LMFDB - Embedded newform 51.2.i.a.29.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(5,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	51.29
Dual form			51.2.i.a.44.3

$q$-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} +(-2.89232 - 2.93845i) q^{17} +(-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} +(-3.18339 - 1.34821i) q^{34} +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} +(-5.09342 + 5.00571i) q^{51} +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} +(5.34735 + 0.0423104i) q^{68} +(-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} +(2.82024 - 1.85232i) q^{85} +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 + 96 * q^34 + 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 - 40 * q^51 - 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 $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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	−0.0916024	−	0.995796i	$-0.529199\pi$
$2$	0.774648	−	0.320870i	0.547759	−	0.226889i	0.639361	+	0.768907i	$0.279199\pi$
$3$	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	$-0.996077\pi$
$5$	−0.159652	+	0.802626i	−0.0713987	+	0.358945i	0.928525	+	0.371269i	$0.121077\pi$
$6$	−0.554726	−	1.34216i	−0.226466	−	0.547934i
$7$	0.191449	−	0.0380817i	0.0723611	−	0.0143935i	−0.158777	−	0.987314i	$-0.550755\pi$
$7$	0.191449	−	0.0380817i	0.0723611	−	0.0143935i	0.231138	+	0.972921i	$0.425755\pi$
$8$	−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	$-0.0806157\pi$
$11$	3.67179	+	2.45341i	1.10709	+	0.739731i	0.138986	+	0.990294i	$0.455616\pi$
$12$	1.58722	+	1.58968i	0.458191	+	0.458900i
$13$	−3.75023	−	3.75023i	−1.04013	−	1.04013i	−0.999161	−	0.0409655i	$-0.986957\pi$
$13$	−3.75023	−	3.75023i	−1.04013	−	1.04013i	−0.0409655	−	0.999161i	$-0.513043\pi$
$14$	0.136087	−	0.0909302i	0.0363707	−	0.0243021i
$15$	1.38998	+	0.277599i	0.358890	+	0.0716759i
$16$		−	0.276039i		−	0.0690098i
$17$	−2.89232	−	2.93845i	−0.701490	−	0.712679i
$17$	−2.89232	−	2.93845i	−0.701490	−	0.712679i
$18$	−2.32543	+	0.959018i	−0.548109	+	0.226043i
$19$	0.210831	+	0.508991i	0.0483680	+	0.116771i	0.946217	−	0.323533i	$-0.104871\pi$
$19$	0.210831	+	0.508991i	0.0483680	+	0.116771i	−0.897849	+	0.440304i	$0.854871\pi$
$20$	−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	$-0.670608\pi$
$23$	2.29752	−	3.43849i	0.479067	−	0.716974i	0.989753	+	0.142793i	$0.0456084\pi$
$24$	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	$-0.419200\pi$
$29$	0.606965	+	0.120733i	0.112711	+	0.0224195i	−0.138413	+	0.990375i	$0.544200\pi$
$30$	1.16581	−	0.230959i	0.212848	−	0.0421672i
$31$	0.369997	+	0.553739i	0.0664533	+	0.0994545i	0.863208	−	0.504849i	$-0.168452\pi$
$31$	0.369997	+	0.553739i	0.0664533	+	0.0994545i	−0.796755	+	0.604303i	$0.793452\pi$
$32$	−2.20436	−	5.32181i	−0.389680	−	0.940771i
$33$	4.25434	−	6.35644i	0.740586	−	1.10651i
$34$	−3.18339	−	1.34821i	−0.545947	−	0.231216i
$35$			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	$-0.635880\pi$
$37$	1.63319	−	1.09126i	0.268495	−	0.179402i	0.682528	+	0.730859i	$0.260880\pi$
$38$	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	0.887965	+	0.459911i	$0.152119\pi$
$41$	1.55975	+	7.84141i	0.243592	+	1.22462i	−0.644373	+	0.764712i	$0.722881\pi$
$42$	−0.157314	−	0.235831i	−0.0242740	−	0.0363895i
$43$	−2.95422	+	7.13212i	−0.450514	+	1.08764i	0.521613	+	0.853182i	$0.325331\pi$
$43$	−2.95422	+	7.13212i	−0.450514	+	1.08764i	−0.972127	+	0.234455i	$0.924669\pi$
$44$	−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	0.0300900	−	0.999547i	$-0.490421\pi$
$47$	7.05884	−	7.05884i	1.02964	−	1.02964i	0.999547	−	0.0300900i	$-0.00957939\pi$
$48$	−0.478114		0.000369245i	−0.0690098		5.32959e-5i
$49$	−6.43195	+	2.66420i	−0.918851	+	0.380600i
$50$	3.63084			0.513479
$51$	−5.09342	+	5.00571i	−0.713221	+	0.700939i
$52$	6.87860			0.953891
$53$	−10.7049	+	4.43410i	−1.47043	+	0.609071i	−0.966957	−	0.254941i	$-0.917944\pi$
$53$	−10.7049	+	4.43410i	−1.47043	+	0.609071i	−0.503471	+	0.864012i	$0.667944\pi$
$54$	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	−0.930226	−	0.366988i	$-0.880389\pi$
$59$	−0.0995233	+	0.240270i	−0.0129568	+	0.0312805i	0.917269	+	0.398269i	$0.130389\pi$
$60$	−1.52932	+	1.02015i	−0.197434	+	0.131701i
$61$	−2.05830	−	10.3478i	−0.263539	−	1.32490i	−0.855026	−	0.518584i	$-0.826459\pi$
$61$	−2.05830	−	10.3478i	−0.263539	−	1.32490i	0.591488	−	0.806314i	$-0.298541\pi$
$62$	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	$0.107205\pi$
$67$			5.40994i			0.660929i	−0.943818	+	0.330465i	$0.892795\pi$
$68$	5.34735	+	0.0423104i	0.648461	+	0.00513089i
$69$	−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	$-0.0611554\pi$
$71$	3.61943	+	5.41686i	0.429548	+	0.642864i	−0.552053	+	0.833809i	$0.686155\pi$
$72$	3.18552	−	7.65705i	0.375417	−	0.902392i
$73$	11.3822	+	2.26406i	1.33218	+	0.264988i	0.809290	−	0.587409i	$-0.199852\pi$
$73$	11.3822	+	2.26406i	1.33218	+	0.264988i	0.522895	+	0.852397i	$0.324852\pi$
$74$	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	−0.322266	−	0.946649i	$-0.604444\pi$
$79$	6.00531	−	8.98758i	0.675650	−	1.01118i	0.997916	−	0.0645322i	$-0.0205555\pi$
$80$	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	0.971229	−	0.238149i	$-0.0765408\pi$
$83$	1.05744	+	2.55289i	0.116069	+	0.280216i	−0.855159	+	0.518365i	$0.826541\pi$
$84$	0.364410	+	0.243898i	0.0397604	+	0.0266115i
$85$	2.82024	−	1.85232i	0.305898	−	0.200912i
$86$			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	0.483503	−	0.875343i	$-0.339364\pi$
$89$	−3.69661	−	3.69661i	−0.391839	−	0.391839i	−0.875343	+	0.483503i	$0.839364\pi$
$90$	−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	$-0.897495\pi$
$97$	0.481692	−	2.42163i	0.0489084	−	0.245879i	0.997504	+	0.0706120i	$0.0224952\pi$
$98$	−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	$0.609731\pi$
$102$	−2.33942	+	5.51198i	−0.231638	+	0.545768i
$103$	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	−0.922402	−	0.386232i	$-0.873776\pi$
$107$	0.802606	−	4.03497i	0.0775909	−	0.390076i	0.999993	−	0.00384387i	$-0.00122355\pi$
$108$	−4.75429	−	4.77637i	−0.457482	−	0.459607i
$109$	−12.4053	+	2.46757i	−1.18821	+	0.236350i	−0.749332	−	0.662195i	$-0.769625\pi$
$109$	−12.4053	+	2.46757i	−1.18821	+	0.236350i	−0.438881	+	0.898545i	$0.644625\pi$
$110$	−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	$-0.293980\pi$
$113$	1.02794	+	0.686845i	0.0967001	+	0.0646130i	−0.506280	+	0.862369i	$0.668980\pi$
$114$	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
$119$	−0.665634	−	0.452421i	−0.0610185	−	0.0414734i
$120$	−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	−0.0110047	−	0.999939i	$-0.503503\pi$
$127$	−8.17992	−	3.38823i	−0.725850	−	0.300657i	−0.714845	+	0.699282i	$0.753503\pi$
$128$	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	$-0.578820\pi$
$131$	−9.64343	−	1.91820i	−0.842551	−	0.167594i	−0.597452	+	0.801904i	$0.703820\pi$
$132$	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
$136$	10.5645	−	4.27836i	0.905901	−	0.366866i
$137$		−	12.6644i		−	1.08200i	−0.841024	−	0.540998i	$-0.818047\pi$
$137$		−	12.6644i		−	1.08200i	0.841024	−	0.540998i	$-0.181953\pi$
$138$	−5.88949	−	1.17622i	−0.501347	−	0.100127i
$139$	9.89935	−	6.61453i	0.839652	−	0.561038i	−0.0597233	−	0.998215i	$-0.519022\pi$
$139$	9.89935	−	6.61453i	0.839652	−	0.561038i	0.899375	+	0.437177i	$0.144022\pi$
$140$	−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	−0.971754	−	0.235998i	$-0.924164\pi$
$149$	−8.98104	+	8.98104i	−0.735756	+	0.735756i	0.235998	+	0.971754i	$0.424164\pi$
$150$	0.00485680	−	6.28880i	0.000396556	−	0.513478i
$151$	0.732249	−	0.303307i	0.0595895	−	0.0246828i	−0.352690	−	0.935740i	$-0.614733\pi$
$151$	0.732249	−	0.303307i	0.0595895	−	0.0246828i	0.412279	+	0.911058i	$0.364733\pi$
$152$	−1.52299			−0.123531
$153$	8.66332	+	8.82875i	0.700388	+	0.713762i
$154$	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	−0.770516	−	0.637421i	$-0.780001\pi$
$157$	−1.66767	+	1.66767i	−0.133095	+	0.133095i	0.637421	+	0.770516i	$0.280001\pi$
$158$	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	−0.883515	−	0.468403i	$-0.844830\pi$
$163$	−3.14715	−	15.8218i	−0.246504	−	1.23926i	0.637012	−	0.770854i	$-0.280170\pi$
$164$	−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	$-0.802917\pi$
$167$	−7.62247	+	5.09317i	−0.589844	+	0.394121i	0.224525	+	0.974468i	$0.427917\pi$
$168$	0.916539	+	0.183047i	0.0707125	+	0.0141224i
$169$			15.1284i			1.16372i
$170$	1.59034	−	2.33983i	0.121974	−	0.179456i
$171$	−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	$-0.201610\pi$
$173$	−0.647630	−	0.969247i	−0.0492384	−	0.0736905i	−0.855272	+	0.518179i	$0.826610\pi$
$174$	−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	0.708476	−	0.705735i	$-0.249383\pi$
$179$	9.50468	+	3.93697i	0.710413	+	0.294263i	0.00193768	+	0.999998i	$0.499383\pi$
$180$	1.76491	+	2.65022i	0.131548	+	0.197536i
$181$	−7.15635	+	10.7102i	−0.531928	+	0.796086i	−0.995966	−	0.0897290i	$-0.971400\pi$
$181$	−7.15635	+	10.7102i	−0.531928	+	0.796086i	0.464039	+	0.885815i	$0.346400\pi$
$182$	−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
$187$	−3.41075	−	17.8854i	−0.249419	−	1.30791i
$188$			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	0.990296	−	0.138977i	$-0.0443814\pi$
$191$	11.7655	+	11.7655i	0.851319	+	0.851319i	−0.138977	+	0.990296i	$0.544381\pi$
$192$	−5.24321	+	5.23512i	−0.378396	+	0.377812i
$193$	−2.47380	−	1.65294i	−0.178068	−	0.118981i	0.463342	−	0.886180i	$-0.346650\pi$
$193$	−2.47380	−	1.65294i	−0.178068	−	0.118981i	−0.641410	+	0.767198i	$0.721650\pi$
$194$	−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	$-0.401908\pi$
$197$	13.3085	−	2.64722i	0.948190	−	0.188607i	0.644879	+	0.764285i	$0.276908\pi$
$198$	−10.8914	−	2.18392i	−0.774015	−	0.155204i
$199$	−0.839234	+	4.21912i	−0.0594917	+	0.299085i	−0.999064	−	0.0432667i	$-0.986223\pi$
$199$	−0.839234	+	4.21912i	−0.0594917	+	0.299085i	0.939572	+	0.342352i	$0.111223\pi$
$200$	−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
$204$	0.0804367	−	9.26182i	0.00563169	−	0.648457i
$205$	−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	$-0.741989\pi$
$211$	−15.2290	+	3.02923i	−1.04840	+	0.208541i	−0.359314	+	0.933217i	$0.616989\pi$
$212$	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
$221$	−0.173018	+	21.8667i	−0.0116385	+	1.47091i
$222$	−2.37062	−	1.58665i	−0.159106	−	0.106489i
$223$	6.37645	+	15.3941i	0.426999	+	1.03087i	0.980234	+	0.197841i	$0.0633931\pi$
$223$	6.37645	+	15.3941i	0.426999	+	1.03087i	−0.553235	+	0.833025i	$0.686607\pi$
$224$	−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	0.284827	+	0.958579i	$0.408064\pi$
$227$	−10.6940	+	16.0046i	−0.709783	+	1.06227i	−0.994610	+	0.103687i	$0.966936\pi$
$228$	−0.474495	+	1.14303i	−0.0314242	+	0.0756993i
$229$	10.1448	+	4.20213i	0.670391	+	0.277685i	0.691803	−	0.722086i	$-0.256816\pi$
$229$	10.1448	+	4.20213i	0.670391	+	0.277685i	−0.0214129	+	0.999771i	$0.506816\pi$
$230$	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	$-0.158089\pi$
$233$	23.0354	+	4.58203i	1.50910	+	0.300179i	0.629917	+	0.776662i	$0.283089\pi$
$234$	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
$238$	−0.660800	−	0.136885i	−0.0428333	−	0.00887295i
$239$		−	13.7217i		−	0.887582i	−0.896130	−	0.443791i	$-0.853633\pi$
$239$		−	13.7217i		−	0.887582i	0.896130	−	0.443791i	$-0.146367\pi$
$240$	0.0766283	−	0.383688i	0.00494634	−	0.0247669i
$241$	3.55549	−	2.37570i	0.229029	−	0.153032i	−0.435761	−	0.900062i	$-0.643521\pi$
$241$	3.55549	−	2.37570i	0.229029	−	0.153032i	0.664790	+	0.747030i	$0.268521\pi$
$242$	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	−0.468609	−	0.883406i	$-0.655245\pi$
$251$	6.57161	−	6.57161i	0.414796	−	0.414796i	0.883406	+	0.468609i	$0.155245\pi$
$252$	0.422932	−	0.630851i	0.0266422	−	0.0397398i
$253$	16.8721	−	6.98863i	1.06074	−	0.439372i
$254$	−7.42374			−0.465807
$255$	−3.20454	−	4.88728i	−0.200676	−	0.306053i
$256$	15.2078			0.950486
$257$	−14.5315	+	6.01912i	−0.906447	+	0.375463i	−0.786696	−	0.617341i	$-0.788210\pi$
$257$	−14.5315	+	6.01912i	−0.906447	+	0.375463i	−0.119752	+	0.992804i	$0.538210\pi$
$258$	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	−0.630264	−	0.776381i	$-0.717053\pi$
$263$	5.90932	−	14.2664i	0.364384	−	0.879701i	0.994648	−	0.103320i	$-0.0329466\pi$
$264$	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	$-0.421395\pi$
$269$	20.2365	−	13.5216i	1.23384	−	0.824426i	0.989397	+	0.145237i	$0.0463945\pi$
$270$	−3.49851	+	0.687475i	−0.212913	+	0.0418384i
$271$		−	5.62528i		−	0.341711i	−0.985296	−	0.170856i	$-0.945347\pi$
$271$		−	5.62528i		−	0.341711i	0.985296	−	0.170856i	$-0.0546532\pi$
$272$	−0.811128	+	0.798393i	−0.0491819	+	0.0484097i
$273$	−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	$-0.523302\pi$
$277$	−8.69401	−	1.72935i	−0.522373	−	0.103906i	−0.449232	+	0.893415i	$0.648302\pi$
$278$	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	0.174794	−	0.984605i	$-0.444074\pi$
$281$	−6.66883	−	2.76232i	−0.397829	−	0.164786i	−0.572623	+	0.819819i	$0.694074\pi$
$282$	−13.3898	−	5.55836i	−0.797351	−	0.330995i
$283$	2.74547	−	4.10889i	0.163201	−	0.244248i	−0.740851	−	0.671669i	$-0.765578\pi$
$283$	2.74547	−	4.10889i	0.163201	−	0.244248i	0.904053	+	0.427421i	$0.140578\pi$
$284$	−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
$289$	−0.269005	+	16.9979i	−0.0158238	+	0.999875i
$290$			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	0.192192	−	0.981357i	$-0.438440\pi$
$293$	−13.5083	−	13.5083i	−0.789165	−	0.789165i	−0.981357	+	0.192192i	$0.938440\pi$
$294$	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
$306$	9.54391	+	4.05937i	0.545589	+	0.232059i
$307$	−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	0.878717	+	0.477343i	$0.158400\pi$
$311$	−2.04185	+	10.2651i	−0.115783	+	0.582080i	−0.994500	+	0.104737i	$0.966600\pi$
$312$	−9.69986	−	23.4688i	−0.549146	−	1.32866i
$313$	23.5532	−	4.68503i	1.33131	−	0.264814i	0.522375	−	0.852716i	$-0.325046\pi$
$313$	23.5532	−	4.68503i	1.33131	−	0.264814i	0.808932	+	0.587902i	$0.200046\pi$
$314$	−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	$-0.401582\pi$
$317$	−8.17832	−	5.46458i	−0.459340	−	0.306921i	−0.763625	+	0.645660i	$0.776582\pi$
$318$	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
$323$	0.885856	−	2.09168i	0.0492904	−	0.116384i
$324$	−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	0.273512	−	0.961869i	$-0.411815\pi$
$331$	−3.87936	−	1.60689i	−0.213229	−	0.0883224i	−0.486741	+	0.873546i	$0.661815\pi$
$332$	−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	$-0.237870\pi$
$337$	−3.21434	−	4.81060i	−0.175096	−	0.262050i	−0.908629	+	0.417604i	$0.862870\pi$
$338$	4.85425	+	11.7192i	0.264036	+	0.637440i
$339$	1.19103	−	1.77952i	0.0646876	−	0.0966502i
$340$	−0.887676	+	4.28517i	−0.0481410	+	0.232396i
$341$			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	$-0.0623382\pi$
$347$	0.00369437	+	0.0185728i	0.000198324	+	0.000997042i	−0.980686	+	0.195589i	$0.937338\pi$
$348$	0.771462	+	1.15651i	0.0413547	+	0.0619953i
$349$	2.37825	−	5.74159i	0.127305	−	0.307340i	−0.847358	−	0.531023i	$-0.821808\pi$
$349$	2.37825	−	5.74159i	0.127305	−	0.307340i	0.974662	+	0.223682i	$0.0718078\pi$
$350$	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	−0.439781	−	0.898105i	$-0.644944\pi$
$353$	8.61113	−	8.61113i	0.458324	−	0.458324i	0.898105	+	0.439781i	$0.144944\pi$
$354$	0.377689		0.000291687i	0.0200740		1.55030e-5i
$355$	−4.92557	+	2.04024i	−0.261422	+	0.108285i
$356$	6.78025			0.359352
$357$	−0.784506	+	1.15231i	−0.0415205	+	0.0609865i
$358$	8.62604			0.455900
$359$	29.4053	−	12.1801i	1.55195	−	0.642840i	0.568284	−	0.822832i	$-0.307607\pi$
$359$	29.4053	−	12.1801i	1.55195	−	0.642840i	0.983668	+	0.179992i	$0.0576073\pi$
$360$	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	0.641359	+	0.767241i	$0.278371\pi$
$367$	6.56004	+	32.9795i	0.342431	+	1.72152i	−0.298928	+	0.954276i	$0.596629\pi$
$368$	−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	$0.129425\pi$
$373$			15.2764i			0.790981i	−0.918470	+	0.395490i	$0.870575\pi$
$374$	−8.38102	−	12.7605i	−0.433372	−	0.659830i
$375$	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	$-0.00682782\pi$
$379$	37.2855	+	7.41655i	1.91523	+	0.380963i	0.915459	+	0.402411i	$0.131828\pi$
$380$	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	−0.631465	−	0.775404i	$-0.717546\pi$
$383$	−31.8268	−	13.1831i	−1.62627	−	0.673624i	−0.994807	+	0.101781i	$0.967546\pi$
$384$	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	0.916389	−	0.400290i	$-0.131091\pi$
$389$	−0.288821	−	0.697275i	−0.0146438	−	0.0353532i	−0.931032	+	0.364937i	$0.881091\pi$
$390$	−5.23822	−	3.50592i	−0.265248	−	0.177529i
$391$	−16.7490	+	3.19403i	−0.847033	+	0.161529i
$392$		−	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	$-0.481218\pi$
$397$	−16.7515	−	11.1930i	−0.840734	−	0.561761i	−0.899705	+	0.436499i	$0.856218\pi$
$398$	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	$-0.433687\pi$
$401$	15.4656	−	3.07630i	0.772315	−	0.153623i	0.565490	+	0.824755i	$0.308687\pi$
$402$	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
$408$	−7.39620	−	18.3040i	−0.366167	−	0.906185i
$409$	−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	0.998506	+	0.0546430i	$0.0174021\pi$
$419$	29.2939	+	19.5736i	1.43110	+	0.956231i	0.432595	+	0.901588i	$0.357598\pi$
$420$	−0.253938	+	0.253546i	−0.0123909	+	0.0123718i
$421$	−0.00892902	−	0.00892902i	−0.000435174	−	0.000435174i	0.706889	−	0.707324i	$-0.250098\pi$
$421$	−0.00892902	−	0.00892902i	−0.000435174	−	0.000435174i	−0.707324	+	0.706889i	$0.750098\pi$
$422$	−10.8251	+	7.23309i	−0.526957	+	0.352102i
$423$	−21.2092	+	21.1438i	−1.03123	+	1.02805i
$424$		−	32.0309i		−	1.55556i
$425$	−6.70182	−	16.5488i	−0.325086	−	0.802733i
$426$	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	$-0.720318\pi$
$431$	6.58741	−	9.85875i	0.317304	−	0.474879i	0.955499	+	0.294996i	$0.0953183\pi$
$432$	1.43434	+	0.00332320i	0.0690096	+	0.000159887i
$433$	−0.501414	−	0.207692i	−0.0240964	−	0.00998106i	0.370603	−	0.928791i	$-0.379151\pi$
$433$	−0.501414	−	0.207692i	−0.0240964	−	0.00998106i	−0.394699	+	0.918810i	$0.629151\pi$
$434$	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	−0.974924	−	0.222540i	$-0.928565\pi$
$439$	−16.9177	−	25.3191i	−0.807436	−	1.20841i	0.167487	−	0.985874i	$-0.446435\pi$
$440$	−3.82308	−	9.22974i	−0.182258	−	0.440010i
$441$	19.3082	−	7.96279i	0.919437	−	0.379181i
$442$	6.88234	+	16.9945i	0.327359	+	0.808347i
$443$			40.2451i			1.91210i	0.293203	+	0.956050i	$0.405279\pi$
$443$			40.2451i			1.91210i	−0.293203	+	0.956050i	$0.594721\pi$
$444$	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	0.668604	+	0.743619i	$0.266892\pi$
$449$	7.10838	+	35.7362i	0.335465	+	1.68650i	−0.333139	+	0.942878i	$0.608108\pi$
$450$	−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	−0.792318	−	0.610108i	$-0.791126\pi$
$457$	−19.6921	+	8.15675i	−0.921160	+	0.381557i	−0.128842	+	0.991665i	$0.541126\pi$
$458$	9.20703			0.430216
$459$	15.3034	−	14.9935i	0.714303	−	0.699837i
$460$	−4.38923			−0.204649
$461$	5.67952	−	2.35253i	0.264521	−	0.109568i	−0.246481	−	0.969148i	$-0.579274\pi$
$461$	5.67952	−	2.35253i	0.264521	−	0.109568i	0.511002	+	0.859579i	$0.329274\pi$
$462$	0.000966816	−	1.25188i	4.49804e−5	−	0.0582425i
$463$	25.6637	−	25.6637i	1.19270	−	1.19270i	0.216388	−	0.976307i	$-0.430572\pi$
$463$	25.6637	−	25.6637i	1.19270	−	1.19270i	0.976307	−	0.216388i	$-0.0694277\pi$
$464$	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	−0.977228	−	0.212190i	$-0.931940\pi$
$467$	−2.94293	+	7.10485i	−0.136182	+	0.328773i	0.841046	+	0.540964i	$0.181940\pi$
$468$	−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
$476$	1.02536	−	0.195536i	0.0469972	−	0.00896236i
$477$	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	$-0.204204\pi$
$479$	−1.27558	−	1.90904i	−0.0582826	−	0.0872260i	−0.859466	+	0.511192i	$0.829204\pi$
$480$	−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	0.288118	+	0.957595i	$0.406970\pi$
$487$	−15.5987	+	23.3450i	−0.706842	+	1.05786i	−0.994960	+	0.100269i	$0.968030\pi$
$488$	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	0.763035	−	0.646357i	$-0.223709\pi$
$491$	−5.17526	−	12.4942i	−0.233556	−	0.563854i	−0.996591	+	0.0825033i	$0.973709\pi$
$492$	−9.98962	+	14.9256i	−0.450367	+	0.672896i
$493$	−1.40077	−	2.13273i	−0.0630874	−	0.0960535i
$494$		−	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	$-0.423254\pi$
$499$	−12.6659	−	8.46309i	−0.567004	−	0.378860i	−0.805780	+	0.592215i	$0.798254\pi$
$500$	−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	$-0.745538\pi$
$503$	−23.9263	+	4.75924i	−1.06682	+	0.212204i	−0.369696	+	0.929153i	$0.620538\pi$
$504$	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	$0.362715\pi$
$510$	−4.05057	−	2.75768i	−0.179362	−	0.122112i
$511$	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	$-0.569442\pi$
$521$	−27.4188	−	18.3207i	−1.20124	−	0.802643i	−0.984807	+	0.173655i	$0.944442\pi$
$522$	−1.52724	+	0.301335i	−0.0668454	+	0.0131891i
$523$	9.24397	+	9.24397i	0.404211	+	0.404211i	0.879714	−	0.475503i	$-0.157734\pi$
$523$	9.24397	+	9.24397i	0.404211	+	0.404211i	−0.475503	+	0.879714i	$0.657734\pi$
$524$	10.6031	−	7.08475i	0.463197	−	0.309499i
$525$	0.286733	−	1.43571i	0.0125141	−	0.0626594i
$526$		−	12.9475i		−	0.564539i
$527$	0.556988	−	2.68881i	0.0242628	−	0.117126i
$528$	−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	$-0.0707383\pi$
$541$	9.26903	+	13.8721i	0.398507	+	0.596408i	−0.576901	+	0.816814i	$0.695738\pi$
$542$	−1.80498	−	4.35761i	−0.0775306	−	0.187176i
$543$	18.5411	+	12.4095i	0.795675	+	0.532542i
$544$	−9.26215	+	21.8698i	−0.397111	+	0.937658i
$545$		−	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	$-0.613036\pi$
$547$	9.01564	−	6.02406i	0.385481	−	0.257570i	0.733178	+	0.680037i	$0.238036\pi$
$548$	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	−0.500079	−	0.865980i	$-0.666696\pi$
$557$	8.63556	−	8.63556i	0.365900	−	0.365900i	0.865980	+	0.500079i	$0.166696\pi$
$558$	−1.39145	−	0.932847i	−0.0589046	−	0.0394905i
$559$	37.8261	−	15.6681i	1.59987	−	0.662689i
$560$	0.0440951			0.00186336
$561$	−30.9830	+	5.88366i	−1.30810	+	0.248408i
$562$	−6.05234			−0.255302
$563$	−21.7414	+	9.00559i	−0.916292	+	0.379541i	−0.790462	−	0.612511i	$-0.790159\pi$
$563$	−21.7414	+	9.00559i	−0.916292	+	0.379541i	−0.125830	+	0.992052i	$0.540159\pi$
$564$	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	−0.938209	−	0.346069i	$-0.887516\pi$
$569$	−0.717701	+	1.73268i	−0.0300876	+	0.0726379i	0.908122	+	0.418707i	$0.137516\pi$
$570$	0.363346	+	0.544696i	0.0152189	+	0.0228148i
$571$	7.81421	+	39.2847i	0.327014	+	1.64401i	0.698526	+	0.715584i	$0.253839\pi$
$571$	7.81421	+	39.2847i	0.327014	+	1.64401i	−0.371512	+	0.928428i	$0.621161\pi$
$572$	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	$-0.769357\pi$
$577$		−	31.8433i		−	1.32565i	0.748773	−	0.662826i	$-0.230643\pi$
$578$	5.24572	+	13.2537i	0.218193	+	0.551281i
$579$	−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	0.609673	−	0.792653i	$-0.291301\pi$
$587$	11.6364	+	4.81996i	0.480286	+	0.198941i	−0.129387	+	0.991594i	$0.541301\pi$
$588$	−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	0.710357	−	0.703841i	$-0.248533\pi$
$593$	−7.05301	−	17.0275i	−0.289632	−	0.699234i	−0.999989	+	0.00460731i	$0.998533\pi$
$594$	−3.79722	+	18.8614i	−0.155802	+	0.773895i
$595$	0.469395	−	0.462025i	0.0192433	−	0.0189412i
$596$		−	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	0.406937	−	0.913456i	$-0.366597\pi$
$599$	−12.3968	−	12.3968i	−0.506519	−	0.506519i	−0.913456	+	0.406937i	$0.866597\pi$
$600$	14.6498	+	14.6724i	0.598075	+	0.599000i
$601$	−11.2873	−	7.54195i	−0.460419	−	0.307642i	0.303642	−	0.952786i	$-0.401797\pi$
$601$	−11.2873	−	7.54195i	−0.460419	−	0.307642i	−0.764061	+	0.645144i	$0.776797\pi$
$602$	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	$-0.964253\pi$
$607$	−0.807003	+	4.05708i	−0.0327552	+	0.164672i	0.960946	+	0.276737i	$0.0892532\pi$
$608$	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
$612$	−16.0418	−	0.151709i	−0.648453	−	0.00613249i
$613$	−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	−0.897792	−	0.440420i	$-0.854830\pi$
$617$	2.48894	−	12.5128i	0.100201	−	0.503745i	0.997993	−	0.0633250i	$-0.0201705\pi$
$618$	−1.37441	−	3.32537i	−0.0552867	−	0.133766i
$619$	−3.81263	+	0.758379i	−0.153243	+	0.0304818i	−0.271115	−	0.962547i	$-0.587392\pi$
$619$	−3.81263	+	0.758379i	−0.153243	+	0.0304818i	0.117873	+	0.993029i	$0.462392\pi$
$620$	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
$629$	−7.93033	−	1.64277i	−0.316203	−	0.0655017i
$630$	−0.153196	−	0.371469i	−0.00610346	−	0.0147997i
$631$	−13.4198	−	32.3983i	−0.534234	−	1.28976i	−0.928696	−	0.370843i	$-0.879069\pi$
$631$	−13.4198	−	32.3983i	−0.534234	−	1.28976i	0.394461	−	0.918913i	$-0.370931\pi$
$632$	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	$-0.423436\pi$
$641$	2.19355	+	0.436325i	0.0866402	+	0.0172338i	−0.151580	+	0.988445i	$0.548436\pi$
$642$	−5.86080	+	1.16108i	−0.231307	+	0.0458242i
$643$	2.03342	+	3.04323i	0.0801904	+	0.120013i	0.869397	−	0.494115i	$-0.164508\pi$
$643$	2.03342	+	3.04323i	0.0801904	+	0.120013i	−0.789206	+	0.614128i	$0.789508\pi$
$644$	0.400653	+	0.967262i	0.0157879	+	0.0381155i
$645$	−6.08617	+	9.09338i	−0.239643	+	0.358051i
$646$	0.0150697	−	1.90456i	0.000592908	−	0.0749340i
$647$			28.3391i			1.11413i	0.830470	+	0.557063i	$0.188072\pi$
$647$			28.3391i			1.11413i	−0.830470	+	0.557063i	$0.811928\pi$
$648$	−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	0.999990	+	0.00447157i	$0.00142335\pi$
$653$	1.98888	+	9.99878i	0.0778309	+	0.391282i	−0.922159	+	0.386811i	$0.873577\pi$
$654$	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	−0.0789501	+	0.996879i	$0.525157\pi$
$659$	−27.6176	+	27.6176i	−1.07583	+	1.07583i	−0.996879	+	0.0789501i	$0.974843\pi$
$660$	−8.11819	−	0.00626963i	−0.316000	−	0.000244045i
$661$	1.89254	−	0.783917i	0.0736114	−	0.0304909i	−0.345574	−	0.938392i	$-0.612316\pi$
$661$	1.89254	−	0.783917i	0.0736114	−	0.0304909i	0.419185	+	0.907901i	$0.362316\pi$
$662$	−3.52074			−0.136838
$663$	37.8740	+	0.328927i	1.47090	+	0.0127745i
$664$	−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	−0.990553	−	0.137129i	$-0.956213\pi$
$673$	−3.31745	−	16.6779i	−0.127878	−	0.642887i	0.862675	−	0.505759i	$-0.168787\pi$
$674$	−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	$-0.549148\pi$
$677$	18.2198	−	12.1741i	0.700245	−	0.467889i	0.854035	+	0.520215i	$0.174148\pi$
$678$	0.351632	−	1.76066i	0.0135043	−	0.0676179i
$679$		−	0.481963i		−	0.0184960i
$680$	1.74727	+	9.16242i	0.0670048	+	0.351363i
$681$	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	−0.984044	−	0.177923i	$-0.943062\pi$
$683$	−20.1716	−	30.1890i	−0.771847	−	1.15515i	0.212198	−	0.977227i	$-0.431938\pi$
$684$	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	$-0.795089\pi$
$691$	1.59686	−	2.38987i	0.0607475	−	0.0909151i	0.860600	+	0.509282i	$0.170089\pi$
$692$	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
$697$	18.5303	−	27.2631i	0.701885	−	1.03266i
$698$		−	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	0.630142	−	0.776480i	$-0.282997\pi$
$701$	−3.87452	−	3.87452i	−0.146339	−	0.146339i	−0.776480	+	0.630142i	$0.782997\pi$
$702$	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	0.557463	+	0.830202i	$0.311775\pi$
$709$	−7.32963	+	36.8486i	−0.275270	+	1.38388i	−0.832733	+	0.553675i	$0.813225\pi$
$710$	−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
$714$	−0.237976	+	1.14436i	−0.00890603	+	0.0428264i
$715$	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	0.782225	+	0.622996i	$0.214085\pi$
$719$	−4.79617	+	24.1120i	−0.178867	+	0.899225i	−0.961092	+	0.276229i	$0.910915\pi$
$720$	−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	0.999942	−	0.0107310i	$-0.00341584\pi$
$727$	26.6720	+	26.6720i	0.989211	+	0.989211i	−0.0107310	+	0.999942i	$0.503416\pi$
$728$	2.37959	−	1.58999i	0.0881935	−	0.0589290i
$729$	−26.9997	−	0.125111i	−0.999989	−	0.00463375i
$730$			7.96307i			0.294726i
$731$	29.5019	−	11.9475i	1.09117	−	0.441895i
$732$	13.1826	−	19.6963i	0.487244	−	0.727995i
$733$	7.27415	+	17.5613i	0.268677	+	0.648643i	0.999422	−	0.0340076i	$-0.0108270\pi$
$733$	7.27415	+	17.5613i	0.268677	+	0.648643i	−0.730745	+	0.682651i	$0.760827\pi$
$734$	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	−0.331742	−	0.943370i	$-0.607636\pi$
$739$	−33.5289	−	13.8881i	−1.23338	−	0.510884i	−0.901640	+	0.432487i	$0.857636\pi$
$740$	−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	$-0.438541\pi$
$743$	−0.174867	−	0.0347832i	−0.00641525	−	0.00127607i	−0.198297	+	0.980142i	$0.563541\pi$
$744$	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
$748$	19.5305	+	13.2746i	0.714107	+	0.485368i
$749$		−	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	$-0.443770\pi$
$751$	31.5832	−	21.1032i	1.15249	−	0.770067i	0.976752	+	0.214371i	$0.0687701\pi$
$752$	−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	−0.999324	−	0.0367531i	$-0.988299\pi$
$757$	−7.33808	+	17.7157i	−0.266707	+	0.643888i	0.732617	+	0.680641i	$0.238299\pi$
$758$	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	−0.982213	−	0.187770i	$-0.939874\pi$
$761$	−21.9157	+	21.9157i	−0.794443	+	0.794443i	0.187770	+	0.982213i	$0.439874\pi$
$762$	−0.00993038	+	12.8583i	−0.000359740	+	0.465807i
$763$	−2.28102	+	0.944829i	−0.0825785	+	0.0342051i
$764$	−21.5800			−0.780737
$765$	−8.46930	+	5.54388i	−0.306208	+	0.200439i
$766$	−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	−0.902881	−	0.429891i	$-0.858552\pi$
$769$	−13.1164	+	13.1164i	−0.472990	+	0.472990i	0.429891	+	0.902881i	$0.358552\pi$
$770$	−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	0.342017	+	0.939694i	$0.388890\pi$
$773$	−15.6889	+	37.8763i	−0.564289	+	1.36232i	−0.906306	+	0.422621i	$0.861110\pi$
$774$	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
$782$	−11.9497	+	7.84850i	−0.427321	+	0.280662i
$783$	−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	$-0.523862\pi$
$787$	−14.7477	−	2.93350i	−0.525700	−	0.104568i	−0.450804	+	0.892623i	$0.648862\pi$
$788$	−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	0.994894	−	0.100922i	$-0.0321794\pi$
$797$	6.21185	+	14.9967i	0.220035	+	0.531211i	−0.774859	+	0.632134i	$0.782179\pi$
$798$	0.0868691	−	0.129792i	0.00307513	−	0.00459458i
$799$	−41.1585	−	0.325663i	−1.45608	−	0.0115211i
$800$		−	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	$-0.330972\pi$
$809$	37.0970	−	7.37905i	1.30426	−	0.259434i	0.797848	+	0.602858i	$0.205972\pi$
$810$	1.18606	+	6.06052i	0.0416739	+	0.212945i
$811$	6.74744	−	33.9217i	0.236935	−	1.19115i	−0.660782	−	0.750578i	$-0.729775\pi$
$811$	6.74744	−	33.9217i	0.236935	−	1.19115i	0.897717	−	0.440573i	$-0.145225\pi$
$812$	−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
$816$	1.38177	+	1.40598i	0.0483717	+	0.0492192i
$817$	−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	−0.296813	−	0.954936i	$-0.595924\pi$
$821$	9.82356	−	49.3864i	0.342845	−	1.72360i	0.639657	−	0.768660i	$-0.279076\pi$
$822$	−16.9977	+	7.02529i	−0.592862	+	0.245035i
$823$	−23.4287	+	4.66026i	−0.816674	+	0.162447i	−0.585715	−	0.810517i	$-0.699186\pi$
$823$	−23.4287	+	4.66026i	−0.816674	+	0.162447i	−0.230959	+	0.972963i	$0.574186\pi$
$824$	−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	$-0.275246\pi$
$827$	5.58417	+	3.73122i	0.194181	+	0.129747i	−0.454679	+	0.890655i	$0.650246\pi$
$828$	−3.11472	−	15.7862i	−0.108244	−	0.548607i
$829$	17.6880	+	17.6880i	0.614331	+	0.614331i	0.944072	−	0.329741i	$-0.106961\pi$
$829$	17.6880	+	17.6880i	0.614331	+	0.614331i	−0.329741	+	0.944072i	$0.606961\pi$
$830$	−1.57649	+	1.05338i	−0.0547208	+	0.0365632i
$831$	−3.00694	+	15.0562i	−0.104310	+	0.522292i
$832$			22.6876i			0.786552i
$833$	26.4319	+	11.1943i	0.915810	+	0.387859i
$834$	−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	0.117895	+	0.993026i	$0.462385\pi$
$839$	−24.4659	+	36.6159i	−0.844658	+	1.26412i	−0.962553	+	0.271094i	$0.912615\pi$
$840$	−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
$850$	−10.5015	−	10.6691i	−0.360200	−	0.365946i
$851$		−	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	$-0.874417\pi$
$853$	−26.9089	+	17.9800i	−0.921344	+	0.615623i	0.00183231	+	0.999998i	$0.499417\pi$
$854$	−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	−0.971095	−	0.238693i	$-0.923281\pi$
$857$	−4.83803	−	24.3224i	−0.165264	−	0.830838i	0.805831	−	0.592145i	$-0.201719\pi$
$858$	−28.2959	+	18.8751i	−0.966007	+	0.644387i
$859$	16.0644	−	38.7830i	0.548112	−	1.32326i	−0.370770	−	0.928725i	$-0.620906\pi$
$859$	16.0644	−	38.7830i	0.548112	−	1.32326i	0.918881	−	0.394534i	$-0.129094\pi$
$860$	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	−0.709626	−	0.704578i	$-0.751136\pi$
$863$	−0.148288	+	0.148288i	−0.00504779	+	0.00504779i	0.704578	+	0.709626i	$0.251136\pi$
$864$	27.6794	−	11.3901i	0.941671	−	0.387499i
$865$	0.881339	−	0.365062i	0.0299664	−	0.0124125i
$866$	−0.455061			−0.0154636
$867$	29.4408	+	0.488668i	0.999862	+	0.0165960i
$868$	−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	$-0.0226541\pi$
$877$	1.44266	+	7.25275i	0.0487152	+	0.244908i	−0.948753	+	0.316018i	$0.897654\pi$
$878$	−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	−0.394790	+	0.918772i	$0.629183\pi$
$881$	−41.3971	+	27.6606i	−1.39470	+	0.931911i	−0.999914	+	0.0131394i	$0.995817\pi$
$882$	12.4020	−	12.3638i	0.417598	−	0.416310i
$883$		−	28.6327i		−	0.963566i	−0.876291	−	0.481783i	$-0.839989\pi$
$883$		−	28.6327i		−	0.963566i	0.876291	−	0.481783i	$-0.160011\pi$
$884$	−19.8951	−	20.2124i	−0.669145	−	0.679818i
$885$	−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	−0.977634	−	0.210315i	$-0.932551\pi$
$887$	−23.7610	−	35.5608i	−0.797816	−	1.19402i	0.179818	−	0.983700i	$-0.442449\pi$
$888$	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
$901$	43.9913	+	18.6309i	1.46556	+	0.620686i
$902$			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	$-0.269374\pi$
$907$	6.76450	+	4.51990i	0.224612	+	0.150081i	−0.438173	+	0.898891i	$0.644374\pi$
$908$	−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	$-0.546860\pi$
$911$	2.90793	−	0.578423i	0.0963440	−	0.0191640i	0.243027	+	0.970020i	$0.421860\pi$
$912$	−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
$918$	7.04381	−	16.5251i	0.232480	−	0.545409i
$919$	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	$-0.465295\pi$
$929$	−23.4065	−	15.6397i	−0.767941	−	0.513122i	−0.876753	+	0.480940i	$0.840295\pi$
$930$	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
$935$	14.8998	+	0.117894i	0.487277	+	0.00385554i
$936$	−40.6621	+	16.7693i	−1.32908	+	0.548120i
$937$	−14.2493	−	34.4010i	−0.465506	−	1.12383i	−0.966105	−	0.258151i	$-0.916887\pi$
$937$	−14.2493	−	34.4010i	−0.465506	−	1.12383i	0.500599	−	0.865679i	$-0.333113\pi$
$938$	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	−0.146249	−	0.989248i	$-0.546720\pi$
$941$	25.2665	−	37.8140i	0.823664	−	1.23270i	0.969913	−	0.243452i	$-0.0782798\pi$
$942$	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	$-0.351392\pi$
$947$	16.1310	+	3.20866i	0.524188	+	0.104267i	0.0740985	+	0.997251i	$0.476392\pi$
$948$	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
$952$	1.85965	−	1.22141i	0.0602715	−	0.0395860i
$953$		−	15.3092i		−	0.495915i	−0.968771	−	0.247958i	$-0.920241\pi$
$953$		−	15.3092i		−	0.495915i	0.968771	−	0.247958i	$-0.0797593\pi$
$954$	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	−0.958527	−	0.285001i	$-0.908006\pi$
$967$	−44.6169	+	18.4809i	−1.43478	+	0.594306i	−0.476255	+	0.879307i	$0.658006\pi$
$968$	−23.5010			−0.755352
$969$	−3.62171	−	1.53715i	−0.116346	−	0.0493802i
$970$	1.69419			0.0543972
$971$	−3.06636	+	1.27013i	−0.0984041	+	0.0407603i	−0.431342	−	0.902188i	$-0.641960\pi$
$971$	−3.06636	+	1.27013i	−0.0984041	+	0.0407603i	0.332938	+	0.942949i	$0.391960\pi$
$972$	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	0.631823	+	0.775113i	$0.282307\pi$
$977$	−11.3473	+	27.3947i	−0.363031	+	0.876434i	−0.994854	+	0.101321i	$0.967693\pi$
$978$	−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	$-0.674803\pi$
$983$	2.07918	−	1.38926i	0.0663155	−	0.0443106i	0.588286	+	0.808653i	$0.299803\pi$
$984$	−7.49726	+	37.5397i	−0.239004	+	1.19672i
$985$			11.1044i			0.353815i
$986$	−1.76943	−	1.20265i	−0.0563502	−	0.0383003i
$987$	−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	$-0.230251\pi$
$991$	37.4243	+	7.44416i	1.18882	+	0.236471i	0.439232	+	0.898374i	$0.355251\pi$
$992$	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	−0.194197	−	0.980963i	$-0.562210\pi$
$997$	24.8311	−	37.1624i	0.786410	−	1.17695i	0.980607	−	0.195984i	$-0.0627899\pi$
$998$	−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	51.2.i.a.29.3	yes	32
3.2	odd	2	inner	51.2.i.a.29.2	✓	32
4.3	odd	2		816.2.cj.c.641.2		32
12.11	even	2		816.2.cj.c.641.1		32
17.2	even	8		867.2.i.i.65.3		32
17.3	odd	16		867.2.i.g.329.3		32
17.4	even	4		867.2.i.d.158.2		32
17.5	odd	16		867.2.i.i.827.2		32
17.6	odd	16		867.2.i.c.653.3		32
17.7	odd	16		867.2.i.h.503.2		32
17.8	even	8		867.2.i.f.224.2		32
17.9	even	8		867.2.i.g.224.2		32
17.10	odd	16	inner	51.2.i.a.44.2	yes	32
17.11	odd	16		867.2.i.d.653.3		32
17.12	odd	16		867.2.i.b.827.2		32
17.13	even	4		867.2.i.c.158.2		32
17.14	odd	16		867.2.i.f.329.3		32
17.15	even	8		867.2.i.b.65.3		32
17.16	even	2		867.2.i.h.131.3		32
51.2	odd	8		867.2.i.i.65.2		32
51.5	even	16		867.2.i.i.827.3		32
51.8	odd	8		867.2.i.f.224.3		32
51.11	even	16		867.2.i.d.653.2		32
51.14	even	16		867.2.i.f.329.2		32
51.20	even	16		867.2.i.g.329.2		32
51.23	even	16		867.2.i.c.653.2		32
51.26	odd	8		867.2.i.g.224.3		32
51.29	even	16		867.2.i.b.827.3		32
51.32	odd	8		867.2.i.b.65.2		32
51.38	odd	4		867.2.i.d.158.3		32
51.41	even	16		867.2.i.h.503.3		32
51.44	even	16	inner	51.2.i.a.44.3	yes	32
51.47	odd	4		867.2.i.c.158.3		32
51.50	odd	2		867.2.i.h.131.2		32
68.27	even	16		816.2.cj.c.401.1		32
204.95	odd	16		816.2.cj.c.401.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.2	✓	32	3.2	odd	2	inner
51.2.i.a.29.3	yes	32	1.1	even	1	trivial
51.2.i.a.44.2	yes	32	17.10	odd	16	inner
51.2.i.a.44.3	yes	32	51.44	even	16	inner
816.2.cj.c.401.1		32	68.27	even	16
816.2.cj.c.401.2		32	204.95	odd	16
816.2.cj.c.641.1		32	12.11	even	2
816.2.cj.c.641.2		32	4.3	odd	2
867.2.i.b.65.2		32	51.32	odd	8
867.2.i.b.65.3		32	17.15	even	8
867.2.i.b.827.2		32	17.12	odd	16
867.2.i.b.827.3		32	51.29	even	16
867.2.i.c.158.2		32	17.13	even	4
867.2.i.c.158.3		32	51.47	odd	4
867.2.i.c.653.2		32	51.23	even	16
867.2.i.c.653.3		32	17.6	odd	16
867.2.i.d.158.2		32	17.4	even	4
867.2.i.d.158.3		32	51.38	odd	4
867.2.i.d.653.2		32	51.11	even	16
867.2.i.d.653.3		32	17.11	odd	16
867.2.i.f.224.2		32	17.8	even	8
867.2.i.f.224.3		32	51.8	odd	8
867.2.i.f.329.2		32	51.14	even	16
867.2.i.f.329.3		32	17.14	odd	16
867.2.i.g.224.2		32	17.9	even	8
867.2.i.g.224.3		32	51.26	odd	8
867.2.i.g.329.2		32	51.20	even	16
867.2.i.g.329.3		32	17.3	odd	16
867.2.i.h.131.2		32	51.50	odd	2
867.2.i.h.131.3		32	17.16	even	2
867.2.i.h.503.2		32	17.7	odd	16
867.2.i.h.503.3		32	51.41	even	16
867.2.i.i.65.2		32	51.2	odd	8
867.2.i.i.65.3		32	17.2	even	8
867.2.i.i.827.2		32	17.5	odd	16
867.2.i.i.827.3		32	51.5	even	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.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} +(-2.89232 - 2.93845i) q^{17} +(-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} +(-3.18339 - 1.34821i) q^{34} +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} +(-5.09342 + 5.00571i) q^{51} +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} +(5.34735 + 0.0423104i) q^{68} +(-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} +(2.82024 - 1.85232i) q^{85} +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 + 96 * q^34 + 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 - 40 * q^51 - 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more