LMFDB - Embedded newform 558.2.g.a.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	558.211
Dual form			558.2.g.a.439.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.69035 - 0.377782i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17303 - 2.03175i) q^{5} +(0.518006 + 1.65278i) q^{6} +(1.52021 - 2.63308i) q^{7} +1.00000 q^{8} +(2.71456 + 1.27717i) q^{9} +(-1.17303 + 2.03175i) q^{10} +5.84199 q^{11} +(1.17234 - 1.27499i) q^{12} +(-2.70313 - 4.68195i) q^{13} -3.04042 q^{14} +(1.21527 + 3.87751i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83888 + 3.18503i) q^{17} +(-0.251223 - 2.98946i) q^{18} +(-2.58676 - 4.48039i) q^{19} +2.34606 q^{20} +(-3.56442 + 3.87652i) q^{21} +(-2.92100 - 5.05931i) q^{22} +(-2.63277 + 4.56010i) q^{23} +(-1.69035 - 0.377782i) q^{24} +(-0.251992 + 0.436463i) q^{25} +(-2.70313 + 4.68195i) q^{26} +(-4.10607 - 3.18437i) q^{27} +(1.52021 + 2.63308i) q^{28} +(-0.623172 - 1.07937i) q^{29} +(2.75038 - 2.99121i) q^{30} +(-4.74093 - 2.91951i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.87501 - 2.20700i) q^{33} +(1.83888 - 3.18503i) q^{34} -7.13300 q^{35} +(-2.46334 + 1.71230i) q^{36} +(-2.03817 - 3.53022i) q^{37} +(-2.58676 + 4.48039i) q^{38} +(2.80047 + 8.93532i) q^{39} +(-1.17303 - 2.03175i) q^{40} +(1.47475 + 2.55433i) q^{41} +(5.13937 + 1.14861i) q^{42} +(-4.91997 + 8.52163i) q^{43} +(-2.92100 + 5.05931i) q^{44} +(-0.589384 - 7.01345i) q^{45} +5.26555 q^{46} +(-4.27777 - 7.40932i) q^{47} +(0.518006 + 1.65278i) q^{48} +(-1.12208 - 1.94350i) q^{49} +0.503984 q^{50} +(-1.90510 - 6.07851i) q^{51} +5.40625 q^{52} +(5.39327 - 9.34142i) q^{53} +(-0.704708 + 5.14814i) q^{54} +(-6.85282 - 11.8694i) q^{55} +(1.52021 - 2.63308i) q^{56} +(2.67991 + 8.55066i) q^{57} +(-0.623172 + 1.07937i) q^{58} +4.76336 q^{59} +(-3.96566 - 0.886297i) q^{60} +(7.03656 + 12.1877i) q^{61} +(-0.157906 + 5.56552i) q^{62} +(7.48959 - 5.20610i) q^{63} +1.00000 q^{64} +(-6.34169 + 10.9841i) q^{65} +(3.02619 + 9.65551i) q^{66} +(-5.06714 - 8.77655i) q^{67} -3.67775 q^{68} +(6.17303 - 6.71354i) q^{69} +(3.56650 + 6.17736i) q^{70} +(-3.74130 + 6.48012i) q^{71} +(2.71456 + 1.27717i) q^{72} +(-2.09806 + 3.63394i) q^{73} +(-2.03817 + 3.53022i) q^{74} +(0.590842 - 0.642577i) q^{75} +5.17351 q^{76} +(8.88106 - 15.3824i) q^{77} +(6.33798 - 6.89294i) q^{78} +(-1.33943 + 2.31997i) q^{79} +(-1.17303 + 2.03175i) q^{80} +(5.73770 + 6.93389i) q^{81} +(1.47475 - 2.55433i) q^{82} -8.77082 q^{83} +(-1.57496 - 5.02514i) q^{84} +(4.31411 - 7.47226i) q^{85} +9.83993 q^{86} +(0.645614 + 2.05993i) q^{87} +5.84199 q^{88} +3.52297 q^{89} +(-5.77913 + 4.01715i) q^{90} -16.4373 q^{91} +(-2.63277 - 4.56010i) q^{92} +(6.91089 + 6.72603i) q^{93} +(-4.27777 + 7.40932i) q^{94} +(-6.06868 + 10.5113i) q^{95} +(1.17234 - 1.27499i) q^{96} +(-1.79211 - 3.10403i) q^{97} +(-1.12208 + 1.94350i) q^{98} +(15.8585 + 7.46119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.69035	−	0.377782i	−0.975924	−	0.218112i
$3$	−1.69035	−	0.377782i	−0.975924	−	0.218112i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.17303	−	2.03175i	−0.524594	−	0.908624i	−0.999590	−	0.0286358i	$-0.990884\pi$
$5$	−1.17303	−	2.03175i	−0.524594	−	0.908624i	0.474996	−	0.879988i	$-0.342450\pi$
$6$	0.518006	+	1.65278i	0.211475	+	0.674743i
$7$	1.52021	−	2.63308i	0.574586	−	0.995211i	−0.421501	−	0.906828i	$-0.638497\pi$
$7$	1.52021	−	2.63308i	0.574586	−	0.995211i	0.996087	−	0.0883835i	$-0.0281701\pi$
$8$	1.00000			0.353553
$9$	2.71456	+	1.27717i	0.904854	+	0.425722i
$10$	−1.17303	+	2.03175i	−0.370944	+	0.642494i
$11$	5.84199			1.76143			0.880714	−	0.473649i	$-0.157064\pi$
$11$	5.84199			1.76143			0.880714	+	0.473649i	$0.157064\pi$
$12$	1.17234	−	1.27499i	0.338426	−	0.368059i
$13$	−2.70313	−	4.68195i	−0.749712	−	1.29854i	−0.947961	−	0.318388i	$-0.896859\pi$
$13$	−2.70313	−	4.68195i	−0.749712	−	1.29854i	0.198248	−	0.980152i	$-0.436475\pi$
$14$	−3.04042			−0.812587
$15$	1.21527	+	3.87751i	0.313782	+	1.00117i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.83888	+	3.18503i	0.445993	+	0.772483i	0.998121	−	0.0612767i	$-0.0195172\pi$
$17$	1.83888	+	3.18503i	0.445993	+	0.772483i	−0.552128	+	0.833760i	$0.686184\pi$
$18$	−0.251223	−	2.98946i	−0.0592139	−	0.704623i
$19$	−2.58676	−	4.48039i	−0.593442	−	1.02787i	−0.993765	−	0.111498i	$-0.964435\pi$
$19$	−2.58676	−	4.48039i	−0.593442	−	1.02787i	0.400322	−	0.916374i	$-0.368898\pi$
$20$	2.34606			0.524594
$21$	−3.56442	+	3.87652i	−0.777820	+	0.845926i
$22$	−2.92100	−	5.05931i	−0.622759	−	1.07865i
$23$	−2.63277	+	4.56010i	−0.548971	+	0.950846i	0.449374	+	0.893344i	$0.351647\pi$
$23$	−2.63277	+	4.56010i	−0.548971	+	0.950846i	−0.998345	+	0.0575023i	$0.981686\pi$
$24$	−1.69035	−	0.377782i	−0.345041	−	0.0771143i
$25$	−0.251992	+	0.436463i	−0.0503984	+	0.0872926i
$26$	−2.70313	+	4.68195i	−0.530127	+	0.918206i
$27$	−4.10607	−	3.18437i	−0.790213	−	0.612832i
$28$	1.52021	+	2.63308i	0.287293	+	0.497606i
$29$	−0.623172	−	1.07937i	−0.115720	−	0.200433i	0.802347	−	0.596857i	$-0.203584\pi$
$29$	−0.623172	−	1.07937i	−0.115720	−	0.200433i	−0.918067	+	0.396424i	$0.870251\pi$
$30$	2.75038	−	2.99121i	0.502149	−	0.546118i
$31$	−4.74093	−	2.91951i	−0.851497	−	0.524360i
$31$	−4.74093	−	2.91951i	−0.851497	−	0.524360i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−9.87501	−	2.20700i	−1.71902	−	0.384189i
$34$	1.83888	−	3.18503i	0.315365	−	0.546228i
$35$	−7.13300			−1.20570
$36$	−2.46334	+	1.71230i	−0.410556	+	0.285383i
$37$	−2.03817	−	3.53022i	−0.335074	−	0.580365i	0.648425	−	0.761278i	$-0.275428\pi$
$37$	−2.03817	−	3.53022i	−0.335074	−	0.580365i	−0.983499	+	0.180914i	$0.942095\pi$
$38$	−2.58676	+	4.48039i	−0.419627	+	0.726815i
$39$	2.80047	+	8.93532i	0.448434	+	1.43080i
$40$	−1.17303	−	2.03175i	−0.185472	−	0.321247i
$41$	1.47475	+	2.55433i	0.230317	+	0.398920i	0.957901	−	0.287098i	$-0.0926905\pi$
$41$	1.47475	+	2.55433i	0.230317	+	0.398920i	−0.727585	+	0.686018i	$0.759357\pi$
$42$	5.13937	+	1.14861i	0.793023	+	0.177235i
$43$	−4.91997	+	8.52163i	−0.750288	+	1.29954i	0.197395	+	0.980324i	$0.436752\pi$
$43$	−4.91997	+	8.52163i	−0.750288	+	1.29954i	−0.947683	+	0.319213i	$0.896582\pi$
$44$	−2.92100	+	5.05931i	−0.440357	+	0.762720i
$45$	−0.589384	−	7.01345i	−0.0878602	−	1.04550i
$46$	5.26555			0.776362
$47$	−4.27777	−	7.40932i	−0.623977	−	1.08076i	−0.988738	−	0.149659i	$-0.952182\pi$
$47$	−4.27777	−	7.40932i	−0.623977	−	1.08076i	0.364760	−	0.931101i	$-0.381151\pi$
$48$	0.518006	+	1.65278i	0.0747678	+	0.238558i
$49$	−1.12208	−	1.94350i	−0.160297	−	0.277643i
$50$	0.503984			0.0712741
$51$	−1.90510	−	6.07851i	−0.266767	−	0.851161i
$52$	5.40625			0.749712
$53$	5.39327	−	9.34142i	0.740823	−	1.28314i	−0.211298	−	0.977422i	$-0.567769\pi$
$53$	5.39327	−	9.34142i	0.740823	−	1.28314i	0.952121	−	0.305721i	$-0.0988975\pi$
$54$	−0.704708	+	5.14814i	−0.0958987	+	0.700574i
$55$	−6.85282	−	11.8694i	−0.924035	−	1.60047i
$56$	1.52021	−	2.63308i	0.203147	−	0.351860i
$57$	2.67991	+	8.55066i	0.354963	+	1.13256i
$58$	−0.623172	+	1.07937i	−0.0818265	+	0.141728i
$59$	4.76336			0.620137			0.310068	−	0.950714i	$-0.399648\pi$
$59$	4.76336			0.620137			0.310068	+	0.950714i	$0.399648\pi$
$60$	−3.96566	−	0.886297i	−0.511964	−	0.114420i
$61$	7.03656	+	12.1877i	0.900939	+	1.56047i	0.826277	+	0.563264i	$0.190455\pi$
$61$	7.03656	+	12.1877i	0.900939	+	1.56047i	0.0746624	+	0.997209i	$0.476212\pi$
$62$	−0.157906	+	5.56552i	−0.0200541	+	0.706822i
$63$	7.48959	−	5.20610i	0.943599	−	0.655908i
$64$	1.00000			0.125000
$65$	−6.34169	+	10.9841i	−0.786589	+	1.36241i
$66$	3.02619	+	9.65551i	0.372498	+	1.18851i
$67$	−5.06714	−	8.77655i	−0.619050	−	1.07223i	−0.989659	−	0.143438i	$-0.954184\pi$
$67$	−5.06714	−	8.77655i	−0.619050	−	1.07223i	0.370609	−	0.928789i	$-0.379149\pi$
$68$	−3.67775			−0.445993
$69$	6.17303	−	6.71354i	0.743145	−	0.808216i
$70$	3.56650	+	6.17736i	0.426278	+	0.738336i
$71$	−3.74130	+	6.48012i	−0.444010	+	0.769049i	−0.997983	−	0.0634865i	$-0.979778\pi$
$71$	−3.74130	+	6.48012i	−0.444010	+	0.769049i	0.553972	+	0.832535i	$0.313111\pi$
$72$	2.71456	+	1.27717i	0.319914	+	0.150515i
$73$	−2.09806	+	3.63394i	−0.245559	+	0.425321i	−0.962289	−	0.272030i	$-0.912305\pi$
$73$	−2.09806	+	3.63394i	−0.245559	+	0.425321i	0.716730	+	0.697351i	$0.245638\pi$
$74$	−2.03817	+	3.53022i	−0.236933	+	0.410380i
$75$	0.590842	−	0.642577i	0.0682246	−	0.0741984i
$76$	5.17351			0.593442
$77$	8.88106	−	15.3824i	1.01209	−	1.75299i
$78$	6.33798	−	6.89294i	0.717635	−	0.780472i
$79$	−1.33943	+	2.31997i	−0.150698	+	0.261017i	−0.931484	−	0.363782i	$-0.881485\pi$
$79$	−1.33943	+	2.31997i	−0.150698	+	0.261017i	0.780786	+	0.624798i	$0.214819\pi$
$80$	−1.17303	+	2.03175i	−0.131149	+	0.227156i
$81$	5.73770	+	6.93389i	0.637522	+	0.770432i
$82$	1.47475	−	2.55433i	0.162858	−	0.282079i
$83$	−8.77082			−0.962723			−0.481362	−	0.876522i	$-0.659858\pi$
$83$	−8.77082			−0.962723			−0.481362	+	0.876522i	$0.659858\pi$
$84$	−1.57496	−	5.02514i	−0.171842	−	0.548287i
$85$	4.31411	−	7.47226i	0.467931	−	0.810480i
$86$	9.83993			1.06107
$87$	0.645614	+	2.05993i	0.0692171	+	0.220847i
$88$	5.84199			0.622759
$89$	3.52297			0.373434			0.186717	−	0.982414i	$-0.440215\pi$
$89$	3.52297			0.373434			0.186717	+	0.982414i	$0.440215\pi$
$90$	−5.77913	+	4.01715i	−0.609174	+	0.423444i
$91$	−16.4373			−1.72310
$92$	−2.63277	−	4.56010i	−0.274486	−	0.475423i
$93$	6.91089	+	6.72603i	0.716626	+	0.697457i
$94$	−4.27777	+	7.40932i	−0.441219	+	0.764213i
$95$	−6.06868	+	10.5113i	−0.622633	+	1.07843i
$96$	1.17234	−	1.27499i	0.119652	−	0.130129i
$97$	−1.79211	−	3.10403i	−0.181961	−	0.315166i	0.760587	−	0.649236i	$-0.224911\pi$
$97$	−1.79211	−	3.10403i	−0.181961	−	0.315166i	−0.942548	+	0.334070i	$0.891578\pi$
$98$	−1.12208	+	1.94350i	−0.113347	+	0.196323i
$99$	15.8585	+	7.46119i	1.59383	+	0.749878i
$100$	−0.251992	−	0.436463i	−0.0251992	−	0.0436463i
$101$	−3.51439	−	6.08711i	−0.349695	−	0.605690i	0.636500	−	0.771277i	$-0.280381\pi$
$101$	−3.51439	−	6.08711i	−0.349695	−	0.605690i	−0.986195	+	0.165587i	$0.947048\pi$
$102$	−4.31159	+	4.68912i	−0.426911	+	0.464292i
$103$	−2.18966	−	3.79259i	−0.215753	−	0.373695i	0.737752	−	0.675072i	$-0.235887\pi$
$103$	−2.18966	−	3.79259i	−0.215753	−	0.373695i	−0.953505	+	0.301376i	$0.902554\pi$
$104$	−2.70313	−	4.68195i	−0.265063	−	0.459103i
$105$	12.0573	+	2.69472i	1.17667	+	0.262977i
$106$	−10.7865			−1.04768
$107$	1.77681	+	3.07753i	0.171771	+	0.297516i	0.939039	−	0.343811i	$-0.111718\pi$
$107$	1.77681	+	3.07753i	0.171771	+	0.297516i	−0.767268	+	0.641326i	$0.778384\pi$
$108$	4.81078	−	1.96378i	0.462917	−	0.188964i
$109$	18.3747			1.75998			0.879989	−	0.474993i	$-0.157550\pi$
$109$	18.3747			1.75998			0.879989	+	0.474993i	$0.157550\pi$
$110$	−6.85282	+	11.8694i	−0.653391	+	1.13171i
$111$	2.11157	+	6.73729i	0.200422	+	0.639475i
$112$	−3.04042			−0.287293
$113$	1.84967	+	3.20372i	0.174002	+	0.301380i	0.939815	−	0.341683i	$-0.110997\pi$
$113$	1.84967	+	3.20372i	0.174002	+	0.301380i	−0.765813	+	0.643063i	$0.777663\pi$
$114$	6.06513	−	6.59620i	0.568051	−	0.617791i
$115$	12.3533			1.15195
$116$	1.24634			0.115720
$117$	−1.35818	−	16.1618i	−0.125563	−	1.49416i
$118$	−2.38168	−	4.12519i	−0.219251	−	0.379755i
$119$	11.1819			1.02505
$120$	1.21527	+	3.87751i	0.110939	+	0.353966i
$121$	23.1289			2.10263
$122$	7.03656	−	12.1877i	0.637060	−	1.10342i
$123$	−1.52785	−	4.87485i	−0.137762	−	0.439550i
$124$	4.89884	−	2.64601i	0.439929	−	0.237619i
$125$	−10.5479			−0.943434
$126$	−8.25341	−	3.88312i	−0.735272	−	0.345936i
$127$	−1.95942	−	3.39381i	−0.173870	−	0.301152i	0.765900	−	0.642960i	$-0.222294\pi$
$127$	−1.95942	−	3.39381i	−0.173870	−	0.301152i	−0.939770	+	0.341808i	$0.888961\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	11.5358	−	12.5459i	1.01567	−	1.10460i
$130$	12.6834			1.11241
$131$	−10.8084			−0.944337			−0.472169	−	0.881508i	$-0.656529\pi$
$131$	−10.8084			−0.944337			−0.472169	+	0.881508i	$0.656529\pi$
$132$	6.84882	−	7.44851i	0.596113	−	0.648310i
$133$	−15.7297			−1.36393
$134$	−5.06714	+	8.77655i	−0.437735	+	0.758179i
$135$	−1.65329	+	12.0778i	−0.142292	+	1.03949i
$136$	1.83888	+	3.18503i	0.157682	+	0.273114i
$137$	11.7047			1.00000			0.500001	−	0.866025i	$-0.333333\pi$
$137$	11.7047			1.00000			0.500001	+	0.866025i	$0.333333\pi$
$138$	−8.90061	−	1.98923i	−0.757670	−	0.169334i
$139$	7.78289	−	13.4804i	0.660136	−	1.14339i	−0.320443	−	0.947268i	$-0.603832\pi$
$139$	7.78289	−	13.4804i	0.660136	−	1.14339i	0.980580	−	0.196122i	$-0.0628348\pi$
$140$	3.56650	−	6.17736i	0.301424	−	0.522082i
$141$	4.43183	+	14.1404i	0.373227	+	1.19084i
$142$	7.48260			0.627926
$143$	−15.7916	−	27.3519i	−1.32056	−	2.28728i
$144$	−0.251223	−	2.98946i	−0.0209353	−	0.249122i
$145$	−1.46200	+	2.53225i	−0.121412	+	0.210292i
$146$	4.19611			0.347273
$147$	1.16249	+	3.70910i	0.0958805	+	0.305921i
$148$	4.07635			0.335074
$149$	−6.88872			−0.564346			−0.282173	−	0.959364i	$-0.591055\pi$
$149$	−6.88872			−0.564346			−0.282173	+	0.959364i	$0.591055\pi$
$150$	−0.851909	−	0.190396i	−0.0695581	−	0.0155458i
$151$	−12.2302	−	21.1834i	−0.995283	−	1.72388i	−0.581660	−	0.813432i	$-0.697597\pi$
$151$	−12.2302	−	21.1834i	−0.995283	−	1.72388i	−0.413623	−	0.910448i	$-0.635737\pi$
$152$	−2.58676	−	4.48039i	−0.209814	−	0.363408i
$153$	0.923938	+	10.9945i	0.0746959	+	0.888853i
$154$	−17.7621			−1.43131
$155$	−0.370457	+	13.0570i	−0.0297558	+	1.04877i
$156$	−9.13845	−	2.04238i	−0.731662	−	0.163521i
$157$	5.18717	−	8.98444i	0.413981	−	0.717036i	−0.581340	−	0.813661i	$-0.697471\pi$
$157$	5.18717	−	8.98444i	0.413981	−	0.717036i	0.995321	+	0.0966246i	$0.0308046\pi$
$158$	2.67887			0.213119
$159$	−12.6455	+	13.7528i	−1.00286	+	1.09067i
$160$	2.34606			0.185472
$161$	8.00474	+	13.8646i	0.630862	+	1.09268i
$162$	3.13608	−	8.43594i	0.246393	−	0.662790i
$163$	13.9787			1.09490			0.547448	−	0.836840i	$-0.315599\pi$
$163$	13.9787			1.09490			0.547448	+	0.836840i	$0.315599\pi$
$164$	−2.94949			−0.230317
$165$	7.09961	+	22.6524i	0.552704	+	1.76348i
$166$	4.38541	+	7.59576i	0.340374	+	0.589545i
$167$	17.7304			1.37202			0.686011	−	0.727592i	$-0.259360\pi$
$167$	17.7304			1.37202			0.686011	+	0.727592i	$0.259360\pi$
$168$	−3.56442	+	3.87652i	−0.275001	+	0.299080i
$169$	−8.11378	+	14.0535i	−0.624137	+	1.08104i
$170$	−8.62822			−0.661754
$171$	−1.29971	−	15.4660i	−0.0993911	−	1.18272i
$172$	−4.91997	−	8.52163i	−0.375144	−	0.649768i
$173$	5.49877			0.418064			0.209032	−	0.977909i	$-0.432969\pi$
$173$	5.49877			0.418064			0.209032	+	0.977909i	$0.432969\pi$
$174$	1.46114	−	1.58908i	0.110769	−	0.120468i
$175$	0.766162	+	1.32703i	0.0579164	+	0.100314i
$176$	−2.92100	−	5.05931i	−0.220178	−	0.381360i
$177$	−8.05174	−	1.79951i	−0.605206	−	0.135259i
$178$	−1.76149	−	3.05098i	−0.132029	−	0.228681i
$179$	11.6898	+	20.2473i	0.873735	+	1.51335i	0.858104	+	0.513476i	$0.171643\pi$
$179$	11.6898	+	20.2473i	0.873735	+	1.51335i	0.0156315	+	0.999878i	$0.495024\pi$
$180$	6.36852	+	2.99630i	0.474681	+	0.223331i
$181$	−0.955580	+	1.65511i	−0.0710277	+	0.123024i	−0.899352	−	0.437225i	$-0.855961\pi$
$181$	−0.955580	+	1.65511i	−0.0710277	+	0.123024i	0.828324	+	0.560249i	$0.189295\pi$
$182$	8.21864	+	14.2351i	0.609206	+	1.05518i
$183$	−7.28997	−	23.2597i	−0.538890	−	1.71941i
$184$	−2.63277	+	4.56010i	−0.194091	+	0.336175i
$185$	−4.78167	+	8.28210i	−0.351555	+	0.608912i
$186$	2.36947	−	9.34803i	0.173738	−	0.685431i
$187$	10.7427	+	18.6069i	0.785585	+	1.36067i
$188$	8.55555			0.623977
$189$	−14.6268	+	5.97071i	−1.06394	+	0.434305i
$190$	12.1374			0.880536
$191$	−16.8932			−1.22235			−0.611174	−	0.791496i	$-0.709302\pi$
$191$	−16.8932			−1.22235			−0.611174	+	0.791496i	$0.709302\pi$
$192$	−1.69035	−	0.377782i	−0.121990	−	0.0272640i
$193$	−12.3273			−0.887338			−0.443669	−	0.896191i	$-0.646323\pi$
$193$	−12.3273			−0.887338			−0.443669	+	0.896191i	$0.646323\pi$
$194$	−1.79211	+	3.10403i	−0.128666	+	0.222856i
$195$	14.8693	−	16.1712i	1.06481	−	1.15805i
$196$	2.24416			0.160297
$197$	5.62507	−	9.74291i	0.400770	−	0.694154i	−0.593049	−	0.805166i	$-0.702076\pi$
$197$	5.62507	−	9.74291i	0.400770	−	0.694154i	0.993819	+	0.111012i	$0.0354094\pi$
$198$	−1.46764	−	17.4644i	−0.104301	−	1.24114i
$199$	−3.79423	+	6.57180i	−0.268966	+	0.465862i	−0.968595	−	0.248644i	$-0.920015\pi$
$199$	−3.79423	+	6.57180i	−0.268966	+	0.465862i	0.699629	+	0.714506i	$0.253348\pi$
$200$	−0.251992	+	0.436463i	−0.0178185	+	0.0308626i
$201$	5.24963	+	16.7497i	0.370280	+	1.18143i
$202$	−3.51439	+	6.08711i	−0.247272	+	0.428287i
$203$	−3.78941			−0.265964
$204$	6.21669	+	1.38939i	0.435255	+	0.0972766i
$205$	3.45984	−	5.99261i	0.241645	−	0.418542i
$206$	−2.18966	+	3.79259i	−0.152561	+	0.264243i
$207$	−12.9708	+	9.01618i	−0.901535	+	0.626668i
$208$	−2.70313	+	4.68195i	−0.187428	+	0.324635i
$209$	−15.1118	−	26.1744i	−1.04531	−	1.81052i
$210$	−3.69494	−	11.7893i	−0.254975	−	0.813536i
$211$	−9.82384			−0.676301			−0.338151	−	0.941092i	$-0.609801\pi$
$211$	−9.82384			−0.676301			−0.338151	+	0.941092i	$0.609801\pi$
$212$	5.39327	+	9.34142i	0.370411	+	0.641571i
$213$	8.77217	−	9.54027i	0.601059	−	0.653689i
$214$	1.77681	−	3.07753i	0.121460	−	0.210375i
$215$	23.0850			1.57439
$216$	−4.10607	−	3.18437i	−0.279383	−	0.216669i
$217$	−14.8945	+	8.04499i	−1.01111	+	0.546130i
$218$	−9.18736	−	15.9130i	−0.622246	−	1.07776i
$219$	4.91929	−	5.35002i	0.332415	−	0.361521i
$220$	13.7056			0.924035
$221$	9.94143	−	17.2191i	0.668733	−	1.15828i
$222$	4.77888	−	5.19732i	0.320737	−	0.348821i
$223$	−5.12084	+	8.86956i	−0.342917	+	0.593950i	−0.984973	−	0.172708i	$-0.944748\pi$
$223$	−5.12084	+	8.86956i	−0.342917	+	0.593950i	0.642056	+	0.766658i	$0.278082\pi$
$224$	1.52021	+	2.63308i	0.101573	+	0.175930i
$225$	−1.24148	+	0.862970i	−0.0827655	+	0.0575313i
$226$	1.84967	−	3.20372i	0.123038	−	0.213108i
$227$	17.2741			1.14652			0.573260	−	0.819374i	$-0.305679\pi$
$227$	17.2741			1.14652			0.573260	+	0.819374i	$0.305679\pi$
$228$	−8.74504	−	1.95446i	−0.579154	−	0.129437i
$229$	2.33341			0.154196			0.0770982	−	0.997024i	$-0.475435\pi$
$229$	2.33341			0.154196			0.0770982	+	0.997024i	$0.475435\pi$
$230$	−6.17664	−	10.6982i	−0.407275	−	0.705422i
$231$	−20.8233	+	22.6466i	−1.37007	+	1.49004i
$232$	−0.623172	−	1.07937i	−0.0409132	−	0.0708638i
$233$	−3.49547			−0.228996			−0.114498	−	0.993424i	$-0.536526\pi$
$233$	−3.49547			−0.228996			−0.114498	+	0.993424i	$0.536526\pi$
$234$	−13.3174	+	9.25711i	−0.870588	+	0.605156i
$235$	−10.0359	+	17.3827i	−0.654670	+	1.13392i
$236$	−2.38168	+	4.12519i	−0.155034	+	0.268527i
$237$	3.14055	−	3.41554i	0.204001	−	0.221863i
$238$	−5.59096	−	9.68383i	−0.362408	−	0.627709i
$239$	−2.85451	−	4.94415i	−0.184643	−	0.319810i	0.758813	−	0.651308i	$-0.225779\pi$
$239$	−2.85451	−	4.94415i	−0.184643	−	0.319810i	−0.943456	+	0.331498i	$0.892446\pi$
$240$	2.75038	−	2.99121i	0.177537	−	0.193082i
$241$	8.88226	−	15.3845i	0.572157	−	0.991004i	−0.424188	−	0.905574i	$-0.639440\pi$
$241$	8.88226	−	15.3845i	0.572157	−	0.991004i	0.996344	−	0.0854299i	$-0.0272264\pi$
$242$	−11.5644	−	20.0302i	−0.743390	−	1.28759i
$243$	−7.07922	−	13.8883i	−0.454132	−	0.890934i
$244$	−14.0731			−0.900939
$245$	−2.63247	+	4.55956i	−0.168182	+	0.291300i
$246$	−3.45782	+	3.76059i	−0.220462	+	0.239766i
$247$	−13.9846	+	24.2221i	−0.889822	+	1.54122i
$248$	−4.74093	−	2.91951i	−0.301050	−	0.185389i
$249$	14.8258	+	3.31346i	0.939544	+	0.209982i
$250$	5.27396	+	9.13476i	0.333554	+	0.577733i
$251$	1.50446	+	2.60581i	0.0949609	+	0.164477i	0.909592	−	0.415502i	$-0.136394\pi$
$251$	1.50446	+	2.60581i	0.0949609	+	0.164477i	−0.814631	+	0.579979i	$0.803061\pi$
$252$	0.763825	+	9.08923i	0.0481164	+	0.572567i
$253$	−15.3806	+	26.6401i	−0.966973	+	1.67485i
$254$	−1.95942	+	3.39381i	−0.122945	+	0.212947i
$255$	−10.1152	+	11.0009i	−0.633441	+	0.688905i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.94806	+	3.37414i	0.121517	+	0.210473i	0.920366	−	0.391058i	$-0.127891\pi$
$257$	1.94806	+	3.37414i	0.121517	+	0.210473i	−0.798849	+	0.601531i	$0.794558\pi$
$258$	−16.6329	−	3.71734i	−1.03552	−	0.231432i
$259$	−12.3938			−0.770114
$260$	−6.34169	−	10.9841i	−0.393295	−	0.681206i
$261$	−0.313111	−	3.72590i	−0.0193811	−	0.230627i
$262$	5.40422	+	9.36038i	0.333874	+	0.578286i
$263$	7.02078	+	12.1603i	0.432920	+	0.749839i	0.997123	−	0.0757968i	$-0.0241500\pi$
$263$	7.02078	+	12.1603i	0.432920	+	0.749839i	−0.564204	+	0.825636i	$0.690817\pi$
$264$	−9.87501	−	2.20700i	−0.607765	−	0.135831i
$265$	−25.3058			−1.55453
$266$	7.86483	+	13.6223i	0.482223	+	0.835235i
$267$	−5.95505	−	1.33091i	−0.364443	−	0.0814506i
$268$	10.1343			0.619050
$269$	−2.44252	+	4.23057i	−0.148923	+	0.257943i	−0.930830	−	0.365453i	$-0.880914\pi$
$269$	−2.44252	+	4.23057i	−0.148923	+	0.257943i	0.781907	+	0.623396i	$0.214247\pi$
$270$	11.2864	−	4.60713i	0.686866	−	0.280381i
$271$	13.2408			0.804323			0.402161	−	0.915569i	$-0.368259\pi$
$271$	13.2408			0.804323			0.402161	+	0.915569i	$0.368259\pi$
$272$	1.83888	−	3.18503i	0.111498	−	0.193121i
$273$	27.7847	+	6.20970i	1.68161	+	0.375828i
$274$	−5.85236	−	10.1366i	−0.353554	−	0.612374i
$275$	−1.47214	+	2.54981i	−0.0887731	+	0.153759i
$276$	2.72759	+	8.70277i	0.164181	+	0.523845i
$277$	9.95924	+	17.2499i	0.598393	+	1.03645i	0.993058	+	0.117622i	$0.0375270\pi$
$277$	9.95924	+	17.2499i	0.598393	+	1.03645i	−0.394666	+	0.918825i	$0.629140\pi$
$278$	−15.5658			−0.933574
$279$	−9.14086	−	13.9802i	−0.547249	−	0.836970i
$280$	−7.13300			−0.426278
$281$	9.34766	+	16.1906i	0.557635	+	0.965852i	0.997693	+	0.0678826i	$0.0216243\pi$
$281$	9.34766	+	16.1906i	0.557635	+	0.965852i	−0.440059	+	0.897969i	$0.645042\pi$
$282$	10.0300	−	10.9083i	0.597280	−	0.649579i
$283$	−3.28581	+	5.69119i	−0.195321	+	0.338306i	−0.947006	−	0.321217i	$-0.895908\pi$
$283$	−3.28581	+	5.69119i	−0.195321	+	0.338306i	0.751685	+	0.659523i	$0.229242\pi$
$284$	−3.74130	−	6.48012i	−0.222005	−	0.384524i
$285$	14.2291	−	15.4751i	0.842861	−	0.916663i
$286$	−15.7916	+	27.3519i	−0.933779	+	1.61735i
$287$	8.96769			0.529346
$288$	−2.46334	+	1.71230i	−0.145154	+	0.100898i
$289$	1.73706	−	3.00868i	0.102180	−	0.176981i
$290$	2.92399			0.171703
$291$	1.85665	+	5.92391i	0.108839	+	0.347266i
$292$	−2.09806	−	3.63394i	−0.122780	−	0.212660i
$293$	−15.4708			−0.903812			−0.451906	−	0.892066i	$-0.649256\pi$
$293$	−15.4708			−0.903812			−0.451906	+	0.892066i	$0.649256\pi$
$294$	2.63093	−	2.86129i	0.153439	−	0.166874i
$295$	−5.58756	−	9.67793i	−0.325320	−	0.563471i
$296$	−2.03817	−	3.53022i	−0.118466	−	0.205190i
$297$	−23.9876	−	18.6031i	−1.39190	−	1.07946i
$298$	3.44436	+	5.96581i	0.199526	+	0.345590i
$299$	28.4669			1.64628
$300$	0.261067	+	0.832973i	0.0150727	+	0.0480917i
$301$	14.9588	+	25.9093i	0.862209	+	1.49339i
$302$	−12.2302	+	21.1834i	−0.703771	+	1.21897i
$303$	3.64095	+	11.6170i	0.209167	+	0.667380i
$304$	−2.58676	+	4.48039i	−0.148361	+	0.256968i
$305$	16.5082	−	28.5930i	0.945255	−	1.63723i
$306$	9.05956	−	6.29741i	0.517900	−	0.359999i
$307$	−7.91988	−	13.7176i	−0.452011	−	0.782907i	0.546499	−	0.837459i	$-0.315960\pi$
$307$	−7.91988	−	13.7176i	−0.452011	−	0.782907i	−0.998511	+	0.0545526i	$0.982627\pi$
$308$	8.88106	+	15.3824i	0.506045	+	0.876496i
$309$	2.26851	+	7.23802i	0.129051	+	0.411757i
$310$	11.4930	−	6.20769i	0.652756	−	0.352573i
$311$	−2.91350	+	5.04633i	−0.165209	+	0.286151i	−0.936730	−	0.350054i	$-0.886163\pi$
$311$	−2.91350	+	5.04633i	−0.165209	+	0.286151i	0.771520	+	0.636205i	$0.219497\pi$
$312$	2.80047	+	8.93532i	0.158546	+	0.505863i
$313$	1.69697	−	2.93925i	0.0959187	−	0.166136i	−0.814073	−	0.580763i	$-0.802754\pi$
$313$	1.69697	−	2.93925i	0.0959187	−	0.166136i	0.909992	+	0.414627i	$0.136088\pi$
$314$	−10.3743			−0.585458
$315$	−19.3630	−	9.11002i	−1.09098	−	0.513292i
$316$	−1.33943	−	2.31997i	−0.0753490	−	0.130508i
$317$	10.0037	−	17.3269i	0.561862	−	0.973174i	−0.435472	−	0.900202i	$-0.643418\pi$
$317$	10.0037	−	17.3269i	0.561862	−	0.973174i	0.997334	−	0.0729714i	$-0.0232482\pi$
$318$	18.2330	+	4.07496i	1.02246	+	0.228512i
$319$	−3.64056	−	6.30564i	−0.203832	−	0.353048i
$320$	−1.17303	−	2.03175i	−0.0655743	−	0.113578i
$321$	−1.84080	−	5.87334i	−0.102743	−	0.327818i
$322$	8.00474	−	13.8646i	0.446087	−	0.772645i
$323$	9.51345	−	16.4778i	0.529343	−	0.916848i
$324$	−8.87377	+	1.50205i	−0.492987	+	0.0834470i
$325$	2.72466			0.151137
$326$	−6.98935	−	12.1059i	−0.387104	−	0.670484i
$327$	−31.0597	−	6.94163i	−1.71760	−	0.383873i
$328$	1.47475	+	2.55433i	0.0814292	+	0.141039i
$329$	−26.0125			−1.43411
$330$	16.0677	−	17.4746i	0.884499	−	0.961947i
$331$	31.8747			1.75199			0.875996	−	0.482318i	$-0.160205\pi$
$331$	31.8747			1.75199			0.875996	+	0.482318i	$0.160205\pi$
$332$	4.38541	−	7.59576i	0.240681	−	0.416871i
$333$	−1.02407	−	12.1861i	−0.0561189	−	0.667793i
$334$	−8.86521	−	15.3550i	−0.485083	−	0.840188i
$335$	−11.8878	+	20.5903i	−0.649500	+	1.12497i
$336$	5.13937	+	1.14861i	0.280376	+	0.0626621i
$337$	11.3010	−	19.5740i	0.615606	−	1.06626i	−0.374672	−	0.927158i	$-0.622245\pi$
$337$	11.3010	−	19.5740i	0.615606	−	1.06626i	0.990278	−	0.139104i	$-0.0444221\pi$
$338$	16.2276			0.882662
$339$	−1.91628	−	6.11417i	−0.104078	−	0.332076i
$340$	4.31411	+	7.47226i	0.233966	+	0.405240i
$341$	−27.6965	−	17.0558i	−1.49985	−	0.923622i
$342$	−12.7441	+	8.85859i	−0.689123	+	0.479018i
$343$	14.4598			0.780753
$344$	−4.91997	+	8.52163i	−0.265267	+	0.459456i
$345$	−20.8813	−	4.66684i	−1.12421	−	0.251254i
$346$	−2.74939	−	4.76208i	−0.147808	−	0.256011i
$347$	−13.9730			−0.750112			−0.375056	−	0.927002i	$-0.622376\pi$
$347$	−13.9730			−0.750112			−0.375056	+	0.927002i	$0.622376\pi$
$348$	−2.10676	−	0.470846i	−0.112934	−	0.0252400i
$349$	3.41690	+	5.91825i	0.182903	+	0.316796i	0.942868	−	0.333167i	$-0.108117\pi$
$349$	3.41690	+	5.91825i	0.182903	+	0.316796i	−0.759965	+	0.649964i	$0.774784\pi$
$350$	0.766162	−	1.32703i	0.0409531	−	0.0709328i
$351$	−3.80983	+	27.8322i	−0.203354	+	1.48557i
$352$	−2.92100	+	5.05931i	−0.155690	+	0.269662i
$353$	−0.173175	+	0.299947i	−0.00921715	+	0.0159646i	−0.870597	−	0.491996i	$-0.836267\pi$
$353$	−0.173175	+	0.299947i	−0.00921715	+	0.0159646i	0.861380	+	0.507961i	$0.169601\pi$
$354$	2.46745	+	7.87277i	0.131144	+	0.418433i
$355$	17.5546			0.931701
$356$	−1.76149	+	3.05098i	−0.0933585	+	0.161702i
$357$	−18.9014	−	4.22432i	−1.00037	−	0.223575i
$358$	11.6898	−	20.2473i	0.617824	−	1.07010i
$359$	−10.8440	+	18.7823i	−0.572324	+	0.991293i	0.424003	+	0.905661i	$0.360625\pi$
$359$	−10.8440	+	18.7823i	−0.572324	+	0.991293i	−0.996327	+	0.0856328i	$0.972709\pi$
$360$	−0.589384	−	7.01345i	−0.0310633	−	0.369641i
$361$	−3.88261	+	6.72487i	−0.204348	+	0.353941i
$362$	1.91116			0.100448
$363$	−39.0959	−	8.73766i	−2.05200	−	0.458608i
$364$	8.21864	−	14.2351i	0.430774	−	0.746122i
$365$	9.84432			0.515275
$366$	−16.4985	+	17.9432i	−0.862392	+	0.937904i
$367$	26.7415			1.39590			0.697948	−	0.716149i	$-0.254097\pi$
$367$	26.7415			1.39590			0.697948	+	0.716149i	$0.254097\pi$
$368$	5.26555			0.274486
$369$	0.740981	+	8.81739i	0.0385739	+	0.459015i
$370$	9.56334			0.497175
$371$	−16.3978	−	28.4019i	−0.851332	−	1.47455i
$372$	−9.28036	+	2.62199i	−0.481164	+	0.135944i
$373$	1.69124	−	2.92931i	0.0875690	−	0.151674i	−0.818914	−	0.573916i	$-0.805424\pi$
$373$	1.69124	−	2.92931i	0.0875690	−	0.151674i	0.906483	+	0.422242i	$0.138757\pi$
$374$	10.7427	−	18.6069i	0.555492	−	0.962141i
$375$	17.8297	+	3.98481i	0.920719	+	0.205774i
$376$	−4.27777	−	7.40932i	−0.220609	−	0.382107i
$377$	−3.36902	+	5.83532i	−0.173514	+	0.300534i
$378$	12.4842	+	9.68182i	0.642117	+	0.497979i
$379$	−17.4095	−	30.1541i	−0.894264	−	1.54891i	−0.834713	−	0.550686i	$-0.814366\pi$
$379$	−17.4095	−	30.1541i	−0.894264	−	1.54891i	−0.0595514	−	0.998225i	$-0.518967\pi$
$380$	−6.06868	−	10.5113i	−0.311316	−	0.539216i
$381$	2.02998	+	6.47696i	0.103999	+	0.331825i
$382$	8.44659	+	14.6299i	0.432165	+	0.748532i
$383$	14.8493	+	25.7198i	0.758764	+	1.31422i	0.943481	+	0.331426i	$0.107530\pi$
$383$	14.8493	+	25.7198i	0.758764	+	1.31422i	−0.184717	+	0.982792i	$0.559137\pi$
$384$	0.518006	+	1.65278i	0.0264344	+	0.0843429i
$385$	−41.6709			−2.12375
$386$	6.16365	+	10.6758i	0.313721	+	0.543381i
$387$	−24.2391	+	16.8489i	−1.23214	+	0.856477i
$388$	3.58422			0.181961
$389$	8.08558	−	14.0046i	0.409955	−	0.710063i	−0.584929	−	0.811084i	$-0.698878\pi$
$389$	8.08558	−	14.0046i	0.409955	−	0.710063i	0.994884	+	0.101021i	$0.0322110\pi$
$390$	−21.4393	−	4.79154i	−1.08562	−	0.242629i
$391$	−19.3654			−0.979350
$392$	−1.12208	−	1.94350i	−0.0566736	−	0.0981616i
$393$	18.2700	+	4.08323i	0.921601	+	0.205971i
$394$	−11.2501			−0.566774
$395$	6.28477			0.316221
$396$	−14.3908	+	10.0032i	−0.723165	+	0.502681i
$397$	3.08789	+	5.34838i	0.154977	+	0.268428i	0.933051	−	0.359745i	$-0.117136\pi$
$397$	3.08789	+	5.34838i	0.154977	+	0.268428i	−0.778074	+	0.628173i	$0.783803\pi$
$398$	7.58846			0.380375
$399$	26.5886	+	5.94237i	1.33110	+	0.297491i
$400$	0.503984			0.0251992
$401$	8.67231	−	15.0209i	0.433074	−	0.750107i	−0.564062	−	0.825732i	$-0.690762\pi$
$401$	8.67231	−	15.0209i	0.433074	−	0.750107i	0.997136	+	0.0756258i	$0.0240955\pi$
$402$	11.8809	−	12.9212i	0.592564	−	0.644449i
$403$	−0.853680	+	30.0886i	−0.0425248	+	1.49882i
$404$	7.02878			0.349695
$405$	7.35742	−	19.7912i	0.365593	−	0.983432i
$406$	1.89470	+	3.28172i	0.0940326	+	0.162869i
$407$	−11.9070	−	20.6235i	−0.590208	−	1.02227i
$408$	−1.90510	−	6.07851i	−0.0943165	−	0.300931i
$409$	24.3718			1.20511			0.602554	−	0.798078i	$-0.294150\pi$
$409$	24.3718			1.20511			0.602554	+	0.798078i	$0.294150\pi$
$410$	−6.91967			−0.341738
$411$	−19.7851	−	4.42183i	−0.975926	−	0.218113i
$412$	4.37931			0.215753
$413$	7.24131	−	12.5423i	0.356322	−	0.617167i
$414$	14.2937	+	6.72497i	0.702495	+	0.330514i
$415$	10.2884	+	17.8201i	0.505039	+	0.874753i
$416$	5.40625			0.265063
$417$	−18.2484	+	19.8463i	−0.893630	+	0.971877i
$418$	−15.1118	+	26.1744i	−0.739143	+	1.28023i
$419$	11.3416	−	19.6442i	0.554072	−	0.959681i	−0.443903	−	0.896075i	$-0.646406\pi$
$419$	11.3416	−	19.6442i	0.554072	−	0.959681i	0.997975	−	0.0636063i	$-0.0202602\pi$
$420$	−8.36233	+	9.09454i	−0.408040	+	0.443768i
$421$	−4.96920			−0.242184			−0.121092	−	0.992641i	$-0.538640\pi$
$421$	−4.96920			−0.242184			−0.121092	+	0.992641i	$0.538640\pi$
$422$	4.91192	+	8.50770i	0.239109	+	0.414148i
$423$	−2.14935	−	25.5765i	−0.104505	−	1.24357i
$424$	5.39327	−	9.34142i	0.261920	−	0.453659i
$425$	−1.85353			−0.0899094
$426$	−12.6482	−	2.82679i	−0.612807	−	0.136958i
$427$	42.7882			2.07067
$428$	−3.55362			−0.171771
$429$	16.3603	+	52.2001i	0.789885	+	2.52024i
$430$	−11.5425	−	19.9922i	−0.556630	−	0.964111i
$431$	−19.8668	−	34.4102i	−0.956948	−	1.65748i	−0.729845	−	0.683613i	$-0.760408\pi$
$431$	−19.8668	−	34.4102i	−0.956948	−	1.65748i	−0.227103	−	0.973871i	$-0.572926\pi$
$432$	−0.704708	+	5.14814i	−0.0339053	+	0.247690i
$433$	−26.3343			−1.26555			−0.632773	−	0.774338i	$-0.718083\pi$
$433$	−26.3343			−1.26555			−0.632773	+	0.774338i	$0.718083\pi$
$434$	14.4144	+	8.87655i	0.691915	+	0.426088i
$435$	3.42792	−	3.72808i	0.164356	−	0.178748i
$436$	−9.18736	+	15.9130i	−0.439995	+	0.762093i
$437$	27.2414			1.30313
$438$	−7.09290	−	1.58521i	−0.338912	−	0.0757445i
$439$	27.0844			1.29267			0.646334	−	0.763054i	$-0.276301\pi$
$439$	27.0844			1.29267			0.646334	+	0.763054i	$0.276301\pi$
$440$	−6.85282	−	11.8694i	−0.326696	−	0.565853i
$441$	−0.563786	−	6.70884i	−0.0268469	−	0.319468i
$442$	−19.8829			−0.945731
$443$	3.41649			0.162322			0.0811611	−	0.996701i	$-0.474137\pi$
$443$	3.41649			0.162322			0.0811611	+	0.996701i	$0.474137\pi$
$444$	−6.89045	−	1.53997i	−0.327006	−	0.0730837i
$445$	−4.13255	−	7.15778i	−0.195901	−	0.339311i
$446$	10.2417			0.484958
$447$	11.6443	+	2.60243i	0.550759	+	0.123091i
$448$	1.52021	−	2.63308i	0.0718232	−	0.124401i
$449$	36.5403			1.72444			0.862221	−	0.506532i	$-0.169073\pi$
$449$	36.5403			1.72444			0.862221	+	0.506532i	$0.169073\pi$
$450$	1.36810	+	0.643671i	0.0644926	+	0.0303429i
$451$	8.61545	+	14.9224i	0.405686	+	0.702668i
$452$	−3.69933			−0.174002
$453$	12.6707	+	40.4277i	0.595321	+	1.89946i
$454$	−8.63703	−	14.9598i	−0.405356	−	0.702097i
$455$	19.2814	+	33.3964i	0.903926	+	1.56565i
$456$	2.67991	+	8.55066i	0.125498	+	0.400421i
$457$	−4.40598	−	7.63138i	−0.206103	−	0.356981i	0.744381	−	0.667756i	$-0.232745\pi$
$457$	−4.40598	−	7.63138i	−0.206103	−	0.356981i	−0.950484	+	0.310775i	$0.899412\pi$
$458$	−1.16671	−	2.02080i	−0.0545166	−	0.0944256i
$459$	2.59174	−	18.9336i	0.120972	−	0.883745i
$460$	−6.17664	+	10.6982i	−0.287987	+	0.498808i
$461$	−6.69027	−	11.5879i	−0.311597	−	0.539702i	0.667111	−	0.744958i	$-0.267531\pi$
$461$	−6.69027	−	11.5879i	−0.311597	−	0.539702i	−0.978708	+	0.205256i	$0.934197\pi$
$462$	30.0242	+	6.71020i	1.39685	+	0.312187i
$463$	13.5432	−	23.4576i	0.629407	−	1.09016i	−0.358264	−	0.933620i	$-0.616631\pi$
$463$	13.5432	−	23.4576i	0.629407	−	1.09016i	0.987671	−	0.156544i	$-0.0500355\pi$
$464$	−0.623172	+	1.07937i	−0.0289300	+	0.0501083i
$465$	5.55891	−	21.9310i	0.257788	−	1.01703i
$466$	1.74773	+	3.02716i	0.0809622	+	0.140231i
$467$	5.43494			0.251499			0.125750	−	0.992062i	$-0.459866\pi$
$467$	5.43494			0.251499			0.125750	+	0.992062i	$0.459866\pi$
$468$	14.6756	+	6.90468i	0.678380	+	0.319169i
$469$	−30.8125			−1.42279
$470$	20.0718			0.925843
$471$	−12.1623	+	13.2272i	−0.560408	+	0.609478i
$472$	4.76336			0.219251
$473$	−28.7424	+	49.7833i	−1.32158	+	2.28904i
$474$	−4.52822	−	1.01203i	−0.207988	−	0.0464839i
$475$	2.60737			0.119634
$476$	−5.59096	+	9.68383i	−0.256261	+	0.443858i
$477$	26.5709	−	18.4698i	1.21660	−	0.845673i
$478$	−2.85451	+	4.94415i	−0.130562	+	0.226140i
$479$	1.78335	−	3.08885i	0.0814833	−	0.141133i	−0.822404	−	0.568904i	$-0.807368\pi$
$479$	1.78335	−	3.08885i	0.0814833	−	0.141133i	0.903887	+	0.427771i	$0.140701\pi$
$480$	−3.96566	−	0.886297i	−0.181007	−	0.0404537i
$481$	−11.0189	+	19.0853i	−0.502418	+	0.870213i
$482$	−17.7645			−0.809152
$483$	−8.29301	−	26.4601i	−0.377345	−	1.20398i
$484$	−11.5644	+	20.0302i	−0.525656	+	0.910463i
$485$	−4.20439	+	7.28222i	−0.190912	+	0.330669i
$486$	−8.48801	+	13.0749i	−0.385024	+	0.593091i
$487$	5.23602	−	9.06906i	0.237267	−	0.410958i	−0.722662	−	0.691201i	$-0.757082\pi$
$487$	5.23602	−	9.06906i	0.237267	−	0.410958i	0.959929	+	0.280243i	$0.0904151\pi$
$488$	7.03656	+	12.1877i	0.318530	+	0.551710i
$489$	−23.6289	−	5.28089i	−1.06853	−	0.238810i
$490$	5.26493			0.237845
$491$	−8.32650	−	14.4219i	−0.375770	−	0.650852i	0.614672	−	0.788783i	$-0.289288\pi$
$491$	−8.32650	−	14.4219i	−0.375770	−	0.650852i	−0.990442	+	0.137931i	$0.955955\pi$
$492$	4.98567	+	1.11426i	0.224771	+	0.0502349i
$493$	2.29187	−	3.96964i	0.103221	−	0.178784i
$494$	27.9693			1.25840
$495$	−3.44318	−	40.9725i	−0.154759	−	1.84158i
$496$	−0.157906	+	5.56552i	−0.00709020	+	0.249899i
$497$	11.3751	+	19.7023i	0.510244	+	0.883769i
$498$	−4.54334	−	14.4962i	−0.203592	−	0.649591i
$499$	−16.3686			−0.732759			−0.366380	−	0.930465i	$-0.619403\pi$
$499$	−16.3686			−0.732759			−0.366380	+	0.930465i	$0.619403\pi$
$500$	5.27396	−	9.13476i	0.235858	−	0.408519i
$501$	−29.9706	−	6.69823i	−1.33899	−	0.299255i
$502$	1.50446	−	2.60581i	0.0671475	−	0.116303i
$503$	3.56017	+	6.16640i	0.158740	+	0.274946i	0.934415	−	0.356187i	$-0.115923\pi$
$503$	3.56017	+	6.16640i	0.158740	+	0.274946i	−0.775674	+	0.631133i	$0.782590\pi$
$504$	7.48959	−	5.20610i	0.333613	−	0.231898i
$505$	−8.24496	+	14.2807i	−0.366896	+	0.635483i
$506$	30.7613			1.36751
$507$	19.0243	−	20.6900i	0.844897	−	0.918877i
$508$	3.91883			0.173870
$509$	11.5784	+	20.0543i	0.513202	+	0.888892i	0.999883	+	0.0153124i	$0.00487427\pi$
$509$	11.5784	+	20.0543i	0.513202	+	0.888892i	−0.486680	+	0.873580i	$0.661792\pi$
$510$	14.5847	+	3.25958i	0.645822	+	0.144337i
$511$	6.37898	+	11.0487i	0.282189	+	0.488766i
$512$	1.00000			0.0441942
$513$	−3.64582	+	26.6340i	−0.160967	+	1.17592i
$514$	1.94806	−	3.37414i	0.0859252	−	0.148827i
$515$	−5.13706	+	8.89764i	−0.226366	+	0.392077i
$516$	5.09715	+	16.2632i	0.224389	+	0.715948i
$517$	−24.9907	−	43.2852i	−1.09909	−	1.90368i
$518$	6.19691	+	10.7334i	0.272276	+	0.471597i
$519$	−9.29485	−	2.07734i	−0.407999	−	0.0911849i
$520$	−6.34169	+	10.9841i	−0.278101	+	0.481686i
$521$	20.6348	+	35.7404i	0.904025	+	1.56582i	0.822221	+	0.569169i	$0.192735\pi$
$521$	20.6348	+	35.7404i	0.904025	+	1.56582i	0.0818041	+	0.996648i	$0.473932\pi$
$522$	−3.07017	+	2.13411i	−0.134378	+	0.0934075i
$523$	1.65720			0.0724643			0.0362322	−	0.999343i	$-0.488464\pi$
$523$	1.65720			0.0724643			0.0362322	+	0.999343i	$0.488464\pi$
$524$	5.40422	−	9.36038i	0.236084	−	0.408910i
$525$	−0.793753	−	2.53259i	−0.0346422	−	0.110531i
$526$	7.02078	−	12.1603i	0.306120	−	0.530216i
$527$	0.580740	−	20.4686i	0.0252974	−	0.891628i
$528$	3.02619	+	9.65551i	0.131698	+	0.420202i
$529$	−2.36299	−	4.09282i	−0.102739	−	0.177949i
$530$	12.6529	+	21.9155i	0.549608	+	0.951949i
$531$	12.9304	+	6.08360i	0.561133	+	0.264006i
$532$	7.86483	−	13.6223i	0.340983	−	0.590601i
$533$	7.97284	−	13.8094i	0.345342	−	0.598150i
$534$	1.82492	+	5.82268i	0.0789721	+	0.251972i
$535$	4.16850	−	7.22006i	0.180220	−	0.312150i
$536$	−5.06714	−	8.77655i	−0.218867	−	0.379089i
$537$	−12.1108	−	38.6412i	−0.522618	−	1.66749i
$538$	4.88504			0.210609
$539$	−6.55519	−	11.3539i	−0.282352	−	0.489048i
$540$	−9.63307	−	7.47071i	−0.414541	−	0.321488i
$541$	−5.52047	−	9.56173i	−0.237343	−	0.411091i	0.722608	−	0.691258i	$-0.242943\pi$
$541$	−5.52047	−	9.56173i	−0.237343	−	0.411091i	−0.959951	+	0.280167i	$0.909610\pi$
$542$	−6.62041	−	11.4669i	−0.284371	−	0.492545i
$543$	2.24054	−	2.43672i	0.0961506	−	0.104570i
$544$	−3.67775			−0.157682
$545$	−21.5541	−	37.3327i	−0.923275	−	1.59916i
$546$	−8.51462	−	27.1671i	−0.364392	−	1.16265i
$547$	0.715421			0.0305892			0.0152946	−	0.999883i	$-0.495131\pi$
$547$	0.715421			0.0305892			0.0152946	+	0.999883i	$0.495131\pi$
$548$	−5.85236	+	10.1366i	−0.250001	+	0.433014i
$549$	3.53550	+	42.0711i	0.150891	+	1.79555i
$550$	2.94427			0.125544
$551$	−3.22399	+	5.58411i	−0.137346	+	0.237891i
$552$	6.17303	−	6.71354i	0.262741	−	0.285747i
$553$	4.07244	+	7.05368i	0.173178	+	0.299953i
$554$	9.95924	−	17.2499i	0.423127	−	0.732878i
$555$	11.2115	−	12.1932i	0.475902	−	0.517573i
$556$	7.78289	+	13.4804i	0.330068	+	0.571695i
$557$	46.7111			1.97921			0.989607	−	0.143800i	$-0.0459322\pi$
$557$	46.7111			1.97921			0.989607	+	0.143800i	$0.0459322\pi$
$558$	−7.53674	+	14.9063i	−0.319056	+	0.631034i
$559$	53.1971			2.25000
$560$	3.56650	+	6.17736i	0.150712	+	0.261041i
$561$	−11.1296	−	35.5106i	−0.469891	−	1.49926i
$562$	9.34766	−	16.1906i	0.394307	−	0.682960i
$563$	−4.35465	−	7.54247i	−0.183526	−	0.317877i	0.759553	−	0.650446i	$-0.225418\pi$
$563$	−4.35465	−	7.54247i	−0.183526	−	0.317877i	−0.943079	+	0.332569i	$0.892085\pi$
$564$	−14.4619	−	3.23213i	−0.608954	−	0.136097i
$565$	4.33942	−	7.51610i	0.182561	−	0.316205i
$566$	6.57162			0.276226
$567$	26.9800	−	4.56685i	1.13305	−	0.191790i
$568$	−3.74130	+	6.48012i	−0.156981	+	0.271900i
$569$	18.1441			0.760639			0.380319	−	0.924855i	$-0.375814\pi$
$569$	18.1441			0.760639			0.380319	+	0.924855i	$0.375814\pi$
$570$	−20.5164	−	4.58527i	−0.859336	−	0.192056i
$571$	20.0206	+	34.6767i	0.837836	+	1.45117i	0.891701	+	0.452626i	$0.149513\pi$
$571$	20.0206	+	34.6767i	0.837836	+	1.45117i	−0.0538648	+	0.998548i	$0.517154\pi$
$572$	31.5833			1.32056
$573$	28.5554	+	6.38193i	1.19292	+	0.266609i
$574$	−4.48385	−	7.76625i	−0.187152	−	0.324157i
$575$	−1.32688	−	2.29822i	−0.0553345	−	0.0958422i
$576$	2.71456	+	1.27717i	0.113107	+	0.0532152i
$577$	18.0167	+	31.2059i	0.750047	+	1.29912i	0.947799	+	0.318867i	$0.103302\pi$
$577$	18.0167	+	31.2059i	0.750047	+	1.29912i	−0.197753	+	0.980252i	$0.563364\pi$
$578$	−3.47412			−0.144504
$579$	20.8374	+	4.65702i	0.865974	+	0.193539i
$580$	−1.46200	−	2.53225i	−0.0607061	−	0.105146i
$581$	−13.3335	+	23.0943i	−0.553167	+	0.958113i
$582$	4.20194	−	4.56986i	0.174176	−	0.189427i
$583$	31.5075	−	54.5725i	1.30491	−	2.26016i
$584$	−2.09806	+	3.63394i	−0.0868182	+	0.150374i
$585$	−31.2434	+	21.7177i	−1.29176	+	0.897917i
$586$	7.73539	+	13.3981i	0.319546	+	0.553470i
$587$	8.45075	+	14.6371i	0.348800	+	0.604139i	0.986037	−	0.166529i	$-0.0532560\pi$
$587$	8.45075	+	14.6371i	0.348800	+	0.604139i	−0.637237	+	0.770668i	$0.719923\pi$
$588$	−3.79342	−	0.847803i	−0.156438	−	0.0349628i
$589$	−0.816929	+	28.7933i	−0.0336610	+	1.18641i
$590$	−5.58756	+	9.67793i	−0.230036	+	0.398434i
$591$	−13.1890	+	14.3439i	−0.542524	+	0.590028i
$592$	−2.03817	+	3.53022i	−0.0837684	+	0.145091i
$593$	29.7811			1.22296			0.611481	−	0.791259i	$-0.290574\pi$
$593$	29.7811			1.22296			0.611481	+	0.791259i	$0.290574\pi$
$594$	−4.11690	+	30.0754i	−0.168919	+	1.23401i
$595$	−13.1167	−	22.7188i	−0.537733	−	0.931381i
$596$	3.44436	−	5.96581i	0.141087	−	0.244369i
$597$	8.89627	−	9.67524i	0.364100	−	0.395981i
$598$	−14.2334	−	24.6530i	−0.582048	−	1.00814i
$599$	15.1054	+	26.1634i	0.617191	+	1.06901i	0.989996	+	0.141097i	$0.0450629\pi$
$599$	15.1054	+	26.1634i	0.617191	+	1.06901i	−0.372804	+	0.927910i	$0.621604\pi$
$600$	0.590842	−	0.642577i	0.0241210	−	0.0262331i
$601$	−13.4185	+	23.2415i	−0.547350	+	0.948039i	0.451104	+	0.892471i	$0.351030\pi$
$601$	−13.4185	+	23.2415i	−0.547350	+	0.948039i	−0.998455	+	0.0555677i	$0.982303\pi$
$602$	14.9588	−	25.9093i	0.609674	−	1.05599i
$603$	−2.54597	−	30.2961i	−0.103680	−	1.23375i
$604$	24.4605			0.995283
$605$	−27.1308	−	46.9920i	−1.10303	−	1.91050i
$606$	8.24015	−	8.96166i	0.334733	−	0.364043i
$607$	−11.2221	−	19.4373i	−0.455492	−	0.788936i	0.543224	−	0.839588i	$-0.317203\pi$
$607$	−11.2221	−	19.4373i	−0.455492	−	0.788936i	−0.998716	+	0.0506519i	$0.983870\pi$
$608$	5.17351			0.209814
$609$	6.40543	+	1.43157i	0.259561	+	0.0580101i
$610$	−33.0164			−1.33679
$611$	−23.1267	+	40.0567i	−0.935607	+	1.62052i
$612$	−9.98349	−	4.69710i	−0.403559	−	0.189869i
$613$	−11.6053	−	20.1010i	−0.468734	−	0.811871i	0.530627	−	0.847605i	$-0.321956\pi$
$613$	−11.6053	−	20.1010i	−0.468734	−	0.811871i	−0.999361	+	0.0357343i	$0.988623\pi$
$614$	−7.91988	+	13.7176i	−0.319620	+	0.553599i
$615$	−8.11223	+	8.82255i	−0.327117	+	0.355759i
$616$	8.88106	−	15.3824i	0.357828	−	0.619776i
$617$	−19.5805			−0.788282			−0.394141	−	0.919050i	$-0.628958\pi$
$617$	−19.5805			−0.788282			−0.394141	+	0.919050i	$0.628958\pi$
$618$	5.13405	−	5.58360i	0.206522	−	0.224605i
$619$	−21.8791	−	37.8958i	−0.879396	−	1.52316i	−0.852004	−	0.523535i	$-0.824613\pi$
$619$	−21.8791	−	37.8958i	−0.879396	−	1.52316i	−0.0273920	−	0.999625i	$-0.508720\pi$
$620$	−11.1225	−	6.84934i	−0.446690	−	0.275076i
$621$	25.3314	−	10.3404i	1.01651	−	0.414944i
$622$	5.82700			0.233641
$623$	5.35566	−	9.27627i	0.214570	−	0.371646i
$624$	6.33798	−	6.89294i	0.253722	−	0.275939i
$625$	13.6330	+	23.6130i	0.545318	+	0.944519i
$626$	−3.39395			−0.135649
$627$	15.6560	+	49.9529i	0.625241	+	1.99493i
$628$	5.18717	+	8.98444i	0.206991	+	0.358518i
$629$	7.49590	−	12.9833i	0.298881	−	0.517677i
$630$	1.79198	+	21.3238i	0.0713941	+	0.849562i
$631$	2.46804	−	4.27478i	0.0982513	−	0.170176i	−0.812710	−	0.582669i	$-0.802008\pi$
$631$	2.46804	−	4.27478i	0.0982513	−	0.170176i	0.910961	+	0.412493i	$0.135342\pi$
$632$	−1.33943	+	2.31997i	−0.0532798	+	0.0922833i
$633$	16.6057	+	3.71127i	0.660018	+	0.147510i
$634$	−20.0073			−0.794593
$635$	−4.59690	+	7.96207i	−0.182423	+	0.315965i
$636$	−5.58750	−	17.8277i	−0.221559	−	0.706916i
$637$	−6.06625	+	10.5071i	−0.240354	+	0.416305i
$638$	−3.64056	+	6.30564i	−0.144131	+	0.249643i
$639$	−18.4322	+	12.8124i	−0.729165	+	0.506852i
$640$	−1.17303	+	2.03175i	−0.0463680	+	0.0803118i
$641$	−34.3824			−1.35802			−0.679012	−	0.734127i	$-0.737592\pi$
$641$	−34.3824			−1.35802			−0.679012	+	0.734127i	$0.737592\pi$
$642$	−4.16606	+	4.53085i	−0.164421	+	0.178818i
$643$	10.3052	−	17.8491i	0.406397	−	0.703900i	−0.588086	−	0.808798i	$-0.700118\pi$
$643$	10.3052	−	17.8491i	0.406397	−	0.703900i	0.994483	+	0.104899i	$0.0334518\pi$
$644$	−16.0095			−0.630862
$645$	−39.0218	−	8.72110i	−1.53648	−	0.343393i
$646$	−19.0269			−0.748603
$647$	−31.8242			−1.25114			−0.625570	−	0.780168i	$-0.715134\pi$
$647$	−31.8242			−1.25114			−0.625570	+	0.780168i	$0.715134\pi$
$648$	5.73770	+	6.93389i	0.225398	+	0.272389i
$649$	27.8275			1.09233
$650$	−1.36233	−	2.35963i	−0.0534350	−	0.0925522i
$651$	28.2162	−	7.97196i	1.10588	−	0.312446i
$652$	−6.98935	+	12.1059i	−0.273724	+	0.474104i
$653$	−5.79092	+	10.0302i	−0.226616	+	0.392511i	−0.956803	−	0.290737i	$-0.906100\pi$
$653$	−5.79092	+	10.0302i	−0.226616	+	0.392511i	0.730187	+	0.683247i	$0.239433\pi$
$654$	9.51822	+	30.3693i	0.372192	+	1.18753i
$655$	12.6786	+	21.9600i	0.495394	+	0.858047i
$656$	1.47475	−	2.55433i	0.0575791	−	0.0997300i
$657$	−10.3365	+	7.18499i	−0.403263	+	0.280313i
$658$	13.0062	+	22.5275i	0.507036	+	0.878212i
$659$	−15.8445	−	27.4434i	−0.617213	−	1.06904i	−0.989992	−	0.141124i	$-0.954928\pi$
$659$	−15.8445	−	27.4434i	−0.617213	−	1.06904i	0.372779	−	0.927920i	$-0.378405\pi$
$660$	−23.1673	−	5.17774i	−0.901787	−	0.201543i
$661$	8.71653	+	15.0975i	0.339034	+	0.587223i	0.984251	−	0.176775i	$-0.0565666\pi$
$661$	8.71653	+	15.0975i	0.339034	+	0.587223i	−0.645218	+	0.763999i	$0.723233\pi$
$662$	−15.9374	−	27.6043i	−0.619423	−	1.07287i
$663$	−23.3095	+	25.3505i	−0.905267	+	0.984534i
$664$	−8.77082			−0.340374
$665$	18.4513	+	31.9586i	0.715512	+	1.23930i
$666$	−10.0414	+	6.97992i	−0.389097	+	0.270466i
$667$	6.56268			0.254108
$668$	−8.86521	+	15.3550i	−0.343005	+	0.594103i
$669$	12.0068	−	13.0581i	0.464209	−	0.504855i
$670$	23.7756			0.918532
$671$	41.1075	+	71.2004i	1.58694	+	2.74866i
$672$	−1.57496	−	5.02514i	−0.0607553	−	0.193849i
$673$	12.8271			0.494450			0.247225	−	0.968958i	$-0.420481\pi$
$673$	12.8271			0.494450			0.247225	+	0.968958i	$0.420481\pi$
$674$	−22.6021			−0.870599
$675$	2.42455	−	0.989712i	0.0933211	−	0.0380940i
$676$	−8.11378	−	14.0535i	−0.312068	−	0.540518i
$677$	−20.5857			−0.791174			−0.395587	−	0.918429i	$-0.629459\pi$
$677$	−20.5857			−0.791174			−0.395587	+	0.918429i	$0.629459\pi$
$678$	−4.33689	+	4.71663i	−0.166557	+	0.181141i
$679$	−10.8975			−0.418209
$680$	4.31411	−	7.47226i	0.165439	−	0.286548i
$681$	−29.1992	−	6.52582i	−1.11892	−	0.250070i
$682$	−0.922487	+	32.5138i	−0.0353238	+	1.24502i
$683$	−6.13838			−0.234879			−0.117439	−	0.993080i	$-0.537469\pi$
$683$	−6.13838			−0.234879			−0.117439	+	0.993080i	$0.537469\pi$
$684$	14.0438	+	6.60743i	0.536979	+	0.252641i
$685$	−13.7300	−	23.7810i	−0.524596	−	0.908626i
$686$	−7.22988	−	12.5225i	−0.276038	−	0.478112i
$687$	−3.94428	−	0.881521i	−0.150484	−	0.0336321i
$688$	9.83993			0.375144
$689$	−58.3148			−2.22162
$690$	6.39907	+	20.4172i	0.243609	+	0.777269i
$691$	−20.0938			−0.764404			−0.382202	−	0.924079i	$-0.624834\pi$
$691$	−20.0938			−0.764404			−0.382202	+	0.924079i	$0.624834\pi$
$692$	−2.74939	+	4.76208i	−0.104516	+	0.181027i
$693$	43.7541	−	30.4140i	1.66208	−	1.15533i
$694$	6.98652	+	12.1010i	0.265205	+	0.459348i
$695$	−36.5182			−1.38521
$696$	0.645614	+	2.05993i	0.0244719	+	0.0780813i
$697$	−5.42375	+	9.39421i	−0.205439	+	0.355831i
$698$	3.41690	−	5.91825i	0.129332	−	0.224009i
$699$	5.90856	+	1.32052i	0.223482	+	0.0499467i
$700$	−1.53232			−0.0579164
$701$	−5.99187	−	10.3782i	−0.226310	−	0.391980i	0.730402	−	0.683018i	$-0.239333\pi$
$701$	−5.99187	−	10.3782i	−0.226310	−	0.391980i	−0.956712	+	0.291038i	$0.906000\pi$
$702$	26.0083	−	10.6167i	0.981619	−	0.400700i
$703$	−10.5445	+	18.2636i	−0.397694	+	0.688826i
$704$	5.84199			0.220178
$705$	23.5310	−	25.5914i	0.886230	−	0.963830i
$706$	0.346349			0.0130350
$707$	−21.3705			−0.803719
$708$	5.58429	−	6.07326i	0.209871	−	0.228247i
$709$	−22.1973	−	38.4469i	−0.833638	−	1.44390i	−0.895134	−	0.445797i	$-0.852920\pi$
$709$	−22.1973	−	38.4469i	−0.833638	−	1.44390i	0.0614959	−	0.998107i	$-0.480413\pi$
$710$	−8.77730	−	15.2027i	−0.329406	−	0.570548i
$711$	−6.59896	+	4.58702i	−0.247480	+	0.172027i
$712$	3.52297			0.132029
$713$	25.7951	−	13.9327i	0.966033	−	0.521784i
$714$	5.79231	+	18.4812i	0.216772	+	0.691642i
$715$	−37.0481	+	64.1692i	−1.38552	+	2.39979i
$716$	−23.3796			−0.873735
$717$	2.95730	+	9.43572i	0.110443	+	0.352383i
$718$	21.6880			0.809388
$719$	14.2308	+	24.6485i	0.530720	+	0.919234i	0.999357	+	0.0358436i	$0.0114118\pi$
$719$	14.2308	+	24.6485i	0.530720	+	0.919234i	−0.468637	+	0.883391i	$0.655255\pi$
$720$	−5.77913	+	4.01715i	−0.215376	+	0.149710i
$721$	−13.3149			−0.495875
$722$	7.76521			0.288991
$723$	−20.8261	+	22.6497i	−0.774531	+	0.842350i
$724$	−0.955580	−	1.65511i	−0.0355139	−	0.0615118i
$725$	0.628137			0.0233284
$726$	11.9809	+	38.2269i	0.444653	+	1.41873i
$727$	−8.17180	+	14.1540i	−0.303075	+	0.524942i	−0.976831	−	0.214012i	$-0.931347\pi$
$727$	−8.17180	+	14.1540i	−0.303075	+	0.524942i	0.673756	+	0.738954i	$0.264680\pi$
$728$	−16.4373			−0.609206
$729$	6.71961	+	26.1505i	0.248874	+	0.968536i
$730$	−4.92216	−	8.52543i	−0.182177	−	0.315540i
$731$	−36.1889			−1.33849
$732$	23.7885	+	5.31657i	0.879248	+	0.196506i
$733$	3.48532	+	6.03675i	0.128733	+	0.222973i	0.923186	−	0.384353i	$-0.125576\pi$
$733$	3.48532	+	6.03675i	0.128733	+	0.222973i	−0.794453	+	0.607326i	$0.792242\pi$
$734$	−13.3708	−	23.1588i	−0.493523	−	0.854808i
$735$	6.17231	−	6.71276i	0.227669	−	0.247604i
$736$	−2.63277	−	4.56010i	−0.0970453	−	0.168087i
$737$	−29.6022	−	51.2726i	−1.09041	−	1.88865i
$738$	7.26560	−	5.05040i	0.267450	−	0.185908i
$739$	−9.65514	+	16.7232i	−0.355170	+	0.615173i	−0.987147	−	0.159814i	$-0.948910\pi$
$739$	−9.65514	+	16.7232i	−0.355170	+	0.615173i	0.631977	+	0.774987i	$0.282244\pi$
$740$	−4.78167	−	8.28210i	−0.175778	−	0.304456i
$741$	32.7896	−	35.6607i	1.20456	−	1.31003i
$742$	−16.3978	+	28.4019i	−0.601983	+	1.04266i
$743$	7.75132	−	13.4257i	0.284368	−	0.492540i	−0.688088	−	0.725628i	$-0.741549\pi$
$743$	7.75132	−	13.4257i	0.284368	−	0.492540i	0.972456	+	0.233087i	$0.0748828\pi$
$744$	6.91089	+	6.72603i	0.253366	+	0.246588i
$745$	8.08067	+	13.9961i	0.296053	+	0.512778i
$746$	−3.38248			−0.123841
$747$	−23.8089	−	11.2018i	−0.871124	−	0.409852i
$748$	−21.4854			−0.785585
$749$	10.8045			0.394788
$750$	−5.46388	−	17.4333i	−0.199513	−	0.636575i
$751$	−33.7537			−1.23169			−0.615844	−	0.787868i	$-0.711185\pi$
$751$	−33.7537			−1.23169			−0.615844	+	0.787868i	$0.711185\pi$
$752$	−4.27777	+	7.40932i	−0.155994	+	0.270190i
$753$	−1.55864	−	4.97308i	−0.0568001	−	0.181229i
$754$	6.73805			0.245385
$755$	−28.6928	+	49.6975i	−1.04424	+	1.80868i
$756$	2.14261	−	15.6525i	0.0779260	−	0.569277i
$757$	−2.29901	+	3.98200i	−0.0835588	+	0.144728i	−0.904776	−	0.425887i	$-0.859962\pi$
$757$	−2.29901	+	3.98200i	−0.0835588	+	0.144728i	0.821217	+	0.570615i	$0.193295\pi$
$758$	−17.4095	+	30.1541i	−0.632340	+	1.09525i
$759$	36.0628	−	39.2205i	1.30900	−	1.42361i
$760$	−6.06868	+	10.5113i	−0.220134	+	0.381283i
$761$	1.95845			0.0709938			0.0354969	−	0.999370i	$-0.488699\pi$
$761$	1.95845			0.0709938			0.0354969	+	0.999370i	$0.488699\pi$
$762$	4.59422	−	4.99649i	0.166431	−	0.181004i
$763$	27.9334	−	48.3821i	1.01126	−	1.75155i
$764$	8.44659	−	14.6299i	0.305587	−	0.529292i
$765$	21.2542	−	14.7741i	0.768448	−	0.534158i
$766$	14.8493	−	25.7198i	0.536527	−	0.929293i
$767$	−12.8760	−	22.3018i	−0.464924	−	0.805272i
$768$	1.17234	−	1.27499i	0.0423033	−	0.0460074i
$769$	7.03396			0.253651			0.126826	−	0.991925i	$-0.459521\pi$
$769$	7.03396			0.253651			0.126826	+	0.991925i	$0.459521\pi$
$770$	20.8355	+	36.0881i	0.750858	+	1.30052i
$771$	−2.01821	−	6.43941i	−0.0726842	−	0.231910i
$772$	6.16365	−	10.6758i	0.221835	−	0.384229i
$773$	−15.5206			−0.558239			−0.279119	−	0.960256i	$-0.590043\pi$
$773$	−15.5206			−0.558239			−0.279119	+	0.960256i	$0.590043\pi$
$774$	26.7111	+	12.5672i	0.960111	+	0.451719i
$775$	2.46894	−	1.33355i	0.0886868	−	0.0479024i
$776$	−1.79211	−	3.10403i	−0.0643330	−	0.111428i
$777$	20.9499	+	4.68215i	0.751573	+	0.167971i
$778$	−16.1712			−0.579764
$779$	7.62961	−	13.2149i	0.273359	−	0.473472i
$780$	6.57007	+	20.9628i	0.235246	+	0.750588i
$781$	−21.8566	+	37.8568i	−0.782092	+	1.35462i
$782$	9.68269	+	16.7709i	0.346252	+	0.599727i
$783$	−0.878309	+	6.41636i	−0.0313882	+	0.229302i
$784$	−1.12208	+	1.94350i	−0.0400743	+	0.0694107i
$785$	−24.3388			−0.868688
$786$	−5.59884	−	17.8639i	−0.199704	−	0.637185i
$787$	18.1468			0.646864			0.323432	−	0.946251i	$-0.395163\pi$
$787$	18.1468			0.646864			0.323432	+	0.946251i	$0.395163\pi$
$788$	5.62507	+	9.74291i	0.200385	+	0.347077i
$789$	−7.27361	−	23.2076i	−0.258948	−	0.826211i
$790$	−3.14239	−	5.44277i	−0.111801	−	0.193645i
$791$	11.2475			0.399916
$792$	15.8585	+	7.46119i	0.563506	+	0.265122i
$793$	38.0414	−	65.8897i	1.35089	−	2.33981i
$794$	3.08789	−	5.34838i	0.109585	−	0.189807i
$795$	42.7757	+	9.56008i	1.51710	+	0.339061i
$796$	−3.79423	−	6.57180i	−0.134483	−	0.232931i
$797$	−18.2696	−	31.6439i	−0.647144	−	1.12089i	−0.983802	−	0.179259i	$-0.942630\pi$
$797$	−18.2696	−	31.6439i	−0.647144	−	1.12089i	0.336658	−	0.941627i	$-0.390703\pi$
$798$	−8.14806	−	25.9976i	−0.288438	−	0.920305i
$799$	15.7326	−	27.2497i	0.556579	−	0.964024i
$800$	−0.251992	−	0.436463i	−0.00890926	−	0.0154313i
$801$	9.56332	+	4.49942i	0.337903	+	0.158979i
$802$	−17.3446			−0.612459
$803$	−12.2568	+	21.2295i	−0.432534	+	0.749171i
$804$	−17.1305	−	3.82855i	−0.604146	−	0.135022i
$805$	18.7796	−	32.5272i	0.661893	−	1.14643i
$806$	26.4844	−	14.3050i	0.932872	−	0.503872i
$807$	5.72695	−	6.22841i	0.201598	−	0.219250i
$808$	−3.51439	−	6.08711i	−0.123636	−	0.214144i
$809$	−6.75139	−	11.6938i	−0.237366	−	0.411130i	0.722591	−	0.691275i	$-0.242951\pi$
$809$	−6.75139	−	11.6938i	−0.237366	−	0.411130i	−0.959958	+	0.280145i	$0.909617\pi$
$810$	−20.8184	+	3.52388i	−0.731483	+	0.123817i
$811$	−7.93579	+	13.7452i	−0.278663	+	0.482659i	−0.971053	−	0.238865i	$-0.923225\pi$
$811$	−7.93579	+	13.7452i	−0.278663	+	0.482659i	0.692390	+	0.721524i	$0.256558\pi$
$812$	1.89470	−	3.28172i	0.0664911	−	0.115166i
$813$	−22.3816	−	5.00214i	−0.784958	−	0.175433i
$814$	−11.9070	+	20.6235i	−0.417340	+	0.722854i
$815$	−16.3974	−	28.4011i	−0.574376	−	0.994848i
$816$	−4.31159	+	4.68912i	−0.150936	+	0.164152i
$817$	50.9070			1.78101
$818$	−12.1859	−	21.1066i	−0.426070	−	0.737975i
$819$	−44.6200	−	20.9931i	−1.55915	−	0.733559i
$820$	3.45984	+	5.99261i	0.120823	+	0.209271i
$821$	8.83187	+	15.2973i	0.308235	+	0.533878i	0.977976	−	0.208716i	$-0.0669285\pi$
$821$	8.83187	+	15.2973i	0.308235	+	0.533878i	−0.669742	+	0.742594i	$0.733595\pi$
$822$	6.06312	+	19.3453i	0.211476	+	0.674745i
$823$	−26.6917			−0.930412			−0.465206	−	0.885202i	$-0.654020\pi$
$823$	−26.6917			−0.930412			−0.465206	+	0.885202i	$0.654020\pi$
$824$	−2.18966	−	3.79259i	−0.0762803	−	0.132121i
$825$	3.45169	−	3.75393i	0.120173	−	0.130695i
$826$	−14.4826			−0.503915
$827$	−6.36247	+	11.0201i	−0.221245	+	0.383207i	−0.955186	−	0.296006i	$-0.904345\pi$
$827$	−6.36247	+	11.0201i	−0.221245	+	0.383207i	0.733941	+	0.679213i	$0.237679\pi$
$828$	−1.32283	−	15.7412i	−0.0459715	−	0.547043i
$829$	−35.0188			−1.21625			−0.608126	−	0.793840i	$-0.708079\pi$
$829$	−35.0188			−1.21625			−0.608126	+	0.793840i	$0.708079\pi$
$830$	10.2884	−	17.8201i	0.357117	−	0.618544i
$831$	−10.3179	−	32.9208i	−0.357924	−	1.14201i
$832$	−2.70313	−	4.68195i	−0.0937140	−	0.162317i
$833$	4.12674	−	7.14772i	0.142983	−	0.247654i
$834$	26.3116	+	5.88046i	0.911096	+	0.203624i
$835$	−20.7983	−	36.0237i	−0.719755	−	1.24665i
$836$	30.2236			1.04531
$837$	10.1698	+	27.0846i	0.351520	+	0.936181i
$838$	−22.6831			−0.783576
$839$	−3.33440	−	5.77534i	−0.115116	−	0.199387i	0.802710	−	0.596370i	$-0.203391\pi$
$839$	−3.33440	−	5.77534i	−0.115116	−	0.199387i	−0.917826	+	0.396983i	$0.870057\pi$
$840$	12.0573	+	2.69472i	0.416015	+	0.0929765i
$841$	13.7233	−	23.7695i	0.473218	−	0.819637i
$842$	2.48460	+	4.30346i	0.0856250	+	0.148307i
$843$	−9.68430	−	30.8992i	−0.333545	−	1.06422i
$844$	4.91192	−	8.50770i	0.169075	−	0.292847i
$845$	38.0708			1.30967
$846$	−21.0752	+	14.6496i	−0.724581	+	0.503665i
$847$	35.1608	−	60.9002i	1.20814	−	2.09256i
$848$	−10.7865			−0.370411
$849$	7.70419	−	8.37878i	0.264407	−	0.287559i
$850$	0.926764	+	1.60520i	0.0317878	+	0.0550580i
$851$	21.4642			0.735783
$852$	3.87603	+	12.3671i	0.132791	+	0.423688i
$853$	−6.45115	−	11.1737i	−0.220883	−	0.382581i	0.734193	−	0.678941i	$-0.237561\pi$
$853$	−6.45115	−	11.1737i	−0.220883	−	0.382581i	−0.955076	+	0.296360i	$0.904227\pi$
$854$	−21.3941	−	37.0557i	−0.732091	−	1.26802i
$855$	−29.8984	+	20.7828i	−1.02250	+	0.710755i
$856$	1.77681	+	3.07753i	0.0607302	+	0.105188i
$857$	−17.3374			−0.592236			−0.296118	−	0.955151i	$-0.595692\pi$
$857$	−17.3374			−0.592236			−0.296118	+	0.955151i	$0.595692\pi$
$858$	37.0264	−	40.2685i	1.26406	−	1.37474i
$859$	4.59838	+	7.96462i	0.156895	+	0.271749i	0.933747	−	0.357933i	$-0.116518\pi$
$859$	4.59838	+	7.96462i	0.156895	+	0.271749i	−0.776853	+	0.629682i	$0.783185\pi$
$860$	−11.5425	+	19.9922i	−0.393597	+	0.681730i
$861$	−15.1585	−	3.38783i	−0.516602	−	0.115457i
$862$	−19.8668	+	34.4102i	−0.676665	+	1.17202i
$863$	−23.8716	+	41.3468i	−0.812598	+	1.40746i	0.0984427	+	0.995143i	$0.468614\pi$
$863$	−23.8716	+	41.3468i	−0.812598	+	1.40746i	−0.911040	+	0.412317i	$0.864719\pi$
$864$	4.81078	−	1.96378i	0.163666	−	0.0668090i
$865$	−6.45022	−	11.1721i	−0.219314	−	0.379863i
$866$	13.1671	+	22.8062i	0.447438	+	0.774985i
$867$	−4.07286	+	4.42949i	−0.138322	+	0.150433i
$868$	0.480101	−	16.9215i	0.0162957	−	0.574354i
$869$	−7.82496	+	13.5532i	−0.265444	+	0.459762i
$870$	−4.94257	−	1.10463i	−0.167569	−	0.0374505i
$871$	−27.3943	+	47.4482i	−0.928219	+	1.60772i
$872$	18.3747			0.622246
$873$	−0.900440	−	10.7149i	−0.0304753	−	0.362644i
$874$	−13.6207	−	23.5917i	−0.460726	−	0.798001i
$875$	−16.0350	+	27.7735i	−0.542083	+	0.938916i
$876$	2.17361	+	6.93524i	0.0734396	+	0.234320i
$877$	16.6409	+	28.8229i	0.561923	+	0.973280i	0.997329	+	0.0730451i	$0.0232717\pi$
$877$	16.6409	+	28.8229i	0.561923	+	0.973280i	−0.435405	+	0.900234i	$0.643395\pi$
$878$	−13.5422	−	23.4558i	−0.457027	−	0.791595i
$879$	26.1510	+	5.84457i	0.882052	+	0.197133i
$880$	−6.85282	+	11.8694i	−0.231009	+	0.400119i
$881$	−16.4234	+	28.4461i	−0.553317	+	0.958374i	0.444715	+	0.895672i	$0.353305\pi$
$881$	−16.4234	+	28.4461i	−0.553317	+	0.958374i	−0.998032	+	0.0627018i	$0.980028\pi$
$882$	−5.52813	+	3.84267i	−0.186142	+	0.129389i
$883$	−19.1572			−0.644691			−0.322346	−	0.946622i	$-0.604471\pi$
$883$	−19.1572			−0.644691			−0.322346	+	0.946622i	$0.604471\pi$
$884$	9.94143	+	17.2191i	0.334367	+	0.579140i
$885$	5.78878	+	18.4700i	0.194588	+	0.620861i
$886$	−1.70824	−	2.95877i	−0.0573896	−	0.0994017i
$887$	−4.33508			−0.145558			−0.0727788	−	0.997348i	$-0.523187\pi$
$887$	−4.33508			−0.145558			−0.0727788	+	0.997348i	$0.523187\pi$
$888$	2.11157	+	6.73729i	0.0708598	+	0.226089i
$889$	−11.9149			−0.399613
$890$	−4.13255	+	7.15778i	−0.138523	+	0.239929i
$891$	33.5196	+	40.5077i	1.12295	+	1.35706i
$892$	−5.12084	−	8.86956i	−0.171459	−	0.296975i
$893$	−22.1311	+	38.3322i	−0.740589	+	1.28274i
$894$	−3.56840	−	11.3855i	−0.119345	−	0.380789i
$895$	27.4249	−	47.5013i	0.916713	−	1.58779i
$896$	−3.04042			−0.101573
$897$	−48.1189	−	10.7543i	−1.60664	−	0.359074i
$898$	−18.2701	−	31.6448i	−0.609683	−	1.05600i
$899$	−0.196805	+	6.93656i	−0.00656382	+	0.231347i
$900$	−0.126613	−	1.50664i	−0.00422042	−	0.0502214i
$901$	39.6703			1.32161
$902$	8.61545	−	14.9224i	0.286863	−	0.496862i
$903$	−15.4975	−	49.4470i	−0.515724	−	1.64549i
$904$	1.84967	+	3.20372i	0.0615190	+	0.106554i
$905$	4.48369			0.149043
$906$	28.6761	−	31.1870i	0.952699	−	1.03612i
$907$	10.7856	+	18.6812i	0.358131	+	0.620301i	0.987649	−	0.156685i	$-0.0500809\pi$
$907$	10.7856	+	18.6812i	0.358131	+	0.620301i	−0.629518	+	0.776986i	$0.716748\pi$
$908$	−8.63703	+	14.9598i	−0.286630	+	0.496457i
$909$	−1.76579	−	21.0123i	−0.0585677	−	0.696934i
$910$	19.2814	−	33.3964i	0.639172	−	1.10708i
$911$	−1.35817	+	2.35243i	−0.0449983	+	0.0779394i	−0.887647	−	0.460524i	$-0.847662\pi$
$911$	−1.35817	+	2.35243i	−0.0449983	+	0.0779394i	0.842649	+	0.538463i	$0.180995\pi$
$912$	6.06513	−	6.59620i	0.200836	−	0.218422i
$913$	−51.2391			−1.69577
$914$	−4.40598	+	7.63138i	−0.145737	+	0.252424i
$915$	−38.7065	+	42.0957i	−1.27960	+	1.39164i
$916$	−1.16671	+	2.02080i	−0.0385491	+	0.0667690i
$917$	−16.4311	+	28.4595i	−0.542602	+	0.939815i
$918$	−17.6929	+	7.22229i	−0.583951	+	0.238371i
$919$	15.9728	−	27.6657i	0.526894	−	0.912607i	−0.472615	−	0.881269i	$-0.656690\pi$
$919$	15.9728	−	27.6657i	0.526894	−	0.912607i	0.999509	−	0.0313382i	$-0.00997689\pi$
$920$	12.3533			0.407275
$921$	8.20510	+	26.1796i	0.270367	+	0.862647i
$922$	−6.69027	+	11.5879i	−0.220332	+	0.381627i
$923$	40.4528			1.33152
$924$	−9.20089	−	29.3568i	−0.302687	−	0.965768i
$925$	2.05441			0.0675487
$926$	−27.0864			−0.890116
$927$	−1.10019	−	13.0918i	−0.0361348	−	0.429991i
$928$	1.24634			0.0409132
$929$	−22.6243	−	39.1864i	−0.742279	−	1.28567i	−0.951455	−	0.307787i	$-0.900411\pi$
$929$	−22.6243	−	39.1864i	−0.742279	−	1.28567i	0.209176	−	0.977878i	$-0.432922\pi$
$930$	−21.7723	+	6.15135i	−0.713941	+	0.201711i
$931$	−5.80510	+	10.0547i	−0.190254	+	0.329530i
$932$	1.74773	−	3.02716i	0.0572489	−	0.0991580i
$933$	6.83124	−	7.42939i	0.223645	−	0.243227i
$934$	−2.71747	−	4.70680i	−0.0889184	−	0.154011i
$935$	25.2030	−	43.6529i	0.824226	−	1.42760i
$936$	−1.35818	−	16.1618i	−0.0443934	−	0.528264i
$937$	15.7775	+	27.3274i	0.515427	+	0.892746i	0.999840	+	0.0179062i	$0.00570004\pi$
$937$	15.7775	+	27.3274i	0.515427	+	0.892746i	−0.484413	+	0.874840i	$0.660967\pi$
$938$	15.4063	+	26.6844i	0.503032	+	0.871277i
$939$	−3.97887	+	4.32727i	−0.129846	+	0.141215i
$940$	−10.0359	−	17.3827i	−0.327335	−	0.566961i
$941$	−9.28506	−	16.0822i	−0.302684	−	0.524264i	0.674059	−	0.738678i	$-0.264549\pi$
$941$	−9.28506	−	16.0822i	−0.302684	−	0.524264i	−0.976743	+	0.214413i	$0.931216\pi$
$942$	17.5363	+	3.91923i	0.571362	+	0.127695i
$943$	−15.5307			−0.505749
$944$	−2.38168	−	4.12519i	−0.0775171	−	0.134264i
$945$	29.2886	+	22.7141i	0.952758	+	0.738890i
$946$	57.4848			1.86899
$947$	−20.2488	+	35.0720i	−0.657999	+	1.13969i	0.323134	+	0.946353i	$0.395264\pi$
$947$	−20.2488	+	35.0720i	−0.657999	+	1.13969i	−0.981133	+	0.193334i	$0.938070\pi$
$948$	1.38767	+	4.42757i	0.0450694	+	0.143801i
$949$	22.6852			0.736394
$950$	−1.30368	−	2.25805i	−0.0422971	−	0.0732607i
$951$	−23.4555	+	25.5093i	−0.760596	+	0.827194i
$952$	11.1819			0.362408
$953$	28.2571			0.915336			0.457668	−	0.889123i	$-0.348685\pi$
$953$	28.2571			0.915336			0.457668	+	0.889123i	$0.348685\pi$
$954$	−29.2807	−	13.7762i	−0.947999	−	0.446021i
$955$	19.8162	+	34.3226i	0.641237	+	1.11065i
$956$	5.70901			0.184643
$957$	3.77167	+	12.0341i	0.121921	+	0.389006i
$958$	−3.56670			−0.115235
$959$	17.7937	−	30.8195i	0.574587	−	0.995214i
$960$	1.21527	+	3.87751i	0.0392227	+	0.125146i
$961$	13.9529	+	27.6824i	0.450093	+	0.892982i
$962$	22.0378			0.710526
$963$	0.892753	+	10.6234i	0.0287686	+	0.342335i
$964$	8.88226	+	15.3845i	0.286078	+	0.495502i
$965$	14.4603	+	25.0459i	0.465493	+	0.806257i
$966$	−18.7686	+	20.4120i	−0.603870	+	0.656745i
$967$	4.86983			0.156603			0.0783016	−	0.996930i	$-0.475050\pi$
$967$	4.86983			0.156603			0.0783016	+	0.996930i	$0.475050\pi$
$968$	23.1289			0.743390
$969$	−22.3061	+	24.2592i	−0.716574	+	0.779318i
$970$	8.40879			0.269990
$971$	14.1457	−	24.5011i	0.453957	−	0.786277i	−0.544670	−	0.838650i	$-0.683345\pi$
$971$	14.1457	−	24.5011i	0.453957	−	0.786277i	0.998628	+	0.0523734i	$0.0166786\pi$
$972$	15.5672	+	0.813366i	0.499319	+	0.0260887i
$973$	−23.6633	−	40.9860i	−0.758609	−	1.31395i
$974$	−10.4720			−0.335546
$975$	−4.60563	−	1.02933i	−0.147498	−	0.0329649i
$976$	7.03656	−	12.1877i	0.225235	−	0.390118i
$977$	−14.5551	+	25.2102i	−0.465659	+	0.806545i	−0.999231	−	0.0392095i	$-0.987516\pi$
$977$	−14.5551	+	25.2102i	−0.465659	+	0.806545i	0.533572	+	0.845755i	$0.320849\pi$
$978$	7.24105	+	23.1037i	0.231543	+	0.738773i
$979$	20.5812			0.657777
$980$	−2.63247	−	4.55956i	−0.0840910	−	0.145650i
$981$	49.8793	+	23.4676i	1.59252	+	0.749261i
$982$	−8.32650	+	14.4219i	−0.265709	+	0.460222i
$983$	54.9593			1.75293			0.876465	−	0.481465i	$-0.159895\pi$
$983$	54.9593			1.75293			0.876465	+	0.481465i	$0.159895\pi$
$984$	−1.52785	−	4.87485i	−0.0487062	−	0.155404i
$985$	−26.3935			−0.840966
$986$	−4.58374			−0.145976
$987$	43.9702	+	9.82703i	1.39959	+	0.312798i
$988$	−13.9846	−	24.2221i	−0.444911	−	0.770608i
$989$	−25.9063	−	44.8710i	−0.823773	−	1.42682i
$990$	−33.7617	+	23.4681i	−1.07302	+	0.745867i
$991$	50.0331			1.58935			0.794677	−	0.607033i	$-0.207640\pi$
$991$	50.0331			1.58935			0.794677	+	0.607033i	$0.207640\pi$
$992$	4.89884	−	2.64601i	0.155538	−	0.0840110i
$993$	−53.8794	−	12.0417i	−1.70981	−	0.382131i
$994$	11.3751	−	19.7023i	0.360797	−	0.624919i
$995$	17.8030			0.564392
$996$	−10.2824	+	11.1828i	−0.325811	+	0.354339i
$997$	−1.30768			−0.0414146			−0.0207073	−	0.999786i	$-0.506592\pi$
$997$	−1.30768			−0.0414146			−0.0207073	+	0.999786i	$0.506592\pi$
$998$	8.18430	+	14.1756i	0.259070	+	0.448722i
$999$	−2.87264	+	20.9856i	−0.0908862	+	0.663956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.211.1	✓	32
3.2	odd	2		1674.2.g.b.955.12		32
9.2	odd	6		1674.2.h.b.397.5		32
9.7	even	3		558.2.h.a.25.11	yes	32
31.5	even	3		558.2.h.a.67.11	yes	32
93.5	odd	6		1674.2.h.b.253.5		32
279.160	even	3	inner	558.2.g.a.439.1	yes	32
279.191	odd	6		1674.2.g.b.1369.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.1	✓	32	1.1	even	1	trivial
558.2.g.a.439.1	yes	32	279.160	even	3	inner
558.2.h.a.25.11	yes	32	9.7	even	3
558.2.h.a.67.11	yes	32	31.5	even	3
1674.2.g.b.955.12		32	3.2	odd	2
1674.2.g.b.1369.12		32	279.191	odd	6
1674.2.h.b.253.5		32	93.5	odd	6
1674.2.h.b.397.5		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.69035 - 0.377782i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.17303 - 2.03175i) q^{5} +(0.518006 + 1.65278i) q^{6} +(1.52021 - 2.63308i) q^{7} +1.00000 q^{8} +(2.71456 + 1.27717i) q^{9} +(-1.17303 + 2.03175i) q^{10} +5.84199 q^{11} +(1.17234 - 1.27499i) q^{12} +(-2.70313 - 4.68195i) q^{13} -3.04042 q^{14} +(1.21527 + 3.87751i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83888 + 3.18503i) q^{17} +(-0.251223 - 2.98946i) q^{18} +(-2.58676 - 4.48039i) q^{19} +2.34606 q^{20} +(-3.56442 + 3.87652i) q^{21} +(-2.92100 - 5.05931i) q^{22} +(-2.63277 + 4.56010i) q^{23} +(-1.69035 - 0.377782i) q^{24} +(-0.251992 + 0.436463i) q^{25} +(-2.70313 + 4.68195i) q^{26} +(-4.10607 - 3.18437i) q^{27} +(1.52021 + 2.63308i) q^{28} +(-0.623172 - 1.07937i) q^{29} +(2.75038 - 2.99121i) q^{30} +(-4.74093 - 2.91951i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.87501 - 2.20700i) q^{33} +(1.83888 - 3.18503i) q^{34} -7.13300 q^{35} +(-2.46334 + 1.71230i) q^{36} +(-2.03817 - 3.53022i) q^{37} +(-2.58676 + 4.48039i) q^{38} +(2.80047 + 8.93532i) q^{39} +(-1.17303 - 2.03175i) q^{40} +(1.47475 + 2.55433i) q^{41} +(5.13937 + 1.14861i) q^{42} +(-4.91997 + 8.52163i) q^{43} +(-2.92100 + 5.05931i) q^{44} +(-0.589384 - 7.01345i) q^{45} +5.26555 q^{46} +(-4.27777 - 7.40932i) q^{47} +(0.518006 + 1.65278i) q^{48} +(-1.12208 - 1.94350i) q^{49} +0.503984 q^{50} +(-1.90510 - 6.07851i) q^{51} +5.40625 q^{52} +(5.39327 - 9.34142i) q^{53} +(-0.704708 + 5.14814i) q^{54} +(-6.85282 - 11.8694i) q^{55} +(1.52021 - 2.63308i) q^{56} +(2.67991 + 8.55066i) q^{57} +(-0.623172 + 1.07937i) q^{58} +4.76336 q^{59} +(-3.96566 - 0.886297i) q^{60} +(7.03656 + 12.1877i) q^{61} +(-0.157906 + 5.56552i) q^{62} +(7.48959 - 5.20610i) q^{63} +1.00000 q^{64} +(-6.34169 + 10.9841i) q^{65} +(3.02619 + 9.65551i) q^{66} +(-5.06714 - 8.77655i) q^{67} -3.67775 q^{68} +(6.17303 - 6.71354i) q^{69} +(3.56650 + 6.17736i) q^{70} +(-3.74130 + 6.48012i) q^{71} +(2.71456 + 1.27717i) q^{72} +(-2.09806 + 3.63394i) q^{73} +(-2.03817 + 3.53022i) q^{74} +(0.590842 - 0.642577i) q^{75} +5.17351 q^{76} +(8.88106 - 15.3824i) q^{77} +(6.33798 - 6.89294i) q^{78} +(-1.33943 + 2.31997i) q^{79} +(-1.17303 + 2.03175i) q^{80} +(5.73770 + 6.93389i) q^{81} +(1.47475 - 2.55433i) q^{82} -8.77082 q^{83} +(-1.57496 - 5.02514i) q^{84} +(4.31411 - 7.47226i) q^{85} +9.83993 q^{86} +(0.645614 + 2.05993i) q^{87} +5.84199 q^{88} +3.52297 q^{89} +(-5.77913 + 4.01715i) q^{90} -16.4373 q^{91} +(-2.63277 - 4.56010i) q^{92} +(6.91089 + 6.72603i) q^{93} +(-4.27777 + 7.40932i) q^{94} +(-6.06868 + 10.5113i) q^{95} +(1.17234 - 1.27499i) q^{96} +(-1.79211 - 3.10403i) q^{97} +(-1.12208 + 1.94350i) q^{98} +(15.8585 + 7.46119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

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