LMFDB - Embedded newform 550.2.l.d.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(181,550)] 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("550.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,12,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	550.191
Dual form			550.2.l.d.311.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} -3.34776 q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.814715 - 2.08236i) q^{5} +(1.03451 + 3.18391i) q^{6} +(-1.27708 - 3.93046i) q^{7} +(0.809017 + 0.587785i) q^{8} +8.20748 q^{9} +(-2.23221 - 0.131355i) q^{10} +(1.39097 - 3.01085i) q^{11} +(2.70839 - 1.96776i) q^{12} +4.03985 q^{13} +(-3.34345 + 2.42916i) q^{14} +(-2.72747 + 6.97125i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.959041 - 2.95163i) q^{17} +(-2.53625 - 7.80578i) q^{18} +(-1.27041 - 0.923006i) q^{19} +(0.564864 + 2.16355i) q^{20} +(4.27537 + 13.1582i) q^{21} +(-3.29332 - 0.392489i) q^{22} +(-0.580276 - 0.421595i) q^{23} +(-2.70839 - 1.96776i) q^{24} +(-3.67248 - 3.39307i) q^{25} +(-1.24838 - 3.84212i) q^{26} -17.4334 q^{27} +(3.34345 + 2.42916i) q^{28} +(-1.02795 + 0.746846i) q^{29} +(7.47289 + 0.439744i) q^{30} +(1.93176 - 1.40351i) q^{31} -1.00000 q^{32} +(-4.65663 + 10.0796i) q^{33} +(-2.51080 + 1.82421i) q^{34} +(-9.22511 - 0.542854i) q^{35} +(-6.63999 + 4.82423i) q^{36} +(-6.78083 - 4.92656i) q^{37} +(-0.485253 + 1.49346i) q^{38} -13.5244 q^{39} +(1.88310 - 1.20579i) q^{40} +(2.42568 + 7.46546i) q^{41} +(11.1931 - 8.13223i) q^{42} -1.98798 q^{43} +(0.644412 + 3.25342i) q^{44} +(6.68676 - 17.0910i) q^{45} +(-0.221646 + 0.682156i) q^{46} +13.0062 q^{47} +(-1.03451 + 3.18391i) q^{48} +(-8.15446 + 5.92456i) q^{49} +(-2.09214 + 4.54125i) q^{50} +(3.21064 + 9.88133i) q^{51} +(-3.26831 + 2.37456i) q^{52} +(-1.88559 + 5.80323i) q^{53} +(5.38721 + 16.5801i) q^{54} +(-5.13643 - 5.34949i) q^{55} +(1.27708 - 3.93046i) q^{56} +(4.25302 + 3.09000i) q^{57} +(1.02795 + 0.746846i) q^{58} +(-0.296335 - 0.215300i) q^{59} +(-1.89103 - 7.24302i) q^{60} +6.35337 q^{61} +(-1.93176 - 1.40351i) q^{62} +(-10.4816 - 32.2592i) q^{63} +(0.309017 + 0.951057i) q^{64} +(3.29133 - 8.41243i) q^{65} +(11.0252 + 1.31396i) q^{66} +(-3.73009 + 11.4800i) q^{67} +(2.51080 + 1.82421i) q^{68} +(1.94262 + 1.41140i) q^{69} +(2.33443 + 8.94135i) q^{70} +(-6.08820 - 4.42333i) q^{71} +(6.63999 + 4.82423i) q^{72} +(3.37033 - 10.3728i) q^{73} +(-2.59005 + 7.97135i) q^{74} +(12.2946 + 11.3592i) q^{75} +1.57031 q^{76} +(-13.6104 - 1.62205i) q^{77} +(4.17928 + 12.8625i) q^{78} +(-0.768966 + 2.36664i) q^{79} +(-1.72868 - 1.41833i) q^{80} +33.7403 q^{81} +(6.35050 - 4.61391i) q^{82} +(1.58810 + 4.88768i) q^{83} +(-11.1931 - 8.13223i) q^{84} +(-6.92770 - 0.407662i) q^{85} +(0.614321 + 1.89069i) q^{86} +(3.44131 - 2.50026i) q^{87} +(2.89505 - 1.61823i) q^{88} +(-6.79755 - 4.93871i) q^{89} +(-18.3208 - 1.07809i) q^{90} +(-5.15923 - 15.8785i) q^{91} +0.717261 q^{92} +(-6.46707 + 4.69860i) q^{93} +(-4.01914 - 12.3697i) q^{94} +(-2.95706 + 1.89347i) q^{95} +3.34776 q^{96} +(-0.562674 + 1.73173i) q^{97} +(8.15446 + 5.92456i) q^{98} +(11.4164 - 24.7115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 22 q^{3} - 12 q^{4} - q^{5} - 3 q^{6} + 11 q^{7} + 12 q^{8} + 70 q^{9} + 6 q^{10} + 3 q^{11} + 8 q^{12} - 34 q^{13} - q^{14} + 7 q^{15} - 12 q^{16} - 9 q^{17} + 10 q^{18} - 6 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) $ 48 * q + 12 * q^2 - 22 * q^3 - 12 * q^4 - q^5 - 3 * q^6 + 11 * q^7 + 12 * q^8 + 70 * q^9 + 6 * q^10 + 3 * q^11 + 8 * q^12 - 34 * q^13 - q^14 + 7 * q^15 - 12 * q^16 - 9 * q^17 + 10 * q^18 - 6 * q^19 + 19 * q^20 - 15 * q^21 - 8 * q^22 + 14 * q^23 - 8 * q^24 + 7 * q^25 - 16 * q^26 - 34 * q^27 + q^28 - q^29 - 12 * q^30 + 17 * q^31 - 48 * q^32 + 4 * q^34 - 41 * q^35 - 25 * q^36 - 23 * q^37 + q^38 - 20 * q^39 + 6 * q^40 + 29 * q^41 + 22 * q^43 + 13 * q^44 + 62 * q^45 - 9 * q^46 - 52 * q^47 + 3 * q^48 - 23 * q^49 - 2 * q^50 + 4 * q^51 + q^52 + 44 * q^53 - 11 * q^54 - 7 * q^55 - 11 * q^56 - 5 * q^57 + q^58 - 18 * q^59 + 2 * q^60 + 16 * q^61 - 17 * q^62 - 13 * q^63 - 12 * q^64 - 2 * q^65 + 20 * q^67 - 4 * q^68 - 2 * q^69 - 59 * q^70 + 39 * q^71 + 25 * q^72 - 42 * q^73 - 37 * q^74 + 20 * q^75 + 14 * q^76 - 13 * q^77 - 15 * q^78 + 53 * q^79 - 6 * q^80 + 56 * q^81 + 36 * q^82 + 14 * q^83 + 6 * q^85 + 13 * q^86 - 18 * q^87 + 17 * q^88 - 8 * q^89 + 28 * q^90 - 5 * q^91 - 46 * q^92 + 15 * q^93 - 13 * q^94 - 24 * q^95 + 22 * q^96 - 16 * q^97 + 23 * q^98 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−3.34776			−1.93283			−0.966414	−	0.256989i	$-0.917269\pi$
$3$	−3.34776			−1.93283			−0.966414	+	0.256989i	$0.917269\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.814715	−	2.08236i	0.364352	−	0.931261i
$5$	0.814715	−	2.08236i	0.364352	−	0.931261i
$6$	1.03451	+	3.18391i	0.422339	+	1.29982i
$7$	−1.27708	−	3.93046i	−0.482692	−	1.48557i	−0.835295	−	0.549801i	$-0.814703\pi$
$7$	−1.27708	−	3.93046i	−0.482692	−	1.48557i	0.352603	−	0.935773i	$-0.385297\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	8.20748			2.73583
$10$	−2.23221	−	0.131355i	−0.705886	−	0.0415380i
$11$	1.39097	−	3.01085i	0.419394	−	0.907804i
$11$	1.39097	−	3.01085i	0.419394	−	0.907804i
$12$	2.70839	−	1.96776i	0.781846	−	0.568044i
$13$	4.03985			1.12045			0.560226	−	0.828340i	$-0.310714\pi$
$13$	4.03985			1.12045			0.560226	+	0.828340i	$0.310714\pi$
$14$	−3.34345	+	2.42916i	−0.893574	+	0.649220i
$15$	−2.72747	+	6.97125i	−0.704230	+	1.79997i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.959041	−	2.95163i	−0.232602	−	0.715874i	−0.997430	−	0.0716408i	$-0.977176\pi$
$17$	−0.959041	−	2.95163i	−0.232602	−	0.715874i	0.764829	−	0.644234i	$-0.222824\pi$
$18$	−2.53625	−	7.80578i	−0.597800	−	1.83984i
$19$	−1.27041	−	0.923006i	−0.291452	−	0.211752i	0.432445	−	0.901660i	$-0.357651\pi$
$19$	−1.27041	−	0.923006i	−0.291452	−	0.211752i	−0.723897	+	0.689908i	$0.757651\pi$
$20$	0.564864	+	2.16355i	0.126307	+	0.483783i
$21$	4.27537	+	13.1582i	0.932962	+	2.87136i
$22$	−3.29332	−	0.392489i	−0.702138	−	0.0836790i
$23$	−0.580276	−	0.421595i	−0.120996	−	0.0879087i	0.525642	−	0.850706i	$-0.323825\pi$
$23$	−0.580276	−	0.421595i	−0.120996	−	0.0879087i	−0.646637	+	0.762797i	$0.723825\pi$
$24$	−2.70839	−	1.96776i	−0.552848	−	0.401668i
$25$	−3.67248	−	3.39307i	−0.734495	−	0.678614i
$26$	−1.24838	−	3.84212i	−0.244828	−	0.753502i
$27$	−17.4334			−3.35505
$28$	3.34345	+	2.42916i	0.631853	+	0.459068i
$29$	−1.02795	+	0.746846i	−0.190885	+	0.138686i	−0.679123	−	0.734025i	$-0.737640\pi$
$29$	−1.02795	+	0.746846i	−0.190885	+	0.138686i	0.488238	+	0.872710i	$0.337640\pi$
$30$	7.47289	+	0.439744i	1.36436	+	0.0802858i
$31$	1.93176	−	1.40351i	0.346955	−	0.252078i	−0.400636	−	0.916238i	$-0.631211\pi$
$31$	1.93176	−	1.40351i	0.346955	−	0.252078i	0.747590	+	0.664160i	$0.231211\pi$
$32$	−1.00000			−0.176777
$33$	−4.65663	+	10.0796i	−0.810616	+	1.75463i
$34$	−2.51080	+	1.82421i	−0.430599	+	0.312849i
$35$	−9.22511	−	0.542854i	−1.55933	−	0.0917590i
$36$	−6.63999	+	4.82423i	−1.10666	+	0.804039i
$37$	−6.78083	−	4.92656i	−1.11476	−	0.809922i	−0.131355	−	0.991335i	$-0.541933\pi$
$37$	−6.78083	−	4.92656i	−1.11476	−	0.809922i	−0.983407	+	0.181413i	$0.941933\pi$
$38$	−0.485253	+	1.49346i	−0.0787185	+	0.242270i
$39$	−13.5244			−2.16564
$40$	1.88310	−	1.20579i	0.297744	−	0.190652i
$41$	2.42568	+	7.46546i	0.378827	+	1.16591i	0.940860	+	0.338795i	$0.110019\pi$
$41$	2.42568	+	7.46546i	0.378827	+	1.16591i	−0.562034	+	0.827114i	$0.689981\pi$
$42$	11.1931	−	8.13223i	1.72713	−	1.25483i
$43$	−1.98798			−0.303165			−0.151582	−	0.988445i	$-0.548437\pi$
$43$	−1.98798			−0.303165			−0.151582	+	0.988445i	$0.548437\pi$
$44$	0.644412	+	3.25342i	0.0971488	+	0.490471i
$45$	6.68676	−	17.0910i	0.996803	−	2.54777i
$46$	−0.221646	+	0.682156i	−0.0326799	+	0.100578i
$47$	13.0062			1.89715			0.948576	−	0.316548i	$-0.102524\pi$
$47$	13.0062			1.89715			0.948576	+	0.316548i	$0.102524\pi$
$48$	−1.03451	+	3.18391i	−0.149319	+	0.459557i
$49$	−8.15446	+	5.92456i	−1.16492	+	0.846366i
$50$	−2.09214	+	4.54125i	−0.295873	+	0.642230i
$51$	3.21064	+	9.88133i	0.449579	+	1.38366i
$52$	−3.26831	+	2.37456i	−0.453232	+	0.329293i
$53$	−1.88559	+	5.80323i	−0.259005	+	0.797136i	0.734009	+	0.679140i	$0.237647\pi$
$53$	−1.88559	+	5.80323i	−0.259005	+	0.797136i	−0.993014	+	0.117996i	$0.962353\pi$
$54$	5.38721	+	16.5801i	0.733106	+	2.25627i
$55$	−5.13643	−	5.34949i	−0.692596	−	0.721325i
$56$	1.27708	−	3.93046i	0.170658	−	0.525230i
$57$	4.25302	+	3.09000i	0.563326	+	0.409281i
$58$	1.02795	+	0.746846i	0.134976	+	0.0980657i
$59$	−0.296335	−	0.215300i	−0.0385796	−	0.0280297i	0.568328	−	0.822802i	$-0.307590\pi$
$59$	−0.296335	−	0.215300i	−0.0385796	−	0.0280297i	−0.606908	+	0.794772i	$0.707590\pi$
$60$	−1.89103	−	7.24302i	−0.244131	−	0.935070i
$61$	6.35337			0.813466			0.406733	−	0.913547i	$-0.366668\pi$
$61$	6.35337			0.813466			0.406733	+	0.913547i	$0.366668\pi$
$62$	−1.93176	−	1.40351i	−0.245334	−	0.178246i
$63$	−10.4816	−	32.2592i	−1.32056	−	4.06427i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	3.29133	−	8.41243i	0.408239	−	1.04343i
$66$	11.0252	+	1.31396i	1.35711	+	0.161737i
$67$	−3.73009	+	11.4800i	−0.455703	+	1.40251i	0.414605	+	0.910002i	$0.363920\pi$
$67$	−3.73009	+	11.4800i	−0.455703	+	1.40251i	−0.870308	+	0.492508i	$0.836080\pi$
$68$	2.51080	+	1.82421i	0.304480	+	0.221217i
$69$	1.94262	+	1.41140i	0.233864	+	0.169912i
$70$	2.33443	+	8.94135i	0.279018	+	1.06870i
$71$	−6.08820	−	4.42333i	−0.722536	−	0.524953i	0.164657	−	0.986351i	$-0.447348\pi$
$71$	−6.08820	−	4.42333i	−0.722536	−	0.524953i	−0.887193	+	0.461398i	$0.847348\pi$
$72$	6.63999	+	4.82423i	0.782530	+	0.568541i
$73$	3.37033	−	10.3728i	0.394467	−	1.21404i	−0.534909	−	0.844910i	$-0.679654\pi$
$73$	3.37033	−	10.3728i	0.394467	−	1.21404i	0.929376	−	0.369135i	$-0.120346\pi$
$74$	−2.59005	+	7.97135i	−0.301087	+	0.926650i
$75$	12.2946	+	11.3592i	1.41965	+	1.31164i
$76$	1.57031			0.180127
$77$	−13.6104	−	1.62205i	−1.55105	−	0.184850i
$78$	4.17928	+	12.8625i	0.473210	+	1.45639i
$79$	−0.768966	+	2.36664i	−0.0865155	+	0.266267i	−0.984950	−	0.172841i	$-0.944705\pi$
$79$	−0.768966	+	2.36664i	−0.0865155	+	0.266267i	0.898434	+	0.439108i	$0.144705\pi$
$80$	−1.72868	−	1.41833i	−0.193273	−	0.158574i
$81$	33.7403			3.74892
$82$	6.35050	−	4.61391i	0.701295	−	0.509521i
$83$	1.58810	+	4.88768i	0.174317	+	0.536492i	0.999602	−	0.0282246i	$-0.00898536\pi$
$83$	1.58810	+	4.88768i	0.174317	+	0.536492i	−0.825285	+	0.564717i	$0.808985\pi$
$84$	−11.1931	−	8.13223i	−1.22126	−	0.887299i
$85$	−6.92770	−	0.407662i	−0.751415	−	0.0442172i
$86$	0.614321	+	1.89069i	0.0662439	+	0.203878i
$87$	3.44131	−	2.50026i	0.368947	−	0.268056i
$88$	2.89505	−	1.61823i	0.308613	−	0.172504i
$89$	−6.79755	−	4.93871i	−0.720539	−	0.523502i	0.166017	−	0.986123i	$-0.446909\pi$
$89$	−6.79755	−	4.93871i	−0.720539	−	0.523502i	−0.886556	+	0.462621i	$0.846909\pi$
$90$	−18.3208	−	1.07809i	−1.93118	−	0.113641i
$91$	−5.15923	−	15.8785i	−0.540834	−	1.66452i
$92$	0.717261			0.0747796
$93$	−6.46707	+	4.69860i	−0.670604	+	0.487223i
$94$	−4.01914	−	12.3697i	−0.414543	−	1.27583i
$95$	−2.95706	+	1.89347i	−0.303388	+	0.194266i
$96$	3.34776			0.341679
$97$	−0.562674	+	1.73173i	−0.0571308	+	0.175831i	−0.975550	−	0.219779i	$-0.929467\pi$
$97$	−0.562674	+	1.73173i	−0.0571308	+	0.175831i	0.918419	+	0.395609i	$0.129467\pi$
$98$	8.15446	+	5.92456i	0.823725	+	0.598471i
$99$	11.4164	−	24.7115i	1.14739	−	2.48360i
$100$	4.96549	+	0.586422i	0.496549	+	0.0586422i
$101$	−3.67338	−	2.66887i	−0.365515	−	0.265562i	0.389834	−	0.920885i	$-0.372533\pi$
$101$	−3.67338	−	2.66887i	−0.365515	−	0.265562i	−0.755349	+	0.655323i	$0.772533\pi$
$102$	8.40556	−	6.10700i	0.832274	−	0.604683i
$103$	5.85553	−	4.25429i	0.576962	−	0.419188i	−0.260665	−	0.965429i	$-0.583942\pi$
$103$	5.85553	−	4.25429i	0.576962	−	0.419188i	0.837628	+	0.546241i	$0.183942\pi$
$104$	3.26831	+	2.37456i	0.320484	+	0.232845i
$105$	30.8834	+	1.81734i	3.01391	+	0.177354i
$106$	6.10188			0.592667
$107$	−3.98522	+	12.2653i	−0.385266	+	1.18573i	0.551021	+	0.834492i	$0.314238\pi$
$107$	−3.98522	+	12.2653i	−0.385266	+	1.18573i	−0.936287	+	0.351236i	$0.885762\pi$
$108$	14.1039	−	10.2471i	1.35715	−	0.986026i
$109$	7.35439	−	5.34328i	0.704423	−	0.511793i	−0.176947	−	0.984220i	$-0.556622\pi$
$109$	7.35439	−	5.34328i	0.704423	−	0.511793i	0.881370	+	0.472427i	$0.156622\pi$
$110$	−3.50042	+	6.53812i	−0.333752	+	0.623385i
$111$	22.7006	+	16.4929i	2.15464	+	1.56544i
$112$	−4.13273			−0.390506
$113$	2.02763	+	6.24041i	0.190743	+	0.587048i	1.00000		0.000407506i	$-0.000129713\pi$
$113$	2.02763	+	6.24041i	0.190743	+	0.587048i	−0.809256	+	0.587456i	$0.800130\pi$
$114$	1.62451	−	4.99973i	0.152149	−	0.468267i
$115$	−1.35067	+	0.864866i	−0.125951	+	0.0806492i
$116$	0.392640	−	1.20842i	0.0364557	−	0.112199i
$117$	33.1570			3.06536
$118$	−0.113190	+	0.348363i	−0.0104200	+	0.0320694i
$119$	−10.3765	+	7.53895i	−0.951210	+	0.691094i
$120$	−6.30417	+	4.03669i	−0.575489	+	0.368498i
$121$	−7.13040	−	8.37600i	−0.648218	−	0.761455i
$122$	−1.96330	−	6.04241i	−0.177749	−	0.547055i
$123$	−8.12057	−	24.9925i	−0.732207	−	2.25350i
$124$	−0.737868	+	2.27092i	−0.0662625	+	0.203935i
$125$	−10.0576	+	4.88305i	−0.899581	+	0.436753i
$126$	−27.4413	+	19.9373i	−2.44466	+	1.77615i
$127$	12.5986			1.11794			0.558972	−	0.829187i	$-0.311196\pi$
$127$	12.5986			1.11794			0.558972	+	0.829187i	$0.311196\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	6.65529			0.585966
$130$	−9.01777	−	0.530653i	−0.790911	−	0.0465413i
$131$	0.765348	−	2.35550i	0.0668688	−	0.205801i	−0.912039	−	0.410103i	$-0.865493\pi$
$131$	0.765348	−	2.35550i	0.0668688	−	0.205801i	0.978908	+	0.204302i	$0.0654926\pi$
$132$	−2.15733	−	10.8917i	−0.187772	−	0.947997i
$133$	−2.00542	+	6.17205i	−0.173892	+	0.535185i
$134$	12.0708			1.04276
$135$	−14.2032	+	36.3026i	−1.22242	+	3.12443i
$136$	0.959041	−	2.95163i	0.0822371	−	0.253100i
$137$	−2.59567	+	7.98865i	−0.221763	+	0.682516i	0.776841	+	0.629697i	$0.216821\pi$
$137$	−2.59567	+	7.98865i	−0.221763	+	0.682516i	−0.998604	+	0.0528195i	$0.983179\pi$
$138$	0.742016	−	2.28369i	0.0631646	−	0.194401i
$139$	5.65195	−	17.3949i	0.479392	−	1.47542i	−0.360549	−	0.932740i	$-0.617411\pi$
$139$	5.65195	−	17.3949i	0.479392	−	1.47542i	0.839941	−	0.542677i	$-0.182589\pi$
$140$	7.78235	−	4.98321i	0.657729	−	0.421158i
$141$	−43.5417			−3.66687
$142$	−2.32548	+	7.15710i	−0.195150	+	0.600611i
$143$	5.61931	−	12.1634i	0.469911	−	1.01715i
$144$	2.53625	−	7.80578i	0.211354	−	0.650481i
$145$	0.717722	+	2.74902i	0.0596036	+	0.228294i
$146$	−10.9066			−0.902637
$147$	27.2991	−	19.8340i	2.25160	−	1.63588i
$148$	8.38157			0.688961
$149$	−10.6536	+	7.74026i	−0.872773	+	0.634107i	−0.931330	−	0.364177i	$-0.881350\pi$
$149$	−10.6536	+	7.74026i	−0.872773	+	0.634107i	0.0585563	+	0.998284i	$0.481350\pi$
$150$	7.00398	−	15.2030i	0.571873	−	1.24132i
$151$	−3.72657	+	11.4692i	−0.303264	+	0.933351i	0.677055	+	0.735932i	$0.263256\pi$
$151$	−3.72657	+	11.4692i	−0.303264	+	0.933351i	−0.980319	+	0.197418i	$0.936744\pi$
$152$	−0.485253	−	1.49346i	−0.0393592	−	0.121135i
$153$	−7.87131	−	24.2254i	−0.636358	−	1.95851i
$154$	2.66318	+	13.4455i	0.214605	+	1.08347i
$155$	−1.34878	−	5.16609i	−0.108336	−	0.414951i
$156$	10.9415	−	7.94946i	0.876021	−	0.636466i
$157$	3.98053	−	12.2508i	0.317681	−	0.977722i	−0.656956	−	0.753929i	$-0.728156\pi$
$157$	3.98053	−	12.2508i	0.317681	−	0.977722i	0.974637	−	0.223793i	$-0.0718438\pi$
$158$	2.48843			0.197969
$159$	6.31248	−	19.4278i	0.500612	−	1.54073i
$160$	−0.814715	+	2.08236i	−0.0644089	+	0.164625i
$161$	−0.916002	+	2.81917i	−0.0721911	+	0.222181i
$162$	−10.4263	−	32.0889i	−0.819169	−	2.52114i
$163$	−14.5330			−1.13831			−0.569155	−	0.822230i	$-0.692730\pi$
$163$	−14.5330			−1.13831			−0.569155	+	0.822230i	$0.692730\pi$
$164$	−6.35050	−	4.61391i	−0.495891	−	0.360286i
$165$	17.1955	+	17.9088i	1.33867	+	1.39420i
$166$	4.15771	−	3.02075i	0.322701	−	0.234456i
$167$	2.75843	−	2.00411i	0.213453	−	0.155083i	−0.475921	−	0.879488i	$-0.657885\pi$
$167$	2.75843	−	2.00411i	0.213453	−	0.155083i	0.689375	+	0.724405i	$0.257885\pi$
$168$	−4.27537	+	13.1582i	−0.329852	+	1.01518i
$169$	3.32037			0.255413
$170$	1.75307	+	6.71461i	0.134454	+	0.514987i
$171$	−10.4269	−	7.57555i	−0.797362	−	0.579317i
$172$	1.60831	−	1.16851i	0.122633	−	0.0890979i
$173$	−12.9159	+	9.38394i	−0.981977	+	0.713448i	−0.958149	−	0.286268i	$-0.907585\pi$
$173$	−12.9159	+	9.38394i	−0.981977	+	0.713448i	−0.0238271	+	0.999716i	$0.507585\pi$
$174$	−3.44131	−	2.50026i	−0.260885	−	0.189544i
$175$	−8.64626	+	18.7678i	−0.653596	+	1.41871i
$176$	−2.43365	−	2.25330i	−0.183443	−	0.169849i
$177$	0.992059	+	0.720773i	0.0745677	+	0.0541766i
$178$	−2.59643	+	7.99100i	−0.194611	+	0.598951i
$179$	−14.1821			−1.06002			−0.530008	−	0.847992i	$-0.677811\pi$
$179$	−14.1821			−1.06002			−0.530008	+	0.847992i	$0.677811\pi$
$180$	4.63611	+	17.7573i	0.345555	+	1.32355i
$181$	0.612716	+	1.88575i	0.0455428	+	0.140166i	0.971242	−	0.238094i	$-0.0765225\pi$
$181$	0.612716	+	1.88575i	0.0455428	+	0.140166i	−0.925699	+	0.378260i	$0.876523\pi$
$182$	−13.5070	+	9.81343i	−1.00121	+	0.727420i
$183$	−21.2695			−1.57229
$184$	−0.221646	−	0.682156i	−0.0163399	−	0.0502892i
$185$	−15.7833	+	10.1064i	−1.16041	+	0.743038i
$186$	6.46707	+	4.69860i	0.474189	+	0.344518i
$187$	−10.2209	−	1.21810i	−0.747426	−	0.0890763i
$188$	−10.5223	+	7.64487i	−0.767414	+	0.557559i
$189$	22.2639	+	68.5212i	1.61946	+	4.98418i
$190$	2.71457	+	2.22721i	0.196936	+	0.161579i
$191$	5.51871	+	4.00958i	0.399320	+	0.290123i	0.769264	−	0.638931i	$-0.220623\pi$
$191$	5.51871	+	4.00958i	0.399320	+	0.290123i	−0.369944	+	0.929054i	$0.620623\pi$
$192$	−1.03451	−	3.18391i	−0.0746596	−	0.229779i
$193$	14.4535	−	10.5011i	1.04038	−	0.755883i	0.0700238	−	0.997545i	$-0.477692\pi$
$193$	14.4535	−	10.5011i	1.04038	−	0.755883i	0.970361	+	0.241662i	$0.0776925\pi$
$194$	1.82085			0.130729
$195$	−11.0186	+	28.1628i	−0.789056	+	2.01678i
$196$	3.11473	−	9.58614i	0.222480	−	0.684724i
$197$	4.09200	+	12.5939i	0.291543	+	0.897276i	0.984361	+	0.176164i	$0.0563688\pi$
$197$	4.09200	+	12.5939i	0.291543	+	0.897276i	−0.692818	+	0.721112i	$0.743631\pi$
$198$	−27.0298	−	3.22135i	−1.92093	−	0.228931i
$199$	23.1188			1.63885			0.819424	−	0.573188i	$-0.194293\pi$
$199$	23.1188			1.63885			0.819424	+	0.573188i	$0.194293\pi$
$200$	−0.976701	−	4.90368i	−0.0690632	−	0.346742i
$201$	12.4874	−	38.4324i	0.880796	−	2.71081i
$202$	−1.40311	+	4.31832i	−0.0987223	+	0.303836i
$203$	4.24822	+	3.08651i	0.298167	+	0.216631i
$204$	−8.40556	−	6.10700i	−0.588507	−	0.427575i
$205$	17.5220	+	1.03109i	1.22379	+	0.0720143i
$206$	−5.85553	−	4.25429i	−0.407974	−	0.296410i
$207$	−4.76260	−	3.46023i	−0.331024	−	0.240503i
$208$	1.24838	−	3.84212i	0.0865597	−	0.266403i
$209$	−4.54613	+	2.54113i	−0.314463	+	0.175774i
$210$	−7.81511	−	29.9335i	−0.539294	−	2.06561i
$211$	1.75797	+	5.41048i	0.121024	+	0.372473i	0.993156	−	0.116798i	$-0.0372630\pi$
$211$	1.75797	+	5.41048i	0.121024	+	0.372473i	−0.872132	+	0.489271i	$0.837263\pi$
$212$	−1.88559	−	5.80323i	−0.129503	−	0.398568i
$213$	20.3818	+	14.8082i	1.39654	+	1.01464i
$214$	12.8965			0.881584
$215$	−1.61964	+	4.13971i	−0.110459	+	0.282326i
$216$	−14.1039	−	10.2471i	−0.959648	−	0.697225i
$217$	−7.98346	−	5.80032i	−0.541952	−	0.393751i
$218$	−7.35439	−	5.34328i	−0.498102	−	0.361893i
$219$	−11.2830	+	34.7256i	−0.762437	+	2.34654i
$220$	7.29981	+	1.30871i	0.492153	+	0.0882332i
$221$	−3.87438	−	11.9241i	−0.260619	−	0.802103i
$222$	8.67085	−	26.6861i	0.581949	−	1.79106i
$223$	−5.58914	+	4.06075i	−0.374276	+	0.271928i	−0.758982	−	0.651112i	$-0.774303\pi$
$223$	−5.58914	+	4.06075i	−0.374276	+	0.271928i	0.384706	+	0.923039i	$0.374303\pi$
$224$	1.27708	+	3.93046i	0.0853288	+	0.262615i
$225$	−30.1418	−	27.8485i	−2.00945	−	1.85657i
$226$	5.30841	−	3.85678i	0.353110	−	0.256549i
$227$	−4.12934	+	12.7088i	−0.274074	+	0.843512i	0.715389	+	0.698726i	$0.246249\pi$
$227$	−4.12934	+	12.7088i	−0.274074	+	0.843512i	−0.989463	+	0.144786i	$0.953751\pi$
$228$	−5.25702			−0.348155
$229$	5.22534	−	16.0819i	0.345300	−	1.06272i	−0.616123	−	0.787650i	$-0.711298\pi$
$229$	5.22534	−	16.0819i	0.345300	−	1.06272i	0.961423	−	0.275074i	$-0.0887024\pi$
$230$	1.23992	+	1.01731i	0.0817578	+	0.0670794i
$231$	45.5643	+	5.43024i	2.99791	+	0.357284i
$232$	−1.27061			−0.0834197
$233$	6.84962	−	4.97654i	0.448734	−	0.326024i	−0.340362	−	0.940295i	$-0.610550\pi$
$233$	6.84962	−	4.97654i	0.448734	−	0.326024i	0.789096	+	0.614270i	$0.210550\pi$
$234$	−10.2461	−	31.5341i	−0.669806	−	2.06145i
$235$	10.5964	−	27.0837i	0.691231	−	1.76675i
$236$	0.366291			0.0238435
$237$	2.57431	−	7.92292i	0.167220	−	0.514649i
$238$	10.3765	+	7.53895i	0.672607	+	0.488677i
$239$	6.49170	−	4.71650i	0.419913	−	0.305085i	−0.357690	−	0.933841i	$-0.616435\pi$
$239$	6.49170	−	4.71650i	0.419913	−	0.305085i	0.777603	+	0.628756i	$0.216435\pi$
$240$	5.78722	+	4.74821i	0.373563	+	0.306496i
$241$	22.4055	−	16.2786i	1.44327	−	1.04859i	0.455919	−	0.890022i	$-0.349311\pi$
$241$	22.4055	−	16.2786i	1.44327	−	1.04859i	0.987347	−	0.158573i	$-0.0506892\pi$
$242$	−5.76264	+	9.36974i	−0.370436	+	0.602310i
$243$	−60.6541			−3.89096
$244$	−5.13998	+	3.73442i	−0.329054	+	0.239072i
$245$	5.69353	+	21.8074i	0.363746	+	1.39322i
$246$	−21.2599	+	15.4462i	−1.35548	+	0.984817i
$247$	−5.13226	−	3.72881i	−0.326558	−	0.237258i
$248$	2.38779			0.151625
$249$	−5.31658	−	16.3628i	−0.336925	−	1.03695i
$250$	7.75203	+	8.05643i	0.490282	+	0.509533i
$251$	12.1104	+	8.79874i	0.764403	+	0.555371i	0.900258	−	0.435357i	$-0.143378\pi$
$251$	12.1104	+	8.79874i	0.764403	+	0.555371i	−0.135855	+	0.990729i	$0.543378\pi$
$252$	27.4413	+	19.9373i	1.72864	+	1.25593i
$253$	−2.07651	+	1.16070i	−0.130549	+	0.0729723i
$254$	−3.89318	−	11.9820i	−0.244280	−	0.751816i
$255$	23.1923	+	1.36475i	1.45236	+	0.0854642i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.18691	−	3.65293i	−0.0740373	−	0.227863i	0.907189	−	0.420723i	$-0.138224\pi$
$257$	−1.18691	−	3.65293i	−0.0740373	−	0.227863i	−0.981226	+	0.192860i	$0.938224\pi$
$258$	−2.05660	−	6.32956i	−0.128038	−	0.394061i
$259$	−10.7040	+	32.9434i	−0.665112	+	2.04701i
$260$	2.28196	+	8.74039i	0.141521	+	0.542056i
$261$	−8.43684	+	6.12972i	−0.522227	+	0.379420i
$262$	−2.47672			−0.153012
$263$	8.66997	−	6.29910i	0.534613	−	0.388419i	−0.287467	−	0.957790i	$-0.592813\pi$
$263$	8.66997	−	6.29910i	0.534613	−	0.388419i	0.822081	+	0.569371i	$0.192813\pi$
$264$	−9.69193	+	5.41745i	−0.596497	+	0.333421i
$265$	10.5482	+	8.65446i	0.647973	+	0.531639i
$266$	6.48968			0.397908
$267$	22.7565	+	16.5336i	1.39268	+	1.01184i
$268$	−3.73009	−	11.4800i	−0.227852	−	0.701255i
$269$	−3.15503	−	9.71019i	−0.192366	−	0.592041i	−0.999997	−	0.00235315i	$-0.999251\pi$
$269$	−3.15503	−	9.71019i	−0.192366	−	0.592041i	0.807632	−	0.589687i	$-0.200749\pi$
$270$	38.9149	+	2.28995i	2.36828	+	0.139362i
$271$	−25.2823	+	18.3687i	−1.53579	+	1.11582i	−0.582886	+	0.812554i	$0.698077\pi$
$271$	−25.2823	+	18.3687i	−1.53579	+	1.11582i	−0.952906	+	0.303265i	$0.901923\pi$
$272$	−3.10352			−0.188179
$273$	17.2718	+	53.1572i	1.04534	+	3.21722i
$274$	8.39976			0.507448
$275$	−15.3243	+	6.33761i	−0.924091	+	0.382172i
$276$	−2.40122			−0.144536
$277$	3.06325	+	9.42772i	0.184053	+	0.566457i	0.999931	−	0.0117674i	$-0.00374578\pi$
$277$	3.06325	+	9.42772i	0.184053	+	0.566457i	−0.815878	+	0.578225i	$0.803746\pi$
$278$	−18.2901			−1.09697
$279$	15.8549	−	11.5193i	0.949208	−	0.689640i
$280$	−7.14419	−	5.86156i	−0.426947	−	0.350295i
$281$	1.43537	+	4.41762i	0.0856271	+	0.263533i	0.984698	−	0.174270i	$-0.0557566\pi$
$281$	1.43537	+	4.41762i	0.0856271	+	0.263533i	−0.899071	+	0.437803i	$0.855757\pi$
$282$	13.4551	+	41.4106i	0.801241	+	2.46597i
$283$	8.18000	+	5.94312i	0.486250	+	0.353282i	0.803741	−	0.594980i	$-0.202840\pi$
$283$	8.18000	+	5.94312i	0.486250	+	0.353282i	−0.317490	+	0.948262i	$0.602840\pi$
$284$	7.52543			0.446552
$285$	9.89951	−	6.33887i	0.586396	−	0.375482i
$286$	−13.3045	−	1.58560i	−0.786712	−	0.0937584i
$287$	26.2449	−	19.0680i	1.54919	−	1.12555i
$288$	−8.20748			−0.483630
$289$	5.96095	−	4.33089i	0.350644	−	0.254758i
$290$	2.39269	−	1.53209i	0.140503	−	0.0899674i
$291$	1.88369	−	5.79742i	0.110424	−	0.339851i
$292$	3.37033	+	10.3728i	0.197234	+	0.607022i
$293$	−0.824760	−	2.53835i	−0.0481830	−	0.148292i	0.924070	−	0.382222i	$-0.124841\pi$
$293$	−0.824760	−	2.53835i	−0.0481830	−	0.148292i	−0.972253	+	0.233930i	$0.924841\pi$
$294$	−27.2991	−	19.8340i	−1.59212	−	1.15674i
$295$	−0.689763	+	0.441670i	−0.0401595	+	0.0257150i
$296$	−2.59005	−	7.97135i	−0.150543	−	0.463325i
$297$	−24.2493	+	52.4892i	−1.40709	+	3.04573i
$298$	10.6536	+	7.74026i	0.617144	+	0.448381i
$299$	−2.34423	−	1.70318i	−0.135570	−	0.0984975i
$300$	−16.6233	−	1.96320i	−0.959744	−	0.113345i
$301$	2.53882	+	7.81370i	0.146335	+	0.450374i
$302$	12.0594			0.693942
$303$	12.2976	+	8.93473i	0.706478	+	0.513287i
$304$	−1.27041	+	0.923006i	−0.0728630	+	0.0529380i
$305$	5.17619	−	13.2300i	0.296388	−	0.757549i
$306$	−20.6074	+	14.9721i	−1.17804	+	0.855899i
$307$	−12.1548			−0.693711			−0.346855	−	0.937919i	$-0.612751\pi$
$307$	−12.1548			−0.693711			−0.346855	+	0.937919i	$0.612751\pi$
$308$	11.9645	−	6.68772i	0.681739	−	0.381068i
$309$	−19.6029	+	14.2423i	−1.11517	+	0.810218i
$310$	−4.49645	+	2.87917i	−0.255381	+	0.163526i
$311$	19.7003	−	14.3131i	1.11710	−	0.811621i	0.133333	−	0.991071i	$-0.457432\pi$
$311$	19.7003	−	14.3131i	1.11710	−	0.811621i	0.983767	+	0.179451i	$0.0574321\pi$
$312$	−10.9415	−	7.94946i	−0.619440	−	0.450050i
$313$	7.30040	−	22.4683i	0.412643	−	1.26998i	−0.501699	−	0.865042i	$-0.667292\pi$
$313$	7.30040	−	22.4683i	0.412643	−	1.26998i	0.914342	−	0.404942i	$-0.132708\pi$
$314$	−12.8813			−0.726932
$315$	−75.7149	−	4.45546i	−4.26605	−	0.251037i
$316$	−0.768966	−	2.36664i	−0.0432577	−	0.133134i
$317$	−2.08042	+	1.51151i	−0.116848	+	0.0848949i	−0.644674	−	0.764457i	$-0.723007\pi$
$317$	−2.08042	+	1.51151i	−0.116848	+	0.0848949i	0.527827	+	0.849352i	$0.323007\pi$
$318$	−20.4276			−1.14552
$319$	0.818796	+	4.13383i	0.0458438	+	0.231450i
$320$	2.23221	+	0.131355i	0.124784	+	0.00734295i
$321$	13.3416	−	41.0611i	0.744654	−	2.29181i
$322$	2.96425			0.165191
$323$	−1.50599	+	4.63497i	−0.0837958	+	0.257897i
$324$	−27.2964	+	19.8320i	−1.51647	+	1.10178i
$325$	−14.8363	−	13.7075i	−0.822967	−	0.760354i
$326$	4.49094	+	13.8217i	0.248730	+	0.765512i
$327$	−24.6207	+	17.8880i	−1.36153	+	0.989209i
$328$	−2.42568	+	7.46546i	−0.133936	+	0.412211i
$329$	−16.6100	−	51.1205i	−0.915741	−	2.81836i
$330$	11.7186	−	21.8880i	0.645086	−	1.20490i
$331$	5.84892	−	18.0011i	0.321486	−	0.989431i	−0.651516	−	0.758635i	$-0.725867\pi$
$331$	5.84892	−	18.0011i	0.321486	−	0.989431i	0.973002	−	0.230796i	$-0.0741331\pi$
$332$	−4.15771	−	3.02075i	−0.228184	−	0.165785i
$333$	−55.6535	−	40.4347i	−3.04979	−	2.21581i
$334$	−2.75843	−	2.00411i	−0.150934	−	0.109660i
$335$	20.8666	+	17.1204i	1.14007	+	0.935386i
$336$	13.8354			0.754782
$337$	4.89288	+	3.55488i	0.266532	+	0.193647i	0.713022	−	0.701142i	$-0.247326\pi$
$337$	4.89288	+	3.55488i	0.266532	+	0.193647i	−0.446490	+	0.894789i	$0.647326\pi$
$338$	−1.02605	−	3.15786i	−0.0558098	−	0.171765i
$339$	−6.78802	−	20.8914i	−0.368674	−	1.13466i
$340$	5.84425	−	3.74220i	0.316949	−	0.202949i
$341$	−1.53872	−	7.76848i	−0.0833264	−	0.420687i
$342$	−3.98270	+	12.2575i	−0.215360	+	0.662810i
$343$	10.2960	+	7.48051i	0.555933	+	0.403909i
$344$	−1.60831	−	1.16851i	−0.0867145	−	0.0630017i
$345$	4.52173	−	2.89536i	0.243442	−	0.155881i
$346$	12.9159	+	9.38394i	0.694362	+	0.504484i
$347$	−4.83434	−	3.51235i	−0.259521	−	0.188553i	0.450415	−	0.892819i	$-0.351276\pi$
$347$	−4.83434	−	3.51235i	−0.259521	−	0.188553i	−0.709936	+	0.704266i	$0.751276\pi$
$348$	−1.31446	+	4.04550i	−0.0704627	+	0.216862i
$349$	−5.06503	+	15.5886i	−0.271125	+	0.834436i	0.719094	+	0.694913i	$0.244557\pi$
$349$	−5.06503	+	15.5886i	−0.271125	+	0.834436i	−0.990219	+	0.139523i	$0.955443\pi$
$350$	20.5210	+	2.42352i	1.09690	+	0.129543i
$351$	−70.4282			−3.75918
$352$	−1.39097	+	3.01085i	−0.0741390	+	0.160479i
$353$	2.52949	+	7.78498i	0.134631	+	0.414353i	0.995532	−	0.0944196i	$-0.0300995\pi$
$353$	2.52949	+	7.78498i	0.134631	+	0.414353i	−0.860901	+	0.508772i	$0.830100\pi$
$354$	0.378933	−	1.16624i	0.0201401	−	0.0619847i
$355$	−14.1711	+	9.07408i	−0.752126	+	0.481602i
$356$	8.40223			0.445318
$357$	34.7379	−	25.2386i	1.83853	−	1.33577i
$358$	4.38250	+	13.4879i	0.231622	+	0.712860i
$359$	−12.9502	−	9.40885i	−0.683484	−	0.496580i	0.191028	−	0.981585i	$-0.438818\pi$
$359$	−12.9502	−	9.40885i	−0.683484	−	0.496580i	−0.874512	+	0.485004i	$0.838818\pi$
$360$	15.4555	−	9.89649i	0.814577	−	0.521591i
$361$	−5.10932	−	15.7249i	−0.268912	−	0.827625i
$362$	1.60411	−	1.16545i	0.0843102	−	0.0612549i
$363$	23.8708	+	28.0408i	1.25289	+	1.47176i
$364$	13.5070	+	9.81343i	0.707961	+	0.514363i
$365$	−18.8541	−	15.4691i	−0.986868	−	0.809691i
$366$	6.57265	+	20.2285i	0.343558	+	1.05736i
$367$	−9.84441			−0.513874			−0.256937	−	0.966428i	$-0.582713\pi$
$367$	−9.84441			−0.513874			−0.256937	+	0.966428i	$0.582713\pi$
$368$	−0.580276	+	0.421595i	−0.0302490	+	0.0219772i
$369$	19.9087	+	61.2726i	1.03640	+	3.18972i
$370$	14.4891	+	11.8878i	0.753252	+	0.618017i
$371$	25.2174			1.30922
$372$	2.47020	−	7.60250i	0.128074	−	0.394171i
$373$	−4.77316	−	3.46790i	−0.247145	−	0.179561i	0.457316	−	0.889304i	$-0.348811\pi$
$373$	−4.77316	−	3.46790i	−0.247145	−	0.179561i	−0.704460	+	0.709743i	$0.748811\pi$
$374$	1.99995	+	10.0971i	0.103415	+	0.522107i
$375$	33.6705	−	16.3473i	1.73874	−	0.844169i
$376$	10.5223	+	7.64487i	0.542644	+	0.394254i
$377$	−4.15274	+	3.01714i	−0.213877	+	0.155391i
$378$	58.2876	−	42.3484i	2.99799	−	2.17817i
$379$	−26.4119	−	19.1894i	−1.35669	−	0.985693i	−0.998648	−	0.0519884i	$-0.983444\pi$
$379$	−26.4119	−	19.1894i	−1.35669	−	0.985693i	−0.358043	−	0.933705i	$-0.616556\pi$
$380$	1.27936	−	3.26996i	0.0656297	−	0.167745i
$381$	−42.1770			−2.16079
$382$	2.10796	−	6.48763i	0.107853	−	0.331936i
$383$	11.8107	−	8.58101i	0.603501	−	0.438469i	−0.243619	−	0.969871i	$-0.578335\pi$
$383$	11.8107	−	8.58101i	0.603501	−	0.438469i	0.847120	+	0.531402i	$0.178335\pi$
$384$	−2.70839	+	1.96776i	−0.138212	+	0.100417i
$385$	−14.4663	+	27.0203i	−0.737271	+	1.37708i
$386$	−14.4535	−	10.5011i	−0.735663	−	0.534490i
$387$	−16.3163			−0.829406
$388$	−0.562674	−	1.73173i	−0.0285654	−	0.0879153i
$389$	8.20804	−	25.2617i	0.416164	−	1.28082i	−0.495042	−	0.868869i	$-0.664847\pi$
$389$	8.20804	−	25.2617i	0.416164	−	1.28082i	0.911206	−	0.411952i	$-0.135153\pi$
$390$	30.1893	+	1.77650i	1.52870	+	0.0899564i
$391$	−0.687883	+	2.11709i	−0.0347877	+	0.107066i
$392$	−10.0795			−0.509090
$393$	−2.56220	+	7.88564i	−0.129246	+	0.397778i
$394$	10.7130	−	7.78344i	0.539712	−	0.392124i
$395$	4.30171	+	3.52940i	0.216442	+	0.177584i
$396$	5.28900	+	26.7024i	0.265782	+	1.34184i
$397$	−9.28946	−	28.5900i	−0.466225	−	1.43489i	−0.857436	−	0.514591i	$-0.827944\pi$
$397$	−9.28946	−	28.5900i	−0.466225	−	1.43489i	0.391211	−	0.920301i	$-0.372056\pi$
$398$	−7.14410	−	21.9873i	−0.358101	−	1.10212i
$399$	6.71366	−	20.6625i	0.336103	−	1.03442i
$400$	−4.36186	+	2.44422i	−0.218093	+	0.122211i
$401$	−5.99518	+	4.35576i	−0.299385	+	0.217516i	−0.727328	−	0.686290i	$-0.759238\pi$
$401$	−5.99518	+	4.35576i	−0.299385	+	0.217516i	0.427943	+	0.903806i	$0.359238\pi$
$402$	−40.4102			−2.01548
$403$	7.80403	−	5.66996i	0.388746	−	0.282441i
$404$	4.54055			0.225901
$405$	27.4887	−	70.2595i	1.36593	−	3.49122i
$406$	1.62268	−	4.99408i	0.0805321	−	0.247852i
$407$	−24.2651	+	13.5633i	−1.20277	+	0.672310i
$408$	−3.21064	+	9.88133i	−0.158950	+	0.489199i
$409$	11.1763			0.552635			0.276317	−	0.961066i	$-0.410886\pi$
$409$	11.1763			0.552635			0.276317	+	0.961066i	$0.410886\pi$
$410$	−4.43398	−	16.9831i	−0.218979	−	0.838734i
$411$	8.68967	−	26.7441i	0.428630	−	1.31919i
$412$	−2.23661	+	6.88359i	−0.110190	+	0.339130i
$413$	−0.467784	+	1.43969i	−0.0230181	+	0.0708426i
$414$	−1.81915	+	5.59878i	−0.0894065	+	0.275165i
$415$	11.4718	+	0.675059i	0.563127	+	0.0331373i
$416$	−4.03985			−0.198070
$417$	−18.9214	+	58.2340i	−0.926583	+	2.85173i
$418$	3.82159	+	3.53838i	0.186920	+	0.173068i
$419$	−2.34945	+	7.23086i	−0.114778	+	0.353251i	−0.991901	−	0.127016i	$-0.959460\pi$
$419$	−2.34945	+	7.23086i	−0.114778	+	0.353251i	0.877123	+	0.480267i	$0.159460\pi$
$420$	−26.0534	+	16.6826i	−1.27128	+	0.814026i
$421$	−4.67913			−0.228047			−0.114024	−	0.993478i	$-0.536374\pi$
$421$	−4.67913			−0.228047			−0.114024	+	0.993478i	$0.536374\pi$
$422$	4.60243	−	3.34386i	0.224043	−	0.162777i
$423$	106.748			5.19028
$424$	−4.93653	+	3.58660i	−0.239739	+	0.174180i
$425$	−6.49301	+	14.0939i	−0.314957	+	0.683653i
$426$	7.78516	−	23.9602i	0.377192	−	1.16088i
$427$	−8.11379	−	24.9717i	−0.392654	−	1.20846i
$428$	−3.98522	−	12.2653i	−0.192633	−	0.592864i
$429$	−18.8121	+	40.7200i	−0.908256	+	1.96598i
$430$	4.43759	+	0.261131i	0.214000	+	0.0125929i
$431$	9.96999	−	7.24362i	0.480238	−	0.348913i	−0.321180	−	0.947018i	$-0.604079\pi$
$431$	9.96999	−	7.24362i	0.480238	−	0.348913i	0.801418	+	0.598105i	$0.204079\pi$
$432$	−5.38721	+	16.5801i	−0.259192	+	0.797711i
$433$	−14.0796			−0.676620			−0.338310	−	0.941035i	$-0.609855\pi$
$433$	−14.0796			−0.676620			−0.338310	+	0.941035i	$0.609855\pi$
$434$	−3.04941	+	9.38512i	−0.146376	+	0.450500i
$435$	−2.40276	−	9.20306i	−0.115203	−	0.441253i
$436$	−2.80913	+	8.64561i	−0.134533	+	0.414050i
$437$	0.348053	+	1.07120i	0.0166496	+	0.0512423i
$438$	36.5127			1.74464
$439$	1.31673	+	0.956658i	0.0628439	+	0.0456588i	0.618764	−	0.785577i	$-0.287634\pi$
$439$	1.31673	+	0.956658i	0.0628439	+	0.0456588i	−0.555920	+	0.831236i	$0.687634\pi$
$440$	−1.01111	−	7.34695i	−0.0482027	−	0.350252i
$441$	−66.9275	+	48.6257i	−3.18703	+	2.31551i
$442$	−10.1433	+	7.36951i	−0.482466	+	0.350532i
$443$	3.49371	−	10.7525i	0.165991	−	0.510869i	−0.833117	−	0.553097i	$-0.813446\pi$
$443$	3.49371	−	10.7525i	0.165991	−	0.510869i	0.999108	+	0.0422285i	$0.0134457\pi$
$444$	−28.0595			−1.33164
$445$	−15.8223	+	10.1313i	−0.750047	+	0.480271i
$446$	5.58914	+	4.06075i	0.264653	+	0.192282i
$447$	35.6655	−	25.9125i	1.68692	−	1.22562i
$448$	3.34345	−	2.42916i	0.157963	−	0.114767i
$449$	−1.64323	−	1.19388i	−0.0775488	−	0.0563425i	0.548335	−	0.836259i	$-0.315262\pi$
$449$	−1.64323	−	1.19388i	−0.0775488	−	0.0563425i	−0.625884	+	0.779916i	$0.715262\pi$
$450$	−17.1712	+	37.2722i	−0.809458	+	1.75703i
$451$	25.8514	+	3.08090i	1.21730	+	0.145074i
$452$	−5.30841	−	3.85678i	−0.249686	−	0.181408i
$453$	12.4757	−	38.3961i	0.586157	−	1.80401i
$454$	13.3628			0.627148
$455$	−37.2680	−	2.19305i	−1.74715	−	0.102812i
$456$	1.62451	+	4.99973i	0.0760746	+	0.234134i
$457$	−3.80668	+	2.76571i	−0.178069	+	0.129375i	−0.673249	−	0.739416i	$-0.735102\pi$
$457$	−3.80668	+	2.76571i	−0.178069	+	0.129375i	0.495180	+	0.868790i	$0.335102\pi$
$458$	−16.9095			−0.790131
$459$	16.7193	+	51.4568i	0.780391	+	2.40180i
$460$	0.584363	−	1.49360i	0.0272461	−	0.0696394i
$461$	28.2367	+	20.5152i	1.31511	+	0.955486i	0.999979	+	0.00643949i	$0.00204977\pi$
$461$	28.2367	+	20.5152i	1.31511	+	0.955486i	0.315135	+	0.949047i	$0.397950\pi$
$462$	−8.91568	−	45.0123i	−0.414795	−	2.09416i
$463$	33.2061	−	24.1256i	1.54322	−	1.12121i	0.594941	−	0.803770i	$-0.297176\pi$
$463$	33.2061	−	24.1256i	1.54322	−	1.12121i	0.948277	−	0.317444i	$-0.102824\pi$
$464$	0.392640	+	1.20842i	0.0182279	+	0.0560996i
$465$	4.51538	+	17.2948i	0.209396	+	0.802028i
$466$	−6.84962	−	4.97654i	−0.317303	−	0.230534i
$467$	−6.06158	−	18.6556i	−0.280497	−	0.863280i	−0.987712	−	0.156282i	$-0.950049\pi$
$467$	−6.06158	−	18.6556i	−0.280497	−	0.863280i	0.707216	−	0.706998i	$-0.249951\pi$
$468$	−26.8245	+	19.4892i	−1.23997	+	0.900887i
$469$	49.8855			2.30350
$470$	−29.0326	−	1.70843i	−1.33917	−	0.0788039i
$471$	−13.3259	+	41.0128i	−0.614023	+	1.88977i
$472$	−0.113190	−	0.348363i	−0.00520999	−	0.0160347i
$473$	−2.76523	+	5.98552i	−0.127145	+	0.275214i
$474$	−8.33065			−0.382640
$475$	1.53373	+	7.70030i	0.0703722	+	0.353314i
$476$	3.96346	−	12.1983i	0.181665	−	0.559107i
$477$	−15.4759	+	47.6299i	−0.708593	+	2.18082i
$478$	−6.49170	−	4.71650i	−0.296924	−	0.215728i
$479$	−3.79062	−	2.75404i	−0.173198	−	0.125835i	0.497809	−	0.867287i	$-0.334138\pi$
$479$	−3.79062	−	2.75404i	−0.173198	−	0.125835i	−0.671007	+	0.741451i	$0.734138\pi$
$480$	2.72747	−	6.97125i	0.124491	−	0.318192i
$481$	−27.3935	−	19.9026i	−1.24904	−	0.907479i
$482$	−22.4055	−	16.2786i	−1.02054	−	0.741468i
$483$	3.06655	−	9.43788i	0.139533	−	0.429438i
$484$	10.6919	+	2.58519i	0.485996	+	0.117508i
$485$	3.14768	+	2.58256i	0.142929	+	0.117268i
$486$	18.7431	+	57.6855i	0.850206	+	2.61667i
$487$	5.13693	+	15.8098i	0.232776	+	0.716412i	0.997409	+	0.0719452i	$0.0229207\pi$
$487$	5.13693	+	15.8098i	0.232776	+	0.716412i	−0.764632	+	0.644467i	$0.777079\pi$
$488$	5.13998	+	3.73442i	0.232676	+	0.169049i
$489$	48.6529			2.20016
$490$	18.9807	−	12.1537i	0.857458	−	0.549049i
$491$	17.5140	+	12.7247i	0.790398	+	0.574258i	0.908082	−	0.418793i	$-0.137547\pi$
$491$	17.5140	+	12.7247i	0.790398	+	0.574258i	−0.117684	+	0.993051i	$0.537547\pi$
$492$	21.2599	+	15.4462i	0.958472	+	0.696371i
$493$	3.19025	+	2.31785i	0.143682	+	0.104391i
$494$	−1.96035	+	6.03333i	−0.0882003	+	0.271453i
$495$	−42.1572	−	43.9058i	−1.89482	−	1.97342i
$496$	−0.737868	−	2.27092i	−0.0331312	−	0.101967i
$497$	−9.61060	+	29.5784i	−0.431094	+	1.32677i
$498$	−13.9190	+	10.1127i	−0.623725	+	0.453163i
$499$	−1.00997	−	3.10836i	−0.0452123	−	0.139149i	0.925902	−	0.377764i	$-0.123307\pi$
$499$	−1.00997	−	3.10836i	−0.0452123	−	0.139149i	−0.971114	+	0.238614i	$0.923307\pi$
$500$	5.26661	−	9.86219i	0.235530	−	0.441051i
$501$	−9.23454	+	6.70928i	−0.412569	+	0.299749i
$502$	4.62577	−	14.2367i	0.206458	−	0.635413i
$503$	23.7751			1.06008			0.530040	−	0.847972i	$-0.322177\pi$
$503$	23.7751			1.06008			0.530040	+	0.847972i	$0.322177\pi$
$504$	10.4816	−	32.2592i	0.466889	−	1.43694i
$505$	−8.55032	+	5.47495i	−0.380484	+	0.243632i
$506$	1.74556	+	1.61620i	0.0775997	+	0.0718489i
$507$	−11.1158			−0.493670
$508$	−10.1925	+	7.40527i	−0.452218	+	0.328556i
$509$	0.970712	+	2.98754i	0.0430260	+	0.132421i	0.970262	−	0.242057i	$-0.0778221\pi$
$509$	0.970712	+	2.98754i	0.0430260	+	0.132421i	−0.927236	+	0.374478i	$0.877822\pi$
$510$	−5.86885	−	22.4789i	−0.259877	−	0.995382i
$511$	−45.0741			−1.99396
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	22.1475	+	16.0911i	0.977837	+	0.710440i
$514$	−3.10736	+	2.25763i	−0.137060	+	0.0995799i
$515$	−4.08839	−	15.6594i	−0.180156	−	0.690035i
$516$	−5.38424	+	3.91188i	−0.237028	+	0.172211i
$517$	18.0913	−	39.1598i	0.795654	−	1.72224i
$518$	34.6388			1.52194
$519$	43.2392	−	31.4152i	1.89799	−	1.37897i
$520$	7.60744	−	4.87121i	0.333608	−	0.213617i
$521$	7.55292	−	5.48751i	0.330899	−	0.240412i	−0.409913	−	0.912125i	$-0.634441\pi$
$521$	7.55292	−	5.48751i	0.330899	−	0.240412i	0.740812	+	0.671712i	$0.234441\pi$
$522$	8.43684	+	6.12972i	0.369270	+	0.268291i
$523$	21.6002			0.944509			0.472254	−	0.881462i	$-0.343440\pi$
$523$	21.6002			0.944509			0.472254	+	0.881462i	$0.343440\pi$
$524$	0.765348	+	2.35550i	0.0334344	+	0.102900i
$525$	28.9456	−	62.8299i	1.26329	−	2.74212i
$526$	−8.66997	−	6.29910i	−0.378029	−	0.274654i
$527$	−5.99527	−	4.35582i	−0.261158	−	0.189743i
$528$	8.14728	+	7.54349i	0.354565	+	0.328288i
$529$	−6.94841	−	21.3850i	−0.302105	−	0.929783i
$530$	4.97130	−	12.7063i	0.215939	−	0.551928i
$531$	−2.43217	−	1.76707i	−0.105547	−	0.0766844i
$532$	−2.00542	−	6.17205i	−0.0869460	−	0.267592i
$533$	9.79936	+	30.1593i	0.424457	+	1.30635i
$534$	8.69223	−	26.7519i	0.376149	−	1.15767i
$535$	22.2939	+	18.2914i	0.963850	+	0.790806i
$536$	−9.76550	+	7.09505i	−0.421805	+	0.306460i
$537$	47.4781			2.04883
$538$	−8.25998	+	6.00123i	−0.356113	+	0.258731i
$539$	6.49533	+	32.7927i	0.279774	+	1.41248i
$540$	−9.84748	−	37.7179i	−0.423768	−	1.62312i
$541$	−40.7265			−1.75097			−0.875485	−	0.483245i	$-0.839458\pi$
$541$	−40.7265			−1.75097			−0.875485	+	0.483245i	$0.839458\pi$
$542$	25.2823	+	18.3687i	1.08597	+	0.789003i
$543$	−2.05122	−	6.31302i	−0.0880264	−	0.270917i
$544$	0.959041	+	2.95163i	0.0411186	+	0.126550i
$545$	−5.13491	−	19.6678i	−0.219956	−	0.842475i
$546$	45.2182	−	32.8530i	1.93516	−	1.40598i
$547$	21.9602			0.938950			0.469475	−	0.882946i	$-0.344443\pi$
$547$	21.9602			0.938950			0.469475	+	0.882946i	$0.344443\pi$
$548$	−2.59567	−	7.98865i	−0.110881	−	0.341258i
$549$	52.1452			2.22550
$550$	10.7629	+	12.6159i	0.458931	+	0.537942i
$551$	1.99525			0.0850007
$552$	0.742016	+	2.28369i	0.0315823	+	0.0972004i
$553$	10.2840			0.437320
$554$	8.01970	−	5.82665i	0.340724	−	0.247551i
$555$	52.8388	−	33.8338i	2.24288	−	1.43617i
$556$	5.65195	+	17.3949i	0.239696	+	0.737709i
$557$	11.1107	+	34.1952i	0.470775	+	1.44890i	0.851572	+	0.524238i	$0.175650\pi$
$557$	11.1107	+	34.1952i	0.470775	+	1.44890i	−0.380796	+	0.924659i	$0.624350\pi$
$558$	−15.8549	−	11.5193i	−0.671192	−	0.487649i
$559$	−8.03116			−0.339682
$560$	−3.36700	+	8.60585i	−0.142282	+	0.363663i
$561$	34.2171	+	4.07790i	1.44465	+	0.172169i
$562$	3.75785	−	2.73024i	0.158515	−	0.115168i
$563$	−28.2260			−1.18958			−0.594791	−	0.803880i	$-0.702765\pi$
$563$	−28.2260			−1.18958			−0.594791	+	0.803880i	$0.702765\pi$
$564$	35.2260	−	25.5932i	1.48328	−	1.07767i
$565$	14.6467	+	0.861890i	0.616193	+	0.0362600i
$566$	3.12448	−	9.61616i	0.131332	−	0.404198i
$567$	−43.0892	−	132.615i	−1.80957	−	5.56930i
$568$	−2.32548	−	7.15710i	−0.0975752	−	0.300305i
$569$	4.49051	+	3.26255i	0.188252	+	0.136773i	0.677919	−	0.735136i	$-0.262882\pi$
$569$	4.49051	+	3.26255i	0.188252	+	0.136773i	−0.489667	+	0.871909i	$0.662882\pi$
$570$	−9.08774	−	7.45617i	−0.380643	−	0.312305i
$571$	6.87911	+	21.1717i	0.287882	+	0.886008i	0.985520	+	0.169559i	$0.0542342\pi$
$571$	6.87911	+	21.1717i	0.287882	+	0.886008i	−0.697639	+	0.716450i	$0.745766\pi$
$572$	2.60333	+	13.1433i	0.108851	+	0.549550i
$573$	−18.4753	−	13.4231i	−0.771817	−	0.560758i
$574$	−26.2449	−	19.0680i	−1.09544	−	0.795885i
$575$	0.700550	+	3.51722i	0.0292149	+	0.146678i
$576$	2.53625	+	7.80578i	0.105677	+	0.325241i
$577$	−16.3840			−0.682075			−0.341037	−	0.940050i	$-0.610778\pi$
$577$	−16.3840			−0.682075			−0.341037	+	0.940050i	$0.610778\pi$
$578$	−5.96095	−	4.33089i	−0.247943	−	0.180141i
$579$	−48.3867	+	35.1550i	−2.01088	+	1.46099i
$580$	−2.19648	−	1.80214i	−0.0912041	−	0.0748298i
$581$	17.1827	−	12.4839i	0.712858	−	0.517922i
$582$	−6.09576			−0.252678
$583$	14.8499	+	13.7493i	0.615018	+	0.569439i
$584$	8.82363	−	6.41074i	0.365125	−	0.265278i
$585$	27.0135	−	69.0449i	1.11687	−	2.85465i
$586$	−2.15925	+	1.56879i	−0.0891978	+	0.0648060i
$587$	14.8157	+	10.7642i	0.611509	+	0.444287i	0.849945	−	0.526871i	$-0.176635\pi$
$587$	14.8157	+	10.7642i	0.611509	+	0.444287i	−0.238437	+	0.971158i	$0.576635\pi$
$588$	−10.4273	+	32.0921i	−0.430016	+	1.32345i
$589$	−3.74958			−0.154499
$590$	0.633201	+	0.519520i	0.0260685	+	0.0213883i
$591$	−13.6990	−	42.1612i	−0.563502	−	1.73428i
$592$	−6.78083	+	4.92656i	−0.278690	+	0.202480i
$593$	−15.4029			−0.632521			−0.316260	−	0.948672i	$-0.602427\pi$
$593$	−15.4029			−0.632521			−0.316260	+	0.948672i	$0.602427\pi$
$594$	57.4137	+	6.84241i	2.35571	+	0.280748i
$595$	7.24496	+	27.7497i	0.297014	+	1.13763i
$596$	4.06930	−	12.5240i	0.166685	−	0.513003i
$597$	−77.3961			−3.16761
$598$	−0.895415	+	2.75580i	−0.0366163	+	0.112693i
$599$	−33.4833	+	24.3270i	−1.36809	+	0.993976i	−0.370207	+	0.928949i	$0.620713\pi$
$599$	−33.4833	+	24.3270i	−1.36809	+	0.993976i	−0.997884	+	0.0650264i	$0.979287\pi$
$600$	3.26976	+	16.4163i	0.133487	+	0.670194i
$601$	−1.98926	−	6.12231i	−0.0811435	−	0.249734i	0.902252	−	0.431209i	$-0.141913\pi$
$601$	−1.98926	−	6.12231i	−0.0811435	−	0.249734i	−0.983396	+	0.181475i	$0.941913\pi$
$602$	6.64673	−	4.82913i	0.270900	−	0.196821i
$603$	−30.6146	+	94.2221i	−1.24672	+	3.83702i
$604$	−3.72657	−	11.4692i	−0.151632	−	0.466675i
$605$	−23.2511	+	8.02402i	−0.945293	+	0.326223i
$606$	4.69726	−	14.4567i	0.190813	−	0.587263i
$607$	21.8131	+	15.8481i	0.885366	+	0.643256i	0.934666	−	0.355528i	$-0.115699\pi$
$607$	21.8131	+	15.8481i	0.885366	+	0.643256i	−0.0492995	+	0.998784i	$0.515699\pi$
$608$	1.27041	+	0.923006i	0.0515219	+	0.0374329i
$609$	−14.2220	−	10.3329i	−0.576305	−	0.418710i
$610$	−14.1820	−	0.834545i	−0.574214	−	0.0337897i
$611$	52.5432			2.12567
$612$	20.6074	+	14.9721i	0.833003	+	0.605212i
$613$	−1.82779	−	5.62537i	−0.0738238	−	0.227206i	0.907335	−	0.420408i	$-0.138113\pi$
$613$	−1.82779	−	5.62537i	−0.0738238	−	0.227206i	−0.981159	+	0.193201i	$0.938113\pi$
$614$	3.75604	+	11.5599i	0.151581	+	0.466520i
$615$	−58.6595	−	3.45183i	−2.36538	−	0.139191i
$616$	−10.0576	−	9.31226i	−0.405233	−	0.375202i
$617$	1.00509	−	3.09336i	0.0404635	−	0.124534i	−0.928784	−	0.370621i	$-0.879145\pi$
$617$	1.00509	−	3.09336i	0.0404635	−	0.124534i	0.969248	+	0.246087i	$0.0791449\pi$
$618$	19.6029	+	14.2423i	0.788544	+	0.572911i
$619$	−18.0747	−	13.1321i	−0.726485	−	0.527822i	0.161965	−	0.986797i	$-0.448217\pi$
$619$	−18.0747	−	13.1321i	−0.726485	−	0.527822i	−0.888449	+	0.458975i	$0.848217\pi$
$620$	4.12774	+	3.38667i	0.165774	+	0.136012i
$621$	10.1162	+	7.34983i	0.405948	+	0.294938i
$622$	−19.7003	−	14.3131i	−0.789909	−	0.573902i
$623$	−10.7304	+	33.0246i	−0.429903	+	1.32310i
$624$	−4.17928	+	12.8625i	−0.167305	+	0.514912i
$625$	1.97418	+	24.9219i	0.0789672	+	0.996877i
$626$	−23.6246			−0.944228
$627$	15.2194	−	8.50709i	0.607802	−	0.339741i
$628$	3.98053	+	12.2508i	0.158841	+	0.488861i
$629$	−8.03827	+	24.7393i	−0.320507	+	0.986419i
$630$	19.1598	+	73.3859i	0.763344	+	2.92377i
$631$	12.1508			0.483716			0.241858	−	0.970312i	$-0.422243\pi$
$631$	12.1508			0.483716			0.241858	+	0.970312i	$0.422243\pi$
$632$	−2.01318	+	1.46266i	−0.0800800	+	0.0581815i
$633$	−5.88526	−	18.1130i	−0.233918	−	0.719926i
$634$	2.08042	+	1.51151i	0.0826239	+	0.0600298i
$635$	10.2643	−	26.2348i	0.407325	−	1.04110i
$636$	6.31248	+	19.4278i	0.250306	+	0.770363i
$637$	−32.9428	+	23.9343i	−1.30524	+	0.948312i
$638$	3.67848	−	2.05614i	0.145632	−	0.0814035i
$639$	−49.9687	−	36.3044i	−1.97673	−	1.43618i
$640$	−0.564864	−	2.16355i	−0.0223282	−	0.0855216i
$641$	−12.4204	−	38.2259i	−0.490575	−	1.50983i	−0.823742	−	0.566965i	$-0.808117\pi$
$641$	−12.4204	−	38.2259i	−0.490575	−	1.50983i	0.333167	−	0.942868i	$-0.391883\pi$
$642$	−43.1742			−1.70395
$643$	16.0809	−	11.6835i	0.634170	−	0.460751i	−0.223673	−	0.974664i	$-0.571805\pi$
$643$	16.0809	−	11.6835i	0.634170	−	0.460751i	0.857842	+	0.513913i	$0.171805\pi$
$644$	−0.916002	−	2.81917i	−0.0360955	−	0.111091i
$645$	5.42217	−	13.8587i	0.213498	−	0.545687i
$646$	4.87350			0.191745
$647$	−15.5010	+	47.7073i	−0.609409	+	1.87557i	−0.146369	+	0.989230i	$0.546759\pi$
$647$	−15.5010	+	47.7073i	−0.609409	+	1.87557i	−0.463040	+	0.886338i	$0.653241\pi$
$648$	27.2964	+	19.8320i	1.07231	+	0.779076i
$649$	−1.06043	+	0.592744i	−0.0416255	+	0.0232672i
$650$	−8.45193	+	18.3460i	−0.331512	+	0.719588i
$651$	26.7267	+	19.4181i	1.04750	+	0.761054i
$652$	11.7574	−	8.54227i	0.460456	−	0.334541i
$653$	−12.5528	+	9.12016i	−0.491230	+	0.356900i	−0.805657	−	0.592382i	$-0.798188\pi$
$653$	−12.5528	+	9.12016i	−0.491230	+	0.356900i	0.314427	+	0.949282i	$0.398188\pi$
$654$	24.6207	+	17.8880i	0.962747	+	0.699476i
$655$	−4.28146	−	3.51279i	−0.167291	−	0.137256i
$656$	7.84965			0.306477
$657$	27.6619	−	85.1346i	1.07919	−	3.32142i
$658$	−43.4857	+	31.5942i	−1.69525	+	1.23167i
$659$	36.8328	−	26.7606i	1.43480	−	1.04245i	0.445707	−	0.895179i	$-0.352952\pi$
$659$	36.8328	−	26.7606i	1.43480	−	1.04245i	0.989097	−	0.147267i	$-0.0470475\pi$
$660$	−24.4380	−	4.38124i	−0.951248	−	0.170540i
$661$	−12.6386	−	9.18247i	−0.491584	−	0.357157i	0.314209	−	0.949354i	$-0.398261\pi$
$661$	−12.6386	−	9.18247i	−0.491584	−	0.357157i	−0.805793	+	0.592197i	$0.798261\pi$
$662$	−18.9275			−0.735638
$663$	12.9705	+	39.9191i	0.503732	+	1.55033i
$664$	−1.58810	+	4.88768i	−0.0616303	+	0.189679i
$665$	11.2186	+	9.20448i	0.435039	+	0.356934i
$666$	−21.2578	+	65.4247i	−0.823721	+	2.53515i
$667$	0.911359			0.0352880
$668$	−1.05362	+	3.24272i	−0.0407660	+	0.125465i
$669$	18.7111	−	13.5944i	0.723412	−	0.525590i
$670$	9.83429	−	25.1358i	0.379932	−	0.971083i
$671$	8.83736	−	19.1290i	0.341162	−	0.738468i
$672$	−4.27537	−	13.1582i	−0.164926	−	0.507590i
$673$	6.42493	+	19.7739i	0.247663	+	0.762228i	0.995187	+	0.0979933i	$0.0312424\pi$
$673$	6.42493	+	19.7739i	0.247663	+	0.762228i	−0.747524	+	0.664235i	$0.768758\pi$
$674$	1.86891	−	5.75192i	0.0719878	−	0.221556i
$675$	64.0237	+	59.1526i	2.46427	+	2.27679i
$676$	−2.68624	+	1.95167i	−0.103317	+	0.0750640i
$677$	35.1597			1.35130			0.675649	−	0.737223i	$-0.263863\pi$
$677$	35.1597			1.35130			0.675649	+	0.737223i	$0.263863\pi$
$678$	−17.7713	+	12.9116i	−0.682501	+	0.495866i
$679$	7.52508			0.288786
$680$	−5.36501	−	4.40181i	−0.205739	−	0.168802i
$681$	13.8240	−	42.5459i	0.529737	−	1.63036i
$682$	−6.91278	+	3.86400i	−0.264704	+	0.147960i
$683$	13.5274	−	41.6330i	0.517611	−	1.59304i	−0.260869	−	0.965374i	$-0.584009\pi$
$683$	13.5274	−	41.6330i	0.517611	−	1.59304i	0.778480	−	0.627669i	$-0.215991\pi$
$684$	12.8883			0.492797
$685$	14.5205	+	11.9136i	0.554801	+	0.455195i
$686$	3.93273	−	12.1037i	0.150152	−	0.462122i
$687$	−17.4932	+	53.8384i	−0.667405	+	2.05406i
$688$	−0.614321	+	1.89069i	−0.0234208	+	0.0720817i
$689$	−7.61748	+	23.4442i	−0.290203	+	0.893152i
$690$	−4.15094	−	3.40571i	−0.158024	−	0.129653i
$691$	−17.4207			−0.662717			−0.331358	−	0.943505i	$-0.607507\pi$
$691$	−17.4207			−0.662717			−0.331358	+	0.943505i	$0.607507\pi$
$692$	4.93343	−	15.1835i	0.187541	−	0.577191i
$693$	−111.707	−	13.3130i	−4.24340	−	0.505718i
$694$	−1.84655	+	5.68311i	−0.0700942	+	0.215728i
$695$	−31.6178	−	25.9413i	−1.19933	−	0.984011i
$696$	4.25369			0.161236
$697$	19.7089	−	14.3194i	0.746529	−	0.542385i
$698$	16.3908			0.620400
$699$	−22.9309	+	16.6603i	−0.867325	+	0.630149i
$700$	−4.03644	−	20.2656i	−0.152563	−	0.765967i
$701$	−2.95475	+	9.09379i	−0.111599	+	0.343468i	−0.991223	−	0.132203i	$-0.957795\pi$
$701$	−2.95475	+	9.09379i	−0.111599	+	0.343468i	0.879623	+	0.475671i	$0.157795\pi$
$702$	21.7635	+	66.9812i	0.821410	+	2.52804i
$703$	4.06718	+	12.5175i	0.153397	+	0.472107i
$704$	3.29332	+	0.392489i	0.124122	+	0.0147925i
$705$	−35.4741	+	90.6696i	−1.33603	+	3.41482i
$706$	6.62230	−	4.81138i	0.249233	−	0.181079i
$707$	−5.79867	+	17.8465i	−0.218081	+	0.671185i
$708$	−1.22625			−0.0460854
$709$	−14.4752	+	44.5502i	−0.543629	+	1.67312i	0.180597	+	0.983557i	$0.442197\pi$
$709$	−14.4752	+	44.5502i	−0.543629	+	1.67312i	−0.724227	+	0.689562i	$0.757803\pi$
$710$	13.0091	+	10.6735i	0.488222	+	0.400570i
$711$	−6.31128	+	19.4241i	−0.236691	+	0.728461i
$712$	−2.59643	−	7.99100i	−0.0973054	−	0.299475i
$713$	−1.71267			−0.0641399
$714$	−34.7379	−	25.2386i	−1.30003	−	0.944530i
$715$	−20.7504	−	21.6111i	−0.776021	−	0.808211i
$716$	11.4735	−	8.33600i	0.428786	−	0.311531i
$717$	−21.7326	+	15.7897i	−0.811621	+	0.589677i
$718$	−4.94653	+	15.2238i	−0.184603	+	0.568149i
$719$	−10.8743			−0.405544			−0.202772	−	0.979226i	$-0.564995\pi$
$719$	−10.8743			−0.405544			−0.202772	+	0.979226i	$0.564995\pi$
$720$	−14.1881	−	11.6409i	−0.528761	−	0.433830i
$721$	−24.1993	−	17.5818i	−0.901230	−	0.654782i
$722$	−13.3764	+	9.71851i	−0.497817	+	0.361686i
$723$	−75.0082	+	54.4967i	−2.78959	+	2.02675i
$724$	−1.60411	−	1.16545i	−0.0596163	−	0.0433138i
$725$	6.30921	+	0.745113i	0.234318	+	0.0276728i
$726$	19.2919	−	31.3676i	0.715990	−	1.16416i
$727$	−27.0464	−	19.6504i	−1.00310	−	0.728791i	−0.0403455	−	0.999186i	$-0.512846\pi$
$727$	−27.0464	−	19.6504i	−1.00310	−	0.728791i	−0.962750	+	0.270395i	$0.912846\pi$
$728$	5.15923	−	15.8785i	0.191214	−	0.588495i
$729$	101.834			3.77164
$730$	−8.88578	+	22.7115i	−0.328878	+	0.840591i
$731$	1.90656	+	5.86779i	0.0705167	+	0.217028i
$732$	17.2074	−	12.5019i	0.636005	−	0.462084i
$733$	32.3989			1.19668			0.598341	−	0.801242i	$-0.295827\pi$
$733$	32.3989			1.19668			0.598341	+	0.801242i	$0.295827\pi$
$734$	3.04209	+	9.36259i	0.112286	+	0.345579i
$735$	−19.0605	−	73.0058i	−0.703059	−	2.69286i
$736$	0.580276	+	0.421595i	0.0213893	+	0.0155402i
$737$	29.3762	+	27.1991i	1.08209	+	1.00189i
$738$	52.1216	−	37.8686i	1.91862	−	1.39396i
$739$	−16.1977	−	49.8515i	−0.595844	−	1.83382i	−0.550482	−	0.834847i	$-0.685556\pi$
$739$	−16.1977	−	49.8515i	−0.595844	−	1.83382i	−0.0453616	−	0.998971i	$-0.514444\pi$
$740$	6.82859	−	17.4535i	0.251024	−	0.641603i
$741$	17.1816	+	12.4831i	0.631180	+	0.458579i
$742$	−7.79262	−	23.9832i	−0.286076	−	0.880451i
$743$	−7.49588	+	5.44607i	−0.274997	+	0.199797i	−0.716732	−	0.697348i	$-0.754363\pi$
$743$	−7.49588	+	5.44607i	−0.274997	+	0.199797i	0.441735	+	0.897145i	$0.354363\pi$
$744$	−7.99374			−0.293065
$745$	7.43842	+	28.4907i	0.272523	+	1.04382i
$746$	−1.82318	+	5.61118i	−0.0667515	+	0.205440i
$747$	13.0343	+	40.1155i	0.476901	+	1.46775i
$748$	8.98486	−	5.02223i	0.328519	−	0.183631i
$749$	53.2976			1.94745
$750$	−25.9519	−	26.9710i	−0.947630	−	0.984840i
$751$	−3.12172	+	9.60765i	−0.113913	+	0.350588i	−0.991719	−	0.128429i	$-0.959007\pi$
$751$	−3.12172	+	9.60765i	−0.113913	+	0.350588i	0.877806	+	0.479017i	$0.159007\pi$
$752$	4.01914	−	12.3697i	0.146563	−	0.451075i
$753$	−40.5427	−	29.4560i	−1.47746	−	1.07344i
$754$	4.15274	+	3.01714i	0.151234	+	0.109878i
$755$	20.8470	+	17.1042i	0.758698	+	0.622486i
$756$	−58.2876	−	42.3484i	−2.11990	−	1.54020i
$757$	−2.79648	−	2.03176i	−0.101640	−	0.0738456i	0.535805	−	0.844342i	$-0.320008\pi$
$757$	−2.79648	−	2.03176i	−0.101640	−	0.0738456i	−0.637444	+	0.770496i	$0.720008\pi$
$758$	−10.0885	+	31.0491i	−0.366430	+	1.12775i
$759$	6.95164	−	3.88573i	0.252329	−	0.141043i
$760$	−3.50526	−	0.206268i	−0.127149	−	0.00748212i
$761$	12.5111	+	38.5053i	0.453528	+	1.39582i	0.872854	+	0.487981i	$0.162267\pi$
$761$	12.5111	+	38.5053i	0.453528	+	1.39582i	−0.419326	+	0.907836i	$0.637733\pi$
$762$	13.0334	+	40.1127i	0.472151	+	1.45313i
$763$	−30.3937	−	22.0823i	−1.10033	−	0.799434i
$764$	−6.82150			−0.246793
$765$	−56.8590	−	3.34588i	−2.05574	−	0.120971i
$766$	−11.8107	−	8.58101i	−0.426740	−	0.310044i
$767$	−1.19715	−	0.869780i	−0.0432266	−	0.0314060i
$768$	2.70839	+	1.96776i	0.0977307	+	0.0710055i
$769$	−16.2751	+	50.0895i	−0.586894	+	1.80627i	0.00463502	+	0.999989i	$0.498525\pi$
$769$	−16.2751	+	50.0895i	−0.586894	+	1.80627i	−0.591529	+	0.806284i	$0.701475\pi$
$770$	30.1682	+	5.40855i	1.08719	+	0.194911i
$771$	3.97348	+	12.2291i	0.143101	+	0.440421i
$772$	−5.52074	+	16.9911i	−0.198696	+	0.611523i
$773$	7.12134	−	5.17396i	0.256137	−	0.186094i	−0.452305	−	0.891863i	$-0.649398\pi$
$773$	7.12134	−	5.17396i	0.256137	−	0.186094i	0.708442	+	0.705769i	$0.249398\pi$
$774$	5.04203	+	15.5178i	0.181232	+	0.557774i
$775$	−11.8566	−	1.40025i	−0.425900	−	0.0502985i
$776$	−1.47310	+	1.07027i	−0.0528812	+	0.0384204i
$777$	35.8343	−	110.287i	1.28555	−	3.95651i
$778$	−26.5618			−0.952285
$779$	3.80907	−	11.7231i	0.136474	−	0.420024i
$780$	−7.63946	−	29.2607i	−0.273537	−	1.04770i
$781$	−21.7865	+	12.1779i	−0.779582	+	0.435759i
$782$	2.22604			0.0796029
$783$	17.9206	−	13.0200i	0.640428	−	0.465298i
$784$	3.11473	+	9.58614i	0.111240	+	0.342362i
$785$	−22.2677	−	18.2698i	−0.794767	−	0.652079i
$786$	8.29145			0.295746
$787$	6.55555	−	20.1759i	0.233680	−	0.719193i	−0.763614	−	0.645673i	$-0.776577\pi$
$787$	6.55555	−	20.1759i	0.233680	−	0.719193i	0.997294	−	0.0735197i	$-0.0234232\pi$
$788$	−10.7130	−	7.78344i	−0.381634	−	0.277274i
$789$	−29.0249	+	21.0879i	−1.03332	+	0.750748i
$790$	2.02736	−	5.18181i	0.0721303	−	0.184361i
$791$	21.9382	−	15.9390i	0.780033	−	0.566727i
$792$	23.7611	−	13.2816i	0.844313	−	0.471942i
$793$	25.6667			0.911450
$794$	−24.3201	+	17.6696i	−0.863089	+	0.627071i
$795$	−35.3129	−	28.9730i	−1.25242	−	1.02757i
$796$	−18.7035	+	13.5889i	−0.662928	+	0.481645i
$797$	13.1682	+	9.56727i	0.466442	+	0.338890i	0.796053	−	0.605227i	$-0.206918\pi$
$797$	13.1682	+	9.56727i	0.466442	+	0.338890i	−0.329611	+	0.944117i	$0.606918\pi$
$798$	−21.7259			−0.769087
$799$	−12.4735	−	38.3895i	−0.441281	−	1.35812i
$800$	3.67248	+	3.39307i	0.129842	+	0.119963i
$801$	−55.7907	−	40.5343i	−1.97127	−	1.43221i
$802$	5.99518	+	4.35576i	0.211697	+	0.153807i
$803$	−26.5429	−	24.5758i	−0.936678	−	0.867262i
$804$	12.4874	+	38.4324i	0.440398	+	1.35541i
$805$	5.12425	+	4.20427i	0.180606	+	0.148181i
$806$	−7.80403	−	5.66996i	−0.274885	−	0.199716i
$807$	10.5623	+	32.5073i	0.371810	+	1.14431i
$808$	−1.40311	−	4.31832i	−0.0493612	−	0.151918i
$809$	12.6655	−	38.9804i	0.445296	−	1.37048i	−0.436863	−	0.899528i	$-0.643911\pi$
$809$	12.6655	−	38.9804i	0.445296	−	1.37048i	0.882159	−	0.470952i	$-0.156089\pi$
$810$	−75.3152	−	4.43194i	−2.64631	−	0.155723i
$811$	−18.9527	+	13.7699i	−0.665518	+	0.483527i	−0.868522	−	0.495651i	$-0.834930\pi$
$811$	−18.9527	+	13.7699i	−0.665518	+	0.483527i	0.203004	+	0.979178i	$0.434930\pi$
$812$	−5.25109			−0.184277
$813$	84.6391	−	61.4939i	2.96842	−	2.15669i
$814$	20.3978	+	18.8862i	0.714943	+	0.661959i
$815$	−11.8402	+	30.2630i	−0.414746	+	1.06007i
$816$	10.3898			0.363717
$817$	2.52555	+	1.83492i	0.0883580	+	0.0641958i
$818$	−3.45368	−	10.6293i	−0.120755	−	0.371646i
$819$	−42.3442	−	130.322i	−1.47963	−	4.55382i
$820$	−14.7817	+	9.46503i	−0.516199	+	0.330533i
$821$	−14.0702	+	10.2226i	−0.491054	+	0.356772i	−0.805590	−	0.592474i	$-0.798151\pi$
$821$	−14.0702	+	10.2226i	−0.491054	+	0.356772i	0.314535	+	0.949246i	$0.398151\pi$
$822$	−28.1204			−0.980810
$823$	−5.88131	−	18.1008i	−0.205010	−	0.630955i	−0.999713	−	0.0239569i	$-0.992374\pi$
$823$	−5.88131	−	18.1008i	−0.205010	−	0.630955i	0.794703	−	0.606998i	$-0.207626\pi$
$824$	7.23783			0.252142
$825$	51.3021	−	21.2168i	1.78611	−	0.738673i
$826$	1.51378			0.0526712
$827$	−1.89125	−	5.82066i	−0.0657651	−	0.202404i	0.912774	−	0.408465i	$-0.133936\pi$
$827$	−1.89125	−	5.82066i	−0.0657651	−	0.202404i	−0.978539	+	0.206060i	$0.933936\pi$
$828$	5.88690			0.204584
$829$	−0.295799	+	0.214910i	−0.0102735	+	0.00746414i	−0.592910	−	0.805269i	$-0.702021\pi$
$829$	−0.295799	+	0.214910i	−0.0102735	+	0.00746414i	0.582637	+	0.812733i	$0.302021\pi$
$830$	−2.90295	−	11.1189i	−0.100763	−	0.385943i
$831$	−10.2550	−	31.5617i	−0.355743	−	1.09486i
$832$	1.24838	+	3.84212i	0.0432798	+	0.133202i
$833$	25.3075	+	18.3870i	0.876855	+	0.637072i
$834$	61.2308			2.12025
$835$	−1.92596	−	7.37683i	−0.0666506	−	0.255286i
$836$	2.18426	−	4.72797i	0.0755442	−	0.163520i
$837$	−33.6771	+	24.4679i	−1.16405	+	0.845734i
$838$	7.60297			0.262640
$839$	34.6239	−	25.1557i	1.19535	−	0.868473i	0.201531	−	0.979482i	$-0.435408\pi$
$839$	34.6239	−	25.1557i	1.19535	−	0.868473i	0.993819	+	0.111009i	$0.0354084\pi$
$840$	23.9170	+	19.6231i	0.825215	+	0.677061i
$841$	−8.46260	+	26.0452i	−0.291814	+	0.898111i
$842$	1.44593	+	4.45012i	0.0498301	+	0.153361i
$843$	−4.80528	−	14.7891i	−0.165503	−	0.509364i
$844$	−4.60243	−	3.34386i	−0.158422	−	0.115100i
$845$	2.70516	−	6.91422i	0.0930603	−	0.237856i
$846$	−32.9870	−	101.524i	−1.13412	−	3.49046i
$847$	−23.8154	+	38.7226i	−0.818308	+	1.33052i
$848$	4.93653	+	3.58660i	0.169521	+	0.123164i
$849$	−27.3846	−	19.8961i	−0.939839	−	0.682833i
$850$	15.4105	+	1.81997i	0.528576	+	0.0624246i
$851$	1.85774	+	5.71753i	0.0636825	+	0.195995i
$852$	−25.1933			−0.863108
$853$	−15.2680	−	11.0928i	−0.522765	−	0.379811i	0.294879	−	0.955535i	$-0.404721\pi$
$853$	−15.2680	−	11.0928i	−0.522765	−	0.379811i	−0.817645	+	0.575723i	$0.804721\pi$
$854$	−21.2422	+	15.4333i	−0.726892	+	0.528118i
$855$	−24.2700	+	15.5406i	−0.830016	+	0.531477i
$856$	−10.4335	+	7.58035i	−0.356608	+	0.259091i
$857$	−47.4027			−1.61924			−0.809622	−	0.586952i	$-0.800328\pi$
$857$	−47.4027			−1.61924			−0.809622	+	0.586952i	$0.800328\pi$
$858$	44.5403	+	5.30820i	1.52058	+	0.181219i
$859$	30.3724	−	22.0669i	1.03629	−	0.752912i	0.0667358	−	0.997771i	$-0.478742\pi$
$859$	30.3724	−	22.0669i	1.03629	−	0.752912i	0.969559	+	0.244859i	$0.0787415\pi$
$860$	−1.12294	−	4.30110i	−0.0382920	−	0.146666i
$861$	−87.8616	+	63.8352i	−2.99431	+	2.17550i
$862$	−9.96999	−	7.24362i	−0.339579	−	0.246719i
$863$	−7.67589	+	23.6240i	−0.261290	+	0.804169i	0.731235	+	0.682126i	$0.238945\pi$
$863$	−7.67589	+	23.6240i	−0.261290	+	0.804169i	−0.992525	+	0.122043i	$0.961055\pi$
$864$	17.4334			0.593095
$865$	9.01800	+	34.5408i	0.306621	+	1.17442i
$866$	4.35082	+	13.3905i	0.147847	+	0.455026i
$867$	−19.9558	+	14.4988i	−0.677735	+	0.492404i
$868$	9.86810			0.334945
$869$	6.05597	+	5.60716i	0.205435	+	0.190210i
$870$	−8.01014	+	5.12906i	−0.271569	+	0.173891i
$871$	−15.0690	+	46.3776i	−0.510593	+	1.57145i
$872$	9.09053			0.307844
$873$	−4.61813	+	14.2131i	−0.156300	+	0.481042i
$874$	0.911215	−	0.662036i	0.0308223	−	0.0223937i
$875$	32.0371	+	33.2950i	1.08305	+	1.12558i
$876$	−11.2830	−	34.7256i	−0.381219	−	1.17327i
$877$	13.1183	−	9.53098i	0.442972	−	0.321838i	−0.343843	−	0.939027i	$-0.611729\pi$
$877$	13.1183	−	9.53098i	0.442972	−	0.321838i	0.786815	+	0.617189i	$0.211729\pi$
$878$	0.502945	−	1.54790i	0.0169736	−	0.0522393i
$879$	2.76110	+	8.49779i	0.0931295	+	0.286623i
$880$	−6.67491	+	3.23195i	−0.225011	+	0.108949i
$881$	−10.7582	+	33.1103i	−0.362453	+	1.11552i	0.589108	+	0.808055i	$0.299479\pi$
$881$	−10.7582	+	33.1103i	−0.362453	+	1.11552i	−0.951561	+	0.307461i	$0.900521\pi$
$882$	66.9275	+	48.6257i	2.25357	+	1.63731i
$883$	38.9126	+	28.2716i	1.30951	+	0.951416i	1.00000		0.000521034i	$0.000165850\pi$
$883$	38.9126	+	28.2716i	1.30951	+	0.951416i	0.309512	+	0.950895i	$0.399834\pi$
$884$	10.1433	+	7.36951i	0.341155	+	0.247863i
$885$	2.30916	−	1.47860i	0.0776215	−	0.0497027i
$886$	−11.3059			−0.379829
$887$	−41.6897	−	30.2893i	−1.39980	−	1.01702i	−0.994708	−	0.102742i	$-0.967238\pi$
$887$	−41.6897	−	30.2893i	−1.39980	−	1.01702i	−0.405095	−	0.914275i	$-0.632762\pi$
$888$	8.67085	+	26.6861i	0.290975	+	0.895528i
$889$	−16.0895	−	49.5183i	−0.539623	−	1.66079i
$890$	14.5248	+	11.9171i	0.486873	+	0.399462i
$891$	46.9317	−	101.587i	1.57227	−	3.40328i
$892$	2.13486	−	6.57043i	0.0714804	−	0.219994i
$893$	−16.5232	−	12.0048i	−0.552929	−	0.401726i
$894$	−35.6655	−	25.9125i	−1.19283	−	0.866644i
$895$	−11.5543	+	29.5322i	−0.386219	+	0.987153i
$896$	−3.34345	−	2.42916i	−0.111697	−	0.0811525i
$897$	7.84790	+	5.70184i	0.262034	+	0.190379i
$898$	−0.627658	+	1.93173i	−0.0209452	+	0.0644627i
$899$	−0.937543	+	2.88546i	−0.0312688	+	0.0962355i
$900$	40.7542	+	4.81304i	1.35847	+	0.160435i
$901$	18.9373			0.630894
$902$	−5.05841	−	25.5382i	−0.168427	−	0.850329i
$903$	−8.49937	−	26.1584i	−0.282841	−	0.870496i
$904$	−2.02763	+	6.24041i	−0.0674380	+	0.207553i
$905$	4.42600	+	0.260449i	0.147125	+	0.00865761i
$906$	−40.3721			−1.34127
$907$	42.7452	−	31.0562i	1.41933	−	1.03120i	0.427448	−	0.904040i	$-0.359413\pi$
$907$	42.7452	−	31.0562i	1.41933	−	1.03120i	0.991882	−	0.127164i	$-0.0405873\pi$
$908$	−4.12934	−	12.7088i	−0.137037	−	0.421756i
$909$	−30.1492	−	21.9047i	−0.999986	−	0.726533i
$910$	9.43075	+	36.1217i	0.312626	+	1.19742i
$911$	−0.995658	−	3.06432i	−0.0329876	−	0.101525i	0.933207	−	0.359339i	$-0.116998\pi$
$911$	−0.995658	−	3.06432i	−0.0329876	−	0.101525i	−0.966195	+	0.257814i	$0.916998\pi$
$912$	4.25302	−	3.09000i	0.140832	−	0.102320i
$913$	16.9251	+	2.01709i	0.560138	+	0.0667558i
$914$	3.80668	+	2.76571i	0.125914	+	0.0914817i
$915$	−17.3286	+	44.2909i	−0.572867	+	1.46421i
$916$	5.22534	+	16.0819i	0.172650	+	0.531362i
$917$	−10.2356			−0.338010
$918$	43.7718	−	31.8020i	1.44468	−	1.04962i
$919$	3.90994	+	12.0335i	0.128977	+	0.396950i	0.994605	−	0.103738i	$-0.0330803\pi$
$919$	3.90994	+	12.0335i	0.128977	+	0.396950i	−0.865628	+	0.500688i	$0.833080\pi$
$920$	−1.60107	−	0.0942156i	−0.0527859	−	0.00310620i
$921$	40.6913			1.34082
$922$	10.7855	−	33.1942i	0.355200	−	1.09319i
$923$	−24.5954	−	17.8696i	−0.809567	−	0.588185i
$924$	−40.0541	+	22.3889i	−1.31768	+	0.736540i
$925$	8.18629	+	41.1005i	0.269164	+	1.35138i
$926$	−33.2061	−	24.1256i	−1.09122	−	0.792818i
$927$	48.0591	−	34.9170i	1.57847	−	1.14682i
$928$	1.02795	−	0.746846i	0.0337440	−	0.0245164i
$929$	8.27228	+	6.01016i	0.271405	+	0.197187i	0.715160	−	0.698961i	$-0.246354\pi$
$929$	8.27228	+	6.01016i	0.271405	+	0.197187i	−0.443755	+	0.896148i	$0.646354\pi$
$930$	15.0530	−	9.63878i	0.493608	−	0.316068i
$931$	15.8279			0.518739
$932$	−2.61632	+	8.05221i	−0.0857005	+	0.263759i
$933$	−65.9517	+	47.9167i	−2.15916	+	1.56872i
$934$	−15.8694	+	11.5298i	−0.519264	+	0.377267i
$935$	−10.8636	+	20.2912i	−0.355279	+	0.663594i
$936$	26.8245	+	19.4892i	0.876788	+	0.637024i
$937$	−21.6352			−0.706792			−0.353396	−	0.935474i	$-0.614973\pi$
$937$	−21.6352			−0.706792			−0.353396	+	0.935474i	$0.614973\pi$
$938$	−15.4155	−	47.4439i	−0.503333	−	1.54910i
$939$	−24.4400	+	75.2185i	−0.797568	+	2.45466i
$940$	7.34675	+	28.1396i	0.239625	+	0.917811i
$941$	−6.96626	+	21.4400i	−0.227094	+	0.698922i	0.770979	+	0.636861i	$0.219767\pi$
$941$	−6.96626	+	21.4400i	−0.227094	+	0.698922i	−0.998072	+	0.0620615i	$0.980233\pi$
$942$	43.1234			1.40504
$943$	1.73984	−	5.35468i	0.0566570	−	0.174372i
$944$	−0.296335	+	0.215300i	−0.00964490	+	0.00700743i
$945$	160.825	+	9.46377i	5.23163	+	0.307856i
$946$	6.54707	+	0.780263i	0.212864	+	0.0253685i
$947$	−8.68240	−	26.7217i	−0.282140	−	0.868337i	−0.987241	−	0.159231i	$-0.949099\pi$
$947$	−8.68240	−	26.7217i	−0.282140	−	0.868337i	0.705101	−	0.709106i	$-0.250901\pi$
$948$	2.57431	+	7.92292i	0.0836098	+	0.257324i
$949$	13.6156	−	41.9045i	0.441981	−	1.36028i
$950$	6.84948	−	3.83819i	0.222226	−	0.124527i
$951$	6.96473	−	5.06017i	0.225847	−	0.164087i
$952$	−12.8260			−0.415694
$953$	42.4969	−	30.8758i	1.37661	−	1.00016i	0.379420	−	0.925224i	$-0.376123\pi$
$953$	42.4969	−	30.8758i	1.37661	−	1.00016i	0.997188	−	0.0749401i	$-0.0238766\pi$
$954$	50.0811			1.62143
$955$	12.8456	−	8.22530i	0.415673	−	0.266164i
$956$	−2.47961	+	7.63145i	−0.0801963	+	0.246819i
$957$	−2.74113	−	13.8390i	−0.0886082	−	0.447353i
$958$	−1.44789	+	4.45614i	−0.0467791	+	0.143971i
$959$	34.7139			1.12097
$960$	−7.47289	−	0.439744i	−0.241186	−	0.0141927i
$961$	−7.81765	+	24.0603i	−0.252182	+	0.776137i
$962$	−10.4634	+	32.2030i	−0.337353	+	1.03827i
$963$	−32.7086	+	100.667i	−1.05402	+	3.24394i
$964$	−8.55814	+	26.3393i	−0.275639	+	0.848330i
$965$	−10.0916	−	38.6528i	−0.324859	−	1.24428i
$966$	−9.92358			−0.319286
$967$	−2.62523	+	8.07964i	−0.0844218	+	0.259824i	−0.984353	−	0.176209i	$-0.943617\pi$
$967$	−2.62523	+	8.07964i	−0.0844218	+	0.259824i	0.899931	+	0.436032i	$0.143617\pi$
$968$	−0.845322	−	10.9675i	−0.0271697	−	0.352508i
$969$	5.04170	−	15.5168i	0.161963	−	0.498470i
$970$	1.48347	−	3.79167i	0.0476315	−	0.121743i
$971$	48.9032			1.56938			0.784689	−	0.619890i	$-0.212823\pi$
$971$	48.9032			1.56938			0.784689	+	0.619890i	$0.212823\pi$
$972$	49.0702	−	35.6516i	1.57393	−	1.14352i
$973$	−75.5881			−2.42324
$974$	13.4487	−	9.77102i	0.430923	−	0.313084i
$975$	49.6682	+	45.8893i	1.59065	+	1.46963i
$976$	1.96330	−	6.04241i	0.0628437	−	0.193413i
$977$	−6.82318	−	20.9996i	−0.218293	−	0.671836i	−0.998903	−	0.0468185i	$-0.985092\pi$
$977$	−6.82318	−	20.9996i	−0.218293	−	0.671836i	0.780611	−	0.625018i	$-0.214908\pi$
$978$	−15.0346	−	46.2716i	−0.480753	−	1.47960i
$979$	−24.3249	+	13.5968i	−0.777427	+	0.434555i
$980$	−17.4242	−	14.2960i	−0.556596	−	0.456668i
$981$	60.3610	−	43.8549i	1.92718	−	1.40018i
$982$	6.68977	−	20.5890i	0.213479	−	0.657021i
$983$	−40.2611			−1.28413			−0.642064	−	0.766651i	$-0.721922\pi$
$983$	−40.2611			−1.28413			−0.642064	+	0.766651i	$0.721922\pi$
$984$	8.12057	−	24.9925i	0.258874	−	0.796733i
$985$	29.5588	+	1.73940i	0.941823	+	0.0554218i
$986$	1.21857	−	3.75037i	0.0388071	−	0.119436i
$987$	55.6064	+	171.139i	1.76997	+	5.44741i
$988$	6.34382			0.201824
$989$	1.15358	+	0.838125i	0.0366817	+	0.0266508i
$990$	−28.7297	+	53.6615i	−0.913088	+	1.70547i
$991$	−22.2701	+	16.1802i	−0.707435	+	0.513981i	−0.882345	−	0.470603i	$-0.844036\pi$
$991$	−22.2701	+	16.1802i	−0.707435	+	0.513981i	0.174910	+	0.984584i	$0.444036\pi$
$992$	−1.93176	+	1.40351i	−0.0613335	+	0.0445614i
$993$	−19.5808	+	60.2634i	−0.621377	+	1.91240i
$994$	31.1006			0.986450
$995$	18.8352	−	48.1418i	0.597117	−	1.52620i
$996$	13.9190	+	10.1127i	0.441040	+	0.320434i
$997$	−42.5404	+	30.9074i	−1.34727	+	0.978846i	−0.348124	+	0.937449i	$0.613181\pi$
$997$	−42.5404	+	30.9074i	−1.34727	+	0.978846i	−0.999143	+	0.0413977i	$0.986819\pi$
$998$	−2.64413	+	1.92107i	−0.0836984	+	0.0608104i
$999$	118.213	+	85.8866i	3.74009	+	2.71733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.l.d.191.1	yes	48
11.3	even	5		550.2.i.d.91.12	✓	48
25.11	even	5		550.2.i.d.411.12	yes	48
275.36	even	5	inner	550.2.l.d.311.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.i.d.91.12	✓	48	11.3	even	5
550.2.i.d.411.12	yes	48	25.11	even	5
550.2.l.d.191.1	yes	48	1.1	even	1	trivial
550.2.l.d.311.1	yes	48	275.36	even	5	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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} -3.34776 q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.814715 - 2.08236i) q^{5} +(1.03451 + 3.18391i) q^{6} +(-1.27708 - 3.93046i) q^{7} +(0.809017 + 0.587785i) q^{8} +8.20748 q^{9} +(-2.23221 - 0.131355i) q^{10} +(1.39097 - 3.01085i) q^{11} +(2.70839 - 1.96776i) q^{12} +4.03985 q^{13} +(-3.34345 + 2.42916i) q^{14} +(-2.72747 + 6.97125i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.959041 - 2.95163i) q^{17} +(-2.53625 - 7.80578i) q^{18} +(-1.27041 - 0.923006i) q^{19} +(0.564864 + 2.16355i) q^{20} +(4.27537 + 13.1582i) q^{21} +(-3.29332 - 0.392489i) q^{22} +(-0.580276 - 0.421595i) q^{23} +(-2.70839 - 1.96776i) q^{24} +(-3.67248 - 3.39307i) q^{25} +(-1.24838 - 3.84212i) q^{26} -17.4334 q^{27} +(3.34345 + 2.42916i) q^{28} +(-1.02795 + 0.746846i) q^{29} +(7.47289 + 0.439744i) q^{30} +(1.93176 - 1.40351i) q^{31} -1.00000 q^{32} +(-4.65663 + 10.0796i) q^{33} +(-2.51080 + 1.82421i) q^{34} +(-9.22511 - 0.542854i) q^{35} +(-6.63999 + 4.82423i) q^{36} +(-6.78083 - 4.92656i) q^{37} +(-0.485253 + 1.49346i) q^{38} -13.5244 q^{39} +(1.88310 - 1.20579i) q^{40} +(2.42568 + 7.46546i) q^{41} +(11.1931 - 8.13223i) q^{42} -1.98798 q^{43} +(0.644412 + 3.25342i) q^{44} +(6.68676 - 17.0910i) q^{45} +(-0.221646 + 0.682156i) q^{46} +13.0062 q^{47} +(-1.03451 + 3.18391i) q^{48} +(-8.15446 + 5.92456i) q^{49} +(-2.09214 + 4.54125i) q^{50} +(3.21064 + 9.88133i) q^{51} +(-3.26831 + 2.37456i) q^{52} +(-1.88559 + 5.80323i) q^{53} +(5.38721 + 16.5801i) q^{54} +(-5.13643 - 5.34949i) q^{55} +(1.27708 - 3.93046i) q^{56} +(4.25302 + 3.09000i) q^{57} +(1.02795 + 0.746846i) q^{58} +(-0.296335 - 0.215300i) q^{59} +(-1.89103 - 7.24302i) q^{60} +6.35337 q^{61} +(-1.93176 - 1.40351i) q^{62} +(-10.4816 - 32.2592i) q^{63} +(0.309017 + 0.951057i) q^{64} +(3.29133 - 8.41243i) q^{65} +(11.0252 + 1.31396i) q^{66} +(-3.73009 + 11.4800i) q^{67} +(2.51080 + 1.82421i) q^{68} +(1.94262 + 1.41140i) q^{69} +(2.33443 + 8.94135i) q^{70} +(-6.08820 - 4.42333i) q^{71} +(6.63999 + 4.82423i) q^{72} +(3.37033 - 10.3728i) q^{73} +(-2.59005 + 7.97135i) q^{74} +(12.2946 + 11.3592i) q^{75} +1.57031 q^{76} +(-13.6104 - 1.62205i) q^{77} +(4.17928 + 12.8625i) q^{78} +(-0.768966 + 2.36664i) q^{79} +(-1.72868 - 1.41833i) q^{80} +33.7403 q^{81} +(6.35050 - 4.61391i) q^{82} +(1.58810 + 4.88768i) q^{83} +(-11.1931 - 8.13223i) q^{84} +(-6.92770 - 0.407662i) q^{85} +(0.614321 + 1.89069i) q^{86} +(3.44131 - 2.50026i) q^{87} +(2.89505 - 1.61823i) q^{88} +(-6.79755 - 4.93871i) q^{89} +(-18.3208 - 1.07809i) q^{90} +(-5.15923 - 15.8785i) q^{91} +0.717261 q^{92} +(-6.46707 + 4.69860i) q^{93} +(-4.01914 - 12.3697i) q^{94} +(-2.95706 + 1.89347i) q^{95} +3.34776 q^{96} +(-0.562674 + 1.73173i) q^{97} +(8.15446 + 5.92456i) q^{98} +(11.4164 - 24.7115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 22 q^{3} - 12 q^{4} - q^{5} - 3 q^{6} + 11 q^{7} + 12 q^{8} + 70 q^{9} + 6 q^{10} + 3 q^{11} + 8 q^{12} - 34 q^{13} - q^{14} + 7 q^{15} - 12 q^{16} - 9 q^{17} + 10 q^{18} - 6 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) \) 48 * q + 12 * q^2 - 22 * q^3 - 12 * q^4 - q^5 - 3 * q^6 + 11 * q^7 + 12 * q^8 + 70 * q^9 + 6 * q^10 + 3 * q^11 + 8 * q^12 - 34 * q^13 - q^14 + 7 * q^15 - 12 * q^16 - 9 * q^17 + 10 * q^18 - 6 * q^19 + 19 * q^20 - 15 * q^21 - 8 * q^22 + 14 * q^23 - 8 * q^24 + 7 * q^25 - 16 * q^26 - 34 * q^27 + q^28 - q^29 - 12 * q^30 + 17 * q^31 - 48 * q^32 + 4 * q^34 - 41 * q^35 - 25 * q^36 - 23 * q^37 + q^38 - 20 * q^39 + 6 * q^40 + 29 * q^41 + 22 * q^43 + 13 * q^44 + 62 * q^45 - 9 * q^46 - 52 * q^47 + 3 * q^48 - 23 * q^49 - 2 * q^50 + 4 * q^51 + q^52 + 44 * q^53 - 11 * q^54 - 7 * q^55 - 11 * q^56 - 5 * q^57 + q^58 - 18 * q^59 + 2 * q^60 + 16 * q^61 - 17 * q^62 - 13 * q^63 - 12 * q^64 - 2 * q^65 + 20 * q^67 - 4 * q^68 - 2 * q^69 - 59 * q^70 + 39 * q^71 + 25 * q^72 - 42 * q^73 - 37 * q^74 + 20 * q^75 + 14 * q^76 - 13 * q^77 - 15 * q^78 + 53 * q^79 - 6 * q^80 + 56 * q^81 + 36 * q^82 + 14 * q^83 + 6 * q^85 + 13 * q^86 - 18 * q^87 + 17 * q^88 - 8 * q^89 + 28 * q^90 - 5 * q^91 - 46 * q^92 + 15 * q^93 - 13 * q^94 - 24 * q^95 + 22 * q^96 - 16 * q^97 + 23 * q^98 - 54 * q^99

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