LMFDB - Embedded newform 456.2.bk.a.61.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.16
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.292311 + 1.38367i) q^{2} +(0.984808 - 0.173648i) q^{3} +(-1.82911 - 0.808927i) q^{4} +(0.464877 + 0.554019i) q^{5} +(-0.0475977 + 1.41341i) q^{6} +(1.23281 - 2.13529i) q^{7} +(1.65396 - 2.29443i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.902471 + 0.481293i) q^{10} +(-1.77865 + 1.02690i) q^{11} +(-1.94179 - 0.479016i) q^{12} +(5.57221 + 0.982531i) q^{13} +(2.59418 + 2.32998i) q^{14} +(0.554019 + 0.464877i) q^{15} +(2.69128 + 2.95923i) q^{16} +(-0.425987 - 0.155047i) q^{17} +(0.198562 + 1.40020i) q^{18} +(4.15091 - 1.33041i) q^{19} +(-0.402150 - 1.38941i) q^{20} +(0.843292 - 2.31692i) q^{21} +(-0.900981 - 2.76124i) q^{22} +(-0.0104611 - 0.00877787i) q^{23} +(1.23041 - 2.54678i) q^{24} +(0.777415 - 4.40894i) q^{25} +(-2.98832 + 7.42292i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.98224 + 2.90842i) q^{28} +(3.24117 + 8.90505i) q^{29} +(-0.805184 + 0.630693i) q^{30} +(-3.48007 + 6.02766i) q^{31} +(-4.88130 + 2.85883i) q^{32} +(-1.57331 + 1.32016i) q^{33} +(0.339055 - 0.544106i) q^{34} +(1.75610 - 0.309647i) q^{35} +(-1.99547 - 0.134550i) q^{36} +0.127493i q^{37} +(0.627494 + 6.13239i) q^{38} +5.65817 q^{39} +(2.04005 - 0.150304i) q^{40} +(-1.39084 - 7.88786i) q^{41} +(2.95937 + 1.84410i) q^{42} +(-7.71060 - 9.18914i) q^{43} +(4.08403 - 0.439521i) q^{44} +(0.626327 + 0.361610i) q^{45} +(0.0152036 - 0.0119088i) q^{46} +(8.05271 - 2.93095i) q^{47} +(3.16425 + 2.44694i) q^{48} +(0.460360 + 0.797367i) q^{49} +(5.87329 + 2.36447i) q^{50} +(-0.446439 - 0.0787193i) q^{51} +(-9.39738 - 6.30467i) q^{52} +(-5.30500 + 6.32226i) q^{53} +(0.438688 + 1.34445i) q^{54} +(-1.39578 - 0.508021i) q^{55} +(-2.86026 - 6.36028i) q^{56} +(3.85682 - 2.03099i) q^{57} +(-13.2691 + 1.88168i) q^{58} +(-2.65372 + 7.29104i) q^{59} +(-0.637309 - 1.29847i) q^{60} +(-3.71349 + 4.42556i) q^{61} +(-7.32306 - 6.57724i) q^{62} +(0.428150 - 2.42816i) q^{63} +(-2.52883 - 7.58980i) q^{64} +(2.04605 + 3.54387i) q^{65} +(-1.36678 - 2.56284i) q^{66} +(-0.577827 - 1.58757i) q^{67} +(0.653755 + 0.628190i) q^{68} +(-0.0118264 - 0.00682797i) q^{69} +(-0.0848757 + 2.52038i) q^{70} +(0.599965 - 0.503430i) q^{71} +(0.769472 - 2.72175i) q^{72} +(1.07041 + 6.07061i) q^{73} +(-0.176408 - 0.0372675i) q^{74} -4.47695i q^{75} +(-8.66866 - 0.924319i) q^{76} +5.06390i q^{77} +(-1.65395 + 7.82907i) q^{78} +(-2.86635 - 16.2559i) q^{79} +(-0.388357 + 2.86670i) q^{80} +(0.766044 - 0.642788i) q^{81} +(11.3208 + 0.381236i) q^{82} +(-12.7140 - 7.34042i) q^{83} +(-3.41669 + 3.55575i) q^{84} +(-0.112133 - 0.308083i) q^{85} +(14.9687 - 7.98287i) q^{86} +(4.73828 + 8.20694i) q^{87} +(-0.585653 + 5.77944i) q^{88} +(-0.517439 + 2.93454i) q^{89} +(-0.683433 + 0.760930i) q^{90} +(8.96746 - 10.6870i) q^{91} +(0.0120338 + 0.0245179i) q^{92} +(-2.38051 + 6.54040i) q^{93} +(1.70158 + 11.9991i) q^{94} +(2.66673 + 1.68120i) q^{95} +(-4.31071 + 3.66303i) q^{96} +(-2.06031 - 0.749893i) q^{97} +(-1.23786 + 0.403909i) q^{98} +(-1.32016 + 1.57331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.292311	+	1.38367i	−0.206695	+	0.978405i
$2$	−0.292311	+	1.38367i	−0.206695	+	0.978405i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$4$	−1.82911	−	0.808927i	−0.914554	−	0.404463i
$5$	0.464877	+	0.554019i	0.207899	+	0.247765i	0.859911	−	0.510444i	$-0.170519\pi$
$5$	0.464877	+	0.554019i	0.207899	+	0.247765i	−0.652011	+	0.758209i	$0.726075\pi$
$6$	−0.0475977	+	1.41341i	−0.0194317	+	0.577023i
$7$	1.23281	−	2.13529i	0.465958	−	0.807063i	−0.533286	−	0.845935i	$-0.679043\pi$
$7$	1.23281	−	2.13529i	0.465958	−	0.807063i	0.999244	+	0.0388716i	$0.0123763\pi$
$8$	1.65396	−	2.29443i	0.584763	−	0.811204i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	−0.902471	+	0.481293i	−0.285386	+	0.152198i
$11$	−1.77865	+	1.02690i	−0.536283	+	0.309623i	−0.743571	−	0.668657i	$-0.766869\pi$
$11$	−1.77865	+	1.02690i	−0.536283	+	0.309623i	0.207288	+	0.978280i	$0.433536\pi$
$12$	−1.94179	−	0.479016i	−0.560546	−	0.138280i
$13$	5.57221	+	0.982531i	1.54545	+	0.272505i	0.880379	−	0.474272i	$-0.157289\pi$
$13$	5.57221	+	0.982531i	1.54545	+	0.272505i	0.665075	+	0.746777i	$0.268400\pi$
$14$	2.59418	+	2.32998i	0.693324	+	0.622712i
$15$	0.554019	+	0.464877i	0.143047	+	0.120031i
$16$	2.69128	+	2.95923i	0.672819	+	0.739807i
$17$	−0.425987	−	0.155047i	−0.103317	−	0.0376043i	0.289844	−	0.957074i	$-0.406396\pi$
$17$	−0.425987	−	0.155047i	−0.103317	−	0.0376043i	−0.393161	+	0.919469i	$0.628619\pi$
$18$	0.198562	+	1.40020i	0.0468015	+	0.330031i
$19$	4.15091	−	1.33041i	0.952283	−	0.305216i
$19$	4.15091	−	1.33041i	0.952283	−	0.305216i
$20$	−0.402150	−	1.38941i	−0.0899235	−	0.310682i
$21$	0.843292	−	2.31692i	0.184021	−	0.505594i
$22$	−0.900981	−	2.76124i	−0.192090	−	0.588699i
$23$	−0.0104611	−	0.00877787i	−0.00218128	−	0.00183031i	0.641696	−	0.766959i	$-0.278231\pi$
$23$	−0.0104611	−	0.00877787i	−0.00218128	−	0.00183031i	−0.643878	+	0.765129i	$0.722675\pi$
$24$	1.23041	−	2.54678i	0.251156	−	0.519860i
$25$	0.777415	−	4.40894i	0.155483	−	0.881787i
$26$	−2.98832	+	7.42292i	−0.586058	+	1.45575i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	−3.98224	+	2.90842i	−0.752572	+	0.549640i
$29$	3.24117	+	8.90505i	0.601871	+	1.65363i	0.747480	+	0.664284i	$0.231263\pi$
$29$	3.24117	+	8.90505i	0.601871	+	1.65363i	−0.145610	+	0.989342i	$0.546514\pi$
$30$	−0.805184	+	0.630693i	−0.147006	+	0.115148i
$31$	−3.48007	+	6.02766i	−0.625040	+	1.08260i	0.363494	+	0.931597i	$0.381584\pi$
$31$	−3.48007	+	6.02766i	−0.625040	+	1.08260i	−0.988533	+	0.151004i	$0.951749\pi$
$32$	−4.88130	+	2.85883i	−0.862900	+	0.505375i
$33$	−1.57331	+	1.32016i	−0.273878	+	0.229811i
$34$	0.339055	−	0.544106i	0.0581474	−	0.0933133i
$35$	1.75610	−	0.309647i	0.296834	−	0.0523399i
$36$	−1.99547	−	0.134550i	−0.332578	−	0.0224251i
$37$			0.127493i			0.0209597i	0.999945	+	0.0104798i	$0.00333589\pi$
$37$			0.127493i			0.0209597i	−0.999945	+	0.0104798i	$0.996664\pi$
$38$	0.627494	+	6.13239i	0.101793	+	0.994806i
$39$	5.65817			0.906033
$40$	2.04005	−	0.150304i	0.322560	−	0.0237651i
$41$	−1.39084	−	7.88786i	−0.217213	−	1.23188i	−0.877024	−	0.480446i	$-0.840475\pi$
$41$	−1.39084	−	7.88786i	−0.217213	−	1.23188i	0.659811	−	0.751431i	$-0.270636\pi$
$42$	2.95937	+	1.84410i	0.456640	+	0.284551i
$43$	−7.71060	−	9.18914i	−1.17586	−	1.40133i	−0.897593	−	0.440825i	$-0.854686\pi$
$43$	−7.71060	−	9.18914i	−1.17586	−	1.40133i	−0.278262	−	0.960505i	$-0.589758\pi$
$44$	4.08403	−	0.439521i	0.615691	−	0.0662603i
$45$	0.626327	+	0.361610i	0.0933674	+	0.0539057i
$46$	0.0152036	−	0.0119088i	0.00224165	−	0.00175586i
$47$	8.05271	−	2.93095i	1.17461	−	0.427523i	0.320314	−	0.947311i	$-0.396212\pi$
$47$	8.05271	−	2.93095i	1.17461	−	0.427523i	0.854295	+	0.519789i	$0.173989\pi$
$48$	3.16425	+	2.44694i	0.456721	+	0.353185i
$49$	0.460360	+	0.797367i	0.0657657	+	0.113910i
$50$	5.87329	+	2.36447i	0.830608	+	0.334387i
$51$	−0.446439	−	0.0787193i	−0.0625140	−	0.0110229i
$52$	−9.39738	−	6.30467i	−1.30318	−	0.874300i
$53$	−5.30500	+	6.32226i	−0.728698	+	0.868429i	−0.995445	−	0.0953379i	$-0.969607\pi$
$53$	−5.30500	+	6.32226i	−0.728698	+	0.868429i	0.266747	+	0.963767i	$0.414051\pi$
$54$	0.438688	+	1.34445i	0.0596979	+	0.182957i
$55$	−1.39578	−	0.508021i	−0.188206	−	0.0685016i
$56$	−2.86026	−	6.36028i	−0.382218	−	0.849928i
$57$	3.85682	−	2.03099i	0.510848	−	0.269012i
$58$	−13.2691	+	1.88168i	−1.74232	+	0.247077i
$59$	−2.65372	+	7.29104i	−0.345485	+	0.949213i	0.638288	+	0.769798i	$0.279643\pi$
$59$	−2.65372	+	7.29104i	−0.345485	+	0.949213i	−0.983773	+	0.179416i	$0.942579\pi$
$60$	−0.637309	−	1.29847i	−0.0822763	−	0.167632i
$61$	−3.71349	+	4.42556i	−0.475463	+	0.566635i	−0.949459	−	0.313892i	$-0.898367\pi$
$61$	−3.71349	+	4.42556i	−0.475463	+	0.566635i	0.473995	+	0.880527i	$0.342811\pi$
$62$	−7.32306	−	6.57724i	−0.930029	−	0.835310i
$63$	0.428150	−	2.42816i	0.0539419	−	0.305920i
$64$	−2.52883	−	7.58980i	−0.316104	−	0.948724i
$65$	2.04605	+	3.54387i	0.253782	+	0.439563i
$66$	−1.36678	−	2.56284i	−0.168239	−	0.315464i
$67$	−0.577827	−	1.58757i	−0.0705928	−	0.193952i	0.899379	−	0.437170i	$-0.144019\pi$
$67$	−0.577827	−	1.58757i	−0.0705928	−	0.193952i	−0.969972	+	0.243218i	$0.921797\pi$
$68$	0.653755	+	0.628190i	0.0792795	+	0.0761792i
$69$	−0.0118264	−	0.00682797i	−0.00142373	−	0.000821991i
$70$	−0.0848757	+	2.52038i	−0.0101446	+	0.301243i
$71$	0.599965	−	0.503430i	0.0712027	−	0.0597462i	−0.606492	−	0.795090i	$-0.707424\pi$
$71$	0.599965	−	0.503430i	0.0712027	−	0.0597462i	0.677694	+	0.735344i	$0.262979\pi$
$72$	0.769472	−	2.72175i	0.0906831	−	0.320761i
$73$	1.07041	+	6.07061i	0.125282	+	0.710511i	0.981140	+	0.193300i	$0.0619190\pi$
$73$	1.07041	+	6.07061i	0.125282	+	0.710511i	−0.855857	+	0.517212i	$0.826970\pi$
$74$	−0.176408	−	0.0372675i	−0.0205070	−	0.00433226i
$75$		−	4.47695i		−	0.516954i
$76$	−8.66866	−	0.924319i	−0.994363	−	0.106027i
$77$			5.06390i			0.577085i
$78$	−1.65395	+	7.82907i	−0.187273	+	0.886467i
$79$	−2.86635	−	16.2559i	−0.322489	−	1.82893i	−0.526762	−	0.850013i	$-0.676594\pi$
$79$	−2.86635	−	16.2559i	−0.322489	−	1.82893i	0.204273	−	0.978914i	$-0.434517\pi$
$80$	−0.388357	+	2.86670i	−0.0434196	+	0.320506i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	11.3208	+	0.381236i	1.25017	+	0.0421005i
$83$	−12.7140	−	7.34042i	−1.39554	−	0.805716i	−0.401619	−	0.915807i	$-0.631552\pi$
$83$	−12.7140	−	7.34042i	−1.39554	−	0.805716i	−0.993921	+	0.110091i	$0.964886\pi$
$84$	−3.41669	+	3.55575i	−0.372792	+	0.387964i
$85$	−0.112133	−	0.308083i	−0.0121625	−	0.0334163i
$86$	14.9687	−	7.98287i	1.61411	−	0.860815i
$87$	4.73828	+	8.20694i	0.507997	+	0.879876i
$88$	−0.585653	+	5.77944i	−0.0624309	+	0.616091i
$89$	−0.517439	+	2.93454i	−0.0548484	+	0.311061i	−0.999873	−	0.0159385i	$-0.994926\pi$
$89$	−0.517439	+	2.93454i	−0.0548484	+	0.311061i	0.945025	+	0.326999i	$0.106038\pi$
$90$	−0.683433	+	0.760930i	−0.0720402	+	0.0802091i
$91$	8.96746	−	10.6870i	0.940046	−	1.12030i
$92$	0.0120338	+	0.0245179i	0.00125461	+	0.00255617i
$93$	−2.38051	+	6.54040i	−0.246847	+	0.678208i
$94$	1.70158	+	11.9991i	0.175504	+	1.23761i
$95$	2.66673	+	1.68120i	0.273601	+	0.172488i
$96$	−4.31071	+	3.66303i	−0.439960	+	0.373856i
$97$	−2.06031	−	0.749893i	−0.209193	−	0.0761401i	0.235298	−	0.971923i	$-0.424393\pi$
$97$	−2.06031	−	0.749893i	−0.209193	−	0.0761401i	−0.444491	+	0.895783i	$0.646616\pi$
$98$	−1.23786	+	0.403909i	−0.125043	+	0.0408010i
$99$	−1.32016	+	1.57331i	−0.132681	+	0.158123i
$100$	−4.98848	+	7.43555i	−0.498848	+	0.743555i
$101$	6.36564	+	1.12243i	0.633405	+	0.111686i	0.481126	−	0.876651i	$-0.340228\pi$
$101$	6.36564	+	1.12243i	0.633405	+	0.111686i	0.152279	+	0.988338i	$0.451339\pi$
$102$	0.239421	−	0.594716i	0.0237062	−	0.0588856i
$103$	−4.42124	−	7.65781i	−0.435638	−	0.754547i	0.561710	−	0.827334i	$-0.310144\pi$
$103$	−4.42124	−	7.65781i	−0.435638	−	0.754547i	−0.997347	+	0.0727877i	$0.976810\pi$
$104$	11.4706	−	11.1600i	1.12478	−	1.09433i
$105$	1.67565	−	0.609886i	0.163526	−	0.0595188i
$106$	−7.19723	−	9.18846i	−0.699057	−	0.892462i
$107$	−5.13167	−	2.96277i	−0.496097	−	0.286422i	0.231003	−	0.972953i	$-0.425799\pi$
$107$	−5.13167	−	2.96277i	−0.496097	−	0.286422i	−0.727100	+	0.686531i	$0.759133\pi$
$108$	−1.98852	+	0.214003i	−0.191345	+	0.0205925i
$109$	−3.51344	−	4.18715i	−0.336526	−	0.401056i	0.571069	−	0.820902i	$-0.306529\pi$
$109$	−3.51344	−	4.18715i	−0.336526	−	0.401056i	−0.907596	+	0.419846i	$0.862084\pi$
$110$	1.11094	−	1.78280i	0.105924	−	0.169983i
$111$	0.0221389	+	0.125556i	0.00210133	+	0.0119172i
$112$	9.63664	−	2.09848i	0.910577	−	0.198288i
$113$	5.75840			0.541705			0.270852	−	0.962621i	$-0.412694\pi$
$113$	5.75840			0.541705			0.270852	+	0.962621i	$0.412694\pi$
$114$	1.68284	+	5.93027i	0.157612	+	0.555420i
$115$		−	0.00987626i		−	0.000920966i
$116$	1.27508	−	18.9102i	0.118388	−	1.75577i
$117$	5.57221	−	0.982531i	0.515151	−	0.0908350i
$118$	−9.31272	−	5.80314i	−0.857305	−	0.534222i
$119$	−0.856231	+	0.718463i	−0.0784905	+	0.0658614i
$120$	1.98295	−	0.502271i	0.181018	−	0.0458508i
$121$	−3.39094	+	5.87328i	−0.308267	+	0.533935i
$122$	−5.03804	−	6.43189i	−0.456123	−	0.582316i
$123$	−2.73943	−	7.52651i	−0.247006	−	0.678643i
$124$	11.2414	−	8.21013i	1.00950	−	0.737291i
$125$	5.93567	−	3.42696i	0.530903	−	0.306517i
$126$	3.23463	+	1.30220i	0.288164	+	0.116009i
$127$	0.871665	−	4.94346i	0.0773477	−	0.438661i	−0.921399	−	0.388617i	$-0.872953\pi$
$127$	0.871665	−	4.94346i	0.0773477	−	0.438661i	0.998747	−	0.0500436i	$-0.0159360\pi$
$128$	11.2410	−	1.28050i	0.993574	−	0.113181i
$129$	−9.18914	−	7.71060i	−0.809058	−	0.678880i
$130$	−5.50164	+	1.79516i	−0.482526	+	0.157446i
$131$	−0.292415	+	0.803405i	−0.0255485	+	0.0701938i	−0.951811	−	0.306685i	$-0.900780\pi$
$131$	−0.292415	+	0.803405i	−0.0255485	+	0.0701938i	0.926263	+	0.376878i	$0.123003\pi$
$132$	3.94566	−	1.14203i	0.343426	−	0.0994008i
$133$	2.27647	−	10.5035i	0.197395	−	0.910771i
$134$	2.36558	−	0.335461i	0.204355	−	0.0289794i
$135$	0.679605	+	0.247356i	0.0584911	+	0.0212890i
$136$	−1.06031	+	0.720958i	−0.0909208	+	0.0618216i
$137$	−15.0588	−	12.6358i	−1.28656	−	1.07955i	−0.992304	−	0.123825i	$-0.960484\pi$
$137$	−15.0588	−	12.6358i	−1.28656	−	1.07955i	−0.294255	−	0.955727i	$-0.595072\pi$
$138$	0.0129047	−	0.0143680i	0.00109852	−	0.00122308i
$139$	7.02472	+	1.23865i	0.595829	+	0.105061i	0.463427	−	0.886135i	$-0.346620\pi$
$139$	7.02472	+	1.23865i	0.595829	+	0.105061i	0.132403	+	0.991196i	$0.457731\pi$
$140$	−3.46257	−	0.854175i	−0.292641	−	0.0721909i
$141$	7.42142	−	4.28476i	0.624996	−	0.360842i
$142$	0.521207	+	0.977314i	0.0437387	+	0.0820144i
$143$	−10.9200	+	3.97454i	−0.913174	+	0.332368i
$144$	3.54109	+	1.86030i	0.295091	+	0.155025i
$145$	−3.42682	+	5.93543i	−0.284582	+	0.492910i
$146$	−8.71264	−	0.293405i	−0.721064	−	0.0242824i
$147$	0.591828	+	0.705313i	0.0488131	+	0.0581732i
$148$	0.103132	−	0.233198i	0.00847741	−	0.0191687i
$149$	−16.3327	+	2.87990i	−1.33803	+	0.235930i	−0.796441	−	0.604716i	$-0.793287\pi$
$149$	−16.3327	+	2.87990i	−1.33803	+	0.235930i	−0.541585	+	0.840646i	$0.682176\pi$
$150$	6.19464	+	1.30866i	0.505790	+	0.106852i
$151$	4.17798			0.339999			0.170000	−	0.985444i	$-0.445623\pi$
$151$	4.17798			0.339999			0.170000	+	0.985444i	$0.445623\pi$
$152$	3.81290	−	11.7244i	0.309267	−	0.950975i
$153$	−0.453326			−0.0366492
$154$	−7.00679	−	1.48024i	−0.564624	−	0.119281i
$155$	−4.95725	+	0.874096i	−0.398176	+	0.0702091i
$156$	−10.3494	−	4.57705i	−0.828616	−	0.366457i
$157$	8.69001	+	10.3564i	0.693538	+	0.826527i	0.991779	−	0.127964i	$-0.0408442\pi$
$157$	8.69001	+	10.3564i	0.693538	+	0.826527i	−0.298240	+	0.954491i	$0.596400\pi$
$158$	23.3307	+	0.785678i	1.85609	+	0.0625052i
$159$	−4.12656	+	7.14741i	−0.327257	+	0.566827i
$160$	−3.85305	−	1.37533i	−0.304611	−	0.108729i
$161$	−0.0316398	+	0.0115159i	−0.00249356	+	0.000907583i
$162$	0.665485	+	1.24785i	0.0522855	+	0.0980403i
$163$	−15.1690	+	8.75783i	−1.18813	+	0.685966i	−0.957881	−	0.287166i	$-0.907287\pi$
$163$	−15.1690	+	8.75783i	−1.18813	+	0.685966i	−0.230248	+	0.973132i	$0.573954\pi$
$164$	−3.83670	+	15.5528i	−0.299596	+	1.21447i
$165$	−1.46279	−	0.257929i	−0.113878	−	0.0200798i
$166$	13.8732	−	15.4463i	1.07677	−	1.19887i
$167$	13.2222	+	11.0947i	1.02316	+	0.858535i	0.990022	−	0.140916i	$-0.0450047\pi$
$167$	13.2222	+	11.0947i	1.02316	+	0.858535i	0.0331404	+	0.999451i	$0.489449\pi$
$168$	−3.92126	−	5.76697i	−0.302531	−	0.444932i
$169$	17.8682	+	6.50348i	1.37447	+	0.500268i
$170$	0.459064	−	0.0650994i	0.0352086	−	0.00499290i
$171$	3.44555	−	2.66987i	0.263488	−	0.204170i
$172$	6.67019	+	23.0452i	0.508597	+	1.75718i
$173$	−0.794010	+	2.18153i	−0.0603675	+	0.165858i	−0.966210	−	0.257757i	$-0.917017\pi$
$173$	−0.794010	+	2.18153i	−0.0603675	+	0.165858i	0.905842	+	0.423615i	$0.139239\pi$
$174$	−12.7408	+	4.15725i	−0.965876	+	0.315161i
$175$	−8.45595	−	7.09539i	−0.639210	−	0.536361i
$176$	−7.82567	−	2.49975i	−0.589882	−	0.188426i
$177$	−1.34733	+	7.64109i	−0.101272	+	0.574340i
$178$	−3.90920	−	1.57377i	−0.293007	−	0.117959i
$179$	−4.02856	+	2.32589i	−0.301108	+	0.173845i	−0.642941	−	0.765916i	$-0.722286\pi$
$179$	−4.02856	+	2.32589i	−0.301108	+	0.173845i	0.341832	+	0.939761i	$0.388953\pi$
$180$	−0.853104	−	1.16808i	−0.0635866	−	0.0870633i
$181$	3.12739	+	8.59244i	0.232457	+	0.638671i	0.999997	−	0.00232979i	$-0.000741596\pi$
$181$	3.12739	+	8.59244i	0.232457	+	0.638671i	−0.767540	+	0.641001i	$0.778519\pi$
$182$	12.1660	+	15.5320i	0.901807	+	1.15131i
$183$	−2.88858	+	5.00317i	−0.213530	+	0.369845i
$184$	−0.0374424	+	0.00948394i	−0.00276029	+	0.000699165i
$185$	−0.0706333	+	0.0592684i	−0.00519307	+	0.00435750i
$186$	−8.35393	−	5.20568i	−0.612540	−	0.381699i
$187$	0.916899	−	0.161674i	0.0670503	−	0.0118228i
$188$	−17.1002	−	1.15303i	−1.24716	−	0.0840935i
$189$		−	2.46562i		−	0.179347i
$190$	−3.10576	+	3.19845i	−0.225315	+	0.232040i
$191$	−17.0861			−1.23630			−0.618152	−	0.786059i	$-0.712118\pi$
$191$	−17.0861			−1.23630			−0.618152	+	0.786059i	$0.712118\pi$
$192$	−3.80837	−	7.03536i	−0.274845	−	0.507733i
$193$	3.71591	+	21.0740i	0.267477	+	1.51694i	0.761888	+	0.647709i	$0.224273\pi$
$193$	3.71591	+	21.0740i	0.267477	+	1.51694i	−0.494411	+	0.869228i	$0.664616\pi$
$194$	1.63986	−	2.63160i	0.117735	−	0.188938i
$195$	2.63035	+	3.13473i	0.188364	+	0.224483i
$196$	−0.197037	−	1.83087i	−0.0140741	−	0.130776i
$197$	−10.1902	−	5.88329i	−0.726018	−	0.419167i	0.0909455	−	0.995856i	$-0.471011\pi$
$197$	−10.1902	−	5.88329i	−0.726018	−	0.419167i	−0.816964	+	0.576689i	$0.804344\pi$
$198$	−1.79105	−	2.28657i	−0.127284	−	0.162499i
$199$	−17.2729	+	6.28683i	−1.22444	+	0.445661i	−0.871691	−	0.490055i	$-0.836977\pi$
$199$	−17.2729	+	6.28683i	−1.22444	+	0.445661i	−0.352753	+	0.935717i	$0.614754\pi$
$200$	−8.83019	−	9.07593i	−0.624389	−	0.641765i
$201$	−0.844727	−	1.46311i	−0.0595824	−	0.103200i
$202$	−3.41383	+	8.47987i	−0.240196	+	0.596642i
$203$	23.0106	+	4.05739i	1.61503	+	0.284773i
$204$	0.752907	+	0.505123i	0.0527141	+	0.0353656i
$205$	3.72345	−	4.43744i	0.260057	−	0.309924i
$206$	11.8883	−	3.87909i	0.828297	−	0.270269i
$207$	−0.0128324	−	0.00467061i	−0.000891912	−	0.000324630i
$208$	12.0888	+	19.1337i	0.838209	+	1.32668i
$209$	−6.01680	+	6.62890i	−0.416191	+	0.458531i
$210$	0.354073	+	2.49683i	0.0244333	+	0.172297i
$211$	6.07209	−	16.6829i	0.418020	−	1.14850i	−0.534804	−	0.844976i	$-0.679615\pi$
$211$	6.07209	−	16.6829i	0.418020	−	1.14850i	0.952824	−	0.303524i	$-0.0981632\pi$
$212$	14.8177	−	7.27273i	1.01768	−	0.499493i
$213$	0.503430	−	0.599965i	0.0344945	−	0.0411089i
$214$	5.59955	−	6.23451i	0.382778	−	0.426182i
$215$	1.50647	−	8.54364i	0.102741	−	0.582671i
$216$	0.285155	−	2.81402i	0.0194024	−	0.191470i
$217$	8.58054	+	14.8619i	0.582485	+	1.00889i
$218$	6.82067	−	3.63750i	0.461954	−	0.246363i
$219$	2.10830	+	5.79251i	0.142466	+	0.391422i
$220$	2.14208	+	2.05831i	0.144419	+	0.138771i
$221$	−2.22135	−	1.28250i	−0.149424	−	0.0862702i
$222$	−0.180200	−	0.00606836i	−0.0120942	−	0.000407282i
$223$	−6.04597	+	5.07317i	−0.404868	+	0.339724i	−0.822372	−	0.568951i	$-0.807349\pi$
$223$	−6.04597	+	5.07317i	−0.404868	+	0.339724i	0.417504	+	0.908675i	$0.362905\pi$
$224$	0.0867215	+	13.9474i	0.00579433	+	0.931899i
$225$	−0.777415	−	4.40894i	−0.0518276	−	0.293929i
$226$	−1.68324	+	7.96775i	−0.111968	+	0.530007i
$227$		−	12.2651i		−	0.814066i	−0.913413	−	0.407033i	$-0.866563\pi$
$227$		−	12.2651i		−	0.814066i	0.913413	−	0.407033i	$-0.133437\pi$
$228$	−8.69747	+	0.595020i	−0.576004	+	0.0394062i
$229$			9.09425i			0.600965i	0.953787	+	0.300482i	$0.0971477\pi$
$229$			9.09425i			0.600965i	−0.953787	+	0.300482i	$0.902852\pi$
$230$	0.0136655	+	0.00288694i	0.000901078	+	0.000190359i
$231$	0.879338	+	4.98697i	0.0578562	+	0.328119i
$232$	25.7928	+	7.29194i	1.69338	+	0.478739i
$233$	−11.2519	+	9.44145i	−0.737135	+	0.618530i	−0.932067	−	0.362287i	$-0.881996\pi$
$233$	−11.2519	+	9.44145i	−0.737135	+	0.618530i	0.194932	+	0.980817i	$0.437552\pi$
$234$	−0.269316	+	7.99733i	−0.0176058	+	0.522802i
$235$	5.36732	+	3.09882i	0.350125	+	0.202145i
$236$	10.7519	−	11.1894i	0.699887	−	0.728371i
$237$	−5.64560	−	15.5112i	−0.366721	−	1.00756i
$238$	−0.743833	−	1.39476i	−0.0482155	−	0.0904088i
$239$	4.25397	+	7.36810i	0.275167	+	0.476602i	0.970177	−	0.242397i	$-0.0779337\pi$
$239$	4.25397	+	7.36810i	0.275167	+	0.476602i	−0.695011	+	0.719000i	$0.744600\pi$
$240$	0.115340	+	2.89058i	0.00744514	+	0.186586i
$241$	−3.26922	+	18.5407i	−0.210589	+	1.19431i	0.677809	+	0.735238i	$0.262930\pi$
$241$	−3.26922	+	18.5407i	−0.210589	+	1.19431i	−0.888398	+	0.459073i	$0.848182\pi$
$242$	−7.13550	−	6.40878i	−0.458687	−	0.411972i
$243$	0.642788	−	0.766044i	0.0412348	−	0.0491418i
$244$	10.3723	−	5.09089i	0.664020	−	0.325911i
$245$	−0.227746	+	0.625726i	−0.0145501	+	0.0399762i
$246$	11.2150	−	1.59039i	0.715042	−	0.101400i
$247$	24.4369	−	3.33492i	1.55488	−	0.212196i
$248$	8.07416	+	17.9543i	0.512710	+	1.14010i
$249$	−13.7955	−	5.02114i	−0.874253	−	0.318202i
$250$	3.00674	+	9.21478i	0.190163	+	0.582794i
$251$	−10.1676	+	12.1172i	−0.641770	+	0.764832i	−0.984649	−	0.174548i	$-0.944154\pi$
$251$	−10.1676	+	12.1172i	−0.641770	+	0.764832i	0.342878	+	0.939380i	$0.388598\pi$
$252$	−2.74734	+	4.09503i	−0.173066	+	0.257963i
$253$	0.0276206	+	0.00487025i	0.00173649	+	0.000306190i
$254$	6.58534	+	2.65113i	0.413201	+	0.166347i
$255$	−0.163927	−	0.283931i	−0.0102655	−	0.0177804i
$256$	−1.51407	+	15.9282i	−0.0946297	+	0.995513i
$257$	16.5020	−	6.00622i	1.02936	−	0.374658i	0.228525	−	0.973538i	$-0.426610\pi$
$257$	16.5020	−	6.00622i	1.02936	−	0.374658i	0.800839	+	0.598880i	$0.204387\pi$
$258$	13.3550	−	10.4609i	0.831449	−	0.651266i
$259$	0.272234	+	0.157174i	0.0169158	+	0.00976633i
$260$	−0.875724	−	8.13722i	−0.0543101	−	0.504649i
$261$	6.09141	+	7.25946i	0.377049	+	0.449349i
$262$	−1.02617	−	0.639452i	−0.0633973	−	0.0395055i
$263$	4.23149	+	23.9980i	0.260925	+	1.47978i	0.780394	+	0.625289i	$0.215019\pi$
$263$	4.23149	+	23.9980i	0.260925	+	1.47978i	−0.519469	+	0.854489i	$0.673870\pi$
$264$	0.426834	+	5.79334i	0.0262698	+	0.356555i
$265$	−5.96883			−0.366662
$266$	13.8680	+	6.22019i	0.850303	+	0.381385i
$267$			2.97981i			0.182362i
$268$	−0.227317	+	3.37125i	−0.0138856	+	0.205932i
$269$	−4.13937	+	0.729883i	−0.252382	+	0.0445018i	−0.298408	−	0.954439i	$-0.596456\pi$
$269$	−4.13937	+	0.729883i	−0.252382	+	0.0445018i	0.0460257	+	0.998940i	$0.485344\pi$
$270$	−0.540916	+	0.868047i	−0.0329191	+	0.0528277i
$271$	−0.556596	+	0.467039i	−0.0338108	+	0.0283706i	−0.659536	−	0.751673i	$-0.729247\pi$
$271$	−0.556596	+	0.467039i	−0.0338108	+	0.0283706i	0.625726	+	0.780043i	$0.284803\pi$
$272$	−0.687630	−	1.67787i	−0.0416937	−	0.101736i
$273$	6.97545	−	12.0818i	0.422173	−	0.731226i
$274$	21.8857	−	17.1429i	1.32216	−	1.03564i
$275$	3.14480	+	8.64028i	0.189639	+	0.521028i
$276$	0.0161084	+	0.0220558i	0.000969613	+	0.00132760i
$277$	−0.379663	+	0.219198i	−0.0228117	+	0.0131704i	−0.511363	−	0.859365i	$-0.670859\pi$
$277$	−0.379663	+	0.219198i	−0.0228117	+	0.0131704i	0.488551	+	0.872535i	$0.337526\pi$
$278$	−3.76729	+	9.35786i	−0.225947	+	0.561247i
$279$	−1.20862	+	6.85441i	−0.0723580	+	0.410363i
$280$	2.19405	−	4.54139i	0.131119	−	0.271400i
$281$	−21.4439	−	17.9936i	−1.27924	−	1.07341i	−0.993349	−	0.115146i	$-0.963266\pi$
$281$	−21.4439	−	17.9936i	−1.27924	−	1.07341i	−0.285890	−	0.958262i	$-0.592289\pi$
$282$	3.75935	+	11.5213i	0.223866	+	0.686084i
$283$	−6.67524	+	18.3401i	−0.396802	+	1.09020i	0.567031	+	0.823697i	$0.308092\pi$
$283$	−6.67524	+	18.3401i	−0.396802	+	1.09020i	−0.963833	+	0.266508i	$0.914130\pi$
$284$	−1.50464	+	0.435501i	−0.0892839	+	0.0258422i
$285$	2.91816	+	1.19259i	0.172857	+	0.0706430i
$286$	−2.30744	−	16.2715i	−0.136442	−	0.962153i
$287$	−18.5575	−	6.75438i	−1.09542	−	0.398699i
$288$	−3.60914	+	4.35593i	−0.212671	+	0.256675i
$289$	−12.8653	−	10.7953i	−0.756784	−	0.635017i
$290$	−7.21100	−	6.47659i	−0.423444	−	0.380319i
$291$	−2.15923	−	0.380731i	−0.126576	−	0.0223188i
$292$	2.95278	−	11.9697i	0.172798	−	0.700473i
$293$	3.96292	−	2.28799i	0.231516	−	0.133666i	−0.379755	−	0.925087i	$-0.623992\pi$
$293$	3.96292	−	2.28799i	0.231516	−	0.133666i	0.611271	+	0.791421i	$0.290658\pi$
$294$	−1.14892	+	0.612726i	−0.0670064	+	0.0357349i
$295$	−5.27303	+	1.91923i	−0.307008	+	0.111742i
$296$	0.292523	+	0.210868i	0.0170026	+	0.0122564i
$297$	−1.02690	+	1.77865i	−0.0595870	+	0.103208i
$298$	0.789392	−	23.4410i	0.0457283	−	1.35790i
$299$	−0.0496667	−	0.0591905i	−0.00287230	−	0.00342307i
$300$	−3.62153	+	8.18883i	−0.209089	+	0.472782i
$301$	−29.1272	+	5.13590i	−1.67886	+	0.296029i
$302$	−1.22127	+	5.78096i	−0.0702762	+	0.332657i
$303$	6.46384			0.371338
$304$	15.1082	+	8.70299i	0.866515	+	0.499151i
$305$	−4.17816			−0.239241
$306$	0.132512	−	0.627256i	0.00757522	−	0.0358578i
$307$	9.92877	−	1.75071i	0.566665	−	0.0999183i	0.117026	−	0.993129i	$-0.462664\pi$
$307$	9.92877	−	1.75071i	0.566665	−	0.0999183i	0.449639	+	0.893210i	$0.351553\pi$
$308$	4.09633	−	9.26243i	0.233410	−	0.527776i
$309$	−5.68384	−	6.77373i	−0.323342	−	0.385344i
$310$	0.239594	−	7.11472i	0.0136080	−	0.404089i
$311$	−2.64079	+	4.57398i	−0.149745	+	0.259367i	−0.931133	−	0.364679i	$-0.881179\pi$
$311$	−2.64079	+	4.57398i	−0.149745	+	0.259367i	0.781388	+	0.624046i	$0.214512\pi$
$312$	9.35839	−	12.9823i	0.529814	−	0.734977i
$313$	14.1485	−	5.14962i	0.799719	−	0.291074i	0.0903490	−	0.995910i	$-0.471202\pi$
$313$	14.1485	−	5.14962i	0.799719	−	0.291074i	0.709370	+	0.704836i	$0.248980\pi$
$314$	−16.8700	+	8.99687i	−0.952029	+	0.507723i
$315$	1.54428	−	0.891593i	0.0870106	−	0.0502356i
$316$	−7.90694	+	32.0524i	−0.444800	+	1.80309i
$317$	19.5773	+	3.45200i	1.09957	+	0.193884i	0.693854	−	0.720116i	$-0.255911\pi$
$317$	19.5773	+	3.45200i	1.09957	+	0.193884i	0.405715	+	0.914000i	$0.367022\pi$
$318$	−8.68345	−	7.79908i	−0.486944	−	0.437351i
$319$	−14.9095	−	12.5106i	−0.834773	−	0.700458i
$320$	3.02929	−	4.92935i	0.169343	−	0.275559i
$321$	−5.56819	−	2.02665i	−0.310786	−	0.113117i
$322$	−0.00668565	−	0.0471454i	−0.000372577	−	0.00262731i
$323$	−1.97451	−	0.0768476i	−0.109865	−	0.00427592i
$324$	−1.92115	+	0.556054i	−0.106730	+	0.0308919i
$325$	8.66384	−	23.8037i	0.480583	−	1.32039i
$326$	−7.68391	−	23.5490i	−0.425573	−	1.30426i
$327$	−4.18715	−	3.51344i	−0.231550	−	0.194293i
$328$	−20.3986	−	9.85501i	−1.12632	−	0.544152i
$329$	3.66904	−	20.8082i	0.202281	−	1.14719i
$330$	0.784479	−	1.94863i	0.0431842	−	0.107268i
$331$	3.27615	−	1.89149i	0.180074	−	0.103966i	−0.407254	−	0.913315i	$-0.633514\pi$
$331$	3.27615	−	1.89149i	0.180074	−	0.103966i	0.587327	+	0.809350i	$0.300180\pi$
$332$	17.3174	+	23.7111i	0.950415	+	1.30132i
$333$	0.0436050	+	0.119804i	0.00238954	+	0.00656521i
$334$	−19.2165	+	15.0521i	−1.05148	+	0.823612i
$335$	0.610924	−	1.05815i	0.0333783	−	0.0578130i
$336$	9.12584	−	3.73999i	0.497855	−	0.204033i
$337$	20.3691	−	17.0917i	1.10957	−	0.931043i	0.111542	−	0.993760i	$-0.464421\pi$
$337$	20.3691	−	17.0917i	1.10957	−	0.931043i	0.998031	+	0.0627172i	$0.0199766\pi$
$338$	−14.2218	+	22.8227i	−0.773562	+	1.24139i
$339$	5.67092	−	0.999936i	0.308002	−	0.0543091i
$340$	−0.0441130	+	0.654224i	−0.00239236	+	0.0354803i
$341$		−	14.2948i		−	0.774106i
$342$	2.68705	+	5.54795i	0.145299	+	0.299999i
$343$	19.5295			1.05449
$344$	−33.8369	+	2.49299i	−1.82436	+	0.134413i
$345$	−0.00171499	−	0.00972621i	−9.23322e−5	−	0.000523642i
$346$	−2.78642	−	1.73634i	−0.149799	−	0.0933460i
$347$	12.0416	+	14.3506i	0.646427	+	0.770382i	0.985371	−	0.170425i	$-0.0545141\pi$
$347$	12.0416	+	14.3506i	0.646427	+	0.770382i	−0.338944	+	0.940807i	$0.610070\pi$
$348$	−2.02801	−	18.8443i	−0.108713	−	1.01016i
$349$	−4.14936	−	2.39564i	−0.222110	−	0.128235i	0.384817	−	0.922993i	$-0.374265\pi$
$349$	−4.14936	−	2.39564i	−0.222110	−	0.128235i	−0.606927	+	0.794758i	$0.707598\pi$
$350$	12.2895	−	9.62622i	0.656900	−	0.514543i
$351$	5.31694	−	1.93521i	0.283797	−	0.103294i
$352$	5.74637	−	10.0975i	0.306283	−	0.538197i
$353$	−15.2290	−	26.3774i	−0.810558	−	1.40393i	−0.912474	−	0.409135i	$-0.865831\pi$
$353$	−15.2290	−	26.3774i	−0.810558	−	1.40393i	0.101916	−	0.994793i	$-0.467503\pi$
$354$	−10.1789	−	4.09784i	−0.541005	−	0.217798i
$355$	0.557820	+	0.0983587i	0.0296060	+	0.00522034i
$356$	3.32028	−	4.94903i	0.175975	−	0.262298i
$357$	−0.718463	+	0.856231i	−0.0380251	+	0.0453165i
$358$	−2.04068	−	6.25409i	−0.107853	−	0.330539i
$359$	21.6529	+	7.88102i	1.14280	+	0.415945i	0.842923	−	0.538034i	$-0.180833\pi$
$359$	21.6529	+	7.88102i	1.14280	+	0.415945i	0.299875	+	0.953978i	$0.403055\pi$
$360$	1.86561	−	0.838977i	0.0983263	−	0.0442179i
$361$	15.4600	−	11.0448i	0.813686	−	0.581305i
$362$	−12.8033	+	1.81563i	−0.672927	+	0.0954273i
$363$	−2.31954	+	6.37288i	−0.121744	+	0.334490i
$364$	−25.0475	+	12.2937i	−1.31284	+	0.644364i
$365$	−2.86562	+	3.41512i	−0.149994	+	0.178755i
$366$	−6.07839	−	5.45933i	−0.317722	−	0.285364i
$367$	−0.383179	+	2.17312i	−0.0200018	+	0.113436i	−0.993174	−	0.116642i	$-0.962787\pi$
$367$	−0.383179	+	2.17312i	−0.0200018	+	0.113436i	0.973172	+	0.230078i	$0.0738981\pi$
$368$	−0.00217786	−	0.0545803i	−0.000113529	−	0.00284520i
$369$	−4.00477	−	6.93647i	−0.208480	−	0.361098i
$370$	−0.0613613	−	0.115058i	−0.00319002	−	0.00598160i
$371$	6.95979	+	19.1219i	0.361334	+	0.992757i
$372$	9.64491	−	10.0374i	0.500065	−	0.520417i
$373$	−4.80519	−	2.77428i	−0.248804	−	0.143647i	0.370413	−	0.928867i	$-0.379216\pi$
$373$	−4.80519	−	2.77428i	−0.248804	−	0.143647i	−0.619216	+	0.785220i	$0.712550\pi$
$374$	−0.0443156	+	1.31595i	−0.00229150	+	0.0680461i
$375$	5.25041	−	4.40562i	0.271130	−	0.227505i
$376$	6.59400	−	23.3241i	0.340060	−	1.20285i
$377$	9.31101	+	52.8054i	0.479541	+	2.71961i
$378$	3.41161	+	0.720728i	0.175474	+	0.0370702i
$379$			12.6828i			0.651470i	0.945461	+	0.325735i	$0.105612\pi$
$379$			12.6828i			0.651470i	−0.945461	+	0.325735i	$0.894388\pi$
$380$	−3.51777	−	5.23230i	−0.180458	−	0.268411i
$381$		−	5.01972i		−	0.257168i
$382$	4.99444	−	23.6415i	0.255538	−	1.20961i
$383$	−1.17657	−	6.67268i	−0.0601201	−	0.340958i	0.939880	−	0.341506i	$-0.110937\pi$
$383$	−1.17657	−	6.67268i	−0.0601201	−	0.340958i	−1.00000		0.000547502i	$0.999826\pi$
$384$	10.8479	−	3.21303i	0.553578	−	0.163964i
$385$	−2.80550	+	2.35409i	−0.142981	+	0.119976i
$386$	−30.2457	−	1.01855i	−1.53947	−	0.0518427i
$387$	−10.3885	−	5.99778i	−0.528075	−	0.304884i
$388$	3.16193	+	3.03828i	0.160523	+	0.154245i
$389$	−10.6596	−	29.2871i	−0.540465	−	1.48492i	−0.846235	−	0.532810i	$-0.821136\pi$
$389$	−10.6596	−	29.2871i	−0.540465	−	1.48492i	0.305770	−	0.952105i	$-0.401086\pi$
$390$	−5.10633	+	2.72324i	−0.258569	+	0.137896i
$391$	0.00309530	+	0.00536121i	0.000156536	+	0.000271128i
$392$	2.59092	+	0.262548i	0.130861	+	0.0132607i
$393$	−0.148463	+	0.841977i	−0.00748898	+	0.0424721i
$394$	11.1192	−	12.3801i	0.560180	−	0.623700i
$395$	7.67356	−	9.14499i	0.386098	−	0.460134i
$396$	3.68741	−	1.80984i	0.185299	−	0.0909476i
$397$	12.2678	−	33.7055i	0.615702	−	1.69163i	−0.101564	−	0.994829i	$-0.532385\pi$
$397$	12.2678	−	33.7055i	0.615702	−	1.69163i	0.717266	−	0.696799i	$-0.245393\pi$
$398$	−3.64985	−	25.7378i	−0.182951	−	1.29012i
$399$	0.417971	−	10.7393i	0.0209247	−	0.537635i
$400$	15.1393	−	9.56512i	0.756965	−	0.478256i
$401$	−6.86170	−	2.49746i	−0.342657	−	0.124717i	0.164959	−	0.986300i	$-0.447251\pi$
$401$	−6.86170	−	2.49746i	−0.342657	−	0.124717i	−0.507616	+	0.861583i	$0.669473\pi$
$402$	2.27139	−	0.741144i	0.113287	−	0.0369649i
$403$	−25.3141	+	30.1681i	−1.26098	+	1.50278i
$404$	−10.7355	−	7.20239i	−0.534110	−	0.358332i
$405$	0.712233	+	0.125586i	0.0353911	+	0.00624041i
$406$	−12.3404	+	30.6532i	−0.612442	+	1.52129i
$407$	−0.130923	−	0.226764i	−0.00648959	−	0.0112403i
$408$	−0.919008	+	0.894126i	−0.0454977	+	0.0442658i
$409$	15.6785	−	5.70651i	0.775253	−	0.282169i	0.0760609	−	0.997103i	$-0.475766\pi$
$409$	15.6785	−	5.70651i	0.775253	−	0.282169i	0.699192	+	0.714934i	$0.253543\pi$
$410$	5.05156	+	6.44916i	0.249479	+	0.318501i
$411$	−17.0242	−	9.82893i	−0.839742	−	0.484825i
$412$	1.89232	+	17.5834i	0.0932279	+	0.866273i
$413$	12.2970	+	14.6549i	0.605093	+	0.721122i
$414$	0.0102136	−	0.0163906i	0.000501973	−	0.000805553i
$415$	−1.84371	−	10.4562i	−0.0905040	−	0.513274i
$416$	−30.0085	+	11.1340i	−1.47129	+	0.545889i
$417$	7.13309			0.349309
$418$	−7.41346	−	10.2630i	−0.362604	−	0.501979i
$419$		−	4.36739i		−	0.213361i	−0.994293	−	0.106681i	$-0.965978\pi$
$419$		−	4.36739i		−	0.213361i	0.994293	−	0.106681i	$-0.0340222\pi$
$420$	−3.55829	−	0.239929i	−0.173627	−	0.0117073i
$421$	−28.1592	+	4.96523i	−1.37240	+	0.241990i	−0.810752	−	0.585390i	$-0.800942\pi$
$421$	−28.1592	+	4.96523i	−1.37240	+	0.241990i	−0.561643	+	0.827380i	$0.689830\pi$
$422$	21.3088	+	13.2784i	1.03730	+	0.646382i
$423$	6.56463	−	5.50838i	0.319183	−	0.267827i
$424$	5.73173	+	22.6287i	0.278357	+	1.09895i
$425$	−1.01476	+	1.75762i	−0.0492231	+	0.0852569i
$426$	0.682998	+	0.871960i	0.0330913	+	0.0422466i
$427$	4.87183	+	13.3852i	0.235764	+	0.647757i
$428$	6.98972	+	9.57037i	0.337861	+	0.462601i
$429$	−10.0639	+	5.81039i	−0.485890	+	0.280528i
$430$	11.3813	+	4.58187i	0.548853	+	0.220957i
$431$	4.82246	−	27.3495i	0.232290	−	1.31738i	−0.615958	−	0.787779i	$-0.711231\pi$
$431$	4.82246	−	27.3495i	0.232290	−	1.31738i	0.848247	−	0.529600i	$-0.177658\pi$
$432$	3.81033	+	1.21713i	0.183324	+	0.0585592i
$433$	19.9336	+	16.7263i	0.957949	+	0.803814i	0.980618	−	0.195929i	$-0.0627721\pi$
$433$	19.9336	+	16.7263i	0.957949	+	0.803814i	−0.0226696	+	0.999743i	$0.507217\pi$
$434$	−23.0722	+	7.52836i	−1.10750	+	0.361373i
$435$	−2.34408	+	6.44031i	−0.112390	+	0.308789i
$436$	3.03936	+	10.5009i	0.145559	+	0.502900i
$437$	−0.0551010	−	0.0225186i	−0.00263584	−	0.00107721i
$438$	−8.63123	+	1.22399i	−0.412416	+	0.0584844i
$439$	1.09587	+	0.398865i	0.0523031	+	0.0190368i	0.368039	−	0.929810i	$-0.380029\pi$
$439$	1.09587	+	0.398865i	0.0523031	+	0.0190368i	−0.315736	+	0.948847i	$0.602251\pi$
$440$	−3.47418	+	2.36227i	−0.165625	+	0.112617i
$441$	0.705313	+	0.591828i	0.0335863	+	0.0281823i
$442$	2.42389	−	2.69874i	0.115293	−	0.128366i
$443$	14.3933	+	2.53793i	0.683847	+	0.120581i	0.504769	−	0.863254i	$-0.331578\pi$
$443$	14.3933	+	2.53793i	0.683847	+	0.120581i	0.179077	+	0.983835i	$0.442689\pi$
$444$	0.0610710	−	0.247564i	0.00289830	−	0.0117489i
$445$	−1.86634	+	1.07753i	−0.0884729	+	0.0510799i
$446$	−5.25231	−	9.84859i	−0.248704	−	0.466344i
$447$	−15.5845	+	5.67229i	−0.737121	+	0.268290i
$448$	−19.3240	−	3.95698i	−0.912972	−	0.186950i
$449$	16.9014	−	29.2740i	0.797625	−	1.38153i	−0.123534	−	0.992340i	$-0.539423\pi$
$449$	16.9014	−	29.2740i	0.797625	−	1.38153i	0.921159	−	0.389187i	$-0.127244\pi$
$450$	6.32778	+	0.213093i	0.298294	+	0.0100453i
$451$	10.5739	+	12.6015i	0.497905	+	0.593380i
$452$	−10.5327	−	4.65812i	−0.495418	−	0.219100i
$453$	4.11451	−	0.725499i	0.193316	−	0.0340869i
$454$	16.9710	+	3.58524i	0.796486	+	0.168263i
$455$	10.0896			0.473007
$456$	1.71905	−	12.2084i	0.0805020	−	0.571710i
$457$	8.40186			0.393022			0.196511	−	0.980502i	$-0.437039\pi$
$457$	8.40186			0.393022			0.196511	+	0.980502i	$0.437039\pi$
$458$	−12.5835	−	2.65835i	−0.587987	−	0.124217i
$459$	−0.446439	+	0.0787193i	−0.0208380	+	0.00367430i
$460$	−0.00798917	+	0.0180647i	−0.000372497	+	0.000842273i
$461$	−8.76348	−	10.4439i	−0.408156	−	0.486421i	0.522333	−	0.852742i	$-0.325062\pi$
$461$	−8.76348	−	10.4439i	−0.408156	−	0.486421i	−0.930489	+	0.366320i	$0.880617\pi$
$462$	−7.15738	−	0.241030i	−0.332992	−	0.0112138i
$463$	−4.99738	+	8.65572i	−0.232248	+	0.402266i	−0.958469	−	0.285196i	$-0.907941\pi$
$463$	−4.99738	+	8.65572i	−0.232248	+	0.402266i	0.726221	+	0.687461i	$0.241275\pi$
$464$	−17.6292	+	33.5573i	−0.818415	+	1.55786i
$465$	−4.73015	+	1.72163i	−0.219355	+	0.0798389i
$466$	−9.77484	−	18.3288i	−0.452810	−	0.849064i
$467$	15.8076	−	9.12652i	0.731488	−	0.422325i	−0.0874782	−	0.996166i	$-0.527881\pi$
$467$	15.8076	−	9.12652i	0.731488	−	0.422325i	0.818966	+	0.573842i	$0.194547\pi$
$468$	−10.9870	−	2.71035i	−0.507873	−	0.125286i
$469$	−4.10227	−	0.723340i	−0.189425	−	0.0334007i
$470$	−5.85669	+	6.52080i	−0.270149	+	0.300782i
$471$	10.3564	+	8.69001i	0.477195	+	0.400415i
$472$	12.3397	+	18.1479i	0.567979	+	0.835324i
$473$	23.1508	+	8.42620i	1.06447	+	0.387437i
$474$	23.1127	−	3.27759i	1.06160	−	0.150545i
$475$	−2.63871	−	19.3354i	−0.121072	−	0.887167i
$476$	2.14732	−	0.621519i	0.0984224	−	0.0284873i
$477$	−2.82273	+	7.75540i	−0.129244	+	0.355095i
$478$	−11.4385	+	3.73233i	−0.523186	+	0.170713i
$479$	−13.5823	−	11.3969i	−0.620591	−	0.520737i	0.277398	−	0.960755i	$-0.410528\pi$
$479$	−13.5823	−	11.3969i	−0.620591	−	0.520737i	−0.897989	+	0.440018i	$0.854972\pi$
$480$	−4.03334	−	0.685357i	−0.184096	−	0.0312821i
$481$	−0.125265	+	0.710416i	−0.00571161	+	0.0323922i
$482$	−24.6986	−	9.94319i	−1.12499	−	0.452900i
$483$	−0.0291594	+	0.0168352i	−0.00132680	+	0.000766027i
$484$	10.9535	−	7.99985i	0.497884	−	0.363629i
$485$	−0.542338	−	1.49006i	−0.0246263	−	0.0676602i
$486$	0.872062	+	1.11333i	0.0395575	+	0.0505018i
$487$	−3.66952	+	6.35580i	−0.166282	+	0.288009i	−0.937110	−	0.349035i	$-0.886509\pi$
$487$	−3.66952	+	6.35580i	−0.166282	+	0.288009i	0.770828	+	0.637043i	$0.219843\pi$
$488$	4.01219	+	15.8400i	0.181623	+	0.717045i
$489$	−13.4178	+	11.2589i	−0.606773	+	0.509143i
$490$	−0.799228	−	0.498033i	−0.0361055	−	0.0224988i
$491$	−33.1520	+	5.84560i	−1.49613	+	0.263808i	−0.861003	−	0.508599i	$-0.830164\pi$
$491$	−33.1520	+	5.84560i	−1.49613	+	0.263808i	−0.635127	+	0.772407i	$0.719052\pi$
$492$	−1.07769	+	15.9828i	−0.0485859	+	0.720560i
$493$		−	4.29597i		−	0.193481i
$494$	−2.52874	+	34.7875i	−0.113773	+	1.56516i
$495$	−1.48535			−0.0667617
$496$	−27.2031	+	5.92377i	−1.22145	+	0.265985i
$497$	−0.335327	−	1.90173i	−0.0150415	−	0.0853043i
$498$	10.9802	−	17.6207i	0.492034	−	0.789603i
$499$	27.1211	+	32.3217i	1.21411	+	1.44692i	0.858912	+	0.512124i	$0.171141\pi$
$499$	27.1211	+	32.3217i	1.21411	+	1.44692i	0.355195	+	0.934792i	$0.384414\pi$
$500$	−13.6292	+	1.46676i	−0.609514	+	0.0655956i
$501$	14.9479	+	8.63016i	0.667822	+	0.385567i
$502$	−13.7942	−	17.6106i	−0.615665	−	0.785999i
$503$	9.58950	−	3.49029i	0.427575	−	0.155625i	−0.119264	−	0.992863i	$-0.538053\pi$
$503$	9.58950	−	3.49029i	0.427575	−	0.155625i	0.546839	+	0.837238i	$0.315831\pi$
$504$	−4.86311	−	4.99844i	−0.216620	−	0.222648i
$505$	2.33739	+	4.04848i	0.104013	+	0.180155i
$506$	−0.0148126	+	0.0367942i	−0.000658502	+	0.00163570i
$507$	18.7260	+	3.30190i	0.831652	+	0.146643i
$508$	−5.59326	+	8.33701i	−0.248161	+	0.369895i
$509$	22.8973	−	27.2879i	1.01490	−	1.20952i	0.0372479	−	0.999306i	$-0.488141\pi$
$509$	22.8973	−	27.2879i	1.01490	−	1.20952i	0.977656	−	0.210210i	$-0.0674147\pi$
$510$	0.440785	−	0.143826i	0.0195183	−	0.00636872i
$511$	14.2821	+	5.19827i	0.631804	+	0.229958i
$512$	−21.5969	−	6.75098i	−0.954455	−	0.298354i
$513$	2.92959	−	3.22762i	0.129344	−	0.142503i
$514$	3.48695	+	24.5890i	0.153803	+	1.08457i
$515$	2.18724	−	6.00939i	0.0963813	−	0.264806i
$516$	10.5706	+	21.5369i	0.465345	+	0.948107i
$517$	−11.3131	+	13.4825i	−0.497551	+	0.592959i
$518$	−0.297055	+	0.330739i	−0.0130518	+	0.0145318i
$519$	−0.403130	+	2.28626i	−0.0176954	+	0.100356i
$520$	11.5153	+	1.16689i	0.504977	+	0.0511713i
$521$	2.44008	+	4.22634i	0.106902	+	0.185159i	0.914514	−	0.404555i	$-0.132574\pi$
$521$	2.44008	+	4.22634i	0.106902	+	0.185159i	−0.807612	+	0.589714i	$0.799240\pi$
$522$	−11.8253	+	6.30651i	−0.517580	+	0.276028i
$523$	−9.49308	−	26.0820i	−0.415103	−	1.14049i	−0.954442	−	0.298398i	$-0.903548\pi$
$523$	−9.49308	−	26.0820i	−0.415103	−	1.14049i	0.539338	−	0.842089i	$-0.318674\pi$
$524$	1.18476	−	1.23297i	0.0517563	−	0.0538626i
$525$	−9.55959	−	5.51923i	−0.417215	−	0.240879i
$526$	−34.4423	−	1.15987i	−1.50175	−	0.0505727i
$527$	2.41704	−	2.02813i	0.105288	−	0.0883469i
$528$	−8.14086	−	1.10286i	−0.354285	−	0.0479957i
$529$	−3.99388	−	22.6504i	−0.173647	−	0.984800i
$530$	1.74475	−	8.25891i	0.0757873	−	0.358744i
$531$			7.75897i			0.336711i
$532$	−12.6605	+	17.3706i	−0.548902	+	0.753110i
$533$		−	45.3194i		−	1.96300i
$534$	−4.12309	−	0.871033i	−0.178424	−	0.0376933i
$535$	−0.744165	−	4.22037i	−0.0321730	−	0.182462i
$536$	−4.59827	−	1.29999i	−0.198615	−	0.0561509i
$537$	−3.56347	+	2.99010i	−0.153775	+	0.129032i
$538$	0.200064	−	5.94090i	0.00862538	−	0.256130i
$539$	−1.63764	−	0.945490i	−0.0705380	−	0.0407252i
$540$	−1.04298	−	1.00219i	−0.0448826	−	0.0431275i
$541$	0.922810	+	2.53540i	0.0396747	+	0.109005i	0.957948	−	0.286942i	$-0.0926386\pi$
$541$	0.922810	+	2.53540i	0.0396747	+	0.109005i	−0.918273	+	0.395947i	$0.870416\pi$
$542$	−0.483531	−	0.906668i	−0.0207694	−	0.0389447i
$543$	4.57194	+	7.91884i	0.196201	+	0.339830i
$544$	2.52262	−	0.460997i	0.108157	−	0.0197651i
$545$	0.686445	−	3.89302i	0.0294041	−	0.166759i
$546$	14.6783	+	13.1834i	0.628174	+	0.564198i
$547$	21.1496	−	25.2052i	0.904293	−	1.07769i	−0.0923420	−	0.995727i	$-0.529435\pi$
$547$	21.1496	−	25.2052i	0.904293	−	1.07769i	0.996635	−	0.0819671i	$-0.0261203\pi$
$548$	17.3227	+	35.2938i	0.739989	+	1.50767i
$549$	−1.97590	+	5.42875i	−0.0843295	+	0.231694i
$550$	−12.8746	+	1.82573i	−0.548974	+	0.0778496i
$551$	25.3011	+	32.6519i	1.07786	+	1.39102i
$552$	−0.0352267	+	0.0158417i	−0.00149935	+	0.000674266i
$553$	−38.2446	−	13.9199i	−1.62633	−	0.591934i
$554$	−0.192320	−	0.589404i	−0.00817088	−	0.0250414i
$555$	−0.0592684	+	0.0706333i	−0.00251580	+	0.00299822i
$556$	−11.8470	−	7.94811i	−0.502425	−	0.337075i
$557$	7.18321	+	1.26659i	0.304362	+	0.0536673i	0.323744	−	0.946145i	$-0.395058\pi$
$557$	7.18321	+	1.26659i	0.304362	+	0.0536673i	−0.0193812	+	0.999812i	$0.506170\pi$
$558$	−9.13097	−	3.67595i	−0.386545	−	0.155615i
$559$	−33.9365	−	58.7797i	−1.43536	−	2.48612i
$560$	5.64245	+	4.36334i	0.238437	+	0.184385i
$561$	0.874895	−	0.318436i	0.0369381	−	0.0134444i
$562$	31.1656	−	24.4117i	1.31464	−	1.02975i
$563$	−28.4129	−	16.4042i	−1.19746	−	0.691354i	−0.237472	−	0.971394i	$-0.576319\pi$
$563$	−28.4129	−	16.4042i	−1.19746	−	0.691354i	−0.959988	+	0.280041i	$0.909652\pi$
$564$	−17.0406	+	1.83390i	−0.717540	+	0.0772213i
$565$	2.67695	+	3.19026i	0.112620	+	0.134215i
$566$	−23.4255	−	14.5974i	−0.984645	−	0.613573i
$567$	−0.428150	−	2.42816i	−0.0179806	−	0.101973i
$568$	−0.162769	−	2.20923i	−0.00682963	−	0.0926973i
$569$	−7.37976			−0.309376			−0.154688	−	0.987963i	$-0.549437\pi$
$569$	−7.37976			−0.309376			−0.154688	+	0.987963i	$0.549437\pi$
$570$	−2.50317	+	3.68917i	−0.104846	+	0.154522i
$571$		−	1.73292i		−	0.0725206i	−0.999342	−	0.0362603i	$-0.988455\pi$
$571$		−	1.73292i		−	0.0725206i	0.999342	−	0.0362603i	$-0.0115445\pi$
$572$	23.1889	+	1.56358i	0.969577	+	0.0653767i
$573$	−16.8265	+	2.96696i	−0.702936	+	0.123947i
$574$	14.7704	−	23.7032i	0.616506	−	0.989351i
$575$	−0.0468336	+	0.0392981i	−0.00195310	+	0.00163884i
$576$	−4.97219	−	6.26716i	−0.207175	−	0.261132i
$577$	3.82041	−	6.61715i	0.159046	−	0.275476i	−0.775479	−	0.631373i	$-0.782492\pi$
$577$	3.82041	−	6.61715i	0.159046	−	0.275476i	0.934525	+	0.355898i	$0.115825\pi$
$578$	18.6978	−	14.6458i	0.777728	−	0.609187i
$579$	7.31891	+	20.1085i	0.304164	+	0.835682i
$580$	11.0693	−	8.08449i	0.459630	−	0.335690i
$581$	−31.3478	+	18.0987i	−1.30053	+	0.750860i
$582$	1.15797	−	2.87638i	0.0479996	−	0.119230i
$583$	2.94339	−	16.6928i	0.121903	−	0.691345i
$584$	15.6990	+	7.58456i	0.649630	+	0.313851i
$585$	3.13473	+	2.63035i	0.129605	+	0.108752i
$586$	2.00743	+	6.15220i	0.0829262	+	0.254145i
$587$	1.26850	−	3.48518i	0.0523566	−	0.143849i	−0.910758	−	0.412941i	$-0.864502\pi$
$587$	1.26850	−	3.48518i	0.0523566	−	0.143849i	0.963114	+	0.269092i	$0.0867237\pi$
$588$	−0.511971	−	1.76884i	−0.0211133	−	0.0729457i
$589$	−6.42621	+	29.6502i	−0.264787	+	1.22171i
$590$	−1.11422	−	7.85717i	−0.0458717	−	0.323475i
$591$	−11.0570	−	4.02441i	−0.454823	−	0.165542i
$592$	−0.377280	+	0.343118i	−0.0155061	+	0.0141021i
$593$	23.9875	+	20.1279i	0.985048	+	0.826553i	0.984843	−	0.173447i	$-0.0554904\pi$
$593$	23.9875	+	20.1279i	0.985048	+	0.826553i	0.000204730		1.00000i	$0.499935\pi$
$594$	−2.16089	−	1.94082i	−0.0886626	−	0.0796327i
$595$	−0.796084	−	0.140371i	−0.0326363	−	0.00575465i
$596$	32.2039	+	7.94431i	1.31912	+	0.325412i
$597$	−15.9188	+	9.19072i	−0.651513	+	0.376151i
$598$	0.0964184	−	0.0514205i	0.00394284	−	0.00210274i
$599$	10.9103	−	3.97102i	0.445783	−	0.162252i	−0.109368	−	0.994001i	$-0.534883\pi$
$599$	10.9103	−	3.97102i	0.445783	−	0.162252i	0.555151	+	0.831750i	$0.312661\pi$
$600$	−10.2721	−	7.40470i	−0.419355	−	0.302296i
$601$	−18.4827	+	32.0130i	−0.753927	+	1.30584i	0.191980	+	0.981399i	$0.438509\pi$
$601$	−18.4827	+	32.0130i	−0.753927	+	1.30584i	−0.945906	+	0.324440i	$0.894824\pi$
$602$	1.40777	−	41.8038i	0.0573766	−	1.70380i
$603$	−1.08596	−	1.29420i	−0.0442237	−	0.0527038i
$604$	−7.64198	−	3.37968i	−0.310948	−	0.137517i
$605$	−4.83028	+	0.851709i	−0.196379	+	0.0346269i
$606$	−1.88945	+	8.94385i	−0.0767538	+	0.363319i
$607$	−12.4635			−0.505877			−0.252939	−	0.967482i	$-0.581397\pi$
$607$	−12.4635			−0.505877			−0.252939	+	0.967482i	$0.581397\pi$
$608$	−16.4584	+	18.3609i	−0.667476	+	0.744631i
$609$	23.3656			0.946821
$610$	1.22132	−	5.78121i	0.0494499	−	0.234074i
$611$	47.7512	−	8.41982i	1.93181	−	0.340629i
$612$	0.829183	+	0.366708i	0.0335177	+	0.0148233i
$613$	29.2549	+	34.8646i	1.18159	+	1.40817i	0.892606	+	0.450837i	$0.148874\pi$
$613$	29.2549	+	34.8646i	1.18159	+	1.40817i	0.288988	+	0.957333i	$0.406681\pi$
$614$	−0.479878	+	14.2499i	−0.0193663	+	0.575081i
$615$	2.89633	−	5.01660i	0.116791	−	0.202289i
$616$	11.6188	+	8.37549i	0.468134	+	0.337458i
$617$	36.5681	−	13.3097i	1.47218	−	0.535828i	0.523486	−	0.852034i	$-0.324631\pi$
$617$	36.5681	−	13.3097i	1.47218	−	0.535828i	0.948691	+	0.316206i	$0.102409\pi$
$618$	11.0341	−	5.88454i	0.443856	−	0.236711i
$619$	−19.3984	+	11.1997i	−0.779689	+	0.450154i	−0.836320	−	0.548242i	$-0.815297\pi$
$619$	−19.3984	+	11.1997i	−0.779689	+	0.450154i	0.0566312	+	0.998395i	$0.481964\pi$
$620$	9.77442	+	2.41123i	0.392550	+	0.0968374i
$621$	−0.0134485	−	0.00237133i	−0.000539669	−	9.51582e-5i
$622$	−5.55697	−	4.99102i	−0.222814	−	0.200122i
$623$	5.62819	+	4.72262i	0.225489	+	0.189208i
$624$	15.2277	+	16.7438i	0.609596	+	0.670290i
$625$	−16.3768	−	5.96068i	−0.655073	−	0.238427i
$626$	2.98964	+	21.0822i	0.119490	+	0.842613i
$627$	−4.77430	+	7.57300i	−0.190667	+	0.302437i
$628$	−7.51744	−	25.9725i	−0.299979	−	1.03641i
$629$	0.0197673	−	0.0543102i	0.000788174	−	0.00216549i
$630$	0.782263	+	2.39741i	0.0311661	+	0.0955151i
$631$	22.9591	+	19.2650i	0.913987	+	0.766926i	0.972873	−	0.231339i	$-0.0743106\pi$
$631$	22.9591	+	19.2650i	0.913987	+	0.766926i	−0.0588866	+	0.998265i	$0.518755\pi$
$632$	−42.0388	−	20.3099i	−1.67221	−	0.807884i
$633$	3.08288	−	17.4839i	0.122533	−	0.694922i
$634$	−10.4991	+	26.0795i	−0.416972	+	1.03575i
$635$	3.14399	−	1.81518i	0.124765	−	0.0720333i
$636$	13.3297	−	9.73531i	0.528555	−	0.386030i
$637$	1.78179	+	4.89542i	0.0705969	+	0.193963i
$638$	21.6688	−	16.9729i	0.857875	−	0.671965i
$639$	0.391599	−	0.678270i	0.0154914	−	0.0268319i
$640$	5.93511	+	5.63246i	0.234606	+	0.222642i
$641$	−15.5908	+	13.0822i	−0.615798	+	0.516716i	−0.896480	−	0.443085i	$-0.853884\pi$
$641$	−15.5908	+	13.0822i	−0.615798	+	0.516716i	0.280681	+	0.959801i	$0.409440\pi$
$642$	4.43187	−	7.11214i	0.174912	−	0.280694i
$643$	−30.5279	+	5.38289i	−1.20390	+	0.212280i	−0.739384	−	0.673284i	$-0.764883\pi$
$643$	−30.5279	+	5.38289i	−1.20390	+	0.212280i	−0.464517	+	0.885564i	$0.653772\pi$
$644$	0.0671881	+	0.00453036i	0.00264758	+	0.000178521i
$645$		−	8.67544i		−	0.341595i
$646$	0.683503	−	2.70961i	0.0268921	−	0.106608i
$647$	−45.0696			−1.77187			−0.885934	−	0.463812i	$-0.846481\pi$
$647$	−45.0696			−1.77187			−0.885934	+	0.463812i	$0.846481\pi$
$648$	−0.207826	−	2.82078i	−0.00816417	−	0.110811i
$649$	−2.76716	−	15.6933i	−0.108620	−	0.616017i
$650$	30.4040	+	18.9460i	1.19254	+	0.743124i
$651$	11.0309	+	13.1461i	0.432336	+	0.515238i
$652$	34.8302	−	3.74841i	1.36406	−	0.146799i
$653$	35.6715	+	20.5950i	1.39594	+	0.805944i	0.993964	−	0.109708i	$-0.0349917\pi$
$653$	35.6715	+	20.5950i	1.39594	+	0.805944i	0.401972	+	0.915652i	$0.368325\pi$
$654$	6.08540	−	4.76664i	0.237958	−	0.186390i
$655$	−0.581039	+	0.211481i	−0.0227031	+	0.00826324i
$656$	19.5988	−	25.3442i	0.765207	−	0.989526i
$657$	3.08213	+	5.33841i	0.120245	+	0.208271i
$658$	27.7192	+	11.1592i	1.08061	+	0.435032i
$659$	10.9672	+	1.93382i	0.427222	+	0.0753308i	0.383125	−	0.923696i	$-0.374848\pi$
$659$	10.9672	+	1.93382i	0.427222	+	0.0753308i	0.0440970	+	0.999027i	$0.485959\pi$
$660$	2.46695	+	1.65507i	0.0960260	+	0.0644235i
$661$	12.1279	−	14.4535i	0.471721	−	0.562175i	−0.476750	−	0.879039i	$-0.658185\pi$
$661$	12.1279	−	14.4535i	0.471721	−	0.562175i	0.948471	+	0.316864i	$0.102630\pi$
$662$	1.65955	+	5.08603i	0.0645001	+	0.197674i
$663$	−2.41031	−	0.877281i	−0.0936086	−	0.0340708i
$664$	−37.8705	+	17.0306i	−1.46966	+	0.660915i
$665$	6.87743	−	3.62164i	0.266695	−	0.140441i
$666$	−0.178516	+	0.0253152i	−0.00691734	+	0.000980943i
$667$	0.0442613	−	0.121607i	0.00171380	−	0.00470863i
$668$	−15.2100	−	30.9892i	−0.588491	−	1.19901i
$669$	−5.07317	+	6.04597i	−0.196140	+	0.233751i
$670$	1.28556	+	1.15463i	0.0496654	+	0.0446072i
$671$	2.06036	−	11.6849i	0.0795395	−	0.451091i
$672$	2.50734	+	13.7204i	0.0967228	+	0.529277i
$673$	11.8989	+	20.6095i	0.458670	+	0.794439i	0.998891	−	0.0470839i	$-0.0149928\pi$
$673$	11.8989	+	20.6095i	0.458670	+	0.794439i	−0.540221	+	0.841523i	$0.681659\pi$
$674$	17.6952	+	33.1802i	0.681594	+	1.27805i
$675$	−1.53121	−	4.20696i	−0.0589362	−	0.161926i
$676$	−27.4220	−	26.3496i	−1.05469	−	1.01345i
$677$	−3.86235	−	2.22993i	−0.148442	−	0.0857031i	0.423939	−	0.905691i	$-0.360647\pi$
$677$	−3.86235	−	2.22993i	−0.148442	−	0.0857031i	−0.572381	+	0.819988i	$0.693980\pi$
$678$	−0.274087	+	8.13900i	−0.0105262	+	0.312576i
$679$	−4.14122	+	3.47489i	−0.158925	+	0.133354i
$680$	−0.892338	−	0.252275i	−0.0342196	−	0.00967430i
$681$	−2.12982	−	12.0788i	−0.0816148	−	0.462861i
$682$	19.7793	+	4.17853i	0.757390	+	0.160004i
$683$		−	6.10752i		−	0.233698i	−0.993150	−	0.116849i	$-0.962721\pi$
$683$		−	6.10752i		−	0.233698i	0.993150	−	0.116849i	$-0.0372793\pi$
$684$	−8.46201	+	2.09628i	−0.323553	+	0.0801533i
$685$		−	14.2170i		−	0.543202i
$686$	−5.70868	+	27.0224i	−0.217959	+	1.03172i
$687$	1.57920	+	8.95609i	0.0602502	+	0.341696i
$688$	6.44141	−	47.5479i	0.245576	−	1.81275i
$689$	−35.7724	+	30.0166i	−1.36282	+	1.14354i
$690$	0.0139592		0.000470088i	0.000531418		1.78959e-5i
$691$	23.1935	+	13.3908i	0.882322	+	0.509409i	0.871423	−	0.490532i	$-0.163197\pi$
$691$	23.1935	+	13.3908i	0.882322	+	0.509409i	0.0108986	+	0.999941i	$0.496531\pi$
$692$	3.21702	−	3.34795i	0.122293	−	0.127270i
$693$	1.73196	+	4.75851i	0.0657916	+	0.180761i
$694$	−23.3765	+	12.4668i	−0.887359	+	0.473233i
$695$	2.57940	+	4.46765i	0.0978422	+	0.169468i
$696$	26.6672	+	2.70229i	1.01082	+	0.102430i
$697$	−0.630505	+	3.57577i	−0.0238821	+	0.135442i
$698$	4.52769	−	5.04110i	0.171375	−	0.190808i
$699$	−9.44145	+	11.2519i	−0.357108	+	0.425585i
$700$	9.72721	+	19.8185i	0.367654	+	0.749068i
$701$	0.127078	−	0.349143i	0.00479966	−	0.0131870i	−0.937270	−	0.348605i	$-0.886655\pi$
$701$	0.127078	−	0.349143i	0.00479966	−	0.0131870i	0.942069	+	0.335418i	$0.108878\pi$
$702$	1.12350	+	7.92260i	0.0424037	+	0.299019i
$703$	0.169617	+	0.529210i	0.00639723	+	0.0199595i
$704$	12.2919	+	10.9027i	0.463268	+	0.410911i
$705$	5.82389	+	2.11972i	0.219340	+	0.0798333i
$706$	40.9493	−	13.3616i	1.54115	−	0.502869i
$707$	10.2443	−	12.2087i	0.385278	−	0.459157i
$708$	8.64550	−	12.8865i	0.324918	−	0.484304i
$709$	38.6284	+	6.81123i	1.45072	+	0.255801i	0.842812	−	0.538207i	$-0.180898\pi$
$709$	38.6284	+	6.81123i	1.45072	+	0.255801i	0.607907	+	0.794008i	$0.292009\pi$
$710$	−0.299153	+	0.743090i	−0.0112270	+	0.0278877i
$711$	−8.25332	−	14.2952i	−0.309524	−	0.536110i
$712$	5.87729	+	6.04085i	0.220261	+	0.226390i
$713$	0.0893153	−	0.0325081i	0.00334488	−	0.00121744i
$714$	−0.974730	−	1.24440i	−0.0364783	−	0.0465707i
$715$	−7.27842	−	4.20220i	−0.272197	−	0.157153i
$716$	9.25014	−	0.995495i	0.345694	−	0.0372034i
$717$	5.46880	+	6.51746i	0.204236	+	0.243399i
$718$	−17.2342	+	27.6569i	−0.643173	+	1.03215i
$719$	−3.27157	−	18.5540i	−0.122009	−	0.691946i	−0.983040	−	0.183393i	$-0.941292\pi$
$719$	−3.27157	−	18.5540i	−0.122009	−	0.691946i	0.861031	−	0.508553i	$-0.169819\pi$
$720$	0.615532	+	2.82664i	0.0229395	+	0.105343i
$721$	−21.8022			−0.811956
$722$	10.7632	+	24.6202i	0.400567	+	0.916268i
$723$			18.8267i			0.700173i
$724$	1.23031	−	18.2463i	0.0457243	−	0.678120i
$725$	41.7815	−	7.36721i	1.55173	−	0.273611i
$726$	−8.13997	−	5.07235i	−0.302103	−	0.188253i
$727$	−9.20622	+	7.72494i	−0.341440	+	0.286502i	−0.797342	−	0.603528i	$-0.793761\pi$
$727$	−9.20622	+	7.72494i	−0.341440	+	0.286502i	0.455902	+	0.890030i	$0.349317\pi$
$728$	−9.68879	−	38.2511i	−0.359090	−	1.41768i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−3.88776	−	4.96337i	−0.143892	−	0.183702i
$731$	1.85987	+	5.10996i	0.0687899	+	0.188999i
$732$	9.33072	−	6.81468i	0.344873	−	0.251878i
$733$	−12.6236	+	7.28824i	−0.466263	+	0.269197i	−0.714674	−	0.699457i	$-0.753425\pi$
$733$	−12.6236	+	7.28824i	−0.466263	+	0.269197i	0.248411	+	0.968655i	$0.420092\pi$
$734$	−2.89488	−	1.16542i	−0.106852	−	0.0430165i
$735$	−0.115630	+	0.655768i	−0.00426506	+	0.0241884i
$736$	0.0761580	+	0.0129410i	0.00280722	+	0.000477011i
$737$	2.65803	+	2.23035i	0.0979098	+	0.0821560i
$738$	10.7685	−	3.51369i	0.396392	−	0.129341i
$739$	14.7982	−	40.6578i	0.544361	−	1.49562i	−0.296856	−	0.954922i	$-0.595938\pi$
$739$	14.7982	−	40.6578i	0.544361	−	1.49562i	0.841217	−	0.540697i	$-0.181840\pi$
$740$	0.177140	−	0.0512712i	0.00651179	−	0.00188476i
$741$	23.4865	−	7.52767i	0.862799	−	0.276536i
$742$	−28.4928	+	4.04055i	−1.04601	+	0.148333i
$743$	42.1519	+	15.3421i	1.54640	+	0.562845i	0.967571	−	0.252600i	$-0.0812857\pi$
$743$	42.1519	+	15.3421i	1.54640	+	0.562845i	0.578834	+	0.815445i	$0.303508\pi$
$744$	11.0692	+	16.2795i	0.405818	+	0.596834i
$745$	−9.18821	−	7.70983i	−0.336630	−	0.282466i
$746$	5.24331	−	5.83787i	0.191971	−	0.213740i
$747$	−14.4578	−	2.54930i	−0.528983	−	0.0932740i
$748$	−1.80789	−	0.445985i	−0.0661030	−	0.0163068i
$749$	−12.6527	+	7.30507i	−0.462321	+	0.266921i
$750$	4.56119	+	8.55267i	0.166551	+	0.312299i
$751$	−28.7492	+	10.4639i	−1.04907	+	0.381832i	−0.808313	−	0.588753i	$-0.799619\pi$
$751$	−28.7492	+	10.4639i	−1.04907	+	0.381832i	−0.240761	+	0.970584i	$0.577397\pi$
$752$	30.3454	+	15.9418i	1.10658	+	0.581339i
$753$	−7.90895	+	13.6987i	−0.288218	+	0.499209i
$754$	−75.7871	−	2.55219i	−2.76000	−	0.0929453i
$755$	1.94225	+	2.31468i	0.0706856	+	0.0842399i
$756$	−1.99451	+	4.50989i	−0.0725395	+	0.164023i
$757$	−17.5021	+	3.08610i	−0.636126	+	0.112166i	−0.482405	−	0.875948i	$-0.660237\pi$
$757$	−17.5021	+	3.08610i	−0.636126	+	0.112166i	−0.153721	+	0.988114i	$0.549126\pi$
$758$	−17.5488	−	3.70732i	−0.637402	−	0.134656i
$759$	0.0280467			0.00101803
$760$	8.26808	−	3.33799i	0.299915	−	0.121082i
$761$	33.6060			1.21822			0.609108	−	0.793087i	$-0.291527\pi$
$761$	33.6060			1.21822			0.609108	+	0.793087i	$0.291527\pi$
$762$	6.94565	+	1.46732i	0.251614	+	0.0531554i
$763$	−13.2722	+	2.34024i	−0.480485	+	0.0847225i
$764$	31.2523	+	13.8214i	1.13067	+	0.500040i
$765$	−0.210741	−	0.251151i	−0.00761936	−	0.00908039i
$766$	9.57674	+	0.322504i	0.346022	+	0.0116525i
$767$	−21.9508	+	38.0199i	−0.792597	+	1.37282i
$768$	1.27483	+	15.9491i	0.0460015	+	0.575515i
$769$	11.4756	−	4.17679i	0.413822	−	0.150619i	−0.126715	−	0.991939i	$-0.540443\pi$
$769$	11.4756	−	4.17679i	0.413822	−	0.150619i	0.540537	+	0.841320i	$0.318221\pi$
$770$	−2.43722	−	4.57002i	−0.0878313	−	0.164692i
$771$	15.2083	−	8.78051i	0.547713	−	0.316222i
$772$	10.2505	−	41.5525i	0.368923	−	1.49551i
$773$	0.245601	+	0.0433061i	0.00883366	+	0.00155761i	0.178063	−	0.984019i	$-0.443017\pi$
$773$	0.245601	+	0.0433061i	0.00883366	+	0.00155761i	−0.169230	+	0.985577i	$0.554128\pi$
$774$	11.3356	−	12.6210i	0.407451	−	0.453654i
$775$	23.8701	+	20.0294i	0.857440	+	0.719478i
$776$	−5.12826	+	3.48696i	−0.184094	+	0.125175i
$777$	0.295391	+	0.107513i	0.0105971	+	0.00385702i
$778$	43.6398	−	6.18852i	1.56456	−	0.221869i
$779$	−16.2673	−	30.8914i	−0.582837	−	1.10680i
$780$	−2.27543	−	7.86153i	−0.0814736	−	0.281488i
$781$	−0.550152	+	1.51153i	−0.0196860	+	0.0540868i
$782$	−0.00832296	+	0.00271574i	−0.000297628	+	9.71147e-5i
$783$	7.25946	+	6.09141i	0.259432	+	0.217689i
$784$	−1.12064	+	3.50825i	−0.0400227	+	0.125294i
$785$	−1.69783	+	9.62886i	−0.0605981	+	0.343669i
$786$	−1.12162	−	0.451544i	−0.0400070	−	0.0161060i
$787$	−30.1787	+	17.4237i	−1.07575	+	0.621087i	−0.929748	−	0.368196i	$-0.879975\pi$
$787$	−30.1787	+	17.4237i	−1.07575	+	0.621087i	−0.146007	+	0.989284i	$0.546642\pi$
$788$	13.8797	+	19.0043i	0.494445	+	0.676999i
$789$	8.33441	+	22.8986i	0.296713	+	0.815211i
$790$	10.4106	+	13.2909i	0.370393	+	0.472868i
$791$	7.09901	−	12.2959i	0.252412	−	0.437190i
$792$	1.42635	+	5.63121i	0.0506832	+	0.200096i
$793$	−25.0406	+	21.0115i	−0.889217	+	0.746142i
$794$	43.0514	+	26.8271i	1.52784	+	0.952058i
$795$	−5.87815	+	1.03648i	−0.208476	+	0.0367600i
$796$	36.6796	+	2.47323i	1.30007	+	0.0876614i
$797$		−	28.1577i		−	0.997396i	−0.866776	−	0.498698i	$-0.833812\pi$
$797$		−	28.1577i		−	0.997396i	0.866776	−	0.498698i	$-0.166188\pi$
$798$	14.7375	+	3.71754i	0.521700	+	0.131599i
$799$	−3.88479			−0.137434
$800$	8.80962	+	23.7438i	0.311467	+	0.839471i
$801$	0.517439	+	2.93454i	0.0182828	+	0.103687i
$802$	5.46142	−	8.76432i	0.192849	−	0.309479i
$803$	−8.13782	−	9.69827i	−0.287177	−	0.342245i
$804$	0.361548	+	3.35951i	0.0127508	+	0.118481i
$805$	−0.0210887	−	0.0121755i	−0.000743278	−	0.000429132i
$806$	−34.3433	−	43.8449i	−1.20969	−	1.54437i
$807$	−3.94974	+	1.43759i	−0.139038	+	0.0506055i
$808$	13.1039	−	12.7491i	0.460992	−	0.448511i
$809$	−10.2691	−	17.7865i	−0.361041	−	0.625341i	0.627092	−	0.778946i	$-0.284245\pi$
$809$	−10.2691	−	17.7865i	−0.361041	−	0.625341i	−0.988132	+	0.153604i	$0.950912\pi$
$810$	−0.381964	+	0.948788i	−0.0134208	+	0.0333370i
$811$	11.3984	+	2.00984i	0.400251	+	0.0705751i	0.370151	−	0.928972i	$-0.379306\pi$
$811$	11.3984	+	2.00984i	0.400251	+	0.0705751i	0.0301008	+	0.999547i	$0.490417\pi$
$812$	−38.8068	−	26.0353i	−1.36185	−	0.913660i
$813$	−0.467039	+	0.556596i	−0.0163798	+	0.0195207i
$814$	0.352038	−	0.114868i	0.0123389	−	0.00402613i
$815$	−11.9037	−	4.33260i	−0.416969	−	0.151764i
$816$	−0.968542	−	1.53297i	−0.0339058	−	0.0536647i
$817$	−44.2313	−	27.8850i	−1.54746	−	0.975572i
$818$	3.31295	+	23.3620i	0.115835	+	0.816834i
$819$	4.77149	−	13.1096i	0.166729	−	0.458085i
$820$	−10.4002	+	5.10456i	−0.363190	+	0.178259i
$821$	−25.4687	+	30.3525i	−0.888865	+	1.05931i	0.109003	+	0.994041i	$0.465234\pi$
$821$	−25.4687	+	30.3525i	−0.888865	+	1.05931i	−0.997868	+	0.0652665i	$0.979210\pi$
$822$	18.5764	−	20.6828i	0.647926	−	0.721397i
$823$	−3.25863	+	18.4806i	−0.113589	+	0.644193i	0.873851	+	0.486194i	$0.161615\pi$
$823$	−3.25863	+	18.4806i	−0.113589	+	0.644193i	−0.987439	+	0.157998i	$0.949496\pi$
$824$	−24.8829	−	2.52148i	−0.866836	−	0.0878399i
$825$	4.59740	+	7.96292i	0.160061	+	0.277233i
$826$	−23.8722	+	12.7312i	−0.830620	+	0.442974i
$827$	2.37349	+	6.52111i	0.0825344	+	0.226761i	0.974095	−	0.226141i	$-0.0726109\pi$
$827$	2.37349	+	6.52111i	0.0825344	+	0.226761i	−0.891560	+	0.452902i	$0.850389\pi$
$828$	0.0196936	+	0.0189235i	0.000684402	+	0.000657637i
$829$	−42.5444	−	24.5630i	−1.47763	−	0.853110i	−0.477949	−	0.878387i	$-0.658620\pi$
$829$	−42.5444	−	24.5630i	−1.47763	−	0.853110i	−0.999680	+	0.0252776i	$0.991953\pi$
$830$	15.0069	+	0.505368i	0.520896	+	0.0175416i
$831$	−0.335832	+	0.281796i	−0.0116499	+	0.00977540i
$832$	−6.63399	−	44.7766i	−0.229992	−	1.55235i
$833$	−0.0724784	−	0.411046i	−0.00251123	−	0.0142419i
$834$	−2.08508	+	9.86987i	−0.0722005	+	0.341766i
$835$			12.4830i			0.431992i
$836$	16.3677	−	7.25783i	0.566088	−	0.251017i
$837$			6.96015i			0.240578i
$838$	6.04305	+	1.27664i	0.208754	+	0.0441007i
$839$	−2.61059	−	14.8054i	−0.0901274	−	0.511138i	−0.996132	−	0.0878701i	$-0.971994\pi$
$839$	−2.61059	−	14.8054i	−0.0901274	−	0.511138i	0.906004	−	0.423268i	$-0.139117\pi$
$840$	1.37211	−	4.85338i	0.0473424	−	0.167458i
$841$	−46.5794	+	39.0848i	−1.60619	+	1.34775i
$842$	1.36099	−	40.4145i	0.0469028	−	1.39278i
$843$	−24.2427	−	13.9965i	−0.834964	−	0.482067i
$844$	−24.6018	+	25.6030i	−0.846828	+	0.881292i
$845$	4.70345	+	12.9226i	0.161804	+	0.444552i
$846$	5.70289	+	10.6935i	0.196069	+	0.367649i
$847$	8.36077	+	14.4813i	0.287279	+	0.497583i
$848$	−32.9862	+	1.31621i	−1.13275	+	0.0451989i
$849$	−3.38911	+	19.2206i	−0.116314	+	0.659649i
$850$	−2.13534	−	1.91787i	−0.0732416	−	0.0657823i
$851$	0.00111911	−	0.00133371i	3.83627e−5	−	4.57189e-5i
$852$	−1.40616	+	0.690163i	−0.0481741	+	0.0236446i
$853$	13.0802	−	35.9375i	0.447857	−	1.23048i	−0.486356	−	0.873761i	$-0.661674\pi$
$853$	13.0802	−	35.9375i	0.447857	−	1.23048i	0.934213	−	0.356715i	$-0.116103\pi$
$854$	−19.9449	+	2.82837i	−0.682500	+	0.0967848i
$855$	3.08091	+	0.667740i	0.105365	+	0.0228362i
$856$	−15.2855	+	6.87396i	−0.522446	+	0.234947i
$857$	−9.11837	−	3.31881i	−0.311478	−	0.113369i	0.181551	−	0.983381i	$-0.441888\pi$
$857$	−9.11837	−	3.31881i	−0.311478	−	0.113369i	−0.493029	+	0.870013i	$0.664110\pi$
$858$	−5.09790	−	15.6236i	−0.174040	−	0.533381i
$859$	−7.04361	+	8.39425i	−0.240325	+	0.286408i	−0.872703	−	0.488252i	$-0.837635\pi$
$859$	−7.04361	+	8.39425i	−0.240325	+	0.286408i	0.632378	+	0.774660i	$0.282079\pi$
$860$	−9.66668	+	14.4086i	−0.329631	+	0.491330i
$861$	−19.4485	−	3.42929i	−0.662802	−	0.116870i
$862$	36.4332	+	14.6673i	1.24092	+	0.499569i
$863$	−8.47575	−	14.6804i	−0.288518	−	0.499727i	0.684938	−	0.728601i	$-0.259829\pi$
$863$	−8.47575	−	14.6804i	−0.288518	−	0.499727i	−0.973456	+	0.228874i	$0.926496\pi$
$864$	−2.79791	+	4.91647i	−0.0951869	+	0.167262i
$865$	−1.57772	+	0.574244i	−0.0536442	+	0.0195249i
$866$	−28.9706	+	22.6924i	−0.984460	+	0.771118i
$867$	−14.5445	−	8.39725i	−0.493956	−	0.285185i
$868$	−3.67252	−	34.1251i	−0.124654	−	1.15828i
$869$	21.7914	+	25.9700i	0.739223	+	0.880972i
$870$	−8.22609	−	5.12602i	−0.278891	−	0.173788i
$871$	−1.65994	−	9.41399i	−0.0562450	−	0.318981i
$872$	−15.4182	+	1.13596i	−0.522127	+	0.0384685i
$873$	−2.19254			−0.0742063
$874$	0.0472651	−	0.0696594i	0.00159877	−	0.00235626i
$875$		−	16.8992i		−	0.571296i
$876$	0.829404	−	12.3006i	0.0280230	−	0.415599i
$877$	−4.09907	+	0.722776i	−0.138416	+	0.0244064i	−0.242427	−	0.970170i	$-0.577943\pi$
$877$	−4.09907	+	0.722776i	−0.138416	+	0.0244064i	0.104011	+	0.994576i	$0.466832\pi$
$878$	−0.872234	+	1.39974i	−0.0294365	+	0.0472388i
$879$	3.50541	−	2.94139i	0.118235	−	0.0992105i
$880$	−2.25307	−	5.49765i	−0.0759509	−	0.185326i
$881$	12.8704	−	22.2922i	0.433615	−	0.751043i	−0.563567	−	0.826071i	$-0.690571\pi$
$881$	12.8704	−	22.2922i	0.433615	−	0.751043i	0.997181	+	0.0750276i	$0.0239045\pi$
$882$	−1.02507	+	0.802925i	−0.0345158	+	0.0270359i
$883$	−15.8239	−	43.4759i	−0.532518	−	1.46308i	−0.856065	−	0.516869i	$-0.827098\pi$
$883$	−15.8239	−	43.4759i	−0.532518	−	1.46308i	0.323547	−	0.946212i	$-0.395125\pi$
$884$	3.02565	+	4.14274i	0.101764	+	0.139335i
$885$	−4.85965	+	2.80572i	−0.163355	+	0.0943133i
$886$	−7.71899	+	19.1738i	−0.259325	+	0.644156i
$887$	−6.21295	+	35.2354i	−0.208610	+	1.18309i	0.683046	+	0.730376i	$0.260655\pi$
$887$	−6.21295	+	35.2354i	−0.208610	+	1.18309i	−0.891656	+	0.452713i	$0.850456\pi$
$888$	0.324696	+	0.156868i	0.0108961	+	0.00526414i
$889$	−9.48111	−	7.95560i	−0.317986	−	0.266822i
$890$	−0.945400	−	2.89738i	−0.0316899	−	0.0971204i
$891$	−0.702443	+	1.92995i	−0.0235327	+	0.0646556i
$892$	15.1625	−	4.38863i	0.507680	−	0.146942i
$893$	29.5267	−	22.8795i	0.988073	−	0.765632i
$894$	−3.29308	−	23.2219i	−0.110137	−	0.776657i
$895$	−3.16137	−	1.15064i	−0.105673	−	0.0384618i
$896$	11.1238	−	25.5814i	0.371620	−	0.854615i
$897$	−0.0591905	−	0.0496667i	−0.00197631	−	0.00165832i
$898$	35.5653	+	31.9431i	1.18683	+	1.06596i
$899$	−64.9562	−	11.4535i	−2.16641	−	0.381996i
$900$	−2.14453	+	8.69330i	−0.0714844	+	0.289777i
$901$	3.24011	−	1.87068i	0.107944	−	0.0623213i
$902$	−20.5272	+	10.9473i	−0.683481	+	0.364504i
$903$	−27.7928	+	10.1158i	−0.924887	+	0.336631i
$904$	9.52416	−	13.2123i	0.316769	−	0.439433i
$905$	−3.30652	+	5.72707i	−0.109913	+	0.190374i
$906$	−0.198862	+	5.90521i	−0.00660676	+	0.196187i
$907$	3.34569	+	3.98724i	0.111092	+	0.132394i	0.818725	−	0.574186i	$-0.194681\pi$
$907$	3.34569	+	3.98724i	0.111092	+	0.132394i	−0.707633	+	0.706580i	$0.750237\pi$
$908$	−9.92160	+	22.4343i	−0.329260	+	0.744507i
$909$	6.36564	−	1.12243i	0.211135	−	0.0372288i
$910$	−2.94930	+	13.9607i	−0.0977682	+	0.462792i
$911$	28.7891			0.953826			0.476913	−	0.878950i	$-0.341756\pi$
$911$	28.7891			0.953826			0.476913	+	0.878950i	$0.341756\pi$
$912$	16.3899	+	5.94726i	0.542725	+	0.196933i
$913$	30.1516			0.997872
$914$	−2.45596	+	11.6254i	−0.0812359	+	0.384535i
$915$	−4.11468	+	0.725530i	−0.136027	+	0.0239853i
$916$	7.35658	−	16.6344i	0.243068	−	0.549615i
$917$	1.35501	+	1.61484i	0.0447463	+	0.0533266i
$918$	0.0215773	−	0.640737i	0.000712157	−	0.0211475i
$919$	−19.3725	+	33.5542i	−0.639040	+	1.10685i	0.346603	+	0.938012i	$0.387335\pi$
$919$	−19.3725	+	33.5542i	−0.639040	+	1.10685i	−0.985644	+	0.168839i	$0.945998\pi$
$920$	−0.0226604	−	0.0163349i	−0.000747091	−	0.000538547i
$921$	9.47392	−	3.44823i	0.312176	−	0.113623i
$922$	17.0126	−	9.07293i	0.560281	−	0.298801i
$923$	3.83777	−	2.21574i	0.126322	−	0.0729318i
$924$	2.42569	−	9.83303i	0.0797994	−	0.323483i
$925$	0.562107	+	0.0991146i	0.0184820	+	0.00325887i
$926$	−10.5159	−	9.44491i	−0.345574	−	0.310379i
$927$	−6.77373	−	5.68384i	−0.222479	−	0.186682i
$928$	−41.2792	−	34.2022i	−1.35506	−	1.12274i
$929$	−47.6013	−	17.3254i	−1.56175	−	0.568429i	−0.590611	−	0.806956i	$-0.701113\pi$
$929$	−47.6013	−	17.3254i	−1.56175	−	0.568429i	−0.971136	+	0.238527i	$0.923336\pi$
$930$	−0.999505	−	7.04824i	−0.0327751	−	0.231121i
$931$	2.97173	+	2.69733i	0.0973947	+	0.0884014i
$932$	28.2183	−	8.16748i	0.924322	−	0.267535i
$933$	−1.80641	+	4.96306i	−0.0591391	+	0.162483i
$934$	8.00739	+	24.5403i	0.262010	+	0.802984i
$935$	0.515816	+	0.432821i	0.0168690	+	0.0141548i
$936$	6.96186	−	14.4101i	0.227556	−	0.471010i
$937$	6.85759	−	38.8913i	0.224028	−	1.27052i	−0.640507	−	0.767952i	$-0.721276\pi$
$937$	6.85759	−	38.8913i	0.224028	−	1.27052i	0.864535	−	0.502572i	$-0.167613\pi$
$938$	2.20001	−	5.46476i	0.0718327	−	0.178431i
$939$	13.0393	−	7.52825i	0.425522	−	0.245675i
$940$	−7.31069	−	10.0099i	−0.238448	−	0.326486i
$941$	20.5022	+	56.3292i	0.668351	+	1.83628i	0.534280	+	0.845308i	$0.320583\pi$
$941$	20.5022	+	56.3292i	0.668351	+	1.83628i	0.134071	+	0.990972i	$0.457195\pi$
$942$	−15.0514	+	11.7896i	−0.490402	+	0.384127i
$943$	−0.0546889	+	0.0947240i	−0.00178092	+	0.00308464i
$944$	−28.7178	+	11.7692i	−0.934684	+	0.383056i
$945$	1.36600	−	1.14621i	0.0444360	−	0.0372862i
$946$	−18.4264	+	29.5701i	−0.599092	+	0.961406i
$947$	26.4104	−	4.65687i	0.858224	−	0.151328i	0.272815	−	0.962066i	$-0.412045\pi$
$947$	26.4104	−	4.65687i	0.858224	−	0.151328i	0.585409	+	0.810738i	$0.300934\pi$
$948$	−2.22098	+	32.9385i	−0.0721339	+	1.06979i
$949$			34.8785i			1.13220i
$950$	27.5252	+	2.00083i	0.893034	+	0.0649155i
$951$	19.8793			0.644630
$952$	0.232293	+	3.15287i	0.00752866	+	0.102185i
$953$	8.21216	+	46.5735i	0.266018	+	1.50866i	0.766120	+	0.642697i	$0.222185\pi$
$953$	8.21216	+	46.5735i	0.266018	+	1.50866i	−0.500102	+	0.865966i	$0.666704\pi$
$954$	−9.90582	−	6.17273i	−0.320713	−	0.199850i
$955$	−7.94292	−	9.46600i	−0.257027	−	0.306313i
$956$	−1.82073	−	16.9182i	−0.0588865	−	0.547174i
$957$	−16.8555	−	9.73150i	−0.544860	−	0.314575i
$958$	19.7398	−	15.4620i	0.637765	−	0.499555i
$959$	−45.5458	+	16.5773i	−1.47075	+	0.535309i
$960$	2.12730	−	5.38049i	0.0686583	−	0.173655i
$961$	−8.72182	−	15.1066i	−0.281349	−	0.487311i
$962$	−0.946367	−	0.380989i	−0.0305121	−	0.0122836i
$963$	−5.83552	−	1.02896i	−0.188047	−	0.0331578i
$964$	20.9778	−	31.2684i	0.675650	−	1.00709i
$965$	−9.94793	+	11.8555i	−0.320235	+	0.381642i
$966$	−0.0147708	−	0.0452682i	−0.000475242	−	0.00145648i
$967$	50.8763	+	18.5175i	1.63607	+	0.595481i	0.986346	−	0.164688i	$-0.0526616\pi$
$967$	50.8763	+	18.5175i	1.63607	+	0.595481i	0.649726	+	0.760169i	$0.274884\pi$
$968$	7.86736	+	17.4945i	0.252867	+	0.562293i
$969$	−1.95786	+	0.267190i	−0.0628954	+	0.00858336i
$970$	2.22029	−	0.314858i	0.0712893	−	0.0101095i
$971$	13.2313	−	36.3527i	0.424613	−	1.16661i	−0.524427	−	0.851456i	$-0.675720\pi$
$971$	13.2313	−	36.3527i	0.424613	−	1.16661i	0.949039	−	0.315158i	$-0.102058\pi$
$972$	−1.79540	+	0.881210i	−0.0575875	+	0.0282648i
$973$	11.3050	−	13.4728i	0.362422	−	0.431918i
$974$	−7.72171	−	6.93529i	−0.247420	−	0.222221i
$975$	4.39875	−	24.9465i	0.140873	−	0.798928i
$976$	−23.0903	+	0.921345i	−0.739101	+	0.0294915i
$977$	21.0792	+	36.5102i	0.674382	+	1.16806i	0.976649	+	0.214841i	$0.0689233\pi$
$977$	21.0792	+	36.5102i	0.674382	+	1.16806i	−0.302267	+	0.953223i	$0.597743\pi$
$978$	−11.6564	−	21.8569i	−0.372731	−	0.698907i
$979$	−2.09315	−	5.75088i	−0.0668973	−	0.183799i
$980$	0.922738	−	0.960291i	0.0294758	−	0.0306754i
$981$	−4.73364	−	2.73297i	−0.151133	−	0.0872570i
$982$	1.60231	−	47.5804i	0.0511316	−	1.51835i
$983$	13.3372	−	11.1912i	0.425390	−	0.356944i	−0.404819	−	0.914397i	$-0.632666\pi$
$983$	13.3372	−	11.1912i	0.425390	−	0.356944i	0.830209	+	0.557452i	$0.188221\pi$
$984$	−21.8000	−	6.16312i	−0.694957	−	0.196473i
$985$	−1.47772	−	8.38054i	−0.0470839	−	0.267026i
$986$	5.94422	+	1.25576i	0.189303	+	0.0399915i
$987$		−	21.1292i		−	0.672549i
$988$	−47.3954	−	13.6677i	−1.50785	−	0.434828i
$989$			0.163811i			0.00520888i
$990$	0.434186	−	2.05525i	0.0137993	−	0.0653200i
$991$	5.91198	+	33.5285i	0.187800	+	1.06507i	0.922304	+	0.386464i	$0.126304\pi$
$991$	5.91198	+	33.5285i	0.187800	+	1.06507i	−0.734504	+	0.678604i	$0.762585\pi$
$992$	−0.244804	−	39.3718i	−0.00777255	−	1.25006i
$993$	2.89793	−	2.43165i	0.0919629	−	0.0771660i
$994$	2.72940	+	0.0919146i	0.0865712	+	0.00291535i
$995$	−11.5128	−	6.64692i	−0.364980	−	0.210722i
$996$	21.1717	+	20.3437i	0.670850	+	0.644616i
$997$	3.32012	+	9.12194i	0.105149	+	0.288895i	0.981099	−	0.193508i	$-0.0619865\pi$
$997$	3.32012	+	9.12194i	0.105149	+	0.288895i	−0.875950	+	0.482403i	$0.839764\pi$
$998$	−52.6504	+	28.0788i	−1.66662	+	0.888818i
$999$	0.0637463	+	0.110412i	0.00201684	+	0.00349328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.61.16	✓	240
8.5	even	2	inner	456.2.bk.a.61.26	yes	240
19.5	even	9	inner	456.2.bk.a.157.26	yes	240
152.5	even	18	inner	456.2.bk.a.157.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.16	✓	240	1.1	even	1	trivial
456.2.bk.a.61.26	yes	240	8.5	even	2	inner
456.2.bk.a.157.16	yes	240	152.5	even	18	inner
456.2.bk.a.157.26	yes	240	19.5	even	9	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292311 + 1.38367i) q^{2} +(0.984808 - 0.173648i) q^{3} +(-1.82911 - 0.808927i) q^{4} +(0.464877 + 0.554019i) q^{5} +(-0.0475977 + 1.41341i) q^{6} +(1.23281 - 2.13529i) q^{7} +(1.65396 - 2.29443i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.902471 + 0.481293i) q^{10} +(-1.77865 + 1.02690i) q^{11} +(-1.94179 - 0.479016i) q^{12} +(5.57221 + 0.982531i) q^{13} +(2.59418 + 2.32998i) q^{14} +(0.554019 + 0.464877i) q^{15} +(2.69128 + 2.95923i) q^{16} +(-0.425987 - 0.155047i) q^{17} +(0.198562 + 1.40020i) q^{18} +(4.15091 - 1.33041i) q^{19} +(-0.402150 - 1.38941i) q^{20} +(0.843292 - 2.31692i) q^{21} +(-0.900981 - 2.76124i) q^{22} +(-0.0104611 - 0.00877787i) q^{23} +(1.23041 - 2.54678i) q^{24} +(0.777415 - 4.40894i) q^{25} +(-2.98832 + 7.42292i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.98224 + 2.90842i) q^{28} +(3.24117 + 8.90505i) q^{29} +(-0.805184 + 0.630693i) q^{30} +(-3.48007 + 6.02766i) q^{31} +(-4.88130 + 2.85883i) q^{32} +(-1.57331 + 1.32016i) q^{33} +(0.339055 - 0.544106i) q^{34} +(1.75610 - 0.309647i) q^{35} +(-1.99547 - 0.134550i) q^{36} +0.127493i q^{37} +(0.627494 + 6.13239i) q^{38} +5.65817 q^{39} +(2.04005 - 0.150304i) q^{40} +(-1.39084 - 7.88786i) q^{41} +(2.95937 + 1.84410i) q^{42} +(-7.71060 - 9.18914i) q^{43} +(4.08403 - 0.439521i) q^{44} +(0.626327 + 0.361610i) q^{45} +(0.0152036 - 0.0119088i) q^{46} +(8.05271 - 2.93095i) q^{47} +(3.16425 + 2.44694i) q^{48} +(0.460360 + 0.797367i) q^{49} +(5.87329 + 2.36447i) q^{50} +(-0.446439 - 0.0787193i) q^{51} +(-9.39738 - 6.30467i) q^{52} +(-5.30500 + 6.32226i) q^{53} +(0.438688 + 1.34445i) q^{54} +(-1.39578 - 0.508021i) q^{55} +(-2.86026 - 6.36028i) q^{56} +(3.85682 - 2.03099i) q^{57} +(-13.2691 + 1.88168i) q^{58} +(-2.65372 + 7.29104i) q^{59} +(-0.637309 - 1.29847i) q^{60} +(-3.71349 + 4.42556i) q^{61} +(-7.32306 - 6.57724i) q^{62} +(0.428150 - 2.42816i) q^{63} +(-2.52883 - 7.58980i) q^{64} +(2.04605 + 3.54387i) q^{65} +(-1.36678 - 2.56284i) q^{66} +(-0.577827 - 1.58757i) q^{67} +(0.653755 + 0.628190i) q^{68} +(-0.0118264 - 0.00682797i) q^{69} +(-0.0848757 + 2.52038i) q^{70} +(0.599965 - 0.503430i) q^{71} +(0.769472 - 2.72175i) q^{72} +(1.07041 + 6.07061i) q^{73} +(-0.176408 - 0.0372675i) q^{74} -4.47695i q^{75} +(-8.66866 - 0.924319i) q^{76} +5.06390i q^{77} +(-1.65395 + 7.82907i) q^{78} +(-2.86635 - 16.2559i) q^{79} +(-0.388357 + 2.86670i) q^{80} +(0.766044 - 0.642788i) q^{81} +(11.3208 + 0.381236i) q^{82} +(-12.7140 - 7.34042i) q^{83} +(-3.41669 + 3.55575i) q^{84} +(-0.112133 - 0.308083i) q^{85} +(14.9687 - 7.98287i) q^{86} +(4.73828 + 8.20694i) q^{87} +(-0.585653 + 5.77944i) q^{88} +(-0.517439 + 2.93454i) q^{89} +(-0.683433 + 0.760930i) q^{90} +(8.96746 - 10.6870i) q^{91} +(0.0120338 + 0.0245179i) q^{92} +(-2.38051 + 6.54040i) q^{93} +(1.70158 + 11.9991i) q^{94} +(2.66673 + 1.68120i) q^{95} +(-4.31071 + 3.66303i) q^{96} +(-2.06031 - 0.749893i) q^{97} +(-1.23786 + 0.403909i) q^{98} +(-1.32016 + 1.57331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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