LMFDB - Embedded newform 820.2.s.c.583.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			583.8
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37024 - 0.349906i) q^{2} +2.06782 q^{3} +(1.75513 + 0.958912i) q^{4} +(-0.600491 + 2.15393i) q^{5} +(-2.83341 - 0.723542i) q^{6} -3.38406i q^{7} +(-2.06943 - 1.92807i) q^{8} +1.27587 q^{9} +(1.57649 - 2.74129i) q^{10} +(3.69062 - 3.69062i) q^{11} +(3.62929 + 1.98286i) q^{12} +0.425062i q^{13} +(-1.18410 + 4.63699i) q^{14} +(-1.24171 + 4.45394i) q^{15} +(2.16098 + 3.36603i) q^{16} -3.34792i q^{17} +(-1.74826 - 0.446436i) q^{18} +(-0.684819 + 0.684819i) q^{19} +(-3.11937 + 3.20461i) q^{20} -6.99763i q^{21} +(-6.34841 + 3.76568i) q^{22} +(5.31453 - 5.31453i) q^{23} +(-4.27920 - 3.98691i) q^{24} +(-4.27882 - 2.58683i) q^{25} +(0.148732 - 0.582438i) q^{26} -3.56518 q^{27} +(3.24502 - 5.93948i) q^{28} +(3.38159 - 3.38159i) q^{29} +(3.25990 - 5.66849i) q^{30} +6.18545i q^{31} +(-1.78327 - 5.36842i) q^{32} +(7.63153 - 7.63153i) q^{33} +(-1.17146 + 4.58747i) q^{34} +(7.28903 + 2.03210i) q^{35} +(2.23933 + 1.22345i) q^{36} +(-3.00501 + 3.00501i) q^{37} +(1.17799 - 0.698746i) q^{38} +0.878951i q^{39} +(5.39561 - 3.29961i) q^{40} +(6.32040 - 1.02593i) q^{41} +(-2.44851 + 9.58845i) q^{42} +(-1.80499 - 1.80499i) q^{43} +(10.0165 - 2.93854i) q^{44} +(-0.766151 + 2.74814i) q^{45} +(-9.14179 + 5.42262i) q^{46} +8.57237 q^{47} +(4.46851 + 6.96035i) q^{48} -4.45188 q^{49} +(4.95788 + 5.04177i) q^{50} -6.92289i q^{51} +(-0.407597 + 0.746040i) q^{52} +9.32035i q^{53} +(4.88516 + 1.24748i) q^{54} +(5.73315 + 10.1655i) q^{55} +(-6.52472 + 7.00308i) q^{56} +(-1.41608 + 1.41608i) q^{57} +(-5.81684 + 3.45036i) q^{58} +0.468941 q^{59} +(-6.45029 + 6.62656i) q^{60} -0.208691i q^{61} +(2.16432 - 8.47557i) q^{62} -4.31764i q^{63} +(0.565069 + 7.98002i) q^{64} +(-0.915554 - 0.255246i) q^{65} +(-13.1274 + 7.78673i) q^{66} -4.16083 q^{67} +(3.21036 - 5.87604i) q^{68} +(10.9895 - 10.9895i) q^{69} +(-9.27670 - 5.33494i) q^{70} +(-5.60857 + 5.60857i) q^{71} +(-2.64033 - 2.45998i) q^{72} +(3.45071 - 3.45071i) q^{73} +(5.16907 - 3.06613i) q^{74} +(-8.84783 - 5.34910i) q^{75} +(-1.85863 + 0.545267i) q^{76} +(-12.4893 - 12.4893i) q^{77} +(0.307550 - 1.20438i) q^{78} +(10.8014 + 10.8014i) q^{79} +(-8.54784 + 2.63332i) q^{80} -11.1998 q^{81} +(-9.01946 - 0.805764i) q^{82} +(5.42477 - 5.42477i) q^{83} +(6.71011 - 12.2818i) q^{84} +(7.21119 + 2.01040i) q^{85} +(1.84170 + 3.10486i) q^{86} +(6.99252 - 6.99252i) q^{87} +(-14.7533 + 0.521689i) q^{88} +(2.57886 - 2.57886i) q^{89} +(2.01140 - 3.49754i) q^{90} +1.43844 q^{91} +(14.4239 - 4.23154i) q^{92} +12.7904i q^{93} +(-11.7462 - 2.99952i) q^{94} +(-1.06382 - 1.88628i) q^{95} +(-3.68747 - 11.1009i) q^{96} -13.1254i q^{97} +(6.10016 + 1.55774i) q^{98} +(4.70877 - 4.70877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37024	−	0.349906i	−0.968908	−	0.247421i
$2$	−1.37024	−	0.349906i	−0.968908	−	0.247421i
$3$	2.06782			1.19386			0.596928	−	0.802295i	$-0.296388\pi$
$3$	2.06782			1.19386			0.596928	+	0.802295i	$0.296388\pi$
$4$	1.75513	+	0.958912i	0.877566	+	0.479456i
$5$	−0.600491	+	2.15393i	−0.268548	+	0.963266i
$5$	−0.600491	+	2.15393i	−0.268548	+	0.963266i
$6$	−2.83341	−	0.723542i	−1.15674	−	0.295385i
$7$		−	3.38406i		−	1.27906i	−0.768768	−	0.639528i	$-0.779130\pi$
$7$		−	3.38406i		−	1.27906i	0.768768	−	0.639528i	$-0.220870\pi$
$8$	−2.06943	−	1.92807i	−0.731653	−	0.681677i
$9$	1.27587			0.425291
$10$	1.57649	−	2.74129i	0.498530	−	0.866872i
$11$	3.69062	−	3.69062i	1.11276	−	1.11276i	0.119988	−	0.992775i	$-0.461714\pi$
$11$	3.69062	−	3.69062i	1.11276	−	1.11276i	0.992775	−	0.119988i	$-0.0382856\pi$
$12$	3.62929	+	1.98286i	1.04769	+	0.572401i
$13$			0.425062i			0.117891i	0.998261	+	0.0589455i	$0.0187738\pi$
$13$			0.425062i			0.117891i	−0.998261	+	0.0589455i	$0.981226\pi$
$14$	−1.18410	+	4.63699i	−0.316465	+	1.23929i
$15$	−1.24171	+	4.45394i	−0.320607	+	1.15000i
$16$	2.16098	+	3.36603i	0.540244	+	0.841508i
$17$		−	3.34792i		−	0.811990i	−0.913875	−	0.405995i	$-0.866925\pi$
$17$		−	3.34792i		−	0.811990i	0.913875	−	0.405995i	$-0.133075\pi$
$18$	−1.74826	−	0.446436i	−0.412068	−	0.105226i
$19$	−0.684819	+	0.684819i	−0.157108	+	0.157108i	−0.781284	−	0.624176i	$-0.785435\pi$
$19$	−0.684819	+	0.684819i	−0.157108	+	0.157108i	0.624176	+	0.781284i	$0.285435\pi$
$20$	−3.11937	+	3.20461i	−0.697512	+	0.716573i
$21$		−	6.99763i		−	1.52701i
$22$	−6.34841	+	3.76568i	−1.35349	+	0.802845i
$23$	5.31453	−	5.31453i	1.10816	−	1.10816i	0.114764	−	0.993393i	$-0.463389\pi$
$23$	5.31453	−	5.31453i	1.10816	−	1.10816i	0.993393	−	0.114764i	$-0.0366112\pi$
$24$	−4.27920	−	3.98691i	−0.873489	−	0.813824i
$25$	−4.27882	−	2.58683i	−0.855764	−	0.517366i
$26$	0.148732	−	0.582438i	0.0291687	−	0.114226i
$27$	−3.56518			−0.686119
$28$	3.24502	−	5.93948i	0.613251	−	1.12246i
$29$	3.38159	−	3.38159i	0.627946	−	0.627946i	−0.319605	−	0.947551i	$-0.603550\pi$
$29$	3.38159	−	3.38159i	0.627946	−	0.627946i	0.947551	+	0.319605i	$0.103550\pi$
$30$	3.25990	−	5.66849i	0.595173	−	1.03492i
$31$			6.18545i			1.11094i	0.831537	+	0.555470i	$0.187462\pi$
$31$			6.18545i			1.11094i	−0.831537	+	0.555470i	$0.812538\pi$
$32$	−1.78327	−	5.36842i	−0.315240	−	0.949012i
$33$	7.63153	−	7.63153i	1.32848	−	1.32848i
$34$	−1.17146	+	4.58747i	−0.200903	+	0.786744i
$35$	7.28903	+	2.03210i	1.23207	+	0.343487i
$36$	2.23933	+	1.22345i	0.373221	+	0.203909i
$37$	−3.00501	+	3.00501i	−0.494021	+	0.494021i	−0.909571	−	0.415549i	$-0.863589\pi$
$37$	−3.00501	+	3.00501i	−0.494021	+	0.494021i	0.415549	+	0.909571i	$0.363589\pi$
$38$	1.17799	−	0.698746i	0.191095	−	0.113352i
$39$			0.878951i			0.140745i
$40$	5.39561	−	3.29961i	0.853120	−	0.521714i
$41$	6.32040	−	1.02593i	0.987081	−	0.160224i
$41$	6.32040	−	1.02593i	0.987081	−	0.160224i
$42$	−2.44851	+	9.58845i	−0.377813	+	1.47953i
$43$	−1.80499	−	1.80499i	−0.275259	−	0.275259i	0.555954	−	0.831213i	$-0.312353\pi$
$43$	−1.80499	−	1.80499i	−0.275259	−	0.275259i	−0.831213	+	0.555954i	$0.812353\pi$
$44$	10.0165	−	2.93854i	1.51004	−	0.443002i
$45$	−0.766151	+	2.74814i	−0.114211	+	0.409669i
$46$	−9.14179	+	5.42262i	−1.34788	+	0.799521i
$47$	8.57237			1.25041			0.625204	−	0.780461i	$-0.285016\pi$
$47$	8.57237			1.25041			0.625204	+	0.780461i	$0.285016\pi$
$48$	4.46851	+	6.96035i	0.644973	+	1.00464i
$49$	−4.45188			−0.635983
$50$	4.95788	+	5.04177i	0.701150	+	0.713014i
$51$		−	6.92289i		−	0.969399i
$52$	−0.407597	+	0.746040i	−0.0565235	+	0.103457i
$53$			9.32035i			1.28025i	0.768271	+	0.640124i	$0.221117\pi$
$53$			9.32035i			1.28025i	−0.768271	+	0.640124i	$0.778883\pi$
$54$	4.88516	+	1.24748i	0.664786	+	0.169760i
$55$	5.73315	+	10.1655i	0.773057	+	1.37072i
$56$	−6.52472	+	7.00308i	−0.871902	+	0.935825i
$57$	−1.41608	+	1.41608i	−0.187565	+	0.187565i
$58$	−5.81684	+	3.45036i	−0.763789	+	0.453055i
$59$	0.468941			0.0610509			0.0305255	−	0.999534i	$-0.490282\pi$
$59$	0.468941			0.0610509			0.0305255	+	0.999534i	$0.490282\pi$
$60$	−6.45029	+	6.62656i	−0.832729	+	0.855485i
$61$		−	0.208691i		−	0.0267202i	−0.999911	−	0.0133601i	$-0.995747\pi$
$61$		−	0.208691i		−	0.0267202i	0.999911	−	0.0133601i	$-0.00425278\pi$
$62$	2.16432	−	8.47557i	0.274870	−	1.07640i
$63$		−	4.31764i		−	0.543971i
$64$	0.565069	+	7.98002i	0.0706336	+	0.997502i
$65$	−0.915554	−	0.255246i	−0.113560	−	0.0316594i
$66$	−13.1274	+	7.78673i	−1.61587	+	0.958481i
$67$	−4.16083			−0.508327			−0.254163	−	0.967161i	$-0.581800\pi$
$67$	−4.16083			−0.508327			−0.254163	+	0.967161i	$0.581800\pi$
$68$	3.21036	−	5.87604i	0.389314	−	0.712575i
$69$	10.9895	−	10.9895i	1.32298	−	1.32298i
$70$	−9.27670	−	5.33494i	−1.10878	−	0.637648i
$71$	−5.60857	+	5.60857i	−0.665615	+	0.665615i	−0.956698	−	0.291083i	$-0.905984\pi$
$71$	−5.60857	+	5.60857i	−0.665615	+	0.665615i	0.291083	+	0.956698i	$0.405984\pi$
$72$	−2.64033	−	2.45998i	−0.311166	−	0.289911i
$73$	3.45071	−	3.45071i	0.403875	−	0.403875i	−0.475721	−	0.879596i	$-0.657813\pi$
$73$	3.45071	−	3.45071i	0.403875	−	0.403875i	0.879596	+	0.475721i	$0.157813\pi$
$74$	5.16907	−	3.06613i	0.600892	−	0.356430i
$75$	−8.84783	−	5.34910i	−1.02166	−	0.617660i
$76$	−1.85863	+	0.545267i	−0.213199	+	0.0625464i
$77$	−12.4893	−	12.4893i	−1.42329	−	1.42329i
$78$	0.307550	−	1.20438i	0.0348232	−	0.136369i
$79$	10.8014	+	10.8014i	1.21525	+	1.21525i	0.969275	+	0.245980i	$0.0791098\pi$
$79$	10.8014	+	10.8014i	1.21525	+	1.21525i	0.245980	+	0.969275i	$0.420890\pi$
$80$	−8.54784	+	2.63332i	−0.955678	+	0.294414i
$81$	−11.1998			−1.24442
$82$	−9.01946	−	0.805764i	−0.996033	−	0.0889818i
$83$	5.42477	−	5.42477i	0.595446	−	0.595446i	−0.343651	−	0.939097i	$-0.611664\pi$
$83$	5.42477	−	5.42477i	0.595446	−	0.595446i	0.939097	+	0.343651i	$0.111664\pi$
$84$	6.71011	−	12.2818i	0.732133	−	1.34005i
$85$	7.21119	+	2.01040i	0.782163	+	0.218058i
$86$	1.84170	+	3.10486i	0.198596	+	0.334805i
$87$	6.99252	−	6.99252i	0.749677	−	0.749677i
$88$	−14.7533	+	0.521689i	−1.57270	+	0.0556122i
$89$	2.57886	−	2.57886i	0.273358	−	0.273358i	−0.557092	−	0.830451i	$-0.688083\pi$
$89$	2.57886	−	2.57886i	0.273358	−	0.273358i	0.830451	+	0.557092i	$0.188083\pi$
$90$	2.01140	−	3.49754i	0.212021	−	0.368673i
$91$	1.43844			0.150789
$92$	14.4239	−	4.23154i	1.50379	−	0.441168i
$93$			12.7904i			1.32630i
$94$	−11.7462	−	2.99952i	−1.21153	−	0.309377i
$95$	−1.06382	−	1.88628i	−0.109146	−	0.193528i
$96$	−3.68747	−	11.1009i	−0.376351	−	1.13298i
$97$		−	13.1254i		−	1.33268i	−0.745649	−	0.666339i	$-0.767860\pi$
$97$		−	13.1254i		−	1.33268i	0.745649	−	0.666339i	$-0.232140\pi$
$98$	6.10016	+	1.55774i	0.616209	+	0.157355i
$99$	4.70877	−	4.70877i	0.473249	−	0.473249i
$100$	−5.02935	−	8.64324i	−0.502935	−	0.864324i
$101$	−8.00287	+	8.00287i	−0.796315	+	0.796315i	−0.982512	−	0.186197i	$-0.940384\pi$
$101$	−8.00287	+	8.00287i	−0.796315	+	0.796315i	0.186197	+	0.982512i	$0.440384\pi$
$102$	−2.42236	+	9.48605i	−0.239849	+	0.939259i
$103$	−4.86602	−	4.86602i	−0.479463	−	0.479463i	0.425497	−	0.904960i	$-0.360099\pi$
$103$	−4.86602	−	4.86602i	−0.479463	−	0.479463i	−0.904960	+	0.425497i	$0.860099\pi$
$104$	0.819551	−	0.879636i	0.0803636	−	0.0862554i
$105$	15.0724	+	4.20201i	1.47092	+	0.410074i
$106$	3.26124	−	12.7711i	0.316760	−	1.24044i
$107$	−0.734209	−	0.734209i	−0.0709787	−	0.0709787i	0.670726	−	0.741705i	$-0.265983\pi$
$107$	−0.734209	−	0.734209i	−0.0709787	−	0.0709787i	−0.741705	+	0.670726i	$0.765983\pi$
$108$	−6.25736	−	3.41869i	−0.602115	−	0.328964i
$109$	−0.315628	−	0.315628i	−0.0302317	−	0.0302317i	0.691829	−	0.722061i	$-0.256805\pi$
$109$	−0.315628	−	0.315628i	−0.0302317	−	0.0302317i	−0.722061	+	0.691829i	$0.756805\pi$
$110$	−4.29883	−	15.9353i	−0.409878	−	1.51937i
$111$	−6.21383	+	6.21383i	−0.589790	+	0.589790i
$112$	11.3909	−	7.31288i	1.07634	−	0.691002i
$113$	5.84978	+	5.84978i	0.550301	+	0.550301i	0.926528	−	0.376227i	$-0.122779\pi$
$113$	5.84978	+	5.84978i	0.550301	+	0.550301i	−0.376227	+	0.926528i	$0.622779\pi$
$114$	2.43587	−	1.44488i	0.228140	−	0.135325i
$115$	8.25580	+	14.6385i	0.769857	+	1.36504i
$116$	9.17779	−	2.69249i	0.852136	−	0.249992i
$117$			0.542326i			0.0501380i
$118$	−0.642563	−	0.164085i	−0.0591527	−	0.0151053i
$119$	−11.3296			−1.03858
$120$	11.1571	−	6.82300i	1.01850	−	0.622852i
$121$		−	16.2413i		−	1.47648i
$122$	−0.0730223	+	0.285958i	−0.00661113	+	0.0258894i
$123$	13.0694	−	2.12145i	1.17843	−	0.191284i
$124$	−5.93130	+	10.8563i	−0.532647	+	0.974923i
$125$	8.14124	−	7.66291i	0.728175	−	0.685391i
$126$	−1.51077	+	5.91621i	−0.134590	+	0.527058i
$127$	15.0544	+	15.0544i	1.33586	+	1.33586i	0.900027	+	0.435834i	$0.143547\pi$
$127$	15.0544	+	15.0544i	1.33586	+	1.33586i	0.435834	+	0.900027i	$0.356453\pi$
$128$	2.01797	−	11.1323i	0.178365	−	0.983964i
$129$	−3.73240	−	3.73240i	−0.328619	−	0.328619i
$130$	1.16522	+	0.670106i	0.102196	+	0.0587722i
$131$	−6.94210			−0.606534			−0.303267	−	0.952906i	$-0.598077\pi$
$131$	−6.94210			−0.606534			−0.303267	+	0.952906i	$0.598077\pi$
$132$	20.7123	−	6.07638i	1.80277	−	0.528881i
$133$	2.31747	+	2.31747i	0.200950	+	0.200950i
$134$	5.70135	+	1.45590i	0.492522	+	0.125771i
$135$	2.14086	−	7.67914i	0.184256	−	0.660915i
$136$	−6.45504	+	6.92828i	−0.553515	+	0.594095i
$137$		−	3.88148i		−	0.331617i	−0.986158	−	0.165809i	$-0.946977\pi$
$137$		−	3.88148i		−	0.331617i	0.986158	−	0.165809i	$-0.0530234\pi$
$138$	−18.9036	+	11.2130i	−1.60918	+	0.954513i
$139$	−18.9708			−1.60908			−0.804540	−	0.593898i	$-0.797588\pi$
$139$	−18.9708			−1.60908			−0.804540	+	0.593898i	$0.797588\pi$
$140$	10.8446	+	10.5561i	0.916537	+	0.892157i
$141$	17.7261			1.49281
$142$	9.64758	−	5.72263i	0.809607	−	0.480233i
$143$	1.56874	+	1.56874i	0.131185	+	0.131185i
$144$	2.75713	+	4.29464i	0.229761	+	0.357886i
$145$	5.25309	+	9.31432i	0.436246	+	0.773512i
$146$	−5.93574	+	3.52089i	−0.491245	+	0.291391i
$147$	−9.20568			−0.759272
$148$	−8.15574	+	2.39265i	−0.670398	+	0.196675i
$149$	−13.8184	−	13.8184i	−1.13205	−	1.13205i	−0.989836	−	0.142212i	$-0.954578\pi$
$149$	−13.8184	−	13.8184i	−1.13205	−	1.13205i	−0.142212	−	0.989836i	$-0.545422\pi$
$150$	10.2520	+	10.4255i	0.837072	+	0.851236i
$151$	−10.4426	+	10.4426i	−0.849804	+	0.849804i	−0.990108	−	0.140305i	$-0.955192\pi$
$151$	−10.4426	+	10.4426i	−0.849804	+	0.849804i	0.140305	+	0.990108i	$0.455192\pi$
$152$	2.73756	−	0.0968029i	0.222046	−	0.00785175i
$153$		−	4.27153i		−	0.345333i
$154$	12.7433	+	21.4834i	1.02688	+	1.73118i
$155$	−13.3230	−	3.71431i	−1.07013	−	0.298340i
$156$	−0.842837	+	1.54268i	−0.0674810	+	0.123513i
$157$	−19.0040			−1.51669			−0.758343	−	0.651856i	$-0.773991\pi$
$157$	−19.0040			−1.51669			−0.758343	+	0.651856i	$0.773991\pi$
$158$	−11.0211	−	18.5801i	−0.876791	−	1.47815i
$159$			19.2728i			1.52843i
$160$	12.6340	−	0.617344i	0.998808	−	0.0488053i
$161$	−17.9847	−	17.9847i	−1.41739	−	1.41739i
$162$	15.3464	+	3.91886i	1.20573	+	0.307895i
$163$	−1.86716	+	1.86716i	−0.146247	+	0.146247i	−0.776439	−	0.630192i	$-0.782976\pi$
$163$	−1.86716	+	1.86716i	−0.146247	+	0.146247i	0.630192	+	0.776439i	$0.282976\pi$
$164$	12.0769	+	4.26006i	0.943049	+	0.332654i
$165$	11.8551	+	21.0204i	0.922919	+	1.63644i
$166$	−9.33142	+	5.53510i	−0.724259	+	0.429607i
$167$		−	22.3685i		−	1.73093i	−0.500972	−	0.865463i	$-0.667024\pi$
$167$		−	22.3685i		−	1.73093i	0.500972	−	0.865463i	$-0.332976\pi$
$168$	−13.4919	+	14.4811i	−1.04093	+	1.11724i
$169$	12.8193			0.986102
$170$	−9.17763	−	5.27797i	−0.703892	−	0.404802i
$171$	−0.873743	+	0.873743i	−0.0668168	+	0.0668168i
$172$	−1.43717	−	4.89883i	−0.109583	−	0.373532i
$173$	−10.8233	+	10.8233i	−0.822883	+	0.822883i	−0.986520	−	0.163638i	$-0.947677\pi$
$173$	−10.8233	+	10.8233i	−0.822883	+	0.822883i	0.163638	+	0.986520i	$0.447677\pi$
$174$	−12.0282	+	7.13473i	−0.911853	+	0.540882i
$175$	−8.75399	+	14.4798i	−0.661740	+	1.09457i
$176$	20.3981	+	4.44741i	1.53756	+	0.335236i
$177$	0.969685			0.0728860
$178$	−4.43602	+	2.63131i	−0.332494	+	0.197225i
$179$	−7.55200	+	7.55200i	−0.564463	+	0.564463i	−0.930572	−	0.366109i	$-0.880690\pi$
$179$	−7.55200	+	7.55200i	−0.564463	+	0.564463i	0.366109	+	0.930572i	$0.380690\pi$
$180$	−3.97992	+	4.08868i	−0.296646	+	0.304752i
$181$	−15.1028	+	15.1028i	−1.12258	+	1.12258i	−0.131227	+	0.991352i	$0.541892\pi$
$181$	−15.1028	+	15.1028i	−1.12258	+	1.12258i	−0.991352	+	0.131227i	$0.958108\pi$
$182$	−1.97101	−	0.503317i	−0.146101	−	0.0373084i
$183$		−	0.431536i		−	0.0319001i
$184$	−21.2449	+	0.751238i	−1.56619	+	0.0553820i
$185$	−4.66810	−	8.27707i	−0.343206	−	0.608543i
$186$	4.47543	−	17.5259i	0.328155	−	1.28506i
$187$	−12.3559	−	12.3559i	−0.903553	−	0.903553i
$188$	15.0456	+	8.22014i	1.09732	+	0.599516i
$189$			12.0648i			0.877584i
$190$	0.797677	+	2.95690i	0.0578696	+	0.214516i
$191$	19.3766	+	19.3766i	1.40204	+	1.40204i	0.793591	+	0.608452i	$0.208209\pi$
$191$	19.3766	+	19.3766i	1.40204	+	1.40204i	0.608452	+	0.793591i	$0.291791\pi$
$192$	1.16846	+	16.5012i	0.0843263	+	1.19087i
$193$		−	5.00474i		−	0.360249i	−0.983644	−	0.180125i	$-0.942350\pi$
$193$		−	5.00474i		−	0.360249i	0.983644	−	0.180125i	$-0.0576501\pi$
$194$	−4.59264	+	17.9849i	−0.329732	+	1.29124i
$195$	−1.89320	−	0.527802i	−0.135575	−	0.0377967i
$196$	−7.81363	−	4.26896i	−0.558117	−	0.304926i
$197$	−0.711380	−	0.711380i	−0.0506837	−	0.0506837i	0.681311	−	0.731994i	$-0.261410\pi$
$197$	−0.711380	−	0.711380i	−0.0506837	−	0.0506837i	−0.731994	+	0.681311i	$0.761410\pi$
$198$	−8.09978	+	4.80453i	−0.575626	+	0.341443i
$199$	3.44585	−	3.44585i	0.244270	−	0.244270i	−0.574344	−	0.818614i	$-0.694743\pi$
$199$	3.44585	−	3.44585i	0.244270	−	0.244270i	0.818614	+	0.574344i	$0.194743\pi$
$200$	3.86712	+	13.6031i	0.273446	+	0.961887i
$201$	−8.60385			−0.606869
$202$	13.7661	−	8.16563i	0.968581	−	0.574531i
$203$	−11.4435	−	11.4435i	−0.803177	−	0.803177i
$204$	6.63845	−	12.1506i	0.464784	−	0.850712i
$205$	−1.58555	+	14.2298i	−0.110740	+	0.993849i
$206$	4.96498	+	8.37028i	0.345927	+	0.583185i
$207$	6.78068	−	6.78068i	0.471290	−	0.471290i
$208$	−1.43077	+	0.918549i	−0.0992063	+	0.0636899i
$209$			5.05481i			0.349649i
$210$	−19.1825	−	11.0317i	−1.32372	−	0.761259i
$211$	4.84316	+	4.84316i	0.333417	+	0.333417i	0.853883	−	0.520466i	$-0.174242\pi$
$211$	4.84316	+	4.84316i	0.333417	+	0.333417i	−0.520466	+	0.853883i	$0.674242\pi$
$212$	−8.93740	+	16.3584i	−0.613823	+	1.12350i
$213$	−11.5975	+	11.5975i	−0.794648	+	0.794648i
$214$	0.749141	+	1.26295i	0.0512102	+	0.0863334i
$215$	4.97171	−	2.80395i	0.339068	−	0.191228i
$216$	7.37788	+	6.87393i	0.502001	+	0.467711i
$217$	20.9319			1.42095
$218$	0.322047	+	0.542927i	0.0218118	+	0.0367717i
$219$	7.13545	−	7.13545i	0.482169	−	0.482169i
$220$	0.314599	+	23.3394i	0.0212102	+	1.57354i
$221$	1.42307			0.0957263
$222$	10.6887	−	6.34020i	0.717379	−	0.425526i
$223$	−0.307241	+	0.307241i	−0.0205744	+	0.0205744i	−0.717319	−	0.696745i	$-0.754631\pi$
$223$	−0.307241	+	0.307241i	−0.0205744	+	0.0205744i	0.696745	+	0.717319i	$0.254631\pi$
$224$	−18.1671	+	6.03469i	−1.21384	+	0.403210i
$225$	−5.45924	−	3.30047i	−0.363949	−	0.220031i
$226$	−5.96875	−	10.0625i	−0.397035	−	0.669347i
$227$	8.88097			0.589451			0.294725	−	0.955582i	$-0.404772\pi$
$227$	8.88097			0.589451			0.294725	+	0.955582i	$0.404772\pi$
$228$	−3.84331	+	1.12751i	−0.254529	+	0.0746713i
$229$	6.28380	+	6.28380i	0.415245	+	0.415245i	0.883561	−	0.468316i	$-0.155139\pi$
$229$	6.28380	+	6.28380i	0.415245	+	0.415245i	−0.468316	+	0.883561i	$0.655139\pi$
$230$	−6.19037	−	22.9470i	−0.408181	−	1.51308i
$231$	−25.8256	−	25.8256i	−1.69920	−	1.69920i
$232$	−13.5179	+	0.478006i	−0.887495	+	0.0313827i
$233$			18.2587i			1.19617i	0.801433	+	0.598085i	$0.204072\pi$
$233$			18.2587i			1.19617i	−0.801433	+	0.598085i	$0.795928\pi$
$234$	0.189763	−	0.743118i	0.0124052	−	0.0485792i
$235$	−5.14763	+	18.4643i	−0.335794	+	1.20448i
$236$	0.823053	+	0.449673i	0.0535762	+	0.0292712i
$237$	22.3354	+	22.3354i	1.45084	+	1.45084i
$238$	15.5243	+	3.96428i	1.00629	+	0.256966i
$239$	−4.72912	−	4.72912i	−0.305902	−	0.305902i	0.537416	−	0.843317i	$-0.319401\pi$
$239$	−4.72912	−	4.72912i	−0.305902	−	0.305902i	−0.843317	+	0.537416i	$0.819401\pi$
$240$	−17.6754	+	5.44522i	−1.14094	+	0.351488i
$241$			18.6068i			1.19857i	0.800536	+	0.599284i	$0.204548\pi$
$241$			18.6068i			1.19857i	−0.800536	+	0.599284i	$0.795452\pi$
$242$	−5.68293	+	22.2546i	−0.365313	+	1.43058i
$243$	−12.4636			−0.799537
$244$	0.200117	−	0.366281i	0.0128112	−	0.0234487i
$245$	2.67331	−	9.58903i	0.170792	−	0.612621i
$246$	−18.6506	−	1.66617i	−1.18912	−	0.106231i
$247$	−0.291091	−	0.291091i	−0.0185216	−	0.0185216i
$248$	11.9260	−	12.8003i	0.757302	−	0.812823i
$249$	11.2174	−	11.2174i	0.710877	−	0.710877i
$250$	−13.8368	+	7.65138i	−0.875115	+	0.483916i
$251$	6.58820			0.415844			0.207922	−	0.978145i	$-0.433330\pi$
$251$	6.58820			0.415844			0.207922	+	0.978145i	$0.433330\pi$
$252$	4.14024	−	7.57803i	0.260810	−	0.477371i
$253$		−	39.2278i		−	2.46623i
$254$	−15.3606	−	25.8958i	−0.963807	−	1.62485i
$255$	14.9114	+	4.15714i	0.933790	+	0.260330i
$256$	−6.66036	+	14.5478i	−0.416273	+	0.909240i
$257$	−12.7653			−0.796275			−0.398137	−	0.917326i	$-0.630343\pi$
$257$	−12.7653			−0.796275			−0.398137	+	0.917326i	$0.630343\pi$
$258$	3.80831	+	6.42028i	0.237095	+	0.399709i
$259$	10.1692	+	10.1692i	0.631881	+	0.631881i
$260$	−1.36216	−	1.32593i	−0.0844775	−	0.0822304i
$261$	4.31449	−	4.31449i	0.267060	−	0.267060i
$262$	9.51236	+	2.42908i	0.587676	+	0.150069i
$263$			4.82813i			0.297715i	0.988859	+	0.148858i	$0.0475596\pi$
$263$			4.82813i			0.297715i	−0.988859	+	0.148858i	$0.952440\pi$
$264$	−30.5071	+	1.07876i	−1.87758	+	0.0663930i
$265$	−20.0754	−	5.59679i	−1.23322	−	0.343808i
$266$	−2.36460	−	3.98639i	−0.144983	−	0.244421i
$267$	5.33261	−	5.33261i	0.326351	−	0.326351i
$268$	−7.30281	−	3.98987i	−0.446090	−	0.243720i
$269$			12.5270i			0.763783i	0.924207	+	0.381891i	$0.124727\pi$
$269$			12.5270i			0.763783i	−0.924207	+	0.381891i	$0.875273\pi$
$270$	−5.62047	+	9.77319i	−0.342051	+	0.594778i
$271$		−	8.44587i		−	0.513050i	−0.966538	−	0.256525i	$-0.917422\pi$
$271$		−	8.44587i		−	0.513050i	0.966538	−	0.256525i	$-0.0825776\pi$
$272$	11.2692	−	7.23478i	0.683297	−	0.438673i
$273$	2.97443			0.180020
$274$	−1.35815	+	5.31857i	−0.0820490	+	0.321307i
$275$	−25.3385	+	6.24449i	−1.52797	+	0.376557i
$276$	29.8260	−	8.75005i	1.79531	−	0.526691i
$277$	17.8144	−	17.8144i	1.07036	−	1.07036i	0.0730342	−	0.997329i	$-0.476732\pi$
$277$	17.8144	−	17.8144i	1.07036	−	1.07036i	0.997329	−	0.0730342i	$-0.0232682\pi$
$278$	25.9946	+	6.63798i	1.55905	+	0.398120i
$279$			7.89186i			0.472473i
$280$	−11.1661	−	18.2591i	−0.667302	−	1.09119i
$281$	−22.3301	+	22.3301i	−1.33210	+	1.33210i	−0.428610	+	0.903489i	$0.640997\pi$
$281$	−22.3301	+	22.3301i	−1.33210	+	1.33210i	−0.903489	+	0.428610i	$0.859003\pi$
$282$	−24.2891	−	6.20246i	−1.44639	−	0.369351i
$283$	−13.3311	+	13.3311i	−0.792450	+	0.792450i	−0.981892	−	0.189442i	$-0.939332\pi$
$283$	−13.3311	+	13.3311i	−0.792450	+	0.792450i	0.189442	+	0.981892i	$0.439332\pi$
$284$	−15.2219	+	4.46566i	−0.903254	+	0.264988i
$285$	−2.19979	−	3.90048i	−0.130305	−	0.231045i
$286$	−1.60065	−	2.69847i	−0.0946482	−	0.159564i
$287$	−3.47183	−	21.3886i	−0.204935	−	1.26253i
$288$	−2.27523	−	6.84943i	−0.134069	−	0.403607i
$289$	5.79142			0.340672
$290$	−3.93888	−	14.6010i	−0.231299	−	0.857399i
$291$		−	27.1409i		−	1.59102i
$292$	9.36539	−	2.74753i	0.548068	−	0.160787i
$293$	15.7494			0.920089			0.460044	−	0.887896i	$-0.347834\pi$
$293$	15.7494			0.920089			0.460044	+	0.887896i	$0.347834\pi$
$294$	12.6140	+	3.22112i	0.735664	+	0.187860i
$295$	−0.281595	+	1.01007i	−0.0163951	+	0.0588083i
$296$	12.0126	−	0.424775i	0.698215	−	0.0246896i
$297$	−13.1577	+	13.1577i	−0.763488	+	0.763488i
$298$	14.0994	+	23.7697i	0.816759	+	1.37694i
$299$	2.25901	+	2.25901i	0.130642	+	0.130642i
$300$	−10.3998	−	17.8727i	−0.600432	−	1.03188i
$301$	−6.10821	+	6.10821i	−0.352071	+	0.352071i
$302$	17.9628	−	10.6549i	1.03364	−	0.613123i
$303$	−16.5485	+	16.5485i	−0.950686	+	0.950686i
$304$	−3.78500	−	0.825246i	−0.217085	−	0.0473311i
$305$	0.449506	+	0.125317i	0.0257387	+	0.00717565i
$306$	−1.49463	+	5.85303i	−0.0854424	+	0.334595i
$307$	−4.51824	+	4.51824i	−0.257870	+	0.257870i	−0.824187	−	0.566317i	$-0.808368\pi$
$307$	−4.51824	+	4.51824i	−0.257870	+	0.257870i	0.566317	+	0.824187i	$0.308368\pi$
$308$	−9.94422	−	33.8965i	−0.566624	−	1.93143i
$309$	−10.0620	−	10.0620i	−0.572410	−	0.572410i
$310$	16.9561	+	9.75131i	0.963043	+	0.553837i
$311$	1.66046	+	1.66046i	0.0941563	+	0.0941563i	0.752616	−	0.658460i	$-0.228792\pi$
$311$	1.66046	+	1.66046i	0.0941563	+	0.0941563i	−0.658460	+	0.752616i	$0.728792\pi$
$312$	1.69468	−	1.81893i	0.0959425	−	0.102976i
$313$	−14.8719			−0.840612			−0.420306	−	0.907382i	$-0.638077\pi$
$313$	−14.8719			−0.840612			−0.420306	+	0.907382i	$0.638077\pi$
$314$	26.0401	+	6.64961i	1.46953	+	0.375259i
$315$	9.29989	+	2.59270i	0.523989	+	0.146082i
$316$	8.60031	+	29.3155i	0.483805	+	1.64913i
$317$	−6.55187			−0.367990			−0.183995	−	0.982927i	$-0.558903\pi$
$317$	−6.55187			−0.367990			−0.183995	+	0.982927i	$0.558903\pi$
$318$	6.74366	−	26.4084i	0.378166	−	1.48091i
$319$		−	24.9603i		−	1.39751i
$320$	−17.5277	−	3.57481i	−0.979829	−	0.199838i
$321$	−1.51821	−	1.51821i	−0.0847383	−	0.0847383i
$322$	18.3505	+	30.9364i	1.02263	+	1.72402i
$323$	2.29272	+	2.29272i	0.127570	+	0.127570i
$324$	−19.6571	−	10.7396i	−1.09206	−	0.596644i
$325$	1.09956	−	1.81876i	0.0609928	−	0.100887i
$326$	3.21179	−	1.90513i	0.177885	−	0.105516i
$327$	−0.652662	−	0.652662i	−0.0360923	−	0.0360923i
$328$	−15.0577	−	10.0631i	−0.831422	−	0.555641i
$329$		−	29.0094i		−	1.59934i
$330$	−8.88921	−	32.9513i	−0.489335	−	1.81391i
$331$	12.2573	−	12.2573i	0.673721	−	0.673721i	−0.284851	−	0.958572i	$-0.591944\pi$
$331$	12.2573	−	12.2573i	0.673721	−	0.673721i	0.958572	+	0.284851i	$0.0919442\pi$
$332$	14.7231	−	4.31931i	0.808034	−	0.237053i
$333$	−3.83402	+	3.83402i	−0.210103	+	0.210103i
$334$	−7.82687	+	30.6503i	−0.428267	+	1.67711i
$335$	2.49854	−	8.96214i	0.136510	−	0.489654i
$336$	23.5543	−	15.1217i	1.28499	−	0.824957i
$337$	22.0976	+	22.0976i	1.20373	+	1.20373i	0.973023	+	0.230709i	$0.0741044\pi$
$337$	22.0976	+	22.0976i	1.20373	+	1.20373i	0.230709	+	0.973023i	$0.425896\pi$
$338$	−17.5656	−	4.48555i	−0.955442	−	0.243982i
$339$	12.0963	+	12.0963i	0.656980	+	0.656980i
$340$	10.7288	+	10.4434i	0.581850	+	0.566373i
$341$	22.8281	+	22.8281i	1.23621	+	1.23621i
$342$	1.50297	−	0.891512i	0.0812712	−	0.0482075i
$343$		−	8.62300i		−	0.465598i
$344$	0.255146	+	7.21546i	0.0137565	+	0.389032i
$345$	17.0715	+	30.2697i	0.919098	+	1.62966i
$346$	18.6177	−	11.0434i	1.00090	−	0.593699i
$347$	4.29289			0.230454			0.115227	−	0.993339i	$-0.463240\pi$
$347$	4.29289			0.230454			0.115227	+	0.993339i	$0.463240\pi$
$348$	18.9780	−	5.56758i	1.01733	−	0.298454i
$349$	20.3710			1.09044			0.545218	−	0.838294i	$-0.316447\pi$
$349$	20.3710			1.09044			0.545218	+	0.838294i	$0.316447\pi$
$350$	17.0617	−	16.7778i	0.911984	−	0.896810i
$351$		−	1.51542i		−	0.0808873i
$352$	−26.3942	−	13.2314i	−1.40681	−	0.705238i
$353$	−6.80856	−	6.80856i	−0.362383	−	0.362383i	0.502307	−	0.864690i	$-0.332485\pi$
$353$	−6.80856	−	6.80856i	−0.362383	−	0.362383i	−0.864690	+	0.502307i	$0.832485\pi$
$354$	−1.32870	−	0.339298i	−0.0706198	−	0.0180335i
$355$	−8.71257	−	15.4484i	−0.462415	−	0.819914i
$356$	6.99913	−	2.05334i	0.370953	−	0.108827i
$357$	−23.4275			−1.23992
$358$	12.9906	−	7.70559i	0.686573	−	0.407253i
$359$	25.3606			1.33848			0.669242	−	0.743045i	$-0.266619\pi$
$359$	25.3606			1.33848			0.669242	+	0.743045i	$0.266619\pi$
$360$	6.88412	−	4.20989i	0.362825	−	0.221881i
$361$			18.0620i			0.950634i
$362$	25.9790	−	15.4099i	1.36543	−	0.809927i
$363$		−	33.5841i		−	1.76271i
$364$	2.52465	+	1.37933i	0.132327	+	0.0722967i
$365$	5.36047	+	9.50471i	0.280580	+	0.497499i
$366$	−0.150997	+	0.591309i	−0.00789273	+	0.0309082i
$367$	−11.0994	+	11.0994i	−0.579385	+	0.579385i	−0.934734	−	0.355349i	$-0.884362\pi$
$367$	−11.0994	+	11.0994i	−0.579385	+	0.579385i	0.355349	+	0.934734i	$0.384362\pi$
$368$	29.3735	+	6.40432i	1.53120	+	0.333848i
$369$	8.06404	−	1.30896i	0.419797	−	0.0681419i
$370$	3.50024	+	12.9750i	0.181969	+	0.674538i
$371$	31.5407			1.63751
$372$	−12.2649	+	22.4488i	−0.635903	+	1.16392i
$373$	19.6251	+	19.6251i	1.01615	+	1.01615i	0.999867	+	0.0162796i	$0.00518218\pi$
$373$	19.6251	+	19.6251i	1.01615	+	1.01615i	0.0162796	+	0.999867i	$0.494818\pi$
$374$	12.6072	+	21.2540i	0.651902	+	1.09902i
$375$	16.8346	−	15.8455i	0.869336	−	0.818259i
$376$	−17.7399	−	16.5281i	−0.914865	−	0.852374i
$377$	1.43739	+	1.43739i	0.0740292	+	0.0740292i
$378$	4.22154	−	16.5317i	0.217133	−	0.850299i
$379$	28.8118			1.47996			0.739982	−	0.672626i	$-0.234834\pi$
$379$	28.8118			1.47996			0.739982	+	0.672626i	$0.234834\pi$
$380$	−0.0583759	−	4.33078i	−0.00299462	−	0.222164i
$381$	31.1298	+	31.1298i	1.59483	+	1.59483i
$382$	−19.7707	−	33.3307i	−1.01156	−	1.70534i
$383$			13.0719i			0.667944i	0.942583	+	0.333972i	$0.108389\pi$
$383$			13.0719i			0.667944i	−0.942583	+	0.333972i	$0.891611\pi$
$384$	4.17280	−	23.0195i	0.212942	−	1.17471i
$385$	34.4007	−	19.4013i	1.75322	−	0.988783i
$386$	−1.75119	+	6.85772i	−0.0891332	+	0.349049i
$387$	−2.30295	−	2.30295i	−0.117065	−	0.117065i
$388$	12.5861	−	23.0367i	0.638960	−	1.16951i
$389$	−35.9288			−1.82166			−0.910831	−	0.412779i	$-0.864558\pi$
$389$	−35.9288			−1.82166			−0.910831	+	0.412779i	$0.864558\pi$
$390$	2.40946	+	1.38566i	0.122008	+	0.0701656i
$391$	−17.7926	−	17.7926i	−0.899812	−	0.899812i
$392$	9.21284	+	8.58355i	0.465319	+	0.433535i
$393$	−14.3550			−0.724114
$394$	0.725847	+	1.22368i	0.0365677	+	0.0616481i
$395$	−29.7517	+	16.7793i	−1.49697	+	0.844260i
$396$	12.7798	−	3.74921i	0.642209	−	0.188405i
$397$	−32.4990			−1.63108			−0.815539	−	0.578702i	$-0.803560\pi$
$397$	−32.4990			−1.63108			−0.815539	+	0.578702i	$0.803560\pi$
$398$	−5.92737	+	3.51593i	−0.297112	+	0.176238i
$399$	4.79211	+	4.79211i	0.239905	+	0.239905i
$400$	−0.539074	−	19.9927i	−0.0269537	−	0.999637i
$401$		−	30.1757i		−	1.50690i	−0.657505	−	0.753450i	$-0.728388\pi$
$401$		−	30.1757i		−	1.50690i	0.657505	−	0.753450i	$-0.271612\pi$
$402$	11.7894	+	3.01054i	0.588000	+	0.150152i
$403$	−2.62920			−0.130970
$404$	−21.7201	+	6.37205i	−1.08062	+	0.317021i
$405$	6.72536	−	24.1235i	0.334186	−	1.19871i
$406$	11.6762	+	19.6846i	0.579482	+	0.976928i
$407$			22.1807i			1.09946i
$408$	−13.3478	+	14.3264i	−0.660817	+	0.709264i
$409$		−	24.3353i		−	1.20330i	−0.798758	−	0.601652i	$-0.794509\pi$
$409$		−	24.3353i		−	1.20330i	0.798758	−	0.601652i	$-0.205491\pi$
$410$	7.15167	−	18.9434i	0.353196	−	0.935549i
$411$		−	8.02619i		−	0.395903i
$412$	−3.87442	−	13.2066i	−0.190879	−	0.650642i
$413$		−	1.58693i		−	0.0780875i
$414$	−11.6638	+	6.91858i	−0.573243	+	0.340030i
$415$	8.42705	+	14.9421i	0.413668	+	0.733479i
$416$	2.28191	−	0.758000i	0.111880	−	0.0371640i
$417$	−39.2281			−1.92101
$418$	1.76871	−	6.92632i	0.0865103	−	0.338777i
$419$		−	31.6294i		−	1.54520i	−0.634893	−	0.772600i	$-0.718956\pi$
$419$		−	31.6294i		−	1.54520i	0.634893	−	0.772600i	$-0.281044\pi$
$420$	22.4247	+	21.8282i	1.09421	+	1.06511i
$421$	−10.1879	−	10.1879i	−0.496529	−	0.496529i	0.413827	−	0.910356i	$-0.364192\pi$
$421$	−10.1879	−	10.1879i	−0.496529	−	0.496529i	−0.910356	+	0.413827i	$0.864192\pi$
$422$	−4.94166	−	8.33096i	−0.240556	−	0.405545i
$423$	10.9373			0.531788
$424$	17.9703	−	19.2878i	0.872716	−	0.936698i
$425$	−8.66050	+	14.3252i	−0.420096	+	0.694872i
$426$	19.9494	−	11.8334i	0.966554	−	0.573329i
$427$	−0.706225			−0.0341766
$428$	−0.584592	−	1.99268i	−0.0282573	−	0.0963196i
$429$	3.24387	+	3.24387i	0.156616	+	0.156616i
$430$	−7.79357	+	2.10246i	−0.375839	+	0.101389i
$431$	2.97987			0.143535			0.0717676	−	0.997421i	$-0.477136\pi$
$431$	2.97987			0.143535			0.0717676	+	0.997421i	$0.477136\pi$
$432$	−7.70427	−	12.0005i	−0.370672	−	0.577375i
$433$	−9.51380	−	9.51380i	−0.457204	−	0.457204i	0.440533	−	0.897737i	$-0.354790\pi$
$433$	−9.51380	−	9.51380i	−0.457204	−	0.457204i	−0.897737	+	0.440533i	$0.854790\pi$
$434$	−28.6819	−	7.32421i	−1.37677	−	0.351573i
$435$	10.8624	+	19.2603i	0.520814	+	0.923462i
$436$	−0.251309	−	0.856628i	−0.0120355	−	0.0410251i
$437$			7.27898i			0.348201i
$438$	−12.2740	+	7.28056i	−0.586476	+	0.347879i
$439$	5.31814	+	5.31814i	0.253821	+	0.253821i	0.822535	−	0.568714i	$-0.192559\pi$
$439$	5.31814	+	5.31814i	0.253821	+	0.253821i	−0.568714	+	0.822535i	$0.692559\pi$
$440$	7.73551	−	32.0907i	0.368776	−	1.52987i
$441$	−5.68004			−0.270478
$442$	−1.94996	−	0.497942i	−0.0927500	−	0.0236847i
$443$	17.8204	+	17.8204i	0.846675	+	0.846675i	0.989717	−	0.143042i	$-0.0456883\pi$
$443$	17.8204	+	17.8204i	0.846675	+	0.846675i	−0.143042	+	0.989717i	$0.545688\pi$
$444$	−16.8646	+	4.94757i	−0.800358	+	0.234801i
$445$	4.00610	+	7.10326i	0.189907	+	0.336727i
$446$	0.528500	−	0.313489i	0.0250252	−	0.0148441i
$447$	−28.5740	−	28.5740i	−1.35150	−	1.35150i
$448$	27.0049	−	1.91223i	1.27586	−	0.0903442i
$449$	5.00475			0.236189			0.118094	−	0.993002i	$-0.462321\pi$
$449$	5.00475			0.236189			0.118094	+	0.993002i	$0.462321\pi$
$450$	6.32563	+	6.43267i	0.298193	+	0.303239i
$451$	19.5399	−	27.1125i	0.920096	−	1.27668i
$452$	4.65771	+	15.8766i	0.219080	+	0.746771i
$453$	−21.5933	+	21.5933i	−1.01454	+	1.01454i
$454$	−12.1691	−	3.10750i	−0.571124	−	0.145842i
$455$	−0.863768	+	3.09829i	−0.0404941	+	0.145250i
$456$	5.66079	−	0.200171i	0.265091	−	0.00937386i
$457$			3.28010i			0.153436i	0.997053	+	0.0767182i	$0.0244442\pi$
$457$			3.28010i			0.153436i	−0.997053	+	0.0767182i	$0.975556\pi$
$458$	−6.41159	−	10.8091i	−0.299594	−	0.505075i
$459$			11.9359i			0.557122i
$460$	0.453026	+	33.6090i	0.0211224	+	1.56703i
$461$	−31.6581			−1.47447			−0.737233	−	0.675638i	$-0.763868\pi$
$461$	−31.6581			−1.47447			−0.737233	+	0.675638i	$0.763868\pi$
$462$	26.3508	+	44.4238i	1.22595	+	2.06678i
$463$	−24.3680			−1.13248			−0.566238	−	0.824241i	$-0.691602\pi$
$463$	−24.3680			−1.13248			−0.566238	+	0.824241i	$0.691602\pi$
$464$	18.6901	+	4.07501i	0.867666	+	0.189178i
$465$	−27.5496	−	7.68051i	−1.27758	−	0.356175i
$466$	6.38884	−	25.0189i	0.295957	−	1.15898i
$467$	15.9882	+	15.9882i	0.739844	+	0.739844i	0.972548	−	0.232703i	$-0.0747571\pi$
$467$	15.9882	+	15.9882i	0.739844	+	0.739844i	−0.232703	+	0.972548i	$0.574757\pi$
$468$	−0.520043	+	0.951853i	−0.0240390	+	0.0439994i
$469$			14.0805i			0.650178i
$470$	13.5143	−	23.4993i	0.623366	−	1.08394i
$471$	−39.2969			−1.81070
$472$	−0.970440	−	0.904153i	−0.0446681	−	0.0416170i
$473$	−13.3231			−0.612596
$474$	−22.7896	−	38.4202i	−1.04676	−	1.76470i
$475$	4.70173	−	1.15871i	0.215730	−	0.0531652i
$476$	−19.8849	−	10.8641i	−0.911423	−	0.497954i
$477$			11.8916i			0.544479i
$478$	4.82530	+	8.13479i	0.220704	+	0.372077i
$479$	−15.9255	−	15.9255i	−0.727655	−	0.727655i	0.242497	−	0.970152i	$-0.422033\pi$
$479$	−15.9255	−	15.9255i	−0.727655	−	0.727655i	−0.970152	+	0.242497i	$0.922033\pi$
$480$	26.1249	−	1.27655i	1.19243	−	0.0582665i
$481$	−1.27732	−	1.27732i	−0.0582407	−	0.0582407i
$482$	6.51062	−	25.4958i	0.296551	−	1.16130i
$483$	−37.1891	−	37.1891i	−1.69216	−	1.69216i
$484$	15.5740	−	28.5057i	0.707909	−	1.29571i
$485$	28.2711	+	7.88166i	1.28372	+	0.357888i
$486$	17.0781	+	4.36107i	0.774678	+	0.197822i
$487$	−10.1928	+	10.1928i	−0.461879	+	0.461879i	−0.899271	−	0.437392i	$-0.855902\pi$
$487$	−10.1928	+	10.1928i	−0.461879	+	0.461879i	0.437392	+	0.899271i	$0.355902\pi$
$488$	−0.402372	+	0.431872i	−0.0182145	+	0.0195499i
$489$	−3.86095	+	3.86095i	−0.174598	+	0.174598i
$490$	−7.01835	+	12.2039i	−0.317057	+	0.551316i
$491$		−	16.0820i		−	0.725769i	−0.931834	−	0.362884i	$-0.881792\pi$
$491$		−	16.0820i		−	0.725769i	0.931834	−	0.362884i	$-0.118208\pi$
$492$	24.9729	+	8.80902i	1.12586	+	0.397141i
$493$	−11.3213	−	11.3213i	−0.509886	−	0.509886i
$494$	0.297011	+	0.500719i	0.0133631	+	0.0225284i
$495$	7.31478	+	12.9699i	0.328775	+	0.582954i
$496$	−20.8204	+	13.3666i	−0.934865	+	0.600179i
$497$	18.9798	+	18.9798i	0.851358	+	0.851358i
$498$	−19.2957	+	11.4456i	−0.864660	+	0.512889i
$499$	16.4691	+	16.4691i	0.737259	+	0.737259i	0.972047	−	0.234788i	$-0.0754395\pi$
$499$	16.4691	+	16.4691i	0.737259	+	0.737259i	−0.234788	+	0.972047i	$0.575439\pi$
$500$	21.6370	−	5.64268i	0.967636	−	0.252348i
$501$		−	46.2540i		−	2.06648i
$502$	−9.02744	−	2.30525i	−0.402914	−	0.102888i
$503$	27.9393			1.24575			0.622877	−	0.782320i	$-0.285964\pi$
$503$	27.9393			1.24575			0.622877	+	0.782320i	$0.285964\pi$
$504$	−8.32472	+	8.93504i	−0.370813	+	0.397999i
$505$	−12.4320	−	22.0433i	−0.553215	−	0.980912i
$506$	−13.7260	+	53.7517i	−0.610197	+	2.38955i
$507$	26.5080			1.17726
$508$	11.9866	+	40.8583i	0.531820	+	1.81279i
$509$	22.7655	+	22.7655i	1.00906	+	1.00906i	0.999959	+	0.00910388i	$0.00289790\pi$
$509$	22.7655	+	22.7655i	1.00906	+	1.00906i	0.00910388	+	0.999959i	$0.497102\pi$
$510$	−18.9777	−	10.9139i	−0.840345	−	0.483275i
$511$	−11.6774	−	11.6774i	−0.516579	−	0.516579i
$512$	14.2167	−	17.6036i	0.628295	−	0.777975i
$513$	2.44150	−	2.44150i	0.107795	−	0.107795i
$514$	17.4915	+	4.46664i	0.771517	+	0.197015i
$515$	13.4031	−	7.55906i	0.590610	−	0.333092i
$516$	−2.97181	−	10.1299i	−0.130827	−	0.445944i
$517$	31.6373	−	31.6373i	1.39141	−	1.39141i
$518$	−10.3760	−	17.4925i	−0.455894	−	0.768575i
$519$	−22.3807	+	22.3807i	−0.982403	+	0.982403i
$520$	1.40254	+	2.29347i	0.0615054	+	0.100575i
$521$	−10.9539	−	10.9539i	−0.479897	−	0.479897i	0.425202	−	0.905099i	$-0.360203\pi$
$521$	−10.9539	−	10.9539i	−0.479897	−	0.479897i	−0.905099	+	0.425202i	$0.860203\pi$
$522$	−7.42156	+	4.40223i	−0.324833	+	0.192680i
$523$	15.8783	−	15.8783i	0.694308	−	0.694308i	−0.268869	−	0.963177i	$-0.586650\pi$
$523$	15.8783	−	15.8783i	0.694308	−	0.694308i	0.963177	+	0.268869i	$0.0866498\pi$
$524$	−12.1843	−	6.65686i	−0.532274	−	0.290806i
$525$	−18.1017	+	29.9416i	−0.790022	+	1.30676i
$526$	1.68939	−	6.61571i	0.0736609	−	0.288459i
$527$	20.7084			0.902072
$528$	42.1795	+	9.19643i	1.83563	+	0.400223i
$529$		−	33.4885i		−	1.45602i
$530$	25.5498	+	14.6934i	1.10981	+	0.638243i
$531$	0.598310			0.0259644
$532$	1.84522	+	6.28971i	0.0800003	+	0.272694i
$533$	0.436086	+	2.68656i	0.0188890	+	0.116368i
$534$	−9.17289	+	5.44106i	−0.396950	+	0.235458i
$535$	2.02232	−	1.14055i	0.0874325	−	0.0493102i
$536$	8.61055	+	8.02239i	0.371919	+	0.346515i
$537$	−15.6162	+	15.6162i	−0.673888	+	0.673888i
$538$	4.38326	−	17.1650i	0.188976	−	0.740035i
$539$	−16.4302	+	16.4302i	−0.707698	+	0.707698i
$540$	11.1211	−	11.4250i	0.478576	−	0.491654i
$541$		−	28.8087i		−	1.23858i	−0.785162	−	0.619291i	$-0.787420\pi$
$541$		−	28.8087i		−	1.23858i	0.785162	−	0.619291i	$-0.212580\pi$
$542$	−2.95526	+	11.5729i	−0.126939	+	0.497098i
$543$	−31.2298	+	31.2298i	−1.34020	+	1.34020i
$544$	−17.9731	+	5.97024i	−0.770588	+	0.255972i
$545$	0.869372	−	0.490309i	0.0372398	−	0.0210025i
$546$	−4.07569	−	1.04077i	−0.174423	−	0.0445408i
$547$	−24.4985			−1.04748			−0.523741	−	0.851877i	$-0.675464\pi$
$547$	−24.4985			−1.04748			−0.523741	+	0.851877i	$0.675464\pi$
$548$	3.72200	−	6.81251i	0.158996	−	0.291016i
$549$		−	0.266264i		−	0.0113639i
$550$	36.9049	+	0.309612i	1.57363	+	0.0132019i
$551$			4.63156i			0.197311i
$552$	−43.9305	+	1.55342i	−1.86981	+	0.0661181i
$553$	36.5527	−	36.5527i	1.55438	−	1.55438i
$554$	−30.6434	+	18.1767i	−1.30191	+	0.772254i
$555$	−9.65279	−	17.1155i	−0.409738	−	0.726512i
$556$	−33.2962	−	18.1913i	−1.41207	−	0.771483i
$557$			15.6020i			0.661080i	0.943792	+	0.330540i	$0.107231\pi$
$557$			15.6020i			0.661080i	−0.943792	+	0.330540i	$0.892769\pi$
$558$	2.76141	−	10.8138i	0.116900	−	0.457783i
$559$	0.767234	−	0.767234i	0.0324506	−	0.0324506i
$560$	8.91131	+	28.9264i	0.376571	+	1.22237i
$561$	−25.5498	−	25.5498i	−1.07871	−	1.07871i
$562$	38.4110	−	22.7842i	1.62027	−	0.961093i
$563$	−34.3618			−1.44818			−0.724089	−	0.689707i	$-0.757740\pi$
$563$	−34.3618			−1.44818			−0.724089	+	0.689707i	$0.757740\pi$
$564$	31.1116	+	16.9978i	1.31004	+	0.715735i
$565$	−16.1128	+	9.08727i	−0.677869	+	0.382304i
$566$	22.9314	−	13.6022i	0.963880	−	0.571743i
$567$			37.9007i			1.59168i
$568$	22.4203	−	0.792802i	0.940734	−	0.0332652i
$569$	18.2622			0.765593			0.382796	−	0.923833i	$-0.374961\pi$
$569$	18.2622			0.765593			0.382796	+	0.923833i	$0.374961\pi$
$570$	1.64945	+	6.11433i	0.0690879	+	0.256101i
$571$	1.16438	−	1.16438i	0.0487279	−	0.0487279i	−0.682323	−	0.731051i	$-0.739030\pi$
$571$	1.16438	−	1.16438i	0.0487279	−	0.0487279i	0.731051	+	0.682323i	$0.239030\pi$
$572$	1.24906	+	4.25763i	0.0522260	+	0.178021i
$573$	40.0673	+	40.0673i	1.67384	+	1.67384i
$574$	−2.72676	+	30.5224i	−0.113813	+	1.27398i
$575$	−36.4877	+	8.99214i	−1.52164	+	0.374998i
$576$	0.720957	+	10.1815i	0.0300399	+	0.424229i
$577$	−39.3687			−1.63894			−0.819470	−	0.573122i	$-0.805732\pi$
$577$	−39.3687			−1.63894			−0.819470	+	0.573122i	$0.805732\pi$
$578$	−7.93566	−	2.02645i	−0.330080	−	0.0842893i
$579$		−	10.3489i		−	0.430086i
$580$	0.288256	+	21.3851i	0.0119692	+	0.887969i
$581$	−18.3578	−	18.3578i	−0.761609	−	0.761609i
$582$	−9.49674	+	37.1896i	−0.393653	+	1.54156i
$583$	34.3979	+	34.3979i	1.42461	+	1.42461i
$584$	−13.7942	+	0.487777i	−0.570809	+	0.0201844i
$585$	−1.16813	−	0.325662i	−0.0482963	−	0.0134645i
$586$	−21.5805	−	5.51080i	−0.891481	−	0.227649i
$587$			5.74840i			0.237262i	0.992938	+	0.118631i	$0.0378506\pi$
$587$			5.74840i			0.237262i	−0.992938	+	0.118631i	$0.962149\pi$
$588$	−16.1572	−	8.82743i	−0.666311	−	0.364037i
$589$	−4.23591	−	4.23591i	−0.174538	−	0.174538i
$590$	0.739281	−	1.28550i	0.0304357	−	0.0529234i
$591$	−1.47100	−	1.47100i	−0.0605090	−	0.0605090i
$592$	−16.6087	−	3.62122i	−0.682615	−	0.148831i
$593$	−22.1695			−0.910391			−0.455195	−	0.890392i	$-0.650431\pi$
$593$	−22.1695			−0.910391			−0.455195	+	0.890392i	$0.650431\pi$
$594$	22.6332	−	13.4253i	0.928653	−	0.550847i
$595$	6.80331	−	24.4031i	0.278908	−	1.00043i
$596$	−11.0025	−	37.5038i	−0.450680	−	1.53621i
$597$	7.12539	−	7.12539i	0.291623	−	0.291623i
$598$	−2.30495	−	3.88583i	−0.0942563	−	0.158903i
$599$	36.2303			1.48033			0.740166	−	0.672425i	$-0.234747\pi$
$599$	36.2303			1.48033			0.740166	+	0.672425i	$0.234747\pi$
$600$	7.99650	+	28.1288i	0.326456	+	1.14835i
$601$	11.4756	−	11.4756i	0.468099	−	0.468099i	−0.433199	−	0.901298i	$-0.642615\pi$
$601$	11.4756	−	11.4756i	0.468099	−	0.468099i	0.901298	+	0.433199i	$0.142615\pi$
$602$	10.5070	−	6.23244i	0.428235	−	0.254015i
$603$	−5.30870			−0.216187
$604$	−28.3416	+	8.31458i	−1.15320	+	0.338315i
$605$	34.9827	+	9.75277i	1.42225	+	0.396506i
$606$	28.4659	−	16.8850i	1.15635	−	0.685908i
$607$	−27.7777	+	27.7777i	−1.12746	+	1.12746i	−0.136873	+	0.990589i	$0.543705\pi$
$607$	−27.7777	+	27.7777i	−1.12746	+	1.12746i	−0.990589	+	0.136873i	$0.956295\pi$
$608$	4.89761	+	2.45518i	0.198624	+	0.0995708i
$609$	−23.6631	−	23.6631i	−0.958878	−	0.958878i
$610$	−0.572084	−	0.329000i	−0.0231630	−	0.0133208i
$611$			3.64379i			0.147412i
$612$	4.09602	−	7.49709i	0.165572	−	0.303052i
$613$	−23.3151	+	23.3151i	−0.941690	+	0.941690i	−0.998391	−	0.0567016i	$-0.981942\pi$
$613$	−23.3151	+	23.3151i	−0.941690	+	0.941690i	0.0567016	+	0.998391i	$0.481942\pi$
$614$	7.77205	−	4.61013i	0.313654	−	0.186050i
$615$	−3.27864	+	29.4246i	−0.132207	+	1.18651i
$616$	1.76543	+	49.9259i	0.0711311	+	2.01157i
$617$	7.81689	+	7.81689i	0.314696	+	0.314696i	0.846726	−	0.532030i	$-0.178571\pi$
$617$	7.81689	+	7.81689i	0.314696	+	0.314696i	−0.532030	+	0.846726i	$0.678571\pi$
$618$	10.2667	+	17.3082i	0.412987	+	0.696239i
$619$	−12.1833			−0.489689			−0.244844	−	0.969562i	$-0.578737\pi$
$619$	−12.1833			−0.489689			−0.244844	+	0.969562i	$0.578737\pi$
$620$	−19.8220	−	19.2947i	−0.796069	−	0.774894i
$621$	−18.9473	+	18.9473i	−0.760327	+	0.760327i
$622$	−1.69423	−	2.85625i	−0.0679326	−	0.114525i
$623$	−8.72702	−	8.72702i	−0.349641	−	0.349641i
$624$	−2.95858	+	1.89939i	−0.118438	+	0.0760366i
$625$	11.6166	+	22.1372i	0.464665	+	0.885487i
$626$	20.3782	+	5.20378i	0.814476	+	0.207985i
$627$			10.4524i			0.417430i
$628$	−33.3546	−	18.2232i	−1.33099	−	0.727184i
$629$	10.0606	+	10.0606i	0.401141	+	0.401141i
$630$	−11.8359	−	6.80672i	−0.471554	−	0.271186i
$631$			11.6522i			0.463867i	0.972732	+	0.231933i	$0.0745051\pi$
$631$			11.6522i			0.463867i	−0.972732	+	0.231933i	$0.925495\pi$
$632$	−1.52684	−	43.1787i	−0.0607344	−	1.71756i
$633$	10.0148	+	10.0148i	0.398052	+	0.398052i
$634$	8.97766	+	2.29254i	0.356548	+	0.0910483i
$635$	−41.4661	+	23.3861i	−1.64553	+	0.928048i
$636$	−18.4809	+	33.8263i	−0.732816	+	1.34130i
$637$		−	1.89232i		−	0.0749766i
$638$	−8.73376	+	34.2017i	−0.345773	+	1.35406i
$639$	−7.15583	+	7.15583i	−0.283080	+	0.283080i
$640$	22.7664	+	11.0314i	0.899920	+	0.436055i
$641$	20.0509	−	20.0509i	0.791961	−	0.791961i	−0.189852	−	0.981813i	$-0.560801\pi$
$641$	20.0509	−	20.0509i	0.791961	−	0.791961i	0.981813	+	0.189852i	$0.0608007\pi$
$642$	1.54909	+	2.61155i	0.0611376	+	0.103070i
$643$	24.9600			0.984326			0.492163	−	0.870503i	$-0.336206\pi$
$643$	24.9600			0.984326			0.492163	+	0.870503i	$0.336206\pi$
$644$	−14.3198	−	48.8113i	−0.564279	−	1.92343i
$645$	10.2806	−	5.79805i	0.404798	−	0.228298i
$646$	−2.33935	−	3.94382i	−0.0920404	−	0.155167i
$647$	29.0538	−	29.0538i	1.14222	−	1.14222i	0.154178	−	0.988043i	$-0.450727\pi$
$647$	29.0538	−	29.0538i	1.14222	−	1.14222i	0.988043	−	0.154178i	$-0.0492730\pi$
$648$	23.1771	+	21.5940i	0.910483	+	0.848291i
$649$	1.73068	−	1.73068i	0.0679352	−	0.0679352i
$650$	−2.14307	+	2.10741i	−0.0840579	+	0.0826593i
$651$	43.2835			1.69641
$652$	−5.06755	+	1.48667i	−0.198461	+	0.0582225i
$653$		−	15.9494i		−	0.624150i	−0.950057	−	0.312075i	$-0.898976\pi$
$653$		−	15.9494i		−	0.624150i	0.950057	−	0.312075i	$-0.101024\pi$
$654$	0.665935	+	1.12268i	0.0260401	+	0.0439001i
$655$	4.16867	−	14.9528i	0.162883	−	0.584254i
$656$	17.1116	+	19.0577i	0.668094	+	0.744077i
$657$	4.40268	−	4.40268i	0.171765	−	0.171765i
$658$	−10.1506	+	39.7500i	−0.395710	+	1.54961i
$659$	−2.75615	−	2.75615i	−0.107365	−	0.107365i	0.651384	−	0.758748i	$-0.274189\pi$
$659$	−2.75615	−	2.75615i	−0.107365	−	0.107365i	−0.758748	+	0.651384i	$0.774189\pi$
$660$	0.650533	+	48.2616i	0.0253220	+	1.87858i
$661$			34.4292i			1.33914i	0.742749	+	0.669570i	$0.233521\pi$
$661$			34.4292i			1.33914i	−0.742749	+	0.669570i	$0.766479\pi$
$662$	−21.0843	+	12.5066i	−0.819466	+	0.486081i
$663$	2.94266			0.114283
$664$	−21.6855	+	0.766821i	−0.841562	+	0.0297584i
$665$	−6.38329	+	3.60005i	−0.247533	+	0.139604i
$666$	6.59509	−	3.91200i	0.255554	−	0.151587i
$667$		−	35.9432i		−	1.39172i
$668$	21.4494	−	39.2597i	0.829903	−	1.51900i
$669$	−0.635318	+	0.635318i	−0.0245628	+	0.0245628i
$670$	−6.55952	+	11.4061i	−0.253416	+	0.440654i
$671$	−0.770200	−	0.770200i	−0.0297332	−	0.0297332i
$672$	−37.5662	+	12.4786i	−1.44915	+	0.481374i
$673$	−25.2810			−0.974512			−0.487256	−	0.873259i	$-0.662002\pi$
$673$	−25.2810			−0.974512			−0.487256	+	0.873259i	$0.662002\pi$
$674$	−22.5470	−	38.0111i	−0.868477	−	1.46413i
$675$	15.2548	+	9.22251i	0.587156	+	0.354975i
$676$	22.4996	+	12.2926i	0.865369	+	0.472792i
$677$	−11.4071	−	11.4071i	−0.438412	−	0.438412i	0.453066	−	0.891477i	$-0.350330\pi$
$677$	−11.4071	−	11.4071i	−0.438412	−	0.438412i	−0.891477	+	0.453066i	$0.850330\pi$
$678$	−12.3423	−	20.8074i	−0.474003	−	0.799104i
$679$	−44.4170			−1.70457
$680$	−11.0468	−	18.0641i	−0.423627	−	0.692725i
$681$	18.3642			0.703719
$682$	−23.2924	−	39.2678i	−0.891912	−	1.50364i
$683$			38.2037i			1.46182i	0.682472	+	0.730911i	$0.260905\pi$
$683$			38.2037i			1.46182i	−0.682472	+	0.730911i	$0.739095\pi$
$684$	−2.37138	+	0.695692i	−0.0906719	+	0.0266004i
$685$	8.36043	+	2.33079i	0.319436	+	0.0890550i
$686$	−3.01724	+	11.8156i	−0.115199	+	0.451122i
$687$	12.9938	+	12.9938i	0.495743	+	0.495743i
$688$	2.17512	−	9.97622i	0.0829257	−	0.380340i
$689$	−3.96173			−0.150930
$690$	−12.8006	−	47.4502i	−0.487309	−	1.80640i
$691$	25.6067	+	25.6067i	0.974123	+	0.974123i	0.999674	−	0.0255504i	$-0.00813382\pi$
$691$	25.6067	+	25.6067i	0.974123	+	0.974123i	−0.0255504	+	0.999674i	$0.508134\pi$
$692$	−29.3750	+	8.61775i	−1.11667	+	0.327598i
$693$	−15.9348	−	15.9348i	−0.605311	−	0.605311i
$694$	−5.88230	−	1.50211i	−0.223289	−	0.0570192i
$695$	11.3918	−	40.8617i	0.432115	−	1.54997i
$696$	−27.9526	+	0.988430i	−1.05954	+	0.0374664i
$697$	−3.43475	−	21.1602i	−0.130100	−	0.801500i
$698$	−27.9133	−	7.12794i	−1.05653	−	0.269796i
$699$			37.7558i			1.42805i
$700$	−29.2493	+	17.0196i	−1.10552	+	0.643282i
$701$	48.7303			1.84052			0.920259	−	0.391310i	$-0.127978\pi$
$701$	48.7303			1.84052			0.920259	+	0.391310i	$0.127978\pi$
$702$	−0.530255	+	2.07650i	−0.0200132	+	0.0783723i
$703$		−	4.11578i		−	0.155230i
$704$	31.5367	+	27.3658i	1.18858	+	1.03139i
$705$	−10.6444	+	38.1808i	−0.400890	+	1.43797i
$706$	6.94703	+	11.7117i	0.261455	+	0.440777i
$707$	27.0822	+	27.0822i	1.01853	+	1.01853i
$708$	1.70193	+	0.929843i	0.0639623	+	0.0349456i
$709$	10.2025	−	10.2025i	0.383163	−	0.383163i	−0.489077	−	0.872240i	$-0.662666\pi$
$709$	10.2025	−	10.2025i	0.383163	−	0.383163i	0.872240	+	0.489077i	$0.162666\pi$
$710$	6.53287	+	24.2166i	0.245174	+	0.908832i
$711$	13.7813	+	13.7813i	0.516838	+	0.516838i
$712$	−10.3090	+	0.364536i	−0.386346	+	0.0136616i
$713$	32.8728	+	32.8728i	1.23110	+	1.23110i
$714$	32.1014	+	8.19742i	1.20136	+	0.306781i
$715$	−4.32097	+	2.43694i	−0.161595	+	0.0911365i
$716$	−20.4965	+	6.01306i	−0.765989	+	0.224718i
$717$	−9.77897	−	9.77897i	−0.365202	−	0.365202i
$718$	−34.7502	−	8.87383i	−1.29687	−	0.331168i
$719$	−2.55264	+	2.55264i	−0.0951974	+	0.0951974i	−0.753102	−	0.657904i	$-0.771443\pi$
$719$	−2.55264	+	2.55264i	−0.0951974	+	0.0951974i	0.657904	+	0.753102i	$0.271443\pi$
$720$	−10.9060	+	3.35978i	−0.406442	+	0.125212i
$721$	−16.4669	+	16.4669i	−0.613260	+	0.613260i
$722$	6.32001	−	24.7494i	0.235207	−	0.921077i
$723$			38.4755i			1.43092i
$724$	−40.9896	+	12.0251i	−1.52336	+	0.446910i
$725$	−23.2168	+	5.72162i	−0.862251	+	0.212496i
$726$	−11.7513	+	46.0184i	−0.436131	+	1.70790i
$727$		−	21.0340i		−	0.780108i	−0.920792	−	0.390054i	$-0.872456\pi$
$727$		−	21.0340i		−	0.780108i	0.920792	−	0.390054i	$-0.127544\pi$
$728$	−2.97674	−	2.77341i	−0.110325	−	0.102789i
$729$	7.82694			0.289887
$730$	−4.01939	−	14.8994i	−0.148764	−	0.551452i
$731$	−6.04298	+	6.04298i	−0.223508	+	0.223508i
$732$	0.413805	−	0.757402i	0.0152947	−	0.0279944i
$733$	15.6779	−	15.6779i	0.579076	−	0.579076i	−0.355572	−	0.934649i	$-0.615714\pi$
$733$	15.6779	−	15.6779i	0.579076	−	0.579076i	0.934649	+	0.355572i	$0.115714\pi$
$734$	19.0927	−	11.3252i	0.704723	−	0.418019i
$735$	5.52793	−	19.8284i	0.203901	−	0.731381i
$736$	−38.0079	−	19.0534i	−1.40099	−	0.702318i
$737$	−15.3560	+	15.3560i	−0.565647	+	0.565647i
$738$	−11.5077	−	1.02805i	−0.423604	−	0.0378432i
$739$	17.4890			0.643342			0.321671	−	0.946852i	$-0.395756\pi$
$739$	17.4890			0.643342			0.321671	+	0.946852i	$0.395756\pi$
$740$	−0.256156	−	19.0037i	−0.00941648	−	0.698588i
$741$	−0.601922	−	0.601922i	−0.0221122	−	0.0221122i
$742$	−43.2184	−	11.0363i	−1.58660	−	0.405154i
$743$	5.66456	+	5.66456i	0.207813	+	0.207813i	0.803337	−	0.595524i	$-0.203056\pi$
$743$	5.66456	+	5.66456i	0.207813	+	0.207813i	−0.595524	+	0.803337i	$0.703056\pi$
$744$	24.6608	−	26.4688i	0.904109	−	0.970393i
$745$	38.0617	−	21.4661i	1.39447	−	0.786455i
$746$	−20.0242	−	33.7580i	−0.733137	−	1.23597i
$747$	6.92133	−	6.92133i	0.253238	−	0.253238i
$748$	−9.83802	−	33.5345i	−0.359713	−	1.22614i
$749$	−2.48461	+	2.48461i	−0.0907857	+	0.0907857i
$750$	−28.6119	+	15.8217i	−1.04476	+	0.577726i
$751$	−29.8104	+	29.8104i	−1.08780	+	1.08780i	−0.0920412	+	0.995755i	$0.529339\pi$
$751$	−29.8104	+	29.8104i	−1.08780	+	1.08780i	−0.995755	+	0.0920412i	$0.970661\pi$
$752$	18.5247	+	28.8549i	0.675525	+	1.05223i
$753$	13.6232			0.496457
$754$	−1.46662	−	2.47252i	−0.0534111	−	0.0900438i
$755$	−16.2219	−	28.7632i	−0.590374	−	1.04680i
$756$	−11.5691	+	21.1753i	−0.420763	+	0.770138i
$757$		−	9.54778i		−	0.347020i	−0.984832	−	0.173510i	$-0.944489\pi$
$757$		−	9.54778i		−	0.347020i	0.984832	−	0.173510i	$-0.0555109\pi$
$758$	−39.4792	−	10.0814i	−1.43395	−	0.366174i
$759$		−	81.1160i		−	2.94433i
$760$	−1.43538	+	5.95465i	−0.0520666	+	0.215998i
$761$	45.4193			1.64645			0.823225	−	0.567716i	$-0.192173\pi$
$761$	45.4193			1.64645			0.823225	+	0.567716i	$0.192173\pi$
$762$	−31.7628	−	53.5478i	−1.15065	−	1.93983i
$763$	−1.06811	+	1.06811i	−0.0386680	+	0.0386680i
$764$	15.4280	+	52.5890i	0.558167	+	1.90260i
$765$	9.20057	+	2.56501i	0.332647	+	0.0927383i
$766$	4.57394	−	17.9117i	0.165263	−	0.647177i
$767$			0.199329i			0.00719736i
$768$	−13.7724	+	30.0823i	−0.496970	+	1.08550i
$769$		−	3.30422i		−	0.119153i	−0.998224	−	0.0595767i	$-0.981025\pi$
$769$		−	3.30422i		−	0.119153i	0.998224	−	0.0595767i	$-0.0189751\pi$
$770$	−53.9260	+	14.5475i	−1.94336	+	0.524256i
$771$	−26.3962			−0.950637
$772$	4.79911	−	8.78399i	0.172724	−	0.316143i
$773$	29.3349			1.05510			0.527551	−	0.849523i	$-0.323110\pi$
$773$	29.3349			1.05510			0.527551	+	0.849523i	$0.323110\pi$
$774$	2.34978	+	3.96141i	0.0844611	+	0.142390i
$775$	16.0007	−	26.4664i	0.574762	−	0.950702i
$776$	−25.3066	+	27.1620i	−0.908455	+	0.975058i
$777$	21.0280	+	21.0280i	0.754374	+	0.754374i
$778$	49.2312	+	12.5717i	1.76502	+	0.450717i
$779$	−3.62575	+	5.03091i	−0.129906	+	0.180251i
$780$	−2.81670	−	2.74177i	−0.100854	−	0.0981712i
$781$			41.3982i			1.48134i
$782$	18.1545	+	30.6060i	0.649203	+	1.09447i
$783$	−12.0560	+	12.0560i	−0.430846	+	0.430846i
$784$	−9.62040	−	14.9852i	−0.343586	−	0.535185i
$785$	11.4117	−	40.9333i	0.407302	−	1.46097i
$786$	19.6698	+	5.02290i	0.701600	+	0.179161i
$787$	16.1923	−	16.1923i	0.577195	−	0.577195i	−0.356935	−	0.934129i	$-0.616178\pi$
$787$	16.1923	−	16.1923i	0.577195	−	0.577195i	0.934129	+	0.356935i	$0.116178\pi$
$788$	−0.566415	−	1.93072i	−0.0201777	−	0.0687789i
$789$			9.98370i			0.355429i
$790$	46.6382	−	12.5815i	1.65931	−	0.447630i
$791$	19.7960	−	19.7960i	0.703865	−	0.703865i
$792$	−18.8233	+	0.665610i	−0.668857	+	0.0236514i
$793$	0.0887068			0.00315007
$794$	44.5315	+	11.3716i	1.58037	+	0.403563i
$795$	−41.5122	−	11.5731i	−1.47229	−	0.410457i
$796$	9.35219	−	2.74365i	0.331479	−	0.0972463i
$797$	1.10655	−	1.10655i	0.0391960	−	0.0391960i	−0.687237	−	0.726433i	$-0.741177\pi$
$797$	1.10655	−	1.10655i	0.0391960	−	0.0391960i	0.726433	+	0.687237i	$0.241177\pi$
$798$	−4.88957	−	8.24314i	−0.173089	−	0.291804i
$799$		−	28.6996i		−	1.01532i
$800$	−6.25691	+	27.5835i	−0.221215	+	0.975225i
$801$	3.29030	−	3.29030i	0.116257	−	0.116257i
$802$	−10.5586	+	41.3480i	−0.372838	+	1.46005i
$803$		−	25.4705i		−	0.898835i
$804$	−15.1009	−	8.25033i	−0.532567	−	0.290967i
$805$	49.5374	−	27.9381i	1.74597	−	0.984690i
$806$	3.60264	+	0.919972i	0.126898	+	0.0324046i
$807$			25.9035i			0.911846i
$808$	31.9915	−	1.13125i	1.12546	−	0.0397972i
$809$	−14.4832	+	14.4832i	−0.509204	+	0.509204i	−0.914282	−	0.405078i	$-0.867244\pi$
$809$	−14.4832	+	14.4832i	−0.509204	+	0.509204i	0.405078	+	0.914282i	$0.367244\pi$
$810$	−17.6563	+	30.7018i	−0.620380	+	1.07875i
$811$	7.05461			0.247721			0.123860	−	0.992300i	$-0.460473\pi$
$811$	7.05461			0.247721			0.123860	+	0.992300i	$0.460473\pi$
$812$	−9.11156	−	31.0582i	−0.319753	−	1.08993i
$813$		−	17.4645i		−	0.612508i
$814$	7.76116	−	30.3930i	0.272029	−	1.06527i
$815$	−2.90052	−	5.14294i	−0.101601	−	0.180149i
$816$	23.3027	−	14.9602i	0.815758	−	0.523712i
$817$	2.47219			0.0864909
$818$	−8.51507	+	33.3453i	−0.297723	+	1.16589i
$819$	1.83526			0.0641293
$820$	−16.4279	+	23.4547i	−0.573688	+	0.819074i
$821$	14.8675			0.518880			0.259440	−	0.965759i	$-0.416462\pi$
$821$	14.8675			0.518880			0.259440	+	0.965759i	$0.416462\pi$
$822$	−2.80841	+	10.9978i	−0.0979546	+	0.383594i
$823$	37.3427			1.30168			0.650842	−	0.759213i	$-0.274416\pi$
$823$	37.3427			1.30168			0.650842	+	0.759213i	$0.274416\pi$
$824$	0.687838	+	19.4519i	0.0239620	+	0.677640i
$825$	−52.3954	+	12.9125i	−1.82417	+	0.449555i
$826$	−0.555275	+	2.17447i	−0.0193205	+	0.0756596i
$827$			39.4208i			1.37080i	0.728169	+	0.685398i	$0.240372\pi$
$827$			39.4208i			1.37080i	−0.728169	+	0.685398i	$0.759628\pi$
$828$	18.4031	−	5.39891i	0.639550	−	0.187625i
$829$	−19.0341			−0.661080			−0.330540	−	0.943792i	$-0.607231\pi$
$829$	−19.0341			−0.661080			−0.330540	+	0.943792i	$0.607231\pi$
$830$	−6.31878	−	23.4230i	−0.219328	−	0.813024i
$831$	36.8370	−	36.8370i	1.27786	−	1.27786i
$832$	−3.39200	+	0.240189i	−0.117597	+	0.00832706i
$833$			14.9045i			0.516412i
$834$	53.7521	+	13.7261i	1.86128	+	0.475298i
$835$	48.1802	+	13.4321i	1.66734	+	0.464836i
$836$	−4.84712	+	8.87186i	−0.167641	+	0.306840i
$837$		−	22.0522i		−	0.762237i
$838$	−11.0673	+	43.3400i	−0.382314	+	1.49716i
$839$	17.9725	−	17.9725i	0.620480	−	0.620480i	−0.325174	−	0.945654i	$-0.605423\pi$
$839$	17.9725	−	17.9725i	0.620480	−	0.620480i	0.945654	+	0.325174i	$0.105423\pi$
$840$	−23.0895	−	37.7564i	−0.796662	−	1.30272i
$841$			6.12968i			0.211368i
$842$	10.3951	+	17.5247i	0.358239	+	0.603942i
$843$	−46.1745	+	46.1745i	−1.59033	+	1.59033i
$844$	3.85622	+	13.1445i	0.132737	+	0.452454i
$845$	−7.69789	+	27.6119i	−0.264815	+	0.949879i
$846$	−14.9867	−	3.82701i	−0.515254	−	0.131575i
$847$	−54.9617			−1.88851
$848$	−31.3726	+	20.1411i	−1.07734	+	0.691647i
$849$	−27.5663	+	27.5663i	−0.946071	+	0.946071i
$850$	16.8794	−	16.5986i	0.578960	−	0.569327i
$851$			31.9405i			1.09491i
$852$	−31.4761	+	9.23417i	−1.07836	+	0.316357i
$853$	20.2190	−	20.2190i	0.692286	−	0.692286i	−0.270448	−	0.962735i	$-0.587172\pi$
$853$	20.2190	−	20.2190i	0.692286	−	0.692286i	0.962735	+	0.270448i	$0.0871719\pi$
$854$	0.967699	+	0.247112i	0.0331140	+	0.00845600i
$855$	−1.35731	−	2.40666i	−0.0464189	−	0.0823059i
$856$	0.103784	+	2.93500i	0.00354728	+	0.100316i
$857$	−11.0226	+	11.0226i	−0.376526	+	0.376526i	−0.869847	−	0.493321i	$-0.835783\pi$
$857$	−11.0226	+	11.0226i	−0.376526	+	0.376526i	0.493321	+	0.869847i	$0.335783\pi$
$858$	−3.30985	−	5.57995i	−0.112996	−	0.190496i
$859$		−	43.7306i		−	1.49207i	−0.665908	−	0.746034i	$-0.731956\pi$
$859$		−	43.7306i		−	1.49207i	0.665908	−	0.746034i	$-0.268044\pi$
$860$	11.4147	−	0.153863i	0.389240	−	0.00524668i
$861$	−7.17911	−	44.2278i	−0.244663	−	1.50728i
$862$	−4.08315	−	1.04267i	−0.139073	−	0.0355136i
$863$	−25.3477	−	25.3477i	−0.862844	−	0.862844i	0.128823	−	0.991668i	$-0.458880\pi$
$863$	−25.3477	−	25.3477i	−0.862844	−	0.862844i	−0.991668	+	0.128823i	$0.958880\pi$
$864$	6.35767	+	19.1394i	0.216292	+	0.651135i
$865$	−16.8134	−	29.8120i	−0.571672	−	1.01364i
$866$	9.70728	+	16.3651i	0.329867	+	0.556110i
$867$	11.9756			0.406713
$868$	36.7383	+	20.0719i	1.24698	+	0.681284i
$869$	79.7279			2.70458
$870$	−8.14489	−	30.1922i	−0.276138	−	1.02361i
$871$		−	1.76861i		−	0.0599272i
$872$	0.0446157	+	1.26172i	0.00151088	+	0.0427274i
$873$		−	16.7463i		−	0.566776i
$874$	2.54696	−	9.97398i	0.0861522	−	0.337375i
$875$	−25.9318	−	27.5505i	−0.876654	−	0.931376i
$876$	19.3659	−	5.68139i	0.654314	−	0.191956i
$877$	2.43394	−	2.43394i	0.0821884	−	0.0821884i	−0.664817	−	0.747006i	$-0.731491\pi$
$877$	2.43394	−	2.43394i	0.0821884	−	0.0821884i	0.747006	+	0.664817i	$0.231491\pi$
$878$	−5.42630	−	9.14799i	−0.183129	−	0.308730i
$879$	32.5669			1.09845
$880$	−21.8283	+	41.2654i	−0.735831	+	1.39106i
$881$		−	45.4208i		−	1.53026i	−0.643873	−	0.765132i	$-0.722674\pi$
$881$		−	45.4208i		−	1.53026i	0.643873	−	0.765132i	$-0.277326\pi$
$882$	7.78303	+	1.98748i	0.262068	+	0.0669219i
$883$			19.5241i			0.657039i	0.944497	+	0.328519i	$0.106550\pi$
$883$			19.5241i			0.657039i	−0.944497	+	0.328519i	$0.893450\pi$
$884$	2.49768	+	1.36460i	0.0840062	+	0.0458966i
$885$	−0.582287	+	2.08863i	−0.0195734	+	0.0702086i
$886$	−18.1829	−	30.6538i	−0.610865	−	1.02984i
$887$	−34.7765			−1.16768			−0.583840	−	0.811869i	$-0.698450\pi$
$887$	−34.7765			−1.16768			−0.583840	+	0.811869i	$0.698450\pi$
$888$	24.8398	−	0.878358i	0.833568	−	0.0294758i
$889$	50.9450	−	50.9450i	1.70864	−	1.70864i
$890$	−3.00386	−	11.1349i	−0.100689	−	0.373244i
$891$	−41.3341	+	41.3341i	−1.38474	+	1.38474i
$892$	−0.833865	+	0.244631i	−0.0279199	+	0.00819086i
$893$	−5.87052	+	5.87052i	−0.196449	+	0.196449i
$894$	29.1551	+	49.1515i	0.975092	+	1.64387i
$895$	−11.7316	−	20.8014i	−0.392143	−	0.695314i
$896$	−37.6723	−	6.82895i	−1.25854	−	0.228139i
$897$	4.67122	+	4.67122i	0.155967	+	0.155967i
$898$	−6.85773	−	1.75119i	−0.228845	−	0.0584380i
$899$	20.9167	+	20.9167i	0.697610	+	0.697610i
$900$	−6.41682	−	11.0277i	−0.213894	−	0.367590i
$901$	31.2038			1.03955
$902$	−36.2612	+	30.3136i	−1.20736	+	1.00933i
$903$	−12.6307	+	12.6307i	−0.420322	+	0.420322i
$904$	−0.826898	−	23.3845i	−0.0275022	−	0.777757i
$905$	−23.4612	−	41.5994i	−0.779877	−	1.38281i
$906$	37.1437	−	22.0325i	1.23402	−	0.731980i
$907$	11.4830	−	11.4830i	0.381288	−	0.381288i	−0.490278	−	0.871566i	$-0.663105\pi$
$907$	11.4830	−	11.4830i	0.381288	−	0.381288i	0.871566	+	0.490278i	$0.163105\pi$
$908$	15.5873	+	8.51607i	0.517282	+	0.282616i
$909$	−10.2107	+	10.2107i	−0.338666	+	0.338666i
$910$	2.26768	−	3.94317i	0.0751729	−	0.130715i
$911$	24.0407			0.796505			0.398252	−	0.917276i	$-0.369617\pi$
$911$	24.0407			0.796505			0.398252	+	0.917276i	$0.369617\pi$
$912$	−7.82670	−	1.70646i	−0.259168	−	0.0565065i
$913$		−	40.0415i		−	1.32518i
$914$	1.14772	−	4.49453i	0.0379634	−	0.148666i
$915$	0.929498	+	0.259133i	0.0307282	+	0.00856669i
$916$	5.00329	+	17.0545i	0.165313	+	0.563497i
$917$			23.4925i			0.775791i
$918$	4.17645	−	16.3551i	0.137844	−	0.539800i
$919$	39.5730	−	39.5730i	1.30539	−	1.30539i	0.380687	−	0.924704i	$-0.375687\pi$
$919$	39.5730	−	39.5730i	1.30539	−	1.30539i	0.924704	−	0.380687i	$-0.124313\pi$
$920$	11.1392	−	46.2110i	0.367249	−	1.52353i
$921$	−9.34291	+	9.34291i	−0.307859	+	0.307859i
$922$	43.3794	+	11.0774i	1.42862	+	0.364814i
$923$	−2.38399	−	2.38399i	−0.0784700	−	0.0784700i
$924$	−20.5628	−	70.0917i	−0.676468	−	2.30585i
$925$	20.6314	−	5.08446i	0.678356	−	0.167176i
$926$	33.3901	+	8.52650i	1.09727	+	0.280198i
$927$	−6.20843	−	6.20843i	−0.203912	−	0.203912i
$928$	−24.1841	−	12.1235i	−0.793882	−	0.397974i
$929$	−6.05660	−	6.05660i	−0.198711	−	0.198711i	0.600737	−	0.799447i	$-0.294874\pi$
$929$	−6.05660	−	6.05660i	−0.198711	−	0.198711i	−0.799447	+	0.600737i	$0.794874\pi$
$930$	35.0622	+	20.1639i	1.14973	+	0.661201i
$931$	3.04873	−	3.04873i	0.0999181	−	0.0999181i
$932$	−17.5085	+	32.0465i	−0.573511	+	1.04972i
$933$	3.43354	+	3.43354i	0.112409	+	0.112409i
$934$	−16.3133	−	27.5020i	−0.533788	−	0.899894i
$935$	34.0333	−	19.1941i	1.11301	−	0.627715i
$936$	1.04564	−	1.12230i	0.0341779	−	0.0366837i
$937$			25.7234i			0.840348i	0.907444	+	0.420174i	$0.138031\pi$
$937$			25.7234i			0.840348i	−0.907444	+	0.420174i	$0.861969\pi$
$938$	4.92686	−	19.2937i	0.160868	−	0.629963i
$939$	−30.7525			−1.00357
$940$	−26.7404	+	27.4711i	−0.872175	+	0.896009i
$941$		−	16.8282i		−	0.548585i	−0.961646	−	0.274293i	$-0.911556\pi$
$941$		−	16.8282i		−	0.548585i	0.961646	−	0.274293i	$-0.0884437\pi$
$942$	53.8462	+	13.7502i	1.75441	+	0.448006i
$943$	28.1376	−	39.0423i	0.916287	−	1.27139i
$944$	1.01337	+	1.57847i	0.0329824	+	0.0513749i
$945$	−25.9867	−	7.24480i	−0.845347	−	0.235673i
$946$	18.2559	+	4.66182i	0.593549	+	0.151569i
$947$	−2.13068	−	2.13068i	−0.0692377	−	0.0692377i	0.671640	−	0.740878i	$-0.265590\pi$
$947$	−2.13068	−	2.13068i	−0.0692377	−	0.0692377i	−0.740878	+	0.671640i	$0.765590\pi$
$948$	17.7839	+	60.6192i	0.577594	+	1.96882i
$949$	1.46677	+	1.46677i	0.0476133	+	0.0476133i
$950$	−6.84795	−	0.0574505i	−0.222177	−	0.00186394i
$951$	−13.5481			−0.439327
$952$	23.4457	+	21.8442i	0.759881	+	0.707976i
$953$	−28.9977	−	28.9977i	−0.939327	−	0.939327i	0.0589353	−	0.998262i	$-0.481229\pi$
$953$	−28.9977	−	28.9977i	−0.939327	−	0.939327i	−0.998262	+	0.0589353i	$0.981229\pi$
$954$	4.16094	−	16.2944i	0.134715	−	0.527550i
$955$	−53.3713	+	30.1004i	−1.72706	+	0.974025i
$956$	−3.76542	−	12.8350i	−0.121782	−	0.415115i
$957$		−	51.6134i		−	1.66843i
$958$	16.2494	+	27.3942i	0.524994	+	0.885067i
$959$	−13.1352			−0.424157
$960$	−36.2441	−	7.39206i	−1.16977	−	0.238578i
$961$	−7.25979			−0.234187
$962$	1.30329	+	2.19718i	0.0420199	+	0.0708398i
$963$	−0.936759	−	0.936759i	−0.0301866	−	0.0301866i
$964$	−17.8423	+	32.6574i	−0.574661	+	1.05182i
$965$	10.7799	+	3.00530i	0.347016	+	0.0967441i
$966$	37.9454	+	63.9708i	1.22087	+	2.05823i
$967$	6.48310			0.208482			0.104241	−	0.994552i	$-0.466759\pi$
$967$	6.48310			0.208482			0.104241	+	0.994552i	$0.466759\pi$
$968$	−31.3145	+	33.6103i	−1.00649	+	1.08027i
$969$	4.74093	+	4.74093i	0.152301	+	0.152301i
$970$	−35.9804	−	20.6920i	−1.15526	−	0.664380i
$971$	−3.85798	+	3.85798i	−0.123809	+	0.123809i	−0.766296	−	0.642488i	$-0.777902\pi$
$971$	−3.85798	+	3.85798i	−0.123809	+	0.123809i	0.642488	+	0.766296i	$0.277902\pi$
$972$	−21.8752	−	11.9514i	−0.701647	−	0.383343i
$973$			64.1983i			2.05810i
$974$	17.5331	−	10.4001i	0.561797	−	0.333240i
$975$	2.27370	−	3.76088i	0.0728166	−	0.120444i
$976$	0.702462	−	0.450977i	0.0224853	−	0.0144354i
$977$	−24.7565			−0.792032			−0.396016	−	0.918244i	$-0.629607\pi$
$977$	−24.7565			−0.792032			−0.396016	+	0.918244i	$0.629607\pi$
$978$	6.64141	−	3.93947i	0.212369	−	0.125970i
$979$		−	19.0352i		−	0.608366i
$980$	13.8871	−	14.2665i	0.443606	−	0.455728i
$981$	−0.402702	−	0.402702i	−0.0128573	−	0.0128573i
$982$	−5.62717	+	22.0362i	−0.179570	+	0.703203i
$983$	18.0539	−	18.0539i	0.575830	−	0.575830i	−0.357922	−	0.933752i	$-0.616515\pi$
$983$	18.0539	−	18.0539i	0.575830	−	0.575830i	0.933752	+	0.357922i	$0.116515\pi$
$984$	−31.1366	−	20.8087i	−0.992598	−	0.663356i
$985$	1.95944	−	1.10508i	0.0624329	−	0.0352109i
$986$	11.5515	+	19.4743i	0.367876	+	0.620189i
$987$		−	59.9862i		−	1.90938i
$988$	−0.231772	−	0.790032i	−0.00737365	−	0.0251343i
$989$	−19.1854			−0.610060
$990$	−5.48477	−	20.3314i	−0.174317	−	0.646175i
$991$	20.1485	−	20.1485i	0.640040	−	0.640040i	−0.310525	−	0.950565i	$-0.600505\pi$
$991$	20.1485	−	20.1485i	0.640040	−	0.640040i	0.950565	+	0.310525i	$0.100505\pi$
$992$	33.2061	−	11.0303i	1.05429	−	0.350213i
$993$	25.3458	−	25.3458i	0.804325	−	0.804325i
$994$	−19.3658	−	32.6480i	−0.614244	−	1.03553i
$995$	5.35291	+	9.49132i	0.169699	+	0.300895i
$996$	30.4446	−	8.93156i	0.964676	−	0.283007i
$997$	−41.2931			−1.30777			−0.653883	−	0.756596i	$-0.726861\pi$
$997$	−41.2931			−1.30777			−0.653883	+	0.756596i	$0.726861\pi$
$998$	−16.8041	−	28.3293i	−0.531923	−	0.896749i
$999$	10.7134	−	10.7134i	0.338957	−	0.338957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.8	yes	240
4.3	odd	2	inner	820.2.s.c.583.54	yes	240
5.2	odd	4		820.2.j.c.747.67	yes	240
20.7	even	4		820.2.j.c.747.113	yes	240
41.32	even	4		820.2.j.c.483.113	yes	240
164.155	odd	4		820.2.j.c.483.67	✓	240
205.32	odd	4	inner	820.2.s.c.647.54	yes	240
820.647	even	4	inner	820.2.s.c.647.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.67	✓	240	164.155	odd	4
820.2.j.c.483.113	yes	240	41.32	even	4
820.2.j.c.747.67	yes	240	5.2	odd	4
820.2.j.c.747.113	yes	240	20.7	even	4
820.2.s.c.583.8	yes	240	1.1	even	1	trivial
820.2.s.c.583.54	yes	240	4.3	odd	2	inner
820.2.s.c.647.8	yes	240	820.647	even	4	inner
820.2.s.c.647.54	yes	240	205.32	odd	4	inner

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37024 - 0.349906i) q^{2} +2.06782 q^{3} +(1.75513 + 0.958912i) q^{4} +(-0.600491 + 2.15393i) q^{5} +(-2.83341 - 0.723542i) q^{6} -3.38406i q^{7} +(-2.06943 - 1.92807i) q^{8} +1.27587 q^{9} +(1.57649 - 2.74129i) q^{10} +(3.69062 - 3.69062i) q^{11} +(3.62929 + 1.98286i) q^{12} +0.425062i q^{13} +(-1.18410 + 4.63699i) q^{14} +(-1.24171 + 4.45394i) q^{15} +(2.16098 + 3.36603i) q^{16} -3.34792i q^{17} +(-1.74826 - 0.446436i) q^{18} +(-0.684819 + 0.684819i) q^{19} +(-3.11937 + 3.20461i) q^{20} -6.99763i q^{21} +(-6.34841 + 3.76568i) q^{22} +(5.31453 - 5.31453i) q^{23} +(-4.27920 - 3.98691i) q^{24} +(-4.27882 - 2.58683i) q^{25} +(0.148732 - 0.582438i) q^{26} -3.56518 q^{27} +(3.24502 - 5.93948i) q^{28} +(3.38159 - 3.38159i) q^{29} +(3.25990 - 5.66849i) q^{30} +6.18545i q^{31} +(-1.78327 - 5.36842i) q^{32} +(7.63153 - 7.63153i) q^{33} +(-1.17146 + 4.58747i) q^{34} +(7.28903 + 2.03210i) q^{35} +(2.23933 + 1.22345i) q^{36} +(-3.00501 + 3.00501i) q^{37} +(1.17799 - 0.698746i) q^{38} +0.878951i q^{39} +(5.39561 - 3.29961i) q^{40} +(6.32040 - 1.02593i) q^{41} +(-2.44851 + 9.58845i) q^{42} +(-1.80499 - 1.80499i) q^{43} +(10.0165 - 2.93854i) q^{44} +(-0.766151 + 2.74814i) q^{45} +(-9.14179 + 5.42262i) q^{46} +8.57237 q^{47} +(4.46851 + 6.96035i) q^{48} -4.45188 q^{49} +(4.95788 + 5.04177i) q^{50} -6.92289i q^{51} +(-0.407597 + 0.746040i) q^{52} +9.32035i q^{53} +(4.88516 + 1.24748i) q^{54} +(5.73315 + 10.1655i) q^{55} +(-6.52472 + 7.00308i) q^{56} +(-1.41608 + 1.41608i) q^{57} +(-5.81684 + 3.45036i) q^{58} +0.468941 q^{59} +(-6.45029 + 6.62656i) q^{60} -0.208691i q^{61} +(2.16432 - 8.47557i) q^{62} -4.31764i q^{63} +(0.565069 + 7.98002i) q^{64} +(-0.915554 - 0.255246i) q^{65} +(-13.1274 + 7.78673i) q^{66} -4.16083 q^{67} +(3.21036 - 5.87604i) q^{68} +(10.9895 - 10.9895i) q^{69} +(-9.27670 - 5.33494i) q^{70} +(-5.60857 + 5.60857i) q^{71} +(-2.64033 - 2.45998i) q^{72} +(3.45071 - 3.45071i) q^{73} +(5.16907 - 3.06613i) q^{74} +(-8.84783 - 5.34910i) q^{75} +(-1.85863 + 0.545267i) q^{76} +(-12.4893 - 12.4893i) q^{77} +(0.307550 - 1.20438i) q^{78} +(10.8014 + 10.8014i) q^{79} +(-8.54784 + 2.63332i) q^{80} -11.1998 q^{81} +(-9.01946 - 0.805764i) q^{82} +(5.42477 - 5.42477i) q^{83} +(6.71011 - 12.2818i) q^{84} +(7.21119 + 2.01040i) q^{85} +(1.84170 + 3.10486i) q^{86} +(6.99252 - 6.99252i) q^{87} +(-14.7533 + 0.521689i) q^{88} +(2.57886 - 2.57886i) q^{89} +(2.01140 - 3.49754i) q^{90} +1.43844 q^{91} +(14.4239 - 4.23154i) q^{92} +12.7904i q^{93} +(-11.7462 - 2.99952i) q^{94} +(-1.06382 - 1.88628i) q^{95} +(-3.68747 - 11.1009i) q^{96} -13.1254i q^{97} +(6.10016 + 1.55774i) q^{98} +(4.70877 - 4.70877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

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