi$
$929$	23.4065	−	15.6397i	0.767941	−	0.513122i	0.876753	+	0.480940i	$0.159705\pi$
$930$	−0.559239	+	0.560103i	−0.0183382	+	0.0183665i
$931$	−2.71211	+	2.71211i	−0.0888859	+	0.0888859i
$932$	25.3277	+	16.9234i	0.829637	+	0.554346i
$933$	17.7769	−	3.55032i	0.581990	−	0.116232i
$934$		−	6.44805i		−	0.210987i
$935$		0			0
$936$	−40.6621	−	16.7693i	−1.32908	−	0.548120i
$937$	−14.2493	+	34.4010i	−0.465506	+	1.12383i	0.500599	+	0.865679i	$0.333113\pi$
$937$	−14.2493	+	34.4010i	−0.465506	+	1.12383i	−0.966105	+	0.258151i	$0.916887\pi$
$938$	−0.491927	+	0.736221i	−0.0160620	+	0.0240385i
$939$	−8.08320	+	40.8017i	−0.263785	+	1.33151i
$940$	10.3918	−	2.06705i	0.338942	−	0.0674197i
$941$	−25.2665	−	37.8140i	−0.823664	−	1.23270i	−0.969913	−	0.243452i	$-0.921720\pi$
$941$	−25.2665	−	37.8140i	−0.823664	−	1.23270i	0.146249	−	0.989248i	$-0.453280\pi$
$942$	−3.16339	+	1.31318i	−0.103069	+	0.0427857i
$943$	30.5462	−	12.6526i	0.994720	−	0.412026i
$944$	0.0663241	−	0.0274723i	0.00215867	−	0.000894148i
$945$	0.830043	−	0.00192311i	0.0270013	−	6.25589e-5i
$946$	15.8804	+	23.7668i	0.516318	+	0.772724i
$947$	−16.1310	+	3.20866i	−0.524188	+	0.104267i	−0.450089	−	0.892983i	$-0.648608\pi$
$947$	−16.1310	+	3.20866i	−0.524188	+	0.104267i	−0.0740985	+	0.997251i	$0.523608\pi$
$948$	23.8191	+	4.71879i	0.773608	+	0.153259i
$949$	34.1951	−	51.1766i	1.11002	−	1.66126i
$950$	0.765494	−	1.84807i	0.0248359	−	0.0599592i
$951$	−9.47587	−	14.1580i	−0.307276	−	0.459103i
$952$		0			0
$953$			15.3092i			0.495915i	0.968771	+	0.247958i	$0.0797593\pi$
$953$			15.3092i			0.495915i	−0.968771	+	0.247958i	$0.920241\pi$
$954$	20.6410	+	20.5774i	0.668278	+	0.666217i
$955$	11.3216	+	7.56488i	0.366360	+	0.244794i
$956$	12.5840	−	12.5840i	0.406997	−	0.406997i
$957$	−3.34967	−	3.34450i	−0.108279	−	0.108112i
$958$	1.60067	−	1.06954i	0.0517154	−	0.0345552i
$959$	0.482282	−	2.42460i	0.0155737	−	0.0782943i
$960$	−3.36475	+	5.04414i	−0.108597	+	0.162799i
$961$	11.6935	+	28.2305i	0.377208	+	0.910661i
$962$	8.56694	+	1.70407i	0.276209	+	0.0549415i
$963$	2.42651	+	12.1012i	0.0781933	+	0.389955i
$964$	1.08197	+	5.43944i	0.0348480	+	0.175193i
$965$	1.72164	+	1.72164i	0.0554216	+	0.0554216i
$966$	1.17233		0.000905386i	0.0377192		2.91303e-5i
$967$	−44.6169	−	18.4809i	−1.43478	−	0.594306i	−0.476255	−	0.879307i	$-0.658006\pi$
$967$	−44.6169	−	18.4809i	−1.43478	−	0.594306i	−0.958527	+	0.285001i	$0.908006\pi$
$968$	−23.5010			−0.755352
$969$		0			0
$970$	1.69419			0.0543972
$971$	−3.06636	−	1.27013i	−0.0984041	−	0.0407603i	0.332938	−	0.942949i	$-0.391960\pi$
$971$	−3.06636	−	1.27013i	−0.0984041	−	0.0407603i	−0.431342	+	0.902188i	$0.641960\pi$
$972$	−14.2407	+	14.3511i	−0.456772	+	0.460313i
$973$	1.64333	+	1.64333i	0.0526828	+	0.0526828i
$974$	4.59275	+	23.0893i	0.147161	+	0.739829i
$975$	36.7625	+	15.1943i	1.17734	+	0.486607i
$976$	2.85640	+	0.568172i	0.0914310	+	0.0181868i
$977$	−11.3473	−	27.3947i	−0.363031	−	0.876434i	−0.994854	−	0.101321i	$-0.967693\pi$
$977$	−11.3473	−	27.3947i	−0.363031	−	0.876434i	0.631823	−	0.775113i	$-0.282307\pi$
$978$	−19.4895	−	13.0007i	−0.623206	−	0.415717i
$979$	4.50386	−	22.6425i	0.143944	−	0.723656i
$980$	−6.14386	+	4.10519i	−0.196258	+	0.131136i
$981$	−37.2273	−	7.34521i	−1.18858	−	0.234515i
$982$	−8.01800	+	8.01800i	−0.255865	+	0.255865i
$983$	−2.07918	−	1.38926i	−0.0663155	−	0.0443106i	0.521971	−	0.852964i	$-0.325197\pi$
$983$	−2.07918	−	1.38926i	−0.0663155	−	0.0443106i	−0.588286	+	0.808653i	$0.700197\pi$
$984$	−7.49726	−	37.5397i	−0.239004	−	1.19672i
$985$		−	11.1044i		−	0.353815i
$986$		0			0
$987$	−2.80486	+	1.87728i	−0.0892797	+	0.0597545i
$988$	1.45022	−	3.50115i	0.0461377	−	0.111386i
$989$	−17.7363	+	26.5443i	−0.563982	+	0.844059i
$990$	3.49170	+	8.39302i	0.110973	+	0.266748i
$991$	−37.4243	+	7.44416i	−1.18882	+	0.236471i	−0.749590	−	0.661902i	$-0.769749\pi$
$991$	−37.4243	+	7.44416i	−1.18882	+	0.236471i	−0.439232	+	0.898374i	$0.644749\pi$
$992$	−2.13128	−	3.18969i	−0.0676683	−	0.101273i
$993$	2.78840	+	6.71711i	0.0884871	+	0.213161i
$994$	0.985113	−	0.408047i	0.0312459	−	0.0129425i
$995$	−3.25239	+	1.34718i	−0.103108	+	0.0427086i
$996$	2.37987	+	5.73299i	0.0754090	+	0.181657i
$997$	−24.8311	−	37.1624i	−0.786410	−	1.17695i	−0.980607	−	0.195984i	$-0.937210\pi$
$997$	−24.8311	−	37.1624i	−0.786410	−	1.17695i	0.194197	−	0.980963i	$-0.437790\pi$
$998$	12.5272	−	2.49181i	0.396541	−	0.0788769i
$999$	5.65069	−	8.49942i	0.178780	−	0.268910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.h.503.3		32
3.2	odd	2	inner	867.2.i.h.503.2		32
17.2	even	8		867.2.i.f.329.2		32
17.3	odd	16		867.2.i.d.158.3		32
17.4	even	4		867.2.i.d.653.2		32
17.5	odd	16		51.2.i.a.29.2	✓	32
17.6	odd	16		867.2.i.f.224.3		32
17.7	odd	16		867.2.i.b.65.2		32
17.8	even	8		867.2.i.i.827.3		32
17.9	even	8		867.2.i.b.827.3		32
17.10	odd	16		867.2.i.i.65.2		32
17.11	odd	16		867.2.i.g.224.3		32
17.12	odd	16	inner	867.2.i.h.131.2		32
17.13	even	4		867.2.i.c.653.2		32
17.14	odd	16		867.2.i.c.158.3		32
17.15	even	8		867.2.i.g.329.2		32
17.16	even	2		51.2.i.a.44.3	yes	32
51.2	odd	8		867.2.i.f.329.3		32
51.5	even	16		51.2.i.a.29.3	yes	32
51.8	odd	8		867.2.i.i.827.2		32
51.11	even	16		867.2.i.g.224.2		32
51.14	even	16		867.2.i.c.158.2		32
51.20	even	16		867.2.i.d.158.2		32
51.23	even	16		867.2.i.f.224.2		32
51.26	odd	8		867.2.i.b.827.2		32
51.29	even	16	inner	867.2.i.h.131.3		32
51.32	odd	8		867.2.i.g.329.3		32
51.38	odd	4		867.2.i.d.653.3		32
51.41	even	16		867.2.i.b.65.3		32
51.44	even	16		867.2.i.i.65.3		32
51.47	odd	4		867.2.i.c.653.3		32
51.50	odd	2		51.2.i.a.44.2	yes	32
68.39	even	16		816.2.cj.c.641.1		32
68.67	odd	2		816.2.cj.c.401.2		32
204.107	odd	16		816.2.cj.c.641.2		32
204.203	even	2		816.2.cj.c.401.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.2	✓	32	17.5	odd	16
51.2.i.a.29.3	yes	32	51.5	even	16
51.2.i.a.44.2	yes	32	51.50	odd	2
51.2.i.a.44.3	yes	32	17.16	even	2
816.2.cj.c.401.1		32	204.203	even	2
816.2.cj.c.401.2		32	68.67	odd	2
816.2.cj.c.641.1		32	68.39	even	16
816.2.cj.c.641.2		32	204.107	odd	16
867.2.i.b.65.2		32	17.7	odd	16
867.2.i.b.65.3		32	51.41	even	16
867.2.i.b.827.2		32	51.26	odd	8
867.2.i.b.827.3		32	17.9	even	8
867.2.i.c.158.2		32	51.14	even	16
867.2.i.c.158.3		32	17.14	odd	16
867.2.i.c.653.2		32	17.13	even	4
867.2.i.c.653.3		32	51.47	odd	4
867.2.i.d.158.2		32	51.20	even	16
867.2.i.d.158.3		32	17.3	odd	16
867.2.i.d.653.2		32	17.4	even	4
867.2.i.d.653.3		32	51.38	odd	4
867.2.i.f.224.2		32	51.23	even	16
867.2.i.f.224.3		32	17.6	odd	16
867.2.i.f.329.2		32	17.2	even	8
867.2.i.f.329.3		32	51.2	odd	8
867.2.i.g.224.2		32	51.11	even	16
867.2.i.g.224.3		32	17.11	odd	16
867.2.i.g.329.2		32	17.15	even	8
867.2.i.g.329.3		32	51.32	odd	8
867.2.i.h.131.2		32	17.12	odd	16	inner
867.2.i.h.131.3		32	51.29	even	16	inner
867.2.i.h.503.2		32	3.2	odd	2	inner
867.2.i.h.503.3		32	1.1	even	1	trivial
867.2.i.i.65.2		32	17.10	odd	16
867.2.i.i.65.3		32	51.44	even	16
867.2.i.i.827.2		32	51.8	odd	8
867.2.i.i.827.3		32	17.8	even	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.774648 + 0.320870i) q^{2} +(-0.00133765 - 1.73205i) q^{3} +(-0.917091 - 0.917091i) q^{4} +(0.159652 + 0.802626i) q^{5} +(0.554726 - 1.34216i) q^{6} +(-0.191449 - 0.0380817i) q^{7} +(-1.05790 - 2.55399i) q^{8} +(-3.00000 + 0.00463376i) q^{9} +(-0.133864 + 0.672980i) q^{10} +(-3.67179 + 2.45341i) q^{11} +(-1.58722 + 1.58968i) q^{12} +(-3.75023 + 3.75023i) q^{13} +(-0.136087 - 0.0909302i) q^{14} +(1.38998 - 0.277599i) q^{15} +0.276039i q^{16} +(-2.32543 - 0.959018i) q^{18} +(0.210831 - 0.508991i) q^{19} +(0.589666 - 0.882497i) q^{20} +(-0.0657033 + 0.331651i) q^{21} +(-3.63157 + 0.722364i) q^{22} +(-2.29752 - 3.43849i) q^{23} +(-4.42222 + 1.83574i) q^{24} +(4.00068 - 1.65713i) q^{25} +(-4.10844 + 1.70177i) q^{26} +(0.0120389 + 5.19614i) q^{27} +(0.140652 + 0.210501i) q^{28} +(-0.606965 + 0.120733i) q^{29} +(1.16581 + 0.230959i) q^{30} +(-0.369997 + 0.553739i) q^{31} +(-2.20436 + 5.32181i) q^{32} +(4.25434 + 6.35644i) q^{33} -0.159742i q^{35} +(2.75552 + 2.74702i) q^{36} +(-1.63319 - 1.09126i) q^{37} +(0.326640 - 0.326640i) q^{38} +(6.50060 + 6.49057i) q^{39} +(1.88100 - 1.25684i) q^{40} +(-1.55975 + 7.84141i) q^{41} +(-0.157314 + 0.235831i) q^{42} +(-2.95422 - 7.13212i) q^{43} +(5.61737 + 1.11736i) q^{44} +(-0.482675 - 2.40714i) q^{45} +(-0.676466 - 3.40082i) q^{46} +(7.05884 + 7.05884i) q^{47} +(0.478114 - 0.000369245i) q^{48} +(-6.43195 - 2.66420i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(-10.7049 - 4.43410i) q^{53} +(-1.65796 + 4.02904i) q^{54} +(-2.55538 - 2.55538i) q^{55} +(0.105274 + 0.529246i) q^{56} +(-0.881880 - 0.364489i) q^{57} +(-0.508924 - 0.101231i) q^{58} +(-0.0995233 - 0.240270i) q^{59} +(-1.52932 - 1.02015i) q^{60} +(2.05830 - 10.3478i) q^{61} +(-0.464295 + 0.310232i) q^{62} +(0.574524 + 0.113358i) q^{63} +(-3.02483 + 3.02483i) q^{64} +(-3.60876 - 2.41130i) q^{65} +(1.25603 + 6.28910i) q^{66} -5.40994i q^{67} +(-5.95256 + 3.98403i) q^{69} +(0.0512564 - 0.123744i) q^{70} +(-3.61943 + 5.41686i) q^{71} +(3.18552 + 7.65705i) q^{72} +(-11.3822 + 2.26406i) q^{73} +(-0.914994 - 1.36939i) q^{74} +(-2.87559 - 6.92716i) q^{75} +(-0.660143 + 0.273440i) q^{76} +(0.796392 - 0.329876i) q^{77} +(2.95305 + 7.11375i) q^{78} +(-6.00531 - 8.98758i) q^{79} +(-0.221556 + 0.0440703i) q^{80} +(8.99996 - 0.0278025i) q^{81} +(-3.72433 + 5.57385i) q^{82} +(1.05744 - 2.55289i) q^{83} +(0.364410 - 0.243898i) q^{84} -6.47280i q^{86} +(0.209927 + 1.05113i) q^{87} +(10.1503 + 6.78225i) q^{88} +(-3.69661 + 3.69661i) q^{89} +(0.398473 - 2.01956i) q^{90} +(0.860794 - 0.575164i) q^{91} +(-1.04637 + 5.26045i) q^{92} +(0.959599 + 0.640112i) q^{93} +(3.20315 + 7.73308i) q^{94} +(0.442189 + 0.0879569i) q^{95} +(9.22058 + 3.81095i) q^{96} +(-0.481692 - 2.42163i) q^{97} +(-4.12764 - 4.12764i) q^{98} +(11.0040 - 7.37724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

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