LMFDB - Embedded newform 820.2.s.c.583.54

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			583.54
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.54

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.349906 - 1.37024i) q^{2} -2.06782 q^{3} +(-1.75513 + 0.958912i) q^{4} +(-0.600491 + 2.15393i) q^{5} +(0.723542 + 2.83341i) q^{6} +3.38406i q^{7} +(1.92807 + 2.06943i) q^{8} +1.27587 q^{9} +(3.16152 + 0.0691463i) q^{10} +(-3.69062 + 3.69062i) q^{11} +(3.62929 - 1.98286i) q^{12} +0.425062i q^{13} +(4.63699 - 1.18410i) q^{14} +(1.24171 - 4.45394i) q^{15} +(2.16098 - 3.36603i) q^{16} -3.34792i q^{17} +(-0.446436 - 1.74826i) q^{18} +(0.684819 - 0.684819i) q^{19} +(-1.01149 - 4.35625i) q^{20} -6.99763i q^{21} +(6.34841 + 3.76568i) q^{22} +(-5.31453 + 5.31453i) q^{23} +(-3.98691 - 4.27920i) q^{24} +(-4.27882 - 2.58683i) q^{25} +(0.582438 - 0.148732i) q^{26} +3.56518 q^{27} +(-3.24502 - 5.93948i) q^{28} +(3.38159 - 3.38159i) q^{29} +(-6.53745 - 0.142982i) q^{30} -6.18545i q^{31} +(-5.36842 - 1.78327i) q^{32} +(7.63153 - 7.63153i) q^{33} +(-4.58747 + 1.17146i) 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} +(-5.61519 + 2.91026i) q^{40} +(6.32040 - 1.02593i) q^{41} +(-9.58845 + 2.44851i) q^{42} +(1.80499 + 1.80499i) q^{43} +(2.93854 - 10.0165i) 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} +(-2.04740 + 6.76817i) q^{50} +6.92289i q^{51} +(-0.407597 - 0.746040i) q^{52} +9.32035i q^{53} +(-1.24748 - 4.88516i) q^{54} +(-5.73315 - 10.1655i) q^{55} +(-7.00308 + 6.52472i) q^{56} +(-1.41608 + 1.41608i) q^{57} +(-5.81684 - 3.45036i) q^{58} -0.468941 q^{59} +(2.09157 + 9.00793i) q^{60} -0.208691i q^{61} +(-8.47557 + 2.16432i) 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} +(-0.233996 + 10.6988i) q^{70} +(5.60857 - 5.60857i) q^{71} +(2.45998 + 2.64033i) q^{72} +(3.45071 - 3.45071i) q^{73} +(5.16907 + 3.06613i) q^{74} +(8.84783 + 5.34910i) q^{75} +(-0.545267 + 1.85863i) q^{76} +(-12.4893 - 12.4893i) q^{77} +(-1.20438 + 0.307550i) q^{78} +(-10.8014 - 10.8014i) q^{79} +(5.95255 + 6.67586i) q^{80} -11.1998 q^{81} +(-3.61732 - 8.30150i) 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} +(4.03370 + 0.0882221i) q^{90} -1.43844 q^{91} +(4.23154 - 14.4239i) q^{92} +12.7904i q^{93} +(2.99952 + 11.7462i) q^{94} +(1.06382 + 1.88628i) q^{95} +(11.1009 + 3.68747i) q^{96} -13.1254i q^{97} +(1.55774 + 6.10016i) 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 $

$2$	−0.349906	−	1.37024i	−0.247421	−	0.968908i
$2$	−0.349906	−	1.37024i	−0.247421	−	0.968908i
$3$	−2.06782			−1.19386			−0.596928	−	0.802295i	$-0.703612\pi$
$3$	−2.06782			−1.19386			−0.596928	+	0.802295i	$0.703612\pi$
$4$	−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
$6$	0.723542	+	2.83341i	0.295385	+	1.15674i
$7$			3.38406i			1.27906i	0.768768	+	0.639528i	$0.220870\pi$
$7$			3.38406i			1.27906i	−0.768768	+	0.639528i	$0.779130\pi$
$8$	1.92807	+	2.06943i	0.681677	+	0.731653i
$9$	1.27587			0.425291
$10$	3.16152	+	0.0691463i	0.999761	+	0.0218660i
$11$	−3.69062	+	3.69062i	−1.11276	+	1.11276i	−0.119988	+	0.992775i	$0.538286\pi$
$11$	−3.69062	+	3.69062i	−1.11276	+	1.11276i	−0.992775	+	0.119988i	$0.961714\pi$
$12$	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	$0.981226\pi$
$14$	4.63699	−	1.18410i	1.23929	−	0.316465i
$15$	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	$-0.133075\pi$
$18$	−0.446436	−	1.74826i	−0.105226	−	0.412068i
$19$	0.684819	−	0.684819i	0.157108	−	0.157108i	−0.624176	−	0.781284i	$-0.714565\pi$
$19$	0.684819	−	0.684819i	0.157108	−	0.157108i	0.781284	+	0.624176i	$0.214565\pi$
$20$	−1.01149	−	4.35625i	−0.226175	−	0.974087i
$21$		−	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	$0.536611\pi$
$23$	−5.31453	+	5.31453i	−1.10816	+	1.10816i	−0.993393	+	0.114764i	$0.963389\pi$
$24$	−3.98691	−	4.27920i	−0.813824	−	0.873489i
$25$	−4.27882	−	2.58683i	−0.855764	−	0.517366i
$26$	0.582438	−	0.148732i	0.114226	−	0.0291687i
$27$	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	$0.103550\pi$
$30$	−6.53745	−	0.142982i	−1.19357	−	0.0261048i
$31$		−	6.18545i		−	1.11094i	−0.831537	−	0.555470i	$-0.812538\pi$
$31$		−	6.18545i		−	1.11094i	0.831537	−	0.555470i	$-0.187462\pi$
$32$	−5.36842	−	1.78327i	−0.949012	−	0.315240i
$33$	7.63153	−	7.63153i	1.32848	−	1.32848i
$34$	−4.58747	+	1.17146i	−0.786744	+	0.200903i
$35$	−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
$40$	−5.61519	+	2.91026i	−0.887840	+	0.460152i
$41$	6.32040	−	1.02593i	0.987081	−	0.160224i
$41$	6.32040	−	1.02593i	0.987081	−	0.160224i
$42$	−9.58845	+	2.44851i	−1.47953	+	0.377813i
$43$	1.80499	+	1.80499i	0.275259	+	0.275259i	0.831213	−	0.555954i	$-0.187647\pi$
$43$	1.80499	+	1.80499i	0.275259	+	0.275259i	−0.555954	+	0.831213i	$0.687647\pi$
$44$	2.93854	−	10.0165i	0.443002	−	1.51004i
$45$	−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	$-0.714984\pi$
$47$	−8.57237			−1.25041			−0.625204	+	0.780461i	$0.714984\pi$
$48$	−4.46851	+	6.96035i	−0.644973	+	1.00464i
$49$	−4.45188			−0.635983
$50$	−2.04740	+	6.76817i	−0.289546	+	0.957164i
$51$			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	$0.778883\pi$
$54$	−1.24748	−	4.88516i	−0.169760	−	0.664786i
$55$	−5.73315	−	10.1655i	−0.773057	−	1.37072i
$56$	−7.00308	+	6.52472i	−0.935825	+	0.871902i
$57$	−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	$-0.509718\pi$
$59$	−0.468941			−0.0610509			−0.0305255	+	0.999534i	$0.509718\pi$
$60$	2.09157	+	9.00793i	0.270021	+	1.16292i
$61$		−	0.208691i		−	0.0267202i	−0.999911	−	0.0133601i	$-0.995747\pi$
$61$		−	0.208691i		−	0.0267202i	0.999911	−	0.0133601i	$-0.00425278\pi$
$62$	−8.47557	+	2.16432i	−1.07640	+	0.274870i
$63$			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	$-0.418200\pi$
$67$	4.16083			0.508327			0.254163	+	0.967161i	$0.418200\pi$
$68$	3.21036	+	5.87604i	0.389314	+	0.712575i
$69$	10.9895	−	10.9895i	1.32298	−	1.32298i
$70$	−0.233996	+	10.6988i	−0.0279678	+	1.27875i
$71$	5.60857	−	5.60857i	0.665615	−	0.665615i	−0.291083	−	0.956698i	$-0.594016\pi$
$71$	5.60857	−	5.60857i	0.665615	−	0.665615i	0.956698	+	0.291083i	$0.0940155\pi$
$72$	2.45998	+	2.64033i	0.289911	+	0.311166i
$73$	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
$76$	−0.545267	+	1.85863i	−0.0625464	+	0.213199i
$77$	−12.4893	−	12.4893i	−1.42329	−	1.42329i
$78$	−1.20438	+	0.307550i	−0.136369	+	0.0348232i
$79$	−10.8014	−	10.8014i	−1.21525	−	1.21525i	−0.969275	−	0.245980i	$-0.920890\pi$
$79$	−10.8014	−	10.8014i	−1.21525	−	1.21525i	−0.245980	−	0.969275i	$-0.579110\pi$
$80$	5.95255	+	6.67586i	0.665515	+	0.746384i
$81$	−11.1998			−1.24442
$82$	−3.61732	−	8.30150i	−0.399467	−	0.916748i
$83$	−5.42477	+	5.42477i	−0.595446	+	0.595446i	−0.939097	−	0.343651i	$-0.888336\pi$
$83$	−5.42477	+	5.42477i	−0.595446	+	0.595446i	0.343651	+	0.939097i	$0.388336\pi$
$84$	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	$0.188083\pi$
$90$	4.03370	+	0.0882221i	0.425190	+	0.00929942i
$91$	−1.43844			−0.150789
$92$	4.23154	−	14.4239i	0.441168	−	1.50379i
$93$			12.7904i			1.32630i
$94$	2.99952	+	11.7462i	0.309377	+	1.21153i
$95$	1.06382	+	1.88628i	0.109146	+	0.193528i
$96$	11.1009	+	3.68747i	1.13298	+	0.376351i
$97$		−	13.1254i		−	1.33268i	−0.745649	−	0.666339i	$-0.767860\pi$
$97$		−	13.1254i		−	1.33268i	0.745649	−	0.666339i	$-0.232140\pi$
$98$	1.55774	+	6.10016i	0.157355	+	0.616209i
$99$	−4.70877	+	4.70877i	−0.473249	+	0.473249i
$100$	9.99044	+	0.437215i	0.999044	+	0.0437215i
$101$	−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	$0.440384\pi$
$102$	9.48605	−	2.42236i	0.939259	−	0.239849i
$103$	4.86602	+	4.86602i	0.479463	+	0.479463i	0.904960	−	0.425497i	$-0.139901\pi$
$103$	4.86602	+	4.86602i	0.479463	+	0.479463i	−0.425497	+	0.904960i	$0.639901\pi$
$104$	−0.879636	+	0.819551i	−0.0862554	+	0.0803636i
$105$	15.0724	+	4.20201i	1.47092	+	0.410074i
$106$	12.7711	−	3.26124i	1.24044	−	0.316760i
$107$	0.734209	+	0.734209i	0.0709787	+	0.0709787i	0.741705	−	0.670726i	$-0.234017\pi$
$107$	0.734209	+	0.734209i	0.0709787	+	0.0709787i	−0.670726	+	0.741705i	$0.734017\pi$
$108$	−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	$0.756805\pi$
$110$	−11.9232	+	11.4128i	−1.13683	+	1.08817i
$111$	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
$116$	−2.69249	+	9.17779i	−0.249992	+	0.852136i
$117$			0.542326i			0.0501380i
$118$	0.164085	+	0.642563i	0.0151053	+	0.0591527i
$119$	11.3296			1.03858
$120$	11.6112	−	6.01789i	1.05995	−	0.549356i
$121$		−	16.2413i		−	1.47648i
$122$	−0.285958	+	0.0730223i	−0.0258894	+	0.00661113i
$123$	−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
$126$	5.91621	−	1.51077i	0.527058	−	0.134590i
$127$	−15.0544	−	15.0544i	−1.33586	−	1.33586i	−0.900027	−	0.435834i	$-0.856453\pi$
$127$	−15.0544	−	15.0544i	−1.33586	−	1.33586i	−0.435834	−	0.900027i	$-0.643547\pi$
$128$	11.1323	−	2.01797i	0.983964	−	0.178365i
$129$	−3.73240	−	3.73240i	−0.328619	−	0.328619i
$130$	−0.0293915	+	1.34384i	−0.00257780	+	0.117863i
$131$	6.94210			0.606534			0.303267	−	0.952906i	$-0.401923\pi$
$131$	6.94210			0.606534			0.303267	+	0.952906i	$0.401923\pi$
$132$	−6.07638	+	20.7123i	−0.528881	+	1.80277i
$133$	2.31747	+	2.31747i	0.200950	+	0.200950i
$134$	−1.45590	−	5.70135i	−0.125771	−	0.492522i
$135$	−2.14086	+	7.67914i	−0.184256	+	0.660915i
$136$	6.92828	−	6.45504i	0.594095	−	0.553515i
$137$		−	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	$-0.202412\pi$
$139$	18.9708			1.60908			0.804540	+	0.593898i	$0.202412\pi$
$140$	14.7418	−	3.42294i	1.24591	−	0.289291i
$141$	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
$148$	2.39265	−	8.15574i	0.196675	−	0.670398i
$149$	−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	$-0.545422\pi$
$150$	4.23366	−	13.9954i	0.345676	−	1.14272i
$151$	10.4426	−	10.4426i	0.849804	−	0.849804i	−0.140305	−	0.990108i	$-0.544808\pi$
$151$	10.4426	−	10.4426i	0.849804	−	0.849804i	0.990108	+	0.140305i	$0.0448082\pi$
$152$	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
$160$	7.06472	−	10.4924i	0.558515	−	0.829494i
$161$	−17.9847	−	17.9847i	−1.41739	−	1.41739i
$162$	3.91886	+	15.3464i	0.307895	+	1.20573i
$163$	1.86716	−	1.86716i	0.146247	−	0.146247i	−0.630192	−	0.776439i	$-0.717024\pi$
$163$	1.86716	−	1.86716i	0.146247	−	0.146247i	0.776439	+	0.630192i	$0.217024\pi$
$164$	−10.1094	+	7.86136i	−0.789408	+	0.613869i
$165$	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	$0.332976\pi$
$167$			22.3685i			1.73093i	−0.500972	+	0.865463i	$0.667024\pi$
$168$	14.4811	−	13.4919i	1.11724	−	1.04093i
$169$	12.8193			0.986102
$170$	0.231497	−	10.5845i	0.0177550	−	0.811796i
$171$	0.873743	−	0.873743i	0.0668168	−	0.0668168i
$172$	−4.89883	−	1.43717i	−0.373532	−	0.109583i
$173$	−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
$176$	4.44741	+	20.3981i	0.335236	+	1.53756i
$177$	0.969685			0.0728860
$178$	−4.43602	−	2.63131i	−0.332494	−	0.197225i
$179$	7.55200	−	7.55200i	0.564463	−	0.564463i	−0.366109	−	0.930572i	$-0.619310\pi$
$179$	7.55200	−	7.55200i	0.564463	−	0.564463i	0.930572	+	0.366109i	$0.119310\pi$
$180$	−1.29053	−	5.55803i	−0.0961905	−	0.414271i
$181$	−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	$0.958108\pi$
$182$	0.503317	+	1.97101i	0.0373084	+	0.146101i
$183$			0.431536i			0.0319001i
$184$	−21.2449	−	0.751238i	−1.56619	−	0.0553820i
$185$	−4.66810	−	8.27707i	−0.343206	−	0.608543i
$186$	17.5259	−	4.47543i	1.28506	−	0.328155i
$187$	12.3559	+	12.3559i	0.903553	+	0.903553i
$188$	15.0456	−	8.22014i	1.09732	−	0.599516i
$189$			12.0648i			0.877584i
$190$	2.21242	−	2.11772i	0.160506	−	0.153635i
$191$	−19.3766	−	19.3766i	−1.40204	−	1.40204i	−0.793591	−	0.608452i	$-0.791791\pi$
$191$	−19.3766	−	19.3766i	−1.40204	−	1.40204i	−0.608452	−	0.793591i	$-0.708209\pi$
$192$	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	$-0.0576501\pi$
$194$	−17.9849	+	4.59264i	−1.29124	+	0.329732i
$195$	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	−0.818614	−	0.574344i	$-0.805257\pi$
$199$	−3.44585	+	3.44585i	−0.244270	+	0.244270i	0.574344	+	0.818614i	$0.305257\pi$
$200$	−2.89662	−	13.8423i	−0.204822	−	0.978799i
$201$	−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
$210$	0.483860	−	22.1232i	0.0333895	−	1.52664i
$211$	−4.84316	−	4.84316i	−0.333417	−	0.333417i	0.520466	−	0.853883i	$-0.325758\pi$
$211$	−4.84316	−	4.84316i	−0.333417	−	0.333417i	−0.853883	+	0.520466i	$0.825758\pi$
$212$	−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
$216$	6.87393	+	7.37788i	0.467711	+	0.502001i
$217$	20.9319			1.42095
$218$	−0.322047	+	0.542927i	−0.0218118	+	0.0367717i
$219$	−7.13545	+	7.13545i	−0.482169	+	0.482169i
$220$	19.8103	+	12.3442i	1.33561	+	0.832248i
$221$	1.42307			0.0957263
$222$	−10.6887	−	6.34020i	−0.717379	−	0.425526i
$223$	0.307241	−	0.307241i	0.0205744	−	0.0205744i	−0.696745	−	0.717319i	$-0.745369\pi$
$223$	0.307241	−	0.307241i	0.0205744	−	0.0205744i	0.717319	+	0.696745i	$0.245369\pi$
$224$	6.03469	−	18.1671i	0.403210	−	1.21384i
$225$	−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	$-0.595228\pi$
$227$	−8.88097			−0.589451			−0.294725	+	0.955582i	$0.595228\pi$
$228$	1.12751	−	3.84331i	0.0746713	−	0.254529i
$229$	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	$0.655139\pi$
$230$	−17.1695	+	16.4345i	−1.13212	+	1.08366i
$231$	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	$0.795928\pi$
$234$	0.743118	−	0.189763i	0.0485792	−	0.0124052i
$235$	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
$238$	−3.96428	−	15.5243i	−0.256966	−	1.00629i
$239$	4.72912	+	4.72912i	0.305902	+	0.305902i	0.843317	−	0.537416i	$-0.180599\pi$
$239$	4.72912	+	4.72912i	0.305902	+	0.305902i	−0.537416	+	0.843317i	$0.680599\pi$
$240$	−12.3088	−	13.8045i	−0.794529	−	0.891075i
$241$			18.6068i			1.19857i	0.800536	+	0.599284i	$0.204548\pi$
$241$			18.6068i			1.19857i	−0.800536	+	0.599284i	$0.795452\pi$
$242$	−22.2546	+	5.68293i	−1.43058	+	0.365313i
$243$	12.4636			0.799537
$244$	0.200117	+	0.366281i	0.0128112	+	0.0234487i
$245$	2.67331	−	9.58903i	0.170792	−	0.612621i
$246$	7.47997	+	17.1660i	0.476906	+	1.09446i
$247$	0.291091	+	0.291091i	0.0185216	+	0.0185216i
$248$	12.8003	−	11.9260i	0.812823	−	0.757302i
$249$	11.2174	−	11.2174i	0.710877	−	0.710877i
$250$	−13.3487	−	8.47418i	−0.844247	−	0.535954i
$251$	−6.58820			−0.415844			−0.207922	−	0.978145i	$-0.566670\pi$
$251$	−6.58820			−0.415844			−0.207922	+	0.978145i	$0.566670\pi$
$252$	−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
$260$	1.85168	−	0.429945i	0.114836	−	0.0266640i
$261$	4.31449	−	4.31449i	0.267060	−	0.267060i
$262$	−2.42908	−	9.51236i	−0.150069	−	0.587676i
$263$		−	4.82813i		−	0.297715i	−0.988859	−	0.148858i	$-0.952440\pi$
$263$		−	4.82813i		−	0.297715i	0.988859	−	0.148858i	$-0.0475596\pi$
$264$	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	$0.875273\pi$
$270$	11.2714	+	0.246519i	0.685955	+	0.0150027i
$271$			8.44587i			0.513050i	0.966538	+	0.256525i	$0.0825776\pi$
$271$			8.44587i			0.513050i	−0.966538	+	0.256525i	$0.917422\pi$
$272$	−11.2692	−	7.23478i	−0.683297	−	0.438673i
$273$	2.97443			0.180020
$274$	−5.31857	+	1.35815i	−0.321307	+	0.0820490i
$275$	25.3385	−	6.24449i	1.52797	−	0.376557i
$276$	−8.75005	+	29.8260i	−0.526691	+	1.79531i
$277$	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	$-0.0232682\pi$
$278$	−6.63798	−	25.9946i	−0.398120	−	1.55905i
$279$		−	7.89186i		−	0.472473i
$280$	−9.84850	−	19.0022i	−0.588560	−	1.13560i
$281$	−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	$0.859003\pi$
$282$	−6.20246	−	24.2891i	−0.369351	−	1.44639i
$283$	13.3311	−	13.3311i	0.792450	−	0.792450i	−0.189442	−	0.981892i	$-0.560668\pi$
$283$	13.3311	−	13.3311i	0.792450	−	0.792450i	0.981892	+	0.189442i	$0.0606678\pi$
$284$	−4.46566	+	15.2219i	−0.264988	+	0.903254i
$285$	−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
$288$	−6.84943	−	2.27523i	−0.403607	−	0.134069i
$289$	5.79142			0.340672
$290$	10.9248	−	10.4572i	0.641526	−	0.614065i
$291$			27.1409i			1.59102i
$292$	−2.74753	+	9.36539i	−0.160787	+	0.548068i
$293$	15.7494			0.920089			0.460044	−	0.887896i	$-0.347834\pi$
$293$	15.7494			0.920089			0.460044	+	0.887896i	$0.347834\pi$
$294$	−3.22112	−	12.6140i	−0.187860	−	0.735664i
$295$	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
$300$	−20.6584	−	0.904082i	−1.19271	−	0.0521972i
$301$	−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
$304$	−0.825246	−	3.78500i	−0.0473311	−	0.217085i
$305$	0.449506	+	0.125317i	0.0257387	+	0.00717565i
$306$	−5.85303	+	1.49463i	−0.334595	+	0.0854424i
$307$	4.51824	−	4.51824i	0.257870	−	0.257870i	−0.566317	−	0.824187i	$-0.691632\pi$
$307$	4.51824	−	4.51824i	0.257870	−	0.257870i	0.824187	+	0.566317i	$0.191632\pi$
$308$	33.8965	+	9.94422i	1.93143	+	0.566624i
$309$	−10.0620	−	10.0620i	−0.572410	−	0.572410i
$310$	0.427701	−	19.5554i	0.0242918	−	1.11067i
$311$	−1.66046	−	1.66046i	−0.0941563	−	0.0941563i	0.658460	−	0.752616i	$-0.271208\pi$
$311$	−1.66046	−	1.66046i	−0.0941563	−	0.0941563i	−0.752616	+	0.658460i	$0.771208\pi$
$312$	1.81893	−	1.69468i	0.102976	−	0.0959425i
$313$	−14.8719			−0.840612			−0.420306	−	0.907382i	$-0.638077\pi$
$313$	−14.8719			−0.840612			−0.420306	+	0.907382i	$0.638077\pi$
$314$	6.64961	+	26.0401i	0.375259	+	1.46953i
$315$	−9.29989	−	2.59270i	−0.523989	−	0.146082i
$316$	29.3155	+	8.60031i	1.64913	+	0.483805i
$317$	−6.55187			−0.367990			−0.183995	−	0.982927i	$-0.558903\pi$
$317$	−6.55187			−0.367990			−0.183995	+	0.982927i	$0.558903\pi$
$318$	−26.4084	+	6.74366i	−1.48091	+	0.378166i
$319$			24.9603i			1.39751i
$320$	−16.8491	−	6.00905i	−0.941892	−	0.335916i
$321$	−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
$328$	14.3093	+	11.1015i	0.790098	+	0.612980i
$329$		−	29.0094i		−	1.59934i
$330$	24.6549	−	23.5996i	1.35721	−	1.29911i
$331$	−12.2573	+	12.2573i	−0.673721	+	0.673721i	−0.958572	−	0.284851i	$-0.908056\pi$
$331$	−12.2573	+	12.2573i	−0.673721	+	0.673721i	0.284851	+	0.958572i	$0.408056\pi$
$332$	4.31931	−	14.7231i	0.237053	−	0.808034i
$333$	−3.83402	+	3.83402i	−0.210103	+	0.210103i
$334$	30.6503	−	7.82687i	1.67711	−	0.428267i
$335$	−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	$0.425896\pi$
$338$	−4.48555	−	17.5656i	−0.243982	−	0.955442i
$339$	−12.0963	−	12.0963i	−0.656980	−	0.656980i
$340$	−14.5844	+	3.38638i	−0.790949	+	0.183652i
$341$	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	$-0.536760\pi$
$347$	−4.29289			−0.230454			−0.115227	+	0.993339i	$0.536760\pi$
$348$	5.56758	−	18.9780i	0.298454	−	1.01733i
$349$	20.3710			1.09044			0.545218	−	0.838294i	$-0.316447\pi$
$349$	20.3710			1.09044			0.545218	+	0.838294i	$0.316447\pi$
$350$	−22.9039	−	6.92853i	−1.22427	−	0.370346i
$351$			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	$0.832485\pi$
$354$	−0.339298	−	1.32870i	−0.0180335	−	0.0706198i
$355$	8.71257	+	15.4484i	0.462415	+	0.819914i
$356$	−2.05334	+	6.99913i	−0.108827	+	0.370953i
$357$	−23.4275			−1.23992
$358$	−12.9906	−	7.70559i	−0.686573	−	0.407253i
$359$	−25.3606			−1.33848			−0.669242	−	0.743045i	$-0.733381\pi$
$359$	−25.3606			−1.33848			−0.669242	+	0.743045i	$0.733381\pi$
$360$	−7.16428	+	3.71313i	−0.377591	+	0.195699i
$361$			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
$366$	0.591309	−	0.150997i	0.0309082	−	0.00789273i
$367$	11.0994	−	11.0994i	0.579385	−	0.579385i	−0.355349	−	0.934734i	$-0.615638\pi$
$367$	11.0994	−	11.0994i	0.579385	−	0.579385i	0.934734	+	0.355349i	$0.115638\pi$
$368$	6.40432	+	29.3735i	0.333848	+	1.53120i
$369$	8.06404	−	1.30896i	0.419797	−	0.0681419i
$370$	−9.70821	+	9.29263i	−0.504706	+	0.483101i
$371$	−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
$376$	−16.5281	−	17.7399i	−0.852374	−	0.914865i
$377$	1.43739	+	1.43739i	0.0740292	+	0.0740292i
$378$	16.5317	−	4.22154i	0.850299	−	0.217133i
$379$	−28.8118			−1.47996			−0.739982	−	0.672626i	$-0.765166\pi$
$379$	−28.8118			−1.47996			−0.739982	+	0.672626i	$0.765166\pi$
$380$	−3.67593	−	2.29056i	−0.188571	−	0.117503i
$381$	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	$-0.891611\pi$
$383$		−	13.0719i		−	0.667944i	0.942583	−	0.333972i	$-0.108389\pi$
$384$	−23.0195	+	4.17280i	−1.17471	+	0.212942i
$385$	34.4007	−	19.4013i	1.75322	−	0.988783i
$386$	−6.85772	+	1.75119i	−0.349049	+	0.0891332i
$387$	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	$0.864558\pi$
$390$	0.0607763	−	2.77882i	0.00307753	−	0.140711i
$391$	17.7926	+	17.7926i	0.899812	+	0.899812i
$392$	−8.58355	−	9.21284i	−0.433535	−	0.465319i
$393$	−14.3550			−0.724114
$394$	−0.725847	+	1.22368i	−0.0365677	+	0.0616481i
$395$	29.7517	−	16.7793i	1.49697	−	0.844260i
$396$	3.74921	−	12.7798i	0.188405	−	0.642209i
$397$	−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
$400$	−17.9538	+	8.81258i	−0.897689	+	0.440629i
$401$		−	30.1757i		−	1.50690i	−0.657505	−	0.753450i	$-0.728388\pi$
$401$		−	30.1757i		−	1.50690i	0.657505	−	0.753450i	$-0.271612\pi$
$402$	3.01054	+	11.7894i	0.150152	+	0.588000i
$403$	2.62920			0.130970
$404$	6.37205	−	21.7201i	0.317021	−	1.08062i
$405$	6.72536	−	24.1235i	0.334186	−	1.19871i
$406$	11.6762	−	19.6846i	0.579482	−	0.976928i
$407$		−	22.1807i		−	1.09946i
$408$	−14.3264	+	13.3478i	−0.709264	+	0.660817i
$409$		−	24.3353i		−	1.20330i	−0.798758	−	0.601652i	$-0.794509\pi$
$409$		−	24.3353i		−	1.20330i	0.798758	−	0.601652i	$-0.205491\pi$
$410$	20.0530	−	2.80648i	0.990348	−	0.138602i
$411$			8.02619i			0.395903i
$412$	−13.2066	−	3.87442i	−0.650642	−	0.190879i
$413$		−	1.58693i		−	0.0780875i
$414$	11.6638	+	6.91858i	0.573243	+	0.340030i
$415$	−8.42705	−	14.9421i	−0.413668	−	0.733479i
$416$	0.758000	−	2.28191i	0.0371640	−	0.111880i
$417$	−39.2281			−1.92101
$418$	6.92632	−	1.76871i	0.338777	−	0.0865103i
$419$			31.6294i			1.54520i	0.634893	+	0.772600i	$0.281044\pi$
$419$			31.6294i			1.54520i	−0.634893	+	0.772600i	$0.718956\pi$
$420$	−30.4834	+	7.07801i	−1.48744	+	0.345372i
$421$	−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
$424$	−19.2878	+	17.9703i	−0.936698	+	0.872716i
$425$	−8.66050	+	14.3252i	−0.420096	+	0.694872i
$426$	19.9494	+	11.8334i	0.966554	+	0.573329i
$427$	0.706225			0.0341766
$428$	−1.99268	−	0.584592i	−0.0963196	−	0.0282573i
$429$	3.24387	+	3.24387i	0.156616	+	0.156616i
$430$	5.58172	+	5.83133i	0.269174	+	0.281212i
$431$	−2.97987			−0.143535			−0.0717676	−	0.997421i	$-0.522864\pi$
$431$	−2.97987			−0.143535			−0.0717676	+	0.997421i	$0.522864\pi$
$432$	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	$0.854790\pi$
$434$	−7.32421	−	28.6819i	−0.351573	−	1.37677i
$435$	−10.8624	−	19.2603i	−0.520814	−	0.923462i
$436$	0.856628	+	0.251309i	0.0410251	+	0.0120355i
$437$			7.27898i			0.348201i
$438$	12.2740	+	7.28056i	0.586476	+	0.347879i
$439$	−5.31814	−	5.31814i	−0.253821	−	0.253821i	0.568714	−	0.822535i	$-0.307441\pi$
$439$	−5.31814	−	5.31814i	−0.253821	−	0.253821i	−0.822535	+	0.568714i	$0.807441\pi$
$440$	9.98288	−	31.4642i	0.475915	−	1.50000i
$441$	−5.68004			−0.270478
$442$	−0.497942	−	1.94996i	−0.0236847	−	0.0927500i
$443$	−17.8204	−	17.8204i	−0.846675	−	0.846675i	0.143042	−	0.989717i	$-0.454312\pi$
$443$	−17.8204	−	17.8204i	−0.846675	−	0.846675i	−0.989717	+	0.143042i	$0.954312\pi$
$444$	−4.94757	+	16.8646i	−0.234801	+	0.800358i
$445$	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	$0.462321\pi$
$450$	−2.61223	+	8.63534i	−0.123142	+	0.407074i
$451$	−19.5399	+	27.1125i	−0.920096	+	1.27668i
$452$	−15.8766	−	4.65771i	−0.746771	−	0.219080i
$453$	−21.5933	+	21.5933i	−1.01454	+	1.01454i
$454$	3.10750	+	12.1691i	0.145842	+	0.571124i
$455$	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
$460$	28.5270	+	17.7758i	1.33008	+	0.828803i
$461$	−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	$-0.308398\pi$
$463$	24.3680			1.13248			0.566238	+	0.824241i	$0.308398\pi$
$464$	−4.07501	−	18.6901i	−0.189178	−	0.867666i
$465$	−27.5496	−	7.68051i	−1.27758	−	0.356175i
$466$	25.0189	−	6.38884i	1.15898	−	0.295957i
$467$	−15.9882	−	15.9882i	−0.739844	−	0.739844i	0.232703	−	0.972548i	$-0.425243\pi$
$467$	−15.9882	−	15.9882i	−0.739844	−	0.739844i	−0.972548	+	0.232703i	$0.925243\pi$
$468$	−0.520043	−	0.951853i	−0.0240390	−	0.0439994i
$469$			14.0805i			0.650178i
$470$	−27.1017	−	0.592748i	−1.25011	−	0.0273414i
$471$	39.2969			1.81070
$472$	−0.904153	−	0.970440i	−0.0416170	−	0.0446681i
$473$	−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	0.970152	−	0.242497i	$-0.0779666\pi$
$479$	15.9255	+	15.9255i	0.727655	+	0.727655i	−0.242497	+	0.970152i	$0.577967\pi$
$480$	−14.6086	+	21.6963i	−0.666787	+	0.990296i
$481$	−1.27732	−	1.27732i	−0.0582407	−	0.0582407i
$482$	25.4958	−	6.51062i	1.16130	−	0.296551i
$483$	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
$486$	−4.36107	−	17.0781i	−0.197822	−	0.774678i
$487$	10.1928	−	10.1928i	0.461879	−	0.461879i	−0.437392	−	0.899271i	$-0.644098\pi$
$487$	10.1928	−	10.1928i	0.461879	−	0.461879i	0.899271	+	0.437392i	$0.144098\pi$
$488$	0.431872	−	0.402372i	0.0195499	−	0.0182145i
$489$	−3.86095	+	3.86095i	−0.174598	+	0.174598i
$490$	−14.0747	−	0.307831i	−0.635831	−	0.0139064i
$491$			16.0820i			0.725769i	0.931834	+	0.362884i	$0.118208\pi$
$491$			16.0820i			0.725769i	−0.931834	+	0.362884i	$0.881792\pi$
$492$	20.9043	−	16.2559i	0.942439	−	0.732871i
$493$	−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	0.234788	−	0.972047i	$-0.424561\pi$
$499$	−16.4691	−	16.4691i	−0.737259	−	0.737259i	−0.972047	+	0.234788i	$0.924561\pi$
$500$	−6.94090	+	21.2562i	−0.310406	+	0.950604i
$501$		−	46.2540i		−	2.06648i
$502$	2.30525	+	9.02744i	0.102888	+	0.402914i
$503$	−27.9393			−1.24575			−0.622877	−	0.782320i	$-0.714036\pi$
$503$	−27.9393			−1.24575			−0.622877	+	0.782320i	$0.714036\pi$
$504$	−8.93504	+	8.32472i	−0.397999	+	0.370813i
$505$	−12.4320	−	22.0433i	−0.553215	−	0.980912i
$506$	−53.7517	+	13.7260i	−2.38955	+	0.610197i
$507$	−26.5080			−1.17726
$508$	40.8583	+	11.9866i	1.81279	+	0.531820i
$509$	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	$0.497102\pi$
$510$	−0.478693	+	21.8869i	−0.0211969	+	0.969167i
$511$	11.6774	+	11.6774i	0.516579	+	0.516579i
$512$	−17.6036	+	14.2167i	−0.777975	+	0.628295i
$513$	2.44150	−	2.44150i	0.107795	−	0.107795i
$514$	4.46664	+	17.4915i	0.197015	+	0.771517i
$515$	−13.4031	+	7.55906i	−0.590610	+	0.333092i
$516$	10.1299	+	2.97181i	0.445944	+	0.130827i
$517$	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
$520$	−1.23704	−	2.38681i	−0.0542478	−	0.104668i
$521$	−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	−0.963177	−	0.268869i	$-0.913350\pi$
$523$	−15.8783	+	15.8783i	−0.694308	+	0.694308i	0.268869	+	0.963177i	$0.413350\pi$
$524$	−12.1843	+	6.65686i	−0.532274	+	0.290806i
$525$	−18.1017	+	29.9416i	−0.790022	+	1.30676i
$526$	−6.61571	+	1.68939i	−0.288459	+	0.0736609i
$527$	−20.7084			−0.902072
$528$	−9.19643	−	42.1795i	−0.400223	−	1.83563i
$529$		−	33.4885i		−	1.45602i
$530$	−0.644468	+	29.4665i	−0.0279939	+	1.27994i
$531$	−0.598310			−0.0259644
$532$	−6.28971	−	1.84522i	−0.272694	−	0.0800003i
$533$	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
$536$	8.02239	+	8.61055i	0.346515	+	0.371919i
$537$	−15.6162	+	15.6162i	−0.673888	+	0.673888i
$538$	17.1650	−	4.38326i	0.740035	−	0.188976i
$539$	16.4302	−	16.4302i	0.707698	−	0.707698i
$540$	−3.60613	−	15.5308i	−0.155183	−	0.668339i
$541$		−	28.8087i		−	1.23858i	−0.785162	−	0.619291i	$-0.787420\pi$
$541$		−	28.8087i		−	1.23858i	0.785162	−	0.619291i	$-0.212580\pi$
$542$	11.5729	−	2.95526i	0.497098	−	0.126939i
$543$	31.2298	−	31.2298i	1.34020	−	1.34020i
$544$	−5.97024	+	17.9731i	−0.255972	+	0.770588i
$545$	0.869372	−	0.490309i	0.0372398	−	0.0210025i
$546$	−1.04077	−	4.07569i	−0.0445408	−	0.174423i
$547$	24.4985			1.04748			0.523741	−	0.851877i	$-0.324536\pi$
$547$	24.4985			1.04748			0.523741	+	0.851877i	$0.324536\pi$
$548$	3.72200	+	6.81251i	0.158996	+	0.291016i
$549$		−	0.266264i		−	0.0113639i
$550$	−17.4226	−	32.5349i	−0.742900	−	1.38729i
$551$		−	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	$0.892769\pi$
$558$	−10.8138	+	2.76141i	−0.457783	+	0.116900i
$559$	−0.767234	+	0.767234i	−0.0324506	+	0.0324506i
$560$	−22.5915	+	20.1438i	−0.954667	+	0.851231i
$561$	−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	$-0.242260\pi$
$563$	34.3618			1.44818			0.724089	+	0.689707i	$0.242260\pi$
$564$	−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	$0.374961\pi$
$570$	−4.57489	+	4.37905i	−0.191621	+	0.183418i
$571$	−1.16438	+	1.16438i	−0.0487279	+	0.0487279i	−0.731051	−	0.682323i	$-0.760970\pi$
$571$	−1.16438	+	1.16438i	−0.0487279	+	0.0487279i	0.682323	+	0.731051i	$0.260970\pi$
$572$	4.25763	+	1.24906i	0.178021	+	0.0522260i
$573$	40.0673	+	40.0673i	1.67384	+	1.67384i
$574$	28.0928	−	12.2413i	1.17257	−	0.510940i
$575$	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	$0.805732\pi$
$578$	−2.02645	−	7.93566i	−0.0842893	−	0.330080i
$579$			10.3489i			0.430086i
$580$	−18.1515	−	11.3106i	−0.753699	−	0.469648i
$581$	−18.3578	−	18.3578i	−0.761609	−	0.761609i
$582$	37.1896	−	9.49674i	1.54156	−	0.393653i
$583$	−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
$586$	−5.51080	−	21.5805i	−0.227649	−	0.891481i
$587$		−	5.74840i		−	0.237262i	−0.992938	−	0.118631i	$-0.962149\pi$
$587$		−	5.74840i		−	0.237262i	0.992938	−	0.118631i	$-0.0378506\pi$
$588$	−16.1572	+	8.82743i	−0.666311	+	0.364037i
$589$	−4.23591	−	4.23591i	−0.174538	−	0.174538i
$590$	−1.48257	−	0.0324256i	−0.0610363	−	0.00133494i
$591$	1.47100	+	1.47100i	0.0605090	+	0.0605090i
$592$	3.62122	+	16.6087i	0.148831	+	0.682615i
$593$	−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
$596$	37.5038	+	11.0025i	1.53621	+	0.450680i
$597$	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	$-0.765253\pi$
$599$	−36.2303			−1.48033			−0.740166	+	0.672425i	$0.765253\pi$
$600$	5.98969	+	28.6234i	0.244528	+	1.16855i
$601$	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
$604$	−8.31458	+	28.3416i	−0.338315	+	1.15320i
$605$	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	$-0.456295\pi$
$607$	27.7777	−	27.7777i	1.12746	−	1.12746i	0.990589	−	0.136873i	$-0.0437051\pi$
$608$	−4.89761	+	2.45518i	−0.198624	+	0.0995708i
$609$	−23.6631	−	23.6631i	−0.958878	−	0.958878i
$610$	0.0144302	−	0.659782i	0.000584264	−	0.0267138i
$611$		−	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	$-0.421263\pi$
$619$	12.1833			0.489689			0.244844	+	0.969562i	$0.421263\pi$
$620$	−26.9454	+	6.25650i	−1.08215	+	0.251267i
$621$	−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
$626$	5.20378	+	20.3782i	0.207985	+	0.814476i
$627$		−	10.4524i		−	0.417430i
$628$	33.3546	−	18.2232i	1.33099	−	0.727184i
$629$	10.0606	+	10.0606i	0.401141	+	0.401141i
$630$	−0.298549	+	13.6503i	−0.0118945	+	0.543841i
$631$		−	11.6522i		−	0.463867i	−0.972732	−	0.231933i	$-0.925495\pi$
$631$		−	11.6522i		−	0.463867i	0.972732	−	0.231933i	$-0.0745051\pi$
$632$	1.52684	−	43.1787i	0.0607344	−	1.71756i
$633$	10.0148	+	10.0148i	0.398052	+	0.398052i
$634$	2.29254	+	8.97766i	0.0910483	+	0.356548i
$635$	41.4661	−	23.3861i	1.64553	−	0.928048i
$636$	18.4809	+	33.8263i	0.732816	+	1.34130i
$637$		−	1.89232i		−	0.0749766i
$638$	34.2017	−	8.73376i	1.35406	−	0.345773i
$639$	7.15583	−	7.15583i	0.283080	−	0.283080i
$640$	−2.33827	+	25.1899i	−0.0924281	+	0.995719i
$641$	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	$-0.663794\pi$
$643$	−24.9600			−0.984326			−0.492163	+	0.870503i	$0.663794\pi$
$644$	48.8113	+	14.3198i	1.92343	+	0.564279i
$645$	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	$0.549273\pi$
$647$	−29.0538	+	29.0538i	−1.14222	+	1.14222i	−0.988043	+	0.154178i	$0.950727\pi$
$648$	−21.5940	−	23.1771i	−0.848291	−	0.910483i
$649$	1.73068	−	1.73068i	0.0679352	−	0.0679352i
$650$	−2.87689	−	0.870273i	−0.112841	−	0.0341349i
$651$	−43.2835			−1.69641
$652$	−1.48667	+	5.06755i	−0.0582225	+	0.198461i
$653$		−	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
$656$	10.2049	−	23.4917i	0.398435	−	0.917197i
$657$	4.40268	−	4.40268i	0.171765	−	0.171765i
$658$	−39.7500	+	10.1506i	−1.54961	+	0.395710i
$659$	2.75615	+	2.75615i	0.107365	+	0.107365i	0.758748	−	0.651384i	$-0.225811\pi$
$659$	2.75615	+	2.75615i	0.107365	+	0.107365i	−0.651384	+	0.758748i	$0.725811\pi$
$660$	−40.9640	−	25.5256i	−1.59452	−	0.993584i
$661$			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
$670$	13.1546	+	0.287706i	0.508205	+	0.0111151i
$671$	0.770200	+	0.770200i	0.0297332	+	0.0297332i
$672$	−12.4786	+	37.5662i	−0.481374	+	1.44915i
$673$	−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
$680$	9.74332	+	18.7992i	0.373639	+	0.720917i
$681$	18.3642			0.703719
$682$	23.2924	−	39.2678i	0.891912	−	1.50364i
$683$		−	38.2037i		−	1.46182i	−0.682472	−	0.730911i	$-0.739095\pi$
$683$		−	38.2037i		−	1.46182i	0.682472	−	0.730911i	$-0.260905\pi$
$684$	−0.695692	+	2.37138i	−0.0266004	+	0.0906719i
$685$	8.36043	+	2.33079i	0.319436	+	0.0890550i
$686$	11.8156	−	3.01724i	0.451122	−	0.115199i
$687$	−12.9938	−	12.9938i	−0.495743	−	0.495743i
$688$	9.97622	−	2.17512i	0.380340	−	0.0829257i
$689$	−3.96173			−0.150930
$690$	35.5034	−	33.9836i	1.35159	−	1.29373i
$691$	−25.6067	−	25.6067i	−0.974123	−	0.974123i	0.0255504	−	0.999674i	$-0.491866\pi$
$691$	−25.6067	−	25.6067i	−0.974123	−	0.974123i	−0.999674	+	0.0255504i	$0.991866\pi$
$692$	8.61775	−	29.3750i	0.327598	−	1.11667i
$693$	−15.9348	−	15.9348i	−0.605311	−	0.605311i
$694$	1.50211	+	5.88230i	0.0570192	+	0.223289i
$695$	−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
$698$	−7.12794	−	27.9133i	−0.269796	−	1.05653i
$699$		−	37.7558i		−	1.42805i
$700$	−1.47956	+	33.8083i	−0.0559223	+	1.27783i
$701$	48.7303			1.84052			0.920259	−	0.391310i	$-0.127978\pi$
$701$	48.7303			1.84052			0.920259	+	0.391310i	$0.127978\pi$
$702$	2.07650	−	0.530255i	0.0783723	−	0.0200132i
$703$			4.11578i			0.155230i
$704$	−27.3658	−	31.5367i	−1.03139	−	1.18858i
$705$	−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	$0.162666\pi$
$710$	18.1194	−	17.3438i	0.680010	−	0.650901i
$711$	−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
$714$	8.19742	+	32.1014i	0.306781	+	1.20136i
$715$	4.32097	−	2.43694i	0.161595	−	0.0911365i
$716$	−6.01306	+	20.4965i	−0.224718	+	0.765989i
$717$	−9.77897	−	9.77897i	−0.365202	−	0.365202i
$718$	8.87383	+	34.7502i	0.331168	+	1.29687i
$719$	2.55264	−	2.55264i	0.0951974	−	0.0951974i	−0.657904	−	0.753102i	$-0.728557\pi$
$719$	2.55264	−	2.55264i	0.0951974	−	0.0951974i	0.753102	+	0.657904i	$0.228557\pi$
$720$	7.59471	+	8.51756i	0.283038	+	0.317431i
$721$	−16.4669	+	16.4669i	−0.613260	+	0.613260i
$722$	24.7494	−	6.32001i	0.921077	−	0.235207i
$723$		−	38.4755i		−	1.43092i
$724$	12.0251	−	40.9896i	0.446910	−	1.52336i
$725$	−23.2168	+	5.72162i	−0.862251	+	0.212496i
$726$	46.0184	−	11.7513i	1.70790	−	0.436131i
$727$			21.0340i			0.780108i	0.920792	+	0.390054i	$0.127544\pi$
$727$			21.0340i			0.780108i	−0.920792	+	0.390054i	$0.872456\pi$
$728$	−2.77341	−	2.97674i	−0.102789	−	0.110325i
$729$	7.82694			0.289887
$730$	11.1481	−	10.6709i	0.412610	−	0.394948i
$731$	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
$738$	−4.61525	−	10.5917i	−0.169890	−	0.389885i
$739$	−17.4890			−0.643342			−0.321671	−	0.946852i	$-0.604244\pi$
$739$	−17.4890			−0.643342			−0.321671	+	0.946852i	$0.604244\pi$
$740$	16.1301	+	10.0511i	0.592955	+	0.369484i
$741$	−0.601922	−	0.601922i	−0.0221122	−	0.0221122i
$742$	11.0363	+	43.2184i	0.405154	+	1.58660i
$743$	−5.66456	−	5.66456i	−0.207813	−	0.207813i	0.595524	−	0.803337i	$-0.296944\pi$
$743$	−5.66456	−	5.66456i	−0.207813	−	0.207813i	−0.803337	+	0.595524i	$0.796944\pi$
$744$	−26.4688	+	24.6608i	−0.970393	+	0.904109i
$745$	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
$748$	−33.5345	−	9.83802i	−1.22614	−	0.359713i
$749$	−2.48461	+	2.48461i	−0.0907857	+	0.0907857i
$750$	27.6027	+	17.5231i	1.00791	+	0.639852i
$751$	29.8104	−	29.8104i	1.08780	−	1.08780i	0.0920412	−	0.995755i	$-0.470661\pi$
$751$	29.8104	−	29.8104i	1.08780	−	1.08780i	0.995755	−	0.0920412i	$-0.0293391\pi$
$752$	−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	$-0.0555109\pi$
$758$	10.0814	+	39.4792i	0.366174	+	1.43395i
$759$			81.1160i			2.94433i
$760$	−1.85239	+	5.83839i	−0.0671932	+	0.211781i
$761$	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
$764$	52.5890	+	15.4280i	1.90260	+	0.558167i
$765$	9.20057	+	2.56501i	0.332647	+	0.0927383i
$766$	−17.9117	+	4.57394i	−0.647177	+	0.165263i
$767$		−	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	$-0.0189751\pi$
$770$	−38.6215	−	40.3487i	−1.39182	−	1.45407i
$771$	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
$776$	27.1620	−	25.3066i	0.975058	−	0.908455i
$777$	21.0280	+	21.0280i	0.754374	+	0.754374i
$778$	12.5717	+	49.2312i	0.450717	+	1.76502i
$779$	3.62575	−	5.03091i	0.129906	−	0.180251i
$780$	−3.82893	+	0.889048i	−0.137098	+	0.0318330i
$781$			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
$786$	5.02290	+	19.6698i	0.179161	+	0.701600i
$787$	−16.1923	+	16.1923i	−0.577195	+	0.577195i	−0.934129	−	0.356935i	$-0.883822\pi$
$787$	−16.1923	+	16.1923i	−0.577195	+	0.577195i	0.356935	+	0.934129i	$0.383822\pi$
$788$	1.93072	+	0.566415i	0.0687789	+	0.0201777i
$789$			9.98370i			0.355429i
$790$	−33.4021	−	34.8958i	−1.18839	−	1.24154i
$791$	−19.7960	+	19.7960i	−0.703865	+	0.703865i
$792$	−18.8233	−	0.665610i	−0.668857	−	0.0236514i
$793$	0.0887068			0.00315007
$794$	11.3716	+	44.5315i	0.403563	+	1.58037i
$795$	41.5122	+	11.5731i	1.47229	+	0.410457i
$796$	2.74365	−	9.35219i	0.0972463	−	0.331479i
$797$	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
$800$	18.3575	+	21.5175i	0.649036	+	0.760758i
$801$	3.29030	−	3.29030i	0.116257	−	0.116257i
$802$	−41.3480	+	10.5586i	−1.46005	+	0.372838i
$803$			25.4705i			0.898835i
$804$	15.1009	−	8.25033i	0.532567	−	0.290967i
$805$	49.5374	−	27.9381i	1.74597	−	0.984690i
$806$	−0.919972	−	3.60264i	−0.0324046	−	0.126898i
$807$		−	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	$0.367244\pi$
$810$	−35.4083	−	0.774423i	−1.24412	−	0.0272105i
$811$	−7.05461			−0.247721			−0.123860	−	0.992300i	$-0.539527\pi$
$811$	−7.05461			−0.247721			−0.123860	+	0.992300i	$0.539527\pi$
$812$	−31.0582	−	9.11156i	−1.08993	−	0.319753i
$813$		−	17.4645i		−	0.612508i
$814$	−30.3930	+	7.76116i	−1.06527	+	0.272029i
$815$	2.90052	+	5.14294i	0.101601	+	0.180149i
$816$	23.3027	+	14.9602i	0.815758	+	0.523712i
$817$	2.47219			0.0864909
$818$	−33.3453	+	8.51507i	−1.16589	+	0.297723i
$819$	−1.83526			−0.0641293
$820$	−10.8622	−	26.4955i	−0.379326	−	0.925263i
$821$	14.8675			0.518880			0.259440	−	0.965759i	$-0.416462\pi$
$821$	14.8675			0.518880			0.259440	+	0.965759i	$0.416462\pi$
$822$	10.9978	−	2.80841i	0.383594	−	0.0979546i
$823$	−37.3427			−1.30168			−0.650842	−	0.759213i	$-0.725584\pi$
$823$	−37.3427			−1.30168			−0.650842	+	0.759213i	$0.725584\pi$
$824$	−0.687838	+	19.4519i	−0.0239620	+	0.677640i
$825$	−52.3954	+	12.9125i	−1.82417	+	0.449555i
$826$	−2.17447	+	0.555275i	−0.0756596	+	0.0193205i
$827$		−	39.4208i		−	1.37080i	−0.728169	−	0.685398i	$-0.759628\pi$
$827$		−	39.4208i		−	1.37080i	0.728169	−	0.685398i	$-0.240372\pi$
$828$	5.39891	−	18.4031i	0.187625	−	0.639550i
$829$	−19.0341			−0.661080			−0.330540	−	0.943792i	$-0.607231\pi$
$829$	−19.0341			−0.661080			−0.330540	+	0.943792i	$0.607231\pi$
$830$	−17.5256	+	16.7754i	−0.608324	+	0.582284i
$831$	−36.8370	+	36.8370i	−1.27786	+	1.27786i
$832$	−3.39200	−	0.240189i	−0.117597	−	0.00832706i
$833$			14.9045i			0.516412i
$834$	13.7261	+	53.7521i	0.475298	+	1.86128i
$835$	−48.1802	−	13.4321i	−1.66734	−	0.464836i
$836$	−4.84712	−	8.87186i	−0.167641	−	0.306840i
$837$		−	22.0522i		−	0.762237i
$838$	43.3400	−	11.0673i	1.49716	−	0.382314i
$839$	−17.9725	+	17.9725i	−0.620480	+	0.620480i	−0.945654	−	0.325174i	$-0.894577\pi$
$839$	−17.9725	+	17.9725i	−0.620480	+	0.620480i	0.325174	+	0.945654i	$0.394577\pi$
$840$	20.3649	+	39.2930i	0.702656	+	1.35574i
$841$			6.12968i			0.211368i
$842$	−10.3951	+	17.5247i	−0.358239	+	0.603942i
$843$	46.1745	−	46.1745i	1.59033	−	1.59033i
$844$	13.1445	+	3.85622i	0.452454	+	0.132737i
$845$	−7.69789	+	27.6119i	−0.264815	+	0.949879i
$846$	3.82701	+	14.9867i	0.131575	+	0.515254i
$847$	54.9617			1.88851
$848$	31.3726	+	20.1411i	1.07734	+	0.691647i
$849$	−27.5663	+	27.5663i	−0.946071	+	0.946071i
$850$	22.6593	+	6.85454i	0.777208	+	0.235109i
$851$		−	31.9405i		−	1.09491i
$852$	9.23417	−	31.4761i	0.316357	−	1.07836i
$853$	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	$0.0871719\pi$
$854$	−0.247112	−	0.967699i	−0.00845600	−	0.0331140i
$855$	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	$0.268044\pi$
$859$			43.7306i			1.49207i	−0.665908	+	0.746034i	$0.731956\pi$
$860$	6.03727	−	9.68873i	0.205869	−	0.330383i
$861$	−7.17911	−	44.2278i	−0.244663	−	1.50728i
$862$	1.04267	+	4.08315i	0.0355136	+	0.139073i
$863$	25.3477	+	25.3477i	0.862844	+	0.862844i	0.991668	−	0.128823i	$-0.0411200\pi$
$863$	25.3477	+	25.3477i	0.862844	+	0.862844i	−0.128823	+	0.991668i	$0.541120\pi$
$864$	−19.1394	−	6.35767i	−0.651135	−	0.216292i
$865$	−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
$870$	−22.5905	+	21.6235i	−0.765890	+	0.733105i
$871$			1.76861i			0.0599272i
$872$	0.0446157	−	1.26172i	0.00151088	−	0.0427274i
$873$		−	16.7463i		−	0.566776i
$874$	9.97398	−	2.54696i	0.337375	−	0.0861522i
$875$	25.9318	+	27.5505i	0.876654	+	0.931376i
$876$	5.68139	−	19.3659i	0.191956	−	0.654314i
$877$	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
$880$	−46.6067	−	2.66946i	−1.57111	−	0.0899876i
$881$		−	45.4208i		−	1.53026i	−0.643873	−	0.765132i	$-0.722674\pi$
$881$		−	45.4208i		−	1.53026i	0.643873	−	0.765132i	$-0.277326\pi$
$882$	1.98748	+	7.78303i	0.0669219	+	0.262068i
$883$		−	19.5241i		−	0.657039i	−0.944497	−	0.328519i	$-0.893450\pi$
$883$		−	19.5241i		−	0.657039i	0.944497	−	0.328519i	$-0.106550\pi$
$884$	−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	$-0.301550\pi$
$887$	34.7765			1.16768			0.583840	+	0.811869i	$0.301550\pi$
$888$	24.8398	+	0.878358i	0.833568	+	0.0294758i
$889$	50.9450	−	50.9450i	1.70864	−	1.70864i
$890$	8.33144	−	7.97480i	0.279270	−	0.267316i
$891$	41.3341	−	41.3341i	1.38474	−	1.38474i
$892$	−0.244631	+	0.833865i	−0.00819086	+	0.0279199i
$893$	−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
$896$	6.82895	+	37.6723i	0.228139	+	1.25854i
$897$	4.67122	+	4.67122i	0.155967	+	0.155967i
$898$	−1.75119	−	6.85773i	−0.0584380	−	0.228845i
$899$	−20.9167	−	20.9167i	−0.697610	−	0.697610i
$900$	12.7465	+	0.557832i	0.424885	+	0.0185944i
$901$	31.2038			1.03955
$902$	43.9878	+	17.2875i	1.46464	+	0.575611i
$903$	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	−0.871566	−	0.490278i	$-0.836895\pi$
$907$	−11.4830	+	11.4830i	−0.381288	+	0.381288i	0.490278	+	0.871566i	$0.336895\pi$
$908$	15.5873	−	8.51607i	0.517282	−	0.282616i
$909$	−10.2107	+	10.2107i	−0.338666	+	0.338666i
$910$	−4.54765	−	0.0994626i	−0.150753	−	0.00329715i
$911$	−24.0407			−0.796505			−0.398252	−	0.917276i	$-0.630383\pi$
$911$	−24.0407			−0.796505			−0.398252	+	0.917276i	$0.630383\pi$
$912$	1.70646	+	7.82670i	0.0565065	+	0.259168i
$913$		−	40.0415i		−	1.32518i
$914$	4.49453	−	1.14772i	0.148666	−	0.0379634i
$915$	−0.929498	−	0.259133i	−0.0307282	−	0.00856669i
$916$	−17.0545	−	5.00329i	−0.563497	−	0.165313i
$917$			23.4925i			0.775791i
$918$	−16.3551	+	4.17645i	−0.539800	+	0.137844i
$919$	−39.5730	+	39.5730i	−1.30539	+	1.30539i	−0.380687	+	0.924704i	$0.624313\pi$
$919$	−39.5730	+	39.5730i	−1.30539	+	1.30539i	−0.924704	+	0.380687i	$0.875687\pi$
$920$	14.3755	−	45.3088i	0.473945	−	1.49379i
$921$	−9.34291	+	9.34291i	−0.307859	+	0.307859i
$922$	11.0774	+	43.3794i	0.364814	+	1.42862i
$923$	2.38399	+	2.38399i	0.0784700	+	0.0784700i
$924$	−70.0917	−	20.5628i	−2.30585	−	0.676468i
$925$	20.6314	−	5.08446i	0.678356	−	0.167176i
$926$	−8.52650	−	33.3901i	−0.280198	−	1.09727i
$927$	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	$0.794874\pi$
$930$	−0.884409	+	40.4371i	−0.0290009	+	1.32598i
$931$	−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
$936$	−1.12230	+	1.04564i	−0.0366837	+	0.0341779i
$937$			25.7234i			0.840348i	0.907444	+	0.420174i	$0.138031\pi$
$937$			25.7234i			0.840348i	−0.907444	+	0.420174i	$0.861969\pi$
$938$	19.2937	−	4.92686i	0.629963	−	0.160868i
$939$	30.7525			1.00357
$940$	8.67084	+	37.3433i	0.282812	+	1.21801i
$941$		−	16.8282i		−	0.548585i	−0.961646	−	0.274293i	$-0.911556\pi$
$941$		−	16.8282i		−	0.548585i	0.961646	−	0.274293i	$-0.0884437\pi$
$942$	−13.7502	−	53.8462i	−0.448006	−	1.75441i
$943$	−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
$946$	4.66182	+	18.2559i	0.151569	+	0.593549i
$947$	2.13068	+	2.13068i	0.0692377	+	0.0692377i	0.740878	−	0.671640i	$-0.234410\pi$
$947$	2.13068	+	2.13068i	0.0692377	+	0.0692377i	−0.671640	+	0.740878i	$0.734410\pi$
$948$	−60.6192	−	17.7839i	−1.96882	−	0.577594i
$949$	1.46677	+	1.46677i	0.0476133	+	0.0476133i
$950$	3.23287	+	6.03707i	0.104888	+	0.195868i
$951$	13.5481			0.439327
$952$	21.8442	+	23.4457i	0.707976	+	0.759881i
$953$	−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	$0.981229\pi$
$954$	16.2944	−	4.16094i	0.527550	−	0.134715i
$955$	53.3713	−	30.1004i	1.72706	−	0.974025i
$956$	−12.8350	−	3.76542i	−0.415115	−	0.121782i
$957$		−	51.6134i		−	1.66843i
$958$	16.2494	−	27.3942i	0.524994	−	0.885067i
$959$	13.1352			0.424157
$960$	34.8408	+	12.4256i	1.12448	+	0.401035i
$961$	−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	$-0.533241\pi$
$967$	−6.48310			−0.208482			−0.104241	+	0.994552i	$0.533241\pi$
$968$	33.6103	−	31.3145i	1.08027	−	1.00649i
$969$	4.74093	+	4.74093i	0.152301	+	0.152301i
$970$	0.907570	−	41.4961i	0.0291403	−	1.33236i
$971$	3.85798	−	3.85798i	0.123809	−	0.123809i	−0.642488	−	0.766296i	$-0.722098\pi$
$971$	3.85798	−	3.85798i	0.123809	−	0.123809i	0.766296	+	0.642488i	$0.222098\pi$
$972$	−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
$980$	4.50302	+	19.3935i	0.143844	+	0.619502i
$981$	−0.402702	−	0.402702i	−0.0128573	−	0.0128573i
$982$	22.0362	−	5.62717i	0.703203	−	0.179570i
$983$	−18.0539	+	18.0539i	−0.575830	+	0.575830i	−0.933752	−	0.357922i	$-0.883485\pi$
$983$	−18.0539	+	18.0539i	−0.575830	+	0.575830i	0.357922	+	0.933752i	$0.383485\pi$
$984$	−29.5890	−	22.9560i	−0.943264	−	0.731810i
$985$	1.95944	−	1.10508i	0.0624329	−	0.0352109i
$986$	−11.5515	+	19.4743i	−0.367876	+	0.620189i
$987$			59.9862i			1.90938i
$988$	−0.790032	−	0.231772i	−0.0251343	−	0.00737365i
$989$	−19.1854			−0.610060
$990$	−15.2125	+	14.5613i	−0.483484	+	0.462788i
$991$	−20.1485	+	20.1485i	−0.640040	+	0.640040i	−0.950565	−	0.310525i	$-0.899495\pi$
$991$	−20.1485	+	20.1485i	−0.640040	+	0.640040i	0.310525	+	0.950565i	$0.399495\pi$
$992$	−11.0303	+	33.2061i	−0.350213	+	1.05429i
$993$	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
$996$	−8.93156	+	30.4446i	−0.283007	+	0.964676i
$997$	−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.583.54	yes	240
4.3	odd	2	inner	820.2.s.c.583.8	yes	240
5.2	odd	4		820.2.j.c.747.113	yes	240
20.7	even	4		820.2.j.c.747.67	yes	240
41.32	even	4		820.2.j.c.483.67	✓	240
164.155	odd	4		820.2.j.c.483.113	yes	240
205.32	odd	4	inner	820.2.s.c.647.8	yes	240
820.647	even	4	inner	820.2.s.c.647.54	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.67	✓	240	41.32	even	4
820.2.j.c.483.113	yes	240	164.155	odd	4
820.2.j.c.747.67	yes	240	20.7	even	4
820.2.j.c.747.113	yes	240	5.2	odd	4
820.2.s.c.583.8	yes	240	4.3	odd	2	inner
820.2.s.c.583.54	yes	240	1.1	even	1	trivial
820.2.s.c.647.8	yes	240	205.32	odd	4	inner
820.2.s.c.647.54	yes	240	820.647	even	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+(-0.349906 - 1.37024i) q^{2} -2.06782 q^{3} +(-1.75513 + 0.958912i) q^{4} +(-0.600491 + 2.15393i) q^{5} +(0.723542 + 2.83341i) q^{6} +3.38406i q^{7} +(1.92807 + 2.06943i) q^{8} +1.27587 q^{9} +(3.16152 + 0.0691463i) q^{10} +(-3.69062 + 3.69062i) q^{11} +(3.62929 - 1.98286i) q^{12} +0.425062i q^{13} +(4.63699 - 1.18410i) q^{14} +(1.24171 - 4.45394i) q^{15} +(2.16098 - 3.36603i) q^{16} -3.34792i q^{17} +(-0.446436 - 1.74826i) q^{18} +(0.684819 - 0.684819i) q^{19} +(-1.01149 - 4.35625i) q^{20} -6.99763i q^{21} +(6.34841 + 3.76568i) q^{22} +(-5.31453 + 5.31453i) q^{23} +(-3.98691 - 4.27920i) q^{24} +(-4.27882 - 2.58683i) q^{25} +(0.582438 - 0.148732i) q^{26} +3.56518 q^{27} +(-3.24502 - 5.93948i) q^{28} +(3.38159 - 3.38159i) q^{29} +(-6.53745 - 0.142982i) q^{30} -6.18545i q^{31} +(-5.36842 - 1.78327i) q^{32} +(7.63153 - 7.63153i) q^{33} +(-4.58747 + 1.17146i) 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} +(-5.61519 + 2.91026i) q^{40} +(6.32040 - 1.02593i) q^{41} +(-9.58845 + 2.44851i) q^{42} +(1.80499 + 1.80499i) q^{43} +(2.93854 - 10.0165i) 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} +(-2.04740 + 6.76817i) q^{50} +6.92289i q^{51} +(-0.407597 - 0.746040i) q^{52} +9.32035i q^{53} +(-1.24748 - 4.88516i) q^{54} +(-5.73315 - 10.1655i) q^{55} +(-7.00308 + 6.52472i) q^{56} +(-1.41608 + 1.41608i) q^{57} +(-5.81684 - 3.45036i) q^{58} -0.468941 q^{59} +(2.09157 + 9.00793i) q^{60} -0.208691i q^{61} +(-8.47557 + 2.16432i) 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} +(-0.233996 + 10.6988i) q^{70} +(5.60857 - 5.60857i) q^{71} +(2.45998 + 2.64033i) q^{72} +(3.45071 - 3.45071i) q^{73} +(5.16907 + 3.06613i) q^{74} +(8.84783 + 5.34910i) q^{75} +(-0.545267 + 1.85863i) q^{76} +(-12.4893 - 12.4893i) q^{77} +(-1.20438 + 0.307550i) q^{78} +(-10.8014 - 10.8014i) q^{79} +(5.95255 + 6.67586i) q^{80} -11.1998 q^{81} +(-3.61732 - 8.30150i) 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} +(4.03370 + 0.0882221i) q^{90} -1.43844 q^{91} +(4.23154 - 14.4239i) q^{92} +12.7904i q^{93} +(2.99952 + 11.7462i) q^{94} +(1.06382 + 1.88628i) q^{95} +(11.1009 + 3.68747i) q^{96} -13.1254i q^{97} +(1.55774 + 6.10016i) 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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