LMFDB - Embedded newform 558.2.h.a.67.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(25,558)] 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([4, 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("558.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.h (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			67.11
Character	$\chi$	$=$	558.67
Dual form			558.2.h.a.25.11

$q$-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} +(0.518006 + 1.65278i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.34606 q^{5} +(1.17234 - 1.27499i) q^{6} -3.04042 q^{7} +1.00000 q^{8} +(-2.46334 + 1.71230i) q^{9} +(-1.17303 - 2.03175i) q^{10} +(-2.92100 + 5.05931i) q^{11} +(-1.69035 - 0.377782i) q^{12} +5.40625 q^{13} +(1.52021 + 2.63308i) q^{14} +(1.21527 + 3.87751i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83888 - 3.18503i) q^{17} +(2.71456 + 1.27717i) q^{18} +(-2.58676 + 4.48039i) q^{19} +(-1.17303 + 2.03175i) q^{20} +(-1.57496 - 5.02514i) q^{21} +5.84199 q^{22} +(-2.63277 + 4.56010i) q^{23} +(0.518006 + 1.65278i) q^{24} +0.503984 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} +(4.89884 + 2.64601i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.87501 - 2.20700i) q^{33} -3.67775 q^{34} -7.13300 q^{35} +(-0.251223 - 2.98946i) q^{36} +(-2.03817 + 3.53022i) q^{37} +5.17351 q^{38} +(2.80047 + 8.93532i) q^{39} +2.34606 q^{40} -2.94949 q^{41} +(-3.56442 + 3.87652i) q^{42} +9.83993 q^{43} +(-2.92100 - 5.05931i) q^{44} +(-5.77913 + 4.01715i) q^{45} +5.26555 q^{46} +(-4.27777 - 7.40932i) q^{47} +(1.17234 - 1.27499i) q^{48} +2.24416 q^{49} +(-0.251992 - 0.436463i) q^{50} +(6.21669 + 1.38939i) q^{51} +(-2.70313 + 4.68195i) q^{52} +(5.39327 + 9.34142i) q^{53} +(-0.704708 + 5.14814i) q^{54} +(-6.85282 + 11.8694i) q^{55} -3.04042 q^{56} +(-8.74504 - 1.95446i) q^{57} +(-0.623172 + 1.07937i) q^{58} +(-2.38168 - 4.12519i) 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} +12.6834 q^{65} +(3.02619 + 9.65551i) q^{66} +10.1343 q^{67} +(1.83888 + 3.18503i) q^{68} +(-8.90061 - 1.98923i) q^{69} +(3.56650 + 6.17736i) q^{70} +(-3.74130 - 6.48012i) q^{71} +(-2.46334 + 1.71230i) q^{72} +(-2.09806 - 3.63394i) q^{73} +4.07635 q^{74} +(0.261067 + 0.832973i) q^{75} +(-2.58676 - 4.48039i) q^{76} +(8.88106 - 15.3824i) q^{77} +(6.33798 - 6.89294i) q^{78} +2.67887 q^{79} +(-1.17303 - 2.03175i) q^{80} +(3.13608 - 8.43594i) q^{81} +(1.47475 + 2.55433i) q^{82} +(4.38541 - 7.59576i) q^{83} +(5.13937 + 1.14861i) q^{84} +(4.31411 - 7.47226i) q^{85} +(-4.91997 - 8.52163i) q^{86} +(1.46114 - 1.58908i) q^{87} +(-2.92100 + 5.05931i) q^{88} +3.52297 q^{89} +(6.36852 + 2.99630i) q^{90} -16.4373 q^{91} +(-2.63277 - 4.56010i) q^{92} +(-1.83564 + 9.46734i) q^{93} +(-4.27777 + 7.40932i) q^{94} +(-6.06868 + 10.5113i) q^{95} +(-1.69035 - 0.377782i) q^{96} +(-1.79211 - 3.10403i) q^{97} +(-1.12208 - 1.94350i) q^{98} +(-1.46764 - 17.4644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 2 q^{3} - 16 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 32 q^{8} - 6 q^{9} - q^{10} - 2 q^{11} + 4 q^{12} + 20 q^{13} + q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} + 12 q^{18} + 4 q^{19} - q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 2 * q^3 - 16 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 32 * q^8 - 6 * q^9 - q^10 - 2 * q^11 + 4 * q^12 + 20 * q^13 + q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 + 12 * q^18 + 4 * q^19 - q^20 + q^21 + 4 * q^22 - q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - 10 * q^31 - 16 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^36 - 19 * q^37 - 8 * q^38 + 19 * q^39 + 2 * q^40 - 20 * q^41 + 10 * q^42 + 26 * q^43 - 2 * q^44 - 19 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 + 26 * q^49 - 19 * q^50 - 37 * q^51 - 10 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 - 2 * q^56 - 5 * q^57 - 3 * q^58 - 6 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 + 16 * q^65 + 5 * q^66 + 16 * q^67 - 4 * q^68 - 32 * q^69 + 7 * q^71 - 6 * q^72 + 7 * q^73 + 38 * q^74 + q^75 + 4 * q^76 - q^77 - 11 * q^78 + 68 * q^79 - q^80 - 6 * q^81 + 10 * q^82 + 14 * q^83 - 11 * q^84 + 13 * q^85 - 13 * q^86 - 6 * q^87 - 2 * q^88 + 2 * q^89 + 5 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 + 4 * q^96 + 10 * q^97 - 13 * q^98 + 10 * q^99

Character values

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

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	0.518006	+	1.65278i	0.299071	+	0.954231i
$3$	0.518006	+	1.65278i	0.299071	+	0.954231i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.34606			1.04919			0.524594	−	0.851352i	$-0.324217\pi$
$5$	2.34606			1.04919			0.524594	+	0.851352i	$0.324217\pi$
$6$	1.17234	−	1.27499i	0.478607	−	0.520514i
$7$	−3.04042			−1.14917			−0.574586	−	0.818444i	$-0.694837\pi$
$7$	−3.04042			−1.14917			−0.574586	+	0.818444i	$0.694837\pi$
$8$	1.00000			0.353553
$9$	−2.46334	+	1.71230i	−0.821113	+	0.570766i
$10$	−1.17303	−	2.03175i	−0.370944	−	0.642494i
$11$	−2.92100	+	5.05931i	−0.880714	+	1.52544i	−0.0301644	+	0.999545i	$0.509603\pi$
$11$	−2.92100	+	5.05931i	−0.880714	+	1.52544i	−0.850549	+	0.525896i	$0.823730\pi$
$12$	−1.69035	−	0.377782i	−0.487962	−	0.109056i
$13$	5.40625			1.49942			0.749712	−	0.661764i	$-0.230192\pi$
$13$	5.40625			1.49942			0.749712	+	0.661764i	$0.230192\pi$
$14$	1.52021	+	2.63308i	0.406293	+	0.703721i
$15$	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	−0.552128	−	0.833760i	$-0.686184\pi$
$17$	1.83888	−	3.18503i	0.445993	−	0.772483i	0.998121	+	0.0612767i	$0.0195172\pi$
$18$	2.71456	+	1.27717i	0.639828	+	0.301031i
$19$	−2.58676	+	4.48039i	−0.593442	+	1.02787i	0.400322	+	0.916374i	$0.368898\pi$
$19$	−2.58676	+	4.48039i	−0.593442	+	1.02787i	−0.993765	+	0.111498i	$0.964435\pi$
$20$	−1.17303	+	2.03175i	−0.262297	+	0.454312i
$21$	−1.57496	−	5.02514i	−0.343684	−	1.09657i
$22$	5.84199			1.24552
$23$	−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	$0.981686\pi$
$24$	0.518006	+	1.65278i	0.105738	+	0.337372i
$25$	0.503984			0.100797
$26$	−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
$31$	4.89884	+	2.64601i	0.879857	+	0.475238i
$31$	4.89884	+	2.64601i	0.879857	+	0.475238i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−9.87501	−	2.20700i	−1.71902	−	0.384189i
$34$	−3.67775			−0.630730
$35$	−7.13300			−1.20570
$36$	−0.251223	−	2.98946i	−0.0418706	−	0.498244i
$37$	−2.03817	+	3.53022i	−0.335074	+	0.580365i	−0.983499	−	0.180914i	$-0.942095\pi$
$37$	−2.03817	+	3.53022i	−0.335074	+	0.580365i	0.648425	+	0.761278i	$0.275428\pi$
$38$	5.17351			0.839254
$39$	2.80047	+	8.93532i	0.448434	+	1.43080i
$40$	2.34606			0.370944
$41$	−2.94949			−0.460633			−0.230317	−	0.973116i	$-0.573976\pi$
$41$	−2.94949			−0.460633			−0.230317	+	0.973116i	$0.573976\pi$
$42$	−3.56442	+	3.87652i	−0.550001	+	0.598160i
$43$	9.83993			1.50058			0.750288	−	0.661111i	$-0.229915\pi$
$43$	9.83993			1.50058			0.750288	+	0.661111i	$0.229915\pi$
$44$	−2.92100	−	5.05931i	−0.440357	−	0.762720i
$45$	−5.77913	+	4.01715i	−0.861502	+	0.598841i
$46$	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	$-0.381151\pi$
$48$	1.17234	−	1.27499i	0.169213	−	0.184030i
$49$	2.24416			0.320594
$50$	−0.251992	−	0.436463i	−0.0356370	−	0.0617252i
$51$	6.21669	+	1.38939i	0.870511	+	0.194553i
$52$	−2.70313	+	4.68195i	−0.374856	+	0.649270i
$53$	5.39327	+	9.34142i	0.740823	+	1.28314i	0.952121	+	0.305721i	$0.0988975\pi$
$53$	5.39327	+	9.34142i	0.740823	+	1.28314i	−0.211298	+	0.977422i	$0.567769\pi$
$54$	−0.704708	+	5.14814i	−0.0958987	+	0.700574i
$55$	−6.85282	+	11.8694i	−0.924035	+	1.60047i
$56$	−3.04042			−0.406293
$57$	−8.74504	−	1.95446i	−1.15831	−	0.258874i
$58$	−0.623172	+	1.07937i	−0.0818265	+	0.141728i
$59$	−2.38168	−	4.12519i	−0.310068	−	0.537054i	0.668309	−	0.743884i	$-0.267019\pi$
$59$	−2.38168	−	4.12519i	−0.310068	−	0.537054i	−0.978377	+	0.206830i	$0.933685\pi$
$60$	−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
$65$	12.6834			1.57318
$66$	3.02619	+	9.65551i	0.372498	+	1.18851i
$67$	10.1343			1.23810			0.619050	−	0.785351i	$-0.287518\pi$
$67$	10.1343			1.23810			0.619050	+	0.785351i	$0.287518\pi$
$68$	1.83888	+	3.18503i	0.222997	+	0.386241i
$69$	−8.90061	−	1.98923i	−1.07151	−	0.239475i
$70$	3.56650	+	6.17736i	0.426278	+	0.738336i
$71$	−3.74130	−	6.48012i	−0.444010	−	0.769049i	0.553972	−	0.832535i	$-0.313111\pi$
$71$	−3.74130	−	6.48012i	−0.444010	−	0.769049i	−0.997983	+	0.0634865i	$0.979778\pi$
$72$	−2.46334	+	1.71230i	−0.290307	+	0.201796i
$73$	−2.09806	−	3.63394i	−0.245559	−	0.425321i	0.716730	−	0.697351i	$-0.245638\pi$
$73$	−2.09806	−	3.63394i	−0.245559	−	0.425321i	−0.962289	+	0.272030i	$0.912305\pi$
$74$	4.07635			0.473866
$75$	0.261067	+	0.832973i	0.0301454	+	0.0961834i
$76$	−2.58676	−	4.48039i	−0.296721	−	0.513936i
$77$	8.88106	−	15.3824i	1.01209	−	1.75299i
$78$	6.33798	−	6.89294i	0.717635	−	0.780472i
$79$	2.67887			0.301396			0.150698	−	0.988580i	$-0.451848\pi$
$79$	2.67887			0.301396			0.150698	+	0.988580i	$0.451848\pi$
$80$	−1.17303	−	2.03175i	−0.131149	−	0.227156i
$81$	3.13608	−	8.43594i	0.348453	−	0.937326i
$82$	1.47475	+	2.55433i	0.162858	+	0.282079i
$83$	4.38541	−	7.59576i	0.481362	−	0.833743i	−0.518410	−	0.855132i	$-0.673476\pi$
$83$	4.38541	−	7.59576i	0.481362	−	0.833743i	0.999771	+	0.0213898i	$0.00680910\pi$
$84$	5.13937	+	1.14861i	0.560752	+	0.125324i
$85$	4.31411	−	7.47226i	0.467931	−	0.810480i
$86$	−4.91997	−	8.52163i	−0.530534	−	0.918911i
$87$	1.46114	−	1.58908i	0.156651	−	0.170367i
$88$	−2.92100	+	5.05931i	−0.311379	+	0.539325i
$89$	3.52297			0.373434			0.186717	−	0.982414i	$-0.440215\pi$
$89$	3.52297			0.373434			0.186717	+	0.982414i	$0.440215\pi$
$90$	6.36852	+	2.99630i	0.671301	+	0.315838i
$91$	−16.4373			−1.72310
$92$	−2.63277	−	4.56010i	−0.274486	−	0.475423i
$93$	−1.83564	+	9.46734i	−0.190347	+	0.981717i
$94$	−4.27777	+	7.40932i	−0.441219	+	0.764213i
$95$	−6.06868	+	10.5113i	−0.622633	+	1.07843i
$96$	−1.69035	−	0.377782i	−0.172521	−	0.0385572i
$97$	−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
$99$	−1.46764	−	17.4644i	−0.147504	−	1.75524i
$100$	−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	$0.947048\pi$
$102$	−1.90510	−	6.07851i	−0.188633	−	0.601862i
$103$	4.37931			0.431506			0.215753	−	0.976448i	$-0.430779\pi$
$103$	4.37931			0.431506			0.215753	+	0.976448i	$0.430779\pi$
$104$	5.40625			0.530127
$105$	−3.69494	−	11.7893i	−0.360589	−	1.15051i
$106$	5.39327	−	9.34142i	0.523841	−	0.907319i
$107$	1.77681	−	3.07753i	0.171771	−	0.297516i	−0.767268	−	0.641326i	$-0.778384\pi$
$107$	1.77681	−	3.07753i	0.171771	−	0.297516i	0.939039	+	0.343811i	$0.111718\pi$
$108$	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	$0.157550\pi$
$110$	13.7056			1.30678
$111$	−6.89045	−	1.53997i	−0.654013	−	0.146167i
$112$	1.52021	+	2.63308i	0.143646	+	0.248803i
$113$	−3.69933			−0.348004			−0.174002	−	0.984745i	$-0.555670\pi$
$113$	−3.69933			−0.348004			−0.174002	+	0.984745i	$0.555670\pi$
$114$	2.67991	+	8.55066i	0.250997	+	0.800842i
$115$	−6.17664	+	10.6982i	−0.575974	+	0.997617i
$116$	1.24634			0.115720
$117$	−13.3174	+	9.25711i	−1.23120	+	0.855820i
$118$	−2.38168	+	4.12519i	−0.219251	+	0.379755i
$119$	−5.59096	+	9.68383i	−0.512523	+	0.887715i
$120$	1.21527	+	3.87751i	0.110939	+	0.353966i
$121$	−11.5644	−	20.0302i	−1.05131	−	1.82093i
$122$	7.03656	−	12.1877i	0.637060	−	1.10342i
$123$	−1.52785	−	4.87485i	−0.137762	−	0.439550i
$124$	−4.74093	+	2.91951i	−0.425748	+	0.262180i
$125$	−10.5479			−0.943434
$126$	−8.25341	−	3.88312i	−0.735272	−	0.345936i
$127$	−1.95942	+	3.39381i	−0.173870	+	0.301152i	−0.939770	−	0.341808i	$-0.888961\pi$
$127$	−1.95942	+	3.39381i	−0.173870	+	0.301152i	0.765900	+	0.642960i	$0.222294\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.09715	+	16.2632i	0.448779	+	1.43190i
$130$	−6.34169	−	10.9841i	−0.556203	−	0.963371i
$131$	5.40422	+	9.36038i	0.472169	+	0.817820i	0.999493	−	0.0318442i	$-0.0101380\pi$
$131$	5.40422	+	9.36038i	0.472169	+	0.817820i	−0.527324	+	0.849664i	$0.676805\pi$
$132$	6.84882	−	7.44851i	0.596113	−	0.648310i
$133$	7.86483	−	13.6223i	0.681967	−	1.18120i
$134$	−5.06714	−	8.77655i	−0.437735	−	0.758179i
$135$	−9.63307	−	7.47071i	−0.829083	−	0.642976i
$136$	1.83888	−	3.18503i	0.157682	−	0.273114i
$137$	−5.85236	+	10.1366i	−0.500001	+	0.866028i	0.499999	+	0.866026i	$0.333334\pi$
$137$	−5.85236	+	10.1366i	−0.500001	+	0.866028i	−1.00000		1.41469e-6i	$1.00000\pi$
$138$	2.72759	+	8.70277i	0.232188	+	0.740829i
$139$	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
$141$	10.0300	−	10.9083i	0.844681	−	0.918643i
$142$	−3.74130	+	6.48012i	−0.313963	+	0.543799i
$143$	−15.7916	+	27.3519i	−1.32056	+	2.28728i
$144$	2.71456	+	1.27717i	0.226214	+	0.106430i
$145$	−1.46200	−	2.53225i	−0.121412	−	0.210292i
$146$	−2.09806	+	3.63394i	−0.173636	+	0.300747i
$147$	1.16249	+	3.70910i	0.0958805	+	0.305921i
$148$	−2.03817	−	3.53022i	−0.167537	−	0.290182i
$149$	3.44436	+	5.96581i	0.282173	+	0.488738i	0.971920	−	0.235313i	$-0.0756114\pi$
$149$	3.44436	+	5.96581i	0.282173	+	0.488738i	−0.689747	+	0.724051i	$0.742278\pi$
$150$	0.590842	−	0.642577i	0.0482421	−	0.0524662i
$151$	−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
$155$	11.4930	+	6.20769i	0.923136	+	0.498614i
$156$	−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	$0.0308046\pi$
$158$	−1.33943	−	2.31997i	−0.106560	−	0.184567i
$159$	−12.6455	+	13.7528i	−1.00286	+	1.09067i
$160$	−1.17303	+	2.03175i	−0.0927360	+	0.160624i
$161$	8.00474	−	13.8646i	0.630862	−	1.09268i
$162$	−8.87377	+	1.50205i	−0.697190	+	0.118012i
$163$	13.9787			1.09490			0.547448	−	0.836840i	$-0.315599\pi$
$163$	13.9787			1.09490			0.547448	+	0.836840i	$0.315599\pi$
$164$	1.47475	−	2.55433i	0.115158	−	0.199460i
$165$	−23.1673	−	5.17774i	−1.80357	−	0.403087i
$166$	−8.77082			−0.680748
$167$	−8.86521	−	15.3550i	−0.686011	−	1.18821i	−0.973118	−	0.230307i	$-0.926027\pi$
$167$	−8.86521	−	15.3550i	−0.686011	−	1.18821i	0.287107	−	0.957898i	$-0.407306\pi$
$168$	−1.57496	−	5.02514i	−0.121511	−	0.387698i
$169$	16.2276			1.24827
$170$	−8.62822			−0.661754
$171$	−1.29971	−	15.4660i	−0.0993911	−	1.18272i
$172$	−4.91997	+	8.52163i	−0.375144	+	0.649768i
$173$	−2.74939	+	4.76208i	−0.209032	+	0.362054i	−0.951410	−	0.307927i	$-0.900365\pi$
$173$	−2.74939	+	4.76208i	−0.209032	+	0.362054i	0.742378	+	0.669981i	$0.233698\pi$
$174$	−2.10676	−	0.470846i	−0.159713	−	0.0356947i
$175$	−1.53232			−0.115833
$176$	5.84199			0.440357
$177$	5.58429	−	6.07326i	0.419741	−	0.456494i
$178$	−1.76149	−	3.05098i	−0.132029	−	0.228681i
$179$	11.6898	−	20.2473i	0.873735	−	1.51335i	0.0156315	−	0.999878i	$-0.495024\pi$
$179$	11.6898	−	20.2473i	0.873735	−	1.51335i	0.858104	−	0.513476i	$-0.171643\pi$
$180$	−0.589384	−	7.01345i	−0.0439301	−	0.522752i
$181$	−0.955580	−	1.65511i	−0.0710277	−	0.123024i	0.828324	−	0.560249i	$-0.189295\pi$
$181$	−0.955580	−	1.65511i	−0.0710277	−	0.123024i	−0.899352	+	0.437225i	$0.855961\pi$
$182$	8.21864	+	14.2351i	0.609206	+	1.05518i
$183$	−16.4985	+	17.9432i	−1.21961	+	1.32640i
$184$	−2.63277	+	4.56010i	−0.194091	+	0.336175i
$185$	−4.78167	+	8.28210i	−0.351555	+	0.608912i
$186$	9.11677	−	3.14396i	0.668474	−	0.230526i
$187$	10.7427	+	18.6069i	0.785585	+	1.36067i
$188$	8.55555			0.623977
$189$	12.4842	+	9.68182i	0.908090	+	0.704249i
$190$	12.1374			0.880536
$191$	8.44659	−	14.6299i	0.611174	−	1.05858i	−0.379869	−	0.925040i	$-0.624031\pi$
$191$	8.44659	−	14.6299i	0.611174	−	1.05858i	0.991043	−	0.133544i	$-0.0426358\pi$
$192$	0.518006	+	1.65278i	0.0373839	+	0.119279i
$193$	6.16365	+	10.6758i	0.443669	+	0.768457i	0.997958	−	0.0638666i	$-0.0203432\pi$
$193$	6.16365	+	10.6758i	0.443669	+	0.768457i	−0.554289	+	0.832324i	$0.687010\pi$
$194$	−1.79211	+	3.10403i	−0.128666	+	0.222856i
$195$	6.57007	+	20.9628i	0.470492	+	1.50118i
$196$	−1.12208	+	1.94350i	−0.0801486	+	0.138821i
$197$	5.62507	+	9.74291i	0.400770	+	0.694154i	0.993819	−	0.111012i	$-0.0354094\pi$
$197$	5.62507	+	9.74291i	0.400770	+	0.694154i	−0.593049	+	0.805166i	$0.702076\pi$
$198$	−14.3908	+	10.0032i	−1.02271	+	0.710898i
$199$	−3.79423	−	6.57180i	−0.268966	−	0.465862i	0.699629	−	0.714506i	$-0.253348\pi$
$199$	−3.79423	−	6.57180i	−0.268966	−	0.465862i	−0.968595	+	0.248644i	$0.920015\pi$
$200$	0.503984			0.0356370
$201$	5.24963	+	16.7497i	0.370280	+	1.18143i
$202$	−3.51439	+	6.08711i	−0.247272	+	0.428287i
$203$	1.89470	+	3.28172i	0.132982	+	0.230332i
$204$	−4.31159	+	4.68912i	−0.301872	+	0.328304i
$205$	−6.91967			−0.483291
$206$	−2.18966	−	3.79259i	−0.152561	−	0.264243i
$207$	−1.32283	−	15.7412i	−0.0919429	−	1.09409i
$208$	−2.70313	−	4.68195i	−0.187428	−	0.324635i
$209$	−15.1118	−	26.1744i	−1.04531	−	1.81052i
$210$	−8.36233	+	9.09454i	−0.577055	+	0.627583i
$211$	4.91192	+	8.50770i	0.338151	+	0.585694i	0.984085	−	0.177699i	$-0.0568653\pi$
$211$	4.91192	+	8.50770i	0.338151	+	0.585694i	−0.645934	+	0.763393i	$0.723532\pi$
$212$	−10.7865			−0.740823
$213$	8.77217	−	9.54027i	0.601059	−	0.653689i
$214$	−3.55362			−0.242921
$215$	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
$220$	−6.85282	−	11.8694i	−0.462017	−	0.800237i
$221$	9.94143	−	17.2191i	0.668733	−	1.15828i
$222$	2.11157	+	6.73729i	0.141720	+	0.452177i
$223$	10.2417			0.685834			0.342917	−	0.939366i	$-0.388585\pi$
$223$	10.2417			0.685834			0.342917	+	0.939366i	$0.388585\pi$
$224$	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
$227$	−8.63703	+	14.9598i	−0.573260	+	0.992915i	0.422969	+	0.906144i	$0.360988\pi$
$227$	−8.63703	+	14.9598i	−0.573260	+	0.992915i	−0.996228	+	0.0867704i	$0.972345\pi$
$228$	6.06513	−	6.59620i	0.401673	−	0.436844i
$229$	−1.16671	−	2.02080i	−0.0770982	−	0.133538i	0.824899	−	0.565281i	$-0.191232\pi$
$229$	−1.16671	−	2.02080i	−0.0770982	−	0.133538i	−0.901997	+	0.431743i	$0.857899\pi$
$230$	12.3533			0.814551
$231$	30.0242	+	6.71020i	1.97545	+	0.441499i
$232$	−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	$0.536526\pi$
$234$	14.6756	+	6.90468i	0.959374	+	0.451373i
$235$	−10.0359	−	17.3827i	−0.654670	−	1.13392i
$236$	4.76336			0.310068
$237$	1.38767	+	4.42757i	0.0901388	+	0.287601i
$238$	11.1819			0.724816
$239$	5.70901			0.369285			0.184643	−	0.982806i	$-0.440887\pi$
$239$	5.70901			0.369285			0.184643	+	0.982806i	$0.440887\pi$
$240$	2.75038	−	2.99121i	0.177537	−	0.193082i
$241$	−17.7645			−1.14431			−0.572157	−	0.820144i	$-0.693893\pi$
$241$	−17.7645			−1.14431			−0.572157	+	0.820144i	$0.693893\pi$
$242$	−11.5644	+	20.0302i	−0.743390	+	1.28759i
$243$	15.5672	+	0.813366i	0.998638	+	0.0521774i
$244$	−14.0731			−0.900939
$245$	5.26493			0.336364
$246$	−3.45782	+	3.76059i	−0.220462	+	0.239766i
$247$	−13.9846	+	24.2221i	−0.889822	+	1.54122i
$248$	4.89884	+	2.64601i	0.311077	+	0.168022i
$249$	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	−0.814631	−	0.579979i	$-0.803061\pi$
$251$	1.50446	−	2.60581i	0.0949609	−	0.164477i	0.909592	+	0.415502i	$0.136394\pi$
$252$	0.763825	+	9.08923i	0.0481164	+	0.572567i
$253$	−15.3806	−	26.6401i	−0.966973	−	1.67485i
$254$	3.91883			0.245890
$255$	14.5847	+	3.25958i	0.913330	+	0.204123i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.89612			−0.243033			−0.121517	−	0.992589i	$-0.538776\pi$
$257$	−3.89612			−0.243033			−0.121517	+	0.992589i	$0.538776\pi$
$258$	11.5358	−	12.5459i	0.718186	−	0.781071i
$259$	6.19691	−	10.7334i	0.385057	−	0.666938i
$260$	−6.34169	+	10.9841i	−0.393295	+	0.681206i
$261$	3.38328	+	1.59179i	0.209420	+	0.0985291i
$262$	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
$265$	12.6529	+	21.9155i	0.777263	+	1.34626i
$266$	−15.7297			−0.964447
$267$	1.82492	+	5.82268i	0.111683	+	0.356342i
$268$	−5.06714	+	8.77655i	−0.309525	+	0.536113i
$269$	−2.44252	−	4.23057i	−0.148923	−	0.257943i	0.781907	−	0.623396i	$-0.214247\pi$
$269$	−2.44252	−	4.23057i	−0.148923	−	0.257943i	−0.930830	+	0.365453i	$0.880914\pi$
$270$	−1.65329	+	12.0778i	−0.100616	+	0.735034i
$271$	13.2408			0.804323			0.402161	−	0.915569i	$-0.368259\pi$
$271$	13.2408			0.804323			0.402161	+	0.915569i	$0.368259\pi$
$272$	−3.67775			−0.222997
$273$	−8.51462	−	27.1671i	−0.515328	−	1.64423i
$274$	11.7047			0.707109
$275$	−1.47214	+	2.54981i	−0.0887731	+	0.153759i
$276$	6.17303	−	6.71354i	0.371573	−	0.404108i
$277$	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
$279$	−16.5983	+	1.87024i	−0.993712	+	0.111969i
$280$	−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	$0.645042\pi$
$282$	−14.4619	−	3.23213i	−0.861191	−	0.192470i
$283$	−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	$0.229242\pi$
$284$	7.48260			0.444010
$285$	−20.5164	−	4.58527i	−1.21528	−	0.271608i
$286$	31.5833			1.86756
$287$	8.96769			0.529346
$288$	−0.251223	−	2.98946i	−0.0148035	−	0.176156i
$289$	1.73706	+	3.00868i	0.102180	+	0.176981i
$290$	−1.46200	+	2.53225i	−0.0858514	+	0.148699i
$291$	4.20194	−	4.56986i	0.246322	−	0.267890i
$292$	4.19611			0.245559
$293$	7.73539	+	13.3981i	0.451906	+	0.782724i	0.998504	−	0.0546706i	$-0.0174109\pi$
$293$	7.73539	+	13.3981i	0.451906	+	0.782724i	−0.546598	+	0.837395i	$0.684078\pi$
$294$	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
$297$	28.1045	−	11.4724i	1.63079	−	0.665694i
$298$	3.44436	−	5.96581i	0.199526	−	0.345590i
$299$	−14.2334	+	24.6530i	−0.823141	+	1.42572i
$300$	−0.851909	−	0.190396i	−0.0491850	−	0.0109925i
$301$	−29.9175			−1.72442
$302$	−12.2302	+	21.1834i	−0.703771	+	1.21897i
$303$	8.24015	−	8.96166i	0.473384	−	0.514834i
$304$	5.17351			0.296721
$305$	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	−0.998511	−	0.0545526i	$-0.982627\pi$
$307$	−7.91988	+	13.7176i	−0.452011	+	0.782907i	0.546499	+	0.837459i	$0.315960\pi$
$308$	8.88106	+	15.3824i	0.506045	+	0.876496i
$309$	2.26851	+	7.23802i	0.129051	+	0.411757i
$310$	−0.370457	−	13.0570i	−0.0210405	−	0.741590i
$311$	−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
$313$	−3.39395			−0.191837			−0.0959187	−	0.995389i	$-0.530579\pi$
$313$	−3.39395			−0.191837			−0.0959187	+	0.995389i	$0.530579\pi$
$314$	−10.3743			−0.585458
$315$	17.5710	−	12.2138i	0.990014	−	0.688171i
$316$	−1.33943	+	2.31997i	−0.0753490	+	0.130508i
$317$	−20.0073			−1.12372			−0.561862	−	0.827231i	$-0.689915\pi$
$317$	−20.0073			−1.12372			−0.561862	+	0.827231i	$0.689915\pi$
$318$	18.2330	+	4.07496i	1.02246	+	0.228512i
$319$	7.28113			0.407665
$320$	2.34606			0.131149
$321$	6.00686	+	1.34249i	0.335270	+	0.0749306i
$322$	−16.0095			−0.892173
$323$	9.51345	+	16.4778i	0.529343	+	0.916848i
$324$	5.73770	+	6.93389i	0.318761	+	0.385216i
$325$	2.72466			0.151137
$326$	−6.98935	−	12.1059i	−0.387104	−	0.670484i
$327$	9.51822	+	30.3693i	0.526359	+	1.67943i
$328$	−2.94949			−0.162858
$329$	13.0062	+	22.5275i	0.717057	+	1.24198i
$330$	7.09961	+	22.6524i	0.390821	+	1.24697i
$331$	−15.9374	+	27.6043i	−0.875996	+	1.51727i	−0.0202982	+	0.999794i	$0.506462\pi$
$331$	−15.9374	+	27.6043i	−0.875996	+	1.51727i	−0.855698	+	0.517476i	$0.826872\pi$
$332$	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
$335$	23.7756			1.29900
$336$	−3.56442	+	3.87652i	−0.194455	+	0.211482i
$337$	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	$-0.0444221\pi$
$338$	−8.11378	−	14.0535i	−0.441331	−	0.764408i
$339$	−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
$344$	9.83993			0.530534
$345$	−20.8813	−	4.66684i	−1.12421	−	0.251254i
$346$	5.49877			0.295616
$347$	6.98652	+	12.1010i	0.375056	+	0.649616i	0.990335	−	0.138693i	$-0.0442902\pi$
$347$	6.98652	+	12.1010i	0.375056	+	0.649616i	−0.615280	+	0.788309i	$0.710957\pi$
$348$	0.645614	+	2.05993i	0.0346085	+	0.110424i
$349$	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
$351$	−22.1984	−	17.2155i	−1.18487	−	0.918895i
$352$	−2.92100	−	5.05931i	−0.155690	−	0.269662i
$353$	0.346349			0.0184343			0.00921715	−	0.999958i	$-0.497066\pi$
$353$	0.346349			0.0184343			0.00921715	+	0.999958i	$0.497066\pi$
$354$	−8.05174	−	1.79951i	−0.427945	−	0.0956429i
$355$	−8.77730	−	15.2027i	−0.465851	−	0.806877i
$356$	−1.76149	+	3.05098i	−0.0933585	+	0.161702i
$357$	−18.9014	−	4.22432i	−1.00037	−	0.223575i
$358$	−23.3796			−1.23565
$359$	−10.8440	−	18.7823i	−0.572324	−	0.991293i	−0.996327	−	0.0856328i	$-0.972709\pi$
$359$	−10.8440	−	18.7823i	−0.572324	−	0.991293i	0.424003	−	0.905661i	$-0.360625\pi$
$360$	−5.77913	+	4.01715i	−0.304587	+	0.211722i
$361$	−3.88261	−	6.72487i	−0.204348	−	0.353941i
$362$	−0.955580	+	1.65511i	−0.0502242	+	0.0869908i
$363$	27.1150	−	29.4892i	1.42317	−	1.54778i
$364$	8.21864	−	14.2351i	0.430774	−	0.746122i
$365$	−4.92216	−	8.52543i	−0.257638	−	0.446242i
$366$	23.7885	+	5.31657i	1.24344	+	0.277901i
$367$	−13.3708	+	23.1588i	−0.697948	+	1.20888i	0.271229	+	0.962515i	$0.412570\pi$
$367$	−13.3708	+	23.1588i	−0.697948	+	1.20888i	−0.969177	+	0.246366i	$0.920763\pi$
$368$	5.26555			0.274486
$369$	7.26560	−	5.05040i	0.378232	−	0.262914i
$370$	9.56334			0.497175
$371$	−16.3978	−	28.4019i	−0.851332	−	1.47455i
$372$	−7.28114	−	6.32337i	−0.377509	−	0.327852i
$373$	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
$375$	−5.46388	−	17.4333i	−0.282154	−	0.900254i
$376$	−4.27777	−	7.40932i	−0.220609	−	0.382107i
$377$	−3.36902	−	5.83532i	−0.173514	−	0.300534i
$378$	2.14261	−	15.6525i	0.110204	−	0.805079i
$379$	−17.4095	+	30.1541i	−0.894264	+	1.54891i	−0.0595514	+	0.998225i	$0.518967\pi$
$379$	−17.4095	+	30.1541i	−0.894264	+	1.54891i	−0.834713	+	0.550686i	$0.814366\pi$
$380$	−6.06868	−	10.5113i	−0.311316	−	0.539216i
$381$	−6.62420	−	1.48046i	−0.339368	−	0.0758464i
$382$	−16.8932			−0.864331
$383$	−29.6986			−1.51753			−0.758764	−	0.651365i	$-0.774197\pi$
$383$	−29.6986			−1.51753			−0.758764	+	0.651365i	$0.774197\pi$
$384$	1.17234	−	1.27499i	0.0598259	−	0.0650643i
$385$	20.8355	−	36.0881i	1.06187	−	1.83922i
$386$	6.16365	−	10.6758i	0.313721	−	0.543381i
$387$	−24.2391	+	16.8489i	−1.23214	+	0.856477i
$388$	3.58422			0.181961
$389$	−16.1712			−0.819910			−0.409955	−	0.912106i	$-0.634456\pi$
$389$	−16.1712			−0.819910			−0.409955	+	0.912106i	$0.634456\pi$
$390$	14.8693	−	16.1712i	0.752935	−	0.818862i
$391$	9.68269	+	16.7709i	0.489675	+	0.848142i
$392$	2.24416			0.113347
$393$	−12.6712	+	13.7807i	−0.639177	+	0.695144i
$394$	5.62507	−	9.74291i	0.283387	−	0.490841i
$395$	6.28477			0.316221
$396$	15.8585	+	7.46119i	0.796917	+	0.374939i
$397$	3.08789	−	5.34838i	0.154977	−	0.268428i	−0.778074	−	0.628173i	$-0.783803\pi$
$397$	3.08789	−	5.34838i	0.154977	−	0.268428i	0.933051	+	0.359745i	$0.117136\pi$
$398$	−3.79423	+	6.57180i	−0.190187	+	0.329414i
$399$	26.5886	+	5.94237i	1.33110	+	0.297491i
$400$	−0.251992	−	0.436463i	−0.0125996	−	0.0218231i
$401$	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
$403$	26.4844	+	14.3050i	1.31928	+	0.712583i
$404$	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
$408$	6.21669	+	1.38939i	0.307772	+	0.0687849i
$409$	−12.1859	−	21.1066i	−0.602554	−	1.04365i	−0.992433	−	0.122788i	$-0.960817\pi$
$409$	−12.1859	−	21.1066i	−0.602554	−	1.04365i	0.389879	−	0.920866i	$-0.372517\pi$
$410$	3.45984	+	5.99261i	0.170869	+	0.295954i
$411$	−19.7851	−	4.42183i	−0.975926	−	0.218113i
$412$	−2.18966	+	3.79259i	−0.107877	+	0.186848i
$413$	7.24131	+	12.5423i	0.356322	+	0.617167i
$414$	−12.9708	+	9.01618i	−0.637481	+	0.443121i
$415$	10.2884	−	17.8201i	0.505039	−	0.874753i
$416$	−2.70313	+	4.68195i	−0.132532	+	0.229552i
$417$	26.3116	+	5.88046i	1.28849	+	0.287968i
$418$	−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	$-0.0202602\pi$
$420$	12.0573	+	2.69472i	0.588334	+	0.131489i
$421$	2.48460	−	4.30346i	0.121092	−	0.209738i	−0.799107	−	0.601189i	$-0.794694\pi$
$421$	2.48460	−	4.30346i	0.121092	−	0.209738i	0.920199	+	0.391452i	$0.128027\pi$
$422$	4.91192	−	8.50770i	0.239109	−	0.414148i
$423$	23.2246	+	10.9268i	1.12922	+	0.531282i
$424$	5.39327	+	9.34142i	0.261920	+	0.453659i
$425$	0.926764	−	1.60520i	0.0449547	−	0.0778638i
$426$	−12.6482	−	2.82679i	−0.612807	−	0.136958i
$427$	−21.3941	−	37.0557i	−1.03533	−	1.79325i
$428$	1.77681	+	3.07753i	0.0858854	+	0.148758i
$429$	−53.3868	−	11.9316i	−2.57754	−	0.576062i
$430$	−11.5425	−	19.9922i	−0.556630	−	0.964111i
$431$	−19.8668	+	34.4102i	−0.956948	+	1.65748i	−0.227103	+	0.973871i	$0.572926\pi$
$431$	−19.8668	+	34.4102i	−0.956948	+	1.65748i	−0.729845	+	0.683613i	$0.760408\pi$
$432$	−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	$0.718083\pi$
$434$	0.480101	+	16.9215i	0.0230456	+	0.812260i
$435$	3.42792	−	3.72808i	0.164356	−	0.178748i
$436$	−9.18736	+	15.9130i	−0.439995	+	0.762093i
$437$	−13.6207	−	23.5917i	−0.651565	−	1.12854i
$438$	−7.09290	−	1.58521i	−0.338912	−	0.0757445i
$439$	−13.5422	+	23.4558i	−0.646334	+	1.11948i	0.337657	+	0.941269i	$0.390366\pi$
$439$	−13.5422	+	23.4558i	−0.646334	+	1.11948i	−0.983992	+	0.178215i	$0.942968\pi$
$440$	−6.85282	+	11.8694i	−0.326696	+	0.565853i
$441$	−5.52813	+	3.84267i	−0.263244	+	0.182984i
$442$	−19.8829			−0.945731
$443$	−1.70824	+	2.95877i	−0.0811611	+	0.140575i	−0.903749	−	0.428063i	$-0.859196\pi$
$443$	−1.70824	+	2.95877i	−0.0811611	+	0.140575i	0.822588	+	0.568638i	$0.192530\pi$
$444$	4.77888	−	5.19732i	0.226795	−	0.246654i
$445$	8.26509			0.391803
$446$	−5.12084	−	8.86956i	−0.242479	−	0.419986i
$447$	−8.07595	+	8.78308i	−0.381979	+	0.415426i
$448$	−3.04042			−0.143646
$449$	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
$452$	1.84967	−	3.20372i	0.0870010	−	0.150690i
$453$	28.6761	−	31.1870i	1.34732	−	1.46529i
$454$	17.2741			0.810711
$455$	−38.5628			−1.80785
$456$	−8.74504	−	1.95446i	−0.409524	−	0.0915258i
$457$	−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
$459$	−17.6929	+	7.22229i	−0.825832	+	0.337108i
$460$	−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	$0.934197\pi$
$462$	−9.20089	−	29.3568i	−0.428064	−	1.36580i
$463$	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
$465$	−4.30651	+	22.2109i	−0.199709	+	1.03001i
$466$	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	$0.459866\pi$
$468$	−1.35818	−	16.1618i	−0.0627817	−	0.747079i
$469$	−30.8125			−1.42279
$470$	−10.0359	+	17.3827i	−0.462922	+	0.801804i
$471$	17.5363	+	3.91923i	0.808028	+	0.180589i
$472$	−2.38168	−	4.12519i	−0.109626	−	0.189877i
$473$	−28.7424	+	49.7833i	−1.32158	+	2.28904i
$474$	3.14055	−	3.41554i	0.144250	−	0.156881i
$475$	−1.30368	+	2.25805i	−0.0598171	+	0.103606i
$476$	−5.59096	−	9.68383i	−0.256261	−	0.443858i
$477$	−29.2807	−	13.7762i	−1.34067	−	0.630769i
$478$	−2.85451	−	4.94415i	−0.130562	−	0.226140i
$479$	−3.56670			−0.162967			−0.0814833	−	0.996675i	$-0.525966\pi$
$479$	−3.56670			−0.162967			−0.0814833	+	0.996675i	$0.525966\pi$
$480$	−3.96566	−	0.886297i	−0.181007	−	0.0404537i
$481$	−11.0189	+	19.0853i	−0.502418	+	0.870213i
$482$	8.88226	+	15.3845i	0.404576	+	0.700746i
$483$	27.0616	+	6.04809i	1.23135	+	0.275197i
$484$	23.1289			1.05131
$485$	−4.20439	−	7.28222i	−0.190912	−	0.330669i
$486$	−7.07922	−	13.8883i	−0.321120	−	0.629986i
$487$	5.23602	+	9.06906i	0.237267	+	0.410958i	0.959929	−	0.280243i	$-0.0904151\pi$
$487$	5.23602	+	9.06906i	0.237267	+	0.410958i	−0.722662	+	0.691201i	$0.757082\pi$
$488$	7.03656	+	12.1877i	0.318530	+	0.551710i
$489$	7.24105	+	23.1037i	0.327452	+	1.04478i
$490$	−2.63247	−	4.55956i	−0.118923	−	0.205980i
$491$	16.6530			0.751539			0.375770	−	0.926713i	$-0.377378\pi$
$491$	16.6530			0.751539			0.375770	+	0.926713i	$0.377378\pi$
$492$	4.98567	+	1.11426i	0.224771	+	0.0502349i
$493$	−4.58374			−0.206441
$494$	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
$499$	8.18430	+	14.1756i	0.366380	+	0.634588i	0.988997	−	0.147939i	$-0.0472638\pi$
$499$	8.18430	+	14.1756i	0.366380	+	0.634588i	−0.622617	+	0.782527i	$0.713930\pi$
$500$	5.27396	−	9.13476i	0.235858	−	0.408519i
$501$	20.7861	−	22.6062i	0.928656	−	1.00997i
$502$	−3.00893			−0.134295
$503$	3.56017	−	6.16640i	0.158740	−	0.274946i	−0.775674	−	0.631133i	$-0.782590\pi$
$503$	3.56017	−	6.16640i	0.158740	−	0.274946i	0.934415	+	0.356187i	$0.115923\pi$
$504$	7.48959	−	5.20610i	0.333613	−	0.231898i
$505$	−8.24496	−	14.2807i	−0.366896	−	0.635483i
$506$	−15.3806	+	26.6401i	−0.683753	+	1.18429i
$507$	8.40597	+	26.8205i	0.373322	+	1.19114i
$508$	−1.95942	−	3.39381i	−0.0869351	−	0.150576i
$509$	−23.1567			−1.02640			−0.513202	−	0.858268i	$-0.671541\pi$
$509$	−23.1567			−1.02640			−0.513202	+	0.858268i	$0.671541\pi$
$510$	−4.46947	−	14.2605i	−0.197912	−	0.631466i
$511$	6.37898	+	11.0487i	0.282189	+	0.488766i
$512$	1.00000			0.0441942
$513$	24.8886	−	10.1596i	1.09886	−	0.448558i
$514$	1.94806	+	3.37414i	0.0859252	+	0.148827i
$515$	10.2741			0.452732
$516$	−16.6329	−	3.71734i	−0.732224	−	0.163647i
$517$	49.9814			2.19818
$518$	−12.3938			−0.544553
$519$	−9.29485	−	2.07734i	−0.407999	−	0.0911849i
$520$	12.6834			0.556203
$521$	20.6348	−	35.7404i	0.904025	−	1.56582i	0.0818041	−	0.996648i	$-0.473932\pi$
$521$	20.6348	−	35.7404i	0.904025	−	1.56582i	0.822221	−	0.569169i	$-0.192735\pi$
$522$	−0.313111	−	3.72590i	−0.0137045	−	0.163078i
$523$	1.65720			0.0724643			0.0362322	−	0.999343i	$-0.488464\pi$
$523$	1.65720			0.0724643			0.0362322	+	0.999343i	$0.488464\pi$
$524$	−10.8084			−0.472169
$525$	−0.793753	−	2.53259i	−0.0346422	−	0.110531i
$526$	7.02078	−	12.1603i	0.306120	−	0.530216i
$527$	17.4360	−	10.7373i	0.759523	−	0.467722i
$528$	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
$533$	−15.9457			−0.690684
$534$	4.13013	−	4.49177i	0.178728	−	0.194378i
$535$	4.16850	−	7.22006i	0.180220	−	0.312150i
$536$	10.1343			0.437735
$537$	39.5196	+	8.83237i	1.70540	+	0.381145i
$538$	−2.44252	+	4.23057i	−0.105305	+	0.182393i
$539$	−6.55519	+	11.3539i	−0.282352	+	0.489048i
$540$	11.2864	−	4.60713i	0.485688	−	0.198259i
$541$	−5.52047	+	9.56173i	−0.237343	+	0.411091i	−0.959951	−	0.280167i	$-0.909610\pi$
$541$	−5.52047	+	9.56173i	−0.237343	+	0.411091i	0.722608	+	0.691258i	$0.242943\pi$
$542$	−6.62041	−	11.4669i	−0.284371	−	0.492545i
$543$	2.24054	−	2.43672i	0.0961506	−	0.104570i
$544$	1.83888	+	3.18503i	0.0788412	+	0.136557i
$545$	43.1081			1.84655
$546$	−19.2701	+	20.9574i	−0.824686	+	0.896896i
$547$	−0.357710	+	0.619573i	−0.0152946	+	0.0264910i	−0.873571	−	0.486696i	$-0.838202\pi$
$547$	−0.357710	+	0.619573i	−0.0152946	+	0.0264910i	0.858277	+	0.513187i	$0.171535\pi$
$548$	−5.85236	−	10.1366i	−0.250001	−	0.433014i
$549$	−38.2024	−	17.9737i	−1.63044	−	0.767099i
$550$	2.94427			0.125544
$551$	6.44797			0.274693
$552$	−8.90061	−	1.98923i	−0.378835	−	0.0846671i
$553$	−8.14488			−0.346356
$554$	9.95924	−	17.2499i	0.423127	−	0.732878i
$555$	−16.1654	−	3.61285i	−0.686183	−	0.153357i
$556$	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	$0.0459322\pi$
$558$	9.91881	+	13.4394i	0.419897	+	0.568935i
$559$	53.1971			2.25000
$560$	3.56650	+	6.17736i	0.150712	+	0.261041i
$561$	−25.1883	+	27.3938i	−1.06345	+	1.15657i
$562$	9.34766	−	16.1906i	0.394307	−	0.682960i
$563$	8.70929			0.367053			0.183526	−	0.983015i	$-0.441249\pi$
$563$	8.70929			0.367053			0.183526	+	0.983015i	$0.441249\pi$
$564$	4.43183	+	14.1404i	0.186614	+	0.595418i
$565$	−8.67884			−0.365122
$566$	6.57162			0.276226
$567$	−9.53500	+	25.6488i	−0.400432	+	1.07715i
$568$	−3.74130	−	6.48012i	−0.156981	−	0.271900i
$569$	−9.07203	+	15.7132i	−0.380319	+	0.658732i	−0.991108	−	0.133061i	$-0.957519\pi$
$569$	−9.07203	+	15.7132i	−0.380319	+	0.658732i	0.610789	+	0.791794i	$0.290853\pi$
$570$	6.28722	+	20.0603i	0.263343	+	0.840235i
$571$	−40.0412			−1.67567			−0.837836	−	0.545922i	$-0.816179\pi$
$571$	−40.0412			−1.67567			−0.837836	+	0.545922i	$0.816179\pi$
$572$	−15.7916	−	27.3519i	−0.660282	−	1.14364i
$573$	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
$576$	−2.46334	+	1.71230i	−0.102639	+	0.0713457i
$577$	18.0167	−	31.2059i	0.750047	−	1.29912i	−0.197753	−	0.980252i	$-0.563364\pi$
$577$	18.0167	−	31.2059i	0.750047	−	1.29912i	0.947799	−	0.318867i	$-0.103302\pi$
$578$	1.73706	−	3.00868i	0.0722522	−	0.125145i
$579$	−14.4518	+	15.7172i	−0.600597	+	0.653186i
$580$	2.92399			0.121412
$581$	−13.3335	+	23.0943i	−0.553167	+	0.958113i
$582$	−6.05858	−	1.35405i	−0.251136	−	0.0561273i
$583$	−63.0149			−2.60981
$584$	−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
$589$	−24.5273	+	15.1041i	−1.01063	+	0.622355i
$590$	−5.58756	+	9.67793i	−0.230036	+	0.398434i
$591$	−13.1890	+	14.3439i	−0.542524	+	0.590028i
$592$	4.07635			0.167537
$593$	29.7811			1.22296			0.611481	−	0.791259i	$-0.290574\pi$
$593$	29.7811			1.22296			0.611481	+	0.791259i	$0.290574\pi$
$594$	−23.9876	−	18.6031i	−0.984224	−	0.763292i
$595$	−13.1167	+	22.7188i	−0.537733	+	0.931381i
$596$	−6.88872			−0.282173
$597$	8.89627	−	9.67524i	0.364100	−	0.395981i
$598$	28.4669			1.16410
$599$	−30.2109			−1.23438			−0.617191	−	0.786813i	$-0.711730\pi$
$599$	−30.2109			−1.23438			−0.617191	+	0.786813i	$0.711730\pi$
$600$	0.261067	+	0.832973i	0.0106580	+	0.0340060i
$601$	26.8369			1.09470			0.547350	−	0.836903i	$-0.315636\pi$
$601$	26.8369			1.09470			0.547350	+	0.836903i	$0.315636\pi$
$602$	14.9588	+	25.9093i	0.609674	+	1.05599i
$603$	−24.9642	+	17.3529i	−1.01662	+	0.706665i
$604$	24.4605			0.995283
$605$	−27.1308	−	46.9920i	−1.10303	−	1.91050i
$606$	−11.8811	−	2.65534i	−0.482637	−	0.107866i
$607$	22.4443			0.910985			0.455492	−	0.890240i	$-0.349463\pi$
$607$	22.4443			0.910985			0.455492	+	0.890240i	$0.349463\pi$
$608$	−2.58676	−	4.48039i	−0.104907	−	0.181704i
$609$	−4.44249	+	4.83148i	−0.180019	+	0.195781i
$610$	16.5082	−	28.5930i	0.668397	−	1.15770i
$611$	−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	−0.999361	−	0.0357343i	$-0.988623\pi$
$613$	−11.6053	+	20.1010i	−0.468734	+	0.811871i	0.530627	+	0.847605i	$0.321956\pi$
$614$	15.8398			0.639241
$615$	−3.58443	−	11.4367i	−0.144538	−	0.461171i
$616$	8.88106	−	15.3824i	0.357828	−	0.619776i
$617$	9.79026	+	16.9572i	0.394141	+	0.682672i	0.992991	−	0.118189i	$-0.0377089\pi$
$617$	9.79026	+	16.9572i	0.394141	+	0.682672i	−0.598850	+	0.800861i	$0.704376\pi$
$618$	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
$623$	−10.7113			−0.429140
$624$	6.33798	−	6.89294i	0.253722	−	0.275939i
$625$	−27.2659			−1.09064
$626$	1.69697	+	2.93925i	0.0678247	+	0.117476i
$627$	35.4324	−	38.5349i	1.41504	−	1.53894i
$628$	5.18717	+	8.98444i	0.206991	+	0.358518i
$629$	7.49590	+	12.9833i	0.298881	+	0.517677i
$630$	−19.3630	−	9.11002i	−0.771439	−	0.362952i
$631$	2.46804	+	4.27478i	0.0982513	+	0.170176i	0.910961	−	0.412493i	$-0.135342\pi$
$631$	2.46804	+	4.27478i	0.0982513	+	0.170176i	−0.812710	+	0.582669i	$0.802008\pi$
$632$	2.67887			0.106560
$633$	−11.5169	+	12.5253i	−0.457756	+	0.497838i
$634$	10.0037	+	17.3269i	0.397297	+	0.688138i
$635$	−4.59690	+	7.96207i	−0.182423	+	0.315965i
$636$	−5.58750	−	17.8277i	−0.221559	−	0.706916i
$637$	12.1325			0.480707
$638$	−3.64056	−	6.30564i	−0.144131	−	0.249643i
$639$	20.3120	+	9.55651i	0.803529	+	0.378050i
$640$	−1.17303	−	2.03175i	−0.0463680	−	0.0803118i
$641$	17.1912	−	29.7761i	0.679012	−	1.17608i	−0.296267	−	0.955105i	$-0.595742\pi$
$641$	17.1912	−	29.7761i	0.679012	−	1.17608i	0.975279	−	0.220978i	$-0.0709249\pi$
$642$	−1.84080	−	5.87334i	−0.0726505	−	0.231802i
$643$	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	$0.0334518\pi$
$644$	8.00474	+	13.8646i	0.315431	+	0.546342i
$645$	11.9582	+	38.1544i	0.470854	+	1.50233i
$646$	9.51345	−	16.4778i	0.374302	−	0.648310i
$647$	−31.8242			−1.25114			−0.625570	−	0.780168i	$-0.715134\pi$
$647$	−31.8242			−1.25114			−0.625570	+	0.780168i	$0.715134\pi$
$648$	3.13608	−	8.43594i	0.123197	−	0.331395i
$649$	27.8275			1.09233
$650$	−1.36233	−	2.35963i	−0.0534350	−	0.0925522i
$651$	5.58111	−	28.7847i	0.218741	−	1.12816i
$652$	−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	$0.239433\pi$
$654$	21.5415	−	23.4277i	0.842338	−	0.916094i
$655$	12.6786	+	21.9600i	0.495394	+	0.858047i
$656$	1.47475	+	2.55433i	0.0575791	+	0.0997300i
$657$	11.3906	+	5.35913i	0.444390	+	0.209080i
$658$	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	$-0.378405\pi$
$660$	16.0677	−	17.4746i	0.625435	−	0.680199i
$661$	−17.4331			−0.678067			−0.339034	−	0.940774i	$-0.610100\pi$
$661$	−17.4331			−0.678067			−0.339034	+	0.940774i	$0.610100\pi$
$662$	31.8747			1.23885
$663$	33.6090	+	7.51138i	1.30526	+	0.291718i
$664$	4.38541	−	7.59576i	0.170187	−	0.294773i
$665$	18.4513	−	31.9586i	0.715512	−	1.23930i
$666$	−10.0414	+	6.97992i	−0.389097	+	0.270466i
$667$	6.56268			0.254108
$668$	17.7304			0.686011
$669$	5.30526	+	16.9272i	0.205113	+	0.654444i
$670$	−11.8878	−	20.5903i	−0.459266	−	0.795472i
$671$	−82.2151			−3.17388
$672$	5.13937	+	1.14861i	0.198256	+	0.0443088i
$673$	−6.41357	+	11.1086i	−0.247225	+	0.428206i	−0.962755	−	0.270376i	$-0.912852\pi$
$673$	−6.41357	+	11.1086i	−0.247225	+	0.428206i	0.715530	+	0.698582i	$0.246185\pi$
$674$	−22.6021			−0.870599
$675$	−2.06939	−	1.60487i	−0.0796510	−	0.0617715i
$676$	−8.11378	+	14.0535i	−0.312068	+	0.540518i
$677$	10.2929	−	17.8278i	0.395587	−	0.685177i	−0.597589	−	0.801803i	$-0.703875\pi$
$677$	10.2929	−	17.8278i	0.395587	−	0.685177i	0.993176	+	0.116626i	$0.0372079\pi$
$678$	−4.33689	+	4.71663i	−0.166557	+	0.181141i
$679$	5.44877	+	9.43755i	0.209105	+	0.362180i
$680$	4.31411	−	7.47226i	0.165439	−	0.286548i
$681$	−29.1992	−	6.52582i	−1.11892	−	0.250070i
$682$	28.6190	+	15.4580i	1.09588	+	0.591917i
$683$	−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
$687$	2.73556	−	2.97509i	0.104368	−	0.113507i
$688$	−4.91997	−	8.52163i	−0.187572	−	0.324884i
$689$	29.1574	+	50.5021i	1.11081	+	1.92398i
$690$	6.39907	+	20.4172i	0.243609	+	0.777269i
$691$	10.0469	−	17.4017i	0.382202	−	0.661993i	−0.609175	−	0.793036i	$-0.708499\pi$
$691$	10.0469	−	17.4017i	0.382202	−	0.661993i	0.991377	+	0.131043i	$0.0418325\pi$
$692$	−2.74939	−	4.76208i	−0.104516	−	0.181027i
$693$	4.46226	+	53.0992i	0.169507	+	2.01707i
$694$	6.98652	−	12.1010i	0.265205	−	0.459348i
$695$	18.2591	−	31.6257i	0.692607	−	1.19963i
$696$	1.46114	−	1.58908i	0.0553844	−	0.0602340i
$697$	−5.42375	+	9.39421i	−0.205439	+	0.355831i
$698$	3.41690	−	5.91825i	0.129332	−	0.224009i
$699$	−1.81067	−	5.77722i	−0.0684860	−	0.218515i
$700$	0.766162	−	1.32703i	0.0289582	−	0.0501571i
$701$	−5.99187	+	10.3782i	−0.226310	+	0.391980i	−0.956712	−	0.291038i	$-0.906000\pi$
$701$	−5.99187	+	10.3782i	−0.226310	+	0.391980i	0.730402	+	0.683018i	$0.239333\pi$
$702$	−3.80983	+	27.8322i	−0.143793	+	1.05046i
$703$	−10.5445	−	18.2636i	−0.397694	−	0.688826i
$704$	−2.92100	+	5.05931i	−0.110089	+	0.190680i
$705$	23.5310	−	25.5914i	0.886230	−	0.963830i
$706$	−0.173175	−	0.299947i	−0.00651751	−	0.0112887i
$707$	10.6852	+	18.5074i	0.401860	+	0.696041i
$708$	2.46745	+	7.87277i	0.0927325	+	0.295877i
$709$	−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
$713$	−24.9636	+	15.3728i	−0.934894	+	0.575717i
$714$	5.79231	+	18.4812i	0.216772	+	0.691642i
$715$	−37.0481	+	64.1692i	−1.38552	+	2.39979i
$716$	11.6898	+	20.2473i	0.436868	+	0.756677i
$717$	2.95730	+	9.43572i	0.110443	+	0.352383i
$718$	−10.8440	+	18.7823i	−0.404694	+	0.700950i
$719$	14.2308	−	24.6485i	0.530720	−	0.919234i	−0.468637	−	0.883391i	$-0.655255\pi$
$719$	14.2308	−	24.6485i	0.530720	−	0.919234i	0.999357	−	0.0358436i	$-0.0114118\pi$
$720$	6.36852	+	2.99630i	0.237341	+	0.111666i
$721$	−13.3149			−0.495875
$722$	−3.88261	+	6.72487i	−0.144496	+	0.250274i
$723$	−9.20213	−	29.3608i	−0.342231	−	1.09194i
$724$	1.91116			0.0710277
$725$	−0.314069	−	0.543983i	−0.0116642	−	0.0202030i
$726$	−39.0959	−	8.73766i	−1.45098	−	0.324285i
$727$	16.3436			0.606151			0.303075	−	0.952967i	$-0.401987\pi$
$727$	16.3436			0.606151			0.303075	+	0.952967i	$0.401987\pi$
$728$	−16.4373			−0.609206
$729$	6.71961	+	26.1505i	0.248874	+	0.968536i
$730$	−4.92216	+	8.52543i	−0.182177	+	0.315540i
$731$	18.0944	−	31.3405i	0.669247	−	1.15917i
$732$	−7.28997	−	23.2597i	−0.269445	−	0.859704i
$733$	−6.97064			−0.257467			−0.128733	−	0.991679i	$-0.541091\pi$
$733$	−6.97064			−0.257467			−0.128733	+	0.991679i	$0.541091\pi$
$734$	26.7415			0.987047
$735$	2.72727	+	8.70175i	0.100597	+	0.320969i
$736$	−2.63277	−	4.56010i	−0.0970453	−	0.168087i
$737$	−29.6022	+	51.2726i	−1.09041	+	1.88865i
$738$	−8.00658	−	3.76699i	−0.294726	−	0.138665i
$739$	−9.65514	−	16.7232i	−0.355170	−	0.615173i	0.631977	−	0.774987i	$-0.282244\pi$
$739$	−9.65514	−	16.7232i	−0.355170	−	0.615173i	−0.987147	+	0.159814i	$0.948910\pi$
$740$	−4.78167	−	8.28210i	−0.175778	−	0.304456i
$741$	−47.2779	−	10.5663i	−1.73680	−	0.388162i
$742$	−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	$0.0748828\pi$
$744$	−1.83564	+	9.46734i	−0.0672977	+	0.347089i
$745$	8.08067	+	13.9961i	0.296053	+	0.512778i
$746$	−3.38248			−0.123841
$747$	2.20344	+	26.2201i	0.0806195	+	0.959342i
$748$	−21.4854			−0.785585
$749$	−5.40225	+	9.35698i	−0.197394	+	0.341897i
$750$	−12.3658	+	13.4485i	−0.451534	+	0.491071i
$751$	16.8768	+	29.2315i	0.615844	+	1.06667i	0.990236	+	0.139403i	$0.0445182\pi$
$751$	16.8768	+	29.2315i	0.615844	+	1.06667i	−0.374392	+	0.927271i	$0.622148\pi$
$752$	−4.27777	+	7.40932i	−0.155994	+	0.270190i
$753$	5.08614	+	1.13672i	0.185349	+	0.0414243i
$754$	−3.36902	+	5.83532i	−0.122693	+	0.212510i
$755$	−28.6928	−	49.6975i	−1.04424	−	1.80868i
$756$	−14.6268	+	5.97071i	−0.531971	+	0.217153i
$757$	−2.29901	−	3.98200i	−0.0835588	−	0.144728i	0.821217	−	0.570615i	$-0.193295\pi$
$757$	−2.29901	−	3.98200i	−0.0835588	−	0.144728i	−0.904776	+	0.425887i	$0.859962\pi$
$758$	34.8189			1.26468
$759$	36.0628	−	39.2205i	1.30900	−	1.42361i
$760$	−6.06868	+	10.5113i	−0.220134	+	0.381283i
$761$	−0.979226	−	1.69607i	−0.0354969	−	0.0614824i	0.847731	−	0.530426i	$-0.177968\pi$
$761$	−0.979226	−	1.69607i	−0.0354969	−	0.0614824i	−0.883228	+	0.468944i	$0.844635\pi$
$762$	2.02998	+	6.47696i	0.0735385	+	0.234635i
$763$	−55.8669			−2.02252
$764$	8.44659	+	14.6299i	0.305587	+	0.529292i
$765$	2.16761	+	25.7937i	0.0783701	+	0.932575i
$766$	14.8493	+	25.7198i	0.536527	+	0.929293i
$767$	−12.8760	−	22.3018i	−0.464924	−	0.805272i
$768$	−1.69035	−	0.377782i	−0.0609952	−	0.0136320i
$769$	−3.51698	−	6.09159i	−0.126826	−	0.219668i	0.795619	−	0.605797i	$-0.207146\pi$
$769$	−3.51698	−	6.09159i	−0.126826	−	0.219668i	−0.922445	+	0.386128i	$0.873812\pi$
$770$	−41.6709			−1.50172
$771$	−2.01821	−	6.43941i	−0.0726842	−	0.231910i
$772$	−12.3273			−0.443669
$773$	−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
$778$	8.08558	+	14.0046i	0.289882	+	0.502090i
$779$	7.62961	−	13.2149i	0.273359	−	0.473472i
$780$	−21.4393	−	4.79154i	−0.767651	−	0.171565i
$781$	43.7133			1.56418
$782$	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
$785$	12.1694	−	21.0780i	0.434344	−	0.752306i
$786$	18.2700	+	4.08323i	0.651670	+	0.145644i
$787$	−9.07341	−	15.7156i	−0.323432	−	0.560201i	0.657762	−	0.753226i	$-0.271503\pi$
$787$	−9.07341	−	15.7156i	−0.323432	−	0.560201i	−0.981194	+	0.193025i	$0.938170\pi$
$788$	−11.2501			−0.400770
$789$	−16.4615	+	17.9029i	−0.586046	+	0.637360i
$790$	−3.14239	−	5.44277i	−0.111801	−	0.193645i
$791$	11.2475			0.399916
$792$	−1.46764	−	17.4644i	−0.0521505	−	0.620571i
$793$	38.0414	+	65.8897i	1.35089	+	2.33981i
$794$	−6.17578			−0.219170
$795$	−29.6671	+	32.2648i	−1.05218	+	1.14432i
$796$	7.58846			0.268966
$797$	36.5393			1.29429			0.647144	−	0.762368i	$-0.275963\pi$
$797$	36.5393			1.29429			0.647144	+	0.762368i	$0.275963\pi$
$798$	−8.14806	−	25.9976i	−0.288438	−	0.920305i
$799$	−31.4652			−1.11316
$800$	−0.251992	+	0.436463i	−0.00890926	+	0.0154313i
$801$	−8.67827	+	6.03237i	−0.306632	+	0.213143i
$802$	−17.3446			−0.612459
$803$	24.5137			0.865069
$804$	−17.1305	−	3.82855i	−0.604146	−	0.135022i
$805$	18.7796	−	32.5272i	0.661893	−	1.14643i
$806$	−0.853680	−	30.0886i	−0.0300696	−	1.05983i
$807$	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	−0.959958	−	0.280145i	$-0.909617\pi$
$809$	−6.75139	+	11.6938i	−0.237366	+	0.411130i	0.722591	+	0.691275i	$0.242951\pi$
$810$	−20.8184	+	3.52388i	−0.731483	+	0.123817i
$811$	−7.93579	−	13.7452i	−0.278663	−	0.482659i	0.692390	−	0.721524i	$-0.256558\pi$
$811$	−7.93579	−	13.7452i	−0.278663	−	0.482659i	−0.971053	+	0.238865i	$0.923225\pi$
$812$	−3.78941			−0.132982
$813$	6.85883	+	21.8841i	0.240550	+	0.767510i
$814$	−11.9070	+	20.6235i	−0.417340	+	0.722854i
$815$	32.7948			1.14875
$816$	−1.90510	−	6.07851i	−0.0666918	−	0.212790i
$817$	−25.4535	+	44.0867i	−0.890505	+	1.54240i
$818$	−12.1859	+	21.1066i	−0.426070	+	0.737975i
$819$	40.4906	−	28.1455i	1.41486	−	0.983484i
$820$	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
$823$	13.3458	+	23.1156i	0.465206	+	0.805761i	0.999211	−	0.0397207i	$-0.0126468\pi$
$823$	13.3458	+	23.1156i	0.465206	+	0.805761i	−0.534005	+	0.845482i	$0.679313\pi$
$824$	4.37931			0.152561
$825$	−4.97685	−	1.11229i	−0.173272	−	0.0387250i
$826$	7.24131	−	12.5423i	0.251957	−	0.436403i
$827$	−6.36247	−	11.0201i	−0.221245	−	0.383207i	0.733941	−	0.679213i	$-0.237679\pi$
$827$	−6.36247	−	11.0201i	−0.221245	−	0.383207i	−0.955186	+	0.296006i	$0.904345\pi$
$828$	14.2937	+	6.72497i	0.496739	+	0.233709i
$829$	−35.0188			−1.21625			−0.608126	−	0.793840i	$-0.708079\pi$
$829$	−35.0188			−1.21625			−0.608126	+	0.793840i	$0.708079\pi$
$830$	−20.5769			−0.714233
$831$	−23.3513	+	25.3960i	−0.810047	+	0.880976i
$832$	5.40625			0.187428
$833$	4.12674	−	7.14772i	0.142983	−	0.247654i
$834$	−8.06317	−	25.7268i	−0.279205	−	0.890845i
$835$	−20.7983	−	36.0237i	−0.719755	−	1.24665i
$836$	30.2236			1.04531
$837$	−11.6891	−	26.4644i	−0.404034	−	0.914744i
$838$	−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	$0.870057\pi$
$840$	−3.69494	−	11.7893i	−0.127488	−	0.406768i
$841$	13.7233	−	23.7695i	0.473218	−	0.819637i
$842$	−4.96920			−0.171250
$843$	−21.9173	+	23.8364i	−0.754873	+	0.820971i
$844$	−9.82384			−0.338151
$845$	38.0708			1.30967
$846$	−2.14935	−	25.5765i	−0.0738963	−	0.879338i
$847$	35.1608	+	60.9002i	1.20814	+	2.09256i
$848$	5.39327	−	9.34142i	0.185206	−	0.320786i
$849$	−11.1083	−	2.48264i	−0.381237	−	0.0852038i
$850$	−1.85353			−0.0635755
$851$	−10.7321	−	18.5885i	−0.367892	−	0.637207i
$852$	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
$855$	−3.04919	−	36.2842i	−0.104280	−	1.24089i
$856$	1.77681	−	3.07753i	0.0607302	−	0.105188i
$857$	8.66872	−	15.0147i	0.296118	−	0.512891i	−0.679127	−	0.734021i	$-0.737641\pi$
$857$	8.66872	−	15.0147i	0.296118	−	0.512891i	0.975244	+	0.221130i	$0.0709746\pi$
$858$	16.3603	+	52.2001i	0.558533	+	1.78208i
$859$	−9.19675			−0.313789			−0.156895	−	0.987615i	$-0.550148\pi$
$859$	−9.19675			−0.313789			−0.156895	+	0.987615i	$0.550148\pi$
$860$	−11.5425	+	19.9922i	−0.393597	+	0.681730i
$861$	4.64532	+	14.8216i	0.158312	+	0.505119i
$862$	39.7335			1.35333
$863$	−23.8716	−	41.3468i	−0.812598	−	1.40746i	−0.911040	−	0.412317i	$-0.864719\pi$
$863$	−23.8716	−	41.3468i	−0.812598	−	1.40746i	0.0984427	−	0.995143i	$-0.468614\pi$
$864$	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
$868$	14.4144	−	8.87655i	0.489258	−	0.301290i
$869$	−7.82496	+	13.5532i	−0.265444	+	0.459762i
$870$	−4.94257	−	1.10463i	−0.167569	−	0.0374505i
$871$	54.7885			1.85644
$872$	18.3747			0.622246
$873$	9.72959	+	4.57764i	0.329297	+	0.154930i
$874$	−13.6207	+	23.5917i	−0.460726	+	0.798001i
$875$	32.0701			1.08417
$876$	2.17361	+	6.93524i	0.0734396	+	0.234320i
$877$	−33.2818			−1.12385			−0.561923	−	0.827189i	$-0.689938\pi$
$877$	−33.2818			−1.12385			−0.561923	+	0.827189i	$0.689938\pi$
$878$	27.0844			0.914055
$879$	−18.1371	+	19.7252i	−0.611748	+	0.665313i
$880$	13.7056			0.462017
$881$	−16.4234	−	28.4461i	−0.553317	−	0.958374i	−0.998032	−	0.0627018i	$-0.980028\pi$
$881$	−16.4234	−	28.4461i	−0.553317	−	0.958374i	0.444715	−	0.895672i	$-0.353305\pi$
$882$	6.09192	+	2.86617i	0.205125	+	0.0965088i
$883$	−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
$885$	13.1011	−	14.2482i	0.440388	−	0.478949i
$886$	3.41649			0.114779
$887$	2.16754	+	3.75429i	0.0727788	+	0.126057i	0.900118	−	0.435646i	$-0.143480\pi$
$887$	2.16754	+	3.75429i	0.0727788	+	0.126057i	−0.827339	+	0.561702i	$0.810147\pi$
$888$	−6.89045	−	1.53997i	−0.231228	−	0.0516780i
$889$	5.95745	−	10.3186i	0.199807	−	0.346075i
$890$	−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
$893$	44.2622			1.48118
$894$	11.6443	+	2.60243i	0.389445	+	0.0870383i
$895$	27.4249	−	47.5013i	0.916713	−	1.58779i
$896$	1.52021	+	2.63308i	0.0507867	+	0.0879651i
$897$	−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
$902$	−17.2309			−0.573726
$903$	−15.4975	−	49.4470i	−0.515724	−	1.64549i
$904$	−3.69933			−0.123038
$905$	−2.24185	−	3.88299i	−0.0745215	−	0.129075i
$906$	−41.3468	−	9.24072i	−1.37365	−	0.307002i
$907$	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
$909$	19.0801	+	8.97692i	0.632846	+	0.297746i
$910$	19.2814	+	33.3964i	0.639172	+	1.10708i
$911$	2.71635			0.0899967			0.0449983	−	0.998987i	$-0.485672\pi$
$911$	2.71635			0.0899967			0.0449983	+	0.998987i	$0.485672\pi$
$912$	2.67991	+	8.55066i	0.0887407	+	0.283140i
$913$	25.6195	+	44.3744i	0.847883	+	1.46858i
$914$	−4.40598	+	7.63138i	−0.145737	+	0.252424i
$915$	−38.7065	+	42.0957i	−1.27960	+	1.39164i
$916$	2.33341			0.0770982
$917$	−16.4311	−	28.4595i	−0.542602	−	0.939815i
$918$	15.1011	+	11.7113i	0.498411	+	0.386531i
$919$	15.9728	+	27.6657i	0.526894	+	0.912607i	0.999509	+	0.0313382i	$0.00997689\pi$
$919$	15.9728	+	27.6657i	0.526894	+	0.912607i	−0.472615	+	0.881269i	$0.656690\pi$
$920$	−6.17664	+	10.6982i	−0.203638	+	0.352711i
$921$	−26.7747	−	5.98397i	−0.882257	−	0.197178i
$922$	−6.69027	+	11.5879i	−0.220332	+	0.381627i
$923$	−20.2264	−	35.0331i	−0.665760	−	1.15313i
$924$	−20.8233	+	22.6466i	−0.685036	+	0.745019i
$925$	−1.02721	+	1.77917i	−0.0337743	+	0.0584989i
$926$	−27.0864			−0.890116
$927$	−10.7877	+	7.49868i	−0.354315	+	0.246289i
$928$	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	$-0.432922\pi$
$930$	21.3885	−	7.37591i	0.701355	−	0.241866i
$931$	−5.80510	+	10.0547i	−0.190254	+	0.329530i
$932$	1.74773	−	3.02716i	0.0572489	−	0.0991580i
$933$	−9.84966	−	2.20133i	−0.322463	−	0.0720683i
$934$	−2.71747	−	4.70680i	−0.0889184	−	0.154011i
$935$	25.2030	+	43.6529i	0.824226	+	1.42760i
$936$	−13.3174	+	9.25711i	−0.435294	+	0.302578i
$937$	15.7775	−	27.3274i	0.515427	−	0.892746i	−0.484413	−	0.874840i	$-0.660967\pi$
$937$	15.7775	−	27.3274i	0.515427	−	0.892746i	0.999840	−	0.0179062i	$-0.00570004\pi$
$938$	15.4063	+	26.6844i	0.503032	+	0.871277i
$939$	−1.75809	−	5.60944i	−0.0573730	−	0.183057i
$940$	20.0718			0.654670
$941$	18.5701			0.605368			0.302684	−	0.953091i	$-0.402117\pi$
$941$	18.5701			0.605368			0.302684	+	0.953091i	$0.402117\pi$
$942$	−5.37397	−	17.1465i	−0.175093	−	0.558662i
$943$	7.76534	−	13.4500i	0.252874	−	0.437991i
$944$	−2.38168	+	4.12519i	−0.0775171	+	0.134264i
$945$	29.2886	+	22.7141i	0.952758	+	0.738890i
$946$	57.4848			1.86899
$947$	40.4977			1.31600			0.657999	−	0.753019i	$-0.271403\pi$
$947$	40.4977			1.31600			0.657999	+	0.753019i	$0.271403\pi$
$948$	−4.52822	−	1.01203i	−0.147070	−	0.0328691i
$949$	−11.3426	−	19.6460i	−0.368197	−	0.637736i
$950$	2.60737			0.0845941
$951$	−10.3639	−	33.0677i	−0.336073	−	1.07229i
$952$	−5.59096	+	9.68383i	−0.181204	+	0.313855i
$953$	28.2571			0.915336			0.457668	−	0.889123i	$-0.348685\pi$
$953$	28.2571			0.915336			0.457668	+	0.889123i	$0.348685\pi$
$954$	2.70983	+	32.2460i	0.0877340	+	1.04400i
$955$	19.8162	−	34.3226i	0.641237	−	1.11065i
$956$	−2.85451	+	4.94415i	−0.0923213	+	0.159905i
$957$	3.77167	+	12.0341i	0.121921	+	0.389006i
$958$	1.78335	+	3.08885i	0.0576174	+	0.0997962i
$959$	17.7937	−	30.8195i	0.574587	−	0.995214i
$960$	1.21527	+	3.87751i	0.0392227	+	0.125146i
$961$	16.9972	+	25.9248i	0.548298	+	0.836283i
$962$	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
$966$	−8.29301	−	26.4601i	−0.266823	−	0.851339i
$967$	−2.43491	−	4.21740i	−0.0783016	−	0.135622i	0.824216	−	0.566276i	$-0.191616\pi$
$967$	−2.43491	−	4.21740i	−0.0783016	−	0.135622i	−0.902517	+	0.430654i	$0.858283\pi$
$968$	−11.5644	−	20.0302i	−0.371695	−	0.643795i
$969$	−22.3061	+	24.2592i	−0.716574	+	0.779318i
$970$	−4.20439	+	7.28222i	−0.134995	+	0.233818i
$971$	14.1457	+	24.5011i	0.453957	+	0.786277i	0.998628	−	0.0523734i	$-0.0166786\pi$
$971$	14.1457	+	24.5011i	0.453957	+	0.786277i	−0.544670	+	0.838650i	$0.683345\pi$
$972$	−8.48801	+	13.0749i	−0.272253	+	0.419379i
$973$	−23.6633	+	40.9860i	−0.758609	+	1.31395i
$974$	5.23602	−	9.06906i	0.167773	−	0.290591i
$975$	1.41139	+	4.50326i	0.0452007	+	0.144220i
$976$	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	$0.320849\pi$
$978$	16.3878	−	17.8228i	0.524025	−	0.569909i
$979$	−10.2906	+	17.8238i	−0.328889	+	0.569652i
$980$	−2.63247	+	4.55956i	−0.0840910	+	0.145650i
$981$	−45.2632	+	31.4630i	−1.44514	+	1.00454i
$982$	−8.32650	−	14.4219i	−0.265709	−	0.460222i
$983$	−27.4797	+	47.5962i	−0.876465	+	1.51808i	−0.0212716	+	0.999774i	$0.506771\pi$
$983$	−27.4797	+	47.5962i	−0.876465	+	1.51808i	−0.855194	+	0.518309i	$0.826562\pi$
$984$	−1.52785	−	4.87485i	−0.0487062	−	0.155404i
$985$	13.1967	+	22.8574i	0.420483	+	0.728298i
$986$	2.29187	+	3.96964i	0.0729881	+	0.126419i
$987$	−30.4955	+	33.1658i	−0.970684	+	1.05568i
$988$	−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	$0.207640\pi$
$992$	−4.74093	+	2.91951i	−0.150525	+	0.0926946i
$993$	−53.8794	−	12.0417i	−1.70981	−	0.382131i
$994$	11.3751	−	19.7023i	0.360797	−	0.624919i
$995$	−8.90148	−	15.4178i	−0.282196	−	0.488777i
$996$	−10.2824	+	11.1828i	−0.325811	+	0.354339i
$997$	0.653839	−	1.13248i	0.0207073	−	0.0358661i	−0.855486	−	0.517826i	$-0.826742\pi$
$997$	0.653839	−	1.13248i	0.0207073	−	0.0358661i	0.876193	+	0.481960i	$0.160075\pi$
$998$	8.18430	−	14.1756i	0.259070	−	0.448722i
$999$	19.6104	−	8.00504i	0.620446	−	0.253268i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.1	✓	32	31.25	even	3
558.2.g.a.439.1	yes	32	9.7	even	3
558.2.h.a.25.11	yes	32	279.25	even	3	inner
558.2.h.a.67.11	yes	32	1.1	even	1	trivial
1674.2.g.b.955.12		32	93.56	odd	6
1674.2.g.b.1369.12		32	9.2	odd	6
1674.2.h.b.253.5		32	3.2	odd	2
1674.2.h.b.397.5		32	279.56	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.518006 + 1.65278i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.34606 q^{5} +(1.17234 - 1.27499i) q^{6} -3.04042 q^{7} +1.00000 q^{8} +(-2.46334 + 1.71230i) q^{9} +(-1.17303 - 2.03175i) q^{10} +(-2.92100 + 5.05931i) q^{11} +(-1.69035 - 0.377782i) q^{12} +5.40625 q^{13} +(1.52021 + 2.63308i) q^{14} +(1.21527 + 3.87751i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.83888 - 3.18503i) q^{17} +(2.71456 + 1.27717i) q^{18} +(-2.58676 + 4.48039i) q^{19} +(-1.17303 + 2.03175i) q^{20} +(-1.57496 - 5.02514i) q^{21} +5.84199 q^{22} +(-2.63277 + 4.56010i) q^{23} +(0.518006 + 1.65278i) q^{24} +0.503984 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} +(4.89884 + 2.64601i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.87501 - 2.20700i) q^{33} -3.67775 q^{34} -7.13300 q^{35} +(-0.251223 - 2.98946i) q^{36} +(-2.03817 + 3.53022i) q^{37} +5.17351 q^{38} +(2.80047 + 8.93532i) q^{39} +2.34606 q^{40} -2.94949 q^{41} +(-3.56442 + 3.87652i) q^{42} +9.83993 q^{43} +(-2.92100 - 5.05931i) q^{44} +(-5.77913 + 4.01715i) q^{45} +5.26555 q^{46} +(-4.27777 - 7.40932i) q^{47} +(1.17234 - 1.27499i) q^{48} +2.24416 q^{49} +(-0.251992 - 0.436463i) q^{50} +(6.21669 + 1.38939i) q^{51} +(-2.70313 + 4.68195i) q^{52} +(5.39327 + 9.34142i) q^{53} +(-0.704708 + 5.14814i) q^{54} +(-6.85282 + 11.8694i) q^{55} -3.04042 q^{56} +(-8.74504 - 1.95446i) q^{57} +(-0.623172 + 1.07937i) q^{58} +(-2.38168 - 4.12519i) 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} +12.6834 q^{65} +(3.02619 + 9.65551i) q^{66} +10.1343 q^{67} +(1.83888 + 3.18503i) q^{68} +(-8.90061 - 1.98923i) q^{69} +(3.56650 + 6.17736i) q^{70} +(-3.74130 - 6.48012i) q^{71} +(-2.46334 + 1.71230i) q^{72} +(-2.09806 - 3.63394i) q^{73} +4.07635 q^{74} +(0.261067 + 0.832973i) q^{75} +(-2.58676 - 4.48039i) q^{76} +(8.88106 - 15.3824i) q^{77} +(6.33798 - 6.89294i) q^{78} +2.67887 q^{79} +(-1.17303 - 2.03175i) q^{80} +(3.13608 - 8.43594i) q^{81} +(1.47475 + 2.55433i) q^{82} +(4.38541 - 7.59576i) q^{83} +(5.13937 + 1.14861i) q^{84} +(4.31411 - 7.47226i) q^{85} +(-4.91997 - 8.52163i) q^{86} +(1.46114 - 1.58908i) q^{87} +(-2.92100 + 5.05931i) q^{88} +3.52297 q^{89} +(6.36852 + 2.99630i) q^{90} -16.4373 q^{91} +(-2.63277 - 4.56010i) q^{92} +(-1.83564 + 9.46734i) q^{93} +(-4.27777 + 7.40932i) q^{94} +(-6.06868 + 10.5113i) q^{95} +(-1.69035 - 0.377782i) q^{96} +(-1.79211 - 3.10403i) q^{97} +(-1.12208 - 1.94350i) q^{98} +(-1.46764 - 17.4644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 2 q^{3} - 16 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 32 q^{8} - 6 q^{9} - q^{10} - 2 q^{11} + 4 q^{12} + 20 q^{13} + q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} + 12 q^{18} + 4 q^{19} - q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 2 * q^3 - 16 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 32 * q^8 - 6 * q^9 - q^10 - 2 * q^11 + 4 * q^12 + 20 * q^13 + q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 + 12 * q^18 + 4 * q^19 - q^20 + q^21 + 4 * q^22 - q^23 - 2 * q^24 + 38 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - 10 * q^31 - 16 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^36 - 19 * q^37 - 8 * q^38 + 19 * q^39 + 2 * q^40 - 20 * q^41 + 10 * q^42 + 26 * q^43 - 2 * q^44 - 19 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 + 26 * q^49 - 19 * q^50 - 37 * q^51 - 10 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 - 2 * q^56 - 5 * q^57 - 3 * q^58 - 6 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 + 16 * q^65 + 5 * q^66 + 16 * q^67 - 4 * q^68 - 32 * q^69 + 7 * q^71 - 6 * q^72 + 7 * q^73 + 38 * q^74 + q^75 + 4 * q^76 - q^77 - 11 * q^78 + 68 * q^79 - q^80 - 6 * q^81 + 10 * q^82 + 14 * q^83 - 11 * q^84 + 13 * q^85 - 13 * q^86 - 6 * q^87 - 2 * q^88 + 2 * q^89 + 5 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 + 4 * q^96 + 10 * q^97 - 13 * q^98 + 10 * q^99

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