LMFDB - Embedded newform 867.2.i.d.158.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			158.2
Character	$\chi$	$=$	867.158
Dual form			867.2.i.d.653.2

$q$-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} +(-1.73205 - 0.00133765i) q^{3} +(-0.917091 + 0.917091i) q^{4} +(0.802626 + 0.159652i) q^{5} +(1.34216 - 0.554726i) q^{6} +(0.0380817 + 0.191449i) q^{7} +(1.05790 - 2.55399i) q^{8} +(3.00000 + 0.00463376i) q^{9} +(-0.672980 + 0.133864i) q^{10} +(-2.45341 + 3.67179i) q^{11} +(1.58968 - 1.58722i) q^{12} +(-3.75023 - 3.75023i) q^{13} +(-0.0909302 - 0.136087i) q^{14} +(-1.38998 - 0.277599i) q^{15} -0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(-0.210831 - 0.508991i) q^{19} +(-0.882497 + 0.589666i) q^{20} +(-0.0657033 - 0.331651i) q^{21} +(0.722364 - 3.63157i) q^{22} +(3.43849 + 2.29752i) q^{23} +(-1.83574 + 4.42222i) q^{24} +(-4.00068 - 1.65713i) q^{25} +(4.10844 + 1.70177i) q^{26} +(-5.19614 - 0.0120389i) q^{27} +(-0.210501 - 0.140652i) q^{28} +(0.120733 - 0.606965i) q^{29} +(1.16581 - 0.230959i) q^{30} +(0.553739 - 0.369997i) q^{31} +(2.20436 + 5.32181i) q^{32} +(4.25434 - 6.35644i) q^{33} +0.159742i q^{35} +(-2.75552 + 2.74702i) q^{36} +(-1.09126 - 1.63319i) q^{37} +(0.326640 + 0.326640i) q^{38} +(6.49057 + 6.50060i) q^{39} +(1.25684 - 1.88100i) q^{40} +(-7.84141 + 1.55975i) q^{41} +(0.157314 + 0.235831i) q^{42} +(2.95422 - 7.13212i) q^{43} +(-1.11736 - 5.61737i) q^{44} +(2.40714 + 0.482675i) q^{45} +(-3.40082 - 0.676466i) q^{46} +(7.05884 - 7.05884i) q^{47} +(-0.000369245 + 0.478114i) q^{48} +(6.43195 - 2.66420i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(10.7049 - 4.43410i) q^{53} +(4.02904 - 1.65796i) q^{54} +(-2.55538 + 2.55538i) q^{55} +(0.529246 + 0.105274i) q^{56} +(0.364489 + 0.881880i) q^{57} +(0.101231 + 0.508924i) q^{58} +(0.0995233 - 0.240270i) q^{59} +(1.52932 - 1.02015i) q^{60} +(10.3478 - 2.05830i) q^{61} +(-0.310232 + 0.464295i) q^{62} +(0.113358 + 0.574524i) q^{63} +(-3.02483 - 3.02483i) q^{64} +(-2.41130 - 3.60876i) q^{65} +(-1.25603 + 6.28910i) q^{66} +5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(-0.0512564 - 0.123744i) q^{70} +(5.41686 - 3.61943i) q^{71} +(3.18552 - 7.65705i) q^{72} +(2.26406 - 11.3822i) q^{73} +(1.36939 + 0.914994i) q^{74} +(6.92716 + 2.87559i) q^{75} +(0.660143 + 0.273440i) q^{76} +(-0.796392 - 0.329876i) q^{77} +(-7.11375 - 2.95305i) q^{78} +(8.98758 + 6.00531i) q^{79} +(0.0440703 - 0.221556i) q^{80} +(8.99996 + 0.0278025i) q^{81} +(5.57385 - 3.72433i) q^{82} +(-1.05744 - 2.55289i) q^{83} +(0.364410 + 0.243898i) q^{84} +6.47280i q^{86} +(-0.209927 + 1.05113i) q^{87} +(6.78225 + 10.1503i) q^{88} +(-3.69661 - 3.69661i) q^{89} +(-2.01956 + 0.398473i) q^{90} +(0.575164 - 0.860794i) q^{91} +(-5.26045 + 1.04637i) q^{92} +(-0.959599 + 0.640112i) q^{93} +(-3.20315 + 7.73308i) q^{94} +(-0.0879569 - 0.442189i) q^{95} +(-3.81095 - 9.22058i) q^{96} +(-2.42163 - 0.481692i) q^{97} +(-4.12764 + 4.12764i) q^{98} +(-7.37724 + 11.0040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{5}{16}\right)$

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	$-0.720801\pi$
$2$	−0.774648	+	0.320870i	−0.547759	+	0.226889i	0.0916024	+	0.995796i	$0.470801\pi$
$3$	−1.73205	−	0.00133765i	−1.00000	−	0.000772294i
$3$	−1.73205	−	0.00133765i	−1.00000	−	0.000772294i
$4$	−0.917091	+	0.917091i	−0.458546	+	0.458546i
$5$	0.802626	+	0.159652i	0.358945	+	0.0713987i	0.371269	−	0.928525i	$-0.378923\pi$
$5$	0.802626	+	0.159652i	0.358945	+	0.0713987i	−0.0123235	+	0.999924i	$0.503923\pi$
$6$	1.34216	−	0.554726i	0.547934	−	0.226466i
$7$	0.0380817	+	0.191449i	0.0143935	+	0.0723611i	0.987314	−	0.158777i	$-0.0507551\pi$
$7$	0.0380817	+	0.191449i	0.0143935	+	0.0723611i	−0.972921	+	0.231138i	$0.925755\pi$
$8$	1.05790	−	2.55399i	0.374023	−	0.902970i
$9$	3.00000	+	0.00463376i	0.999999	+	0.00154459i
$10$	−0.672980	+	0.133864i	−0.212815	+	0.0423316i
$11$	−2.45341	+	3.67179i	−0.739731	+	1.10709i	0.250563	+	0.968100i	$0.419384\pi$
$11$	−2.45341	+	3.67179i	−0.739731	+	1.10709i	−0.990294	+	0.138986i	$0.955616\pi$
$12$	1.58968	−	1.58722i	0.458900	−	0.458191i
$13$	−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	$-0.513043\pi$
$14$	−0.0909302	−	0.136087i	−0.0243021	−	0.0363707i
$15$	−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	$-0.145129\pi$
$19$	−0.210831	−	0.508991i	−0.0483680	−	0.116771i	−0.946217	+	0.323533i	$0.895129\pi$
$20$	−0.882497	+	0.589666i	−0.197332	+	0.131853i
$21$	−0.0657033	−	0.331651i	−0.0143376	−	0.0723722i
$22$	0.722364	−	3.63157i	0.154009	−	0.774253i
$23$	3.43849	+	2.29752i	0.716974	+	0.479067i	0.859768	−	0.510686i	$-0.170608\pi$
$23$	3.43849	+	2.29752i	0.716974	+	0.479067i	−0.142793	+	0.989753i	$0.545608\pi$
$24$	−1.83574	+	4.42222i	−0.374720	+	0.902681i
$25$	−4.00068	−	1.65713i	−0.800136	−	0.331427i
$26$	4.10844	+	1.70177i	0.805732	+	0.333745i
$27$	−5.19614	−	0.0120389i	−0.999997	−	0.00231688i
$28$	−0.210501	−	0.140652i	−0.0397810	−	0.0265808i
$29$	0.120733	−	0.606965i	0.0224195	−	0.112711i	−0.967955	−	0.251123i	$-0.919200\pi$
$29$	0.120733	−	0.606965i	0.0224195	−	0.112711i	0.990375	+	0.138413i	$0.0442000\pi$
$30$	1.16581	−	0.230959i	0.212848	−	0.0421672i
$31$	0.553739	−	0.369997i	0.0994545	−	0.0664533i	−0.504849	−	0.863208i	$-0.668452\pi$
$31$	0.553739	−	0.369997i	0.0994545	−	0.0664533i	0.604303	+	0.796755i	$0.293452\pi$
$32$	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
$37$	−1.09126	−	1.63319i	−0.179402	−	0.268495i	0.730859	−	0.682528i	$-0.239120\pi$
$37$	−1.09126	−	1.63319i	−0.179402	−	0.268495i	−0.910262	+	0.414034i	$0.864120\pi$
$38$	0.326640	+	0.326640i	0.0529880	+	0.0529880i
$39$	6.49057	+	6.50060i	1.03932	+	1.04093i
$40$	1.25684	−	1.88100i	0.198725	−	0.297412i
$41$	−7.84141	+	1.55975i	−1.22462	+	0.243592i	−0.764712	−	0.644373i	$-0.777119\pi$
$41$	−7.84141	+	1.55975i	−1.22462	+	0.243592i	−0.459911	+	0.887965i	$0.652119\pi$
$42$	0.157314	+	0.235831i	0.0242740	+	0.0363895i
$43$	2.95422	−	7.13212i	0.450514	−	1.08764i	−0.521613	−	0.853182i	$-0.674669\pi$
$43$	2.95422	−	7.13212i	0.450514	−	1.08764i	0.972127	−	0.234455i	$-0.0753307\pi$
$44$	−1.11736	−	5.61737i	−0.168449	−	0.846850i
$45$	2.40714	+	0.482675i	0.358835	+	0.0719530i
$46$	−3.40082	−	0.676466i	−0.501424	−	0.0997395i
$47$	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	$-0.00957939\pi$
$48$	−0.000369245		0.478114i	−5.32959e−5		0.0690098i
$49$	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	$-0.332056\pi$
$53$	10.7049	−	4.43410i	1.47043	−	0.609071i	0.966957	+	0.254941i	$0.0820561\pi$
$54$	4.02904	−	1.65796i	0.548283	−	0.225619i
$55$	−2.55538	+	2.55538i	−0.344568	+	0.344568i
$56$	0.529246	+	0.105274i	0.0707234	+	0.0140678i
$57$	0.364489	+	0.881880i	0.0482778	+	0.116808i
$58$	0.101231	+	0.508924i	0.0132923	+	0.0668249i
$59$	0.0995233	−	0.240270i	0.0129568	−	0.0312805i	−0.917269	−	0.398269i	$-0.869611\pi$
$59$	0.0995233	−	0.240270i	0.0129568	−	0.0312805i	0.930226	+	0.366988i	$0.119611\pi$
$60$	1.52932	−	1.02015i	0.197434	−	0.131701i
$61$	10.3478	−	2.05830i	1.32490	−	0.263539i	0.518584	−	0.855026i	$-0.326459\pi$
$61$	10.3478	−	2.05830i	1.32490	−	0.263539i	0.806314	+	0.591488i	$0.201459\pi$
$62$	−0.310232	+	0.464295i	−0.0393995	+	0.0589655i
$63$	0.113358	+	0.574524i	0.0142817	+	0.0723832i
$64$	−3.02483	−	3.02483i	−0.378104	−	0.378104i
$65$	−2.41130	−	3.60876i	−0.299085	−	0.447612i
$66$	−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	$0.892795\pi$
$68$		0			0
$69$	−5.95256	−	3.98403i	−0.716604	−	0.479621i
$70$	−0.0512564	−	0.123744i	−0.00612632	−	0.0147902i
$71$	5.41686	−	3.61943i	0.642864	−	0.429548i	−0.190945	−	0.981601i	$-0.561155\pi$
$71$	5.41686	−	3.61943i	0.642864	−	0.429548i	0.833809	+	0.552053i	$0.186155\pi$
$72$	3.18552	−	7.65705i	0.375417	−	0.902392i
$73$	2.26406	−	11.3822i	0.264988	−	1.33218i	−0.587409	−	0.809290i	$-0.699852\pi$
$73$	2.26406	−	11.3822i	0.264988	−	1.33218i	0.852397	−	0.522895i	$-0.175148\pi$
$74$	1.36939	+	0.914994i	0.159188	+	0.106366i
$75$	6.92716	+	2.87559i	0.799879	+	0.332045i
$76$	0.660143	+	0.273440i	0.0757236	+	0.0313657i
$77$	−0.796392	−	0.329876i	−0.0907573	−	0.0375929i
$78$	−7.11375	−	2.95305i	−0.805474	−	0.334367i
$79$	8.98758	+	6.00531i	1.01118	+	0.675650i	0.946649	−	0.322266i	$-0.104444\pi$
$79$	8.98758	+	6.00531i	1.01118	+	0.675650i	0.0645322	+	0.997916i	$0.479444\pi$
$80$	0.0440703	−	0.221556i	0.00492721	−	0.0247708i
$81$	8.99996	+	0.0278025i	0.999995	+	0.00308917i
$82$	5.57385	−	3.72433i	0.615529	−	0.411283i
$83$	−1.05744	−	2.55289i	−0.116069	−	0.280216i	0.855159	−	0.518365i	$-0.173459\pi$
$83$	−1.05744	−	2.55289i	−0.116069	−	0.280216i	−0.971229	+	0.238149i	$0.923459\pi$
$84$	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
$88$	6.78225	+	10.1503i	0.722990	+	1.08203i
$89$	−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	$0.839364\pi$
$90$	−2.01956	+	0.398473i	−0.212880	+	0.0420028i
$91$	0.575164	−	0.860794i	0.0602936	−	0.0902357i
$92$	−5.26045	+	1.04637i	−0.548440	+	0.109091i
$93$	−0.959599	+	0.640112i	−0.0995057	+	0.0663765i
$94$	−3.20315	+	7.73308i	−0.330379	+	0.797606i
$95$	−0.0879569	−	0.442189i	−0.00902419	−	0.0453677i
$96$	−3.81095	−	9.22058i	−0.388953	−	0.941072i
$97$	−2.42163	−	0.481692i	−0.245879	−	0.0489084i	0.0706120	−	0.997504i	$-0.477505\pi$
$97$	−2.42163	−	0.481692i	−0.245879	−	0.0489084i	−0.316491	+	0.948595i	$0.602505\pi$
$98$	−4.12764	+	4.12764i	−0.416954	+	0.416954i
$99$	−7.37724	+	11.0040i	−0.741441	+	1.10594i
$100$	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
$105$	0.000213679	−	0.276681i	2.08530e−5	−	0.0270013i
$106$	−6.86974	+	6.86974i	−0.667248	+	0.667248i
$107$	−4.03497	−	0.802606i	−0.390076	−	0.0775909i	−0.00384387	−	0.999993i	$-0.501224\pi$
$107$	−4.03497	−	0.802606i	−0.390076	−	0.0775909i	−0.386232	+	0.922402i	$0.626224\pi$
$108$	4.77637	−	4.75429i	0.459607	−	0.457482i
$109$	−2.46757	−	12.4053i	−0.236350	−	1.18821i	−0.898545	−	0.438881i	$-0.855375\pi$
$109$	−2.46757	−	12.4053i	−0.236350	−	1.18821i	0.662195	−	0.749332i	$-0.269625\pi$
$110$	1.15958	−	2.79947i	0.110561	−	0.266919i
$111$	1.88794	+	2.83023i	0.179195	+	0.268633i
$112$	0.0528476	−	0.0105120i	0.00499363	−	0.000993294i
$113$	−0.686845	+	1.02794i	−0.0646130	+	0.0967001i	−0.862369	−	0.506280i	$-0.831020\pi$
$113$	−0.686845	+	1.02794i	−0.0646130	+	0.0967001i	0.797756	+	0.602980i	$0.206020\pi$
$114$	−0.565320	−	0.566193i	−0.0529470	−	0.0530289i
$115$	2.39302	+	2.39302i	0.223150	+	0.223150i
$116$	0.445919	+	0.667365i	0.0414026	+	0.0619633i
$117$	−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
$122$	−7.35545	+	4.91475i	−0.665931	+	0.444961i
$123$	13.5838	−	2.69108i	1.22481	−	0.242647i
$124$	−0.168509	+	0.847150i	−0.0151325	+	0.0760763i
$125$	−6.34865	−	4.24203i	−0.567841	−	0.379419i
$126$	−0.272160	−	0.408681i	−0.0242459	−	0.0364082i
$127$	8.17992	+	3.38823i	0.725850	+	0.300657i	0.714845	−	0.699282i	$-0.246497\pi$
$127$	8.17992	+	3.38823i	0.725850	+	0.300657i	0.0110047	+	0.999939i	$0.496497\pi$
$128$	−7.32985	−	3.03612i	−0.647873	−	0.268358i
$129$	−5.12640	+	12.3492i	−0.451354	+	1.08729i
$130$	3.02585	+	2.02181i	0.265385	+	0.177324i
$131$	−1.91820	+	9.64343i	−0.167594	+	0.842551i	0.801904	+	0.597452i	$0.203820\pi$
$131$	−1.91820	+	9.64343i	−0.167594	+	0.842551i	−0.969498	+	0.245098i	$0.921180\pi$
$132$	1.92782	+	9.73106i	0.167795	+	0.846980i
$133$	0.0894173	−	0.0597467i	0.00775346	−	0.00518070i
$134$	−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	$-0.818047\pi$
$137$		−	12.6644i		−	1.08200i	0.841024	−	0.540998i	$-0.181953\pi$
$138$	5.88949	+	1.17622i	0.501347	+	0.100127i
$139$	−6.61453	−	9.89935i	−0.561038	−	0.839652i	0.437177	−	0.899375i	$-0.355978\pi$
$139$	−6.61453	−	9.89935i	−0.561038	−	0.839652i	−0.998215	+	0.0597233i	$0.980978\pi$
$140$	−0.146498	−	0.146498i	−0.0123814	−	0.0123814i
$141$	−12.2357	+	12.2168i	−1.03043	+	1.02884i
$142$	−3.03480	+	4.54189i	−0.254675	+	0.381147i
$143$	22.9709	−	4.56920i	1.92092	−	0.382095i
$144$	0.00127910	−	0.828117i	0.000106592	−	0.0690097i
$145$	0.193807	−	0.467891i	0.0160948	−	0.0388562i
$146$	1.89835	+	9.54366i	0.157109	+	0.789839i
$147$	−11.1440	+	4.60593i	−0.919144	+	0.379891i
$148$	2.49857	+	0.496997i	0.205381	+	0.0408529i
$149$	−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	$0.424164\pi$
$150$	−6.28880	−	0.00485680i	−0.513478	−	0.000396556i
$151$	−0.732249	+	0.303307i	−0.0595895	+	0.0246828i	−0.412279	−	0.911058i	$-0.635267\pi$
$151$	−0.732249	+	0.303307i	−0.0595895	+	0.0246828i	0.352690	+	0.935740i	$0.385267\pi$
$152$	−1.52299			−0.123531
$153$		0			0
$154$	0.722771			0.0582426
$155$	0.503516	−	0.208563i	0.0404434	−	0.0167522i
$156$	−11.9141	−	0.00920118i	−0.953890	−	0.000736684i
$157$	−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	$0.280001\pi$
$158$	−8.88913	−	1.76816i	−0.707181	−	0.140667i
$159$	−18.5473	+	7.66577i	−1.47090	+	0.607935i
$160$	0.919642	+	4.62335i	0.0727041	+	0.365508i
$161$	−0.308916	+	0.745790i	−0.0243460	+	0.0587765i
$162$	−6.98072	+	2.86628i	−0.548457	+	0.225196i
$163$	15.8218	−	3.14715i	1.23926	−	0.246504i	0.468403	−	0.883515i	$-0.344830\pi$
$163$	15.8218	−	3.14715i	1.23926	−	0.246504i	0.770854	+	0.637012i	$0.219830\pi$
$164$	5.76085	−	8.62172i	0.449847	−	0.673243i
$165$	4.42947	−	4.42263i	0.344834	−	0.344301i
$166$	1.63829	+	1.63829i	0.127156	+	0.127156i
$167$	5.09317	+	7.62247i	0.394121	+	0.589844i	0.974468	−	0.224525i	$-0.0720831\pi$
$167$	5.09317	+	7.62247i	0.394121	+	0.589844i	−0.580347	+	0.814369i	$0.697083\pi$
$168$	−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
$173$	−0.969247	+	0.647630i	−0.0736905	+	0.0492384i	−0.591870	−	0.806034i	$-0.701610\pi$
$173$	−0.969247	+	0.647630i	−0.0736905	+	0.0492384i	0.518179	+	0.855272i	$0.326610\pi$
$174$	−0.174657	−	0.881617i	−0.0132407	−	0.0668352i
$175$	0.164905	−	0.829034i	0.0124657	−	0.0626691i
$176$	1.01356	+	0.677238i	0.0763998	+	0.0510487i
$177$	−0.172701	+	0.416027i	−0.0129810	+	0.0312705i
$178$	4.04970	+	1.67744i	0.303538	+	0.125729i
$179$	−9.50468	−	3.93697i	−0.710413	−	0.294263i	−0.00193768	−	0.999998i	$-0.500617\pi$
$179$	−9.50468	−	3.93697i	−0.710413	−	0.294263i	−0.708476	+	0.705735i	$0.750617\pi$
$180$	−2.65022	+	1.76491i	−0.197536	+	0.131548i
$181$	−10.7102	−	7.15635i	−0.796086	−	0.531928i	0.0897290	−	0.995966i	$-0.471400\pi$
$181$	−10.7102	−	7.15635i	−0.796086	−	0.531928i	−0.885815	+	0.464039i	$0.846400\pi$
$182$	−0.169347	+	0.851365i	−0.0125528	+	0.0631074i
$183$	−17.9256	+	3.55124i	−1.32510	+	0.262515i
$184$	9.50541	−	6.35131i	0.700748	−	0.468225i
$185$	−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
$190$	0.210021	+	0.314318i	0.0152365	+	0.0228031i
$191$	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	$0.544381\pi$
$192$	5.23512	+	5.24321i	0.377812	+	0.378396i
$193$	1.65294	−	2.47380i	0.118981	−	0.178068i	−0.767198	−	0.641410i	$-0.778350\pi$
$193$	1.65294	−	2.47380i	0.118981	−	0.178068i	0.886180	+	0.463342i	$0.153350\pi$
$194$	2.03047	−	0.403886i	0.145779	−	0.0289973i
$195$	4.17166	+	6.25379i	0.298739	+	0.447843i
$196$	−3.45537	+	8.34201i	−0.246812	+	0.595858i
$197$	2.64722	+	13.3085i	0.188607	+	0.948190i	0.952892	+	0.303311i	$0.0980922\pi$
$197$	2.64722	+	13.3085i	0.188607	+	0.948190i	−0.764285	+	0.644879i	$0.776908\pi$
$198$	2.18392	−	10.8914i	0.155204	−	0.774015i
$199$	4.21912	+	0.839234i	0.299085	+	0.0594917i	0.342352	−	0.939572i	$-0.388777\pi$
$199$	4.21912	+	0.839234i	0.299085	+	0.0594917i	−0.0432667	+	0.999064i	$0.513777\pi$
$200$	−8.46460	+	8.46460i	−0.598538	+	0.598538i
$201$	0.00723662	−	9.37029i	0.000510432	−	0.660929i
$202$	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
$207$	10.3048	+	6.90850i	0.716234	+	0.480174i
$208$	−1.03521	+	1.03521i	−0.0717789	+	0.0717789i
$209$	2.38616	+	0.474638i	0.165054	+	0.0328314i
$210$	0.0886132	+	0.214399i	0.00611489	+	0.0147950i
$211$	−3.02923	−	15.2290i	−0.208541	−	1.04840i	−0.933217	−	0.359314i	$-0.883011\pi$
$211$	−3.02923	−	15.2290i	−0.208541	−	1.04840i	0.724676	−	0.689090i	$-0.241989\pi$
$212$	−5.75087	+	13.8838i	−0.394971	+	0.953545i
$213$	−9.38712	+	6.26179i	−0.643195	+	0.429051i
$214$	3.38322	−	0.672964i	0.231272	−	0.0460029i
$215$	3.50979	−	5.25278i	0.239366	−	0.358236i
$216$	−5.52772	+	13.2581i	−0.376114	+	0.902101i
$217$	0.0919229	+	0.0919229i	0.00624014	+	0.00624014i
$218$	5.89198	+	8.81798i	0.399056	+	0.597229i
$219$	−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	−0.980234	−	0.197841i	$-0.936607\pi$
$223$	−6.37645	−	15.3941i	−0.426999	−	1.03087i	0.553235	−	0.833025i	$-0.313393\pi$
$224$	−0.934911	+	0.624687i	−0.0624664	+	0.0417387i
$225$	−11.9943	−	4.98994i	−0.799623	−	0.332662i
$226$	0.202230	−	1.01668i	0.0134521	−	0.0676283i
$227$	−16.0046	−	10.6940i	−1.06227	−	0.709783i	−0.103687	−	0.994610i	$-0.533064\pi$
$227$	−16.0046	−	10.6940i	−1.06227	−	0.709783i	−0.958579	+	0.284827i	$0.908064\pi$
$228$	−1.14303	−	0.474495i	−0.0756993	−	0.0314242i
$229$	−10.1448	−	4.20213i	−0.670391	−	0.277685i	0.0214129	−	0.999771i	$-0.493184\pi$
$229$	−10.1448	−	4.20213i	−0.670391	−	0.277685i	−0.691803	+	0.722086i	$0.743184\pi$
$230$	−2.62159	−	1.08590i	−0.172863	−	0.0716020i
$231$	1.37895	+	0.572428i	0.0907283	+	0.0376630i
$232$	−1.42246	−	0.950455i	−0.0933889	−	0.0624004i
$233$	4.58203	−	23.0354i	0.300179	−	1.50910i	−0.476484	−	0.879183i	$-0.658089\pi$
$233$	4.58203	−	23.0354i	0.300179	−	1.50910i	0.776662	−	0.629917i	$-0.216911\pi$
$234$	12.3174	+	5.12435i	0.805215	+	0.334989i
$235$	6.79257	−	4.53865i	0.443098	−	0.296069i
$236$	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	$-0.853633\pi$
$239$		−	13.7217i		−	0.887582i	0.896130	−	0.443791i	$-0.146367\pi$
$240$	−0.0766283	+	0.383688i	−0.00494634	+	0.0247669i
$241$	−2.37570	−	3.55549i	−0.153032	−	0.229029i	0.747030	−	0.664790i	$-0.231479\pi$
$241$	−2.37570	−	3.55549i	−0.153032	−	0.229029i	−0.900062	+	0.435761i	$0.856479\pi$
$242$	5.04032	+	5.04032i	0.324004	+	0.324004i
$243$	−15.5883	−	0.0601942i	−0.999993	−	0.00386146i
$244$	−7.60221	+	11.3775i	−0.486682	+	0.728371i
$245$	5.58780	−	1.11148i	0.356992	−	0.0710100i
$246$	−9.65918	+	6.44327i	−0.615847	+	0.410808i
$247$	−1.11817	+	2.69950i	−0.0711474	+	0.171765i
$248$	−0.359168	−	1.80566i	−0.0228072	−	0.114659i
$249$	1.82813	+	4.42314i	0.115853	+	0.280305i
$250$	6.27911	+	1.24899i	0.397126	+	0.0789932i
$251$	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	$0.155245\pi$
$252$	−0.630851	−	0.422932i	−0.0397398	−	0.0266422i
$253$	−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	$-0.461790\pi$
$257$	14.5315	−	6.01912i	0.906447	−	0.375463i	0.786696	+	0.617341i	$0.211790\pi$
$258$	0.00865836	−	11.2112i	0.000539046	−	0.697980i
$259$	0.271116	−	0.271116i	0.0168463	−	0.0168463i
$260$	5.52095	+	1.09818i	0.342395	+	0.0681065i
$261$	0.365010	−	1.82033i	0.0225936	−	0.112676i
$262$	−1.60836	−	8.08576i	−0.0993647	−	0.499540i
$263$	−5.90932	+	14.2664i	−0.364384	+	0.879701i	0.630264	+	0.776381i	$0.282947\pi$
$263$	−5.90932	+	14.2664i	−0.364384	+	0.879701i	−0.994648	+	0.103320i	$0.967053\pi$
$264$	−11.7336	−	17.5900i	−0.722154	−	1.08259i
$265$	9.29993	−	1.84987i	0.571290	−	0.113637i
$266$	−0.0500960	+	0.0749740i	−0.00307158	+	0.00459695i
$267$	6.39776	+	6.40765i	0.391537	+	0.392142i
$268$	−4.96141	−	4.96141i	−0.303066	−	0.303066i
$269$	−13.5216	−	20.2365i	−0.824426	−	1.23384i	−0.969663	−	0.244444i	$-0.921395\pi$
$269$	−13.5216	−	20.2365i	−0.824426	−	1.23384i	0.145237	−	0.989397i	$-0.453605\pi$
$270$	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			0
$273$	−0.997365	+	1.49017i	−0.0603633	+	0.0901891i
$274$	4.06363	+	9.81047i	0.245493	+	0.592672i
$275$	15.9000	−	10.6240i	0.958804	−	0.640652i
$276$	9.11276	−	1.80533i	0.548524	−	0.108668i
$277$	−1.72935	+	8.69401i	−0.103906	+	0.522373i	0.893415	+	0.449232i	$0.148302\pi$
$277$	−1.72935	+	8.69401i	−0.103906	+	0.522373i	−0.997322	+	0.0731408i	$0.976698\pi$
$278$	8.30034	+	5.54611i	0.497821	+	0.332633i
$279$	1.66293	−	1.10742i	0.0995570	−	0.0662996i
$280$	0.407979	+	0.168991i	0.0243814	+	0.0100991i
$281$	6.66883	+	2.76232i	0.397829	+	0.164786i	0.572623	−	0.819819i	$-0.305926\pi$
$281$	6.66883	+	2.76232i	0.397829	+	0.164786i	−0.174794	+	0.984605i	$0.555926\pi$
$282$	5.55836	−	13.3898i	0.330995	−	0.797351i
$283$	4.10889	+	2.74547i	0.244248	+	0.163201i	0.671669	−	0.740851i	$-0.265578\pi$
$283$	4.10889	+	2.74547i	0.244248	+	0.163201i	−0.427421	+	0.904053i	$0.640578\pi$
$284$	−1.64841	+	8.28711i	−0.0978151	+	0.491750i
$285$	0.151754	+	0.766012i	0.00898915	+	0.0453746i
$286$	−16.3282	+	10.9102i	−0.965509	+	0.645133i
$287$	−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
$292$	8.36216	+	12.5149i	0.489359	+	0.732377i
$293$	−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	$0.938440\pi$
$294$	7.15480	−	7.14376i	0.417276	−	0.416632i
$295$	0.118240	−	0.176958i	0.00688418	−	0.0103029i
$296$	−5.32559	+	1.05932i	−0.309543	+	0.0615720i
$297$	12.7925	−	19.0496i	0.742294	−	1.10537i
$298$	4.07540	−	9.83889i	0.236082	−	0.569952i
$299$	−4.27887	−	21.5114i	−0.247454	−	1.24403i
$300$	−8.99002	+	3.71566i	−0.519039	+	0.214523i
$301$	1.47794	+	0.293981i	0.0851872	+	0.0169448i
$302$	0.469913	−	0.469913i	0.0270404	−	0.0270404i
$303$	11.7651	+	0.00908610i	0.675886	+	0.000521983i
$304$	−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
$309$	−4.29138	−	0.00331421i	−0.244128	−	0.000188539i
$310$	−0.323126	+	0.323126i	−0.0183523	+	0.0183523i
$311$	10.2651	+	2.04185i	0.582080	+	0.115783i	0.477343	−	0.878717i	$-0.341600\pi$
$311$	10.2651	+	2.04185i	0.582080	+	0.115783i	0.104737	+	0.994500i	$0.466600\pi$
$312$	23.4688	−	9.69986i	1.32866	−	0.549146i
$313$	4.68503	+	23.5532i	0.264814	+	1.33131i	0.852716	+	0.522375i	$0.174954\pi$
$313$	4.68503	+	23.5532i	0.264814	+	1.33131i	−0.587902	+	0.808932i	$0.700046\pi$
$314$	0.756754	−	1.82697i	0.0427061	−	0.103102i
$315$	−0.000740207		0.479226i	−4.17060e−5		0.0270013i
$316$	−13.7498	+	2.73501i	−0.773489	+	0.153857i
$317$	5.46458	−	8.17832i	0.306921	−	0.459340i	−0.645660	−	0.763625i	$-0.723418\pi$
$317$	5.46458	−	8.17832i	0.306921	−	0.459340i	0.952581	+	0.304285i	$0.0984175\pi$
$318$	11.9079	−	11.8895i	0.667763	−	0.666733i
$319$	1.93244	+	1.93244i	0.108196	+	0.108196i
$320$	−1.94489	−	2.91073i	−0.108723	−	0.162715i
$321$	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
$326$	−11.2465	+	7.51466i	−0.622885	+	0.416198i
$327$	4.25736	+	21.4899i	0.235432	+	1.18839i
$328$	−4.31180	+	21.6769i	−0.238080	+	1.19691i
$329$	1.62022	+	1.08260i	0.0893258	+	0.0596856i
$330$	−2.01219	+	4.84727i	−0.110767	+	0.266833i
$331$	3.87936	+	1.60689i	0.213229	+	0.0883224i	0.486741	−	0.873546i	$-0.338185\pi$
$331$	3.87936	+	1.60689i	0.213229	+	0.0883224i	−0.273512	+	0.961869i	$0.588185\pi$
$332$	3.31100	+	1.37146i	0.181715	+	0.0752687i
$333$	−3.26622	−	4.90462i	−0.178988	−	0.268772i
$334$	−6.39123	−	4.27048i	−0.349713	−	0.233671i
$335$	−0.863709	+	4.34216i	−0.0471895	+	0.237238i
$336$	−0.0915487	+	0.0181367i	−0.00499439	+	0.000989437i
$337$	−4.81060	+	3.21434i	−0.262050	+	0.175096i	−0.679654	−	0.733533i	$-0.737870\pi$
$337$	−4.81060	+	3.21434i	−0.262050	+	0.175096i	0.417604	+	0.908629i	$0.362870\pi$
$338$	−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
$343$	1.51413	+	2.26606i	0.0817554	+	0.122356i
$344$	−15.0901	−	15.0901i	−0.813602	−	0.813602i
$345$	−4.14162	−	4.14802i	−0.222977	−	0.223322i
$346$	0.543020	−	0.812687i	0.0291930	−	0.0436903i
$347$	−0.0185728	+	0.00369437i	−0.000997042	+	0.000198324i	−0.195589	−	0.980686i	$-0.562662\pi$
$347$	−0.0185728	+	0.00369437i	−0.000997042	+	0.000198324i	0.194592	+	0.980884i	$0.437662\pi$
$348$	−0.771462	−	1.15651i	−0.0413547	−	0.0619953i
$349$	−2.37825	+	5.74159i	−0.127305	+	0.307340i	−0.974662	−	0.223682i	$-0.928192\pi$
$349$	−2.37825	+	5.74159i	−0.127305	+	0.307340i	0.847358	+	0.531023i	$0.178192\pi$
$350$	0.138268	+	0.695123i	0.00739076	+	0.0371559i
$351$	19.4416	+	19.5319i	1.03771	+	1.04253i
$352$	−24.9488	−	4.96262i	−1.32977	−	0.264508i
$353$	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	$0.144944\pi$
$354$	0.000291687	−	0.377689i	1.55030e−5	−	0.0200740i
$355$	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	$-0.942393\pi$
$359$	−29.4053	+	12.1801i	−1.55195	+	0.642840i	−0.568284	+	0.822832i	$0.692393\pi$
$360$	3.77924	−	5.63717i	0.199184	−	0.297105i
$361$	13.2204	−	13.2204i	0.695811	−	0.695811i
$362$	10.5929	+	2.10706i	0.556752	+	0.110745i
$363$	5.62437	+	13.6081i	0.295203	+	0.714242i
$364$	0.261949	+	1.31690i	0.0137298	+	0.0690246i
$365$	3.63439	−	8.77418i	0.190232	−	0.459262i
$366$	12.7466	−	8.50276i	0.666274	−	0.444446i
$367$	−32.9795	+	6.56004i	−1.72152	+	0.342431i	−0.954276	−	0.298928i	$-0.903371\pi$
$367$	−32.9795	+	6.56004i	−1.72152	+	0.342431i	−0.767241	+	0.641359i	$0.778371\pi$
$368$	0.634207	−	0.949158i	0.0330603	−	0.0494783i
$369$	−23.5314	+	4.64292i	−1.22500	+	0.241701i
$370$	0.953024	+	0.953024i	0.0495453	+	0.0495453i
$371$	1.25657	+	1.88058i	0.0652377	+	0.0976351i
$372$	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	$0.870575\pi$
$374$		0			0
$375$	10.9905	+	7.35591i	0.567547	+	0.379857i
$376$	−10.5607	−	25.4957i	−0.544624	−	1.31484i
$377$	−2.72903	+	1.82348i	−0.140552	+	0.0939140i
$378$	0.470848	+	0.708220i	0.0242178	+	0.0364269i
$379$	7.41655	−	37.2855i	0.380963	−	1.91523i	−0.0214486	−	0.999770i	$-0.506828\pi$
$379$	7.41655	−	37.2855i	0.380963	−	1.91523i	0.402411	−	0.915459i	$-0.368172\pi$
$380$	0.486193	+	0.324864i	0.0249412	+	0.0166651i
$381$	−14.1635	−	5.87953i	−0.725618	−	0.301217i
$382$	−12.8893	−	5.33891i	−0.659472	−	0.273162i
$383$	31.8268	+	13.1831i	1.62627	+	0.673624i	0.994807	−	0.101781i	$-0.0324540\pi$
$383$	31.8268	+	13.1831i	1.62627	+	0.673624i	0.631465	+	0.775404i	$0.282454\pi$
$384$	12.6916	+	5.26852i	0.647666	+	0.268858i
$385$	−0.586540	−	0.391913i	−0.0298928	−	0.0199738i
$386$	−0.486680	+	2.44670i	−0.0247714	+	0.124534i
$387$	8.89570	−	21.3826i	0.452194	−	1.08694i
$388$	2.66261	−	1.77910i	0.135174	−	0.0903201i
$389$	0.288821	+	0.697275i	0.0146438	+	0.0353532i	0.931032	−	0.364937i	$-0.118909\pi$
$389$	0.288821	+	0.697275i	0.0146438	+	0.0353532i	−0.916389	+	0.400290i	$0.868909\pi$
$390$	−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
$394$	−6.32096	−	9.45998i	−0.318445	−	0.476587i
$395$	6.25490	+	6.25490i	0.314718	+	0.314718i
$396$	−3.32606	−	16.8573i	−0.167141	−	0.847110i
$397$	11.1930	−	16.7515i	0.561761	−	0.840734i	−0.436499	−	0.899705i	$-0.643782\pi$
$397$	11.1930	−	16.7515i	0.561761	−	0.840734i	0.998260	+	0.0589706i	$0.0187818\pi$
$398$	−3.53761	+	0.703675i	−0.177325	+	0.0352720i
$399$	−0.154955	+	0.103365i	−0.00775746	+	0.00517471i
$400$	−0.457434	+	1.10434i	−0.0228717	+	0.0552172i
$401$	3.07630	+	15.4656i	0.153623	+	0.772315i	0.978378	+	0.206825i	$0.0663130\pi$
$401$	3.07630	+	15.4656i	0.153623	+	0.772315i	−0.824755	+	0.565490i	$0.808687\pi$
$402$	3.00104	+	7.26100i	0.149678	+	0.362146i
$403$	−3.46422	−	0.689076i	−0.172565	−	0.0343253i
$404$	6.22941	−	6.22941i	0.309925	−	0.309925i
$405$	7.21916	+	1.45918i	0.358723	+	0.0725072i
$406$	−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
$411$	−0.0169406	+	21.9354i	−0.000835618	+	1.08199i
$412$	−2.27221	+	2.27221i	−0.111944	+	0.111944i
$413$	0.0497897	+	0.00990378i	0.00244999	+	0.000487333i
$414$	−10.1993	−	2.04515i	−0.501270	−	0.100514i
$415$	−0.441155	−	2.21784i	−0.0216555	−	0.108869i
$416$	11.6911	−	28.2248i	0.573204	−	1.38384i
$417$	11.4435	+	17.1550i	0.560389	+	0.840085i
$418$	−2.00073	+	0.397971i	−0.0978591	+	0.0194654i
$419$	−19.5736	+	29.2939i	−0.956231	+	1.43110i	−0.0546430	+	0.998506i	$0.517402\pi$
$419$	−19.5736	+	29.2939i	−0.956231	+	1.43110i	−0.901588	+	0.432595i	$0.857598\pi$
$420$	0.253546	+	0.253938i	0.0123718	+	0.0123909i
$421$	−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	$0.750098\pi$
$422$	7.23309	+	10.8251i	0.352102	+	0.526957i
$423$	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
$428$	4.43650	−	2.96438i	0.214447	−	0.143289i
$429$	−39.7929	+	7.88335i	−1.92122	+	0.380612i
$430$	−1.03340	+	5.19524i	−0.0498349	+	0.250537i
$431$	9.85875	+	6.58741i	0.474879	+	0.317304i	0.769875	−	0.638194i	$-0.220318\pi$
$431$	9.85875	+	6.58741i	0.474879	+	0.317304i	−0.294996	+	0.955499i	$0.595318\pi$
$432$	−0.00332320	+	1.43434i	−0.000159887	+	0.0690096i
$433$	0.501414	+	0.207692i	0.0240964	+	0.00998106i	0.394699	−	0.918810i	$-0.370849\pi$
$433$	0.501414	+	0.207692i	0.0240964	+	0.00998106i	−0.370603	+	0.928791i	$0.620849\pi$
$434$	−0.100703	−	0.0417126i	−0.00483391	−	0.00200227i
$435$	−0.336309	+	0.810151i	−0.0161248	+	0.0388438i
$436$	13.6398	+	9.11381i	0.653227	+	0.436472i
$437$	0.444480	−	2.23455i	0.0212623	−	0.106893i
$438$	−3.27528	−	16.5326i	−0.156499	−	0.789960i
$439$	−25.3191	+	16.9177i	−1.20841	+	0.807436i	−0.985874	−	0.167487i	$-0.946435\pi$
$439$	−25.3191	+	16.9177i	−1.20841	+	0.807436i	−0.222540	+	0.974924i	$0.571435\pi$
$440$	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	$0.405279\pi$
$443$			40.2451i			1.91210i	−0.293203	+	0.956050i	$0.594721\pi$
$444$	−4.32699	−	0.864166i	−0.205350	−	0.0410115i
$445$	−2.37682	−	3.55716i	−0.112672	−	0.168626i
$446$	9.87902	+	9.87902i	0.467785	+	0.467785i
$447$	15.5676	−	15.5436i	0.736324	−	0.735187i
$448$	0.463912	−	0.694294i	0.0219178	−	0.0328023i
$449$	−35.7362	+	7.10838i	−1.68650	+	0.335465i	−0.942878	−	0.333139i	$-0.891892\pi$
$449$	−35.7362	+	7.10838i	−1.68650	+	0.335465i	−0.743619	+	0.668604i	$0.766892\pi$
$450$	10.8925	+	0.0168245i	0.513478	+	0.000793112i
$451$	13.5111	−	32.6187i	0.636214	−	1.53596i
$452$	−0.312812	−	1.57261i	−0.0147134	−	0.0739694i
$453$	1.26870	−	0.524364i	0.0596086	−	0.0246368i
$454$	15.8293	+	3.14865i	0.742908	+	0.147774i
$455$	0.599070	−	0.599070i	0.0280848	−	0.0280848i
$456$	2.63790	+	0.00203724i	0.123531	+	9.54023e-5i
$457$	19.6921	−	8.15675i	0.921160	−	0.381557i	0.128842	−	0.991665i	$-0.458874\pi$
$457$	19.6921	−	8.15675i	0.921160	−	0.381557i	0.792318	+	0.610108i	$0.208874\pi$
$458$	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	$-0.670726\pi$
$461$	−5.67952	+	2.35253i	−0.264521	+	0.109568i	0.246481	+	0.969148i	$0.420726\pi$
$462$	−1.25188		0.000966816i	−0.0582425		4.49804e-5i
$463$	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	$-0.0694277\pi$
$464$	−0.167546	−	0.0333270i	−0.00777813	−	0.00154717i
$465$	−0.872394	+	0.360569i	−0.0404563	+	0.0167210i
$466$	3.84191	+	19.3146i	0.177973	+	0.894730i
$467$	2.94293	−	7.10485i	0.136182	−	0.328773i	−0.841046	−	0.540964i	$-0.818060\pi$
$467$	2.94293	−	7.10485i	0.136182	−	0.328773i	0.977228	+	0.212190i	$0.0680597\pi$
$468$	20.6358	+	0.0318738i	0.953889	+	0.00147337i
$469$	−1.03573	+	0.206020i	−0.0478256	+	0.00951310i
$470$	−3.80553	+	5.69538i	−0.175536	+	0.262708i
$471$	2.89073	−	2.88626i	0.133198	−	0.132992i
$472$	−0.508362	−	0.508362i	−0.0233993	−	0.0233993i
$473$	18.9397	+	28.3453i	0.870849	+	1.30332i
$474$	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
$479$	−1.90904	+	1.27558i	−0.0872260	+	0.0582826i	−0.598418	−	0.801184i	$-0.704204\pi$
$479$	−1.90904	+	1.27558i	−0.0872260	+	0.0582826i	0.511192	+	0.859466i	$0.329204\pi$
$480$	−1.58668	−	8.00911i	−0.0724218	−	0.365564i
$481$	−2.03235	+	10.2173i	−0.0926672	+	0.465870i
$482$	2.98118	+	1.99196i	0.135789	+	0.0907313i
$483$	0.536056	−	1.29133i	0.0243914	−	0.0587577i
$484$	10.1865	+	4.21940i	0.463025	+	0.191791i
$485$	−1.86676	−	0.773237i	−0.0847652	−	0.0351109i
$486$	12.0948	−	4.95520i	0.548631	−	0.224772i
$487$	−23.3450	−	15.5987i	−1.05786	−	0.706842i	−0.100269	−	0.994960i	$-0.531970\pi$
$487$	−23.3450	−	15.5987i	−1.05786	−	0.706842i	−0.957595	+	0.288118i	$0.906970\pi$
$488$	5.69000	−	28.6056i	0.257574	−	1.29491i
$489$	−27.4083	+	5.42985i	−1.23945	+	0.245546i
$490$	−3.97194	+	2.65396i	−0.179434	+	0.119894i
$491$	5.17526	+	12.4942i	0.233556	+	0.563854i	0.996591	−	0.0825033i	$-0.0262915\pi$
$491$	5.17526	+	12.4942i	0.233556	+	0.563854i	−0.763035	+	0.646357i	$0.776291\pi$
$492$	−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
$496$	−0.102134	−	0.152854i	−0.00458593	−	0.00686333i
$497$	0.899222	+	0.899222i	0.0403356	+	0.0403356i
$498$	−2.83541	−	2.83979i	−0.127058	−	0.127254i
$499$	8.46309	−	12.6659i	0.378860	−	0.567004i	−0.592215	−	0.805780i	$-0.701746\pi$
$499$	8.46309	−	12.6659i	0.378860	−	0.567004i	0.971075	+	0.238776i	$0.0767462\pi$
$500$	9.71263	−	1.93196i	0.434362	−	0.0863999i
$501$	−8.81143	−	13.2093i	−0.393666	−	0.590148i
$502$	−2.98205	+	7.19931i	−0.133096	+	0.321321i
$503$	−4.75924	−	23.9263i	−0.212204	−	1.06682i	−0.929153	−	0.369696i	$-0.879462\pi$
$503$	−4.75924	−	23.9263i	−0.212204	−	1.06682i	0.716949	−	0.697126i	$-0.245538\pi$
$504$	1.58725	+	0.318273i	0.0707016	+	0.0141770i
$505$	−5.45190	−	1.08445i	−0.242606	−	0.0482574i
$506$	10.8275	−	10.8275i	0.481339	−	0.481339i
$507$	0.0202366	−	26.2032i	0.000898737	−	1.16372i
$508$	−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
$513$	1.08938	+	2.64733i	0.0480973	+	0.116882i
$514$	−9.32541	+	9.32541i	−0.411326	+	0.411326i
$515$	1.98861	+	0.395559i	0.0876286	+	0.0174304i
$516$	−6.62400	−	16.0268i	−0.291605	−	0.705538i
$517$	8.60033	+	43.2368i	0.378242	+	1.90155i
$518$	−0.123027	+	0.297013i	−0.00540548	+	0.0130500i
$519$	1.67965	−	1.12043i	0.0737285	−	0.0491815i
$520$	−11.7676	+	2.34073i	−0.516045	+	0.102648i
$521$	18.3207	−	27.4188i	0.802643	−	1.20124i	−0.173655	−	0.984807i	$-0.555558\pi$
$521$	18.3207	−	27.4188i	0.802643	−	1.20124i	0.976298	−	0.216433i	$-0.0694422\pi$
$522$	0.301335	+	1.52724i	0.0131891	+	0.0668454i
$523$	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	$0.657734\pi$
$524$	−7.08475	−	10.6031i	−0.309499	−	0.463197i
$525$	−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
$530$	−6.61060	+	4.41706i	−0.287146	+	0.191865i
$531$	0.299683	−	0.720349i	0.0130051	−	0.0312605i
$532$	−0.0272106	+	0.136797i	−0.00117973	+	0.00593090i
$533$	35.2565	+	23.5576i	1.52713	+	1.02039i
$534$	−7.01203	−	2.91083i	−0.303440	−	0.125964i
$535$	−3.11044	−	1.28839i	−0.134476	−	0.0557018i
$536$	13.8169	+	5.72315i	0.596800	+	0.247202i
$537$	16.4573	+	6.83174i	0.710186	+	0.294811i
$538$	16.9678	+	11.3375i	0.731532	+	0.488794i
$539$	−5.99784	+	30.1532i	−0.258345	+	1.29879i
$540$	4.59268	−	3.05336i	0.197637	−	0.131396i
$541$	13.8721	−	9.26903i	0.596408	−	0.398507i	−0.220406	−	0.975408i	$-0.570738\pi$
$541$	13.8721	−	9.26903i	0.596408	−	0.398507i	0.816814	+	0.576901i	$0.195738\pi$
$542$	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
$547$	−6.02406	−	9.01564i	−0.257570	−	0.385481i	0.680037	−	0.733178i	$-0.261964\pi$
$547$	−6.02406	−	9.01564i	−0.257570	−	0.385481i	−0.937607	+	0.347697i	$0.886964\pi$
$548$	11.6144	+	11.6144i	0.496144	+	0.496144i
$549$	31.0529	−	6.12695i	1.32530	−	0.261492i
$550$	−8.90795	+	13.3317i	−0.379836	+	0.568465i
$551$	−0.334394	+	0.0665151i	−0.0142457	+	0.00283364i
$552$	−16.4723	+	10.9881i	−0.701109	+	0.467683i
$553$	−0.807451	+	1.94936i	−0.0343363	+	0.0828952i
$554$	−1.45001	−	7.28969i	−0.0616050	−	0.309709i
$555$	1.06346	+	2.57303i	0.0451412	+	0.109219i
$556$	15.1447	+	3.01248i	0.642280	+	0.127757i
$557$	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	$0.166696\pi$
$558$	−0.932847	+	1.39145i	−0.0394905	+	0.0589046i
$559$	−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	$-0.459841\pi$
$563$	21.7414	−	9.00559i	0.916292	−	0.379541i	0.790462	+	0.612511i	$0.209841\pi$
$564$	0.0173188	−	22.4252i	0.000729255	−	0.944271i
$565$	−0.715392	+	0.715392i	−0.0300968	+	0.0300968i
$566$	−4.06388	−	0.808357i	−0.170818	−	0.0339778i
$567$	0.337411	+	1.72410i	0.0141699	+	0.0724052i
$568$	−3.51350	−	17.6636i	−0.147423	−	0.741147i
$569$	0.717701	−	1.73268i	0.0300876	−	0.0726379i	−0.908122	−	0.418707i	$-0.862484\pi$
$569$	0.717701	−	1.73268i	0.0300876	−	0.0726379i	0.938209	+	0.346069i	$0.112484\pi$
$570$	−0.363346	−	0.544696i	−0.0152189	−	0.0228148i
$571$	−39.2847	+	7.81421i	−1.64401	+	0.327014i	−0.928428	−	0.371512i	$-0.878839\pi$
$571$	−39.2847	+	7.81421i	−1.64401	+	0.327014i	−0.715584	+	0.698526i	$0.753839\pi$
$572$	−16.8760	+	25.2568i	−0.705623	+	1.05604i
$573$	−20.3626	−	20.3941i	−0.850661	−	0.851976i
$574$	0.925283	+	0.925283i	0.0386205	+	0.0386205i
$575$	−9.94898	−	14.8897i	−0.414901	−	0.620943i
$576$	−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	$-0.230643\pi$
$578$		0			0
$579$	−2.86629	+	4.28254i	−0.119119	+	0.177976i
$580$	0.251360	+	0.606837i	0.0104372	+	0.0251975i
$581$	0.448480	−	0.299665i	0.0186061	−	0.0124322i
$582$	−3.51742	+	0.696834i	−0.145802	+	0.0288847i
$583$	−9.98236	+	50.1847i	−0.413427	+	2.07844i
$584$	−26.6748	−	17.8235i	−1.10381	−	0.737544i
$585$	−7.21717	−	10.8375i	−0.298393	−	0.448073i
$586$	14.7986	+	6.12978i	0.611325	+	0.253219i
$587$	−11.6364	−	4.81996i	−0.480286	−	0.198941i	0.129387	−	0.991594i	$-0.458699\pi$
$587$	−11.6364	−	4.81996i	−0.480286	−	0.198941i	−0.609673	+	0.792653i	$0.708699\pi$
$588$	5.99604	−	14.4442i	0.247272	−	0.595667i
$589$	−0.305070	−	0.203842i	−0.0125702	−	0.00839914i
$590$	−0.0348136	+	0.175020i	−0.00143325	+	0.00720546i
$591$	−4.56732	−	23.0545i	−0.187874	−	0.948336i
$592$	−0.450825	+	0.301231i	−0.0185288	+	0.0123805i
$593$	7.05301	+	17.0275i	0.289632	+	0.699234i	0.999989	−	0.00460731i	$-0.00146656\pi$
$593$	7.05301	+	17.0275i	0.289632	+	0.699234i	−0.710357	+	0.703841i	$0.751467\pi$
$594$	−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
$598$	10.2170	+	15.2908i	0.417803	+	0.625286i
$599$	−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	$0.866597\pi$
$600$	14.6724	−	14.6498i	0.599000	−	0.598075i
$601$	7.54195	−	11.2873i	0.307642	−	0.460419i	−0.645144	−	0.764061i	$-0.723203\pi$
$601$	7.54195	−	11.2873i	0.307642	−	0.460419i	0.952786	+	0.303642i	$0.0982026\pi$
$602$	−1.23921	+	0.246495i	−0.0505066	+	0.0100464i
$603$	−0.0250684	+	16.2298i	−0.00102086	+	0.660929i
$604$	0.393378	−	0.949699i	0.0160063	−	0.0386427i
$605$	−1.35725	−	6.82334i	−0.0551800	−	0.277408i
$606$	−9.11671	+	3.76802i	−0.370341	+	0.153065i
$607$	4.05708	+	0.807003i	0.164672	+	0.0327552i	0.276737	−	0.960946i	$-0.410747\pi$
$607$	4.05708	+	0.807003i	0.164672	+	0.0327552i	−0.112066	+	0.993701i	$0.535747\pi$
$608$	2.24400	−	2.24400i	0.0910064	−	0.0910064i
$609$	−0.209233		0.000161589i	−0.00847855		6.54793e-6i
$610$	−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
$615$	11.3323	+	0.00875191i	0.456964	+	0.000352911i
$616$	−1.68500	+	1.68500i	−0.0678906	+	0.0678906i
$617$	−12.5128	−	2.48894i	−0.503745	−	0.100201i	−0.0633250	−	0.997993i	$-0.520170\pi$
$617$	−12.5128	−	2.48894i	−0.503745	−	0.100201i	−0.440420	+	0.897792i	$0.645170\pi$
$618$	3.32537	−	1.37441i	0.133766	−	0.0552867i
$619$	−0.758379	−	3.81263i	−0.0304818	−	0.153243i	0.962547	−	0.271115i	$-0.0873925\pi$
$619$	−0.758379	−	3.81263i	−0.0304818	−	0.153243i	−0.993029	+	0.117873i	$0.962392\pi$
$620$	−0.270499	+	0.653042i	−0.0108635	+	0.0262268i
$621$	−17.8392	−	11.9797i	−0.715863	−	0.480727i
$622$	−8.60700	+	1.71204i	−0.345109	+	0.0686465i
$623$	0.566940	−	0.848486i	0.0227140	−	0.0339939i
$624$	1.79442	−	1.79165i	0.0718343	−	0.0717235i
$625$	10.8916	+	10.8916i	0.435663	+	0.435663i
$626$	−11.1868	−	16.7422i	−0.447113	−	0.669152i
$627$	−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	0.928696	+	0.370843i	$0.120931\pi$
$631$	13.4198	+	32.3983i	0.534234	+	1.28976i	−0.394461	+	0.918913i	$0.629069\pi$
$632$	24.8454	−	16.6012i	0.988296	−	0.660359i
$633$	5.22640	+	26.3814i	0.207731	+	1.04857i
$634$	−1.60895	+	8.08874i	−0.0638996	+	0.321245i
$635$	6.02448	+	4.02543i	0.239074	+	0.159744i
$636$	9.97937	−	24.0398i	0.395708	−	0.953240i
$637$	−34.1127	−	14.1299i	−1.35159	−	0.559848i
$638$	−2.11702	−	0.876899i	−0.0838137	−	0.0347168i
$639$	16.2673	−	10.8332i	0.643526	−	0.428554i
$640$	−5.39841	−	3.60710i	−0.213391	−	0.142583i
$641$	0.436325	−	2.19355i	0.0172338	−	0.0866402i	−0.971211	−	0.238220i	$-0.923436\pi$
$641$	0.436325	−	2.19355i	0.0172338	−	0.0866402i	0.988445	+	0.151580i	$0.0484361\pi$
$642$	−5.86080	+	1.16108i	−0.231307	+	0.0458242i
$643$	3.04323	−	2.03342i	0.120013	−	0.0801904i	−0.494115	−	0.869397i	$-0.664508\pi$
$643$	3.04323	−	2.03342i	0.120013	−	0.0801904i	0.614128	+	0.789206i	$0.289508\pi$
$644$	−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	$0.188072\pi$
$647$			28.3391i			1.11413i	−0.830470	+	0.557063i	$0.811928\pi$
$648$	9.59202	−	22.9564i	0.376810	−	0.901811i
$649$	0.638051	+	0.954911i	0.0250457	+	0.0374835i
$650$	−13.6165	−	13.6165i	−0.534082	−	0.534082i
$651$	−0.159092	−	0.159338i	−0.00623532	−	0.00624495i
$652$	−11.6238	+	17.3962i	−0.455223	+	0.681289i
$653$	−9.99878	+	1.98888i	−0.391282	+	0.0778309i	−0.386811	−	0.922159i	$-0.626423\pi$
$653$	−9.99878	+	1.98888i	−0.391282	+	0.0778309i	−0.00447157	+	0.999990i	$0.501423\pi$
$654$	−10.1934	−	15.2811i	−0.398594	−	0.597537i
$655$	−3.07919	+	7.43383i	−0.120314	+	0.290464i
$656$	0.430553	+	2.16454i	0.0168103	+	0.0845109i
$657$	6.84491	−	34.1360i	0.267045	−	1.33177i
$658$	−1.60248	−	0.318752i	−0.0624710	−	0.0124263i
$659$	−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	$0.974843\pi$
$660$	−0.00626963	+	8.11819i	−0.000244045	+	0.316000i
$661$	−1.89254	+	0.783917i	−0.0736114	+	0.0304909i	−0.419185	−	0.907901i	$-0.637684\pi$
$661$	−1.89254	+	0.783917i	−0.0736114	+	0.0304909i	0.345574	+	0.938392i	$0.387684\pi$
$662$	−3.52074			−0.136838
$663$		0			0
$664$	−7.63870			−0.296439
$665$	0.0813074	−	0.0336786i	0.00315296	−	0.00130600i
$666$	4.10391	+	2.75132i	0.159023	+	0.106612i
$667$	1.80965	−	1.80965i	0.0700701	−	0.0700701i
$668$	−11.6614	−	2.31960i	−0.451193	−	0.0897479i
$669$	11.0237	+	26.6719i	0.426203	+	1.03120i
$670$	−0.724197	−	3.64078i	−0.0279782	−	0.140656i
$671$	−17.8297	+	43.0448i	−0.688309	+	1.66172i
$672$	1.62015	−	1.08074i	0.0624986	−	0.0416904i
$673$	16.6779	−	3.31745i	0.642887	−	0.127878i	0.137129	−	0.990553i	$-0.456213\pi$
$673$	16.6779	−	3.31745i	0.642887	−	0.127878i	0.505759	+	0.862675i	$0.331213\pi$
$674$	2.69514	−	4.03356i	0.103813	−	0.155367i
$675$	20.7681	+	8.65887i	0.799366	+	0.333280i
$676$	−13.8741	−	13.8741i	−0.533621	−	0.533621i
$677$	−12.1741	−	18.2198i	−0.467889	−	0.700245i	0.520215	−	0.854035i	$-0.325852\pi$
$677$	−12.1741	−	18.2198i	−0.467889	−	0.700245i	−0.988103	+	0.153791i	$0.950852\pi$
$678$	−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
$683$	−30.1890	+	20.1716i	−1.15515	+	0.771847i	−0.977227	−	0.212198i	$-0.931938\pi$
$683$	−30.1890	+	20.1716i	−1.15515	+	0.771847i	−0.177923	+	0.984044i	$0.556938\pi$
$684$	1.97916	+	0.823378i	0.0756750	+	0.0314827i
$685$	2.02190	−	10.1648i	0.0772530	−	0.388377i
$686$	−1.90003	−	1.26956i	−0.0725434	−	0.0484720i
$687$	17.5658	+	7.29188i	0.670176	+	0.278202i
$688$	−1.96874	−	0.815481i	−0.0750577	−	0.0310899i
$689$	−56.7746	−	23.5168i	−2.16294	−	0.895919i
$690$	4.53928	+	1.88434i	0.172807	+	0.0717355i
$691$	2.38987	+	1.59686i	0.0909151	+	0.0607475i	0.600197	−	0.799852i	$-0.295089\pi$
$691$	2.38987	+	1.59686i	0.0909151	+	0.0607475i	−0.509282	+	0.860600i	$0.670089\pi$
$692$	0.294952	−	1.48282i	0.0112124	−	0.0563685i
$693$	−2.38765	−	0.993319i	−0.0906991	−	0.0377331i
$694$	0.0132020	−	0.00882130i	0.000501141	−	0.000334852i
$695$	−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
$700$	0.609067	+	0.911533i	0.0230206	+	0.0344527i
$701$	−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	$0.782997\pi$
$702$	−21.3275	−	8.89210i	−0.804956	−	0.335611i
$703$	−0.601207	+	0.899770i	−0.0226750	+	0.0339355i
$704$	18.5277	−	3.68539i	0.698290	−	0.138898i
$705$	−11.7711	+	7.85208i	−0.443327	+	0.295726i
$706$	−3.90754	+	9.43364i	−0.147062	+	0.355040i
$707$	−0.258672	−	1.30043i	−0.00972838	−	0.0489079i
$708$	−0.223153	−	0.539917i	−0.00838659	−	0.0202913i
$709$	36.8486	+	7.32963i	1.38388	+	0.275270i	0.830202	−	0.557463i	$-0.188225\pi$
$709$	36.8486	+	7.32963i	1.38388	+	0.275270i	0.553675	+	0.832733i	$0.313225\pi$
$710$	−3.16093	+	3.16093i	−0.118628	+	0.118628i
$711$	26.9349	+	18.0575i	1.01014	+	0.677211i
$712$	−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
$717$	−0.0183548	+	23.7667i	−0.000685474	+	0.887582i
$718$	18.8705	−	18.8705i	0.704242	−	0.704242i
$719$	24.1120	+	4.79617i	0.899225	+	0.178867i	0.622996	−	0.782225i	$-0.285915\pi$
$719$	24.1120	+	4.79617i	0.899225	+	0.178867i	0.276229	+	0.961092i	$0.410915\pi$
$720$	0.133237	−	0.664464i	0.00496546	−	0.0247631i
$721$	0.0943522	+	0.474341i	0.00351386	+	0.0176654i
$722$	−5.99913	+	14.4832i	−0.223265	+	0.539009i
$723$	4.11008	+	6.16146i	0.152855	+	0.229147i
$724$	16.3853	−	3.25924i	0.608955	−	0.121129i
$725$	−1.48884	+	2.22820i	−0.0552940	+	0.0827533i
$726$	−8.72334	−	8.73683i	−0.323754	−	0.324254i
$727$	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	$0.503416\pi$
$728$	−1.58999	−	2.37959i	−0.0589290	−	0.0881935i
$729$	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	$-0.239173\pi$
$733$	−7.27415	−	17.5613i	−0.268677	−	0.648643i	−0.999422	+	0.0340076i	$0.989173\pi$
$734$	23.4426	−	15.6638i	0.865282	−	0.578163i
$735$	−9.67984	+	1.91767i	−0.357046	+	0.0707343i
$736$	−4.64730	+	23.3635i	−0.171302	+	0.861192i
$737$	−19.8642	−	13.2728i	−0.731706	−	0.488910i
$738$	16.7388	−	11.1471i	0.616164	−	0.410332i
$739$	33.5289	+	13.8881i	1.23338	+	0.510884i	0.901640	−	0.432487i	$-0.142364\pi$
$739$	33.5289	+	13.8881i	1.23338	+	0.510884i	0.331742	+	0.943370i	$0.392364\pi$
$740$	1.92607	+	0.797805i	0.0708038	+	0.0293279i
$741$	1.94034	−	4.67417i	0.0712800	−	0.171710i
$742$	−1.57682	−	1.05360i	−0.0578868	−	0.0386788i
$743$	−0.0347832	+	0.174867i	−0.00127607	+	0.00641525i	−0.981418	−	0.191882i	$-0.938541\pi$
$743$	−0.0347832	+	0.174867i	−0.00127607	+	0.00641525i	0.980142	+	0.198297i	$0.0635410\pi$
$744$	0.619682	+	3.12797i	0.0227186	+	0.114677i
$745$	−8.64227	+	5.77458i	−0.316628	+	0.211564i
$746$	−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
$751$	−21.1032	−	31.5832i	−0.770067	−	1.15249i	−0.984438	−	0.175734i	$-0.943770\pi$
$751$	−21.1032	−	31.5832i	−0.770067	−	1.15249i	0.214371	−	0.976752i	$-0.431230\pi$
$752$	−1.94852	−	1.94852i	−0.0710551	−	0.0710551i
$753$	−11.3911	+	11.3736i	−0.415116	+	0.414476i
$754$	1.52894	−	2.28822i	0.0556807	−	0.0833320i
$755$	−0.636146	+	0.126537i	−0.0231517	+	0.00460516i
$756$	1.09210	+	0.733383i	0.0397193	+	0.0266729i
$757$	7.33808	−	17.7157i	0.266707	−	0.643888i	−0.732617	−	0.680641i	$-0.761701\pi$
$757$	7.33808	−	17.7157i	0.266707	−	0.643888i	0.999324	+	0.0367531i	$0.0117015\pi$
$758$	6.21858	+	31.2629i	0.225869	+	1.13552i
$759$	29.2326	−	12.0821i	1.06108	−	0.438552i
$760$	−1.22239	−	0.243149i	−0.0443409	−	0.00881996i
$761$	−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	$0.439874\pi$
$762$	12.8583	+	0.00993038i	0.465807	+	0.000359740i
$763$	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
$768$	−26.3406	−	0.0203427i	−0.950486	−	0.000734055i
$769$	−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	$0.358552\pi$
$770$	0.580115	+	0.115392i	0.0209059	+	0.00415844i
$771$	−25.1773	+	10.4060i	−0.906737	+	0.374763i
$772$	0.752804	+	3.78460i	0.0270940	+	0.136211i
$773$	15.6889	−	37.8763i	0.564289	−	1.36232i	−0.342017	−	0.939694i	$-0.611110\pi$
$773$	15.6889	−	37.8763i	0.564289	−	1.36232i	0.906306	−	0.422621i	$-0.138890\pi$
$774$	−0.0299934	+	19.4184i	−0.00107809	+	0.697979i
$775$	−2.82847	+	0.562617i	−0.101601	+	0.0202098i
$776$	−3.79206	+	5.67523i	−0.136127	+	0.203729i
$777$	−0.469950	+	0.469224i	−0.0168593	+	0.0168333i
$778$	−0.447469	−	0.447469i	−0.0160425	−	0.0160425i
$779$	2.44711	+	3.66236i	0.0876769	+	0.131218i
$780$	−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
$785$	−1.60477	+	1.07227i	−0.0572766	+	0.0382710i
$786$	2.77494	+	14.0071i	0.0989788	+	0.499616i
$787$	−2.93350	+	14.7477i	−0.104568	+	0.525700i	0.892623	+	0.450804i	$0.148862\pi$
$787$	−2.93350	+	14.7477i	−0.104568	+	0.525700i	−0.997191	+	0.0748960i	$0.976138\pi$
$788$	−14.6328	−	9.77735i	−0.521273	−	0.348304i
$789$	10.2543	−	24.7021i	0.365063	−	0.879419i
$790$	−6.85236	−	2.83834i	−0.243796	−	0.100984i
$791$	−0.222954	−	0.0923506i	−0.00792734	−	0.00328361i
$792$	20.2997	+	30.4824i	0.721318	+	1.08315i
$793$	−46.5257	−	31.0875i	−1.65217	−	1.10395i
$794$	−3.29558	+	16.5680i	−0.116956	+	0.587977i
$795$	−16.1104	+	3.19163i	−0.571378	+	0.113195i
$796$	−4.63897	+	3.09966i	−0.164424	+	0.109865i
$797$	−6.21185	−	14.9967i	−0.220035	−	0.531211i	0.774859	−	0.632134i	$-0.217821\pi$
$797$	−6.21185	−	14.9967i	−0.220035	−	0.531211i	−0.994894	+	0.100922i	$0.967821\pi$
$798$	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
$802$	−7.34549	−	10.9933i	−0.259378	−	0.388187i
$803$	36.2384	+	36.2384i	1.27882	+	1.27882i
$804$	8.58677	+	8.60005i	0.302832	+	0.303300i
$805$	−0.367012	+	0.549272i	−0.0129355	+	0.0193593i
$806$	2.90465	−	0.577772i	0.102312	−	0.0203511i
$807$	23.3930	+	35.0687i	0.823473	+	1.23448i
$808$	−7.18583	+	17.3481i	−0.252797	+	0.610305i
$809$	7.37905	+	37.0970i	0.259434	+	1.30426i	0.862292	+	0.506412i	$0.169028\pi$
$809$	7.37905	+	37.0970i	0.259434	+	1.30426i	−0.602858	+	0.797848i	$0.705972\pi$
$810$	−6.06052	+	1.18606i	−0.212945	+	0.0416739i
$811$	−33.9217	−	6.74744i	−1.19115	−	0.236935i	−0.440573	−	0.897717i	$-0.645225\pi$
$811$	−33.9217	−	6.74744i	−1.19115	−	0.236935i	−0.750578	+	0.660782i	$0.770225\pi$
$812$	−0.110785	+	0.110785i	−0.00388780	+	0.00388780i
$813$	−0.00752467	+	9.74327i	−0.000263902	+	0.341711i
$814$	−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
$819$	1.72948	−	2.57971i	0.0604329	−	0.0901425i
$820$	6.00029	−	6.00029i	0.209539	−	0.209539i
$821$	−49.3864	−	9.82356i	−1.72360	−	0.342845i	−0.768660	−	0.639657i	$-0.779076\pi$
$821$	−49.3864	−	9.82356i	−1.72360	−	0.342845i	−0.954936	+	0.296813i	$0.904076\pi$
$822$	−7.02529	−	16.9977i	−0.245035	−	0.592862i
$823$	−4.66026	−	23.4287i	−0.162447	−	0.816674i	−0.972963	−	0.230959i	$-0.925814\pi$
$823$	−4.66026	−	23.4287i	−0.162447	−	0.816674i	0.810517	−	0.585715i	$-0.199186\pi$
$824$	2.62107	−	6.32783i	0.0913094	−	0.220440i
$825$	−27.5537	+	18.3801i	−0.959298	+	0.639912i
$826$	−0.0417473	+	0.00830405i	−0.00145257	+	0.000288935i
$827$	−3.73122	+	5.58417i	−0.129747	+	0.194181i	−0.890655	−	0.454679i	$-0.849754\pi$
$827$	−3.73122	+	5.58417i	−0.129747	+	0.194181i	0.760908	+	0.648860i	$0.224754\pi$
$828$	−15.7862	+	3.11472i	−0.548607	+	0.108244i
$829$	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	$0.606961\pi$
$830$	1.05338	+	1.57649i	0.0365632	+	0.0547208i
$831$	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
$836$	−2.62362	+	1.75304i	−0.0907397	+	0.0606303i
$837$	−2.88176	+	1.91589i	−0.0996082	+	0.0662227i
$838$	5.76309	−	28.9730i	0.199083	−	1.00086i
$839$	−36.6159	−	24.4659i	−1.26412	−	0.844658i	−0.271094	−	0.962553i	$-0.587385\pi$
$839$	−36.6159	−	24.4659i	−1.26412	−	0.844658i	−0.993026	+	0.117895i	$0.962385\pi$
$840$	−0.706415	−	0.293246i	−0.0243736	−	0.0101179i
$841$	26.4387	+	10.9513i	0.911679	+	0.377630i
$842$	0.00978190	+	0.00405180i	0.000337107	+	0.000139634i
$843$	−11.5470	−	4.79339i	−0.397701	−	0.165093i
$844$	16.7444	+	11.1883i	0.576367	+	0.385116i
$845$	−2.41529	+	12.1425i	−0.0830884	+	0.417713i
$846$	−9.64526	+	23.1844i	−0.331611	+	0.797095i
$847$	1.37978	−	0.921941i	0.0474099	−	0.0316783i
$848$	−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
$853$	17.9800	+	26.9089i	0.615623	+	0.921344i	0.999998	−	0.00183231i	$-0.000583244\pi$
$853$	17.9800	+	26.9089i	0.615623	+	0.921344i	−0.384376	+	0.923177i	$0.625583\pi$
$854$	−1.22103	−	1.22103i	−0.0417829	−	0.0417829i
$855$	−0.261821	−	1.32697i	−0.00895411	−	0.0453816i
$856$	−6.31843	+	9.45620i	−0.215959	+	0.323206i
$857$	24.3224	−	4.83803i	0.830838	−	0.165264i	0.238693	−	0.971095i	$-0.423281\pi$
$857$	24.3224	−	4.83803i	0.830838	−	0.165264i	0.592145	+	0.805831i	$0.298281\pi$
$858$	28.2959	−	18.8751i	0.966007	−	0.644387i
$859$	−16.0644	+	38.7830i	−0.548112	+	1.32326i	0.370770	+	0.928725i	$0.379094\pi$
$859$	−16.0644	+	38.7830i	−0.548112	+	1.32326i	−0.918881	+	0.394534i	$0.870906\pi$
$860$	1.59848	+	8.03608i	0.0545076	+	0.274028i
$861$	1.03250	+	2.49813i	0.0351875	+	0.0851360i
$862$	−9.75076	−	1.93955i	−0.332112	−	0.0660613i
$863$	−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	$0.251136\pi$
$864$	−11.3901	−	27.6794i	−0.387499	−	0.941671i
$865$	−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
$870$	0.000568017	−	0.735493i	1.92576e−5	−	0.0249355i
$871$	20.2885	−	20.2885i	0.687450	−	0.687450i
$872$	−34.2934	−	6.82138i	−1.16132	−	0.231001i
$873$	−7.26265	−	1.45630i	−0.245803	−	0.0492881i
$874$	0.372684	+	1.87361i	0.0126062	+	0.0633758i
$875$	0.570368	−	1.37699i	0.0192820	−	0.0465507i
$876$	−14.4669	−	21.6876i	−0.488793	−	0.732755i
$877$	−7.25275	+	1.44266i	−0.244908	+	0.0487152i	−0.316018	−	0.948753i	$-0.602346\pi$
$877$	−7.25275	+	1.44266i	−0.244908	+	0.0487152i	0.0711099	+	0.997468i	$0.477346\pi$
$878$	14.1850	−	21.2294i	0.478721	−	0.716456i
$879$	23.3790	+	23.4152i	0.788555	+	0.789774i
$880$	0.705386	+	0.705386i	0.0237786	+	0.0237786i
$881$	27.6606	+	41.3971i	0.931911	+	1.39470i	0.918772	+	0.394790i	$0.129183\pi$
$881$	27.6606	+	41.3971i	0.931911	+	1.39470i	0.0131394	+	0.999914i	$0.495817\pi$
$882$	−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	$-0.160011\pi$
$884$		0			0
$885$	−0.205034	+	0.306342i	−0.00689214	+	0.0102976i
$886$	−12.9134	−	31.1758i	−0.433835	−	1.04737i
$887$	−35.5608	+	23.7610i	−1.19402	+	0.797816i	−0.983700	−	0.179818i	$-0.942449\pi$
$887$	−35.5608	+	23.7610i	−1.19402	+	0.797816i	−0.210315	+	0.977634i	$0.567449\pi$
$888$	9.22560	−	1.82768i	0.309591	−	0.0613329i
$889$	−0.337170	+	1.69507i	−0.0113083	+	0.0568508i
$890$	2.98259	+	1.99290i	0.0999765	+	0.0668022i
$891$	−22.1827	+	32.9777i	−0.743148	+	1.10480i
$892$	19.9656	+	8.27003i	0.668498	+	0.276901i
$893$	−5.08111	−	2.10466i	−0.170033	−	0.0704299i
$894$	−7.07196	+	17.0360i	−0.236522	+	0.569769i
$895$	−7.00016	−	4.67736i	−0.233990	−	0.156347i
$896$	0.302131	−	1.51892i	0.0100935	−	0.0507434i
$897$	7.38245	+	37.2645i	0.246493	+	1.24422i
$898$	25.4021	−	16.9732i	0.847680	−	0.566402i
$899$	−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
$904$	1.89872	+	2.84164i	0.0631506	+	0.0945116i
$905$	−7.45379	−	7.45379i	−0.247772	−	0.247772i
$906$	−0.814541	+	0.813284i	−0.0270613	+	0.0270196i
$907$	−4.51990	+	6.76450i	−0.150081	+	0.224612i	−0.898891	−	0.438173i	$-0.855626\pi$
$907$	−4.51990	+	6.76450i	−0.150081	+	0.224612i	0.748810	+	0.662785i	$0.230626\pi$
$908$	24.4851	−	4.87038i	0.812565	−	0.161629i
$909$	−20.3777	−	0.0314752i	−0.675885	−	0.00104396i
$910$	−0.271845	+	0.656291i	−0.00901157	+	0.0217558i
$911$	0.578423	+	2.90793i	0.0191640	+	0.0963440i	0.989184	−	0.146683i	$-0.0468597\pi$
$911$	0.578423	+	2.90793i	0.0191640	+	0.0963440i	−0.970020	+	0.243027i	$0.921860\pi$
$912$	0.243434	−	0.100613i	0.00806089	−	0.00333164i
$913$	11.9680	+	2.38058i	0.396083	+	0.0787858i
$914$	−12.6372	+	12.6372i	−0.418002	+	0.418002i
$915$	−14.9546	−	0.0115493i	−0.494382	−	0.000381809i
$916$	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
$921$	8.63966	+	0.00667236i	0.284687	+	0.000219862i
$922$	3.64477	−	3.64477i	0.120034	−	0.120034i
$923$	−33.8882	−	6.74078i	−1.11544	−	0.221875i
$924$	−1.78959	+	0.739655i	−0.0588733	+	0.0243328i
$925$	1.65937	+	8.34224i	0.0545599	+	0.274291i
$926$	−11.6457	+	28.1151i	−0.382700	+	0.923919i
$927$	7.43288	+	0.0114807i	0.244128	+	0.000377077i
$928$	3.49629	−	0.695455i	0.114771	−	0.0228294i
$929$	15.6397	−	23.4065i	0.513122	−	0.767941i	−0.480940	−	0.876753i	$-0.659705\pi$
$929$	15.6397	−	23.4065i	0.513122	−	0.767941i	0.994062	+	0.108812i	$0.0347046\pi$
$930$	0.560103	−	0.559239i	0.0183665	−	0.0183382i
$931$	−2.71211	−	2.71211i	−0.0888859	−	0.0888859i
$932$	16.9234	+	25.3277i	0.554346	+	0.829637i
$933$	−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	0.966105	+	0.258151i	$0.0831132\pi$
$937$	14.2493	+	34.4010i	0.465506	+	1.12383i	−0.500599	+	0.865679i	$0.666887\pi$
$938$	0.736221	−	0.491927i	0.0240385	−	0.0160620i
$939$	−8.08320	−	40.8017i	−0.263785	−	1.33151i
$940$	−2.06705	+	10.3918i	−0.0674197	+	0.338942i
$941$	37.8140	+	25.2665i	1.23270	+	0.823664i	0.989248	−	0.146249i	$-0.0467202\pi$
$941$	37.8140	+	25.2665i	1.23270	+	0.823664i	0.243452	+	0.969913i	$0.421720\pi$
$942$	−1.31318	+	3.16339i	−0.0427857	+	0.103069i
$943$	−30.5462	−	12.6526i	−0.994720	−	0.412026i
$944$	−0.0663241	−	0.0274723i	−0.00215867	−	0.000894148i
$945$	0.00192311	−	0.830043i	6.25589e−5	−	0.0270013i
$946$	−23.7668	−	15.8804i	−0.772724	−	0.516318i
$947$	3.20866	−	16.1310i	0.104267	−	0.524188i	−0.892983	−	0.450089i	$-0.851392\pi$
$947$	3.20866	−	16.1310i	0.104267	−	0.524188i	0.997251	−	0.0740985i	$-0.0236079\pi$
$948$	23.8191	−	4.71879i	0.773608	−	0.153259i
$949$	−51.1766	+	34.1951i	−1.66126	+	1.11002i
$950$	−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	$-0.920241\pi$
$953$		−	15.3092i		−	0.495915i	0.968771	−	0.247958i	$-0.0797593\pi$
$954$	−20.6410	+	20.5774i	−0.668278	+	0.666217i
$955$	7.56488	+	11.3216i	0.244794	+	0.366360i
$956$	12.5840	+	12.5840i	0.406997	+	0.406997i
$957$	−3.34450	−	3.34967i	−0.108112	−	0.108279i
$958$	1.06954	−	1.60067i	0.0345552	−	0.0517154i
$959$	2.42460	−	0.482282i	0.0782943	−	0.0155737i
$960$	3.36475	+	5.04414i	0.108597	+	0.162799i
$961$	−11.6935	+	28.2305i	−0.377208	+	0.910661i
$962$	−1.70407	−	8.56694i	−0.0549415	−	0.276209i
$963$	−12.1012	−	2.42651i	−0.389955	−	0.0781933i
$964$	5.43944	+	1.08197i	0.175193	+	0.0348480i
$965$	1.72164	−	1.72164i	0.0554216	−	0.0554216i
$966$	−0.000905386		1.17233i	−2.91303e−5		0.0377192i
$967$	44.6169	−	18.4809i	1.43478	−	0.594306i	0.476255	−	0.879307i	$-0.341994\pi$
$967$	44.6169	−	18.4809i	1.43478	−	0.594306i	0.958527	+	0.285001i	$0.0919939\pi$
$968$	−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	$-0.608040\pi$
$971$	3.06636	−	1.27013i	0.0984041	−	0.0407603i	0.431342	+	0.902188i	$0.358040\pi$
$972$	14.3511	−	14.2407i	0.460313	−	0.456772i
$973$	1.64333	−	1.64333i	0.0526828	−	0.0526828i
$974$	23.0893	+	4.59275i	0.739829	+	0.147161i
$975$	−15.1943	−	36.7625i	−0.486607	−	1.17734i
$976$	−0.568172	−	2.85640i	−0.0181868	−	0.0914310i
$977$	11.3473	−	27.3947i	0.363031	−	0.876434i	−0.631823	−	0.775113i	$-0.717693\pi$
$977$	11.3473	−	27.3947i	0.363031	−	0.876434i	0.994854	−	0.101321i	$-0.0323070\pi$
$978$	19.4895	−	13.0007i	0.623206	−	0.415717i
$979$	22.6425	−	4.50386i	0.723656	−	0.143944i
$980$	−4.10519	+	6.14386i	−0.131136	+	0.196258i
$981$	−7.34521	−	37.2273i	−0.234515	−	1.18858i
$982$	−8.01800	−	8.01800i	−0.255865	−	0.255865i
$983$	−1.38926	−	2.07918i	−0.0443106	−	0.0663155i	0.808653	−	0.588286i	$-0.200197\pi$
$983$	−1.38926	−	2.07918i	−0.0443106	−	0.0663155i	−0.852964	+	0.521971i	$0.825197\pi$
$984$	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
$989$	26.5443	−	17.7363i	0.844059	−	0.563982i
$990$	3.49170	−	8.39302i	0.110973	−	0.266748i
$991$	7.44416	−	37.4243i	0.236471	−	1.18882i	−0.661902	−	0.749590i	$-0.730251\pi$
$991$	7.44416	−	37.4243i	0.236471	−	1.18882i	0.898374	−	0.439232i	$-0.144749\pi$
$992$	3.18969	+	2.13128i	0.101273	+	0.0676683i
$993$	−6.71711	−	2.78840i	−0.213161	−	0.0884871i
$994$	−0.985113	−	0.408047i	−0.0312459	−	0.0129425i
$995$	3.25239	+	1.34718i	0.103108	+	0.0427086i
$996$	−5.73299	−	2.37987i	−0.181657	−	0.0754090i
$997$	37.1624	+	24.8311i	1.17695	+	0.786410i	0.980963	−	0.194197i	$-0.0622101\pi$
$997$	37.1624	+	24.8311i	1.17695	+	0.786410i	0.195984	+	0.980607i	$0.437210\pi$
$998$	−2.49181	+	12.5272i	−0.0788769	+	0.396541i
$999$	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.d.158.2		32
3.2	odd	2	inner	867.2.i.d.158.3		32
17.2	even	8		867.2.i.f.224.2		32
17.3	odd	16		867.2.i.b.827.2		32
17.4	even	4		867.2.i.h.131.3		32
17.5	odd	16		867.2.i.g.329.3		32
17.6	odd	16		867.2.i.h.503.2		32
17.7	odd	16	inner	867.2.i.d.653.3		32
17.8	even	8		867.2.i.b.65.3		32
17.9	even	8		867.2.i.i.65.3		32
17.10	odd	16		867.2.i.c.653.3		32
17.11	odd	16		51.2.i.a.44.2	yes	32
17.12	odd	16		867.2.i.f.329.3		32
17.13	even	4		51.2.i.a.29.3	yes	32
17.14	odd	16		867.2.i.i.827.2		32
17.15	even	8		867.2.i.g.224.2		32
17.16	even	2		867.2.i.c.158.2		32
51.2	odd	8		867.2.i.f.224.3		32
51.5	even	16		867.2.i.g.329.2		32
51.8	odd	8		867.2.i.b.65.2		32
51.11	even	16		51.2.i.a.44.3	yes	32
51.14	even	16		867.2.i.i.827.3		32
51.20	even	16		867.2.i.b.827.3		32
51.23	even	16		867.2.i.h.503.3		32
51.26	odd	8		867.2.i.i.65.2		32
51.29	even	16		867.2.i.f.329.2		32
51.32	odd	8		867.2.i.g.224.3		32
51.38	odd	4		867.2.i.h.131.2		32
51.41	even	16	inner	867.2.i.d.653.2		32
51.44	even	16		867.2.i.c.653.2		32
51.47	odd	4		51.2.i.a.29.2	✓	32
51.50	odd	2		867.2.i.c.158.3		32
68.11	even	16		816.2.cj.c.401.1		32
68.47	odd	4		816.2.cj.c.641.2		32
204.11	odd	16		816.2.cj.c.401.2		32
204.47	even	4		816.2.cj.c.641.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.2	✓	32	51.47	odd	4
51.2.i.a.29.3	yes	32	17.13	even	4
51.2.i.a.44.2	yes	32	17.11	odd	16
51.2.i.a.44.3	yes	32	51.11	even	16
816.2.cj.c.401.1		32	68.11	even	16
816.2.cj.c.401.2		32	204.11	odd	16
816.2.cj.c.641.1		32	204.47	even	4
816.2.cj.c.641.2		32	68.47	odd	4
867.2.i.b.65.2		32	51.8	odd	8
867.2.i.b.65.3		32	17.8	even	8
867.2.i.b.827.2		32	17.3	odd	16
867.2.i.b.827.3		32	51.20	even	16
867.2.i.c.158.2		32	17.16	even	2
867.2.i.c.158.3		32	51.50	odd	2
867.2.i.c.653.2		32	51.44	even	16
867.2.i.c.653.3		32	17.10	odd	16
867.2.i.d.158.2		32	1.1	even	1	trivial
867.2.i.d.158.3		32	3.2	odd	2	inner
867.2.i.d.653.2		32	51.41	even	16	inner
867.2.i.d.653.3		32	17.7	odd	16	inner
867.2.i.f.224.2		32	17.2	even	8
867.2.i.f.224.3		32	51.2	odd	8
867.2.i.f.329.2		32	51.29	even	16
867.2.i.f.329.3		32	17.12	odd	16
867.2.i.g.224.2		32	17.15	even	8
867.2.i.g.224.3		32	51.32	odd	8
867.2.i.g.329.2		32	51.5	even	16
867.2.i.g.329.3		32	17.5	odd	16
867.2.i.h.131.2		32	51.38	odd	4
867.2.i.h.131.3		32	17.4	even	4
867.2.i.h.503.2		32	17.6	odd	16
867.2.i.h.503.3		32	51.23	even	16
867.2.i.i.65.2		32	51.26	odd	8
867.2.i.i.65.3		32	17.9	even	8
867.2.i.i.827.2		32	17.14	odd	16
867.2.i.i.827.3		32	51.14	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 $\F_{q}$

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} +(-1.73205 - 0.00133765i) q^{3} +(-0.917091 + 0.917091i) q^{4} +(0.802626 + 0.159652i) q^{5} +(1.34216 - 0.554726i) q^{6} +(0.0380817 + 0.191449i) q^{7} +(1.05790 - 2.55399i) q^{8} +(3.00000 + 0.00463376i) q^{9} +(-0.672980 + 0.133864i) q^{10} +(-2.45341 + 3.67179i) q^{11} +(1.58968 - 1.58722i) q^{12} +(-3.75023 - 3.75023i) q^{13} +(-0.0909302 - 0.136087i) q^{14} +(-1.38998 - 0.277599i) q^{15} -0.276039i q^{16} +(-2.32543 + 0.959018i) q^{18} +(-0.210831 - 0.508991i) q^{19} +(-0.882497 + 0.589666i) q^{20} +(-0.0657033 - 0.331651i) q^{21} +(0.722364 - 3.63157i) q^{22} +(3.43849 + 2.29752i) q^{23} +(-1.83574 + 4.42222i) q^{24} +(-4.00068 - 1.65713i) q^{25} +(4.10844 + 1.70177i) q^{26} +(-5.19614 - 0.0120389i) q^{27} +(-0.210501 - 0.140652i) q^{28} +(0.120733 - 0.606965i) q^{29} +(1.16581 - 0.230959i) q^{30} +(0.553739 - 0.369997i) q^{31} +(2.20436 + 5.32181i) q^{32} +(4.25434 - 6.35644i) q^{33} +0.159742i q^{35} +(-2.75552 + 2.74702i) q^{36} +(-1.09126 - 1.63319i) q^{37} +(0.326640 + 0.326640i) q^{38} +(6.49057 + 6.50060i) q^{39} +(1.25684 - 1.88100i) q^{40} +(-7.84141 + 1.55975i) q^{41} +(0.157314 + 0.235831i) q^{42} +(2.95422 - 7.13212i) q^{43} +(-1.11736 - 5.61737i) q^{44} +(2.40714 + 0.482675i) q^{45} +(-3.40082 - 0.676466i) q^{46} +(7.05884 - 7.05884i) q^{47} +(-0.000369245 + 0.478114i) q^{48} +(6.43195 - 2.66420i) q^{49} +3.63084 q^{50} +6.87860 q^{52} +(10.7049 - 4.43410i) q^{53} +(4.02904 - 1.65796i) q^{54} +(-2.55538 + 2.55538i) q^{55} +(0.529246 + 0.105274i) q^{56} +(0.364489 + 0.881880i) q^{57} +(0.101231 + 0.508924i) q^{58} +(0.0995233 - 0.240270i) q^{59} +(1.52932 - 1.02015i) q^{60} +(10.3478 - 2.05830i) q^{61} +(-0.310232 + 0.464295i) q^{62} +(0.113358 + 0.574524i) q^{63} +(-3.02483 - 3.02483i) q^{64} +(-2.41130 - 3.60876i) q^{65} +(-1.25603 + 6.28910i) q^{66} +5.40994i q^{67} +(-5.95256 - 3.98403i) q^{69} +(-0.0512564 - 0.123744i) q^{70} +(5.41686 - 3.61943i) q^{71} +(3.18552 - 7.65705i) q^{72} +(2.26406 - 11.3822i) q^{73} +(1.36939 + 0.914994i) q^{74} +(6.92716 + 2.87559i) q^{75} +(0.660143 + 0.273440i) q^{76} +(-0.796392 - 0.329876i) q^{77} +(-7.11375 - 2.95305i) q^{78} +(8.98758 + 6.00531i) q^{79} +(0.0440703 - 0.221556i) q^{80} +(8.99996 + 0.0278025i) q^{81} +(5.57385 - 3.72433i) q^{82} +(-1.05744 - 2.55289i) q^{83} +(0.364410 + 0.243898i) q^{84} +6.47280i q^{86} +(-0.209927 + 1.05113i) q^{87} +(6.78225 + 10.1503i) q^{88} +(-3.69661 - 3.69661i) q^{89} +(-2.01956 + 0.398473i) q^{90} +(0.575164 - 0.860794i) q^{91} +(-5.26045 + 1.04637i) q^{92} +(-0.959599 + 0.640112i) q^{93} +(-3.20315 + 7.73308i) q^{94} +(-0.0879569 - 0.442189i) q^{95} +(-3.81095 - 9.22058i) q^{96} +(-2.42163 - 0.481692i) q^{97} +(-4.12764 + 4.12764i) q^{98} +(-7.37724 + 11.0040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

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