LMFDB - Embedded newform 820.2.s.c.647.54

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			647.54
Character	$\chi$	$=$	820.647
Dual form			820.2.s.c.583.54

$q$-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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

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

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	$-0.779130\pi$
$7$		−	3.38406i		−	1.27906i	0.768768	−	0.639528i	$-0.220870\pi$
$8$	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	−0.992775	−	0.119988i	$-0.961714\pi$
$11$	−3.69062	−	3.69062i	−1.11276	−	1.11276i	−0.119988	−	0.992775i	$-0.538286\pi$
$12$	3.62929	+	1.98286i	1.04769	+	0.572401i
$13$		−	0.425062i		−	0.117891i	−0.998261	−	0.0589455i	$-0.981226\pi$
$13$		−	0.425062i		−	0.117891i	0.998261	−	0.0589455i	$-0.0187738\pi$
$14$	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	$0.133075\pi$
$17$			3.34792i			0.811990i	−0.913875	+	0.405995i	$0.866925\pi$
$18$	−0.446436	+	1.74826i	−0.105226	+	0.412068i
$19$	0.684819	+	0.684819i	0.157108	+	0.157108i	0.781284	−	0.624176i	$-0.214565\pi$
$19$	0.684819	+	0.684819i	0.157108	+	0.157108i	−0.624176	+	0.781284i	$0.714565\pi$
$20$	−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	−0.993393	−	0.114764i	$-0.963389\pi$
$23$	−5.31453	−	5.31453i	−1.10816	−	1.10816i	−0.114764	−	0.993393i	$-0.536611\pi$
$24$	−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	0.947551	−	0.319605i	$-0.103550\pi$
$29$	3.38159	+	3.38159i	0.627946	+	0.627946i	−0.319605	+	0.947551i	$0.603550\pi$
$30$	−6.53745	+	0.142982i	−1.19357	+	0.0261048i
$31$			6.18545i			1.11094i	0.831537	+	0.555470i	$0.187462\pi$
$31$			6.18545i			1.11094i	−0.831537	+	0.555470i	$0.812538\pi$
$32$	−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	0.415549	−	0.909571i	$-0.363589\pi$
$37$	−3.00501	−	3.00501i	−0.494021	−	0.494021i	−0.909571	+	0.415549i	$0.863589\pi$
$38$	−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	−0.555954	−	0.831213i	$-0.687647\pi$
$43$	1.80499	−	1.80499i	0.275259	−	0.275259i	0.831213	+	0.555954i	$0.187647\pi$
$44$	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	$-0.778883\pi$
$53$		−	9.32035i		−	1.28025i	0.768271	−	0.640124i	$-0.221117\pi$
$54$	−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	$0.00425278\pi$
$61$			0.208691i			0.0267202i	−0.999911	+	0.0133601i	$0.995747\pi$
$62$	−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	0.956698	−	0.291083i	$-0.0940155\pi$
$71$	5.60857	+	5.60857i	0.665615	+	0.665615i	−0.291083	+	0.956698i	$0.594016\pi$
$72$	2.45998	−	2.64033i	0.289911	−	0.311166i
$73$	3.45071	+	3.45071i	0.403875	+	0.403875i	0.879596	−	0.475721i	$-0.157813\pi$
$73$	3.45071	+	3.45071i	0.403875	+	0.403875i	−0.475721	+	0.879596i	$0.657813\pi$
$74$	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	−0.245980	+	0.969275i	$0.579110\pi$
$79$	−10.8014	+	10.8014i	−1.21525	+	1.21525i	−0.969275	+	0.245980i	$0.920890\pi$
$80$	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	0.343651	−	0.939097i	$-0.388336\pi$
$83$	−5.42477	−	5.42477i	−0.595446	−	0.595446i	−0.939097	+	0.343651i	$0.888336\pi$
$84$	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	0.830451	−	0.557092i	$-0.188083\pi$
$89$	2.57886	+	2.57886i	0.273358	+	0.273358i	−0.557092	+	0.830451i	$0.688083\pi$
$90$	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	$0.232140\pi$
$97$			13.1254i			1.33268i	−0.745649	+	0.666339i	$0.767860\pi$
$98$	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	0.186197	−	0.982512i	$-0.440384\pi$
$101$	−8.00287	−	8.00287i	−0.796315	−	0.796315i	−0.982512	+	0.186197i	$0.940384\pi$
$102$	9.48605	+	2.42236i	0.939259	+	0.239849i
$103$	4.86602	−	4.86602i	0.479463	−	0.479463i	−0.425497	−	0.904960i	$-0.639901\pi$
$103$	4.86602	−	4.86602i	0.479463	−	0.479463i	0.904960	+	0.425497i	$0.139901\pi$
$104$	−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	−0.670726	−	0.741705i	$-0.734017\pi$
$107$	0.734209	−	0.734209i	0.0709787	−	0.0709787i	0.741705	+	0.670726i	$0.234017\pi$
$108$	−6.25736	−	3.41869i	−0.602115	−	0.328964i
$109$	−0.315628	+	0.315628i	−0.0302317	+	0.0302317i	−0.722061	−	0.691829i	$-0.756805\pi$
$109$	−0.315628	+	0.315628i	−0.0302317	+	0.0302317i	0.691829	+	0.722061i	$0.256805\pi$
$110$	−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	−0.376227	−	0.926528i	$-0.622779\pi$
$113$	5.84978	−	5.84978i	0.550301	−	0.550301i	0.926528	+	0.376227i	$0.122779\pi$
$114$	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	−0.435834	+	0.900027i	$0.643547\pi$
$127$	−15.0544	+	15.0544i	−1.33586	+	1.33586i	−0.900027	+	0.435834i	$0.856453\pi$
$128$	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	$0.0530234\pi$
$137$			3.88148i			0.331617i	−0.986158	+	0.165809i	$0.946977\pi$
$138$	−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	−0.142212	+	0.989836i	$0.545422\pi$
$149$	−13.8184	+	13.8184i	−1.13205	+	1.13205i	−0.989836	+	0.142212i	$0.954578\pi$
$150$	4.23366	+	13.9954i	0.345676	+	1.14272i
$151$	10.4426	+	10.4426i	0.849804	+	0.849804i	0.990108	−	0.140305i	$-0.0448082\pi$
$151$	10.4426	+	10.4426i	0.849804	+	0.849804i	−0.140305	+	0.990108i	$0.544808\pi$
$152$	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	0.776439	−	0.630192i	$-0.217024\pi$
$163$	1.86716	+	1.86716i	0.146247	+	0.146247i	−0.630192	+	0.776439i	$0.717024\pi$
$164$	−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	$-0.667024\pi$
$167$		−	22.3685i		−	1.73093i	0.500972	−	0.865463i	$-0.332976\pi$
$168$	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	0.163638	−	0.986520i	$-0.447677\pi$
$173$	−10.8233	−	10.8233i	−0.822883	−	0.822883i	−0.986520	+	0.163638i	$0.947677\pi$
$174$	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	0.930572	−	0.366109i	$-0.119310\pi$
$179$	7.55200	+	7.55200i	0.564463	+	0.564463i	−0.366109	+	0.930572i	$0.619310\pi$
$180$	−1.29053	+	5.55803i	−0.0961905	+	0.414271i
$181$	−15.1028	−	15.1028i	−1.12258	−	1.12258i	−0.991352	−	0.131227i	$-0.958108\pi$
$181$	−15.1028	−	15.1028i	−1.12258	−	1.12258i	−0.131227	−	0.991352i	$-0.541892\pi$
$182$	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	−0.608452	+	0.793591i	$0.708209\pi$
$191$	−19.3766	+	19.3766i	−1.40204	+	1.40204i	−0.793591	+	0.608452i	$0.791791\pi$
$192$	1.16846	+	16.5012i	0.0843263	+	1.19087i
$193$			5.00474i			0.360249i	0.983644	+	0.180125i	$0.0576501\pi$
$193$			5.00474i			0.360249i	−0.983644	+	0.180125i	$0.942350\pi$
$194$	−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	−0.731994	−	0.681311i	$-0.761410\pi$
$197$	−0.711380	+	0.711380i	−0.0506837	+	0.0506837i	0.681311	+	0.731994i	$0.261410\pi$
$198$	8.09978	−	4.80453i	0.575626	−	0.341443i
$199$	−3.44585	−	3.44585i	−0.244270	−	0.244270i	0.574344	−	0.818614i	$-0.305257\pi$
$199$	−3.44585	−	3.44585i	−0.244270	−	0.244270i	−0.818614	+	0.574344i	$0.805257\pi$
$200$	−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	−0.853883	−	0.520466i	$-0.825758\pi$
$211$	−4.84316	+	4.84316i	−0.333417	+	0.333417i	0.520466	+	0.853883i	$0.325758\pi$
$212$	−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	0.717319	−	0.696745i	$-0.245369\pi$
$223$	0.307241	+	0.307241i	0.0205744	+	0.0205744i	−0.696745	+	0.717319i	$0.745369\pi$
$224$	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	−0.468316	−	0.883561i	$-0.655139\pi$
$229$	6.28380	−	6.28380i	0.415245	−	0.415245i	0.883561	+	0.468316i	$0.155139\pi$
$230$	−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	$-0.795928\pi$
$233$		−	18.2587i		−	1.19617i	0.801433	−	0.598085i	$-0.204072\pi$
$234$	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	−0.537416	−	0.843317i	$-0.680599\pi$
$239$	4.72912	−	4.72912i	0.305902	−	0.305902i	0.843317	+	0.537416i	$0.180599\pi$
$240$	−12.3088	+	13.8045i	−0.794529	+	0.891075i
$241$		−	18.6068i		−	1.19857i	−0.800536	−	0.599284i	$-0.795452\pi$
$241$		−	18.6068i		−	1.19857i	0.800536	−	0.599284i	$-0.204548\pi$
$242$	−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	$0.0475596\pi$
$263$			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	$-0.875273\pi$
$269$		−	12.5270i		−	0.763783i	0.924207	−	0.381891i	$-0.124727\pi$
$270$	11.2714	−	0.246519i	0.685955	−	0.0150027i
$271$		−	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
$274$	−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	0.997329	+	0.0730342i	$0.0232682\pi$
$277$	17.8144	+	17.8144i	1.07036	+	1.07036i	0.0730342	+	0.997329i	$0.476732\pi$
$278$	−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	−0.903489	−	0.428610i	$-0.859003\pi$
$281$	−22.3301	−	22.3301i	−1.33210	−	1.33210i	−0.428610	−	0.903489i	$-0.640997\pi$
$282$	−6.20246	+	24.2891i	−0.369351	+	1.44639i
$283$	13.3311	+	13.3311i	0.792450	+	0.792450i	0.981892	−	0.189442i	$-0.0606678\pi$
$283$	13.3311	+	13.3311i	0.792450	+	0.792450i	−0.189442	+	0.981892i	$0.560668\pi$
$284$	−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	0.824187	−	0.566317i	$-0.191632\pi$
$307$	4.51824	+	4.51824i	0.257870	+	0.257870i	−0.566317	+	0.824187i	$0.691632\pi$
$308$	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	−0.752616	−	0.658460i	$-0.771208\pi$
$311$	−1.66046	+	1.66046i	−0.0941563	+	0.0941563i	0.658460	+	0.752616i	$0.271208\pi$
$312$	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	0.284851	−	0.958572i	$-0.408056\pi$
$331$	−12.2573	−	12.2573i	−0.673721	−	0.673721i	−0.958572	+	0.284851i	$0.908056\pi$
$332$	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	0.230709	−	0.973023i	$-0.425896\pi$
$337$	22.0976	−	22.0976i	1.20373	−	1.20373i	0.973023	−	0.230709i	$-0.0741044\pi$
$338$	−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	−0.864690	−	0.502307i	$-0.832485\pi$
$353$	−6.80856	+	6.80856i	−0.362383	+	0.362383i	0.502307	+	0.864690i	$0.332485\pi$
$354$	−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	0.934734	−	0.355349i	$-0.115638\pi$
$367$	11.0994	+	11.0994i	0.579385	+	0.579385i	−0.355349	+	0.934734i	$0.615638\pi$
$368$	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	0.0162796	−	0.999867i	$-0.494818\pi$
$373$	19.6251	−	19.6251i	1.01615	−	1.01615i	0.999867	−	0.0162796i	$-0.00518218\pi$
$374$	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	$0.108389\pi$
$383$			13.0719i			0.667944i	−0.942583	+	0.333972i	$0.891611\pi$
$384$	−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	$0.271612\pi$
$401$			30.1757i			1.50690i	−0.657505	+	0.753450i	$0.728388\pi$
$402$	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	$0.205491\pi$
$409$			24.3353i			1.20330i	−0.798758	+	0.601652i	$0.794509\pi$
$410$	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	$-0.718956\pi$
$419$		−	31.6294i		−	1.54520i	0.634893	−	0.772600i	$-0.281044\pi$
$420$	−30.4834	−	7.07801i	−1.48744	−	0.345372i
$421$	−10.1879	+	10.1879i	−0.496529	+	0.496529i	−0.910356	−	0.413827i	$-0.864192\pi$
$421$	−10.1879	+	10.1879i	−0.496529	+	0.496529i	0.413827	+	0.910356i	$0.364192\pi$
$422$	−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	−0.897737	−	0.440533i	$-0.854790\pi$
$433$	−9.51380	+	9.51380i	−0.457204	+	0.457204i	0.440533	+	0.897737i	$0.354790\pi$
$434$	−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	−0.822535	−	0.568714i	$-0.807441\pi$
$439$	−5.31814	+	5.31814i	−0.253821	+	0.253821i	0.568714	+	0.822535i	$0.307441\pi$
$440$	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	−0.989717	−	0.143042i	$-0.954312\pi$
$443$	−17.8204	+	17.8204i	−0.846675	+	0.846675i	0.143042	+	0.989717i	$0.454312\pi$
$444$	−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	$-0.975556\pi$
$457$		−	3.28010i		−	0.153436i	0.997053	−	0.0767182i	$-0.0244442\pi$
$458$	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	−0.972548	−	0.232703i	$-0.925243\pi$
$467$	−15.9882	+	15.9882i	−0.739844	+	0.739844i	0.232703	+	0.972548i	$0.425243\pi$
$468$	−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	−0.242497	−	0.970152i	$-0.577967\pi$
$479$	15.9255	−	15.9255i	0.727655	−	0.727655i	0.970152	+	0.242497i	$0.0779666\pi$
$480$	−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	0.899271	−	0.437392i	$-0.144098\pi$
$487$	10.1928	+	10.1928i	0.461879	+	0.461879i	−0.437392	+	0.899271i	$0.644098\pi$
$488$	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	$-0.881792\pi$
$491$		−	16.0820i		−	0.725769i	0.931834	−	0.362884i	$-0.118208\pi$
$492$	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	−0.972047	−	0.234788i	$-0.924561\pi$
$499$	−16.4691	+	16.4691i	−0.737259	+	0.737259i	0.234788	+	0.972047i	$0.424561\pi$
$500$	−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	0.00910388	−	0.999959i	$-0.497102\pi$
$509$	22.7655	−	22.7655i	1.00906	−	1.00906i	0.999959	−	0.00910388i	$-0.00289790\pi$
$510$	−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	−0.905099	−	0.425202i	$-0.860203\pi$
$521$	−10.9539	+	10.9539i	−0.479897	+	0.479897i	0.425202	+	0.905099i	$0.360203\pi$
$522$	−7.42156	+	4.40223i	−0.324833	+	0.192680i
$523$	−15.8783	−	15.8783i	−0.694308	−	0.694308i	0.268869	−	0.963177i	$-0.413350\pi$
$523$	−15.8783	−	15.8783i	−0.694308	−	0.694308i	−0.963177	+	0.268869i	$0.913350\pi$
$524$	−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	$0.212580\pi$
$541$			28.8087i			1.23858i	−0.785162	+	0.619291i	$0.787420\pi$
$542$	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	$-0.892769\pi$
$557$		−	15.6020i		−	0.661080i	0.943792	−	0.330540i	$-0.107231\pi$
$558$	−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	0.682323	−	0.731051i	$-0.260970\pi$
$571$	−1.16438	−	1.16438i	−0.0487279	−	0.0487279i	−0.731051	+	0.682323i	$0.760970\pi$
$572$	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	$0.0378506\pi$
$587$			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
$590$	−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	0.901298	−	0.433199i	$-0.142615\pi$
$601$	11.4756	+	11.4756i	0.468099	+	0.468099i	−0.433199	+	0.901298i	$0.642615\pi$
$602$	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	0.990589	+	0.136873i	$0.0437051\pi$
$607$	27.7777	+	27.7777i	1.12746	+	1.12746i	0.136873	+	0.990589i	$0.456295\pi$
$608$	−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	0.0567016	−	0.998391i	$-0.481942\pi$
$613$	−23.3151	−	23.3151i	−0.941690	−	0.941690i	−0.998391	+	0.0567016i	$0.981942\pi$
$614$	−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	−0.532030	−	0.846726i	$-0.678571\pi$
$617$	7.81689	−	7.81689i	0.314696	−	0.314696i	0.846726	+	0.532030i	$0.178571\pi$
$618$	−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	$0.0745051\pi$
$631$			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
$634$	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	0.981813	−	0.189852i	$-0.0608007\pi$
$641$	20.0509	+	20.0509i	0.791961	+	0.791961i	−0.189852	+	0.981813i	$0.560801\pi$
$642$	−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	−0.988043	−	0.154178i	$-0.950727\pi$
$647$	−29.0538	−	29.0538i	−1.14222	−	1.14222i	−0.154178	−	0.988043i	$-0.549273\pi$
$648$	−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	$0.101024\pi$
$653$			15.9494i			0.624150i	−0.950057	+	0.312075i	$0.898976\pi$
$654$	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	−0.651384	−	0.758748i	$-0.725811\pi$
$659$	2.75615	−	2.75615i	0.107365	−	0.107365i	0.758748	+	0.651384i	$0.225811\pi$
$660$	−40.9640	+	25.5256i	−1.59452	+	0.993584i
$661$		−	34.4292i		−	1.33914i	−0.742749	−	0.669570i	$-0.766479\pi$
$661$		−	34.4292i		−	1.33914i	0.742749	−	0.669570i	$-0.233521\pi$
$662$	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	−0.891477	−	0.453066i	$-0.850330\pi$
$677$	−11.4071	+	11.4071i	−0.438412	+	0.438412i	0.453066	+	0.891477i	$0.350330\pi$
$678$	−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	$0.260905\pi$
$683$			38.2037i			1.46182i	−0.682472	+	0.730911i	$0.739095\pi$
$684$	−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	−0.999674	−	0.0255504i	$-0.991866\pi$
$691$	−25.6067	+	25.6067i	−0.974123	+	0.974123i	0.0255504	+	0.999674i	$0.491866\pi$
$692$	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	0.872240	−	0.489077i	$-0.162666\pi$
$709$	10.2025	+	10.2025i	0.383163	+	0.383163i	−0.489077	+	0.872240i	$0.662666\pi$
$710$	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	0.753102	−	0.657904i	$-0.228557\pi$
$719$	2.55264	+	2.55264i	0.0951974	+	0.0951974i	−0.657904	+	0.753102i	$0.728557\pi$
$720$	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	$-0.872456\pi$
$727$		−	21.0340i		−	0.780108i	0.920792	−	0.390054i	$-0.127544\pi$
$728$	−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	0.934649	−	0.355572i	$-0.115714\pi$
$733$	15.6779	+	15.6779i	0.579076	+	0.579076i	−0.355572	+	0.934649i	$0.615714\pi$
$734$	−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	−0.803337	−	0.595524i	$-0.796944\pi$
$743$	−5.66456	+	5.66456i	−0.207813	+	0.207813i	0.595524	+	0.803337i	$0.296944\pi$
$744$	−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	0.995755	+	0.0920412i	$0.0293391\pi$
$751$	29.8104	+	29.8104i	1.08780	+	1.08780i	0.0920412	+	0.995755i	$0.470661\pi$
$752$	−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	$0.0555109\pi$
$757$			9.54778i			0.347020i	−0.984832	+	0.173510i	$0.944489\pi$
$758$	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	$0.0189751\pi$
$769$			3.30422i			0.119153i	−0.998224	+	0.0595767i	$0.981025\pi$
$770$	−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	0.356935	−	0.934129i	$-0.383822\pi$
$787$	−16.1923	−	16.1923i	−0.577195	−	0.577195i	−0.934129	+	0.356935i	$0.883822\pi$
$788$	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	0.726433	−	0.687237i	$-0.241177\pi$
$797$	1.10655	+	1.10655i	0.0391960	+	0.0391960i	−0.687237	+	0.726433i	$0.741177\pi$
$798$	−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	0.405078	−	0.914282i	$-0.367244\pi$
$809$	−14.4832	−	14.4832i	−0.509204	−	0.509204i	−0.914282	+	0.405078i	$0.867244\pi$
$810$	−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	$0.240372\pi$
$827$			39.4208i			1.37080i	−0.728169	+	0.685398i	$0.759628\pi$
$828$	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	0.325174	−	0.945654i	$-0.394577\pi$
$839$	−17.9725	−	17.9725i	−0.620480	−	0.620480i	−0.945654	+	0.325174i	$0.894577\pi$
$840$	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	0.962735	−	0.270448i	$-0.0871719\pi$
$853$	20.2190	+	20.2190i	0.692286	+	0.692286i	−0.270448	+	0.962735i	$0.587172\pi$
$854$	−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	0.493321	−	0.869847i	$-0.335783\pi$
$857$	−11.0226	−	11.0226i	−0.376526	−	0.376526i	−0.869847	+	0.493321i	$0.835783\pi$
$858$	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	$-0.268044\pi$
$860$	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	−0.128823	−	0.991668i	$-0.541120\pi$
$863$	25.3477	−	25.3477i	0.862844	−	0.862844i	0.991668	+	0.128823i	$0.0411200\pi$
$864$	−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	0.747006	−	0.664817i	$-0.231491\pi$
$877$	2.43394	+	2.43394i	0.0821884	+	0.0821884i	−0.664817	+	0.747006i	$0.731491\pi$
$878$	−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	$0.277326\pi$
$881$			45.4208i			1.53026i	−0.643873	+	0.765132i	$0.722674\pi$
$882$	1.98748	−	7.78303i	0.0669219	−	0.262068i
$883$			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	$-0.301550\pi$
$887$	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	0.490278	−	0.871566i	$-0.336895\pi$
$907$	−11.4830	−	11.4830i	−0.381288	−	0.381288i	−0.871566	+	0.490278i	$0.836895\pi$
$908$	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	−0.924704	−	0.380687i	$-0.875687\pi$
$919$	−39.5730	−	39.5730i	−1.30539	−	1.30539i	−0.380687	−	0.924704i	$-0.624313\pi$
$920$	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	−0.799447	−	0.600737i	$-0.794874\pi$
$929$	−6.05660	+	6.05660i	−0.198711	+	0.198711i	0.600737	+	0.799447i	$0.294874\pi$
$930$	−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	$-0.861969\pi$
$937$		−	25.7234i		−	0.840348i	0.907444	−	0.420174i	$-0.138031\pi$
$938$	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	$0.0884437\pi$
$941$			16.8282i			0.548585i	−0.961646	+	0.274293i	$0.911556\pi$
$942$	−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	−0.671640	−	0.740878i	$-0.734410\pi$
$947$	2.13068	−	2.13068i	0.0692377	−	0.0692377i	0.740878	+	0.671640i	$0.234410\pi$
$948$	−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	−0.998262	−	0.0589353i	$-0.981229\pi$
$953$	−28.9977	+	28.9977i	−0.939327	+	0.939327i	0.0589353	+	0.998262i	$0.481229\pi$
$954$	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	0.766296	−	0.642488i	$-0.222098\pi$
$971$	3.85798	+	3.85798i	0.123809	+	0.123809i	−0.642488	+	0.766296i	$0.722098\pi$
$972$	−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	0.357922	−	0.933752i	$-0.383485\pi$
$983$	−18.0539	−	18.0539i	−0.575830	−	0.575830i	−0.933752	+	0.357922i	$0.883485\pi$
$984$	−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	0.310525	−	0.950565i	$-0.399495\pi$
$991$	−20.1485	−	20.1485i	−0.640040	−	0.640040i	−0.950565	+	0.310525i	$0.899495\pi$
$992$	−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.647.54	yes	240
4.3	odd	2	inner	820.2.s.c.647.8	yes	240
5.3	odd	4		820.2.j.c.483.113	yes	240
20.3	even	4		820.2.j.c.483.67	✓	240
41.9	even	4		820.2.j.c.747.67	yes	240
164.91	odd	4		820.2.j.c.747.113	yes	240
205.173	odd	4	inner	820.2.s.c.583.8	yes	240
820.583	even	4	inner	820.2.s.c.583.54	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.67	✓	240	20.3	even	4
820.2.j.c.483.113	yes	240	5.3	odd	4
820.2.j.c.747.67	yes	240	41.9	even	4
820.2.j.c.747.113	yes	240	164.91	odd	4
820.2.s.c.583.8	yes	240	205.173	odd	4	inner
820.2.s.c.583.54	yes	240	820.583	even	4	inner
820.2.s.c.647.8	yes	240	4.3	odd	2	inner
820.2.s.c.647.54	yes	240	1.1	even	1	trivial

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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